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Properties

Label 9450.2.a.cd.1.1
Level $9450$
Weight $2$
Character 9450.1
Self dual yes
Analytic conductor $75.459$
Analytic rank $1$
Dimension $1$
CM no
Inner twists $1$

Related objects

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [9450,2,Mod(1,9450)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(9450, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 0, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("9450.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 9450 = 2 \cdot 3^{3} \cdot 5^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 9450.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: \(75.4586299101\)
Analytic rank: \(1\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Character \(\chi\) \(=\) 9450.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+1.00000 q^{2} +1.00000 q^{4} -1.00000 q^{7} +1.00000 q^{8} +O(q^{10})\) \(q+1.00000 q^{2} +1.00000 q^{4} -1.00000 q^{7} +1.00000 q^{8} -4.00000 q^{11} -1.00000 q^{13} -1.00000 q^{14} +1.00000 q^{16} -1.00000 q^{17} +5.00000 q^{19} -4.00000 q^{22} +4.00000 q^{23} -1.00000 q^{26} -1.00000 q^{28} +3.00000 q^{29} -8.00000 q^{31} +1.00000 q^{32} -1.00000 q^{34} -4.00000 q^{37} +5.00000 q^{38} -2.00000 q^{41} -4.00000 q^{44} +4.00000 q^{46} +7.00000 q^{47} +1.00000 q^{49} -1.00000 q^{52} -9.00000 q^{53} -1.00000 q^{56} +3.00000 q^{58} -10.0000 q^{59} +13.0000 q^{61} -8.00000 q^{62} +1.00000 q^{64} +6.00000 q^{67} -1.00000 q^{68} -8.00000 q^{71} +2.00000 q^{73} -4.00000 q^{74} +5.00000 q^{76} +4.00000 q^{77} -3.00000 q^{79} -2.00000 q^{82} -12.0000 q^{83} -4.00000 q^{88} -11.0000 q^{89} +1.00000 q^{91} +4.00000 q^{92} +7.00000 q^{94} -10.0000 q^{97} +1.00000 q^{98} +O(q^{100})\)

Display 100 coefficients 10 coefficients

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000 0.707107
\(3\) 0 0
\(4\) 1.00000 0.500000
\(5\) 0 0
\(6\) 0 0
\(7\) −1.00000 −0.377964
\(8\) 1.00000 0.353553
\(9\) 0 0
\(10\) 0 0
\(11\) −4.00000 −1.20605 −0.603023 − 0.797724i \(-0.706037\pi\)
−0.603023 + 0.797724i \(0.706037\pi\)
\(12\) 0 0
\(13\) −1.00000 −0.277350 −0.138675 − 0.990338i \(-0.544284\pi\)
−0.138675 + 0.990338i \(0.544284\pi\)
\(14\) −1.00000 −0.267261
\(15\) 0 0
\(16\) 1.00000 0.250000
\(17\) −1.00000 −0.242536 −0.121268 − 0.992620i \(-0.538696\pi\)
−0.121268 + 0.992620i \(0.538696\pi\)
\(18\) 0 0
\(19\) 5.00000 1.14708 0.573539 − 0.819178i \(-0.305570\pi\)
0.573539 + 0.819178i \(0.305570\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) −4.00000 −0.852803
\(23\) 4.00000 0.834058 0.417029 − 0.908893i \(-0.363071\pi\)
0.417029 + 0.908893i \(0.363071\pi\)
\(24\) 0 0
\(25\) 0 0
\(26\) −1.00000 −0.196116
\(27\) 0 0
\(28\) −1.00000 −0.188982
\(29\) 3.00000 0.557086 0.278543 − 0.960424i \(-0.410149\pi\)
0.278543 + 0.960424i \(0.410149\pi\)
\(30\) 0 0
\(31\) −8.00000 −1.43684 −0.718421 − 0.695608i \(-0.755135\pi\)
−0.718421 + 0.695608i \(0.755135\pi\)
\(32\) 1.00000 0.176777
\(33\) 0 0
\(34\) −1.00000 −0.171499
\(35\) 0 0
\(36\) 0 0
\(37\) −4.00000 −0.657596 −0.328798 − 0.944400i \(-0.606644\pi\)
−0.328798 + 0.944400i \(0.606644\pi\)
\(38\) 5.00000 0.811107
\(39\) 0 0
\(40\) 0 0
\(41\) −2.00000 −0.312348 −0.156174 − 0.987730i \(-0.549916\pi\)
−0.156174 + 0.987730i \(0.549916\pi\)
\(42\) 0 0
\(43\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(44\) −4.00000 −0.603023
\(45\) 0 0
\(46\) 4.00000 0.589768
\(47\) 7.00000 1.02105 0.510527 − 0.859861i \(-0.329450\pi\)
0.510527 + 0.859861i \(0.329450\pi\)
\(48\) 0 0
\(49\) 1.00000 0.142857
\(50\) 0 0
\(51\) 0 0
\(52\) −1.00000 −0.138675
\(53\) −9.00000 −1.23625 −0.618123 − 0.786082i \(-0.712106\pi\)
−0.618123 + 0.786082i \(0.712106\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) −1.00000 −0.133631
\(57\) 0 0
\(58\) 3.00000 0.393919
\(59\) −10.0000 −1.30189 −0.650945 − 0.759125i \(-0.725627\pi\)
−0.650945 + 0.759125i \(0.725627\pi\)
\(60\) 0 0
\(61\) 13.0000 1.66448 0.832240 − 0.554416i \(-0.187058\pi\)
0.832240 + 0.554416i \(0.187058\pi\)
\(62\) −8.00000 −1.01600
\(63\) 0 0
\(64\) 1.00000 0.125000
\(65\) 0 0
\(66\) 0 0
\(67\) 6.00000 0.733017 0.366508 − 0.930415i \(-0.380553\pi\)
0.366508 + 0.930415i \(0.380553\pi\)
\(68\) −1.00000 −0.121268
\(69\) 0 0
\(70\) 0 0
\(71\) −8.00000 −0.949425 −0.474713 − 0.880141i \(-0.657448\pi\)
−0.474713 + 0.880141i \(0.657448\pi\)
\(72\) 0 0
\(73\) 2.00000 0.234082 0.117041 − 0.993127i \(-0.462659\pi\)
0.117041 + 0.993127i \(0.462659\pi\)
\(74\) −4.00000 −0.464991
\(75\) 0 0
\(76\) 5.00000 0.573539
\(77\) 4.00000 0.455842
\(78\) 0 0
\(79\) −3.00000 −0.337526 −0.168763 − 0.985657i \(-0.553977\pi\)
−0.168763 + 0.985657i \(0.553977\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) −2.00000 −0.220863
\(83\) −12.0000 −1.31717 −0.658586 − 0.752506i \(-0.728845\pi\)
−0.658586 + 0.752506i \(0.728845\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 0 0
\(87\) 0 0
\(88\) −4.00000 −0.426401
\(89\) −11.0000 −1.16600 −0.582999 − 0.812473i \(-0.698121\pi\)
−0.582999 + 0.812473i \(0.698121\pi\)
\(90\) 0 0
\(91\) 1.00000 0.104828
\(92\) 4.00000 0.417029
\(93\) 0 0
\(94\) 7.00000 0.721995
\(95\) 0 0
\(96\) 0 0
\(97\) −10.0000 −1.01535 −0.507673 − 0.861550i \(-0.669494\pi\)
−0.507673 + 0.861550i \(0.669494\pi\)
\(98\) 1.00000 0.101015
\(99\) 0 0
\(100\) 0 0
\(101\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(102\) 0 0
\(103\) 4.00000 0.394132 0.197066 − 0.980390i \(-0.436859\pi\)
0.197066 + 0.980390i \(0.436859\pi\)
\(104\) −1.00000 −0.0980581
\(105\) 0 0
\(106\) −9.00000 −0.874157
\(107\) 4.00000 0.386695 0.193347 − 0.981130i \(-0.438066\pi\)
0.193347 + 0.981130i \(0.438066\pi\)
\(108\) 0 0
\(109\) −20.0000 −1.91565 −0.957826 − 0.287348i \(-0.907226\pi\)
−0.957826 + 0.287348i \(0.907226\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) −1.00000 −0.0944911
\(113\) −2.00000 −0.188144 −0.0940721 − 0.995565i \(-0.529988\pi\)
−0.0940721 + 0.995565i \(0.529988\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 3.00000 0.278543
\(117\) 0 0
\(118\) −10.0000 −0.920575
\(119\) 1.00000 0.0916698
\(120\) 0 0
\(121\) 5.00000 0.454545
\(122\) 13.0000 1.17696
\(123\) 0 0
\(124\) −8.00000 −0.718421
\(125\) 0 0
\(126\) 0 0
\(127\) −3.00000 −0.266207 −0.133103 − 0.991102i \(-0.542494\pi\)
−0.133103 + 0.991102i \(0.542494\pi\)
\(128\) 1.00000 0.0883883
\(129\) 0 0
\(130\) 0 0
\(131\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(132\) 0 0
\(133\) −5.00000 −0.433555
\(134\) 6.00000 0.518321
\(135\) 0 0
\(136\) −1.00000 −0.0857493
\(137\) −20.0000 −1.70872 −0.854358 − 0.519685i \(-0.826049\pi\)
−0.854358 + 0.519685i \(0.826049\pi\)
\(138\) 0 0
\(139\) −4.00000 −0.339276 −0.169638 − 0.985506i \(-0.554260\pi\)
−0.169638 + 0.985506i \(0.554260\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) −8.00000 −0.671345
\(143\) 4.00000 0.334497
\(144\) 0 0
\(145\) 0 0
\(146\) 2.00000 0.165521
\(147\) 0 0
\(148\) −4.00000 −0.328798
\(149\) 15.0000 1.22885 0.614424 − 0.788976i \(-0.289388\pi\)
0.614424 + 0.788976i \(0.289388\pi\)
\(150\) 0 0
\(151\) 11.0000 0.895167 0.447584 − 0.894242i \(-0.352285\pi\)
0.447584 + 0.894242i \(0.352285\pi\)
\(152\) 5.00000 0.405554
\(153\) 0 0
\(154\) 4.00000 0.322329
\(155\) 0 0
\(156\) 0 0
\(157\) −11.0000 −0.877896 −0.438948 − 0.898513i \(-0.644649\pi\)
−0.438948 + 0.898513i \(0.644649\pi\)
\(158\) −3.00000 −0.238667
\(159\) 0 0
\(160\) 0 0
\(161\) −4.00000 −0.315244
\(162\) 0 0
\(163\) −6.00000 −0.469956 −0.234978 − 0.972001i \(-0.575502\pi\)
−0.234978 + 0.972001i \(0.575502\pi\)
\(164\) −2.00000 −0.156174
\(165\) 0 0
\(166\) −12.0000 −0.931381
\(167\) 8.00000 0.619059 0.309529 − 0.950890i \(-0.399829\pi\)
0.309529 + 0.950890i \(0.399829\pi\)
\(168\) 0 0
\(169\) −12.0000 −0.923077
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) 2.00000 0.152057 0.0760286 − 0.997106i \(-0.475776\pi\)
0.0760286 + 0.997106i \(0.475776\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) −4.00000 −0.301511
\(177\) 0 0
\(178\) −11.0000 −0.824485
\(179\) −19.0000 −1.42013 −0.710063 − 0.704138i \(-0.751334\pi\)
−0.710063 + 0.704138i \(0.751334\pi\)
\(180\) 0 0
\(181\) −7.00000 −0.520306 −0.260153 − 0.965567i \(-0.583773\pi\)
−0.260153 + 0.965567i \(0.583773\pi\)
\(182\) 1.00000 0.0741249
\(183\) 0 0
\(184\) 4.00000 0.294884
\(185\) 0 0
\(186\) 0 0
\(187\) 4.00000 0.292509
\(188\) 7.00000 0.510527
\(189\) 0 0
\(190\) 0 0
\(191\) −20.0000 −1.44715 −0.723575 − 0.690246i \(-0.757502\pi\)
−0.723575 + 0.690246i \(0.757502\pi\)
\(192\) 0 0
\(193\) 23.0000 1.65558 0.827788 − 0.561041i \(-0.189599\pi\)
0.827788 + 0.561041i \(0.189599\pi\)
\(194\) −10.0000 −0.717958
\(195\) 0 0
\(196\) 1.00000 0.0714286
\(197\) 3.00000 0.213741 0.106871 − 0.994273i \(-0.465917\pi\)
0.106871 + 0.994273i \(0.465917\pi\)
\(198\) 0 0
\(199\) −16.0000 −1.13421 −0.567105 − 0.823646i \(-0.691937\pi\)
−0.567105 + 0.823646i \(0.691937\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) −3.00000 −0.210559
\(204\) 0 0
\(205\) 0 0
\(206\) 4.00000 0.278693
\(207\) 0 0
\(208\) −1.00000 −0.0693375
\(209\) −20.0000 −1.38343
\(210\) 0 0
\(211\) −10.0000 −0.688428 −0.344214 − 0.938891i \(-0.611855\pi\)
−0.344214 + 0.938891i \(0.611855\pi\)
\(212\) −9.00000 −0.618123
\(213\) 0 0
\(214\) 4.00000 0.273434
\(215\) 0 0
\(216\) 0 0
\(217\) 8.00000 0.543075
\(218\) −20.0000 −1.35457
\(219\) 0 0
\(220\) 0 0
\(221\) 1.00000 0.0672673
\(222\) 0 0
\(223\) −6.00000 −0.401790 −0.200895 − 0.979613i \(-0.564385\pi\)
−0.200895 + 0.979613i \(0.564385\pi\)
\(224\) −1.00000 −0.0668153
\(225\) 0 0
\(226\) −2.00000 −0.133038
\(227\) 6.00000 0.398234 0.199117 − 0.979976i \(-0.436193\pi\)
0.199117 + 0.979976i \(0.436193\pi\)
\(228\) 0 0
\(229\) −11.0000 −0.726900 −0.363450 − 0.931614i \(-0.618401\pi\)
−0.363450 + 0.931614i \(0.618401\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 3.00000 0.196960
\(233\) −14.0000 −0.917170 −0.458585 − 0.888650i \(-0.651644\pi\)
−0.458585 + 0.888650i \(0.651644\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) −10.0000 −0.650945
\(237\) 0 0
\(238\) 1.00000 0.0648204
\(239\) −8.00000 −0.517477 −0.258738 − 0.965947i \(-0.583307\pi\)
−0.258738 + 0.965947i \(0.583307\pi\)
\(240\) 0 0
\(241\) 18.0000 1.15948 0.579741 − 0.814801i \(-0.303154\pi\)
0.579741 + 0.814801i \(0.303154\pi\)
\(242\) 5.00000 0.321412
\(243\) 0 0
\(244\) 13.0000 0.832240
\(245\) 0 0
\(246\) 0 0
\(247\) −5.00000 −0.318142
\(248\) −8.00000 −0.508001
\(249\) 0 0
\(250\) 0 0
\(251\) 2.00000 0.126239 0.0631194 − 0.998006i \(-0.479895\pi\)
0.0631194 + 0.998006i \(0.479895\pi\)
\(252\) 0 0
\(253\) −16.0000 −1.00591
\(254\) −3.00000 −0.188237
\(255\) 0 0
\(256\) 1.00000 0.0625000
\(257\) 11.0000 0.686161 0.343081 − 0.939306i \(-0.388530\pi\)
0.343081 + 0.939306i \(0.388530\pi\)
\(258\) 0 0
\(259\) 4.00000 0.248548
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) 6.00000 0.369976 0.184988 − 0.982741i \(-0.440775\pi\)
0.184988 + 0.982741i \(0.440775\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) −5.00000 −0.306570
\(267\) 0 0
\(268\) 6.00000 0.366508
\(269\) −30.0000 −1.82913 −0.914566 − 0.404436i \(-0.867468\pi\)
−0.914566 + 0.404436i \(0.867468\pi\)
\(270\) 0 0
\(271\) 24.0000 1.45790 0.728948 − 0.684569i \(-0.240010\pi\)
0.728948 + 0.684569i \(0.240010\pi\)
\(272\) −1.00000 −0.0606339
\(273\) 0 0
\(274\) −20.0000 −1.20824
\(275\) 0 0
\(276\) 0 0
\(277\) −2.00000 −0.120168 −0.0600842 − 0.998193i \(-0.519137\pi\)
−0.0600842 + 0.998193i \(0.519137\pi\)
\(278\) −4.00000 −0.239904
\(279\) 0 0
\(280\) 0 0
\(281\) −16.0000 −0.954480 −0.477240 − 0.878773i \(-0.658363\pi\)
−0.477240 + 0.878773i \(0.658363\pi\)
\(282\) 0 0
\(283\) −17.0000 −1.01055 −0.505273 − 0.862960i \(-0.668608\pi\)
−0.505273 + 0.862960i \(0.668608\pi\)
\(284\) −8.00000 −0.474713
\(285\) 0 0
\(286\) 4.00000 0.236525
\(287\) 2.00000 0.118056
\(288\) 0 0
\(289\) −16.0000 −0.941176
\(290\) 0 0
\(291\) 0 0
\(292\) 2.00000 0.117041
\(293\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) −4.00000 −0.232495
\(297\) 0 0
\(298\) 15.0000 0.868927
\(299\) −4.00000 −0.231326
\(300\) 0 0
\(301\) 0 0
\(302\) 11.0000 0.632979
\(303\) 0 0
\(304\) 5.00000 0.286770
\(305\) 0 0
\(306\) 0 0
\(307\) −8.00000 −0.456584 −0.228292 − 0.973593i \(-0.573314\pi\)
−0.228292 + 0.973593i \(0.573314\pi\)
\(308\) 4.00000 0.227921
\(309\) 0 0
\(310\) 0 0
\(311\) −20.0000 −1.13410 −0.567048 − 0.823685i \(-0.691915\pi\)
−0.567048 + 0.823685i \(0.691915\pi\)
\(312\) 0 0
\(313\) 14.0000 0.791327 0.395663 − 0.918396i \(-0.370515\pi\)
0.395663 + 0.918396i \(0.370515\pi\)
\(314\) −11.0000 −0.620766
\(315\) 0 0
\(316\) −3.00000 −0.168763
\(317\) 11.0000 0.617822 0.308911 − 0.951091i \(-0.400036\pi\)
0.308911 + 0.951091i \(0.400036\pi\)
\(318\) 0 0
\(319\) −12.0000 −0.671871
\(320\) 0 0
\(321\) 0 0
\(322\) −4.00000 −0.222911
\(323\) −5.00000 −0.278207
\(324\) 0 0
\(325\) 0 0
\(326\) −6.00000 −0.332309
\(327\) 0 0
\(328\) −2.00000 −0.110432
\(329\) −7.00000 −0.385922
\(330\) 0 0
\(331\) 10.0000 0.549650 0.274825 − 0.961494i \(-0.411380\pi\)
0.274825 + 0.961494i \(0.411380\pi\)
\(332\) −12.0000 −0.658586
\(333\) 0 0
\(334\) 8.00000 0.437741
\(335\) 0 0
\(336\) 0 0
\(337\) 1.00000 0.0544735 0.0272367 − 0.999629i \(-0.491329\pi\)
0.0272367 + 0.999629i \(0.491329\pi\)
\(338\) −12.0000 −0.652714
\(339\) 0 0
\(340\) 0 0
\(341\) 32.0000 1.73290
\(342\) 0 0
\(343\) −1.00000 −0.0539949
\(344\) 0 0
\(345\) 0 0
\(346\) 2.00000 0.107521
\(347\) 27.0000 1.44944 0.724718 − 0.689046i \(-0.241970\pi\)
0.724718 + 0.689046i \(0.241970\pi\)
\(348\) 0 0
\(349\) 23.0000 1.23116 0.615581 − 0.788074i \(-0.288921\pi\)
0.615581 + 0.788074i \(0.288921\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) −4.00000 −0.213201
\(353\) −18.0000 −0.958043 −0.479022 − 0.877803i \(-0.659008\pi\)
−0.479022 + 0.877803i \(0.659008\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) −11.0000 −0.582999
\(357\) 0 0
\(358\) −19.0000 −1.00418
\(359\) −22.0000 −1.16112 −0.580558 − 0.814219i \(-0.697165\pi\)
−0.580558 + 0.814219i \(0.697165\pi\)
\(360\) 0 0
\(361\) 6.00000 0.315789
\(362\) −7.00000 −0.367912
\(363\) 0 0
\(364\) 1.00000 0.0524142
\(365\) 0 0
\(366\) 0 0
\(367\) 8.00000 0.417597 0.208798 − 0.977959i \(-0.433045\pi\)
0.208798 + 0.977959i \(0.433045\pi\)
\(368\) 4.00000 0.208514
\(369\) 0 0
\(370\) 0 0
\(371\) 9.00000 0.467257
\(372\) 0 0
\(373\) 22.0000 1.13912 0.569558 − 0.821951i \(-0.307114\pi\)
0.569558 + 0.821951i \(0.307114\pi\)
\(374\) 4.00000 0.206835
\(375\) 0 0
\(376\) 7.00000 0.360997
\(377\) −3.00000 −0.154508
\(378\) 0 0
\(379\) 4.00000 0.205466 0.102733 − 0.994709i \(-0.467241\pi\)
0.102733 + 0.994709i \(0.467241\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) −20.0000 −1.02329
\(383\) −12.0000 −0.613171 −0.306586 − 0.951843i \(-0.599187\pi\)
−0.306586 + 0.951843i \(0.599187\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 23.0000 1.17067
\(387\) 0 0
\(388\) −10.0000 −0.507673
\(389\) −27.0000 −1.36895 −0.684477 − 0.729034i \(-0.739969\pi\)
−0.684477 + 0.729034i \(0.739969\pi\)
\(390\) 0 0
\(391\) −4.00000 −0.202289
\(392\) 1.00000 0.0505076
\(393\) 0 0
\(394\) 3.00000 0.151138
\(395\) 0 0
\(396\) 0 0
\(397\) −19.0000 −0.953583 −0.476791 − 0.879017i \(-0.658200\pi\)
−0.476791 + 0.879017i \(0.658200\pi\)
\(398\) −16.0000 −0.802008
\(399\) 0 0
\(400\) 0 0
\(401\) 6.00000 0.299626 0.149813 − 0.988714i \(-0.452133\pi\)
0.149813 + 0.988714i \(0.452133\pi\)
\(402\) 0 0
\(403\) 8.00000 0.398508
\(404\) 0 0
\(405\) 0 0
\(406\) −3.00000 −0.148888
\(407\) 16.0000 0.793091
\(408\) 0 0
\(409\) 10.0000 0.494468 0.247234 − 0.968956i \(-0.420478\pi\)
0.247234 + 0.968956i \(0.420478\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 4.00000 0.197066
\(413\) 10.0000 0.492068
\(414\) 0 0
\(415\) 0 0
\(416\) −1.00000 −0.0490290
\(417\) 0 0
\(418\) −20.0000 −0.978232
\(419\) 30.0000 1.46560 0.732798 − 0.680446i \(-0.238214\pi\)
0.732798 + 0.680446i \(0.238214\pi\)
\(420\) 0 0
\(421\) 10.0000 0.487370 0.243685 − 0.969854i \(-0.421644\pi\)
0.243685 + 0.969854i \(0.421644\pi\)
\(422\) −10.0000 −0.486792
\(423\) 0 0
\(424\) −9.00000 −0.437079
\(425\) 0 0
\(426\) 0 0
\(427\) −13.0000 −0.629114
\(428\) 4.00000 0.193347
\(429\) 0 0
\(430\) 0 0
\(431\) 36.0000 1.73406 0.867029 − 0.498257i \(-0.166026\pi\)
0.867029 + 0.498257i \(0.166026\pi\)
\(432\) 0 0
\(433\) 36.0000 1.73005 0.865025 − 0.501729i \(-0.167303\pi\)
0.865025 + 0.501729i \(0.167303\pi\)
\(434\) 8.00000 0.384012
\(435\) 0 0
\(436\) −20.0000 −0.957826
\(437\) 20.0000 0.956730
\(438\) 0 0
\(439\) 20.0000 0.954548 0.477274 − 0.878755i \(-0.341625\pi\)
0.477274 + 0.878755i \(0.341625\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 1.00000 0.0475651
\(443\) −31.0000 −1.47285 −0.736427 − 0.676517i \(-0.763489\pi\)
−0.736427 + 0.676517i \(0.763489\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) −6.00000 −0.284108
\(447\) 0 0
\(448\) −1.00000 −0.0472456
\(449\) −34.0000 −1.60456 −0.802280 − 0.596948i \(-0.796380\pi\)
−0.802280 + 0.596948i \(0.796380\pi\)
\(450\) 0 0
\(451\) 8.00000 0.376705
\(452\) −2.00000 −0.0940721
\(453\) 0 0
\(454\) 6.00000 0.281594
\(455\) 0 0
\(456\) 0 0
\(457\) 17.0000 0.795226 0.397613 − 0.917553i \(-0.369839\pi\)
0.397613 + 0.917553i \(0.369839\pi\)
\(458\) −11.0000 −0.513996
\(459\) 0 0
\(460\) 0 0
\(461\) 4.00000 0.186299 0.0931493 − 0.995652i \(-0.470307\pi\)
0.0931493 + 0.995652i \(0.470307\pi\)
\(462\) 0 0
\(463\) 13.0000 0.604161 0.302081 − 0.953282i \(-0.402319\pi\)
0.302081 + 0.953282i \(0.402319\pi\)
\(464\) 3.00000 0.139272
\(465\) 0 0
\(466\) −14.0000 −0.648537
\(467\) −8.00000 −0.370196 −0.185098 − 0.982720i \(-0.559260\pi\)
−0.185098 + 0.982720i \(0.559260\pi\)
\(468\) 0 0
\(469\) −6.00000 −0.277054
\(470\) 0 0
\(471\) 0 0
\(472\) −10.0000 −0.460287
\(473\) 0 0
\(474\) 0 0
\(475\) 0 0
\(476\) 1.00000 0.0458349
\(477\) 0 0
\(478\) −8.00000 −0.365911
\(479\) 21.0000 0.959514 0.479757 − 0.877401i \(-0.340725\pi\)
0.479757 + 0.877401i \(0.340725\pi\)
\(480\) 0 0
\(481\) 4.00000 0.182384
\(482\) 18.0000 0.819878
\(483\) 0 0
\(484\) 5.00000 0.227273
\(485\) 0 0
\(486\) 0 0
\(487\) 36.0000 1.63132 0.815658 − 0.578535i \(-0.196375\pi\)
0.815658 + 0.578535i \(0.196375\pi\)
\(488\) 13.0000 0.588482
\(489\) 0 0
\(490\) 0 0
\(491\) −15.0000 −0.676941 −0.338470 − 0.940977i \(-0.609909\pi\)
−0.338470 + 0.940977i \(0.609909\pi\)
\(492\) 0 0
\(493\) −3.00000 −0.135113
\(494\) −5.00000 −0.224961
\(495\) 0 0
\(496\) −8.00000 −0.359211
\(497\) 8.00000 0.358849
\(498\) 0 0
\(499\) 4.00000 0.179065 0.0895323 − 0.995984i \(-0.471463\pi\)
0.0895323 + 0.995984i \(0.471463\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 2.00000 0.0892644
\(503\) −20.0000 −0.891756 −0.445878 − 0.895094i \(-0.647108\pi\)
−0.445878 + 0.895094i \(0.647108\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) −16.0000 −0.711287
\(507\) 0 0
\(508\) −3.00000 −0.133103
\(509\) −20.0000 −0.886484 −0.443242 − 0.896402i \(-0.646172\pi\)
−0.443242 + 0.896402i \(0.646172\pi\)
\(510\) 0 0
\(511\) −2.00000 −0.0884748
\(512\) 1.00000 0.0441942
\(513\) 0 0
\(514\) 11.0000 0.485189
\(515\) 0 0
\(516\) 0 0
\(517\) −28.0000 −1.23144
\(518\) 4.00000 0.175750
\(519\) 0 0
\(520\) 0 0
\(521\) −3.00000 −0.131432 −0.0657162 − 0.997838i \(-0.520933\pi\)
−0.0657162 + 0.997838i \(0.520933\pi\)
\(522\) 0 0
\(523\) 37.0000 1.61790 0.808949 − 0.587879i \(-0.200037\pi\)
0.808949 + 0.587879i \(0.200037\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 6.00000 0.261612
\(527\) 8.00000 0.348485
\(528\) 0 0
\(529\) −7.00000 −0.304348
\(530\) 0 0
\(531\) 0 0
\(532\) −5.00000 −0.216777
\(533\) 2.00000 0.0866296
\(534\) 0 0
\(535\) 0 0
\(536\) 6.00000 0.259161
\(537\) 0 0
\(538\) −30.0000 −1.29339
\(539\) −4.00000 −0.172292
\(540\) 0 0
\(541\) 8.00000 0.343947 0.171973 − 0.985102i \(-0.444986\pi\)
0.171973 + 0.985102i \(0.444986\pi\)
\(542\) 24.0000 1.03089
\(543\) 0 0
\(544\) −1.00000 −0.0428746
\(545\) 0 0
\(546\) 0 0
\(547\) 8.00000 0.342055 0.171028 − 0.985266i \(-0.445291\pi\)
0.171028 + 0.985266i \(0.445291\pi\)
\(548\) −20.0000 −0.854358
\(549\) 0 0
\(550\) 0 0
\(551\) 15.0000 0.639021
\(552\) 0 0
\(553\) 3.00000 0.127573
\(554\) −2.00000 −0.0849719
\(555\) 0 0
\(556\) −4.00000 −0.169638
\(557\) −23.0000 −0.974541 −0.487271 − 0.873251i \(-0.662007\pi\)
−0.487271 + 0.873251i \(0.662007\pi\)
\(558\) 0 0
\(559\) 0 0
\(560\) 0 0
\(561\) 0 0
\(562\) −16.0000 −0.674919
\(563\) 30.0000 1.26435 0.632175 − 0.774826i \(-0.282163\pi\)
0.632175 + 0.774826i \(0.282163\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) −17.0000 −0.714563
\(567\) 0 0
\(568\) −8.00000 −0.335673
\(569\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(570\) 0 0
\(571\) 34.0000 1.42286 0.711428 − 0.702759i \(-0.248049\pi\)
0.711428 + 0.702759i \(0.248049\pi\)
\(572\) 4.00000 0.167248
\(573\) 0 0
\(574\) 2.00000 0.0834784
\(575\) 0 0
\(576\) 0 0
\(577\) 4.00000 0.166522 0.0832611 − 0.996528i \(-0.473466\pi\)
0.0832611 + 0.996528i \(0.473466\pi\)
\(578\) −16.0000 −0.665512
\(579\) 0 0
\(580\) 0 0
\(581\) 12.0000 0.497844
\(582\) 0 0
\(583\) 36.0000 1.49097
\(584\) 2.00000 0.0827606
\(585\) 0 0
\(586\) 0 0
\(587\) 42.0000 1.73353 0.866763 − 0.498721i \(-0.166197\pi\)
0.866763 + 0.498721i \(0.166197\pi\)
\(588\) 0 0
\(589\) −40.0000 −1.64817
\(590\) 0 0
\(591\) 0 0
\(592\) −4.00000 −0.164399
\(593\) −15.0000 −0.615976 −0.307988 − 0.951390i \(-0.599656\pi\)
−0.307988 + 0.951390i \(0.599656\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 15.0000 0.614424
\(597\) 0 0
\(598\) −4.00000 −0.163572
\(599\) −20.0000 −0.817178 −0.408589 − 0.912719i \(-0.633979\pi\)
−0.408589 + 0.912719i \(0.633979\pi\)
\(600\) 0 0
\(601\) −16.0000 −0.652654 −0.326327 − 0.945257i \(-0.605811\pi\)
−0.326327 + 0.945257i \(0.605811\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 11.0000 0.447584
\(605\) 0 0
\(606\) 0 0
\(607\) −6.00000 −0.243532 −0.121766 − 0.992559i \(-0.538856\pi\)
−0.121766 + 0.992559i \(0.538856\pi\)
\(608\) 5.00000 0.202777
\(609\) 0 0
\(610\) 0 0
\(611\) −7.00000 −0.283190
\(612\) 0 0
\(613\) −38.0000 −1.53481 −0.767403 − 0.641165i \(-0.778451\pi\)
−0.767403 + 0.641165i \(0.778451\pi\)
\(614\) −8.00000 −0.322854
\(615\) 0 0
\(616\) 4.00000 0.161165
\(617\) 16.0000 0.644136 0.322068 − 0.946717i \(-0.395622\pi\)
0.322068 + 0.946717i \(0.395622\pi\)
\(618\) 0 0
\(619\) −20.0000 −0.803868 −0.401934 − 0.915669i \(-0.631662\pi\)
−0.401934 + 0.915669i \(0.631662\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) −20.0000 −0.801927
\(623\) 11.0000 0.440706
\(624\) 0 0
\(625\) 0 0
\(626\) 14.0000 0.559553
\(627\) 0 0
\(628\) −11.0000 −0.438948
\(629\) 4.00000 0.159490
\(630\) 0 0
\(631\) −15.0000 −0.597141 −0.298570 − 0.954388i \(-0.596510\pi\)
−0.298570 + 0.954388i \(0.596510\pi\)
\(632\) −3.00000 −0.119334
\(633\) 0 0
\(634\) 11.0000 0.436866
\(635\) 0 0
\(636\) 0 0
\(637\) −1.00000 −0.0396214
\(638\) −12.0000 −0.475085
\(639\) 0 0
\(640\) 0 0
\(641\) −24.0000 −0.947943 −0.473972 − 0.880540i \(-0.657180\pi\)
−0.473972 + 0.880540i \(0.657180\pi\)
\(642\) 0 0
\(643\) 11.0000 0.433798 0.216899 − 0.976194i \(-0.430406\pi\)
0.216899 + 0.976194i \(0.430406\pi\)
\(644\) −4.00000 −0.157622
\(645\) 0 0
\(646\) −5.00000 −0.196722
\(647\) 7.00000 0.275198 0.137599 − 0.990488i \(-0.456061\pi\)
0.137599 + 0.990488i \(0.456061\pi\)
\(648\) 0 0
\(649\) 40.0000 1.57014
\(650\) 0 0
\(651\) 0 0
\(652\) −6.00000 −0.234978
\(653\) −49.0000 −1.91752 −0.958759 − 0.284220i \(-0.908265\pi\)
−0.958759 + 0.284220i \(0.908265\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) −2.00000 −0.0780869
\(657\) 0 0
\(658\) −7.00000 −0.272888
\(659\) −1.00000 −0.0389545 −0.0194772 − 0.999810i \(-0.506200\pi\)
−0.0194772 + 0.999810i \(0.506200\pi\)
\(660\) 0 0
\(661\) −34.0000 −1.32245 −0.661223 − 0.750189i \(-0.729962\pi\)
−0.661223 + 0.750189i \(0.729962\pi\)
\(662\) 10.0000 0.388661
\(663\) 0 0
\(664\) −12.0000 −0.465690
\(665\) 0 0
\(666\) 0 0
\(667\) 12.0000 0.464642
\(668\) 8.00000 0.309529
\(669\) 0 0
\(670\) 0 0
\(671\) −52.0000 −2.00744
\(672\) 0 0
\(673\) −14.0000 −0.539660 −0.269830 − 0.962908i \(-0.586968\pi\)
−0.269830 + 0.962908i \(0.586968\pi\)
\(674\) 1.00000 0.0385186
\(675\) 0 0
\(676\) −12.0000 −0.461538
\(677\) 6.00000 0.230599 0.115299 − 0.993331i \(-0.463217\pi\)
0.115299 + 0.993331i \(0.463217\pi\)
\(678\) 0 0
\(679\) 10.0000 0.383765
\(680\) 0 0
\(681\) 0 0
\(682\) 32.0000 1.22534
\(683\) −4.00000 −0.153056 −0.0765279 − 0.997067i \(-0.524383\pi\)
−0.0765279 + 0.997067i \(0.524383\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) −1.00000 −0.0381802
\(687\) 0 0
\(688\) 0 0
\(689\) 9.00000 0.342873
\(690\) 0 0
\(691\) −8.00000 −0.304334 −0.152167 − 0.988355i \(-0.548625\pi\)
−0.152167 + 0.988355i \(0.548625\pi\)
\(692\) 2.00000 0.0760286
\(693\) 0 0
\(694\) 27.0000 1.02491
\(695\) 0 0
\(696\) 0 0
\(697\) 2.00000 0.0757554
\(698\) 23.0000 0.870563
\(699\) 0 0
\(700\) 0 0
\(701\) −30.0000 −1.13308 −0.566542 − 0.824033i \(-0.691719\pi\)
−0.566542 + 0.824033i \(0.691719\pi\)
\(702\) 0 0
\(703\) −20.0000 −0.754314
\(704\) −4.00000 −0.150756
\(705\) 0 0
\(706\) −18.0000 −0.677439
\(707\) 0 0
\(708\) 0 0
\(709\) 28.0000 1.05156 0.525781 − 0.850620i \(-0.323773\pi\)
0.525781 + 0.850620i \(0.323773\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) −11.0000 −0.412242
\(713\) −32.0000 −1.19841
\(714\) 0 0
\(715\) 0 0
\(716\) −19.0000 −0.710063
\(717\) 0 0
\(718\) −22.0000 −0.821033
\(719\) −33.0000 −1.23069 −0.615346 − 0.788257i \(-0.710984\pi\)
−0.615346 + 0.788257i \(0.710984\pi\)
\(720\) 0 0
\(721\) −4.00000 −0.148968
\(722\) 6.00000 0.223297
\(723\) 0 0
\(724\) −7.00000 −0.260153
\(725\) 0 0
\(726\) 0 0
\(727\) 24.0000 0.890111 0.445055 − 0.895503i \(-0.353184\pi\)
0.445055 + 0.895503i \(0.353184\pi\)
\(728\) 1.00000 0.0370625
\(729\) 0 0
\(730\) 0 0
\(731\) 0 0
\(732\) 0 0
\(733\) 9.00000 0.332423 0.166211 − 0.986090i \(-0.446847\pi\)
0.166211 + 0.986090i \(0.446847\pi\)
\(734\) 8.00000 0.295285
\(735\) 0 0
\(736\) 4.00000 0.147442
\(737\) −24.0000 −0.884051
\(738\) 0 0
\(739\) 18.0000 0.662141 0.331070 − 0.943606i \(-0.392590\pi\)
0.331070 + 0.943606i \(0.392590\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 9.00000 0.330400
\(743\) 18.0000 0.660356 0.330178 − 0.943919i \(-0.392891\pi\)
0.330178 + 0.943919i \(0.392891\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 22.0000 0.805477
\(747\) 0 0
\(748\) 4.00000 0.146254
\(749\) −4.00000 −0.146157
\(750\) 0 0
\(751\) −32.0000 −1.16770 −0.583848 − 0.811863i \(-0.698454\pi\)
−0.583848 + 0.811863i \(0.698454\pi\)
\(752\) 7.00000 0.255264
\(753\) 0 0
\(754\) −3.00000 −0.109254
\(755\) 0 0
\(756\) 0 0
\(757\) 34.0000 1.23575 0.617876 − 0.786276i \(-0.287994\pi\)
0.617876 + 0.786276i \(0.287994\pi\)
\(758\) 4.00000 0.145287
\(759\) 0 0
\(760\) 0 0
\(761\) −17.0000 −0.616250 −0.308125 − 0.951346i \(-0.599701\pi\)
−0.308125 + 0.951346i \(0.599701\pi\)
\(762\) 0 0
\(763\) 20.0000 0.724049
\(764\) −20.0000 −0.723575
\(765\) 0 0
\(766\) −12.0000 −0.433578
\(767\) 10.0000 0.361079
\(768\) 0 0
\(769\) −32.0000 −1.15395 −0.576975 − 0.816762i \(-0.695767\pi\)
−0.576975 + 0.816762i \(0.695767\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 23.0000 0.827788
\(773\) 28.0000 1.00709 0.503545 − 0.863969i \(-0.332029\pi\)
0.503545 + 0.863969i \(0.332029\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) −10.0000 −0.358979
\(777\) 0 0
\(778\) −27.0000 −0.967997
\(779\) −10.0000 −0.358287
\(780\) 0 0
\(781\) 32.0000 1.14505
\(782\) −4.00000 −0.143040
\(783\) 0 0
\(784\) 1.00000 0.0357143
\(785\) 0 0
\(786\) 0 0
\(787\) 52.0000 1.85360 0.926800 − 0.375555i \(-0.122548\pi\)
0.926800 + 0.375555i \(0.122548\pi\)
\(788\) 3.00000 0.106871
\(789\) 0 0
\(790\) 0 0
\(791\) 2.00000 0.0711118
\(792\) 0 0
\(793\) −13.0000 −0.461644
\(794\) −19.0000 −0.674285
\(795\) 0 0
\(796\) −16.0000 −0.567105
\(797\) 42.0000 1.48772 0.743858 − 0.668338i \(-0.232994\pi\)
0.743858 + 0.668338i \(0.232994\pi\)
\(798\) 0 0
\(799\) −7.00000 −0.247642
\(800\) 0 0
\(801\) 0 0
\(802\) 6.00000 0.211867
\(803\) −8.00000 −0.282314
\(804\) 0 0
\(805\) 0 0
\(806\) 8.00000 0.281788
\(807\) 0 0
\(808\) 0 0
\(809\) 38.0000 1.33601 0.668004 − 0.744157i \(-0.267149\pi\)
0.668004 + 0.744157i \(0.267149\pi\)
\(810\) 0 0
\(811\) 36.0000 1.26413 0.632065 − 0.774915i \(-0.282207\pi\)
0.632065 + 0.774915i \(0.282207\pi\)
\(812\) −3.00000 −0.105279
\(813\) 0 0
\(814\) 16.0000 0.560800
\(815\) 0 0
\(816\) 0 0
\(817\) 0 0
\(818\) 10.0000 0.349642
\(819\) 0 0
\(820\) 0 0
\(821\) −7.00000 −0.244302 −0.122151 − 0.992512i \(-0.538979\pi\)
−0.122151 + 0.992512i \(0.538979\pi\)
\(822\) 0 0
\(823\) −4.00000 −0.139431 −0.0697156 − 0.997567i \(-0.522209\pi\)
−0.0697156 + 0.997567i \(0.522209\pi\)
\(824\) 4.00000 0.139347
\(825\) 0 0
\(826\) 10.0000 0.347945
\(827\) −45.0000 −1.56480 −0.782402 − 0.622774i \(-0.786006\pi\)
−0.782402 + 0.622774i \(0.786006\pi\)
\(828\) 0 0
\(829\) −49.0000 −1.70184 −0.850920 − 0.525295i \(-0.823955\pi\)
−0.850920 + 0.525295i \(0.823955\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) −1.00000 −0.0346688
\(833\) −1.00000 −0.0346479
\(834\) 0 0
\(835\) 0 0
\(836\) −20.0000 −0.691714
\(837\) 0 0
\(838\) 30.0000 1.03633
\(839\) 9.00000 0.310715 0.155357 − 0.987858i \(-0.450347\pi\)
0.155357 + 0.987858i \(0.450347\pi\)
\(840\) 0 0
\(841\) −20.0000 −0.689655
\(842\) 10.0000 0.344623
\(843\) 0 0
\(844\) −10.0000 −0.344214
\(845\) 0 0
\(846\) 0 0
\(847\) −5.00000 −0.171802
\(848\) −9.00000 −0.309061
\(849\) 0 0
\(850\) 0 0
\(851\) −16.0000 −0.548473
\(852\) 0 0
\(853\) 14.0000 0.479351 0.239675 − 0.970853i \(-0.422959\pi\)
0.239675 + 0.970853i \(0.422959\pi\)
\(854\) −13.0000 −0.444851
\(855\) 0 0
\(856\) 4.00000 0.136717
\(857\) 5.00000 0.170797 0.0853984 − 0.996347i \(-0.472784\pi\)
0.0853984 + 0.996347i \(0.472784\pi\)
\(858\) 0 0
\(859\) −40.0000 −1.36478 −0.682391 − 0.730987i \(-0.739060\pi\)
−0.682391 + 0.730987i \(0.739060\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 36.0000 1.22616
\(863\) −54.0000 −1.83818 −0.919091 − 0.394046i \(-0.871075\pi\)
−0.919091 + 0.394046i \(0.871075\pi\)
\(864\) 0 0
\(865\) 0 0
\(866\) 36.0000 1.22333
\(867\) 0 0
\(868\) 8.00000 0.271538
\(869\) 12.0000 0.407072
\(870\) 0 0
\(871\) −6.00000 −0.203302
\(872\) −20.0000 −0.677285
\(873\) 0 0
\(874\) 20.0000 0.676510
\(875\) 0 0
\(876\) 0 0
\(877\) −44.0000 −1.48577 −0.742887 − 0.669417i \(-0.766544\pi\)
−0.742887 + 0.669417i \(0.766544\pi\)
\(878\) 20.0000 0.674967
\(879\) 0 0
\(880\) 0 0
\(881\) 3.00000 0.101073 0.0505363 − 0.998722i \(-0.483907\pi\)
0.0505363 + 0.998722i \(0.483907\pi\)
\(882\) 0 0
\(883\) 44.0000 1.48072 0.740359 − 0.672212i \(-0.234656\pi\)
0.740359 + 0.672212i \(0.234656\pi\)
\(884\) 1.00000 0.0336336
\(885\) 0 0
\(886\) −31.0000 −1.04147
\(887\) 4.00000 0.134307 0.0671534 − 0.997743i \(-0.478608\pi\)
0.0671534 + 0.997743i \(0.478608\pi\)
\(888\) 0 0
\(889\) 3.00000 0.100617
\(890\) 0 0
\(891\) 0 0
\(892\) −6.00000 −0.200895
\(893\) 35.0000 1.17123
\(894\) 0 0
\(895\) 0 0
\(896\) −1.00000 −0.0334077
\(897\) 0 0
\(898\) −34.0000 −1.13459
\(899\) −24.0000 −0.800445
\(900\) 0 0
\(901\) 9.00000 0.299833
\(902\) 8.00000 0.266371
\(903\) 0 0
\(904\) −2.00000 −0.0665190
\(905\) 0 0
\(906\) 0 0
\(907\) 24.0000 0.796907 0.398453 − 0.917189i \(-0.369547\pi\)
0.398453 + 0.917189i \(0.369547\pi\)
\(908\) 6.00000 0.199117
\(909\) 0 0
\(910\) 0 0
\(911\) 24.0000 0.795155 0.397578 − 0.917568i \(-0.369851\pi\)
0.397578 + 0.917568i \(0.369851\pi\)
\(912\) 0 0
\(913\) 48.0000 1.58857
\(914\) 17.0000 0.562310
\(915\) 0 0
\(916\) −11.0000 −0.363450
\(917\) 0 0
\(918\) 0 0
\(919\) −32.0000 −1.05558 −0.527791 − 0.849374i \(-0.676980\pi\)
−0.527791 + 0.849374i \(0.676980\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 4.00000 0.131733
\(923\) 8.00000 0.263323
\(924\) 0 0
\(925\) 0 0
\(926\) 13.0000 0.427207
\(927\) 0 0
\(928\) 3.00000 0.0984798
\(929\) 23.0000 0.754606 0.377303 − 0.926090i \(-0.376852\pi\)
0.377303 + 0.926090i \(0.376852\pi\)
\(930\) 0 0
\(931\) 5.00000 0.163868
\(932\) −14.0000 −0.458585
\(933\) 0 0
\(934\) −8.00000 −0.261768
\(935\) 0 0
\(936\) 0 0
\(937\) 18.0000 0.588034 0.294017 − 0.955800i \(-0.405008\pi\)
0.294017 + 0.955800i \(0.405008\pi\)
\(938\) −6.00000 −0.195907
\(939\) 0 0
\(940\) 0 0
\(941\) 30.0000 0.977972 0.488986 − 0.872292i \(-0.337367\pi\)
0.488986 + 0.872292i \(0.337367\pi\)
\(942\) 0 0
\(943\) −8.00000 −0.260516
\(944\) −10.0000 −0.325472
\(945\) 0 0
\(946\) 0 0
\(947\) −48.0000 −1.55979 −0.779895 − 0.625910i \(-0.784728\pi\)
−0.779895 + 0.625910i \(0.784728\pi\)
\(948\) 0 0
\(949\) −2.00000 −0.0649227
\(950\) 0 0
\(951\) 0 0
\(952\) 1.00000 0.0324102
\(953\) −42.0000 −1.36051 −0.680257 − 0.732974i \(-0.738132\pi\)
−0.680257 + 0.732974i \(0.738132\pi\)
\(954\) 0 0
\(955\) 0 0
\(956\) −8.00000 −0.258738
\(957\) 0 0
\(958\) 21.0000 0.678479
\(959\) 20.0000 0.645834
\(960\) 0 0
\(961\) 33.0000 1.06452
\(962\) 4.00000 0.128965
\(963\) 0 0
\(964\) 18.0000 0.579741
\(965\) 0 0
\(966\) 0 0
\(967\) 59.0000 1.89731 0.948656 − 0.316310i \(-0.102444\pi\)
0.948656 + 0.316310i \(0.102444\pi\)
\(968\) 5.00000 0.160706
\(969\) 0 0
\(970\) 0 0
\(971\) 18.0000 0.577647 0.288824 − 0.957382i \(-0.406736\pi\)
0.288824 + 0.957382i \(0.406736\pi\)
\(972\) 0 0
\(973\) 4.00000 0.128234
\(974\) 36.0000 1.15351
\(975\) 0 0
\(976\) 13.0000 0.416120
\(977\) 12.0000 0.383914 0.191957 − 0.981403i \(-0.438517\pi\)
0.191957 + 0.981403i \(0.438517\pi\)
\(978\) 0 0
\(979\) 44.0000 1.40625
\(980\) 0 0
\(981\) 0 0
\(982\) −15.0000 −0.478669
\(983\) 23.0000 0.733586 0.366793 − 0.930303i \(-0.380456\pi\)
0.366793 + 0.930303i \(0.380456\pi\)
\(984\) 0 0
\(985\) 0 0
\(986\) −3.00000 −0.0955395
\(987\) 0 0
\(988\) −5.00000 −0.159071
\(989\) 0 0
\(990\) 0 0
\(991\) −47.0000 −1.49300 −0.746502 − 0.665383i \(-0.768268\pi\)
−0.746502 + 0.665383i \(0.768268\pi\)
\(992\) −8.00000 −0.254000
\(993\) 0 0
\(994\) 8.00000 0.253745
\(995\) 0 0
\(996\) 0 0
\(997\) −38.0000 −1.20347 −0.601736 − 0.798695i \(-0.705524\pi\)
−0.601736 + 0.798695i \(0.705524\pi\)
\(998\) 4.00000 0.126618
\(999\) 0 0
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 9450.2.a.cd.1.1 yes 1
3.2 odd 2 9450.2.a.x.1.1 ✓ 1
5.4 even 2 9450.2.a.bd.1.1 yes 1
15.14 odd 2 9450.2.a.dw.1.1 yes 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
9450.2.a.x.1.1 ✓ 1 3.2 odd 2
9450.2.a.bd.1.1 yes 1 5.4 even 2
9450.2.a.cd.1.1 yes 1 1.1 even 1 trivial
9450.2.a.dw.1.1 yes 1 15.14 odd 2