Properties

Label 6004.2.a.g.1.3
Level 6004
Weight 2
Character 6004.1
Self dual Yes
Analytic conductor 47.942
Analytic rank 1
Dimension 27
CM No

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Newspace parameters

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

Newform invariants

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

Embedding invariants

Embedding label 1.3
Character \(\chi\) = 6004.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-2.74782 q^{3}\) \(-0.322226 q^{5}\) \(-1.10048 q^{7}\) \(+4.55049 q^{9}\) \(+O(q^{10})\) \(q\)\(-2.74782 q^{3}\) \(-0.322226 q^{5}\) \(-1.10048 q^{7}\) \(+4.55049 q^{9}\) \(-1.90455 q^{11}\) \(-3.46075 q^{13}\) \(+0.885416 q^{15}\) \(+0.596613 q^{17}\) \(+1.00000 q^{19}\) \(+3.02391 q^{21}\) \(+3.97163 q^{23}\) \(-4.89617 q^{25}\) \(-4.26046 q^{27}\) \(+4.48417 q^{29}\) \(-0.142441 q^{31}\) \(+5.23334 q^{33}\) \(+0.354603 q^{35}\) \(+1.73291 q^{37}\) \(+9.50951 q^{39}\) \(-2.38206 q^{41}\) \(+5.85585 q^{43}\) \(-1.46628 q^{45}\) \(-1.46562 q^{47}\) \(-5.78895 q^{49}\) \(-1.63938 q^{51}\) \(-2.82437 q^{53}\) \(+0.613693 q^{55}\) \(-2.74782 q^{57}\) \(+10.6456 q^{59}\) \(-3.06513 q^{61}\) \(-5.00772 q^{63}\) \(+1.11514 q^{65}\) \(+3.30641 q^{67}\) \(-10.9133 q^{69}\) \(+9.93768 q^{71}\) \(+1.31446 q^{73}\) \(+13.4538 q^{75}\) \(+2.09591 q^{77}\) \(-1.00000 q^{79}\) \(-1.94452 q^{81}\) \(+12.5240 q^{83}\) \(-0.192244 q^{85}\) \(-12.3217 q^{87}\) \(-16.0319 q^{89}\) \(+3.80849 q^{91}\) \(+0.391402 q^{93}\) \(-0.322226 q^{95}\) \(+14.2275 q^{97}\) \(-8.66661 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(27q \) \(\mathstrut -\mathstrut 4q^{3} \) \(\mathstrut -\mathstrut 10q^{5} \) \(\mathstrut -\mathstrut 8q^{7} \) \(\mathstrut +\mathstrut 19q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(27q \) \(\mathstrut -\mathstrut 4q^{3} \) \(\mathstrut -\mathstrut 10q^{5} \) \(\mathstrut -\mathstrut 8q^{7} \) \(\mathstrut +\mathstrut 19q^{9} \) \(\mathstrut +\mathstrut 3q^{11} \) \(\mathstrut -\mathstrut 5q^{13} \) \(\mathstrut -\mathstrut 11q^{15} \) \(\mathstrut -\mathstrut 17q^{17} \) \(\mathstrut +\mathstrut 27q^{19} \) \(\mathstrut -\mathstrut 28q^{21} \) \(\mathstrut -\mathstrut 11q^{23} \) \(\mathstrut +\mathstrut 13q^{25} \) \(\mathstrut -\mathstrut 7q^{27} \) \(\mathstrut -\mathstrut 39q^{29} \) \(\mathstrut -\mathstrut 27q^{31} \) \(\mathstrut -\mathstrut 18q^{33} \) \(\mathstrut -\mathstrut 5q^{35} \) \(\mathstrut -\mathstrut q^{37} \) \(\mathstrut -\mathstrut 22q^{39} \) \(\mathstrut -\mathstrut 36q^{41} \) \(\mathstrut -\mathstrut 2q^{43} \) \(\mathstrut -\mathstrut 18q^{45} \) \(\mathstrut -\mathstrut 12q^{47} \) \(\mathstrut +\mathstrut 15q^{49} \) \(\mathstrut +\mathstrut 4q^{51} \) \(\mathstrut -\mathstrut 28q^{53} \) \(\mathstrut +\mathstrut 5q^{55} \) \(\mathstrut -\mathstrut 4q^{57} \) \(\mathstrut -\mathstrut 30q^{59} \) \(\mathstrut -\mathstrut 6q^{61} \) \(\mathstrut -\mathstrut 4q^{63} \) \(\mathstrut -\mathstrut 32q^{65} \) \(\mathstrut +\mathstrut 13q^{67} \) \(\mathstrut -\mathstrut 27q^{69} \) \(\mathstrut -\mathstrut 59q^{71} \) \(\mathstrut -\mathstrut 30q^{73} \) \(\mathstrut -\mathstrut 21q^{75} \) \(\mathstrut -\mathstrut 39q^{77} \) \(\mathstrut -\mathstrut 27q^{79} \) \(\mathstrut -\mathstrut 5q^{81} \) \(\mathstrut +\mathstrut 4q^{83} \) \(\mathstrut -\mathstrut 3q^{85} \) \(\mathstrut +\mathstrut 22q^{87} \) \(\mathstrut -\mathstrut 56q^{89} \) \(\mathstrut -\mathstrut 8q^{91} \) \(\mathstrut -\mathstrut 38q^{93} \) \(\mathstrut -\mathstrut 10q^{95} \) \(\mathstrut -\mathstrut 30q^{97} \) \(\mathstrut +\mathstrut 31q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) −2.74782 −1.58645 −0.793226 0.608927i \(-0.791600\pi\)
−0.793226 + 0.608927i \(0.791600\pi\)
\(4\) 0 0
\(5\) −0.322226 −0.144104 −0.0720518 0.997401i \(-0.522955\pi\)
−0.0720518 + 0.997401i \(0.522955\pi\)
\(6\) 0 0
\(7\) −1.10048 −0.415942 −0.207971 0.978135i \(-0.566686\pi\)
−0.207971 + 0.978135i \(0.566686\pi\)
\(8\) 0 0
\(9\) 4.55049 1.51683
\(10\) 0 0
\(11\) −1.90455 −0.574242 −0.287121 0.957894i \(-0.592698\pi\)
−0.287121 + 0.957894i \(0.592698\pi\)
\(12\) 0 0
\(13\) −3.46075 −0.959840 −0.479920 0.877312i \(-0.659334\pi\)
−0.479920 + 0.877312i \(0.659334\pi\)
\(14\) 0 0
\(15\) 0.885416 0.228614
\(16\) 0 0
\(17\) 0.596613 0.144700 0.0723499 0.997379i \(-0.476950\pi\)
0.0723499 + 0.997379i \(0.476950\pi\)
\(18\) 0 0
\(19\) 1.00000 0.229416
\(20\) 0 0
\(21\) 3.02391 0.659872
\(22\) 0 0
\(23\) 3.97163 0.828143 0.414071 0.910244i \(-0.364106\pi\)
0.414071 + 0.910244i \(0.364106\pi\)
\(24\) 0 0
\(25\) −4.89617 −0.979234
\(26\) 0 0
\(27\) −4.26046 −0.819925
\(28\) 0 0
\(29\) 4.48417 0.832690 0.416345 0.909207i \(-0.363311\pi\)
0.416345 + 0.909207i \(0.363311\pi\)
\(30\) 0 0
\(31\) −0.142441 −0.0255832 −0.0127916 0.999918i \(-0.504072\pi\)
−0.0127916 + 0.999918i \(0.504072\pi\)
\(32\) 0 0
\(33\) 5.23334 0.911007
\(34\) 0 0
\(35\) 0.354603 0.0599388
\(36\) 0 0
\(37\) 1.73291 0.284889 0.142444 0.989803i \(-0.454504\pi\)
0.142444 + 0.989803i \(0.454504\pi\)
\(38\) 0 0
\(39\) 9.50951 1.52274
\(40\) 0 0
\(41\) −2.38206 −0.372015 −0.186007 0.982548i \(-0.559555\pi\)
−0.186007 + 0.982548i \(0.559555\pi\)
\(42\) 0 0
\(43\) 5.85585 0.893009 0.446504 0.894781i \(-0.352669\pi\)
0.446504 + 0.894781i \(0.352669\pi\)
\(44\) 0 0
\(45\) −1.46628 −0.218581
\(46\) 0 0
\(47\) −1.46562 −0.213782 −0.106891 0.994271i \(-0.534090\pi\)
−0.106891 + 0.994271i \(0.534090\pi\)
\(48\) 0 0
\(49\) −5.78895 −0.826992
\(50\) 0 0
\(51\) −1.63938 −0.229559
\(52\) 0 0
\(53\) −2.82437 −0.387957 −0.193979 0.981006i \(-0.562139\pi\)
−0.193979 + 0.981006i \(0.562139\pi\)
\(54\) 0 0
\(55\) 0.613693 0.0827504
\(56\) 0 0
\(57\) −2.74782 −0.363957
\(58\) 0 0
\(59\) 10.6456 1.38594 0.692968 0.720969i \(-0.256303\pi\)
0.692968 + 0.720969i \(0.256303\pi\)
\(60\) 0 0
\(61\) −3.06513 −0.392449 −0.196225 0.980559i \(-0.562868\pi\)
−0.196225 + 0.980559i \(0.562868\pi\)
\(62\) 0 0
\(63\) −5.00772 −0.630913
\(64\) 0 0
\(65\) 1.11514 0.138317
\(66\) 0 0
\(67\) 3.30641 0.403943 0.201971 0.979391i \(-0.435265\pi\)
0.201971 + 0.979391i \(0.435265\pi\)
\(68\) 0 0
\(69\) −10.9133 −1.31381
\(70\) 0 0
\(71\) 9.93768 1.17939 0.589693 0.807628i \(-0.299249\pi\)
0.589693 + 0.807628i \(0.299249\pi\)
\(72\) 0 0
\(73\) 1.31446 0.153846 0.0769228 0.997037i \(-0.475490\pi\)
0.0769228 + 0.997037i \(0.475490\pi\)
\(74\) 0 0
\(75\) 13.4538 1.55351
\(76\) 0 0
\(77\) 2.09591 0.238851
\(78\) 0 0
\(79\) −1.00000 −0.112509
\(80\) 0 0
\(81\) −1.94452 −0.216058
\(82\) 0 0
\(83\) 12.5240 1.37468 0.687341 0.726334i \(-0.258778\pi\)
0.687341 + 0.726334i \(0.258778\pi\)
\(84\) 0 0
\(85\) −0.192244 −0.0208518
\(86\) 0 0
\(87\) −12.3217 −1.32102
\(88\) 0 0
\(89\) −16.0319 −1.69938 −0.849688 0.527287i \(-0.823209\pi\)
−0.849688 + 0.527287i \(0.823209\pi\)
\(90\) 0 0
\(91\) 3.80849 0.399238
\(92\) 0 0
\(93\) 0.391402 0.0405865
\(94\) 0 0
\(95\) −0.322226 −0.0330597
\(96\) 0 0
\(97\) 14.2275 1.44459 0.722294 0.691586i \(-0.243088\pi\)
0.722294 + 0.691586i \(0.243088\pi\)
\(98\) 0 0
\(99\) −8.66661 −0.871027
\(100\) 0 0
\(101\) 9.75462 0.970621 0.485311 0.874342i \(-0.338707\pi\)
0.485311 + 0.874342i \(0.338707\pi\)
\(102\) 0 0
\(103\) 8.82932 0.869978 0.434989 0.900436i \(-0.356752\pi\)
0.434989 + 0.900436i \(0.356752\pi\)
\(104\) 0 0
\(105\) −0.974382 −0.0950900
\(106\) 0 0
\(107\) 1.59907 0.154588 0.0772941 0.997008i \(-0.475372\pi\)
0.0772941 + 0.997008i \(0.475372\pi\)
\(108\) 0 0
\(109\) −18.1592 −1.73934 −0.869670 0.493634i \(-0.835668\pi\)
−0.869670 + 0.493634i \(0.835668\pi\)
\(110\) 0 0
\(111\) −4.76172 −0.451962
\(112\) 0 0
\(113\) −10.6686 −1.00362 −0.501809 0.864978i \(-0.667332\pi\)
−0.501809 + 0.864978i \(0.667332\pi\)
\(114\) 0 0
\(115\) −1.27976 −0.119338
\(116\) 0 0
\(117\) −15.7481 −1.45591
\(118\) 0 0
\(119\) −0.656560 −0.0601867
\(120\) 0 0
\(121\) −7.37271 −0.670246
\(122\) 0 0
\(123\) 6.54545 0.590183
\(124\) 0 0
\(125\) 3.18880 0.285215
\(126\) 0 0
\(127\) −4.33340 −0.384527 −0.192263 0.981343i \(-0.561583\pi\)
−0.192263 + 0.981343i \(0.561583\pi\)
\(128\) 0 0
\(129\) −16.0908 −1.41672
\(130\) 0 0
\(131\) 0.0882175 0.00770760 0.00385380 0.999993i \(-0.498773\pi\)
0.00385380 + 0.999993i \(0.498773\pi\)
\(132\) 0 0
\(133\) −1.10048 −0.0954236
\(134\) 0 0
\(135\) 1.37283 0.118154
\(136\) 0 0
\(137\) 19.5661 1.67165 0.835823 0.548999i \(-0.184991\pi\)
0.835823 + 0.548999i \(0.184991\pi\)
\(138\) 0 0
\(139\) 8.38056 0.710830 0.355415 0.934709i \(-0.384340\pi\)
0.355415 + 0.934709i \(0.384340\pi\)
\(140\) 0 0
\(141\) 4.02724 0.339155
\(142\) 0 0
\(143\) 6.59116 0.551181
\(144\) 0 0
\(145\) −1.44491 −0.119994
\(146\) 0 0
\(147\) 15.9070 1.31198
\(148\) 0 0
\(149\) 6.43262 0.526981 0.263490 0.964662i \(-0.415126\pi\)
0.263490 + 0.964662i \(0.415126\pi\)
\(150\) 0 0
\(151\) 5.40288 0.439680 0.219840 0.975536i \(-0.429446\pi\)
0.219840 + 0.975536i \(0.429446\pi\)
\(152\) 0 0
\(153\) 2.71488 0.219485
\(154\) 0 0
\(155\) 0.0458982 0.00368663
\(156\) 0 0
\(157\) 11.7271 0.935928 0.467964 0.883748i \(-0.344988\pi\)
0.467964 + 0.883748i \(0.344988\pi\)
\(158\) 0 0
\(159\) 7.76085 0.615476
\(160\) 0 0
\(161\) −4.37070 −0.344459
\(162\) 0 0
\(163\) −12.0793 −0.946121 −0.473061 0.881030i \(-0.656851\pi\)
−0.473061 + 0.881030i \(0.656851\pi\)
\(164\) 0 0
\(165\) −1.68632 −0.131279
\(166\) 0 0
\(167\) −15.6644 −1.21215 −0.606073 0.795409i \(-0.707256\pi\)
−0.606073 + 0.795409i \(0.707256\pi\)
\(168\) 0 0
\(169\) −1.02318 −0.0787064
\(170\) 0 0
\(171\) 4.55049 0.347985
\(172\) 0 0
\(173\) −4.05671 −0.308426 −0.154213 0.988038i \(-0.549284\pi\)
−0.154213 + 0.988038i \(0.549284\pi\)
\(174\) 0 0
\(175\) 5.38813 0.407305
\(176\) 0 0
\(177\) −29.2521 −2.19872
\(178\) 0 0
\(179\) −18.4769 −1.38103 −0.690513 0.723320i \(-0.742615\pi\)
−0.690513 + 0.723320i \(0.742615\pi\)
\(180\) 0 0
\(181\) 17.7692 1.32077 0.660385 0.750927i \(-0.270393\pi\)
0.660385 + 0.750927i \(0.270393\pi\)
\(182\) 0 0
\(183\) 8.42240 0.622602
\(184\) 0 0
\(185\) −0.558388 −0.0410535
\(186\) 0 0
\(187\) −1.13628 −0.0830927
\(188\) 0 0
\(189\) 4.68854 0.341041
\(190\) 0 0
\(191\) 11.2665 0.815217 0.407609 0.913157i \(-0.366363\pi\)
0.407609 + 0.913157i \(0.366363\pi\)
\(192\) 0 0
\(193\) 10.2092 0.734871 0.367436 0.930049i \(-0.380236\pi\)
0.367436 + 0.930049i \(0.380236\pi\)
\(194\) 0 0
\(195\) −3.06421 −0.219433
\(196\) 0 0
\(197\) 2.20613 0.157180 0.0785900 0.996907i \(-0.474958\pi\)
0.0785900 + 0.996907i \(0.474958\pi\)
\(198\) 0 0
\(199\) 8.02285 0.568725 0.284363 0.958717i \(-0.408218\pi\)
0.284363 + 0.958717i \(0.408218\pi\)
\(200\) 0 0
\(201\) −9.08541 −0.640836
\(202\) 0 0
\(203\) −4.93474 −0.346351
\(204\) 0 0
\(205\) 0.767559 0.0536087
\(206\) 0 0
\(207\) 18.0729 1.25615
\(208\) 0 0
\(209\) −1.90455 −0.131740
\(210\) 0 0
\(211\) −26.9577 −1.85584 −0.927922 0.372775i \(-0.878406\pi\)
−0.927922 + 0.372775i \(0.878406\pi\)
\(212\) 0 0
\(213\) −27.3069 −1.87104
\(214\) 0 0
\(215\) −1.88690 −0.128686
\(216\) 0 0
\(217\) 0.156754 0.0106411
\(218\) 0 0
\(219\) −3.61189 −0.244069
\(220\) 0 0
\(221\) −2.06473 −0.138889
\(222\) 0 0
\(223\) −17.5112 −1.17264 −0.586319 0.810080i \(-0.699423\pi\)
−0.586319 + 0.810080i \(0.699423\pi\)
\(224\) 0 0
\(225\) −22.2800 −1.48533
\(226\) 0 0
\(227\) 15.9225 1.05681 0.528406 0.848992i \(-0.322790\pi\)
0.528406 + 0.848992i \(0.322790\pi\)
\(228\) 0 0
\(229\) −10.2773 −0.679141 −0.339571 0.940581i \(-0.610282\pi\)
−0.339571 + 0.940581i \(0.610282\pi\)
\(230\) 0 0
\(231\) −5.75918 −0.378926
\(232\) 0 0
\(233\) −19.2565 −1.26154 −0.630768 0.775971i \(-0.717260\pi\)
−0.630768 + 0.775971i \(0.717260\pi\)
\(234\) 0 0
\(235\) 0.472259 0.0308068
\(236\) 0 0
\(237\) 2.74782 0.178490
\(238\) 0 0
\(239\) −9.33202 −0.603638 −0.301819 0.953365i \(-0.597594\pi\)
−0.301819 + 0.953365i \(0.597594\pi\)
\(240\) 0 0
\(241\) −4.26126 −0.274492 −0.137246 0.990537i \(-0.543825\pi\)
−0.137246 + 0.990537i \(0.543825\pi\)
\(242\) 0 0
\(243\) 18.1245 1.16269
\(244\) 0 0
\(245\) 1.86535 0.119173
\(246\) 0 0
\(247\) −3.46075 −0.220202
\(248\) 0 0
\(249\) −34.4135 −2.18087
\(250\) 0 0
\(251\) 3.99243 0.252000 0.126000 0.992030i \(-0.459786\pi\)
0.126000 + 0.992030i \(0.459786\pi\)
\(252\) 0 0
\(253\) −7.56416 −0.475554
\(254\) 0 0
\(255\) 0.528251 0.0330803
\(256\) 0 0
\(257\) 6.04628 0.377157 0.188578 0.982058i \(-0.439612\pi\)
0.188578 + 0.982058i \(0.439612\pi\)
\(258\) 0 0
\(259\) −1.90703 −0.118497
\(260\) 0 0
\(261\) 20.4052 1.26305
\(262\) 0 0
\(263\) −28.4841 −1.75640 −0.878201 0.478291i \(-0.841256\pi\)
−0.878201 + 0.478291i \(0.841256\pi\)
\(264\) 0 0
\(265\) 0.910085 0.0559061
\(266\) 0 0
\(267\) 44.0526 2.69598
\(268\) 0 0
\(269\) 25.6804 1.56576 0.782879 0.622173i \(-0.213750\pi\)
0.782879 + 0.622173i \(0.213750\pi\)
\(270\) 0 0
\(271\) 5.47566 0.332623 0.166311 0.986073i \(-0.446814\pi\)
0.166311 + 0.986073i \(0.446814\pi\)
\(272\) 0 0
\(273\) −10.4650 −0.633372
\(274\) 0 0
\(275\) 9.32498 0.562317
\(276\) 0 0
\(277\) 6.23158 0.374419 0.187210 0.982320i \(-0.440056\pi\)
0.187210 + 0.982320i \(0.440056\pi\)
\(278\) 0 0
\(279\) −0.648177 −0.0388054
\(280\) 0 0
\(281\) −12.5009 −0.745739 −0.372870 0.927884i \(-0.621626\pi\)
−0.372870 + 0.927884i \(0.621626\pi\)
\(282\) 0 0
\(283\) 23.8462 1.41751 0.708753 0.705456i \(-0.249258\pi\)
0.708753 + 0.705456i \(0.249258\pi\)
\(284\) 0 0
\(285\) 0.885416 0.0524475
\(286\) 0 0
\(287\) 2.62140 0.154736
\(288\) 0 0
\(289\) −16.6441 −0.979062
\(290\) 0 0
\(291\) −39.0947 −2.29177
\(292\) 0 0
\(293\) −6.44855 −0.376728 −0.188364 0.982099i \(-0.560319\pi\)
−0.188364 + 0.982099i \(0.560319\pi\)
\(294\) 0 0
\(295\) −3.43028 −0.199718
\(296\) 0 0
\(297\) 8.11423 0.470836
\(298\) 0 0
\(299\) −13.7448 −0.794885
\(300\) 0 0
\(301\) −6.44424 −0.371440
\(302\) 0 0
\(303\) −26.8039 −1.53984
\(304\) 0 0
\(305\) 0.987663 0.0565534
\(306\) 0 0
\(307\) −24.6078 −1.40444 −0.702221 0.711959i \(-0.747808\pi\)
−0.702221 + 0.711959i \(0.747808\pi\)
\(308\) 0 0
\(309\) −24.2613 −1.38018
\(310\) 0 0
\(311\) −33.4895 −1.89901 −0.949506 0.313748i \(-0.898415\pi\)
−0.949506 + 0.313748i \(0.898415\pi\)
\(312\) 0 0
\(313\) −17.4341 −0.985436 −0.492718 0.870189i \(-0.663997\pi\)
−0.492718 + 0.870189i \(0.663997\pi\)
\(314\) 0 0
\(315\) 1.61361 0.0909169
\(316\) 0 0
\(317\) −8.81607 −0.495160 −0.247580 0.968867i \(-0.579635\pi\)
−0.247580 + 0.968867i \(0.579635\pi\)
\(318\) 0 0
\(319\) −8.54031 −0.478165
\(320\) 0 0
\(321\) −4.39396 −0.245247
\(322\) 0 0
\(323\) 0.596613 0.0331964
\(324\) 0 0
\(325\) 16.9444 0.939908
\(326\) 0 0
\(327\) 49.8982 2.75938
\(328\) 0 0
\(329\) 1.61288 0.0889209
\(330\) 0 0
\(331\) −12.4641 −0.685089 −0.342544 0.939502i \(-0.611289\pi\)
−0.342544 + 0.939502i \(0.611289\pi\)
\(332\) 0 0
\(333\) 7.88559 0.432128
\(334\) 0 0
\(335\) −1.06541 −0.0582096
\(336\) 0 0
\(337\) −32.5786 −1.77467 −0.887334 0.461127i \(-0.847445\pi\)
−0.887334 + 0.461127i \(0.847445\pi\)
\(338\) 0 0
\(339\) 29.3154 1.59219
\(340\) 0 0
\(341\) 0.271286 0.0146909
\(342\) 0 0
\(343\) 14.0740 0.759923
\(344\) 0 0
\(345\) 3.51655 0.189325
\(346\) 0 0
\(347\) 9.25713 0.496949 0.248474 0.968638i \(-0.420071\pi\)
0.248474 + 0.968638i \(0.420071\pi\)
\(348\) 0 0
\(349\) 3.00026 0.160600 0.0803001 0.996771i \(-0.474412\pi\)
0.0803001 + 0.996771i \(0.474412\pi\)
\(350\) 0 0
\(351\) 14.7444 0.786997
\(352\) 0 0
\(353\) −2.16535 −0.115250 −0.0576250 0.998338i \(-0.518353\pi\)
−0.0576250 + 0.998338i \(0.518353\pi\)
\(354\) 0 0
\(355\) −3.20218 −0.169954
\(356\) 0 0
\(357\) 1.80410 0.0954834
\(358\) 0 0
\(359\) −31.0025 −1.63625 −0.818125 0.575041i \(-0.804986\pi\)
−0.818125 + 0.575041i \(0.804986\pi\)
\(360\) 0 0
\(361\) 1.00000 0.0526316
\(362\) 0 0
\(363\) 20.2588 1.06331
\(364\) 0 0
\(365\) −0.423552 −0.0221697
\(366\) 0 0
\(367\) 30.4518 1.58957 0.794784 0.606892i \(-0.207584\pi\)
0.794784 + 0.606892i \(0.207584\pi\)
\(368\) 0 0
\(369\) −10.8395 −0.564283
\(370\) 0 0
\(371\) 3.10816 0.161368
\(372\) 0 0
\(373\) −21.3117 −1.10348 −0.551740 0.834016i \(-0.686036\pi\)
−0.551740 + 0.834016i \(0.686036\pi\)
\(374\) 0 0
\(375\) −8.76223 −0.452480
\(376\) 0 0
\(377\) −15.5186 −0.799249
\(378\) 0 0
\(379\) 10.8481 0.557228 0.278614 0.960403i \(-0.410125\pi\)
0.278614 + 0.960403i \(0.410125\pi\)
\(380\) 0 0
\(381\) 11.9074 0.610034
\(382\) 0 0
\(383\) −6.10185 −0.311790 −0.155895 0.987774i \(-0.549826\pi\)
−0.155895 + 0.987774i \(0.549826\pi\)
\(384\) 0 0
\(385\) −0.675357 −0.0344194
\(386\) 0 0
\(387\) 26.6470 1.35454
\(388\) 0 0
\(389\) −13.7729 −0.698312 −0.349156 0.937065i \(-0.613532\pi\)
−0.349156 + 0.937065i \(0.613532\pi\)
\(390\) 0 0
\(391\) 2.36953 0.119832
\(392\) 0 0
\(393\) −0.242405 −0.0122277
\(394\) 0 0
\(395\) 0.322226 0.0162129
\(396\) 0 0
\(397\) −18.0140 −0.904095 −0.452047 0.891994i \(-0.649306\pi\)
−0.452047 + 0.891994i \(0.649306\pi\)
\(398\) 0 0
\(399\) 3.02391 0.151385
\(400\) 0 0
\(401\) −26.4039 −1.31855 −0.659274 0.751903i \(-0.729136\pi\)
−0.659274 + 0.751903i \(0.729136\pi\)
\(402\) 0 0
\(403\) 0.492954 0.0245558
\(404\) 0 0
\(405\) 0.626574 0.0311347
\(406\) 0 0
\(407\) −3.30041 −0.163595
\(408\) 0 0
\(409\) −25.3726 −1.25459 −0.627297 0.778780i \(-0.715839\pi\)
−0.627297 + 0.778780i \(0.715839\pi\)
\(410\) 0 0
\(411\) −53.7641 −2.65199
\(412\) 0 0
\(413\) −11.7152 −0.576469
\(414\) 0 0
\(415\) −4.03554 −0.198097
\(416\) 0 0
\(417\) −23.0282 −1.12770
\(418\) 0 0
\(419\) −17.5022 −0.855039 −0.427519 0.904006i \(-0.640612\pi\)
−0.427519 + 0.904006i \(0.640612\pi\)
\(420\) 0 0
\(421\) −16.5524 −0.806715 −0.403358 0.915042i \(-0.632157\pi\)
−0.403358 + 0.915042i \(0.632157\pi\)
\(422\) 0 0
\(423\) −6.66927 −0.324271
\(424\) 0 0
\(425\) −2.92112 −0.141695
\(426\) 0 0
\(427\) 3.37311 0.163236
\(428\) 0 0
\(429\) −18.1113 −0.874422
\(430\) 0 0
\(431\) −19.6764 −0.947778 −0.473889 0.880585i \(-0.657150\pi\)
−0.473889 + 0.880585i \(0.657150\pi\)
\(432\) 0 0
\(433\) −10.3389 −0.496857 −0.248429 0.968650i \(-0.579914\pi\)
−0.248429 + 0.968650i \(0.579914\pi\)
\(434\) 0 0
\(435\) 3.97036 0.190364
\(436\) 0 0
\(437\) 3.97163 0.189989
\(438\) 0 0
\(439\) −35.8829 −1.71260 −0.856298 0.516482i \(-0.827241\pi\)
−0.856298 + 0.516482i \(0.827241\pi\)
\(440\) 0 0
\(441\) −26.3425 −1.25441
\(442\) 0 0
\(443\) 23.9914 1.13987 0.569934 0.821691i \(-0.306969\pi\)
0.569934 + 0.821691i \(0.306969\pi\)
\(444\) 0 0
\(445\) 5.16588 0.244886
\(446\) 0 0
\(447\) −17.6757 −0.836030
\(448\) 0 0
\(449\) −1.95556 −0.0922887 −0.0461443 0.998935i \(-0.514693\pi\)
−0.0461443 + 0.998935i \(0.514693\pi\)
\(450\) 0 0
\(451\) 4.53673 0.213626
\(452\) 0 0
\(453\) −14.8461 −0.697531
\(454\) 0 0
\(455\) −1.22719 −0.0575317
\(456\) 0 0
\(457\) 30.9199 1.44637 0.723186 0.690653i \(-0.242677\pi\)
0.723186 + 0.690653i \(0.242677\pi\)
\(458\) 0 0
\(459\) −2.54184 −0.118643
\(460\) 0 0
\(461\) −32.9900 −1.53650 −0.768248 0.640153i \(-0.778871\pi\)
−0.768248 + 0.640153i \(0.778871\pi\)
\(462\) 0 0
\(463\) 35.6325 1.65599 0.827993 0.560739i \(-0.189483\pi\)
0.827993 + 0.560739i \(0.189483\pi\)
\(464\) 0 0
\(465\) −0.126120 −0.00584867
\(466\) 0 0
\(467\) 26.8577 1.24283 0.621414 0.783483i \(-0.286559\pi\)
0.621414 + 0.783483i \(0.286559\pi\)
\(468\) 0 0
\(469\) −3.63864 −0.168017
\(470\) 0 0
\(471\) −32.2240 −1.48480
\(472\) 0 0
\(473\) −11.1527 −0.512803
\(474\) 0 0
\(475\) −4.89617 −0.224652
\(476\) 0 0
\(477\) −12.8523 −0.588465
\(478\) 0 0
\(479\) 10.6099 0.484776 0.242388 0.970179i \(-0.422069\pi\)
0.242388 + 0.970179i \(0.422069\pi\)
\(480\) 0 0
\(481\) −5.99718 −0.273448
\(482\) 0 0
\(483\) 12.0099 0.546468
\(484\) 0 0
\(485\) −4.58448 −0.208170
\(486\) 0 0
\(487\) −15.1683 −0.687341 −0.343670 0.939090i \(-0.611670\pi\)
−0.343670 + 0.939090i \(0.611670\pi\)
\(488\) 0 0
\(489\) 33.1916 1.50098
\(490\) 0 0
\(491\) −36.0083 −1.62503 −0.812516 0.582938i \(-0.801903\pi\)
−0.812516 + 0.582938i \(0.801903\pi\)
\(492\) 0 0
\(493\) 2.67531 0.120490
\(494\) 0 0
\(495\) 2.79260 0.125518
\(496\) 0 0
\(497\) −10.9362 −0.490556
\(498\) 0 0
\(499\) −0.380587 −0.0170374 −0.00851870 0.999964i \(-0.502712\pi\)
−0.00851870 + 0.999964i \(0.502712\pi\)
\(500\) 0 0
\(501\) 43.0428 1.92301
\(502\) 0 0
\(503\) −40.0370 −1.78516 −0.892581 0.450886i \(-0.851108\pi\)
−0.892581 + 0.450886i \(0.851108\pi\)
\(504\) 0 0
\(505\) −3.14319 −0.139870
\(506\) 0 0
\(507\) 2.81152 0.124864
\(508\) 0 0
\(509\) −33.3739 −1.47927 −0.739636 0.673007i \(-0.765002\pi\)
−0.739636 + 0.673007i \(0.765002\pi\)
\(510\) 0 0
\(511\) −1.44653 −0.0639909
\(512\) 0 0
\(513\) −4.26046 −0.188104
\(514\) 0 0
\(515\) −2.84503 −0.125367
\(516\) 0 0
\(517\) 2.79133 0.122763
\(518\) 0 0
\(519\) 11.1471 0.489303
\(520\) 0 0
\(521\) 21.2022 0.928886 0.464443 0.885603i \(-0.346255\pi\)
0.464443 + 0.885603i \(0.346255\pi\)
\(522\) 0 0
\(523\) 3.24994 0.142110 0.0710549 0.997472i \(-0.477363\pi\)
0.0710549 + 0.997472i \(0.477363\pi\)
\(524\) 0 0
\(525\) −14.8056 −0.646169
\(526\) 0 0
\(527\) −0.0849823 −0.00370189
\(528\) 0 0
\(529\) −7.22612 −0.314179
\(530\) 0 0
\(531\) 48.4426 2.10223
\(532\) 0 0
\(533\) 8.24371 0.357075
\(534\) 0 0
\(535\) −0.515262 −0.0222767
\(536\) 0 0
\(537\) 50.7710 2.19093
\(538\) 0 0
\(539\) 11.0253 0.474894
\(540\) 0 0
\(541\) 31.1466 1.33910 0.669550 0.742767i \(-0.266487\pi\)
0.669550 + 0.742767i \(0.266487\pi\)
\(542\) 0 0
\(543\) −48.8264 −2.09534
\(544\) 0 0
\(545\) 5.85137 0.250645
\(546\) 0 0
\(547\) −4.03247 −0.172416 −0.0862079 0.996277i \(-0.527475\pi\)
−0.0862079 + 0.996277i \(0.527475\pi\)
\(548\) 0 0
\(549\) −13.9478 −0.595279
\(550\) 0 0
\(551\) 4.48417 0.191032
\(552\) 0 0
\(553\) 1.10048 0.0467971
\(554\) 0 0
\(555\) 1.53435 0.0651295
\(556\) 0 0
\(557\) 8.20095 0.347485 0.173743 0.984791i \(-0.444414\pi\)
0.173743 + 0.984791i \(0.444414\pi\)
\(558\) 0 0
\(559\) −20.2657 −0.857146
\(560\) 0 0
\(561\) 3.12228 0.131823
\(562\) 0 0
\(563\) 11.6848 0.492458 0.246229 0.969212i \(-0.420809\pi\)
0.246229 + 0.969212i \(0.420809\pi\)
\(564\) 0 0
\(565\) 3.43770 0.144625
\(566\) 0 0
\(567\) 2.13990 0.0898674
\(568\) 0 0
\(569\) −24.0710 −1.00911 −0.504555 0.863380i \(-0.668343\pi\)
−0.504555 + 0.863380i \(0.668343\pi\)
\(570\) 0 0
\(571\) 31.8220 1.33171 0.665856 0.746081i \(-0.268067\pi\)
0.665856 + 0.746081i \(0.268067\pi\)
\(572\) 0 0
\(573\) −30.9583 −1.29330
\(574\) 0 0
\(575\) −19.4458 −0.810946
\(576\) 0 0
\(577\) 8.11051 0.337645 0.168823 0.985646i \(-0.446004\pi\)
0.168823 + 0.985646i \(0.446004\pi\)
\(578\) 0 0
\(579\) −28.0529 −1.16584
\(580\) 0 0
\(581\) −13.7824 −0.571788
\(582\) 0 0
\(583\) 5.37915 0.222781
\(584\) 0 0
\(585\) 5.07445 0.209803
\(586\) 0 0
\(587\) −31.3012 −1.29194 −0.645969 0.763364i \(-0.723546\pi\)
−0.645969 + 0.763364i \(0.723546\pi\)
\(588\) 0 0
\(589\) −0.142441 −0.00586919
\(590\) 0 0
\(591\) −6.06203 −0.249359
\(592\) 0 0
\(593\) 18.2853 0.750886 0.375443 0.926845i \(-0.377491\pi\)
0.375443 + 0.926845i \(0.377491\pi\)
\(594\) 0 0
\(595\) 0.211560 0.00867313
\(596\) 0 0
\(597\) −22.0453 −0.902255
\(598\) 0 0
\(599\) 41.7951 1.70770 0.853852 0.520517i \(-0.174261\pi\)
0.853852 + 0.520517i \(0.174261\pi\)
\(600\) 0 0
\(601\) −26.9296 −1.09848 −0.549240 0.835665i \(-0.685083\pi\)
−0.549240 + 0.835665i \(0.685083\pi\)
\(602\) 0 0
\(603\) 15.0458 0.612712
\(604\) 0 0
\(605\) 2.37568 0.0965849
\(606\) 0 0
\(607\) −5.20348 −0.211203 −0.105601 0.994409i \(-0.533677\pi\)
−0.105601 + 0.994409i \(0.533677\pi\)
\(608\) 0 0
\(609\) 13.5597 0.549469
\(610\) 0 0
\(611\) 5.07213 0.205197
\(612\) 0 0
\(613\) −37.5556 −1.51685 −0.758427 0.651758i \(-0.774032\pi\)
−0.758427 + 0.651758i \(0.774032\pi\)
\(614\) 0 0
\(615\) −2.10911 −0.0850476
\(616\) 0 0
\(617\) 1.11484 0.0448818 0.0224409 0.999748i \(-0.492856\pi\)
0.0224409 + 0.999748i \(0.492856\pi\)
\(618\) 0 0
\(619\) 32.3564 1.30051 0.650256 0.759715i \(-0.274661\pi\)
0.650256 + 0.759715i \(0.274661\pi\)
\(620\) 0 0
\(621\) −16.9210 −0.679015
\(622\) 0 0
\(623\) 17.6427 0.706841
\(624\) 0 0
\(625\) 23.4533 0.938134
\(626\) 0 0
\(627\) 5.23334 0.208999
\(628\) 0 0
\(629\) 1.03388 0.0412234
\(630\) 0 0
\(631\) −21.2398 −0.845542 −0.422771 0.906237i \(-0.638942\pi\)
−0.422771 + 0.906237i \(0.638942\pi\)
\(632\) 0 0
\(633\) 74.0747 2.94421
\(634\) 0 0
\(635\) 1.39633 0.0554118
\(636\) 0 0
\(637\) 20.0341 0.793781
\(638\) 0 0
\(639\) 45.2213 1.78893
\(640\) 0 0
\(641\) 37.6080 1.48542 0.742712 0.669610i \(-0.233539\pi\)
0.742712 + 0.669610i \(0.233539\pi\)
\(642\) 0 0
\(643\) 25.8329 1.01875 0.509376 0.860544i \(-0.329876\pi\)
0.509376 + 0.860544i \(0.329876\pi\)
\(644\) 0 0
\(645\) 5.18487 0.204154
\(646\) 0 0
\(647\) −10.4698 −0.411609 −0.205804 0.978593i \(-0.565981\pi\)
−0.205804 + 0.978593i \(0.565981\pi\)
\(648\) 0 0
\(649\) −20.2750 −0.795862
\(650\) 0 0
\(651\) −0.430730 −0.0168816
\(652\) 0 0
\(653\) 6.18617 0.242083 0.121042 0.992647i \(-0.461377\pi\)
0.121042 + 0.992647i \(0.461377\pi\)
\(654\) 0 0
\(655\) −0.0284259 −0.00111069
\(656\) 0 0
\(657\) 5.98143 0.233358
\(658\) 0 0
\(659\) −12.7354 −0.496100 −0.248050 0.968747i \(-0.579790\pi\)
−0.248050 + 0.968747i \(0.579790\pi\)
\(660\) 0 0
\(661\) 41.4179 1.61097 0.805485 0.592616i \(-0.201905\pi\)
0.805485 + 0.592616i \(0.201905\pi\)
\(662\) 0 0
\(663\) 5.67350 0.220340
\(664\) 0 0
\(665\) 0.354603 0.0137509
\(666\) 0 0
\(667\) 17.8095 0.689586
\(668\) 0 0
\(669\) 48.1176 1.86033
\(670\) 0 0
\(671\) 5.83767 0.225361
\(672\) 0 0
\(673\) −15.7266 −0.606216 −0.303108 0.952956i \(-0.598024\pi\)
−0.303108 + 0.952956i \(0.598024\pi\)
\(674\) 0 0
\(675\) 20.8599 0.802899
\(676\) 0 0
\(677\) −23.9547 −0.920653 −0.460327 0.887750i \(-0.652268\pi\)
−0.460327 + 0.887750i \(0.652268\pi\)
\(678\) 0 0
\(679\) −15.6571 −0.600865
\(680\) 0 0
\(681\) −43.7520 −1.67658
\(682\) 0 0
\(683\) −5.49575 −0.210289 −0.105144 0.994457i \(-0.533530\pi\)
−0.105144 + 0.994457i \(0.533530\pi\)
\(684\) 0 0
\(685\) −6.30470 −0.240890
\(686\) 0 0
\(687\) 28.2400 1.07742
\(688\) 0 0
\(689\) 9.77446 0.372377
\(690\) 0 0
\(691\) −41.4625 −1.57731 −0.788653 0.614838i \(-0.789221\pi\)
−0.788653 + 0.614838i \(0.789221\pi\)
\(692\) 0 0
\(693\) 9.53742 0.362297
\(694\) 0 0
\(695\) −2.70043 −0.102433
\(696\) 0 0
\(697\) −1.42116 −0.0538304
\(698\) 0 0
\(699\) 52.9134 2.00137
\(700\) 0 0
\(701\) 34.4107 1.29967 0.649836 0.760074i \(-0.274837\pi\)
0.649836 + 0.760074i \(0.274837\pi\)
\(702\) 0 0
\(703\) 1.73291 0.0653580
\(704\) 0 0
\(705\) −1.29768 −0.0488735
\(706\) 0 0
\(707\) −10.7348 −0.403722
\(708\) 0 0
\(709\) 1.23435 0.0463568 0.0231784 0.999731i \(-0.492621\pi\)
0.0231784 + 0.999731i \(0.492621\pi\)
\(710\) 0 0
\(711\) −4.55049 −0.170657
\(712\) 0 0
\(713\) −0.565725 −0.0211866
\(714\) 0 0
\(715\) −2.12384 −0.0794272
\(716\) 0 0
\(717\) 25.6427 0.957643
\(718\) 0 0
\(719\) −28.9956 −1.08135 −0.540677 0.841230i \(-0.681832\pi\)
−0.540677 + 0.841230i \(0.681832\pi\)
\(720\) 0 0
\(721\) −9.71648 −0.361860
\(722\) 0 0
\(723\) 11.7092 0.435468
\(724\) 0 0
\(725\) −21.9553 −0.815398
\(726\) 0 0
\(727\) 23.0888 0.856315 0.428157 0.903704i \(-0.359163\pi\)
0.428157 + 0.903704i \(0.359163\pi\)
\(728\) 0 0
\(729\) −43.9694 −1.62849
\(730\) 0 0
\(731\) 3.49367 0.129218
\(732\) 0 0
\(733\) 51.6398 1.90736 0.953680 0.300824i \(-0.0972617\pi\)
0.953680 + 0.300824i \(0.0972617\pi\)
\(734\) 0 0
\(735\) −5.12563 −0.189062
\(736\) 0 0
\(737\) −6.29721 −0.231961
\(738\) 0 0
\(739\) −7.46711 −0.274682 −0.137341 0.990524i \(-0.543856\pi\)
−0.137341 + 0.990524i \(0.543856\pi\)
\(740\) 0 0
\(741\) 9.50951 0.349341
\(742\) 0 0
\(743\) 12.9801 0.476195 0.238098 0.971241i \(-0.423476\pi\)
0.238098 + 0.971241i \(0.423476\pi\)
\(744\) 0 0
\(745\) −2.07276 −0.0759399
\(746\) 0 0
\(747\) 56.9901 2.08516
\(748\) 0 0
\(749\) −1.75975 −0.0642997
\(750\) 0 0
\(751\) 6.29746 0.229798 0.114899 0.993377i \(-0.463346\pi\)
0.114899 + 0.993377i \(0.463346\pi\)
\(752\) 0 0
\(753\) −10.9705 −0.399786
\(754\) 0 0
\(755\) −1.74095 −0.0633595
\(756\) 0 0
\(757\) 15.3741 0.558780 0.279390 0.960178i \(-0.409868\pi\)
0.279390 + 0.960178i \(0.409868\pi\)
\(758\) 0 0
\(759\) 20.7849 0.754444
\(760\) 0 0
\(761\) 22.5592 0.817770 0.408885 0.912586i \(-0.365918\pi\)
0.408885 + 0.912586i \(0.365918\pi\)
\(762\) 0 0
\(763\) 19.9839 0.723465
\(764\) 0 0
\(765\) −0.874804 −0.0316286
\(766\) 0 0
\(767\) −36.8417 −1.33028
\(768\) 0 0
\(769\) 39.2098 1.41394 0.706971 0.707243i \(-0.250061\pi\)
0.706971 + 0.707243i \(0.250061\pi\)
\(770\) 0 0
\(771\) −16.6141 −0.598341
\(772\) 0 0
\(773\) 4.23161 0.152200 0.0761002 0.997100i \(-0.475753\pi\)
0.0761002 + 0.997100i \(0.475753\pi\)
\(774\) 0 0
\(775\) 0.697417 0.0250519
\(776\) 0 0
\(777\) 5.24017 0.187990
\(778\) 0 0
\(779\) −2.38206 −0.0853460
\(780\) 0 0
\(781\) −18.9268 −0.677253
\(782\) 0 0
\(783\) −19.1046 −0.682743
\(784\) 0 0
\(785\) −3.77879 −0.134871
\(786\) 0 0
\(787\) 22.4768 0.801212 0.400606 0.916251i \(-0.368800\pi\)
0.400606 + 0.916251i \(0.368800\pi\)
\(788\) 0 0
\(789\) 78.2690 2.78645
\(790\) 0 0
\(791\) 11.7406 0.417447
\(792\) 0 0
\(793\) 10.6077 0.376689
\(794\) 0 0
\(795\) −2.50075 −0.0886923
\(796\) 0 0
\(797\) −38.8015 −1.37442 −0.687209 0.726459i \(-0.741164\pi\)
−0.687209 + 0.726459i \(0.741164\pi\)
\(798\) 0 0
\(799\) −0.874405 −0.0309342
\(800\) 0 0
\(801\) −72.9529 −2.57766
\(802\) 0 0
\(803\) −2.50344 −0.0883446
\(804\) 0 0
\(805\) 1.40835 0.0496379
\(806\) 0 0
\(807\) −70.5649 −2.48400
\(808\) 0 0
\(809\) 30.9845 1.08936 0.544678 0.838645i \(-0.316652\pi\)
0.544678 + 0.838645i \(0.316652\pi\)
\(810\) 0 0
\(811\) −13.8246 −0.485448 −0.242724 0.970095i \(-0.578041\pi\)
−0.242724 + 0.970095i \(0.578041\pi\)
\(812\) 0 0
\(813\) −15.0461 −0.527690
\(814\) 0 0
\(815\) 3.89225 0.136340
\(816\) 0 0
\(817\) 5.85585 0.204870
\(818\) 0 0
\(819\) 17.3305 0.605576
\(820\) 0 0
\(821\) −48.7769 −1.70233 −0.851163 0.524901i \(-0.824102\pi\)
−0.851163 + 0.524901i \(0.824102\pi\)
\(822\) 0 0
\(823\) 16.7394 0.583497 0.291749 0.956495i \(-0.405763\pi\)
0.291749 + 0.956495i \(0.405763\pi\)
\(824\) 0 0
\(825\) −25.6233 −0.892089
\(826\) 0 0
\(827\) 12.6269 0.439081 0.219540 0.975603i \(-0.429544\pi\)
0.219540 + 0.975603i \(0.429544\pi\)
\(828\) 0 0
\(829\) 10.2351 0.355479 0.177739 0.984078i \(-0.443122\pi\)
0.177739 + 0.984078i \(0.443122\pi\)
\(830\) 0 0
\(831\) −17.1232 −0.593998
\(832\) 0 0
\(833\) −3.45376 −0.119666
\(834\) 0 0
\(835\) 5.04747 0.174675
\(836\) 0 0
\(837\) 0.606865 0.0209763
\(838\) 0 0
\(839\) −7.64201 −0.263832 −0.131916 0.991261i \(-0.542113\pi\)
−0.131916 + 0.991261i \(0.542113\pi\)
\(840\) 0 0
\(841\) −8.89221 −0.306628
\(842\) 0 0
\(843\) 34.3501 1.18308
\(844\) 0 0
\(845\) 0.329696 0.0113419
\(846\) 0 0
\(847\) 8.11351 0.278784
\(848\) 0 0
\(849\) −65.5248 −2.24881
\(850\) 0 0
\(851\) 6.88249 0.235929
\(852\) 0 0
\(853\) −34.8680 −1.19386 −0.596929 0.802294i \(-0.703613\pi\)
−0.596929 + 0.802294i \(0.703613\pi\)
\(854\) 0 0
\(855\) −1.46628 −0.0501459
\(856\) 0 0
\(857\) −45.3258 −1.54830 −0.774149 0.633003i \(-0.781822\pi\)
−0.774149 + 0.633003i \(0.781822\pi\)
\(858\) 0 0
\(859\) 16.9737 0.579135 0.289568 0.957158i \(-0.406488\pi\)
0.289568 + 0.957158i \(0.406488\pi\)
\(860\) 0 0
\(861\) −7.20313 −0.245482
\(862\) 0 0
\(863\) −16.6412 −0.566472 −0.283236 0.959050i \(-0.591408\pi\)
−0.283236 + 0.959050i \(0.591408\pi\)
\(864\) 0 0
\(865\) 1.30718 0.0444453
\(866\) 0 0
\(867\) 45.7348 1.55323
\(868\) 0 0
\(869\) 1.90455 0.0646073
\(870\) 0 0
\(871\) −11.4427 −0.387721
\(872\) 0 0
\(873\) 64.7423 2.19119
\(874\) 0 0
\(875\) −3.50921 −0.118633
\(876\) 0 0
\(877\) 22.8014 0.769948 0.384974 0.922927i \(-0.374210\pi\)
0.384974 + 0.922927i \(0.374210\pi\)
\(878\) 0 0
\(879\) 17.7194 0.597661
\(880\) 0 0
\(881\) 30.1721 1.01653 0.508263 0.861202i \(-0.330288\pi\)
0.508263 + 0.861202i \(0.330288\pi\)
\(882\) 0 0
\(883\) −42.7120 −1.43737 −0.718686 0.695334i \(-0.755256\pi\)
−0.718686 + 0.695334i \(0.755256\pi\)
\(884\) 0 0
\(885\) 9.42576 0.316844
\(886\) 0 0
\(887\) −17.9941 −0.604182 −0.302091 0.953279i \(-0.597685\pi\)
−0.302091 + 0.953279i \(0.597685\pi\)
\(888\) 0 0
\(889\) 4.76881 0.159941
\(890\) 0 0
\(891\) 3.70342 0.124069
\(892\) 0 0
\(893\) −1.46562 −0.0490449
\(894\) 0 0
\(895\) 5.95372 0.199011
\(896\) 0 0
\(897\) 37.7683 1.26105
\(898\) 0 0
\(899\) −0.638731 −0.0213029
\(900\) 0 0
\(901\) −1.68506 −0.0561374
\(902\) 0 0
\(903\) 17.7076 0.589271
\(904\) 0 0
\(905\) −5.72568 −0.190328
\(906\) 0 0
\(907\) −34.6271 −1.14978 −0.574888 0.818232i \(-0.694954\pi\)
−0.574888 + 0.818232i \(0.694954\pi\)
\(908\) 0 0
\(909\) 44.3883 1.47227
\(910\) 0 0
\(911\) −44.5789 −1.47697 −0.738483 0.674272i \(-0.764457\pi\)
−0.738483 + 0.674272i \(0.764457\pi\)
\(912\) 0 0
\(913\) −23.8524 −0.789401
\(914\) 0 0
\(915\) −2.71391 −0.0897192
\(916\) 0 0
\(917\) −0.0970815 −0.00320591
\(918\) 0 0
\(919\) 42.3848 1.39815 0.699073 0.715050i \(-0.253596\pi\)
0.699073 + 0.715050i \(0.253596\pi\)
\(920\) 0 0
\(921\) 67.6177 2.22808
\(922\) 0 0
\(923\) −34.3919 −1.13202
\(924\) 0 0
\(925\) −8.48463 −0.278973
\(926\) 0 0
\(927\) 40.1777 1.31961
\(928\) 0 0
\(929\) −1.53086 −0.0502260 −0.0251130 0.999685i \(-0.507995\pi\)
−0.0251130 + 0.999685i \(0.507995\pi\)
\(930\) 0 0
\(931\) −5.78895 −0.189725
\(932\) 0 0
\(933\) 92.0228 3.01269
\(934\) 0 0
\(935\) 0.366137 0.0119740
\(936\) 0 0
\(937\) 16.3179 0.533081 0.266541 0.963824i \(-0.414119\pi\)
0.266541 + 0.963824i \(0.414119\pi\)
\(938\) 0 0
\(939\) 47.9058 1.56335
\(940\) 0 0
\(941\) −3.40682 −0.111059 −0.0555296 0.998457i \(-0.517685\pi\)
−0.0555296 + 0.998457i \(0.517685\pi\)
\(942\) 0 0
\(943\) −9.46065 −0.308081
\(944\) 0 0
\(945\) −1.51077 −0.0491453
\(946\) 0 0
\(947\) −16.3858 −0.532468 −0.266234 0.963908i \(-0.585779\pi\)
−0.266234 + 0.963908i \(0.585779\pi\)
\(948\) 0 0
\(949\) −4.54902 −0.147667
\(950\) 0 0
\(951\) 24.2249 0.785548
\(952\) 0 0
\(953\) 2.25457 0.0730327 0.0365164 0.999333i \(-0.488374\pi\)
0.0365164 + 0.999333i \(0.488374\pi\)
\(954\) 0 0
\(955\) −3.63036 −0.117476
\(956\) 0 0
\(957\) 23.4672 0.758586
\(958\) 0 0
\(959\) −21.5321 −0.695308
\(960\) 0 0
\(961\) −30.9797 −0.999345
\(962\) 0 0
\(963\) 7.27656 0.234484
\(964\) 0 0
\(965\) −3.28965 −0.105898
\(966\) 0 0
\(967\) 35.3853 1.13792 0.568958 0.822367i \(-0.307347\pi\)
0.568958 + 0.822367i \(0.307347\pi\)
\(968\) 0 0
\(969\) −1.63938 −0.0526645
\(970\) 0 0
\(971\) −23.8146 −0.764245 −0.382123 0.924112i \(-0.624807\pi\)
−0.382123 + 0.924112i \(0.624807\pi\)
\(972\) 0 0
\(973\) −9.22263 −0.295664
\(974\) 0 0
\(975\) −46.5602 −1.49112
\(976\) 0 0
\(977\) 37.9373 1.21372 0.606861 0.794808i \(-0.292428\pi\)
0.606861 + 0.794808i \(0.292428\pi\)
\(978\) 0 0
\(979\) 30.5334 0.975852
\(980\) 0 0
\(981\) −82.6334 −2.63828
\(982\) 0 0
\(983\) 6.03830 0.192592 0.0962959 0.995353i \(-0.469300\pi\)
0.0962959 + 0.995353i \(0.469300\pi\)
\(984\) 0 0
\(985\) −0.710871 −0.0226502
\(986\) 0 0
\(987\) −4.43189 −0.141069
\(988\) 0 0
\(989\) 23.2573 0.739539
\(990\) 0 0
\(991\) 22.2803 0.707757 0.353879 0.935291i \(-0.384863\pi\)
0.353879 + 0.935291i \(0.384863\pi\)
\(992\) 0 0
\(993\) 34.2490 1.08686
\(994\) 0 0
\(995\) −2.58517 −0.0819554
\(996\) 0 0
\(997\) 33.8602 1.07236 0.536181 0.844103i \(-0.319866\pi\)
0.536181 + 0.844103i \(0.319866\pi\)
\(998\) 0 0
\(999\) −7.38299 −0.233588
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 \(a_p\))