Properties

Label 4560.2.a.t.1.1
Level $4560$
Weight $2$
Character 4560.1
Self dual yes
Analytic conductor $36.412$
Analytic rank $1$
Dimension $1$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 4560 = 2^{4} \cdot 3 \cdot 5 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 4560.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(36.4117833217\)
Analytic rank: \(1\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 570)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Character \(\chi\) \(=\) 4560.1

$q$-expansion

\(f(q)\) \(=\) \(q+1.00000 q^{3} -1.00000 q^{5} +2.00000 q^{7} +1.00000 q^{9} +O(q^{10})\) \(q+1.00000 q^{3} -1.00000 q^{5} +2.00000 q^{7} +1.00000 q^{9} -4.00000 q^{11} -6.00000 q^{13} -1.00000 q^{15} +4.00000 q^{17} -1.00000 q^{19} +2.00000 q^{21} -4.00000 q^{23} +1.00000 q^{25} +1.00000 q^{27} +6.00000 q^{29} +6.00000 q^{31} -4.00000 q^{33} -2.00000 q^{35} +10.0000 q^{37} -6.00000 q^{39} +4.00000 q^{41} -12.0000 q^{43} -1.00000 q^{45} -4.00000 q^{47} -3.00000 q^{49} +4.00000 q^{51} -10.0000 q^{53} +4.00000 q^{55} -1.00000 q^{57} -10.0000 q^{59} +2.00000 q^{61} +2.00000 q^{63} +6.00000 q^{65} -12.0000 q^{67} -4.00000 q^{69} -8.00000 q^{71} -2.00000 q^{73} +1.00000 q^{75} -8.00000 q^{77} -10.0000 q^{79} +1.00000 q^{81} -2.00000 q^{83} -4.00000 q^{85} +6.00000 q^{87} -8.00000 q^{89} -12.0000 q^{91} +6.00000 q^{93} +1.00000 q^{95} +2.00000 q^{97} -4.00000 q^{99} +O(q^{100})\)

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
\(3\) 1.00000 0.577350
\(4\) 0 0
\(5\) −1.00000 −0.447214
\(6\) 0 0
\(7\) 2.00000 0.755929 0.377964 0.925820i \(-0.376624\pi\)
0.377964 + 0.925820i \(0.376624\pi\)
\(8\) 0 0
\(9\) 1.00000 0.333333
\(10\) 0 0
\(11\) −4.00000 −1.20605 −0.603023 0.797724i \(-0.706037\pi\)
−0.603023 + 0.797724i \(0.706037\pi\)
\(12\) 0 0
\(13\) −6.00000 −1.66410 −0.832050 0.554700i \(-0.812833\pi\)
−0.832050 + 0.554700i \(0.812833\pi\)
\(14\) 0 0
\(15\) −1.00000 −0.258199
\(16\) 0 0
\(17\) 4.00000 0.970143 0.485071 0.874475i \(-0.338794\pi\)
0.485071 + 0.874475i \(0.338794\pi\)
\(18\) 0 0
\(19\) −1.00000 −0.229416
\(20\) 0 0
\(21\) 2.00000 0.436436
\(22\) 0 0
\(23\) −4.00000 −0.834058 −0.417029 0.908893i \(-0.636929\pi\)
−0.417029 + 0.908893i \(0.636929\pi\)
\(24\) 0 0
\(25\) 1.00000 0.200000
\(26\) 0 0
\(27\) 1.00000 0.192450
\(28\) 0 0
\(29\) 6.00000 1.11417 0.557086 0.830455i \(-0.311919\pi\)
0.557086 + 0.830455i \(0.311919\pi\)
\(30\) 0 0
\(31\) 6.00000 1.07763 0.538816 0.842424i \(-0.318872\pi\)
0.538816 + 0.842424i \(0.318872\pi\)
\(32\) 0 0
\(33\) −4.00000 −0.696311
\(34\) 0 0
\(35\) −2.00000 −0.338062
\(36\) 0 0
\(37\) 10.0000 1.64399 0.821995 0.569495i \(-0.192861\pi\)
0.821995 + 0.569495i \(0.192861\pi\)
\(38\) 0 0
\(39\) −6.00000 −0.960769
\(40\) 0 0
\(41\) 4.00000 0.624695 0.312348 0.949968i \(-0.398885\pi\)
0.312348 + 0.949968i \(0.398885\pi\)
\(42\) 0 0
\(43\) −12.0000 −1.82998 −0.914991 0.403473i \(-0.867803\pi\)
−0.914991 + 0.403473i \(0.867803\pi\)
\(44\) 0 0
\(45\) −1.00000 −0.149071
\(46\) 0 0
\(47\) −4.00000 −0.583460 −0.291730 0.956501i \(-0.594231\pi\)
−0.291730 + 0.956501i \(0.594231\pi\)
\(48\) 0 0
\(49\) −3.00000 −0.428571
\(50\) 0 0
\(51\) 4.00000 0.560112
\(52\) 0 0
\(53\) −10.0000 −1.37361 −0.686803 0.726844i \(-0.740986\pi\)
−0.686803 + 0.726844i \(0.740986\pi\)
\(54\) 0 0
\(55\) 4.00000 0.539360
\(56\) 0 0
\(57\) −1.00000 −0.132453
\(58\) 0 0
\(59\) −10.0000 −1.30189 −0.650945 0.759125i \(-0.725627\pi\)
−0.650945 + 0.759125i \(0.725627\pi\)
\(60\) 0 0
\(61\) 2.00000 0.256074 0.128037 0.991769i \(-0.459132\pi\)
0.128037 + 0.991769i \(0.459132\pi\)
\(62\) 0 0
\(63\) 2.00000 0.251976
\(64\) 0 0
\(65\) 6.00000 0.744208
\(66\) 0 0
\(67\) −12.0000 −1.46603 −0.733017 0.680211i \(-0.761888\pi\)
−0.733017 + 0.680211i \(0.761888\pi\)
\(68\) 0 0
\(69\) −4.00000 −0.481543
\(70\) 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 \(-0.537341\pi\)
−0.117041 + 0.993127i \(0.537341\pi\)
\(74\) 0 0
\(75\) 1.00000 0.115470
\(76\) 0 0
\(77\) −8.00000 −0.911685
\(78\) 0 0
\(79\) −10.0000 −1.12509 −0.562544 0.826767i \(-0.690177\pi\)
−0.562544 + 0.826767i \(0.690177\pi\)
\(80\) 0 0
\(81\) 1.00000 0.111111
\(82\) 0 0
\(83\) −2.00000 −0.219529 −0.109764 0.993958i \(-0.535010\pi\)
−0.109764 + 0.993958i \(0.535010\pi\)
\(84\) 0 0
\(85\) −4.00000 −0.433861
\(86\) 0 0
\(87\) 6.00000 0.643268
\(88\) 0 0
\(89\) −8.00000 −0.847998 −0.423999 0.905663i \(-0.639374\pi\)
−0.423999 + 0.905663i \(0.639374\pi\)
\(90\) 0 0
\(91\) −12.0000 −1.25794
\(92\) 0 0
\(93\) 6.00000 0.622171
\(94\) 0 0
\(95\) 1.00000 0.102598
\(96\) 0 0
\(97\) 2.00000 0.203069 0.101535 0.994832i \(-0.467625\pi\)
0.101535 + 0.994832i \(0.467625\pi\)
\(98\) 0 0
\(99\) −4.00000 −0.402015
\(100\) 0 0
\(101\) −10.0000 −0.995037 −0.497519 0.867453i \(-0.665755\pi\)
−0.497519 + 0.867453i \(0.665755\pi\)
\(102\) 0 0
\(103\) 12.0000 1.18240 0.591198 0.806527i \(-0.298655\pi\)
0.591198 + 0.806527i \(0.298655\pi\)
\(104\) 0 0
\(105\) −2.00000 −0.195180
\(106\) 0 0
\(107\) −8.00000 −0.773389 −0.386695 0.922208i \(-0.626383\pi\)
−0.386695 + 0.922208i \(0.626383\pi\)
\(108\) 0 0
\(109\) −16.0000 −1.53252 −0.766261 0.642529i \(-0.777885\pi\)
−0.766261 + 0.642529i \(0.777885\pi\)
\(110\) 0 0
\(111\) 10.0000 0.949158
\(112\) 0 0
\(113\) −14.0000 −1.31701 −0.658505 0.752577i \(-0.728811\pi\)
−0.658505 + 0.752577i \(0.728811\pi\)
\(114\) 0 0
\(115\) 4.00000 0.373002
\(116\) 0 0
\(117\) −6.00000 −0.554700
\(118\) 0 0
\(119\) 8.00000 0.733359
\(120\) 0 0
\(121\) 5.00000 0.454545
\(122\) 0 0
\(123\) 4.00000 0.360668
\(124\) 0 0
\(125\) −1.00000 −0.0894427
\(126\) 0 0
\(127\) 20.0000 1.77471 0.887357 0.461084i \(-0.152539\pi\)
0.887357 + 0.461084i \(0.152539\pi\)
\(128\) 0 0
\(129\) −12.0000 −1.05654
\(130\) 0 0
\(131\) −12.0000 −1.04844 −0.524222 0.851581i \(-0.675644\pi\)
−0.524222 + 0.851581i \(0.675644\pi\)
\(132\) 0 0
\(133\) −2.00000 −0.173422
\(134\) 0 0
\(135\) −1.00000 −0.0860663
\(136\) 0 0
\(137\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(138\) 0 0
\(139\) 4.00000 0.339276 0.169638 0.985506i \(-0.445740\pi\)
0.169638 + 0.985506i \(0.445740\pi\)
\(140\) 0 0
\(141\) −4.00000 −0.336861
\(142\) 0 0
\(143\) 24.0000 2.00698
\(144\) 0 0
\(145\) −6.00000 −0.498273
\(146\) 0 0
\(147\) −3.00000 −0.247436
\(148\) 0 0
\(149\) 14.0000 1.14692 0.573462 0.819232i \(-0.305600\pi\)
0.573462 + 0.819232i \(0.305600\pi\)
\(150\) 0 0
\(151\) 2.00000 0.162758 0.0813788 0.996683i \(-0.474068\pi\)
0.0813788 + 0.996683i \(0.474068\pi\)
\(152\) 0 0
\(153\) 4.00000 0.323381
\(154\) 0 0
\(155\) −6.00000 −0.481932
\(156\) 0 0
\(157\) 12.0000 0.957704 0.478852 0.877896i \(-0.341053\pi\)
0.478852 + 0.877896i \(0.341053\pi\)
\(158\) 0 0
\(159\) −10.0000 −0.793052
\(160\) 0 0
\(161\) −8.00000 −0.630488
\(162\) 0 0
\(163\) 16.0000 1.25322 0.626608 0.779334i \(-0.284443\pi\)
0.626608 + 0.779334i \(0.284443\pi\)
\(164\) 0 0
\(165\) 4.00000 0.311400
\(166\) 0 0
\(167\) −24.0000 −1.85718 −0.928588 0.371113i \(-0.878976\pi\)
−0.928588 + 0.371113i \(0.878976\pi\)
\(168\) 0 0
\(169\) 23.0000 1.76923
\(170\) 0 0
\(171\) −1.00000 −0.0764719
\(172\) 0 0
\(173\) −18.0000 −1.36851 −0.684257 0.729241i \(-0.739873\pi\)
−0.684257 + 0.729241i \(0.739873\pi\)
\(174\) 0 0
\(175\) 2.00000 0.151186
\(176\) 0 0
\(177\) −10.0000 −0.751646
\(178\) 0 0
\(179\) 2.00000 0.149487 0.0747435 0.997203i \(-0.476186\pi\)
0.0747435 + 0.997203i \(0.476186\pi\)
\(180\) 0 0
\(181\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(182\) 0 0
\(183\) 2.00000 0.147844
\(184\) 0 0
\(185\) −10.0000 −0.735215
\(186\) 0 0
\(187\) −16.0000 −1.17004
\(188\) 0 0
\(189\) 2.00000 0.145479
\(190\) 0 0
\(191\) 8.00000 0.578860 0.289430 0.957199i \(-0.406534\pi\)
0.289430 + 0.957199i \(0.406534\pi\)
\(192\) 0 0
\(193\) 14.0000 1.00774 0.503871 0.863779i \(-0.331909\pi\)
0.503871 + 0.863779i \(0.331909\pi\)
\(194\) 0 0
\(195\) 6.00000 0.429669
\(196\) 0 0
\(197\) 22.0000 1.56744 0.783718 0.621117i \(-0.213321\pi\)
0.783718 + 0.621117i \(0.213321\pi\)
\(198\) 0 0
\(199\) 4.00000 0.283552 0.141776 0.989899i \(-0.454719\pi\)
0.141776 + 0.989899i \(0.454719\pi\)
\(200\) 0 0
\(201\) −12.0000 −0.846415
\(202\) 0 0
\(203\) 12.0000 0.842235
\(204\) 0 0
\(205\) −4.00000 −0.279372
\(206\) 0 0
\(207\) −4.00000 −0.278019
\(208\) 0 0
\(209\) 4.00000 0.276686
\(210\) 0 0
\(211\) 8.00000 0.550743 0.275371 0.961338i \(-0.411199\pi\)
0.275371 + 0.961338i \(0.411199\pi\)
\(212\) 0 0
\(213\) −8.00000 −0.548151
\(214\) 0 0
\(215\) 12.0000 0.818393
\(216\) 0 0
\(217\) 12.0000 0.814613
\(218\) 0 0
\(219\) −2.00000 −0.135147
\(220\) 0 0
\(221\) −24.0000 −1.61441
\(222\) 0 0
\(223\) −24.0000 −1.60716 −0.803579 0.595198i \(-0.797074\pi\)
−0.803579 + 0.595198i \(0.797074\pi\)
\(224\) 0 0
\(225\) 1.00000 0.0666667
\(226\) 0 0
\(227\) −20.0000 −1.32745 −0.663723 0.747978i \(-0.731025\pi\)
−0.663723 + 0.747978i \(0.731025\pi\)
\(228\) 0 0
\(229\) −26.0000 −1.71813 −0.859064 0.511868i \(-0.828954\pi\)
−0.859064 + 0.511868i \(0.828954\pi\)
\(230\) 0 0
\(231\) −8.00000 −0.526361
\(232\) 0 0
\(233\) −12.0000 −0.786146 −0.393073 0.919507i \(-0.628588\pi\)
−0.393073 + 0.919507i \(0.628588\pi\)
\(234\) 0 0
\(235\) 4.00000 0.260931
\(236\) 0 0
\(237\) −10.0000 −0.649570
\(238\) 0 0
\(239\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(240\) 0 0
\(241\) 10.0000 0.644157 0.322078 0.946713i \(-0.395619\pi\)
0.322078 + 0.946713i \(0.395619\pi\)
\(242\) 0 0
\(243\) 1.00000 0.0641500
\(244\) 0 0
\(245\) 3.00000 0.191663
\(246\) 0 0
\(247\) 6.00000 0.381771
\(248\) 0 0
\(249\) −2.00000 −0.126745
\(250\) 0 0
\(251\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(252\) 0 0
\(253\) 16.0000 1.00591
\(254\) 0 0
\(255\) −4.00000 −0.250490
\(256\) 0 0
\(257\) −18.0000 −1.12281 −0.561405 0.827541i \(-0.689739\pi\)
−0.561405 + 0.827541i \(0.689739\pi\)
\(258\) 0 0
\(259\) 20.0000 1.24274
\(260\) 0 0
\(261\) 6.00000 0.371391
\(262\) 0 0
\(263\) −12.0000 −0.739952 −0.369976 0.929041i \(-0.620634\pi\)
−0.369976 + 0.929041i \(0.620634\pi\)
\(264\) 0 0
\(265\) 10.0000 0.614295
\(266\) 0 0
\(267\) −8.00000 −0.489592
\(268\) 0 0
\(269\) 14.0000 0.853595 0.426798 0.904347i \(-0.359642\pi\)
0.426798 + 0.904347i \(0.359642\pi\)
\(270\) 0 0
\(271\) −20.0000 −1.21491 −0.607457 0.794353i \(-0.707810\pi\)
−0.607457 + 0.794353i \(0.707810\pi\)
\(272\) 0 0
\(273\) −12.0000 −0.726273
\(274\) 0 0
\(275\) −4.00000 −0.241209
\(276\) 0 0
\(277\) 28.0000 1.68236 0.841178 0.540758i \(-0.181862\pi\)
0.841178 + 0.540758i \(0.181862\pi\)
\(278\) 0 0
\(279\) 6.00000 0.359211
\(280\) 0 0
\(281\) 4.00000 0.238620 0.119310 0.992857i \(-0.461932\pi\)
0.119310 + 0.992857i \(0.461932\pi\)
\(282\) 0 0
\(283\) −28.0000 −1.66443 −0.832214 0.554455i \(-0.812927\pi\)
−0.832214 + 0.554455i \(0.812927\pi\)
\(284\) 0 0
\(285\) 1.00000 0.0592349
\(286\) 0 0
\(287\) 8.00000 0.472225
\(288\) 0 0
\(289\) −1.00000 −0.0588235
\(290\) 0 0
\(291\) 2.00000 0.117242
\(292\) 0 0
\(293\) 2.00000 0.116841 0.0584206 0.998292i \(-0.481394\pi\)
0.0584206 + 0.998292i \(0.481394\pi\)
\(294\) 0 0
\(295\) 10.0000 0.582223
\(296\) 0 0
\(297\) −4.00000 −0.232104
\(298\) 0 0
\(299\) 24.0000 1.38796
\(300\) 0 0
\(301\) −24.0000 −1.38334
\(302\) 0 0
\(303\) −10.0000 −0.574485
\(304\) 0 0
\(305\) −2.00000 −0.114520
\(306\) 0 0
\(307\) 12.0000 0.684876 0.342438 0.939540i \(-0.388747\pi\)
0.342438 + 0.939540i \(0.388747\pi\)
\(308\) 0 0
\(309\) 12.0000 0.682656
\(310\) 0 0
\(311\) −16.0000 −0.907277 −0.453638 0.891186i \(-0.649874\pi\)
−0.453638 + 0.891186i \(0.649874\pi\)
\(312\) 0 0
\(313\) 6.00000 0.339140 0.169570 0.985518i \(-0.445762\pi\)
0.169570 + 0.985518i \(0.445762\pi\)
\(314\) 0 0
\(315\) −2.00000 −0.112687
\(316\) 0 0
\(317\) 18.0000 1.01098 0.505490 0.862832i \(-0.331312\pi\)
0.505490 + 0.862832i \(0.331312\pi\)
\(318\) 0 0
\(319\) −24.0000 −1.34374
\(320\) 0 0
\(321\) −8.00000 −0.446516
\(322\) 0 0
\(323\) −4.00000 −0.222566
\(324\) 0 0
\(325\) −6.00000 −0.332820
\(326\) 0 0
\(327\) −16.0000 −0.884802
\(328\) 0 0
\(329\) −8.00000 −0.441054
\(330\) 0 0
\(331\) 12.0000 0.659580 0.329790 0.944054i \(-0.393022\pi\)
0.329790 + 0.944054i \(0.393022\pi\)
\(332\) 0 0
\(333\) 10.0000 0.547997
\(334\) 0 0
\(335\) 12.0000 0.655630
\(336\) 0 0
\(337\) −34.0000 −1.85210 −0.926049 0.377403i \(-0.876817\pi\)
−0.926049 + 0.377403i \(0.876817\pi\)
\(338\) 0 0
\(339\) −14.0000 −0.760376
\(340\) 0 0
\(341\) −24.0000 −1.29967
\(342\) 0 0
\(343\) −20.0000 −1.07990
\(344\) 0 0
\(345\) 4.00000 0.215353
\(346\) 0 0
\(347\) 2.00000 0.107366 0.0536828 0.998558i \(-0.482904\pi\)
0.0536828 + 0.998558i \(0.482904\pi\)
\(348\) 0 0
\(349\) 22.0000 1.17763 0.588817 0.808267i \(-0.299594\pi\)
0.588817 + 0.808267i \(0.299594\pi\)
\(350\) 0 0
\(351\) −6.00000 −0.320256
\(352\) 0 0
\(353\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(354\) 0 0
\(355\) 8.00000 0.424596
\(356\) 0 0
\(357\) 8.00000 0.423405
\(358\) 0 0
\(359\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(360\) 0 0
\(361\) 1.00000 0.0526316
\(362\) 0 0
\(363\) 5.00000 0.262432
\(364\) 0 0
\(365\) 2.00000 0.104685
\(366\) 0 0
\(367\) 22.0000 1.14839 0.574195 0.818718i \(-0.305315\pi\)
0.574195 + 0.818718i \(0.305315\pi\)
\(368\) 0 0
\(369\) 4.00000 0.208232
\(370\) 0 0
\(371\) −20.0000 −1.03835
\(372\) 0 0
\(373\) 14.0000 0.724893 0.362446 0.932005i \(-0.381942\pi\)
0.362446 + 0.932005i \(0.381942\pi\)
\(374\) 0 0
\(375\) −1.00000 −0.0516398
\(376\) 0 0
\(377\) −36.0000 −1.85409
\(378\) 0 0
\(379\) −8.00000 −0.410932 −0.205466 0.978664i \(-0.565871\pi\)
−0.205466 + 0.978664i \(0.565871\pi\)
\(380\) 0 0
\(381\) 20.0000 1.02463
\(382\) 0 0
\(383\) 16.0000 0.817562 0.408781 0.912633i \(-0.365954\pi\)
0.408781 + 0.912633i \(0.365954\pi\)
\(384\) 0 0
\(385\) 8.00000 0.407718
\(386\) 0 0
\(387\) −12.0000 −0.609994
\(388\) 0 0
\(389\) −10.0000 −0.507020 −0.253510 0.967333i \(-0.581585\pi\)
−0.253510 + 0.967333i \(0.581585\pi\)
\(390\) 0 0
\(391\) −16.0000 −0.809155
\(392\) 0 0
\(393\) −12.0000 −0.605320
\(394\) 0 0
\(395\) 10.0000 0.503155
\(396\) 0 0
\(397\) −24.0000 −1.20453 −0.602263 0.798298i \(-0.705734\pi\)
−0.602263 + 0.798298i \(0.705734\pi\)
\(398\) 0 0
\(399\) −2.00000 −0.100125
\(400\) 0 0
\(401\) −24.0000 −1.19850 −0.599251 0.800561i \(-0.704535\pi\)
−0.599251 + 0.800561i \(0.704535\pi\)
\(402\) 0 0
\(403\) −36.0000 −1.79329
\(404\) 0 0
\(405\) −1.00000 −0.0496904
\(406\) 0 0
\(407\) −40.0000 −1.98273
\(408\) 0 0
\(409\) −6.00000 −0.296681 −0.148340 0.988936i \(-0.547393\pi\)
−0.148340 + 0.988936i \(0.547393\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) −20.0000 −0.984136
\(414\) 0 0
\(415\) 2.00000 0.0981761
\(416\) 0 0
\(417\) 4.00000 0.195881
\(418\) 0 0
\(419\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(420\) 0 0
\(421\) −8.00000 −0.389896 −0.194948 0.980814i \(-0.562454\pi\)
−0.194948 + 0.980814i \(0.562454\pi\)
\(422\) 0 0
\(423\) −4.00000 −0.194487
\(424\) 0 0
\(425\) 4.00000 0.194029
\(426\) 0 0
\(427\) 4.00000 0.193574
\(428\) 0 0
\(429\) 24.0000 1.15873
\(430\) 0 0
\(431\) 40.0000 1.92673 0.963366 0.268190i \(-0.0864254\pi\)
0.963366 + 0.268190i \(0.0864254\pi\)
\(432\) 0 0
\(433\) 30.0000 1.44171 0.720854 0.693087i \(-0.243750\pi\)
0.720854 + 0.693087i \(0.243750\pi\)
\(434\) 0 0
\(435\) −6.00000 −0.287678
\(436\) 0 0
\(437\) 4.00000 0.191346
\(438\) 0 0
\(439\) 38.0000 1.81364 0.906821 0.421517i \(-0.138502\pi\)
0.906821 + 0.421517i \(0.138502\pi\)
\(440\) 0 0
\(441\) −3.00000 −0.142857
\(442\) 0 0
\(443\) −6.00000 −0.285069 −0.142534 0.989790i \(-0.545525\pi\)
−0.142534 + 0.989790i \(0.545525\pi\)
\(444\) 0 0
\(445\) 8.00000 0.379236
\(446\) 0 0
\(447\) 14.0000 0.662177
\(448\) 0 0
\(449\) 12.0000 0.566315 0.283158 0.959073i \(-0.408618\pi\)
0.283158 + 0.959073i \(0.408618\pi\)
\(450\) 0 0
\(451\) −16.0000 −0.753411
\(452\) 0 0
\(453\) 2.00000 0.0939682
\(454\) 0 0
\(455\) 12.0000 0.562569
\(456\) 0 0
\(457\) −22.0000 −1.02912 −0.514558 0.857455i \(-0.672044\pi\)
−0.514558 + 0.857455i \(0.672044\pi\)
\(458\) 0 0
\(459\) 4.00000 0.186704
\(460\) 0 0
\(461\) 18.0000 0.838344 0.419172 0.907907i \(-0.362320\pi\)
0.419172 + 0.907907i \(0.362320\pi\)
\(462\) 0 0
\(463\) 18.0000 0.836531 0.418265 0.908325i \(-0.362638\pi\)
0.418265 + 0.908325i \(0.362638\pi\)
\(464\) 0 0
\(465\) −6.00000 −0.278243
\(466\) 0 0
\(467\) 22.0000 1.01804 0.509019 0.860755i \(-0.330008\pi\)
0.509019 + 0.860755i \(0.330008\pi\)
\(468\) 0 0
\(469\) −24.0000 −1.10822
\(470\) 0 0
\(471\) 12.0000 0.552931
\(472\) 0 0
\(473\) 48.0000 2.20704
\(474\) 0 0
\(475\) −1.00000 −0.0458831
\(476\) 0 0
\(477\) −10.0000 −0.457869
\(478\) 0 0
\(479\) 24.0000 1.09659 0.548294 0.836286i \(-0.315277\pi\)
0.548294 + 0.836286i \(0.315277\pi\)
\(480\) 0 0
\(481\) −60.0000 −2.73576
\(482\) 0 0
\(483\) −8.00000 −0.364013
\(484\) 0 0
\(485\) −2.00000 −0.0908153
\(486\) 0 0
\(487\) −20.0000 −0.906287 −0.453143 0.891438i \(-0.649697\pi\)
−0.453143 + 0.891438i \(0.649697\pi\)
\(488\) 0 0
\(489\) 16.0000 0.723545
\(490\) 0 0
\(491\) −12.0000 −0.541552 −0.270776 0.962642i \(-0.587280\pi\)
−0.270776 + 0.962642i \(0.587280\pi\)
\(492\) 0 0
\(493\) 24.0000 1.08091
\(494\) 0 0
\(495\) 4.00000 0.179787
\(496\) 0 0
\(497\) −16.0000 −0.717698
\(498\) 0 0
\(499\) 4.00000 0.179065 0.0895323 0.995984i \(-0.471463\pi\)
0.0895323 + 0.995984i \(0.471463\pi\)
\(500\) 0 0
\(501\) −24.0000 −1.07224
\(502\) 0 0
\(503\) 8.00000 0.356702 0.178351 0.983967i \(-0.442924\pi\)
0.178351 + 0.983967i \(0.442924\pi\)
\(504\) 0 0
\(505\) 10.0000 0.444994
\(506\) 0 0
\(507\) 23.0000 1.02147
\(508\) 0 0
\(509\) 38.0000 1.68432 0.842160 0.539227i \(-0.181284\pi\)
0.842160 + 0.539227i \(0.181284\pi\)
\(510\) 0 0
\(511\) −4.00000 −0.176950
\(512\) 0 0
\(513\) −1.00000 −0.0441511
\(514\) 0 0
\(515\) −12.0000 −0.528783
\(516\) 0 0
\(517\) 16.0000 0.703679
\(518\) 0 0
\(519\) −18.0000 −0.790112
\(520\) 0 0
\(521\) 40.0000 1.75243 0.876216 0.481919i \(-0.160060\pi\)
0.876216 + 0.481919i \(0.160060\pi\)
\(522\) 0 0
\(523\) −4.00000 −0.174908 −0.0874539 0.996169i \(-0.527873\pi\)
−0.0874539 + 0.996169i \(0.527873\pi\)
\(524\) 0 0
\(525\) 2.00000 0.0872872
\(526\) 0 0
\(527\) 24.0000 1.04546
\(528\) 0 0
\(529\) −7.00000 −0.304348
\(530\) 0 0
\(531\) −10.0000 −0.433963
\(532\) 0 0
\(533\) −24.0000 −1.03956
\(534\) 0 0
\(535\) 8.00000 0.345870
\(536\) 0 0
\(537\) 2.00000 0.0863064
\(538\) 0 0
\(539\) 12.0000 0.516877
\(540\) 0 0
\(541\) 38.0000 1.63375 0.816874 0.576816i \(-0.195705\pi\)
0.816874 + 0.576816i \(0.195705\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) 16.0000 0.685365
\(546\) 0 0
\(547\) 4.00000 0.171028 0.0855138 0.996337i \(-0.472747\pi\)
0.0855138 + 0.996337i \(0.472747\pi\)
\(548\) 0 0
\(549\) 2.00000 0.0853579
\(550\) 0 0
\(551\) −6.00000 −0.255609
\(552\) 0 0
\(553\) −20.0000 −0.850487
\(554\) 0 0
\(555\) −10.0000 −0.424476
\(556\) 0 0
\(557\) 10.0000 0.423714 0.211857 0.977301i \(-0.432049\pi\)
0.211857 + 0.977301i \(0.432049\pi\)
\(558\) 0 0
\(559\) 72.0000 3.04528
\(560\) 0 0
\(561\) −16.0000 −0.675521
\(562\) 0 0
\(563\) −24.0000 −1.01148 −0.505740 0.862686i \(-0.668780\pi\)
−0.505740 + 0.862686i \(0.668780\pi\)
\(564\) 0 0
\(565\) 14.0000 0.588984
\(566\) 0 0
\(567\) 2.00000 0.0839921
\(568\) 0 0
\(569\) 12.0000 0.503066 0.251533 0.967849i \(-0.419065\pi\)
0.251533 + 0.967849i \(0.419065\pi\)
\(570\) 0 0
\(571\) 28.0000 1.17176 0.585882 0.810397i \(-0.300748\pi\)
0.585882 + 0.810397i \(0.300748\pi\)
\(572\) 0 0
\(573\) 8.00000 0.334205
\(574\) 0 0
\(575\) −4.00000 −0.166812
\(576\) 0 0
\(577\) 10.0000 0.416305 0.208153 0.978096i \(-0.433255\pi\)
0.208153 + 0.978096i \(0.433255\pi\)
\(578\) 0 0
\(579\) 14.0000 0.581820
\(580\) 0 0
\(581\) −4.00000 −0.165948
\(582\) 0 0
\(583\) 40.0000 1.65663
\(584\) 0 0
\(585\) 6.00000 0.248069
\(586\) 0 0
\(587\) −22.0000 −0.908037 −0.454019 0.890992i \(-0.650010\pi\)
−0.454019 + 0.890992i \(0.650010\pi\)
\(588\) 0 0
\(589\) −6.00000 −0.247226
\(590\) 0 0
\(591\) 22.0000 0.904959
\(592\) 0 0
\(593\) −8.00000 −0.328521 −0.164260 0.986417i \(-0.552524\pi\)
−0.164260 + 0.986417i \(0.552524\pi\)
\(594\) 0 0
\(595\) −8.00000 −0.327968
\(596\) 0 0
\(597\) 4.00000 0.163709
\(598\) 0 0
\(599\) 28.0000 1.14405 0.572024 0.820237i \(-0.306158\pi\)
0.572024 + 0.820237i \(0.306158\pi\)
\(600\) 0 0
\(601\) −6.00000 −0.244745 −0.122373 0.992484i \(-0.539050\pi\)
−0.122373 + 0.992484i \(0.539050\pi\)
\(602\) 0 0
\(603\) −12.0000 −0.488678
\(604\) 0 0
\(605\) −5.00000 −0.203279
\(606\) 0 0
\(607\) 28.0000 1.13648 0.568242 0.822861i \(-0.307624\pi\)
0.568242 + 0.822861i \(0.307624\pi\)
\(608\) 0 0
\(609\) 12.0000 0.486265
\(610\) 0 0
\(611\) 24.0000 0.970936
\(612\) 0 0
\(613\) −16.0000 −0.646234 −0.323117 0.946359i \(-0.604731\pi\)
−0.323117 + 0.946359i \(0.604731\pi\)
\(614\) 0 0
\(615\) −4.00000 −0.161296
\(616\) 0 0
\(617\) −48.0000 −1.93241 −0.966204 0.257780i \(-0.917009\pi\)
−0.966204 + 0.257780i \(0.917009\pi\)
\(618\) 0 0
\(619\) −4.00000 −0.160774 −0.0803868 0.996764i \(-0.525616\pi\)
−0.0803868 + 0.996764i \(0.525616\pi\)
\(620\) 0 0
\(621\) −4.00000 −0.160514
\(622\) 0 0
\(623\) −16.0000 −0.641026
\(624\) 0 0
\(625\) 1.00000 0.0400000
\(626\) 0 0
\(627\) 4.00000 0.159745
\(628\) 0 0
\(629\) 40.0000 1.59490
\(630\) 0 0
\(631\) −8.00000 −0.318475 −0.159237 0.987240i \(-0.550904\pi\)
−0.159237 + 0.987240i \(0.550904\pi\)
\(632\) 0 0
\(633\) 8.00000 0.317971
\(634\) 0 0
\(635\) −20.0000 −0.793676
\(636\) 0 0
\(637\) 18.0000 0.713186
\(638\) 0 0
\(639\) −8.00000 −0.316475
\(640\) 0 0
\(641\) −20.0000 −0.789953 −0.394976 0.918691i \(-0.629247\pi\)
−0.394976 + 0.918691i \(0.629247\pi\)
\(642\) 0 0
\(643\) 20.0000 0.788723 0.394362 0.918955i \(-0.370966\pi\)
0.394362 + 0.918955i \(0.370966\pi\)
\(644\) 0 0
\(645\) 12.0000 0.472500
\(646\) 0 0
\(647\) 24.0000 0.943537 0.471769 0.881722i \(-0.343616\pi\)
0.471769 + 0.881722i \(0.343616\pi\)
\(648\) 0 0
\(649\) 40.0000 1.57014
\(650\) 0 0
\(651\) 12.0000 0.470317
\(652\) 0 0
\(653\) −6.00000 −0.234798 −0.117399 0.993085i \(-0.537456\pi\)
−0.117399 + 0.993085i \(0.537456\pi\)
\(654\) 0 0
\(655\) 12.0000 0.468879
\(656\) 0 0
\(657\) −2.00000 −0.0780274
\(658\) 0 0
\(659\) −22.0000 −0.856998 −0.428499 0.903542i \(-0.640958\pi\)
−0.428499 + 0.903542i \(0.640958\pi\)
\(660\) 0 0
\(661\) −8.00000 −0.311164 −0.155582 0.987823i \(-0.549725\pi\)
−0.155582 + 0.987823i \(0.549725\pi\)
\(662\) 0 0
\(663\) −24.0000 −0.932083
\(664\) 0 0
\(665\) 2.00000 0.0775567
\(666\) 0 0
\(667\) −24.0000 −0.929284
\(668\) 0 0
\(669\) −24.0000 −0.927894
\(670\) 0 0
\(671\) −8.00000 −0.308837
\(672\) 0 0
\(673\) 26.0000 1.00223 0.501113 0.865382i \(-0.332924\pi\)
0.501113 + 0.865382i \(0.332924\pi\)
\(674\) 0 0
\(675\) 1.00000 0.0384900
\(676\) 0 0
\(677\) −6.00000 −0.230599 −0.115299 0.993331i \(-0.536783\pi\)
−0.115299 + 0.993331i \(0.536783\pi\)
\(678\) 0 0
\(679\) 4.00000 0.153506
\(680\) 0 0
\(681\) −20.0000 −0.766402
\(682\) 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
\(687\) −26.0000 −0.991962
\(688\) 0 0
\(689\) 60.0000 2.28582
\(690\) 0 0
\(691\) −4.00000 −0.152167 −0.0760836 0.997101i \(-0.524242\pi\)
−0.0760836 + 0.997101i \(0.524242\pi\)
\(692\) 0 0
\(693\) −8.00000 −0.303895
\(694\) 0 0
\(695\) −4.00000 −0.151729
\(696\) 0 0
\(697\) 16.0000 0.606043
\(698\) 0 0
\(699\) −12.0000 −0.453882
\(700\) 0 0
\(701\) 10.0000 0.377695 0.188847 0.982006i \(-0.439525\pi\)
0.188847 + 0.982006i \(0.439525\pi\)
\(702\) 0 0
\(703\) −10.0000 −0.377157
\(704\) 0 0
\(705\) 4.00000 0.150649
\(706\) 0 0
\(707\) −20.0000 −0.752177
\(708\) 0 0
\(709\) 14.0000 0.525781 0.262891 0.964826i \(-0.415324\pi\)
0.262891 + 0.964826i \(0.415324\pi\)
\(710\) 0 0
\(711\) −10.0000 −0.375029
\(712\) 0 0
\(713\) −24.0000 −0.898807
\(714\) 0 0
\(715\) −24.0000 −0.897549
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) −40.0000 −1.49175 −0.745874 0.666087i \(-0.767968\pi\)
−0.745874 + 0.666087i \(0.767968\pi\)
\(720\) 0 0
\(721\) 24.0000 0.893807
\(722\) 0 0
\(723\) 10.0000 0.371904
\(724\) 0 0
\(725\) 6.00000 0.222834
\(726\) 0 0
\(727\) −26.0000 −0.964287 −0.482143 0.876092i \(-0.660142\pi\)
−0.482143 + 0.876092i \(0.660142\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) 0 0
\(731\) −48.0000 −1.77534
\(732\) 0 0
\(733\) −8.00000 −0.295487 −0.147743 0.989026i \(-0.547201\pi\)
−0.147743 + 0.989026i \(0.547201\pi\)
\(734\) 0 0
\(735\) 3.00000 0.110657
\(736\) 0 0
\(737\) 48.0000 1.76810
\(738\) 0 0
\(739\) 20.0000 0.735712 0.367856 0.929883i \(-0.380092\pi\)
0.367856 + 0.929883i \(0.380092\pi\)
\(740\) 0 0
\(741\) 6.00000 0.220416
\(742\) 0 0
\(743\) −48.0000 −1.76095 −0.880475 0.474093i \(-0.842776\pi\)
−0.880475 + 0.474093i \(0.842776\pi\)
\(744\) 0 0
\(745\) −14.0000 −0.512920
\(746\) 0 0
\(747\) −2.00000 −0.0731762
\(748\) 0 0
\(749\) −16.0000 −0.584627
\(750\) 0 0
\(751\) 38.0000 1.38664 0.693320 0.720630i \(-0.256147\pi\)
0.693320 + 0.720630i \(0.256147\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) −2.00000 −0.0727875
\(756\) 0 0
\(757\) 8.00000 0.290765 0.145382 0.989376i \(-0.453559\pi\)
0.145382 + 0.989376i \(0.453559\pi\)
\(758\) 0 0
\(759\) 16.0000 0.580763
\(760\) 0 0
\(761\) −34.0000 −1.23250 −0.616250 0.787551i \(-0.711349\pi\)
−0.616250 + 0.787551i \(0.711349\pi\)
\(762\) 0 0
\(763\) −32.0000 −1.15848
\(764\) 0 0
\(765\) −4.00000 −0.144620
\(766\) 0 0
\(767\) 60.0000 2.16647
\(768\) 0 0
\(769\) −18.0000 −0.649097 −0.324548 0.945869i \(-0.605212\pi\)
−0.324548 + 0.945869i \(0.605212\pi\)
\(770\) 0 0
\(771\) −18.0000 −0.648254
\(772\) 0 0
\(773\) 6.00000 0.215805 0.107903 0.994161i \(-0.465587\pi\)
0.107903 + 0.994161i \(0.465587\pi\)
\(774\) 0 0
\(775\) 6.00000 0.215526
\(776\) 0 0
\(777\) 20.0000 0.717496
\(778\) 0 0
\(779\) −4.00000 −0.143315
\(780\) 0 0
\(781\) 32.0000 1.14505
\(782\) 0 0
\(783\) 6.00000 0.214423
\(784\) 0 0
\(785\) −12.0000 −0.428298
\(786\) 0 0
\(787\) −4.00000 −0.142585 −0.0712923 0.997455i \(-0.522712\pi\)
−0.0712923 + 0.997455i \(0.522712\pi\)
\(788\) 0 0
\(789\) −12.0000 −0.427211
\(790\) 0 0
\(791\) −28.0000 −0.995565
\(792\) 0 0
\(793\) −12.0000 −0.426132
\(794\) 0 0
\(795\) 10.0000 0.354663
\(796\) 0 0
\(797\) 2.00000 0.0708436 0.0354218 0.999372i \(-0.488723\pi\)
0.0354218 + 0.999372i \(0.488723\pi\)
\(798\) 0 0
\(799\) −16.0000 −0.566039
\(800\) 0 0
\(801\) −8.00000 −0.282666
\(802\) 0 0
\(803\) 8.00000 0.282314
\(804\) 0 0
\(805\) 8.00000 0.281963
\(806\) 0 0
\(807\) 14.0000 0.492823
\(808\) 0 0
\(809\) −42.0000 −1.47664 −0.738321 0.674450i \(-0.764381\pi\)
−0.738321 + 0.674450i \(0.764381\pi\)
\(810\) 0 0
\(811\) 8.00000 0.280918 0.140459 0.990086i \(-0.455142\pi\)
0.140459 + 0.990086i \(0.455142\pi\)
\(812\) 0 0
\(813\) −20.0000 −0.701431
\(814\) 0 0
\(815\) −16.0000 −0.560456
\(816\) 0 0
\(817\) 12.0000 0.419827
\(818\) 0 0
\(819\) −12.0000 −0.419314
\(820\) 0 0
\(821\) −42.0000 −1.46581 −0.732905 0.680331i \(-0.761836\pi\)
−0.732905 + 0.680331i \(0.761836\pi\)
\(822\) 0 0
\(823\) 26.0000 0.906303 0.453152 0.891434i \(-0.350300\pi\)
0.453152 + 0.891434i \(0.350300\pi\)
\(824\) 0 0
\(825\) −4.00000 −0.139262
\(826\) 0 0
\(827\) −48.0000 −1.66912 −0.834562 0.550914i \(-0.814279\pi\)
−0.834562 + 0.550914i \(0.814279\pi\)
\(828\) 0 0
\(829\) −40.0000 −1.38926 −0.694629 0.719368i \(-0.744431\pi\)
−0.694629 + 0.719368i \(0.744431\pi\)
\(830\) 0 0
\(831\) 28.0000 0.971309
\(832\) 0 0
\(833\) −12.0000 −0.415775
\(834\) 0 0
\(835\) 24.0000 0.830554
\(836\) 0 0
\(837\) 6.00000 0.207390
\(838\) 0 0
\(839\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(840\) 0 0
\(841\) 7.00000 0.241379
\(842\) 0 0
\(843\) 4.00000 0.137767
\(844\) 0 0
\(845\) −23.0000 −0.791224
\(846\) 0 0
\(847\) 10.0000 0.343604
\(848\) 0 0
\(849\) −28.0000 −0.960958
\(850\) 0 0
\(851\) −40.0000 −1.37118
\(852\) 0 0
\(853\) −36.0000 −1.23262 −0.616308 0.787505i \(-0.711372\pi\)
−0.616308 + 0.787505i \(0.711372\pi\)
\(854\) 0 0
\(855\) 1.00000 0.0341993
\(856\) 0 0
\(857\) 30.0000 1.02478 0.512390 0.858753i \(-0.328760\pi\)
0.512390 + 0.858753i \(0.328760\pi\)
\(858\) 0 0
\(859\) −4.00000 −0.136478 −0.0682391 0.997669i \(-0.521738\pi\)
−0.0682391 + 0.997669i \(0.521738\pi\)
\(860\) 0 0
\(861\) 8.00000 0.272639
\(862\) 0 0
\(863\) −32.0000 −1.08929 −0.544646 0.838666i \(-0.683336\pi\)
−0.544646 + 0.838666i \(0.683336\pi\)
\(864\) 0 0
\(865\) 18.0000 0.612018
\(866\) 0 0
\(867\) −1.00000 −0.0339618
\(868\) 0 0
\(869\) 40.0000 1.35691
\(870\) 0 0
\(871\) 72.0000 2.43963
\(872\) 0 0
\(873\) 2.00000 0.0676897
\(874\) 0 0
\(875\) −2.00000 −0.0676123
\(876\) 0 0
\(877\) −34.0000 −1.14810 −0.574049 0.818821i \(-0.694628\pi\)
−0.574049 + 0.818821i \(0.694628\pi\)
\(878\) 0 0
\(879\) 2.00000 0.0674583
\(880\) 0 0
\(881\) 18.0000 0.606435 0.303218 0.952921i \(-0.401939\pi\)
0.303218 + 0.952921i \(0.401939\pi\)
\(882\) 0 0
\(883\) −36.0000 −1.21150 −0.605748 0.795656i \(-0.707126\pi\)
−0.605748 + 0.795656i \(0.707126\pi\)
\(884\) 0 0
\(885\) 10.0000 0.336146
\(886\) 0 0
\(887\) −48.0000 −1.61168 −0.805841 0.592132i \(-0.798286\pi\)
−0.805841 + 0.592132i \(0.798286\pi\)
\(888\) 0 0
\(889\) 40.0000 1.34156
\(890\) 0 0
\(891\) −4.00000 −0.134005
\(892\) 0 0
\(893\) 4.00000 0.133855
\(894\) 0 0
\(895\) −2.00000 −0.0668526
\(896\) 0 0
\(897\) 24.0000 0.801337
\(898\) 0 0
\(899\) 36.0000 1.20067
\(900\) 0 0
\(901\) −40.0000 −1.33259
\(902\) 0 0
\(903\) −24.0000 −0.798670
\(904\) 0 0
\(905\) 0 0
\(906\) 0 0
\(907\) 20.0000 0.664089 0.332045 0.943264i \(-0.392262\pi\)
0.332045 + 0.943264i \(0.392262\pi\)
\(908\) 0 0
\(909\) −10.0000 −0.331679
\(910\) 0 0
\(911\) −12.0000 −0.397578 −0.198789 0.980042i \(-0.563701\pi\)
−0.198789 + 0.980042i \(0.563701\pi\)
\(912\) 0 0
\(913\) 8.00000 0.264761
\(914\) 0 0
\(915\) −2.00000 −0.0661180
\(916\) 0 0
\(917\) −24.0000 −0.792550
\(918\) 0 0
\(919\) −16.0000 −0.527791 −0.263896 0.964551i \(-0.585007\pi\)
−0.263896 + 0.964551i \(0.585007\pi\)
\(920\) 0 0
\(921\) 12.0000 0.395413
\(922\) 0 0
\(923\) 48.0000 1.57994
\(924\) 0 0
\(925\) 10.0000 0.328798
\(926\) 0 0
\(927\) 12.0000 0.394132
\(928\) 0 0
\(929\) 42.0000 1.37798 0.688988 0.724773i \(-0.258055\pi\)
0.688988 + 0.724773i \(0.258055\pi\)
\(930\) 0 0
\(931\) 3.00000 0.0983210
\(932\) 0 0
\(933\) −16.0000 −0.523816
\(934\) 0 0
\(935\) 16.0000 0.523256
\(936\) 0 0
\(937\) 26.0000 0.849383 0.424691 0.905338i \(-0.360383\pi\)
0.424691 + 0.905338i \(0.360383\pi\)
\(938\) 0 0
\(939\) 6.00000 0.195803
\(940\) 0 0
\(941\) 10.0000 0.325991 0.162995 0.986627i \(-0.447884\pi\)
0.162995 + 0.986627i \(0.447884\pi\)
\(942\) 0 0
\(943\) −16.0000 −0.521032
\(944\) 0 0
\(945\) −2.00000 −0.0650600
\(946\) 0 0
\(947\) 38.0000 1.23483 0.617417 0.786636i \(-0.288179\pi\)
0.617417 + 0.786636i \(0.288179\pi\)
\(948\) 0 0
\(949\) 12.0000 0.389536
\(950\) 0 0
\(951\) 18.0000 0.583690
\(952\) 0 0
\(953\) 6.00000 0.194359 0.0971795 0.995267i \(-0.469018\pi\)
0.0971795 + 0.995267i \(0.469018\pi\)
\(954\) 0 0
\(955\) −8.00000 −0.258874
\(956\) 0 0
\(957\) −24.0000 −0.775810
\(958\) 0 0
\(959\) 0 0
\(960\) 0 0
\(961\) 5.00000 0.161290
\(962\) 0 0
\(963\) −8.00000 −0.257796
\(964\) 0 0
\(965\) −14.0000 −0.450676
\(966\) 0 0
\(967\) 18.0000 0.578841 0.289420 0.957202i \(-0.406537\pi\)
0.289420 + 0.957202i \(0.406537\pi\)
\(968\) 0 0
\(969\) −4.00000 −0.128499
\(970\) 0 0
\(971\) 42.0000 1.34784 0.673922 0.738802i \(-0.264608\pi\)
0.673922 + 0.738802i \(0.264608\pi\)
\(972\) 0 0
\(973\) 8.00000 0.256468
\(974\) 0 0
\(975\) −6.00000 −0.192154
\(976\) 0 0
\(977\) −42.0000 −1.34370 −0.671850 0.740688i \(-0.734500\pi\)
−0.671850 + 0.740688i \(0.734500\pi\)
\(978\) 0 0
\(979\) 32.0000 1.02272
\(980\) 0 0
\(981\) −16.0000 −0.510841
\(982\) 0 0
\(983\) −24.0000 −0.765481 −0.382741 0.923856i \(-0.625020\pi\)
−0.382741 + 0.923856i \(0.625020\pi\)
\(984\) 0 0
\(985\) −22.0000 −0.700978
\(986\) 0 0
\(987\) −8.00000 −0.254643
\(988\) 0 0
\(989\) 48.0000 1.52631
\(990\) 0 0
\(991\) 2.00000 0.0635321 0.0317660 0.999495i \(-0.489887\pi\)
0.0317660 + 0.999495i \(0.489887\pi\)
\(992\) 0 0
\(993\) 12.0000 0.380808
\(994\) 0 0
\(995\) −4.00000 −0.126809
\(996\) 0 0
\(997\) −52.0000 −1.64686 −0.823428 0.567420i \(-0.807941\pi\)
−0.823428 + 0.567420i \(0.807941\pi\)
\(998\) 0 0
\(999\) 10.0000 0.316386
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 4560.2.a.t.1.1 1
4.3 odd 2 570.2.a.a.1.1 1
12.11 even 2 1710.2.a.q.1.1 1
20.3 even 4 2850.2.d.r.799.2 2
20.7 even 4 2850.2.d.r.799.1 2
20.19 odd 2 2850.2.a.bb.1.1 1
60.59 even 2 8550.2.a.n.1.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
570.2.a.a.1.1 1 4.3 odd 2
1710.2.a.q.1.1 1 12.11 even 2
2850.2.a.bb.1.1 1 20.19 odd 2
2850.2.d.r.799.1 2 20.7 even 4
2850.2.d.r.799.2 2 20.3 even 4
4560.2.a.t.1.1 1 1.1 even 1 trivial
8550.2.a.n.1.1 1 60.59 even 2