Properties

Label 9702.2.a.f.1.1
Level $9702$
Weight $2$
Character 9702.1
Self dual yes
Analytic conductor $77.471$
Analytic rank $0$
Dimension $1$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 9702 = 2 \cdot 3^{2} \cdot 7^{2} \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 9702.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(77.4708600410\)
Analytic rank: \(0\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 1386)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Character \(\chi\) \(=\) 9702.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.00000 q^{2} +1.00000 q^{4} -2.00000 q^{5} -1.00000 q^{8} +O(q^{10})\) \(q-1.00000 q^{2} +1.00000 q^{4} -2.00000 q^{5} -1.00000 q^{8} +2.00000 q^{10} -1.00000 q^{11} -2.00000 q^{13} +1.00000 q^{16} +1.00000 q^{17} +3.00000 q^{19} -2.00000 q^{20} +1.00000 q^{22} +1.00000 q^{23} -1.00000 q^{25} +2.00000 q^{26} +1.00000 q^{29} +2.00000 q^{31} -1.00000 q^{32} -1.00000 q^{34} -5.00000 q^{37} -3.00000 q^{38} +2.00000 q^{40} -10.0000 q^{41} +1.00000 q^{43} -1.00000 q^{44} -1.00000 q^{46} +7.00000 q^{47} +1.00000 q^{50} -2.00000 q^{52} -12.0000 q^{53} +2.00000 q^{55} -1.00000 q^{58} -3.00000 q^{59} +14.0000 q^{61} -2.00000 q^{62} +1.00000 q^{64} +4.00000 q^{65} +12.0000 q^{67} +1.00000 q^{68} -5.00000 q^{71} +8.00000 q^{73} +5.00000 q^{74} +3.00000 q^{76} -2.00000 q^{80} +10.0000 q^{82} -6.00000 q^{83} -2.00000 q^{85} -1.00000 q^{86} +1.00000 q^{88} -6.00000 q^{89} +1.00000 q^{92} -7.00000 q^{94} -6.00000 q^{95} -7.00000 q^{97} +O(q^{100})\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.00000 −0.707107
\(3\) 0 0
\(4\) 1.00000 0.500000
\(5\) −2.00000 −0.894427 −0.447214 0.894427i \(-0.647584\pi\)
−0.447214 + 0.894427i \(0.647584\pi\)
\(6\) 0 0
\(7\) 0 0
\(8\) −1.00000 −0.353553
\(9\) 0 0
\(10\) 2.00000 0.632456
\(11\) −1.00000 −0.301511
\(12\) 0 0
\(13\) −2.00000 −0.554700 −0.277350 0.960769i \(-0.589456\pi\)
−0.277350 + 0.960769i \(0.589456\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 1.00000 0.250000
\(17\) 1.00000 0.242536 0.121268 0.992620i \(-0.461304\pi\)
0.121268 + 0.992620i \(0.461304\pi\)
\(18\) 0 0
\(19\) 3.00000 0.688247 0.344124 0.938924i \(-0.388176\pi\)
0.344124 + 0.938924i \(0.388176\pi\)
\(20\) −2.00000 −0.447214
\(21\) 0 0
\(22\) 1.00000 0.213201
\(23\) 1.00000 0.208514 0.104257 0.994550i \(-0.466753\pi\)
0.104257 + 0.994550i \(0.466753\pi\)
\(24\) 0 0
\(25\) −1.00000 −0.200000
\(26\) 2.00000 0.392232
\(27\) 0 0
\(28\) 0 0
\(29\) 1.00000 0.185695 0.0928477 0.995680i \(-0.470403\pi\)
0.0928477 + 0.995680i \(0.470403\pi\)
\(30\) 0 0
\(31\) 2.00000 0.359211 0.179605 0.983739i \(-0.442518\pi\)
0.179605 + 0.983739i \(0.442518\pi\)
\(32\) −1.00000 −0.176777
\(33\) 0 0
\(34\) −1.00000 −0.171499
\(35\) 0 0
\(36\) 0 0
\(37\) −5.00000 −0.821995 −0.410997 0.911636i \(-0.634819\pi\)
−0.410997 + 0.911636i \(0.634819\pi\)
\(38\) −3.00000 −0.486664
\(39\) 0 0
\(40\) 2.00000 0.316228
\(41\) −10.0000 −1.56174 −0.780869 0.624695i \(-0.785223\pi\)
−0.780869 + 0.624695i \(0.785223\pi\)
\(42\) 0 0
\(43\) 1.00000 0.152499 0.0762493 0.997089i \(-0.475706\pi\)
0.0762493 + 0.997089i \(0.475706\pi\)
\(44\) −1.00000 −0.150756
\(45\) 0 0
\(46\) −1.00000 −0.147442
\(47\) 7.00000 1.02105 0.510527 0.859861i \(-0.329450\pi\)
0.510527 + 0.859861i \(0.329450\pi\)
\(48\) 0 0
\(49\) 0 0
\(50\) 1.00000 0.141421
\(51\) 0 0
\(52\) −2.00000 −0.277350
\(53\) −12.0000 −1.64833 −0.824163 0.566352i \(-0.808354\pi\)
−0.824163 + 0.566352i \(0.808354\pi\)
\(54\) 0 0
\(55\) 2.00000 0.269680
\(56\) 0 0
\(57\) 0 0
\(58\) −1.00000 −0.131306
\(59\) −3.00000 −0.390567 −0.195283 0.980747i \(-0.562563\pi\)
−0.195283 + 0.980747i \(0.562563\pi\)
\(60\) 0 0
\(61\) 14.0000 1.79252 0.896258 0.443533i \(-0.146275\pi\)
0.896258 + 0.443533i \(0.146275\pi\)
\(62\) −2.00000 −0.254000
\(63\) 0 0
\(64\) 1.00000 0.125000
\(65\) 4.00000 0.496139
\(66\) 0 0
\(67\) 12.0000 1.46603 0.733017 0.680211i \(-0.238112\pi\)
0.733017 + 0.680211i \(0.238112\pi\)
\(68\) 1.00000 0.121268
\(69\) 0 0
\(70\) 0 0
\(71\) −5.00000 −0.593391 −0.296695 0.954972i \(-0.595885\pi\)
−0.296695 + 0.954972i \(0.595885\pi\)
\(72\) 0 0
\(73\) 8.00000 0.936329 0.468165 0.883641i \(-0.344915\pi\)
0.468165 + 0.883641i \(0.344915\pi\)
\(74\) 5.00000 0.581238
\(75\) 0 0
\(76\) 3.00000 0.344124
\(77\) 0 0
\(78\) 0 0
\(79\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(80\) −2.00000 −0.223607
\(81\) 0 0
\(82\) 10.0000 1.10432
\(83\) −6.00000 −0.658586 −0.329293 0.944228i \(-0.606810\pi\)
−0.329293 + 0.944228i \(0.606810\pi\)
\(84\) 0 0
\(85\) −2.00000 −0.216930
\(86\) −1.00000 −0.107833
\(87\) 0 0
\(88\) 1.00000 0.106600
\(89\) −6.00000 −0.635999 −0.317999 0.948091i \(-0.603011\pi\)
−0.317999 + 0.948091i \(0.603011\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 1.00000 0.104257
\(93\) 0 0
\(94\) −7.00000 −0.721995
\(95\) −6.00000 −0.615587
\(96\) 0 0
\(97\) −7.00000 −0.710742 −0.355371 0.934725i \(-0.615646\pi\)
−0.355371 + 0.934725i \(0.615646\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) −1.00000 −0.100000
\(101\) −9.00000 −0.895533 −0.447767 0.894150i \(-0.647781\pi\)
−0.447767 + 0.894150i \(0.647781\pi\)
\(102\) 0 0
\(103\) 6.00000 0.591198 0.295599 0.955312i \(-0.404481\pi\)
0.295599 + 0.955312i \(0.404481\pi\)
\(104\) 2.00000 0.196116
\(105\) 0 0
\(106\) 12.0000 1.16554
\(107\) 2.00000 0.193347 0.0966736 0.995316i \(-0.469180\pi\)
0.0966736 + 0.995316i \(0.469180\pi\)
\(108\) 0 0
\(109\) −20.0000 −1.91565 −0.957826 0.287348i \(-0.907226\pi\)
−0.957826 + 0.287348i \(0.907226\pi\)
\(110\) −2.00000 −0.190693
\(111\) 0 0
\(112\) 0 0
\(113\) −10.0000 −0.940721 −0.470360 0.882474i \(-0.655876\pi\)
−0.470360 + 0.882474i \(0.655876\pi\)
\(114\) 0 0
\(115\) −2.00000 −0.186501
\(116\) 1.00000 0.0928477
\(117\) 0 0
\(118\) 3.00000 0.276172
\(119\) 0 0
\(120\) 0 0
\(121\) 1.00000 0.0909091
\(122\) −14.0000 −1.26750
\(123\) 0 0
\(124\) 2.00000 0.179605
\(125\) 12.0000 1.07331
\(126\) 0 0
\(127\) −1.00000 −0.0887357 −0.0443678 0.999015i \(-0.514127\pi\)
−0.0443678 + 0.999015i \(0.514127\pi\)
\(128\) −1.00000 −0.0883883
\(129\) 0 0
\(130\) −4.00000 −0.350823
\(131\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) −12.0000 −1.03664
\(135\) 0 0
\(136\) −1.00000 −0.0857493
\(137\) −6.00000 −0.512615 −0.256307 0.966595i \(-0.582506\pi\)
−0.256307 + 0.966595i \(0.582506\pi\)
\(138\) 0 0
\(139\) 13.0000 1.10265 0.551323 0.834292i \(-0.314123\pi\)
0.551323 + 0.834292i \(0.314123\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 5.00000 0.419591
\(143\) 2.00000 0.167248
\(144\) 0 0
\(145\) −2.00000 −0.166091
\(146\) −8.00000 −0.662085
\(147\) 0 0
\(148\) −5.00000 −0.410997
\(149\) 11.0000 0.901155 0.450578 0.892737i \(-0.351218\pi\)
0.450578 + 0.892737i \(0.351218\pi\)
\(150\) 0 0
\(151\) −15.0000 −1.22068 −0.610341 0.792139i \(-0.708968\pi\)
−0.610341 + 0.792139i \(0.708968\pi\)
\(152\) −3.00000 −0.243332
\(153\) 0 0
\(154\) 0 0
\(155\) −4.00000 −0.321288
\(156\) 0 0
\(157\) −1.00000 −0.0798087 −0.0399043 0.999204i \(-0.512705\pi\)
−0.0399043 + 0.999204i \(0.512705\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 2.00000 0.158114
\(161\) 0 0
\(162\) 0 0
\(163\) 10.0000 0.783260 0.391630 0.920123i \(-0.371911\pi\)
0.391630 + 0.920123i \(0.371911\pi\)
\(164\) −10.0000 −0.780869
\(165\) 0 0
\(166\) 6.00000 0.465690
\(167\) 2.00000 0.154765 0.0773823 0.997001i \(-0.475344\pi\)
0.0773823 + 0.997001i \(0.475344\pi\)
\(168\) 0 0
\(169\) −9.00000 −0.692308
\(170\) 2.00000 0.153393
\(171\) 0 0
\(172\) 1.00000 0.0762493
\(173\) 14.0000 1.06440 0.532200 0.846619i \(-0.321365\pi\)
0.532200 + 0.846619i \(0.321365\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) −1.00000 −0.0753778
\(177\) 0 0
\(178\) 6.00000 0.449719
\(179\) 7.00000 0.523205 0.261602 0.965176i \(-0.415749\pi\)
0.261602 + 0.965176i \(0.415749\pi\)
\(180\) 0 0
\(181\) 10.0000 0.743294 0.371647 0.928374i \(-0.378793\pi\)
0.371647 + 0.928374i \(0.378793\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) −1.00000 −0.0737210
\(185\) 10.0000 0.735215
\(186\) 0 0
\(187\) −1.00000 −0.0731272
\(188\) 7.00000 0.510527
\(189\) 0 0
\(190\) 6.00000 0.435286
\(191\) 8.00000 0.578860 0.289430 0.957199i \(-0.406534\pi\)
0.289430 + 0.957199i \(0.406534\pi\)
\(192\) 0 0
\(193\) 8.00000 0.575853 0.287926 0.957653i \(-0.407034\pi\)
0.287926 + 0.957653i \(0.407034\pi\)
\(194\) 7.00000 0.502571
\(195\) 0 0
\(196\) 0 0
\(197\) −27.0000 −1.92367 −0.961835 0.273629i \(-0.911776\pi\)
−0.961835 + 0.273629i \(0.911776\pi\)
\(198\) 0 0
\(199\) 2.00000 0.141776 0.0708881 0.997484i \(-0.477417\pi\)
0.0708881 + 0.997484i \(0.477417\pi\)
\(200\) 1.00000 0.0707107
\(201\) 0 0
\(202\) 9.00000 0.633238
\(203\) 0 0
\(204\) 0 0
\(205\) 20.0000 1.39686
\(206\) −6.00000 −0.418040
\(207\) 0 0
\(208\) −2.00000 −0.138675
\(209\) −3.00000 −0.207514
\(210\) 0 0
\(211\) 4.00000 0.275371 0.137686 0.990476i \(-0.456034\pi\)
0.137686 + 0.990476i \(0.456034\pi\)
\(212\) −12.0000 −0.824163
\(213\) 0 0
\(214\) −2.00000 −0.136717
\(215\) −2.00000 −0.136399
\(216\) 0 0
\(217\) 0 0
\(218\) 20.0000 1.35457
\(219\) 0 0
\(220\) 2.00000 0.134840
\(221\) −2.00000 −0.134535
\(222\) 0 0
\(223\) 26.0000 1.74109 0.870544 0.492090i \(-0.163767\pi\)
0.870544 + 0.492090i \(0.163767\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 10.0000 0.665190
\(227\) −10.0000 −0.663723 −0.331862 0.943328i \(-0.607677\pi\)
−0.331862 + 0.943328i \(0.607677\pi\)
\(228\) 0 0
\(229\) 10.0000 0.660819 0.330409 0.943838i \(-0.392813\pi\)
0.330409 + 0.943838i \(0.392813\pi\)
\(230\) 2.00000 0.131876
\(231\) 0 0
\(232\) −1.00000 −0.0656532
\(233\) 21.0000 1.37576 0.687878 0.725826i \(-0.258542\pi\)
0.687878 + 0.725826i \(0.258542\pi\)
\(234\) 0 0
\(235\) −14.0000 −0.913259
\(236\) −3.00000 −0.195283
\(237\) 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
\(241\) 12.0000 0.772988 0.386494 0.922292i \(-0.373686\pi\)
0.386494 + 0.922292i \(0.373686\pi\)
\(242\) −1.00000 −0.0642824
\(243\) 0 0
\(244\) 14.0000 0.896258
\(245\) 0 0
\(246\) 0 0
\(247\) −6.00000 −0.381771
\(248\) −2.00000 −0.127000
\(249\) 0 0
\(250\) −12.0000 −0.758947
\(251\) −21.0000 −1.32551 −0.662754 0.748837i \(-0.730613\pi\)
−0.662754 + 0.748837i \(0.730613\pi\)
\(252\) 0 0
\(253\) −1.00000 −0.0628695
\(254\) 1.00000 0.0627456
\(255\) 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
\(260\) 4.00000 0.248069
\(261\) 0 0
\(262\) 0 0
\(263\) 6.00000 0.369976 0.184988 0.982741i \(-0.440775\pi\)
0.184988 + 0.982741i \(0.440775\pi\)
\(264\) 0 0
\(265\) 24.0000 1.47431
\(266\) 0 0
\(267\) 0 0
\(268\) 12.0000 0.733017
\(269\) 12.0000 0.731653 0.365826 0.930683i \(-0.380786\pi\)
0.365826 + 0.930683i \(0.380786\pi\)
\(270\) 0 0
\(271\) −16.0000 −0.971931 −0.485965 0.873978i \(-0.661532\pi\)
−0.485965 + 0.873978i \(0.661532\pi\)
\(272\) 1.00000 0.0606339
\(273\) 0 0
\(274\) 6.00000 0.362473
\(275\) 1.00000 0.0603023
\(276\) 0 0
\(277\) −24.0000 −1.44202 −0.721010 0.692925i \(-0.756322\pi\)
−0.721010 + 0.692925i \(0.756322\pi\)
\(278\) −13.0000 −0.779688
\(279\) 0 0
\(280\) 0 0
\(281\) −7.00000 −0.417585 −0.208792 0.977960i \(-0.566953\pi\)
−0.208792 + 0.977960i \(0.566953\pi\)
\(282\) 0 0
\(283\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(284\) −5.00000 −0.296695
\(285\) 0 0
\(286\) −2.00000 −0.118262
\(287\) 0 0
\(288\) 0 0
\(289\) −16.0000 −0.941176
\(290\) 2.00000 0.117444
\(291\) 0 0
\(292\) 8.00000 0.468165
\(293\) 9.00000 0.525786 0.262893 0.964825i \(-0.415323\pi\)
0.262893 + 0.964825i \(0.415323\pi\)
\(294\) 0 0
\(295\) 6.00000 0.349334
\(296\) 5.00000 0.290619
\(297\) 0 0
\(298\) −11.0000 −0.637213
\(299\) −2.00000 −0.115663
\(300\) 0 0
\(301\) 0 0
\(302\) 15.0000 0.863153
\(303\) 0 0
\(304\) 3.00000 0.172062
\(305\) −28.0000 −1.60328
\(306\) 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
\(310\) 4.00000 0.227185
\(311\) 13.0000 0.737162 0.368581 0.929596i \(-0.379844\pi\)
0.368581 + 0.929596i \(0.379844\pi\)
\(312\) 0 0
\(313\) −7.00000 −0.395663 −0.197832 0.980236i \(-0.563390\pi\)
−0.197832 + 0.980236i \(0.563390\pi\)
\(314\) 1.00000 0.0564333
\(315\) 0 0
\(316\) 0 0
\(317\) −6.00000 −0.336994 −0.168497 0.985702i \(-0.553891\pi\)
−0.168497 + 0.985702i \(0.553891\pi\)
\(318\) 0 0
\(319\) −1.00000 −0.0559893
\(320\) −2.00000 −0.111803
\(321\) 0 0
\(322\) 0 0
\(323\) 3.00000 0.166924
\(324\) 0 0
\(325\) 2.00000 0.110940
\(326\) −10.0000 −0.553849
\(327\) 0 0
\(328\) 10.0000 0.552158
\(329\) 0 0
\(330\) 0 0
\(331\) −2.00000 −0.109930 −0.0549650 0.998488i \(-0.517505\pi\)
−0.0549650 + 0.998488i \(0.517505\pi\)
\(332\) −6.00000 −0.329293
\(333\) 0 0
\(334\) −2.00000 −0.109435
\(335\) −24.0000 −1.31126
\(336\) 0 0
\(337\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(338\) 9.00000 0.489535
\(339\) 0 0
\(340\) −2.00000 −0.108465
\(341\) −2.00000 −0.108306
\(342\) 0 0
\(343\) 0 0
\(344\) −1.00000 −0.0539164
\(345\) 0 0
\(346\) −14.0000 −0.752645
\(347\) 32.0000 1.71785 0.858925 0.512101i \(-0.171133\pi\)
0.858925 + 0.512101i \(0.171133\pi\)
\(348\) 0 0
\(349\) 16.0000 0.856460 0.428230 0.903670i \(-0.359137\pi\)
0.428230 + 0.903670i \(0.359137\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 1.00000 0.0533002
\(353\) −6.00000 −0.319348 −0.159674 0.987170i \(-0.551044\pi\)
−0.159674 + 0.987170i \(0.551044\pi\)
\(354\) 0 0
\(355\) 10.0000 0.530745
\(356\) −6.00000 −0.317999
\(357\) 0 0
\(358\) −7.00000 −0.369961
\(359\) −10.0000 −0.527780 −0.263890 0.964553i \(-0.585006\pi\)
−0.263890 + 0.964553i \(0.585006\pi\)
\(360\) 0 0
\(361\) −10.0000 −0.526316
\(362\) −10.0000 −0.525588
\(363\) 0 0
\(364\) 0 0
\(365\) −16.0000 −0.837478
\(366\) 0 0
\(367\) 32.0000 1.67039 0.835193 0.549957i \(-0.185356\pi\)
0.835193 + 0.549957i \(0.185356\pi\)
\(368\) 1.00000 0.0521286
\(369\) 0 0
\(370\) −10.0000 −0.519875
\(371\) 0 0
\(372\) 0 0
\(373\) 26.0000 1.34623 0.673114 0.739538i \(-0.264956\pi\)
0.673114 + 0.739538i \(0.264956\pi\)
\(374\) 1.00000 0.0517088
\(375\) 0 0
\(376\) −7.00000 −0.360997
\(377\) −2.00000 −0.103005
\(378\) 0 0
\(379\) −8.00000 −0.410932 −0.205466 0.978664i \(-0.565871\pi\)
−0.205466 + 0.978664i \(0.565871\pi\)
\(380\) −6.00000 −0.307794
\(381\) 0 0
\(382\) −8.00000 −0.409316
\(383\) 25.0000 1.27744 0.638720 0.769439i \(-0.279464\pi\)
0.638720 + 0.769439i \(0.279464\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) −8.00000 −0.407189
\(387\) 0 0
\(388\) −7.00000 −0.355371
\(389\) 30.0000 1.52106 0.760530 0.649303i \(-0.224939\pi\)
0.760530 + 0.649303i \(0.224939\pi\)
\(390\) 0 0
\(391\) 1.00000 0.0505722
\(392\) 0 0
\(393\) 0 0
\(394\) 27.0000 1.36024
\(395\) 0 0
\(396\) 0 0
\(397\) 27.0000 1.35509 0.677546 0.735481i \(-0.263044\pi\)
0.677546 + 0.735481i \(0.263044\pi\)
\(398\) −2.00000 −0.100251
\(399\) 0 0
\(400\) −1.00000 −0.0500000
\(401\) 24.0000 1.19850 0.599251 0.800561i \(-0.295465\pi\)
0.599251 + 0.800561i \(0.295465\pi\)
\(402\) 0 0
\(403\) −4.00000 −0.199254
\(404\) −9.00000 −0.447767
\(405\) 0 0
\(406\) 0 0
\(407\) 5.00000 0.247841
\(408\) 0 0
\(409\) −16.0000 −0.791149 −0.395575 0.918434i \(-0.629455\pi\)
−0.395575 + 0.918434i \(0.629455\pi\)
\(410\) −20.0000 −0.987730
\(411\) 0 0
\(412\) 6.00000 0.295599
\(413\) 0 0
\(414\) 0 0
\(415\) 12.0000 0.589057
\(416\) 2.00000 0.0980581
\(417\) 0 0
\(418\) 3.00000 0.146735
\(419\) 29.0000 1.41674 0.708371 0.705840i \(-0.249430\pi\)
0.708371 + 0.705840i \(0.249430\pi\)
\(420\) 0 0
\(421\) −17.0000 −0.828529 −0.414265 0.910156i \(-0.635961\pi\)
−0.414265 + 0.910156i \(0.635961\pi\)
\(422\) −4.00000 −0.194717
\(423\) 0 0
\(424\) 12.0000 0.582772
\(425\) −1.00000 −0.0485071
\(426\) 0 0
\(427\) 0 0
\(428\) 2.00000 0.0966736
\(429\) 0 0
\(430\) 2.00000 0.0964486
\(431\) 16.0000 0.770693 0.385346 0.922772i \(-0.374082\pi\)
0.385346 + 0.922772i \(0.374082\pi\)
\(432\) 0 0
\(433\) 19.0000 0.913082 0.456541 0.889702i \(-0.349088\pi\)
0.456541 + 0.889702i \(0.349088\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) −20.0000 −0.957826
\(437\) 3.00000 0.143509
\(438\) 0 0
\(439\) −31.0000 −1.47955 −0.739775 0.672855i \(-0.765068\pi\)
−0.739775 + 0.672855i \(0.765068\pi\)
\(440\) −2.00000 −0.0953463
\(441\) 0 0
\(442\) 2.00000 0.0951303
\(443\) −15.0000 −0.712672 −0.356336 0.934358i \(-0.615974\pi\)
−0.356336 + 0.934358i \(0.615974\pi\)
\(444\) 0 0
\(445\) 12.0000 0.568855
\(446\) −26.0000 −1.23114
\(447\) 0 0
\(448\) 0 0
\(449\) 12.0000 0.566315 0.283158 0.959073i \(-0.408618\pi\)
0.283158 + 0.959073i \(0.408618\pi\)
\(450\) 0 0
\(451\) 10.0000 0.470882
\(452\) −10.0000 −0.470360
\(453\) 0 0
\(454\) 10.0000 0.469323
\(455\) 0 0
\(456\) 0 0
\(457\) 32.0000 1.49690 0.748448 0.663193i \(-0.230799\pi\)
0.748448 + 0.663193i \(0.230799\pi\)
\(458\) −10.0000 −0.467269
\(459\) 0 0
\(460\) −2.00000 −0.0932505
\(461\) 33.0000 1.53696 0.768482 0.639872i \(-0.221013\pi\)
0.768482 + 0.639872i \(0.221013\pi\)
\(462\) 0 0
\(463\) 16.0000 0.743583 0.371792 0.928316i \(-0.378744\pi\)
0.371792 + 0.928316i \(0.378744\pi\)
\(464\) 1.00000 0.0464238
\(465\) 0 0
\(466\) −21.0000 −0.972806
\(467\) 27.0000 1.24941 0.624705 0.780860i \(-0.285219\pi\)
0.624705 + 0.780860i \(0.285219\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 14.0000 0.645772
\(471\) 0 0
\(472\) 3.00000 0.138086
\(473\) −1.00000 −0.0459800
\(474\) 0 0
\(475\) −3.00000 −0.137649
\(476\) 0 0
\(477\) 0 0
\(478\) −22.0000 −1.00626
\(479\) −26.0000 −1.18797 −0.593985 0.804476i \(-0.702446\pi\)
−0.593985 + 0.804476i \(0.702446\pi\)
\(480\) 0 0
\(481\) 10.0000 0.455961
\(482\) −12.0000 −0.546585
\(483\) 0 0
\(484\) 1.00000 0.0454545
\(485\) 14.0000 0.635707
\(486\) 0 0
\(487\) −34.0000 −1.54069 −0.770344 0.637629i \(-0.779915\pi\)
−0.770344 + 0.637629i \(0.779915\pi\)
\(488\) −14.0000 −0.633750
\(489\) 0 0
\(490\) 0 0
\(491\) 6.00000 0.270776 0.135388 0.990793i \(-0.456772\pi\)
0.135388 + 0.990793i \(0.456772\pi\)
\(492\) 0 0
\(493\) 1.00000 0.0450377
\(494\) 6.00000 0.269953
\(495\) 0 0
\(496\) 2.00000 0.0898027
\(497\) 0 0
\(498\) 0 0
\(499\) 8.00000 0.358129 0.179065 0.983837i \(-0.442693\pi\)
0.179065 + 0.983837i \(0.442693\pi\)
\(500\) 12.0000 0.536656
\(501\) 0 0
\(502\) 21.0000 0.937276
\(503\) −42.0000 −1.87269 −0.936344 0.351085i \(-0.885813\pi\)
−0.936344 + 0.351085i \(0.885813\pi\)
\(504\) 0 0
\(505\) 18.0000 0.800989
\(506\) 1.00000 0.0444554
\(507\) 0 0
\(508\) −1.00000 −0.0443678
\(509\) −20.0000 −0.886484 −0.443242 0.896402i \(-0.646172\pi\)
−0.443242 + 0.896402i \(0.646172\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) −1.00000 −0.0441942
\(513\) 0 0
\(514\) 6.00000 0.264649
\(515\) −12.0000 −0.528783
\(516\) 0 0
\(517\) −7.00000 −0.307860
\(518\) 0 0
\(519\) 0 0
\(520\) −4.00000 −0.175412
\(521\) 14.0000 0.613351 0.306676 0.951814i \(-0.400783\pi\)
0.306676 + 0.951814i \(0.400783\pi\)
\(522\) 0 0
\(523\) 4.00000 0.174908 0.0874539 0.996169i \(-0.472127\pi\)
0.0874539 + 0.996169i \(0.472127\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) −6.00000 −0.261612
\(527\) 2.00000 0.0871214
\(528\) 0 0
\(529\) −22.0000 −0.956522
\(530\) −24.0000 −1.04249
\(531\) 0 0
\(532\) 0 0
\(533\) 20.0000 0.866296
\(534\) 0 0
\(535\) −4.00000 −0.172935
\(536\) −12.0000 −0.518321
\(537\) 0 0
\(538\) −12.0000 −0.517357
\(539\) 0 0
\(540\) 0 0
\(541\) −16.0000 −0.687894 −0.343947 0.938989i \(-0.611764\pi\)
−0.343947 + 0.938989i \(0.611764\pi\)
\(542\) 16.0000 0.687259
\(543\) 0 0
\(544\) −1.00000 −0.0428746
\(545\) 40.0000 1.71341
\(546\) 0 0
\(547\) 39.0000 1.66752 0.833760 0.552127i \(-0.186184\pi\)
0.833760 + 0.552127i \(0.186184\pi\)
\(548\) −6.00000 −0.256307
\(549\) 0 0
\(550\) −1.00000 −0.0426401
\(551\) 3.00000 0.127804
\(552\) 0 0
\(553\) 0 0
\(554\) 24.0000 1.01966
\(555\) 0 0
\(556\) 13.0000 0.551323
\(557\) 35.0000 1.48300 0.741499 0.670954i \(-0.234115\pi\)
0.741499 + 0.670954i \(0.234115\pi\)
\(558\) 0 0
\(559\) −2.00000 −0.0845910
\(560\) 0 0
\(561\) 0 0
\(562\) 7.00000 0.295277
\(563\) −38.0000 −1.60151 −0.800755 0.598993i \(-0.795568\pi\)
−0.800755 + 0.598993i \(0.795568\pi\)
\(564\) 0 0
\(565\) 20.0000 0.841406
\(566\) 0 0
\(567\) 0 0
\(568\) 5.00000 0.209795
\(569\) 15.0000 0.628833 0.314416 0.949285i \(-0.398191\pi\)
0.314416 + 0.949285i \(0.398191\pi\)
\(570\) 0 0
\(571\) 7.00000 0.292941 0.146470 0.989215i \(-0.453209\pi\)
0.146470 + 0.989215i \(0.453209\pi\)
\(572\) 2.00000 0.0836242
\(573\) 0 0
\(574\) 0 0
\(575\) −1.00000 −0.0417029
\(576\) 0 0
\(577\) −14.0000 −0.582828 −0.291414 0.956597i \(-0.594126\pi\)
−0.291414 + 0.956597i \(0.594126\pi\)
\(578\) 16.0000 0.665512
\(579\) 0 0
\(580\) −2.00000 −0.0830455
\(581\) 0 0
\(582\) 0 0
\(583\) 12.0000 0.496989
\(584\) −8.00000 −0.331042
\(585\) 0 0
\(586\) −9.00000 −0.371787
\(587\) 12.0000 0.495293 0.247647 0.968850i \(-0.420343\pi\)
0.247647 + 0.968850i \(0.420343\pi\)
\(588\) 0 0
\(589\) 6.00000 0.247226
\(590\) −6.00000 −0.247016
\(591\) 0 0
\(592\) −5.00000 −0.205499
\(593\) 15.0000 0.615976 0.307988 0.951390i \(-0.400344\pi\)
0.307988 + 0.951390i \(0.400344\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 11.0000 0.450578
\(597\) 0 0
\(598\) 2.00000 0.0817861
\(599\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(600\) 0 0
\(601\) −8.00000 −0.326327 −0.163163 0.986599i \(-0.552170\pi\)
−0.163163 + 0.986599i \(0.552170\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) −15.0000 −0.610341
\(605\) −2.00000 −0.0813116
\(606\) 0 0
\(607\) 28.0000 1.13648 0.568242 0.822861i \(-0.307624\pi\)
0.568242 + 0.822861i \(0.307624\pi\)
\(608\) −3.00000 −0.121666
\(609\) 0 0
\(610\) 28.0000 1.13369
\(611\) −14.0000 −0.566379
\(612\) 0 0
\(613\) −14.0000 −0.565455 −0.282727 0.959200i \(-0.591239\pi\)
−0.282727 + 0.959200i \(0.591239\pi\)
\(614\) −4.00000 −0.161427
\(615\) 0 0
\(616\) 0 0
\(617\) −36.0000 −1.44931 −0.724653 0.689114i \(-0.758000\pi\)
−0.724653 + 0.689114i \(0.758000\pi\)
\(618\) 0 0
\(619\) −26.0000 −1.04503 −0.522514 0.852631i \(-0.675006\pi\)
−0.522514 + 0.852631i \(0.675006\pi\)
\(620\) −4.00000 −0.160644
\(621\) 0 0
\(622\) −13.0000 −0.521253
\(623\) 0 0
\(624\) 0 0
\(625\) −19.0000 −0.760000
\(626\) 7.00000 0.279776
\(627\) 0 0
\(628\) −1.00000 −0.0399043
\(629\) −5.00000 −0.199363
\(630\) 0 0
\(631\) 18.0000 0.716569 0.358284 0.933613i \(-0.383362\pi\)
0.358284 + 0.933613i \(0.383362\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 6.00000 0.238290
\(635\) 2.00000 0.0793676
\(636\) 0 0
\(637\) 0 0
\(638\) 1.00000 0.0395904
\(639\) 0 0
\(640\) 2.00000 0.0790569
\(641\) 12.0000 0.473972 0.236986 0.971513i \(-0.423841\pi\)
0.236986 + 0.971513i \(0.423841\pi\)
\(642\) 0 0
\(643\) 32.0000 1.26196 0.630978 0.775800i \(-0.282654\pi\)
0.630978 + 0.775800i \(0.282654\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) −3.00000 −0.118033
\(647\) 48.0000 1.88707 0.943537 0.331266i \(-0.107476\pi\)
0.943537 + 0.331266i \(0.107476\pi\)
\(648\) 0 0
\(649\) 3.00000 0.117760
\(650\) −2.00000 −0.0784465
\(651\) 0 0
\(652\) 10.0000 0.391630
\(653\) −14.0000 −0.547862 −0.273931 0.961749i \(-0.588324\pi\)
−0.273931 + 0.961749i \(0.588324\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) −10.0000 −0.390434
\(657\) 0 0
\(658\) 0 0
\(659\) −44.0000 −1.71400 −0.856998 0.515319i \(-0.827673\pi\)
−0.856998 + 0.515319i \(0.827673\pi\)
\(660\) 0 0
\(661\) −5.00000 −0.194477 −0.0972387 0.995261i \(-0.531001\pi\)
−0.0972387 + 0.995261i \(0.531001\pi\)
\(662\) 2.00000 0.0777322
\(663\) 0 0
\(664\) 6.00000 0.232845
\(665\) 0 0
\(666\) 0 0
\(667\) 1.00000 0.0387202
\(668\) 2.00000 0.0773823
\(669\) 0 0
\(670\) 24.0000 0.927201
\(671\) −14.0000 −0.540464
\(672\) 0 0
\(673\) 22.0000 0.848038 0.424019 0.905653i \(-0.360619\pi\)
0.424019 + 0.905653i \(0.360619\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) −9.00000 −0.346154
\(677\) 7.00000 0.269032 0.134516 0.990911i \(-0.457052\pi\)
0.134516 + 0.990911i \(0.457052\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 2.00000 0.0766965
\(681\) 0 0
\(682\) 2.00000 0.0765840
\(683\) 39.0000 1.49229 0.746147 0.665782i \(-0.231902\pi\)
0.746147 + 0.665782i \(0.231902\pi\)
\(684\) 0 0
\(685\) 12.0000 0.458496
\(686\) 0 0
\(687\) 0 0
\(688\) 1.00000 0.0381246
\(689\) 24.0000 0.914327
\(690\) 0 0
\(691\) 18.0000 0.684752 0.342376 0.939563i \(-0.388768\pi\)
0.342376 + 0.939563i \(0.388768\pi\)
\(692\) 14.0000 0.532200
\(693\) 0 0
\(694\) −32.0000 −1.21470
\(695\) −26.0000 −0.986236
\(696\) 0 0
\(697\) −10.0000 −0.378777
\(698\) −16.0000 −0.605609
\(699\) 0 0
\(700\) 0 0
\(701\) −9.00000 −0.339925 −0.169963 0.985451i \(-0.554365\pi\)
−0.169963 + 0.985451i \(0.554365\pi\)
\(702\) 0 0
\(703\) −15.0000 −0.565736
\(704\) −1.00000 −0.0376889
\(705\) 0 0
\(706\) 6.00000 0.225813
\(707\) 0 0
\(708\) 0 0
\(709\) 9.00000 0.338002 0.169001 0.985616i \(-0.445946\pi\)
0.169001 + 0.985616i \(0.445946\pi\)
\(710\) −10.0000 −0.375293
\(711\) 0 0
\(712\) 6.00000 0.224860
\(713\) 2.00000 0.0749006
\(714\) 0 0
\(715\) −4.00000 −0.149592
\(716\) 7.00000 0.261602
\(717\) 0 0
\(718\) 10.0000 0.373197
\(719\) 23.0000 0.857755 0.428878 0.903363i \(-0.358909\pi\)
0.428878 + 0.903363i \(0.358909\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) 10.0000 0.372161
\(723\) 0 0
\(724\) 10.0000 0.371647
\(725\) −1.00000 −0.0371391
\(726\) 0 0
\(727\) −14.0000 −0.519231 −0.259616 0.965712i \(-0.583596\pi\)
−0.259616 + 0.965712i \(0.583596\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 16.0000 0.592187
\(731\) 1.00000 0.0369863
\(732\) 0 0
\(733\) 10.0000 0.369358 0.184679 0.982799i \(-0.440875\pi\)
0.184679 + 0.982799i \(0.440875\pi\)
\(734\) −32.0000 −1.18114
\(735\) 0 0
\(736\) −1.00000 −0.0368605
\(737\) −12.0000 −0.442026
\(738\) 0 0
\(739\) 36.0000 1.32428 0.662141 0.749380i \(-0.269648\pi\)
0.662141 + 0.749380i \(0.269648\pi\)
\(740\) 10.0000 0.367607
\(741\) 0 0
\(742\) 0 0
\(743\) −36.0000 −1.32071 −0.660356 0.750953i \(-0.729595\pi\)
−0.660356 + 0.750953i \(0.729595\pi\)
\(744\) 0 0
\(745\) −22.0000 −0.806018
\(746\) −26.0000 −0.951928
\(747\) 0 0
\(748\) −1.00000 −0.0365636
\(749\) 0 0
\(750\) 0 0
\(751\) −32.0000 −1.16770 −0.583848 0.811863i \(-0.698454\pi\)
−0.583848 + 0.811863i \(0.698454\pi\)
\(752\) 7.00000 0.255264
\(753\) 0 0
\(754\) 2.00000 0.0728357
\(755\) 30.0000 1.09181
\(756\) 0 0
\(757\) 47.0000 1.70824 0.854122 0.520073i \(-0.174095\pi\)
0.854122 + 0.520073i \(0.174095\pi\)
\(758\) 8.00000 0.290573
\(759\) 0 0
\(760\) 6.00000 0.217643
\(761\) 18.0000 0.652499 0.326250 0.945284i \(-0.394215\pi\)
0.326250 + 0.945284i \(0.394215\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 8.00000 0.289430
\(765\) 0 0
\(766\) −25.0000 −0.903287
\(767\) 6.00000 0.216647
\(768\) 0 0
\(769\) 20.0000 0.721218 0.360609 0.932717i \(-0.382569\pi\)
0.360609 + 0.932717i \(0.382569\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 8.00000 0.287926
\(773\) 36.0000 1.29483 0.647415 0.762138i \(-0.275850\pi\)
0.647415 + 0.762138i \(0.275850\pi\)
\(774\) 0 0
\(775\) −2.00000 −0.0718421
\(776\) 7.00000 0.251285
\(777\) 0 0
\(778\) −30.0000 −1.07555
\(779\) −30.0000 −1.07486
\(780\) 0 0
\(781\) 5.00000 0.178914
\(782\) −1.00000 −0.0357599
\(783\) 0 0
\(784\) 0 0
\(785\) 2.00000 0.0713831
\(786\) 0 0
\(787\) 31.0000 1.10503 0.552515 0.833503i \(-0.313668\pi\)
0.552515 + 0.833503i \(0.313668\pi\)
\(788\) −27.0000 −0.961835
\(789\) 0 0
\(790\) 0 0
\(791\) 0 0
\(792\) 0 0
\(793\) −28.0000 −0.994309
\(794\) −27.0000 −0.958194
\(795\) 0 0
\(796\) 2.00000 0.0708881
\(797\) 22.0000 0.779280 0.389640 0.920967i \(-0.372599\pi\)
0.389640 + 0.920967i \(0.372599\pi\)
\(798\) 0 0
\(799\) 7.00000 0.247642
\(800\) 1.00000 0.0353553
\(801\) 0 0
\(802\) −24.0000 −0.847469
\(803\) −8.00000 −0.282314
\(804\) 0 0
\(805\) 0 0
\(806\) 4.00000 0.140894
\(807\) 0 0
\(808\) 9.00000 0.316619
\(809\) −18.0000 −0.632846 −0.316423 0.948618i \(-0.602482\pi\)
−0.316423 + 0.948618i \(0.602482\pi\)
\(810\) 0 0
\(811\) 28.0000 0.983213 0.491606 0.870817i \(-0.336410\pi\)
0.491606 + 0.870817i \(0.336410\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) −5.00000 −0.175250
\(815\) −20.0000 −0.700569
\(816\) 0 0
\(817\) 3.00000 0.104957
\(818\) 16.0000 0.559427
\(819\) 0 0
\(820\) 20.0000 0.698430
\(821\) 30.0000 1.04701 0.523504 0.852023i \(-0.324625\pi\)
0.523504 + 0.852023i \(0.324625\pi\)
\(822\) 0 0
\(823\) 44.0000 1.53374 0.766872 0.641800i \(-0.221812\pi\)
0.766872 + 0.641800i \(0.221812\pi\)
\(824\) −6.00000 −0.209020
\(825\) 0 0
\(826\) 0 0
\(827\) −34.0000 −1.18230 −0.591148 0.806563i \(-0.701325\pi\)
−0.591148 + 0.806563i \(0.701325\pi\)
\(828\) 0 0
\(829\) −7.00000 −0.243120 −0.121560 0.992584i \(-0.538790\pi\)
−0.121560 + 0.992584i \(0.538790\pi\)
\(830\) −12.0000 −0.416526
\(831\) 0 0
\(832\) −2.00000 −0.0693375
\(833\) 0 0
\(834\) 0 0
\(835\) −4.00000 −0.138426
\(836\) −3.00000 −0.103757
\(837\) 0 0
\(838\) −29.0000 −1.00179
\(839\) −24.0000 −0.828572 −0.414286 0.910147i \(-0.635969\pi\)
−0.414286 + 0.910147i \(0.635969\pi\)
\(840\) 0 0
\(841\) −28.0000 −0.965517
\(842\) 17.0000 0.585859
\(843\) 0 0
\(844\) 4.00000 0.137686
\(845\) 18.0000 0.619219
\(846\) 0 0
\(847\) 0 0
\(848\) −12.0000 −0.412082
\(849\) 0 0
\(850\) 1.00000 0.0342997
\(851\) −5.00000 −0.171398
\(852\) 0 0
\(853\) −14.0000 −0.479351 −0.239675 0.970853i \(-0.577041\pi\)
−0.239675 + 0.970853i \(0.577041\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) −2.00000 −0.0683586
\(857\) −47.0000 −1.60549 −0.802745 0.596323i \(-0.796628\pi\)
−0.802745 + 0.596323i \(0.796628\pi\)
\(858\) 0 0
\(859\) 26.0000 0.887109 0.443554 0.896248i \(-0.353717\pi\)
0.443554 + 0.896248i \(0.353717\pi\)
\(860\) −2.00000 −0.0681994
\(861\) 0 0
\(862\) −16.0000 −0.544962
\(863\) −44.0000 −1.49778 −0.748889 0.662696i \(-0.769412\pi\)
−0.748889 + 0.662696i \(0.769412\pi\)
\(864\) 0 0
\(865\) −28.0000 −0.952029
\(866\) −19.0000 −0.645646
\(867\) 0 0
\(868\) 0 0
\(869\) 0 0
\(870\) 0 0
\(871\) −24.0000 −0.813209
\(872\) 20.0000 0.677285
\(873\) 0 0
\(874\) −3.00000 −0.101477
\(875\) 0 0
\(876\) 0 0
\(877\) −14.0000 −0.472746 −0.236373 0.971662i \(-0.575959\pi\)
−0.236373 + 0.971662i \(0.575959\pi\)
\(878\) 31.0000 1.04620
\(879\) 0 0
\(880\) 2.00000 0.0674200
\(881\) 12.0000 0.404290 0.202145 0.979356i \(-0.435209\pi\)
0.202145 + 0.979356i \(0.435209\pi\)
\(882\) 0 0
\(883\) 40.0000 1.34611 0.673054 0.739594i \(-0.264982\pi\)
0.673054 + 0.739594i \(0.264982\pi\)
\(884\) −2.00000 −0.0672673
\(885\) 0 0
\(886\) 15.0000 0.503935
\(887\) 44.0000 1.47738 0.738688 0.674048i \(-0.235446\pi\)
0.738688 + 0.674048i \(0.235446\pi\)
\(888\) 0 0
\(889\) 0 0
\(890\) −12.0000 −0.402241
\(891\) 0 0
\(892\) 26.0000 0.870544
\(893\) 21.0000 0.702738
\(894\) 0 0
\(895\) −14.0000 −0.467968
\(896\) 0 0
\(897\) 0 0
\(898\) −12.0000 −0.400445
\(899\) 2.00000 0.0667037
\(900\) 0 0
\(901\) −12.0000 −0.399778
\(902\) −10.0000 −0.332964
\(903\) 0 0
\(904\) 10.0000 0.332595
\(905\) −20.0000 −0.664822
\(906\) 0 0
\(907\) −40.0000 −1.32818 −0.664089 0.747653i \(-0.731180\pi\)
−0.664089 + 0.747653i \(0.731180\pi\)
\(908\) −10.0000 −0.331862
\(909\) 0 0
\(910\) 0 0
\(911\) 45.0000 1.49092 0.745458 0.666552i \(-0.232231\pi\)
0.745458 + 0.666552i \(0.232231\pi\)
\(912\) 0 0
\(913\) 6.00000 0.198571
\(914\) −32.0000 −1.05847
\(915\) 0 0
\(916\) 10.0000 0.330409
\(917\) 0 0
\(918\) 0 0
\(919\) 57.0000 1.88026 0.940128 0.340821i \(-0.110705\pi\)
0.940128 + 0.340821i \(0.110705\pi\)
\(920\) 2.00000 0.0659380
\(921\) 0 0
\(922\) −33.0000 −1.08680
\(923\) 10.0000 0.329154
\(924\) 0 0
\(925\) 5.00000 0.164399
\(926\) −16.0000 −0.525793
\(927\) 0 0
\(928\) −1.00000 −0.0328266
\(929\) 36.0000 1.18112 0.590561 0.806993i \(-0.298907\pi\)
0.590561 + 0.806993i \(0.298907\pi\)
\(930\) 0 0
\(931\) 0 0
\(932\) 21.0000 0.687878
\(933\) 0 0
\(934\) −27.0000 −0.883467
\(935\) 2.00000 0.0654070
\(936\) 0 0
\(937\) −18.0000 −0.588034 −0.294017 0.955800i \(-0.594992\pi\)
−0.294017 + 0.955800i \(0.594992\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) −14.0000 −0.456630
\(941\) 35.0000 1.14097 0.570484 0.821309i \(-0.306756\pi\)
0.570484 + 0.821309i \(0.306756\pi\)
\(942\) 0 0
\(943\) −10.0000 −0.325645
\(944\) −3.00000 −0.0976417
\(945\) 0 0
\(946\) 1.00000 0.0325128
\(947\) 53.0000 1.72227 0.861134 0.508378i \(-0.169755\pi\)
0.861134 + 0.508378i \(0.169755\pi\)
\(948\) 0 0
\(949\) −16.0000 −0.519382
\(950\) 3.00000 0.0973329
\(951\) 0 0
\(952\) 0 0
\(953\) 26.0000 0.842223 0.421111 0.907009i \(-0.361640\pi\)
0.421111 + 0.907009i \(0.361640\pi\)
\(954\) 0 0
\(955\) −16.0000 −0.517748
\(956\) 22.0000 0.711531
\(957\) 0 0
\(958\) 26.0000 0.840022
\(959\) 0 0
\(960\) 0 0
\(961\) −27.0000 −0.870968
\(962\) −10.0000 −0.322413
\(963\) 0 0
\(964\) 12.0000 0.386494
\(965\) −16.0000 −0.515058
\(966\) 0 0
\(967\) −1.00000 −0.0321578 −0.0160789 0.999871i \(-0.505118\pi\)
−0.0160789 + 0.999871i \(0.505118\pi\)
\(968\) −1.00000 −0.0321412
\(969\) 0 0
\(970\) −14.0000 −0.449513
\(971\) 4.00000 0.128366 0.0641831 0.997938i \(-0.479556\pi\)
0.0641831 + 0.997938i \(0.479556\pi\)
\(972\) 0 0
\(973\) 0 0
\(974\) 34.0000 1.08943
\(975\) 0 0
\(976\) 14.0000 0.448129
\(977\) −28.0000 −0.895799 −0.447900 0.894084i \(-0.647828\pi\)
−0.447900 + 0.894084i \(0.647828\pi\)
\(978\) 0 0
\(979\) 6.00000 0.191761
\(980\) 0 0
\(981\) 0 0
\(982\) −6.00000 −0.191468
\(983\) 39.0000 1.24391 0.621953 0.783054i \(-0.286339\pi\)
0.621953 + 0.783054i \(0.286339\pi\)
\(984\) 0 0
\(985\) 54.0000 1.72058
\(986\) −1.00000 −0.0318465
\(987\) 0 0
\(988\) −6.00000 −0.190885
\(989\) 1.00000 0.0317982
\(990\) 0 0
\(991\) 16.0000 0.508257 0.254128 0.967170i \(-0.418211\pi\)
0.254128 + 0.967170i \(0.418211\pi\)
\(992\) −2.00000 −0.0635001
\(993\) 0 0
\(994\) 0 0
\(995\) −4.00000 −0.126809
\(996\) 0 0
\(997\) 42.0000 1.33015 0.665077 0.746775i \(-0.268399\pi\)
0.665077 + 0.746775i \(0.268399\pi\)
\(998\) −8.00000 −0.253236
\(999\) 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 9702.2.a.f.1.1 1
3.2 odd 2 9702.2.a.ca.1.1 1
7.3 odd 6 1386.2.k.l.793.1 yes 2
7.5 odd 6 1386.2.k.l.991.1 yes 2
7.6 odd 2 9702.2.a.s.1.1 1
21.5 even 6 1386.2.k.h.991.1 yes 2
21.17 even 6 1386.2.k.h.793.1 2
21.20 even 2 9702.2.a.bi.1.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1386.2.k.h.793.1 2 21.17 even 6
1386.2.k.h.991.1 yes 2 21.5 even 6
1386.2.k.l.793.1 yes 2 7.3 odd 6
1386.2.k.l.991.1 yes 2 7.5 odd 6
9702.2.a.f.1.1 1 1.1 even 1 trivial
9702.2.a.s.1.1 1 7.6 odd 2
9702.2.a.bi.1.1 1 21.20 even 2
9702.2.a.ca.1.1 1 3.2 odd 2