Properties

Label 4011.2.a.j.1.9
Level $4011$
Weight $2$
Character 4011.1
Self dual yes
Analytic conductor $32.028$
Analytic rank $0$
Dimension $26$
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] = [4011,2,Mod(1,4011)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(4011, 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("4011.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 4011 = 3 \cdot 7 \cdot 191 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 4011.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: \(32.0279962507\)
Analytic rank: \(0\)
Dimension: \(26\)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.9
Character \(\chi\) \(=\) 4011.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-1.07123 q^{2} -1.00000 q^{3} -0.852471 q^{4} -1.60541 q^{5} +1.07123 q^{6} -1.00000 q^{7} +3.05565 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q-1.07123 q^{2} -1.00000 q^{3} -0.852471 q^{4} -1.60541 q^{5} +1.07123 q^{6} -1.00000 q^{7} +3.05565 q^{8} +1.00000 q^{9} +1.71976 q^{10} +3.95375 q^{11} +0.852471 q^{12} +2.25813 q^{13} +1.07123 q^{14} +1.60541 q^{15} -1.56835 q^{16} +7.21920 q^{17} -1.07123 q^{18} +3.29499 q^{19} +1.36856 q^{20} +1.00000 q^{21} -4.23537 q^{22} +7.63636 q^{23} -3.05565 q^{24} -2.42267 q^{25} -2.41897 q^{26} -1.00000 q^{27} +0.852471 q^{28} +2.20779 q^{29} -1.71976 q^{30} +3.76529 q^{31} -4.43123 q^{32} -3.95375 q^{33} -7.73341 q^{34} +1.60541 q^{35} -0.852471 q^{36} +7.13126 q^{37} -3.52969 q^{38} -2.25813 q^{39} -4.90556 q^{40} +2.60553 q^{41} -1.07123 q^{42} -4.92670 q^{43} -3.37046 q^{44} -1.60541 q^{45} -8.18029 q^{46} -3.37970 q^{47} +1.56835 q^{48} +1.00000 q^{49} +2.59523 q^{50} -7.21920 q^{51} -1.92499 q^{52} -6.43059 q^{53} +1.07123 q^{54} -6.34738 q^{55} -3.05565 q^{56} -3.29499 q^{57} -2.36504 q^{58} +7.10117 q^{59} -1.36856 q^{60} +9.46455 q^{61} -4.03348 q^{62} -1.00000 q^{63} +7.88356 q^{64} -3.62521 q^{65} +4.23537 q^{66} -2.59510 q^{67} -6.15416 q^{68} -7.63636 q^{69} -1.71976 q^{70} -3.53690 q^{71} +3.05565 q^{72} -12.6813 q^{73} -7.63920 q^{74} +2.42267 q^{75} -2.80889 q^{76} -3.95375 q^{77} +2.41897 q^{78} +9.03996 q^{79} +2.51784 q^{80} +1.00000 q^{81} -2.79112 q^{82} +1.94384 q^{83} -0.852471 q^{84} -11.5898 q^{85} +5.27761 q^{86} -2.20779 q^{87} +12.0813 q^{88} -1.89187 q^{89} +1.71976 q^{90} -2.25813 q^{91} -6.50978 q^{92} -3.76529 q^{93} +3.62043 q^{94} -5.28981 q^{95} +4.43123 q^{96} +10.9501 q^{97} -1.07123 q^{98} +3.95375 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 26 q - 26 q^{3} + 34 q^{4} + 2 q^{5} - 26 q^{7} + 26 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 26 q - 26 q^{3} + 34 q^{4} + 2 q^{5} - 26 q^{7} + 26 q^{9} - q^{10} + 13 q^{11} - 34 q^{12} - q^{13} - 2 q^{15} + 54 q^{16} + q^{19} - 22 q^{20} + 26 q^{21} + 17 q^{22} - 3 q^{23} + 48 q^{25} + 6 q^{26} - 26 q^{27} - 34 q^{28} + 23 q^{29} + q^{30} + 18 q^{31} + 10 q^{32} - 13 q^{33} - 19 q^{34} - 2 q^{35} + 34 q^{36} + 23 q^{37} - 15 q^{38} + q^{39} + 14 q^{40} - 4 q^{41} + 5 q^{43} + 60 q^{44} + 2 q^{45} + 8 q^{46} - 20 q^{47} - 54 q^{48} + 26 q^{49} + 26 q^{50} + 19 q^{52} + 31 q^{53} + 41 q^{55} - q^{57} + 19 q^{58} - 2 q^{59} + 22 q^{60} - 2 q^{61} - 35 q^{62} - 26 q^{63} + 132 q^{64} + 40 q^{65} - 17 q^{66} + 47 q^{67} - 60 q^{68} + 3 q^{69} + q^{70} + 16 q^{71} - 23 q^{73} + 34 q^{74} - 48 q^{75} + 72 q^{76} - 13 q^{77} - 6 q^{78} + 14 q^{79} - 21 q^{80} + 26 q^{81} + 60 q^{82} - 4 q^{83} + 34 q^{84} + 36 q^{85} + 21 q^{86} - 23 q^{87} + 67 q^{88} + 14 q^{89} - q^{90} + q^{91} + 20 q^{92} - 18 q^{93} + 58 q^{94} - 4 q^{95} - 10 q^{96} + 48 q^{97} + 13 q^{99}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.07123 −0.757472 −0.378736 0.925505i \(-0.623641\pi\)
−0.378736 + 0.925505i \(0.623641\pi\)
\(3\) −1.00000 −0.577350
\(4\) −0.852471 −0.426236
\(5\) −1.60541 −0.717960 −0.358980 0.933345i \(-0.616875\pi\)
−0.358980 + 0.933345i \(0.616875\pi\)
\(6\) 1.07123 0.437327
\(7\) −1.00000 −0.377964
\(8\) 3.05565 1.08033
\(9\) 1.00000 0.333333
\(10\) 1.71976 0.543835
\(11\) 3.95375 1.19210 0.596050 0.802947i \(-0.296736\pi\)
0.596050 + 0.802947i \(0.296736\pi\)
\(12\) 0.852471 0.246087
\(13\) 2.25813 0.626292 0.313146 0.949705i \(-0.398617\pi\)
0.313146 + 0.949705i \(0.398617\pi\)
\(14\) 1.07123 0.286298
\(15\) 1.60541 0.414514
\(16\) −1.56835 −0.392088
\(17\) 7.21920 1.75091 0.875456 0.483297i \(-0.160561\pi\)
0.875456 + 0.483297i \(0.160561\pi\)
\(18\) −1.07123 −0.252491
\(19\) 3.29499 0.755924 0.377962 0.925821i \(-0.376625\pi\)
0.377962 + 0.925821i \(0.376625\pi\)
\(20\) 1.36856 0.306020
\(21\) 1.00000 0.218218
\(22\) −4.23537 −0.902983
\(23\) 7.63636 1.59229 0.796146 0.605105i \(-0.206869\pi\)
0.796146 + 0.605105i \(0.206869\pi\)
\(24\) −3.05565 −0.623731
\(25\) −2.42267 −0.484533
\(26\) −2.41897 −0.474399
\(27\) −1.00000 −0.192450
\(28\) 0.852471 0.161102
\(29\) 2.20779 0.409975 0.204988 0.978765i \(-0.434285\pi\)
0.204988 + 0.978765i \(0.434285\pi\)
\(30\) −1.71976 −0.313983
\(31\) 3.76529 0.676265 0.338133 0.941098i \(-0.390205\pi\)
0.338133 + 0.941098i \(0.390205\pi\)
\(32\) −4.43123 −0.783338
\(33\) −3.95375 −0.688259
\(34\) −7.73341 −1.32627
\(35\) 1.60541 0.271363
\(36\) −0.852471 −0.142079
\(37\) 7.13126 1.17237 0.586186 0.810177i \(-0.300629\pi\)
0.586186 + 0.810177i \(0.300629\pi\)
\(38\) −3.52969 −0.572591
\(39\) −2.25813 −0.361590
\(40\) −4.90556 −0.775637
\(41\) 2.60553 0.406915 0.203458 0.979084i \(-0.434782\pi\)
0.203458 + 0.979084i \(0.434782\pi\)
\(42\) −1.07123 −0.165294
\(43\) −4.92670 −0.751314 −0.375657 0.926759i \(-0.622583\pi\)
−0.375657 + 0.926759i \(0.622583\pi\)
\(44\) −3.37046 −0.508116
\(45\) −1.60541 −0.239320
\(46\) −8.18029 −1.20612
\(47\) −3.37970 −0.492980 −0.246490 0.969145i \(-0.579277\pi\)
−0.246490 + 0.969145i \(0.579277\pi\)
\(48\) 1.56835 0.226372
\(49\) 1.00000 0.142857
\(50\) 2.59523 0.367021
\(51\) −7.21920 −1.01089
\(52\) −1.92499 −0.266948
\(53\) −6.43059 −0.883309 −0.441655 0.897185i \(-0.645608\pi\)
−0.441655 + 0.897185i \(0.645608\pi\)
\(54\) 1.07123 0.145776
\(55\) −6.34738 −0.855880
\(56\) −3.05565 −0.408328
\(57\) −3.29499 −0.436433
\(58\) −2.36504 −0.310545
\(59\) 7.10117 0.924494 0.462247 0.886751i \(-0.347043\pi\)
0.462247 + 0.886751i \(0.347043\pi\)
\(60\) −1.36856 −0.176681
\(61\) 9.46455 1.21181 0.605906 0.795536i \(-0.292811\pi\)
0.605906 + 0.795536i \(0.292811\pi\)
\(62\) −4.03348 −0.512252
\(63\) −1.00000 −0.125988
\(64\) 7.88356 0.985445
\(65\) −3.62521 −0.449652
\(66\) 4.23537 0.521338
\(67\) −2.59510 −0.317042 −0.158521 0.987356i \(-0.550673\pi\)
−0.158521 + 0.987356i \(0.550673\pi\)
\(68\) −6.15416 −0.746301
\(69\) −7.63636 −0.919310
\(70\) −1.71976 −0.205550
\(71\) −3.53690 −0.419753 −0.209877 0.977728i \(-0.567306\pi\)
−0.209877 + 0.977728i \(0.567306\pi\)
\(72\) 3.05565 0.360111
\(73\) −12.6813 −1.48424 −0.742119 0.670268i \(-0.766179\pi\)
−0.742119 + 0.670268i \(0.766179\pi\)
\(74\) −7.63920 −0.888039
\(75\) 2.42267 0.279745
\(76\) −2.80889 −0.322202
\(77\) −3.95375 −0.450572
\(78\) 2.41897 0.273894
\(79\) 9.03996 1.01707 0.508537 0.861040i \(-0.330186\pi\)
0.508537 + 0.861040i \(0.330186\pi\)
\(80\) 2.51784 0.281503
\(81\) 1.00000 0.111111
\(82\) −2.79112 −0.308227
\(83\) 1.94384 0.213364 0.106682 0.994293i \(-0.465977\pi\)
0.106682 + 0.994293i \(0.465977\pi\)
\(84\) −0.852471 −0.0930122
\(85\) −11.5898 −1.25709
\(86\) 5.27761 0.569100
\(87\) −2.20779 −0.236699
\(88\) 12.0813 1.28787
\(89\) −1.89187 −0.200538 −0.100269 0.994960i \(-0.531970\pi\)
−0.100269 + 0.994960i \(0.531970\pi\)
\(90\) 1.71976 0.181278
\(91\) −2.25813 −0.236716
\(92\) −6.50978 −0.678691
\(93\) −3.76529 −0.390442
\(94\) 3.62043 0.373419
\(95\) −5.28981 −0.542723
\(96\) 4.43123 0.452261
\(97\) 10.9501 1.11181 0.555906 0.831245i \(-0.312372\pi\)
0.555906 + 0.831245i \(0.312372\pi\)
\(98\) −1.07123 −0.108210
\(99\) 3.95375 0.397367
\(100\) 2.06525 0.206525
\(101\) −16.7754 −1.66921 −0.834606 0.550847i \(-0.814305\pi\)
−0.834606 + 0.550847i \(0.814305\pi\)
\(102\) 7.73341 0.765721
\(103\) 7.97639 0.785937 0.392968 0.919552i \(-0.371448\pi\)
0.392968 + 0.919552i \(0.371448\pi\)
\(104\) 6.90004 0.676604
\(105\) −1.60541 −0.156672
\(106\) 6.88862 0.669082
\(107\) −5.72343 −0.553305 −0.276653 0.960970i \(-0.589225\pi\)
−0.276653 + 0.960970i \(0.589225\pi\)
\(108\) 0.852471 0.0820291
\(109\) 4.81420 0.461117 0.230558 0.973058i \(-0.425945\pi\)
0.230558 + 0.973058i \(0.425945\pi\)
\(110\) 6.79949 0.648306
\(111\) −7.13126 −0.676869
\(112\) 1.56835 0.148195
\(113\) 6.71853 0.632026 0.316013 0.948755i \(-0.397656\pi\)
0.316013 + 0.948755i \(0.397656\pi\)
\(114\) 3.52969 0.330586
\(115\) −12.2595 −1.14320
\(116\) −1.88207 −0.174746
\(117\) 2.25813 0.208764
\(118\) −7.60697 −0.700279
\(119\) −7.21920 −0.661783
\(120\) 4.90556 0.447814
\(121\) 4.63214 0.421103
\(122\) −10.1387 −0.917914
\(123\) −2.60553 −0.234933
\(124\) −3.20980 −0.288248
\(125\) 11.9164 1.06584
\(126\) 1.07123 0.0954326
\(127\) 8.46541 0.751184 0.375592 0.926785i \(-0.377439\pi\)
0.375592 + 0.926785i \(0.377439\pi\)
\(128\) 0.417375 0.0368911
\(129\) 4.92670 0.433771
\(130\) 3.88343 0.340599
\(131\) −7.42020 −0.648306 −0.324153 0.946005i \(-0.605079\pi\)
−0.324153 + 0.946005i \(0.605079\pi\)
\(132\) 3.37046 0.293361
\(133\) −3.29499 −0.285712
\(134\) 2.77995 0.240151
\(135\) 1.60541 0.138171
\(136\) 22.0593 1.89157
\(137\) 1.68559 0.144010 0.0720050 0.997404i \(-0.477060\pi\)
0.0720050 + 0.997404i \(0.477060\pi\)
\(138\) 8.18029 0.696352
\(139\) −9.79050 −0.830419 −0.415210 0.909726i \(-0.636292\pi\)
−0.415210 + 0.909726i \(0.636292\pi\)
\(140\) −1.36856 −0.115665
\(141\) 3.37970 0.284622
\(142\) 3.78883 0.317952
\(143\) 8.92807 0.746602
\(144\) −1.56835 −0.130696
\(145\) −3.54439 −0.294346
\(146\) 13.5846 1.12427
\(147\) −1.00000 −0.0824786
\(148\) −6.07919 −0.499706
\(149\) 0.674214 0.0552338 0.0276169 0.999619i \(-0.491208\pi\)
0.0276169 + 0.999619i \(0.491208\pi\)
\(150\) −2.59523 −0.211899
\(151\) 6.29611 0.512370 0.256185 0.966628i \(-0.417534\pi\)
0.256185 + 0.966628i \(0.417534\pi\)
\(152\) 10.0683 0.816650
\(153\) 7.21920 0.583638
\(154\) 4.23537 0.341296
\(155\) −6.04482 −0.485531
\(156\) 1.92499 0.154122
\(157\) −17.4938 −1.39616 −0.698078 0.716022i \(-0.745961\pi\)
−0.698078 + 0.716022i \(0.745961\pi\)
\(158\) −9.68385 −0.770406
\(159\) 6.43059 0.509979
\(160\) 7.11393 0.562406
\(161\) −7.63636 −0.601830
\(162\) −1.07123 −0.0841636
\(163\) 22.3848 1.75332 0.876658 0.481114i \(-0.159768\pi\)
0.876658 + 0.481114i \(0.159768\pi\)
\(164\) −2.22114 −0.173442
\(165\) 6.34738 0.494143
\(166\) −2.08229 −0.161617
\(167\) −24.6831 −1.91004 −0.955018 0.296548i \(-0.904165\pi\)
−0.955018 + 0.296548i \(0.904165\pi\)
\(168\) 3.05565 0.235748
\(169\) −7.90087 −0.607759
\(170\) 12.4153 0.952207
\(171\) 3.29499 0.251975
\(172\) 4.19987 0.320237
\(173\) 11.6998 0.889519 0.444759 0.895650i \(-0.353289\pi\)
0.444759 + 0.895650i \(0.353289\pi\)
\(174\) 2.36504 0.179293
\(175\) 2.42267 0.183136
\(176\) −6.20087 −0.467408
\(177\) −7.10117 −0.533757
\(178\) 2.02663 0.151902
\(179\) −8.71883 −0.651676 −0.325838 0.945426i \(-0.605646\pi\)
−0.325838 + 0.945426i \(0.605646\pi\)
\(180\) 1.36856 0.102007
\(181\) 15.5238 1.15387 0.576936 0.816790i \(-0.304248\pi\)
0.576936 + 0.816790i \(0.304248\pi\)
\(182\) 2.41897 0.179306
\(183\) −9.46455 −0.699640
\(184\) 23.3340 1.72021
\(185\) −11.4486 −0.841716
\(186\) 4.03348 0.295749
\(187\) 28.5429 2.08726
\(188\) 2.88110 0.210126
\(189\) 1.00000 0.0727393
\(190\) 5.66659 0.411098
\(191\) 1.00000 0.0723575
\(192\) −7.88356 −0.568947
\(193\) 8.77267 0.631470 0.315735 0.948847i \(-0.397749\pi\)
0.315735 + 0.948847i \(0.397749\pi\)
\(194\) −11.7300 −0.842166
\(195\) 3.62521 0.259607
\(196\) −0.852471 −0.0608908
\(197\) 20.1146 1.43311 0.716554 0.697532i \(-0.245718\pi\)
0.716554 + 0.697532i \(0.245718\pi\)
\(198\) −4.23537 −0.300994
\(199\) −9.89253 −0.701263 −0.350631 0.936514i \(-0.614033\pi\)
−0.350631 + 0.936514i \(0.614033\pi\)
\(200\) −7.40281 −0.523458
\(201\) 2.59510 0.183044
\(202\) 17.9702 1.26438
\(203\) −2.20779 −0.154956
\(204\) 6.15416 0.430877
\(205\) −4.18294 −0.292149
\(206\) −8.54453 −0.595325
\(207\) 7.63636 0.530764
\(208\) −3.54153 −0.245561
\(209\) 13.0276 0.901137
\(210\) 1.71976 0.118675
\(211\) 10.9634 0.754750 0.377375 0.926061i \(-0.376827\pi\)
0.377375 + 0.926061i \(0.376827\pi\)
\(212\) 5.48189 0.376498
\(213\) 3.53690 0.242345
\(214\) 6.13110 0.419113
\(215\) 7.90935 0.539413
\(216\) −3.05565 −0.207910
\(217\) −3.76529 −0.255604
\(218\) −5.15710 −0.349283
\(219\) 12.6813 0.856925
\(220\) 5.41096 0.364807
\(221\) 16.3019 1.09658
\(222\) 7.63920 0.512709
\(223\) 5.73082 0.383764 0.191882 0.981418i \(-0.438541\pi\)
0.191882 + 0.981418i \(0.438541\pi\)
\(224\) 4.43123 0.296074
\(225\) −2.42267 −0.161511
\(226\) −7.19708 −0.478743
\(227\) −18.8079 −1.24832 −0.624162 0.781295i \(-0.714560\pi\)
−0.624162 + 0.781295i \(0.714560\pi\)
\(228\) 2.80889 0.186023
\(229\) −6.31690 −0.417432 −0.208716 0.977976i \(-0.566928\pi\)
−0.208716 + 0.977976i \(0.566928\pi\)
\(230\) 13.1327 0.865944
\(231\) 3.95375 0.260138
\(232\) 6.74621 0.442910
\(233\) −1.27413 −0.0834710 −0.0417355 0.999129i \(-0.513289\pi\)
−0.0417355 + 0.999129i \(0.513289\pi\)
\(234\) −2.41897 −0.158133
\(235\) 5.42579 0.353940
\(236\) −6.05354 −0.394052
\(237\) −9.03996 −0.587208
\(238\) 7.73341 0.501282
\(239\) −22.0775 −1.42807 −0.714036 0.700109i \(-0.753135\pi\)
−0.714036 + 0.700109i \(0.753135\pi\)
\(240\) −2.51784 −0.162526
\(241\) −18.2835 −1.17774 −0.588871 0.808227i \(-0.700427\pi\)
−0.588871 + 0.808227i \(0.700427\pi\)
\(242\) −4.96207 −0.318974
\(243\) −1.00000 −0.0641500
\(244\) −8.06826 −0.516517
\(245\) −1.60541 −0.102566
\(246\) 2.79112 0.177955
\(247\) 7.44051 0.473429
\(248\) 11.5054 0.730592
\(249\) −1.94384 −0.123186
\(250\) −12.7652 −0.807341
\(251\) 24.5159 1.54743 0.773715 0.633533i \(-0.218396\pi\)
0.773715 + 0.633533i \(0.218396\pi\)
\(252\) 0.852471 0.0537006
\(253\) 30.1923 1.89817
\(254\) −9.06839 −0.569001
\(255\) 11.5898 0.725779
\(256\) −16.2142 −1.01339
\(257\) 1.86568 0.116378 0.0581889 0.998306i \(-0.481467\pi\)
0.0581889 + 0.998306i \(0.481467\pi\)
\(258\) −5.27761 −0.328570
\(259\) −7.13126 −0.443115
\(260\) 3.09039 0.191658
\(261\) 2.20779 0.136658
\(262\) 7.94872 0.491074
\(263\) −13.3481 −0.823076 −0.411538 0.911392i \(-0.635008\pi\)
−0.411538 + 0.911392i \(0.635008\pi\)
\(264\) −12.0813 −0.743550
\(265\) 10.3237 0.634181
\(266\) 3.52969 0.216419
\(267\) 1.89187 0.115781
\(268\) 2.21225 0.135135
\(269\) 8.19868 0.499883 0.249941 0.968261i \(-0.419589\pi\)
0.249941 + 0.968261i \(0.419589\pi\)
\(270\) −1.71976 −0.104661
\(271\) −24.3911 −1.48165 −0.740826 0.671697i \(-0.765566\pi\)
−0.740826 + 0.671697i \(0.765566\pi\)
\(272\) −11.3222 −0.686511
\(273\) 2.25813 0.136668
\(274\) −1.80565 −0.109084
\(275\) −9.57862 −0.577612
\(276\) 6.50978 0.391843
\(277\) −1.15495 −0.0693943 −0.0346972 0.999398i \(-0.511047\pi\)
−0.0346972 + 0.999398i \(0.511047\pi\)
\(278\) 10.4879 0.629020
\(279\) 3.76529 0.225422
\(280\) 4.90556 0.293163
\(281\) −7.98233 −0.476186 −0.238093 0.971242i \(-0.576522\pi\)
−0.238093 + 0.971242i \(0.576522\pi\)
\(282\) −3.62043 −0.215593
\(283\) 27.6027 1.64081 0.820406 0.571781i \(-0.193747\pi\)
0.820406 + 0.571781i \(0.193747\pi\)
\(284\) 3.01511 0.178914
\(285\) 5.28981 0.313341
\(286\) −9.56399 −0.565531
\(287\) −2.60553 −0.153800
\(288\) −4.43123 −0.261113
\(289\) 35.1168 2.06570
\(290\) 3.79685 0.222959
\(291\) −10.9501 −0.641904
\(292\) 10.8105 0.632635
\(293\) 10.6042 0.619505 0.309752 0.950817i \(-0.399754\pi\)
0.309752 + 0.950817i \(0.399754\pi\)
\(294\) 1.07123 0.0624753
\(295\) −11.4003 −0.663750
\(296\) 21.7906 1.26655
\(297\) −3.95375 −0.229420
\(298\) −0.722237 −0.0418381
\(299\) 17.2439 0.997239
\(300\) −2.06525 −0.119237
\(301\) 4.92670 0.283970
\(302\) −6.74457 −0.388106
\(303\) 16.7754 0.963720
\(304\) −5.16771 −0.296388
\(305\) −15.1945 −0.870033
\(306\) −7.73341 −0.442089
\(307\) −0.647153 −0.0369350 −0.0184675 0.999829i \(-0.505879\pi\)
−0.0184675 + 0.999829i \(0.505879\pi\)
\(308\) 3.37046 0.192050
\(309\) −7.97639 −0.453761
\(310\) 6.47538 0.367777
\(311\) 1.95496 0.110856 0.0554279 0.998463i \(-0.482348\pi\)
0.0554279 + 0.998463i \(0.482348\pi\)
\(312\) −6.90004 −0.390638
\(313\) 4.32445 0.244432 0.122216 0.992503i \(-0.461000\pi\)
0.122216 + 0.992503i \(0.461000\pi\)
\(314\) 18.7398 1.05755
\(315\) 1.60541 0.0904545
\(316\) −7.70630 −0.433513
\(317\) −8.61346 −0.483780 −0.241890 0.970304i \(-0.577767\pi\)
−0.241890 + 0.970304i \(0.577767\pi\)
\(318\) −6.88862 −0.386295
\(319\) 8.72903 0.488732
\(320\) −12.6563 −0.707510
\(321\) 5.72343 0.319451
\(322\) 8.18029 0.455869
\(323\) 23.7872 1.32356
\(324\) −0.852471 −0.0473595
\(325\) −5.47069 −0.303459
\(326\) −23.9793 −1.32809
\(327\) −4.81420 −0.266226
\(328\) 7.96158 0.439605
\(329\) 3.37970 0.186329
\(330\) −6.79949 −0.374300
\(331\) 33.1706 1.82322 0.911610 0.411057i \(-0.134840\pi\)
0.911610 + 0.411057i \(0.134840\pi\)
\(332\) −1.65706 −0.0909433
\(333\) 7.13126 0.390790
\(334\) 26.4412 1.44680
\(335\) 4.16620 0.227624
\(336\) −1.56835 −0.0855605
\(337\) 24.7860 1.35018 0.675090 0.737735i \(-0.264105\pi\)
0.675090 + 0.737735i \(0.264105\pi\)
\(338\) 8.46363 0.460361
\(339\) −6.71853 −0.364901
\(340\) 9.87993 0.535814
\(341\) 14.8870 0.806176
\(342\) −3.52969 −0.190864
\(343\) −1.00000 −0.0539949
\(344\) −15.0542 −0.811670
\(345\) 12.2595 0.660028
\(346\) −12.5331 −0.673786
\(347\) −15.3519 −0.824134 −0.412067 0.911154i \(-0.635193\pi\)
−0.412067 + 0.911154i \(0.635193\pi\)
\(348\) 1.88207 0.100890
\(349\) −31.4705 −1.68458 −0.842288 0.539027i \(-0.818792\pi\)
−0.842288 + 0.539027i \(0.818792\pi\)
\(350\) −2.59523 −0.138721
\(351\) −2.25813 −0.120530
\(352\) −17.5200 −0.933818
\(353\) −26.5844 −1.41495 −0.707474 0.706740i \(-0.750165\pi\)
−0.707474 + 0.706740i \(0.750165\pi\)
\(354\) 7.60697 0.404306
\(355\) 5.67817 0.301366
\(356\) 1.61277 0.0854765
\(357\) 7.21920 0.382080
\(358\) 9.33985 0.493626
\(359\) 7.32424 0.386559 0.193279 0.981144i \(-0.438088\pi\)
0.193279 + 0.981144i \(0.438088\pi\)
\(360\) −4.90556 −0.258546
\(361\) −8.14301 −0.428580
\(362\) −16.6295 −0.874026
\(363\) −4.63214 −0.243124
\(364\) 1.92499 0.100897
\(365\) 20.3587 1.06562
\(366\) 10.1387 0.529958
\(367\) −36.3112 −1.89543 −0.947714 0.319121i \(-0.896612\pi\)
−0.947714 + 0.319121i \(0.896612\pi\)
\(368\) −11.9765 −0.624318
\(369\) 2.60553 0.135638
\(370\) 12.2640 0.637576
\(371\) 6.43059 0.333859
\(372\) 3.20980 0.166420
\(373\) 9.04125 0.468138 0.234069 0.972220i \(-0.424796\pi\)
0.234069 + 0.972220i \(0.424796\pi\)
\(374\) −30.5759 −1.58104
\(375\) −11.9164 −0.615360
\(376\) −10.3272 −0.532583
\(377\) 4.98546 0.256764
\(378\) −1.07123 −0.0550980
\(379\) 16.9931 0.872879 0.436440 0.899734i \(-0.356239\pi\)
0.436440 + 0.899734i \(0.356239\pi\)
\(380\) 4.50941 0.231328
\(381\) −8.46541 −0.433696
\(382\) −1.07123 −0.0548088
\(383\) −2.75744 −0.140899 −0.0704494 0.997515i \(-0.522443\pi\)
−0.0704494 + 0.997515i \(0.522443\pi\)
\(384\) −0.417375 −0.0212991
\(385\) 6.34738 0.323492
\(386\) −9.39752 −0.478321
\(387\) −4.92670 −0.250438
\(388\) −9.33462 −0.473893
\(389\) 24.7868 1.25674 0.628369 0.777915i \(-0.283723\pi\)
0.628369 + 0.777915i \(0.283723\pi\)
\(390\) −3.88343 −0.196645
\(391\) 55.1284 2.78796
\(392\) 3.05565 0.154333
\(393\) 7.42020 0.374299
\(394\) −21.5473 −1.08554
\(395\) −14.5128 −0.730219
\(396\) −3.37046 −0.169372
\(397\) −22.4693 −1.12770 −0.563851 0.825877i \(-0.690681\pi\)
−0.563851 + 0.825877i \(0.690681\pi\)
\(398\) 10.5972 0.531187
\(399\) 3.29499 0.164956
\(400\) 3.79959 0.189980
\(401\) 13.0849 0.653431 0.326715 0.945123i \(-0.394058\pi\)
0.326715 + 0.945123i \(0.394058\pi\)
\(402\) −2.77995 −0.138651
\(403\) 8.50249 0.423539
\(404\) 14.3005 0.711478
\(405\) −1.60541 −0.0797733
\(406\) 2.36504 0.117375
\(407\) 28.1952 1.39758
\(408\) −22.0593 −1.09210
\(409\) −9.41484 −0.465534 −0.232767 0.972533i \(-0.574778\pi\)
−0.232767 + 0.972533i \(0.574778\pi\)
\(410\) 4.48088 0.221295
\(411\) −1.68559 −0.0831442
\(412\) −6.79964 −0.334994
\(413\) −7.10117 −0.349426
\(414\) −8.18029 −0.402039
\(415\) −3.12065 −0.153187
\(416\) −10.0063 −0.490598
\(417\) 9.79050 0.479443
\(418\) −13.9555 −0.682586
\(419\) −27.5630 −1.34654 −0.673270 0.739397i \(-0.735111\pi\)
−0.673270 + 0.739397i \(0.735111\pi\)
\(420\) 1.36856 0.0667791
\(421\) −0.485100 −0.0236423 −0.0118212 0.999930i \(-0.503763\pi\)
−0.0118212 + 0.999930i \(0.503763\pi\)
\(422\) −11.7443 −0.571702
\(423\) −3.37970 −0.164327
\(424\) −19.6496 −0.954269
\(425\) −17.4897 −0.848376
\(426\) −3.78883 −0.183569
\(427\) −9.46455 −0.458022
\(428\) 4.87906 0.235838
\(429\) −8.92807 −0.431051
\(430\) −8.47272 −0.408591
\(431\) 40.3460 1.94340 0.971699 0.236224i \(-0.0759099\pi\)
0.971699 + 0.236224i \(0.0759099\pi\)
\(432\) 1.56835 0.0754573
\(433\) 3.01364 0.144826 0.0724132 0.997375i \(-0.476930\pi\)
0.0724132 + 0.997375i \(0.476930\pi\)
\(434\) 4.03348 0.193613
\(435\) 3.54439 0.169941
\(436\) −4.10397 −0.196544
\(437\) 25.1618 1.20365
\(438\) −13.5846 −0.649097
\(439\) 10.7374 0.512469 0.256235 0.966615i \(-0.417518\pi\)
0.256235 + 0.966615i \(0.417518\pi\)
\(440\) −19.3953 −0.924637
\(441\) 1.00000 0.0476190
\(442\) −17.4630 −0.830631
\(443\) −22.1940 −1.05447 −0.527234 0.849720i \(-0.676771\pi\)
−0.527234 + 0.849720i \(0.676771\pi\)
\(444\) 6.07919 0.288506
\(445\) 3.03723 0.143978
\(446\) −6.13902 −0.290691
\(447\) −0.674214 −0.0318892
\(448\) −7.88356 −0.372463
\(449\) 24.0274 1.13392 0.566962 0.823744i \(-0.308119\pi\)
0.566962 + 0.823744i \(0.308119\pi\)
\(450\) 2.59523 0.122340
\(451\) 10.3016 0.485084
\(452\) −5.72736 −0.269392
\(453\) −6.29611 −0.295817
\(454\) 20.1475 0.945571
\(455\) 3.62521 0.169953
\(456\) −10.0683 −0.471493
\(457\) −20.1053 −0.940484 −0.470242 0.882537i \(-0.655833\pi\)
−0.470242 + 0.882537i \(0.655833\pi\)
\(458\) 6.76684 0.316194
\(459\) −7.21920 −0.336963
\(460\) 10.4508 0.487273
\(461\) −30.3736 −1.41464 −0.707319 0.706895i \(-0.750095\pi\)
−0.707319 + 0.706895i \(0.750095\pi\)
\(462\) −4.23537 −0.197047
\(463\) 14.1708 0.658574 0.329287 0.944230i \(-0.393192\pi\)
0.329287 + 0.944230i \(0.393192\pi\)
\(464\) −3.46258 −0.160746
\(465\) 6.04482 0.280322
\(466\) 1.36488 0.0632270
\(467\) −36.9095 −1.70797 −0.853984 0.520300i \(-0.825820\pi\)
−0.853984 + 0.520300i \(0.825820\pi\)
\(468\) −1.92499 −0.0889826
\(469\) 2.59510 0.119831
\(470\) −5.81226 −0.268100
\(471\) 17.4938 0.806071
\(472\) 21.6987 0.998762
\(473\) −19.4789 −0.895642
\(474\) 9.68385 0.444794
\(475\) −7.98267 −0.366270
\(476\) 6.15416 0.282075
\(477\) −6.43059 −0.294436
\(478\) 23.6500 1.08173
\(479\) −31.4445 −1.43674 −0.718368 0.695664i \(-0.755110\pi\)
−0.718368 + 0.695664i \(0.755110\pi\)
\(480\) −7.11393 −0.324705
\(481\) 16.1033 0.734246
\(482\) 19.5858 0.892107
\(483\) 7.63636 0.347467
\(484\) −3.94876 −0.179489
\(485\) −17.5793 −0.798236
\(486\) 1.07123 0.0485919
\(487\) 17.6044 0.797732 0.398866 0.917009i \(-0.369404\pi\)
0.398866 + 0.917009i \(0.369404\pi\)
\(488\) 28.9203 1.30916
\(489\) −22.3848 −1.01228
\(490\) 1.71976 0.0776907
\(491\) 0.926528 0.0418136 0.0209068 0.999781i \(-0.493345\pi\)
0.0209068 + 0.999781i \(0.493345\pi\)
\(492\) 2.22114 0.100137
\(493\) 15.9384 0.717831
\(494\) −7.97048 −0.358609
\(495\) −6.34738 −0.285293
\(496\) −5.90529 −0.265155
\(497\) 3.53690 0.158652
\(498\) 2.08229 0.0933097
\(499\) −16.1234 −0.721780 −0.360890 0.932608i \(-0.617527\pi\)
−0.360890 + 0.932608i \(0.617527\pi\)
\(500\) −10.1584 −0.454297
\(501\) 24.6831 1.10276
\(502\) −26.2621 −1.17214
\(503\) 40.0355 1.78509 0.892547 0.450954i \(-0.148916\pi\)
0.892547 + 0.450954i \(0.148916\pi\)
\(504\) −3.05565 −0.136109
\(505\) 26.9313 1.19843
\(506\) −32.3428 −1.43781
\(507\) 7.90087 0.350890
\(508\) −7.21652 −0.320181
\(509\) −10.9560 −0.485617 −0.242809 0.970074i \(-0.578069\pi\)
−0.242809 + 0.970074i \(0.578069\pi\)
\(510\) −12.4153 −0.549757
\(511\) 12.6813 0.560989
\(512\) 16.5344 0.730723
\(513\) −3.29499 −0.145478
\(514\) −1.99857 −0.0881530
\(515\) −12.8053 −0.564271
\(516\) −4.19987 −0.184889
\(517\) −13.3625 −0.587681
\(518\) 7.63920 0.335647
\(519\) −11.6998 −0.513564
\(520\) −11.0774 −0.485775
\(521\) −3.93778 −0.172517 −0.0862585 0.996273i \(-0.527491\pi\)
−0.0862585 + 0.996273i \(0.527491\pi\)
\(522\) −2.36504 −0.103515
\(523\) 15.8233 0.691903 0.345952 0.938252i \(-0.387556\pi\)
0.345952 + 0.938252i \(0.387556\pi\)
\(524\) 6.32550 0.276331
\(525\) −2.42267 −0.105734
\(526\) 14.2988 0.623458
\(527\) 27.1823 1.18408
\(528\) 6.20087 0.269858
\(529\) 35.3141 1.53539
\(530\) −11.0590 −0.480374
\(531\) 7.10117 0.308165
\(532\) 2.80889 0.121781
\(533\) 5.88361 0.254848
\(534\) −2.02663 −0.0877007
\(535\) 9.18844 0.397251
\(536\) −7.92971 −0.342511
\(537\) 8.71883 0.376245
\(538\) −8.78266 −0.378647
\(539\) 3.95375 0.170300
\(540\) −1.36856 −0.0588936
\(541\) 31.8076 1.36752 0.683758 0.729709i \(-0.260344\pi\)
0.683758 + 0.729709i \(0.260344\pi\)
\(542\) 26.1284 1.12231
\(543\) −15.5238 −0.666188
\(544\) −31.9899 −1.37156
\(545\) −7.72875 −0.331063
\(546\) −2.41897 −0.103522
\(547\) −7.75499 −0.331579 −0.165790 0.986161i \(-0.553017\pi\)
−0.165790 + 0.986161i \(0.553017\pi\)
\(548\) −1.43692 −0.0613822
\(549\) 9.46455 0.403937
\(550\) 10.2609 0.437525
\(551\) 7.27464 0.309910
\(552\) −23.3340 −0.993162
\(553\) −9.03996 −0.384418
\(554\) 1.23722 0.0525643
\(555\) 11.4486 0.485965
\(556\) 8.34612 0.353954
\(557\) −40.0002 −1.69486 −0.847431 0.530905i \(-0.821852\pi\)
−0.847431 + 0.530905i \(0.821852\pi\)
\(558\) −4.03348 −0.170751
\(559\) −11.1251 −0.470542
\(560\) −2.51784 −0.106398
\(561\) −28.5429 −1.20508
\(562\) 8.55089 0.360698
\(563\) −15.8098 −0.666302 −0.333151 0.942873i \(-0.608112\pi\)
−0.333151 + 0.942873i \(0.608112\pi\)
\(564\) −2.88110 −0.121316
\(565\) −10.7860 −0.453770
\(566\) −29.5688 −1.24287
\(567\) −1.00000 −0.0419961
\(568\) −10.8075 −0.453474
\(569\) −6.48696 −0.271947 −0.135974 0.990712i \(-0.543416\pi\)
−0.135974 + 0.990712i \(0.543416\pi\)
\(570\) −5.66659 −0.237347
\(571\) 25.5999 1.07132 0.535661 0.844433i \(-0.320063\pi\)
0.535661 + 0.844433i \(0.320063\pi\)
\(572\) −7.61092 −0.318228
\(573\) −1.00000 −0.0417756
\(574\) 2.79112 0.116499
\(575\) −18.5004 −0.771519
\(576\) 7.88356 0.328482
\(577\) 42.8974 1.78584 0.892920 0.450215i \(-0.148653\pi\)
0.892920 + 0.450215i \(0.148653\pi\)
\(578\) −37.6181 −1.56471
\(579\) −8.77267 −0.364580
\(580\) 3.02149 0.125461
\(581\) −1.94384 −0.0806439
\(582\) 11.7300 0.486225
\(583\) −25.4249 −1.05299
\(584\) −38.7497 −1.60347
\(585\) −3.62521 −0.149884
\(586\) −11.3595 −0.469258
\(587\) 12.3490 0.509698 0.254849 0.966981i \(-0.417974\pi\)
0.254849 + 0.966981i \(0.417974\pi\)
\(588\) 0.852471 0.0351553
\(589\) 12.4066 0.511205
\(590\) 12.2123 0.502772
\(591\) −20.1146 −0.827405
\(592\) −11.1843 −0.459672
\(593\) 18.0381 0.740736 0.370368 0.928885i \(-0.379232\pi\)
0.370368 + 0.928885i \(0.379232\pi\)
\(594\) 4.23537 0.173779
\(595\) 11.5898 0.475134
\(596\) −0.574748 −0.0235426
\(597\) 9.89253 0.404874
\(598\) −18.4721 −0.755381
\(599\) 28.1439 1.14993 0.574964 0.818179i \(-0.305016\pi\)
0.574964 + 0.818179i \(0.305016\pi\)
\(600\) 7.40281 0.302219
\(601\) 39.4164 1.60783 0.803915 0.594744i \(-0.202747\pi\)
0.803915 + 0.594744i \(0.202747\pi\)
\(602\) −5.27761 −0.215099
\(603\) −2.59510 −0.105681
\(604\) −5.36725 −0.218390
\(605\) −7.43647 −0.302335
\(606\) −17.9702 −0.729991
\(607\) −30.3092 −1.23021 −0.615106 0.788445i \(-0.710887\pi\)
−0.615106 + 0.788445i \(0.710887\pi\)
\(608\) −14.6009 −0.592144
\(609\) 2.20779 0.0894640
\(610\) 16.2767 0.659026
\(611\) −7.63179 −0.308749
\(612\) −6.15416 −0.248767
\(613\) 6.88568 0.278110 0.139055 0.990285i \(-0.455594\pi\)
0.139055 + 0.990285i \(0.455594\pi\)
\(614\) 0.693249 0.0279772
\(615\) 4.18294 0.168672
\(616\) −12.0813 −0.486768
\(617\) 2.49816 0.100572 0.0502860 0.998735i \(-0.483987\pi\)
0.0502860 + 0.998735i \(0.483987\pi\)
\(618\) 8.54453 0.343711
\(619\) 3.82063 0.153564 0.0767820 0.997048i \(-0.475535\pi\)
0.0767820 + 0.997048i \(0.475535\pi\)
\(620\) 5.15303 0.206951
\(621\) −7.63636 −0.306437
\(622\) −2.09421 −0.0839702
\(623\) 1.89187 0.0757963
\(624\) 3.54153 0.141775
\(625\) −7.01735 −0.280694
\(626\) −4.63247 −0.185151
\(627\) −13.0276 −0.520272
\(628\) 14.9129 0.595091
\(629\) 51.4819 2.05272
\(630\) −1.71976 −0.0685168
\(631\) −4.87731 −0.194163 −0.0970813 0.995276i \(-0.530951\pi\)
−0.0970813 + 0.995276i \(0.530951\pi\)
\(632\) 27.6229 1.09878
\(633\) −10.9634 −0.435755
\(634\) 9.22697 0.366450
\(635\) −13.5904 −0.539320
\(636\) −5.48189 −0.217371
\(637\) 2.25813 0.0894702
\(638\) −9.35078 −0.370201
\(639\) −3.53690 −0.139918
\(640\) −0.670057 −0.0264863
\(641\) 4.66421 0.184225 0.0921127 0.995749i \(-0.470638\pi\)
0.0921127 + 0.995749i \(0.470638\pi\)
\(642\) −6.13110 −0.241975
\(643\) 3.55725 0.140284 0.0701421 0.997537i \(-0.477655\pi\)
0.0701421 + 0.997537i \(0.477655\pi\)
\(644\) 6.50978 0.256521
\(645\) −7.90935 −0.311431
\(646\) −25.4815 −1.00256
\(647\) 16.0468 0.630866 0.315433 0.948948i \(-0.397850\pi\)
0.315433 + 0.948948i \(0.397850\pi\)
\(648\) 3.05565 0.120037
\(649\) 28.0763 1.10209
\(650\) 5.86035 0.229862
\(651\) 3.76529 0.147573
\(652\) −19.0824 −0.747326
\(653\) 25.5154 0.998496 0.499248 0.866459i \(-0.333610\pi\)
0.499248 + 0.866459i \(0.333610\pi\)
\(654\) 5.15710 0.201659
\(655\) 11.9124 0.465458
\(656\) −4.08638 −0.159546
\(657\) −12.6813 −0.494746
\(658\) −3.62043 −0.141139
\(659\) −27.3209 −1.06427 −0.532135 0.846660i \(-0.678610\pi\)
−0.532135 + 0.846660i \(0.678610\pi\)
\(660\) −5.41096 −0.210621
\(661\) 25.3809 0.987204 0.493602 0.869688i \(-0.335680\pi\)
0.493602 + 0.869688i \(0.335680\pi\)
\(662\) −35.5332 −1.38104
\(663\) −16.3019 −0.633112
\(664\) 5.93968 0.230504
\(665\) 5.28981 0.205130
\(666\) −7.63920 −0.296013
\(667\) 16.8595 0.652801
\(668\) 21.0416 0.814125
\(669\) −5.73082 −0.221566
\(670\) −4.46294 −0.172419
\(671\) 37.4205 1.44460
\(672\) −4.43123 −0.170938
\(673\) −2.95341 −0.113846 −0.0569229 0.998379i \(-0.518129\pi\)
−0.0569229 + 0.998379i \(0.518129\pi\)
\(674\) −26.5515 −1.02272
\(675\) 2.42267 0.0932485
\(676\) 6.73526 0.259048
\(677\) −37.7680 −1.45154 −0.725770 0.687937i \(-0.758516\pi\)
−0.725770 + 0.687937i \(0.758516\pi\)
\(678\) 7.19708 0.276402
\(679\) −10.9501 −0.420225
\(680\) −35.4142 −1.35807
\(681\) 18.8079 0.720720
\(682\) −15.9474 −0.610656
\(683\) −15.4844 −0.592493 −0.296246 0.955112i \(-0.595735\pi\)
−0.296246 + 0.955112i \(0.595735\pi\)
\(684\) −2.80889 −0.107401
\(685\) −2.70606 −0.103393
\(686\) 1.07123 0.0408997
\(687\) 6.31690 0.241005
\(688\) 7.72679 0.294581
\(689\) −14.5211 −0.553209
\(690\) −13.1327 −0.499953
\(691\) −1.27832 −0.0486297 −0.0243148 0.999704i \(-0.507740\pi\)
−0.0243148 + 0.999704i \(0.507740\pi\)
\(692\) −9.97373 −0.379144
\(693\) −3.95375 −0.150191
\(694\) 16.4454 0.624259
\(695\) 15.7177 0.596208
\(696\) −6.74621 −0.255714
\(697\) 18.8098 0.712473
\(698\) 33.7121 1.27602
\(699\) 1.27413 0.0481920
\(700\) −2.06525 −0.0780593
\(701\) 17.6475 0.666536 0.333268 0.942832i \(-0.391849\pi\)
0.333268 + 0.942832i \(0.391849\pi\)
\(702\) 2.41897 0.0912980
\(703\) 23.4974 0.886223
\(704\) 31.1696 1.17475
\(705\) −5.42579 −0.204347
\(706\) 28.4780 1.07178
\(707\) 16.7754 0.630903
\(708\) 6.05354 0.227506
\(709\) 53.1278 1.99526 0.997628 0.0688293i \(-0.0219264\pi\)
0.997628 + 0.0688293i \(0.0219264\pi\)
\(710\) −6.08262 −0.228277
\(711\) 9.03996 0.339025
\(712\) −5.78089 −0.216648
\(713\) 28.7531 1.07681
\(714\) −7.73341 −0.289415
\(715\) −14.3332 −0.536031
\(716\) 7.43255 0.277767
\(717\) 22.0775 0.824498
\(718\) −7.84593 −0.292808
\(719\) −3.94431 −0.147098 −0.0735490 0.997292i \(-0.523433\pi\)
−0.0735490 + 0.997292i \(0.523433\pi\)
\(720\) 2.51784 0.0938344
\(721\) −7.97639 −0.297056
\(722\) 8.72302 0.324637
\(723\) 18.2835 0.679970
\(724\) −13.2335 −0.491821
\(725\) −5.34873 −0.198647
\(726\) 4.96207 0.184160
\(727\) −26.8457 −0.995650 −0.497825 0.867277i \(-0.665868\pi\)
−0.497825 + 0.867277i \(0.665868\pi\)
\(728\) −6.90004 −0.255732
\(729\) 1.00000 0.0370370
\(730\) −21.8088 −0.807180
\(731\) −35.5668 −1.31549
\(732\) 8.06826 0.298211
\(733\) −11.1232 −0.410845 −0.205423 0.978673i \(-0.565857\pi\)
−0.205423 + 0.978673i \(0.565857\pi\)
\(734\) 38.8975 1.43573
\(735\) 1.60541 0.0592163
\(736\) −33.8385 −1.24730
\(737\) −10.2604 −0.377946
\(738\) −2.79112 −0.102742
\(739\) −27.5864 −1.01478 −0.507391 0.861716i \(-0.669390\pi\)
−0.507391 + 0.861716i \(0.669390\pi\)
\(740\) 9.75958 0.358769
\(741\) −7.44051 −0.273334
\(742\) −6.88862 −0.252889
\(743\) −26.4082 −0.968823 −0.484411 0.874840i \(-0.660966\pi\)
−0.484411 + 0.874840i \(0.660966\pi\)
\(744\) −11.5054 −0.421808
\(745\) −1.08239 −0.0396557
\(746\) −9.68524 −0.354602
\(747\) 1.94384 0.0711213
\(748\) −24.3320 −0.889666
\(749\) 5.72343 0.209130
\(750\) 12.7652 0.466119
\(751\) −53.4551 −1.95060 −0.975301 0.220878i \(-0.929108\pi\)
−0.975301 + 0.220878i \(0.929108\pi\)
\(752\) 5.30055 0.193291
\(753\) −24.5159 −0.893410
\(754\) −5.34056 −0.194492
\(755\) −10.1078 −0.367861
\(756\) −0.852471 −0.0310041
\(757\) −50.7130 −1.84320 −0.921598 0.388145i \(-0.873116\pi\)
−0.921598 + 0.388145i \(0.873116\pi\)
\(758\) −18.2035 −0.661182
\(759\) −30.1923 −1.09591
\(760\) −16.1638 −0.586322
\(761\) 32.0694 1.16251 0.581257 0.813720i \(-0.302561\pi\)
0.581257 + 0.813720i \(0.302561\pi\)
\(762\) 9.06839 0.328513
\(763\) −4.81420 −0.174286
\(764\) −0.852471 −0.0308413
\(765\) −11.5898 −0.419028
\(766\) 2.95385 0.106727
\(767\) 16.0353 0.579003
\(768\) 16.2142 0.585080
\(769\) 22.0829 0.796330 0.398165 0.917314i \(-0.369647\pi\)
0.398165 + 0.917314i \(0.369647\pi\)
\(770\) −6.79949 −0.245037
\(771\) −1.86568 −0.0671908
\(772\) −7.47844 −0.269155
\(773\) −16.9475 −0.609558 −0.304779 0.952423i \(-0.598583\pi\)
−0.304779 + 0.952423i \(0.598583\pi\)
\(774\) 5.27761 0.189700
\(775\) −9.12203 −0.327673
\(776\) 33.4595 1.20113
\(777\) 7.13126 0.255832
\(778\) −26.5523 −0.951945
\(779\) 8.58521 0.307597
\(780\) −3.09039 −0.110654
\(781\) −13.9840 −0.500388
\(782\) −59.0551 −2.11181
\(783\) −2.20779 −0.0788998
\(784\) −1.56835 −0.0560125
\(785\) 28.0846 1.00238
\(786\) −7.94872 −0.283522
\(787\) −13.6816 −0.487696 −0.243848 0.969813i \(-0.578410\pi\)
−0.243848 + 0.969813i \(0.578410\pi\)
\(788\) −17.1471 −0.610841
\(789\) 13.3481 0.475203
\(790\) 15.5465 0.553121
\(791\) −6.71853 −0.238884
\(792\) 12.0813 0.429289
\(793\) 21.3722 0.758948
\(794\) 24.0697 0.854202
\(795\) −10.3237 −0.366144
\(796\) 8.43310 0.298903
\(797\) −23.7100 −0.839853 −0.419926 0.907558i \(-0.637944\pi\)
−0.419926 + 0.907558i \(0.637944\pi\)
\(798\) −3.52969 −0.124950
\(799\) −24.3987 −0.863165
\(800\) 10.7354 0.379554
\(801\) −1.89187 −0.0668460
\(802\) −14.0169 −0.494956
\(803\) −50.1388 −1.76936
\(804\) −2.21225 −0.0780200
\(805\) 12.2595 0.432090
\(806\) −9.10810 −0.320819
\(807\) −8.19868 −0.288607
\(808\) −51.2596 −1.80331
\(809\) 11.4257 0.401707 0.200854 0.979621i \(-0.435628\pi\)
0.200854 + 0.979621i \(0.435628\pi\)
\(810\) 1.71976 0.0604261
\(811\) 21.8387 0.766859 0.383430 0.923570i \(-0.374743\pi\)
0.383430 + 0.923570i \(0.374743\pi\)
\(812\) 1.88207 0.0660478
\(813\) 24.3911 0.855432
\(814\) −30.2035 −1.05863
\(815\) −35.9368 −1.25881
\(816\) 11.3222 0.396358
\(817\) −16.2334 −0.567936
\(818\) 10.0854 0.352629
\(819\) −2.25813 −0.0789053
\(820\) 3.56583 0.124524
\(821\) 10.4364 0.364233 0.182116 0.983277i \(-0.441705\pi\)
0.182116 + 0.983277i \(0.441705\pi\)
\(822\) 1.80565 0.0629794
\(823\) −34.9451 −1.21811 −0.609055 0.793128i \(-0.708451\pi\)
−0.609055 + 0.793128i \(0.708451\pi\)
\(824\) 24.3730 0.849074
\(825\) 9.57862 0.333485
\(826\) 7.60697 0.264680
\(827\) −30.0929 −1.04643 −0.523217 0.852200i \(-0.675268\pi\)
−0.523217 + 0.852200i \(0.675268\pi\)
\(828\) −6.50978 −0.226230
\(829\) 33.1864 1.15261 0.576306 0.817234i \(-0.304493\pi\)
0.576306 + 0.817234i \(0.304493\pi\)
\(830\) 3.34293 0.116035
\(831\) 1.15495 0.0400648
\(832\) 17.8021 0.617176
\(833\) 7.21920 0.250130
\(834\) −10.4879 −0.363165
\(835\) 39.6264 1.37133
\(836\) −11.1056 −0.384097
\(837\) −3.76529 −0.130147
\(838\) 29.5262 1.01997
\(839\) 37.8509 1.30676 0.653380 0.757031i \(-0.273351\pi\)
0.653380 + 0.757031i \(0.273351\pi\)
\(840\) −4.90556 −0.169258
\(841\) −24.1257 −0.831920
\(842\) 0.519653 0.0179084
\(843\) 7.98233 0.274926
\(844\) −9.34596 −0.321701
\(845\) 12.6841 0.436347
\(846\) 3.62043 0.124473
\(847\) −4.63214 −0.159162
\(848\) 10.0854 0.346335
\(849\) −27.6027 −0.947323
\(850\) 18.7355 0.642621
\(851\) 54.4569 1.86676
\(852\) −3.01511 −0.103296
\(853\) 29.5727 1.01255 0.506275 0.862372i \(-0.331022\pi\)
0.506275 + 0.862372i \(0.331022\pi\)
\(854\) 10.1387 0.346939
\(855\) −5.28981 −0.180908
\(856\) −17.4888 −0.597755
\(857\) −2.93843 −0.100375 −0.0501873 0.998740i \(-0.515982\pi\)
−0.0501873 + 0.998740i \(0.515982\pi\)
\(858\) 9.56399 0.326509
\(859\) 13.2384 0.451687 0.225844 0.974164i \(-0.427486\pi\)
0.225844 + 0.974164i \(0.427486\pi\)
\(860\) −6.74250 −0.229917
\(861\) 2.60553 0.0887962
\(862\) −43.2197 −1.47207
\(863\) −55.8000 −1.89945 −0.949727 0.313079i \(-0.898640\pi\)
−0.949727 + 0.313079i \(0.898640\pi\)
\(864\) 4.43123 0.150754
\(865\) −18.7829 −0.638639
\(866\) −3.22830 −0.109702
\(867\) −35.1168 −1.19263
\(868\) 3.20980 0.108948
\(869\) 35.7417 1.21246
\(870\) −3.79685 −0.128725
\(871\) −5.86007 −0.198561
\(872\) 14.7105 0.498160
\(873\) 10.9501 0.370604
\(874\) −26.9540 −0.911732
\(875\) −11.9164 −0.402848
\(876\) −10.8105 −0.365252
\(877\) 54.4379 1.83824 0.919119 0.393979i \(-0.128902\pi\)
0.919119 + 0.393979i \(0.128902\pi\)
\(878\) −11.5022 −0.388181
\(879\) −10.6042 −0.357671
\(880\) 9.95492 0.335580
\(881\) −5.81193 −0.195809 −0.0979044 0.995196i \(-0.531214\pi\)
−0.0979044 + 0.995196i \(0.531214\pi\)
\(882\) −1.07123 −0.0360701
\(883\) −50.2967 −1.69262 −0.846309 0.532692i \(-0.821180\pi\)
−0.846309 + 0.532692i \(0.821180\pi\)
\(884\) −13.8969 −0.467402
\(885\) 11.4003 0.383216
\(886\) 23.7748 0.798731
\(887\) −24.5730 −0.825079 −0.412540 0.910940i \(-0.635358\pi\)
−0.412540 + 0.910940i \(0.635358\pi\)
\(888\) −21.7906 −0.731244
\(889\) −8.46541 −0.283921
\(890\) −3.25356 −0.109060
\(891\) 3.95375 0.132456
\(892\) −4.88536 −0.163574
\(893\) −11.1361 −0.372655
\(894\) 0.722237 0.0241552
\(895\) 13.9973 0.467877
\(896\) −0.417375 −0.0139435
\(897\) −17.2439 −0.575756
\(898\) −25.7388 −0.858916
\(899\) 8.31294 0.277252
\(900\) 2.06525 0.0688418
\(901\) −46.4237 −1.54660
\(902\) −11.0354 −0.367438
\(903\) −4.92670 −0.163950
\(904\) 20.5295 0.682800
\(905\) −24.9219 −0.828433
\(906\) 6.74457 0.224073
\(907\) 22.0175 0.731079 0.365539 0.930796i \(-0.380885\pi\)
0.365539 + 0.930796i \(0.380885\pi\)
\(908\) 16.0332 0.532080
\(909\) −16.7754 −0.556404
\(910\) −3.88343 −0.128734
\(911\) −6.73977 −0.223298 −0.111649 0.993748i \(-0.535613\pi\)
−0.111649 + 0.993748i \(0.535613\pi\)
\(912\) 5.16771 0.171120
\(913\) 7.68545 0.254351
\(914\) 21.5373 0.712391
\(915\) 15.1945 0.502314
\(916\) 5.38497 0.177925
\(917\) 7.42020 0.245037
\(918\) 7.73341 0.255240
\(919\) 33.3112 1.09884 0.549418 0.835548i \(-0.314849\pi\)
0.549418 + 0.835548i \(0.314849\pi\)
\(920\) −37.4606 −1.23504
\(921\) 0.647153 0.0213244
\(922\) 32.5370 1.07155
\(923\) −7.98678 −0.262888
\(924\) −3.37046 −0.110880
\(925\) −17.2767 −0.568053
\(926\) −15.1802 −0.498852
\(927\) 7.97639 0.261979
\(928\) −9.78321 −0.321150
\(929\) 34.3536 1.12711 0.563553 0.826080i \(-0.309434\pi\)
0.563553 + 0.826080i \(0.309434\pi\)
\(930\) −6.47538 −0.212336
\(931\) 3.29499 0.107989
\(932\) 1.08616 0.0355783
\(933\) −1.95496 −0.0640026
\(934\) 39.5385 1.29374
\(935\) −45.8230 −1.49857
\(936\) 6.90004 0.225535
\(937\) −26.1880 −0.855525 −0.427763 0.903891i \(-0.640698\pi\)
−0.427763 + 0.903891i \(0.640698\pi\)
\(938\) −2.77995 −0.0907684
\(939\) −4.32445 −0.141123
\(940\) −4.62533 −0.150862
\(941\) 9.53035 0.310681 0.155340 0.987861i \(-0.450353\pi\)
0.155340 + 0.987861i \(0.450353\pi\)
\(942\) −18.7398 −0.610576
\(943\) 19.8968 0.647928
\(944\) −11.1371 −0.362483
\(945\) −1.60541 −0.0522239
\(946\) 20.8664 0.678424
\(947\) −15.5422 −0.505054 −0.252527 0.967590i \(-0.581262\pi\)
−0.252527 + 0.967590i \(0.581262\pi\)
\(948\) 7.70630 0.250289
\(949\) −28.6361 −0.929566
\(950\) 8.55126 0.277440
\(951\) 8.61346 0.279310
\(952\) −22.0593 −0.714947
\(953\) −0.154260 −0.00499696 −0.00249848 0.999997i \(-0.500795\pi\)
−0.00249848 + 0.999997i \(0.500795\pi\)
\(954\) 6.88862 0.223027
\(955\) −1.60541 −0.0519498
\(956\) 18.8204 0.608695
\(957\) −8.72903 −0.282169
\(958\) 33.6842 1.08829
\(959\) −1.68559 −0.0544306
\(960\) 12.6563 0.408481
\(961\) −16.8226 −0.542665
\(962\) −17.2503 −0.556171
\(963\) −5.72343 −0.184435
\(964\) 15.5861 0.501995
\(965\) −14.0837 −0.453370
\(966\) −8.18029 −0.263196
\(967\) −22.9884 −0.739256 −0.369628 0.929180i \(-0.620515\pi\)
−0.369628 + 0.929180i \(0.620515\pi\)
\(968\) 14.1542 0.454932
\(969\) −23.7872 −0.764156
\(970\) 18.8315 0.604642
\(971\) 55.8595 1.79262 0.896308 0.443432i \(-0.146239\pi\)
0.896308 + 0.443432i \(0.146239\pi\)
\(972\) 0.852471 0.0273430
\(973\) 9.79050 0.313869
\(974\) −18.8583 −0.604260
\(975\) 5.47069 0.175202
\(976\) −14.8437 −0.475137
\(977\) −23.8934 −0.764416 −0.382208 0.924076i \(-0.624836\pi\)
−0.382208 + 0.924076i \(0.624836\pi\)
\(978\) 23.9793 0.766772
\(979\) −7.47999 −0.239062
\(980\) 1.36856 0.0437172
\(981\) 4.81420 0.153706
\(982\) −0.992522 −0.0316727
\(983\) −36.3132 −1.15821 −0.579106 0.815252i \(-0.696598\pi\)
−0.579106 + 0.815252i \(0.696598\pi\)
\(984\) −7.96158 −0.253806
\(985\) −32.2922 −1.02891
\(986\) −17.0737 −0.543737
\(987\) −3.37970 −0.107577
\(988\) −6.34282 −0.201792
\(989\) −37.6220 −1.19631
\(990\) 6.79949 0.216102
\(991\) 3.43443 0.109098 0.0545492 0.998511i \(-0.482628\pi\)
0.0545492 + 0.998511i \(0.482628\pi\)
\(992\) −16.6849 −0.529745
\(993\) −33.1706 −1.05264
\(994\) −3.78883 −0.120174
\(995\) 15.8815 0.503479
\(996\) 1.65706 0.0525061
\(997\) −16.2980 −0.516161 −0.258081 0.966123i \(-0.583090\pi\)
−0.258081 + 0.966123i \(0.583090\pi\)
\(998\) 17.2718 0.546729
\(999\) −7.13126 −0.225623
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 4011.2.a.j.1.9 26
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
4011.2.a.j.1.9 26 1.1 even 1 trivial