Properties

Label 6004.2.a.d.1.2
Level 6004
Weight 2
Character 6004.1
Self dual Yes
Analytic conductor 47.942
Analytic rank 0
Dimension 8
CM No
Inner twists 1

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Newspace parameters

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

Newform invariants

Self dual: Yes
Analytic conductor: \(47.9421813736\)
Analytic rank: \(0\)
Dimension: \(8\)
Coefficient field: \(\mathbb{Q}[x]/(x^{8} - \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{29}]\)
Coefficient ring index: \( 1 \)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.2
Root \(-1.94482\)
Character \(\chi\) = 6004.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-1.94482 q^{5}\) \(-0.969069 q^{7}\) \(-3.00000 q^{9}\) \(+O(q^{10})\) \(q\)\(-1.94482 q^{5}\) \(-0.969069 q^{7}\) \(-3.00000 q^{9}\) \(+0.202183 q^{11}\) \(-5.56979 q^{13}\) \(+3.01217 q^{17}\) \(+1.00000 q^{19}\) \(+6.09105 q^{23}\) \(-1.21766 q^{25}\) \(-6.46811 q^{29}\) \(-5.83369 q^{31}\) \(+1.88467 q^{35}\) \(+8.65467 q^{37}\) \(-7.53148 q^{41}\) \(+2.75737 q^{43}\) \(+5.83447 q^{45}\) \(-5.67933 q^{47}\) \(-6.06091 q^{49}\) \(-12.1865 q^{53}\) \(-0.393210 q^{55}\) \(-10.5931 q^{59}\) \(+1.88233 q^{61}\) \(+2.90721 q^{63}\) \(+10.8323 q^{65}\) \(+8.95699 q^{67}\) \(+5.27497 q^{71}\) \(-9.05092 q^{73}\) \(-0.195929 q^{77}\) \(+1.00000 q^{79}\) \(+9.00000 q^{81}\) \(+4.23359 q^{83}\) \(-5.85814 q^{85}\) \(-7.91293 q^{89}\) \(+5.39751 q^{91}\) \(-1.94482 q^{95}\) \(-12.3246 q^{97}\) \(-0.606548 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(8q \) \(\mathstrut +\mathstrut 4q^{5} \) \(\mathstrut +\mathstrut q^{7} \) \(\mathstrut -\mathstrut 24q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(8q \) \(\mathstrut +\mathstrut 4q^{5} \) \(\mathstrut +\mathstrut q^{7} \) \(\mathstrut -\mathstrut 24q^{9} \) \(\mathstrut -\mathstrut 7q^{11} \) \(\mathstrut -\mathstrut 12q^{13} \) \(\mathstrut -\mathstrut 7q^{17} \) \(\mathstrut +\mathstrut 8q^{19} \) \(\mathstrut +\mathstrut 10q^{23} \) \(\mathstrut +\mathstrut 6q^{25} \) \(\mathstrut +\mathstrut 5q^{29} \) \(\mathstrut +\mathstrut 3q^{31} \) \(\mathstrut -\mathstrut 11q^{35} \) \(\mathstrut -\mathstrut 15q^{37} \) \(\mathstrut -\mathstrut 5q^{41} \) \(\mathstrut +\mathstrut 10q^{43} \) \(\mathstrut -\mathstrut 12q^{45} \) \(\mathstrut +\mathstrut 18q^{47} \) \(\mathstrut +\mathstrut 31q^{49} \) \(\mathstrut +\mathstrut 9q^{53} \) \(\mathstrut -\mathstrut 17q^{55} \) \(\mathstrut +\mathstrut 8q^{59} \) \(\mathstrut +\mathstrut 13q^{61} \) \(\mathstrut -\mathstrut 3q^{63} \) \(\mathstrut +\mathstrut 4q^{65} \) \(\mathstrut +\mathstrut 21q^{67} \) \(\mathstrut +\mathstrut 44q^{71} \) \(\mathstrut -\mathstrut 20q^{73} \) \(\mathstrut +\mathstrut 15q^{77} \) \(\mathstrut +\mathstrut 8q^{79} \) \(\mathstrut +\mathstrut 72q^{81} \) \(\mathstrut -\mathstrut 4q^{83} \) \(\mathstrut -\mathstrut 9q^{85} \) \(\mathstrut -\mathstrut 10q^{89} \) \(\mathstrut +\mathstrut 48q^{91} \) \(\mathstrut +\mathstrut 4q^{95} \) \(\mathstrut -\mathstrut 22q^{97} \) \(\mathstrut +\mathstrut 21q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(4\) 0 0
\(5\) −1.94482 −0.869752 −0.434876 0.900490i \(-0.643208\pi\)
−0.434876 + 0.900490i \(0.643208\pi\)
\(6\) 0 0
\(7\) −0.969069 −0.366274 −0.183137 0.983087i \(-0.558625\pi\)
−0.183137 + 0.983087i \(0.558625\pi\)
\(8\) 0 0
\(9\) −3.00000 −1.00000
\(10\) 0 0
\(11\) 0.202183 0.0609604 0.0304802 0.999535i \(-0.490296\pi\)
0.0304802 + 0.999535i \(0.490296\pi\)
\(12\) 0 0
\(13\) −5.56979 −1.54478 −0.772391 0.635147i \(-0.780939\pi\)
−0.772391 + 0.635147i \(0.780939\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 3.01217 0.730558 0.365279 0.930898i \(-0.380974\pi\)
0.365279 + 0.930898i \(0.380974\pi\)
\(18\) 0 0
\(19\) 1.00000 0.229416
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) 6.09105 1.27007 0.635036 0.772483i \(-0.280985\pi\)
0.635036 + 0.772483i \(0.280985\pi\)
\(24\) 0 0
\(25\) −1.21766 −0.243531
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) −6.46811 −1.20110 −0.600549 0.799588i \(-0.705051\pi\)
−0.600549 + 0.799588i \(0.705051\pi\)
\(30\) 0 0
\(31\) −5.83369 −1.04776 −0.523881 0.851791i \(-0.675516\pi\)
−0.523881 + 0.851791i \(0.675516\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) 1.88467 0.318567
\(36\) 0 0
\(37\) 8.65467 1.42282 0.711410 0.702777i \(-0.248057\pi\)
0.711410 + 0.702777i \(0.248057\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) −7.53148 −1.17622 −0.588110 0.808781i \(-0.700128\pi\)
−0.588110 + 0.808781i \(0.700128\pi\)
\(42\) 0 0
\(43\) 2.75737 0.420495 0.210247 0.977648i \(-0.432573\pi\)
0.210247 + 0.977648i \(0.432573\pi\)
\(44\) 0 0
\(45\) 5.83447 0.869752
\(46\) 0 0
\(47\) −5.67933 −0.828416 −0.414208 0.910182i \(-0.635941\pi\)
−0.414208 + 0.910182i \(0.635941\pi\)
\(48\) 0 0
\(49\) −6.06091 −0.865844
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) −12.1865 −1.67395 −0.836975 0.547241i \(-0.815678\pi\)
−0.836975 + 0.547241i \(0.815678\pi\)
\(54\) 0 0
\(55\) −0.393210 −0.0530204
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) −10.5931 −1.37910 −0.689551 0.724237i \(-0.742192\pi\)
−0.689551 + 0.724237i \(0.742192\pi\)
\(60\) 0 0
\(61\) 1.88233 0.241007 0.120504 0.992713i \(-0.461549\pi\)
0.120504 + 0.992713i \(0.461549\pi\)
\(62\) 0 0
\(63\) 2.90721 0.366274
\(64\) 0 0
\(65\) 10.8323 1.34358
\(66\) 0 0
\(67\) 8.95699 1.09427 0.547135 0.837044i \(-0.315718\pi\)
0.547135 + 0.837044i \(0.315718\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 5.27497 0.626024 0.313012 0.949749i \(-0.398662\pi\)
0.313012 + 0.949749i \(0.398662\pi\)
\(72\) 0 0
\(73\) −9.05092 −1.05933 −0.529665 0.848207i \(-0.677682\pi\)
−0.529665 + 0.848207i \(0.677682\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) −0.195929 −0.0223282
\(78\) 0 0
\(79\) 1.00000 0.112509
\(80\) 0 0
\(81\) 9.00000 1.00000
\(82\) 0 0
\(83\) 4.23359 0.464697 0.232348 0.972633i \(-0.425359\pi\)
0.232348 + 0.972633i \(0.425359\pi\)
\(84\) 0 0
\(85\) −5.85814 −0.635404
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) −7.91293 −0.838768 −0.419384 0.907809i \(-0.637754\pi\)
−0.419384 + 0.907809i \(0.637754\pi\)
\(90\) 0 0
\(91\) 5.39751 0.565813
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) −1.94482 −0.199535
\(96\) 0 0
\(97\) −12.3246 −1.25138 −0.625689 0.780073i \(-0.715182\pi\)
−0.625689 + 0.780073i \(0.715182\pi\)
\(98\) 0 0
\(99\) −0.606548 −0.0609604
\(100\) 0 0
\(101\) 6.68432 0.665115 0.332557 0.943083i \(-0.392089\pi\)
0.332557 + 0.943083i \(0.392089\pi\)
\(102\) 0 0
\(103\) 15.1474 1.49251 0.746257 0.665658i \(-0.231849\pi\)
0.746257 + 0.665658i \(0.231849\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 13.2790 1.28373 0.641866 0.766817i \(-0.278161\pi\)
0.641866 + 0.766817i \(0.278161\pi\)
\(108\) 0 0
\(109\) 3.19533 0.306057 0.153029 0.988222i \(-0.451097\pi\)
0.153029 + 0.988222i \(0.451097\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) 19.6953 1.85277 0.926387 0.376573i \(-0.122898\pi\)
0.926387 + 0.376573i \(0.122898\pi\)
\(114\) 0 0
\(115\) −11.8460 −1.10465
\(116\) 0 0
\(117\) 16.7094 1.54478
\(118\) 0 0
\(119\) −2.91900 −0.267584
\(120\) 0 0
\(121\) −10.9591 −0.996284
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) 12.0923 1.08156
\(126\) 0 0
\(127\) 20.7327 1.83973 0.919863 0.392240i \(-0.128300\pi\)
0.919863 + 0.392240i \(0.128300\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) 4.19154 0.366217 0.183108 0.983093i \(-0.441384\pi\)
0.183108 + 0.983093i \(0.441384\pi\)
\(132\) 0 0
\(133\) −0.969069 −0.0840289
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 6.02851 0.515051 0.257525 0.966272i \(-0.417093\pi\)
0.257525 + 0.966272i \(0.417093\pi\)
\(138\) 0 0
\(139\) −15.9788 −1.35531 −0.677654 0.735381i \(-0.737003\pi\)
−0.677654 + 0.735381i \(0.737003\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) −1.12612 −0.0941705
\(144\) 0 0
\(145\) 12.5793 1.04466
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) 7.01337 0.574558 0.287279 0.957847i \(-0.407249\pi\)
0.287279 + 0.957847i \(0.407249\pi\)
\(150\) 0 0
\(151\) 14.7433 1.19979 0.599895 0.800079i \(-0.295209\pi\)
0.599895 + 0.800079i \(0.295209\pi\)
\(152\) 0 0
\(153\) −9.03650 −0.730558
\(154\) 0 0
\(155\) 11.3455 0.911293
\(156\) 0 0
\(157\) −7.06136 −0.563557 −0.281779 0.959479i \(-0.590924\pi\)
−0.281779 + 0.959479i \(0.590924\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) −5.90265 −0.465194
\(162\) 0 0
\(163\) 12.3905 0.970497 0.485248 0.874376i \(-0.338729\pi\)
0.485248 + 0.874376i \(0.338729\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 23.8319 1.84417 0.922084 0.386990i \(-0.126485\pi\)
0.922084 + 0.386990i \(0.126485\pi\)
\(168\) 0 0
\(169\) 18.0226 1.38635
\(170\) 0 0
\(171\) −3.00000 −0.229416
\(172\) 0 0
\(173\) −10.0368 −0.763084 −0.381542 0.924352i \(-0.624607\pi\)
−0.381542 + 0.924352i \(0.624607\pi\)
\(174\) 0 0
\(175\) 1.17999 0.0891991
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) −5.48749 −0.410155 −0.205077 0.978746i \(-0.565745\pi\)
−0.205077 + 0.978746i \(0.565745\pi\)
\(180\) 0 0
\(181\) 12.2243 0.908625 0.454312 0.890842i \(-0.349885\pi\)
0.454312 + 0.890842i \(0.349885\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) −16.8318 −1.23750
\(186\) 0 0
\(187\) 0.609008 0.0445351
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 7.55204 0.546447 0.273223 0.961951i \(-0.411910\pi\)
0.273223 + 0.961951i \(0.411910\pi\)
\(192\) 0 0
\(193\) 18.6413 1.34183 0.670914 0.741535i \(-0.265902\pi\)
0.670914 + 0.741535i \(0.265902\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) −14.1324 −1.00689 −0.503445 0.864027i \(-0.667934\pi\)
−0.503445 + 0.864027i \(0.667934\pi\)
\(198\) 0 0
\(199\) −12.9218 −0.916001 −0.458000 0.888952i \(-0.651434\pi\)
−0.458000 + 0.888952i \(0.651434\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) 6.26804 0.439931
\(204\) 0 0
\(205\) 14.6474 1.02302
\(206\) 0 0
\(207\) −18.2732 −1.27007
\(208\) 0 0
\(209\) 0.202183 0.0139853
\(210\) 0 0
\(211\) 12.4115 0.854444 0.427222 0.904147i \(-0.359492\pi\)
0.427222 + 0.904147i \(0.359492\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) −5.36260 −0.365726
\(216\) 0 0
\(217\) 5.65325 0.383768
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) −16.7771 −1.12855
\(222\) 0 0
\(223\) 23.3449 1.56329 0.781645 0.623723i \(-0.214381\pi\)
0.781645 + 0.623723i \(0.214381\pi\)
\(224\) 0 0
\(225\) 3.65297 0.243531
\(226\) 0 0
\(227\) −9.73366 −0.646046 −0.323023 0.946391i \(-0.604699\pi\)
−0.323023 + 0.946391i \(0.604699\pi\)
\(228\) 0 0
\(229\) 16.9689 1.12133 0.560667 0.828041i \(-0.310545\pi\)
0.560667 + 0.828041i \(0.310545\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) −8.09564 −0.530363 −0.265181 0.964199i \(-0.585432\pi\)
−0.265181 + 0.964199i \(0.585432\pi\)
\(234\) 0 0
\(235\) 11.0453 0.720517
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) 9.56166 0.618492 0.309246 0.950982i \(-0.399923\pi\)
0.309246 + 0.950982i \(0.399923\pi\)
\(240\) 0 0
\(241\) 13.8100 0.889582 0.444791 0.895634i \(-0.353278\pi\)
0.444791 + 0.895634i \(0.353278\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) 11.7874 0.753069
\(246\) 0 0
\(247\) −5.56979 −0.354397
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 4.14231 0.261461 0.130730 0.991418i \(-0.458268\pi\)
0.130730 + 0.991418i \(0.458268\pi\)
\(252\) 0 0
\(253\) 1.23150 0.0774240
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) −4.39737 −0.274301 −0.137150 0.990550i \(-0.543794\pi\)
−0.137150 + 0.990550i \(0.543794\pi\)
\(258\) 0 0
\(259\) −8.38698 −0.521141
\(260\) 0 0
\(261\) 19.4043 1.20110
\(262\) 0 0
\(263\) −12.0955 −0.745842 −0.372921 0.927863i \(-0.621644\pi\)
−0.372921 + 0.927863i \(0.621644\pi\)
\(264\) 0 0
\(265\) 23.7007 1.45592
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) −0.368422 −0.0224631 −0.0112315 0.999937i \(-0.503575\pi\)
−0.0112315 + 0.999937i \(0.503575\pi\)
\(270\) 0 0
\(271\) −18.3494 −1.11465 −0.557324 0.830295i \(-0.688172\pi\)
−0.557324 + 0.830295i \(0.688172\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) −0.246189 −0.0148458
\(276\) 0 0
\(277\) 32.7165 1.96574 0.982871 0.184293i \(-0.0589995\pi\)
0.982871 + 0.184293i \(0.0589995\pi\)
\(278\) 0 0
\(279\) 17.5011 1.04776
\(280\) 0 0
\(281\) −13.9586 −0.832703 −0.416351 0.909204i \(-0.636691\pi\)
−0.416351 + 0.909204i \(0.636691\pi\)
\(282\) 0 0
\(283\) −22.7577 −1.35281 −0.676404 0.736531i \(-0.736463\pi\)
−0.676404 + 0.736531i \(0.736463\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 7.29852 0.430818
\(288\) 0 0
\(289\) −7.92685 −0.466285
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) 19.6839 1.14995 0.574973 0.818172i \(-0.305012\pi\)
0.574973 + 0.818172i \(0.305012\pi\)
\(294\) 0 0
\(295\) 20.6017 1.19948
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) −33.9259 −1.96198
\(300\) 0 0
\(301\) −2.67208 −0.154016
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) −3.66079 −0.209616
\(306\) 0 0
\(307\) −20.1331 −1.14906 −0.574528 0.818485i \(-0.694815\pi\)
−0.574528 + 0.818485i \(0.694815\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) −12.7448 −0.722689 −0.361344 0.932432i \(-0.617682\pi\)
−0.361344 + 0.932432i \(0.617682\pi\)
\(312\) 0 0
\(313\) −11.0674 −0.625568 −0.312784 0.949824i \(-0.601262\pi\)
−0.312784 + 0.949824i \(0.601262\pi\)
\(314\) 0 0
\(315\) −5.65401 −0.318567
\(316\) 0 0
\(317\) −6.62769 −0.372248 −0.186124 0.982526i \(-0.559593\pi\)
−0.186124 + 0.982526i \(0.559593\pi\)
\(318\) 0 0
\(319\) −1.30774 −0.0732194
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) 3.01217 0.167601
\(324\) 0 0
\(325\) 6.78209 0.376203
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) 5.50367 0.303427
\(330\) 0 0
\(331\) −18.2445 −1.00281 −0.501405 0.865213i \(-0.667183\pi\)
−0.501405 + 0.865213i \(0.667183\pi\)
\(332\) 0 0
\(333\) −25.9640 −1.42282
\(334\) 0 0
\(335\) −17.4198 −0.951744
\(336\) 0 0
\(337\) −30.8573 −1.68091 −0.840453 0.541884i \(-0.817711\pi\)
−0.840453 + 0.541884i \(0.817711\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) −1.17947 −0.0638720
\(342\) 0 0
\(343\) 12.6569 0.683409
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) −11.7593 −0.631273 −0.315637 0.948880i \(-0.602218\pi\)
−0.315637 + 0.948880i \(0.602218\pi\)
\(348\) 0 0
\(349\) −20.3591 −1.08980 −0.544898 0.838503i \(-0.683431\pi\)
−0.544898 + 0.838503i \(0.683431\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) 24.8354 1.32186 0.660929 0.750449i \(-0.270163\pi\)
0.660929 + 0.750449i \(0.270163\pi\)
\(354\) 0 0
\(355\) −10.2589 −0.544486
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 23.1124 1.21983 0.609913 0.792469i \(-0.291205\pi\)
0.609913 + 0.792469i \(0.291205\pi\)
\(360\) 0 0
\(361\) 1.00000 0.0526316
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) 17.6024 0.921354
\(366\) 0 0
\(367\) 25.8920 1.35155 0.675775 0.737108i \(-0.263809\pi\)
0.675775 + 0.737108i \(0.263809\pi\)
\(368\) 0 0
\(369\) 22.5944 1.17622
\(370\) 0 0
\(371\) 11.8096 0.613124
\(372\) 0 0
\(373\) −33.1282 −1.71531 −0.857656 0.514224i \(-0.828080\pi\)
−0.857656 + 0.514224i \(0.828080\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 36.0260 1.85544
\(378\) 0 0
\(379\) −4.51614 −0.231978 −0.115989 0.993250i \(-0.537004\pi\)
−0.115989 + 0.993250i \(0.537004\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) −21.7382 −1.11077 −0.555385 0.831593i \(-0.687429\pi\)
−0.555385 + 0.831593i \(0.687429\pi\)
\(384\) 0 0
\(385\) 0.381047 0.0194200
\(386\) 0 0
\(387\) −8.27211 −0.420495
\(388\) 0 0
\(389\) 19.5420 0.990820 0.495410 0.868659i \(-0.335018\pi\)
0.495410 + 0.868659i \(0.335018\pi\)
\(390\) 0 0
\(391\) 18.3473 0.927861
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) −1.94482 −0.0978548
\(396\) 0 0
\(397\) −13.5986 −0.682496 −0.341248 0.939973i \(-0.610850\pi\)
−0.341248 + 0.939973i \(0.610850\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 35.7974 1.78763 0.893817 0.448431i \(-0.148017\pi\)
0.893817 + 0.448431i \(0.148017\pi\)
\(402\) 0 0
\(403\) 32.4925 1.61856
\(404\) 0 0
\(405\) −17.5034 −0.869752
\(406\) 0 0
\(407\) 1.74983 0.0867356
\(408\) 0 0
\(409\) 0.401479 0.0198519 0.00992594 0.999951i \(-0.496840\pi\)
0.00992594 + 0.999951i \(0.496840\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) 10.2654 0.505129
\(414\) 0 0
\(415\) −8.23359 −0.404171
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 0.924684 0.0451738 0.0225869 0.999745i \(-0.492810\pi\)
0.0225869 + 0.999745i \(0.492810\pi\)
\(420\) 0 0
\(421\) −19.3875 −0.944888 −0.472444 0.881361i \(-0.656628\pi\)
−0.472444 + 0.881361i \(0.656628\pi\)
\(422\) 0 0
\(423\) 17.0380 0.828416
\(424\) 0 0
\(425\) −3.66778 −0.177914
\(426\) 0 0
\(427\) −1.82410 −0.0882745
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 10.7203 0.516380 0.258190 0.966094i \(-0.416874\pi\)
0.258190 + 0.966094i \(0.416874\pi\)
\(432\) 0 0
\(433\) 33.5768 1.61360 0.806800 0.590825i \(-0.201198\pi\)
0.806800 + 0.590825i \(0.201198\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 6.09105 0.291374
\(438\) 0 0
\(439\) 22.9305 1.09441 0.547206 0.836998i \(-0.315691\pi\)
0.547206 + 0.836998i \(0.315691\pi\)
\(440\) 0 0
\(441\) 18.1827 0.865844
\(442\) 0 0
\(443\) 22.7061 1.07880 0.539399 0.842050i \(-0.318651\pi\)
0.539399 + 0.842050i \(0.318651\pi\)
\(444\) 0 0
\(445\) 15.3893 0.729521
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) 13.4201 0.633335 0.316668 0.948537i \(-0.397436\pi\)
0.316668 + 0.948537i \(0.397436\pi\)
\(450\) 0 0
\(451\) −1.52274 −0.0717028
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) −10.4972 −0.492117
\(456\) 0 0
\(457\) −5.34889 −0.250210 −0.125105 0.992143i \(-0.539927\pi\)
−0.125105 + 0.992143i \(0.539927\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 17.0556 0.794360 0.397180 0.917741i \(-0.369989\pi\)
0.397180 + 0.917741i \(0.369989\pi\)
\(462\) 0 0
\(463\) −17.2936 −0.803703 −0.401852 0.915705i \(-0.631633\pi\)
−0.401852 + 0.915705i \(0.631633\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 18.0380 0.834701 0.417350 0.908746i \(-0.362959\pi\)
0.417350 + 0.908746i \(0.362959\pi\)
\(468\) 0 0
\(469\) −8.67994 −0.400802
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) 0.557492 0.0256335
\(474\) 0 0
\(475\) −1.21766 −0.0558699
\(476\) 0 0
\(477\) 36.5596 1.67395
\(478\) 0 0
\(479\) −13.2513 −0.605468 −0.302734 0.953075i \(-0.597899\pi\)
−0.302734 + 0.953075i \(0.597899\pi\)
\(480\) 0 0
\(481\) −48.2047 −2.19795
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 23.9693 1.08839
\(486\) 0 0
\(487\) 34.8466 1.57905 0.789525 0.613719i \(-0.210327\pi\)
0.789525 + 0.613719i \(0.210327\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) 3.28039 0.148042 0.0740210 0.997257i \(-0.476417\pi\)
0.0740210 + 0.997257i \(0.476417\pi\)
\(492\) 0 0
\(493\) −19.4830 −0.877471
\(494\) 0 0
\(495\) 1.17963 0.0530204
\(496\) 0 0
\(497\) −5.11181 −0.229296
\(498\) 0 0
\(499\) −24.4043 −1.09248 −0.546242 0.837627i \(-0.683942\pi\)
−0.546242 + 0.837627i \(0.683942\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) −4.92788 −0.219723 −0.109862 0.993947i \(-0.535041\pi\)
−0.109862 + 0.993947i \(0.535041\pi\)
\(504\) 0 0
\(505\) −12.9998 −0.578485
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) −2.19457 −0.0972728 −0.0486364 0.998817i \(-0.515488\pi\)
−0.0486364 + 0.998817i \(0.515488\pi\)
\(510\) 0 0
\(511\) 8.77096 0.388004
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) −29.4590 −1.29812
\(516\) 0 0
\(517\) −1.14826 −0.0505006
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 22.2667 0.975524 0.487762 0.872977i \(-0.337813\pi\)
0.487762 + 0.872977i \(0.337813\pi\)
\(522\) 0 0
\(523\) 14.2664 0.623826 0.311913 0.950111i \(-0.399030\pi\)
0.311913 + 0.950111i \(0.399030\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −17.5721 −0.765451
\(528\) 0 0
\(529\) 14.1009 0.613082
\(530\) 0 0
\(531\) 31.7793 1.37910
\(532\) 0 0
\(533\) 41.9488 1.81700
\(534\) 0 0
\(535\) −25.8254 −1.11653
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) −1.22541 −0.0527822
\(540\) 0 0
\(541\) −29.0710 −1.24986 −0.624931 0.780680i \(-0.714873\pi\)
−0.624931 + 0.780680i \(0.714873\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) −6.21436 −0.266194
\(546\) 0 0
\(547\) −39.2386 −1.67772 −0.838862 0.544345i \(-0.816778\pi\)
−0.838862 + 0.544345i \(0.816778\pi\)
\(548\) 0 0
\(549\) −5.64698 −0.241007
\(550\) 0 0
\(551\) −6.46811 −0.275551
\(552\) 0 0
\(553\) −0.969069 −0.0412090
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 5.35817 0.227033 0.113517 0.993536i \(-0.463789\pi\)
0.113517 + 0.993536i \(0.463789\pi\)
\(558\) 0 0
\(559\) −15.3580 −0.649573
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) −26.4894 −1.11640 −0.558198 0.829708i \(-0.688507\pi\)
−0.558198 + 0.829708i \(0.688507\pi\)
\(564\) 0 0
\(565\) −38.3038 −1.61145
\(566\) 0 0
\(567\) −8.72162 −0.366274
\(568\) 0 0
\(569\) 38.4626 1.61243 0.806217 0.591620i \(-0.201511\pi\)
0.806217 + 0.591620i \(0.201511\pi\)
\(570\) 0 0
\(571\) −13.4314 −0.562088 −0.281044 0.959695i \(-0.590681\pi\)
−0.281044 + 0.959695i \(0.590681\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) −7.41681 −0.309302
\(576\) 0 0
\(577\) 26.0959 1.08639 0.543194 0.839607i \(-0.317215\pi\)
0.543194 + 0.839607i \(0.317215\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) −4.10264 −0.170206
\(582\) 0 0
\(583\) −2.46391 −0.102045
\(584\) 0 0
\(585\) −32.4968 −1.34358
\(586\) 0 0
\(587\) 29.5272 1.21872 0.609360 0.792894i \(-0.291427\pi\)
0.609360 + 0.792894i \(0.291427\pi\)
\(588\) 0 0
\(589\) −5.83369 −0.240373
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) −21.9870 −0.902898 −0.451449 0.892297i \(-0.649093\pi\)
−0.451449 + 0.892297i \(0.649093\pi\)
\(594\) 0 0
\(595\) 5.67694 0.232732
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) −39.5233 −1.61488 −0.807440 0.589950i \(-0.799148\pi\)
−0.807440 + 0.589950i \(0.799148\pi\)
\(600\) 0 0
\(601\) −3.24732 −0.132461 −0.0662305 0.997804i \(-0.521097\pi\)
−0.0662305 + 0.997804i \(0.521097\pi\)
\(602\) 0 0
\(603\) −26.8710 −1.09427
\(604\) 0 0
\(605\) 21.3136 0.866520
\(606\) 0 0
\(607\) −13.4957 −0.547773 −0.273887 0.961762i \(-0.588309\pi\)
−0.273887 + 0.961762i \(0.588309\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 31.6327 1.27972
\(612\) 0 0
\(613\) 12.3846 0.500209 0.250104 0.968219i \(-0.419535\pi\)
0.250104 + 0.968219i \(0.419535\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) −41.3042 −1.66285 −0.831423 0.555640i \(-0.812473\pi\)
−0.831423 + 0.555640i \(0.812473\pi\)
\(618\) 0 0
\(619\) −25.6149 −1.02955 −0.514775 0.857326i \(-0.672124\pi\)
−0.514775 + 0.857326i \(0.672124\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 7.66817 0.307219
\(624\) 0 0
\(625\) −17.4290 −0.697161
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 26.0693 1.03945
\(630\) 0 0
\(631\) 33.7156 1.34220 0.671099 0.741368i \(-0.265823\pi\)
0.671099 + 0.741368i \(0.265823\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) −40.3214 −1.60011
\(636\) 0 0
\(637\) 33.7580 1.33754
\(638\) 0 0
\(639\) −15.8249 −0.626024
\(640\) 0 0
\(641\) −1.97060 −0.0778342 −0.0389171 0.999242i \(-0.512391\pi\)
−0.0389171 + 0.999242i \(0.512391\pi\)
\(642\) 0 0
\(643\) −36.2746 −1.43053 −0.715266 0.698853i \(-0.753694\pi\)
−0.715266 + 0.698853i \(0.753694\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) −6.81188 −0.267803 −0.133901 0.990995i \(-0.542750\pi\)
−0.133901 + 0.990995i \(0.542750\pi\)
\(648\) 0 0
\(649\) −2.14174 −0.0840706
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 35.3988 1.38526 0.692631 0.721292i \(-0.256452\pi\)
0.692631 + 0.721292i \(0.256452\pi\)
\(654\) 0 0
\(655\) −8.15182 −0.318518
\(656\) 0 0
\(657\) 27.1527 1.05933
\(658\) 0 0
\(659\) −11.4679 −0.446725 −0.223362 0.974735i \(-0.571703\pi\)
−0.223362 + 0.974735i \(0.571703\pi\)
\(660\) 0 0
\(661\) −30.6931 −1.19382 −0.596911 0.802308i \(-0.703605\pi\)
−0.596911 + 0.802308i \(0.703605\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 1.88467 0.0730843
\(666\) 0 0
\(667\) −39.3976 −1.52548
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 0.380574 0.0146919
\(672\) 0 0
\(673\) −26.2566 −1.01212 −0.506059 0.862499i \(-0.668898\pi\)
−0.506059 + 0.862499i \(0.668898\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 24.0683 0.925021 0.462510 0.886614i \(-0.346949\pi\)
0.462510 + 0.886614i \(0.346949\pi\)
\(678\) 0 0
\(679\) 11.9434 0.458347
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) −19.2822 −0.737813 −0.368907 0.929466i \(-0.620268\pi\)
−0.368907 + 0.929466i \(0.620268\pi\)
\(684\) 0 0
\(685\) −11.7244 −0.447966
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) 67.8765 2.58589
\(690\) 0 0
\(691\) 20.9343 0.796378 0.398189 0.917303i \(-0.369639\pi\)
0.398189 + 0.917303i \(0.369639\pi\)
\(692\) 0 0
\(693\) 0.587787 0.0223282
\(694\) 0 0
\(695\) 31.0761 1.17878
\(696\) 0 0
\(697\) −22.6861 −0.859297
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) −19.8817 −0.750922 −0.375461 0.926838i \(-0.622516\pi\)
−0.375461 + 0.926838i \(0.622516\pi\)
\(702\) 0 0
\(703\) 8.65467 0.326417
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) −6.47756 −0.243614
\(708\) 0 0
\(709\) −23.8869 −0.897090 −0.448545 0.893760i \(-0.648058\pi\)
−0.448545 + 0.893760i \(0.648058\pi\)
\(710\) 0 0
\(711\) −3.00000 −0.112509
\(712\) 0 0
\(713\) −35.5333 −1.33073
\(714\) 0 0
\(715\) 2.19010 0.0819050
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) 18.9661 0.707316 0.353658 0.935375i \(-0.384938\pi\)
0.353658 + 0.935375i \(0.384938\pi\)
\(720\) 0 0
\(721\) −14.6788 −0.546669
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) 7.87594 0.292505
\(726\) 0 0
\(727\) 22.3342 0.828328 0.414164 0.910202i \(-0.364074\pi\)
0.414164 + 0.910202i \(0.364074\pi\)
\(728\) 0 0
\(729\) −27.0000 −1.00000
\(730\) 0 0
\(731\) 8.30565 0.307196
\(732\) 0 0
\(733\) 44.6152 1.64790 0.823949 0.566663i \(-0.191766\pi\)
0.823949 + 0.566663i \(0.191766\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 1.81095 0.0667071
\(738\) 0 0
\(739\) −16.1349 −0.593531 −0.296766 0.954950i \(-0.595908\pi\)
−0.296766 + 0.954950i \(0.595908\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 45.1469 1.65628 0.828139 0.560523i \(-0.189400\pi\)
0.828139 + 0.560523i \(0.189400\pi\)
\(744\) 0 0
\(745\) −13.6398 −0.499723
\(746\) 0 0
\(747\) −12.7008 −0.464697
\(748\) 0 0
\(749\) −12.8683 −0.470197
\(750\) 0 0
\(751\) 18.9280 0.690694 0.345347 0.938475i \(-0.387761\pi\)
0.345347 + 0.938475i \(0.387761\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) −28.6731 −1.04352
\(756\) 0 0
\(757\) −44.8498 −1.63010 −0.815048 0.579394i \(-0.803289\pi\)
−0.815048 + 0.579394i \(0.803289\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 2.18519 0.0792129 0.0396065 0.999215i \(-0.487390\pi\)
0.0396065 + 0.999215i \(0.487390\pi\)
\(762\) 0 0
\(763\) −3.09650 −0.112101
\(764\) 0 0
\(765\) 17.5744 0.635404
\(766\) 0 0
\(767\) 59.0013 2.13041
\(768\) 0 0
\(769\) 20.1606 0.727009 0.363504 0.931593i \(-0.381580\pi\)
0.363504 + 0.931593i \(0.381580\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) −16.4852 −0.592933 −0.296466 0.955043i \(-0.595808\pi\)
−0.296466 + 0.955043i \(0.595808\pi\)
\(774\) 0 0
\(775\) 7.10343 0.255163
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) −7.53148 −0.269843
\(780\) 0 0
\(781\) 1.06651 0.0381626
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) 13.7331 0.490155
\(786\) 0 0
\(787\) −24.5662 −0.875691 −0.437846 0.899050i \(-0.644258\pi\)
−0.437846 + 0.899050i \(0.644258\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) −19.0861 −0.678622
\(792\) 0 0
\(793\) −10.4842 −0.372303
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) −21.6913 −0.768347 −0.384173 0.923261i \(-0.625513\pi\)
−0.384173 + 0.923261i \(0.625513\pi\)
\(798\) 0 0
\(799\) −17.1071 −0.605206
\(800\) 0 0
\(801\) 23.7388 0.838768
\(802\) 0 0
\(803\) −1.82994 −0.0645771
\(804\) 0 0
\(805\) 11.4796 0.404603
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) 3.94747 0.138786 0.0693928 0.997589i \(-0.477894\pi\)
0.0693928 + 0.997589i \(0.477894\pi\)
\(810\) 0 0
\(811\) 45.2087 1.58749 0.793747 0.608248i \(-0.208128\pi\)
0.793747 + 0.608248i \(0.208128\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) −24.0973 −0.844092
\(816\) 0 0
\(817\) 2.75737 0.0964681
\(818\) 0 0
\(819\) −16.1925 −0.565813
\(820\) 0 0
\(821\) 50.2213 1.75273 0.876367 0.481643i \(-0.159960\pi\)
0.876367 + 0.481643i \(0.159960\pi\)
\(822\) 0 0
\(823\) −29.1103 −1.01472 −0.507361 0.861733i \(-0.669379\pi\)
−0.507361 + 0.861733i \(0.669379\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) 14.2082 0.494068 0.247034 0.969007i \(-0.420544\pi\)
0.247034 + 0.969007i \(0.420544\pi\)
\(828\) 0 0
\(829\) 38.9336 1.35222 0.676109 0.736801i \(-0.263665\pi\)
0.676109 + 0.736801i \(0.263665\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) −18.2565 −0.632549
\(834\) 0 0
\(835\) −46.3489 −1.60397
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) −9.01237 −0.311141 −0.155571 0.987825i \(-0.549722\pi\)
−0.155571 + 0.987825i \(0.549722\pi\)
\(840\) 0 0
\(841\) 12.8365 0.442637
\(842\) 0 0
\(843\) 0 0
\(844\) 0 0
\(845\) −35.0508 −1.20578
\(846\) 0 0
\(847\) 10.6201 0.364912
\(848\) 0 0
\(849\) 0 0
\(850\) 0 0
\(851\) 52.7161 1.80708
\(852\) 0 0
\(853\) −19.0696 −0.652931 −0.326465 0.945209i \(-0.605858\pi\)
−0.326465 + 0.945209i \(0.605858\pi\)
\(854\) 0 0
\(855\) 5.83447 0.199535
\(856\) 0 0
\(857\) −7.43388 −0.253937 −0.126968 0.991907i \(-0.540525\pi\)
−0.126968 + 0.991907i \(0.540525\pi\)
\(858\) 0 0
\(859\) −27.5873 −0.941267 −0.470634 0.882329i \(-0.655975\pi\)
−0.470634 + 0.882329i \(0.655975\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) −4.59800 −0.156518 −0.0782588 0.996933i \(-0.524936\pi\)
−0.0782588 + 0.996933i \(0.524936\pi\)
\(864\) 0 0
\(865\) 19.5198 0.663694
\(866\) 0 0
\(867\) 0 0
\(868\) 0 0
\(869\) 0.202183 0.00685858
\(870\) 0 0
\(871\) −49.8886 −1.69041
\(872\) 0 0
\(873\) 36.9739 1.25138
\(874\) 0 0
\(875\) −11.7182 −0.396148
\(876\) 0 0
\(877\) 42.4654 1.43396 0.716978 0.697096i \(-0.245525\pi\)
0.716978 + 0.697096i \(0.245525\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) −44.8572 −1.51128 −0.755640 0.654988i \(-0.772674\pi\)
−0.755640 + 0.654988i \(0.772674\pi\)
\(882\) 0 0
\(883\) −55.7323 −1.87554 −0.937770 0.347256i \(-0.887113\pi\)
−0.937770 + 0.347256i \(0.887113\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) 52.9354 1.77740 0.888699 0.458492i \(-0.151610\pi\)
0.888699 + 0.458492i \(0.151610\pi\)
\(888\) 0 0
\(889\) −20.0914 −0.673843
\(890\) 0 0
\(891\) 1.81964 0.0609604
\(892\) 0 0
\(893\) −5.67933 −0.190052
\(894\) 0 0
\(895\) 10.6722 0.356733
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) 37.7330 1.25847
\(900\) 0 0
\(901\) −36.7079 −1.22292
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) −23.7741 −0.790278
\(906\) 0 0
\(907\) −6.64552 −0.220661 −0.110330 0.993895i \(-0.535191\pi\)
−0.110330 + 0.993895i \(0.535191\pi\)
\(908\) 0 0
\(909\) −20.0530 −0.665115
\(910\) 0 0
\(911\) 22.9453 0.760213 0.380107 0.924943i \(-0.375887\pi\)
0.380107 + 0.924943i \(0.375887\pi\)
\(912\) 0 0
\(913\) 0.855958 0.0283281
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) −4.06189 −0.134136
\(918\) 0 0
\(919\) −38.1037 −1.25693 −0.628463 0.777839i \(-0.716316\pi\)
−0.628463 + 0.777839i \(0.716316\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 0 0
\(923\) −29.3805 −0.967071
\(924\) 0 0
\(925\) −10.5384 −0.346501
\(926\) 0 0
\(927\) −45.4421 −1.49251
\(928\) 0 0
\(929\) 35.0523 1.15003 0.575014 0.818143i \(-0.304996\pi\)
0.575014 + 0.818143i \(0.304996\pi\)
\(930\) 0 0
\(931\) −6.06091 −0.198638
\(932\) 0 0
\(933\) 0 0
\(934\) 0 0
\(935\) −1.18441 −0.0387345
\(936\) 0 0
\(937\) 25.5571 0.834914 0.417457 0.908697i \(-0.362921\pi\)
0.417457 + 0.908697i \(0.362921\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0 0
\(941\) 32.6856 1.06552 0.532760 0.846266i \(-0.321155\pi\)
0.532760 + 0.846266i \(0.321155\pi\)
\(942\) 0 0
\(943\) −45.8746 −1.49388
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) 10.6671 0.346635 0.173318 0.984866i \(-0.444551\pi\)
0.173318 + 0.984866i \(0.444551\pi\)
\(948\) 0 0
\(949\) 50.4117 1.63643
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) 47.5537 1.54041 0.770207 0.637794i \(-0.220153\pi\)
0.770207 + 0.637794i \(0.220153\pi\)
\(954\) 0 0
\(955\) −14.6874 −0.475273
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) −5.84204 −0.188649
\(960\) 0 0
\(961\) 3.03196 0.0978053
\(962\) 0 0
\(963\) −39.8371 −1.28373
\(964\) 0 0
\(965\) −36.2540 −1.16706
\(966\) 0 0
\(967\) 13.9357 0.448141 0.224071 0.974573i \(-0.428065\pi\)
0.224071 + 0.974573i \(0.428065\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) 14.2793 0.458245 0.229122 0.973398i \(-0.426414\pi\)
0.229122 + 0.973398i \(0.426414\pi\)
\(972\) 0 0
\(973\) 15.4846 0.496413
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) 33.0764 1.05821 0.529104 0.848557i \(-0.322528\pi\)
0.529104 + 0.848557i \(0.322528\pi\)
\(978\) 0 0
\(979\) −1.59986 −0.0511316
\(980\) 0 0
\(981\) −9.58600 −0.306057
\(982\) 0 0
\(983\) −34.6310 −1.10456 −0.552279 0.833660i \(-0.686242\pi\)
−0.552279 + 0.833660i \(0.686242\pi\)
\(984\) 0 0
\(985\) 27.4850 0.875745
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) 16.7953 0.534059
\(990\) 0 0
\(991\) 21.1870 0.673026 0.336513 0.941679i \(-0.390752\pi\)
0.336513 + 0.941679i \(0.390752\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0 0
\(995\) 25.1306 0.796694
\(996\) 0 0
\(997\) 17.2962 0.547777 0.273889 0.961761i \(-0.411690\pi\)
0.273889 + 0.961761i \(0.411690\pi\)
\(998\) 0 0
\(999\) 0 0
Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))