Properties

Label 4011.2.a.l.1.6
Level $4011$
Weight $2$
Character 4011.1
Self dual yes
Analytic conductor $32.028$
Analytic rank $0$
Dimension $28$
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: \(28\)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.6
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)
 
\(f(q)\) \(=\) \(q-2.23874 q^{2} -1.00000 q^{3} +3.01194 q^{4} +1.19635 q^{5} +2.23874 q^{6} +1.00000 q^{7} -2.26547 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q-2.23874 q^{2} -1.00000 q^{3} +3.01194 q^{4} +1.19635 q^{5} +2.23874 q^{6} +1.00000 q^{7} -2.26547 q^{8} +1.00000 q^{9} -2.67832 q^{10} +4.91098 q^{11} -3.01194 q^{12} +4.83040 q^{13} -2.23874 q^{14} -1.19635 q^{15} -0.952086 q^{16} -6.57397 q^{17} -2.23874 q^{18} -2.90324 q^{19} +3.60335 q^{20} -1.00000 q^{21} -10.9944 q^{22} -6.64434 q^{23} +2.26547 q^{24} -3.56874 q^{25} -10.8140 q^{26} -1.00000 q^{27} +3.01194 q^{28} +5.61643 q^{29} +2.67832 q^{30} +8.36935 q^{31} +6.66242 q^{32} -4.91098 q^{33} +14.7174 q^{34} +1.19635 q^{35} +3.01194 q^{36} +6.18380 q^{37} +6.49959 q^{38} -4.83040 q^{39} -2.71031 q^{40} +9.01478 q^{41} +2.23874 q^{42} -0.0607989 q^{43} +14.7916 q^{44} +1.19635 q^{45} +14.8749 q^{46} -7.86001 q^{47} +0.952086 q^{48} +1.00000 q^{49} +7.98946 q^{50} +6.57397 q^{51} +14.5489 q^{52} +0.959377 q^{53} +2.23874 q^{54} +5.87527 q^{55} -2.26547 q^{56} +2.90324 q^{57} -12.5737 q^{58} +4.62990 q^{59} -3.60335 q^{60} +1.52750 q^{61} -18.7368 q^{62} +1.00000 q^{63} -13.0112 q^{64} +5.77887 q^{65} +10.9944 q^{66} +5.11522 q^{67} -19.8004 q^{68} +6.64434 q^{69} -2.67832 q^{70} -7.71447 q^{71} -2.26547 q^{72} +5.82688 q^{73} -13.8439 q^{74} +3.56874 q^{75} -8.74439 q^{76} +4.91098 q^{77} +10.8140 q^{78} +8.80672 q^{79} -1.13903 q^{80} +1.00000 q^{81} -20.1817 q^{82} -3.10269 q^{83} -3.01194 q^{84} -7.86480 q^{85} +0.136113 q^{86} -5.61643 q^{87} -11.1257 q^{88} -1.15416 q^{89} -2.67832 q^{90} +4.83040 q^{91} -20.0124 q^{92} -8.36935 q^{93} +17.5965 q^{94} -3.47330 q^{95} -6.66242 q^{96} +11.1893 q^{97} -2.23874 q^{98} +4.91098 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 28 q - 6 q^{2} - 28 q^{3} + 34 q^{4} + 8 q^{5} + 6 q^{6} + 28 q^{7} - 15 q^{8} + 28 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 28 q - 6 q^{2} - 28 q^{3} + 34 q^{4} + 8 q^{5} + 6 q^{6} + 28 q^{7} - 15 q^{8} + 28 q^{9} + 4 q^{10} - 8 q^{11} - 34 q^{12} + 26 q^{13} - 6 q^{14} - 8 q^{15} + 62 q^{16} + 9 q^{17} - 6 q^{18} + 25 q^{19} + 20 q^{20} - 28 q^{21} + 3 q^{22} - 30 q^{23} + 15 q^{24} + 42 q^{25} + 25 q^{26} - 28 q^{27} + 34 q^{28} - 5 q^{29} - 4 q^{30} + 18 q^{31} - 26 q^{32} + 8 q^{33} + 30 q^{34} + 8 q^{35} + 34 q^{36} + 36 q^{37} - 2 q^{38} - 26 q^{39} + 28 q^{40} + 21 q^{41} + 6 q^{42} + 8 q^{43} - 20 q^{44} + 8 q^{45} + 24 q^{46} + 6 q^{47} - 62 q^{48} + 28 q^{49} - 48 q^{50} - 9 q^{51} + 54 q^{52} - 12 q^{53} + 6 q^{54} + 15 q^{55} - 15 q^{56} - 25 q^{57} + 19 q^{58} + 33 q^{59} - 20 q^{60} + 48 q^{61} + 28 q^{63} + 75 q^{64} + 21 q^{65} - 3 q^{66} + 27 q^{67} + 19 q^{68} + 30 q^{69} + 4 q^{70} - 45 q^{71} - 15 q^{72} + 61 q^{73} - 31 q^{74} - 42 q^{75} + 63 q^{76} - 8 q^{77} - 25 q^{78} + 35 q^{79} + 84 q^{80} + 28 q^{81} + 11 q^{82} + 43 q^{83} - 34 q^{84} + 43 q^{85} - q^{86} + 5 q^{87} - 27 q^{88} + 25 q^{89} + 4 q^{90} + 26 q^{91} - 102 q^{92} - 18 q^{93} + 55 q^{94} - 43 q^{95} + 26 q^{96} + 40 q^{97} - 6 q^{98} - 8 q^{99}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.23874 −1.58303 −0.791513 0.611152i \(-0.790706\pi\)
−0.791513 + 0.611152i \(0.790706\pi\)
\(3\) −1.00000 −0.577350
\(4\) 3.01194 1.50597
\(5\) 1.19635 0.535026 0.267513 0.963554i \(-0.413798\pi\)
0.267513 + 0.963554i \(0.413798\pi\)
\(6\) 2.23874 0.913961
\(7\) 1.00000 0.377964
\(8\) −2.26547 −0.800966
\(9\) 1.00000 0.333333
\(10\) −2.67832 −0.846960
\(11\) 4.91098 1.48072 0.740358 0.672213i \(-0.234656\pi\)
0.740358 + 0.672213i \(0.234656\pi\)
\(12\) −3.01194 −0.869473
\(13\) 4.83040 1.33971 0.669856 0.742491i \(-0.266356\pi\)
0.669856 + 0.742491i \(0.266356\pi\)
\(14\) −2.23874 −0.598328
\(15\) −1.19635 −0.308897
\(16\) −0.952086 −0.238022
\(17\) −6.57397 −1.59442 −0.797211 0.603701i \(-0.793692\pi\)
−0.797211 + 0.603701i \(0.793692\pi\)
\(18\) −2.23874 −0.527675
\(19\) −2.90324 −0.666049 −0.333024 0.942918i \(-0.608069\pi\)
−0.333024 + 0.942918i \(0.608069\pi\)
\(20\) 3.60335 0.805734
\(21\) −1.00000 −0.218218
\(22\) −10.9944 −2.34401
\(23\) −6.64434 −1.38544 −0.692720 0.721206i \(-0.743588\pi\)
−0.692720 + 0.721206i \(0.743588\pi\)
\(24\) 2.26547 0.462438
\(25\) −3.56874 −0.713747
\(26\) −10.8140 −2.12080
\(27\) −1.00000 −0.192450
\(28\) 3.01194 0.569204
\(29\) 5.61643 1.04294 0.521472 0.853268i \(-0.325383\pi\)
0.521472 + 0.853268i \(0.325383\pi\)
\(30\) 2.67832 0.488993
\(31\) 8.36935 1.50318 0.751590 0.659631i \(-0.229287\pi\)
0.751590 + 0.659631i \(0.229287\pi\)
\(32\) 6.66242 1.17776
\(33\) −4.91098 −0.854892
\(34\) 14.7174 2.52401
\(35\) 1.19635 0.202221
\(36\) 3.01194 0.501990
\(37\) 6.18380 1.01661 0.508306 0.861177i \(-0.330272\pi\)
0.508306 + 0.861177i \(0.330272\pi\)
\(38\) 6.49959 1.05437
\(39\) −4.83040 −0.773483
\(40\) −2.71031 −0.428538
\(41\) 9.01478 1.40787 0.703936 0.710263i \(-0.251424\pi\)
0.703936 + 0.710263i \(0.251424\pi\)
\(42\) 2.23874 0.345445
\(43\) −0.0607989 −0.00927174 −0.00463587 0.999989i \(-0.501476\pi\)
−0.00463587 + 0.999989i \(0.501476\pi\)
\(44\) 14.7916 2.22992
\(45\) 1.19635 0.178342
\(46\) 14.8749 2.19319
\(47\) −7.86001 −1.14650 −0.573250 0.819381i \(-0.694318\pi\)
−0.573250 + 0.819381i \(0.694318\pi\)
\(48\) 0.952086 0.137422
\(49\) 1.00000 0.142857
\(50\) 7.98946 1.12988
\(51\) 6.57397 0.920540
\(52\) 14.5489 2.01757
\(53\) 0.959377 0.131781 0.0658903 0.997827i \(-0.479011\pi\)
0.0658903 + 0.997827i \(0.479011\pi\)
\(54\) 2.23874 0.304654
\(55\) 5.87527 0.792222
\(56\) −2.26547 −0.302737
\(57\) 2.90324 0.384544
\(58\) −12.5737 −1.65101
\(59\) 4.62990 0.602762 0.301381 0.953504i \(-0.402552\pi\)
0.301381 + 0.953504i \(0.402552\pi\)
\(60\) −3.60335 −0.465191
\(61\) 1.52750 0.195577 0.0977883 0.995207i \(-0.468823\pi\)
0.0977883 + 0.995207i \(0.468823\pi\)
\(62\) −18.7368 −2.37957
\(63\) 1.00000 0.125988
\(64\) −13.0112 −1.62640
\(65\) 5.77887 0.716780
\(66\) 10.9944 1.35332
\(67\) 5.11522 0.624924 0.312462 0.949930i \(-0.398846\pi\)
0.312462 + 0.949930i \(0.398846\pi\)
\(68\) −19.8004 −2.40115
\(69\) 6.64434 0.799885
\(70\) −2.67832 −0.320121
\(71\) −7.71447 −0.915539 −0.457769 0.889071i \(-0.651351\pi\)
−0.457769 + 0.889071i \(0.651351\pi\)
\(72\) −2.26547 −0.266989
\(73\) 5.82688 0.681984 0.340992 0.940066i \(-0.389237\pi\)
0.340992 + 0.940066i \(0.389237\pi\)
\(74\) −13.8439 −1.60932
\(75\) 3.56874 0.412082
\(76\) −8.74439 −1.00305
\(77\) 4.91098 0.559658
\(78\) 10.8140 1.22444
\(79\) 8.80672 0.990833 0.495417 0.868656i \(-0.335015\pi\)
0.495417 + 0.868656i \(0.335015\pi\)
\(80\) −1.13903 −0.127348
\(81\) 1.00000 0.111111
\(82\) −20.1817 −2.22870
\(83\) −3.10269 −0.340564 −0.170282 0.985395i \(-0.554468\pi\)
−0.170282 + 0.985395i \(0.554468\pi\)
\(84\) −3.01194 −0.328630
\(85\) −7.86480 −0.853057
\(86\) 0.136113 0.0146774
\(87\) −5.61643 −0.602144
\(88\) −11.1257 −1.18600
\(89\) −1.15416 −0.122341 −0.0611703 0.998127i \(-0.519483\pi\)
−0.0611703 + 0.998127i \(0.519483\pi\)
\(90\) −2.67832 −0.282320
\(91\) 4.83040 0.506363
\(92\) −20.0124 −2.08643
\(93\) −8.36935 −0.867861
\(94\) 17.5965 1.81494
\(95\) −3.47330 −0.356354
\(96\) −6.66242 −0.679980
\(97\) 11.1893 1.13610 0.568050 0.822994i \(-0.307698\pi\)
0.568050 + 0.822994i \(0.307698\pi\)
\(98\) −2.23874 −0.226147
\(99\) 4.91098 0.493572
\(100\) −10.7488 −1.07488
\(101\) −7.91000 −0.787074 −0.393537 0.919309i \(-0.628749\pi\)
−0.393537 + 0.919309i \(0.628749\pi\)
\(102\) −14.7174 −1.45724
\(103\) −0.523257 −0.0515580 −0.0257790 0.999668i \(-0.508207\pi\)
−0.0257790 + 0.999668i \(0.508207\pi\)
\(104\) −10.9431 −1.07306
\(105\) −1.19635 −0.116752
\(106\) −2.14779 −0.208612
\(107\) −3.71914 −0.359543 −0.179771 0.983708i \(-0.557536\pi\)
−0.179771 + 0.983708i \(0.557536\pi\)
\(108\) −3.01194 −0.289824
\(109\) −11.0066 −1.05424 −0.527119 0.849791i \(-0.676728\pi\)
−0.527119 + 0.849791i \(0.676728\pi\)
\(110\) −13.1532 −1.25411
\(111\) −6.18380 −0.586941
\(112\) −0.952086 −0.0899637
\(113\) 2.50026 0.235204 0.117602 0.993061i \(-0.462479\pi\)
0.117602 + 0.993061i \(0.462479\pi\)
\(114\) −6.49959 −0.608742
\(115\) −7.94899 −0.741247
\(116\) 16.9164 1.57064
\(117\) 4.83040 0.446570
\(118\) −10.3651 −0.954188
\(119\) −6.57397 −0.602635
\(120\) 2.71031 0.247416
\(121\) 13.1177 1.19252
\(122\) −3.41967 −0.309603
\(123\) −9.01478 −0.812836
\(124\) 25.2080 2.26375
\(125\) −10.2512 −0.916899
\(126\) −2.23874 −0.199443
\(127\) 15.0444 1.33498 0.667489 0.744620i \(-0.267369\pi\)
0.667489 + 0.744620i \(0.267369\pi\)
\(128\) 15.8039 1.39688
\(129\) 0.0607989 0.00535304
\(130\) −12.9374 −1.13468
\(131\) 16.1545 1.41142 0.705712 0.708499i \(-0.250627\pi\)
0.705712 + 0.708499i \(0.250627\pi\)
\(132\) −14.7916 −1.28744
\(133\) −2.90324 −0.251743
\(134\) −11.4516 −0.989270
\(135\) −1.19635 −0.102966
\(136\) 14.8932 1.27708
\(137\) −16.9693 −1.44979 −0.724895 0.688860i \(-0.758112\pi\)
−0.724895 + 0.688860i \(0.758112\pi\)
\(138\) −14.8749 −1.26624
\(139\) −1.57636 −0.133705 −0.0668526 0.997763i \(-0.521296\pi\)
−0.0668526 + 0.997763i \(0.521296\pi\)
\(140\) 3.60335 0.304539
\(141\) 7.86001 0.661932
\(142\) 17.2707 1.44932
\(143\) 23.7220 1.98373
\(144\) −0.952086 −0.0793405
\(145\) 6.71924 0.558002
\(146\) −13.0448 −1.07960
\(147\) −1.00000 −0.0824786
\(148\) 18.6253 1.53099
\(149\) 22.4293 1.83748 0.918742 0.394859i \(-0.129207\pi\)
0.918742 + 0.394859i \(0.129207\pi\)
\(150\) −7.98946 −0.652337
\(151\) 16.8263 1.36931 0.684654 0.728868i \(-0.259953\pi\)
0.684654 + 0.728868i \(0.259953\pi\)
\(152\) 6.57721 0.533483
\(153\) −6.57397 −0.531474
\(154\) −10.9944 −0.885953
\(155\) 10.0127 0.804240
\(156\) −14.5489 −1.16484
\(157\) 11.6691 0.931294 0.465647 0.884970i \(-0.345822\pi\)
0.465647 + 0.884970i \(0.345822\pi\)
\(158\) −19.7159 −1.56851
\(159\) −0.959377 −0.0760835
\(160\) 7.97061 0.630132
\(161\) −6.64434 −0.523647
\(162\) −2.23874 −0.175892
\(163\) −19.6438 −1.53862 −0.769309 0.638877i \(-0.779399\pi\)
−0.769309 + 0.638877i \(0.779399\pi\)
\(164\) 27.1520 2.12022
\(165\) −5.87527 −0.457389
\(166\) 6.94611 0.539122
\(167\) 2.58695 0.200184 0.100092 0.994978i \(-0.468086\pi\)
0.100092 + 0.994978i \(0.468086\pi\)
\(168\) 2.26547 0.174785
\(169\) 10.3327 0.794827
\(170\) 17.6072 1.35041
\(171\) −2.90324 −0.222016
\(172\) −0.183123 −0.0139630
\(173\) −9.38849 −0.713793 −0.356897 0.934144i \(-0.616165\pi\)
−0.356897 + 0.934144i \(0.616165\pi\)
\(174\) 12.5737 0.953210
\(175\) −3.56874 −0.269771
\(176\) −4.67568 −0.352442
\(177\) −4.62990 −0.348005
\(178\) 2.58386 0.193668
\(179\) −21.6483 −1.61807 −0.809034 0.587762i \(-0.800009\pi\)
−0.809034 + 0.587762i \(0.800009\pi\)
\(180\) 3.60335 0.268578
\(181\) 14.7432 1.09586 0.547929 0.836525i \(-0.315417\pi\)
0.547929 + 0.836525i \(0.315417\pi\)
\(182\) −10.8140 −0.801586
\(183\) −1.52750 −0.112916
\(184\) 15.0526 1.10969
\(185\) 7.39802 0.543913
\(186\) 18.7368 1.37385
\(187\) −32.2846 −2.36089
\(188\) −23.6739 −1.72660
\(189\) −1.00000 −0.0727393
\(190\) 7.77581 0.564117
\(191\) −1.00000 −0.0723575
\(192\) 13.0112 0.939004
\(193\) 24.6200 1.77219 0.886093 0.463507i \(-0.153409\pi\)
0.886093 + 0.463507i \(0.153409\pi\)
\(194\) −25.0499 −1.79847
\(195\) −5.77887 −0.413833
\(196\) 3.01194 0.215139
\(197\) −3.36933 −0.240055 −0.120027 0.992771i \(-0.538298\pi\)
−0.120027 + 0.992771i \(0.538298\pi\)
\(198\) −10.9944 −0.781338
\(199\) −22.3704 −1.58580 −0.792900 0.609352i \(-0.791429\pi\)
−0.792900 + 0.609352i \(0.791429\pi\)
\(200\) 8.08488 0.571687
\(201\) −5.11522 −0.360800
\(202\) 17.7084 1.24596
\(203\) 5.61643 0.394196
\(204\) 19.8004 1.38631
\(205\) 10.7849 0.753249
\(206\) 1.17143 0.0816177
\(207\) −6.64434 −0.461814
\(208\) −4.59895 −0.318880
\(209\) −14.2578 −0.986230
\(210\) 2.67832 0.184822
\(211\) −11.9024 −0.819394 −0.409697 0.912222i \(-0.634366\pi\)
−0.409697 + 0.912222i \(0.634366\pi\)
\(212\) 2.88959 0.198458
\(213\) 7.71447 0.528587
\(214\) 8.32618 0.569166
\(215\) −0.0727370 −0.00496062
\(216\) 2.26547 0.154146
\(217\) 8.36935 0.568148
\(218\) 24.6408 1.66889
\(219\) −5.82688 −0.393744
\(220\) 17.6960 1.19306
\(221\) −31.7549 −2.13607
\(222\) 13.8439 0.929143
\(223\) 22.0537 1.47682 0.738412 0.674350i \(-0.235576\pi\)
0.738412 + 0.674350i \(0.235576\pi\)
\(224\) 6.66242 0.445152
\(225\) −3.56874 −0.237916
\(226\) −5.59742 −0.372335
\(227\) 0.496506 0.0329542 0.0164771 0.999864i \(-0.494755\pi\)
0.0164771 + 0.999864i \(0.494755\pi\)
\(228\) 8.74439 0.579112
\(229\) −25.4168 −1.67959 −0.839796 0.542902i \(-0.817326\pi\)
−0.839796 + 0.542902i \(0.817326\pi\)
\(230\) 17.7957 1.17341
\(231\) −4.91098 −0.323119
\(232\) −12.7239 −0.835363
\(233\) −24.5871 −1.61075 −0.805377 0.592764i \(-0.798037\pi\)
−0.805377 + 0.592764i \(0.798037\pi\)
\(234\) −10.8140 −0.706933
\(235\) −9.40335 −0.613407
\(236\) 13.9450 0.907743
\(237\) −8.80672 −0.572058
\(238\) 14.7174 0.953987
\(239\) 2.27952 0.147450 0.0737250 0.997279i \(-0.476511\pi\)
0.0737250 + 0.997279i \(0.476511\pi\)
\(240\) 1.13903 0.0735242
\(241\) 17.7901 1.14596 0.572979 0.819570i \(-0.305788\pi\)
0.572979 + 0.819570i \(0.305788\pi\)
\(242\) −29.3671 −1.88779
\(243\) −1.00000 −0.0641500
\(244\) 4.60075 0.294533
\(245\) 1.19635 0.0764323
\(246\) 20.1817 1.28674
\(247\) −14.0238 −0.892313
\(248\) −18.9605 −1.20400
\(249\) 3.10269 0.196625
\(250\) 22.9498 1.45148
\(251\) 15.8080 0.997793 0.498896 0.866662i \(-0.333739\pi\)
0.498896 + 0.866662i \(0.333739\pi\)
\(252\) 3.01194 0.189735
\(253\) −32.6302 −2.05144
\(254\) −33.6805 −2.11330
\(255\) 7.86480 0.492513
\(256\) −9.35827 −0.584892
\(257\) 2.60548 0.162525 0.0812627 0.996693i \(-0.474105\pi\)
0.0812627 + 0.996693i \(0.474105\pi\)
\(258\) −0.136113 −0.00847400
\(259\) 6.18380 0.384243
\(260\) 17.4056 1.07945
\(261\) 5.61643 0.347648
\(262\) −36.1656 −2.23432
\(263\) 10.6186 0.654772 0.327386 0.944891i \(-0.393832\pi\)
0.327386 + 0.944891i \(0.393832\pi\)
\(264\) 11.1257 0.684739
\(265\) 1.14775 0.0705060
\(266\) 6.49959 0.398515
\(267\) 1.15416 0.0706334
\(268\) 15.4068 0.941117
\(269\) 11.9894 0.731007 0.365503 0.930810i \(-0.380897\pi\)
0.365503 + 0.930810i \(0.380897\pi\)
\(270\) 2.67832 0.162998
\(271\) 24.2998 1.47611 0.738055 0.674741i \(-0.235745\pi\)
0.738055 + 0.674741i \(0.235745\pi\)
\(272\) 6.25899 0.379507
\(273\) −4.83040 −0.292349
\(274\) 37.9899 2.29505
\(275\) −17.5260 −1.05686
\(276\) 20.0124 1.20460
\(277\) 3.63746 0.218554 0.109277 0.994011i \(-0.465147\pi\)
0.109277 + 0.994011i \(0.465147\pi\)
\(278\) 3.52906 0.211659
\(279\) 8.36935 0.501060
\(280\) −2.71031 −0.161972
\(281\) −27.9140 −1.66521 −0.832606 0.553866i \(-0.813152\pi\)
−0.832606 + 0.553866i \(0.813152\pi\)
\(282\) −17.5965 −1.04786
\(283\) 5.72185 0.340129 0.170064 0.985433i \(-0.445602\pi\)
0.170064 + 0.985433i \(0.445602\pi\)
\(284\) −23.2355 −1.37878
\(285\) 3.47330 0.205741
\(286\) −53.1073 −3.14030
\(287\) 9.01478 0.532126
\(288\) 6.66242 0.392587
\(289\) 26.2171 1.54218
\(290\) −15.0426 −0.883332
\(291\) −11.1893 −0.655927
\(292\) 17.5502 1.02705
\(293\) −23.7777 −1.38911 −0.694553 0.719441i \(-0.744398\pi\)
−0.694553 + 0.719441i \(0.744398\pi\)
\(294\) 2.23874 0.130566
\(295\) 5.53901 0.322493
\(296\) −14.0092 −0.814271
\(297\) −4.91098 −0.284964
\(298\) −50.2134 −2.90878
\(299\) −32.0948 −1.85609
\(300\) 10.7488 0.620584
\(301\) −0.0607989 −0.00350439
\(302\) −37.6698 −2.16765
\(303\) 7.91000 0.454418
\(304\) 2.76413 0.158534
\(305\) 1.82743 0.104639
\(306\) 14.7174 0.841337
\(307\) −8.40496 −0.479696 −0.239848 0.970810i \(-0.577098\pi\)
−0.239848 + 0.970810i \(0.577098\pi\)
\(308\) 14.7916 0.842829
\(309\) 0.523257 0.0297670
\(310\) −22.4158 −1.27313
\(311\) 23.4356 1.32891 0.664455 0.747328i \(-0.268664\pi\)
0.664455 + 0.747328i \(0.268664\pi\)
\(312\) 10.9431 0.619533
\(313\) 20.2103 1.14235 0.571176 0.820828i \(-0.306487\pi\)
0.571176 + 0.820828i \(0.306487\pi\)
\(314\) −26.1240 −1.47426
\(315\) 1.19635 0.0674069
\(316\) 26.5253 1.49217
\(317\) 13.1251 0.737177 0.368588 0.929593i \(-0.379841\pi\)
0.368588 + 0.929593i \(0.379841\pi\)
\(318\) 2.14779 0.120442
\(319\) 27.5822 1.54430
\(320\) −15.5660 −0.870168
\(321\) 3.71914 0.207582
\(322\) 14.8749 0.828947
\(323\) 19.0858 1.06196
\(324\) 3.01194 0.167330
\(325\) −17.2384 −0.956215
\(326\) 43.9772 2.43567
\(327\) 11.0066 0.608665
\(328\) −20.4228 −1.12766
\(329\) −7.86001 −0.433336
\(330\) 13.1532 0.724059
\(331\) 7.57883 0.416570 0.208285 0.978068i \(-0.433212\pi\)
0.208285 + 0.978068i \(0.433212\pi\)
\(332\) −9.34513 −0.512880
\(333\) 6.18380 0.338870
\(334\) −5.79149 −0.316896
\(335\) 6.11962 0.334350
\(336\) 0.952086 0.0519406
\(337\) 27.4532 1.49547 0.747736 0.663997i \(-0.231141\pi\)
0.747736 + 0.663997i \(0.231141\pi\)
\(338\) −23.1323 −1.25823
\(339\) −2.50026 −0.135795
\(340\) −23.6883 −1.28468
\(341\) 41.1017 2.22578
\(342\) 6.49959 0.351458
\(343\) 1.00000 0.0539949
\(344\) 0.137738 0.00742635
\(345\) 7.94899 0.427959
\(346\) 21.0183 1.12995
\(347\) 0.500520 0.0268693 0.0134347 0.999910i \(-0.495723\pi\)
0.0134347 + 0.999910i \(0.495723\pi\)
\(348\) −16.9164 −0.906812
\(349\) −1.22673 −0.0656656 −0.0328328 0.999461i \(-0.510453\pi\)
−0.0328328 + 0.999461i \(0.510453\pi\)
\(350\) 7.98946 0.427055
\(351\) −4.83040 −0.257828
\(352\) 32.7190 1.74393
\(353\) 19.9347 1.06102 0.530509 0.847679i \(-0.322001\pi\)
0.530509 + 0.847679i \(0.322001\pi\)
\(354\) 10.3651 0.550901
\(355\) −9.22924 −0.489837
\(356\) −3.47626 −0.184242
\(357\) 6.57397 0.347931
\(358\) 48.4648 2.56144
\(359\) 3.05808 0.161399 0.0806996 0.996738i \(-0.474285\pi\)
0.0806996 + 0.996738i \(0.474285\pi\)
\(360\) −2.71031 −0.142846
\(361\) −10.5712 −0.556379
\(362\) −33.0063 −1.73477
\(363\) −13.1177 −0.688502
\(364\) 14.5489 0.762569
\(365\) 6.97101 0.364879
\(366\) 3.41967 0.178749
\(367\) −7.70950 −0.402432 −0.201216 0.979547i \(-0.564489\pi\)
−0.201216 + 0.979547i \(0.564489\pi\)
\(368\) 6.32598 0.329765
\(369\) 9.01478 0.469291
\(370\) −16.5622 −0.861029
\(371\) 0.959377 0.0498083
\(372\) −25.2080 −1.30697
\(373\) −21.3810 −1.10707 −0.553534 0.832826i \(-0.686721\pi\)
−0.553534 + 0.832826i \(0.686721\pi\)
\(374\) 72.2768 3.73735
\(375\) 10.2512 0.529372
\(376\) 17.8066 0.918307
\(377\) 27.1296 1.39724
\(378\) 2.23874 0.115148
\(379\) 4.48857 0.230563 0.115281 0.993333i \(-0.463223\pi\)
0.115281 + 0.993333i \(0.463223\pi\)
\(380\) −10.4614 −0.536658
\(381\) −15.0444 −0.770749
\(382\) 2.23874 0.114544
\(383\) 3.51289 0.179500 0.0897501 0.995964i \(-0.471393\pi\)
0.0897501 + 0.995964i \(0.471393\pi\)
\(384\) −15.8039 −0.806488
\(385\) 5.87527 0.299432
\(386\) −55.1177 −2.80542
\(387\) −0.0607989 −0.00309058
\(388\) 33.7015 1.71093
\(389\) 15.1081 0.766011 0.383006 0.923746i \(-0.374889\pi\)
0.383006 + 0.923746i \(0.374889\pi\)
\(390\) 12.9374 0.655109
\(391\) 43.6797 2.20898
\(392\) −2.26547 −0.114424
\(393\) −16.1545 −0.814886
\(394\) 7.54304 0.380013
\(395\) 10.5360 0.530121
\(396\) 14.7916 0.743306
\(397\) −5.62601 −0.282361 −0.141181 0.989984i \(-0.545090\pi\)
−0.141181 + 0.989984i \(0.545090\pi\)
\(398\) 50.0815 2.51036
\(399\) 2.90324 0.145344
\(400\) 3.39774 0.169887
\(401\) 31.9834 1.59717 0.798587 0.601880i \(-0.205581\pi\)
0.798587 + 0.601880i \(0.205581\pi\)
\(402\) 11.4516 0.571156
\(403\) 40.4273 2.01383
\(404\) −23.8245 −1.18531
\(405\) 1.19635 0.0594473
\(406\) −12.5737 −0.624022
\(407\) 30.3685 1.50531
\(408\) −14.8932 −0.737321
\(409\) −11.1229 −0.549991 −0.274995 0.961446i \(-0.588676\pi\)
−0.274995 + 0.961446i \(0.588676\pi\)
\(410\) −24.1445 −1.19241
\(411\) 16.9693 0.837036
\(412\) −1.57602 −0.0776449
\(413\) 4.62990 0.227823
\(414\) 14.8749 0.731063
\(415\) −3.71192 −0.182211
\(416\) 32.1821 1.57786
\(417\) 1.57636 0.0771947
\(418\) 31.9194 1.56123
\(419\) 27.1097 1.32440 0.662198 0.749329i \(-0.269624\pi\)
0.662198 + 0.749329i \(0.269624\pi\)
\(420\) −3.60335 −0.175826
\(421\) 10.3542 0.504631 0.252316 0.967645i \(-0.418808\pi\)
0.252316 + 0.967645i \(0.418808\pi\)
\(422\) 26.6463 1.29712
\(423\) −7.86001 −0.382167
\(424\) −2.17344 −0.105552
\(425\) 23.4608 1.13801
\(426\) −17.2707 −0.836766
\(427\) 1.52750 0.0739210
\(428\) −11.2018 −0.541461
\(429\) −23.7220 −1.14531
\(430\) 0.162839 0.00785279
\(431\) −15.8290 −0.762457 −0.381228 0.924481i \(-0.624499\pi\)
−0.381228 + 0.924481i \(0.624499\pi\)
\(432\) 0.952086 0.0458073
\(433\) 14.1026 0.677729 0.338864 0.940835i \(-0.389957\pi\)
0.338864 + 0.940835i \(0.389957\pi\)
\(434\) −18.7368 −0.899394
\(435\) −6.71924 −0.322163
\(436\) −33.1512 −1.58765
\(437\) 19.2901 0.922771
\(438\) 13.0448 0.623307
\(439\) −6.85407 −0.327127 −0.163563 0.986533i \(-0.552299\pi\)
−0.163563 + 0.986533i \(0.552299\pi\)
\(440\) −13.3103 −0.634543
\(441\) 1.00000 0.0476190
\(442\) 71.0909 3.38145
\(443\) −25.6061 −1.21658 −0.608291 0.793714i \(-0.708145\pi\)
−0.608291 + 0.793714i \(0.708145\pi\)
\(444\) −18.6253 −0.883916
\(445\) −1.38078 −0.0654554
\(446\) −49.3724 −2.33785
\(447\) −22.4293 −1.06087
\(448\) −13.0112 −0.614723
\(449\) −1.95832 −0.0924188 −0.0462094 0.998932i \(-0.514714\pi\)
−0.0462094 + 0.998932i \(0.514714\pi\)
\(450\) 7.98946 0.376627
\(451\) 44.2714 2.08466
\(452\) 7.53063 0.354211
\(453\) −16.8263 −0.790571
\(454\) −1.11155 −0.0521674
\(455\) 5.77887 0.270918
\(456\) −6.57721 −0.308006
\(457\) −30.2629 −1.41564 −0.707820 0.706393i \(-0.750321\pi\)
−0.707820 + 0.706393i \(0.750321\pi\)
\(458\) 56.9016 2.65884
\(459\) 6.57397 0.306847
\(460\) −23.9419 −1.11630
\(461\) 11.3263 0.527520 0.263760 0.964588i \(-0.415037\pi\)
0.263760 + 0.964588i \(0.415037\pi\)
\(462\) 10.9944 0.511505
\(463\) −37.7584 −1.75478 −0.877392 0.479775i \(-0.840718\pi\)
−0.877392 + 0.479775i \(0.840718\pi\)
\(464\) −5.34732 −0.248243
\(465\) −10.0127 −0.464328
\(466\) 55.0440 2.54986
\(467\) −28.9505 −1.33967 −0.669834 0.742511i \(-0.733635\pi\)
−0.669834 + 0.742511i \(0.733635\pi\)
\(468\) 14.5489 0.672522
\(469\) 5.11522 0.236199
\(470\) 21.0516 0.971039
\(471\) −11.6691 −0.537683
\(472\) −10.4889 −0.482792
\(473\) −0.298582 −0.0137288
\(474\) 19.7159 0.905582
\(475\) 10.3609 0.475391
\(476\) −19.8004 −0.907551
\(477\) 0.959377 0.0439268
\(478\) −5.10325 −0.233417
\(479\) −36.1868 −1.65342 −0.826708 0.562631i \(-0.809789\pi\)
−0.826708 + 0.562631i \(0.809789\pi\)
\(480\) −7.97061 −0.363807
\(481\) 29.8702 1.36197
\(482\) −39.8273 −1.81408
\(483\) 6.64434 0.302328
\(484\) 39.5099 1.79590
\(485\) 13.3863 0.607843
\(486\) 2.23874 0.101551
\(487\) −20.5250 −0.930079 −0.465039 0.885290i \(-0.653960\pi\)
−0.465039 + 0.885290i \(0.653960\pi\)
\(488\) −3.46052 −0.156650
\(489\) 19.6438 0.888322
\(490\) −2.67832 −0.120994
\(491\) −17.9234 −0.808872 −0.404436 0.914566i \(-0.632532\pi\)
−0.404436 + 0.914566i \(0.632532\pi\)
\(492\) −27.1520 −1.22411
\(493\) −36.9222 −1.66289
\(494\) 31.3956 1.41256
\(495\) 5.87527 0.264074
\(496\) −7.96834 −0.357789
\(497\) −7.71447 −0.346041
\(498\) −6.94611 −0.311262
\(499\) 17.5046 0.783612 0.391806 0.920048i \(-0.371850\pi\)
0.391806 + 0.920048i \(0.371850\pi\)
\(500\) −30.8762 −1.38082
\(501\) −2.58695 −0.115576
\(502\) −35.3900 −1.57953
\(503\) −4.97229 −0.221703 −0.110852 0.993837i \(-0.535358\pi\)
−0.110852 + 0.993837i \(0.535358\pi\)
\(504\) −2.26547 −0.100912
\(505\) −9.46316 −0.421105
\(506\) 73.0505 3.24749
\(507\) −10.3327 −0.458894
\(508\) 45.3130 2.01044
\(509\) 14.9079 0.660783 0.330391 0.943844i \(-0.392819\pi\)
0.330391 + 0.943844i \(0.392819\pi\)
\(510\) −17.6072 −0.779661
\(511\) 5.82688 0.257766
\(512\) −10.6570 −0.470979
\(513\) 2.90324 0.128181
\(514\) −5.83299 −0.257282
\(515\) −0.626001 −0.0275849
\(516\) 0.183123 0.00806153
\(517\) −38.6003 −1.69764
\(518\) −13.8439 −0.608267
\(519\) 9.38849 0.412109
\(520\) −13.0919 −0.574117
\(521\) 41.2809 1.80855 0.904275 0.426950i \(-0.140412\pi\)
0.904275 + 0.426950i \(0.140412\pi\)
\(522\) −12.5737 −0.550336
\(523\) −1.66264 −0.0727022 −0.0363511 0.999339i \(-0.511573\pi\)
−0.0363511 + 0.999339i \(0.511573\pi\)
\(524\) 48.6564 2.12556
\(525\) 3.56874 0.155752
\(526\) −23.7723 −1.03652
\(527\) −55.0198 −2.39670
\(528\) 4.67568 0.203483
\(529\) 21.1473 0.919446
\(530\) −2.56952 −0.111613
\(531\) 4.62990 0.200921
\(532\) −8.74439 −0.379118
\(533\) 43.5450 1.88614
\(534\) −2.58386 −0.111815
\(535\) −4.44941 −0.192365
\(536\) −11.5884 −0.500543
\(537\) 21.6483 0.934192
\(538\) −26.8411 −1.15720
\(539\) 4.91098 0.211531
\(540\) −3.60335 −0.155064
\(541\) 1.33991 0.0576074 0.0288037 0.999585i \(-0.490830\pi\)
0.0288037 + 0.999585i \(0.490830\pi\)
\(542\) −54.4009 −2.33672
\(543\) −14.7432 −0.632693
\(544\) −43.7985 −1.87785
\(545\) −13.1678 −0.564045
\(546\) 10.8140 0.462796
\(547\) 18.8298 0.805103 0.402551 0.915397i \(-0.368123\pi\)
0.402551 + 0.915397i \(0.368123\pi\)
\(548\) −51.1107 −2.18334
\(549\) 1.52750 0.0651922
\(550\) 39.2361 1.67303
\(551\) −16.3058 −0.694652
\(552\) −15.0526 −0.640680
\(553\) 8.80672 0.374500
\(554\) −8.14331 −0.345976
\(555\) −7.39802 −0.314029
\(556\) −4.74791 −0.201356
\(557\) 34.8852 1.47813 0.739066 0.673633i \(-0.235267\pi\)
0.739066 + 0.673633i \(0.235267\pi\)
\(558\) −18.7368 −0.793191
\(559\) −0.293683 −0.0124215
\(560\) −1.13903 −0.0481329
\(561\) 32.2846 1.36306
\(562\) 62.4922 2.63607
\(563\) 23.1043 0.973730 0.486865 0.873477i \(-0.338140\pi\)
0.486865 + 0.873477i \(0.338140\pi\)
\(564\) 23.6739 0.996851
\(565\) 2.99119 0.125840
\(566\) −12.8097 −0.538432
\(567\) 1.00000 0.0419961
\(568\) 17.4769 0.733315
\(569\) −18.0716 −0.757602 −0.378801 0.925478i \(-0.623664\pi\)
−0.378801 + 0.925478i \(0.623664\pi\)
\(570\) −7.77581 −0.325693
\(571\) 38.6685 1.61823 0.809114 0.587652i \(-0.199948\pi\)
0.809114 + 0.587652i \(0.199948\pi\)
\(572\) 71.4493 2.98744
\(573\) 1.00000 0.0417756
\(574\) −20.1817 −0.842369
\(575\) 23.7119 0.988854
\(576\) −13.0112 −0.542134
\(577\) 20.5957 0.857410 0.428705 0.903445i \(-0.358970\pi\)
0.428705 + 0.903445i \(0.358970\pi\)
\(578\) −58.6932 −2.44131
\(579\) −24.6200 −1.02317
\(580\) 20.2380 0.840336
\(581\) −3.10269 −0.128721
\(582\) 25.0499 1.03835
\(583\) 4.71148 0.195130
\(584\) −13.2006 −0.546246
\(585\) 5.77887 0.238927
\(586\) 53.2320 2.19899
\(587\) 10.6936 0.441371 0.220685 0.975345i \(-0.429171\pi\)
0.220685 + 0.975345i \(0.429171\pi\)
\(588\) −3.01194 −0.124210
\(589\) −24.2982 −1.00119
\(590\) −12.4004 −0.510515
\(591\) 3.36933 0.138596
\(592\) −5.88751 −0.241975
\(593\) 15.1318 0.621387 0.310694 0.950510i \(-0.399439\pi\)
0.310694 + 0.950510i \(0.399439\pi\)
\(594\) 10.9944 0.451105
\(595\) −7.86480 −0.322425
\(596\) 67.5559 2.76720
\(597\) 22.3704 0.915562
\(598\) 71.8518 2.93824
\(599\) −18.3890 −0.751352 −0.375676 0.926751i \(-0.622589\pi\)
−0.375676 + 0.926751i \(0.622589\pi\)
\(600\) −8.08488 −0.330064
\(601\) −10.3429 −0.421895 −0.210947 0.977497i \(-0.567655\pi\)
−0.210947 + 0.977497i \(0.567655\pi\)
\(602\) 0.136113 0.00554754
\(603\) 5.11522 0.208308
\(604\) 50.6800 2.06214
\(605\) 15.6935 0.638030
\(606\) −17.7084 −0.719355
\(607\) −45.1902 −1.83421 −0.917107 0.398641i \(-0.869482\pi\)
−0.917107 + 0.398641i \(0.869482\pi\)
\(608\) −19.3426 −0.784446
\(609\) −5.61643 −0.227589
\(610\) −4.09114 −0.165646
\(611\) −37.9670 −1.53598
\(612\) −19.8004 −0.800385
\(613\) −14.7884 −0.597299 −0.298649 0.954363i \(-0.596536\pi\)
−0.298649 + 0.954363i \(0.596536\pi\)
\(614\) 18.8165 0.759372
\(615\) −10.7849 −0.434888
\(616\) −11.1257 −0.448267
\(617\) 18.6415 0.750479 0.375240 0.926928i \(-0.377560\pi\)
0.375240 + 0.926928i \(0.377560\pi\)
\(618\) −1.17143 −0.0471220
\(619\) −27.6771 −1.11244 −0.556218 0.831037i \(-0.687748\pi\)
−0.556218 + 0.831037i \(0.687748\pi\)
\(620\) 30.1577 1.21116
\(621\) 6.64434 0.266628
\(622\) −52.4661 −2.10370
\(623\) −1.15416 −0.0462404
\(624\) 4.59895 0.184106
\(625\) 5.57956 0.223182
\(626\) −45.2455 −1.80837
\(627\) 14.2578 0.569400
\(628\) 35.1466 1.40250
\(629\) −40.6521 −1.62091
\(630\) −2.67832 −0.106707
\(631\) −1.04580 −0.0416327 −0.0208163 0.999783i \(-0.506627\pi\)
−0.0208163 + 0.999783i \(0.506627\pi\)
\(632\) −19.9514 −0.793624
\(633\) 11.9024 0.473077
\(634\) −29.3836 −1.16697
\(635\) 17.9985 0.714248
\(636\) −2.88959 −0.114580
\(637\) 4.83040 0.191387
\(638\) −61.7492 −2.44467
\(639\) −7.71447 −0.305180
\(640\) 18.9070 0.747367
\(641\) 39.2122 1.54879 0.774394 0.632703i \(-0.218055\pi\)
0.774394 + 0.632703i \(0.218055\pi\)
\(642\) −8.32618 −0.328608
\(643\) 30.1716 1.18985 0.594927 0.803780i \(-0.297181\pi\)
0.594927 + 0.803780i \(0.297181\pi\)
\(644\) −20.0124 −0.788598
\(645\) 0.0727370 0.00286402
\(646\) −42.7281 −1.68112
\(647\) 36.8140 1.44731 0.723653 0.690164i \(-0.242461\pi\)
0.723653 + 0.690164i \(0.242461\pi\)
\(648\) −2.26547 −0.0889962
\(649\) 22.7374 0.892520
\(650\) 38.5923 1.51371
\(651\) −8.36935 −0.328021
\(652\) −59.1659 −2.31711
\(653\) −19.7365 −0.772348 −0.386174 0.922426i \(-0.626204\pi\)
−0.386174 + 0.922426i \(0.626204\pi\)
\(654\) −24.6408 −0.963532
\(655\) 19.3265 0.755148
\(656\) −8.58285 −0.335104
\(657\) 5.82688 0.227328
\(658\) 17.5965 0.685982
\(659\) 20.3400 0.792333 0.396167 0.918179i \(-0.370340\pi\)
0.396167 + 0.918179i \(0.370340\pi\)
\(660\) −17.6960 −0.688815
\(661\) −11.4093 −0.443770 −0.221885 0.975073i \(-0.571221\pi\)
−0.221885 + 0.975073i \(0.571221\pi\)
\(662\) −16.9670 −0.659441
\(663\) 31.7549 1.23326
\(664\) 7.02906 0.272781
\(665\) −3.47330 −0.134689
\(666\) −13.8439 −0.536441
\(667\) −37.3175 −1.44494
\(668\) 7.79174 0.301471
\(669\) −22.0537 −0.852645
\(670\) −13.7002 −0.529285
\(671\) 7.50153 0.289593
\(672\) −6.66242 −0.257008
\(673\) 47.4217 1.82797 0.913985 0.405747i \(-0.132989\pi\)
0.913985 + 0.405747i \(0.132989\pi\)
\(674\) −61.4605 −2.36737
\(675\) 3.56874 0.137361
\(676\) 31.1217 1.19699
\(677\) −15.0044 −0.576667 −0.288334 0.957530i \(-0.593101\pi\)
−0.288334 + 0.957530i \(0.593101\pi\)
\(678\) 5.59742 0.214967
\(679\) 11.1893 0.429405
\(680\) 17.8175 0.683270
\(681\) −0.496506 −0.0190261
\(682\) −92.0159 −3.52347
\(683\) −39.6557 −1.51738 −0.758691 0.651450i \(-0.774161\pi\)
−0.758691 + 0.651450i \(0.774161\pi\)
\(684\) −8.74439 −0.334350
\(685\) −20.3014 −0.775675
\(686\) −2.23874 −0.0854754
\(687\) 25.4168 0.969713
\(688\) 0.0578857 0.00220687
\(689\) 4.63417 0.176548
\(690\) −17.7957 −0.677470
\(691\) −30.5049 −1.16046 −0.580231 0.814452i \(-0.697038\pi\)
−0.580231 + 0.814452i \(0.697038\pi\)
\(692\) −28.2776 −1.07495
\(693\) 4.91098 0.186553
\(694\) −1.12053 −0.0425349
\(695\) −1.88589 −0.0715357
\(696\) 12.7239 0.482297
\(697\) −59.2629 −2.24474
\(698\) 2.74634 0.103950
\(699\) 24.5871 0.929969
\(700\) −10.7488 −0.406268
\(701\) 36.0614 1.36202 0.681010 0.732274i \(-0.261541\pi\)
0.681010 + 0.732274i \(0.261541\pi\)
\(702\) 10.8140 0.408148
\(703\) −17.9531 −0.677113
\(704\) −63.8979 −2.40824
\(705\) 9.40335 0.354151
\(706\) −44.6286 −1.67962
\(707\) −7.91000 −0.297486
\(708\) −13.9450 −0.524085
\(709\) 18.8618 0.708371 0.354186 0.935175i \(-0.384758\pi\)
0.354186 + 0.935175i \(0.384758\pi\)
\(710\) 20.6618 0.775425
\(711\) 8.80672 0.330278
\(712\) 2.61472 0.0979907
\(713\) −55.6088 −2.08257
\(714\) −14.7174 −0.550784
\(715\) 28.3799 1.06135
\(716\) −65.2034 −2.43676
\(717\) −2.27952 −0.0851303
\(718\) −6.84623 −0.255499
\(719\) 1.43512 0.0535210 0.0267605 0.999642i \(-0.491481\pi\)
0.0267605 + 0.999642i \(0.491481\pi\)
\(720\) −1.13903 −0.0424492
\(721\) −0.523257 −0.0194871
\(722\) 23.6661 0.880762
\(723\) −17.7901 −0.661619
\(724\) 44.4058 1.65033
\(725\) −20.0435 −0.744399
\(726\) 29.3671 1.08992
\(727\) −9.78980 −0.363084 −0.181542 0.983383i \(-0.558109\pi\)
−0.181542 + 0.983383i \(0.558109\pi\)
\(728\) −10.9431 −0.405580
\(729\) 1.00000 0.0370370
\(730\) −15.6063 −0.577613
\(731\) 0.399690 0.0147831
\(732\) −4.60075 −0.170049
\(733\) −12.7193 −0.469797 −0.234898 0.972020i \(-0.575476\pi\)
−0.234898 + 0.972020i \(0.575476\pi\)
\(734\) 17.2595 0.637061
\(735\) −1.19635 −0.0441282
\(736\) −44.2674 −1.63172
\(737\) 25.1207 0.925335
\(738\) −20.1817 −0.742900
\(739\) 33.0733 1.21662 0.608310 0.793700i \(-0.291848\pi\)
0.608310 + 0.793700i \(0.291848\pi\)
\(740\) 22.2824 0.819118
\(741\) 14.0238 0.515177
\(742\) −2.14779 −0.0788479
\(743\) 26.9820 0.989874 0.494937 0.868929i \(-0.335191\pi\)
0.494937 + 0.868929i \(0.335191\pi\)
\(744\) 18.9605 0.695127
\(745\) 26.8334 0.983101
\(746\) 47.8665 1.75252
\(747\) −3.10269 −0.113521
\(748\) −97.2395 −3.55543
\(749\) −3.71914 −0.135894
\(750\) −22.9498 −0.838010
\(751\) 12.5210 0.456897 0.228449 0.973556i \(-0.426635\pi\)
0.228449 + 0.973556i \(0.426635\pi\)
\(752\) 7.48340 0.272892
\(753\) −15.8080 −0.576076
\(754\) −60.7360 −2.21187
\(755\) 20.1303 0.732616
\(756\) −3.01194 −0.109543
\(757\) −9.61090 −0.349314 −0.174657 0.984629i \(-0.555882\pi\)
−0.174657 + 0.984629i \(0.555882\pi\)
\(758\) −10.0487 −0.364987
\(759\) 32.6302 1.18440
\(760\) 7.86868 0.285427
\(761\) 31.2369 1.13234 0.566168 0.824290i \(-0.308425\pi\)
0.566168 + 0.824290i \(0.308425\pi\)
\(762\) 33.6805 1.22012
\(763\) −11.0066 −0.398465
\(764\) −3.01194 −0.108968
\(765\) −7.86480 −0.284352
\(766\) −7.86444 −0.284154
\(767\) 22.3643 0.807527
\(768\) 9.35827 0.337688
\(769\) −46.0230 −1.65963 −0.829816 0.558036i \(-0.811555\pi\)
−0.829816 + 0.558036i \(0.811555\pi\)
\(770\) −13.1532 −0.474008
\(771\) −2.60548 −0.0938341
\(772\) 74.1540 2.66886
\(773\) 26.2347 0.943596 0.471798 0.881707i \(-0.343605\pi\)
0.471798 + 0.881707i \(0.343605\pi\)
\(774\) 0.136113 0.00489247
\(775\) −29.8680 −1.07289
\(776\) −25.3490 −0.909977
\(777\) −6.18380 −0.221843
\(778\) −33.8231 −1.21262
\(779\) −26.1721 −0.937712
\(780\) −17.4056 −0.623221
\(781\) −37.8856 −1.35565
\(782\) −97.7874 −3.49687
\(783\) −5.61643 −0.200715
\(784\) −0.952086 −0.0340031
\(785\) 13.9604 0.498267
\(786\) 36.1656 1.28999
\(787\) 0.577184 0.0205744 0.0102872 0.999947i \(-0.496725\pi\)
0.0102872 + 0.999947i \(0.496725\pi\)
\(788\) −10.1482 −0.361515
\(789\) −10.6186 −0.378033
\(790\) −23.5872 −0.839196
\(791\) 2.50026 0.0888989
\(792\) −11.1257 −0.395334
\(793\) 7.37844 0.262016
\(794\) 12.5952 0.446985
\(795\) −1.14775 −0.0407067
\(796\) −67.3785 −2.38817
\(797\) 29.8531 1.05745 0.528726 0.848792i \(-0.322670\pi\)
0.528726 + 0.848792i \(0.322670\pi\)
\(798\) −6.49959 −0.230083
\(799\) 51.6714 1.82800
\(800\) −23.7764 −0.840623
\(801\) −1.15416 −0.0407802
\(802\) −71.6024 −2.52837
\(803\) 28.6157 1.00983
\(804\) −15.4068 −0.543354
\(805\) −7.94899 −0.280165
\(806\) −90.5061 −3.18794
\(807\) −11.9894 −0.422047
\(808\) 17.9199 0.630420
\(809\) 32.5113 1.14304 0.571519 0.820589i \(-0.306354\pi\)
0.571519 + 0.820589i \(0.306354\pi\)
\(810\) −2.67832 −0.0941067
\(811\) −39.9287 −1.40209 −0.701044 0.713118i \(-0.747282\pi\)
−0.701044 + 0.713118i \(0.747282\pi\)
\(812\) 16.9164 0.593648
\(813\) −24.2998 −0.852232
\(814\) −67.9872 −2.38295
\(815\) −23.5009 −0.823201
\(816\) −6.25899 −0.219108
\(817\) 0.176514 0.00617543
\(818\) 24.9012 0.870649
\(819\) 4.83040 0.168788
\(820\) 32.4834 1.13437
\(821\) −7.86164 −0.274373 −0.137186 0.990545i \(-0.543806\pi\)
−0.137186 + 0.990545i \(0.543806\pi\)
\(822\) −37.9899 −1.32505
\(823\) 9.55136 0.332939 0.166470 0.986047i \(-0.446763\pi\)
0.166470 + 0.986047i \(0.446763\pi\)
\(824\) 1.18542 0.0412962
\(825\) 17.5260 0.610177
\(826\) −10.3651 −0.360649
\(827\) 5.44750 0.189428 0.0947141 0.995505i \(-0.469806\pi\)
0.0947141 + 0.995505i \(0.469806\pi\)
\(828\) −20.0124 −0.695478
\(829\) 1.97167 0.0684790 0.0342395 0.999414i \(-0.489099\pi\)
0.0342395 + 0.999414i \(0.489099\pi\)
\(830\) 8.31001 0.288445
\(831\) −3.63746 −0.126182
\(832\) −62.8494 −2.17891
\(833\) −6.57397 −0.227775
\(834\) −3.52906 −0.122201
\(835\) 3.09491 0.107104
\(836\) −42.9435 −1.48523
\(837\) −8.36935 −0.289287
\(838\) −60.6915 −2.09655
\(839\) −13.9047 −0.480044 −0.240022 0.970767i \(-0.577155\pi\)
−0.240022 + 0.970767i \(0.577155\pi\)
\(840\) 2.71031 0.0935146
\(841\) 2.54425 0.0877329
\(842\) −23.1803 −0.798845
\(843\) 27.9140 0.961410
\(844\) −35.8493 −1.23398
\(845\) 12.3616 0.425253
\(846\) 17.5965 0.604980
\(847\) 13.1177 0.450731
\(848\) −0.913409 −0.0313666
\(849\) −5.72185 −0.196373
\(850\) −52.5225 −1.80151
\(851\) −41.0873 −1.40845
\(852\) 23.2355 0.796036
\(853\) 44.1402 1.51133 0.755665 0.654958i \(-0.227314\pi\)
0.755665 + 0.654958i \(0.227314\pi\)
\(854\) −3.41967 −0.117019
\(855\) −3.47330 −0.118785
\(856\) 8.42562 0.287982
\(857\) 26.9020 0.918954 0.459477 0.888190i \(-0.348037\pi\)
0.459477 + 0.888190i \(0.348037\pi\)
\(858\) 53.1073 1.81305
\(859\) 28.6221 0.976574 0.488287 0.872683i \(-0.337622\pi\)
0.488287 + 0.872683i \(0.337622\pi\)
\(860\) −0.219080 −0.00747055
\(861\) −9.01478 −0.307223
\(862\) 35.4370 1.20699
\(863\) −32.7324 −1.11422 −0.557112 0.830438i \(-0.688090\pi\)
−0.557112 + 0.830438i \(0.688090\pi\)
\(864\) −6.66242 −0.226660
\(865\) −11.2320 −0.381898
\(866\) −31.5721 −1.07286
\(867\) −26.2171 −0.890379
\(868\) 25.2080 0.855615
\(869\) 43.2496 1.46714
\(870\) 15.0426 0.509992
\(871\) 24.7086 0.837217
\(872\) 24.9351 0.844409
\(873\) 11.1893 0.378700
\(874\) −43.1855 −1.46077
\(875\) −10.2512 −0.346555
\(876\) −17.5502 −0.592967
\(877\) −35.4367 −1.19661 −0.598306 0.801268i \(-0.704159\pi\)
−0.598306 + 0.801268i \(0.704159\pi\)
\(878\) 15.3445 0.517850
\(879\) 23.7777 0.802001
\(880\) −5.59377 −0.188566
\(881\) −12.3862 −0.417300 −0.208650 0.977990i \(-0.566907\pi\)
−0.208650 + 0.977990i \(0.566907\pi\)
\(882\) −2.23874 −0.0753822
\(883\) −21.0202 −0.707385 −0.353692 0.935362i \(-0.615074\pi\)
−0.353692 + 0.935362i \(0.615074\pi\)
\(884\) −95.6439 −3.21685
\(885\) −5.53901 −0.186192
\(886\) 57.3253 1.92588
\(887\) 17.4206 0.584925 0.292463 0.956277i \(-0.405525\pi\)
0.292463 + 0.956277i \(0.405525\pi\)
\(888\) 14.0092 0.470120
\(889\) 15.0444 0.504574
\(890\) 3.09121 0.103618
\(891\) 4.91098 0.164524
\(892\) 66.4244 2.22405
\(893\) 22.8195 0.763625
\(894\) 50.2134 1.67939
\(895\) −25.8990 −0.865708
\(896\) 15.8039 0.527971
\(897\) 32.0948 1.07161
\(898\) 4.38416 0.146301
\(899\) 47.0058 1.56773
\(900\) −10.7488 −0.358294
\(901\) −6.30691 −0.210114
\(902\) −99.1121 −3.30007
\(903\) 0.0607989 0.00202326
\(904\) −5.66427 −0.188391
\(905\) 17.6382 0.586312
\(906\) 37.6698 1.25149
\(907\) −24.3911 −0.809894 −0.404947 0.914340i \(-0.632710\pi\)
−0.404947 + 0.914340i \(0.632710\pi\)
\(908\) 1.49545 0.0496281
\(909\) −7.91000 −0.262358
\(910\) −12.9374 −0.428870
\(911\) −9.90018 −0.328008 −0.164004 0.986460i \(-0.552441\pi\)
−0.164004 + 0.986460i \(0.552441\pi\)
\(912\) −2.76413 −0.0915296
\(913\) −15.2373 −0.504279
\(914\) 67.7507 2.24099
\(915\) −1.82743 −0.0604131
\(916\) −76.5541 −2.52942
\(917\) 16.1545 0.533468
\(918\) −14.7174 −0.485746
\(919\) 32.9140 1.08573 0.542867 0.839819i \(-0.317339\pi\)
0.542867 + 0.839819i \(0.317339\pi\)
\(920\) 18.0082 0.593713
\(921\) 8.40496 0.276953
\(922\) −25.3567 −0.835077
\(923\) −37.2640 −1.22656
\(924\) −14.7916 −0.486608
\(925\) −22.0684 −0.725603
\(926\) 84.5312 2.77787
\(927\) −0.523257 −0.0171860
\(928\) 37.4190 1.22834
\(929\) 27.0441 0.887288 0.443644 0.896203i \(-0.353686\pi\)
0.443644 + 0.896203i \(0.353686\pi\)
\(930\) 22.4158 0.735044
\(931\) −2.90324 −0.0951499
\(932\) −74.0549 −2.42575
\(933\) −23.4356 −0.767247
\(934\) 64.8125 2.12073
\(935\) −38.6239 −1.26314
\(936\) −10.9431 −0.357688
\(937\) 56.3376 1.84047 0.920235 0.391366i \(-0.127997\pi\)
0.920235 + 0.391366i \(0.127997\pi\)
\(938\) −11.4516 −0.373909
\(939\) −20.2103 −0.659537
\(940\) −28.3224 −0.923774
\(941\) 6.90321 0.225038 0.112519 0.993650i \(-0.464108\pi\)
0.112519 + 0.993650i \(0.464108\pi\)
\(942\) 26.1240 0.851166
\(943\) −59.8973 −1.95052
\(944\) −4.40807 −0.143470
\(945\) −1.19635 −0.0389174
\(946\) 0.668447 0.0217331
\(947\) −2.80736 −0.0912270 −0.0456135 0.998959i \(-0.514524\pi\)
−0.0456135 + 0.998959i \(0.514524\pi\)
\(948\) −26.5253 −0.861503
\(949\) 28.1461 0.913662
\(950\) −23.1953 −0.752556
\(951\) −13.1251 −0.425609
\(952\) 14.8932 0.482690
\(953\) 5.51651 0.178697 0.0893486 0.996000i \(-0.471521\pi\)
0.0893486 + 0.996000i \(0.471521\pi\)
\(954\) −2.14779 −0.0695373
\(955\) −1.19635 −0.0387131
\(956\) 6.86579 0.222055
\(957\) −27.5822 −0.891605
\(958\) 81.0127 2.61740
\(959\) −16.9693 −0.547969
\(960\) 15.5660 0.502392
\(961\) 39.0460 1.25955
\(962\) −66.8716 −2.15603
\(963\) −3.71914 −0.119848
\(964\) 53.5826 1.72578
\(965\) 29.4542 0.948166
\(966\) −14.8749 −0.478593
\(967\) −42.0701 −1.35288 −0.676442 0.736496i \(-0.736479\pi\)
−0.676442 + 0.736496i \(0.736479\pi\)
\(968\) −29.7179 −0.955169
\(969\) −19.0858 −0.613125
\(970\) −29.9685 −0.962231
\(971\) 21.2806 0.682926 0.341463 0.939895i \(-0.389078\pi\)
0.341463 + 0.939895i \(0.389078\pi\)
\(972\) −3.01194 −0.0966081
\(973\) −1.57636 −0.0505358
\(974\) 45.9502 1.47234
\(975\) 17.2384 0.552071
\(976\) −1.45431 −0.0465514
\(977\) 5.87114 0.187834 0.0939171 0.995580i \(-0.470061\pi\)
0.0939171 + 0.995580i \(0.470061\pi\)
\(978\) −43.9772 −1.40624
\(979\) −5.66806 −0.181152
\(980\) 3.60335 0.115105
\(981\) −11.0066 −0.351413
\(982\) 40.1258 1.28047
\(983\) 0.809028 0.0258040 0.0129020 0.999917i \(-0.495893\pi\)
0.0129020 + 0.999917i \(0.495893\pi\)
\(984\) 20.4228 0.651054
\(985\) −4.03091 −0.128435
\(986\) 82.6591 2.63240
\(987\) 7.86001 0.250187
\(988\) −42.2389 −1.34380
\(989\) 0.403968 0.0128454
\(990\) −13.1532 −0.418036
\(991\) −43.7490 −1.38973 −0.694867 0.719139i \(-0.744537\pi\)
−0.694867 + 0.719139i \(0.744537\pi\)
\(992\) 55.7601 1.77038
\(993\) −7.57883 −0.240507
\(994\) 17.2707 0.547792
\(995\) −26.7630 −0.848444
\(996\) 9.34513 0.296112
\(997\) −24.1816 −0.765838 −0.382919 0.923782i \(-0.625081\pi\)
−0.382919 + 0.923782i \(0.625081\pi\)
\(998\) −39.1881 −1.24048
\(999\) −6.18380 −0.195647
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.l.1.6 28
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
4011.2.a.l.1.6 28 1.1 even 1 trivial