Properties

Label 4017.2.a.g.1.12
Level $4017$
Weight $2$
Character 4017.1
Self dual yes
Analytic conductor $32.076$
Analytic rank $0$
Dimension $24$
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: \(0\)
Dimension: \(24\)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.12
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)
 
\(f(q)\) \(=\) \(q+0.0298243 q^{2} -1.00000 q^{3} -1.99911 q^{4} +3.06004 q^{5} -0.0298243 q^{6} -1.69214 q^{7} -0.119271 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q+0.0298243 q^{2} -1.00000 q^{3} -1.99911 q^{4} +3.06004 q^{5} -0.0298243 q^{6} -1.69214 q^{7} -0.119271 q^{8} +1.00000 q^{9} +0.0912635 q^{10} +4.60629 q^{11} +1.99911 q^{12} -1.00000 q^{13} -0.0504670 q^{14} -3.06004 q^{15} +3.99466 q^{16} +3.22816 q^{17} +0.0298243 q^{18} +3.92996 q^{19} -6.11736 q^{20} +1.69214 q^{21} +0.137379 q^{22} +4.33457 q^{23} +0.119271 q^{24} +4.36384 q^{25} -0.0298243 q^{26} -1.00000 q^{27} +3.38278 q^{28} -0.592940 q^{29} -0.0912635 q^{30} -4.96202 q^{31} +0.357679 q^{32} -4.60629 q^{33} +0.0962775 q^{34} -5.17803 q^{35} -1.99911 q^{36} -2.80816 q^{37} +0.117208 q^{38} +1.00000 q^{39} -0.364973 q^{40} -3.44430 q^{41} +0.0504670 q^{42} +8.82134 q^{43} -9.20848 q^{44} +3.06004 q^{45} +0.129276 q^{46} -0.175510 q^{47} -3.99466 q^{48} -4.13665 q^{49} +0.130149 q^{50} -3.22816 q^{51} +1.99911 q^{52} -0.255619 q^{53} -0.0298243 q^{54} +14.0954 q^{55} +0.201823 q^{56} -3.92996 q^{57} -0.0176840 q^{58} -12.5860 q^{59} +6.11736 q^{60} +12.7051 q^{61} -0.147989 q^{62} -1.69214 q^{63} -7.97866 q^{64} -3.06004 q^{65} -0.137379 q^{66} -5.34184 q^{67} -6.45344 q^{68} -4.33457 q^{69} -0.154431 q^{70} +7.61726 q^{71} -0.119271 q^{72} +2.64161 q^{73} -0.0837513 q^{74} -4.36384 q^{75} -7.85643 q^{76} -7.79451 q^{77} +0.0298243 q^{78} +14.2734 q^{79} +12.2238 q^{80} +1.00000 q^{81} -0.102724 q^{82} -4.88639 q^{83} -3.38278 q^{84} +9.87829 q^{85} +0.263090 q^{86} +0.592940 q^{87} -0.549395 q^{88} -16.4565 q^{89} +0.0912635 q^{90} +1.69214 q^{91} -8.66529 q^{92} +4.96202 q^{93} -0.00523447 q^{94} +12.0258 q^{95} -0.357679 q^{96} +8.65835 q^{97} -0.123373 q^{98} +4.60629 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 24 q + 3 q^{2} - 24 q^{3} + 25 q^{4} + 3 q^{5} - 3 q^{6} + 11 q^{7} + 6 q^{8} + 24 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 24 q + 3 q^{2} - 24 q^{3} + 25 q^{4} + 3 q^{5} - 3 q^{6} + 11 q^{7} + 6 q^{8} + 24 q^{9} - 2 q^{10} + 7 q^{11} - 25 q^{12} - 24 q^{13} + 8 q^{14} - 3 q^{15} + 23 q^{16} + 4 q^{17} + 3 q^{18} - 20 q^{19} + 8 q^{20} - 11 q^{21} + 5 q^{22} + 41 q^{23} - 6 q^{24} + 23 q^{25} - 3 q^{26} - 24 q^{27} + 16 q^{28} + 12 q^{29} + 2 q^{30} + 2 q^{31} + 25 q^{32} - 7 q^{33} - 11 q^{34} + 36 q^{35} + 25 q^{36} + 18 q^{37} + 10 q^{38} + 24 q^{39} + 14 q^{40} - 9 q^{41} - 8 q^{42} + 23 q^{43} + 41 q^{44} + 3 q^{45} + 7 q^{46} + 32 q^{47} - 23 q^{48} + 11 q^{49} + 26 q^{50} - 4 q^{51} - 25 q^{52} + 46 q^{53} - 3 q^{54} + 18 q^{55} + 26 q^{56} + 20 q^{57} + 37 q^{58} - 12 q^{59} - 8 q^{60} - q^{61} + 53 q^{62} + 11 q^{63} + 26 q^{64} - 3 q^{65} - 5 q^{66} + 8 q^{67} + 6 q^{68} - 41 q^{69} + 19 q^{70} + 20 q^{71} + 6 q^{72} + 12 q^{73} + 86 q^{74} - 23 q^{75} - 28 q^{76} + 23 q^{77} + 3 q^{78} + 27 q^{79} + 6 q^{80} + 24 q^{81} - 28 q^{82} + 33 q^{83} - 16 q^{84} - 13 q^{85} + 63 q^{86} - 12 q^{87} + 11 q^{88} - 2 q^{90} - 11 q^{91} + 79 q^{92} - 2 q^{93} - 12 q^{94} + 37 q^{95} - 25 q^{96} - 14 q^{97} + 20 q^{98} + 7 q^{99}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.0298243 0.0210890 0.0105445 0.999944i \(-0.496644\pi\)
0.0105445 + 0.999944i \(0.496644\pi\)
\(3\) −1.00000 −0.577350
\(4\) −1.99911 −0.999555
\(5\) 3.06004 1.36849 0.684246 0.729252i \(-0.260132\pi\)
0.684246 + 0.729252i \(0.260132\pi\)
\(6\) −0.0298243 −0.0121757
\(7\) −1.69214 −0.639571 −0.319785 0.947490i \(-0.603611\pi\)
−0.319785 + 0.947490i \(0.603611\pi\)
\(8\) −0.119271 −0.0421686
\(9\) 1.00000 0.333333
\(10\) 0.0912635 0.0288601
\(11\) 4.60629 1.38885 0.694424 0.719566i \(-0.255659\pi\)
0.694424 + 0.719566i \(0.255659\pi\)
\(12\) 1.99911 0.577093
\(13\) −1.00000 −0.277350
\(14\) −0.0504670 −0.0134879
\(15\) −3.06004 −0.790099
\(16\) 3.99466 0.998666
\(17\) 3.22816 0.782943 0.391472 0.920190i \(-0.371966\pi\)
0.391472 + 0.920190i \(0.371966\pi\)
\(18\) 0.0298243 0.00702966
\(19\) 3.92996 0.901595 0.450797 0.892626i \(-0.351140\pi\)
0.450797 + 0.892626i \(0.351140\pi\)
\(20\) −6.11736 −1.36788
\(21\) 1.69214 0.369256
\(22\) 0.137379 0.0292894
\(23\) 4.33457 0.903821 0.451910 0.892063i \(-0.350743\pi\)
0.451910 + 0.892063i \(0.350743\pi\)
\(24\) 0.119271 0.0243460
\(25\) 4.36384 0.872768
\(26\) −0.0298243 −0.00584903
\(27\) −1.00000 −0.192450
\(28\) 3.38278 0.639286
\(29\) −0.592940 −0.110106 −0.0550531 0.998483i \(-0.517533\pi\)
−0.0550531 + 0.998483i \(0.517533\pi\)
\(30\) −0.0912635 −0.0166624
\(31\) −4.96202 −0.891205 −0.445602 0.895231i \(-0.647010\pi\)
−0.445602 + 0.895231i \(0.647010\pi\)
\(32\) 0.357679 0.0632294
\(33\) −4.60629 −0.801852
\(34\) 0.0962775 0.0165115
\(35\) −5.17803 −0.875247
\(36\) −1.99911 −0.333185
\(37\) −2.80816 −0.461658 −0.230829 0.972994i \(-0.574144\pi\)
−0.230829 + 0.972994i \(0.574144\pi\)
\(38\) 0.117208 0.0190137
\(39\) 1.00000 0.160128
\(40\) −0.364973 −0.0577073
\(41\) −3.44430 −0.537910 −0.268955 0.963153i \(-0.586678\pi\)
−0.268955 + 0.963153i \(0.586678\pi\)
\(42\) 0.0504670 0.00778723
\(43\) 8.82134 1.34524 0.672621 0.739987i \(-0.265169\pi\)
0.672621 + 0.739987i \(0.265169\pi\)
\(44\) −9.20848 −1.38823
\(45\) 3.06004 0.456164
\(46\) 0.129276 0.0190606
\(47\) −0.175510 −0.0256008 −0.0128004 0.999918i \(-0.504075\pi\)
−0.0128004 + 0.999918i \(0.504075\pi\)
\(48\) −3.99466 −0.576580
\(49\) −4.13665 −0.590949
\(50\) 0.130149 0.0184058
\(51\) −3.22816 −0.452032
\(52\) 1.99911 0.277227
\(53\) −0.255619 −0.0351119 −0.0175560 0.999846i \(-0.505589\pi\)
−0.0175560 + 0.999846i \(0.505589\pi\)
\(54\) −0.0298243 −0.00405857
\(55\) 14.0954 1.90063
\(56\) 0.201823 0.0269698
\(57\) −3.92996 −0.520536
\(58\) −0.0176840 −0.00232203
\(59\) −12.5860 −1.63856 −0.819278 0.573397i \(-0.805625\pi\)
−0.819278 + 0.573397i \(0.805625\pi\)
\(60\) 6.11736 0.789747
\(61\) 12.7051 1.62672 0.813362 0.581758i \(-0.197635\pi\)
0.813362 + 0.581758i \(0.197635\pi\)
\(62\) −0.147989 −0.0187946
\(63\) −1.69214 −0.213190
\(64\) −7.97866 −0.997333
\(65\) −3.06004 −0.379551
\(66\) −0.137379 −0.0169102
\(67\) −5.34184 −0.652609 −0.326305 0.945265i \(-0.605804\pi\)
−0.326305 + 0.945265i \(0.605804\pi\)
\(68\) −6.45344 −0.782595
\(69\) −4.33457 −0.521821
\(70\) −0.154431 −0.0184581
\(71\) 7.61726 0.904003 0.452001 0.892017i \(-0.350710\pi\)
0.452001 + 0.892017i \(0.350710\pi\)
\(72\) −0.119271 −0.0140562
\(73\) 2.64161 0.309177 0.154589 0.987979i \(-0.450595\pi\)
0.154589 + 0.987979i \(0.450595\pi\)
\(74\) −0.0837513 −0.00973589
\(75\) −4.36384 −0.503893
\(76\) −7.85643 −0.901194
\(77\) −7.79451 −0.888266
\(78\) 0.0298243 0.00337694
\(79\) 14.2734 1.60588 0.802939 0.596061i \(-0.203268\pi\)
0.802939 + 0.596061i \(0.203268\pi\)
\(80\) 12.2238 1.36667
\(81\) 1.00000 0.111111
\(82\) −0.102724 −0.0113440
\(83\) −4.88639 −0.536351 −0.268176 0.963370i \(-0.586421\pi\)
−0.268176 + 0.963370i \(0.586421\pi\)
\(84\) −3.38278 −0.369092
\(85\) 9.87829 1.07145
\(86\) 0.263090 0.0283698
\(87\) 0.592940 0.0635698
\(88\) −0.549395 −0.0585657
\(89\) −16.4565 −1.74439 −0.872194 0.489160i \(-0.837303\pi\)
−0.872194 + 0.489160i \(0.837303\pi\)
\(90\) 0.0912635 0.00962002
\(91\) 1.69214 0.177385
\(92\) −8.66529 −0.903419
\(93\) 4.96202 0.514537
\(94\) −0.00523447 −0.000539895 0
\(95\) 12.0258 1.23382
\(96\) −0.357679 −0.0365055
\(97\) 8.65835 0.879122 0.439561 0.898213i \(-0.355134\pi\)
0.439561 + 0.898213i \(0.355134\pi\)
\(98\) −0.123373 −0.0124625
\(99\) 4.60629 0.462949
\(100\) −8.72380 −0.872380
\(101\) 12.2260 1.21654 0.608268 0.793731i \(-0.291864\pi\)
0.608268 + 0.793731i \(0.291864\pi\)
\(102\) −0.0962775 −0.00953290
\(103\) 1.00000 0.0985329
\(104\) 0.119271 0.0116955
\(105\) 5.17803 0.505324
\(106\) −0.00762364 −0.000740474 0
\(107\) 11.7861 1.13941 0.569703 0.821851i \(-0.307058\pi\)
0.569703 + 0.821851i \(0.307058\pi\)
\(108\) 1.99911 0.192364
\(109\) −9.11561 −0.873117 −0.436558 0.899676i \(-0.643803\pi\)
−0.436558 + 0.899676i \(0.643803\pi\)
\(110\) 0.420386 0.0400823
\(111\) 2.80816 0.266538
\(112\) −6.75955 −0.638717
\(113\) 10.9023 1.02561 0.512803 0.858506i \(-0.328607\pi\)
0.512803 + 0.858506i \(0.328607\pi\)
\(114\) −0.117208 −0.0109776
\(115\) 13.2640 1.23687
\(116\) 1.18535 0.110057
\(117\) −1.00000 −0.0924500
\(118\) −0.375368 −0.0345555
\(119\) −5.46251 −0.500747
\(120\) 0.364973 0.0333173
\(121\) 10.2179 0.928899
\(122\) 0.378921 0.0343059
\(123\) 3.44430 0.310562
\(124\) 9.91962 0.890808
\(125\) −1.94667 −0.174116
\(126\) −0.0504670 −0.00449596
\(127\) −15.1737 −1.34645 −0.673223 0.739439i \(-0.735091\pi\)
−0.673223 + 0.739439i \(0.735091\pi\)
\(128\) −0.953317 −0.0842621
\(129\) −8.82134 −0.776676
\(130\) −0.0912635 −0.00800434
\(131\) −5.65098 −0.493729 −0.246864 0.969050i \(-0.579400\pi\)
−0.246864 + 0.969050i \(0.579400\pi\)
\(132\) 9.20848 0.801495
\(133\) −6.65006 −0.576634
\(134\) −0.159317 −0.0137629
\(135\) −3.06004 −0.263366
\(136\) −0.385025 −0.0330156
\(137\) 4.42445 0.378006 0.189003 0.981977i \(-0.439474\pi\)
0.189003 + 0.981977i \(0.439474\pi\)
\(138\) −0.129276 −0.0110047
\(139\) 13.9763 1.18545 0.592725 0.805405i \(-0.298052\pi\)
0.592725 + 0.805405i \(0.298052\pi\)
\(140\) 10.3515 0.874857
\(141\) 0.175510 0.0147806
\(142\) 0.227180 0.0190645
\(143\) −4.60629 −0.385197
\(144\) 3.99466 0.332889
\(145\) −1.81442 −0.150679
\(146\) 0.0787843 0.00652023
\(147\) 4.13665 0.341185
\(148\) 5.61381 0.461453
\(149\) 1.51911 0.124451 0.0622253 0.998062i \(-0.480180\pi\)
0.0622253 + 0.998062i \(0.480180\pi\)
\(150\) −0.130149 −0.0106266
\(151\) 5.41580 0.440731 0.220366 0.975417i \(-0.429275\pi\)
0.220366 + 0.975417i \(0.429275\pi\)
\(152\) −0.468729 −0.0380190
\(153\) 3.22816 0.260981
\(154\) −0.232466 −0.0187326
\(155\) −15.1840 −1.21961
\(156\) −1.99911 −0.160057
\(157\) 17.5237 1.39855 0.699273 0.714855i \(-0.253507\pi\)
0.699273 + 0.714855i \(0.253507\pi\)
\(158\) 0.425693 0.0338663
\(159\) 0.255619 0.0202719
\(160\) 1.09451 0.0865289
\(161\) −7.33472 −0.578057
\(162\) 0.0298243 0.00234322
\(163\) 1.82150 0.142671 0.0713355 0.997452i \(-0.477274\pi\)
0.0713355 + 0.997452i \(0.477274\pi\)
\(164\) 6.88555 0.537671
\(165\) −14.0954 −1.09733
\(166\) −0.145733 −0.0113111
\(167\) −19.8258 −1.53416 −0.767081 0.641550i \(-0.778292\pi\)
−0.767081 + 0.641550i \(0.778292\pi\)
\(168\) −0.201823 −0.0155710
\(169\) 1.00000 0.0769231
\(170\) 0.294613 0.0225958
\(171\) 3.92996 0.300532
\(172\) −17.6348 −1.34464
\(173\) −15.1355 −1.15073 −0.575365 0.817897i \(-0.695140\pi\)
−0.575365 + 0.817897i \(0.695140\pi\)
\(174\) 0.0176840 0.00134062
\(175\) −7.38425 −0.558197
\(176\) 18.4006 1.38700
\(177\) 12.5860 0.946021
\(178\) −0.490804 −0.0367873
\(179\) 21.8052 1.62979 0.814897 0.579605i \(-0.196793\pi\)
0.814897 + 0.579605i \(0.196793\pi\)
\(180\) −6.11736 −0.455961
\(181\) −11.6142 −0.863280 −0.431640 0.902046i \(-0.642065\pi\)
−0.431640 + 0.902046i \(0.642065\pi\)
\(182\) 0.0504670 0.00374087
\(183\) −12.7051 −0.939190
\(184\) −0.516987 −0.0381128
\(185\) −8.59307 −0.631775
\(186\) 0.147989 0.0108511
\(187\) 14.8698 1.08739
\(188\) 0.350865 0.0255894
\(189\) 1.69214 0.123085
\(190\) 0.358662 0.0260201
\(191\) 12.1789 0.881236 0.440618 0.897695i \(-0.354759\pi\)
0.440618 + 0.897695i \(0.354759\pi\)
\(192\) 7.97866 0.575810
\(193\) 19.1182 1.37616 0.688079 0.725635i \(-0.258454\pi\)
0.688079 + 0.725635i \(0.258454\pi\)
\(194\) 0.258229 0.0185398
\(195\) 3.06004 0.219134
\(196\) 8.26961 0.590687
\(197\) −14.8035 −1.05471 −0.527354 0.849646i \(-0.676816\pi\)
−0.527354 + 0.849646i \(0.676816\pi\)
\(198\) 0.137379 0.00976313
\(199\) 10.0910 0.715331 0.357665 0.933850i \(-0.383573\pi\)
0.357665 + 0.933850i \(0.383573\pi\)
\(200\) −0.520478 −0.0368034
\(201\) 5.34184 0.376784
\(202\) 0.364633 0.0256555
\(203\) 1.00334 0.0704207
\(204\) 6.45344 0.451831
\(205\) −10.5397 −0.736125
\(206\) 0.0298243 0.00207796
\(207\) 4.33457 0.301274
\(208\) −3.99466 −0.276980
\(209\) 18.1025 1.25218
\(210\) 0.154431 0.0106568
\(211\) 6.26999 0.431644 0.215822 0.976433i \(-0.430757\pi\)
0.215822 + 0.976433i \(0.430757\pi\)
\(212\) 0.511010 0.0350963
\(213\) −7.61726 −0.521926
\(214\) 0.351512 0.0240289
\(215\) 26.9936 1.84095
\(216\) 0.119271 0.00811534
\(217\) 8.39645 0.569988
\(218\) −0.271867 −0.0184131
\(219\) −2.64161 −0.178504
\(220\) −28.1783 −1.89978
\(221\) −3.22816 −0.217149
\(222\) 0.0837513 0.00562102
\(223\) 24.3195 1.62855 0.814277 0.580477i \(-0.197134\pi\)
0.814277 + 0.580477i \(0.197134\pi\)
\(224\) −0.605245 −0.0404397
\(225\) 4.36384 0.290923
\(226\) 0.325155 0.0216290
\(227\) 0.112801 0.00748685 0.00374342 0.999993i \(-0.498808\pi\)
0.00374342 + 0.999993i \(0.498808\pi\)
\(228\) 7.85643 0.520305
\(229\) −2.07740 −0.137278 −0.0686392 0.997642i \(-0.521866\pi\)
−0.0686392 + 0.997642i \(0.521866\pi\)
\(230\) 0.395588 0.0260843
\(231\) 7.79451 0.512841
\(232\) 0.0707203 0.00464302
\(233\) 14.8944 0.975766 0.487883 0.872909i \(-0.337769\pi\)
0.487883 + 0.872909i \(0.337769\pi\)
\(234\) −0.0298243 −0.00194968
\(235\) −0.537069 −0.0350345
\(236\) 25.1608 1.63783
\(237\) −14.2734 −0.927154
\(238\) −0.162916 −0.0105602
\(239\) 9.00916 0.582754 0.291377 0.956608i \(-0.405887\pi\)
0.291377 + 0.956608i \(0.405887\pi\)
\(240\) −12.2238 −0.789045
\(241\) −18.5937 −1.19772 −0.598861 0.800853i \(-0.704380\pi\)
−0.598861 + 0.800853i \(0.704380\pi\)
\(242\) 0.304742 0.0195895
\(243\) −1.00000 −0.0641500
\(244\) −25.3989 −1.62600
\(245\) −12.6583 −0.808709
\(246\) 0.102724 0.00654944
\(247\) −3.92996 −0.250057
\(248\) 0.591823 0.0375808
\(249\) 4.88639 0.309662
\(250\) −0.0580581 −0.00367192
\(251\) 1.63413 0.103145 0.0515726 0.998669i \(-0.483577\pi\)
0.0515726 + 0.998669i \(0.483577\pi\)
\(252\) 3.38278 0.213095
\(253\) 19.9663 1.25527
\(254\) −0.452545 −0.0283952
\(255\) −9.87829 −0.618602
\(256\) 15.9289 0.995556
\(257\) 10.9198 0.681157 0.340578 0.940216i \(-0.389377\pi\)
0.340578 + 0.940216i \(0.389377\pi\)
\(258\) −0.263090 −0.0163793
\(259\) 4.75181 0.295263
\(260\) 6.11736 0.379382
\(261\) −0.592940 −0.0367021
\(262\) −0.168537 −0.0104122
\(263\) 11.6090 0.715839 0.357920 0.933752i \(-0.383486\pi\)
0.357920 + 0.933752i \(0.383486\pi\)
\(264\) 0.549395 0.0338129
\(265\) −0.782203 −0.0480503
\(266\) −0.198333 −0.0121606
\(267\) 16.4565 1.00712
\(268\) 10.6789 0.652319
\(269\) 1.35757 0.0827725 0.0413863 0.999143i \(-0.486823\pi\)
0.0413863 + 0.999143i \(0.486823\pi\)
\(270\) −0.0912635 −0.00555412
\(271\) −20.6130 −1.25215 −0.626076 0.779762i \(-0.715340\pi\)
−0.626076 + 0.779762i \(0.715340\pi\)
\(272\) 12.8954 0.781899
\(273\) −1.69214 −0.102413
\(274\) 0.131956 0.00797176
\(275\) 20.1011 1.21214
\(276\) 8.66529 0.521589
\(277\) 24.1056 1.44837 0.724184 0.689607i \(-0.242217\pi\)
0.724184 + 0.689607i \(0.242217\pi\)
\(278\) 0.416832 0.0249999
\(279\) −4.96202 −0.297068
\(280\) 0.617587 0.0369079
\(281\) −18.7524 −1.11867 −0.559337 0.828940i \(-0.688944\pi\)
−0.559337 + 0.828940i \(0.688944\pi\)
\(282\) 0.00523447 0.000311708 0
\(283\) 27.8394 1.65488 0.827440 0.561555i \(-0.189797\pi\)
0.827440 + 0.561555i \(0.189797\pi\)
\(284\) −15.2277 −0.903601
\(285\) −12.0258 −0.712349
\(286\) −0.137379 −0.00812341
\(287\) 5.82826 0.344031
\(288\) 0.357679 0.0210765
\(289\) −6.57900 −0.387000
\(290\) −0.0541138 −0.00317767
\(291\) −8.65835 −0.507561
\(292\) −5.28088 −0.309040
\(293\) 7.02330 0.410306 0.205153 0.978730i \(-0.434231\pi\)
0.205153 + 0.978730i \(0.434231\pi\)
\(294\) 0.123373 0.00719524
\(295\) −38.5136 −2.24235
\(296\) 0.334931 0.0194674
\(297\) −4.60629 −0.267284
\(298\) 0.0453065 0.00262454
\(299\) −4.33457 −0.250675
\(300\) 8.72380 0.503669
\(301\) −14.9270 −0.860377
\(302\) 0.161522 0.00929457
\(303\) −12.2260 −0.702368
\(304\) 15.6989 0.900392
\(305\) 38.8782 2.22616
\(306\) 0.0962775 0.00550382
\(307\) 17.8124 1.01661 0.508304 0.861178i \(-0.330273\pi\)
0.508304 + 0.861178i \(0.330273\pi\)
\(308\) 15.5821 0.887871
\(309\) −1.00000 −0.0568880
\(310\) −0.452851 −0.0257202
\(311\) 5.03954 0.285766 0.142883 0.989740i \(-0.454363\pi\)
0.142883 + 0.989740i \(0.454363\pi\)
\(312\) −0.119271 −0.00675237
\(313\) −19.7835 −1.11823 −0.559116 0.829089i \(-0.688859\pi\)
−0.559116 + 0.829089i \(0.688859\pi\)
\(314\) 0.522633 0.0294939
\(315\) −5.17803 −0.291749
\(316\) −28.5340 −1.60516
\(317\) 7.66086 0.430277 0.215138 0.976584i \(-0.430980\pi\)
0.215138 + 0.976584i \(0.430980\pi\)
\(318\) 0.00762364 0.000427513 0
\(319\) −2.73125 −0.152921
\(320\) −24.4150 −1.36484
\(321\) −11.7861 −0.657836
\(322\) −0.218753 −0.0121906
\(323\) 12.6865 0.705897
\(324\) −1.99911 −0.111062
\(325\) −4.36384 −0.242062
\(326\) 0.0543250 0.00300878
\(327\) 9.11561 0.504094
\(328\) 0.410805 0.0226829
\(329\) 0.296989 0.0163735
\(330\) −0.420386 −0.0231415
\(331\) −8.34360 −0.458606 −0.229303 0.973355i \(-0.573645\pi\)
−0.229303 + 0.973355i \(0.573645\pi\)
\(332\) 9.76844 0.536113
\(333\) −2.80816 −0.153886
\(334\) −0.591289 −0.0323539
\(335\) −16.3462 −0.893090
\(336\) 6.75955 0.368764
\(337\) −12.9548 −0.705692 −0.352846 0.935681i \(-0.614786\pi\)
−0.352846 + 0.935681i \(0.614786\pi\)
\(338\) 0.0298243 0.00162223
\(339\) −10.9023 −0.592134
\(340\) −19.7478 −1.07097
\(341\) −22.8565 −1.23775
\(342\) 0.117208 0.00633790
\(343\) 18.8448 1.01752
\(344\) −1.05213 −0.0567269
\(345\) −13.2640 −0.714108
\(346\) −0.451406 −0.0242677
\(347\) 29.1738 1.56613 0.783066 0.621939i \(-0.213655\pi\)
0.783066 + 0.621939i \(0.213655\pi\)
\(348\) −1.18535 −0.0635416
\(349\) 12.3398 0.660532 0.330266 0.943888i \(-0.392862\pi\)
0.330266 + 0.943888i \(0.392862\pi\)
\(350\) −0.220230 −0.0117718
\(351\) 1.00000 0.0533761
\(352\) 1.64757 0.0878160
\(353\) −7.51777 −0.400131 −0.200065 0.979783i \(-0.564115\pi\)
−0.200065 + 0.979783i \(0.564115\pi\)
\(354\) 0.375368 0.0199506
\(355\) 23.3091 1.23712
\(356\) 32.8984 1.74361
\(357\) 5.46251 0.289107
\(358\) 0.650324 0.0343707
\(359\) 4.01242 0.211768 0.105884 0.994379i \(-0.466233\pi\)
0.105884 + 0.994379i \(0.466233\pi\)
\(360\) −0.364973 −0.0192358
\(361\) −3.55541 −0.187127
\(362\) −0.346387 −0.0182057
\(363\) −10.2179 −0.536300
\(364\) −3.38278 −0.177306
\(365\) 8.08344 0.423107
\(366\) −0.378921 −0.0198065
\(367\) −28.6589 −1.49598 −0.747990 0.663709i \(-0.768981\pi\)
−0.747990 + 0.663709i \(0.768981\pi\)
\(368\) 17.3152 0.902615
\(369\) −3.44430 −0.179303
\(370\) −0.256282 −0.0133235
\(371\) 0.432544 0.0224565
\(372\) −9.91962 −0.514308
\(373\) −10.8170 −0.560083 −0.280041 0.959988i \(-0.590348\pi\)
−0.280041 + 0.959988i \(0.590348\pi\)
\(374\) 0.443482 0.0229319
\(375\) 1.94667 0.100526
\(376\) 0.0209332 0.00107955
\(377\) 0.592940 0.0305380
\(378\) 0.0504670 0.00259574
\(379\) −1.16673 −0.0599311 −0.0299655 0.999551i \(-0.509540\pi\)
−0.0299655 + 0.999551i \(0.509540\pi\)
\(380\) −24.0410 −1.23328
\(381\) 15.1737 0.777371
\(382\) 0.363228 0.0185844
\(383\) 17.3293 0.885485 0.442743 0.896649i \(-0.354006\pi\)
0.442743 + 0.896649i \(0.354006\pi\)
\(384\) 0.953317 0.0486487
\(385\) −23.8515 −1.21558
\(386\) 0.570187 0.0290218
\(387\) 8.82134 0.448414
\(388\) −17.3090 −0.878731
\(389\) 29.6106 1.50132 0.750658 0.660691i \(-0.229737\pi\)
0.750658 + 0.660691i \(0.229737\pi\)
\(390\) 0.0912635 0.00462131
\(391\) 13.9927 0.707640
\(392\) 0.493381 0.0249195
\(393\) 5.65098 0.285054
\(394\) −0.441505 −0.0222427
\(395\) 43.6770 2.19763
\(396\) −9.20848 −0.462744
\(397\) 5.36573 0.269298 0.134649 0.990893i \(-0.457009\pi\)
0.134649 + 0.990893i \(0.457009\pi\)
\(398\) 0.300956 0.0150856
\(399\) 6.65006 0.332920
\(400\) 17.4321 0.871604
\(401\) −9.60580 −0.479691 −0.239845 0.970811i \(-0.577097\pi\)
−0.239845 + 0.970811i \(0.577097\pi\)
\(402\) 0.159317 0.00794599
\(403\) 4.96202 0.247176
\(404\) −24.4412 −1.21600
\(405\) 3.06004 0.152055
\(406\) 0.0299239 0.00148510
\(407\) −12.9352 −0.641173
\(408\) 0.385025 0.0190616
\(409\) −18.1156 −0.895757 −0.447879 0.894094i \(-0.647820\pi\)
−0.447879 + 0.894094i \(0.647820\pi\)
\(410\) −0.314339 −0.0155241
\(411\) −4.42445 −0.218242
\(412\) −1.99911 −0.0984891
\(413\) 21.2973 1.04797
\(414\) 0.129276 0.00635355
\(415\) −14.9526 −0.733992
\(416\) −0.357679 −0.0175367
\(417\) −13.9763 −0.684420
\(418\) 0.539895 0.0264071
\(419\) −7.10706 −0.347203 −0.173601 0.984816i \(-0.555540\pi\)
−0.173601 + 0.984816i \(0.555540\pi\)
\(420\) −10.3515 −0.505099
\(421\) −19.0647 −0.929157 −0.464579 0.885532i \(-0.653794\pi\)
−0.464579 + 0.885532i \(0.653794\pi\)
\(422\) 0.186998 0.00910292
\(423\) −0.175510 −0.00853361
\(424\) 0.0304878 0.00148062
\(425\) 14.0872 0.683328
\(426\) −0.227180 −0.0110069
\(427\) −21.4989 −1.04040
\(428\) −23.5617 −1.13890
\(429\) 4.60629 0.222394
\(430\) 0.805067 0.0388238
\(431\) 36.5047 1.75837 0.879185 0.476480i \(-0.158088\pi\)
0.879185 + 0.476480i \(0.158088\pi\)
\(432\) −3.99466 −0.192193
\(433\) 25.5072 1.22580 0.612898 0.790162i \(-0.290004\pi\)
0.612898 + 0.790162i \(0.290004\pi\)
\(434\) 0.250418 0.0120205
\(435\) 1.81442 0.0869948
\(436\) 18.2231 0.872729
\(437\) 17.0347 0.814880
\(438\) −0.0787843 −0.00376446
\(439\) −4.65970 −0.222395 −0.111198 0.993798i \(-0.535469\pi\)
−0.111198 + 0.993798i \(0.535469\pi\)
\(440\) −1.68117 −0.0801467
\(441\) −4.13665 −0.196983
\(442\) −0.0962775 −0.00457946
\(443\) −0.143465 −0.00681622 −0.00340811 0.999994i \(-0.501085\pi\)
−0.00340811 + 0.999994i \(0.501085\pi\)
\(444\) −5.61381 −0.266420
\(445\) −50.3576 −2.38718
\(446\) 0.725312 0.0343445
\(447\) −1.51911 −0.0718516
\(448\) 13.5010 0.637865
\(449\) −1.84722 −0.0871759 −0.0435879 0.999050i \(-0.513879\pi\)
−0.0435879 + 0.999050i \(0.513879\pi\)
\(450\) 0.130149 0.00613526
\(451\) −15.8655 −0.747075
\(452\) −21.7950 −1.02515
\(453\) −5.41580 −0.254456
\(454\) 0.00336420 0.000157890 0
\(455\) 5.17803 0.242750
\(456\) 0.468729 0.0219503
\(457\) −1.76511 −0.0825685 −0.0412842 0.999147i \(-0.513145\pi\)
−0.0412842 + 0.999147i \(0.513145\pi\)
\(458\) −0.0619570 −0.00289506
\(459\) −3.22816 −0.150677
\(460\) −26.5161 −1.23632
\(461\) 6.44028 0.299954 0.149977 0.988690i \(-0.452080\pi\)
0.149977 + 0.988690i \(0.452080\pi\)
\(462\) 0.232466 0.0108153
\(463\) 16.4323 0.763675 0.381837 0.924229i \(-0.375291\pi\)
0.381837 + 0.924229i \(0.375291\pi\)
\(464\) −2.36860 −0.109959
\(465\) 15.1840 0.704140
\(466\) 0.444216 0.0205779
\(467\) −9.44012 −0.436836 −0.218418 0.975855i \(-0.570090\pi\)
−0.218418 + 0.975855i \(0.570090\pi\)
\(468\) 1.99911 0.0924089
\(469\) 9.03916 0.417390
\(470\) −0.0160177 −0.000738841 0
\(471\) −17.5237 −0.807451
\(472\) 1.50114 0.0690955
\(473\) 40.6336 1.86834
\(474\) −0.425693 −0.0195527
\(475\) 17.1497 0.786883
\(476\) 10.9202 0.500525
\(477\) −0.255619 −0.0117040
\(478\) 0.268692 0.0122897
\(479\) −12.8252 −0.585998 −0.292999 0.956113i \(-0.594653\pi\)
−0.292999 + 0.956113i \(0.594653\pi\)
\(480\) −1.09451 −0.0499575
\(481\) 2.80816 0.128041
\(482\) −0.554543 −0.0252587
\(483\) 7.33472 0.333742
\(484\) −20.4267 −0.928486
\(485\) 26.4949 1.20307
\(486\) −0.0298243 −0.00135286
\(487\) 35.2979 1.59950 0.799751 0.600332i \(-0.204965\pi\)
0.799751 + 0.600332i \(0.204965\pi\)
\(488\) −1.51535 −0.0685966
\(489\) −1.82150 −0.0823711
\(490\) −0.377525 −0.0170548
\(491\) 29.9174 1.35015 0.675077 0.737747i \(-0.264110\pi\)
0.675077 + 0.737747i \(0.264110\pi\)
\(492\) −6.88555 −0.310424
\(493\) −1.91410 −0.0862069
\(494\) −0.117208 −0.00527345
\(495\) 14.0954 0.633542
\(496\) −19.8216 −0.890016
\(497\) −12.8895 −0.578174
\(498\) 0.145733 0.00653046
\(499\) −4.36023 −0.195190 −0.0975952 0.995226i \(-0.531115\pi\)
−0.0975952 + 0.995226i \(0.531115\pi\)
\(500\) 3.89161 0.174038
\(501\) 19.8258 0.885749
\(502\) 0.0487368 0.00217523
\(503\) −16.3239 −0.727846 −0.363923 0.931429i \(-0.618563\pi\)
−0.363923 + 0.931429i \(0.618563\pi\)
\(504\) 0.201823 0.00898992
\(505\) 37.4122 1.66482
\(506\) 0.595481 0.0264723
\(507\) −1.00000 −0.0444116
\(508\) 30.3339 1.34585
\(509\) −10.9778 −0.486581 −0.243291 0.969953i \(-0.578227\pi\)
−0.243291 + 0.969953i \(0.578227\pi\)
\(510\) −0.294613 −0.0130457
\(511\) −4.46999 −0.197741
\(512\) 2.38170 0.105257
\(513\) −3.92996 −0.173512
\(514\) 0.325675 0.0143649
\(515\) 3.06004 0.134841
\(516\) 17.6348 0.776330
\(517\) −0.808451 −0.0355556
\(518\) 0.141719 0.00622679
\(519\) 15.1355 0.664374
\(520\) 0.364973 0.0160051
\(521\) −34.3218 −1.50367 −0.751833 0.659354i \(-0.770830\pi\)
−0.751833 + 0.659354i \(0.770830\pi\)
\(522\) −0.0176840 −0.000774009 0
\(523\) −22.0037 −0.962152 −0.481076 0.876679i \(-0.659754\pi\)
−0.481076 + 0.876679i \(0.659754\pi\)
\(524\) 11.2969 0.493509
\(525\) 7.38425 0.322275
\(526\) 0.346229 0.0150963
\(527\) −16.0182 −0.697763
\(528\) −18.4006 −0.800782
\(529\) −4.21148 −0.183108
\(530\) −0.0233287 −0.00101333
\(531\) −12.5860 −0.546185
\(532\) 13.2942 0.576377
\(533\) 3.44430 0.149189
\(534\) 0.490804 0.0212392
\(535\) 36.0659 1.55927
\(536\) 0.637124 0.0275196
\(537\) −21.8052 −0.940963
\(538\) 0.0404886 0.00174559
\(539\) −19.0546 −0.820739
\(540\) 6.11736 0.263249
\(541\) −14.5633 −0.626127 −0.313063 0.949732i \(-0.601355\pi\)
−0.313063 + 0.949732i \(0.601355\pi\)
\(542\) −0.614769 −0.0264066
\(543\) 11.6142 0.498415
\(544\) 1.15465 0.0495050
\(545\) −27.8941 −1.19485
\(546\) −0.0504670 −0.00215979
\(547\) −8.56516 −0.366220 −0.183110 0.983092i \(-0.558616\pi\)
−0.183110 + 0.983092i \(0.558616\pi\)
\(548\) −8.84496 −0.377838
\(549\) 12.7051 0.542241
\(550\) 0.599502 0.0255628
\(551\) −2.33023 −0.0992712
\(552\) 0.516987 0.0220044
\(553\) −24.1526 −1.02707
\(554\) 0.718934 0.0305446
\(555\) 8.59307 0.364755
\(556\) −27.9401 −1.18492
\(557\) 9.38728 0.397752 0.198876 0.980025i \(-0.436271\pi\)
0.198876 + 0.980025i \(0.436271\pi\)
\(558\) −0.147989 −0.00626486
\(559\) −8.82134 −0.373103
\(560\) −20.6845 −0.874079
\(561\) −14.8698 −0.627804
\(562\) −0.559277 −0.0235917
\(563\) 11.8967 0.501385 0.250692 0.968067i \(-0.419342\pi\)
0.250692 + 0.968067i \(0.419342\pi\)
\(564\) −0.350865 −0.0147741
\(565\) 33.3616 1.40353
\(566\) 0.830290 0.0348997
\(567\) −1.69214 −0.0710634
\(568\) −0.908516 −0.0381205
\(569\) −16.1566 −0.677320 −0.338660 0.940909i \(-0.609974\pi\)
−0.338660 + 0.940909i \(0.609974\pi\)
\(570\) −0.358662 −0.0150227
\(571\) 27.7464 1.16115 0.580575 0.814207i \(-0.302828\pi\)
0.580575 + 0.814207i \(0.302828\pi\)
\(572\) 9.20848 0.385026
\(573\) −12.1789 −0.508782
\(574\) 0.173824 0.00725527
\(575\) 18.9154 0.788826
\(576\) −7.97866 −0.332444
\(577\) 4.64568 0.193402 0.0967011 0.995313i \(-0.469171\pi\)
0.0967011 + 0.995313i \(0.469171\pi\)
\(578\) −0.196214 −0.00816143
\(579\) −19.1182 −0.794526
\(580\) 3.62722 0.150612
\(581\) 8.26848 0.343034
\(582\) −0.258229 −0.0107039
\(583\) −1.17745 −0.0487651
\(584\) −0.315067 −0.0130376
\(585\) −3.06004 −0.126517
\(586\) 0.209465 0.00865292
\(587\) −15.3149 −0.632112 −0.316056 0.948741i \(-0.602359\pi\)
−0.316056 + 0.948741i \(0.602359\pi\)
\(588\) −8.26961 −0.341033
\(589\) −19.5005 −0.803506
\(590\) −1.14864 −0.0472888
\(591\) 14.8035 0.608936
\(592\) −11.2176 −0.461042
\(593\) −16.8272 −0.691009 −0.345505 0.938417i \(-0.612292\pi\)
−0.345505 + 0.938417i \(0.612292\pi\)
\(594\) −0.137379 −0.00563674
\(595\) −16.7155 −0.685268
\(596\) −3.03688 −0.124395
\(597\) −10.0910 −0.412996
\(598\) −0.129276 −0.00528647
\(599\) 21.0065 0.858301 0.429151 0.903233i \(-0.358813\pi\)
0.429151 + 0.903233i \(0.358813\pi\)
\(600\) 0.520478 0.0212484
\(601\) 38.2296 1.55942 0.779710 0.626141i \(-0.215367\pi\)
0.779710 + 0.626141i \(0.215367\pi\)
\(602\) −0.445187 −0.0181445
\(603\) −5.34184 −0.217536
\(604\) −10.8268 −0.440535
\(605\) 31.2672 1.27119
\(606\) −0.364633 −0.0148122
\(607\) −43.2393 −1.75503 −0.877515 0.479548i \(-0.840801\pi\)
−0.877515 + 0.479548i \(0.840801\pi\)
\(608\) 1.40567 0.0570073
\(609\) −1.00334 −0.0406574
\(610\) 1.15951 0.0469474
\(611\) 0.175510 0.00710039
\(612\) −6.45344 −0.260865
\(613\) −27.6480 −1.11669 −0.558347 0.829608i \(-0.688564\pi\)
−0.558347 + 0.829608i \(0.688564\pi\)
\(614\) 0.531243 0.0214392
\(615\) 10.5397 0.425002
\(616\) 0.929656 0.0374569
\(617\) −38.8213 −1.56289 −0.781444 0.623976i \(-0.785516\pi\)
−0.781444 + 0.623976i \(0.785516\pi\)
\(618\) −0.0298243 −0.00119971
\(619\) −32.6015 −1.31037 −0.655183 0.755470i \(-0.727409\pi\)
−0.655183 + 0.755470i \(0.727409\pi\)
\(620\) 30.3544 1.21906
\(621\) −4.33457 −0.173940
\(622\) 0.150301 0.00602651
\(623\) 27.8468 1.11566
\(624\) 3.99466 0.159915
\(625\) −27.7761 −1.11104
\(626\) −0.590030 −0.0235824
\(627\) −18.1025 −0.722946
\(628\) −35.0319 −1.39792
\(629\) −9.06517 −0.361452
\(630\) −0.154431 −0.00615268
\(631\) 10.9258 0.434950 0.217475 0.976066i \(-0.430218\pi\)
0.217475 + 0.976066i \(0.430218\pi\)
\(632\) −1.70239 −0.0677176
\(633\) −6.26999 −0.249210
\(634\) 0.228480 0.00907410
\(635\) −46.4321 −1.84260
\(636\) −0.511010 −0.0202629
\(637\) 4.13665 0.163900
\(638\) −0.0814577 −0.00322494
\(639\) 7.61726 0.301334
\(640\) −2.91719 −0.115312
\(641\) −28.2294 −1.11499 −0.557497 0.830179i \(-0.688238\pi\)
−0.557497 + 0.830179i \(0.688238\pi\)
\(642\) −0.351512 −0.0138731
\(643\) 20.6457 0.814187 0.407093 0.913387i \(-0.366542\pi\)
0.407093 + 0.913387i \(0.366542\pi\)
\(644\) 14.6629 0.577800
\(645\) −26.9936 −1.06287
\(646\) 0.378367 0.0148866
\(647\) 20.4026 0.802109 0.401054 0.916054i \(-0.368644\pi\)
0.401054 + 0.916054i \(0.368644\pi\)
\(648\) −0.119271 −0.00468540
\(649\) −57.9747 −2.27571
\(650\) −0.130149 −0.00510484
\(651\) −8.39645 −0.329083
\(652\) −3.64138 −0.142607
\(653\) −13.0210 −0.509550 −0.254775 0.967000i \(-0.582001\pi\)
−0.254775 + 0.967000i \(0.582001\pi\)
\(654\) 0.271867 0.0106308
\(655\) −17.2922 −0.675663
\(656\) −13.7588 −0.537192
\(657\) 2.64161 0.103059
\(658\) 0.00885749 0.000345301 0
\(659\) −46.8236 −1.82399 −0.911995 0.410201i \(-0.865458\pi\)
−0.911995 + 0.410201i \(0.865458\pi\)
\(660\) 28.1783 1.09684
\(661\) −38.7458 −1.50704 −0.753519 0.657426i \(-0.771645\pi\)
−0.753519 + 0.657426i \(0.771645\pi\)
\(662\) −0.248842 −0.00967152
\(663\) 3.22816 0.125371
\(664\) 0.582803 0.0226172
\(665\) −20.3495 −0.789118
\(666\) −0.0837513 −0.00324530
\(667\) −2.57014 −0.0995163
\(668\) 39.6339 1.53348
\(669\) −24.3195 −0.940246
\(670\) −0.487515 −0.0188343
\(671\) 58.5235 2.25927
\(672\) 0.605245 0.0233478
\(673\) 16.7438 0.645425 0.322713 0.946497i \(-0.395405\pi\)
0.322713 + 0.946497i \(0.395405\pi\)
\(674\) −0.386367 −0.0148823
\(675\) −4.36384 −0.167964
\(676\) −1.99911 −0.0768889
\(677\) 31.3519 1.20495 0.602475 0.798138i \(-0.294181\pi\)
0.602475 + 0.798138i \(0.294181\pi\)
\(678\) −0.325155 −0.0124875
\(679\) −14.6512 −0.562261
\(680\) −1.17819 −0.0451815
\(681\) −0.112801 −0.00432253
\(682\) −0.681679 −0.0261028
\(683\) 9.45935 0.361952 0.180976 0.983488i \(-0.442074\pi\)
0.180976 + 0.983488i \(0.442074\pi\)
\(684\) −7.85643 −0.300398
\(685\) 13.5390 0.517298
\(686\) 0.562034 0.0214585
\(687\) 2.07740 0.0792578
\(688\) 35.2383 1.34345
\(689\) 0.255619 0.00973829
\(690\) −0.395588 −0.0150598
\(691\) 52.0566 1.98033 0.990163 0.139916i \(-0.0446833\pi\)
0.990163 + 0.139916i \(0.0446833\pi\)
\(692\) 30.2575 1.15022
\(693\) −7.79451 −0.296089
\(694\) 0.870088 0.0330281
\(695\) 42.7679 1.62228
\(696\) −0.0707203 −0.00268065
\(697\) −11.1188 −0.421153
\(698\) 0.368025 0.0139299
\(699\) −14.8944 −0.563359
\(700\) 14.7619 0.557949
\(701\) 6.26342 0.236566 0.118283 0.992980i \(-0.462261\pi\)
0.118283 + 0.992980i \(0.462261\pi\)
\(702\) 0.0298243 0.00112565
\(703\) −11.0359 −0.416228
\(704\) −36.7520 −1.38514
\(705\) 0.537069 0.0202272
\(706\) −0.224212 −0.00843834
\(707\) −20.6882 −0.778061
\(708\) −25.1608 −0.945600
\(709\) −17.8043 −0.668656 −0.334328 0.942457i \(-0.608509\pi\)
−0.334328 + 0.942457i \(0.608509\pi\)
\(710\) 0.695178 0.0260896
\(711\) 14.2734 0.535293
\(712\) 1.96278 0.0735583
\(713\) −21.5082 −0.805489
\(714\) 0.162916 0.00609696
\(715\) −14.0954 −0.527139
\(716\) −43.5909 −1.62907
\(717\) −9.00916 −0.336453
\(718\) 0.119668 0.00446596
\(719\) −43.8075 −1.63375 −0.816873 0.576818i \(-0.804294\pi\)
−0.816873 + 0.576818i \(0.804294\pi\)
\(720\) 12.2238 0.455555
\(721\) −1.69214 −0.0630188
\(722\) −0.106038 −0.00394631
\(723\) 18.5937 0.691506
\(724\) 23.2181 0.862896
\(725\) −2.58750 −0.0960972
\(726\) −0.304742 −0.0113100
\(727\) −15.0653 −0.558740 −0.279370 0.960184i \(-0.590126\pi\)
−0.279370 + 0.960184i \(0.590126\pi\)
\(728\) −0.201823 −0.00748007
\(729\) 1.00000 0.0370370
\(730\) 0.241083 0.00892288
\(731\) 28.4767 1.05325
\(732\) 25.3989 0.938772
\(733\) 3.75227 0.138593 0.0692966 0.997596i \(-0.477925\pi\)
0.0692966 + 0.997596i \(0.477925\pi\)
\(734\) −0.854731 −0.0315487
\(735\) 12.6583 0.466908
\(736\) 1.55039 0.0571480
\(737\) −24.6060 −0.906375
\(738\) −0.102724 −0.00378132
\(739\) −9.36283 −0.344417 −0.172209 0.985061i \(-0.555090\pi\)
−0.172209 + 0.985061i \(0.555090\pi\)
\(740\) 17.1785 0.631494
\(741\) 3.92996 0.144371
\(742\) 0.0129003 0.000473585 0
\(743\) 26.7907 0.982854 0.491427 0.870919i \(-0.336475\pi\)
0.491427 + 0.870919i \(0.336475\pi\)
\(744\) −0.591823 −0.0216973
\(745\) 4.64855 0.170310
\(746\) −0.322609 −0.0118116
\(747\) −4.88639 −0.178784
\(748\) −29.7264 −1.08691
\(749\) −19.9438 −0.728730
\(750\) 0.0580581 0.00211998
\(751\) −18.4998 −0.675067 −0.337534 0.941313i \(-0.609593\pi\)
−0.337534 + 0.941313i \(0.609593\pi\)
\(752\) −0.701105 −0.0255667
\(753\) −1.63413 −0.0595510
\(754\) 0.0176840 0.000644014 0
\(755\) 16.5726 0.603137
\(756\) −3.38278 −0.123031
\(757\) −17.3037 −0.628912 −0.314456 0.949272i \(-0.601822\pi\)
−0.314456 + 0.949272i \(0.601822\pi\)
\(758\) −0.0347970 −0.00126388
\(759\) −19.9663 −0.724730
\(760\) −1.43433 −0.0520286
\(761\) 27.2794 0.988879 0.494439 0.869212i \(-0.335373\pi\)
0.494439 + 0.869212i \(0.335373\pi\)
\(762\) 0.452545 0.0163940
\(763\) 15.4249 0.558420
\(764\) −24.3470 −0.880844
\(765\) 9.87829 0.357150
\(766\) 0.516834 0.0186740
\(767\) 12.5860 0.454454
\(768\) −15.9289 −0.574784
\(769\) −34.8016 −1.25498 −0.627489 0.778626i \(-0.715917\pi\)
−0.627489 + 0.778626i \(0.715917\pi\)
\(770\) −0.711354 −0.0256354
\(771\) −10.9198 −0.393266
\(772\) −38.2194 −1.37555
\(773\) 54.2257 1.95036 0.975181 0.221409i \(-0.0710656\pi\)
0.975181 + 0.221409i \(0.0710656\pi\)
\(774\) 0.263090 0.00945659
\(775\) −21.6535 −0.777815
\(776\) −1.03269 −0.0370713
\(777\) −4.75181 −0.170470
\(778\) 0.883115 0.0316612
\(779\) −13.5360 −0.484977
\(780\) −6.11736 −0.219037
\(781\) 35.0873 1.25552
\(782\) 0.417322 0.0149234
\(783\) 0.592940 0.0211899
\(784\) −16.5245 −0.590161
\(785\) 53.6233 1.91390
\(786\) 0.168537 0.00601150
\(787\) 47.3647 1.68837 0.844184 0.536054i \(-0.180086\pi\)
0.844184 + 0.536054i \(0.180086\pi\)
\(788\) 29.5939 1.05424
\(789\) −11.6090 −0.413290
\(790\) 1.30264 0.0463458
\(791\) −18.4483 −0.655947
\(792\) −0.549395 −0.0195219
\(793\) −12.7051 −0.451172
\(794\) 0.160029 0.00567923
\(795\) 0.782203 0.0277419
\(796\) −20.1730 −0.715012
\(797\) −24.9570 −0.884022 −0.442011 0.897010i \(-0.645735\pi\)
−0.442011 + 0.897010i \(0.645735\pi\)
\(798\) 0.198333 0.00702093
\(799\) −0.566575 −0.0200440
\(800\) 1.56086 0.0551846
\(801\) −16.4565 −0.581463
\(802\) −0.286486 −0.0101162
\(803\) 12.1680 0.429400
\(804\) −10.6789 −0.376617
\(805\) −22.4445 −0.791066
\(806\) 0.147989 0.00521268
\(807\) −1.35757 −0.0477887
\(808\) −1.45821 −0.0512996
\(809\) −44.9595 −1.58069 −0.790346 0.612660i \(-0.790099\pi\)
−0.790346 + 0.612660i \(0.790099\pi\)
\(810\) 0.0912635 0.00320667
\(811\) −38.0789 −1.33713 −0.668566 0.743652i \(-0.733092\pi\)
−0.668566 + 0.743652i \(0.733092\pi\)
\(812\) −2.00579 −0.0703894
\(813\) 20.6130 0.722931
\(814\) −0.385783 −0.0135217
\(815\) 5.57386 0.195244
\(816\) −12.8954 −0.451429
\(817\) 34.6675 1.21286
\(818\) −0.540284 −0.0188906
\(819\) 1.69214 0.0591283
\(820\) 21.0700 0.735798
\(821\) −52.7186 −1.83989 −0.919946 0.392044i \(-0.871768\pi\)
−0.919946 + 0.392044i \(0.871768\pi\)
\(822\) −0.131956 −0.00460250
\(823\) −1.17106 −0.0408206 −0.0204103 0.999792i \(-0.506497\pi\)
−0.0204103 + 0.999792i \(0.506497\pi\)
\(824\) −0.119271 −0.00415499
\(825\) −20.1011 −0.699831
\(826\) 0.635177 0.0221007
\(827\) −52.3926 −1.82187 −0.910934 0.412552i \(-0.864638\pi\)
−0.910934 + 0.412552i \(0.864638\pi\)
\(828\) −8.66529 −0.301140
\(829\) −12.5108 −0.434516 −0.217258 0.976114i \(-0.569711\pi\)
−0.217258 + 0.976114i \(0.569711\pi\)
\(830\) −0.445949 −0.0154791
\(831\) −24.1056 −0.836215
\(832\) 7.97866 0.276610
\(833\) −13.3537 −0.462680
\(834\) −0.416832 −0.0144337
\(835\) −60.6676 −2.09949
\(836\) −36.1890 −1.25162
\(837\) 4.96202 0.171512
\(838\) −0.211963 −0.00732215
\(839\) 6.26052 0.216137 0.108069 0.994143i \(-0.465533\pi\)
0.108069 + 0.994143i \(0.465533\pi\)
\(840\) −0.617587 −0.0213088
\(841\) −28.6484 −0.987877
\(842\) −0.568592 −0.0195950
\(843\) 18.7524 0.645867
\(844\) −12.5344 −0.431452
\(845\) 3.06004 0.105269
\(846\) −0.00523447 −0.000179965 0
\(847\) −17.2902 −0.594097
\(848\) −1.02111 −0.0350651
\(849\) −27.8394 −0.955445
\(850\) 0.420140 0.0144107
\(851\) −12.1722 −0.417256
\(852\) 15.2277 0.521694
\(853\) −32.1438 −1.10058 −0.550291 0.834973i \(-0.685483\pi\)
−0.550291 + 0.834973i \(0.685483\pi\)
\(854\) −0.641190 −0.0219411
\(855\) 12.0258 0.411275
\(856\) −1.40574 −0.0480471
\(857\) 18.3549 0.626991 0.313496 0.949590i \(-0.398500\pi\)
0.313496 + 0.949590i \(0.398500\pi\)
\(858\) 0.137379 0.00469005
\(859\) 25.4143 0.867126 0.433563 0.901123i \(-0.357256\pi\)
0.433563 + 0.901123i \(0.357256\pi\)
\(860\) −53.9633 −1.84013
\(861\) −5.82826 −0.198627
\(862\) 1.08873 0.0370822
\(863\) 12.3570 0.420637 0.210319 0.977633i \(-0.432550\pi\)
0.210319 + 0.977633i \(0.432550\pi\)
\(864\) −0.357679 −0.0121685
\(865\) −46.3152 −1.57476
\(866\) 0.760733 0.0258508
\(867\) 6.57900 0.223435
\(868\) −16.7854 −0.569735
\(869\) 65.7472 2.23032
\(870\) 0.0541138 0.00183463
\(871\) 5.34184 0.181001
\(872\) 1.08722 0.0368181
\(873\) 8.65835 0.293041
\(874\) 0.508048 0.0171850
\(875\) 3.29405 0.111359
\(876\) 5.28088 0.178424
\(877\) 39.3862 1.32998 0.664990 0.746853i \(-0.268436\pi\)
0.664990 + 0.746853i \(0.268436\pi\)
\(878\) −0.138972 −0.00469009
\(879\) −7.02330 −0.236890
\(880\) 56.3065 1.89809
\(881\) −45.8855 −1.54592 −0.772961 0.634453i \(-0.781225\pi\)
−0.772961 + 0.634453i \(0.781225\pi\)
\(882\) −0.123373 −0.00415417
\(883\) −21.3311 −0.717850 −0.358925 0.933366i \(-0.616857\pi\)
−0.358925 + 0.933366i \(0.616857\pi\)
\(884\) 6.45344 0.217053
\(885\) 38.5136 1.29462
\(886\) −0.00427874 −0.000143747 0
\(887\) −29.2078 −0.980701 −0.490351 0.871525i \(-0.663131\pi\)
−0.490351 + 0.871525i \(0.663131\pi\)
\(888\) −0.334931 −0.0112395
\(889\) 25.6761 0.861148
\(890\) −1.50188 −0.0503432
\(891\) 4.60629 0.154316
\(892\) −48.6174 −1.62783
\(893\) −0.689749 −0.0230816
\(894\) −0.0453065 −0.00151528
\(895\) 66.7247 2.23036
\(896\) 1.61315 0.0538916
\(897\) 4.33457 0.144727
\(898\) −0.0550922 −0.00183845
\(899\) 2.94218 0.0981272
\(900\) −8.72380 −0.290793
\(901\) −0.825177 −0.0274906
\(902\) −0.473176 −0.0157550
\(903\) 14.9270 0.496739
\(904\) −1.30033 −0.0432483
\(905\) −35.5400 −1.18139
\(906\) −0.161522 −0.00536622
\(907\) −38.6611 −1.28372 −0.641860 0.766822i \(-0.721837\pi\)
−0.641860 + 0.766822i \(0.721837\pi\)
\(908\) −0.225501 −0.00748352
\(909\) 12.2260 0.405512
\(910\) 0.154431 0.00511934
\(911\) −23.7854 −0.788046 −0.394023 0.919101i \(-0.628917\pi\)
−0.394023 + 0.919101i \(0.628917\pi\)
\(912\) −15.6989 −0.519842
\(913\) −22.5081 −0.744910
\(914\) −0.0526433 −0.00174128
\(915\) −38.8782 −1.28527
\(916\) 4.15295 0.137217
\(917\) 9.56228 0.315774
\(918\) −0.0962775 −0.00317763
\(919\) 51.7768 1.70796 0.853979 0.520307i \(-0.174182\pi\)
0.853979 + 0.520307i \(0.174182\pi\)
\(920\) −1.58200 −0.0521571
\(921\) −17.8124 −0.586939
\(922\) 0.192077 0.00632571
\(923\) −7.61726 −0.250725
\(924\) −15.5821 −0.512613
\(925\) −12.2543 −0.402920
\(926\) 0.490083 0.0161051
\(927\) 1.00000 0.0328443
\(928\) −0.212082 −0.00696195
\(929\) 19.1854 0.629452 0.314726 0.949183i \(-0.398087\pi\)
0.314726 + 0.949183i \(0.398087\pi\)
\(930\) 0.452851 0.0148496
\(931\) −16.2569 −0.532797
\(932\) −29.7756 −0.975332
\(933\) −5.03954 −0.164987
\(934\) −0.281545 −0.00921243
\(935\) 45.5022 1.48808
\(936\) 0.119271 0.00389848
\(937\) −36.9394 −1.20676 −0.603379 0.797454i \(-0.706179\pi\)
−0.603379 + 0.797454i \(0.706179\pi\)
\(938\) 0.269587 0.00880232
\(939\) 19.7835 0.645612
\(940\) 1.07366 0.0350189
\(941\) 46.4950 1.51569 0.757846 0.652433i \(-0.226252\pi\)
0.757846 + 0.652433i \(0.226252\pi\)
\(942\) −0.522633 −0.0170283
\(943\) −14.9296 −0.486174
\(944\) −50.2768 −1.63637
\(945\) 5.17803 0.168441
\(946\) 1.21187 0.0394013
\(947\) −29.6802 −0.964477 −0.482238 0.876040i \(-0.660176\pi\)
−0.482238 + 0.876040i \(0.660176\pi\)
\(948\) 28.5340 0.926742
\(949\) −2.64161 −0.0857504
\(950\) 0.511479 0.0165946
\(951\) −7.66086 −0.248421
\(952\) 0.651517 0.0211158
\(953\) 56.1856 1.82003 0.910015 0.414576i \(-0.136070\pi\)
0.910015 + 0.414576i \(0.136070\pi\)
\(954\) −0.00762364 −0.000246825 0
\(955\) 37.2680 1.20596
\(956\) −18.0103 −0.582495
\(957\) 2.73125 0.0882888
\(958\) −0.382502 −0.0123581
\(959\) −7.48681 −0.241762
\(960\) 24.4150 0.787991
\(961\) −6.37837 −0.205754
\(962\) 0.0837513 0.00270025
\(963\) 11.7861 0.379802
\(964\) 37.1708 1.19719
\(965\) 58.5025 1.88326
\(966\) 0.218753 0.00703826
\(967\) 11.0987 0.356911 0.178455 0.983948i \(-0.442890\pi\)
0.178455 + 0.983948i \(0.442890\pi\)
\(968\) −1.21870 −0.0391703
\(969\) −12.6865 −0.407550
\(970\) 0.790191 0.0253715
\(971\) 24.0228 0.770930 0.385465 0.922722i \(-0.374041\pi\)
0.385465 + 0.922722i \(0.374041\pi\)
\(972\) 1.99911 0.0641215
\(973\) −23.6498 −0.758179
\(974\) 1.05274 0.0337318
\(975\) 4.36384 0.139755
\(976\) 50.7527 1.62455
\(977\) −31.4465 −1.00606 −0.503031 0.864269i \(-0.667782\pi\)
−0.503031 + 0.864269i \(0.667782\pi\)
\(978\) −0.0543250 −0.00173712
\(979\) −75.8035 −2.42269
\(980\) 25.3053 0.808349
\(981\) −9.11561 −0.291039
\(982\) 0.892267 0.0284734
\(983\) −36.8778 −1.17622 −0.588110 0.808781i \(-0.700128\pi\)
−0.588110 + 0.808781i \(0.700128\pi\)
\(984\) −0.410805 −0.0130960
\(985\) −45.2994 −1.44336
\(986\) −0.0570868 −0.00181801
\(987\) −0.296989 −0.00945326
\(988\) 7.85643 0.249946
\(989\) 38.2367 1.21586
\(990\) 0.420386 0.0133608
\(991\) 6.91455 0.219648 0.109824 0.993951i \(-0.464971\pi\)
0.109824 + 0.993951i \(0.464971\pi\)
\(992\) −1.77481 −0.0563503
\(993\) 8.34360 0.264776
\(994\) −0.384421 −0.0121931
\(995\) 30.8788 0.978924
\(996\) −9.76844 −0.309525
\(997\) −18.8800 −0.597935 −0.298968 0.954263i \(-0.596642\pi\)
−0.298968 + 0.954263i \(0.596642\pi\)
\(998\) −0.130041 −0.00411637
\(999\) 2.80816 0.0888461
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.g.1.12 24
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
4017.2.a.g.1.12 24 1.1 even 1 trivial