Properties

Label 5290.2.a.bk.1.12
Level $5290$
Weight $2$
Character 5290.1
Self dual yes
Analytic conductor $42.241$
Analytic rank $0$
Dimension $15$
CM no
Inner twists $1$

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [5290,2,Mod(1,5290)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(5290, 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("5290.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 5290 = 2 \cdot 5 \cdot 23^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 5290.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: \(42.2408626693\)
Analytic rank: \(0\)
Dimension: \(15\)
Coefficient field: \(\mathbb{Q}[x]/(x^{15} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{15} - 5 x^{14} - 24 x^{13} + 142 x^{12} + 184 x^{11} - 1488 x^{10} - 426 x^{9} + 7165 x^{8} - 206 x^{7} - 16453 x^{6} + 637 x^{5} + 16290 x^{4} + 1068 x^{3} - 4992 x^{2} + \cdots - 32 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 230)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.12
Root \(2.75508\) of defining polynomial
Character \(\chi\) \(=\) 5290.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+1.00000 q^{2} +2.75508 q^{3} +1.00000 q^{4} -1.00000 q^{5} +2.75508 q^{6} +4.44855 q^{7} +1.00000 q^{8} +4.59049 q^{9} +O(q^{10})\) \(q+1.00000 q^{2} +2.75508 q^{3} +1.00000 q^{4} -1.00000 q^{5} +2.75508 q^{6} +4.44855 q^{7} +1.00000 q^{8} +4.59049 q^{9} -1.00000 q^{10} +4.40211 q^{11} +2.75508 q^{12} +2.45989 q^{13} +4.44855 q^{14} -2.75508 q^{15} +1.00000 q^{16} -6.98238 q^{17} +4.59049 q^{18} -3.42347 q^{19} -1.00000 q^{20} +12.2561 q^{21} +4.40211 q^{22} +2.75508 q^{24} +1.00000 q^{25} +2.45989 q^{26} +4.38194 q^{27} +4.44855 q^{28} +5.51384 q^{29} -2.75508 q^{30} -2.05611 q^{31} +1.00000 q^{32} +12.1282 q^{33} -6.98238 q^{34} -4.44855 q^{35} +4.59049 q^{36} -6.73053 q^{37} -3.42347 q^{38} +6.77719 q^{39} -1.00000 q^{40} +3.15936 q^{41} +12.2561 q^{42} -2.76141 q^{43} +4.40211 q^{44} -4.59049 q^{45} +6.18748 q^{47} +2.75508 q^{48} +12.7896 q^{49} +1.00000 q^{50} -19.2371 q^{51} +2.45989 q^{52} -1.99036 q^{53} +4.38194 q^{54} -4.40211 q^{55} +4.44855 q^{56} -9.43196 q^{57} +5.51384 q^{58} +2.00254 q^{59} -2.75508 q^{60} -13.8042 q^{61} -2.05611 q^{62} +20.4210 q^{63} +1.00000 q^{64} -2.45989 q^{65} +12.1282 q^{66} +8.90067 q^{67} -6.98238 q^{68} -4.44855 q^{70} -10.8705 q^{71} +4.59049 q^{72} -8.57546 q^{73} -6.73053 q^{74} +2.75508 q^{75} -3.42347 q^{76} +19.5830 q^{77} +6.77719 q^{78} -11.8628 q^{79} -1.00000 q^{80} -1.69886 q^{81} +3.15936 q^{82} +0.319840 q^{83} +12.2561 q^{84} +6.98238 q^{85} -2.76141 q^{86} +15.1911 q^{87} +4.40211 q^{88} +8.69820 q^{89} -4.59049 q^{90} +10.9429 q^{91} -5.66475 q^{93} +6.18748 q^{94} +3.42347 q^{95} +2.75508 q^{96} +7.30395 q^{97} +12.7896 q^{98} +20.2078 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 15 q + 15 q^{2} + 5 q^{3} + 15 q^{4} - 15 q^{5} + 5 q^{6} + 4 q^{7} + 15 q^{8} + 28 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 15 q + 15 q^{2} + 5 q^{3} + 15 q^{4} - 15 q^{5} + 5 q^{6} + 4 q^{7} + 15 q^{8} + 28 q^{9} - 15 q^{10} - 7 q^{11} + 5 q^{12} + 17 q^{13} + 4 q^{14} - 5 q^{15} + 15 q^{16} - 2 q^{17} + 28 q^{18} - 18 q^{19} - 15 q^{20} - 7 q^{22} + 5 q^{24} + 15 q^{25} + 17 q^{26} + 29 q^{27} + 4 q^{28} + 35 q^{29} - 5 q^{30} + 19 q^{31} + 15 q^{32} + 21 q^{33} - 2 q^{34} - 4 q^{35} + 28 q^{36} + 12 q^{37} - 18 q^{38} + 26 q^{39} - 15 q^{40} + 27 q^{41} - 12 q^{43} - 7 q^{44} - 28 q^{45} + 40 q^{47} + 5 q^{48} + 29 q^{49} + 15 q^{50} + 27 q^{51} + 17 q^{52} + 20 q^{53} + 29 q^{54} + 7 q^{55} + 4 q^{56} + 11 q^{57} + 35 q^{58} + 15 q^{59} - 5 q^{60} - 28 q^{61} + 19 q^{62} + 51 q^{63} + 15 q^{64} - 17 q^{65} + 21 q^{66} - 4 q^{67} - 2 q^{68} - 4 q^{70} + 22 q^{71} + 28 q^{72} + 48 q^{73} + 12 q^{74} + 5 q^{75} - 18 q^{76} + 45 q^{77} + 26 q^{78} + 2 q^{79} - 15 q^{80} + 79 q^{81} + 27 q^{82} + 29 q^{83} + 2 q^{85} - 12 q^{86} - 7 q^{87} - 7 q^{88} - 20 q^{89} - 28 q^{90} - 6 q^{91} + 63 q^{93} + 40 q^{94} + 18 q^{95} + 5 q^{96} + 22 q^{97} + 29 q^{98} - 23 q^{99}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000 0.707107
\(3\) 2.75508 1.59065 0.795324 0.606184i \(-0.207300\pi\)
0.795324 + 0.606184i \(0.207300\pi\)
\(4\) 1.00000 0.500000
\(5\) −1.00000 −0.447214
\(6\) 2.75508 1.12476
\(7\) 4.44855 1.68139 0.840696 0.541507i \(-0.182146\pi\)
0.840696 + 0.541507i \(0.182146\pi\)
\(8\) 1.00000 0.353553
\(9\) 4.59049 1.53016
\(10\) −1.00000 −0.316228
\(11\) 4.40211 1.32729 0.663643 0.748050i \(-0.269009\pi\)
0.663643 + 0.748050i \(0.269009\pi\)
\(12\) 2.75508 0.795324
\(13\) 2.45989 0.682249 0.341125 0.940018i \(-0.389192\pi\)
0.341125 + 0.940018i \(0.389192\pi\)
\(14\) 4.44855 1.18892
\(15\) −2.75508 −0.711360
\(16\) 1.00000 0.250000
\(17\) −6.98238 −1.69348 −0.846738 0.532010i \(-0.821437\pi\)
−0.846738 + 0.532010i \(0.821437\pi\)
\(18\) 4.59049 1.08199
\(19\) −3.42347 −0.785399 −0.392699 0.919667i \(-0.628459\pi\)
−0.392699 + 0.919667i \(0.628459\pi\)
\(20\) −1.00000 −0.223607
\(21\) 12.2561 2.67451
\(22\) 4.40211 0.938533
\(23\) 0 0
\(24\) 2.75508 0.562379
\(25\) 1.00000 0.200000
\(26\) 2.45989 0.482423
\(27\) 4.38194 0.843305
\(28\) 4.44855 0.840696
\(29\) 5.51384 1.02389 0.511947 0.859017i \(-0.328924\pi\)
0.511947 + 0.859017i \(0.328924\pi\)
\(30\) −2.75508 −0.503007
\(31\) −2.05611 −0.369288 −0.184644 0.982805i \(-0.559113\pi\)
−0.184644 + 0.982805i \(0.559113\pi\)
\(32\) 1.00000 0.176777
\(33\) 12.1282 2.11125
\(34\) −6.98238 −1.19747
\(35\) −4.44855 −0.751942
\(36\) 4.59049 0.765082
\(37\) −6.73053 −1.10649 −0.553246 0.833018i \(-0.686611\pi\)
−0.553246 + 0.833018i \(0.686611\pi\)
\(38\) −3.42347 −0.555361
\(39\) 6.77719 1.08522
\(40\) −1.00000 −0.158114
\(41\) 3.15936 0.493410 0.246705 0.969091i \(-0.420652\pi\)
0.246705 + 0.969091i \(0.420652\pi\)
\(42\) 12.2561 1.89116
\(43\) −2.76141 −0.421111 −0.210555 0.977582i \(-0.567527\pi\)
−0.210555 + 0.977582i \(0.567527\pi\)
\(44\) 4.40211 0.663643
\(45\) −4.59049 −0.684310
\(46\) 0 0
\(47\) 6.18748 0.902537 0.451268 0.892388i \(-0.350972\pi\)
0.451268 + 0.892388i \(0.350972\pi\)
\(48\) 2.75508 0.397662
\(49\) 12.7896 1.82708
\(50\) 1.00000 0.141421
\(51\) −19.2371 −2.69373
\(52\) 2.45989 0.341125
\(53\) −1.99036 −0.273397 −0.136698 0.990613i \(-0.543649\pi\)
−0.136698 + 0.990613i \(0.543649\pi\)
\(54\) 4.38194 0.596307
\(55\) −4.40211 −0.593580
\(56\) 4.44855 0.594462
\(57\) −9.43196 −1.24929
\(58\) 5.51384 0.724003
\(59\) 2.00254 0.260708 0.130354 0.991467i \(-0.458389\pi\)
0.130354 + 0.991467i \(0.458389\pi\)
\(60\) −2.75508 −0.355680
\(61\) −13.8042 −1.76744 −0.883721 0.468014i \(-0.844970\pi\)
−0.883721 + 0.468014i \(0.844970\pi\)
\(62\) −2.05611 −0.261126
\(63\) 20.4210 2.57281
\(64\) 1.00000 0.125000
\(65\) −2.45989 −0.305111
\(66\) 12.1282 1.49288
\(67\) 8.90067 1.08739 0.543695 0.839283i \(-0.317025\pi\)
0.543695 + 0.839283i \(0.317025\pi\)
\(68\) −6.98238 −0.846738
\(69\) 0 0
\(70\) −4.44855 −0.531703
\(71\) −10.8705 −1.29010 −0.645048 0.764142i \(-0.723162\pi\)
−0.645048 + 0.764142i \(0.723162\pi\)
\(72\) 4.59049 0.540995
\(73\) −8.57546 −1.00368 −0.501841 0.864960i \(-0.667344\pi\)
−0.501841 + 0.864960i \(0.667344\pi\)
\(74\) −6.73053 −0.782408
\(75\) 2.75508 0.318130
\(76\) −3.42347 −0.392699
\(77\) 19.5830 2.23169
\(78\) 6.77719 0.767366
\(79\) −11.8628 −1.33466 −0.667332 0.744760i \(-0.732564\pi\)
−0.667332 + 0.744760i \(0.732564\pi\)
\(80\) −1.00000 −0.111803
\(81\) −1.69886 −0.188762
\(82\) 3.15936 0.348893
\(83\) 0.319840 0.0351069 0.0175535 0.999846i \(-0.494412\pi\)
0.0175535 + 0.999846i \(0.494412\pi\)
\(84\) 12.2561 1.33725
\(85\) 6.98238 0.757345
\(86\) −2.76141 −0.297770
\(87\) 15.1911 1.62866
\(88\) 4.40211 0.469266
\(89\) 8.69820 0.922008 0.461004 0.887398i \(-0.347489\pi\)
0.461004 + 0.887398i \(0.347489\pi\)
\(90\) −4.59049 −0.483880
\(91\) 10.9429 1.14713
\(92\) 0 0
\(93\) −5.66475 −0.587408
\(94\) 6.18748 0.638190
\(95\) 3.42347 0.351241
\(96\) 2.75508 0.281190
\(97\) 7.30395 0.741603 0.370802 0.928712i \(-0.379083\pi\)
0.370802 + 0.928712i \(0.379083\pi\)
\(98\) 12.7896 1.29194
\(99\) 20.2078 2.03097
\(100\) 1.00000 0.100000
\(101\) −9.08953 −0.904442 −0.452221 0.891906i \(-0.649368\pi\)
−0.452221 + 0.891906i \(0.649368\pi\)
\(102\) −19.2371 −1.90475
\(103\) 1.49900 0.147701 0.0738504 0.997269i \(-0.476471\pi\)
0.0738504 + 0.997269i \(0.476471\pi\)
\(104\) 2.45989 0.241212
\(105\) −12.2561 −1.19608
\(106\) −1.99036 −0.193321
\(107\) −17.7755 −1.71842 −0.859211 0.511622i \(-0.829045\pi\)
−0.859211 + 0.511622i \(0.829045\pi\)
\(108\) 4.38194 0.421653
\(109\) 18.9672 1.81673 0.908364 0.418181i \(-0.137332\pi\)
0.908364 + 0.418181i \(0.137332\pi\)
\(110\) −4.40211 −0.419725
\(111\) −18.5432 −1.76004
\(112\) 4.44855 0.420348
\(113\) −3.38804 −0.318720 −0.159360 0.987221i \(-0.550943\pi\)
−0.159360 + 0.987221i \(0.550943\pi\)
\(114\) −9.43196 −0.883384
\(115\) 0 0
\(116\) 5.51384 0.511947
\(117\) 11.2921 1.04395
\(118\) 2.00254 0.184349
\(119\) −31.0614 −2.84740
\(120\) −2.75508 −0.251504
\(121\) 8.37857 0.761688
\(122\) −13.8042 −1.24977
\(123\) 8.70432 0.784842
\(124\) −2.05611 −0.184644
\(125\) −1.00000 −0.0894427
\(126\) 20.4210 1.81925
\(127\) −5.73551 −0.508945 −0.254472 0.967080i \(-0.581902\pi\)
−0.254472 + 0.967080i \(0.581902\pi\)
\(128\) 1.00000 0.0883883
\(129\) −7.60792 −0.669840
\(130\) −2.45989 −0.215746
\(131\) −10.6514 −0.930620 −0.465310 0.885148i \(-0.654057\pi\)
−0.465310 + 0.885148i \(0.654057\pi\)
\(132\) 12.1282 1.05562
\(133\) −15.2295 −1.32056
\(134\) 8.90067 0.768901
\(135\) −4.38194 −0.377137
\(136\) −6.98238 −0.598734
\(137\) 13.7187 1.17207 0.586035 0.810285i \(-0.300688\pi\)
0.586035 + 0.810285i \(0.300688\pi\)
\(138\) 0 0
\(139\) −3.55749 −0.301742 −0.150871 0.988553i \(-0.548208\pi\)
−0.150871 + 0.988553i \(0.548208\pi\)
\(140\) −4.44855 −0.375971
\(141\) 17.0470 1.43562
\(142\) −10.8705 −0.912235
\(143\) 10.8287 0.905540
\(144\) 4.59049 0.382541
\(145\) −5.51384 −0.457899
\(146\) −8.57546 −0.709710
\(147\) 35.2363 2.90624
\(148\) −6.73053 −0.553246
\(149\) −8.65572 −0.709104 −0.354552 0.935036i \(-0.615367\pi\)
−0.354552 + 0.935036i \(0.615367\pi\)
\(150\) 2.75508 0.224952
\(151\) −1.76370 −0.143528 −0.0717640 0.997422i \(-0.522863\pi\)
−0.0717640 + 0.997422i \(0.522863\pi\)
\(152\) −3.42347 −0.277680
\(153\) −32.0526 −2.59130
\(154\) 19.5830 1.57804
\(155\) 2.05611 0.165151
\(156\) 6.77719 0.542610
\(157\) −12.6015 −1.00571 −0.502856 0.864370i \(-0.667717\pi\)
−0.502856 + 0.864370i \(0.667717\pi\)
\(158\) −11.8628 −0.943750
\(159\) −5.48361 −0.434878
\(160\) −1.00000 −0.0790569
\(161\) 0 0
\(162\) −1.69886 −0.133475
\(163\) 2.07678 0.162666 0.0813329 0.996687i \(-0.474082\pi\)
0.0813329 + 0.996687i \(0.474082\pi\)
\(164\) 3.15936 0.246705
\(165\) −12.1282 −0.944178
\(166\) 0.319840 0.0248244
\(167\) 3.48524 0.269696 0.134848 0.990866i \(-0.456945\pi\)
0.134848 + 0.990866i \(0.456945\pi\)
\(168\) 12.2561 0.945580
\(169\) −6.94896 −0.534536
\(170\) 6.98238 0.535524
\(171\) −15.7154 −1.20179
\(172\) −2.76141 −0.210555
\(173\) 23.1699 1.76157 0.880787 0.473513i \(-0.157014\pi\)
0.880787 + 0.473513i \(0.157014\pi\)
\(174\) 15.1911 1.15163
\(175\) 4.44855 0.336278
\(176\) 4.40211 0.331821
\(177\) 5.51717 0.414696
\(178\) 8.69820 0.651958
\(179\) 1.26603 0.0946279 0.0473139 0.998880i \(-0.484934\pi\)
0.0473139 + 0.998880i \(0.484934\pi\)
\(180\) −4.59049 −0.342155
\(181\) −18.3728 −1.36564 −0.682822 0.730585i \(-0.739247\pi\)
−0.682822 + 0.730585i \(0.739247\pi\)
\(182\) 10.9429 0.811143
\(183\) −38.0316 −2.81138
\(184\) 0 0
\(185\) 6.73053 0.494838
\(186\) −5.66475 −0.415360
\(187\) −30.7372 −2.24773
\(188\) 6.18748 0.451268
\(189\) 19.4933 1.41793
\(190\) 3.42347 0.248365
\(191\) 5.84116 0.422652 0.211326 0.977416i \(-0.432222\pi\)
0.211326 + 0.977416i \(0.432222\pi\)
\(192\) 2.75508 0.198831
\(193\) −0.726448 −0.0522908 −0.0261454 0.999658i \(-0.508323\pi\)
−0.0261454 + 0.999658i \(0.508323\pi\)
\(194\) 7.30395 0.524393
\(195\) −6.77719 −0.485325
\(196\) 12.7896 0.913540
\(197\) 10.1195 0.720987 0.360493 0.932762i \(-0.382608\pi\)
0.360493 + 0.932762i \(0.382608\pi\)
\(198\) 20.2078 1.43611
\(199\) 18.5869 1.31759 0.658795 0.752322i \(-0.271066\pi\)
0.658795 + 0.752322i \(0.271066\pi\)
\(200\) 1.00000 0.0707107
\(201\) 24.5221 1.72966
\(202\) −9.08953 −0.639537
\(203\) 24.5286 1.72157
\(204\) −19.2371 −1.34686
\(205\) −3.15936 −0.220660
\(206\) 1.49900 0.104440
\(207\) 0 0
\(208\) 2.45989 0.170562
\(209\) −15.0705 −1.04245
\(210\) −12.2561 −0.845753
\(211\) 4.90443 0.337635 0.168817 0.985647i \(-0.446005\pi\)
0.168817 + 0.985647i \(0.446005\pi\)
\(212\) −1.99036 −0.136698
\(213\) −29.9492 −2.05209
\(214\) −17.7755 −1.21511
\(215\) 2.76141 0.188327
\(216\) 4.38194 0.298153
\(217\) −9.14670 −0.620918
\(218\) 18.9672 1.28462
\(219\) −23.6261 −1.59651
\(220\) −4.40211 −0.296790
\(221\) −17.1759 −1.15537
\(222\) −18.5432 −1.24454
\(223\) 9.71984 0.650888 0.325444 0.945561i \(-0.394486\pi\)
0.325444 + 0.945561i \(0.394486\pi\)
\(224\) 4.44855 0.297231
\(225\) 4.59049 0.306033
\(226\) −3.38804 −0.225369
\(227\) 21.5002 1.42702 0.713509 0.700646i \(-0.247105\pi\)
0.713509 + 0.700646i \(0.247105\pi\)
\(228\) −9.43196 −0.624647
\(229\) −5.38568 −0.355896 −0.177948 0.984040i \(-0.556946\pi\)
−0.177948 + 0.984040i \(0.556946\pi\)
\(230\) 0 0
\(231\) 53.9528 3.54983
\(232\) 5.51384 0.362001
\(233\) −29.3533 −1.92300 −0.961498 0.274811i \(-0.911385\pi\)
−0.961498 + 0.274811i \(0.911385\pi\)
\(234\) 11.2921 0.738187
\(235\) −6.18748 −0.403627
\(236\) 2.00254 0.130354
\(237\) −32.6829 −2.12298
\(238\) −31.0614 −2.01341
\(239\) −8.09013 −0.523307 −0.261653 0.965162i \(-0.584268\pi\)
−0.261653 + 0.965162i \(0.584268\pi\)
\(240\) −2.75508 −0.177840
\(241\) 11.4116 0.735088 0.367544 0.930006i \(-0.380199\pi\)
0.367544 + 0.930006i \(0.380199\pi\)
\(242\) 8.37857 0.538595
\(243\) −17.8263 −1.14356
\(244\) −13.8042 −0.883721
\(245\) −12.7896 −0.817095
\(246\) 8.70432 0.554967
\(247\) −8.42135 −0.535838
\(248\) −2.05611 −0.130563
\(249\) 0.881185 0.0558428
\(250\) −1.00000 −0.0632456
\(251\) 11.7941 0.744436 0.372218 0.928145i \(-0.378597\pi\)
0.372218 + 0.928145i \(0.378597\pi\)
\(252\) 20.4210 1.28640
\(253\) 0 0
\(254\) −5.73551 −0.359878
\(255\) 19.2371 1.20467
\(256\) 1.00000 0.0625000
\(257\) 2.03939 0.127214 0.0636069 0.997975i \(-0.479740\pi\)
0.0636069 + 0.997975i \(0.479740\pi\)
\(258\) −7.60792 −0.473648
\(259\) −29.9411 −1.86045
\(260\) −2.45989 −0.152556
\(261\) 25.3112 1.56673
\(262\) −10.6514 −0.658047
\(263\) 24.7269 1.52473 0.762364 0.647149i \(-0.224039\pi\)
0.762364 + 0.647149i \(0.224039\pi\)
\(264\) 12.1282 0.746438
\(265\) 1.99036 0.122267
\(266\) −15.2295 −0.933779
\(267\) 23.9643 1.46659
\(268\) 8.90067 0.543695
\(269\) 14.4785 0.882770 0.441385 0.897318i \(-0.354487\pi\)
0.441385 + 0.897318i \(0.354487\pi\)
\(270\) −4.38194 −0.266676
\(271\) 19.7153 1.19762 0.598811 0.800890i \(-0.295640\pi\)
0.598811 + 0.800890i \(0.295640\pi\)
\(272\) −6.98238 −0.423369
\(273\) 30.1487 1.82468
\(274\) 13.7187 0.828779
\(275\) 4.40211 0.265457
\(276\) 0 0
\(277\) −22.7803 −1.36874 −0.684368 0.729136i \(-0.739922\pi\)
−0.684368 + 0.729136i \(0.739922\pi\)
\(278\) −3.55749 −0.213364
\(279\) −9.43855 −0.565071
\(280\) −4.44855 −0.265851
\(281\) 13.2608 0.791073 0.395536 0.918450i \(-0.370559\pi\)
0.395536 + 0.918450i \(0.370559\pi\)
\(282\) 17.0470 1.01514
\(283\) 7.87321 0.468014 0.234007 0.972235i \(-0.424816\pi\)
0.234007 + 0.972235i \(0.424816\pi\)
\(284\) −10.8705 −0.645048
\(285\) 9.43196 0.558701
\(286\) 10.8287 0.640314
\(287\) 14.0546 0.829616
\(288\) 4.59049 0.270497
\(289\) 31.7536 1.86786
\(290\) −5.51384 −0.323784
\(291\) 20.1230 1.17963
\(292\) −8.57546 −0.501841
\(293\) 10.7456 0.627763 0.313881 0.949462i \(-0.398371\pi\)
0.313881 + 0.949462i \(0.398371\pi\)
\(294\) 35.2363 2.05502
\(295\) −2.00254 −0.116592
\(296\) −6.73053 −0.391204
\(297\) 19.2898 1.11931
\(298\) −8.65572 −0.501412
\(299\) 0 0
\(300\) 2.75508 0.159065
\(301\) −12.2843 −0.708053
\(302\) −1.76370 −0.101490
\(303\) −25.0424 −1.43865
\(304\) −3.42347 −0.196350
\(305\) 13.8042 0.790424
\(306\) −32.0526 −1.83232
\(307\) 1.33735 0.0763266 0.0381633 0.999272i \(-0.487849\pi\)
0.0381633 + 0.999272i \(0.487849\pi\)
\(308\) 19.5830 1.11584
\(309\) 4.12987 0.234940
\(310\) 2.05611 0.116779
\(311\) 7.12911 0.404255 0.202128 0.979359i \(-0.435214\pi\)
0.202128 + 0.979359i \(0.435214\pi\)
\(312\) 6.77719 0.383683
\(313\) −13.1855 −0.745289 −0.372645 0.927974i \(-0.621549\pi\)
−0.372645 + 0.927974i \(0.621549\pi\)
\(314\) −12.6015 −0.711146
\(315\) −20.4210 −1.15059
\(316\) −11.8628 −0.667332
\(317\) 11.9822 0.672989 0.336494 0.941685i \(-0.390759\pi\)
0.336494 + 0.941685i \(0.390759\pi\)
\(318\) −5.48361 −0.307505
\(319\) 24.2725 1.35900
\(320\) −1.00000 −0.0559017
\(321\) −48.9730 −2.73341
\(322\) 0 0
\(323\) 23.9040 1.33005
\(324\) −1.69886 −0.0943809
\(325\) 2.45989 0.136450
\(326\) 2.07678 0.115022
\(327\) 52.2562 2.88978
\(328\) 3.15936 0.174447
\(329\) 27.5253 1.51752
\(330\) −12.1282 −0.667635
\(331\) 11.5934 0.637229 0.318615 0.947884i \(-0.396782\pi\)
0.318615 + 0.947884i \(0.396782\pi\)
\(332\) 0.319840 0.0175535
\(333\) −30.8964 −1.69311
\(334\) 3.48524 0.190704
\(335\) −8.90067 −0.486296
\(336\) 12.2561 0.668626
\(337\) 6.87330 0.374412 0.187206 0.982321i \(-0.440057\pi\)
0.187206 + 0.982321i \(0.440057\pi\)
\(338\) −6.94896 −0.377974
\(339\) −9.33434 −0.506972
\(340\) 6.98238 0.378673
\(341\) −9.05122 −0.490151
\(342\) −15.7154 −0.849793
\(343\) 25.7551 1.39065
\(344\) −2.76141 −0.148885
\(345\) 0 0
\(346\) 23.1699 1.24562
\(347\) 5.76727 0.309603 0.154802 0.987946i \(-0.450526\pi\)
0.154802 + 0.987946i \(0.450526\pi\)
\(348\) 15.1911 0.814328
\(349\) −16.4626 −0.881220 −0.440610 0.897699i \(-0.645238\pi\)
−0.440610 + 0.897699i \(0.645238\pi\)
\(350\) 4.44855 0.237785
\(351\) 10.7791 0.575344
\(352\) 4.40211 0.234633
\(353\) −22.8572 −1.21657 −0.608283 0.793720i \(-0.708142\pi\)
−0.608283 + 0.793720i \(0.708142\pi\)
\(354\) 5.51717 0.293234
\(355\) 10.8705 0.576948
\(356\) 8.69820 0.461004
\(357\) −85.5769 −4.52921
\(358\) 1.26603 0.0669120
\(359\) 21.1272 1.11505 0.557526 0.830159i \(-0.311751\pi\)
0.557526 + 0.830159i \(0.311751\pi\)
\(360\) −4.59049 −0.241940
\(361\) −7.27983 −0.383149
\(362\) −18.3728 −0.965655
\(363\) 23.0837 1.21158
\(364\) 10.9429 0.573565
\(365\) 8.57546 0.448860
\(366\) −38.0316 −1.98795
\(367\) 12.1222 0.632773 0.316386 0.948630i \(-0.397530\pi\)
0.316386 + 0.948630i \(0.397530\pi\)
\(368\) 0 0
\(369\) 14.5030 0.754998
\(370\) 6.73053 0.349904
\(371\) −8.85420 −0.459687
\(372\) −5.66475 −0.293704
\(373\) −18.1236 −0.938402 −0.469201 0.883091i \(-0.655458\pi\)
−0.469201 + 0.883091i \(0.655458\pi\)
\(374\) −30.7372 −1.58938
\(375\) −2.75508 −0.142272
\(376\) 6.18748 0.319095
\(377\) 13.5634 0.698551
\(378\) 19.4933 1.00263
\(379\) 18.0644 0.927906 0.463953 0.885860i \(-0.346431\pi\)
0.463953 + 0.885860i \(0.346431\pi\)
\(380\) 3.42347 0.175620
\(381\) −15.8018 −0.809552
\(382\) 5.84116 0.298860
\(383\) 20.5709 1.05112 0.525561 0.850756i \(-0.323855\pi\)
0.525561 + 0.850756i \(0.323855\pi\)
\(384\) 2.75508 0.140595
\(385\) −19.5830 −0.998041
\(386\) −0.726448 −0.0369752
\(387\) −12.6762 −0.644369
\(388\) 7.30395 0.370802
\(389\) −4.21880 −0.213902 −0.106951 0.994264i \(-0.534109\pi\)
−0.106951 + 0.994264i \(0.534109\pi\)
\(390\) −6.77719 −0.343177
\(391\) 0 0
\(392\) 12.7896 0.645970
\(393\) −29.3456 −1.48029
\(394\) 10.1195 0.509815
\(395\) 11.8628 0.596880
\(396\) 20.2078 1.01548
\(397\) 22.9773 1.15320 0.576598 0.817028i \(-0.304380\pi\)
0.576598 + 0.817028i \(0.304380\pi\)
\(398\) 18.5869 0.931677
\(399\) −41.9585 −2.10055
\(400\) 1.00000 0.0500000
\(401\) −30.9372 −1.54493 −0.772465 0.635057i \(-0.780977\pi\)
−0.772465 + 0.635057i \(0.780977\pi\)
\(402\) 24.5221 1.22305
\(403\) −5.05779 −0.251947
\(404\) −9.08953 −0.452221
\(405\) 1.69886 0.0844169
\(406\) 24.5286 1.21733
\(407\) −29.6285 −1.46863
\(408\) −19.2371 −0.952376
\(409\) 0.576257 0.0284941 0.0142470 0.999899i \(-0.495465\pi\)
0.0142470 + 0.999899i \(0.495465\pi\)
\(410\) −3.15936 −0.156030
\(411\) 37.7963 1.86435
\(412\) 1.49900 0.0738504
\(413\) 8.90839 0.438353
\(414\) 0 0
\(415\) −0.319840 −0.0157003
\(416\) 2.45989 0.120606
\(417\) −9.80118 −0.479966
\(418\) −15.0705 −0.737122
\(419\) 7.93865 0.387828 0.193914 0.981018i \(-0.437882\pi\)
0.193914 + 0.981018i \(0.437882\pi\)
\(420\) −12.2561 −0.598038
\(421\) 3.08985 0.150590 0.0752951 0.997161i \(-0.476010\pi\)
0.0752951 + 0.997161i \(0.476010\pi\)
\(422\) 4.90443 0.238744
\(423\) 28.4036 1.38103
\(424\) −1.99036 −0.0966603
\(425\) −6.98238 −0.338695
\(426\) −29.9492 −1.45105
\(427\) −61.4085 −2.97176
\(428\) −17.7755 −0.859211
\(429\) 29.8339 1.44040
\(430\) 2.76141 0.133167
\(431\) 3.77328 0.181752 0.0908762 0.995862i \(-0.471033\pi\)
0.0908762 + 0.995862i \(0.471033\pi\)
\(432\) 4.38194 0.210826
\(433\) 8.51858 0.409377 0.204689 0.978827i \(-0.434382\pi\)
0.204689 + 0.978827i \(0.434382\pi\)
\(434\) −9.14670 −0.439055
\(435\) −15.1911 −0.728357
\(436\) 18.9672 0.908364
\(437\) 0 0
\(438\) −23.6261 −1.12890
\(439\) −31.7255 −1.51417 −0.757087 0.653314i \(-0.773378\pi\)
−0.757087 + 0.653314i \(0.773378\pi\)
\(440\) −4.40211 −0.209862
\(441\) 58.7104 2.79573
\(442\) −17.1759 −0.816972
\(443\) 3.57155 0.169690 0.0848448 0.996394i \(-0.472961\pi\)
0.0848448 + 0.996394i \(0.472961\pi\)
\(444\) −18.5432 −0.880020
\(445\) −8.69820 −0.412334
\(446\) 9.71984 0.460248
\(447\) −23.8472 −1.12794
\(448\) 4.44855 0.210174
\(449\) 31.6916 1.49562 0.747810 0.663913i \(-0.231106\pi\)
0.747810 + 0.663913i \(0.231106\pi\)
\(450\) 4.59049 0.216398
\(451\) 13.9079 0.654896
\(452\) −3.38804 −0.159360
\(453\) −4.85915 −0.228303
\(454\) 21.5002 1.00905
\(455\) −10.9429 −0.513012
\(456\) −9.43196 −0.441692
\(457\) −35.5083 −1.66101 −0.830503 0.557014i \(-0.811947\pi\)
−0.830503 + 0.557014i \(0.811947\pi\)
\(458\) −5.38568 −0.251656
\(459\) −30.5964 −1.42812
\(460\) 0 0
\(461\) −35.4649 −1.65177 −0.825883 0.563842i \(-0.809323\pi\)
−0.825883 + 0.563842i \(0.809323\pi\)
\(462\) 53.9528 2.51011
\(463\) 3.37272 0.156744 0.0783719 0.996924i \(-0.475028\pi\)
0.0783719 + 0.996924i \(0.475028\pi\)
\(464\) 5.51384 0.255974
\(465\) 5.66475 0.262697
\(466\) −29.3533 −1.35976
\(467\) 17.6398 0.816273 0.408136 0.912921i \(-0.366179\pi\)
0.408136 + 0.912921i \(0.366179\pi\)
\(468\) 11.2921 0.521977
\(469\) 39.5951 1.82833
\(470\) −6.18748 −0.285407
\(471\) −34.7183 −1.59973
\(472\) 2.00254 0.0921744
\(473\) −12.1560 −0.558935
\(474\) −32.6829 −1.50118
\(475\) −3.42347 −0.157080
\(476\) −31.0614 −1.42370
\(477\) −9.13673 −0.418342
\(478\) −8.09013 −0.370034
\(479\) −31.4181 −1.43553 −0.717766 0.696285i \(-0.754835\pi\)
−0.717766 + 0.696285i \(0.754835\pi\)
\(480\) −2.75508 −0.125752
\(481\) −16.5563 −0.754904
\(482\) 11.4116 0.519786
\(483\) 0 0
\(484\) 8.37857 0.380844
\(485\) −7.30395 −0.331655
\(486\) −17.8263 −0.808618
\(487\) −2.67284 −0.121118 −0.0605590 0.998165i \(-0.519288\pi\)
−0.0605590 + 0.998165i \(0.519288\pi\)
\(488\) −13.8042 −0.624885
\(489\) 5.72170 0.258744
\(490\) −12.7896 −0.577774
\(491\) 6.39355 0.288537 0.144268 0.989539i \(-0.453917\pi\)
0.144268 + 0.989539i \(0.453917\pi\)
\(492\) 8.70432 0.392421
\(493\) −38.4997 −1.73394
\(494\) −8.42135 −0.378895
\(495\) −20.2078 −0.908275
\(496\) −2.05611 −0.0923220
\(497\) −48.3581 −2.16916
\(498\) 0.881185 0.0394868
\(499\) −2.98791 −0.133757 −0.0668785 0.997761i \(-0.521304\pi\)
−0.0668785 + 0.997761i \(0.521304\pi\)
\(500\) −1.00000 −0.0447214
\(501\) 9.60214 0.428992
\(502\) 11.7941 0.526396
\(503\) −32.6689 −1.45663 −0.728316 0.685241i \(-0.759697\pi\)
−0.728316 + 0.685241i \(0.759697\pi\)
\(504\) 20.4210 0.909624
\(505\) 9.08953 0.404479
\(506\) 0 0
\(507\) −19.1450 −0.850259
\(508\) −5.73551 −0.254472
\(509\) 6.90839 0.306209 0.153105 0.988210i \(-0.451073\pi\)
0.153105 + 0.988210i \(0.451073\pi\)
\(510\) 19.2371 0.851831
\(511\) −38.1483 −1.68758
\(512\) 1.00000 0.0441942
\(513\) −15.0015 −0.662331
\(514\) 2.03939 0.0899538
\(515\) −1.49900 −0.0660538
\(516\) −7.60792 −0.334920
\(517\) 27.2380 1.19792
\(518\) −29.9411 −1.31554
\(519\) 63.8350 2.80205
\(520\) −2.45989 −0.107873
\(521\) −25.5985 −1.12149 −0.560746 0.827988i \(-0.689485\pi\)
−0.560746 + 0.827988i \(0.689485\pi\)
\(522\) 25.3112 1.10784
\(523\) −38.7838 −1.69590 −0.847948 0.530080i \(-0.822162\pi\)
−0.847948 + 0.530080i \(0.822162\pi\)
\(524\) −10.6514 −0.465310
\(525\) 12.2561 0.534901
\(526\) 24.7269 1.07815
\(527\) 14.3565 0.625380
\(528\) 12.1282 0.527811
\(529\) 0 0
\(530\) 1.99036 0.0864556
\(531\) 9.19264 0.398927
\(532\) −15.2295 −0.660282
\(533\) 7.77168 0.336629
\(534\) 23.9643 1.03704
\(535\) 17.7755 0.768501
\(536\) 8.90067 0.384451
\(537\) 3.48803 0.150520
\(538\) 14.4785 0.624213
\(539\) 56.3011 2.42506
\(540\) −4.38194 −0.188569
\(541\) −12.2853 −0.528186 −0.264093 0.964497i \(-0.585073\pi\)
−0.264093 + 0.964497i \(0.585073\pi\)
\(542\) 19.7153 0.846847
\(543\) −50.6188 −2.17226
\(544\) −6.98238 −0.299367
\(545\) −18.9672 −0.812465
\(546\) 30.1487 1.29024
\(547\) −40.4153 −1.72803 −0.864016 0.503465i \(-0.832058\pi\)
−0.864016 + 0.503465i \(0.832058\pi\)
\(548\) 13.7187 0.586035
\(549\) −63.3679 −2.70448
\(550\) 4.40211 0.187707
\(551\) −18.8765 −0.804165
\(552\) 0 0
\(553\) −52.7720 −2.24409
\(554\) −22.7803 −0.967843
\(555\) 18.5432 0.787114
\(556\) −3.55749 −0.150871
\(557\) 20.7658 0.879874 0.439937 0.898029i \(-0.355001\pi\)
0.439937 + 0.898029i \(0.355001\pi\)
\(558\) −9.43855 −0.399566
\(559\) −6.79275 −0.287303
\(560\) −4.44855 −0.187985
\(561\) −84.6836 −3.57534
\(562\) 13.2608 0.559373
\(563\) −9.46288 −0.398813 −0.199406 0.979917i \(-0.563901\pi\)
−0.199406 + 0.979917i \(0.563901\pi\)
\(564\) 17.0470 0.717809
\(565\) 3.38804 0.142536
\(566\) 7.87321 0.330936
\(567\) −7.55744 −0.317383
\(568\) −10.8705 −0.456118
\(569\) 21.9043 0.918276 0.459138 0.888365i \(-0.348158\pi\)
0.459138 + 0.888365i \(0.348158\pi\)
\(570\) 9.43196 0.395061
\(571\) 15.5220 0.649575 0.324788 0.945787i \(-0.394707\pi\)
0.324788 + 0.945787i \(0.394707\pi\)
\(572\) 10.8287 0.452770
\(573\) 16.0929 0.672291
\(574\) 14.0546 0.586627
\(575\) 0 0
\(576\) 4.59049 0.191271
\(577\) −42.9640 −1.78862 −0.894308 0.447452i \(-0.852331\pi\)
−0.894308 + 0.447452i \(0.852331\pi\)
\(578\) 31.7536 1.32078
\(579\) −2.00142 −0.0831764
\(580\) −5.51384 −0.228950
\(581\) 1.42282 0.0590286
\(582\) 20.1230 0.834125
\(583\) −8.76178 −0.362876
\(584\) −8.57546 −0.354855
\(585\) −11.2921 −0.466870
\(586\) 10.7456 0.443895
\(587\) 35.7584 1.47591 0.737954 0.674852i \(-0.235792\pi\)
0.737954 + 0.674852i \(0.235792\pi\)
\(588\) 35.2363 1.45312
\(589\) 7.03903 0.290038
\(590\) −2.00254 −0.0824433
\(591\) 27.8802 1.14684
\(592\) −6.73053 −0.276623
\(593\) −35.7883 −1.46965 −0.734824 0.678258i \(-0.762735\pi\)
−0.734824 + 0.678258i \(0.762735\pi\)
\(594\) 19.2898 0.791469
\(595\) 31.0614 1.27339
\(596\) −8.65572 −0.354552
\(597\) 51.2085 2.09582
\(598\) 0 0
\(599\) 43.5055 1.77759 0.888794 0.458307i \(-0.151544\pi\)
0.888794 + 0.458307i \(0.151544\pi\)
\(600\) 2.75508 0.112476
\(601\) −34.9867 −1.42714 −0.713569 0.700585i \(-0.752923\pi\)
−0.713569 + 0.700585i \(0.752923\pi\)
\(602\) −12.2843 −0.500669
\(603\) 40.8585 1.66389
\(604\) −1.76370 −0.0717640
\(605\) −8.37857 −0.340637
\(606\) −25.0424 −1.01728
\(607\) 18.5267 0.751974 0.375987 0.926625i \(-0.377304\pi\)
0.375987 + 0.926625i \(0.377304\pi\)
\(608\) −3.42347 −0.138840
\(609\) 67.5783 2.73841
\(610\) 13.8042 0.558914
\(611\) 15.2205 0.615755
\(612\) −32.0526 −1.29565
\(613\) 16.0330 0.647568 0.323784 0.946131i \(-0.395045\pi\)
0.323784 + 0.946131i \(0.395045\pi\)
\(614\) 1.33735 0.0539711
\(615\) −8.70432 −0.350992
\(616\) 19.5830 0.789021
\(617\) 11.4406 0.460581 0.230291 0.973122i \(-0.426032\pi\)
0.230291 + 0.973122i \(0.426032\pi\)
\(618\) 4.12987 0.166128
\(619\) −9.90379 −0.398067 −0.199033 0.979993i \(-0.563780\pi\)
−0.199033 + 0.979993i \(0.563780\pi\)
\(620\) 2.05611 0.0825753
\(621\) 0 0
\(622\) 7.12911 0.285851
\(623\) 38.6944 1.55026
\(624\) 6.77719 0.271305
\(625\) 1.00000 0.0400000
\(626\) −13.1855 −0.526999
\(627\) −41.5205 −1.65817
\(628\) −12.6015 −0.502856
\(629\) 46.9951 1.87382
\(630\) −20.4210 −0.813593
\(631\) −23.1560 −0.921828 −0.460914 0.887445i \(-0.652478\pi\)
−0.460914 + 0.887445i \(0.652478\pi\)
\(632\) −11.8628 −0.471875
\(633\) 13.5121 0.537058
\(634\) 11.9822 0.475875
\(635\) 5.73551 0.227607
\(636\) −5.48361 −0.217439
\(637\) 31.4609 1.24652
\(638\) 24.2725 0.960958
\(639\) −49.9011 −1.97406
\(640\) −1.00000 −0.0395285
\(641\) 10.8851 0.429938 0.214969 0.976621i \(-0.431035\pi\)
0.214969 + 0.976621i \(0.431035\pi\)
\(642\) −48.9730 −1.93281
\(643\) −38.3078 −1.51071 −0.755356 0.655315i \(-0.772536\pi\)
−0.755356 + 0.655315i \(0.772536\pi\)
\(644\) 0 0
\(645\) 7.60792 0.299561
\(646\) 23.9040 0.940490
\(647\) −31.6382 −1.24382 −0.621912 0.783087i \(-0.713644\pi\)
−0.621912 + 0.783087i \(0.713644\pi\)
\(648\) −1.69886 −0.0667374
\(649\) 8.81540 0.346035
\(650\) 2.45989 0.0964846
\(651\) −25.1999 −0.987663
\(652\) 2.07678 0.0813329
\(653\) −21.8844 −0.856404 −0.428202 0.903683i \(-0.640853\pi\)
−0.428202 + 0.903683i \(0.640853\pi\)
\(654\) 52.2562 2.04338
\(655\) 10.6514 0.416186
\(656\) 3.15936 0.123352
\(657\) −39.3656 −1.53580
\(658\) 27.5253 1.07305
\(659\) 14.4063 0.561191 0.280595 0.959826i \(-0.409468\pi\)
0.280595 + 0.959826i \(0.409468\pi\)
\(660\) −12.1282 −0.472089
\(661\) −2.90302 −0.112914 −0.0564571 0.998405i \(-0.517980\pi\)
−0.0564571 + 0.998405i \(0.517980\pi\)
\(662\) 11.5934 0.450589
\(663\) −47.3209 −1.83779
\(664\) 0.319840 0.0124122
\(665\) 15.2295 0.590574
\(666\) −30.8964 −1.19721
\(667\) 0 0
\(668\) 3.48524 0.134848
\(669\) 26.7790 1.03533
\(670\) −8.90067 −0.343863
\(671\) −60.7674 −2.34590
\(672\) 12.2561 0.472790
\(673\) 13.9422 0.537433 0.268717 0.963219i \(-0.413400\pi\)
0.268717 + 0.963219i \(0.413400\pi\)
\(674\) 6.87330 0.264749
\(675\) 4.38194 0.168661
\(676\) −6.94896 −0.267268
\(677\) −14.1958 −0.545591 −0.272795 0.962072i \(-0.587948\pi\)
−0.272795 + 0.962072i \(0.587948\pi\)
\(678\) −9.33434 −0.358483
\(679\) 32.4919 1.24693
\(680\) 6.98238 0.267762
\(681\) 59.2349 2.26988
\(682\) −9.05122 −0.346589
\(683\) −0.587432 −0.0224775 −0.0112387 0.999937i \(-0.503577\pi\)
−0.0112387 + 0.999937i \(0.503577\pi\)
\(684\) −15.7154 −0.600894
\(685\) −13.7187 −0.524166
\(686\) 25.7551 0.983336
\(687\) −14.8380 −0.566105
\(688\) −2.76141 −0.105278
\(689\) −4.89605 −0.186525
\(690\) 0 0
\(691\) −37.3834 −1.42213 −0.711066 0.703126i \(-0.751787\pi\)
−0.711066 + 0.703126i \(0.751787\pi\)
\(692\) 23.1699 0.880787
\(693\) 89.8955 3.41485
\(694\) 5.76727 0.218923
\(695\) 3.55749 0.134943
\(696\) 15.1911 0.575817
\(697\) −22.0599 −0.835578
\(698\) −16.4626 −0.623117
\(699\) −80.8707 −3.05881
\(700\) 4.44855 0.168139
\(701\) 18.6885 0.705857 0.352928 0.935650i \(-0.385186\pi\)
0.352928 + 0.935650i \(0.385186\pi\)
\(702\) 10.7791 0.406830
\(703\) 23.0418 0.869037
\(704\) 4.40211 0.165911
\(705\) −17.0470 −0.642028
\(706\) −22.8572 −0.860243
\(707\) −40.4352 −1.52072
\(708\) 5.51717 0.207348
\(709\) 41.3053 1.55125 0.775627 0.631192i \(-0.217434\pi\)
0.775627 + 0.631192i \(0.217434\pi\)
\(710\) 10.8705 0.407964
\(711\) −54.4559 −2.04226
\(712\) 8.69820 0.325979
\(713\) 0 0
\(714\) −85.5769 −3.20264
\(715\) −10.8287 −0.404970
\(716\) 1.26603 0.0473139
\(717\) −22.2890 −0.832397
\(718\) 21.1272 0.788461
\(719\) 36.3270 1.35477 0.677383 0.735630i \(-0.263114\pi\)
0.677383 + 0.735630i \(0.263114\pi\)
\(720\) −4.59049 −0.171078
\(721\) 6.66837 0.248343
\(722\) −7.27983 −0.270927
\(723\) 31.4400 1.16927
\(724\) −18.3728 −0.682822
\(725\) 5.51384 0.204779
\(726\) 23.0837 0.856715
\(727\) −5.17645 −0.191984 −0.0959920 0.995382i \(-0.530602\pi\)
−0.0959920 + 0.995382i \(0.530602\pi\)
\(728\) 10.9429 0.405571
\(729\) −44.0165 −1.63024
\(730\) 8.57546 0.317392
\(731\) 19.2812 0.713141
\(732\) −38.0316 −1.40569
\(733\) −3.74165 −0.138201 −0.0691006 0.997610i \(-0.522013\pi\)
−0.0691006 + 0.997610i \(0.522013\pi\)
\(734\) 12.1222 0.447438
\(735\) −35.2363 −1.29971
\(736\) 0 0
\(737\) 39.1817 1.44328
\(738\) 14.5030 0.533864
\(739\) −15.7153 −0.578097 −0.289049 0.957314i \(-0.593339\pi\)
−0.289049 + 0.957314i \(0.593339\pi\)
\(740\) 6.73053 0.247419
\(741\) −23.2015 −0.852330
\(742\) −8.85420 −0.325048
\(743\) 48.5703 1.78187 0.890936 0.454130i \(-0.150050\pi\)
0.890936 + 0.454130i \(0.150050\pi\)
\(744\) −5.66475 −0.207680
\(745\) 8.65572 0.317121
\(746\) −18.1236 −0.663551
\(747\) 1.46822 0.0537194
\(748\) −30.7372 −1.12386
\(749\) −79.0751 −2.88934
\(750\) −2.75508 −0.100601
\(751\) −36.1176 −1.31795 −0.658975 0.752165i \(-0.729010\pi\)
−0.658975 + 0.752165i \(0.729010\pi\)
\(752\) 6.18748 0.225634
\(753\) 32.4937 1.18414
\(754\) 13.5634 0.493950
\(755\) 1.76370 0.0641877
\(756\) 19.4933 0.708963
\(757\) 16.6016 0.603397 0.301698 0.953403i \(-0.402446\pi\)
0.301698 + 0.953403i \(0.402446\pi\)
\(758\) 18.0644 0.656129
\(759\) 0 0
\(760\) 3.42347 0.124182
\(761\) −10.6287 −0.385291 −0.192645 0.981268i \(-0.561707\pi\)
−0.192645 + 0.981268i \(0.561707\pi\)
\(762\) −15.8018 −0.572440
\(763\) 84.3764 3.05463
\(764\) 5.84116 0.211326
\(765\) 32.0526 1.15886
\(766\) 20.5709 0.743256
\(767\) 4.92602 0.177868
\(768\) 2.75508 0.0994156
\(769\) −42.5639 −1.53489 −0.767446 0.641113i \(-0.778473\pi\)
−0.767446 + 0.641113i \(0.778473\pi\)
\(770\) −19.5830 −0.705722
\(771\) 5.61870 0.202353
\(772\) −0.726448 −0.0261454
\(773\) −23.6457 −0.850475 −0.425238 0.905082i \(-0.639810\pi\)
−0.425238 + 0.905082i \(0.639810\pi\)
\(774\) −12.6762 −0.455638
\(775\) −2.05611 −0.0738576
\(776\) 7.30395 0.262196
\(777\) −82.4902 −2.95932
\(778\) −4.21880 −0.151251
\(779\) −10.8160 −0.387523
\(780\) −6.77719 −0.242662
\(781\) −47.8533 −1.71233
\(782\) 0 0
\(783\) 24.1613 0.863455
\(784\) 12.7896 0.456770
\(785\) 12.6015 0.449768
\(786\) −29.3456 −1.04672
\(787\) −47.0801 −1.67822 −0.839112 0.543959i \(-0.816925\pi\)
−0.839112 + 0.543959i \(0.816925\pi\)
\(788\) 10.1195 0.360493
\(789\) 68.1248 2.42531
\(790\) 11.8628 0.422058
\(791\) −15.0719 −0.535893
\(792\) 20.2078 0.718055
\(793\) −33.9567 −1.20584
\(794\) 22.9773 0.815433
\(795\) 5.48361 0.194483
\(796\) 18.5869 0.658795
\(797\) −15.0160 −0.531894 −0.265947 0.963988i \(-0.585685\pi\)
−0.265947 + 0.963988i \(0.585685\pi\)
\(798\) −41.9585 −1.48531
\(799\) −43.2033 −1.52842
\(800\) 1.00000 0.0353553
\(801\) 39.9290 1.41082
\(802\) −30.9372 −1.09243
\(803\) −37.7501 −1.33217
\(804\) 24.5221 0.864828
\(805\) 0 0
\(806\) −5.05779 −0.178153
\(807\) 39.8895 1.40418
\(808\) −9.08953 −0.319769
\(809\) −47.7657 −1.67935 −0.839675 0.543088i \(-0.817255\pi\)
−0.839675 + 0.543088i \(0.817255\pi\)
\(810\) 1.69886 0.0596917
\(811\) 55.8820 1.96228 0.981142 0.193289i \(-0.0619154\pi\)
0.981142 + 0.193289i \(0.0619154\pi\)
\(812\) 24.5286 0.860784
\(813\) 54.3174 1.90500
\(814\) −29.6285 −1.03848
\(815\) −2.07678 −0.0727464
\(816\) −19.2371 −0.673431
\(817\) 9.45361 0.330740
\(818\) 0.576257 0.0201484
\(819\) 50.2334 1.75530
\(820\) −3.15936 −0.110330
\(821\) −7.19232 −0.251014 −0.125507 0.992093i \(-0.540056\pi\)
−0.125507 + 0.992093i \(0.540056\pi\)
\(822\) 37.7963 1.31830
\(823\) 12.3438 0.430278 0.215139 0.976583i \(-0.430980\pi\)
0.215139 + 0.976583i \(0.430980\pi\)
\(824\) 1.49900 0.0522201
\(825\) 12.1282 0.422249
\(826\) 8.90839 0.309963
\(827\) 48.0835 1.67203 0.836013 0.548710i \(-0.184881\pi\)
0.836013 + 0.548710i \(0.184881\pi\)
\(828\) 0 0
\(829\) 36.8346 1.27932 0.639658 0.768659i \(-0.279076\pi\)
0.639658 + 0.768659i \(0.279076\pi\)
\(830\) −0.319840 −0.0111018
\(831\) −62.7617 −2.17718
\(832\) 2.45989 0.0852812
\(833\) −89.3016 −3.09412
\(834\) −9.80118 −0.339387
\(835\) −3.48524 −0.120612
\(836\) −15.0705 −0.521224
\(837\) −9.00975 −0.311422
\(838\) 7.93865 0.274236
\(839\) −15.9647 −0.551164 −0.275582 0.961278i \(-0.588870\pi\)
−0.275582 + 0.961278i \(0.588870\pi\)
\(840\) −12.2561 −0.422876
\(841\) 1.40242 0.0483595
\(842\) 3.08985 0.106483
\(843\) 36.5346 1.25832
\(844\) 4.90443 0.168817
\(845\) 6.94896 0.239052
\(846\) 28.4036 0.976535
\(847\) 37.2724 1.28070
\(848\) −1.99036 −0.0683492
\(849\) 21.6914 0.744446
\(850\) −6.98238 −0.239494
\(851\) 0 0
\(852\) −29.9492 −1.02604
\(853\) 28.0441 0.960213 0.480107 0.877210i \(-0.340598\pi\)
0.480107 + 0.877210i \(0.340598\pi\)
\(854\) −61.4085 −2.10135
\(855\) 15.7154 0.537456
\(856\) −17.7755 −0.607554
\(857\) −4.37547 −0.149463 −0.0747316 0.997204i \(-0.523810\pi\)
−0.0747316 + 0.997204i \(0.523810\pi\)
\(858\) 29.8339 1.01851
\(859\) −6.77691 −0.231225 −0.115613 0.993294i \(-0.536883\pi\)
−0.115613 + 0.993294i \(0.536883\pi\)
\(860\) 2.76141 0.0941633
\(861\) 38.7216 1.31963
\(862\) 3.77328 0.128518
\(863\) 25.2591 0.859830 0.429915 0.902869i \(-0.358544\pi\)
0.429915 + 0.902869i \(0.358544\pi\)
\(864\) 4.38194 0.149077
\(865\) −23.1699 −0.787800
\(866\) 8.51858 0.289473
\(867\) 87.4840 2.97111
\(868\) −9.14670 −0.310459
\(869\) −52.2211 −1.77148
\(870\) −15.1911 −0.515026
\(871\) 21.8946 0.741872
\(872\) 18.9672 0.642310
\(873\) 33.5287 1.13478
\(874\) 0 0
\(875\) −4.44855 −0.150388
\(876\) −23.6261 −0.798253
\(877\) 56.1429 1.89581 0.947906 0.318550i \(-0.103196\pi\)
0.947906 + 0.318550i \(0.103196\pi\)
\(878\) −31.7255 −1.07068
\(879\) 29.6050 0.998550
\(880\) −4.40211 −0.148395
\(881\) −16.0725 −0.541497 −0.270749 0.962650i \(-0.587271\pi\)
−0.270749 + 0.962650i \(0.587271\pi\)
\(882\) 58.7104 1.97688
\(883\) −51.9366 −1.74781 −0.873903 0.486100i \(-0.838419\pi\)
−0.873903 + 0.486100i \(0.838419\pi\)
\(884\) −17.1759 −0.577687
\(885\) −5.51717 −0.185458
\(886\) 3.57155 0.119989
\(887\) 9.49221 0.318717 0.159359 0.987221i \(-0.449057\pi\)
0.159359 + 0.987221i \(0.449057\pi\)
\(888\) −18.5432 −0.622268
\(889\) −25.5147 −0.855736
\(890\) −8.69820 −0.291564
\(891\) −7.47855 −0.250541
\(892\) 9.71984 0.325444
\(893\) −21.1827 −0.708851
\(894\) −23.8472 −0.797571
\(895\) −1.26603 −0.0423189
\(896\) 4.44855 0.148615
\(897\) 0 0
\(898\) 31.6916 1.05756
\(899\) −11.3371 −0.378112
\(900\) 4.59049 0.153016
\(901\) 13.8974 0.462991
\(902\) 13.9079 0.463081
\(903\) −33.8442 −1.12626
\(904\) −3.38804 −0.112685
\(905\) 18.3728 0.610734
\(906\) −4.85915 −0.161434
\(907\) 22.6681 0.752680 0.376340 0.926482i \(-0.377182\pi\)
0.376340 + 0.926482i \(0.377182\pi\)
\(908\) 21.5002 0.713509
\(909\) −41.7254 −1.38394
\(910\) −10.9429 −0.362754
\(911\) 18.0437 0.597815 0.298908 0.954282i \(-0.403378\pi\)
0.298908 + 0.954282i \(0.403378\pi\)
\(912\) −9.43196 −0.312323
\(913\) 1.40797 0.0465970
\(914\) −35.5083 −1.17451
\(915\) 38.0316 1.25729
\(916\) −5.38568 −0.177948
\(917\) −47.3834 −1.56474
\(918\) −30.5964 −1.00983
\(919\) −3.42259 −0.112901 −0.0564505 0.998405i \(-0.517978\pi\)
−0.0564505 + 0.998405i \(0.517978\pi\)
\(920\) 0 0
\(921\) 3.68451 0.121409
\(922\) −35.4649 −1.16797
\(923\) −26.7403 −0.880167
\(924\) 53.9528 1.77492
\(925\) −6.73053 −0.221298
\(926\) 3.37272 0.110835
\(927\) 6.88115 0.226007
\(928\) 5.51384 0.181001
\(929\) 5.28457 0.173381 0.0866906 0.996235i \(-0.472371\pi\)
0.0866906 + 0.996235i \(0.472371\pi\)
\(930\) 5.66475 0.185755
\(931\) −43.7847 −1.43499
\(932\) −29.3533 −0.961498
\(933\) 19.6413 0.643028
\(934\) 17.6398 0.577192
\(935\) 30.7372 1.00521
\(936\) 11.2921 0.369093
\(937\) −9.57867 −0.312921 −0.156461 0.987684i \(-0.550008\pi\)
−0.156461 + 0.987684i \(0.550008\pi\)
\(938\) 39.5951 1.29282
\(939\) −36.3272 −1.18549
\(940\) −6.18748 −0.201813
\(941\) −18.7350 −0.610744 −0.305372 0.952233i \(-0.598781\pi\)
−0.305372 + 0.952233i \(0.598781\pi\)
\(942\) −34.7183 −1.13118
\(943\) 0 0
\(944\) 2.00254 0.0651771
\(945\) −19.4933 −0.634116
\(946\) −12.1560 −0.395226
\(947\) 48.5733 1.57842 0.789211 0.614122i \(-0.210490\pi\)
0.789211 + 0.614122i \(0.210490\pi\)
\(948\) −32.6829 −1.06149
\(949\) −21.0947 −0.684761
\(950\) −3.42347 −0.111072
\(951\) 33.0120 1.07049
\(952\) −31.0614 −1.00671
\(953\) 3.40802 0.110397 0.0551983 0.998475i \(-0.482421\pi\)
0.0551983 + 0.998475i \(0.482421\pi\)
\(954\) −9.13673 −0.295812
\(955\) −5.84116 −0.189016
\(956\) −8.09013 −0.261653
\(957\) 66.8729 2.16169
\(958\) −31.4181 −1.01507
\(959\) 61.0284 1.97071
\(960\) −2.75508 −0.0889200
\(961\) −26.7724 −0.863626
\(962\) −16.5563 −0.533798
\(963\) −81.5982 −2.62947
\(964\) 11.4116 0.367544
\(965\) 0.726448 0.0233852
\(966\) 0 0
\(967\) −13.2945 −0.427524 −0.213762 0.976886i \(-0.568572\pi\)
−0.213762 + 0.976886i \(0.568572\pi\)
\(968\) 8.37857 0.269297
\(969\) 65.8575 2.11565
\(970\) −7.30395 −0.234516
\(971\) −9.61364 −0.308516 −0.154258 0.988031i \(-0.549299\pi\)
−0.154258 + 0.988031i \(0.549299\pi\)
\(972\) −17.8263 −0.571779
\(973\) −15.8256 −0.507347
\(974\) −2.67284 −0.0856434
\(975\) 6.77719 0.217044
\(976\) −13.8042 −0.441861
\(977\) −49.8942 −1.59626 −0.798129 0.602487i \(-0.794177\pi\)
−0.798129 + 0.602487i \(0.794177\pi\)
\(978\) 5.72170 0.182960
\(979\) 38.2904 1.22377
\(980\) −12.7896 −0.408548
\(981\) 87.0688 2.77989
\(982\) 6.39355 0.204026
\(983\) −28.8271 −0.919443 −0.459721 0.888063i \(-0.652051\pi\)
−0.459721 + 0.888063i \(0.652051\pi\)
\(984\) 8.70432 0.277484
\(985\) −10.1195 −0.322435
\(986\) −38.4997 −1.22608
\(987\) 75.8345 2.41384
\(988\) −8.42135 −0.267919
\(989\) 0 0
\(990\) −20.2078 −0.642248
\(991\) −6.23589 −0.198090 −0.0990448 0.995083i \(-0.531579\pi\)
−0.0990448 + 0.995083i \(0.531579\pi\)
\(992\) −2.05611 −0.0652815
\(993\) 31.9407 1.01361
\(994\) −48.3581 −1.53383
\(995\) −18.5869 −0.589244
\(996\) 0.881185 0.0279214
\(997\) −43.3422 −1.37266 −0.686330 0.727290i \(-0.740779\pi\)
−0.686330 + 0.727290i \(0.740779\pi\)
\(998\) −2.98791 −0.0945805
\(999\) −29.4928 −0.933110
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 5290.2.a.bk.1.12 15
23.3 even 11 230.2.g.d.101.1 yes 30
23.8 even 11 230.2.g.d.41.1 30
23.22 odd 2 5290.2.a.bl.1.12 15
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
230.2.g.d.41.1 30 23.8 even 11
230.2.g.d.101.1 yes 30 23.3 even 11
5290.2.a.bk.1.12 15 1.1 even 1 trivial
5290.2.a.bl.1.12 15 23.22 odd 2