Properties

Label 8020.2.a.d.1.17
Level $8020$
Weight $2$
Character 8020.1
Self dual yes
Analytic conductor $64.040$
Analytic rank $1$
Dimension $29$
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] = [8020,2,Mod(1,8020)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(8020, 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("8020.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 8020 = 2^{2} \cdot 5 \cdot 401 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 8020.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: \(64.0400224211\)
Analytic rank: \(1\)
Dimension: \(29\)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.17
Character \(\chi\) \(=\) 8020.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+0.121745 q^{3} +1.00000 q^{5} +5.25775 q^{7} -2.98518 q^{9} +O(q^{10})\) \(q+0.121745 q^{3} +1.00000 q^{5} +5.25775 q^{7} -2.98518 q^{9} -2.85102 q^{11} -2.22012 q^{13} +0.121745 q^{15} -7.47382 q^{17} -0.221168 q^{19} +0.640103 q^{21} +1.75744 q^{23} +1.00000 q^{25} -0.728663 q^{27} +0.610881 q^{29} -3.10415 q^{31} -0.347096 q^{33} +5.25775 q^{35} +1.19893 q^{37} -0.270288 q^{39} +4.15702 q^{41} +7.47381 q^{43} -2.98518 q^{45} -10.1133 q^{47} +20.6440 q^{49} -0.909897 q^{51} +6.80692 q^{53} -2.85102 q^{55} -0.0269260 q^{57} +0.527712 q^{59} -0.958908 q^{61} -15.6953 q^{63} -2.22012 q^{65} +4.05123 q^{67} +0.213959 q^{69} -8.66014 q^{71} -11.3527 q^{73} +0.121745 q^{75} -14.9900 q^{77} -7.00612 q^{79} +8.86682 q^{81} -16.9997 q^{83} -7.47382 q^{85} +0.0743715 q^{87} -9.23370 q^{89} -11.6728 q^{91} -0.377913 q^{93} -0.221168 q^{95} +0.669863 q^{97} +8.51080 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 29 q - 3 q^{3} + 29 q^{5} - 8 q^{7} + 10 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 29 q - 3 q^{3} + 29 q^{5} - 8 q^{7} + 10 q^{9} + 2 q^{11} - 23 q^{13} - 3 q^{15} - 30 q^{17} - 6 q^{19} - 16 q^{21} - 21 q^{23} + 29 q^{25} - 15 q^{27} - 35 q^{29} - 7 q^{31} - 36 q^{33} - 8 q^{35} - 31 q^{37} - 11 q^{39} - 24 q^{41} - 17 q^{43} + 10 q^{45} - 17 q^{47} + q^{49} + 8 q^{51} - 57 q^{53} + 2 q^{55} - 46 q^{57} - 9 q^{59} - 27 q^{61} - 34 q^{63} - 23 q^{65} - 21 q^{67} - 28 q^{69} - 19 q^{71} - 81 q^{73} - 3 q^{75} - 66 q^{77} - 17 q^{79} - 39 q^{81} - 30 q^{83} - 30 q^{85} - 20 q^{87} - 38 q^{89} + q^{91} - 75 q^{93} - 6 q^{95} - 48 q^{97} - 7 q^{99}+O(q^{100}) \) 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
\(3\) 0.121745 0.0702893 0.0351447 0.999382i \(-0.488811\pi\)
0.0351447 + 0.999382i \(0.488811\pi\)
\(4\) 0 0
\(5\) 1.00000 0.447214
\(6\) 0 0
\(7\) 5.25775 1.98724 0.993622 0.112763i \(-0.0359702\pi\)
0.993622 + 0.112763i \(0.0359702\pi\)
\(8\) 0 0
\(9\) −2.98518 −0.995059
\(10\) 0 0
\(11\) −2.85102 −0.859615 −0.429807 0.902921i \(-0.641419\pi\)
−0.429807 + 0.902921i \(0.641419\pi\)
\(12\) 0 0
\(13\) −2.22012 −0.615751 −0.307875 0.951427i \(-0.599618\pi\)
−0.307875 + 0.951427i \(0.599618\pi\)
\(14\) 0 0
\(15\) 0.121745 0.0314343
\(16\) 0 0
\(17\) −7.47382 −1.81267 −0.906333 0.422563i \(-0.861130\pi\)
−0.906333 + 0.422563i \(0.861130\pi\)
\(18\) 0 0
\(19\) −0.221168 −0.0507393 −0.0253697 0.999678i \(-0.508076\pi\)
−0.0253697 + 0.999678i \(0.508076\pi\)
\(20\) 0 0
\(21\) 0.640103 0.139682
\(22\) 0 0
\(23\) 1.75744 0.366452 0.183226 0.983071i \(-0.441346\pi\)
0.183226 + 0.983071i \(0.441346\pi\)
\(24\) 0 0
\(25\) 1.00000 0.200000
\(26\) 0 0
\(27\) −0.728663 −0.140231
\(28\) 0 0
\(29\) 0.610881 0.113438 0.0567189 0.998390i \(-0.481936\pi\)
0.0567189 + 0.998390i \(0.481936\pi\)
\(30\) 0 0
\(31\) −3.10415 −0.557522 −0.278761 0.960361i \(-0.589924\pi\)
−0.278761 + 0.960361i \(0.589924\pi\)
\(32\) 0 0
\(33\) −0.347096 −0.0604217
\(34\) 0 0
\(35\) 5.25775 0.888722
\(36\) 0 0
\(37\) 1.19893 0.197102 0.0985512 0.995132i \(-0.468579\pi\)
0.0985512 + 0.995132i \(0.468579\pi\)
\(38\) 0 0
\(39\) −0.270288 −0.0432807
\(40\) 0 0
\(41\) 4.15702 0.649217 0.324608 0.945848i \(-0.394767\pi\)
0.324608 + 0.945848i \(0.394767\pi\)
\(42\) 0 0
\(43\) 7.47381 1.13975 0.569873 0.821733i \(-0.306992\pi\)
0.569873 + 0.821733i \(0.306992\pi\)
\(44\) 0 0
\(45\) −2.98518 −0.445004
\(46\) 0 0
\(47\) −10.1133 −1.47517 −0.737587 0.675252i \(-0.764035\pi\)
−0.737587 + 0.675252i \(0.764035\pi\)
\(48\) 0 0
\(49\) 20.6440 2.94914
\(50\) 0 0
\(51\) −0.909897 −0.127411
\(52\) 0 0
\(53\) 6.80692 0.935002 0.467501 0.883992i \(-0.345154\pi\)
0.467501 + 0.883992i \(0.345154\pi\)
\(54\) 0 0
\(55\) −2.85102 −0.384431
\(56\) 0 0
\(57\) −0.0269260 −0.00356643
\(58\) 0 0
\(59\) 0.527712 0.0687023 0.0343511 0.999410i \(-0.489064\pi\)
0.0343511 + 0.999410i \(0.489064\pi\)
\(60\) 0 0
\(61\) −0.958908 −0.122776 −0.0613878 0.998114i \(-0.519553\pi\)
−0.0613878 + 0.998114i \(0.519553\pi\)
\(62\) 0 0
\(63\) −15.6953 −1.97743
\(64\) 0 0
\(65\) −2.22012 −0.275372
\(66\) 0 0
\(67\) 4.05123 0.494936 0.247468 0.968896i \(-0.420401\pi\)
0.247468 + 0.968896i \(0.420401\pi\)
\(68\) 0 0
\(69\) 0.213959 0.0257577
\(70\) 0 0
\(71\) −8.66014 −1.02777 −0.513885 0.857859i \(-0.671794\pi\)
−0.513885 + 0.857859i \(0.671794\pi\)
\(72\) 0 0
\(73\) −11.3527 −1.32874 −0.664368 0.747406i \(-0.731299\pi\)
−0.664368 + 0.747406i \(0.731299\pi\)
\(74\) 0 0
\(75\) 0.121745 0.0140579
\(76\) 0 0
\(77\) −14.9900 −1.70826
\(78\) 0 0
\(79\) −7.00612 −0.788250 −0.394125 0.919057i \(-0.628952\pi\)
−0.394125 + 0.919057i \(0.628952\pi\)
\(80\) 0 0
\(81\) 8.86682 0.985203
\(82\) 0 0
\(83\) −16.9997 −1.86596 −0.932979 0.359930i \(-0.882801\pi\)
−0.932979 + 0.359930i \(0.882801\pi\)
\(84\) 0 0
\(85\) −7.47382 −0.810649
\(86\) 0 0
\(87\) 0.0743715 0.00797346
\(88\) 0 0
\(89\) −9.23370 −0.978770 −0.489385 0.872068i \(-0.662779\pi\)
−0.489385 + 0.872068i \(0.662779\pi\)
\(90\) 0 0
\(91\) −11.6728 −1.22365
\(92\) 0 0
\(93\) −0.377913 −0.0391878
\(94\) 0 0
\(95\) −0.221168 −0.0226913
\(96\) 0 0
\(97\) 0.669863 0.0680143 0.0340071 0.999422i \(-0.489173\pi\)
0.0340071 + 0.999422i \(0.489173\pi\)
\(98\) 0 0
\(99\) 8.51080 0.855368
\(100\) 0 0
\(101\) −6.29915 −0.626789 −0.313394 0.949623i \(-0.601466\pi\)
−0.313394 + 0.949623i \(0.601466\pi\)
\(102\) 0 0
\(103\) 0.756974 0.0745868 0.0372934 0.999304i \(-0.488126\pi\)
0.0372934 + 0.999304i \(0.488126\pi\)
\(104\) 0 0
\(105\) 0.640103 0.0624677
\(106\) 0 0
\(107\) −12.1406 −1.17367 −0.586836 0.809705i \(-0.699627\pi\)
−0.586836 + 0.809705i \(0.699627\pi\)
\(108\) 0 0
\(109\) −15.2467 −1.46037 −0.730183 0.683251i \(-0.760565\pi\)
−0.730183 + 0.683251i \(0.760565\pi\)
\(110\) 0 0
\(111\) 0.145963 0.0138542
\(112\) 0 0
\(113\) 10.8551 1.02116 0.510581 0.859830i \(-0.329430\pi\)
0.510581 + 0.859830i \(0.329430\pi\)
\(114\) 0 0
\(115\) 1.75744 0.163883
\(116\) 0 0
\(117\) 6.62746 0.612709
\(118\) 0 0
\(119\) −39.2955 −3.60221
\(120\) 0 0
\(121\) −2.87169 −0.261062
\(122\) 0 0
\(123\) 0.506094 0.0456330
\(124\) 0 0
\(125\) 1.00000 0.0894427
\(126\) 0 0
\(127\) 14.2572 1.26512 0.632560 0.774512i \(-0.282004\pi\)
0.632560 + 0.774512i \(0.282004\pi\)
\(128\) 0 0
\(129\) 0.909897 0.0801120
\(130\) 0 0
\(131\) −11.7172 −1.02373 −0.511867 0.859064i \(-0.671046\pi\)
−0.511867 + 0.859064i \(0.671046\pi\)
\(132\) 0 0
\(133\) −1.16284 −0.100831
\(134\) 0 0
\(135\) −0.728663 −0.0627134
\(136\) 0 0
\(137\) 1.69608 0.144906 0.0724530 0.997372i \(-0.476917\pi\)
0.0724530 + 0.997372i \(0.476917\pi\)
\(138\) 0 0
\(139\) −15.2897 −1.29686 −0.648428 0.761276i \(-0.724573\pi\)
−0.648428 + 0.761276i \(0.724573\pi\)
\(140\) 0 0
\(141\) −1.23124 −0.103689
\(142\) 0 0
\(143\) 6.32961 0.529309
\(144\) 0 0
\(145\) 0.610881 0.0507309
\(146\) 0 0
\(147\) 2.51329 0.207293
\(148\) 0 0
\(149\) −8.12919 −0.665969 −0.332984 0.942932i \(-0.608056\pi\)
−0.332984 + 0.942932i \(0.608056\pi\)
\(150\) 0 0
\(151\) −15.9517 −1.29813 −0.649067 0.760732i \(-0.724840\pi\)
−0.649067 + 0.760732i \(0.724840\pi\)
\(152\) 0 0
\(153\) 22.3107 1.80371
\(154\) 0 0
\(155\) −3.10415 −0.249331
\(156\) 0 0
\(157\) 20.5204 1.63770 0.818851 0.574006i \(-0.194611\pi\)
0.818851 + 0.574006i \(0.194611\pi\)
\(158\) 0 0
\(159\) 0.828706 0.0657207
\(160\) 0 0
\(161\) 9.24021 0.728230
\(162\) 0 0
\(163\) −5.71269 −0.447452 −0.223726 0.974652i \(-0.571822\pi\)
−0.223726 + 0.974652i \(0.571822\pi\)
\(164\) 0 0
\(165\) −0.347096 −0.0270214
\(166\) 0 0
\(167\) 12.4923 0.966683 0.483341 0.875432i \(-0.339423\pi\)
0.483341 + 0.875432i \(0.339423\pi\)
\(168\) 0 0
\(169\) −8.07106 −0.620851
\(170\) 0 0
\(171\) 0.660225 0.0504887
\(172\) 0 0
\(173\) −6.53177 −0.496601 −0.248301 0.968683i \(-0.579872\pi\)
−0.248301 + 0.968683i \(0.579872\pi\)
\(174\) 0 0
\(175\) 5.25775 0.397449
\(176\) 0 0
\(177\) 0.0642461 0.00482904
\(178\) 0 0
\(179\) −11.8243 −0.883791 −0.441895 0.897067i \(-0.645694\pi\)
−0.441895 + 0.897067i \(0.645694\pi\)
\(180\) 0 0
\(181\) 3.73893 0.277912 0.138956 0.990299i \(-0.455625\pi\)
0.138956 + 0.990299i \(0.455625\pi\)
\(182\) 0 0
\(183\) −0.116742 −0.00862981
\(184\) 0 0
\(185\) 1.19893 0.0881469
\(186\) 0 0
\(187\) 21.3080 1.55820
\(188\) 0 0
\(189\) −3.83113 −0.278674
\(190\) 0 0
\(191\) 16.5632 1.19847 0.599234 0.800574i \(-0.295472\pi\)
0.599234 + 0.800574i \(0.295472\pi\)
\(192\) 0 0
\(193\) −20.6257 −1.48467 −0.742336 0.670028i \(-0.766282\pi\)
−0.742336 + 0.670028i \(0.766282\pi\)
\(194\) 0 0
\(195\) −0.270288 −0.0193557
\(196\) 0 0
\(197\) 9.39504 0.669369 0.334684 0.942330i \(-0.391370\pi\)
0.334684 + 0.942330i \(0.391370\pi\)
\(198\) 0 0
\(199\) −3.39683 −0.240795 −0.120397 0.992726i \(-0.538417\pi\)
−0.120397 + 0.992726i \(0.538417\pi\)
\(200\) 0 0
\(201\) 0.493215 0.0347887
\(202\) 0 0
\(203\) 3.21186 0.225428
\(204\) 0 0
\(205\) 4.15702 0.290339
\(206\) 0 0
\(207\) −5.24628 −0.364642
\(208\) 0 0
\(209\) 0.630553 0.0436163
\(210\) 0 0
\(211\) −23.7190 −1.63288 −0.816441 0.577428i \(-0.804056\pi\)
−0.816441 + 0.577428i \(0.804056\pi\)
\(212\) 0 0
\(213\) −1.05433 −0.0722412
\(214\) 0 0
\(215\) 7.47381 0.509710
\(216\) 0 0
\(217\) −16.3208 −1.10793
\(218\) 0 0
\(219\) −1.38213 −0.0933959
\(220\) 0 0
\(221\) 16.5928 1.11615
\(222\) 0 0
\(223\) 16.4313 1.10032 0.550160 0.835059i \(-0.314567\pi\)
0.550160 + 0.835059i \(0.314567\pi\)
\(224\) 0 0
\(225\) −2.98518 −0.199012
\(226\) 0 0
\(227\) −23.9022 −1.58645 −0.793223 0.608932i \(-0.791598\pi\)
−0.793223 + 0.608932i \(0.791598\pi\)
\(228\) 0 0
\(229\) −13.3058 −0.879273 −0.439636 0.898176i \(-0.644893\pi\)
−0.439636 + 0.898176i \(0.644893\pi\)
\(230\) 0 0
\(231\) −1.82495 −0.120073
\(232\) 0 0
\(233\) −2.15936 −0.141465 −0.0707323 0.997495i \(-0.522534\pi\)
−0.0707323 + 0.997495i \(0.522534\pi\)
\(234\) 0 0
\(235\) −10.1133 −0.659718
\(236\) 0 0
\(237\) −0.852957 −0.0554055
\(238\) 0 0
\(239\) −22.8319 −1.47688 −0.738438 0.674322i \(-0.764436\pi\)
−0.738438 + 0.674322i \(0.764436\pi\)
\(240\) 0 0
\(241\) 23.4028 1.50751 0.753753 0.657158i \(-0.228241\pi\)
0.753753 + 0.657158i \(0.228241\pi\)
\(242\) 0 0
\(243\) 3.26548 0.209481
\(244\) 0 0
\(245\) 20.6440 1.31889
\(246\) 0 0
\(247\) 0.491019 0.0312428
\(248\) 0 0
\(249\) −2.06962 −0.131157
\(250\) 0 0
\(251\) 27.6817 1.74726 0.873628 0.486595i \(-0.161761\pi\)
0.873628 + 0.486595i \(0.161761\pi\)
\(252\) 0 0
\(253\) −5.01051 −0.315008
\(254\) 0 0
\(255\) −0.909897 −0.0569800
\(256\) 0 0
\(257\) −25.3831 −1.58335 −0.791676 0.610941i \(-0.790791\pi\)
−0.791676 + 0.610941i \(0.790791\pi\)
\(258\) 0 0
\(259\) 6.30366 0.391690
\(260\) 0 0
\(261\) −1.82359 −0.112877
\(262\) 0 0
\(263\) −10.6763 −0.658330 −0.329165 0.944272i \(-0.606767\pi\)
−0.329165 + 0.944272i \(0.606767\pi\)
\(264\) 0 0
\(265\) 6.80692 0.418146
\(266\) 0 0
\(267\) −1.12415 −0.0687971
\(268\) 0 0
\(269\) 3.05826 0.186465 0.0932327 0.995644i \(-0.470280\pi\)
0.0932327 + 0.995644i \(0.470280\pi\)
\(270\) 0 0
\(271\) 8.21259 0.498879 0.249440 0.968390i \(-0.419754\pi\)
0.249440 + 0.968390i \(0.419754\pi\)
\(272\) 0 0
\(273\) −1.42111 −0.0860093
\(274\) 0 0
\(275\) −2.85102 −0.171923
\(276\) 0 0
\(277\) −13.1239 −0.788540 −0.394270 0.918995i \(-0.629002\pi\)
−0.394270 + 0.918995i \(0.629002\pi\)
\(278\) 0 0
\(279\) 9.26644 0.554767
\(280\) 0 0
\(281\) −24.9232 −1.48680 −0.743398 0.668850i \(-0.766787\pi\)
−0.743398 + 0.668850i \(0.766787\pi\)
\(282\) 0 0
\(283\) −17.5782 −1.04491 −0.522457 0.852666i \(-0.674984\pi\)
−0.522457 + 0.852666i \(0.674984\pi\)
\(284\) 0 0
\(285\) −0.0269260 −0.00159496
\(286\) 0 0
\(287\) 21.8566 1.29015
\(288\) 0 0
\(289\) 38.8579 2.28576
\(290\) 0 0
\(291\) 0.0815522 0.00478068
\(292\) 0 0
\(293\) 4.62159 0.269996 0.134998 0.990846i \(-0.456897\pi\)
0.134998 + 0.990846i \(0.456897\pi\)
\(294\) 0 0
\(295\) 0.527712 0.0307246
\(296\) 0 0
\(297\) 2.07743 0.120545
\(298\) 0 0
\(299\) −3.90174 −0.225643
\(300\) 0 0
\(301\) 39.2955 2.26495
\(302\) 0 0
\(303\) −0.766888 −0.0440566
\(304\) 0 0
\(305\) −0.958908 −0.0549069
\(306\) 0 0
\(307\) 29.7975 1.70063 0.850316 0.526273i \(-0.176411\pi\)
0.850316 + 0.526273i \(0.176411\pi\)
\(308\) 0 0
\(309\) 0.0921575 0.00524266
\(310\) 0 0
\(311\) 20.3896 1.15619 0.578095 0.815969i \(-0.303796\pi\)
0.578095 + 0.815969i \(0.303796\pi\)
\(312\) 0 0
\(313\) 12.0868 0.683186 0.341593 0.939848i \(-0.389034\pi\)
0.341593 + 0.939848i \(0.389034\pi\)
\(314\) 0 0
\(315\) −15.6953 −0.884332
\(316\) 0 0
\(317\) −11.2249 −0.630452 −0.315226 0.949017i \(-0.602080\pi\)
−0.315226 + 0.949017i \(0.602080\pi\)
\(318\) 0 0
\(319\) −1.74163 −0.0975127
\(320\) 0 0
\(321\) −1.47805 −0.0824967
\(322\) 0 0
\(323\) 1.65297 0.0919735
\(324\) 0 0
\(325\) −2.22012 −0.123150
\(326\) 0 0
\(327\) −1.85620 −0.102648
\(328\) 0 0
\(329\) −53.1731 −2.93153
\(330\) 0 0
\(331\) 13.5472 0.744621 0.372310 0.928108i \(-0.378566\pi\)
0.372310 + 0.928108i \(0.378566\pi\)
\(332\) 0 0
\(333\) −3.57901 −0.196129
\(334\) 0 0
\(335\) 4.05123 0.221342
\(336\) 0 0
\(337\) −24.0585 −1.31055 −0.655275 0.755390i \(-0.727447\pi\)
−0.655275 + 0.755390i \(0.727447\pi\)
\(338\) 0 0
\(339\) 1.32155 0.0717768
\(340\) 0 0
\(341\) 8.84999 0.479254
\(342\) 0 0
\(343\) 71.7366 3.87341
\(344\) 0 0
\(345\) 0.213959 0.0115192
\(346\) 0 0
\(347\) 7.16350 0.384557 0.192278 0.981340i \(-0.438412\pi\)
0.192278 + 0.981340i \(0.438412\pi\)
\(348\) 0 0
\(349\) 4.33325 0.231953 0.115977 0.993252i \(-0.463000\pi\)
0.115977 + 0.993252i \(0.463000\pi\)
\(350\) 0 0
\(351\) 1.61772 0.0863476
\(352\) 0 0
\(353\) 6.09350 0.324324 0.162162 0.986764i \(-0.448153\pi\)
0.162162 + 0.986764i \(0.448153\pi\)
\(354\) 0 0
\(355\) −8.66014 −0.459633
\(356\) 0 0
\(357\) −4.78402 −0.253197
\(358\) 0 0
\(359\) 7.81009 0.412201 0.206100 0.978531i \(-0.433923\pi\)
0.206100 + 0.978531i \(0.433923\pi\)
\(360\) 0 0
\(361\) −18.9511 −0.997426
\(362\) 0 0
\(363\) −0.349612 −0.0183499
\(364\) 0 0
\(365\) −11.3527 −0.594229
\(366\) 0 0
\(367\) 34.1452 1.78237 0.891183 0.453645i \(-0.149877\pi\)
0.891183 + 0.453645i \(0.149877\pi\)
\(368\) 0 0
\(369\) −12.4094 −0.646009
\(370\) 0 0
\(371\) 35.7891 1.85808
\(372\) 0 0
\(373\) −12.9968 −0.672951 −0.336476 0.941692i \(-0.609235\pi\)
−0.336476 + 0.941692i \(0.609235\pi\)
\(374\) 0 0
\(375\) 0.121745 0.00628687
\(376\) 0 0
\(377\) −1.35623 −0.0698494
\(378\) 0 0
\(379\) −13.1953 −0.677799 −0.338900 0.940822i \(-0.610055\pi\)
−0.338900 + 0.940822i \(0.610055\pi\)
\(380\) 0 0
\(381\) 1.73573 0.0889243
\(382\) 0 0
\(383\) −9.26583 −0.473462 −0.236731 0.971575i \(-0.576076\pi\)
−0.236731 + 0.971575i \(0.576076\pi\)
\(384\) 0 0
\(385\) −14.9900 −0.763959
\(386\) 0 0
\(387\) −22.3107 −1.13411
\(388\) 0 0
\(389\) −19.3487 −0.981019 −0.490509 0.871436i \(-0.663189\pi\)
−0.490509 + 0.871436i \(0.663189\pi\)
\(390\) 0 0
\(391\) −13.1348 −0.664256
\(392\) 0 0
\(393\) −1.42650 −0.0719576
\(394\) 0 0
\(395\) −7.00612 −0.352516
\(396\) 0 0
\(397\) 13.3736 0.671200 0.335600 0.942005i \(-0.391061\pi\)
0.335600 + 0.942005i \(0.391061\pi\)
\(398\) 0 0
\(399\) −0.141570 −0.00708737
\(400\) 0 0
\(401\) −1.00000 −0.0499376
\(402\) 0 0
\(403\) 6.89159 0.343294
\(404\) 0 0
\(405\) 8.86682 0.440596
\(406\) 0 0
\(407\) −3.41816 −0.169432
\(408\) 0 0
\(409\) −5.92283 −0.292865 −0.146433 0.989221i \(-0.546779\pi\)
−0.146433 + 0.989221i \(0.546779\pi\)
\(410\) 0 0
\(411\) 0.206489 0.0101853
\(412\) 0 0
\(413\) 2.77458 0.136528
\(414\) 0 0
\(415\) −16.9997 −0.834482
\(416\) 0 0
\(417\) −1.86144 −0.0911551
\(418\) 0 0
\(419\) 2.49806 0.122038 0.0610191 0.998137i \(-0.480565\pi\)
0.0610191 + 0.998137i \(0.480565\pi\)
\(420\) 0 0
\(421\) 33.7368 1.64423 0.822115 0.569321i \(-0.192794\pi\)
0.822115 + 0.569321i \(0.192794\pi\)
\(422\) 0 0
\(423\) 30.1899 1.46789
\(424\) 0 0
\(425\) −7.47382 −0.362533
\(426\) 0 0
\(427\) −5.04170 −0.243985
\(428\) 0 0
\(429\) 0.770596 0.0372047
\(430\) 0 0
\(431\) −29.4626 −1.41917 −0.709583 0.704622i \(-0.751117\pi\)
−0.709583 + 0.704622i \(0.751117\pi\)
\(432\) 0 0
\(433\) −0.0820591 −0.00394351 −0.00197176 0.999998i \(-0.500628\pi\)
−0.00197176 + 0.999998i \(0.500628\pi\)
\(434\) 0 0
\(435\) 0.0743715 0.00356584
\(436\) 0 0
\(437\) −0.388690 −0.0185936
\(438\) 0 0
\(439\) 18.4428 0.880228 0.440114 0.897942i \(-0.354938\pi\)
0.440114 + 0.897942i \(0.354938\pi\)
\(440\) 0 0
\(441\) −61.6259 −2.93457
\(442\) 0 0
\(443\) −16.9358 −0.804645 −0.402322 0.915498i \(-0.631797\pi\)
−0.402322 + 0.915498i \(0.631797\pi\)
\(444\) 0 0
\(445\) −9.23370 −0.437719
\(446\) 0 0
\(447\) −0.989685 −0.0468105
\(448\) 0 0
\(449\) 16.4738 0.777445 0.388722 0.921355i \(-0.372917\pi\)
0.388722 + 0.921355i \(0.372917\pi\)
\(450\) 0 0
\(451\) −11.8517 −0.558076
\(452\) 0 0
\(453\) −1.94204 −0.0912449
\(454\) 0 0
\(455\) −11.6728 −0.547232
\(456\) 0 0
\(457\) −1.35231 −0.0632584 −0.0316292 0.999500i \(-0.510070\pi\)
−0.0316292 + 0.999500i \(0.510070\pi\)
\(458\) 0 0
\(459\) 5.44590 0.254193
\(460\) 0 0
\(461\) 21.9966 1.02449 0.512243 0.858841i \(-0.328815\pi\)
0.512243 + 0.858841i \(0.328815\pi\)
\(462\) 0 0
\(463\) −19.6477 −0.913104 −0.456552 0.889697i \(-0.650916\pi\)
−0.456552 + 0.889697i \(0.650916\pi\)
\(464\) 0 0
\(465\) −0.377913 −0.0175253
\(466\) 0 0
\(467\) −3.16680 −0.146542 −0.0732711 0.997312i \(-0.523344\pi\)
−0.0732711 + 0.997312i \(0.523344\pi\)
\(468\) 0 0
\(469\) 21.3004 0.983559
\(470\) 0 0
\(471\) 2.49824 0.115113
\(472\) 0 0
\(473\) −21.3080 −0.979742
\(474\) 0 0
\(475\) −0.221168 −0.0101479
\(476\) 0 0
\(477\) −20.3199 −0.930383
\(478\) 0 0
\(479\) −21.9142 −1.00128 −0.500642 0.865654i \(-0.666903\pi\)
−0.500642 + 0.865654i \(0.666903\pi\)
\(480\) 0 0
\(481\) −2.66176 −0.121366
\(482\) 0 0
\(483\) 1.12495 0.0511868
\(484\) 0 0
\(485\) 0.669863 0.0304169
\(486\) 0 0
\(487\) 42.5948 1.93015 0.965077 0.261966i \(-0.0843709\pi\)
0.965077 + 0.261966i \(0.0843709\pi\)
\(488\) 0 0
\(489\) −0.695489 −0.0314511
\(490\) 0 0
\(491\) −6.35002 −0.286572 −0.143286 0.989681i \(-0.545767\pi\)
−0.143286 + 0.989681i \(0.545767\pi\)
\(492\) 0 0
\(493\) −4.56561 −0.205625
\(494\) 0 0
\(495\) 8.51080 0.382532
\(496\) 0 0
\(497\) −45.5329 −2.04243
\(498\) 0 0
\(499\) −16.6397 −0.744896 −0.372448 0.928053i \(-0.621482\pi\)
−0.372448 + 0.928053i \(0.621482\pi\)
\(500\) 0 0
\(501\) 1.52087 0.0679475
\(502\) 0 0
\(503\) 10.4627 0.466507 0.233253 0.972416i \(-0.425063\pi\)
0.233253 + 0.972416i \(0.425063\pi\)
\(504\) 0 0
\(505\) −6.29915 −0.280309
\(506\) 0 0
\(507\) −0.982609 −0.0436392
\(508\) 0 0
\(509\) 34.5559 1.53167 0.765833 0.643040i \(-0.222327\pi\)
0.765833 + 0.643040i \(0.222327\pi\)
\(510\) 0 0
\(511\) −59.6898 −2.64052
\(512\) 0 0
\(513\) 0.161157 0.00711525
\(514\) 0 0
\(515\) 0.756974 0.0333562
\(516\) 0 0
\(517\) 28.8332 1.26808
\(518\) 0 0
\(519\) −0.795208 −0.0349058
\(520\) 0 0
\(521\) 14.9805 0.656307 0.328153 0.944624i \(-0.393574\pi\)
0.328153 + 0.944624i \(0.393574\pi\)
\(522\) 0 0
\(523\) −27.4264 −1.19927 −0.599636 0.800273i \(-0.704688\pi\)
−0.599636 + 0.800273i \(0.704688\pi\)
\(524\) 0 0
\(525\) 0.640103 0.0279364
\(526\) 0 0
\(527\) 23.1998 1.01060
\(528\) 0 0
\(529\) −19.9114 −0.865713
\(530\) 0 0
\(531\) −1.57531 −0.0683628
\(532\) 0 0
\(533\) −9.22908 −0.399756
\(534\) 0 0
\(535\) −12.1406 −0.524882
\(536\) 0 0
\(537\) −1.43955 −0.0621211
\(538\) 0 0
\(539\) −58.8563 −2.53512
\(540\) 0 0
\(541\) 7.42242 0.319115 0.159557 0.987189i \(-0.448993\pi\)
0.159557 + 0.987189i \(0.448993\pi\)
\(542\) 0 0
\(543\) 0.455194 0.0195343
\(544\) 0 0
\(545\) −15.2467 −0.653096
\(546\) 0 0
\(547\) 15.8172 0.676297 0.338148 0.941093i \(-0.390199\pi\)
0.338148 + 0.941093i \(0.390199\pi\)
\(548\) 0 0
\(549\) 2.86251 0.122169
\(550\) 0 0
\(551\) −0.135107 −0.00575575
\(552\) 0 0
\(553\) −36.8364 −1.56644
\(554\) 0 0
\(555\) 0.145963 0.00619578
\(556\) 0 0
\(557\) 23.7864 1.00786 0.503930 0.863744i \(-0.331887\pi\)
0.503930 + 0.863744i \(0.331887\pi\)
\(558\) 0 0
\(559\) −16.5928 −0.701800
\(560\) 0 0
\(561\) 2.59414 0.109524
\(562\) 0 0
\(563\) 11.2900 0.475817 0.237908 0.971288i \(-0.423538\pi\)
0.237908 + 0.971288i \(0.423538\pi\)
\(564\) 0 0
\(565\) 10.8551 0.456678
\(566\) 0 0
\(567\) 46.6196 1.95784
\(568\) 0 0
\(569\) −11.1065 −0.465609 −0.232805 0.972524i \(-0.574790\pi\)
−0.232805 + 0.972524i \(0.574790\pi\)
\(570\) 0 0
\(571\) 17.5404 0.734041 0.367021 0.930213i \(-0.380378\pi\)
0.367021 + 0.930213i \(0.380378\pi\)
\(572\) 0 0
\(573\) 2.01648 0.0842395
\(574\) 0 0
\(575\) 1.75744 0.0732905
\(576\) 0 0
\(577\) −4.06969 −0.169423 −0.0847117 0.996406i \(-0.526997\pi\)
−0.0847117 + 0.996406i \(0.526997\pi\)
\(578\) 0 0
\(579\) −2.51107 −0.104357
\(580\) 0 0
\(581\) −89.3802 −3.70811
\(582\) 0 0
\(583\) −19.4067 −0.803742
\(584\) 0 0
\(585\) 6.62746 0.274012
\(586\) 0 0
\(587\) 22.0592 0.910482 0.455241 0.890368i \(-0.349553\pi\)
0.455241 + 0.890368i \(0.349553\pi\)
\(588\) 0 0
\(589\) 0.686537 0.0282883
\(590\) 0 0
\(591\) 1.14380 0.0470495
\(592\) 0 0
\(593\) −16.8222 −0.690807 −0.345403 0.938454i \(-0.612258\pi\)
−0.345403 + 0.938454i \(0.612258\pi\)
\(594\) 0 0
\(595\) −39.2955 −1.61096
\(596\) 0 0
\(597\) −0.413545 −0.0169253
\(598\) 0 0
\(599\) −7.55428 −0.308659 −0.154330 0.988019i \(-0.549322\pi\)
−0.154330 + 0.988019i \(0.549322\pi\)
\(600\) 0 0
\(601\) −24.5529 −1.00153 −0.500766 0.865583i \(-0.666948\pi\)
−0.500766 + 0.865583i \(0.666948\pi\)
\(602\) 0 0
\(603\) −12.0936 −0.492491
\(604\) 0 0
\(605\) −2.87169 −0.116751
\(606\) 0 0
\(607\) −31.7767 −1.28978 −0.644889 0.764277i \(-0.723096\pi\)
−0.644889 + 0.764277i \(0.723096\pi\)
\(608\) 0 0
\(609\) 0.391027 0.0158452
\(610\) 0 0
\(611\) 22.4527 0.908339
\(612\) 0 0
\(613\) 41.8595 1.69069 0.845345 0.534221i \(-0.179395\pi\)
0.845345 + 0.534221i \(0.179395\pi\)
\(614\) 0 0
\(615\) 0.506094 0.0204077
\(616\) 0 0
\(617\) −26.8914 −1.08261 −0.541303 0.840828i \(-0.682069\pi\)
−0.541303 + 0.840828i \(0.682069\pi\)
\(618\) 0 0
\(619\) 15.9722 0.641976 0.320988 0.947083i \(-0.395985\pi\)
0.320988 + 0.947083i \(0.395985\pi\)
\(620\) 0 0
\(621\) −1.28059 −0.0513881
\(622\) 0 0
\(623\) −48.5485 −1.94506
\(624\) 0 0
\(625\) 1.00000 0.0400000
\(626\) 0 0
\(627\) 0.0767665 0.00306576
\(628\) 0 0
\(629\) −8.96056 −0.357281
\(630\) 0 0
\(631\) 30.5843 1.21754 0.608772 0.793346i \(-0.291663\pi\)
0.608772 + 0.793346i \(0.291663\pi\)
\(632\) 0 0
\(633\) −2.88766 −0.114774
\(634\) 0 0
\(635\) 14.2572 0.565778
\(636\) 0 0
\(637\) −45.8321 −1.81593
\(638\) 0 0
\(639\) 25.8521 1.02269
\(640\) 0 0
\(641\) 27.8408 1.09964 0.549822 0.835282i \(-0.314696\pi\)
0.549822 + 0.835282i \(0.314696\pi\)
\(642\) 0 0
\(643\) −5.03072 −0.198392 −0.0991961 0.995068i \(-0.531627\pi\)
−0.0991961 + 0.995068i \(0.531627\pi\)
\(644\) 0 0
\(645\) 0.909897 0.0358272
\(646\) 0 0
\(647\) −28.4014 −1.11658 −0.558288 0.829647i \(-0.688542\pi\)
−0.558288 + 0.829647i \(0.688542\pi\)
\(648\) 0 0
\(649\) −1.50452 −0.0590575
\(650\) 0 0
\(651\) −1.98698 −0.0778757
\(652\) 0 0
\(653\) −18.3180 −0.716837 −0.358419 0.933561i \(-0.616684\pi\)
−0.358419 + 0.933561i \(0.616684\pi\)
\(654\) 0 0
\(655\) −11.7172 −0.457828
\(656\) 0 0
\(657\) 33.8899 1.32217
\(658\) 0 0
\(659\) 43.3127 1.68722 0.843611 0.536954i \(-0.180425\pi\)
0.843611 + 0.536954i \(0.180425\pi\)
\(660\) 0 0
\(661\) 38.7535 1.50734 0.753669 0.657254i \(-0.228282\pi\)
0.753669 + 0.657254i \(0.228282\pi\)
\(662\) 0 0
\(663\) 2.02008 0.0784535
\(664\) 0 0
\(665\) −1.16284 −0.0450932
\(666\) 0 0
\(667\) 1.07359 0.0415695
\(668\) 0 0
\(669\) 2.00042 0.0773407
\(670\) 0 0
\(671\) 2.73386 0.105540
\(672\) 0 0
\(673\) −27.4072 −1.05647 −0.528235 0.849098i \(-0.677146\pi\)
−0.528235 + 0.849098i \(0.677146\pi\)
\(674\) 0 0
\(675\) −0.728663 −0.0280463
\(676\) 0 0
\(677\) −41.5573 −1.59718 −0.798588 0.601878i \(-0.794419\pi\)
−0.798588 + 0.601878i \(0.794419\pi\)
\(678\) 0 0
\(679\) 3.52197 0.135161
\(680\) 0 0
\(681\) −2.90997 −0.111510
\(682\) 0 0
\(683\) −7.94348 −0.303949 −0.151974 0.988384i \(-0.548563\pi\)
−0.151974 + 0.988384i \(0.548563\pi\)
\(684\) 0 0
\(685\) 1.69608 0.0648039
\(686\) 0 0
\(687\) −1.61991 −0.0618035
\(688\) 0 0
\(689\) −15.1122 −0.575729
\(690\) 0 0
\(691\) 41.6262 1.58354 0.791768 0.610823i \(-0.209161\pi\)
0.791768 + 0.610823i \(0.209161\pi\)
\(692\) 0 0
\(693\) 44.7477 1.69982
\(694\) 0 0
\(695\) −15.2897 −0.579972
\(696\) 0 0
\(697\) −31.0688 −1.17681
\(698\) 0 0
\(699\) −0.262891 −0.00994345
\(700\) 0 0
\(701\) 24.4480 0.923389 0.461694 0.887039i \(-0.347242\pi\)
0.461694 + 0.887039i \(0.347242\pi\)
\(702\) 0 0
\(703\) −0.265164 −0.0100008
\(704\) 0 0
\(705\) −1.23124 −0.0463711
\(706\) 0 0
\(707\) −33.1194 −1.24558
\(708\) 0 0
\(709\) −24.1347 −0.906397 −0.453198 0.891410i \(-0.649717\pi\)
−0.453198 + 0.891410i \(0.649717\pi\)
\(710\) 0 0
\(711\) 20.9145 0.784355
\(712\) 0 0
\(713\) −5.45537 −0.204305
\(714\) 0 0
\(715\) 6.32961 0.236714
\(716\) 0 0
\(717\) −2.77967 −0.103809
\(718\) 0 0
\(719\) −5.49446 −0.204909 −0.102454 0.994738i \(-0.532670\pi\)
−0.102454 + 0.994738i \(0.532670\pi\)
\(720\) 0 0
\(721\) 3.97998 0.148222
\(722\) 0 0
\(723\) 2.84916 0.105962
\(724\) 0 0
\(725\) 0.610881 0.0226875
\(726\) 0 0
\(727\) 39.8304 1.47723 0.738613 0.674130i \(-0.235481\pi\)
0.738613 + 0.674130i \(0.235481\pi\)
\(728\) 0 0
\(729\) −26.2029 −0.970478
\(730\) 0 0
\(731\) −55.8579 −2.06598
\(732\) 0 0
\(733\) 30.1024 1.11186 0.555929 0.831230i \(-0.312363\pi\)
0.555929 + 0.831230i \(0.312363\pi\)
\(734\) 0 0
\(735\) 2.51329 0.0927042
\(736\) 0 0
\(737\) −11.5501 −0.425455
\(738\) 0 0
\(739\) 11.9335 0.438981 0.219490 0.975615i \(-0.429561\pi\)
0.219490 + 0.975615i \(0.429561\pi\)
\(740\) 0 0
\(741\) 0.0597789 0.00219603
\(742\) 0 0
\(743\) −5.94786 −0.218206 −0.109103 0.994030i \(-0.534798\pi\)
−0.109103 + 0.994030i \(0.534798\pi\)
\(744\) 0 0
\(745\) −8.12919 −0.297830
\(746\) 0 0
\(747\) 50.7471 1.85674
\(748\) 0 0
\(749\) −63.8321 −2.33237
\(750\) 0 0
\(751\) −9.54531 −0.348313 −0.174157 0.984718i \(-0.555720\pi\)
−0.174157 + 0.984718i \(0.555720\pi\)
\(752\) 0 0
\(753\) 3.37010 0.122813
\(754\) 0 0
\(755\) −15.9517 −0.580543
\(756\) 0 0
\(757\) −35.1181 −1.27639 −0.638195 0.769875i \(-0.720319\pi\)
−0.638195 + 0.769875i \(0.720319\pi\)
\(758\) 0 0
\(759\) −0.610003 −0.0221417
\(760\) 0 0
\(761\) −28.1653 −1.02099 −0.510495 0.859881i \(-0.670538\pi\)
−0.510495 + 0.859881i \(0.670538\pi\)
\(762\) 0 0
\(763\) −80.1632 −2.90210
\(764\) 0 0
\(765\) 22.3107 0.806644
\(766\) 0 0
\(767\) −1.17159 −0.0423035
\(768\) 0 0
\(769\) −28.6462 −1.03301 −0.516505 0.856284i \(-0.672767\pi\)
−0.516505 + 0.856284i \(0.672767\pi\)
\(770\) 0 0
\(771\) −3.09025 −0.111293
\(772\) 0 0
\(773\) 3.87121 0.139238 0.0696189 0.997574i \(-0.477822\pi\)
0.0696189 + 0.997574i \(0.477822\pi\)
\(774\) 0 0
\(775\) −3.10415 −0.111504
\(776\) 0 0
\(777\) 0.767437 0.0275317
\(778\) 0 0
\(779\) −0.919398 −0.0329408
\(780\) 0 0
\(781\) 24.6902 0.883486
\(782\) 0 0
\(783\) −0.445126 −0.0159075
\(784\) 0 0
\(785\) 20.5204 0.732403
\(786\) 0 0
\(787\) 41.7115 1.48685 0.743426 0.668818i \(-0.233199\pi\)
0.743426 + 0.668818i \(0.233199\pi\)
\(788\) 0 0
\(789\) −1.29978 −0.0462736
\(790\) 0 0
\(791\) 57.0735 2.02930
\(792\) 0 0
\(793\) 2.12889 0.0755992
\(794\) 0 0
\(795\) 0.828706 0.0293912
\(796\) 0 0
\(797\) 38.0464 1.34767 0.673836 0.738881i \(-0.264645\pi\)
0.673836 + 0.738881i \(0.264645\pi\)
\(798\) 0 0
\(799\) 75.5848 2.67400
\(800\) 0 0
\(801\) 27.5642 0.973935
\(802\) 0 0
\(803\) 32.3668 1.14220
\(804\) 0 0
\(805\) 9.24021 0.325675
\(806\) 0 0
\(807\) 0.372327 0.0131065
\(808\) 0 0
\(809\) 4.45585 0.156659 0.0783297 0.996928i \(-0.475041\pi\)
0.0783297 + 0.996928i \(0.475041\pi\)
\(810\) 0 0
\(811\) −16.3150 −0.572896 −0.286448 0.958096i \(-0.592475\pi\)
−0.286448 + 0.958096i \(0.592475\pi\)
\(812\) 0 0
\(813\) 0.999838 0.0350659
\(814\) 0 0
\(815\) −5.71269 −0.200107
\(816\) 0 0
\(817\) −1.65297 −0.0578300
\(818\) 0 0
\(819\) 34.8455 1.21760
\(820\) 0 0
\(821\) 28.5436 0.996179 0.498090 0.867126i \(-0.334035\pi\)
0.498090 + 0.867126i \(0.334035\pi\)
\(822\) 0 0
\(823\) 45.1112 1.57248 0.786239 0.617922i \(-0.212025\pi\)
0.786239 + 0.617922i \(0.212025\pi\)
\(824\) 0 0
\(825\) −0.347096 −0.0120843
\(826\) 0 0
\(827\) −27.0250 −0.939750 −0.469875 0.882733i \(-0.655701\pi\)
−0.469875 + 0.882733i \(0.655701\pi\)
\(828\) 0 0
\(829\) 4.59653 0.159644 0.0798221 0.996809i \(-0.474565\pi\)
0.0798221 + 0.996809i \(0.474565\pi\)
\(830\) 0 0
\(831\) −1.59777 −0.0554259
\(832\) 0 0
\(833\) −154.289 −5.34580
\(834\) 0 0
\(835\) 12.4923 0.432314
\(836\) 0 0
\(837\) 2.26188 0.0781820
\(838\) 0 0
\(839\) 7.87295 0.271804 0.135902 0.990722i \(-0.456607\pi\)
0.135902 + 0.990722i \(0.456607\pi\)
\(840\) 0 0
\(841\) −28.6268 −0.987132
\(842\) 0 0
\(843\) −3.03427 −0.104506
\(844\) 0 0
\(845\) −8.07106 −0.277653
\(846\) 0 0
\(847\) −15.0986 −0.518795
\(848\) 0 0
\(849\) −2.14005 −0.0734462
\(850\) 0 0
\(851\) 2.10705 0.0722287
\(852\) 0 0
\(853\) −30.6219 −1.04847 −0.524236 0.851573i \(-0.675649\pi\)
−0.524236 + 0.851573i \(0.675649\pi\)
\(854\) 0 0
\(855\) 0.660225 0.0225792
\(856\) 0 0
\(857\) −9.99842 −0.341540 −0.170770 0.985311i \(-0.554625\pi\)
−0.170770 + 0.985311i \(0.554625\pi\)
\(858\) 0 0
\(859\) −19.2232 −0.655887 −0.327944 0.944697i \(-0.606356\pi\)
−0.327944 + 0.944697i \(0.606356\pi\)
\(860\) 0 0
\(861\) 2.66092 0.0906839
\(862\) 0 0
\(863\) −53.0999 −1.80754 −0.903771 0.428015i \(-0.859213\pi\)
−0.903771 + 0.428015i \(0.859213\pi\)
\(864\) 0 0
\(865\) −6.53177 −0.222087
\(866\) 0 0
\(867\) 4.73075 0.160665
\(868\) 0 0
\(869\) 19.9746 0.677591
\(870\) 0 0
\(871\) −8.99422 −0.304758
\(872\) 0 0
\(873\) −1.99966 −0.0676782
\(874\) 0 0
\(875\) 5.25775 0.177744
\(876\) 0 0
\(877\) −31.2618 −1.05563 −0.527817 0.849358i \(-0.676989\pi\)
−0.527817 + 0.849358i \(0.676989\pi\)
\(878\) 0 0
\(879\) 0.562654 0.0189779
\(880\) 0 0
\(881\) 39.3521 1.32580 0.662902 0.748706i \(-0.269324\pi\)
0.662902 + 0.748706i \(0.269324\pi\)
\(882\) 0 0
\(883\) −42.3262 −1.42439 −0.712195 0.701981i \(-0.752299\pi\)
−0.712195 + 0.701981i \(0.752299\pi\)
\(884\) 0 0
\(885\) 0.0642461 0.00215961
\(886\) 0 0
\(887\) 41.3401 1.38807 0.694033 0.719944i \(-0.255832\pi\)
0.694033 + 0.719944i \(0.255832\pi\)
\(888\) 0 0
\(889\) 74.9607 2.51410
\(890\) 0 0
\(891\) −25.2795 −0.846895
\(892\) 0 0
\(893\) 2.23673 0.0748493
\(894\) 0 0
\(895\) −11.8243 −0.395243
\(896\) 0 0
\(897\) −0.475016 −0.0158603
\(898\) 0 0
\(899\) −1.89626 −0.0632440
\(900\) 0 0
\(901\) −50.8737 −1.69485
\(902\) 0 0
\(903\) 4.78401 0.159202
\(904\) 0 0
\(905\) 3.73893 0.124286
\(906\) 0 0
\(907\) 50.3739 1.67264 0.836319 0.548243i \(-0.184703\pi\)
0.836319 + 0.548243i \(0.184703\pi\)
\(908\) 0 0
\(909\) 18.8041 0.623692
\(910\) 0 0
\(911\) −6.59547 −0.218518 −0.109259 0.994013i \(-0.534848\pi\)
−0.109259 + 0.994013i \(0.534848\pi\)
\(912\) 0 0
\(913\) 48.4665 1.60401
\(914\) 0 0
\(915\) −0.116742 −0.00385937
\(916\) 0 0
\(917\) −61.6060 −2.03441
\(918\) 0 0
\(919\) −27.2272 −0.898144 −0.449072 0.893496i \(-0.648245\pi\)
−0.449072 + 0.893496i \(0.648245\pi\)
\(920\) 0 0
\(921\) 3.62768 0.119536
\(922\) 0 0
\(923\) 19.2266 0.632850
\(924\) 0 0
\(925\) 1.19893 0.0394205
\(926\) 0 0
\(927\) −2.25970 −0.0742183
\(928\) 0 0
\(929\) −40.3297 −1.32318 −0.661588 0.749868i \(-0.730117\pi\)
−0.661588 + 0.749868i \(0.730117\pi\)
\(930\) 0 0
\(931\) −4.56578 −0.149637
\(932\) 0 0
\(933\) 2.48233 0.0812678
\(934\) 0 0
\(935\) 21.3080 0.696846
\(936\) 0 0
\(937\) 0.165480 0.00540600 0.00270300 0.999996i \(-0.499140\pi\)
0.00270300 + 0.999996i \(0.499140\pi\)
\(938\) 0 0
\(939\) 1.47150 0.0480206
\(940\) 0 0
\(941\) 47.4796 1.54779 0.773895 0.633314i \(-0.218306\pi\)
0.773895 + 0.633314i \(0.218306\pi\)
\(942\) 0 0
\(943\) 7.30572 0.237907
\(944\) 0 0
\(945\) −3.83113 −0.124627
\(946\) 0 0
\(947\) 30.0973 0.978029 0.489015 0.872276i \(-0.337356\pi\)
0.489015 + 0.872276i \(0.337356\pi\)
\(948\) 0 0
\(949\) 25.2044 0.818170
\(950\) 0 0
\(951\) −1.36657 −0.0443140
\(952\) 0 0
\(953\) 38.9511 1.26175 0.630875 0.775884i \(-0.282696\pi\)
0.630875 + 0.775884i \(0.282696\pi\)
\(954\) 0 0
\(955\) 16.5632 0.535971
\(956\) 0 0
\(957\) −0.212035 −0.00685410
\(958\) 0 0
\(959\) 8.91757 0.287963
\(960\) 0 0
\(961\) −21.3643 −0.689170
\(962\) 0 0
\(963\) 36.2418 1.16787
\(964\) 0 0
\(965\) −20.6257 −0.663966
\(966\) 0 0
\(967\) 35.4556 1.14017 0.570087 0.821584i \(-0.306909\pi\)
0.570087 + 0.821584i \(0.306909\pi\)
\(968\) 0 0
\(969\) 0.201240 0.00646476
\(970\) 0 0
\(971\) −18.8874 −0.606125 −0.303063 0.952971i \(-0.598009\pi\)
−0.303063 + 0.952971i \(0.598009\pi\)
\(972\) 0 0
\(973\) −80.3895 −2.57717
\(974\) 0 0
\(975\) −0.270288 −0.00865614
\(976\) 0 0
\(977\) 54.5149 1.74409 0.872044 0.489428i \(-0.162794\pi\)
0.872044 + 0.489428i \(0.162794\pi\)
\(978\) 0 0
\(979\) 26.3255 0.841366
\(980\) 0 0
\(981\) 45.5140 1.45315
\(982\) 0 0
\(983\) 1.32748 0.0423402 0.0211701 0.999776i \(-0.493261\pi\)
0.0211701 + 0.999776i \(0.493261\pi\)
\(984\) 0 0
\(985\) 9.39504 0.299351
\(986\) 0 0
\(987\) −6.47354 −0.206055
\(988\) 0 0
\(989\) 13.1348 0.417663
\(990\) 0 0
\(991\) −11.7720 −0.373950 −0.186975 0.982365i \(-0.559868\pi\)
−0.186975 + 0.982365i \(0.559868\pi\)
\(992\) 0 0
\(993\) 1.64930 0.0523389
\(994\) 0 0
\(995\) −3.39683 −0.107687
\(996\) 0 0
\(997\) −12.3756 −0.391940 −0.195970 0.980610i \(-0.562786\pi\)
−0.195970 + 0.980610i \(0.562786\pi\)
\(998\) 0 0
\(999\) −0.873614 −0.0276399
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 8020.2.a.d.1.17 29
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
8020.2.a.d.1.17 29 1.1 even 1 trivial