Properties

Label 4018.2.a.bo.1.3
Level $4018$
Weight $2$
Character 4018.1
Self dual yes
Analytic conductor $32.084$
Analytic rank $0$
Dimension $6$
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] = [4018,2,Mod(1,4018)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(4018, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([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("4018.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 4018 = 2 \cdot 7^{2} \cdot 41 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 4018.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: \(32.0838915322\)
Analytic rank: \(0\)
Dimension: \(6\)
Coefficient field: 6.6.52046292.1
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{6} - x^{5} - 10x^{4} + 9x^{3} + 24x^{2} - 18x + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{13}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 574)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.3
Root \(2.28320\) of defining polynomial
Character \(\chi\) \(=\) 4018.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-1.00000 q^{2} -0.486321 q^{3} +1.00000 q^{4} +0.616311 q^{5} +0.486321 q^{6} -1.00000 q^{8} -2.76349 q^{9} +O(q^{10})\) \(q-1.00000 q^{2} -0.486321 q^{3} +1.00000 q^{4} +0.616311 q^{5} +0.486321 q^{6} -1.00000 q^{8} -2.76349 q^{9} -0.616311 q^{10} -1.68048 q^{11} -0.486321 q^{12} +5.11251 q^{13} -0.299725 q^{15} +1.00000 q^{16} -4.37980 q^{17} +2.76349 q^{18} -7.65697 q^{19} +0.616311 q^{20} +1.68048 q^{22} +2.40331 q^{23} +0.486321 q^{24} -4.62016 q^{25} -5.11251 q^{26} +2.80291 q^{27} +4.00988 q^{29} +0.299725 q^{30} +4.02347 q^{31} -1.00000 q^{32} +0.817254 q^{33} +4.37980 q^{34} -2.76349 q^{36} +4.15268 q^{37} +7.65697 q^{38} -2.48632 q^{39} -0.616311 q^{40} +1.00000 q^{41} -9.35336 q^{43} -1.68048 q^{44} -1.70317 q^{45} -2.40331 q^{46} +2.90939 q^{47} -0.486321 q^{48} +4.62016 q^{50} +2.12999 q^{51} +5.11251 q^{52} -5.83023 q^{53} -2.80291 q^{54} -1.03570 q^{55} +3.72375 q^{57} -4.00988 q^{58} +11.3459 q^{59} -0.299725 q^{60} -1.07916 q^{61} -4.02347 q^{62} +1.00000 q^{64} +3.15090 q^{65} -0.817254 q^{66} +12.6312 q^{67} -4.37980 q^{68} -1.16878 q^{69} +6.87059 q^{71} +2.76349 q^{72} -4.58524 q^{73} -4.15268 q^{74} +2.24688 q^{75} -7.65697 q^{76} +2.48632 q^{78} +9.49284 q^{79} +0.616311 q^{80} +6.92736 q^{81} -1.00000 q^{82} +4.98021 q^{83} -2.69932 q^{85} +9.35336 q^{86} -1.95009 q^{87} +1.68048 q^{88} -2.21593 q^{89} +1.70317 q^{90} +2.40331 q^{92} -1.95670 q^{93} -2.90939 q^{94} -4.71908 q^{95} +0.486321 q^{96} -15.8435 q^{97} +4.64400 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6 q - 6 q^{2} + q^{3} + 6 q^{4} - q^{6} - 6 q^{8} + 5 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 6 q - 6 q^{2} + q^{3} + 6 q^{4} - q^{6} - 6 q^{8} + 5 q^{9} + q^{11} + q^{12} + 4 q^{13} + 2 q^{15} + 6 q^{16} - q^{17} - 5 q^{18} - 3 q^{19} - q^{22} + 21 q^{23} - q^{24} - 4 q^{26} + 13 q^{27} + 5 q^{29} - 2 q^{30} + 3 q^{31} - 6 q^{32} - 19 q^{33} + q^{34} + 5 q^{36} - 2 q^{37} + 3 q^{38} - 11 q^{39} + 6 q^{41} + 12 q^{43} + q^{44} + 28 q^{45} - 21 q^{46} - 18 q^{47} + q^{48} + 13 q^{51} + 4 q^{52} + 14 q^{53} - 13 q^{54} - 7 q^{55} + 5 q^{57} - 5 q^{58} + 16 q^{59} + 2 q^{60} - 20 q^{61} - 3 q^{62} + 6 q^{64} + 18 q^{65} + 19 q^{66} - 13 q^{67} - q^{68} + 15 q^{69} + 11 q^{71} - 5 q^{72} + q^{73} + 2 q^{74} - 23 q^{75} - 3 q^{76} + 11 q^{78} + 19 q^{79} - 6 q^{81} - 6 q^{82} + 15 q^{83} - 2 q^{85} - 12 q^{86} + 10 q^{87} - q^{88} - 14 q^{89} - 28 q^{90} + 21 q^{92} + 35 q^{93} + 18 q^{94} + 24 q^{95} - q^{96} + q^{97} + 10 q^{99}+O(q^{100}) \) 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
\(3\) −0.486321 −0.280778 −0.140389 0.990096i \(-0.544835\pi\)
−0.140389 + 0.990096i \(0.544835\pi\)
\(4\) 1.00000 0.500000
\(5\) 0.616311 0.275623 0.137811 0.990458i \(-0.455993\pi\)
0.137811 + 0.990458i \(0.455993\pi\)
\(6\) 0.486321 0.198540
\(7\) 0 0
\(8\) −1.00000 −0.353553
\(9\) −2.76349 −0.921164
\(10\) −0.616311 −0.194895
\(11\) −1.68048 −0.506684 −0.253342 0.967377i \(-0.581530\pi\)
−0.253342 + 0.967377i \(0.581530\pi\)
\(12\) −0.486321 −0.140389
\(13\) 5.11251 1.41796 0.708978 0.705231i \(-0.249157\pi\)
0.708978 + 0.705231i \(0.249157\pi\)
\(14\) 0 0
\(15\) −0.299725 −0.0773887
\(16\) 1.00000 0.250000
\(17\) −4.37980 −1.06226 −0.531129 0.847291i \(-0.678232\pi\)
−0.531129 + 0.847291i \(0.678232\pi\)
\(18\) 2.76349 0.651361
\(19\) −7.65697 −1.75663 −0.878315 0.478082i \(-0.841332\pi\)
−0.878315 + 0.478082i \(0.841332\pi\)
\(20\) 0.616311 0.137811
\(21\) 0 0
\(22\) 1.68048 0.358280
\(23\) 2.40331 0.501125 0.250563 0.968100i \(-0.419384\pi\)
0.250563 + 0.968100i \(0.419384\pi\)
\(24\) 0.486321 0.0992699
\(25\) −4.62016 −0.924032
\(26\) −5.11251 −1.00265
\(27\) 2.80291 0.539420
\(28\) 0 0
\(29\) 4.00988 0.744616 0.372308 0.928109i \(-0.378567\pi\)
0.372308 + 0.928109i \(0.378567\pi\)
\(30\) 0.299725 0.0547220
\(31\) 4.02347 0.722637 0.361318 0.932442i \(-0.382327\pi\)
0.361318 + 0.932442i \(0.382327\pi\)
\(32\) −1.00000 −0.176777
\(33\) 0.817254 0.142266
\(34\) 4.37980 0.751130
\(35\) 0 0
\(36\) −2.76349 −0.460582
\(37\) 4.15268 0.682696 0.341348 0.939937i \(-0.389117\pi\)
0.341348 + 0.939937i \(0.389117\pi\)
\(38\) 7.65697 1.24213
\(39\) −2.48632 −0.398130
\(40\) −0.616311 −0.0974473
\(41\) 1.00000 0.156174
\(42\) 0 0
\(43\) −9.35336 −1.42637 −0.713187 0.700974i \(-0.752749\pi\)
−0.713187 + 0.700974i \(0.752749\pi\)
\(44\) −1.68048 −0.253342
\(45\) −1.70317 −0.253894
\(46\) −2.40331 −0.354349
\(47\) 2.90939 0.424378 0.212189 0.977229i \(-0.431941\pi\)
0.212189 + 0.977229i \(0.431941\pi\)
\(48\) −0.486321 −0.0701944
\(49\) 0 0
\(50\) 4.62016 0.653389
\(51\) 2.12999 0.298258
\(52\) 5.11251 0.708978
\(53\) −5.83023 −0.800844 −0.400422 0.916331i \(-0.631136\pi\)
−0.400422 + 0.916331i \(0.631136\pi\)
\(54\) −2.80291 −0.381427
\(55\) −1.03570 −0.139654
\(56\) 0 0
\(57\) 3.72375 0.493222
\(58\) −4.00988 −0.526523
\(59\) 11.3459 1.47711 0.738554 0.674194i \(-0.235509\pi\)
0.738554 + 0.674194i \(0.235509\pi\)
\(60\) −0.299725 −0.0386943
\(61\) −1.07916 −0.138172 −0.0690861 0.997611i \(-0.522008\pi\)
−0.0690861 + 0.997611i \(0.522008\pi\)
\(62\) −4.02347 −0.510981
\(63\) 0 0
\(64\) 1.00000 0.125000
\(65\) 3.15090 0.390821
\(66\) −0.817254 −0.100597
\(67\) 12.6312 1.54315 0.771575 0.636138i \(-0.219469\pi\)
0.771575 + 0.636138i \(0.219469\pi\)
\(68\) −4.37980 −0.531129
\(69\) −1.16878 −0.140705
\(70\) 0 0
\(71\) 6.87059 0.815389 0.407695 0.913118i \(-0.366333\pi\)
0.407695 + 0.913118i \(0.366333\pi\)
\(72\) 2.76349 0.325681
\(73\) −4.58524 −0.536661 −0.268331 0.963327i \(-0.586472\pi\)
−0.268331 + 0.963327i \(0.586472\pi\)
\(74\) −4.15268 −0.482739
\(75\) 2.24688 0.259447
\(76\) −7.65697 −0.878315
\(77\) 0 0
\(78\) 2.48632 0.281520
\(79\) 9.49284 1.06803 0.534014 0.845476i \(-0.320683\pi\)
0.534014 + 0.845476i \(0.320683\pi\)
\(80\) 0.616311 0.0689057
\(81\) 6.92736 0.769707
\(82\) −1.00000 −0.110432
\(83\) 4.98021 0.546649 0.273324 0.961922i \(-0.411877\pi\)
0.273324 + 0.961922i \(0.411877\pi\)
\(84\) 0 0
\(85\) −2.69932 −0.292782
\(86\) 9.35336 1.00860
\(87\) −1.95009 −0.209071
\(88\) 1.68048 0.179140
\(89\) −2.21593 −0.234888 −0.117444 0.993079i \(-0.537470\pi\)
−0.117444 + 0.993079i \(0.537470\pi\)
\(90\) 1.70317 0.179530
\(91\) 0 0
\(92\) 2.40331 0.250563
\(93\) −1.95670 −0.202900
\(94\) −2.90939 −0.300081
\(95\) −4.71908 −0.484167
\(96\) 0.486321 0.0496349
\(97\) −15.8435 −1.60867 −0.804334 0.594178i \(-0.797477\pi\)
−0.804334 + 0.594178i \(0.797477\pi\)
\(98\) 0 0
\(99\) 4.64400 0.466739
\(100\) −4.62016 −0.462016
\(101\) 2.90010 0.288571 0.144286 0.989536i \(-0.453912\pi\)
0.144286 + 0.989536i \(0.453912\pi\)
\(102\) −2.12999 −0.210900
\(103\) −9.44397 −0.930542 −0.465271 0.885168i \(-0.654043\pi\)
−0.465271 + 0.885168i \(0.654043\pi\)
\(104\) −5.11251 −0.501323
\(105\) 0 0
\(106\) 5.83023 0.566282
\(107\) 19.1366 1.85001 0.925005 0.379955i \(-0.124061\pi\)
0.925005 + 0.379955i \(0.124061\pi\)
\(108\) 2.80291 0.269710
\(109\) 5.33986 0.511466 0.255733 0.966748i \(-0.417683\pi\)
0.255733 + 0.966748i \(0.417683\pi\)
\(110\) 1.03570 0.0987501
\(111\) −2.01953 −0.191686
\(112\) 0 0
\(113\) 7.95104 0.747971 0.373986 0.927435i \(-0.377991\pi\)
0.373986 + 0.927435i \(0.377991\pi\)
\(114\) −3.72375 −0.348761
\(115\) 1.48119 0.138121
\(116\) 4.00988 0.372308
\(117\) −14.1284 −1.30617
\(118\) −11.3459 −1.04447
\(119\) 0 0
\(120\) 0.299725 0.0273610
\(121\) −8.17598 −0.743271
\(122\) 1.07916 0.0977026
\(123\) −0.486321 −0.0438501
\(124\) 4.02347 0.361318
\(125\) −5.92901 −0.530307
\(126\) 0 0
\(127\) −12.2391 −1.08605 −0.543023 0.839718i \(-0.682720\pi\)
−0.543023 + 0.839718i \(0.682720\pi\)
\(128\) −1.00000 −0.0883883
\(129\) 4.54874 0.400494
\(130\) −3.15090 −0.276352
\(131\) 1.23803 0.108167 0.0540837 0.998536i \(-0.482776\pi\)
0.0540837 + 0.998536i \(0.482776\pi\)
\(132\) 0.817254 0.0711328
\(133\) 0 0
\(134\) −12.6312 −1.09117
\(135\) 1.72746 0.148676
\(136\) 4.37980 0.375565
\(137\) 15.5136 1.32542 0.662708 0.748878i \(-0.269407\pi\)
0.662708 + 0.748878i \(0.269407\pi\)
\(138\) 1.16878 0.0994932
\(139\) 17.9970 1.52649 0.763243 0.646112i \(-0.223606\pi\)
0.763243 + 0.646112i \(0.223606\pi\)
\(140\) 0 0
\(141\) −1.41490 −0.119156
\(142\) −6.87059 −0.576567
\(143\) −8.59148 −0.718456
\(144\) −2.76349 −0.230291
\(145\) 2.47133 0.205233
\(146\) 4.58524 0.379477
\(147\) 0 0
\(148\) 4.15268 0.341348
\(149\) 14.4679 1.18526 0.592628 0.805476i \(-0.298091\pi\)
0.592628 + 0.805476i \(0.298091\pi\)
\(150\) −2.24688 −0.183457
\(151\) 2.14126 0.174253 0.0871265 0.996197i \(-0.472232\pi\)
0.0871265 + 0.996197i \(0.472232\pi\)
\(152\) 7.65697 0.621063
\(153\) 12.1035 0.978514
\(154\) 0 0
\(155\) 2.47971 0.199175
\(156\) −2.48632 −0.199065
\(157\) −5.37832 −0.429236 −0.214618 0.976698i \(-0.568851\pi\)
−0.214618 + 0.976698i \(0.568851\pi\)
\(158\) −9.49284 −0.755210
\(159\) 2.83536 0.224859
\(160\) −0.616311 −0.0487237
\(161\) 0 0
\(162\) −6.92736 −0.544265
\(163\) 8.44420 0.661400 0.330700 0.943736i \(-0.392715\pi\)
0.330700 + 0.943736i \(0.392715\pi\)
\(164\) 1.00000 0.0780869
\(165\) 0.503682 0.0392116
\(166\) −4.98021 −0.386539
\(167\) −13.3726 −1.03481 −0.517403 0.855742i \(-0.673101\pi\)
−0.517403 + 0.855742i \(0.673101\pi\)
\(168\) 0 0
\(169\) 13.1378 1.01060
\(170\) 2.69932 0.207028
\(171\) 21.1600 1.61814
\(172\) −9.35336 −0.713187
\(173\) −3.71068 −0.282118 −0.141059 0.990001i \(-0.545051\pi\)
−0.141059 + 0.990001i \(0.545051\pi\)
\(174\) 1.95009 0.147836
\(175\) 0 0
\(176\) −1.68048 −0.126671
\(177\) −5.51774 −0.414739
\(178\) 2.21593 0.166091
\(179\) −6.02645 −0.450438 −0.225219 0.974308i \(-0.572310\pi\)
−0.225219 + 0.974308i \(0.572310\pi\)
\(180\) −1.70317 −0.126947
\(181\) −11.8265 −0.879053 −0.439527 0.898230i \(-0.644854\pi\)
−0.439527 + 0.898230i \(0.644854\pi\)
\(182\) 0 0
\(183\) 0.524818 0.0387957
\(184\) −2.40331 −0.177174
\(185\) 2.55934 0.188167
\(186\) 1.95670 0.143472
\(187\) 7.36018 0.538230
\(188\) 2.90939 0.212189
\(189\) 0 0
\(190\) 4.71908 0.342358
\(191\) 7.52434 0.544442 0.272221 0.962235i \(-0.412242\pi\)
0.272221 + 0.962235i \(0.412242\pi\)
\(192\) −0.486321 −0.0350972
\(193\) 1.71959 0.123778 0.0618892 0.998083i \(-0.480287\pi\)
0.0618892 + 0.998083i \(0.480287\pi\)
\(194\) 15.8435 1.13750
\(195\) −1.53235 −0.109734
\(196\) 0 0
\(197\) 17.3709 1.23763 0.618813 0.785538i \(-0.287614\pi\)
0.618813 + 0.785538i \(0.287614\pi\)
\(198\) −4.64400 −0.330035
\(199\) 20.0315 1.41999 0.709997 0.704204i \(-0.248696\pi\)
0.709997 + 0.704204i \(0.248696\pi\)
\(200\) 4.62016 0.326695
\(201\) −6.14283 −0.433282
\(202\) −2.90010 −0.204051
\(203\) 0 0
\(204\) 2.12999 0.149129
\(205\) 0.616311 0.0430450
\(206\) 9.44397 0.657993
\(207\) −6.64153 −0.461618
\(208\) 5.11251 0.354489
\(209\) 12.8674 0.890057
\(210\) 0 0
\(211\) −3.19398 −0.219883 −0.109941 0.993938i \(-0.535066\pi\)
−0.109941 + 0.993938i \(0.535066\pi\)
\(212\) −5.83023 −0.400422
\(213\) −3.34131 −0.228943
\(214\) −19.1366 −1.30815
\(215\) −5.76458 −0.393141
\(216\) −2.80291 −0.190714
\(217\) 0 0
\(218\) −5.33986 −0.361661
\(219\) 2.22990 0.150682
\(220\) −1.03570 −0.0698269
\(221\) −22.3918 −1.50623
\(222\) 2.01953 0.135542
\(223\) 3.67068 0.245807 0.122903 0.992419i \(-0.460779\pi\)
0.122903 + 0.992419i \(0.460779\pi\)
\(224\) 0 0
\(225\) 12.7678 0.851185
\(226\) −7.95104 −0.528895
\(227\) −9.06526 −0.601682 −0.300841 0.953674i \(-0.597267\pi\)
−0.300841 + 0.953674i \(0.597267\pi\)
\(228\) 3.72375 0.246611
\(229\) −17.0097 −1.12403 −0.562017 0.827126i \(-0.689974\pi\)
−0.562017 + 0.827126i \(0.689974\pi\)
\(230\) −1.48119 −0.0976666
\(231\) 0 0
\(232\) −4.00988 −0.263261
\(233\) 4.83435 0.316709 0.158354 0.987382i \(-0.449381\pi\)
0.158354 + 0.987382i \(0.449381\pi\)
\(234\) 14.1284 0.923601
\(235\) 1.79309 0.116968
\(236\) 11.3459 0.738554
\(237\) −4.61657 −0.299878
\(238\) 0 0
\(239\) 9.41859 0.609238 0.304619 0.952474i \(-0.401471\pi\)
0.304619 + 0.952474i \(0.401471\pi\)
\(240\) −0.299725 −0.0193472
\(241\) 27.3729 1.76324 0.881620 0.471959i \(-0.156453\pi\)
0.881620 + 0.471959i \(0.156453\pi\)
\(242\) 8.17598 0.525572
\(243\) −11.7776 −0.755536
\(244\) −1.07916 −0.0690861
\(245\) 0 0
\(246\) 0.486321 0.0310067
\(247\) −39.1464 −2.49082
\(248\) −4.02347 −0.255491
\(249\) −2.42198 −0.153487
\(250\) 5.92901 0.374984
\(251\) −27.5767 −1.74062 −0.870311 0.492502i \(-0.836083\pi\)
−0.870311 + 0.492502i \(0.836083\pi\)
\(252\) 0 0
\(253\) −4.03872 −0.253912
\(254\) 12.2391 0.767950
\(255\) 1.31274 0.0822067
\(256\) 1.00000 0.0625000
\(257\) −4.82258 −0.300824 −0.150412 0.988623i \(-0.548060\pi\)
−0.150412 + 0.988623i \(0.548060\pi\)
\(258\) −4.54874 −0.283192
\(259\) 0 0
\(260\) 3.15090 0.195410
\(261\) −11.0813 −0.685913
\(262\) −1.23803 −0.0764859
\(263\) 26.6507 1.64336 0.821678 0.569952i \(-0.193038\pi\)
0.821678 + 0.569952i \(0.193038\pi\)
\(264\) −0.817254 −0.0502985
\(265\) −3.59323 −0.220731
\(266\) 0 0
\(267\) 1.07765 0.0659514
\(268\) 12.6312 0.771575
\(269\) −20.9088 −1.27483 −0.637416 0.770519i \(-0.719997\pi\)
−0.637416 + 0.770519i \(0.719997\pi\)
\(270\) −1.72746 −0.105130
\(271\) −21.0168 −1.27668 −0.638341 0.769754i \(-0.720379\pi\)
−0.638341 + 0.769754i \(0.720379\pi\)
\(272\) −4.37980 −0.265565
\(273\) 0 0
\(274\) −15.5136 −0.937211
\(275\) 7.76410 0.468193
\(276\) −1.16878 −0.0703523
\(277\) −0.898457 −0.0539830 −0.0269915 0.999636i \(-0.508593\pi\)
−0.0269915 + 0.999636i \(0.508593\pi\)
\(278\) −17.9970 −1.07939
\(279\) −11.1188 −0.665667
\(280\) 0 0
\(281\) 30.0786 1.79434 0.897171 0.441684i \(-0.145619\pi\)
0.897171 + 0.441684i \(0.145619\pi\)
\(282\) 1.41490 0.0842559
\(283\) 19.6019 1.16521 0.582605 0.812755i \(-0.302033\pi\)
0.582605 + 0.812755i \(0.302033\pi\)
\(284\) 6.87059 0.407695
\(285\) 2.29499 0.135943
\(286\) 8.59148 0.508025
\(287\) 0 0
\(288\) 2.76349 0.162840
\(289\) 2.18267 0.128393
\(290\) −2.47133 −0.145122
\(291\) 7.70504 0.451678
\(292\) −4.58524 −0.268331
\(293\) 25.7367 1.50356 0.751778 0.659417i \(-0.229197\pi\)
0.751778 + 0.659417i \(0.229197\pi\)
\(294\) 0 0
\(295\) 6.99259 0.407125
\(296\) −4.15268 −0.241370
\(297\) −4.71024 −0.273316
\(298\) −14.4679 −0.838102
\(299\) 12.2870 0.710573
\(300\) 2.24688 0.129724
\(301\) 0 0
\(302\) −2.14126 −0.123216
\(303\) −1.41038 −0.0810243
\(304\) −7.65697 −0.439158
\(305\) −0.665098 −0.0380834
\(306\) −12.1035 −0.691914
\(307\) 17.4198 0.994199 0.497100 0.867694i \(-0.334398\pi\)
0.497100 + 0.867694i \(0.334398\pi\)
\(308\) 0 0
\(309\) 4.59280 0.261275
\(310\) −2.47971 −0.140838
\(311\) −23.0089 −1.30471 −0.652357 0.757912i \(-0.726220\pi\)
−0.652357 + 0.757912i \(0.726220\pi\)
\(312\) 2.48632 0.140760
\(313\) 7.66554 0.433282 0.216641 0.976251i \(-0.430490\pi\)
0.216641 + 0.976251i \(0.430490\pi\)
\(314\) 5.37832 0.303516
\(315\) 0 0
\(316\) 9.49284 0.534014
\(317\) −4.13124 −0.232033 −0.116017 0.993247i \(-0.537013\pi\)
−0.116017 + 0.993247i \(0.537013\pi\)
\(318\) −2.83536 −0.158999
\(319\) −6.73853 −0.377285
\(320\) 0.616311 0.0344528
\(321\) −9.30655 −0.519441
\(322\) 0 0
\(323\) 33.5360 1.86599
\(324\) 6.92736 0.384854
\(325\) −23.6206 −1.31024
\(326\) −8.44420 −0.467681
\(327\) −2.59688 −0.143608
\(328\) −1.00000 −0.0552158
\(329\) 0 0
\(330\) −0.503682 −0.0277268
\(331\) −3.92192 −0.215568 −0.107784 0.994174i \(-0.534376\pi\)
−0.107784 + 0.994174i \(0.534376\pi\)
\(332\) 4.98021 0.273324
\(333\) −11.4759 −0.628875
\(334\) 13.3726 0.731719
\(335\) 7.78476 0.425327
\(336\) 0 0
\(337\) −32.3835 −1.76404 −0.882021 0.471210i \(-0.843818\pi\)
−0.882021 + 0.471210i \(0.843818\pi\)
\(338\) −13.1378 −0.714600
\(339\) −3.86676 −0.210013
\(340\) −2.69932 −0.146391
\(341\) −6.76137 −0.366149
\(342\) −21.1600 −1.14420
\(343\) 0 0
\(344\) 9.35336 0.504300
\(345\) −0.720332 −0.0387814
\(346\) 3.71068 0.199488
\(347\) 24.2908 1.30400 0.651999 0.758219i \(-0.273930\pi\)
0.651999 + 0.758219i \(0.273930\pi\)
\(348\) −1.95009 −0.104536
\(349\) 15.8847 0.850287 0.425143 0.905126i \(-0.360224\pi\)
0.425143 + 0.905126i \(0.360224\pi\)
\(350\) 0 0
\(351\) 14.3299 0.764873
\(352\) 1.68048 0.0895700
\(353\) 23.3079 1.24056 0.620278 0.784382i \(-0.287020\pi\)
0.620278 + 0.784382i \(0.287020\pi\)
\(354\) 5.51774 0.293265
\(355\) 4.23442 0.224740
\(356\) −2.21593 −0.117444
\(357\) 0 0
\(358\) 6.02645 0.318508
\(359\) 30.9375 1.63282 0.816408 0.577475i \(-0.195962\pi\)
0.816408 + 0.577475i \(0.195962\pi\)
\(360\) 1.70317 0.0897650
\(361\) 39.6292 2.08575
\(362\) 11.8265 0.621584
\(363\) 3.97615 0.208694
\(364\) 0 0
\(365\) −2.82593 −0.147916
\(366\) −0.524818 −0.0274327
\(367\) 19.0487 0.994334 0.497167 0.867655i \(-0.334374\pi\)
0.497167 + 0.867655i \(0.334374\pi\)
\(368\) 2.40331 0.125281
\(369\) −2.76349 −0.143862
\(370\) −2.55934 −0.133054
\(371\) 0 0
\(372\) −1.95670 −0.101450
\(373\) 16.8532 0.872625 0.436312 0.899795i \(-0.356284\pi\)
0.436312 + 0.899795i \(0.356284\pi\)
\(374\) −7.36018 −0.380586
\(375\) 2.88340 0.148898
\(376\) −2.90939 −0.150040
\(377\) 20.5005 1.05583
\(378\) 0 0
\(379\) 26.6798 1.37045 0.685224 0.728332i \(-0.259704\pi\)
0.685224 + 0.728332i \(0.259704\pi\)
\(380\) −4.71908 −0.242084
\(381\) 5.95214 0.304937
\(382\) −7.52434 −0.384979
\(383\) 30.6768 1.56751 0.783755 0.621071i \(-0.213302\pi\)
0.783755 + 0.621071i \(0.213302\pi\)
\(384\) 0.486321 0.0248175
\(385\) 0 0
\(386\) −1.71959 −0.0875246
\(387\) 25.8479 1.31392
\(388\) −15.8435 −0.804334
\(389\) 15.5832 0.790100 0.395050 0.918660i \(-0.370727\pi\)
0.395050 + 0.918660i \(0.370727\pi\)
\(390\) 1.53235 0.0775934
\(391\) −10.5260 −0.532324
\(392\) 0 0
\(393\) −0.602081 −0.0303710
\(394\) −17.3709 −0.875134
\(395\) 5.85054 0.294373
\(396\) 4.64400 0.233370
\(397\) −6.00501 −0.301383 −0.150691 0.988581i \(-0.548150\pi\)
−0.150691 + 0.988581i \(0.548150\pi\)
\(398\) −20.0315 −1.00409
\(399\) 0 0
\(400\) −4.62016 −0.231008
\(401\) 9.75645 0.487214 0.243607 0.969874i \(-0.421669\pi\)
0.243607 + 0.969874i \(0.421669\pi\)
\(402\) 6.14283 0.306377
\(403\) 20.5700 1.02467
\(404\) 2.90010 0.144286
\(405\) 4.26941 0.212149
\(406\) 0 0
\(407\) −6.97850 −0.345911
\(408\) −2.12999 −0.105450
\(409\) −2.43844 −0.120573 −0.0602866 0.998181i \(-0.519201\pi\)
−0.0602866 + 0.998181i \(0.519201\pi\)
\(410\) −0.616311 −0.0304374
\(411\) −7.54459 −0.372147
\(412\) −9.44397 −0.465271
\(413\) 0 0
\(414\) 6.64153 0.326413
\(415\) 3.06936 0.150669
\(416\) −5.11251 −0.250661
\(417\) −8.75232 −0.428603
\(418\) −12.8674 −0.629365
\(419\) 4.49210 0.219453 0.109727 0.993962i \(-0.465002\pi\)
0.109727 + 0.993962i \(0.465002\pi\)
\(420\) 0 0
\(421\) −38.1666 −1.86013 −0.930064 0.367398i \(-0.880249\pi\)
−0.930064 + 0.367398i \(0.880249\pi\)
\(422\) 3.19398 0.155481
\(423\) −8.04007 −0.390922
\(424\) 5.83023 0.283141
\(425\) 20.2354 0.981561
\(426\) 3.34131 0.161887
\(427\) 0 0
\(428\) 19.1366 0.925005
\(429\) 4.17822 0.201726
\(430\) 5.76458 0.277993
\(431\) −31.1582 −1.50084 −0.750420 0.660962i \(-0.770149\pi\)
−0.750420 + 0.660962i \(0.770149\pi\)
\(432\) 2.80291 0.134855
\(433\) 11.5301 0.554101 0.277051 0.960855i \(-0.410643\pi\)
0.277051 + 0.960855i \(0.410643\pi\)
\(434\) 0 0
\(435\) −1.20186 −0.0576248
\(436\) 5.33986 0.255733
\(437\) −18.4021 −0.880291
\(438\) −2.22990 −0.106549
\(439\) 27.9140 1.33226 0.666131 0.745835i \(-0.267949\pi\)
0.666131 + 0.745835i \(0.267949\pi\)
\(440\) 1.03570 0.0493750
\(441\) 0 0
\(442\) 22.3918 1.06507
\(443\) 12.6944 0.603130 0.301565 0.953446i \(-0.402491\pi\)
0.301565 + 0.953446i \(0.402491\pi\)
\(444\) −2.01953 −0.0958429
\(445\) −1.36570 −0.0647405
\(446\) −3.67068 −0.173812
\(447\) −7.03604 −0.332793
\(448\) 0 0
\(449\) −38.5081 −1.81731 −0.908656 0.417546i \(-0.862890\pi\)
−0.908656 + 0.417546i \(0.862890\pi\)
\(450\) −12.7678 −0.601879
\(451\) −1.68048 −0.0791308
\(452\) 7.95104 0.373986
\(453\) −1.04134 −0.0489264
\(454\) 9.06526 0.425454
\(455\) 0 0
\(456\) −3.72375 −0.174380
\(457\) −5.36824 −0.251116 −0.125558 0.992086i \(-0.540072\pi\)
−0.125558 + 0.992086i \(0.540072\pi\)
\(458\) 17.0097 0.794812
\(459\) −12.2762 −0.573003
\(460\) 1.48119 0.0690607
\(461\) 29.6642 1.38160 0.690799 0.723047i \(-0.257259\pi\)
0.690799 + 0.723047i \(0.257259\pi\)
\(462\) 0 0
\(463\) 26.0446 1.21039 0.605197 0.796076i \(-0.293094\pi\)
0.605197 + 0.796076i \(0.293094\pi\)
\(464\) 4.00988 0.186154
\(465\) −1.20594 −0.0559239
\(466\) −4.83435 −0.223947
\(467\) −10.5096 −0.486326 −0.243163 0.969985i \(-0.578185\pi\)
−0.243163 + 0.969985i \(0.578185\pi\)
\(468\) −14.1284 −0.653085
\(469\) 0 0
\(470\) −1.79309 −0.0827090
\(471\) 2.61559 0.120520
\(472\) −11.3459 −0.522237
\(473\) 15.7182 0.722722
\(474\) 4.61657 0.212046
\(475\) 35.3764 1.62318
\(476\) 0 0
\(477\) 16.1118 0.737708
\(478\) −9.41859 −0.430796
\(479\) −10.6171 −0.485106 −0.242553 0.970138i \(-0.577985\pi\)
−0.242553 + 0.970138i \(0.577985\pi\)
\(480\) 0.299725 0.0136805
\(481\) 21.2306 0.968033
\(482\) −27.3729 −1.24680
\(483\) 0 0
\(484\) −8.17598 −0.371635
\(485\) −9.76454 −0.443385
\(486\) 11.7776 0.534245
\(487\) 0.350326 0.0158748 0.00793739 0.999968i \(-0.497473\pi\)
0.00793739 + 0.999968i \(0.497473\pi\)
\(488\) 1.07916 0.0488513
\(489\) −4.10659 −0.185706
\(490\) 0 0
\(491\) −29.9266 −1.35057 −0.675285 0.737557i \(-0.735979\pi\)
−0.675285 + 0.737557i \(0.735979\pi\)
\(492\) −0.486321 −0.0219250
\(493\) −17.5625 −0.790974
\(494\) 39.1464 1.76128
\(495\) 2.86215 0.128644
\(496\) 4.02347 0.180659
\(497\) 0 0
\(498\) 2.42198 0.108531
\(499\) 34.4378 1.54165 0.770823 0.637049i \(-0.219845\pi\)
0.770823 + 0.637049i \(0.219845\pi\)
\(500\) −5.92901 −0.265153
\(501\) 6.50340 0.290550
\(502\) 27.5767 1.23081
\(503\) −12.7817 −0.569907 −0.284953 0.958541i \(-0.591978\pi\)
−0.284953 + 0.958541i \(0.591978\pi\)
\(504\) 0 0
\(505\) 1.78737 0.0795368
\(506\) 4.03872 0.179543
\(507\) −6.38917 −0.283753
\(508\) −12.2391 −0.543023
\(509\) 36.6635 1.62508 0.812541 0.582905i \(-0.198084\pi\)
0.812541 + 0.582905i \(0.198084\pi\)
\(510\) −1.31274 −0.0581289
\(511\) 0 0
\(512\) −1.00000 −0.0441942
\(513\) −21.4618 −0.947561
\(514\) 4.82258 0.212715
\(515\) −5.82043 −0.256479
\(516\) 4.54874 0.200247
\(517\) −4.88918 −0.215026
\(518\) 0 0
\(519\) 1.80458 0.0792124
\(520\) −3.15090 −0.138176
\(521\) 3.36045 0.147224 0.0736119 0.997287i \(-0.476547\pi\)
0.0736119 + 0.997287i \(0.476547\pi\)
\(522\) 11.0813 0.485014
\(523\) 23.7576 1.03885 0.519423 0.854517i \(-0.326147\pi\)
0.519423 + 0.854517i \(0.326147\pi\)
\(524\) 1.23803 0.0540837
\(525\) 0 0
\(526\) −26.6507 −1.16203
\(527\) −17.6220 −0.767627
\(528\) 0.817254 0.0355664
\(529\) −17.2241 −0.748874
\(530\) 3.59323 0.156080
\(531\) −31.3543 −1.36066
\(532\) 0 0
\(533\) 5.11251 0.221447
\(534\) −1.07765 −0.0466346
\(535\) 11.7941 0.509905
\(536\) −12.6312 −0.545586
\(537\) 2.93079 0.126473
\(538\) 20.9088 0.901443
\(539\) 0 0
\(540\) 1.72746 0.0743381
\(541\) −4.33577 −0.186409 −0.0932047 0.995647i \(-0.529711\pi\)
−0.0932047 + 0.995647i \(0.529711\pi\)
\(542\) 21.0168 0.902751
\(543\) 5.75145 0.246818
\(544\) 4.37980 0.187783
\(545\) 3.29101 0.140971
\(546\) 0 0
\(547\) 25.3371 1.08334 0.541669 0.840592i \(-0.317793\pi\)
0.541669 + 0.840592i \(0.317793\pi\)
\(548\) 15.5136 0.662708
\(549\) 2.98225 0.127279
\(550\) −7.76410 −0.331062
\(551\) −30.7035 −1.30801
\(552\) 1.16878 0.0497466
\(553\) 0 0
\(554\) 0.898457 0.0381718
\(555\) −1.24466 −0.0528329
\(556\) 17.9970 0.763243
\(557\) 33.5582 1.42191 0.710953 0.703239i \(-0.248264\pi\)
0.710953 + 0.703239i \(0.248264\pi\)
\(558\) 11.1188 0.470698
\(559\) −47.8192 −2.02254
\(560\) 0 0
\(561\) −3.57941 −0.151123
\(562\) −30.0786 −1.26879
\(563\) 8.07654 0.340385 0.170193 0.985411i \(-0.445561\pi\)
0.170193 + 0.985411i \(0.445561\pi\)
\(564\) −1.41490 −0.0595779
\(565\) 4.90031 0.206158
\(566\) −19.6019 −0.823928
\(567\) 0 0
\(568\) −6.87059 −0.288284
\(569\) 23.4628 0.983611 0.491806 0.870705i \(-0.336337\pi\)
0.491806 + 0.870705i \(0.336337\pi\)
\(570\) −2.29499 −0.0961264
\(571\) 5.05564 0.211572 0.105786 0.994389i \(-0.466264\pi\)
0.105786 + 0.994389i \(0.466264\pi\)
\(572\) −8.59148 −0.359228
\(573\) −3.65924 −0.152867
\(574\) 0 0
\(575\) −11.1037 −0.463056
\(576\) −2.76349 −0.115145
\(577\) −15.0464 −0.626389 −0.313195 0.949689i \(-0.601399\pi\)
−0.313195 + 0.949689i \(0.601399\pi\)
\(578\) −2.18267 −0.0907873
\(579\) −0.836270 −0.0347542
\(580\) 2.47133 0.102616
\(581\) 0 0
\(582\) −7.70504 −0.319384
\(583\) 9.79760 0.405775
\(584\) 4.58524 0.189738
\(585\) −8.70748 −0.360010
\(586\) −25.7367 −1.06317
\(587\) 9.33886 0.385456 0.192728 0.981252i \(-0.438266\pi\)
0.192728 + 0.981252i \(0.438266\pi\)
\(588\) 0 0
\(589\) −30.8076 −1.26941
\(590\) −6.99259 −0.287881
\(591\) −8.44784 −0.347498
\(592\) 4.15268 0.170674
\(593\) −47.9053 −1.96723 −0.983617 0.180273i \(-0.942302\pi\)
−0.983617 + 0.180273i \(0.942302\pi\)
\(594\) 4.71024 0.193263
\(595\) 0 0
\(596\) 14.4679 0.592628
\(597\) −9.74173 −0.398703
\(598\) −12.2870 −0.502451
\(599\) 26.2578 1.07287 0.536433 0.843943i \(-0.319772\pi\)
0.536433 + 0.843943i \(0.319772\pi\)
\(600\) −2.24688 −0.0917285
\(601\) −34.5798 −1.41054 −0.705269 0.708939i \(-0.749174\pi\)
−0.705269 + 0.708939i \(0.749174\pi\)
\(602\) 0 0
\(603\) −34.9063 −1.42149
\(604\) 2.14126 0.0871265
\(605\) −5.03895 −0.204862
\(606\) 1.41038 0.0572928
\(607\) −8.02107 −0.325565 −0.162783 0.986662i \(-0.552047\pi\)
−0.162783 + 0.986662i \(0.552047\pi\)
\(608\) 7.65697 0.310531
\(609\) 0 0
\(610\) 0.665098 0.0269290
\(611\) 14.8743 0.601749
\(612\) 12.1035 0.489257
\(613\) −2.25023 −0.0908861 −0.0454430 0.998967i \(-0.514470\pi\)
−0.0454430 + 0.998967i \(0.514470\pi\)
\(614\) −17.4198 −0.703005
\(615\) −0.299725 −0.0120861
\(616\) 0 0
\(617\) −38.9683 −1.56880 −0.784402 0.620252i \(-0.787030\pi\)
−0.784402 + 0.620252i \(0.787030\pi\)
\(618\) −4.59280 −0.184750
\(619\) 15.9889 0.642649 0.321324 0.946969i \(-0.395872\pi\)
0.321324 + 0.946969i \(0.395872\pi\)
\(620\) 2.47971 0.0995876
\(621\) 6.73626 0.270317
\(622\) 23.0089 0.922572
\(623\) 0 0
\(624\) −2.48632 −0.0995325
\(625\) 19.4467 0.777868
\(626\) −7.66554 −0.306376
\(627\) −6.25769 −0.249908
\(628\) −5.37832 −0.214618
\(629\) −18.1879 −0.725200
\(630\) 0 0
\(631\) 9.44784 0.376113 0.188056 0.982158i \(-0.439781\pi\)
0.188056 + 0.982158i \(0.439781\pi\)
\(632\) −9.49284 −0.377605
\(633\) 1.55330 0.0617382
\(634\) 4.13124 0.164072
\(635\) −7.54310 −0.299339
\(636\) 2.83536 0.112429
\(637\) 0 0
\(638\) 6.73853 0.266781
\(639\) −18.9868 −0.751107
\(640\) −0.616311 −0.0243618
\(641\) 12.8091 0.505928 0.252964 0.967476i \(-0.418595\pi\)
0.252964 + 0.967476i \(0.418595\pi\)
\(642\) 9.30655 0.367300
\(643\) 12.3360 0.486486 0.243243 0.969965i \(-0.421789\pi\)
0.243243 + 0.969965i \(0.421789\pi\)
\(644\) 0 0
\(645\) 2.80344 0.110385
\(646\) −33.5360 −1.31946
\(647\) −49.7158 −1.95453 −0.977265 0.212022i \(-0.931995\pi\)
−0.977265 + 0.212022i \(0.931995\pi\)
\(648\) −6.92736 −0.272133
\(649\) −19.0666 −0.748428
\(650\) 23.6206 0.926477
\(651\) 0 0
\(652\) 8.44420 0.330700
\(653\) 45.3400 1.77429 0.887145 0.461491i \(-0.152685\pi\)
0.887145 + 0.461491i \(0.152685\pi\)
\(654\) 2.59688 0.101546
\(655\) 0.763013 0.0298134
\(656\) 1.00000 0.0390434
\(657\) 12.6713 0.494353
\(658\) 0 0
\(659\) 2.23227 0.0869570 0.0434785 0.999054i \(-0.486156\pi\)
0.0434785 + 0.999054i \(0.486156\pi\)
\(660\) 0.503682 0.0196058
\(661\) −44.1283 −1.71639 −0.858195 0.513323i \(-0.828414\pi\)
−0.858195 + 0.513323i \(0.828414\pi\)
\(662\) 3.92192 0.152430
\(663\) 10.8896 0.422917
\(664\) −4.98021 −0.193270
\(665\) 0 0
\(666\) 11.4759 0.444682
\(667\) 9.63699 0.373146
\(668\) −13.3726 −0.517403
\(669\) −1.78513 −0.0690170
\(670\) −7.78476 −0.300752
\(671\) 1.81351 0.0700097
\(672\) 0 0
\(673\) −27.0400 −1.04231 −0.521157 0.853461i \(-0.674499\pi\)
−0.521157 + 0.853461i \(0.674499\pi\)
\(674\) 32.3835 1.24737
\(675\) −12.9499 −0.498441
\(676\) 13.1378 0.505299
\(677\) 11.5874 0.445342 0.222671 0.974894i \(-0.428522\pi\)
0.222671 + 0.974894i \(0.428522\pi\)
\(678\) 3.86676 0.148502
\(679\) 0 0
\(680\) 2.69932 0.103514
\(681\) 4.40863 0.168939
\(682\) 6.76137 0.258906
\(683\) −42.0044 −1.60725 −0.803627 0.595134i \(-0.797099\pi\)
−0.803627 + 0.595134i \(0.797099\pi\)
\(684\) 21.1600 0.809072
\(685\) 9.56121 0.365315
\(686\) 0 0
\(687\) 8.27218 0.315603
\(688\) −9.35336 −0.356594
\(689\) −29.8071 −1.13556
\(690\) 0.720332 0.0274226
\(691\) −2.00125 −0.0761311 −0.0380655 0.999275i \(-0.512120\pi\)
−0.0380655 + 0.999275i \(0.512120\pi\)
\(692\) −3.71068 −0.141059
\(693\) 0 0
\(694\) −24.2908 −0.922066
\(695\) 11.0917 0.420734
\(696\) 1.95009 0.0739179
\(697\) −4.37980 −0.165897
\(698\) −15.8847 −0.601244
\(699\) −2.35104 −0.0889247
\(700\) 0 0
\(701\) −44.6984 −1.68823 −0.844117 0.536159i \(-0.819875\pi\)
−0.844117 + 0.536159i \(0.819875\pi\)
\(702\) −14.3299 −0.540847
\(703\) −31.7969 −1.19924
\(704\) −1.68048 −0.0633356
\(705\) −0.872016 −0.0328420
\(706\) −23.3079 −0.877205
\(707\) 0 0
\(708\) −5.51774 −0.207369
\(709\) −13.1363 −0.493343 −0.246671 0.969099i \(-0.579337\pi\)
−0.246671 + 0.969099i \(0.579337\pi\)
\(710\) −4.23442 −0.158915
\(711\) −26.2334 −0.983829
\(712\) 2.21593 0.0830455
\(713\) 9.66966 0.362131
\(714\) 0 0
\(715\) −5.29503 −0.198023
\(716\) −6.02645 −0.225219
\(717\) −4.58046 −0.171060
\(718\) −30.9375 −1.15458
\(719\) −14.1812 −0.528868 −0.264434 0.964404i \(-0.585185\pi\)
−0.264434 + 0.964404i \(0.585185\pi\)
\(720\) −1.70317 −0.0634734
\(721\) 0 0
\(722\) −39.6292 −1.47485
\(723\) −13.3120 −0.495078
\(724\) −11.8265 −0.439527
\(725\) −18.5263 −0.688049
\(726\) −3.97615 −0.147569
\(727\) −19.8678 −0.736857 −0.368428 0.929656i \(-0.620104\pi\)
−0.368428 + 0.929656i \(0.620104\pi\)
\(728\) 0 0
\(729\) −15.0544 −0.557569
\(730\) 2.82593 0.104592
\(731\) 40.9659 1.51518
\(732\) 0.524818 0.0193978
\(733\) 4.39927 0.162491 0.0812453 0.996694i \(-0.474110\pi\)
0.0812453 + 0.996694i \(0.474110\pi\)
\(734\) −19.0487 −0.703101
\(735\) 0 0
\(736\) −2.40331 −0.0885872
\(737\) −21.2266 −0.781890
\(738\) 2.76349 0.101726
\(739\) −49.6085 −1.82488 −0.912440 0.409211i \(-0.865804\pi\)
−0.912440 + 0.409211i \(0.865804\pi\)
\(740\) 2.55934 0.0940833
\(741\) 19.0377 0.699367
\(742\) 0 0
\(743\) 37.2462 1.36643 0.683215 0.730217i \(-0.260581\pi\)
0.683215 + 0.730217i \(0.260581\pi\)
\(744\) 1.95670 0.0717361
\(745\) 8.91672 0.326683
\(746\) −16.8532 −0.617039
\(747\) −13.7628 −0.503553
\(748\) 7.36018 0.269115
\(749\) 0 0
\(750\) −2.88340 −0.105287
\(751\) −44.0789 −1.60846 −0.804230 0.594318i \(-0.797422\pi\)
−0.804230 + 0.594318i \(0.797422\pi\)
\(752\) 2.90939 0.106094
\(753\) 13.4111 0.488728
\(754\) −20.5005 −0.746586
\(755\) 1.31968 0.0480281
\(756\) 0 0
\(757\) 49.7382 1.80777 0.903883 0.427779i \(-0.140704\pi\)
0.903883 + 0.427779i \(0.140704\pi\)
\(758\) −26.6798 −0.969053
\(759\) 1.96412 0.0712929
\(760\) 4.71908 0.171179
\(761\) −9.17555 −0.332614 −0.166307 0.986074i \(-0.553184\pi\)
−0.166307 + 0.986074i \(0.553184\pi\)
\(762\) −5.95214 −0.215623
\(763\) 0 0
\(764\) 7.52434 0.272221
\(765\) 7.45955 0.269701
\(766\) −30.6768 −1.10840
\(767\) 58.0060 2.09447
\(768\) −0.486321 −0.0175486
\(769\) 6.52990 0.235474 0.117737 0.993045i \(-0.462436\pi\)
0.117737 + 0.993045i \(0.462436\pi\)
\(770\) 0 0
\(771\) 2.34532 0.0844647
\(772\) 1.71959 0.0618892
\(773\) −3.57177 −0.128468 −0.0642338 0.997935i \(-0.520460\pi\)
−0.0642338 + 0.997935i \(0.520460\pi\)
\(774\) −25.8479 −0.929085
\(775\) −18.5891 −0.667740
\(776\) 15.8435 0.568750
\(777\) 0 0
\(778\) −15.5832 −0.558685
\(779\) −7.65697 −0.274340
\(780\) −1.53235 −0.0548668
\(781\) −11.5459 −0.413145
\(782\) 10.5260 0.376410
\(783\) 11.2393 0.401660
\(784\) 0 0
\(785\) −3.31472 −0.118307
\(786\) 0.602081 0.0214755
\(787\) −10.3998 −0.370714 −0.185357 0.982671i \(-0.559344\pi\)
−0.185357 + 0.982671i \(0.559344\pi\)
\(788\) 17.3709 0.618813
\(789\) −12.9608 −0.461417
\(790\) −5.85054 −0.208153
\(791\) 0 0
\(792\) −4.64400 −0.165017
\(793\) −5.51722 −0.195922
\(794\) 6.00501 0.213110
\(795\) 1.74747 0.0619762
\(796\) 20.0315 0.709997
\(797\) 18.3777 0.650971 0.325485 0.945547i \(-0.394472\pi\)
0.325485 + 0.945547i \(0.394472\pi\)
\(798\) 0 0
\(799\) −12.7425 −0.450799
\(800\) 4.62016 0.163347
\(801\) 6.12371 0.216371
\(802\) −9.75645 −0.344512
\(803\) 7.70541 0.271918
\(804\) −6.14283 −0.216641
\(805\) 0 0
\(806\) −20.5700 −0.724549
\(807\) 10.1684 0.357944
\(808\) −2.90010 −0.102025
\(809\) 9.73379 0.342222 0.171111 0.985252i \(-0.445264\pi\)
0.171111 + 0.985252i \(0.445264\pi\)
\(810\) −4.26941 −0.150012
\(811\) 31.2917 1.09880 0.549401 0.835559i \(-0.314856\pi\)
0.549401 + 0.835559i \(0.314856\pi\)
\(812\) 0 0
\(813\) 10.2209 0.358464
\(814\) 6.97850 0.244596
\(815\) 5.20425 0.182297
\(816\) 2.12999 0.0745646
\(817\) 71.6185 2.50561
\(818\) 2.43844 0.0852581
\(819\) 0 0
\(820\) 0.616311 0.0215225
\(821\) −37.2984 −1.30172 −0.650861 0.759197i \(-0.725592\pi\)
−0.650861 + 0.759197i \(0.725592\pi\)
\(822\) 7.54459 0.263148
\(823\) 4.25887 0.148455 0.0742274 0.997241i \(-0.476351\pi\)
0.0742274 + 0.997241i \(0.476351\pi\)
\(824\) 9.44397 0.328996
\(825\) −3.77584 −0.131458
\(826\) 0 0
\(827\) −7.45576 −0.259262 −0.129631 0.991562i \(-0.541379\pi\)
−0.129631 + 0.991562i \(0.541379\pi\)
\(828\) −6.64153 −0.230809
\(829\) −49.3494 −1.71397 −0.856987 0.515338i \(-0.827666\pi\)
−0.856987 + 0.515338i \(0.827666\pi\)
\(830\) −3.06936 −0.106539
\(831\) 0.436938 0.0151572
\(832\) 5.11251 0.177244
\(833\) 0 0
\(834\) 8.75232 0.303068
\(835\) −8.24171 −0.285216
\(836\) 12.8674 0.445029
\(837\) 11.2774 0.389805
\(838\) −4.49210 −0.155177
\(839\) 33.1222 1.14351 0.571753 0.820426i \(-0.306264\pi\)
0.571753 + 0.820426i \(0.306264\pi\)
\(840\) 0 0
\(841\) −12.9209 −0.445547
\(842\) 38.1666 1.31531
\(843\) −14.6279 −0.503811
\(844\) −3.19398 −0.109941
\(845\) 8.09695 0.278543
\(846\) 8.04007 0.276423
\(847\) 0 0
\(848\) −5.83023 −0.200211
\(849\) −9.53280 −0.327165
\(850\) −20.2354 −0.694068
\(851\) 9.98018 0.342116
\(852\) −3.34131 −0.114472
\(853\) 18.9524 0.648917 0.324458 0.945900i \(-0.394818\pi\)
0.324458 + 0.945900i \(0.394818\pi\)
\(854\) 0 0
\(855\) 13.0411 0.445997
\(856\) −19.1366 −0.654077
\(857\) 0.0245596 0.000838940 0 0.000419470 1.00000i \(-0.499866\pi\)
0.000419470 1.00000i \(0.499866\pi\)
\(858\) −4.17822 −0.142642
\(859\) 4.64751 0.158571 0.0792855 0.996852i \(-0.474736\pi\)
0.0792855 + 0.996852i \(0.474736\pi\)
\(860\) −5.76458 −0.196571
\(861\) 0 0
\(862\) 31.1582 1.06125
\(863\) 1.51904 0.0517088 0.0258544 0.999666i \(-0.491769\pi\)
0.0258544 + 0.999666i \(0.491769\pi\)
\(864\) −2.80291 −0.0953568
\(865\) −2.28694 −0.0777581
\(866\) −11.5301 −0.391809
\(867\) −1.06148 −0.0360497
\(868\) 0 0
\(869\) −15.9526 −0.541153
\(870\) 1.20186 0.0407469
\(871\) 64.5773 2.18812
\(872\) −5.33986 −0.180830
\(873\) 43.7835 1.48185
\(874\) 18.4021 0.622460
\(875\) 0 0
\(876\) 2.22990 0.0753412
\(877\) −37.1405 −1.25415 −0.627073 0.778961i \(-0.715747\pi\)
−0.627073 + 0.778961i \(0.715747\pi\)
\(878\) −27.9140 −0.942051
\(879\) −12.5163 −0.422165
\(880\) −1.03570 −0.0349134
\(881\) 27.1593 0.915021 0.457511 0.889204i \(-0.348741\pi\)
0.457511 + 0.889204i \(0.348741\pi\)
\(882\) 0 0
\(883\) −22.3915 −0.753534 −0.376767 0.926308i \(-0.622964\pi\)
−0.376767 + 0.926308i \(0.622964\pi\)
\(884\) −22.3918 −0.753117
\(885\) −3.40065 −0.114311
\(886\) −12.6944 −0.426477
\(887\) −16.7315 −0.561788 −0.280894 0.959739i \(-0.590631\pi\)
−0.280894 + 0.959739i \(0.590631\pi\)
\(888\) 2.01953 0.0677711
\(889\) 0 0
\(890\) 1.36570 0.0457785
\(891\) −11.6413 −0.389999
\(892\) 3.67068 0.122903
\(893\) −22.2771 −0.745475
\(894\) 7.03604 0.235320
\(895\) −3.71417 −0.124151
\(896\) 0 0
\(897\) −5.97540 −0.199513
\(898\) 38.5081 1.28503
\(899\) 16.1336 0.538087
\(900\) 12.7678 0.425593
\(901\) 25.5353 0.850703
\(902\) 1.68048 0.0559539
\(903\) 0 0
\(904\) −7.95104 −0.264448
\(905\) −7.28877 −0.242287
\(906\) 1.04134 0.0345962
\(907\) 10.7326 0.356370 0.178185 0.983997i \(-0.442977\pi\)
0.178185 + 0.983997i \(0.442977\pi\)
\(908\) −9.06526 −0.300841
\(909\) −8.01441 −0.265821
\(910\) 0 0
\(911\) −3.97142 −0.131579 −0.0657896 0.997834i \(-0.520957\pi\)
−0.0657896 + 0.997834i \(0.520957\pi\)
\(912\) 3.72375 0.123306
\(913\) −8.36915 −0.276978
\(914\) 5.36824 0.177566
\(915\) 0.323451 0.0106930
\(916\) −17.0097 −0.562017
\(917\) 0 0
\(918\) 12.2762 0.405174
\(919\) −41.5804 −1.37161 −0.685805 0.727785i \(-0.740550\pi\)
−0.685805 + 0.727785i \(0.740550\pi\)
\(920\) −1.48119 −0.0488333
\(921\) −8.47160 −0.279149
\(922\) −29.6642 −0.976938
\(923\) 35.1260 1.15619
\(924\) 0 0
\(925\) −19.1860 −0.630833
\(926\) −26.0446 −0.855878
\(927\) 26.0983 0.857182
\(928\) −4.00988 −0.131631
\(929\) −45.6831 −1.49881 −0.749406 0.662111i \(-0.769661\pi\)
−0.749406 + 0.662111i \(0.769661\pi\)
\(930\) 1.20594 0.0395442
\(931\) 0 0
\(932\) 4.83435 0.158354
\(933\) 11.1897 0.366334
\(934\) 10.5096 0.343885
\(935\) 4.53616 0.148348
\(936\) 14.1284 0.461801
\(937\) 6.29104 0.205519 0.102760 0.994706i \(-0.467233\pi\)
0.102760 + 0.994706i \(0.467233\pi\)
\(938\) 0 0
\(939\) −3.72791 −0.121656
\(940\) 1.79309 0.0584841
\(941\) 31.8867 1.03948 0.519739 0.854325i \(-0.326029\pi\)
0.519739 + 0.854325i \(0.326029\pi\)
\(942\) −2.61559 −0.0852205
\(943\) 2.40331 0.0782626
\(944\) 11.3459 0.369277
\(945\) 0 0
\(946\) −15.7182 −0.511041
\(947\) −15.3656 −0.499316 −0.249658 0.968334i \(-0.580318\pi\)
−0.249658 + 0.968334i \(0.580318\pi\)
\(948\) −4.61657 −0.149939
\(949\) −23.4421 −0.760962
\(950\) −35.3764 −1.14776
\(951\) 2.00911 0.0651498
\(952\) 0 0
\(953\) 25.8172 0.836301 0.418150 0.908378i \(-0.362679\pi\)
0.418150 + 0.908378i \(0.362679\pi\)
\(954\) −16.1118 −0.521638
\(955\) 4.63733 0.150061
\(956\) 9.41859 0.304619
\(957\) 3.27709 0.105933
\(958\) 10.6171 0.343021
\(959\) 0 0
\(960\) −0.299725 −0.00967358
\(961\) −14.8117 −0.477796
\(962\) −21.2306 −0.684502
\(963\) −52.8840 −1.70416
\(964\) 27.3729 0.881620
\(965\) 1.05980 0.0341161
\(966\) 0 0
\(967\) 18.6448 0.599577 0.299789 0.954006i \(-0.403084\pi\)
0.299789 + 0.954006i \(0.403084\pi\)
\(968\) 8.17598 0.262786
\(969\) −16.3093 −0.523929
\(970\) 9.76454 0.313521
\(971\) −11.2870 −0.362218 −0.181109 0.983463i \(-0.557969\pi\)
−0.181109 + 0.983463i \(0.557969\pi\)
\(972\) −11.7776 −0.377768
\(973\) 0 0
\(974\) −0.350326 −0.0112252
\(975\) 11.4872 0.367885
\(976\) −1.07916 −0.0345431
\(977\) −35.5003 −1.13575 −0.567877 0.823113i \(-0.692235\pi\)
−0.567877 + 0.823113i \(0.692235\pi\)
\(978\) 4.10659 0.131314
\(979\) 3.72383 0.119014
\(980\) 0 0
\(981\) −14.7567 −0.471144
\(982\) 29.9266 0.954997
\(983\) −11.7626 −0.375169 −0.187585 0.982248i \(-0.560066\pi\)
−0.187585 + 0.982248i \(0.560066\pi\)
\(984\) 0.486321 0.0155033
\(985\) 10.7059 0.341118
\(986\) 17.5625 0.559303
\(987\) 0 0
\(988\) −39.1464 −1.24541
\(989\) −22.4790 −0.714792
\(990\) −2.86215 −0.0909650
\(991\) 31.6807 1.00637 0.503185 0.864179i \(-0.332162\pi\)
0.503185 + 0.864179i \(0.332162\pi\)
\(992\) −4.02347 −0.127745
\(993\) 1.90731 0.0605267
\(994\) 0 0
\(995\) 12.3456 0.391383
\(996\) −2.42198 −0.0767433
\(997\) −6.98898 −0.221343 −0.110672 0.993857i \(-0.535300\pi\)
−0.110672 + 0.993857i \(0.535300\pi\)
\(998\) −34.4378 −1.09011
\(999\) 11.6396 0.368260
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 4018.2.a.bo.1.3 6
7.2 even 3 574.2.e.g.165.4 12
7.4 even 3 574.2.e.g.247.4 yes 12
7.6 odd 2 4018.2.a.bn.1.4 6
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
574.2.e.g.165.4 12 7.2 even 3
574.2.e.g.247.4 yes 12 7.4 even 3
4018.2.a.bn.1.4 6 7.6 odd 2
4018.2.a.bo.1.3 6 1.1 even 1 trivial