Properties

Label 4018.2.a.bt.1.10
Level $4018$
Weight $2$
Character 4018.1
Self dual yes
Analytic conductor $32.084$
Analytic rank $0$
Dimension $10$
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] = [4018,2,Mod(1,4018)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(4018, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("4018.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 4018 = 2 \cdot 7^{2} \cdot 41 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 4018.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: \(32.0838915322\)
Analytic rank: \(0\)
Dimension: \(10\)
Coefficient field: \(\mathbb{Q}[x]/(x^{10} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{10} - x^{9} - 23x^{8} + 19x^{7} + 181x^{6} - 109x^{5} - 579x^{4} + 231x^{3} + 608x^{2} - 204x - 12 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{13}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 574)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.10
Root \(-3.24091\) of defining polynomial
Character \(\chi\) \(=\) 4018.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+1.00000 q^{2} +3.24091 q^{3} +1.00000 q^{4} +1.45353 q^{5} +3.24091 q^{6} +1.00000 q^{8} +7.50351 q^{9} +O(q^{10})\) \(q+1.00000 q^{2} +3.24091 q^{3} +1.00000 q^{4} +1.45353 q^{5} +3.24091 q^{6} +1.00000 q^{8} +7.50351 q^{9} +1.45353 q^{10} +4.18274 q^{11} +3.24091 q^{12} -5.22423 q^{13} +4.71076 q^{15} +1.00000 q^{16} -5.04998 q^{17} +7.50351 q^{18} +4.31873 q^{19} +1.45353 q^{20} +4.18274 q^{22} -3.03034 q^{23} +3.24091 q^{24} -2.88726 q^{25} -5.22423 q^{26} +14.5955 q^{27} +2.29501 q^{29} +4.71076 q^{30} -7.50317 q^{31} +1.00000 q^{32} +13.5559 q^{33} -5.04998 q^{34} +7.50351 q^{36} +2.48890 q^{37} +4.31873 q^{38} -16.9313 q^{39} +1.45353 q^{40} -1.00000 q^{41} +9.36993 q^{43} +4.18274 q^{44} +10.9066 q^{45} -3.03034 q^{46} +7.57920 q^{47} +3.24091 q^{48} -2.88726 q^{50} -16.3665 q^{51} -5.22423 q^{52} +1.22893 q^{53} +14.5955 q^{54} +6.07973 q^{55} +13.9966 q^{57} +2.29501 q^{58} +2.55484 q^{59} +4.71076 q^{60} +10.3886 q^{61} -7.50317 q^{62} +1.00000 q^{64} -7.59356 q^{65} +13.5559 q^{66} -4.10815 q^{67} -5.04998 q^{68} -9.82105 q^{69} -8.47279 q^{71} +7.50351 q^{72} -4.49215 q^{73} +2.48890 q^{74} -9.35734 q^{75} +4.31873 q^{76} -16.9313 q^{78} -10.1084 q^{79} +1.45353 q^{80} +24.7921 q^{81} -1.00000 q^{82} -2.86502 q^{83} -7.34029 q^{85} +9.36993 q^{86} +7.43793 q^{87} +4.18274 q^{88} -15.4950 q^{89} +10.9066 q^{90} -3.03034 q^{92} -24.3171 q^{93} +7.57920 q^{94} +6.27739 q^{95} +3.24091 q^{96} -14.7885 q^{97} +31.3852 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 10 q + 10 q^{2} - q^{3} + 10 q^{4} + 2 q^{5} - q^{6} + 10 q^{8} + 17 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 10 q + 10 q^{2} - q^{3} + 10 q^{4} + 2 q^{5} - q^{6} + 10 q^{8} + 17 q^{9} + 2 q^{10} + 11 q^{11} - q^{12} - 4 q^{13} + 4 q^{15} + 10 q^{16} - 5 q^{17} + 17 q^{18} + q^{19} + 2 q^{20} + 11 q^{22} + 9 q^{23} - q^{24} + 24 q^{25} - 4 q^{26} - 7 q^{27} + 23 q^{29} + 4 q^{30} + 5 q^{31} + 10 q^{32} + 5 q^{33} - 5 q^{34} + 17 q^{36} + 16 q^{37} + q^{38} - 7 q^{39} + 2 q^{40} - 10 q^{41} + 20 q^{43} + 11 q^{44} + 42 q^{45} + 9 q^{46} + 16 q^{47} - q^{48} + 24 q^{50} + 13 q^{51} - 4 q^{52} + 26 q^{53} - 7 q^{54} - 7 q^{55} + 37 q^{57} + 23 q^{58} + 10 q^{59} + 4 q^{60} + 5 q^{62} + 10 q^{64} + 18 q^{65} + 5 q^{66} + 7 q^{67} - 5 q^{68} - 39 q^{69} + 5 q^{71} + 17 q^{72} + 13 q^{73} + 16 q^{74} - 19 q^{75} + q^{76} - 7 q^{78} - q^{79} + 2 q^{80} + 18 q^{81} - 10 q^{82} - 21 q^{83} + 34 q^{85} + 20 q^{86} - 2 q^{87} + 11 q^{88} - 6 q^{89} + 42 q^{90} + 9 q^{92} - 5 q^{93} + 16 q^{94} + 24 q^{95} - q^{96} - 29 q^{97} + 48 q^{99}+O(q^{100}) \) 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
\(3\) 3.24091 1.87114 0.935571 0.353140i \(-0.114886\pi\)
0.935571 + 0.353140i \(0.114886\pi\)
\(4\) 1.00000 0.500000
\(5\) 1.45353 0.650038 0.325019 0.945708i \(-0.394629\pi\)
0.325019 + 0.945708i \(0.394629\pi\)
\(6\) 3.24091 1.32310
\(7\) 0 0
\(8\) 1.00000 0.353553
\(9\) 7.50351 2.50117
\(10\) 1.45353 0.459646
\(11\) 4.18274 1.26114 0.630572 0.776131i \(-0.282820\pi\)
0.630572 + 0.776131i \(0.282820\pi\)
\(12\) 3.24091 0.935571
\(13\) −5.22423 −1.44894 −0.724470 0.689307i \(-0.757915\pi\)
−0.724470 + 0.689307i \(0.757915\pi\)
\(14\) 0 0
\(15\) 4.71076 1.21631
\(16\) 1.00000 0.250000
\(17\) −5.04998 −1.22480 −0.612400 0.790548i \(-0.709796\pi\)
−0.612400 + 0.790548i \(0.709796\pi\)
\(18\) 7.50351 1.76859
\(19\) 4.31873 0.990784 0.495392 0.868670i \(-0.335024\pi\)
0.495392 + 0.868670i \(0.335024\pi\)
\(20\) 1.45353 0.325019
\(21\) 0 0
\(22\) 4.18274 0.891764
\(23\) −3.03034 −0.631869 −0.315934 0.948781i \(-0.602318\pi\)
−0.315934 + 0.948781i \(0.602318\pi\)
\(24\) 3.24091 0.661548
\(25\) −2.88726 −0.577451
\(26\) −5.22423 −1.02456
\(27\) 14.5955 2.80890
\(28\) 0 0
\(29\) 2.29501 0.426173 0.213086 0.977033i \(-0.431648\pi\)
0.213086 + 0.977033i \(0.431648\pi\)
\(30\) 4.71076 0.860063
\(31\) −7.50317 −1.34761 −0.673804 0.738910i \(-0.735341\pi\)
−0.673804 + 0.738910i \(0.735341\pi\)
\(32\) 1.00000 0.176777
\(33\) 13.5559 2.35978
\(34\) −5.04998 −0.866065
\(35\) 0 0
\(36\) 7.50351 1.25058
\(37\) 2.48890 0.409173 0.204586 0.978849i \(-0.434415\pi\)
0.204586 + 0.978849i \(0.434415\pi\)
\(38\) 4.31873 0.700590
\(39\) −16.9313 −2.71117
\(40\) 1.45353 0.229823
\(41\) −1.00000 −0.156174
\(42\) 0 0
\(43\) 9.36993 1.42890 0.714451 0.699686i \(-0.246677\pi\)
0.714451 + 0.699686i \(0.246677\pi\)
\(44\) 4.18274 0.630572
\(45\) 10.9066 1.62585
\(46\) −3.03034 −0.446799
\(47\) 7.57920 1.10554 0.552770 0.833334i \(-0.313571\pi\)
0.552770 + 0.833334i \(0.313571\pi\)
\(48\) 3.24091 0.467785
\(49\) 0 0
\(50\) −2.88726 −0.408320
\(51\) −16.3665 −2.29177
\(52\) −5.22423 −0.724470
\(53\) 1.22893 0.168806 0.0844031 0.996432i \(-0.473102\pi\)
0.0844031 + 0.996432i \(0.473102\pi\)
\(54\) 14.5955 1.98619
\(55\) 6.07973 0.819791
\(56\) 0 0
\(57\) 13.9966 1.85390
\(58\) 2.29501 0.301350
\(59\) 2.55484 0.332611 0.166306 0.986074i \(-0.446816\pi\)
0.166306 + 0.986074i \(0.446816\pi\)
\(60\) 4.71076 0.608156
\(61\) 10.3886 1.33013 0.665065 0.746786i \(-0.268404\pi\)
0.665065 + 0.746786i \(0.268404\pi\)
\(62\) −7.50317 −0.952903
\(63\) 0 0
\(64\) 1.00000 0.125000
\(65\) −7.59356 −0.941865
\(66\) 13.5559 1.66862
\(67\) −4.10815 −0.501891 −0.250945 0.968001i \(-0.580741\pi\)
−0.250945 + 0.968001i \(0.580741\pi\)
\(68\) −5.04998 −0.612400
\(69\) −9.82105 −1.18232
\(70\) 0 0
\(71\) −8.47279 −1.00554 −0.502768 0.864421i \(-0.667685\pi\)
−0.502768 + 0.864421i \(0.667685\pi\)
\(72\) 7.50351 0.884297
\(73\) −4.49215 −0.525766 −0.262883 0.964828i \(-0.584673\pi\)
−0.262883 + 0.964828i \(0.584673\pi\)
\(74\) 2.48890 0.289329
\(75\) −9.35734 −1.08049
\(76\) 4.31873 0.495392
\(77\) 0 0
\(78\) −16.9313 −1.91709
\(79\) −10.1084 −1.13728 −0.568640 0.822586i \(-0.692530\pi\)
−0.568640 + 0.822586i \(0.692530\pi\)
\(80\) 1.45353 0.162509
\(81\) 24.7921 2.75468
\(82\) −1.00000 −0.110432
\(83\) −2.86502 −0.314476 −0.157238 0.987561i \(-0.550259\pi\)
−0.157238 + 0.987561i \(0.550259\pi\)
\(84\) 0 0
\(85\) −7.34029 −0.796166
\(86\) 9.36993 1.01039
\(87\) 7.43793 0.797430
\(88\) 4.18274 0.445882
\(89\) −15.4950 −1.64247 −0.821233 0.570594i \(-0.806713\pi\)
−0.821233 + 0.570594i \(0.806713\pi\)
\(90\) 10.9066 1.14965
\(91\) 0 0
\(92\) −3.03034 −0.315934
\(93\) −24.3171 −2.52157
\(94\) 7.57920 0.781735
\(95\) 6.27739 0.644047
\(96\) 3.24091 0.330774
\(97\) −14.7885 −1.50155 −0.750775 0.660558i \(-0.770320\pi\)
−0.750775 + 0.660558i \(0.770320\pi\)
\(98\) 0 0
\(99\) 31.3852 3.15434
\(100\) −2.88726 −0.288726
\(101\) −3.63661 −0.361856 −0.180928 0.983496i \(-0.557910\pi\)
−0.180928 + 0.983496i \(0.557910\pi\)
\(102\) −16.3665 −1.62053
\(103\) 13.7935 1.35911 0.679556 0.733624i \(-0.262173\pi\)
0.679556 + 0.733624i \(0.262173\pi\)
\(104\) −5.22423 −0.512278
\(105\) 0 0
\(106\) 1.22893 0.119364
\(107\) 20.2757 1.96013 0.980065 0.198676i \(-0.0636640\pi\)
0.980065 + 0.198676i \(0.0636640\pi\)
\(108\) 14.5955 1.40445
\(109\) −8.86423 −0.849039 −0.424520 0.905419i \(-0.639557\pi\)
−0.424520 + 0.905419i \(0.639557\pi\)
\(110\) 6.07973 0.579680
\(111\) 8.06631 0.765620
\(112\) 0 0
\(113\) −7.33107 −0.689649 −0.344825 0.938667i \(-0.612062\pi\)
−0.344825 + 0.938667i \(0.612062\pi\)
\(114\) 13.9966 1.31090
\(115\) −4.40468 −0.410738
\(116\) 2.29501 0.213086
\(117\) −39.2000 −3.62404
\(118\) 2.55484 0.235192
\(119\) 0 0
\(120\) 4.71076 0.430031
\(121\) 6.49533 0.590485
\(122\) 10.3886 0.940544
\(123\) −3.24091 −0.292223
\(124\) −7.50317 −0.673804
\(125\) −11.4643 −1.02540
\(126\) 0 0
\(127\) −0.797302 −0.0707491 −0.0353746 0.999374i \(-0.511262\pi\)
−0.0353746 + 0.999374i \(0.511262\pi\)
\(128\) 1.00000 0.0883883
\(129\) 30.3671 2.67368
\(130\) −7.59356 −0.665999
\(131\) −9.27577 −0.810428 −0.405214 0.914222i \(-0.632803\pi\)
−0.405214 + 0.914222i \(0.632803\pi\)
\(132\) 13.5559 1.17989
\(133\) 0 0
\(134\) −4.10815 −0.354890
\(135\) 21.2149 1.82589
\(136\) −5.04998 −0.433032
\(137\) −5.22892 −0.446737 −0.223368 0.974734i \(-0.571705\pi\)
−0.223368 + 0.974734i \(0.571705\pi\)
\(138\) −9.82105 −0.836024
\(139\) −12.9221 −1.09604 −0.548021 0.836465i \(-0.684618\pi\)
−0.548021 + 0.836465i \(0.684618\pi\)
\(140\) 0 0
\(141\) 24.5635 2.06862
\(142\) −8.47279 −0.711021
\(143\) −21.8516 −1.82732
\(144\) 7.50351 0.625292
\(145\) 3.33586 0.277028
\(146\) −4.49215 −0.371773
\(147\) 0 0
\(148\) 2.48890 0.204586
\(149\) −8.42101 −0.689876 −0.344938 0.938625i \(-0.612100\pi\)
−0.344938 + 0.938625i \(0.612100\pi\)
\(150\) −9.35734 −0.764024
\(151\) −2.37428 −0.193216 −0.0966079 0.995323i \(-0.530799\pi\)
−0.0966079 + 0.995323i \(0.530799\pi\)
\(152\) 4.31873 0.350295
\(153\) −37.8926 −3.06343
\(154\) 0 0
\(155\) −10.9061 −0.875996
\(156\) −16.9313 −1.35559
\(157\) −23.3643 −1.86468 −0.932339 0.361586i \(-0.882235\pi\)
−0.932339 + 0.361586i \(0.882235\pi\)
\(158\) −10.1084 −0.804179
\(159\) 3.98285 0.315860
\(160\) 1.45353 0.114911
\(161\) 0 0
\(162\) 24.7921 1.94785
\(163\) 19.3371 1.51460 0.757301 0.653066i \(-0.226518\pi\)
0.757301 + 0.653066i \(0.226518\pi\)
\(164\) −1.00000 −0.0780869
\(165\) 19.7039 1.53395
\(166\) −2.86502 −0.222368
\(167\) −2.00988 −0.155529 −0.0777646 0.996972i \(-0.524778\pi\)
−0.0777646 + 0.996972i \(0.524778\pi\)
\(168\) 0 0
\(169\) 14.2925 1.09943
\(170\) −7.34029 −0.562975
\(171\) 32.4056 2.47812
\(172\) 9.36993 0.714451
\(173\) −10.8809 −0.827258 −0.413629 0.910446i \(-0.635739\pi\)
−0.413629 + 0.910446i \(0.635739\pi\)
\(174\) 7.43793 0.563868
\(175\) 0 0
\(176\) 4.18274 0.315286
\(177\) 8.28000 0.622363
\(178\) −15.4950 −1.16140
\(179\) 6.59120 0.492649 0.246325 0.969187i \(-0.420777\pi\)
0.246325 + 0.969187i \(0.420777\pi\)
\(180\) 10.9066 0.812927
\(181\) −10.3441 −0.768875 −0.384437 0.923151i \(-0.625604\pi\)
−0.384437 + 0.923151i \(0.625604\pi\)
\(182\) 0 0
\(183\) 33.6687 2.48886
\(184\) −3.03034 −0.223399
\(185\) 3.61769 0.265978
\(186\) −24.3171 −1.78302
\(187\) −21.1228 −1.54465
\(188\) 7.57920 0.552770
\(189\) 0 0
\(190\) 6.27739 0.455410
\(191\) −4.11146 −0.297495 −0.148747 0.988875i \(-0.547524\pi\)
−0.148747 + 0.988875i \(0.547524\pi\)
\(192\) 3.24091 0.233893
\(193\) 17.4496 1.25605 0.628026 0.778192i \(-0.283863\pi\)
0.628026 + 0.778192i \(0.283863\pi\)
\(194\) −14.7885 −1.06176
\(195\) −24.6101 −1.76236
\(196\) 0 0
\(197\) −21.9669 −1.56508 −0.782538 0.622603i \(-0.786075\pi\)
−0.782538 + 0.622603i \(0.786075\pi\)
\(198\) 31.3852 2.23045
\(199\) 9.23644 0.654754 0.327377 0.944894i \(-0.393835\pi\)
0.327377 + 0.944894i \(0.393835\pi\)
\(200\) −2.88726 −0.204160
\(201\) −13.3142 −0.939108
\(202\) −3.63661 −0.255871
\(203\) 0 0
\(204\) −16.3665 −1.14589
\(205\) −1.45353 −0.101519
\(206\) 13.7935 0.961037
\(207\) −22.7382 −1.58041
\(208\) −5.22423 −0.362235
\(209\) 18.0641 1.24952
\(210\) 0 0
\(211\) 22.8202 1.57101 0.785505 0.618856i \(-0.212403\pi\)
0.785505 + 0.618856i \(0.212403\pi\)
\(212\) 1.22893 0.0844031
\(213\) −27.4596 −1.88150
\(214\) 20.2757 1.38602
\(215\) 13.6195 0.928840
\(216\) 14.5955 0.993097
\(217\) 0 0
\(218\) −8.86423 −0.600361
\(219\) −14.5587 −0.983783
\(220\) 6.07973 0.409896
\(221\) 26.3822 1.77466
\(222\) 8.06631 0.541375
\(223\) 18.1731 1.21696 0.608479 0.793570i \(-0.291780\pi\)
0.608479 + 0.793570i \(0.291780\pi\)
\(224\) 0 0
\(225\) −21.6646 −1.44430
\(226\) −7.33107 −0.487656
\(227\) 11.2158 0.744417 0.372208 0.928149i \(-0.378601\pi\)
0.372208 + 0.928149i \(0.378601\pi\)
\(228\) 13.9966 0.926948
\(229\) 7.14061 0.471865 0.235932 0.971769i \(-0.424186\pi\)
0.235932 + 0.971769i \(0.424186\pi\)
\(230\) −4.40468 −0.290436
\(231\) 0 0
\(232\) 2.29501 0.150675
\(233\) 12.4071 0.812819 0.406409 0.913691i \(-0.366781\pi\)
0.406409 + 0.913691i \(0.366781\pi\)
\(234\) −39.2000 −2.56259
\(235\) 11.0166 0.718643
\(236\) 2.55484 0.166306
\(237\) −32.7603 −2.12801
\(238\) 0 0
\(239\) 18.9128 1.22336 0.611682 0.791103i \(-0.290493\pi\)
0.611682 + 0.791103i \(0.290493\pi\)
\(240\) 4.71076 0.304078
\(241\) 23.3723 1.50554 0.752772 0.658282i \(-0.228716\pi\)
0.752772 + 0.658282i \(0.228716\pi\)
\(242\) 6.49533 0.417536
\(243\) 36.5627 2.34550
\(244\) 10.3886 0.665065
\(245\) 0 0
\(246\) −3.24091 −0.206633
\(247\) −22.5620 −1.43559
\(248\) −7.50317 −0.476452
\(249\) −9.28526 −0.588430
\(250\) −11.4643 −0.725069
\(251\) −3.44847 −0.217666 −0.108833 0.994060i \(-0.534711\pi\)
−0.108833 + 0.994060i \(0.534711\pi\)
\(252\) 0 0
\(253\) −12.6751 −0.796878
\(254\) −0.797302 −0.0500272
\(255\) −23.7892 −1.48974
\(256\) 1.00000 0.0625000
\(257\) 26.0084 1.62236 0.811180 0.584797i \(-0.198826\pi\)
0.811180 + 0.584797i \(0.198826\pi\)
\(258\) 30.3671 1.89057
\(259\) 0 0
\(260\) −7.59356 −0.470933
\(261\) 17.2206 1.06593
\(262\) −9.27577 −0.573059
\(263\) −0.875593 −0.0539914 −0.0269957 0.999636i \(-0.508594\pi\)
−0.0269957 + 0.999636i \(0.508594\pi\)
\(264\) 13.5559 0.834308
\(265\) 1.78628 0.109730
\(266\) 0 0
\(267\) −50.2179 −3.07328
\(268\) −4.10815 −0.250945
\(269\) −27.9132 −1.70190 −0.850949 0.525248i \(-0.823972\pi\)
−0.850949 + 0.525248i \(0.823972\pi\)
\(270\) 21.2149 1.29110
\(271\) 9.10994 0.553389 0.276695 0.960958i \(-0.410761\pi\)
0.276695 + 0.960958i \(0.410761\pi\)
\(272\) −5.04998 −0.306200
\(273\) 0 0
\(274\) −5.22892 −0.315890
\(275\) −12.0766 −0.728249
\(276\) −9.82105 −0.591158
\(277\) −0.0967641 −0.00581399 −0.00290699 0.999996i \(-0.500925\pi\)
−0.00290699 + 0.999996i \(0.500925\pi\)
\(278\) −12.9221 −0.775018
\(279\) −56.3001 −3.37060
\(280\) 0 0
\(281\) 16.4020 0.978462 0.489231 0.872154i \(-0.337278\pi\)
0.489231 + 0.872154i \(0.337278\pi\)
\(282\) 24.5635 1.46274
\(283\) −2.48341 −0.147623 −0.0738116 0.997272i \(-0.523516\pi\)
−0.0738116 + 0.997272i \(0.523516\pi\)
\(284\) −8.47279 −0.502768
\(285\) 20.3445 1.20510
\(286\) −21.8516 −1.29211
\(287\) 0 0
\(288\) 7.50351 0.442149
\(289\) 8.50231 0.500136
\(290\) 3.33586 0.195889
\(291\) −47.9284 −2.80961
\(292\) −4.49215 −0.262883
\(293\) −9.32569 −0.544813 −0.272406 0.962182i \(-0.587820\pi\)
−0.272406 + 0.962182i \(0.587820\pi\)
\(294\) 0 0
\(295\) 3.71353 0.216210
\(296\) 2.48890 0.144664
\(297\) 61.0491 3.54243
\(298\) −8.42101 −0.487816
\(299\) 15.8312 0.915540
\(300\) −9.35734 −0.540246
\(301\) 0 0
\(302\) −2.37428 −0.136624
\(303\) −11.7859 −0.677084
\(304\) 4.31873 0.247696
\(305\) 15.1002 0.864634
\(306\) −37.8926 −2.16618
\(307\) 15.8969 0.907286 0.453643 0.891184i \(-0.350124\pi\)
0.453643 + 0.891184i \(0.350124\pi\)
\(308\) 0 0
\(309\) 44.7034 2.54309
\(310\) −10.9061 −0.619423
\(311\) 16.9719 0.962387 0.481194 0.876614i \(-0.340203\pi\)
0.481194 + 0.876614i \(0.340203\pi\)
\(312\) −16.9313 −0.958544
\(313\) −31.6976 −1.79165 −0.895827 0.444404i \(-0.853416\pi\)
−0.895827 + 0.444404i \(0.853416\pi\)
\(314\) −23.3643 −1.31853
\(315\) 0 0
\(316\) −10.1084 −0.568640
\(317\) 16.7818 0.942557 0.471279 0.881984i \(-0.343793\pi\)
0.471279 + 0.881984i \(0.343793\pi\)
\(318\) 3.98285 0.223347
\(319\) 9.59944 0.537466
\(320\) 1.45353 0.0812547
\(321\) 65.7119 3.66768
\(322\) 0 0
\(323\) −21.8095 −1.21351
\(324\) 24.7921 1.37734
\(325\) 15.0837 0.836692
\(326\) 19.3371 1.07099
\(327\) −28.7282 −1.58867
\(328\) −1.00000 −0.0552158
\(329\) 0 0
\(330\) 19.7039 1.08466
\(331\) −20.5312 −1.12850 −0.564248 0.825605i \(-0.690834\pi\)
−0.564248 + 0.825605i \(0.690834\pi\)
\(332\) −2.86502 −0.157238
\(333\) 18.6755 1.02341
\(334\) −2.00988 −0.109976
\(335\) −5.97131 −0.326248
\(336\) 0 0
\(337\) −2.71983 −0.148158 −0.0740792 0.997252i \(-0.523602\pi\)
−0.0740792 + 0.997252i \(0.523602\pi\)
\(338\) 14.2925 0.777412
\(339\) −23.7594 −1.29043
\(340\) −7.34029 −0.398083
\(341\) −31.3838 −1.69953
\(342\) 32.4056 1.75229
\(343\) 0 0
\(344\) 9.36993 0.505193
\(345\) −14.2752 −0.768550
\(346\) −10.8809 −0.584960
\(347\) 12.9347 0.694368 0.347184 0.937797i \(-0.387138\pi\)
0.347184 + 0.937797i \(0.387138\pi\)
\(348\) 7.43793 0.398715
\(349\) 19.9087 1.06569 0.532843 0.846214i \(-0.321124\pi\)
0.532843 + 0.846214i \(0.321124\pi\)
\(350\) 0 0
\(351\) −76.2501 −4.06993
\(352\) 4.18274 0.222941
\(353\) 0.487930 0.0259699 0.0129849 0.999916i \(-0.495867\pi\)
0.0129849 + 0.999916i \(0.495867\pi\)
\(354\) 8.28000 0.440077
\(355\) −12.3154 −0.653636
\(356\) −15.4950 −0.821233
\(357\) 0 0
\(358\) 6.59120 0.348356
\(359\) −7.91222 −0.417591 −0.208795 0.977959i \(-0.566954\pi\)
−0.208795 + 0.977959i \(0.566954\pi\)
\(360\) 10.9066 0.574826
\(361\) −0.348598 −0.0183473
\(362\) −10.3441 −0.543676
\(363\) 21.0508 1.10488
\(364\) 0 0
\(365\) −6.52946 −0.341768
\(366\) 33.6687 1.75989
\(367\) −14.4797 −0.755835 −0.377918 0.925839i \(-0.623360\pi\)
−0.377918 + 0.925839i \(0.623360\pi\)
\(368\) −3.03034 −0.157967
\(369\) −7.50351 −0.390617
\(370\) 3.61769 0.188075
\(371\) 0 0
\(372\) −24.3171 −1.26078
\(373\) 18.9631 0.981874 0.490937 0.871195i \(-0.336655\pi\)
0.490937 + 0.871195i \(0.336655\pi\)
\(374\) −21.1228 −1.09223
\(375\) −37.1549 −1.91867
\(376\) 7.57920 0.390868
\(377\) −11.9897 −0.617499
\(378\) 0 0
\(379\) −28.3181 −1.45461 −0.727303 0.686317i \(-0.759226\pi\)
−0.727303 + 0.686317i \(0.759226\pi\)
\(380\) 6.27739 0.322023
\(381\) −2.58399 −0.132382
\(382\) −4.11146 −0.210361
\(383\) −13.0221 −0.665400 −0.332700 0.943033i \(-0.607960\pi\)
−0.332700 + 0.943033i \(0.607960\pi\)
\(384\) 3.24091 0.165387
\(385\) 0 0
\(386\) 17.4496 0.888163
\(387\) 70.3074 3.57392
\(388\) −14.7885 −0.750775
\(389\) −35.3836 −1.79402 −0.897009 0.442012i \(-0.854265\pi\)
−0.897009 + 0.442012i \(0.854265\pi\)
\(390\) −24.6101 −1.24618
\(391\) 15.3031 0.773913
\(392\) 0 0
\(393\) −30.0620 −1.51642
\(394\) −21.9669 −1.10668
\(395\) −14.6928 −0.739275
\(396\) 31.3852 1.57717
\(397\) −20.0384 −1.00570 −0.502850 0.864374i \(-0.667715\pi\)
−0.502850 + 0.864374i \(0.667715\pi\)
\(398\) 9.23644 0.462981
\(399\) 0 0
\(400\) −2.88726 −0.144363
\(401\) −14.8916 −0.743652 −0.371826 0.928302i \(-0.621268\pi\)
−0.371826 + 0.928302i \(0.621268\pi\)
\(402\) −13.3142 −0.664050
\(403\) 39.1982 1.95260
\(404\) −3.63661 −0.180928
\(405\) 36.0361 1.79065
\(406\) 0 0
\(407\) 10.4104 0.516026
\(408\) −16.3665 −0.810265
\(409\) 22.5833 1.11667 0.558336 0.829615i \(-0.311440\pi\)
0.558336 + 0.829615i \(0.311440\pi\)
\(410\) −1.45353 −0.0717846
\(411\) −16.9465 −0.835907
\(412\) 13.7935 0.679556
\(413\) 0 0
\(414\) −22.7382 −1.11752
\(415\) −4.16438 −0.204421
\(416\) −5.22423 −0.256139
\(417\) −41.8795 −2.05085
\(418\) 18.0641 0.883545
\(419\) 19.4523 0.950305 0.475153 0.879903i \(-0.342393\pi\)
0.475153 + 0.879903i \(0.342393\pi\)
\(420\) 0 0
\(421\) −14.7322 −0.718005 −0.359003 0.933337i \(-0.616883\pi\)
−0.359003 + 0.933337i \(0.616883\pi\)
\(422\) 22.8202 1.11087
\(423\) 56.8706 2.76514
\(424\) 1.22893 0.0596820
\(425\) 14.5806 0.707262
\(426\) −27.4596 −1.33042
\(427\) 0 0
\(428\) 20.2757 0.980065
\(429\) −70.8191 −3.41918
\(430\) 13.6195 0.656789
\(431\) 8.85046 0.426311 0.213156 0.977018i \(-0.431626\pi\)
0.213156 + 0.977018i \(0.431626\pi\)
\(432\) 14.5955 0.702225
\(433\) 2.99616 0.143986 0.0719931 0.997405i \(-0.477064\pi\)
0.0719931 + 0.997405i \(0.477064\pi\)
\(434\) 0 0
\(435\) 10.8112 0.518359
\(436\) −8.86423 −0.424520
\(437\) −13.0872 −0.626045
\(438\) −14.5587 −0.695640
\(439\) −11.2325 −0.536096 −0.268048 0.963406i \(-0.586379\pi\)
−0.268048 + 0.963406i \(0.586379\pi\)
\(440\) 6.07973 0.289840
\(441\) 0 0
\(442\) 26.3822 1.25488
\(443\) −30.2403 −1.43676 −0.718381 0.695650i \(-0.755116\pi\)
−0.718381 + 0.695650i \(0.755116\pi\)
\(444\) 8.06631 0.382810
\(445\) −22.5224 −1.06766
\(446\) 18.1731 0.860520
\(447\) −27.2918 −1.29086
\(448\) 0 0
\(449\) −19.5454 −0.922403 −0.461202 0.887295i \(-0.652582\pi\)
−0.461202 + 0.887295i \(0.652582\pi\)
\(450\) −21.6646 −1.02128
\(451\) −4.18274 −0.196958
\(452\) −7.33107 −0.344825
\(453\) −7.69482 −0.361534
\(454\) 11.2158 0.526382
\(455\) 0 0
\(456\) 13.9966 0.655451
\(457\) 27.1077 1.26804 0.634022 0.773315i \(-0.281403\pi\)
0.634022 + 0.773315i \(0.281403\pi\)
\(458\) 7.14061 0.333659
\(459\) −73.7069 −3.44034
\(460\) −4.40468 −0.205369
\(461\) −9.69624 −0.451599 −0.225800 0.974174i \(-0.572499\pi\)
−0.225800 + 0.974174i \(0.572499\pi\)
\(462\) 0 0
\(463\) 24.3349 1.13094 0.565468 0.824770i \(-0.308695\pi\)
0.565468 + 0.824770i \(0.308695\pi\)
\(464\) 2.29501 0.106543
\(465\) −35.3456 −1.63911
\(466\) 12.4071 0.574750
\(467\) −21.6468 −1.00170 −0.500848 0.865535i \(-0.666979\pi\)
−0.500848 + 0.865535i \(0.666979\pi\)
\(468\) −39.2000 −1.81202
\(469\) 0 0
\(470\) 11.0166 0.508157
\(471\) −75.7218 −3.48908
\(472\) 2.55484 0.117596
\(473\) 39.1920 1.80205
\(474\) −32.7603 −1.50473
\(475\) −12.4693 −0.572129
\(476\) 0 0
\(477\) 9.22128 0.422213
\(478\) 18.9128 0.865050
\(479\) −5.40224 −0.246834 −0.123417 0.992355i \(-0.539385\pi\)
−0.123417 + 0.992355i \(0.539385\pi\)
\(480\) 4.71076 0.215016
\(481\) −13.0026 −0.592867
\(482\) 23.3723 1.06458
\(483\) 0 0
\(484\) 6.49533 0.295242
\(485\) −21.4956 −0.976064
\(486\) 36.5627 1.65852
\(487\) −0.808632 −0.0366426 −0.0183213 0.999832i \(-0.505832\pi\)
−0.0183213 + 0.999832i \(0.505832\pi\)
\(488\) 10.3886 0.470272
\(489\) 62.6700 2.83403
\(490\) 0 0
\(491\) 7.24205 0.326829 0.163415 0.986557i \(-0.447749\pi\)
0.163415 + 0.986557i \(0.447749\pi\)
\(492\) −3.24091 −0.146112
\(493\) −11.5898 −0.521977
\(494\) −22.5620 −1.01511
\(495\) 45.6193 2.05044
\(496\) −7.50317 −0.336902
\(497\) 0 0
\(498\) −9.28526 −0.416083
\(499\) −7.70718 −0.345021 −0.172510 0.985008i \(-0.555188\pi\)
−0.172510 + 0.985008i \(0.555188\pi\)
\(500\) −11.4643 −0.512701
\(501\) −6.51384 −0.291017
\(502\) −3.44847 −0.153913
\(503\) −4.34375 −0.193678 −0.0968391 0.995300i \(-0.530873\pi\)
−0.0968391 + 0.995300i \(0.530873\pi\)
\(504\) 0 0
\(505\) −5.28591 −0.235220
\(506\) −12.6751 −0.563478
\(507\) 46.3209 2.05718
\(508\) −0.797302 −0.0353746
\(509\) −22.1583 −0.982148 −0.491074 0.871118i \(-0.663395\pi\)
−0.491074 + 0.871118i \(0.663395\pi\)
\(510\) −23.7892 −1.05341
\(511\) 0 0
\(512\) 1.00000 0.0441942
\(513\) 63.0339 2.78301
\(514\) 26.0084 1.14718
\(515\) 20.0492 0.883474
\(516\) 30.3671 1.33684
\(517\) 31.7018 1.39425
\(518\) 0 0
\(519\) −35.2640 −1.54792
\(520\) −7.59356 −0.333000
\(521\) −35.9075 −1.57314 −0.786569 0.617503i \(-0.788144\pi\)
−0.786569 + 0.617503i \(0.788144\pi\)
\(522\) 17.2206 0.753727
\(523\) 35.7784 1.56448 0.782241 0.622976i \(-0.214076\pi\)
0.782241 + 0.622976i \(0.214076\pi\)
\(524\) −9.27577 −0.405214
\(525\) 0 0
\(526\) −0.875593 −0.0381777
\(527\) 37.8909 1.65055
\(528\) 13.5559 0.589945
\(529\) −13.8171 −0.600742
\(530\) 1.78628 0.0775911
\(531\) 19.1702 0.831918
\(532\) 0 0
\(533\) 5.22423 0.226286
\(534\) −50.2179 −2.17314
\(535\) 29.4714 1.27416
\(536\) −4.10815 −0.177445
\(537\) 21.3615 0.921816
\(538\) −27.9132 −1.20342
\(539\) 0 0
\(540\) 21.2149 0.912946
\(541\) 13.7164 0.589716 0.294858 0.955541i \(-0.404728\pi\)
0.294858 + 0.955541i \(0.404728\pi\)
\(542\) 9.10994 0.391305
\(543\) −33.5245 −1.43867
\(544\) −5.04998 −0.216516
\(545\) −12.8844 −0.551907
\(546\) 0 0
\(547\) 35.7038 1.52658 0.763292 0.646054i \(-0.223582\pi\)
0.763292 + 0.646054i \(0.223582\pi\)
\(548\) −5.22892 −0.223368
\(549\) 77.9513 3.32688
\(550\) −12.0766 −0.514950
\(551\) 9.91153 0.422245
\(552\) −9.82105 −0.418012
\(553\) 0 0
\(554\) −0.0967641 −0.00411111
\(555\) 11.7246 0.497682
\(556\) −12.9221 −0.548021
\(557\) 3.47414 0.147204 0.0736020 0.997288i \(-0.476551\pi\)
0.0736020 + 0.997288i \(0.476551\pi\)
\(558\) −56.3001 −2.38337
\(559\) −48.9506 −2.07039
\(560\) 0 0
\(561\) −68.4570 −2.89026
\(562\) 16.4020 0.691877
\(563\) −35.2600 −1.48603 −0.743015 0.669274i \(-0.766605\pi\)
−0.743015 + 0.669274i \(0.766605\pi\)
\(564\) 24.5635 1.03431
\(565\) −10.6559 −0.448298
\(566\) −2.48341 −0.104385
\(567\) 0 0
\(568\) −8.47279 −0.355511
\(569\) 25.4642 1.06752 0.533758 0.845637i \(-0.320779\pi\)
0.533758 + 0.845637i \(0.320779\pi\)
\(570\) 20.3445 0.852136
\(571\) 2.68312 0.112285 0.0561425 0.998423i \(-0.482120\pi\)
0.0561425 + 0.998423i \(0.482120\pi\)
\(572\) −21.8516 −0.913661
\(573\) −13.3249 −0.556655
\(574\) 0 0
\(575\) 8.74936 0.364873
\(576\) 7.50351 0.312646
\(577\) 16.3197 0.679396 0.339698 0.940535i \(-0.389675\pi\)
0.339698 + 0.940535i \(0.389675\pi\)
\(578\) 8.50231 0.353650
\(579\) 56.5527 2.35025
\(580\) 3.33586 0.138514
\(581\) 0 0
\(582\) −47.9284 −1.98670
\(583\) 5.14029 0.212889
\(584\) −4.49215 −0.185886
\(585\) −56.9784 −2.35576
\(586\) −9.32569 −0.385241
\(587\) 3.21883 0.132855 0.0664277 0.997791i \(-0.478840\pi\)
0.0664277 + 0.997791i \(0.478840\pi\)
\(588\) 0 0
\(589\) −32.4041 −1.33519
\(590\) 3.71353 0.152884
\(591\) −71.1927 −2.92848
\(592\) 2.48890 0.102293
\(593\) 3.30169 0.135584 0.0677920 0.997699i \(-0.478405\pi\)
0.0677920 + 0.997699i \(0.478405\pi\)
\(594\) 61.0491 2.50488
\(595\) 0 0
\(596\) −8.42101 −0.344938
\(597\) 29.9345 1.22514
\(598\) 15.8312 0.647384
\(599\) 24.7427 1.01096 0.505480 0.862838i \(-0.331315\pi\)
0.505480 + 0.862838i \(0.331315\pi\)
\(600\) −9.35734 −0.382012
\(601\) −19.4774 −0.794500 −0.397250 0.917710i \(-0.630035\pi\)
−0.397250 + 0.917710i \(0.630035\pi\)
\(602\) 0 0
\(603\) −30.8256 −1.25531
\(604\) −2.37428 −0.0966079
\(605\) 9.44115 0.383837
\(606\) −11.7859 −0.478771
\(607\) 24.1581 0.980547 0.490274 0.871569i \(-0.336897\pi\)
0.490274 + 0.871569i \(0.336897\pi\)
\(608\) 4.31873 0.175148
\(609\) 0 0
\(610\) 15.1002 0.611389
\(611\) −39.5955 −1.60186
\(612\) −37.8926 −1.53172
\(613\) −13.3981 −0.541144 −0.270572 0.962700i \(-0.587213\pi\)
−0.270572 + 0.962700i \(0.587213\pi\)
\(614\) 15.8969 0.641548
\(615\) −4.71076 −0.189956
\(616\) 0 0
\(617\) 42.9785 1.73025 0.865125 0.501557i \(-0.167239\pi\)
0.865125 + 0.501557i \(0.167239\pi\)
\(618\) 44.7034 1.79824
\(619\) 13.1401 0.528145 0.264073 0.964503i \(-0.414934\pi\)
0.264073 + 0.964503i \(0.414934\pi\)
\(620\) −10.9061 −0.437998
\(621\) −44.2292 −1.77486
\(622\) 16.9719 0.680511
\(623\) 0 0
\(624\) −16.9313 −0.677793
\(625\) −2.22748 −0.0890990
\(626\) −31.6976 −1.26689
\(627\) 58.5442 2.33803
\(628\) −23.3643 −0.932339
\(629\) −12.5689 −0.501155
\(630\) 0 0
\(631\) 25.7634 1.02562 0.512812 0.858501i \(-0.328604\pi\)
0.512812 + 0.858501i \(0.328604\pi\)
\(632\) −10.1084 −0.402089
\(633\) 73.9584 2.93958
\(634\) 16.7818 0.666489
\(635\) −1.15890 −0.0459896
\(636\) 3.98285 0.157930
\(637\) 0 0
\(638\) 9.59944 0.380046
\(639\) −63.5757 −2.51502
\(640\) 1.45353 0.0574557
\(641\) 43.8275 1.73108 0.865542 0.500837i \(-0.166974\pi\)
0.865542 + 0.500837i \(0.166974\pi\)
\(642\) 65.7119 2.59344
\(643\) 45.7881 1.80571 0.902853 0.429949i \(-0.141468\pi\)
0.902853 + 0.429949i \(0.141468\pi\)
\(644\) 0 0
\(645\) 44.1395 1.73799
\(646\) −21.8095 −0.858083
\(647\) −12.6013 −0.495410 −0.247705 0.968836i \(-0.579676\pi\)
−0.247705 + 0.968836i \(0.579676\pi\)
\(648\) 24.7921 0.973927
\(649\) 10.6862 0.419471
\(650\) 15.0837 0.591630
\(651\) 0 0
\(652\) 19.3371 0.757301
\(653\) 41.4853 1.62344 0.811722 0.584044i \(-0.198531\pi\)
0.811722 + 0.584044i \(0.198531\pi\)
\(654\) −28.7282 −1.12336
\(655\) −13.4826 −0.526808
\(656\) −1.00000 −0.0390434
\(657\) −33.7069 −1.31503
\(658\) 0 0
\(659\) 20.3880 0.794206 0.397103 0.917774i \(-0.370016\pi\)
0.397103 + 0.917774i \(0.370016\pi\)
\(660\) 19.7039 0.766973
\(661\) −39.5463 −1.53817 −0.769086 0.639145i \(-0.779288\pi\)
−0.769086 + 0.639145i \(0.779288\pi\)
\(662\) −20.5312 −0.797968
\(663\) 85.5025 3.32064
\(664\) −2.86502 −0.111184
\(665\) 0 0
\(666\) 18.6755 0.723661
\(667\) −6.95466 −0.269285
\(668\) −2.00988 −0.0777646
\(669\) 58.8973 2.27710
\(670\) −5.97131 −0.230692
\(671\) 43.4530 1.67749
\(672\) 0 0
\(673\) −18.9729 −0.731352 −0.365676 0.930742i \(-0.619162\pi\)
−0.365676 + 0.930742i \(0.619162\pi\)
\(674\) −2.71983 −0.104764
\(675\) −42.1409 −1.62200
\(676\) 14.2925 0.549713
\(677\) 11.6773 0.448794 0.224397 0.974498i \(-0.427959\pi\)
0.224397 + 0.974498i \(0.427959\pi\)
\(678\) −23.7594 −0.912473
\(679\) 0 0
\(680\) −7.34029 −0.281487
\(681\) 36.3493 1.39291
\(682\) −31.3838 −1.20175
\(683\) 15.6257 0.597899 0.298949 0.954269i \(-0.403364\pi\)
0.298949 + 0.954269i \(0.403364\pi\)
\(684\) 32.4056 1.23906
\(685\) −7.60038 −0.290396
\(686\) 0 0
\(687\) 23.1421 0.882925
\(688\) 9.36993 0.357225
\(689\) −6.42020 −0.244590
\(690\) −14.2752 −0.543447
\(691\) −14.3995 −0.547784 −0.273892 0.961760i \(-0.588311\pi\)
−0.273892 + 0.961760i \(0.588311\pi\)
\(692\) −10.8809 −0.413629
\(693\) 0 0
\(694\) 12.9347 0.490993
\(695\) −18.7827 −0.712468
\(696\) 7.43793 0.281934
\(697\) 5.04998 0.191282
\(698\) 19.9087 0.753554
\(699\) 40.2105 1.52090
\(700\) 0 0
\(701\) 12.2708 0.463462 0.231731 0.972780i \(-0.425561\pi\)
0.231731 + 0.972780i \(0.425561\pi\)
\(702\) −76.2501 −2.87787
\(703\) 10.7489 0.405402
\(704\) 4.18274 0.157643
\(705\) 35.7038 1.34468
\(706\) 0.487930 0.0183635
\(707\) 0 0
\(708\) 8.28000 0.311182
\(709\) 17.7056 0.664948 0.332474 0.943112i \(-0.392117\pi\)
0.332474 + 0.943112i \(0.392117\pi\)
\(710\) −12.3154 −0.462190
\(711\) −75.8483 −2.84453
\(712\) −15.4950 −0.580699
\(713\) 22.7371 0.851512
\(714\) 0 0
\(715\) −31.7619 −1.18783
\(716\) 6.59120 0.246325
\(717\) 61.2946 2.28909
\(718\) −7.91222 −0.295281
\(719\) 48.6849 1.81564 0.907819 0.419362i \(-0.137746\pi\)
0.907819 + 0.419362i \(0.137746\pi\)
\(720\) 10.9066 0.406464
\(721\) 0 0
\(722\) −0.348598 −0.0129735
\(723\) 75.7476 2.81708
\(724\) −10.3441 −0.384437
\(725\) −6.62629 −0.246094
\(726\) 21.0508 0.781268
\(727\) −48.2554 −1.78970 −0.894848 0.446372i \(-0.852716\pi\)
−0.894848 + 0.446372i \(0.852716\pi\)
\(728\) 0 0
\(729\) 44.1200 1.63407
\(730\) −6.52946 −0.241666
\(731\) −47.3180 −1.75012
\(732\) 33.6687 1.24443
\(733\) −23.1361 −0.854550 −0.427275 0.904122i \(-0.640526\pi\)
−0.427275 + 0.904122i \(0.640526\pi\)
\(734\) −14.4797 −0.534456
\(735\) 0 0
\(736\) −3.03034 −0.111700
\(737\) −17.1833 −0.632956
\(738\) −7.50351 −0.276208
\(739\) 1.81517 0.0667721 0.0333861 0.999443i \(-0.489371\pi\)
0.0333861 + 0.999443i \(0.489371\pi\)
\(740\) 3.61769 0.132989
\(741\) −73.1215 −2.68618
\(742\) 0 0
\(743\) 3.27732 0.120233 0.0601165 0.998191i \(-0.480853\pi\)
0.0601165 + 0.998191i \(0.480853\pi\)
\(744\) −24.3171 −0.891508
\(745\) −12.2402 −0.448446
\(746\) 18.9631 0.694290
\(747\) −21.4977 −0.786559
\(748\) −21.1228 −0.772325
\(749\) 0 0
\(750\) −37.1549 −1.35671
\(751\) −40.2715 −1.46953 −0.734765 0.678322i \(-0.762707\pi\)
−0.734765 + 0.678322i \(0.762707\pi\)
\(752\) 7.57920 0.276385
\(753\) −11.1762 −0.407283
\(754\) −11.9897 −0.436638
\(755\) −3.45108 −0.125598
\(756\) 0 0
\(757\) 13.1294 0.477195 0.238597 0.971119i \(-0.423312\pi\)
0.238597 + 0.971119i \(0.423312\pi\)
\(758\) −28.3181 −1.02856
\(759\) −41.0789 −1.49107
\(760\) 6.27739 0.227705
\(761\) 2.72300 0.0987088 0.0493544 0.998781i \(-0.484284\pi\)
0.0493544 + 0.998781i \(0.484284\pi\)
\(762\) −2.58399 −0.0936079
\(763\) 0 0
\(764\) −4.11146 −0.148747
\(765\) −55.0779 −1.99135
\(766\) −13.0221 −0.470509
\(767\) −13.3470 −0.481934
\(768\) 3.24091 0.116946
\(769\) 11.1411 0.401758 0.200879 0.979616i \(-0.435620\pi\)
0.200879 + 0.979616i \(0.435620\pi\)
\(770\) 0 0
\(771\) 84.2909 3.03566
\(772\) 17.4496 0.628026
\(773\) 28.6395 1.03009 0.515045 0.857163i \(-0.327775\pi\)
0.515045 + 0.857163i \(0.327775\pi\)
\(774\) 70.3074 2.52715
\(775\) 21.6636 0.778178
\(776\) −14.7885 −0.530878
\(777\) 0 0
\(778\) −35.3836 −1.26856
\(779\) −4.31873 −0.154734
\(780\) −24.6101 −0.881181
\(781\) −35.4395 −1.26813
\(782\) 15.3031 0.547239
\(783\) 33.4968 1.19708
\(784\) 0 0
\(785\) −33.9607 −1.21211
\(786\) −30.0620 −1.07227
\(787\) 39.7506 1.41696 0.708479 0.705732i \(-0.249382\pi\)
0.708479 + 0.705732i \(0.249382\pi\)
\(788\) −21.9669 −0.782538
\(789\) −2.83772 −0.101025
\(790\) −14.6928 −0.522746
\(791\) 0 0
\(792\) 31.3852 1.11523
\(793\) −54.2726 −1.92728
\(794\) −20.0384 −0.711137
\(795\) 5.78918 0.205321
\(796\) 9.23644 0.327377
\(797\) 54.7109 1.93796 0.968981 0.247137i \(-0.0794898\pi\)
0.968981 + 0.247137i \(0.0794898\pi\)
\(798\) 0 0
\(799\) −38.2748 −1.35407
\(800\) −2.88726 −0.102080
\(801\) −116.267 −4.10808
\(802\) −14.8916 −0.525841
\(803\) −18.7895 −0.663067
\(804\) −13.3142 −0.469554
\(805\) 0 0
\(806\) 39.1982 1.38070
\(807\) −90.4642 −3.18449
\(808\) −3.63661 −0.127935
\(809\) −19.5057 −0.685784 −0.342892 0.939375i \(-0.611406\pi\)
−0.342892 + 0.939375i \(0.611406\pi\)
\(810\) 36.0361 1.26618
\(811\) −31.6037 −1.10976 −0.554879 0.831931i \(-0.687235\pi\)
−0.554879 + 0.831931i \(0.687235\pi\)
\(812\) 0 0
\(813\) 29.5245 1.03547
\(814\) 10.4104 0.364885
\(815\) 28.1071 0.984548
\(816\) −16.3665 −0.572944
\(817\) 40.4662 1.41573
\(818\) 22.5833 0.789606
\(819\) 0 0
\(820\) −1.45353 −0.0507594
\(821\) 11.9842 0.418250 0.209125 0.977889i \(-0.432938\pi\)
0.209125 + 0.977889i \(0.432938\pi\)
\(822\) −16.9465 −0.591076
\(823\) −7.39458 −0.257759 −0.128879 0.991660i \(-0.541138\pi\)
−0.128879 + 0.991660i \(0.541138\pi\)
\(824\) 13.7935 0.480519
\(825\) −39.1393 −1.36266
\(826\) 0 0
\(827\) 26.5511 0.923272 0.461636 0.887069i \(-0.347263\pi\)
0.461636 + 0.887069i \(0.347263\pi\)
\(828\) −22.7382 −0.790206
\(829\) 13.9729 0.485300 0.242650 0.970114i \(-0.421983\pi\)
0.242650 + 0.970114i \(0.421983\pi\)
\(830\) −4.16438 −0.144548
\(831\) −0.313604 −0.0108788
\(832\) −5.22423 −0.181117
\(833\) 0 0
\(834\) −41.8795 −1.45017
\(835\) −2.92142 −0.101100
\(836\) 18.0641 0.624761
\(837\) −109.512 −3.78530
\(838\) 19.4523 0.671967
\(839\) 9.50824 0.328261 0.164130 0.986439i \(-0.447518\pi\)
0.164130 + 0.986439i \(0.447518\pi\)
\(840\) 0 0
\(841\) −23.7329 −0.818377
\(842\) −14.7322 −0.507707
\(843\) 53.1575 1.83084
\(844\) 22.8202 0.785505
\(845\) 20.7746 0.714668
\(846\) 56.8706 1.95525
\(847\) 0 0
\(848\) 1.22893 0.0422016
\(849\) −8.04850 −0.276224
\(850\) 14.5806 0.500110
\(851\) −7.54221 −0.258544
\(852\) −27.4596 −0.940750
\(853\) −39.8656 −1.36497 −0.682485 0.730899i \(-0.739101\pi\)
−0.682485 + 0.730899i \(0.739101\pi\)
\(854\) 0 0
\(855\) 47.1025 1.61087
\(856\) 20.2757 0.693011
\(857\) 12.5114 0.427381 0.213691 0.976901i \(-0.431452\pi\)
0.213691 + 0.976901i \(0.431452\pi\)
\(858\) −70.8191 −2.41772
\(859\) −1.99659 −0.0681227 −0.0340613 0.999420i \(-0.510844\pi\)
−0.0340613 + 0.999420i \(0.510844\pi\)
\(860\) 13.6195 0.464420
\(861\) 0 0
\(862\) 8.85046 0.301448
\(863\) −16.5835 −0.564510 −0.282255 0.959339i \(-0.591082\pi\)
−0.282255 + 0.959339i \(0.591082\pi\)
\(864\) 14.5955 0.496548
\(865\) −15.8157 −0.537749
\(866\) 2.99616 0.101814
\(867\) 27.5553 0.935825
\(868\) 0 0
\(869\) −42.2807 −1.43427
\(870\) 10.8112 0.366535
\(871\) 21.4619 0.727209
\(872\) −8.86423 −0.300181
\(873\) −110.966 −3.75563
\(874\) −13.0872 −0.442681
\(875\) 0 0
\(876\) −14.5587 −0.491891
\(877\) −33.8770 −1.14395 −0.571973 0.820272i \(-0.693822\pi\)
−0.571973 + 0.820272i \(0.693822\pi\)
\(878\) −11.2325 −0.379077
\(879\) −30.2238 −1.01942
\(880\) 6.07973 0.204948
\(881\) −35.6178 −1.19999 −0.599997 0.800002i \(-0.704832\pi\)
−0.599997 + 0.800002i \(0.704832\pi\)
\(882\) 0 0
\(883\) 5.66968 0.190800 0.0953999 0.995439i \(-0.469587\pi\)
0.0953999 + 0.995439i \(0.469587\pi\)
\(884\) 26.3822 0.887331
\(885\) 12.0352 0.404559
\(886\) −30.2403 −1.01594
\(887\) −27.1241 −0.910738 −0.455369 0.890303i \(-0.650493\pi\)
−0.455369 + 0.890303i \(0.650493\pi\)
\(888\) 8.06631 0.270688
\(889\) 0 0
\(890\) −22.5224 −0.754953
\(891\) 103.699 3.47405
\(892\) 18.1731 0.608479
\(893\) 32.7325 1.09535
\(894\) −27.2918 −0.912773
\(895\) 9.58049 0.320240
\(896\) 0 0
\(897\) 51.3074 1.71310
\(898\) −19.5454 −0.652238
\(899\) −17.2199 −0.574314
\(900\) −21.6646 −0.722152
\(901\) −6.20607 −0.206754
\(902\) −4.18274 −0.139270
\(903\) 0 0
\(904\) −7.33107 −0.243828
\(905\) −15.0355 −0.499797
\(906\) −7.69482 −0.255643
\(907\) −5.03235 −0.167096 −0.0835482 0.996504i \(-0.526625\pi\)
−0.0835482 + 0.996504i \(0.526625\pi\)
\(908\) 11.2158 0.372208
\(909\) −27.2873 −0.905063
\(910\) 0 0
\(911\) 54.0700 1.79142 0.895710 0.444639i \(-0.146668\pi\)
0.895710 + 0.444639i \(0.146668\pi\)
\(912\) 13.9966 0.463474
\(913\) −11.9836 −0.396600
\(914\) 27.1077 0.896642
\(915\) 48.9384 1.61785
\(916\) 7.14061 0.235932
\(917\) 0 0
\(918\) −73.7069 −2.43269
\(919\) −55.6099 −1.83440 −0.917200 0.398427i \(-0.869556\pi\)
−0.917200 + 0.398427i \(0.869556\pi\)
\(920\) −4.40468 −0.145218
\(921\) 51.5205 1.69766
\(922\) −9.69624 −0.319329
\(923\) 44.2638 1.45696
\(924\) 0 0
\(925\) −7.18609 −0.236277
\(926\) 24.3349 0.799693
\(927\) 103.499 3.39937
\(928\) 2.29501 0.0753374
\(929\) 9.62188 0.315684 0.157842 0.987464i \(-0.449546\pi\)
0.157842 + 0.987464i \(0.449546\pi\)
\(930\) −35.3456 −1.15903
\(931\) 0 0
\(932\) 12.4071 0.406409
\(933\) 55.0044 1.80076
\(934\) −21.6468 −0.708306
\(935\) −30.7025 −1.00408
\(936\) −39.2000 −1.28129
\(937\) 6.63826 0.216863 0.108431 0.994104i \(-0.465417\pi\)
0.108431 + 0.994104i \(0.465417\pi\)
\(938\) 0 0
\(939\) −102.729 −3.35244
\(940\) 11.0166 0.359321
\(941\) −13.9901 −0.456065 −0.228032 0.973654i \(-0.573229\pi\)
−0.228032 + 0.973654i \(0.573229\pi\)
\(942\) −75.7218 −2.46715
\(943\) 3.03034 0.0986813
\(944\) 2.55484 0.0831529
\(945\) 0 0
\(946\) 39.1920 1.27424
\(947\) 13.8264 0.449299 0.224649 0.974440i \(-0.427876\pi\)
0.224649 + 0.974440i \(0.427876\pi\)
\(948\) −32.7603 −1.06401
\(949\) 23.4680 0.761804
\(950\) −12.4693 −0.404557
\(951\) 54.3882 1.76366
\(952\) 0 0
\(953\) −3.27602 −0.106121 −0.0530604 0.998591i \(-0.516898\pi\)
−0.0530604 + 0.998591i \(0.516898\pi\)
\(954\) 9.22128 0.298550
\(955\) −5.97613 −0.193383
\(956\) 18.9128 0.611682
\(957\) 31.1109 1.00567
\(958\) −5.40224 −0.174538
\(959\) 0 0
\(960\) 4.71076 0.152039
\(961\) 25.2975 0.816049
\(962\) −13.0026 −0.419220
\(963\) 152.139 4.90262
\(964\) 23.3723 0.752772
\(965\) 25.3635 0.816481
\(966\) 0 0
\(967\) −28.8513 −0.927795 −0.463898 0.885889i \(-0.653549\pi\)
−0.463898 + 0.885889i \(0.653549\pi\)
\(968\) 6.49533 0.208768
\(969\) −70.6826 −2.27065
\(970\) −21.4956 −0.690181
\(971\) −23.7272 −0.761442 −0.380721 0.924690i \(-0.624324\pi\)
−0.380721 + 0.924690i \(0.624324\pi\)
\(972\) 36.5627 1.17275
\(973\) 0 0
\(974\) −0.808632 −0.0259102
\(975\) 48.8849 1.56557
\(976\) 10.3886 0.332532
\(977\) 0.886915 0.0283749 0.0141875 0.999899i \(-0.495484\pi\)
0.0141875 + 0.999899i \(0.495484\pi\)
\(978\) 62.6700 2.00396
\(979\) −64.8115 −2.07139
\(980\) 0 0
\(981\) −66.5128 −2.12359
\(982\) 7.24205 0.231103
\(983\) 10.3852 0.331235 0.165618 0.986190i \(-0.447038\pi\)
0.165618 + 0.986190i \(0.447038\pi\)
\(984\) −3.24091 −0.103316
\(985\) −31.9295 −1.01736
\(986\) −11.5898 −0.369093
\(987\) 0 0
\(988\) −22.5620 −0.717793
\(989\) −28.3940 −0.902878
\(990\) 45.6193 1.44988
\(991\) −21.9812 −0.698255 −0.349128 0.937075i \(-0.613522\pi\)
−0.349128 + 0.937075i \(0.613522\pi\)
\(992\) −7.50317 −0.238226
\(993\) −66.5398 −2.11158
\(994\) 0 0
\(995\) 13.4254 0.425615
\(996\) −9.28526 −0.294215
\(997\) −24.1310 −0.764236 −0.382118 0.924114i \(-0.624805\pi\)
−0.382118 + 0.924114i \(0.624805\pi\)
\(998\) −7.70718 −0.243967
\(999\) 36.3267 1.14933
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 4018.2.a.bt.1.10 10
7.2 even 3 574.2.e.h.165.1 20
7.4 even 3 574.2.e.h.247.1 yes 20
7.6 odd 2 4018.2.a.bu.1.1 10
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
574.2.e.h.165.1 20 7.2 even 3
574.2.e.h.247.1 yes 20 7.4 even 3
4018.2.a.bt.1.10 10 1.1 even 1 trivial
4018.2.a.bu.1.1 10 7.6 odd 2