Properties

Label 6018.2.a.bc.1.10
Level $6018$
Weight $2$
Character 6018.1
Self dual yes
Analytic conductor $48.054$
Analytic rank $0$
Dimension $14$
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: \(14\)
Coefficient field: \(\mathbb{Q}[x]/(x^{14} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{14} - 2 x^{13} - 49 x^{12} + 79 x^{11} + 956 x^{10} - 1179 x^{9} - 9396 x^{8} + 8315 x^{7} + 48570 x^{6} - 28124 x^{5} - 125592 x^{4} + 40576 x^{3} + 138096 x^{2} + \cdots - 43744 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 2^{2} \)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.10
Root \(2.33625\) 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)
 
\(f(q)\) \(=\) \(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +2.33625 q^{5} -1.00000 q^{6} -0.683869 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +2.33625 q^{5} -1.00000 q^{6} -0.683869 q^{7} +1.00000 q^{8} +1.00000 q^{9} +2.33625 q^{10} +1.93698 q^{11} -1.00000 q^{12} +0.480780 q^{13} -0.683869 q^{14} -2.33625 q^{15} +1.00000 q^{16} +1.00000 q^{17} +1.00000 q^{18} -0.134424 q^{19} +2.33625 q^{20} +0.683869 q^{21} +1.93698 q^{22} +6.84029 q^{23} -1.00000 q^{24} +0.458066 q^{25} +0.480780 q^{26} -1.00000 q^{27} -0.683869 q^{28} +7.79476 q^{29} -2.33625 q^{30} +2.80957 q^{31} +1.00000 q^{32} -1.93698 q^{33} +1.00000 q^{34} -1.59769 q^{35} +1.00000 q^{36} -0.709000 q^{37} -0.134424 q^{38} -0.480780 q^{39} +2.33625 q^{40} -2.73813 q^{41} +0.683869 q^{42} -6.44381 q^{43} +1.93698 q^{44} +2.33625 q^{45} +6.84029 q^{46} -8.90316 q^{47} -1.00000 q^{48} -6.53232 q^{49} +0.458066 q^{50} -1.00000 q^{51} +0.480780 q^{52} +13.4888 q^{53} -1.00000 q^{54} +4.52526 q^{55} -0.683869 q^{56} +0.134424 q^{57} +7.79476 q^{58} +1.00000 q^{59} -2.33625 q^{60} -11.1555 q^{61} +2.80957 q^{62} -0.683869 q^{63} +1.00000 q^{64} +1.12322 q^{65} -1.93698 q^{66} +8.92916 q^{67} +1.00000 q^{68} -6.84029 q^{69} -1.59769 q^{70} +5.82347 q^{71} +1.00000 q^{72} -2.58810 q^{73} -0.709000 q^{74} -0.458066 q^{75} -0.134424 q^{76} -1.32464 q^{77} -0.480780 q^{78} +12.0018 q^{79} +2.33625 q^{80} +1.00000 q^{81} -2.73813 q^{82} -5.79142 q^{83} +0.683869 q^{84} +2.33625 q^{85} -6.44381 q^{86} -7.79476 q^{87} +1.93698 q^{88} +13.5600 q^{89} +2.33625 q^{90} -0.328790 q^{91} +6.84029 q^{92} -2.80957 q^{93} -8.90316 q^{94} -0.314048 q^{95} -1.00000 q^{96} +3.01760 q^{97} -6.53232 q^{98} +1.93698 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 14 q + 14 q^{2} - 14 q^{3} + 14 q^{4} + 2 q^{5} - 14 q^{6} + q^{7} + 14 q^{8} + 14 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 14 q + 14 q^{2} - 14 q^{3} + 14 q^{4} + 2 q^{5} - 14 q^{6} + q^{7} + 14 q^{8} + 14 q^{9} + 2 q^{10} + 3 q^{11} - 14 q^{12} + 16 q^{13} + q^{14} - 2 q^{15} + 14 q^{16} + 14 q^{17} + 14 q^{18} + 13 q^{19} + 2 q^{20} - q^{21} + 3 q^{22} + 4 q^{23} - 14 q^{24} + 32 q^{25} + 16 q^{26} - 14 q^{27} + q^{28} - 2 q^{30} - 13 q^{31} + 14 q^{32} - 3 q^{33} + 14 q^{34} + 14 q^{36} + 12 q^{37} + 13 q^{38} - 16 q^{39} + 2 q^{40} - 18 q^{41} - q^{42} + 29 q^{43} + 3 q^{44} + 2 q^{45} + 4 q^{46} - 14 q^{48} + 49 q^{49} + 32 q^{50} - 14 q^{51} + 16 q^{52} + 24 q^{53} - 14 q^{54} + 15 q^{55} + q^{56} - 13 q^{57} + 14 q^{59} - 2 q^{60} + 29 q^{61} - 13 q^{62} + q^{63} + 14 q^{64} + 6 q^{65} - 3 q^{66} + 4 q^{67} + 14 q^{68} - 4 q^{69} - 10 q^{71} + 14 q^{72} + 18 q^{73} + 12 q^{74} - 32 q^{75} + 13 q^{76} + 20 q^{77} - 16 q^{78} + 7 q^{79} + 2 q^{80} + 14 q^{81} - 18 q^{82} + 28 q^{83} - q^{84} + 2 q^{85} + 29 q^{86} + 3 q^{88} + 23 q^{89} + 2 q^{90} + 9 q^{91} + 4 q^{92} + 13 q^{93} + 5 q^{95} - 14 q^{96} - 7 q^{97} + 49 q^{98} + 3 q^{99}+O(q^{100}) \) 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
\(5\) 2.33625 1.04480 0.522401 0.852700i \(-0.325036\pi\)
0.522401 + 0.852700i \(0.325036\pi\)
\(6\) −1.00000 −0.408248
\(7\) −0.683869 −0.258478 −0.129239 0.991613i \(-0.541253\pi\)
−0.129239 + 0.991613i \(0.541253\pi\)
\(8\) 1.00000 0.353553
\(9\) 1.00000 0.333333
\(10\) 2.33625 0.738787
\(11\) 1.93698 0.584020 0.292010 0.956415i \(-0.405676\pi\)
0.292010 + 0.956415i \(0.405676\pi\)
\(12\) −1.00000 −0.288675
\(13\) 0.480780 0.133344 0.0666721 0.997775i \(-0.478762\pi\)
0.0666721 + 0.997775i \(0.478762\pi\)
\(14\) −0.683869 −0.182772
\(15\) −2.33625 −0.603217
\(16\) 1.00000 0.250000
\(17\) 1.00000 0.242536
\(18\) 1.00000 0.235702
\(19\) −0.134424 −0.0308390 −0.0154195 0.999881i \(-0.504908\pi\)
−0.0154195 + 0.999881i \(0.504908\pi\)
\(20\) 2.33625 0.522401
\(21\) 0.683869 0.149232
\(22\) 1.93698 0.412965
\(23\) 6.84029 1.42630 0.713150 0.701012i \(-0.247268\pi\)
0.713150 + 0.701012i \(0.247268\pi\)
\(24\) −1.00000 −0.204124
\(25\) 0.458066 0.0916132
\(26\) 0.480780 0.0942886
\(27\) −1.00000 −0.192450
\(28\) −0.683869 −0.129239
\(29\) 7.79476 1.44745 0.723725 0.690088i \(-0.242428\pi\)
0.723725 + 0.690088i \(0.242428\pi\)
\(30\) −2.33625 −0.426539
\(31\) 2.80957 0.504614 0.252307 0.967647i \(-0.418811\pi\)
0.252307 + 0.967647i \(0.418811\pi\)
\(32\) 1.00000 0.176777
\(33\) −1.93698 −0.337184
\(34\) 1.00000 0.171499
\(35\) −1.59769 −0.270059
\(36\) 1.00000 0.166667
\(37\) −0.709000 −0.116559 −0.0582795 0.998300i \(-0.518561\pi\)
−0.0582795 + 0.998300i \(0.518561\pi\)
\(38\) −0.134424 −0.0218064
\(39\) −0.480780 −0.0769863
\(40\) 2.33625 0.369394
\(41\) −2.73813 −0.427624 −0.213812 0.976875i \(-0.568588\pi\)
−0.213812 + 0.976875i \(0.568588\pi\)
\(42\) 0.683869 0.105523
\(43\) −6.44381 −0.982672 −0.491336 0.870970i \(-0.663491\pi\)
−0.491336 + 0.870970i \(0.663491\pi\)
\(44\) 1.93698 0.292010
\(45\) 2.33625 0.348268
\(46\) 6.84029 1.00855
\(47\) −8.90316 −1.29866 −0.649329 0.760507i \(-0.724950\pi\)
−0.649329 + 0.760507i \(0.724950\pi\)
\(48\) −1.00000 −0.144338
\(49\) −6.53232 −0.933189
\(50\) 0.458066 0.0647803
\(51\) −1.00000 −0.140028
\(52\) 0.480780 0.0666721
\(53\) 13.4888 1.85283 0.926413 0.376508i \(-0.122875\pi\)
0.926413 + 0.376508i \(0.122875\pi\)
\(54\) −1.00000 −0.136083
\(55\) 4.52526 0.610186
\(56\) −0.683869 −0.0913858
\(57\) 0.134424 0.0178049
\(58\) 7.79476 1.02350
\(59\) 1.00000 0.130189
\(60\) −2.33625 −0.301609
\(61\) −11.1555 −1.42831 −0.714157 0.699986i \(-0.753190\pi\)
−0.714157 + 0.699986i \(0.753190\pi\)
\(62\) 2.80957 0.356816
\(63\) −0.683869 −0.0861594
\(64\) 1.00000 0.125000
\(65\) 1.12322 0.139318
\(66\) −1.93698 −0.238425
\(67\) 8.92916 1.09087 0.545435 0.838153i \(-0.316364\pi\)
0.545435 + 0.838153i \(0.316364\pi\)
\(68\) 1.00000 0.121268
\(69\) −6.84029 −0.823474
\(70\) −1.59769 −0.190960
\(71\) 5.82347 0.691119 0.345559 0.938397i \(-0.387689\pi\)
0.345559 + 0.938397i \(0.387689\pi\)
\(72\) 1.00000 0.117851
\(73\) −2.58810 −0.302915 −0.151457 0.988464i \(-0.548397\pi\)
−0.151457 + 0.988464i \(0.548397\pi\)
\(74\) −0.709000 −0.0824196
\(75\) −0.458066 −0.0528929
\(76\) −0.134424 −0.0154195
\(77\) −1.32464 −0.150956
\(78\) −0.480780 −0.0544376
\(79\) 12.0018 1.35030 0.675151 0.737679i \(-0.264078\pi\)
0.675151 + 0.737679i \(0.264078\pi\)
\(80\) 2.33625 0.261201
\(81\) 1.00000 0.111111
\(82\) −2.73813 −0.302376
\(83\) −5.79142 −0.635691 −0.317846 0.948142i \(-0.602959\pi\)
−0.317846 + 0.948142i \(0.602959\pi\)
\(84\) 0.683869 0.0746162
\(85\) 2.33625 0.253402
\(86\) −6.44381 −0.694854
\(87\) −7.79476 −0.835686
\(88\) 1.93698 0.206482
\(89\) 13.5600 1.43736 0.718678 0.695343i \(-0.244748\pi\)
0.718678 + 0.695343i \(0.244748\pi\)
\(90\) 2.33625 0.246262
\(91\) −0.328790 −0.0344666
\(92\) 6.84029 0.713150
\(93\) −2.80957 −0.291339
\(94\) −8.90316 −0.918290
\(95\) −0.314048 −0.0322206
\(96\) −1.00000 −0.102062
\(97\) 3.01760 0.306390 0.153195 0.988196i \(-0.451044\pi\)
0.153195 + 0.988196i \(0.451044\pi\)
\(98\) −6.53232 −0.659864
\(99\) 1.93698 0.194673
\(100\) 0.458066 0.0458066
\(101\) 1.42039 0.141334 0.0706671 0.997500i \(-0.477487\pi\)
0.0706671 + 0.997500i \(0.477487\pi\)
\(102\) −1.00000 −0.0990148
\(103\) −14.5482 −1.43348 −0.716740 0.697340i \(-0.754367\pi\)
−0.716740 + 0.697340i \(0.754367\pi\)
\(104\) 0.480780 0.0471443
\(105\) 1.59769 0.155918
\(106\) 13.4888 1.31015
\(107\) 6.16423 0.595919 0.297959 0.954579i \(-0.403694\pi\)
0.297959 + 0.954579i \(0.403694\pi\)
\(108\) −1.00000 −0.0962250
\(109\) 12.1410 1.16290 0.581450 0.813582i \(-0.302485\pi\)
0.581450 + 0.813582i \(0.302485\pi\)
\(110\) 4.52526 0.431467
\(111\) 0.709000 0.0672953
\(112\) −0.683869 −0.0646195
\(113\) 10.7865 1.01471 0.507353 0.861738i \(-0.330624\pi\)
0.507353 + 0.861738i \(0.330624\pi\)
\(114\) 0.134424 0.0125900
\(115\) 15.9806 1.49020
\(116\) 7.79476 0.723725
\(117\) 0.480780 0.0444481
\(118\) 1.00000 0.0920575
\(119\) −0.683869 −0.0626902
\(120\) −2.33625 −0.213270
\(121\) −7.24813 −0.658921
\(122\) −11.1555 −1.00997
\(123\) 2.73813 0.246889
\(124\) 2.80957 0.252307
\(125\) −10.6111 −0.949085
\(126\) −0.683869 −0.0609239
\(127\) −3.99253 −0.354280 −0.177140 0.984186i \(-0.556685\pi\)
−0.177140 + 0.984186i \(0.556685\pi\)
\(128\) 1.00000 0.0883883
\(129\) 6.44381 0.567346
\(130\) 1.12322 0.0985130
\(131\) −9.37785 −0.819347 −0.409673 0.912232i \(-0.634357\pi\)
−0.409673 + 0.912232i \(0.634357\pi\)
\(132\) −1.93698 −0.168592
\(133\) 0.0919283 0.00797120
\(134\) 8.92916 0.771362
\(135\) −2.33625 −0.201072
\(136\) 1.00000 0.0857493
\(137\) 17.3272 1.48036 0.740181 0.672407i \(-0.234740\pi\)
0.740181 + 0.672407i \(0.234740\pi\)
\(138\) −6.84029 −0.582284
\(139\) −18.9097 −1.60390 −0.801949 0.597392i \(-0.796204\pi\)
−0.801949 + 0.597392i \(0.796204\pi\)
\(140\) −1.59769 −0.135029
\(141\) 8.90316 0.749781
\(142\) 5.82347 0.488695
\(143\) 0.931258 0.0778757
\(144\) 1.00000 0.0833333
\(145\) 18.2105 1.51230
\(146\) −2.58810 −0.214193
\(147\) 6.53232 0.538777
\(148\) −0.709000 −0.0582795
\(149\) 0.845331 0.0692522 0.0346261 0.999400i \(-0.488976\pi\)
0.0346261 + 0.999400i \(0.488976\pi\)
\(150\) −0.458066 −0.0374009
\(151\) 20.7691 1.69017 0.845085 0.534633i \(-0.179550\pi\)
0.845085 + 0.534633i \(0.179550\pi\)
\(152\) −0.134424 −0.0109032
\(153\) 1.00000 0.0808452
\(154\) −1.32464 −0.106742
\(155\) 6.56386 0.527222
\(156\) −0.480780 −0.0384932
\(157\) 4.90486 0.391451 0.195725 0.980659i \(-0.437294\pi\)
0.195725 + 0.980659i \(0.437294\pi\)
\(158\) 12.0018 0.954808
\(159\) −13.4888 −1.06973
\(160\) 2.33625 0.184697
\(161\) −4.67786 −0.368667
\(162\) 1.00000 0.0785674
\(163\) −0.793255 −0.0621325 −0.0310663 0.999517i \(-0.509890\pi\)
−0.0310663 + 0.999517i \(0.509890\pi\)
\(164\) −2.73813 −0.213812
\(165\) −4.52526 −0.352291
\(166\) −5.79142 −0.449502
\(167\) −1.71195 −0.132475 −0.0662374 0.997804i \(-0.521099\pi\)
−0.0662374 + 0.997804i \(0.521099\pi\)
\(168\) 0.683869 0.0527616
\(169\) −12.7689 −0.982219
\(170\) 2.33625 0.179182
\(171\) −0.134424 −0.0102797
\(172\) −6.44381 −0.491336
\(173\) 23.6118 1.79517 0.897585 0.440842i \(-0.145320\pi\)
0.897585 + 0.440842i \(0.145320\pi\)
\(174\) −7.79476 −0.590919
\(175\) −0.313257 −0.0236800
\(176\) 1.93698 0.146005
\(177\) −1.00000 −0.0751646
\(178\) 13.5600 1.01636
\(179\) −21.7180 −1.62328 −0.811640 0.584157i \(-0.801425\pi\)
−0.811640 + 0.584157i \(0.801425\pi\)
\(180\) 2.33625 0.174134
\(181\) 14.4439 1.07361 0.536805 0.843707i \(-0.319631\pi\)
0.536805 + 0.843707i \(0.319631\pi\)
\(182\) −0.328790 −0.0243715
\(183\) 11.1555 0.824637
\(184\) 6.84029 0.504273
\(185\) −1.65640 −0.121781
\(186\) −2.80957 −0.206008
\(187\) 1.93698 0.141646
\(188\) −8.90316 −0.649329
\(189\) 0.683869 0.0497441
\(190\) −0.314048 −0.0227834
\(191\) 0.474135 0.0343072 0.0171536 0.999853i \(-0.494540\pi\)
0.0171536 + 0.999853i \(0.494540\pi\)
\(192\) −1.00000 −0.0721688
\(193\) 7.01099 0.504662 0.252331 0.967641i \(-0.418803\pi\)
0.252331 + 0.967641i \(0.418803\pi\)
\(194\) 3.01760 0.216651
\(195\) −1.12322 −0.0804356
\(196\) −6.53232 −0.466595
\(197\) −1.46125 −0.104110 −0.0520550 0.998644i \(-0.516577\pi\)
−0.0520550 + 0.998644i \(0.516577\pi\)
\(198\) 1.93698 0.137655
\(199\) −12.2073 −0.865354 −0.432677 0.901549i \(-0.642431\pi\)
−0.432677 + 0.901549i \(0.642431\pi\)
\(200\) 0.458066 0.0323902
\(201\) −8.92916 −0.629815
\(202\) 1.42039 0.0999384
\(203\) −5.33059 −0.374134
\(204\) −1.00000 −0.0700140
\(205\) −6.39696 −0.446783
\(206\) −14.5482 −1.01362
\(207\) 6.84029 0.475433
\(208\) 0.480780 0.0333361
\(209\) −0.260376 −0.0180106
\(210\) 1.59769 0.110251
\(211\) −12.4282 −0.855596 −0.427798 0.903874i \(-0.640710\pi\)
−0.427798 + 0.903874i \(0.640710\pi\)
\(212\) 13.4888 0.926413
\(213\) −5.82347 −0.399017
\(214\) 6.16423 0.421378
\(215\) −15.0544 −1.02670
\(216\) −1.00000 −0.0680414
\(217\) −1.92138 −0.130432
\(218\) 12.1410 0.822295
\(219\) 2.58810 0.174888
\(220\) 4.52526 0.305093
\(221\) 0.480780 0.0323407
\(222\) 0.709000 0.0475850
\(223\) 5.55345 0.371886 0.185943 0.982561i \(-0.440466\pi\)
0.185943 + 0.982561i \(0.440466\pi\)
\(224\) −0.683869 −0.0456929
\(225\) 0.458066 0.0305377
\(226\) 10.7865 0.717506
\(227\) 12.3784 0.821580 0.410790 0.911730i \(-0.365253\pi\)
0.410790 + 0.911730i \(0.365253\pi\)
\(228\) 0.134424 0.00890244
\(229\) −2.70403 −0.178687 −0.0893435 0.996001i \(-0.528477\pi\)
−0.0893435 + 0.996001i \(0.528477\pi\)
\(230\) 15.9806 1.05373
\(231\) 1.32464 0.0871547
\(232\) 7.79476 0.511751
\(233\) −9.87308 −0.646807 −0.323404 0.946261i \(-0.604827\pi\)
−0.323404 + 0.946261i \(0.604827\pi\)
\(234\) 0.480780 0.0314295
\(235\) −20.8000 −1.35684
\(236\) 1.00000 0.0650945
\(237\) −12.0018 −0.779597
\(238\) −0.683869 −0.0443286
\(239\) 3.27930 0.212120 0.106060 0.994360i \(-0.466176\pi\)
0.106060 + 0.994360i \(0.466176\pi\)
\(240\) −2.33625 −0.150804
\(241\) −6.96482 −0.448644 −0.224322 0.974515i \(-0.572017\pi\)
−0.224322 + 0.974515i \(0.572017\pi\)
\(242\) −7.24813 −0.465927
\(243\) −1.00000 −0.0641500
\(244\) −11.1555 −0.714157
\(245\) −15.2611 −0.974999
\(246\) 2.73813 0.174577
\(247\) −0.0646283 −0.00411220
\(248\) 2.80957 0.178408
\(249\) 5.79142 0.367017
\(250\) −10.6111 −0.671105
\(251\) −20.2352 −1.27723 −0.638616 0.769525i \(-0.720493\pi\)
−0.638616 + 0.769525i \(0.720493\pi\)
\(252\) −0.683869 −0.0430797
\(253\) 13.2495 0.832987
\(254\) −3.99253 −0.250514
\(255\) −2.33625 −0.146302
\(256\) 1.00000 0.0625000
\(257\) −0.910524 −0.0567969 −0.0283985 0.999597i \(-0.509041\pi\)
−0.0283985 + 0.999597i \(0.509041\pi\)
\(258\) 6.44381 0.401174
\(259\) 0.484863 0.0301279
\(260\) 1.12322 0.0696592
\(261\) 7.79476 0.482483
\(262\) −9.37785 −0.579365
\(263\) 15.6632 0.965834 0.482917 0.875666i \(-0.339577\pi\)
0.482917 + 0.875666i \(0.339577\pi\)
\(264\) −1.93698 −0.119213
\(265\) 31.5132 1.93584
\(266\) 0.0919283 0.00563649
\(267\) −13.5600 −0.829858
\(268\) 8.92916 0.545435
\(269\) 15.6658 0.955158 0.477579 0.878589i \(-0.341514\pi\)
0.477579 + 0.878589i \(0.341514\pi\)
\(270\) −2.33625 −0.142180
\(271\) 0.951602 0.0578057 0.0289028 0.999582i \(-0.490799\pi\)
0.0289028 + 0.999582i \(0.490799\pi\)
\(272\) 1.00000 0.0606339
\(273\) 0.328790 0.0198993
\(274\) 17.3272 1.04677
\(275\) 0.887263 0.0535040
\(276\) −6.84029 −0.411737
\(277\) −8.23112 −0.494560 −0.247280 0.968944i \(-0.579537\pi\)
−0.247280 + 0.968944i \(0.579537\pi\)
\(278\) −18.9097 −1.13413
\(279\) 2.80957 0.168205
\(280\) −1.59769 −0.0954802
\(281\) 12.9741 0.773972 0.386986 0.922086i \(-0.373516\pi\)
0.386986 + 0.922086i \(0.373516\pi\)
\(282\) 8.90316 0.530175
\(283\) −3.83895 −0.228202 −0.114101 0.993469i \(-0.536399\pi\)
−0.114101 + 0.993469i \(0.536399\pi\)
\(284\) 5.82347 0.345559
\(285\) 0.314048 0.0186026
\(286\) 0.931258 0.0550665
\(287\) 1.87252 0.110532
\(288\) 1.00000 0.0589256
\(289\) 1.00000 0.0588235
\(290\) 18.2105 1.06936
\(291\) −3.01760 −0.176895
\(292\) −2.58810 −0.151457
\(293\) 20.7091 1.20984 0.604920 0.796286i \(-0.293205\pi\)
0.604920 + 0.796286i \(0.293205\pi\)
\(294\) 6.53232 0.380973
\(295\) 2.33625 0.136022
\(296\) −0.709000 −0.0412098
\(297\) −1.93698 −0.112395
\(298\) 0.845331 0.0489687
\(299\) 3.28867 0.190189
\(300\) −0.458066 −0.0264465
\(301\) 4.40672 0.253999
\(302\) 20.7691 1.19513
\(303\) −1.42039 −0.0815993
\(304\) −0.134424 −0.00770974
\(305\) −26.0620 −1.49231
\(306\) 1.00000 0.0571662
\(307\) 6.93896 0.396027 0.198014 0.980199i \(-0.436551\pi\)
0.198014 + 0.980199i \(0.436551\pi\)
\(308\) −1.32464 −0.0754782
\(309\) 14.5482 0.827621
\(310\) 6.56386 0.372802
\(311\) 3.79474 0.215180 0.107590 0.994195i \(-0.465687\pi\)
0.107590 + 0.994195i \(0.465687\pi\)
\(312\) −0.480780 −0.0272188
\(313\) −5.69740 −0.322036 −0.161018 0.986951i \(-0.551478\pi\)
−0.161018 + 0.986951i \(0.551478\pi\)
\(314\) 4.90486 0.276797
\(315\) −1.59769 −0.0900196
\(316\) 12.0018 0.675151
\(317\) −19.0607 −1.07056 −0.535278 0.844676i \(-0.679793\pi\)
−0.535278 + 0.844676i \(0.679793\pi\)
\(318\) −13.4888 −0.756413
\(319\) 15.0983 0.845340
\(320\) 2.33625 0.130600
\(321\) −6.16423 −0.344054
\(322\) −4.67786 −0.260687
\(323\) −0.134424 −0.00747955
\(324\) 1.00000 0.0555556
\(325\) 0.220229 0.0122161
\(326\) −0.793255 −0.0439343
\(327\) −12.1410 −0.671401
\(328\) −2.73813 −0.151188
\(329\) 6.08859 0.335675
\(330\) −4.52526 −0.249107
\(331\) 7.10042 0.390274 0.195137 0.980776i \(-0.437485\pi\)
0.195137 + 0.980776i \(0.437485\pi\)
\(332\) −5.79142 −0.317846
\(333\) −0.709000 −0.0388530
\(334\) −1.71195 −0.0936738
\(335\) 20.8608 1.13974
\(336\) 0.683869 0.0373081
\(337\) −2.63257 −0.143405 −0.0717025 0.997426i \(-0.522843\pi\)
−0.0717025 + 0.997426i \(0.522843\pi\)
\(338\) −12.7689 −0.694534
\(339\) −10.7865 −0.585841
\(340\) 2.33625 0.126701
\(341\) 5.44207 0.294704
\(342\) −0.134424 −0.00726881
\(343\) 9.25433 0.499687
\(344\) −6.44381 −0.347427
\(345\) −15.9806 −0.860368
\(346\) 23.6118 1.26938
\(347\) −15.7899 −0.847645 −0.423823 0.905745i \(-0.639312\pi\)
−0.423823 + 0.905745i \(0.639312\pi\)
\(348\) −7.79476 −0.417843
\(349\) −11.5109 −0.616164 −0.308082 0.951360i \(-0.599687\pi\)
−0.308082 + 0.951360i \(0.599687\pi\)
\(350\) −0.313257 −0.0167443
\(351\) −0.480780 −0.0256621
\(352\) 1.93698 0.103241
\(353\) 31.0633 1.65333 0.826666 0.562694i \(-0.190235\pi\)
0.826666 + 0.562694i \(0.190235\pi\)
\(354\) −1.00000 −0.0531494
\(355\) 13.6051 0.722083
\(356\) 13.5600 0.718678
\(357\) 0.683869 0.0361942
\(358\) −21.7180 −1.14783
\(359\) 23.5865 1.24485 0.622425 0.782680i \(-0.286148\pi\)
0.622425 + 0.782680i \(0.286148\pi\)
\(360\) 2.33625 0.123131
\(361\) −18.9819 −0.999049
\(362\) 14.4439 0.759156
\(363\) 7.24813 0.380428
\(364\) −0.328790 −0.0172333
\(365\) −6.04646 −0.316486
\(366\) 11.1555 0.583107
\(367\) −7.13232 −0.372304 −0.186152 0.982521i \(-0.559602\pi\)
−0.186152 + 0.982521i \(0.559602\pi\)
\(368\) 6.84029 0.356575
\(369\) −2.73813 −0.142541
\(370\) −1.65640 −0.0861122
\(371\) −9.22456 −0.478915
\(372\) −2.80957 −0.145669
\(373\) 28.1071 1.45533 0.727665 0.685933i \(-0.240606\pi\)
0.727665 + 0.685933i \(0.240606\pi\)
\(374\) 1.93698 0.100159
\(375\) 10.6111 0.547955
\(376\) −8.90316 −0.459145
\(377\) 3.74756 0.193009
\(378\) 0.683869 0.0351744
\(379\) −3.21621 −0.165206 −0.0826028 0.996583i \(-0.526323\pi\)
−0.0826028 + 0.996583i \(0.526323\pi\)
\(380\) −0.314048 −0.0161103
\(381\) 3.99253 0.204544
\(382\) 0.474135 0.0242589
\(383\) −17.9314 −0.916252 −0.458126 0.888887i \(-0.651479\pi\)
−0.458126 + 0.888887i \(0.651479\pi\)
\(384\) −1.00000 −0.0510310
\(385\) −3.09468 −0.157720
\(386\) 7.01099 0.356850
\(387\) −6.44381 −0.327557
\(388\) 3.01760 0.153195
\(389\) 24.8722 1.26107 0.630536 0.776160i \(-0.282835\pi\)
0.630536 + 0.776160i \(0.282835\pi\)
\(390\) −1.12322 −0.0568765
\(391\) 6.84029 0.345928
\(392\) −6.53232 −0.329932
\(393\) 9.37785 0.473050
\(394\) −1.46125 −0.0736169
\(395\) 28.0391 1.41080
\(396\) 1.93698 0.0973367
\(397\) 22.0814 1.10823 0.554116 0.832439i \(-0.313056\pi\)
0.554116 + 0.832439i \(0.313056\pi\)
\(398\) −12.2073 −0.611898
\(399\) −0.0919283 −0.00460217
\(400\) 0.458066 0.0229033
\(401\) −20.6434 −1.03088 −0.515441 0.856925i \(-0.672372\pi\)
−0.515441 + 0.856925i \(0.672372\pi\)
\(402\) −8.92916 −0.445346
\(403\) 1.35078 0.0672873
\(404\) 1.42039 0.0706671
\(405\) 2.33625 0.116089
\(406\) −5.33059 −0.264553
\(407\) −1.37332 −0.0680727
\(408\) −1.00000 −0.0495074
\(409\) 31.1858 1.54204 0.771020 0.636811i \(-0.219747\pi\)
0.771020 + 0.636811i \(0.219747\pi\)
\(410\) −6.39696 −0.315923
\(411\) −17.3272 −0.854688
\(412\) −14.5482 −0.716740
\(413\) −0.683869 −0.0336510
\(414\) 6.84029 0.336182
\(415\) −13.5302 −0.664172
\(416\) 0.480780 0.0235722
\(417\) 18.9097 0.926011
\(418\) −0.260376 −0.0127354
\(419\) 32.5126 1.58835 0.794173 0.607691i \(-0.207904\pi\)
0.794173 + 0.607691i \(0.207904\pi\)
\(420\) 1.59769 0.0779592
\(421\) 10.5978 0.516505 0.258253 0.966077i \(-0.416853\pi\)
0.258253 + 0.966077i \(0.416853\pi\)
\(422\) −12.4282 −0.604998
\(423\) −8.90316 −0.432886
\(424\) 13.4888 0.655073
\(425\) 0.458066 0.0222195
\(426\) −5.82347 −0.282148
\(427\) 7.62889 0.369188
\(428\) 6.16423 0.297959
\(429\) −0.931258 −0.0449616
\(430\) −15.0544 −0.725985
\(431\) 10.0321 0.483227 0.241614 0.970373i \(-0.422323\pi\)
0.241614 + 0.970373i \(0.422323\pi\)
\(432\) −1.00000 −0.0481125
\(433\) −18.5634 −0.892099 −0.446050 0.895008i \(-0.647170\pi\)
−0.446050 + 0.895008i \(0.647170\pi\)
\(434\) −1.92138 −0.0922290
\(435\) −18.2105 −0.873127
\(436\) 12.1410 0.581450
\(437\) −0.919499 −0.0439856
\(438\) 2.58810 0.123664
\(439\) −24.9087 −1.18883 −0.594415 0.804159i \(-0.702616\pi\)
−0.594415 + 0.804159i \(0.702616\pi\)
\(440\) 4.52526 0.215733
\(441\) −6.53232 −0.311063
\(442\) 0.480780 0.0228684
\(443\) −10.3404 −0.491285 −0.245642 0.969361i \(-0.578999\pi\)
−0.245642 + 0.969361i \(0.578999\pi\)
\(444\) 0.709000 0.0336477
\(445\) 31.6795 1.50175
\(446\) 5.55345 0.262963
\(447\) −0.845331 −0.0399828
\(448\) −0.683869 −0.0323098
\(449\) −22.0314 −1.03973 −0.519864 0.854249i \(-0.674017\pi\)
−0.519864 + 0.854249i \(0.674017\pi\)
\(450\) 0.458066 0.0215934
\(451\) −5.30369 −0.249741
\(452\) 10.7865 0.507353
\(453\) −20.7691 −0.975820
\(454\) 12.3784 0.580945
\(455\) −0.768136 −0.0360108
\(456\) 0.134424 0.00629498
\(457\) 21.8148 1.02045 0.510227 0.860040i \(-0.329561\pi\)
0.510227 + 0.860040i \(0.329561\pi\)
\(458\) −2.70403 −0.126351
\(459\) −1.00000 −0.0466760
\(460\) 15.9806 0.745101
\(461\) −23.1270 −1.07713 −0.538566 0.842583i \(-0.681034\pi\)
−0.538566 + 0.842583i \(0.681034\pi\)
\(462\) 1.32464 0.0616277
\(463\) −2.30556 −0.107149 −0.0535743 0.998564i \(-0.517061\pi\)
−0.0535743 + 0.998564i \(0.517061\pi\)
\(464\) 7.79476 0.361863
\(465\) −6.56386 −0.304392
\(466\) −9.87308 −0.457362
\(467\) 18.8292 0.871310 0.435655 0.900114i \(-0.356517\pi\)
0.435655 + 0.900114i \(0.356517\pi\)
\(468\) 0.480780 0.0222240
\(469\) −6.10638 −0.281966
\(470\) −20.8000 −0.959433
\(471\) −4.90486 −0.226004
\(472\) 1.00000 0.0460287
\(473\) −12.4815 −0.573900
\(474\) −12.0018 −0.551259
\(475\) −0.0615750 −0.00282526
\(476\) −0.683869 −0.0313451
\(477\) 13.4888 0.617609
\(478\) 3.27930 0.149992
\(479\) 40.4771 1.84945 0.924724 0.380639i \(-0.124296\pi\)
0.924724 + 0.380639i \(0.124296\pi\)
\(480\) −2.33625 −0.106635
\(481\) −0.340873 −0.0155425
\(482\) −6.96482 −0.317239
\(483\) 4.67786 0.212850
\(484\) −7.24813 −0.329460
\(485\) 7.04986 0.320118
\(486\) −1.00000 −0.0453609
\(487\) −11.7648 −0.533112 −0.266556 0.963819i \(-0.585886\pi\)
−0.266556 + 0.963819i \(0.585886\pi\)
\(488\) −11.1555 −0.504985
\(489\) 0.793255 0.0358722
\(490\) −15.2611 −0.689428
\(491\) −26.3139 −1.18753 −0.593765 0.804638i \(-0.702359\pi\)
−0.593765 + 0.804638i \(0.702359\pi\)
\(492\) 2.73813 0.123444
\(493\) 7.79476 0.351058
\(494\) −0.0646283 −0.00290776
\(495\) 4.52526 0.203395
\(496\) 2.80957 0.126153
\(497\) −3.98249 −0.178639
\(498\) 5.79142 0.259520
\(499\) −3.10849 −0.139155 −0.0695775 0.997577i \(-0.522165\pi\)
−0.0695775 + 0.997577i \(0.522165\pi\)
\(500\) −10.6111 −0.474543
\(501\) 1.71195 0.0764843
\(502\) −20.2352 −0.903140
\(503\) 1.13272 0.0505055 0.0252528 0.999681i \(-0.491961\pi\)
0.0252528 + 0.999681i \(0.491961\pi\)
\(504\) −0.683869 −0.0304619
\(505\) 3.31839 0.147666
\(506\) 13.2495 0.589011
\(507\) 12.7689 0.567085
\(508\) −3.99253 −0.177140
\(509\) 11.7618 0.521334 0.260667 0.965429i \(-0.416058\pi\)
0.260667 + 0.965429i \(0.416058\pi\)
\(510\) −2.33625 −0.103451
\(511\) 1.76992 0.0782968
\(512\) 1.00000 0.0441942
\(513\) 0.134424 0.00593496
\(514\) −0.910524 −0.0401615
\(515\) −33.9883 −1.49771
\(516\) 6.44381 0.283673
\(517\) −17.2452 −0.758443
\(518\) 0.484863 0.0213037
\(519\) −23.6118 −1.03644
\(520\) 1.12322 0.0492565
\(521\) −15.5802 −0.682580 −0.341290 0.939958i \(-0.610864\pi\)
−0.341290 + 0.939958i \(0.610864\pi\)
\(522\) 7.79476 0.341167
\(523\) −39.8744 −1.74359 −0.871793 0.489875i \(-0.837043\pi\)
−0.871793 + 0.489875i \(0.837043\pi\)
\(524\) −9.37785 −0.409673
\(525\) 0.313257 0.0136717
\(526\) 15.6632 0.682948
\(527\) 2.80957 0.122387
\(528\) −1.93698 −0.0842960
\(529\) 23.7896 1.03433
\(530\) 31.5132 1.36884
\(531\) 1.00000 0.0433963
\(532\) 0.0919283 0.00398560
\(533\) −1.31644 −0.0570212
\(534\) −13.5600 −0.586798
\(535\) 14.4012 0.622618
\(536\) 8.92916 0.385681
\(537\) 21.7180 0.937202
\(538\) 15.6658 0.675399
\(539\) −12.6530 −0.545001
\(540\) −2.33625 −0.100536
\(541\) 27.4040 1.17819 0.589094 0.808064i \(-0.299485\pi\)
0.589094 + 0.808064i \(0.299485\pi\)
\(542\) 0.951602 0.0408748
\(543\) −14.4439 −0.619849
\(544\) 1.00000 0.0428746
\(545\) 28.3645 1.21500
\(546\) 0.328790 0.0140709
\(547\) −25.6204 −1.09545 −0.547724 0.836659i \(-0.684505\pi\)
−0.547724 + 0.836659i \(0.684505\pi\)
\(548\) 17.3272 0.740181
\(549\) −11.1555 −0.476105
\(550\) 0.887263 0.0378330
\(551\) −1.04780 −0.0446379
\(552\) −6.84029 −0.291142
\(553\) −8.20762 −0.349024
\(554\) −8.23112 −0.349707
\(555\) 1.65640 0.0703103
\(556\) −18.9097 −0.801949
\(557\) −10.5851 −0.448503 −0.224252 0.974531i \(-0.571994\pi\)
−0.224252 + 0.974531i \(0.571994\pi\)
\(558\) 2.80957 0.118939
\(559\) −3.09805 −0.131034
\(560\) −1.59769 −0.0675147
\(561\) −1.93698 −0.0817792
\(562\) 12.9741 0.547281
\(563\) −18.0402 −0.760303 −0.380151 0.924924i \(-0.624128\pi\)
−0.380151 + 0.924924i \(0.624128\pi\)
\(564\) 8.90316 0.374891
\(565\) 25.1999 1.06017
\(566\) −3.83895 −0.161363
\(567\) −0.683869 −0.0287198
\(568\) 5.82347 0.244347
\(569\) −10.5867 −0.443820 −0.221910 0.975067i \(-0.571229\pi\)
−0.221910 + 0.975067i \(0.571229\pi\)
\(570\) 0.314048 0.0131540
\(571\) 8.89154 0.372099 0.186050 0.982540i \(-0.440431\pi\)
0.186050 + 0.982540i \(0.440431\pi\)
\(572\) 0.931258 0.0389379
\(573\) −0.474135 −0.0198073
\(574\) 1.87252 0.0781576
\(575\) 3.13330 0.130668
\(576\) 1.00000 0.0416667
\(577\) 34.1238 1.42059 0.710296 0.703903i \(-0.248561\pi\)
0.710296 + 0.703903i \(0.248561\pi\)
\(578\) 1.00000 0.0415945
\(579\) −7.01099 −0.291367
\(580\) 18.2105 0.756150
\(581\) 3.96057 0.164312
\(582\) −3.01760 −0.125083
\(583\) 26.1274 1.08209
\(584\) −2.58810 −0.107097
\(585\) 1.12322 0.0464395
\(586\) 20.7091 0.855486
\(587\) −11.2691 −0.465125 −0.232563 0.972581i \(-0.574711\pi\)
−0.232563 + 0.972581i \(0.574711\pi\)
\(588\) 6.53232 0.269388
\(589\) −0.377673 −0.0155618
\(590\) 2.33625 0.0961819
\(591\) 1.46125 0.0601079
\(592\) −0.709000 −0.0291397
\(593\) 10.9643 0.450252 0.225126 0.974330i \(-0.427721\pi\)
0.225126 + 0.974330i \(0.427721\pi\)
\(594\) −1.93698 −0.0794751
\(595\) −1.59769 −0.0654989
\(596\) 0.845331 0.0346261
\(597\) 12.2073 0.499613
\(598\) 3.28867 0.134484
\(599\) −40.7716 −1.66588 −0.832941 0.553362i \(-0.813345\pi\)
−0.832941 + 0.553362i \(0.813345\pi\)
\(600\) −0.458066 −0.0187005
\(601\) −26.7629 −1.09168 −0.545841 0.837889i \(-0.683790\pi\)
−0.545841 + 0.837889i \(0.683790\pi\)
\(602\) 4.40672 0.179605
\(603\) 8.92916 0.363624
\(604\) 20.7691 0.845085
\(605\) −16.9334 −0.688442
\(606\) −1.42039 −0.0576994
\(607\) −21.8331 −0.886176 −0.443088 0.896478i \(-0.646117\pi\)
−0.443088 + 0.896478i \(0.646117\pi\)
\(608\) −0.134424 −0.00545161
\(609\) 5.33059 0.216007
\(610\) −26.0620 −1.05522
\(611\) −4.28046 −0.173169
\(612\) 1.00000 0.0404226
\(613\) 21.7308 0.877698 0.438849 0.898561i \(-0.355386\pi\)
0.438849 + 0.898561i \(0.355386\pi\)
\(614\) 6.93896 0.280034
\(615\) 6.39696 0.257950
\(616\) −1.32464 −0.0533712
\(617\) 4.18038 0.168296 0.0841478 0.996453i \(-0.473183\pi\)
0.0841478 + 0.996453i \(0.473183\pi\)
\(618\) 14.5482 0.585216
\(619\) −19.2345 −0.773100 −0.386550 0.922268i \(-0.626333\pi\)
−0.386550 + 0.922268i \(0.626333\pi\)
\(620\) 6.56386 0.263611
\(621\) −6.84029 −0.274491
\(622\) 3.79474 0.152155
\(623\) −9.27325 −0.371525
\(624\) −0.480780 −0.0192466
\(625\) −27.0805 −1.08322
\(626\) −5.69740 −0.227714
\(627\) 0.260376 0.0103984
\(628\) 4.90486 0.195725
\(629\) −0.709000 −0.0282697
\(630\) −1.59769 −0.0636534
\(631\) −18.9098 −0.752785 −0.376393 0.926460i \(-0.622836\pi\)
−0.376393 + 0.926460i \(0.622836\pi\)
\(632\) 12.0018 0.477404
\(633\) 12.4282 0.493978
\(634\) −19.0607 −0.756998
\(635\) −9.32756 −0.370153
\(636\) −13.4888 −0.534865
\(637\) −3.14061 −0.124435
\(638\) 15.0983 0.597746
\(639\) 5.82347 0.230373
\(640\) 2.33625 0.0923484
\(641\) −30.7190 −1.21333 −0.606664 0.794958i \(-0.707493\pi\)
−0.606664 + 0.794958i \(0.707493\pi\)
\(642\) −6.16423 −0.243283
\(643\) −38.4980 −1.51821 −0.759106 0.650967i \(-0.774364\pi\)
−0.759106 + 0.650967i \(0.774364\pi\)
\(644\) −4.67786 −0.184334
\(645\) 15.0544 0.592765
\(646\) −0.134424 −0.00528884
\(647\) −42.8012 −1.68269 −0.841345 0.540498i \(-0.818236\pi\)
−0.841345 + 0.540498i \(0.818236\pi\)
\(648\) 1.00000 0.0392837
\(649\) 1.93698 0.0760329
\(650\) 0.220229 0.00863808
\(651\) 1.92138 0.0753047
\(652\) −0.793255 −0.0310663
\(653\) −45.9452 −1.79797 −0.898987 0.437976i \(-0.855695\pi\)
−0.898987 + 0.437976i \(0.855695\pi\)
\(654\) −12.1410 −0.474752
\(655\) −21.9090 −0.856056
\(656\) −2.73813 −0.106906
\(657\) −2.58810 −0.100972
\(658\) 6.08859 0.237358
\(659\) −13.1101 −0.510696 −0.255348 0.966849i \(-0.582190\pi\)
−0.255348 + 0.966849i \(0.582190\pi\)
\(660\) −4.52526 −0.176145
\(661\) −16.0578 −0.624576 −0.312288 0.949987i \(-0.601095\pi\)
−0.312288 + 0.949987i \(0.601095\pi\)
\(662\) 7.10042 0.275966
\(663\) −0.480780 −0.0186719
\(664\) −5.79142 −0.224751
\(665\) 0.214768 0.00832833
\(666\) −0.709000 −0.0274732
\(667\) 53.3184 2.06450
\(668\) −1.71195 −0.0662374
\(669\) −5.55345 −0.214709
\(670\) 20.8608 0.805921
\(671\) −21.6079 −0.834164
\(672\) 0.683869 0.0263808
\(673\) −14.6881 −0.566184 −0.283092 0.959093i \(-0.591360\pi\)
−0.283092 + 0.959093i \(0.591360\pi\)
\(674\) −2.63257 −0.101403
\(675\) −0.458066 −0.0176310
\(676\) −12.7689 −0.491110
\(677\) 3.08551 0.118586 0.0592930 0.998241i \(-0.481115\pi\)
0.0592930 + 0.998241i \(0.481115\pi\)
\(678\) −10.7865 −0.414252
\(679\) −2.06364 −0.0791952
\(680\) 2.33625 0.0895911
\(681\) −12.3784 −0.474340
\(682\) 5.44207 0.208388
\(683\) −31.0309 −1.18736 −0.593682 0.804700i \(-0.702326\pi\)
−0.593682 + 0.804700i \(0.702326\pi\)
\(684\) −0.134424 −0.00513983
\(685\) 40.4807 1.54669
\(686\) 9.25433 0.353332
\(687\) 2.70403 0.103165
\(688\) −6.44381 −0.245668
\(689\) 6.48513 0.247064
\(690\) −15.9806 −0.608372
\(691\) 1.91114 0.0727032 0.0363516 0.999339i \(-0.488426\pi\)
0.0363516 + 0.999339i \(0.488426\pi\)
\(692\) 23.6118 0.897585
\(693\) −1.32464 −0.0503188
\(694\) −15.7899 −0.599376
\(695\) −44.1778 −1.67576
\(696\) −7.79476 −0.295460
\(697\) −2.73813 −0.103714
\(698\) −11.5109 −0.435694
\(699\) 9.87308 0.373434
\(700\) −0.313257 −0.0118400
\(701\) −32.7563 −1.23719 −0.618593 0.785711i \(-0.712297\pi\)
−0.618593 + 0.785711i \(0.712297\pi\)
\(702\) −0.480780 −0.0181459
\(703\) 0.0953066 0.00359456
\(704\) 1.93698 0.0730025
\(705\) 20.8000 0.783373
\(706\) 31.0633 1.16908
\(707\) −0.971361 −0.0365318
\(708\) −1.00000 −0.0375823
\(709\) −18.9454 −0.711510 −0.355755 0.934579i \(-0.615776\pi\)
−0.355755 + 0.934579i \(0.615776\pi\)
\(710\) 13.6051 0.510590
\(711\) 12.0018 0.450101
\(712\) 13.5600 0.508182
\(713\) 19.2183 0.719730
\(714\) 0.683869 0.0255931
\(715\) 2.17565 0.0813648
\(716\) −21.7180 −0.811640
\(717\) −3.27930 −0.122468
\(718\) 23.5865 0.880242
\(719\) −24.1272 −0.899791 −0.449896 0.893081i \(-0.648539\pi\)
−0.449896 + 0.893081i \(0.648539\pi\)
\(720\) 2.33625 0.0870669
\(721\) 9.94909 0.370523
\(722\) −18.9819 −0.706434
\(723\) 6.96482 0.259025
\(724\) 14.4439 0.536805
\(725\) 3.57051 0.132606
\(726\) 7.24813 0.269003
\(727\) 50.8356 1.88539 0.942694 0.333659i \(-0.108283\pi\)
0.942694 + 0.333659i \(0.108283\pi\)
\(728\) −0.328790 −0.0121858
\(729\) 1.00000 0.0370370
\(730\) −6.04646 −0.223789
\(731\) −6.44381 −0.238333
\(732\) 11.1555 0.412319
\(733\) 39.5771 1.46181 0.730906 0.682478i \(-0.239098\pi\)
0.730906 + 0.682478i \(0.239098\pi\)
\(734\) −7.13232 −0.263259
\(735\) 15.2611 0.562916
\(736\) 6.84029 0.252136
\(737\) 17.2956 0.637090
\(738\) −2.73813 −0.100792
\(739\) −2.39046 −0.0879346 −0.0439673 0.999033i \(-0.514000\pi\)
−0.0439673 + 0.999033i \(0.514000\pi\)
\(740\) −1.65640 −0.0608905
\(741\) 0.0646283 0.00237418
\(742\) −9.22456 −0.338644
\(743\) 11.2795 0.413804 0.206902 0.978362i \(-0.433662\pi\)
0.206902 + 0.978362i \(0.433662\pi\)
\(744\) −2.80957 −0.103004
\(745\) 1.97491 0.0723549
\(746\) 28.1071 1.02907
\(747\) −5.79142 −0.211897
\(748\) 1.93698 0.0708228
\(749\) −4.21553 −0.154032
\(750\) 10.6111 0.387462
\(751\) 15.3530 0.560238 0.280119 0.959965i \(-0.409626\pi\)
0.280119 + 0.959965i \(0.409626\pi\)
\(752\) −8.90316 −0.324665
\(753\) 20.2352 0.737411
\(754\) 3.74756 0.136478
\(755\) 48.5219 1.76589
\(756\) 0.683869 0.0248721
\(757\) −15.6544 −0.568969 −0.284484 0.958681i \(-0.591822\pi\)
−0.284484 + 0.958681i \(0.591822\pi\)
\(758\) −3.21621 −0.116818
\(759\) −13.2495 −0.480926
\(760\) −0.314048 −0.0113917
\(761\) 2.16738 0.0785674 0.0392837 0.999228i \(-0.487492\pi\)
0.0392837 + 0.999228i \(0.487492\pi\)
\(762\) 3.99253 0.144634
\(763\) −8.30288 −0.300584
\(764\) 0.474135 0.0171536
\(765\) 2.33625 0.0844673
\(766\) −17.9314 −0.647888
\(767\) 0.480780 0.0173599
\(768\) −1.00000 −0.0360844
\(769\) 34.5419 1.24561 0.622806 0.782376i \(-0.285993\pi\)
0.622806 + 0.782376i \(0.285993\pi\)
\(770\) −3.09468 −0.111525
\(771\) 0.910524 0.0327917
\(772\) 7.01099 0.252331
\(773\) −3.30022 −0.118701 −0.0593503 0.998237i \(-0.518903\pi\)
−0.0593503 + 0.998237i \(0.518903\pi\)
\(774\) −6.44381 −0.231618
\(775\) 1.28697 0.0462293
\(776\) 3.01760 0.108325
\(777\) −0.484863 −0.0173944
\(778\) 24.8722 0.891713
\(779\) 0.368070 0.0131875
\(780\) −1.12322 −0.0402178
\(781\) 11.2799 0.403627
\(782\) 6.84029 0.244608
\(783\) −7.79476 −0.278562
\(784\) −6.53232 −0.233297
\(785\) 11.4590 0.408989
\(786\) 9.37785 0.334497
\(787\) 12.5418 0.447067 0.223533 0.974696i \(-0.428241\pi\)
0.223533 + 0.974696i \(0.428241\pi\)
\(788\) −1.46125 −0.0520550
\(789\) −15.6632 −0.557625
\(790\) 28.0391 0.997586
\(791\) −7.37654 −0.262280
\(792\) 1.93698 0.0688274
\(793\) −5.36333 −0.190457
\(794\) 22.0814 0.783639
\(795\) −31.5132 −1.11766
\(796\) −12.2073 −0.432677
\(797\) −54.6473 −1.93571 −0.967853 0.251517i \(-0.919070\pi\)
−0.967853 + 0.251517i \(0.919070\pi\)
\(798\) −0.0919283 −0.00325423
\(799\) −8.90316 −0.314971
\(800\) 0.458066 0.0161951
\(801\) 13.5600 0.479119
\(802\) −20.6434 −0.728944
\(803\) −5.01309 −0.176908
\(804\) −8.92916 −0.314907
\(805\) −10.9287 −0.385185
\(806\) 1.35078 0.0475793
\(807\) −15.6658 −0.551461
\(808\) 1.42039 0.0499692
\(809\) −47.6421 −1.67501 −0.837504 0.546431i \(-0.815986\pi\)
−0.837504 + 0.546431i \(0.815986\pi\)
\(810\) 2.33625 0.0820875
\(811\) −18.9398 −0.665067 −0.332533 0.943092i \(-0.607903\pi\)
−0.332533 + 0.943092i \(0.607903\pi\)
\(812\) −5.33059 −0.187067
\(813\) −0.951602 −0.0333741
\(814\) −1.37332 −0.0481347
\(815\) −1.85324 −0.0649163
\(816\) −1.00000 −0.0350070
\(817\) 0.866202 0.0303046
\(818\) 31.1858 1.09039
\(819\) −0.328790 −0.0114889
\(820\) −6.39696 −0.223392
\(821\) 9.34226 0.326047 0.163024 0.986622i \(-0.447875\pi\)
0.163024 + 0.986622i \(0.447875\pi\)
\(822\) −17.3272 −0.604356
\(823\) −39.9866 −1.39385 −0.696923 0.717146i \(-0.745448\pi\)
−0.696923 + 0.717146i \(0.745448\pi\)
\(824\) −14.5482 −0.506812
\(825\) −0.887263 −0.0308905
\(826\) −0.683869 −0.0237948
\(827\) 42.0276 1.46144 0.730722 0.682675i \(-0.239184\pi\)
0.730722 + 0.682675i \(0.239184\pi\)
\(828\) 6.84029 0.237717
\(829\) −29.0685 −1.00959 −0.504796 0.863239i \(-0.668432\pi\)
−0.504796 + 0.863239i \(0.668432\pi\)
\(830\) −13.5302 −0.469641
\(831\) 8.23112 0.285534
\(832\) 0.480780 0.0166680
\(833\) −6.53232 −0.226332
\(834\) 18.9097 0.654789
\(835\) −3.99955 −0.138410
\(836\) −0.260376 −0.00900529
\(837\) −2.80957 −0.0971129
\(838\) 32.5126 1.12313
\(839\) −41.3546 −1.42772 −0.713860 0.700289i \(-0.753055\pi\)
−0.713860 + 0.700289i \(0.753055\pi\)
\(840\) 1.59769 0.0551255
\(841\) 31.7583 1.09511
\(842\) 10.5978 0.365224
\(843\) −12.9741 −0.446853
\(844\) −12.4282 −0.427798
\(845\) −29.8312 −1.02623
\(846\) −8.90316 −0.306097
\(847\) 4.95677 0.170317
\(848\) 13.4888 0.463207
\(849\) 3.83895 0.131752
\(850\) 0.458066 0.0157115
\(851\) −4.84977 −0.166248
\(852\) −5.82347 −0.199509
\(853\) 5.71145 0.195556 0.0977781 0.995208i \(-0.468826\pi\)
0.0977781 + 0.995208i \(0.468826\pi\)
\(854\) 7.62889 0.261055
\(855\) −0.314048 −0.0107402
\(856\) 6.16423 0.210689
\(857\) 40.9247 1.39796 0.698981 0.715141i \(-0.253637\pi\)
0.698981 + 0.715141i \(0.253637\pi\)
\(858\) −0.931258 −0.0317926
\(859\) −31.5340 −1.07593 −0.537963 0.842968i \(-0.680806\pi\)
−0.537963 + 0.842968i \(0.680806\pi\)
\(860\) −15.0544 −0.513349
\(861\) −1.87252 −0.0638154
\(862\) 10.0321 0.341693
\(863\) 13.3177 0.453338 0.226669 0.973972i \(-0.427216\pi\)
0.226669 + 0.973972i \(0.427216\pi\)
\(864\) −1.00000 −0.0340207
\(865\) 55.1630 1.87560
\(866\) −18.5634 −0.630809
\(867\) −1.00000 −0.0339618
\(868\) −1.92138 −0.0652158
\(869\) 23.2471 0.788604
\(870\) −18.2105 −0.617394
\(871\) 4.29296 0.145461
\(872\) 12.1410 0.411148
\(873\) 3.01760 0.102130
\(874\) −0.919499 −0.0311025
\(875\) 7.25660 0.245318
\(876\) 2.58810 0.0874439
\(877\) 45.2580 1.52825 0.764127 0.645066i \(-0.223170\pi\)
0.764127 + 0.645066i \(0.223170\pi\)
\(878\) −24.9087 −0.840629
\(879\) −20.7091 −0.698501
\(880\) 4.52526 0.152546
\(881\) −1.92725 −0.0649306 −0.0324653 0.999473i \(-0.510336\pi\)
−0.0324653 + 0.999473i \(0.510336\pi\)
\(882\) −6.53232 −0.219955
\(883\) 11.8267 0.398001 0.199000 0.979999i \(-0.436231\pi\)
0.199000 + 0.979999i \(0.436231\pi\)
\(884\) 0.480780 0.0161704
\(885\) −2.33625 −0.0785322
\(886\) −10.3404 −0.347391
\(887\) 19.3000 0.648032 0.324016 0.946052i \(-0.394967\pi\)
0.324016 + 0.946052i \(0.394967\pi\)
\(888\) 0.709000 0.0237925
\(889\) 2.73037 0.0915737
\(890\) 31.6795 1.06190
\(891\) 1.93698 0.0648911
\(892\) 5.55345 0.185943
\(893\) 1.19680 0.0400493
\(894\) −0.845331 −0.0282721
\(895\) −50.7387 −1.69601
\(896\) −0.683869 −0.0228465
\(897\) −3.28867 −0.109806
\(898\) −22.0314 −0.735198
\(899\) 21.8999 0.730403
\(900\) 0.458066 0.0152689
\(901\) 13.4888 0.449377
\(902\) −5.30369 −0.176594
\(903\) −4.40672 −0.146646
\(904\) 10.7865 0.358753
\(905\) 33.7447 1.12171
\(906\) −20.7691 −0.690009
\(907\) 29.5964 0.982733 0.491367 0.870953i \(-0.336497\pi\)
0.491367 + 0.870953i \(0.336497\pi\)
\(908\) 12.3784 0.410790
\(909\) 1.42039 0.0471114
\(910\) −0.768136 −0.0254635
\(911\) 47.5967 1.57695 0.788474 0.615068i \(-0.210871\pi\)
0.788474 + 0.615068i \(0.210871\pi\)
\(912\) 0.134424 0.00445122
\(913\) −11.2178 −0.371256
\(914\) 21.8148 0.721570
\(915\) 26.0620 0.861583
\(916\) −2.70403 −0.0893435
\(917\) 6.41322 0.211783
\(918\) −1.00000 −0.0330049
\(919\) −33.8497 −1.11660 −0.558300 0.829639i \(-0.688546\pi\)
−0.558300 + 0.829639i \(0.688546\pi\)
\(920\) 15.9806 0.526866
\(921\) −6.93896 −0.228646
\(922\) −23.1270 −0.761648
\(923\) 2.79980 0.0921567
\(924\) 1.32464 0.0435774
\(925\) −0.324769 −0.0106783
\(926\) −2.30556 −0.0757655
\(927\) −14.5482 −0.477827
\(928\) 7.79476 0.255875
\(929\) −21.3804 −0.701467 −0.350734 0.936475i \(-0.614068\pi\)
−0.350734 + 0.936475i \(0.614068\pi\)
\(930\) −6.56386 −0.215237
\(931\) 0.878100 0.0287786
\(932\) −9.87308 −0.323404
\(933\) −3.79474 −0.124234
\(934\) 18.8292 0.616109
\(935\) 4.52526 0.147992
\(936\) 0.480780 0.0157148
\(937\) −13.6256 −0.445128 −0.222564 0.974918i \(-0.571443\pi\)
−0.222564 + 0.974918i \(0.571443\pi\)
\(938\) −6.10638 −0.199380
\(939\) 5.69740 0.185928
\(940\) −20.8000 −0.678421
\(941\) −1.26926 −0.0413767 −0.0206883 0.999786i \(-0.506586\pi\)
−0.0206883 + 0.999786i \(0.506586\pi\)
\(942\) −4.90486 −0.159809
\(943\) −18.7296 −0.609920
\(944\) 1.00000 0.0325472
\(945\) 1.59769 0.0519728
\(946\) −12.4815 −0.405809
\(947\) −51.7861 −1.68282 −0.841412 0.540395i \(-0.818275\pi\)
−0.841412 + 0.540395i \(0.818275\pi\)
\(948\) −12.0018 −0.389799
\(949\) −1.24431 −0.0403919
\(950\) −0.0615750 −0.00199776
\(951\) 19.0607 0.618086
\(952\) −0.683869 −0.0221643
\(953\) −13.7380 −0.445017 −0.222509 0.974931i \(-0.571425\pi\)
−0.222509 + 0.974931i \(0.571425\pi\)
\(954\) 13.4888 0.436716
\(955\) 1.10770 0.0358443
\(956\) 3.27930 0.106060
\(957\) −15.0983 −0.488057
\(958\) 40.4771 1.30776
\(959\) −11.8495 −0.382641
\(960\) −2.33625 −0.0754022
\(961\) −23.1063 −0.745365
\(962\) −0.340873 −0.0109902
\(963\) 6.16423 0.198640
\(964\) −6.96482 −0.224322
\(965\) 16.3794 0.527272
\(966\) 4.67786 0.150508
\(967\) 42.7342 1.37424 0.687120 0.726544i \(-0.258875\pi\)
0.687120 + 0.726544i \(0.258875\pi\)
\(968\) −7.24813 −0.232964
\(969\) 0.134424 0.00431832
\(970\) 7.04986 0.226357
\(971\) −29.9598 −0.961454 −0.480727 0.876870i \(-0.659627\pi\)
−0.480727 + 0.876870i \(0.659627\pi\)
\(972\) −1.00000 −0.0320750
\(973\) 12.9317 0.414573
\(974\) −11.7648 −0.376967
\(975\) −0.220229 −0.00705297
\(976\) −11.1555 −0.357078
\(977\) 24.9595 0.798524 0.399262 0.916837i \(-0.369266\pi\)
0.399262 + 0.916837i \(0.369266\pi\)
\(978\) 0.793255 0.0253655
\(979\) 26.2654 0.839445
\(980\) −15.2611 −0.487499
\(981\) 12.1410 0.387634
\(982\) −26.3139 −0.839711
\(983\) −48.3918 −1.54346 −0.771730 0.635951i \(-0.780608\pi\)
−0.771730 + 0.635951i \(0.780608\pi\)
\(984\) 2.73813 0.0872884
\(985\) −3.41385 −0.108774
\(986\) 7.79476 0.248236
\(987\) −6.08859 −0.193802
\(988\) −0.0646283 −0.00205610
\(989\) −44.0775 −1.40158
\(990\) 4.52526 0.143822
\(991\) 21.7193 0.689938 0.344969 0.938614i \(-0.387890\pi\)
0.344969 + 0.938614i \(0.387890\pi\)
\(992\) 2.80957 0.0892039
\(993\) −7.10042 −0.225325
\(994\) −3.98249 −0.126317
\(995\) −28.5194 −0.904125
\(996\) 5.79142 0.183508
\(997\) −49.4539 −1.56622 −0.783110 0.621884i \(-0.786368\pi\)
−0.783110 + 0.621884i \(0.786368\pi\)
\(998\) −3.10849 −0.0983975
\(999\) 0.709000 0.0224318
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.bc.1.10 14
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
6018.2.a.bc.1.10 14 1.1 even 1 trivial