Properties

Label 8026.2.a.a.1.16
Level $8026$
Weight $2$
Character 8026.1
Self dual yes
Analytic conductor $64.088$
Analytic rank $1$
Dimension $71$
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] = [8026,2,Mod(1,8026)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(8026, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("8026.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 8026 = 2 \cdot 4013 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 8026.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: \(64.0879326623\)
Analytic rank: \(1\)
Dimension: \(71\)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.16
Character \(\chi\) \(=\) 8026.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+1.00000 q^{2} -1.97637 q^{3} +1.00000 q^{4} -0.168031 q^{5} -1.97637 q^{6} -1.30361 q^{7} +1.00000 q^{8} +0.906032 q^{9} +O(q^{10})\) \(q+1.00000 q^{2} -1.97637 q^{3} +1.00000 q^{4} -0.168031 q^{5} -1.97637 q^{6} -1.30361 q^{7} +1.00000 q^{8} +0.906032 q^{9} -0.168031 q^{10} -4.48117 q^{11} -1.97637 q^{12} +2.33495 q^{13} -1.30361 q^{14} +0.332092 q^{15} +1.00000 q^{16} +3.76866 q^{17} +0.906032 q^{18} +1.05517 q^{19} -0.168031 q^{20} +2.57641 q^{21} -4.48117 q^{22} +4.38036 q^{23} -1.97637 q^{24} -4.97177 q^{25} +2.33495 q^{26} +4.13845 q^{27} -1.30361 q^{28} -6.31021 q^{29} +0.332092 q^{30} +1.19262 q^{31} +1.00000 q^{32} +8.85645 q^{33} +3.76866 q^{34} +0.219048 q^{35} +0.906032 q^{36} -5.98531 q^{37} +1.05517 q^{38} -4.61472 q^{39} -0.168031 q^{40} +7.86206 q^{41} +2.57641 q^{42} +2.84566 q^{43} -4.48117 q^{44} -0.152242 q^{45} +4.38036 q^{46} +6.14204 q^{47} -1.97637 q^{48} -5.30060 q^{49} -4.97177 q^{50} -7.44825 q^{51} +2.33495 q^{52} -0.518989 q^{53} +4.13845 q^{54} +0.752978 q^{55} -1.30361 q^{56} -2.08540 q^{57} -6.31021 q^{58} +5.21300 q^{59} +0.332092 q^{60} +7.76239 q^{61} +1.19262 q^{62} -1.18111 q^{63} +1.00000 q^{64} -0.392345 q^{65} +8.85645 q^{66} -5.81318 q^{67} +3.76866 q^{68} -8.65720 q^{69} +0.219048 q^{70} -2.67321 q^{71} +0.906032 q^{72} -10.0953 q^{73} -5.98531 q^{74} +9.82604 q^{75} +1.05517 q^{76} +5.84170 q^{77} -4.61472 q^{78} +3.11698 q^{79} -0.168031 q^{80} -10.8972 q^{81} +7.86206 q^{82} +15.6884 q^{83} +2.57641 q^{84} -0.633253 q^{85} +2.84566 q^{86} +12.4713 q^{87} -4.48117 q^{88} -1.95686 q^{89} -0.152242 q^{90} -3.04387 q^{91} +4.38036 q^{92} -2.35705 q^{93} +6.14204 q^{94} -0.177302 q^{95} -1.97637 q^{96} +0.204240 q^{97} -5.30060 q^{98} -4.06009 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 71 q + 71 q^{2} - 9 q^{3} + 71 q^{4} - 34 q^{5} - 9 q^{6} - 19 q^{7} + 71 q^{8} + 34 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 71 q + 71 q^{2} - 9 q^{3} + 71 q^{4} - 34 q^{5} - 9 q^{6} - 19 q^{7} + 71 q^{8} + 34 q^{9} - 34 q^{10} - 37 q^{11} - 9 q^{12} - 62 q^{13} - 19 q^{14} - 29 q^{15} + 71 q^{16} - 52 q^{17} + 34 q^{18} - 30 q^{19} - 34 q^{20} - 51 q^{21} - 37 q^{22} - 45 q^{23} - 9 q^{24} + 27 q^{25} - 62 q^{26} - 27 q^{27} - 19 q^{28} - 55 q^{29} - 29 q^{30} - 61 q^{31} + 71 q^{32} - 73 q^{33} - 52 q^{34} - 33 q^{35} + 34 q^{36} - 43 q^{37} - 30 q^{38} - 40 q^{39} - 34 q^{40} - 87 q^{41} - 51 q^{42} - 4 q^{43} - 37 q^{44} - 81 q^{45} - 45 q^{46} - 89 q^{47} - 9 q^{48} - 2 q^{49} + 27 q^{50} - 19 q^{51} - 62 q^{52} - 50 q^{53} - 27 q^{54} - 66 q^{55} - 19 q^{56} - 45 q^{57} - 55 q^{58} - 118 q^{59} - 29 q^{60} - 92 q^{61} - 61 q^{62} - 54 q^{63} + 71 q^{64} - 51 q^{65} - 73 q^{66} - 17 q^{67} - 52 q^{68} - 89 q^{69} - 33 q^{70} - 95 q^{71} + 34 q^{72} - 114 q^{73} - 43 q^{74} - 38 q^{75} - 30 q^{76} - 73 q^{77} - 40 q^{78} - 47 q^{79} - 34 q^{80} - 57 q^{81} - 87 q^{82} - 68 q^{83} - 51 q^{84} - 67 q^{85} - 4 q^{86} - 55 q^{87} - 37 q^{88} - 150 q^{89} - 81 q^{90} - 23 q^{91} - 45 q^{92} - 59 q^{93} - 89 q^{94} - 47 q^{95} - 9 q^{96} - 97 q^{97} - 2 q^{98} - 57 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000 0.707107
\(3\) −1.97637 −1.14106 −0.570528 0.821278i \(-0.693262\pi\)
−0.570528 + 0.821278i \(0.693262\pi\)
\(4\) 1.00000 0.500000
\(5\) −0.168031 −0.0751460 −0.0375730 0.999294i \(-0.511963\pi\)
−0.0375730 + 0.999294i \(0.511963\pi\)
\(6\) −1.97637 −0.806849
\(7\) −1.30361 −0.492718 −0.246359 0.969179i \(-0.579234\pi\)
−0.246359 + 0.969179i \(0.579234\pi\)
\(8\) 1.00000 0.353553
\(9\) 0.906032 0.302011
\(10\) −0.168031 −0.0531362
\(11\) −4.48117 −1.35113 −0.675563 0.737303i \(-0.736099\pi\)
−0.675563 + 0.737303i \(0.736099\pi\)
\(12\) −1.97637 −0.570528
\(13\) 2.33495 0.647599 0.323800 0.946126i \(-0.395040\pi\)
0.323800 + 0.946126i \(0.395040\pi\)
\(14\) −1.30361 −0.348404
\(15\) 0.332092 0.0857458
\(16\) 1.00000 0.250000
\(17\) 3.76866 0.914033 0.457017 0.889458i \(-0.348918\pi\)
0.457017 + 0.889458i \(0.348918\pi\)
\(18\) 0.906032 0.213554
\(19\) 1.05517 0.242073 0.121036 0.992648i \(-0.461378\pi\)
0.121036 + 0.992648i \(0.461378\pi\)
\(20\) −0.168031 −0.0375730
\(21\) 2.57641 0.562220
\(22\) −4.48117 −0.955390
\(23\) 4.38036 0.913368 0.456684 0.889629i \(-0.349037\pi\)
0.456684 + 0.889629i \(0.349037\pi\)
\(24\) −1.97637 −0.403425
\(25\) −4.97177 −0.994353
\(26\) 2.33495 0.457922
\(27\) 4.13845 0.796446
\(28\) −1.30361 −0.246359
\(29\) −6.31021 −1.17178 −0.585888 0.810392i \(-0.699254\pi\)
−0.585888 + 0.810392i \(0.699254\pi\)
\(30\) 0.332092 0.0606314
\(31\) 1.19262 0.214201 0.107100 0.994248i \(-0.465843\pi\)
0.107100 + 0.994248i \(0.465843\pi\)
\(32\) 1.00000 0.176777
\(33\) 8.85645 1.54171
\(34\) 3.76866 0.646319
\(35\) 0.219048 0.0370258
\(36\) 0.906032 0.151005
\(37\) −5.98531 −0.983979 −0.491990 0.870601i \(-0.663730\pi\)
−0.491990 + 0.870601i \(0.663730\pi\)
\(38\) 1.05517 0.171171
\(39\) −4.61472 −0.738947
\(40\) −0.168031 −0.0265681
\(41\) 7.86206 1.22785 0.613923 0.789366i \(-0.289590\pi\)
0.613923 + 0.789366i \(0.289590\pi\)
\(42\) 2.57641 0.397549
\(43\) 2.84566 0.433959 0.216980 0.976176i \(-0.430379\pi\)
0.216980 + 0.976176i \(0.430379\pi\)
\(44\) −4.48117 −0.675563
\(45\) −0.152242 −0.0226949
\(46\) 4.38036 0.645849
\(47\) 6.14204 0.895908 0.447954 0.894057i \(-0.352153\pi\)
0.447954 + 0.894057i \(0.352153\pi\)
\(48\) −1.97637 −0.285264
\(49\) −5.30060 −0.757229
\(50\) −4.97177 −0.703114
\(51\) −7.44825 −1.04296
\(52\) 2.33495 0.323800
\(53\) −0.518989 −0.0712887 −0.0356443 0.999365i \(-0.511348\pi\)
−0.0356443 + 0.999365i \(0.511348\pi\)
\(54\) 4.13845 0.563172
\(55\) 0.752978 0.101532
\(56\) −1.30361 −0.174202
\(57\) −2.08540 −0.276219
\(58\) −6.31021 −0.828571
\(59\) 5.21300 0.678674 0.339337 0.940665i \(-0.389797\pi\)
0.339337 + 0.940665i \(0.389797\pi\)
\(60\) 0.332092 0.0428729
\(61\) 7.76239 0.993873 0.496936 0.867787i \(-0.334458\pi\)
0.496936 + 0.867787i \(0.334458\pi\)
\(62\) 1.19262 0.151463
\(63\) −1.18111 −0.148806
\(64\) 1.00000 0.125000
\(65\) −0.392345 −0.0486645
\(66\) 8.85645 1.09015
\(67\) −5.81318 −0.710193 −0.355096 0.934830i \(-0.615552\pi\)
−0.355096 + 0.934830i \(0.615552\pi\)
\(68\) 3.76866 0.457017
\(69\) −8.65720 −1.04220
\(70\) 0.219048 0.0261812
\(71\) −2.67321 −0.317252 −0.158626 0.987339i \(-0.550706\pi\)
−0.158626 + 0.987339i \(0.550706\pi\)
\(72\) 0.906032 0.106777
\(73\) −10.0953 −1.18157 −0.590785 0.806829i \(-0.701182\pi\)
−0.590785 + 0.806829i \(0.701182\pi\)
\(74\) −5.98531 −0.695778
\(75\) 9.82604 1.13461
\(76\) 1.05517 0.121036
\(77\) 5.84170 0.665724
\(78\) −4.61472 −0.522515
\(79\) 3.11698 0.350687 0.175344 0.984507i \(-0.443896\pi\)
0.175344 + 0.984507i \(0.443896\pi\)
\(80\) −0.168031 −0.0187865
\(81\) −10.8972 −1.21080
\(82\) 7.86206 0.868219
\(83\) 15.6884 1.72202 0.861011 0.508586i \(-0.169832\pi\)
0.861011 + 0.508586i \(0.169832\pi\)
\(84\) 2.57641 0.281110
\(85\) −0.633253 −0.0686859
\(86\) 2.84566 0.306855
\(87\) 12.4713 1.33706
\(88\) −4.48117 −0.477695
\(89\) −1.95686 −0.207427 −0.103713 0.994607i \(-0.533072\pi\)
−0.103713 + 0.994607i \(0.533072\pi\)
\(90\) −0.152242 −0.0160477
\(91\) −3.04387 −0.319084
\(92\) 4.38036 0.456684
\(93\) −2.35705 −0.244415
\(94\) 6.14204 0.633503
\(95\) −0.177302 −0.0181908
\(96\) −1.97637 −0.201712
\(97\) 0.204240 0.0207374 0.0103687 0.999946i \(-0.496699\pi\)
0.0103687 + 0.999946i \(0.496699\pi\)
\(98\) −5.30060 −0.535442
\(99\) −4.06009 −0.408054
\(100\) −4.97177 −0.497177
\(101\) 1.62093 0.161289 0.0806443 0.996743i \(-0.474302\pi\)
0.0806443 + 0.996743i \(0.474302\pi\)
\(102\) −7.44825 −0.737487
\(103\) −19.5068 −1.92206 −0.961032 0.276437i \(-0.910846\pi\)
−0.961032 + 0.276437i \(0.910846\pi\)
\(104\) 2.33495 0.228961
\(105\) −0.432919 −0.0422485
\(106\) −0.518989 −0.0504087
\(107\) −15.1972 −1.46917 −0.734586 0.678515i \(-0.762624\pi\)
−0.734586 + 0.678515i \(0.762624\pi\)
\(108\) 4.13845 0.398223
\(109\) 10.6327 1.01843 0.509214 0.860640i \(-0.329936\pi\)
0.509214 + 0.860640i \(0.329936\pi\)
\(110\) 0.752978 0.0717937
\(111\) 11.8292 1.12278
\(112\) −1.30361 −0.123180
\(113\) −3.37491 −0.317485 −0.158742 0.987320i \(-0.550744\pi\)
−0.158742 + 0.987320i \(0.550744\pi\)
\(114\) −2.08540 −0.195316
\(115\) −0.736038 −0.0686359
\(116\) −6.31021 −0.585888
\(117\) 2.11554 0.195582
\(118\) 5.21300 0.479895
\(119\) −4.91286 −0.450361
\(120\) 0.332092 0.0303157
\(121\) 9.08093 0.825539
\(122\) 7.76239 0.702774
\(123\) −15.5383 −1.40104
\(124\) 1.19262 0.107100
\(125\) 1.67557 0.149868
\(126\) −1.18111 −0.105222
\(127\) −8.66633 −0.769013 −0.384506 0.923122i \(-0.625628\pi\)
−0.384506 + 0.923122i \(0.625628\pi\)
\(128\) 1.00000 0.0883883
\(129\) −5.62407 −0.495172
\(130\) −0.392345 −0.0344110
\(131\) 13.8235 1.20777 0.603883 0.797073i \(-0.293619\pi\)
0.603883 + 0.797073i \(0.293619\pi\)
\(132\) 8.85645 0.770855
\(133\) −1.37553 −0.119274
\(134\) −5.81318 −0.502182
\(135\) −0.695390 −0.0598497
\(136\) 3.76866 0.323160
\(137\) 3.07452 0.262674 0.131337 0.991338i \(-0.458073\pi\)
0.131337 + 0.991338i \(0.458073\pi\)
\(138\) −8.65720 −0.736950
\(139\) −11.0174 −0.934488 −0.467244 0.884128i \(-0.654753\pi\)
−0.467244 + 0.884128i \(0.654753\pi\)
\(140\) 0.219048 0.0185129
\(141\) −12.1389 −1.02228
\(142\) −2.67321 −0.224331
\(143\) −10.4633 −0.874987
\(144\) 0.906032 0.0755027
\(145\) 1.06031 0.0880542
\(146\) −10.0953 −0.835496
\(147\) 10.4759 0.864041
\(148\) −5.98531 −0.491990
\(149\) −13.8344 −1.13336 −0.566679 0.823939i \(-0.691772\pi\)
−0.566679 + 0.823939i \(0.691772\pi\)
\(150\) 9.82604 0.802293
\(151\) −2.43642 −0.198273 −0.0991366 0.995074i \(-0.531608\pi\)
−0.0991366 + 0.995074i \(0.531608\pi\)
\(152\) 1.05517 0.0855856
\(153\) 3.41452 0.276048
\(154\) 5.84170 0.470738
\(155\) −0.200398 −0.0160963
\(156\) −4.61472 −0.369474
\(157\) −18.6718 −1.49017 −0.745086 0.666968i \(-0.767592\pi\)
−0.745086 + 0.666968i \(0.767592\pi\)
\(158\) 3.11698 0.247973
\(159\) 1.02571 0.0813444
\(160\) −0.168031 −0.0132841
\(161\) −5.71028 −0.450033
\(162\) −10.8972 −0.856165
\(163\) −0.807239 −0.0632278 −0.0316139 0.999500i \(-0.510065\pi\)
−0.0316139 + 0.999500i \(0.510065\pi\)
\(164\) 7.86206 0.613923
\(165\) −1.48816 −0.115853
\(166\) 15.6884 1.21765
\(167\) 14.3175 1.10792 0.553960 0.832543i \(-0.313116\pi\)
0.553960 + 0.832543i \(0.313116\pi\)
\(168\) 2.57641 0.198775
\(169\) −7.54800 −0.580615
\(170\) −0.633253 −0.0485683
\(171\) 0.956017 0.0731085
\(172\) 2.84566 0.216980
\(173\) −15.2909 −1.16254 −0.581272 0.813709i \(-0.697445\pi\)
−0.581272 + 0.813709i \(0.697445\pi\)
\(174\) 12.4713 0.945446
\(175\) 6.48124 0.489936
\(176\) −4.48117 −0.337781
\(177\) −10.3028 −0.774406
\(178\) −1.95686 −0.146673
\(179\) −9.35245 −0.699035 −0.349517 0.936930i \(-0.613654\pi\)
−0.349517 + 0.936930i \(0.613654\pi\)
\(180\) −0.152242 −0.0113474
\(181\) 24.0169 1.78516 0.892580 0.450889i \(-0.148893\pi\)
0.892580 + 0.450889i \(0.148893\pi\)
\(182\) −3.04387 −0.225626
\(183\) −15.3414 −1.13407
\(184\) 4.38036 0.322924
\(185\) 1.00572 0.0739421
\(186\) −2.35705 −0.172828
\(187\) −16.8880 −1.23497
\(188\) 6.14204 0.447954
\(189\) −5.39493 −0.392423
\(190\) −0.177302 −0.0128628
\(191\) −16.8777 −1.22123 −0.610614 0.791928i \(-0.709077\pi\)
−0.610614 + 0.791928i \(0.709077\pi\)
\(192\) −1.97637 −0.142632
\(193\) −24.0536 −1.73142 −0.865710 0.500546i \(-0.833132\pi\)
−0.865710 + 0.500546i \(0.833132\pi\)
\(194\) 0.204240 0.0146636
\(195\) 0.775419 0.0555289
\(196\) −5.30060 −0.378614
\(197\) −10.6357 −0.757764 −0.378882 0.925445i \(-0.623691\pi\)
−0.378882 + 0.925445i \(0.623691\pi\)
\(198\) −4.06009 −0.288538
\(199\) 8.49276 0.602036 0.301018 0.953618i \(-0.402674\pi\)
0.301018 + 0.953618i \(0.402674\pi\)
\(200\) −4.97177 −0.351557
\(201\) 11.4890 0.810370
\(202\) 1.62093 0.114048
\(203\) 8.22605 0.577355
\(204\) −7.44825 −0.521482
\(205\) −1.32107 −0.0922677
\(206\) −19.5068 −1.35910
\(207\) 3.96875 0.275847
\(208\) 2.33495 0.161900
\(209\) −4.72840 −0.327070
\(210\) −0.432919 −0.0298742
\(211\) 18.6669 1.28508 0.642540 0.766252i \(-0.277881\pi\)
0.642540 + 0.766252i \(0.277881\pi\)
\(212\) −0.518989 −0.0356443
\(213\) 5.28326 0.362003
\(214\) −15.1972 −1.03886
\(215\) −0.478161 −0.0326103
\(216\) 4.13845 0.281586
\(217\) −1.55471 −0.105541
\(218\) 10.6327 0.720137
\(219\) 19.9521 1.34824
\(220\) 0.752978 0.0507658
\(221\) 8.79963 0.591927
\(222\) 11.8292 0.793922
\(223\) 20.2007 1.35274 0.676370 0.736562i \(-0.263552\pi\)
0.676370 + 0.736562i \(0.263552\pi\)
\(224\) −1.30361 −0.0871011
\(225\) −4.50458 −0.300305
\(226\) −3.37491 −0.224496
\(227\) 18.1102 1.20202 0.601008 0.799243i \(-0.294766\pi\)
0.601008 + 0.799243i \(0.294766\pi\)
\(228\) −2.08540 −0.138109
\(229\) 2.03970 0.134787 0.0673937 0.997726i \(-0.478532\pi\)
0.0673937 + 0.997726i \(0.478532\pi\)
\(230\) −0.736038 −0.0485329
\(231\) −11.5454 −0.759629
\(232\) −6.31021 −0.414285
\(233\) −7.97305 −0.522332 −0.261166 0.965294i \(-0.584107\pi\)
−0.261166 + 0.965294i \(0.584107\pi\)
\(234\) 2.11554 0.138297
\(235\) −1.03206 −0.0673239
\(236\) 5.21300 0.339337
\(237\) −6.16029 −0.400154
\(238\) −4.91286 −0.318453
\(239\) −17.1569 −1.10979 −0.554894 0.831921i \(-0.687241\pi\)
−0.554894 + 0.831921i \(0.687241\pi\)
\(240\) 0.332092 0.0214365
\(241\) −22.8505 −1.47193 −0.735965 0.677020i \(-0.763271\pi\)
−0.735965 + 0.677020i \(0.763271\pi\)
\(242\) 9.08093 0.583744
\(243\) 9.12153 0.585146
\(244\) 7.76239 0.496936
\(245\) 0.890668 0.0569027
\(246\) −15.5383 −0.990687
\(247\) 2.46377 0.156766
\(248\) 1.19262 0.0757314
\(249\) −31.0060 −1.96493
\(250\) 1.67557 0.105972
\(251\) −16.0932 −1.01579 −0.507897 0.861418i \(-0.669577\pi\)
−0.507897 + 0.861418i \(0.669577\pi\)
\(252\) −1.18111 −0.0744031
\(253\) −19.6292 −1.23407
\(254\) −8.66633 −0.543774
\(255\) 1.25154 0.0783745
\(256\) 1.00000 0.0625000
\(257\) −23.7996 −1.48458 −0.742290 0.670078i \(-0.766261\pi\)
−0.742290 + 0.670078i \(0.766261\pi\)
\(258\) −5.62407 −0.350140
\(259\) 7.80251 0.484824
\(260\) −0.392345 −0.0243322
\(261\) −5.71725 −0.353889
\(262\) 13.8235 0.854020
\(263\) 8.33080 0.513699 0.256850 0.966451i \(-0.417315\pi\)
0.256850 + 0.966451i \(0.417315\pi\)
\(264\) 8.85645 0.545077
\(265\) 0.0872065 0.00535706
\(266\) −1.37553 −0.0843391
\(267\) 3.86747 0.236685
\(268\) −5.81318 −0.355096
\(269\) −13.8061 −0.841775 −0.420887 0.907113i \(-0.638281\pi\)
−0.420887 + 0.907113i \(0.638281\pi\)
\(270\) −0.695390 −0.0423201
\(271\) 5.14386 0.312467 0.156234 0.987720i \(-0.450065\pi\)
0.156234 + 0.987720i \(0.450065\pi\)
\(272\) 3.76866 0.228508
\(273\) 6.01580 0.364093
\(274\) 3.07452 0.185739
\(275\) 22.2794 1.34350
\(276\) −8.65720 −0.521102
\(277\) −8.24857 −0.495608 −0.247804 0.968810i \(-0.579709\pi\)
−0.247804 + 0.968810i \(0.579709\pi\)
\(278\) −11.0174 −0.660783
\(279\) 1.08055 0.0646909
\(280\) 0.219048 0.0130906
\(281\) 21.1214 1.26000 0.630000 0.776595i \(-0.283055\pi\)
0.630000 + 0.776595i \(0.283055\pi\)
\(282\) −12.1389 −0.722863
\(283\) 8.10533 0.481812 0.240906 0.970548i \(-0.422555\pi\)
0.240906 + 0.970548i \(0.422555\pi\)
\(284\) −2.67321 −0.158626
\(285\) 0.350414 0.0207567
\(286\) −10.4633 −0.618709
\(287\) −10.2491 −0.604983
\(288\) 0.906032 0.0533884
\(289\) −2.79724 −0.164543
\(290\) 1.06031 0.0622637
\(291\) −0.403653 −0.0236626
\(292\) −10.0953 −0.590785
\(293\) −30.8519 −1.80239 −0.901194 0.433417i \(-0.857308\pi\)
−0.901194 + 0.433417i \(0.857308\pi\)
\(294\) 10.4759 0.610969
\(295\) −0.875948 −0.0509996
\(296\) −5.98531 −0.347889
\(297\) −18.5451 −1.07610
\(298\) −13.8344 −0.801404
\(299\) 10.2279 0.591496
\(300\) 9.82604 0.567307
\(301\) −3.70963 −0.213820
\(302\) −2.43642 −0.140200
\(303\) −3.20356 −0.184040
\(304\) 1.05517 0.0605181
\(305\) −1.30433 −0.0746855
\(306\) 3.41452 0.195195
\(307\) 0.307125 0.0175286 0.00876429 0.999962i \(-0.497210\pi\)
0.00876429 + 0.999962i \(0.497210\pi\)
\(308\) 5.84170 0.332862
\(309\) 38.5527 2.19318
\(310\) −0.200398 −0.0113818
\(311\) −21.5954 −1.22457 −0.612283 0.790639i \(-0.709749\pi\)
−0.612283 + 0.790639i \(0.709749\pi\)
\(312\) −4.61472 −0.261257
\(313\) −26.7242 −1.51054 −0.755269 0.655415i \(-0.772494\pi\)
−0.755269 + 0.655415i \(0.772494\pi\)
\(314\) −18.6718 −1.05371
\(315\) 0.198464 0.0111822
\(316\) 3.11698 0.175344
\(317\) −15.0854 −0.847279 −0.423639 0.905831i \(-0.639248\pi\)
−0.423639 + 0.905831i \(0.639248\pi\)
\(318\) 1.02571 0.0575192
\(319\) 28.2771 1.58322
\(320\) −0.168031 −0.00939325
\(321\) 30.0353 1.67641
\(322\) −5.71028 −0.318221
\(323\) 3.97657 0.221262
\(324\) −10.8972 −0.605400
\(325\) −11.6088 −0.643942
\(326\) −0.807239 −0.0447088
\(327\) −21.0141 −1.16208
\(328\) 7.86206 0.434109
\(329\) −8.00682 −0.441430
\(330\) −1.48816 −0.0819207
\(331\) −27.7004 −1.52255 −0.761275 0.648429i \(-0.775426\pi\)
−0.761275 + 0.648429i \(0.775426\pi\)
\(332\) 15.6884 0.861011
\(333\) −5.42288 −0.297172
\(334\) 14.3175 0.783418
\(335\) 0.976797 0.0533681
\(336\) 2.57641 0.140555
\(337\) −22.6359 −1.23306 −0.616528 0.787333i \(-0.711461\pi\)
−0.616528 + 0.787333i \(0.711461\pi\)
\(338\) −7.54800 −0.410557
\(339\) 6.67007 0.362268
\(340\) −0.633253 −0.0343430
\(341\) −5.34433 −0.289412
\(342\) 0.956017 0.0516955
\(343\) 16.0352 0.865819
\(344\) 2.84566 0.153428
\(345\) 1.45468 0.0783175
\(346\) −15.2909 −0.822043
\(347\) −1.80578 −0.0969393 −0.0484696 0.998825i \(-0.515434\pi\)
−0.0484696 + 0.998825i \(0.515434\pi\)
\(348\) 12.4713 0.668531
\(349\) 18.3573 0.982642 0.491321 0.870978i \(-0.336514\pi\)
0.491321 + 0.870978i \(0.336514\pi\)
\(350\) 6.48124 0.346437
\(351\) 9.66309 0.515777
\(352\) −4.48117 −0.238847
\(353\) 22.8849 1.21804 0.609020 0.793155i \(-0.291563\pi\)
0.609020 + 0.793155i \(0.291563\pi\)
\(354\) −10.3028 −0.547588
\(355\) 0.449184 0.0238402
\(356\) −1.95686 −0.103713
\(357\) 9.70961 0.513887
\(358\) −9.35245 −0.494292
\(359\) −30.5646 −1.61314 −0.806569 0.591140i \(-0.798678\pi\)
−0.806569 + 0.591140i \(0.798678\pi\)
\(360\) −0.152242 −0.00802385
\(361\) −17.8866 −0.941401
\(362\) 24.0169 1.26230
\(363\) −17.9473 −0.941987
\(364\) −3.04387 −0.159542
\(365\) 1.69633 0.0887902
\(366\) −15.3414 −0.801905
\(367\) 27.3795 1.42920 0.714599 0.699534i \(-0.246609\pi\)
0.714599 + 0.699534i \(0.246609\pi\)
\(368\) 4.38036 0.228342
\(369\) 7.12327 0.370823
\(370\) 1.00572 0.0522849
\(371\) 0.676560 0.0351252
\(372\) −2.35705 −0.122208
\(373\) 8.47849 0.438999 0.219500 0.975613i \(-0.429557\pi\)
0.219500 + 0.975613i \(0.429557\pi\)
\(374\) −16.8880 −0.873258
\(375\) −3.31154 −0.171007
\(376\) 6.14204 0.316751
\(377\) −14.7340 −0.758841
\(378\) −5.39493 −0.277485
\(379\) 29.1535 1.49752 0.748758 0.662843i \(-0.230650\pi\)
0.748758 + 0.662843i \(0.230650\pi\)
\(380\) −0.177302 −0.00909539
\(381\) 17.1279 0.877487
\(382\) −16.8777 −0.863538
\(383\) −17.6296 −0.900829 −0.450415 0.892820i \(-0.648724\pi\)
−0.450415 + 0.892820i \(0.648724\pi\)
\(384\) −1.97637 −0.100856
\(385\) −0.981590 −0.0500265
\(386\) −24.0536 −1.22430
\(387\) 2.57826 0.131060
\(388\) 0.204240 0.0103687
\(389\) 11.6697 0.591678 0.295839 0.955238i \(-0.404401\pi\)
0.295839 + 0.955238i \(0.404401\pi\)
\(390\) 0.775419 0.0392649
\(391\) 16.5081 0.834849
\(392\) −5.30060 −0.267721
\(393\) −27.3204 −1.37813
\(394\) −10.6357 −0.535820
\(395\) −0.523750 −0.0263527
\(396\) −4.06009 −0.204027
\(397\) −5.76210 −0.289192 −0.144596 0.989491i \(-0.546188\pi\)
−0.144596 + 0.989491i \(0.546188\pi\)
\(398\) 8.49276 0.425704
\(399\) 2.71855 0.136098
\(400\) −4.97177 −0.248588
\(401\) 6.15823 0.307527 0.153764 0.988108i \(-0.450861\pi\)
0.153764 + 0.988108i \(0.450861\pi\)
\(402\) 11.4890 0.573018
\(403\) 2.78471 0.138716
\(404\) 1.62093 0.0806443
\(405\) 1.83107 0.0909868
\(406\) 8.22605 0.408252
\(407\) 26.8212 1.32948
\(408\) −7.44825 −0.368743
\(409\) 11.7294 0.579981 0.289991 0.957029i \(-0.406348\pi\)
0.289991 + 0.957029i \(0.406348\pi\)
\(410\) −1.32107 −0.0652431
\(411\) −6.07639 −0.299726
\(412\) −19.5068 −0.961032
\(413\) −6.79572 −0.334395
\(414\) 3.96875 0.195053
\(415\) −2.63614 −0.129403
\(416\) 2.33495 0.114480
\(417\) 21.7745 1.06630
\(418\) −4.72840 −0.231274
\(419\) 4.04766 0.197741 0.0988705 0.995100i \(-0.468477\pi\)
0.0988705 + 0.995100i \(0.468477\pi\)
\(420\) −0.432919 −0.0211243
\(421\) 10.9475 0.533548 0.266774 0.963759i \(-0.414042\pi\)
0.266774 + 0.963759i \(0.414042\pi\)
\(422\) 18.6669 0.908689
\(423\) 5.56488 0.270574
\(424\) −0.518989 −0.0252043
\(425\) −18.7369 −0.908872
\(426\) 5.28326 0.255975
\(427\) −10.1191 −0.489699
\(428\) −15.1972 −0.734586
\(429\) 20.6794 0.998410
\(430\) −0.478161 −0.0230590
\(431\) −27.5446 −1.32678 −0.663388 0.748276i \(-0.730882\pi\)
−0.663388 + 0.748276i \(0.730882\pi\)
\(432\) 4.13845 0.199111
\(433\) −27.4780 −1.32051 −0.660255 0.751041i \(-0.729552\pi\)
−0.660255 + 0.751041i \(0.729552\pi\)
\(434\) −1.55471 −0.0746285
\(435\) −2.09557 −0.100475
\(436\) 10.6327 0.509214
\(437\) 4.62202 0.221101
\(438\) 19.9521 0.953349
\(439\) 13.5683 0.647578 0.323789 0.946129i \(-0.395043\pi\)
0.323789 + 0.946129i \(0.395043\pi\)
\(440\) 0.752978 0.0358968
\(441\) −4.80251 −0.228691
\(442\) 8.79963 0.418556
\(443\) −0.790011 −0.0375345 −0.0187673 0.999824i \(-0.505974\pi\)
−0.0187673 + 0.999824i \(0.505974\pi\)
\(444\) 11.8292 0.561388
\(445\) 0.328814 0.0155873
\(446\) 20.2007 0.956531
\(447\) 27.3418 1.29322
\(448\) −1.30361 −0.0615898
\(449\) 39.0557 1.84315 0.921576 0.388199i \(-0.126903\pi\)
0.921576 + 0.388199i \(0.126903\pi\)
\(450\) −4.50458 −0.212348
\(451\) −35.2312 −1.65897
\(452\) −3.37491 −0.158742
\(453\) 4.81527 0.226241
\(454\) 18.1102 0.849954
\(455\) 0.511465 0.0239779
\(456\) −2.08540 −0.0976580
\(457\) 3.85746 0.180444 0.0902221 0.995922i \(-0.471242\pi\)
0.0902221 + 0.995922i \(0.471242\pi\)
\(458\) 2.03970 0.0953090
\(459\) 15.5964 0.727978
\(460\) −0.736038 −0.0343180
\(461\) −20.8437 −0.970790 −0.485395 0.874295i \(-0.661324\pi\)
−0.485395 + 0.874295i \(0.661324\pi\)
\(462\) −11.5454 −0.537139
\(463\) 12.5445 0.582990 0.291495 0.956572i \(-0.405847\pi\)
0.291495 + 0.956572i \(0.405847\pi\)
\(464\) −6.31021 −0.292944
\(465\) 0.396059 0.0183668
\(466\) −7.97305 −0.369345
\(467\) 16.7817 0.776564 0.388282 0.921541i \(-0.373069\pi\)
0.388282 + 0.921541i \(0.373069\pi\)
\(468\) 2.11554 0.0977909
\(469\) 7.57812 0.349925
\(470\) −1.03206 −0.0476052
\(471\) 36.9024 1.70037
\(472\) 5.21300 0.239948
\(473\) −12.7519 −0.586333
\(474\) −6.16029 −0.282952
\(475\) −5.24606 −0.240706
\(476\) −4.91286 −0.225180
\(477\) −0.470221 −0.0215299
\(478\) −17.1569 −0.784738
\(479\) −42.5719 −1.94516 −0.972580 0.232568i \(-0.925287\pi\)
−0.972580 + 0.232568i \(0.925287\pi\)
\(480\) 0.332092 0.0151579
\(481\) −13.9754 −0.637224
\(482\) −22.8505 −1.04081
\(483\) 11.2856 0.513513
\(484\) 9.08093 0.412769
\(485\) −0.0343187 −0.00155833
\(486\) 9.12153 0.413761
\(487\) −17.4778 −0.791993 −0.395996 0.918252i \(-0.629601\pi\)
−0.395996 + 0.918252i \(0.629601\pi\)
\(488\) 7.76239 0.351387
\(489\) 1.59540 0.0721465
\(490\) 0.890668 0.0402363
\(491\) −8.76263 −0.395452 −0.197726 0.980257i \(-0.563356\pi\)
−0.197726 + 0.980257i \(0.563356\pi\)
\(492\) −15.5383 −0.700522
\(493\) −23.7810 −1.07104
\(494\) 2.46377 0.110850
\(495\) 0.682223 0.0306636
\(496\) 1.19262 0.0535502
\(497\) 3.48483 0.156316
\(498\) −31.0060 −1.38941
\(499\) −13.6928 −0.612975 −0.306488 0.951875i \(-0.599154\pi\)
−0.306488 + 0.951875i \(0.599154\pi\)
\(500\) 1.67557 0.0749338
\(501\) −28.2966 −1.26420
\(502\) −16.0932 −0.718274
\(503\) −16.6337 −0.741659 −0.370829 0.928701i \(-0.620927\pi\)
−0.370829 + 0.928701i \(0.620927\pi\)
\(504\) −1.18111 −0.0526109
\(505\) −0.272367 −0.0121202
\(506\) −19.6292 −0.872622
\(507\) 14.9176 0.662515
\(508\) −8.66633 −0.384506
\(509\) −17.6916 −0.784167 −0.392084 0.919930i \(-0.628246\pi\)
−0.392084 + 0.919930i \(0.628246\pi\)
\(510\) 1.25154 0.0554192
\(511\) 13.1604 0.582181
\(512\) 1.00000 0.0441942
\(513\) 4.36677 0.192798
\(514\) −23.7996 −1.04976
\(515\) 3.27776 0.144435
\(516\) −5.62407 −0.247586
\(517\) −27.5235 −1.21048
\(518\) 7.80251 0.342823
\(519\) 30.2204 1.32653
\(520\) −0.392345 −0.0172055
\(521\) 8.65584 0.379219 0.189610 0.981860i \(-0.439278\pi\)
0.189610 + 0.981860i \(0.439278\pi\)
\(522\) −5.71725 −0.250237
\(523\) 7.15968 0.313071 0.156536 0.987672i \(-0.449967\pi\)
0.156536 + 0.987672i \(0.449967\pi\)
\(524\) 13.8235 0.603883
\(525\) −12.8093 −0.559045
\(526\) 8.33080 0.363240
\(527\) 4.49457 0.195787
\(528\) 8.85645 0.385428
\(529\) −3.81245 −0.165759
\(530\) 0.0872065 0.00378801
\(531\) 4.72314 0.204967
\(532\) −1.37553 −0.0596368
\(533\) 18.3575 0.795153
\(534\) 3.86747 0.167362
\(535\) 2.55361 0.110402
\(536\) −5.81318 −0.251091
\(537\) 18.4839 0.797639
\(538\) −13.8061 −0.595225
\(539\) 23.7529 1.02311
\(540\) −0.695390 −0.0299248
\(541\) 30.2707 1.30144 0.650719 0.759318i \(-0.274467\pi\)
0.650719 + 0.759318i \(0.274467\pi\)
\(542\) 5.14386 0.220948
\(543\) −47.4662 −2.03697
\(544\) 3.76866 0.161580
\(545\) −1.78663 −0.0765308
\(546\) 6.01580 0.257453
\(547\) 25.9528 1.10966 0.554830 0.831964i \(-0.312783\pi\)
0.554830 + 0.831964i \(0.312783\pi\)
\(548\) 3.07452 0.131337
\(549\) 7.03298 0.300160
\(550\) 22.2794 0.949995
\(551\) −6.65834 −0.283655
\(552\) −8.65720 −0.368475
\(553\) −4.06332 −0.172790
\(554\) −8.24857 −0.350448
\(555\) −1.98767 −0.0843721
\(556\) −11.0174 −0.467244
\(557\) −1.49382 −0.0632954 −0.0316477 0.999499i \(-0.510075\pi\)
−0.0316477 + 0.999499i \(0.510075\pi\)
\(558\) 1.08055 0.0457434
\(559\) 6.64448 0.281032
\(560\) 0.219048 0.00925645
\(561\) 33.3769 1.40917
\(562\) 21.1214 0.890954
\(563\) −6.75713 −0.284779 −0.142389 0.989811i \(-0.545479\pi\)
−0.142389 + 0.989811i \(0.545479\pi\)
\(564\) −12.1389 −0.511141
\(565\) 0.567091 0.0238577
\(566\) 8.10533 0.340692
\(567\) 14.2057 0.596583
\(568\) −2.67321 −0.112166
\(569\) 3.12500 0.131007 0.0655033 0.997852i \(-0.479135\pi\)
0.0655033 + 0.997852i \(0.479135\pi\)
\(570\) 0.350414 0.0146772
\(571\) 22.1690 0.927744 0.463872 0.885902i \(-0.346460\pi\)
0.463872 + 0.885902i \(0.346460\pi\)
\(572\) −10.4633 −0.437494
\(573\) 33.3566 1.39349
\(574\) −10.2491 −0.427787
\(575\) −21.7781 −0.908210
\(576\) 0.906032 0.0377513
\(577\) 15.0891 0.628169 0.314084 0.949395i \(-0.398303\pi\)
0.314084 + 0.949395i \(0.398303\pi\)
\(578\) −2.79724 −0.116350
\(579\) 47.5389 1.97565
\(580\) 1.06031 0.0440271
\(581\) −20.4515 −0.848472
\(582\) −0.403653 −0.0167320
\(583\) 2.32568 0.0963199
\(584\) −10.0953 −0.417748
\(585\) −0.355477 −0.0146972
\(586\) −30.8519 −1.27448
\(587\) −2.04081 −0.0842333 −0.0421167 0.999113i \(-0.513410\pi\)
−0.0421167 + 0.999113i \(0.513410\pi\)
\(588\) 10.4759 0.432020
\(589\) 1.25842 0.0518521
\(590\) −0.875948 −0.0360622
\(591\) 21.0201 0.864652
\(592\) −5.98531 −0.245995
\(593\) −27.8250 −1.14263 −0.571317 0.820729i \(-0.693567\pi\)
−0.571317 + 0.820729i \(0.693567\pi\)
\(594\) −18.5451 −0.760916
\(595\) 0.825515 0.0338428
\(596\) −13.8344 −0.566679
\(597\) −16.7848 −0.686957
\(598\) 10.2279 0.418251
\(599\) 16.6896 0.681919 0.340959 0.940078i \(-0.389248\pi\)
0.340959 + 0.940078i \(0.389248\pi\)
\(600\) 9.82604 0.401146
\(601\) 17.4131 0.710296 0.355148 0.934810i \(-0.384430\pi\)
0.355148 + 0.934810i \(0.384430\pi\)
\(602\) −3.70963 −0.151193
\(603\) −5.26692 −0.214486
\(604\) −2.43642 −0.0991366
\(605\) −1.52588 −0.0620359
\(606\) −3.20356 −0.130136
\(607\) −32.8203 −1.33214 −0.666068 0.745891i \(-0.732024\pi\)
−0.666068 + 0.745891i \(0.732024\pi\)
\(608\) 1.05517 0.0427928
\(609\) −16.2577 −0.658795
\(610\) −1.30433 −0.0528106
\(611\) 14.3414 0.580189
\(612\) 3.41452 0.138024
\(613\) 43.2006 1.74486 0.872428 0.488742i \(-0.162544\pi\)
0.872428 + 0.488742i \(0.162544\pi\)
\(614\) 0.307125 0.0123946
\(615\) 2.61093 0.105283
\(616\) 5.84170 0.235369
\(617\) −12.7481 −0.513221 −0.256610 0.966515i \(-0.582606\pi\)
−0.256610 + 0.966515i \(0.582606\pi\)
\(618\) 38.5527 1.55082
\(619\) 18.0393 0.725061 0.362531 0.931972i \(-0.381913\pi\)
0.362531 + 0.931972i \(0.381913\pi\)
\(620\) −0.200398 −0.00804816
\(621\) 18.1279 0.727448
\(622\) −21.5954 −0.865899
\(623\) 2.55098 0.102203
\(624\) −4.61472 −0.184737
\(625\) 24.5773 0.983091
\(626\) −26.7242 −1.06811
\(627\) 9.34506 0.373206
\(628\) −18.6718 −0.745086
\(629\) −22.5566 −0.899389
\(630\) 0.198464 0.00790700
\(631\) −21.1879 −0.843475 −0.421738 0.906718i \(-0.638580\pi\)
−0.421738 + 0.906718i \(0.638580\pi\)
\(632\) 3.11698 0.123987
\(633\) −36.8926 −1.46635
\(634\) −15.0854 −0.599116
\(635\) 1.45622 0.0577882
\(636\) 1.02571 0.0406722
\(637\) −12.3766 −0.490381
\(638\) 28.2771 1.11950
\(639\) −2.42202 −0.0958135
\(640\) −0.168031 −0.00664203
\(641\) −36.0637 −1.42443 −0.712216 0.701960i \(-0.752308\pi\)
−0.712216 + 0.701960i \(0.752308\pi\)
\(642\) 30.0353 1.18540
\(643\) 28.0858 1.10760 0.553798 0.832651i \(-0.313178\pi\)
0.553798 + 0.832651i \(0.313178\pi\)
\(644\) −5.71028 −0.225017
\(645\) 0.945021 0.0372102
\(646\) 3.97657 0.156456
\(647\) 13.9193 0.547225 0.273613 0.961840i \(-0.411781\pi\)
0.273613 + 0.961840i \(0.411781\pi\)
\(648\) −10.8972 −0.428083
\(649\) −23.3604 −0.916974
\(650\) −11.6088 −0.455336
\(651\) 3.07268 0.120428
\(652\) −0.807239 −0.0316139
\(653\) −39.8089 −1.55784 −0.778921 0.627122i \(-0.784233\pi\)
−0.778921 + 0.627122i \(0.784233\pi\)
\(654\) −21.0141 −0.821718
\(655\) −2.32279 −0.0907588
\(656\) 7.86206 0.306962
\(657\) −9.14670 −0.356847
\(658\) −8.00682 −0.312138
\(659\) −46.3426 −1.80525 −0.902625 0.430427i \(-0.858363\pi\)
−0.902625 + 0.430427i \(0.858363\pi\)
\(660\) −1.48816 −0.0579267
\(661\) −30.8679 −1.20062 −0.600311 0.799766i \(-0.704957\pi\)
−0.600311 + 0.799766i \(0.704957\pi\)
\(662\) −27.7004 −1.07661
\(663\) −17.3913 −0.675422
\(664\) 15.6884 0.608827
\(665\) 0.231132 0.00896293
\(666\) −5.42288 −0.210132
\(667\) −27.6410 −1.07026
\(668\) 14.3175 0.553960
\(669\) −39.9240 −1.54355
\(670\) 0.976797 0.0377369
\(671\) −34.7846 −1.34285
\(672\) 2.57641 0.0993873
\(673\) −15.7020 −0.605269 −0.302634 0.953107i \(-0.597866\pi\)
−0.302634 + 0.953107i \(0.597866\pi\)
\(674\) −22.6359 −0.871903
\(675\) −20.5754 −0.791948
\(676\) −7.54800 −0.290308
\(677\) −43.8194 −1.68412 −0.842058 0.539387i \(-0.818656\pi\)
−0.842058 + 0.539387i \(0.818656\pi\)
\(678\) 6.67007 0.256162
\(679\) −0.266249 −0.0102177
\(680\) −0.633253 −0.0242841
\(681\) −35.7924 −1.37157
\(682\) −5.34433 −0.204645
\(683\) 28.4584 1.08893 0.544465 0.838784i \(-0.316733\pi\)
0.544465 + 0.838784i \(0.316733\pi\)
\(684\) 0.956017 0.0365542
\(685\) −0.516616 −0.0197389
\(686\) 16.0352 0.612226
\(687\) −4.03120 −0.153800
\(688\) 2.84566 0.108490
\(689\) −1.21181 −0.0461665
\(690\) 1.45468 0.0553788
\(691\) −6.24695 −0.237645 −0.118822 0.992916i \(-0.537912\pi\)
−0.118822 + 0.992916i \(0.537912\pi\)
\(692\) −15.2909 −0.581272
\(693\) 5.29277 0.201056
\(694\) −1.80578 −0.0685464
\(695\) 1.85128 0.0702230
\(696\) 12.4713 0.472723
\(697\) 29.6294 1.12229
\(698\) 18.3573 0.694833
\(699\) 15.7577 0.596011
\(700\) 6.48124 0.244968
\(701\) 8.70130 0.328644 0.164322 0.986407i \(-0.447456\pi\)
0.164322 + 0.986407i \(0.447456\pi\)
\(702\) 9.66309 0.364710
\(703\) −6.31552 −0.238194
\(704\) −4.48117 −0.168891
\(705\) 2.03972 0.0768204
\(706\) 22.8849 0.861284
\(707\) −2.11306 −0.0794699
\(708\) −10.3028 −0.387203
\(709\) −51.3155 −1.92719 −0.963597 0.267360i \(-0.913849\pi\)
−0.963597 + 0.267360i \(0.913849\pi\)
\(710\) 0.449184 0.0168576
\(711\) 2.82408 0.105911
\(712\) −1.95686 −0.0733364
\(713\) 5.22410 0.195644
\(714\) 9.70961 0.363373
\(715\) 1.75817 0.0657518
\(716\) −9.35245 −0.349517
\(717\) 33.9083 1.26633
\(718\) −30.5646 −1.14066
\(719\) 12.1836 0.454372 0.227186 0.973851i \(-0.427048\pi\)
0.227186 + 0.973851i \(0.427048\pi\)
\(720\) −0.152242 −0.00567372
\(721\) 25.4293 0.947036
\(722\) −17.8866 −0.665671
\(723\) 45.1610 1.67956
\(724\) 24.0169 0.892580
\(725\) 31.3729 1.16516
\(726\) −17.9473 −0.666085
\(727\) −44.2616 −1.64157 −0.820786 0.571236i \(-0.806464\pi\)
−0.820786 + 0.571236i \(0.806464\pi\)
\(728\) −3.04387 −0.112813
\(729\) 14.6641 0.543115
\(730\) 1.69633 0.0627842
\(731\) 10.7243 0.396653
\(732\) −15.3414 −0.567033
\(733\) 26.5028 0.978903 0.489451 0.872031i \(-0.337197\pi\)
0.489451 + 0.872031i \(0.337197\pi\)
\(734\) 27.3795 1.01060
\(735\) −1.76029 −0.0649292
\(736\) 4.38036 0.161462
\(737\) 26.0499 0.959559
\(738\) 7.12327 0.262211
\(739\) −41.5250 −1.52752 −0.763762 0.645498i \(-0.776650\pi\)
−0.763762 + 0.645498i \(0.776650\pi\)
\(740\) 1.00572 0.0369710
\(741\) −4.86932 −0.178879
\(742\) 0.676560 0.0248373
\(743\) 5.76455 0.211481 0.105740 0.994394i \(-0.466279\pi\)
0.105740 + 0.994394i \(0.466279\pi\)
\(744\) −2.35705 −0.0864138
\(745\) 2.32461 0.0851672
\(746\) 8.47849 0.310420
\(747\) 14.2142 0.520069
\(748\) −16.8880 −0.617487
\(749\) 19.8113 0.723888
\(750\) −3.31154 −0.120921
\(751\) −17.3145 −0.631815 −0.315907 0.948790i \(-0.602309\pi\)
−0.315907 + 0.948790i \(0.602309\pi\)
\(752\) 6.14204 0.223977
\(753\) 31.8061 1.15908
\(754\) −14.7340 −0.536582
\(755\) 0.409396 0.0148994
\(756\) −5.39493 −0.196212
\(757\) 17.4218 0.633208 0.316604 0.948558i \(-0.397457\pi\)
0.316604 + 0.948558i \(0.397457\pi\)
\(758\) 29.1535 1.05890
\(759\) 38.7944 1.40815
\(760\) −0.177302 −0.00643141
\(761\) −46.9236 −1.70098 −0.850489 0.525993i \(-0.823694\pi\)
−0.850489 + 0.525993i \(0.823694\pi\)
\(762\) 17.1279 0.620477
\(763\) −13.8609 −0.501798
\(764\) −16.8777 −0.610614
\(765\) −0.573747 −0.0207439
\(766\) −17.6296 −0.636982
\(767\) 12.1721 0.439509
\(768\) −1.97637 −0.0713161
\(769\) −6.81037 −0.245588 −0.122794 0.992432i \(-0.539186\pi\)
−0.122794 + 0.992432i \(0.539186\pi\)
\(770\) −0.981590 −0.0353741
\(771\) 47.0369 1.69399
\(772\) −24.0536 −0.865710
\(773\) −11.8880 −0.427582 −0.213791 0.976879i \(-0.568581\pi\)
−0.213791 + 0.976879i \(0.568581\pi\)
\(774\) 2.57826 0.0926736
\(775\) −5.92942 −0.212991
\(776\) 0.204240 0.00733178
\(777\) −15.4206 −0.553212
\(778\) 11.6697 0.418380
\(779\) 8.29580 0.297228
\(780\) 0.775419 0.0277645
\(781\) 11.9791 0.428647
\(782\) 16.5081 0.590327
\(783\) −26.1145 −0.933255
\(784\) −5.30060 −0.189307
\(785\) 3.13745 0.111980
\(786\) −27.3204 −0.974486
\(787\) −38.9054 −1.38683 −0.693414 0.720540i \(-0.743894\pi\)
−0.693414 + 0.720540i \(0.743894\pi\)
\(788\) −10.6357 −0.378882
\(789\) −16.4647 −0.586160
\(790\) −0.523750 −0.0186342
\(791\) 4.39957 0.156431
\(792\) −4.06009 −0.144269
\(793\) 18.1248 0.643631
\(794\) −5.76210 −0.204489
\(795\) −0.172352 −0.00611270
\(796\) 8.49276 0.301018
\(797\) −10.0987 −0.357715 −0.178858 0.983875i \(-0.557240\pi\)
−0.178858 + 0.983875i \(0.557240\pi\)
\(798\) 2.71855 0.0962358
\(799\) 23.1472 0.818890
\(800\) −4.97177 −0.175778
\(801\) −1.77298 −0.0626450
\(802\) 6.15823 0.217455
\(803\) 45.2390 1.59645
\(804\) 11.4890 0.405185
\(805\) 0.959507 0.0338182
\(806\) 2.78471 0.0980871
\(807\) 27.2860 0.960513
\(808\) 1.62093 0.0570242
\(809\) −26.5634 −0.933918 −0.466959 0.884279i \(-0.654650\pi\)
−0.466959 + 0.884279i \(0.654650\pi\)
\(810\) 1.83107 0.0643373
\(811\) 51.4445 1.80646 0.903231 0.429156i \(-0.141189\pi\)
0.903231 + 0.429156i \(0.141189\pi\)
\(812\) 8.22605 0.288678
\(813\) −10.1662 −0.356543
\(814\) 26.8212 0.940083
\(815\) 0.135641 0.00475131
\(816\) −7.44825 −0.260741
\(817\) 3.00265 0.105050
\(818\) 11.7294 0.410109
\(819\) −2.75784 −0.0963667
\(820\) −1.32107 −0.0461339
\(821\) −43.6714 −1.52414 −0.762071 0.647494i \(-0.775817\pi\)
−0.762071 + 0.647494i \(0.775817\pi\)
\(822\) −6.07639 −0.211938
\(823\) 46.6151 1.62490 0.812450 0.583031i \(-0.198133\pi\)
0.812450 + 0.583031i \(0.198133\pi\)
\(824\) −19.5068 −0.679552
\(825\) −44.0322 −1.53300
\(826\) −6.79572 −0.236453
\(827\) 17.7647 0.617740 0.308870 0.951104i \(-0.400049\pi\)
0.308870 + 0.951104i \(0.400049\pi\)
\(828\) 3.96875 0.137923
\(829\) 37.4854 1.30192 0.650961 0.759111i \(-0.274366\pi\)
0.650961 + 0.759111i \(0.274366\pi\)
\(830\) −2.63614 −0.0915018
\(831\) 16.3022 0.565517
\(832\) 2.33495 0.0809499
\(833\) −19.9761 −0.692132
\(834\) 21.7745 0.753991
\(835\) −2.40579 −0.0832557
\(836\) −4.72840 −0.163535
\(837\) 4.93560 0.170599
\(838\) 4.04766 0.139824
\(839\) 30.8409 1.06474 0.532372 0.846510i \(-0.321301\pi\)
0.532372 + 0.846510i \(0.321301\pi\)
\(840\) −0.432919 −0.0149371
\(841\) 10.8187 0.373058
\(842\) 10.9475 0.377276
\(843\) −41.7437 −1.43773
\(844\) 18.6669 0.642540
\(845\) 1.26830 0.0436309
\(846\) 5.56488 0.191325
\(847\) −11.8380 −0.406758
\(848\) −0.518989 −0.0178222
\(849\) −16.0191 −0.549775
\(850\) −18.7369 −0.642669
\(851\) −26.2178 −0.898735
\(852\) 5.28326 0.181001
\(853\) 40.1040 1.37314 0.686568 0.727066i \(-0.259116\pi\)
0.686568 + 0.727066i \(0.259116\pi\)
\(854\) −10.1191 −0.346270
\(855\) −0.160641 −0.00549381
\(856\) −15.1972 −0.519431
\(857\) −18.9045 −0.645766 −0.322883 0.946439i \(-0.604652\pi\)
−0.322883 + 0.946439i \(0.604652\pi\)
\(858\) 20.6794 0.705983
\(859\) 30.8310 1.05194 0.525970 0.850503i \(-0.323702\pi\)
0.525970 + 0.850503i \(0.323702\pi\)
\(860\) −0.478161 −0.0163051
\(861\) 20.2559 0.690320
\(862\) −27.5446 −0.938172
\(863\) −24.3604 −0.829238 −0.414619 0.909995i \(-0.636085\pi\)
−0.414619 + 0.909995i \(0.636085\pi\)
\(864\) 4.13845 0.140793
\(865\) 2.56935 0.0873605
\(866\) −27.4780 −0.933742
\(867\) 5.52837 0.187753
\(868\) −1.55471 −0.0527703
\(869\) −13.9677 −0.473822
\(870\) −2.09557 −0.0710465
\(871\) −13.5735 −0.459920
\(872\) 10.6327 0.360069
\(873\) 0.185048 0.00626292
\(874\) 4.62202 0.156342
\(875\) −2.18429 −0.0738425
\(876\) 19.9521 0.674119
\(877\) 34.0992 1.15145 0.575725 0.817644i \(-0.304720\pi\)
0.575725 + 0.817644i \(0.304720\pi\)
\(878\) 13.5683 0.457907
\(879\) 60.9747 2.05663
\(880\) 0.752978 0.0253829
\(881\) −1.04893 −0.0353394 −0.0176697 0.999844i \(-0.505625\pi\)
−0.0176697 + 0.999844i \(0.505625\pi\)
\(882\) −4.80251 −0.161709
\(883\) −37.6484 −1.26697 −0.633484 0.773755i \(-0.718376\pi\)
−0.633484 + 0.773755i \(0.718376\pi\)
\(884\) 8.79963 0.295964
\(885\) 1.73120 0.0581935
\(886\) −0.790011 −0.0265409
\(887\) 27.7832 0.932868 0.466434 0.884556i \(-0.345539\pi\)
0.466434 + 0.884556i \(0.345539\pi\)
\(888\) 11.8292 0.396961
\(889\) 11.2975 0.378907
\(890\) 0.328814 0.0110219
\(891\) 48.8323 1.63594
\(892\) 20.2007 0.676370
\(893\) 6.48089 0.216875
\(894\) 27.3418 0.914448
\(895\) 1.57151 0.0525297
\(896\) −1.30361 −0.0435506
\(897\) −20.2142 −0.674931
\(898\) 39.0557 1.30330
\(899\) −7.52567 −0.250995
\(900\) −4.50458 −0.150153
\(901\) −1.95589 −0.0651602
\(902\) −35.2312 −1.17307
\(903\) 7.33160 0.243980
\(904\) −3.37491 −0.112248
\(905\) −4.03559 −0.134148
\(906\) 4.81527 0.159977
\(907\) 7.46053 0.247723 0.123861 0.992300i \(-0.460472\pi\)
0.123861 + 0.992300i \(0.460472\pi\)
\(908\) 18.1102 0.601008
\(909\) 1.46862 0.0487109
\(910\) 0.511465 0.0169549
\(911\) 7.81434 0.258901 0.129450 0.991586i \(-0.458679\pi\)
0.129450 + 0.991586i \(0.458679\pi\)
\(912\) −2.08540 −0.0690546
\(913\) −70.3023 −2.32667
\(914\) 3.85746 0.127593
\(915\) 2.57783 0.0852204
\(916\) 2.03970 0.0673937
\(917\) −18.0205 −0.595089
\(918\) 15.5964 0.514758
\(919\) −57.4085 −1.89373 −0.946865 0.321631i \(-0.895769\pi\)
−0.946865 + 0.321631i \(0.895769\pi\)
\(920\) −0.736038 −0.0242665
\(921\) −0.606993 −0.0200011
\(922\) −20.8437 −0.686452
\(923\) −6.24183 −0.205452
\(924\) −11.5454 −0.379814
\(925\) 29.7576 0.978423
\(926\) 12.5445 0.412236
\(927\) −17.6738 −0.580484
\(928\) −6.31021 −0.207143
\(929\) −37.9459 −1.24497 −0.622483 0.782633i \(-0.713876\pi\)
−0.622483 + 0.782633i \(0.713876\pi\)
\(930\) 0.396059 0.0129873
\(931\) −5.59303 −0.183304
\(932\) −7.97305 −0.261166
\(933\) 42.6806 1.39730
\(934\) 16.7817 0.549114
\(935\) 2.83772 0.0928032
\(936\) 2.11554 0.0691486
\(937\) 29.6653 0.969125 0.484562 0.874757i \(-0.338979\pi\)
0.484562 + 0.874757i \(0.338979\pi\)
\(938\) 7.57812 0.247434
\(939\) 52.8168 1.72361
\(940\) −1.03206 −0.0336619
\(941\) 49.4730 1.61277 0.806387 0.591388i \(-0.201420\pi\)
0.806387 + 0.591388i \(0.201420\pi\)
\(942\) 36.9024 1.20234
\(943\) 34.4386 1.12148
\(944\) 5.21300 0.169669
\(945\) 0.906518 0.0294890
\(946\) −12.7519 −0.414600
\(947\) 35.5162 1.15412 0.577061 0.816701i \(-0.304199\pi\)
0.577061 + 0.816701i \(0.304199\pi\)
\(948\) −6.16029 −0.200077
\(949\) −23.5721 −0.765184
\(950\) −5.24606 −0.170205
\(951\) 29.8142 0.966793
\(952\) −4.91286 −0.159227
\(953\) 20.5083 0.664329 0.332165 0.943221i \(-0.392221\pi\)
0.332165 + 0.943221i \(0.392221\pi\)
\(954\) −0.470221 −0.0152240
\(955\) 2.83599 0.0917703
\(956\) −17.1569 −0.554894
\(957\) −55.8860 −1.80654
\(958\) −42.5719 −1.37544
\(959\) −4.00798 −0.129424
\(960\) 0.332092 0.0107182
\(961\) −29.5777 −0.954118
\(962\) −13.9754 −0.450585
\(963\) −13.7692 −0.443706
\(964\) −22.8505 −0.735965
\(965\) 4.04177 0.130109
\(966\) 11.2856 0.363109
\(967\) −10.7690 −0.346307 −0.173153 0.984895i \(-0.555396\pi\)
−0.173153 + 0.984895i \(0.555396\pi\)
\(968\) 9.08093 0.291872
\(969\) −7.85917 −0.252473
\(970\) −0.0343187 −0.00110191
\(971\) −13.1794 −0.422947 −0.211474 0.977384i \(-0.567826\pi\)
−0.211474 + 0.977384i \(0.567826\pi\)
\(972\) 9.12153 0.292573
\(973\) 14.3625 0.460439
\(974\) −17.4778 −0.560023
\(975\) 22.9433 0.734775
\(976\) 7.76239 0.248468
\(977\) −32.7763 −1.04861 −0.524303 0.851532i \(-0.675674\pi\)
−0.524303 + 0.851532i \(0.675674\pi\)
\(978\) 1.59540 0.0510153
\(979\) 8.76902 0.280259
\(980\) 0.890668 0.0284513
\(981\) 9.63357 0.307576
\(982\) −8.76263 −0.279627
\(983\) −36.9148 −1.17740 −0.588700 0.808351i \(-0.700360\pi\)
−0.588700 + 0.808351i \(0.700360\pi\)
\(984\) −15.5383 −0.495344
\(985\) 1.78714 0.0569429
\(986\) −23.7810 −0.757341
\(987\) 15.8244 0.503697
\(988\) 2.46377 0.0783830
\(989\) 12.4650 0.396364
\(990\) 0.682223 0.0216825
\(991\) −2.15837 −0.0685630 −0.0342815 0.999412i \(-0.510914\pi\)
−0.0342815 + 0.999412i \(0.510914\pi\)
\(992\) 1.19262 0.0378657
\(993\) 54.7461 1.73732
\(994\) 3.48483 0.110532
\(995\) −1.42705 −0.0452406
\(996\) −31.0060 −0.982463
\(997\) −5.17430 −0.163872 −0.0819358 0.996638i \(-0.526110\pi\)
−0.0819358 + 0.996638i \(0.526110\pi\)
\(998\) −13.6928 −0.433439
\(999\) −24.7699 −0.783686
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 8026.2.a.a.1.16 71
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
8026.2.a.a.1.16 71 1.1 even 1 trivial