Properties

Label 6018.2.a.bb.1.13
Level $6018$
Weight $2$
Character 6018.1
Self dual yes
Analytic conductor $48.054$
Analytic rank $0$
Dimension $13$
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: \(13\)
Coefficient field: \(\mathbb{Q}[x]/(x^{13} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{13} - 4 x^{12} - 41 x^{11} + 179 x^{10} + 540 x^{9} - 2773 x^{8} - 2260 x^{7} + 17621 x^{6} - 838 x^{5} - 44478 x^{4} + 16472 x^{3} + 29944 x^{2} - 6856 x + 128 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2 \)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.13
Root \(4.08702\) 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)
 
\(f(q)\) \(=\) \(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +4.08702 q^{5} +1.00000 q^{6} -2.27776 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +4.08702 q^{5} +1.00000 q^{6} -2.27776 q^{7} +1.00000 q^{8} +1.00000 q^{9} +4.08702 q^{10} -4.97741 q^{11} +1.00000 q^{12} +3.14470 q^{13} -2.27776 q^{14} +4.08702 q^{15} +1.00000 q^{16} +1.00000 q^{17} +1.00000 q^{18} -1.30689 q^{19} +4.08702 q^{20} -2.27776 q^{21} -4.97741 q^{22} +3.59338 q^{23} +1.00000 q^{24} +11.7038 q^{25} +3.14470 q^{26} +1.00000 q^{27} -2.27776 q^{28} +0.323318 q^{29} +4.08702 q^{30} -1.53298 q^{31} +1.00000 q^{32} -4.97741 q^{33} +1.00000 q^{34} -9.30924 q^{35} +1.00000 q^{36} +6.77537 q^{37} -1.30689 q^{38} +3.14470 q^{39} +4.08702 q^{40} +8.35887 q^{41} -2.27776 q^{42} +5.11297 q^{43} -4.97741 q^{44} +4.08702 q^{45} +3.59338 q^{46} +3.42062 q^{47} +1.00000 q^{48} -1.81183 q^{49} +11.7038 q^{50} +1.00000 q^{51} +3.14470 q^{52} +2.94049 q^{53} +1.00000 q^{54} -20.3428 q^{55} -2.27776 q^{56} -1.30689 q^{57} +0.323318 q^{58} -1.00000 q^{59} +4.08702 q^{60} -7.45651 q^{61} -1.53298 q^{62} -2.27776 q^{63} +1.00000 q^{64} +12.8525 q^{65} -4.97741 q^{66} -11.1237 q^{67} +1.00000 q^{68} +3.59338 q^{69} -9.30924 q^{70} +6.20001 q^{71} +1.00000 q^{72} +8.75380 q^{73} +6.77537 q^{74} +11.7038 q^{75} -1.30689 q^{76} +11.3373 q^{77} +3.14470 q^{78} +9.24674 q^{79} +4.08702 q^{80} +1.00000 q^{81} +8.35887 q^{82} +1.66129 q^{83} -2.27776 q^{84} +4.08702 q^{85} +5.11297 q^{86} +0.323318 q^{87} -4.97741 q^{88} -3.42829 q^{89} +4.08702 q^{90} -7.16287 q^{91} +3.59338 q^{92} -1.53298 q^{93} +3.42062 q^{94} -5.34130 q^{95} +1.00000 q^{96} -8.73640 q^{97} -1.81183 q^{98} -4.97741 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 13 q + 13 q^{2} + 13 q^{3} + 13 q^{4} + 4 q^{5} + 13 q^{6} + 11 q^{7} + 13 q^{8} + 13 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 13 q + 13 q^{2} + 13 q^{3} + 13 q^{4} + 4 q^{5} + 13 q^{6} + 11 q^{7} + 13 q^{8} + 13 q^{9} + 4 q^{10} + 7 q^{11} + 13 q^{12} + 6 q^{13} + 11 q^{14} + 4 q^{15} + 13 q^{16} + 13 q^{17} + 13 q^{18} + 9 q^{19} + 4 q^{20} + 11 q^{21} + 7 q^{22} + 2 q^{23} + 13 q^{24} + 33 q^{25} + 6 q^{26} + 13 q^{27} + 11 q^{28} + 14 q^{29} + 4 q^{30} - 5 q^{31} + 13 q^{32} + 7 q^{33} + 13 q^{34} + 24 q^{35} + 13 q^{36} + 4 q^{37} + 9 q^{38} + 6 q^{39} + 4 q^{40} + 28 q^{41} + 11 q^{42} + q^{43} + 7 q^{44} + 4 q^{45} + 2 q^{46} + 12 q^{47} + 13 q^{48} + 32 q^{49} + 33 q^{50} + 13 q^{51} + 6 q^{52} + 22 q^{53} + 13 q^{54} - 7 q^{55} + 11 q^{56} + 9 q^{57} + 14 q^{58} - 13 q^{59} + 4 q^{60} - 9 q^{61} - 5 q^{62} + 11 q^{63} + 13 q^{64} + 34 q^{65} + 7 q^{66} + 26 q^{67} + 13 q^{68} + 2 q^{69} + 24 q^{70} + 8 q^{71} + 13 q^{72} + 4 q^{73} + 4 q^{74} + 33 q^{75} + 9 q^{76} + 38 q^{77} + 6 q^{78} - 17 q^{79} + 4 q^{80} + 13 q^{81} + 28 q^{82} + 14 q^{83} + 11 q^{84} + 4 q^{85} + q^{86} + 14 q^{87} + 7 q^{88} + 19 q^{89} + 4 q^{90} - 5 q^{91} + 2 q^{92} - 5 q^{93} + 12 q^{94} + 25 q^{95} + 13 q^{96} - 5 q^{97} + 32 q^{98} + 7 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000 0.707107
\(3\) 1.00000 0.577350
\(4\) 1.00000 0.500000
\(5\) 4.08702 1.82777 0.913886 0.405971i \(-0.133067\pi\)
0.913886 + 0.405971i \(0.133067\pi\)
\(6\) 1.00000 0.408248
\(7\) −2.27776 −0.860911 −0.430455 0.902612i \(-0.641647\pi\)
−0.430455 + 0.902612i \(0.641647\pi\)
\(8\) 1.00000 0.353553
\(9\) 1.00000 0.333333
\(10\) 4.08702 1.29243
\(11\) −4.97741 −1.50075 −0.750373 0.661015i \(-0.770126\pi\)
−0.750373 + 0.661015i \(0.770126\pi\)
\(12\) 1.00000 0.288675
\(13\) 3.14470 0.872184 0.436092 0.899902i \(-0.356362\pi\)
0.436092 + 0.899902i \(0.356362\pi\)
\(14\) −2.27776 −0.608756
\(15\) 4.08702 1.05526
\(16\) 1.00000 0.250000
\(17\) 1.00000 0.242536
\(18\) 1.00000 0.235702
\(19\) −1.30689 −0.299822 −0.149911 0.988699i \(-0.547899\pi\)
−0.149911 + 0.988699i \(0.547899\pi\)
\(20\) 4.08702 0.913886
\(21\) −2.27776 −0.497047
\(22\) −4.97741 −1.06119
\(23\) 3.59338 0.749272 0.374636 0.927172i \(-0.377768\pi\)
0.374636 + 0.927172i \(0.377768\pi\)
\(24\) 1.00000 0.204124
\(25\) 11.7038 2.34075
\(26\) 3.14470 0.616727
\(27\) 1.00000 0.192450
\(28\) −2.27776 −0.430455
\(29\) 0.323318 0.0600386 0.0300193 0.999549i \(-0.490443\pi\)
0.0300193 + 0.999549i \(0.490443\pi\)
\(30\) 4.08702 0.746185
\(31\) −1.53298 −0.275332 −0.137666 0.990479i \(-0.543960\pi\)
−0.137666 + 0.990479i \(0.543960\pi\)
\(32\) 1.00000 0.176777
\(33\) −4.97741 −0.866456
\(34\) 1.00000 0.171499
\(35\) −9.30924 −1.57355
\(36\) 1.00000 0.166667
\(37\) 6.77537 1.11386 0.556932 0.830558i \(-0.311978\pi\)
0.556932 + 0.830558i \(0.311978\pi\)
\(38\) −1.30689 −0.212006
\(39\) 3.14470 0.503556
\(40\) 4.08702 0.646215
\(41\) 8.35887 1.30544 0.652718 0.757601i \(-0.273629\pi\)
0.652718 + 0.757601i \(0.273629\pi\)
\(42\) −2.27776 −0.351465
\(43\) 5.11297 0.779720 0.389860 0.920874i \(-0.372523\pi\)
0.389860 + 0.920874i \(0.372523\pi\)
\(44\) −4.97741 −0.750373
\(45\) 4.08702 0.609257
\(46\) 3.59338 0.529816
\(47\) 3.42062 0.498948 0.249474 0.968381i \(-0.419742\pi\)
0.249474 + 0.968381i \(0.419742\pi\)
\(48\) 1.00000 0.144338
\(49\) −1.81183 −0.258832
\(50\) 11.7038 1.65516
\(51\) 1.00000 0.140028
\(52\) 3.14470 0.436092
\(53\) 2.94049 0.403907 0.201953 0.979395i \(-0.435271\pi\)
0.201953 + 0.979395i \(0.435271\pi\)
\(54\) 1.00000 0.136083
\(55\) −20.3428 −2.74302
\(56\) −2.27776 −0.304378
\(57\) −1.30689 −0.173102
\(58\) 0.323318 0.0424537
\(59\) −1.00000 −0.130189
\(60\) 4.08702 0.527632
\(61\) −7.45651 −0.954708 −0.477354 0.878711i \(-0.658404\pi\)
−0.477354 + 0.878711i \(0.658404\pi\)
\(62\) −1.53298 −0.194689
\(63\) −2.27776 −0.286970
\(64\) 1.00000 0.125000
\(65\) 12.8525 1.59415
\(66\) −4.97741 −0.612677
\(67\) −11.1237 −1.35898 −0.679488 0.733686i \(-0.737798\pi\)
−0.679488 + 0.733686i \(0.737798\pi\)
\(68\) 1.00000 0.121268
\(69\) 3.59338 0.432593
\(70\) −9.30924 −1.11267
\(71\) 6.20001 0.735806 0.367903 0.929864i \(-0.380076\pi\)
0.367903 + 0.929864i \(0.380076\pi\)
\(72\) 1.00000 0.117851
\(73\) 8.75380 1.02455 0.512277 0.858820i \(-0.328802\pi\)
0.512277 + 0.858820i \(0.328802\pi\)
\(74\) 6.77537 0.787621
\(75\) 11.7038 1.35143
\(76\) −1.30689 −0.149911
\(77\) 11.3373 1.29201
\(78\) 3.14470 0.356068
\(79\) 9.24674 1.04034 0.520170 0.854063i \(-0.325869\pi\)
0.520170 + 0.854063i \(0.325869\pi\)
\(80\) 4.08702 0.456943
\(81\) 1.00000 0.111111
\(82\) 8.35887 0.923082
\(83\) 1.66129 0.182350 0.0911752 0.995835i \(-0.470938\pi\)
0.0911752 + 0.995835i \(0.470938\pi\)
\(84\) −2.27776 −0.248524
\(85\) 4.08702 0.443300
\(86\) 5.11297 0.551345
\(87\) 0.323318 0.0346633
\(88\) −4.97741 −0.530594
\(89\) −3.42829 −0.363398 −0.181699 0.983354i \(-0.558160\pi\)
−0.181699 + 0.983354i \(0.558160\pi\)
\(90\) 4.08702 0.430810
\(91\) −7.16287 −0.750873
\(92\) 3.59338 0.374636
\(93\) −1.53298 −0.158963
\(94\) 3.42062 0.352810
\(95\) −5.34130 −0.548006
\(96\) 1.00000 0.102062
\(97\) −8.73640 −0.887047 −0.443524 0.896263i \(-0.646272\pi\)
−0.443524 + 0.896263i \(0.646272\pi\)
\(98\) −1.81183 −0.183022
\(99\) −4.97741 −0.500249
\(100\) 11.7038 1.17038
\(101\) 3.85469 0.383556 0.191778 0.981438i \(-0.438575\pi\)
0.191778 + 0.981438i \(0.438575\pi\)
\(102\) 1.00000 0.0990148
\(103\) −2.37041 −0.233563 −0.116782 0.993158i \(-0.537258\pi\)
−0.116782 + 0.993158i \(0.537258\pi\)
\(104\) 3.14470 0.308364
\(105\) −9.30924 −0.908489
\(106\) 2.94049 0.285605
\(107\) 0.620217 0.0599587 0.0299793 0.999551i \(-0.490456\pi\)
0.0299793 + 0.999551i \(0.490456\pi\)
\(108\) 1.00000 0.0962250
\(109\) 16.0601 1.53827 0.769137 0.639084i \(-0.220686\pi\)
0.769137 + 0.639084i \(0.220686\pi\)
\(110\) −20.3428 −1.93961
\(111\) 6.77537 0.643090
\(112\) −2.27776 −0.215228
\(113\) −2.60248 −0.244821 −0.122411 0.992480i \(-0.539062\pi\)
−0.122411 + 0.992480i \(0.539062\pi\)
\(114\) −1.30689 −0.122402
\(115\) 14.6862 1.36950
\(116\) 0.323318 0.0300193
\(117\) 3.14470 0.290728
\(118\) −1.00000 −0.0920575
\(119\) −2.27776 −0.208802
\(120\) 4.08702 0.373092
\(121\) 13.7746 1.25224
\(122\) −7.45651 −0.675080
\(123\) 8.35887 0.753693
\(124\) −1.53298 −0.137666
\(125\) 27.3984 2.45059
\(126\) −2.27776 −0.202919
\(127\) 20.7461 1.84092 0.920458 0.390841i \(-0.127816\pi\)
0.920458 + 0.390841i \(0.127816\pi\)
\(128\) 1.00000 0.0883883
\(129\) 5.11297 0.450172
\(130\) 12.8525 1.12724
\(131\) −20.2666 −1.77070 −0.885349 0.464928i \(-0.846080\pi\)
−0.885349 + 0.464928i \(0.846080\pi\)
\(132\) −4.97741 −0.433228
\(133\) 2.97679 0.258120
\(134\) −11.1237 −0.960942
\(135\) 4.08702 0.351755
\(136\) 1.00000 0.0857493
\(137\) −11.6936 −0.999053 −0.499526 0.866299i \(-0.666493\pi\)
−0.499526 + 0.866299i \(0.666493\pi\)
\(138\) 3.59338 0.305889
\(139\) −6.48633 −0.550163 −0.275082 0.961421i \(-0.588705\pi\)
−0.275082 + 0.961421i \(0.588705\pi\)
\(140\) −9.30924 −0.786774
\(141\) 3.42062 0.288068
\(142\) 6.20001 0.520293
\(143\) −15.6525 −1.30893
\(144\) 1.00000 0.0833333
\(145\) 1.32141 0.109737
\(146\) 8.75380 0.724469
\(147\) −1.81183 −0.149437
\(148\) 6.77537 0.556932
\(149\) 0.843435 0.0690969 0.0345485 0.999403i \(-0.489001\pi\)
0.0345485 + 0.999403i \(0.489001\pi\)
\(150\) 11.7038 0.955607
\(151\) −4.52554 −0.368284 −0.184142 0.982900i \(-0.558951\pi\)
−0.184142 + 0.982900i \(0.558951\pi\)
\(152\) −1.30689 −0.106003
\(153\) 1.00000 0.0808452
\(154\) 11.3373 0.913588
\(155\) −6.26534 −0.503244
\(156\) 3.14470 0.251778
\(157\) −18.8717 −1.50612 −0.753061 0.657951i \(-0.771423\pi\)
−0.753061 + 0.657951i \(0.771423\pi\)
\(158\) 9.24674 0.735631
\(159\) 2.94049 0.233196
\(160\) 4.08702 0.323107
\(161\) −8.18485 −0.645057
\(162\) 1.00000 0.0785674
\(163\) 7.35972 0.576458 0.288229 0.957562i \(-0.406934\pi\)
0.288229 + 0.957562i \(0.406934\pi\)
\(164\) 8.35887 0.652718
\(165\) −20.3428 −1.58368
\(166\) 1.66129 0.128941
\(167\) −7.07794 −0.547708 −0.273854 0.961771i \(-0.588298\pi\)
−0.273854 + 0.961771i \(0.588298\pi\)
\(168\) −2.27776 −0.175733
\(169\) −3.11083 −0.239295
\(170\) 4.08702 0.313460
\(171\) −1.30689 −0.0999407
\(172\) 5.11297 0.389860
\(173\) −1.83515 −0.139524 −0.0697620 0.997564i \(-0.522224\pi\)
−0.0697620 + 0.997564i \(0.522224\pi\)
\(174\) 0.323318 0.0245107
\(175\) −26.6583 −2.01518
\(176\) −4.97741 −0.375186
\(177\) −1.00000 −0.0751646
\(178\) −3.42829 −0.256961
\(179\) 8.48650 0.634311 0.317155 0.948374i \(-0.397272\pi\)
0.317155 + 0.948374i \(0.397272\pi\)
\(180\) 4.08702 0.304629
\(181\) 18.8006 1.39744 0.698719 0.715396i \(-0.253754\pi\)
0.698719 + 0.715396i \(0.253754\pi\)
\(182\) −7.16287 −0.530947
\(183\) −7.45651 −0.551201
\(184\) 3.59338 0.264908
\(185\) 27.6911 2.03589
\(186\) −1.53298 −0.112404
\(187\) −4.97741 −0.363984
\(188\) 3.42062 0.249474
\(189\) −2.27776 −0.165682
\(190\) −5.34130 −0.387499
\(191\) 7.35714 0.532344 0.266172 0.963926i \(-0.414241\pi\)
0.266172 + 0.963926i \(0.414241\pi\)
\(192\) 1.00000 0.0721688
\(193\) −0.399035 −0.0287232 −0.0143616 0.999897i \(-0.504572\pi\)
−0.0143616 + 0.999897i \(0.504572\pi\)
\(194\) −8.73640 −0.627237
\(195\) 12.8525 0.920385
\(196\) −1.81183 −0.129416
\(197\) −23.3060 −1.66048 −0.830242 0.557403i \(-0.811798\pi\)
−0.830242 + 0.557403i \(0.811798\pi\)
\(198\) −4.97741 −0.353729
\(199\) −23.2534 −1.64839 −0.824195 0.566307i \(-0.808372\pi\)
−0.824195 + 0.566307i \(0.808372\pi\)
\(200\) 11.7038 0.827580
\(201\) −11.1237 −0.784606
\(202\) 3.85469 0.271215
\(203\) −0.736440 −0.0516879
\(204\) 1.00000 0.0700140
\(205\) 34.1629 2.38604
\(206\) −2.37041 −0.165154
\(207\) 3.59338 0.249757
\(208\) 3.14470 0.218046
\(209\) 6.50495 0.449957
\(210\) −9.30924 −0.642399
\(211\) 20.0614 1.38109 0.690543 0.723291i \(-0.257372\pi\)
0.690543 + 0.723291i \(0.257372\pi\)
\(212\) 2.94049 0.201953
\(213\) 6.20001 0.424818
\(214\) 0.620217 0.0423972
\(215\) 20.8968 1.42515
\(216\) 1.00000 0.0680414
\(217\) 3.49176 0.237036
\(218\) 16.0601 1.08772
\(219\) 8.75380 0.591527
\(220\) −20.3428 −1.37151
\(221\) 3.14470 0.211536
\(222\) 6.77537 0.454733
\(223\) −10.2655 −0.687425 −0.343713 0.939075i \(-0.611685\pi\)
−0.343713 + 0.939075i \(0.611685\pi\)
\(224\) −2.27776 −0.152189
\(225\) 11.7038 0.780250
\(226\) −2.60248 −0.173115
\(227\) −23.0457 −1.52960 −0.764799 0.644269i \(-0.777162\pi\)
−0.764799 + 0.644269i \(0.777162\pi\)
\(228\) −1.30689 −0.0865512
\(229\) −20.9627 −1.38526 −0.692628 0.721295i \(-0.743547\pi\)
−0.692628 + 0.721295i \(0.743547\pi\)
\(230\) 14.6862 0.968382
\(231\) 11.3373 0.745941
\(232\) 0.323318 0.0212269
\(233\) −17.8963 −1.17242 −0.586212 0.810158i \(-0.699381\pi\)
−0.586212 + 0.810158i \(0.699381\pi\)
\(234\) 3.14470 0.205576
\(235\) 13.9801 0.911964
\(236\) −1.00000 −0.0650945
\(237\) 9.24674 0.600641
\(238\) −2.27776 −0.147645
\(239\) 0.642085 0.0415331 0.0207665 0.999784i \(-0.493389\pi\)
0.0207665 + 0.999784i \(0.493389\pi\)
\(240\) 4.08702 0.263816
\(241\) −4.52390 −0.291410 −0.145705 0.989328i \(-0.546545\pi\)
−0.145705 + 0.989328i \(0.546545\pi\)
\(242\) 13.7746 0.885466
\(243\) 1.00000 0.0641500
\(244\) −7.45651 −0.477354
\(245\) −7.40498 −0.473087
\(246\) 8.35887 0.532942
\(247\) −4.10980 −0.261500
\(248\) −1.53298 −0.0973446
\(249\) 1.66129 0.105280
\(250\) 27.3984 1.73283
\(251\) −23.0526 −1.45507 −0.727534 0.686072i \(-0.759334\pi\)
−0.727534 + 0.686072i \(0.759334\pi\)
\(252\) −2.27776 −0.143485
\(253\) −17.8857 −1.12447
\(254\) 20.7461 1.30172
\(255\) 4.08702 0.255939
\(256\) 1.00000 0.0625000
\(257\) 14.5705 0.908882 0.454441 0.890777i \(-0.349839\pi\)
0.454441 + 0.890777i \(0.349839\pi\)
\(258\) 5.11297 0.318319
\(259\) −15.4326 −0.958938
\(260\) 12.8525 0.797077
\(261\) 0.323318 0.0200129
\(262\) −20.2666 −1.25207
\(263\) 8.13918 0.501883 0.250942 0.968002i \(-0.419260\pi\)
0.250942 + 0.968002i \(0.419260\pi\)
\(264\) −4.97741 −0.306338
\(265\) 12.0178 0.738249
\(266\) 2.97679 0.182518
\(267\) −3.42829 −0.209808
\(268\) −11.1237 −0.679488
\(269\) 20.6899 1.26149 0.630744 0.775991i \(-0.282750\pi\)
0.630744 + 0.775991i \(0.282750\pi\)
\(270\) 4.08702 0.248728
\(271\) −9.74484 −0.591957 −0.295978 0.955195i \(-0.595646\pi\)
−0.295978 + 0.955195i \(0.595646\pi\)
\(272\) 1.00000 0.0606339
\(273\) −7.16287 −0.433517
\(274\) −11.6936 −0.706437
\(275\) −58.2544 −3.51287
\(276\) 3.59338 0.216296
\(277\) 3.66544 0.220235 0.110117 0.993919i \(-0.464877\pi\)
0.110117 + 0.993919i \(0.464877\pi\)
\(278\) −6.48633 −0.389024
\(279\) −1.53298 −0.0917773
\(280\) −9.30924 −0.556334
\(281\) −10.0881 −0.601807 −0.300904 0.953655i \(-0.597288\pi\)
−0.300904 + 0.953655i \(0.597288\pi\)
\(282\) 3.42062 0.203695
\(283\) −22.8465 −1.35809 −0.679043 0.734099i \(-0.737605\pi\)
−0.679043 + 0.734099i \(0.737605\pi\)
\(284\) 6.20001 0.367903
\(285\) −5.34130 −0.316392
\(286\) −15.6525 −0.925551
\(287\) −19.0395 −1.12386
\(288\) 1.00000 0.0589256
\(289\) 1.00000 0.0588235
\(290\) 1.32141 0.0775957
\(291\) −8.73640 −0.512137
\(292\) 8.75380 0.512277
\(293\) −16.9859 −0.992329 −0.496164 0.868229i \(-0.665259\pi\)
−0.496164 + 0.868229i \(0.665259\pi\)
\(294\) −1.81183 −0.105668
\(295\) −4.08702 −0.237956
\(296\) 6.77537 0.393810
\(297\) −4.97741 −0.288819
\(298\) 0.843435 0.0488589
\(299\) 11.3001 0.653504
\(300\) 11.7038 0.675716
\(301\) −11.6461 −0.671269
\(302\) −4.52554 −0.260416
\(303\) 3.85469 0.221446
\(304\) −1.30689 −0.0749555
\(305\) −30.4749 −1.74499
\(306\) 1.00000 0.0571662
\(307\) 28.6640 1.63594 0.817970 0.575261i \(-0.195100\pi\)
0.817970 + 0.575261i \(0.195100\pi\)
\(308\) 11.3373 0.646004
\(309\) −2.37041 −0.134848
\(310\) −6.26534 −0.355847
\(311\) −12.3768 −0.701826 −0.350913 0.936408i \(-0.614129\pi\)
−0.350913 + 0.936408i \(0.614129\pi\)
\(312\) 3.14470 0.178034
\(313\) −21.1662 −1.19638 −0.598191 0.801353i \(-0.704114\pi\)
−0.598191 + 0.801353i \(0.704114\pi\)
\(314\) −18.8717 −1.06499
\(315\) −9.30924 −0.524516
\(316\) 9.24674 0.520170
\(317\) −20.5229 −1.15268 −0.576340 0.817210i \(-0.695520\pi\)
−0.576340 + 0.817210i \(0.695520\pi\)
\(318\) 2.94049 0.164894
\(319\) −1.60929 −0.0901027
\(320\) 4.08702 0.228471
\(321\) 0.620217 0.0346172
\(322\) −8.18485 −0.456124
\(323\) −1.30689 −0.0727175
\(324\) 1.00000 0.0555556
\(325\) 36.8048 2.04157
\(326\) 7.35972 0.407617
\(327\) 16.0601 0.888123
\(328\) 8.35887 0.461541
\(329\) −7.79133 −0.429550
\(330\) −20.3428 −1.11983
\(331\) −2.43796 −0.134003 −0.0670013 0.997753i \(-0.521343\pi\)
−0.0670013 + 0.997753i \(0.521343\pi\)
\(332\) 1.66129 0.0911752
\(333\) 6.77537 0.371288
\(334\) −7.07794 −0.387288
\(335\) −45.4628 −2.48390
\(336\) −2.27776 −0.124262
\(337\) −13.2121 −0.719708 −0.359854 0.933009i \(-0.617173\pi\)
−0.359854 + 0.933009i \(0.617173\pi\)
\(338\) −3.11083 −0.169207
\(339\) −2.60248 −0.141348
\(340\) 4.08702 0.221650
\(341\) 7.63029 0.413203
\(342\) −1.30689 −0.0706687
\(343\) 20.0712 1.08374
\(344\) 5.11297 0.275673
\(345\) 14.6862 0.790681
\(346\) −1.83515 −0.0986583
\(347\) −20.3262 −1.09117 −0.545584 0.838056i \(-0.683692\pi\)
−0.545584 + 0.838056i \(0.683692\pi\)
\(348\) 0.323318 0.0173317
\(349\) 33.8846 1.81380 0.906901 0.421343i \(-0.138441\pi\)
0.906901 + 0.421343i \(0.138441\pi\)
\(350\) −26.6583 −1.42495
\(351\) 3.14470 0.167852
\(352\) −4.97741 −0.265297
\(353\) 22.9604 1.22206 0.611031 0.791607i \(-0.290755\pi\)
0.611031 + 0.791607i \(0.290755\pi\)
\(354\) −1.00000 −0.0531494
\(355\) 25.3396 1.34488
\(356\) −3.42829 −0.181699
\(357\) −2.27776 −0.120552
\(358\) 8.48650 0.448525
\(359\) 0.852062 0.0449701 0.0224851 0.999747i \(-0.492842\pi\)
0.0224851 + 0.999747i \(0.492842\pi\)
\(360\) 4.08702 0.215405
\(361\) −17.2920 −0.910107
\(362\) 18.8006 0.988138
\(363\) 13.7746 0.722980
\(364\) −7.16287 −0.375436
\(365\) 35.7770 1.87265
\(366\) −7.45651 −0.389758
\(367\) −20.1729 −1.05301 −0.526507 0.850171i \(-0.676499\pi\)
−0.526507 + 0.850171i \(0.676499\pi\)
\(368\) 3.59338 0.187318
\(369\) 8.35887 0.435145
\(370\) 27.6911 1.43959
\(371\) −6.69771 −0.347728
\(372\) −1.53298 −0.0794815
\(373\) 6.92011 0.358310 0.179155 0.983821i \(-0.442664\pi\)
0.179155 + 0.983821i \(0.442664\pi\)
\(374\) −4.97741 −0.257376
\(375\) 27.3984 1.41485
\(376\) 3.42062 0.176405
\(377\) 1.01674 0.0523648
\(378\) −2.27776 −0.117155
\(379\) 19.8059 1.01736 0.508679 0.860956i \(-0.330134\pi\)
0.508679 + 0.860956i \(0.330134\pi\)
\(380\) −5.34130 −0.274003
\(381\) 20.7461 1.06285
\(382\) 7.35714 0.376424
\(383\) −3.88159 −0.198340 −0.0991700 0.995071i \(-0.531619\pi\)
−0.0991700 + 0.995071i \(0.531619\pi\)
\(384\) 1.00000 0.0510310
\(385\) 46.3359 2.36150
\(386\) −0.399035 −0.0203104
\(387\) 5.11297 0.259907
\(388\) −8.73640 −0.443524
\(389\) 29.4234 1.49182 0.745912 0.666044i \(-0.232014\pi\)
0.745912 + 0.666044i \(0.232014\pi\)
\(390\) 12.8525 0.650811
\(391\) 3.59338 0.181725
\(392\) −1.81183 −0.0915111
\(393\) −20.2666 −1.02231
\(394\) −23.3060 −1.17414
\(395\) 37.7917 1.90150
\(396\) −4.97741 −0.250124
\(397\) −25.6566 −1.28767 −0.643834 0.765165i \(-0.722657\pi\)
−0.643834 + 0.765165i \(0.722657\pi\)
\(398\) −23.2534 −1.16559
\(399\) 2.97679 0.149026
\(400\) 11.7038 0.585188
\(401\) −18.3323 −0.915472 −0.457736 0.889088i \(-0.651339\pi\)
−0.457736 + 0.889088i \(0.651339\pi\)
\(402\) −11.1237 −0.554800
\(403\) −4.82078 −0.240140
\(404\) 3.85469 0.191778
\(405\) 4.08702 0.203086
\(406\) −0.736440 −0.0365489
\(407\) −33.7238 −1.67163
\(408\) 1.00000 0.0495074
\(409\) −19.2136 −0.950053 −0.475027 0.879971i \(-0.657562\pi\)
−0.475027 + 0.879971i \(0.657562\pi\)
\(410\) 34.1629 1.68718
\(411\) −11.6936 −0.576803
\(412\) −2.37041 −0.116782
\(413\) 2.27776 0.112081
\(414\) 3.59338 0.176605
\(415\) 6.78973 0.333295
\(416\) 3.14470 0.154182
\(417\) −6.48633 −0.317637
\(418\) 6.50495 0.318167
\(419\) 9.40926 0.459672 0.229836 0.973229i \(-0.426181\pi\)
0.229836 + 0.973229i \(0.426181\pi\)
\(420\) −9.30924 −0.454244
\(421\) 9.54620 0.465253 0.232627 0.972566i \(-0.425268\pi\)
0.232627 + 0.972566i \(0.425268\pi\)
\(422\) 20.0614 0.976575
\(423\) 3.42062 0.166316
\(424\) 2.94049 0.142803
\(425\) 11.7038 0.567715
\(426\) 6.20001 0.300391
\(427\) 16.9841 0.821918
\(428\) 0.620217 0.0299793
\(429\) −15.6525 −0.755709
\(430\) 20.8968 1.00773
\(431\) −3.13096 −0.150813 −0.0754066 0.997153i \(-0.524025\pi\)
−0.0754066 + 0.997153i \(0.524025\pi\)
\(432\) 1.00000 0.0481125
\(433\) 16.1020 0.773812 0.386906 0.922119i \(-0.373544\pi\)
0.386906 + 0.922119i \(0.373544\pi\)
\(434\) 3.49176 0.167610
\(435\) 1.32141 0.0633567
\(436\) 16.0601 0.769137
\(437\) −4.69617 −0.224648
\(438\) 8.75380 0.418273
\(439\) −35.1537 −1.67779 −0.838897 0.544291i \(-0.816799\pi\)
−0.838897 + 0.544291i \(0.816799\pi\)
\(440\) −20.3428 −0.969804
\(441\) −1.81183 −0.0862775
\(442\) 3.14470 0.149578
\(443\) 17.5708 0.834812 0.417406 0.908720i \(-0.362939\pi\)
0.417406 + 0.908720i \(0.362939\pi\)
\(444\) 6.77537 0.321545
\(445\) −14.0115 −0.664209
\(446\) −10.2655 −0.486083
\(447\) 0.843435 0.0398931
\(448\) −2.27776 −0.107614
\(449\) −26.6121 −1.25590 −0.627951 0.778253i \(-0.716106\pi\)
−0.627951 + 0.778253i \(0.716106\pi\)
\(450\) 11.7038 0.551720
\(451\) −41.6055 −1.95913
\(452\) −2.60248 −0.122411
\(453\) −4.52554 −0.212629
\(454\) −23.0457 −1.08159
\(455\) −29.2748 −1.37242
\(456\) −1.30689 −0.0612009
\(457\) 7.42520 0.347336 0.173668 0.984804i \(-0.444438\pi\)
0.173668 + 0.984804i \(0.444438\pi\)
\(458\) −20.9627 −0.979524
\(459\) 1.00000 0.0466760
\(460\) 14.6862 0.684750
\(461\) −5.40610 −0.251787 −0.125893 0.992044i \(-0.540180\pi\)
−0.125893 + 0.992044i \(0.540180\pi\)
\(462\) 11.3373 0.527460
\(463\) −15.3768 −0.714619 −0.357309 0.933986i \(-0.616306\pi\)
−0.357309 + 0.933986i \(0.616306\pi\)
\(464\) 0.323318 0.0150097
\(465\) −6.26534 −0.290548
\(466\) −17.8963 −0.829028
\(467\) −28.9318 −1.33881 −0.669403 0.742900i \(-0.733450\pi\)
−0.669403 + 0.742900i \(0.733450\pi\)
\(468\) 3.14470 0.145364
\(469\) 25.3371 1.16996
\(470\) 13.9801 0.644856
\(471\) −18.8717 −0.869560
\(472\) −1.00000 −0.0460287
\(473\) −25.4493 −1.17016
\(474\) 9.24674 0.424717
\(475\) −15.2956 −0.701809
\(476\) −2.27776 −0.104401
\(477\) 2.94049 0.134636
\(478\) 0.642085 0.0293683
\(479\) −9.35258 −0.427330 −0.213665 0.976907i \(-0.568540\pi\)
−0.213665 + 0.976907i \(0.568540\pi\)
\(480\) 4.08702 0.186546
\(481\) 21.3065 0.971495
\(482\) −4.52390 −0.206058
\(483\) −8.18485 −0.372424
\(484\) 13.7746 0.626119
\(485\) −35.7059 −1.62132
\(486\) 1.00000 0.0453609
\(487\) −14.9865 −0.679103 −0.339551 0.940588i \(-0.610275\pi\)
−0.339551 + 0.940588i \(0.610275\pi\)
\(488\) −7.45651 −0.337540
\(489\) 7.35972 0.332818
\(490\) −7.40498 −0.334523
\(491\) 11.4391 0.516241 0.258121 0.966113i \(-0.416897\pi\)
0.258121 + 0.966113i \(0.416897\pi\)
\(492\) 8.35887 0.376847
\(493\) 0.323318 0.0145615
\(494\) −4.10980 −0.184908
\(495\) −20.3428 −0.914340
\(496\) −1.53298 −0.0688330
\(497\) −14.1221 −0.633463
\(498\) 1.66129 0.0744442
\(499\) −25.4224 −1.13806 −0.569031 0.822316i \(-0.692681\pi\)
−0.569031 + 0.822316i \(0.692681\pi\)
\(500\) 27.3984 1.22529
\(501\) −7.07794 −0.316219
\(502\) −23.0526 −1.02889
\(503\) −11.5767 −0.516178 −0.258089 0.966121i \(-0.583093\pi\)
−0.258089 + 0.966121i \(0.583093\pi\)
\(504\) −2.27776 −0.101459
\(505\) 15.7542 0.701053
\(506\) −17.8857 −0.795118
\(507\) −3.11083 −0.138157
\(508\) 20.7461 0.920458
\(509\) 34.6216 1.53457 0.767287 0.641304i \(-0.221606\pi\)
0.767287 + 0.641304i \(0.221606\pi\)
\(510\) 4.08702 0.180976
\(511\) −19.9390 −0.882050
\(512\) 1.00000 0.0441942
\(513\) −1.30689 −0.0577008
\(514\) 14.5705 0.642677
\(515\) −9.68791 −0.426900
\(516\) 5.11297 0.225086
\(517\) −17.0258 −0.748794
\(518\) −15.4326 −0.678071
\(519\) −1.83515 −0.0805542
\(520\) 12.8525 0.563618
\(521\) 26.1044 1.14366 0.571828 0.820374i \(-0.306235\pi\)
0.571828 + 0.820374i \(0.306235\pi\)
\(522\) 0.323318 0.0141512
\(523\) 18.1012 0.791510 0.395755 0.918356i \(-0.370483\pi\)
0.395755 + 0.918356i \(0.370483\pi\)
\(524\) −20.2666 −0.885349
\(525\) −26.6583 −1.16346
\(526\) 8.13918 0.354885
\(527\) −1.53298 −0.0667778
\(528\) −4.97741 −0.216614
\(529\) −10.0876 −0.438591
\(530\) 12.0178 0.522021
\(531\) −1.00000 −0.0433963
\(532\) 2.97679 0.129060
\(533\) 26.2862 1.13858
\(534\) −3.42829 −0.148357
\(535\) 2.53484 0.109591
\(536\) −11.1237 −0.480471
\(537\) 8.48650 0.366219
\(538\) 20.6899 0.892006
\(539\) 9.01821 0.388442
\(540\) 4.08702 0.175877
\(541\) 26.4961 1.13916 0.569578 0.821937i \(-0.307107\pi\)
0.569578 + 0.821937i \(0.307107\pi\)
\(542\) −9.74484 −0.418577
\(543\) 18.8006 0.806812
\(544\) 1.00000 0.0428746
\(545\) 65.6378 2.81161
\(546\) −7.16287 −0.306543
\(547\) 18.8129 0.804383 0.402191 0.915556i \(-0.368249\pi\)
0.402191 + 0.915556i \(0.368249\pi\)
\(548\) −11.6936 −0.499526
\(549\) −7.45651 −0.318236
\(550\) −58.2544 −2.48397
\(551\) −0.422542 −0.0180009
\(552\) 3.59338 0.152945
\(553\) −21.0618 −0.895640
\(554\) 3.66544 0.155730
\(555\) 27.6911 1.17542
\(556\) −6.48633 −0.275082
\(557\) 38.2073 1.61889 0.809447 0.587192i \(-0.199767\pi\)
0.809447 + 0.587192i \(0.199767\pi\)
\(558\) −1.53298 −0.0648964
\(559\) 16.0788 0.680059
\(560\) −9.30924 −0.393387
\(561\) −4.97741 −0.210146
\(562\) −10.0881 −0.425542
\(563\) −0.923939 −0.0389394 −0.0194697 0.999810i \(-0.506198\pi\)
−0.0194697 + 0.999810i \(0.506198\pi\)
\(564\) 3.42062 0.144034
\(565\) −10.6364 −0.447477
\(566\) −22.8465 −0.960311
\(567\) −2.27776 −0.0956568
\(568\) 6.20001 0.260147
\(569\) −25.0704 −1.05101 −0.525503 0.850792i \(-0.676123\pi\)
−0.525503 + 0.850792i \(0.676123\pi\)
\(570\) −5.34130 −0.223723
\(571\) 8.40864 0.351891 0.175945 0.984400i \(-0.443702\pi\)
0.175945 + 0.984400i \(0.443702\pi\)
\(572\) −15.6525 −0.654463
\(573\) 7.35714 0.307349
\(574\) −19.0395 −0.794692
\(575\) 42.0561 1.75386
\(576\) 1.00000 0.0416667
\(577\) −21.7603 −0.905893 −0.452946 0.891538i \(-0.649627\pi\)
−0.452946 + 0.891538i \(0.649627\pi\)
\(578\) 1.00000 0.0415945
\(579\) −0.399035 −0.0165833
\(580\) 1.32141 0.0548685
\(581\) −3.78401 −0.156987
\(582\) −8.73640 −0.362135
\(583\) −14.6360 −0.606161
\(584\) 8.75380 0.362235
\(585\) 12.8525 0.531385
\(586\) −16.9859 −0.701682
\(587\) −33.9917 −1.40299 −0.701495 0.712675i \(-0.747484\pi\)
−0.701495 + 0.712675i \(0.747484\pi\)
\(588\) −1.81183 −0.0747185
\(589\) 2.00345 0.0825506
\(590\) −4.08702 −0.168260
\(591\) −23.3060 −0.958681
\(592\) 6.77537 0.278466
\(593\) 35.6982 1.46595 0.732975 0.680256i \(-0.238131\pi\)
0.732975 + 0.680256i \(0.238131\pi\)
\(594\) −4.97741 −0.204226
\(595\) −9.30924 −0.381642
\(596\) 0.843435 0.0345485
\(597\) −23.2534 −0.951698
\(598\) 11.3001 0.462097
\(599\) 46.8489 1.91419 0.957097 0.289767i \(-0.0935777\pi\)
0.957097 + 0.289767i \(0.0935777\pi\)
\(600\) 11.7038 0.477804
\(601\) 2.25594 0.0920218 0.0460109 0.998941i \(-0.485349\pi\)
0.0460109 + 0.998941i \(0.485349\pi\)
\(602\) −11.6461 −0.474659
\(603\) −11.1237 −0.452992
\(604\) −4.52554 −0.184142
\(605\) 56.2972 2.28880
\(606\) 3.85469 0.156586
\(607\) 11.6408 0.472487 0.236243 0.971694i \(-0.424084\pi\)
0.236243 + 0.971694i \(0.424084\pi\)
\(608\) −1.30689 −0.0530015
\(609\) −0.736440 −0.0298420
\(610\) −30.4749 −1.23389
\(611\) 10.7568 0.435175
\(612\) 1.00000 0.0404226
\(613\) −23.4298 −0.946322 −0.473161 0.880976i \(-0.656887\pi\)
−0.473161 + 0.880976i \(0.656887\pi\)
\(614\) 28.6640 1.15678
\(615\) 34.1629 1.37758
\(616\) 11.3373 0.456794
\(617\) −33.3785 −1.34377 −0.671883 0.740657i \(-0.734514\pi\)
−0.671883 + 0.740657i \(0.734514\pi\)
\(618\) −2.37041 −0.0953518
\(619\) −13.7098 −0.551044 −0.275522 0.961295i \(-0.588851\pi\)
−0.275522 + 0.961295i \(0.588851\pi\)
\(620\) −6.26534 −0.251622
\(621\) 3.59338 0.144198
\(622\) −12.3768 −0.496266
\(623\) 7.80881 0.312854
\(624\) 3.14470 0.125889
\(625\) 53.4591 2.13836
\(626\) −21.1662 −0.845970
\(627\) 6.50495 0.259783
\(628\) −18.8717 −0.753061
\(629\) 6.77537 0.270152
\(630\) −9.30924 −0.370889
\(631\) 34.2957 1.36529 0.682645 0.730750i \(-0.260829\pi\)
0.682645 + 0.730750i \(0.260829\pi\)
\(632\) 9.24674 0.367816
\(633\) 20.0614 0.797370
\(634\) −20.5229 −0.815068
\(635\) 84.7897 3.36478
\(636\) 2.94049 0.116598
\(637\) −5.69766 −0.225750
\(638\) −1.60929 −0.0637123
\(639\) 6.20001 0.245269
\(640\) 4.08702 0.161554
\(641\) −32.1423 −1.26955 −0.634773 0.772699i \(-0.718906\pi\)
−0.634773 + 0.772699i \(0.718906\pi\)
\(642\) 0.620217 0.0244780
\(643\) −20.6692 −0.815112 −0.407556 0.913180i \(-0.633619\pi\)
−0.407556 + 0.913180i \(0.633619\pi\)
\(644\) −8.18485 −0.322528
\(645\) 20.8968 0.822811
\(646\) −1.30689 −0.0514191
\(647\) 31.1376 1.22415 0.612073 0.790801i \(-0.290336\pi\)
0.612073 + 0.790801i \(0.290336\pi\)
\(648\) 1.00000 0.0392837
\(649\) 4.97741 0.195380
\(650\) 36.8048 1.44360
\(651\) 3.49176 0.136853
\(652\) 7.35972 0.288229
\(653\) 31.7537 1.24262 0.621310 0.783565i \(-0.286601\pi\)
0.621310 + 0.783565i \(0.286601\pi\)
\(654\) 16.0601 0.627998
\(655\) −82.8299 −3.23643
\(656\) 8.35887 0.326359
\(657\) 8.75380 0.341518
\(658\) −7.79133 −0.303738
\(659\) 7.07348 0.275544 0.137772 0.990464i \(-0.456006\pi\)
0.137772 + 0.990464i \(0.456006\pi\)
\(660\) −20.3428 −0.791842
\(661\) 37.4356 1.45608 0.728038 0.685536i \(-0.240432\pi\)
0.728038 + 0.685536i \(0.240432\pi\)
\(662\) −2.43796 −0.0947541
\(663\) 3.14470 0.122130
\(664\) 1.66129 0.0644706
\(665\) 12.1662 0.471785
\(666\) 6.77537 0.262540
\(667\) 1.16181 0.0449853
\(668\) −7.07794 −0.273854
\(669\) −10.2655 −0.396885
\(670\) −45.4628 −1.75638
\(671\) 37.1141 1.43277
\(672\) −2.27776 −0.0878664
\(673\) 35.5240 1.36935 0.684675 0.728848i \(-0.259944\pi\)
0.684675 + 0.728848i \(0.259944\pi\)
\(674\) −13.2121 −0.508910
\(675\) 11.7038 0.450478
\(676\) −3.11083 −0.119647
\(677\) −13.5173 −0.519512 −0.259756 0.965674i \(-0.583642\pi\)
−0.259756 + 0.965674i \(0.583642\pi\)
\(678\) −2.60248 −0.0999478
\(679\) 19.8994 0.763669
\(680\) 4.08702 0.156730
\(681\) −23.0457 −0.883114
\(682\) 7.63029 0.292179
\(683\) 35.3464 1.35249 0.676247 0.736675i \(-0.263605\pi\)
0.676247 + 0.736675i \(0.263605\pi\)
\(684\) −1.30689 −0.0499703
\(685\) −47.7921 −1.82604
\(686\) 20.0712 0.766322
\(687\) −20.9627 −0.799778
\(688\) 5.11297 0.194930
\(689\) 9.24696 0.352281
\(690\) 14.6862 0.559096
\(691\) −17.5813 −0.668825 −0.334413 0.942427i \(-0.608538\pi\)
−0.334413 + 0.942427i \(0.608538\pi\)
\(692\) −1.83515 −0.0697620
\(693\) 11.3373 0.430669
\(694\) −20.3262 −0.771572
\(695\) −26.5098 −1.00557
\(696\) 0.323318 0.0122553
\(697\) 8.35887 0.316615
\(698\) 33.8846 1.28255
\(699\) −17.8963 −0.676899
\(700\) −26.6583 −1.00759
\(701\) −23.5462 −0.889328 −0.444664 0.895697i \(-0.646677\pi\)
−0.444664 + 0.895697i \(0.646677\pi\)
\(702\) 3.14470 0.118689
\(703\) −8.85469 −0.333961
\(704\) −4.97741 −0.187593
\(705\) 13.9801 0.526522
\(706\) 22.9604 0.864128
\(707\) −8.78004 −0.330207
\(708\) −1.00000 −0.0375823
\(709\) −17.9998 −0.675996 −0.337998 0.941147i \(-0.609750\pi\)
−0.337998 + 0.941147i \(0.609750\pi\)
\(710\) 25.3396 0.950977
\(711\) 9.24674 0.346780
\(712\) −3.42829 −0.128481
\(713\) −5.50860 −0.206299
\(714\) −2.27776 −0.0852429
\(715\) −63.9721 −2.39242
\(716\) 8.48650 0.317155
\(717\) 0.642085 0.0239791
\(718\) 0.852062 0.0317987
\(719\) 40.7379 1.51927 0.759635 0.650350i \(-0.225378\pi\)
0.759635 + 0.650350i \(0.225378\pi\)
\(720\) 4.08702 0.152314
\(721\) 5.39921 0.201077
\(722\) −17.2920 −0.643543
\(723\) −4.52390 −0.168246
\(724\) 18.8006 0.698719
\(725\) 3.78403 0.140535
\(726\) 13.7746 0.511224
\(727\) −13.5112 −0.501102 −0.250551 0.968103i \(-0.580612\pi\)
−0.250551 + 0.968103i \(0.580612\pi\)
\(728\) −7.16287 −0.265474
\(729\) 1.00000 0.0370370
\(730\) 35.7770 1.32416
\(731\) 5.11297 0.189110
\(732\) −7.45651 −0.275600
\(733\) −7.94022 −0.293279 −0.146639 0.989190i \(-0.546846\pi\)
−0.146639 + 0.989190i \(0.546846\pi\)
\(734\) −20.1729 −0.744594
\(735\) −7.40498 −0.273137
\(736\) 3.59338 0.132454
\(737\) 55.3672 2.03948
\(738\) 8.35887 0.307694
\(739\) −23.1235 −0.850612 −0.425306 0.905050i \(-0.639833\pi\)
−0.425306 + 0.905050i \(0.639833\pi\)
\(740\) 27.6911 1.01794
\(741\) −4.10980 −0.150977
\(742\) −6.69771 −0.245881
\(743\) 26.6774 0.978699 0.489349 0.872088i \(-0.337234\pi\)
0.489349 + 0.872088i \(0.337234\pi\)
\(744\) −1.53298 −0.0562019
\(745\) 3.44714 0.126293
\(746\) 6.92011 0.253363
\(747\) 1.66129 0.0607834
\(748\) −4.97741 −0.181992
\(749\) −1.41270 −0.0516191
\(750\) 27.3984 1.00045
\(751\) 22.2657 0.812488 0.406244 0.913765i \(-0.366838\pi\)
0.406244 + 0.913765i \(0.366838\pi\)
\(752\) 3.42062 0.124737
\(753\) −23.0526 −0.840084
\(754\) 1.01674 0.0370275
\(755\) −18.4960 −0.673138
\(756\) −2.27776 −0.0828412
\(757\) −15.3625 −0.558359 −0.279179 0.960239i \(-0.590062\pi\)
−0.279179 + 0.960239i \(0.590062\pi\)
\(758\) 19.8059 0.719381
\(759\) −17.8857 −0.649212
\(760\) −5.34130 −0.193749
\(761\) 20.4615 0.741729 0.370865 0.928687i \(-0.379061\pi\)
0.370865 + 0.928687i \(0.379061\pi\)
\(762\) 20.7461 0.751551
\(763\) −36.5809 −1.32432
\(764\) 7.35714 0.266172
\(765\) 4.08702 0.147767
\(766\) −3.88159 −0.140248
\(767\) −3.14470 −0.113549
\(768\) 1.00000 0.0360844
\(769\) −10.8477 −0.391180 −0.195590 0.980686i \(-0.562662\pi\)
−0.195590 + 0.980686i \(0.562662\pi\)
\(770\) 46.3359 1.66983
\(771\) 14.5705 0.524743
\(772\) −0.399035 −0.0143616
\(773\) 12.2794 0.441661 0.220830 0.975312i \(-0.429123\pi\)
0.220830 + 0.975312i \(0.429123\pi\)
\(774\) 5.11297 0.183782
\(775\) −17.9417 −0.644483
\(776\) −8.73640 −0.313619
\(777\) −15.4326 −0.553643
\(778\) 29.4234 1.05488
\(779\) −10.9242 −0.391398
\(780\) 12.8525 0.460193
\(781\) −30.8600 −1.10426
\(782\) 3.59338 0.128499
\(783\) 0.323318 0.0115544
\(784\) −1.81183 −0.0647081
\(785\) −77.1289 −2.75285
\(786\) −20.2666 −0.722884
\(787\) −10.0093 −0.356793 −0.178397 0.983959i \(-0.557091\pi\)
−0.178397 + 0.983959i \(0.557091\pi\)
\(788\) −23.3060 −0.830242
\(789\) 8.13918 0.289762
\(790\) 37.7917 1.34457
\(791\) 5.92782 0.210769
\(792\) −4.97741 −0.176865
\(793\) −23.4485 −0.832681
\(794\) −25.6566 −0.910519
\(795\) 12.0178 0.426228
\(796\) −23.2534 −0.824195
\(797\) 10.4321 0.369523 0.184761 0.982783i \(-0.440849\pi\)
0.184761 + 0.982783i \(0.440849\pi\)
\(798\) 2.97679 0.105377
\(799\) 3.42062 0.121013
\(800\) 11.7038 0.413790
\(801\) −3.42829 −0.121133
\(802\) −18.3323 −0.647336
\(803\) −43.5712 −1.53760
\(804\) −11.1237 −0.392303
\(805\) −33.4517 −1.17902
\(806\) −4.82078 −0.169805
\(807\) 20.6899 0.728320
\(808\) 3.85469 0.135607
\(809\) 47.4844 1.66946 0.834731 0.550657i \(-0.185623\pi\)
0.834731 + 0.550657i \(0.185623\pi\)
\(810\) 4.08702 0.143603
\(811\) 4.66901 0.163951 0.0819756 0.996634i \(-0.473877\pi\)
0.0819756 + 0.996634i \(0.473877\pi\)
\(812\) −0.736440 −0.0258440
\(813\) −9.74484 −0.341766
\(814\) −33.7238 −1.18202
\(815\) 30.0793 1.05363
\(816\) 1.00000 0.0350070
\(817\) −6.68210 −0.233777
\(818\) −19.2136 −0.671789
\(819\) −7.16287 −0.250291
\(820\) 34.1629 1.19302
\(821\) 12.4665 0.435085 0.217542 0.976051i \(-0.430196\pi\)
0.217542 + 0.976051i \(0.430196\pi\)
\(822\) −11.6936 −0.407862
\(823\) −2.85465 −0.0995069 −0.0497535 0.998762i \(-0.515844\pi\)
−0.0497535 + 0.998762i \(0.515844\pi\)
\(824\) −2.37041 −0.0825771
\(825\) −58.2544 −2.02816
\(826\) 2.27776 0.0792533
\(827\) 37.7515 1.31275 0.656375 0.754435i \(-0.272089\pi\)
0.656375 + 0.754435i \(0.272089\pi\)
\(828\) 3.59338 0.124879
\(829\) −17.9797 −0.624461 −0.312231 0.950006i \(-0.601076\pi\)
−0.312231 + 0.950006i \(0.601076\pi\)
\(830\) 6.78973 0.235675
\(831\) 3.66544 0.127153
\(832\) 3.14470 0.109023
\(833\) −1.81183 −0.0627761
\(834\) −6.48633 −0.224603
\(835\) −28.9277 −1.00108
\(836\) 6.50495 0.224978
\(837\) −1.53298 −0.0529877
\(838\) 9.40926 0.325037
\(839\) 39.3767 1.35943 0.679717 0.733475i \(-0.262103\pi\)
0.679717 + 0.733475i \(0.262103\pi\)
\(840\) −9.30924 −0.321199
\(841\) −28.8955 −0.996395
\(842\) 9.54620 0.328984
\(843\) −10.0881 −0.347453
\(844\) 20.0614 0.690543
\(845\) −12.7140 −0.437376
\(846\) 3.42062 0.117603
\(847\) −31.3752 −1.07807
\(848\) 2.94049 0.100977
\(849\) −22.8465 −0.784091
\(850\) 11.7038 0.401435
\(851\) 24.3465 0.834588
\(852\) 6.20001 0.212409
\(853\) 32.6317 1.11729 0.558644 0.829407i \(-0.311322\pi\)
0.558644 + 0.829407i \(0.311322\pi\)
\(854\) 16.9841 0.581184
\(855\) −5.34130 −0.182669
\(856\) 0.620217 0.0211986
\(857\) −5.78268 −0.197533 −0.0987663 0.995111i \(-0.531490\pi\)
−0.0987663 + 0.995111i \(0.531490\pi\)
\(858\) −15.6525 −0.534367
\(859\) 43.7052 1.49120 0.745601 0.666393i \(-0.232163\pi\)
0.745601 + 0.666393i \(0.232163\pi\)
\(860\) 20.8968 0.712575
\(861\) −19.0395 −0.648863
\(862\) −3.13096 −0.106641
\(863\) 28.7751 0.979516 0.489758 0.871858i \(-0.337085\pi\)
0.489758 + 0.871858i \(0.337085\pi\)
\(864\) 1.00000 0.0340207
\(865\) −7.50030 −0.255018
\(866\) 16.1020 0.547168
\(867\) 1.00000 0.0339618
\(868\) 3.49176 0.118518
\(869\) −46.0248 −1.56129
\(870\) 1.32141 0.0447999
\(871\) −34.9808 −1.18528
\(872\) 16.0601 0.543862
\(873\) −8.73640 −0.295682
\(874\) −4.69617 −0.158850
\(875\) −62.4068 −2.10974
\(876\) 8.75380 0.295763
\(877\) 42.7561 1.44377 0.721885 0.692013i \(-0.243276\pi\)
0.721885 + 0.692013i \(0.243276\pi\)
\(878\) −35.1537 −1.18638
\(879\) −16.9859 −0.572921
\(880\) −20.3428 −0.685755
\(881\) 5.44662 0.183501 0.0917506 0.995782i \(-0.470754\pi\)
0.0917506 + 0.995782i \(0.470754\pi\)
\(882\) −1.81183 −0.0610074
\(883\) 8.28943 0.278961 0.139481 0.990225i \(-0.455457\pi\)
0.139481 + 0.990225i \(0.455457\pi\)
\(884\) 3.14470 0.105768
\(885\) −4.08702 −0.137384
\(886\) 17.5708 0.590302
\(887\) −18.8214 −0.631959 −0.315980 0.948766i \(-0.602333\pi\)
−0.315980 + 0.948766i \(0.602333\pi\)
\(888\) 6.77537 0.227367
\(889\) −47.2545 −1.58487
\(890\) −14.0115 −0.469667
\(891\) −4.97741 −0.166750
\(892\) −10.2655 −0.343713
\(893\) −4.47038 −0.149596
\(894\) 0.843435 0.0282087
\(895\) 34.6845 1.15938
\(896\) −2.27776 −0.0760945
\(897\) 11.3001 0.377300
\(898\) −26.6121 −0.888056
\(899\) −0.495641 −0.0165306
\(900\) 11.7038 0.390125
\(901\) 2.94049 0.0979618
\(902\) −41.6055 −1.38531
\(903\) −11.6461 −0.387558
\(904\) −2.60248 −0.0865573
\(905\) 76.8385 2.55420
\(906\) −4.52554 −0.150351
\(907\) −36.0394 −1.19667 −0.598334 0.801247i \(-0.704170\pi\)
−0.598334 + 0.801247i \(0.704170\pi\)
\(908\) −23.0457 −0.764799
\(909\) 3.85469 0.127852
\(910\) −29.2748 −0.970451
\(911\) 41.8005 1.38491 0.692456 0.721460i \(-0.256529\pi\)
0.692456 + 0.721460i \(0.256529\pi\)
\(912\) −1.30689 −0.0432756
\(913\) −8.26892 −0.273661
\(914\) 7.42520 0.245604
\(915\) −30.4749 −1.00747
\(916\) −20.9627 −0.692628
\(917\) 46.1623 1.52441
\(918\) 1.00000 0.0330049
\(919\) −4.09329 −0.135025 −0.0675125 0.997718i \(-0.521506\pi\)
−0.0675125 + 0.997718i \(0.521506\pi\)
\(920\) 14.6862 0.484191
\(921\) 28.6640 0.944510
\(922\) −5.40610 −0.178040
\(923\) 19.4972 0.641758
\(924\) 11.3373 0.372971
\(925\) 79.2973 2.60728
\(926\) −15.3768 −0.505312
\(927\) −2.37041 −0.0778544
\(928\) 0.323318 0.0106134
\(929\) −44.1156 −1.44739 −0.723694 0.690122i \(-0.757557\pi\)
−0.723694 + 0.690122i \(0.757557\pi\)
\(930\) −6.26534 −0.205449
\(931\) 2.36787 0.0776037
\(932\) −17.8963 −0.586212
\(933\) −12.3768 −0.405199
\(934\) −28.9318 −0.946678
\(935\) −20.3428 −0.665280
\(936\) 3.14470 0.102788
\(937\) −38.7818 −1.26695 −0.633473 0.773764i \(-0.718371\pi\)
−0.633473 + 0.773764i \(0.718371\pi\)
\(938\) 25.3371 0.827285
\(939\) −21.1662 −0.690732
\(940\) 13.9801 0.455982
\(941\) 18.1112 0.590408 0.295204 0.955434i \(-0.404612\pi\)
0.295204 + 0.955434i \(0.404612\pi\)
\(942\) −18.8717 −0.614872
\(943\) 30.0366 0.978127
\(944\) −1.00000 −0.0325472
\(945\) −9.30924 −0.302830
\(946\) −25.4493 −0.827429
\(947\) −36.1922 −1.17609 −0.588045 0.808828i \(-0.700102\pi\)
−0.588045 + 0.808828i \(0.700102\pi\)
\(948\) 9.24674 0.300320
\(949\) 27.5281 0.893600
\(950\) −15.2956 −0.496254
\(951\) −20.5229 −0.665500
\(952\) −2.27776 −0.0738225
\(953\) −31.3283 −1.01482 −0.507411 0.861704i \(-0.669397\pi\)
−0.507411 + 0.861704i \(0.669397\pi\)
\(954\) 2.94049 0.0952017
\(955\) 30.0688 0.973003
\(956\) 0.642085 0.0207665
\(957\) −1.60929 −0.0520208
\(958\) −9.35258 −0.302168
\(959\) 26.6352 0.860095
\(960\) 4.08702 0.131908
\(961\) −28.6500 −0.924192
\(962\) 21.3065 0.686950
\(963\) 0.620217 0.0199862
\(964\) −4.52390 −0.145705
\(965\) −1.63087 −0.0524994
\(966\) −8.18485 −0.263343
\(967\) −39.5048 −1.27039 −0.635194 0.772353i \(-0.719080\pi\)
−0.635194 + 0.772353i \(0.719080\pi\)
\(968\) 13.7746 0.442733
\(969\) −1.30689 −0.0419835
\(970\) −35.7059 −1.14645
\(971\) −5.97866 −0.191864 −0.0959322 0.995388i \(-0.530583\pi\)
−0.0959322 + 0.995388i \(0.530583\pi\)
\(972\) 1.00000 0.0320750
\(973\) 14.7743 0.473642
\(974\) −14.9865 −0.480198
\(975\) 36.8048 1.17870
\(976\) −7.45651 −0.238677
\(977\) 7.40254 0.236828 0.118414 0.992964i \(-0.462219\pi\)
0.118414 + 0.992964i \(0.462219\pi\)
\(978\) 7.35972 0.235338
\(979\) 17.0640 0.545368
\(980\) −7.40498 −0.236543
\(981\) 16.0601 0.512758
\(982\) 11.4391 0.365038
\(983\) −54.0107 −1.72267 −0.861337 0.508033i \(-0.830373\pi\)
−0.861337 + 0.508033i \(0.830373\pi\)
\(984\) 8.35887 0.266471
\(985\) −95.2522 −3.03499
\(986\) 0.323318 0.0102965
\(987\) −7.79133 −0.248001
\(988\) −4.10980 −0.130750
\(989\) 18.3729 0.584223
\(990\) −20.3428 −0.646536
\(991\) −7.86198 −0.249744 −0.124872 0.992173i \(-0.539852\pi\)
−0.124872 + 0.992173i \(0.539852\pi\)
\(992\) −1.53298 −0.0486723
\(993\) −2.43796 −0.0773664
\(994\) −14.1221 −0.447926
\(995\) −95.0371 −3.01288
\(996\) 1.66129 0.0526400
\(997\) 15.4399 0.488987 0.244493 0.969651i \(-0.421378\pi\)
0.244493 + 0.969651i \(0.421378\pi\)
\(998\) −25.4224 −0.804731
\(999\) 6.77537 0.214363
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.bb.1.13 13
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
6018.2.a.bb.1.13 13 1.1 even 1 trivial