Properties

Label 8043.2.a.o.1.18
Level $8043$
Weight $2$
Character 8043.1
Self dual yes
Analytic conductor $64.224$
Analytic rank $1$
Dimension $41$
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] = [8043,2,Mod(1,8043)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(8043, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 0, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("8043.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 8043 = 3 \cdot 7 \cdot 383 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 8043.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: \(64.2236783457\)
Analytic rank: \(1\)
Dimension: \(41\)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.18
Character \(\chi\) \(=\) 8043.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-0.555636 q^{2} -1.00000 q^{3} -1.69127 q^{4} -1.46250 q^{5} +0.555636 q^{6} +1.00000 q^{7} +2.05100 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q-0.555636 q^{2} -1.00000 q^{3} -1.69127 q^{4} -1.46250 q^{5} +0.555636 q^{6} +1.00000 q^{7} +2.05100 q^{8} +1.00000 q^{9} +0.812618 q^{10} +4.65121 q^{11} +1.69127 q^{12} -1.76814 q^{13} -0.555636 q^{14} +1.46250 q^{15} +2.24292 q^{16} +0.856481 q^{17} -0.555636 q^{18} +1.84003 q^{19} +2.47348 q^{20} -1.00000 q^{21} -2.58438 q^{22} -5.80371 q^{23} -2.05100 q^{24} -2.86110 q^{25} +0.982444 q^{26} -1.00000 q^{27} -1.69127 q^{28} +3.84513 q^{29} -0.812618 q^{30} +0.134605 q^{31} -5.34826 q^{32} -4.65121 q^{33} -0.475892 q^{34} -1.46250 q^{35} -1.69127 q^{36} -5.11266 q^{37} -1.02239 q^{38} +1.76814 q^{39} -2.99959 q^{40} -7.45941 q^{41} +0.555636 q^{42} +4.27274 q^{43} -7.86644 q^{44} -1.46250 q^{45} +3.22475 q^{46} +0.949635 q^{47} -2.24292 q^{48} +1.00000 q^{49} +1.58973 q^{50} -0.856481 q^{51} +2.99040 q^{52} +0.392595 q^{53} +0.555636 q^{54} -6.80239 q^{55} +2.05100 q^{56} -1.84003 q^{57} -2.13650 q^{58} +1.60517 q^{59} -2.47348 q^{60} +15.5098 q^{61} -0.0747912 q^{62} +1.00000 q^{63} -1.51416 q^{64} +2.58591 q^{65} +2.58438 q^{66} -12.8432 q^{67} -1.44854 q^{68} +5.80371 q^{69} +0.812618 q^{70} -3.57750 q^{71} +2.05100 q^{72} +2.62361 q^{73} +2.84078 q^{74} +2.86110 q^{75} -3.11198 q^{76} +4.65121 q^{77} -0.982444 q^{78} -2.90361 q^{79} -3.28028 q^{80} +1.00000 q^{81} +4.14472 q^{82} -11.0965 q^{83} +1.69127 q^{84} -1.25260 q^{85} -2.37409 q^{86} -3.84513 q^{87} +9.53965 q^{88} -7.10905 q^{89} +0.812618 q^{90} -1.76814 q^{91} +9.81563 q^{92} -0.134605 q^{93} -0.527652 q^{94} -2.69104 q^{95} +5.34826 q^{96} -12.3661 q^{97} -0.555636 q^{98} +4.65121 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 41 q - 4 q^{2} - 41 q^{3} + 34 q^{4} + 5 q^{5} + 4 q^{6} + 41 q^{7} - 15 q^{8} + 41 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 41 q - 4 q^{2} - 41 q^{3} + 34 q^{4} + 5 q^{5} + 4 q^{6} + 41 q^{7} - 15 q^{8} + 41 q^{9} - 18 q^{10} - 17 q^{11} - 34 q^{12} - 38 q^{13} - 4 q^{14} - 5 q^{15} + 16 q^{16} + 4 q^{17} - 4 q^{18} - 15 q^{19} + 23 q^{20} - 41 q^{21} - 31 q^{22} - 8 q^{23} + 15 q^{24} + 16 q^{25} + 15 q^{26} - 41 q^{27} + 34 q^{28} - 27 q^{29} + 18 q^{30} - 23 q^{31} - 24 q^{32} + 17 q^{33} - 9 q^{34} + 5 q^{35} + 34 q^{36} - 81 q^{37} + 38 q^{39} - 52 q^{40} + 29 q^{41} + 4 q^{42} - 47 q^{43} - 20 q^{44} + 5 q^{45} - 40 q^{46} + 26 q^{47} - 16 q^{48} + 41 q^{49} - 23 q^{50} - 4 q^{51} - 64 q^{52} - 66 q^{53} + 4 q^{54} - 14 q^{55} - 15 q^{56} + 15 q^{57} - 50 q^{58} + 41 q^{59} - 23 q^{60} - 47 q^{61} + 5 q^{62} + 41 q^{63} - 37 q^{64} - 24 q^{65} + 31 q^{66} - 73 q^{67} + 10 q^{68} + 8 q^{69} - 18 q^{70} + q^{71} - 15 q^{72} - 14 q^{73} + 18 q^{74} - 16 q^{75} - 37 q^{76} - 17 q^{77} - 15 q^{78} - 80 q^{79} + 63 q^{80} + 41 q^{81} - 31 q^{82} + 20 q^{83} - 34 q^{84} - 82 q^{85} - 39 q^{86} + 27 q^{87} - 132 q^{88} + 17 q^{89} - 18 q^{90} - 38 q^{91} - 26 q^{92} + 23 q^{93} - 9 q^{94} - q^{95} + 24 q^{96} - 73 q^{97} - 4 q^{98} - 17 q^{99}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.555636 −0.392894 −0.196447 0.980514i \(-0.562940\pi\)
−0.196447 + 0.980514i \(0.562940\pi\)
\(3\) −1.00000 −0.577350
\(4\) −1.69127 −0.845634
\(5\) −1.46250 −0.654050 −0.327025 0.945016i \(-0.606046\pi\)
−0.327025 + 0.945016i \(0.606046\pi\)
\(6\) 0.555636 0.226838
\(7\) 1.00000 0.377964
\(8\) 2.05100 0.725139
\(9\) 1.00000 0.333333
\(10\) 0.812618 0.256972
\(11\) 4.65121 1.40239 0.701196 0.712968i \(-0.252650\pi\)
0.701196 + 0.712968i \(0.252650\pi\)
\(12\) 1.69127 0.488227
\(13\) −1.76814 −0.490394 −0.245197 0.969473i \(-0.578853\pi\)
−0.245197 + 0.969473i \(0.578853\pi\)
\(14\) −0.555636 −0.148500
\(15\) 1.46250 0.377616
\(16\) 2.24292 0.560731
\(17\) 0.856481 0.207727 0.103864 0.994592i \(-0.466879\pi\)
0.103864 + 0.994592i \(0.466879\pi\)
\(18\) −0.555636 −0.130965
\(19\) 1.84003 0.422132 0.211066 0.977472i \(-0.432307\pi\)
0.211066 + 0.977472i \(0.432307\pi\)
\(20\) 2.47348 0.553087
\(21\) −1.00000 −0.218218
\(22\) −2.58438 −0.550992
\(23\) −5.80371 −1.21016 −0.605079 0.796166i \(-0.706858\pi\)
−0.605079 + 0.796166i \(0.706858\pi\)
\(24\) −2.05100 −0.418659
\(25\) −2.86110 −0.572219
\(26\) 0.982444 0.192673
\(27\) −1.00000 −0.192450
\(28\) −1.69127 −0.319620
\(29\) 3.84513 0.714023 0.357012 0.934100i \(-0.383796\pi\)
0.357012 + 0.934100i \(0.383796\pi\)
\(30\) −0.812618 −0.148363
\(31\) 0.134605 0.0241757 0.0120878 0.999927i \(-0.496152\pi\)
0.0120878 + 0.999927i \(0.496152\pi\)
\(32\) −5.34826 −0.945447
\(33\) −4.65121 −0.809672
\(34\) −0.475892 −0.0816148
\(35\) −1.46250 −0.247208
\(36\) −1.69127 −0.281878
\(37\) −5.11266 −0.840515 −0.420258 0.907405i \(-0.638060\pi\)
−0.420258 + 0.907405i \(0.638060\pi\)
\(38\) −1.02239 −0.165853
\(39\) 1.76814 0.283129
\(40\) −2.99959 −0.474277
\(41\) −7.45941 −1.16496 −0.582482 0.812844i \(-0.697918\pi\)
−0.582482 + 0.812844i \(0.697918\pi\)
\(42\) 0.555636 0.0857366
\(43\) 4.27274 0.651586 0.325793 0.945441i \(-0.394369\pi\)
0.325793 + 0.945441i \(0.394369\pi\)
\(44\) −7.86644 −1.18591
\(45\) −1.46250 −0.218017
\(46\) 3.22475 0.475464
\(47\) 0.949635 0.138519 0.0692593 0.997599i \(-0.477936\pi\)
0.0692593 + 0.997599i \(0.477936\pi\)
\(48\) −2.24292 −0.323738
\(49\) 1.00000 0.142857
\(50\) 1.58973 0.224822
\(51\) −0.856481 −0.119931
\(52\) 2.99040 0.414694
\(53\) 0.392595 0.0539271 0.0269635 0.999636i \(-0.491416\pi\)
0.0269635 + 0.999636i \(0.491416\pi\)
\(54\) 0.555636 0.0756125
\(55\) −6.80239 −0.917234
\(56\) 2.05100 0.274077
\(57\) −1.84003 −0.243718
\(58\) −2.13650 −0.280536
\(59\) 1.60517 0.208976 0.104488 0.994526i \(-0.466680\pi\)
0.104488 + 0.994526i \(0.466680\pi\)
\(60\) −2.47348 −0.319325
\(61\) 15.5098 1.98583 0.992916 0.118818i \(-0.0379106\pi\)
0.992916 + 0.118818i \(0.0379106\pi\)
\(62\) −0.0747912 −0.00949849
\(63\) 1.00000 0.125988
\(64\) −1.51416 −0.189270
\(65\) 2.58591 0.320742
\(66\) 2.58438 0.318115
\(67\) −12.8432 −1.56905 −0.784523 0.620100i \(-0.787092\pi\)
−0.784523 + 0.620100i \(0.787092\pi\)
\(68\) −1.44854 −0.175661
\(69\) 5.80371 0.698685
\(70\) 0.812618 0.0971264
\(71\) −3.57750 −0.424572 −0.212286 0.977208i \(-0.568091\pi\)
−0.212286 + 0.977208i \(0.568091\pi\)
\(72\) 2.05100 0.241713
\(73\) 2.62361 0.307070 0.153535 0.988143i \(-0.450934\pi\)
0.153535 + 0.988143i \(0.450934\pi\)
\(74\) 2.84078 0.330234
\(75\) 2.86110 0.330371
\(76\) −3.11198 −0.356969
\(77\) 4.65121 0.530055
\(78\) −0.982444 −0.111240
\(79\) −2.90361 −0.326682 −0.163341 0.986570i \(-0.552227\pi\)
−0.163341 + 0.986570i \(0.552227\pi\)
\(80\) −3.28028 −0.366746
\(81\) 1.00000 0.111111
\(82\) 4.14472 0.457708
\(83\) −11.0965 −1.21800 −0.609000 0.793170i \(-0.708429\pi\)
−0.609000 + 0.793170i \(0.708429\pi\)
\(84\) 1.69127 0.184532
\(85\) −1.25260 −0.135864
\(86\) −2.37409 −0.256005
\(87\) −3.84513 −0.412242
\(88\) 9.53965 1.01693
\(89\) −7.10905 −0.753558 −0.376779 0.926303i \(-0.622968\pi\)
−0.376779 + 0.926303i \(0.622968\pi\)
\(90\) 0.812618 0.0856575
\(91\) −1.76814 −0.185352
\(92\) 9.81563 1.02335
\(93\) −0.134605 −0.0139578
\(94\) −0.527652 −0.0544231
\(95\) −2.69104 −0.276095
\(96\) 5.34826 0.545854
\(97\) −12.3661 −1.25559 −0.627793 0.778380i \(-0.716042\pi\)
−0.627793 + 0.778380i \(0.716042\pi\)
\(98\) −0.555636 −0.0561278
\(99\) 4.65121 0.467464
\(100\) 4.83888 0.483888
\(101\) −0.917518 −0.0912964 −0.0456482 0.998958i \(-0.514535\pi\)
−0.0456482 + 0.998958i \(0.514535\pi\)
\(102\) 0.475892 0.0471203
\(103\) 15.7448 1.55138 0.775691 0.631113i \(-0.217401\pi\)
0.775691 + 0.631113i \(0.217401\pi\)
\(104\) −3.62646 −0.355604
\(105\) 1.46250 0.142725
\(106\) −0.218140 −0.0211877
\(107\) 4.49317 0.434371 0.217186 0.976130i \(-0.430312\pi\)
0.217186 + 0.976130i \(0.430312\pi\)
\(108\) 1.69127 0.162742
\(109\) 2.12822 0.203847 0.101923 0.994792i \(-0.467500\pi\)
0.101923 + 0.994792i \(0.467500\pi\)
\(110\) 3.77966 0.360376
\(111\) 5.11266 0.485272
\(112\) 2.24292 0.211936
\(113\) 5.65973 0.532422 0.266211 0.963915i \(-0.414228\pi\)
0.266211 + 0.963915i \(0.414228\pi\)
\(114\) 1.02239 0.0957554
\(115\) 8.48792 0.791503
\(116\) −6.50315 −0.603803
\(117\) −1.76814 −0.163465
\(118\) −0.891893 −0.0821055
\(119\) 0.856481 0.0785135
\(120\) 2.99959 0.273824
\(121\) 10.6338 0.966705
\(122\) −8.61783 −0.780222
\(123\) 7.45941 0.672592
\(124\) −0.227652 −0.0204438
\(125\) 11.4968 1.02831
\(126\) −0.555636 −0.0495000
\(127\) −3.68860 −0.327311 −0.163655 0.986518i \(-0.552329\pi\)
−0.163655 + 0.986518i \(0.552329\pi\)
\(128\) 11.5378 1.01981
\(129\) −4.27274 −0.376193
\(130\) −1.43682 −0.126018
\(131\) 9.84593 0.860243 0.430121 0.902771i \(-0.358471\pi\)
0.430121 + 0.902771i \(0.358471\pi\)
\(132\) 7.86644 0.684686
\(133\) 1.84003 0.159551
\(134\) 7.13614 0.616469
\(135\) 1.46250 0.125872
\(136\) 1.75665 0.150631
\(137\) 2.63093 0.224775 0.112388 0.993664i \(-0.464150\pi\)
0.112388 + 0.993664i \(0.464150\pi\)
\(138\) −3.22475 −0.274509
\(139\) 21.1677 1.79542 0.897711 0.440584i \(-0.145229\pi\)
0.897711 + 0.440584i \(0.145229\pi\)
\(140\) 2.47348 0.209047
\(141\) −0.949635 −0.0799737
\(142\) 1.98779 0.166812
\(143\) −8.22400 −0.687725
\(144\) 2.24292 0.186910
\(145\) −5.62351 −0.467007
\(146\) −1.45777 −0.120646
\(147\) −1.00000 −0.0824786
\(148\) 8.64687 0.710768
\(149\) 23.6277 1.93566 0.967828 0.251615i \(-0.0809615\pi\)
0.967828 + 0.251615i \(0.0809615\pi\)
\(150\) −1.58973 −0.129801
\(151\) −4.20556 −0.342244 −0.171122 0.985250i \(-0.554739\pi\)
−0.171122 + 0.985250i \(0.554739\pi\)
\(152\) 3.77391 0.306104
\(153\) 0.856481 0.0692424
\(154\) −2.58438 −0.208255
\(155\) −0.196859 −0.0158121
\(156\) −2.99040 −0.239424
\(157\) −6.04298 −0.482282 −0.241141 0.970490i \(-0.577522\pi\)
−0.241141 + 0.970490i \(0.577522\pi\)
\(158\) 1.61335 0.128351
\(159\) −0.392595 −0.0311348
\(160\) 7.82182 0.618369
\(161\) −5.80371 −0.457396
\(162\) −0.555636 −0.0436549
\(163\) −3.97417 −0.311281 −0.155640 0.987814i \(-0.549744\pi\)
−0.155640 + 0.987814i \(0.549744\pi\)
\(164\) 12.6159 0.985133
\(165\) 6.80239 0.529565
\(166\) 6.16562 0.478545
\(167\) 14.5862 1.12871 0.564356 0.825532i \(-0.309125\pi\)
0.564356 + 0.825532i \(0.309125\pi\)
\(168\) −2.05100 −0.158238
\(169\) −9.87368 −0.759514
\(170\) 0.695992 0.0533801
\(171\) 1.84003 0.140711
\(172\) −7.22634 −0.551004
\(173\) −20.6262 −1.56818 −0.784091 0.620646i \(-0.786870\pi\)
−0.784091 + 0.620646i \(0.786870\pi\)
\(174\) 2.13650 0.161967
\(175\) −2.86110 −0.216278
\(176\) 10.4323 0.786365
\(177\) −1.60517 −0.120652
\(178\) 3.95005 0.296069
\(179\) −11.8629 −0.886673 −0.443336 0.896355i \(-0.646205\pi\)
−0.443336 + 0.896355i \(0.646205\pi\)
\(180\) 2.47348 0.184362
\(181\) 6.37482 0.473837 0.236918 0.971530i \(-0.423863\pi\)
0.236918 + 0.971530i \(0.423863\pi\)
\(182\) 0.982444 0.0728236
\(183\) −15.5098 −1.14652
\(184\) −11.9034 −0.877532
\(185\) 7.47726 0.549739
\(186\) 0.0747912 0.00548396
\(187\) 3.98367 0.291315
\(188\) −1.60609 −0.117136
\(189\) −1.00000 −0.0727393
\(190\) 1.49524 0.108476
\(191\) −13.6925 −0.990755 −0.495377 0.868678i \(-0.664970\pi\)
−0.495377 + 0.868678i \(0.664970\pi\)
\(192\) 1.51416 0.109275
\(193\) −8.62461 −0.620813 −0.310406 0.950604i \(-0.600465\pi\)
−0.310406 + 0.950604i \(0.600465\pi\)
\(194\) 6.87105 0.493313
\(195\) −2.58591 −0.185181
\(196\) −1.69127 −0.120805
\(197\) −7.15316 −0.509641 −0.254821 0.966988i \(-0.582016\pi\)
−0.254821 + 0.966988i \(0.582016\pi\)
\(198\) −2.58438 −0.183664
\(199\) −22.3739 −1.58605 −0.793024 0.609191i \(-0.791494\pi\)
−0.793024 + 0.609191i \(0.791494\pi\)
\(200\) −5.86812 −0.414938
\(201\) 12.8432 0.905889
\(202\) 0.509806 0.0358698
\(203\) 3.84513 0.269875
\(204\) 1.44854 0.101418
\(205\) 10.9094 0.761944
\(206\) −8.74839 −0.609529
\(207\) −5.80371 −0.403386
\(208\) −3.96581 −0.274979
\(209\) 8.55836 0.591994
\(210\) −0.812618 −0.0560760
\(211\) 13.7259 0.944930 0.472465 0.881349i \(-0.343364\pi\)
0.472465 + 0.881349i \(0.343364\pi\)
\(212\) −0.663984 −0.0456026
\(213\) 3.57750 0.245127
\(214\) −2.49657 −0.170662
\(215\) −6.24887 −0.426170
\(216\) −2.05100 −0.139553
\(217\) 0.134605 0.00913755
\(218\) −1.18252 −0.0800902
\(219\) −2.62361 −0.177287
\(220\) 11.5047 0.775645
\(221\) −1.51438 −0.101868
\(222\) −2.84078 −0.190661
\(223\) 6.73340 0.450902 0.225451 0.974255i \(-0.427615\pi\)
0.225451 + 0.974255i \(0.427615\pi\)
\(224\) −5.34826 −0.357345
\(225\) −2.86110 −0.190740
\(226\) −3.14475 −0.209186
\(227\) 6.06777 0.402732 0.201366 0.979516i \(-0.435462\pi\)
0.201366 + 0.979516i \(0.435462\pi\)
\(228\) 3.11198 0.206096
\(229\) 16.8701 1.11481 0.557404 0.830241i \(-0.311797\pi\)
0.557404 + 0.830241i \(0.311797\pi\)
\(230\) −4.71620 −0.310977
\(231\) −4.65121 −0.306027
\(232\) 7.88638 0.517766
\(233\) −4.58341 −0.300269 −0.150135 0.988666i \(-0.547971\pi\)
−0.150135 + 0.988666i \(0.547971\pi\)
\(234\) 0.982444 0.0642244
\(235\) −1.38884 −0.0905980
\(236\) −2.71478 −0.176717
\(237\) 2.90361 0.188610
\(238\) −0.475892 −0.0308475
\(239\) −5.32334 −0.344338 −0.172169 0.985067i \(-0.555078\pi\)
−0.172169 + 0.985067i \(0.555078\pi\)
\(240\) 3.28028 0.211741
\(241\) 0.657764 0.0423703 0.0211852 0.999776i \(-0.493256\pi\)
0.0211852 + 0.999776i \(0.493256\pi\)
\(242\) −5.90850 −0.379813
\(243\) −1.00000 −0.0641500
\(244\) −26.2313 −1.67929
\(245\) −1.46250 −0.0934357
\(246\) −4.14472 −0.264258
\(247\) −3.25343 −0.207011
\(248\) 0.276074 0.0175307
\(249\) 11.0965 0.703213
\(250\) −6.38807 −0.404017
\(251\) 27.1568 1.71412 0.857062 0.515214i \(-0.172287\pi\)
0.857062 + 0.515214i \(0.172287\pi\)
\(252\) −1.69127 −0.106540
\(253\) −26.9943 −1.69712
\(254\) 2.04952 0.128599
\(255\) 1.25260 0.0784411
\(256\) −3.38252 −0.211407
\(257\) −1.67942 −0.104759 −0.0523797 0.998627i \(-0.516681\pi\)
−0.0523797 + 0.998627i \(0.516681\pi\)
\(258\) 2.37409 0.147804
\(259\) −5.11266 −0.317685
\(260\) −4.37346 −0.271230
\(261\) 3.84513 0.238008
\(262\) −5.47076 −0.337984
\(263\) −16.8518 −1.03913 −0.519563 0.854432i \(-0.673905\pi\)
−0.519563 + 0.854432i \(0.673905\pi\)
\(264\) −9.53965 −0.587125
\(265\) −0.574170 −0.0352710
\(266\) −1.02239 −0.0626866
\(267\) 7.10905 0.435067
\(268\) 21.7213 1.32684
\(269\) −5.47293 −0.333691 −0.166845 0.985983i \(-0.553358\pi\)
−0.166845 + 0.985983i \(0.553358\pi\)
\(270\) −0.812618 −0.0494544
\(271\) −15.6762 −0.952261 −0.476131 0.879375i \(-0.657961\pi\)
−0.476131 + 0.879375i \(0.657961\pi\)
\(272\) 1.92102 0.116479
\(273\) 1.76814 0.107013
\(274\) −1.46184 −0.0883129
\(275\) −13.3076 −0.802476
\(276\) −9.81563 −0.590832
\(277\) −2.66248 −0.159973 −0.0799865 0.996796i \(-0.525488\pi\)
−0.0799865 + 0.996796i \(0.525488\pi\)
\(278\) −11.7616 −0.705411
\(279\) 0.134605 0.00805856
\(280\) −2.99959 −0.179260
\(281\) 26.0334 1.55302 0.776511 0.630104i \(-0.216988\pi\)
0.776511 + 0.630104i \(0.216988\pi\)
\(282\) 0.527652 0.0314212
\(283\) −8.80119 −0.523176 −0.261588 0.965180i \(-0.584246\pi\)
−0.261588 + 0.965180i \(0.584246\pi\)
\(284\) 6.05052 0.359032
\(285\) 2.69104 0.159404
\(286\) 4.56955 0.270203
\(287\) −7.45941 −0.440315
\(288\) −5.34826 −0.315149
\(289\) −16.2664 −0.956849
\(290\) 3.12462 0.183484
\(291\) 12.3661 0.724913
\(292\) −4.43722 −0.259669
\(293\) 22.3910 1.30809 0.654047 0.756454i \(-0.273070\pi\)
0.654047 + 0.756454i \(0.273070\pi\)
\(294\) 0.555636 0.0324054
\(295\) −2.34757 −0.136681
\(296\) −10.4861 −0.609491
\(297\) −4.65121 −0.269891
\(298\) −13.1284 −0.760508
\(299\) 10.2618 0.593454
\(300\) −4.83888 −0.279373
\(301\) 4.27274 0.246276
\(302\) 2.33676 0.134466
\(303\) 0.917518 0.0527100
\(304\) 4.12705 0.236702
\(305\) −22.6831 −1.29883
\(306\) −0.475892 −0.0272049
\(307\) −24.7055 −1.41002 −0.705008 0.709199i \(-0.749057\pi\)
−0.705008 + 0.709199i \(0.749057\pi\)
\(308\) −7.86644 −0.448232
\(309\) −15.7448 −0.895691
\(310\) 0.109382 0.00621248
\(311\) 21.3674 1.21164 0.605818 0.795604i \(-0.292846\pi\)
0.605818 + 0.795604i \(0.292846\pi\)
\(312\) 3.62646 0.205308
\(313\) 19.2229 1.08654 0.543272 0.839557i \(-0.317185\pi\)
0.543272 + 0.839557i \(0.317185\pi\)
\(314\) 3.35770 0.189486
\(315\) −1.46250 −0.0824025
\(316\) 4.91078 0.276253
\(317\) −5.92136 −0.332577 −0.166288 0.986077i \(-0.553178\pi\)
−0.166288 + 0.986077i \(0.553178\pi\)
\(318\) 0.218140 0.0122327
\(319\) 17.8845 1.00134
\(320\) 2.21446 0.123792
\(321\) −4.49317 −0.250784
\(322\) 3.22475 0.179708
\(323\) 1.57595 0.0876882
\(324\) −1.69127 −0.0939593
\(325\) 5.05882 0.280613
\(326\) 2.20819 0.122300
\(327\) −2.12822 −0.117691
\(328\) −15.2993 −0.844761
\(329\) 0.949635 0.0523551
\(330\) −3.77966 −0.208063
\(331\) −35.5887 −1.95613 −0.978065 0.208300i \(-0.933207\pi\)
−0.978065 + 0.208300i \(0.933207\pi\)
\(332\) 18.7672 1.02998
\(333\) −5.11266 −0.280172
\(334\) −8.10460 −0.443464
\(335\) 18.7832 1.02623
\(336\) −2.24292 −0.122362
\(337\) −20.4464 −1.11379 −0.556894 0.830584i \(-0.688007\pi\)
−0.556894 + 0.830584i \(0.688007\pi\)
\(338\) 5.48617 0.298409
\(339\) −5.65973 −0.307394
\(340\) 2.11849 0.114891
\(341\) 0.626074 0.0339038
\(342\) −1.02239 −0.0552844
\(343\) 1.00000 0.0539949
\(344\) 8.76340 0.472491
\(345\) −8.48792 −0.456974
\(346\) 11.4607 0.616130
\(347\) −15.2764 −0.820081 −0.410040 0.912067i \(-0.634485\pi\)
−0.410040 + 0.912067i \(0.634485\pi\)
\(348\) 6.50315 0.348606
\(349\) 2.24275 0.120052 0.0600259 0.998197i \(-0.480882\pi\)
0.0600259 + 0.998197i \(0.480882\pi\)
\(350\) 1.58973 0.0849746
\(351\) 1.76814 0.0943764
\(352\) −24.8759 −1.32589
\(353\) −19.8671 −1.05742 −0.528710 0.848803i \(-0.677324\pi\)
−0.528710 + 0.848803i \(0.677324\pi\)
\(354\) 0.891893 0.0474036
\(355\) 5.23210 0.277691
\(356\) 12.0233 0.637234
\(357\) −0.856481 −0.0453298
\(358\) 6.59145 0.348369
\(359\) −28.3125 −1.49428 −0.747140 0.664667i \(-0.768573\pi\)
−0.747140 + 0.664667i \(0.768573\pi\)
\(360\) −2.99959 −0.158092
\(361\) −15.6143 −0.821805
\(362\) −3.54208 −0.186168
\(363\) −10.6338 −0.558127
\(364\) 2.99040 0.156740
\(365\) −3.83702 −0.200839
\(366\) 8.61783 0.450461
\(367\) −37.7960 −1.97293 −0.986467 0.163957i \(-0.947574\pi\)
−0.986467 + 0.163957i \(0.947574\pi\)
\(368\) −13.0173 −0.678573
\(369\) −7.45941 −0.388321
\(370\) −4.15464 −0.215989
\(371\) 0.392595 0.0203825
\(372\) 0.227652 0.0118032
\(373\) −18.8834 −0.977746 −0.488873 0.872355i \(-0.662592\pi\)
−0.488873 + 0.872355i \(0.662592\pi\)
\(374\) −2.21347 −0.114456
\(375\) −11.4968 −0.593695
\(376\) 1.94771 0.100445
\(377\) −6.79874 −0.350153
\(378\) 0.555636 0.0285789
\(379\) −24.1038 −1.23813 −0.619064 0.785341i \(-0.712488\pi\)
−0.619064 + 0.785341i \(0.712488\pi\)
\(380\) 4.55127 0.233475
\(381\) 3.68860 0.188973
\(382\) 7.60805 0.389262
\(383\) 1.00000 0.0510976
\(384\) −11.5378 −0.588788
\(385\) −6.80239 −0.346682
\(386\) 4.79215 0.243914
\(387\) 4.27274 0.217195
\(388\) 20.9144 1.06177
\(389\) 33.1997 1.68329 0.841645 0.540031i \(-0.181587\pi\)
0.841645 + 0.540031i \(0.181587\pi\)
\(390\) 1.43682 0.0727564
\(391\) −4.97077 −0.251383
\(392\) 2.05100 0.103591
\(393\) −9.84593 −0.496661
\(394\) 3.97455 0.200235
\(395\) 4.24653 0.213666
\(396\) −7.86644 −0.395304
\(397\) −13.2321 −0.664100 −0.332050 0.943262i \(-0.607740\pi\)
−0.332050 + 0.943262i \(0.607740\pi\)
\(398\) 12.4318 0.623149
\(399\) −1.84003 −0.0921167
\(400\) −6.41722 −0.320861
\(401\) −0.0873597 −0.00436253 −0.00218127 0.999998i \(-0.500694\pi\)
−0.00218127 + 0.999998i \(0.500694\pi\)
\(402\) −7.13614 −0.355919
\(403\) −0.238000 −0.0118556
\(404\) 1.55177 0.0772034
\(405\) −1.46250 −0.0726722
\(406\) −2.13650 −0.106033
\(407\) −23.7800 −1.17873
\(408\) −1.75665 −0.0869669
\(409\) −11.1622 −0.551934 −0.275967 0.961167i \(-0.588998\pi\)
−0.275967 + 0.961167i \(0.588998\pi\)
\(410\) −6.06165 −0.299364
\(411\) −2.63093 −0.129774
\(412\) −26.6287 −1.31190
\(413\) 1.60517 0.0789855
\(414\) 3.22475 0.158488
\(415\) 16.2286 0.796632
\(416\) 9.45647 0.463642
\(417\) −21.1677 −1.03659
\(418\) −4.75534 −0.232591
\(419\) −18.4227 −0.900006 −0.450003 0.893027i \(-0.648577\pi\)
−0.450003 + 0.893027i \(0.648577\pi\)
\(420\) −2.47348 −0.120693
\(421\) 21.6951 1.05735 0.528677 0.848823i \(-0.322688\pi\)
0.528677 + 0.848823i \(0.322688\pi\)
\(422\) −7.62661 −0.371258
\(423\) 0.949635 0.0461728
\(424\) 0.805214 0.0391046
\(425\) −2.45047 −0.118865
\(426\) −1.98779 −0.0963088
\(427\) 15.5098 0.750574
\(428\) −7.59916 −0.367319
\(429\) 8.22400 0.397058
\(430\) 3.47210 0.167440
\(431\) −1.85014 −0.0891180 −0.0445590 0.999007i \(-0.514188\pi\)
−0.0445590 + 0.999007i \(0.514188\pi\)
\(432\) −2.24292 −0.107913
\(433\) 16.3739 0.786880 0.393440 0.919350i \(-0.371285\pi\)
0.393440 + 0.919350i \(0.371285\pi\)
\(434\) −0.0747912 −0.00359009
\(435\) 5.62351 0.269626
\(436\) −3.59940 −0.172380
\(437\) −10.6790 −0.510846
\(438\) 1.45777 0.0696550
\(439\) 10.6218 0.506953 0.253476 0.967342i \(-0.418426\pi\)
0.253476 + 0.967342i \(0.418426\pi\)
\(440\) −13.9517 −0.665122
\(441\) 1.00000 0.0476190
\(442\) 0.841445 0.0400234
\(443\) −10.6566 −0.506310 −0.253155 0.967426i \(-0.581468\pi\)
−0.253155 + 0.967426i \(0.581468\pi\)
\(444\) −8.64687 −0.410362
\(445\) 10.3970 0.492864
\(446\) −3.74132 −0.177157
\(447\) −23.6277 −1.11755
\(448\) −1.51416 −0.0715374
\(449\) 26.0557 1.22964 0.614822 0.788666i \(-0.289228\pi\)
0.614822 + 0.788666i \(0.289228\pi\)
\(450\) 1.58973 0.0749405
\(451\) −34.6953 −1.63374
\(452\) −9.57212 −0.450235
\(453\) 4.20556 0.197595
\(454\) −3.37148 −0.158231
\(455\) 2.58591 0.121229
\(456\) −3.77391 −0.176729
\(457\) −14.3730 −0.672340 −0.336170 0.941801i \(-0.609132\pi\)
−0.336170 + 0.941801i \(0.609132\pi\)
\(458\) −9.37365 −0.438002
\(459\) −0.856481 −0.0399771
\(460\) −14.3554 −0.669322
\(461\) −1.36651 −0.0636445 −0.0318222 0.999494i \(-0.510131\pi\)
−0.0318222 + 0.999494i \(0.510131\pi\)
\(462\) 2.58438 0.120236
\(463\) 2.90746 0.135121 0.0675605 0.997715i \(-0.478478\pi\)
0.0675605 + 0.997715i \(0.478478\pi\)
\(464\) 8.62434 0.400375
\(465\) 0.196859 0.00912912
\(466\) 2.54671 0.117974
\(467\) −30.4342 −1.40833 −0.704163 0.710038i \(-0.748678\pi\)
−0.704163 + 0.710038i \(0.748678\pi\)
\(468\) 2.99040 0.138231
\(469\) −12.8432 −0.593043
\(470\) 0.771691 0.0355954
\(471\) 6.04298 0.278446
\(472\) 3.29222 0.151537
\(473\) 19.8734 0.913780
\(474\) −1.61335 −0.0741037
\(475\) −5.26450 −0.241552
\(476\) −1.44854 −0.0663937
\(477\) 0.392595 0.0179757
\(478\) 2.95784 0.135289
\(479\) −2.08302 −0.0951754 −0.0475877 0.998867i \(-0.515153\pi\)
−0.0475877 + 0.998867i \(0.515153\pi\)
\(480\) −7.82182 −0.357016
\(481\) 9.03990 0.412184
\(482\) −0.365478 −0.0166471
\(483\) 5.80371 0.264078
\(484\) −17.9845 −0.817478
\(485\) 18.0854 0.821216
\(486\) 0.555636 0.0252042
\(487\) 12.0897 0.547838 0.273919 0.961753i \(-0.411680\pi\)
0.273919 + 0.961753i \(0.411680\pi\)
\(488\) 31.8107 1.44000
\(489\) 3.97417 0.179718
\(490\) 0.812618 0.0367103
\(491\) 15.3064 0.690768 0.345384 0.938462i \(-0.387749\pi\)
0.345384 + 0.938462i \(0.387749\pi\)
\(492\) −12.6159 −0.568767
\(493\) 3.29328 0.148322
\(494\) 1.80773 0.0813334
\(495\) −6.80239 −0.305745
\(496\) 0.301908 0.0135561
\(497\) −3.57750 −0.160473
\(498\) −6.16562 −0.276288
\(499\) −34.7558 −1.55588 −0.777941 0.628337i \(-0.783736\pi\)
−0.777941 + 0.628337i \(0.783736\pi\)
\(500\) −19.4443 −0.869573
\(501\) −14.5862 −0.651662
\(502\) −15.0893 −0.673469
\(503\) 6.72402 0.299809 0.149905 0.988700i \(-0.452103\pi\)
0.149905 + 0.988700i \(0.452103\pi\)
\(504\) 2.05100 0.0913589
\(505\) 1.34187 0.0597124
\(506\) 14.9990 0.666787
\(507\) 9.87368 0.438505
\(508\) 6.23842 0.276785
\(509\) −29.0825 −1.28906 −0.644529 0.764580i \(-0.722946\pi\)
−0.644529 + 0.764580i \(0.722946\pi\)
\(510\) −0.695992 −0.0308190
\(511\) 2.62361 0.116062
\(512\) −21.1962 −0.936750
\(513\) −1.84003 −0.0812393
\(514\) 0.933147 0.0411594
\(515\) −23.0268 −1.01468
\(516\) 7.22634 0.318122
\(517\) 4.41695 0.194257
\(518\) 2.84078 0.124817
\(519\) 20.6262 0.905390
\(520\) 5.30370 0.232583
\(521\) −32.3456 −1.41709 −0.708544 0.705666i \(-0.750648\pi\)
−0.708544 + 0.705666i \(0.750648\pi\)
\(522\) −2.13650 −0.0935119
\(523\) 18.2443 0.797767 0.398883 0.917002i \(-0.369398\pi\)
0.398883 + 0.917002i \(0.369398\pi\)
\(524\) −16.6521 −0.727451
\(525\) 2.86110 0.124868
\(526\) 9.36348 0.408267
\(527\) 0.115286 0.00502195
\(528\) −10.4323 −0.454008
\(529\) 10.6831 0.464481
\(530\) 0.319030 0.0138578
\(531\) 1.60517 0.0696586
\(532\) −3.11198 −0.134922
\(533\) 13.1893 0.571291
\(534\) −3.95005 −0.170935
\(535\) −6.57126 −0.284100
\(536\) −26.3414 −1.13778
\(537\) 11.8629 0.511921
\(538\) 3.04096 0.131105
\(539\) 4.65121 0.200342
\(540\) −2.47348 −0.106442
\(541\) −16.4744 −0.708288 −0.354144 0.935191i \(-0.615228\pi\)
−0.354144 + 0.935191i \(0.615228\pi\)
\(542\) 8.71027 0.374138
\(543\) −6.37482 −0.273570
\(544\) −4.58068 −0.196395
\(545\) −3.11252 −0.133326
\(546\) −0.982444 −0.0420447
\(547\) −16.8111 −0.718789 −0.359395 0.933186i \(-0.617017\pi\)
−0.359395 + 0.933186i \(0.617017\pi\)
\(548\) −4.44960 −0.190078
\(549\) 15.5098 0.661944
\(550\) 7.39416 0.315288
\(551\) 7.07516 0.301412
\(552\) 11.9034 0.506644
\(553\) −2.90361 −0.123474
\(554\) 1.47937 0.0628525
\(555\) −7.47726 −0.317392
\(556\) −35.8003 −1.51827
\(557\) −10.5162 −0.445587 −0.222793 0.974866i \(-0.571518\pi\)
−0.222793 + 0.974866i \(0.571518\pi\)
\(558\) −0.0747912 −0.00316616
\(559\) −7.55480 −0.319534
\(560\) −3.28028 −0.138617
\(561\) −3.98367 −0.168191
\(562\) −14.4651 −0.610173
\(563\) −17.5388 −0.739173 −0.369586 0.929196i \(-0.620501\pi\)
−0.369586 + 0.929196i \(0.620501\pi\)
\(564\) 1.60609 0.0676285
\(565\) −8.27735 −0.348231
\(566\) 4.89026 0.205553
\(567\) 1.00000 0.0419961
\(568\) −7.33747 −0.307873
\(569\) 44.7599 1.87643 0.938217 0.346048i \(-0.112477\pi\)
0.938217 + 0.346048i \(0.112477\pi\)
\(570\) −1.49524 −0.0626288
\(571\) −32.0670 −1.34196 −0.670980 0.741475i \(-0.734126\pi\)
−0.670980 + 0.741475i \(0.734126\pi\)
\(572\) 13.9090 0.581564
\(573\) 13.6925 0.572013
\(574\) 4.14472 0.172997
\(575\) 16.6050 0.692475
\(576\) −1.51416 −0.0630901
\(577\) 23.3379 0.971571 0.485785 0.874078i \(-0.338534\pi\)
0.485785 + 0.874078i \(0.338534\pi\)
\(578\) 9.03823 0.375941
\(579\) 8.62461 0.358427
\(580\) 9.51086 0.394917
\(581\) −11.0965 −0.460361
\(582\) −6.87105 −0.284814
\(583\) 1.82604 0.0756270
\(584\) 5.38103 0.222668
\(585\) 2.58591 0.106914
\(586\) −12.4412 −0.513943
\(587\) 5.91881 0.244295 0.122148 0.992512i \(-0.461022\pi\)
0.122148 + 0.992512i \(0.461022\pi\)
\(588\) 1.69127 0.0697467
\(589\) 0.247676 0.0102053
\(590\) 1.30439 0.0537010
\(591\) 7.15316 0.294242
\(592\) −11.4673 −0.471303
\(593\) 20.5245 0.842842 0.421421 0.906865i \(-0.361532\pi\)
0.421421 + 0.906865i \(0.361532\pi\)
\(594\) 2.58438 0.106038
\(595\) −1.25260 −0.0513517
\(596\) −39.9607 −1.63686
\(597\) 22.3739 0.915705
\(598\) −5.70182 −0.233165
\(599\) −7.73670 −0.316113 −0.158057 0.987430i \(-0.550523\pi\)
−0.158057 + 0.987430i \(0.550523\pi\)
\(600\) 5.86812 0.239565
\(601\) 21.0734 0.859603 0.429802 0.902923i \(-0.358583\pi\)
0.429802 + 0.902923i \(0.358583\pi\)
\(602\) −2.37409 −0.0967606
\(603\) −12.8432 −0.523015
\(604\) 7.11274 0.289413
\(605\) −15.5519 −0.632273
\(606\) −0.509806 −0.0207095
\(607\) 3.29943 0.133920 0.0669599 0.997756i \(-0.478670\pi\)
0.0669599 + 0.997756i \(0.478670\pi\)
\(608\) −9.84095 −0.399103
\(609\) −3.84513 −0.155813
\(610\) 12.6036 0.510304
\(611\) −1.67909 −0.0679287
\(612\) −1.44854 −0.0585537
\(613\) −43.3915 −1.75257 −0.876284 0.481795i \(-0.839985\pi\)
−0.876284 + 0.481795i \(0.839985\pi\)
\(614\) 13.7273 0.553987
\(615\) −10.9094 −0.439909
\(616\) 9.53965 0.384363
\(617\) 38.2327 1.53919 0.769595 0.638532i \(-0.220458\pi\)
0.769595 + 0.638532i \(0.220458\pi\)
\(618\) 8.74839 0.351912
\(619\) −8.87287 −0.356631 −0.178315 0.983973i \(-0.557065\pi\)
−0.178315 + 0.983973i \(0.557065\pi\)
\(620\) 0.332941 0.0133713
\(621\) 5.80371 0.232895
\(622\) −11.8725 −0.476045
\(623\) −7.10905 −0.284818
\(624\) 3.96581 0.158759
\(625\) −2.50866 −0.100346
\(626\) −10.6810 −0.426897
\(627\) −8.55836 −0.341788
\(628\) 10.2203 0.407834
\(629\) −4.37889 −0.174598
\(630\) 0.812618 0.0323755
\(631\) −31.1276 −1.23917 −0.619586 0.784929i \(-0.712699\pi\)
−0.619586 + 0.784929i \(0.712699\pi\)
\(632\) −5.95531 −0.236890
\(633\) −13.7259 −0.545556
\(634\) 3.29012 0.130667
\(635\) 5.39458 0.214077
\(636\) 0.663984 0.0263287
\(637\) −1.76814 −0.0700563
\(638\) −9.93729 −0.393421
\(639\) −3.57750 −0.141524
\(640\) −16.8741 −0.667007
\(641\) 3.23986 0.127967 0.0639834 0.997951i \(-0.479620\pi\)
0.0639834 + 0.997951i \(0.479620\pi\)
\(642\) 2.49657 0.0985318
\(643\) 38.5643 1.52083 0.760415 0.649438i \(-0.224996\pi\)
0.760415 + 0.649438i \(0.224996\pi\)
\(644\) 9.81563 0.386790
\(645\) 6.24887 0.246049
\(646\) −0.875656 −0.0344522
\(647\) 35.5087 1.39599 0.697996 0.716102i \(-0.254075\pi\)
0.697996 + 0.716102i \(0.254075\pi\)
\(648\) 2.05100 0.0805710
\(649\) 7.46600 0.293066
\(650\) −2.81087 −0.110251
\(651\) −0.134605 −0.00527557
\(652\) 6.72138 0.263230
\(653\) −12.3139 −0.481879 −0.240939 0.970540i \(-0.577456\pi\)
−0.240939 + 0.970540i \(0.577456\pi\)
\(654\) 1.18252 0.0462401
\(655\) −14.3997 −0.562641
\(656\) −16.7309 −0.653231
\(657\) 2.62361 0.102357
\(658\) −0.527652 −0.0205700
\(659\) −32.7962 −1.27756 −0.638780 0.769390i \(-0.720560\pi\)
−0.638780 + 0.769390i \(0.720560\pi\)
\(660\) −11.5047 −0.447819
\(661\) 29.1908 1.13539 0.567696 0.823239i \(-0.307835\pi\)
0.567696 + 0.823239i \(0.307835\pi\)
\(662\) 19.7744 0.768552
\(663\) 1.51438 0.0588136
\(664\) −22.7590 −0.883219
\(665\) −2.69104 −0.104354
\(666\) 2.84078 0.110078
\(667\) −22.3160 −0.864081
\(668\) −24.6691 −0.954477
\(669\) −6.73340 −0.260328
\(670\) −10.4366 −0.403201
\(671\) 72.1395 2.78492
\(672\) 5.34826 0.206313
\(673\) −44.6600 −1.72152 −0.860759 0.509013i \(-0.830010\pi\)
−0.860759 + 0.509013i \(0.830010\pi\)
\(674\) 11.3608 0.437601
\(675\) 2.86110 0.110124
\(676\) 16.6990 0.642271
\(677\) −36.0719 −1.38636 −0.693179 0.720766i \(-0.743790\pi\)
−0.693179 + 0.720766i \(0.743790\pi\)
\(678\) 3.14475 0.120773
\(679\) −12.3661 −0.474567
\(680\) −2.56909 −0.0985202
\(681\) −6.06777 −0.232518
\(682\) −0.347869 −0.0133206
\(683\) −11.0664 −0.423443 −0.211722 0.977330i \(-0.567907\pi\)
−0.211722 + 0.977330i \(0.567907\pi\)
\(684\) −3.11198 −0.118990
\(685\) −3.84773 −0.147014
\(686\) −0.555636 −0.0212143
\(687\) −16.8701 −0.643635
\(688\) 9.58342 0.365365
\(689\) −0.694164 −0.0264455
\(690\) 4.71620 0.179543
\(691\) 44.7972 1.70417 0.852083 0.523406i \(-0.175339\pi\)
0.852083 + 0.523406i \(0.175339\pi\)
\(692\) 34.8845 1.32611
\(693\) 4.65121 0.176685
\(694\) 8.48813 0.322205
\(695\) −30.9578 −1.17430
\(696\) −7.88638 −0.298933
\(697\) −6.38884 −0.241995
\(698\) −1.24616 −0.0471677
\(699\) 4.58341 0.173360
\(700\) 4.83888 0.182892
\(701\) 21.2884 0.804051 0.402026 0.915628i \(-0.368306\pi\)
0.402026 + 0.915628i \(0.368306\pi\)
\(702\) −0.982444 −0.0370799
\(703\) −9.40744 −0.354808
\(704\) −7.04268 −0.265431
\(705\) 1.38884 0.0523068
\(706\) 11.0389 0.415454
\(707\) −0.917518 −0.0345068
\(708\) 2.71478 0.102028
\(709\) 3.37390 0.126710 0.0633548 0.997991i \(-0.479820\pi\)
0.0633548 + 0.997991i \(0.479820\pi\)
\(710\) −2.90714 −0.109103
\(711\) −2.90361 −0.108894
\(712\) −14.5807 −0.546435
\(713\) −0.781206 −0.0292564
\(714\) 0.475892 0.0178098
\(715\) 12.0276 0.449806
\(716\) 20.0633 0.749801
\(717\) 5.32334 0.198804
\(718\) 15.7315 0.587094
\(719\) 7.42172 0.276783 0.138392 0.990378i \(-0.455807\pi\)
0.138392 + 0.990378i \(0.455807\pi\)
\(720\) −3.28028 −0.122249
\(721\) 15.7448 0.586367
\(722\) 8.67587 0.322882
\(723\) −0.657764 −0.0244625
\(724\) −10.7815 −0.400693
\(725\) −11.0013 −0.408578
\(726\) 5.90850 0.219285
\(727\) −19.5424 −0.724789 −0.362395 0.932025i \(-0.618041\pi\)
−0.362395 + 0.932025i \(0.618041\pi\)
\(728\) −3.62646 −0.134406
\(729\) 1.00000 0.0370370
\(730\) 2.13199 0.0789085
\(731\) 3.65952 0.135352
\(732\) 26.2313 0.969537
\(733\) 19.0737 0.704505 0.352252 0.935905i \(-0.385416\pi\)
0.352252 + 0.935905i \(0.385416\pi\)
\(734\) 21.0008 0.775155
\(735\) 1.46250 0.0539451
\(736\) 31.0397 1.14414
\(737\) −59.7364 −2.20042
\(738\) 4.14472 0.152569
\(739\) −16.1755 −0.595027 −0.297513 0.954718i \(-0.596157\pi\)
−0.297513 + 0.954718i \(0.596157\pi\)
\(740\) −12.6460 −0.464878
\(741\) 3.25343 0.119518
\(742\) −0.218140 −0.00800818
\(743\) 35.0169 1.28464 0.642322 0.766435i \(-0.277971\pi\)
0.642322 + 0.766435i \(0.277971\pi\)
\(744\) −0.276074 −0.0101214
\(745\) −34.5555 −1.26601
\(746\) 10.4923 0.384151
\(747\) −11.0965 −0.406000
\(748\) −6.73746 −0.246346
\(749\) 4.49317 0.164177
\(750\) 6.38807 0.233259
\(751\) −39.5907 −1.44468 −0.722342 0.691536i \(-0.756934\pi\)
−0.722342 + 0.691536i \(0.756934\pi\)
\(752\) 2.12996 0.0776716
\(753\) −27.1568 −0.989650
\(754\) 3.77763 0.137573
\(755\) 6.15064 0.223845
\(756\) 1.69127 0.0615108
\(757\) −6.56100 −0.238464 −0.119232 0.992866i \(-0.538043\pi\)
−0.119232 + 0.992866i \(0.538043\pi\)
\(758\) 13.3929 0.486453
\(759\) 26.9943 0.979830
\(760\) −5.51934 −0.200207
\(761\) 17.4495 0.632543 0.316272 0.948669i \(-0.397569\pi\)
0.316272 + 0.948669i \(0.397569\pi\)
\(762\) −2.04952 −0.0742464
\(763\) 2.12822 0.0770468
\(764\) 23.1577 0.837816
\(765\) −1.25260 −0.0452880
\(766\) −0.555636 −0.0200760
\(767\) −2.83818 −0.102481
\(768\) 3.38252 0.122056
\(769\) −37.4459 −1.35033 −0.675167 0.737665i \(-0.735928\pi\)
−0.675167 + 0.737665i \(0.735928\pi\)
\(770\) 3.77966 0.136209
\(771\) 1.67942 0.0604828
\(772\) 14.5865 0.524981
\(773\) −3.44275 −0.123827 −0.0619135 0.998082i \(-0.519720\pi\)
−0.0619135 + 0.998082i \(0.519720\pi\)
\(774\) −2.37409 −0.0853348
\(775\) −0.385116 −0.0138338
\(776\) −25.3629 −0.910475
\(777\) 5.11266 0.183415
\(778\) −18.4469 −0.661355
\(779\) −13.7255 −0.491768
\(780\) 4.37346 0.156595
\(781\) −16.6397 −0.595416
\(782\) 2.76194 0.0987668
\(783\) −3.84513 −0.137414
\(784\) 2.24292 0.0801044
\(785\) 8.83785 0.315436
\(786\) 5.47076 0.195135
\(787\) −6.30267 −0.224666 −0.112333 0.993671i \(-0.535832\pi\)
−0.112333 + 0.993671i \(0.535832\pi\)
\(788\) 12.0979 0.430970
\(789\) 16.8518 0.599940
\(790\) −2.35953 −0.0839482
\(791\) 5.65973 0.201237
\(792\) 9.53965 0.338977
\(793\) −27.4236 −0.973840
\(794\) 7.35224 0.260921
\(795\) 0.574170 0.0203637
\(796\) 37.8403 1.34122
\(797\) −21.6823 −0.768027 −0.384014 0.923327i \(-0.625458\pi\)
−0.384014 + 0.923327i \(0.625458\pi\)
\(798\) 1.02239 0.0361921
\(799\) 0.813345 0.0287741
\(800\) 15.3019 0.541003
\(801\) −7.10905 −0.251186
\(802\) 0.0485402 0.00171402
\(803\) 12.2029 0.430633
\(804\) −21.7213 −0.766050
\(805\) 8.48792 0.299160
\(806\) 0.132241 0.00465800
\(807\) 5.47293 0.192656
\(808\) −1.88183 −0.0662026
\(809\) −32.4724 −1.14167 −0.570834 0.821066i \(-0.693380\pi\)
−0.570834 + 0.821066i \(0.693380\pi\)
\(810\) 0.812618 0.0285525
\(811\) −36.8771 −1.29493 −0.647466 0.762095i \(-0.724171\pi\)
−0.647466 + 0.762095i \(0.724171\pi\)
\(812\) −6.50315 −0.228216
\(813\) 15.6762 0.549788
\(814\) 13.2131 0.463117
\(815\) 5.81222 0.203593
\(816\) −1.92102 −0.0672492
\(817\) 7.86196 0.275055
\(818\) 6.20211 0.216852
\(819\) −1.76814 −0.0617839
\(820\) −18.4507 −0.644326
\(821\) 26.6529 0.930194 0.465097 0.885260i \(-0.346019\pi\)
0.465097 + 0.885260i \(0.346019\pi\)
\(822\) 1.46184 0.0509875
\(823\) −50.7607 −1.76941 −0.884703 0.466156i \(-0.845639\pi\)
−0.884703 + 0.466156i \(0.845639\pi\)
\(824\) 32.2927 1.12497
\(825\) 13.3076 0.463310
\(826\) −0.891893 −0.0310329
\(827\) 28.9588 1.00700 0.503498 0.863996i \(-0.332046\pi\)
0.503498 + 0.863996i \(0.332046\pi\)
\(828\) 9.81563 0.341117
\(829\) −42.4799 −1.47539 −0.737694 0.675135i \(-0.764085\pi\)
−0.737694 + 0.675135i \(0.764085\pi\)
\(830\) −9.01722 −0.312992
\(831\) 2.66248 0.0923605
\(832\) 2.67725 0.0928170
\(833\) 0.856481 0.0296753
\(834\) 11.7616 0.407269
\(835\) −21.3323 −0.738233
\(836\) −14.4745 −0.500611
\(837\) −0.134605 −0.00465261
\(838\) 10.2363 0.353607
\(839\) −33.2494 −1.14790 −0.573948 0.818892i \(-0.694589\pi\)
−0.573948 + 0.818892i \(0.694589\pi\)
\(840\) 2.99959 0.103496
\(841\) −14.2149 −0.490171
\(842\) −12.0546 −0.415428
\(843\) −26.0334 −0.896637
\(844\) −23.2142 −0.799065
\(845\) 14.4402 0.496760
\(846\) −0.527652 −0.0181410
\(847\) 10.6338 0.365380
\(848\) 0.880561 0.0302386
\(849\) 8.80119 0.302056
\(850\) 1.36157 0.0467016
\(851\) 29.6724 1.01716
\(852\) −6.05052 −0.207287
\(853\) −14.8558 −0.508651 −0.254326 0.967119i \(-0.581854\pi\)
−0.254326 + 0.967119i \(0.581854\pi\)
\(854\) −8.61783 −0.294896
\(855\) −2.69104 −0.0920317
\(856\) 9.21551 0.314980
\(857\) −18.3348 −0.626304 −0.313152 0.949703i \(-0.601385\pi\)
−0.313152 + 0.949703i \(0.601385\pi\)
\(858\) −4.56955 −0.156002
\(859\) 43.6975 1.49094 0.745470 0.666539i \(-0.232225\pi\)
0.745470 + 0.666539i \(0.232225\pi\)
\(860\) 10.5685 0.360384
\(861\) 7.45941 0.254216
\(862\) 1.02800 0.0350139
\(863\) 53.6603 1.82662 0.913309 0.407268i \(-0.133518\pi\)
0.913309 + 0.407268i \(0.133518\pi\)
\(864\) 5.34826 0.181951
\(865\) 30.1658 1.02567
\(866\) −9.09795 −0.309161
\(867\) 16.2664 0.552437
\(868\) −0.227652 −0.00772702
\(869\) −13.5053 −0.458136
\(870\) −3.12462 −0.105935
\(871\) 22.7086 0.769451
\(872\) 4.36499 0.147817
\(873\) −12.3661 −0.418529
\(874\) 5.93364 0.200708
\(875\) 11.4968 0.388664
\(876\) 4.43722 0.149920
\(877\) −14.5423 −0.491057 −0.245529 0.969389i \(-0.578962\pi\)
−0.245529 + 0.969389i \(0.578962\pi\)
\(878\) −5.90188 −0.199179
\(879\) −22.3910 −0.755229
\(880\) −15.2572 −0.514322
\(881\) 14.2821 0.481176 0.240588 0.970627i \(-0.422660\pi\)
0.240588 + 0.970627i \(0.422660\pi\)
\(882\) −0.555636 −0.0187093
\(883\) 53.2177 1.79092 0.895459 0.445144i \(-0.146847\pi\)
0.895459 + 0.445144i \(0.146847\pi\)
\(884\) 2.56122 0.0861432
\(885\) 2.34757 0.0789126
\(886\) 5.92119 0.198926
\(887\) −29.2156 −0.980965 −0.490482 0.871451i \(-0.663179\pi\)
−0.490482 + 0.871451i \(0.663179\pi\)
\(888\) 10.4861 0.351890
\(889\) −3.68860 −0.123712
\(890\) −5.77694 −0.193644
\(891\) 4.65121 0.155821
\(892\) −11.3880 −0.381298
\(893\) 1.74736 0.0584731
\(894\) 13.1284 0.439079
\(895\) 17.3494 0.579928
\(896\) 11.5378 0.385452
\(897\) −10.2618 −0.342631
\(898\) −14.4775 −0.483120
\(899\) 0.517572 0.0172620
\(900\) 4.83888 0.161296
\(901\) 0.336250 0.0112021
\(902\) 19.2780 0.641886
\(903\) −4.27274 −0.142188
\(904\) 11.6081 0.386080
\(905\) −9.32317 −0.309913
\(906\) −2.33676 −0.0776338
\(907\) −8.61836 −0.286168 −0.143084 0.989711i \(-0.545702\pi\)
−0.143084 + 0.989711i \(0.545702\pi\)
\(908\) −10.2622 −0.340564
\(909\) −0.917518 −0.0304321
\(910\) −1.43682 −0.0476302
\(911\) −3.05285 −0.101145 −0.0505726 0.998720i \(-0.516105\pi\)
−0.0505726 + 0.998720i \(0.516105\pi\)
\(912\) −4.12705 −0.136660
\(913\) −51.6122 −1.70811
\(914\) 7.98616 0.264159
\(915\) 22.6831 0.749881
\(916\) −28.5319 −0.942720
\(917\) 9.84593 0.325141
\(918\) 0.475892 0.0157068
\(919\) 56.5586 1.86570 0.932848 0.360270i \(-0.117316\pi\)
0.932848 + 0.360270i \(0.117316\pi\)
\(920\) 17.4088 0.573950
\(921\) 24.7055 0.814073
\(922\) 0.759280 0.0250056
\(923\) 6.32553 0.208207
\(924\) 7.86644 0.258787
\(925\) 14.6278 0.480959
\(926\) −1.61549 −0.0530883
\(927\) 15.7448 0.517127
\(928\) −20.5648 −0.675071
\(929\) 4.13974 0.135820 0.0679102 0.997691i \(-0.478367\pi\)
0.0679102 + 0.997691i \(0.478367\pi\)
\(930\) −0.109382 −0.00358678
\(931\) 1.84003 0.0603045
\(932\) 7.75177 0.253918
\(933\) −21.3674 −0.699538
\(934\) 16.9103 0.553324
\(935\) −5.82612 −0.190534
\(936\) −3.62646 −0.118535
\(937\) 37.8494 1.23649 0.618243 0.785987i \(-0.287845\pi\)
0.618243 + 0.785987i \(0.287845\pi\)
\(938\) 7.13614 0.233003
\(939\) −19.2229 −0.627317
\(940\) 2.34890 0.0766128
\(941\) 1.43847 0.0468928 0.0234464 0.999725i \(-0.492536\pi\)
0.0234464 + 0.999725i \(0.492536\pi\)
\(942\) −3.35770 −0.109400
\(943\) 43.2922 1.40979
\(944\) 3.60028 0.117179
\(945\) 1.46250 0.0475751
\(946\) −11.0424 −0.359019
\(947\) −8.20248 −0.266545 −0.133272 0.991079i \(-0.542549\pi\)
−0.133272 + 0.991079i \(0.542549\pi\)
\(948\) −4.91078 −0.159495
\(949\) −4.63891 −0.150585
\(950\) 2.92515 0.0949043
\(951\) 5.92136 0.192013
\(952\) 1.75665 0.0569332
\(953\) 25.9608 0.840953 0.420476 0.907303i \(-0.361863\pi\)
0.420476 + 0.907303i \(0.361863\pi\)
\(954\) −0.218140 −0.00706255
\(955\) 20.0253 0.648003
\(956\) 9.00319 0.291184
\(957\) −17.8845 −0.578125
\(958\) 1.15740 0.0373939
\(959\) 2.63093 0.0849571
\(960\) −2.21446 −0.0714714
\(961\) −30.9819 −0.999416
\(962\) −5.02290 −0.161945
\(963\) 4.49317 0.144790
\(964\) −1.11246 −0.0358298
\(965\) 12.6135 0.406042
\(966\) −3.22475 −0.103755
\(967\) 35.0051 1.12569 0.562844 0.826563i \(-0.309707\pi\)
0.562844 + 0.826563i \(0.309707\pi\)
\(968\) 21.8099 0.700995
\(969\) −1.57595 −0.0506268
\(970\) −10.0489 −0.322651
\(971\) 26.1983 0.840744 0.420372 0.907352i \(-0.361900\pi\)
0.420372 + 0.907352i \(0.361900\pi\)
\(972\) 1.69127 0.0542475
\(973\) 21.1677 0.678606
\(974\) −6.71749 −0.215242
\(975\) −5.05882 −0.162012
\(976\) 34.7874 1.11352
\(977\) −28.1719 −0.901298 −0.450649 0.892701i \(-0.648807\pi\)
−0.450649 + 0.892701i \(0.648807\pi\)
\(978\) −2.20819 −0.0706102
\(979\) −33.0657 −1.05678
\(980\) 2.47348 0.0790124
\(981\) 2.12822 0.0679489
\(982\) −8.50479 −0.271399
\(983\) −20.7021 −0.660294 −0.330147 0.943929i \(-0.607098\pi\)
−0.330147 + 0.943929i \(0.607098\pi\)
\(984\) 15.2993 0.487723
\(985\) 10.4615 0.333331
\(986\) −1.82987 −0.0582749
\(987\) −0.949635 −0.0302272
\(988\) 5.50243 0.175056
\(989\) −24.7977 −0.788522
\(990\) 3.77966 0.120125
\(991\) −31.6952 −1.00683 −0.503415 0.864045i \(-0.667923\pi\)
−0.503415 + 0.864045i \(0.667923\pi\)
\(992\) −0.719900 −0.0228568
\(993\) 35.5887 1.12937
\(994\) 1.98779 0.0630489
\(995\) 32.7219 1.03735
\(996\) −18.7672 −0.594660
\(997\) −7.17055 −0.227094 −0.113547 0.993533i \(-0.536221\pi\)
−0.113547 + 0.993533i \(0.536221\pi\)
\(998\) 19.3116 0.611297
\(999\) 5.11266 0.161757
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 8043.2.a.o.1.18 41
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
8043.2.a.o.1.18 41 1.1 even 1 trivial