Properties

Label 8008.2.a.k.1.4
Level 8008
Weight 2
Character 8008.1
Self dual Yes
Analytic conductor 63.944
Analytic rank 0
Dimension 6
CM No
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 8008 = 2^{3} \cdot 7 \cdot 11 \cdot 13 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8008.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(63.9442019386\)
Analytic rank: \(0\)
Dimension: \(6\)
Coefficient field: 6.6.244558277.1
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 2^{2} \)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.4
Root \(-0.676795\)
Character \(\chi\) = 8008.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(+0.676795 q^{3}\) \(+3.59312 q^{5}\) \(+1.00000 q^{7}\) \(-2.54195 q^{9}\) \(+O(q^{10})\) \(q\)\(+0.676795 q^{3}\) \(+3.59312 q^{5}\) \(+1.00000 q^{7}\) \(-2.54195 q^{9}\) \(-1.00000 q^{11}\) \(-1.00000 q^{13}\) \(+2.43181 q^{15}\) \(-5.62384 q^{17}\) \(-5.78115 q^{19}\) \(+0.676795 q^{21}\) \(+8.70173 q^{23}\) \(+7.91054 q^{25}\) \(-3.75076 q^{27}\) \(+9.58734 q^{29}\) \(+3.11439 q^{31}\) \(-0.676795 q^{33}\) \(+3.59312 q^{35}\) \(-5.39931 q^{37}\) \(-0.676795 q^{39}\) \(+8.94093 q^{41}\) \(-4.02493 q^{43}\) \(-9.13354 q^{45}\) \(+1.80586 q^{47}\) \(+1.00000 q^{49}\) \(-3.80619 q^{51}\) \(-4.67067 q^{53}\) \(-3.59312 q^{55}\) \(-3.91265 q^{57}\) \(+3.19237 q^{59}\) \(+9.66345 q^{61}\) \(-2.54195 q^{63}\) \(-3.59312 q^{65}\) \(+11.3992 q^{67}\) \(+5.88929 q^{69}\) \(-4.18836 q^{71}\) \(+12.6610 q^{73}\) \(+5.35382 q^{75}\) \(-1.00000 q^{77}\) \(+11.1859 q^{79}\) \(+5.08735 q^{81}\) \(-0.112281 q^{83}\) \(-20.2072 q^{85}\) \(+6.48866 q^{87}\) \(+10.6256 q^{89}\) \(-1.00000 q^{91}\) \(+2.10780 q^{93}\) \(-20.7724 q^{95}\) \(+16.7285 q^{97}\) \(+2.54195 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(6q \) \(\mathstrut -\mathstrut q^{3} \) \(\mathstrut +\mathstrut q^{5} \) \(\mathstrut +\mathstrut 6q^{7} \) \(\mathstrut +\mathstrut 9q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(6q \) \(\mathstrut -\mathstrut q^{3} \) \(\mathstrut +\mathstrut q^{5} \) \(\mathstrut +\mathstrut 6q^{7} \) \(\mathstrut +\mathstrut 9q^{9} \) \(\mathstrut -\mathstrut 6q^{11} \) \(\mathstrut -\mathstrut 6q^{13} \) \(\mathstrut -\mathstrut q^{15} \) \(\mathstrut +\mathstrut 2q^{19} \) \(\mathstrut -\mathstrut q^{21} \) \(\mathstrut +\mathstrut 11q^{23} \) \(\mathstrut +\mathstrut 9q^{25} \) \(\mathstrut -\mathstrut q^{27} \) \(\mathstrut +\mathstrut 14q^{29} \) \(\mathstrut +\mathstrut 21q^{31} \) \(\mathstrut +\mathstrut q^{33} \) \(\mathstrut +\mathstrut q^{35} \) \(\mathstrut -\mathstrut 5q^{37} \) \(\mathstrut +\mathstrut q^{39} \) \(\mathstrut +\mathstrut 12q^{43} \) \(\mathstrut +\mathstrut 2q^{45} \) \(\mathstrut +\mathstrut 2q^{47} \) \(\mathstrut +\mathstrut 6q^{49} \) \(\mathstrut -\mathstrut 16q^{51} \) \(\mathstrut +\mathstrut 2q^{53} \) \(\mathstrut -\mathstrut q^{55} \) \(\mathstrut -\mathstrut 12q^{57} \) \(\mathstrut +\mathstrut 3q^{59} \) \(\mathstrut -\mathstrut 18q^{61} \) \(\mathstrut +\mathstrut 9q^{63} \) \(\mathstrut -\mathstrut q^{65} \) \(\mathstrut -\mathstrut 25q^{67} \) \(\mathstrut +\mathstrut 29q^{69} \) \(\mathstrut -\mathstrut 11q^{71} \) \(\mathstrut +\mathstrut 14q^{73} \) \(\mathstrut -\mathstrut 42q^{75} \) \(\mathstrut -\mathstrut 6q^{77} \) \(\mathstrut +\mathstrut 24q^{79} \) \(\mathstrut +\mathstrut 42q^{81} \) \(\mathstrut +\mathstrut 24q^{83} \) \(\mathstrut -\mathstrut 46q^{85} \) \(\mathstrut -\mathstrut 16q^{87} \) \(\mathstrut +\mathstrut 55q^{89} \) \(\mathstrut -\mathstrut 6q^{91} \) \(\mathstrut +\mathstrut 41q^{93} \) \(\mathstrut -\mathstrut 30q^{95} \) \(\mathstrut +\mathstrut 37q^{97} \) \(\mathstrut -\mathstrut 9q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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
\(3\) 0.676795 0.390748 0.195374 0.980729i \(-0.437408\pi\)
0.195374 + 0.980729i \(0.437408\pi\)
\(4\) 0 0
\(5\) 3.59312 1.60689 0.803447 0.595376i \(-0.202997\pi\)
0.803447 + 0.595376i \(0.202997\pi\)
\(6\) 0 0
\(7\) 1.00000 0.377964
\(8\) 0 0
\(9\) −2.54195 −0.847316
\(10\) 0 0
\(11\) −1.00000 −0.301511
\(12\) 0 0
\(13\) −1.00000 −0.277350
\(14\) 0 0
\(15\) 2.43181 0.627890
\(16\) 0 0
\(17\) −5.62384 −1.36398 −0.681991 0.731360i \(-0.738886\pi\)
−0.681991 + 0.731360i \(0.738886\pi\)
\(18\) 0 0
\(19\) −5.78115 −1.32629 −0.663143 0.748493i \(-0.730778\pi\)
−0.663143 + 0.748493i \(0.730778\pi\)
\(20\) 0 0
\(21\) 0.676795 0.147689
\(22\) 0 0
\(23\) 8.70173 1.81444 0.907218 0.420661i \(-0.138202\pi\)
0.907218 + 0.420661i \(0.138202\pi\)
\(24\) 0 0
\(25\) 7.91054 1.58211
\(26\) 0 0
\(27\) −3.75076 −0.721835
\(28\) 0 0
\(29\) 9.58734 1.78032 0.890162 0.455644i \(-0.150591\pi\)
0.890162 + 0.455644i \(0.150591\pi\)
\(30\) 0 0
\(31\) 3.11439 0.559361 0.279680 0.960093i \(-0.409771\pi\)
0.279680 + 0.960093i \(0.409771\pi\)
\(32\) 0 0
\(33\) −0.676795 −0.117815
\(34\) 0 0
\(35\) 3.59312 0.607349
\(36\) 0 0
\(37\) −5.39931 −0.887642 −0.443821 0.896116i \(-0.646377\pi\)
−0.443821 + 0.896116i \(0.646377\pi\)
\(38\) 0 0
\(39\) −0.676795 −0.108374
\(40\) 0 0
\(41\) 8.94093 1.39634 0.698169 0.715933i \(-0.253998\pi\)
0.698169 + 0.715933i \(0.253998\pi\)
\(42\) 0 0
\(43\) −4.02493 −0.613797 −0.306898 0.951742i \(-0.599291\pi\)
−0.306898 + 0.951742i \(0.599291\pi\)
\(44\) 0 0
\(45\) −9.13354 −1.36155
\(46\) 0 0
\(47\) 1.80586 0.263411 0.131706 0.991289i \(-0.457955\pi\)
0.131706 + 0.991289i \(0.457955\pi\)
\(48\) 0 0
\(49\) 1.00000 0.142857
\(50\) 0 0
\(51\) −3.80619 −0.532973
\(52\) 0 0
\(53\) −4.67067 −0.641566 −0.320783 0.947153i \(-0.603946\pi\)
−0.320783 + 0.947153i \(0.603946\pi\)
\(54\) 0 0
\(55\) −3.59312 −0.484497
\(56\) 0 0
\(57\) −3.91265 −0.518244
\(58\) 0 0
\(59\) 3.19237 0.415611 0.207806 0.978170i \(-0.433368\pi\)
0.207806 + 0.978170i \(0.433368\pi\)
\(60\) 0 0
\(61\) 9.66345 1.23728 0.618639 0.785676i \(-0.287684\pi\)
0.618639 + 0.785676i \(0.287684\pi\)
\(62\) 0 0
\(63\) −2.54195 −0.320255
\(64\) 0 0
\(65\) −3.59312 −0.445672
\(66\) 0 0
\(67\) 11.3992 1.39263 0.696317 0.717734i \(-0.254821\pi\)
0.696317 + 0.717734i \(0.254821\pi\)
\(68\) 0 0
\(69\) 5.88929 0.708987
\(70\) 0 0
\(71\) −4.18836 −0.497067 −0.248533 0.968623i \(-0.579949\pi\)
−0.248533 + 0.968623i \(0.579949\pi\)
\(72\) 0 0
\(73\) 12.6610 1.48185 0.740927 0.671585i \(-0.234386\pi\)
0.740927 + 0.671585i \(0.234386\pi\)
\(74\) 0 0
\(75\) 5.35382 0.618205
\(76\) 0 0
\(77\) −1.00000 −0.113961
\(78\) 0 0
\(79\) 11.1859 1.25851 0.629257 0.777197i \(-0.283359\pi\)
0.629257 + 0.777197i \(0.283359\pi\)
\(80\) 0 0
\(81\) 5.08735 0.565261
\(82\) 0 0
\(83\) −0.112281 −0.0123244 −0.00616220 0.999981i \(-0.501962\pi\)
−0.00616220 + 0.999981i \(0.501962\pi\)
\(84\) 0 0
\(85\) −20.2072 −2.19178
\(86\) 0 0
\(87\) 6.48866 0.695658
\(88\) 0 0
\(89\) 10.6256 1.12631 0.563157 0.826350i \(-0.309587\pi\)
0.563157 + 0.826350i \(0.309587\pi\)
\(90\) 0 0
\(91\) −1.00000 −0.104828
\(92\) 0 0
\(93\) 2.10780 0.218569
\(94\) 0 0
\(95\) −20.7724 −2.13120
\(96\) 0 0
\(97\) 16.7285 1.69853 0.849263 0.527971i \(-0.177047\pi\)
0.849263 + 0.527971i \(0.177047\pi\)
\(98\) 0 0
\(99\) 2.54195 0.255475
\(100\) 0 0
\(101\) −17.2870 −1.72012 −0.860058 0.510196i \(-0.829573\pi\)
−0.860058 + 0.510196i \(0.829573\pi\)
\(102\) 0 0
\(103\) 8.00000 0.788263 0.394132 0.919054i \(-0.371045\pi\)
0.394132 + 0.919054i \(0.371045\pi\)
\(104\) 0 0
\(105\) 2.43181 0.237320
\(106\) 0 0
\(107\) −5.79615 −0.560335 −0.280168 0.959951i \(-0.590390\pi\)
−0.280168 + 0.959951i \(0.590390\pi\)
\(108\) 0 0
\(109\) −2.19381 −0.210129 −0.105064 0.994465i \(-0.533505\pi\)
−0.105064 + 0.994465i \(0.533505\pi\)
\(110\) 0 0
\(111\) −3.65423 −0.346844
\(112\) 0 0
\(113\) 8.35215 0.785704 0.392852 0.919602i \(-0.371488\pi\)
0.392852 + 0.919602i \(0.371488\pi\)
\(114\) 0 0
\(115\) 31.2664 2.91561
\(116\) 0 0
\(117\) 2.54195 0.235003
\(118\) 0 0
\(119\) −5.62384 −0.515537
\(120\) 0 0
\(121\) 1.00000 0.0909091
\(122\) 0 0
\(123\) 6.05118 0.545616
\(124\) 0 0
\(125\) 10.4579 0.935387
\(126\) 0 0
\(127\) 11.6650 1.03510 0.517550 0.855653i \(-0.326844\pi\)
0.517550 + 0.855653i \(0.326844\pi\)
\(128\) 0 0
\(129\) −2.72405 −0.239840
\(130\) 0 0
\(131\) 10.6828 0.933361 0.466681 0.884426i \(-0.345450\pi\)
0.466681 + 0.884426i \(0.345450\pi\)
\(132\) 0 0
\(133\) −5.78115 −0.501289
\(134\) 0 0
\(135\) −13.4770 −1.15991
\(136\) 0 0
\(137\) 9.11439 0.778695 0.389347 0.921091i \(-0.372701\pi\)
0.389347 + 0.921091i \(0.372701\pi\)
\(138\) 0 0
\(139\) −3.83266 −0.325082 −0.162541 0.986702i \(-0.551969\pi\)
−0.162541 + 0.986702i \(0.551969\pi\)
\(140\) 0 0
\(141\) 1.22219 0.102927
\(142\) 0 0
\(143\) 1.00000 0.0836242
\(144\) 0 0
\(145\) 34.4485 2.86079
\(146\) 0 0
\(147\) 0.676795 0.0558211
\(148\) 0 0
\(149\) 8.90099 0.729198 0.364599 0.931165i \(-0.381206\pi\)
0.364599 + 0.931165i \(0.381206\pi\)
\(150\) 0 0
\(151\) −4.34140 −0.353298 −0.176649 0.984274i \(-0.556526\pi\)
−0.176649 + 0.984274i \(0.556526\pi\)
\(152\) 0 0
\(153\) 14.2955 1.15572
\(154\) 0 0
\(155\) 11.1904 0.898834
\(156\) 0 0
\(157\) 10.0712 0.803768 0.401884 0.915690i \(-0.368355\pi\)
0.401884 + 0.915690i \(0.368355\pi\)
\(158\) 0 0
\(159\) −3.16109 −0.250691
\(160\) 0 0
\(161\) 8.70173 0.685792
\(162\) 0 0
\(163\) 3.80552 0.298071 0.149036 0.988832i \(-0.452383\pi\)
0.149036 + 0.988832i \(0.452383\pi\)
\(164\) 0 0
\(165\) −2.43181 −0.189316
\(166\) 0 0
\(167\) 15.8820 1.22898 0.614492 0.788923i \(-0.289361\pi\)
0.614492 + 0.788923i \(0.289361\pi\)
\(168\) 0 0
\(169\) 1.00000 0.0769231
\(170\) 0 0
\(171\) 14.6954 1.12378
\(172\) 0 0
\(173\) −10.4883 −0.797413 −0.398706 0.917079i \(-0.630541\pi\)
−0.398706 + 0.917079i \(0.630541\pi\)
\(174\) 0 0
\(175\) 7.91054 0.597981
\(176\) 0 0
\(177\) 2.16058 0.162399
\(178\) 0 0
\(179\) 12.2756 0.917521 0.458761 0.888560i \(-0.348294\pi\)
0.458761 + 0.888560i \(0.348294\pi\)
\(180\) 0 0
\(181\) 20.1320 1.49640 0.748199 0.663474i \(-0.230919\pi\)
0.748199 + 0.663474i \(0.230919\pi\)
\(182\) 0 0
\(183\) 6.54017 0.483464
\(184\) 0 0
\(185\) −19.4004 −1.42635
\(186\) 0 0
\(187\) 5.62384 0.411256
\(188\) 0 0
\(189\) −3.75076 −0.272828
\(190\) 0 0
\(191\) −9.80150 −0.709211 −0.354606 0.935016i \(-0.615385\pi\)
−0.354606 + 0.935016i \(0.615385\pi\)
\(192\) 0 0
\(193\) 3.00779 0.216505 0.108253 0.994123i \(-0.465474\pi\)
0.108253 + 0.994123i \(0.465474\pi\)
\(194\) 0 0
\(195\) −2.43181 −0.174145
\(196\) 0 0
\(197\) −16.2336 −1.15660 −0.578299 0.815825i \(-0.696283\pi\)
−0.578299 + 0.815825i \(0.696283\pi\)
\(198\) 0 0
\(199\) −18.8354 −1.33520 −0.667602 0.744519i \(-0.732679\pi\)
−0.667602 + 0.744519i \(0.732679\pi\)
\(200\) 0 0
\(201\) 7.71493 0.544169
\(202\) 0 0
\(203\) 9.58734 0.672899
\(204\) 0 0
\(205\) 32.1259 2.24377
\(206\) 0 0
\(207\) −22.1193 −1.53740
\(208\) 0 0
\(209\) 5.78115 0.399890
\(210\) 0 0
\(211\) −26.6591 −1.83529 −0.917644 0.397403i \(-0.869911\pi\)
−0.917644 + 0.397403i \(0.869911\pi\)
\(212\) 0 0
\(213\) −2.83466 −0.194228
\(214\) 0 0
\(215\) −14.4621 −0.986306
\(216\) 0 0
\(217\) 3.11439 0.211419
\(218\) 0 0
\(219\) 8.56888 0.579031
\(220\) 0 0
\(221\) 5.62384 0.378301
\(222\) 0 0
\(223\) −10.1514 −0.679789 −0.339894 0.940464i \(-0.610391\pi\)
−0.339894 + 0.940464i \(0.610391\pi\)
\(224\) 0 0
\(225\) −20.1082 −1.34055
\(226\) 0 0
\(227\) −21.5691 −1.43159 −0.715796 0.698309i \(-0.753936\pi\)
−0.715796 + 0.698309i \(0.753936\pi\)
\(228\) 0 0
\(229\) −2.89330 −0.191194 −0.0955972 0.995420i \(-0.530476\pi\)
−0.0955972 + 0.995420i \(0.530476\pi\)
\(230\) 0 0
\(231\) −0.676795 −0.0445298
\(232\) 0 0
\(233\) 15.3688 1.00684 0.503422 0.864040i \(-0.332074\pi\)
0.503422 + 0.864040i \(0.332074\pi\)
\(234\) 0 0
\(235\) 6.48866 0.423274
\(236\) 0 0
\(237\) 7.57057 0.491761
\(238\) 0 0
\(239\) −18.1509 −1.17408 −0.587042 0.809556i \(-0.699708\pi\)
−0.587042 + 0.809556i \(0.699708\pi\)
\(240\) 0 0
\(241\) −3.04429 −0.196100 −0.0980501 0.995181i \(-0.531261\pi\)
−0.0980501 + 0.995181i \(0.531261\pi\)
\(242\) 0 0
\(243\) 14.6954 0.942709
\(244\) 0 0
\(245\) 3.59312 0.229556
\(246\) 0 0
\(247\) 5.78115 0.367846
\(248\) 0 0
\(249\) −0.0759910 −0.00481573
\(250\) 0 0
\(251\) −15.8103 −0.997939 −0.498970 0.866619i \(-0.666288\pi\)
−0.498970 + 0.866619i \(0.666288\pi\)
\(252\) 0 0
\(253\) −8.70173 −0.547073
\(254\) 0 0
\(255\) −13.6761 −0.856431
\(256\) 0 0
\(257\) −8.07424 −0.503657 −0.251829 0.967772i \(-0.581032\pi\)
−0.251829 + 0.967772i \(0.581032\pi\)
\(258\) 0 0
\(259\) −5.39931 −0.335497
\(260\) 0 0
\(261\) −24.3705 −1.50850
\(262\) 0 0
\(263\) 6.60516 0.407292 0.203646 0.979045i \(-0.434721\pi\)
0.203646 + 0.979045i \(0.434721\pi\)
\(264\) 0 0
\(265\) −16.7823 −1.03093
\(266\) 0 0
\(267\) 7.19137 0.440104
\(268\) 0 0
\(269\) −5.85703 −0.357110 −0.178555 0.983930i \(-0.557142\pi\)
−0.178555 + 0.983930i \(0.557142\pi\)
\(270\) 0 0
\(271\) −13.6007 −0.826184 −0.413092 0.910689i \(-0.635551\pi\)
−0.413092 + 0.910689i \(0.635551\pi\)
\(272\) 0 0
\(273\) −0.676795 −0.0409615
\(274\) 0 0
\(275\) −7.91054 −0.477024
\(276\) 0 0
\(277\) 0.244652 0.0146997 0.00734985 0.999973i \(-0.497660\pi\)
0.00734985 + 0.999973i \(0.497660\pi\)
\(278\) 0 0
\(279\) −7.91662 −0.473956
\(280\) 0 0
\(281\) −15.7613 −0.940239 −0.470120 0.882603i \(-0.655789\pi\)
−0.470120 + 0.882603i \(0.655789\pi\)
\(282\) 0 0
\(283\) −21.5368 −1.28023 −0.640116 0.768278i \(-0.721114\pi\)
−0.640116 + 0.768278i \(0.721114\pi\)
\(284\) 0 0
\(285\) −14.0586 −0.832762
\(286\) 0 0
\(287\) 8.94093 0.527766
\(288\) 0 0
\(289\) 14.6276 0.860448
\(290\) 0 0
\(291\) 11.3218 0.663695
\(292\) 0 0
\(293\) 24.6207 1.43836 0.719179 0.694825i \(-0.244518\pi\)
0.719179 + 0.694825i \(0.244518\pi\)
\(294\) 0 0
\(295\) 11.4706 0.667843
\(296\) 0 0
\(297\) 3.75076 0.217641
\(298\) 0 0
\(299\) −8.70173 −0.503234
\(300\) 0 0
\(301\) −4.02493 −0.231993
\(302\) 0 0
\(303\) −11.6997 −0.672132
\(304\) 0 0
\(305\) 34.7220 1.98817
\(306\) 0 0
\(307\) −24.0388 −1.37197 −0.685984 0.727616i \(-0.740628\pi\)
−0.685984 + 0.727616i \(0.740628\pi\)
\(308\) 0 0
\(309\) 5.41436 0.308012
\(310\) 0 0
\(311\) −15.6375 −0.886723 −0.443362 0.896343i \(-0.646214\pi\)
−0.443362 + 0.896343i \(0.646214\pi\)
\(312\) 0 0
\(313\) 8.49347 0.480080 0.240040 0.970763i \(-0.422840\pi\)
0.240040 + 0.970763i \(0.422840\pi\)
\(314\) 0 0
\(315\) −9.13354 −0.514617
\(316\) 0 0
\(317\) −35.1209 −1.97259 −0.986293 0.165005i \(-0.947236\pi\)
−0.986293 + 0.165005i \(0.947236\pi\)
\(318\) 0 0
\(319\) −9.58734 −0.536788
\(320\) 0 0
\(321\) −3.92281 −0.218950
\(322\) 0 0
\(323\) 32.5123 1.80903
\(324\) 0 0
\(325\) −7.91054 −0.438798
\(326\) 0 0
\(327\) −1.48476 −0.0821074
\(328\) 0 0
\(329\) 1.80586 0.0995600
\(330\) 0 0
\(331\) −25.5645 −1.40515 −0.702577 0.711608i \(-0.747967\pi\)
−0.702577 + 0.711608i \(0.747967\pi\)
\(332\) 0 0
\(333\) 13.7248 0.752113
\(334\) 0 0
\(335\) 40.9588 2.23782
\(336\) 0 0
\(337\) 23.9641 1.30541 0.652703 0.757614i \(-0.273635\pi\)
0.652703 + 0.757614i \(0.273635\pi\)
\(338\) 0 0
\(339\) 5.65269 0.307012
\(340\) 0 0
\(341\) −3.11439 −0.168654
\(342\) 0 0
\(343\) 1.00000 0.0539949
\(344\) 0 0
\(345\) 21.1609 1.13927
\(346\) 0 0
\(347\) −31.0331 −1.66595 −0.832973 0.553314i \(-0.813363\pi\)
−0.832973 + 0.553314i \(0.813363\pi\)
\(348\) 0 0
\(349\) 35.0480 1.87608 0.938039 0.346530i \(-0.112640\pi\)
0.938039 + 0.346530i \(0.112640\pi\)
\(350\) 0 0
\(351\) 3.75076 0.200201
\(352\) 0 0
\(353\) −2.15133 −0.114504 −0.0572519 0.998360i \(-0.518234\pi\)
−0.0572519 + 0.998360i \(0.518234\pi\)
\(354\) 0 0
\(355\) −15.0493 −0.798734
\(356\) 0 0
\(357\) −3.80619 −0.201445
\(358\) 0 0
\(359\) 4.61897 0.243780 0.121890 0.992544i \(-0.461105\pi\)
0.121890 + 0.992544i \(0.461105\pi\)
\(360\) 0 0
\(361\) 14.4217 0.759036
\(362\) 0 0
\(363\) 0.676795 0.0355225
\(364\) 0 0
\(365\) 45.4924 2.38118
\(366\) 0 0
\(367\) 18.2909 0.954779 0.477390 0.878692i \(-0.341583\pi\)
0.477390 + 0.878692i \(0.341583\pi\)
\(368\) 0 0
\(369\) −22.7274 −1.18314
\(370\) 0 0
\(371\) −4.67067 −0.242489
\(372\) 0 0
\(373\) −9.59338 −0.496726 −0.248363 0.968667i \(-0.579893\pi\)
−0.248363 + 0.968667i \(0.579893\pi\)
\(374\) 0 0
\(375\) 7.07788 0.365500
\(376\) 0 0
\(377\) −9.58734 −0.493773
\(378\) 0 0
\(379\) −9.93124 −0.510133 −0.255067 0.966923i \(-0.582097\pi\)
−0.255067 + 0.966923i \(0.582097\pi\)
\(380\) 0 0
\(381\) 7.89480 0.404463
\(382\) 0 0
\(383\) −18.9342 −0.967491 −0.483745 0.875209i \(-0.660724\pi\)
−0.483745 + 0.875209i \(0.660724\pi\)
\(384\) 0 0
\(385\) −3.59312 −0.183123
\(386\) 0 0
\(387\) 10.2312 0.520080
\(388\) 0 0
\(389\) 9.41346 0.477281 0.238641 0.971108i \(-0.423298\pi\)
0.238641 + 0.971108i \(0.423298\pi\)
\(390\) 0 0
\(391\) −48.9372 −2.47486
\(392\) 0 0
\(393\) 7.23007 0.364709
\(394\) 0 0
\(395\) 40.1924 2.02230
\(396\) 0 0
\(397\) −1.77670 −0.0891702 −0.0445851 0.999006i \(-0.514197\pi\)
−0.0445851 + 0.999006i \(0.514197\pi\)
\(398\) 0 0
\(399\) −3.91265 −0.195878
\(400\) 0 0
\(401\) −5.37013 −0.268172 −0.134086 0.990970i \(-0.542810\pi\)
−0.134086 + 0.990970i \(0.542810\pi\)
\(402\) 0 0
\(403\) −3.11439 −0.155139
\(404\) 0 0
\(405\) 18.2795 0.908314
\(406\) 0 0
\(407\) 5.39931 0.267634
\(408\) 0 0
\(409\) −24.0341 −1.18841 −0.594204 0.804314i \(-0.702533\pi\)
−0.594204 + 0.804314i \(0.702533\pi\)
\(410\) 0 0
\(411\) 6.16857 0.304273
\(412\) 0 0
\(413\) 3.19237 0.157086
\(414\) 0 0
\(415\) −0.403438 −0.0198040
\(416\) 0 0
\(417\) −2.59392 −0.127025
\(418\) 0 0
\(419\) 14.9227 0.729022 0.364511 0.931199i \(-0.381236\pi\)
0.364511 + 0.931199i \(0.381236\pi\)
\(420\) 0 0
\(421\) 1.18689 0.0578455 0.0289227 0.999582i \(-0.490792\pi\)
0.0289227 + 0.999582i \(0.490792\pi\)
\(422\) 0 0
\(423\) −4.59039 −0.223192
\(424\) 0 0
\(425\) −44.4877 −2.15797
\(426\) 0 0
\(427\) 9.66345 0.467647
\(428\) 0 0
\(429\) 0.676795 0.0326760
\(430\) 0 0
\(431\) −36.1150 −1.73960 −0.869798 0.493407i \(-0.835751\pi\)
−0.869798 + 0.493407i \(0.835751\pi\)
\(432\) 0 0
\(433\) −20.0523 −0.963650 −0.481825 0.876267i \(-0.660026\pi\)
−0.481825 + 0.876267i \(0.660026\pi\)
\(434\) 0 0
\(435\) 23.3146 1.11785
\(436\) 0 0
\(437\) −50.3060 −2.40646
\(438\) 0 0
\(439\) 13.3196 0.635711 0.317855 0.948139i \(-0.397037\pi\)
0.317855 + 0.948139i \(0.397037\pi\)
\(440\) 0 0
\(441\) −2.54195 −0.121045
\(442\) 0 0
\(443\) 34.4034 1.63456 0.817278 0.576243i \(-0.195482\pi\)
0.817278 + 0.576243i \(0.195482\pi\)
\(444\) 0 0
\(445\) 38.1792 1.80987
\(446\) 0 0
\(447\) 6.02415 0.284932
\(448\) 0 0
\(449\) 16.8444 0.794934 0.397467 0.917616i \(-0.369889\pi\)
0.397467 + 0.917616i \(0.369889\pi\)
\(450\) 0 0
\(451\) −8.94093 −0.421012
\(452\) 0 0
\(453\) −2.93823 −0.138050
\(454\) 0 0
\(455\) −3.59312 −0.168448
\(456\) 0 0
\(457\) −35.3150 −1.65197 −0.825983 0.563695i \(-0.809379\pi\)
−0.825983 + 0.563695i \(0.809379\pi\)
\(458\) 0 0
\(459\) 21.0937 0.984570
\(460\) 0 0
\(461\) 11.0321 0.513814 0.256907 0.966436i \(-0.417297\pi\)
0.256907 + 0.966436i \(0.417297\pi\)
\(462\) 0 0
\(463\) −7.28844 −0.338723 −0.169361 0.985554i \(-0.554170\pi\)
−0.169361 + 0.985554i \(0.554170\pi\)
\(464\) 0 0
\(465\) 7.57360 0.351217
\(466\) 0 0
\(467\) 6.03039 0.279053 0.139526 0.990218i \(-0.455442\pi\)
0.139526 + 0.990218i \(0.455442\pi\)
\(468\) 0 0
\(469\) 11.3992 0.526366
\(470\) 0 0
\(471\) 6.81613 0.314071
\(472\) 0 0
\(473\) 4.02493 0.185067
\(474\) 0 0
\(475\) −45.7320 −2.09833
\(476\) 0 0
\(477\) 11.8726 0.543610
\(478\) 0 0
\(479\) −13.5920 −0.621032 −0.310516 0.950568i \(-0.600502\pi\)
−0.310516 + 0.950568i \(0.600502\pi\)
\(480\) 0 0
\(481\) 5.39931 0.246188
\(482\) 0 0
\(483\) 5.88929 0.267972
\(484\) 0 0
\(485\) 60.1077 2.72935
\(486\) 0 0
\(487\) 7.55386 0.342298 0.171149 0.985245i \(-0.445252\pi\)
0.171149 + 0.985245i \(0.445252\pi\)
\(488\) 0 0
\(489\) 2.57556 0.116471
\(490\) 0 0
\(491\) 18.5708 0.838088 0.419044 0.907966i \(-0.362365\pi\)
0.419044 + 0.907966i \(0.362365\pi\)
\(492\) 0 0
\(493\) −53.9177 −2.42833
\(494\) 0 0
\(495\) 9.13354 0.410522
\(496\) 0 0
\(497\) −4.18836 −0.187874
\(498\) 0 0
\(499\) 25.8928 1.15912 0.579559 0.814930i \(-0.303225\pi\)
0.579559 + 0.814930i \(0.303225\pi\)
\(500\) 0 0
\(501\) 10.7488 0.480223
\(502\) 0 0
\(503\) 3.66225 0.163291 0.0816457 0.996661i \(-0.473982\pi\)
0.0816457 + 0.996661i \(0.473982\pi\)
\(504\) 0 0
\(505\) −62.1142 −2.76405
\(506\) 0 0
\(507\) 0.676795 0.0300575
\(508\) 0 0
\(509\) 32.9982 1.46262 0.731310 0.682045i \(-0.238909\pi\)
0.731310 + 0.682045i \(0.238909\pi\)
\(510\) 0 0
\(511\) 12.6610 0.560088
\(512\) 0 0
\(513\) 21.6837 0.957360
\(514\) 0 0
\(515\) 28.7450 1.26666
\(516\) 0 0
\(517\) −1.80586 −0.0794214
\(518\) 0 0
\(519\) −7.09845 −0.311587
\(520\) 0 0
\(521\) 28.4607 1.24689 0.623443 0.781869i \(-0.285733\pi\)
0.623443 + 0.781869i \(0.285733\pi\)
\(522\) 0 0
\(523\) 22.1522 0.968649 0.484324 0.874888i \(-0.339065\pi\)
0.484324 + 0.874888i \(0.339065\pi\)
\(524\) 0 0
\(525\) 5.35382 0.233660
\(526\) 0 0
\(527\) −17.5148 −0.762959
\(528\) 0 0
\(529\) 52.7201 2.29218
\(530\) 0 0
\(531\) −8.11484 −0.352154
\(532\) 0 0
\(533\) −8.94093 −0.387275
\(534\) 0 0
\(535\) −20.8263 −0.900399
\(536\) 0 0
\(537\) 8.30806 0.358519
\(538\) 0 0
\(539\) −1.00000 −0.0430730
\(540\) 0 0
\(541\) −24.8923 −1.07020 −0.535101 0.844788i \(-0.679726\pi\)
−0.535101 + 0.844788i \(0.679726\pi\)
\(542\) 0 0
\(543\) 13.6252 0.584715
\(544\) 0 0
\(545\) −7.88263 −0.337655
\(546\) 0 0
\(547\) −18.6048 −0.795485 −0.397743 0.917497i \(-0.630206\pi\)
−0.397743 + 0.917497i \(0.630206\pi\)
\(548\) 0 0
\(549\) −24.5640 −1.04837
\(550\) 0 0
\(551\) −55.4258 −2.36122
\(552\) 0 0
\(553\) 11.1859 0.475673
\(554\) 0 0
\(555\) −13.1301 −0.557342
\(556\) 0 0
\(557\) 13.8700 0.587692 0.293846 0.955853i \(-0.405065\pi\)
0.293846 + 0.955853i \(0.405065\pi\)
\(558\) 0 0
\(559\) 4.02493 0.170237
\(560\) 0 0
\(561\) 3.80619 0.160697
\(562\) 0 0
\(563\) −28.4856 −1.20052 −0.600262 0.799803i \(-0.704937\pi\)
−0.600262 + 0.799803i \(0.704937\pi\)
\(564\) 0 0
\(565\) 30.0103 1.26254
\(566\) 0 0
\(567\) 5.08735 0.213649
\(568\) 0 0
\(569\) −30.1583 −1.26430 −0.632150 0.774846i \(-0.717827\pi\)
−0.632150 + 0.774846i \(0.717827\pi\)
\(570\) 0 0
\(571\) −5.48529 −0.229552 −0.114776 0.993391i \(-0.536615\pi\)
−0.114776 + 0.993391i \(0.536615\pi\)
\(572\) 0 0
\(573\) −6.63360 −0.277123
\(574\) 0 0
\(575\) 68.8354 2.87063
\(576\) 0 0
\(577\) 33.9648 1.41397 0.706986 0.707228i \(-0.250055\pi\)
0.706986 + 0.707228i \(0.250055\pi\)
\(578\) 0 0
\(579\) 2.03566 0.0845990
\(580\) 0 0
\(581\) −0.112281 −0.00465818
\(582\) 0 0
\(583\) 4.67067 0.193440
\(584\) 0 0
\(585\) 9.13354 0.377625
\(586\) 0 0
\(587\) 27.0359 1.11589 0.557946 0.829877i \(-0.311590\pi\)
0.557946 + 0.829877i \(0.311590\pi\)
\(588\) 0 0
\(589\) −18.0048 −0.741873
\(590\) 0 0
\(591\) −10.9868 −0.451939
\(592\) 0 0
\(593\) −14.4237 −0.592309 −0.296155 0.955140i \(-0.595704\pi\)
−0.296155 + 0.955140i \(0.595704\pi\)
\(594\) 0 0
\(595\) −20.2072 −0.828413
\(596\) 0 0
\(597\) −12.7477 −0.521728
\(598\) 0 0
\(599\) 2.67784 0.109414 0.0547068 0.998502i \(-0.482578\pi\)
0.0547068 + 0.998502i \(0.482578\pi\)
\(600\) 0 0
\(601\) −19.2928 −0.786969 −0.393484 0.919331i \(-0.628730\pi\)
−0.393484 + 0.919331i \(0.628730\pi\)
\(602\) 0 0
\(603\) −28.9762 −1.18000
\(604\) 0 0
\(605\) 3.59312 0.146081
\(606\) 0 0
\(607\) 18.6095 0.755334 0.377667 0.925941i \(-0.376726\pi\)
0.377667 + 0.925941i \(0.376726\pi\)
\(608\) 0 0
\(609\) 6.48866 0.262934
\(610\) 0 0
\(611\) −1.80586 −0.0730571
\(612\) 0 0
\(613\) 32.4517 1.31071 0.655356 0.755320i \(-0.272519\pi\)
0.655356 + 0.755320i \(0.272519\pi\)
\(614\) 0 0
\(615\) 21.7426 0.876747
\(616\) 0 0
\(617\) 0.435725 0.0175416 0.00877081 0.999962i \(-0.497208\pi\)
0.00877081 + 0.999962i \(0.497208\pi\)
\(618\) 0 0
\(619\) −40.9744 −1.64690 −0.823450 0.567388i \(-0.807954\pi\)
−0.823450 + 0.567388i \(0.807954\pi\)
\(620\) 0 0
\(621\) −32.6381 −1.30972
\(622\) 0 0
\(623\) 10.6256 0.425706
\(624\) 0 0
\(625\) −1.97602 −0.0790409
\(626\) 0 0
\(627\) 3.91265 0.156256
\(628\) 0 0
\(629\) 30.3649 1.21073
\(630\) 0 0
\(631\) 8.35558 0.332630 0.166315 0.986073i \(-0.446813\pi\)
0.166315 + 0.986073i \(0.446813\pi\)
\(632\) 0 0
\(633\) −18.0427 −0.717135
\(634\) 0 0
\(635\) 41.9137 1.66330
\(636\) 0 0
\(637\) −1.00000 −0.0396214
\(638\) 0 0
\(639\) 10.6466 0.421173
\(640\) 0 0
\(641\) −29.2121 −1.15381 −0.576905 0.816811i \(-0.695740\pi\)
−0.576905 + 0.816811i \(0.695740\pi\)
\(642\) 0 0
\(643\) −5.46796 −0.215635 −0.107818 0.994171i \(-0.534386\pi\)
−0.107818 + 0.994171i \(0.534386\pi\)
\(644\) 0 0
\(645\) −9.78787 −0.385397
\(646\) 0 0
\(647\) −35.5057 −1.39588 −0.697938 0.716159i \(-0.745899\pi\)
−0.697938 + 0.716159i \(0.745899\pi\)
\(648\) 0 0
\(649\) −3.19237 −0.125311
\(650\) 0 0
\(651\) 2.10780 0.0826113
\(652\) 0 0
\(653\) −13.4593 −0.526703 −0.263352 0.964700i \(-0.584828\pi\)
−0.263352 + 0.964700i \(0.584828\pi\)
\(654\) 0 0
\(655\) 38.3847 1.49981
\(656\) 0 0
\(657\) −32.1835 −1.25560
\(658\) 0 0
\(659\) 11.4237 0.445002 0.222501 0.974932i \(-0.428578\pi\)
0.222501 + 0.974932i \(0.428578\pi\)
\(660\) 0 0
\(661\) −36.5377 −1.42115 −0.710576 0.703621i \(-0.751565\pi\)
−0.710576 + 0.703621i \(0.751565\pi\)
\(662\) 0 0
\(663\) 3.80619 0.147820
\(664\) 0 0
\(665\) −20.7724 −0.805519
\(666\) 0 0
\(667\) 83.4264 3.23028
\(668\) 0 0
\(669\) −6.87042 −0.265626
\(670\) 0 0
\(671\) −9.66345 −0.373053
\(672\) 0 0
\(673\) −40.9767 −1.57954 −0.789768 0.613406i \(-0.789799\pi\)
−0.789768 + 0.613406i \(0.789799\pi\)
\(674\) 0 0
\(675\) −29.6706 −1.14202
\(676\) 0 0
\(677\) −4.97586 −0.191238 −0.0956190 0.995418i \(-0.530483\pi\)
−0.0956190 + 0.995418i \(0.530483\pi\)
\(678\) 0 0
\(679\) 16.7285 0.641982
\(680\) 0 0
\(681\) −14.5979 −0.559392
\(682\) 0 0
\(683\) −0.526478 −0.0201451 −0.0100726 0.999949i \(-0.503206\pi\)
−0.0100726 + 0.999949i \(0.503206\pi\)
\(684\) 0 0
\(685\) 32.7491 1.25128
\(686\) 0 0
\(687\) −1.95817 −0.0747088
\(688\) 0 0
\(689\) 4.67067 0.177939
\(690\) 0 0
\(691\) −7.68151 −0.292218 −0.146109 0.989268i \(-0.546675\pi\)
−0.146109 + 0.989268i \(0.546675\pi\)
\(692\) 0 0
\(693\) 2.54195 0.0965606
\(694\) 0 0
\(695\) −13.7712 −0.522372
\(696\) 0 0
\(697\) −50.2824 −1.90458
\(698\) 0 0
\(699\) 10.4015 0.393422
\(700\) 0 0
\(701\) 3.29151 0.124319 0.0621593 0.998066i \(-0.480201\pi\)
0.0621593 + 0.998066i \(0.480201\pi\)
\(702\) 0 0
\(703\) 31.2142 1.17727
\(704\) 0 0
\(705\) 4.39149 0.165393
\(706\) 0 0
\(707\) −17.2870 −0.650143
\(708\) 0 0
\(709\) 37.4374 1.40599 0.702995 0.711194i \(-0.251845\pi\)
0.702995 + 0.711194i \(0.251845\pi\)
\(710\) 0 0
\(711\) −28.4340 −1.06636
\(712\) 0 0
\(713\) 27.1006 1.01492
\(714\) 0 0
\(715\) 3.59312 0.134375
\(716\) 0 0
\(717\) −12.2844 −0.458771
\(718\) 0 0
\(719\) −35.8954 −1.33867 −0.669335 0.742960i \(-0.733421\pi\)
−0.669335 + 0.742960i \(0.733421\pi\)
\(720\) 0 0
\(721\) 8.00000 0.297936
\(722\) 0 0
\(723\) −2.06036 −0.0766257
\(724\) 0 0
\(725\) 75.8411 2.81667
\(726\) 0 0
\(727\) 1.15310 0.0427661 0.0213831 0.999771i \(-0.493193\pi\)
0.0213831 + 0.999771i \(0.493193\pi\)
\(728\) 0 0
\(729\) −5.31628 −0.196899
\(730\) 0 0
\(731\) 22.6356 0.837208
\(732\) 0 0
\(733\) −24.5439 −0.906550 −0.453275 0.891371i \(-0.649745\pi\)
−0.453275 + 0.891371i \(0.649745\pi\)
\(734\) 0 0
\(735\) 2.43181 0.0896986
\(736\) 0 0
\(737\) −11.3992 −0.419895
\(738\) 0 0
\(739\) 48.0467 1.76743 0.883714 0.468027i \(-0.155035\pi\)
0.883714 + 0.468027i \(0.155035\pi\)
\(740\) 0 0
\(741\) 3.91265 0.143735
\(742\) 0 0
\(743\) −25.9216 −0.950970 −0.475485 0.879724i \(-0.657727\pi\)
−0.475485 + 0.879724i \(0.657727\pi\)
\(744\) 0 0
\(745\) 31.9824 1.17174
\(746\) 0 0
\(747\) 0.285412 0.0104427
\(748\) 0 0
\(749\) −5.79615 −0.211787
\(750\) 0 0
\(751\) 12.0776 0.440718 0.220359 0.975419i \(-0.429277\pi\)
0.220359 + 0.975419i \(0.429277\pi\)
\(752\) 0 0
\(753\) −10.7004 −0.389943
\(754\) 0 0
\(755\) −15.5992 −0.567712
\(756\) 0 0
\(757\) 11.3929 0.414081 0.207041 0.978332i \(-0.433617\pi\)
0.207041 + 0.978332i \(0.433617\pi\)
\(758\) 0 0
\(759\) −5.88929 −0.213768
\(760\) 0 0
\(761\) 23.5386 0.853273 0.426637 0.904423i \(-0.359698\pi\)
0.426637 + 0.904423i \(0.359698\pi\)
\(762\) 0 0
\(763\) −2.19381 −0.0794213
\(764\) 0 0
\(765\) 51.3656 1.85713
\(766\) 0 0
\(767\) −3.19237 −0.115270
\(768\) 0 0
\(769\) 22.2843 0.803592 0.401796 0.915729i \(-0.368386\pi\)
0.401796 + 0.915729i \(0.368386\pi\)
\(770\) 0 0
\(771\) −5.46460 −0.196803
\(772\) 0 0
\(773\) 22.3364 0.803384 0.401692 0.915775i \(-0.368422\pi\)
0.401692 + 0.915775i \(0.368422\pi\)
\(774\) 0 0
\(775\) 24.6365 0.884970
\(776\) 0 0
\(777\) −3.65423 −0.131095
\(778\) 0 0
\(779\) −51.6888 −1.85194
\(780\) 0 0
\(781\) 4.18836 0.149871
\(782\) 0 0
\(783\) −35.9598 −1.28510
\(784\) 0 0
\(785\) 36.1870 1.29157
\(786\) 0 0
\(787\) −47.3562 −1.68806 −0.844032 0.536292i \(-0.819824\pi\)
−0.844032 + 0.536292i \(0.819824\pi\)
\(788\) 0 0
\(789\) 4.47034 0.159148
\(790\) 0 0
\(791\) 8.35215 0.296968
\(792\) 0 0
\(793\) −9.66345 −0.343159
\(794\) 0 0
\(795\) −11.3582 −0.402833
\(796\) 0 0
\(797\) −6.23258 −0.220769 −0.110385 0.993889i \(-0.535208\pi\)
−0.110385 + 0.993889i \(0.535208\pi\)
\(798\) 0 0
\(799\) −10.1558 −0.359288
\(800\) 0 0
\(801\) −27.0098 −0.954344
\(802\) 0 0
\(803\) −12.6610 −0.446796
\(804\) 0 0
\(805\) 31.2664 1.10200
\(806\) 0 0
\(807\) −3.96401 −0.139540
\(808\) 0 0
\(809\) 4.55541 0.160160 0.0800799 0.996788i \(-0.474482\pi\)
0.0800799 + 0.996788i \(0.474482\pi\)
\(810\) 0 0
\(811\) 4.57597 0.160684 0.0803421 0.996767i \(-0.474399\pi\)
0.0803421 + 0.996767i \(0.474399\pi\)
\(812\) 0 0
\(813\) −9.20489 −0.322829
\(814\) 0 0
\(815\) 13.6737 0.478969
\(816\) 0 0
\(817\) 23.2687 0.814070
\(818\) 0 0
\(819\) 2.54195 0.0888229
\(820\) 0 0
\(821\) 26.2506 0.916153 0.458076 0.888913i \(-0.348539\pi\)
0.458076 + 0.888913i \(0.348539\pi\)
\(822\) 0 0
\(823\) 11.5873 0.403907 0.201953 0.979395i \(-0.435271\pi\)
0.201953 + 0.979395i \(0.435271\pi\)
\(824\) 0 0
\(825\) −5.35382 −0.186396
\(826\) 0 0
\(827\) −32.9718 −1.14654 −0.573271 0.819366i \(-0.694326\pi\)
−0.573271 + 0.819366i \(0.694326\pi\)
\(828\) 0 0
\(829\) 7.36535 0.255809 0.127905 0.991786i \(-0.459175\pi\)
0.127905 + 0.991786i \(0.459175\pi\)
\(830\) 0 0
\(831\) 0.165579 0.00574388
\(832\) 0 0
\(833\) −5.62384 −0.194855
\(834\) 0 0
\(835\) 57.0659 1.97485
\(836\) 0 0
\(837\) −11.6813 −0.403766
\(838\) 0 0
\(839\) 2.74972 0.0949307 0.0474654 0.998873i \(-0.484886\pi\)
0.0474654 + 0.998873i \(0.484886\pi\)
\(840\) 0 0
\(841\) 62.9171 2.16955
\(842\) 0 0
\(843\) −10.6672 −0.367396
\(844\) 0 0
\(845\) 3.59312 0.123607
\(846\) 0 0
\(847\) 1.00000 0.0343604
\(848\) 0 0
\(849\) −14.5760 −0.500248
\(850\) 0 0
\(851\) −46.9834 −1.61057
\(852\) 0 0
\(853\) −21.0998 −0.722443 −0.361222 0.932480i \(-0.617640\pi\)
−0.361222 + 0.932480i \(0.617640\pi\)
\(854\) 0 0
\(855\) 52.8023 1.80580
\(856\) 0 0
\(857\) 4.65459 0.158998 0.0794989 0.996835i \(-0.474668\pi\)
0.0794989 + 0.996835i \(0.474668\pi\)
\(858\) 0 0
\(859\) −38.1289 −1.30094 −0.650471 0.759531i \(-0.725428\pi\)
−0.650471 + 0.759531i \(0.725428\pi\)
\(860\) 0 0
\(861\) 6.05118 0.206224
\(862\) 0 0
\(863\) −26.2902 −0.894929 −0.447464 0.894302i \(-0.647673\pi\)
−0.447464 + 0.894302i \(0.647673\pi\)
\(864\) 0 0
\(865\) −37.6859 −1.28136
\(866\) 0 0
\(867\) 9.89990 0.336218
\(868\) 0 0
\(869\) −11.1859 −0.379456
\(870\) 0 0
\(871\) −11.3992 −0.386247
\(872\) 0 0
\(873\) −42.5231 −1.43919
\(874\) 0 0
\(875\) 10.4579 0.353543
\(876\) 0 0
\(877\) 21.9230 0.740288 0.370144 0.928974i \(-0.379308\pi\)
0.370144 + 0.928974i \(0.379308\pi\)
\(878\) 0 0
\(879\) 16.6632 0.562035
\(880\) 0 0
\(881\) 34.8363 1.17366 0.586832 0.809709i \(-0.300375\pi\)
0.586832 + 0.809709i \(0.300375\pi\)
\(882\) 0 0
\(883\) 57.2116 1.92532 0.962662 0.270707i \(-0.0872573\pi\)
0.962662 + 0.270707i \(0.0872573\pi\)
\(884\) 0 0
\(885\) 7.76323 0.260958
\(886\) 0 0
\(887\) 22.5586 0.757444 0.378722 0.925510i \(-0.376364\pi\)
0.378722 + 0.925510i \(0.376364\pi\)
\(888\) 0 0
\(889\) 11.6650 0.391231
\(890\) 0 0
\(891\) −5.08735 −0.170433
\(892\) 0 0
\(893\) −10.4399 −0.349359
\(894\) 0 0
\(895\) 44.1077 1.47436
\(896\) 0 0
\(897\) −5.88929 −0.196638
\(898\) 0 0
\(899\) 29.8587 0.995844
\(900\) 0 0
\(901\) 26.2671 0.875085
\(902\) 0 0
\(903\) −2.72405 −0.0906509
\(904\) 0 0
\(905\) 72.3367 2.40455
\(906\) 0 0
\(907\) −26.6878 −0.886152 −0.443076 0.896484i \(-0.646113\pi\)
−0.443076 + 0.896484i \(0.646113\pi\)
\(908\) 0 0
\(909\) 43.9426 1.45748
\(910\) 0 0
\(911\) −1.47959 −0.0490211 −0.0245106 0.999700i \(-0.507803\pi\)
−0.0245106 + 0.999700i \(0.507803\pi\)
\(912\) 0 0
\(913\) 0.112281 0.00371595
\(914\) 0 0
\(915\) 23.4997 0.776875
\(916\) 0 0
\(917\) 10.6828 0.352777
\(918\) 0 0
\(919\) 39.1529 1.29154 0.645768 0.763534i \(-0.276537\pi\)
0.645768 + 0.763534i \(0.276537\pi\)
\(920\) 0 0
\(921\) −16.2694 −0.536094
\(922\) 0 0
\(923\) 4.18836 0.137861
\(924\) 0 0
\(925\) −42.7115 −1.40435
\(926\) 0 0
\(927\) −20.3356 −0.667908
\(928\) 0 0
\(929\) 53.2474 1.74699 0.873495 0.486834i \(-0.161848\pi\)
0.873495 + 0.486834i \(0.161848\pi\)
\(930\) 0 0
\(931\) −5.78115 −0.189469
\(932\) 0 0
\(933\) −10.5834 −0.346485
\(934\) 0 0
\(935\) 20.2072 0.660845
\(936\) 0 0
\(937\) 14.0294 0.458322 0.229161 0.973389i \(-0.426402\pi\)
0.229161 + 0.973389i \(0.426402\pi\)
\(938\) 0 0
\(939\) 5.74834 0.187590
\(940\) 0 0
\(941\) 59.0549 1.92513 0.962567 0.271044i \(-0.0873688\pi\)
0.962567 + 0.271044i \(0.0873688\pi\)
\(942\) 0 0
\(943\) 77.8015 2.53357
\(944\) 0 0
\(945\) −13.4770 −0.438406
\(946\) 0 0
\(947\) −13.9227 −0.452428 −0.226214 0.974078i \(-0.572635\pi\)
−0.226214 + 0.974078i \(0.572635\pi\)
\(948\) 0 0
\(949\) −12.6610 −0.410993
\(950\) 0 0
\(951\) −23.7696 −0.770783
\(952\) 0 0
\(953\) −37.7030 −1.22132 −0.610659 0.791893i \(-0.709096\pi\)
−0.610659 + 0.791893i \(0.709096\pi\)
\(954\) 0 0
\(955\) −35.2180 −1.13963
\(956\) 0 0
\(957\) −6.48866 −0.209749
\(958\) 0 0
\(959\) 9.11439 0.294319
\(960\) 0 0
\(961\) −21.3006 −0.687115
\(962\) 0 0
\(963\) 14.7335 0.474781
\(964\) 0 0
\(965\) 10.8074 0.347901
\(966\) 0 0
\(967\) −42.5027 −1.36679 −0.683397 0.730047i \(-0.739498\pi\)
−0.683397 + 0.730047i \(0.739498\pi\)
\(968\) 0 0
\(969\) 22.0041 0.706875
\(970\) 0 0
\(971\) 57.4572 1.84389 0.921945 0.387320i \(-0.126599\pi\)
0.921945 + 0.387320i \(0.126599\pi\)
\(972\) 0 0
\(973\) −3.83266 −0.122869
\(974\) 0 0
\(975\) −5.35382 −0.171459
\(976\) 0 0
\(977\) −20.6200 −0.659691 −0.329845 0.944035i \(-0.606997\pi\)
−0.329845 + 0.944035i \(0.606997\pi\)
\(978\) 0 0
\(979\) −10.6256 −0.339596
\(980\) 0 0
\(981\) 5.57655 0.178046
\(982\) 0 0
\(983\) −33.2574 −1.06075 −0.530373 0.847764i \(-0.677948\pi\)
−0.530373 + 0.847764i \(0.677948\pi\)
\(984\) 0 0
\(985\) −58.3295 −1.85853
\(986\) 0 0
\(987\) 1.22219 0.0389029
\(988\) 0 0
\(989\) −35.0239 −1.11369
\(990\) 0 0
\(991\) 17.6901 0.561946 0.280973 0.959716i \(-0.409343\pi\)
0.280973 + 0.959716i \(0.409343\pi\)
\(992\) 0 0
\(993\) −17.3019 −0.549061
\(994\) 0 0
\(995\) −67.6778 −2.14553
\(996\) 0 0
\(997\) 28.4947 0.902437 0.451218 0.892414i \(-0.350990\pi\)
0.451218 + 0.892414i \(0.350990\pi\)
\(998\) 0 0
\(999\) 20.2515 0.640731
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 \(a_p\))