Properties

Label 4900.2.a.be.1.2
Level $4900$
Weight $2$
Character 4900.1
Self dual yes
Analytic conductor $39.127$
Analytic rank $1$
Dimension $4$
CM no
Inner twists $2$

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [4900,2,Mod(1,4900)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(4900, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 0, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("4900.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 4900 = 2^{2} \cdot 5^{2} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 4900.a (trivial)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: yes
Analytic conductor: \(39.1266969904\)
Analytic rank: \(1\)
Dimension: \(4\)
Coefficient field: \(\Q(\sqrt{3}, \sqrt{19})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{4} - 11x^{2} + 16 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{13}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 140)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.2
Root \(1.31342\) of defining polynomial
Character \(\chi\) \(=\) 4900.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-1.73205 q^{3} +O(q^{10})\) \(q-1.73205 q^{3} +2.27492 q^{11} +6.09095 q^{13} -4.77753 q^{17} -4.27492 q^{19} -0.894797 q^{23} +5.19615 q^{27} -3.27492 q^{29} -4.27492 q^{31} -3.94027 q^{33} +5.61478 q^{37} -10.5498 q^{39} -11.2749 q^{41} +6.50958 q^{43} -2.15068 q^{47} +8.27492 q^{51} -7.40437 q^{53} +7.40437 q^{57} +4.27492 q^{59} +1.54983 q^{61} +13.9140 q^{67} +1.54983 q^{69} +10.5498 q^{71} -2.15068 q^{73} -0.274917 q^{79} -9.00000 q^{81} -5.67232 q^{83} +5.67232 q^{87} -7.00000 q^{89} +7.40437 q^{93} +6.92820 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q+O(q^{10}) \) Copy content Toggle raw display \( 4 q - 6 q^{11} - 2 q^{19} + 2 q^{29} - 2 q^{31} - 12 q^{39} - 30 q^{41} + 18 q^{51} + 2 q^{59} - 24 q^{61} - 24 q^{69} + 12 q^{71} + 14 q^{79} - 36 q^{81} - 28 q^{89}+O(q^{100}) \) 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
\(3\) −1.73205 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(4\) 0 0
\(5\) 0 0
\(6\) 0 0
\(7\) 0 0
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) 2.27492 0.685913 0.342957 0.939351i \(-0.388572\pi\)
0.342957 + 0.939351i \(0.388572\pi\)
\(12\) 0 0
\(13\) 6.09095 1.68933 0.844663 0.535299i \(-0.179801\pi\)
0.844663 + 0.535299i \(0.179801\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) −4.77753 −1.15872 −0.579360 0.815072i \(-0.696697\pi\)
−0.579360 + 0.815072i \(0.696697\pi\)
\(18\) 0 0
\(19\) −4.27492 −0.980733 −0.490367 0.871516i \(-0.663137\pi\)
−0.490367 + 0.871516i \(0.663137\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) −0.894797 −0.186578 −0.0932891 0.995639i \(-0.529738\pi\)
−0.0932891 + 0.995639i \(0.529738\pi\)
\(24\) 0 0
\(25\) 0 0
\(26\) 0 0
\(27\) 5.19615 1.00000
\(28\) 0 0
\(29\) −3.27492 −0.608137 −0.304068 0.952650i \(-0.598345\pi\)
−0.304068 + 0.952650i \(0.598345\pi\)
\(30\) 0 0
\(31\) −4.27492 −0.767798 −0.383899 0.923375i \(-0.625419\pi\)
−0.383899 + 0.923375i \(0.625419\pi\)
\(32\) 0 0
\(33\) −3.94027 −0.685913
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) 5.61478 0.923064 0.461532 0.887124i \(-0.347300\pi\)
0.461532 + 0.887124i \(0.347300\pi\)
\(38\) 0 0
\(39\) −10.5498 −1.68933
\(40\) 0 0
\(41\) −11.2749 −1.76085 −0.880423 0.474189i \(-0.842741\pi\)
−0.880423 + 0.474189i \(0.842741\pi\)
\(42\) 0 0
\(43\) 6.50958 0.992701 0.496351 0.868122i \(-0.334673\pi\)
0.496351 + 0.868122i \(0.334673\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) −2.15068 −0.313709 −0.156854 0.987622i \(-0.550135\pi\)
−0.156854 + 0.987622i \(0.550135\pi\)
\(48\) 0 0
\(49\) 0 0
\(50\) 0 0
\(51\) 8.27492 1.15872
\(52\) 0 0
\(53\) −7.40437 −1.01707 −0.508534 0.861042i \(-0.669813\pi\)
−0.508534 + 0.861042i \(0.669813\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 0 0
\(57\) 7.40437 0.980733
\(58\) 0 0
\(59\) 4.27492 0.556547 0.278273 0.960502i \(-0.410238\pi\)
0.278273 + 0.960502i \(0.410238\pi\)
\(60\) 0 0
\(61\) 1.54983 0.198436 0.0992180 0.995066i \(-0.468366\pi\)
0.0992180 + 0.995066i \(0.468366\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) 0 0
\(66\) 0 0
\(67\) 13.9140 1.69986 0.849930 0.526896i \(-0.176644\pi\)
0.849930 + 0.526896i \(0.176644\pi\)
\(68\) 0 0
\(69\) 1.54983 0.186578
\(70\) 0 0
\(71\) 10.5498 1.25204 0.626018 0.779809i \(-0.284684\pi\)
0.626018 + 0.779809i \(0.284684\pi\)
\(72\) 0 0
\(73\) −2.15068 −0.251718 −0.125859 0.992048i \(-0.540169\pi\)
−0.125859 + 0.992048i \(0.540169\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 0 0
\(78\) 0 0
\(79\) −0.274917 −0.0309306 −0.0154653 0.999880i \(-0.504923\pi\)
−0.0154653 + 0.999880i \(0.504923\pi\)
\(80\) 0 0
\(81\) −9.00000 −1.00000
\(82\) 0 0
\(83\) −5.67232 −0.622618 −0.311309 0.950309i \(-0.600767\pi\)
−0.311309 + 0.950309i \(0.600767\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 0 0
\(87\) 5.67232 0.608137
\(88\) 0 0
\(89\) −7.00000 −0.741999 −0.370999 0.928633i \(-0.620985\pi\)
−0.370999 + 0.928633i \(0.620985\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 0 0
\(93\) 7.40437 0.767798
\(94\) 0 0
\(95\) 0 0
\(96\) 0 0
\(97\) 6.92820 0.703452 0.351726 0.936103i \(-0.385595\pi\)
0.351726 + 0.936103i \(0.385595\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) 1.54983 0.154214 0.0771071 0.997023i \(-0.475432\pi\)
0.0771071 + 0.997023i \(0.475432\pi\)
\(102\) 0 0
\(103\) −2.56930 −0.253161 −0.126581 0.991956i \(-0.540400\pi\)
−0.126581 + 0.991956i \(0.540400\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 13.9140 1.34511 0.672556 0.740046i \(-0.265196\pi\)
0.672556 + 0.740046i \(0.265196\pi\)
\(108\) 0 0
\(109\) 3.54983 0.340012 0.170006 0.985443i \(-0.445621\pi\)
0.170006 + 0.985443i \(0.445621\pi\)
\(110\) 0 0
\(111\) −9.72508 −0.923064
\(112\) 0 0
\(113\) −13.0192 −1.22474 −0.612369 0.790572i \(-0.709783\pi\)
−0.612369 + 0.790572i \(0.709783\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) 0 0
\(120\) 0 0
\(121\) −5.82475 −0.529523
\(122\) 0 0
\(123\) 19.5287 1.76085
\(124\) 0 0
\(125\) 0 0
\(126\) 0 0
\(127\) −1.78959 −0.158801 −0.0794004 0.996843i \(-0.525301\pi\)
−0.0794004 + 0.996843i \(0.525301\pi\)
\(128\) 0 0
\(129\) −11.2749 −0.992701
\(130\) 0 0
\(131\) −18.2749 −1.59669 −0.798343 0.602202i \(-0.794290\pi\)
−0.798343 + 0.602202i \(0.794290\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) −9.19397 −0.785494 −0.392747 0.919647i \(-0.628475\pi\)
−0.392747 + 0.919647i \(0.628475\pi\)
\(138\) 0 0
\(139\) −17.0997 −1.45037 −0.725187 0.688551i \(-0.758247\pi\)
−0.725187 + 0.688551i \(0.758247\pi\)
\(140\) 0 0
\(141\) 3.72508 0.313709
\(142\) 0 0
\(143\) 13.8564 1.15873
\(144\) 0 0
\(145\) 0 0
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) 7.54983 0.618507 0.309253 0.950980i \(-0.399921\pi\)
0.309253 + 0.950980i \(0.399921\pi\)
\(150\) 0 0
\(151\) −20.2749 −1.64995 −0.824975 0.565170i \(-0.808811\pi\)
−0.824975 + 0.565170i \(0.808811\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 0 0
\(156\) 0 0
\(157\) −10.8685 −0.867399 −0.433699 0.901058i \(-0.642792\pi\)
−0.433699 + 0.901058i \(0.642792\pi\)
\(158\) 0 0
\(159\) 12.8248 1.01707
\(160\) 0 0
\(161\) 0 0
\(162\) 0 0
\(163\) 7.40437 0.579955 0.289978 0.957033i \(-0.406352\pi\)
0.289978 + 0.957033i \(0.406352\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) −12.6005 −0.975058 −0.487529 0.873107i \(-0.662102\pi\)
−0.487529 + 0.873107i \(0.662102\pi\)
\(168\) 0 0
\(169\) 24.0997 1.85382
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) 18.7490 1.42546 0.712731 0.701438i \(-0.247458\pi\)
0.712731 + 0.701438i \(0.247458\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) −7.40437 −0.556547
\(178\) 0 0
\(179\) 0.274917 0.0205483 0.0102741 0.999947i \(-0.496730\pi\)
0.0102741 + 0.999947i \(0.496730\pi\)
\(180\) 0 0
\(181\) −16.7251 −1.24317 −0.621583 0.783348i \(-0.713510\pi\)
−0.621583 + 0.783348i \(0.713510\pi\)
\(182\) 0 0
\(183\) −2.68439 −0.198436
\(184\) 0 0
\(185\) 0 0
\(186\) 0 0
\(187\) −10.8685 −0.794782
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 22.8248 1.65154 0.825771 0.564006i \(-0.190741\pi\)
0.825771 + 0.564006i \(0.190741\pi\)
\(192\) 0 0
\(193\) 9.19397 0.661796 0.330898 0.943666i \(-0.392648\pi\)
0.330898 + 0.943666i \(0.392648\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) −26.0383 −1.85515 −0.927576 0.373634i \(-0.878112\pi\)
−0.927576 + 0.373634i \(0.878112\pi\)
\(198\) 0 0
\(199\) 9.72508 0.689393 0.344696 0.938714i \(-0.387982\pi\)
0.344696 + 0.938714i \(0.387982\pi\)
\(200\) 0 0
\(201\) −24.0997 −1.69986
\(202\) 0 0
\(203\) 0 0
\(204\) 0 0
\(205\) 0 0
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) −9.72508 −0.672698
\(210\) 0 0
\(211\) −19.6495 −1.35273 −0.676364 0.736568i \(-0.736445\pi\)
−0.676364 + 0.736568i \(0.736445\pi\)
\(212\) 0 0
\(213\) −18.2728 −1.25204
\(214\) 0 0
\(215\) 0 0
\(216\) 0 0
\(217\) 0 0
\(218\) 0 0
\(219\) 3.72508 0.251718
\(220\) 0 0
\(221\) −29.0997 −1.95746
\(222\) 0 0
\(223\) −8.71780 −0.583787 −0.291893 0.956451i \(-0.594285\pi\)
−0.291893 + 0.956451i \(0.594285\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 6.45203 0.428236 0.214118 0.976808i \(-0.431312\pi\)
0.214118 + 0.976808i \(0.431312\pi\)
\(228\) 0 0
\(229\) −4.27492 −0.282494 −0.141247 0.989974i \(-0.545111\pi\)
−0.141247 + 0.989974i \(0.545111\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) −18.6339 −1.22075 −0.610375 0.792113i \(-0.708981\pi\)
−0.610375 + 0.792113i \(0.708981\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 0 0
\(237\) 0.476171 0.0309306
\(238\) 0 0
\(239\) −14.5498 −0.941151 −0.470575 0.882360i \(-0.655954\pi\)
−0.470575 + 0.882360i \(0.655954\pi\)
\(240\) 0 0
\(241\) −12.8248 −0.826115 −0.413057 0.910705i \(-0.635539\pi\)
−0.413057 + 0.910705i \(0.635539\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) −26.0383 −1.65678
\(248\) 0 0
\(249\) 9.82475 0.622618
\(250\) 0 0
\(251\) −5.45017 −0.344011 −0.172006 0.985096i \(-0.555025\pi\)
−0.172006 + 0.985096i \(0.555025\pi\)
\(252\) 0 0
\(253\) −2.03559 −0.127976
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 24.7249 1.54230 0.771148 0.636656i \(-0.219683\pi\)
0.771148 + 0.636656i \(0.219683\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) −26.9331 −1.66077 −0.830383 0.557193i \(-0.811878\pi\)
−0.830383 + 0.557193i \(0.811878\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) 12.1244 0.741999
\(268\) 0 0
\(269\) −29.5498 −1.80169 −0.900843 0.434146i \(-0.857050\pi\)
−0.900843 + 0.434146i \(0.857050\pi\)
\(270\) 0 0
\(271\) −12.8248 −0.779048 −0.389524 0.921016i \(-0.627361\pi\)
−0.389524 + 0.921016i \(0.627361\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 0 0
\(276\) 0 0
\(277\) −18.6339 −1.11960 −0.559802 0.828626i \(-0.689123\pi\)
−0.559802 + 0.828626i \(0.689123\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) 6.00000 0.357930 0.178965 0.983855i \(-0.442725\pi\)
0.178965 + 0.983855i \(0.442725\pi\)
\(282\) 0 0
\(283\) 19.5863 1.16428 0.582142 0.813087i \(-0.302215\pi\)
0.582142 + 0.813087i \(0.302215\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 0 0
\(288\) 0 0
\(289\) 5.82475 0.342632
\(290\) 0 0
\(291\) −12.0000 −0.703452
\(292\) 0 0
\(293\) −6.92820 −0.404750 −0.202375 0.979308i \(-0.564866\pi\)
−0.202375 + 0.979308i \(0.564866\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 0 0
\(297\) 11.8208 0.685913
\(298\) 0 0
\(299\) −5.45017 −0.315191
\(300\) 0 0
\(301\) 0 0
\(302\) 0 0
\(303\) −2.68439 −0.154214
\(304\) 0 0
\(305\) 0 0
\(306\) 0 0
\(307\) 3.99782 0.228167 0.114084 0.993471i \(-0.463607\pi\)
0.114084 + 0.993471i \(0.463607\pi\)
\(308\) 0 0
\(309\) 4.45017 0.253161
\(310\) 0 0
\(311\) 12.8248 0.727225 0.363612 0.931550i \(-0.381543\pi\)
0.363612 + 0.931550i \(0.381543\pi\)
\(312\) 0 0
\(313\) −14.4477 −0.816630 −0.408315 0.912841i \(-0.633884\pi\)
−0.408315 + 0.912841i \(0.633884\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −3.82518 −0.214844 −0.107422 0.994214i \(-0.534260\pi\)
−0.107422 + 0.994214i \(0.534260\pi\)
\(318\) 0 0
\(319\) −7.45017 −0.417129
\(320\) 0 0
\(321\) −24.0997 −1.34511
\(322\) 0 0
\(323\) 20.4235 1.13640
\(324\) 0 0
\(325\) 0 0
\(326\) 0 0
\(327\) −6.14849 −0.340012
\(328\) 0 0
\(329\) 0 0
\(330\) 0 0
\(331\) −4.82475 −0.265192 −0.132596 0.991170i \(-0.542331\pi\)
−0.132596 + 0.991170i \(0.542331\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) 0 0
\(336\) 0 0
\(337\) 13.0192 0.709198 0.354599 0.935018i \(-0.384617\pi\)
0.354599 + 0.935018i \(0.384617\pi\)
\(338\) 0 0
\(339\) 22.5498 1.22474
\(340\) 0 0
\(341\) −9.72508 −0.526643
\(342\) 0 0
\(343\) 0 0
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) −12.1244 −0.650870 −0.325435 0.945564i \(-0.605511\pi\)
−0.325435 + 0.945564i \(0.605511\pi\)
\(348\) 0 0
\(349\) −11.2749 −0.603532 −0.301766 0.953382i \(-0.597576\pi\)
−0.301766 + 0.953382i \(0.597576\pi\)
\(350\) 0 0
\(351\) 31.6495 1.68933
\(352\) 0 0
\(353\) −21.2608 −1.13160 −0.565799 0.824543i \(-0.691432\pi\)
−0.565799 + 0.824543i \(0.691432\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) −1.37459 −0.0725479 −0.0362739 0.999342i \(-0.511549\pi\)
−0.0362739 + 0.999342i \(0.511549\pi\)
\(360\) 0 0
\(361\) −0.725083 −0.0381623
\(362\) 0 0
\(363\) 10.0888 0.529523
\(364\) 0 0
\(365\) 0 0
\(366\) 0 0
\(367\) 14.7512 0.770007 0.385003 0.922915i \(-0.374200\pi\)
0.385003 + 0.922915i \(0.374200\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) 0 0
\(372\) 0 0
\(373\) −5.61478 −0.290722 −0.145361 0.989379i \(-0.546434\pi\)
−0.145361 + 0.989379i \(0.546434\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) −19.9474 −1.02734
\(378\) 0 0
\(379\) 23.6495 1.21479 0.607397 0.794399i \(-0.292214\pi\)
0.607397 + 0.794399i \(0.292214\pi\)
\(380\) 0 0
\(381\) 3.09967 0.158801
\(382\) 0 0
\(383\) −20.0049 −1.02220 −0.511101 0.859520i \(-0.670762\pi\)
−0.511101 + 0.859520i \(0.670762\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) −5.37459 −0.272502 −0.136251 0.990674i \(-0.543505\pi\)
−0.136251 + 0.990674i \(0.543505\pi\)
\(390\) 0 0
\(391\) 4.27492 0.216192
\(392\) 0 0
\(393\) 31.6531 1.59669
\(394\) 0 0
\(395\) 0 0
\(396\) 0 0
\(397\) −15.1698 −0.761352 −0.380676 0.924708i \(-0.624309\pi\)
−0.380676 + 0.924708i \(0.624309\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 3.00000 0.149813 0.0749064 0.997191i \(-0.476134\pi\)
0.0749064 + 0.997191i \(0.476134\pi\)
\(402\) 0 0
\(403\) −26.0383 −1.29706
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 12.7732 0.633142
\(408\) 0 0
\(409\) 10.0997 0.499396 0.249698 0.968324i \(-0.419669\pi\)
0.249698 + 0.968324i \(0.419669\pi\)
\(410\) 0 0
\(411\) 15.9244 0.785494
\(412\) 0 0
\(413\) 0 0
\(414\) 0 0
\(415\) 0 0
\(416\) 0 0
\(417\) 29.6175 1.45037
\(418\) 0 0
\(419\) 17.0997 0.835373 0.417687 0.908591i \(-0.362841\pi\)
0.417687 + 0.908591i \(0.362841\pi\)
\(420\) 0 0
\(421\) 3.27492 0.159610 0.0798048 0.996811i \(-0.474570\pi\)
0.0798048 + 0.996811i \(0.474570\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) 0 0
\(426\) 0 0
\(427\) 0 0
\(428\) 0 0
\(429\) −24.0000 −1.15873
\(430\) 0 0
\(431\) 19.3746 0.933241 0.466620 0.884458i \(-0.345471\pi\)
0.466620 + 0.884458i \(0.345471\pi\)
\(432\) 0 0
\(433\) 26.8756 1.29156 0.645778 0.763525i \(-0.276533\pi\)
0.645778 + 0.763525i \(0.276533\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 3.82518 0.182983
\(438\) 0 0
\(439\) 1.17525 0.0560915 0.0280458 0.999607i \(-0.491072\pi\)
0.0280458 + 0.999607i \(0.491072\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 12.1244 0.576046 0.288023 0.957624i \(-0.407002\pi\)
0.288023 + 0.957624i \(0.407002\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 0 0
\(447\) −13.0767 −0.618507
\(448\) 0 0
\(449\) −25.8248 −1.21875 −0.609373 0.792884i \(-0.708579\pi\)
−0.609373 + 0.792884i \(0.708579\pi\)
\(450\) 0 0
\(451\) −25.6495 −1.20779
\(452\) 0 0
\(453\) 35.1172 1.64995
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) −20.4235 −0.955372 −0.477686 0.878531i \(-0.658524\pi\)
−0.477686 + 0.878531i \(0.658524\pi\)
\(458\) 0 0
\(459\) −24.8248 −1.15872
\(460\) 0 0
\(461\) −14.0000 −0.652045 −0.326023 0.945362i \(-0.605709\pi\)
−0.326023 + 0.945362i \(0.605709\pi\)
\(462\) 0 0
\(463\) −6.50958 −0.302526 −0.151263 0.988494i \(-0.548334\pi\)
−0.151263 + 0.988494i \(0.548334\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 19.1676 0.886973 0.443486 0.896281i \(-0.353741\pi\)
0.443486 + 0.896281i \(0.353741\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 0 0
\(471\) 18.8248 0.867399
\(472\) 0 0
\(473\) 14.8087 0.680907
\(474\) 0 0
\(475\) 0 0
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) −12.8248 −0.585978 −0.292989 0.956116i \(-0.594650\pi\)
−0.292989 + 0.956116i \(0.594650\pi\)
\(480\) 0 0
\(481\) 34.1993 1.55936
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 0 0
\(486\) 0 0
\(487\) −33.4427 −1.51543 −0.757716 0.652584i \(-0.773685\pi\)
−0.757716 + 0.652584i \(0.773685\pi\)
\(488\) 0 0
\(489\) −12.8248 −0.579955
\(490\) 0 0
\(491\) −13.4502 −0.606997 −0.303499 0.952832i \(-0.598155\pi\)
−0.303499 + 0.952832i \(0.598155\pi\)
\(492\) 0 0
\(493\) 15.6460 0.704660
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 0 0
\(498\) 0 0
\(499\) 39.3746 1.76265 0.881324 0.472512i \(-0.156653\pi\)
0.881324 + 0.472512i \(0.156653\pi\)
\(500\) 0 0
\(501\) 21.8248 0.975058
\(502\) 0 0
\(503\) 16.1797 0.721418 0.360709 0.932678i \(-0.382535\pi\)
0.360709 + 0.932678i \(0.382535\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) −41.7419 −1.85382
\(508\) 0 0
\(509\) −29.5498 −1.30977 −0.654887 0.755727i \(-0.727284\pi\)
−0.654887 + 0.755727i \(0.727284\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 0 0
\(513\) −22.2131 −0.980733
\(514\) 0 0
\(515\) 0 0
\(516\) 0 0
\(517\) −4.89261 −0.215177
\(518\) 0 0
\(519\) −32.4743 −1.42546
\(520\) 0 0
\(521\) −12.8248 −0.561863 −0.280931 0.959728i \(-0.590643\pi\)
−0.280931 + 0.959728i \(0.590643\pi\)
\(522\) 0 0
\(523\) −11.7057 −0.511856 −0.255928 0.966696i \(-0.582381\pi\)
−0.255928 + 0.966696i \(0.582381\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 20.4235 0.889663
\(528\) 0 0
\(529\) −22.1993 −0.965189
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) −68.6750 −2.97464
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) −0.476171 −0.0205483
\(538\) 0 0
\(539\) 0 0
\(540\) 0 0
\(541\) −2.45017 −0.105341 −0.0526704 0.998612i \(-0.516773\pi\)
−0.0526704 + 0.998612i \(0.516773\pi\)
\(542\) 0 0
\(543\) 28.9687 1.24317
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) −36.1271 −1.54468 −0.772341 0.635208i \(-0.780914\pi\)
−0.772341 + 0.635208i \(0.780914\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) 14.0000 0.596420
\(552\) 0 0
\(553\) 0 0
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) −5.61478 −0.237906 −0.118953 0.992900i \(-0.537954\pi\)
−0.118953 + 0.992900i \(0.537954\pi\)
\(558\) 0 0
\(559\) 39.6495 1.67700
\(560\) 0 0
\(561\) 18.8248 0.794782
\(562\) 0 0
\(563\) −12.2394 −0.515831 −0.257916 0.966167i \(-0.583036\pi\)
−0.257916 + 0.966167i \(0.583036\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) −29.3746 −1.23145 −0.615723 0.787962i \(-0.711136\pi\)
−0.615723 + 0.787962i \(0.711136\pi\)
\(570\) 0 0
\(571\) −0.274917 −0.0115049 −0.00575246 0.999983i \(-0.501831\pi\)
−0.00575246 + 0.999983i \(0.501831\pi\)
\(572\) 0 0
\(573\) −39.5336 −1.65154
\(574\) 0 0
\(575\) 0 0
\(576\) 0 0
\(577\) 8.24163 0.343103 0.171552 0.985175i \(-0.445122\pi\)
0.171552 + 0.985175i \(0.445122\pi\)
\(578\) 0 0
\(579\) −15.9244 −0.661796
\(580\) 0 0
\(581\) 0 0
\(582\) 0 0
\(583\) −16.8443 −0.697621
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 13.9715 0.576665 0.288333 0.957530i \(-0.406899\pi\)
0.288333 + 0.957530i \(0.406899\pi\)
\(588\) 0 0
\(589\) 18.2749 0.753005
\(590\) 0 0
\(591\) 45.0997 1.85515
\(592\) 0 0
\(593\) −20.3084 −0.833968 −0.416984 0.908914i \(-0.636913\pi\)
−0.416984 + 0.908914i \(0.636913\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) −16.8443 −0.689393
\(598\) 0 0
\(599\) −2.27492 −0.0929506 −0.0464753 0.998919i \(-0.514799\pi\)
−0.0464753 + 0.998919i \(0.514799\pi\)
\(600\) 0 0
\(601\) 14.0000 0.571072 0.285536 0.958368i \(-0.407828\pi\)
0.285536 + 0.958368i \(0.407828\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) 0 0
\(606\) 0 0
\(607\) 32.1868 1.30642 0.653211 0.757176i \(-0.273421\pi\)
0.653211 + 0.757176i \(0.273421\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) −13.0997 −0.529956
\(612\) 0 0
\(613\) −37.0219 −1.49530 −0.747650 0.664093i \(-0.768818\pi\)
−0.747650 + 0.664093i \(0.768818\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) −3.57919 −0.144093 −0.0720464 0.997401i \(-0.522953\pi\)
−0.0720464 + 0.997401i \(0.522953\pi\)
\(618\) 0 0
\(619\) 43.9244 1.76547 0.882736 0.469870i \(-0.155699\pi\)
0.882736 + 0.469870i \(0.155699\pi\)
\(620\) 0 0
\(621\) −4.64950 −0.186578
\(622\) 0 0
\(623\) 0 0
\(624\) 0 0
\(625\) 0 0
\(626\) 0 0
\(627\) 16.8443 0.672698
\(628\) 0 0
\(629\) −26.8248 −1.06957
\(630\) 0 0
\(631\) 2.90033 0.115460 0.0577302 0.998332i \(-0.481614\pi\)
0.0577302 + 0.998332i \(0.481614\pi\)
\(632\) 0 0
\(633\) 34.0339 1.35273
\(634\) 0 0
\(635\) 0 0
\(636\) 0 0
\(637\) 0 0
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) 28.0997 1.10987 0.554935 0.831894i \(-0.312743\pi\)
0.554935 + 0.831894i \(0.312743\pi\)
\(642\) 0 0
\(643\) −38.3353 −1.51180 −0.755898 0.654689i \(-0.772800\pi\)
−0.755898 + 0.654689i \(0.772800\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) −0.779710 −0.0306535 −0.0153268 0.999883i \(-0.504879\pi\)
−0.0153268 + 0.999883i \(0.504879\pi\)
\(648\) 0 0
\(649\) 9.72508 0.381743
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 37.0219 1.44878 0.724389 0.689392i \(-0.242122\pi\)
0.724389 + 0.689392i \(0.242122\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) −25.4502 −0.991398 −0.495699 0.868494i \(-0.665088\pi\)
−0.495699 + 0.868494i \(0.665088\pi\)
\(660\) 0 0
\(661\) −15.5498 −0.604818 −0.302409 0.953178i \(-0.597791\pi\)
−0.302409 + 0.953178i \(0.597791\pi\)
\(662\) 0 0
\(663\) 50.4021 1.95746
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) 2.93039 0.113465
\(668\) 0 0
\(669\) 15.0997 0.583787
\(670\) 0 0
\(671\) 3.52575 0.136110
\(672\) 0 0
\(673\) −3.57919 −0.137968 −0.0689838 0.997618i \(-0.521976\pi\)
−0.0689838 + 0.997618i \(0.521976\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) −24.6098 −0.945831 −0.472916 0.881108i \(-0.656798\pi\)
−0.472916 + 0.881108i \(0.656798\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 0 0
\(681\) −11.1752 −0.428236
\(682\) 0 0
\(683\) 15.7035 0.600879 0.300440 0.953801i \(-0.402867\pi\)
0.300440 + 0.953801i \(0.402867\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 0 0
\(687\) 7.40437 0.282494
\(688\) 0 0
\(689\) −45.0997 −1.71816
\(690\) 0 0
\(691\) −7.37459 −0.280542 −0.140271 0.990113i \(-0.544797\pi\)
−0.140271 + 0.990113i \(0.544797\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 0 0
\(696\) 0 0
\(697\) 53.8662 2.04033
\(698\) 0 0
\(699\) 32.2749 1.22075
\(700\) 0 0
\(701\) −13.8248 −0.522154 −0.261077 0.965318i \(-0.584078\pi\)
−0.261077 + 0.965318i \(0.584078\pi\)
\(702\) 0 0
\(703\) −24.0027 −0.905280
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 0 0
\(708\) 0 0
\(709\) −25.5498 −0.959544 −0.479772 0.877393i \(-0.659281\pi\)
−0.479772 + 0.877393i \(0.659281\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) 3.82518 0.143254
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) 25.2011 0.941151
\(718\) 0 0
\(719\) 7.37459 0.275026 0.137513 0.990500i \(-0.456089\pi\)
0.137513 + 0.990500i \(0.456089\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) 0 0
\(723\) 22.2131 0.826115
\(724\) 0 0
\(725\) 0 0
\(726\) 0 0
\(727\) 18.6915 0.693228 0.346614 0.938008i \(-0.387331\pi\)
0.346614 + 0.938008i \(0.387331\pi\)
\(728\) 0 0
\(729\) 27.0000 1.00000
\(730\) 0 0
\(731\) −31.0997 −1.15026
\(732\) 0 0
\(733\) −33.3276 −1.23098 −0.615491 0.788144i \(-0.711042\pi\)
−0.615491 + 0.788144i \(0.711042\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 31.6531 1.16596
\(738\) 0 0
\(739\) 31.9244 1.17436 0.587179 0.809457i \(-0.300238\pi\)
0.587179 + 0.809457i \(0.300238\pi\)
\(740\) 0 0
\(741\) 45.0997 1.65678
\(742\) 0 0
\(743\) 19.5287 0.716440 0.358220 0.933637i \(-0.383384\pi\)
0.358220 + 0.933637i \(0.383384\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) 0 0
\(750\) 0 0
\(751\) −22.2749 −0.812823 −0.406412 0.913690i \(-0.633220\pi\)
−0.406412 + 0.913690i \(0.633220\pi\)
\(752\) 0 0
\(753\) 9.43996 0.344011
\(754\) 0 0
\(755\) 0 0
\(756\) 0 0
\(757\) −9.43996 −0.343101 −0.171551 0.985175i \(-0.554878\pi\)
−0.171551 + 0.985175i \(0.554878\pi\)
\(758\) 0 0
\(759\) 3.52575 0.127976
\(760\) 0 0
\(761\) −29.9244 −1.08476 −0.542380 0.840133i \(-0.682477\pi\)
−0.542380 + 0.840133i \(0.682477\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 26.0383 0.940189
\(768\) 0 0
\(769\) −14.0000 −0.504853 −0.252426 0.967616i \(-0.581229\pi\)
−0.252426 + 0.967616i \(0.581229\pi\)
\(770\) 0 0
\(771\) −42.8248 −1.54230
\(772\) 0 0
\(773\) 27.2366 0.979634 0.489817 0.871825i \(-0.337064\pi\)
0.489817 + 0.871825i \(0.337064\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 48.1993 1.72692
\(780\) 0 0
\(781\) 24.0000 0.858788
\(782\) 0 0
\(783\) −17.0170 −0.608137
\(784\) 0 0
\(785\) 0 0
\(786\) 0 0
\(787\) 1.73205 0.0617409 0.0308705 0.999523i \(-0.490172\pi\)
0.0308705 + 0.999523i \(0.490172\pi\)
\(788\) 0 0
\(789\) 46.6495 1.66077
\(790\) 0 0
\(791\) 0 0
\(792\) 0 0
\(793\) 9.43996 0.335223
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 29.3873 1.04095 0.520476 0.853876i \(-0.325754\pi\)
0.520476 + 0.853876i \(0.325754\pi\)
\(798\) 0 0
\(799\) 10.2749 0.363500
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) −4.89261 −0.172657
\(804\) 0 0
\(805\) 0 0
\(806\) 0 0
\(807\) 51.1818 1.80169
\(808\) 0 0
\(809\) 43.1993 1.51881 0.759404 0.650619i \(-0.225491\pi\)
0.759404 + 0.650619i \(0.225491\pi\)
\(810\) 0 0
\(811\) 22.5498 0.791832 0.395916 0.918287i \(-0.370427\pi\)
0.395916 + 0.918287i \(0.370427\pi\)
\(812\) 0 0
\(813\) 22.2131 0.779048
\(814\) 0 0
\(815\) 0 0
\(816\) 0 0
\(817\) −27.8279 −0.973575
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) 17.3746 0.606377 0.303189 0.952931i \(-0.401949\pi\)
0.303189 + 0.952931i \(0.401949\pi\)
\(822\) 0 0
\(823\) 32.3019 1.12597 0.562987 0.826466i \(-0.309652\pi\)
0.562987 + 0.826466i \(0.309652\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) 45.5670 1.58452 0.792261 0.610183i \(-0.208904\pi\)
0.792261 + 0.610183i \(0.208904\pi\)
\(828\) 0 0
\(829\) 1.92442 0.0668379 0.0334189 0.999441i \(-0.489360\pi\)
0.0334189 + 0.999441i \(0.489360\pi\)
\(830\) 0 0
\(831\) 32.2749 1.11960
\(832\) 0 0
\(833\) 0 0
\(834\) 0 0
\(835\) 0 0
\(836\) 0 0
\(837\) −22.2131 −0.767798
\(838\) 0 0
\(839\) 10.9003 0.376321 0.188161 0.982138i \(-0.439747\pi\)
0.188161 + 0.982138i \(0.439747\pi\)
\(840\) 0 0
\(841\) −18.2749 −0.630170
\(842\) 0 0
\(843\) −10.3923 −0.357930
\(844\) 0 0
\(845\) 0 0
\(846\) 0 0
\(847\) 0 0
\(848\) 0 0
\(849\) −33.9244 −1.16428
\(850\) 0 0
\(851\) −5.02409 −0.172224
\(852\) 0 0
\(853\) 30.4547 1.04275 0.521375 0.853327i \(-0.325419\pi\)
0.521375 + 0.853327i \(0.325419\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) −33.3276 −1.13845 −0.569224 0.822182i \(-0.692756\pi\)
−0.569224 + 0.822182i \(0.692756\pi\)
\(858\) 0 0
\(859\) 35.3746 1.20697 0.603483 0.797376i \(-0.293779\pi\)
0.603483 + 0.797376i \(0.293779\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) 25.1435 0.855895 0.427947 0.903804i \(-0.359237\pi\)
0.427947 + 0.903804i \(0.359237\pi\)
\(864\) 0 0
\(865\) 0 0
\(866\) 0 0
\(867\) −10.0888 −0.342632
\(868\) 0 0
\(869\) −0.625414 −0.0212157
\(870\) 0 0
\(871\) 84.7492 2.87162
\(872\) 0 0
\(873\) 0 0
\(874\) 0 0
\(875\) 0 0
\(876\) 0 0
\(877\) 44.6722 1.50847 0.754237 0.656602i \(-0.228007\pi\)
0.754237 + 0.656602i \(0.228007\pi\)
\(878\) 0 0
\(879\) 12.0000 0.404750
\(880\) 0 0
\(881\) 40.0241 1.34845 0.674223 0.738528i \(-0.264479\pi\)
0.674223 + 0.738528i \(0.264479\pi\)
\(882\) 0 0
\(883\) −20.6695 −0.695585 −0.347792 0.937572i \(-0.613069\pi\)
−0.347792 + 0.937572i \(0.613069\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) −39.2301 −1.31722 −0.658609 0.752486i \(-0.728855\pi\)
−0.658609 + 0.752486i \(0.728855\pi\)
\(888\) 0 0
\(889\) 0 0
\(890\) 0 0
\(891\) −20.4743 −0.685913
\(892\) 0 0
\(893\) 9.19397 0.307664
\(894\) 0 0
\(895\) 0 0
\(896\) 0 0
\(897\) 9.43996 0.315191
\(898\) 0 0
\(899\) 14.0000 0.466926
\(900\) 0 0
\(901\) 35.3746 1.17850
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) 0 0
\(906\) 0 0
\(907\) −45.3210 −1.50486 −0.752430 0.658672i \(-0.771119\pi\)
−0.752430 + 0.658672i \(0.771119\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) 5.09967 0.168960 0.0844798 0.996425i \(-0.473077\pi\)
0.0844798 + 0.996425i \(0.473077\pi\)
\(912\) 0 0
\(913\) −12.9041 −0.427062
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) 0 0
\(918\) 0 0
\(919\) 5.92442 0.195429 0.0977143 0.995215i \(-0.468847\pi\)
0.0977143 + 0.995215i \(0.468847\pi\)
\(920\) 0 0
\(921\) −6.92442 −0.228167
\(922\) 0 0
\(923\) 64.2585 2.11509
\(924\) 0 0
\(925\) 0 0
\(926\) 0 0
\(927\) 0 0
\(928\) 0 0
\(929\) −17.9003 −0.587291 −0.293645 0.955914i \(-0.594868\pi\)
−0.293645 + 0.955914i \(0.594868\pi\)
\(930\) 0 0
\(931\) 0 0
\(932\) 0 0
\(933\) −22.2131 −0.727225
\(934\) 0 0
\(935\) 0 0
\(936\) 0 0
\(937\) 10.5074 0.343262 0.171631 0.985161i \(-0.445096\pi\)
0.171631 + 0.985161i \(0.445096\pi\)
\(938\) 0 0
\(939\) 25.0241 0.816630
\(940\) 0 0
\(941\) 4.27492 0.139358 0.0696792 0.997569i \(-0.477802\pi\)
0.0696792 + 0.997569i \(0.477802\pi\)
\(942\) 0 0
\(943\) 10.0888 0.328535
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) −41.7419 −1.35643 −0.678214 0.734865i \(-0.737246\pi\)
−0.678214 + 0.734865i \(0.737246\pi\)
\(948\) 0 0
\(949\) −13.0997 −0.425233
\(950\) 0 0
\(951\) 6.62541 0.214844
\(952\) 0 0
\(953\) 29.6175 0.959405 0.479702 0.877431i \(-0.340745\pi\)
0.479702 + 0.877431i \(0.340745\pi\)
\(954\) 0 0
\(955\) 0 0
\(956\) 0 0
\(957\) 12.9041 0.417129
\(958\) 0 0
\(959\) 0 0
\(960\) 0 0
\(961\) −12.7251 −0.410487
\(962\) 0 0
\(963\) 0 0
\(964\) 0 0
\(965\) 0 0
\(966\) 0 0
\(967\) 6.50958 0.209334 0.104667 0.994507i \(-0.466622\pi\)
0.104667 + 0.994507i \(0.466622\pi\)
\(968\) 0 0
\(969\) −35.3746 −1.13640
\(970\) 0 0
\(971\) 15.9244 0.511039 0.255519 0.966804i \(-0.417754\pi\)
0.255519 + 0.966804i \(0.417754\pi\)
\(972\) 0 0
\(973\) 0 0
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) 16.8443 0.538898 0.269449 0.963015i \(-0.413158\pi\)
0.269449 + 0.963015i \(0.413158\pi\)
\(978\) 0 0
\(979\) −15.9244 −0.508947
\(980\) 0 0
\(981\) 0 0
\(982\) 0 0
\(983\) −37.2103 −1.18682 −0.593412 0.804899i \(-0.702220\pi\)
−0.593412 + 0.804899i \(0.702220\pi\)
\(984\) 0 0
\(985\) 0 0
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) −5.82475 −0.185216
\(990\) 0 0
\(991\) −34.4743 −1.09511 −0.547555 0.836769i \(-0.684441\pi\)
−0.547555 + 0.836769i \(0.684441\pi\)
\(992\) 0 0
\(993\) 8.35671 0.265192
\(994\) 0 0
\(995\) 0 0
\(996\) 0 0
\(997\) −4.77753 −0.151306 −0.0756529 0.997134i \(-0.524104\pi\)
−0.0756529 + 0.997134i \(0.524104\pi\)
\(998\) 0 0
\(999\) 29.1752 0.923064
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 4900.2.a.be.1.2 4
5.2 odd 4 980.2.e.f.589.4 4
5.3 odd 4 980.2.e.f.589.2 4
5.4 even 2 inner 4900.2.a.be.1.4 4
7.2 even 3 700.2.i.f.501.4 8
7.4 even 3 700.2.i.f.401.4 8
7.6 odd 2 4900.2.a.bf.1.4 4
35.2 odd 12 140.2.q.a.109.1 yes 4
35.3 even 12 980.2.q.g.569.2 4
35.4 even 6 700.2.i.f.401.1 8
35.9 even 6 700.2.i.f.501.1 8
35.12 even 12 980.2.q.g.949.2 4
35.13 even 4 980.2.e.c.589.3 4
35.17 even 12 980.2.q.b.569.1 4
35.18 odd 12 140.2.q.a.9.1 4
35.23 odd 12 140.2.q.b.109.1 yes 4
35.27 even 4 980.2.e.c.589.1 4
35.32 odd 12 140.2.q.b.9.2 yes 4
35.33 even 12 980.2.q.b.949.2 4
35.34 odd 2 4900.2.a.bf.1.2 4
105.2 even 12 1260.2.bm.a.109.2 4
105.23 even 12 1260.2.bm.b.109.2 4
105.32 even 12 1260.2.bm.b.289.1 4
105.53 even 12 1260.2.bm.a.289.2 4
140.23 even 12 560.2.bw.a.529.1 4
140.67 even 12 560.2.bw.a.289.2 4
140.107 even 12 560.2.bw.e.529.1 4
140.123 even 12 560.2.bw.e.289.1 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
140.2.q.a.9.1 4 35.18 odd 12
140.2.q.a.109.1 yes 4 35.2 odd 12
140.2.q.b.9.2 yes 4 35.32 odd 12
140.2.q.b.109.1 yes 4 35.23 odd 12
560.2.bw.a.289.2 4 140.67 even 12
560.2.bw.a.529.1 4 140.23 even 12
560.2.bw.e.289.1 4 140.123 even 12
560.2.bw.e.529.1 4 140.107 even 12
700.2.i.f.401.1 8 35.4 even 6
700.2.i.f.401.4 8 7.4 even 3
700.2.i.f.501.1 8 35.9 even 6
700.2.i.f.501.4 8 7.2 even 3
980.2.e.c.589.1 4 35.27 even 4
980.2.e.c.589.3 4 35.13 even 4
980.2.e.f.589.2 4 5.3 odd 4
980.2.e.f.589.4 4 5.2 odd 4
980.2.q.b.569.1 4 35.17 even 12
980.2.q.b.949.2 4 35.33 even 12
980.2.q.g.569.2 4 35.3 even 12
980.2.q.g.949.2 4 35.12 even 12
1260.2.bm.a.109.2 4 105.2 even 12
1260.2.bm.a.289.2 4 105.53 even 12
1260.2.bm.b.109.2 4 105.23 even 12
1260.2.bm.b.289.1 4 105.32 even 12
4900.2.a.be.1.2 4 1.1 even 1 trivial
4900.2.a.be.1.4 4 5.4 even 2 inner
4900.2.a.bf.1.2 4 35.34 odd 2
4900.2.a.bf.1.4 4 7.6 odd 2