Properties

Label 6016.2.a.n.1.1
Level $6016$
Weight $2$
Character 6016.1
Self dual yes
Analytic conductor $48.038$
Analytic rank $0$
Dimension $13$
CM no
Inner twists $1$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [6016,2,Mod(1,6016)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(6016, 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("6016.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 6016 = 2^{7} \cdot 47 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 6016.a (trivial)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: yes
Analytic conductor: \(48.0380018560\)
Analytic rank: \(0\)
Dimension: \(13\)
Coefficient field: \(\mathbb{Q}[x]/(x^{13} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{13} - 4 x^{12} - 22 x^{11} + 96 x^{10} + 163 x^{9} - 840 x^{8} - 438 x^{7} + 3358 x^{6} + 5 x^{5} + \cdots - 832 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 2 \)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Root \(3.29402\) of defining polynomial
Character \(\chi\) \(=\) 6016.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-3.29402 q^{3} -3.40346 q^{5} -1.01019 q^{7} +7.85059 q^{9} +O(q^{10})\) \(q-3.29402 q^{3} -3.40346 q^{5} -1.01019 q^{7} +7.85059 q^{9} -5.72520 q^{11} +2.46556 q^{13} +11.2111 q^{15} +5.23012 q^{17} +4.81048 q^{19} +3.32760 q^{21} +5.25423 q^{23} +6.58356 q^{25} -15.9780 q^{27} +5.28804 q^{29} -8.08188 q^{31} +18.8589 q^{33} +3.43816 q^{35} -4.26903 q^{37} -8.12160 q^{39} -12.5727 q^{41} -3.79762 q^{43} -26.7192 q^{45} -1.00000 q^{47} -5.97951 q^{49} -17.2281 q^{51} +4.27708 q^{53} +19.4855 q^{55} -15.8458 q^{57} +4.14200 q^{59} +5.15979 q^{61} -7.93062 q^{63} -8.39143 q^{65} +5.15333 q^{67} -17.3075 q^{69} +10.5001 q^{71} -5.30202 q^{73} -21.6864 q^{75} +5.78356 q^{77} -14.3486 q^{79} +29.0800 q^{81} -9.84381 q^{83} -17.8005 q^{85} -17.4189 q^{87} -7.70282 q^{89} -2.49069 q^{91} +26.6219 q^{93} -16.3723 q^{95} -10.2647 q^{97} -44.9462 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 13 q - 4 q^{3} + 6 q^{5} - 2 q^{7} + 21 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 13 q - 4 q^{3} + 6 q^{5} - 2 q^{7} + 21 q^{9} - 10 q^{11} + 4 q^{13} + 14 q^{15} + 10 q^{17} - 8 q^{19} + 10 q^{21} + 18 q^{23} + 23 q^{25} - 16 q^{27} + 14 q^{29} + 4 q^{31} + 14 q^{33} - 14 q^{35} + 16 q^{37} + 12 q^{39} + 10 q^{41} - 12 q^{43} + 10 q^{45} - 13 q^{47} + 9 q^{49} - 22 q^{51} + 26 q^{53} - 2 q^{55} + 20 q^{57} - 30 q^{59} + 18 q^{61} + 12 q^{63} - 4 q^{65} - 4 q^{67} + 2 q^{69} + 36 q^{71} + 10 q^{73} - 38 q^{75} + 42 q^{77} + 21 q^{81} - 12 q^{83} + 4 q^{85} + 6 q^{87} + 50 q^{89} + 4 q^{91} + 52 q^{93} + 8 q^{95} - 10 q^{97} - 34 q^{99}+O(q^{100}) \) 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 0
\(3\) −3.29402 −1.90181 −0.950903 0.309490i \(-0.899842\pi\)
−0.950903 + 0.309490i \(0.899842\pi\)
\(4\) 0 0
\(5\) −3.40346 −1.52207 −0.761037 0.648708i \(-0.775310\pi\)
−0.761037 + 0.648708i \(0.775310\pi\)
\(6\) 0 0
\(7\) −1.01019 −0.381817 −0.190909 0.981608i \(-0.561143\pi\)
−0.190909 + 0.981608i \(0.561143\pi\)
\(8\) 0 0
\(9\) 7.85059 2.61686
\(10\) 0 0
\(11\) −5.72520 −1.72621 −0.863106 0.505023i \(-0.831484\pi\)
−0.863106 + 0.505023i \(0.831484\pi\)
\(12\) 0 0
\(13\) 2.46556 0.683822 0.341911 0.939732i \(-0.388926\pi\)
0.341911 + 0.939732i \(0.388926\pi\)
\(14\) 0 0
\(15\) 11.2111 2.89469
\(16\) 0 0
\(17\) 5.23012 1.26849 0.634246 0.773132i \(-0.281311\pi\)
0.634246 + 0.773132i \(0.281311\pi\)
\(18\) 0 0
\(19\) 4.81048 1.10360 0.551799 0.833977i \(-0.313941\pi\)
0.551799 + 0.833977i \(0.313941\pi\)
\(20\) 0 0
\(21\) 3.32760 0.726142
\(22\) 0 0
\(23\) 5.25423 1.09558 0.547791 0.836615i \(-0.315469\pi\)
0.547791 + 0.836615i \(0.315469\pi\)
\(24\) 0 0
\(25\) 6.58356 1.31671
\(26\) 0 0
\(27\) −15.9780 −3.07496
\(28\) 0 0
\(29\) 5.28804 0.981964 0.490982 0.871170i \(-0.336638\pi\)
0.490982 + 0.871170i \(0.336638\pi\)
\(30\) 0 0
\(31\) −8.08188 −1.45155 −0.725774 0.687933i \(-0.758518\pi\)
−0.725774 + 0.687933i \(0.758518\pi\)
\(32\) 0 0
\(33\) 18.8589 3.28292
\(34\) 0 0
\(35\) 3.43816 0.581154
\(36\) 0 0
\(37\) −4.26903 −0.701824 −0.350912 0.936408i \(-0.614128\pi\)
−0.350912 + 0.936408i \(0.614128\pi\)
\(38\) 0 0
\(39\) −8.12160 −1.30050
\(40\) 0 0
\(41\) −12.5727 −1.96352 −0.981760 0.190123i \(-0.939111\pi\)
−0.981760 + 0.190123i \(0.939111\pi\)
\(42\) 0 0
\(43\) −3.79762 −0.579131 −0.289566 0.957158i \(-0.593511\pi\)
−0.289566 + 0.957158i \(0.593511\pi\)
\(44\) 0 0
\(45\) −26.7192 −3.98306
\(46\) 0 0
\(47\) −1.00000 −0.145865
\(48\) 0 0
\(49\) −5.97951 −0.854216
\(50\) 0 0
\(51\) −17.2281 −2.41242
\(52\) 0 0
\(53\) 4.27708 0.587502 0.293751 0.955882i \(-0.405096\pi\)
0.293751 + 0.955882i \(0.405096\pi\)
\(54\) 0 0
\(55\) 19.4855 2.62742
\(56\) 0 0
\(57\) −15.8458 −2.09883
\(58\) 0 0
\(59\) 4.14200 0.539243 0.269621 0.962966i \(-0.413101\pi\)
0.269621 + 0.962966i \(0.413101\pi\)
\(60\) 0 0
\(61\) 5.15979 0.660643 0.330322 0.943868i \(-0.392843\pi\)
0.330322 + 0.943868i \(0.392843\pi\)
\(62\) 0 0
\(63\) −7.93062 −0.999164
\(64\) 0 0
\(65\) −8.39143 −1.04083
\(66\) 0 0
\(67\) 5.15333 0.629579 0.314789 0.949162i \(-0.398066\pi\)
0.314789 + 0.949162i \(0.398066\pi\)
\(68\) 0 0
\(69\) −17.3075 −2.08358
\(70\) 0 0
\(71\) 10.5001 1.24613 0.623065 0.782170i \(-0.285887\pi\)
0.623065 + 0.782170i \(0.285887\pi\)
\(72\) 0 0
\(73\) −5.30202 −0.620554 −0.310277 0.950646i \(-0.600422\pi\)
−0.310277 + 0.950646i \(0.600422\pi\)
\(74\) 0 0
\(75\) −21.6864 −2.50413
\(76\) 0 0
\(77\) 5.78356 0.659097
\(78\) 0 0
\(79\) −14.3486 −1.61435 −0.807173 0.590315i \(-0.799003\pi\)
−0.807173 + 0.590315i \(0.799003\pi\)
\(80\) 0 0
\(81\) 29.0800 3.23111
\(82\) 0 0
\(83\) −9.84381 −1.08050 −0.540250 0.841505i \(-0.681670\pi\)
−0.540250 + 0.841505i \(0.681670\pi\)
\(84\) 0 0
\(85\) −17.8005 −1.93074
\(86\) 0 0
\(87\) −17.4189 −1.86750
\(88\) 0 0
\(89\) −7.70282 −0.816497 −0.408248 0.912871i \(-0.633860\pi\)
−0.408248 + 0.912871i \(0.633860\pi\)
\(90\) 0 0
\(91\) −2.49069 −0.261095
\(92\) 0 0
\(93\) 26.6219 2.76056
\(94\) 0 0
\(95\) −16.3723 −1.67976
\(96\) 0 0
\(97\) −10.2647 −1.04222 −0.521110 0.853490i \(-0.674482\pi\)
−0.521110 + 0.853490i \(0.674482\pi\)
\(98\) 0 0
\(99\) −44.9462 −4.51726
\(100\) 0 0
\(101\) 19.7066 1.96088 0.980438 0.196828i \(-0.0630640\pi\)
0.980438 + 0.196828i \(0.0630640\pi\)
\(102\) 0 0
\(103\) −6.98446 −0.688199 −0.344100 0.938933i \(-0.611816\pi\)
−0.344100 + 0.938933i \(0.611816\pi\)
\(104\) 0 0
\(105\) −11.3254 −1.10524
\(106\) 0 0
\(107\) −6.50926 −0.629273 −0.314637 0.949212i \(-0.601883\pi\)
−0.314637 + 0.949212i \(0.601883\pi\)
\(108\) 0 0
\(109\) −16.5829 −1.58835 −0.794177 0.607686i \(-0.792098\pi\)
−0.794177 + 0.607686i \(0.792098\pi\)
\(110\) 0 0
\(111\) 14.0623 1.33473
\(112\) 0 0
\(113\) 5.91614 0.556543 0.278272 0.960502i \(-0.410238\pi\)
0.278272 + 0.960502i \(0.410238\pi\)
\(114\) 0 0
\(115\) −17.8826 −1.66756
\(116\) 0 0
\(117\) 19.3561 1.78947
\(118\) 0 0
\(119\) −5.28344 −0.484332
\(120\) 0 0
\(121\) 21.7779 1.97981
\(122\) 0 0
\(123\) 41.4147 3.73423
\(124\) 0 0
\(125\) −5.38958 −0.482058
\(126\) 0 0
\(127\) −1.84506 −0.163722 −0.0818612 0.996644i \(-0.526086\pi\)
−0.0818612 + 0.996644i \(0.526086\pi\)
\(128\) 0 0
\(129\) 12.5094 1.10140
\(130\) 0 0
\(131\) 10.5001 0.917396 0.458698 0.888592i \(-0.348316\pi\)
0.458698 + 0.888592i \(0.348316\pi\)
\(132\) 0 0
\(133\) −4.85951 −0.421373
\(134\) 0 0
\(135\) 54.3804 4.68032
\(136\) 0 0
\(137\) 11.4238 0.976004 0.488002 0.872843i \(-0.337726\pi\)
0.488002 + 0.872843i \(0.337726\pi\)
\(138\) 0 0
\(139\) 7.91429 0.671281 0.335641 0.941990i \(-0.391047\pi\)
0.335641 + 0.941990i \(0.391047\pi\)
\(140\) 0 0
\(141\) 3.29402 0.277407
\(142\) 0 0
\(143\) −14.1158 −1.18042
\(144\) 0 0
\(145\) −17.9976 −1.49462
\(146\) 0 0
\(147\) 19.6966 1.62455
\(148\) 0 0
\(149\) 18.0805 1.48121 0.740605 0.671940i \(-0.234539\pi\)
0.740605 + 0.671940i \(0.234539\pi\)
\(150\) 0 0
\(151\) 0.949002 0.0772287 0.0386144 0.999254i \(-0.487706\pi\)
0.0386144 + 0.999254i \(0.487706\pi\)
\(152\) 0 0
\(153\) 41.0596 3.31947
\(154\) 0 0
\(155\) 27.5064 2.20936
\(156\) 0 0
\(157\) −10.0579 −0.802710 −0.401355 0.915923i \(-0.631461\pi\)
−0.401355 + 0.915923i \(0.631461\pi\)
\(158\) 0 0
\(159\) −14.0888 −1.11731
\(160\) 0 0
\(161\) −5.30779 −0.418312
\(162\) 0 0
\(163\) −7.61522 −0.596470 −0.298235 0.954492i \(-0.596398\pi\)
−0.298235 + 0.954492i \(0.596398\pi\)
\(164\) 0 0
\(165\) −64.1857 −4.99685
\(166\) 0 0
\(167\) −7.71566 −0.597056 −0.298528 0.954401i \(-0.596496\pi\)
−0.298528 + 0.954401i \(0.596496\pi\)
\(168\) 0 0
\(169\) −6.92103 −0.532387
\(170\) 0 0
\(171\) 37.7651 2.88797
\(172\) 0 0
\(173\) −9.15546 −0.696077 −0.348038 0.937480i \(-0.613152\pi\)
−0.348038 + 0.937480i \(0.613152\pi\)
\(174\) 0 0
\(175\) −6.65067 −0.502743
\(176\) 0 0
\(177\) −13.6439 −1.02554
\(178\) 0 0
\(179\) −12.9473 −0.967727 −0.483863 0.875144i \(-0.660767\pi\)
−0.483863 + 0.875144i \(0.660767\pi\)
\(180\) 0 0
\(181\) −0.263246 −0.0195669 −0.00978347 0.999952i \(-0.503114\pi\)
−0.00978347 + 0.999952i \(0.503114\pi\)
\(182\) 0 0
\(183\) −16.9965 −1.25641
\(184\) 0 0
\(185\) 14.5295 1.06823
\(186\) 0 0
\(187\) −29.9435 −2.18968
\(188\) 0 0
\(189\) 16.1408 1.17407
\(190\) 0 0
\(191\) −7.74895 −0.560695 −0.280347 0.959899i \(-0.590450\pi\)
−0.280347 + 0.959899i \(0.590450\pi\)
\(192\) 0 0
\(193\) 20.2678 1.45891 0.729455 0.684028i \(-0.239774\pi\)
0.729455 + 0.684028i \(0.239774\pi\)
\(194\) 0 0
\(195\) 27.6416 1.97945
\(196\) 0 0
\(197\) −1.16480 −0.0829889 −0.0414944 0.999139i \(-0.513212\pi\)
−0.0414944 + 0.999139i \(0.513212\pi\)
\(198\) 0 0
\(199\) 21.5395 1.52689 0.763447 0.645871i \(-0.223506\pi\)
0.763447 + 0.645871i \(0.223506\pi\)
\(200\) 0 0
\(201\) −16.9752 −1.19734
\(202\) 0 0
\(203\) −5.34194 −0.374931
\(204\) 0 0
\(205\) 42.7906 2.98863
\(206\) 0 0
\(207\) 41.2488 2.86699
\(208\) 0 0
\(209\) −27.5409 −1.90505
\(210\) 0 0
\(211\) −11.1401 −0.766916 −0.383458 0.923558i \(-0.625267\pi\)
−0.383458 + 0.923558i \(0.625267\pi\)
\(212\) 0 0
\(213\) −34.5875 −2.36990
\(214\) 0 0
\(215\) 12.9251 0.881481
\(216\) 0 0
\(217\) 8.16426 0.554226
\(218\) 0 0
\(219\) 17.4650 1.18017
\(220\) 0 0
\(221\) 12.8952 0.867423
\(222\) 0 0
\(223\) 2.86516 0.191865 0.0959327 0.995388i \(-0.469417\pi\)
0.0959327 + 0.995388i \(0.469417\pi\)
\(224\) 0 0
\(225\) 51.6848 3.44565
\(226\) 0 0
\(227\) 7.92238 0.525827 0.262913 0.964819i \(-0.415317\pi\)
0.262913 + 0.964819i \(0.415317\pi\)
\(228\) 0 0
\(229\) −10.1286 −0.669319 −0.334659 0.942339i \(-0.608621\pi\)
−0.334659 + 0.942339i \(0.608621\pi\)
\(230\) 0 0
\(231\) −19.0512 −1.25347
\(232\) 0 0
\(233\) −5.45696 −0.357497 −0.178749 0.983895i \(-0.557205\pi\)
−0.178749 + 0.983895i \(0.557205\pi\)
\(234\) 0 0
\(235\) 3.40346 0.222017
\(236\) 0 0
\(237\) 47.2647 3.07017
\(238\) 0 0
\(239\) −2.47493 −0.160090 −0.0800450 0.996791i \(-0.525506\pi\)
−0.0800450 + 0.996791i \(0.525506\pi\)
\(240\) 0 0
\(241\) −17.7997 −1.14658 −0.573291 0.819352i \(-0.694333\pi\)
−0.573291 + 0.819352i \(0.694333\pi\)
\(242\) 0 0
\(243\) −47.8563 −3.06998
\(244\) 0 0
\(245\) 20.3510 1.30018
\(246\) 0 0
\(247\) 11.8605 0.754666
\(248\) 0 0
\(249\) 32.4258 2.05490
\(250\) 0 0
\(251\) −16.3045 −1.02913 −0.514566 0.857451i \(-0.672047\pi\)
−0.514566 + 0.857451i \(0.672047\pi\)
\(252\) 0 0
\(253\) −30.0815 −1.89121
\(254\) 0 0
\(255\) 58.6354 3.67189
\(256\) 0 0
\(257\) 0.476521 0.0297246 0.0148623 0.999890i \(-0.495269\pi\)
0.0148623 + 0.999890i \(0.495269\pi\)
\(258\) 0 0
\(259\) 4.31255 0.267969
\(260\) 0 0
\(261\) 41.5142 2.56967
\(262\) 0 0
\(263\) 0.982319 0.0605724 0.0302862 0.999541i \(-0.490358\pi\)
0.0302862 + 0.999541i \(0.490358\pi\)
\(264\) 0 0
\(265\) −14.5569 −0.894221
\(266\) 0 0
\(267\) 25.3733 1.55282
\(268\) 0 0
\(269\) 10.2190 0.623064 0.311532 0.950236i \(-0.399158\pi\)
0.311532 + 0.950236i \(0.399158\pi\)
\(270\) 0 0
\(271\) 5.62542 0.341720 0.170860 0.985295i \(-0.445345\pi\)
0.170860 + 0.985295i \(0.445345\pi\)
\(272\) 0 0
\(273\) 8.20439 0.496552
\(274\) 0 0
\(275\) −37.6922 −2.27292
\(276\) 0 0
\(277\) −12.2346 −0.735107 −0.367553 0.930002i \(-0.619805\pi\)
−0.367553 + 0.930002i \(0.619805\pi\)
\(278\) 0 0
\(279\) −63.4475 −3.79850
\(280\) 0 0
\(281\) −14.7699 −0.881096 −0.440548 0.897729i \(-0.645216\pi\)
−0.440548 + 0.897729i \(0.645216\pi\)
\(282\) 0 0
\(283\) −19.4910 −1.15862 −0.579311 0.815107i \(-0.696678\pi\)
−0.579311 + 0.815107i \(0.696678\pi\)
\(284\) 0 0
\(285\) 53.9307 3.19458
\(286\) 0 0
\(287\) 12.7008 0.749706
\(288\) 0 0
\(289\) 10.3542 0.609070
\(290\) 0 0
\(291\) 33.8121 1.98210
\(292\) 0 0
\(293\) −11.5024 −0.671975 −0.335988 0.941866i \(-0.609070\pi\)
−0.335988 + 0.941866i \(0.609070\pi\)
\(294\) 0 0
\(295\) −14.0972 −0.820768
\(296\) 0 0
\(297\) 91.4770 5.30803
\(298\) 0 0
\(299\) 12.9546 0.749184
\(300\) 0 0
\(301\) 3.83633 0.221122
\(302\) 0 0
\(303\) −64.9139 −3.72920
\(304\) 0 0
\(305\) −17.5611 −1.00555
\(306\) 0 0
\(307\) −27.1455 −1.54927 −0.774637 0.632407i \(-0.782067\pi\)
−0.774637 + 0.632407i \(0.782067\pi\)
\(308\) 0 0
\(309\) 23.0070 1.30882
\(310\) 0 0
\(311\) 29.2076 1.65621 0.828105 0.560573i \(-0.189419\pi\)
0.828105 + 0.560573i \(0.189419\pi\)
\(312\) 0 0
\(313\) 17.3355 0.979862 0.489931 0.871761i \(-0.337022\pi\)
0.489931 + 0.871761i \(0.337022\pi\)
\(314\) 0 0
\(315\) 26.9916 1.52080
\(316\) 0 0
\(317\) 8.16893 0.458813 0.229406 0.973331i \(-0.426322\pi\)
0.229406 + 0.973331i \(0.426322\pi\)
\(318\) 0 0
\(319\) −30.2750 −1.69508
\(320\) 0 0
\(321\) 21.4416 1.19676
\(322\) 0 0
\(323\) 25.1594 1.39991
\(324\) 0 0
\(325\) 16.2321 0.900397
\(326\) 0 0
\(327\) 54.6245 3.02074
\(328\) 0 0
\(329\) 1.01019 0.0556938
\(330\) 0 0
\(331\) −8.54399 −0.469620 −0.234810 0.972041i \(-0.575447\pi\)
−0.234810 + 0.972041i \(0.575447\pi\)
\(332\) 0 0
\(333\) −33.5144 −1.83658
\(334\) 0 0
\(335\) −17.5392 −0.958266
\(336\) 0 0
\(337\) 14.5188 0.790888 0.395444 0.918490i \(-0.370591\pi\)
0.395444 + 0.918490i \(0.370591\pi\)
\(338\) 0 0
\(339\) −19.4879 −1.05844
\(340\) 0 0
\(341\) 46.2703 2.50568
\(342\) 0 0
\(343\) 13.1118 0.707972
\(344\) 0 0
\(345\) 58.9056 3.17137
\(346\) 0 0
\(347\) −9.43033 −0.506247 −0.253123 0.967434i \(-0.581458\pi\)
−0.253123 + 0.967434i \(0.581458\pi\)
\(348\) 0 0
\(349\) −7.36249 −0.394105 −0.197052 0.980393i \(-0.563137\pi\)
−0.197052 + 0.980393i \(0.563137\pi\)
\(350\) 0 0
\(351\) −39.3946 −2.10273
\(352\) 0 0
\(353\) −13.0551 −0.694853 −0.347426 0.937707i \(-0.612944\pi\)
−0.347426 + 0.937707i \(0.612944\pi\)
\(354\) 0 0
\(355\) −35.7366 −1.89670
\(356\) 0 0
\(357\) 17.4038 0.921105
\(358\) 0 0
\(359\) 27.7361 1.46386 0.731929 0.681381i \(-0.238620\pi\)
0.731929 + 0.681381i \(0.238620\pi\)
\(360\) 0 0
\(361\) 4.14068 0.217931
\(362\) 0 0
\(363\) −71.7368 −3.76521
\(364\) 0 0
\(365\) 18.0452 0.944530
\(366\) 0 0
\(367\) 36.6642 1.91386 0.956929 0.290323i \(-0.0937627\pi\)
0.956929 + 0.290323i \(0.0937627\pi\)
\(368\) 0 0
\(369\) −98.7029 −5.13827
\(370\) 0 0
\(371\) −4.32067 −0.224318
\(372\) 0 0
\(373\) 9.01404 0.466729 0.233365 0.972389i \(-0.425026\pi\)
0.233365 + 0.972389i \(0.425026\pi\)
\(374\) 0 0
\(375\) 17.7534 0.916781
\(376\) 0 0
\(377\) 13.0380 0.671489
\(378\) 0 0
\(379\) 11.2137 0.576010 0.288005 0.957629i \(-0.407008\pi\)
0.288005 + 0.957629i \(0.407008\pi\)
\(380\) 0 0
\(381\) 6.07766 0.311368
\(382\) 0 0
\(383\) −12.3247 −0.629760 −0.314880 0.949131i \(-0.601964\pi\)
−0.314880 + 0.949131i \(0.601964\pi\)
\(384\) 0 0
\(385\) −19.6841 −1.00320
\(386\) 0 0
\(387\) −29.8135 −1.51551
\(388\) 0 0
\(389\) 11.6693 0.591658 0.295829 0.955241i \(-0.404404\pi\)
0.295829 + 0.955241i \(0.404404\pi\)
\(390\) 0 0
\(391\) 27.4803 1.38974
\(392\) 0 0
\(393\) −34.5875 −1.74471
\(394\) 0 0
\(395\) 48.8350 2.45715
\(396\) 0 0
\(397\) 5.65277 0.283705 0.141852 0.989888i \(-0.454694\pi\)
0.141852 + 0.989888i \(0.454694\pi\)
\(398\) 0 0
\(399\) 16.0073 0.801370
\(400\) 0 0
\(401\) 39.7695 1.98599 0.992997 0.118139i \(-0.0376929\pi\)
0.992997 + 0.118139i \(0.0376929\pi\)
\(402\) 0 0
\(403\) −19.9263 −0.992601
\(404\) 0 0
\(405\) −98.9727 −4.91799
\(406\) 0 0
\(407\) 24.4410 1.21150
\(408\) 0 0
\(409\) −14.0369 −0.694078 −0.347039 0.937851i \(-0.612813\pi\)
−0.347039 + 0.937851i \(0.612813\pi\)
\(410\) 0 0
\(411\) −37.6304 −1.85617
\(412\) 0 0
\(413\) −4.18423 −0.205892
\(414\) 0 0
\(415\) 33.5031 1.64460
\(416\) 0 0
\(417\) −26.0699 −1.27665
\(418\) 0 0
\(419\) 38.8002 1.89551 0.947756 0.318996i \(-0.103346\pi\)
0.947756 + 0.318996i \(0.103346\pi\)
\(420\) 0 0
\(421\) 8.76782 0.427317 0.213659 0.976908i \(-0.431462\pi\)
0.213659 + 0.976908i \(0.431462\pi\)
\(422\) 0 0
\(423\) −7.85059 −0.381709
\(424\) 0 0
\(425\) 34.4328 1.67024
\(426\) 0 0
\(427\) −5.21239 −0.252245
\(428\) 0 0
\(429\) 46.4978 2.24493
\(430\) 0 0
\(431\) 15.9651 0.769011 0.384505 0.923123i \(-0.374372\pi\)
0.384505 + 0.923123i \(0.374372\pi\)
\(432\) 0 0
\(433\) −35.6916 −1.71523 −0.857615 0.514292i \(-0.828055\pi\)
−0.857615 + 0.514292i \(0.828055\pi\)
\(434\) 0 0
\(435\) 59.2846 2.84248
\(436\) 0 0
\(437\) 25.2753 1.20908
\(438\) 0 0
\(439\) −27.1930 −1.29785 −0.648925 0.760852i \(-0.724781\pi\)
−0.648925 + 0.760852i \(0.724781\pi\)
\(440\) 0 0
\(441\) −46.9427 −2.23537
\(442\) 0 0
\(443\) 16.9119 0.803507 0.401753 0.915748i \(-0.368401\pi\)
0.401753 + 0.915748i \(0.368401\pi\)
\(444\) 0 0
\(445\) 26.2162 1.24277
\(446\) 0 0
\(447\) −59.5575 −2.81697
\(448\) 0 0
\(449\) −5.54470 −0.261671 −0.130835 0.991404i \(-0.541766\pi\)
−0.130835 + 0.991404i \(0.541766\pi\)
\(450\) 0 0
\(451\) 71.9810 3.38945
\(452\) 0 0
\(453\) −3.12604 −0.146874
\(454\) 0 0
\(455\) 8.47697 0.397406
\(456\) 0 0
\(457\) −16.4027 −0.767286 −0.383643 0.923481i \(-0.625331\pi\)
−0.383643 + 0.923481i \(0.625331\pi\)
\(458\) 0 0
\(459\) −83.5667 −3.90056
\(460\) 0 0
\(461\) 8.06731 0.375732 0.187866 0.982195i \(-0.439843\pi\)
0.187866 + 0.982195i \(0.439843\pi\)
\(462\) 0 0
\(463\) 35.3959 1.64499 0.822493 0.568776i \(-0.192583\pi\)
0.822493 + 0.568776i \(0.192583\pi\)
\(464\) 0 0
\(465\) −90.6066 −4.20178
\(466\) 0 0
\(467\) 0.348500 0.0161267 0.00806334 0.999967i \(-0.497433\pi\)
0.00806334 + 0.999967i \(0.497433\pi\)
\(468\) 0 0
\(469\) −5.20586 −0.240384
\(470\) 0 0
\(471\) 33.1311 1.52660
\(472\) 0 0
\(473\) 21.7421 0.999703
\(474\) 0 0
\(475\) 31.6700 1.45312
\(476\) 0 0
\(477\) 33.5776 1.53741
\(478\) 0 0
\(479\) −17.7205 −0.809669 −0.404835 0.914390i \(-0.632671\pi\)
−0.404835 + 0.914390i \(0.632671\pi\)
\(480\) 0 0
\(481\) −10.5255 −0.479923
\(482\) 0 0
\(483\) 17.4840 0.795548
\(484\) 0 0
\(485\) 34.9354 1.58634
\(486\) 0 0
\(487\) −1.44876 −0.0656495 −0.0328247 0.999461i \(-0.510450\pi\)
−0.0328247 + 0.999461i \(0.510450\pi\)
\(488\) 0 0
\(489\) 25.0847 1.13437
\(490\) 0 0
\(491\) −2.15520 −0.0972627 −0.0486313 0.998817i \(-0.515486\pi\)
−0.0486313 + 0.998817i \(0.515486\pi\)
\(492\) 0 0
\(493\) 27.6571 1.24561
\(494\) 0 0
\(495\) 152.973 6.87561
\(496\) 0 0
\(497\) −10.6071 −0.475794
\(498\) 0 0
\(499\) 22.5468 1.00933 0.504666 0.863314i \(-0.331616\pi\)
0.504666 + 0.863314i \(0.331616\pi\)
\(500\) 0 0
\(501\) 25.4156 1.13548
\(502\) 0 0
\(503\) 12.1442 0.541483 0.270742 0.962652i \(-0.412731\pi\)
0.270742 + 0.962652i \(0.412731\pi\)
\(504\) 0 0
\(505\) −67.0705 −2.98460
\(506\) 0 0
\(507\) 22.7980 1.01250
\(508\) 0 0
\(509\) 1.45073 0.0643027 0.0321513 0.999483i \(-0.489764\pi\)
0.0321513 + 0.999483i \(0.489764\pi\)
\(510\) 0 0
\(511\) 5.35606 0.236938
\(512\) 0 0
\(513\) −76.8616 −3.39352
\(514\) 0 0
\(515\) 23.7713 1.04749
\(516\) 0 0
\(517\) 5.72520 0.251794
\(518\) 0 0
\(519\) 30.1583 1.32380
\(520\) 0 0
\(521\) −14.2519 −0.624388 −0.312194 0.950018i \(-0.601064\pi\)
−0.312194 + 0.950018i \(0.601064\pi\)
\(522\) 0 0
\(523\) 1.78280 0.0779565 0.0389782 0.999240i \(-0.487590\pi\)
0.0389782 + 0.999240i \(0.487590\pi\)
\(524\) 0 0
\(525\) 21.9075 0.956120
\(526\) 0 0
\(527\) −42.2692 −1.84128
\(528\) 0 0
\(529\) 4.60691 0.200300
\(530\) 0 0
\(531\) 32.5172 1.41113
\(532\) 0 0
\(533\) −30.9986 −1.34270
\(534\) 0 0
\(535\) 22.1540 0.957801
\(536\) 0 0
\(537\) 42.6487 1.84043
\(538\) 0 0
\(539\) 34.2339 1.47456
\(540\) 0 0
\(541\) −1.55369 −0.0667982 −0.0333991 0.999442i \(-0.510633\pi\)
−0.0333991 + 0.999442i \(0.510633\pi\)
\(542\) 0 0
\(543\) 0.867140 0.0372125
\(544\) 0 0
\(545\) 56.4393 2.41759
\(546\) 0 0
\(547\) −23.8059 −1.01787 −0.508933 0.860806i \(-0.669960\pi\)
−0.508933 + 0.860806i \(0.669960\pi\)
\(548\) 0 0
\(549\) 40.5074 1.72881
\(550\) 0 0
\(551\) 25.4380 1.08369
\(552\) 0 0
\(553\) 14.4949 0.616385
\(554\) 0 0
\(555\) −47.8605 −2.03156
\(556\) 0 0
\(557\) 24.3308 1.03093 0.515465 0.856911i \(-0.327619\pi\)
0.515465 + 0.856911i \(0.327619\pi\)
\(558\) 0 0
\(559\) −9.36324 −0.396023
\(560\) 0 0
\(561\) 98.6345 4.16435
\(562\) 0 0
\(563\) 6.88333 0.290098 0.145049 0.989424i \(-0.453666\pi\)
0.145049 + 0.989424i \(0.453666\pi\)
\(564\) 0 0
\(565\) −20.1353 −0.847101
\(566\) 0 0
\(567\) −29.3764 −1.23369
\(568\) 0 0
\(569\) 6.32305 0.265076 0.132538 0.991178i \(-0.457687\pi\)
0.132538 + 0.991178i \(0.457687\pi\)
\(570\) 0 0
\(571\) −6.32641 −0.264752 −0.132376 0.991200i \(-0.542261\pi\)
−0.132376 + 0.991200i \(0.542261\pi\)
\(572\) 0 0
\(573\) 25.5252 1.06633
\(574\) 0 0
\(575\) 34.5915 1.44257
\(576\) 0 0
\(577\) 24.5472 1.02191 0.510957 0.859606i \(-0.329291\pi\)
0.510957 + 0.859606i \(0.329291\pi\)
\(578\) 0 0
\(579\) −66.7627 −2.77456
\(580\) 0 0
\(581\) 9.94416 0.412553
\(582\) 0 0
\(583\) −24.4871 −1.01415
\(584\) 0 0
\(585\) −65.8777 −2.72371
\(586\) 0 0
\(587\) −34.4747 −1.42293 −0.711463 0.702724i \(-0.751967\pi\)
−0.711463 + 0.702724i \(0.751967\pi\)
\(588\) 0 0
\(589\) −38.8777 −1.60193
\(590\) 0 0
\(591\) 3.83689 0.157829
\(592\) 0 0
\(593\) −16.5677 −0.680354 −0.340177 0.940361i \(-0.610487\pi\)
−0.340177 + 0.940361i \(0.610487\pi\)
\(594\) 0 0
\(595\) 17.9820 0.737189
\(596\) 0 0
\(597\) −70.9515 −2.90385
\(598\) 0 0
\(599\) 3.33391 0.136220 0.0681099 0.997678i \(-0.478303\pi\)
0.0681099 + 0.997678i \(0.478303\pi\)
\(600\) 0 0
\(601\) −22.6444 −0.923684 −0.461842 0.886962i \(-0.652811\pi\)
−0.461842 + 0.886962i \(0.652811\pi\)
\(602\) 0 0
\(603\) 40.4566 1.64752
\(604\) 0 0
\(605\) −74.1202 −3.01341
\(606\) 0 0
\(607\) 39.5991 1.60728 0.803639 0.595117i \(-0.202894\pi\)
0.803639 + 0.595117i \(0.202894\pi\)
\(608\) 0 0
\(609\) 17.5965 0.713045
\(610\) 0 0
\(611\) −2.46556 −0.0997457
\(612\) 0 0
\(613\) −5.24650 −0.211904 −0.105952 0.994371i \(-0.533789\pi\)
−0.105952 + 0.994371i \(0.533789\pi\)
\(614\) 0 0
\(615\) −140.953 −5.68378
\(616\) 0 0
\(617\) 3.90461 0.157194 0.0785969 0.996906i \(-0.474956\pi\)
0.0785969 + 0.996906i \(0.474956\pi\)
\(618\) 0 0
\(619\) 0.752490 0.0302451 0.0151226 0.999886i \(-0.495186\pi\)
0.0151226 + 0.999886i \(0.495186\pi\)
\(620\) 0 0
\(621\) −83.9518 −3.36887
\(622\) 0 0
\(623\) 7.78134 0.311753
\(624\) 0 0
\(625\) −14.5746 −0.582982
\(626\) 0 0
\(627\) 90.7204 3.62303
\(628\) 0 0
\(629\) −22.3276 −0.890258
\(630\) 0 0
\(631\) 16.1111 0.641373 0.320686 0.947185i \(-0.396086\pi\)
0.320686 + 0.947185i \(0.396086\pi\)
\(632\) 0 0
\(633\) 36.6958 1.45853
\(634\) 0 0
\(635\) 6.27958 0.249198
\(636\) 0 0
\(637\) −14.7428 −0.584132
\(638\) 0 0
\(639\) 82.4318 3.26095
\(640\) 0 0
\(641\) 3.57148 0.141065 0.0705325 0.997509i \(-0.477530\pi\)
0.0705325 + 0.997509i \(0.477530\pi\)
\(642\) 0 0
\(643\) −17.1521 −0.676411 −0.338206 0.941072i \(-0.609820\pi\)
−0.338206 + 0.941072i \(0.609820\pi\)
\(644\) 0 0
\(645\) −42.5754 −1.67641
\(646\) 0 0
\(647\) 16.7145 0.657114 0.328557 0.944484i \(-0.393438\pi\)
0.328557 + 0.944484i \(0.393438\pi\)
\(648\) 0 0
\(649\) −23.7138 −0.930847
\(650\) 0 0
\(651\) −26.8933 −1.05403
\(652\) 0 0
\(653\) −40.0870 −1.56873 −0.784364 0.620301i \(-0.787010\pi\)
−0.784364 + 0.620301i \(0.787010\pi\)
\(654\) 0 0
\(655\) −35.7366 −1.39635
\(656\) 0 0
\(657\) −41.6240 −1.62391
\(658\) 0 0
\(659\) −18.5765 −0.723638 −0.361819 0.932248i \(-0.617844\pi\)
−0.361819 + 0.932248i \(0.617844\pi\)
\(660\) 0 0
\(661\) 25.8030 1.00362 0.501811 0.864977i \(-0.332667\pi\)
0.501811 + 0.864977i \(0.332667\pi\)
\(662\) 0 0
\(663\) −42.4770 −1.64967
\(664\) 0 0
\(665\) 16.5392 0.641361
\(666\) 0 0
\(667\) 27.7845 1.07582
\(668\) 0 0
\(669\) −9.43791 −0.364891
\(670\) 0 0
\(671\) −29.5408 −1.14041
\(672\) 0 0
\(673\) −10.0161 −0.386092 −0.193046 0.981190i \(-0.561837\pi\)
−0.193046 + 0.981190i \(0.561837\pi\)
\(674\) 0 0
\(675\) −105.192 −4.04883
\(676\) 0 0
\(677\) −48.0177 −1.84547 −0.922736 0.385433i \(-0.874052\pi\)
−0.922736 + 0.385433i \(0.874052\pi\)
\(678\) 0 0
\(679\) 10.3693 0.397937
\(680\) 0 0
\(681\) −26.0965 −1.00002
\(682\) 0 0
\(683\) 20.3988 0.780537 0.390268 0.920701i \(-0.372382\pi\)
0.390268 + 0.920701i \(0.372382\pi\)
\(684\) 0 0
\(685\) −38.8806 −1.48555
\(686\) 0 0
\(687\) 33.3639 1.27291
\(688\) 0 0
\(689\) 10.5454 0.401747
\(690\) 0 0
\(691\) 3.07747 0.117072 0.0585362 0.998285i \(-0.481357\pi\)
0.0585362 + 0.998285i \(0.481357\pi\)
\(692\) 0 0
\(693\) 45.4043 1.72477
\(694\) 0 0
\(695\) −26.9360 −1.02174
\(696\) 0 0
\(697\) −65.7566 −2.49071
\(698\) 0 0
\(699\) 17.9754 0.679890
\(700\) 0 0
\(701\) 11.7014 0.441956 0.220978 0.975279i \(-0.429075\pi\)
0.220978 + 0.975279i \(0.429075\pi\)
\(702\) 0 0
\(703\) −20.5361 −0.774533
\(704\) 0 0
\(705\) −11.2111 −0.422234
\(706\) 0 0
\(707\) −19.9074 −0.748696
\(708\) 0 0
\(709\) 39.4191 1.48042 0.740209 0.672377i \(-0.234727\pi\)
0.740209 + 0.672377i \(0.234727\pi\)
\(710\) 0 0
\(711\) −112.645 −4.22452
\(712\) 0 0
\(713\) −42.4640 −1.59029
\(714\) 0 0
\(715\) 48.0426 1.79669
\(716\) 0 0
\(717\) 8.15248 0.304460
\(718\) 0 0
\(719\) 41.1251 1.53371 0.766854 0.641822i \(-0.221821\pi\)
0.766854 + 0.641822i \(0.221821\pi\)
\(720\) 0 0
\(721\) 7.05566 0.262766
\(722\) 0 0
\(723\) 58.6327 2.18057
\(724\) 0 0
\(725\) 34.8141 1.29296
\(726\) 0 0
\(727\) −29.8097 −1.10558 −0.552790 0.833321i \(-0.686437\pi\)
−0.552790 + 0.833321i \(0.686437\pi\)
\(728\) 0 0
\(729\) 70.3999 2.60740
\(730\) 0 0
\(731\) −19.8620 −0.734623
\(732\) 0 0
\(733\) −2.39218 −0.0883573 −0.0441786 0.999024i \(-0.514067\pi\)
−0.0441786 + 0.999024i \(0.514067\pi\)
\(734\) 0 0
\(735\) −67.0368 −2.47269
\(736\) 0 0
\(737\) −29.5038 −1.08679
\(738\) 0 0
\(739\) 29.4914 1.08486 0.542428 0.840102i \(-0.317505\pi\)
0.542428 + 0.840102i \(0.317505\pi\)
\(740\) 0 0
\(741\) −39.0688 −1.43523
\(742\) 0 0
\(743\) 18.1362 0.665353 0.332677 0.943041i \(-0.392048\pi\)
0.332677 + 0.943041i \(0.392048\pi\)
\(744\) 0 0
\(745\) −61.5362 −2.25451
\(746\) 0 0
\(747\) −77.2798 −2.82752
\(748\) 0 0
\(749\) 6.57561 0.240267
\(750\) 0 0
\(751\) 36.7238 1.34007 0.670035 0.742329i \(-0.266279\pi\)
0.670035 + 0.742329i \(0.266279\pi\)
\(752\) 0 0
\(753\) 53.7075 1.95721
\(754\) 0 0
\(755\) −3.22989 −0.117548
\(756\) 0 0
\(757\) −16.3203 −0.593173 −0.296587 0.955006i \(-0.595848\pi\)
−0.296587 + 0.955006i \(0.595848\pi\)
\(758\) 0 0
\(759\) 99.0891 3.59671
\(760\) 0 0
\(761\) 34.0552 1.23450 0.617250 0.786767i \(-0.288247\pi\)
0.617250 + 0.786767i \(0.288247\pi\)
\(762\) 0 0
\(763\) 16.7519 0.606461
\(764\) 0 0
\(765\) −139.745 −5.05248
\(766\) 0 0
\(767\) 10.2123 0.368746
\(768\) 0 0
\(769\) −1.76745 −0.0637360 −0.0318680 0.999492i \(-0.510146\pi\)
−0.0318680 + 0.999492i \(0.510146\pi\)
\(770\) 0 0
\(771\) −1.56967 −0.0565303
\(772\) 0 0
\(773\) −15.3189 −0.550984 −0.275492 0.961303i \(-0.588841\pi\)
−0.275492 + 0.961303i \(0.588841\pi\)
\(774\) 0 0
\(775\) −53.2075 −1.91127
\(776\) 0 0
\(777\) −14.2056 −0.509624
\(778\) 0 0
\(779\) −60.4805 −2.16694
\(780\) 0 0
\(781\) −60.1150 −2.15108
\(782\) 0 0
\(783\) −84.4920 −3.01950
\(784\) 0 0
\(785\) 34.2318 1.22178
\(786\) 0 0
\(787\) 49.6113 1.76845 0.884226 0.467059i \(-0.154686\pi\)
0.884226 + 0.467059i \(0.154686\pi\)
\(788\) 0 0
\(789\) −3.23578 −0.115197
\(790\) 0 0
\(791\) −5.97644 −0.212498
\(792\) 0 0
\(793\) 12.7218 0.451763
\(794\) 0 0
\(795\) 47.9507 1.70063
\(796\) 0 0
\(797\) 28.4624 1.00819 0.504096 0.863648i \(-0.331826\pi\)
0.504096 + 0.863648i \(0.331826\pi\)
\(798\) 0 0
\(799\) −5.23012 −0.185028
\(800\) 0 0
\(801\) −60.4717 −2.13666
\(802\) 0 0
\(803\) 30.3551 1.07121
\(804\) 0 0
\(805\) 18.0649 0.636702
\(806\) 0 0
\(807\) −33.6617 −1.18495
\(808\) 0 0
\(809\) 55.0741 1.93630 0.968151 0.250366i \(-0.0805509\pi\)
0.968151 + 0.250366i \(0.0805509\pi\)
\(810\) 0 0
\(811\) −14.1223 −0.495902 −0.247951 0.968773i \(-0.579757\pi\)
−0.247951 + 0.968773i \(0.579757\pi\)
\(812\) 0 0
\(813\) −18.5303 −0.649885
\(814\) 0 0
\(815\) 25.9181 0.907872
\(816\) 0 0
\(817\) −18.2684 −0.639129
\(818\) 0 0
\(819\) −19.5534 −0.683250
\(820\) 0 0
\(821\) −42.8827 −1.49662 −0.748308 0.663352i \(-0.769133\pi\)
−0.748308 + 0.663352i \(0.769133\pi\)
\(822\) 0 0
\(823\) 39.9210 1.39156 0.695779 0.718256i \(-0.255059\pi\)
0.695779 + 0.718256i \(0.255059\pi\)
\(824\) 0 0
\(825\) 124.159 4.32266
\(826\) 0 0
\(827\) −48.2874 −1.67912 −0.839558 0.543270i \(-0.817186\pi\)
−0.839558 + 0.543270i \(0.817186\pi\)
\(828\) 0 0
\(829\) −7.12920 −0.247607 −0.123804 0.992307i \(-0.539509\pi\)
−0.123804 + 0.992307i \(0.539509\pi\)
\(830\) 0 0
\(831\) 40.3011 1.39803
\(832\) 0 0
\(833\) −31.2736 −1.08356
\(834\) 0 0
\(835\) 26.2600 0.908764
\(836\) 0 0
\(837\) 129.132 4.46345
\(838\) 0 0
\(839\) −33.3109 −1.15002 −0.575010 0.818146i \(-0.695002\pi\)
−0.575010 + 0.818146i \(0.695002\pi\)
\(840\) 0 0
\(841\) −1.03666 −0.0357471
\(842\) 0 0
\(843\) 48.6523 1.67567
\(844\) 0 0
\(845\) 23.5555 0.810333
\(846\) 0 0
\(847\) −21.9999 −0.755924
\(848\) 0 0
\(849\) 64.2039 2.20347
\(850\) 0 0
\(851\) −22.4305 −0.768906
\(852\) 0 0
\(853\) −9.10908 −0.311889 −0.155944 0.987766i \(-0.549842\pi\)
−0.155944 + 0.987766i \(0.549842\pi\)
\(854\) 0 0
\(855\) −128.532 −4.39570
\(856\) 0 0
\(857\) −7.22096 −0.246663 −0.123332 0.992366i \(-0.539358\pi\)
−0.123332 + 0.992366i \(0.539358\pi\)
\(858\) 0 0
\(859\) −15.4990 −0.528818 −0.264409 0.964411i \(-0.585177\pi\)
−0.264409 + 0.964411i \(0.585177\pi\)
\(860\) 0 0
\(861\) −41.8368 −1.42580
\(862\) 0 0
\(863\) −8.22895 −0.280117 −0.140058 0.990143i \(-0.544729\pi\)
−0.140058 + 0.990143i \(0.544729\pi\)
\(864\) 0 0
\(865\) 31.1603 1.05948
\(866\) 0 0
\(867\) −34.1069 −1.15833
\(868\) 0 0
\(869\) 82.1486 2.78670
\(870\) 0 0
\(871\) 12.7058 0.430520
\(872\) 0 0
\(873\) −80.5837 −2.72735
\(874\) 0 0
\(875\) 5.44452 0.184058
\(876\) 0 0
\(877\) −27.2276 −0.919411 −0.459706 0.888071i \(-0.652045\pi\)
−0.459706 + 0.888071i \(0.652045\pi\)
\(878\) 0 0
\(879\) 37.8890 1.27797
\(880\) 0 0
\(881\) 35.2731 1.18838 0.594191 0.804324i \(-0.297472\pi\)
0.594191 + 0.804324i \(0.297472\pi\)
\(882\) 0 0
\(883\) 26.3181 0.885674 0.442837 0.896602i \(-0.353972\pi\)
0.442837 + 0.896602i \(0.353972\pi\)
\(884\) 0 0
\(885\) 46.4364 1.56094
\(886\) 0 0
\(887\) −52.0204 −1.74667 −0.873337 0.487116i \(-0.838049\pi\)
−0.873337 + 0.487116i \(0.838049\pi\)
\(888\) 0 0
\(889\) 1.86386 0.0625120
\(890\) 0 0
\(891\) −166.489 −5.57758
\(892\) 0 0
\(893\) −4.81048 −0.160976
\(894\) 0 0
\(895\) 44.0657 1.47295
\(896\) 0 0
\(897\) −42.6727 −1.42480
\(898\) 0 0
\(899\) −42.7373 −1.42537
\(900\) 0 0
\(901\) 22.3696 0.745241
\(902\) 0 0
\(903\) −12.6370 −0.420532
\(904\) 0 0
\(905\) 0.895949 0.0297824
\(906\) 0 0
\(907\) 46.2955 1.53722 0.768608 0.639720i \(-0.220950\pi\)
0.768608 + 0.639720i \(0.220950\pi\)
\(908\) 0 0
\(909\) 154.708 5.13135
\(910\) 0 0
\(911\) 34.5338 1.14416 0.572079 0.820199i \(-0.306137\pi\)
0.572079 + 0.820199i \(0.306137\pi\)
\(912\) 0 0
\(913\) 56.3578 1.86517
\(914\) 0 0
\(915\) 57.8468 1.91236
\(916\) 0 0
\(917\) −10.6071 −0.350278
\(918\) 0 0
\(919\) 35.4876 1.17063 0.585315 0.810806i \(-0.300971\pi\)
0.585315 + 0.810806i \(0.300971\pi\)
\(920\) 0 0
\(921\) 89.4178 2.94642
\(922\) 0 0
\(923\) 25.8885 0.852131
\(924\) 0 0
\(925\) −28.1054 −0.924100
\(926\) 0 0
\(927\) −54.8321 −1.80092
\(928\) 0 0
\(929\) −27.0523 −0.887557 −0.443779 0.896136i \(-0.646362\pi\)
−0.443779 + 0.896136i \(0.646362\pi\)
\(930\) 0 0
\(931\) −28.7643 −0.942711
\(932\) 0 0
\(933\) −96.2105 −3.14979
\(934\) 0 0
\(935\) 101.912 3.33286
\(936\) 0 0
\(937\) −51.6534 −1.68744 −0.843722 0.536780i \(-0.819640\pi\)
−0.843722 + 0.536780i \(0.819640\pi\)
\(938\) 0 0
\(939\) −57.1036 −1.86351
\(940\) 0 0
\(941\) 45.5605 1.48523 0.742615 0.669718i \(-0.233585\pi\)
0.742615 + 0.669718i \(0.233585\pi\)
\(942\) 0 0
\(943\) −66.0596 −2.15120
\(944\) 0 0
\(945\) −54.9347 −1.78703
\(946\) 0 0
\(947\) −16.6145 −0.539898 −0.269949 0.962875i \(-0.587007\pi\)
−0.269949 + 0.962875i \(0.587007\pi\)
\(948\) 0 0
\(949\) −13.0724 −0.424349
\(950\) 0 0
\(951\) −26.9086 −0.872572
\(952\) 0 0
\(953\) 4.18754 0.135648 0.0678239 0.997697i \(-0.478394\pi\)
0.0678239 + 0.997697i \(0.478394\pi\)
\(954\) 0 0
\(955\) 26.3733 0.853419
\(956\) 0 0
\(957\) 99.7267 3.22371
\(958\) 0 0
\(959\) −11.5403 −0.372655
\(960\) 0 0
\(961\) 34.3167 1.10699
\(962\) 0 0
\(963\) −51.1015 −1.64672
\(964\) 0 0
\(965\) −68.9808 −2.22057
\(966\) 0 0
\(967\) 39.4921 1.26998 0.634990 0.772520i \(-0.281004\pi\)
0.634990 + 0.772520i \(0.281004\pi\)
\(968\) 0 0
\(969\) −82.8756 −2.66235
\(970\) 0 0
\(971\) 10.5070 0.337185 0.168592 0.985686i \(-0.446078\pi\)
0.168592 + 0.985686i \(0.446078\pi\)
\(972\) 0 0
\(973\) −7.99496 −0.256307
\(974\) 0 0
\(975\) −53.4690 −1.71238
\(976\) 0 0
\(977\) −43.7558 −1.39987 −0.699937 0.714205i \(-0.746788\pi\)
−0.699937 + 0.714205i \(0.746788\pi\)
\(978\) 0 0
\(979\) 44.1001 1.40945
\(980\) 0 0
\(981\) −130.186 −4.15651
\(982\) 0 0
\(983\) −61.6919 −1.96767 −0.983833 0.179089i \(-0.942685\pi\)
−0.983833 + 0.179089i \(0.942685\pi\)
\(984\) 0 0
\(985\) 3.96437 0.126315
\(986\) 0 0
\(987\) −3.32760 −0.105919
\(988\) 0 0
\(989\) −19.9536 −0.634486
\(990\) 0 0
\(991\) 52.9225 1.68114 0.840569 0.541705i \(-0.182221\pi\)
0.840569 + 0.541705i \(0.182221\pi\)
\(992\) 0 0
\(993\) 28.1441 0.893127
\(994\) 0 0
\(995\) −73.3088 −2.32405
\(996\) 0 0
\(997\) −58.6863 −1.85861 −0.929306 0.369310i \(-0.879594\pi\)
−0.929306 + 0.369310i \(0.879594\pi\)
\(998\) 0 0
\(999\) 68.2104 2.15808
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 6016.2.a.n.1.1 yes 13
4.3 odd 2 6016.2.a.p.1.13 yes 13
8.3 odd 2 6016.2.a.m.1.1 13
8.5 even 2 6016.2.a.o.1.13 yes 13
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
6016.2.a.m.1.1 13 8.3 odd 2
6016.2.a.n.1.1 yes 13 1.1 even 1 trivial
6016.2.a.o.1.13 yes 13 8.5 even 2
6016.2.a.p.1.13 yes 13 4.3 odd 2