Properties

Label 6018.2.a.s.1.7
Level $6018$
Weight $2$
Character 6018.1
Self dual yes
Analytic conductor $48.054$
Analytic rank $0$
Dimension $8$
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] = [6018,2,Mod(1,6018)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(6018, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 0, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("6018.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 6018 = 2 \cdot 3 \cdot 17 \cdot 59 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 6018.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: \(48.0539719364\)
Analytic rank: \(0\)
Dimension: \(8\)
Coefficient field: \(\mathbb{Q}[x]/(x^{8} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{8} - 3x^{7} - 17x^{6} + 37x^{5} + 105x^{4} - 117x^{3} - 238x^{2} + 42x + 90 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.7
Root \(-1.32287\) of defining polynomial
Character \(\chi\) \(=\) 6018.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +2.86769 q^{5} +1.00000 q^{6} +0.636539 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +2.86769 q^{5} +1.00000 q^{6} +0.636539 q^{7} -1.00000 q^{8} +1.00000 q^{9} -2.86769 q^{10} -3.08318 q^{11} -1.00000 q^{12} +1.26426 q^{13} -0.636539 q^{14} -2.86769 q^{15} +1.00000 q^{16} -1.00000 q^{17} -1.00000 q^{18} +6.75412 q^{19} +2.86769 q^{20} -0.636539 q^{21} +3.08318 q^{22} -6.12526 q^{23} +1.00000 q^{24} +3.22366 q^{25} -1.26426 q^{26} -1.00000 q^{27} +0.636539 q^{28} +2.06981 q^{29} +2.86769 q^{30} +8.03376 q^{31} -1.00000 q^{32} +3.08318 q^{33} +1.00000 q^{34} +1.82540 q^{35} +1.00000 q^{36} -0.884221 q^{37} -6.75412 q^{38} -1.26426 q^{39} -2.86769 q^{40} -7.06013 q^{41} +0.636539 q^{42} +6.55402 q^{43} -3.08318 q^{44} +2.86769 q^{45} +6.12526 q^{46} -0.660560 q^{47} -1.00000 q^{48} -6.59482 q^{49} -3.22366 q^{50} +1.00000 q^{51} +1.26426 q^{52} +2.83430 q^{53} +1.00000 q^{54} -8.84161 q^{55} -0.636539 q^{56} -6.75412 q^{57} -2.06981 q^{58} +1.00000 q^{59} -2.86769 q^{60} -10.1283 q^{61} -8.03376 q^{62} +0.636539 q^{63} +1.00000 q^{64} +3.62550 q^{65} -3.08318 q^{66} +0.0139862 q^{67} -1.00000 q^{68} +6.12526 q^{69} -1.82540 q^{70} +5.73708 q^{71} -1.00000 q^{72} +6.30289 q^{73} +0.884221 q^{74} -3.22366 q^{75} +6.75412 q^{76} -1.96256 q^{77} +1.26426 q^{78} +7.12879 q^{79} +2.86769 q^{80} +1.00000 q^{81} +7.06013 q^{82} +14.6054 q^{83} -0.636539 q^{84} -2.86769 q^{85} -6.55402 q^{86} -2.06981 q^{87} +3.08318 q^{88} +1.32107 q^{89} -2.86769 q^{90} +0.804748 q^{91} -6.12526 q^{92} -8.03376 q^{93} +0.660560 q^{94} +19.3687 q^{95} +1.00000 q^{96} +15.2562 q^{97} +6.59482 q^{98} -3.08318 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q - 8 q^{2} - 8 q^{3} + 8 q^{4} - q^{5} + 8 q^{6} + 6 q^{7} - 8 q^{8} + 8 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 8 q - 8 q^{2} - 8 q^{3} + 8 q^{4} - q^{5} + 8 q^{6} + 6 q^{7} - 8 q^{8} + 8 q^{9} + q^{10} - 8 q^{12} + 6 q^{13} - 6 q^{14} + q^{15} + 8 q^{16} - 8 q^{17} - 8 q^{18} - 7 q^{19} - q^{20} - 6 q^{21} - 5 q^{23} + 8 q^{24} + 9 q^{25} - 6 q^{26} - 8 q^{27} + 6 q^{28} - 15 q^{29} - q^{30} + 21 q^{31} - 8 q^{32} + 8 q^{34} - 2 q^{35} + 8 q^{36} + 7 q^{37} + 7 q^{38} - 6 q^{39} + q^{40} - q^{41} + 6 q^{42} + 14 q^{43} - q^{45} + 5 q^{46} - 8 q^{47} - 8 q^{48} + 2 q^{49} - 9 q^{50} + 8 q^{51} + 6 q^{52} + 8 q^{53} + 8 q^{54} + 24 q^{55} - 6 q^{56} + 7 q^{57} + 15 q^{58} + 8 q^{59} + q^{60} - 21 q^{62} + 6 q^{63} + 8 q^{64} + 6 q^{65} + 15 q^{67} - 8 q^{68} + 5 q^{69} + 2 q^{70} - 22 q^{71} - 8 q^{72} + 13 q^{73} - 7 q^{74} - 9 q^{75} - 7 q^{76} - 6 q^{77} + 6 q^{78} + 26 q^{79} - q^{80} + 8 q^{81} + q^{82} + 30 q^{83} - 6 q^{84} + q^{85} - 14 q^{86} + 15 q^{87} - 6 q^{89} + q^{90} + 3 q^{91} - 5 q^{92} - 21 q^{93} + 8 q^{94} + 37 q^{95} + 8 q^{96} + 23 q^{97} - 2 q^{98}+O(q^{100}) \) 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
\(3\) −1.00000 −0.577350
\(4\) 1.00000 0.500000
\(5\) 2.86769 1.28247 0.641236 0.767344i \(-0.278422\pi\)
0.641236 + 0.767344i \(0.278422\pi\)
\(6\) 1.00000 0.408248
\(7\) 0.636539 0.240589 0.120295 0.992738i \(-0.461616\pi\)
0.120295 + 0.992738i \(0.461616\pi\)
\(8\) −1.00000 −0.353553
\(9\) 1.00000 0.333333
\(10\) −2.86769 −0.906844
\(11\) −3.08318 −0.929613 −0.464807 0.885412i \(-0.653876\pi\)
−0.464807 + 0.885412i \(0.653876\pi\)
\(12\) −1.00000 −0.288675
\(13\) 1.26426 0.350642 0.175321 0.984511i \(-0.443904\pi\)
0.175321 + 0.984511i \(0.443904\pi\)
\(14\) −0.636539 −0.170122
\(15\) −2.86769 −0.740435
\(16\) 1.00000 0.250000
\(17\) −1.00000 −0.242536
\(18\) −1.00000 −0.235702
\(19\) 6.75412 1.54950 0.774751 0.632266i \(-0.217875\pi\)
0.774751 + 0.632266i \(0.217875\pi\)
\(20\) 2.86769 0.641236
\(21\) −0.636539 −0.138904
\(22\) 3.08318 0.657336
\(23\) −6.12526 −1.27720 −0.638602 0.769537i \(-0.720487\pi\)
−0.638602 + 0.769537i \(0.720487\pi\)
\(24\) 1.00000 0.204124
\(25\) 3.22366 0.644732
\(26\) −1.26426 −0.247941
\(27\) −1.00000 −0.192450
\(28\) 0.636539 0.120295
\(29\) 2.06981 0.384354 0.192177 0.981360i \(-0.438445\pi\)
0.192177 + 0.981360i \(0.438445\pi\)
\(30\) 2.86769 0.523567
\(31\) 8.03376 1.44291 0.721453 0.692463i \(-0.243475\pi\)
0.721453 + 0.692463i \(0.243475\pi\)
\(32\) −1.00000 −0.176777
\(33\) 3.08318 0.536712
\(34\) 1.00000 0.171499
\(35\) 1.82540 0.308549
\(36\) 1.00000 0.166667
\(37\) −0.884221 −0.145365 −0.0726825 0.997355i \(-0.523156\pi\)
−0.0726825 + 0.997355i \(0.523156\pi\)
\(38\) −6.75412 −1.09566
\(39\) −1.26426 −0.202443
\(40\) −2.86769 −0.453422
\(41\) −7.06013 −1.10261 −0.551303 0.834305i \(-0.685869\pi\)
−0.551303 + 0.834305i \(0.685869\pi\)
\(42\) 0.636539 0.0982201
\(43\) 6.55402 0.999479 0.499739 0.866176i \(-0.333429\pi\)
0.499739 + 0.866176i \(0.333429\pi\)
\(44\) −3.08318 −0.464807
\(45\) 2.86769 0.427490
\(46\) 6.12526 0.903120
\(47\) −0.660560 −0.0963526 −0.0481763 0.998839i \(-0.515341\pi\)
−0.0481763 + 0.998839i \(0.515341\pi\)
\(48\) −1.00000 −0.144338
\(49\) −6.59482 −0.942117
\(50\) −3.22366 −0.455894
\(51\) 1.00000 0.140028
\(52\) 1.26426 0.175321
\(53\) 2.83430 0.389321 0.194661 0.980871i \(-0.437639\pi\)
0.194661 + 0.980871i \(0.437639\pi\)
\(54\) 1.00000 0.136083
\(55\) −8.84161 −1.19220
\(56\) −0.636539 −0.0850611
\(57\) −6.75412 −0.894605
\(58\) −2.06981 −0.271779
\(59\) 1.00000 0.130189
\(60\) −2.86769 −0.370218
\(61\) −10.1283 −1.29679 −0.648396 0.761303i \(-0.724560\pi\)
−0.648396 + 0.761303i \(0.724560\pi\)
\(62\) −8.03376 −1.02029
\(63\) 0.636539 0.0801964
\(64\) 1.00000 0.125000
\(65\) 3.62550 0.449688
\(66\) −3.08318 −0.379513
\(67\) 0.0139862 0.00170868 0.000854342 1.00000i \(-0.499728\pi\)
0.000854342 1.00000i \(0.499728\pi\)
\(68\) −1.00000 −0.121268
\(69\) 6.12526 0.737395
\(70\) −1.82540 −0.218177
\(71\) 5.73708 0.680867 0.340433 0.940269i \(-0.389426\pi\)
0.340433 + 0.940269i \(0.389426\pi\)
\(72\) −1.00000 −0.117851
\(73\) 6.30289 0.737697 0.368849 0.929489i \(-0.379752\pi\)
0.368849 + 0.929489i \(0.379752\pi\)
\(74\) 0.884221 0.102789
\(75\) −3.22366 −0.372236
\(76\) 6.75412 0.774751
\(77\) −1.96256 −0.223655
\(78\) 1.26426 0.143149
\(79\) 7.12879 0.802052 0.401026 0.916067i \(-0.368654\pi\)
0.401026 + 0.916067i \(0.368654\pi\)
\(80\) 2.86769 0.320618
\(81\) 1.00000 0.111111
\(82\) 7.06013 0.779661
\(83\) 14.6054 1.60315 0.801574 0.597895i \(-0.203996\pi\)
0.801574 + 0.597895i \(0.203996\pi\)
\(84\) −0.636539 −0.0694521
\(85\) −2.86769 −0.311045
\(86\) −6.55402 −0.706738
\(87\) −2.06981 −0.221907
\(88\) 3.08318 0.328668
\(89\) 1.32107 0.140033 0.0700164 0.997546i \(-0.477695\pi\)
0.0700164 + 0.997546i \(0.477695\pi\)
\(90\) −2.86769 −0.302281
\(91\) 0.804748 0.0843605
\(92\) −6.12526 −0.638602
\(93\) −8.03376 −0.833062
\(94\) 0.660560 0.0681316
\(95\) 19.3687 1.98719
\(96\) 1.00000 0.102062
\(97\) 15.2562 1.54903 0.774517 0.632553i \(-0.217993\pi\)
0.774517 + 0.632553i \(0.217993\pi\)
\(98\) 6.59482 0.666177
\(99\) −3.08318 −0.309871
\(100\) 3.22366 0.322366
\(101\) 4.52152 0.449908 0.224954 0.974369i \(-0.427777\pi\)
0.224954 + 0.974369i \(0.427777\pi\)
\(102\) −1.00000 −0.0990148
\(103\) 18.1452 1.78790 0.893948 0.448171i \(-0.147924\pi\)
0.893948 + 0.448171i \(0.147924\pi\)
\(104\) −1.26426 −0.123971
\(105\) −1.82540 −0.178141
\(106\) −2.83430 −0.275292
\(107\) 6.90533 0.667564 0.333782 0.942650i \(-0.391675\pi\)
0.333782 + 0.942650i \(0.391675\pi\)
\(108\) −1.00000 −0.0962250
\(109\) 2.23129 0.213719 0.106859 0.994274i \(-0.465921\pi\)
0.106859 + 0.994274i \(0.465921\pi\)
\(110\) 8.84161 0.843014
\(111\) 0.884221 0.0839265
\(112\) 0.636539 0.0601473
\(113\) 9.41503 0.885691 0.442846 0.896598i \(-0.353969\pi\)
0.442846 + 0.896598i \(0.353969\pi\)
\(114\) 6.75412 0.632582
\(115\) −17.5654 −1.63798
\(116\) 2.06981 0.192177
\(117\) 1.26426 0.116881
\(118\) −1.00000 −0.0920575
\(119\) −0.636539 −0.0583514
\(120\) 2.86769 0.261783
\(121\) −1.49402 −0.135820
\(122\) 10.1283 0.916971
\(123\) 7.06013 0.636590
\(124\) 8.03376 0.721453
\(125\) −5.09400 −0.455621
\(126\) −0.636539 −0.0567074
\(127\) −9.67015 −0.858087 −0.429044 0.903284i \(-0.641149\pi\)
−0.429044 + 0.903284i \(0.641149\pi\)
\(128\) −1.00000 −0.0883883
\(129\) −6.55402 −0.577049
\(130\) −3.62550 −0.317977
\(131\) 12.1575 1.06220 0.531101 0.847308i \(-0.321778\pi\)
0.531101 + 0.847308i \(0.321778\pi\)
\(132\) 3.08318 0.268356
\(133\) 4.29926 0.372793
\(134\) −0.0139862 −0.00120822
\(135\) −2.86769 −0.246812
\(136\) 1.00000 0.0857493
\(137\) −16.0035 −1.36727 −0.683634 0.729825i \(-0.739601\pi\)
−0.683634 + 0.729825i \(0.739601\pi\)
\(138\) −6.12526 −0.521417
\(139\) −20.1857 −1.71213 −0.856066 0.516866i \(-0.827098\pi\)
−0.856066 + 0.516866i \(0.827098\pi\)
\(140\) 1.82540 0.154274
\(141\) 0.660560 0.0556292
\(142\) −5.73708 −0.481445
\(143\) −3.89793 −0.325961
\(144\) 1.00000 0.0833333
\(145\) 5.93557 0.492922
\(146\) −6.30289 −0.521631
\(147\) 6.59482 0.543931
\(148\) −0.884221 −0.0726825
\(149\) −16.2296 −1.32958 −0.664792 0.747029i \(-0.731480\pi\)
−0.664792 + 0.747029i \(0.731480\pi\)
\(150\) 3.22366 0.263211
\(151\) −4.37879 −0.356341 −0.178170 0.984000i \(-0.557018\pi\)
−0.178170 + 0.984000i \(0.557018\pi\)
\(152\) −6.75412 −0.547832
\(153\) −1.00000 −0.0808452
\(154\) 1.96256 0.158148
\(155\) 23.0384 1.85049
\(156\) −1.26426 −0.101221
\(157\) 10.5021 0.838155 0.419078 0.907950i \(-0.362354\pi\)
0.419078 + 0.907950i \(0.362354\pi\)
\(158\) −7.12879 −0.567136
\(159\) −2.83430 −0.224775
\(160\) −2.86769 −0.226711
\(161\) −3.89897 −0.307282
\(162\) −1.00000 −0.0785674
\(163\) 14.2087 1.11291 0.556454 0.830878i \(-0.312162\pi\)
0.556454 + 0.830878i \(0.312162\pi\)
\(164\) −7.06013 −0.551303
\(165\) 8.84161 0.688318
\(166\) −14.6054 −1.13360
\(167\) 9.29493 0.719264 0.359632 0.933094i \(-0.382902\pi\)
0.359632 + 0.933094i \(0.382902\pi\)
\(168\) 0.636539 0.0491100
\(169\) −11.4017 −0.877051
\(170\) 2.86769 0.219942
\(171\) 6.75412 0.516501
\(172\) 6.55402 0.499739
\(173\) 13.4939 1.02592 0.512961 0.858412i \(-0.328549\pi\)
0.512961 + 0.858412i \(0.328549\pi\)
\(174\) 2.06981 0.156912
\(175\) 2.05199 0.155116
\(176\) −3.08318 −0.232403
\(177\) −1.00000 −0.0751646
\(178\) −1.32107 −0.0990182
\(179\) −10.8405 −0.810254 −0.405127 0.914260i \(-0.632773\pi\)
−0.405127 + 0.914260i \(0.632773\pi\)
\(180\) 2.86769 0.213745
\(181\) −0.350673 −0.0260653 −0.0130327 0.999915i \(-0.504149\pi\)
−0.0130327 + 0.999915i \(0.504149\pi\)
\(182\) −0.804748 −0.0596519
\(183\) 10.1283 0.748703
\(184\) 6.12526 0.451560
\(185\) −2.53567 −0.186426
\(186\) 8.03376 0.589064
\(187\) 3.08318 0.225464
\(188\) −0.660560 −0.0481763
\(189\) −0.636539 −0.0463014
\(190\) −19.3687 −1.40516
\(191\) −5.71664 −0.413642 −0.206821 0.978379i \(-0.566312\pi\)
−0.206821 + 0.978379i \(0.566312\pi\)
\(192\) −1.00000 −0.0721688
\(193\) −18.2524 −1.31384 −0.656920 0.753960i \(-0.728141\pi\)
−0.656920 + 0.753960i \(0.728141\pi\)
\(194\) −15.2562 −1.09533
\(195\) −3.62550 −0.259627
\(196\) −6.59482 −0.471058
\(197\) 16.0335 1.14234 0.571170 0.820832i \(-0.306490\pi\)
0.571170 + 0.820832i \(0.306490\pi\)
\(198\) 3.08318 0.219112
\(199\) 14.7301 1.04419 0.522094 0.852888i \(-0.325151\pi\)
0.522094 + 0.852888i \(0.325151\pi\)
\(200\) −3.22366 −0.227947
\(201\) −0.0139862 −0.000986509 0
\(202\) −4.52152 −0.318133
\(203\) 1.31751 0.0924713
\(204\) 1.00000 0.0700140
\(205\) −20.2463 −1.41406
\(206\) −18.1452 −1.26423
\(207\) −6.12526 −0.425735
\(208\) 1.26426 0.0876604
\(209\) −20.8242 −1.44044
\(210\) 1.82540 0.125964
\(211\) 18.1318 1.24825 0.624124 0.781325i \(-0.285456\pi\)
0.624124 + 0.781325i \(0.285456\pi\)
\(212\) 2.83430 0.194661
\(213\) −5.73708 −0.393099
\(214\) −6.90533 −0.472039
\(215\) 18.7949 1.28180
\(216\) 1.00000 0.0680414
\(217\) 5.11380 0.347147
\(218\) −2.23129 −0.151122
\(219\) −6.30289 −0.425910
\(220\) −8.84161 −0.596101
\(221\) −1.26426 −0.0850431
\(222\) −0.884221 −0.0593450
\(223\) 5.29242 0.354407 0.177203 0.984174i \(-0.443295\pi\)
0.177203 + 0.984174i \(0.443295\pi\)
\(224\) −0.636539 −0.0425305
\(225\) 3.22366 0.214911
\(226\) −9.41503 −0.626278
\(227\) 5.38961 0.357721 0.178860 0.983874i \(-0.442759\pi\)
0.178860 + 0.983874i \(0.442759\pi\)
\(228\) −6.75412 −0.447303
\(229\) −7.41385 −0.489921 −0.244960 0.969533i \(-0.578775\pi\)
−0.244960 + 0.969533i \(0.578775\pi\)
\(230\) 17.5654 1.15823
\(231\) 1.96256 0.129127
\(232\) −2.06981 −0.135890
\(233\) −23.6396 −1.54868 −0.774342 0.632768i \(-0.781919\pi\)
−0.774342 + 0.632768i \(0.781919\pi\)
\(234\) −1.26426 −0.0826470
\(235\) −1.89428 −0.123569
\(236\) 1.00000 0.0650945
\(237\) −7.12879 −0.463065
\(238\) 0.636539 0.0412607
\(239\) 20.6309 1.33450 0.667252 0.744832i \(-0.267471\pi\)
0.667252 + 0.744832i \(0.267471\pi\)
\(240\) −2.86769 −0.185109
\(241\) 19.8421 1.27814 0.639072 0.769147i \(-0.279319\pi\)
0.639072 + 0.769147i \(0.279319\pi\)
\(242\) 1.49402 0.0960389
\(243\) −1.00000 −0.0641500
\(244\) −10.1283 −0.648396
\(245\) −18.9119 −1.20824
\(246\) −7.06013 −0.450137
\(247\) 8.53894 0.543320
\(248\) −8.03376 −0.510144
\(249\) −14.6054 −0.925578
\(250\) 5.09400 0.322173
\(251\) 15.3852 0.971104 0.485552 0.874208i \(-0.338619\pi\)
0.485552 + 0.874208i \(0.338619\pi\)
\(252\) 0.636539 0.0400982
\(253\) 18.8853 1.18731
\(254\) 9.67015 0.606759
\(255\) 2.86769 0.179582
\(256\) 1.00000 0.0625000
\(257\) −19.7400 −1.23135 −0.615673 0.788002i \(-0.711116\pi\)
−0.615673 + 0.788002i \(0.711116\pi\)
\(258\) 6.55402 0.408035
\(259\) −0.562841 −0.0349732
\(260\) 3.62550 0.224844
\(261\) 2.06981 0.128118
\(262\) −12.1575 −0.751091
\(263\) −9.87594 −0.608977 −0.304488 0.952516i \(-0.598485\pi\)
−0.304488 + 0.952516i \(0.598485\pi\)
\(264\) −3.08318 −0.189756
\(265\) 8.12791 0.499293
\(266\) −4.29926 −0.263605
\(267\) −1.32107 −0.0808480
\(268\) 0.0139862 0.000854342 0
\(269\) 14.3719 0.876268 0.438134 0.898910i \(-0.355639\pi\)
0.438134 + 0.898910i \(0.355639\pi\)
\(270\) 2.86769 0.174522
\(271\) −20.9059 −1.26994 −0.634971 0.772536i \(-0.718988\pi\)
−0.634971 + 0.772536i \(0.718988\pi\)
\(272\) −1.00000 −0.0606339
\(273\) −0.804748 −0.0487056
\(274\) 16.0035 0.966804
\(275\) −9.93912 −0.599351
\(276\) 6.12526 0.368697
\(277\) 20.3650 1.22361 0.611807 0.791007i \(-0.290443\pi\)
0.611807 + 0.791007i \(0.290443\pi\)
\(278\) 20.1857 1.21066
\(279\) 8.03376 0.480969
\(280\) −1.82540 −0.109088
\(281\) −6.13616 −0.366053 −0.183026 0.983108i \(-0.558589\pi\)
−0.183026 + 0.983108i \(0.558589\pi\)
\(282\) −0.660560 −0.0393358
\(283\) −4.66780 −0.277472 −0.138736 0.990329i \(-0.544304\pi\)
−0.138736 + 0.990329i \(0.544304\pi\)
\(284\) 5.73708 0.340433
\(285\) −19.3687 −1.14731
\(286\) 3.89793 0.230489
\(287\) −4.49405 −0.265275
\(288\) −1.00000 −0.0589256
\(289\) 1.00000 0.0588235
\(290\) −5.93557 −0.348549
\(291\) −15.2562 −0.894335
\(292\) 6.30289 0.368849
\(293\) −25.8627 −1.51091 −0.755457 0.655199i \(-0.772585\pi\)
−0.755457 + 0.655199i \(0.772585\pi\)
\(294\) −6.59482 −0.384618
\(295\) 2.86769 0.166964
\(296\) 0.884221 0.0513943
\(297\) 3.08318 0.178904
\(298\) 16.2296 0.940158
\(299\) −7.74390 −0.447841
\(300\) −3.22366 −0.186118
\(301\) 4.17189 0.240464
\(302\) 4.37879 0.251971
\(303\) −4.52152 −0.259754
\(304\) 6.75412 0.387376
\(305\) −29.0448 −1.66310
\(306\) 1.00000 0.0571662
\(307\) 2.39542 0.136714 0.0683568 0.997661i \(-0.478224\pi\)
0.0683568 + 0.997661i \(0.478224\pi\)
\(308\) −1.96256 −0.111827
\(309\) −18.1452 −1.03224
\(310\) −23.0384 −1.30849
\(311\) −2.92768 −0.166013 −0.0830067 0.996549i \(-0.526452\pi\)
−0.0830067 + 0.996549i \(0.526452\pi\)
\(312\) 1.26426 0.0715744
\(313\) 9.91154 0.560233 0.280117 0.959966i \(-0.409627\pi\)
0.280117 + 0.959966i \(0.409627\pi\)
\(314\) −10.5021 −0.592665
\(315\) 1.82540 0.102850
\(316\) 7.12879 0.401026
\(317\) 7.04898 0.395910 0.197955 0.980211i \(-0.436570\pi\)
0.197955 + 0.980211i \(0.436570\pi\)
\(318\) 2.83430 0.158940
\(319\) −6.38159 −0.357300
\(320\) 2.86769 0.160309
\(321\) −6.90533 −0.385418
\(322\) 3.89897 0.217281
\(323\) −6.75412 −0.375809
\(324\) 1.00000 0.0555556
\(325\) 4.07553 0.226070
\(326\) −14.2087 −0.786945
\(327\) −2.23129 −0.123391
\(328\) 7.06013 0.389830
\(329\) −0.420472 −0.0231814
\(330\) −8.84161 −0.486714
\(331\) 19.4349 1.06824 0.534120 0.845409i \(-0.320643\pi\)
0.534120 + 0.845409i \(0.320643\pi\)
\(332\) 14.6054 0.801574
\(333\) −0.884221 −0.0484550
\(334\) −9.29493 −0.508596
\(335\) 0.0401080 0.00219134
\(336\) −0.636539 −0.0347260
\(337\) 8.43905 0.459704 0.229852 0.973226i \(-0.426176\pi\)
0.229852 + 0.973226i \(0.426176\pi\)
\(338\) 11.4017 0.620168
\(339\) −9.41503 −0.511354
\(340\) −2.86769 −0.155522
\(341\) −24.7695 −1.34134
\(342\) −6.75412 −0.365221
\(343\) −8.65363 −0.467252
\(344\) −6.55402 −0.353369
\(345\) 17.5654 0.945687
\(346\) −13.4939 −0.725436
\(347\) 20.3612 1.09305 0.546524 0.837443i \(-0.315951\pi\)
0.546524 + 0.837443i \(0.315951\pi\)
\(348\) −2.06981 −0.110953
\(349\) 23.9847 1.28387 0.641935 0.766759i \(-0.278132\pi\)
0.641935 + 0.766759i \(0.278132\pi\)
\(350\) −2.05199 −0.109683
\(351\) −1.26426 −0.0674810
\(352\) 3.08318 0.164334
\(353\) 1.45037 0.0771956 0.0385978 0.999255i \(-0.487711\pi\)
0.0385978 + 0.999255i \(0.487711\pi\)
\(354\) 1.00000 0.0531494
\(355\) 16.4522 0.873192
\(356\) 1.32107 0.0700164
\(357\) 0.636539 0.0336892
\(358\) 10.8405 0.572936
\(359\) −28.2900 −1.49309 −0.746543 0.665337i \(-0.768288\pi\)
−0.746543 + 0.665337i \(0.768288\pi\)
\(360\) −2.86769 −0.151141
\(361\) 26.6182 1.40096
\(362\) 0.350673 0.0184310
\(363\) 1.49402 0.0784155
\(364\) 0.804748 0.0421803
\(365\) 18.0748 0.946076
\(366\) −10.1283 −0.529413
\(367\) 19.5178 1.01882 0.509411 0.860523i \(-0.329863\pi\)
0.509411 + 0.860523i \(0.329863\pi\)
\(368\) −6.12526 −0.319301
\(369\) −7.06013 −0.367536
\(370\) 2.53567 0.131823
\(371\) 1.80414 0.0936665
\(372\) −8.03376 −0.416531
\(373\) −6.22265 −0.322196 −0.161098 0.986938i \(-0.551504\pi\)
−0.161098 + 0.986938i \(0.551504\pi\)
\(374\) −3.08318 −0.159427
\(375\) 5.09400 0.263053
\(376\) 0.660560 0.0340658
\(377\) 2.61677 0.134770
\(378\) 0.636539 0.0327400
\(379\) −20.5389 −1.05501 −0.527507 0.849551i \(-0.676873\pi\)
−0.527507 + 0.849551i \(0.676873\pi\)
\(380\) 19.3687 0.993596
\(381\) 9.67015 0.495417
\(382\) 5.71664 0.292489
\(383\) 24.5322 1.25354 0.626769 0.779205i \(-0.284377\pi\)
0.626769 + 0.779205i \(0.284377\pi\)
\(384\) 1.00000 0.0510310
\(385\) −5.62803 −0.286831
\(386\) 18.2524 0.929025
\(387\) 6.55402 0.333160
\(388\) 15.2562 0.774517
\(389\) −14.9943 −0.760241 −0.380120 0.924937i \(-0.624117\pi\)
−0.380120 + 0.924937i \(0.624117\pi\)
\(390\) 3.62550 0.183584
\(391\) 6.12526 0.309768
\(392\) 6.59482 0.333089
\(393\) −12.1575 −0.613263
\(394\) −16.0335 −0.807756
\(395\) 20.4432 1.02861
\(396\) −3.08318 −0.154936
\(397\) 16.9911 0.852757 0.426378 0.904545i \(-0.359789\pi\)
0.426378 + 0.904545i \(0.359789\pi\)
\(398\) −14.7301 −0.738352
\(399\) −4.29926 −0.215232
\(400\) 3.22366 0.161183
\(401\) 9.16169 0.457513 0.228756 0.973484i \(-0.426534\pi\)
0.228756 + 0.973484i \(0.426534\pi\)
\(402\) 0.0139862 0.000697567 0
\(403\) 10.1567 0.505943
\(404\) 4.52152 0.224954
\(405\) 2.86769 0.142497
\(406\) −1.31751 −0.0653871
\(407\) 2.72621 0.135133
\(408\) −1.00000 −0.0495074
\(409\) 9.77838 0.483510 0.241755 0.970337i \(-0.422277\pi\)
0.241755 + 0.970337i \(0.422277\pi\)
\(410\) 20.2463 0.999892
\(411\) 16.0035 0.789392
\(412\) 18.1452 0.893948
\(413\) 0.636539 0.0313220
\(414\) 6.12526 0.301040
\(415\) 41.8837 2.05599
\(416\) −1.26426 −0.0619853
\(417\) 20.1857 0.988500
\(418\) 20.8242 1.01854
\(419\) −12.0030 −0.586385 −0.293193 0.956053i \(-0.594718\pi\)
−0.293193 + 0.956053i \(0.594718\pi\)
\(420\) −1.82540 −0.0890703
\(421\) −16.6688 −0.812386 −0.406193 0.913787i \(-0.633144\pi\)
−0.406193 + 0.913787i \(0.633144\pi\)
\(422\) −18.1318 −0.882644
\(423\) −0.660560 −0.0321175
\(424\) −2.83430 −0.137646
\(425\) −3.22366 −0.156371
\(426\) 5.73708 0.277963
\(427\) −6.44704 −0.311994
\(428\) 6.90533 0.333782
\(429\) 3.89793 0.188194
\(430\) −18.7949 −0.906371
\(431\) −8.75516 −0.421721 −0.210860 0.977516i \(-0.567627\pi\)
−0.210860 + 0.977516i \(0.567627\pi\)
\(432\) −1.00000 −0.0481125
\(433\) −29.7186 −1.42819 −0.714093 0.700051i \(-0.753161\pi\)
−0.714093 + 0.700051i \(0.753161\pi\)
\(434\) −5.11380 −0.245470
\(435\) −5.93557 −0.284589
\(436\) 2.23129 0.106859
\(437\) −41.3708 −1.97903
\(438\) 6.30289 0.301164
\(439\) −33.6068 −1.60396 −0.801982 0.597348i \(-0.796221\pi\)
−0.801982 + 0.597348i \(0.796221\pi\)
\(440\) 8.84161 0.421507
\(441\) −6.59482 −0.314039
\(442\) 1.26426 0.0601345
\(443\) 21.8571 1.03846 0.519232 0.854634i \(-0.326218\pi\)
0.519232 + 0.854634i \(0.326218\pi\)
\(444\) 0.884221 0.0419633
\(445\) 3.78842 0.179588
\(446\) −5.29242 −0.250604
\(447\) 16.2296 0.767635
\(448\) 0.636539 0.0300736
\(449\) 0.330027 0.0155750 0.00778748 0.999970i \(-0.497521\pi\)
0.00778748 + 0.999970i \(0.497521\pi\)
\(450\) −3.22366 −0.151965
\(451\) 21.7676 1.02500
\(452\) 9.41503 0.442846
\(453\) 4.37879 0.205733
\(454\) −5.38961 −0.252947
\(455\) 2.30777 0.108190
\(456\) 6.75412 0.316291
\(457\) 23.9610 1.12085 0.560423 0.828207i \(-0.310639\pi\)
0.560423 + 0.828207i \(0.310639\pi\)
\(458\) 7.41385 0.346426
\(459\) 1.00000 0.0466760
\(460\) −17.5654 −0.818989
\(461\) 15.4035 0.717411 0.358705 0.933451i \(-0.383218\pi\)
0.358705 + 0.933451i \(0.383218\pi\)
\(462\) −1.96256 −0.0913067
\(463\) 9.07029 0.421532 0.210766 0.977537i \(-0.432404\pi\)
0.210766 + 0.977537i \(0.432404\pi\)
\(464\) 2.06981 0.0960884
\(465\) −23.0384 −1.06838
\(466\) 23.6396 1.09508
\(467\) 9.37346 0.433752 0.216876 0.976199i \(-0.430413\pi\)
0.216876 + 0.976199i \(0.430413\pi\)
\(468\) 1.26426 0.0584403
\(469\) 0.00890274 0.000411091 0
\(470\) 1.89428 0.0873768
\(471\) −10.5021 −0.483909
\(472\) −1.00000 −0.0460287
\(473\) −20.2072 −0.929128
\(474\) 7.12879 0.327436
\(475\) 21.7730 0.999014
\(476\) −0.636539 −0.0291757
\(477\) 2.83430 0.129774
\(478\) −20.6309 −0.943636
\(479\) 19.9688 0.912399 0.456199 0.889878i \(-0.349210\pi\)
0.456199 + 0.889878i \(0.349210\pi\)
\(480\) 2.86769 0.130892
\(481\) −1.11788 −0.0509710
\(482\) −19.8421 −0.903784
\(483\) 3.89897 0.177409
\(484\) −1.49402 −0.0679098
\(485\) 43.7501 1.98659
\(486\) 1.00000 0.0453609
\(487\) 2.20781 0.100046 0.0500228 0.998748i \(-0.484071\pi\)
0.0500228 + 0.998748i \(0.484071\pi\)
\(488\) 10.1283 0.458485
\(489\) −14.2087 −0.642538
\(490\) 18.9119 0.854353
\(491\) −7.72087 −0.348438 −0.174219 0.984707i \(-0.555740\pi\)
−0.174219 + 0.984707i \(0.555740\pi\)
\(492\) 7.06013 0.318295
\(493\) −2.06981 −0.0932195
\(494\) −8.53894 −0.384185
\(495\) −8.84161 −0.397401
\(496\) 8.03376 0.360726
\(497\) 3.65188 0.163809
\(498\) 14.6054 0.654483
\(499\) 23.7571 1.06351 0.531757 0.846897i \(-0.321532\pi\)
0.531757 + 0.846897i \(0.321532\pi\)
\(500\) −5.09400 −0.227810
\(501\) −9.29493 −0.415267
\(502\) −15.3852 −0.686674
\(503\) −16.5416 −0.737555 −0.368777 0.929518i \(-0.620224\pi\)
−0.368777 + 0.929518i \(0.620224\pi\)
\(504\) −0.636539 −0.0283537
\(505\) 12.9663 0.576994
\(506\) −18.8853 −0.839552
\(507\) 11.4017 0.506365
\(508\) −9.67015 −0.429044
\(509\) 37.4627 1.66050 0.830252 0.557388i \(-0.188196\pi\)
0.830252 + 0.557388i \(0.188196\pi\)
\(510\) −2.86769 −0.126984
\(511\) 4.01203 0.177482
\(512\) −1.00000 −0.0441942
\(513\) −6.75412 −0.298202
\(514\) 19.7400 0.870693
\(515\) 52.0347 2.29292
\(516\) −6.55402 −0.288525
\(517\) 2.03662 0.0895707
\(518\) 0.562841 0.0247298
\(519\) −13.4939 −0.592316
\(520\) −3.62550 −0.158989
\(521\) −29.0834 −1.27417 −0.637083 0.770795i \(-0.719859\pi\)
−0.637083 + 0.770795i \(0.719859\pi\)
\(522\) −2.06981 −0.0905930
\(523\) −7.03125 −0.307455 −0.153728 0.988113i \(-0.549128\pi\)
−0.153728 + 0.988113i \(0.549128\pi\)
\(524\) 12.1575 0.531101
\(525\) −2.05199 −0.0895560
\(526\) 9.87594 0.430612
\(527\) −8.03376 −0.349956
\(528\) 3.08318 0.134178
\(529\) 14.5188 0.631252
\(530\) −8.12791 −0.353054
\(531\) 1.00000 0.0433963
\(532\) 4.29926 0.186397
\(533\) −8.92581 −0.386620
\(534\) 1.32107 0.0571682
\(535\) 19.8024 0.856131
\(536\) −0.0139862 −0.000604111 0
\(537\) 10.8405 0.467800
\(538\) −14.3719 −0.619615
\(539\) 20.3330 0.875804
\(540\) −2.86769 −0.123406
\(541\) 23.3056 1.00198 0.500992 0.865452i \(-0.332969\pi\)
0.500992 + 0.865452i \(0.332969\pi\)
\(542\) 20.9059 0.897984
\(543\) 0.350673 0.0150488
\(544\) 1.00000 0.0428746
\(545\) 6.39865 0.274088
\(546\) 0.804748 0.0344400
\(547\) 16.2453 0.694599 0.347300 0.937754i \(-0.387099\pi\)
0.347300 + 0.937754i \(0.387099\pi\)
\(548\) −16.0035 −0.683634
\(549\) −10.1283 −0.432264
\(550\) 9.93912 0.423805
\(551\) 13.9797 0.595557
\(552\) −6.12526 −0.260708
\(553\) 4.53775 0.192965
\(554\) −20.3650 −0.865226
\(555\) 2.53567 0.107633
\(556\) −20.1857 −0.856066
\(557\) −33.3654 −1.41374 −0.706868 0.707345i \(-0.749893\pi\)
−0.706868 + 0.707345i \(0.749893\pi\)
\(558\) −8.03376 −0.340096
\(559\) 8.28596 0.350459
\(560\) 1.82540 0.0771371
\(561\) −3.08318 −0.130172
\(562\) 6.13616 0.258838
\(563\) 0.176635 0.00744427 0.00372214 0.999993i \(-0.498815\pi\)
0.00372214 + 0.999993i \(0.498815\pi\)
\(564\) 0.660560 0.0278146
\(565\) 26.9994 1.13587
\(566\) 4.66780 0.196202
\(567\) 0.636539 0.0267321
\(568\) −5.73708 −0.240723
\(569\) 21.3506 0.895062 0.447531 0.894268i \(-0.352303\pi\)
0.447531 + 0.894268i \(0.352303\pi\)
\(570\) 19.3687 0.811268
\(571\) 8.10989 0.339388 0.169694 0.985497i \(-0.445722\pi\)
0.169694 + 0.985497i \(0.445722\pi\)
\(572\) −3.89793 −0.162980
\(573\) 5.71664 0.238816
\(574\) 4.49405 0.187578
\(575\) −19.7458 −0.823455
\(576\) 1.00000 0.0416667
\(577\) 21.7216 0.904284 0.452142 0.891946i \(-0.350660\pi\)
0.452142 + 0.891946i \(0.350660\pi\)
\(578\) −1.00000 −0.0415945
\(579\) 18.2524 0.758546
\(580\) 5.93557 0.246461
\(581\) 9.29689 0.385700
\(582\) 15.2562 0.632390
\(583\) −8.73866 −0.361918
\(584\) −6.30289 −0.260815
\(585\) 3.62550 0.149896
\(586\) 25.8627 1.06838
\(587\) 3.88011 0.160149 0.0800746 0.996789i \(-0.474484\pi\)
0.0800746 + 0.996789i \(0.474484\pi\)
\(588\) 6.59482 0.271966
\(589\) 54.2610 2.23579
\(590\) −2.86769 −0.118061
\(591\) −16.0335 −0.659530
\(592\) −0.884221 −0.0363413
\(593\) 32.1503 1.32025 0.660126 0.751155i \(-0.270503\pi\)
0.660126 + 0.751155i \(0.270503\pi\)
\(594\) −3.08318 −0.126504
\(595\) −1.82540 −0.0748340
\(596\) −16.2296 −0.664792
\(597\) −14.7301 −0.602862
\(598\) 7.74390 0.316671
\(599\) 32.2735 1.31866 0.659329 0.751854i \(-0.270840\pi\)
0.659329 + 0.751854i \(0.270840\pi\)
\(600\) 3.22366 0.131605
\(601\) 35.6452 1.45400 0.726999 0.686639i \(-0.240915\pi\)
0.726999 + 0.686639i \(0.240915\pi\)
\(602\) −4.17189 −0.170033
\(603\) 0.0139862 0.000569561 0
\(604\) −4.37879 −0.178170
\(605\) −4.28438 −0.174185
\(606\) 4.52152 0.183674
\(607\) 32.5590 1.32153 0.660765 0.750593i \(-0.270232\pi\)
0.660765 + 0.750593i \(0.270232\pi\)
\(608\) −6.75412 −0.273916
\(609\) −1.31751 −0.0533883
\(610\) 29.0448 1.17599
\(611\) −0.835117 −0.0337852
\(612\) −1.00000 −0.0404226
\(613\) −13.6814 −0.552588 −0.276294 0.961073i \(-0.589106\pi\)
−0.276294 + 0.961073i \(0.589106\pi\)
\(614\) −2.39542 −0.0966711
\(615\) 20.2463 0.816409
\(616\) 1.96256 0.0790739
\(617\) −20.4629 −0.823803 −0.411902 0.911228i \(-0.635135\pi\)
−0.411902 + 0.911228i \(0.635135\pi\)
\(618\) 18.1452 0.729905
\(619\) 33.8274 1.35964 0.679819 0.733380i \(-0.262058\pi\)
0.679819 + 0.733380i \(0.262058\pi\)
\(620\) 23.0384 0.925243
\(621\) 6.12526 0.245798
\(622\) 2.92768 0.117389
\(623\) 0.840911 0.0336904
\(624\) −1.26426 −0.0506107
\(625\) −30.7263 −1.22905
\(626\) −9.91154 −0.396145
\(627\) 20.8242 0.831637
\(628\) 10.5021 0.419078
\(629\) 0.884221 0.0352562
\(630\) −1.82540 −0.0727256
\(631\) −35.3128 −1.40578 −0.702890 0.711298i \(-0.748107\pi\)
−0.702890 + 0.711298i \(0.748107\pi\)
\(632\) −7.12879 −0.283568
\(633\) −18.1318 −0.720676
\(634\) −7.04898 −0.279951
\(635\) −27.7310 −1.10047
\(636\) −2.83430 −0.112387
\(637\) −8.33754 −0.330345
\(638\) 6.38159 0.252649
\(639\) 5.73708 0.226956
\(640\) −2.86769 −0.113356
\(641\) −10.1247 −0.399902 −0.199951 0.979806i \(-0.564078\pi\)
−0.199951 + 0.979806i \(0.564078\pi\)
\(642\) 6.90533 0.272532
\(643\) 17.8410 0.703579 0.351790 0.936079i \(-0.385573\pi\)
0.351790 + 0.936079i \(0.385573\pi\)
\(644\) −3.89897 −0.153641
\(645\) −18.7949 −0.740049
\(646\) 6.75412 0.265737
\(647\) −9.26085 −0.364082 −0.182041 0.983291i \(-0.558270\pi\)
−0.182041 + 0.983291i \(0.558270\pi\)
\(648\) −1.00000 −0.0392837
\(649\) −3.08318 −0.121025
\(650\) −4.07553 −0.159856
\(651\) −5.11380 −0.200426
\(652\) 14.2087 0.556454
\(653\) 48.0871 1.88179 0.940897 0.338694i \(-0.109985\pi\)
0.940897 + 0.338694i \(0.109985\pi\)
\(654\) 2.23129 0.0872503
\(655\) 34.8639 1.36224
\(656\) −7.06013 −0.275652
\(657\) 6.30289 0.245899
\(658\) 0.420472 0.0163917
\(659\) −35.8621 −1.39699 −0.698495 0.715615i \(-0.746146\pi\)
−0.698495 + 0.715615i \(0.746146\pi\)
\(660\) 8.84161 0.344159
\(661\) 20.9952 0.816620 0.408310 0.912843i \(-0.366118\pi\)
0.408310 + 0.912843i \(0.366118\pi\)
\(662\) −19.4349 −0.755359
\(663\) 1.26426 0.0490996
\(664\) −14.6054 −0.566799
\(665\) 12.3290 0.478097
\(666\) 0.884221 0.0342629
\(667\) −12.6781 −0.490898
\(668\) 9.29493 0.359632
\(669\) −5.29242 −0.204617
\(670\) −0.0401080 −0.00154951
\(671\) 31.2273 1.20552
\(672\) 0.636539 0.0245550
\(673\) 0.321940 0.0124099 0.00620494 0.999981i \(-0.498025\pi\)
0.00620494 + 0.999981i \(0.498025\pi\)
\(674\) −8.43905 −0.325060
\(675\) −3.22366 −0.124079
\(676\) −11.4017 −0.438525
\(677\) 20.9026 0.803354 0.401677 0.915781i \(-0.368427\pi\)
0.401677 + 0.915781i \(0.368427\pi\)
\(678\) 9.41503 0.361582
\(679\) 9.71117 0.372681
\(680\) 2.86769 0.109971
\(681\) −5.38961 −0.206530
\(682\) 24.7695 0.948474
\(683\) −14.4561 −0.553146 −0.276573 0.960993i \(-0.589199\pi\)
−0.276573 + 0.960993i \(0.589199\pi\)
\(684\) 6.75412 0.258250
\(685\) −45.8930 −1.75348
\(686\) 8.65363 0.330397
\(687\) 7.41385 0.282856
\(688\) 6.55402 0.249870
\(689\) 3.58328 0.136512
\(690\) −17.5654 −0.668702
\(691\) 9.18531 0.349426 0.174713 0.984619i \(-0.444100\pi\)
0.174713 + 0.984619i \(0.444100\pi\)
\(692\) 13.4939 0.512961
\(693\) −1.96256 −0.0745516
\(694\) −20.3612 −0.772902
\(695\) −57.8865 −2.19576
\(696\) 2.06981 0.0784559
\(697\) 7.06013 0.267421
\(698\) −23.9847 −0.907833
\(699\) 23.6396 0.894133
\(700\) 2.05199 0.0775578
\(701\) −16.3096 −0.616004 −0.308002 0.951386i \(-0.599660\pi\)
−0.308002 + 0.951386i \(0.599660\pi\)
\(702\) 1.26426 0.0477163
\(703\) −5.97214 −0.225243
\(704\) −3.08318 −0.116202
\(705\) 1.89428 0.0713429
\(706\) −1.45037 −0.0545855
\(707\) 2.87812 0.108243
\(708\) −1.00000 −0.0375823
\(709\) −15.7670 −0.592142 −0.296071 0.955166i \(-0.595677\pi\)
−0.296071 + 0.955166i \(0.595677\pi\)
\(710\) −16.4522 −0.617440
\(711\) 7.12879 0.267351
\(712\) −1.32107 −0.0495091
\(713\) −49.2089 −1.84289
\(714\) −0.636539 −0.0238219
\(715\) −11.1781 −0.418036
\(716\) −10.8405 −0.405127
\(717\) −20.6309 −0.770476
\(718\) 28.2900 1.05577
\(719\) −19.5878 −0.730500 −0.365250 0.930909i \(-0.619017\pi\)
−0.365250 + 0.930909i \(0.619017\pi\)
\(720\) 2.86769 0.106873
\(721\) 11.5501 0.430148
\(722\) −26.6182 −0.990626
\(723\) −19.8421 −0.737937
\(724\) −0.350673 −0.0130327
\(725\) 6.67236 0.247805
\(726\) −1.49402 −0.0554481
\(727\) −38.1925 −1.41648 −0.708241 0.705970i \(-0.750511\pi\)
−0.708241 + 0.705970i \(0.750511\pi\)
\(728\) −0.804748 −0.0298260
\(729\) 1.00000 0.0370370
\(730\) −18.0748 −0.668977
\(731\) −6.55402 −0.242409
\(732\) 10.1283 0.374352
\(733\) 30.8428 1.13921 0.569603 0.821920i \(-0.307097\pi\)
0.569603 + 0.821920i \(0.307097\pi\)
\(734\) −19.5178 −0.720416
\(735\) 18.9119 0.697576
\(736\) 6.12526 0.225780
\(737\) −0.0431219 −0.00158841
\(738\) 7.06013 0.259887
\(739\) −33.1652 −1.22000 −0.610001 0.792400i \(-0.708831\pi\)
−0.610001 + 0.792400i \(0.708831\pi\)
\(740\) −2.53567 −0.0932132
\(741\) −8.53894 −0.313686
\(742\) −1.80414 −0.0662322
\(743\) −6.83482 −0.250745 −0.125373 0.992110i \(-0.540013\pi\)
−0.125373 + 0.992110i \(0.540013\pi\)
\(744\) 8.03376 0.294532
\(745\) −46.5416 −1.70515
\(746\) 6.22265 0.227827
\(747\) 14.6054 0.534383
\(748\) 3.08318 0.112732
\(749\) 4.39551 0.160609
\(750\) −5.09400 −0.186006
\(751\) 24.7062 0.901543 0.450771 0.892639i \(-0.351149\pi\)
0.450771 + 0.892639i \(0.351149\pi\)
\(752\) −0.660560 −0.0240882
\(753\) −15.3852 −0.560667
\(754\) −2.61677 −0.0952970
\(755\) −12.5570 −0.456997
\(756\) −0.636539 −0.0231507
\(757\) −31.9271 −1.16041 −0.580205 0.814471i \(-0.697027\pi\)
−0.580205 + 0.814471i \(0.697027\pi\)
\(758\) 20.5389 0.746007
\(759\) −18.8853 −0.685492
\(760\) −19.3687 −0.702578
\(761\) 46.0195 1.66820 0.834102 0.551610i \(-0.185986\pi\)
0.834102 + 0.551610i \(0.185986\pi\)
\(762\) −9.67015 −0.350313
\(763\) 1.42030 0.0514184
\(764\) −5.71664 −0.206821
\(765\) −2.86769 −0.103682
\(766\) −24.5322 −0.886385
\(767\) 1.26426 0.0456496
\(768\) −1.00000 −0.0360844
\(769\) −3.55901 −0.128341 −0.0641707 0.997939i \(-0.520440\pi\)
−0.0641707 + 0.997939i \(0.520440\pi\)
\(770\) 5.62803 0.202820
\(771\) 19.7400 0.710918
\(772\) −18.2524 −0.656920
\(773\) 13.7187 0.493427 0.246714 0.969088i \(-0.420649\pi\)
0.246714 + 0.969088i \(0.420649\pi\)
\(774\) −6.55402 −0.235579
\(775\) 25.8981 0.930288
\(776\) −15.2562 −0.547666
\(777\) 0.562841 0.0201918
\(778\) 14.9943 0.537572
\(779\) −47.6850 −1.70849
\(780\) −3.62550 −0.129814
\(781\) −17.6885 −0.632943
\(782\) −6.12526 −0.219039
\(783\) −2.06981 −0.0739689
\(784\) −6.59482 −0.235529
\(785\) 30.1167 1.07491
\(786\) 12.1575 0.433642
\(787\) 19.6825 0.701606 0.350803 0.936449i \(-0.385909\pi\)
0.350803 + 0.936449i \(0.385909\pi\)
\(788\) 16.0335 0.571170
\(789\) 9.87594 0.351593
\(790\) −20.4432 −0.727336
\(791\) 5.99303 0.213088
\(792\) 3.08318 0.109556
\(793\) −12.8047 −0.454709
\(794\) −16.9911 −0.602990
\(795\) −8.12791 −0.288267
\(796\) 14.7301 0.522094
\(797\) −8.88139 −0.314595 −0.157297 0.987551i \(-0.550278\pi\)
−0.157297 + 0.987551i \(0.550278\pi\)
\(798\) 4.29926 0.152192
\(799\) 0.660560 0.0233689
\(800\) −3.22366 −0.113974
\(801\) 1.32107 0.0466776
\(802\) −9.16169 −0.323510
\(803\) −19.4329 −0.685773
\(804\) −0.0139862 −0.000493254 0
\(805\) −11.1810 −0.394080
\(806\) −10.1567 −0.357756
\(807\) −14.3719 −0.505914
\(808\) −4.52152 −0.159066
\(809\) −10.7058 −0.376395 −0.188198 0.982131i \(-0.560265\pi\)
−0.188198 + 0.982131i \(0.560265\pi\)
\(810\) −2.86769 −0.100760
\(811\) 0.293301 0.0102992 0.00514960 0.999987i \(-0.498361\pi\)
0.00514960 + 0.999987i \(0.498361\pi\)
\(812\) 1.31751 0.0462356
\(813\) 20.9059 0.733201
\(814\) −2.72621 −0.0955536
\(815\) 40.7461 1.42727
\(816\) 1.00000 0.0350070
\(817\) 44.2667 1.54869
\(818\) −9.77838 −0.341893
\(819\) 0.804748 0.0281202
\(820\) −20.2463 −0.707031
\(821\) 40.8843 1.42687 0.713436 0.700720i \(-0.247138\pi\)
0.713436 + 0.700720i \(0.247138\pi\)
\(822\) −16.0035 −0.558185
\(823\) 17.2997 0.603029 0.301514 0.953462i \(-0.402508\pi\)
0.301514 + 0.953462i \(0.402508\pi\)
\(824\) −18.1452 −0.632117
\(825\) 9.93912 0.346036
\(826\) −0.636539 −0.0221480
\(827\) 2.63202 0.0915243 0.0457622 0.998952i \(-0.485428\pi\)
0.0457622 + 0.998952i \(0.485428\pi\)
\(828\) −6.12526 −0.212867
\(829\) −57.2712 −1.98911 −0.994555 0.104213i \(-0.966768\pi\)
−0.994555 + 0.104213i \(0.966768\pi\)
\(830\) −41.8837 −1.45381
\(831\) −20.3650 −0.706454
\(832\) 1.26426 0.0438302
\(833\) 6.59482 0.228497
\(834\) −20.1857 −0.698975
\(835\) 26.6550 0.922435
\(836\) −20.8242 −0.720219
\(837\) −8.03376 −0.277687
\(838\) 12.0030 0.414637
\(839\) −23.8197 −0.822349 −0.411174 0.911557i \(-0.634881\pi\)
−0.411174 + 0.911557i \(0.634881\pi\)
\(840\) 1.82540 0.0629822
\(841\) −24.7159 −0.852272
\(842\) 16.6688 0.574443
\(843\) 6.13616 0.211341
\(844\) 18.1318 0.624124
\(845\) −32.6964 −1.12479
\(846\) 0.660560 0.0227105
\(847\) −0.950999 −0.0326767
\(848\) 2.83430 0.0973303
\(849\) 4.66780 0.160198
\(850\) 3.22366 0.110571
\(851\) 5.41608 0.185661
\(852\) −5.73708 −0.196549
\(853\) 13.3256 0.456260 0.228130 0.973631i \(-0.426739\pi\)
0.228130 + 0.973631i \(0.426739\pi\)
\(854\) 6.44704 0.220613
\(855\) 19.3687 0.662397
\(856\) −6.90533 −0.236019
\(857\) −12.1185 −0.413961 −0.206980 0.978345i \(-0.566364\pi\)
−0.206980 + 0.978345i \(0.566364\pi\)
\(858\) −3.89793 −0.133073
\(859\) 28.5240 0.973226 0.486613 0.873618i \(-0.338232\pi\)
0.486613 + 0.873618i \(0.338232\pi\)
\(860\) 18.7949 0.640901
\(861\) 4.49405 0.153157
\(862\) 8.75516 0.298202
\(863\) 50.5592 1.72105 0.860527 0.509405i \(-0.170135\pi\)
0.860527 + 0.509405i \(0.170135\pi\)
\(864\) 1.00000 0.0340207
\(865\) 38.6963 1.31571
\(866\) 29.7186 1.00988
\(867\) −1.00000 −0.0339618
\(868\) 5.11380 0.173574
\(869\) −21.9793 −0.745598
\(870\) 5.93557 0.201235
\(871\) 0.0176821 0.000599135 0
\(872\) −2.23129 −0.0755610
\(873\) 15.2562 0.516345
\(874\) 41.3708 1.39939
\(875\) −3.24253 −0.109617
\(876\) −6.30289 −0.212955
\(877\) 9.00840 0.304192 0.152096 0.988366i \(-0.451398\pi\)
0.152096 + 0.988366i \(0.451398\pi\)
\(878\) 33.6068 1.13417
\(879\) 25.8627 0.872326
\(880\) −8.84161 −0.298050
\(881\) 3.85028 0.129719 0.0648595 0.997894i \(-0.479340\pi\)
0.0648595 + 0.997894i \(0.479340\pi\)
\(882\) 6.59482 0.222059
\(883\) −12.8248 −0.431589 −0.215795 0.976439i \(-0.569234\pi\)
−0.215795 + 0.976439i \(0.569234\pi\)
\(884\) −1.26426 −0.0425215
\(885\) −2.86769 −0.0963964
\(886\) −21.8571 −0.734304
\(887\) −6.34607 −0.213080 −0.106540 0.994308i \(-0.533977\pi\)
−0.106540 + 0.994308i \(0.533977\pi\)
\(888\) −0.884221 −0.0296725
\(889\) −6.15543 −0.206446
\(890\) −3.78842 −0.126988
\(891\) −3.08318 −0.103290
\(892\) 5.29242 0.177203
\(893\) −4.46151 −0.149299
\(894\) −16.2296 −0.542800
\(895\) −31.0871 −1.03913
\(896\) −0.636539 −0.0212653
\(897\) 7.74390 0.258561
\(898\) −0.330027 −0.0110132
\(899\) 16.6283 0.554586
\(900\) 3.22366 0.107455
\(901\) −2.83430 −0.0944243
\(902\) −21.7676 −0.724783
\(903\) −4.17189 −0.138832
\(904\) −9.41503 −0.313139
\(905\) −1.00562 −0.0334280
\(906\) −4.37879 −0.145475
\(907\) −33.6554 −1.11751 −0.558754 0.829334i \(-0.688720\pi\)
−0.558754 + 0.829334i \(0.688720\pi\)
\(908\) 5.38961 0.178860
\(909\) 4.52152 0.149969
\(910\) −2.30777 −0.0765018
\(911\) 5.90483 0.195636 0.0978179 0.995204i \(-0.468814\pi\)
0.0978179 + 0.995204i \(0.468814\pi\)
\(912\) −6.75412 −0.223651
\(913\) −45.0310 −1.49031
\(914\) −23.9610 −0.792558
\(915\) 29.0448 0.960190
\(916\) −7.41385 −0.244960
\(917\) 7.73870 0.255554
\(918\) −1.00000 −0.0330049
\(919\) 2.81640 0.0929045 0.0464522 0.998921i \(-0.485208\pi\)
0.0464522 + 0.998921i \(0.485208\pi\)
\(920\) 17.5654 0.579113
\(921\) −2.39542 −0.0789317
\(922\) −15.4035 −0.507286
\(923\) 7.25314 0.238740
\(924\) 1.96256 0.0645636
\(925\) −2.85043 −0.0937215
\(926\) −9.07029 −0.298068
\(927\) 18.1452 0.595965
\(928\) −2.06981 −0.0679448
\(929\) −28.6049 −0.938497 −0.469249 0.883066i \(-0.655475\pi\)
−0.469249 + 0.883066i \(0.655475\pi\)
\(930\) 23.0384 0.755457
\(931\) −44.5422 −1.45981
\(932\) −23.6396 −0.774342
\(933\) 2.92768 0.0958478
\(934\) −9.37346 −0.306709
\(935\) 8.84161 0.289151
\(936\) −1.26426 −0.0413235
\(937\) 44.7778 1.46283 0.731414 0.681934i \(-0.238861\pi\)
0.731414 + 0.681934i \(0.238861\pi\)
\(938\) −0.00890274 −0.000290685 0
\(939\) −9.91154 −0.323451
\(940\) −1.89428 −0.0617847
\(941\) −32.3694 −1.05521 −0.527606 0.849489i \(-0.676910\pi\)
−0.527606 + 0.849489i \(0.676910\pi\)
\(942\) 10.5021 0.342175
\(943\) 43.2451 1.40825
\(944\) 1.00000 0.0325472
\(945\) −1.82540 −0.0593802
\(946\) 20.2072 0.656993
\(947\) 18.1673 0.590357 0.295179 0.955442i \(-0.404621\pi\)
0.295179 + 0.955442i \(0.404621\pi\)
\(948\) −7.12879 −0.231532
\(949\) 7.96847 0.258667
\(950\) −21.7730 −0.706409
\(951\) −7.04898 −0.228579
\(952\) 0.636539 0.0206303
\(953\) 44.9009 1.45448 0.727242 0.686382i \(-0.240802\pi\)
0.727242 + 0.686382i \(0.240802\pi\)
\(954\) −2.83430 −0.0917639
\(955\) −16.3936 −0.530483
\(956\) 20.6309 0.667252
\(957\) 6.38159 0.206287
\(958\) −19.9688 −0.645163
\(959\) −10.1868 −0.328950
\(960\) −2.86769 −0.0925544
\(961\) 33.5413 1.08198
\(962\) 1.11788 0.0360419
\(963\) 6.90533 0.222521
\(964\) 19.8421 0.639072
\(965\) −52.3424 −1.68496
\(966\) −3.89897 −0.125447
\(967\) 21.3686 0.687169 0.343585 0.939122i \(-0.388359\pi\)
0.343585 + 0.939122i \(0.388359\pi\)
\(968\) 1.49402 0.0480195
\(969\) 6.75412 0.216974
\(970\) −43.7501 −1.40473
\(971\) −53.7462 −1.72480 −0.862400 0.506228i \(-0.831039\pi\)
−0.862400 + 0.506228i \(0.831039\pi\)
\(972\) −1.00000 −0.0320750
\(973\) −12.8490 −0.411920
\(974\) −2.20781 −0.0707429
\(975\) −4.07553 −0.130521
\(976\) −10.1283 −0.324198
\(977\) −40.8608 −1.30725 −0.653626 0.756818i \(-0.726753\pi\)
−0.653626 + 0.756818i \(0.726753\pi\)
\(978\) 14.2087 0.454343
\(979\) −4.07309 −0.130176
\(980\) −18.9119 −0.604119
\(981\) 2.23129 0.0712396
\(982\) 7.72087 0.246383
\(983\) 39.2707 1.25254 0.626270 0.779606i \(-0.284581\pi\)
0.626270 + 0.779606i \(0.284581\pi\)
\(984\) −7.06013 −0.225069
\(985\) 45.9791 1.46502
\(986\) 2.06981 0.0659161
\(987\) 0.420472 0.0133838
\(988\) 8.53894 0.271660
\(989\) −40.1451 −1.27654
\(990\) 8.84161 0.281005
\(991\) −45.1682 −1.43481 −0.717407 0.696654i \(-0.754671\pi\)
−0.717407 + 0.696654i \(0.754671\pi\)
\(992\) −8.03376 −0.255072
\(993\) −19.4349 −0.616748
\(994\) −3.65188 −0.115831
\(995\) 42.2413 1.33914
\(996\) −14.6054 −0.462789
\(997\) −2.33896 −0.0740755 −0.0370377 0.999314i \(-0.511792\pi\)
−0.0370377 + 0.999314i \(0.511792\pi\)
\(998\) −23.7571 −0.752019
\(999\) 0.884221 0.0279755
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 6018.2.a.s.1.7 8
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
6018.2.a.s.1.7 8 1.1 even 1 trivial