Properties

Label 6026.2.a.h.1.24
Level $6026$
Weight $2$
Character 6026.1
Self dual yes
Analytic conductor $48.118$
Analytic rank $1$
Dimension $24$
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] = [6026,2,Mod(1,6026)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(6026, 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("6026.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 6026 = 2 \cdot 23 \cdot 131 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 6026.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: \(48.1178522580\)
Analytic rank: \(1\)
Dimension: \(24\)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.24
Character \(\chi\) \(=\) 6026.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-1.00000 q^{2} +3.27738 q^{3} +1.00000 q^{4} +0.672993 q^{5} -3.27738 q^{6} -2.46940 q^{7} -1.00000 q^{8} +7.74119 q^{9} +O(q^{10})\) \(q-1.00000 q^{2} +3.27738 q^{3} +1.00000 q^{4} +0.672993 q^{5} -3.27738 q^{6} -2.46940 q^{7} -1.00000 q^{8} +7.74119 q^{9} -0.672993 q^{10} -2.72025 q^{11} +3.27738 q^{12} -4.85867 q^{13} +2.46940 q^{14} +2.20565 q^{15} +1.00000 q^{16} -5.69100 q^{17} -7.74119 q^{18} +4.50325 q^{19} +0.672993 q^{20} -8.09315 q^{21} +2.72025 q^{22} -1.00000 q^{23} -3.27738 q^{24} -4.54708 q^{25} +4.85867 q^{26} +15.5387 q^{27} -2.46940 q^{28} -0.111652 q^{29} -2.20565 q^{30} +0.359190 q^{31} -1.00000 q^{32} -8.91528 q^{33} +5.69100 q^{34} -1.66189 q^{35} +7.74119 q^{36} +3.00619 q^{37} -4.50325 q^{38} -15.9237 q^{39} -0.672993 q^{40} -5.58923 q^{41} +8.09315 q^{42} -3.52544 q^{43} -2.72025 q^{44} +5.20976 q^{45} +1.00000 q^{46} +4.33998 q^{47} +3.27738 q^{48} -0.902057 q^{49} +4.54708 q^{50} -18.6515 q^{51} -4.85867 q^{52} +4.79375 q^{53} -15.5387 q^{54} -1.83071 q^{55} +2.46940 q^{56} +14.7588 q^{57} +0.111652 q^{58} -2.17382 q^{59} +2.20565 q^{60} -0.654976 q^{61} -0.359190 q^{62} -19.1161 q^{63} +1.00000 q^{64} -3.26985 q^{65} +8.91528 q^{66} -0.983839 q^{67} -5.69100 q^{68} -3.27738 q^{69} +1.66189 q^{70} +11.3274 q^{71} -7.74119 q^{72} -8.31522 q^{73} -3.00619 q^{74} -14.9025 q^{75} +4.50325 q^{76} +6.71739 q^{77} +15.9237 q^{78} -14.9928 q^{79} +0.672993 q^{80} +27.7024 q^{81} +5.58923 q^{82} +3.35089 q^{83} -8.09315 q^{84} -3.83000 q^{85} +3.52544 q^{86} -0.365925 q^{87} +2.72025 q^{88} -14.5057 q^{89} -5.20976 q^{90} +11.9980 q^{91} -1.00000 q^{92} +1.17720 q^{93} -4.33998 q^{94} +3.03065 q^{95} -3.27738 q^{96} -9.65785 q^{97} +0.902057 q^{98} -21.0580 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 24 q - 24 q^{2} - q^{3} + 24 q^{4} - q^{5} + q^{6} - 7 q^{7} - 24 q^{8} + 27 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 24 q - 24 q^{2} - q^{3} + 24 q^{4} - q^{5} + q^{6} - 7 q^{7} - 24 q^{8} + 27 q^{9} + q^{10} - 4 q^{11} - q^{12} - 5 q^{13} + 7 q^{14} - 6 q^{15} + 24 q^{16} + 5 q^{17} - 27 q^{18} - 20 q^{19} - q^{20} + 4 q^{22} - 24 q^{23} + q^{24} + q^{25} + 5 q^{26} - q^{27} - 7 q^{28} - 6 q^{29} + 6 q^{30} - 23 q^{31} - 24 q^{32} - 6 q^{33} - 5 q^{34} + 5 q^{35} + 27 q^{36} - 6 q^{37} + 20 q^{38} - 39 q^{39} + q^{40} - q^{41} - 44 q^{43} - 4 q^{44} - 13 q^{45} + 24 q^{46} + 32 q^{47} - q^{48} - 13 q^{49} - q^{50} - 44 q^{51} - 5 q^{52} + 21 q^{53} + q^{54} - 13 q^{55} + 7 q^{56} + 10 q^{57} + 6 q^{58} - 24 q^{59} - 6 q^{60} - 40 q^{61} + 23 q^{62} - 54 q^{63} + 24 q^{64} - 29 q^{65} + 6 q^{66} - 17 q^{67} + 5 q^{68} + q^{69} - 5 q^{70} + 4 q^{71} - 27 q^{72} - 16 q^{73} + 6 q^{74} - 36 q^{75} - 20 q^{76} + 24 q^{77} + 39 q^{78} - 53 q^{79} - q^{80} + 24 q^{81} + q^{82} - 9 q^{83} - 37 q^{85} + 44 q^{86} + 7 q^{87} + 4 q^{88} - 46 q^{89} + 13 q^{90} - 44 q^{91} - 24 q^{92} + 23 q^{93} - 32 q^{94} + 28 q^{95} + q^{96} - 20 q^{97} + 13 q^{98} - 78 q^{99}+O(q^{100}) \) 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
\(3\) 3.27738 1.89219 0.946097 0.323884i \(-0.104989\pi\)
0.946097 + 0.323884i \(0.104989\pi\)
\(4\) 1.00000 0.500000
\(5\) 0.672993 0.300971 0.150486 0.988612i \(-0.451916\pi\)
0.150486 + 0.988612i \(0.451916\pi\)
\(6\) −3.27738 −1.33798
\(7\) −2.46940 −0.933346 −0.466673 0.884430i \(-0.654547\pi\)
−0.466673 + 0.884430i \(0.654547\pi\)
\(8\) −1.00000 −0.353553
\(9\) 7.74119 2.58040
\(10\) −0.672993 −0.212819
\(11\) −2.72025 −0.820187 −0.410093 0.912044i \(-0.634504\pi\)
−0.410093 + 0.912044i \(0.634504\pi\)
\(12\) 3.27738 0.946097
\(13\) −4.85867 −1.34755 −0.673776 0.738935i \(-0.735329\pi\)
−0.673776 + 0.738935i \(0.735329\pi\)
\(14\) 2.46940 0.659975
\(15\) 2.20565 0.569496
\(16\) 1.00000 0.250000
\(17\) −5.69100 −1.38027 −0.690135 0.723681i \(-0.742449\pi\)
−0.690135 + 0.723681i \(0.742449\pi\)
\(18\) −7.74119 −1.82462
\(19\) 4.50325 1.03312 0.516558 0.856252i \(-0.327213\pi\)
0.516558 + 0.856252i \(0.327213\pi\)
\(20\) 0.672993 0.150486
\(21\) −8.09315 −1.76607
\(22\) 2.72025 0.579960
\(23\) −1.00000 −0.208514
\(24\) −3.27738 −0.668991
\(25\) −4.54708 −0.909416
\(26\) 4.85867 0.952864
\(27\) 15.5387 2.99042
\(28\) −2.46940 −0.466673
\(29\) −0.111652 −0.0207332 −0.0103666 0.999946i \(-0.503300\pi\)
−0.0103666 + 0.999946i \(0.503300\pi\)
\(30\) −2.20565 −0.402695
\(31\) 0.359190 0.0645124 0.0322562 0.999480i \(-0.489731\pi\)
0.0322562 + 0.999480i \(0.489731\pi\)
\(32\) −1.00000 −0.176777
\(33\) −8.91528 −1.55195
\(34\) 5.69100 0.975998
\(35\) −1.66189 −0.280910
\(36\) 7.74119 1.29020
\(37\) 3.00619 0.494214 0.247107 0.968988i \(-0.420520\pi\)
0.247107 + 0.968988i \(0.420520\pi\)
\(38\) −4.50325 −0.730523
\(39\) −15.9237 −2.54983
\(40\) −0.672993 −0.106409
\(41\) −5.58923 −0.872891 −0.436446 0.899731i \(-0.643763\pi\)
−0.436446 + 0.899731i \(0.643763\pi\)
\(42\) 8.09315 1.24880
\(43\) −3.52544 −0.537624 −0.268812 0.963193i \(-0.586631\pi\)
−0.268812 + 0.963193i \(0.586631\pi\)
\(44\) −2.72025 −0.410093
\(45\) 5.20976 0.776625
\(46\) 1.00000 0.147442
\(47\) 4.33998 0.633051 0.316526 0.948584i \(-0.397484\pi\)
0.316526 + 0.948584i \(0.397484\pi\)
\(48\) 3.27738 0.473048
\(49\) −0.902057 −0.128865
\(50\) 4.54708 0.643054
\(51\) −18.6515 −2.61174
\(52\) −4.85867 −0.673776
\(53\) 4.79375 0.658472 0.329236 0.944248i \(-0.393209\pi\)
0.329236 + 0.944248i \(0.393209\pi\)
\(54\) −15.5387 −2.11454
\(55\) −1.83071 −0.246853
\(56\) 2.46940 0.329988
\(57\) 14.7588 1.95486
\(58\) 0.111652 0.0146606
\(59\) −2.17382 −0.283007 −0.141504 0.989938i \(-0.545194\pi\)
−0.141504 + 0.989938i \(0.545194\pi\)
\(60\) 2.20565 0.284748
\(61\) −0.654976 −0.0838611 −0.0419305 0.999121i \(-0.513351\pi\)
−0.0419305 + 0.999121i \(0.513351\pi\)
\(62\) −0.359190 −0.0456172
\(63\) −19.1161 −2.40840
\(64\) 1.00000 0.125000
\(65\) −3.26985 −0.405575
\(66\) 8.91528 1.09740
\(67\) −0.983839 −0.120195 −0.0600975 0.998193i \(-0.519141\pi\)
−0.0600975 + 0.998193i \(0.519141\pi\)
\(68\) −5.69100 −0.690135
\(69\) −3.27738 −0.394550
\(70\) 1.66189 0.198634
\(71\) 11.3274 1.34432 0.672160 0.740406i \(-0.265367\pi\)
0.672160 + 0.740406i \(0.265367\pi\)
\(72\) −7.74119 −0.912308
\(73\) −8.31522 −0.973223 −0.486611 0.873619i \(-0.661767\pi\)
−0.486611 + 0.873619i \(0.661767\pi\)
\(74\) −3.00619 −0.349462
\(75\) −14.9025 −1.72079
\(76\) 4.50325 0.516558
\(77\) 6.71739 0.765518
\(78\) 15.9237 1.80300
\(79\) −14.9928 −1.68682 −0.843409 0.537271i \(-0.819455\pi\)
−0.843409 + 0.537271i \(0.819455\pi\)
\(80\) 0.672993 0.0752429
\(81\) 27.7024 3.07805
\(82\) 5.58923 0.617227
\(83\) 3.35089 0.367808 0.183904 0.982944i \(-0.441126\pi\)
0.183904 + 0.982944i \(0.441126\pi\)
\(84\) −8.09315 −0.883036
\(85\) −3.83000 −0.415422
\(86\) 3.52544 0.380157
\(87\) −0.365925 −0.0392313
\(88\) 2.72025 0.289980
\(89\) −14.5057 −1.53760 −0.768801 0.639488i \(-0.779146\pi\)
−0.768801 + 0.639488i \(0.779146\pi\)
\(90\) −5.20976 −0.549157
\(91\) 11.9980 1.25773
\(92\) −1.00000 −0.104257
\(93\) 1.17720 0.122070
\(94\) −4.33998 −0.447635
\(95\) 3.03065 0.310938
\(96\) −3.27738 −0.334496
\(97\) −9.65785 −0.980606 −0.490303 0.871552i \(-0.663114\pi\)
−0.490303 + 0.871552i \(0.663114\pi\)
\(98\) 0.902057 0.0911215
\(99\) −21.0580 −2.11641
\(100\) −4.54708 −0.454708
\(101\) −11.8330 −1.17743 −0.588714 0.808342i \(-0.700365\pi\)
−0.588714 + 0.808342i \(0.700365\pi\)
\(102\) 18.6515 1.84678
\(103\) −0.537652 −0.0529764 −0.0264882 0.999649i \(-0.508432\pi\)
−0.0264882 + 0.999649i \(0.508432\pi\)
\(104\) 4.85867 0.476432
\(105\) −5.44663 −0.531537
\(106\) −4.79375 −0.465610
\(107\) −13.4091 −1.29631 −0.648153 0.761510i \(-0.724458\pi\)
−0.648153 + 0.761510i \(0.724458\pi\)
\(108\) 15.5387 1.49521
\(109\) −14.8228 −1.41977 −0.709886 0.704317i \(-0.751253\pi\)
−0.709886 + 0.704317i \(0.751253\pi\)
\(110\) 1.83071 0.174551
\(111\) 9.85240 0.935149
\(112\) −2.46940 −0.233337
\(113\) −0.929835 −0.0874715 −0.0437357 0.999043i \(-0.513926\pi\)
−0.0437357 + 0.999043i \(0.513926\pi\)
\(114\) −14.7588 −1.38229
\(115\) −0.672993 −0.0627569
\(116\) −0.111652 −0.0103666
\(117\) −37.6119 −3.47722
\(118\) 2.17382 0.200116
\(119\) 14.0534 1.28827
\(120\) −2.20565 −0.201347
\(121\) −3.60023 −0.327294
\(122\) 0.654976 0.0592988
\(123\) −18.3180 −1.65168
\(124\) 0.359190 0.0322562
\(125\) −6.42511 −0.574680
\(126\) 19.1161 1.70300
\(127\) 13.0317 1.15638 0.578190 0.815902i \(-0.303759\pi\)
0.578190 + 0.815902i \(0.303759\pi\)
\(128\) −1.00000 −0.0883883
\(129\) −11.5542 −1.01729
\(130\) 3.26985 0.286785
\(131\) −1.00000 −0.0873704
\(132\) −8.91528 −0.775976
\(133\) −11.1203 −0.964255
\(134\) 0.983839 0.0849907
\(135\) 10.4574 0.900029
\(136\) 5.69100 0.487999
\(137\) −2.90262 −0.247987 −0.123994 0.992283i \(-0.539570\pi\)
−0.123994 + 0.992283i \(0.539570\pi\)
\(138\) 3.27738 0.278989
\(139\) 17.9545 1.52288 0.761441 0.648235i \(-0.224492\pi\)
0.761441 + 0.648235i \(0.224492\pi\)
\(140\) −1.66189 −0.140455
\(141\) 14.2237 1.19786
\(142\) −11.3274 −0.950578
\(143\) 13.2168 1.10524
\(144\) 7.74119 0.645099
\(145\) −0.0751408 −0.00624010
\(146\) 8.31522 0.688172
\(147\) −2.95638 −0.243838
\(148\) 3.00619 0.247107
\(149\) −5.76602 −0.472371 −0.236185 0.971708i \(-0.575897\pi\)
−0.236185 + 0.971708i \(0.575897\pi\)
\(150\) 14.9025 1.21678
\(151\) 11.3445 0.923203 0.461601 0.887088i \(-0.347275\pi\)
0.461601 + 0.887088i \(0.347275\pi\)
\(152\) −4.50325 −0.365262
\(153\) −44.0551 −3.56164
\(154\) −6.71739 −0.541303
\(155\) 0.241732 0.0194164
\(156\) −15.9237 −1.27492
\(157\) 6.21486 0.496000 0.248000 0.968760i \(-0.420227\pi\)
0.248000 + 0.968760i \(0.420227\pi\)
\(158\) 14.9928 1.19276
\(159\) 15.7109 1.24596
\(160\) −0.672993 −0.0532047
\(161\) 2.46940 0.194616
\(162\) −27.7024 −2.17651
\(163\) −6.87668 −0.538623 −0.269312 0.963053i \(-0.586796\pi\)
−0.269312 + 0.963053i \(0.586796\pi\)
\(164\) −5.58923 −0.436446
\(165\) −5.99992 −0.467093
\(166\) −3.35089 −0.260079
\(167\) −4.59332 −0.355442 −0.177721 0.984081i \(-0.556872\pi\)
−0.177721 + 0.984081i \(0.556872\pi\)
\(168\) 8.09315 0.624400
\(169\) 10.6067 0.815899
\(170\) 3.83000 0.293748
\(171\) 34.8605 2.66585
\(172\) −3.52544 −0.268812
\(173\) 21.8306 1.65975 0.829875 0.557949i \(-0.188412\pi\)
0.829875 + 0.557949i \(0.188412\pi\)
\(174\) 0.365925 0.0277407
\(175\) 11.2286 0.848800
\(176\) −2.72025 −0.205047
\(177\) −7.12442 −0.535504
\(178\) 14.5057 1.08725
\(179\) 0.596979 0.0446203 0.0223102 0.999751i \(-0.492898\pi\)
0.0223102 + 0.999751i \(0.492898\pi\)
\(180\) 5.20976 0.388313
\(181\) −8.26363 −0.614231 −0.307115 0.951672i \(-0.599364\pi\)
−0.307115 + 0.951672i \(0.599364\pi\)
\(182\) −11.9980 −0.889352
\(183\) −2.14660 −0.158681
\(184\) 1.00000 0.0737210
\(185\) 2.02314 0.148744
\(186\) −1.17720 −0.0863165
\(187\) 15.4809 1.13208
\(188\) 4.33998 0.316526
\(189\) −38.3712 −2.79109
\(190\) −3.03065 −0.219867
\(191\) 6.65464 0.481513 0.240757 0.970586i \(-0.422604\pi\)
0.240757 + 0.970586i \(0.422604\pi\)
\(192\) 3.27738 0.236524
\(193\) 0.746691 0.0537480 0.0268740 0.999639i \(-0.491445\pi\)
0.0268740 + 0.999639i \(0.491445\pi\)
\(194\) 9.65785 0.693393
\(195\) −10.7165 −0.767426
\(196\) −0.902057 −0.0644326
\(197\) −15.2183 −1.08426 −0.542130 0.840294i \(-0.682382\pi\)
−0.542130 + 0.840294i \(0.682382\pi\)
\(198\) 21.0580 1.49653
\(199\) −24.2595 −1.71971 −0.859856 0.510537i \(-0.829447\pi\)
−0.859856 + 0.510537i \(0.829447\pi\)
\(200\) 4.54708 0.321527
\(201\) −3.22441 −0.227432
\(202\) 11.8330 0.832567
\(203\) 0.275713 0.0193513
\(204\) −18.6515 −1.30587
\(205\) −3.76151 −0.262715
\(206\) 0.537652 0.0374600
\(207\) −7.74119 −0.538050
\(208\) −4.85867 −0.336888
\(209\) −12.2500 −0.847348
\(210\) 5.44663 0.375853
\(211\) −10.6607 −0.733913 −0.366957 0.930238i \(-0.619600\pi\)
−0.366957 + 0.930238i \(0.619600\pi\)
\(212\) 4.79375 0.329236
\(213\) 37.1243 2.54371
\(214\) 13.4091 0.916627
\(215\) −2.37259 −0.161809
\(216\) −15.5387 −1.05727
\(217\) −0.886984 −0.0602124
\(218\) 14.8228 1.00393
\(219\) −27.2521 −1.84153
\(220\) −1.83071 −0.123426
\(221\) 27.6507 1.85999
\(222\) −9.85240 −0.661250
\(223\) −24.3145 −1.62822 −0.814110 0.580711i \(-0.802775\pi\)
−0.814110 + 0.580711i \(0.802775\pi\)
\(224\) 2.46940 0.164994
\(225\) −35.1998 −2.34665
\(226\) 0.929835 0.0618517
\(227\) −9.02089 −0.598737 −0.299369 0.954138i \(-0.596776\pi\)
−0.299369 + 0.954138i \(0.596776\pi\)
\(228\) 14.7588 0.977428
\(229\) −7.30526 −0.482745 −0.241373 0.970433i \(-0.577598\pi\)
−0.241373 + 0.970433i \(0.577598\pi\)
\(230\) 0.672993 0.0443758
\(231\) 22.0154 1.44851
\(232\) 0.111652 0.00733030
\(233\) −6.99032 −0.457951 −0.228976 0.973432i \(-0.573538\pi\)
−0.228976 + 0.973432i \(0.573538\pi\)
\(234\) 37.6119 2.45877
\(235\) 2.92077 0.190530
\(236\) −2.17382 −0.141504
\(237\) −49.1369 −3.19179
\(238\) −14.0534 −0.910944
\(239\) −15.1187 −0.977948 −0.488974 0.872298i \(-0.662629\pi\)
−0.488974 + 0.872298i \(0.662629\pi\)
\(240\) 2.20565 0.142374
\(241\) −14.3638 −0.925251 −0.462626 0.886554i \(-0.653093\pi\)
−0.462626 + 0.886554i \(0.653093\pi\)
\(242\) 3.60023 0.231432
\(243\) 44.1753 2.83385
\(244\) −0.654976 −0.0419305
\(245\) −0.607077 −0.0387848
\(246\) 18.3180 1.16791
\(247\) −21.8798 −1.39218
\(248\) −0.359190 −0.0228086
\(249\) 10.9821 0.695963
\(250\) 6.42511 0.406360
\(251\) 9.79525 0.618271 0.309135 0.951018i \(-0.399960\pi\)
0.309135 + 0.951018i \(0.399960\pi\)
\(252\) −19.1161 −1.20420
\(253\) 2.72025 0.171021
\(254\) −13.0317 −0.817684
\(255\) −12.5523 −0.786058
\(256\) 1.00000 0.0625000
\(257\) −7.41344 −0.462438 −0.231219 0.972902i \(-0.574271\pi\)
−0.231219 + 0.972902i \(0.574271\pi\)
\(258\) 11.5542 0.719332
\(259\) −7.42348 −0.461273
\(260\) −3.26985 −0.202787
\(261\) −0.864317 −0.0534999
\(262\) 1.00000 0.0617802
\(263\) 14.3565 0.885263 0.442631 0.896704i \(-0.354045\pi\)
0.442631 + 0.896704i \(0.354045\pi\)
\(264\) 8.91528 0.548698
\(265\) 3.22616 0.198181
\(266\) 11.1203 0.681831
\(267\) −47.5406 −2.90944
\(268\) −0.983839 −0.0600975
\(269\) 23.3541 1.42393 0.711963 0.702217i \(-0.247806\pi\)
0.711963 + 0.702217i \(0.247806\pi\)
\(270\) −10.4574 −0.636417
\(271\) −17.3327 −1.05288 −0.526442 0.850211i \(-0.676474\pi\)
−0.526442 + 0.850211i \(0.676474\pi\)
\(272\) −5.69100 −0.345068
\(273\) 39.3220 2.37987
\(274\) 2.90262 0.175354
\(275\) 12.3692 0.745891
\(276\) −3.27738 −0.197275
\(277\) 26.1333 1.57020 0.785100 0.619369i \(-0.212612\pi\)
0.785100 + 0.619369i \(0.212612\pi\)
\(278\) −17.9545 −1.07684
\(279\) 2.78056 0.166468
\(280\) 1.66189 0.0993168
\(281\) −17.6203 −1.05114 −0.525569 0.850751i \(-0.676148\pi\)
−0.525569 + 0.850751i \(0.676148\pi\)
\(282\) −14.2237 −0.847012
\(283\) 17.5816 1.04512 0.522559 0.852603i \(-0.324977\pi\)
0.522559 + 0.852603i \(0.324977\pi\)
\(284\) 11.3274 0.672160
\(285\) 9.93259 0.588356
\(286\) −13.2168 −0.781526
\(287\) 13.8021 0.814710
\(288\) −7.74119 −0.456154
\(289\) 15.3875 0.905146
\(290\) 0.0751408 0.00441242
\(291\) −31.6524 −1.85550
\(292\) −8.31522 −0.486611
\(293\) 19.9662 1.16644 0.583220 0.812315i \(-0.301793\pi\)
0.583220 + 0.812315i \(0.301793\pi\)
\(294\) 2.95638 0.172419
\(295\) −1.46296 −0.0851770
\(296\) −3.00619 −0.174731
\(297\) −42.2690 −2.45270
\(298\) 5.76602 0.334017
\(299\) 4.85867 0.280984
\(300\) −14.9025 −0.860396
\(301\) 8.70572 0.501789
\(302\) −11.3445 −0.652803
\(303\) −38.7812 −2.22792
\(304\) 4.50325 0.258279
\(305\) −0.440794 −0.0252398
\(306\) 44.0551 2.51846
\(307\) 30.0142 1.71300 0.856502 0.516144i \(-0.172633\pi\)
0.856502 + 0.516144i \(0.172633\pi\)
\(308\) 6.71739 0.382759
\(309\) −1.76209 −0.100242
\(310\) −0.241732 −0.0137295
\(311\) −6.98218 −0.395923 −0.197962 0.980210i \(-0.563432\pi\)
−0.197962 + 0.980210i \(0.563432\pi\)
\(312\) 15.9237 0.901501
\(313\) 9.82075 0.555101 0.277551 0.960711i \(-0.410477\pi\)
0.277551 + 0.960711i \(0.410477\pi\)
\(314\) −6.21486 −0.350725
\(315\) −12.8650 −0.724860
\(316\) −14.9928 −0.843409
\(317\) 8.47516 0.476012 0.238006 0.971264i \(-0.423506\pi\)
0.238006 + 0.971264i \(0.423506\pi\)
\(318\) −15.7109 −0.881024
\(319\) 0.303721 0.0170051
\(320\) 0.672993 0.0376214
\(321\) −43.9466 −2.45286
\(322\) −2.46940 −0.137614
\(323\) −25.6280 −1.42598
\(324\) 27.7024 1.53902
\(325\) 22.0928 1.22549
\(326\) 6.87668 0.380864
\(327\) −48.5800 −2.68648
\(328\) 5.58923 0.308614
\(329\) −10.7172 −0.590856
\(330\) 5.99992 0.330285
\(331\) −16.9272 −0.930402 −0.465201 0.885205i \(-0.654018\pi\)
−0.465201 + 0.885205i \(0.654018\pi\)
\(332\) 3.35089 0.183904
\(333\) 23.2715 1.27527
\(334\) 4.59332 0.251335
\(335\) −0.662116 −0.0361753
\(336\) −8.09315 −0.441518
\(337\) 19.0862 1.03969 0.519844 0.854261i \(-0.325990\pi\)
0.519844 + 0.854261i \(0.325990\pi\)
\(338\) −10.6067 −0.576928
\(339\) −3.04742 −0.165513
\(340\) −3.83000 −0.207711
\(341\) −0.977087 −0.0529122
\(342\) −34.8605 −1.88504
\(343\) 19.5133 1.05362
\(344\) 3.52544 0.190079
\(345\) −2.20565 −0.118748
\(346\) −21.8306 −1.17362
\(347\) 3.48175 0.186910 0.0934550 0.995624i \(-0.470209\pi\)
0.0934550 + 0.995624i \(0.470209\pi\)
\(348\) −0.365925 −0.0196156
\(349\) 20.5414 1.09956 0.549779 0.835310i \(-0.314712\pi\)
0.549779 + 0.835310i \(0.314712\pi\)
\(350\) −11.2286 −0.600192
\(351\) −75.4972 −4.02974
\(352\) 2.72025 0.144990
\(353\) 13.9928 0.744759 0.372380 0.928080i \(-0.378542\pi\)
0.372380 + 0.928080i \(0.378542\pi\)
\(354\) 7.12442 0.378659
\(355\) 7.62328 0.404602
\(356\) −14.5057 −0.768801
\(357\) 46.0581 2.43766
\(358\) −0.596979 −0.0315513
\(359\) −10.9137 −0.576002 −0.288001 0.957630i \(-0.592991\pi\)
−0.288001 + 0.957630i \(0.592991\pi\)
\(360\) −5.20976 −0.274579
\(361\) 1.27925 0.0673291
\(362\) 8.26363 0.434327
\(363\) −11.7993 −0.619303
\(364\) 11.9980 0.628867
\(365\) −5.59608 −0.292912
\(366\) 2.14660 0.112205
\(367\) 14.1246 0.737301 0.368650 0.929568i \(-0.379820\pi\)
0.368650 + 0.929568i \(0.379820\pi\)
\(368\) −1.00000 −0.0521286
\(369\) −43.2673 −2.25241
\(370\) −2.02314 −0.105178
\(371\) −11.8377 −0.614582
\(372\) 1.17720 0.0610350
\(373\) 15.7652 0.816289 0.408145 0.912917i \(-0.366176\pi\)
0.408145 + 0.912917i \(0.366176\pi\)
\(374\) −15.4809 −0.800501
\(375\) −21.0575 −1.08741
\(376\) −4.33998 −0.223817
\(377\) 0.542479 0.0279391
\(378\) 38.3712 1.97360
\(379\) 14.5518 0.747476 0.373738 0.927534i \(-0.378076\pi\)
0.373738 + 0.927534i \(0.378076\pi\)
\(380\) 3.03065 0.155469
\(381\) 42.7099 2.18809
\(382\) −6.65464 −0.340481
\(383\) 32.2612 1.64847 0.824234 0.566249i \(-0.191606\pi\)
0.824234 + 0.566249i \(0.191606\pi\)
\(384\) −3.27738 −0.167248
\(385\) 4.52075 0.230399
\(386\) −0.746691 −0.0380056
\(387\) −27.2911 −1.38728
\(388\) −9.65785 −0.490303
\(389\) 22.0284 1.11688 0.558442 0.829544i \(-0.311399\pi\)
0.558442 + 0.829544i \(0.311399\pi\)
\(390\) 10.7165 0.542652
\(391\) 5.69100 0.287806
\(392\) 0.902057 0.0455607
\(393\) −3.27738 −0.165322
\(394\) 15.2183 0.766688
\(395\) −10.0900 −0.507684
\(396\) −21.0580 −1.05820
\(397\) −14.4906 −0.727262 −0.363631 0.931543i \(-0.618463\pi\)
−0.363631 + 0.931543i \(0.618463\pi\)
\(398\) 24.2595 1.21602
\(399\) −36.4455 −1.82456
\(400\) −4.54708 −0.227354
\(401\) 19.0287 0.950246 0.475123 0.879919i \(-0.342404\pi\)
0.475123 + 0.879919i \(0.342404\pi\)
\(402\) 3.22441 0.160819
\(403\) −1.74519 −0.0869339
\(404\) −11.8330 −0.588714
\(405\) 18.6435 0.926404
\(406\) −0.275713 −0.0136834
\(407\) −8.17759 −0.405348
\(408\) 18.6515 0.923389
\(409\) −5.15006 −0.254654 −0.127327 0.991861i \(-0.540640\pi\)
−0.127327 + 0.991861i \(0.540640\pi\)
\(410\) 3.76151 0.185768
\(411\) −9.51297 −0.469240
\(412\) −0.537652 −0.0264882
\(413\) 5.36803 0.264144
\(414\) 7.74119 0.380459
\(415\) 2.25512 0.110700
\(416\) 4.85867 0.238216
\(417\) 58.8436 2.88159
\(418\) 12.2500 0.599166
\(419\) 2.49870 0.122069 0.0610347 0.998136i \(-0.480560\pi\)
0.0610347 + 0.998136i \(0.480560\pi\)
\(420\) −5.44663 −0.265768
\(421\) 11.4990 0.560429 0.280215 0.959937i \(-0.409594\pi\)
0.280215 + 0.959937i \(0.409594\pi\)
\(422\) 10.6607 0.518955
\(423\) 33.5966 1.63352
\(424\) −4.79375 −0.232805
\(425\) 25.8774 1.25524
\(426\) −37.1243 −1.79868
\(427\) 1.61740 0.0782714
\(428\) −13.4091 −0.648153
\(429\) 43.3164 2.09134
\(430\) 2.37259 0.114417
\(431\) −10.0914 −0.486087 −0.243043 0.970015i \(-0.578146\pi\)
−0.243043 + 0.970015i \(0.578146\pi\)
\(432\) 15.5387 0.747604
\(433\) 0.00882162 0.000423940 0 0.000211970 1.00000i \(-0.499933\pi\)
0.000211970 1.00000i \(0.499933\pi\)
\(434\) 0.886984 0.0425766
\(435\) −0.246265 −0.0118075
\(436\) −14.8228 −0.709886
\(437\) −4.50325 −0.215420
\(438\) 27.2521 1.30216
\(439\) 6.07524 0.289956 0.144978 0.989435i \(-0.453689\pi\)
0.144978 + 0.989435i \(0.453689\pi\)
\(440\) 1.83071 0.0872756
\(441\) −6.98299 −0.332523
\(442\) −27.6507 −1.31521
\(443\) −4.58827 −0.217995 −0.108998 0.994042i \(-0.534764\pi\)
−0.108998 + 0.994042i \(0.534764\pi\)
\(444\) 9.85240 0.467574
\(445\) −9.76223 −0.462774
\(446\) 24.3145 1.15132
\(447\) −18.8974 −0.893817
\(448\) −2.46940 −0.116668
\(449\) −26.4659 −1.24900 −0.624501 0.781024i \(-0.714698\pi\)
−0.624501 + 0.781024i \(0.714698\pi\)
\(450\) 35.1998 1.65933
\(451\) 15.2041 0.715934
\(452\) −0.929835 −0.0437357
\(453\) 37.1802 1.74688
\(454\) 9.02089 0.423371
\(455\) 8.07457 0.378542
\(456\) −14.7588 −0.691146
\(457\) 14.5427 0.680279 0.340140 0.940375i \(-0.389526\pi\)
0.340140 + 0.940375i \(0.389526\pi\)
\(458\) 7.30526 0.341352
\(459\) −88.4305 −4.12758
\(460\) −0.672993 −0.0313784
\(461\) 36.9130 1.71921 0.859604 0.510960i \(-0.170710\pi\)
0.859604 + 0.510960i \(0.170710\pi\)
\(462\) −22.0154 −1.02425
\(463\) 27.8713 1.29529 0.647646 0.761942i \(-0.275754\pi\)
0.647646 + 0.761942i \(0.275754\pi\)
\(464\) −0.111652 −0.00518330
\(465\) 0.792247 0.0367396
\(466\) 6.99032 0.323821
\(467\) 16.8556 0.779985 0.389993 0.920818i \(-0.372478\pi\)
0.389993 + 0.920818i \(0.372478\pi\)
\(468\) −37.6119 −1.73861
\(469\) 2.42949 0.112184
\(470\) −2.92077 −0.134725
\(471\) 20.3684 0.938528
\(472\) 2.17382 0.100058
\(473\) 9.59007 0.440952
\(474\) 49.1369 2.25693
\(475\) −20.4766 −0.939533
\(476\) 14.0534 0.644135
\(477\) 37.1093 1.69912
\(478\) 15.1187 0.691514
\(479\) −18.3078 −0.836507 −0.418253 0.908330i \(-0.637358\pi\)
−0.418253 + 0.908330i \(0.637358\pi\)
\(480\) −2.20565 −0.100674
\(481\) −14.6061 −0.665980
\(482\) 14.3638 0.654251
\(483\) 8.09315 0.368251
\(484\) −3.60023 −0.163647
\(485\) −6.49966 −0.295134
\(486\) −44.1753 −2.00383
\(487\) 39.1360 1.77342 0.886710 0.462326i \(-0.152985\pi\)
0.886710 + 0.462326i \(0.152985\pi\)
\(488\) 0.654976 0.0296494
\(489\) −22.5375 −1.01918
\(490\) 0.607077 0.0274250
\(491\) 28.3155 1.27786 0.638930 0.769265i \(-0.279377\pi\)
0.638930 + 0.769265i \(0.279377\pi\)
\(492\) −18.3180 −0.825840
\(493\) 0.635410 0.0286174
\(494\) 21.8798 0.984419
\(495\) −14.1719 −0.636978
\(496\) 0.359190 0.0161281
\(497\) −27.9720 −1.25472
\(498\) −10.9821 −0.492120
\(499\) −16.3453 −0.731716 −0.365858 0.930671i \(-0.619224\pi\)
−0.365858 + 0.930671i \(0.619224\pi\)
\(500\) −6.42511 −0.287340
\(501\) −15.0540 −0.672565
\(502\) −9.79525 −0.437184
\(503\) 31.2967 1.39545 0.697725 0.716366i \(-0.254196\pi\)
0.697725 + 0.716366i \(0.254196\pi\)
\(504\) 19.1161 0.851499
\(505\) −7.96352 −0.354372
\(506\) −2.72025 −0.120930
\(507\) 34.7621 1.54384
\(508\) 13.0317 0.578190
\(509\) −3.79992 −0.168428 −0.0842142 0.996448i \(-0.526838\pi\)
−0.0842142 + 0.996448i \(0.526838\pi\)
\(510\) 12.5523 0.555827
\(511\) 20.5336 0.908354
\(512\) −1.00000 −0.0441942
\(513\) 69.9744 3.08945
\(514\) 7.41344 0.326993
\(515\) −0.361836 −0.0159444
\(516\) −11.5542 −0.508644
\(517\) −11.8058 −0.519220
\(518\) 7.42348 0.326169
\(519\) 71.5471 3.14057
\(520\) 3.26985 0.143392
\(521\) −24.1039 −1.05601 −0.528005 0.849241i \(-0.677060\pi\)
−0.528005 + 0.849241i \(0.677060\pi\)
\(522\) 0.864317 0.0378301
\(523\) −17.6879 −0.773438 −0.386719 0.922198i \(-0.626392\pi\)
−0.386719 + 0.922198i \(0.626392\pi\)
\(524\) −1.00000 −0.0436852
\(525\) 36.8002 1.60609
\(526\) −14.3565 −0.625975
\(527\) −2.04415 −0.0890445
\(528\) −8.91528 −0.387988
\(529\) 1.00000 0.0434783
\(530\) −3.22616 −0.140135
\(531\) −16.8279 −0.730270
\(532\) −11.1203 −0.482127
\(533\) 27.1562 1.17627
\(534\) 47.5406 2.05728
\(535\) −9.02422 −0.390151
\(536\) 0.983839 0.0424954
\(537\) 1.95652 0.0844302
\(538\) −23.3541 −1.00687
\(539\) 2.45382 0.105694
\(540\) 10.4574 0.450015
\(541\) −29.3569 −1.26215 −0.631077 0.775721i \(-0.717387\pi\)
−0.631077 + 0.775721i \(0.717387\pi\)
\(542\) 17.3327 0.744501
\(543\) −27.0830 −1.16224
\(544\) 5.69100 0.244000
\(545\) −9.97567 −0.427311
\(546\) −39.3220 −1.68283
\(547\) −12.4978 −0.534365 −0.267183 0.963646i \(-0.586093\pi\)
−0.267183 + 0.963646i \(0.586093\pi\)
\(548\) −2.90262 −0.123994
\(549\) −5.07029 −0.216395
\(550\) −12.3692 −0.527425
\(551\) −0.502796 −0.0214198
\(552\) 3.27738 0.139494
\(553\) 37.0232 1.57439
\(554\) −26.1333 −1.11030
\(555\) 6.63059 0.281453
\(556\) 17.9545 0.761441
\(557\) 21.0701 0.892770 0.446385 0.894841i \(-0.352711\pi\)
0.446385 + 0.894841i \(0.352711\pi\)
\(558\) −2.78056 −0.117710
\(559\) 17.1289 0.724477
\(560\) −1.66189 −0.0702276
\(561\) 50.7369 2.14211
\(562\) 17.6203 0.743267
\(563\) −7.06310 −0.297674 −0.148837 0.988862i \(-0.547553\pi\)
−0.148837 + 0.988862i \(0.547553\pi\)
\(564\) 14.2237 0.598928
\(565\) −0.625772 −0.0263264
\(566\) −17.5816 −0.739010
\(567\) −68.4084 −2.87288
\(568\) −11.3274 −0.475289
\(569\) 8.74373 0.366556 0.183278 0.983061i \(-0.441329\pi\)
0.183278 + 0.983061i \(0.441329\pi\)
\(570\) −9.93259 −0.416030
\(571\) 16.3004 0.682150 0.341075 0.940036i \(-0.389209\pi\)
0.341075 + 0.940036i \(0.389209\pi\)
\(572\) 13.2168 0.552622
\(573\) 21.8098 0.911116
\(574\) −13.8021 −0.576087
\(575\) 4.54708 0.189626
\(576\) 7.74119 0.322550
\(577\) 9.42179 0.392234 0.196117 0.980580i \(-0.437167\pi\)
0.196117 + 0.980580i \(0.437167\pi\)
\(578\) −15.3875 −0.640035
\(579\) 2.44719 0.101702
\(580\) −0.0751408 −0.00312005
\(581\) −8.27469 −0.343292
\(582\) 31.6524 1.31203
\(583\) −13.0402 −0.540070
\(584\) 8.31522 0.344086
\(585\) −25.3125 −1.04654
\(586\) −19.9662 −0.824797
\(587\) 9.10497 0.375802 0.187901 0.982188i \(-0.439832\pi\)
0.187901 + 0.982188i \(0.439832\pi\)
\(588\) −2.95638 −0.121919
\(589\) 1.61752 0.0666488
\(590\) 1.46296 0.0602293
\(591\) −49.8762 −2.05163
\(592\) 3.00619 0.123554
\(593\) 16.0222 0.657954 0.328977 0.944338i \(-0.393296\pi\)
0.328977 + 0.944338i \(0.393296\pi\)
\(594\) 42.2690 1.73432
\(595\) 9.45781 0.387732
\(596\) −5.76602 −0.236185
\(597\) −79.5075 −3.25403
\(598\) −4.85867 −0.198686
\(599\) 32.0481 1.30945 0.654725 0.755868i \(-0.272785\pi\)
0.654725 + 0.755868i \(0.272785\pi\)
\(600\) 14.9025 0.608392
\(601\) −12.3117 −0.502203 −0.251102 0.967961i \(-0.580793\pi\)
−0.251102 + 0.967961i \(0.580793\pi\)
\(602\) −8.70572 −0.354818
\(603\) −7.61608 −0.310151
\(604\) 11.3445 0.461601
\(605\) −2.42293 −0.0985061
\(606\) 38.7812 1.57538
\(607\) 4.28885 0.174079 0.0870395 0.996205i \(-0.472259\pi\)
0.0870395 + 0.996205i \(0.472259\pi\)
\(608\) −4.50325 −0.182631
\(609\) 0.903615 0.0366163
\(610\) 0.440794 0.0178472
\(611\) −21.0865 −0.853070
\(612\) −44.0551 −1.78082
\(613\) −20.7929 −0.839816 −0.419908 0.907567i \(-0.637938\pi\)
−0.419908 + 0.907567i \(0.637938\pi\)
\(614\) −30.0142 −1.21128
\(615\) −12.3279 −0.497108
\(616\) −6.71739 −0.270651
\(617\) −23.9447 −0.963978 −0.481989 0.876177i \(-0.660085\pi\)
−0.481989 + 0.876177i \(0.660085\pi\)
\(618\) 1.76209 0.0708816
\(619\) −37.0862 −1.49062 −0.745310 0.666718i \(-0.767698\pi\)
−0.745310 + 0.666718i \(0.767698\pi\)
\(620\) 0.241732 0.00970819
\(621\) −15.5387 −0.623545
\(622\) 6.98218 0.279960
\(623\) 35.8204 1.43511
\(624\) −15.9237 −0.637458
\(625\) 18.4114 0.736454
\(626\) −9.82075 −0.392516
\(627\) −40.1477 −1.60335
\(628\) 6.21486 0.248000
\(629\) −17.1082 −0.682149
\(630\) 12.8650 0.512554
\(631\) −42.7507 −1.70188 −0.850940 0.525263i \(-0.823967\pi\)
−0.850940 + 0.525263i \(0.823967\pi\)
\(632\) 14.9928 0.596381
\(633\) −34.9391 −1.38871
\(634\) −8.47516 −0.336592
\(635\) 8.77026 0.348037
\(636\) 15.7109 0.622978
\(637\) 4.38280 0.173653
\(638\) −0.303721 −0.0120244
\(639\) 87.6878 3.46888
\(640\) −0.672993 −0.0266024
\(641\) 12.4701 0.492538 0.246269 0.969202i \(-0.420795\pi\)
0.246269 + 0.969202i \(0.420795\pi\)
\(642\) 43.9466 1.73444
\(643\) −32.7766 −1.29258 −0.646292 0.763090i \(-0.723681\pi\)
−0.646292 + 0.763090i \(0.723681\pi\)
\(644\) 2.46940 0.0973080
\(645\) −7.77587 −0.306175
\(646\) 25.6280 1.00832
\(647\) −8.36783 −0.328973 −0.164487 0.986379i \(-0.552597\pi\)
−0.164487 + 0.986379i \(0.552597\pi\)
\(648\) −27.7024 −1.08825
\(649\) 5.91333 0.232119
\(650\) −22.0928 −0.866550
\(651\) −2.90698 −0.113933
\(652\) −6.87668 −0.269312
\(653\) 38.4140 1.50326 0.751629 0.659586i \(-0.229268\pi\)
0.751629 + 0.659586i \(0.229268\pi\)
\(654\) 48.5800 1.89963
\(655\) −0.672993 −0.0262960
\(656\) −5.58923 −0.218223
\(657\) −64.3697 −2.51130
\(658\) 10.7172 0.417798
\(659\) −9.08750 −0.353999 −0.176999 0.984211i \(-0.556639\pi\)
−0.176999 + 0.984211i \(0.556639\pi\)
\(660\) −5.99992 −0.233547
\(661\) 24.1992 0.941239 0.470619 0.882336i \(-0.344031\pi\)
0.470619 + 0.882336i \(0.344031\pi\)
\(662\) 16.9272 0.657894
\(663\) 90.6217 3.51946
\(664\) −3.35089 −0.130040
\(665\) −7.48390 −0.290213
\(666\) −23.2715 −0.901751
\(667\) 0.111652 0.00432317
\(668\) −4.59332 −0.177721
\(669\) −79.6877 −3.08091
\(670\) 0.662116 0.0255798
\(671\) 1.78170 0.0687818
\(672\) 8.09315 0.312200
\(673\) 10.5822 0.407913 0.203956 0.978980i \(-0.434620\pi\)
0.203956 + 0.978980i \(0.434620\pi\)
\(674\) −19.0862 −0.735171
\(675\) −70.6555 −2.71953
\(676\) 10.6067 0.407950
\(677\) 16.8689 0.648323 0.324162 0.946002i \(-0.394918\pi\)
0.324162 + 0.946002i \(0.394918\pi\)
\(678\) 3.04742 0.117035
\(679\) 23.8491 0.915244
\(680\) 3.83000 0.146874
\(681\) −29.5648 −1.13293
\(682\) 0.977087 0.0374146
\(683\) 31.7281 1.21404 0.607021 0.794685i \(-0.292364\pi\)
0.607021 + 0.794685i \(0.292364\pi\)
\(684\) 34.8605 1.33292
\(685\) −1.95344 −0.0746371
\(686\) −19.5133 −0.745023
\(687\) −23.9421 −0.913447
\(688\) −3.52544 −0.134406
\(689\) −23.2912 −0.887326
\(690\) 2.20565 0.0839676
\(691\) 48.5547 1.84711 0.923554 0.383468i \(-0.125270\pi\)
0.923554 + 0.383468i \(0.125270\pi\)
\(692\) 21.8306 0.829875
\(693\) 52.0006 1.97534
\(694\) −3.48175 −0.132165
\(695\) 12.0832 0.458344
\(696\) 0.365925 0.0138703
\(697\) 31.8083 1.20483
\(698\) −20.5414 −0.777504
\(699\) −22.9099 −0.866533
\(700\) 11.2286 0.424400
\(701\) 6.67303 0.252037 0.126018 0.992028i \(-0.459780\pi\)
0.126018 + 0.992028i \(0.459780\pi\)
\(702\) 75.4972 2.84946
\(703\) 13.5376 0.510581
\(704\) −2.72025 −0.102523
\(705\) 9.57248 0.360520
\(706\) −13.9928 −0.526624
\(707\) 29.2204 1.09895
\(708\) −7.12442 −0.267752
\(709\) −40.6096 −1.52512 −0.762562 0.646915i \(-0.776059\pi\)
−0.762562 + 0.646915i \(0.776059\pi\)
\(710\) −7.62328 −0.286097
\(711\) −116.062 −4.35266
\(712\) 14.5057 0.543624
\(713\) −0.359190 −0.0134518
\(714\) −46.0581 −1.72368
\(715\) 8.89481 0.332647
\(716\) 0.596979 0.0223102
\(717\) −49.5497 −1.85047
\(718\) 10.9137 0.407295
\(719\) −27.8501 −1.03863 −0.519316 0.854582i \(-0.673813\pi\)
−0.519316 + 0.854582i \(0.673813\pi\)
\(720\) 5.20976 0.194156
\(721\) 1.32768 0.0494453
\(722\) −1.27925 −0.0476088
\(723\) −47.0754 −1.75075
\(724\) −8.26363 −0.307115
\(725\) 0.507690 0.0188551
\(726\) 11.7993 0.437914
\(727\) −42.2871 −1.56834 −0.784171 0.620545i \(-0.786911\pi\)
−0.784171 + 0.620545i \(0.786911\pi\)
\(728\) −11.9980 −0.444676
\(729\) 61.6717 2.28414
\(730\) 5.59608 0.207120
\(731\) 20.0633 0.742066
\(732\) −2.14660 −0.0793407
\(733\) −8.61628 −0.318250 −0.159125 0.987258i \(-0.550867\pi\)
−0.159125 + 0.987258i \(0.550867\pi\)
\(734\) −14.1246 −0.521350
\(735\) −1.98962 −0.0733883
\(736\) 1.00000 0.0368605
\(737\) 2.67629 0.0985823
\(738\) 43.2673 1.59269
\(739\) −24.5546 −0.903257 −0.451629 0.892206i \(-0.649157\pi\)
−0.451629 + 0.892206i \(0.649157\pi\)
\(740\) 2.02314 0.0743722
\(741\) −71.7083 −2.63427
\(742\) 11.8377 0.434575
\(743\) 15.6730 0.574988 0.287494 0.957783i \(-0.407178\pi\)
0.287494 + 0.957783i \(0.407178\pi\)
\(744\) −1.17720 −0.0431582
\(745\) −3.88049 −0.142170
\(746\) −15.7652 −0.577204
\(747\) 25.9399 0.949090
\(748\) 15.4809 0.566040
\(749\) 33.1124 1.20990
\(750\) 21.0575 0.768912
\(751\) −34.9767 −1.27632 −0.638160 0.769904i \(-0.720304\pi\)
−0.638160 + 0.769904i \(0.720304\pi\)
\(752\) 4.33998 0.158263
\(753\) 32.1027 1.16989
\(754\) −0.542479 −0.0197559
\(755\) 7.63477 0.277858
\(756\) −38.3712 −1.39555
\(757\) −34.8799 −1.26773 −0.633866 0.773443i \(-0.718533\pi\)
−0.633866 + 0.773443i \(0.718533\pi\)
\(758\) −14.5518 −0.528545
\(759\) 8.91528 0.323604
\(760\) −3.03065 −0.109933
\(761\) −45.3665 −1.64453 −0.822267 0.569102i \(-0.807291\pi\)
−0.822267 + 0.569102i \(0.807291\pi\)
\(762\) −42.7099 −1.54722
\(763\) 36.6036 1.32514
\(764\) 6.65464 0.240757
\(765\) −29.6488 −1.07195
\(766\) −32.2612 −1.16564
\(767\) 10.5619 0.381367
\(768\) 3.27738 0.118262
\(769\) −39.4821 −1.42376 −0.711881 0.702300i \(-0.752156\pi\)
−0.711881 + 0.702300i \(0.752156\pi\)
\(770\) −4.52075 −0.162917
\(771\) −24.2966 −0.875022
\(772\) 0.746691 0.0268740
\(773\) 4.57562 0.164574 0.0822868 0.996609i \(-0.473778\pi\)
0.0822868 + 0.996609i \(0.473778\pi\)
\(774\) 27.2911 0.980957
\(775\) −1.63327 −0.0586686
\(776\) 9.65785 0.346696
\(777\) −24.3295 −0.872817
\(778\) −22.0284 −0.789756
\(779\) −25.1697 −0.901798
\(780\) −10.7165 −0.383713
\(781\) −30.8135 −1.10259
\(782\) −5.69100 −0.203510
\(783\) −1.73492 −0.0620009
\(784\) −0.902057 −0.0322163
\(785\) 4.18256 0.149282
\(786\) 3.27738 0.116900
\(787\) −41.4280 −1.47675 −0.738375 0.674390i \(-0.764406\pi\)
−0.738375 + 0.674390i \(0.764406\pi\)
\(788\) −15.2183 −0.542130
\(789\) 47.0518 1.67509
\(790\) 10.0900 0.358987
\(791\) 2.29613 0.0816412
\(792\) 21.0580 0.748263
\(793\) 3.18231 0.113007
\(794\) 14.4906 0.514252
\(795\) 10.5733 0.374997
\(796\) −24.2595 −0.859856
\(797\) 5.52648 0.195758 0.0978790 0.995198i \(-0.468794\pi\)
0.0978790 + 0.995198i \(0.468794\pi\)
\(798\) 36.4455 1.29016
\(799\) −24.6988 −0.873782
\(800\) 4.54708 0.160764
\(801\) −112.291 −3.96762
\(802\) −19.0287 −0.671925
\(803\) 22.6195 0.798224
\(804\) −3.22441 −0.113716
\(805\) 1.66189 0.0585739
\(806\) 1.74519 0.0614715
\(807\) 76.5403 2.69435
\(808\) 11.8330 0.416284
\(809\) −19.7025 −0.692703 −0.346352 0.938105i \(-0.612580\pi\)
−0.346352 + 0.938105i \(0.612580\pi\)
\(810\) −18.6435 −0.655067
\(811\) −1.43028 −0.0502238 −0.0251119 0.999685i \(-0.507994\pi\)
−0.0251119 + 0.999685i \(0.507994\pi\)
\(812\) 0.275713 0.00967563
\(813\) −56.8056 −1.99226
\(814\) 8.17759 0.286624
\(815\) −4.62796 −0.162110
\(816\) −18.6515 −0.652935
\(817\) −15.8759 −0.555428
\(818\) 5.15006 0.180068
\(819\) 92.8789 3.24545
\(820\) −3.76151 −0.131358
\(821\) 31.1573 1.08740 0.543698 0.839281i \(-0.317024\pi\)
0.543698 + 0.839281i \(0.317024\pi\)
\(822\) 9.51297 0.331803
\(823\) 36.2094 1.26218 0.631091 0.775709i \(-0.282608\pi\)
0.631091 + 0.775709i \(0.282608\pi\)
\(824\) 0.537652 0.0187300
\(825\) 40.5385 1.41137
\(826\) −5.36803 −0.186778
\(827\) −7.98323 −0.277604 −0.138802 0.990320i \(-0.544325\pi\)
−0.138802 + 0.990320i \(0.544325\pi\)
\(828\) −7.74119 −0.269025
\(829\) −13.6966 −0.475704 −0.237852 0.971301i \(-0.576443\pi\)
−0.237852 + 0.971301i \(0.576443\pi\)
\(830\) −2.25512 −0.0782764
\(831\) 85.6487 2.97112
\(832\) −4.85867 −0.168444
\(833\) 5.13360 0.177869
\(834\) −58.8436 −2.03759
\(835\) −3.09127 −0.106978
\(836\) −12.2500 −0.423674
\(837\) 5.58133 0.192919
\(838\) −2.49870 −0.0863161
\(839\) 23.4688 0.810232 0.405116 0.914265i \(-0.367231\pi\)
0.405116 + 0.914265i \(0.367231\pi\)
\(840\) 5.44663 0.187927
\(841\) −28.9875 −0.999570
\(842\) −11.4990 −0.396283
\(843\) −57.7483 −1.98896
\(844\) −10.6607 −0.366957
\(845\) 7.13822 0.245562
\(846\) −33.5966 −1.15508
\(847\) 8.89042 0.305478
\(848\) 4.79375 0.164618
\(849\) 57.6215 1.97757
\(850\) −25.8774 −0.887589
\(851\) −3.00619 −0.103051
\(852\) 37.1243 1.27186
\(853\) 6.32032 0.216404 0.108202 0.994129i \(-0.465491\pi\)
0.108202 + 0.994129i \(0.465491\pi\)
\(854\) −1.61740 −0.0553463
\(855\) 23.4609 0.802344
\(856\) 13.4091 0.458313
\(857\) 36.3089 1.24029 0.620145 0.784488i \(-0.287074\pi\)
0.620145 + 0.784488i \(0.287074\pi\)
\(858\) −43.3164 −1.47880
\(859\) −33.2645 −1.13497 −0.567484 0.823384i \(-0.692083\pi\)
−0.567484 + 0.823384i \(0.692083\pi\)
\(860\) −2.37259 −0.0809047
\(861\) 45.2345 1.54159
\(862\) 10.0914 0.343715
\(863\) −29.1074 −0.990826 −0.495413 0.868658i \(-0.664983\pi\)
−0.495413 + 0.868658i \(0.664983\pi\)
\(864\) −15.5387 −0.528636
\(865\) 14.6918 0.499537
\(866\) −0.00882162 −0.000299771 0
\(867\) 50.4305 1.71271
\(868\) −0.886984 −0.0301062
\(869\) 40.7841 1.38351
\(870\) 0.246265 0.00834915
\(871\) 4.78015 0.161969
\(872\) 14.8228 0.501965
\(873\) −74.7632 −2.53035
\(874\) 4.50325 0.152325
\(875\) 15.8662 0.536375
\(876\) −27.2521 −0.920763
\(877\) 46.6843 1.57642 0.788208 0.615409i \(-0.211009\pi\)
0.788208 + 0.615409i \(0.211009\pi\)
\(878\) −6.07524 −0.205030
\(879\) 65.4368 2.20713
\(880\) −1.83071 −0.0617132
\(881\) −4.70238 −0.158427 −0.0792135 0.996858i \(-0.525241\pi\)
−0.0792135 + 0.996858i \(0.525241\pi\)
\(882\) 6.98299 0.235130
\(883\) 41.1212 1.38384 0.691919 0.721975i \(-0.256766\pi\)
0.691919 + 0.721975i \(0.256766\pi\)
\(884\) 27.6507 0.929994
\(885\) −4.79468 −0.161171
\(886\) 4.58827 0.154146
\(887\) 2.54416 0.0854245 0.0427122 0.999087i \(-0.486400\pi\)
0.0427122 + 0.999087i \(0.486400\pi\)
\(888\) −9.85240 −0.330625
\(889\) −32.1806 −1.07930
\(890\) 9.76223 0.327231
\(891\) −75.3576 −2.52457
\(892\) −24.3145 −0.814110
\(893\) 19.5440 0.654016
\(894\) 18.8974 0.632024
\(895\) 0.401762 0.0134294
\(896\) 2.46940 0.0824969
\(897\) 15.9237 0.531677
\(898\) 26.4659 0.883178
\(899\) −0.0401042 −0.00133755
\(900\) −35.1998 −1.17333
\(901\) −27.2812 −0.908869
\(902\) −15.2041 −0.506242
\(903\) 28.5319 0.949482
\(904\) 0.929835 0.0309258
\(905\) −5.56136 −0.184866
\(906\) −37.1802 −1.23523
\(907\) −34.8929 −1.15860 −0.579301 0.815114i \(-0.696674\pi\)
−0.579301 + 0.815114i \(0.696674\pi\)
\(908\) −9.02089 −0.299369
\(909\) −91.6015 −3.03823
\(910\) −8.07457 −0.267669
\(911\) 33.6596 1.11519 0.557597 0.830112i \(-0.311724\pi\)
0.557597 + 0.830112i \(0.311724\pi\)
\(912\) 14.7588 0.488714
\(913\) −9.11526 −0.301671
\(914\) −14.5427 −0.481030
\(915\) −1.44465 −0.0477586
\(916\) −7.30526 −0.241373
\(917\) 2.46940 0.0815468
\(918\) 88.4305 2.91864
\(919\) 10.1870 0.336039 0.168020 0.985784i \(-0.446263\pi\)
0.168020 + 0.985784i \(0.446263\pi\)
\(920\) 0.672993 0.0221879
\(921\) 98.3679 3.24133
\(922\) −36.9130 −1.21566
\(923\) −55.0363 −1.81154
\(924\) 22.0154 0.724254
\(925\) −13.6694 −0.449446
\(926\) −27.8713 −0.915909
\(927\) −4.16207 −0.136700
\(928\) 0.111652 0.00366515
\(929\) 49.2609 1.61620 0.808100 0.589046i \(-0.200496\pi\)
0.808100 + 0.589046i \(0.200496\pi\)
\(930\) −0.792247 −0.0259788
\(931\) −4.06219 −0.133133
\(932\) −6.99032 −0.228976
\(933\) −22.8832 −0.749163
\(934\) −16.8556 −0.551533
\(935\) 10.4186 0.340723
\(936\) 37.6119 1.22938
\(937\) 18.8856 0.616967 0.308483 0.951230i \(-0.400179\pi\)
0.308483 + 0.951230i \(0.400179\pi\)
\(938\) −2.42949 −0.0793257
\(939\) 32.1863 1.05036
\(940\) 2.92077 0.0952652
\(941\) −7.55427 −0.246262 −0.123131 0.992390i \(-0.539294\pi\)
−0.123131 + 0.992390i \(0.539294\pi\)
\(942\) −20.3684 −0.663640
\(943\) 5.58923 0.182010
\(944\) −2.17382 −0.0707518
\(945\) −25.8235 −0.840039
\(946\) −9.59007 −0.311800
\(947\) −60.5605 −1.96795 −0.983977 0.178298i \(-0.942941\pi\)
−0.983977 + 0.178298i \(0.942941\pi\)
\(948\) −49.1369 −1.59589
\(949\) 40.4009 1.31147
\(950\) 20.4766 0.664350
\(951\) 27.7763 0.900707
\(952\) −14.0534 −0.455472
\(953\) −45.1368 −1.46212 −0.731062 0.682311i \(-0.760975\pi\)
−0.731062 + 0.682311i \(0.760975\pi\)
\(954\) −37.1093 −1.20146
\(955\) 4.47852 0.144922
\(956\) −15.1187 −0.488974
\(957\) 0.995407 0.0321769
\(958\) 18.3078 0.591500
\(959\) 7.16773 0.231458
\(960\) 2.20565 0.0711870
\(961\) −30.8710 −0.995838
\(962\) 14.6061 0.470919
\(963\) −103.802 −3.34498
\(964\) −14.3638 −0.462626
\(965\) 0.502518 0.0161766
\(966\) −8.09315 −0.260393
\(967\) −20.9549 −0.673864 −0.336932 0.941529i \(-0.609389\pi\)
−0.336932 + 0.941529i \(0.609389\pi\)
\(968\) 3.60023 0.115716
\(969\) −83.9925 −2.69823
\(970\) 6.49966 0.208691
\(971\) 52.2202 1.67583 0.837913 0.545803i \(-0.183775\pi\)
0.837913 + 0.545803i \(0.183775\pi\)
\(972\) 44.1753 1.41692
\(973\) −44.3369 −1.42137
\(974\) −39.1360 −1.25400
\(975\) 72.4063 2.31886
\(976\) −0.654976 −0.0209653
\(977\) −19.4881 −0.623480 −0.311740 0.950167i \(-0.600912\pi\)
−0.311740 + 0.950167i \(0.600912\pi\)
\(978\) 22.5375 0.720669
\(979\) 39.4592 1.26112
\(980\) −0.607077 −0.0193924
\(981\) −114.746 −3.66357
\(982\) −28.3155 −0.903583
\(983\) −60.6859 −1.93558 −0.967790 0.251760i \(-0.918991\pi\)
−0.967790 + 0.251760i \(0.918991\pi\)
\(984\) 18.3180 0.583957
\(985\) −10.2418 −0.326331
\(986\) −0.635410 −0.0202356
\(987\) −35.1241 −1.11801
\(988\) −21.8798 −0.696089
\(989\) 3.52544 0.112102
\(990\) 14.1719 0.450411
\(991\) −44.4645 −1.41246 −0.706230 0.707982i \(-0.749606\pi\)
−0.706230 + 0.707982i \(0.749606\pi\)
\(992\) −0.359190 −0.0114043
\(993\) −55.4767 −1.76050
\(994\) 27.9720 0.887218
\(995\) −16.3265 −0.517584
\(996\) 10.9821 0.347982
\(997\) −23.8697 −0.755962 −0.377981 0.925813i \(-0.623382\pi\)
−0.377981 + 0.925813i \(0.623382\pi\)
\(998\) 16.3453 0.517402
\(999\) 46.7121 1.47791
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 6026.2.a.h.1.24 24
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
6026.2.a.h.1.24 24 1.1 even 1 trivial