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Properties

Label 8325.2.a.i.1.1
Level $8325$
Weight $2$
Character 8325.1
Self dual yes
Analytic conductor $66.475$
Analytic rank $2$
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] = [8325,2,Mod(1,8325)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(8325, 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("8325.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 8325 = 3^{2} \cdot 5^{2} \cdot 37 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 8325.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: \(66.4754596827\)
Analytic rank: \(2\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 2775)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Character \(\chi\) \(=\) 8325.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-2.00000 q^{4} -3.00000 q^{7} -4.00000 q^{11} -5.00000 q^{13} +4.00000 q^{16} -2.00000 q^{17} +1.00000 q^{19} -4.00000 q^{23} +6.00000 q^{28} +2.00000 q^{29} -1.00000 q^{31} +1.00000 q^{37} -10.0000 q^{41} -9.00000 q^{43} +8.00000 q^{44} -6.00000 q^{47} +2.00000 q^{49} +10.0000 q^{52} -12.0000 q^{53} -4.00000 q^{59} -7.00000 q^{61} -8.00000 q^{64} -7.00000 q^{67} +4.00000 q^{68} -2.00000 q^{71} -6.00000 q^{73} -2.00000 q^{76} +12.0000 q^{77} -8.00000 q^{79} +4.00000 q^{83} +14.0000 q^{89} +15.0000 q^{91} +8.00000 q^{92} -17.0000 q^{97} +O(q^{100})\)

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 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(3\) 0 0
\(4\) −2.00000 −1.00000
\(5\) 0 0
\(6\) 0 0
\(7\) −3.00000 −1.13389 −0.566947 − 0.823754i \(-0.691875\pi\)
−0.566947 + 0.823754i \(0.691875\pi\)
\(8\) 0 0
\(9\) 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
\(13\) −5.00000 −1.38675 −0.693375 − 0.720577i \(-0.743877\pi\)
−0.693375 + 0.720577i \(0.743877\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 4.00000 1.00000
\(17\) −2.00000 −0.485071 −0.242536 − 0.970143i \(-0.577979\pi\)
−0.242536 + 0.970143i \(0.577979\pi\)
\(18\) 0 0
\(19\) 1.00000 0.229416 0.114708 − 0.993399i \(-0.463407\pi\)
0.114708 + 0.993399i \(0.463407\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) −4.00000 −0.834058 −0.417029 − 0.908893i \(-0.636929\pi\)
−0.417029 + 0.908893i \(0.636929\pi\)
\(24\) 0 0
\(25\) 0 0
\(26\) 0 0
\(27\) 0 0
\(28\) 6.00000 1.13389
\(29\) 2.00000 0.371391 0.185695 − 0.982607i \(-0.440546\pi\)
0.185695 + 0.982607i \(0.440546\pi\)
\(30\) 0 0
\(31\) −1.00000 −0.179605 −0.0898027 − 0.995960i \(-0.528624\pi\)
−0.0898027 + 0.995960i \(0.528624\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) 1.00000 0.164399
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) −10.0000 −1.56174 −0.780869 − 0.624695i \(-0.785223\pi\)
−0.780869 + 0.624695i \(0.785223\pi\)
\(42\) 0 0
\(43\) −9.00000 −1.37249 −0.686244 − 0.727372i \(-0.740742\pi\)
−0.686244 + 0.727372i \(0.740742\pi\)
\(44\) 8.00000 1.20605
\(45\) 0 0
\(46\) 0 0
\(47\) −6.00000 −0.875190 −0.437595 − 0.899172i \(-0.644170\pi\)
−0.437595 + 0.899172i \(0.644170\pi\)
\(48\) 0 0
\(49\) 2.00000 0.285714
\(50\) 0 0
\(51\) 0 0
\(52\) 10.0000 1.38675
\(53\) −12.0000 −1.64833 −0.824163 − 0.566352i \(-0.808354\pi\)
−0.824163 + 0.566352i \(0.808354\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) −4.00000 −0.520756 −0.260378 − 0.965507i \(-0.583847\pi\)
−0.260378 + 0.965507i \(0.583847\pi\)
\(60\) 0 0
\(61\) −7.00000 −0.896258 −0.448129 − 0.893969i \(-0.647910\pi\)
−0.448129 + 0.893969i \(0.647910\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) −8.00000 −1.00000
\(65\) 0 0
\(66\) 0 0
\(67\) −7.00000 −0.855186 −0.427593 − 0.903971i \(-0.640638\pi\)
−0.427593 + 0.903971i \(0.640638\pi\)
\(68\) 4.00000 0.485071
\(69\) 0 0
\(70\) 0 0
\(71\) −2.00000 −0.237356 −0.118678 − 0.992933i \(-0.537866\pi\)
−0.118678 + 0.992933i \(0.537866\pi\)
\(72\) 0 0
\(73\) −6.00000 −0.702247 −0.351123 − 0.936329i \(-0.614200\pi\)
−0.351123 + 0.936329i \(0.614200\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) −2.00000 −0.229416
\(77\) 12.0000 1.36753
\(78\) 0 0
\(79\) −8.00000 −0.900070 −0.450035 − 0.893011i \(-0.648589\pi\)
−0.450035 + 0.893011i \(0.648589\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) 4.00000 0.439057 0.219529 − 0.975606i \(-0.429548\pi\)
0.219529 + 0.975606i \(0.429548\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 14.0000 1.48400 0.741999 − 0.670402i \(-0.233878\pi\)
0.741999 + 0.670402i \(0.233878\pi\)
\(90\) 0 0
\(91\) 15.0000 1.57243
\(92\) 8.00000 0.834058
\(93\) 0 0
\(94\) 0 0
\(95\) 0 0
\(96\) 0 0
\(97\) −17.0000 −1.72609 −0.863044 − 0.505128i \(-0.831445\pi\)
−0.863044 + 0.505128i \(0.831445\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) −18.0000 −1.79107 −0.895533 − 0.444994i \(-0.853206\pi\)
−0.895533 + 0.444994i \(0.853206\pi\)
\(102\) 0 0
\(103\) −4.00000 −0.394132 −0.197066 − 0.980390i \(-0.563141\pi\)
−0.197066 + 0.980390i \(0.563141\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 10.0000 0.966736 0.483368 − 0.875417i \(-0.339413\pi\)
0.483368 + 0.875417i \(0.339413\pi\)
\(108\) 0 0
\(109\) −1.00000 −0.0957826 −0.0478913 − 0.998853i \(-0.515250\pi\)
−0.0478913 + 0.998853i \(0.515250\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) −12.0000 −1.13389
\(113\) 2.00000 0.188144 0.0940721 − 0.995565i \(-0.470012\pi\)
0.0940721 + 0.995565i \(0.470012\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) −4.00000 −0.371391
\(117\) 0 0
\(118\) 0 0
\(119\) 6.00000 0.550019
\(120\) 0 0
\(121\) 5.00000 0.454545
\(122\) 0 0
\(123\) 0 0
\(124\) 2.00000 0.179605
\(125\) 0 0
\(126\) 0 0
\(127\) 16.0000 1.41977 0.709885 − 0.704317i \(-0.248747\pi\)
0.709885 + 0.704317i \(0.248747\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) 6.00000 0.524222 0.262111 − 0.965038i \(-0.415581\pi\)
0.262111 + 0.965038i \(0.415581\pi\)
\(132\) 0 0
\(133\) −3.00000 −0.260133
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 16.0000 1.36697 0.683486 − 0.729964i \(-0.260463\pi\)
0.683486 + 0.729964i \(0.260463\pi\)
\(138\) 0 0
\(139\) 12.0000 1.01783 0.508913 − 0.860818i \(-0.330047\pi\)
0.508913 + 0.860818i \(0.330047\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 20.0000 1.67248
\(144\) 0 0
\(145\) 0 0
\(146\) 0 0
\(147\) 0 0
\(148\) −2.00000 −0.164399
\(149\) 12.0000 0.983078 0.491539 − 0.870855i \(-0.336434\pi\)
0.491539 + 0.870855i \(0.336434\pi\)
\(150\) 0 0
\(151\) −17.0000 −1.38344 −0.691720 − 0.722166i \(-0.743147\pi\)
−0.691720 + 0.722166i \(0.743147\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 0 0
\(156\) 0 0
\(157\) 7.00000 0.558661 0.279330 − 0.960195i \(-0.409888\pi\)
0.279330 + 0.960195i \(0.409888\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 12.0000 0.945732
\(162\) 0 0
\(163\) −15.0000 −1.17489 −0.587445 − 0.809264i \(-0.699866\pi\)
−0.587445 + 0.809264i \(0.699866\pi\)
\(164\) 20.0000 1.56174
\(165\) 0 0
\(166\) 0 0
\(167\) 10.0000 0.773823 0.386912 − 0.922117i \(-0.373542\pi\)
0.386912 + 0.922117i \(0.373542\pi\)
\(168\) 0 0
\(169\) 12.0000 0.923077
\(170\) 0 0
\(171\) 0 0
\(172\) 18.0000 1.37249
\(173\) 8.00000 0.608229 0.304114 − 0.952636i \(-0.401639\pi\)
0.304114 + 0.952636i \(0.401639\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) −16.0000 −1.20605
\(177\) 0 0
\(178\) 0 0
\(179\) −12.0000 −0.896922 −0.448461 − 0.893802i \(-0.648028\pi\)
−0.448461 + 0.893802i \(0.648028\pi\)
\(180\) 0 0
\(181\) 5.00000 0.371647 0.185824 − 0.982583i \(-0.440505\pi\)
0.185824 + 0.982583i \(0.440505\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 0 0
\(186\) 0 0
\(187\) 8.00000 0.585018
\(188\) 12.0000 0.875190
\(189\) 0 0
\(190\) 0 0
\(191\) 10.0000 0.723575 0.361787 − 0.932261i \(-0.382167\pi\)
0.361787 + 0.932261i \(0.382167\pi\)
\(192\) 0 0
\(193\) −19.0000 −1.36765 −0.683825 − 0.729646i \(-0.739685\pi\)
−0.683825 + 0.729646i \(0.739685\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) −4.00000 −0.285714
\(197\) 8.00000 0.569976 0.284988 − 0.958531i \(-0.408010\pi\)
0.284988 + 0.958531i \(0.408010\pi\)
\(198\) 0 0
\(199\) 13.0000 0.921546 0.460773 − 0.887518i \(-0.347572\pi\)
0.460773 + 0.887518i \(0.347572\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) −6.00000 −0.421117
\(204\) 0 0
\(205\) 0 0
\(206\) 0 0
\(207\) 0 0
\(208\) −20.0000 −1.38675
\(209\) −4.00000 −0.276686
\(210\) 0 0
\(211\) 11.0000 0.757271 0.378636 − 0.925546i \(-0.376393\pi\)
0.378636 + 0.925546i \(0.376393\pi\)
\(212\) 24.0000 1.64833
\(213\) 0 0
\(214\) 0 0
\(215\) 0 0
\(216\) 0 0
\(217\) 3.00000 0.203653
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) 10.0000 0.672673
\(222\) 0 0
\(223\) −15.0000 −1.00447 −0.502237 − 0.864730i \(-0.667490\pi\)
−0.502237 + 0.864730i \(0.667490\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) −14.0000 −0.929213 −0.464606 − 0.885517i \(-0.653804\pi\)
−0.464606 + 0.885517i \(0.653804\pi\)
\(228\) 0 0
\(229\) −7.00000 −0.462573 −0.231287 − 0.972886i \(-0.574293\pi\)
−0.231287 + 0.972886i \(0.574293\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) −16.0000 −1.04819 −0.524097 − 0.851658i \(-0.675597\pi\)
−0.524097 + 0.851658i \(0.675597\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 8.00000 0.520756
\(237\) 0 0
\(238\) 0 0
\(239\) 22.0000 1.42306 0.711531 − 0.702655i \(-0.248002\pi\)
0.711531 + 0.702655i \(0.248002\pi\)
\(240\) 0 0
\(241\) −17.0000 −1.09507 −0.547533 − 0.836784i \(-0.684433\pi\)
−0.547533 + 0.836784i \(0.684433\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 14.0000 0.896258
\(245\) 0 0
\(246\) 0 0
\(247\) −5.00000 −0.318142
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 24.0000 1.51487 0.757433 − 0.652913i \(-0.226453\pi\)
0.757433 + 0.652913i \(0.226453\pi\)
\(252\) 0 0
\(253\) 16.0000 1.00591
\(254\) 0 0
\(255\) 0 0
\(256\) 16.0000 1.00000
\(257\) −14.0000 −0.873296 −0.436648 − 0.899632i \(-0.643834\pi\)
−0.436648 + 0.899632i \(0.643834\pi\)
\(258\) 0 0
\(259\) −3.00000 −0.186411
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) −14.0000 −0.863277 −0.431638 − 0.902047i \(-0.642064\pi\)
−0.431638 + 0.902047i \(0.642064\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) 0 0
\(268\) 14.0000 0.855186
\(269\) −10.0000 −0.609711 −0.304855 − 0.952399i \(-0.598608\pi\)
−0.304855 + 0.952399i \(0.598608\pi\)
\(270\) 0 0
\(271\) 20.0000 1.21491 0.607457 − 0.794353i \(-0.292190\pi\)
0.607457 + 0.794353i \(0.292190\pi\)
\(272\) −8.00000 −0.485071
\(273\) 0 0
\(274\) 0 0
\(275\) 0 0
\(276\) 0 0
\(277\) −17.0000 −1.02143 −0.510716 − 0.859750i \(-0.670619\pi\)
−0.510716 + 0.859750i \(0.670619\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) 32.0000 1.90896 0.954480 − 0.298275i \(-0.0964112\pi\)
0.954480 + 0.298275i \(0.0964112\pi\)
\(282\) 0 0
\(283\) −15.0000 −0.891657 −0.445829 − 0.895118i \(-0.647091\pi\)
−0.445829 + 0.895118i \(0.647091\pi\)
\(284\) 4.00000 0.237356
\(285\) 0 0
\(286\) 0 0
\(287\) 30.0000 1.77084
\(288\) 0 0
\(289\) −13.0000 −0.764706
\(290\) 0 0
\(291\) 0 0
\(292\) 12.0000 0.702247
\(293\) −18.0000 −1.05157 −0.525786 − 0.850617i \(-0.676229\pi\)
−0.525786 + 0.850617i \(0.676229\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 20.0000 1.15663
\(300\) 0 0
\(301\) 27.0000 1.55625
\(302\) 0 0
\(303\) 0 0
\(304\) 4.00000 0.229416
\(305\) 0 0
\(306\) 0 0
\(307\) 27.0000 1.54097 0.770486 − 0.637457i \(-0.220014\pi\)
0.770486 + 0.637457i \(0.220014\pi\)
\(308\) −24.0000 −1.36753
\(309\) 0 0
\(310\) 0 0
\(311\) −12.0000 −0.680458 −0.340229 − 0.940343i \(-0.610505\pi\)
−0.340229 + 0.940343i \(0.610505\pi\)
\(312\) 0 0
\(313\) 29.0000 1.63918 0.819588 − 0.572953i \(-0.194202\pi\)
0.819588 + 0.572953i \(0.194202\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 16.0000 0.900070
\(317\) −12.0000 −0.673987 −0.336994 − 0.941507i \(-0.609410\pi\)
−0.336994 + 0.941507i \(0.609410\pi\)
\(318\) 0 0
\(319\) −8.00000 −0.447914
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) −2.00000 −0.111283
\(324\) 0 0
\(325\) 0 0
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) 18.0000 0.992372
\(330\) 0 0
\(331\) −24.0000 −1.31916 −0.659580 − 0.751635i \(-0.729266\pi\)
−0.659580 + 0.751635i \(0.729266\pi\)
\(332\) −8.00000 −0.439057
\(333\) 0 0
\(334\) 0 0
\(335\) 0 0
\(336\) 0 0
\(337\) −7.00000 −0.381314 −0.190657 − 0.981657i \(-0.561062\pi\)
−0.190657 + 0.981657i \(0.561062\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) 4.00000 0.216612
\(342\) 0 0
\(343\) 15.0000 0.809924
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 18.0000 0.966291 0.483145 − 0.875540i \(-0.339494\pi\)
0.483145 + 0.875540i \(0.339494\pi\)
\(348\) 0 0
\(349\) 2.00000 0.107058 0.0535288 − 0.998566i \(-0.482953\pi\)
0.0535288 + 0.998566i \(0.482953\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) 22.0000 1.17094 0.585471 − 0.810693i \(-0.300910\pi\)
0.585471 + 0.810693i \(0.300910\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) −28.0000 −1.48400
\(357\) 0 0
\(358\) 0 0
\(359\) −16.0000 −0.844448 −0.422224 − 0.906492i \(-0.638750\pi\)
−0.422224 + 0.906492i \(0.638750\pi\)
\(360\) 0 0
\(361\) −18.0000 −0.947368
\(362\) 0 0
\(363\) 0 0
\(364\) −30.0000 −1.57243
\(365\) 0 0
\(366\) 0 0
\(367\) −13.0000 −0.678594 −0.339297 − 0.940679i \(-0.610189\pi\)
−0.339297 + 0.940679i \(0.610189\pi\)
\(368\) −16.0000 −0.834058
\(369\) 0 0
\(370\) 0 0
\(371\) 36.0000 1.86903
\(372\) 0 0
\(373\) −17.0000 −0.880227 −0.440113 − 0.897942i \(-0.645062\pi\)
−0.440113 + 0.897942i \(0.645062\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) −10.0000 −0.515026
\(378\) 0 0
\(379\) 25.0000 1.28416 0.642082 − 0.766636i \(-0.278071\pi\)
0.642082 + 0.766636i \(0.278071\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) −16.0000 −0.817562 −0.408781 − 0.912633i \(-0.634046\pi\)
−0.408781 + 0.912633i \(0.634046\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) 0 0
\(388\) 34.0000 1.72609
\(389\) 10.0000 0.507020 0.253510 − 0.967333i \(-0.418415\pi\)
0.253510 + 0.967333i \(0.418415\pi\)
\(390\) 0 0
\(391\) 8.00000 0.404577
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) 0 0
\(396\) 0 0
\(397\) −13.0000 −0.652451 −0.326226 − 0.945292i \(-0.605777\pi\)
−0.326226 + 0.945292i \(0.605777\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 2.00000 0.0998752 0.0499376 − 0.998752i \(-0.484098\pi\)
0.0499376 + 0.998752i \(0.484098\pi\)
\(402\) 0 0
\(403\) 5.00000 0.249068
\(404\) 36.0000 1.79107
\(405\) 0 0
\(406\) 0 0
\(407\) −4.00000 −0.198273
\(408\) 0 0
\(409\) −29.0000 −1.43396 −0.716979 − 0.697095i \(-0.754476\pi\)
−0.716979 + 0.697095i \(0.754476\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 8.00000 0.394132
\(413\) 12.0000 0.590481
\(414\) 0 0
\(415\) 0 0
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) −20.0000 −0.977064 −0.488532 − 0.872546i \(-0.662467\pi\)
−0.488532 + 0.872546i \(0.662467\pi\)
\(420\) 0 0
\(421\) −26.0000 −1.26716 −0.633581 − 0.773676i \(-0.718416\pi\)
−0.633581 + 0.773676i \(0.718416\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) 0 0
\(426\) 0 0
\(427\) 21.0000 1.01626
\(428\) −20.0000 −0.966736
\(429\) 0 0
\(430\) 0 0
\(431\) −24.0000 −1.15604 −0.578020 − 0.816023i \(-0.696174\pi\)
−0.578020 + 0.816023i \(0.696174\pi\)
\(432\) 0 0
\(433\) −13.0000 −0.624740 −0.312370 − 0.949960i \(-0.601123\pi\)
−0.312370 + 0.949960i \(0.601123\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 2.00000 0.0957826
\(437\) −4.00000 −0.191346
\(438\) 0 0
\(439\) 27.0000 1.28864 0.644320 − 0.764756i \(-0.277141\pi\)
0.644320 + 0.764756i \(0.277141\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) −6.00000 −0.285069 −0.142534 − 0.989790i \(-0.545525\pi\)
−0.142534 + 0.989790i \(0.545525\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 0 0
\(447\) 0 0
\(448\) 24.0000 1.13389
\(449\) 12.0000 0.566315 0.283158 − 0.959073i \(-0.408618\pi\)
0.283158 + 0.959073i \(0.408618\pi\)
\(450\) 0 0
\(451\) 40.0000 1.88353
\(452\) −4.00000 −0.188144
\(453\) 0 0
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) 6.00000 0.280668 0.140334 − 0.990104i \(-0.455182\pi\)
0.140334 + 0.990104i \(0.455182\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 36.0000 1.67669 0.838344 − 0.545142i \(-0.183524\pi\)
0.838344 + 0.545142i \(0.183524\pi\)
\(462\) 0 0
\(463\) 24.0000 1.11537 0.557687 − 0.830051i \(-0.311689\pi\)
0.557687 + 0.830051i \(0.311689\pi\)
\(464\) 8.00000 0.371391
\(465\) 0 0
\(466\) 0 0
\(467\) 6.00000 0.277647 0.138823 − 0.990317i \(-0.455668\pi\)
0.138823 + 0.990317i \(0.455668\pi\)
\(468\) 0 0
\(469\) 21.0000 0.969690
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) 36.0000 1.65528
\(474\) 0 0
\(475\) 0 0
\(476\) −12.0000 −0.550019
\(477\) 0 0
\(478\) 0 0
\(479\) 18.0000 0.822441 0.411220 − 0.911536i \(-0.365103\pi\)
0.411220 + 0.911536i \(0.365103\pi\)
\(480\) 0 0
\(481\) −5.00000 −0.227980
\(482\) 0 0
\(483\) 0 0
\(484\) −10.0000 −0.454545
\(485\) 0 0
\(486\) 0 0
\(487\) −15.0000 −0.679715 −0.339857 − 0.940477i \(-0.610379\pi\)
−0.339857 + 0.940477i \(0.610379\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) 32.0000 1.44414 0.722070 − 0.691820i \(-0.243191\pi\)
0.722070 + 0.691820i \(0.243191\pi\)
\(492\) 0 0
\(493\) −4.00000 −0.180151
\(494\) 0 0
\(495\) 0 0
\(496\) −4.00000 −0.179605
\(497\) 6.00000 0.269137
\(498\) 0 0
\(499\) 37.0000 1.65635 0.828174 − 0.560471i \(-0.189380\pi\)
0.828174 + 0.560471i \(0.189380\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) −36.0000 −1.60516 −0.802580 − 0.596544i \(-0.796540\pi\)
−0.802580 + 0.596544i \(0.796540\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) 0 0
\(508\) −32.0000 −1.41977
\(509\) −34.0000 −1.50702 −0.753512 − 0.657434i \(-0.771642\pi\)
−0.753512 + 0.657434i \(0.771642\pi\)
\(510\) 0 0
\(511\) 18.0000 0.796273
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) 0 0
\(516\) 0 0
\(517\) 24.0000 1.05552
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 30.0000 1.31432 0.657162 − 0.753749i \(-0.271757\pi\)
0.657162 + 0.753749i \(0.271757\pi\)
\(522\) 0 0
\(523\) −11.0000 −0.480996 −0.240498 − 0.970650i \(-0.577311\pi\)
−0.240498 + 0.970650i \(0.577311\pi\)
\(524\) −12.0000 −0.524222
\(525\) 0 0
\(526\) 0 0
\(527\) 2.00000 0.0871214
\(528\) 0 0
\(529\) −7.00000 −0.304348
\(530\) 0 0
\(531\) 0 0
\(532\) 6.00000 0.260133
\(533\) 50.0000 2.16574
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) −8.00000 −0.344584
\(540\) 0 0
\(541\) 3.00000 0.128980 0.0644900 − 0.997918i \(-0.479458\pi\)
0.0644900 + 0.997918i \(0.479458\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) −28.0000 −1.19719 −0.598597 − 0.801050i \(-0.704275\pi\)
−0.598597 + 0.801050i \(0.704275\pi\)
\(548\) −32.0000 −1.36697
\(549\) 0 0
\(550\) 0 0
\(551\) 2.00000 0.0852029
\(552\) 0 0
\(553\) 24.0000 1.02058
\(554\) 0 0
\(555\) 0 0
\(556\) −24.0000 −1.01783
\(557\) −36.0000 −1.52537 −0.762684 − 0.646771i \(-0.776119\pi\)
−0.762684 + 0.646771i \(0.776119\pi\)
\(558\) 0 0
\(559\) 45.0000 1.90330
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) −36.0000 −1.51722 −0.758610 − 0.651546i \(-0.774121\pi\)
−0.758610 + 0.651546i \(0.774121\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 10.0000 0.419222 0.209611 − 0.977785i \(-0.432780\pi\)
0.209611 + 0.977785i \(0.432780\pi\)
\(570\) 0 0
\(571\) −33.0000 −1.38101 −0.690504 − 0.723329i \(-0.742611\pi\)
−0.690504 + 0.723329i \(0.742611\pi\)
\(572\) −40.0000 −1.67248
\(573\) 0 0
\(574\) 0 0
\(575\) 0 0
\(576\) 0 0
\(577\) −23.0000 −0.957503 −0.478751 − 0.877951i \(-0.658910\pi\)
−0.478751 + 0.877951i \(0.658910\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) −12.0000 −0.497844
\(582\) 0 0
\(583\) 48.0000 1.98796
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(588\) 0 0
\(589\) −1.00000 −0.0412043
\(590\) 0 0
\(591\) 0 0
\(592\) 4.00000 0.164399
\(593\) −4.00000 −0.164260 −0.0821302 − 0.996622i \(-0.526172\pi\)
−0.0821302 + 0.996622i \(0.526172\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) −24.0000 −0.983078
\(597\) 0 0
\(598\) 0 0
\(599\) 6.00000 0.245153 0.122577 − 0.992459i \(-0.460884\pi\)
0.122577 + 0.992459i \(0.460884\pi\)
\(600\) 0 0
\(601\) 11.0000 0.448699 0.224350 − 0.974509i \(-0.427974\pi\)
0.224350 + 0.974509i \(0.427974\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 34.0000 1.38344
\(605\) 0 0
\(606\) 0 0
\(607\) −8.00000 −0.324710 −0.162355 − 0.986732i \(-0.551909\pi\)
−0.162355 + 0.986732i \(0.551909\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 30.0000 1.21367
\(612\) 0 0
\(613\) 10.0000 0.403896 0.201948 − 0.979396i \(-0.435273\pi\)
0.201948 + 0.979396i \(0.435273\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 24.0000 0.966204 0.483102 − 0.875564i \(-0.339510\pi\)
0.483102 + 0.875564i \(0.339510\pi\)
\(618\) 0 0
\(619\) 11.0000 0.442127 0.221064 − 0.975259i \(-0.429047\pi\)
0.221064 + 0.975259i \(0.429047\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) −42.0000 −1.68269
\(624\) 0 0
\(625\) 0 0
\(626\) 0 0
\(627\) 0 0
\(628\) −14.0000 −0.558661
\(629\) −2.00000 −0.0797452
\(630\) 0 0
\(631\) −1.00000 −0.0398094 −0.0199047 − 0.999802i \(-0.506336\pi\)
−0.0199047 + 0.999802i \(0.506336\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) 0 0
\(636\) 0 0
\(637\) −10.0000 −0.396214
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) −38.0000 −1.50091 −0.750455 − 0.660922i \(-0.770166\pi\)
−0.750455 + 0.660922i \(0.770166\pi\)
\(642\) 0 0
\(643\) 20.0000 0.788723 0.394362 − 0.918955i \(-0.370966\pi\)
0.394362 + 0.918955i \(0.370966\pi\)
\(644\) −24.0000 −0.945732
\(645\) 0 0
\(646\) 0 0
\(647\) −28.0000 −1.10079 −0.550397 − 0.834903i \(-0.685524\pi\)
−0.550397 + 0.834903i \(0.685524\pi\)
\(648\) 0 0
\(649\) 16.0000 0.628055
\(650\) 0 0
\(651\) 0 0
\(652\) 30.0000 1.17489
\(653\) 6.00000 0.234798 0.117399 − 0.993085i \(-0.462544\pi\)
0.117399 + 0.993085i \(0.462544\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) −40.0000 −1.56174
\(657\) 0 0
\(658\) 0 0
\(659\) −24.0000 −0.934907 −0.467454 − 0.884018i \(-0.654829\pi\)
−0.467454 + 0.884018i \(0.654829\pi\)
\(660\) 0 0
\(661\) 10.0000 0.388955 0.194477 − 0.980907i \(-0.437699\pi\)
0.194477 + 0.980907i \(0.437699\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) −8.00000 −0.309761
\(668\) −20.0000 −0.773823
\(669\) 0 0
\(670\) 0 0
\(671\) 28.0000 1.08093
\(672\) 0 0
\(673\) −2.00000 −0.0770943 −0.0385472 − 0.999257i \(-0.512273\pi\)
−0.0385472 + 0.999257i \(0.512273\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) −24.0000 −0.923077
\(677\) 30.0000 1.15299 0.576497 − 0.817099i \(-0.304419\pi\)
0.576497 + 0.817099i \(0.304419\pi\)
\(678\) 0 0
\(679\) 51.0000 1.95720
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 14.0000 0.535695 0.267848 − 0.963461i \(-0.413688\pi\)
0.267848 + 0.963461i \(0.413688\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 0 0
\(687\) 0 0
\(688\) −36.0000 −1.37249
\(689\) 60.0000 2.28582
\(690\) 0 0
\(691\) 4.00000 0.152167 0.0760836 − 0.997101i \(-0.475758\pi\)
0.0760836 + 0.997101i \(0.475758\pi\)
\(692\) −16.0000 −0.608229
\(693\) 0 0
\(694\) 0 0
\(695\) 0 0
\(696\) 0 0
\(697\) 20.0000 0.757554
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) 22.0000 0.830929 0.415464 − 0.909610i \(-0.363619\pi\)
0.415464 + 0.909610i \(0.363619\pi\)
\(702\) 0 0
\(703\) 1.00000 0.0377157
\(704\) 32.0000 1.20605
\(705\) 0 0
\(706\) 0 0
\(707\) 54.0000 2.03088
\(708\) 0 0
\(709\) 3.00000 0.112667 0.0563337 − 0.998412i \(-0.482059\pi\)
0.0563337 + 0.998412i \(0.482059\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) 4.00000 0.149801
\(714\) 0 0
\(715\) 0 0
\(716\) 24.0000 0.896922
\(717\) 0 0
\(718\) 0 0
\(719\) 50.0000 1.86469 0.932343 − 0.361576i \(-0.117761\pi\)
0.932343 + 0.361576i \(0.117761\pi\)
\(720\) 0 0
\(721\) 12.0000 0.446903
\(722\) 0 0
\(723\) 0 0
\(724\) −10.0000 −0.371647
\(725\) 0 0
\(726\) 0 0
\(727\) 3.00000 0.111264 0.0556319 − 0.998451i \(-0.482283\pi\)
0.0556319 + 0.998451i \(0.482283\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) 18.0000 0.665754
\(732\) 0 0
\(733\) −34.0000 −1.25582 −0.627909 − 0.778287i \(-0.716089\pi\)
−0.627909 + 0.778287i \(0.716089\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 28.0000 1.03139
\(738\) 0 0
\(739\) −12.0000 −0.441427 −0.220714 − 0.975339i \(-0.570839\pi\)
−0.220714 + 0.975339i \(0.570839\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) −14.0000 −0.513610 −0.256805 − 0.966463i \(-0.582670\pi\)
−0.256805 + 0.966463i \(0.582670\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0 0
\(747\) 0 0
\(748\) −16.0000 −0.585018
\(749\) −30.0000 −1.09618
\(750\) 0 0
\(751\) −40.0000 −1.45962 −0.729810 − 0.683650i \(-0.760392\pi\)
−0.729810 + 0.683650i \(0.760392\pi\)
\(752\) −24.0000 −0.875190
\(753\) 0 0
\(754\) 0 0
\(755\) 0 0
\(756\) 0 0
\(757\) −29.0000 −1.05402 −0.527011 − 0.849858i \(-0.676688\pi\)
−0.527011 + 0.849858i \(0.676688\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 8.00000 0.290000 0.145000 − 0.989432i \(-0.453682\pi\)
0.145000 + 0.989432i \(0.453682\pi\)
\(762\) 0 0
\(763\) 3.00000 0.108607
\(764\) −20.0000 −0.723575
\(765\) 0 0
\(766\) 0 0
\(767\) 20.0000 0.722158
\(768\) 0 0
\(769\) 5.00000 0.180305 0.0901523 − 0.995928i \(-0.471265\pi\)
0.0901523 + 0.995928i \(0.471265\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 38.0000 1.36765
\(773\) 18.0000 0.647415 0.323708 − 0.946157i \(-0.395071\pi\)
0.323708 + 0.946157i \(0.395071\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) −10.0000 −0.358287
\(780\) 0 0
\(781\) 8.00000 0.286263
\(782\) 0 0
\(783\) 0 0
\(784\) 8.00000 0.285714
\(785\) 0 0
\(786\) 0 0
\(787\) 23.0000 0.819861 0.409931 − 0.912117i \(-0.365553\pi\)
0.409931 + 0.912117i \(0.365553\pi\)
\(788\) −16.0000 −0.569976
\(789\) 0 0
\(790\) 0 0
\(791\) −6.00000 −0.213335
\(792\) 0 0
\(793\) 35.0000 1.24289
\(794\) 0 0
\(795\) 0 0
\(796\) −26.0000 −0.921546
\(797\) −38.0000 −1.34603 −0.673015 − 0.739629i \(-0.735001\pi\)
−0.673015 + 0.739629i \(0.735001\pi\)
\(798\) 0 0
\(799\) 12.0000 0.424529
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) 24.0000 0.846942
\(804\) 0 0
\(805\) 0 0
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) 46.0000 1.61727 0.808637 − 0.588308i \(-0.200206\pi\)
0.808637 + 0.588308i \(0.200206\pi\)
\(810\) 0 0
\(811\) −25.0000 −0.877869 −0.438934 − 0.898519i \(-0.644644\pi\)
−0.438934 + 0.898519i \(0.644644\pi\)
\(812\) 12.0000 0.421117
\(813\) 0 0
\(814\) 0 0
\(815\) 0 0
\(816\) 0 0
\(817\) −9.00000 −0.314870
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) 24.0000 0.837606 0.418803 − 0.908077i \(-0.362450\pi\)
0.418803 + 0.908077i \(0.362450\pi\)
\(822\) 0 0
\(823\) −23.0000 −0.801730 −0.400865 − 0.916137i \(-0.631290\pi\)
−0.400865 + 0.916137i \(0.631290\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) 24.0000 0.834562 0.417281 − 0.908778i \(-0.362983\pi\)
0.417281 + 0.908778i \(0.362983\pi\)
\(828\) 0 0
\(829\) 2.00000 0.0694629 0.0347314 − 0.999397i \(-0.488942\pi\)
0.0347314 + 0.999397i \(0.488942\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 40.0000 1.38675
\(833\) −4.00000 −0.138592
\(834\) 0 0
\(835\) 0 0
\(836\) 8.00000 0.276686
\(837\) 0 0
\(838\) 0 0
\(839\) −12.0000 −0.414286 −0.207143 − 0.978311i \(-0.566417\pi\)
−0.207143 + 0.978311i \(0.566417\pi\)
\(840\) 0 0
\(841\) −25.0000 −0.862069
\(842\) 0 0
\(843\) 0 0
\(844\) −22.0000 −0.757271
\(845\) 0 0
\(846\) 0 0
\(847\) −15.0000 −0.515406
\(848\) −48.0000 −1.64833
\(849\) 0 0
\(850\) 0 0
\(851\) −4.00000 −0.137118
\(852\) 0 0
\(853\) 21.0000 0.719026 0.359513 − 0.933140i \(-0.382943\pi\)
0.359513 + 0.933140i \(0.382943\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) 24.0000 0.819824 0.409912 − 0.912125i \(-0.365559\pi\)
0.409912 + 0.912125i \(0.365559\pi\)
\(858\) 0 0
\(859\) −12.0000 −0.409435 −0.204717 − 0.978821i \(-0.565628\pi\)
−0.204717 + 0.978821i \(0.565628\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) −18.0000 −0.612727 −0.306364 − 0.951915i \(-0.599112\pi\)
−0.306364 + 0.951915i \(0.599112\pi\)
\(864\) 0 0
\(865\) 0 0
\(866\) 0 0
\(867\) 0 0
\(868\) −6.00000 −0.203653
\(869\) 32.0000 1.08553
\(870\) 0 0
\(871\) 35.0000 1.18593
\(872\) 0 0
\(873\) 0 0
\(874\) 0 0
\(875\) 0 0
\(876\) 0 0
\(877\) −57.0000 −1.92475 −0.962377 − 0.271719i \(-0.912408\pi\)
−0.962377 + 0.271719i \(0.912408\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) −42.0000 −1.41502 −0.707508 − 0.706705i \(-0.750181\pi\)
−0.707508 + 0.706705i \(0.750181\pi\)
\(882\) 0 0
\(883\) −13.0000 −0.437485 −0.218742 − 0.975783i \(-0.570195\pi\)
−0.218742 + 0.975783i \(0.570195\pi\)
\(884\) −20.0000 −0.672673
\(885\) 0 0
\(886\) 0 0
\(887\) −36.0000 −1.20876 −0.604381 − 0.796696i \(-0.706579\pi\)
−0.604381 + 0.796696i \(0.706579\pi\)
\(888\) 0 0
\(889\) −48.0000 −1.60987
\(890\) 0 0
\(891\) 0 0
\(892\) 30.0000 1.00447
\(893\) −6.00000 −0.200782
\(894\) 0 0
\(895\) 0 0
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) −2.00000 −0.0667037
\(900\) 0 0
\(901\) 24.0000 0.799556
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) 0 0
\(906\) 0 0
\(907\) 12.0000 0.398453 0.199227 − 0.979953i \(-0.436157\pi\)
0.199227 + 0.979953i \(0.436157\pi\)
\(908\) 28.0000 0.929213
\(909\) 0 0
\(910\) 0 0
\(911\) 46.0000 1.52405 0.762024 − 0.647549i \(-0.224206\pi\)
0.762024 + 0.647549i \(0.224206\pi\)
\(912\) 0 0
\(913\) −16.0000 −0.529523
\(914\) 0 0
\(915\) 0 0
\(916\) 14.0000 0.462573
\(917\) −18.0000 −0.594412
\(918\) 0 0
\(919\) −3.00000 −0.0989609 −0.0494804 − 0.998775i \(-0.515757\pi\)
−0.0494804 + 0.998775i \(0.515757\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 0 0
\(923\) 10.0000 0.329154
\(924\) 0 0
\(925\) 0 0
\(926\) 0 0
\(927\) 0 0
\(928\) 0 0
\(929\) 26.0000 0.853032 0.426516 − 0.904480i \(-0.359741\pi\)
0.426516 + 0.904480i \(0.359741\pi\)
\(930\) 0 0
\(931\) 2.00000 0.0655474
\(932\) 32.0000 1.04819
\(933\) 0 0
\(934\) 0 0
\(935\) 0 0
\(936\) 0 0
\(937\) 23.0000 0.751377 0.375689 − 0.926746i \(-0.377406\pi\)
0.375689 + 0.926746i \(0.377406\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0 0
\(941\) 6.00000 0.195594 0.0977972 − 0.995206i \(-0.468820\pi\)
0.0977972 + 0.995206i \(0.468820\pi\)
\(942\) 0 0
\(943\) 40.0000 1.30258
\(944\) −16.0000 −0.520756
\(945\) 0 0
\(946\) 0 0
\(947\) −46.0000 −1.49480 −0.747400 − 0.664375i \(-0.768698\pi\)
−0.747400 + 0.664375i \(0.768698\pi\)
\(948\) 0 0
\(949\) 30.0000 0.973841
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) −2.00000 −0.0647864 −0.0323932 − 0.999475i \(-0.510313\pi\)
−0.0323932 + 0.999475i \(0.510313\pi\)
\(954\) 0 0
\(955\) 0 0
\(956\) −44.0000 −1.42306
\(957\) 0 0
\(958\) 0 0
\(959\) −48.0000 −1.55000
\(960\) 0 0
\(961\) −30.0000 −0.967742
\(962\) 0 0
\(963\) 0 0
\(964\) 34.0000 1.09507
\(965\) 0 0
\(966\) 0 0
\(967\) −40.0000 −1.28631 −0.643157 − 0.765735i \(-0.722376\pi\)
−0.643157 + 0.765735i \(0.722376\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) 40.0000 1.28366 0.641831 − 0.766846i \(-0.278175\pi\)
0.641831 + 0.766846i \(0.278175\pi\)
\(972\) 0 0
\(973\) −36.0000 −1.15411
\(974\) 0 0
\(975\) 0 0
\(976\) −28.0000 −0.896258
\(977\) −32.0000 −1.02377 −0.511885 − 0.859054i \(-0.671053\pi\)
−0.511885 + 0.859054i \(0.671053\pi\)
\(978\) 0 0
\(979\) −56.0000 −1.78977
\(980\) 0 0
\(981\) 0 0
\(982\) 0 0
\(983\) −48.0000 −1.53096 −0.765481 − 0.643458i \(-0.777499\pi\)
−0.765481 + 0.643458i \(0.777499\pi\)
\(984\) 0 0
\(985\) 0 0
\(986\) 0 0
\(987\) 0 0
\(988\) 10.0000 0.318142
\(989\) 36.0000 1.14473
\(990\) 0 0
\(991\) 43.0000 1.36594 0.682970 − 0.730446i \(-0.260688\pi\)
0.682970 + 0.730446i \(0.260688\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0 0
\(995\) 0 0
\(996\) 0 0
\(997\) −6.00000 −0.190022 −0.0950110 − 0.995476i \(-0.530289\pi\)
−0.0950110 + 0.995476i \(0.530289\pi\)
\(998\) 0 0
\(999\) 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 8325.2.a.i.1.1 1
3.2 odd 2 2775.2.a.c.1.1 ✓ 1
5.4 even 2 8325.2.a.v.1.1 1
15.14 odd 2 2775.2.a.h.1.1 yes 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
2775.2.a.c.1.1 ✓ 1 3.2 odd 2
2775.2.a.h.1.1 yes 1 15.14 odd 2
8325.2.a.i.1.1 1 1.1 even 1 trivial
8325.2.a.v.1.1 1 5.4 even 2