Properties

Label 6018.2.a.bb.1.7
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 1.7
Root \(0.197152\) 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)
 
\(f(q)\) \(=\) \(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +0.197152 q^{5} +1.00000 q^{6} +1.50880 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +0.197152 q^{5} +1.00000 q^{6} +1.50880 q^{7} +1.00000 q^{8} +1.00000 q^{9} +0.197152 q^{10} -1.06748 q^{11} +1.00000 q^{12} -3.56974 q^{13} +1.50880 q^{14} +0.197152 q^{15} +1.00000 q^{16} +1.00000 q^{17} +1.00000 q^{18} -3.08651 q^{19} +0.197152 q^{20} +1.50880 q^{21} -1.06748 q^{22} +2.60504 q^{23} +1.00000 q^{24} -4.96113 q^{25} -3.56974 q^{26} +1.00000 q^{27} +1.50880 q^{28} +1.69549 q^{29} +0.197152 q^{30} +8.35472 q^{31} +1.00000 q^{32} -1.06748 q^{33} +1.00000 q^{34} +0.297463 q^{35} +1.00000 q^{36} +10.5779 q^{37} -3.08651 q^{38} -3.56974 q^{39} +0.197152 q^{40} +10.3617 q^{41} +1.50880 q^{42} +3.49884 q^{43} -1.06748 q^{44} +0.197152 q^{45} +2.60504 q^{46} +8.36241 q^{47} +1.00000 q^{48} -4.72353 q^{49} -4.96113 q^{50} +1.00000 q^{51} -3.56974 q^{52} -9.48041 q^{53} +1.00000 q^{54} -0.210456 q^{55} +1.50880 q^{56} -3.08651 q^{57} +1.69549 q^{58} -1.00000 q^{59} +0.197152 q^{60} +13.8381 q^{61} +8.35472 q^{62} +1.50880 q^{63} +1.00000 q^{64} -0.703783 q^{65} -1.06748 q^{66} +13.1934 q^{67} +1.00000 q^{68} +2.60504 q^{69} +0.297463 q^{70} +0.742176 q^{71} +1.00000 q^{72} -7.50498 q^{73} +10.5779 q^{74} -4.96113 q^{75} -3.08651 q^{76} -1.61061 q^{77} -3.56974 q^{78} +10.8576 q^{79} +0.197152 q^{80} +1.00000 q^{81} +10.3617 q^{82} -1.77582 q^{83} +1.50880 q^{84} +0.197152 q^{85} +3.49884 q^{86} +1.69549 q^{87} -1.06748 q^{88} +4.46785 q^{89} +0.197152 q^{90} -5.38602 q^{91} +2.60504 q^{92} +8.35472 q^{93} +8.36241 q^{94} -0.608512 q^{95} +1.00000 q^{96} +15.6563 q^{97} -4.72353 q^{98} -1.06748 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 13 q + 13 q^{2} + 13 q^{3} + 13 q^{4} + 4 q^{5} + 13 q^{6} + 11 q^{7} + 13 q^{8} + 13 q^{9}+O(q^{10}) \) 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
\(5\) 0.197152 0.0881692 0.0440846 0.999028i \(-0.485963\pi\)
0.0440846 + 0.999028i \(0.485963\pi\)
\(6\) 1.00000 0.408248
\(7\) 1.50880 0.570272 0.285136 0.958487i \(-0.407961\pi\)
0.285136 + 0.958487i \(0.407961\pi\)
\(8\) 1.00000 0.353553
\(9\) 1.00000 0.333333
\(10\) 0.197152 0.0623450
\(11\) −1.06748 −0.321857 −0.160928 0.986966i \(-0.551449\pi\)
−0.160928 + 0.986966i \(0.551449\pi\)
\(12\) 1.00000 0.288675
\(13\) −3.56974 −0.990068 −0.495034 0.868874i \(-0.664844\pi\)
−0.495034 + 0.868874i \(0.664844\pi\)
\(14\) 1.50880 0.403243
\(15\) 0.197152 0.0509045
\(16\) 1.00000 0.250000
\(17\) 1.00000 0.242536
\(18\) 1.00000 0.235702
\(19\) −3.08651 −0.708094 −0.354047 0.935228i \(-0.615195\pi\)
−0.354047 + 0.935228i \(0.615195\pi\)
\(20\) 0.197152 0.0440846
\(21\) 1.50880 0.329247
\(22\) −1.06748 −0.227587
\(23\) 2.60504 0.543189 0.271594 0.962412i \(-0.412449\pi\)
0.271594 + 0.962412i \(0.412449\pi\)
\(24\) 1.00000 0.204124
\(25\) −4.96113 −0.992226
\(26\) −3.56974 −0.700084
\(27\) 1.00000 0.192450
\(28\) 1.50880 0.285136
\(29\) 1.69549 0.314845 0.157423 0.987531i \(-0.449682\pi\)
0.157423 + 0.987531i \(0.449682\pi\)
\(30\) 0.197152 0.0359949
\(31\) 8.35472 1.50055 0.750276 0.661124i \(-0.229920\pi\)
0.750276 + 0.661124i \(0.229920\pi\)
\(32\) 1.00000 0.176777
\(33\) −1.06748 −0.185824
\(34\) 1.00000 0.171499
\(35\) 0.297463 0.0502804
\(36\) 1.00000 0.166667
\(37\) 10.5779 1.73900 0.869498 0.493936i \(-0.164442\pi\)
0.869498 + 0.493936i \(0.164442\pi\)
\(38\) −3.08651 −0.500698
\(39\) −3.56974 −0.571616
\(40\) 0.197152 0.0311725
\(41\) 10.3617 1.61823 0.809114 0.587651i \(-0.199947\pi\)
0.809114 + 0.587651i \(0.199947\pi\)
\(42\) 1.50880 0.232812
\(43\) 3.49884 0.533568 0.266784 0.963756i \(-0.414039\pi\)
0.266784 + 0.963756i \(0.414039\pi\)
\(44\) −1.06748 −0.160928
\(45\) 0.197152 0.0293897
\(46\) 2.60504 0.384093
\(47\) 8.36241 1.21978 0.609892 0.792485i \(-0.291213\pi\)
0.609892 + 0.792485i \(0.291213\pi\)
\(48\) 1.00000 0.144338
\(49\) −4.72353 −0.674790
\(50\) −4.96113 −0.701610
\(51\) 1.00000 0.140028
\(52\) −3.56974 −0.495034
\(53\) −9.48041 −1.30223 −0.651117 0.758977i \(-0.725699\pi\)
−0.651117 + 0.758977i \(0.725699\pi\)
\(54\) 1.00000 0.136083
\(55\) −0.210456 −0.0283778
\(56\) 1.50880 0.201622
\(57\) −3.08651 −0.408818
\(58\) 1.69549 0.222629
\(59\) −1.00000 −0.130189
\(60\) 0.197152 0.0254522
\(61\) 13.8381 1.77179 0.885894 0.463887i \(-0.153546\pi\)
0.885894 + 0.463887i \(0.153546\pi\)
\(62\) 8.35472 1.06105
\(63\) 1.50880 0.190091
\(64\) 1.00000 0.125000
\(65\) −0.703783 −0.0872935
\(66\) −1.06748 −0.131397
\(67\) 13.1934 1.61183 0.805914 0.592033i \(-0.201674\pi\)
0.805914 + 0.592033i \(0.201674\pi\)
\(68\) 1.00000 0.121268
\(69\) 2.60504 0.313610
\(70\) 0.297463 0.0355536
\(71\) 0.742176 0.0880801 0.0440401 0.999030i \(-0.485977\pi\)
0.0440401 + 0.999030i \(0.485977\pi\)
\(72\) 1.00000 0.117851
\(73\) −7.50498 −0.878391 −0.439196 0.898391i \(-0.644736\pi\)
−0.439196 + 0.898391i \(0.644736\pi\)
\(74\) 10.5779 1.22966
\(75\) −4.96113 −0.572862
\(76\) −3.08651 −0.354047
\(77\) −1.61061 −0.183546
\(78\) −3.56974 −0.404194
\(79\) 10.8576 1.22157 0.610786 0.791795i \(-0.290853\pi\)
0.610786 + 0.791795i \(0.290853\pi\)
\(80\) 0.197152 0.0220423
\(81\) 1.00000 0.111111
\(82\) 10.3617 1.14426
\(83\) −1.77582 −0.194921 −0.0974607 0.995239i \(-0.531072\pi\)
−0.0974607 + 0.995239i \(0.531072\pi\)
\(84\) 1.50880 0.164623
\(85\) 0.197152 0.0213842
\(86\) 3.49884 0.377290
\(87\) 1.69549 0.181776
\(88\) −1.06748 −0.113794
\(89\) 4.46785 0.473592 0.236796 0.971559i \(-0.423903\pi\)
0.236796 + 0.971559i \(0.423903\pi\)
\(90\) 0.197152 0.0207817
\(91\) −5.38602 −0.564608
\(92\) 2.60504 0.271594
\(93\) 8.35472 0.866345
\(94\) 8.36241 0.862517
\(95\) −0.608512 −0.0624320
\(96\) 1.00000 0.102062
\(97\) 15.6563 1.58966 0.794830 0.606832i \(-0.207560\pi\)
0.794830 + 0.606832i \(0.207560\pi\)
\(98\) −4.72353 −0.477149
\(99\) −1.06748 −0.107286
\(100\) −4.96113 −0.496113
\(101\) 9.50176 0.945460 0.472730 0.881207i \(-0.343269\pi\)
0.472730 + 0.881207i \(0.343269\pi\)
\(102\) 1.00000 0.0990148
\(103\) −3.93030 −0.387264 −0.193632 0.981074i \(-0.562027\pi\)
−0.193632 + 0.981074i \(0.562027\pi\)
\(104\) −3.56974 −0.350042
\(105\) 0.297463 0.0290294
\(106\) −9.48041 −0.920819
\(107\) 6.77958 0.655407 0.327703 0.944781i \(-0.393725\pi\)
0.327703 + 0.944781i \(0.393725\pi\)
\(108\) 1.00000 0.0962250
\(109\) 7.32838 0.701932 0.350966 0.936388i \(-0.385853\pi\)
0.350966 + 0.936388i \(0.385853\pi\)
\(110\) −0.210456 −0.0200662
\(111\) 10.5779 1.00401
\(112\) 1.50880 0.142568
\(113\) −15.0982 −1.42032 −0.710161 0.704039i \(-0.751378\pi\)
−0.710161 + 0.704039i \(0.751378\pi\)
\(114\) −3.08651 −0.289078
\(115\) 0.513590 0.0478925
\(116\) 1.69549 0.157423
\(117\) −3.56974 −0.330023
\(118\) −1.00000 −0.0920575
\(119\) 1.50880 0.138311
\(120\) 0.197152 0.0179975
\(121\) −9.86049 −0.896408
\(122\) 13.8381 1.25284
\(123\) 10.3617 0.934285
\(124\) 8.35472 0.750276
\(125\) −1.96386 −0.175653
\(126\) 1.50880 0.134414
\(127\) −3.70663 −0.328910 −0.164455 0.986385i \(-0.552587\pi\)
−0.164455 + 0.986385i \(0.552587\pi\)
\(128\) 1.00000 0.0883883
\(129\) 3.49884 0.308056
\(130\) −0.703783 −0.0617258
\(131\) 5.11961 0.447302 0.223651 0.974669i \(-0.428202\pi\)
0.223651 + 0.974669i \(0.428202\pi\)
\(132\) −1.06748 −0.0929120
\(133\) −4.65692 −0.403806
\(134\) 13.1934 1.13973
\(135\) 0.197152 0.0169682
\(136\) 1.00000 0.0857493
\(137\) −3.58744 −0.306495 −0.153248 0.988188i \(-0.548973\pi\)
−0.153248 + 0.988188i \(0.548973\pi\)
\(138\) 2.60504 0.221756
\(139\) −14.0373 −1.19063 −0.595313 0.803494i \(-0.702972\pi\)
−0.595313 + 0.803494i \(0.702972\pi\)
\(140\) 0.297463 0.0251402
\(141\) 8.36241 0.704242
\(142\) 0.742176 0.0622821
\(143\) 3.81062 0.318660
\(144\) 1.00000 0.0833333
\(145\) 0.334270 0.0277596
\(146\) −7.50498 −0.621116
\(147\) −4.72353 −0.389590
\(148\) 10.5779 0.869498
\(149\) −15.8542 −1.29883 −0.649413 0.760436i \(-0.724985\pi\)
−0.649413 + 0.760436i \(0.724985\pi\)
\(150\) −4.96113 −0.405075
\(151\) −12.8033 −1.04192 −0.520958 0.853582i \(-0.674425\pi\)
−0.520958 + 0.853582i \(0.674425\pi\)
\(152\) −3.08651 −0.250349
\(153\) 1.00000 0.0808452
\(154\) −1.61061 −0.129786
\(155\) 1.64715 0.132302
\(156\) −3.56974 −0.285808
\(157\) −5.34695 −0.426733 −0.213367 0.976972i \(-0.568443\pi\)
−0.213367 + 0.976972i \(0.568443\pi\)
\(158\) 10.8576 0.863782
\(159\) −9.48041 −0.751845
\(160\) 0.197152 0.0155863
\(161\) 3.93048 0.309765
\(162\) 1.00000 0.0785674
\(163\) 1.99629 0.156362 0.0781808 0.996939i \(-0.475089\pi\)
0.0781808 + 0.996939i \(0.475089\pi\)
\(164\) 10.3617 0.809114
\(165\) −0.210456 −0.0163840
\(166\) −1.77582 −0.137830
\(167\) 12.1067 0.936846 0.468423 0.883504i \(-0.344822\pi\)
0.468423 + 0.883504i \(0.344822\pi\)
\(168\) 1.50880 0.116406
\(169\) −0.256942 −0.0197648
\(170\) 0.197152 0.0151209
\(171\) −3.08651 −0.236031
\(172\) 3.49884 0.266784
\(173\) −9.44184 −0.717849 −0.358925 0.933367i \(-0.616857\pi\)
−0.358925 + 0.933367i \(0.616857\pi\)
\(174\) 1.69549 0.128535
\(175\) −7.48534 −0.565839
\(176\) −1.06748 −0.0804642
\(177\) −1.00000 −0.0751646
\(178\) 4.46785 0.334880
\(179\) −25.1291 −1.87823 −0.939117 0.343597i \(-0.888355\pi\)
−0.939117 + 0.343597i \(0.888355\pi\)
\(180\) 0.197152 0.0146949
\(181\) −0.499522 −0.0371292 −0.0185646 0.999828i \(-0.505910\pi\)
−0.0185646 + 0.999828i \(0.505910\pi\)
\(182\) −5.38602 −0.399238
\(183\) 13.8381 1.02294
\(184\) 2.60504 0.192046
\(185\) 2.08546 0.153326
\(186\) 8.35472 0.612598
\(187\) −1.06748 −0.0780617
\(188\) 8.36241 0.609892
\(189\) 1.50880 0.109749
\(190\) −0.608512 −0.0441461
\(191\) −23.2793 −1.68443 −0.842217 0.539139i \(-0.818750\pi\)
−0.842217 + 0.539139i \(0.818750\pi\)
\(192\) 1.00000 0.0721688
\(193\) −24.5273 −1.76551 −0.882755 0.469833i \(-0.844314\pi\)
−0.882755 + 0.469833i \(0.844314\pi\)
\(194\) 15.6563 1.12406
\(195\) −0.703783 −0.0503989
\(196\) −4.72353 −0.337395
\(197\) 21.4206 1.52615 0.763077 0.646308i \(-0.223688\pi\)
0.763077 + 0.646308i \(0.223688\pi\)
\(198\) −1.06748 −0.0758624
\(199\) −3.94881 −0.279924 −0.139962 0.990157i \(-0.544698\pi\)
−0.139962 + 0.990157i \(0.544698\pi\)
\(200\) −4.96113 −0.350805
\(201\) 13.1934 0.930589
\(202\) 9.50176 0.668541
\(203\) 2.55815 0.179547
\(204\) 1.00000 0.0700140
\(205\) 2.04284 0.142678
\(206\) −3.93030 −0.273837
\(207\) 2.60504 0.181063
\(208\) −3.56974 −0.247517
\(209\) 3.29478 0.227905
\(210\) 0.297463 0.0205269
\(211\) −1.28881 −0.0887251 −0.0443626 0.999015i \(-0.514126\pi\)
−0.0443626 + 0.999015i \(0.514126\pi\)
\(212\) −9.48041 −0.651117
\(213\) 0.742176 0.0508531
\(214\) 6.77958 0.463442
\(215\) 0.689804 0.0470443
\(216\) 1.00000 0.0680414
\(217\) 12.6056 0.855723
\(218\) 7.32838 0.496341
\(219\) −7.50498 −0.507139
\(220\) −0.210456 −0.0141889
\(221\) −3.56974 −0.240127
\(222\) 10.5779 0.709942
\(223\) −15.7214 −1.05278 −0.526392 0.850242i \(-0.676455\pi\)
−0.526392 + 0.850242i \(0.676455\pi\)
\(224\) 1.50880 0.100811
\(225\) −4.96113 −0.330742
\(226\) −15.0982 −1.00432
\(227\) 18.9667 1.25886 0.629432 0.777055i \(-0.283287\pi\)
0.629432 + 0.777055i \(0.283287\pi\)
\(228\) −3.08651 −0.204409
\(229\) −7.27448 −0.480711 −0.240355 0.970685i \(-0.577264\pi\)
−0.240355 + 0.970685i \(0.577264\pi\)
\(230\) 0.513590 0.0338651
\(231\) −1.61061 −0.105970
\(232\) 1.69549 0.111315
\(233\) 4.19965 0.275128 0.137564 0.990493i \(-0.456073\pi\)
0.137564 + 0.990493i \(0.456073\pi\)
\(234\) −3.56974 −0.233361
\(235\) 1.64867 0.107547
\(236\) −1.00000 −0.0650945
\(237\) 10.8576 0.705275
\(238\) 1.50880 0.0978008
\(239\) 16.3762 1.05929 0.529645 0.848219i \(-0.322325\pi\)
0.529645 + 0.848219i \(0.322325\pi\)
\(240\) 0.197152 0.0127261
\(241\) −1.50349 −0.0968480 −0.0484240 0.998827i \(-0.515420\pi\)
−0.0484240 + 0.998827i \(0.515420\pi\)
\(242\) −9.86049 −0.633856
\(243\) 1.00000 0.0641500
\(244\) 13.8381 0.885894
\(245\) −0.931255 −0.0594957
\(246\) 10.3617 0.660639
\(247\) 11.0180 0.701061
\(248\) 8.35472 0.530526
\(249\) −1.77582 −0.112538
\(250\) −1.96386 −0.124205
\(251\) 4.65482 0.293810 0.146905 0.989151i \(-0.453069\pi\)
0.146905 + 0.989151i \(0.453069\pi\)
\(252\) 1.50880 0.0950453
\(253\) −2.78083 −0.174829
\(254\) −3.70663 −0.232575
\(255\) 0.197152 0.0123462
\(256\) 1.00000 0.0625000
\(257\) −6.74375 −0.420664 −0.210332 0.977630i \(-0.567454\pi\)
−0.210332 + 0.977630i \(0.567454\pi\)
\(258\) 3.49884 0.217828
\(259\) 15.9599 0.991701
\(260\) −0.703783 −0.0436467
\(261\) 1.69549 0.104948
\(262\) 5.11961 0.316291
\(263\) 27.3944 1.68921 0.844606 0.535388i \(-0.179835\pi\)
0.844606 + 0.535388i \(0.179835\pi\)
\(264\) −1.06748 −0.0656987
\(265\) −1.86908 −0.114817
\(266\) −4.65692 −0.285534
\(267\) 4.46785 0.273428
\(268\) 13.1934 0.805914
\(269\) 4.62812 0.282181 0.141091 0.989997i \(-0.454939\pi\)
0.141091 + 0.989997i \(0.454939\pi\)
\(270\) 0.197152 0.0119983
\(271\) −14.6545 −0.890196 −0.445098 0.895482i \(-0.646831\pi\)
−0.445098 + 0.895482i \(0.646831\pi\)
\(272\) 1.00000 0.0606339
\(273\) −5.38602 −0.325977
\(274\) −3.58744 −0.216725
\(275\) 5.29590 0.319355
\(276\) 2.60504 0.156805
\(277\) −15.0346 −0.903340 −0.451670 0.892185i \(-0.649172\pi\)
−0.451670 + 0.892185i \(0.649172\pi\)
\(278\) −14.0373 −0.841900
\(279\) 8.35472 0.500184
\(280\) 0.297463 0.0177768
\(281\) −17.4883 −1.04326 −0.521632 0.853170i \(-0.674677\pi\)
−0.521632 + 0.853170i \(0.674677\pi\)
\(282\) 8.36241 0.497974
\(283\) −33.2804 −1.97832 −0.989158 0.146855i \(-0.953085\pi\)
−0.989158 + 0.146855i \(0.953085\pi\)
\(284\) 0.742176 0.0440401
\(285\) −0.608512 −0.0360451
\(286\) 3.81062 0.225327
\(287\) 15.6337 0.922830
\(288\) 1.00000 0.0589256
\(289\) 1.00000 0.0588235
\(290\) 0.334270 0.0196290
\(291\) 15.6563 0.917790
\(292\) −7.50498 −0.439196
\(293\) −1.05772 −0.0617928 −0.0308964 0.999523i \(-0.509836\pi\)
−0.0308964 + 0.999523i \(0.509836\pi\)
\(294\) −4.72353 −0.275482
\(295\) −0.197152 −0.0114786
\(296\) 10.5779 0.614828
\(297\) −1.06748 −0.0619414
\(298\) −15.8542 −0.918409
\(299\) −9.29933 −0.537794
\(300\) −4.96113 −0.286431
\(301\) 5.27904 0.304279
\(302\) −12.8033 −0.736746
\(303\) 9.50176 0.545862
\(304\) −3.08651 −0.177023
\(305\) 2.72821 0.156217
\(306\) 1.00000 0.0571662
\(307\) −20.8598 −1.19053 −0.595266 0.803529i \(-0.702953\pi\)
−0.595266 + 0.803529i \(0.702953\pi\)
\(308\) −1.61061 −0.0917729
\(309\) −3.93030 −0.223587
\(310\) 1.64715 0.0935520
\(311\) −2.33820 −0.132587 −0.0662935 0.997800i \(-0.521117\pi\)
−0.0662935 + 0.997800i \(0.521117\pi\)
\(312\) −3.56974 −0.202097
\(313\) −2.49236 −0.140877 −0.0704384 0.997516i \(-0.522440\pi\)
−0.0704384 + 0.997516i \(0.522440\pi\)
\(314\) −5.34695 −0.301746
\(315\) 0.297463 0.0167601
\(316\) 10.8576 0.610786
\(317\) 23.3541 1.31170 0.655850 0.754891i \(-0.272310\pi\)
0.655850 + 0.754891i \(0.272310\pi\)
\(318\) −9.48041 −0.531635
\(319\) −1.80990 −0.101335
\(320\) 0.197152 0.0110211
\(321\) 6.77958 0.378399
\(322\) 3.93048 0.219037
\(323\) −3.08651 −0.171738
\(324\) 1.00000 0.0555556
\(325\) 17.7100 0.982372
\(326\) 1.99629 0.110564
\(327\) 7.32838 0.405260
\(328\) 10.3617 0.572130
\(329\) 12.6172 0.695608
\(330\) −0.210456 −0.0115852
\(331\) 15.3552 0.843999 0.422000 0.906596i \(-0.361328\pi\)
0.422000 + 0.906596i \(0.361328\pi\)
\(332\) −1.77582 −0.0974607
\(333\) 10.5779 0.579665
\(334\) 12.1067 0.662450
\(335\) 2.60110 0.142114
\(336\) 1.50880 0.0823116
\(337\) −27.4294 −1.49418 −0.747088 0.664725i \(-0.768549\pi\)
−0.747088 + 0.664725i \(0.768549\pi\)
\(338\) −0.256942 −0.0139758
\(339\) −15.0982 −0.820023
\(340\) 0.197152 0.0106921
\(341\) −8.91848 −0.482963
\(342\) −3.08651 −0.166899
\(343\) −17.6884 −0.955086
\(344\) 3.49884 0.188645
\(345\) 0.513590 0.0276507
\(346\) −9.44184 −0.507596
\(347\) −4.95564 −0.266033 −0.133016 0.991114i \(-0.542466\pi\)
−0.133016 + 0.991114i \(0.542466\pi\)
\(348\) 1.69549 0.0908879
\(349\) −4.68176 −0.250609 −0.125304 0.992118i \(-0.539991\pi\)
−0.125304 + 0.992118i \(0.539991\pi\)
\(350\) −7.48534 −0.400108
\(351\) −3.56974 −0.190539
\(352\) −1.06748 −0.0568968
\(353\) −7.74350 −0.412145 −0.206073 0.978537i \(-0.566068\pi\)
−0.206073 + 0.978537i \(0.566068\pi\)
\(354\) −1.00000 −0.0531494
\(355\) 0.146322 0.00776595
\(356\) 4.46785 0.236796
\(357\) 1.50880 0.0798540
\(358\) −25.1291 −1.32811
\(359\) 20.8428 1.10004 0.550022 0.835150i \(-0.314619\pi\)
0.550022 + 0.835150i \(0.314619\pi\)
\(360\) 0.197152 0.0103908
\(361\) −9.47346 −0.498603
\(362\) −0.499522 −0.0262543
\(363\) −9.86049 −0.517542
\(364\) −5.38602 −0.282304
\(365\) −1.47962 −0.0774470
\(366\) 13.8381 0.723330
\(367\) −26.4124 −1.37872 −0.689358 0.724421i \(-0.742107\pi\)
−0.689358 + 0.724421i \(0.742107\pi\)
\(368\) 2.60504 0.135797
\(369\) 10.3617 0.539410
\(370\) 2.08546 0.108418
\(371\) −14.3040 −0.742627
\(372\) 8.35472 0.433172
\(373\) 27.4940 1.42358 0.711792 0.702390i \(-0.247884\pi\)
0.711792 + 0.702390i \(0.247884\pi\)
\(374\) −1.06748 −0.0551980
\(375\) −1.96386 −0.101413
\(376\) 8.36241 0.431258
\(377\) −6.05247 −0.311718
\(378\) 1.50880 0.0776042
\(379\) 18.5566 0.953187 0.476593 0.879124i \(-0.341871\pi\)
0.476593 + 0.879124i \(0.341871\pi\)
\(380\) −0.608512 −0.0312160
\(381\) −3.70663 −0.189896
\(382\) −23.2793 −1.19107
\(383\) −30.7392 −1.57070 −0.785349 0.619054i \(-0.787516\pi\)
−0.785349 + 0.619054i \(0.787516\pi\)
\(384\) 1.00000 0.0510310
\(385\) −0.317535 −0.0161831
\(386\) −24.5273 −1.24840
\(387\) 3.49884 0.177856
\(388\) 15.6563 0.794830
\(389\) −20.5958 −1.04425 −0.522125 0.852869i \(-0.674861\pi\)
−0.522125 + 0.852869i \(0.674861\pi\)
\(390\) −0.703783 −0.0356374
\(391\) 2.60504 0.131743
\(392\) −4.72353 −0.238574
\(393\) 5.11961 0.258250
\(394\) 21.4206 1.07915
\(395\) 2.14060 0.107705
\(396\) −1.06748 −0.0536428
\(397\) −0.324755 −0.0162990 −0.00814949 0.999967i \(-0.502594\pi\)
−0.00814949 + 0.999967i \(0.502594\pi\)
\(398\) −3.94881 −0.197936
\(399\) −4.65692 −0.233137
\(400\) −4.96113 −0.248057
\(401\) 33.6158 1.67869 0.839347 0.543596i \(-0.182937\pi\)
0.839347 + 0.543596i \(0.182937\pi\)
\(402\) 13.1934 0.658026
\(403\) −29.8242 −1.48565
\(404\) 9.50176 0.472730
\(405\) 0.197152 0.00979657
\(406\) 2.55815 0.126959
\(407\) −11.2917 −0.559708
\(408\) 1.00000 0.0495074
\(409\) −12.5737 −0.621728 −0.310864 0.950454i \(-0.600618\pi\)
−0.310864 + 0.950454i \(0.600618\pi\)
\(410\) 2.04284 0.100888
\(411\) −3.58744 −0.176955
\(412\) −3.93030 −0.193632
\(413\) −1.50880 −0.0742431
\(414\) 2.60504 0.128031
\(415\) −0.350107 −0.0171861
\(416\) −3.56974 −0.175021
\(417\) −14.0373 −0.687408
\(418\) 3.29478 0.161153
\(419\) 37.5244 1.83319 0.916594 0.399819i \(-0.130927\pi\)
0.916594 + 0.399819i \(0.130927\pi\)
\(420\) 0.297463 0.0145147
\(421\) 29.0179 1.41424 0.707122 0.707091i \(-0.249993\pi\)
0.707122 + 0.707091i \(0.249993\pi\)
\(422\) −1.28881 −0.0627381
\(423\) 8.36241 0.406594
\(424\) −9.48041 −0.460409
\(425\) −4.96113 −0.240650
\(426\) 0.742176 0.0359586
\(427\) 20.8789 1.01040
\(428\) 6.77958 0.327703
\(429\) 3.81062 0.183979
\(430\) 0.689804 0.0332653
\(431\) −14.4178 −0.694482 −0.347241 0.937776i \(-0.612881\pi\)
−0.347241 + 0.937776i \(0.612881\pi\)
\(432\) 1.00000 0.0481125
\(433\) 35.7355 1.71734 0.858670 0.512528i \(-0.171291\pi\)
0.858670 + 0.512528i \(0.171291\pi\)
\(434\) 12.6056 0.605087
\(435\) 0.334270 0.0160270
\(436\) 7.32838 0.350966
\(437\) −8.04049 −0.384629
\(438\) −7.50498 −0.358602
\(439\) −9.07090 −0.432930 −0.216465 0.976290i \(-0.569453\pi\)
−0.216465 + 0.976290i \(0.569453\pi\)
\(440\) −0.210456 −0.0100331
\(441\) −4.72353 −0.224930
\(442\) −3.56974 −0.169795
\(443\) 20.7004 0.983507 0.491753 0.870735i \(-0.336356\pi\)
0.491753 + 0.870735i \(0.336356\pi\)
\(444\) 10.5779 0.502005
\(445\) 0.880847 0.0417562
\(446\) −15.7214 −0.744430
\(447\) −15.8542 −0.749878
\(448\) 1.50880 0.0712840
\(449\) −1.92736 −0.0909577 −0.0454788 0.998965i \(-0.514481\pi\)
−0.0454788 + 0.998965i \(0.514481\pi\)
\(450\) −4.96113 −0.233870
\(451\) −11.0609 −0.520838
\(452\) −15.0982 −0.710161
\(453\) −12.8033 −0.601551
\(454\) 18.9667 0.890152
\(455\) −1.06187 −0.0497810
\(456\) −3.08651 −0.144539
\(457\) −20.5877 −0.963053 −0.481527 0.876431i \(-0.659918\pi\)
−0.481527 + 0.876431i \(0.659918\pi\)
\(458\) −7.27448 −0.339914
\(459\) 1.00000 0.0466760
\(460\) 0.513590 0.0239463
\(461\) 21.2081 0.987758 0.493879 0.869531i \(-0.335579\pi\)
0.493879 + 0.869531i \(0.335579\pi\)
\(462\) −1.61061 −0.0749323
\(463\) 33.2158 1.54367 0.771835 0.635823i \(-0.219339\pi\)
0.771835 + 0.635823i \(0.219339\pi\)
\(464\) 1.69549 0.0787113
\(465\) 1.64715 0.0763849
\(466\) 4.19965 0.194545
\(467\) 36.7332 1.69981 0.849905 0.526936i \(-0.176659\pi\)
0.849905 + 0.526936i \(0.176659\pi\)
\(468\) −3.56974 −0.165011
\(469\) 19.9061 0.919180
\(470\) 1.64867 0.0760474
\(471\) −5.34695 −0.246375
\(472\) −1.00000 −0.0460287
\(473\) −3.73494 −0.171733
\(474\) 10.8576 0.498705
\(475\) 15.3126 0.702589
\(476\) 1.50880 0.0691556
\(477\) −9.48041 −0.434078
\(478\) 16.3762 0.749031
\(479\) −28.4509 −1.29995 −0.649977 0.759954i \(-0.725222\pi\)
−0.649977 + 0.759954i \(0.725222\pi\)
\(480\) 0.197152 0.00899873
\(481\) −37.7604 −1.72173
\(482\) −1.50349 −0.0684819
\(483\) 3.93048 0.178843
\(484\) −9.86049 −0.448204
\(485\) 3.08668 0.140159
\(486\) 1.00000 0.0453609
\(487\) 35.4163 1.60487 0.802433 0.596743i \(-0.203539\pi\)
0.802433 + 0.596743i \(0.203539\pi\)
\(488\) 13.8381 0.626422
\(489\) 1.99629 0.0902754
\(490\) −0.931255 −0.0420698
\(491\) 26.6887 1.20444 0.602221 0.798329i \(-0.294283\pi\)
0.602221 + 0.798329i \(0.294283\pi\)
\(492\) 10.3617 0.467142
\(493\) 1.69549 0.0763611
\(494\) 11.0180 0.495725
\(495\) −0.210456 −0.00945928
\(496\) 8.35472 0.375138
\(497\) 1.11979 0.0502296
\(498\) −1.77582 −0.0795764
\(499\) −0.942608 −0.0421969 −0.0210985 0.999777i \(-0.506716\pi\)
−0.0210985 + 0.999777i \(0.506716\pi\)
\(500\) −1.96386 −0.0878264
\(501\) 12.1067 0.540888
\(502\) 4.65482 0.207755
\(503\) −8.62835 −0.384719 −0.192360 0.981325i \(-0.561614\pi\)
−0.192360 + 0.981325i \(0.561614\pi\)
\(504\) 1.50880 0.0672072
\(505\) 1.87329 0.0833604
\(506\) −2.78083 −0.123623
\(507\) −0.256942 −0.0114112
\(508\) −3.70663 −0.164455
\(509\) −1.60098 −0.0709622 −0.0354811 0.999370i \(-0.511296\pi\)
−0.0354811 + 0.999370i \(0.511296\pi\)
\(510\) 0.197152 0.00873005
\(511\) −11.3235 −0.500922
\(512\) 1.00000 0.0441942
\(513\) −3.08651 −0.136273
\(514\) −6.74375 −0.297454
\(515\) −0.774867 −0.0341447
\(516\) 3.49884 0.154028
\(517\) −8.92669 −0.392595
\(518\) 15.9599 0.701238
\(519\) −9.44184 −0.414451
\(520\) −0.703783 −0.0308629
\(521\) 18.4489 0.808263 0.404131 0.914701i \(-0.367574\pi\)
0.404131 + 0.914701i \(0.367574\pi\)
\(522\) 1.69549 0.0742097
\(523\) 21.0391 0.919976 0.459988 0.887925i \(-0.347854\pi\)
0.459988 + 0.887925i \(0.347854\pi\)
\(524\) 5.11961 0.223651
\(525\) −7.48534 −0.326687
\(526\) 27.3944 1.19445
\(527\) 8.35472 0.363938
\(528\) −1.06748 −0.0464560
\(529\) −16.2138 −0.704946
\(530\) −1.86908 −0.0811878
\(531\) −1.00000 −0.0433963
\(532\) −4.65692 −0.201903
\(533\) −36.9887 −1.60216
\(534\) 4.46785 0.193343
\(535\) 1.33661 0.0577866
\(536\) 13.1934 0.569867
\(537\) −25.1291 −1.08440
\(538\) 4.62812 0.199532
\(539\) 5.04226 0.217186
\(540\) 0.197152 0.00848408
\(541\) 19.0472 0.818903 0.409452 0.912332i \(-0.365720\pi\)
0.409452 + 0.912332i \(0.365720\pi\)
\(542\) −14.6545 −0.629464
\(543\) −0.499522 −0.0214365
\(544\) 1.00000 0.0428746
\(545\) 1.44481 0.0618887
\(546\) −5.38602 −0.230500
\(547\) −31.5093 −1.34724 −0.673621 0.739077i \(-0.735262\pi\)
−0.673621 + 0.739077i \(0.735262\pi\)
\(548\) −3.58744 −0.153248
\(549\) 13.8381 0.590596
\(550\) 5.29590 0.225818
\(551\) −5.23315 −0.222940
\(552\) 2.60504 0.110878
\(553\) 16.3819 0.696629
\(554\) −15.0346 −0.638758
\(555\) 2.08546 0.0885227
\(556\) −14.0373 −0.595313
\(557\) −23.7863 −1.00786 −0.503929 0.863745i \(-0.668113\pi\)
−0.503929 + 0.863745i \(0.668113\pi\)
\(558\) 8.35472 0.353684
\(559\) −12.4900 −0.528269
\(560\) 0.297463 0.0125701
\(561\) −1.06748 −0.0450690
\(562\) −17.4883 −0.737699
\(563\) −10.4358 −0.439816 −0.219908 0.975521i \(-0.570576\pi\)
−0.219908 + 0.975521i \(0.570576\pi\)
\(564\) 8.36241 0.352121
\(565\) −2.97665 −0.125229
\(566\) −33.2804 −1.39888
\(567\) 1.50880 0.0633635
\(568\) 0.742176 0.0311410
\(569\) −4.85639 −0.203590 −0.101795 0.994805i \(-0.532459\pi\)
−0.101795 + 0.994805i \(0.532459\pi\)
\(570\) −0.608512 −0.0254878
\(571\) −10.7132 −0.448333 −0.224166 0.974551i \(-0.571966\pi\)
−0.224166 + 0.974551i \(0.571966\pi\)
\(572\) 3.81062 0.159330
\(573\) −23.2793 −0.972508
\(574\) 15.6337 0.652539
\(575\) −12.9240 −0.538966
\(576\) 1.00000 0.0416667
\(577\) −37.1189 −1.54528 −0.772640 0.634844i \(-0.781064\pi\)
−0.772640 + 0.634844i \(0.781064\pi\)
\(578\) 1.00000 0.0415945
\(579\) −24.5273 −1.01932
\(580\) 0.334270 0.0138798
\(581\) −2.67935 −0.111158
\(582\) 15.6563 0.648976
\(583\) 10.1201 0.419133
\(584\) −7.50498 −0.310558
\(585\) −0.703783 −0.0290978
\(586\) −1.05772 −0.0436941
\(587\) −4.23721 −0.174889 −0.0874443 0.996169i \(-0.527870\pi\)
−0.0874443 + 0.996169i \(0.527870\pi\)
\(588\) −4.72353 −0.194795
\(589\) −25.7869 −1.06253
\(590\) −0.197152 −0.00811663
\(591\) 21.4206 0.881125
\(592\) 10.5779 0.434749
\(593\) 17.0811 0.701437 0.350719 0.936481i \(-0.385937\pi\)
0.350719 + 0.936481i \(0.385937\pi\)
\(594\) −1.06748 −0.0437992
\(595\) 0.297463 0.0121948
\(596\) −15.8542 −0.649413
\(597\) −3.94881 −0.161614
\(598\) −9.29933 −0.380278
\(599\) 1.37562 0.0562065 0.0281032 0.999605i \(-0.491053\pi\)
0.0281032 + 0.999605i \(0.491053\pi\)
\(600\) −4.96113 −0.202537
\(601\) −12.1746 −0.496614 −0.248307 0.968681i \(-0.579874\pi\)
−0.248307 + 0.968681i \(0.579874\pi\)
\(602\) 5.27904 0.215158
\(603\) 13.1934 0.537276
\(604\) −12.8033 −0.520958
\(605\) −1.94402 −0.0790356
\(606\) 9.50176 0.385983
\(607\) −19.7047 −0.799787 −0.399894 0.916562i \(-0.630953\pi\)
−0.399894 + 0.916562i \(0.630953\pi\)
\(608\) −3.08651 −0.125174
\(609\) 2.55815 0.103662
\(610\) 2.72821 0.110462
\(611\) −29.8517 −1.20767
\(612\) 1.00000 0.0404226
\(613\) 19.9816 0.807047 0.403524 0.914969i \(-0.367785\pi\)
0.403524 + 0.914969i \(0.367785\pi\)
\(614\) −20.8598 −0.841833
\(615\) 2.04284 0.0823751
\(616\) −1.61061 −0.0648932
\(617\) −0.388897 −0.0156564 −0.00782821 0.999969i \(-0.502492\pi\)
−0.00782821 + 0.999969i \(0.502492\pi\)
\(618\) −3.93030 −0.158100
\(619\) 5.29120 0.212671 0.106336 0.994330i \(-0.466088\pi\)
0.106336 + 0.994330i \(0.466088\pi\)
\(620\) 1.64715 0.0661512
\(621\) 2.60504 0.104537
\(622\) −2.33820 −0.0937531
\(623\) 6.74109 0.270076
\(624\) −3.56974 −0.142904
\(625\) 24.4185 0.976739
\(626\) −2.49236 −0.0996149
\(627\) 3.29478 0.131581
\(628\) −5.34695 −0.213367
\(629\) 10.5779 0.421769
\(630\) 0.297463 0.0118512
\(631\) −24.1983 −0.963318 −0.481659 0.876359i \(-0.659966\pi\)
−0.481659 + 0.876359i \(0.659966\pi\)
\(632\) 10.8576 0.431891
\(633\) −1.28881 −0.0512255
\(634\) 23.3541 0.927512
\(635\) −0.730770 −0.0289997
\(636\) −9.48041 −0.375923
\(637\) 16.8618 0.668088
\(638\) −1.80990 −0.0716547
\(639\) 0.742176 0.0293600
\(640\) 0.197152 0.00779313
\(641\) 25.0424 0.989117 0.494558 0.869144i \(-0.335330\pi\)
0.494558 + 0.869144i \(0.335330\pi\)
\(642\) 6.77958 0.267569
\(643\) 20.5535 0.810550 0.405275 0.914195i \(-0.367176\pi\)
0.405275 + 0.914195i \(0.367176\pi\)
\(644\) 3.93048 0.154883
\(645\) 0.689804 0.0271610
\(646\) −3.08651 −0.121437
\(647\) 4.98493 0.195978 0.0979889 0.995188i \(-0.468759\pi\)
0.0979889 + 0.995188i \(0.468759\pi\)
\(648\) 1.00000 0.0392837
\(649\) 1.06748 0.0419022
\(650\) 17.7100 0.694642
\(651\) 12.6056 0.494052
\(652\) 1.99629 0.0781808
\(653\) −39.8724 −1.56033 −0.780163 0.625576i \(-0.784864\pi\)
−0.780163 + 0.625576i \(0.784864\pi\)
\(654\) 7.32838 0.286562
\(655\) 1.00934 0.0394383
\(656\) 10.3617 0.404557
\(657\) −7.50498 −0.292797
\(658\) 12.6172 0.491869
\(659\) −28.3875 −1.10582 −0.552909 0.833242i \(-0.686482\pi\)
−0.552909 + 0.833242i \(0.686482\pi\)
\(660\) −0.210456 −0.00819198
\(661\) 1.44575 0.0562331 0.0281166 0.999605i \(-0.491049\pi\)
0.0281166 + 0.999605i \(0.491049\pi\)
\(662\) 15.3552 0.596798
\(663\) −3.56974 −0.138637
\(664\) −1.77582 −0.0689152
\(665\) −0.918121 −0.0356032
\(666\) 10.5779 0.409885
\(667\) 4.41683 0.171020
\(668\) 12.1067 0.468423
\(669\) −15.7214 −0.607825
\(670\) 2.60110 0.100489
\(671\) −14.7719 −0.570262
\(672\) 1.50880 0.0582031
\(673\) 10.9909 0.423668 0.211834 0.977306i \(-0.432056\pi\)
0.211834 + 0.977306i \(0.432056\pi\)
\(674\) −27.4294 −1.05654
\(675\) −4.96113 −0.190954
\(676\) −0.256942 −0.00988240
\(677\) 3.92845 0.150983 0.0754913 0.997146i \(-0.475947\pi\)
0.0754913 + 0.997146i \(0.475947\pi\)
\(678\) −15.0982 −0.579844
\(679\) 23.6222 0.906538
\(680\) 0.197152 0.00756044
\(681\) 18.9667 0.726806
\(682\) −8.91848 −0.341506
\(683\) 20.3112 0.777186 0.388593 0.921409i \(-0.372961\pi\)
0.388593 + 0.921409i \(0.372961\pi\)
\(684\) −3.08651 −0.118016
\(685\) −0.707271 −0.0270234
\(686\) −17.6884 −0.675347
\(687\) −7.27448 −0.277539
\(688\) 3.49884 0.133392
\(689\) 33.8426 1.28930
\(690\) 0.513590 0.0195520
\(691\) −39.0453 −1.48535 −0.742677 0.669649i \(-0.766444\pi\)
−0.742677 + 0.669649i \(0.766444\pi\)
\(692\) −9.44184 −0.358925
\(693\) −1.61061 −0.0611819
\(694\) −4.95564 −0.188114
\(695\) −2.76748 −0.104976
\(696\) 1.69549 0.0642675
\(697\) 10.3617 0.392478
\(698\) −4.68176 −0.177207
\(699\) 4.19965 0.158845
\(700\) −7.48534 −0.282919
\(701\) 40.3399 1.52362 0.761808 0.647803i \(-0.224312\pi\)
0.761808 + 0.647803i \(0.224312\pi\)
\(702\) −3.56974 −0.134731
\(703\) −32.6488 −1.23137
\(704\) −1.06748 −0.0402321
\(705\) 1.64867 0.0620924
\(706\) −7.74350 −0.291431
\(707\) 14.3362 0.539169
\(708\) −1.00000 −0.0375823
\(709\) −15.6377 −0.587288 −0.293644 0.955915i \(-0.594868\pi\)
−0.293644 + 0.955915i \(0.594868\pi\)
\(710\) 0.146322 0.00549136
\(711\) 10.8576 0.407191
\(712\) 4.46785 0.167440
\(713\) 21.7644 0.815084
\(714\) 1.50880 0.0564653
\(715\) 0.751272 0.0280960
\(716\) −25.1291 −0.939117
\(717\) 16.3762 0.611581
\(718\) 20.8428 0.777848
\(719\) −37.4057 −1.39500 −0.697499 0.716586i \(-0.745704\pi\)
−0.697499 + 0.716586i \(0.745704\pi\)
\(720\) 0.197152 0.00734743
\(721\) −5.93003 −0.220846
\(722\) −9.47346 −0.352566
\(723\) −1.50349 −0.0559152
\(724\) −0.499522 −0.0185646
\(725\) −8.41156 −0.312397
\(726\) −9.86049 −0.365957
\(727\) −26.0435 −0.965901 −0.482951 0.875648i \(-0.660435\pi\)
−0.482951 + 0.875648i \(0.660435\pi\)
\(728\) −5.38602 −0.199619
\(729\) 1.00000 0.0370370
\(730\) −1.47962 −0.0547633
\(731\) 3.49884 0.129409
\(732\) 13.8381 0.511471
\(733\) 10.3141 0.380959 0.190480 0.981691i \(-0.438996\pi\)
0.190480 + 0.981691i \(0.438996\pi\)
\(734\) −26.4124 −0.974899
\(735\) −0.931255 −0.0343498
\(736\) 2.60504 0.0960231
\(737\) −14.0836 −0.518778
\(738\) 10.3617 0.381420
\(739\) −5.75525 −0.211710 −0.105855 0.994382i \(-0.533758\pi\)
−0.105855 + 0.994382i \(0.533758\pi\)
\(740\) 2.08546 0.0766629
\(741\) 11.0180 0.404758
\(742\) −14.3040 −0.525117
\(743\) −27.4435 −1.00681 −0.503403 0.864052i \(-0.667919\pi\)
−0.503403 + 0.864052i \(0.667919\pi\)
\(744\) 8.35472 0.306299
\(745\) −3.12569 −0.114516
\(746\) 27.4940 1.00663
\(747\) −1.77582 −0.0649738
\(748\) −1.06748 −0.0390309
\(749\) 10.2290 0.373760
\(750\) −1.96386 −0.0717100
\(751\) −6.48953 −0.236806 −0.118403 0.992966i \(-0.537778\pi\)
−0.118403 + 0.992966i \(0.537778\pi\)
\(752\) 8.36241 0.304946
\(753\) 4.65482 0.169631
\(754\) −6.05247 −0.220418
\(755\) −2.52420 −0.0918649
\(756\) 1.50880 0.0548744
\(757\) −9.12616 −0.331696 −0.165848 0.986151i \(-0.553036\pi\)
−0.165848 + 0.986151i \(0.553036\pi\)
\(758\) 18.5566 0.674005
\(759\) −2.78083 −0.100938
\(760\) −0.608512 −0.0220731
\(761\) 45.1557 1.63689 0.818446 0.574583i \(-0.194836\pi\)
0.818446 + 0.574583i \(0.194836\pi\)
\(762\) −3.70663 −0.134277
\(763\) 11.0570 0.400292
\(764\) −23.2793 −0.842217
\(765\) 0.197152 0.00712805
\(766\) −30.7392 −1.11065
\(767\) 3.56974 0.128896
\(768\) 1.00000 0.0360844
\(769\) −36.0909 −1.30147 −0.650735 0.759305i \(-0.725539\pi\)
−0.650735 + 0.759305i \(0.725539\pi\)
\(770\) −0.317535 −0.0114432
\(771\) −6.74375 −0.242870
\(772\) −24.5273 −0.882755
\(773\) −31.7772 −1.14295 −0.571473 0.820621i \(-0.693628\pi\)
−0.571473 + 0.820621i \(0.693628\pi\)
\(774\) 3.49884 0.125763
\(775\) −41.4489 −1.48889
\(776\) 15.6563 0.562030
\(777\) 15.9599 0.572559
\(778\) −20.5958 −0.738397
\(779\) −31.9815 −1.14586
\(780\) −0.703783 −0.0251995
\(781\) −0.792257 −0.0283492
\(782\) 2.60504 0.0931561
\(783\) 1.69549 0.0605920
\(784\) −4.72353 −0.168698
\(785\) −1.05416 −0.0376247
\(786\) 5.11961 0.182610
\(787\) 21.4904 0.766050 0.383025 0.923738i \(-0.374882\pi\)
0.383025 + 0.923738i \(0.374882\pi\)
\(788\) 21.4206 0.763077
\(789\) 27.3944 0.975267
\(790\) 2.14060 0.0761590
\(791\) −22.7802 −0.809970
\(792\) −1.06748 −0.0379312
\(793\) −49.3985 −1.75419
\(794\) −0.324755 −0.0115251
\(795\) −1.86908 −0.0662896
\(796\) −3.94881 −0.139962
\(797\) −21.6325 −0.766262 −0.383131 0.923694i \(-0.625154\pi\)
−0.383131 + 0.923694i \(0.625154\pi\)
\(798\) −4.65692 −0.164853
\(799\) 8.36241 0.295841
\(800\) −4.96113 −0.175402
\(801\) 4.46785 0.157864
\(802\) 33.6158 1.18702
\(803\) 8.01140 0.282716
\(804\) 13.1934 0.465295
\(805\) 0.774903 0.0273117
\(806\) −29.8242 −1.05051
\(807\) 4.62812 0.162917
\(808\) 9.50176 0.334271
\(809\) 4.20447 0.147821 0.0739107 0.997265i \(-0.476452\pi\)
0.0739107 + 0.997265i \(0.476452\pi\)
\(810\) 0.197152 0.00692722
\(811\) −6.84292 −0.240287 −0.120144 0.992757i \(-0.538336\pi\)
−0.120144 + 0.992757i \(0.538336\pi\)
\(812\) 2.55815 0.0897736
\(813\) −14.6545 −0.513955
\(814\) −11.2917 −0.395773
\(815\) 0.393573 0.0137863
\(816\) 1.00000 0.0350070
\(817\) −10.7992 −0.377816
\(818\) −12.5737 −0.439628
\(819\) −5.38602 −0.188203
\(820\) 2.04284 0.0713389
\(821\) 29.7525 1.03837 0.519184 0.854663i \(-0.326236\pi\)
0.519184 + 0.854663i \(0.326236\pi\)
\(822\) −3.58744 −0.125126
\(823\) 15.6663 0.546093 0.273046 0.962001i \(-0.411969\pi\)
0.273046 + 0.962001i \(0.411969\pi\)
\(824\) −3.93030 −0.136918
\(825\) 5.29590 0.184379
\(826\) −1.50880 −0.0524978
\(827\) −2.66571 −0.0926957 −0.0463479 0.998925i \(-0.514758\pi\)
−0.0463479 + 0.998925i \(0.514758\pi\)
\(828\) 2.60504 0.0905315
\(829\) −46.8431 −1.62693 −0.813465 0.581614i \(-0.802421\pi\)
−0.813465 + 0.581614i \(0.802421\pi\)
\(830\) −0.350107 −0.0121524
\(831\) −15.0346 −0.521544
\(832\) −3.56974 −0.123759
\(833\) −4.72353 −0.163661
\(834\) −14.0373 −0.486071
\(835\) 2.38687 0.0826009
\(836\) 3.29478 0.113952
\(837\) 8.35472 0.288782
\(838\) 37.5244 1.29626
\(839\) 16.8031 0.580107 0.290054 0.957010i \(-0.406327\pi\)
0.290054 + 0.957010i \(0.406327\pi\)
\(840\) 0.297463 0.0102634
\(841\) −26.1253 −0.900873
\(842\) 29.0179 1.00002
\(843\) −17.4883 −0.602329
\(844\) −1.28881 −0.0443626
\(845\) −0.0506568 −0.00174265
\(846\) 8.36241 0.287506
\(847\) −14.8775 −0.511196
\(848\) −9.48041 −0.325559
\(849\) −33.2804 −1.14218
\(850\) −4.96113 −0.170165
\(851\) 27.5559 0.944603
\(852\) 0.742176 0.0254265
\(853\) 18.3976 0.629923 0.314961 0.949104i \(-0.398008\pi\)
0.314961 + 0.949104i \(0.398008\pi\)
\(854\) 20.8789 0.714462
\(855\) −0.608512 −0.0208107
\(856\) 6.77958 0.231721
\(857\) −13.3510 −0.456061 −0.228031 0.973654i \(-0.573229\pi\)
−0.228031 + 0.973654i \(0.573229\pi\)
\(858\) 3.81062 0.130092
\(859\) −27.1022 −0.924716 −0.462358 0.886693i \(-0.652996\pi\)
−0.462358 + 0.886693i \(0.652996\pi\)
\(860\) 0.689804 0.0235221
\(861\) 15.6337 0.532796
\(862\) −14.4178 −0.491073
\(863\) −31.7467 −1.08067 −0.540336 0.841449i \(-0.681703\pi\)
−0.540336 + 0.841449i \(0.681703\pi\)
\(864\) 1.00000 0.0340207
\(865\) −1.86148 −0.0632922
\(866\) 35.7355 1.21434
\(867\) 1.00000 0.0339618
\(868\) 12.6056 0.427861
\(869\) −11.5902 −0.393171
\(870\) 0.334270 0.0113328
\(871\) −47.0970 −1.59582
\(872\) 7.32838 0.248170
\(873\) 15.6563 0.529887
\(874\) −8.04049 −0.271973
\(875\) −2.96307 −0.100170
\(876\) −7.50498 −0.253570
\(877\) 32.2350 1.08850 0.544249 0.838924i \(-0.316815\pi\)
0.544249 + 0.838924i \(0.316815\pi\)
\(878\) −9.07090 −0.306128
\(879\) −1.05772 −0.0356761
\(880\) −0.210456 −0.00709446
\(881\) −18.2954 −0.616388 −0.308194 0.951324i \(-0.599725\pi\)
−0.308194 + 0.951324i \(0.599725\pi\)
\(882\) −4.72353 −0.159050
\(883\) −38.7349 −1.30353 −0.651766 0.758420i \(-0.725972\pi\)
−0.651766 + 0.758420i \(0.725972\pi\)
\(884\) −3.56974 −0.120063
\(885\) −0.197152 −0.00662720
\(886\) 20.7004 0.695444
\(887\) −4.45066 −0.149439 −0.0747193 0.997205i \(-0.523806\pi\)
−0.0747193 + 0.997205i \(0.523806\pi\)
\(888\) 10.5779 0.354971
\(889\) −5.59255 −0.187568
\(890\) 0.880847 0.0295261
\(891\) −1.06748 −0.0357619
\(892\) −15.7214 −0.526392
\(893\) −25.8107 −0.863721
\(894\) −15.8542 −0.530244
\(895\) −4.95425 −0.165602
\(896\) 1.50880 0.0504054
\(897\) −9.29933 −0.310496
\(898\) −1.92736 −0.0643168
\(899\) 14.1654 0.472442
\(900\) −4.96113 −0.165371
\(901\) −9.48041 −0.315838
\(902\) −11.0609 −0.368288
\(903\) 5.27904 0.175676
\(904\) −15.0982 −0.502160
\(905\) −0.0984818 −0.00327365
\(906\) −12.8033 −0.425361
\(907\) −3.99083 −0.132513 −0.0662567 0.997803i \(-0.521106\pi\)
−0.0662567 + 0.997803i \(0.521106\pi\)
\(908\) 18.9667 0.629432
\(909\) 9.50176 0.315153
\(910\) −1.06187 −0.0352005
\(911\) −2.13351 −0.0706864 −0.0353432 0.999375i \(-0.511252\pi\)
−0.0353432 + 0.999375i \(0.511252\pi\)
\(912\) −3.08651 −0.102205
\(913\) 1.89565 0.0627368
\(914\) −20.5877 −0.680981
\(915\) 2.72821 0.0901920
\(916\) −7.27448 −0.240355
\(917\) 7.72445 0.255084
\(918\) 1.00000 0.0330049
\(919\) −32.1332 −1.05998 −0.529988 0.848005i \(-0.677804\pi\)
−0.529988 + 0.848005i \(0.677804\pi\)
\(920\) 0.513590 0.0169326
\(921\) −20.8598 −0.687354
\(922\) 21.2081 0.698450
\(923\) −2.64938 −0.0872053
\(924\) −1.61061 −0.0529851
\(925\) −52.4784 −1.72548
\(926\) 33.2158 1.09154
\(927\) −3.93030 −0.129088
\(928\) 1.69549 0.0556573
\(929\) −5.96853 −0.195821 −0.0979106 0.995195i \(-0.531216\pi\)
−0.0979106 + 0.995195i \(0.531216\pi\)
\(930\) 1.64715 0.0540123
\(931\) 14.5792 0.477815
\(932\) 4.19965 0.137564
\(933\) −2.33820 −0.0765491
\(934\) 36.7332 1.20195
\(935\) −0.210456 −0.00688264
\(936\) −3.56974 −0.116681
\(937\) 33.3139 1.08832 0.544158 0.838982i \(-0.316849\pi\)
0.544158 + 0.838982i \(0.316849\pi\)
\(938\) 19.9061 0.649958
\(939\) −2.49236 −0.0813352
\(940\) 1.64867 0.0537736
\(941\) 46.8492 1.52724 0.763621 0.645665i \(-0.223420\pi\)
0.763621 + 0.645665i \(0.223420\pi\)
\(942\) −5.34695 −0.174213
\(943\) 26.9927 0.879004
\(944\) −1.00000 −0.0325472
\(945\) 0.297463 0.00967646
\(946\) −3.73494 −0.121433
\(947\) 10.9315 0.355226 0.177613 0.984100i \(-0.443163\pi\)
0.177613 + 0.984100i \(0.443163\pi\)
\(948\) 10.8576 0.352638
\(949\) 26.7908 0.869667
\(950\) 15.3126 0.496805
\(951\) 23.3541 0.757310
\(952\) 1.50880 0.0489004
\(953\) −41.1242 −1.33214 −0.666072 0.745888i \(-0.732026\pi\)
−0.666072 + 0.745888i \(0.732026\pi\)
\(954\) −9.48041 −0.306940
\(955\) −4.58957 −0.148515
\(956\) 16.3762 0.529645
\(957\) −1.80990 −0.0585058
\(958\) −28.4509 −0.919206
\(959\) −5.41271 −0.174786
\(960\) 0.197152 0.00636306
\(961\) 38.8014 1.25166
\(962\) −37.7604 −1.21744
\(963\) 6.77958 0.218469
\(964\) −1.50349 −0.0484240
\(965\) −4.83560 −0.155664
\(966\) 3.93048 0.126461
\(967\) 11.0062 0.353937 0.176968 0.984217i \(-0.443371\pi\)
0.176968 + 0.984217i \(0.443371\pi\)
\(968\) −9.86049 −0.316928
\(969\) −3.08651 −0.0991529
\(970\) 3.08668 0.0991073
\(971\) 48.5171 1.55699 0.778495 0.627651i \(-0.215984\pi\)
0.778495 + 0.627651i \(0.215984\pi\)
\(972\) 1.00000 0.0320750
\(973\) −21.1794 −0.678980
\(974\) 35.4163 1.13481
\(975\) 17.7100 0.567173
\(976\) 13.8381 0.442947
\(977\) −2.74376 −0.0877805 −0.0438903 0.999036i \(-0.513975\pi\)
−0.0438903 + 0.999036i \(0.513975\pi\)
\(978\) 1.99629 0.0638344
\(979\) −4.76934 −0.152429
\(980\) −0.931255 −0.0297478
\(981\) 7.32838 0.233977
\(982\) 26.6887 0.851669
\(983\) 18.8604 0.601552 0.300776 0.953695i \(-0.402754\pi\)
0.300776 + 0.953695i \(0.402754\pi\)
\(984\) 10.3617 0.330320
\(985\) 4.22312 0.134560
\(986\) 1.69549 0.0539955
\(987\) 12.6172 0.401609
\(988\) 11.0180 0.350531
\(989\) 9.11463 0.289828
\(990\) −0.210456 −0.00668872
\(991\) −18.6297 −0.591793 −0.295897 0.955220i \(-0.595618\pi\)
−0.295897 + 0.955220i \(0.595618\pi\)
\(992\) 8.35472 0.265263
\(993\) 15.3552 0.487283
\(994\) 1.11979 0.0355177
\(995\) −0.778517 −0.0246807
\(996\) −1.77582 −0.0562690
\(997\) −6.25843 −0.198207 −0.0991033 0.995077i \(-0.531597\pi\)
−0.0991033 + 0.995077i \(0.531597\pi\)
\(998\) −0.942608 −0.0298377
\(999\) 10.5779 0.334670
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.1.7 13
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
6018.2.a.bb.1.7 13 1.1 even 1 trivial