Properties

Label 8024.2.a.bb.1.16
Level $8024$
Weight $2$
Character 8024.1
Self dual yes
Analytic conductor $64.072$
Analytic rank $0$
Dimension $32$
CM no
Inner twists $1$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [8024,2,Mod(1,8024)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(8024, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 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("8024.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 8024 = 2^{3} \cdot 17 \cdot 59 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 8024.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: \(64.0719625819\)
Analytic rank: \(0\)
Dimension: \(32\)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.16
Character \(\chi\) \(=\) 8024.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-0.159636 q^{3} -1.22368 q^{5} +3.18149 q^{7} -2.97452 q^{9} +O(q^{10})\) \(q-0.159636 q^{3} -1.22368 q^{5} +3.18149 q^{7} -2.97452 q^{9} -4.68772 q^{11} -4.84748 q^{13} +0.195343 q^{15} +1.00000 q^{17} -5.27761 q^{19} -0.507880 q^{21} -0.783934 q^{23} -3.50261 q^{25} +0.953748 q^{27} -3.96119 q^{29} +7.08691 q^{31} +0.748328 q^{33} -3.89312 q^{35} -9.25275 q^{37} +0.773833 q^{39} -2.85024 q^{41} -6.32832 q^{43} +3.63985 q^{45} +2.34943 q^{47} +3.12188 q^{49} -0.159636 q^{51} +14.2699 q^{53} +5.73625 q^{55} +0.842496 q^{57} +1.00000 q^{59} -1.63395 q^{61} -9.46340 q^{63} +5.93176 q^{65} +13.5888 q^{67} +0.125144 q^{69} +11.9418 q^{71} +5.14024 q^{73} +0.559143 q^{75} -14.9139 q^{77} +0.220834 q^{79} +8.77130 q^{81} +7.78113 q^{83} -1.22368 q^{85} +0.632348 q^{87} -11.9465 q^{89} -15.4222 q^{91} -1.13132 q^{93} +6.45809 q^{95} -1.18393 q^{97} +13.9437 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 32 q + 8 q^{5} - 3 q^{7} + 40 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 32 q + 8 q^{5} - 3 q^{7} + 40 q^{9} + 3 q^{11} + 13 q^{13} + 4 q^{15} + 32 q^{17} + 14 q^{19} - 7 q^{21} + 7 q^{23} + 38 q^{25} + 9 q^{27} + 17 q^{29} + 15 q^{31} + 18 q^{33} + 6 q^{35} + 21 q^{37} + 16 q^{39} + 49 q^{41} - 7 q^{43} + 14 q^{45} - 25 q^{47} + 37 q^{49} + 12 q^{53} + 15 q^{55} + 45 q^{57} + 32 q^{59} + 5 q^{61} - 12 q^{63} + 39 q^{65} + 12 q^{69} - 13 q^{71} + 70 q^{73} - 47 q^{75} - 10 q^{77} - q^{79} + 84 q^{81} - 17 q^{83} + 8 q^{85} + 20 q^{87} + 42 q^{89} + 36 q^{91} + 2 q^{93} - q^{95} + 58 q^{97} + 7 q^{99}+O(q^{100}) \) 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
\(3\) −0.159636 −0.0921659 −0.0460829 0.998938i \(-0.514674\pi\)
−0.0460829 + 0.998938i \(0.514674\pi\)
\(4\) 0 0
\(5\) −1.22368 −0.547245 −0.273623 0.961837i \(-0.588222\pi\)
−0.273623 + 0.961837i \(0.588222\pi\)
\(6\) 0 0
\(7\) 3.18149 1.20249 0.601245 0.799065i \(-0.294671\pi\)
0.601245 + 0.799065i \(0.294671\pi\)
\(8\) 0 0
\(9\) −2.97452 −0.991505
\(10\) 0 0
\(11\) −4.68772 −1.41340 −0.706700 0.707514i \(-0.749817\pi\)
−0.706700 + 0.707514i \(0.749817\pi\)
\(12\) 0 0
\(13\) −4.84748 −1.34445 −0.672225 0.740347i \(-0.734661\pi\)
−0.672225 + 0.740347i \(0.734661\pi\)
\(14\) 0 0
\(15\) 0.195343 0.0504373
\(16\) 0 0
\(17\) 1.00000 0.242536
\(18\) 0 0
\(19\) −5.27761 −1.21077 −0.605383 0.795934i \(-0.706980\pi\)
−0.605383 + 0.795934i \(0.706980\pi\)
\(20\) 0 0
\(21\) −0.507880 −0.110829
\(22\) 0 0
\(23\) −0.783934 −0.163462 −0.0817308 0.996654i \(-0.526045\pi\)
−0.0817308 + 0.996654i \(0.526045\pi\)
\(24\) 0 0
\(25\) −3.50261 −0.700523
\(26\) 0 0
\(27\) 0.953748 0.183549
\(28\) 0 0
\(29\) −3.96119 −0.735574 −0.367787 0.929910i \(-0.619884\pi\)
−0.367787 + 0.929910i \(0.619884\pi\)
\(30\) 0 0
\(31\) 7.08691 1.27285 0.636423 0.771340i \(-0.280413\pi\)
0.636423 + 0.771340i \(0.280413\pi\)
\(32\) 0 0
\(33\) 0.748328 0.130267
\(34\) 0 0
\(35\) −3.89312 −0.658057
\(36\) 0 0
\(37\) −9.25275 −1.52114 −0.760572 0.649254i \(-0.775081\pi\)
−0.760572 + 0.649254i \(0.775081\pi\)
\(38\) 0 0
\(39\) 0.773833 0.123912
\(40\) 0 0
\(41\) −2.85024 −0.445132 −0.222566 0.974918i \(-0.571443\pi\)
−0.222566 + 0.974918i \(0.571443\pi\)
\(42\) 0 0
\(43\) −6.32832 −0.965060 −0.482530 0.875880i \(-0.660282\pi\)
−0.482530 + 0.875880i \(0.660282\pi\)
\(44\) 0 0
\(45\) 3.63985 0.542597
\(46\) 0 0
\(47\) 2.34943 0.342700 0.171350 0.985210i \(-0.445187\pi\)
0.171350 + 0.985210i \(0.445187\pi\)
\(48\) 0 0
\(49\) 3.12188 0.445983
\(50\) 0 0
\(51\) −0.159636 −0.0223535
\(52\) 0 0
\(53\) 14.2699 1.96012 0.980060 0.198704i \(-0.0636732\pi\)
0.980060 + 0.198704i \(0.0636732\pi\)
\(54\) 0 0
\(55\) 5.73625 0.773476
\(56\) 0 0
\(57\) 0.842496 0.111591
\(58\) 0 0
\(59\) 1.00000 0.130189
\(60\) 0 0
\(61\) −1.63395 −0.209206 −0.104603 0.994514i \(-0.533357\pi\)
−0.104603 + 0.994514i \(0.533357\pi\)
\(62\) 0 0
\(63\) −9.46340 −1.19228
\(64\) 0 0
\(65\) 5.93176 0.735744
\(66\) 0 0
\(67\) 13.5888 1.66013 0.830067 0.557663i \(-0.188302\pi\)
0.830067 + 0.557663i \(0.188302\pi\)
\(68\) 0 0
\(69\) 0.125144 0.0150656
\(70\) 0 0
\(71\) 11.9418 1.41724 0.708618 0.705592i \(-0.249319\pi\)
0.708618 + 0.705592i \(0.249319\pi\)
\(72\) 0 0
\(73\) 5.14024 0.601619 0.300810 0.953684i \(-0.402743\pi\)
0.300810 + 0.953684i \(0.402743\pi\)
\(74\) 0 0
\(75\) 0.559143 0.0645643
\(76\) 0 0
\(77\) −14.9139 −1.69960
\(78\) 0 0
\(79\) 0.220834 0.0248458 0.0124229 0.999923i \(-0.496046\pi\)
0.0124229 + 0.999923i \(0.496046\pi\)
\(80\) 0 0
\(81\) 8.77130 0.974589
\(82\) 0 0
\(83\) 7.78113 0.854090 0.427045 0.904230i \(-0.359555\pi\)
0.427045 + 0.904230i \(0.359555\pi\)
\(84\) 0 0
\(85\) −1.22368 −0.132726
\(86\) 0 0
\(87\) 0.632348 0.0677948
\(88\) 0 0
\(89\) −11.9465 −1.26632 −0.633162 0.774019i \(-0.718243\pi\)
−0.633162 + 0.774019i \(0.718243\pi\)
\(90\) 0 0
\(91\) −15.4222 −1.61669
\(92\) 0 0
\(93\) −1.13132 −0.117313
\(94\) 0 0
\(95\) 6.45809 0.662586
\(96\) 0 0
\(97\) −1.18393 −0.120209 −0.0601047 0.998192i \(-0.519143\pi\)
−0.0601047 + 0.998192i \(0.519143\pi\)
\(98\) 0 0
\(99\) 13.9437 1.40139
\(100\) 0 0
\(101\) −3.42739 −0.341038 −0.170519 0.985354i \(-0.554544\pi\)
−0.170519 + 0.985354i \(0.554544\pi\)
\(102\) 0 0
\(103\) 5.95890 0.587148 0.293574 0.955936i \(-0.405155\pi\)
0.293574 + 0.955936i \(0.405155\pi\)
\(104\) 0 0
\(105\) 0.621482 0.0606504
\(106\) 0 0
\(107\) 0.0903576 0.00873520 0.00436760 0.999990i \(-0.498610\pi\)
0.00436760 + 0.999990i \(0.498610\pi\)
\(108\) 0 0
\(109\) 13.7381 1.31588 0.657938 0.753072i \(-0.271429\pi\)
0.657938 + 0.753072i \(0.271429\pi\)
\(110\) 0 0
\(111\) 1.47707 0.140197
\(112\) 0 0
\(113\) 5.40931 0.508865 0.254433 0.967091i \(-0.418111\pi\)
0.254433 + 0.967091i \(0.418111\pi\)
\(114\) 0 0
\(115\) 0.959283 0.0894536
\(116\) 0 0
\(117\) 14.4189 1.33303
\(118\) 0 0
\(119\) 3.18149 0.291647
\(120\) 0 0
\(121\) 10.9747 0.997698
\(122\) 0 0
\(123\) 0.455000 0.0410260
\(124\) 0 0
\(125\) 10.4045 0.930603
\(126\) 0 0
\(127\) −2.26004 −0.200546 −0.100273 0.994960i \(-0.531972\pi\)
−0.100273 + 0.994960i \(0.531972\pi\)
\(128\) 0 0
\(129\) 1.01023 0.0889456
\(130\) 0 0
\(131\) −16.6204 −1.45213 −0.726065 0.687626i \(-0.758653\pi\)
−0.726065 + 0.687626i \(0.758653\pi\)
\(132\) 0 0
\(133\) −16.7907 −1.45593
\(134\) 0 0
\(135\) −1.16708 −0.100446
\(136\) 0 0
\(137\) −5.42987 −0.463905 −0.231953 0.972727i \(-0.574511\pi\)
−0.231953 + 0.972727i \(0.574511\pi\)
\(138\) 0 0
\(139\) −7.11995 −0.603906 −0.301953 0.953323i \(-0.597639\pi\)
−0.301953 + 0.953323i \(0.597639\pi\)
\(140\) 0 0
\(141\) −0.375054 −0.0315852
\(142\) 0 0
\(143\) 22.7236 1.90025
\(144\) 0 0
\(145\) 4.84722 0.402539
\(146\) 0 0
\(147\) −0.498365 −0.0411044
\(148\) 0 0
\(149\) −22.3437 −1.83047 −0.915235 0.402921i \(-0.867995\pi\)
−0.915235 + 0.402921i \(0.867995\pi\)
\(150\) 0 0
\(151\) 9.27022 0.754399 0.377200 0.926132i \(-0.376887\pi\)
0.377200 + 0.926132i \(0.376887\pi\)
\(152\) 0 0
\(153\) −2.97452 −0.240475
\(154\) 0 0
\(155\) −8.67208 −0.696559
\(156\) 0 0
\(157\) 18.7248 1.49440 0.747200 0.664599i \(-0.231398\pi\)
0.747200 + 0.664599i \(0.231398\pi\)
\(158\) 0 0
\(159\) −2.27799 −0.180656
\(160\) 0 0
\(161\) −2.49408 −0.196561
\(162\) 0 0
\(163\) −16.2420 −1.27217 −0.636085 0.771619i \(-0.719447\pi\)
−0.636085 + 0.771619i \(0.719447\pi\)
\(164\) 0 0
\(165\) −0.915712 −0.0712881
\(166\) 0 0
\(167\) 10.7205 0.829580 0.414790 0.909917i \(-0.363855\pi\)
0.414790 + 0.909917i \(0.363855\pi\)
\(168\) 0 0
\(169\) 10.4981 0.807546
\(170\) 0 0
\(171\) 15.6983 1.20048
\(172\) 0 0
\(173\) 2.79839 0.212757 0.106379 0.994326i \(-0.466074\pi\)
0.106379 + 0.994326i \(0.466074\pi\)
\(174\) 0 0
\(175\) −11.1435 −0.842372
\(176\) 0 0
\(177\) −0.159636 −0.0119990
\(178\) 0 0
\(179\) −2.84113 −0.212356 −0.106178 0.994347i \(-0.533861\pi\)
−0.106178 + 0.994347i \(0.533861\pi\)
\(180\) 0 0
\(181\) 3.93917 0.292796 0.146398 0.989226i \(-0.453232\pi\)
0.146398 + 0.989226i \(0.453232\pi\)
\(182\) 0 0
\(183\) 0.260837 0.0192817
\(184\) 0 0
\(185\) 11.3224 0.832438
\(186\) 0 0
\(187\) −4.68772 −0.342800
\(188\) 0 0
\(189\) 3.03434 0.220716
\(190\) 0 0
\(191\) 22.0138 1.59286 0.796430 0.604731i \(-0.206719\pi\)
0.796430 + 0.604731i \(0.206719\pi\)
\(192\) 0 0
\(193\) 10.1683 0.731933 0.365966 0.930628i \(-0.380738\pi\)
0.365966 + 0.930628i \(0.380738\pi\)
\(194\) 0 0
\(195\) −0.946922 −0.0678105
\(196\) 0 0
\(197\) 8.86530 0.631627 0.315813 0.948821i \(-0.397723\pi\)
0.315813 + 0.948821i \(0.397723\pi\)
\(198\) 0 0
\(199\) 22.6876 1.60828 0.804141 0.594438i \(-0.202626\pi\)
0.804141 + 0.594438i \(0.202626\pi\)
\(200\) 0 0
\(201\) −2.16926 −0.153008
\(202\) 0 0
\(203\) −12.6025 −0.884521
\(204\) 0 0
\(205\) 3.48777 0.243596
\(206\) 0 0
\(207\) 2.33183 0.162073
\(208\) 0 0
\(209\) 24.7399 1.71130
\(210\) 0 0
\(211\) 13.7486 0.946495 0.473248 0.880930i \(-0.343082\pi\)
0.473248 + 0.880930i \(0.343082\pi\)
\(212\) 0 0
\(213\) −1.90635 −0.130621
\(214\) 0 0
\(215\) 7.74382 0.528124
\(216\) 0 0
\(217\) 22.5469 1.53058
\(218\) 0 0
\(219\) −0.820567 −0.0554488
\(220\) 0 0
\(221\) −4.84748 −0.326077
\(222\) 0 0
\(223\) 0.793664 0.0531477 0.0265738 0.999647i \(-0.491540\pi\)
0.0265738 + 0.999647i \(0.491540\pi\)
\(224\) 0 0
\(225\) 10.4186 0.694572
\(226\) 0 0
\(227\) −8.78020 −0.582762 −0.291381 0.956607i \(-0.594115\pi\)
−0.291381 + 0.956607i \(0.594115\pi\)
\(228\) 0 0
\(229\) 1.98371 0.131087 0.0655436 0.997850i \(-0.479122\pi\)
0.0655436 + 0.997850i \(0.479122\pi\)
\(230\) 0 0
\(231\) 2.38080 0.156645
\(232\) 0 0
\(233\) −18.1934 −1.19189 −0.595946 0.803025i \(-0.703223\pi\)
−0.595946 + 0.803025i \(0.703223\pi\)
\(234\) 0 0
\(235\) −2.87495 −0.187541
\(236\) 0 0
\(237\) −0.0352531 −0.00228993
\(238\) 0 0
\(239\) −24.5927 −1.59077 −0.795384 0.606106i \(-0.792731\pi\)
−0.795384 + 0.606106i \(0.792731\pi\)
\(240\) 0 0
\(241\) −16.4395 −1.05896 −0.529480 0.848323i \(-0.677613\pi\)
−0.529480 + 0.848323i \(0.677613\pi\)
\(242\) 0 0
\(243\) −4.26146 −0.273373
\(244\) 0 0
\(245\) −3.82018 −0.244062
\(246\) 0 0
\(247\) 25.5831 1.62782
\(248\) 0 0
\(249\) −1.24215 −0.0787179
\(250\) 0 0
\(251\) 1.30009 0.0820612 0.0410306 0.999158i \(-0.486936\pi\)
0.0410306 + 0.999158i \(0.486936\pi\)
\(252\) 0 0
\(253\) 3.67486 0.231037
\(254\) 0 0
\(255\) 0.195343 0.0122328
\(256\) 0 0
\(257\) −13.5662 −0.846239 −0.423119 0.906074i \(-0.639065\pi\)
−0.423119 + 0.906074i \(0.639065\pi\)
\(258\) 0 0
\(259\) −29.4375 −1.82916
\(260\) 0 0
\(261\) 11.7826 0.729326
\(262\) 0 0
\(263\) 16.0744 0.991189 0.495595 0.868554i \(-0.334950\pi\)
0.495595 + 0.868554i \(0.334950\pi\)
\(264\) 0 0
\(265\) −17.4617 −1.07267
\(266\) 0 0
\(267\) 1.90709 0.116712
\(268\) 0 0
\(269\) −17.6739 −1.07760 −0.538798 0.842435i \(-0.681121\pi\)
−0.538798 + 0.842435i \(0.681121\pi\)
\(270\) 0 0
\(271\) −2.84698 −0.172942 −0.0864708 0.996254i \(-0.527559\pi\)
−0.0864708 + 0.996254i \(0.527559\pi\)
\(272\) 0 0
\(273\) 2.46194 0.149003
\(274\) 0 0
\(275\) 16.4193 0.990119
\(276\) 0 0
\(277\) 3.46116 0.207961 0.103980 0.994579i \(-0.466842\pi\)
0.103980 + 0.994579i \(0.466842\pi\)
\(278\) 0 0
\(279\) −21.0801 −1.26203
\(280\) 0 0
\(281\) −10.4336 −0.622415 −0.311207 0.950342i \(-0.600733\pi\)
−0.311207 + 0.950342i \(0.600733\pi\)
\(282\) 0 0
\(283\) 5.56408 0.330750 0.165375 0.986231i \(-0.447117\pi\)
0.165375 + 0.986231i \(0.447117\pi\)
\(284\) 0 0
\(285\) −1.03094 −0.0610678
\(286\) 0 0
\(287\) −9.06800 −0.535267
\(288\) 0 0
\(289\) 1.00000 0.0588235
\(290\) 0 0
\(291\) 0.188997 0.0110792
\(292\) 0 0
\(293\) −10.3845 −0.606667 −0.303333 0.952885i \(-0.598100\pi\)
−0.303333 + 0.952885i \(0.598100\pi\)
\(294\) 0 0
\(295\) −1.22368 −0.0712452
\(296\) 0 0
\(297\) −4.47090 −0.259428
\(298\) 0 0
\(299\) 3.80011 0.219766
\(300\) 0 0
\(301\) −20.1335 −1.16048
\(302\) 0 0
\(303\) 0.547135 0.0314321
\(304\) 0 0
\(305\) 1.99943 0.114487
\(306\) 0 0
\(307\) 7.67646 0.438119 0.219059 0.975712i \(-0.429701\pi\)
0.219059 + 0.975712i \(0.429701\pi\)
\(308\) 0 0
\(309\) −0.951254 −0.0541150
\(310\) 0 0
\(311\) 15.5562 0.882112 0.441056 0.897480i \(-0.354604\pi\)
0.441056 + 0.897480i \(0.354604\pi\)
\(312\) 0 0
\(313\) 9.92757 0.561140 0.280570 0.959834i \(-0.409477\pi\)
0.280570 + 0.959834i \(0.409477\pi\)
\(314\) 0 0
\(315\) 11.5801 0.652467
\(316\) 0 0
\(317\) −29.3994 −1.65124 −0.825619 0.564229i \(-0.809174\pi\)
−0.825619 + 0.564229i \(0.809174\pi\)
\(318\) 0 0
\(319\) 18.5689 1.03966
\(320\) 0 0
\(321\) −0.0144243 −0.000805087 0
\(322\) 0 0
\(323\) −5.27761 −0.293654
\(324\) 0 0
\(325\) 16.9789 0.941818
\(326\) 0 0
\(327\) −2.19310 −0.121279
\(328\) 0 0
\(329\) 7.47469 0.412093
\(330\) 0 0
\(331\) −18.0149 −0.990189 −0.495094 0.868839i \(-0.664867\pi\)
−0.495094 + 0.868839i \(0.664867\pi\)
\(332\) 0 0
\(333\) 27.5225 1.50822
\(334\) 0 0
\(335\) −16.6283 −0.908500
\(336\) 0 0
\(337\) −7.83733 −0.426927 −0.213463 0.976951i \(-0.568474\pi\)
−0.213463 + 0.976951i \(0.568474\pi\)
\(338\) 0 0
\(339\) −0.863521 −0.0469000
\(340\) 0 0
\(341\) −33.2214 −1.79904
\(342\) 0 0
\(343\) −12.3382 −0.666200
\(344\) 0 0
\(345\) −0.153136 −0.00824456
\(346\) 0 0
\(347\) −5.37196 −0.288382 −0.144191 0.989550i \(-0.546058\pi\)
−0.144191 + 0.989550i \(0.546058\pi\)
\(348\) 0 0
\(349\) 31.1222 1.66593 0.832966 0.553325i \(-0.186641\pi\)
0.832966 + 0.553325i \(0.186641\pi\)
\(350\) 0 0
\(351\) −4.62328 −0.246772
\(352\) 0 0
\(353\) 30.8396 1.64143 0.820713 0.571341i \(-0.193577\pi\)
0.820713 + 0.571341i \(0.193577\pi\)
\(354\) 0 0
\(355\) −14.6130 −0.775576
\(356\) 0 0
\(357\) −0.507880 −0.0268799
\(358\) 0 0
\(359\) −10.3567 −0.546603 −0.273302 0.961928i \(-0.588116\pi\)
−0.273302 + 0.961928i \(0.588116\pi\)
\(360\) 0 0
\(361\) 8.85314 0.465955
\(362\) 0 0
\(363\) −1.75195 −0.0919537
\(364\) 0 0
\(365\) −6.28999 −0.329233
\(366\) 0 0
\(367\) −21.5607 −1.12546 −0.562730 0.826641i \(-0.690249\pi\)
−0.562730 + 0.826641i \(0.690249\pi\)
\(368\) 0 0
\(369\) 8.47807 0.441351
\(370\) 0 0
\(371\) 45.3995 2.35702
\(372\) 0 0
\(373\) 30.3603 1.57200 0.785999 0.618228i \(-0.212149\pi\)
0.785999 + 0.618228i \(0.212149\pi\)
\(374\) 0 0
\(375\) −1.66093 −0.0857698
\(376\) 0 0
\(377\) 19.2018 0.988943
\(378\) 0 0
\(379\) −10.8141 −0.555485 −0.277743 0.960655i \(-0.589586\pi\)
−0.277743 + 0.960655i \(0.589586\pi\)
\(380\) 0 0
\(381\) 0.360784 0.0184835
\(382\) 0 0
\(383\) −16.4602 −0.841075 −0.420537 0.907275i \(-0.638158\pi\)
−0.420537 + 0.907275i \(0.638158\pi\)
\(384\) 0 0
\(385\) 18.2498 0.930097
\(386\) 0 0
\(387\) 18.8237 0.956862
\(388\) 0 0
\(389\) −11.4768 −0.581894 −0.290947 0.956739i \(-0.593970\pi\)
−0.290947 + 0.956739i \(0.593970\pi\)
\(390\) 0 0
\(391\) −0.783934 −0.0396453
\(392\) 0 0
\(393\) 2.65321 0.133837
\(394\) 0 0
\(395\) −0.270230 −0.0135967
\(396\) 0 0
\(397\) 29.7362 1.49242 0.746208 0.665713i \(-0.231872\pi\)
0.746208 + 0.665713i \(0.231872\pi\)
\(398\) 0 0
\(399\) 2.68039 0.134187
\(400\) 0 0
\(401\) −7.69858 −0.384449 −0.192224 0.981351i \(-0.561570\pi\)
−0.192224 + 0.981351i \(0.561570\pi\)
\(402\) 0 0
\(403\) −34.3537 −1.71128
\(404\) 0 0
\(405\) −10.7332 −0.533339
\(406\) 0 0
\(407\) 43.3743 2.14998
\(408\) 0 0
\(409\) 5.56107 0.274977 0.137489 0.990503i \(-0.456097\pi\)
0.137489 + 0.990503i \(0.456097\pi\)
\(410\) 0 0
\(411\) 0.866803 0.0427562
\(412\) 0 0
\(413\) 3.18149 0.156551
\(414\) 0 0
\(415\) −9.52159 −0.467396
\(416\) 0 0
\(417\) 1.13660 0.0556595
\(418\) 0 0
\(419\) −30.5828 −1.49407 −0.747034 0.664786i \(-0.768523\pi\)
−0.747034 + 0.664786i \(0.768523\pi\)
\(420\) 0 0
\(421\) 27.9069 1.36010 0.680051 0.733165i \(-0.261958\pi\)
0.680051 + 0.733165i \(0.261958\pi\)
\(422\) 0 0
\(423\) −6.98842 −0.339789
\(424\) 0 0
\(425\) −3.50261 −0.169902
\(426\) 0 0
\(427\) −5.19840 −0.251568
\(428\) 0 0
\(429\) −3.62751 −0.175138
\(430\) 0 0
\(431\) −27.0068 −1.30087 −0.650436 0.759561i \(-0.725414\pi\)
−0.650436 + 0.759561i \(0.725414\pi\)
\(432\) 0 0
\(433\) 0.283178 0.0136087 0.00680433 0.999977i \(-0.497834\pi\)
0.00680433 + 0.999977i \(0.497834\pi\)
\(434\) 0 0
\(435\) −0.773790 −0.0371004
\(436\) 0 0
\(437\) 4.13730 0.197914
\(438\) 0 0
\(439\) −27.6030 −1.31742 −0.658709 0.752398i \(-0.728897\pi\)
−0.658709 + 0.752398i \(0.728897\pi\)
\(440\) 0 0
\(441\) −9.28609 −0.442195
\(442\) 0 0
\(443\) −26.0375 −1.23708 −0.618541 0.785753i \(-0.712276\pi\)
−0.618541 + 0.785753i \(0.712276\pi\)
\(444\) 0 0
\(445\) 14.6186 0.692990
\(446\) 0 0
\(447\) 3.56686 0.168707
\(448\) 0 0
\(449\) −4.46706 −0.210814 −0.105407 0.994429i \(-0.533614\pi\)
−0.105407 + 0.994429i \(0.533614\pi\)
\(450\) 0 0
\(451\) 13.3611 0.629149
\(452\) 0 0
\(453\) −1.47986 −0.0695299
\(454\) 0 0
\(455\) 18.8718 0.884725
\(456\) 0 0
\(457\) 28.1249 1.31563 0.657813 0.753182i \(-0.271482\pi\)
0.657813 + 0.753182i \(0.271482\pi\)
\(458\) 0 0
\(459\) 0.953748 0.0445171
\(460\) 0 0
\(461\) 33.0219 1.53798 0.768991 0.639260i \(-0.220759\pi\)
0.768991 + 0.639260i \(0.220759\pi\)
\(462\) 0 0
\(463\) 6.77577 0.314897 0.157448 0.987527i \(-0.449673\pi\)
0.157448 + 0.987527i \(0.449673\pi\)
\(464\) 0 0
\(465\) 1.38438 0.0641989
\(466\) 0 0
\(467\) −29.2140 −1.35186 −0.675932 0.736964i \(-0.736259\pi\)
−0.675932 + 0.736964i \(0.736259\pi\)
\(468\) 0 0
\(469\) 43.2326 1.99630
\(470\) 0 0
\(471\) −2.98915 −0.137733
\(472\) 0 0
\(473\) 29.6654 1.36401
\(474\) 0 0
\(475\) 18.4854 0.848169
\(476\) 0 0
\(477\) −42.4460 −1.94347
\(478\) 0 0
\(479\) −42.9076 −1.96050 −0.980249 0.197769i \(-0.936631\pi\)
−0.980249 + 0.197769i \(0.936631\pi\)
\(480\) 0 0
\(481\) 44.8526 2.04510
\(482\) 0 0
\(483\) 0.398145 0.0181162
\(484\) 0 0
\(485\) 1.44874 0.0657840
\(486\) 0 0
\(487\) −1.54390 −0.0699608 −0.0349804 0.999388i \(-0.511137\pi\)
−0.0349804 + 0.999388i \(0.511137\pi\)
\(488\) 0 0
\(489\) 2.59280 0.117251
\(490\) 0 0
\(491\) −14.0195 −0.632689 −0.316345 0.948644i \(-0.602456\pi\)
−0.316345 + 0.948644i \(0.602456\pi\)
\(492\) 0 0
\(493\) −3.96119 −0.178403
\(494\) 0 0
\(495\) −17.0626 −0.766906
\(496\) 0 0
\(497\) 37.9929 1.70421
\(498\) 0 0
\(499\) 8.41653 0.376776 0.188388 0.982095i \(-0.439674\pi\)
0.188388 + 0.982095i \(0.439674\pi\)
\(500\) 0 0
\(501\) −1.71138 −0.0764590
\(502\) 0 0
\(503\) 7.08466 0.315889 0.157945 0.987448i \(-0.449513\pi\)
0.157945 + 0.987448i \(0.449513\pi\)
\(504\) 0 0
\(505\) 4.19402 0.186632
\(506\) 0 0
\(507\) −1.67587 −0.0744282
\(508\) 0 0
\(509\) −20.3061 −0.900050 −0.450025 0.893016i \(-0.648585\pi\)
−0.450025 + 0.893016i \(0.648585\pi\)
\(510\) 0 0
\(511\) 16.3536 0.723442
\(512\) 0 0
\(513\) −5.03351 −0.222235
\(514\) 0 0
\(515\) −7.29177 −0.321314
\(516\) 0 0
\(517\) −11.0135 −0.484372
\(518\) 0 0
\(519\) −0.446723 −0.0196090
\(520\) 0 0
\(521\) 27.9533 1.22465 0.612327 0.790604i \(-0.290234\pi\)
0.612327 + 0.790604i \(0.290234\pi\)
\(522\) 0 0
\(523\) 41.6435 1.82094 0.910472 0.413570i \(-0.135718\pi\)
0.910472 + 0.413570i \(0.135718\pi\)
\(524\) 0 0
\(525\) 1.77891 0.0776379
\(526\) 0 0
\(527\) 7.08691 0.308710
\(528\) 0 0
\(529\) −22.3854 −0.973280
\(530\) 0 0
\(531\) −2.97452 −0.129083
\(532\) 0 0
\(533\) 13.8165 0.598458
\(534\) 0 0
\(535\) −0.110569 −0.00478029
\(536\) 0 0
\(537\) 0.453547 0.0195720
\(538\) 0 0
\(539\) −14.6345 −0.630353
\(540\) 0 0
\(541\) 25.2704 1.08646 0.543229 0.839585i \(-0.317202\pi\)
0.543229 + 0.839585i \(0.317202\pi\)
\(542\) 0 0
\(543\) −0.628833 −0.0269858
\(544\) 0 0
\(545\) −16.8111 −0.720107
\(546\) 0 0
\(547\) 16.7958 0.718137 0.359068 0.933311i \(-0.383094\pi\)
0.359068 + 0.933311i \(0.383094\pi\)
\(548\) 0 0
\(549\) 4.86022 0.207429
\(550\) 0 0
\(551\) 20.9056 0.890608
\(552\) 0 0
\(553\) 0.702582 0.0298768
\(554\) 0 0
\(555\) −1.80746 −0.0767224
\(556\) 0 0
\(557\) 20.1116 0.852157 0.426078 0.904686i \(-0.359895\pi\)
0.426078 + 0.904686i \(0.359895\pi\)
\(558\) 0 0
\(559\) 30.6764 1.29747
\(560\) 0 0
\(561\) 0.748328 0.0315944
\(562\) 0 0
\(563\) 19.7409 0.831979 0.415990 0.909369i \(-0.363435\pi\)
0.415990 + 0.909369i \(0.363435\pi\)
\(564\) 0 0
\(565\) −6.61925 −0.278474
\(566\) 0 0
\(567\) 27.9058 1.17193
\(568\) 0 0
\(569\) 26.3605 1.10509 0.552546 0.833483i \(-0.313656\pi\)
0.552546 + 0.833483i \(0.313656\pi\)
\(570\) 0 0
\(571\) 42.1151 1.76246 0.881230 0.472687i \(-0.156716\pi\)
0.881230 + 0.472687i \(0.156716\pi\)
\(572\) 0 0
\(573\) −3.51419 −0.146807
\(574\) 0 0
\(575\) 2.74582 0.114509
\(576\) 0 0
\(577\) −12.7502 −0.530797 −0.265398 0.964139i \(-0.585503\pi\)
−0.265398 + 0.964139i \(0.585503\pi\)
\(578\) 0 0
\(579\) −1.62323 −0.0674592
\(580\) 0 0
\(581\) 24.7556 1.02703
\(582\) 0 0
\(583\) −66.8932 −2.77043
\(584\) 0 0
\(585\) −17.6441 −0.729494
\(586\) 0 0
\(587\) −24.5005 −1.01124 −0.505621 0.862755i \(-0.668737\pi\)
−0.505621 + 0.862755i \(0.668737\pi\)
\(588\) 0 0
\(589\) −37.4019 −1.54112
\(590\) 0 0
\(591\) −1.41522 −0.0582144
\(592\) 0 0
\(593\) 42.6831 1.75279 0.876393 0.481597i \(-0.159943\pi\)
0.876393 + 0.481597i \(0.159943\pi\)
\(594\) 0 0
\(595\) −3.89312 −0.159602
\(596\) 0 0
\(597\) −3.62176 −0.148229
\(598\) 0 0
\(599\) −36.3736 −1.48619 −0.743093 0.669188i \(-0.766642\pi\)
−0.743093 + 0.669188i \(0.766642\pi\)
\(600\) 0 0
\(601\) 3.42501 0.139709 0.0698545 0.997557i \(-0.477746\pi\)
0.0698545 + 0.997557i \(0.477746\pi\)
\(602\) 0 0
\(603\) −40.4201 −1.64603
\(604\) 0 0
\(605\) −13.4295 −0.545985
\(606\) 0 0
\(607\) 3.78328 0.153559 0.0767793 0.997048i \(-0.475536\pi\)
0.0767793 + 0.997048i \(0.475536\pi\)
\(608\) 0 0
\(609\) 2.01181 0.0815226
\(610\) 0 0
\(611\) −11.3888 −0.460743
\(612\) 0 0
\(613\) 6.93993 0.280301 0.140151 0.990130i \(-0.455241\pi\)
0.140151 + 0.990130i \(0.455241\pi\)
\(614\) 0 0
\(615\) −0.556773 −0.0224513
\(616\) 0 0
\(617\) 35.5832 1.43253 0.716263 0.697831i \(-0.245851\pi\)
0.716263 + 0.697831i \(0.245851\pi\)
\(618\) 0 0
\(619\) −6.52750 −0.262362 −0.131181 0.991358i \(-0.541877\pi\)
−0.131181 + 0.991358i \(0.541877\pi\)
\(620\) 0 0
\(621\) −0.747675 −0.0300032
\(622\) 0 0
\(623\) −38.0076 −1.52274
\(624\) 0 0
\(625\) 4.78137 0.191255
\(626\) 0 0
\(627\) −3.94938 −0.157723
\(628\) 0 0
\(629\) −9.25275 −0.368931
\(630\) 0 0
\(631\) 35.0434 1.39506 0.697528 0.716557i \(-0.254283\pi\)
0.697528 + 0.716557i \(0.254283\pi\)
\(632\) 0 0
\(633\) −2.19478 −0.0872345
\(634\) 0 0
\(635\) 2.76556 0.109748
\(636\) 0 0
\(637\) −15.1333 −0.599602
\(638\) 0 0
\(639\) −35.5212 −1.40520
\(640\) 0 0
\(641\) −18.8738 −0.745469 −0.372735 0.927938i \(-0.621580\pi\)
−0.372735 + 0.927938i \(0.621580\pi\)
\(642\) 0 0
\(643\) −28.6814 −1.13108 −0.565541 0.824720i \(-0.691333\pi\)
−0.565541 + 0.824720i \(0.691333\pi\)
\(644\) 0 0
\(645\) −1.23619 −0.0486750
\(646\) 0 0
\(647\) 29.6276 1.16478 0.582390 0.812909i \(-0.302118\pi\)
0.582390 + 0.812909i \(0.302118\pi\)
\(648\) 0 0
\(649\) −4.68772 −0.184009
\(650\) 0 0
\(651\) −3.59930 −0.141068
\(652\) 0 0
\(653\) −4.06063 −0.158905 −0.0794523 0.996839i \(-0.525317\pi\)
−0.0794523 + 0.996839i \(0.525317\pi\)
\(654\) 0 0
\(655\) 20.3380 0.794671
\(656\) 0 0
\(657\) −15.2897 −0.596509
\(658\) 0 0
\(659\) 41.5565 1.61881 0.809405 0.587250i \(-0.199790\pi\)
0.809405 + 0.587250i \(0.199790\pi\)
\(660\) 0 0
\(661\) −6.98492 −0.271682 −0.135841 0.990731i \(-0.543374\pi\)
−0.135841 + 0.990731i \(0.543374\pi\)
\(662\) 0 0
\(663\) 0.773833 0.0300532
\(664\) 0 0
\(665\) 20.5463 0.796753
\(666\) 0 0
\(667\) 3.10531 0.120238
\(668\) 0 0
\(669\) −0.126697 −0.00489840
\(670\) 0 0
\(671\) 7.65950 0.295692
\(672\) 0 0
\(673\) 45.6607 1.76009 0.880046 0.474888i \(-0.157511\pi\)
0.880046 + 0.474888i \(0.157511\pi\)
\(674\) 0 0
\(675\) −3.34061 −0.128580
\(676\) 0 0
\(677\) −2.97767 −0.114441 −0.0572207 0.998362i \(-0.518224\pi\)
−0.0572207 + 0.998362i \(0.518224\pi\)
\(678\) 0 0
\(679\) −3.76665 −0.144551
\(680\) 0 0
\(681\) 1.40163 0.0537108
\(682\) 0 0
\(683\) 25.0810 0.959697 0.479849 0.877351i \(-0.340692\pi\)
0.479849 + 0.877351i \(0.340692\pi\)
\(684\) 0 0
\(685\) 6.64441 0.253870
\(686\) 0 0
\(687\) −0.316671 −0.0120818
\(688\) 0 0
\(689\) −69.1730 −2.63528
\(690\) 0 0
\(691\) −6.91079 −0.262899 −0.131449 0.991323i \(-0.541963\pi\)
−0.131449 + 0.991323i \(0.541963\pi\)
\(692\) 0 0
\(693\) 44.3617 1.68516
\(694\) 0 0
\(695\) 8.71252 0.330485
\(696\) 0 0
\(697\) −2.85024 −0.107960
\(698\) 0 0
\(699\) 2.90433 0.109852
\(700\) 0 0
\(701\) 47.1939 1.78249 0.891244 0.453524i \(-0.149833\pi\)
0.891244 + 0.453524i \(0.149833\pi\)
\(702\) 0 0
\(703\) 48.8324 1.84175
\(704\) 0 0
\(705\) 0.458945 0.0172849
\(706\) 0 0
\(707\) −10.9042 −0.410095
\(708\) 0 0
\(709\) 49.2058 1.84796 0.923982 0.382437i \(-0.124915\pi\)
0.923982 + 0.382437i \(0.124915\pi\)
\(710\) 0 0
\(711\) −0.656875 −0.0246347
\(712\) 0 0
\(713\) −5.55567 −0.208061
\(714\) 0 0
\(715\) −27.8064 −1.03990
\(716\) 0 0
\(717\) 3.92587 0.146614
\(718\) 0 0
\(719\) −26.1746 −0.976147 −0.488073 0.872803i \(-0.662300\pi\)
−0.488073 + 0.872803i \(0.662300\pi\)
\(720\) 0 0
\(721\) 18.9582 0.706039
\(722\) 0 0
\(723\) 2.62433 0.0975999
\(724\) 0 0
\(725\) 13.8745 0.515286
\(726\) 0 0
\(727\) 27.0554 1.00343 0.501715 0.865033i \(-0.332703\pi\)
0.501715 + 0.865033i \(0.332703\pi\)
\(728\) 0 0
\(729\) −25.6336 −0.949393
\(730\) 0 0
\(731\) −6.32832 −0.234061
\(732\) 0 0
\(733\) 13.9986 0.517050 0.258525 0.966005i \(-0.416764\pi\)
0.258525 + 0.966005i \(0.416764\pi\)
\(734\) 0 0
\(735\) 0.609838 0.0224942
\(736\) 0 0
\(737\) −63.7004 −2.34643
\(738\) 0 0
\(739\) 24.6598 0.907126 0.453563 0.891224i \(-0.350153\pi\)
0.453563 + 0.891224i \(0.350153\pi\)
\(740\) 0 0
\(741\) −4.08399 −0.150029
\(742\) 0 0
\(743\) 34.5789 1.26858 0.634288 0.773097i \(-0.281293\pi\)
0.634288 + 0.773097i \(0.281293\pi\)
\(744\) 0 0
\(745\) 27.3415 1.00172
\(746\) 0 0
\(747\) −23.1451 −0.846835
\(748\) 0 0
\(749\) 0.287472 0.0105040
\(750\) 0 0
\(751\) 28.8076 1.05120 0.525602 0.850731i \(-0.323840\pi\)
0.525602 + 0.850731i \(0.323840\pi\)
\(752\) 0 0
\(753\) −0.207542 −0.00756324
\(754\) 0 0
\(755\) −11.3438 −0.412841
\(756\) 0 0
\(757\) −4.75998 −0.173004 −0.0865021 0.996252i \(-0.527569\pi\)
−0.0865021 + 0.996252i \(0.527569\pi\)
\(758\) 0 0
\(759\) −0.586640 −0.0212937
\(760\) 0 0
\(761\) 19.4235 0.704101 0.352050 0.935981i \(-0.385485\pi\)
0.352050 + 0.935981i \(0.385485\pi\)
\(762\) 0 0
\(763\) 43.7078 1.58233
\(764\) 0 0
\(765\) 3.63985 0.131599
\(766\) 0 0
\(767\) −4.84748 −0.175033
\(768\) 0 0
\(769\) 28.0219 1.01049 0.505247 0.862975i \(-0.331401\pi\)
0.505247 + 0.862975i \(0.331401\pi\)
\(770\) 0 0
\(771\) 2.16566 0.0779943
\(772\) 0 0
\(773\) 26.6224 0.957541 0.478770 0.877940i \(-0.341083\pi\)
0.478770 + 0.877940i \(0.341083\pi\)
\(774\) 0 0
\(775\) −24.8227 −0.891657
\(776\) 0 0
\(777\) 4.69929 0.168586
\(778\) 0 0
\(779\) 15.0424 0.538951
\(780\) 0 0
\(781\) −55.9800 −2.00312
\(782\) 0 0
\(783\) −3.77797 −0.135014
\(784\) 0 0
\(785\) −22.9131 −0.817803
\(786\) 0 0
\(787\) 43.3373 1.54481 0.772405 0.635131i \(-0.219054\pi\)
0.772405 + 0.635131i \(0.219054\pi\)
\(788\) 0 0
\(789\) −2.56605 −0.0913538
\(790\) 0 0
\(791\) 17.2097 0.611906
\(792\) 0 0
\(793\) 7.92055 0.281267
\(794\) 0 0
\(795\) 2.78752 0.0988631
\(796\) 0 0
\(797\) 23.1631 0.820479 0.410240 0.911978i \(-0.365445\pi\)
0.410240 + 0.911978i \(0.365445\pi\)
\(798\) 0 0
\(799\) 2.34943 0.0831169
\(800\) 0 0
\(801\) 35.5350 1.25557
\(802\) 0 0
\(803\) −24.0960 −0.850329
\(804\) 0 0
\(805\) 3.05195 0.107567
\(806\) 0 0
\(807\) 2.82139 0.0993176
\(808\) 0 0
\(809\) −23.8654 −0.839064 −0.419532 0.907741i \(-0.637806\pi\)
−0.419532 + 0.907741i \(0.637806\pi\)
\(810\) 0 0
\(811\) −39.0771 −1.37218 −0.686092 0.727515i \(-0.740675\pi\)
−0.686092 + 0.727515i \(0.740675\pi\)
\(812\) 0 0
\(813\) 0.454480 0.0159393
\(814\) 0 0
\(815\) 19.8749 0.696189
\(816\) 0 0
\(817\) 33.3984 1.16846
\(818\) 0 0
\(819\) 45.8737 1.60296
\(820\) 0 0
\(821\) −21.8685 −0.763214 −0.381607 0.924325i \(-0.624629\pi\)
−0.381607 + 0.924325i \(0.624629\pi\)
\(822\) 0 0
\(823\) 7.21602 0.251535 0.125767 0.992060i \(-0.459861\pi\)
0.125767 + 0.992060i \(0.459861\pi\)
\(824\) 0 0
\(825\) −2.62110 −0.0912551
\(826\) 0 0
\(827\) −3.47242 −0.120748 −0.0603739 0.998176i \(-0.519229\pi\)
−0.0603739 + 0.998176i \(0.519229\pi\)
\(828\) 0 0
\(829\) −25.2692 −0.877634 −0.438817 0.898576i \(-0.644602\pi\)
−0.438817 + 0.898576i \(0.644602\pi\)
\(830\) 0 0
\(831\) −0.552525 −0.0191669
\(832\) 0 0
\(833\) 3.12188 0.108167
\(834\) 0 0
\(835\) −13.1185 −0.453984
\(836\) 0 0
\(837\) 6.75912 0.233629
\(838\) 0 0
\(839\) −0.360262 −0.0124376 −0.00621882 0.999981i \(-0.501980\pi\)
−0.00621882 + 0.999981i \(0.501980\pi\)
\(840\) 0 0
\(841\) −13.3090 −0.458931
\(842\) 0 0
\(843\) 1.66557 0.0573654
\(844\) 0 0
\(845\) −12.8463 −0.441926
\(846\) 0 0
\(847\) 34.9158 1.19972
\(848\) 0 0
\(849\) −0.888227 −0.0304839
\(850\) 0 0
\(851\) 7.25355 0.248648
\(852\) 0 0
\(853\) −21.2029 −0.725973 −0.362987 0.931794i \(-0.618243\pi\)
−0.362987 + 0.931794i \(0.618243\pi\)
\(854\) 0 0
\(855\) −19.2097 −0.656958
\(856\) 0 0
\(857\) 33.7746 1.15372 0.576859 0.816844i \(-0.304278\pi\)
0.576859 + 0.816844i \(0.304278\pi\)
\(858\) 0 0
\(859\) −6.90816 −0.235703 −0.117852 0.993031i \(-0.537601\pi\)
−0.117852 + 0.993031i \(0.537601\pi\)
\(860\) 0 0
\(861\) 1.44758 0.0493333
\(862\) 0 0
\(863\) 32.2974 1.09942 0.549708 0.835357i \(-0.314739\pi\)
0.549708 + 0.835357i \(0.314739\pi\)
\(864\) 0 0
\(865\) −3.42432 −0.116430
\(866\) 0 0
\(867\) −0.159636 −0.00542152
\(868\) 0 0
\(869\) −1.03521 −0.0351170
\(870\) 0 0
\(871\) −65.8714 −2.23197
\(872\) 0 0
\(873\) 3.52161 0.119188
\(874\) 0 0
\(875\) 33.1017 1.11904
\(876\) 0 0
\(877\) 29.8357 1.00748 0.503740 0.863856i \(-0.331957\pi\)
0.503740 + 0.863856i \(0.331957\pi\)
\(878\) 0 0
\(879\) 1.65773 0.0559139
\(880\) 0 0
\(881\) −49.8307 −1.67884 −0.839419 0.543485i \(-0.817105\pi\)
−0.839419 + 0.543485i \(0.817105\pi\)
\(882\) 0 0
\(883\) 29.5600 0.994773 0.497387 0.867529i \(-0.334293\pi\)
0.497387 + 0.867529i \(0.334293\pi\)
\(884\) 0 0
\(885\) 0.195343 0.00656638
\(886\) 0 0
\(887\) −45.2555 −1.51953 −0.759766 0.650197i \(-0.774686\pi\)
−0.759766 + 0.650197i \(0.774686\pi\)
\(888\) 0 0
\(889\) −7.19030 −0.241155
\(890\) 0 0
\(891\) −41.1173 −1.37748
\(892\) 0 0
\(893\) −12.3994 −0.414929
\(894\) 0 0
\(895\) 3.47663 0.116211
\(896\) 0 0
\(897\) −0.606634 −0.0202549
\(898\) 0 0
\(899\) −28.0726 −0.936272
\(900\) 0 0
\(901\) 14.2699 0.475399
\(902\) 0 0
\(903\) 3.21403 0.106956
\(904\) 0 0
\(905\) −4.82027 −0.160231
\(906\) 0 0
\(907\) −0.155456 −0.00516185 −0.00258092 0.999997i \(-0.500822\pi\)
−0.00258092 + 0.999997i \(0.500822\pi\)
\(908\) 0 0
\(909\) 10.1948 0.338141
\(910\) 0 0
\(911\) 38.8398 1.28682 0.643410 0.765522i \(-0.277519\pi\)
0.643410 + 0.765522i \(0.277519\pi\)
\(912\) 0 0
\(913\) −36.4757 −1.20717
\(914\) 0 0
\(915\) −0.319181 −0.0105518
\(916\) 0 0
\(917\) −52.8776 −1.74617
\(918\) 0 0
\(919\) −41.5612 −1.37098 −0.685489 0.728083i \(-0.740411\pi\)
−0.685489 + 0.728083i \(0.740411\pi\)
\(920\) 0 0
\(921\) −1.22544 −0.0403796
\(922\) 0 0
\(923\) −57.8879 −1.90540
\(924\) 0 0
\(925\) 32.4088 1.06560
\(926\) 0 0
\(927\) −17.7248 −0.582160
\(928\) 0 0
\(929\) 8.44937 0.277215 0.138607 0.990347i \(-0.455737\pi\)
0.138607 + 0.990347i \(0.455737\pi\)
\(930\) 0 0
\(931\) −16.4761 −0.539982
\(932\) 0 0
\(933\) −2.48333 −0.0813006
\(934\) 0 0
\(935\) 5.73625 0.187595
\(936\) 0 0
\(937\) −15.2953 −0.499676 −0.249838 0.968288i \(-0.580377\pi\)
−0.249838 + 0.968288i \(0.580377\pi\)
\(938\) 0 0
\(939\) −1.58480 −0.0517179
\(940\) 0 0
\(941\) −14.8519 −0.484160 −0.242080 0.970256i \(-0.577830\pi\)
−0.242080 + 0.970256i \(0.577830\pi\)
\(942\) 0 0
\(943\) 2.23440 0.0727620
\(944\) 0 0
\(945\) −3.71305 −0.120786
\(946\) 0 0
\(947\) 21.0834 0.685118 0.342559 0.939496i \(-0.388706\pi\)
0.342559 + 0.939496i \(0.388706\pi\)
\(948\) 0 0
\(949\) −24.9172 −0.808847
\(950\) 0 0
\(951\) 4.69321 0.152188
\(952\) 0 0
\(953\) 13.6820 0.443202 0.221601 0.975137i \(-0.428872\pi\)
0.221601 + 0.975137i \(0.428872\pi\)
\(954\) 0 0
\(955\) −26.9377 −0.871685
\(956\) 0 0
\(957\) −2.96427 −0.0958212
\(958\) 0 0
\(959\) −17.2751 −0.557842
\(960\) 0 0
\(961\) 19.2242 0.620136
\(962\) 0 0
\(963\) −0.268770 −0.00866099
\(964\) 0 0
\(965\) −12.4428 −0.400547
\(966\) 0 0
\(967\) −27.3058 −0.878096 −0.439048 0.898464i \(-0.644684\pi\)
−0.439048 + 0.898464i \(0.644684\pi\)
\(968\) 0 0
\(969\) 0.842496 0.0270649
\(970\) 0 0
\(971\) −40.4805 −1.29908 −0.649541 0.760327i \(-0.725039\pi\)
−0.649541 + 0.760327i \(0.725039\pi\)
\(972\) 0 0
\(973\) −22.6521 −0.726192
\(974\) 0 0
\(975\) −2.71044 −0.0868035
\(976\) 0 0
\(977\) −27.6264 −0.883847 −0.441923 0.897053i \(-0.645704\pi\)
−0.441923 + 0.897053i \(0.645704\pi\)
\(978\) 0 0
\(979\) 56.0017 1.78982
\(980\) 0 0
\(981\) −40.8644 −1.30470
\(982\) 0 0
\(983\) 23.1145 0.737237 0.368619 0.929581i \(-0.379831\pi\)
0.368619 + 0.929581i \(0.379831\pi\)
\(984\) 0 0
\(985\) −10.8483 −0.345655
\(986\) 0 0
\(987\) −1.19323 −0.0379809
\(988\) 0 0
\(989\) 4.96099 0.157750
\(990\) 0 0
\(991\) −56.2053 −1.78542 −0.892710 0.450633i \(-0.851198\pi\)
−0.892710 + 0.450633i \(0.851198\pi\)
\(992\) 0 0
\(993\) 2.87583 0.0912616
\(994\) 0 0
\(995\) −27.7623 −0.880125
\(996\) 0 0
\(997\) 26.8504 0.850360 0.425180 0.905109i \(-0.360211\pi\)
0.425180 + 0.905109i \(0.360211\pi\)
\(998\) 0 0
\(999\) −8.82479 −0.279204
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 8024.2.a.bb.1.16 32
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
8024.2.a.bb.1.16 32 1.1 even 1 trivial