Properties

Label 8001.2.a.o.1.5
Level 8001
Weight 2
Character 8001.1
Self dual Yes
Analytic conductor 63.888
Analytic rank 1
Dimension 13
CM No
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 8001 = 3^{2} \cdot 7 \cdot 127 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8001.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(63.8883066572\)
Analytic rank: \(1\)
Dimension: \(13\)
Coefficient field: \(\mathbb{Q}[x]/(x^{13} - \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{17}]\)
Coefficient ring index: \( 2^{2} \)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.5
Root \(1.27342\)
Character \(\chi\) = 8001.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-1.27342 q^{2}\) \(-0.378389 q^{4}\) \(+2.08575 q^{5}\) \(+1.00000 q^{7}\) \(+3.02870 q^{8}\) \(+O(q^{10})\) \(q\)\(-1.27342 q^{2}\) \(-0.378389 q^{4}\) \(+2.08575 q^{5}\) \(+1.00000 q^{7}\) \(+3.02870 q^{8}\) \(-2.65604 q^{10}\) \(+2.11092 q^{11}\) \(-3.46613 q^{13}\) \(-1.27342 q^{14}\) \(-3.10004 q^{16}\) \(-5.03226 q^{17}\) \(+0.224274 q^{19}\) \(-0.789224 q^{20}\) \(-2.68810 q^{22}\) \(+7.75804 q^{23}\) \(-0.649667 q^{25}\) \(+4.41385 q^{26}\) \(-0.378389 q^{28}\) \(-5.57528 q^{29}\) \(-0.678920 q^{31}\) \(-2.10973 q^{32}\) \(+6.40821 q^{34}\) \(+2.08575 q^{35}\) \(+10.9322 q^{37}\) \(-0.285596 q^{38}\) \(+6.31710 q^{40}\) \(-1.33740 q^{41}\) \(-5.86968 q^{43}\) \(-0.798750 q^{44}\) \(-9.87928 q^{46}\) \(-0.612915 q^{47}\) \(+1.00000 q^{49}\) \(+0.827302 q^{50}\) \(+1.31155 q^{52}\) \(-9.19649 q^{53}\) \(+4.40284 q^{55}\) \(+3.02870 q^{56}\) \(+7.09970 q^{58}\) \(-9.06930 q^{59}\) \(+0.604535 q^{61}\) \(+0.864553 q^{62}\) \(+8.88667 q^{64}\) \(-7.22946 q^{65}\) \(-1.65675 q^{67}\) \(+1.90415 q^{68}\) \(-2.65604 q^{70}\) \(+7.12563 q^{71}\) \(-7.49595 q^{73}\) \(-13.9214 q^{74}\) \(-0.0848630 q^{76}\) \(+2.11092 q^{77}\) \(+5.41599 q^{79}\) \(-6.46590 q^{80}\) \(+1.70308 q^{82}\) \(-5.01259 q^{83}\) \(-10.4960 q^{85}\) \(+7.47460 q^{86}\) \(+6.39335 q^{88}\) \(-8.62166 q^{89}\) \(-3.46613 q^{91}\) \(-2.93556 q^{92}\) \(+0.780501 q^{94}\) \(+0.467779 q^{95}\) \(+6.43694 q^{97}\) \(-1.27342 q^{98}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(13q \) \(\mathstrut -\mathstrut 4q^{2} \) \(\mathstrut +\mathstrut 10q^{4} \) \(\mathstrut -\mathstrut 12q^{5} \) \(\mathstrut +\mathstrut 13q^{7} \) \(\mathstrut -\mathstrut 9q^{8} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(13q \) \(\mathstrut -\mathstrut 4q^{2} \) \(\mathstrut +\mathstrut 10q^{4} \) \(\mathstrut -\mathstrut 12q^{5} \) \(\mathstrut +\mathstrut 13q^{7} \) \(\mathstrut -\mathstrut 9q^{8} \) \(\mathstrut +\mathstrut 6q^{10} \) \(\mathstrut -\mathstrut 3q^{11} \) \(\mathstrut +\mathstrut 21q^{13} \) \(\mathstrut -\mathstrut 4q^{14} \) \(\mathstrut +\mathstrut 8q^{16} \) \(\mathstrut -\mathstrut 17q^{17} \) \(\mathstrut +\mathstrut 5q^{19} \) \(\mathstrut -\mathstrut 29q^{20} \) \(\mathstrut +\mathstrut q^{22} \) \(\mathstrut -\mathstrut 4q^{23} \) \(\mathstrut +\mathstrut q^{25} \) \(\mathstrut -\mathstrut 22q^{26} \) \(\mathstrut +\mathstrut 10q^{28} \) \(\mathstrut -\mathstrut 21q^{29} \) \(\mathstrut -\mathstrut 7q^{31} \) \(\mathstrut -\mathstrut 12q^{32} \) \(\mathstrut +\mathstrut 2q^{34} \) \(\mathstrut -\mathstrut 12q^{35} \) \(\mathstrut +\mathstrut 7q^{37} \) \(\mathstrut +\mathstrut 9q^{38} \) \(\mathstrut +\mathstrut 29q^{40} \) \(\mathstrut -\mathstrut 21q^{41} \) \(\mathstrut -\mathstrut 9q^{43} \) \(\mathstrut +\mathstrut 2q^{44} \) \(\mathstrut -\mathstrut 28q^{46} \) \(\mathstrut -\mathstrut 23q^{47} \) \(\mathstrut +\mathstrut 13q^{49} \) \(\mathstrut -\mathstrut 15q^{50} \) \(\mathstrut +\mathstrut 15q^{52} \) \(\mathstrut -\mathstrut 31q^{53} \) \(\mathstrut -\mathstrut 8q^{55} \) \(\mathstrut -\mathstrut 9q^{56} \) \(\mathstrut -\mathstrut 25q^{58} \) \(\mathstrut -\mathstrut 28q^{59} \) \(\mathstrut +\mathstrut 29q^{61} \) \(\mathstrut +\mathstrut 3q^{62} \) \(\mathstrut +\mathstrut 9q^{64} \) \(\mathstrut -\mathstrut 30q^{65} \) \(\mathstrut -\mathstrut 18q^{67} \) \(\mathstrut -\mathstrut 34q^{68} \) \(\mathstrut +\mathstrut 6q^{70} \) \(\mathstrut -\mathstrut 10q^{71} \) \(\mathstrut +\mathstrut 24q^{73} \) \(\mathstrut +\mathstrut 19q^{74} \) \(\mathstrut -\mathstrut 3q^{77} \) \(\mathstrut -\mathstrut 28q^{79} \) \(\mathstrut -\mathstrut 26q^{80} \) \(\mathstrut +\mathstrut 18q^{82} \) \(\mathstrut -\mathstrut 26q^{83} \) \(\mathstrut +\mathstrut 20q^{85} \) \(\mathstrut +\mathstrut 2q^{86} \) \(\mathstrut -\mathstrut 17q^{88} \) \(\mathstrut -\mathstrut 44q^{89} \) \(\mathstrut +\mathstrut 21q^{91} \) \(\mathstrut -\mathstrut 6q^{92} \) \(\mathstrut -\mathstrut 9q^{94} \) \(\mathstrut +\mathstrut 2q^{95} \) \(\mathstrut +\mathstrut 17q^{97} \) \(\mathstrut -\mathstrut 4q^{98} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.27342 −0.900447 −0.450224 0.892916i \(-0.648656\pi\)
−0.450224 + 0.892916i \(0.648656\pi\)
\(3\) 0 0
\(4\) −0.378389 −0.189195
\(5\) 2.08575 0.932774 0.466387 0.884581i \(-0.345555\pi\)
0.466387 + 0.884581i \(0.345555\pi\)
\(6\) 0 0
\(7\) 1.00000 0.377964
\(8\) 3.02870 1.07081
\(9\) 0 0
\(10\) −2.65604 −0.839914
\(11\) 2.11092 0.636467 0.318233 0.948012i \(-0.396910\pi\)
0.318233 + 0.948012i \(0.396910\pi\)
\(12\) 0 0
\(13\) −3.46613 −0.961331 −0.480666 0.876904i \(-0.659605\pi\)
−0.480666 + 0.876904i \(0.659605\pi\)
\(14\) −1.27342 −0.340337
\(15\) 0 0
\(16\) −3.10004 −0.775011
\(17\) −5.03226 −1.22050 −0.610252 0.792208i \(-0.708932\pi\)
−0.610252 + 0.792208i \(0.708932\pi\)
\(18\) 0 0
\(19\) 0.224274 0.0514520 0.0257260 0.999669i \(-0.491810\pi\)
0.0257260 + 0.999669i \(0.491810\pi\)
\(20\) −0.789224 −0.176476
\(21\) 0 0
\(22\) −2.68810 −0.573105
\(23\) 7.75804 1.61766 0.808832 0.588040i \(-0.200100\pi\)
0.808832 + 0.588040i \(0.200100\pi\)
\(24\) 0 0
\(25\) −0.649667 −0.129933
\(26\) 4.41385 0.865628
\(27\) 0 0
\(28\) −0.378389 −0.0715088
\(29\) −5.57528 −1.03530 −0.517651 0.855592i \(-0.673194\pi\)
−0.517651 + 0.855592i \(0.673194\pi\)
\(30\) 0 0
\(31\) −0.678920 −0.121938 −0.0609688 0.998140i \(-0.519419\pi\)
−0.0609688 + 0.998140i \(0.519419\pi\)
\(32\) −2.10973 −0.372951
\(33\) 0 0
\(34\) 6.40821 1.09900
\(35\) 2.08575 0.352555
\(36\) 0 0
\(37\) 10.9322 1.79725 0.898625 0.438718i \(-0.144567\pi\)
0.898625 + 0.438718i \(0.144567\pi\)
\(38\) −0.285596 −0.0463299
\(39\) 0 0
\(40\) 6.31710 0.998821
\(41\) −1.33740 −0.208867 −0.104433 0.994532i \(-0.533303\pi\)
−0.104433 + 0.994532i \(0.533303\pi\)
\(42\) 0 0
\(43\) −5.86968 −0.895118 −0.447559 0.894254i \(-0.647707\pi\)
−0.447559 + 0.894254i \(0.647707\pi\)
\(44\) −0.798750 −0.120416
\(45\) 0 0
\(46\) −9.87928 −1.45662
\(47\) −0.612915 −0.0894028 −0.0447014 0.999000i \(-0.514234\pi\)
−0.0447014 + 0.999000i \(0.514234\pi\)
\(48\) 0 0
\(49\) 1.00000 0.142857
\(50\) 0.827302 0.116998
\(51\) 0 0
\(52\) 1.31155 0.181879
\(53\) −9.19649 −1.26324 −0.631618 0.775280i \(-0.717609\pi\)
−0.631618 + 0.775280i \(0.717609\pi\)
\(54\) 0 0
\(55\) 4.40284 0.593679
\(56\) 3.02870 0.404727
\(57\) 0 0
\(58\) 7.09970 0.932236
\(59\) −9.06930 −1.18072 −0.590361 0.807139i \(-0.701015\pi\)
−0.590361 + 0.807139i \(0.701015\pi\)
\(60\) 0 0
\(61\) 0.604535 0.0774028 0.0387014 0.999251i \(-0.487678\pi\)
0.0387014 + 0.999251i \(0.487678\pi\)
\(62\) 0.864553 0.109798
\(63\) 0 0
\(64\) 8.88667 1.11083
\(65\) −7.22946 −0.896704
\(66\) 0 0
\(67\) −1.65675 −0.202404 −0.101202 0.994866i \(-0.532269\pi\)
−0.101202 + 0.994866i \(0.532269\pi\)
\(68\) 1.90415 0.230913
\(69\) 0 0
\(70\) −2.65604 −0.317457
\(71\) 7.12563 0.845657 0.422829 0.906210i \(-0.361037\pi\)
0.422829 + 0.906210i \(0.361037\pi\)
\(72\) 0 0
\(73\) −7.49595 −0.877335 −0.438667 0.898650i \(-0.644549\pi\)
−0.438667 + 0.898650i \(0.644549\pi\)
\(74\) −13.9214 −1.61833
\(75\) 0 0
\(76\) −0.0848630 −0.00973445
\(77\) 2.11092 0.240562
\(78\) 0 0
\(79\) 5.41599 0.609346 0.304673 0.952457i \(-0.401453\pi\)
0.304673 + 0.952457i \(0.401453\pi\)
\(80\) −6.46590 −0.722910
\(81\) 0 0
\(82\) 1.70308 0.188074
\(83\) −5.01259 −0.550204 −0.275102 0.961415i \(-0.588712\pi\)
−0.275102 + 0.961415i \(0.588712\pi\)
\(84\) 0 0
\(85\) −10.4960 −1.13845
\(86\) 7.47460 0.806007
\(87\) 0 0
\(88\) 6.39335 0.681533
\(89\) −8.62166 −0.913894 −0.456947 0.889494i \(-0.651057\pi\)
−0.456947 + 0.889494i \(0.651057\pi\)
\(90\) 0 0
\(91\) −3.46613 −0.363349
\(92\) −2.93556 −0.306053
\(93\) 0 0
\(94\) 0.780501 0.0805025
\(95\) 0.467779 0.0479931
\(96\) 0 0
\(97\) 6.43694 0.653572 0.326786 0.945098i \(-0.394034\pi\)
0.326786 + 0.945098i \(0.394034\pi\)
\(98\) −1.27342 −0.128635
\(99\) 0 0
\(100\) 0.245827 0.0245827
\(101\) −12.0226 −1.19629 −0.598145 0.801388i \(-0.704095\pi\)
−0.598145 + 0.801388i \(0.704095\pi\)
\(102\) 0 0
\(103\) 9.25231 0.911657 0.455829 0.890068i \(-0.349343\pi\)
0.455829 + 0.890068i \(0.349343\pi\)
\(104\) −10.4979 −1.02940
\(105\) 0 0
\(106\) 11.7110 1.13748
\(107\) −10.2336 −0.989324 −0.494662 0.869085i \(-0.664708\pi\)
−0.494662 + 0.869085i \(0.664708\pi\)
\(108\) 0 0
\(109\) −9.22482 −0.883577 −0.441789 0.897119i \(-0.645656\pi\)
−0.441789 + 0.897119i \(0.645656\pi\)
\(110\) −5.60669 −0.534577
\(111\) 0 0
\(112\) −3.10004 −0.292927
\(113\) −16.8813 −1.58806 −0.794032 0.607876i \(-0.792022\pi\)
−0.794032 + 0.607876i \(0.792022\pi\)
\(114\) 0 0
\(115\) 16.1813 1.50891
\(116\) 2.10962 0.195874
\(117\) 0 0
\(118\) 11.5491 1.06318
\(119\) −5.03226 −0.461307
\(120\) 0 0
\(121\) −6.54401 −0.594910
\(122\) −0.769830 −0.0696971
\(123\) 0 0
\(124\) 0.256896 0.0230699
\(125\) −11.7838 −1.05397
\(126\) 0 0
\(127\) −1.00000 −0.0887357
\(128\) −7.09705 −0.627296
\(129\) 0 0
\(130\) 9.20618 0.807435
\(131\) −1.55514 −0.135874 −0.0679368 0.997690i \(-0.521642\pi\)
−0.0679368 + 0.997690i \(0.521642\pi\)
\(132\) 0 0
\(133\) 0.224274 0.0194470
\(134\) 2.10975 0.182254
\(135\) 0 0
\(136\) −15.2412 −1.30692
\(137\) 6.31696 0.539694 0.269847 0.962903i \(-0.413027\pi\)
0.269847 + 0.962903i \(0.413027\pi\)
\(138\) 0 0
\(139\) 16.4399 1.39441 0.697205 0.716872i \(-0.254427\pi\)
0.697205 + 0.716872i \(0.254427\pi\)
\(140\) −0.789224 −0.0667016
\(141\) 0 0
\(142\) −9.07396 −0.761470
\(143\) −7.31672 −0.611855
\(144\) 0 0
\(145\) −11.6286 −0.965703
\(146\) 9.54553 0.789994
\(147\) 0 0
\(148\) −4.13664 −0.340030
\(149\) 8.62637 0.706700 0.353350 0.935491i \(-0.385042\pi\)
0.353350 + 0.935491i \(0.385042\pi\)
\(150\) 0 0
\(151\) −21.7050 −1.76632 −0.883162 0.469068i \(-0.844590\pi\)
−0.883162 + 0.469068i \(0.844590\pi\)
\(152\) 0.679259 0.0550952
\(153\) 0 0
\(154\) −2.68810 −0.216613
\(155\) −1.41605 −0.113740
\(156\) 0 0
\(157\) 9.92251 0.791902 0.395951 0.918272i \(-0.370415\pi\)
0.395951 + 0.918272i \(0.370415\pi\)
\(158\) −6.89685 −0.548684
\(159\) 0 0
\(160\) −4.40035 −0.347879
\(161\) 7.75804 0.611419
\(162\) 0 0
\(163\) −10.0861 −0.790005 −0.395003 0.918680i \(-0.629256\pi\)
−0.395003 + 0.918680i \(0.629256\pi\)
\(164\) 0.506058 0.0395165
\(165\) 0 0
\(166\) 6.38316 0.495429
\(167\) 2.52578 0.195451 0.0977254 0.995213i \(-0.468843\pi\)
0.0977254 + 0.995213i \(0.468843\pi\)
\(168\) 0 0
\(169\) −0.985951 −0.0758424
\(170\) 13.3659 1.02512
\(171\) 0 0
\(172\) 2.22102 0.169352
\(173\) −10.7804 −0.819618 −0.409809 0.912171i \(-0.634405\pi\)
−0.409809 + 0.912171i \(0.634405\pi\)
\(174\) 0 0
\(175\) −0.649667 −0.0491102
\(176\) −6.54394 −0.493268
\(177\) 0 0
\(178\) 10.9790 0.822913
\(179\) 21.7204 1.62346 0.811728 0.584036i \(-0.198527\pi\)
0.811728 + 0.584036i \(0.198527\pi\)
\(180\) 0 0
\(181\) 5.87464 0.436659 0.218329 0.975875i \(-0.429939\pi\)
0.218329 + 0.975875i \(0.429939\pi\)
\(182\) 4.41385 0.327177
\(183\) 0 0
\(184\) 23.4968 1.73221
\(185\) 22.8019 1.67643
\(186\) 0 0
\(187\) −10.6227 −0.776809
\(188\) 0.231920 0.0169145
\(189\) 0 0
\(190\) −0.595681 −0.0432153
\(191\) −8.92458 −0.645760 −0.322880 0.946440i \(-0.604651\pi\)
−0.322880 + 0.946440i \(0.604651\pi\)
\(192\) 0 0
\(193\) −23.3225 −1.67879 −0.839396 0.543521i \(-0.817091\pi\)
−0.839396 + 0.543521i \(0.817091\pi\)
\(194\) −8.19696 −0.588507
\(195\) 0 0
\(196\) −0.378389 −0.0270278
\(197\) −19.0659 −1.35839 −0.679195 0.733957i \(-0.737671\pi\)
−0.679195 + 0.733957i \(0.737671\pi\)
\(198\) 0 0
\(199\) 7.14093 0.506207 0.253104 0.967439i \(-0.418549\pi\)
0.253104 + 0.967439i \(0.418549\pi\)
\(200\) −1.96765 −0.139134
\(201\) 0 0
\(202\) 15.3098 1.07720
\(203\) −5.57528 −0.391308
\(204\) 0 0
\(205\) −2.78948 −0.194825
\(206\) −11.7821 −0.820900
\(207\) 0 0
\(208\) 10.7451 0.745042
\(209\) 0.473425 0.0327475
\(210\) 0 0
\(211\) 10.8604 0.747664 0.373832 0.927496i \(-0.378044\pi\)
0.373832 + 0.927496i \(0.378044\pi\)
\(212\) 3.47985 0.238997
\(213\) 0 0
\(214\) 13.0318 0.890834
\(215\) −12.2427 −0.834943
\(216\) 0 0
\(217\) −0.678920 −0.0460881
\(218\) 11.7471 0.795615
\(219\) 0 0
\(220\) −1.66599 −0.112321
\(221\) 17.4425 1.17331
\(222\) 0 0
\(223\) 26.1985 1.75438 0.877190 0.480144i \(-0.159416\pi\)
0.877190 + 0.480144i \(0.159416\pi\)
\(224\) −2.10973 −0.140962
\(225\) 0 0
\(226\) 21.4971 1.42997
\(227\) 1.57740 0.104696 0.0523480 0.998629i \(-0.483329\pi\)
0.0523480 + 0.998629i \(0.483329\pi\)
\(228\) 0 0
\(229\) −6.07326 −0.401333 −0.200666 0.979660i \(-0.564311\pi\)
−0.200666 + 0.979660i \(0.564311\pi\)
\(230\) −20.6057 −1.35870
\(231\) 0 0
\(232\) −16.8858 −1.10861
\(233\) 2.10427 0.137856 0.0689278 0.997622i \(-0.478042\pi\)
0.0689278 + 0.997622i \(0.478042\pi\)
\(234\) 0 0
\(235\) −1.27838 −0.0833926
\(236\) 3.43173 0.223386
\(237\) 0 0
\(238\) 6.40821 0.415383
\(239\) −22.6997 −1.46832 −0.734161 0.678976i \(-0.762424\pi\)
−0.734161 + 0.678976i \(0.762424\pi\)
\(240\) 0 0
\(241\) 22.8242 1.47023 0.735117 0.677941i \(-0.237127\pi\)
0.735117 + 0.677941i \(0.237127\pi\)
\(242\) 8.33331 0.535685
\(243\) 0 0
\(244\) −0.228750 −0.0146442
\(245\) 2.08575 0.133253
\(246\) 0 0
\(247\) −0.777364 −0.0494625
\(248\) −2.05624 −0.130572
\(249\) 0 0
\(250\) 15.0057 0.949046
\(251\) −0.360572 −0.0227591 −0.0113795 0.999935i \(-0.503622\pi\)
−0.0113795 + 0.999935i \(0.503622\pi\)
\(252\) 0 0
\(253\) 16.3766 1.02959
\(254\) 1.27342 0.0799018
\(255\) 0 0
\(256\) −8.73578 −0.545986
\(257\) 11.3934 0.710700 0.355350 0.934733i \(-0.384362\pi\)
0.355350 + 0.934733i \(0.384362\pi\)
\(258\) 0 0
\(259\) 10.9322 0.679296
\(260\) 2.73555 0.169652
\(261\) 0 0
\(262\) 1.98036 0.122347
\(263\) 26.8294 1.65437 0.827187 0.561926i \(-0.189940\pi\)
0.827187 + 0.561926i \(0.189940\pi\)
\(264\) 0 0
\(265\) −19.1815 −1.17831
\(266\) −0.285596 −0.0175110
\(267\) 0 0
\(268\) 0.626896 0.0382938
\(269\) 29.0339 1.77023 0.885113 0.465377i \(-0.154081\pi\)
0.885113 + 0.465377i \(0.154081\pi\)
\(270\) 0 0
\(271\) −12.7987 −0.777464 −0.388732 0.921351i \(-0.627087\pi\)
−0.388732 + 0.921351i \(0.627087\pi\)
\(272\) 15.6002 0.945903
\(273\) 0 0
\(274\) −8.04417 −0.485966
\(275\) −1.37140 −0.0826983
\(276\) 0 0
\(277\) −11.1286 −0.668655 −0.334327 0.942457i \(-0.608509\pi\)
−0.334327 + 0.942457i \(0.608509\pi\)
\(278\) −20.9349 −1.25559
\(279\) 0 0
\(280\) 6.31710 0.377519
\(281\) −26.3268 −1.57052 −0.785262 0.619164i \(-0.787472\pi\)
−0.785262 + 0.619164i \(0.787472\pi\)
\(282\) 0 0
\(283\) −3.23400 −0.192241 −0.0961207 0.995370i \(-0.530643\pi\)
−0.0961207 + 0.995370i \(0.530643\pi\)
\(284\) −2.69626 −0.159994
\(285\) 0 0
\(286\) 9.31730 0.550943
\(287\) −1.33740 −0.0789442
\(288\) 0 0
\(289\) 8.32368 0.489628
\(290\) 14.8082 0.869565
\(291\) 0 0
\(292\) 2.83639 0.165987
\(293\) 23.3615 1.36479 0.682396 0.730982i \(-0.260938\pi\)
0.682396 + 0.730982i \(0.260938\pi\)
\(294\) 0 0
\(295\) −18.9163 −1.10135
\(296\) 33.1105 1.92451
\(297\) 0 0
\(298\) −10.9850 −0.636346
\(299\) −26.8904 −1.55511
\(300\) 0 0
\(301\) −5.86968 −0.338323
\(302\) 27.6396 1.59048
\(303\) 0 0
\(304\) −0.695260 −0.0398759
\(305\) 1.26091 0.0721993
\(306\) 0 0
\(307\) 31.9099 1.82119 0.910596 0.413297i \(-0.135623\pi\)
0.910596 + 0.413297i \(0.135623\pi\)
\(308\) −0.798750 −0.0455130
\(309\) 0 0
\(310\) 1.80324 0.102417
\(311\) 27.5284 1.56099 0.780496 0.625160i \(-0.214966\pi\)
0.780496 + 0.625160i \(0.214966\pi\)
\(312\) 0 0
\(313\) −20.7307 −1.17177 −0.585886 0.810394i \(-0.699253\pi\)
−0.585886 + 0.810394i \(0.699253\pi\)
\(314\) −12.6356 −0.713066
\(315\) 0 0
\(316\) −2.04935 −0.115285
\(317\) −3.97581 −0.223304 −0.111652 0.993747i \(-0.535614\pi\)
−0.111652 + 0.993747i \(0.535614\pi\)
\(318\) 0 0
\(319\) −11.7690 −0.658936
\(320\) 18.5353 1.03616
\(321\) 0 0
\(322\) −9.87928 −0.550551
\(323\) −1.12861 −0.0627974
\(324\) 0 0
\(325\) 2.25183 0.124909
\(326\) 12.8439 0.711358
\(327\) 0 0
\(328\) −4.05058 −0.223656
\(329\) −0.612915 −0.0337911
\(330\) 0 0
\(331\) −6.45118 −0.354589 −0.177295 0.984158i \(-0.556735\pi\)
−0.177295 + 0.984158i \(0.556735\pi\)
\(332\) 1.89671 0.104096
\(333\) 0 0
\(334\) −3.21639 −0.175993
\(335\) −3.45556 −0.188797
\(336\) 0 0
\(337\) −23.4825 −1.27917 −0.639586 0.768720i \(-0.720894\pi\)
−0.639586 + 0.768720i \(0.720894\pi\)
\(338\) 1.25553 0.0682921
\(339\) 0 0
\(340\) 3.97158 0.215389
\(341\) −1.43315 −0.0776092
\(342\) 0 0
\(343\) 1.00000 0.0539949
\(344\) −17.7775 −0.958499
\(345\) 0 0
\(346\) 13.7280 0.738023
\(347\) −19.3384 −1.03814 −0.519070 0.854732i \(-0.673722\pi\)
−0.519070 + 0.854732i \(0.673722\pi\)
\(348\) 0 0
\(349\) 17.9941 0.963204 0.481602 0.876390i \(-0.340055\pi\)
0.481602 + 0.876390i \(0.340055\pi\)
\(350\) 0.827302 0.0442212
\(351\) 0 0
\(352\) −4.45347 −0.237371
\(353\) −32.3822 −1.72353 −0.861765 0.507307i \(-0.830641\pi\)
−0.861765 + 0.507307i \(0.830641\pi\)
\(354\) 0 0
\(355\) 14.8623 0.788807
\(356\) 3.26234 0.172904
\(357\) 0 0
\(358\) −27.6592 −1.46184
\(359\) 7.91949 0.417975 0.208987 0.977918i \(-0.432983\pi\)
0.208987 + 0.977918i \(0.432983\pi\)
\(360\) 0 0
\(361\) −18.9497 −0.997353
\(362\) −7.48091 −0.393188
\(363\) 0 0
\(364\) 1.31155 0.0687437
\(365\) −15.6346 −0.818355
\(366\) 0 0
\(367\) 27.4206 1.43134 0.715672 0.698436i \(-0.246120\pi\)
0.715672 + 0.698436i \(0.246120\pi\)
\(368\) −24.0503 −1.25371
\(369\) 0 0
\(370\) −29.0365 −1.50953
\(371\) −9.19649 −0.477458
\(372\) 0 0
\(373\) 3.79509 0.196502 0.0982511 0.995162i \(-0.468675\pi\)
0.0982511 + 0.995162i \(0.468675\pi\)
\(374\) 13.5272 0.699476
\(375\) 0 0
\(376\) −1.85633 −0.0957331
\(377\) 19.3246 0.995269
\(378\) 0 0
\(379\) −35.9912 −1.84874 −0.924371 0.381494i \(-0.875410\pi\)
−0.924371 + 0.381494i \(0.875410\pi\)
\(380\) −0.177003 −0.00908004
\(381\) 0 0
\(382\) 11.3648 0.581473
\(383\) 1.34990 0.0689768 0.0344884 0.999405i \(-0.489020\pi\)
0.0344884 + 0.999405i \(0.489020\pi\)
\(384\) 0 0
\(385\) 4.40284 0.224390
\(386\) 29.6995 1.51166
\(387\) 0 0
\(388\) −2.43567 −0.123652
\(389\) 3.58741 0.181889 0.0909445 0.995856i \(-0.471011\pi\)
0.0909445 + 0.995856i \(0.471011\pi\)
\(390\) 0 0
\(391\) −39.0405 −1.97436
\(392\) 3.02870 0.152972
\(393\) 0 0
\(394\) 24.2790 1.22316
\(395\) 11.2964 0.568382
\(396\) 0 0
\(397\) 8.38007 0.420584 0.210292 0.977639i \(-0.432559\pi\)
0.210292 + 0.977639i \(0.432559\pi\)
\(398\) −9.09344 −0.455813
\(399\) 0 0
\(400\) 2.01400 0.100700
\(401\) −9.89210 −0.493988 −0.246994 0.969017i \(-0.579443\pi\)
−0.246994 + 0.969017i \(0.579443\pi\)
\(402\) 0 0
\(403\) 2.35322 0.117222
\(404\) 4.54921 0.226332
\(405\) 0 0
\(406\) 7.09970 0.352352
\(407\) 23.0771 1.14389
\(408\) 0 0
\(409\) −4.56659 −0.225804 −0.112902 0.993606i \(-0.536015\pi\)
−0.112902 + 0.993606i \(0.536015\pi\)
\(410\) 3.55219 0.175430
\(411\) 0 0
\(412\) −3.50098 −0.172481
\(413\) −9.06930 −0.446271
\(414\) 0 0
\(415\) −10.4550 −0.513215
\(416\) 7.31259 0.358529
\(417\) 0 0
\(418\) −0.602871 −0.0294874
\(419\) 0.445636 0.0217707 0.0108854 0.999941i \(-0.496535\pi\)
0.0108854 + 0.999941i \(0.496535\pi\)
\(420\) 0 0
\(421\) 7.72563 0.376524 0.188262 0.982119i \(-0.439715\pi\)
0.188262 + 0.982119i \(0.439715\pi\)
\(422\) −13.8300 −0.673232
\(423\) 0 0
\(424\) −27.8534 −1.35268
\(425\) 3.26930 0.158584
\(426\) 0 0
\(427\) 0.604535 0.0292555
\(428\) 3.87230 0.187175
\(429\) 0 0
\(430\) 15.5901 0.751822
\(431\) −33.6636 −1.62152 −0.810760 0.585379i \(-0.800946\pi\)
−0.810760 + 0.585379i \(0.800946\pi\)
\(432\) 0 0
\(433\) −22.2388 −1.06873 −0.534364 0.845255i \(-0.679449\pi\)
−0.534364 + 0.845255i \(0.679449\pi\)
\(434\) 0.864553 0.0414999
\(435\) 0 0
\(436\) 3.49057 0.167168
\(437\) 1.73993 0.0832321
\(438\) 0 0
\(439\) −2.92254 −0.139485 −0.0697425 0.997565i \(-0.522218\pi\)
−0.0697425 + 0.997565i \(0.522218\pi\)
\(440\) 13.3349 0.635716
\(441\) 0 0
\(442\) −22.2117 −1.05650
\(443\) −1.86532 −0.0886242 −0.0443121 0.999018i \(-0.514110\pi\)
−0.0443121 + 0.999018i \(0.514110\pi\)
\(444\) 0 0
\(445\) −17.9826 −0.852456
\(446\) −33.3618 −1.57973
\(447\) 0 0
\(448\) 8.88667 0.419856
\(449\) −8.85530 −0.417908 −0.208954 0.977926i \(-0.567006\pi\)
−0.208954 + 0.977926i \(0.567006\pi\)
\(450\) 0 0
\(451\) −2.82314 −0.132937
\(452\) 6.38772 0.300453
\(453\) 0 0
\(454\) −2.00871 −0.0942732
\(455\) −7.22946 −0.338922
\(456\) 0 0
\(457\) 32.9290 1.54035 0.770177 0.637830i \(-0.220168\pi\)
0.770177 + 0.637830i \(0.220168\pi\)
\(458\) 7.73384 0.361379
\(459\) 0 0
\(460\) −6.12283 −0.285478
\(461\) −24.4113 −1.13695 −0.568474 0.822701i \(-0.692466\pi\)
−0.568474 + 0.822701i \(0.692466\pi\)
\(462\) 0 0
\(463\) −29.9222 −1.39060 −0.695300 0.718719i \(-0.744729\pi\)
−0.695300 + 0.718719i \(0.744729\pi\)
\(464\) 17.2836 0.802371
\(465\) 0 0
\(466\) −2.67963 −0.124132
\(467\) −14.9090 −0.689905 −0.344952 0.938620i \(-0.612105\pi\)
−0.344952 + 0.938620i \(0.612105\pi\)
\(468\) 0 0
\(469\) −1.65675 −0.0765016
\(470\) 1.62793 0.0750906
\(471\) 0 0
\(472\) −27.4682 −1.26433
\(473\) −12.3904 −0.569713
\(474\) 0 0
\(475\) −0.145704 −0.00668534
\(476\) 1.90415 0.0872768
\(477\) 0 0
\(478\) 28.9064 1.32215
\(479\) 10.2536 0.468497 0.234249 0.972177i \(-0.424737\pi\)
0.234249 + 0.972177i \(0.424737\pi\)
\(480\) 0 0
\(481\) −37.8926 −1.72775
\(482\) −29.0649 −1.32387
\(483\) 0 0
\(484\) 2.47618 0.112554
\(485\) 13.4258 0.609635
\(486\) 0 0
\(487\) 13.5403 0.613569 0.306784 0.951779i \(-0.400747\pi\)
0.306784 + 0.951779i \(0.400747\pi\)
\(488\) 1.83095 0.0828834
\(489\) 0 0
\(490\) −2.65604 −0.119988
\(491\) −9.12846 −0.411962 −0.205981 0.978556i \(-0.566038\pi\)
−0.205981 + 0.978556i \(0.566038\pi\)
\(492\) 0 0
\(493\) 28.0563 1.26359
\(494\) 0.989914 0.0445383
\(495\) 0 0
\(496\) 2.10468 0.0945029
\(497\) 7.12563 0.319628
\(498\) 0 0
\(499\) 30.3752 1.35978 0.679890 0.733314i \(-0.262028\pi\)
0.679890 + 0.733314i \(0.262028\pi\)
\(500\) 4.45885 0.199406
\(501\) 0 0
\(502\) 0.459161 0.0204934
\(503\) −34.1012 −1.52050 −0.760250 0.649631i \(-0.774923\pi\)
−0.760250 + 0.649631i \(0.774923\pi\)
\(504\) 0 0
\(505\) −25.0760 −1.11587
\(506\) −20.8544 −0.927090
\(507\) 0 0
\(508\) 0.378389 0.0167883
\(509\) 28.9661 1.28390 0.641951 0.766746i \(-0.278125\pi\)
0.641951 + 0.766746i \(0.278125\pi\)
\(510\) 0 0
\(511\) −7.49595 −0.331601
\(512\) 25.3184 1.11893
\(513\) 0 0
\(514\) −14.5086 −0.639948
\(515\) 19.2980 0.850370
\(516\) 0 0
\(517\) −1.29381 −0.0569019
\(518\) −13.9214 −0.611671
\(519\) 0 0
\(520\) −21.8959 −0.960197
\(521\) −19.5947 −0.858461 −0.429231 0.903195i \(-0.641215\pi\)
−0.429231 + 0.903195i \(0.641215\pi\)
\(522\) 0 0
\(523\) 19.2890 0.843448 0.421724 0.906724i \(-0.361425\pi\)
0.421724 + 0.906724i \(0.361425\pi\)
\(524\) 0.588450 0.0257066
\(525\) 0 0
\(526\) −34.1653 −1.48968
\(527\) 3.41650 0.148825
\(528\) 0 0
\(529\) 37.1872 1.61684
\(530\) 24.4263 1.06101
\(531\) 0 0
\(532\) −0.0848630 −0.00367928
\(533\) 4.63560 0.200790
\(534\) 0 0
\(535\) −21.3448 −0.922815
\(536\) −5.01780 −0.216736
\(537\) 0 0
\(538\) −36.9724 −1.59399
\(539\) 2.11092 0.0909238
\(540\) 0 0
\(541\) −2.87389 −0.123558 −0.0617792 0.998090i \(-0.519677\pi\)
−0.0617792 + 0.998090i \(0.519677\pi\)
\(542\) 16.2981 0.700065
\(543\) 0 0
\(544\) 10.6167 0.455188
\(545\) −19.2406 −0.824177
\(546\) 0 0
\(547\) −25.9189 −1.10821 −0.554105 0.832447i \(-0.686939\pi\)
−0.554105 + 0.832447i \(0.686939\pi\)
\(548\) −2.39027 −0.102107
\(549\) 0 0
\(550\) 1.74637 0.0744654
\(551\) −1.25039 −0.0532684
\(552\) 0 0
\(553\) 5.41599 0.230311
\(554\) 14.1715 0.602088
\(555\) 0 0
\(556\) −6.22066 −0.263815
\(557\) −37.5358 −1.59044 −0.795222 0.606319i \(-0.792646\pi\)
−0.795222 + 0.606319i \(0.792646\pi\)
\(558\) 0 0
\(559\) 20.3451 0.860505
\(560\) −6.46590 −0.273234
\(561\) 0 0
\(562\) 33.5252 1.41417
\(563\) 39.2104 1.65252 0.826260 0.563289i \(-0.190464\pi\)
0.826260 + 0.563289i \(0.190464\pi\)
\(564\) 0 0
\(565\) −35.2102 −1.48130
\(566\) 4.11826 0.173103
\(567\) 0 0
\(568\) 21.5814 0.905536
\(569\) −35.4013 −1.48410 −0.742050 0.670344i \(-0.766146\pi\)
−0.742050 + 0.670344i \(0.766146\pi\)
\(570\) 0 0
\(571\) −2.89890 −0.121315 −0.0606576 0.998159i \(-0.519320\pi\)
−0.0606576 + 0.998159i \(0.519320\pi\)
\(572\) 2.76857 0.115760
\(573\) 0 0
\(574\) 1.70308 0.0710851
\(575\) −5.04014 −0.210189
\(576\) 0 0
\(577\) −22.5791 −0.939978 −0.469989 0.882672i \(-0.655742\pi\)
−0.469989 + 0.882672i \(0.655742\pi\)
\(578\) −10.5996 −0.440884
\(579\) 0 0
\(580\) 4.40014 0.182706
\(581\) −5.01259 −0.207957
\(582\) 0 0
\(583\) −19.4131 −0.804007
\(584\) −22.7030 −0.939456
\(585\) 0 0
\(586\) −29.7491 −1.22892
\(587\) −14.5897 −0.602181 −0.301091 0.953596i \(-0.597351\pi\)
−0.301091 + 0.953596i \(0.597351\pi\)
\(588\) 0 0
\(589\) −0.152264 −0.00627394
\(590\) 24.0884 0.991705
\(591\) 0 0
\(592\) −33.8904 −1.39289
\(593\) 16.4282 0.674627 0.337314 0.941392i \(-0.390482\pi\)
0.337314 + 0.941392i \(0.390482\pi\)
\(594\) 0 0
\(595\) −10.4960 −0.430295
\(596\) −3.26413 −0.133704
\(597\) 0 0
\(598\) 34.2429 1.40030
\(599\) 22.5507 0.921395 0.460698 0.887557i \(-0.347599\pi\)
0.460698 + 0.887557i \(0.347599\pi\)
\(600\) 0 0
\(601\) −41.7123 −1.70148 −0.850741 0.525586i \(-0.823846\pi\)
−0.850741 + 0.525586i \(0.823846\pi\)
\(602\) 7.47460 0.304642
\(603\) 0 0
\(604\) 8.21292 0.334179
\(605\) −13.6491 −0.554917
\(606\) 0 0
\(607\) 8.02170 0.325591 0.162795 0.986660i \(-0.447949\pi\)
0.162795 + 0.986660i \(0.447949\pi\)
\(608\) −0.473158 −0.0191891
\(609\) 0 0
\(610\) −1.60567 −0.0650116
\(611\) 2.12444 0.0859457
\(612\) 0 0
\(613\) 23.1953 0.936848 0.468424 0.883504i \(-0.344822\pi\)
0.468424 + 0.883504i \(0.344822\pi\)
\(614\) −40.6348 −1.63989
\(615\) 0 0
\(616\) 6.39335 0.257595
\(617\) −18.3473 −0.738635 −0.369317 0.929303i \(-0.620408\pi\)
−0.369317 + 0.929303i \(0.620408\pi\)
\(618\) 0 0
\(619\) −28.2358 −1.13489 −0.567446 0.823411i \(-0.692069\pi\)
−0.567446 + 0.823411i \(0.692069\pi\)
\(620\) 0.535819 0.0215190
\(621\) 0 0
\(622\) −35.0554 −1.40559
\(623\) −8.62166 −0.345419
\(624\) 0 0
\(625\) −21.3296 −0.853184
\(626\) 26.3990 1.05512
\(627\) 0 0
\(628\) −3.75457 −0.149824
\(629\) −55.0139 −2.19355
\(630\) 0 0
\(631\) 36.8484 1.46691 0.733455 0.679738i \(-0.237907\pi\)
0.733455 + 0.679738i \(0.237907\pi\)
\(632\) 16.4034 0.652492
\(633\) 0 0
\(634\) 5.06290 0.201073
\(635\) −2.08575 −0.0827703
\(636\) 0 0
\(637\) −3.46613 −0.137333
\(638\) 14.9869 0.593337
\(639\) 0 0
\(640\) −14.8026 −0.585125
\(641\) −36.0974 −1.42576 −0.712881 0.701285i \(-0.752610\pi\)
−0.712881 + 0.701285i \(0.752610\pi\)
\(642\) 0 0
\(643\) 1.75159 0.0690760 0.0345380 0.999403i \(-0.489004\pi\)
0.0345380 + 0.999403i \(0.489004\pi\)
\(644\) −2.93556 −0.115677
\(645\) 0 0
\(646\) 1.43720 0.0565457
\(647\) −5.69840 −0.224027 −0.112014 0.993707i \(-0.535730\pi\)
−0.112014 + 0.993707i \(0.535730\pi\)
\(648\) 0 0
\(649\) −19.1446 −0.751491
\(650\) −2.86754 −0.112474
\(651\) 0 0
\(652\) 3.81648 0.149465
\(653\) −17.8696 −0.699290 −0.349645 0.936882i \(-0.613698\pi\)
−0.349645 + 0.936882i \(0.613698\pi\)
\(654\) 0 0
\(655\) −3.24364 −0.126739
\(656\) 4.14600 0.161874
\(657\) 0 0
\(658\) 0.780501 0.0304271
\(659\) −32.0714 −1.24932 −0.624662 0.780895i \(-0.714763\pi\)
−0.624662 + 0.780895i \(0.714763\pi\)
\(660\) 0 0
\(661\) −5.79459 −0.225383 −0.112692 0.993630i \(-0.535947\pi\)
−0.112692 + 0.993630i \(0.535947\pi\)
\(662\) 8.21510 0.319289
\(663\) 0 0
\(664\) −15.1816 −0.589162
\(665\) 0.467779 0.0181397
\(666\) 0 0
\(667\) −43.2532 −1.67477
\(668\) −0.955728 −0.0369782
\(669\) 0 0
\(670\) 4.40039 0.170002
\(671\) 1.27613 0.0492643
\(672\) 0 0
\(673\) −20.3555 −0.784648 −0.392324 0.919827i \(-0.628329\pi\)
−0.392324 + 0.919827i \(0.628329\pi\)
\(674\) 29.9032 1.15183
\(675\) 0 0
\(676\) 0.373073 0.0143490
\(677\) −42.8044 −1.64511 −0.822553 0.568689i \(-0.807451\pi\)
−0.822553 + 0.568689i \(0.807451\pi\)
\(678\) 0 0
\(679\) 6.43694 0.247027
\(680\) −31.7893 −1.21906
\(681\) 0 0
\(682\) 1.82500 0.0698830
\(683\) −9.59767 −0.367245 −0.183622 0.982997i \(-0.558782\pi\)
−0.183622 + 0.982997i \(0.558782\pi\)
\(684\) 0 0
\(685\) 13.1756 0.503412
\(686\) −1.27342 −0.0486196
\(687\) 0 0
\(688\) 18.1963 0.693726
\(689\) 31.8762 1.21439
\(690\) 0 0
\(691\) −21.2390 −0.807969 −0.403984 0.914766i \(-0.632375\pi\)
−0.403984 + 0.914766i \(0.632375\pi\)
\(692\) 4.07919 0.155067
\(693\) 0 0
\(694\) 24.6260 0.934791
\(695\) 34.2893 1.30067
\(696\) 0 0
\(697\) 6.73015 0.254923
\(698\) −22.9142 −0.867315
\(699\) 0 0
\(700\) 0.245827 0.00929139
\(701\) −33.2723 −1.25668 −0.628338 0.777940i \(-0.716265\pi\)
−0.628338 + 0.777940i \(0.716265\pi\)
\(702\) 0 0
\(703\) 2.45182 0.0924722
\(704\) 18.7590 0.707008
\(705\) 0 0
\(706\) 41.2363 1.55195
\(707\) −12.0226 −0.452155
\(708\) 0 0
\(709\) 29.3845 1.10356 0.551779 0.833990i \(-0.313949\pi\)
0.551779 + 0.833990i \(0.313949\pi\)
\(710\) −18.9260 −0.710279
\(711\) 0 0
\(712\) −26.1124 −0.978604
\(713\) −5.26709 −0.197254
\(714\) 0 0
\(715\) −15.2608 −0.570722
\(716\) −8.21875 −0.307149
\(717\) 0 0
\(718\) −10.0849 −0.376364
\(719\) 10.3787 0.387059 0.193530 0.981094i \(-0.438006\pi\)
0.193530 + 0.981094i \(0.438006\pi\)
\(720\) 0 0
\(721\) 9.25231 0.344574
\(722\) 24.1310 0.898064
\(723\) 0 0
\(724\) −2.22290 −0.0826135
\(725\) 3.62207 0.134520
\(726\) 0 0
\(727\) 50.7802 1.88333 0.941666 0.336549i \(-0.109260\pi\)
0.941666 + 0.336549i \(0.109260\pi\)
\(728\) −10.4979 −0.389077
\(729\) 0 0
\(730\) 19.9095 0.736885
\(731\) 29.5378 1.09249
\(732\) 0 0
\(733\) 37.5120 1.38554 0.692768 0.721161i \(-0.256391\pi\)
0.692768 + 0.721161i \(0.256391\pi\)
\(734\) −34.9181 −1.28885
\(735\) 0 0
\(736\) −16.3674 −0.603309
\(737\) −3.49727 −0.128824
\(738\) 0 0
\(739\) −27.5500 −1.01344 −0.506722 0.862109i \(-0.669143\pi\)
−0.506722 + 0.862109i \(0.669143\pi\)
\(740\) −8.62798 −0.317171
\(741\) 0 0
\(742\) 11.7110 0.429926
\(743\) 43.0316 1.57868 0.789338 0.613959i \(-0.210424\pi\)
0.789338 + 0.613959i \(0.210424\pi\)
\(744\) 0 0
\(745\) 17.9924 0.659191
\(746\) −4.83276 −0.176940
\(747\) 0 0
\(748\) 4.01952 0.146968
\(749\) −10.2336 −0.373929
\(750\) 0 0
\(751\) 5.07746 0.185279 0.0926396 0.995700i \(-0.470470\pi\)
0.0926396 + 0.995700i \(0.470470\pi\)
\(752\) 1.90006 0.0692881
\(753\) 0 0
\(754\) −24.6085 −0.896187
\(755\) −45.2710 −1.64758
\(756\) 0 0
\(757\) 37.1949 1.35187 0.675936 0.736961i \(-0.263740\pi\)
0.675936 + 0.736961i \(0.263740\pi\)
\(758\) 45.8321 1.66470
\(759\) 0 0
\(760\) 1.41676 0.0513914
\(761\) −33.4225 −1.21156 −0.605781 0.795631i \(-0.707139\pi\)
−0.605781 + 0.795631i \(0.707139\pi\)
\(762\) 0 0
\(763\) −9.22482 −0.333961
\(764\) 3.37697 0.122174
\(765\) 0 0
\(766\) −1.71900 −0.0621100
\(767\) 31.4354 1.13507
\(768\) 0 0
\(769\) 46.3925 1.67296 0.836479 0.547999i \(-0.184610\pi\)
0.836479 + 0.547999i \(0.184610\pi\)
\(770\) −5.60669 −0.202051
\(771\) 0 0
\(772\) 8.82499 0.317618
\(773\) −22.3827 −0.805048 −0.402524 0.915409i \(-0.631867\pi\)
−0.402524 + 0.915409i \(0.631867\pi\)
\(774\) 0 0
\(775\) 0.441072 0.0158438
\(776\) 19.4956 0.699850
\(777\) 0 0
\(778\) −4.56830 −0.163781
\(779\) −0.299944 −0.0107466
\(780\) 0 0
\(781\) 15.0416 0.538232
\(782\) 49.7152 1.77781
\(783\) 0 0
\(784\) −3.10004 −0.110716
\(785\) 20.6958 0.738666
\(786\) 0 0
\(787\) −35.3014 −1.25836 −0.629179 0.777260i \(-0.716609\pi\)
−0.629179 + 0.777260i \(0.716609\pi\)
\(788\) 7.21434 0.257000
\(789\) 0 0
\(790\) −14.3851 −0.511798
\(791\) −16.8813 −0.600232
\(792\) 0 0
\(793\) −2.09540 −0.0744097
\(794\) −10.6714 −0.378713
\(795\) 0 0
\(796\) −2.70205 −0.0957716
\(797\) 17.4912 0.619570 0.309785 0.950807i \(-0.399743\pi\)
0.309785 + 0.950807i \(0.399743\pi\)
\(798\) 0 0
\(799\) 3.08435 0.109116
\(800\) 1.37062 0.0484588
\(801\) 0 0
\(802\) 12.5969 0.444810
\(803\) −15.8234 −0.558394
\(804\) 0 0
\(805\) 16.1813 0.570316
\(806\) −2.99665 −0.105553
\(807\) 0 0
\(808\) −36.4128 −1.28100
\(809\) 52.4987 1.84575 0.922877 0.385094i \(-0.125831\pi\)
0.922877 + 0.385094i \(0.125831\pi\)
\(810\) 0 0
\(811\) 5.96928 0.209610 0.104805 0.994493i \(-0.466578\pi\)
0.104805 + 0.994493i \(0.466578\pi\)
\(812\) 2.10962 0.0740333
\(813\) 0 0
\(814\) −29.3869 −1.03001
\(815\) −21.0371 −0.736896
\(816\) 0 0
\(817\) −1.31642 −0.0460557
\(818\) 5.81521 0.203324
\(819\) 0 0
\(820\) 1.05551 0.0368599
\(821\) −20.6990 −0.722399 −0.361199 0.932489i \(-0.617633\pi\)
−0.361199 + 0.932489i \(0.617633\pi\)
\(822\) 0 0
\(823\) −38.2152 −1.33210 −0.666050 0.745907i \(-0.732016\pi\)
−0.666050 + 0.745907i \(0.732016\pi\)
\(824\) 28.0225 0.976209
\(825\) 0 0
\(826\) 11.5491 0.401844
\(827\) 27.2185 0.946479 0.473239 0.880934i \(-0.343085\pi\)
0.473239 + 0.880934i \(0.343085\pi\)
\(828\) 0 0
\(829\) 11.3121 0.392886 0.196443 0.980515i \(-0.437061\pi\)
0.196443 + 0.980515i \(0.437061\pi\)
\(830\) 13.3136 0.462123
\(831\) 0 0
\(832\) −30.8023 −1.06788
\(833\) −5.03226 −0.174358
\(834\) 0 0
\(835\) 5.26813 0.182311
\(836\) −0.179139 −0.00619565
\(837\) 0 0
\(838\) −0.567483 −0.0196034
\(839\) −18.7066 −0.645824 −0.322912 0.946429i \(-0.604662\pi\)
−0.322912 + 0.946429i \(0.604662\pi\)
\(840\) 0 0
\(841\) 2.08370 0.0718519
\(842\) −9.83800 −0.339040
\(843\) 0 0
\(844\) −4.10948 −0.141454
\(845\) −2.05644 −0.0707438
\(846\) 0 0
\(847\) −6.54401 −0.224855
\(848\) 28.5095 0.979021
\(849\) 0 0
\(850\) −4.16320 −0.142797
\(851\) 84.8128 2.90734
\(852\) 0 0
\(853\) 14.1464 0.484365 0.242182 0.970231i \(-0.422137\pi\)
0.242182 + 0.970231i \(0.422137\pi\)
\(854\) −0.769830 −0.0263430
\(855\) 0 0
\(856\) −30.9946 −1.05938
\(857\) 7.84138 0.267857 0.133928 0.990991i \(-0.457241\pi\)
0.133928 + 0.990991i \(0.457241\pi\)
\(858\) 0 0
\(859\) −21.2444 −0.724851 −0.362426 0.932013i \(-0.618051\pi\)
−0.362426 + 0.932013i \(0.618051\pi\)
\(860\) 4.63249 0.157967
\(861\) 0 0
\(862\) 42.8681 1.46009
\(863\) −31.6439 −1.07717 −0.538586 0.842571i \(-0.681041\pi\)
−0.538586 + 0.842571i \(0.681041\pi\)
\(864\) 0 0
\(865\) −22.4852 −0.764518
\(866\) 28.3194 0.962333
\(867\) 0 0
\(868\) 0.256896 0.00871962
\(869\) 11.4327 0.387828
\(870\) 0 0
\(871\) 5.74251 0.194578
\(872\) −27.9392 −0.946141
\(873\) 0 0
\(874\) −2.21567 −0.0749461
\(875\) −11.7838 −0.398364
\(876\) 0 0
\(877\) 4.23316 0.142944 0.0714718 0.997443i \(-0.477230\pi\)
0.0714718 + 0.997443i \(0.477230\pi\)
\(878\) 3.72163 0.125599
\(879\) 0 0
\(880\) −13.6490 −0.460108
\(881\) −41.2980 −1.39136 −0.695682 0.718350i \(-0.744898\pi\)
−0.695682 + 0.718350i \(0.744898\pi\)
\(882\) 0 0
\(883\) 23.9434 0.805761 0.402881 0.915253i \(-0.368009\pi\)
0.402881 + 0.915253i \(0.368009\pi\)
\(884\) −6.60004 −0.221984
\(885\) 0 0
\(886\) 2.37535 0.0798015
\(887\) 0.000719418 0 2.41557e−5 0 1.20778e−5 1.00000i \(-0.499996\pi\)
1.20778e−5 1.00000i \(0.499996\pi\)
\(888\) 0 0
\(889\) −1.00000 −0.0335389
\(890\) 22.8995 0.767592
\(891\) 0 0
\(892\) −9.91322 −0.331919
\(893\) −0.137461 −0.00459996
\(894\) 0 0
\(895\) 45.3031 1.51432
\(896\) −7.09705 −0.237096
\(897\) 0 0
\(898\) 11.2766 0.376304
\(899\) 3.78517 0.126242
\(900\) 0 0
\(901\) 46.2792 1.54178
\(902\) 3.59506 0.119702
\(903\) 0 0
\(904\) −51.1285 −1.70051
\(905\) 12.2530 0.407304
\(906\) 0 0
\(907\) 24.5697 0.815822 0.407911 0.913022i \(-0.366257\pi\)
0.407911 + 0.913022i \(0.366257\pi\)
\(908\) −0.596873 −0.0198079
\(909\) 0 0
\(910\) 9.20618 0.305182
\(911\) −12.3580 −0.409440 −0.204720 0.978821i \(-0.565628\pi\)
−0.204720 + 0.978821i \(0.565628\pi\)
\(912\) 0 0
\(913\) −10.5812 −0.350186
\(914\) −41.9326 −1.38701
\(915\) 0 0
\(916\) 2.29806 0.0759300
\(917\) −1.55514 −0.0513554
\(918\) 0 0
\(919\) −18.0428 −0.595178 −0.297589 0.954694i \(-0.596183\pi\)
−0.297589 + 0.954694i \(0.596183\pi\)
\(920\) 49.0083 1.61576
\(921\) 0 0
\(922\) 31.0859 1.02376
\(923\) −24.6984 −0.812957
\(924\) 0 0
\(925\) −7.10232 −0.233523
\(926\) 38.1036 1.25216
\(927\) 0 0
\(928\) 11.7623 0.386117
\(929\) 36.3068 1.19119 0.595595 0.803285i \(-0.296917\pi\)
0.595595 + 0.803285i \(0.296917\pi\)
\(930\) 0 0
\(931\) 0.224274 0.00735029
\(932\) −0.796234 −0.0260815
\(933\) 0 0
\(934\) 18.9854 0.621223
\(935\) −22.1563 −0.724587
\(936\) 0 0
\(937\) −13.0953 −0.427804 −0.213902 0.976855i \(-0.568617\pi\)
−0.213902 + 0.976855i \(0.568617\pi\)
\(938\) 2.10975 0.0688857
\(939\) 0 0
\(940\) 0.483727 0.0157774
\(941\) −7.84886 −0.255866 −0.127933 0.991783i \(-0.540834\pi\)
−0.127933 + 0.991783i \(0.540834\pi\)
\(942\) 0 0
\(943\) −10.3756 −0.337876
\(944\) 28.1152 0.915073
\(945\) 0 0
\(946\) 15.7783 0.512996
\(947\) −13.3476 −0.433738 −0.216869 0.976201i \(-0.569584\pi\)
−0.216869 + 0.976201i \(0.569584\pi\)
\(948\) 0 0
\(949\) 25.9819 0.843409
\(950\) 0.185543 0.00601980
\(951\) 0 0
\(952\) −15.2412 −0.493971
\(953\) 19.4366 0.629612 0.314806 0.949156i \(-0.398061\pi\)
0.314806 + 0.949156i \(0.398061\pi\)
\(954\) 0 0
\(955\) −18.6144 −0.602348
\(956\) 8.58932 0.277799
\(957\) 0 0
\(958\) −13.0571 −0.421857
\(959\) 6.31696 0.203985
\(960\) 0 0
\(961\) −30.5391 −0.985131
\(962\) 48.2533 1.55575
\(963\) 0 0
\(964\) −8.63642 −0.278160
\(965\) −48.6448 −1.56593
\(966\) 0 0
\(967\) −6.70164 −0.215510 −0.107755 0.994177i \(-0.534366\pi\)
−0.107755 + 0.994177i \(0.534366\pi\)
\(968\) −19.8199 −0.637034
\(969\) 0 0
\(970\) −17.0968 −0.548944
\(971\) −40.7514 −1.30778 −0.653888 0.756591i \(-0.726863\pi\)
−0.653888 + 0.756591i \(0.726863\pi\)
\(972\) 0 0
\(973\) 16.4399 0.527037
\(974\) −17.2425 −0.552486
\(975\) 0 0
\(976\) −1.87408 −0.0599880
\(977\) 47.8398 1.53053 0.765266 0.643715i \(-0.222608\pi\)
0.765266 + 0.643715i \(0.222608\pi\)
\(978\) 0 0
\(979\) −18.1996 −0.581663
\(980\) −0.789224 −0.0252108
\(981\) 0 0
\(982\) 11.6244 0.370950
\(983\) −44.1662 −1.40868 −0.704342 0.709861i \(-0.748758\pi\)
−0.704342 + 0.709861i \(0.748758\pi\)
\(984\) 0 0
\(985\) −39.7667 −1.26707
\(986\) −35.7275 −1.13780
\(987\) 0 0
\(988\) 0.294146 0.00935803
\(989\) −45.5372 −1.44800
\(990\) 0 0
\(991\) −20.3201 −0.645490 −0.322745 0.946486i \(-0.604606\pi\)
−0.322745 + 0.946486i \(0.604606\pi\)
\(992\) 1.43234 0.0454767
\(993\) 0 0
\(994\) −9.07396 −0.287809
\(995\) 14.8942 0.472177
\(996\) 0 0
\(997\) 13.1177 0.415443 0.207721 0.978188i \(-0.433395\pi\)
0.207721 + 0.978188i \(0.433395\pi\)
\(998\) −38.6805 −1.22441
\(999\) 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 \(a_p\))