Properties

Label 8024.2.a.w.1.11
Level $8024$
Weight $2$
Character 8024.1
Self dual yes
Analytic conductor $64.072$
Analytic rank $1$
Dimension $20$
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: \(1\)
Dimension: \(20\)
Coefficient field: \(\mathbb{Q}[x]/(x^{20} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{20} - 2 x^{19} - 29 x^{18} + 51 x^{17} + 341 x^{16} - 514 x^{15} - 2114 x^{14} + 2629 x^{13} + 7532 x^{12} - 7342 x^{11} - 15668 x^{10} + 11260 x^{9} + 18269 x^{8} - 9059 x^{7} + \cdots + 4 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{8} \)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.11
Root \(-0.126023\) of defining polynomial
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)
 
\(f(q)\) \(=\) \(q+0.126023 q^{3} -3.00184 q^{5} +1.14075 q^{7} -2.98412 q^{9} +O(q^{10})\) \(q+0.126023 q^{3} -3.00184 q^{5} +1.14075 q^{7} -2.98412 q^{9} -5.21479 q^{11} +2.40906 q^{13} -0.378302 q^{15} +1.00000 q^{17} +6.00813 q^{19} +0.143761 q^{21} +4.99584 q^{23} +4.01106 q^{25} -0.754139 q^{27} +5.63999 q^{29} -7.10972 q^{31} -0.657185 q^{33} -3.42434 q^{35} -10.3994 q^{37} +0.303598 q^{39} +4.25539 q^{41} +4.05492 q^{43} +8.95785 q^{45} +3.59029 q^{47} -5.69870 q^{49} +0.126023 q^{51} +11.4309 q^{53} +15.6540 q^{55} +0.757164 q^{57} -1.00000 q^{59} +0.689168 q^{61} -3.40412 q^{63} -7.23162 q^{65} -0.334220 q^{67} +0.629593 q^{69} +0.447166 q^{71} -6.96383 q^{73} +0.505487 q^{75} -5.94874 q^{77} -8.97581 q^{79} +8.85732 q^{81} +3.58416 q^{83} -3.00184 q^{85} +0.710770 q^{87} +13.2105 q^{89} +2.74812 q^{91} -0.895991 q^{93} -18.0354 q^{95} +14.0084 q^{97} +15.5615 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 20 q - 2 q^{3} - 2 q^{5} + 5 q^{7} + 2 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 20 q - 2 q^{3} - 2 q^{5} + 5 q^{7} + 2 q^{9} + 8 q^{11} - 3 q^{13} - 2 q^{15} + 20 q^{17} - 9 q^{19} - 31 q^{21} - 8 q^{23} - 4 q^{25} - 17 q^{27} - 37 q^{29} - 9 q^{31} - 8 q^{33} - 8 q^{35} - 11 q^{37} - 12 q^{39} - 27 q^{41} + 17 q^{43} - 4 q^{45} + 7 q^{47} - 9 q^{49} - 2 q^{51} - q^{53} - 21 q^{55} - 57 q^{57} - 20 q^{59} - 12 q^{61} - 14 q^{63} - 59 q^{65} - 26 q^{67} + 14 q^{69} - 3 q^{71} - 45 q^{73} + 15 q^{75} + 6 q^{77} + 5 q^{79} + 12 q^{81} - 17 q^{83} - 2 q^{85} - 32 q^{87} - 40 q^{89} - 36 q^{91} - 4 q^{93} + 5 q^{95} - 77 q^{97} + 54 q^{99}+O(q^{100}) \) 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
\(3\) 0.126023 0.0727596 0.0363798 0.999338i \(-0.488417\pi\)
0.0363798 + 0.999338i \(0.488417\pi\)
\(4\) 0 0
\(5\) −3.00184 −1.34246 −0.671232 0.741247i \(-0.734235\pi\)
−0.671232 + 0.741247i \(0.734235\pi\)
\(6\) 0 0
\(7\) 1.14075 0.431161 0.215581 0.976486i \(-0.430836\pi\)
0.215581 + 0.976486i \(0.430836\pi\)
\(8\) 0 0
\(9\) −2.98412 −0.994706
\(10\) 0 0
\(11\) −5.21479 −1.57232 −0.786159 0.618025i \(-0.787933\pi\)
−0.786159 + 0.618025i \(0.787933\pi\)
\(12\) 0 0
\(13\) 2.40906 0.668153 0.334076 0.942546i \(-0.391576\pi\)
0.334076 + 0.942546i \(0.391576\pi\)
\(14\) 0 0
\(15\) −0.378302 −0.0976773
\(16\) 0 0
\(17\) 1.00000 0.242536
\(18\) 0 0
\(19\) 6.00813 1.37836 0.689179 0.724591i \(-0.257971\pi\)
0.689179 + 0.724591i \(0.257971\pi\)
\(20\) 0 0
\(21\) 0.143761 0.0313711
\(22\) 0 0
\(23\) 4.99584 1.04171 0.520853 0.853647i \(-0.325614\pi\)
0.520853 + 0.853647i \(0.325614\pi\)
\(24\) 0 0
\(25\) 4.01106 0.802212
\(26\) 0 0
\(27\) −0.754139 −0.145134
\(28\) 0 0
\(29\) 5.63999 1.04732 0.523660 0.851928i \(-0.324566\pi\)
0.523660 + 0.851928i \(0.324566\pi\)
\(30\) 0 0
\(31\) −7.10972 −1.27694 −0.638471 0.769646i \(-0.720433\pi\)
−0.638471 + 0.769646i \(0.720433\pi\)
\(32\) 0 0
\(33\) −0.657185 −0.114401
\(34\) 0 0
\(35\) −3.42434 −0.578819
\(36\) 0 0
\(37\) −10.3994 −1.70965 −0.854823 0.518920i \(-0.826334\pi\)
−0.854823 + 0.518920i \(0.826334\pi\)
\(38\) 0 0
\(39\) 0.303598 0.0486146
\(40\) 0 0
\(41\) 4.25539 0.664581 0.332290 0.943177i \(-0.392179\pi\)
0.332290 + 0.943177i \(0.392179\pi\)
\(42\) 0 0
\(43\) 4.05492 0.618369 0.309184 0.951002i \(-0.399944\pi\)
0.309184 + 0.951002i \(0.399944\pi\)
\(44\) 0 0
\(45\) 8.95785 1.33536
\(46\) 0 0
\(47\) 3.59029 0.523698 0.261849 0.965109i \(-0.415668\pi\)
0.261849 + 0.965109i \(0.415668\pi\)
\(48\) 0 0
\(49\) −5.69870 −0.814100
\(50\) 0 0
\(51\) 0.126023 0.0176468
\(52\) 0 0
\(53\) 11.4309 1.57015 0.785077 0.619398i \(-0.212623\pi\)
0.785077 + 0.619398i \(0.212623\pi\)
\(54\) 0 0
\(55\) 15.6540 2.11078
\(56\) 0 0
\(57\) 0.757164 0.100289
\(58\) 0 0
\(59\) −1.00000 −0.130189
\(60\) 0 0
\(61\) 0.689168 0.0882389 0.0441194 0.999026i \(-0.485952\pi\)
0.0441194 + 0.999026i \(0.485952\pi\)
\(62\) 0 0
\(63\) −3.40412 −0.428879
\(64\) 0 0
\(65\) −7.23162 −0.896972
\(66\) 0 0
\(67\) −0.334220 −0.0408315 −0.0204157 0.999792i \(-0.506499\pi\)
−0.0204157 + 0.999792i \(0.506499\pi\)
\(68\) 0 0
\(69\) 0.629593 0.0757941
\(70\) 0 0
\(71\) 0.447166 0.0530689 0.0265344 0.999648i \(-0.491553\pi\)
0.0265344 + 0.999648i \(0.491553\pi\)
\(72\) 0 0
\(73\) −6.96383 −0.815054 −0.407527 0.913193i \(-0.633609\pi\)
−0.407527 + 0.913193i \(0.633609\pi\)
\(74\) 0 0
\(75\) 0.505487 0.0583687
\(76\) 0 0
\(77\) −5.94874 −0.677922
\(78\) 0 0
\(79\) −8.97581 −1.00986 −0.504929 0.863161i \(-0.668481\pi\)
−0.504929 + 0.863161i \(0.668481\pi\)
\(80\) 0 0
\(81\) 8.85732 0.984146
\(82\) 0 0
\(83\) 3.58416 0.393413 0.196707 0.980462i \(-0.436975\pi\)
0.196707 + 0.980462i \(0.436975\pi\)
\(84\) 0 0
\(85\) −3.00184 −0.325596
\(86\) 0 0
\(87\) 0.710770 0.0762026
\(88\) 0 0
\(89\) 13.2105 1.40031 0.700153 0.713993i \(-0.253115\pi\)
0.700153 + 0.713993i \(0.253115\pi\)
\(90\) 0 0
\(91\) 2.74812 0.288082
\(92\) 0 0
\(93\) −0.895991 −0.0929099
\(94\) 0 0
\(95\) −18.0354 −1.85040
\(96\) 0 0
\(97\) 14.0084 1.42234 0.711170 0.703021i \(-0.248166\pi\)
0.711170 + 0.703021i \(0.248166\pi\)
\(98\) 0 0
\(99\) 15.5615 1.56399
\(100\) 0 0
\(101\) 0.275049 0.0273684 0.0136842 0.999906i \(-0.495644\pi\)
0.0136842 + 0.999906i \(0.495644\pi\)
\(102\) 0 0
\(103\) −12.4016 −1.22196 −0.610981 0.791646i \(-0.709225\pi\)
−0.610981 + 0.791646i \(0.709225\pi\)
\(104\) 0 0
\(105\) −0.431547 −0.0421147
\(106\) 0 0
\(107\) 5.37705 0.519819 0.259909 0.965633i \(-0.416307\pi\)
0.259909 + 0.965633i \(0.416307\pi\)
\(108\) 0 0
\(109\) −6.90115 −0.661010 −0.330505 0.943804i \(-0.607219\pi\)
−0.330505 + 0.943804i \(0.607219\pi\)
\(110\) 0 0
\(111\) −1.31056 −0.124393
\(112\) 0 0
\(113\) −10.2548 −0.964692 −0.482346 0.875981i \(-0.660215\pi\)
−0.482346 + 0.875981i \(0.660215\pi\)
\(114\) 0 0
\(115\) −14.9967 −1.39845
\(116\) 0 0
\(117\) −7.18892 −0.664616
\(118\) 0 0
\(119\) 1.14075 0.104572
\(120\) 0 0
\(121\) 16.1940 1.47218
\(122\) 0 0
\(123\) 0.536279 0.0483547
\(124\) 0 0
\(125\) 2.96864 0.265523
\(126\) 0 0
\(127\) 10.4271 0.925254 0.462627 0.886553i \(-0.346907\pi\)
0.462627 + 0.886553i \(0.346907\pi\)
\(128\) 0 0
\(129\) 0.511014 0.0449923
\(130\) 0 0
\(131\) 7.42500 0.648725 0.324363 0.945933i \(-0.394850\pi\)
0.324363 + 0.945933i \(0.394850\pi\)
\(132\) 0 0
\(133\) 6.85374 0.594295
\(134\) 0 0
\(135\) 2.26381 0.194837
\(136\) 0 0
\(137\) 1.38079 0.117969 0.0589844 0.998259i \(-0.481214\pi\)
0.0589844 + 0.998259i \(0.481214\pi\)
\(138\) 0 0
\(139\) −11.7283 −0.994784 −0.497392 0.867526i \(-0.665709\pi\)
−0.497392 + 0.867526i \(0.665709\pi\)
\(140\) 0 0
\(141\) 0.452461 0.0381040
\(142\) 0 0
\(143\) −12.5627 −1.05055
\(144\) 0 0
\(145\) −16.9303 −1.40599
\(146\) 0 0
\(147\) −0.718170 −0.0592336
\(148\) 0 0
\(149\) −15.8805 −1.30098 −0.650489 0.759515i \(-0.725436\pi\)
−0.650489 + 0.759515i \(0.725436\pi\)
\(150\) 0 0
\(151\) 2.54563 0.207160 0.103580 0.994621i \(-0.466970\pi\)
0.103580 + 0.994621i \(0.466970\pi\)
\(152\) 0 0
\(153\) −2.98412 −0.241252
\(154\) 0 0
\(155\) 21.3422 1.71425
\(156\) 0 0
\(157\) −0.671821 −0.0536172 −0.0268086 0.999641i \(-0.508534\pi\)
−0.0268086 + 0.999641i \(0.508534\pi\)
\(158\) 0 0
\(159\) 1.44056 0.114244
\(160\) 0 0
\(161\) 5.69899 0.449143
\(162\) 0 0
\(163\) −13.7045 −1.07342 −0.536711 0.843766i \(-0.680333\pi\)
−0.536711 + 0.843766i \(0.680333\pi\)
\(164\) 0 0
\(165\) 1.97277 0.153580
\(166\) 0 0
\(167\) −16.1333 −1.24843 −0.624215 0.781253i \(-0.714581\pi\)
−0.624215 + 0.781253i \(0.714581\pi\)
\(168\) 0 0
\(169\) −7.19643 −0.553572
\(170\) 0 0
\(171\) −17.9290 −1.37106
\(172\) 0 0
\(173\) 7.71861 0.586835 0.293417 0.955984i \(-0.405207\pi\)
0.293417 + 0.955984i \(0.405207\pi\)
\(174\) 0 0
\(175\) 4.57560 0.345883
\(176\) 0 0
\(177\) −0.126023 −0.00947250
\(178\) 0 0
\(179\) −8.46639 −0.632808 −0.316404 0.948625i \(-0.602475\pi\)
−0.316404 + 0.948625i \(0.602475\pi\)
\(180\) 0 0
\(181\) 2.59899 0.193182 0.0965909 0.995324i \(-0.469206\pi\)
0.0965909 + 0.995324i \(0.469206\pi\)
\(182\) 0 0
\(183\) 0.0868513 0.00642023
\(184\) 0 0
\(185\) 31.2173 2.29514
\(186\) 0 0
\(187\) −5.21479 −0.381343
\(188\) 0 0
\(189\) −0.860281 −0.0625762
\(190\) 0 0
\(191\) −23.4647 −1.69785 −0.848924 0.528515i \(-0.822749\pi\)
−0.848924 + 0.528515i \(0.822749\pi\)
\(192\) 0 0
\(193\) −21.2687 −1.53095 −0.765476 0.643464i \(-0.777497\pi\)
−0.765476 + 0.643464i \(0.777497\pi\)
\(194\) 0 0
\(195\) −0.911353 −0.0652634
\(196\) 0 0
\(197\) −1.99334 −0.142019 −0.0710096 0.997476i \(-0.522622\pi\)
−0.0710096 + 0.997476i \(0.522622\pi\)
\(198\) 0 0
\(199\) −22.7503 −1.61272 −0.806362 0.591422i \(-0.798567\pi\)
−0.806362 + 0.591422i \(0.798567\pi\)
\(200\) 0 0
\(201\) −0.0421195 −0.00297088
\(202\) 0 0
\(203\) 6.43379 0.451563
\(204\) 0 0
\(205\) −12.7740 −0.892176
\(206\) 0 0
\(207\) −14.9082 −1.03619
\(208\) 0 0
\(209\) −31.3311 −2.16722
\(210\) 0 0
\(211\) −7.07579 −0.487118 −0.243559 0.969886i \(-0.578315\pi\)
−0.243559 + 0.969886i \(0.578315\pi\)
\(212\) 0 0
\(213\) 0.0563534 0.00386127
\(214\) 0 0
\(215\) −12.1722 −0.830139
\(216\) 0 0
\(217\) −8.11038 −0.550568
\(218\) 0 0
\(219\) −0.877605 −0.0593031
\(220\) 0 0
\(221\) 2.40906 0.162051
\(222\) 0 0
\(223\) 13.3477 0.893830 0.446915 0.894576i \(-0.352523\pi\)
0.446915 + 0.894576i \(0.352523\pi\)
\(224\) 0 0
\(225\) −11.9695 −0.797965
\(226\) 0 0
\(227\) 5.44827 0.361614 0.180807 0.983519i \(-0.442129\pi\)
0.180807 + 0.983519i \(0.442129\pi\)
\(228\) 0 0
\(229\) −16.6875 −1.10274 −0.551370 0.834261i \(-0.685895\pi\)
−0.551370 + 0.834261i \(0.685895\pi\)
\(230\) 0 0
\(231\) −0.749681 −0.0493254
\(232\) 0 0
\(233\) −10.4889 −0.687149 −0.343574 0.939125i \(-0.611638\pi\)
−0.343574 + 0.939125i \(0.611638\pi\)
\(234\) 0 0
\(235\) −10.7775 −0.703046
\(236\) 0 0
\(237\) −1.13116 −0.0734769
\(238\) 0 0
\(239\) 6.36138 0.411484 0.205742 0.978606i \(-0.434039\pi\)
0.205742 + 0.978606i \(0.434039\pi\)
\(240\) 0 0
\(241\) −20.3695 −1.31212 −0.656058 0.754711i \(-0.727777\pi\)
−0.656058 + 0.754711i \(0.727777\pi\)
\(242\) 0 0
\(243\) 3.37865 0.216740
\(244\) 0 0
\(245\) 17.1066 1.09290
\(246\) 0 0
\(247\) 14.4739 0.920954
\(248\) 0 0
\(249\) 0.451688 0.0286246
\(250\) 0 0
\(251\) 0.481594 0.0303979 0.0151990 0.999884i \(-0.495162\pi\)
0.0151990 + 0.999884i \(0.495162\pi\)
\(252\) 0 0
\(253\) −26.0523 −1.63789
\(254\) 0 0
\(255\) −0.378302 −0.0236902
\(256\) 0 0
\(257\) −24.4666 −1.52618 −0.763092 0.646290i \(-0.776320\pi\)
−0.763092 + 0.646290i \(0.776320\pi\)
\(258\) 0 0
\(259\) −11.8630 −0.737133
\(260\) 0 0
\(261\) −16.8304 −1.04177
\(262\) 0 0
\(263\) −15.3833 −0.948578 −0.474289 0.880369i \(-0.657295\pi\)
−0.474289 + 0.880369i \(0.657295\pi\)
\(264\) 0 0
\(265\) −34.3138 −2.10788
\(266\) 0 0
\(267\) 1.66483 0.101886
\(268\) 0 0
\(269\) 9.73616 0.593624 0.296812 0.954936i \(-0.404077\pi\)
0.296812 + 0.954936i \(0.404077\pi\)
\(270\) 0 0
\(271\) −2.06324 −0.125333 −0.0626665 0.998035i \(-0.519960\pi\)
−0.0626665 + 0.998035i \(0.519960\pi\)
\(272\) 0 0
\(273\) 0.346328 0.0209607
\(274\) 0 0
\(275\) −20.9168 −1.26133
\(276\) 0 0
\(277\) −4.52104 −0.271643 −0.135821 0.990733i \(-0.543367\pi\)
−0.135821 + 0.990733i \(0.543367\pi\)
\(278\) 0 0
\(279\) 21.2162 1.27018
\(280\) 0 0
\(281\) 26.1254 1.55851 0.779256 0.626706i \(-0.215597\pi\)
0.779256 + 0.626706i \(0.215597\pi\)
\(282\) 0 0
\(283\) 16.5260 0.982368 0.491184 0.871056i \(-0.336564\pi\)
0.491184 + 0.871056i \(0.336564\pi\)
\(284\) 0 0
\(285\) −2.27289 −0.134634
\(286\) 0 0
\(287\) 4.85432 0.286541
\(288\) 0 0
\(289\) 1.00000 0.0588235
\(290\) 0 0
\(291\) 1.76539 0.103489
\(292\) 0 0
\(293\) 8.10585 0.473549 0.236774 0.971565i \(-0.423910\pi\)
0.236774 + 0.971565i \(0.423910\pi\)
\(294\) 0 0
\(295\) 3.00184 0.174774
\(296\) 0 0
\(297\) 3.93267 0.228197
\(298\) 0 0
\(299\) 12.0353 0.696019
\(300\) 0 0
\(301\) 4.62563 0.266617
\(302\) 0 0
\(303\) 0.0346626 0.00199131
\(304\) 0 0
\(305\) −2.06877 −0.118458
\(306\) 0 0
\(307\) −23.8670 −1.36216 −0.681081 0.732208i \(-0.738490\pi\)
−0.681081 + 0.732208i \(0.738490\pi\)
\(308\) 0 0
\(309\) −1.56289 −0.0889095
\(310\) 0 0
\(311\) 22.7334 1.28909 0.644547 0.764565i \(-0.277046\pi\)
0.644547 + 0.764565i \(0.277046\pi\)
\(312\) 0 0
\(313\) −15.3489 −0.867570 −0.433785 0.901017i \(-0.642822\pi\)
−0.433785 + 0.901017i \(0.642822\pi\)
\(314\) 0 0
\(315\) 10.2186 0.575755
\(316\) 0 0
\(317\) 15.1405 0.850378 0.425189 0.905105i \(-0.360208\pi\)
0.425189 + 0.905105i \(0.360208\pi\)
\(318\) 0 0
\(319\) −29.4113 −1.64672
\(320\) 0 0
\(321\) 0.677634 0.0378218
\(322\) 0 0
\(323\) 6.00813 0.334301
\(324\) 0 0
\(325\) 9.66288 0.536000
\(326\) 0 0
\(327\) −0.869706 −0.0480949
\(328\) 0 0
\(329\) 4.09561 0.225798
\(330\) 0 0
\(331\) 26.3595 1.44885 0.724426 0.689353i \(-0.242105\pi\)
0.724426 + 0.689353i \(0.242105\pi\)
\(332\) 0 0
\(333\) 31.0329 1.70059
\(334\) 0 0
\(335\) 1.00328 0.0548148
\(336\) 0 0
\(337\) 6.14816 0.334912 0.167456 0.985880i \(-0.446445\pi\)
0.167456 + 0.985880i \(0.446445\pi\)
\(338\) 0 0
\(339\) −1.29235 −0.0701906
\(340\) 0 0
\(341\) 37.0756 2.00776
\(342\) 0 0
\(343\) −14.4860 −0.782170
\(344\) 0 0
\(345\) −1.88994 −0.101751
\(346\) 0 0
\(347\) −16.3568 −0.878080 −0.439040 0.898467i \(-0.644681\pi\)
−0.439040 + 0.898467i \(0.644681\pi\)
\(348\) 0 0
\(349\) 13.0756 0.699920 0.349960 0.936765i \(-0.386195\pi\)
0.349960 + 0.936765i \(0.386195\pi\)
\(350\) 0 0
\(351\) −1.81677 −0.0969718
\(352\) 0 0
\(353\) −20.5458 −1.09354 −0.546772 0.837282i \(-0.684143\pi\)
−0.546772 + 0.837282i \(0.684143\pi\)
\(354\) 0 0
\(355\) −1.34232 −0.0712431
\(356\) 0 0
\(357\) 0.143761 0.00760862
\(358\) 0 0
\(359\) 16.8851 0.891162 0.445581 0.895242i \(-0.352997\pi\)
0.445581 + 0.895242i \(0.352997\pi\)
\(360\) 0 0
\(361\) 17.0976 0.899872
\(362\) 0 0
\(363\) 2.04082 0.107115
\(364\) 0 0
\(365\) 20.9043 1.09418
\(366\) 0 0
\(367\) −7.49308 −0.391136 −0.195568 0.980690i \(-0.562655\pi\)
−0.195568 + 0.980690i \(0.562655\pi\)
\(368\) 0 0
\(369\) −12.6986 −0.661062
\(370\) 0 0
\(371\) 13.0397 0.676990
\(372\) 0 0
\(373\) −36.2372 −1.87629 −0.938147 0.346238i \(-0.887459\pi\)
−0.938147 + 0.346238i \(0.887459\pi\)
\(374\) 0 0
\(375\) 0.374118 0.0193194
\(376\) 0 0
\(377\) 13.5871 0.699769
\(378\) 0 0
\(379\) 19.1070 0.981462 0.490731 0.871311i \(-0.336730\pi\)
0.490731 + 0.871311i \(0.336730\pi\)
\(380\) 0 0
\(381\) 1.31406 0.0673212
\(382\) 0 0
\(383\) 24.2104 1.23709 0.618547 0.785748i \(-0.287722\pi\)
0.618547 + 0.785748i \(0.287722\pi\)
\(384\) 0 0
\(385\) 17.8572 0.910087
\(386\) 0 0
\(387\) −12.1003 −0.615095
\(388\) 0 0
\(389\) −35.6273 −1.80637 −0.903187 0.429247i \(-0.858779\pi\)
−0.903187 + 0.429247i \(0.858779\pi\)
\(390\) 0 0
\(391\) 4.99584 0.252651
\(392\) 0 0
\(393\) 0.935724 0.0472010
\(394\) 0 0
\(395\) 26.9440 1.35570
\(396\) 0 0
\(397\) −4.47236 −0.224461 −0.112231 0.993682i \(-0.535800\pi\)
−0.112231 + 0.993682i \(0.535800\pi\)
\(398\) 0 0
\(399\) 0.863732 0.0432407
\(400\) 0 0
\(401\) 13.8281 0.690543 0.345271 0.938503i \(-0.387787\pi\)
0.345271 + 0.938503i \(0.387787\pi\)
\(402\) 0 0
\(403\) −17.1277 −0.853193
\(404\) 0 0
\(405\) −26.5883 −1.32118
\(406\) 0 0
\(407\) 54.2305 2.68810
\(408\) 0 0
\(409\) −4.69046 −0.231928 −0.115964 0.993253i \(-0.536996\pi\)
−0.115964 + 0.993253i \(0.536996\pi\)
\(410\) 0 0
\(411\) 0.174012 0.00858337
\(412\) 0 0
\(413\) −1.14075 −0.0561324
\(414\) 0 0
\(415\) −10.7591 −0.528143
\(416\) 0 0
\(417\) −1.47804 −0.0723801
\(418\) 0 0
\(419\) −20.9370 −1.02284 −0.511419 0.859332i \(-0.670880\pi\)
−0.511419 + 0.859332i \(0.670880\pi\)
\(420\) 0 0
\(421\) 20.6293 1.00541 0.502706 0.864457i \(-0.332338\pi\)
0.502706 + 0.864457i \(0.332338\pi\)
\(422\) 0 0
\(423\) −10.7138 −0.520925
\(424\) 0 0
\(425\) 4.01106 0.194565
\(426\) 0 0
\(427\) 0.786165 0.0380452
\(428\) 0 0
\(429\) −1.58320 −0.0764375
\(430\) 0 0
\(431\) −9.83905 −0.473930 −0.236965 0.971518i \(-0.576153\pi\)
−0.236965 + 0.971518i \(0.576153\pi\)
\(432\) 0 0
\(433\) −22.1984 −1.06679 −0.533393 0.845867i \(-0.679083\pi\)
−0.533393 + 0.845867i \(0.679083\pi\)
\(434\) 0 0
\(435\) −2.13362 −0.102299
\(436\) 0 0
\(437\) 30.0157 1.43584
\(438\) 0 0
\(439\) −23.0419 −1.09973 −0.549864 0.835254i \(-0.685320\pi\)
−0.549864 + 0.835254i \(0.685320\pi\)
\(440\) 0 0
\(441\) 17.0056 0.809790
\(442\) 0 0
\(443\) −31.3020 −1.48720 −0.743601 0.668624i \(-0.766884\pi\)
−0.743601 + 0.668624i \(0.766884\pi\)
\(444\) 0 0
\(445\) −39.6557 −1.87986
\(446\) 0 0
\(447\) −2.00131 −0.0946587
\(448\) 0 0
\(449\) −39.8384 −1.88009 −0.940046 0.341048i \(-0.889218\pi\)
−0.940046 + 0.341048i \(0.889218\pi\)
\(450\) 0 0
\(451\) −22.1910 −1.04493
\(452\) 0 0
\(453\) 0.320808 0.0150729
\(454\) 0 0
\(455\) −8.24944 −0.386740
\(456\) 0 0
\(457\) −37.8326 −1.76973 −0.884867 0.465844i \(-0.845751\pi\)
−0.884867 + 0.465844i \(0.845751\pi\)
\(458\) 0 0
\(459\) −0.754139 −0.0352002
\(460\) 0 0
\(461\) 17.4266 0.811636 0.405818 0.913954i \(-0.366987\pi\)
0.405818 + 0.913954i \(0.366987\pi\)
\(462\) 0 0
\(463\) 16.3715 0.760848 0.380424 0.924812i \(-0.375778\pi\)
0.380424 + 0.924812i \(0.375778\pi\)
\(464\) 0 0
\(465\) 2.68962 0.124728
\(466\) 0 0
\(467\) 24.3207 1.12543 0.562713 0.826652i \(-0.309758\pi\)
0.562713 + 0.826652i \(0.309758\pi\)
\(468\) 0 0
\(469\) −0.381260 −0.0176049
\(470\) 0 0
\(471\) −0.0846652 −0.00390117
\(472\) 0 0
\(473\) −21.1455 −0.972272
\(474\) 0 0
\(475\) 24.0990 1.10574
\(476\) 0 0
\(477\) −34.1112 −1.56184
\(478\) 0 0
\(479\) −4.15815 −0.189991 −0.0949953 0.995478i \(-0.530284\pi\)
−0.0949953 + 0.995478i \(0.530284\pi\)
\(480\) 0 0
\(481\) −25.0527 −1.14230
\(482\) 0 0
\(483\) 0.718206 0.0326795
\(484\) 0 0
\(485\) −42.0511 −1.90944
\(486\) 0 0
\(487\) −27.9326 −1.26575 −0.632873 0.774255i \(-0.718125\pi\)
−0.632873 + 0.774255i \(0.718125\pi\)
\(488\) 0 0
\(489\) −1.72709 −0.0781017
\(490\) 0 0
\(491\) −16.0768 −0.725535 −0.362767 0.931880i \(-0.618168\pi\)
−0.362767 + 0.931880i \(0.618168\pi\)
\(492\) 0 0
\(493\) 5.63999 0.254012
\(494\) 0 0
\(495\) −46.7133 −2.09961
\(496\) 0 0
\(497\) 0.510103 0.0228812
\(498\) 0 0
\(499\) 6.93251 0.310342 0.155171 0.987888i \(-0.450407\pi\)
0.155171 + 0.987888i \(0.450407\pi\)
\(500\) 0 0
\(501\) −2.03317 −0.0908353
\(502\) 0 0
\(503\) 26.7818 1.19414 0.597071 0.802189i \(-0.296331\pi\)
0.597071 + 0.802189i \(0.296331\pi\)
\(504\) 0 0
\(505\) −0.825653 −0.0367411
\(506\) 0 0
\(507\) −0.906919 −0.0402777
\(508\) 0 0
\(509\) 13.6604 0.605488 0.302744 0.953072i \(-0.402097\pi\)
0.302744 + 0.953072i \(0.402097\pi\)
\(510\) 0 0
\(511\) −7.94395 −0.351420
\(512\) 0 0
\(513\) −4.53096 −0.200047
\(514\) 0 0
\(515\) 37.2275 1.64044
\(516\) 0 0
\(517\) −18.7226 −0.823419
\(518\) 0 0
\(519\) 0.972725 0.0426979
\(520\) 0 0
\(521\) −1.64880 −0.0722354 −0.0361177 0.999348i \(-0.511499\pi\)
−0.0361177 + 0.999348i \(0.511499\pi\)
\(522\) 0 0
\(523\) 10.3043 0.450573 0.225287 0.974293i \(-0.427668\pi\)
0.225287 + 0.974293i \(0.427668\pi\)
\(524\) 0 0
\(525\) 0.576633 0.0251663
\(526\) 0 0
\(527\) −7.10972 −0.309704
\(528\) 0 0
\(529\) 1.95846 0.0851505
\(530\) 0 0
\(531\) 2.98412 0.129500
\(532\) 0 0
\(533\) 10.2515 0.444042
\(534\) 0 0
\(535\) −16.1411 −0.697839
\(536\) 0 0
\(537\) −1.06696 −0.0460429
\(538\) 0 0
\(539\) 29.7175 1.28002
\(540\) 0 0
\(541\) 30.7994 1.32417 0.662085 0.749429i \(-0.269672\pi\)
0.662085 + 0.749429i \(0.269672\pi\)
\(542\) 0 0
\(543\) 0.327534 0.0140558
\(544\) 0 0
\(545\) 20.7162 0.887383
\(546\) 0 0
\(547\) −12.3941 −0.529933 −0.264967 0.964258i \(-0.585361\pi\)
−0.264967 + 0.964258i \(0.585361\pi\)
\(548\) 0 0
\(549\) −2.05656 −0.0877717
\(550\) 0 0
\(551\) 33.8857 1.44358
\(552\) 0 0
\(553\) −10.2391 −0.435412
\(554\) 0 0
\(555\) 3.93411 0.166993
\(556\) 0 0
\(557\) −41.9431 −1.77718 −0.888592 0.458698i \(-0.848316\pi\)
−0.888592 + 0.458698i \(0.848316\pi\)
\(558\) 0 0
\(559\) 9.76853 0.413165
\(560\) 0 0
\(561\) −0.657185 −0.0277464
\(562\) 0 0
\(563\) −32.4203 −1.36635 −0.683177 0.730253i \(-0.739402\pi\)
−0.683177 + 0.730253i \(0.739402\pi\)
\(564\) 0 0
\(565\) 30.7833 1.29506
\(566\) 0 0
\(567\) 10.1039 0.424326
\(568\) 0 0
\(569\) 28.4154 1.19123 0.595617 0.803269i \(-0.296908\pi\)
0.595617 + 0.803269i \(0.296908\pi\)
\(570\) 0 0
\(571\) 26.1767 1.09546 0.547731 0.836654i \(-0.315492\pi\)
0.547731 + 0.836654i \(0.315492\pi\)
\(572\) 0 0
\(573\) −2.95710 −0.123535
\(574\) 0 0
\(575\) 20.0386 0.835669
\(576\) 0 0
\(577\) −5.80115 −0.241505 −0.120752 0.992683i \(-0.538531\pi\)
−0.120752 + 0.992683i \(0.538531\pi\)
\(578\) 0 0
\(579\) −2.68035 −0.111392
\(580\) 0 0
\(581\) 4.08862 0.169624
\(582\) 0 0
\(583\) −59.6097 −2.46878
\(584\) 0 0
\(585\) 21.5800 0.892223
\(586\) 0 0
\(587\) 41.6575 1.71939 0.859694 0.510809i \(-0.170654\pi\)
0.859694 + 0.510809i \(0.170654\pi\)
\(588\) 0 0
\(589\) −42.7161 −1.76008
\(590\) 0 0
\(591\) −0.251207 −0.0103333
\(592\) 0 0
\(593\) −38.5296 −1.58222 −0.791111 0.611673i \(-0.790497\pi\)
−0.791111 + 0.611673i \(0.790497\pi\)
\(594\) 0 0
\(595\) −3.42434 −0.140384
\(596\) 0 0
\(597\) −2.86707 −0.117341
\(598\) 0 0
\(599\) 28.7536 1.17484 0.587419 0.809283i \(-0.300144\pi\)
0.587419 + 0.809283i \(0.300144\pi\)
\(600\) 0 0
\(601\) 26.2114 1.06919 0.534593 0.845110i \(-0.320465\pi\)
0.534593 + 0.845110i \(0.320465\pi\)
\(602\) 0 0
\(603\) 0.997352 0.0406153
\(604\) 0 0
\(605\) −48.6118 −1.97635
\(606\) 0 0
\(607\) 12.0482 0.489020 0.244510 0.969647i \(-0.421373\pi\)
0.244510 + 0.969647i \(0.421373\pi\)
\(608\) 0 0
\(609\) 0.810808 0.0328556
\(610\) 0 0
\(611\) 8.64922 0.349910
\(612\) 0 0
\(613\) 24.5112 0.989999 0.495000 0.868893i \(-0.335168\pi\)
0.495000 + 0.868893i \(0.335168\pi\)
\(614\) 0 0
\(615\) −1.60983 −0.0649144
\(616\) 0 0
\(617\) −35.0974 −1.41297 −0.706484 0.707729i \(-0.749720\pi\)
−0.706484 + 0.707729i \(0.749720\pi\)
\(618\) 0 0
\(619\) −25.5434 −1.02667 −0.513337 0.858187i \(-0.671591\pi\)
−0.513337 + 0.858187i \(0.671591\pi\)
\(620\) 0 0
\(621\) −3.76756 −0.151187
\(622\) 0 0
\(623\) 15.0698 0.603758
\(624\) 0 0
\(625\) −28.9667 −1.15867
\(626\) 0 0
\(627\) −3.94845 −0.157686
\(628\) 0 0
\(629\) −10.3994 −0.414650
\(630\) 0 0
\(631\) −31.0208 −1.23492 −0.617459 0.786603i \(-0.711838\pi\)
−0.617459 + 0.786603i \(0.711838\pi\)
\(632\) 0 0
\(633\) −0.891715 −0.0354425
\(634\) 0 0
\(635\) −31.3005 −1.24212
\(636\) 0 0
\(637\) −13.7285 −0.543943
\(638\) 0 0
\(639\) −1.33440 −0.0527879
\(640\) 0 0
\(641\) −4.31634 −0.170485 −0.0852425 0.996360i \(-0.527166\pi\)
−0.0852425 + 0.996360i \(0.527166\pi\)
\(642\) 0 0
\(643\) 40.6051 1.60131 0.800654 0.599127i \(-0.204486\pi\)
0.800654 + 0.599127i \(0.204486\pi\)
\(644\) 0 0
\(645\) −1.53398 −0.0604006
\(646\) 0 0
\(647\) 33.0506 1.29935 0.649677 0.760210i \(-0.274904\pi\)
0.649677 + 0.760210i \(0.274904\pi\)
\(648\) 0 0
\(649\) 5.21479 0.204698
\(650\) 0 0
\(651\) −1.02210 −0.0400591
\(652\) 0 0
\(653\) −42.1162 −1.64813 −0.824067 0.566492i \(-0.808300\pi\)
−0.824067 + 0.566492i \(0.808300\pi\)
\(654\) 0 0
\(655\) −22.2887 −0.870891
\(656\) 0 0
\(657\) 20.7809 0.810739
\(658\) 0 0
\(659\) 24.7841 0.965453 0.482727 0.875771i \(-0.339646\pi\)
0.482727 + 0.875771i \(0.339646\pi\)
\(660\) 0 0
\(661\) −41.9877 −1.63313 −0.816567 0.577251i \(-0.804125\pi\)
−0.816567 + 0.577251i \(0.804125\pi\)
\(662\) 0 0
\(663\) 0.303598 0.0117908
\(664\) 0 0
\(665\) −20.5739 −0.797820
\(666\) 0 0
\(667\) 28.1765 1.09100
\(668\) 0 0
\(669\) 1.68213 0.0650347
\(670\) 0 0
\(671\) −3.59386 −0.138740
\(672\) 0 0
\(673\) −23.2743 −0.897159 −0.448579 0.893743i \(-0.648070\pi\)
−0.448579 + 0.893743i \(0.648070\pi\)
\(674\) 0 0
\(675\) −3.02490 −0.116428
\(676\) 0 0
\(677\) −18.4973 −0.710910 −0.355455 0.934693i \(-0.615674\pi\)
−0.355455 + 0.934693i \(0.615674\pi\)
\(678\) 0 0
\(679\) 15.9800 0.613258
\(680\) 0 0
\(681\) 0.686609 0.0263109
\(682\) 0 0
\(683\) 35.3211 1.35153 0.675763 0.737119i \(-0.263814\pi\)
0.675763 + 0.737119i \(0.263814\pi\)
\(684\) 0 0
\(685\) −4.14492 −0.158369
\(686\) 0 0
\(687\) −2.10301 −0.0802349
\(688\) 0 0
\(689\) 27.5377 1.04910
\(690\) 0 0
\(691\) 44.2119 1.68190 0.840950 0.541112i \(-0.181997\pi\)
0.840950 + 0.541112i \(0.181997\pi\)
\(692\) 0 0
\(693\) 17.7518 0.674333
\(694\) 0 0
\(695\) 35.2066 1.33546
\(696\) 0 0
\(697\) 4.25539 0.161184
\(698\) 0 0
\(699\) −1.32184 −0.0499967
\(700\) 0 0
\(701\) −12.1992 −0.460756 −0.230378 0.973101i \(-0.573996\pi\)
−0.230378 + 0.973101i \(0.573996\pi\)
\(702\) 0 0
\(703\) −62.4807 −2.35650
\(704\) 0 0
\(705\) −1.35822 −0.0511533
\(706\) 0 0
\(707\) 0.313761 0.0118002
\(708\) 0 0
\(709\) 28.4867 1.06984 0.534920 0.844903i \(-0.320342\pi\)
0.534920 + 0.844903i \(0.320342\pi\)
\(710\) 0 0
\(711\) 26.7849 1.00451
\(712\) 0 0
\(713\) −35.5190 −1.33020
\(714\) 0 0
\(715\) 37.7113 1.41032
\(716\) 0 0
\(717\) 0.801683 0.0299394
\(718\) 0 0
\(719\) 10.4564 0.389956 0.194978 0.980808i \(-0.437536\pi\)
0.194978 + 0.980808i \(0.437536\pi\)
\(720\) 0 0
\(721\) −14.1470 −0.526862
\(722\) 0 0
\(723\) −2.56703 −0.0954691
\(724\) 0 0
\(725\) 22.6223 0.840172
\(726\) 0 0
\(727\) −28.5216 −1.05781 −0.528904 0.848682i \(-0.677397\pi\)
−0.528904 + 0.848682i \(0.677397\pi\)
\(728\) 0 0
\(729\) −26.1462 −0.968376
\(730\) 0 0
\(731\) 4.05492 0.149976
\(732\) 0 0
\(733\) 45.5121 1.68103 0.840514 0.541789i \(-0.182253\pi\)
0.840514 + 0.541789i \(0.182253\pi\)
\(734\) 0 0
\(735\) 2.15583 0.0795191
\(736\) 0 0
\(737\) 1.74289 0.0642000
\(738\) 0 0
\(739\) 10.3813 0.381880 0.190940 0.981602i \(-0.438846\pi\)
0.190940 + 0.981602i \(0.438846\pi\)
\(740\) 0 0
\(741\) 1.82405 0.0670083
\(742\) 0 0
\(743\) −0.917458 −0.0336583 −0.0168291 0.999858i \(-0.505357\pi\)
−0.0168291 + 0.999858i \(0.505357\pi\)
\(744\) 0 0
\(745\) 47.6707 1.74652
\(746\) 0 0
\(747\) −10.6956 −0.391330
\(748\) 0 0
\(749\) 6.13384 0.224126
\(750\) 0 0
\(751\) −13.5297 −0.493706 −0.246853 0.969053i \(-0.579396\pi\)
−0.246853 + 0.969053i \(0.579396\pi\)
\(752\) 0 0
\(753\) 0.0606921 0.00221174
\(754\) 0 0
\(755\) −7.64157 −0.278105
\(756\) 0 0
\(757\) −21.2041 −0.770678 −0.385339 0.922775i \(-0.625915\pi\)
−0.385339 + 0.922775i \(0.625915\pi\)
\(758\) 0 0
\(759\) −3.28319 −0.119172
\(760\) 0 0
\(761\) −32.4935 −1.17789 −0.588944 0.808174i \(-0.700456\pi\)
−0.588944 + 0.808174i \(0.700456\pi\)
\(762\) 0 0
\(763\) −7.87246 −0.285002
\(764\) 0 0
\(765\) 8.95785 0.323872
\(766\) 0 0
\(767\) −2.40906 −0.0869861
\(768\) 0 0
\(769\) −33.6599 −1.21381 −0.606903 0.794776i \(-0.707589\pi\)
−0.606903 + 0.794776i \(0.707589\pi\)
\(770\) 0 0
\(771\) −3.08336 −0.111045
\(772\) 0 0
\(773\) 46.9565 1.68891 0.844454 0.535628i \(-0.179925\pi\)
0.844454 + 0.535628i \(0.179925\pi\)
\(774\) 0 0
\(775\) −28.5175 −1.02438
\(776\) 0 0
\(777\) −1.49502 −0.0536335
\(778\) 0 0
\(779\) 25.5669 0.916030
\(780\) 0 0
\(781\) −2.33188 −0.0834411
\(782\) 0 0
\(783\) −4.25333 −0.152002
\(784\) 0 0
\(785\) 2.01670 0.0719792
\(786\) 0 0
\(787\) 22.6165 0.806191 0.403096 0.915158i \(-0.367934\pi\)
0.403096 + 0.915158i \(0.367934\pi\)
\(788\) 0 0
\(789\) −1.93866 −0.0690182
\(790\) 0 0
\(791\) −11.6981 −0.415938
\(792\) 0 0
\(793\) 1.66025 0.0589571
\(794\) 0 0
\(795\) −4.32434 −0.153368
\(796\) 0 0
\(797\) −33.1861 −1.17551 −0.587757 0.809038i \(-0.699989\pi\)
−0.587757 + 0.809038i \(0.699989\pi\)
\(798\) 0 0
\(799\) 3.59029 0.127015
\(800\) 0 0
\(801\) −39.4216 −1.39289
\(802\) 0 0
\(803\) 36.3149 1.28152
\(804\) 0 0
\(805\) −17.1075 −0.602959
\(806\) 0 0
\(807\) 1.22698 0.0431919
\(808\) 0 0
\(809\) −26.8722 −0.944777 −0.472389 0.881390i \(-0.656608\pi\)
−0.472389 + 0.881390i \(0.656608\pi\)
\(810\) 0 0
\(811\) 26.9582 0.946629 0.473315 0.880893i \(-0.343057\pi\)
0.473315 + 0.880893i \(0.343057\pi\)
\(812\) 0 0
\(813\) −0.260017 −0.00911918
\(814\) 0 0
\(815\) 41.1388 1.44103
\(816\) 0 0
\(817\) 24.3624 0.852334
\(818\) 0 0
\(819\) −8.20073 −0.286557
\(820\) 0 0
\(821\) 5.41068 0.188834 0.0944169 0.995533i \(-0.469901\pi\)
0.0944169 + 0.995533i \(0.469901\pi\)
\(822\) 0 0
\(823\) −5.67516 −0.197824 −0.0989119 0.995096i \(-0.531536\pi\)
−0.0989119 + 0.995096i \(0.531536\pi\)
\(824\) 0 0
\(825\) −2.63601 −0.0917740
\(826\) 0 0
\(827\) −12.9948 −0.451874 −0.225937 0.974142i \(-0.572544\pi\)
−0.225937 + 0.974142i \(0.572544\pi\)
\(828\) 0 0
\(829\) −38.9845 −1.35399 −0.676995 0.735988i \(-0.736718\pi\)
−0.676995 + 0.735988i \(0.736718\pi\)
\(830\) 0 0
\(831\) −0.569756 −0.0197646
\(832\) 0 0
\(833\) −5.69870 −0.197448
\(834\) 0 0
\(835\) 48.4295 1.67597
\(836\) 0 0
\(837\) 5.36171 0.185328
\(838\) 0 0
\(839\) 46.8082 1.61600 0.808000 0.589183i \(-0.200550\pi\)
0.808000 + 0.589183i \(0.200550\pi\)
\(840\) 0 0
\(841\) 2.80944 0.0968771
\(842\) 0 0
\(843\) 3.29241 0.113397
\(844\) 0 0
\(845\) 21.6026 0.743151
\(846\) 0 0
\(847\) 18.4732 0.634747
\(848\) 0 0
\(849\) 2.08266 0.0714768
\(850\) 0 0
\(851\) −51.9536 −1.78095
\(852\) 0 0
\(853\) −19.1224 −0.654739 −0.327369 0.944896i \(-0.606162\pi\)
−0.327369 + 0.944896i \(0.606162\pi\)
\(854\) 0 0
\(855\) 53.8199 1.84060
\(856\) 0 0
\(857\) −23.7980 −0.812923 −0.406461 0.913668i \(-0.633237\pi\)
−0.406461 + 0.913668i \(0.633237\pi\)
\(858\) 0 0
\(859\) 53.8438 1.83713 0.918564 0.395273i \(-0.129350\pi\)
0.918564 + 0.395273i \(0.129350\pi\)
\(860\) 0 0
\(861\) 0.611758 0.0208487
\(862\) 0 0
\(863\) 19.5791 0.666480 0.333240 0.942842i \(-0.391858\pi\)
0.333240 + 0.942842i \(0.391858\pi\)
\(864\) 0 0
\(865\) −23.1700 −0.787805
\(866\) 0 0
\(867\) 0.126023 0.00427998
\(868\) 0 0
\(869\) 46.8069 1.58782
\(870\) 0 0
\(871\) −0.805156 −0.0272817
\(872\) 0 0
\(873\) −41.8028 −1.41481
\(874\) 0 0
\(875\) 3.38646 0.114483
\(876\) 0 0
\(877\) 2.61615 0.0883411 0.0441706 0.999024i \(-0.485935\pi\)
0.0441706 + 0.999024i \(0.485935\pi\)
\(878\) 0 0
\(879\) 1.02153 0.0344553
\(880\) 0 0
\(881\) −56.2447 −1.89493 −0.947467 0.319854i \(-0.896366\pi\)
−0.947467 + 0.319854i \(0.896366\pi\)
\(882\) 0 0
\(883\) −50.6355 −1.70402 −0.852011 0.523524i \(-0.824617\pi\)
−0.852011 + 0.523524i \(0.824617\pi\)
\(884\) 0 0
\(885\) 0.378302 0.0127165
\(886\) 0 0
\(887\) −8.80356 −0.295595 −0.147797 0.989018i \(-0.547218\pi\)
−0.147797 + 0.989018i \(0.547218\pi\)
\(888\) 0 0
\(889\) 11.8947 0.398934
\(890\) 0 0
\(891\) −46.1890 −1.54739
\(892\) 0 0
\(893\) 21.5709 0.721843
\(894\) 0 0
\(895\) 25.4148 0.849522
\(896\) 0 0
\(897\) 1.51673 0.0506421
\(898\) 0 0
\(899\) −40.0987 −1.33737
\(900\) 0 0
\(901\) 11.4309 0.380819
\(902\) 0 0
\(903\) 0.582937 0.0193989
\(904\) 0 0
\(905\) −7.80177 −0.259340
\(906\) 0 0
\(907\) 2.08465 0.0692197 0.0346099 0.999401i \(-0.488981\pi\)
0.0346099 + 0.999401i \(0.488981\pi\)
\(908\) 0 0
\(909\) −0.820778 −0.0272235
\(910\) 0 0
\(911\) −38.1870 −1.26519 −0.632596 0.774482i \(-0.718011\pi\)
−0.632596 + 0.774482i \(0.718011\pi\)
\(912\) 0 0
\(913\) −18.6906 −0.618570
\(914\) 0 0
\(915\) −0.260714 −0.00861893
\(916\) 0 0
\(917\) 8.47004 0.279705
\(918\) 0 0
\(919\) 20.2009 0.666367 0.333183 0.942862i \(-0.391877\pi\)
0.333183 + 0.942862i \(0.391877\pi\)
\(920\) 0 0
\(921\) −3.00780 −0.0991104
\(922\) 0 0
\(923\) 1.07725 0.0354581
\(924\) 0 0
\(925\) −41.7125 −1.37150
\(926\) 0 0
\(927\) 37.0077 1.21549
\(928\) 0 0
\(929\) −5.30223 −0.173961 −0.0869803 0.996210i \(-0.527722\pi\)
−0.0869803 + 0.996210i \(0.527722\pi\)
\(930\) 0 0
\(931\) −34.2385 −1.12212
\(932\) 0 0
\(933\) 2.86494 0.0937940
\(934\) 0 0
\(935\) 15.6540 0.511939
\(936\) 0 0
\(937\) −20.4181 −0.667030 −0.333515 0.942745i \(-0.608235\pi\)
−0.333515 + 0.942745i \(0.608235\pi\)
\(938\) 0 0
\(939\) −1.93432 −0.0631240
\(940\) 0 0
\(941\) 8.26900 0.269562 0.134781 0.990875i \(-0.456967\pi\)
0.134781 + 0.990875i \(0.456967\pi\)
\(942\) 0 0
\(943\) 21.2593 0.692297
\(944\) 0 0
\(945\) 2.58243 0.0840064
\(946\) 0 0
\(947\) −51.1722 −1.66287 −0.831436 0.555620i \(-0.812481\pi\)
−0.831436 + 0.555620i \(0.812481\pi\)
\(948\) 0 0
\(949\) −16.7763 −0.544581
\(950\) 0 0
\(951\) 1.90806 0.0618732
\(952\) 0 0
\(953\) 10.1308 0.328170 0.164085 0.986446i \(-0.447533\pi\)
0.164085 + 0.986446i \(0.447533\pi\)
\(954\) 0 0
\(955\) 70.4374 2.27930
\(956\) 0 0
\(957\) −3.70651 −0.119815
\(958\) 0 0
\(959\) 1.57513 0.0508636
\(960\) 0 0
\(961\) 19.5481 0.630582
\(962\) 0 0
\(963\) −16.0457 −0.517067
\(964\) 0 0
\(965\) 63.8452 2.05525
\(966\) 0 0
\(967\) 49.6026 1.59511 0.797556 0.603245i \(-0.206126\pi\)
0.797556 + 0.603245i \(0.206126\pi\)
\(968\) 0 0
\(969\) 0.757164 0.0243236
\(970\) 0 0
\(971\) −33.3721 −1.07096 −0.535480 0.844548i \(-0.679869\pi\)
−0.535480 + 0.844548i \(0.679869\pi\)
\(972\) 0 0
\(973\) −13.3790 −0.428912
\(974\) 0 0
\(975\) 1.21775 0.0389992
\(976\) 0 0
\(977\) −5.87049 −0.187814 −0.0939069 0.995581i \(-0.529936\pi\)
−0.0939069 + 0.995581i \(0.529936\pi\)
\(978\) 0 0
\(979\) −68.8897 −2.20173
\(980\) 0 0
\(981\) 20.5938 0.657511
\(982\) 0 0
\(983\) 53.4357 1.70433 0.852167 0.523269i \(-0.175288\pi\)
0.852167 + 0.523269i \(0.175288\pi\)
\(984\) 0 0
\(985\) 5.98368 0.190656
\(986\) 0 0
\(987\) 0.516142 0.0164290
\(988\) 0 0
\(989\) 20.2577 0.644158
\(990\) 0 0
\(991\) 2.14776 0.0682260 0.0341130 0.999418i \(-0.489139\pi\)
0.0341130 + 0.999418i \(0.489139\pi\)
\(992\) 0 0
\(993\) 3.32192 0.105418
\(994\) 0 0
\(995\) 68.2927 2.16503
\(996\) 0 0
\(997\) 30.5213 0.966618 0.483309 0.875450i \(-0.339435\pi\)
0.483309 + 0.875450i \(0.339435\pi\)
\(998\) 0 0
\(999\) 7.84257 0.248128
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.w.1.11 20
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
8024.2.a.w.1.11 20 1.1 even 1 trivial