Properties

Label 4005.2.a.l.1.2
Level 4005
Weight 2
Character 4005.1
Self dual Yes
Analytic conductor 31.980
Analytic rank 0
Dimension 4
CM No
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 4005 = 3^{2} \cdot 5 \cdot 89 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 4005.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(31.9800860095\)
Analytic rank: \(0\)
Dimension: \(4\)
Coefficient field: 4.4.725.1
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.2
Root \(0.737640\)
Character \(\chi\) = 4005.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.45589 q^{2} +0.119606 q^{4} +1.00000 q^{5} +3.71135 q^{7} +2.73764 q^{8} +O(q^{10})\) \(q-1.45589 q^{2} +0.119606 q^{4} +1.00000 q^{5} +3.71135 q^{7} +2.73764 q^{8} -1.45589 q^{10} +1.80647 q^{11} -6.78527 q^{13} -5.40330 q^{14} -4.22491 q^{16} +1.92293 q^{17} -6.21801 q^{19} +0.119606 q^{20} -2.63002 q^{22} -1.39822 q^{23} +1.00000 q^{25} +9.87858 q^{26} +0.443901 q^{28} +4.99310 q^{29} +1.92427 q^{31} +0.675706 q^{32} -2.79958 q^{34} +3.71135 q^{35} +2.70709 q^{37} +9.05272 q^{38} +2.73764 q^{40} -2.91604 q^{41} +0.211586 q^{43} +0.216066 q^{44} +2.03564 q^{46} +9.61114 q^{47} +6.77411 q^{49} -1.45589 q^{50} -0.811561 q^{52} -10.9331 q^{53} +1.80647 q^{55} +10.1603 q^{56} -7.26939 q^{58} +12.0984 q^{59} +10.1997 q^{61} -2.80152 q^{62} +7.46606 q^{64} -6.78527 q^{65} +2.88548 q^{67} +0.229995 q^{68} -5.40330 q^{70} +3.85919 q^{71} +11.5899 q^{73} -3.94121 q^{74} -0.743713 q^{76} +6.70445 q^{77} -10.8158 q^{79} -4.22491 q^{80} +4.24542 q^{82} +5.59257 q^{83} +1.92293 q^{85} -0.308045 q^{86} +4.94547 q^{88} +1.00000 q^{89} -25.1825 q^{91} -0.167235 q^{92} -13.9927 q^{94} -6.21801 q^{95} +1.07064 q^{97} -9.86233 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4q - q^{2} + 3q^{4} + 4q^{5} + 2q^{7} + 9q^{8} + O(q^{10}) \) \( 4q - q^{2} + 3q^{4} + 4q^{5} + 2q^{7} + 9q^{8} - q^{10} + 14q^{11} - 5q^{13} + 5q^{14} - 3q^{16} + 3q^{17} - q^{19} + 3q^{20} + 2q^{22} + 3q^{23} + 4q^{25} + 9q^{26} + 5q^{28} + 10q^{29} - 11q^{31} + 2q^{32} - 8q^{34} + 2q^{35} + 3q^{37} - 2q^{38} + 9q^{40} + 3q^{41} + 9q^{43} + 9q^{44} - 4q^{46} + 24q^{47} - q^{50} + 8q^{52} - 3q^{53} + 14q^{55} + 13q^{56} + 19q^{58} + 22q^{59} - 3q^{61} + 24q^{62} - 11q^{64} - 5q^{65} - 9q^{67} - 31q^{68} + 5q^{70} - 16q^{71} + 3q^{73} - 31q^{74} - 24q^{76} + 4q^{77} - 27q^{79} - 3q^{80} - 15q^{82} - 6q^{83} + 3q^{85} - 15q^{86} + 30q^{88} + 4q^{89} - 29q^{91} + 17q^{92} + 13q^{94} - q^{95} + 41q^{97} - 22q^{98} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.45589 −1.02947 −0.514734 0.857350i \(-0.672109\pi\)
−0.514734 + 0.857350i \(0.672109\pi\)
\(3\) 0 0
\(4\) 0.119606 0.0598032
\(5\) 1.00000 0.447214
\(6\) 0 0
\(7\) 3.71135 1.40276 0.701379 0.712789i \(-0.252568\pi\)
0.701379 + 0.712789i \(0.252568\pi\)
\(8\) 2.73764 0.967902
\(9\) 0 0
\(10\) −1.45589 −0.460392
\(11\) 1.80647 0.544672 0.272336 0.962202i \(-0.412204\pi\)
0.272336 + 0.962202i \(0.412204\pi\)
\(12\) 0 0
\(13\) −6.78527 −1.88190 −0.940948 0.338552i \(-0.890063\pi\)
−0.940948 + 0.338552i \(0.890063\pi\)
\(14\) −5.40330 −1.44409
\(15\) 0 0
\(16\) −4.22491 −1.05623
\(17\) 1.92293 0.466380 0.233190 0.972431i \(-0.425084\pi\)
0.233190 + 0.972431i \(0.425084\pi\)
\(18\) 0 0
\(19\) −6.21801 −1.42651 −0.713255 0.700905i \(-0.752780\pi\)
−0.713255 + 0.700905i \(0.752780\pi\)
\(20\) 0.119606 0.0267448
\(21\) 0 0
\(22\) −2.63002 −0.560722
\(23\) −1.39822 −0.291548 −0.145774 0.989318i \(-0.546567\pi\)
−0.145774 + 0.989318i \(0.546567\pi\)
\(24\) 0 0
\(25\) 1.00000 0.200000
\(26\) 9.87858 1.93735
\(27\) 0 0
\(28\) 0.443901 0.0838894
\(29\) 4.99310 0.927196 0.463598 0.886046i \(-0.346558\pi\)
0.463598 + 0.886046i \(0.346558\pi\)
\(30\) 0 0
\(31\) 1.92427 0.345609 0.172805 0.984956i \(-0.444717\pi\)
0.172805 + 0.984956i \(0.444717\pi\)
\(32\) 0.675706 0.119449
\(33\) 0 0
\(34\) −2.79958 −0.480123
\(35\) 3.71135 0.627332
\(36\) 0 0
\(37\) 2.70709 0.445042 0.222521 0.974928i \(-0.428571\pi\)
0.222521 + 0.974928i \(0.428571\pi\)
\(38\) 9.05272 1.46854
\(39\) 0 0
\(40\) 2.73764 0.432859
\(41\) −2.91604 −0.455408 −0.227704 0.973730i \(-0.573122\pi\)
−0.227704 + 0.973730i \(0.573122\pi\)
\(42\) 0 0
\(43\) 0.211586 0.0322666 0.0161333 0.999870i \(-0.494864\pi\)
0.0161333 + 0.999870i \(0.494864\pi\)
\(44\) 0.216066 0.0325731
\(45\) 0 0
\(46\) 2.03564 0.300139
\(47\) 9.61114 1.40193 0.700964 0.713197i \(-0.252753\pi\)
0.700964 + 0.713197i \(0.252753\pi\)
\(48\) 0 0
\(49\) 6.77411 0.967730
\(50\) −1.45589 −0.205893
\(51\) 0 0
\(52\) −0.811561 −0.112543
\(53\) −10.9331 −1.50178 −0.750889 0.660428i \(-0.770375\pi\)
−0.750889 + 0.660428i \(0.770375\pi\)
\(54\) 0 0
\(55\) 1.80647 0.243585
\(56\) 10.1603 1.35773
\(57\) 0 0
\(58\) −7.26939 −0.954518
\(59\) 12.0984 1.57508 0.787539 0.616265i \(-0.211355\pi\)
0.787539 + 0.616265i \(0.211355\pi\)
\(60\) 0 0
\(61\) 10.1997 1.30594 0.652971 0.757383i \(-0.273522\pi\)
0.652971 + 0.757383i \(0.273522\pi\)
\(62\) −2.80152 −0.355793
\(63\) 0 0
\(64\) 7.46606 0.933258
\(65\) −6.78527 −0.841609
\(66\) 0 0
\(67\) 2.88548 0.352518 0.176259 0.984344i \(-0.443600\pi\)
0.176259 + 0.984344i \(0.443600\pi\)
\(68\) 0.229995 0.0278910
\(69\) 0 0
\(70\) −5.40330 −0.645818
\(71\) 3.85919 0.458002 0.229001 0.973426i \(-0.426454\pi\)
0.229001 + 0.973426i \(0.426454\pi\)
\(72\) 0 0
\(73\) 11.5899 1.35650 0.678250 0.734832i \(-0.262739\pi\)
0.678250 + 0.734832i \(0.262739\pi\)
\(74\) −3.94121 −0.458156
\(75\) 0 0
\(76\) −0.743713 −0.0853098
\(77\) 6.70445 0.764043
\(78\) 0 0
\(79\) −10.8158 −1.21688 −0.608438 0.793602i \(-0.708203\pi\)
−0.608438 + 0.793602i \(0.708203\pi\)
\(80\) −4.22491 −0.472359
\(81\) 0 0
\(82\) 4.24542 0.468828
\(83\) 5.59257 0.613864 0.306932 0.951731i \(-0.400698\pi\)
0.306932 + 0.951731i \(0.400698\pi\)
\(84\) 0 0
\(85\) 1.92293 0.208572
\(86\) −0.308045 −0.0332174
\(87\) 0 0
\(88\) 4.94547 0.527189
\(89\) 1.00000 0.106000
\(90\) 0 0
\(91\) −25.1825 −2.63984
\(92\) −0.167235 −0.0174355
\(93\) 0 0
\(94\) −13.9927 −1.44324
\(95\) −6.21801 −0.637954
\(96\) 0 0
\(97\) 1.07064 0.108707 0.0543536 0.998522i \(-0.482690\pi\)
0.0543536 + 0.998522i \(0.482690\pi\)
\(98\) −9.86233 −0.996246
\(99\) 0 0
\(100\) 0.119606 0.0119606
\(101\) 13.8603 1.37915 0.689576 0.724213i \(-0.257797\pi\)
0.689576 + 0.724213i \(0.257797\pi\)
\(102\) 0 0
\(103\) 2.85216 0.281032 0.140516 0.990078i \(-0.455124\pi\)
0.140516 + 0.990078i \(0.455124\pi\)
\(104\) −18.5756 −1.82149
\(105\) 0 0
\(106\) 15.9174 1.54603
\(107\) 1.48908 0.143954 0.0719772 0.997406i \(-0.477069\pi\)
0.0719772 + 0.997406i \(0.477069\pi\)
\(108\) 0 0
\(109\) 9.40330 0.900673 0.450337 0.892859i \(-0.351304\pi\)
0.450337 + 0.892859i \(0.351304\pi\)
\(110\) −2.63002 −0.250763
\(111\) 0 0
\(112\) −15.6801 −1.48163
\(113\) −12.6841 −1.19322 −0.596609 0.802532i \(-0.703485\pi\)
−0.596609 + 0.802532i \(0.703485\pi\)
\(114\) 0 0
\(115\) −1.39822 −0.130384
\(116\) 0.597207 0.0554492
\(117\) 0 0
\(118\) −17.6139 −1.62149
\(119\) 7.13668 0.654218
\(120\) 0 0
\(121\) −7.73666 −0.703332
\(122\) −14.8497 −1.34442
\(123\) 0 0
\(124\) 0.230155 0.0206685
\(125\) 1.00000 0.0894427
\(126\) 0 0
\(127\) 1.25413 0.111286 0.0556429 0.998451i \(-0.482279\pi\)
0.0556429 + 0.998451i \(0.482279\pi\)
\(128\) −12.2212 −1.08021
\(129\) 0 0
\(130\) 9.87858 0.866409
\(131\) 2.27240 0.198541 0.0992704 0.995060i \(-0.468349\pi\)
0.0992704 + 0.995060i \(0.468349\pi\)
\(132\) 0 0
\(133\) −23.0772 −2.00105
\(134\) −4.20093 −0.362905
\(135\) 0 0
\(136\) 5.26430 0.451410
\(137\) 15.5836 1.33140 0.665700 0.746219i \(-0.268133\pi\)
0.665700 + 0.746219i \(0.268133\pi\)
\(138\) 0 0
\(139\) −21.5004 −1.82364 −0.911819 0.410593i \(-0.865322\pi\)
−0.911819 + 0.410593i \(0.865322\pi\)
\(140\) 0.443901 0.0375165
\(141\) 0 0
\(142\) −5.61854 −0.471498
\(143\) −12.2574 −1.02502
\(144\) 0 0
\(145\) 4.99310 0.414655
\(146\) −16.8736 −1.39647
\(147\) 0 0
\(148\) 0.323785 0.0266149
\(149\) 17.0028 1.39292 0.696461 0.717595i \(-0.254757\pi\)
0.696461 + 0.717595i \(0.254757\pi\)
\(150\) 0 0
\(151\) −17.7866 −1.44745 −0.723727 0.690087i \(-0.757572\pi\)
−0.723727 + 0.690087i \(0.757572\pi\)
\(152\) −17.0227 −1.38072
\(153\) 0 0
\(154\) −9.76092 −0.786557
\(155\) 1.92427 0.154561
\(156\) 0 0
\(157\) −8.13061 −0.648893 −0.324447 0.945904i \(-0.605178\pi\)
−0.324447 + 0.945904i \(0.605178\pi\)
\(158\) 15.7466 1.25273
\(159\) 0 0
\(160\) 0.675706 0.0534192
\(161\) −5.18926 −0.408971
\(162\) 0 0
\(163\) 23.0135 1.80255 0.901276 0.433244i \(-0.142631\pi\)
0.901276 + 0.433244i \(0.142631\pi\)
\(164\) −0.348776 −0.0272349
\(165\) 0 0
\(166\) −8.14214 −0.631953
\(167\) −5.88974 −0.455762 −0.227881 0.973689i \(-0.573180\pi\)
−0.227881 + 0.973689i \(0.573180\pi\)
\(168\) 0 0
\(169\) 33.0399 2.54153
\(170\) −2.79958 −0.214718
\(171\) 0 0
\(172\) 0.0253070 0.00192964
\(173\) 15.0723 1.14593 0.572964 0.819581i \(-0.305794\pi\)
0.572964 + 0.819581i \(0.305794\pi\)
\(174\) 0 0
\(175\) 3.71135 0.280552
\(176\) −7.63218 −0.575297
\(177\) 0 0
\(178\) −1.45589 −0.109123
\(179\) −4.65562 −0.347977 −0.173989 0.984748i \(-0.555666\pi\)
−0.173989 + 0.984748i \(0.555666\pi\)
\(180\) 0 0
\(181\) 9.62070 0.715101 0.357551 0.933894i \(-0.383612\pi\)
0.357551 + 0.933894i \(0.383612\pi\)
\(182\) 36.6629 2.71763
\(183\) 0 0
\(184\) −3.82781 −0.282190
\(185\) 2.70709 0.199029
\(186\) 0 0
\(187\) 3.47373 0.254024
\(188\) 1.14955 0.0838397
\(189\) 0 0
\(190\) 9.05272 0.656753
\(191\) −13.3629 −0.966907 −0.483454 0.875370i \(-0.660618\pi\)
−0.483454 + 0.875370i \(0.660618\pi\)
\(192\) 0 0
\(193\) 0.449680 0.0323687 0.0161843 0.999869i \(-0.494848\pi\)
0.0161843 + 0.999869i \(0.494848\pi\)
\(194\) −1.55873 −0.111911
\(195\) 0 0
\(196\) 0.810226 0.0578733
\(197\) −8.56942 −0.610546 −0.305273 0.952265i \(-0.598748\pi\)
−0.305273 + 0.952265i \(0.598748\pi\)
\(198\) 0 0
\(199\) −8.67704 −0.615099 −0.307550 0.951532i \(-0.599509\pi\)
−0.307550 + 0.951532i \(0.599509\pi\)
\(200\) 2.73764 0.193580
\(201\) 0 0
\(202\) −20.1790 −1.41979
\(203\) 18.5311 1.30063
\(204\) 0 0
\(205\) −2.91604 −0.203665
\(206\) −4.15242 −0.289313
\(207\) 0 0
\(208\) 28.6671 1.98771
\(209\) −11.2327 −0.776980
\(210\) 0 0
\(211\) 25.1953 1.73452 0.867258 0.497858i \(-0.165880\pi\)
0.867258 + 0.497858i \(0.165880\pi\)
\(212\) −1.30767 −0.0898111
\(213\) 0 0
\(214\) −2.16793 −0.148196
\(215\) 0.211586 0.0144300
\(216\) 0 0
\(217\) 7.14163 0.484806
\(218\) −13.6901 −0.927214
\(219\) 0 0
\(220\) 0.216066 0.0145671
\(221\) −13.0476 −0.877679
\(222\) 0 0
\(223\) 16.2438 1.08777 0.543884 0.839161i \(-0.316953\pi\)
0.543884 + 0.839161i \(0.316953\pi\)
\(224\) 2.50778 0.167558
\(225\) 0 0
\(226\) 18.4666 1.22838
\(227\) 13.1941 0.875726 0.437863 0.899042i \(-0.355736\pi\)
0.437863 + 0.899042i \(0.355736\pi\)
\(228\) 0 0
\(229\) 2.36998 0.156613 0.0783063 0.996929i \(-0.475049\pi\)
0.0783063 + 0.996929i \(0.475049\pi\)
\(230\) 2.03564 0.134226
\(231\) 0 0
\(232\) 13.6693 0.897435
\(233\) 9.67877 0.634077 0.317039 0.948413i \(-0.397312\pi\)
0.317039 + 0.948413i \(0.397312\pi\)
\(234\) 0 0
\(235\) 9.61114 0.626961
\(236\) 1.44705 0.0941946
\(237\) 0 0
\(238\) −10.3902 −0.673497
\(239\) 23.8871 1.54513 0.772564 0.634936i \(-0.218974\pi\)
0.772564 + 0.634936i \(0.218974\pi\)
\(240\) 0 0
\(241\) −15.7221 −1.01275 −0.506376 0.862313i \(-0.669015\pi\)
−0.506376 + 0.862313i \(0.669015\pi\)
\(242\) 11.2637 0.724058
\(243\) 0 0
\(244\) 1.21995 0.0780995
\(245\) 6.77411 0.432782
\(246\) 0 0
\(247\) 42.1909 2.68454
\(248\) 5.26796 0.334516
\(249\) 0 0
\(250\) −1.45589 −0.0920784
\(251\) −14.2933 −0.902183 −0.451091 0.892478i \(-0.648965\pi\)
−0.451091 + 0.892478i \(0.648965\pi\)
\(252\) 0 0
\(253\) −2.52584 −0.158798
\(254\) −1.82587 −0.114565
\(255\) 0 0
\(256\) 2.86049 0.178781
\(257\) 8.51369 0.531070 0.265535 0.964101i \(-0.414451\pi\)
0.265535 + 0.964101i \(0.414451\pi\)
\(258\) 0 0
\(259\) 10.0469 0.624286
\(260\) −0.811561 −0.0503309
\(261\) 0 0
\(262\) −3.30836 −0.204391
\(263\) 19.3754 1.19474 0.597370 0.801966i \(-0.296212\pi\)
0.597370 + 0.801966i \(0.296212\pi\)
\(264\) 0 0
\(265\) −10.9331 −0.671616
\(266\) 33.5978 2.06001
\(267\) 0 0
\(268\) 0.345122 0.0210817
\(269\) 7.39853 0.451096 0.225548 0.974232i \(-0.427583\pi\)
0.225548 + 0.974232i \(0.427583\pi\)
\(270\) 0 0
\(271\) −27.2477 −1.65518 −0.827590 0.561333i \(-0.810289\pi\)
−0.827590 + 0.561333i \(0.810289\pi\)
\(272\) −8.12422 −0.492603
\(273\) 0 0
\(274\) −22.6880 −1.37063
\(275\) 1.80647 0.108934
\(276\) 0 0
\(277\) 28.4582 1.70989 0.854943 0.518722i \(-0.173592\pi\)
0.854943 + 0.518722i \(0.173592\pi\)
\(278\) 31.3021 1.87738
\(279\) 0 0
\(280\) 10.1603 0.607196
\(281\) −22.1815 −1.32323 −0.661617 0.749842i \(-0.730130\pi\)
−0.661617 + 0.749842i \(0.730130\pi\)
\(282\) 0 0
\(283\) 0.247445 0.0147091 0.00735455 0.999973i \(-0.497659\pi\)
0.00735455 + 0.999973i \(0.497659\pi\)
\(284\) 0.461584 0.0273899
\(285\) 0 0
\(286\) 17.8454 1.05522
\(287\) −10.8224 −0.638828
\(288\) 0 0
\(289\) −13.3023 −0.782490
\(290\) −7.26939 −0.426873
\(291\) 0 0
\(292\) 1.38623 0.0811229
\(293\) 11.3844 0.665085 0.332542 0.943088i \(-0.392094\pi\)
0.332542 + 0.943088i \(0.392094\pi\)
\(294\) 0 0
\(295\) 12.0984 0.704396
\(296\) 7.41103 0.430757
\(297\) 0 0
\(298\) −24.7541 −1.43397
\(299\) 9.48727 0.548663
\(300\) 0 0
\(301\) 0.785269 0.0452622
\(302\) 25.8953 1.49011
\(303\) 0 0
\(304\) 26.2705 1.50672
\(305\) 10.1997 0.584035
\(306\) 0 0
\(307\) −6.37110 −0.363618 −0.181809 0.983334i \(-0.558195\pi\)
−0.181809 + 0.983334i \(0.558195\pi\)
\(308\) 0.801895 0.0456922
\(309\) 0 0
\(310\) −2.80152 −0.159116
\(311\) 30.5996 1.73514 0.867572 0.497312i \(-0.165679\pi\)
0.867572 + 0.497312i \(0.165679\pi\)
\(312\) 0 0
\(313\) −19.2316 −1.08704 −0.543518 0.839398i \(-0.682908\pi\)
−0.543518 + 0.839398i \(0.682908\pi\)
\(314\) 11.8372 0.668014
\(315\) 0 0
\(316\) −1.29364 −0.0727730
\(317\) 9.70429 0.545047 0.272524 0.962149i \(-0.412142\pi\)
0.272524 + 0.962149i \(0.412142\pi\)
\(318\) 0 0
\(319\) 9.01990 0.505018
\(320\) 7.46606 0.417366
\(321\) 0 0
\(322\) 7.55498 0.421023
\(323\) −11.9568 −0.665296
\(324\) 0 0
\(325\) −6.78527 −0.376379
\(326\) −33.5050 −1.85567
\(327\) 0 0
\(328\) −7.98306 −0.440791
\(329\) 35.6703 1.96657
\(330\) 0 0
\(331\) −28.9275 −1.59000 −0.795001 0.606608i \(-0.792530\pi\)
−0.795001 + 0.606608i \(0.792530\pi\)
\(332\) 0.668906 0.0367110
\(333\) 0 0
\(334\) 8.57480 0.469192
\(335\) 2.88548 0.157651
\(336\) 0 0
\(337\) 2.30865 0.125760 0.0628802 0.998021i \(-0.479971\pi\)
0.0628802 + 0.998021i \(0.479971\pi\)
\(338\) −48.1023 −2.61642
\(339\) 0 0
\(340\) 0.229995 0.0124732
\(341\) 3.47614 0.188244
\(342\) 0 0
\(343\) −0.838363 −0.0452673
\(344\) 0.579246 0.0312309
\(345\) 0 0
\(346\) −21.9436 −1.17970
\(347\) 34.4649 1.85017 0.925085 0.379759i \(-0.123993\pi\)
0.925085 + 0.379759i \(0.123993\pi\)
\(348\) 0 0
\(349\) 19.3154 1.03393 0.516965 0.856007i \(-0.327062\pi\)
0.516965 + 0.856007i \(0.327062\pi\)
\(350\) −5.40330 −0.288819
\(351\) 0 0
\(352\) 1.22064 0.0650605
\(353\) −1.41183 −0.0751441 −0.0375721 0.999294i \(-0.511962\pi\)
−0.0375721 + 0.999294i \(0.511962\pi\)
\(354\) 0 0
\(355\) 3.85919 0.204825
\(356\) 0.119606 0.00633912
\(357\) 0 0
\(358\) 6.77806 0.358231
\(359\) 17.2200 0.908834 0.454417 0.890789i \(-0.349848\pi\)
0.454417 + 0.890789i \(0.349848\pi\)
\(360\) 0 0
\(361\) 19.6636 1.03493
\(362\) −14.0067 −0.736173
\(363\) 0 0
\(364\) −3.01199 −0.157871
\(365\) 11.5899 0.606645
\(366\) 0 0
\(367\) −20.4193 −1.06588 −0.532939 0.846154i \(-0.678913\pi\)
−0.532939 + 0.846154i \(0.678913\pi\)
\(368\) 5.90733 0.307941
\(369\) 0 0
\(370\) −3.94121 −0.204894
\(371\) −40.5766 −2.10663
\(372\) 0 0
\(373\) −0.00410346 −0.000212469 0 −0.000106235 1.00000i \(-0.500034\pi\)
−0.000106235 1.00000i \(0.500034\pi\)
\(374\) −5.05736 −0.261510
\(375\) 0 0
\(376\) 26.3118 1.35693
\(377\) −33.8795 −1.74489
\(378\) 0 0
\(379\) 33.3456 1.71285 0.856424 0.516273i \(-0.172681\pi\)
0.856424 + 0.516273i \(0.172681\pi\)
\(380\) −0.743713 −0.0381517
\(381\) 0 0
\(382\) 19.4549 0.995399
\(383\) −34.6473 −1.77039 −0.885196 0.465218i \(-0.845976\pi\)
−0.885196 + 0.465218i \(0.845976\pi\)
\(384\) 0 0
\(385\) 6.70445 0.341690
\(386\) −0.654683 −0.0333225
\(387\) 0 0
\(388\) 0.128056 0.00650104
\(389\) −30.7954 −1.56139 −0.780696 0.624912i \(-0.785135\pi\)
−0.780696 + 0.624912i \(0.785135\pi\)
\(390\) 0 0
\(391\) −2.68868 −0.135972
\(392\) 18.5451 0.936668
\(393\) 0 0
\(394\) 12.4761 0.628537
\(395\) −10.8158 −0.544203
\(396\) 0 0
\(397\) 30.1664 1.51401 0.757004 0.653411i \(-0.226662\pi\)
0.757004 + 0.653411i \(0.226662\pi\)
\(398\) 12.6328 0.633224
\(399\) 0 0
\(400\) −4.22491 −0.211245
\(401\) 7.51947 0.375504 0.187752 0.982216i \(-0.439880\pi\)
0.187752 + 0.982216i \(0.439880\pi\)
\(402\) 0 0
\(403\) −13.0567 −0.650400
\(404\) 1.65778 0.0824777
\(405\) 0 0
\(406\) −26.9792 −1.33896
\(407\) 4.89028 0.242402
\(408\) 0 0
\(409\) 32.8936 1.62648 0.813241 0.581927i \(-0.197701\pi\)
0.813241 + 0.581927i \(0.197701\pi\)
\(410\) 4.24542 0.209666
\(411\) 0 0
\(412\) 0.341136 0.0168066
\(413\) 44.9014 2.20945
\(414\) 0 0
\(415\) 5.59257 0.274528
\(416\) −4.58484 −0.224790
\(417\) 0 0
\(418\) 16.3535 0.799875
\(419\) −15.0851 −0.736957 −0.368479 0.929636i \(-0.620121\pi\)
−0.368479 + 0.929636i \(0.620121\pi\)
\(420\) 0 0
\(421\) −23.0575 −1.12375 −0.561876 0.827221i \(-0.689920\pi\)
−0.561876 + 0.827221i \(0.689920\pi\)
\(422\) −36.6815 −1.78563
\(423\) 0 0
\(424\) −29.9309 −1.45357
\(425\) 1.92293 0.0932760
\(426\) 0 0
\(427\) 37.8548 1.83192
\(428\) 0.178103 0.00860893
\(429\) 0 0
\(430\) −0.308045 −0.0148553
\(431\) 12.8238 0.617703 0.308851 0.951110i \(-0.400055\pi\)
0.308851 + 0.951110i \(0.400055\pi\)
\(432\) 0 0
\(433\) −28.7231 −1.38034 −0.690171 0.723646i \(-0.742465\pi\)
−0.690171 + 0.723646i \(0.742465\pi\)
\(434\) −10.3974 −0.499092
\(435\) 0 0
\(436\) 1.12469 0.0538631
\(437\) 8.69411 0.415896
\(438\) 0 0
\(439\) −23.6489 −1.12870 −0.564349 0.825536i \(-0.690873\pi\)
−0.564349 + 0.825536i \(0.690873\pi\)
\(440\) 4.94547 0.235766
\(441\) 0 0
\(442\) 18.9959 0.903541
\(443\) 35.5043 1.68686 0.843430 0.537239i \(-0.180533\pi\)
0.843430 + 0.537239i \(0.180533\pi\)
\(444\) 0 0
\(445\) 1.00000 0.0474045
\(446\) −23.6492 −1.11982
\(447\) 0 0
\(448\) 27.7092 1.30913
\(449\) −32.7779 −1.54688 −0.773442 0.633867i \(-0.781467\pi\)
−0.773442 + 0.633867i \(0.781467\pi\)
\(450\) 0 0
\(451\) −5.26774 −0.248048
\(452\) −1.51710 −0.0713582
\(453\) 0 0
\(454\) −19.2092 −0.901531
\(455\) −25.1825 −1.18057
\(456\) 0 0
\(457\) 28.7506 1.34490 0.672448 0.740145i \(-0.265243\pi\)
0.672448 + 0.740145i \(0.265243\pi\)
\(458\) −3.45042 −0.161228
\(459\) 0 0
\(460\) −0.167235 −0.00779739
\(461\) 11.6097 0.540717 0.270358 0.962760i \(-0.412858\pi\)
0.270358 + 0.962760i \(0.412858\pi\)
\(462\) 0 0
\(463\) −18.7448 −0.871145 −0.435573 0.900154i \(-0.643454\pi\)
−0.435573 + 0.900154i \(0.643454\pi\)
\(464\) −21.0954 −0.979329
\(465\) 0 0
\(466\) −14.0912 −0.652762
\(467\) 0.634016 0.0293387 0.0146694 0.999892i \(-0.495330\pi\)
0.0146694 + 0.999892i \(0.495330\pi\)
\(468\) 0 0
\(469\) 10.7090 0.494497
\(470\) −13.9927 −0.645436
\(471\) 0 0
\(472\) 33.1211 1.52452
\(473\) 0.382224 0.0175747
\(474\) 0 0
\(475\) −6.21801 −0.285302
\(476\) 0.853592 0.0391243
\(477\) 0 0
\(478\) −34.7769 −1.59066
\(479\) −29.2698 −1.33737 −0.668686 0.743545i \(-0.733143\pi\)
−0.668686 + 0.743545i \(0.733143\pi\)
\(480\) 0 0
\(481\) −18.3683 −0.837523
\(482\) 22.8896 1.04259
\(483\) 0 0
\(484\) −0.925353 −0.0420615
\(485\) 1.07064 0.0486154
\(486\) 0 0
\(487\) 8.96526 0.406255 0.203127 0.979152i \(-0.434889\pi\)
0.203127 + 0.979152i \(0.434889\pi\)
\(488\) 27.9232 1.26402
\(489\) 0 0
\(490\) −9.86233 −0.445535
\(491\) −21.4601 −0.968479 −0.484240 0.874935i \(-0.660904\pi\)
−0.484240 + 0.874935i \(0.660904\pi\)
\(492\) 0 0
\(493\) 9.60141 0.432426
\(494\) −61.4251 −2.76365
\(495\) 0 0
\(496\) −8.12986 −0.365041
\(497\) 14.3228 0.642465
\(498\) 0 0
\(499\) 21.8821 0.979576 0.489788 0.871841i \(-0.337074\pi\)
0.489788 + 0.871841i \(0.337074\pi\)
\(500\) 0.119606 0.00534896
\(501\) 0 0
\(502\) 20.8094 0.928768
\(503\) 8.91940 0.397696 0.198848 0.980030i \(-0.436280\pi\)
0.198848 + 0.980030i \(0.436280\pi\)
\(504\) 0 0
\(505\) 13.8603 0.616776
\(506\) 3.67733 0.163477
\(507\) 0 0
\(508\) 0.150001 0.00665524
\(509\) 5.76572 0.255561 0.127780 0.991802i \(-0.459215\pi\)
0.127780 + 0.991802i \(0.459215\pi\)
\(510\) 0 0
\(511\) 43.0143 1.90284
\(512\) 20.2778 0.896159
\(513\) 0 0
\(514\) −12.3950 −0.546719
\(515\) 2.85216 0.125681
\(516\) 0 0
\(517\) 17.3623 0.763591
\(518\) −14.6272 −0.642682
\(519\) 0 0
\(520\) −18.5756 −0.814595
\(521\) −14.8063 −0.648676 −0.324338 0.945941i \(-0.605142\pi\)
−0.324338 + 0.945941i \(0.605142\pi\)
\(522\) 0 0
\(523\) 34.3182 1.50063 0.750315 0.661081i \(-0.229902\pi\)
0.750315 + 0.661081i \(0.229902\pi\)
\(524\) 0.271794 0.0118734
\(525\) 0 0
\(526\) −28.2084 −1.22995
\(527\) 3.70024 0.161185
\(528\) 0 0
\(529\) −21.0450 −0.915000
\(530\) 15.9174 0.691406
\(531\) 0 0
\(532\) −2.76018 −0.119669
\(533\) 19.7861 0.857031
\(534\) 0 0
\(535\) 1.48908 0.0643784
\(536\) 7.89941 0.341203
\(537\) 0 0
\(538\) −10.7714 −0.464389
\(539\) 12.2372 0.527095
\(540\) 0 0
\(541\) −19.0816 −0.820384 −0.410192 0.911999i \(-0.634538\pi\)
−0.410192 + 0.911999i \(0.634538\pi\)
\(542\) 39.6696 1.70395
\(543\) 0 0
\(544\) 1.29934 0.0557086
\(545\) 9.40330 0.402793
\(546\) 0 0
\(547\) −16.2497 −0.694789 −0.347394 0.937719i \(-0.612933\pi\)
−0.347394 + 0.937719i \(0.612933\pi\)
\(548\) 1.86390 0.0796220
\(549\) 0 0
\(550\) −2.63002 −0.112144
\(551\) −31.0472 −1.32265
\(552\) 0 0
\(553\) −40.1413 −1.70698
\(554\) −41.4319 −1.76027
\(555\) 0 0
\(556\) −2.57158 −0.109059
\(557\) −34.7023 −1.47038 −0.735191 0.677860i \(-0.762908\pi\)
−0.735191 + 0.677860i \(0.762908\pi\)
\(558\) 0 0
\(559\) −1.43567 −0.0607223
\(560\) −15.6801 −0.662605
\(561\) 0 0
\(562\) 32.2937 1.36223
\(563\) −11.6228 −0.489842 −0.244921 0.969543i \(-0.578762\pi\)
−0.244921 + 0.969543i \(0.578762\pi\)
\(564\) 0 0
\(565\) −12.6841 −0.533623
\(566\) −0.360253 −0.0151425
\(567\) 0 0
\(568\) 10.5651 0.443301
\(569\) −42.6106 −1.78633 −0.893164 0.449732i \(-0.851520\pi\)
−0.893164 + 0.449732i \(0.851520\pi\)
\(570\) 0 0
\(571\) −3.41985 −0.143116 −0.0715582 0.997436i \(-0.522797\pi\)
−0.0715582 + 0.997436i \(0.522797\pi\)
\(572\) −1.46606 −0.0612992
\(573\) 0 0
\(574\) 15.7562 0.657652
\(575\) −1.39822 −0.0583096
\(576\) 0 0
\(577\) 6.58744 0.274239 0.137119 0.990555i \(-0.456216\pi\)
0.137119 + 0.990555i \(0.456216\pi\)
\(578\) 19.3667 0.805548
\(579\) 0 0
\(580\) 0.597207 0.0247977
\(581\) 20.7560 0.861103
\(582\) 0 0
\(583\) −19.7504 −0.817977
\(584\) 31.7291 1.31296
\(585\) 0 0
\(586\) −16.5744 −0.684683
\(587\) 3.93893 0.162577 0.0812884 0.996691i \(-0.474097\pi\)
0.0812884 + 0.996691i \(0.474097\pi\)
\(588\) 0 0
\(589\) −11.9651 −0.493014
\(590\) −17.6139 −0.725153
\(591\) 0 0
\(592\) −11.4372 −0.470065
\(593\) 20.9067 0.858537 0.429269 0.903177i \(-0.358771\pi\)
0.429269 + 0.903177i \(0.358771\pi\)
\(594\) 0 0
\(595\) 7.13668 0.292575
\(596\) 2.03364 0.0833011
\(597\) 0 0
\(598\) −13.8124 −0.564830
\(599\) −8.80091 −0.359595 −0.179798 0.983704i \(-0.557544\pi\)
−0.179798 + 0.983704i \(0.557544\pi\)
\(600\) 0 0
\(601\) 3.04731 0.124303 0.0621513 0.998067i \(-0.480204\pi\)
0.0621513 + 0.998067i \(0.480204\pi\)
\(602\) −1.14326 −0.0465959
\(603\) 0 0
\(604\) −2.12739 −0.0865623
\(605\) −7.73666 −0.314540
\(606\) 0 0
\(607\) −37.2207 −1.51074 −0.755371 0.655298i \(-0.772543\pi\)
−0.755371 + 0.655298i \(0.772543\pi\)
\(608\) −4.20154 −0.170395
\(609\) 0 0
\(610\) −14.8497 −0.601245
\(611\) −65.2141 −2.63828
\(612\) 0 0
\(613\) 7.03831 0.284275 0.142137 0.989847i \(-0.454603\pi\)
0.142137 + 0.989847i \(0.454603\pi\)
\(614\) 9.27560 0.374333
\(615\) 0 0
\(616\) 18.3544 0.739519
\(617\) 41.9256 1.68786 0.843931 0.536452i \(-0.180236\pi\)
0.843931 + 0.536452i \(0.180236\pi\)
\(618\) 0 0
\(619\) −7.92233 −0.318425 −0.159213 0.987244i \(-0.550896\pi\)
−0.159213 + 0.987244i \(0.550896\pi\)
\(620\) 0.230155 0.00924324
\(621\) 0 0
\(622\) −44.5496 −1.78627
\(623\) 3.71135 0.148692
\(624\) 0 0
\(625\) 1.00000 0.0400000
\(626\) 27.9991 1.11907
\(627\) 0 0
\(628\) −0.972472 −0.0388059
\(629\) 5.20555 0.207559
\(630\) 0 0
\(631\) 27.9812 1.11391 0.556956 0.830542i \(-0.311969\pi\)
0.556956 + 0.830542i \(0.311969\pi\)
\(632\) −29.6098 −1.17782
\(633\) 0 0
\(634\) −14.1283 −0.561108
\(635\) 1.25413 0.0497685
\(636\) 0 0
\(637\) −45.9641 −1.82117
\(638\) −13.1320 −0.519899
\(639\) 0 0
\(640\) −12.2212 −0.483084
\(641\) 10.8328 0.427868 0.213934 0.976848i \(-0.431372\pi\)
0.213934 + 0.976848i \(0.431372\pi\)
\(642\) 0 0
\(643\) 33.1604 1.30772 0.653859 0.756616i \(-0.273149\pi\)
0.653859 + 0.756616i \(0.273149\pi\)
\(644\) −0.620669 −0.0244578
\(645\) 0 0
\(646\) 17.4078 0.684900
\(647\) −7.80677 −0.306916 −0.153458 0.988155i \(-0.549041\pi\)
−0.153458 + 0.988155i \(0.549041\pi\)
\(648\) 0 0
\(649\) 21.8554 0.857901
\(650\) 9.87858 0.387470
\(651\) 0 0
\(652\) 2.75255 0.107798
\(653\) 9.79178 0.383182 0.191591 0.981475i \(-0.438635\pi\)
0.191591 + 0.981475i \(0.438635\pi\)
\(654\) 0 0
\(655\) 2.27240 0.0887901
\(656\) 12.3200 0.481015
\(657\) 0 0
\(658\) −51.9319 −2.02452
\(659\) 33.0449 1.28725 0.643623 0.765342i \(-0.277430\pi\)
0.643623 + 0.765342i \(0.277430\pi\)
\(660\) 0 0
\(661\) 21.9348 0.853165 0.426582 0.904449i \(-0.359717\pi\)
0.426582 + 0.904449i \(0.359717\pi\)
\(662\) 42.1152 1.63686
\(663\) 0 0
\(664\) 15.3104 0.594160
\(665\) −23.0772 −0.894895
\(666\) 0 0
\(667\) −6.98143 −0.270322
\(668\) −0.704451 −0.0272560
\(669\) 0 0
\(670\) −4.20093 −0.162296
\(671\) 18.4255 0.711310
\(672\) 0 0
\(673\) 12.6202 0.486472 0.243236 0.969967i \(-0.421791\pi\)
0.243236 + 0.969967i \(0.421791\pi\)
\(674\) −3.36114 −0.129466
\(675\) 0 0
\(676\) 3.95178 0.151991
\(677\) 43.1296 1.65761 0.828803 0.559541i \(-0.189023\pi\)
0.828803 + 0.559541i \(0.189023\pi\)
\(678\) 0 0
\(679\) 3.97353 0.152490
\(680\) 5.26430 0.201877
\(681\) 0 0
\(682\) −5.06087 −0.193791
\(683\) 33.1031 1.26666 0.633328 0.773884i \(-0.281689\pi\)
0.633328 + 0.773884i \(0.281689\pi\)
\(684\) 0 0
\(685\) 15.5836 0.595420
\(686\) 1.22056 0.0466012
\(687\) 0 0
\(688\) −0.893931 −0.0340808
\(689\) 74.1841 2.82619
\(690\) 0 0
\(691\) 11.4778 0.436637 0.218319 0.975878i \(-0.429943\pi\)
0.218319 + 0.975878i \(0.429943\pi\)
\(692\) 1.80275 0.0685301
\(693\) 0 0
\(694\) −50.1769 −1.90469
\(695\) −21.5004 −0.815556
\(696\) 0 0
\(697\) −5.60735 −0.212393
\(698\) −28.1210 −1.06440
\(699\) 0 0
\(700\) 0.443901 0.0167779
\(701\) −27.7156 −1.04680 −0.523401 0.852087i \(-0.675337\pi\)
−0.523401 + 0.852087i \(0.675337\pi\)
\(702\) 0 0
\(703\) −16.8327 −0.634857
\(704\) 13.4872 0.508320
\(705\) 0 0
\(706\) 2.05546 0.0773584
\(707\) 51.4404 1.93462
\(708\) 0 0
\(709\) 21.6735 0.813965 0.406983 0.913436i \(-0.366581\pi\)
0.406983 + 0.913436i \(0.366581\pi\)
\(710\) −5.61854 −0.210860
\(711\) 0 0
\(712\) 2.73764 0.102597
\(713\) −2.69054 −0.100762
\(714\) 0 0
\(715\) −12.2574 −0.458401
\(716\) −0.556842 −0.0208101
\(717\) 0 0
\(718\) −25.0703 −0.935615
\(719\) −13.5991 −0.507160 −0.253580 0.967314i \(-0.581608\pi\)
−0.253580 + 0.967314i \(0.581608\pi\)
\(720\) 0 0
\(721\) 10.5854 0.394219
\(722\) −28.6280 −1.06542
\(723\) 0 0
\(724\) 1.15070 0.0427653
\(725\) 4.99310 0.185439
\(726\) 0 0
\(727\) 22.5512 0.836379 0.418189 0.908360i \(-0.362665\pi\)
0.418189 + 0.908360i \(0.362665\pi\)
\(728\) −68.9406 −2.55511
\(729\) 0 0
\(730\) −16.8736 −0.624521
\(731\) 0.406866 0.0150485
\(732\) 0 0
\(733\) 11.3716 0.420019 0.210009 0.977699i \(-0.432651\pi\)
0.210009 + 0.977699i \(0.432651\pi\)
\(734\) 29.7282 1.09729
\(735\) 0 0
\(736\) −0.944782 −0.0348251
\(737\) 5.21254 0.192007
\(738\) 0 0
\(739\) −51.8437 −1.90710 −0.953551 0.301232i \(-0.902602\pi\)
−0.953551 + 0.301232i \(0.902602\pi\)
\(740\) 0.323785 0.0119026
\(741\) 0 0
\(742\) 59.0749 2.16871
\(743\) −20.9239 −0.767623 −0.383812 0.923411i \(-0.625389\pi\)
−0.383812 + 0.923411i \(0.625389\pi\)
\(744\) 0 0
\(745\) 17.0028 0.622933
\(746\) 0.00597418 0.000218730 0
\(747\) 0 0
\(748\) 0.415480 0.0151915
\(749\) 5.52648 0.201933
\(750\) 0 0
\(751\) 27.2392 0.993972 0.496986 0.867759i \(-0.334440\pi\)
0.496986 + 0.867759i \(0.334440\pi\)
\(752\) −40.6062 −1.48075
\(753\) 0 0
\(754\) 49.3248 1.79630
\(755\) −17.7866 −0.647321
\(756\) 0 0
\(757\) −18.6306 −0.677142 −0.338571 0.940941i \(-0.609943\pi\)
−0.338571 + 0.940941i \(0.609943\pi\)
\(758\) −48.5474 −1.76332
\(759\) 0 0
\(760\) −17.0227 −0.617477
\(761\) 4.06378 0.147312 0.0736559 0.997284i \(-0.476533\pi\)
0.0736559 + 0.997284i \(0.476533\pi\)
\(762\) 0 0
\(763\) 34.8989 1.26343
\(764\) −1.59829 −0.0578241
\(765\) 0 0
\(766\) 50.4425 1.82256
\(767\) −82.0909 −2.96413
\(768\) 0 0
\(769\) −32.7396 −1.18062 −0.590310 0.807177i \(-0.700994\pi\)
−0.590310 + 0.807177i \(0.700994\pi\)
\(770\) −9.76092 −0.351759
\(771\) 0 0
\(772\) 0.0537846 0.00193575
\(773\) −19.0463 −0.685049 −0.342524 0.939509i \(-0.611282\pi\)
−0.342524 + 0.939509i \(0.611282\pi\)
\(774\) 0 0
\(775\) 1.92427 0.0691218
\(776\) 2.93103 0.105218
\(777\) 0 0
\(778\) 44.8347 1.60740
\(779\) 18.1319 0.649644
\(780\) 0 0
\(781\) 6.97152 0.249461
\(782\) 3.91441 0.139979
\(783\) 0 0
\(784\) −28.6200 −1.02214
\(785\) −8.13061 −0.290194
\(786\) 0 0
\(787\) 36.9703 1.31785 0.658924 0.752210i \(-0.271012\pi\)
0.658924 + 0.752210i \(0.271012\pi\)
\(788\) −1.02496 −0.0365126
\(789\) 0 0
\(790\) 15.7466 0.560239
\(791\) −47.0750 −1.67379
\(792\) 0 0
\(793\) −69.2079 −2.45765
\(794\) −43.9188 −1.55862
\(795\) 0 0
\(796\) −1.03783 −0.0367849
\(797\) 10.1404 0.359191 0.179596 0.983741i \(-0.442521\pi\)
0.179596 + 0.983741i \(0.442521\pi\)
\(798\) 0 0
\(799\) 18.4816 0.653832
\(800\) 0.675706 0.0238898
\(801\) 0 0
\(802\) −10.9475 −0.386570
\(803\) 20.9369 0.738847
\(804\) 0 0
\(805\) −5.18926 −0.182898
\(806\) 19.0091 0.669566
\(807\) 0 0
\(808\) 37.9445 1.33488
\(809\) −0.167200 −0.00587845 −0.00293922 0.999996i \(-0.500936\pi\)
−0.00293922 + 0.999996i \(0.500936\pi\)
\(810\) 0 0
\(811\) −41.1102 −1.44357 −0.721787 0.692115i \(-0.756679\pi\)
−0.721787 + 0.692115i \(0.756679\pi\)
\(812\) 2.21644 0.0777819
\(813\) 0 0
\(814\) −7.11969 −0.249545
\(815\) 23.0135 0.806126
\(816\) 0 0
\(817\) −1.31564 −0.0460285
\(818\) −47.8893 −1.67441
\(819\) 0 0
\(820\) −0.348776 −0.0121798
\(821\) 43.1698 1.50664 0.753318 0.657656i \(-0.228452\pi\)
0.753318 + 0.657656i \(0.228452\pi\)
\(822\) 0 0
\(823\) −8.46445 −0.295052 −0.147526 0.989058i \(-0.547131\pi\)
−0.147526 + 0.989058i \(0.547131\pi\)
\(824\) 7.80818 0.272011
\(825\) 0 0
\(826\) −65.3713 −2.27456
\(827\) −6.41763 −0.223163 −0.111581 0.993755i \(-0.535592\pi\)
−0.111581 + 0.993755i \(0.535592\pi\)
\(828\) 0 0
\(829\) −16.7935 −0.583261 −0.291631 0.956531i \(-0.594198\pi\)
−0.291631 + 0.956531i \(0.594198\pi\)
\(830\) −8.14214 −0.282618
\(831\) 0 0
\(832\) −50.6592 −1.75629
\(833\) 13.0262 0.451330
\(834\) 0 0
\(835\) −5.88974 −0.203823
\(836\) −1.34350 −0.0464658
\(837\) 0 0
\(838\) 21.9623 0.758673
\(839\) 7.92834 0.273717 0.136858 0.990591i \(-0.456299\pi\)
0.136858 + 0.990591i \(0.456299\pi\)
\(840\) 0 0
\(841\) −4.06893 −0.140308
\(842\) 33.5691 1.15687
\(843\) 0 0
\(844\) 3.01352 0.103730
\(845\) 33.0399 1.13661
\(846\) 0 0
\(847\) −28.7134 −0.986605
\(848\) 46.1914 1.58622
\(849\) 0 0
\(850\) −2.79958 −0.0960246
\(851\) −3.78509 −0.129751
\(852\) 0 0
\(853\) −27.1727 −0.930375 −0.465187 0.885212i \(-0.654013\pi\)
−0.465187 + 0.885212i \(0.654013\pi\)
\(854\) −55.1123 −1.88590
\(855\) 0 0
\(856\) 4.07656 0.139334
\(857\) 43.2642 1.47788 0.738938 0.673773i \(-0.235328\pi\)
0.738938 + 0.673773i \(0.235328\pi\)
\(858\) 0 0
\(859\) 18.4487 0.629463 0.314731 0.949181i \(-0.398086\pi\)
0.314731 + 0.949181i \(0.398086\pi\)
\(860\) 0.0253070 0.000862962 0
\(861\) 0 0
\(862\) −18.6701 −0.635905
\(863\) −1.54533 −0.0526037 −0.0263018 0.999654i \(-0.508373\pi\)
−0.0263018 + 0.999654i \(0.508373\pi\)
\(864\) 0 0
\(865\) 15.0723 0.512475
\(866\) 41.8175 1.42102
\(867\) 0 0
\(868\) 0.854185 0.0289929
\(869\) −19.5385 −0.662798
\(870\) 0 0
\(871\) −19.5788 −0.663401
\(872\) 25.7429 0.871763
\(873\) 0 0
\(874\) −12.6576 −0.428151
\(875\) 3.71135 0.125466
\(876\) 0 0
\(877\) 47.7230 1.61149 0.805745 0.592262i \(-0.201765\pi\)
0.805745 + 0.592262i \(0.201765\pi\)
\(878\) 34.4301 1.16196
\(879\) 0 0
\(880\) −7.63218 −0.257281
\(881\) −28.2004 −0.950095 −0.475047 0.879960i \(-0.657569\pi\)
−0.475047 + 0.879960i \(0.657569\pi\)
\(882\) 0 0
\(883\) −11.2269 −0.377816 −0.188908 0.981995i \(-0.560495\pi\)
−0.188908 + 0.981995i \(0.560495\pi\)
\(884\) −1.56058 −0.0524879
\(885\) 0 0
\(886\) −51.6902 −1.73657
\(887\) −12.8249 −0.430619 −0.215309 0.976546i \(-0.569076\pi\)
−0.215309 + 0.976546i \(0.569076\pi\)
\(888\) 0 0
\(889\) 4.65450 0.156107
\(890\) −1.45589 −0.0488014
\(891\) 0 0
\(892\) 1.94286 0.0650519
\(893\) −59.7621 −1.99986
\(894\) 0 0
\(895\) −4.65562 −0.155620
\(896\) −45.3570 −1.51527
\(897\) 0 0
\(898\) 47.7209 1.59247
\(899\) 9.60807 0.320447
\(900\) 0 0
\(901\) −21.0237 −0.700400
\(902\) 7.66923 0.255358
\(903\) 0 0
\(904\) −34.7244 −1.15492
\(905\) 9.62070 0.319803
\(906\) 0 0
\(907\) −45.9112 −1.52446 −0.762229 0.647308i \(-0.775895\pi\)
−0.762229 + 0.647308i \(0.775895\pi\)
\(908\) 1.57810 0.0523712
\(909\) 0 0
\(910\) 36.6629 1.21536
\(911\) −55.7475 −1.84700 −0.923499 0.383600i \(-0.874684\pi\)
−0.923499 + 0.383600i \(0.874684\pi\)
\(912\) 0 0
\(913\) 10.1028 0.334355
\(914\) −41.8576 −1.38453
\(915\) 0 0
\(916\) 0.283465 0.00936593
\(917\) 8.43368 0.278505
\(918\) 0 0
\(919\) −49.0675 −1.61859 −0.809293 0.587405i \(-0.800150\pi\)
−0.809293 + 0.587405i \(0.800150\pi\)
\(920\) −3.82781 −0.126199
\(921\) 0 0
\(922\) −16.9024 −0.556650
\(923\) −26.1856 −0.861911
\(924\) 0 0
\(925\) 2.70709 0.0890084
\(926\) 27.2903 0.896815
\(927\) 0 0
\(928\) 3.37387 0.110753
\(929\) 0.564626 0.0185248 0.00926238 0.999957i \(-0.497052\pi\)
0.00926238 + 0.999957i \(0.497052\pi\)
\(930\) 0 0
\(931\) −42.1215 −1.38048
\(932\) 1.15764 0.0379198
\(933\) 0 0
\(934\) −0.923055 −0.0302033
\(935\) 3.47373 0.113603
\(936\) 0 0
\(937\) 21.4710 0.701426 0.350713 0.936483i \(-0.385939\pi\)
0.350713 + 0.936483i \(0.385939\pi\)
\(938\) −15.5911 −0.509069
\(939\) 0 0
\(940\) 1.14955 0.0374943
\(941\) −32.9258 −1.07335 −0.536676 0.843789i \(-0.680320\pi\)
−0.536676 + 0.843789i \(0.680320\pi\)
\(942\) 0 0
\(943\) 4.07725 0.132773
\(944\) −51.1146 −1.66364
\(945\) 0 0
\(946\) −0.556475 −0.0180926
\(947\) 46.4200 1.50845 0.754224 0.656617i \(-0.228013\pi\)
0.754224 + 0.656617i \(0.228013\pi\)
\(948\) 0 0
\(949\) −78.6408 −2.55279
\(950\) 9.05272 0.293709
\(951\) 0 0
\(952\) 19.5377 0.633219
\(953\) −40.6651 −1.31727 −0.658636 0.752462i \(-0.728866\pi\)
−0.658636 + 0.752462i \(0.728866\pi\)
\(954\) 0 0
\(955\) −13.3629 −0.432414
\(956\) 2.85705 0.0924036
\(957\) 0 0
\(958\) 42.6135 1.37678
\(959\) 57.8363 1.86763
\(960\) 0 0
\(961\) −27.2972 −0.880554
\(962\) 26.7422 0.862202
\(963\) 0 0
\(964\) −1.88047 −0.0605657
\(965\) 0.449680 0.0144757
\(966\) 0 0
\(967\) 13.7463 0.442051 0.221026 0.975268i \(-0.429060\pi\)
0.221026 + 0.975268i \(0.429060\pi\)
\(968\) −21.1802 −0.680757
\(969\) 0 0
\(970\) −1.55873 −0.0500479
\(971\) 10.4871 0.336548 0.168274 0.985740i \(-0.446181\pi\)
0.168274 + 0.985740i \(0.446181\pi\)
\(972\) 0 0
\(973\) −79.7954 −2.55812
\(974\) −13.0524 −0.418226
\(975\) 0 0
\(976\) −43.0929 −1.37937
\(977\) −26.8721 −0.859716 −0.429858 0.902897i \(-0.641436\pi\)
−0.429858 + 0.902897i \(0.641436\pi\)
\(978\) 0 0
\(979\) 1.80647 0.0577351
\(980\) 0.810226 0.0258817
\(981\) 0 0
\(982\) 31.2434 0.997018
\(983\) −5.47408 −0.174596 −0.0872980 0.996182i \(-0.527823\pi\)
−0.0872980 + 0.996182i \(0.527823\pi\)
\(984\) 0 0
\(985\) −8.56942 −0.273044
\(986\) −13.9786 −0.445168
\(987\) 0 0
\(988\) 5.04629 0.160544
\(989\) −0.295843 −0.00940725
\(990\) 0 0
\(991\) 25.1620 0.799296 0.399648 0.916669i \(-0.369132\pi\)
0.399648 + 0.916669i \(0.369132\pi\)
\(992\) 1.30024 0.0412827
\(993\) 0 0
\(994\) −20.8524 −0.661397
\(995\) −8.67704 −0.275081
\(996\) 0 0
\(997\) 11.3414 0.359186 0.179593 0.983741i \(-0.442522\pi\)
0.179593 + 0.983741i \(0.442522\pi\)
\(998\) −31.8578 −1.00844
\(999\) 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 \(a_p\))