Properties

Label 4023.2.a.f.1.10
Level $4023$
Weight $2$
Character 4023.1
Self dual yes
Analytic conductor $32.124$
Analytic rank $0$
Dimension $25$
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] = [4023,2,Mod(1,4023)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(4023, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([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("4023.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 4023 = 3^{3} \cdot 149 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 4023.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: \(32.1238167332\)
Analytic rank: \(0\)
Dimension: \(25\)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.10
Character \(\chi\) \(=\) 4023.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-0.530451 q^{2} -1.71862 q^{4} +3.35792 q^{5} +3.91494 q^{7} +1.97255 q^{8} +O(q^{10})\) \(q-0.530451 q^{2} -1.71862 q^{4} +3.35792 q^{5} +3.91494 q^{7} +1.97255 q^{8} -1.78121 q^{10} -0.0181339 q^{11} -5.92757 q^{13} -2.07668 q^{14} +2.39091 q^{16} +2.80172 q^{17} +8.42725 q^{19} -5.77100 q^{20} +0.00961916 q^{22} -7.23843 q^{23} +6.27566 q^{25} +3.14428 q^{26} -6.72830 q^{28} +0.873804 q^{29} +0.822902 q^{31} -5.21335 q^{32} -1.48618 q^{34} +13.1461 q^{35} -0.327675 q^{37} -4.47024 q^{38} +6.62366 q^{40} +8.66885 q^{41} -1.00666 q^{43} +0.0311654 q^{44} +3.83963 q^{46} +7.71226 q^{47} +8.32675 q^{49} -3.32892 q^{50} +10.1872 q^{52} +4.76237 q^{53} -0.0608924 q^{55} +7.72239 q^{56} -0.463510 q^{58} -11.5774 q^{59} +4.56273 q^{61} -0.436509 q^{62} -2.01639 q^{64} -19.9043 q^{65} +7.44129 q^{67} -4.81511 q^{68} -6.97334 q^{70} +11.7175 q^{71} -5.83597 q^{73} +0.173816 q^{74} -14.4833 q^{76} -0.0709933 q^{77} -0.209454 q^{79} +8.02848 q^{80} -4.59840 q^{82} +0.907761 q^{83} +9.40798 q^{85} +0.533985 q^{86} -0.0357700 q^{88} +4.48048 q^{89} -23.2061 q^{91} +12.4401 q^{92} -4.09097 q^{94} +28.2981 q^{95} -6.76631 q^{97} -4.41693 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 25 q + 7 q^{2} + 27 q^{4} + 12 q^{5} - 2 q^{7} + 21 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 25 q + 7 q^{2} + 27 q^{4} + 12 q^{5} - 2 q^{7} + 21 q^{8} - 4 q^{10} + 12 q^{11} + 10 q^{14} + 35 q^{16} + 26 q^{17} + 30 q^{20} + 8 q^{22} + 26 q^{23} + 27 q^{25} + 16 q^{26} + 4 q^{28} + 20 q^{29} - 6 q^{31} + 49 q^{32} - 14 q^{34} + 16 q^{35} - 2 q^{37} + 27 q^{38} + 2 q^{40} + 35 q^{41} + 4 q^{43} + 22 q^{44} + 6 q^{46} + 38 q^{47} + 19 q^{49} + 22 q^{50} + 4 q^{52} + 36 q^{53} + 10 q^{55} + 79 q^{56} - 22 q^{58} + 15 q^{59} + 10 q^{61} - 14 q^{62} + 41 q^{64} + 80 q^{65} - 6 q^{67} + 33 q^{68} + 8 q^{70} + 26 q^{71} - 6 q^{73} + 75 q^{74} - 10 q^{76} + 47 q^{77} - 6 q^{79} + 66 q^{80} + 12 q^{82} + 40 q^{83} - 12 q^{85} + 4 q^{86} + 12 q^{88} + 30 q^{89} + 158 q^{92} + 18 q^{94} + 22 q^{95} - 20 q^{97} + 35 q^{98}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.530451 −0.375085 −0.187543 0.982256i \(-0.560052\pi\)
−0.187543 + 0.982256i \(0.560052\pi\)
\(3\) 0 0
\(4\) −1.71862 −0.859311
\(5\) 3.35792 1.50171 0.750855 0.660467i \(-0.229642\pi\)
0.750855 + 0.660467i \(0.229642\pi\)
\(6\) 0 0
\(7\) 3.91494 1.47971 0.739854 0.672767i \(-0.234895\pi\)
0.739854 + 0.672767i \(0.234895\pi\)
\(8\) 1.97255 0.697400
\(9\) 0 0
\(10\) −1.78121 −0.563269
\(11\) −0.0181339 −0.00546759 −0.00273380 0.999996i \(-0.500870\pi\)
−0.00273380 + 0.999996i \(0.500870\pi\)
\(12\) 0 0
\(13\) −5.92757 −1.64401 −0.822006 0.569479i \(-0.807145\pi\)
−0.822006 + 0.569479i \(0.807145\pi\)
\(14\) −2.07668 −0.555017
\(15\) 0 0
\(16\) 2.39091 0.597727
\(17\) 2.80172 0.679518 0.339759 0.940513i \(-0.389655\pi\)
0.339759 + 0.940513i \(0.389655\pi\)
\(18\) 0 0
\(19\) 8.42725 1.93334 0.966672 0.256020i \(-0.0824112\pi\)
0.966672 + 0.256020i \(0.0824112\pi\)
\(20\) −5.77100 −1.29044
\(21\) 0 0
\(22\) 0.00961916 0.00205081
\(23\) −7.23843 −1.50932 −0.754658 0.656118i \(-0.772197\pi\)
−0.754658 + 0.656118i \(0.772197\pi\)
\(24\) 0 0
\(25\) 6.27566 1.25513
\(26\) 3.14428 0.616644
\(27\) 0 0
\(28\) −6.72830 −1.27153
\(29\) 0.873804 0.162261 0.0811307 0.996703i \(-0.474147\pi\)
0.0811307 + 0.996703i \(0.474147\pi\)
\(30\) 0 0
\(31\) 0.822902 0.147798 0.0738988 0.997266i \(-0.476456\pi\)
0.0738988 + 0.997266i \(0.476456\pi\)
\(32\) −5.21335 −0.921598
\(33\) 0 0
\(34\) −1.48618 −0.254877
\(35\) 13.1461 2.22209
\(36\) 0 0
\(37\) −0.327675 −0.0538695 −0.0269347 0.999637i \(-0.508575\pi\)
−0.0269347 + 0.999637i \(0.508575\pi\)
\(38\) −4.47024 −0.725168
\(39\) 0 0
\(40\) 6.62366 1.04729
\(41\) 8.66885 1.35385 0.676924 0.736053i \(-0.263313\pi\)
0.676924 + 0.736053i \(0.263313\pi\)
\(42\) 0 0
\(43\) −1.00666 −0.153515 −0.0767574 0.997050i \(-0.524457\pi\)
−0.0767574 + 0.997050i \(0.524457\pi\)
\(44\) 0.0311654 0.00469836
\(45\) 0 0
\(46\) 3.83963 0.566122
\(47\) 7.71226 1.12495 0.562474 0.826815i \(-0.309850\pi\)
0.562474 + 0.826815i \(0.309850\pi\)
\(48\) 0 0
\(49\) 8.32675 1.18954
\(50\) −3.32892 −0.470781
\(51\) 0 0
\(52\) 10.1872 1.41272
\(53\) 4.76237 0.654161 0.327081 0.944996i \(-0.393935\pi\)
0.327081 + 0.944996i \(0.393935\pi\)
\(54\) 0 0
\(55\) −0.0608924 −0.00821073
\(56\) 7.72239 1.03195
\(57\) 0 0
\(58\) −0.463510 −0.0608618
\(59\) −11.5774 −1.50725 −0.753627 0.657302i \(-0.771697\pi\)
−0.753627 + 0.657302i \(0.771697\pi\)
\(60\) 0 0
\(61\) 4.56273 0.584198 0.292099 0.956388i \(-0.405646\pi\)
0.292099 + 0.956388i \(0.405646\pi\)
\(62\) −0.436509 −0.0554367
\(63\) 0 0
\(64\) −2.01639 −0.252049
\(65\) −19.9043 −2.46883
\(66\) 0 0
\(67\) 7.44129 0.909098 0.454549 0.890722i \(-0.349801\pi\)
0.454549 + 0.890722i \(0.349801\pi\)
\(68\) −4.81511 −0.583917
\(69\) 0 0
\(70\) −6.97334 −0.833474
\(71\) 11.7175 1.39062 0.695309 0.718711i \(-0.255268\pi\)
0.695309 + 0.718711i \(0.255268\pi\)
\(72\) 0 0
\(73\) −5.83597 −0.683049 −0.341524 0.939873i \(-0.610943\pi\)
−0.341524 + 0.939873i \(0.610943\pi\)
\(74\) 0.173816 0.0202056
\(75\) 0 0
\(76\) −14.4833 −1.66134
\(77\) −0.0709933 −0.00809044
\(78\) 0 0
\(79\) −0.209454 −0.0235654 −0.0117827 0.999931i \(-0.503751\pi\)
−0.0117827 + 0.999931i \(0.503751\pi\)
\(80\) 8.02848 0.897612
\(81\) 0 0
\(82\) −4.59840 −0.507808
\(83\) 0.907761 0.0996397 0.0498199 0.998758i \(-0.484135\pi\)
0.0498199 + 0.998758i \(0.484135\pi\)
\(84\) 0 0
\(85\) 9.40798 1.02044
\(86\) 0.533985 0.0575811
\(87\) 0 0
\(88\) −0.0357700 −0.00381310
\(89\) 4.48048 0.474930 0.237465 0.971396i \(-0.423684\pi\)
0.237465 + 0.971396i \(0.423684\pi\)
\(90\) 0 0
\(91\) −23.2061 −2.43266
\(92\) 12.4401 1.29697
\(93\) 0 0
\(94\) −4.09097 −0.421951
\(95\) 28.2981 2.90332
\(96\) 0 0
\(97\) −6.76631 −0.687014 −0.343507 0.939150i \(-0.611615\pi\)
−0.343507 + 0.939150i \(0.611615\pi\)
\(98\) −4.41693 −0.446177
\(99\) 0 0
\(100\) −10.7855 −1.07855
\(101\) −10.2494 −1.01986 −0.509929 0.860216i \(-0.670328\pi\)
−0.509929 + 0.860216i \(0.670328\pi\)
\(102\) 0 0
\(103\) −0.864367 −0.0851686 −0.0425843 0.999093i \(-0.513559\pi\)
−0.0425843 + 0.999093i \(0.513559\pi\)
\(104\) −11.6924 −1.14653
\(105\) 0 0
\(106\) −2.52620 −0.245366
\(107\) 11.8683 1.14735 0.573674 0.819084i \(-0.305518\pi\)
0.573674 + 0.819084i \(0.305518\pi\)
\(108\) 0 0
\(109\) −10.6983 −1.02472 −0.512358 0.858772i \(-0.671228\pi\)
−0.512358 + 0.858772i \(0.671228\pi\)
\(110\) 0.0323004 0.00307972
\(111\) 0 0
\(112\) 9.36026 0.884461
\(113\) 5.67368 0.533735 0.266868 0.963733i \(-0.414011\pi\)
0.266868 + 0.963733i \(0.414011\pi\)
\(114\) 0 0
\(115\) −24.3061 −2.26655
\(116\) −1.50174 −0.139433
\(117\) 0 0
\(118\) 6.14126 0.565349
\(119\) 10.9686 1.00549
\(120\) 0 0
\(121\) −10.9997 −0.999970
\(122\) −2.42030 −0.219124
\(123\) 0 0
\(124\) −1.41426 −0.127004
\(125\) 4.28355 0.383133
\(126\) 0 0
\(127\) 5.16460 0.458284 0.229142 0.973393i \(-0.426408\pi\)
0.229142 + 0.973393i \(0.426408\pi\)
\(128\) 11.4963 1.01614
\(129\) 0 0
\(130\) 10.5583 0.926020
\(131\) 0.843924 0.0737340 0.0368670 0.999320i \(-0.488262\pi\)
0.0368670 + 0.999320i \(0.488262\pi\)
\(132\) 0 0
\(133\) 32.9922 2.86078
\(134\) −3.94723 −0.340989
\(135\) 0 0
\(136\) 5.52653 0.473896
\(137\) 12.5066 1.06851 0.534255 0.845323i \(-0.320592\pi\)
0.534255 + 0.845323i \(0.320592\pi\)
\(138\) 0 0
\(139\) −6.72761 −0.570629 −0.285314 0.958434i \(-0.592098\pi\)
−0.285314 + 0.958434i \(0.592098\pi\)
\(140\) −22.5931 −1.90947
\(141\) 0 0
\(142\) −6.21558 −0.521600
\(143\) 0.107490 0.00898878
\(144\) 0 0
\(145\) 2.93417 0.243669
\(146\) 3.09569 0.256201
\(147\) 0 0
\(148\) 0.563150 0.0462906
\(149\) 1.00000 0.0819232
\(150\) 0 0
\(151\) −19.0650 −1.55149 −0.775745 0.631046i \(-0.782626\pi\)
−0.775745 + 0.631046i \(0.782626\pi\)
\(152\) 16.6231 1.34831
\(153\) 0 0
\(154\) 0.0376584 0.00303460
\(155\) 2.76324 0.221949
\(156\) 0 0
\(157\) 13.3633 1.06651 0.533255 0.845954i \(-0.320969\pi\)
0.533255 + 0.845954i \(0.320969\pi\)
\(158\) 0.111105 0.00883903
\(159\) 0 0
\(160\) −17.5060 −1.38397
\(161\) −28.3380 −2.23335
\(162\) 0 0
\(163\) −17.6010 −1.37862 −0.689308 0.724469i \(-0.742085\pi\)
−0.689308 + 0.724469i \(0.742085\pi\)
\(164\) −14.8985 −1.16338
\(165\) 0 0
\(166\) −0.481522 −0.0373734
\(167\) 21.0164 1.62630 0.813150 0.582054i \(-0.197751\pi\)
0.813150 + 0.582054i \(0.197751\pi\)
\(168\) 0 0
\(169\) 22.1360 1.70277
\(170\) −4.99047 −0.382751
\(171\) 0 0
\(172\) 1.73007 0.131917
\(173\) −19.6201 −1.49169 −0.745843 0.666122i \(-0.767953\pi\)
−0.745843 + 0.666122i \(0.767953\pi\)
\(174\) 0 0
\(175\) 24.5688 1.85723
\(176\) −0.0433566 −0.00326813
\(177\) 0 0
\(178\) −2.37667 −0.178139
\(179\) −13.3659 −0.999017 −0.499508 0.866309i \(-0.666486\pi\)
−0.499508 + 0.866309i \(0.666486\pi\)
\(180\) 0 0
\(181\) −17.8820 −1.32916 −0.664578 0.747219i \(-0.731389\pi\)
−0.664578 + 0.747219i \(0.731389\pi\)
\(182\) 12.3097 0.912453
\(183\) 0 0
\(184\) −14.2781 −1.05260
\(185\) −1.10031 −0.0808963
\(186\) 0 0
\(187\) −0.0508063 −0.00371533
\(188\) −13.2545 −0.966681
\(189\) 0 0
\(190\) −15.0107 −1.08899
\(191\) −12.6985 −0.918828 −0.459414 0.888222i \(-0.651941\pi\)
−0.459414 + 0.888222i \(0.651941\pi\)
\(192\) 0 0
\(193\) −22.4742 −1.61773 −0.808863 0.587998i \(-0.799916\pi\)
−0.808863 + 0.587998i \(0.799916\pi\)
\(194\) 3.58919 0.257689
\(195\) 0 0
\(196\) −14.3105 −1.02218
\(197\) 19.1471 1.36418 0.682089 0.731270i \(-0.261072\pi\)
0.682089 + 0.731270i \(0.261072\pi\)
\(198\) 0 0
\(199\) −5.62488 −0.398737 −0.199369 0.979925i \(-0.563889\pi\)
−0.199369 + 0.979925i \(0.563889\pi\)
\(200\) 12.3790 0.875328
\(201\) 0 0
\(202\) 5.43682 0.382534
\(203\) 3.42089 0.240099
\(204\) 0 0
\(205\) 29.1094 2.03309
\(206\) 0.458504 0.0319455
\(207\) 0 0
\(208\) −14.1723 −0.982669
\(209\) −0.152819 −0.0105707
\(210\) 0 0
\(211\) 6.28633 0.432769 0.216384 0.976308i \(-0.430574\pi\)
0.216384 + 0.976308i \(0.430574\pi\)
\(212\) −8.18471 −0.562128
\(213\) 0 0
\(214\) −6.29552 −0.430353
\(215\) −3.38030 −0.230535
\(216\) 0 0
\(217\) 3.22161 0.218697
\(218\) 5.67494 0.384356
\(219\) 0 0
\(220\) 0.104651 0.00705557
\(221\) −16.6074 −1.11714
\(222\) 0 0
\(223\) 14.5550 0.974676 0.487338 0.873213i \(-0.337968\pi\)
0.487338 + 0.873213i \(0.337968\pi\)
\(224\) −20.4099 −1.36370
\(225\) 0 0
\(226\) −3.00961 −0.200196
\(227\) 22.2592 1.47740 0.738698 0.674036i \(-0.235441\pi\)
0.738698 + 0.674036i \(0.235441\pi\)
\(228\) 0 0
\(229\) 19.4305 1.28400 0.642001 0.766704i \(-0.278104\pi\)
0.642001 + 0.766704i \(0.278104\pi\)
\(230\) 12.8932 0.850151
\(231\) 0 0
\(232\) 1.72362 0.113161
\(233\) 25.4141 1.66493 0.832465 0.554077i \(-0.186929\pi\)
0.832465 + 0.554077i \(0.186929\pi\)
\(234\) 0 0
\(235\) 25.8972 1.68935
\(236\) 19.8972 1.29520
\(237\) 0 0
\(238\) −5.81829 −0.377144
\(239\) 21.7018 1.40377 0.701885 0.712290i \(-0.252342\pi\)
0.701885 + 0.712290i \(0.252342\pi\)
\(240\) 0 0
\(241\) 21.7521 1.40118 0.700588 0.713566i \(-0.252921\pi\)
0.700588 + 0.713566i \(0.252921\pi\)
\(242\) 5.83478 0.375074
\(243\) 0 0
\(244\) −7.84162 −0.502008
\(245\) 27.9606 1.78634
\(246\) 0 0
\(247\) −49.9531 −3.17844
\(248\) 1.62321 0.103074
\(249\) 0 0
\(250\) −2.27221 −0.143707
\(251\) 24.7699 1.56347 0.781733 0.623614i \(-0.214336\pi\)
0.781733 + 0.623614i \(0.214336\pi\)
\(252\) 0 0
\(253\) 0.131261 0.00825232
\(254\) −2.73956 −0.171896
\(255\) 0 0
\(256\) −2.06543 −0.129090
\(257\) −7.92098 −0.494097 −0.247049 0.969003i \(-0.579461\pi\)
−0.247049 + 0.969003i \(0.579461\pi\)
\(258\) 0 0
\(259\) −1.28283 −0.0797111
\(260\) 34.2080 2.12149
\(261\) 0 0
\(262\) −0.447660 −0.0276565
\(263\) −8.65342 −0.533593 −0.266796 0.963753i \(-0.585965\pi\)
−0.266796 + 0.963753i \(0.585965\pi\)
\(264\) 0 0
\(265\) 15.9917 0.982360
\(266\) −17.5007 −1.07304
\(267\) 0 0
\(268\) −12.7888 −0.781198
\(269\) −23.4545 −1.43005 −0.715023 0.699101i \(-0.753584\pi\)
−0.715023 + 0.699101i \(0.753584\pi\)
\(270\) 0 0
\(271\) 30.4032 1.84686 0.923431 0.383766i \(-0.125373\pi\)
0.923431 + 0.383766i \(0.125373\pi\)
\(272\) 6.69866 0.406166
\(273\) 0 0
\(274\) −6.63413 −0.400782
\(275\) −0.113802 −0.00686254
\(276\) 0 0
\(277\) −8.43685 −0.506921 −0.253460 0.967346i \(-0.581569\pi\)
−0.253460 + 0.967346i \(0.581569\pi\)
\(278\) 3.56867 0.214034
\(279\) 0 0
\(280\) 25.9312 1.54969
\(281\) 19.5511 1.16632 0.583162 0.812356i \(-0.301815\pi\)
0.583162 + 0.812356i \(0.301815\pi\)
\(282\) 0 0
\(283\) −21.5020 −1.27816 −0.639081 0.769139i \(-0.720685\pi\)
−0.639081 + 0.769139i \(0.720685\pi\)
\(284\) −20.1380 −1.19497
\(285\) 0 0
\(286\) −0.0570182 −0.00337156
\(287\) 33.9380 2.00330
\(288\) 0 0
\(289\) −9.15034 −0.538255
\(290\) −1.55643 −0.0913968
\(291\) 0 0
\(292\) 10.0298 0.586951
\(293\) −0.525326 −0.0306899 −0.0153449 0.999882i \(-0.504885\pi\)
−0.0153449 + 0.999882i \(0.504885\pi\)
\(294\) 0 0
\(295\) −38.8762 −2.26346
\(296\) −0.646354 −0.0375686
\(297\) 0 0
\(298\) −0.530451 −0.0307282
\(299\) 42.9063 2.48133
\(300\) 0 0
\(301\) −3.94103 −0.227157
\(302\) 10.1131 0.581941
\(303\) 0 0
\(304\) 20.1488 1.15561
\(305\) 15.3213 0.877296
\(306\) 0 0
\(307\) 21.6144 1.23360 0.616799 0.787121i \(-0.288429\pi\)
0.616799 + 0.787121i \(0.288429\pi\)
\(308\) 0.122011 0.00695220
\(309\) 0 0
\(310\) −1.46576 −0.0832498
\(311\) 2.46662 0.139869 0.0699345 0.997552i \(-0.477721\pi\)
0.0699345 + 0.997552i \(0.477721\pi\)
\(312\) 0 0
\(313\) 28.4135 1.60603 0.803014 0.595960i \(-0.203228\pi\)
0.803014 + 0.595960i \(0.203228\pi\)
\(314\) −7.08859 −0.400032
\(315\) 0 0
\(316\) 0.359972 0.0202500
\(317\) 22.7136 1.27572 0.637860 0.770152i \(-0.279820\pi\)
0.637860 + 0.770152i \(0.279820\pi\)
\(318\) 0 0
\(319\) −0.0158455 −0.000887178 0
\(320\) −6.77089 −0.378504
\(321\) 0 0
\(322\) 15.0319 0.837695
\(323\) 23.6108 1.31374
\(324\) 0 0
\(325\) −37.1994 −2.06345
\(326\) 9.33645 0.517098
\(327\) 0 0
\(328\) 17.0997 0.944173
\(329\) 30.1930 1.66460
\(330\) 0 0
\(331\) 7.79546 0.428477 0.214239 0.976781i \(-0.431273\pi\)
0.214239 + 0.976781i \(0.431273\pi\)
\(332\) −1.56010 −0.0856215
\(333\) 0 0
\(334\) −11.1482 −0.610001
\(335\) 24.9873 1.36520
\(336\) 0 0
\(337\) −26.0560 −1.41936 −0.709679 0.704525i \(-0.751160\pi\)
−0.709679 + 0.704525i \(0.751160\pi\)
\(338\) −11.7421 −0.638685
\(339\) 0 0
\(340\) −16.1688 −0.876874
\(341\) −0.0149225 −0.000808097 0
\(342\) 0 0
\(343\) 5.19415 0.280458
\(344\) −1.98569 −0.107061
\(345\) 0 0
\(346\) 10.4075 0.559509
\(347\) −14.5930 −0.783392 −0.391696 0.920095i \(-0.628111\pi\)
−0.391696 + 0.920095i \(0.628111\pi\)
\(348\) 0 0
\(349\) −8.52698 −0.456439 −0.228219 0.973610i \(-0.573290\pi\)
−0.228219 + 0.973610i \(0.573290\pi\)
\(350\) −13.0325 −0.696619
\(351\) 0 0
\(352\) 0.0945386 0.00503892
\(353\) 29.7193 1.58180 0.790900 0.611946i \(-0.209613\pi\)
0.790900 + 0.611946i \(0.209613\pi\)
\(354\) 0 0
\(355\) 39.3466 2.08830
\(356\) −7.70025 −0.408112
\(357\) 0 0
\(358\) 7.08997 0.374716
\(359\) −7.58639 −0.400394 −0.200197 0.979756i \(-0.564158\pi\)
−0.200197 + 0.979756i \(0.564158\pi\)
\(360\) 0 0
\(361\) 52.0185 2.73782
\(362\) 9.48550 0.498547
\(363\) 0 0
\(364\) 39.8825 2.09041
\(365\) −19.5967 −1.02574
\(366\) 0 0
\(367\) 1.18734 0.0619786 0.0309893 0.999520i \(-0.490134\pi\)
0.0309893 + 0.999520i \(0.490134\pi\)
\(368\) −17.3064 −0.902159
\(369\) 0 0
\(370\) 0.583659 0.0303430
\(371\) 18.6444 0.967968
\(372\) 0 0
\(373\) 15.9023 0.823389 0.411695 0.911322i \(-0.364937\pi\)
0.411695 + 0.911322i \(0.364937\pi\)
\(374\) 0.0269502 0.00139356
\(375\) 0 0
\(376\) 15.2128 0.784539
\(377\) −5.17953 −0.266759
\(378\) 0 0
\(379\) −10.0065 −0.514001 −0.257000 0.966411i \(-0.582734\pi\)
−0.257000 + 0.966411i \(0.582734\pi\)
\(380\) −48.6337 −2.49485
\(381\) 0 0
\(382\) 6.73591 0.344639
\(383\) −34.7613 −1.77622 −0.888111 0.459630i \(-0.847982\pi\)
−0.888111 + 0.459630i \(0.847982\pi\)
\(384\) 0 0
\(385\) −0.238390 −0.0121495
\(386\) 11.9214 0.606785
\(387\) 0 0
\(388\) 11.6287 0.590359
\(389\) −13.7771 −0.698527 −0.349264 0.937024i \(-0.613568\pi\)
−0.349264 + 0.937024i \(0.613568\pi\)
\(390\) 0 0
\(391\) −20.2801 −1.02561
\(392\) 16.4249 0.829582
\(393\) 0 0
\(394\) −10.1566 −0.511683
\(395\) −0.703330 −0.0353884
\(396\) 0 0
\(397\) −11.0908 −0.556629 −0.278315 0.960490i \(-0.589776\pi\)
−0.278315 + 0.960490i \(0.589776\pi\)
\(398\) 2.98372 0.149560
\(399\) 0 0
\(400\) 15.0045 0.750225
\(401\) 4.79005 0.239203 0.119602 0.992822i \(-0.461838\pi\)
0.119602 + 0.992822i \(0.461838\pi\)
\(402\) 0 0
\(403\) −4.87781 −0.242981
\(404\) 17.6149 0.876375
\(405\) 0 0
\(406\) −1.81461 −0.0900577
\(407\) 0.00594205 0.000294536 0
\(408\) 0 0
\(409\) −31.7677 −1.57081 −0.785406 0.618981i \(-0.787546\pi\)
−0.785406 + 0.618981i \(0.787546\pi\)
\(410\) −15.4411 −0.762580
\(411\) 0 0
\(412\) 1.48552 0.0731863
\(413\) −45.3250 −2.23030
\(414\) 0 0
\(415\) 3.04819 0.149630
\(416\) 30.9025 1.51512
\(417\) 0 0
\(418\) 0.0810631 0.00396492
\(419\) 38.3410 1.87308 0.936541 0.350557i \(-0.114008\pi\)
0.936541 + 0.350557i \(0.114008\pi\)
\(420\) 0 0
\(421\) −0.145307 −0.00708184 −0.00354092 0.999994i \(-0.501127\pi\)
−0.00354092 + 0.999994i \(0.501127\pi\)
\(422\) −3.33459 −0.162325
\(423\) 0 0
\(424\) 9.39398 0.456212
\(425\) 17.5827 0.852884
\(426\) 0 0
\(427\) 17.8628 0.864443
\(428\) −20.3970 −0.985928
\(429\) 0 0
\(430\) 1.79308 0.0864701
\(431\) 0.439138 0.0211526 0.0105763 0.999944i \(-0.496633\pi\)
0.0105763 + 0.999944i \(0.496633\pi\)
\(432\) 0 0
\(433\) 3.35091 0.161034 0.0805171 0.996753i \(-0.474343\pi\)
0.0805171 + 0.996753i \(0.474343\pi\)
\(434\) −1.70891 −0.0820301
\(435\) 0 0
\(436\) 18.3864 0.880549
\(437\) −61.0000 −2.91803
\(438\) 0 0
\(439\) 4.64091 0.221498 0.110749 0.993848i \(-0.464675\pi\)
0.110749 + 0.993848i \(0.464675\pi\)
\(440\) −0.120113 −0.00572616
\(441\) 0 0
\(442\) 8.80941 0.419021
\(443\) 18.0312 0.856689 0.428344 0.903616i \(-0.359097\pi\)
0.428344 + 0.903616i \(0.359097\pi\)
\(444\) 0 0
\(445\) 15.0451 0.713207
\(446\) −7.72071 −0.365586
\(447\) 0 0
\(448\) −7.89405 −0.372959
\(449\) 7.47507 0.352770 0.176385 0.984321i \(-0.443560\pi\)
0.176385 + 0.984321i \(0.443560\pi\)
\(450\) 0 0
\(451\) −0.157201 −0.00740228
\(452\) −9.75092 −0.458644
\(453\) 0 0
\(454\) −11.8074 −0.554149
\(455\) −77.9242 −3.65314
\(456\) 0 0
\(457\) 2.32153 0.108597 0.0542983 0.998525i \(-0.482708\pi\)
0.0542983 + 0.998525i \(0.482708\pi\)
\(458\) −10.3069 −0.481610
\(459\) 0 0
\(460\) 41.7730 1.94768
\(461\) −28.3889 −1.32220 −0.661101 0.750297i \(-0.729911\pi\)
−0.661101 + 0.750297i \(0.729911\pi\)
\(462\) 0 0
\(463\) −38.0681 −1.76917 −0.884587 0.466375i \(-0.845560\pi\)
−0.884587 + 0.466375i \(0.845560\pi\)
\(464\) 2.08918 0.0969879
\(465\) 0 0
\(466\) −13.4809 −0.624491
\(467\) −33.2327 −1.53783 −0.768913 0.639354i \(-0.779202\pi\)
−0.768913 + 0.639354i \(0.779202\pi\)
\(468\) 0 0
\(469\) 29.1322 1.34520
\(470\) −13.7372 −0.633648
\(471\) 0 0
\(472\) −22.8370 −1.05116
\(473\) 0.0182548 0.000839356 0
\(474\) 0 0
\(475\) 52.8865 2.42660
\(476\) −18.8508 −0.864027
\(477\) 0 0
\(478\) −11.5117 −0.526533
\(479\) −21.6861 −0.990862 −0.495431 0.868647i \(-0.664990\pi\)
−0.495431 + 0.868647i \(0.664990\pi\)
\(480\) 0 0
\(481\) 1.94232 0.0885620
\(482\) −11.5384 −0.525560
\(483\) 0 0
\(484\) 18.9043 0.859285
\(485\) −22.7207 −1.03170
\(486\) 0 0
\(487\) −38.9044 −1.76292 −0.881462 0.472254i \(-0.843440\pi\)
−0.881462 + 0.472254i \(0.843440\pi\)
\(488\) 9.00020 0.407420
\(489\) 0 0
\(490\) −14.8317 −0.670029
\(491\) −5.59325 −0.252420 −0.126210 0.992004i \(-0.540281\pi\)
−0.126210 + 0.992004i \(0.540281\pi\)
\(492\) 0 0
\(493\) 2.44816 0.110259
\(494\) 26.4976 1.19218
\(495\) 0 0
\(496\) 1.96748 0.0883426
\(497\) 45.8735 2.05771
\(498\) 0 0
\(499\) −21.8271 −0.977115 −0.488558 0.872532i \(-0.662477\pi\)
−0.488558 + 0.872532i \(0.662477\pi\)
\(500\) −7.36181 −0.329230
\(501\) 0 0
\(502\) −13.1392 −0.586433
\(503\) 25.7315 1.14731 0.573655 0.819097i \(-0.305525\pi\)
0.573655 + 0.819097i \(0.305525\pi\)
\(504\) 0 0
\(505\) −34.4169 −1.53153
\(506\) −0.0696276 −0.00309532
\(507\) 0 0
\(508\) −8.87600 −0.393809
\(509\) 13.2495 0.587273 0.293637 0.955917i \(-0.405134\pi\)
0.293637 + 0.955917i \(0.405134\pi\)
\(510\) 0 0
\(511\) −22.8475 −1.01071
\(512\) −21.8970 −0.967719
\(513\) 0 0
\(514\) 4.20169 0.185328
\(515\) −2.90248 −0.127898
\(516\) 0 0
\(517\) −0.139854 −0.00615076
\(518\) 0.680477 0.0298985
\(519\) 0 0
\(520\) −39.2622 −1.72176
\(521\) −41.7311 −1.82827 −0.914136 0.405407i \(-0.867130\pi\)
−0.914136 + 0.405407i \(0.867130\pi\)
\(522\) 0 0
\(523\) 16.0286 0.700881 0.350441 0.936585i \(-0.386032\pi\)
0.350441 + 0.936585i \(0.386032\pi\)
\(524\) −1.45039 −0.0633605
\(525\) 0 0
\(526\) 4.59021 0.200143
\(527\) 2.30554 0.100431
\(528\) 0 0
\(529\) 29.3948 1.27804
\(530\) −8.48279 −0.368469
\(531\) 0 0
\(532\) −56.7011 −2.45830
\(533\) −51.3852 −2.22574
\(534\) 0 0
\(535\) 39.8527 1.72298
\(536\) 14.6783 0.634005
\(537\) 0 0
\(538\) 12.4415 0.536389
\(539\) −0.150997 −0.00650390
\(540\) 0 0
\(541\) 36.8842 1.58578 0.792888 0.609368i \(-0.208577\pi\)
0.792888 + 0.609368i \(0.208577\pi\)
\(542\) −16.1274 −0.692730
\(543\) 0 0
\(544\) −14.6064 −0.626243
\(545\) −35.9242 −1.53882
\(546\) 0 0
\(547\) 22.9918 0.983058 0.491529 0.870861i \(-0.336438\pi\)
0.491529 + 0.870861i \(0.336438\pi\)
\(548\) −21.4941 −0.918182
\(549\) 0 0
\(550\) 0.0603665 0.00257404
\(551\) 7.36376 0.313707
\(552\) 0 0
\(553\) −0.819999 −0.0348699
\(554\) 4.47533 0.190139
\(555\) 0 0
\(556\) 11.5622 0.490347
\(557\) 16.3802 0.694050 0.347025 0.937856i \(-0.387192\pi\)
0.347025 + 0.937856i \(0.387192\pi\)
\(558\) 0 0
\(559\) 5.96706 0.252380
\(560\) 31.4310 1.32820
\(561\) 0 0
\(562\) −10.3709 −0.437471
\(563\) 10.8411 0.456897 0.228448 0.973556i \(-0.426635\pi\)
0.228448 + 0.973556i \(0.426635\pi\)
\(564\) 0 0
\(565\) 19.0518 0.801515
\(566\) 11.4058 0.479420
\(567\) 0 0
\(568\) 23.1134 0.969816
\(569\) −14.2012 −0.595347 −0.297673 0.954668i \(-0.596211\pi\)
−0.297673 + 0.954668i \(0.596211\pi\)
\(570\) 0 0
\(571\) −40.2664 −1.68510 −0.842548 0.538621i \(-0.818946\pi\)
−0.842548 + 0.538621i \(0.818946\pi\)
\(572\) −0.184735 −0.00772416
\(573\) 0 0
\(574\) −18.0024 −0.751408
\(575\) −45.4259 −1.89439
\(576\) 0 0
\(577\) −20.7821 −0.865171 −0.432585 0.901593i \(-0.642399\pi\)
−0.432585 + 0.901593i \(0.642399\pi\)
\(578\) 4.85380 0.201892
\(579\) 0 0
\(580\) −5.04273 −0.209388
\(581\) 3.55383 0.147438
\(582\) 0 0
\(583\) −0.0863605 −0.00357669
\(584\) −11.5117 −0.476358
\(585\) 0 0
\(586\) 0.278659 0.0115113
\(587\) −10.0202 −0.413577 −0.206789 0.978386i \(-0.566301\pi\)
−0.206789 + 0.978386i \(0.566301\pi\)
\(588\) 0 0
\(589\) 6.93480 0.285743
\(590\) 20.6219 0.848989
\(591\) 0 0
\(592\) −0.783441 −0.0321992
\(593\) −3.38206 −0.138885 −0.0694423 0.997586i \(-0.522122\pi\)
−0.0694423 + 0.997586i \(0.522122\pi\)
\(594\) 0 0
\(595\) 36.8317 1.50995
\(596\) −1.71862 −0.0703975
\(597\) 0 0
\(598\) −22.7596 −0.930711
\(599\) −14.6166 −0.597217 −0.298609 0.954376i \(-0.596523\pi\)
−0.298609 + 0.954376i \(0.596523\pi\)
\(600\) 0 0
\(601\) 8.46074 0.345121 0.172560 0.984999i \(-0.444796\pi\)
0.172560 + 0.984999i \(0.444796\pi\)
\(602\) 2.09052 0.0852032
\(603\) 0 0
\(604\) 32.7656 1.33321
\(605\) −36.9361 −1.50166
\(606\) 0 0
\(607\) −13.0077 −0.527967 −0.263983 0.964527i \(-0.585036\pi\)
−0.263983 + 0.964527i \(0.585036\pi\)
\(608\) −43.9342 −1.78177
\(609\) 0 0
\(610\) −8.12720 −0.329061
\(611\) −45.7149 −1.84943
\(612\) 0 0
\(613\) 21.6052 0.872626 0.436313 0.899795i \(-0.356284\pi\)
0.436313 + 0.899795i \(0.356284\pi\)
\(614\) −11.4654 −0.462704
\(615\) 0 0
\(616\) −0.140037 −0.00564227
\(617\) 35.3363 1.42258 0.711292 0.702896i \(-0.248110\pi\)
0.711292 + 0.702896i \(0.248110\pi\)
\(618\) 0 0
\(619\) −16.4083 −0.659505 −0.329752 0.944067i \(-0.606965\pi\)
−0.329752 + 0.944067i \(0.606965\pi\)
\(620\) −4.74897 −0.190723
\(621\) 0 0
\(622\) −1.30842 −0.0524628
\(623\) 17.5408 0.702757
\(624\) 0 0
\(625\) −16.9944 −0.679777
\(626\) −15.0720 −0.602398
\(627\) 0 0
\(628\) −22.9665 −0.916464
\(629\) −0.918056 −0.0366053
\(630\) 0 0
\(631\) 0.317511 0.0126399 0.00631996 0.999980i \(-0.497988\pi\)
0.00631996 + 0.999980i \(0.497988\pi\)
\(632\) −0.413157 −0.0164345
\(633\) 0 0
\(634\) −12.0484 −0.478504
\(635\) 17.3423 0.688210
\(636\) 0 0
\(637\) −49.3574 −1.95561
\(638\) 0.00840526 0.000332767 0
\(639\) 0 0
\(640\) 38.6037 1.52594
\(641\) −18.1436 −0.716628 −0.358314 0.933601i \(-0.616648\pi\)
−0.358314 + 0.933601i \(0.616648\pi\)
\(642\) 0 0
\(643\) 26.2642 1.03576 0.517879 0.855454i \(-0.326722\pi\)
0.517879 + 0.855454i \(0.326722\pi\)
\(644\) 48.7023 1.91914
\(645\) 0 0
\(646\) −12.5244 −0.492765
\(647\) 19.7059 0.774720 0.387360 0.921929i \(-0.373387\pi\)
0.387360 + 0.921929i \(0.373387\pi\)
\(648\) 0 0
\(649\) 0.209945 0.00824105
\(650\) 19.7324 0.773969
\(651\) 0 0
\(652\) 30.2494 1.18466
\(653\) 34.9563 1.36795 0.683974 0.729507i \(-0.260250\pi\)
0.683974 + 0.729507i \(0.260250\pi\)
\(654\) 0 0
\(655\) 2.83383 0.110727
\(656\) 20.7264 0.809231
\(657\) 0 0
\(658\) −16.0159 −0.624365
\(659\) −38.8782 −1.51448 −0.757239 0.653137i \(-0.773452\pi\)
−0.757239 + 0.653137i \(0.773452\pi\)
\(660\) 0 0
\(661\) −23.7519 −0.923840 −0.461920 0.886922i \(-0.652839\pi\)
−0.461920 + 0.886922i \(0.652839\pi\)
\(662\) −4.13511 −0.160715
\(663\) 0 0
\(664\) 1.79060 0.0694887
\(665\) 110.785 4.29607
\(666\) 0 0
\(667\) −6.32496 −0.244904
\(668\) −36.1193 −1.39750
\(669\) 0 0
\(670\) −13.2545 −0.512066
\(671\) −0.0827404 −0.00319416
\(672\) 0 0
\(673\) −1.61288 −0.0621720 −0.0310860 0.999517i \(-0.509897\pi\)
−0.0310860 + 0.999517i \(0.509897\pi\)
\(674\) 13.8214 0.532380
\(675\) 0 0
\(676\) −38.0435 −1.46321
\(677\) −26.4378 −1.01609 −0.508044 0.861331i \(-0.669631\pi\)
−0.508044 + 0.861331i \(0.669631\pi\)
\(678\) 0 0
\(679\) −26.4897 −1.01658
\(680\) 18.5577 0.711654
\(681\) 0 0
\(682\) 0.00791563 0.000303105 0
\(683\) −26.1063 −0.998931 −0.499465 0.866334i \(-0.666470\pi\)
−0.499465 + 0.866334i \(0.666470\pi\)
\(684\) 0 0
\(685\) 41.9962 1.60459
\(686\) −2.75524 −0.105196
\(687\) 0 0
\(688\) −2.40684 −0.0917599
\(689\) −28.2292 −1.07545
\(690\) 0 0
\(691\) −10.4534 −0.397664 −0.198832 0.980034i \(-0.563715\pi\)
−0.198832 + 0.980034i \(0.563715\pi\)
\(692\) 33.7195 1.28182
\(693\) 0 0
\(694\) 7.74085 0.293839
\(695\) −22.5908 −0.856918
\(696\) 0 0
\(697\) 24.2877 0.919964
\(698\) 4.52314 0.171203
\(699\) 0 0
\(700\) −42.2245 −1.59594
\(701\) 44.1917 1.66910 0.834548 0.550936i \(-0.185729\pi\)
0.834548 + 0.550936i \(0.185729\pi\)
\(702\) 0 0
\(703\) −2.76140 −0.104148
\(704\) 0.0365651 0.00137810
\(705\) 0 0
\(706\) −15.7646 −0.593309
\(707\) −40.1260 −1.50909
\(708\) 0 0
\(709\) −22.6858 −0.851984 −0.425992 0.904727i \(-0.640075\pi\)
−0.425992 + 0.904727i \(0.640075\pi\)
\(710\) −20.8714 −0.783291
\(711\) 0 0
\(712\) 8.83795 0.331216
\(713\) −5.95652 −0.223073
\(714\) 0 0
\(715\) 0.360944 0.0134985
\(716\) 22.9710 0.858466
\(717\) 0 0
\(718\) 4.02421 0.150182
\(719\) −43.1259 −1.60833 −0.804163 0.594409i \(-0.797386\pi\)
−0.804163 + 0.594409i \(0.797386\pi\)
\(720\) 0 0
\(721\) −3.38394 −0.126025
\(722\) −27.5932 −1.02691
\(723\) 0 0
\(724\) 30.7324 1.14216
\(725\) 5.48369 0.203659
\(726\) 0 0
\(727\) −16.5706 −0.614570 −0.307285 0.951617i \(-0.599421\pi\)
−0.307285 + 0.951617i \(0.599421\pi\)
\(728\) −45.7750 −1.69653
\(729\) 0 0
\(730\) 10.3951 0.384740
\(731\) −2.82039 −0.104316
\(732\) 0 0
\(733\) 51.6534 1.90786 0.953931 0.300026i \(-0.0969954\pi\)
0.953931 + 0.300026i \(0.0969954\pi\)
\(734\) −0.629825 −0.0232473
\(735\) 0 0
\(736\) 37.7364 1.39098
\(737\) −0.134940 −0.00497057
\(738\) 0 0
\(739\) 21.9045 0.805768 0.402884 0.915251i \(-0.368008\pi\)
0.402884 + 0.915251i \(0.368008\pi\)
\(740\) 1.89102 0.0695151
\(741\) 0 0
\(742\) −9.88992 −0.363070
\(743\) −47.9102 −1.75765 −0.878827 0.477140i \(-0.841673\pi\)
−0.878827 + 0.477140i \(0.841673\pi\)
\(744\) 0 0
\(745\) 3.35792 0.123025
\(746\) −8.43538 −0.308841
\(747\) 0 0
\(748\) 0.0873169 0.00319262
\(749\) 46.4635 1.69774
\(750\) 0 0
\(751\) −27.2207 −0.993299 −0.496650 0.867951i \(-0.665437\pi\)
−0.496650 + 0.867951i \(0.665437\pi\)
\(752\) 18.4393 0.672412
\(753\) 0 0
\(754\) 2.74749 0.100058
\(755\) −64.0189 −2.32989
\(756\) 0 0
\(757\) 13.9698 0.507742 0.253871 0.967238i \(-0.418296\pi\)
0.253871 + 0.967238i \(0.418296\pi\)
\(758\) 5.30797 0.192794
\(759\) 0 0
\(760\) 55.8192 2.02478
\(761\) 7.46960 0.270773 0.135386 0.990793i \(-0.456772\pi\)
0.135386 + 0.990793i \(0.456772\pi\)
\(762\) 0 0
\(763\) −41.8834 −1.51628
\(764\) 21.8239 0.789559
\(765\) 0 0
\(766\) 18.4392 0.666234
\(767\) 68.6260 2.47794
\(768\) 0 0
\(769\) 23.6443 0.852635 0.426318 0.904574i \(-0.359811\pi\)
0.426318 + 0.904574i \(0.359811\pi\)
\(770\) 0.126454 0.00455709
\(771\) 0 0
\(772\) 38.6246 1.39013
\(773\) −30.3897 −1.09304 −0.546521 0.837445i \(-0.684048\pi\)
−0.546521 + 0.837445i \(0.684048\pi\)
\(774\) 0 0
\(775\) 5.16425 0.185505
\(776\) −13.3468 −0.479124
\(777\) 0 0
\(778\) 7.30808 0.262007
\(779\) 73.0546 2.61745
\(780\) 0 0
\(781\) −0.212485 −0.00760333
\(782\) 10.7576 0.384690
\(783\) 0 0
\(784\) 19.9085 0.711017
\(785\) 44.8731 1.60159
\(786\) 0 0
\(787\) −10.7757 −0.384112 −0.192056 0.981384i \(-0.561516\pi\)
−0.192056 + 0.981384i \(0.561516\pi\)
\(788\) −32.9067 −1.17225
\(789\) 0 0
\(790\) 0.373082 0.0132737
\(791\) 22.2121 0.789772
\(792\) 0 0
\(793\) −27.0459 −0.960428
\(794\) 5.88310 0.208783
\(795\) 0 0
\(796\) 9.66704 0.342639
\(797\) −8.93814 −0.316605 −0.158303 0.987391i \(-0.550602\pi\)
−0.158303 + 0.987391i \(0.550602\pi\)
\(798\) 0 0
\(799\) 21.6076 0.764422
\(800\) −32.7172 −1.15673
\(801\) 0 0
\(802\) −2.54088 −0.0897217
\(803\) 0.105829 0.00373463
\(804\) 0 0
\(805\) −95.1569 −3.35384
\(806\) 2.58744 0.0911385
\(807\) 0 0
\(808\) −20.2175 −0.711249
\(809\) −37.5114 −1.31883 −0.659416 0.751778i \(-0.729196\pi\)
−0.659416 + 0.751778i \(0.729196\pi\)
\(810\) 0 0
\(811\) −4.39395 −0.154292 −0.0771462 0.997020i \(-0.524581\pi\)
−0.0771462 + 0.997020i \(0.524581\pi\)
\(812\) −5.87922 −0.206320
\(813\) 0 0
\(814\) −0.00315196 −0.000110476 0
\(815\) −59.1028 −2.07028
\(816\) 0 0
\(817\) −8.48340 −0.296797
\(818\) 16.8512 0.589188
\(819\) 0 0
\(820\) −50.0280 −1.74705
\(821\) −13.9328 −0.486257 −0.243128 0.969994i \(-0.578174\pi\)
−0.243128 + 0.969994i \(0.578174\pi\)
\(822\) 0 0
\(823\) 15.6850 0.546746 0.273373 0.961908i \(-0.411861\pi\)
0.273373 + 0.961908i \(0.411861\pi\)
\(824\) −1.70500 −0.0593966
\(825\) 0 0
\(826\) 24.0427 0.836551
\(827\) 32.1864 1.11923 0.559616 0.828752i \(-0.310949\pi\)
0.559616 + 0.828752i \(0.310949\pi\)
\(828\) 0 0
\(829\) −42.2221 −1.46643 −0.733217 0.679994i \(-0.761982\pi\)
−0.733217 + 0.679994i \(0.761982\pi\)
\(830\) −1.61692 −0.0561240
\(831\) 0 0
\(832\) 11.9523 0.414371
\(833\) 23.3293 0.808311
\(834\) 0 0
\(835\) 70.5716 2.44223
\(836\) 0.262639 0.00908354
\(837\) 0 0
\(838\) −20.3380 −0.702566
\(839\) 7.36583 0.254297 0.127148 0.991884i \(-0.459418\pi\)
0.127148 + 0.991884i \(0.459418\pi\)
\(840\) 0 0
\(841\) −28.2365 −0.973671
\(842\) 0.0770783 0.00265629
\(843\) 0 0
\(844\) −10.8038 −0.371883
\(845\) 74.3312 2.55707
\(846\) 0 0
\(847\) −43.0630 −1.47966
\(848\) 11.3864 0.391010
\(849\) 0 0
\(850\) −9.32673 −0.319904
\(851\) 2.37185 0.0813061
\(852\) 0 0
\(853\) 38.4496 1.31649 0.658245 0.752804i \(-0.271299\pi\)
0.658245 + 0.752804i \(0.271299\pi\)
\(854\) −9.47535 −0.324240
\(855\) 0 0
\(856\) 23.4107 0.800160
\(857\) 1.92317 0.0656942 0.0328471 0.999460i \(-0.489543\pi\)
0.0328471 + 0.999460i \(0.489543\pi\)
\(858\) 0 0
\(859\) −23.1582 −0.790149 −0.395075 0.918649i \(-0.629281\pi\)
−0.395075 + 0.918649i \(0.629281\pi\)
\(860\) 5.80946 0.198101
\(861\) 0 0
\(862\) −0.232941 −0.00793401
\(863\) −9.21594 −0.313714 −0.156857 0.987621i \(-0.550136\pi\)
−0.156857 + 0.987621i \(0.550136\pi\)
\(864\) 0 0
\(865\) −65.8827 −2.24008
\(866\) −1.77749 −0.0604015
\(867\) 0 0
\(868\) −5.53673 −0.187929
\(869\) 0.00379822 0.000128846 0
\(870\) 0 0
\(871\) −44.1087 −1.49457
\(872\) −21.1030 −0.714637
\(873\) 0 0
\(874\) 32.3575 1.09451
\(875\) 16.7699 0.566925
\(876\) 0 0
\(877\) −35.5672 −1.20102 −0.600509 0.799618i \(-0.705035\pi\)
−0.600509 + 0.799618i \(0.705035\pi\)
\(878\) −2.46177 −0.0830807
\(879\) 0 0
\(880\) −0.145588 −0.00490777
\(881\) 13.3847 0.450943 0.225471 0.974250i \(-0.427608\pi\)
0.225471 + 0.974250i \(0.427608\pi\)
\(882\) 0 0
\(883\) −48.2966 −1.62531 −0.812655 0.582745i \(-0.801979\pi\)
−0.812655 + 0.582745i \(0.801979\pi\)
\(884\) 28.5419 0.959967
\(885\) 0 0
\(886\) −9.56467 −0.321331
\(887\) 11.8976 0.399481 0.199741 0.979849i \(-0.435990\pi\)
0.199741 + 0.979849i \(0.435990\pi\)
\(888\) 0 0
\(889\) 20.2191 0.678127
\(890\) −7.98069 −0.267513
\(891\) 0 0
\(892\) −25.0146 −0.837550
\(893\) 64.9931 2.17491
\(894\) 0 0
\(895\) −44.8818 −1.50023
\(896\) 45.0073 1.50359
\(897\) 0 0
\(898\) −3.96516 −0.132319
\(899\) 0.719055 0.0239818
\(900\) 0 0
\(901\) 13.3428 0.444514
\(902\) 0.0833871 0.00277649
\(903\) 0 0
\(904\) 11.1916 0.372227
\(905\) −60.0463 −1.99601
\(906\) 0 0
\(907\) 7.28699 0.241961 0.120980 0.992655i \(-0.461396\pi\)
0.120980 + 0.992655i \(0.461396\pi\)
\(908\) −38.2552 −1.26954
\(909\) 0 0
\(910\) 41.3349 1.37024
\(911\) −43.2137 −1.43173 −0.715867 0.698236i \(-0.753968\pi\)
−0.715867 + 0.698236i \(0.753968\pi\)
\(912\) 0 0
\(913\) −0.0164613 −0.000544789 0
\(914\) −1.23146 −0.0407330
\(915\) 0 0
\(916\) −33.3937 −1.10336
\(917\) 3.30391 0.109105
\(918\) 0 0
\(919\) −39.3602 −1.29837 −0.649187 0.760629i \(-0.724891\pi\)
−0.649187 + 0.760629i \(0.724891\pi\)
\(920\) −47.9448 −1.58069
\(921\) 0 0
\(922\) 15.0589 0.495939
\(923\) −69.4565 −2.28619
\(924\) 0 0
\(925\) −2.05638 −0.0676133
\(926\) 20.1932 0.663591
\(927\) 0 0
\(928\) −4.55544 −0.149540
\(929\) 52.3627 1.71797 0.858983 0.512004i \(-0.171097\pi\)
0.858983 + 0.512004i \(0.171097\pi\)
\(930\) 0 0
\(931\) 70.1716 2.29978
\(932\) −43.6772 −1.43069
\(933\) 0 0
\(934\) 17.6283 0.576816
\(935\) −0.170604 −0.00557934
\(936\) 0 0
\(937\) −0.642958 −0.0210045 −0.0105023 0.999945i \(-0.503343\pi\)
−0.0105023 + 0.999945i \(0.503343\pi\)
\(938\) −15.4532 −0.504564
\(939\) 0 0
\(940\) −44.5075 −1.45167
\(941\) 6.85566 0.223488 0.111744 0.993737i \(-0.464356\pi\)
0.111744 + 0.993737i \(0.464356\pi\)
\(942\) 0 0
\(943\) −62.7488 −2.04338
\(944\) −27.6806 −0.900926
\(945\) 0 0
\(946\) −0.00968326 −0.000314830 0
\(947\) −23.8132 −0.773826 −0.386913 0.922116i \(-0.626459\pi\)
−0.386913 + 0.922116i \(0.626459\pi\)
\(948\) 0 0
\(949\) 34.5931 1.12294
\(950\) −28.0537 −0.910181
\(951\) 0 0
\(952\) 21.6360 0.701227
\(953\) −8.89776 −0.288227 −0.144113 0.989561i \(-0.546033\pi\)
−0.144113 + 0.989561i \(0.546033\pi\)
\(954\) 0 0
\(955\) −42.6405 −1.37981
\(956\) −37.2971 −1.20628
\(957\) 0 0
\(958\) 11.5034 0.371658
\(959\) 48.9625 1.58108
\(960\) 0 0
\(961\) −30.3228 −0.978156
\(962\) −1.03030 −0.0332183
\(963\) 0 0
\(964\) −37.3836 −1.20405
\(965\) −75.4665 −2.42935
\(966\) 0 0
\(967\) 1.99362 0.0641105 0.0320552 0.999486i \(-0.489795\pi\)
0.0320552 + 0.999486i \(0.489795\pi\)
\(968\) −21.6973 −0.697379
\(969\) 0 0
\(970\) 12.0522 0.386974
\(971\) −24.8965 −0.798965 −0.399483 0.916741i \(-0.630810\pi\)
−0.399483 + 0.916741i \(0.630810\pi\)
\(972\) 0 0
\(973\) −26.3382 −0.844364
\(974\) 20.6368 0.661247
\(975\) 0 0
\(976\) 10.9091 0.349191
\(977\) 49.8050 1.59340 0.796701 0.604374i \(-0.206577\pi\)
0.796701 + 0.604374i \(0.206577\pi\)
\(978\) 0 0
\(979\) −0.0812488 −0.00259672
\(980\) −48.0537 −1.53502
\(981\) 0 0
\(982\) 2.96694 0.0946789
\(983\) 18.3355 0.584812 0.292406 0.956294i \(-0.405544\pi\)
0.292406 + 0.956294i \(0.405544\pi\)
\(984\) 0 0
\(985\) 64.2946 2.04860
\(986\) −1.29863 −0.0413567
\(987\) 0 0
\(988\) 85.8505 2.73127
\(989\) 7.28666 0.231702
\(990\) 0 0
\(991\) −11.1904 −0.355476 −0.177738 0.984078i \(-0.556878\pi\)
−0.177738 + 0.984078i \(0.556878\pi\)
\(992\) −4.29008 −0.136210
\(993\) 0 0
\(994\) −24.3336 −0.771815
\(995\) −18.8879 −0.598787
\(996\) 0 0
\(997\) −37.9659 −1.20239 −0.601195 0.799102i \(-0.705309\pi\)
−0.601195 + 0.799102i \(0.705309\pi\)
\(998\) 11.5782 0.366501
\(999\) 0 0
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 4023.2.a.f.1.10 yes 25
3.2 odd 2 4023.2.a.e.1.16 25
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
4023.2.a.e.1.16 25 3.2 odd 2
4023.2.a.f.1.10 yes 25 1.1 even 1 trivial