Properties

Label 8048.2.a.p.1.6
Level 8048
Weight 2
Character 8048.1
Self dual Yes
Analytic conductor 64.264
Analytic rank 1
Dimension 10
CM No
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 8048 = 2^{4} \cdot 503 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8048.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(64.2636035467\)
Analytic rank: \(1\)
Dimension: \(10\)
Coefficient field: \(\mathbb{Q}[x]/(x^{10} - \cdots)\)
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.6
Root \(-0.489003\)
Character \(\chi\) = 8048.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(+1.48900 q^{3}\) \(-1.79865 q^{5}\) \(-0.552233 q^{7}\) \(-0.782869 q^{9}\) \(+O(q^{10})\) \(q\)\(+1.48900 q^{3}\) \(-1.79865 q^{5}\) \(-0.552233 q^{7}\) \(-0.782869 q^{9}\) \(-4.33718 q^{11}\) \(+2.54873 q^{13}\) \(-2.67819 q^{15}\) \(+2.52304 q^{17}\) \(+5.11893 q^{19}\) \(-0.822276 q^{21}\) \(+3.78409 q^{23}\) \(-1.76486 q^{25}\) \(-5.63270 q^{27}\) \(+0.907287 q^{29}\) \(-0.380820 q^{31}\) \(-6.45807 q^{33}\) \(+0.993273 q^{35}\) \(-5.43266 q^{37}\) \(+3.79507 q^{39}\) \(+5.72459 q^{41}\) \(+9.21553 q^{43}\) \(+1.40811 q^{45}\) \(+8.81077 q^{47}\) \(-6.69504 q^{49}\) \(+3.75682 q^{51}\) \(-6.46357 q^{53}\) \(+7.80106 q^{55}\) \(+7.62210 q^{57}\) \(-3.40568 q^{59}\) \(-1.06109 q^{61}\) \(+0.432326 q^{63}\) \(-4.58427 q^{65}\) \(+0.253929 q^{67}\) \(+5.63451 q^{69}\) \(-11.7311 q^{71}\) \(-16.1271 q^{73}\) \(-2.62789 q^{75}\) \(+2.39513 q^{77}\) \(-7.76447 q^{79}\) \(-6.03851 q^{81}\) \(+16.3846 q^{83}\) \(-4.53807 q^{85}\) \(+1.35095 q^{87}\) \(-3.09992 q^{89}\) \(-1.40749 q^{91}\) \(-0.567042 q^{93}\) \(-9.20715 q^{95}\) \(-4.28605 q^{97}\) \(+3.39544 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(10q \) \(\mathstrut +\mathstrut 8q^{3} \) \(\mathstrut -\mathstrut q^{5} \) \(\mathstrut +\mathstrut 5q^{7} \) \(\mathstrut -\mathstrut 2q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(10q \) \(\mathstrut +\mathstrut 8q^{3} \) \(\mathstrut -\mathstrut q^{5} \) \(\mathstrut +\mathstrut 5q^{7} \) \(\mathstrut -\mathstrut 2q^{9} \) \(\mathstrut +\mathstrut 3q^{11} \) \(\mathstrut -\mathstrut 18q^{13} \) \(\mathstrut +\mathstrut 2q^{15} \) \(\mathstrut -\mathstrut 11q^{17} \) \(\mathstrut +\mathstrut q^{21} \) \(\mathstrut +\mathstrut 2q^{23} \) \(\mathstrut -\mathstrut 27q^{25} \) \(\mathstrut +\mathstrut 2q^{27} \) \(\mathstrut -\mathstrut 9q^{29} \) \(\mathstrut +\mathstrut 22q^{31} \) \(\mathstrut -\mathstrut 10q^{33} \) \(\mathstrut +\mathstrut 6q^{35} \) \(\mathstrut -\mathstrut 35q^{37} \) \(\mathstrut -\mathstrut 8q^{39} \) \(\mathstrut -\mathstrut 4q^{41} \) \(\mathstrut +\mathstrut 20q^{43} \) \(\mathstrut +\mathstrut 2q^{45} \) \(\mathstrut -\mathstrut 7q^{47} \) \(\mathstrut -\mathstrut 27q^{49} \) \(\mathstrut -\mathstrut 9q^{51} \) \(\mathstrut -\mathstrut 24q^{53} \) \(\mathstrut +\mathstrut 11q^{55} \) \(\mathstrut -\mathstrut 23q^{57} \) \(\mathstrut -\mathstrut 17q^{59} \) \(\mathstrut -\mathstrut 4q^{61} \) \(\mathstrut -\mathstrut 10q^{63} \) \(\mathstrut -\mathstrut 16q^{65} \) \(\mathstrut +\mathstrut 6q^{67} \) \(\mathstrut -\mathstrut 2q^{69} \) \(\mathstrut +\mathstrut q^{71} \) \(\mathstrut -\mathstrut 31q^{73} \) \(\mathstrut -\mathstrut 30q^{75} \) \(\mathstrut +\mathstrut 3q^{77} \) \(\mathstrut +\mathstrut 10q^{79} \) \(\mathstrut -\mathstrut 6q^{81} \) \(\mathstrut -\mathstrut 22q^{83} \) \(\mathstrut -\mathstrut 6q^{85} \) \(\mathstrut -\mathstrut 25q^{87} \) \(\mathstrut +\mathstrut q^{89} \) \(\mathstrut -\mathstrut 10q^{91} \) \(\mathstrut -\mathstrut 6q^{93} \) \(\mathstrut -\mathstrut 39q^{95} \) \(\mathstrut -\mathstrut 57q^{97} \) \(\mathstrut -\mathstrut 35q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) 1.48900 0.859676 0.429838 0.902906i \(-0.358571\pi\)
0.429838 + 0.902906i \(0.358571\pi\)
\(4\) 0 0
\(5\) −1.79865 −0.804380 −0.402190 0.915556i \(-0.631751\pi\)
−0.402190 + 0.915556i \(0.631751\pi\)
\(6\) 0 0
\(7\) −0.552233 −0.208724 −0.104362 0.994539i \(-0.533280\pi\)
−0.104362 + 0.994539i \(0.533280\pi\)
\(8\) 0 0
\(9\) −0.782869 −0.260956
\(10\) 0 0
\(11\) −4.33718 −1.30771 −0.653854 0.756620i \(-0.726849\pi\)
−0.653854 + 0.756620i \(0.726849\pi\)
\(12\) 0 0
\(13\) 2.54873 0.706891 0.353445 0.935455i \(-0.385010\pi\)
0.353445 + 0.935455i \(0.385010\pi\)
\(14\) 0 0
\(15\) −2.67819 −0.691507
\(16\) 0 0
\(17\) 2.52304 0.611928 0.305964 0.952043i \(-0.401021\pi\)
0.305964 + 0.952043i \(0.401021\pi\)
\(18\) 0 0
\(19\) 5.11893 1.17436 0.587181 0.809455i \(-0.300238\pi\)
0.587181 + 0.809455i \(0.300238\pi\)
\(20\) 0 0
\(21\) −0.822276 −0.179435
\(22\) 0 0
\(23\) 3.78409 0.789036 0.394518 0.918888i \(-0.370912\pi\)
0.394518 + 0.918888i \(0.370912\pi\)
\(24\) 0 0
\(25\) −1.76486 −0.352972
\(26\) 0 0
\(27\) −5.63270 −1.08401
\(28\) 0 0
\(29\) 0.907287 0.168479 0.0842395 0.996446i \(-0.473154\pi\)
0.0842395 + 0.996446i \(0.473154\pi\)
\(30\) 0 0
\(31\) −0.380820 −0.0683972 −0.0341986 0.999415i \(-0.510888\pi\)
−0.0341986 + 0.999415i \(0.510888\pi\)
\(32\) 0 0
\(33\) −6.45807 −1.12421
\(34\) 0 0
\(35\) 0.993273 0.167894
\(36\) 0 0
\(37\) −5.43266 −0.893124 −0.446562 0.894753i \(-0.647352\pi\)
−0.446562 + 0.894753i \(0.647352\pi\)
\(38\) 0 0
\(39\) 3.79507 0.607697
\(40\) 0 0
\(41\) 5.72459 0.894031 0.447015 0.894526i \(-0.352487\pi\)
0.447015 + 0.894526i \(0.352487\pi\)
\(42\) 0 0
\(43\) 9.21553 1.40536 0.702678 0.711508i \(-0.251988\pi\)
0.702678 + 0.711508i \(0.251988\pi\)
\(44\) 0 0
\(45\) 1.40811 0.209908
\(46\) 0 0
\(47\) 8.81077 1.28518 0.642592 0.766209i \(-0.277859\pi\)
0.642592 + 0.766209i \(0.277859\pi\)
\(48\) 0 0
\(49\) −6.69504 −0.956434
\(50\) 0 0
\(51\) 3.75682 0.526060
\(52\) 0 0
\(53\) −6.46357 −0.887840 −0.443920 0.896066i \(-0.646413\pi\)
−0.443920 + 0.896066i \(0.646413\pi\)
\(54\) 0 0
\(55\) 7.80106 1.05190
\(56\) 0 0
\(57\) 7.62210 1.00957
\(58\) 0 0
\(59\) −3.40568 −0.443381 −0.221691 0.975117i \(-0.571157\pi\)
−0.221691 + 0.975117i \(0.571157\pi\)
\(60\) 0 0
\(61\) −1.06109 −0.135859 −0.0679294 0.997690i \(-0.521639\pi\)
−0.0679294 + 0.997690i \(0.521639\pi\)
\(62\) 0 0
\(63\) 0.432326 0.0544679
\(64\) 0 0
\(65\) −4.58427 −0.568609
\(66\) 0 0
\(67\) 0.253929 0.0310223 0.0155112 0.999880i \(-0.495062\pi\)
0.0155112 + 0.999880i \(0.495062\pi\)
\(68\) 0 0
\(69\) 5.63451 0.678316
\(70\) 0 0
\(71\) −11.7311 −1.39222 −0.696112 0.717933i \(-0.745088\pi\)
−0.696112 + 0.717933i \(0.745088\pi\)
\(72\) 0 0
\(73\) −16.1271 −1.88753 −0.943765 0.330617i \(-0.892743\pi\)
−0.943765 + 0.330617i \(0.892743\pi\)
\(74\) 0 0
\(75\) −2.62789 −0.303442
\(76\) 0 0
\(77\) 2.39513 0.272951
\(78\) 0 0
\(79\) −7.76447 −0.873571 −0.436785 0.899566i \(-0.643883\pi\)
−0.436785 + 0.899566i \(0.643883\pi\)
\(80\) 0 0
\(81\) −6.03851 −0.670945
\(82\) 0 0
\(83\) 16.3846 1.79844 0.899222 0.437492i \(-0.144133\pi\)
0.899222 + 0.437492i \(0.144133\pi\)
\(84\) 0 0
\(85\) −4.53807 −0.492223
\(86\) 0 0
\(87\) 1.35095 0.144837
\(88\) 0 0
\(89\) −3.09992 −0.328590 −0.164295 0.986411i \(-0.552535\pi\)
−0.164295 + 0.986411i \(0.552535\pi\)
\(90\) 0 0
\(91\) −1.40749 −0.147545
\(92\) 0 0
\(93\) −0.567042 −0.0587995
\(94\) 0 0
\(95\) −9.20715 −0.944634
\(96\) 0 0
\(97\) −4.28605 −0.435183 −0.217591 0.976040i \(-0.569820\pi\)
−0.217591 + 0.976040i \(0.569820\pi\)
\(98\) 0 0
\(99\) 3.39544 0.341255
\(100\) 0 0
\(101\) −3.73446 −0.371592 −0.185796 0.982588i \(-0.559486\pi\)
−0.185796 + 0.982588i \(0.559486\pi\)
\(102\) 0 0
\(103\) −2.83220 −0.279065 −0.139533 0.990217i \(-0.544560\pi\)
−0.139533 + 0.990217i \(0.544560\pi\)
\(104\) 0 0
\(105\) 1.47899 0.144334
\(106\) 0 0
\(107\) −10.0994 −0.976343 −0.488172 0.872748i \(-0.662336\pi\)
−0.488172 + 0.872748i \(0.662336\pi\)
\(108\) 0 0
\(109\) −6.86764 −0.657800 −0.328900 0.944365i \(-0.606678\pi\)
−0.328900 + 0.944365i \(0.606678\pi\)
\(110\) 0 0
\(111\) −8.08925 −0.767798
\(112\) 0 0
\(113\) 2.80558 0.263927 0.131963 0.991255i \(-0.457872\pi\)
0.131963 + 0.991255i \(0.457872\pi\)
\(114\) 0 0
\(115\) −6.80624 −0.634685
\(116\) 0 0
\(117\) −1.99532 −0.184468
\(118\) 0 0
\(119\) −1.39331 −0.127724
\(120\) 0 0
\(121\) 7.81112 0.710102
\(122\) 0 0
\(123\) 8.52393 0.768577
\(124\) 0 0
\(125\) 12.1676 1.08830
\(126\) 0 0
\(127\) 14.9147 1.32347 0.661734 0.749739i \(-0.269821\pi\)
0.661734 + 0.749739i \(0.269821\pi\)
\(128\) 0 0
\(129\) 13.7220 1.20815
\(130\) 0 0
\(131\) −13.5207 −1.18131 −0.590654 0.806925i \(-0.701130\pi\)
−0.590654 + 0.806925i \(0.701130\pi\)
\(132\) 0 0
\(133\) −2.82684 −0.245118
\(134\) 0 0
\(135\) 10.1313 0.871960
\(136\) 0 0
\(137\) −12.4479 −1.06350 −0.531750 0.846901i \(-0.678465\pi\)
−0.531750 + 0.846901i \(0.678465\pi\)
\(138\) 0 0
\(139\) −2.15443 −0.182736 −0.0913681 0.995817i \(-0.529124\pi\)
−0.0913681 + 0.995817i \(0.529124\pi\)
\(140\) 0 0
\(141\) 13.1193 1.10484
\(142\) 0 0
\(143\) −11.0543 −0.924407
\(144\) 0 0
\(145\) −1.63189 −0.135521
\(146\) 0 0
\(147\) −9.96894 −0.822224
\(148\) 0 0
\(149\) −8.59253 −0.703927 −0.351964 0.936014i \(-0.614486\pi\)
−0.351964 + 0.936014i \(0.614486\pi\)
\(150\) 0 0
\(151\) −0.527862 −0.0429568 −0.0214784 0.999769i \(-0.506837\pi\)
−0.0214784 + 0.999769i \(0.506837\pi\)
\(152\) 0 0
\(153\) −1.97521 −0.159687
\(154\) 0 0
\(155\) 0.684961 0.0550174
\(156\) 0 0
\(157\) 11.1711 0.891554 0.445777 0.895144i \(-0.352927\pi\)
0.445777 + 0.895144i \(0.352927\pi\)
\(158\) 0 0
\(159\) −9.62428 −0.763255
\(160\) 0 0
\(161\) −2.08970 −0.164691
\(162\) 0 0
\(163\) −20.0109 −1.56738 −0.783689 0.621153i \(-0.786664\pi\)
−0.783689 + 0.621153i \(0.786664\pi\)
\(164\) 0 0
\(165\) 11.6158 0.904289
\(166\) 0 0
\(167\) 11.9520 0.924877 0.462439 0.886651i \(-0.346975\pi\)
0.462439 + 0.886651i \(0.346975\pi\)
\(168\) 0 0
\(169\) −6.50397 −0.500305
\(170\) 0 0
\(171\) −4.00745 −0.306457
\(172\) 0 0
\(173\) 3.14561 0.239156 0.119578 0.992825i \(-0.461846\pi\)
0.119578 + 0.992825i \(0.461846\pi\)
\(174\) 0 0
\(175\) 0.974615 0.0736739
\(176\) 0 0
\(177\) −5.07106 −0.381164
\(178\) 0 0
\(179\) 6.02096 0.450028 0.225014 0.974356i \(-0.427757\pi\)
0.225014 + 0.974356i \(0.427757\pi\)
\(180\) 0 0
\(181\) −23.0475 −1.71311 −0.856553 0.516059i \(-0.827398\pi\)
−0.856553 + 0.516059i \(0.827398\pi\)
\(182\) 0 0
\(183\) −1.57997 −0.116795
\(184\) 0 0
\(185\) 9.77145 0.718412
\(186\) 0 0
\(187\) −10.9429 −0.800224
\(188\) 0 0
\(189\) 3.11056 0.226260
\(190\) 0 0
\(191\) 17.9774 1.30080 0.650398 0.759594i \(-0.274602\pi\)
0.650398 + 0.759594i \(0.274602\pi\)
\(192\) 0 0
\(193\) −10.4429 −0.751697 −0.375848 0.926681i \(-0.622649\pi\)
−0.375848 + 0.926681i \(0.622649\pi\)
\(194\) 0 0
\(195\) −6.82600 −0.488820
\(196\) 0 0
\(197\) −4.36026 −0.310656 −0.155328 0.987863i \(-0.549643\pi\)
−0.155328 + 0.987863i \(0.549643\pi\)
\(198\) 0 0
\(199\) −14.0205 −0.993888 −0.496944 0.867783i \(-0.665545\pi\)
−0.496944 + 0.867783i \(0.665545\pi\)
\(200\) 0 0
\(201\) 0.378101 0.0266692
\(202\) 0 0
\(203\) −0.501034 −0.0351657
\(204\) 0 0
\(205\) −10.2965 −0.719141
\(206\) 0 0
\(207\) −2.96244 −0.205904
\(208\) 0 0
\(209\) −22.2017 −1.53572
\(210\) 0 0
\(211\) 11.0580 0.761265 0.380633 0.924726i \(-0.375706\pi\)
0.380633 + 0.924726i \(0.375706\pi\)
\(212\) 0 0
\(213\) −17.4676 −1.19686
\(214\) 0 0
\(215\) −16.5755 −1.13044
\(216\) 0 0
\(217\) 0.210301 0.0142762
\(218\) 0 0
\(219\) −24.0133 −1.62267
\(220\) 0 0
\(221\) 6.43056 0.432566
\(222\) 0 0
\(223\) 15.5502 1.04132 0.520658 0.853765i \(-0.325687\pi\)
0.520658 + 0.853765i \(0.325687\pi\)
\(224\) 0 0
\(225\) 1.38166 0.0921104
\(226\) 0 0
\(227\) −1.27577 −0.0846759 −0.0423379 0.999103i \(-0.513481\pi\)
−0.0423379 + 0.999103i \(0.513481\pi\)
\(228\) 0 0
\(229\) −15.5232 −1.02580 −0.512901 0.858448i \(-0.671429\pi\)
−0.512901 + 0.858448i \(0.671429\pi\)
\(230\) 0 0
\(231\) 3.56636 0.234649
\(232\) 0 0
\(233\) −27.8010 −1.82130 −0.910651 0.413177i \(-0.864419\pi\)
−0.910651 + 0.413177i \(0.864419\pi\)
\(234\) 0 0
\(235\) −15.8475 −1.03378
\(236\) 0 0
\(237\) −11.5613 −0.750988
\(238\) 0 0
\(239\) −1.20369 −0.0778601 −0.0389301 0.999242i \(-0.512395\pi\)
−0.0389301 + 0.999242i \(0.512395\pi\)
\(240\) 0 0
\(241\) −25.6025 −1.64920 −0.824602 0.565713i \(-0.808601\pi\)
−0.824602 + 0.565713i \(0.808601\pi\)
\(242\) 0 0
\(243\) 7.90676 0.507219
\(244\) 0 0
\(245\) 12.0420 0.769337
\(246\) 0 0
\(247\) 13.0468 0.830146
\(248\) 0 0
\(249\) 24.3967 1.54608
\(250\) 0 0
\(251\) −13.2638 −0.837205 −0.418603 0.908170i \(-0.637480\pi\)
−0.418603 + 0.908170i \(0.637480\pi\)
\(252\) 0 0
\(253\) −16.4123 −1.03183
\(254\) 0 0
\(255\) −6.75720 −0.423152
\(256\) 0 0
\(257\) −16.1006 −1.00433 −0.502163 0.864773i \(-0.667462\pi\)
−0.502163 + 0.864773i \(0.667462\pi\)
\(258\) 0 0
\(259\) 3.00009 0.186417
\(260\) 0 0
\(261\) −0.710288 −0.0439657
\(262\) 0 0
\(263\) −6.77336 −0.417663 −0.208832 0.977952i \(-0.566966\pi\)
−0.208832 + 0.977952i \(0.566966\pi\)
\(264\) 0 0
\(265\) 11.6257 0.714161
\(266\) 0 0
\(267\) −4.61579 −0.282481
\(268\) 0 0
\(269\) 23.4853 1.43192 0.715962 0.698139i \(-0.245988\pi\)
0.715962 + 0.698139i \(0.245988\pi\)
\(270\) 0 0
\(271\) −17.5886 −1.06843 −0.534216 0.845348i \(-0.679393\pi\)
−0.534216 + 0.845348i \(0.679393\pi\)
\(272\) 0 0
\(273\) −2.09576 −0.126841
\(274\) 0 0
\(275\) 7.65452 0.461585
\(276\) 0 0
\(277\) −11.3448 −0.681645 −0.340823 0.940128i \(-0.610706\pi\)
−0.340823 + 0.940128i \(0.610706\pi\)
\(278\) 0 0
\(279\) 0.298132 0.0178487
\(280\) 0 0
\(281\) −9.36752 −0.558820 −0.279410 0.960172i \(-0.590139\pi\)
−0.279410 + 0.960172i \(0.590139\pi\)
\(282\) 0 0
\(283\) −26.8789 −1.59778 −0.798892 0.601474i \(-0.794580\pi\)
−0.798892 + 0.601474i \(0.794580\pi\)
\(284\) 0 0
\(285\) −13.7095 −0.812080
\(286\) 0 0
\(287\) −3.16131 −0.186606
\(288\) 0 0
\(289\) −10.6342 −0.625544
\(290\) 0 0
\(291\) −6.38195 −0.374117
\(292\) 0 0
\(293\) 17.2365 1.00697 0.503485 0.864004i \(-0.332051\pi\)
0.503485 + 0.864004i \(0.332051\pi\)
\(294\) 0 0
\(295\) 6.12561 0.356647
\(296\) 0 0
\(297\) 24.4301 1.41758
\(298\) 0 0
\(299\) 9.64462 0.557763
\(300\) 0 0
\(301\) −5.08912 −0.293332
\(302\) 0 0
\(303\) −5.56062 −0.319449
\(304\) 0 0
\(305\) 1.90853 0.109282
\(306\) 0 0
\(307\) −29.0001 −1.65512 −0.827561 0.561376i \(-0.810272\pi\)
−0.827561 + 0.561376i \(0.810272\pi\)
\(308\) 0 0
\(309\) −4.21716 −0.239906
\(310\) 0 0
\(311\) −27.2312 −1.54414 −0.772071 0.635536i \(-0.780779\pi\)
−0.772071 + 0.635536i \(0.780779\pi\)
\(312\) 0 0
\(313\) 5.53059 0.312607 0.156304 0.987709i \(-0.450042\pi\)
0.156304 + 0.987709i \(0.450042\pi\)
\(314\) 0 0
\(315\) −0.777603 −0.0438129
\(316\) 0 0
\(317\) 31.2030 1.75253 0.876267 0.481826i \(-0.160026\pi\)
0.876267 + 0.481826i \(0.160026\pi\)
\(318\) 0 0
\(319\) −3.93507 −0.220322
\(320\) 0 0
\(321\) −15.0380 −0.839339
\(322\) 0 0
\(323\) 12.9153 0.718626
\(324\) 0 0
\(325\) −4.49816 −0.249513
\(326\) 0 0
\(327\) −10.2259 −0.565495
\(328\) 0 0
\(329\) −4.86560 −0.268249
\(330\) 0 0
\(331\) −16.8025 −0.923551 −0.461775 0.886997i \(-0.652787\pi\)
−0.461775 + 0.886997i \(0.652787\pi\)
\(332\) 0 0
\(333\) 4.25307 0.233067
\(334\) 0 0
\(335\) −0.456729 −0.0249538
\(336\) 0 0
\(337\) 7.57943 0.412878 0.206439 0.978459i \(-0.433813\pi\)
0.206439 + 0.978459i \(0.433813\pi\)
\(338\) 0 0
\(339\) 4.17752 0.226892
\(340\) 0 0
\(341\) 1.65168 0.0894437
\(342\) 0 0
\(343\) 7.56285 0.408355
\(344\) 0 0
\(345\) −10.1345 −0.545624
\(346\) 0 0
\(347\) 28.0855 1.50771 0.753853 0.657043i \(-0.228193\pi\)
0.753853 + 0.657043i \(0.228193\pi\)
\(348\) 0 0
\(349\) 11.6230 0.622164 0.311082 0.950383i \(-0.399309\pi\)
0.311082 + 0.950383i \(0.399309\pi\)
\(350\) 0 0
\(351\) −14.3563 −0.766280
\(352\) 0 0
\(353\) −6.16556 −0.328160 −0.164080 0.986447i \(-0.552465\pi\)
−0.164080 + 0.986447i \(0.552465\pi\)
\(354\) 0 0
\(355\) 21.1001 1.11988
\(356\) 0 0
\(357\) −2.07464 −0.109802
\(358\) 0 0
\(359\) 10.3896 0.548344 0.274172 0.961681i \(-0.411596\pi\)
0.274172 + 0.961681i \(0.411596\pi\)
\(360\) 0 0
\(361\) 7.20342 0.379127
\(362\) 0 0
\(363\) 11.6308 0.610458
\(364\) 0 0
\(365\) 29.0069 1.51829
\(366\) 0 0
\(367\) −0.571294 −0.0298213 −0.0149107 0.999889i \(-0.504746\pi\)
−0.0149107 + 0.999889i \(0.504746\pi\)
\(368\) 0 0
\(369\) −4.48161 −0.233303
\(370\) 0 0
\(371\) 3.56940 0.185314
\(372\) 0 0
\(373\) 2.95332 0.152917 0.0764586 0.997073i \(-0.475639\pi\)
0.0764586 + 0.997073i \(0.475639\pi\)
\(374\) 0 0
\(375\) 18.1176 0.935590
\(376\) 0 0
\(377\) 2.31243 0.119096
\(378\) 0 0
\(379\) 26.2705 1.34942 0.674711 0.738082i \(-0.264268\pi\)
0.674711 + 0.738082i \(0.264268\pi\)
\(380\) 0 0
\(381\) 22.2081 1.13775
\(382\) 0 0
\(383\) −3.44503 −0.176033 −0.0880164 0.996119i \(-0.528053\pi\)
−0.0880164 + 0.996119i \(0.528053\pi\)
\(384\) 0 0
\(385\) −4.30800 −0.219556
\(386\) 0 0
\(387\) −7.21456 −0.366736
\(388\) 0 0
\(389\) −7.95150 −0.403157 −0.201578 0.979472i \(-0.564607\pi\)
−0.201578 + 0.979472i \(0.564607\pi\)
\(390\) 0 0
\(391\) 9.54742 0.482834
\(392\) 0 0
\(393\) −20.1323 −1.01554
\(394\) 0 0
\(395\) 13.9656 0.702683
\(396\) 0 0
\(397\) 21.7255 1.09037 0.545186 0.838315i \(-0.316459\pi\)
0.545186 + 0.838315i \(0.316459\pi\)
\(398\) 0 0
\(399\) −4.20917 −0.210722
\(400\) 0 0
\(401\) 14.1072 0.704481 0.352241 0.935909i \(-0.385420\pi\)
0.352241 + 0.935909i \(0.385420\pi\)
\(402\) 0 0
\(403\) −0.970607 −0.0483494
\(404\) 0 0
\(405\) 10.8612 0.539695
\(406\) 0 0
\(407\) 23.5624 1.16795
\(408\) 0 0
\(409\) −10.2905 −0.508834 −0.254417 0.967095i \(-0.581884\pi\)
−0.254417 + 0.967095i \(0.581884\pi\)
\(410\) 0 0
\(411\) −18.5350 −0.914266
\(412\) 0 0
\(413\) 1.88072 0.0925444
\(414\) 0 0
\(415\) −29.4702 −1.44663
\(416\) 0 0
\(417\) −3.20795 −0.157094
\(418\) 0 0
\(419\) −19.0965 −0.932925 −0.466463 0.884541i \(-0.654472\pi\)
−0.466463 + 0.884541i \(0.654472\pi\)
\(420\) 0 0
\(421\) 26.3025 1.28191 0.640953 0.767580i \(-0.278539\pi\)
0.640953 + 0.767580i \(0.278539\pi\)
\(422\) 0 0
\(423\) −6.89768 −0.335377
\(424\) 0 0
\(425\) −4.45283 −0.215994
\(426\) 0 0
\(427\) 0.585969 0.0283570
\(428\) 0 0
\(429\) −16.4599 −0.794691
\(430\) 0 0
\(431\) 16.5246 0.795963 0.397982 0.917393i \(-0.369711\pi\)
0.397982 + 0.917393i \(0.369711\pi\)
\(432\) 0 0
\(433\) 4.52467 0.217442 0.108721 0.994072i \(-0.465325\pi\)
0.108721 + 0.994072i \(0.465325\pi\)
\(434\) 0 0
\(435\) −2.42989 −0.116504
\(436\) 0 0
\(437\) 19.3705 0.926615
\(438\) 0 0
\(439\) 9.06783 0.432784 0.216392 0.976307i \(-0.430571\pi\)
0.216392 + 0.976307i \(0.430571\pi\)
\(440\) 0 0
\(441\) 5.24134 0.249588
\(442\) 0 0
\(443\) 12.6542 0.601219 0.300609 0.953747i \(-0.402810\pi\)
0.300609 + 0.953747i \(0.402810\pi\)
\(444\) 0 0
\(445\) 5.57566 0.264312
\(446\) 0 0
\(447\) −12.7943 −0.605150
\(448\) 0 0
\(449\) 34.8336 1.64390 0.821950 0.569560i \(-0.192886\pi\)
0.821950 + 0.569560i \(0.192886\pi\)
\(450\) 0 0
\(451\) −24.8286 −1.16913
\(452\) 0 0
\(453\) −0.785988 −0.0369290
\(454\) 0 0
\(455\) 2.53158 0.118683
\(456\) 0 0
\(457\) −14.3718 −0.672283 −0.336141 0.941812i \(-0.609122\pi\)
−0.336141 + 0.941812i \(0.609122\pi\)
\(458\) 0 0
\(459\) −14.2116 −0.663339
\(460\) 0 0
\(461\) −20.9323 −0.974914 −0.487457 0.873147i \(-0.662075\pi\)
−0.487457 + 0.873147i \(0.662075\pi\)
\(462\) 0 0
\(463\) −19.4204 −0.902541 −0.451271 0.892387i \(-0.649029\pi\)
−0.451271 + 0.892387i \(0.649029\pi\)
\(464\) 0 0
\(465\) 1.01991 0.0472971
\(466\) 0 0
\(467\) −22.0847 −1.02196 −0.510980 0.859593i \(-0.670717\pi\)
−0.510980 + 0.859593i \(0.670717\pi\)
\(468\) 0 0
\(469\) −0.140228 −0.00647512
\(470\) 0 0
\(471\) 16.6339 0.766448
\(472\) 0 0
\(473\) −39.9694 −1.83780
\(474\) 0 0
\(475\) −9.03420 −0.414518
\(476\) 0 0
\(477\) 5.06013 0.231688
\(478\) 0 0
\(479\) −25.4118 −1.16109 −0.580547 0.814227i \(-0.697161\pi\)
−0.580547 + 0.814227i \(0.697161\pi\)
\(480\) 0 0
\(481\) −13.8464 −0.631342
\(482\) 0 0
\(483\) −3.11156 −0.141581
\(484\) 0 0
\(485\) 7.70911 0.350053
\(486\) 0 0
\(487\) 36.7671 1.66608 0.833039 0.553214i \(-0.186599\pi\)
0.833039 + 0.553214i \(0.186599\pi\)
\(488\) 0 0
\(489\) −29.7964 −1.34744
\(490\) 0 0
\(491\) 12.6572 0.571212 0.285606 0.958347i \(-0.407805\pi\)
0.285606 + 0.958347i \(0.407805\pi\)
\(492\) 0 0
\(493\) 2.28913 0.103097
\(494\) 0 0
\(495\) −6.10721 −0.274499
\(496\) 0 0
\(497\) 6.47829 0.290591
\(498\) 0 0
\(499\) −2.39500 −0.107215 −0.0536074 0.998562i \(-0.517072\pi\)
−0.0536074 + 0.998562i \(0.517072\pi\)
\(500\) 0 0
\(501\) 17.7966 0.795095
\(502\) 0 0
\(503\) 1.00000 0.0445878
\(504\) 0 0
\(505\) 6.71697 0.298901
\(506\) 0 0
\(507\) −9.68443 −0.430101
\(508\) 0 0
\(509\) 6.46329 0.286480 0.143240 0.989688i \(-0.454248\pi\)
0.143240 + 0.989688i \(0.454248\pi\)
\(510\) 0 0
\(511\) 8.90589 0.393973
\(512\) 0 0
\(513\) −28.8334 −1.27303
\(514\) 0 0
\(515\) 5.09414 0.224475
\(516\) 0 0
\(517\) −38.2139 −1.68065
\(518\) 0 0
\(519\) 4.68382 0.205597
\(520\) 0 0
\(521\) 34.3036 1.50287 0.751434 0.659808i \(-0.229363\pi\)
0.751434 + 0.659808i \(0.229363\pi\)
\(522\) 0 0
\(523\) −30.3662 −1.32782 −0.663910 0.747812i \(-0.731104\pi\)
−0.663910 + 0.747812i \(0.731104\pi\)
\(524\) 0 0
\(525\) 1.45120 0.0633357
\(526\) 0 0
\(527\) −0.960825 −0.0418542
\(528\) 0 0
\(529\) −8.68070 −0.377422
\(530\) 0 0
\(531\) 2.66620 0.115703
\(532\) 0 0
\(533\) 14.5904 0.631982
\(534\) 0 0
\(535\) 18.1652 0.785351
\(536\) 0 0
\(537\) 8.96523 0.386878
\(538\) 0 0
\(539\) 29.0376 1.25074
\(540\) 0 0
\(541\) 39.1371 1.68263 0.841317 0.540542i \(-0.181781\pi\)
0.841317 + 0.540542i \(0.181781\pi\)
\(542\) 0 0
\(543\) −34.3178 −1.47272
\(544\) 0 0
\(545\) 12.3525 0.529121
\(546\) 0 0
\(547\) −24.0487 −1.02825 −0.514125 0.857715i \(-0.671883\pi\)
−0.514125 + 0.857715i \(0.671883\pi\)
\(548\) 0 0
\(549\) 0.830696 0.0354532
\(550\) 0 0
\(551\) 4.64434 0.197855
\(552\) 0 0
\(553\) 4.28779 0.182335
\(554\) 0 0
\(555\) 14.5497 0.617602
\(556\) 0 0
\(557\) −17.2987 −0.732971 −0.366486 0.930424i \(-0.619439\pi\)
−0.366486 + 0.930424i \(0.619439\pi\)
\(558\) 0 0
\(559\) 23.4879 0.993433
\(560\) 0 0
\(561\) −16.2940 −0.687934
\(562\) 0 0
\(563\) −5.63944 −0.237674 −0.118837 0.992914i \(-0.537917\pi\)
−0.118837 + 0.992914i \(0.537917\pi\)
\(564\) 0 0
\(565\) −5.04626 −0.212298
\(566\) 0 0
\(567\) 3.33466 0.140043
\(568\) 0 0
\(569\) −12.0350 −0.504535 −0.252268 0.967658i \(-0.581176\pi\)
−0.252268 + 0.967658i \(0.581176\pi\)
\(570\) 0 0
\(571\) −29.9404 −1.25297 −0.626484 0.779434i \(-0.715507\pi\)
−0.626484 + 0.779434i \(0.715507\pi\)
\(572\) 0 0
\(573\) 26.7683 1.11826
\(574\) 0 0
\(575\) −6.67839 −0.278508
\(576\) 0 0
\(577\) 17.6080 0.733032 0.366516 0.930412i \(-0.380551\pi\)
0.366516 + 0.930412i \(0.380551\pi\)
\(578\) 0 0
\(579\) −15.5495 −0.646216
\(580\) 0 0
\(581\) −9.04811 −0.375379
\(582\) 0 0
\(583\) 28.0337 1.16104
\(584\) 0 0
\(585\) 3.58889 0.148382
\(586\) 0 0
\(587\) 21.2268 0.876125 0.438062 0.898945i \(-0.355665\pi\)
0.438062 + 0.898945i \(0.355665\pi\)
\(588\) 0 0
\(589\) −1.94939 −0.0803231
\(590\) 0 0
\(591\) −6.49244 −0.267063
\(592\) 0 0
\(593\) 1.78783 0.0734175 0.0367087 0.999326i \(-0.488313\pi\)
0.0367087 + 0.999326i \(0.488313\pi\)
\(594\) 0 0
\(595\) 2.50607 0.102739
\(596\) 0 0
\(597\) −20.8766 −0.854422
\(598\) 0 0
\(599\) 4.15199 0.169646 0.0848228 0.996396i \(-0.472968\pi\)
0.0848228 + 0.996396i \(0.472968\pi\)
\(600\) 0 0
\(601\) −4.87221 −0.198742 −0.0993708 0.995050i \(-0.531683\pi\)
−0.0993708 + 0.995050i \(0.531683\pi\)
\(602\) 0 0
\(603\) −0.198793 −0.00809548
\(604\) 0 0
\(605\) −14.0495 −0.571192
\(606\) 0 0
\(607\) 22.0579 0.895303 0.447652 0.894208i \(-0.352261\pi\)
0.447652 + 0.894208i \(0.352261\pi\)
\(608\) 0 0
\(609\) −0.746041 −0.0302311
\(610\) 0 0
\(611\) 22.4563 0.908484
\(612\) 0 0
\(613\) −19.0369 −0.768895 −0.384447 0.923147i \(-0.625608\pi\)
−0.384447 + 0.923147i \(0.625608\pi\)
\(614\) 0 0
\(615\) −15.3316 −0.618228
\(616\) 0 0
\(617\) −22.0697 −0.888494 −0.444247 0.895904i \(-0.646529\pi\)
−0.444247 + 0.895904i \(0.646529\pi\)
\(618\) 0 0
\(619\) 5.69372 0.228850 0.114425 0.993432i \(-0.463497\pi\)
0.114425 + 0.993432i \(0.463497\pi\)
\(620\) 0 0
\(621\) −21.3146 −0.855327
\(622\) 0 0
\(623\) 1.71187 0.0685848
\(624\) 0 0
\(625\) −13.0609 −0.522438
\(626\) 0 0
\(627\) −33.0584 −1.32023
\(628\) 0 0
\(629\) −13.7069 −0.546528
\(630\) 0 0
\(631\) −37.6327 −1.49813 −0.749067 0.662494i \(-0.769498\pi\)
−0.749067 + 0.662494i \(0.769498\pi\)
\(632\) 0 0
\(633\) 16.4654 0.654442
\(634\) 0 0
\(635\) −26.8263 −1.06457
\(636\) 0 0
\(637\) −17.0639 −0.676095
\(638\) 0 0
\(639\) 9.18391 0.363310
\(640\) 0 0
\(641\) 6.63550 0.262086 0.131043 0.991377i \(-0.458167\pi\)
0.131043 + 0.991377i \(0.458167\pi\)
\(642\) 0 0
\(643\) 29.4970 1.16325 0.581625 0.813457i \(-0.302417\pi\)
0.581625 + 0.813457i \(0.302417\pi\)
\(644\) 0 0
\(645\) −24.6810 −0.971813
\(646\) 0 0
\(647\) 45.6726 1.79558 0.897788 0.440427i \(-0.145173\pi\)
0.897788 + 0.440427i \(0.145173\pi\)
\(648\) 0 0
\(649\) 14.7710 0.579813
\(650\) 0 0
\(651\) 0.313139 0.0122729
\(652\) 0 0
\(653\) −31.6691 −1.23931 −0.619655 0.784875i \(-0.712727\pi\)
−0.619655 + 0.784875i \(0.712727\pi\)
\(654\) 0 0
\(655\) 24.3190 0.950220
\(656\) 0 0
\(657\) 12.6254 0.492563
\(658\) 0 0
\(659\) −9.73186 −0.379099 −0.189550 0.981871i \(-0.560703\pi\)
−0.189550 + 0.981871i \(0.560703\pi\)
\(660\) 0 0
\(661\) −14.5544 −0.566100 −0.283050 0.959105i \(-0.591346\pi\)
−0.283050 + 0.959105i \(0.591346\pi\)
\(662\) 0 0
\(663\) 9.57513 0.371867
\(664\) 0 0
\(665\) 5.08449 0.197168
\(666\) 0 0
\(667\) 3.43325 0.132936
\(668\) 0 0
\(669\) 23.1542 0.895195
\(670\) 0 0
\(671\) 4.60214 0.177664
\(672\) 0 0
\(673\) −46.1914 −1.78055 −0.890273 0.455427i \(-0.849486\pi\)
−0.890273 + 0.455427i \(0.849486\pi\)
\(674\) 0 0
\(675\) 9.94095 0.382627
\(676\) 0 0
\(677\) −10.6087 −0.407725 −0.203863 0.978999i \(-0.565350\pi\)
−0.203863 + 0.978999i \(0.565350\pi\)
\(678\) 0 0
\(679\) 2.36690 0.0908333
\(680\) 0 0
\(681\) −1.89963 −0.0727939
\(682\) 0 0
\(683\) 35.9985 1.37745 0.688723 0.725025i \(-0.258172\pi\)
0.688723 + 0.725025i \(0.258172\pi\)
\(684\) 0 0
\(685\) 22.3895 0.855458
\(686\) 0 0
\(687\) −23.1141 −0.881858
\(688\) 0 0
\(689\) −16.4739 −0.627606
\(690\) 0 0
\(691\) −24.7115 −0.940070 −0.470035 0.882648i \(-0.655759\pi\)
−0.470035 + 0.882648i \(0.655759\pi\)
\(692\) 0 0
\(693\) −1.87508 −0.0712282
\(694\) 0 0
\(695\) 3.87506 0.146989
\(696\) 0 0
\(697\) 14.4434 0.547083
\(698\) 0 0
\(699\) −41.3957 −1.56573
\(700\) 0 0
\(701\) 28.8712 1.09045 0.545225 0.838290i \(-0.316444\pi\)
0.545225 + 0.838290i \(0.316444\pi\)
\(702\) 0 0
\(703\) −27.8094 −1.04885
\(704\) 0 0
\(705\) −23.5970 −0.888713
\(706\) 0 0
\(707\) 2.06229 0.0775603
\(708\) 0 0
\(709\) −31.6656 −1.18923 −0.594614 0.804012i \(-0.702695\pi\)
−0.594614 + 0.804012i \(0.702695\pi\)
\(710\) 0 0
\(711\) 6.07856 0.227964
\(712\) 0 0
\(713\) −1.44105 −0.0539679
\(714\) 0 0
\(715\) 19.8828 0.743575
\(716\) 0 0
\(717\) −1.79230 −0.0669345
\(718\) 0 0
\(719\) −30.1524 −1.12449 −0.562247 0.826969i \(-0.690063\pi\)
−0.562247 + 0.826969i \(0.690063\pi\)
\(720\) 0 0
\(721\) 1.56403 0.0582477
\(722\) 0 0
\(723\) −38.1222 −1.41778
\(724\) 0 0
\(725\) −1.60124 −0.0594685
\(726\) 0 0
\(727\) −15.1905 −0.563384 −0.281692 0.959505i \(-0.590896\pi\)
−0.281692 + 0.959505i \(0.590896\pi\)
\(728\) 0 0
\(729\) 29.8887 1.10699
\(730\) 0 0
\(731\) 23.2512 0.859977
\(732\) 0 0
\(733\) 39.8270 1.47104 0.735522 0.677501i \(-0.236937\pi\)
0.735522 + 0.677501i \(0.236937\pi\)
\(734\) 0 0
\(735\) 17.9306 0.661381
\(736\) 0 0
\(737\) −1.10134 −0.0405682
\(738\) 0 0
\(739\) 26.4367 0.972489 0.486245 0.873823i \(-0.338366\pi\)
0.486245 + 0.873823i \(0.338366\pi\)
\(740\) 0 0
\(741\) 19.4267 0.713657
\(742\) 0 0
\(743\) 26.5745 0.974923 0.487462 0.873144i \(-0.337923\pi\)
0.487462 + 0.873144i \(0.337923\pi\)
\(744\) 0 0
\(745\) 15.4549 0.566225
\(746\) 0 0
\(747\) −12.8270 −0.469316
\(748\) 0 0
\(749\) 5.57720 0.203787
\(750\) 0 0
\(751\) 30.1977 1.10193 0.550964 0.834529i \(-0.314260\pi\)
0.550964 + 0.834529i \(0.314260\pi\)
\(752\) 0 0
\(753\) −19.7499 −0.719725
\(754\) 0 0
\(755\) 0.949439 0.0345536
\(756\) 0 0
\(757\) 31.3606 1.13982 0.569911 0.821706i \(-0.306978\pi\)
0.569911 + 0.821706i \(0.306978\pi\)
\(758\) 0 0
\(759\) −24.4379 −0.887040
\(760\) 0 0
\(761\) 40.3426 1.46242 0.731210 0.682153i \(-0.238956\pi\)
0.731210 + 0.682153i \(0.238956\pi\)
\(762\) 0 0
\(763\) 3.79253 0.137299
\(764\) 0 0
\(765\) 3.55272 0.128449
\(766\) 0 0
\(767\) −8.68015 −0.313422
\(768\) 0 0
\(769\) −20.4304 −0.736739 −0.368369 0.929680i \(-0.620084\pi\)
−0.368369 + 0.929680i \(0.620084\pi\)
\(770\) 0 0
\(771\) −23.9738 −0.863395
\(772\) 0 0
\(773\) 45.6859 1.64321 0.821605 0.570058i \(-0.193079\pi\)
0.821605 + 0.570058i \(0.193079\pi\)
\(774\) 0 0
\(775\) 0.672094 0.0241423
\(776\) 0 0
\(777\) 4.46715 0.160258
\(778\) 0 0
\(779\) 29.3038 1.04992
\(780\) 0 0
\(781\) 50.8798 1.82062
\(782\) 0 0
\(783\) −5.11048 −0.182634
\(784\) 0 0
\(785\) −20.0930 −0.717149
\(786\) 0 0
\(787\) −15.1038 −0.538392 −0.269196 0.963085i \(-0.586758\pi\)
−0.269196 + 0.963085i \(0.586758\pi\)
\(788\) 0 0
\(789\) −10.0856 −0.359055
\(790\) 0 0
\(791\) −1.54933 −0.0550880
\(792\) 0 0
\(793\) −2.70444 −0.0960373
\(794\) 0 0
\(795\) 17.3107 0.613947
\(796\) 0 0
\(797\) 13.0697 0.462954 0.231477 0.972840i \(-0.425644\pi\)
0.231477 + 0.972840i \(0.425644\pi\)
\(798\) 0 0
\(799\) 22.2300 0.786440
\(800\) 0 0
\(801\) 2.42683 0.0857478
\(802\) 0 0
\(803\) 69.9460 2.46834
\(804\) 0 0
\(805\) 3.75863 0.132474
\(806\) 0 0
\(807\) 34.9697 1.23099
\(808\) 0 0
\(809\) −19.0282 −0.668996 −0.334498 0.942396i \(-0.608567\pi\)
−0.334498 + 0.942396i \(0.608567\pi\)
\(810\) 0 0
\(811\) −21.0749 −0.740042 −0.370021 0.929023i \(-0.620649\pi\)
−0.370021 + 0.929023i \(0.620649\pi\)
\(812\) 0 0
\(813\) −26.1895 −0.918506
\(814\) 0 0
\(815\) 35.9927 1.26077
\(816\) 0 0
\(817\) 47.1736 1.65040
\(818\) 0 0
\(819\) 1.10188 0.0385029
\(820\) 0 0
\(821\) 10.5704 0.368909 0.184454 0.982841i \(-0.440948\pi\)
0.184454 + 0.982841i \(0.440948\pi\)
\(822\) 0 0
\(823\) −40.5293 −1.41276 −0.706381 0.707832i \(-0.749673\pi\)
−0.706381 + 0.707832i \(0.749673\pi\)
\(824\) 0 0
\(825\) 11.3976 0.396814
\(826\) 0 0
\(827\) 47.1057 1.63803 0.819013 0.573775i \(-0.194522\pi\)
0.819013 + 0.573775i \(0.194522\pi\)
\(828\) 0 0
\(829\) −9.69487 −0.336717 −0.168358 0.985726i \(-0.553847\pi\)
−0.168358 + 0.985726i \(0.553847\pi\)
\(830\) 0 0
\(831\) −16.8925 −0.585994
\(832\) 0 0
\(833\) −16.8919 −0.585269
\(834\) 0 0
\(835\) −21.4975 −0.743953
\(836\) 0 0
\(837\) 2.14504 0.0741436
\(838\) 0 0
\(839\) −29.2517 −1.00988 −0.504940 0.863154i \(-0.668485\pi\)
−0.504940 + 0.863154i \(0.668485\pi\)
\(840\) 0 0
\(841\) −28.1768 −0.971615
\(842\) 0 0
\(843\) −13.9483 −0.480404
\(844\) 0 0
\(845\) 11.6984 0.402436
\(846\) 0 0
\(847\) −4.31356 −0.148216
\(848\) 0 0
\(849\) −40.0228 −1.37358
\(850\) 0 0
\(851\) −20.5577 −0.704708
\(852\) 0 0
\(853\) −31.0610 −1.06351 −0.531754 0.846899i \(-0.678467\pi\)
−0.531754 + 0.846899i \(0.678467\pi\)
\(854\) 0 0
\(855\) 7.20800 0.246508
\(856\) 0 0
\(857\) −27.3567 −0.934486 −0.467243 0.884129i \(-0.654753\pi\)
−0.467243 + 0.884129i \(0.654753\pi\)
\(858\) 0 0
\(859\) 37.0124 1.26285 0.631424 0.775438i \(-0.282471\pi\)
0.631424 + 0.775438i \(0.282471\pi\)
\(860\) 0 0
\(861\) −4.70719 −0.160421
\(862\) 0 0
\(863\) 37.6253 1.28078 0.640389 0.768051i \(-0.278773\pi\)
0.640389 + 0.768051i \(0.278773\pi\)
\(864\) 0 0
\(865\) −5.65785 −0.192373
\(866\) 0 0
\(867\) −15.8344 −0.537765
\(868\) 0 0
\(869\) 33.6759 1.14238
\(870\) 0 0
\(871\) 0.647196 0.0219294
\(872\) 0 0
\(873\) 3.35542 0.113564
\(874\) 0 0
\(875\) −6.71935 −0.227156
\(876\) 0 0
\(877\) 35.6727 1.20458 0.602291 0.798277i \(-0.294255\pi\)
0.602291 + 0.798277i \(0.294255\pi\)
\(878\) 0 0
\(879\) 25.6653 0.865668
\(880\) 0 0
\(881\) −30.3930 −1.02397 −0.511984 0.858995i \(-0.671089\pi\)
−0.511984 + 0.858995i \(0.671089\pi\)
\(882\) 0 0
\(883\) −23.6017 −0.794260 −0.397130 0.917762i \(-0.629994\pi\)
−0.397130 + 0.917762i \(0.629994\pi\)
\(884\) 0 0
\(885\) 9.12106 0.306601
\(886\) 0 0
\(887\) 18.1804 0.610437 0.305219 0.952282i \(-0.401270\pi\)
0.305219 + 0.952282i \(0.401270\pi\)
\(888\) 0 0
\(889\) −8.23639 −0.276240
\(890\) 0 0
\(891\) 26.1901 0.877401
\(892\) 0 0
\(893\) 45.1017 1.50927
\(894\) 0 0
\(895\) −10.8296 −0.361993
\(896\) 0 0
\(897\) 14.3609 0.479495
\(898\) 0 0
\(899\) −0.345513 −0.0115235
\(900\) 0 0
\(901\) −16.3079 −0.543294
\(902\) 0 0
\(903\) −7.57771 −0.252170
\(904\) 0 0
\(905\) 41.4543 1.37799
\(906\) 0 0
\(907\) 26.8615 0.891921 0.445961 0.895053i \(-0.352862\pi\)
0.445961 + 0.895053i \(0.352862\pi\)
\(908\) 0 0
\(909\) 2.92359 0.0969694
\(910\) 0 0
\(911\) −42.7019 −1.41478 −0.707388 0.706825i \(-0.750127\pi\)
−0.707388 + 0.706825i \(0.750127\pi\)
\(912\) 0 0
\(913\) −71.0630 −2.35184
\(914\) 0 0
\(915\) 2.84181 0.0939473
\(916\) 0 0
\(917\) 7.46656 0.246568
\(918\) 0 0
\(919\) 7.59767 0.250624 0.125312 0.992117i \(-0.460007\pi\)
0.125312 + 0.992117i \(0.460007\pi\)
\(920\) 0 0
\(921\) −43.1812 −1.42287
\(922\) 0 0
\(923\) −29.8994 −0.984151
\(924\) 0 0
\(925\) 9.58790 0.315248
\(926\) 0 0
\(927\) 2.21724 0.0728239
\(928\) 0 0
\(929\) −34.5765 −1.13442 −0.567210 0.823574i \(-0.691977\pi\)
−0.567210 + 0.823574i \(0.691977\pi\)
\(930\) 0 0
\(931\) −34.2714 −1.12320
\(932\) 0 0
\(933\) −40.5474 −1.32746
\(934\) 0 0
\(935\) 19.6824 0.643684
\(936\) 0 0
\(937\) 40.4353 1.32096 0.660482 0.750842i \(-0.270352\pi\)
0.660482 + 0.750842i \(0.270352\pi\)
\(938\) 0 0
\(939\) 8.23506 0.268741
\(940\) 0 0
\(941\) −22.3193 −0.727587 −0.363794 0.931480i \(-0.618519\pi\)
−0.363794 + 0.931480i \(0.618519\pi\)
\(942\) 0 0
\(943\) 21.6623 0.705423
\(944\) 0 0
\(945\) −5.59481 −0.181999
\(946\) 0 0
\(947\) 40.0277 1.30073 0.650363 0.759623i \(-0.274617\pi\)
0.650363 + 0.759623i \(0.274617\pi\)
\(948\) 0 0
\(949\) −41.1036 −1.33428
\(950\) 0 0
\(951\) 46.4613 1.50661
\(952\) 0 0
\(953\) −6.33099 −0.205081 −0.102540 0.994729i \(-0.532697\pi\)
−0.102540 + 0.994729i \(0.532697\pi\)
\(954\) 0 0
\(955\) −32.3349 −1.04633
\(956\) 0 0
\(957\) −5.85933 −0.189405
\(958\) 0 0
\(959\) 6.87416 0.221978
\(960\) 0 0
\(961\) −30.8550 −0.995322
\(962\) 0 0
\(963\) 7.90649 0.254783
\(964\) 0 0
\(965\) 18.7831 0.604650
\(966\) 0 0
\(967\) 12.8388 0.412867 0.206433 0.978461i \(-0.433814\pi\)
0.206433 + 0.978461i \(0.433814\pi\)
\(968\) 0 0
\(969\) 19.2309 0.617785
\(970\) 0 0
\(971\) −22.1505 −0.710842 −0.355421 0.934706i \(-0.615662\pi\)
−0.355421 + 0.934706i \(0.615662\pi\)
\(972\) 0 0
\(973\) 1.18975 0.0381415
\(974\) 0 0
\(975\) −6.69778 −0.214500
\(976\) 0 0
\(977\) 41.0297 1.31266 0.656328 0.754475i \(-0.272109\pi\)
0.656328 + 0.754475i \(0.272109\pi\)
\(978\) 0 0
\(979\) 13.4449 0.429701
\(980\) 0 0
\(981\) 5.37646 0.171657
\(982\) 0 0
\(983\) −43.9691 −1.40240 −0.701199 0.712966i \(-0.747351\pi\)
−0.701199 + 0.712966i \(0.747351\pi\)
\(984\) 0 0
\(985\) 7.84258 0.249885
\(986\) 0 0
\(987\) −7.24489 −0.230607
\(988\) 0 0
\(989\) 34.8724 1.10888
\(990\) 0 0
\(991\) −20.6965 −0.657446 −0.328723 0.944426i \(-0.606618\pi\)
−0.328723 + 0.944426i \(0.606618\pi\)
\(992\) 0 0
\(993\) −25.0190 −0.793955
\(994\) 0 0
\(995\) 25.2180 0.799464
\(996\) 0 0
\(997\) 52.9018 1.67542 0.837709 0.546117i \(-0.183895\pi\)
0.837709 + 0.546117i \(0.183895\pi\)
\(998\) 0 0
\(999\) 30.6006 0.968160
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 \(a_p\))