Properties

Label 1840.2.a.l.1.1
Level $1840$
Weight $2$
Character 1840.1
Self dual yes
Analytic conductor $14.692$
Analytic rank $1$
Dimension $2$
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] = [1840,2,Mod(1,1840)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1840, 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("1840.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1840 = 2^{4} \cdot 5 \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1840.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: \(14.6924739719\)
Analytic rank: \(1\)
Dimension: \(2\)
Coefficient field: \(\Q(\zeta_{10})^+\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{2} - x - 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 230)
Fricke sign: \(+1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Root \(1.61803\) of defining polynomial
Character \(\chi\) \(=\) 1840.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-1.61803 q^{3} +1.00000 q^{5} +0.618034 q^{7} -0.381966 q^{9} +O(q^{10})\) \(q-1.61803 q^{3} +1.00000 q^{5} +0.618034 q^{7} -0.381966 q^{9} +2.85410 q^{11} -7.09017 q^{13} -1.61803 q^{15} +6.09017 q^{17} -1.85410 q^{19} -1.00000 q^{21} -1.00000 q^{23} +1.00000 q^{25} +5.47214 q^{27} -9.23607 q^{29} -9.09017 q^{31} -4.61803 q^{33} +0.618034 q^{35} +6.47214 q^{37} +11.4721 q^{39} +3.32624 q^{41} -0.381966 q^{45} +3.70820 q^{47} -6.61803 q^{49} -9.85410 q^{51} +0.472136 q^{53} +2.85410 q^{55} +3.00000 q^{57} -1.70820 q^{59} -9.32624 q^{61} -0.236068 q^{63} -7.09017 q^{65} -14.4721 q^{67} +1.61803 q^{69} +4.09017 q^{71} +3.23607 q^{73} -1.61803 q^{75} +1.76393 q^{77} -1.52786 q^{79} -7.70820 q^{81} +6.94427 q^{83} +6.09017 q^{85} +14.9443 q^{87} -10.4721 q^{89} -4.38197 q^{91} +14.7082 q^{93} -1.85410 q^{95} +12.3820 q^{97} -1.09017 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q - q^{3} + 2 q^{5} - q^{7} - 3 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 2 q - q^{3} + 2 q^{5} - q^{7} - 3 q^{9} - q^{11} - 3 q^{13} - q^{15} + q^{17} + 3 q^{19} - 2 q^{21} - 2 q^{23} + 2 q^{25} + 2 q^{27} - 14 q^{29} - 7 q^{31} - 7 q^{33} - q^{35} + 4 q^{37} + 14 q^{39} - 9 q^{41} - 3 q^{45} - 6 q^{47} - 11 q^{49} - 13 q^{51} - 8 q^{53} - q^{55} + 6 q^{57} + 10 q^{59} - 3 q^{61} + 4 q^{63} - 3 q^{65} - 20 q^{67} + q^{69} - 3 q^{71} + 2 q^{73} - q^{75} + 8 q^{77} - 12 q^{79} - 2 q^{81} - 4 q^{83} + q^{85} + 12 q^{87} - 12 q^{89} - 11 q^{91} + 16 q^{93} + 3 q^{95} + 27 q^{97} + 9 q^{99}+O(q^{100}) \) 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
\(3\) −1.61803 −0.934172 −0.467086 0.884212i \(-0.654696\pi\)
−0.467086 + 0.884212i \(0.654696\pi\)
\(4\) 0 0
\(5\) 1.00000 0.447214
\(6\) 0 0
\(7\) 0.618034 0.233595 0.116797 0.993156i \(-0.462737\pi\)
0.116797 + 0.993156i \(0.462737\pi\)
\(8\) 0 0
\(9\) −0.381966 −0.127322
\(10\) 0 0
\(11\) 2.85410 0.860544 0.430272 0.902699i \(-0.358418\pi\)
0.430272 + 0.902699i \(0.358418\pi\)
\(12\) 0 0
\(13\) −7.09017 −1.96646 −0.983230 0.182372i \(-0.941623\pi\)
−0.983230 + 0.182372i \(0.941623\pi\)
\(14\) 0 0
\(15\) −1.61803 −0.417775
\(16\) 0 0
\(17\) 6.09017 1.47708 0.738542 0.674208i \(-0.235515\pi\)
0.738542 + 0.674208i \(0.235515\pi\)
\(18\) 0 0
\(19\) −1.85410 −0.425360 −0.212680 0.977122i \(-0.568219\pi\)
−0.212680 + 0.977122i \(0.568219\pi\)
\(20\) 0 0
\(21\) −1.00000 −0.218218
\(22\) 0 0
\(23\) −1.00000 −0.208514
\(24\) 0 0
\(25\) 1.00000 0.200000
\(26\) 0 0
\(27\) 5.47214 1.05311
\(28\) 0 0
\(29\) −9.23607 −1.71509 −0.857547 0.514405i \(-0.828013\pi\)
−0.857547 + 0.514405i \(0.828013\pi\)
\(30\) 0 0
\(31\) −9.09017 −1.63264 −0.816321 0.577598i \(-0.803990\pi\)
−0.816321 + 0.577598i \(0.803990\pi\)
\(32\) 0 0
\(33\) −4.61803 −0.803897
\(34\) 0 0
\(35\) 0.618034 0.104467
\(36\) 0 0
\(37\) 6.47214 1.06401 0.532006 0.846740i \(-0.321438\pi\)
0.532006 + 0.846740i \(0.321438\pi\)
\(38\) 0 0
\(39\) 11.4721 1.83701
\(40\) 0 0
\(41\) 3.32624 0.519471 0.259736 0.965680i \(-0.416365\pi\)
0.259736 + 0.965680i \(0.416365\pi\)
\(42\) 0 0
\(43\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(44\) 0 0
\(45\) −0.381966 −0.0569401
\(46\) 0 0
\(47\) 3.70820 0.540897 0.270449 0.962734i \(-0.412828\pi\)
0.270449 + 0.962734i \(0.412828\pi\)
\(48\) 0 0
\(49\) −6.61803 −0.945433
\(50\) 0 0
\(51\) −9.85410 −1.37985
\(52\) 0 0
\(53\) 0.472136 0.0648529 0.0324264 0.999474i \(-0.489677\pi\)
0.0324264 + 0.999474i \(0.489677\pi\)
\(54\) 0 0
\(55\) 2.85410 0.384847
\(56\) 0 0
\(57\) 3.00000 0.397360
\(58\) 0 0
\(59\) −1.70820 −0.222389 −0.111195 0.993799i \(-0.535468\pi\)
−0.111195 + 0.993799i \(0.535468\pi\)
\(60\) 0 0
\(61\) −9.32624 −1.19410 −0.597051 0.802203i \(-0.703661\pi\)
−0.597051 + 0.802203i \(0.703661\pi\)
\(62\) 0 0
\(63\) −0.236068 −0.0297418
\(64\) 0 0
\(65\) −7.09017 −0.879427
\(66\) 0 0
\(67\) −14.4721 −1.76805 −0.884026 0.467437i \(-0.845177\pi\)
−0.884026 + 0.467437i \(0.845177\pi\)
\(68\) 0 0
\(69\) 1.61803 0.194788
\(70\) 0 0
\(71\) 4.09017 0.485414 0.242707 0.970100i \(-0.421965\pi\)
0.242707 + 0.970100i \(0.421965\pi\)
\(72\) 0 0
\(73\) 3.23607 0.378753 0.189377 0.981905i \(-0.439353\pi\)
0.189377 + 0.981905i \(0.439353\pi\)
\(74\) 0 0
\(75\) −1.61803 −0.186834
\(76\) 0 0
\(77\) 1.76393 0.201019
\(78\) 0 0
\(79\) −1.52786 −0.171898 −0.0859491 0.996300i \(-0.527392\pi\)
−0.0859491 + 0.996300i \(0.527392\pi\)
\(80\) 0 0
\(81\) −7.70820 −0.856467
\(82\) 0 0
\(83\) 6.94427 0.762233 0.381116 0.924527i \(-0.375540\pi\)
0.381116 + 0.924527i \(0.375540\pi\)
\(84\) 0 0
\(85\) 6.09017 0.660572
\(86\) 0 0
\(87\) 14.9443 1.60219
\(88\) 0 0
\(89\) −10.4721 −1.11004 −0.555022 0.831836i \(-0.687290\pi\)
−0.555022 + 0.831836i \(0.687290\pi\)
\(90\) 0 0
\(91\) −4.38197 −0.459355
\(92\) 0 0
\(93\) 14.7082 1.52517
\(94\) 0 0
\(95\) −1.85410 −0.190227
\(96\) 0 0
\(97\) 12.3820 1.25720 0.628599 0.777730i \(-0.283629\pi\)
0.628599 + 0.777730i \(0.283629\pi\)
\(98\) 0 0
\(99\) −1.09017 −0.109566
\(100\) 0 0
\(101\) −0.291796 −0.0290348 −0.0145174 0.999895i \(-0.504621\pi\)
−0.0145174 + 0.999895i \(0.504621\pi\)
\(102\) 0 0
\(103\) −16.5623 −1.63193 −0.815966 0.578100i \(-0.803795\pi\)
−0.815966 + 0.578100i \(0.803795\pi\)
\(104\) 0 0
\(105\) −1.00000 −0.0975900
\(106\) 0 0
\(107\) −18.1803 −1.75756 −0.878780 0.477227i \(-0.841642\pi\)
−0.878780 + 0.477227i \(0.841642\pi\)
\(108\) 0 0
\(109\) −11.5623 −1.10747 −0.553734 0.832694i \(-0.686798\pi\)
−0.553734 + 0.832694i \(0.686798\pi\)
\(110\) 0 0
\(111\) −10.4721 −0.993971
\(112\) 0 0
\(113\) 1.05573 0.0993145 0.0496573 0.998766i \(-0.484187\pi\)
0.0496573 + 0.998766i \(0.484187\pi\)
\(114\) 0 0
\(115\) −1.00000 −0.0932505
\(116\) 0 0
\(117\) 2.70820 0.250374
\(118\) 0 0
\(119\) 3.76393 0.345039
\(120\) 0 0
\(121\) −2.85410 −0.259464
\(122\) 0 0
\(123\) −5.38197 −0.485276
\(124\) 0 0
\(125\) 1.00000 0.0894427
\(126\) 0 0
\(127\) −16.1803 −1.43577 −0.717886 0.696160i \(-0.754890\pi\)
−0.717886 + 0.696160i \(0.754890\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) −2.94427 −0.257242 −0.128621 0.991694i \(-0.541055\pi\)
−0.128621 + 0.991694i \(0.541055\pi\)
\(132\) 0 0
\(133\) −1.14590 −0.0993620
\(134\) 0 0
\(135\) 5.47214 0.470966
\(136\) 0 0
\(137\) −10.3262 −0.882230 −0.441115 0.897451i \(-0.645417\pi\)
−0.441115 + 0.897451i \(0.645417\pi\)
\(138\) 0 0
\(139\) −12.7639 −1.08262 −0.541311 0.840822i \(-0.682072\pi\)
−0.541311 + 0.840822i \(0.682072\pi\)
\(140\) 0 0
\(141\) −6.00000 −0.505291
\(142\) 0 0
\(143\) −20.2361 −1.69223
\(144\) 0 0
\(145\) −9.23607 −0.767014
\(146\) 0 0
\(147\) 10.7082 0.883198
\(148\) 0 0
\(149\) −7.85410 −0.643433 −0.321717 0.946836i \(-0.604260\pi\)
−0.321717 + 0.946836i \(0.604260\pi\)
\(150\) 0 0
\(151\) 2.56231 0.208517 0.104259 0.994550i \(-0.466753\pi\)
0.104259 + 0.994550i \(0.466753\pi\)
\(152\) 0 0
\(153\) −2.32624 −0.188065
\(154\) 0 0
\(155\) −9.09017 −0.730140
\(156\) 0 0
\(157\) −3.70820 −0.295947 −0.147973 0.988991i \(-0.547275\pi\)
−0.147973 + 0.988991i \(0.547275\pi\)
\(158\) 0 0
\(159\) −0.763932 −0.0605838
\(160\) 0 0
\(161\) −0.618034 −0.0487079
\(162\) 0 0
\(163\) −1.38197 −0.108244 −0.0541220 0.998534i \(-0.517236\pi\)
−0.0541220 + 0.998534i \(0.517236\pi\)
\(164\) 0 0
\(165\) −4.61803 −0.359513
\(166\) 0 0
\(167\) 8.00000 0.619059 0.309529 0.950890i \(-0.399829\pi\)
0.309529 + 0.950890i \(0.399829\pi\)
\(168\) 0 0
\(169\) 37.2705 2.86696
\(170\) 0 0
\(171\) 0.708204 0.0541577
\(172\) 0 0
\(173\) −1.43769 −0.109306 −0.0546529 0.998505i \(-0.517405\pi\)
−0.0546529 + 0.998505i \(0.517405\pi\)
\(174\) 0 0
\(175\) 0.618034 0.0467190
\(176\) 0 0
\(177\) 2.76393 0.207750
\(178\) 0 0
\(179\) −2.18034 −0.162966 −0.0814831 0.996675i \(-0.525966\pi\)
−0.0814831 + 0.996675i \(0.525966\pi\)
\(180\) 0 0
\(181\) −12.1459 −0.902797 −0.451399 0.892322i \(-0.649075\pi\)
−0.451399 + 0.892322i \(0.649075\pi\)
\(182\) 0 0
\(183\) 15.0902 1.11550
\(184\) 0 0
\(185\) 6.47214 0.475841
\(186\) 0 0
\(187\) 17.3820 1.27110
\(188\) 0 0
\(189\) 3.38197 0.246002
\(190\) 0 0
\(191\) 13.7082 0.991891 0.495945 0.868354i \(-0.334822\pi\)
0.495945 + 0.868354i \(0.334822\pi\)
\(192\) 0 0
\(193\) 0.763932 0.0549890 0.0274945 0.999622i \(-0.491247\pi\)
0.0274945 + 0.999622i \(0.491247\pi\)
\(194\) 0 0
\(195\) 11.4721 0.821537
\(196\) 0 0
\(197\) −22.5623 −1.60750 −0.803749 0.594969i \(-0.797164\pi\)
−0.803749 + 0.594969i \(0.797164\pi\)
\(198\) 0 0
\(199\) −2.00000 −0.141776 −0.0708881 0.997484i \(-0.522583\pi\)
−0.0708881 + 0.997484i \(0.522583\pi\)
\(200\) 0 0
\(201\) 23.4164 1.65167
\(202\) 0 0
\(203\) −5.70820 −0.400637
\(204\) 0 0
\(205\) 3.32624 0.232315
\(206\) 0 0
\(207\) 0.381966 0.0265485
\(208\) 0 0
\(209\) −5.29180 −0.366041
\(210\) 0 0
\(211\) −14.0000 −0.963800 −0.481900 0.876226i \(-0.660053\pi\)
−0.481900 + 0.876226i \(0.660053\pi\)
\(212\) 0 0
\(213\) −6.61803 −0.453460
\(214\) 0 0
\(215\) 0 0
\(216\) 0 0
\(217\) −5.61803 −0.381377
\(218\) 0 0
\(219\) −5.23607 −0.353821
\(220\) 0 0
\(221\) −43.1803 −2.90462
\(222\) 0 0
\(223\) 20.9443 1.40253 0.701266 0.712900i \(-0.252618\pi\)
0.701266 + 0.712900i \(0.252618\pi\)
\(224\) 0 0
\(225\) −0.381966 −0.0254644
\(226\) 0 0
\(227\) 18.7639 1.24541 0.622703 0.782458i \(-0.286035\pi\)
0.622703 + 0.782458i \(0.286035\pi\)
\(228\) 0 0
\(229\) 10.0000 0.660819 0.330409 0.943838i \(-0.392813\pi\)
0.330409 + 0.943838i \(0.392813\pi\)
\(230\) 0 0
\(231\) −2.85410 −0.187786
\(232\) 0 0
\(233\) 6.29180 0.412189 0.206095 0.978532i \(-0.433925\pi\)
0.206095 + 0.978532i \(0.433925\pi\)
\(234\) 0 0
\(235\) 3.70820 0.241897
\(236\) 0 0
\(237\) 2.47214 0.160582
\(238\) 0 0
\(239\) 20.3607 1.31702 0.658511 0.752571i \(-0.271186\pi\)
0.658511 + 0.752571i \(0.271186\pi\)
\(240\) 0 0
\(241\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(242\) 0 0
\(243\) −3.94427 −0.253025
\(244\) 0 0
\(245\) −6.61803 −0.422811
\(246\) 0 0
\(247\) 13.1459 0.836453
\(248\) 0 0
\(249\) −11.2361 −0.712057
\(250\) 0 0
\(251\) −6.14590 −0.387926 −0.193963 0.981009i \(-0.562134\pi\)
−0.193963 + 0.981009i \(0.562134\pi\)
\(252\) 0 0
\(253\) −2.85410 −0.179436
\(254\) 0 0
\(255\) −9.85410 −0.617088
\(256\) 0 0
\(257\) −7.81966 −0.487777 −0.243888 0.969803i \(-0.578423\pi\)
−0.243888 + 0.969803i \(0.578423\pi\)
\(258\) 0 0
\(259\) 4.00000 0.248548
\(260\) 0 0
\(261\) 3.52786 0.218369
\(262\) 0 0
\(263\) −20.7426 −1.27905 −0.639523 0.768772i \(-0.720868\pi\)
−0.639523 + 0.768772i \(0.720868\pi\)
\(264\) 0 0
\(265\) 0.472136 0.0290031
\(266\) 0 0
\(267\) 16.9443 1.03697
\(268\) 0 0
\(269\) −14.1803 −0.864591 −0.432295 0.901732i \(-0.642296\pi\)
−0.432295 + 0.901732i \(0.642296\pi\)
\(270\) 0 0
\(271\) 30.3262 1.84219 0.921094 0.389341i \(-0.127297\pi\)
0.921094 + 0.389341i \(0.127297\pi\)
\(272\) 0 0
\(273\) 7.09017 0.429117
\(274\) 0 0
\(275\) 2.85410 0.172109
\(276\) 0 0
\(277\) 29.4164 1.76746 0.883730 0.467996i \(-0.155024\pi\)
0.883730 + 0.467996i \(0.155024\pi\)
\(278\) 0 0
\(279\) 3.47214 0.207871
\(280\) 0 0
\(281\) 22.7639 1.35798 0.678991 0.734146i \(-0.262417\pi\)
0.678991 + 0.734146i \(0.262417\pi\)
\(282\) 0 0
\(283\) 26.9443 1.60167 0.800835 0.598885i \(-0.204389\pi\)
0.800835 + 0.598885i \(0.204389\pi\)
\(284\) 0 0
\(285\) 3.00000 0.177705
\(286\) 0 0
\(287\) 2.05573 0.121346
\(288\) 0 0
\(289\) 20.0902 1.18177
\(290\) 0 0
\(291\) −20.0344 −1.17444
\(292\) 0 0
\(293\) −19.8885 −1.16190 −0.580951 0.813939i \(-0.697319\pi\)
−0.580951 + 0.813939i \(0.697319\pi\)
\(294\) 0 0
\(295\) −1.70820 −0.0994555
\(296\) 0 0
\(297\) 15.6180 0.906250
\(298\) 0 0
\(299\) 7.09017 0.410035
\(300\) 0 0
\(301\) 0 0
\(302\) 0 0
\(303\) 0.472136 0.0271235
\(304\) 0 0
\(305\) −9.32624 −0.534019
\(306\) 0 0
\(307\) 28.4508 1.62378 0.811888 0.583813i \(-0.198440\pi\)
0.811888 + 0.583813i \(0.198440\pi\)
\(308\) 0 0
\(309\) 26.7984 1.52451
\(310\) 0 0
\(311\) −4.00000 −0.226819 −0.113410 0.993548i \(-0.536177\pi\)
−0.113410 + 0.993548i \(0.536177\pi\)
\(312\) 0 0
\(313\) 12.7984 0.723407 0.361703 0.932293i \(-0.382195\pi\)
0.361703 + 0.932293i \(0.382195\pi\)
\(314\) 0 0
\(315\) −0.236068 −0.0133009
\(316\) 0 0
\(317\) −11.0902 −0.622886 −0.311443 0.950265i \(-0.600812\pi\)
−0.311443 + 0.950265i \(0.600812\pi\)
\(318\) 0 0
\(319\) −26.3607 −1.47591
\(320\) 0 0
\(321\) 29.4164 1.64186
\(322\) 0 0
\(323\) −11.2918 −0.628292
\(324\) 0 0
\(325\) −7.09017 −0.393292
\(326\) 0 0
\(327\) 18.7082 1.03457
\(328\) 0 0
\(329\) 2.29180 0.126351
\(330\) 0 0
\(331\) −19.2361 −1.05731 −0.528655 0.848837i \(-0.677303\pi\)
−0.528655 + 0.848837i \(0.677303\pi\)
\(332\) 0 0
\(333\) −2.47214 −0.135472
\(334\) 0 0
\(335\) −14.4721 −0.790697
\(336\) 0 0
\(337\) 13.6738 0.744857 0.372429 0.928061i \(-0.378525\pi\)
0.372429 + 0.928061i \(0.378525\pi\)
\(338\) 0 0
\(339\) −1.70820 −0.0927769
\(340\) 0 0
\(341\) −25.9443 −1.40496
\(342\) 0 0
\(343\) −8.41641 −0.454443
\(344\) 0 0
\(345\) 1.61803 0.0871120
\(346\) 0 0
\(347\) 6.38197 0.342602 0.171301 0.985219i \(-0.445203\pi\)
0.171301 + 0.985219i \(0.445203\pi\)
\(348\) 0 0
\(349\) −2.00000 −0.107058 −0.0535288 0.998566i \(-0.517047\pi\)
−0.0535288 + 0.998566i \(0.517047\pi\)
\(350\) 0 0
\(351\) −38.7984 −2.07090
\(352\) 0 0
\(353\) 24.0000 1.27739 0.638696 0.769460i \(-0.279474\pi\)
0.638696 + 0.769460i \(0.279474\pi\)
\(354\) 0 0
\(355\) 4.09017 0.217084
\(356\) 0 0
\(357\) −6.09017 −0.322326
\(358\) 0 0
\(359\) −26.3607 −1.39126 −0.695632 0.718399i \(-0.744875\pi\)
−0.695632 + 0.718399i \(0.744875\pi\)
\(360\) 0 0
\(361\) −15.5623 −0.819069
\(362\) 0 0
\(363\) 4.61803 0.242384
\(364\) 0 0
\(365\) 3.23607 0.169384
\(366\) 0 0
\(367\) −6.47214 −0.337843 −0.168921 0.985630i \(-0.554028\pi\)
−0.168921 + 0.985630i \(0.554028\pi\)
\(368\) 0 0
\(369\) −1.27051 −0.0661401
\(370\) 0 0
\(371\) 0.291796 0.0151493
\(372\) 0 0
\(373\) 20.1803 1.04490 0.522449 0.852670i \(-0.325018\pi\)
0.522449 + 0.852670i \(0.325018\pi\)
\(374\) 0 0
\(375\) −1.61803 −0.0835549
\(376\) 0 0
\(377\) 65.4853 3.37266
\(378\) 0 0
\(379\) 22.4508 1.15322 0.576611 0.817019i \(-0.304375\pi\)
0.576611 + 0.817019i \(0.304375\pi\)
\(380\) 0 0
\(381\) 26.1803 1.34126
\(382\) 0 0
\(383\) 17.8885 0.914062 0.457031 0.889451i \(-0.348913\pi\)
0.457031 + 0.889451i \(0.348913\pi\)
\(384\) 0 0
\(385\) 1.76393 0.0898983
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) 21.3262 1.08128 0.540642 0.841253i \(-0.318182\pi\)
0.540642 + 0.841253i \(0.318182\pi\)
\(390\) 0 0
\(391\) −6.09017 −0.307993
\(392\) 0 0
\(393\) 4.76393 0.240309
\(394\) 0 0
\(395\) −1.52786 −0.0768752
\(396\) 0 0
\(397\) 7.32624 0.367693 0.183847 0.982955i \(-0.441145\pi\)
0.183847 + 0.982955i \(0.441145\pi\)
\(398\) 0 0
\(399\) 1.85410 0.0928212
\(400\) 0 0
\(401\) −1.70820 −0.0853036 −0.0426518 0.999090i \(-0.513581\pi\)
−0.0426518 + 0.999090i \(0.513581\pi\)
\(402\) 0 0
\(403\) 64.4508 3.21053
\(404\) 0 0
\(405\) −7.70820 −0.383024
\(406\) 0 0
\(407\) 18.4721 0.915630
\(408\) 0 0
\(409\) −30.2148 −1.49402 −0.747012 0.664810i \(-0.768512\pi\)
−0.747012 + 0.664810i \(0.768512\pi\)
\(410\) 0 0
\(411\) 16.7082 0.824155
\(412\) 0 0
\(413\) −1.05573 −0.0519490
\(414\) 0 0
\(415\) 6.94427 0.340881
\(416\) 0 0
\(417\) 20.6525 1.01136
\(418\) 0 0
\(419\) −14.4721 −0.707010 −0.353505 0.935433i \(-0.615010\pi\)
−0.353505 + 0.935433i \(0.615010\pi\)
\(420\) 0 0
\(421\) 13.7426 0.669776 0.334888 0.942258i \(-0.391302\pi\)
0.334888 + 0.942258i \(0.391302\pi\)
\(422\) 0 0
\(423\) −1.41641 −0.0688681
\(424\) 0 0
\(425\) 6.09017 0.295417
\(426\) 0 0
\(427\) −5.76393 −0.278936
\(428\) 0 0
\(429\) 32.7426 1.58083
\(430\) 0 0
\(431\) −3.34752 −0.161245 −0.0806223 0.996745i \(-0.525691\pi\)
−0.0806223 + 0.996745i \(0.525691\pi\)
\(432\) 0 0
\(433\) 8.50658 0.408800 0.204400 0.978887i \(-0.434476\pi\)
0.204400 + 0.978887i \(0.434476\pi\)
\(434\) 0 0
\(435\) 14.9443 0.716523
\(436\) 0 0
\(437\) 1.85410 0.0886937
\(438\) 0 0
\(439\) 13.3820 0.638686 0.319343 0.947639i \(-0.396538\pi\)
0.319343 + 0.947639i \(0.396538\pi\)
\(440\) 0 0
\(441\) 2.52786 0.120374
\(442\) 0 0
\(443\) −25.0902 −1.19207 −0.596035 0.802958i \(-0.703258\pi\)
−0.596035 + 0.802958i \(0.703258\pi\)
\(444\) 0 0
\(445\) −10.4721 −0.496427
\(446\) 0 0
\(447\) 12.7082 0.601077
\(448\) 0 0
\(449\) −1.56231 −0.0737298 −0.0368649 0.999320i \(-0.511737\pi\)
−0.0368649 + 0.999320i \(0.511737\pi\)
\(450\) 0 0
\(451\) 9.49342 0.447028
\(452\) 0 0
\(453\) −4.14590 −0.194791
\(454\) 0 0
\(455\) −4.38197 −0.205430
\(456\) 0 0
\(457\) −37.7771 −1.76714 −0.883569 0.468301i \(-0.844866\pi\)
−0.883569 + 0.468301i \(0.844866\pi\)
\(458\) 0 0
\(459\) 33.3262 1.55554
\(460\) 0 0
\(461\) −39.2361 −1.82741 −0.913703 0.406383i \(-0.866790\pi\)
−0.913703 + 0.406383i \(0.866790\pi\)
\(462\) 0 0
\(463\) −2.00000 −0.0929479 −0.0464739 0.998920i \(-0.514798\pi\)
−0.0464739 + 0.998920i \(0.514798\pi\)
\(464\) 0 0
\(465\) 14.7082 0.682077
\(466\) 0 0
\(467\) 17.1246 0.792433 0.396216 0.918157i \(-0.370323\pi\)
0.396216 + 0.918157i \(0.370323\pi\)
\(468\) 0 0
\(469\) −8.94427 −0.413008
\(470\) 0 0
\(471\) 6.00000 0.276465
\(472\) 0 0
\(473\) 0 0
\(474\) 0 0
\(475\) −1.85410 −0.0850720
\(476\) 0 0
\(477\) −0.180340 −0.00825720
\(478\) 0 0
\(479\) 31.8885 1.45702 0.728512 0.685033i \(-0.240212\pi\)
0.728512 + 0.685033i \(0.240212\pi\)
\(480\) 0 0
\(481\) −45.8885 −2.09234
\(482\) 0 0
\(483\) 1.00000 0.0455016
\(484\) 0 0
\(485\) 12.3820 0.562236
\(486\) 0 0
\(487\) 19.8197 0.898115 0.449057 0.893503i \(-0.351760\pi\)
0.449057 + 0.893503i \(0.351760\pi\)
\(488\) 0 0
\(489\) 2.23607 0.101118
\(490\) 0 0
\(491\) −6.18034 −0.278915 −0.139457 0.990228i \(-0.544536\pi\)
−0.139457 + 0.990228i \(0.544536\pi\)
\(492\) 0 0
\(493\) −56.2492 −2.53334
\(494\) 0 0
\(495\) −1.09017 −0.0489995
\(496\) 0 0
\(497\) 2.52786 0.113390
\(498\) 0 0
\(499\) −12.3607 −0.553340 −0.276670 0.960965i \(-0.589231\pi\)
−0.276670 + 0.960965i \(0.589231\pi\)
\(500\) 0 0
\(501\) −12.9443 −0.578307
\(502\) 0 0
\(503\) −36.3262 −1.61971 −0.809853 0.586632i \(-0.800453\pi\)
−0.809853 + 0.586632i \(0.800453\pi\)
\(504\) 0 0
\(505\) −0.291796 −0.0129848
\(506\) 0 0
\(507\) −60.3050 −2.67824
\(508\) 0 0
\(509\) 36.6525 1.62459 0.812296 0.583245i \(-0.198217\pi\)
0.812296 + 0.583245i \(0.198217\pi\)
\(510\) 0 0
\(511\) 2.00000 0.0884748
\(512\) 0 0
\(513\) −10.1459 −0.447952
\(514\) 0 0
\(515\) −16.5623 −0.729822
\(516\) 0 0
\(517\) 10.5836 0.465466
\(518\) 0 0
\(519\) 2.32624 0.102111
\(520\) 0 0
\(521\) −15.5279 −0.680288 −0.340144 0.940373i \(-0.610476\pi\)
−0.340144 + 0.940373i \(0.610476\pi\)
\(522\) 0 0
\(523\) 26.0000 1.13690 0.568450 0.822718i \(-0.307543\pi\)
0.568450 + 0.822718i \(0.307543\pi\)
\(524\) 0 0
\(525\) −1.00000 −0.0436436
\(526\) 0 0
\(527\) −55.3607 −2.41155
\(528\) 0 0
\(529\) 1.00000 0.0434783
\(530\) 0 0
\(531\) 0.652476 0.0283150
\(532\) 0 0
\(533\) −23.5836 −1.02152
\(534\) 0 0
\(535\) −18.1803 −0.786005
\(536\) 0 0
\(537\) 3.52786 0.152239
\(538\) 0 0
\(539\) −18.8885 −0.813587
\(540\) 0 0
\(541\) 22.8328 0.981659 0.490830 0.871256i \(-0.336694\pi\)
0.490830 + 0.871256i \(0.336694\pi\)
\(542\) 0 0
\(543\) 19.6525 0.843368
\(544\) 0 0
\(545\) −11.5623 −0.495275
\(546\) 0 0
\(547\) −27.9230 −1.19390 −0.596950 0.802278i \(-0.703621\pi\)
−0.596950 + 0.802278i \(0.703621\pi\)
\(548\) 0 0
\(549\) 3.56231 0.152036
\(550\) 0 0
\(551\) 17.1246 0.729533
\(552\) 0 0
\(553\) −0.944272 −0.0401545
\(554\) 0 0
\(555\) −10.4721 −0.444517
\(556\) 0 0
\(557\) −22.8328 −0.967457 −0.483729 0.875218i \(-0.660718\pi\)
−0.483729 + 0.875218i \(0.660718\pi\)
\(558\) 0 0
\(559\) 0 0
\(560\) 0 0
\(561\) −28.1246 −1.18742
\(562\) 0 0
\(563\) 13.8885 0.585332 0.292666 0.956215i \(-0.405458\pi\)
0.292666 + 0.956215i \(0.405458\pi\)
\(564\) 0 0
\(565\) 1.05573 0.0444148
\(566\) 0 0
\(567\) −4.76393 −0.200066
\(568\) 0 0
\(569\) −2.00000 −0.0838444 −0.0419222 0.999121i \(-0.513348\pi\)
−0.0419222 + 0.999121i \(0.513348\pi\)
\(570\) 0 0
\(571\) −15.9787 −0.668688 −0.334344 0.942451i \(-0.608515\pi\)
−0.334344 + 0.942451i \(0.608515\pi\)
\(572\) 0 0
\(573\) −22.1803 −0.926597
\(574\) 0 0
\(575\) −1.00000 −0.0417029
\(576\) 0 0
\(577\) −3.52786 −0.146867 −0.0734335 0.997300i \(-0.523396\pi\)
−0.0734335 + 0.997300i \(0.523396\pi\)
\(578\) 0 0
\(579\) −1.23607 −0.0513692
\(580\) 0 0
\(581\) 4.29180 0.178054
\(582\) 0 0
\(583\) 1.34752 0.0558087
\(584\) 0 0
\(585\) 2.70820 0.111970
\(586\) 0 0
\(587\) −13.6180 −0.562076 −0.281038 0.959697i \(-0.590679\pi\)
−0.281038 + 0.959697i \(0.590679\pi\)
\(588\) 0 0
\(589\) 16.8541 0.694461
\(590\) 0 0
\(591\) 36.5066 1.50168
\(592\) 0 0
\(593\) 39.2361 1.61123 0.805616 0.592438i \(-0.201834\pi\)
0.805616 + 0.592438i \(0.201834\pi\)
\(594\) 0 0
\(595\) 3.76393 0.154306
\(596\) 0 0
\(597\) 3.23607 0.132443
\(598\) 0 0
\(599\) 18.3820 0.751067 0.375533 0.926809i \(-0.377460\pi\)
0.375533 + 0.926809i \(0.377460\pi\)
\(600\) 0 0
\(601\) −33.2705 −1.35713 −0.678566 0.734539i \(-0.737398\pi\)
−0.678566 + 0.734539i \(0.737398\pi\)
\(602\) 0 0
\(603\) 5.52786 0.225112
\(604\) 0 0
\(605\) −2.85410 −0.116036
\(606\) 0 0
\(607\) −26.4721 −1.07447 −0.537235 0.843432i \(-0.680531\pi\)
−0.537235 + 0.843432i \(0.680531\pi\)
\(608\) 0 0
\(609\) 9.23607 0.374264
\(610\) 0 0
\(611\) −26.2918 −1.06365
\(612\) 0 0
\(613\) 19.3050 0.779720 0.389860 0.920874i \(-0.372523\pi\)
0.389860 + 0.920874i \(0.372523\pi\)
\(614\) 0 0
\(615\) −5.38197 −0.217022
\(616\) 0 0
\(617\) 34.0902 1.37242 0.686209 0.727404i \(-0.259273\pi\)
0.686209 + 0.727404i \(0.259273\pi\)
\(618\) 0 0
\(619\) 2.79837 0.112476 0.0562381 0.998417i \(-0.482089\pi\)
0.0562381 + 0.998417i \(0.482089\pi\)
\(620\) 0 0
\(621\) −5.47214 −0.219589
\(622\) 0 0
\(623\) −6.47214 −0.259301
\(624\) 0 0
\(625\) 1.00000 0.0400000
\(626\) 0 0
\(627\) 8.56231 0.341946
\(628\) 0 0
\(629\) 39.4164 1.57164
\(630\) 0 0
\(631\) −42.0689 −1.67474 −0.837368 0.546640i \(-0.815907\pi\)
−0.837368 + 0.546640i \(0.815907\pi\)
\(632\) 0 0
\(633\) 22.6525 0.900355
\(634\) 0 0
\(635\) −16.1803 −0.642097
\(636\) 0 0
\(637\) 46.9230 1.85916
\(638\) 0 0
\(639\) −1.56231 −0.0618039
\(640\) 0 0
\(641\) 0.360680 0.0142460 0.00712300 0.999975i \(-0.497733\pi\)
0.00712300 + 0.999975i \(0.497733\pi\)
\(642\) 0 0
\(643\) 8.29180 0.326997 0.163498 0.986544i \(-0.447722\pi\)
0.163498 + 0.986544i \(0.447722\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 36.2492 1.42510 0.712552 0.701619i \(-0.247539\pi\)
0.712552 + 0.701619i \(0.247539\pi\)
\(648\) 0 0
\(649\) −4.87539 −0.191376
\(650\) 0 0
\(651\) 9.09017 0.356272
\(652\) 0 0
\(653\) −8.03444 −0.314412 −0.157206 0.987566i \(-0.550249\pi\)
−0.157206 + 0.987566i \(0.550249\pi\)
\(654\) 0 0
\(655\) −2.94427 −0.115042
\(656\) 0 0
\(657\) −1.23607 −0.0482236
\(658\) 0 0
\(659\) 46.2492 1.80161 0.900807 0.434220i \(-0.142976\pi\)
0.900807 + 0.434220i \(0.142976\pi\)
\(660\) 0 0
\(661\) 18.6738 0.726325 0.363163 0.931726i \(-0.381697\pi\)
0.363163 + 0.931726i \(0.381697\pi\)
\(662\) 0 0
\(663\) 69.8673 2.71342
\(664\) 0 0
\(665\) −1.14590 −0.0444360
\(666\) 0 0
\(667\) 9.23607 0.357622
\(668\) 0 0
\(669\) −33.8885 −1.31021
\(670\) 0 0
\(671\) −26.6180 −1.02758
\(672\) 0 0
\(673\) −10.9443 −0.421871 −0.210935 0.977500i \(-0.567651\pi\)
−0.210935 + 0.977500i \(0.567651\pi\)
\(674\) 0 0
\(675\) 5.47214 0.210623
\(676\) 0 0
\(677\) −50.9443 −1.95795 −0.978974 0.203986i \(-0.934610\pi\)
−0.978974 + 0.203986i \(0.934610\pi\)
\(678\) 0 0
\(679\) 7.65248 0.293675
\(680\) 0 0
\(681\) −30.3607 −1.16342
\(682\) 0 0
\(683\) 31.5623 1.20770 0.603849 0.797099i \(-0.293633\pi\)
0.603849 + 0.797099i \(0.293633\pi\)
\(684\) 0 0
\(685\) −10.3262 −0.394545
\(686\) 0 0
\(687\) −16.1803 −0.617318
\(688\) 0 0
\(689\) −3.34752 −0.127531
\(690\) 0 0
\(691\) 29.2361 1.11219 0.556096 0.831118i \(-0.312299\pi\)
0.556096 + 0.831118i \(0.312299\pi\)
\(692\) 0 0
\(693\) −0.673762 −0.0255941
\(694\) 0 0
\(695\) −12.7639 −0.484164
\(696\) 0 0
\(697\) 20.2574 0.767302
\(698\) 0 0
\(699\) −10.1803 −0.385056
\(700\) 0 0
\(701\) 43.3394 1.63691 0.818453 0.574573i \(-0.194832\pi\)
0.818453 + 0.574573i \(0.194832\pi\)
\(702\) 0 0
\(703\) −12.0000 −0.452589
\(704\) 0 0
\(705\) −6.00000 −0.225973
\(706\) 0 0
\(707\) −0.180340 −0.00678238
\(708\) 0 0
\(709\) −26.0902 −0.979837 −0.489918 0.871768i \(-0.662973\pi\)
−0.489918 + 0.871768i \(0.662973\pi\)
\(710\) 0 0
\(711\) 0.583592 0.0218864
\(712\) 0 0
\(713\) 9.09017 0.340430
\(714\) 0 0
\(715\) −20.2361 −0.756786
\(716\) 0 0
\(717\) −32.9443 −1.23033
\(718\) 0 0
\(719\) −35.2705 −1.31537 −0.657684 0.753294i \(-0.728464\pi\)
−0.657684 + 0.753294i \(0.728464\pi\)
\(720\) 0 0
\(721\) −10.2361 −0.381211
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) −9.23607 −0.343019
\(726\) 0 0
\(727\) −28.2016 −1.04594 −0.522970 0.852351i \(-0.675176\pi\)
−0.522970 + 0.852351i \(0.675176\pi\)
\(728\) 0 0
\(729\) 29.5066 1.09284
\(730\) 0 0
\(731\) 0 0
\(732\) 0 0
\(733\) −29.4164 −1.08652 −0.543260 0.839565i \(-0.682810\pi\)
−0.543260 + 0.839565i \(0.682810\pi\)
\(734\) 0 0
\(735\) 10.7082 0.394978
\(736\) 0 0
\(737\) −41.3050 −1.52149
\(738\) 0 0
\(739\) 13.8885 0.510898 0.255449 0.966822i \(-0.417777\pi\)
0.255449 + 0.966822i \(0.417777\pi\)
\(740\) 0 0
\(741\) −21.2705 −0.781392
\(742\) 0 0
\(743\) −33.6312 −1.23381 −0.616904 0.787038i \(-0.711613\pi\)
−0.616904 + 0.787038i \(0.711613\pi\)
\(744\) 0 0
\(745\) −7.85410 −0.287752
\(746\) 0 0
\(747\) −2.65248 −0.0970490
\(748\) 0 0
\(749\) −11.2361 −0.410557
\(750\) 0 0
\(751\) 47.0132 1.71553 0.857767 0.514038i \(-0.171851\pi\)
0.857767 + 0.514038i \(0.171851\pi\)
\(752\) 0 0
\(753\) 9.94427 0.362389
\(754\) 0 0
\(755\) 2.56231 0.0932519
\(756\) 0 0
\(757\) −17.8885 −0.650170 −0.325085 0.945685i \(-0.605393\pi\)
−0.325085 + 0.945685i \(0.605393\pi\)
\(758\) 0 0
\(759\) 4.61803 0.167624
\(760\) 0 0
\(761\) 46.8673 1.69894 0.849468 0.527640i \(-0.176923\pi\)
0.849468 + 0.527640i \(0.176923\pi\)
\(762\) 0 0
\(763\) −7.14590 −0.258699
\(764\) 0 0
\(765\) −2.32624 −0.0841053
\(766\) 0 0
\(767\) 12.1115 0.437319
\(768\) 0 0
\(769\) −6.58359 −0.237410 −0.118705 0.992930i \(-0.537874\pi\)
−0.118705 + 0.992930i \(0.537874\pi\)
\(770\) 0 0
\(771\) 12.6525 0.455668
\(772\) 0 0
\(773\) 28.9443 1.04105 0.520527 0.853845i \(-0.325736\pi\)
0.520527 + 0.853845i \(0.325736\pi\)
\(774\) 0 0
\(775\) −9.09017 −0.326529
\(776\) 0 0
\(777\) −6.47214 −0.232187
\(778\) 0 0
\(779\) −6.16718 −0.220962
\(780\) 0 0
\(781\) 11.6738 0.417720
\(782\) 0 0
\(783\) −50.5410 −1.80619
\(784\) 0 0
\(785\) −3.70820 −0.132351
\(786\) 0 0
\(787\) 2.87539 0.102497 0.0512483 0.998686i \(-0.483680\pi\)
0.0512483 + 0.998686i \(0.483680\pi\)
\(788\) 0 0
\(789\) 33.5623 1.19485
\(790\) 0 0
\(791\) 0.652476 0.0231994
\(792\) 0 0
\(793\) 66.1246 2.34815
\(794\) 0 0
\(795\) −0.763932 −0.0270939
\(796\) 0 0
\(797\) 13.7082 0.485569 0.242785 0.970080i \(-0.421939\pi\)
0.242785 + 0.970080i \(0.421939\pi\)
\(798\) 0 0
\(799\) 22.5836 0.798950
\(800\) 0 0
\(801\) 4.00000 0.141333
\(802\) 0 0
\(803\) 9.23607 0.325934
\(804\) 0 0
\(805\) −0.618034 −0.0217828
\(806\) 0 0
\(807\) 22.9443 0.807677
\(808\) 0 0
\(809\) −46.7426 −1.64338 −0.821692 0.569932i \(-0.806970\pi\)
−0.821692 + 0.569932i \(0.806970\pi\)
\(810\) 0 0
\(811\) −21.8197 −0.766192 −0.383096 0.923709i \(-0.625142\pi\)
−0.383096 + 0.923709i \(0.625142\pi\)
\(812\) 0 0
\(813\) −49.0689 −1.72092
\(814\) 0 0
\(815\) −1.38197 −0.0484082
\(816\) 0 0
\(817\) 0 0
\(818\) 0 0
\(819\) 1.67376 0.0584860
\(820\) 0 0
\(821\) −33.0557 −1.15365 −0.576826 0.816867i \(-0.695709\pi\)
−0.576826 + 0.816867i \(0.695709\pi\)
\(822\) 0 0
\(823\) −25.4164 −0.885960 −0.442980 0.896531i \(-0.646079\pi\)
−0.442980 + 0.896531i \(0.646079\pi\)
\(824\) 0 0
\(825\) −4.61803 −0.160779
\(826\) 0 0
\(827\) −21.7082 −0.754868 −0.377434 0.926036i \(-0.623194\pi\)
−0.377434 + 0.926036i \(0.623194\pi\)
\(828\) 0 0
\(829\) 18.9443 0.657962 0.328981 0.944337i \(-0.393295\pi\)
0.328981 + 0.944337i \(0.393295\pi\)
\(830\) 0 0
\(831\) −47.5967 −1.65111
\(832\) 0 0
\(833\) −40.3050 −1.39648
\(834\) 0 0
\(835\) 8.00000 0.276851
\(836\) 0 0
\(837\) −49.7426 −1.71936
\(838\) 0 0
\(839\) −33.0132 −1.13974 −0.569870 0.821735i \(-0.693007\pi\)
−0.569870 + 0.821735i \(0.693007\pi\)
\(840\) 0 0
\(841\) 56.3050 1.94155
\(842\) 0 0
\(843\) −36.8328 −1.26859
\(844\) 0 0
\(845\) 37.2705 1.28214
\(846\) 0 0
\(847\) −1.76393 −0.0606094
\(848\) 0 0
\(849\) −43.5967 −1.49624
\(850\) 0 0
\(851\) −6.47214 −0.221862
\(852\) 0 0
\(853\) −10.7984 −0.369729 −0.184865 0.982764i \(-0.559185\pi\)
−0.184865 + 0.982764i \(0.559185\pi\)
\(854\) 0 0
\(855\) 0.708204 0.0242201
\(856\) 0 0
\(857\) −6.58359 −0.224891 −0.112446 0.993658i \(-0.535868\pi\)
−0.112446 + 0.993658i \(0.535868\pi\)
\(858\) 0 0
\(859\) 24.0689 0.821220 0.410610 0.911811i \(-0.365316\pi\)
0.410610 + 0.911811i \(0.365316\pi\)
\(860\) 0 0
\(861\) −3.32624 −0.113358
\(862\) 0 0
\(863\) −32.7639 −1.11530 −0.557649 0.830077i \(-0.688296\pi\)
−0.557649 + 0.830077i \(0.688296\pi\)
\(864\) 0 0
\(865\) −1.43769 −0.0488831
\(866\) 0 0
\(867\) −32.5066 −1.10398
\(868\) 0 0
\(869\) −4.36068 −0.147926
\(870\) 0 0
\(871\) 102.610 3.47680
\(872\) 0 0
\(873\) −4.72949 −0.160069
\(874\) 0 0
\(875\) 0.618034 0.0208934
\(876\) 0 0
\(877\) 18.7426 0.632894 0.316447 0.948610i \(-0.397510\pi\)
0.316447 + 0.948610i \(0.397510\pi\)
\(878\) 0 0
\(879\) 32.1803 1.08542
\(880\) 0 0
\(881\) 8.58359 0.289189 0.144594 0.989491i \(-0.453812\pi\)
0.144594 + 0.989491i \(0.453812\pi\)
\(882\) 0 0
\(883\) −15.5623 −0.523713 −0.261857 0.965107i \(-0.584335\pi\)
−0.261857 + 0.965107i \(0.584335\pi\)
\(884\) 0 0
\(885\) 2.76393 0.0929086
\(886\) 0 0
\(887\) 5.16718 0.173497 0.0867485 0.996230i \(-0.472352\pi\)
0.0867485 + 0.996230i \(0.472352\pi\)
\(888\) 0 0
\(889\) −10.0000 −0.335389
\(890\) 0 0
\(891\) −22.0000 −0.737028
\(892\) 0 0
\(893\) −6.87539 −0.230076
\(894\) 0 0
\(895\) −2.18034 −0.0728807
\(896\) 0 0
\(897\) −11.4721 −0.383043
\(898\) 0 0
\(899\) 83.9574 2.80014
\(900\) 0 0
\(901\) 2.87539 0.0957931
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) −12.1459 −0.403743
\(906\) 0 0
\(907\) −7.12461 −0.236569 −0.118284 0.992980i \(-0.537739\pi\)
−0.118284 + 0.992980i \(0.537739\pi\)
\(908\) 0 0
\(909\) 0.111456 0.00369677
\(910\) 0 0
\(911\) −36.0689 −1.19502 −0.597508 0.801863i \(-0.703842\pi\)
−0.597508 + 0.801863i \(0.703842\pi\)
\(912\) 0 0
\(913\) 19.8197 0.655935
\(914\) 0 0
\(915\) 15.0902 0.498866
\(916\) 0 0
\(917\) −1.81966 −0.0600905
\(918\) 0 0
\(919\) −40.0000 −1.31948 −0.659739 0.751495i \(-0.729333\pi\)
−0.659739 + 0.751495i \(0.729333\pi\)
\(920\) 0 0
\(921\) −46.0344 −1.51689
\(922\) 0 0
\(923\) −29.0000 −0.954547
\(924\) 0 0
\(925\) 6.47214 0.212803
\(926\) 0 0
\(927\) 6.32624 0.207781
\(928\) 0 0
\(929\) −3.52786 −0.115745 −0.0578727 0.998324i \(-0.518432\pi\)
−0.0578727 + 0.998324i \(0.518432\pi\)
\(930\) 0 0
\(931\) 12.2705 0.402150
\(932\) 0 0
\(933\) 6.47214 0.211888
\(934\) 0 0
\(935\) 17.3820 0.568451
\(936\) 0 0
\(937\) −36.7984 −1.20215 −0.601075 0.799192i \(-0.705261\pi\)
−0.601075 + 0.799192i \(0.705261\pi\)
\(938\) 0 0
\(939\) −20.7082 −0.675787
\(940\) 0 0
\(941\) −22.4934 −0.733265 −0.366632 0.930366i \(-0.619489\pi\)
−0.366632 + 0.930366i \(0.619489\pi\)
\(942\) 0 0
\(943\) −3.32624 −0.108317
\(944\) 0 0
\(945\) 3.38197 0.110015
\(946\) 0 0
\(947\) 54.6869 1.77709 0.888543 0.458793i \(-0.151718\pi\)
0.888543 + 0.458793i \(0.151718\pi\)
\(948\) 0 0
\(949\) −22.9443 −0.744803
\(950\) 0 0
\(951\) 17.9443 0.581883
\(952\) 0 0
\(953\) 3.79837 0.123041 0.0615207 0.998106i \(-0.480405\pi\)
0.0615207 + 0.998106i \(0.480405\pi\)
\(954\) 0 0
\(955\) 13.7082 0.443587
\(956\) 0 0
\(957\) 42.6525 1.37876
\(958\) 0 0
\(959\) −6.38197 −0.206084
\(960\) 0 0
\(961\) 51.6312 1.66552
\(962\) 0 0
\(963\) 6.94427 0.223776
\(964\) 0 0
\(965\) 0.763932 0.0245918
\(966\) 0 0
\(967\) 16.5410 0.531923 0.265962 0.963984i \(-0.414311\pi\)
0.265962 + 0.963984i \(0.414311\pi\)
\(968\) 0 0
\(969\) 18.2705 0.586933
\(970\) 0 0
\(971\) −34.2705 −1.09979 −0.549896 0.835233i \(-0.685333\pi\)
−0.549896 + 0.835233i \(0.685333\pi\)
\(972\) 0 0
\(973\) −7.88854 −0.252895
\(974\) 0 0
\(975\) 11.4721 0.367402
\(976\) 0 0
\(977\) −23.5623 −0.753825 −0.376912 0.926249i \(-0.623014\pi\)
−0.376912 + 0.926249i \(0.623014\pi\)
\(978\) 0 0
\(979\) −29.8885 −0.955242
\(980\) 0 0
\(981\) 4.41641 0.141005
\(982\) 0 0
\(983\) 14.2705 0.455159 0.227579 0.973760i \(-0.426919\pi\)
0.227579 + 0.973760i \(0.426919\pi\)
\(984\) 0 0
\(985\) −22.5623 −0.718895
\(986\) 0 0
\(987\) −3.70820 −0.118033
\(988\) 0 0
\(989\) 0 0
\(990\) 0 0
\(991\) −27.5066 −0.873775 −0.436888 0.899516i \(-0.643919\pi\)
−0.436888 + 0.899516i \(0.643919\pi\)
\(992\) 0 0
\(993\) 31.1246 0.987710
\(994\) 0 0
\(995\) −2.00000 −0.0634043
\(996\) 0 0
\(997\) 57.1935 1.81134 0.905668 0.423987i \(-0.139370\pi\)
0.905668 + 0.423987i \(0.139370\pi\)
\(998\) 0 0
\(999\) 35.4164 1.12053
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 1840.2.a.l.1.1 2
4.3 odd 2 230.2.a.c.1.2 2
5.4 even 2 9200.2.a.bu.1.2 2
8.3 odd 2 7360.2.a.bh.1.1 2
8.5 even 2 7360.2.a.bn.1.2 2
12.11 even 2 2070.2.a.u.1.1 2
20.3 even 4 1150.2.b.i.599.2 4
20.7 even 4 1150.2.b.i.599.3 4
20.19 odd 2 1150.2.a.j.1.1 2
92.91 even 2 5290.2.a.o.1.2 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
230.2.a.c.1.2 2 4.3 odd 2
1150.2.a.j.1.1 2 20.19 odd 2
1150.2.b.i.599.2 4 20.3 even 4
1150.2.b.i.599.3 4 20.7 even 4
1840.2.a.l.1.1 2 1.1 even 1 trivial
2070.2.a.u.1.1 2 12.11 even 2
5290.2.a.o.1.2 2 92.91 even 2
7360.2.a.bh.1.1 2 8.3 odd 2
7360.2.a.bn.1.2 2 8.5 even 2
9200.2.a.bu.1.2 2 5.4 even 2