Properties

Label 6032.2.a.ba.1.10
Level $6032$
Weight $2$
Character 6032.1
Self dual yes
Analytic conductor $48.166$
Analytic rank $0$
Dimension $10$
CM no
Inner twists $1$

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [6032,2,Mod(1,6032)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(6032, 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("6032.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 6032 = 2^{4} \cdot 13 \cdot 29 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 6032.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: \(48.1657624992\)
Analytic rank: \(0\)
Dimension: \(10\)
Coefficient field: \(\mathbb{Q}[x]/(x^{10} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{10} - 2x^{9} - 21x^{8} + 40x^{7} + 138x^{6} - 243x^{5} - 318x^{4} + 448x^{3} + 312x^{2} - 240x - 128 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{2} \)
Twist minimal: no (minimal twist has level 3016)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.10
Root \(-3.19372\) of defining polynomial
Character \(\chi\) \(=\) 6032.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+3.19372 q^{3} +3.55069 q^{5} +0.0377760 q^{7} +7.19984 q^{9} +O(q^{10})\) \(q+3.19372 q^{3} +3.55069 q^{5} +0.0377760 q^{7} +7.19984 q^{9} -2.32931 q^{11} +1.00000 q^{13} +11.3399 q^{15} +4.44877 q^{17} -8.18121 q^{19} +0.120646 q^{21} -3.15419 q^{23} +7.60738 q^{25} +13.4131 q^{27} -1.00000 q^{29} +5.23096 q^{31} -7.43916 q^{33} +0.134131 q^{35} +5.42958 q^{37} +3.19372 q^{39} +11.2645 q^{41} +0.883058 q^{43} +25.5644 q^{45} -6.08755 q^{47} -6.99857 q^{49} +14.2081 q^{51} -13.0163 q^{53} -8.27065 q^{55} -26.1285 q^{57} +1.25215 q^{59} +7.20275 q^{61} +0.271981 q^{63} +3.55069 q^{65} +3.92451 q^{67} -10.0736 q^{69} +7.80178 q^{71} +2.98215 q^{73} +24.2958 q^{75} -0.0879919 q^{77} +10.4220 q^{79} +21.2381 q^{81} +12.2932 q^{83} +15.7962 q^{85} -3.19372 q^{87} -10.6546 q^{89} +0.0377760 q^{91} +16.7062 q^{93} -29.0489 q^{95} -5.83038 q^{97} -16.7707 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 10 q - 2 q^{3} + 5 q^{5} + 2 q^{7} + 16 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 10 q - 2 q^{3} + 5 q^{5} + 2 q^{7} + 16 q^{9} - 4 q^{11} + 10 q^{13} - 8 q^{15} + 10 q^{17} + q^{19} + q^{21} - 23 q^{23} + 25 q^{25} - 2 q^{27} - 10 q^{29} + 13 q^{31} + 15 q^{33} + 12 q^{35} - 7 q^{37} - 2 q^{39} + 16 q^{41} + 12 q^{43} + 55 q^{45} - 11 q^{47} + 25 q^{51} + 11 q^{53} - 22 q^{55} - 6 q^{57} + 11 q^{59} + 34 q^{61} - 37 q^{63} + 5 q^{65} + 23 q^{67} + 2 q^{69} + 4 q^{71} + 39 q^{73} - 11 q^{75} + 32 q^{77} - 5 q^{79} + 38 q^{81} - 6 q^{83} + 45 q^{85} + 2 q^{87} - 24 q^{89} + 2 q^{91} + 13 q^{93} - 33 q^{95} + 19 q^{97}+O(q^{100}) \) 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
\(3\) 3.19372 1.84389 0.921947 0.387316i \(-0.126598\pi\)
0.921947 + 0.387316i \(0.126598\pi\)
\(4\) 0 0
\(5\) 3.55069 1.58792 0.793958 0.607973i \(-0.208017\pi\)
0.793958 + 0.607973i \(0.208017\pi\)
\(6\) 0 0
\(7\) 0.0377760 0.0142780 0.00713898 0.999975i \(-0.497728\pi\)
0.00713898 + 0.999975i \(0.497728\pi\)
\(8\) 0 0
\(9\) 7.19984 2.39995
\(10\) 0 0
\(11\) −2.32931 −0.702314 −0.351157 0.936317i \(-0.614212\pi\)
−0.351157 + 0.936317i \(0.614212\pi\)
\(12\) 0 0
\(13\) 1.00000 0.277350
\(14\) 0 0
\(15\) 11.3399 2.92795
\(16\) 0 0
\(17\) 4.44877 1.07898 0.539492 0.841990i \(-0.318616\pi\)
0.539492 + 0.841990i \(0.318616\pi\)
\(18\) 0 0
\(19\) −8.18121 −1.87690 −0.938449 0.345418i \(-0.887737\pi\)
−0.938449 + 0.345418i \(0.887737\pi\)
\(20\) 0 0
\(21\) 0.120646 0.0263271
\(22\) 0 0
\(23\) −3.15419 −0.657693 −0.328847 0.944383i \(-0.606660\pi\)
−0.328847 + 0.944383i \(0.606660\pi\)
\(24\) 0 0
\(25\) 7.60738 1.52148
\(26\) 0 0
\(27\) 13.4131 2.58135
\(28\) 0 0
\(29\) −1.00000 −0.185695
\(30\) 0 0
\(31\) 5.23096 0.939509 0.469754 0.882797i \(-0.344343\pi\)
0.469754 + 0.882797i \(0.344343\pi\)
\(32\) 0 0
\(33\) −7.43916 −1.29499
\(34\) 0 0
\(35\) 0.134131 0.0226722
\(36\) 0 0
\(37\) 5.42958 0.892617 0.446308 0.894879i \(-0.352738\pi\)
0.446308 + 0.894879i \(0.352738\pi\)
\(38\) 0 0
\(39\) 3.19372 0.511404
\(40\) 0 0
\(41\) 11.2645 1.75922 0.879608 0.475699i \(-0.157805\pi\)
0.879608 + 0.475699i \(0.157805\pi\)
\(42\) 0 0
\(43\) 0.883058 0.134665 0.0673325 0.997731i \(-0.478551\pi\)
0.0673325 + 0.997731i \(0.478551\pi\)
\(44\) 0 0
\(45\) 25.5644 3.81091
\(46\) 0 0
\(47\) −6.08755 −0.887961 −0.443980 0.896036i \(-0.646434\pi\)
−0.443980 + 0.896036i \(0.646434\pi\)
\(48\) 0 0
\(49\) −6.99857 −0.999796
\(50\) 0 0
\(51\) 14.2081 1.98953
\(52\) 0 0
\(53\) −13.0163 −1.78793 −0.893963 0.448141i \(-0.852086\pi\)
−0.893963 + 0.448141i \(0.852086\pi\)
\(54\) 0 0
\(55\) −8.27065 −1.11521
\(56\) 0 0
\(57\) −26.1285 −3.46080
\(58\) 0 0
\(59\) 1.25215 0.163016 0.0815079 0.996673i \(-0.474026\pi\)
0.0815079 + 0.996673i \(0.474026\pi\)
\(60\) 0 0
\(61\) 7.20275 0.922217 0.461109 0.887344i \(-0.347452\pi\)
0.461109 + 0.887344i \(0.347452\pi\)
\(62\) 0 0
\(63\) 0.271981 0.0342663
\(64\) 0 0
\(65\) 3.55069 0.440408
\(66\) 0 0
\(67\) 3.92451 0.479455 0.239727 0.970840i \(-0.422942\pi\)
0.239727 + 0.970840i \(0.422942\pi\)
\(68\) 0 0
\(69\) −10.0736 −1.21272
\(70\) 0 0
\(71\) 7.80178 0.925902 0.462951 0.886384i \(-0.346791\pi\)
0.462951 + 0.886384i \(0.346791\pi\)
\(72\) 0 0
\(73\) 2.98215 0.349035 0.174517 0.984654i \(-0.444163\pi\)
0.174517 + 0.984654i \(0.444163\pi\)
\(74\) 0 0
\(75\) 24.2958 2.80544
\(76\) 0 0
\(77\) −0.0879919 −0.0100276
\(78\) 0 0
\(79\) 10.4220 1.17257 0.586285 0.810105i \(-0.300590\pi\)
0.586285 + 0.810105i \(0.300590\pi\)
\(80\) 0 0
\(81\) 21.2381 2.35979
\(82\) 0 0
\(83\) 12.2932 1.34935 0.674677 0.738113i \(-0.264283\pi\)
0.674677 + 0.738113i \(0.264283\pi\)
\(84\) 0 0
\(85\) 15.7962 1.71334
\(86\) 0 0
\(87\) −3.19372 −0.342403
\(88\) 0 0
\(89\) −10.6546 −1.12938 −0.564690 0.825303i \(-0.691004\pi\)
−0.564690 + 0.825303i \(0.691004\pi\)
\(90\) 0 0
\(91\) 0.0377760 0.00396000
\(92\) 0 0
\(93\) 16.7062 1.73235
\(94\) 0 0
\(95\) −29.0489 −2.98036
\(96\) 0 0
\(97\) −5.83038 −0.591985 −0.295993 0.955190i \(-0.595650\pi\)
−0.295993 + 0.955190i \(0.595650\pi\)
\(98\) 0 0
\(99\) −16.7707 −1.68551
\(100\) 0 0
\(101\) 5.27263 0.524647 0.262323 0.964980i \(-0.415511\pi\)
0.262323 + 0.964980i \(0.415511\pi\)
\(102\) 0 0
\(103\) −9.88582 −0.974079 −0.487040 0.873380i \(-0.661923\pi\)
−0.487040 + 0.873380i \(0.661923\pi\)
\(104\) 0 0
\(105\) 0.428375 0.0418051
\(106\) 0 0
\(107\) 14.7126 1.42232 0.711159 0.703031i \(-0.248171\pi\)
0.711159 + 0.703031i \(0.248171\pi\)
\(108\) 0 0
\(109\) 5.50664 0.527441 0.263720 0.964599i \(-0.415050\pi\)
0.263720 + 0.964599i \(0.415050\pi\)
\(110\) 0 0
\(111\) 17.3405 1.64589
\(112\) 0 0
\(113\) −7.36130 −0.692493 −0.346246 0.938144i \(-0.612544\pi\)
−0.346246 + 0.938144i \(0.612544\pi\)
\(114\) 0 0
\(115\) −11.1995 −1.04436
\(116\) 0 0
\(117\) 7.19984 0.665625
\(118\) 0 0
\(119\) 0.168056 0.0154057
\(120\) 0 0
\(121\) −5.57431 −0.506756
\(122\) 0 0
\(123\) 35.9756 3.24381
\(124\) 0 0
\(125\) 9.25797 0.828058
\(126\) 0 0
\(127\) −10.3678 −0.919990 −0.459995 0.887922i \(-0.652149\pi\)
−0.459995 + 0.887922i \(0.652149\pi\)
\(128\) 0 0
\(129\) 2.82024 0.248308
\(130\) 0 0
\(131\) −14.4737 −1.26457 −0.632285 0.774736i \(-0.717883\pi\)
−0.632285 + 0.774736i \(0.717883\pi\)
\(132\) 0 0
\(133\) −0.309053 −0.0267983
\(134\) 0 0
\(135\) 47.6257 4.09897
\(136\) 0 0
\(137\) 8.88198 0.758839 0.379420 0.925225i \(-0.376124\pi\)
0.379420 + 0.925225i \(0.376124\pi\)
\(138\) 0 0
\(139\) −5.67810 −0.481610 −0.240805 0.970574i \(-0.577411\pi\)
−0.240805 + 0.970574i \(0.577411\pi\)
\(140\) 0 0
\(141\) −19.4419 −1.63731
\(142\) 0 0
\(143\) −2.32931 −0.194787
\(144\) 0 0
\(145\) −3.55069 −0.294868
\(146\) 0 0
\(147\) −22.3515 −1.84352
\(148\) 0 0
\(149\) −0.441665 −0.0361826 −0.0180913 0.999836i \(-0.505759\pi\)
−0.0180913 + 0.999836i \(0.505759\pi\)
\(150\) 0 0
\(151\) −14.0305 −1.14178 −0.570892 0.821025i \(-0.693402\pi\)
−0.570892 + 0.821025i \(0.693402\pi\)
\(152\) 0 0
\(153\) 32.0304 2.58950
\(154\) 0 0
\(155\) 18.5735 1.49186
\(156\) 0 0
\(157\) −18.8799 −1.50678 −0.753392 0.657572i \(-0.771584\pi\)
−0.753392 + 0.657572i \(0.771584\pi\)
\(158\) 0 0
\(159\) −41.5704 −3.29675
\(160\) 0 0
\(161\) −0.119152 −0.00939052
\(162\) 0 0
\(163\) 16.9553 1.32804 0.664021 0.747714i \(-0.268849\pi\)
0.664021 + 0.747714i \(0.268849\pi\)
\(164\) 0 0
\(165\) −26.4141 −2.05634
\(166\) 0 0
\(167\) −0.819711 −0.0634311 −0.0317156 0.999497i \(-0.510097\pi\)
−0.0317156 + 0.999497i \(0.510097\pi\)
\(168\) 0 0
\(169\) 1.00000 0.0769231
\(170\) 0 0
\(171\) −58.9034 −4.50445
\(172\) 0 0
\(173\) −2.83996 −0.215919 −0.107959 0.994155i \(-0.534432\pi\)
−0.107959 + 0.994155i \(0.534432\pi\)
\(174\) 0 0
\(175\) 0.287376 0.0217236
\(176\) 0 0
\(177\) 3.99901 0.300584
\(178\) 0 0
\(179\) −13.6353 −1.01915 −0.509576 0.860426i \(-0.670198\pi\)
−0.509576 + 0.860426i \(0.670198\pi\)
\(180\) 0 0
\(181\) −14.8639 −1.10482 −0.552412 0.833571i \(-0.686293\pi\)
−0.552412 + 0.833571i \(0.686293\pi\)
\(182\) 0 0
\(183\) 23.0035 1.70047
\(184\) 0 0
\(185\) 19.2787 1.41740
\(186\) 0 0
\(187\) −10.3626 −0.757786
\(188\) 0 0
\(189\) 0.506693 0.0368565
\(190\) 0 0
\(191\) −11.6865 −0.845603 −0.422802 0.906222i \(-0.638953\pi\)
−0.422802 + 0.906222i \(0.638953\pi\)
\(192\) 0 0
\(193\) 6.66785 0.479963 0.239981 0.970778i \(-0.422859\pi\)
0.239981 + 0.970778i \(0.422859\pi\)
\(194\) 0 0
\(195\) 11.3399 0.812067
\(196\) 0 0
\(197\) 26.1055 1.85994 0.929969 0.367637i \(-0.119833\pi\)
0.929969 + 0.367637i \(0.119833\pi\)
\(198\) 0 0
\(199\) −21.0213 −1.49016 −0.745080 0.666975i \(-0.767589\pi\)
−0.745080 + 0.666975i \(0.767589\pi\)
\(200\) 0 0
\(201\) 12.5338 0.884064
\(202\) 0 0
\(203\) −0.0377760 −0.00265135
\(204\) 0 0
\(205\) 39.9966 2.79349
\(206\) 0 0
\(207\) −22.7096 −1.57843
\(208\) 0 0
\(209\) 19.0566 1.31817
\(210\) 0 0
\(211\) −19.5071 −1.34292 −0.671462 0.741039i \(-0.734333\pi\)
−0.671462 + 0.741039i \(0.734333\pi\)
\(212\) 0 0
\(213\) 24.9167 1.70726
\(214\) 0 0
\(215\) 3.13546 0.213837
\(216\) 0 0
\(217\) 0.197605 0.0134143
\(218\) 0 0
\(219\) 9.52416 0.643583
\(220\) 0 0
\(221\) 4.44877 0.299257
\(222\) 0 0
\(223\) 10.8263 0.724981 0.362491 0.931987i \(-0.381926\pi\)
0.362491 + 0.931987i \(0.381926\pi\)
\(224\) 0 0
\(225\) 54.7719 3.65146
\(226\) 0 0
\(227\) 14.4455 0.958782 0.479391 0.877601i \(-0.340858\pi\)
0.479391 + 0.877601i \(0.340858\pi\)
\(228\) 0 0
\(229\) −0.687312 −0.0454188 −0.0227094 0.999742i \(-0.507229\pi\)
−0.0227094 + 0.999742i \(0.507229\pi\)
\(230\) 0 0
\(231\) −0.281021 −0.0184899
\(232\) 0 0
\(233\) −21.5573 −1.41227 −0.706133 0.708079i \(-0.749562\pi\)
−0.706133 + 0.708079i \(0.749562\pi\)
\(234\) 0 0
\(235\) −21.6150 −1.41001
\(236\) 0 0
\(237\) 33.2850 2.16209
\(238\) 0 0
\(239\) −29.4262 −1.90342 −0.951711 0.306995i \(-0.900676\pi\)
−0.951711 + 0.306995i \(0.900676\pi\)
\(240\) 0 0
\(241\) 27.5514 1.77474 0.887370 0.461058i \(-0.152530\pi\)
0.887370 + 0.461058i \(0.152530\pi\)
\(242\) 0 0
\(243\) 27.5894 1.76986
\(244\) 0 0
\(245\) −24.8497 −1.58759
\(246\) 0 0
\(247\) −8.18121 −0.520558
\(248\) 0 0
\(249\) 39.2610 2.48806
\(250\) 0 0
\(251\) 27.5958 1.74183 0.870917 0.491431i \(-0.163526\pi\)
0.870917 + 0.491431i \(0.163526\pi\)
\(252\) 0 0
\(253\) 7.34708 0.461907
\(254\) 0 0
\(255\) 50.4486 3.15921
\(256\) 0 0
\(257\) 3.25598 0.203102 0.101551 0.994830i \(-0.467619\pi\)
0.101551 + 0.994830i \(0.467619\pi\)
\(258\) 0 0
\(259\) 0.205107 0.0127448
\(260\) 0 0
\(261\) −7.19984 −0.445659
\(262\) 0 0
\(263\) −1.06561 −0.0657081 −0.0328541 0.999460i \(-0.510460\pi\)
−0.0328541 + 0.999460i \(0.510460\pi\)
\(264\) 0 0
\(265\) −46.2168 −2.83907
\(266\) 0 0
\(267\) −34.0277 −2.08246
\(268\) 0 0
\(269\) −7.15804 −0.436433 −0.218217 0.975900i \(-0.570024\pi\)
−0.218217 + 0.975900i \(0.570024\pi\)
\(270\) 0 0
\(271\) −14.4567 −0.878184 −0.439092 0.898442i \(-0.644700\pi\)
−0.439092 + 0.898442i \(0.644700\pi\)
\(272\) 0 0
\(273\) 0.120646 0.00730181
\(274\) 0 0
\(275\) −17.7199 −1.06855
\(276\) 0 0
\(277\) −6.45236 −0.387685 −0.193842 0.981033i \(-0.562095\pi\)
−0.193842 + 0.981033i \(0.562095\pi\)
\(278\) 0 0
\(279\) 37.6621 2.25477
\(280\) 0 0
\(281\) −8.19756 −0.489025 −0.244513 0.969646i \(-0.578628\pi\)
−0.244513 + 0.969646i \(0.578628\pi\)
\(282\) 0 0
\(283\) 20.0718 1.19314 0.596572 0.802560i \(-0.296529\pi\)
0.596572 + 0.802560i \(0.296529\pi\)
\(284\) 0 0
\(285\) −92.7740 −5.49546
\(286\) 0 0
\(287\) 0.425526 0.0251180
\(288\) 0 0
\(289\) 2.79154 0.164208
\(290\) 0 0
\(291\) −18.6206 −1.09156
\(292\) 0 0
\(293\) −33.2167 −1.94054 −0.970269 0.242028i \(-0.922188\pi\)
−0.970269 + 0.242028i \(0.922188\pi\)
\(294\) 0 0
\(295\) 4.44599 0.258855
\(296\) 0 0
\(297\) −31.2433 −1.81292
\(298\) 0 0
\(299\) −3.15419 −0.182411
\(300\) 0 0
\(301\) 0.0333583 0.00192274
\(302\) 0 0
\(303\) 16.8393 0.967393
\(304\) 0 0
\(305\) 25.5747 1.46440
\(306\) 0 0
\(307\) −22.0435 −1.25809 −0.629045 0.777369i \(-0.716554\pi\)
−0.629045 + 0.777369i \(0.716554\pi\)
\(308\) 0 0
\(309\) −31.5725 −1.79610
\(310\) 0 0
\(311\) 14.4470 0.819212 0.409606 0.912263i \(-0.365666\pi\)
0.409606 + 0.912263i \(0.365666\pi\)
\(312\) 0 0
\(313\) −24.3826 −1.37819 −0.689093 0.724673i \(-0.741991\pi\)
−0.689093 + 0.724673i \(0.741991\pi\)
\(314\) 0 0
\(315\) 0.965718 0.0544121
\(316\) 0 0
\(317\) −19.2482 −1.08109 −0.540544 0.841316i \(-0.681781\pi\)
−0.540544 + 0.841316i \(0.681781\pi\)
\(318\) 0 0
\(319\) 2.32931 0.130416
\(320\) 0 0
\(321\) 46.9878 2.62260
\(322\) 0 0
\(323\) −36.3963 −2.02514
\(324\) 0 0
\(325\) 7.60738 0.421981
\(326\) 0 0
\(327\) 17.5867 0.972545
\(328\) 0 0
\(329\) −0.229963 −0.0126783
\(330\) 0 0
\(331\) −25.3527 −1.39351 −0.696756 0.717309i \(-0.745374\pi\)
−0.696756 + 0.717309i \(0.745374\pi\)
\(332\) 0 0
\(333\) 39.0921 2.14223
\(334\) 0 0
\(335\) 13.9347 0.761334
\(336\) 0 0
\(337\) 13.6008 0.740885 0.370443 0.928855i \(-0.379206\pi\)
0.370443 + 0.928855i \(0.379206\pi\)
\(338\) 0 0
\(339\) −23.5099 −1.27688
\(340\) 0 0
\(341\) −12.1845 −0.659830
\(342\) 0 0
\(343\) −0.528809 −0.0285530
\(344\) 0 0
\(345\) −35.7681 −1.92569
\(346\) 0 0
\(347\) −8.28506 −0.444765 −0.222383 0.974959i \(-0.571383\pi\)
−0.222383 + 0.974959i \(0.571383\pi\)
\(348\) 0 0
\(349\) −15.9737 −0.855055 −0.427528 0.904002i \(-0.640615\pi\)
−0.427528 + 0.904002i \(0.640615\pi\)
\(350\) 0 0
\(351\) 13.4131 0.715938
\(352\) 0 0
\(353\) 10.1717 0.541386 0.270693 0.962666i \(-0.412747\pi\)
0.270693 + 0.962666i \(0.412747\pi\)
\(354\) 0 0
\(355\) 27.7017 1.47025
\(356\) 0 0
\(357\) 0.536725 0.0284065
\(358\) 0 0
\(359\) −9.17392 −0.484181 −0.242090 0.970254i \(-0.577833\pi\)
−0.242090 + 0.970254i \(0.577833\pi\)
\(360\) 0 0
\(361\) 47.9322 2.52275
\(362\) 0 0
\(363\) −17.8028 −0.934404
\(364\) 0 0
\(365\) 10.5887 0.554238
\(366\) 0 0
\(367\) −18.1462 −0.947224 −0.473612 0.880734i \(-0.657050\pi\)
−0.473612 + 0.880734i \(0.657050\pi\)
\(368\) 0 0
\(369\) 81.1024 4.22202
\(370\) 0 0
\(371\) −0.491703 −0.0255279
\(372\) 0 0
\(373\) −34.1562 −1.76854 −0.884271 0.466975i \(-0.845344\pi\)
−0.884271 + 0.466975i \(0.845344\pi\)
\(374\) 0 0
\(375\) 29.5674 1.52685
\(376\) 0 0
\(377\) −1.00000 −0.0515026
\(378\) 0 0
\(379\) 20.0710 1.03098 0.515489 0.856896i \(-0.327610\pi\)
0.515489 + 0.856896i \(0.327610\pi\)
\(380\) 0 0
\(381\) −33.1117 −1.69636
\(382\) 0 0
\(383\) −13.4374 −0.686621 −0.343310 0.939222i \(-0.611548\pi\)
−0.343310 + 0.939222i \(0.611548\pi\)
\(384\) 0 0
\(385\) −0.312432 −0.0159230
\(386\) 0 0
\(387\) 6.35787 0.323189
\(388\) 0 0
\(389\) −4.53820 −0.230096 −0.115048 0.993360i \(-0.536702\pi\)
−0.115048 + 0.993360i \(0.536702\pi\)
\(390\) 0 0
\(391\) −14.0322 −0.709641
\(392\) 0 0
\(393\) −46.2248 −2.33173
\(394\) 0 0
\(395\) 37.0054 1.86194
\(396\) 0 0
\(397\) −4.09663 −0.205604 −0.102802 0.994702i \(-0.532781\pi\)
−0.102802 + 0.994702i \(0.532781\pi\)
\(398\) 0 0
\(399\) −0.987028 −0.0494132
\(400\) 0 0
\(401\) −29.7356 −1.48493 −0.742463 0.669888i \(-0.766342\pi\)
−0.742463 + 0.669888i \(0.766342\pi\)
\(402\) 0 0
\(403\) 5.23096 0.260573
\(404\) 0 0
\(405\) 75.4100 3.74715
\(406\) 0 0
\(407\) −12.6472 −0.626897
\(408\) 0 0
\(409\) 30.4427 1.50529 0.752646 0.658425i \(-0.228777\pi\)
0.752646 + 0.658425i \(0.228777\pi\)
\(410\) 0 0
\(411\) 28.3666 1.39922
\(412\) 0 0
\(413\) 0.0473011 0.00232753
\(414\) 0 0
\(415\) 43.6493 2.14266
\(416\) 0 0
\(417\) −18.1342 −0.888037
\(418\) 0 0
\(419\) 22.4296 1.09576 0.547878 0.836558i \(-0.315436\pi\)
0.547878 + 0.836558i \(0.315436\pi\)
\(420\) 0 0
\(421\) 1.98970 0.0969720 0.0484860 0.998824i \(-0.484560\pi\)
0.0484860 + 0.998824i \(0.484560\pi\)
\(422\) 0 0
\(423\) −43.8294 −2.13106
\(424\) 0 0
\(425\) 33.8434 1.64165
\(426\) 0 0
\(427\) 0.272091 0.0131674
\(428\) 0 0
\(429\) −7.43916 −0.359166
\(430\) 0 0
\(431\) 1.12747 0.0543085 0.0271543 0.999631i \(-0.491355\pi\)
0.0271543 + 0.999631i \(0.491355\pi\)
\(432\) 0 0
\(433\) −14.0873 −0.676992 −0.338496 0.940968i \(-0.609918\pi\)
−0.338496 + 0.940968i \(0.609918\pi\)
\(434\) 0 0
\(435\) −11.3399 −0.543706
\(436\) 0 0
\(437\) 25.8051 1.23442
\(438\) 0 0
\(439\) −2.31341 −0.110413 −0.0552066 0.998475i \(-0.517582\pi\)
−0.0552066 + 0.998475i \(0.517582\pi\)
\(440\) 0 0
\(441\) −50.3886 −2.39946
\(442\) 0 0
\(443\) −17.3531 −0.824471 −0.412236 0.911077i \(-0.635252\pi\)
−0.412236 + 0.911077i \(0.635252\pi\)
\(444\) 0 0
\(445\) −37.8310 −1.79336
\(446\) 0 0
\(447\) −1.41055 −0.0667169
\(448\) 0 0
\(449\) 21.0151 0.991762 0.495881 0.868390i \(-0.334845\pi\)
0.495881 + 0.868390i \(0.334845\pi\)
\(450\) 0 0
\(451\) −26.2385 −1.23552
\(452\) 0 0
\(453\) −44.8094 −2.10533
\(454\) 0 0
\(455\) 0.134131 0.00628814
\(456\) 0 0
\(457\) 2.10681 0.0985523 0.0492761 0.998785i \(-0.484309\pi\)
0.0492761 + 0.998785i \(0.484309\pi\)
\(458\) 0 0
\(459\) 59.6718 2.78524
\(460\) 0 0
\(461\) −24.6745 −1.14921 −0.574603 0.818432i \(-0.694844\pi\)
−0.574603 + 0.818432i \(0.694844\pi\)
\(462\) 0 0
\(463\) −3.79916 −0.176562 −0.0882811 0.996096i \(-0.528137\pi\)
−0.0882811 + 0.996096i \(0.528137\pi\)
\(464\) 0 0
\(465\) 59.3186 2.75083
\(466\) 0 0
\(467\) 25.3345 1.17234 0.586170 0.810188i \(-0.300635\pi\)
0.586170 + 0.810188i \(0.300635\pi\)
\(468\) 0 0
\(469\) 0.148252 0.00684564
\(470\) 0 0
\(471\) −60.2972 −2.77835
\(472\) 0 0
\(473\) −2.05692 −0.0945771
\(474\) 0 0
\(475\) −62.2375 −2.85565
\(476\) 0 0
\(477\) −93.7152 −4.29092
\(478\) 0 0
\(479\) −15.8039 −0.722099 −0.361049 0.932547i \(-0.617581\pi\)
−0.361049 + 0.932547i \(0.617581\pi\)
\(480\) 0 0
\(481\) 5.42958 0.247567
\(482\) 0 0
\(483\) −0.380539 −0.0173151
\(484\) 0 0
\(485\) −20.7018 −0.940022
\(486\) 0 0
\(487\) −16.0835 −0.728813 −0.364406 0.931240i \(-0.618728\pi\)
−0.364406 + 0.931240i \(0.618728\pi\)
\(488\) 0 0
\(489\) 54.1505 2.44877
\(490\) 0 0
\(491\) 15.9636 0.720426 0.360213 0.932870i \(-0.382704\pi\)
0.360213 + 0.932870i \(0.382704\pi\)
\(492\) 0 0
\(493\) −4.44877 −0.200362
\(494\) 0 0
\(495\) −59.5473 −2.67645
\(496\) 0 0
\(497\) 0.294720 0.0132200
\(498\) 0 0
\(499\) 39.8110 1.78219 0.891093 0.453822i \(-0.149940\pi\)
0.891093 + 0.453822i \(0.149940\pi\)
\(500\) 0 0
\(501\) −2.61793 −0.116960
\(502\) 0 0
\(503\) 10.0790 0.449399 0.224700 0.974428i \(-0.427860\pi\)
0.224700 + 0.974428i \(0.427860\pi\)
\(504\) 0 0
\(505\) 18.7215 0.833095
\(506\) 0 0
\(507\) 3.19372 0.141838
\(508\) 0 0
\(509\) −4.69097 −0.207924 −0.103962 0.994581i \(-0.533152\pi\)
−0.103962 + 0.994581i \(0.533152\pi\)
\(510\) 0 0
\(511\) 0.112654 0.00498351
\(512\) 0 0
\(513\) −109.735 −4.84493
\(514\) 0 0
\(515\) −35.1015 −1.54676
\(516\) 0 0
\(517\) 14.1798 0.623627
\(518\) 0 0
\(519\) −9.07005 −0.398131
\(520\) 0 0
\(521\) −8.16585 −0.357752 −0.178876 0.983872i \(-0.557246\pi\)
−0.178876 + 0.983872i \(0.557246\pi\)
\(522\) 0 0
\(523\) 19.2444 0.841498 0.420749 0.907177i \(-0.361767\pi\)
0.420749 + 0.907177i \(0.361767\pi\)
\(524\) 0 0
\(525\) 0.917797 0.0400560
\(526\) 0 0
\(527\) 23.2713 1.01372
\(528\) 0 0
\(529\) −13.0511 −0.567440
\(530\) 0 0
\(531\) 9.01526 0.391229
\(532\) 0 0
\(533\) 11.2645 0.487919
\(534\) 0 0
\(535\) 52.2397 2.25852
\(536\) 0 0
\(537\) −43.5474 −1.87921
\(538\) 0 0
\(539\) 16.3018 0.702170
\(540\) 0 0
\(541\) 6.03172 0.259324 0.129662 0.991558i \(-0.458611\pi\)
0.129662 + 0.991558i \(0.458611\pi\)
\(542\) 0 0
\(543\) −47.4711 −2.03718
\(544\) 0 0
\(545\) 19.5524 0.837532
\(546\) 0 0
\(547\) 33.1719 1.41833 0.709163 0.705045i \(-0.249073\pi\)
0.709163 + 0.705045i \(0.249073\pi\)
\(548\) 0 0
\(549\) 51.8586 2.21327
\(550\) 0 0
\(551\) 8.18121 0.348531
\(552\) 0 0
\(553\) 0.393702 0.0167419
\(554\) 0 0
\(555\) 61.5708 2.61354
\(556\) 0 0
\(557\) 29.2337 1.23867 0.619335 0.785127i \(-0.287402\pi\)
0.619335 + 0.785127i \(0.287402\pi\)
\(558\) 0 0
\(559\) 0.883058 0.0373494
\(560\) 0 0
\(561\) −33.0951 −1.39728
\(562\) 0 0
\(563\) −19.8428 −0.836273 −0.418136 0.908384i \(-0.637317\pi\)
−0.418136 + 0.908384i \(0.637317\pi\)
\(564\) 0 0
\(565\) −26.1377 −1.09962
\(566\) 0 0
\(567\) 0.802291 0.0336931
\(568\) 0 0
\(569\) 8.96656 0.375898 0.187949 0.982179i \(-0.439816\pi\)
0.187949 + 0.982179i \(0.439816\pi\)
\(570\) 0 0
\(571\) 36.8686 1.54290 0.771451 0.636288i \(-0.219531\pi\)
0.771451 + 0.636288i \(0.219531\pi\)
\(572\) 0 0
\(573\) −37.3233 −1.55920
\(574\) 0 0
\(575\) −23.9951 −1.00066
\(576\) 0 0
\(577\) −42.5678 −1.77212 −0.886061 0.463569i \(-0.846569\pi\)
−0.886061 + 0.463569i \(0.846569\pi\)
\(578\) 0 0
\(579\) 21.2952 0.885000
\(580\) 0 0
\(581\) 0.464387 0.0192660
\(582\) 0 0
\(583\) 30.3190 1.25568
\(584\) 0 0
\(585\) 25.5644 1.05696
\(586\) 0 0
\(587\) −28.1990 −1.16390 −0.581949 0.813225i \(-0.697710\pi\)
−0.581949 + 0.813225i \(0.697710\pi\)
\(588\) 0 0
\(589\) −42.7956 −1.76336
\(590\) 0 0
\(591\) 83.3736 3.42953
\(592\) 0 0
\(593\) 18.6955 0.767731 0.383866 0.923389i \(-0.374593\pi\)
0.383866 + 0.923389i \(0.374593\pi\)
\(594\) 0 0
\(595\) 0.596716 0.0244630
\(596\) 0 0
\(597\) −67.1361 −2.74770
\(598\) 0 0
\(599\) 35.5906 1.45419 0.727095 0.686537i \(-0.240870\pi\)
0.727095 + 0.686537i \(0.240870\pi\)
\(600\) 0 0
\(601\) −36.8076 −1.50142 −0.750708 0.660635i \(-0.770287\pi\)
−0.750708 + 0.660635i \(0.770287\pi\)
\(602\) 0 0
\(603\) 28.2558 1.15067
\(604\) 0 0
\(605\) −19.7926 −0.804685
\(606\) 0 0
\(607\) 4.53839 0.184208 0.0921038 0.995749i \(-0.470641\pi\)
0.0921038 + 0.995749i \(0.470641\pi\)
\(608\) 0 0
\(609\) −0.120646 −0.00488881
\(610\) 0 0
\(611\) −6.08755 −0.246276
\(612\) 0 0
\(613\) 26.6161 1.07502 0.537508 0.843259i \(-0.319366\pi\)
0.537508 + 0.843259i \(0.319366\pi\)
\(614\) 0 0
\(615\) 127.738 5.15089
\(616\) 0 0
\(617\) 13.0087 0.523710 0.261855 0.965107i \(-0.415666\pi\)
0.261855 + 0.965107i \(0.415666\pi\)
\(618\) 0 0
\(619\) −29.2205 −1.17447 −0.587235 0.809416i \(-0.699784\pi\)
−0.587235 + 0.809416i \(0.699784\pi\)
\(620\) 0 0
\(621\) −42.3074 −1.69774
\(622\) 0 0
\(623\) −0.402486 −0.0161253
\(624\) 0 0
\(625\) −5.16472 −0.206589
\(626\) 0 0
\(627\) 60.8613 2.43057
\(628\) 0 0
\(629\) 24.1549 0.963120
\(630\) 0 0
\(631\) −44.0809 −1.75483 −0.877417 0.479728i \(-0.840735\pi\)
−0.877417 + 0.479728i \(0.840735\pi\)
\(632\) 0 0
\(633\) −62.3002 −2.47621
\(634\) 0 0
\(635\) −36.8127 −1.46087
\(636\) 0 0
\(637\) −6.99857 −0.277294
\(638\) 0 0
\(639\) 56.1716 2.22211
\(640\) 0 0
\(641\) 45.9291 1.81409 0.907045 0.421034i \(-0.138333\pi\)
0.907045 + 0.421034i \(0.138333\pi\)
\(642\) 0 0
\(643\) −8.53698 −0.336665 −0.168333 0.985730i \(-0.553838\pi\)
−0.168333 + 0.985730i \(0.553838\pi\)
\(644\) 0 0
\(645\) 10.0138 0.394292
\(646\) 0 0
\(647\) 35.1361 1.38134 0.690671 0.723169i \(-0.257315\pi\)
0.690671 + 0.723169i \(0.257315\pi\)
\(648\) 0 0
\(649\) −2.91664 −0.114488
\(650\) 0 0
\(651\) 0.631093 0.0247345
\(652\) 0 0
\(653\) 26.4848 1.03643 0.518215 0.855250i \(-0.326597\pi\)
0.518215 + 0.855250i \(0.326597\pi\)
\(654\) 0 0
\(655\) −51.3914 −2.00803
\(656\) 0 0
\(657\) 21.4710 0.837665
\(658\) 0 0
\(659\) −28.1495 −1.09655 −0.548273 0.836299i \(-0.684715\pi\)
−0.548273 + 0.836299i \(0.684715\pi\)
\(660\) 0 0
\(661\) 33.8455 1.31644 0.658219 0.752827i \(-0.271310\pi\)
0.658219 + 0.752827i \(0.271310\pi\)
\(662\) 0 0
\(663\) 14.2081 0.551797
\(664\) 0 0
\(665\) −1.09735 −0.0425534
\(666\) 0 0
\(667\) 3.15419 0.122131
\(668\) 0 0
\(669\) 34.5761 1.33679
\(670\) 0 0
\(671\) −16.7774 −0.647686
\(672\) 0 0
\(673\) −33.2218 −1.28061 −0.640303 0.768122i \(-0.721191\pi\)
−0.640303 + 0.768122i \(0.721191\pi\)
\(674\) 0 0
\(675\) 102.038 3.92746
\(676\) 0 0
\(677\) 30.2700 1.16337 0.581684 0.813415i \(-0.302394\pi\)
0.581684 + 0.813415i \(0.302394\pi\)
\(678\) 0 0
\(679\) −0.220248 −0.00845235
\(680\) 0 0
\(681\) 46.1349 1.76789
\(682\) 0 0
\(683\) −13.9658 −0.534385 −0.267193 0.963643i \(-0.586096\pi\)
−0.267193 + 0.963643i \(0.586096\pi\)
\(684\) 0 0
\(685\) 31.5371 1.20497
\(686\) 0 0
\(687\) −2.19508 −0.0837475
\(688\) 0 0
\(689\) −13.0163 −0.495881
\(690\) 0 0
\(691\) 43.7373 1.66385 0.831923 0.554892i \(-0.187240\pi\)
0.831923 + 0.554892i \(0.187240\pi\)
\(692\) 0 0
\(693\) −0.633528 −0.0240657
\(694\) 0 0
\(695\) −20.1611 −0.764756
\(696\) 0 0
\(697\) 50.1130 1.89817
\(698\) 0 0
\(699\) −68.8480 −2.60407
\(700\) 0 0
\(701\) 14.8874 0.562289 0.281144 0.959665i \(-0.409286\pi\)
0.281144 + 0.959665i \(0.409286\pi\)
\(702\) 0 0
\(703\) −44.4205 −1.67535
\(704\) 0 0
\(705\) −69.0322 −2.59990
\(706\) 0 0
\(707\) 0.199179 0.00749089
\(708\) 0 0
\(709\) −0.664272 −0.0249473 −0.0124736 0.999922i \(-0.503971\pi\)
−0.0124736 + 0.999922i \(0.503971\pi\)
\(710\) 0 0
\(711\) 75.0369 2.81410
\(712\) 0 0
\(713\) −16.4994 −0.617908
\(714\) 0 0
\(715\) −8.27065 −0.309305
\(716\) 0 0
\(717\) −93.9790 −3.50971
\(718\) 0 0
\(719\) −37.7597 −1.40820 −0.704099 0.710102i \(-0.748649\pi\)
−0.704099 + 0.710102i \(0.748649\pi\)
\(720\) 0 0
\(721\) −0.373446 −0.0139079
\(722\) 0 0
\(723\) 87.9913 3.27243
\(724\) 0 0
\(725\) −7.60738 −0.282531
\(726\) 0 0
\(727\) 32.6139 1.20958 0.604791 0.796384i \(-0.293257\pi\)
0.604791 + 0.796384i \(0.293257\pi\)
\(728\) 0 0
\(729\) 24.3982 0.903638
\(730\) 0 0
\(731\) 3.92852 0.145302
\(732\) 0 0
\(733\) 0.991578 0.0366248 0.0183124 0.999832i \(-0.494171\pi\)
0.0183124 + 0.999832i \(0.494171\pi\)
\(734\) 0 0
\(735\) −79.3631 −2.92735
\(736\) 0 0
\(737\) −9.14139 −0.336728
\(738\) 0 0
\(739\) 50.8377 1.87010 0.935048 0.354521i \(-0.115356\pi\)
0.935048 + 0.354521i \(0.115356\pi\)
\(740\) 0 0
\(741\) −26.1285 −0.959854
\(742\) 0 0
\(743\) −3.88320 −0.142461 −0.0712304 0.997460i \(-0.522693\pi\)
−0.0712304 + 0.997460i \(0.522693\pi\)
\(744\) 0 0
\(745\) −1.56821 −0.0574549
\(746\) 0 0
\(747\) 88.5090 3.23837
\(748\) 0 0
\(749\) 0.555781 0.0203078
\(750\) 0 0
\(751\) −0.720099 −0.0262768 −0.0131384 0.999914i \(-0.504182\pi\)
−0.0131384 + 0.999914i \(0.504182\pi\)
\(752\) 0 0
\(753\) 88.1333 3.21176
\(754\) 0 0
\(755\) −49.8178 −1.81306
\(756\) 0 0
\(757\) 27.5474 1.00123 0.500614 0.865671i \(-0.333108\pi\)
0.500614 + 0.865671i \(0.333108\pi\)
\(758\) 0 0
\(759\) 23.4645 0.851707
\(760\) 0 0
\(761\) 20.2479 0.733987 0.366993 0.930224i \(-0.380387\pi\)
0.366993 + 0.930224i \(0.380387\pi\)
\(762\) 0 0
\(763\) 0.208019 0.00753078
\(764\) 0 0
\(765\) 113.730 4.11191
\(766\) 0 0
\(767\) 1.25215 0.0452124
\(768\) 0 0
\(769\) −22.5959 −0.814830 −0.407415 0.913243i \(-0.633570\pi\)
−0.407415 + 0.913243i \(0.633570\pi\)
\(770\) 0 0
\(771\) 10.3987 0.374499
\(772\) 0 0
\(773\) −16.3845 −0.589308 −0.294654 0.955604i \(-0.595204\pi\)
−0.294654 + 0.955604i \(0.595204\pi\)
\(774\) 0 0
\(775\) 39.7939 1.42944
\(776\) 0 0
\(777\) 0.655055 0.0235000
\(778\) 0 0
\(779\) −92.1570 −3.30187
\(780\) 0 0
\(781\) −18.1728 −0.650273
\(782\) 0 0
\(783\) −13.4131 −0.479345
\(784\) 0 0
\(785\) −67.0368 −2.39265
\(786\) 0 0
\(787\) 1.18929 0.0423935 0.0211967 0.999775i \(-0.493252\pi\)
0.0211967 + 0.999775i \(0.493252\pi\)
\(788\) 0 0
\(789\) −3.40325 −0.121159
\(790\) 0 0
\(791\) −0.278080 −0.00988739
\(792\) 0 0
\(793\) 7.20275 0.255777
\(794\) 0 0
\(795\) −147.603 −5.23495
\(796\) 0 0
\(797\) −22.7655 −0.806396 −0.403198 0.915113i \(-0.632101\pi\)
−0.403198 + 0.915113i \(0.632101\pi\)
\(798\) 0 0
\(799\) −27.0821 −0.958096
\(800\) 0 0
\(801\) −76.7111 −2.71045
\(802\) 0 0
\(803\) −6.94636 −0.245132
\(804\) 0 0
\(805\) −0.423073 −0.0149114
\(806\) 0 0
\(807\) −22.8608 −0.804737
\(808\) 0 0
\(809\) 28.1972 0.991362 0.495681 0.868505i \(-0.334919\pi\)
0.495681 + 0.868505i \(0.334919\pi\)
\(810\) 0 0
\(811\) 19.9733 0.701358 0.350679 0.936496i \(-0.385951\pi\)
0.350679 + 0.936496i \(0.385951\pi\)
\(812\) 0 0
\(813\) −46.1707 −1.61928
\(814\) 0 0
\(815\) 60.2030 2.10882
\(816\) 0 0
\(817\) −7.22448 −0.252753
\(818\) 0 0
\(819\) 0.271981 0.00950378
\(820\) 0 0
\(821\) 40.7669 1.42277 0.711387 0.702801i \(-0.248067\pi\)
0.711387 + 0.702801i \(0.248067\pi\)
\(822\) 0 0
\(823\) −16.5525 −0.576983 −0.288491 0.957483i \(-0.593154\pi\)
−0.288491 + 0.957483i \(0.593154\pi\)
\(824\) 0 0
\(825\) −56.5925 −1.97030
\(826\) 0 0
\(827\) −20.0657 −0.697754 −0.348877 0.937169i \(-0.613437\pi\)
−0.348877 + 0.937169i \(0.613437\pi\)
\(828\) 0 0
\(829\) −10.0835 −0.350213 −0.175107 0.984549i \(-0.556027\pi\)
−0.175107 + 0.984549i \(0.556027\pi\)
\(830\) 0 0
\(831\) −20.6070 −0.714850
\(832\) 0 0
\(833\) −31.1350 −1.07876
\(834\) 0 0
\(835\) −2.91054 −0.100723
\(836\) 0 0
\(837\) 70.1634 2.42520
\(838\) 0 0
\(839\) 40.3002 1.39132 0.695658 0.718373i \(-0.255113\pi\)
0.695658 + 0.718373i \(0.255113\pi\)
\(840\) 0 0
\(841\) 1.00000 0.0344828
\(842\) 0 0
\(843\) −26.1807 −0.901711
\(844\) 0 0
\(845\) 3.55069 0.122147
\(846\) 0 0
\(847\) −0.210575 −0.00723544
\(848\) 0 0
\(849\) 64.1036 2.20003
\(850\) 0 0
\(851\) −17.1259 −0.587068
\(852\) 0 0
\(853\) −29.8835 −1.02319 −0.511596 0.859226i \(-0.670946\pi\)
−0.511596 + 0.859226i \(0.670946\pi\)
\(854\) 0 0
\(855\) −209.147 −7.15269
\(856\) 0 0
\(857\) 46.0659 1.57358 0.786790 0.617221i \(-0.211742\pi\)
0.786790 + 0.617221i \(0.211742\pi\)
\(858\) 0 0
\(859\) −14.0535 −0.479498 −0.239749 0.970835i \(-0.577065\pi\)
−0.239749 + 0.970835i \(0.577065\pi\)
\(860\) 0 0
\(861\) 1.35901 0.0463150
\(862\) 0 0
\(863\) 17.2251 0.586348 0.293174 0.956059i \(-0.405288\pi\)
0.293174 + 0.956059i \(0.405288\pi\)
\(864\) 0 0
\(865\) −10.0838 −0.342860
\(866\) 0 0
\(867\) 8.91538 0.302782
\(868\) 0 0
\(869\) −24.2761 −0.823512
\(870\) 0 0
\(871\) 3.92451 0.132977
\(872\) 0 0
\(873\) −41.9778 −1.42073
\(874\) 0 0
\(875\) 0.349729 0.0118230
\(876\) 0 0
\(877\) 46.9006 1.58372 0.791860 0.610702i \(-0.209113\pi\)
0.791860 + 0.610702i \(0.209113\pi\)
\(878\) 0 0
\(879\) −106.085 −3.57815
\(880\) 0 0
\(881\) −11.7545 −0.396020 −0.198010 0.980200i \(-0.563448\pi\)
−0.198010 + 0.980200i \(0.563448\pi\)
\(882\) 0 0
\(883\) 6.04628 0.203473 0.101737 0.994811i \(-0.467560\pi\)
0.101737 + 0.994811i \(0.467560\pi\)
\(884\) 0 0
\(885\) 14.1992 0.477302
\(886\) 0 0
\(887\) −21.6994 −0.728596 −0.364298 0.931282i \(-0.618691\pi\)
−0.364298 + 0.931282i \(0.618691\pi\)
\(888\) 0 0
\(889\) −0.391652 −0.0131356
\(890\) 0 0
\(891\) −49.4702 −1.65732
\(892\) 0 0
\(893\) 49.8035 1.66661
\(894\) 0 0
\(895\) −48.4148 −1.61833
\(896\) 0 0
\(897\) −10.0736 −0.336347
\(898\) 0 0
\(899\) −5.23096 −0.174462
\(900\) 0 0
\(901\) −57.9065 −1.92914
\(902\) 0 0
\(903\) 0.106537 0.00354533
\(904\) 0 0
\(905\) −52.7770 −1.75437
\(906\) 0 0
\(907\) 30.8716 1.02507 0.512537 0.858665i \(-0.328706\pi\)
0.512537 + 0.858665i \(0.328706\pi\)
\(908\) 0 0
\(909\) 37.9621 1.25912
\(910\) 0 0
\(911\) 4.91820 0.162947 0.0814735 0.996676i \(-0.474037\pi\)
0.0814735 + 0.996676i \(0.474037\pi\)
\(912\) 0 0
\(913\) −28.6347 −0.947669
\(914\) 0 0
\(915\) 81.6784 2.70020
\(916\) 0 0
\(917\) −0.546756 −0.0180555
\(918\) 0 0
\(919\) 23.0447 0.760174 0.380087 0.924951i \(-0.375894\pi\)
0.380087 + 0.924951i \(0.375894\pi\)
\(920\) 0 0
\(921\) −70.4008 −2.31979
\(922\) 0 0
\(923\) 7.80178 0.256799
\(924\) 0 0
\(925\) 41.3048 1.35809
\(926\) 0 0
\(927\) −71.1763 −2.33774
\(928\) 0 0
\(929\) 40.2144 1.31939 0.659695 0.751533i \(-0.270685\pi\)
0.659695 + 0.751533i \(0.270685\pi\)
\(930\) 0 0
\(931\) 57.2568 1.87652
\(932\) 0 0
\(933\) 46.1395 1.51054
\(934\) 0 0
\(935\) −36.7942 −1.20330
\(936\) 0 0
\(937\) 44.9954 1.46994 0.734968 0.678102i \(-0.237197\pi\)
0.734968 + 0.678102i \(0.237197\pi\)
\(938\) 0 0
\(939\) −77.8711 −2.54123
\(940\) 0 0
\(941\) 19.8523 0.647167 0.323583 0.946200i \(-0.395112\pi\)
0.323583 + 0.946200i \(0.395112\pi\)
\(942\) 0 0
\(943\) −35.5303 −1.15702
\(944\) 0 0
\(945\) 1.79911 0.0585249
\(946\) 0 0
\(947\) −6.17415 −0.200633 −0.100317 0.994956i \(-0.531986\pi\)
−0.100317 + 0.994956i \(0.531986\pi\)
\(948\) 0 0
\(949\) 2.98215 0.0968048
\(950\) 0 0
\(951\) −61.4734 −1.99341
\(952\) 0 0
\(953\) −4.21645 −0.136584 −0.0682921 0.997665i \(-0.521755\pi\)
−0.0682921 + 0.997665i \(0.521755\pi\)
\(954\) 0 0
\(955\) −41.4950 −1.34275
\(956\) 0 0
\(957\) 7.43916 0.240474
\(958\) 0 0
\(959\) 0.335525 0.0108347
\(960\) 0 0
\(961\) −3.63703 −0.117324
\(962\) 0 0
\(963\) 105.928 3.41349
\(964\) 0 0
\(965\) 23.6755 0.762140
\(966\) 0 0
\(967\) 20.2560 0.651388 0.325694 0.945475i \(-0.394402\pi\)
0.325694 + 0.945475i \(0.394402\pi\)
\(968\) 0 0
\(969\) −116.240 −3.73415
\(970\) 0 0
\(971\) −2.12516 −0.0681995 −0.0340998 0.999418i \(-0.510856\pi\)
−0.0340998 + 0.999418i \(0.510856\pi\)
\(972\) 0 0
\(973\) −0.214495 −0.00687641
\(974\) 0 0
\(975\) 24.2958 0.778089
\(976\) 0 0
\(977\) 16.0751 0.514289 0.257144 0.966373i \(-0.417218\pi\)
0.257144 + 0.966373i \(0.417218\pi\)
\(978\) 0 0
\(979\) 24.8178 0.793179
\(980\) 0 0
\(981\) 39.6469 1.26583
\(982\) 0 0
\(983\) −18.6455 −0.594700 −0.297350 0.954769i \(-0.596103\pi\)
−0.297350 + 0.954769i \(0.596103\pi\)
\(984\) 0 0
\(985\) 92.6924 2.95343
\(986\) 0 0
\(987\) −0.734437 −0.0233774
\(988\) 0 0
\(989\) −2.78533 −0.0885683
\(990\) 0 0
\(991\) 58.3484 1.85350 0.926748 0.375683i \(-0.122592\pi\)
0.926748 + 0.375683i \(0.122592\pi\)
\(992\) 0 0
\(993\) −80.9694 −2.56949
\(994\) 0 0
\(995\) −74.6400 −2.36625
\(996\) 0 0
\(997\) 43.5110 1.37801 0.689003 0.724758i \(-0.258049\pi\)
0.689003 + 0.724758i \(0.258049\pi\)
\(998\) 0 0
\(999\) 72.8274 2.30416
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 6032.2.a.ba.1.10 10
4.3 odd 2 3016.2.a.g.1.1 10
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
3016.2.a.g.1.1 10 4.3 odd 2
6032.2.a.ba.1.10 10 1.1 even 1 trivial