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Properties

Label 5850.2.a.m.1.1
Level $5850$
Weight $2$
Character 5850.1
Self dual yes
Analytic conductor $46.712$
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] = [5850,2,Mod(1,5850)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(5850, 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("5850.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 5850 = 2 \cdot 3^{2} \cdot 5^{2} \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 5850.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: \(46.7124851824\)
Analytic rank: \(1\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 390)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Character \(\chi\) \(=\) 5850.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-1.00000 q^{2} +1.00000 q^{4} -1.00000 q^{8} +O(q^{10})\) \(q-1.00000 q^{2} +1.00000 q^{4} -1.00000 q^{8} +1.00000 q^{13} +1.00000 q^{16} -6.00000 q^{17} -4.00000 q^{23} -1.00000 q^{26} +10.0000 q^{29} -1.00000 q^{32} +6.00000 q^{34} +6.00000 q^{37} -2.00000 q^{41} +4.00000 q^{43} +4.00000 q^{46} -7.00000 q^{49} +1.00000 q^{52} -6.00000 q^{53} -10.0000 q^{58} +6.00000 q^{61} +1.00000 q^{64} -4.00000 q^{67} -6.00000 q^{68} -16.0000 q^{71} +2.00000 q^{73} -6.00000 q^{74} +2.00000 q^{82} +4.00000 q^{83} -4.00000 q^{86} +6.00000 q^{89} -4.00000 q^{92} -14.0000 q^{97} +7.00000 q^{98} +O(q^{100})\)

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
\(7\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(8\) −1.00000 −0.353553
\(9\) 0 0
\(10\) 0 0
\(11\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(12\) 0 0
\(13\) 1.00000 0.277350
\(14\) 0 0
\(15\) 0 0
\(16\) 1.00000 0.250000
\(17\) −6.00000 −1.45521 −0.727607 − 0.685994i \(-0.759367\pi\)
−0.727607 + 0.685994i \(0.759367\pi\)
\(18\) 0 0
\(19\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(20\) 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
\(26\) −1.00000 −0.196116
\(27\) 0 0
\(28\) 0 0
\(29\) 10.0000 1.85695 0.928477 − 0.371391i \(-0.121119\pi\)
0.928477 + 0.371391i \(0.121119\pi\)
\(30\) 0 0
\(31\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(32\) −1.00000 −0.176777
\(33\) 0 0
\(34\) 6.00000 1.02899
\(35\) 0 0
\(36\) 0 0
\(37\) 6.00000 0.986394 0.493197 − 0.869918i \(-0.335828\pi\)
0.493197 + 0.869918i \(0.335828\pi\)
\(38\) 0 0
\(39\) 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
\(43\) 4.00000 0.609994 0.304997 − 0.952353i \(-0.401344\pi\)
0.304997 + 0.952353i \(0.401344\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 4.00000 0.589768
\(47\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(48\) 0 0
\(49\) −7.00000 −1.00000
\(50\) 0 0
\(51\) 0 0
\(52\) 1.00000 0.138675
\(53\) −6.00000 −0.824163 −0.412082 − 0.911147i \(-0.635198\pi\)
−0.412082 + 0.911147i \(0.635198\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 0 0
\(57\) 0 0
\(58\) −10.0000 −1.31306
\(59\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(60\) 0 0
\(61\) 6.00000 0.768221 0.384111 − 0.923287i \(-0.374508\pi\)
0.384111 + 0.923287i \(0.374508\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 1.00000 0.125000
\(65\) 0 0
\(66\) 0 0
\(67\) −4.00000 −0.488678 −0.244339 − 0.969690i \(-0.578571\pi\)
−0.244339 + 0.969690i \(0.578571\pi\)
\(68\) −6.00000 −0.727607
\(69\) 0 0
\(70\) 0 0
\(71\) −16.0000 −1.89885 −0.949425 − 0.313993i \(-0.898333\pi\)
−0.949425 + 0.313993i \(0.898333\pi\)
\(72\) 0 0
\(73\) 2.00000 0.234082 0.117041 − 0.993127i \(-0.462659\pi\)
0.117041 + 0.993127i \(0.462659\pi\)
\(74\) −6.00000 −0.697486
\(75\) 0 0
\(76\) 0 0
\(77\) 0 0
\(78\) 0 0
\(79\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 2.00000 0.220863
\(83\) 4.00000 0.439057 0.219529 − 0.975606i \(-0.429548\pi\)
0.219529 + 0.975606i \(0.429548\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) −4.00000 −0.431331
\(87\) 0 0
\(88\) 0 0
\(89\) 6.00000 0.635999 0.317999 − 0.948091i \(-0.396989\pi\)
0.317999 + 0.948091i \(0.396989\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) −4.00000 −0.417029
\(93\) 0 0
\(94\) 0 0
\(95\) 0 0
\(96\) 0 0
\(97\) −14.0000 −1.42148 −0.710742 − 0.703452i \(-0.751641\pi\)
−0.710742 + 0.703452i \(0.751641\pi\)
\(98\) 7.00000 0.707107
\(99\) 0 0
\(100\) 0 0
\(101\) −6.00000 −0.597022 −0.298511 − 0.954406i \(-0.596490\pi\)
−0.298511 + 0.954406i \(0.596490\pi\)
\(102\) 0 0
\(103\) −12.0000 −1.18240 −0.591198 − 0.806527i \(-0.701345\pi\)
−0.591198 + 0.806527i \(0.701345\pi\)
\(104\) −1.00000 −0.0980581
\(105\) 0 0
\(106\) 6.00000 0.582772
\(107\) −4.00000 −0.386695 −0.193347 − 0.981130i \(-0.561934\pi\)
−0.193347 + 0.981130i \(0.561934\pi\)
\(108\) 0 0
\(109\) −14.0000 −1.34096 −0.670478 − 0.741929i \(-0.733911\pi\)
−0.670478 + 0.741929i \(0.733911\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) 10.0000 0.940721 0.470360 − 0.882474i \(-0.344124\pi\)
0.470360 + 0.882474i \(0.344124\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 10.0000 0.928477
\(117\) 0 0
\(118\) 0 0
\(119\) 0 0
\(120\) 0 0
\(121\) −11.0000 −1.00000
\(122\) −6.00000 −0.543214
\(123\) 0 0
\(124\) 0 0
\(125\) 0 0
\(126\) 0 0
\(127\) 12.0000 1.06483 0.532414 − 0.846484i \(-0.321285\pi\)
0.532414 + 0.846484i \(0.321285\pi\)
\(128\) −1.00000 −0.0883883
\(129\) 0 0
\(130\) 0 0
\(131\) −12.0000 −1.04844 −0.524222 − 0.851581i \(-0.675644\pi\)
−0.524222 + 0.851581i \(0.675644\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 4.00000 0.345547
\(135\) 0 0
\(136\) 6.00000 0.514496
\(137\) 6.00000 0.512615 0.256307 − 0.966595i \(-0.417494\pi\)
0.256307 + 0.966595i \(0.417494\pi\)
\(138\) 0 0
\(139\) 4.00000 0.339276 0.169638 − 0.985506i \(-0.445740\pi\)
0.169638 + 0.985506i \(0.445740\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 16.0000 1.34269
\(143\) 0 0
\(144\) 0 0
\(145\) 0 0
\(146\) −2.00000 −0.165521
\(147\) 0 0
\(148\) 6.00000 0.493197
\(149\) 14.0000 1.14692 0.573462 − 0.819232i \(-0.305600\pi\)
0.573462 + 0.819232i \(0.305600\pi\)
\(150\) 0 0
\(151\) −16.0000 −1.30206 −0.651031 − 0.759051i \(-0.725663\pi\)
−0.651031 + 0.759051i \(0.725663\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 0 0
\(156\) 0 0
\(157\) 14.0000 1.11732 0.558661 − 0.829396i \(-0.311315\pi\)
0.558661 + 0.829396i \(0.311315\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 0 0
\(162\) 0 0
\(163\) 4.00000 0.313304 0.156652 − 0.987654i \(-0.449930\pi\)
0.156652 + 0.987654i \(0.449930\pi\)
\(164\) −2.00000 −0.156174
\(165\) 0 0
\(166\) −4.00000 −0.310460
\(167\) 24.0000 1.85718 0.928588 − 0.371113i \(-0.121024\pi\)
0.928588 + 0.371113i \(0.121024\pi\)
\(168\) 0 0
\(169\) 1.00000 0.0769231
\(170\) 0 0
\(171\) 0 0
\(172\) 4.00000 0.304997
\(173\) −14.0000 −1.06440 −0.532200 − 0.846619i \(-0.678635\pi\)
−0.532200 + 0.846619i \(0.678635\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) 0 0
\(178\) −6.00000 −0.449719
\(179\) 20.0000 1.49487 0.747435 − 0.664335i \(-0.231285\pi\)
0.747435 + 0.664335i \(0.231285\pi\)
\(180\) 0 0
\(181\) −10.0000 −0.743294 −0.371647 − 0.928374i \(-0.621207\pi\)
−0.371647 + 0.928374i \(0.621207\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 4.00000 0.294884
\(185\) 0 0
\(186\) 0 0
\(187\) 0 0
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) −24.0000 −1.73658 −0.868290 − 0.496058i \(-0.834780\pi\)
−0.868290 + 0.496058i \(0.834780\pi\)
\(192\) 0 0
\(193\) −14.0000 −1.00774 −0.503871 − 0.863779i \(-0.668091\pi\)
−0.503871 + 0.863779i \(0.668091\pi\)
\(194\) 14.0000 1.00514
\(195\) 0 0
\(196\) −7.00000 −0.500000
\(197\) −22.0000 −1.56744 −0.783718 − 0.621117i \(-0.786679\pi\)
−0.783718 + 0.621117i \(0.786679\pi\)
\(198\) 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
\(202\) 6.00000 0.422159
\(203\) 0 0
\(204\) 0 0
\(205\) 0 0
\(206\) 12.0000 0.836080
\(207\) 0 0
\(208\) 1.00000 0.0693375
\(209\) 0 0
\(210\) 0 0
\(211\) −12.0000 −0.826114 −0.413057 − 0.910705i \(-0.635539\pi\)
−0.413057 + 0.910705i \(0.635539\pi\)
\(212\) −6.00000 −0.412082
\(213\) 0 0
\(214\) 4.00000 0.273434
\(215\) 0 0
\(216\) 0 0
\(217\) 0 0
\(218\) 14.0000 0.948200
\(219\) 0 0
\(220\) 0 0
\(221\) −6.00000 −0.403604
\(222\) 0 0
\(223\) −16.0000 −1.07144 −0.535720 − 0.844396i \(-0.679960\pi\)
−0.535720 + 0.844396i \(0.679960\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) −10.0000 −0.665190
\(227\) 20.0000 1.32745 0.663723 − 0.747978i \(-0.268975\pi\)
0.663723 + 0.747978i \(0.268975\pi\)
\(228\) 0 0
\(229\) 2.00000 0.132164 0.0660819 − 0.997814i \(-0.478950\pi\)
0.0660819 + 0.997814i \(0.478950\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) −10.0000 −0.656532
\(233\) 18.0000 1.17922 0.589610 − 0.807688i \(-0.299282\pi\)
0.589610 + 0.807688i \(0.299282\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) −16.0000 −1.03495 −0.517477 − 0.855697i \(-0.673129\pi\)
−0.517477 + 0.855697i \(0.673129\pi\)
\(240\) 0 0
\(241\) −14.0000 −0.901819 −0.450910 − 0.892570i \(-0.648900\pi\)
−0.450910 + 0.892570i \(0.648900\pi\)
\(242\) 11.0000 0.707107
\(243\) 0 0
\(244\) 6.00000 0.384111
\(245\) 0 0
\(246\) 0 0
\(247\) 0 0
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 4.00000 0.252478 0.126239 − 0.992000i \(-0.459709\pi\)
0.126239 + 0.992000i \(0.459709\pi\)
\(252\) 0 0
\(253\) 0 0
\(254\) −12.0000 −0.752947
\(255\) 0 0
\(256\) 1.00000 0.0625000
\(257\) −6.00000 −0.374270 −0.187135 − 0.982334i \(-0.559920\pi\)
−0.187135 + 0.982334i \(0.559920\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 0 0
\(261\) 0 0
\(262\) 12.0000 0.741362
\(263\) −28.0000 −1.72655 −0.863277 − 0.504730i \(-0.831592\pi\)
−0.863277 + 0.504730i \(0.831592\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) 0 0
\(268\) −4.00000 −0.244339
\(269\) −14.0000 −0.853595 −0.426798 − 0.904347i \(-0.640358\pi\)
−0.426798 + 0.904347i \(0.640358\pi\)
\(270\) 0 0
\(271\) −24.0000 −1.45790 −0.728948 − 0.684569i \(-0.759990\pi\)
−0.728948 + 0.684569i \(0.759990\pi\)
\(272\) −6.00000 −0.363803
\(273\) 0 0
\(274\) −6.00000 −0.362473
\(275\) 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
\(281\) 6.00000 0.357930 0.178965 − 0.983855i \(-0.442725\pi\)
0.178965 + 0.983855i \(0.442725\pi\)
\(282\) 0 0
\(283\) 12.0000 0.713326 0.356663 − 0.934233i \(-0.383914\pi\)
0.356663 + 0.934233i \(0.383914\pi\)
\(284\) −16.0000 −0.949425
\(285\) 0 0
\(286\) 0 0
\(287\) 0 0
\(288\) 0 0
\(289\) 19.0000 1.11765
\(290\) 0 0
\(291\) 0 0
\(292\) 2.00000 0.117041
\(293\) 26.0000 1.51894 0.759468 − 0.650545i \(-0.225459\pi\)
0.759468 + 0.650545i \(0.225459\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) −6.00000 −0.348743
\(297\) 0 0
\(298\) −14.0000 −0.810998
\(299\) −4.00000 −0.231326
\(300\) 0 0
\(301\) 0 0
\(302\) 16.0000 0.920697
\(303\) 0 0
\(304\) 0 0
\(305\) 0 0
\(306\) 0 0
\(307\) 4.00000 0.228292 0.114146 − 0.993464i \(-0.463587\pi\)
0.114146 + 0.993464i \(0.463587\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 16.0000 0.907277 0.453638 − 0.891186i \(-0.350126\pi\)
0.453638 + 0.891186i \(0.350126\pi\)
\(312\) 0 0
\(313\) −26.0000 −1.46961 −0.734803 − 0.678280i \(-0.762726\pi\)
−0.734803 + 0.678280i \(0.762726\pi\)
\(314\) −14.0000 −0.790066
\(315\) 0 0
\(316\) 0 0
\(317\) 2.00000 0.112331 0.0561656 − 0.998421i \(-0.482113\pi\)
0.0561656 + 0.998421i \(0.482113\pi\)
\(318\) 0 0
\(319\) 0 0
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) 0 0
\(324\) 0 0
\(325\) 0 0
\(326\) −4.00000 −0.221540
\(327\) 0 0
\(328\) 2.00000 0.110432
\(329\) 0 0
\(330\) 0 0
\(331\) 8.00000 0.439720 0.219860 − 0.975531i \(-0.429440\pi\)
0.219860 + 0.975531i \(0.429440\pi\)
\(332\) 4.00000 0.219529
\(333\) 0 0
\(334\) −24.0000 −1.31322
\(335\) 0 0
\(336\) 0 0
\(337\) −18.0000 −0.980522 −0.490261 − 0.871576i \(-0.663099\pi\)
−0.490261 + 0.871576i \(0.663099\pi\)
\(338\) −1.00000 −0.0543928
\(339\) 0 0
\(340\) 0 0
\(341\) 0 0
\(342\) 0 0
\(343\) 0 0
\(344\) −4.00000 −0.215666
\(345\) 0 0
\(346\) 14.0000 0.752645
\(347\) 12.0000 0.644194 0.322097 − 0.946707i \(-0.395612\pi\)
0.322097 + 0.946707i \(0.395612\pi\)
\(348\) 0 0
\(349\) 34.0000 1.81998 0.909989 − 0.414632i \(-0.136090\pi\)
0.909989 + 0.414632i \(0.136090\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) −26.0000 −1.38384 −0.691920 − 0.721974i \(-0.743235\pi\)
−0.691920 + 0.721974i \(0.743235\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 6.00000 0.317999
\(357\) 0 0
\(358\) −20.0000 −1.05703
\(359\) −24.0000 −1.26667 −0.633336 − 0.773877i \(-0.718315\pi\)
−0.633336 + 0.773877i \(0.718315\pi\)
\(360\) 0 0
\(361\) −19.0000 −1.00000
\(362\) 10.0000 0.525588
\(363\) 0 0
\(364\) 0 0
\(365\) 0 0
\(366\) 0 0
\(367\) −20.0000 −1.04399 −0.521996 − 0.852948i \(-0.674812\pi\)
−0.521996 + 0.852948i \(0.674812\pi\)
\(368\) −4.00000 −0.208514
\(369\) 0 0
\(370\) 0 0
\(371\) 0 0
\(372\) 0 0
\(373\) −10.0000 −0.517780 −0.258890 − 0.965907i \(-0.583357\pi\)
−0.258890 + 0.965907i \(0.583357\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 10.0000 0.515026
\(378\) 0 0
\(379\) 24.0000 1.23280 0.616399 − 0.787434i \(-0.288591\pi\)
0.616399 + 0.787434i \(0.288591\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 24.0000 1.22795
\(383\) −8.00000 −0.408781 −0.204390 − 0.978889i \(-0.565521\pi\)
−0.204390 + 0.978889i \(0.565521\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 14.0000 0.712581
\(387\) 0 0
\(388\) −14.0000 −0.710742
\(389\) 18.0000 0.912636 0.456318 − 0.889817i \(-0.349168\pi\)
0.456318 + 0.889817i \(0.349168\pi\)
\(390\) 0 0
\(391\) 24.0000 1.21373
\(392\) 7.00000 0.353553
\(393\) 0 0
\(394\) 22.0000 1.10834
\(395\) 0 0
\(396\) 0 0
\(397\) 14.0000 0.702640 0.351320 − 0.936255i \(-0.385733\pi\)
0.351320 + 0.936255i \(0.385733\pi\)
\(398\) 16.0000 0.802008
\(399\) 0 0
\(400\) 0 0
\(401\) −18.0000 −0.898877 −0.449439 − 0.893311i \(-0.648376\pi\)
−0.449439 + 0.893311i \(0.648376\pi\)
\(402\) 0 0
\(403\) 0 0
\(404\) −6.00000 −0.298511
\(405\) 0 0
\(406\) 0 0
\(407\) 0 0
\(408\) 0 0
\(409\) 2.00000 0.0988936 0.0494468 − 0.998777i \(-0.484254\pi\)
0.0494468 + 0.998777i \(0.484254\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) −12.0000 −0.591198
\(413\) 0 0
\(414\) 0 0
\(415\) 0 0
\(416\) −1.00000 −0.0490290
\(417\) 0 0
\(418\) 0 0
\(419\) −12.0000 −0.586238 −0.293119 − 0.956076i \(-0.594693\pi\)
−0.293119 + 0.956076i \(0.594693\pi\)
\(420\) 0 0
\(421\) −22.0000 −1.07221 −0.536107 − 0.844150i \(-0.680106\pi\)
−0.536107 + 0.844150i \(0.680106\pi\)
\(422\) 12.0000 0.584151
\(423\) 0 0
\(424\) 6.00000 0.291386
\(425\) 0 0
\(426\) 0 0
\(427\) 0 0
\(428\) −4.00000 −0.193347
\(429\) 0 0
\(430\) 0 0
\(431\) 24.0000 1.15604 0.578020 − 0.816023i \(-0.303826\pi\)
0.578020 + 0.816023i \(0.303826\pi\)
\(432\) 0 0
\(433\) −2.00000 −0.0961139 −0.0480569 − 0.998845i \(-0.515303\pi\)
−0.0480569 + 0.998845i \(0.515303\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) −14.0000 −0.670478
\(437\) 0 0
\(438\) 0 0
\(439\) −24.0000 −1.14546 −0.572729 − 0.819745i \(-0.694115\pi\)
−0.572729 + 0.819745i \(0.694115\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 6.00000 0.285391
\(443\) −4.00000 −0.190046 −0.0950229 − 0.995475i \(-0.530292\pi\)
−0.0950229 + 0.995475i \(0.530292\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 16.0000 0.757622
\(447\) 0 0
\(448\) 0 0
\(449\) 14.0000 0.660701 0.330350 − 0.943858i \(-0.392833\pi\)
0.330350 + 0.943858i \(0.392833\pi\)
\(450\) 0 0
\(451\) 0 0
\(452\) 10.0000 0.470360
\(453\) 0 0
\(454\) −20.0000 −0.938647
\(455\) 0 0
\(456\) 0 0
\(457\) −6.00000 −0.280668 −0.140334 − 0.990104i \(-0.544818\pi\)
−0.140334 + 0.990104i \(0.544818\pi\)
\(458\) −2.00000 −0.0934539
\(459\) 0 0
\(460\) 0 0
\(461\) 14.0000 0.652045 0.326023 − 0.945362i \(-0.394291\pi\)
0.326023 + 0.945362i \(0.394291\pi\)
\(462\) 0 0
\(463\) 24.0000 1.11537 0.557687 − 0.830051i \(-0.311689\pi\)
0.557687 + 0.830051i \(0.311689\pi\)
\(464\) 10.0000 0.464238
\(465\) 0 0
\(466\) −18.0000 −0.833834
\(467\) −28.0000 −1.29569 −0.647843 − 0.761774i \(-0.724329\pi\)
−0.647843 + 0.761774i \(0.724329\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) 0 0
\(474\) 0 0
\(475\) 0 0
\(476\) 0 0
\(477\) 0 0
\(478\) 16.0000 0.731823
\(479\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(480\) 0 0
\(481\) 6.00000 0.273576
\(482\) 14.0000 0.637683
\(483\) 0 0
\(484\) −11.0000 −0.500000
\(485\) 0 0
\(486\) 0 0
\(487\) −8.00000 −0.362515 −0.181257 − 0.983436i \(-0.558017\pi\)
−0.181257 + 0.983436i \(0.558017\pi\)
\(488\) −6.00000 −0.271607
\(489\) 0 0
\(490\) 0 0
\(491\) −20.0000 −0.902587 −0.451294 − 0.892375i \(-0.649037\pi\)
−0.451294 + 0.892375i \(0.649037\pi\)
\(492\) 0 0
\(493\) −60.0000 −2.70226
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 0 0
\(498\) 0 0
\(499\) −40.0000 −1.79065 −0.895323 − 0.445418i \(-0.853055\pi\)
−0.895323 + 0.445418i \(0.853055\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) −4.00000 −0.178529
\(503\) −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
\(508\) 12.0000 0.532414
\(509\) 38.0000 1.68432 0.842160 − 0.539227i \(-0.181284\pi\)
0.842160 + 0.539227i \(0.181284\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) −1.00000 −0.0441942
\(513\) 0 0
\(514\) 6.00000 0.264649
\(515\) 0 0
\(516\) 0 0
\(517\) 0 0
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) −10.0000 −0.438108 −0.219054 − 0.975713i \(-0.570297\pi\)
−0.219054 + 0.975713i \(0.570297\pi\)
\(522\) 0 0
\(523\) 20.0000 0.874539 0.437269 − 0.899331i \(-0.355946\pi\)
0.437269 + 0.899331i \(0.355946\pi\)
\(524\) −12.0000 −0.524222
\(525\) 0 0
\(526\) 28.0000 1.22086
\(527\) 0 0
\(528\) 0 0
\(529\) −7.00000 −0.304348
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) −2.00000 −0.0866296
\(534\) 0 0
\(535\) 0 0
\(536\) 4.00000 0.172774
\(537\) 0 0
\(538\) 14.0000 0.603583
\(539\) 0 0
\(540\) 0 0
\(541\) −22.0000 −0.945854 −0.472927 − 0.881102i \(-0.656803\pi\)
−0.472927 + 0.881102i \(0.656803\pi\)
\(542\) 24.0000 1.03089
\(543\) 0 0
\(544\) 6.00000 0.257248
\(545\) 0 0
\(546\) 0 0
\(547\) −28.0000 −1.19719 −0.598597 − 0.801050i \(-0.704275\pi\)
−0.598597 + 0.801050i \(0.704275\pi\)
\(548\) 6.00000 0.256307
\(549\) 0 0
\(550\) 0 0
\(551\) 0 0
\(552\) 0 0
\(553\) 0 0
\(554\) 2.00000 0.0849719
\(555\) 0 0
\(556\) 4.00000 0.169638
\(557\) −30.0000 −1.27114 −0.635570 − 0.772043i \(-0.719235\pi\)
−0.635570 + 0.772043i \(0.719235\pi\)
\(558\) 0 0
\(559\) 4.00000 0.169182
\(560\) 0 0
\(561\) 0 0
\(562\) −6.00000 −0.253095
\(563\) −28.0000 −1.18006 −0.590030 − 0.807382i \(-0.700884\pi\)
−0.590030 + 0.807382i \(0.700884\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) −12.0000 −0.504398
\(567\) 0 0
\(568\) 16.0000 0.671345
\(569\) 6.00000 0.251533 0.125767 − 0.992060i \(-0.459861\pi\)
0.125767 + 0.992060i \(0.459861\pi\)
\(570\) 0 0
\(571\) −4.00000 −0.167395 −0.0836974 − 0.996491i \(-0.526673\pi\)
−0.0836974 + 0.996491i \(0.526673\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 0 0
\(576\) 0 0
\(577\) −22.0000 −0.915872 −0.457936 − 0.888985i \(-0.651411\pi\)
−0.457936 + 0.888985i \(0.651411\pi\)
\(578\) −19.0000 −0.790296
\(579\) 0 0
\(580\) 0 0
\(581\) 0 0
\(582\) 0 0
\(583\) 0 0
\(584\) −2.00000 −0.0827606
\(585\) 0 0
\(586\) −26.0000 −1.07405
\(587\) −12.0000 −0.495293 −0.247647 − 0.968850i \(-0.579657\pi\)
−0.247647 + 0.968850i \(0.579657\pi\)
\(588\) 0 0
\(589\) 0 0
\(590\) 0 0
\(591\) 0 0
\(592\) 6.00000 0.246598
\(593\) 6.00000 0.246390 0.123195 − 0.992382i \(-0.460686\pi\)
0.123195 + 0.992382i \(0.460686\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 14.0000 0.573462
\(597\) 0 0
\(598\) 4.00000 0.163572
\(599\) −24.0000 −0.980613 −0.490307 − 0.871550i \(-0.663115\pi\)
−0.490307 + 0.871550i \(0.663115\pi\)
\(600\) 0 0
\(601\) 42.0000 1.71322 0.856608 − 0.515968i \(-0.172568\pi\)
0.856608 + 0.515968i \(0.172568\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) −16.0000 −0.651031
\(605\) 0 0
\(606\) 0 0
\(607\) 36.0000 1.46119 0.730597 − 0.682808i \(-0.239242\pi\)
0.730597 + 0.682808i \(0.239242\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 0 0
\(612\) 0 0
\(613\) 22.0000 0.888572 0.444286 − 0.895885i \(-0.353457\pi\)
0.444286 + 0.895885i \(0.353457\pi\)
\(614\) −4.00000 −0.161427
\(615\) 0 0
\(616\) 0 0
\(617\) 30.0000 1.20775 0.603877 − 0.797077i \(-0.293622\pi\)
0.603877 + 0.797077i \(0.293622\pi\)
\(618\) 0 0
\(619\) 40.0000 1.60774 0.803868 − 0.594808i \(-0.202772\pi\)
0.803868 + 0.594808i \(0.202772\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) −16.0000 −0.641542
\(623\) 0 0
\(624\) 0 0
\(625\) 0 0
\(626\) 26.0000 1.03917
\(627\) 0 0
\(628\) 14.0000 0.558661
\(629\) −36.0000 −1.43541
\(630\) 0 0
\(631\) −48.0000 −1.91085 −0.955425 − 0.295234i \(-0.904602\pi\)
−0.955425 + 0.295234i \(0.904602\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) −2.00000 −0.0794301
\(635\) 0 0
\(636\) 0 0
\(637\) −7.00000 −0.277350
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) −2.00000 −0.0789953 −0.0394976 − 0.999220i \(-0.512576\pi\)
−0.0394976 + 0.999220i \(0.512576\pi\)
\(642\) 0 0
\(643\) −4.00000 −0.157745 −0.0788723 − 0.996885i \(-0.525132\pi\)
−0.0788723 + 0.996885i \(0.525132\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) −36.0000 −1.41531 −0.707653 − 0.706560i \(-0.750246\pi\)
−0.707653 + 0.706560i \(0.750246\pi\)
\(648\) 0 0
\(649\) 0 0
\(650\) 0 0
\(651\) 0 0
\(652\) 4.00000 0.156652
\(653\) −6.00000 −0.234798 −0.117399 − 0.993085i \(-0.537456\pi\)
−0.117399 + 0.993085i \(0.537456\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) −2.00000 −0.0780869
\(657\) 0 0
\(658\) 0 0
\(659\) 20.0000 0.779089 0.389545 − 0.921008i \(-0.372632\pi\)
0.389545 + 0.921008i \(0.372632\pi\)
\(660\) 0 0
\(661\) −30.0000 −1.16686 −0.583432 − 0.812162i \(-0.698291\pi\)
−0.583432 + 0.812162i \(0.698291\pi\)
\(662\) −8.00000 −0.310929
\(663\) 0 0
\(664\) −4.00000 −0.155230
\(665\) 0 0
\(666\) 0 0
\(667\) −40.0000 −1.54881
\(668\) 24.0000 0.928588
\(669\) 0 0
\(670\) 0 0
\(671\) 0 0
\(672\) 0 0
\(673\) −42.0000 −1.61898 −0.809491 − 0.587133i \(-0.800257\pi\)
−0.809491 + 0.587133i \(0.800257\pi\)
\(674\) 18.0000 0.693334
\(675\) 0 0
\(676\) 1.00000 0.0384615
\(677\) −30.0000 −1.15299 −0.576497 − 0.817099i \(-0.695581\pi\)
−0.576497 + 0.817099i \(0.695581\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 12.0000 0.459167 0.229584 − 0.973289i \(-0.426264\pi\)
0.229584 + 0.973289i \(0.426264\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 0 0
\(687\) 0 0
\(688\) 4.00000 0.152499
\(689\) −6.00000 −0.228582
\(690\) 0 0
\(691\) 32.0000 1.21734 0.608669 − 0.793424i \(-0.291704\pi\)
0.608669 + 0.793424i \(0.291704\pi\)
\(692\) −14.0000 −0.532200
\(693\) 0 0
\(694\) −12.0000 −0.455514
\(695\) 0 0
\(696\) 0 0
\(697\) 12.0000 0.454532
\(698\) −34.0000 −1.28692
\(699\) 0 0
\(700\) 0 0
\(701\) 18.0000 0.679851 0.339925 − 0.940452i \(-0.389598\pi\)
0.339925 + 0.940452i \(0.389598\pi\)
\(702\) 0 0
\(703\) 0 0
\(704\) 0 0
\(705\) 0 0
\(706\) 26.0000 0.978523
\(707\) 0 0
\(708\) 0 0
\(709\) 2.00000 0.0751116 0.0375558 − 0.999295i \(-0.488043\pi\)
0.0375558 + 0.999295i \(0.488043\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) −6.00000 −0.224860
\(713\) 0 0
\(714\) 0 0
\(715\) 0 0
\(716\) 20.0000 0.747435
\(717\) 0 0
\(718\) 24.0000 0.895672
\(719\) −24.0000 −0.895049 −0.447524 − 0.894272i \(-0.647694\pi\)
−0.447524 + 0.894272i \(0.647694\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) 19.0000 0.707107
\(723\) 0 0
\(724\) −10.0000 −0.371647
\(725\) 0 0
\(726\) 0 0
\(727\) −12.0000 −0.445055 −0.222528 − 0.974926i \(-0.571431\pi\)
−0.222528 + 0.974926i \(0.571431\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) −24.0000 −0.887672
\(732\) 0 0
\(733\) −50.0000 −1.84679 −0.923396 − 0.383849i \(-0.874598\pi\)
−0.923396 + 0.383849i \(0.874598\pi\)
\(734\) 20.0000 0.738213
\(735\) 0 0
\(736\) 4.00000 0.147442
\(737\) 0 0
\(738\) 0 0
\(739\) −40.0000 −1.47142 −0.735712 − 0.677295i \(-0.763152\pi\)
−0.735712 + 0.677295i \(0.763152\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) −48.0000 −1.76095 −0.880475 − 0.474093i \(-0.842776\pi\)
−0.880475 + 0.474093i \(0.842776\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 10.0000 0.366126
\(747\) 0 0
\(748\) 0 0
\(749\) 0 0
\(750\) 0 0
\(751\) 24.0000 0.875772 0.437886 − 0.899030i \(-0.355727\pi\)
0.437886 + 0.899030i \(0.355727\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) −10.0000 −0.364179
\(755\) 0 0
\(756\) 0 0
\(757\) −2.00000 −0.0726912 −0.0363456 − 0.999339i \(-0.511572\pi\)
−0.0363456 + 0.999339i \(0.511572\pi\)
\(758\) −24.0000 −0.871719
\(759\) 0 0
\(760\) 0 0
\(761\) 22.0000 0.797499 0.398750 − 0.917060i \(-0.369444\pi\)
0.398750 + 0.917060i \(0.369444\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) −24.0000 −0.868290
\(765\) 0 0
\(766\) 8.00000 0.289052
\(767\) 0 0
\(768\) 0 0
\(769\) 34.0000 1.22607 0.613036 − 0.790055i \(-0.289948\pi\)
0.613036 + 0.790055i \(0.289948\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) −14.0000 −0.503871
\(773\) 26.0000 0.935155 0.467578 − 0.883952i \(-0.345127\pi\)
0.467578 + 0.883952i \(0.345127\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 14.0000 0.502571
\(777\) 0 0
\(778\) −18.0000 −0.645331
\(779\) 0 0
\(780\) 0 0
\(781\) 0 0
\(782\) −24.0000 −0.858238
\(783\) 0 0
\(784\) −7.00000 −0.250000
\(785\) 0 0
\(786\) 0 0
\(787\) 36.0000 1.28326 0.641631 − 0.767014i \(-0.278258\pi\)
0.641631 + 0.767014i \(0.278258\pi\)
\(788\) −22.0000 −0.783718
\(789\) 0 0
\(790\) 0 0
\(791\) 0 0
\(792\) 0 0
\(793\) 6.00000 0.213066
\(794\) −14.0000 −0.496841
\(795\) 0 0
\(796\) −16.0000 −0.567105
\(797\) 18.0000 0.637593 0.318796 − 0.947823i \(-0.396721\pi\)
0.318796 + 0.947823i \(0.396721\pi\)
\(798\) 0 0
\(799\) 0 0
\(800\) 0 0
\(801\) 0 0
\(802\) 18.0000 0.635602
\(803\) 0 0
\(804\) 0 0
\(805\) 0 0
\(806\) 0 0
\(807\) 0 0
\(808\) 6.00000 0.211079
\(809\) −26.0000 −0.914111 −0.457056 − 0.889438i \(-0.651096\pi\)
−0.457056 + 0.889438i \(0.651096\pi\)
\(810\) 0 0
\(811\) 32.0000 1.12367 0.561836 − 0.827249i \(-0.310095\pi\)
0.561836 + 0.827249i \(0.310095\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) 0 0
\(816\) 0 0
\(817\) 0 0
\(818\) −2.00000 −0.0699284
\(819\) 0 0
\(820\) 0 0
\(821\) 22.0000 0.767805 0.383903 − 0.923374i \(-0.374580\pi\)
0.383903 + 0.923374i \(0.374580\pi\)
\(822\) 0 0
\(823\) 44.0000 1.53374 0.766872 − 0.641800i \(-0.221812\pi\)
0.766872 + 0.641800i \(0.221812\pi\)
\(824\) 12.0000 0.418040
\(825\) 0 0
\(826\) 0 0
\(827\) −12.0000 −0.417281 −0.208640 − 0.977992i \(-0.566904\pi\)
−0.208640 + 0.977992i \(0.566904\pi\)
\(828\) 0 0
\(829\) 54.0000 1.87550 0.937749 − 0.347314i \(-0.112906\pi\)
0.937749 + 0.347314i \(0.112906\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 1.00000 0.0346688
\(833\) 42.0000 1.45521
\(834\) 0 0
\(835\) 0 0
\(836\) 0 0
\(837\) 0 0
\(838\) 12.0000 0.414533
\(839\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(840\) 0 0
\(841\) 71.0000 2.44828
\(842\) 22.0000 0.758170
\(843\) 0 0
\(844\) −12.0000 −0.413057
\(845\) 0 0
\(846\) 0 0
\(847\) 0 0
\(848\) −6.00000 −0.206041
\(849\) 0 0
\(850\) 0 0
\(851\) −24.0000 −0.822709
\(852\) 0 0
\(853\) 38.0000 1.30110 0.650548 − 0.759465i \(-0.274539\pi\)
0.650548 + 0.759465i \(0.274539\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 4.00000 0.136717
\(857\) −38.0000 −1.29806 −0.649028 − 0.760765i \(-0.724824\pi\)
−0.649028 + 0.760765i \(0.724824\pi\)
\(858\) 0 0
\(859\) −20.0000 −0.682391 −0.341196 − 0.939992i \(-0.610832\pi\)
−0.341196 + 0.939992i \(0.610832\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) −24.0000 −0.817443
\(863\) 48.0000 1.63394 0.816970 − 0.576681i \(-0.195652\pi\)
0.816970 + 0.576681i \(0.195652\pi\)
\(864\) 0 0
\(865\) 0 0
\(866\) 2.00000 0.0679628
\(867\) 0 0
\(868\) 0 0
\(869\) 0 0
\(870\) 0 0
\(871\) −4.00000 −0.135535
\(872\) 14.0000 0.474100
\(873\) 0 0
\(874\) 0 0
\(875\) 0 0
\(876\) 0 0
\(877\) 14.0000 0.472746 0.236373 − 0.971662i \(-0.424041\pi\)
0.236373 + 0.971662i \(0.424041\pi\)
\(878\) 24.0000 0.809961
\(879\) 0 0
\(880\) 0 0
\(881\) −34.0000 −1.14549 −0.572745 − 0.819734i \(-0.694121\pi\)
−0.572745 + 0.819734i \(0.694121\pi\)
\(882\) 0 0
\(883\) −52.0000 −1.74994 −0.874970 − 0.484178i \(-0.839119\pi\)
−0.874970 + 0.484178i \(0.839119\pi\)
\(884\) −6.00000 −0.201802
\(885\) 0 0
\(886\) 4.00000 0.134383
\(887\) −36.0000 −1.20876 −0.604381 − 0.796696i \(-0.706579\pi\)
−0.604381 + 0.796696i \(0.706579\pi\)
\(888\) 0 0
\(889\) 0 0
\(890\) 0 0
\(891\) 0 0
\(892\) −16.0000 −0.535720
\(893\) 0 0
\(894\) 0 0
\(895\) 0 0
\(896\) 0 0
\(897\) 0 0
\(898\) −14.0000 −0.467186
\(899\) 0 0
\(900\) 0 0
\(901\) 36.0000 1.19933
\(902\) 0 0
\(903\) 0 0
\(904\) −10.0000 −0.332595
\(905\) 0 0
\(906\) 0 0
\(907\) −28.0000 −0.929725 −0.464862 − 0.885383i \(-0.653896\pi\)
−0.464862 + 0.885383i \(0.653896\pi\)
\(908\) 20.0000 0.663723
\(909\) 0 0
\(910\) 0 0
\(911\) −40.0000 −1.32526 −0.662630 − 0.748947i \(-0.730560\pi\)
−0.662630 + 0.748947i \(0.730560\pi\)
\(912\) 0 0
\(913\) 0 0
\(914\) 6.00000 0.198462
\(915\) 0 0
\(916\) 2.00000 0.0660819
\(917\) 0 0
\(918\) 0 0
\(919\) −16.0000 −0.527791 −0.263896 − 0.964551i \(-0.585007\pi\)
−0.263896 + 0.964551i \(0.585007\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) −14.0000 −0.461065
\(923\) −16.0000 −0.526646
\(924\) 0 0
\(925\) 0 0
\(926\) −24.0000 −0.788689
\(927\) 0 0
\(928\) −10.0000 −0.328266
\(929\) 46.0000 1.50921 0.754606 − 0.656179i \(-0.227828\pi\)
0.754606 + 0.656179i \(0.227828\pi\)
\(930\) 0 0
\(931\) 0 0
\(932\) 18.0000 0.589610
\(933\) 0 0
\(934\) 28.0000 0.916188
\(935\) 0 0
\(936\) 0 0
\(937\) 22.0000 0.718709 0.359354 − 0.933201i \(-0.382997\pi\)
0.359354 + 0.933201i \(0.382997\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0 0
\(941\) −10.0000 −0.325991 −0.162995 − 0.986627i \(-0.552116\pi\)
−0.162995 + 0.986627i \(0.552116\pi\)
\(942\) 0 0
\(943\) 8.00000 0.260516
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) −36.0000 −1.16984 −0.584921 − 0.811090i \(-0.698875\pi\)
−0.584921 + 0.811090i \(0.698875\pi\)
\(948\) 0 0
\(949\) 2.00000 0.0649227
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) 10.0000 0.323932 0.161966 − 0.986796i \(-0.448217\pi\)
0.161966 + 0.986796i \(0.448217\pi\)
\(954\) 0 0
\(955\) 0 0
\(956\) −16.0000 −0.517477
\(957\) 0 0
\(958\) 0 0
\(959\) 0 0
\(960\) 0 0
\(961\) −31.0000 −1.00000
\(962\) −6.00000 −0.193448
\(963\) 0 0
\(964\) −14.0000 −0.450910
\(965\) 0 0
\(966\) 0 0
\(967\) 32.0000 1.02905 0.514525 − 0.857475i \(-0.327968\pi\)
0.514525 + 0.857475i \(0.327968\pi\)
\(968\) 11.0000 0.353553
\(969\) 0 0
\(970\) 0 0
\(971\) −12.0000 −0.385098 −0.192549 − 0.981287i \(-0.561675\pi\)
−0.192549 + 0.981287i \(0.561675\pi\)
\(972\) 0 0
\(973\) 0 0
\(974\) 8.00000 0.256337
\(975\) 0 0
\(976\) 6.00000 0.192055
\(977\) −2.00000 −0.0639857 −0.0319928 − 0.999488i \(-0.510185\pi\)
−0.0319928 + 0.999488i \(0.510185\pi\)
\(978\) 0 0
\(979\) 0 0
\(980\) 0 0
\(981\) 0 0
\(982\) 20.0000 0.638226
\(983\) 16.0000 0.510321 0.255160 − 0.966899i \(-0.417872\pi\)
0.255160 + 0.966899i \(0.417872\pi\)
\(984\) 0 0
\(985\) 0 0
\(986\) 60.0000 1.91079
\(987\) 0 0
\(988\) 0 0
\(989\) −16.0000 −0.508770
\(990\) 0 0
\(991\) −8.00000 −0.254128 −0.127064 − 0.991894i \(-0.540555\pi\)
−0.127064 + 0.991894i \(0.540555\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0 0
\(995\) 0 0
\(996\) 0 0
\(997\) 22.0000 0.696747 0.348373 − 0.937356i \(-0.386734\pi\)
0.348373 + 0.937356i \(0.386734\pi\)
\(998\) 40.0000 1.26618
\(999\) 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 5850.2.a.m.1.1 1
3.2 odd 2 1950.2.a.y.1.1 1
5.2 odd 4 5850.2.e.p.5149.1 2
5.3 odd 4 5850.2.e.p.5149.2 2
5.4 even 2 1170.2.a.m.1.1 1
15.2 even 4 1950.2.e.l.1249.2 2
15.8 even 4 1950.2.e.l.1249.1 2
15.14 odd 2 390.2.a.a.1.1 ✓ 1
20.19 odd 2 9360.2.a.bn.1.1 1
60.59 even 2 3120.2.a.q.1.1 1
195.44 even 4 5070.2.b.c.1351.2 2
195.164 even 4 5070.2.b.c.1351.1 2
195.194 odd 2 5070.2.a.s.1.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
390.2.a.a.1.1 ✓ 1 15.14 odd 2
1170.2.a.m.1.1 1 5.4 even 2
1950.2.a.y.1.1 1 3.2 odd 2
1950.2.e.l.1249.1 2 15.8 even 4
1950.2.e.l.1249.2 2 15.2 even 4
3120.2.a.q.1.1 1 60.59 even 2
5070.2.a.s.1.1 1 195.194 odd 2
5070.2.b.c.1351.1 2 195.164 even 4
5070.2.b.c.1351.2 2 195.44 even 4
5850.2.a.m.1.1 1 1.1 even 1 trivial
5850.2.e.p.5149.1 2 5.2 odd 4
5850.2.e.p.5149.2 2 5.3 odd 4
9360.2.a.bn.1.1 1 20.19 odd 2