Properties

Label 6003.2.a.t.1.20
Level 6003
Weight 2
Character 6003.1
Self dual Yes
Analytic conductor 47.934
Analytic rank 1
Dimension 22
CM No

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Newspace parameters

Level: \( N \) = \( 6003 = 3^{2} \cdot 23 \cdot 29 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 6003.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(47.9341963334\)
Analytic rank: \(1\)
Dimension: \(22\)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.20
Character \(\chi\) = 6003.1

$q$-expansion

\(f(q)\) \(=\) \(q+2.08661 q^{2} +2.35393 q^{4} +1.43041 q^{5} -0.274571 q^{7} +0.738503 q^{8} +O(q^{10})\) \(q+2.08661 q^{2} +2.35393 q^{4} +1.43041 q^{5} -0.274571 q^{7} +0.738503 q^{8} +2.98470 q^{10} -6.10520 q^{11} +0.188265 q^{13} -0.572921 q^{14} -3.16689 q^{16} -2.24526 q^{17} +3.65245 q^{19} +3.36708 q^{20} -12.7391 q^{22} +1.00000 q^{23} -2.95393 q^{25} +0.392834 q^{26} -0.646319 q^{28} +1.00000 q^{29} -4.05707 q^{31} -8.08505 q^{32} -4.68496 q^{34} -0.392749 q^{35} -4.16777 q^{37} +7.62122 q^{38} +1.05636 q^{40} -3.24174 q^{41} -4.69667 q^{43} -14.3712 q^{44} +2.08661 q^{46} +6.10569 q^{47} -6.92461 q^{49} -6.16369 q^{50} +0.443161 q^{52} +3.87730 q^{53} -8.73294 q^{55} -0.202771 q^{56} +2.08661 q^{58} +2.91676 q^{59} -2.77700 q^{61} -8.46551 q^{62} -10.5365 q^{64} +0.269296 q^{65} +7.02715 q^{67} -5.28516 q^{68} -0.819512 q^{70} -3.49275 q^{71} -12.1979 q^{73} -8.69650 q^{74} +8.59759 q^{76} +1.67631 q^{77} -8.81856 q^{79} -4.52994 q^{80} -6.76424 q^{82} -2.42899 q^{83} -3.21163 q^{85} -9.80011 q^{86} -4.50871 q^{88} -1.75647 q^{89} -0.0516920 q^{91} +2.35393 q^{92} +12.7402 q^{94} +5.22450 q^{95} -5.73211 q^{97} -14.4489 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 22q - 3q^{2} + 17q^{4} - 6q^{7} - 6q^{8} + O(q^{10}) \) \( 22q - 3q^{2} + 17q^{4} - 6q^{7} - 6q^{8} - 12q^{10} - 28q^{13} - q^{14} + 3q^{16} - 10q^{17} - 8q^{19} - 11q^{22} + 22q^{23} + 11q^{26} - 21q^{28} + 22q^{29} - 18q^{31} + 5q^{32} - 33q^{34} + 2q^{35} - 28q^{37} + 14q^{38} - 30q^{40} - 10q^{41} - 14q^{43} + 37q^{44} - 3q^{46} - 18q^{47} + 2q^{49} + 7q^{50} - 57q^{52} + 20q^{53} - 42q^{55} - 2q^{56} - 3q^{58} - 20q^{59} - 38q^{61} + 4q^{62} - 24q^{64} + 12q^{65} - 50q^{67} + 11q^{68} - 48q^{70} + 12q^{71} - 46q^{73} - 6q^{74} - 16q^{76} - 14q^{77} - 20q^{79} - 58q^{80} - 42q^{82} + 22q^{83} - 66q^{85} + 22q^{86} - 68q^{88} - 14q^{89} - 16q^{91} + 17q^{92} - 27q^{94} - 20q^{95} - 48q^{97} - 28q^{98} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.08661 1.47545 0.737727 0.675099i \(-0.235899\pi\)
0.737727 + 0.675099i \(0.235899\pi\)
\(3\) 0 0
\(4\) 2.35393 1.17696
\(5\) 1.43041 0.639698 0.319849 0.947468i \(-0.396368\pi\)
0.319849 + 0.947468i \(0.396368\pi\)
\(6\) 0 0
\(7\) −0.274571 −0.103778 −0.0518890 0.998653i \(-0.516524\pi\)
−0.0518890 + 0.998653i \(0.516524\pi\)
\(8\) 0.738503 0.261100
\(9\) 0 0
\(10\) 2.98470 0.943845
\(11\) −6.10520 −1.84079 −0.920394 0.390993i \(-0.872132\pi\)
−0.920394 + 0.390993i \(0.872132\pi\)
\(12\) 0 0
\(13\) 0.188265 0.0522152 0.0261076 0.999659i \(-0.491689\pi\)
0.0261076 + 0.999659i \(0.491689\pi\)
\(14\) −0.572921 −0.153120
\(15\) 0 0
\(16\) −3.16689 −0.791721
\(17\) −2.24526 −0.544554 −0.272277 0.962219i \(-0.587777\pi\)
−0.272277 + 0.962219i \(0.587777\pi\)
\(18\) 0 0
\(19\) 3.65245 0.837929 0.418965 0.908003i \(-0.362393\pi\)
0.418965 + 0.908003i \(0.362393\pi\)
\(20\) 3.36708 0.752901
\(21\) 0 0
\(22\) −12.7391 −2.71600
\(23\) 1.00000 0.208514
\(24\) 0 0
\(25\) −2.95393 −0.590786
\(26\) 0.392834 0.0770412
\(27\) 0 0
\(28\) −0.646319 −0.122143
\(29\) 1.00000 0.185695
\(30\) 0 0
\(31\) −4.05707 −0.728671 −0.364336 0.931268i \(-0.618704\pi\)
−0.364336 + 0.931268i \(0.618704\pi\)
\(32\) −8.08505 −1.42925
\(33\) 0 0
\(34\) −4.68496 −0.803465
\(35\) −0.392749 −0.0663866
\(36\) 0 0
\(37\) −4.16777 −0.685178 −0.342589 0.939485i \(-0.611304\pi\)
−0.342589 + 0.939485i \(0.611304\pi\)
\(38\) 7.62122 1.23633
\(39\) 0 0
\(40\) 1.05636 0.167025
\(41\) −3.24174 −0.506275 −0.253138 0.967430i \(-0.581463\pi\)
−0.253138 + 0.967430i \(0.581463\pi\)
\(42\) 0 0
\(43\) −4.69667 −0.716236 −0.358118 0.933676i \(-0.616581\pi\)
−0.358118 + 0.933676i \(0.616581\pi\)
\(44\) −14.3712 −2.16654
\(45\) 0 0
\(46\) 2.08661 0.307653
\(47\) 6.10569 0.890606 0.445303 0.895380i \(-0.353096\pi\)
0.445303 + 0.895380i \(0.353096\pi\)
\(48\) 0 0
\(49\) −6.92461 −0.989230
\(50\) −6.16369 −0.871677
\(51\) 0 0
\(52\) 0.443161 0.0614554
\(53\) 3.87730 0.532588 0.266294 0.963892i \(-0.414201\pi\)
0.266294 + 0.963892i \(0.414201\pi\)
\(54\) 0 0
\(55\) −8.73294 −1.17755
\(56\) −0.202771 −0.0270965
\(57\) 0 0
\(58\) 2.08661 0.273985
\(59\) 2.91676 0.379730 0.189865 0.981810i \(-0.439195\pi\)
0.189865 + 0.981810i \(0.439195\pi\)
\(60\) 0 0
\(61\) −2.77700 −0.355559 −0.177779 0.984070i \(-0.556891\pi\)
−0.177779 + 0.984070i \(0.556891\pi\)
\(62\) −8.46551 −1.07512
\(63\) 0 0
\(64\) −10.5365 −1.31707
\(65\) 0.269296 0.0334020
\(66\) 0 0
\(67\) 7.02715 0.858502 0.429251 0.903185i \(-0.358778\pi\)
0.429251 + 0.903185i \(0.358778\pi\)
\(68\) −5.28516 −0.640920
\(69\) 0 0
\(70\) −0.819512 −0.0979504
\(71\) −3.49275 −0.414514 −0.207257 0.978287i \(-0.566454\pi\)
−0.207257 + 0.978287i \(0.566454\pi\)
\(72\) 0 0
\(73\) −12.1979 −1.42766 −0.713830 0.700319i \(-0.753041\pi\)
−0.713830 + 0.700319i \(0.753041\pi\)
\(74\) −8.69650 −1.01095
\(75\) 0 0
\(76\) 8.59759 0.986211
\(77\) 1.67631 0.191033
\(78\) 0 0
\(79\) −8.81856 −0.992165 −0.496083 0.868275i \(-0.665229\pi\)
−0.496083 + 0.868275i \(0.665229\pi\)
\(80\) −4.52994 −0.506463
\(81\) 0 0
\(82\) −6.76424 −0.746986
\(83\) −2.42899 −0.266616 −0.133308 0.991075i \(-0.542560\pi\)
−0.133308 + 0.991075i \(0.542560\pi\)
\(84\) 0 0
\(85\) −3.21163 −0.348351
\(86\) −9.80011 −1.05677
\(87\) 0 0
\(88\) −4.50871 −0.480630
\(89\) −1.75647 −0.186185 −0.0930926 0.995657i \(-0.529675\pi\)
−0.0930926 + 0.995657i \(0.529675\pi\)
\(90\) 0 0
\(91\) −0.0516920 −0.00541879
\(92\) 2.35393 0.245414
\(93\) 0 0
\(94\) 12.7402 1.31405
\(95\) 5.22450 0.536022
\(96\) 0 0
\(97\) −5.73211 −0.582008 −0.291004 0.956722i \(-0.593989\pi\)
−0.291004 + 0.956722i \(0.593989\pi\)
\(98\) −14.4489 −1.45956
\(99\) 0 0
\(100\) −6.95333 −0.695333
\(101\) 9.23902 0.919317 0.459659 0.888096i \(-0.347972\pi\)
0.459659 + 0.888096i \(0.347972\pi\)
\(102\) 0 0
\(103\) −7.23178 −0.712568 −0.356284 0.934378i \(-0.615957\pi\)
−0.356284 + 0.934378i \(0.615957\pi\)
\(104\) 0.139034 0.0136334
\(105\) 0 0
\(106\) 8.09040 0.785809
\(107\) −3.16077 −0.305563 −0.152781 0.988260i \(-0.548823\pi\)
−0.152781 + 0.988260i \(0.548823\pi\)
\(108\) 0 0
\(109\) 9.56401 0.916066 0.458033 0.888935i \(-0.348554\pi\)
0.458033 + 0.888935i \(0.348554\pi\)
\(110\) −18.2222 −1.73742
\(111\) 0 0
\(112\) 0.869534 0.0821633
\(113\) −19.3625 −1.82147 −0.910734 0.412994i \(-0.864483\pi\)
−0.910734 + 0.412994i \(0.864483\pi\)
\(114\) 0 0
\(115\) 1.43041 0.133386
\(116\) 2.35393 0.218556
\(117\) 0 0
\(118\) 6.08613 0.560274
\(119\) 0.616482 0.0565128
\(120\) 0 0
\(121\) 26.2735 2.38850
\(122\) −5.79451 −0.524610
\(123\) 0 0
\(124\) −9.55004 −0.857619
\(125\) −11.3774 −1.01762
\(126\) 0 0
\(127\) −12.6479 −1.12232 −0.561161 0.827706i \(-0.689645\pi\)
−0.561161 + 0.827706i \(0.689645\pi\)
\(128\) −5.81552 −0.514024
\(129\) 0 0
\(130\) 0.561914 0.0492831
\(131\) 7.81787 0.683050 0.341525 0.939873i \(-0.389057\pi\)
0.341525 + 0.939873i \(0.389057\pi\)
\(132\) 0 0
\(133\) −1.00286 −0.0869586
\(134\) 14.6629 1.26668
\(135\) 0 0
\(136\) −1.65813 −0.142183
\(137\) −2.22227 −0.189861 −0.0949305 0.995484i \(-0.530263\pi\)
−0.0949305 + 0.995484i \(0.530263\pi\)
\(138\) 0 0
\(139\) 13.7510 1.16635 0.583174 0.812347i \(-0.301811\pi\)
0.583174 + 0.812347i \(0.301811\pi\)
\(140\) −0.924501 −0.0781346
\(141\) 0 0
\(142\) −7.28800 −0.611595
\(143\) −1.14939 −0.0961171
\(144\) 0 0
\(145\) 1.43041 0.118789
\(146\) −25.4523 −2.10645
\(147\) 0 0
\(148\) −9.81063 −0.806428
\(149\) 6.77408 0.554954 0.277477 0.960732i \(-0.410502\pi\)
0.277477 + 0.960732i \(0.410502\pi\)
\(150\) 0 0
\(151\) −10.6096 −0.863395 −0.431698 0.902018i \(-0.642085\pi\)
−0.431698 + 0.902018i \(0.642085\pi\)
\(152\) 2.69734 0.218784
\(153\) 0 0
\(154\) 3.49780 0.281861
\(155\) −5.80327 −0.466130
\(156\) 0 0
\(157\) 17.0603 1.36156 0.680778 0.732489i \(-0.261642\pi\)
0.680778 + 0.732489i \(0.261642\pi\)
\(158\) −18.4009 −1.46389
\(159\) 0 0
\(160\) −11.5649 −0.914288
\(161\) −0.274571 −0.0216392
\(162\) 0 0
\(163\) −24.0671 −1.88508 −0.942539 0.334096i \(-0.891569\pi\)
−0.942539 + 0.334096i \(0.891569\pi\)
\(164\) −7.63082 −0.595867
\(165\) 0 0
\(166\) −5.06835 −0.393380
\(167\) 4.02327 0.311330 0.155665 0.987810i \(-0.450248\pi\)
0.155665 + 0.987810i \(0.450248\pi\)
\(168\) 0 0
\(169\) −12.9646 −0.997274
\(170\) −6.70141 −0.513975
\(171\) 0 0
\(172\) −11.0556 −0.842983
\(173\) −0.0249861 −0.00189966 −0.000949830 1.00000i \(-0.500302\pi\)
−0.000949830 1.00000i \(0.500302\pi\)
\(174\) 0 0
\(175\) 0.811063 0.0613106
\(176\) 19.3345 1.45739
\(177\) 0 0
\(178\) −3.66506 −0.274707
\(179\) −1.00959 −0.0754606 −0.0377303 0.999288i \(-0.512013\pi\)
−0.0377303 + 0.999288i \(0.512013\pi\)
\(180\) 0 0
\(181\) 22.8161 1.69591 0.847955 0.530069i \(-0.177834\pi\)
0.847955 + 0.530069i \(0.177834\pi\)
\(182\) −0.107861 −0.00799518
\(183\) 0 0
\(184\) 0.738503 0.0544432
\(185\) −5.96162 −0.438307
\(186\) 0 0
\(187\) 13.7077 1.00241
\(188\) 14.3723 1.04821
\(189\) 0 0
\(190\) 10.9015 0.790875
\(191\) 2.91312 0.210786 0.105393 0.994431i \(-0.466390\pi\)
0.105393 + 0.994431i \(0.466390\pi\)
\(192\) 0 0
\(193\) −3.51894 −0.253299 −0.126650 0.991948i \(-0.540422\pi\)
−0.126650 + 0.991948i \(0.540422\pi\)
\(194\) −11.9607 −0.858725
\(195\) 0 0
\(196\) −16.3000 −1.16429
\(197\) 14.7731 1.05254 0.526272 0.850317i \(-0.323590\pi\)
0.526272 + 0.850317i \(0.323590\pi\)
\(198\) 0 0
\(199\) 23.7774 1.68553 0.842767 0.538278i \(-0.180925\pi\)
0.842767 + 0.538278i \(0.180925\pi\)
\(200\) −2.18149 −0.154254
\(201\) 0 0
\(202\) 19.2782 1.35641
\(203\) −0.274571 −0.0192711
\(204\) 0 0
\(205\) −4.63702 −0.323864
\(206\) −15.0899 −1.05136
\(207\) 0 0
\(208\) −0.596213 −0.0413399
\(209\) −22.2989 −1.54245
\(210\) 0 0
\(211\) 0.588832 0.0405369 0.0202684 0.999795i \(-0.493548\pi\)
0.0202684 + 0.999795i \(0.493548\pi\)
\(212\) 9.12688 0.626837
\(213\) 0 0
\(214\) −6.59527 −0.450844
\(215\) −6.71817 −0.458175
\(216\) 0 0
\(217\) 1.11395 0.0756201
\(218\) 19.9563 1.35161
\(219\) 0 0
\(220\) −20.5567 −1.38593
\(221\) −0.422702 −0.0284340
\(222\) 0 0
\(223\) −17.5937 −1.17816 −0.589079 0.808075i \(-0.700509\pi\)
−0.589079 + 0.808075i \(0.700509\pi\)
\(224\) 2.21992 0.148325
\(225\) 0 0
\(226\) −40.4018 −2.68749
\(227\) 27.3659 1.81634 0.908169 0.418603i \(-0.137480\pi\)
0.908169 + 0.418603i \(0.137480\pi\)
\(228\) 0 0
\(229\) −20.2749 −1.33980 −0.669900 0.742451i \(-0.733663\pi\)
−0.669900 + 0.742451i \(0.733663\pi\)
\(230\) 2.98470 0.196805
\(231\) 0 0
\(232\) 0.738503 0.0484851
\(233\) −3.03886 −0.199082 −0.0995412 0.995033i \(-0.531737\pi\)
−0.0995412 + 0.995033i \(0.531737\pi\)
\(234\) 0 0
\(235\) 8.73363 0.569719
\(236\) 6.86584 0.446928
\(237\) 0 0
\(238\) 1.28635 0.0833820
\(239\) −1.74365 −0.112787 −0.0563936 0.998409i \(-0.517960\pi\)
−0.0563936 + 0.998409i \(0.517960\pi\)
\(240\) 0 0
\(241\) 3.99474 0.257324 0.128662 0.991689i \(-0.458932\pi\)
0.128662 + 0.991689i \(0.458932\pi\)
\(242\) 54.8224 3.52412
\(243\) 0 0
\(244\) −6.53685 −0.418479
\(245\) −9.90503 −0.632809
\(246\) 0 0
\(247\) 0.687627 0.0437527
\(248\) −2.99616 −0.190256
\(249\) 0 0
\(250\) −23.7401 −1.50146
\(251\) −7.41675 −0.468141 −0.234070 0.972220i \(-0.575205\pi\)
−0.234070 + 0.972220i \(0.575205\pi\)
\(252\) 0 0
\(253\) −6.10520 −0.383831
\(254\) −26.3913 −1.65594
\(255\) 0 0
\(256\) 8.93839 0.558649
\(257\) 19.0615 1.18902 0.594512 0.804087i \(-0.297345\pi\)
0.594512 + 0.804087i \(0.297345\pi\)
\(258\) 0 0
\(259\) 1.14435 0.0711064
\(260\) 0.633902 0.0393129
\(261\) 0 0
\(262\) 16.3128 1.00781
\(263\) 2.53582 0.156365 0.0781827 0.996939i \(-0.475088\pi\)
0.0781827 + 0.996939i \(0.475088\pi\)
\(264\) 0 0
\(265\) 5.54613 0.340696
\(266\) −2.09257 −0.128303
\(267\) 0 0
\(268\) 16.5414 1.01043
\(269\) −4.13080 −0.251859 −0.125930 0.992039i \(-0.540191\pi\)
−0.125930 + 0.992039i \(0.540191\pi\)
\(270\) 0 0
\(271\) −4.10014 −0.249066 −0.124533 0.992215i \(-0.539743\pi\)
−0.124533 + 0.992215i \(0.539743\pi\)
\(272\) 7.11047 0.431135
\(273\) 0 0
\(274\) −4.63700 −0.280131
\(275\) 18.0343 1.08751
\(276\) 0 0
\(277\) 7.14419 0.429253 0.214626 0.976696i \(-0.431147\pi\)
0.214626 + 0.976696i \(0.431147\pi\)
\(278\) 28.6930 1.72089
\(279\) 0 0
\(280\) −0.290046 −0.0173336
\(281\) −15.6506 −0.933635 −0.466817 0.884354i \(-0.654599\pi\)
−0.466817 + 0.884354i \(0.654599\pi\)
\(282\) 0 0
\(283\) 8.24117 0.489887 0.244943 0.969537i \(-0.421231\pi\)
0.244943 + 0.969537i \(0.421231\pi\)
\(284\) −8.22168 −0.487867
\(285\) 0 0
\(286\) −2.39833 −0.141816
\(287\) 0.890088 0.0525403
\(288\) 0 0
\(289\) −11.9588 −0.703461
\(290\) 2.98470 0.175268
\(291\) 0 0
\(292\) −28.7130 −1.68030
\(293\) 20.9302 1.22275 0.611377 0.791340i \(-0.290616\pi\)
0.611377 + 0.791340i \(0.290616\pi\)
\(294\) 0 0
\(295\) 4.17216 0.242913
\(296\) −3.07791 −0.178900
\(297\) 0 0
\(298\) 14.1348 0.818809
\(299\) 0.188265 0.0108876
\(300\) 0 0
\(301\) 1.28957 0.0743296
\(302\) −22.1380 −1.27390
\(303\) 0 0
\(304\) −11.5669 −0.663406
\(305\) −3.97225 −0.227450
\(306\) 0 0
\(307\) 19.1315 1.09189 0.545947 0.837819i \(-0.316170\pi\)
0.545947 + 0.837819i \(0.316170\pi\)
\(308\) 3.94591 0.224839
\(309\) 0 0
\(310\) −12.1091 −0.687753
\(311\) 30.8388 1.74871 0.874353 0.485291i \(-0.161286\pi\)
0.874353 + 0.485291i \(0.161286\pi\)
\(312\) 0 0
\(313\) 0.287106 0.0162282 0.00811409 0.999967i \(-0.497417\pi\)
0.00811409 + 0.999967i \(0.497417\pi\)
\(314\) 35.5980 2.00891
\(315\) 0 0
\(316\) −20.7582 −1.16774
\(317\) 4.79550 0.269342 0.134671 0.990890i \(-0.457002\pi\)
0.134671 + 0.990890i \(0.457002\pi\)
\(318\) 0 0
\(319\) −6.10520 −0.341826
\(320\) −15.0716 −0.842526
\(321\) 0 0
\(322\) −0.572921 −0.0319276
\(323\) −8.20068 −0.456298
\(324\) 0 0
\(325\) −0.556121 −0.0308480
\(326\) −50.2185 −2.78134
\(327\) 0 0
\(328\) −2.39404 −0.132189
\(329\) −1.67644 −0.0924253
\(330\) 0 0
\(331\) −7.68460 −0.422384 −0.211192 0.977445i \(-0.567735\pi\)
−0.211192 + 0.977445i \(0.567735\pi\)
\(332\) −5.71766 −0.313798
\(333\) 0 0
\(334\) 8.39498 0.459353
\(335\) 10.0517 0.549183
\(336\) 0 0
\(337\) 0.712372 0.0388054 0.0194027 0.999812i \(-0.493824\pi\)
0.0194027 + 0.999812i \(0.493824\pi\)
\(338\) −27.0519 −1.47143
\(339\) 0 0
\(340\) −7.55995 −0.409996
\(341\) 24.7692 1.34133
\(342\) 0 0
\(343\) 3.82329 0.206438
\(344\) −3.46851 −0.187009
\(345\) 0 0
\(346\) −0.0521362 −0.00280286
\(347\) −20.4402 −1.09729 −0.548645 0.836056i \(-0.684856\pi\)
−0.548645 + 0.836056i \(0.684856\pi\)
\(348\) 0 0
\(349\) 3.84665 0.205907 0.102953 0.994686i \(-0.467171\pi\)
0.102953 + 0.994686i \(0.467171\pi\)
\(350\) 1.69237 0.0904609
\(351\) 0 0
\(352\) 49.3608 2.63094
\(353\) 6.68615 0.355868 0.177934 0.984042i \(-0.443059\pi\)
0.177934 + 0.984042i \(0.443059\pi\)
\(354\) 0 0
\(355\) −4.99607 −0.265164
\(356\) −4.13459 −0.219133
\(357\) 0 0
\(358\) −2.10662 −0.111339
\(359\) −25.6460 −1.35355 −0.676773 0.736191i \(-0.736622\pi\)
−0.676773 + 0.736191i \(0.736622\pi\)
\(360\) 0 0
\(361\) −5.65962 −0.297875
\(362\) 47.6083 2.50223
\(363\) 0 0
\(364\) −0.121679 −0.00637772
\(365\) −17.4480 −0.913272
\(366\) 0 0
\(367\) 12.3016 0.642141 0.321070 0.947055i \(-0.395957\pi\)
0.321070 + 0.947055i \(0.395957\pi\)
\(368\) −3.16689 −0.165085
\(369\) 0 0
\(370\) −12.4396 −0.646702
\(371\) −1.06459 −0.0552710
\(372\) 0 0
\(373\) −22.4264 −1.16120 −0.580598 0.814190i \(-0.697181\pi\)
−0.580598 + 0.814190i \(0.697181\pi\)
\(374\) 28.6026 1.47901
\(375\) 0 0
\(376\) 4.50907 0.232537
\(377\) 0.188265 0.00969613
\(378\) 0 0
\(379\) 33.7025 1.73118 0.865590 0.500754i \(-0.166944\pi\)
0.865590 + 0.500754i \(0.166944\pi\)
\(380\) 12.2981 0.630878
\(381\) 0 0
\(382\) 6.07853 0.311004
\(383\) 21.0513 1.07567 0.537836 0.843050i \(-0.319242\pi\)
0.537836 + 0.843050i \(0.319242\pi\)
\(384\) 0 0
\(385\) 2.39781 0.122204
\(386\) −7.34265 −0.373731
\(387\) 0 0
\(388\) −13.4930 −0.685001
\(389\) −34.5723 −1.75288 −0.876442 0.481507i \(-0.840090\pi\)
−0.876442 + 0.481507i \(0.840090\pi\)
\(390\) 0 0
\(391\) −2.24526 −0.113547
\(392\) −5.11385 −0.258288
\(393\) 0 0
\(394\) 30.8257 1.55298
\(395\) −12.6141 −0.634686
\(396\) 0 0
\(397\) 12.2736 0.615995 0.307997 0.951387i \(-0.400341\pi\)
0.307997 + 0.951387i \(0.400341\pi\)
\(398\) 49.6140 2.48693
\(399\) 0 0
\(400\) 9.35476 0.467738
\(401\) −9.95916 −0.497337 −0.248668 0.968589i \(-0.579993\pi\)
−0.248668 + 0.968589i \(0.579993\pi\)
\(402\) 0 0
\(403\) −0.763803 −0.0380478
\(404\) 21.7480 1.08200
\(405\) 0 0
\(406\) −0.572921 −0.0284336
\(407\) 25.4451 1.26127
\(408\) 0 0
\(409\) −28.5666 −1.41253 −0.706264 0.707949i \(-0.749621\pi\)
−0.706264 + 0.707949i \(0.749621\pi\)
\(410\) −9.67564 −0.477846
\(411\) 0 0
\(412\) −17.0231 −0.838666
\(413\) −0.800858 −0.0394076
\(414\) 0 0
\(415\) −3.47445 −0.170554
\(416\) −1.52213 −0.0746285
\(417\) 0 0
\(418\) −46.5291 −2.27581
\(419\) 7.55392 0.369033 0.184517 0.982829i \(-0.440928\pi\)
0.184517 + 0.982829i \(0.440928\pi\)
\(420\) 0 0
\(421\) −7.74446 −0.377442 −0.188721 0.982031i \(-0.560434\pi\)
−0.188721 + 0.982031i \(0.560434\pi\)
\(422\) 1.22866 0.0598103
\(423\) 0 0
\(424\) 2.86340 0.139059
\(425\) 6.63233 0.321715
\(426\) 0 0
\(427\) 0.762484 0.0368992
\(428\) −7.44021 −0.359636
\(429\) 0 0
\(430\) −14.0182 −0.676016
\(431\) 38.6217 1.86034 0.930172 0.367124i \(-0.119658\pi\)
0.930172 + 0.367124i \(0.119658\pi\)
\(432\) 0 0
\(433\) −5.41271 −0.260118 −0.130059 0.991506i \(-0.541517\pi\)
−0.130059 + 0.991506i \(0.541517\pi\)
\(434\) 2.32438 0.111574
\(435\) 0 0
\(436\) 22.5130 1.07818
\(437\) 3.65245 0.174720
\(438\) 0 0
\(439\) −12.2447 −0.584407 −0.292203 0.956356i \(-0.594388\pi\)
−0.292203 + 0.956356i \(0.594388\pi\)
\(440\) −6.44930 −0.307458
\(441\) 0 0
\(442\) −0.882013 −0.0419531
\(443\) −11.2775 −0.535808 −0.267904 0.963446i \(-0.586331\pi\)
−0.267904 + 0.963446i \(0.586331\pi\)
\(444\) 0 0
\(445\) −2.51247 −0.119102
\(446\) −36.7110 −1.73832
\(447\) 0 0
\(448\) 2.89303 0.136683
\(449\) −20.3814 −0.961858 −0.480929 0.876760i \(-0.659700\pi\)
−0.480929 + 0.876760i \(0.659700\pi\)
\(450\) 0 0
\(451\) 19.7915 0.931945
\(452\) −45.5778 −2.14380
\(453\) 0 0
\(454\) 57.1019 2.67992
\(455\) −0.0739407 −0.00346639
\(456\) 0 0
\(457\) −14.2683 −0.667442 −0.333721 0.942672i \(-0.608304\pi\)
−0.333721 + 0.942672i \(0.608304\pi\)
\(458\) −42.3057 −1.97681
\(459\) 0 0
\(460\) 3.36708 0.156991
\(461\) −28.9224 −1.34705 −0.673525 0.739164i \(-0.735221\pi\)
−0.673525 + 0.739164i \(0.735221\pi\)
\(462\) 0 0
\(463\) −10.8540 −0.504429 −0.252215 0.967671i \(-0.581159\pi\)
−0.252215 + 0.967671i \(0.581159\pi\)
\(464\) −3.16689 −0.147019
\(465\) 0 0
\(466\) −6.34090 −0.293737
\(467\) −18.3096 −0.847267 −0.423633 0.905834i \(-0.639245\pi\)
−0.423633 + 0.905834i \(0.639245\pi\)
\(468\) 0 0
\(469\) −1.92945 −0.0890937
\(470\) 18.2236 0.840594
\(471\) 0 0
\(472\) 2.15404 0.0991476
\(473\) 28.6741 1.31844
\(474\) 0 0
\(475\) −10.7891 −0.495037
\(476\) 1.45115 0.0665134
\(477\) 0 0
\(478\) −3.63831 −0.166412
\(479\) 29.2790 1.33779 0.668896 0.743356i \(-0.266767\pi\)
0.668896 + 0.743356i \(0.266767\pi\)
\(480\) 0 0
\(481\) −0.784645 −0.0357767
\(482\) 8.33544 0.379669
\(483\) 0 0
\(484\) 61.8458 2.81117
\(485\) −8.19926 −0.372309
\(486\) 0 0
\(487\) 2.51914 0.114153 0.0570766 0.998370i \(-0.481822\pi\)
0.0570766 + 0.998370i \(0.481822\pi\)
\(488\) −2.05082 −0.0928365
\(489\) 0 0
\(490\) −20.6679 −0.933680
\(491\) −18.0791 −0.815896 −0.407948 0.913005i \(-0.633756\pi\)
−0.407948 + 0.913005i \(0.633756\pi\)
\(492\) 0 0
\(493\) −2.24526 −0.101121
\(494\) 1.43481 0.0645550
\(495\) 0 0
\(496\) 12.8483 0.576905
\(497\) 0.959008 0.0430174
\(498\) 0 0
\(499\) 19.8082 0.886736 0.443368 0.896340i \(-0.353784\pi\)
0.443368 + 0.896340i \(0.353784\pi\)
\(500\) −26.7815 −1.19770
\(501\) 0 0
\(502\) −15.4758 −0.690720
\(503\) 12.8927 0.574855 0.287428 0.957802i \(-0.407200\pi\)
0.287428 + 0.957802i \(0.407200\pi\)
\(504\) 0 0
\(505\) 13.2156 0.588086
\(506\) −12.7391 −0.566324
\(507\) 0 0
\(508\) −29.7723 −1.32093
\(509\) 8.87677 0.393456 0.196728 0.980458i \(-0.436968\pi\)
0.196728 + 0.980458i \(0.436968\pi\)
\(510\) 0 0
\(511\) 3.34920 0.148160
\(512\) 30.2819 1.33829
\(513\) 0 0
\(514\) 39.7739 1.75435
\(515\) −10.3444 −0.455829
\(516\) 0 0
\(517\) −37.2764 −1.63942
\(518\) 2.38780 0.104914
\(519\) 0 0
\(520\) 0.198876 0.00872127
\(521\) 4.07848 0.178681 0.0893407 0.996001i \(-0.471524\pi\)
0.0893407 + 0.996001i \(0.471524\pi\)
\(522\) 0 0
\(523\) −41.7215 −1.82436 −0.912178 0.409795i \(-0.865600\pi\)
−0.912178 + 0.409795i \(0.865600\pi\)
\(524\) 18.4027 0.803925
\(525\) 0 0
\(526\) 5.29126 0.230710
\(527\) 9.10916 0.396801
\(528\) 0 0
\(529\) 1.00000 0.0434783
\(530\) 11.5726 0.502681
\(531\) 0 0
\(532\) −2.36065 −0.102347
\(533\) −0.610306 −0.0264353
\(534\) 0 0
\(535\) −4.52119 −0.195468
\(536\) 5.18957 0.224155
\(537\) 0 0
\(538\) −8.61935 −0.371607
\(539\) 42.2761 1.82096
\(540\) 0 0
\(541\) −20.0737 −0.863038 −0.431519 0.902104i \(-0.642022\pi\)
−0.431519 + 0.902104i \(0.642022\pi\)
\(542\) −8.55538 −0.367485
\(543\) 0 0
\(544\) 18.1530 0.778303
\(545\) 13.6804 0.586006
\(546\) 0 0
\(547\) −13.2512 −0.566583 −0.283291 0.959034i \(-0.591426\pi\)
−0.283291 + 0.959034i \(0.591426\pi\)
\(548\) −5.23105 −0.223459
\(549\) 0 0
\(550\) 37.6305 1.60457
\(551\) 3.65245 0.155600
\(552\) 0 0
\(553\) 2.42132 0.102965
\(554\) 14.9071 0.633342
\(555\) 0 0
\(556\) 32.3689 1.37275
\(557\) −29.8454 −1.26459 −0.632295 0.774727i \(-0.717887\pi\)
−0.632295 + 0.774727i \(0.717887\pi\)
\(558\) 0 0
\(559\) −0.884218 −0.0373984
\(560\) 1.24379 0.0525597
\(561\) 0 0
\(562\) −32.6566 −1.37753
\(563\) −6.32526 −0.266578 −0.133289 0.991077i \(-0.542554\pi\)
−0.133289 + 0.991077i \(0.542554\pi\)
\(564\) 0 0
\(565\) −27.6962 −1.16519
\(566\) 17.1961 0.722805
\(567\) 0 0
\(568\) −2.57941 −0.108230
\(569\) −13.4246 −0.562788 −0.281394 0.959592i \(-0.590797\pi\)
−0.281394 + 0.959592i \(0.590797\pi\)
\(570\) 0 0
\(571\) −31.9335 −1.33638 −0.668188 0.743992i \(-0.732930\pi\)
−0.668188 + 0.743992i \(0.732930\pi\)
\(572\) −2.70559 −0.113126
\(573\) 0 0
\(574\) 1.85726 0.0775207
\(575\) −2.95393 −0.123187
\(576\) 0 0
\(577\) 12.4350 0.517677 0.258838 0.965921i \(-0.416660\pi\)
0.258838 + 0.965921i \(0.416660\pi\)
\(578\) −24.9534 −1.03792
\(579\) 0 0
\(580\) 3.36708 0.139810
\(581\) 0.666930 0.0276689
\(582\) 0 0
\(583\) −23.6717 −0.980382
\(584\) −9.00821 −0.372762
\(585\) 0 0
\(586\) 43.6730 1.80412
\(587\) 24.0000 0.990586 0.495293 0.868726i \(-0.335061\pi\)
0.495293 + 0.868726i \(0.335061\pi\)
\(588\) 0 0
\(589\) −14.8182 −0.610575
\(590\) 8.70566 0.358406
\(591\) 0 0
\(592\) 13.1989 0.542470
\(593\) −19.4433 −0.798441 −0.399221 0.916855i \(-0.630719\pi\)
−0.399221 + 0.916855i \(0.630719\pi\)
\(594\) 0 0
\(595\) 0.881821 0.0361511
\(596\) 15.9457 0.653161
\(597\) 0 0
\(598\) 0.392834 0.0160642
\(599\) 13.7703 0.562640 0.281320 0.959614i \(-0.409228\pi\)
0.281320 + 0.959614i \(0.409228\pi\)
\(600\) 0 0
\(601\) −1.23499 −0.0503764 −0.0251882 0.999683i \(-0.508018\pi\)
−0.0251882 + 0.999683i \(0.508018\pi\)
\(602\) 2.69082 0.109670
\(603\) 0 0
\(604\) −24.9742 −1.01618
\(605\) 37.5818 1.52792
\(606\) 0 0
\(607\) −29.5165 −1.19804 −0.599019 0.800735i \(-0.704443\pi\)
−0.599019 + 0.800735i \(0.704443\pi\)
\(608\) −29.5302 −1.19761
\(609\) 0 0
\(610\) −8.28852 −0.335592
\(611\) 1.14949 0.0465032
\(612\) 0 0
\(613\) 11.7152 0.473172 0.236586 0.971611i \(-0.423972\pi\)
0.236586 + 0.971611i \(0.423972\pi\)
\(614\) 39.9200 1.61104
\(615\) 0 0
\(616\) 1.23796 0.0498788
\(617\) 29.9849 1.20715 0.603573 0.797308i \(-0.293743\pi\)
0.603573 + 0.797308i \(0.293743\pi\)
\(618\) 0 0
\(619\) 7.17569 0.288415 0.144208 0.989547i \(-0.453937\pi\)
0.144208 + 0.989547i \(0.453937\pi\)
\(620\) −13.6605 −0.548618
\(621\) 0 0
\(622\) 64.3484 2.58013
\(623\) 0.482275 0.0193219
\(624\) 0 0
\(625\) −1.50465 −0.0601861
\(626\) 0.599077 0.0239439
\(627\) 0 0
\(628\) 40.1586 1.60250
\(629\) 9.35771 0.373116
\(630\) 0 0
\(631\) −22.8076 −0.907955 −0.453977 0.891013i \(-0.649995\pi\)
−0.453977 + 0.891013i \(0.649995\pi\)
\(632\) −6.51253 −0.259055
\(633\) 0 0
\(634\) 10.0063 0.397402
\(635\) −18.0917 −0.717948
\(636\) 0 0
\(637\) −1.30366 −0.0516529
\(638\) −12.7391 −0.504348
\(639\) 0 0
\(640\) −8.31857 −0.328820
\(641\) 2.68538 0.106066 0.0530331 0.998593i \(-0.483111\pi\)
0.0530331 + 0.998593i \(0.483111\pi\)
\(642\) 0 0
\(643\) 8.39727 0.331156 0.165578 0.986197i \(-0.447051\pi\)
0.165578 + 0.986197i \(0.447051\pi\)
\(644\) −0.646319 −0.0254685
\(645\) 0 0
\(646\) −17.1116 −0.673246
\(647\) −13.2389 −0.520476 −0.260238 0.965545i \(-0.583801\pi\)
−0.260238 + 0.965545i \(0.583801\pi\)
\(648\) 0 0
\(649\) −17.8074 −0.699002
\(650\) −1.16040 −0.0455148
\(651\) 0 0
\(652\) −56.6521 −2.21867
\(653\) 30.6244 1.19842 0.599212 0.800591i \(-0.295481\pi\)
0.599212 + 0.800591i \(0.295481\pi\)
\(654\) 0 0
\(655\) 11.1827 0.436946
\(656\) 10.2662 0.400829
\(657\) 0 0
\(658\) −3.49808 −0.136369
\(659\) 33.9602 1.32290 0.661450 0.749989i \(-0.269941\pi\)
0.661450 + 0.749989i \(0.269941\pi\)
\(660\) 0 0
\(661\) 16.1979 0.630027 0.315013 0.949087i \(-0.397991\pi\)
0.315013 + 0.949087i \(0.397991\pi\)
\(662\) −16.0347 −0.623208
\(663\) 0 0
\(664\) −1.79382 −0.0696136
\(665\) −1.43449 −0.0556273
\(666\) 0 0
\(667\) 1.00000 0.0387202
\(668\) 9.47047 0.366424
\(669\) 0 0
\(670\) 20.9739 0.810293
\(671\) 16.9542 0.654508
\(672\) 0 0
\(673\) −38.7576 −1.49400 −0.746998 0.664827i \(-0.768505\pi\)
−0.746998 + 0.664827i \(0.768505\pi\)
\(674\) 1.48644 0.0572555
\(675\) 0 0
\(676\) −30.5176 −1.17375
\(677\) 34.2894 1.31785 0.658925 0.752208i \(-0.271011\pi\)
0.658925 + 0.752208i \(0.271011\pi\)
\(678\) 0 0
\(679\) 1.57387 0.0603996
\(680\) −2.37180 −0.0909544
\(681\) 0 0
\(682\) 51.6836 1.97907
\(683\) 7.15688 0.273851 0.136925 0.990581i \(-0.456278\pi\)
0.136925 + 0.990581i \(0.456278\pi\)
\(684\) 0 0
\(685\) −3.17875 −0.121454
\(686\) 7.97770 0.304590
\(687\) 0 0
\(688\) 14.8738 0.567060
\(689\) 0.729959 0.0278092
\(690\) 0 0
\(691\) −27.4957 −1.04599 −0.522993 0.852337i \(-0.675184\pi\)
−0.522993 + 0.852337i \(0.675184\pi\)
\(692\) −0.0588155 −0.00223583
\(693\) 0 0
\(694\) −42.6507 −1.61900
\(695\) 19.6696 0.746111
\(696\) 0 0
\(697\) 7.27854 0.275694
\(698\) 8.02645 0.303806
\(699\) 0 0
\(700\) 1.90918 0.0721603
\(701\) −13.8109 −0.521630 −0.260815 0.965389i \(-0.583991\pi\)
−0.260815 + 0.965389i \(0.583991\pi\)
\(702\) 0 0
\(703\) −15.2226 −0.574130
\(704\) 64.3277 2.42444
\(705\) 0 0
\(706\) 13.9514 0.525067
\(707\) −2.53677 −0.0954049
\(708\) 0 0
\(709\) −0.924764 −0.0347303 −0.0173651 0.999849i \(-0.505528\pi\)
−0.0173651 + 0.999849i \(0.505528\pi\)
\(710\) −10.4248 −0.391237
\(711\) 0 0
\(712\) −1.29716 −0.0486130
\(713\) −4.05707 −0.151938
\(714\) 0 0
\(715\) −1.64410 −0.0614860
\(716\) −2.37651 −0.0888143
\(717\) 0 0
\(718\) −53.5132 −1.99709
\(719\) 20.1522 0.751552 0.375776 0.926711i \(-0.377376\pi\)
0.375776 + 0.926711i \(0.377376\pi\)
\(720\) 0 0
\(721\) 1.98564 0.0739489
\(722\) −11.8094 −0.439500
\(723\) 0 0
\(724\) 53.7075 1.99602
\(725\) −2.95393 −0.109706
\(726\) 0 0
\(727\) 2.08270 0.0772429 0.0386215 0.999254i \(-0.487703\pi\)
0.0386215 + 0.999254i \(0.487703\pi\)
\(728\) −0.0381747 −0.00141485
\(729\) 0 0
\(730\) −36.4072 −1.34749
\(731\) 10.5452 0.390030
\(732\) 0 0
\(733\) 8.15634 0.301261 0.150631 0.988590i \(-0.451870\pi\)
0.150631 + 0.988590i \(0.451870\pi\)
\(734\) 25.6687 0.947449
\(735\) 0 0
\(736\) −8.08505 −0.298019
\(737\) −42.9021 −1.58032
\(738\) 0 0
\(739\) −25.8699 −0.951638 −0.475819 0.879543i \(-0.657848\pi\)
−0.475819 + 0.879543i \(0.657848\pi\)
\(740\) −14.0332 −0.515871
\(741\) 0 0
\(742\) −2.22139 −0.0815497
\(743\) 34.9391 1.28179 0.640896 0.767628i \(-0.278563\pi\)
0.640896 + 0.767628i \(0.278563\pi\)
\(744\) 0 0
\(745\) 9.68971 0.355003
\(746\) −46.7951 −1.71329
\(747\) 0 0
\(748\) 32.2670 1.17980
\(749\) 0.867854 0.0317107
\(750\) 0 0
\(751\) 10.4297 0.380585 0.190293 0.981727i \(-0.439056\pi\)
0.190293 + 0.981727i \(0.439056\pi\)
\(752\) −19.3360 −0.705112
\(753\) 0 0
\(754\) 0.392834 0.0143062
\(755\) −15.1760 −0.552313
\(756\) 0 0
\(757\) 46.0068 1.67215 0.836073 0.548619i \(-0.184846\pi\)
0.836073 + 0.548619i \(0.184846\pi\)
\(758\) 70.3238 2.55428
\(759\) 0 0
\(760\) 3.85831 0.139956
\(761\) −33.1684 −1.20235 −0.601177 0.799116i \(-0.705301\pi\)
−0.601177 + 0.799116i \(0.705301\pi\)
\(762\) 0 0
\(763\) −2.62600 −0.0950675
\(764\) 6.85726 0.248087
\(765\) 0 0
\(766\) 43.9258 1.58710
\(767\) 0.549123 0.0198277
\(768\) 0 0
\(769\) −23.9544 −0.863816 −0.431908 0.901918i \(-0.642159\pi\)
−0.431908 + 0.901918i \(0.642159\pi\)
\(770\) 5.00328 0.180306
\(771\) 0 0
\(772\) −8.28333 −0.298124
\(773\) −37.4046 −1.34535 −0.672674 0.739939i \(-0.734854\pi\)
−0.672674 + 0.739939i \(0.734854\pi\)
\(774\) 0 0
\(775\) 11.9843 0.430489
\(776\) −4.23318 −0.151962
\(777\) 0 0
\(778\) −72.1387 −2.58630
\(779\) −11.8403 −0.424223
\(780\) 0 0
\(781\) 21.3240 0.763031
\(782\) −4.68496 −0.167534
\(783\) 0 0
\(784\) 21.9295 0.783195
\(785\) 24.4032 0.870986
\(786\) 0 0
\(787\) 4.05977 0.144715 0.0723576 0.997379i \(-0.476948\pi\)
0.0723576 + 0.997379i \(0.476948\pi\)
\(788\) 34.7749 1.23880
\(789\) 0 0
\(790\) −26.3208 −0.936450
\(791\) 5.31637 0.189028
\(792\) 0 0
\(793\) −0.522811 −0.0185656
\(794\) 25.6102 0.908871
\(795\) 0 0
\(796\) 55.9702 1.98381
\(797\) −1.56174 −0.0553196 −0.0276598 0.999617i \(-0.508806\pi\)
−0.0276598 + 0.999617i \(0.508806\pi\)
\(798\) 0 0
\(799\) −13.7088 −0.484983
\(800\) 23.8827 0.844380
\(801\) 0 0
\(802\) −20.7808 −0.733797
\(803\) 74.4708 2.62802
\(804\) 0 0
\(805\) −0.392749 −0.0138426
\(806\) −1.59376 −0.0561377
\(807\) 0 0
\(808\) 6.82305 0.240034
\(809\) −9.09173 −0.319648 −0.159824 0.987146i \(-0.551093\pi\)
−0.159824 + 0.987146i \(0.551093\pi\)
\(810\) 0 0
\(811\) 6.07851 0.213445 0.106723 0.994289i \(-0.465964\pi\)
0.106723 + 0.994289i \(0.465964\pi\)
\(812\) −0.646319 −0.0226814
\(813\) 0 0
\(814\) 53.0939 1.86094
\(815\) −34.4257 −1.20588
\(816\) 0 0
\(817\) −17.1544 −0.600155
\(818\) −59.6073 −2.08412
\(819\) 0 0
\(820\) −10.9152 −0.381175
\(821\) 29.7440 1.03807 0.519036 0.854752i \(-0.326291\pi\)
0.519036 + 0.854752i \(0.326291\pi\)
\(822\) 0 0
\(823\) 12.8740 0.448758 0.224379 0.974502i \(-0.427965\pi\)
0.224379 + 0.974502i \(0.427965\pi\)
\(824\) −5.34069 −0.186052
\(825\) 0 0
\(826\) −1.67107 −0.0581441
\(827\) 36.2049 1.25897 0.629484 0.777014i \(-0.283266\pi\)
0.629484 + 0.777014i \(0.283266\pi\)
\(828\) 0 0
\(829\) −31.7283 −1.10197 −0.550985 0.834515i \(-0.685748\pi\)
−0.550985 + 0.834515i \(0.685748\pi\)
\(830\) −7.24981 −0.251645
\(831\) 0 0
\(832\) −1.98366 −0.0687710
\(833\) 15.5475 0.538690
\(834\) 0 0
\(835\) 5.75492 0.199157
\(836\) −52.4900 −1.81541
\(837\) 0 0
\(838\) 15.7621 0.544491
\(839\) −29.9699 −1.03468 −0.517338 0.855781i \(-0.673077\pi\)
−0.517338 + 0.855781i \(0.673077\pi\)
\(840\) 0 0
\(841\) 1.00000 0.0344828
\(842\) −16.1596 −0.556898
\(843\) 0 0
\(844\) 1.38607 0.0477104
\(845\) −18.5446 −0.637954
\(846\) 0 0
\(847\) −7.21393 −0.247874
\(848\) −12.2790 −0.421662
\(849\) 0 0
\(850\) 13.8391 0.474676
\(851\) −4.16777 −0.142869
\(852\) 0 0
\(853\) −43.0788 −1.47499 −0.737495 0.675352i \(-0.763992\pi\)
−0.737495 + 0.675352i \(0.763992\pi\)
\(854\) 1.59100 0.0544430
\(855\) 0 0
\(856\) −2.33424 −0.0797825
\(857\) −56.4937 −1.92979 −0.964895 0.262637i \(-0.915408\pi\)
−0.964895 + 0.262637i \(0.915408\pi\)
\(858\) 0 0
\(859\) 13.8657 0.473093 0.236547 0.971620i \(-0.423984\pi\)
0.236547 + 0.971620i \(0.423984\pi\)
\(860\) −15.8141 −0.539255
\(861\) 0 0
\(862\) 80.5884 2.74485
\(863\) 12.0348 0.409669 0.204835 0.978797i \(-0.434334\pi\)
0.204835 + 0.978797i \(0.434334\pi\)
\(864\) 0 0
\(865\) −0.0357404 −0.00121521
\(866\) −11.2942 −0.383792
\(867\) 0 0
\(868\) 2.62216 0.0890020
\(869\) 53.8391 1.82636
\(870\) 0 0
\(871\) 1.32296 0.0448269
\(872\) 7.06305 0.239185
\(873\) 0 0
\(874\) 7.62122 0.257792
\(875\) 3.12389 0.105607
\(876\) 0 0
\(877\) −26.0150 −0.878463 −0.439232 0.898374i \(-0.644749\pi\)
−0.439232 + 0.898374i \(0.644749\pi\)
\(878\) −25.5498 −0.862265
\(879\) 0 0
\(880\) 27.6562 0.932291
\(881\) 18.7821 0.632785 0.316392 0.948628i \(-0.397528\pi\)
0.316392 + 0.948628i \(0.397528\pi\)
\(882\) 0 0
\(883\) −8.62443 −0.290235 −0.145118 0.989414i \(-0.546356\pi\)
−0.145118 + 0.989414i \(0.546356\pi\)
\(884\) −0.995010 −0.0334658
\(885\) 0 0
\(886\) −23.5316 −0.790560
\(887\) 39.3782 1.32219 0.661095 0.750302i \(-0.270092\pi\)
0.661095 + 0.750302i \(0.270092\pi\)
\(888\) 0 0
\(889\) 3.47275 0.116472
\(890\) −5.24253 −0.175730
\(891\) 0 0
\(892\) −41.4142 −1.38665
\(893\) 22.3007 0.746265
\(894\) 0 0
\(895\) −1.44413 −0.0482720
\(896\) 1.59677 0.0533444
\(897\) 0 0
\(898\) −42.5280 −1.41918
\(899\) −4.05707 −0.135311
\(900\) 0 0
\(901\) −8.70553 −0.290023
\(902\) 41.2971 1.37504
\(903\) 0 0
\(904\) −14.2992 −0.475586
\(905\) 32.6364 1.08487
\(906\) 0 0
\(907\) 8.33324 0.276701 0.138350 0.990383i \(-0.455820\pi\)
0.138350 + 0.990383i \(0.455820\pi\)
\(908\) 64.4173 2.13776
\(909\) 0 0
\(910\) −0.154285 −0.00511450
\(911\) 40.2510 1.33358 0.666788 0.745247i \(-0.267669\pi\)
0.666788 + 0.745247i \(0.267669\pi\)
\(912\) 0 0
\(913\) 14.8295 0.490784
\(914\) −29.7723 −0.984780
\(915\) 0 0
\(916\) −47.7255 −1.57690
\(917\) −2.14656 −0.0708856
\(918\) 0 0
\(919\) 34.7016 1.14470 0.572351 0.820009i \(-0.306032\pi\)
0.572351 + 0.820009i \(0.306032\pi\)
\(920\) 1.05636 0.0348272
\(921\) 0 0
\(922\) −60.3497 −1.98751
\(923\) −0.657562 −0.0216439
\(924\) 0 0
\(925\) 12.3113 0.404793
\(926\) −22.6481 −0.744262
\(927\) 0 0
\(928\) −8.08505 −0.265405
\(929\) 25.0656 0.822376 0.411188 0.911551i \(-0.365114\pi\)
0.411188 + 0.911551i \(0.365114\pi\)
\(930\) 0 0
\(931\) −25.2918 −0.828905
\(932\) −7.15325 −0.234313
\(933\) 0 0
\(934\) −38.2049 −1.25010
\(935\) 19.6077 0.641239
\(936\) 0 0
\(937\) −48.2923 −1.57764 −0.788821 0.614623i \(-0.789308\pi\)
−0.788821 + 0.614623i \(0.789308\pi\)
\(938\) −4.02600 −0.131454
\(939\) 0 0
\(940\) 20.5583 0.670538
\(941\) 16.0613 0.523582 0.261791 0.965125i \(-0.415687\pi\)
0.261791 + 0.965125i \(0.415687\pi\)
\(942\) 0 0
\(943\) −3.24174 −0.105566
\(944\) −9.23705 −0.300640
\(945\) 0 0
\(946\) 59.8316 1.94529
\(947\) 36.9475 1.20063 0.600316 0.799763i \(-0.295041\pi\)
0.600316 + 0.799763i \(0.295041\pi\)
\(948\) 0 0
\(949\) −2.29644 −0.0745456
\(950\) −22.5126 −0.730404
\(951\) 0 0
\(952\) 0.455274 0.0147555
\(953\) 31.1650 1.00953 0.504766 0.863256i \(-0.331579\pi\)
0.504766 + 0.863256i \(0.331579\pi\)
\(954\) 0 0
\(955\) 4.16695 0.134839
\(956\) −4.10442 −0.132746
\(957\) 0 0
\(958\) 61.0938 1.97385
\(959\) 0.610170 0.0197034
\(960\) 0 0
\(961\) −14.5402 −0.469038
\(962\) −1.63724 −0.0527869
\(963\) 0 0
\(964\) 9.40331 0.302860
\(965\) −5.03353 −0.162035
\(966\) 0 0
\(967\) 57.2912 1.84236 0.921181 0.389134i \(-0.127226\pi\)
0.921181 + 0.389134i \(0.127226\pi\)
\(968\) 19.4030 0.623637
\(969\) 0 0
\(970\) −17.1086 −0.549325
\(971\) −36.2034 −1.16182 −0.580912 0.813966i \(-0.697304\pi\)
−0.580912 + 0.813966i \(0.697304\pi\)
\(972\) 0 0
\(973\) −3.77563 −0.121041
\(974\) 5.25646 0.168428
\(975\) 0 0
\(976\) 8.79445 0.281503
\(977\) −36.0090 −1.15203 −0.576015 0.817439i \(-0.695393\pi\)
−0.576015 + 0.817439i \(0.695393\pi\)
\(978\) 0 0
\(979\) 10.7236 0.342727
\(980\) −23.3157 −0.744793
\(981\) 0 0
\(982\) −37.7239 −1.20382
\(983\) 14.3777 0.458576 0.229288 0.973359i \(-0.426360\pi\)
0.229288 + 0.973359i \(0.426360\pi\)
\(984\) 0 0
\(985\) 21.1316 0.673310
\(986\) −4.68496 −0.149200
\(987\) 0 0
\(988\) 1.61862 0.0514953
\(989\) −4.69667 −0.149346
\(990\) 0 0
\(991\) 5.18303 0.164644 0.0823221 0.996606i \(-0.473766\pi\)
0.0823221 + 0.996606i \(0.473766\pi\)
\(992\) 32.8016 1.04145
\(993\) 0 0
\(994\) 2.00107 0.0634702
\(995\) 34.0114 1.07823
\(996\) 0 0
\(997\) −50.0974 −1.58660 −0.793301 0.608830i \(-0.791639\pi\)
−0.793301 + 0.608830i \(0.791639\pi\)
\(998\) 41.3319 1.30834
\(999\) 0 0
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 \(a_p\))