Properties

Label 6080.2.a.bb.1.2
Level $6080$
Weight $2$
Character 6080.1
Self dual yes
Analytic conductor $48.549$
Analytic rank $0$
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] = [6080,2,Mod(1,6080)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(6080, 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("6080.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 6080 = 2^{6} \cdot 5 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 6080.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: \(48.5490444289\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\sqrt{17}) \)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{2} - x - 4 \) 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 190)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.2
Root \(-1.56155\) of defining polynomial
Character \(\chi\) \(=\) 6080.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+1.56155 q^{3} -1.00000 q^{5} -1.56155 q^{7} -0.561553 q^{9} +O(q^{10})\) \(q+1.56155 q^{3} -1.00000 q^{5} -1.56155 q^{7} -0.561553 q^{9} +4.00000 q^{11} +6.68466 q^{13} -1.56155 q^{15} +7.56155 q^{17} -1.00000 q^{19} -2.43845 q^{21} +4.68466 q^{23} +1.00000 q^{25} -5.56155 q^{27} -6.68466 q^{29} -3.12311 q^{31} +6.24621 q^{33} +1.56155 q^{35} +6.00000 q^{37} +10.4384 q^{39} -4.24621 q^{41} -11.1231 q^{43} +0.561553 q^{45} +10.2462 q^{47} -4.56155 q^{49} +11.8078 q^{51} +0.438447 q^{53} -4.00000 q^{55} -1.56155 q^{57} -1.56155 q^{59} -2.87689 q^{61} +0.876894 q^{63} -6.68466 q^{65} +1.56155 q^{67} +7.31534 q^{69} +6.24621 q^{71} +10.6847 q^{73} +1.56155 q^{75} -6.24621 q^{77} -3.12311 q^{79} -7.00000 q^{81} +11.1231 q^{83} -7.56155 q^{85} -10.4384 q^{87} +2.00000 q^{89} -10.4384 q^{91} -4.87689 q^{93} +1.00000 q^{95} +6.00000 q^{97} -2.24621 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q - q^{3} - 2 q^{5} + q^{7} + 3 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 2 q - q^{3} - 2 q^{5} + q^{7} + 3 q^{9} + 8 q^{11} + q^{13} + q^{15} + 11 q^{17} - 2 q^{19} - 9 q^{21} - 3 q^{23} + 2 q^{25} - 7 q^{27} - q^{29} + 2 q^{31} - 4 q^{33} - q^{35} + 12 q^{37} + 25 q^{39} + 8 q^{41} - 14 q^{43} - 3 q^{45} + 4 q^{47} - 5 q^{49} + 3 q^{51} + 5 q^{53} - 8 q^{55} + q^{57} + q^{59} - 14 q^{61} + 10 q^{63} - q^{65} - q^{67} + 27 q^{69} - 4 q^{71} + 9 q^{73} - q^{75} + 4 q^{77} + 2 q^{79} - 14 q^{81} + 14 q^{83} - 11 q^{85} - 25 q^{87} + 4 q^{89} - 25 q^{91} - 18 q^{93} + 2 q^{95} + 12 q^{97} + 12 q^{99}+O(q^{100}) \) 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
\(3\) 1.56155 0.901563 0.450781 0.892634i \(-0.351145\pi\)
0.450781 + 0.892634i \(0.351145\pi\)
\(4\) 0 0
\(5\) −1.00000 −0.447214
\(6\) 0 0
\(7\) −1.56155 −0.590211 −0.295106 0.955465i \(-0.595355\pi\)
−0.295106 + 0.955465i \(0.595355\pi\)
\(8\) 0 0
\(9\) −0.561553 −0.187184
\(10\) 0 0
\(11\) 4.00000 1.20605 0.603023 0.797724i \(-0.293963\pi\)
0.603023 + 0.797724i \(0.293963\pi\)
\(12\) 0 0
\(13\) 6.68466 1.85399 0.926995 0.375073i \(-0.122382\pi\)
0.926995 + 0.375073i \(0.122382\pi\)
\(14\) 0 0
\(15\) −1.56155 −0.403191
\(16\) 0 0
\(17\) 7.56155 1.83395 0.916973 0.398949i \(-0.130625\pi\)
0.916973 + 0.398949i \(0.130625\pi\)
\(18\) 0 0
\(19\) −1.00000 −0.229416
\(20\) 0 0
\(21\) −2.43845 −0.532113
\(22\) 0 0
\(23\) 4.68466 0.976819 0.488409 0.872615i \(-0.337577\pi\)
0.488409 + 0.872615i \(0.337577\pi\)
\(24\) 0 0
\(25\) 1.00000 0.200000
\(26\) 0 0
\(27\) −5.56155 −1.07032
\(28\) 0 0
\(29\) −6.68466 −1.24131 −0.620655 0.784084i \(-0.713133\pi\)
−0.620655 + 0.784084i \(0.713133\pi\)
\(30\) 0 0
\(31\) −3.12311 −0.560926 −0.280463 0.959865i \(-0.590488\pi\)
−0.280463 + 0.959865i \(0.590488\pi\)
\(32\) 0 0
\(33\) 6.24621 1.08733
\(34\) 0 0
\(35\) 1.56155 0.263951
\(36\) 0 0
\(37\) 6.00000 0.986394 0.493197 0.869918i \(-0.335828\pi\)
0.493197 + 0.869918i \(0.335828\pi\)
\(38\) 0 0
\(39\) 10.4384 1.67149
\(40\) 0 0
\(41\) −4.24621 −0.663147 −0.331573 0.943429i \(-0.607579\pi\)
−0.331573 + 0.943429i \(0.607579\pi\)
\(42\) 0 0
\(43\) −11.1231 −1.69626 −0.848129 0.529790i \(-0.822271\pi\)
−0.848129 + 0.529790i \(0.822271\pi\)
\(44\) 0 0
\(45\) 0.561553 0.0837114
\(46\) 0 0
\(47\) 10.2462 1.49456 0.747282 0.664507i \(-0.231359\pi\)
0.747282 + 0.664507i \(0.231359\pi\)
\(48\) 0 0
\(49\) −4.56155 −0.651650
\(50\) 0 0
\(51\) 11.8078 1.65342
\(52\) 0 0
\(53\) 0.438447 0.0602254 0.0301127 0.999547i \(-0.490413\pi\)
0.0301127 + 0.999547i \(0.490413\pi\)
\(54\) 0 0
\(55\) −4.00000 −0.539360
\(56\) 0 0
\(57\) −1.56155 −0.206833
\(58\) 0 0
\(59\) −1.56155 −0.203297 −0.101648 0.994820i \(-0.532412\pi\)
−0.101648 + 0.994820i \(0.532412\pi\)
\(60\) 0 0
\(61\) −2.87689 −0.368349 −0.184174 0.982894i \(-0.558961\pi\)
−0.184174 + 0.982894i \(0.558961\pi\)
\(62\) 0 0
\(63\) 0.876894 0.110478
\(64\) 0 0
\(65\) −6.68466 −0.829130
\(66\) 0 0
\(67\) 1.56155 0.190774 0.0953870 0.995440i \(-0.469591\pi\)
0.0953870 + 0.995440i \(0.469591\pi\)
\(68\) 0 0
\(69\) 7.31534 0.880664
\(70\) 0 0
\(71\) 6.24621 0.741289 0.370644 0.928775i \(-0.379137\pi\)
0.370644 + 0.928775i \(0.379137\pi\)
\(72\) 0 0
\(73\) 10.6847 1.25054 0.625272 0.780407i \(-0.284988\pi\)
0.625272 + 0.780407i \(0.284988\pi\)
\(74\) 0 0
\(75\) 1.56155 0.180313
\(76\) 0 0
\(77\) −6.24621 −0.711822
\(78\) 0 0
\(79\) −3.12311 −0.351377 −0.175688 0.984446i \(-0.556215\pi\)
−0.175688 + 0.984446i \(0.556215\pi\)
\(80\) 0 0
\(81\) −7.00000 −0.777778
\(82\) 0 0
\(83\) 11.1231 1.22092 0.610460 0.792047i \(-0.290985\pi\)
0.610460 + 0.792047i \(0.290985\pi\)
\(84\) 0 0
\(85\) −7.56155 −0.820166
\(86\) 0 0
\(87\) −10.4384 −1.11912
\(88\) 0 0
\(89\) 2.00000 0.212000 0.106000 0.994366i \(-0.466196\pi\)
0.106000 + 0.994366i \(0.466196\pi\)
\(90\) 0 0
\(91\) −10.4384 −1.09425
\(92\) 0 0
\(93\) −4.87689 −0.505710
\(94\) 0 0
\(95\) 1.00000 0.102598
\(96\) 0 0
\(97\) 6.00000 0.609208 0.304604 0.952479i \(-0.401476\pi\)
0.304604 + 0.952479i \(0.401476\pi\)
\(98\) 0 0
\(99\) −2.24621 −0.225753
\(100\) 0 0
\(101\) −7.36932 −0.733274 −0.366637 0.930364i \(-0.619491\pi\)
−0.366637 + 0.930364i \(0.619491\pi\)
\(102\) 0 0
\(103\) 14.2462 1.40372 0.701860 0.712314i \(-0.252353\pi\)
0.701860 + 0.712314i \(0.252353\pi\)
\(104\) 0 0
\(105\) 2.43845 0.237968
\(106\) 0 0
\(107\) −9.56155 −0.924350 −0.462175 0.886789i \(-0.652931\pi\)
−0.462175 + 0.886789i \(0.652931\pi\)
\(108\) 0 0
\(109\) −3.56155 −0.341135 −0.170567 0.985346i \(-0.554560\pi\)
−0.170567 + 0.985346i \(0.554560\pi\)
\(110\) 0 0
\(111\) 9.36932 0.889296
\(112\) 0 0
\(113\) 17.1231 1.61081 0.805403 0.592727i \(-0.201949\pi\)
0.805403 + 0.592727i \(0.201949\pi\)
\(114\) 0 0
\(115\) −4.68466 −0.436847
\(116\) 0 0
\(117\) −3.75379 −0.347038
\(118\) 0 0
\(119\) −11.8078 −1.08242
\(120\) 0 0
\(121\) 5.00000 0.454545
\(122\) 0 0
\(123\) −6.63068 −0.597869
\(124\) 0 0
\(125\) −1.00000 −0.0894427
\(126\) 0 0
\(127\) −4.87689 −0.432754 −0.216377 0.976310i \(-0.569424\pi\)
−0.216377 + 0.976310i \(0.569424\pi\)
\(128\) 0 0
\(129\) −17.3693 −1.52928
\(130\) 0 0
\(131\) 16.4924 1.44095 0.720475 0.693481i \(-0.243924\pi\)
0.720475 + 0.693481i \(0.243924\pi\)
\(132\) 0 0
\(133\) 1.56155 0.135404
\(134\) 0 0
\(135\) 5.56155 0.478662
\(136\) 0 0
\(137\) 5.80776 0.496191 0.248095 0.968736i \(-0.420195\pi\)
0.248095 + 0.968736i \(0.420195\pi\)
\(138\) 0 0
\(139\) −16.4924 −1.39887 −0.699435 0.714697i \(-0.746565\pi\)
−0.699435 + 0.714697i \(0.746565\pi\)
\(140\) 0 0
\(141\) 16.0000 1.34744
\(142\) 0 0
\(143\) 26.7386 2.23600
\(144\) 0 0
\(145\) 6.68466 0.555131
\(146\) 0 0
\(147\) −7.12311 −0.587504
\(148\) 0 0
\(149\) 11.3693 0.931411 0.465705 0.884940i \(-0.345801\pi\)
0.465705 + 0.884940i \(0.345801\pi\)
\(150\) 0 0
\(151\) 3.12311 0.254155 0.127077 0.991893i \(-0.459440\pi\)
0.127077 + 0.991893i \(0.459440\pi\)
\(152\) 0 0
\(153\) −4.24621 −0.343286
\(154\) 0 0
\(155\) 3.12311 0.250854
\(156\) 0 0
\(157\) 3.75379 0.299585 0.149792 0.988717i \(-0.452139\pi\)
0.149792 + 0.988717i \(0.452139\pi\)
\(158\) 0 0
\(159\) 0.684658 0.0542969
\(160\) 0 0
\(161\) −7.31534 −0.576530
\(162\) 0 0
\(163\) 9.36932 0.733862 0.366931 0.930248i \(-0.380409\pi\)
0.366931 + 0.930248i \(0.380409\pi\)
\(164\) 0 0
\(165\) −6.24621 −0.486267
\(166\) 0 0
\(167\) −17.3693 −1.34408 −0.672039 0.740516i \(-0.734581\pi\)
−0.672039 + 0.740516i \(0.734581\pi\)
\(168\) 0 0
\(169\) 31.6847 2.43728
\(170\) 0 0
\(171\) 0.561553 0.0429430
\(172\) 0 0
\(173\) −3.75379 −0.285395 −0.142698 0.989766i \(-0.545578\pi\)
−0.142698 + 0.989766i \(0.545578\pi\)
\(174\) 0 0
\(175\) −1.56155 −0.118042
\(176\) 0 0
\(177\) −2.43845 −0.183285
\(178\) 0 0
\(179\) −5.75379 −0.430058 −0.215029 0.976608i \(-0.568985\pi\)
−0.215029 + 0.976608i \(0.568985\pi\)
\(180\) 0 0
\(181\) 18.0000 1.33793 0.668965 0.743294i \(-0.266738\pi\)
0.668965 + 0.743294i \(0.266738\pi\)
\(182\) 0 0
\(183\) −4.49242 −0.332089
\(184\) 0 0
\(185\) −6.00000 −0.441129
\(186\) 0 0
\(187\) 30.2462 2.21182
\(188\) 0 0
\(189\) 8.68466 0.631716
\(190\) 0 0
\(191\) −8.68466 −0.628400 −0.314200 0.949357i \(-0.601736\pi\)
−0.314200 + 0.949357i \(0.601736\pi\)
\(192\) 0 0
\(193\) 18.4924 1.33111 0.665557 0.746347i \(-0.268194\pi\)
0.665557 + 0.746347i \(0.268194\pi\)
\(194\) 0 0
\(195\) −10.4384 −0.747513
\(196\) 0 0
\(197\) 3.75379 0.267446 0.133723 0.991019i \(-0.457307\pi\)
0.133723 + 0.991019i \(0.457307\pi\)
\(198\) 0 0
\(199\) 3.80776 0.269925 0.134963 0.990851i \(-0.456909\pi\)
0.134963 + 0.990851i \(0.456909\pi\)
\(200\) 0 0
\(201\) 2.43845 0.171995
\(202\) 0 0
\(203\) 10.4384 0.732635
\(204\) 0 0
\(205\) 4.24621 0.296568
\(206\) 0 0
\(207\) −2.63068 −0.182845
\(208\) 0 0
\(209\) −4.00000 −0.276686
\(210\) 0 0
\(211\) 20.6847 1.42399 0.711995 0.702184i \(-0.247792\pi\)
0.711995 + 0.702184i \(0.247792\pi\)
\(212\) 0 0
\(213\) 9.75379 0.668319
\(214\) 0 0
\(215\) 11.1231 0.758590
\(216\) 0 0
\(217\) 4.87689 0.331065
\(218\) 0 0
\(219\) 16.6847 1.12744
\(220\) 0 0
\(221\) 50.5464 3.40012
\(222\) 0 0
\(223\) −1.36932 −0.0916962 −0.0458481 0.998948i \(-0.514599\pi\)
−0.0458481 + 0.998948i \(0.514599\pi\)
\(224\) 0 0
\(225\) −0.561553 −0.0374369
\(226\) 0 0
\(227\) −2.93087 −0.194529 −0.0972643 0.995259i \(-0.531009\pi\)
−0.0972643 + 0.995259i \(0.531009\pi\)
\(228\) 0 0
\(229\) −18.4924 −1.22201 −0.611007 0.791625i \(-0.709235\pi\)
−0.611007 + 0.791625i \(0.709235\pi\)
\(230\) 0 0
\(231\) −9.75379 −0.641752
\(232\) 0 0
\(233\) 10.0000 0.655122 0.327561 0.944830i \(-0.393773\pi\)
0.327561 + 0.944830i \(0.393773\pi\)
\(234\) 0 0
\(235\) −10.2462 −0.668389
\(236\) 0 0
\(237\) −4.87689 −0.316788
\(238\) 0 0
\(239\) 5.56155 0.359747 0.179873 0.983690i \(-0.442431\pi\)
0.179873 + 0.983690i \(0.442431\pi\)
\(240\) 0 0
\(241\) 14.8769 0.958305 0.479153 0.877732i \(-0.340944\pi\)
0.479153 + 0.877732i \(0.340944\pi\)
\(242\) 0 0
\(243\) 5.75379 0.369106
\(244\) 0 0
\(245\) 4.56155 0.291427
\(246\) 0 0
\(247\) −6.68466 −0.425335
\(248\) 0 0
\(249\) 17.3693 1.10074
\(250\) 0 0
\(251\) −10.2462 −0.646735 −0.323368 0.946273i \(-0.604815\pi\)
−0.323368 + 0.946273i \(0.604815\pi\)
\(252\) 0 0
\(253\) 18.7386 1.17809
\(254\) 0 0
\(255\) −11.8078 −0.739431
\(256\) 0 0
\(257\) 14.0000 0.873296 0.436648 0.899632i \(-0.356166\pi\)
0.436648 + 0.899632i \(0.356166\pi\)
\(258\) 0 0
\(259\) −9.36932 −0.582181
\(260\) 0 0
\(261\) 3.75379 0.232354
\(262\) 0 0
\(263\) 5.75379 0.354794 0.177397 0.984139i \(-0.443232\pi\)
0.177397 + 0.984139i \(0.443232\pi\)
\(264\) 0 0
\(265\) −0.438447 −0.0269336
\(266\) 0 0
\(267\) 3.12311 0.191131
\(268\) 0 0
\(269\) 26.0000 1.58525 0.792624 0.609711i \(-0.208714\pi\)
0.792624 + 0.609711i \(0.208714\pi\)
\(270\) 0 0
\(271\) −6.93087 −0.421020 −0.210510 0.977592i \(-0.567513\pi\)
−0.210510 + 0.977592i \(0.567513\pi\)
\(272\) 0 0
\(273\) −16.3002 −0.986532
\(274\) 0 0
\(275\) 4.00000 0.241209
\(276\) 0 0
\(277\) −9.12311 −0.548154 −0.274077 0.961708i \(-0.588372\pi\)
−0.274077 + 0.961708i \(0.588372\pi\)
\(278\) 0 0
\(279\) 1.75379 0.104997
\(280\) 0 0
\(281\) 2.00000 0.119310 0.0596550 0.998219i \(-0.481000\pi\)
0.0596550 + 0.998219i \(0.481000\pi\)
\(282\) 0 0
\(283\) −12.8769 −0.765452 −0.382726 0.923862i \(-0.625015\pi\)
−0.382726 + 0.923862i \(0.625015\pi\)
\(284\) 0 0
\(285\) 1.56155 0.0924984
\(286\) 0 0
\(287\) 6.63068 0.391397
\(288\) 0 0
\(289\) 40.1771 2.36336
\(290\) 0 0
\(291\) 9.36932 0.549239
\(292\) 0 0
\(293\) −23.1771 −1.35402 −0.677010 0.735974i \(-0.736725\pi\)
−0.677010 + 0.735974i \(0.736725\pi\)
\(294\) 0 0
\(295\) 1.56155 0.0909171
\(296\) 0 0
\(297\) −22.2462 −1.29086
\(298\) 0 0
\(299\) 31.3153 1.81101
\(300\) 0 0
\(301\) 17.3693 1.00115
\(302\) 0 0
\(303\) −11.5076 −0.661093
\(304\) 0 0
\(305\) 2.87689 0.164730
\(306\) 0 0
\(307\) −0.492423 −0.0281040 −0.0140520 0.999901i \(-0.504473\pi\)
−0.0140520 + 0.999901i \(0.504473\pi\)
\(308\) 0 0
\(309\) 22.2462 1.26554
\(310\) 0 0
\(311\) −8.68466 −0.492462 −0.246231 0.969211i \(-0.579192\pi\)
−0.246231 + 0.969211i \(0.579192\pi\)
\(312\) 0 0
\(313\) −32.0540 −1.81180 −0.905899 0.423494i \(-0.860803\pi\)
−0.905899 + 0.423494i \(0.860803\pi\)
\(314\) 0 0
\(315\) −0.876894 −0.0494074
\(316\) 0 0
\(317\) 24.0540 1.35101 0.675503 0.737357i \(-0.263927\pi\)
0.675503 + 0.737357i \(0.263927\pi\)
\(318\) 0 0
\(319\) −26.7386 −1.49708
\(320\) 0 0
\(321\) −14.9309 −0.833360
\(322\) 0 0
\(323\) −7.56155 −0.420736
\(324\) 0 0
\(325\) 6.68466 0.370798
\(326\) 0 0
\(327\) −5.56155 −0.307555
\(328\) 0 0
\(329\) −16.0000 −0.882109
\(330\) 0 0
\(331\) 1.56155 0.0858307 0.0429154 0.999079i \(-0.486335\pi\)
0.0429154 + 0.999079i \(0.486335\pi\)
\(332\) 0 0
\(333\) −3.36932 −0.184637
\(334\) 0 0
\(335\) −1.56155 −0.0853167
\(336\) 0 0
\(337\) −26.0000 −1.41631 −0.708155 0.706057i \(-0.750472\pi\)
−0.708155 + 0.706057i \(0.750472\pi\)
\(338\) 0 0
\(339\) 26.7386 1.45224
\(340\) 0 0
\(341\) −12.4924 −0.676503
\(342\) 0 0
\(343\) 18.0540 0.974823
\(344\) 0 0
\(345\) −7.31534 −0.393845
\(346\) 0 0
\(347\) −33.3693 −1.79136 −0.895679 0.444700i \(-0.853310\pi\)
−0.895679 + 0.444700i \(0.853310\pi\)
\(348\) 0 0
\(349\) −20.2462 −1.08375 −0.541877 0.840458i \(-0.682286\pi\)
−0.541877 + 0.840458i \(0.682286\pi\)
\(350\) 0 0
\(351\) −37.1771 −1.98437
\(352\) 0 0
\(353\) 24.9309 1.32694 0.663468 0.748205i \(-0.269084\pi\)
0.663468 + 0.748205i \(0.269084\pi\)
\(354\) 0 0
\(355\) −6.24621 −0.331514
\(356\) 0 0
\(357\) −18.4384 −0.975866
\(358\) 0 0
\(359\) −5.56155 −0.293528 −0.146764 0.989172i \(-0.546886\pi\)
−0.146764 + 0.989172i \(0.546886\pi\)
\(360\) 0 0
\(361\) 1.00000 0.0526316
\(362\) 0 0
\(363\) 7.80776 0.409801
\(364\) 0 0
\(365\) −10.6847 −0.559261
\(366\) 0 0
\(367\) 10.2462 0.534848 0.267424 0.963579i \(-0.413828\pi\)
0.267424 + 0.963579i \(0.413828\pi\)
\(368\) 0 0
\(369\) 2.38447 0.124131
\(370\) 0 0
\(371\) −0.684658 −0.0355457
\(372\) 0 0
\(373\) 27.5616 1.42708 0.713542 0.700613i \(-0.247090\pi\)
0.713542 + 0.700613i \(0.247090\pi\)
\(374\) 0 0
\(375\) −1.56155 −0.0806382
\(376\) 0 0
\(377\) −44.6847 −2.30138
\(378\) 0 0
\(379\) 6.43845 0.330721 0.165360 0.986233i \(-0.447121\pi\)
0.165360 + 0.986233i \(0.447121\pi\)
\(380\) 0 0
\(381\) −7.61553 −0.390155
\(382\) 0 0
\(383\) −30.2462 −1.54551 −0.772755 0.634705i \(-0.781122\pi\)
−0.772755 + 0.634705i \(0.781122\pi\)
\(384\) 0 0
\(385\) 6.24621 0.318336
\(386\) 0 0
\(387\) 6.24621 0.317513
\(388\) 0 0
\(389\) −1.12311 −0.0569437 −0.0284719 0.999595i \(-0.509064\pi\)
−0.0284719 + 0.999595i \(0.509064\pi\)
\(390\) 0 0
\(391\) 35.4233 1.79143
\(392\) 0 0
\(393\) 25.7538 1.29911
\(394\) 0 0
\(395\) 3.12311 0.157140
\(396\) 0 0
\(397\) −1.12311 −0.0563671 −0.0281835 0.999603i \(-0.508972\pi\)
−0.0281835 + 0.999603i \(0.508972\pi\)
\(398\) 0 0
\(399\) 2.43845 0.122075
\(400\) 0 0
\(401\) −20.2462 −1.01105 −0.505524 0.862813i \(-0.668701\pi\)
−0.505524 + 0.862813i \(0.668701\pi\)
\(402\) 0 0
\(403\) −20.8769 −1.03995
\(404\) 0 0
\(405\) 7.00000 0.347833
\(406\) 0 0
\(407\) 24.0000 1.18964
\(408\) 0 0
\(409\) −24.7386 −1.22325 −0.611623 0.791149i \(-0.709483\pi\)
−0.611623 + 0.791149i \(0.709483\pi\)
\(410\) 0 0
\(411\) 9.06913 0.447347
\(412\) 0 0
\(413\) 2.43845 0.119988
\(414\) 0 0
\(415\) −11.1231 −0.546012
\(416\) 0 0
\(417\) −25.7538 −1.26117
\(418\) 0 0
\(419\) −33.8617 −1.65425 −0.827127 0.562015i \(-0.810026\pi\)
−0.827127 + 0.562015i \(0.810026\pi\)
\(420\) 0 0
\(421\) −4.93087 −0.240316 −0.120158 0.992755i \(-0.538340\pi\)
−0.120158 + 0.992755i \(0.538340\pi\)
\(422\) 0 0
\(423\) −5.75379 −0.279759
\(424\) 0 0
\(425\) 7.56155 0.366789
\(426\) 0 0
\(427\) 4.49242 0.217404
\(428\) 0 0
\(429\) 41.7538 2.01589
\(430\) 0 0
\(431\) 16.0000 0.770693 0.385346 0.922772i \(-0.374082\pi\)
0.385346 + 0.922772i \(0.374082\pi\)
\(432\) 0 0
\(433\) 39.3693 1.89197 0.945984 0.324212i \(-0.105099\pi\)
0.945984 + 0.324212i \(0.105099\pi\)
\(434\) 0 0
\(435\) 10.4384 0.500485
\(436\) 0 0
\(437\) −4.68466 −0.224098
\(438\) 0 0
\(439\) 4.87689 0.232761 0.116381 0.993205i \(-0.462871\pi\)
0.116381 + 0.993205i \(0.462871\pi\)
\(440\) 0 0
\(441\) 2.56155 0.121979
\(442\) 0 0
\(443\) −14.2462 −0.676858 −0.338429 0.940992i \(-0.609895\pi\)
−0.338429 + 0.940992i \(0.609895\pi\)
\(444\) 0 0
\(445\) −2.00000 −0.0948091
\(446\) 0 0
\(447\) 17.7538 0.839725
\(448\) 0 0
\(449\) 20.7386 0.978717 0.489358 0.872083i \(-0.337231\pi\)
0.489358 + 0.872083i \(0.337231\pi\)
\(450\) 0 0
\(451\) −16.9848 −0.799785
\(452\) 0 0
\(453\) 4.87689 0.229136
\(454\) 0 0
\(455\) 10.4384 0.489362
\(456\) 0 0
\(457\) 18.6847 0.874031 0.437016 0.899454i \(-0.356035\pi\)
0.437016 + 0.899454i \(0.356035\pi\)
\(458\) 0 0
\(459\) −42.0540 −1.96291
\(460\) 0 0
\(461\) −20.2462 −0.942960 −0.471480 0.881877i \(-0.656280\pi\)
−0.471480 + 0.881877i \(0.656280\pi\)
\(462\) 0 0
\(463\) 13.7538 0.639193 0.319596 0.947554i \(-0.396453\pi\)
0.319596 + 0.947554i \(0.396453\pi\)
\(464\) 0 0
\(465\) 4.87689 0.226161
\(466\) 0 0
\(467\) 1.75379 0.0811557 0.0405778 0.999176i \(-0.487080\pi\)
0.0405778 + 0.999176i \(0.487080\pi\)
\(468\) 0 0
\(469\) −2.43845 −0.112597
\(470\) 0 0
\(471\) 5.86174 0.270095
\(472\) 0 0
\(473\) −44.4924 −2.04576
\(474\) 0 0
\(475\) −1.00000 −0.0458831
\(476\) 0 0
\(477\) −0.246211 −0.0112732
\(478\) 0 0
\(479\) −32.0000 −1.46212 −0.731059 0.682315i \(-0.760973\pi\)
−0.731059 + 0.682315i \(0.760973\pi\)
\(480\) 0 0
\(481\) 40.1080 1.82877
\(482\) 0 0
\(483\) −11.4233 −0.519778
\(484\) 0 0
\(485\) −6.00000 −0.272446
\(486\) 0 0
\(487\) −23.6155 −1.07012 −0.535061 0.844814i \(-0.679711\pi\)
−0.535061 + 0.844814i \(0.679711\pi\)
\(488\) 0 0
\(489\) 14.6307 0.661622
\(490\) 0 0
\(491\) 7.12311 0.321461 0.160731 0.986998i \(-0.448615\pi\)
0.160731 + 0.986998i \(0.448615\pi\)
\(492\) 0 0
\(493\) −50.5464 −2.27650
\(494\) 0 0
\(495\) 2.24621 0.100960
\(496\) 0 0
\(497\) −9.75379 −0.437517
\(498\) 0 0
\(499\) −32.1080 −1.43735 −0.718675 0.695347i \(-0.755251\pi\)
−0.718675 + 0.695347i \(0.755251\pi\)
\(500\) 0 0
\(501\) −27.1231 −1.21177
\(502\) 0 0
\(503\) −30.0540 −1.34004 −0.670020 0.742343i \(-0.733715\pi\)
−0.670020 + 0.742343i \(0.733715\pi\)
\(504\) 0 0
\(505\) 7.36932 0.327930
\(506\) 0 0
\(507\) 49.4773 2.19736
\(508\) 0 0
\(509\) 30.4924 1.35155 0.675776 0.737107i \(-0.263808\pi\)
0.675776 + 0.737107i \(0.263808\pi\)
\(510\) 0 0
\(511\) −16.6847 −0.738086
\(512\) 0 0
\(513\) 5.56155 0.245549
\(514\) 0 0
\(515\) −14.2462 −0.627763
\(516\) 0 0
\(517\) 40.9848 1.80251
\(518\) 0 0
\(519\) −5.86174 −0.257302
\(520\) 0 0
\(521\) 5.12311 0.224447 0.112224 0.993683i \(-0.464203\pi\)
0.112224 + 0.993683i \(0.464203\pi\)
\(522\) 0 0
\(523\) −19.3153 −0.844601 −0.422300 0.906456i \(-0.638777\pi\)
−0.422300 + 0.906456i \(0.638777\pi\)
\(524\) 0 0
\(525\) −2.43845 −0.106423
\(526\) 0 0
\(527\) −23.6155 −1.02871
\(528\) 0 0
\(529\) −1.05398 −0.0458250
\(530\) 0 0
\(531\) 0.876894 0.0380540
\(532\) 0 0
\(533\) −28.3845 −1.22947
\(534\) 0 0
\(535\) 9.56155 0.413382
\(536\) 0 0
\(537\) −8.98485 −0.387725
\(538\) 0 0
\(539\) −18.2462 −0.785920
\(540\) 0 0
\(541\) 41.6155 1.78919 0.894596 0.446877i \(-0.147464\pi\)
0.894596 + 0.446877i \(0.147464\pi\)
\(542\) 0 0
\(543\) 28.1080 1.20623
\(544\) 0 0
\(545\) 3.56155 0.152560
\(546\) 0 0
\(547\) −16.4924 −0.705165 −0.352583 0.935781i \(-0.614696\pi\)
−0.352583 + 0.935781i \(0.614696\pi\)
\(548\) 0 0
\(549\) 1.61553 0.0689491
\(550\) 0 0
\(551\) 6.68466 0.284776
\(552\) 0 0
\(553\) 4.87689 0.207387
\(554\) 0 0
\(555\) −9.36932 −0.397705
\(556\) 0 0
\(557\) 1.61553 0.0684521 0.0342261 0.999414i \(-0.489103\pi\)
0.0342261 + 0.999414i \(0.489103\pi\)
\(558\) 0 0
\(559\) −74.3542 −3.14485
\(560\) 0 0
\(561\) 47.2311 1.99410
\(562\) 0 0
\(563\) 24.4924 1.03223 0.516116 0.856519i \(-0.327377\pi\)
0.516116 + 0.856519i \(0.327377\pi\)
\(564\) 0 0
\(565\) −17.1231 −0.720374
\(566\) 0 0
\(567\) 10.9309 0.459053
\(568\) 0 0
\(569\) 5.12311 0.214772 0.107386 0.994217i \(-0.465752\pi\)
0.107386 + 0.994217i \(0.465752\pi\)
\(570\) 0 0
\(571\) −19.6155 −0.820884 −0.410442 0.911887i \(-0.634626\pi\)
−0.410442 + 0.911887i \(0.634626\pi\)
\(572\) 0 0
\(573\) −13.5616 −0.566542
\(574\) 0 0
\(575\) 4.68466 0.195364
\(576\) 0 0
\(577\) −22.6847 −0.944375 −0.472187 0.881498i \(-0.656535\pi\)
−0.472187 + 0.881498i \(0.656535\pi\)
\(578\) 0 0
\(579\) 28.8769 1.20008
\(580\) 0 0
\(581\) −17.3693 −0.720601
\(582\) 0 0
\(583\) 1.75379 0.0726345
\(584\) 0 0
\(585\) 3.75379 0.155200
\(586\) 0 0
\(587\) 17.3693 0.716908 0.358454 0.933547i \(-0.383304\pi\)
0.358454 + 0.933547i \(0.383304\pi\)
\(588\) 0 0
\(589\) 3.12311 0.128685
\(590\) 0 0
\(591\) 5.86174 0.241120
\(592\) 0 0
\(593\) 24.2462 0.995673 0.497836 0.867271i \(-0.334128\pi\)
0.497836 + 0.867271i \(0.334128\pi\)
\(594\) 0 0
\(595\) 11.8078 0.484071
\(596\) 0 0
\(597\) 5.94602 0.243355
\(598\) 0 0
\(599\) −45.8617 −1.87386 −0.936930 0.349517i \(-0.886346\pi\)
−0.936930 + 0.349517i \(0.886346\pi\)
\(600\) 0 0
\(601\) 18.0000 0.734235 0.367118 0.930175i \(-0.380345\pi\)
0.367118 + 0.930175i \(0.380345\pi\)
\(602\) 0 0
\(603\) −0.876894 −0.0357099
\(604\) 0 0
\(605\) −5.00000 −0.203279
\(606\) 0 0
\(607\) 12.8769 0.522657 0.261329 0.965250i \(-0.415839\pi\)
0.261329 + 0.965250i \(0.415839\pi\)
\(608\) 0 0
\(609\) 16.3002 0.660517
\(610\) 0 0
\(611\) 68.4924 2.77091
\(612\) 0 0
\(613\) 19.3693 0.782319 0.391160 0.920323i \(-0.372074\pi\)
0.391160 + 0.920323i \(0.372074\pi\)
\(614\) 0 0
\(615\) 6.63068 0.267375
\(616\) 0 0
\(617\) −4.24621 −0.170946 −0.0854730 0.996340i \(-0.527240\pi\)
−0.0854730 + 0.996340i \(0.527240\pi\)
\(618\) 0 0
\(619\) −36.0000 −1.44696 −0.723481 0.690344i \(-0.757459\pi\)
−0.723481 + 0.690344i \(0.757459\pi\)
\(620\) 0 0
\(621\) −26.0540 −1.04551
\(622\) 0 0
\(623\) −3.12311 −0.125125
\(624\) 0 0
\(625\) 1.00000 0.0400000
\(626\) 0 0
\(627\) −6.24621 −0.249450
\(628\) 0 0
\(629\) 45.3693 1.80899
\(630\) 0 0
\(631\) −12.4924 −0.497315 −0.248658 0.968591i \(-0.579989\pi\)
−0.248658 + 0.968591i \(0.579989\pi\)
\(632\) 0 0
\(633\) 32.3002 1.28382
\(634\) 0 0
\(635\) 4.87689 0.193534
\(636\) 0 0
\(637\) −30.4924 −1.20815
\(638\) 0 0
\(639\) −3.50758 −0.138758
\(640\) 0 0
\(641\) −35.8617 −1.41645 −0.708227 0.705985i \(-0.750505\pi\)
−0.708227 + 0.705985i \(0.750505\pi\)
\(642\) 0 0
\(643\) 7.61553 0.300327 0.150164 0.988661i \(-0.452020\pi\)
0.150164 + 0.988661i \(0.452020\pi\)
\(644\) 0 0
\(645\) 17.3693 0.683916
\(646\) 0 0
\(647\) −9.56155 −0.375903 −0.187952 0.982178i \(-0.560185\pi\)
−0.187952 + 0.982178i \(0.560185\pi\)
\(648\) 0 0
\(649\) −6.24621 −0.245185
\(650\) 0 0
\(651\) 7.61553 0.298476
\(652\) 0 0
\(653\) −1.12311 −0.0439505 −0.0219753 0.999759i \(-0.506996\pi\)
−0.0219753 + 0.999759i \(0.506996\pi\)
\(654\) 0 0
\(655\) −16.4924 −0.644412
\(656\) 0 0
\(657\) −6.00000 −0.234082
\(658\) 0 0
\(659\) −42.9309 −1.67235 −0.836175 0.548463i \(-0.815213\pi\)
−0.836175 + 0.548463i \(0.815213\pi\)
\(660\) 0 0
\(661\) −9.80776 −0.381478 −0.190739 0.981641i \(-0.561088\pi\)
−0.190739 + 0.981641i \(0.561088\pi\)
\(662\) 0 0
\(663\) 78.9309 3.06542
\(664\) 0 0
\(665\) −1.56155 −0.0605544
\(666\) 0 0
\(667\) −31.3153 −1.21253
\(668\) 0 0
\(669\) −2.13826 −0.0826699
\(670\) 0 0
\(671\) −11.5076 −0.444245
\(672\) 0 0
\(673\) −3.36932 −0.129878 −0.0649388 0.997889i \(-0.520685\pi\)
−0.0649388 + 0.997889i \(0.520685\pi\)
\(674\) 0 0
\(675\) −5.56155 −0.214064
\(676\) 0 0
\(677\) −36.4384 −1.40044 −0.700222 0.713926i \(-0.746915\pi\)
−0.700222 + 0.713926i \(0.746915\pi\)
\(678\) 0 0
\(679\) −9.36932 −0.359561
\(680\) 0 0
\(681\) −4.57671 −0.175380
\(682\) 0 0
\(683\) 4.00000 0.153056 0.0765279 0.997067i \(-0.475617\pi\)
0.0765279 + 0.997067i \(0.475617\pi\)
\(684\) 0 0
\(685\) −5.80776 −0.221903
\(686\) 0 0
\(687\) −28.8769 −1.10172
\(688\) 0 0
\(689\) 2.93087 0.111657
\(690\) 0 0
\(691\) −8.87689 −0.337693 −0.168846 0.985642i \(-0.554004\pi\)
−0.168846 + 0.985642i \(0.554004\pi\)
\(692\) 0 0
\(693\) 3.50758 0.133242
\(694\) 0 0
\(695\) 16.4924 0.625593
\(696\) 0 0
\(697\) −32.1080 −1.21618
\(698\) 0 0
\(699\) 15.6155 0.590634
\(700\) 0 0
\(701\) 29.1231 1.09996 0.549982 0.835176i \(-0.314634\pi\)
0.549982 + 0.835176i \(0.314634\pi\)
\(702\) 0 0
\(703\) −6.00000 −0.226294
\(704\) 0 0
\(705\) −16.0000 −0.602595
\(706\) 0 0
\(707\) 11.5076 0.432787
\(708\) 0 0
\(709\) −38.0000 −1.42712 −0.713560 0.700594i \(-0.752918\pi\)
−0.713560 + 0.700594i \(0.752918\pi\)
\(710\) 0 0
\(711\) 1.75379 0.0657722
\(712\) 0 0
\(713\) −14.6307 −0.547923
\(714\) 0 0
\(715\) −26.7386 −0.999968
\(716\) 0 0
\(717\) 8.68466 0.324335
\(718\) 0 0
\(719\) 29.5616 1.10246 0.551230 0.834353i \(-0.314159\pi\)
0.551230 + 0.834353i \(0.314159\pi\)
\(720\) 0 0
\(721\) −22.2462 −0.828492
\(722\) 0 0
\(723\) 23.2311 0.863972
\(724\) 0 0
\(725\) −6.68466 −0.248262
\(726\) 0 0
\(727\) 36.6847 1.36056 0.680279 0.732953i \(-0.261858\pi\)
0.680279 + 0.732953i \(0.261858\pi\)
\(728\) 0 0
\(729\) 29.9848 1.11055
\(730\) 0 0
\(731\) −84.1080 −3.11084
\(732\) 0 0
\(733\) 45.1231 1.66666 0.833330 0.552776i \(-0.186431\pi\)
0.833330 + 0.552776i \(0.186431\pi\)
\(734\) 0 0
\(735\) 7.12311 0.262740
\(736\) 0 0
\(737\) 6.24621 0.230082
\(738\) 0 0
\(739\) 16.8769 0.620827 0.310413 0.950602i \(-0.399533\pi\)
0.310413 + 0.950602i \(0.399533\pi\)
\(740\) 0 0
\(741\) −10.4384 −0.383466
\(742\) 0 0
\(743\) −27.1231 −0.995050 −0.497525 0.867450i \(-0.665758\pi\)
−0.497525 + 0.867450i \(0.665758\pi\)
\(744\) 0 0
\(745\) −11.3693 −0.416540
\(746\) 0 0
\(747\) −6.24621 −0.228537
\(748\) 0 0
\(749\) 14.9309 0.545562
\(750\) 0 0
\(751\) 43.1231 1.57358 0.786792 0.617218i \(-0.211740\pi\)
0.786792 + 0.617218i \(0.211740\pi\)
\(752\) 0 0
\(753\) −16.0000 −0.583072
\(754\) 0 0
\(755\) −3.12311 −0.113661
\(756\) 0 0
\(757\) −9.50758 −0.345559 −0.172779 0.984961i \(-0.555275\pi\)
−0.172779 + 0.984961i \(0.555275\pi\)
\(758\) 0 0
\(759\) 29.2614 1.06212
\(760\) 0 0
\(761\) −28.5464 −1.03481 −0.517403 0.855742i \(-0.673101\pi\)
−0.517403 + 0.855742i \(0.673101\pi\)
\(762\) 0 0
\(763\) 5.56155 0.201342
\(764\) 0 0
\(765\) 4.24621 0.153522
\(766\) 0 0
\(767\) −10.4384 −0.376910
\(768\) 0 0
\(769\) 31.5616 1.13814 0.569069 0.822290i \(-0.307304\pi\)
0.569069 + 0.822290i \(0.307304\pi\)
\(770\) 0 0
\(771\) 21.8617 0.787331
\(772\) 0 0
\(773\) 9.80776 0.352761 0.176380 0.984322i \(-0.443561\pi\)
0.176380 + 0.984322i \(0.443561\pi\)
\(774\) 0 0
\(775\) −3.12311 −0.112185
\(776\) 0 0
\(777\) −14.6307 −0.524873
\(778\) 0 0
\(779\) 4.24621 0.152136
\(780\) 0 0
\(781\) 24.9848 0.894028
\(782\) 0 0
\(783\) 37.1771 1.32860
\(784\) 0 0
\(785\) −3.75379 −0.133978
\(786\) 0 0
\(787\) 31.8078 1.13382 0.566912 0.823778i \(-0.308138\pi\)
0.566912 + 0.823778i \(0.308138\pi\)
\(788\) 0 0
\(789\) 8.98485 0.319869
\(790\) 0 0
\(791\) −26.7386 −0.950716
\(792\) 0 0
\(793\) −19.2311 −0.682915
\(794\) 0 0
\(795\) −0.684658 −0.0242823
\(796\) 0 0
\(797\) −42.3002 −1.49835 −0.749175 0.662372i \(-0.769550\pi\)
−0.749175 + 0.662372i \(0.769550\pi\)
\(798\) 0 0
\(799\) 77.4773 2.74095
\(800\) 0 0
\(801\) −1.12311 −0.0396830
\(802\) 0 0
\(803\) 42.7386 1.50821
\(804\) 0 0
\(805\) 7.31534 0.257832
\(806\) 0 0
\(807\) 40.6004 1.42920
\(808\) 0 0
\(809\) −8.43845 −0.296680 −0.148340 0.988936i \(-0.547393\pi\)
−0.148340 + 0.988936i \(0.547393\pi\)
\(810\) 0 0
\(811\) −0.192236 −0.00675032 −0.00337516 0.999994i \(-0.501074\pi\)
−0.00337516 + 0.999994i \(0.501074\pi\)
\(812\) 0 0
\(813\) −10.8229 −0.379576
\(814\) 0 0
\(815\) −9.36932 −0.328193
\(816\) 0 0
\(817\) 11.1231 0.389148
\(818\) 0 0
\(819\) 5.86174 0.204826
\(820\) 0 0
\(821\) −7.36932 −0.257191 −0.128595 0.991697i \(-0.541047\pi\)
−0.128595 + 0.991697i \(0.541047\pi\)
\(822\) 0 0
\(823\) 33.5616 1.16988 0.584941 0.811076i \(-0.301118\pi\)
0.584941 + 0.811076i \(0.301118\pi\)
\(824\) 0 0
\(825\) 6.24621 0.217465
\(826\) 0 0
\(827\) −6.43845 −0.223887 −0.111943 0.993715i \(-0.535708\pi\)
−0.111943 + 0.993715i \(0.535708\pi\)
\(828\) 0 0
\(829\) −16.0540 −0.557578 −0.278789 0.960352i \(-0.589933\pi\)
−0.278789 + 0.960352i \(0.589933\pi\)
\(830\) 0 0
\(831\) −14.2462 −0.494196
\(832\) 0 0
\(833\) −34.4924 −1.19509
\(834\) 0 0
\(835\) 17.3693 0.601090
\(836\) 0 0
\(837\) 17.3693 0.600371
\(838\) 0 0
\(839\) 12.4924 0.431286 0.215643 0.976472i \(-0.430815\pi\)
0.215643 + 0.976472i \(0.430815\pi\)
\(840\) 0 0
\(841\) 15.6847 0.540850
\(842\) 0 0
\(843\) 3.12311 0.107565
\(844\) 0 0
\(845\) −31.6847 −1.08999
\(846\) 0 0
\(847\) −7.80776 −0.268278
\(848\) 0 0
\(849\) −20.1080 −0.690103
\(850\) 0 0
\(851\) 28.1080 0.963528
\(852\) 0 0
\(853\) −24.7386 −0.847035 −0.423517 0.905888i \(-0.639205\pi\)
−0.423517 + 0.905888i \(0.639205\pi\)
\(854\) 0 0
\(855\) −0.561553 −0.0192047
\(856\) 0 0
\(857\) 39.3693 1.34483 0.672415 0.740174i \(-0.265257\pi\)
0.672415 + 0.740174i \(0.265257\pi\)
\(858\) 0 0
\(859\) 12.9848 0.443037 0.221519 0.975156i \(-0.428899\pi\)
0.221519 + 0.975156i \(0.428899\pi\)
\(860\) 0 0
\(861\) 10.3542 0.352869
\(862\) 0 0
\(863\) 14.2462 0.484947 0.242473 0.970158i \(-0.422041\pi\)
0.242473 + 0.970158i \(0.422041\pi\)
\(864\) 0 0
\(865\) 3.75379 0.127633
\(866\) 0 0
\(867\) 62.7386 2.13072
\(868\) 0 0
\(869\) −12.4924 −0.423776
\(870\) 0 0
\(871\) 10.4384 0.353693
\(872\) 0 0
\(873\) −3.36932 −0.114034
\(874\) 0 0
\(875\) 1.56155 0.0527901
\(876\) 0 0
\(877\) −24.9309 −0.841856 −0.420928 0.907094i \(-0.638295\pi\)
−0.420928 + 0.907094i \(0.638295\pi\)
\(878\) 0 0
\(879\) −36.1922 −1.22073
\(880\) 0 0
\(881\) −22.9848 −0.774379 −0.387190 0.922000i \(-0.626554\pi\)
−0.387190 + 0.922000i \(0.626554\pi\)
\(882\) 0 0
\(883\) −47.6155 −1.60239 −0.801195 0.598403i \(-0.795802\pi\)
−0.801195 + 0.598403i \(0.795802\pi\)
\(884\) 0 0
\(885\) 2.43845 0.0819675
\(886\) 0 0
\(887\) 4.49242 0.150841 0.0754204 0.997152i \(-0.475970\pi\)
0.0754204 + 0.997152i \(0.475970\pi\)
\(888\) 0 0
\(889\) 7.61553 0.255417
\(890\) 0 0
\(891\) −28.0000 −0.938035
\(892\) 0 0
\(893\) −10.2462 −0.342876
\(894\) 0 0
\(895\) 5.75379 0.192328
\(896\) 0 0
\(897\) 48.9006 1.63274
\(898\) 0 0
\(899\) 20.8769 0.696283
\(900\) 0 0
\(901\) 3.31534 0.110450
\(902\) 0 0
\(903\) 27.1231 0.902600
\(904\) 0 0
\(905\) −18.0000 −0.598340
\(906\) 0 0
\(907\) 25.1771 0.835991 0.417996 0.908449i \(-0.362733\pi\)
0.417996 + 0.908449i \(0.362733\pi\)
\(908\) 0 0
\(909\) 4.13826 0.137257
\(910\) 0 0
\(911\) 28.4924 0.943996 0.471998 0.881600i \(-0.343533\pi\)
0.471998 + 0.881600i \(0.343533\pi\)
\(912\) 0 0
\(913\) 44.4924 1.47248
\(914\) 0 0
\(915\) 4.49242 0.148515
\(916\) 0 0
\(917\) −25.7538 −0.850465
\(918\) 0 0
\(919\) 30.9309 1.02032 0.510158 0.860081i \(-0.329587\pi\)
0.510158 + 0.860081i \(0.329587\pi\)
\(920\) 0 0
\(921\) −0.768944 −0.0253376
\(922\) 0 0
\(923\) 41.7538 1.37434
\(924\) 0 0
\(925\) 6.00000 0.197279
\(926\) 0 0
\(927\) −8.00000 −0.262754
\(928\) 0 0
\(929\) 34.3002 1.12535 0.562676 0.826677i \(-0.309772\pi\)
0.562676 + 0.826677i \(0.309772\pi\)
\(930\) 0 0
\(931\) 4.56155 0.149499
\(932\) 0 0
\(933\) −13.5616 −0.443985
\(934\) 0 0
\(935\) −30.2462 −0.989157
\(936\) 0 0
\(937\) 36.4384 1.19039 0.595196 0.803580i \(-0.297074\pi\)
0.595196 + 0.803580i \(0.297074\pi\)
\(938\) 0 0
\(939\) −50.0540 −1.63345
\(940\) 0 0
\(941\) −34.1922 −1.11464 −0.557318 0.830299i \(-0.688169\pi\)
−0.557318 + 0.830299i \(0.688169\pi\)
\(942\) 0 0
\(943\) −19.8920 −0.647774
\(944\) 0 0
\(945\) −8.68466 −0.282512
\(946\) 0 0
\(947\) −17.7538 −0.576921 −0.288460 0.957492i \(-0.593143\pi\)
−0.288460 + 0.957492i \(0.593143\pi\)
\(948\) 0 0
\(949\) 71.4233 2.31850
\(950\) 0 0
\(951\) 37.5616 1.21802
\(952\) 0 0
\(953\) −30.1080 −0.975292 −0.487646 0.873041i \(-0.662144\pi\)
−0.487646 + 0.873041i \(0.662144\pi\)
\(954\) 0 0
\(955\) 8.68466 0.281029
\(956\) 0 0
\(957\) −41.7538 −1.34971
\(958\) 0 0
\(959\) −9.06913 −0.292857
\(960\) 0 0
\(961\) −21.2462 −0.685362
\(962\) 0 0
\(963\) 5.36932 0.173024
\(964\) 0 0
\(965\) −18.4924 −0.595292
\(966\) 0 0
\(967\) 48.4924 1.55941 0.779706 0.626146i \(-0.215369\pi\)
0.779706 + 0.626146i \(0.215369\pi\)
\(968\) 0 0
\(969\) −11.8078 −0.379320
\(970\) 0 0
\(971\) −23.5076 −0.754394 −0.377197 0.926133i \(-0.623112\pi\)
−0.377197 + 0.926133i \(0.623112\pi\)
\(972\) 0 0
\(973\) 25.7538 0.825629
\(974\) 0 0
\(975\) 10.4384 0.334298
\(976\) 0 0
\(977\) −20.7386 −0.663488 −0.331744 0.943370i \(-0.607637\pi\)
−0.331744 + 0.943370i \(0.607637\pi\)
\(978\) 0 0
\(979\) 8.00000 0.255681
\(980\) 0 0
\(981\) 2.00000 0.0638551
\(982\) 0 0
\(983\) −27.1231 −0.865093 −0.432546 0.901612i \(-0.642385\pi\)
−0.432546 + 0.901612i \(0.642385\pi\)
\(984\) 0 0
\(985\) −3.75379 −0.119606
\(986\) 0 0
\(987\) −24.9848 −0.795276
\(988\) 0 0
\(989\) −52.1080 −1.65694
\(990\) 0 0
\(991\) −11.1231 −0.353337 −0.176669 0.984270i \(-0.556532\pi\)
−0.176669 + 0.984270i \(0.556532\pi\)
\(992\) 0 0
\(993\) 2.43845 0.0773818
\(994\) 0 0
\(995\) −3.80776 −0.120714
\(996\) 0 0
\(997\) −32.7386 −1.03684 −0.518421 0.855125i \(-0.673480\pi\)
−0.518421 + 0.855125i \(0.673480\pi\)
\(998\) 0 0
\(999\) −33.3693 −1.05576
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 6080.2.a.bb.1.2 2
4.3 odd 2 6080.2.a.bh.1.1 2
8.3 odd 2 190.2.a.d.1.2 2
8.5 even 2 1520.2.a.n.1.1 2
24.11 even 2 1710.2.a.w.1.2 2
40.3 even 4 950.2.b.f.799.4 4
40.19 odd 2 950.2.a.h.1.1 2
40.27 even 4 950.2.b.f.799.1 4
40.29 even 2 7600.2.a.y.1.2 2
56.27 even 2 9310.2.a.bc.1.1 2
120.59 even 2 8550.2.a.br.1.1 2
152.75 even 2 3610.2.a.t.1.1 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
190.2.a.d.1.2 2 8.3 odd 2
950.2.a.h.1.1 2 40.19 odd 2
950.2.b.f.799.1 4 40.27 even 4
950.2.b.f.799.4 4 40.3 even 4
1520.2.a.n.1.1 2 8.5 even 2
1710.2.a.w.1.2 2 24.11 even 2
3610.2.a.t.1.1 2 152.75 even 2
6080.2.a.bb.1.2 2 1.1 even 1 trivial
6080.2.a.bh.1.1 2 4.3 odd 2
7600.2.a.y.1.2 2 40.29 even 2
8550.2.a.br.1.1 2 120.59 even 2
9310.2.a.bc.1.1 2 56.27 even 2