Properties

Label 8048.2.a.p.1.1
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 1.1
Root \(2.78533\)
Character \(\chi\) = 8048.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-1.78533 q^{3}\) \(-0.701114 q^{5}\) \(+2.02991 q^{7}\) \(+0.187388 q^{9}\) \(+O(q^{10})\) \(q\)\(-1.78533 q^{3}\) \(-0.701114 q^{5}\) \(+2.02991 q^{7}\) \(+0.187388 q^{9}\) \(+0.626970 q^{11}\) \(-2.93743 q^{13}\) \(+1.25172 q^{15}\) \(-2.71003 q^{17}\) \(+1.11114 q^{19}\) \(-3.62406 q^{21}\) \(+0.412395 q^{23}\) \(-4.50844 q^{25}\) \(+5.02143 q^{27}\) \(+6.46349 q^{29}\) \(+4.14074 q^{31}\) \(-1.11935 q^{33}\) \(-1.42320 q^{35}\) \(+2.98634 q^{37}\) \(+5.24427 q^{39}\) \(-0.135430 q^{41}\) \(+0.861393 q^{43}\) \(-0.131380 q^{45}\) \(-1.67307 q^{47}\) \(-2.87945 q^{49}\) \(+4.83829 q^{51}\) \(-8.51721 q^{53}\) \(-0.439578 q^{55}\) \(-1.98374 q^{57}\) \(+0.406685 q^{59}\) \(-8.53132 q^{61}\) \(+0.380381 q^{63}\) \(+2.05948 q^{65}\) \(+13.0293 q^{67}\) \(-0.736259 q^{69}\) \(-2.78095 q^{71}\) \(-2.11734 q^{73}\) \(+8.04903 q^{75}\) \(+1.27270 q^{77}\) \(+0.317368 q^{79}\) \(-9.52705 q^{81}\) \(+5.05120 q^{83}\) \(+1.90004 q^{85}\) \(-11.5394 q^{87}\) \(+16.4699 q^{89}\) \(-5.96273 q^{91}\) \(-7.39256 q^{93}\) \(-0.779033 q^{95}\) \(+7.68873 q^{97}\) \(+0.117486 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(10q \) \(\mathstrut +\mathstrut 8q^{3} \) \(\mathstrut -\mathstrut q^{5} \) \(\mathstrut +\mathstrut 5q^{7} \) \(\mathstrut -\mathstrut 2q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(10q \) \(\mathstrut +\mathstrut 8q^{3} \) \(\mathstrut -\mathstrut q^{5} \) \(\mathstrut +\mathstrut 5q^{7} \) \(\mathstrut -\mathstrut 2q^{9} \) \(\mathstrut +\mathstrut 3q^{11} \) \(\mathstrut -\mathstrut 18q^{13} \) \(\mathstrut +\mathstrut 2q^{15} \) \(\mathstrut -\mathstrut 11q^{17} \) \(\mathstrut +\mathstrut q^{21} \) \(\mathstrut +\mathstrut 2q^{23} \) \(\mathstrut -\mathstrut 27q^{25} \) \(\mathstrut +\mathstrut 2q^{27} \) \(\mathstrut -\mathstrut 9q^{29} \) \(\mathstrut +\mathstrut 22q^{31} \) \(\mathstrut -\mathstrut 10q^{33} \) \(\mathstrut +\mathstrut 6q^{35} \) \(\mathstrut -\mathstrut 35q^{37} \) \(\mathstrut -\mathstrut 8q^{39} \) \(\mathstrut -\mathstrut 4q^{41} \) \(\mathstrut +\mathstrut 20q^{43} \) \(\mathstrut +\mathstrut 2q^{45} \) \(\mathstrut -\mathstrut 7q^{47} \) \(\mathstrut -\mathstrut 27q^{49} \) \(\mathstrut -\mathstrut 9q^{51} \) \(\mathstrut -\mathstrut 24q^{53} \) \(\mathstrut +\mathstrut 11q^{55} \) \(\mathstrut -\mathstrut 23q^{57} \) \(\mathstrut -\mathstrut 17q^{59} \) \(\mathstrut -\mathstrut 4q^{61} \) \(\mathstrut -\mathstrut 10q^{63} \) \(\mathstrut -\mathstrut 16q^{65} \) \(\mathstrut +\mathstrut 6q^{67} \) \(\mathstrut -\mathstrut 2q^{69} \) \(\mathstrut +\mathstrut q^{71} \) \(\mathstrut -\mathstrut 31q^{73} \) \(\mathstrut -\mathstrut 30q^{75} \) \(\mathstrut +\mathstrut 3q^{77} \) \(\mathstrut +\mathstrut 10q^{79} \) \(\mathstrut -\mathstrut 6q^{81} \) \(\mathstrut -\mathstrut 22q^{83} \) \(\mathstrut -\mathstrut 6q^{85} \) \(\mathstrut -\mathstrut 25q^{87} \) \(\mathstrut +\mathstrut q^{89} \) \(\mathstrut -\mathstrut 10q^{91} \) \(\mathstrut -\mathstrut 6q^{93} \) \(\mathstrut -\mathstrut 39q^{95} \) \(\mathstrut -\mathstrut 57q^{97} \) \(\mathstrut -\mathstrut 35q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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
\(3\) −1.78533 −1.03076 −0.515379 0.856962i \(-0.672349\pi\)
−0.515379 + 0.856962i \(0.672349\pi\)
\(4\) 0 0
\(5\) −0.701114 −0.313548 −0.156774 0.987635i \(-0.550109\pi\)
−0.156774 + 0.987635i \(0.550109\pi\)
\(6\) 0 0
\(7\) 2.02991 0.767235 0.383618 0.923492i \(-0.374678\pi\)
0.383618 + 0.923492i \(0.374678\pi\)
\(8\) 0 0
\(9\) 0.187388 0.0624625
\(10\) 0 0
\(11\) 0.626970 0.189039 0.0945194 0.995523i \(-0.469869\pi\)
0.0945194 + 0.995523i \(0.469869\pi\)
\(12\) 0 0
\(13\) −2.93743 −0.814697 −0.407349 0.913273i \(-0.633547\pi\)
−0.407349 + 0.913273i \(0.633547\pi\)
\(14\) 0 0
\(15\) 1.25172 0.323192
\(16\) 0 0
\(17\) −2.71003 −0.657280 −0.328640 0.944455i \(-0.606590\pi\)
−0.328640 + 0.944455i \(0.606590\pi\)
\(18\) 0 0
\(19\) 1.11114 0.254912 0.127456 0.991844i \(-0.459319\pi\)
0.127456 + 0.991844i \(0.459319\pi\)
\(20\) 0 0
\(21\) −3.62406 −0.790834
\(22\) 0 0
\(23\) 0.412395 0.0859902 0.0429951 0.999075i \(-0.486310\pi\)
0.0429951 + 0.999075i \(0.486310\pi\)
\(24\) 0 0
\(25\) −4.50844 −0.901688
\(26\) 0 0
\(27\) 5.02143 0.966374
\(28\) 0 0
\(29\) 6.46349 1.20024 0.600120 0.799910i \(-0.295120\pi\)
0.600120 + 0.799910i \(0.295120\pi\)
\(30\) 0 0
\(31\) 4.14074 0.743698 0.371849 0.928293i \(-0.378724\pi\)
0.371849 + 0.928293i \(0.378724\pi\)
\(32\) 0 0
\(33\) −1.11935 −0.194853
\(34\) 0 0
\(35\) −1.42320 −0.240565
\(36\) 0 0
\(37\) 2.98634 0.490951 0.245475 0.969403i \(-0.421056\pi\)
0.245475 + 0.969403i \(0.421056\pi\)
\(38\) 0 0
\(39\) 5.24427 0.839756
\(40\) 0 0
\(41\) −0.135430 −0.0211505 −0.0105753 0.999944i \(-0.503366\pi\)
−0.0105753 + 0.999944i \(0.503366\pi\)
\(42\) 0 0
\(43\) 0.861393 0.131361 0.0656806 0.997841i \(-0.479078\pi\)
0.0656806 + 0.997841i \(0.479078\pi\)
\(44\) 0 0
\(45\) −0.131380 −0.0195850
\(46\) 0 0
\(47\) −1.67307 −0.244043 −0.122021 0.992527i \(-0.538938\pi\)
−0.122021 + 0.992527i \(0.538938\pi\)
\(48\) 0 0
\(49\) −2.87945 −0.411350
\(50\) 0 0
\(51\) 4.83829 0.677497
\(52\) 0 0
\(53\) −8.51721 −1.16993 −0.584964 0.811059i \(-0.698892\pi\)
−0.584964 + 0.811059i \(0.698892\pi\)
\(54\) 0 0
\(55\) −0.439578 −0.0592727
\(56\) 0 0
\(57\) −1.98374 −0.262753
\(58\) 0 0
\(59\) 0.406685 0.0529459 0.0264729 0.999650i \(-0.491572\pi\)
0.0264729 + 0.999650i \(0.491572\pi\)
\(60\) 0 0
\(61\) −8.53132 −1.09232 −0.546162 0.837680i \(-0.683912\pi\)
−0.546162 + 0.837680i \(0.683912\pi\)
\(62\) 0 0
\(63\) 0.380381 0.0479234
\(64\) 0 0
\(65\) 2.05948 0.255446
\(66\) 0 0
\(67\) 13.0293 1.59178 0.795889 0.605443i \(-0.207004\pi\)
0.795889 + 0.605443i \(0.207004\pi\)
\(68\) 0 0
\(69\) −0.736259 −0.0886352
\(70\) 0 0
\(71\) −2.78095 −0.330039 −0.165019 0.986290i \(-0.552769\pi\)
−0.165019 + 0.986290i \(0.552769\pi\)
\(72\) 0 0
\(73\) −2.11734 −0.247816 −0.123908 0.992294i \(-0.539543\pi\)
−0.123908 + 0.992294i \(0.539543\pi\)
\(74\) 0 0
\(75\) 8.04903 0.929422
\(76\) 0 0
\(77\) 1.27270 0.145037
\(78\) 0 0
\(79\) 0.317368 0.0357067 0.0178534 0.999841i \(-0.494317\pi\)
0.0178534 + 0.999841i \(0.494317\pi\)
\(80\) 0 0
\(81\) −9.52705 −1.05856
\(82\) 0 0
\(83\) 5.05120 0.554442 0.277221 0.960806i \(-0.410587\pi\)
0.277221 + 0.960806i \(0.410587\pi\)
\(84\) 0 0
\(85\) 1.90004 0.206089
\(86\) 0 0
\(87\) −11.5394 −1.23716
\(88\) 0 0
\(89\) 16.4699 1.74580 0.872901 0.487897i \(-0.162236\pi\)
0.872901 + 0.487897i \(0.162236\pi\)
\(90\) 0 0
\(91\) −5.96273 −0.625064
\(92\) 0 0
\(93\) −7.39256 −0.766573
\(94\) 0 0
\(95\) −0.779033 −0.0799271
\(96\) 0 0
\(97\) 7.68873 0.780673 0.390336 0.920672i \(-0.372359\pi\)
0.390336 + 0.920672i \(0.372359\pi\)
\(98\) 0 0
\(99\) 0.117486 0.0118078
\(100\) 0 0
\(101\) −0.549020 −0.0546296 −0.0273148 0.999627i \(-0.508696\pi\)
−0.0273148 + 0.999627i \(0.508696\pi\)
\(102\) 0 0
\(103\) −1.32758 −0.130810 −0.0654051 0.997859i \(-0.520834\pi\)
−0.0654051 + 0.997859i \(0.520834\pi\)
\(104\) 0 0
\(105\) 2.54088 0.247964
\(106\) 0 0
\(107\) −2.57528 −0.248961 −0.124481 0.992222i \(-0.539726\pi\)
−0.124481 + 0.992222i \(0.539726\pi\)
\(108\) 0 0
\(109\) 8.89011 0.851518 0.425759 0.904837i \(-0.360007\pi\)
0.425759 + 0.904837i \(0.360007\pi\)
\(110\) 0 0
\(111\) −5.33159 −0.506052
\(112\) 0 0
\(113\) −1.91987 −0.180606 −0.0903032 0.995914i \(-0.528784\pi\)
−0.0903032 + 0.995914i \(0.528784\pi\)
\(114\) 0 0
\(115\) −0.289136 −0.0269621
\(116\) 0 0
\(117\) −0.550438 −0.0508880
\(118\) 0 0
\(119\) −5.50114 −0.504288
\(120\) 0 0
\(121\) −10.6069 −0.964264
\(122\) 0 0
\(123\) 0.241786 0.0218011
\(124\) 0 0
\(125\) 6.66650 0.596270
\(126\) 0 0
\(127\) −21.8010 −1.93452 −0.967261 0.253782i \(-0.918325\pi\)
−0.967261 + 0.253782i \(0.918325\pi\)
\(128\) 0 0
\(129\) −1.53787 −0.135402
\(130\) 0 0
\(131\) −8.78145 −0.767239 −0.383620 0.923491i \(-0.625323\pi\)
−0.383620 + 0.923491i \(0.625323\pi\)
\(132\) 0 0
\(133\) 2.25551 0.195577
\(134\) 0 0
\(135\) −3.52060 −0.303005
\(136\) 0 0
\(137\) −4.26127 −0.364065 −0.182032 0.983293i \(-0.558268\pi\)
−0.182032 + 0.983293i \(0.558268\pi\)
\(138\) 0 0
\(139\) −13.4951 −1.14464 −0.572321 0.820030i \(-0.693957\pi\)
−0.572321 + 0.820030i \(0.693957\pi\)
\(140\) 0 0
\(141\) 2.98698 0.251549
\(142\) 0 0
\(143\) −1.84168 −0.154009
\(144\) 0 0
\(145\) −4.53164 −0.376332
\(146\) 0 0
\(147\) 5.14076 0.424003
\(148\) 0 0
\(149\) 11.2453 0.921253 0.460626 0.887594i \(-0.347625\pi\)
0.460626 + 0.887594i \(0.347625\pi\)
\(150\) 0 0
\(151\) 2.36107 0.192141 0.0960705 0.995375i \(-0.469373\pi\)
0.0960705 + 0.995375i \(0.469373\pi\)
\(152\) 0 0
\(153\) −0.507827 −0.0410554
\(154\) 0 0
\(155\) −2.90313 −0.233185
\(156\) 0 0
\(157\) −17.5242 −1.39859 −0.699293 0.714835i \(-0.746502\pi\)
−0.699293 + 0.714835i \(0.746502\pi\)
\(158\) 0 0
\(159\) 15.2060 1.20591
\(160\) 0 0
\(161\) 0.837126 0.0659747
\(162\) 0 0
\(163\) 7.12153 0.557801 0.278901 0.960320i \(-0.410030\pi\)
0.278901 + 0.960320i \(0.410030\pi\)
\(164\) 0 0
\(165\) 0.784790 0.0610958
\(166\) 0 0
\(167\) −4.56080 −0.352925 −0.176463 0.984307i \(-0.556465\pi\)
−0.176463 + 0.984307i \(0.556465\pi\)
\(168\) 0 0
\(169\) −4.37149 −0.336269
\(170\) 0 0
\(171\) 0.208213 0.0159224
\(172\) 0 0
\(173\) 2.91357 0.221514 0.110757 0.993847i \(-0.464672\pi\)
0.110757 + 0.993847i \(0.464672\pi\)
\(174\) 0 0
\(175\) −9.15174 −0.691807
\(176\) 0 0
\(177\) −0.726065 −0.0545744
\(178\) 0 0
\(179\) 9.01141 0.673544 0.336772 0.941586i \(-0.390665\pi\)
0.336772 + 0.941586i \(0.390665\pi\)
\(180\) 0 0
\(181\) 14.4065 1.07082 0.535412 0.844591i \(-0.320156\pi\)
0.535412 + 0.844591i \(0.320156\pi\)
\(182\) 0 0
\(183\) 15.2312 1.12592
\(184\) 0 0
\(185\) −2.09376 −0.153937
\(186\) 0 0
\(187\) −1.69911 −0.124251
\(188\) 0 0
\(189\) 10.1931 0.741437
\(190\) 0 0
\(191\) −4.40730 −0.318901 −0.159450 0.987206i \(-0.550972\pi\)
−0.159450 + 0.987206i \(0.550972\pi\)
\(192\) 0 0
\(193\) −2.90027 −0.208766 −0.104383 0.994537i \(-0.533287\pi\)
−0.104383 + 0.994537i \(0.533287\pi\)
\(194\) 0 0
\(195\) −3.67683 −0.263304
\(196\) 0 0
\(197\) 5.91510 0.421433 0.210717 0.977547i \(-0.432420\pi\)
0.210717 + 0.977547i \(0.432420\pi\)
\(198\) 0 0
\(199\) 4.73473 0.335636 0.167818 0.985818i \(-0.446328\pi\)
0.167818 + 0.985818i \(0.446328\pi\)
\(200\) 0 0
\(201\) −23.2615 −1.64074
\(202\) 0 0
\(203\) 13.1203 0.920866
\(204\) 0 0
\(205\) 0.0949516 0.00663171
\(206\) 0 0
\(207\) 0.0772776 0.00537117
\(208\) 0 0
\(209\) 0.696649 0.0481882
\(210\) 0 0
\(211\) 1.50671 0.103726 0.0518631 0.998654i \(-0.483484\pi\)
0.0518631 + 0.998654i \(0.483484\pi\)
\(212\) 0 0
\(213\) 4.96491 0.340190
\(214\) 0 0
\(215\) −0.603935 −0.0411880
\(216\) 0 0
\(217\) 8.40534 0.570591
\(218\) 0 0
\(219\) 3.78014 0.255438
\(220\) 0 0
\(221\) 7.96054 0.535484
\(222\) 0 0
\(223\) 9.79220 0.655734 0.327867 0.944724i \(-0.393670\pi\)
0.327867 + 0.944724i \(0.393670\pi\)
\(224\) 0 0
\(225\) −0.844825 −0.0563217
\(226\) 0 0
\(227\) −6.88512 −0.456981 −0.228491 0.973546i \(-0.573379\pi\)
−0.228491 + 0.973546i \(0.573379\pi\)
\(228\) 0 0
\(229\) 12.1880 0.805405 0.402703 0.915331i \(-0.368071\pi\)
0.402703 + 0.915331i \(0.368071\pi\)
\(230\) 0 0
\(231\) −2.27218 −0.149498
\(232\) 0 0
\(233\) −21.0547 −1.37934 −0.689669 0.724125i \(-0.742244\pi\)
−0.689669 + 0.724125i \(0.742244\pi\)
\(234\) 0 0
\(235\) 1.17301 0.0765190
\(236\) 0 0
\(237\) −0.566606 −0.0368050
\(238\) 0 0
\(239\) −9.11944 −0.589888 −0.294944 0.955515i \(-0.595301\pi\)
−0.294944 + 0.955515i \(0.595301\pi\)
\(240\) 0 0
\(241\) 22.7352 1.46450 0.732252 0.681034i \(-0.238469\pi\)
0.732252 + 0.681034i \(0.238469\pi\)
\(242\) 0 0
\(243\) 1.94460 0.124746
\(244\) 0 0
\(245\) 2.01882 0.128978
\(246\) 0 0
\(247\) −3.26388 −0.207676
\(248\) 0 0
\(249\) −9.01804 −0.571495
\(250\) 0 0
\(251\) 11.6824 0.737385 0.368692 0.929551i \(-0.379806\pi\)
0.368692 + 0.929551i \(0.379806\pi\)
\(252\) 0 0
\(253\) 0.258559 0.0162555
\(254\) 0 0
\(255\) −3.39220 −0.212428
\(256\) 0 0
\(257\) −16.3010 −1.01683 −0.508415 0.861112i \(-0.669768\pi\)
−0.508415 + 0.861112i \(0.669768\pi\)
\(258\) 0 0
\(259\) 6.06201 0.376675
\(260\) 0 0
\(261\) 1.21118 0.0749700
\(262\) 0 0
\(263\) 15.7955 0.973993 0.486996 0.873404i \(-0.338093\pi\)
0.486996 + 0.873404i \(0.338093\pi\)
\(264\) 0 0
\(265\) 5.97154 0.366829
\(266\) 0 0
\(267\) −29.4041 −1.79950
\(268\) 0 0
\(269\) 11.2401 0.685323 0.342662 0.939459i \(-0.388672\pi\)
0.342662 + 0.939459i \(0.388672\pi\)
\(270\) 0 0
\(271\) −22.7114 −1.37962 −0.689809 0.723991i \(-0.742306\pi\)
−0.689809 + 0.723991i \(0.742306\pi\)
\(272\) 0 0
\(273\) 10.6454 0.644290
\(274\) 0 0
\(275\) −2.82666 −0.170454
\(276\) 0 0
\(277\) −3.42609 −0.205854 −0.102927 0.994689i \(-0.532821\pi\)
−0.102927 + 0.994689i \(0.532821\pi\)
\(278\) 0 0
\(279\) 0.775923 0.0464533
\(280\) 0 0
\(281\) −6.41168 −0.382488 −0.191244 0.981542i \(-0.561252\pi\)
−0.191244 + 0.981542i \(0.561252\pi\)
\(282\) 0 0
\(283\) 22.3462 1.32834 0.664172 0.747580i \(-0.268784\pi\)
0.664172 + 0.747580i \(0.268784\pi\)
\(284\) 0 0
\(285\) 1.39083 0.0823855
\(286\) 0 0
\(287\) −0.274910 −0.0162274
\(288\) 0 0
\(289\) −9.65571 −0.567983
\(290\) 0 0
\(291\) −13.7269 −0.804685
\(292\) 0 0
\(293\) 4.95366 0.289396 0.144698 0.989476i \(-0.453779\pi\)
0.144698 + 0.989476i \(0.453779\pi\)
\(294\) 0 0
\(295\) −0.285133 −0.0166011
\(296\) 0 0
\(297\) 3.14829 0.182682
\(298\) 0 0
\(299\) −1.21138 −0.0700560
\(300\) 0 0
\(301\) 1.74855 0.100785
\(302\) 0 0
\(303\) 0.980180 0.0563099
\(304\) 0 0
\(305\) 5.98143 0.342496
\(306\) 0 0
\(307\) 1.86937 0.106690 0.0533452 0.998576i \(-0.483012\pi\)
0.0533452 + 0.998576i \(0.483012\pi\)
\(308\) 0 0
\(309\) 2.37016 0.134834
\(310\) 0 0
\(311\) 4.29662 0.243639 0.121819 0.992552i \(-0.461127\pi\)
0.121819 + 0.992552i \(0.461127\pi\)
\(312\) 0 0
\(313\) −24.2378 −1.37000 −0.684999 0.728544i \(-0.740198\pi\)
−0.684999 + 0.728544i \(0.740198\pi\)
\(314\) 0 0
\(315\) −0.266690 −0.0150263
\(316\) 0 0
\(317\) −28.1902 −1.58332 −0.791661 0.610961i \(-0.790783\pi\)
−0.791661 + 0.610961i \(0.790783\pi\)
\(318\) 0 0
\(319\) 4.05242 0.226892
\(320\) 0 0
\(321\) 4.59771 0.256619
\(322\) 0 0
\(323\) −3.01121 −0.167548
\(324\) 0 0
\(325\) 13.2432 0.734602
\(326\) 0 0
\(327\) −15.8717 −0.877709
\(328\) 0 0
\(329\) −3.39619 −0.187238
\(330\) 0 0
\(331\) −13.5185 −0.743046 −0.371523 0.928424i \(-0.621164\pi\)
−0.371523 + 0.928424i \(0.621164\pi\)
\(332\) 0 0
\(333\) 0.559603 0.0306660
\(334\) 0 0
\(335\) −9.13500 −0.499098
\(336\) 0 0
\(337\) −1.73199 −0.0943475 −0.0471738 0.998887i \(-0.515021\pi\)
−0.0471738 + 0.998887i \(0.515021\pi\)
\(338\) 0 0
\(339\) 3.42760 0.186161
\(340\) 0 0
\(341\) 2.59612 0.140588
\(342\) 0 0
\(343\) −20.0544 −1.08284
\(344\) 0 0
\(345\) 0.516202 0.0277914
\(346\) 0 0
\(347\) 27.7262 1.48842 0.744210 0.667946i \(-0.232826\pi\)
0.744210 + 0.667946i \(0.232826\pi\)
\(348\) 0 0
\(349\) −16.0612 −0.859737 −0.429869 0.902891i \(-0.641440\pi\)
−0.429869 + 0.902891i \(0.641440\pi\)
\(350\) 0 0
\(351\) −14.7501 −0.787302
\(352\) 0 0
\(353\) −16.0011 −0.851652 −0.425826 0.904805i \(-0.640016\pi\)
−0.425826 + 0.904805i \(0.640016\pi\)
\(354\) 0 0
\(355\) 1.94977 0.103483
\(356\) 0 0
\(357\) 9.82132 0.519799
\(358\) 0 0
\(359\) −29.2698 −1.54480 −0.772400 0.635136i \(-0.780944\pi\)
−0.772400 + 0.635136i \(0.780944\pi\)
\(360\) 0 0
\(361\) −17.7654 −0.935020
\(362\) 0 0
\(363\) 18.9368 0.993923
\(364\) 0 0
\(365\) 1.48450 0.0777022
\(366\) 0 0
\(367\) −19.5331 −1.01962 −0.509810 0.860287i \(-0.670284\pi\)
−0.509810 + 0.860287i \(0.670284\pi\)
\(368\) 0 0
\(369\) −0.0253778 −0.00132112
\(370\) 0 0
\(371\) −17.2892 −0.897611
\(372\) 0 0
\(373\) −22.0592 −1.14218 −0.571091 0.820887i \(-0.693480\pi\)
−0.571091 + 0.820887i \(0.693480\pi\)
\(374\) 0 0
\(375\) −11.9019 −0.614610
\(376\) 0 0
\(377\) −18.9861 −0.977832
\(378\) 0 0
\(379\) −10.7429 −0.551828 −0.275914 0.961182i \(-0.588980\pi\)
−0.275914 + 0.961182i \(0.588980\pi\)
\(380\) 0 0
\(381\) 38.9218 1.99403
\(382\) 0 0
\(383\) −7.81876 −0.399520 −0.199760 0.979845i \(-0.564016\pi\)
−0.199760 + 0.979845i \(0.564016\pi\)
\(384\) 0 0
\(385\) −0.892305 −0.0454761
\(386\) 0 0
\(387\) 0.161414 0.00820515
\(388\) 0 0
\(389\) −35.0312 −1.77615 −0.888075 0.459698i \(-0.847957\pi\)
−0.888075 + 0.459698i \(0.847957\pi\)
\(390\) 0 0
\(391\) −1.11760 −0.0565197
\(392\) 0 0
\(393\) 15.6778 0.790838
\(394\) 0 0
\(395\) −0.222512 −0.0111958
\(396\) 0 0
\(397\) −0.245438 −0.0123182 −0.00615909 0.999981i \(-0.501961\pi\)
−0.00615909 + 0.999981i \(0.501961\pi\)
\(398\) 0 0
\(399\) −4.02682 −0.201593
\(400\) 0 0
\(401\) −16.3434 −0.816151 −0.408075 0.912948i \(-0.633800\pi\)
−0.408075 + 0.912948i \(0.633800\pi\)
\(402\) 0 0
\(403\) −12.1631 −0.605889
\(404\) 0 0
\(405\) 6.67955 0.331909
\(406\) 0 0
\(407\) 1.87235 0.0928087
\(408\) 0 0
\(409\) 4.60893 0.227897 0.113948 0.993487i \(-0.463650\pi\)
0.113948 + 0.993487i \(0.463650\pi\)
\(410\) 0 0
\(411\) 7.60775 0.375263
\(412\) 0 0
\(413\) 0.825536 0.0406220
\(414\) 0 0
\(415\) −3.54147 −0.173844
\(416\) 0 0
\(417\) 24.0932 1.17985
\(418\) 0 0
\(419\) −11.4509 −0.559414 −0.279707 0.960085i \(-0.590237\pi\)
−0.279707 + 0.960085i \(0.590237\pi\)
\(420\) 0 0
\(421\) −22.2626 −1.08501 −0.542505 0.840052i \(-0.682524\pi\)
−0.542505 + 0.840052i \(0.682524\pi\)
\(422\) 0 0
\(423\) −0.313513 −0.0152435
\(424\) 0 0
\(425\) 12.2180 0.592661
\(426\) 0 0
\(427\) −17.3178 −0.838069
\(428\) 0 0
\(429\) 3.28800 0.158746
\(430\) 0 0
\(431\) 1.13299 0.0545741 0.0272871 0.999628i \(-0.491313\pi\)
0.0272871 + 0.999628i \(0.491313\pi\)
\(432\) 0 0
\(433\) −2.65692 −0.127683 −0.0638417 0.997960i \(-0.520335\pi\)
−0.0638417 + 0.997960i \(0.520335\pi\)
\(434\) 0 0
\(435\) 8.09046 0.387908
\(436\) 0 0
\(437\) 0.458226 0.0219199
\(438\) 0 0
\(439\) −6.57228 −0.313678 −0.156839 0.987624i \(-0.550130\pi\)
−0.156839 + 0.987624i \(0.550130\pi\)
\(440\) 0 0
\(441\) −0.539573 −0.0256940
\(442\) 0 0
\(443\) −1.34406 −0.0638583 −0.0319291 0.999490i \(-0.510165\pi\)
−0.0319291 + 0.999490i \(0.510165\pi\)
\(444\) 0 0
\(445\) −11.5473 −0.547393
\(446\) 0 0
\(447\) −20.0766 −0.949589
\(448\) 0 0
\(449\) 26.3410 1.24311 0.621555 0.783371i \(-0.286501\pi\)
0.621555 + 0.783371i \(0.286501\pi\)
\(450\) 0 0
\(451\) −0.0849103 −0.00399827
\(452\) 0 0
\(453\) −4.21528 −0.198051
\(454\) 0 0
\(455\) 4.18056 0.195988
\(456\) 0 0
\(457\) −30.0693 −1.40658 −0.703290 0.710903i \(-0.748287\pi\)
−0.703290 + 0.710903i \(0.748287\pi\)
\(458\) 0 0
\(459\) −13.6082 −0.635179
\(460\) 0 0
\(461\) −7.72477 −0.359778 −0.179889 0.983687i \(-0.557574\pi\)
−0.179889 + 0.983687i \(0.557574\pi\)
\(462\) 0 0
\(463\) −7.82961 −0.363873 −0.181936 0.983310i \(-0.558236\pi\)
−0.181936 + 0.983310i \(0.558236\pi\)
\(464\) 0 0
\(465\) 5.18303 0.240357
\(466\) 0 0
\(467\) 7.19623 0.333002 0.166501 0.986041i \(-0.446753\pi\)
0.166501 + 0.986041i \(0.446753\pi\)
\(468\) 0 0
\(469\) 26.4483 1.22127
\(470\) 0 0
\(471\) 31.2865 1.44160
\(472\) 0 0
\(473\) 0.540068 0.0248323
\(474\) 0 0
\(475\) −5.00948 −0.229851
\(476\) 0 0
\(477\) −1.59602 −0.0730767
\(478\) 0 0
\(479\) 12.1955 0.557229 0.278614 0.960403i \(-0.410125\pi\)
0.278614 + 0.960403i \(0.410125\pi\)
\(480\) 0 0
\(481\) −8.77217 −0.399976
\(482\) 0 0
\(483\) −1.49454 −0.0680040
\(484\) 0 0
\(485\) −5.39068 −0.244778
\(486\) 0 0
\(487\) −35.9684 −1.62988 −0.814942 0.579543i \(-0.803231\pi\)
−0.814942 + 0.579543i \(0.803231\pi\)
\(488\) 0 0
\(489\) −12.7142 −0.574958
\(490\) 0 0
\(491\) 17.3618 0.783527 0.391763 0.920066i \(-0.371865\pi\)
0.391763 + 0.920066i \(0.371865\pi\)
\(492\) 0 0
\(493\) −17.5163 −0.788893
\(494\) 0 0
\(495\) −0.0823714 −0.00370232
\(496\) 0 0
\(497\) −5.64510 −0.253217
\(498\) 0 0
\(499\) 30.0817 1.34664 0.673320 0.739351i \(-0.264867\pi\)
0.673320 + 0.739351i \(0.264867\pi\)
\(500\) 0 0
\(501\) 8.14251 0.363781
\(502\) 0 0
\(503\) 1.00000 0.0445878
\(504\) 0 0
\(505\) 0.384926 0.0171290
\(506\) 0 0
\(507\) 7.80454 0.346612
\(508\) 0 0
\(509\) −32.5495 −1.44273 −0.721366 0.692554i \(-0.756485\pi\)
−0.721366 + 0.692554i \(0.756485\pi\)
\(510\) 0 0
\(511\) −4.29802 −0.190133
\(512\) 0 0
\(513\) 5.57949 0.246340
\(514\) 0 0
\(515\) 0.930784 0.0410152
\(516\) 0 0
\(517\) −1.04897 −0.0461335
\(518\) 0 0
\(519\) −5.20166 −0.228328
\(520\) 0 0
\(521\) −12.6474 −0.554094 −0.277047 0.960856i \(-0.589356\pi\)
−0.277047 + 0.960856i \(0.589356\pi\)
\(522\) 0 0
\(523\) −14.7294 −0.644073 −0.322036 0.946727i \(-0.604367\pi\)
−0.322036 + 0.946727i \(0.604367\pi\)
\(524\) 0 0
\(525\) 16.3388 0.713085
\(526\) 0 0
\(527\) −11.2215 −0.488818
\(528\) 0 0
\(529\) −22.8299 −0.992606
\(530\) 0 0
\(531\) 0.0762077 0.00330713
\(532\) 0 0
\(533\) 0.397815 0.0172313
\(534\) 0 0
\(535\) 1.80556 0.0780613
\(536\) 0 0
\(537\) −16.0883 −0.694261
\(538\) 0 0
\(539\) −1.80533 −0.0777611
\(540\) 0 0
\(541\) −27.4172 −1.17876 −0.589379 0.807857i \(-0.700627\pi\)
−0.589379 + 0.807857i \(0.700627\pi\)
\(542\) 0 0
\(543\) −25.7202 −1.10376
\(544\) 0 0
\(545\) −6.23298 −0.266992
\(546\) 0 0
\(547\) 16.1884 0.692164 0.346082 0.938204i \(-0.387512\pi\)
0.346082 + 0.938204i \(0.387512\pi\)
\(548\) 0 0
\(549\) −1.59866 −0.0682293
\(550\) 0 0
\(551\) 7.18181 0.305955
\(552\) 0 0
\(553\) 0.644231 0.0273955
\(554\) 0 0
\(555\) 3.73805 0.158671
\(556\) 0 0
\(557\) −13.3858 −0.567176 −0.283588 0.958946i \(-0.591525\pi\)
−0.283588 + 0.958946i \(0.591525\pi\)
\(558\) 0 0
\(559\) −2.53028 −0.107020
\(560\) 0 0
\(561\) 3.03347 0.128073
\(562\) 0 0
\(563\) −23.3845 −0.985538 −0.492769 0.870160i \(-0.664015\pi\)
−0.492769 + 0.870160i \(0.664015\pi\)
\(564\) 0 0
\(565\) 1.34605 0.0566287
\(566\) 0 0
\(567\) −19.3391 −0.812165
\(568\) 0 0
\(569\) 43.0171 1.80337 0.901685 0.432393i \(-0.142331\pi\)
0.901685 + 0.432393i \(0.142331\pi\)
\(570\) 0 0
\(571\) 1.24920 0.0522772 0.0261386 0.999658i \(-0.491679\pi\)
0.0261386 + 0.999658i \(0.491679\pi\)
\(572\) 0 0
\(573\) 7.86846 0.328710
\(574\) 0 0
\(575\) −1.85926 −0.0775364
\(576\) 0 0
\(577\) −38.6392 −1.60857 −0.804284 0.594244i \(-0.797451\pi\)
−0.804284 + 0.594244i \(0.797451\pi\)
\(578\) 0 0
\(579\) 5.17793 0.215187
\(580\) 0 0
\(581\) 10.2535 0.425387
\(582\) 0 0
\(583\) −5.34004 −0.221162
\(584\) 0 0
\(585\) 0.385920 0.0159558
\(586\) 0 0
\(587\) 13.5179 0.557943 0.278972 0.960299i \(-0.410006\pi\)
0.278972 + 0.960299i \(0.410006\pi\)
\(588\) 0 0
\(589\) 4.60092 0.189578
\(590\) 0 0
\(591\) −10.5604 −0.434396
\(592\) 0 0
\(593\) −6.72274 −0.276070 −0.138035 0.990427i \(-0.544079\pi\)
−0.138035 + 0.990427i \(0.544079\pi\)
\(594\) 0 0
\(595\) 3.85692 0.158118
\(596\) 0 0
\(597\) −8.45303 −0.345960
\(598\) 0 0
\(599\) −4.15139 −0.169621 −0.0848106 0.996397i \(-0.527029\pi\)
−0.0848106 + 0.996397i \(0.527029\pi\)
\(600\) 0 0
\(601\) −39.8754 −1.62655 −0.813276 0.581878i \(-0.802318\pi\)
−0.813276 + 0.581878i \(0.802318\pi\)
\(602\) 0 0
\(603\) 2.44152 0.0994264
\(604\) 0 0
\(605\) 7.43665 0.302343
\(606\) 0 0
\(607\) 27.9713 1.13532 0.567660 0.823263i \(-0.307849\pi\)
0.567660 + 0.823263i \(0.307849\pi\)
\(608\) 0 0
\(609\) −23.4240 −0.949190
\(610\) 0 0
\(611\) 4.91454 0.198821
\(612\) 0 0
\(613\) −30.7521 −1.24207 −0.621033 0.783785i \(-0.713287\pi\)
−0.621033 + 0.783785i \(0.713287\pi\)
\(614\) 0 0
\(615\) −0.169520 −0.00683569
\(616\) 0 0
\(617\) −24.4669 −0.984999 −0.492500 0.870313i \(-0.663917\pi\)
−0.492500 + 0.870313i \(0.663917\pi\)
\(618\) 0 0
\(619\) −37.1492 −1.49315 −0.746575 0.665301i \(-0.768303\pi\)
−0.746575 + 0.665301i \(0.768303\pi\)
\(620\) 0 0
\(621\) 2.07081 0.0830988
\(622\) 0 0
\(623\) 33.4324 1.33944
\(624\) 0 0
\(625\) 17.8682 0.714729
\(626\) 0 0
\(627\) −1.24375 −0.0496704
\(628\) 0 0
\(629\) −8.09308 −0.322692
\(630\) 0 0
\(631\) 15.7642 0.627563 0.313781 0.949495i \(-0.398404\pi\)
0.313781 + 0.949495i \(0.398404\pi\)
\(632\) 0 0
\(633\) −2.68997 −0.106917
\(634\) 0 0
\(635\) 15.2850 0.606565
\(636\) 0 0
\(637\) 8.45819 0.335126
\(638\) 0 0
\(639\) −0.521116 −0.0206150
\(640\) 0 0
\(641\) 48.3528 1.90982 0.954911 0.296892i \(-0.0959503\pi\)
0.954911 + 0.296892i \(0.0959503\pi\)
\(642\) 0 0
\(643\) −3.30378 −0.130288 −0.0651441 0.997876i \(-0.520751\pi\)
−0.0651441 + 0.997876i \(0.520751\pi\)
\(644\) 0 0
\(645\) 1.07822 0.0424549
\(646\) 0 0
\(647\) −34.3017 −1.34854 −0.674269 0.738486i \(-0.735541\pi\)
−0.674269 + 0.738486i \(0.735541\pi\)
\(648\) 0 0
\(649\) 0.254980 0.0100088
\(650\) 0 0
\(651\) −15.0063 −0.588142
\(652\) 0 0
\(653\) −13.5211 −0.529120 −0.264560 0.964369i \(-0.585227\pi\)
−0.264560 + 0.964369i \(0.585227\pi\)
\(654\) 0 0
\(655\) 6.15680 0.240566
\(656\) 0 0
\(657\) −0.396763 −0.0154792
\(658\) 0 0
\(659\) −29.2605 −1.13983 −0.569914 0.821704i \(-0.693023\pi\)
−0.569914 + 0.821704i \(0.693023\pi\)
\(660\) 0 0
\(661\) 36.0006 1.40026 0.700131 0.714015i \(-0.253125\pi\)
0.700131 + 0.714015i \(0.253125\pi\)
\(662\) 0 0
\(663\) −14.2122 −0.551955
\(664\) 0 0
\(665\) −1.58137 −0.0613229
\(666\) 0 0
\(667\) 2.66551 0.103209
\(668\) 0 0
\(669\) −17.4823 −0.675903
\(670\) 0 0
\(671\) −5.34889 −0.206491
\(672\) 0 0
\(673\) 14.3874 0.554595 0.277298 0.960784i \(-0.410561\pi\)
0.277298 + 0.960784i \(0.410561\pi\)
\(674\) 0 0
\(675\) −22.6388 −0.871368
\(676\) 0 0
\(677\) 25.3712 0.975094 0.487547 0.873097i \(-0.337892\pi\)
0.487547 + 0.873097i \(0.337892\pi\)
\(678\) 0 0
\(679\) 15.6075 0.598960
\(680\) 0 0
\(681\) 12.2922 0.471037
\(682\) 0 0
\(683\) −31.2549 −1.19594 −0.597968 0.801520i \(-0.704025\pi\)
−0.597968 + 0.801520i \(0.704025\pi\)
\(684\) 0 0
\(685\) 2.98764 0.114152
\(686\) 0 0
\(687\) −21.7595 −0.830178
\(688\) 0 0
\(689\) 25.0187 0.953138
\(690\) 0 0
\(691\) 1.92143 0.0730946 0.0365473 0.999332i \(-0.488364\pi\)
0.0365473 + 0.999332i \(0.488364\pi\)
\(692\) 0 0
\(693\) 0.238487 0.00905939
\(694\) 0 0
\(695\) 9.46162 0.358900
\(696\) 0 0
\(697\) 0.367019 0.0139018
\(698\) 0 0
\(699\) 37.5894 1.42176
\(700\) 0 0
\(701\) 5.22129 0.197205 0.0986027 0.995127i \(-0.468563\pi\)
0.0986027 + 0.995127i \(0.468563\pi\)
\(702\) 0 0
\(703\) 3.31823 0.125149
\(704\) 0 0
\(705\) −2.09421 −0.0788726
\(706\) 0 0
\(707\) −1.11446 −0.0419137
\(708\) 0 0
\(709\) 1.68414 0.0632493 0.0316247 0.999500i \(-0.489932\pi\)
0.0316247 + 0.999500i \(0.489932\pi\)
\(710\) 0 0
\(711\) 0.0594709 0.00223033
\(712\) 0 0
\(713\) 1.70762 0.0639508
\(714\) 0 0
\(715\) 1.29123 0.0482893
\(716\) 0 0
\(717\) 16.2812 0.608032
\(718\) 0 0
\(719\) 38.7868 1.44651 0.723253 0.690583i \(-0.242646\pi\)
0.723253 + 0.690583i \(0.242646\pi\)
\(720\) 0 0
\(721\) −2.69487 −0.100362
\(722\) 0 0
\(723\) −40.5898 −1.50955
\(724\) 0 0
\(725\) −29.1402 −1.08224
\(726\) 0 0
\(727\) 18.0472 0.669333 0.334666 0.942337i \(-0.391376\pi\)
0.334666 + 0.942337i \(0.391376\pi\)
\(728\) 0 0
\(729\) 25.1094 0.929978
\(730\) 0 0
\(731\) −2.33440 −0.0863410
\(732\) 0 0
\(733\) 2.36945 0.0875175 0.0437587 0.999042i \(-0.486067\pi\)
0.0437587 + 0.999042i \(0.486067\pi\)
\(734\) 0 0
\(735\) −3.60426 −0.132945
\(736\) 0 0
\(737\) 8.16896 0.300907
\(738\) 0 0
\(739\) −23.0868 −0.849260 −0.424630 0.905367i \(-0.639596\pi\)
−0.424630 + 0.905367i \(0.639596\pi\)
\(740\) 0 0
\(741\) 5.82710 0.214064
\(742\) 0 0
\(743\) −2.24456 −0.0823449 −0.0411725 0.999152i \(-0.513109\pi\)
−0.0411725 + 0.999152i \(0.513109\pi\)
\(744\) 0 0
\(745\) −7.88426 −0.288857
\(746\) 0 0
\(747\) 0.946533 0.0346318
\(748\) 0 0
\(749\) −5.22759 −0.191012
\(750\) 0 0
\(751\) −54.7798 −1.99894 −0.999472 0.0324826i \(-0.989659\pi\)
−0.999472 + 0.0324826i \(0.989659\pi\)
\(752\) 0 0
\(753\) −20.8568 −0.760065
\(754\) 0 0
\(755\) −1.65538 −0.0602454
\(756\) 0 0
\(757\) −5.96003 −0.216621 −0.108311 0.994117i \(-0.534544\pi\)
−0.108311 + 0.994117i \(0.534544\pi\)
\(758\) 0 0
\(759\) −0.461613 −0.0167555
\(760\) 0 0
\(761\) −33.5210 −1.21513 −0.607567 0.794268i \(-0.707854\pi\)
−0.607567 + 0.794268i \(0.707854\pi\)
\(762\) 0 0
\(763\) 18.0461 0.653314
\(764\) 0 0
\(765\) 0.356045 0.0128728
\(766\) 0 0
\(767\) −1.19461 −0.0431349
\(768\) 0 0
\(769\) −41.9889 −1.51416 −0.757080 0.653322i \(-0.773375\pi\)
−0.757080 + 0.653322i \(0.773375\pi\)
\(770\) 0 0
\(771\) 29.1026 1.04810
\(772\) 0 0
\(773\) 11.9695 0.430512 0.215256 0.976558i \(-0.430941\pi\)
0.215256 + 0.976558i \(0.430941\pi\)
\(774\) 0 0
\(775\) −18.6683 −0.670584
\(776\) 0 0
\(777\) −10.8227 −0.388261
\(778\) 0 0
\(779\) −0.150481 −0.00539153
\(780\) 0 0
\(781\) −1.74358 −0.0623901
\(782\) 0 0
\(783\) 32.4559 1.15988
\(784\) 0 0
\(785\) 12.2865 0.438523
\(786\) 0 0
\(787\) 14.5883 0.520017 0.260008 0.965606i \(-0.416275\pi\)
0.260008 + 0.965606i \(0.416275\pi\)
\(788\) 0 0
\(789\) −28.2001 −1.00395
\(790\) 0 0
\(791\) −3.89717 −0.138568
\(792\) 0 0
\(793\) 25.0602 0.889913
\(794\) 0 0
\(795\) −10.6611 −0.378112
\(796\) 0 0
\(797\) 13.0225 0.461281 0.230641 0.973039i \(-0.425918\pi\)
0.230641 + 0.973039i \(0.425918\pi\)
\(798\) 0 0
\(799\) 4.53408 0.160404
\(800\) 0 0
\(801\) 3.08625 0.109047
\(802\) 0 0
\(803\) −1.32751 −0.0468468
\(804\) 0 0
\(805\) −0.586921 −0.0206862
\(806\) 0 0
\(807\) −20.0673 −0.706403
\(808\) 0 0
\(809\) 23.5857 0.829230 0.414615 0.909997i \(-0.363916\pi\)
0.414615 + 0.909997i \(0.363916\pi\)
\(810\) 0 0
\(811\) −44.3230 −1.55639 −0.778195 0.628023i \(-0.783864\pi\)
−0.778195 + 0.628023i \(0.783864\pi\)
\(812\) 0 0
\(813\) 40.5472 1.42205
\(814\) 0 0
\(815\) −4.99300 −0.174897
\(816\) 0 0
\(817\) 0.957124 0.0334855
\(818\) 0 0
\(819\) −1.11734 −0.0390431
\(820\) 0 0
\(821\) −11.0481 −0.385581 −0.192791 0.981240i \(-0.561754\pi\)
−0.192791 + 0.981240i \(0.561754\pi\)
\(822\) 0 0
\(823\) −8.97374 −0.312805 −0.156403 0.987693i \(-0.549990\pi\)
−0.156403 + 0.987693i \(0.549990\pi\)
\(824\) 0 0
\(825\) 5.04650 0.175697
\(826\) 0 0
\(827\) −36.0996 −1.25531 −0.627654 0.778493i \(-0.715985\pi\)
−0.627654 + 0.778493i \(0.715985\pi\)
\(828\) 0 0
\(829\) −5.63971 −0.195875 −0.0979375 0.995193i \(-0.531225\pi\)
−0.0979375 + 0.995193i \(0.531225\pi\)
\(830\) 0 0
\(831\) 6.11669 0.212186
\(832\) 0 0
\(833\) 7.80341 0.270372
\(834\) 0 0
\(835\) 3.19764 0.110659
\(836\) 0 0
\(837\) 20.7924 0.718691
\(838\) 0 0
\(839\) 19.2580 0.664859 0.332429 0.943128i \(-0.392132\pi\)
0.332429 + 0.943128i \(0.392132\pi\)
\(840\) 0 0
\(841\) 12.7767 0.440575
\(842\) 0 0
\(843\) 11.4469 0.394253
\(844\) 0 0
\(845\) 3.06492 0.105436
\(846\) 0 0
\(847\) −21.5311 −0.739818
\(848\) 0 0
\(849\) −39.8953 −1.36920
\(850\) 0 0
\(851\) 1.23155 0.0422170
\(852\) 0 0
\(853\) 29.1126 0.996796 0.498398 0.866948i \(-0.333922\pi\)
0.498398 + 0.866948i \(0.333922\pi\)
\(854\) 0 0
\(855\) −0.145981 −0.00499245
\(856\) 0 0
\(857\) −18.6286 −0.636342 −0.318171 0.948033i \(-0.603069\pi\)
−0.318171 + 0.948033i \(0.603069\pi\)
\(858\) 0 0
\(859\) −18.5140 −0.631690 −0.315845 0.948811i \(-0.602288\pi\)
−0.315845 + 0.948811i \(0.602288\pi\)
\(860\) 0 0
\(861\) 0.490804 0.0167266
\(862\) 0 0
\(863\) 43.5150 1.48127 0.740635 0.671908i \(-0.234525\pi\)
0.740635 + 0.671908i \(0.234525\pi\)
\(864\) 0 0
\(865\) −2.04274 −0.0694553
\(866\) 0 0
\(867\) 17.2386 0.585453
\(868\) 0 0
\(869\) 0.198981 0.00674996
\(870\) 0 0
\(871\) −38.2726 −1.29682
\(872\) 0 0
\(873\) 1.44077 0.0487628
\(874\) 0 0
\(875\) 13.5324 0.457479
\(876\) 0 0
\(877\) 11.9837 0.404662 0.202331 0.979317i \(-0.435148\pi\)
0.202331 + 0.979317i \(0.435148\pi\)
\(878\) 0 0
\(879\) −8.84390 −0.298297
\(880\) 0 0
\(881\) −8.33770 −0.280904 −0.140452 0.990087i \(-0.544856\pi\)
−0.140452 + 0.990087i \(0.544856\pi\)
\(882\) 0 0
\(883\) −14.7773 −0.497296 −0.248648 0.968594i \(-0.579986\pi\)
−0.248648 + 0.968594i \(0.579986\pi\)
\(884\) 0 0
\(885\) 0.509055 0.0171117
\(886\) 0 0
\(887\) 26.6636 0.895278 0.447639 0.894214i \(-0.352265\pi\)
0.447639 + 0.894214i \(0.352265\pi\)
\(888\) 0 0
\(889\) −44.2541 −1.48423
\(890\) 0 0
\(891\) −5.97318 −0.200109
\(892\) 0 0
\(893\) −1.85901 −0.0622094
\(894\) 0 0
\(895\) −6.31803 −0.211188
\(896\) 0 0
\(897\) 2.16271 0.0722108
\(898\) 0 0
\(899\) 26.7636 0.892616
\(900\) 0 0
\(901\) 23.0819 0.768971
\(902\) 0 0
\(903\) −3.12174 −0.103885
\(904\) 0 0
\(905\) −10.1006 −0.335754
\(906\) 0 0
\(907\) 41.3358 1.37253 0.686266 0.727351i \(-0.259249\pi\)
0.686266 + 0.727351i \(0.259249\pi\)
\(908\) 0 0
\(909\) −0.102880 −0.00341230
\(910\) 0 0
\(911\) 32.2613 1.06887 0.534433 0.845211i \(-0.320525\pi\)
0.534433 + 0.845211i \(0.320525\pi\)
\(912\) 0 0
\(913\) 3.16696 0.104811
\(914\) 0 0
\(915\) −10.6788 −0.353030
\(916\) 0 0
\(917\) −17.8256 −0.588653
\(918\) 0 0
\(919\) 48.5538 1.60164 0.800821 0.598903i \(-0.204397\pi\)
0.800821 + 0.598903i \(0.204397\pi\)
\(920\) 0 0
\(921\) −3.33743 −0.109972
\(922\) 0 0
\(923\) 8.16886 0.268881
\(924\) 0 0
\(925\) −13.4637 −0.442684
\(926\) 0 0
\(927\) −0.248772 −0.00817073
\(928\) 0 0
\(929\) 28.1849 0.924717 0.462358 0.886693i \(-0.347003\pi\)
0.462358 + 0.886693i \(0.347003\pi\)
\(930\) 0 0
\(931\) −3.19946 −0.104858
\(932\) 0 0
\(933\) −7.67087 −0.251133
\(934\) 0 0
\(935\) 1.19127 0.0389587
\(936\) 0 0
\(937\) −59.4487 −1.94211 −0.971053 0.238865i \(-0.923225\pi\)
−0.971053 + 0.238865i \(0.923225\pi\)
\(938\) 0 0
\(939\) 43.2723 1.41214
\(940\) 0 0
\(941\) 24.0890 0.785277 0.392639 0.919693i \(-0.371562\pi\)
0.392639 + 0.919693i \(0.371562\pi\)
\(942\) 0 0
\(943\) −0.0558504 −0.00181874
\(944\) 0 0
\(945\) −7.14650 −0.232476
\(946\) 0 0
\(947\) −40.0415 −1.30117 −0.650586 0.759432i \(-0.725477\pi\)
−0.650586 + 0.759432i \(0.725477\pi\)
\(948\) 0 0
\(949\) 6.21955 0.201895
\(950\) 0 0
\(951\) 50.3288 1.63202
\(952\) 0 0
\(953\) −24.4039 −0.790521 −0.395261 0.918569i \(-0.629346\pi\)
−0.395261 + 0.918569i \(0.629346\pi\)
\(954\) 0 0
\(955\) 3.09002 0.0999907
\(956\) 0 0
\(957\) −7.23488 −0.233870
\(958\) 0 0
\(959\) −8.65001 −0.279323
\(960\) 0 0
\(961\) −13.8543 −0.446913
\(962\) 0 0
\(963\) −0.482575 −0.0155508
\(964\) 0 0
\(965\) 2.03342 0.0654581
\(966\) 0 0
\(967\) 16.2701 0.523212 0.261606 0.965175i \(-0.415748\pi\)
0.261606 + 0.965175i \(0.415748\pi\)
\(968\) 0 0
\(969\) 5.37600 0.172702
\(970\) 0 0
\(971\) 53.0256 1.70167 0.850837 0.525430i \(-0.176096\pi\)
0.850837 + 0.525430i \(0.176096\pi\)
\(972\) 0 0
\(973\) −27.3939 −0.878209
\(974\) 0 0
\(975\) −23.6435 −0.757197
\(976\) 0 0
\(977\) −47.0435 −1.50505 −0.752527 0.658561i \(-0.771165\pi\)
−0.752527 + 0.658561i \(0.771165\pi\)
\(978\) 0 0
\(979\) 10.3261 0.330024
\(980\) 0 0
\(981\) 1.66590 0.0531879
\(982\) 0 0
\(983\) 10.9007 0.347678 0.173839 0.984774i \(-0.444383\pi\)
0.173839 + 0.984774i \(0.444383\pi\)
\(984\) 0 0
\(985\) −4.14716 −0.132139
\(986\) 0 0
\(987\) 6.06331 0.192997
\(988\) 0 0
\(989\) 0.355234 0.0112958
\(990\) 0 0
\(991\) 48.5839 1.54332 0.771659 0.636036i \(-0.219427\pi\)
0.771659 + 0.636036i \(0.219427\pi\)
\(992\) 0 0
\(993\) 24.1350 0.765901
\(994\) 0 0
\(995\) −3.31959 −0.105238
\(996\) 0 0
\(997\) 20.3630 0.644902 0.322451 0.946586i \(-0.395493\pi\)
0.322451 + 0.946586i \(0.395493\pi\)
\(998\) 0 0
\(999\) 14.9957 0.474442
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 \(a_p\))