Properties

Label 4017.2.a.f.1.18
Level $4017$
Weight $2$
Character 4017.1
Self dual yes
Analytic conductor $32.076$
Analytic rank $1$
Dimension $19$
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] = [4017,2,Mod(1,4017)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(4017, 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("4017.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 4017 = 3 \cdot 13 \cdot 103 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 4017.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: \(32.0759064919\)
Analytic rank: \(1\)
Dimension: \(19\)
Coefficient field: \(\mathbb{Q}[x]/(x^{19} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{19} - 4 x^{18} - 16 x^{17} + 77 x^{16} + 88 x^{15} - 594 x^{14} - 154 x^{13} + 2388 x^{12} - 278 x^{11} - 5460 x^{10} + 1491 x^{9} + 7285 x^{8} - 2223 x^{7} - 5579 x^{6} + 1430 x^{5} + \cdots + 4 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.18
Root \(-2.08649\) of defining polynomial
Character \(\chi\) \(=\) 4017.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+2.08649 q^{2} +1.00000 q^{3} +2.35342 q^{4} +0.146235 q^{5} +2.08649 q^{6} -2.80287 q^{7} +0.737414 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q+2.08649 q^{2} +1.00000 q^{3} +2.35342 q^{4} +0.146235 q^{5} +2.08649 q^{6} -2.80287 q^{7} +0.737414 q^{8} +1.00000 q^{9} +0.305116 q^{10} -2.41948 q^{11} +2.35342 q^{12} +1.00000 q^{13} -5.84814 q^{14} +0.146235 q^{15} -3.16824 q^{16} -7.90000 q^{17} +2.08649 q^{18} -1.37004 q^{19} +0.344152 q^{20} -2.80287 q^{21} -5.04821 q^{22} +2.00810 q^{23} +0.737414 q^{24} -4.97862 q^{25} +2.08649 q^{26} +1.00000 q^{27} -6.59633 q^{28} +0.323878 q^{29} +0.305116 q^{30} -2.15569 q^{31} -8.08532 q^{32} -2.41948 q^{33} -16.4832 q^{34} -0.409876 q^{35} +2.35342 q^{36} +8.53857 q^{37} -2.85856 q^{38} +1.00000 q^{39} +0.107835 q^{40} -1.40537 q^{41} -5.84814 q^{42} -3.63358 q^{43} -5.69406 q^{44} +0.146235 q^{45} +4.18988 q^{46} +1.09047 q^{47} -3.16824 q^{48} +0.856054 q^{49} -10.3878 q^{50} -7.90000 q^{51} +2.35342 q^{52} +5.59115 q^{53} +2.08649 q^{54} -0.353811 q^{55} -2.06687 q^{56} -1.37004 q^{57} +0.675767 q^{58} -5.92594 q^{59} +0.344152 q^{60} -5.22961 q^{61} -4.49782 q^{62} -2.80287 q^{63} -10.5334 q^{64} +0.146235 q^{65} -5.04821 q^{66} -15.2322 q^{67} -18.5921 q^{68} +2.00810 q^{69} -0.855200 q^{70} -7.85364 q^{71} +0.737414 q^{72} +5.89036 q^{73} +17.8156 q^{74} -4.97862 q^{75} -3.22428 q^{76} +6.78147 q^{77} +2.08649 q^{78} +10.9860 q^{79} -0.463307 q^{80} +1.00000 q^{81} -2.93229 q^{82} +6.84744 q^{83} -6.59633 q^{84} -1.15525 q^{85} -7.58142 q^{86} +0.323878 q^{87} -1.78416 q^{88} +1.55874 q^{89} +0.305116 q^{90} -2.80287 q^{91} +4.72592 q^{92} -2.15569 q^{93} +2.27525 q^{94} -0.200347 q^{95} -8.08532 q^{96} +3.05667 q^{97} +1.78614 q^{98} -2.41948 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 19 q - 4 q^{2} + 19 q^{3} + 10 q^{4} - 3 q^{5} - 4 q^{6} - 23 q^{7} - 9 q^{8} + 19 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 19 q - 4 q^{2} + 19 q^{3} + 10 q^{4} - 3 q^{5} - 4 q^{6} - 23 q^{7} - 9 q^{8} + 19 q^{9} - 6 q^{10} - 15 q^{11} + 10 q^{12} + 19 q^{13} - 4 q^{14} - 3 q^{15} - 4 q^{16} - 4 q^{18} - 32 q^{19} - 8 q^{20} - 23 q^{21} - 9 q^{22} - 23 q^{23} - 9 q^{24} - 8 q^{25} - 4 q^{26} + 19 q^{27} - 22 q^{28} + 4 q^{29} - 6 q^{30} - 50 q^{31} - 2 q^{32} - 15 q^{33} - 35 q^{34} - 4 q^{35} + 10 q^{36} - 38 q^{37} + 20 q^{38} + 19 q^{39} - 30 q^{40} - 11 q^{41} - 4 q^{42} - 17 q^{43} - 29 q^{44} - 3 q^{45} - 5 q^{46} - 38 q^{47} - 4 q^{48} - 6 q^{49} - 9 q^{50} + 10 q^{52} - 12 q^{53} - 4 q^{54} - 22 q^{55} + 12 q^{56} - 32 q^{57} - 23 q^{58} - 8 q^{59} - 8 q^{60} - 31 q^{61} + 31 q^{62} - 23 q^{63} + 15 q^{64} - 3 q^{65} - 9 q^{66} - 48 q^{67} + 44 q^{68} - 23 q^{69} + 13 q^{70} - 14 q^{71} - 9 q^{72} - 50 q^{73} - 10 q^{74} - 8 q^{75} - 64 q^{76} + 23 q^{77} - 4 q^{78} - 21 q^{79} + 8 q^{80} + 19 q^{81} - 10 q^{82} - 15 q^{83} - 22 q^{84} - 29 q^{85} + 9 q^{86} + 4 q^{87} + 3 q^{88} - 10 q^{89} - 6 q^{90} - 23 q^{91} - 17 q^{92} - 50 q^{93} - 22 q^{94} - 25 q^{95} - 2 q^{96} - 42 q^{97} - q^{98} - 15 q^{99}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.08649 1.47537 0.737684 0.675146i \(-0.235919\pi\)
0.737684 + 0.675146i \(0.235919\pi\)
\(3\) 1.00000 0.577350
\(4\) 2.35342 1.17671
\(5\) 0.146235 0.0653981 0.0326990 0.999465i \(-0.489590\pi\)
0.0326990 + 0.999465i \(0.489590\pi\)
\(6\) 2.08649 0.851804
\(7\) −2.80287 −1.05938 −0.529692 0.848190i \(-0.677692\pi\)
−0.529692 + 0.848190i \(0.677692\pi\)
\(8\) 0.737414 0.260715
\(9\) 1.00000 0.333333
\(10\) 0.305116 0.0964863
\(11\) −2.41948 −0.729500 −0.364750 0.931106i \(-0.618846\pi\)
−0.364750 + 0.931106i \(0.618846\pi\)
\(12\) 2.35342 0.679375
\(13\) 1.00000 0.277350
\(14\) −5.84814 −1.56298
\(15\) 0.146235 0.0377576
\(16\) −3.16824 −0.792061
\(17\) −7.90000 −1.91603 −0.958016 0.286714i \(-0.907437\pi\)
−0.958016 + 0.286714i \(0.907437\pi\)
\(18\) 2.08649 0.491789
\(19\) −1.37004 −0.314308 −0.157154 0.987574i \(-0.550232\pi\)
−0.157154 + 0.987574i \(0.550232\pi\)
\(20\) 0.344152 0.0769547
\(21\) −2.80287 −0.611635
\(22\) −5.04821 −1.07628
\(23\) 2.00810 0.418718 0.209359 0.977839i \(-0.432862\pi\)
0.209359 + 0.977839i \(0.432862\pi\)
\(24\) 0.737414 0.150524
\(25\) −4.97862 −0.995723
\(26\) 2.08649 0.409194
\(27\) 1.00000 0.192450
\(28\) −6.59633 −1.24659
\(29\) 0.323878 0.0601427 0.0300713 0.999548i \(-0.490427\pi\)
0.0300713 + 0.999548i \(0.490427\pi\)
\(30\) 0.305116 0.0557064
\(31\) −2.15569 −0.387174 −0.193587 0.981083i \(-0.562012\pi\)
−0.193587 + 0.981083i \(0.562012\pi\)
\(32\) −8.08532 −1.42930
\(33\) −2.41948 −0.421177
\(34\) −16.4832 −2.82685
\(35\) −0.409876 −0.0692817
\(36\) 2.35342 0.392237
\(37\) 8.53857 1.40373 0.701866 0.712309i \(-0.252350\pi\)
0.701866 + 0.712309i \(0.252350\pi\)
\(38\) −2.85856 −0.463720
\(39\) 1.00000 0.160128
\(40\) 0.107835 0.0170503
\(41\) −1.40537 −0.219483 −0.109741 0.993960i \(-0.535002\pi\)
−0.109741 + 0.993960i \(0.535002\pi\)
\(42\) −5.84814 −0.902387
\(43\) −3.63358 −0.554116 −0.277058 0.960853i \(-0.589359\pi\)
−0.277058 + 0.960853i \(0.589359\pi\)
\(44\) −5.69406 −0.858411
\(45\) 0.146235 0.0217994
\(46\) 4.18988 0.617764
\(47\) 1.09047 0.159062 0.0795308 0.996832i \(-0.474658\pi\)
0.0795308 + 0.996832i \(0.474658\pi\)
\(48\) −3.16824 −0.457297
\(49\) 0.856054 0.122293
\(50\) −10.3878 −1.46906
\(51\) −7.90000 −1.10622
\(52\) 2.35342 0.326361
\(53\) 5.59115 0.768003 0.384002 0.923332i \(-0.374546\pi\)
0.384002 + 0.923332i \(0.374546\pi\)
\(54\) 2.08649 0.283935
\(55\) −0.353811 −0.0477079
\(56\) −2.06687 −0.276197
\(57\) −1.37004 −0.181466
\(58\) 0.675767 0.0887326
\(59\) −5.92594 −0.771491 −0.385746 0.922605i \(-0.626056\pi\)
−0.385746 + 0.922605i \(0.626056\pi\)
\(60\) 0.344152 0.0444298
\(61\) −5.22961 −0.669583 −0.334792 0.942292i \(-0.608666\pi\)
−0.334792 + 0.942292i \(0.608666\pi\)
\(62\) −4.49782 −0.571224
\(63\) −2.80287 −0.353128
\(64\) −10.5334 −1.31668
\(65\) 0.146235 0.0181382
\(66\) −5.04821 −0.621391
\(67\) −15.2322 −1.86091 −0.930456 0.366403i \(-0.880589\pi\)
−0.930456 + 0.366403i \(0.880589\pi\)
\(68\) −18.5921 −2.25462
\(69\) 2.00810 0.241747
\(70\) −0.855200 −0.102216
\(71\) −7.85364 −0.932055 −0.466028 0.884770i \(-0.654315\pi\)
−0.466028 + 0.884770i \(0.654315\pi\)
\(72\) 0.737414 0.0869051
\(73\) 5.89036 0.689415 0.344707 0.938710i \(-0.387978\pi\)
0.344707 + 0.938710i \(0.387978\pi\)
\(74\) 17.8156 2.07102
\(75\) −4.97862 −0.574881
\(76\) −3.22428 −0.369850
\(77\) 6.78147 0.772820
\(78\) 2.08649 0.236248
\(79\) 10.9860 1.23602 0.618010 0.786170i \(-0.287939\pi\)
0.618010 + 0.786170i \(0.287939\pi\)
\(80\) −0.463307 −0.0517993
\(81\) 1.00000 0.111111
\(82\) −2.93229 −0.323818
\(83\) 6.84744 0.751604 0.375802 0.926700i \(-0.377367\pi\)
0.375802 + 0.926700i \(0.377367\pi\)
\(84\) −6.59633 −0.719719
\(85\) −1.15525 −0.125305
\(86\) −7.58142 −0.817526
\(87\) 0.323878 0.0347234
\(88\) −1.78416 −0.190192
\(89\) 1.55874 0.165226 0.0826130 0.996582i \(-0.473673\pi\)
0.0826130 + 0.996582i \(0.473673\pi\)
\(90\) 0.305116 0.0321621
\(91\) −2.80287 −0.293820
\(92\) 4.72592 0.492711
\(93\) −2.15569 −0.223535
\(94\) 2.27525 0.234675
\(95\) −0.200347 −0.0205551
\(96\) −8.08532 −0.825205
\(97\) 3.05667 0.310358 0.155179 0.987886i \(-0.450405\pi\)
0.155179 + 0.987886i \(0.450405\pi\)
\(98\) 1.78614 0.180428
\(99\) −2.41948 −0.243167
\(100\) −11.7168 −1.17168
\(101\) 8.97677 0.893222 0.446611 0.894728i \(-0.352631\pi\)
0.446611 + 0.894728i \(0.352631\pi\)
\(102\) −16.4832 −1.63208
\(103\) −1.00000 −0.0985329
\(104\) 0.737414 0.0723094
\(105\) −0.409876 −0.0399998
\(106\) 11.6659 1.13309
\(107\) 10.9794 1.06142 0.530711 0.847553i \(-0.321925\pi\)
0.530711 + 0.847553i \(0.321925\pi\)
\(108\) 2.35342 0.226458
\(109\) −14.8721 −1.42449 −0.712245 0.701931i \(-0.752322\pi\)
−0.712245 + 0.701931i \(0.752322\pi\)
\(110\) −0.738222 −0.0703867
\(111\) 8.53857 0.810445
\(112\) 8.88016 0.839096
\(113\) 3.10936 0.292504 0.146252 0.989247i \(-0.453279\pi\)
0.146252 + 0.989247i \(0.453279\pi\)
\(114\) −2.85856 −0.267729
\(115\) 0.293654 0.0273834
\(116\) 0.762223 0.0707706
\(117\) 1.00000 0.0924500
\(118\) −12.3644 −1.13823
\(119\) 22.1426 2.02981
\(120\) 0.107835 0.00984398
\(121\) −5.14613 −0.467830
\(122\) −10.9115 −0.987882
\(123\) −1.40537 −0.126718
\(124\) −5.07326 −0.455592
\(125\) −1.45922 −0.130516
\(126\) −5.84814 −0.520994
\(127\) 0.420464 0.0373101 0.0186551 0.999826i \(-0.494062\pi\)
0.0186551 + 0.999826i \(0.494062\pi\)
\(128\) −5.80720 −0.513289
\(129\) −3.63358 −0.319919
\(130\) 0.305116 0.0267605
\(131\) −12.3974 −1.08316 −0.541582 0.840648i \(-0.682174\pi\)
−0.541582 + 0.840648i \(0.682174\pi\)
\(132\) −5.69406 −0.495604
\(133\) 3.84003 0.332973
\(134\) −31.7818 −2.74553
\(135\) 0.146235 0.0125859
\(136\) −5.82557 −0.499539
\(137\) −5.62724 −0.480768 −0.240384 0.970678i \(-0.577273\pi\)
−0.240384 + 0.970678i \(0.577273\pi\)
\(138\) 4.18988 0.356666
\(139\) 16.6873 1.41540 0.707699 0.706514i \(-0.249733\pi\)
0.707699 + 0.706514i \(0.249733\pi\)
\(140\) −0.964612 −0.0815246
\(141\) 1.09047 0.0918343
\(142\) −16.3865 −1.37512
\(143\) −2.41948 −0.202327
\(144\) −3.16824 −0.264020
\(145\) 0.0473622 0.00393322
\(146\) 12.2902 1.01714
\(147\) 0.856054 0.0706061
\(148\) 20.0949 1.65179
\(149\) 18.9510 1.55253 0.776264 0.630409i \(-0.217113\pi\)
0.776264 + 0.630409i \(0.217113\pi\)
\(150\) −10.3878 −0.848161
\(151\) −10.8437 −0.882445 −0.441222 0.897398i \(-0.645455\pi\)
−0.441222 + 0.897398i \(0.645455\pi\)
\(152\) −1.01028 −0.0819449
\(153\) −7.90000 −0.638677
\(154\) 14.1494 1.14019
\(155\) −0.315237 −0.0253204
\(156\) 2.35342 0.188425
\(157\) 6.43435 0.513517 0.256759 0.966476i \(-0.417345\pi\)
0.256759 + 0.966476i \(0.417345\pi\)
\(158\) 22.9221 1.82358
\(159\) 5.59115 0.443407
\(160\) −1.18235 −0.0934733
\(161\) −5.62844 −0.443583
\(162\) 2.08649 0.163930
\(163\) −10.8170 −0.847251 −0.423626 0.905837i \(-0.639243\pi\)
−0.423626 + 0.905837i \(0.639243\pi\)
\(164\) −3.30744 −0.258268
\(165\) −0.353811 −0.0275442
\(166\) 14.2871 1.10889
\(167\) 3.13564 0.242643 0.121322 0.992613i \(-0.461287\pi\)
0.121322 + 0.992613i \(0.461287\pi\)
\(168\) −2.06687 −0.159463
\(169\) 1.00000 0.0769231
\(170\) −2.41042 −0.184871
\(171\) −1.37004 −0.104769
\(172\) −8.55136 −0.652035
\(173\) 12.7567 0.969872 0.484936 0.874550i \(-0.338843\pi\)
0.484936 + 0.874550i \(0.338843\pi\)
\(174\) 0.675767 0.0512298
\(175\) 13.9544 1.05485
\(176\) 7.66550 0.577808
\(177\) −5.92594 −0.445421
\(178\) 3.25229 0.243769
\(179\) −15.1240 −1.13042 −0.565209 0.824948i \(-0.691205\pi\)
−0.565209 + 0.824948i \(0.691205\pi\)
\(180\) 0.344152 0.0256516
\(181\) −21.6386 −1.60838 −0.804192 0.594369i \(-0.797402\pi\)
−0.804192 + 0.594369i \(0.797402\pi\)
\(182\) −5.84814 −0.433493
\(183\) −5.22961 −0.386584
\(184\) 1.48080 0.109166
\(185\) 1.24863 0.0918014
\(186\) −4.49782 −0.329796
\(187\) 19.1139 1.39775
\(188\) 2.56634 0.187170
\(189\) −2.80287 −0.203878
\(190\) −0.418021 −0.0303264
\(191\) −18.6747 −1.35126 −0.675628 0.737243i \(-0.736127\pi\)
−0.675628 + 0.737243i \(0.736127\pi\)
\(192\) −10.5334 −0.760185
\(193\) 6.17826 0.444721 0.222360 0.974965i \(-0.428624\pi\)
0.222360 + 0.974965i \(0.428624\pi\)
\(194\) 6.37770 0.457892
\(195\) 0.146235 0.0104721
\(196\) 2.01466 0.143904
\(197\) 7.93563 0.565390 0.282695 0.959210i \(-0.408772\pi\)
0.282695 + 0.959210i \(0.408772\pi\)
\(198\) −5.04821 −0.358760
\(199\) 18.7223 1.32719 0.663593 0.748094i \(-0.269031\pi\)
0.663593 + 0.748094i \(0.269031\pi\)
\(200\) −3.67130 −0.259600
\(201\) −15.2322 −1.07440
\(202\) 18.7299 1.31783
\(203\) −0.907787 −0.0637142
\(204\) −18.5921 −1.30170
\(205\) −0.205514 −0.0143537
\(206\) −2.08649 −0.145372
\(207\) 2.00810 0.139573
\(208\) −3.16824 −0.219678
\(209\) 3.31477 0.229288
\(210\) −0.855200 −0.0590144
\(211\) 23.7261 1.63337 0.816685 0.577084i \(-0.195809\pi\)
0.816685 + 0.577084i \(0.195809\pi\)
\(212\) 13.1583 0.903719
\(213\) −7.85364 −0.538122
\(214\) 22.9084 1.56599
\(215\) −0.531356 −0.0362382
\(216\) 0.737414 0.0501747
\(217\) 6.04212 0.410166
\(218\) −31.0305 −2.10165
\(219\) 5.89036 0.398034
\(220\) −0.832668 −0.0561385
\(221\) −7.90000 −0.531412
\(222\) 17.8156 1.19571
\(223\) −4.25945 −0.285234 −0.142617 0.989778i \(-0.545552\pi\)
−0.142617 + 0.989778i \(0.545552\pi\)
\(224\) 22.6621 1.51417
\(225\) −4.97862 −0.331908
\(226\) 6.48764 0.431551
\(227\) −11.3346 −0.752304 −0.376152 0.926558i \(-0.622753\pi\)
−0.376152 + 0.926558i \(0.622753\pi\)
\(228\) −3.22428 −0.213533
\(229\) −2.19287 −0.144909 −0.0724545 0.997372i \(-0.523083\pi\)
−0.0724545 + 0.997372i \(0.523083\pi\)
\(230\) 0.612705 0.0404006
\(231\) 6.78147 0.446188
\(232\) 0.238832 0.0156801
\(233\) −17.0845 −1.11924 −0.559621 0.828749i \(-0.689053\pi\)
−0.559621 + 0.828749i \(0.689053\pi\)
\(234\) 2.08649 0.136398
\(235\) 0.159465 0.0104023
\(236\) −13.9462 −0.907823
\(237\) 10.9860 0.713617
\(238\) 46.2003 2.99472
\(239\) −15.7266 −1.01727 −0.508634 0.860983i \(-0.669849\pi\)
−0.508634 + 0.860983i \(0.669849\pi\)
\(240\) −0.463307 −0.0299063
\(241\) −28.3568 −1.82662 −0.913310 0.407266i \(-0.866482\pi\)
−0.913310 + 0.407266i \(0.866482\pi\)
\(242\) −10.7373 −0.690221
\(243\) 1.00000 0.0641500
\(244\) −12.3075 −0.787906
\(245\) 0.125185 0.00799776
\(246\) −2.93229 −0.186956
\(247\) −1.37004 −0.0871734
\(248\) −1.58964 −0.100942
\(249\) 6.84744 0.433939
\(250\) −3.04464 −0.192560
\(251\) −10.1004 −0.637534 −0.318767 0.947833i \(-0.603269\pi\)
−0.318767 + 0.947833i \(0.603269\pi\)
\(252\) −6.59633 −0.415530
\(253\) −4.85856 −0.305455
\(254\) 0.877291 0.0550461
\(255\) −1.15525 −0.0723448
\(256\) 8.95021 0.559388
\(257\) −19.2020 −1.19779 −0.598895 0.800827i \(-0.704394\pi\)
−0.598895 + 0.800827i \(0.704394\pi\)
\(258\) −7.58142 −0.471999
\(259\) −23.9325 −1.48709
\(260\) 0.344152 0.0213434
\(261\) 0.323878 0.0200476
\(262\) −25.8670 −1.59807
\(263\) 1.09765 0.0676842 0.0338421 0.999427i \(-0.489226\pi\)
0.0338421 + 0.999427i \(0.489226\pi\)
\(264\) −1.78416 −0.109807
\(265\) 0.817619 0.0502259
\(266\) 8.01217 0.491258
\(267\) 1.55874 0.0953933
\(268\) −35.8479 −2.18976
\(269\) −4.22283 −0.257471 −0.128735 0.991679i \(-0.541092\pi\)
−0.128735 + 0.991679i \(0.541092\pi\)
\(270\) 0.305116 0.0185688
\(271\) 11.1291 0.676046 0.338023 0.941138i \(-0.390242\pi\)
0.338023 + 0.941138i \(0.390242\pi\)
\(272\) 25.0291 1.51761
\(273\) −2.80287 −0.169637
\(274\) −11.7412 −0.709310
\(275\) 12.0456 0.726380
\(276\) 4.72592 0.284467
\(277\) −26.1321 −1.57012 −0.785062 0.619417i \(-0.787369\pi\)
−0.785062 + 0.619417i \(0.787369\pi\)
\(278\) 34.8178 2.08823
\(279\) −2.15569 −0.129058
\(280\) −0.302248 −0.0180628
\(281\) 12.9257 0.771081 0.385541 0.922691i \(-0.374015\pi\)
0.385541 + 0.922691i \(0.374015\pi\)
\(282\) 2.27525 0.135489
\(283\) −9.74679 −0.579387 −0.289693 0.957120i \(-0.593553\pi\)
−0.289693 + 0.957120i \(0.593553\pi\)
\(284\) −18.4829 −1.09676
\(285\) −0.200347 −0.0118675
\(286\) −5.04821 −0.298507
\(287\) 3.93907 0.232516
\(288\) −8.08532 −0.476432
\(289\) 45.4101 2.67118
\(290\) 0.0988206 0.00580294
\(291\) 3.05667 0.179185
\(292\) 13.8625 0.811243
\(293\) 9.92718 0.579952 0.289976 0.957034i \(-0.406353\pi\)
0.289976 + 0.957034i \(0.406353\pi\)
\(294\) 1.78614 0.104170
\(295\) −0.866577 −0.0504540
\(296\) 6.29646 0.365974
\(297\) −2.41948 −0.140392
\(298\) 39.5410 2.29055
\(299\) 2.00810 0.116132
\(300\) −11.7168 −0.676469
\(301\) 10.1844 0.587022
\(302\) −22.6252 −1.30193
\(303\) 8.97677 0.515702
\(304\) 4.34061 0.248951
\(305\) −0.764750 −0.0437895
\(306\) −16.4832 −0.942285
\(307\) 15.2886 0.872566 0.436283 0.899809i \(-0.356295\pi\)
0.436283 + 0.899809i \(0.356295\pi\)
\(308\) 15.9597 0.909387
\(309\) −1.00000 −0.0568880
\(310\) −0.657737 −0.0373570
\(311\) 7.38549 0.418793 0.209396 0.977831i \(-0.432850\pi\)
0.209396 + 0.977831i \(0.432850\pi\)
\(312\) 0.737414 0.0417478
\(313\) 12.9545 0.732230 0.366115 0.930570i \(-0.380688\pi\)
0.366115 + 0.930570i \(0.380688\pi\)
\(314\) 13.4252 0.757627
\(315\) −0.409876 −0.0230939
\(316\) 25.8547 1.45444
\(317\) 26.3027 1.47731 0.738654 0.674085i \(-0.235462\pi\)
0.738654 + 0.674085i \(0.235462\pi\)
\(318\) 11.6659 0.654188
\(319\) −0.783616 −0.0438741
\(320\) −1.54035 −0.0861083
\(321\) 10.9794 0.612812
\(322\) −11.7437 −0.654449
\(323\) 10.8233 0.602224
\(324\) 2.35342 0.130746
\(325\) −4.97862 −0.276164
\(326\) −22.5695 −1.25001
\(327\) −14.8721 −0.822430
\(328\) −1.03634 −0.0572224
\(329\) −3.05645 −0.168507
\(330\) −0.738222 −0.0406378
\(331\) −6.14631 −0.337832 −0.168916 0.985630i \(-0.554027\pi\)
−0.168916 + 0.985630i \(0.554027\pi\)
\(332\) 16.1149 0.884421
\(333\) 8.53857 0.467911
\(334\) 6.54248 0.357988
\(335\) −2.22748 −0.121700
\(336\) 8.88016 0.484453
\(337\) 1.99702 0.108785 0.0543923 0.998520i \(-0.482678\pi\)
0.0543923 + 0.998520i \(0.482678\pi\)
\(338\) 2.08649 0.113490
\(339\) 3.10936 0.168877
\(340\) −2.71880 −0.147448
\(341\) 5.21565 0.282443
\(342\) −2.85856 −0.154573
\(343\) 17.2207 0.929828
\(344\) −2.67946 −0.144467
\(345\) 0.293654 0.0158098
\(346\) 26.6166 1.43092
\(347\) −2.07380 −0.111327 −0.0556636 0.998450i \(-0.517727\pi\)
−0.0556636 + 0.998450i \(0.517727\pi\)
\(348\) 0.762223 0.0408594
\(349\) −16.6784 −0.892777 −0.446388 0.894839i \(-0.647290\pi\)
−0.446388 + 0.894839i \(0.647290\pi\)
\(350\) 29.1156 1.55630
\(351\) 1.00000 0.0533761
\(352\) 19.5623 1.04267
\(353\) −27.1474 −1.44491 −0.722454 0.691419i \(-0.756986\pi\)
−0.722454 + 0.691419i \(0.756986\pi\)
\(354\) −12.3644 −0.657159
\(355\) −1.14847 −0.0609546
\(356\) 3.66837 0.194423
\(357\) 22.1426 1.17191
\(358\) −31.5559 −1.66778
\(359\) 17.0340 0.899021 0.449511 0.893275i \(-0.351598\pi\)
0.449511 + 0.893275i \(0.351598\pi\)
\(360\) 0.107835 0.00568342
\(361\) −17.1230 −0.901210
\(362\) −45.1486 −2.37296
\(363\) −5.14613 −0.270102
\(364\) −6.59633 −0.345742
\(365\) 0.861375 0.0450864
\(366\) −10.9115 −0.570354
\(367\) 32.0657 1.67382 0.836908 0.547343i \(-0.184361\pi\)
0.836908 + 0.547343i \(0.184361\pi\)
\(368\) −6.36216 −0.331651
\(369\) −1.40537 −0.0731609
\(370\) 2.60526 0.135441
\(371\) −15.6712 −0.813610
\(372\) −5.07326 −0.263036
\(373\) −14.7862 −0.765601 −0.382800 0.923831i \(-0.625040\pi\)
−0.382800 + 0.923831i \(0.625040\pi\)
\(374\) 39.8808 2.06219
\(375\) −1.45922 −0.0753537
\(376\) 0.804129 0.0414698
\(377\) 0.323878 0.0166806
\(378\) −5.84814 −0.300796
\(379\) −30.5037 −1.56687 −0.783435 0.621473i \(-0.786534\pi\)
−0.783435 + 0.621473i \(0.786534\pi\)
\(380\) −0.471501 −0.0241875
\(381\) 0.420464 0.0215410
\(382\) −38.9645 −1.99360
\(383\) 30.7228 1.56986 0.784932 0.619582i \(-0.212698\pi\)
0.784932 + 0.619582i \(0.212698\pi\)
\(384\) −5.80720 −0.296347
\(385\) 0.991685 0.0505410
\(386\) 12.8909 0.656127
\(387\) −3.63358 −0.184705
\(388\) 7.19364 0.365202
\(389\) 18.9137 0.958962 0.479481 0.877552i \(-0.340825\pi\)
0.479481 + 0.877552i \(0.340825\pi\)
\(390\) 0.305116 0.0154502
\(391\) −15.8640 −0.802278
\(392\) 0.631266 0.0318837
\(393\) −12.3974 −0.625365
\(394\) 16.5576 0.834159
\(395\) 1.60653 0.0808334
\(396\) −5.69406 −0.286137
\(397\) −23.7380 −1.19138 −0.595688 0.803216i \(-0.703120\pi\)
−0.595688 + 0.803216i \(0.703120\pi\)
\(398\) 39.0637 1.95809
\(399\) 3.84003 0.192242
\(400\) 15.7735 0.788673
\(401\) 37.0937 1.85237 0.926186 0.377067i \(-0.123067\pi\)
0.926186 + 0.377067i \(0.123067\pi\)
\(402\) −31.7818 −1.58513
\(403\) −2.15569 −0.107383
\(404\) 21.1261 1.05106
\(405\) 0.146235 0.00726645
\(406\) −1.89408 −0.0940019
\(407\) −20.6589 −1.02402
\(408\) −5.82557 −0.288409
\(409\) −20.1546 −0.996582 −0.498291 0.867010i \(-0.666039\pi\)
−0.498291 + 0.867010i \(0.666039\pi\)
\(410\) −0.428803 −0.0211771
\(411\) −5.62724 −0.277571
\(412\) −2.35342 −0.115945
\(413\) 16.6096 0.817305
\(414\) 4.18988 0.205921
\(415\) 1.00133 0.0491534
\(416\) −8.08532 −0.396416
\(417\) 16.6873 0.817181
\(418\) 6.91623 0.338284
\(419\) 5.64622 0.275836 0.137918 0.990444i \(-0.455959\pi\)
0.137918 + 0.990444i \(0.455959\pi\)
\(420\) −0.964612 −0.0470682
\(421\) 32.4072 1.57943 0.789714 0.613475i \(-0.210229\pi\)
0.789714 + 0.613475i \(0.210229\pi\)
\(422\) 49.5041 2.40982
\(423\) 1.09047 0.0530206
\(424\) 4.12299 0.200230
\(425\) 39.3311 1.90784
\(426\) −16.3865 −0.793929
\(427\) 14.6579 0.709345
\(428\) 25.8392 1.24899
\(429\) −2.41948 −0.116813
\(430\) −1.10867 −0.0534646
\(431\) −33.5759 −1.61729 −0.808647 0.588294i \(-0.799800\pi\)
−0.808647 + 0.588294i \(0.799800\pi\)
\(432\) −3.16824 −0.152432
\(433\) 13.3542 0.641762 0.320881 0.947119i \(-0.396021\pi\)
0.320881 + 0.947119i \(0.396021\pi\)
\(434\) 12.6068 0.605146
\(435\) 0.0473622 0.00227084
\(436\) −35.0004 −1.67622
\(437\) −2.75118 −0.131607
\(438\) 12.2902 0.587247
\(439\) −8.79526 −0.419775 −0.209887 0.977726i \(-0.567310\pi\)
−0.209887 + 0.977726i \(0.567310\pi\)
\(440\) −0.260905 −0.0124382
\(441\) 0.856054 0.0407645
\(442\) −16.4832 −0.784028
\(443\) −3.23353 −0.153630 −0.0768149 0.997045i \(-0.524475\pi\)
−0.0768149 + 0.997045i \(0.524475\pi\)
\(444\) 20.0949 0.953660
\(445\) 0.227942 0.0108055
\(446\) −8.88729 −0.420825
\(447\) 18.9510 0.896352
\(448\) 29.5238 1.39487
\(449\) 2.81077 0.132648 0.0663242 0.997798i \(-0.478873\pi\)
0.0663242 + 0.997798i \(0.478873\pi\)
\(450\) −10.3878 −0.489686
\(451\) 3.40027 0.160113
\(452\) 7.31764 0.344193
\(453\) −10.8437 −0.509480
\(454\) −23.6495 −1.10993
\(455\) −0.409876 −0.0192153
\(456\) −1.01028 −0.0473109
\(457\) −4.12736 −0.193070 −0.0965349 0.995330i \(-0.530776\pi\)
−0.0965349 + 0.995330i \(0.530776\pi\)
\(458\) −4.57539 −0.213794
\(459\) −7.90000 −0.368741
\(460\) 0.691093 0.0322224
\(461\) −3.09660 −0.144223 −0.0721116 0.997397i \(-0.522974\pi\)
−0.0721116 + 0.997397i \(0.522974\pi\)
\(462\) 14.1494 0.658292
\(463\) 1.63629 0.0760447 0.0380223 0.999277i \(-0.487894\pi\)
0.0380223 + 0.999277i \(0.487894\pi\)
\(464\) −1.02613 −0.0476367
\(465\) −0.315237 −0.0146188
\(466\) −35.6466 −1.65129
\(467\) −26.3373 −1.21875 −0.609373 0.792884i \(-0.708579\pi\)
−0.609373 + 0.792884i \(0.708579\pi\)
\(468\) 2.35342 0.108787
\(469\) 42.6939 1.97142
\(470\) 0.332721 0.0153473
\(471\) 6.43435 0.296479
\(472\) −4.36987 −0.201139
\(473\) 8.79138 0.404228
\(474\) 22.9221 1.05285
\(475\) 6.82089 0.312964
\(476\) 52.1110 2.38851
\(477\) 5.59115 0.256001
\(478\) −32.8133 −1.50085
\(479\) 11.3171 0.517090 0.258545 0.965999i \(-0.416757\pi\)
0.258545 + 0.965999i \(0.416757\pi\)
\(480\) −1.18235 −0.0539668
\(481\) 8.53857 0.389325
\(482\) −59.1660 −2.69494
\(483\) −5.62844 −0.256103
\(484\) −12.1110 −0.550501
\(485\) 0.446991 0.0202968
\(486\) 2.08649 0.0946449
\(487\) −35.4588 −1.60679 −0.803396 0.595445i \(-0.796976\pi\)
−0.803396 + 0.595445i \(0.796976\pi\)
\(488\) −3.85639 −0.174570
\(489\) −10.8170 −0.489161
\(490\) 0.261196 0.0117996
\(491\) −11.7787 −0.531564 −0.265782 0.964033i \(-0.585630\pi\)
−0.265782 + 0.964033i \(0.585630\pi\)
\(492\) −3.30744 −0.149111
\(493\) −2.55864 −0.115235
\(494\) −2.85856 −0.128613
\(495\) −0.353811 −0.0159026
\(496\) 6.82976 0.306665
\(497\) 22.0127 0.987404
\(498\) 14.2871 0.640219
\(499\) −6.67864 −0.298977 −0.149489 0.988763i \(-0.547763\pi\)
−0.149489 + 0.988763i \(0.547763\pi\)
\(500\) −3.43416 −0.153580
\(501\) 3.13564 0.140090
\(502\) −21.0744 −0.940598
\(503\) −38.2115 −1.70376 −0.851882 0.523733i \(-0.824539\pi\)
−0.851882 + 0.523733i \(0.824539\pi\)
\(504\) −2.06687 −0.0920658
\(505\) 1.31271 0.0584150
\(506\) −10.1373 −0.450659
\(507\) 1.00000 0.0444116
\(508\) 0.989529 0.0439032
\(509\) 14.3663 0.636775 0.318388 0.947961i \(-0.396859\pi\)
0.318388 + 0.947961i \(0.396859\pi\)
\(510\) −2.41042 −0.106735
\(511\) −16.5099 −0.730355
\(512\) 30.2889 1.33859
\(513\) −1.37004 −0.0604886
\(514\) −40.0648 −1.76718
\(515\) −0.146235 −0.00644387
\(516\) −8.55136 −0.376453
\(517\) −2.63837 −0.116035
\(518\) −49.9347 −2.19401
\(519\) 12.7567 0.559956
\(520\) 0.107835 0.00472889
\(521\) −6.96588 −0.305181 −0.152590 0.988290i \(-0.548761\pi\)
−0.152590 + 0.988290i \(0.548761\pi\)
\(522\) 0.675767 0.0295775
\(523\) 17.9076 0.783045 0.391522 0.920169i \(-0.371949\pi\)
0.391522 + 0.920169i \(0.371949\pi\)
\(524\) −29.1763 −1.27457
\(525\) 13.9544 0.609019
\(526\) 2.29024 0.0998591
\(527\) 17.0300 0.741838
\(528\) 7.66550 0.333598
\(529\) −18.9675 −0.824675
\(530\) 1.70595 0.0741018
\(531\) −5.92594 −0.257164
\(532\) 9.03722 0.391813
\(533\) −1.40537 −0.0608735
\(534\) 3.25229 0.140740
\(535\) 1.60557 0.0694149
\(536\) −11.2325 −0.485168
\(537\) −15.1240 −0.652647
\(538\) −8.81089 −0.379864
\(539\) −2.07120 −0.0892130
\(540\) 0.344152 0.0148099
\(541\) −14.2551 −0.612875 −0.306438 0.951891i \(-0.599137\pi\)
−0.306438 + 0.951891i \(0.599137\pi\)
\(542\) 23.2207 0.997416
\(543\) −21.6386 −0.928601
\(544\) 63.8741 2.73858
\(545\) −2.17482 −0.0931590
\(546\) −5.84814 −0.250277
\(547\) −29.1336 −1.24566 −0.622831 0.782357i \(-0.714017\pi\)
−0.622831 + 0.782357i \(0.714017\pi\)
\(548\) −13.2433 −0.565725
\(549\) −5.22961 −0.223194
\(550\) 25.1331 1.07168
\(551\) −0.443725 −0.0189033
\(552\) 1.48080 0.0630272
\(553\) −30.7922 −1.30942
\(554\) −54.5242 −2.31651
\(555\) 1.24863 0.0530016
\(556\) 39.2723 1.66552
\(557\) −30.2608 −1.28219 −0.641095 0.767462i \(-0.721519\pi\)
−0.641095 + 0.767462i \(0.721519\pi\)
\(558\) −4.49782 −0.190408
\(559\) −3.63358 −0.153684
\(560\) 1.29859 0.0548753
\(561\) 19.1139 0.806989
\(562\) 26.9692 1.13763
\(563\) −4.15922 −0.175290 −0.0876451 0.996152i \(-0.527934\pi\)
−0.0876451 + 0.996152i \(0.527934\pi\)
\(564\) 2.56634 0.108063
\(565\) 0.454696 0.0191292
\(566\) −20.3365 −0.854809
\(567\) −2.80287 −0.117709
\(568\) −5.79138 −0.243001
\(569\) 28.3380 1.18799 0.593995 0.804469i \(-0.297550\pi\)
0.593995 + 0.804469i \(0.297550\pi\)
\(570\) −0.418021 −0.0175090
\(571\) −17.5850 −0.735907 −0.367954 0.929844i \(-0.619941\pi\)
−0.367954 + 0.929844i \(0.619941\pi\)
\(572\) −5.69406 −0.238080
\(573\) −18.6747 −0.780148
\(574\) 8.21882 0.343047
\(575\) −9.99757 −0.416928
\(576\) −10.5334 −0.438893
\(577\) 20.1078 0.837098 0.418549 0.908194i \(-0.362539\pi\)
0.418549 + 0.908194i \(0.362539\pi\)
\(578\) 94.7475 3.94098
\(579\) 6.17826 0.256760
\(580\) 0.111463 0.00462826
\(581\) −19.1924 −0.796237
\(582\) 6.37770 0.264364
\(583\) −13.5277 −0.560258
\(584\) 4.34364 0.179741
\(585\) 0.146235 0.00604606
\(586\) 20.7129 0.855643
\(587\) −36.8883 −1.52254 −0.761271 0.648434i \(-0.775424\pi\)
−0.761271 + 0.648434i \(0.775424\pi\)
\(588\) 2.01466 0.0830831
\(589\) 2.95338 0.121692
\(590\) −1.80810 −0.0744383
\(591\) 7.93563 0.326428
\(592\) −27.0523 −1.11184
\(593\) −8.10709 −0.332918 −0.166459 0.986048i \(-0.553233\pi\)
−0.166459 + 0.986048i \(0.553233\pi\)
\(594\) −5.04821 −0.207130
\(595\) 3.23802 0.132746
\(596\) 44.5998 1.82688
\(597\) 18.7223 0.766251
\(598\) 4.18988 0.171337
\(599\) −25.2371 −1.03116 −0.515581 0.856841i \(-0.672424\pi\)
−0.515581 + 0.856841i \(0.672424\pi\)
\(600\) −3.67130 −0.149880
\(601\) 14.9142 0.608363 0.304182 0.952614i \(-0.401617\pi\)
0.304182 + 0.952614i \(0.401617\pi\)
\(602\) 21.2497 0.866073
\(603\) −15.2322 −0.620304
\(604\) −25.5197 −1.03838
\(605\) −0.752542 −0.0305952
\(606\) 18.7299 0.760850
\(607\) −2.66643 −0.108227 −0.0541135 0.998535i \(-0.517233\pi\)
−0.0541135 + 0.998535i \(0.517233\pi\)
\(608\) 11.0772 0.449240
\(609\) −0.907787 −0.0367854
\(610\) −1.59564 −0.0646056
\(611\) 1.09047 0.0441158
\(612\) −18.5921 −0.751539
\(613\) 33.3423 1.34668 0.673341 0.739332i \(-0.264859\pi\)
0.673341 + 0.739332i \(0.264859\pi\)
\(614\) 31.8994 1.28736
\(615\) −0.205514 −0.00828714
\(616\) 5.00075 0.201486
\(617\) 9.02258 0.363235 0.181618 0.983369i \(-0.441867\pi\)
0.181618 + 0.983369i \(0.441867\pi\)
\(618\) −2.08649 −0.0839308
\(619\) −18.6711 −0.750455 −0.375228 0.926933i \(-0.622435\pi\)
−0.375228 + 0.926933i \(0.622435\pi\)
\(620\) −0.741886 −0.0297949
\(621\) 2.00810 0.0805824
\(622\) 15.4097 0.617873
\(623\) −4.36894 −0.175038
\(624\) −3.16824 −0.126831
\(625\) 24.6797 0.987188
\(626\) 27.0293 1.08031
\(627\) 3.31477 0.132379
\(628\) 15.1428 0.604262
\(629\) −67.4547 −2.68960
\(630\) −0.855200 −0.0340720
\(631\) −9.70059 −0.386174 −0.193087 0.981182i \(-0.561850\pi\)
−0.193087 + 0.981182i \(0.561850\pi\)
\(632\) 8.10122 0.322249
\(633\) 23.7261 0.943027
\(634\) 54.8802 2.17957
\(635\) 0.0614863 0.00244001
\(636\) 13.1583 0.521762
\(637\) 0.856054 0.0339181
\(638\) −1.63500 −0.0647304
\(639\) −7.85364 −0.310685
\(640\) −0.849214 −0.0335681
\(641\) −4.30276 −0.169949 −0.0849745 0.996383i \(-0.527081\pi\)
−0.0849745 + 0.996383i \(0.527081\pi\)
\(642\) 22.9084 0.904123
\(643\) −14.7586 −0.582022 −0.291011 0.956720i \(-0.593992\pi\)
−0.291011 + 0.956720i \(0.593992\pi\)
\(644\) −13.2461 −0.521970
\(645\) −0.531356 −0.0209221
\(646\) 22.5827 0.888503
\(647\) 5.11283 0.201006 0.100503 0.994937i \(-0.467955\pi\)
0.100503 + 0.994937i \(0.467955\pi\)
\(648\) 0.737414 0.0289684
\(649\) 14.3377 0.562803
\(650\) −10.3878 −0.407443
\(651\) 6.04212 0.236809
\(652\) −25.4569 −0.996970
\(653\) 24.6570 0.964903 0.482451 0.875923i \(-0.339746\pi\)
0.482451 + 0.875923i \(0.339746\pi\)
\(654\) −31.0305 −1.21339
\(655\) −1.81293 −0.0708369
\(656\) 4.45257 0.173844
\(657\) 5.89036 0.229805
\(658\) −6.37723 −0.248610
\(659\) 7.51441 0.292720 0.146360 0.989231i \(-0.453244\pi\)
0.146360 + 0.989231i \(0.453244\pi\)
\(660\) −0.832668 −0.0324116
\(661\) 30.7298 1.19525 0.597625 0.801776i \(-0.296111\pi\)
0.597625 + 0.801776i \(0.296111\pi\)
\(662\) −12.8242 −0.498426
\(663\) −7.90000 −0.306811
\(664\) 5.04939 0.195954
\(665\) 0.561545 0.0217758
\(666\) 17.8156 0.690341
\(667\) 0.650381 0.0251829
\(668\) 7.37950 0.285521
\(669\) −4.25945 −0.164680
\(670\) −4.64760 −0.179553
\(671\) 12.6529 0.488461
\(672\) 22.6621 0.874209
\(673\) 44.7534 1.72512 0.862559 0.505956i \(-0.168860\pi\)
0.862559 + 0.505956i \(0.168860\pi\)
\(674\) 4.16675 0.160497
\(675\) −4.97862 −0.191627
\(676\) 2.35342 0.0905163
\(677\) −7.23229 −0.277959 −0.138980 0.990295i \(-0.544382\pi\)
−0.138980 + 0.990295i \(0.544382\pi\)
\(678\) 6.48764 0.249156
\(679\) −8.56744 −0.328788
\(680\) −0.851900 −0.0326689
\(681\) −11.3346 −0.434343
\(682\) 10.8824 0.416708
\(683\) −27.9454 −1.06930 −0.534651 0.845073i \(-0.679557\pi\)
−0.534651 + 0.845073i \(0.679557\pi\)
\(684\) −3.22428 −0.123283
\(685\) −0.822898 −0.0314413
\(686\) 35.9307 1.37184
\(687\) −2.19287 −0.0836632
\(688\) 11.5121 0.438894
\(689\) 5.59115 0.213006
\(690\) 0.612705 0.0233253
\(691\) −30.4955 −1.16010 −0.580051 0.814580i \(-0.696967\pi\)
−0.580051 + 0.814580i \(0.696967\pi\)
\(692\) 30.0219 1.14126
\(693\) 6.78147 0.257607
\(694\) −4.32695 −0.164249
\(695\) 2.44026 0.0925644
\(696\) 0.238832 0.00905291
\(697\) 11.1025 0.420536
\(698\) −34.7993 −1.31717
\(699\) −17.0845 −0.646195
\(700\) 32.8406 1.24126
\(701\) 43.0145 1.62463 0.812317 0.583216i \(-0.198206\pi\)
0.812317 + 0.583216i \(0.198206\pi\)
\(702\) 2.08649 0.0787493
\(703\) −11.6982 −0.441204
\(704\) 25.4854 0.960517
\(705\) 0.159465 0.00600579
\(706\) −56.6426 −2.13177
\(707\) −25.1607 −0.946265
\(708\) −13.9462 −0.524132
\(709\) −18.9440 −0.711456 −0.355728 0.934590i \(-0.615767\pi\)
−0.355728 + 0.934590i \(0.615767\pi\)
\(710\) −2.39627 −0.0899305
\(711\) 10.9860 0.412007
\(712\) 1.14944 0.0430769
\(713\) −4.32885 −0.162117
\(714\) 46.2003 1.72900
\(715\) −0.353811 −0.0132318
\(716\) −35.5931 −1.33018
\(717\) −15.7266 −0.587320
\(718\) 35.5412 1.32639
\(719\) −0.439285 −0.0163826 −0.00819128 0.999966i \(-0.502607\pi\)
−0.00819128 + 0.999966i \(0.502607\pi\)
\(720\) −0.463307 −0.0172664
\(721\) 2.80287 0.104384
\(722\) −35.7269 −1.32962
\(723\) −28.3568 −1.05460
\(724\) −50.9248 −1.89261
\(725\) −1.61247 −0.0598855
\(726\) −10.7373 −0.398500
\(727\) 32.6780 1.21196 0.605980 0.795480i \(-0.292781\pi\)
0.605980 + 0.795480i \(0.292781\pi\)
\(728\) −2.06687 −0.0766034
\(729\) 1.00000 0.0370370
\(730\) 1.79725 0.0665191
\(731\) 28.7053 1.06171
\(732\) −12.3075 −0.454898
\(733\) −40.6150 −1.50015 −0.750075 0.661353i \(-0.769983\pi\)
−0.750075 + 0.661353i \(0.769983\pi\)
\(734\) 66.9047 2.46950
\(735\) 0.125185 0.00461751
\(736\) −16.2362 −0.598473
\(737\) 36.8540 1.35754
\(738\) −2.93229 −0.107939
\(739\) −27.7466 −1.02067 −0.510337 0.859974i \(-0.670479\pi\)
−0.510337 + 0.859974i \(0.670479\pi\)
\(740\) 2.93857 0.108024
\(741\) −1.37004 −0.0503296
\(742\) −32.6978 −1.20037
\(743\) −2.39602 −0.0879016 −0.0439508 0.999034i \(-0.513994\pi\)
−0.0439508 + 0.999034i \(0.513994\pi\)
\(744\) −1.58964 −0.0582790
\(745\) 2.77129 0.101532
\(746\) −30.8512 −1.12954
\(747\) 6.84744 0.250535
\(748\) 44.9831 1.64474
\(749\) −30.7739 −1.12445
\(750\) −3.04464 −0.111175
\(751\) 27.5007 1.00351 0.501757 0.865009i \(-0.332687\pi\)
0.501757 + 0.865009i \(0.332687\pi\)
\(752\) −3.45488 −0.125987
\(753\) −10.1004 −0.368081
\(754\) 0.675767 0.0246100
\(755\) −1.58572 −0.0577102
\(756\) −6.59633 −0.239906
\(757\) −35.7589 −1.29968 −0.649839 0.760072i \(-0.725164\pi\)
−0.649839 + 0.760072i \(0.725164\pi\)
\(758\) −63.6456 −2.31171
\(759\) −4.85856 −0.176355
\(760\) −0.147738 −0.00535904
\(761\) 19.3590 0.701762 0.350881 0.936420i \(-0.385882\pi\)
0.350881 + 0.936420i \(0.385882\pi\)
\(762\) 0.877291 0.0317809
\(763\) 41.6845 1.50908
\(764\) −43.9495 −1.59004
\(765\) −1.15525 −0.0417683
\(766\) 64.1028 2.31613
\(767\) −5.92594 −0.213973
\(768\) 8.95021 0.322963
\(769\) −44.5091 −1.60504 −0.802520 0.596625i \(-0.796508\pi\)
−0.802520 + 0.596625i \(0.796508\pi\)
\(770\) 2.06914 0.0745665
\(771\) −19.2020 −0.691545
\(772\) 14.5401 0.523308
\(773\) 8.15875 0.293450 0.146725 0.989177i \(-0.453127\pi\)
0.146725 + 0.989177i \(0.453127\pi\)
\(774\) −7.58142 −0.272509
\(775\) 10.7324 0.385518
\(776\) 2.25403 0.0809150
\(777\) −23.9325 −0.858572
\(778\) 39.4631 1.41482
\(779\) 1.92541 0.0689851
\(780\) 0.344152 0.0123226
\(781\) 19.0017 0.679934
\(782\) −33.1001 −1.18366
\(783\) 0.323878 0.0115745
\(784\) −2.71219 −0.0968638
\(785\) 0.940924 0.0335830
\(786\) −25.8670 −0.922644
\(787\) −9.93833 −0.354263 −0.177132 0.984187i \(-0.556682\pi\)
−0.177132 + 0.984187i \(0.556682\pi\)
\(788\) 18.6759 0.665301
\(789\) 1.09765 0.0390775
\(790\) 3.35200 0.119259
\(791\) −8.71512 −0.309874
\(792\) −1.78416 −0.0633972
\(793\) −5.22961 −0.185709
\(794\) −49.5290 −1.75772
\(795\) 0.817619 0.0289980
\(796\) 44.0614 1.56172
\(797\) 1.76945 0.0626772 0.0313386 0.999509i \(-0.490023\pi\)
0.0313386 + 0.999509i \(0.490023\pi\)
\(798\) 8.01217 0.283628
\(799\) −8.61473 −0.304767
\(800\) 40.2537 1.42318
\(801\) 1.55874 0.0550754
\(802\) 77.3955 2.73293
\(803\) −14.2516 −0.502928
\(804\) −35.8479 −1.26426
\(805\) −0.823073 −0.0290095
\(806\) −4.49782 −0.158429
\(807\) −4.22283 −0.148651
\(808\) 6.61959 0.232876
\(809\) 25.9916 0.913817 0.456908 0.889514i \(-0.348957\pi\)
0.456908 + 0.889514i \(0.348957\pi\)
\(810\) 0.305116 0.0107207
\(811\) −19.4633 −0.683449 −0.341724 0.939800i \(-0.611011\pi\)
−0.341724 + 0.939800i \(0.611011\pi\)
\(812\) −2.13641 −0.0749732
\(813\) 11.1291 0.390315
\(814\) −43.1045 −1.51081
\(815\) −1.58182 −0.0554086
\(816\) 25.0291 0.876195
\(817\) 4.97815 0.174163
\(818\) −42.0523 −1.47033
\(819\) −2.80287 −0.0979400
\(820\) −0.483662 −0.0168902
\(821\) 6.41589 0.223916 0.111958 0.993713i \(-0.464288\pi\)
0.111958 + 0.993713i \(0.464288\pi\)
\(822\) −11.7412 −0.409520
\(823\) 28.1445 0.981057 0.490529 0.871425i \(-0.336804\pi\)
0.490529 + 0.871425i \(0.336804\pi\)
\(824\) −0.737414 −0.0256890
\(825\) 12.0456 0.419376
\(826\) 34.6557 1.20583
\(827\) 34.5645 1.20192 0.600962 0.799277i \(-0.294784\pi\)
0.600962 + 0.799277i \(0.294784\pi\)
\(828\) 4.72592 0.164237
\(829\) 33.4554 1.16195 0.580977 0.813920i \(-0.302671\pi\)
0.580977 + 0.813920i \(0.302671\pi\)
\(830\) 2.08926 0.0725194
\(831\) −26.1321 −0.906512
\(832\) −10.5334 −0.365181
\(833\) −6.76283 −0.234318
\(834\) 34.8178 1.20564
\(835\) 0.458540 0.0158684
\(836\) 7.80107 0.269806
\(837\) −2.15569 −0.0745117
\(838\) 11.7808 0.406960
\(839\) 12.5178 0.432164 0.216082 0.976375i \(-0.430672\pi\)
0.216082 + 0.976375i \(0.430672\pi\)
\(840\) −0.302248 −0.0104285
\(841\) −28.8951 −0.996383
\(842\) 67.6171 2.33024
\(843\) 12.9257 0.445184
\(844\) 55.8375 1.92201
\(845\) 0.146235 0.00503062
\(846\) 2.27525 0.0782249
\(847\) 14.4239 0.495611
\(848\) −17.7141 −0.608305
\(849\) −9.74679 −0.334509
\(850\) 82.0638 2.81476
\(851\) 17.1463 0.587769
\(852\) −18.4829 −0.633215
\(853\) −20.3982 −0.698421 −0.349210 0.937044i \(-0.613550\pi\)
−0.349210 + 0.937044i \(0.613550\pi\)
\(854\) 30.5835 1.04655
\(855\) −0.200347 −0.00685172
\(856\) 8.09638 0.276729
\(857\) 9.18933 0.313901 0.156951 0.987606i \(-0.449834\pi\)
0.156951 + 0.987606i \(0.449834\pi\)
\(858\) −5.04821 −0.172343
\(859\) −4.60595 −0.157153 −0.0785764 0.996908i \(-0.525037\pi\)
−0.0785764 + 0.996908i \(0.525037\pi\)
\(860\) −1.25051 −0.0426419
\(861\) 3.93907 0.134243
\(862\) −70.0556 −2.38610
\(863\) −9.37107 −0.318995 −0.159498 0.987198i \(-0.550987\pi\)
−0.159498 + 0.987198i \(0.550987\pi\)
\(864\) −8.08532 −0.275068
\(865\) 1.86547 0.0634278
\(866\) 27.8634 0.946836
\(867\) 45.4101 1.54221
\(868\) 14.2197 0.482647
\(869\) −26.5803 −0.901677
\(870\) 0.0988206 0.00335033
\(871\) −15.2322 −0.516124
\(872\) −10.9669 −0.371386
\(873\) 3.05667 0.103453
\(874\) −5.74029 −0.194168
\(875\) 4.08999 0.138267
\(876\) 13.8625 0.468371
\(877\) −32.6386 −1.10213 −0.551063 0.834463i \(-0.685778\pi\)
−0.551063 + 0.834463i \(0.685778\pi\)
\(878\) −18.3512 −0.619322
\(879\) 9.92718 0.334836
\(880\) 1.12096 0.0377876
\(881\) 22.9829 0.774312 0.387156 0.922014i \(-0.373457\pi\)
0.387156 + 0.922014i \(0.373457\pi\)
\(882\) 1.78614 0.0601426
\(883\) −20.0153 −0.673569 −0.336784 0.941582i \(-0.609339\pi\)
−0.336784 + 0.941582i \(0.609339\pi\)
\(884\) −18.5921 −0.625319
\(885\) −0.866577 −0.0291297
\(886\) −6.74672 −0.226661
\(887\) 8.18702 0.274893 0.137447 0.990509i \(-0.456110\pi\)
0.137447 + 0.990509i \(0.456110\pi\)
\(888\) 6.29646 0.211295
\(889\) −1.17850 −0.0395257
\(890\) 0.475597 0.0159420
\(891\) −2.41948 −0.0810555
\(892\) −10.0243 −0.335638
\(893\) −1.49399 −0.0499944
\(894\) 39.5410 1.32245
\(895\) −2.21165 −0.0739272
\(896\) 16.2768 0.543770
\(897\) 2.00810 0.0670486
\(898\) 5.86463 0.195705
\(899\) −0.698182 −0.0232857
\(900\) −11.7168 −0.390560
\(901\) −44.1701 −1.47152
\(902\) 7.09462 0.236225
\(903\) 10.1844 0.338917
\(904\) 2.29289 0.0762602
\(905\) −3.16431 −0.105185
\(906\) −22.6252 −0.751670
\(907\) 46.0972 1.53063 0.765316 0.643655i \(-0.222583\pi\)
0.765316 + 0.643655i \(0.222583\pi\)
\(908\) −26.6751 −0.885245
\(909\) 8.97677 0.297741
\(910\) −0.855200 −0.0283496
\(911\) 48.7577 1.61542 0.807708 0.589583i \(-0.200708\pi\)
0.807708 + 0.589583i \(0.200708\pi\)
\(912\) 4.34061 0.143732
\(913\) −16.5672 −0.548295
\(914\) −8.61168 −0.284849
\(915\) −0.764750 −0.0252819
\(916\) −5.16075 −0.170516
\(917\) 34.7482 1.14749
\(918\) −16.4832 −0.544028
\(919\) 21.7702 0.718134 0.359067 0.933312i \(-0.383095\pi\)
0.359067 + 0.933312i \(0.383095\pi\)
\(920\) 0.216545 0.00713926
\(921\) 15.2886 0.503776
\(922\) −6.46102 −0.212782
\(923\) −7.85364 −0.258506
\(924\) 15.9597 0.525035
\(925\) −42.5103 −1.39773
\(926\) 3.41409 0.112194
\(927\) −1.00000 −0.0328443
\(928\) −2.61866 −0.0859617
\(929\) 39.7530 1.30425 0.652127 0.758110i \(-0.273877\pi\)
0.652127 + 0.758110i \(0.273877\pi\)
\(930\) −0.657737 −0.0215681
\(931\) −1.17283 −0.0384378
\(932\) −40.2071 −1.31703
\(933\) 7.38549 0.241790
\(934\) −54.9525 −1.79810
\(935\) 2.79511 0.0914099
\(936\) 0.737414 0.0241031
\(937\) −51.5931 −1.68547 −0.842737 0.538326i \(-0.819057\pi\)
−0.842737 + 0.538326i \(0.819057\pi\)
\(938\) 89.0802 2.90857
\(939\) 12.9545 0.422753
\(940\) 0.375288 0.0122405
\(941\) −44.0246 −1.43516 −0.717580 0.696476i \(-0.754750\pi\)
−0.717580 + 0.696476i \(0.754750\pi\)
\(942\) 13.4252 0.437416
\(943\) −2.82214 −0.0919014
\(944\) 18.7748 0.611068
\(945\) −0.409876 −0.0133333
\(946\) 18.3431 0.596385
\(947\) −36.6363 −1.19052 −0.595260 0.803533i \(-0.702951\pi\)
−0.595260 + 0.803533i \(0.702951\pi\)
\(948\) 25.8547 0.839721
\(949\) 5.89036 0.191209
\(950\) 14.2317 0.461737
\(951\) 26.3027 0.852924
\(952\) 16.3283 0.529203
\(953\) −16.2708 −0.527061 −0.263531 0.964651i \(-0.584887\pi\)
−0.263531 + 0.964651i \(0.584887\pi\)
\(954\) 11.6659 0.377696
\(955\) −2.73089 −0.0883695
\(956\) −37.0113 −1.19703
\(957\) −0.783616 −0.0253307
\(958\) 23.6129 0.762898
\(959\) 15.7724 0.509318
\(960\) −1.54035 −0.0497146
\(961\) −26.3530 −0.850096
\(962\) 17.8156 0.574398
\(963\) 10.9794 0.353807
\(964\) −66.7355 −2.14940
\(965\) 0.903475 0.0290839
\(966\) −11.7437 −0.377846
\(967\) 16.2190 0.521568 0.260784 0.965397i \(-0.416019\pi\)
0.260784 + 0.965397i \(0.416019\pi\)
\(968\) −3.79483 −0.121970
\(969\) 10.8233 0.347694
\(970\) 0.932640 0.0299453
\(971\) −10.3109 −0.330892 −0.165446 0.986219i \(-0.552906\pi\)
−0.165446 + 0.986219i \(0.552906\pi\)
\(972\) 2.35342 0.0754861
\(973\) −46.7723 −1.49945
\(974\) −73.9843 −2.37061
\(975\) −4.97862 −0.159443
\(976\) 16.5687 0.530351
\(977\) −11.0022 −0.351993 −0.175997 0.984391i \(-0.556315\pi\)
−0.175997 + 0.984391i \(0.556315\pi\)
\(978\) −22.5695 −0.721692
\(979\) −3.77134 −0.120532
\(980\) 0.294613 0.00941105
\(981\) −14.8721 −0.474830
\(982\) −24.5760 −0.784253
\(983\) −30.2120 −0.963612 −0.481806 0.876278i \(-0.660019\pi\)
−0.481806 + 0.876278i \(0.660019\pi\)
\(984\) −1.03634 −0.0330374
\(985\) 1.16046 0.0369754
\(986\) −5.33857 −0.170015
\(987\) −3.05645 −0.0972877
\(988\) −3.22428 −0.102578
\(989\) −7.29661 −0.232019
\(990\) −0.738222 −0.0234622
\(991\) −5.35669 −0.170161 −0.0850805 0.996374i \(-0.527115\pi\)
−0.0850805 + 0.996374i \(0.527115\pi\)
\(992\) 17.4295 0.553387
\(993\) −6.14631 −0.195047
\(994\) 45.9292 1.45678
\(995\) 2.73784 0.0867955
\(996\) 16.1149 0.510621
\(997\) 21.8763 0.692828 0.346414 0.938082i \(-0.387399\pi\)
0.346414 + 0.938082i \(0.387399\pi\)
\(998\) −13.9349 −0.441101
\(999\) 8.53857 0.270148
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 4017.2.a.f.1.18 19
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
4017.2.a.f.1.18 19 1.1 even 1 trivial