Properties

Label 2760.2.a.w.1.1
Level $2760$
Weight $2$
Character 2760.1
Self dual yes
Analytic conductor $22.039$
Analytic rank $0$
Dimension $5$
CM no
Inner twists $1$

Related objects

Downloads

Learn more

Newspace parameters

Level: \( N \) \(=\) \( 2760 = 2^{3} \cdot 3 \cdot 5 \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2760.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(22.0387109579\)
Analytic rank: \(0\)
Dimension: \(5\)
Coefficient field: 5.5.20087896.1
Defining polynomial: \( x^{5} - x^{4} - 21x^{3} + 5x^{2} + 84x - 4 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 2^{2} \)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Root \(0.0475116\) of defining polynomial
Character \(\chi\) \(=\) 2760.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.00000 q^{3} +1.00000 q^{5} -5.02263 q^{7} +1.00000 q^{9} +O(q^{10})\) \(q-1.00000 q^{3} +1.00000 q^{5} -5.02263 q^{7} +1.00000 q^{9} -3.71008 q^{11} -6.49408 q^{13} -1.00000 q^{15} +5.37642 q^{17} -8.39905 q^{19} +5.02263 q^{21} -1.00000 q^{23} +1.00000 q^{25} -1.00000 q^{27} +3.31255 q^{29} +7.18153 q^{31} +3.71008 q^{33} -5.02263 q^{35} -3.02263 q^{37} +6.49408 q^{39} +0.782477 q^{41} -0.0950231 q^{43} +1.00000 q^{45} +8.39905 q^{47} +18.2268 q^{49} -5.37642 q^{51} +6.82773 q^{53} -3.71008 q^{55} +8.39905 q^{57} +11.2628 q^{59} -14.6032 q^{61} -5.02263 q^{63} -6.49408 q^{65} -9.71160 q^{67} +1.00000 q^{69} +8.73271 q^{71} +3.64620 q^{73} -1.00000 q^{75} +18.6344 q^{77} +8.59395 q^{79} +1.00000 q^{81} -7.37642 q^{83} +5.37642 q^{85} -3.31255 q^{87} -6.29918 q^{89} +32.6173 q^{91} -7.18153 q^{93} -8.39905 q^{95} -5.32514 q^{97} -3.71008 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 5 q - 5 q^{3} + 5 q^{5} - 4 q^{7} + 5 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 5 q - 5 q^{3} + 5 q^{5} - 4 q^{7} + 5 q^{9} - 4 q^{11} + 4 q^{13} - 5 q^{15} + 10 q^{17} - 4 q^{19} + 4 q^{21} - 5 q^{23} + 5 q^{25} - 5 q^{27} + 10 q^{29} + 6 q^{31} + 4 q^{33} - 4 q^{35} + 6 q^{37} - 4 q^{39} + 12 q^{41} - 2 q^{43} + 5 q^{45} + 4 q^{47} + 19 q^{49} - 10 q^{51} - 4 q^{55} + 4 q^{57} + 6 q^{59} + 16 q^{61} - 4 q^{63} + 4 q^{65} - 4 q^{67} + 5 q^{69} + 8 q^{71} + 14 q^{73} - 5 q^{75} + 16 q^{77} + 18 q^{79} + 5 q^{81} - 20 q^{83} + 10 q^{85} - 10 q^{87} + 18 q^{89} + 20 q^{91} - 6 q^{93} - 4 q^{95} + 4 q^{97} - 4 q^{99}+O(q^{100}) \) Copy content Toggle raw display

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
\(3\) −1.00000 −0.577350
\(4\) 0 0
\(5\) 1.00000 0.447214
\(6\) 0 0
\(7\) −5.02263 −1.89837 −0.949187 0.314712i \(-0.898092\pi\)
−0.949187 + 0.314712i \(0.898092\pi\)
\(8\) 0 0
\(9\) 1.00000 0.333333
\(10\) 0 0
\(11\) −3.71008 −1.11863 −0.559316 0.828955i \(-0.688936\pi\)
−0.559316 + 0.828955i \(0.688936\pi\)
\(12\) 0 0
\(13\) −6.49408 −1.80113 −0.900566 0.434719i \(-0.856848\pi\)
−0.900566 + 0.434719i \(0.856848\pi\)
\(14\) 0 0
\(15\) −1.00000 −0.258199
\(16\) 0 0
\(17\) 5.37642 1.30397 0.651987 0.758230i \(-0.273936\pi\)
0.651987 + 0.758230i \(0.273936\pi\)
\(18\) 0 0
\(19\) −8.39905 −1.92687 −0.963437 0.267934i \(-0.913659\pi\)
−0.963437 + 0.267934i \(0.913659\pi\)
\(20\) 0 0
\(21\) 5.02263 1.09603
\(22\) 0 0
\(23\) −1.00000 −0.208514
\(24\) 0 0
\(25\) 1.00000 0.200000
\(26\) 0 0
\(27\) −1.00000 −0.192450
\(28\) 0 0
\(29\) 3.31255 0.615124 0.307562 0.951528i \(-0.400487\pi\)
0.307562 + 0.951528i \(0.400487\pi\)
\(30\) 0 0
\(31\) 7.18153 1.28984 0.644920 0.764250i \(-0.276891\pi\)
0.644920 + 0.764250i \(0.276891\pi\)
\(32\) 0 0
\(33\) 3.71008 0.645842
\(34\) 0 0
\(35\) −5.02263 −0.848979
\(36\) 0 0
\(37\) −3.02263 −0.496917 −0.248458 0.968643i \(-0.579924\pi\)
−0.248458 + 0.968643i \(0.579924\pi\)
\(38\) 0 0
\(39\) 6.49408 1.03988
\(40\) 0 0
\(41\) 0.782477 0.122202 0.0611012 0.998132i \(-0.480539\pi\)
0.0611012 + 0.998132i \(0.480539\pi\)
\(42\) 0 0
\(43\) −0.0950231 −0.0144909 −0.00724544 0.999974i \(-0.502306\pi\)
−0.00724544 + 0.999974i \(0.502306\pi\)
\(44\) 0 0
\(45\) 1.00000 0.149071
\(46\) 0 0
\(47\) 8.39905 1.22513 0.612564 0.790421i \(-0.290138\pi\)
0.612564 + 0.790421i \(0.290138\pi\)
\(48\) 0 0
\(49\) 18.2268 2.60383
\(50\) 0 0
\(51\) −5.37642 −0.752850
\(52\) 0 0
\(53\) 6.82773 0.937861 0.468930 0.883235i \(-0.344639\pi\)
0.468930 + 0.883235i \(0.344639\pi\)
\(54\) 0 0
\(55\) −3.71008 −0.500267
\(56\) 0 0
\(57\) 8.39905 1.11248
\(58\) 0 0
\(59\) 11.2628 1.46629 0.733144 0.680073i \(-0.238052\pi\)
0.733144 + 0.680073i \(0.238052\pi\)
\(60\) 0 0
\(61\) −14.6032 −1.86975 −0.934875 0.354978i \(-0.884488\pi\)
−0.934875 + 0.354978i \(0.884488\pi\)
\(62\) 0 0
\(63\) −5.02263 −0.632792
\(64\) 0 0
\(65\) −6.49408 −0.805491
\(66\) 0 0
\(67\) −9.71160 −1.18646 −0.593230 0.805033i \(-0.702148\pi\)
−0.593230 + 0.805033i \(0.702148\pi\)
\(68\) 0 0
\(69\) 1.00000 0.120386
\(70\) 0 0
\(71\) 8.73271 1.03638 0.518191 0.855265i \(-0.326606\pi\)
0.518191 + 0.855265i \(0.326606\pi\)
\(72\) 0 0
\(73\) 3.64620 0.426756 0.213378 0.976970i \(-0.431553\pi\)
0.213378 + 0.976970i \(0.431553\pi\)
\(74\) 0 0
\(75\) −1.00000 −0.115470
\(76\) 0 0
\(77\) 18.6344 2.12358
\(78\) 0 0
\(79\) 8.59395 0.966895 0.483447 0.875373i \(-0.339384\pi\)
0.483447 + 0.875373i \(0.339384\pi\)
\(80\) 0 0
\(81\) 1.00000 0.111111
\(82\) 0 0
\(83\) −7.37642 −0.809668 −0.404834 0.914390i \(-0.632671\pi\)
−0.404834 + 0.914390i \(0.632671\pi\)
\(84\) 0 0
\(85\) 5.37642 0.583155
\(86\) 0 0
\(87\) −3.31255 −0.355142
\(88\) 0 0
\(89\) −6.29918 −0.667712 −0.333856 0.942624i \(-0.608350\pi\)
−0.333856 + 0.942624i \(0.608350\pi\)
\(90\) 0 0
\(91\) 32.6173 3.41922
\(92\) 0 0
\(93\) −7.18153 −0.744690
\(94\) 0 0
\(95\) −8.39905 −0.861725
\(96\) 0 0
\(97\) −5.32514 −0.540686 −0.270343 0.962764i \(-0.587137\pi\)
−0.270343 + 0.962764i \(0.587137\pi\)
\(98\) 0 0
\(99\) −3.71008 −0.372877
\(100\) 0 0
\(101\) 10.0654 1.00154 0.500772 0.865579i \(-0.333049\pi\)
0.500772 + 0.865579i \(0.333049\pi\)
\(102\) 0 0
\(103\) 2.15890 0.212723 0.106361 0.994328i \(-0.466080\pi\)
0.106361 + 0.994328i \(0.466080\pi\)
\(104\) 0 0
\(105\) 5.02263 0.490158
\(106\) 0 0
\(107\) −2.00152 −0.193494 −0.0967470 0.995309i \(-0.530844\pi\)
−0.0967470 + 0.995309i \(0.530844\pi\)
\(108\) 0 0
\(109\) 12.4302 1.19060 0.595298 0.803505i \(-0.297034\pi\)
0.595298 + 0.803505i \(0.297034\pi\)
\(110\) 0 0
\(111\) 3.02263 0.286895
\(112\) 0 0
\(113\) −14.0468 −1.32141 −0.660705 0.750646i \(-0.729742\pi\)
−0.660705 + 0.750646i \(0.729742\pi\)
\(114\) 0 0
\(115\) −1.00000 −0.0932505
\(116\) 0 0
\(117\) −6.49408 −0.600377
\(118\) 0 0
\(119\) −27.0038 −2.47543
\(120\) 0 0
\(121\) 2.76470 0.251336
\(122\) 0 0
\(123\) −0.782477 −0.0705536
\(124\) 0 0
\(125\) 1.00000 0.0894427
\(126\) 0 0
\(127\) −11.9142 −1.05722 −0.528609 0.848866i \(-0.677286\pi\)
−0.528609 + 0.848866i \(0.677286\pi\)
\(128\) 0 0
\(129\) 0.0950231 0.00836632
\(130\) 0 0
\(131\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(132\) 0 0
\(133\) 42.1853 3.65793
\(134\) 0 0
\(135\) −1.00000 −0.0860663
\(136\) 0 0
\(137\) −20.2494 −1.73002 −0.865012 0.501751i \(-0.832689\pi\)
−0.865012 + 0.501751i \(0.832689\pi\)
\(138\) 0 0
\(139\) −5.61658 −0.476392 −0.238196 0.971217i \(-0.576556\pi\)
−0.238196 + 0.971217i \(0.576556\pi\)
\(140\) 0 0
\(141\) −8.39905 −0.707328
\(142\) 0 0
\(143\) 24.0935 2.01480
\(144\) 0 0
\(145\) 3.31255 0.275092
\(146\) 0 0
\(147\) −18.2268 −1.50332
\(148\) 0 0
\(149\) 0.226041 0.0185180 0.00925898 0.999957i \(-0.497053\pi\)
0.00925898 + 0.999957i \(0.497053\pi\)
\(150\) 0 0
\(151\) 10.2353 0.832937 0.416468 0.909150i \(-0.363268\pi\)
0.416468 + 0.909150i \(0.363268\pi\)
\(152\) 0 0
\(153\) 5.37642 0.434658
\(154\) 0 0
\(155\) 7.18153 0.576834
\(156\) 0 0
\(157\) 13.7755 1.09940 0.549701 0.835361i \(-0.314742\pi\)
0.549701 + 0.835361i \(0.314742\pi\)
\(158\) 0 0
\(159\) −6.82773 −0.541474
\(160\) 0 0
\(161\) 5.02263 0.395838
\(162\) 0 0
\(163\) −3.33269 −0.261036 −0.130518 0.991446i \(-0.541664\pi\)
−0.130518 + 0.991446i \(0.541664\pi\)
\(164\) 0 0
\(165\) 3.71008 0.288829
\(166\) 0 0
\(167\) 19.5014 1.50906 0.754532 0.656263i \(-0.227864\pi\)
0.754532 + 0.656263i \(0.227864\pi\)
\(168\) 0 0
\(169\) 29.1730 2.24408
\(170\) 0 0
\(171\) −8.39905 −0.642292
\(172\) 0 0
\(173\) −16.0453 −1.21990 −0.609949 0.792441i \(-0.708810\pi\)
−0.609949 + 0.792441i \(0.708810\pi\)
\(174\) 0 0
\(175\) −5.02263 −0.379675
\(176\) 0 0
\(177\) −11.2628 −0.846562
\(178\) 0 0
\(179\) 14.1730 1.05934 0.529670 0.848204i \(-0.322316\pi\)
0.529670 + 0.848204i \(0.322316\pi\)
\(180\) 0 0
\(181\) 4.03114 0.299633 0.149816 0.988714i \(-0.452132\pi\)
0.149816 + 0.988714i \(0.452132\pi\)
\(182\) 0 0
\(183\) 14.6032 1.07950
\(184\) 0 0
\(185\) −3.02263 −0.222228
\(186\) 0 0
\(187\) −19.9470 −1.45867
\(188\) 0 0
\(189\) 5.02263 0.365342
\(190\) 0 0
\(191\) 8.58910 0.621485 0.310743 0.950494i \(-0.399422\pi\)
0.310743 + 0.950494i \(0.399422\pi\)
\(192\) 0 0
\(193\) −16.8434 −1.21241 −0.606206 0.795308i \(-0.707309\pi\)
−0.606206 + 0.795308i \(0.707309\pi\)
\(194\) 0 0
\(195\) 6.49408 0.465050
\(196\) 0 0
\(197\) 0.0422192 0.00300800 0.00150400 0.999999i \(-0.499521\pi\)
0.00150400 + 0.999999i \(0.499521\pi\)
\(198\) 0 0
\(199\) 14.1589 1.00370 0.501849 0.864955i \(-0.332653\pi\)
0.501849 + 0.864955i \(0.332653\pi\)
\(200\) 0 0
\(201\) 9.71160 0.685003
\(202\) 0 0
\(203\) −16.6377 −1.16774
\(204\) 0 0
\(205\) 0.782477 0.0546506
\(206\) 0 0
\(207\) −1.00000 −0.0695048
\(208\) 0 0
\(209\) 31.1612 2.15546
\(210\) 0 0
\(211\) 13.6166 0.937404 0.468702 0.883356i \(-0.344722\pi\)
0.468702 + 0.883356i \(0.344722\pi\)
\(212\) 0 0
\(213\) −8.73271 −0.598355
\(214\) 0 0
\(215\) −0.0950231 −0.00648052
\(216\) 0 0
\(217\) −36.0701 −2.44860
\(218\) 0 0
\(219\) −3.64620 −0.246388
\(220\) 0 0
\(221\) −34.9149 −2.34863
\(222\) 0 0
\(223\) −28.3133 −1.89600 −0.947999 0.318273i \(-0.896897\pi\)
−0.947999 + 0.318273i \(0.896897\pi\)
\(224\) 0 0
\(225\) 1.00000 0.0666667
\(226\) 0 0
\(227\) 12.9118 0.856983 0.428492 0.903546i \(-0.359045\pi\)
0.428492 + 0.903546i \(0.359045\pi\)
\(228\) 0 0
\(229\) 18.6814 1.23450 0.617252 0.786766i \(-0.288246\pi\)
0.617252 + 0.786766i \(0.288246\pi\)
\(230\) 0 0
\(231\) −18.6344 −1.22605
\(232\) 0 0
\(233\) −12.2353 −0.801561 −0.400781 0.916174i \(-0.631261\pi\)
−0.400781 + 0.916174i \(0.631261\pi\)
\(234\) 0 0
\(235\) 8.39905 0.547894
\(236\) 0 0
\(237\) −8.59395 −0.558237
\(238\) 0 0
\(239\) 14.2977 0.924839 0.462419 0.886661i \(-0.346981\pi\)
0.462419 + 0.886661i \(0.346981\pi\)
\(240\) 0 0
\(241\) 4.22604 0.272223 0.136112 0.990694i \(-0.456539\pi\)
0.136112 + 0.990694i \(0.456539\pi\)
\(242\) 0 0
\(243\) −1.00000 −0.0641500
\(244\) 0 0
\(245\) 18.2268 1.16447
\(246\) 0 0
\(247\) 54.5441 3.47056
\(248\) 0 0
\(249\) 7.37642 0.467462
\(250\) 0 0
\(251\) −15.4015 −0.972136 −0.486068 0.873921i \(-0.661569\pi\)
−0.486068 + 0.873921i \(0.661569\pi\)
\(252\) 0 0
\(253\) 3.71008 0.233251
\(254\) 0 0
\(255\) −5.37642 −0.336685
\(256\) 0 0
\(257\) 19.7367 1.23114 0.615571 0.788081i \(-0.288925\pi\)
0.615571 + 0.788081i \(0.288925\pi\)
\(258\) 0 0
\(259\) 15.1815 0.943334
\(260\) 0 0
\(261\) 3.31255 0.205041
\(262\) 0 0
\(263\) 9.81588 0.605273 0.302637 0.953106i \(-0.402133\pi\)
0.302637 + 0.953106i \(0.402133\pi\)
\(264\) 0 0
\(265\) 6.82773 0.419424
\(266\) 0 0
\(267\) 6.29918 0.385503
\(268\) 0 0
\(269\) −6.92275 −0.422088 −0.211044 0.977477i \(-0.567686\pi\)
−0.211044 + 0.977477i \(0.567686\pi\)
\(270\) 0 0
\(271\) −9.22678 −0.560487 −0.280244 0.959929i \(-0.590415\pi\)
−0.280244 + 0.959929i \(0.590415\pi\)
\(272\) 0 0
\(273\) −32.6173 −1.97409
\(274\) 0 0
\(275\) −3.71008 −0.223726
\(276\) 0 0
\(277\) −8.33032 −0.500521 −0.250260 0.968179i \(-0.580516\pi\)
−0.250260 + 0.968179i \(0.580516\pi\)
\(278\) 0 0
\(279\) 7.18153 0.429947
\(280\) 0 0
\(281\) −16.1451 −0.963138 −0.481569 0.876408i \(-0.659933\pi\)
−0.481569 + 0.876408i \(0.659933\pi\)
\(282\) 0 0
\(283\) 28.5550 1.69742 0.848708 0.528862i \(-0.177381\pi\)
0.848708 + 0.528862i \(0.177381\pi\)
\(284\) 0 0
\(285\) 8.39905 0.497517
\(286\) 0 0
\(287\) −3.93009 −0.231986
\(288\) 0 0
\(289\) 11.9059 0.700350
\(290\) 0 0
\(291\) 5.32514 0.312165
\(292\) 0 0
\(293\) 25.5836 1.49461 0.747305 0.664481i \(-0.231347\pi\)
0.747305 + 0.664481i \(0.231347\pi\)
\(294\) 0 0
\(295\) 11.2628 0.655744
\(296\) 0 0
\(297\) 3.71008 0.215281
\(298\) 0 0
\(299\) 6.49408 0.375562
\(300\) 0 0
\(301\) 0.477266 0.0275091
\(302\) 0 0
\(303\) −10.0654 −0.578242
\(304\) 0 0
\(305\) −14.6032 −0.836177
\(306\) 0 0
\(307\) −4.58910 −0.261914 −0.130957 0.991388i \(-0.541805\pi\)
−0.130957 + 0.991388i \(0.541805\pi\)
\(308\) 0 0
\(309\) −2.15890 −0.122816
\(310\) 0 0
\(311\) −23.8360 −1.35162 −0.675808 0.737077i \(-0.736205\pi\)
−0.675808 + 0.737077i \(0.736205\pi\)
\(312\) 0 0
\(313\) 26.0747 1.47383 0.736913 0.675987i \(-0.236283\pi\)
0.736913 + 0.675987i \(0.236283\pi\)
\(314\) 0 0
\(315\) −5.02263 −0.282993
\(316\) 0 0
\(317\) 15.7367 0.883862 0.441931 0.897049i \(-0.354294\pi\)
0.441931 + 0.897049i \(0.354294\pi\)
\(318\) 0 0
\(319\) −12.2898 −0.688098
\(320\) 0 0
\(321\) 2.00152 0.111714
\(322\) 0 0
\(323\) −45.1569 −2.51260
\(324\) 0 0
\(325\) −6.49408 −0.360226
\(326\) 0 0
\(327\) −12.4302 −0.687391
\(328\) 0 0
\(329\) −42.1853 −2.32575
\(330\) 0 0
\(331\) −34.3427 −1.88764 −0.943822 0.330453i \(-0.892799\pi\)
−0.943822 + 0.330453i \(0.892799\pi\)
\(332\) 0 0
\(333\) −3.02263 −0.165639
\(334\) 0 0
\(335\) −9.71160 −0.530601
\(336\) 0 0
\(337\) 9.23767 0.503208 0.251604 0.967830i \(-0.419042\pi\)
0.251604 + 0.967830i \(0.419042\pi\)
\(338\) 0 0
\(339\) 14.0468 0.762916
\(340\) 0 0
\(341\) −26.6441 −1.44286
\(342\) 0 0
\(343\) −56.3879 −3.04466
\(344\) 0 0
\(345\) 1.00000 0.0538382
\(346\) 0 0
\(347\) 16.4803 0.884709 0.442354 0.896840i \(-0.354143\pi\)
0.442354 + 0.896840i \(0.354143\pi\)
\(348\) 0 0
\(349\) 3.48882 0.186752 0.0933761 0.995631i \(-0.470234\pi\)
0.0933761 + 0.995631i \(0.470234\pi\)
\(350\) 0 0
\(351\) 6.49408 0.346628
\(352\) 0 0
\(353\) 29.7503 1.58345 0.791723 0.610880i \(-0.209184\pi\)
0.791723 + 0.610880i \(0.209184\pi\)
\(354\) 0 0
\(355\) 8.73271 0.463484
\(356\) 0 0
\(357\) 27.0038 1.42919
\(358\) 0 0
\(359\) 11.5014 0.607021 0.303511 0.952828i \(-0.401841\pi\)
0.303511 + 0.952828i \(0.401841\pi\)
\(360\) 0 0
\(361\) 51.5441 2.71285
\(362\) 0 0
\(363\) −2.76470 −0.145109
\(364\) 0 0
\(365\) 3.64620 0.190851
\(366\) 0 0
\(367\) 2.58758 0.135071 0.0675353 0.997717i \(-0.478486\pi\)
0.0675353 + 0.997717i \(0.478486\pi\)
\(368\) 0 0
\(369\) 0.782477 0.0407341
\(370\) 0 0
\(371\) −34.2931 −1.78041
\(372\) 0 0
\(373\) −12.6392 −0.654433 −0.327217 0.944949i \(-0.606111\pi\)
−0.327217 + 0.944949i \(0.606111\pi\)
\(374\) 0 0
\(375\) −1.00000 −0.0516398
\(376\) 0 0
\(377\) −21.5119 −1.10792
\(378\) 0 0
\(379\) 13.8858 0.713265 0.356633 0.934245i \(-0.383925\pi\)
0.356633 + 0.934245i \(0.383925\pi\)
\(380\) 0 0
\(381\) 11.9142 0.610385
\(382\) 0 0
\(383\) 6.20264 0.316940 0.158470 0.987364i \(-0.449344\pi\)
0.158470 + 0.987364i \(0.449344\pi\)
\(384\) 0 0
\(385\) 18.6344 0.949695
\(386\) 0 0
\(387\) −0.0950231 −0.00483030
\(388\) 0 0
\(389\) 0.147827 0.00749513 0.00374756 0.999993i \(-0.498807\pi\)
0.00374756 + 0.999993i \(0.498807\pi\)
\(390\) 0 0
\(391\) −5.37642 −0.271897
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) 8.59395 0.432408
\(396\) 0 0
\(397\) 29.0259 1.45677 0.728383 0.685170i \(-0.240272\pi\)
0.728383 + 0.685170i \(0.240272\pi\)
\(398\) 0 0
\(399\) −42.1853 −2.11191
\(400\) 0 0
\(401\) 17.2145 0.859652 0.429826 0.902912i \(-0.358575\pi\)
0.429826 + 0.902912i \(0.358575\pi\)
\(402\) 0 0
\(403\) −46.6374 −2.32317
\(404\) 0 0
\(405\) 1.00000 0.0496904
\(406\) 0 0
\(407\) 11.2142 0.555867
\(408\) 0 0
\(409\) −23.8348 −1.17856 −0.589279 0.807930i \(-0.700588\pi\)
−0.589279 + 0.807930i \(0.700588\pi\)
\(410\) 0 0
\(411\) 20.2494 0.998830
\(412\) 0 0
\(413\) −56.5687 −2.78357
\(414\) 0 0
\(415\) −7.37642 −0.362094
\(416\) 0 0
\(417\) 5.61658 0.275045
\(418\) 0 0
\(419\) 7.99064 0.390368 0.195184 0.980767i \(-0.437470\pi\)
0.195184 + 0.980767i \(0.437470\pi\)
\(420\) 0 0
\(421\) −11.5326 −0.562062 −0.281031 0.959699i \(-0.590676\pi\)
−0.281031 + 0.959699i \(0.590676\pi\)
\(422\) 0 0
\(423\) 8.39905 0.408376
\(424\) 0 0
\(425\) 5.37642 0.260795
\(426\) 0 0
\(427\) 73.3465 3.54948
\(428\) 0 0
\(429\) −24.0935 −1.16325
\(430\) 0 0
\(431\) −26.3661 −1.27001 −0.635005 0.772508i \(-0.719002\pi\)
−0.635005 + 0.772508i \(0.719002\pi\)
\(432\) 0 0
\(433\) 2.24618 0.107945 0.0539723 0.998542i \(-0.482812\pi\)
0.0539723 + 0.998542i \(0.482812\pi\)
\(434\) 0 0
\(435\) −3.31255 −0.158824
\(436\) 0 0
\(437\) 8.39905 0.401781
\(438\) 0 0
\(439\) −15.3512 −0.732673 −0.366337 0.930482i \(-0.619388\pi\)
−0.366337 + 0.930482i \(0.619388\pi\)
\(440\) 0 0
\(441\) 18.2268 0.867942
\(442\) 0 0
\(443\) −26.0948 −1.23980 −0.619901 0.784680i \(-0.712827\pi\)
−0.619901 + 0.784680i \(0.712827\pi\)
\(444\) 0 0
\(445\) −6.29918 −0.298610
\(446\) 0 0
\(447\) −0.226041 −0.0106914
\(448\) 0 0
\(449\) 5.67109 0.267635 0.133818 0.991006i \(-0.457276\pi\)
0.133818 + 0.991006i \(0.457276\pi\)
\(450\) 0 0
\(451\) −2.90305 −0.136699
\(452\) 0 0
\(453\) −10.2353 −0.480896
\(454\) 0 0
\(455\) 32.6173 1.52912
\(456\) 0 0
\(457\) 30.2024 1.41281 0.706405 0.707808i \(-0.250316\pi\)
0.706405 + 0.707808i \(0.250316\pi\)
\(458\) 0 0
\(459\) −5.37642 −0.250950
\(460\) 0 0
\(461\) −27.0526 −1.25996 −0.629982 0.776609i \(-0.716938\pi\)
−0.629982 + 0.776609i \(0.716938\pi\)
\(462\) 0 0
\(463\) 10.6671 0.495742 0.247871 0.968793i \(-0.420269\pi\)
0.247871 + 0.968793i \(0.420269\pi\)
\(464\) 0 0
\(465\) −7.18153 −0.333035
\(466\) 0 0
\(467\) −20.9696 −0.970357 −0.485179 0.874415i \(-0.661245\pi\)
−0.485179 + 0.874415i \(0.661245\pi\)
\(468\) 0 0
\(469\) 48.7777 2.25235
\(470\) 0 0
\(471\) −13.7755 −0.634740
\(472\) 0 0
\(473\) 0.352543 0.0162100
\(474\) 0 0
\(475\) −8.39905 −0.385375
\(476\) 0 0
\(477\) 6.82773 0.312620
\(478\) 0 0
\(479\) −18.7218 −0.855422 −0.427711 0.903916i \(-0.640680\pi\)
−0.427711 + 0.903916i \(0.640680\pi\)
\(480\) 0 0
\(481\) 19.6292 0.895013
\(482\) 0 0
\(483\) −5.02263 −0.228537
\(484\) 0 0
\(485\) −5.32514 −0.241802
\(486\) 0 0
\(487\) −10.5363 −0.477445 −0.238723 0.971088i \(-0.576729\pi\)
−0.238723 + 0.971088i \(0.576729\pi\)
\(488\) 0 0
\(489\) 3.33269 0.150709
\(490\) 0 0
\(491\) 7.77063 0.350683 0.175342 0.984508i \(-0.443897\pi\)
0.175342 + 0.984508i \(0.443897\pi\)
\(492\) 0 0
\(493\) 17.8097 0.802107
\(494\) 0 0
\(495\) −3.71008 −0.166756
\(496\) 0 0
\(497\) −43.8611 −1.96744
\(498\) 0 0
\(499\) 20.8370 0.932792 0.466396 0.884576i \(-0.345552\pi\)
0.466396 + 0.884576i \(0.345552\pi\)
\(500\) 0 0
\(501\) −19.5014 −0.871259
\(502\) 0 0
\(503\) −16.6377 −0.741838 −0.370919 0.928665i \(-0.620957\pi\)
−0.370919 + 0.928665i \(0.620957\pi\)
\(504\) 0 0
\(505\) 10.0654 0.447904
\(506\) 0 0
\(507\) −29.1730 −1.29562
\(508\) 0 0
\(509\) 25.9235 1.14904 0.574519 0.818491i \(-0.305189\pi\)
0.574519 + 0.818491i \(0.305189\pi\)
\(510\) 0 0
\(511\) −18.3135 −0.810142
\(512\) 0 0
\(513\) 8.39905 0.370827
\(514\) 0 0
\(515\) 2.15890 0.0951326
\(516\) 0 0
\(517\) −31.1612 −1.37047
\(518\) 0 0
\(519\) 16.0453 0.704308
\(520\) 0 0
\(521\) −8.91501 −0.390574 −0.195287 0.980746i \(-0.562564\pi\)
−0.195287 + 0.980746i \(0.562564\pi\)
\(522\) 0 0
\(523\) −14.6481 −0.640518 −0.320259 0.947330i \(-0.603770\pi\)
−0.320259 + 0.947330i \(0.603770\pi\)
\(524\) 0 0
\(525\) 5.02263 0.219205
\(526\) 0 0
\(527\) 38.6110 1.68192
\(528\) 0 0
\(529\) 1.00000 0.0434783
\(530\) 0 0
\(531\) 11.2628 0.488763
\(532\) 0 0
\(533\) −5.08146 −0.220103
\(534\) 0 0
\(535\) −2.00152 −0.0865331
\(536\) 0 0
\(537\) −14.1730 −0.611611
\(538\) 0 0
\(539\) −67.6228 −2.91272
\(540\) 0 0
\(541\) −19.0571 −0.819329 −0.409664 0.912236i \(-0.634354\pi\)
−0.409664 + 0.912236i \(0.634354\pi\)
\(542\) 0 0
\(543\) −4.03114 −0.172993
\(544\) 0 0
\(545\) 12.4302 0.532451
\(546\) 0 0
\(547\) 2.84032 0.121443 0.0607217 0.998155i \(-0.480660\pi\)
0.0607217 + 0.998155i \(0.480660\pi\)
\(548\) 0 0
\(549\) −14.6032 −0.623250
\(550\) 0 0
\(551\) −27.8222 −1.18527
\(552\) 0 0
\(553\) −43.1642 −1.83553
\(554\) 0 0
\(555\) 3.02263 0.128303
\(556\) 0 0
\(557\) 35.1365 1.48878 0.744391 0.667744i \(-0.232740\pi\)
0.744391 + 0.667744i \(0.232740\pi\)
\(558\) 0 0
\(559\) 0.617087 0.0261000
\(560\) 0 0
\(561\) 19.9470 0.842162
\(562\) 0 0
\(563\) 4.96960 0.209444 0.104722 0.994502i \(-0.466605\pi\)
0.104722 + 0.994502i \(0.466605\pi\)
\(564\) 0 0
\(565\) −14.0468 −0.590952
\(566\) 0 0
\(567\) −5.02263 −0.210931
\(568\) 0 0
\(569\) −34.6769 −1.45373 −0.726866 0.686780i \(-0.759024\pi\)
−0.726866 + 0.686780i \(0.759024\pi\)
\(570\) 0 0
\(571\) −11.2514 −0.470858 −0.235429 0.971892i \(-0.575650\pi\)
−0.235429 + 0.971892i \(0.575650\pi\)
\(572\) 0 0
\(573\) −8.58910 −0.358815
\(574\) 0 0
\(575\) −1.00000 −0.0417029
\(576\) 0 0
\(577\) −14.2872 −0.594785 −0.297392 0.954755i \(-0.596117\pi\)
−0.297392 + 0.954755i \(0.596117\pi\)
\(578\) 0 0
\(579\) 16.8434 0.699986
\(580\) 0 0
\(581\) 37.0490 1.53705
\(582\) 0 0
\(583\) −25.3314 −1.04912
\(584\) 0 0
\(585\) −6.49408 −0.268497
\(586\) 0 0
\(587\) 28.8856 1.19224 0.596118 0.802897i \(-0.296709\pi\)
0.596118 + 0.802897i \(0.296709\pi\)
\(588\) 0 0
\(589\) −60.3180 −2.48536
\(590\) 0 0
\(591\) −0.0422192 −0.00173667
\(592\) 0 0
\(593\) −37.6225 −1.54497 −0.772486 0.635032i \(-0.780987\pi\)
−0.772486 + 0.635032i \(0.780987\pi\)
\(594\) 0 0
\(595\) −27.0038 −1.10705
\(596\) 0 0
\(597\) −14.1589 −0.579485
\(598\) 0 0
\(599\) 26.7483 1.09291 0.546454 0.837489i \(-0.315977\pi\)
0.546454 + 0.837489i \(0.315977\pi\)
\(600\) 0 0
\(601\) 21.4621 0.875457 0.437728 0.899107i \(-0.355783\pi\)
0.437728 + 0.899107i \(0.355783\pi\)
\(602\) 0 0
\(603\) −9.71160 −0.395487
\(604\) 0 0
\(605\) 2.76470 0.112401
\(606\) 0 0
\(607\) 25.1644 1.02139 0.510696 0.859761i \(-0.329388\pi\)
0.510696 + 0.859761i \(0.329388\pi\)
\(608\) 0 0
\(609\) 16.6377 0.674193
\(610\) 0 0
\(611\) −54.5441 −2.20662
\(612\) 0 0
\(613\) −9.62432 −0.388723 −0.194361 0.980930i \(-0.562263\pi\)
−0.194361 + 0.980930i \(0.562263\pi\)
\(614\) 0 0
\(615\) −0.782477 −0.0315525
\(616\) 0 0
\(617\) −30.2368 −1.21729 −0.608644 0.793443i \(-0.708286\pi\)
−0.608644 + 0.793443i \(0.708286\pi\)
\(618\) 0 0
\(619\) −22.6503 −0.910391 −0.455196 0.890391i \(-0.650431\pi\)
−0.455196 + 0.890391i \(0.650431\pi\)
\(620\) 0 0
\(621\) 1.00000 0.0401286
\(622\) 0 0
\(623\) 31.6384 1.26757
\(624\) 0 0
\(625\) 1.00000 0.0400000
\(626\) 0 0
\(627\) −31.1612 −1.24446
\(628\) 0 0
\(629\) −16.2509 −0.647967
\(630\) 0 0
\(631\) 39.3188 1.56526 0.782629 0.622489i \(-0.213878\pi\)
0.782629 + 0.622489i \(0.213878\pi\)
\(632\) 0 0
\(633\) −13.6166 −0.541210
\(634\) 0 0
\(635\) −11.9142 −0.472802
\(636\) 0 0
\(637\) −118.366 −4.68984
\(638\) 0 0
\(639\) 8.73271 0.345461
\(640\) 0 0
\(641\) −15.9826 −0.631276 −0.315638 0.948880i \(-0.602219\pi\)
−0.315638 + 0.948880i \(0.602219\pi\)
\(642\) 0 0
\(643\) 3.36706 0.132784 0.0663919 0.997794i \(-0.478851\pi\)
0.0663919 + 0.997794i \(0.478851\pi\)
\(644\) 0 0
\(645\) 0.0950231 0.00374153
\(646\) 0 0
\(647\) 13.5839 0.534039 0.267019 0.963691i \(-0.413961\pi\)
0.267019 + 0.963691i \(0.413961\pi\)
\(648\) 0 0
\(649\) −41.7858 −1.64024
\(650\) 0 0
\(651\) 36.0701 1.41370
\(652\) 0 0
\(653\) −24.3754 −0.953881 −0.476941 0.878936i \(-0.658254\pi\)
−0.476941 + 0.878936i \(0.658254\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 0 0
\(657\) 3.64620 0.142252
\(658\) 0 0
\(659\) 41.9766 1.63518 0.817589 0.575803i \(-0.195310\pi\)
0.817589 + 0.575803i \(0.195310\pi\)
\(660\) 0 0
\(661\) −39.8004 −1.54805 −0.774027 0.633152i \(-0.781761\pi\)
−0.774027 + 0.633152i \(0.781761\pi\)
\(662\) 0 0
\(663\) 34.9149 1.35598
\(664\) 0 0
\(665\) 42.1853 1.63588
\(666\) 0 0
\(667\) −3.31255 −0.128262
\(668\) 0 0
\(669\) 28.3133 1.09465
\(670\) 0 0
\(671\) 54.1791 2.09156
\(672\) 0 0
\(673\) 1.60095 0.0617120 0.0308560 0.999524i \(-0.490177\pi\)
0.0308560 + 0.999524i \(0.490177\pi\)
\(674\) 0 0
\(675\) −1.00000 −0.0384900
\(676\) 0 0
\(677\) 8.52044 0.327467 0.163734 0.986505i \(-0.447646\pi\)
0.163734 + 0.986505i \(0.447646\pi\)
\(678\) 0 0
\(679\) 26.7462 1.02642
\(680\) 0 0
\(681\) −12.9118 −0.494779
\(682\) 0 0
\(683\) −41.7050 −1.59580 −0.797899 0.602791i \(-0.794055\pi\)
−0.797899 + 0.602791i \(0.794055\pi\)
\(684\) 0 0
\(685\) −20.2494 −0.773690
\(686\) 0 0
\(687\) −18.6814 −0.712741
\(688\) 0 0
\(689\) −44.3398 −1.68921
\(690\) 0 0
\(691\) −6.01703 −0.228899 −0.114449 0.993429i \(-0.536510\pi\)
−0.114449 + 0.993429i \(0.536510\pi\)
\(692\) 0 0
\(693\) 18.6344 0.707861
\(694\) 0 0
\(695\) −5.61658 −0.213049
\(696\) 0 0
\(697\) 4.20693 0.159349
\(698\) 0 0
\(699\) 12.2353 0.462782
\(700\) 0 0
\(701\) −9.51347 −0.359319 −0.179659 0.983729i \(-0.557500\pi\)
−0.179659 + 0.983729i \(0.557500\pi\)
\(702\) 0 0
\(703\) 25.3872 0.957496
\(704\) 0 0
\(705\) −8.39905 −0.316327
\(706\) 0 0
\(707\) −50.5547 −1.90131
\(708\) 0 0
\(709\) 27.8187 1.04475 0.522376 0.852715i \(-0.325046\pi\)
0.522376 + 0.852715i \(0.325046\pi\)
\(710\) 0 0
\(711\) 8.59395 0.322298
\(712\) 0 0
\(713\) −7.18153 −0.268950
\(714\) 0 0
\(715\) 24.0935 0.901047
\(716\) 0 0
\(717\) −14.2977 −0.533956
\(718\) 0 0
\(719\) 38.1729 1.42361 0.711805 0.702377i \(-0.247878\pi\)
0.711805 + 0.702377i \(0.247878\pi\)
\(720\) 0 0
\(721\) −10.8434 −0.403828
\(722\) 0 0
\(723\) −4.22604 −0.157168
\(724\) 0 0
\(725\) 3.31255 0.123025
\(726\) 0 0
\(727\) −44.3738 −1.64573 −0.822867 0.568234i \(-0.807627\pi\)
−0.822867 + 0.568234i \(0.807627\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) 0 0
\(731\) −0.510885 −0.0188957
\(732\) 0 0
\(733\) 38.5639 1.42439 0.712195 0.701982i \(-0.247701\pi\)
0.712195 + 0.701982i \(0.247701\pi\)
\(734\) 0 0
\(735\) −18.2268 −0.672305
\(736\) 0 0
\(737\) 36.0308 1.32721
\(738\) 0 0
\(739\) −32.9275 −1.21126 −0.605629 0.795747i \(-0.707078\pi\)
−0.605629 + 0.795747i \(0.707078\pi\)
\(740\) 0 0
\(741\) −54.5441 −2.00373
\(742\) 0 0
\(743\) 5.09739 0.187005 0.0935025 0.995619i \(-0.470194\pi\)
0.0935025 + 0.995619i \(0.470194\pi\)
\(744\) 0 0
\(745\) 0.226041 0.00828149
\(746\) 0 0
\(747\) −7.37642 −0.269889
\(748\) 0 0
\(749\) 10.0529 0.367324
\(750\) 0 0
\(751\) −11.9611 −0.436466 −0.218233 0.975897i \(-0.570029\pi\)
−0.218233 + 0.975897i \(0.570029\pi\)
\(752\) 0 0
\(753\) 15.4015 0.561263
\(754\) 0 0
\(755\) 10.2353 0.372501
\(756\) 0 0
\(757\) −9.87805 −0.359024 −0.179512 0.983756i \(-0.557452\pi\)
−0.179512 + 0.983756i \(0.557452\pi\)
\(758\) 0 0
\(759\) −3.71008 −0.134667
\(760\) 0 0
\(761\) 31.9064 1.15661 0.578303 0.815822i \(-0.303715\pi\)
0.578303 + 0.815822i \(0.303715\pi\)
\(762\) 0 0
\(763\) −62.4322 −2.26020
\(764\) 0 0
\(765\) 5.37642 0.194385
\(766\) 0 0
\(767\) −73.1413 −2.64098
\(768\) 0 0
\(769\) −8.75907 −0.315860 −0.157930 0.987450i \(-0.550482\pi\)
−0.157930 + 0.987450i \(0.550482\pi\)
\(770\) 0 0
\(771\) −19.7367 −0.710800
\(772\) 0 0
\(773\) −10.1997 −0.366859 −0.183430 0.983033i \(-0.558720\pi\)
−0.183430 + 0.983033i \(0.558720\pi\)
\(774\) 0 0
\(775\) 7.18153 0.257968
\(776\) 0 0
\(777\) −15.1815 −0.544634
\(778\) 0 0
\(779\) −6.57206 −0.235469
\(780\) 0 0
\(781\) −32.3991 −1.15933
\(782\) 0 0
\(783\) −3.31255 −0.118381
\(784\) 0 0
\(785\) 13.7755 0.491668
\(786\) 0 0
\(787\) 23.4576 0.836172 0.418086 0.908407i \(-0.362701\pi\)
0.418086 + 0.908407i \(0.362701\pi\)
\(788\) 0 0
\(789\) −9.81588 −0.349455
\(790\) 0 0
\(791\) 70.5517 2.50853
\(792\) 0 0
\(793\) 94.8343 3.36767
\(794\) 0 0
\(795\) −6.82773 −0.242155
\(796\) 0 0
\(797\) 48.5265 1.71890 0.859449 0.511222i \(-0.170807\pi\)
0.859449 + 0.511222i \(0.170807\pi\)
\(798\) 0 0
\(799\) 45.1569 1.59754
\(800\) 0 0
\(801\) −6.29918 −0.222571
\(802\) 0 0
\(803\) −13.5277 −0.477382
\(804\) 0 0
\(805\) 5.02263 0.177024
\(806\) 0 0
\(807\) 6.92275 0.243692
\(808\) 0 0
\(809\) 32.1619 1.13075 0.565376 0.824833i \(-0.308731\pi\)
0.565376 + 0.824833i \(0.308731\pi\)
\(810\) 0 0
\(811\) 22.2522 0.781380 0.390690 0.920522i \(-0.372236\pi\)
0.390690 + 0.920522i \(0.372236\pi\)
\(812\) 0 0
\(813\) 9.22678 0.323597
\(814\) 0 0
\(815\) −3.33269 −0.116739
\(816\) 0 0
\(817\) 0.798104 0.0279221
\(818\) 0 0
\(819\) 32.6173 1.13974
\(820\) 0 0
\(821\) 2.10472 0.0734553 0.0367277 0.999325i \(-0.488307\pi\)
0.0367277 + 0.999325i \(0.488307\pi\)
\(822\) 0 0
\(823\) −12.1922 −0.424993 −0.212497 0.977162i \(-0.568159\pi\)
−0.212497 + 0.977162i \(0.568159\pi\)
\(824\) 0 0
\(825\) 3.71008 0.129168
\(826\) 0 0
\(827\) 11.9593 0.415866 0.207933 0.978143i \(-0.433326\pi\)
0.207933 + 0.978143i \(0.433326\pi\)
\(828\) 0 0
\(829\) −2.71590 −0.0943271 −0.0471635 0.998887i \(-0.515018\pi\)
−0.0471635 + 0.998887i \(0.515018\pi\)
\(830\) 0 0
\(831\) 8.33032 0.288976
\(832\) 0 0
\(833\) 97.9949 3.39532
\(834\) 0 0
\(835\) 19.5014 0.674874
\(836\) 0 0
\(837\) −7.18153 −0.248230
\(838\) 0 0
\(839\) 29.9457 1.03384 0.516920 0.856033i \(-0.327078\pi\)
0.516920 + 0.856033i \(0.327078\pi\)
\(840\) 0 0
\(841\) −18.0270 −0.621622
\(842\) 0 0
\(843\) 16.1451 0.556068
\(844\) 0 0
\(845\) 29.1730 1.00358
\(846\) 0 0
\(847\) −13.8861 −0.477130
\(848\) 0 0
\(849\) −28.5550 −0.980004
\(850\) 0 0
\(851\) 3.02263 0.103614
\(852\) 0 0
\(853\) 7.02437 0.240510 0.120255 0.992743i \(-0.461629\pi\)
0.120255 + 0.992743i \(0.461629\pi\)
\(854\) 0 0
\(855\) −8.39905 −0.287242
\(856\) 0 0
\(857\) −3.56799 −0.121880 −0.0609401 0.998141i \(-0.519410\pi\)
−0.0609401 + 0.998141i \(0.519410\pi\)
\(858\) 0 0
\(859\) 22.5711 0.770116 0.385058 0.922892i \(-0.374181\pi\)
0.385058 + 0.922892i \(0.374181\pi\)
\(860\) 0 0
\(861\) 3.93009 0.133937
\(862\) 0 0
\(863\) −19.2607 −0.655642 −0.327821 0.944740i \(-0.606314\pi\)
−0.327821 + 0.944740i \(0.606314\pi\)
\(864\) 0 0
\(865\) −16.0453 −0.545555
\(866\) 0 0
\(867\) −11.9059 −0.404347
\(868\) 0 0
\(869\) −31.8842 −1.08160
\(870\) 0 0
\(871\) 63.0678 2.13697
\(872\) 0 0
\(873\) −5.32514 −0.180229
\(874\) 0 0
\(875\) −5.02263 −0.169796
\(876\) 0 0
\(877\) 26.4441 0.892953 0.446477 0.894795i \(-0.352679\pi\)
0.446477 + 0.894795i \(0.352679\pi\)
\(878\) 0 0
\(879\) −25.5836 −0.862914
\(880\) 0 0
\(881\) 27.2630 0.918513 0.459256 0.888304i \(-0.348116\pi\)
0.459256 + 0.888304i \(0.348116\pi\)
\(882\) 0 0
\(883\) 25.3469 0.852992 0.426496 0.904490i \(-0.359748\pi\)
0.426496 + 0.904490i \(0.359748\pi\)
\(884\) 0 0
\(885\) −11.2628 −0.378594
\(886\) 0 0
\(887\) 48.1308 1.61607 0.808037 0.589132i \(-0.200530\pi\)
0.808037 + 0.589132i \(0.200530\pi\)
\(888\) 0 0
\(889\) 59.8408 2.00699
\(890\) 0 0
\(891\) −3.71008 −0.124292
\(892\) 0 0
\(893\) −70.5441 −2.36067
\(894\) 0 0
\(895\) 14.1730 0.473752
\(896\) 0 0
\(897\) −6.49408 −0.216831
\(898\) 0 0
\(899\) 23.7891 0.793412
\(900\) 0 0
\(901\) 36.7088 1.22295
\(902\) 0 0
\(903\) −0.477266 −0.0158824
\(904\) 0 0
\(905\) 4.03114 0.134000
\(906\) 0 0
\(907\) 18.4071 0.611199 0.305599 0.952160i \(-0.401143\pi\)
0.305599 + 0.952160i \(0.401143\pi\)
\(908\) 0 0
\(909\) 10.0654 0.333848
\(910\) 0 0
\(911\) 40.5984 1.34508 0.672542 0.740059i \(-0.265203\pi\)
0.672542 + 0.740059i \(0.265203\pi\)
\(912\) 0 0
\(913\) 27.3671 0.905720
\(914\) 0 0
\(915\) 14.6032 0.482767
\(916\) 0 0
\(917\) 0 0
\(918\) 0 0
\(919\) 25.5485 0.842767 0.421383 0.906883i \(-0.361545\pi\)
0.421383 + 0.906883i \(0.361545\pi\)
\(920\) 0 0
\(921\) 4.58910 0.151216
\(922\) 0 0
\(923\) −56.7109 −1.86666
\(924\) 0 0
\(925\) −3.02263 −0.0993834
\(926\) 0 0
\(927\) 2.15890 0.0709076
\(928\) 0 0
\(929\) 18.7588 0.615456 0.307728 0.951474i \(-0.400431\pi\)
0.307728 + 0.951474i \(0.400431\pi\)
\(930\) 0 0
\(931\) −153.088 −5.01725
\(932\) 0 0
\(933\) 23.8360 0.780356
\(934\) 0 0
\(935\) −19.9470 −0.652336
\(936\) 0 0
\(937\) 10.4697 0.342031 0.171015 0.985268i \(-0.445295\pi\)
0.171015 + 0.985268i \(0.445295\pi\)
\(938\) 0 0
\(939\) −26.0747 −0.850914
\(940\) 0 0
\(941\) −15.1569 −0.494100 −0.247050 0.969003i \(-0.579461\pi\)
−0.247050 + 0.969003i \(0.579461\pi\)
\(942\) 0 0
\(943\) −0.782477 −0.0254810
\(944\) 0 0
\(945\) 5.02263 0.163386
\(946\) 0 0
\(947\) −11.2362 −0.365127 −0.182563 0.983194i \(-0.558440\pi\)
−0.182563 + 0.983194i \(0.558440\pi\)
\(948\) 0 0
\(949\) −23.6787 −0.768643
\(950\) 0 0
\(951\) −15.7367 −0.510298
\(952\) 0 0
\(953\) −14.5317 −0.470727 −0.235363 0.971907i \(-0.575628\pi\)
−0.235363 + 0.971907i \(0.575628\pi\)
\(954\) 0 0
\(955\) 8.58910 0.277937
\(956\) 0 0
\(957\) 12.2898 0.397273
\(958\) 0 0
\(959\) 101.705 3.28423
\(960\) 0 0
\(961\) 20.5744 0.663689
\(962\) 0 0
\(963\) −2.00152 −0.0644980
\(964\) 0 0
\(965\) −16.8434 −0.542207
\(966\) 0 0
\(967\) −23.8670 −0.767512 −0.383756 0.923434i \(-0.625370\pi\)
−0.383756 + 0.923434i \(0.625370\pi\)
\(968\) 0 0
\(969\) 45.1569 1.45065
\(970\) 0 0
\(971\) 16.8670 0.541286 0.270643 0.962680i \(-0.412764\pi\)
0.270643 + 0.962680i \(0.412764\pi\)
\(972\) 0 0
\(973\) 28.2100 0.904370
\(974\) 0 0
\(975\) 6.49408 0.207977
\(976\) 0 0
\(977\) −28.3073 −0.905629 −0.452815 0.891605i \(-0.649580\pi\)
−0.452815 + 0.891605i \(0.649580\pi\)
\(978\) 0 0
\(979\) 23.3705 0.746923
\(980\) 0 0
\(981\) 12.4302 0.396866
\(982\) 0 0
\(983\) 7.45949 0.237921 0.118960 0.992899i \(-0.462044\pi\)
0.118960 + 0.992899i \(0.462044\pi\)
\(984\) 0 0
\(985\) 0.0422192 0.00134522
\(986\) 0 0
\(987\) 42.1853 1.34277
\(988\) 0 0
\(989\) 0.0950231 0.00302156
\(990\) 0 0
\(991\) 32.6469 1.03706 0.518532 0.855058i \(-0.326479\pi\)
0.518532 + 0.855058i \(0.326479\pi\)
\(992\) 0 0
\(993\) 34.3427 1.08983
\(994\) 0 0
\(995\) 14.1589 0.448867
\(996\) 0 0
\(997\) 28.7800 0.911473 0.455737 0.890115i \(-0.349376\pi\)
0.455737 + 0.890115i \(0.349376\pi\)
\(998\) 0 0
\(999\) 3.02263 0.0956317
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 \(a_p\))

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 2760.2.a.w.1.1 5
3.2 odd 2 8280.2.a.br.1.1 5
4.3 odd 2 5520.2.a.cc.1.5 5
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
2760.2.a.w.1.1 5 1.1 even 1 trivial
5520.2.a.cc.1.5 5 4.3 odd 2
8280.2.a.br.1.1 5 3.2 odd 2