Properties

Label 4840.2.a.u.1.2
Level $4840$
Weight $2$
Character 4840.1
Self dual yes
Analytic conductor $38.648$
Analytic rank $0$
Dimension $3$
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] = [4840,2,Mod(1,4840)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(4840, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 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("4840.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 4840 = 2^{3} \cdot 5 \cdot 11^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 4840.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: \(38.6475945783\)
Analytic rank: \(0\)
Dimension: \(3\)
Coefficient field: 3.3.404.1
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{3} - x^{2} - 5x - 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.2
Root \(-1.65544\) of defining polynomial
Character \(\chi\) \(=\) 4840.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+1.39593 q^{3} -1.00000 q^{5} -1.65544 q^{7} -1.05137 q^{9} +O(q^{10})\) \(q+1.39593 q^{3} -1.00000 q^{5} -1.65544 q^{7} -1.05137 q^{9} -6.36226 q^{13} -1.39593 q^{15} +5.31088 q^{17} +4.36226 q^{19} -2.31088 q^{21} -5.57040 q^{23} +1.00000 q^{25} -5.65544 q^{27} +6.79186 q^{29} +0.259511 q^{31} +1.65544 q^{35} -0.791864 q^{37} -8.88128 q^{39} +2.74049 q^{41} +11.6554 q^{43} +1.05137 q^{45} +7.49868 q^{47} -4.25951 q^{49} +7.41363 q^{51} -1.84324 q^{53} +6.08942 q^{57} -7.15412 q^{59} -8.57040 q^{61} +1.74049 q^{63} +6.36226 q^{65} +15.6014 q^{67} -7.77589 q^{69} +1.05137 q^{71} +11.6865 q^{73} +1.39593 q^{75} +2.27284 q^{79} -4.74049 q^{81} +7.15412 q^{83} -5.31088 q^{85} +9.48098 q^{87} -8.31088 q^{89} +10.5324 q^{91} +0.362259 q^{93} -4.36226 q^{95} +14.3623 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 3 q + q^{3} - 3 q^{5} + q^{7} + 6 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 3 q + q^{3} - 3 q^{5} + q^{7} + 6 q^{9} + 2 q^{13} - q^{15} + 4 q^{17} - 8 q^{19} + 5 q^{21} - 2 q^{23} + 3 q^{25} - 11 q^{27} + 14 q^{29} - 2 q^{31} - q^{35} + 4 q^{37} + 11 q^{41} + 29 q^{43} - 6 q^{45} + q^{47} - 10 q^{49} - 8 q^{51} + 10 q^{53} - 2 q^{57} + 6 q^{59} - 11 q^{61} + 8 q^{63} - 2 q^{65} + 7 q^{67} + 28 q^{69} - 6 q^{71} + 4 q^{73} + q^{75} + 6 q^{79} - 17 q^{81} - 6 q^{83} - 4 q^{85} + 34 q^{87} - 13 q^{89} + 28 q^{91} - 20 q^{93} + 8 q^{95} + 22 q^{97}+O(q^{100}) \) 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 0
\(3\) 1.39593 0.805942 0.402971 0.915213i \(-0.367978\pi\)
0.402971 + 0.915213i \(0.367978\pi\)
\(4\) 0 0
\(5\) −1.00000 −0.447214
\(6\) 0 0
\(7\) −1.65544 −0.625698 −0.312849 0.949803i \(-0.601283\pi\)
−0.312849 + 0.949803i \(0.601283\pi\)
\(8\) 0 0
\(9\) −1.05137 −0.350458
\(10\) 0 0
\(11\) 0 0
\(12\) 0 0
\(13\) −6.36226 −1.76457 −0.882287 0.470713i \(-0.843997\pi\)
−0.882287 + 0.470713i \(0.843997\pi\)
\(14\) 0 0
\(15\) −1.39593 −0.360428
\(16\) 0 0
\(17\) 5.31088 1.28808 0.644039 0.764992i \(-0.277257\pi\)
0.644039 + 0.764992i \(0.277257\pi\)
\(18\) 0 0
\(19\) 4.36226 1.00077 0.500385 0.865803i \(-0.333192\pi\)
0.500385 + 0.865803i \(0.333192\pi\)
\(20\) 0 0
\(21\) −2.31088 −0.504276
\(22\) 0 0
\(23\) −5.57040 −1.16151 −0.580754 0.814079i \(-0.697242\pi\)
−0.580754 + 0.814079i \(0.697242\pi\)
\(24\) 0 0
\(25\) 1.00000 0.200000
\(26\) 0 0
\(27\) −5.65544 −1.08839
\(28\) 0 0
\(29\) 6.79186 1.26122 0.630609 0.776101i \(-0.282805\pi\)
0.630609 + 0.776101i \(0.282805\pi\)
\(30\) 0 0
\(31\) 0.259511 0.0466095 0.0233047 0.999728i \(-0.492581\pi\)
0.0233047 + 0.999728i \(0.492581\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) 1.65544 0.279821
\(36\) 0 0
\(37\) −0.791864 −0.130182 −0.0650908 0.997879i \(-0.520734\pi\)
−0.0650908 + 0.997879i \(0.520734\pi\)
\(38\) 0 0
\(39\) −8.88128 −1.42214
\(40\) 0 0
\(41\) 2.74049 0.427993 0.213996 0.976834i \(-0.431352\pi\)
0.213996 + 0.976834i \(0.431352\pi\)
\(42\) 0 0
\(43\) 11.6554 1.77744 0.888719 0.458452i \(-0.151596\pi\)
0.888719 + 0.458452i \(0.151596\pi\)
\(44\) 0 0
\(45\) 1.05137 0.156730
\(46\) 0 0
\(47\) 7.49868 1.09379 0.546897 0.837200i \(-0.315809\pi\)
0.546897 + 0.837200i \(0.315809\pi\)
\(48\) 0 0
\(49\) −4.25951 −0.608502
\(50\) 0 0
\(51\) 7.41363 1.03812
\(52\) 0 0
\(53\) −1.84324 −0.253188 −0.126594 0.991955i \(-0.540405\pi\)
−0.126594 + 0.991955i \(0.540405\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 0 0
\(57\) 6.08942 0.806563
\(58\) 0 0
\(59\) −7.15412 −0.931387 −0.465694 0.884946i \(-0.654195\pi\)
−0.465694 + 0.884946i \(0.654195\pi\)
\(60\) 0 0
\(61\) −8.57040 −1.09733 −0.548663 0.836043i \(-0.684863\pi\)
−0.548663 + 0.836043i \(0.684863\pi\)
\(62\) 0 0
\(63\) 1.74049 0.219281
\(64\) 0 0
\(65\) 6.36226 0.789141
\(66\) 0 0
\(67\) 15.6014 1.90602 0.953009 0.302942i \(-0.0979689\pi\)
0.953009 + 0.302942i \(0.0979689\pi\)
\(68\) 0 0
\(69\) −7.77589 −0.936107
\(70\) 0 0
\(71\) 1.05137 0.124775 0.0623876 0.998052i \(-0.480129\pi\)
0.0623876 + 0.998052i \(0.480129\pi\)
\(72\) 0 0
\(73\) 11.6865 1.36780 0.683899 0.729576i \(-0.260283\pi\)
0.683899 + 0.729576i \(0.260283\pi\)
\(74\) 0 0
\(75\) 1.39593 0.161188
\(76\) 0 0
\(77\) 0 0
\(78\) 0 0
\(79\) 2.27284 0.255715 0.127857 0.991793i \(-0.459190\pi\)
0.127857 + 0.991793i \(0.459190\pi\)
\(80\) 0 0
\(81\) −4.74049 −0.526721
\(82\) 0 0
\(83\) 7.15412 0.785267 0.392633 0.919695i \(-0.371564\pi\)
0.392633 + 0.919695i \(0.371564\pi\)
\(84\) 0 0
\(85\) −5.31088 −0.576046
\(86\) 0 0
\(87\) 9.48098 1.01647
\(88\) 0 0
\(89\) −8.31088 −0.880952 −0.440476 0.897764i \(-0.645190\pi\)
−0.440476 + 0.897764i \(0.645190\pi\)
\(90\) 0 0
\(91\) 10.5324 1.10409
\(92\) 0 0
\(93\) 0.362259 0.0375645
\(94\) 0 0
\(95\) −4.36226 −0.447558
\(96\) 0 0
\(97\) 14.3623 1.45827 0.729133 0.684372i \(-0.239923\pi\)
0.729133 + 0.684372i \(0.239923\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) −3.79186 −0.377305 −0.188652 0.982044i \(-0.560412\pi\)
−0.188652 + 0.982044i \(0.560412\pi\)
\(102\) 0 0
\(103\) 9.77589 0.963247 0.481624 0.876378i \(-0.340047\pi\)
0.481624 + 0.876378i \(0.340047\pi\)
\(104\) 0 0
\(105\) 2.31088 0.225519
\(106\) 0 0
\(107\) −14.9123 −1.44163 −0.720814 0.693129i \(-0.756232\pi\)
−0.720814 + 0.693129i \(0.756232\pi\)
\(108\) 0 0
\(109\) 10.1541 0.972589 0.486294 0.873795i \(-0.338348\pi\)
0.486294 + 0.873795i \(0.338348\pi\)
\(110\) 0 0
\(111\) −1.10539 −0.104919
\(112\) 0 0
\(113\) 12.6218 1.18736 0.593678 0.804703i \(-0.297675\pi\)
0.593678 + 0.804703i \(0.297675\pi\)
\(114\) 0 0
\(115\) 5.57040 0.519442
\(116\) 0 0
\(117\) 6.68912 0.618409
\(118\) 0 0
\(119\) −8.79186 −0.805949
\(120\) 0 0
\(121\) 0 0
\(122\) 0 0
\(123\) 3.82554 0.344937
\(124\) 0 0
\(125\) −1.00000 −0.0894427
\(126\) 0 0
\(127\) −1.29318 −0.114751 −0.0573757 0.998353i \(-0.518273\pi\)
−0.0573757 + 0.998353i \(0.518273\pi\)
\(128\) 0 0
\(129\) 16.2702 1.43251
\(130\) 0 0
\(131\) 5.74049 0.501549 0.250774 0.968046i \(-0.419315\pi\)
0.250774 + 0.968046i \(0.419315\pi\)
\(132\) 0 0
\(133\) −7.22147 −0.626181
\(134\) 0 0
\(135\) 5.65544 0.486743
\(136\) 0 0
\(137\) −10.1161 −0.864275 −0.432138 0.901808i \(-0.642241\pi\)
−0.432138 + 0.901808i \(0.642241\pi\)
\(138\) 0 0
\(139\) 5.84324 0.495617 0.247808 0.968809i \(-0.420290\pi\)
0.247808 + 0.968809i \(0.420290\pi\)
\(140\) 0 0
\(141\) 10.4676 0.881535
\(142\) 0 0
\(143\) 0 0
\(144\) 0 0
\(145\) −6.79186 −0.564034
\(146\) 0 0
\(147\) −5.94599 −0.490417
\(148\) 0 0
\(149\) 22.0868 1.80942 0.904710 0.426029i \(-0.140088\pi\)
0.904710 + 0.426029i \(0.140088\pi\)
\(150\) 0 0
\(151\) 7.46765 0.607708 0.303854 0.952719i \(-0.401726\pi\)
0.303854 + 0.952719i \(0.401726\pi\)
\(152\) 0 0
\(153\) −5.58373 −0.451418
\(154\) 0 0
\(155\) −0.259511 −0.0208444
\(156\) 0 0
\(157\) 11.1408 0.889132 0.444566 0.895746i \(-0.353358\pi\)
0.444566 + 0.895746i \(0.353358\pi\)
\(158\) 0 0
\(159\) −2.57303 −0.204055
\(160\) 0 0
\(161\) 9.22147 0.726754
\(162\) 0 0
\(163\) −8.55005 −0.669692 −0.334846 0.942273i \(-0.608684\pi\)
−0.334846 + 0.942273i \(0.608684\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 10.0717 0.779373 0.389686 0.920948i \(-0.372583\pi\)
0.389686 + 0.920948i \(0.372583\pi\)
\(168\) 0 0
\(169\) 27.4783 2.11372
\(170\) 0 0
\(171\) −4.58637 −0.350728
\(172\) 0 0
\(173\) 12.7785 0.971534 0.485767 0.874088i \(-0.338540\pi\)
0.485767 + 0.874088i \(0.338540\pi\)
\(174\) 0 0
\(175\) −1.65544 −0.125140
\(176\) 0 0
\(177\) −9.98667 −0.750644
\(178\) 0 0
\(179\) 12.1027 0.904602 0.452301 0.891865i \(-0.350603\pi\)
0.452301 + 0.891865i \(0.350603\pi\)
\(180\) 0 0
\(181\) −19.1382 −1.42253 −0.711264 0.702925i \(-0.751877\pi\)
−0.711264 + 0.702925i \(0.751877\pi\)
\(182\) 0 0
\(183\) −11.9637 −0.884381
\(184\) 0 0
\(185\) 0.791864 0.0582190
\(186\) 0 0
\(187\) 0 0
\(188\) 0 0
\(189\) 9.36226 0.681004
\(190\) 0 0
\(191\) −12.0894 −0.874759 −0.437380 0.899277i \(-0.644093\pi\)
−0.437380 + 0.899277i \(0.644093\pi\)
\(192\) 0 0
\(193\) −13.6191 −0.980326 −0.490163 0.871631i \(-0.663063\pi\)
−0.490163 + 0.871631i \(0.663063\pi\)
\(194\) 0 0
\(195\) 8.88128 0.636002
\(196\) 0 0
\(197\) 14.7919 1.05388 0.526938 0.849904i \(-0.323340\pi\)
0.526938 + 0.849904i \(0.323340\pi\)
\(198\) 0 0
\(199\) −17.6865 −1.25376 −0.626881 0.779115i \(-0.715669\pi\)
−0.626881 + 0.779115i \(0.715669\pi\)
\(200\) 0 0
\(201\) 21.7785 1.53614
\(202\) 0 0
\(203\) −11.2435 −0.789142
\(204\) 0 0
\(205\) −2.74049 −0.191404
\(206\) 0 0
\(207\) 5.85657 0.407060
\(208\) 0 0
\(209\) 0 0
\(210\) 0 0
\(211\) 27.0868 1.86473 0.932365 0.361518i \(-0.117741\pi\)
0.932365 + 0.361518i \(0.117741\pi\)
\(212\) 0 0
\(213\) 1.46765 0.100562
\(214\) 0 0
\(215\) −11.6554 −0.794895
\(216\) 0 0
\(217\) −0.429605 −0.0291635
\(218\) 0 0
\(219\) 16.3135 1.10237
\(220\) 0 0
\(221\) −33.7892 −2.27291
\(222\) 0 0
\(223\) −8.69348 −0.582159 −0.291079 0.956699i \(-0.594014\pi\)
−0.291079 + 0.956699i \(0.594014\pi\)
\(224\) 0 0
\(225\) −1.05137 −0.0700916
\(226\) 0 0
\(227\) −3.40926 −0.226281 −0.113140 0.993579i \(-0.536091\pi\)
−0.113140 + 0.993579i \(0.536091\pi\)
\(228\) 0 0
\(229\) 13.3489 0.882122 0.441061 0.897477i \(-0.354602\pi\)
0.441061 + 0.897477i \(0.354602\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 14.6351 0.958777 0.479389 0.877603i \(-0.340858\pi\)
0.479389 + 0.877603i \(0.340858\pi\)
\(234\) 0 0
\(235\) −7.49868 −0.489160
\(236\) 0 0
\(237\) 3.17273 0.206091
\(238\) 0 0
\(239\) −8.36226 −0.540910 −0.270455 0.962733i \(-0.587174\pi\)
−0.270455 + 0.962733i \(0.587174\pi\)
\(240\) 0 0
\(241\) −11.0487 −0.711712 −0.355856 0.934541i \(-0.615811\pi\)
−0.355856 + 0.934541i \(0.615811\pi\)
\(242\) 0 0
\(243\) 10.3489 0.663884
\(244\) 0 0
\(245\) 4.25951 0.272130
\(246\) 0 0
\(247\) −27.7538 −1.76593
\(248\) 0 0
\(249\) 9.98667 0.632879
\(250\) 0 0
\(251\) −13.5704 −0.856556 −0.428278 0.903647i \(-0.640880\pi\)
−0.428278 + 0.903647i \(0.640880\pi\)
\(252\) 0 0
\(253\) 0 0
\(254\) 0 0
\(255\) −7.41363 −0.464260
\(256\) 0 0
\(257\) −0.881280 −0.0549727 −0.0274864 0.999622i \(-0.508750\pi\)
−0.0274864 + 0.999622i \(0.508750\pi\)
\(258\) 0 0
\(259\) 1.31088 0.0814544
\(260\) 0 0
\(261\) −7.14079 −0.442004
\(262\) 0 0
\(263\) 14.3623 0.885615 0.442807 0.896617i \(-0.353983\pi\)
0.442807 + 0.896617i \(0.353983\pi\)
\(264\) 0 0
\(265\) 1.84324 0.113229
\(266\) 0 0
\(267\) −11.6014 −0.709996
\(268\) 0 0
\(269\) 11.2188 0.684024 0.342012 0.939696i \(-0.388892\pi\)
0.342012 + 0.939696i \(0.388892\pi\)
\(270\) 0 0
\(271\) −14.3756 −0.873255 −0.436627 0.899642i \(-0.643827\pi\)
−0.436627 + 0.899642i \(0.643827\pi\)
\(272\) 0 0
\(273\) 14.7024 0.889833
\(274\) 0 0
\(275\) 0 0
\(276\) 0 0
\(277\) −31.2029 −1.87480 −0.937399 0.348257i \(-0.886774\pi\)
−0.937399 + 0.348257i \(0.886774\pi\)
\(278\) 0 0
\(279\) −0.272843 −0.0163347
\(280\) 0 0
\(281\) −17.1675 −1.02412 −0.512062 0.858948i \(-0.671118\pi\)
−0.512062 + 0.858948i \(0.671118\pi\)
\(282\) 0 0
\(283\) −11.9150 −0.708270 −0.354135 0.935194i \(-0.615225\pi\)
−0.354135 + 0.935194i \(0.615225\pi\)
\(284\) 0 0
\(285\) −6.08942 −0.360706
\(286\) 0 0
\(287\) −4.53672 −0.267794
\(288\) 0 0
\(289\) 11.2055 0.659147
\(290\) 0 0
\(291\) 20.0487 1.17528
\(292\) 0 0
\(293\) 10.5324 0.615307 0.307653 0.951499i \(-0.400456\pi\)
0.307653 + 0.951499i \(0.400456\pi\)
\(294\) 0 0
\(295\) 7.15412 0.416529
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 35.4403 2.04957
\(300\) 0 0
\(301\) −19.2949 −1.11214
\(302\) 0 0
\(303\) −5.29318 −0.304085
\(304\) 0 0
\(305\) 8.57040 0.490739
\(306\) 0 0
\(307\) 11.1541 0.636599 0.318300 0.947990i \(-0.396888\pi\)
0.318300 + 0.947990i \(0.396888\pi\)
\(308\) 0 0
\(309\) 13.6465 0.776321
\(310\) 0 0
\(311\) −10.9840 −0.622847 −0.311424 0.950271i \(-0.600806\pi\)
−0.311424 + 0.950271i \(0.600806\pi\)
\(312\) 0 0
\(313\) 12.3977 0.700757 0.350379 0.936608i \(-0.386053\pi\)
0.350379 + 0.936608i \(0.386053\pi\)
\(314\) 0 0
\(315\) −1.74049 −0.0980655
\(316\) 0 0
\(317\) 6.54569 0.367642 0.183821 0.982960i \(-0.441153\pi\)
0.183821 + 0.982960i \(0.441153\pi\)
\(318\) 0 0
\(319\) 0 0
\(320\) 0 0
\(321\) −20.8166 −1.16187
\(322\) 0 0
\(323\) 23.1675 1.28907
\(324\) 0 0
\(325\) −6.36226 −0.352915
\(326\) 0 0
\(327\) 14.1745 0.783850
\(328\) 0 0
\(329\) −12.4136 −0.684386
\(330\) 0 0
\(331\) −29.8786 −1.64228 −0.821139 0.570728i \(-0.806661\pi\)
−0.821139 + 0.570728i \(0.806661\pi\)
\(332\) 0 0
\(333\) 0.832545 0.0456232
\(334\) 0 0
\(335\) −15.6014 −0.852397
\(336\) 0 0
\(337\) 3.19480 0.174032 0.0870160 0.996207i \(-0.472267\pi\)
0.0870160 + 0.996207i \(0.472267\pi\)
\(338\) 0 0
\(339\) 17.6191 0.956940
\(340\) 0 0
\(341\) 0 0
\(342\) 0 0
\(343\) 18.6395 1.00644
\(344\) 0 0
\(345\) 7.77589 0.418640
\(346\) 0 0
\(347\) −21.3773 −1.14759 −0.573797 0.818997i \(-0.694530\pi\)
−0.573797 + 0.818997i \(0.694530\pi\)
\(348\) 0 0
\(349\) −0.894612 −0.0478875 −0.0239437 0.999713i \(-0.507622\pi\)
−0.0239437 + 0.999713i \(0.507622\pi\)
\(350\) 0 0
\(351\) 35.9814 1.92054
\(352\) 0 0
\(353\) −7.05137 −0.375307 −0.187653 0.982235i \(-0.560088\pi\)
−0.187653 + 0.982235i \(0.560088\pi\)
\(354\) 0 0
\(355\) −1.05137 −0.0558012
\(356\) 0 0
\(357\) −12.2728 −0.649548
\(358\) 0 0
\(359\) 10.5324 0.555876 0.277938 0.960599i \(-0.410349\pi\)
0.277938 + 0.960599i \(0.410349\pi\)
\(360\) 0 0
\(361\) 0.0293036 0.00154230
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) −11.6865 −0.611698
\(366\) 0 0
\(367\) 33.5341 1.75046 0.875232 0.483703i \(-0.160708\pi\)
0.875232 + 0.483703i \(0.160708\pi\)
\(368\) 0 0
\(369\) −2.88128 −0.149993
\(370\) 0 0
\(371\) 3.05137 0.158419
\(372\) 0 0
\(373\) 10.1922 0.527730 0.263865 0.964560i \(-0.415003\pi\)
0.263865 + 0.964560i \(0.415003\pi\)
\(374\) 0 0
\(375\) −1.39593 −0.0720856
\(376\) 0 0
\(377\) −43.2116 −2.22551
\(378\) 0 0
\(379\) −0.170094 −0.00873715 −0.00436858 0.999990i \(-0.501391\pi\)
−0.00436858 + 0.999990i \(0.501391\pi\)
\(380\) 0 0
\(381\) −1.80520 −0.0924830
\(382\) 0 0
\(383\) −12.8052 −0.654315 −0.327157 0.944970i \(-0.606091\pi\)
−0.327157 + 0.944970i \(0.606091\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) −12.2542 −0.622918
\(388\) 0 0
\(389\) 30.1134 1.52681 0.763406 0.645919i \(-0.223526\pi\)
0.763406 + 0.645919i \(0.223526\pi\)
\(390\) 0 0
\(391\) −29.5837 −1.49611
\(392\) 0 0
\(393\) 8.01333 0.404219
\(394\) 0 0
\(395\) −2.27284 −0.114359
\(396\) 0 0
\(397\) −10.1027 −0.507042 −0.253521 0.967330i \(-0.581589\pi\)
−0.253521 + 0.967330i \(0.581589\pi\)
\(398\) 0 0
\(399\) −10.0807 −0.504665
\(400\) 0 0
\(401\) 36.2435 1.80992 0.904958 0.425501i \(-0.139902\pi\)
0.904958 + 0.425501i \(0.139902\pi\)
\(402\) 0 0
\(403\) −1.65107 −0.0822458
\(404\) 0 0
\(405\) 4.74049 0.235557
\(406\) 0 0
\(407\) 0 0
\(408\) 0 0
\(409\) 12.9460 0.640138 0.320069 0.947394i \(-0.396294\pi\)
0.320069 + 0.947394i \(0.396294\pi\)
\(410\) 0 0
\(411\) −14.1214 −0.696555
\(412\) 0 0
\(413\) 11.8432 0.582768
\(414\) 0 0
\(415\) −7.15412 −0.351182
\(416\) 0 0
\(417\) 8.15676 0.399438
\(418\) 0 0
\(419\) −22.2188 −1.08546 −0.542730 0.839907i \(-0.682609\pi\)
−0.542730 + 0.839907i \(0.682609\pi\)
\(420\) 0 0
\(421\) 27.3623 1.33355 0.666777 0.745257i \(-0.267673\pi\)
0.666777 + 0.745257i \(0.267673\pi\)
\(422\) 0 0
\(423\) −7.88392 −0.383329
\(424\) 0 0
\(425\) 5.31088 0.257616
\(426\) 0 0
\(427\) 14.1878 0.686596
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) −34.1382 −1.64438 −0.822188 0.569215i \(-0.807247\pi\)
−0.822188 + 0.569215i \(0.807247\pi\)
\(432\) 0 0
\(433\) 3.63774 0.174819 0.0874093 0.996172i \(-0.472141\pi\)
0.0874093 + 0.996172i \(0.472141\pi\)
\(434\) 0 0
\(435\) −9.48098 −0.454578
\(436\) 0 0
\(437\) −24.2995 −1.16240
\(438\) 0 0
\(439\) −18.0621 −0.862055 −0.431028 0.902339i \(-0.641849\pi\)
−0.431028 + 0.902339i \(0.641849\pi\)
\(440\) 0 0
\(441\) 4.47834 0.213254
\(442\) 0 0
\(443\) 40.3126 1.91531 0.957655 0.287918i \(-0.0929631\pi\)
0.957655 + 0.287918i \(0.0929631\pi\)
\(444\) 0 0
\(445\) 8.31088 0.393974
\(446\) 0 0
\(447\) 30.8316 1.45829
\(448\) 0 0
\(449\) 10.8839 0.513644 0.256822 0.966459i \(-0.417325\pi\)
0.256822 + 0.966459i \(0.417325\pi\)
\(450\) 0 0
\(451\) 0 0
\(452\) 0 0
\(453\) 10.4243 0.489778
\(454\) 0 0
\(455\) −10.5324 −0.493764
\(456\) 0 0
\(457\) 38.6438 1.80768 0.903841 0.427868i \(-0.140735\pi\)
0.903841 + 0.427868i \(0.140735\pi\)
\(458\) 0 0
\(459\) −30.0354 −1.40193
\(460\) 0 0
\(461\) −25.6891 −1.19646 −0.598231 0.801324i \(-0.704129\pi\)
−0.598231 + 0.801324i \(0.704129\pi\)
\(462\) 0 0
\(463\) −2.41190 −0.112091 −0.0560453 0.998428i \(-0.517849\pi\)
−0.0560453 + 0.998428i \(0.517849\pi\)
\(464\) 0 0
\(465\) −0.362259 −0.0167994
\(466\) 0 0
\(467\) −39.8423 −1.84368 −0.921842 0.387567i \(-0.873316\pi\)
−0.921842 + 0.387567i \(0.873316\pi\)
\(468\) 0 0
\(469\) −25.8273 −1.19259
\(470\) 0 0
\(471\) 15.5518 0.716588
\(472\) 0 0
\(473\) 0 0
\(474\) 0 0
\(475\) 4.36226 0.200154
\(476\) 0 0
\(477\) 1.93793 0.0887319
\(478\) 0 0
\(479\) 26.4517 1.20861 0.604304 0.796754i \(-0.293451\pi\)
0.604304 + 0.796754i \(0.293451\pi\)
\(480\) 0 0
\(481\) 5.03804 0.229715
\(482\) 0 0
\(483\) 12.8725 0.585721
\(484\) 0 0
\(485\) −14.3623 −0.652157
\(486\) 0 0
\(487\) −28.5324 −1.29292 −0.646462 0.762946i \(-0.723752\pi\)
−0.646462 + 0.762946i \(0.723752\pi\)
\(488\) 0 0
\(489\) −11.9353 −0.539733
\(490\) 0 0
\(491\) −28.0354 −1.26522 −0.632610 0.774471i \(-0.718016\pi\)
−0.632610 + 0.774471i \(0.718016\pi\)
\(492\) 0 0
\(493\) 36.0708 1.62455
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) −1.74049 −0.0780716
\(498\) 0 0
\(499\) −31.0380 −1.38945 −0.694727 0.719274i \(-0.744475\pi\)
−0.694727 + 0.719274i \(0.744475\pi\)
\(500\) 0 0
\(501\) 14.0594 0.628129
\(502\) 0 0
\(503\) 37.0505 1.65200 0.825999 0.563671i \(-0.190611\pi\)
0.825999 + 0.563671i \(0.190611\pi\)
\(504\) 0 0
\(505\) 3.79186 0.168736
\(506\) 0 0
\(507\) 38.3579 1.70353
\(508\) 0 0
\(509\) 36.7219 1.62767 0.813834 0.581097i \(-0.197376\pi\)
0.813834 + 0.581097i \(0.197376\pi\)
\(510\) 0 0
\(511\) −19.3463 −0.855829
\(512\) 0 0
\(513\) −24.6705 −1.08923
\(514\) 0 0
\(515\) −9.77589 −0.430777
\(516\) 0 0
\(517\) 0 0
\(518\) 0 0
\(519\) 17.8380 0.783000
\(520\) 0 0
\(521\) 23.6572 1.03644 0.518220 0.855247i \(-0.326595\pi\)
0.518220 + 0.855247i \(0.326595\pi\)
\(522\) 0 0
\(523\) −16.7785 −0.733674 −0.366837 0.930285i \(-0.619559\pi\)
−0.366837 + 0.930285i \(0.619559\pi\)
\(524\) 0 0
\(525\) −2.31088 −0.100855
\(526\) 0 0
\(527\) 1.37823 0.0600367
\(528\) 0 0
\(529\) 8.02930 0.349100
\(530\) 0 0
\(531\) 7.52166 0.326412
\(532\) 0 0
\(533\) −17.4357 −0.755224
\(534\) 0 0
\(535\) 14.9123 0.644716
\(536\) 0 0
\(537\) 16.8946 0.729056
\(538\) 0 0
\(539\) 0 0
\(540\) 0 0
\(541\) −5.75646 −0.247490 −0.123745 0.992314i \(-0.539490\pi\)
−0.123745 + 0.992314i \(0.539490\pi\)
\(542\) 0 0
\(543\) −26.7156 −1.14647
\(544\) 0 0
\(545\) −10.1541 −0.434955
\(546\) 0 0
\(547\) −10.9486 −0.468129 −0.234065 0.972221i \(-0.575203\pi\)
−0.234065 + 0.972221i \(0.575203\pi\)
\(548\) 0 0
\(549\) 9.01069 0.384567
\(550\) 0 0
\(551\) 29.6279 1.26219
\(552\) 0 0
\(553\) −3.76256 −0.160000
\(554\) 0 0
\(555\) 1.10539 0.0469211
\(556\) 0 0
\(557\) −1.82991 −0.0775356 −0.0387678 0.999248i \(-0.512343\pi\)
−0.0387678 + 0.999248i \(0.512343\pi\)
\(558\) 0 0
\(559\) −74.1549 −3.13642
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) −1.61476 −0.0680541 −0.0340270 0.999421i \(-0.510833\pi\)
−0.0340270 + 0.999421i \(0.510833\pi\)
\(564\) 0 0
\(565\) −12.6218 −0.531002
\(566\) 0 0
\(567\) 7.84761 0.329569
\(568\) 0 0
\(569\) 23.4296 0.982220 0.491110 0.871098i \(-0.336591\pi\)
0.491110 + 0.871098i \(0.336591\pi\)
\(570\) 0 0
\(571\) −30.1382 −1.26124 −0.630621 0.776091i \(-0.717200\pi\)
−0.630621 + 0.776091i \(0.717200\pi\)
\(572\) 0 0
\(573\) −16.8760 −0.705005
\(574\) 0 0
\(575\) −5.57040 −0.232302
\(576\) 0 0
\(577\) −37.5651 −1.56386 −0.781928 0.623369i \(-0.785764\pi\)
−0.781928 + 0.623369i \(0.785764\pi\)
\(578\) 0 0
\(579\) −19.0114 −0.790086
\(580\) 0 0
\(581\) −11.8432 −0.491340
\(582\) 0 0
\(583\) 0 0
\(584\) 0 0
\(585\) −6.68912 −0.276561
\(586\) 0 0
\(587\) 24.7962 1.02345 0.511725 0.859149i \(-0.329007\pi\)
0.511725 + 0.859149i \(0.329007\pi\)
\(588\) 0 0
\(589\) 1.13205 0.0466454
\(590\) 0 0
\(591\) 20.6484 0.849363
\(592\) 0 0
\(593\) −46.2542 −1.89943 −0.949717 0.313110i \(-0.898629\pi\)
−0.949717 + 0.313110i \(0.898629\pi\)
\(594\) 0 0
\(595\) 8.79186 0.360431
\(596\) 0 0
\(597\) −24.6891 −1.01046
\(598\) 0 0
\(599\) −3.01069 −0.123014 −0.0615068 0.998107i \(-0.519591\pi\)
−0.0615068 + 0.998107i \(0.519591\pi\)
\(600\) 0 0
\(601\) −5.52166 −0.225233 −0.112617 0.993639i \(-0.535923\pi\)
−0.112617 + 0.993639i \(0.535923\pi\)
\(602\) 0 0
\(603\) −16.4029 −0.667979
\(604\) 0 0
\(605\) 0 0
\(606\) 0 0
\(607\) 14.3356 0.581864 0.290932 0.956744i \(-0.406035\pi\)
0.290932 + 0.956744i \(0.406035\pi\)
\(608\) 0 0
\(609\) −15.6952 −0.636002
\(610\) 0 0
\(611\) −47.7085 −1.93008
\(612\) 0 0
\(613\) −41.3056 −1.66832 −0.834159 0.551524i \(-0.814046\pi\)
−0.834159 + 0.551524i \(0.814046\pi\)
\(614\) 0 0
\(615\) −3.82554 −0.154261
\(616\) 0 0
\(617\) 40.1869 1.61786 0.808932 0.587903i \(-0.200046\pi\)
0.808932 + 0.587903i \(0.200046\pi\)
\(618\) 0 0
\(619\) −47.3463 −1.90301 −0.951504 0.307636i \(-0.900462\pi\)
−0.951504 + 0.307636i \(0.900462\pi\)
\(620\) 0 0
\(621\) 31.5030 1.26417
\(622\) 0 0
\(623\) 13.7582 0.551210
\(624\) 0 0
\(625\) 1.00000 0.0400000
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) −4.20550 −0.167684
\(630\) 0 0
\(631\) −33.9681 −1.35225 −0.676124 0.736788i \(-0.736341\pi\)
−0.676124 + 0.736788i \(0.736341\pi\)
\(632\) 0 0
\(633\) 37.8113 1.50286
\(634\) 0 0
\(635\) 1.29318 0.0513184
\(636\) 0 0
\(637\) 27.1001 1.07375
\(638\) 0 0
\(639\) −1.10539 −0.0437285
\(640\) 0 0
\(641\) 24.3082 0.960118 0.480059 0.877236i \(-0.340615\pi\)
0.480059 + 0.877236i \(0.340615\pi\)
\(642\) 0 0
\(643\) 38.6209 1.52306 0.761529 0.648131i \(-0.224449\pi\)
0.761529 + 0.648131i \(0.224449\pi\)
\(644\) 0 0
\(645\) −16.2702 −0.640639
\(646\) 0 0
\(647\) −34.9663 −1.37467 −0.687334 0.726341i \(-0.741219\pi\)
−0.687334 + 0.726341i \(0.741219\pi\)
\(648\) 0 0
\(649\) 0 0
\(650\) 0 0
\(651\) −0.599699 −0.0235041
\(652\) 0 0
\(653\) −9.44030 −0.369427 −0.184714 0.982792i \(-0.559136\pi\)
−0.184714 + 0.982792i \(0.559136\pi\)
\(654\) 0 0
\(655\) −5.74049 −0.224299
\(656\) 0 0
\(657\) −12.2869 −0.479356
\(658\) 0 0
\(659\) 14.7652 0.575171 0.287585 0.957755i \(-0.407148\pi\)
0.287585 + 0.957755i \(0.407148\pi\)
\(660\) 0 0
\(661\) −8.32422 −0.323775 −0.161887 0.986809i \(-0.551758\pi\)
−0.161887 + 0.986809i \(0.551758\pi\)
\(662\) 0 0
\(663\) −47.1675 −1.83183
\(664\) 0 0
\(665\) 7.22147 0.280037
\(666\) 0 0
\(667\) −37.8334 −1.46491
\(668\) 0 0
\(669\) −12.1355 −0.469186
\(670\) 0 0
\(671\) 0 0
\(672\) 0 0
\(673\) 0.388923 0.0149919 0.00749595 0.999972i \(-0.497614\pi\)
0.00749595 + 0.999972i \(0.497614\pi\)
\(674\) 0 0
\(675\) −5.65544 −0.217678
\(676\) 0 0
\(677\) 41.5837 1.59819 0.799096 0.601203i \(-0.205312\pi\)
0.799096 + 0.601203i \(0.205312\pi\)
\(678\) 0 0
\(679\) −23.7759 −0.912435
\(680\) 0 0
\(681\) −4.75910 −0.182369
\(682\) 0 0
\(683\) −13.3153 −0.509494 −0.254747 0.967008i \(-0.581992\pi\)
−0.254747 + 0.967008i \(0.581992\pi\)
\(684\) 0 0
\(685\) 10.1161 0.386516
\(686\) 0 0
\(687\) 18.6342 0.710939
\(688\) 0 0
\(689\) 11.7272 0.446769
\(690\) 0 0
\(691\) 3.54373 0.134810 0.0674049 0.997726i \(-0.478528\pi\)
0.0674049 + 0.997726i \(0.478528\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) −5.84324 −0.221647
\(696\) 0 0
\(697\) 14.5544 0.551288
\(698\) 0 0
\(699\) 20.4296 0.772719
\(700\) 0 0
\(701\) 24.3489 0.919646 0.459823 0.888011i \(-0.347913\pi\)
0.459823 + 0.888011i \(0.347913\pi\)
\(702\) 0 0
\(703\) −3.45431 −0.130282
\(704\) 0 0
\(705\) −10.4676 −0.394234
\(706\) 0 0
\(707\) 6.27721 0.236079
\(708\) 0 0
\(709\) 21.6484 0.813024 0.406512 0.913645i \(-0.366745\pi\)
0.406512 + 0.913645i \(0.366745\pi\)
\(710\) 0 0
\(711\) −2.38961 −0.0896173
\(712\) 0 0
\(713\) −1.44558 −0.0541373
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) −11.6731 −0.435942
\(718\) 0 0
\(719\) 35.2302 1.31387 0.656933 0.753949i \(-0.271854\pi\)
0.656933 + 0.753949i \(0.271854\pi\)
\(720\) 0 0
\(721\) −16.1834 −0.602702
\(722\) 0 0
\(723\) −15.4233 −0.573598
\(724\) 0 0
\(725\) 6.79186 0.252243
\(726\) 0 0
\(727\) 22.3446 0.828714 0.414357 0.910114i \(-0.364007\pi\)
0.414357 + 0.910114i \(0.364007\pi\)
\(728\) 0 0
\(729\) 28.6679 1.06177
\(730\) 0 0
\(731\) 61.9007 2.28948
\(732\) 0 0
\(733\) 51.5111 1.90261 0.951303 0.308257i \(-0.0997458\pi\)
0.951303 + 0.308257i \(0.0997458\pi\)
\(734\) 0 0
\(735\) 5.94599 0.219321
\(736\) 0 0
\(737\) 0 0
\(738\) 0 0
\(739\) −15.7219 −0.578339 −0.289169 0.957278i \(-0.593379\pi\)
−0.289169 + 0.957278i \(0.593379\pi\)
\(740\) 0 0
\(741\) −38.7424 −1.42324
\(742\) 0 0
\(743\) 22.6041 0.829263 0.414631 0.909989i \(-0.363911\pi\)
0.414631 + 0.909989i \(0.363911\pi\)
\(744\) 0 0
\(745\) −22.0868 −0.809197
\(746\) 0 0
\(747\) −7.52166 −0.275203
\(748\) 0 0
\(749\) 24.6865 0.902024
\(750\) 0 0
\(751\) 27.4490 1.00163 0.500815 0.865554i \(-0.333034\pi\)
0.500815 + 0.865554i \(0.333034\pi\)
\(752\) 0 0
\(753\) −18.9433 −0.690334
\(754\) 0 0
\(755\) −7.46765 −0.271775
\(756\) 0 0
\(757\) 13.5704 0.493224 0.246612 0.969114i \(-0.420683\pi\)
0.246612 + 0.969114i \(0.420683\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 27.7892 1.00736 0.503679 0.863891i \(-0.331979\pi\)
0.503679 + 0.863891i \(0.331979\pi\)
\(762\) 0 0
\(763\) −16.8096 −0.608547
\(764\) 0 0
\(765\) 5.58373 0.201880
\(766\) 0 0
\(767\) 45.5164 1.64350
\(768\) 0 0
\(769\) 6.13815 0.221347 0.110674 0.993857i \(-0.464699\pi\)
0.110674 + 0.993857i \(0.464699\pi\)
\(770\) 0 0
\(771\) −1.23021 −0.0443048
\(772\) 0 0
\(773\) −21.9867 −0.790805 −0.395403 0.918508i \(-0.629395\pi\)
−0.395403 + 0.918508i \(0.629395\pi\)
\(774\) 0 0
\(775\) 0.259511 0.00932189
\(776\) 0 0
\(777\) 1.82991 0.0656475
\(778\) 0 0
\(779\) 11.9547 0.428322
\(780\) 0 0
\(781\) 0 0
\(782\) 0 0
\(783\) −38.4110 −1.37270
\(784\) 0 0
\(785\) −11.1408 −0.397632
\(786\) 0 0
\(787\) 19.3959 0.691390 0.345695 0.938347i \(-0.387643\pi\)
0.345695 + 0.938347i \(0.387643\pi\)
\(788\) 0 0
\(789\) 20.0487 0.713754
\(790\) 0 0
\(791\) −20.8946 −0.742927
\(792\) 0 0
\(793\) 54.5271 1.93631
\(794\) 0 0
\(795\) 2.57303 0.0912561
\(796\) 0 0
\(797\) 41.2516 1.46121 0.730603 0.682802i \(-0.239239\pi\)
0.730603 + 0.682802i \(0.239239\pi\)
\(798\) 0 0
\(799\) 39.8246 1.40889
\(800\) 0 0
\(801\) 8.73785 0.308737
\(802\) 0 0
\(803\) 0 0
\(804\) 0 0
\(805\) −9.22147 −0.325014
\(806\) 0 0
\(807\) 15.6607 0.551283
\(808\) 0 0
\(809\) −31.0682 −1.09230 −0.546149 0.837688i \(-0.683907\pi\)
−0.546149 + 0.837688i \(0.683907\pi\)
\(810\) 0 0
\(811\) 3.29227 0.115607 0.0578037 0.998328i \(-0.481590\pi\)
0.0578037 + 0.998328i \(0.481590\pi\)
\(812\) 0 0
\(813\) −20.0673 −0.703793
\(814\) 0 0
\(815\) 8.55005 0.299495
\(816\) 0 0
\(817\) 50.8441 1.77881
\(818\) 0 0
\(819\) −11.0734 −0.386937
\(820\) 0 0
\(821\) 31.2276 1.08985 0.544925 0.838485i \(-0.316558\pi\)
0.544925 + 0.838485i \(0.316558\pi\)
\(822\) 0 0
\(823\) −8.04437 −0.280409 −0.140204 0.990123i \(-0.544776\pi\)
−0.140204 + 0.990123i \(0.544776\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) 55.3286 1.92396 0.961982 0.273114i \(-0.0880536\pi\)
0.961982 + 0.273114i \(0.0880536\pi\)
\(828\) 0 0
\(829\) 52.1895 1.81262 0.906309 0.422617i \(-0.138888\pi\)
0.906309 + 0.422617i \(0.138888\pi\)
\(830\) 0 0
\(831\) −43.5571 −1.51098
\(832\) 0 0
\(833\) −22.6218 −0.783798
\(834\) 0 0
\(835\) −10.0717 −0.348546
\(836\) 0 0
\(837\) −1.46765 −0.0507293
\(838\) 0 0
\(839\) −51.1355 −1.76539 −0.882697 0.469943i \(-0.844275\pi\)
−0.882697 + 0.469943i \(0.844275\pi\)
\(840\) 0 0
\(841\) 17.1294 0.590669
\(842\) 0 0
\(843\) −23.9646 −0.825385
\(844\) 0 0
\(845\) −27.4783 −0.945284
\(846\) 0 0
\(847\) 0 0
\(848\) 0 0
\(849\) −16.6325 −0.570825
\(850\) 0 0
\(851\) 4.41099 0.151207
\(852\) 0 0
\(853\) 13.7892 0.472134 0.236067 0.971737i \(-0.424142\pi\)
0.236067 + 0.971737i \(0.424142\pi\)
\(854\) 0 0
\(855\) 4.58637 0.156850
\(856\) 0 0
\(857\) −20.3756 −0.696017 −0.348008 0.937491i \(-0.613142\pi\)
−0.348008 + 0.937491i \(0.613142\pi\)
\(858\) 0 0
\(859\) 39.2302 1.33852 0.669259 0.743029i \(-0.266612\pi\)
0.669259 + 0.743029i \(0.266612\pi\)
\(860\) 0 0
\(861\) −6.33296 −0.215827
\(862\) 0 0
\(863\) 36.6395 1.24722 0.623611 0.781735i \(-0.285665\pi\)
0.623611 + 0.781735i \(0.285665\pi\)
\(864\) 0 0
\(865\) −12.7785 −0.434483
\(866\) 0 0
\(867\) 15.6421 0.531234
\(868\) 0 0
\(869\) 0 0
\(870\) 0 0
\(871\) −99.2603 −3.36331
\(872\) 0 0
\(873\) −15.1001 −0.511061
\(874\) 0 0
\(875\) 1.65544 0.0559642
\(876\) 0 0
\(877\) −46.1108 −1.55705 −0.778526 0.627613i \(-0.784032\pi\)
−0.778526 + 0.627613i \(0.784032\pi\)
\(878\) 0 0
\(879\) 14.7024 0.495901
\(880\) 0 0
\(881\) 1.32158 0.0445251 0.0222625 0.999752i \(-0.492913\pi\)
0.0222625 + 0.999752i \(0.492913\pi\)
\(882\) 0 0
\(883\) −17.2302 −0.579843 −0.289921 0.957050i \(-0.593629\pi\)
−0.289921 + 0.957050i \(0.593629\pi\)
\(884\) 0 0
\(885\) 9.98667 0.335698
\(886\) 0 0
\(887\) 17.7175 0.594896 0.297448 0.954738i \(-0.403865\pi\)
0.297448 + 0.954738i \(0.403865\pi\)
\(888\) 0 0
\(889\) 2.14079 0.0717998
\(890\) 0 0
\(891\) 0 0
\(892\) 0 0
\(893\) 32.7112 1.09464
\(894\) 0 0
\(895\) −12.1027 −0.404550
\(896\) 0 0
\(897\) 49.4722 1.65183
\(898\) 0 0
\(899\) 1.76256 0.0587847
\(900\) 0 0
\(901\) −9.78922 −0.326126
\(902\) 0 0
\(903\) −26.9344 −0.896320
\(904\) 0 0
\(905\) 19.1382 0.636174
\(906\) 0 0
\(907\) −20.2011 −0.670767 −0.335384 0.942082i \(-0.608866\pi\)
−0.335384 + 0.942082i \(0.608866\pi\)
\(908\) 0 0
\(909\) 3.98667 0.132229
\(910\) 0 0
\(911\) −45.1001 −1.49423 −0.747117 0.664693i \(-0.768562\pi\)
−0.747117 + 0.664693i \(0.768562\pi\)
\(912\) 0 0
\(913\) 0 0
\(914\) 0 0
\(915\) 11.9637 0.395507
\(916\) 0 0
\(917\) −9.50305 −0.313818
\(918\) 0 0
\(919\) −3.77589 −0.124555 −0.0622776 0.998059i \(-0.519836\pi\)
−0.0622776 + 0.998059i \(0.519836\pi\)
\(920\) 0 0
\(921\) 15.5704 0.513062
\(922\) 0 0
\(923\) −6.68912 −0.220175
\(924\) 0 0
\(925\) −0.791864 −0.0260363
\(926\) 0 0
\(927\) −10.2781 −0.337578
\(928\) 0 0
\(929\) 26.7245 0.876803 0.438401 0.898779i \(-0.355545\pi\)
0.438401 + 0.898779i \(0.355545\pi\)
\(930\) 0 0
\(931\) −18.5811 −0.608971
\(932\) 0 0
\(933\) −15.3330 −0.501978
\(934\) 0 0
\(935\) 0 0
\(936\) 0 0
\(937\) 6.68384 0.218351 0.109176 0.994022i \(-0.465179\pi\)
0.109176 + 0.994022i \(0.465179\pi\)
\(938\) 0 0
\(939\) 17.3063 0.564769
\(940\) 0 0
\(941\) −13.1027 −0.427137 −0.213569 0.976928i \(-0.568509\pi\)
−0.213569 + 0.976928i \(0.568509\pi\)
\(942\) 0 0
\(943\) −15.2656 −0.497117
\(944\) 0 0
\(945\) −9.36226 −0.304554
\(946\) 0 0
\(947\) 47.6058 1.54698 0.773490 0.633808i \(-0.218509\pi\)
0.773490 + 0.633808i \(0.218509\pi\)
\(948\) 0 0
\(949\) −74.3524 −2.41358
\(950\) 0 0
\(951\) 9.13733 0.296298
\(952\) 0 0
\(953\) 15.2348 0.493504 0.246752 0.969079i \(-0.420637\pi\)
0.246752 + 0.969079i \(0.420637\pi\)
\(954\) 0 0
\(955\) 12.0894 0.391204
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) 16.7466 0.540776
\(960\) 0 0
\(961\) −30.9327 −0.997828
\(962\) 0 0
\(963\) 15.6784 0.505230
\(964\) 0 0
\(965\) 13.6191 0.438415
\(966\) 0 0
\(967\) −36.4243 −1.17133 −0.585664 0.810554i \(-0.699166\pi\)
−0.585664 + 0.810554i \(0.699166\pi\)
\(968\) 0 0
\(969\) 32.3402 1.03892
\(970\) 0 0
\(971\) 35.1001 1.12642 0.563208 0.826315i \(-0.309567\pi\)
0.563208 + 0.826315i \(0.309567\pi\)
\(972\) 0 0
\(973\) −9.67314 −0.310107
\(974\) 0 0
\(975\) −8.88128 −0.284429
\(976\) 0 0
\(977\) −42.8946 −1.37232 −0.686160 0.727451i \(-0.740705\pi\)
−0.686160 + 0.727451i \(0.740705\pi\)
\(978\) 0 0
\(979\) 0 0
\(980\) 0 0
\(981\) −10.6758 −0.340852
\(982\) 0 0
\(983\) −28.1559 −0.898032 −0.449016 0.893524i \(-0.648225\pi\)
−0.449016 + 0.893524i \(0.648225\pi\)
\(984\) 0 0
\(985\) −14.7919 −0.471308
\(986\) 0 0
\(987\) −17.3286 −0.551575
\(988\) 0 0
\(989\) −64.9254 −2.06451
\(990\) 0 0
\(991\) −43.7085 −1.38845 −0.694224 0.719759i \(-0.744252\pi\)
−0.694224 + 0.719759i \(0.744252\pi\)
\(992\) 0 0
\(993\) −41.7085 −1.32358
\(994\) 0 0
\(995\) 17.6865 0.560699
\(996\) 0 0
\(997\) −13.0247 −0.412497 −0.206248 0.978500i \(-0.566125\pi\)
−0.206248 + 0.978500i \(0.566125\pi\)
\(998\) 0 0
\(999\) 4.47834 0.141688
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 4840.2.a.u.1.2 yes 3
4.3 odd 2 9680.2.a.ca.1.2 3
11.10 odd 2 4840.2.a.t.1.2 3
44.43 even 2 9680.2.a.cc.1.2 3
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
4840.2.a.t.1.2 3 11.10 odd 2
4840.2.a.u.1.2 yes 3 1.1 even 1 trivial
9680.2.a.ca.1.2 3 4.3 odd 2
9680.2.a.cc.1.2 3 44.43 even 2