Properties

Label 9702.2.a.ca.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 \(-0.352416\pi\)
0.447214 + 0.894427i \(0.352416\pi\)
\(6\) 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 \(-0.538696\pi\)
−0.121268 + 0.992620i \(0.538696\pi\)
\(18\) 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 \(-0.533247\pi\)
−0.104257 + 0.994550i \(0.533247\pi\)
\(24\) 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 \(-0.529597\pi\)
−0.0928477 + 0.995680i \(0.529597\pi\)
\(30\) 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 \(-0.214777\pi\)
0.780869 + 0.624695i \(0.214777\pi\)
\(42\) 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 \(-0.670550\pi\)
−0.510527 + 0.859861i \(0.670550\pi\)
\(48\) 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 \(-0.191646\pi\)
0.824163 + 0.566352i \(0.191646\pi\)
\(54\) 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 \(-0.437437\pi\)
0.195283 + 0.980747i \(0.437437\pi\)
\(60\) 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 \(-0.404115\pi\)
0.296695 + 0.954972i \(0.404115\pi\)
\(72\) 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 \(-0.393190\pi\)
0.329293 + 0.944228i \(0.393190\pi\)
\(84\) 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 \(-0.396989\pi\)
0.317999 + 0.948091i \(0.396989\pi\)
\(90\) 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 \(-0.352219\pi\)
0.447767 + 0.894150i \(0.352219\pi\)
\(102\) 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 \(-0.530820\pi\)
−0.0966736 + 0.995316i \(0.530820\pi\)
\(108\) 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 \(-0.344124\pi\)
0.470360 + 0.882474i \(0.344124\pi\)
\(114\) 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 \(-0.417494\pi\)
0.256307 + 0.966595i \(0.417494\pi\)
\(138\) 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 \(-0.648782\pi\)
−0.450578 + 0.892737i \(0.648782\pi\)
\(150\) 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 \(-0.524656\pi\)
−0.0773823 + 0.997001i \(0.524656\pi\)
\(168\) 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 \(-0.678635\pi\)
−0.532200 + 0.846619i \(0.678635\pi\)
\(174\) 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 \(-0.584251\pi\)
−0.261602 + 0.965176i \(0.584251\pi\)
\(180\) 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 \(-0.593466\pi\)
−0.289430 + 0.957199i \(0.593466\pi\)
\(192\) 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 \(-0.0882242\pi\)
0.961835 + 0.273629i \(0.0882242\pi\)
\(198\) 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 \(-0.392323\pi\)
0.331862 + 0.943328i \(0.392323\pi\)
\(228\) 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 \(-0.741458\pi\)
−0.687878 + 0.725826i \(0.741458\pi\)
\(234\) 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 \(-0.751998\pi\)
−0.711531 + 0.702655i \(0.751998\pi\)
\(240\) 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 \(-0.269387\pi\)
0.662754 + 0.748837i \(0.269387\pi\)
\(252\) 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 \(-0.440080\pi\)
0.187135 + 0.982334i \(0.440080\pi\)
\(258\) 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 \(-0.559225\pi\)
−0.184988 + 0.982741i \(0.559225\pi\)
\(264\) 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 \(-0.619214\pi\)
−0.365826 + 0.930683i \(0.619214\pi\)
\(270\) 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 \(-0.433047\pi\)
0.208792 + 0.977960i \(0.433047\pi\)
\(282\) 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 \(-0.584677\pi\)
−0.262893 + 0.964825i \(0.584677\pi\)
\(294\) 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 \(-0.620156\pi\)
−0.368581 + 0.929596i \(0.620156\pi\)
\(312\) 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 \(-0.446109\pi\)
0.168497 + 0.985702i \(0.446109\pi\)
\(318\) 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 \(-0.828867\pi\)
−0.858925 + 0.512101i \(0.828867\pi\)
\(348\) 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 \(-0.448956\pi\)
0.159674 + 0.987170i \(0.448956\pi\)
\(354\) 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 \(-0.414994\pi\)
0.263890 + 0.964553i \(0.414994\pi\)
\(360\) 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 \(-0.720536\pi\)
−0.638720 + 0.769439i \(0.720536\pi\)
\(384\) 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 \(-0.775061\pi\)
−0.760530 + 0.649303i \(0.775061\pi\)
\(390\) 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 \(-0.704535\pi\)
−0.599251 + 0.800561i \(0.704535\pi\)
\(402\) 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 \(-0.750570\pi\)
−0.708371 + 0.705840i \(0.750570\pi\)
\(420\) 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 \(-0.625918\pi\)
−0.385346 + 0.922772i \(0.625918\pi\)
\(432\) 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 \(-0.384026\pi\)
0.356336 + 0.934358i \(0.384026\pi\)
\(444\) 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 \(-0.591382\pi\)
−0.283158 + 0.959073i \(0.591382\pi\)
\(450\) 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 \(-0.778987\pi\)
−0.768482 + 0.639872i \(0.778987\pi\)
\(462\) 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 \(-0.714781\pi\)
−0.624705 + 0.780860i \(0.714781\pi\)
\(468\) 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 \(-0.297554\pi\)
0.593985 + 0.804476i \(0.297554\pi\)
\(480\) 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 \(-0.543228\pi\)
−0.135388 + 0.990793i \(0.543228\pi\)
\(492\) 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 \(-0.114187\pi\)
0.936344 + 0.351085i \(0.114187\pi\)
\(504\) 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 \(-0.353828\pi\)
0.443242 + 0.896402i \(0.353828\pi\)
\(510\) 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 \(-0.599217\pi\)
−0.306676 + 0.951814i \(0.599217\pi\)
\(522\) 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 \(-0.765885\pi\)
−0.741499 + 0.670954i \(0.765885\pi\)
\(558\) 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 \(-0.204432\pi\)
0.800755 + 0.598993i \(0.204432\pi\)
\(564\) 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 \(-0.601809\pi\)
−0.314416 + 0.949285i \(0.601809\pi\)
\(570\) 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 \(-0.579657\pi\)
−0.247647 + 0.968850i \(0.579657\pi\)
\(588\) 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 \(-0.599656\pi\)
−0.307988 + 0.951390i \(0.599656\pi\)
\(594\) 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 \(-0.242000\pi\)
0.724653 + 0.689114i \(0.242000\pi\)
\(618\) 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 \(-0.576159\pi\)
−0.236986 + 0.971513i \(0.576159\pi\)
\(642\) 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 \(-0.892524\pi\)
−0.943537 + 0.331266i \(0.892524\pi\)
\(648\) 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 \(-0.411676\pi\)
0.273931 + 0.961749i \(0.411676\pi\)
\(654\) 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 \(-0.172327\pi\)
0.856998 + 0.515319i \(0.172327\pi\)
\(660\) 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 \(-0.542948\pi\)
−0.134516 + 0.990911i \(0.542948\pi\)
\(678\) 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 \(-0.768098\pi\)
−0.746147 + 0.665782i \(0.768098\pi\)
\(684\) 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 \(-0.445635\pi\)
0.169963 + 0.985451i \(0.445635\pi\)
\(702\) 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 \(-0.641091\pi\)
−0.428878 + 0.903363i \(0.641091\pi\)
\(720\) 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 \(-0.270405\pi\)
0.660356 + 0.750953i \(0.270405\pi\)
\(744\) 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 \(-0.605785\pi\)
−0.326250 + 0.945284i \(0.605785\pi\)
\(762\) 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 \(-0.724150\pi\)
−0.647415 + 0.762138i \(0.724150\pi\)
\(774\) 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 \(-0.627401\pi\)
−0.389640 + 0.920967i \(0.627401\pi\)
\(798\) 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 \(-0.397518\pi\)
0.316423 + 0.948618i \(0.397518\pi\)
\(810\) 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 \(-0.675375\pi\)
−0.523504 + 0.852023i \(0.675375\pi\)
\(822\) 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 \(-0.298675\pi\)
0.591148 + 0.806563i \(0.298675\pi\)
\(828\) 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 \(-0.364031\pi\)
0.414286 + 0.910147i \(0.364031\pi\)
\(840\) 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 \(-0.203372\pi\)
0.802745 + 0.596323i \(0.203372\pi\)
\(858\) 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 \(-0.230588\pi\)
0.748889 + 0.662696i \(0.230588\pi\)
\(864\) 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 \(-0.564791\pi\)
−0.202145 + 0.979356i \(0.564791\pi\)
\(882\) 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 \(-0.764554\pi\)
−0.738688 + 0.674048i \(0.764554\pi\)
\(888\) 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 \(-0.767769\pi\)
−0.745458 + 0.666552i \(0.767769\pi\)
\(912\) 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 \(-0.701093\pi\)
−0.590561 + 0.806993i \(0.701093\pi\)
\(930\) 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 \(-0.693244\pi\)
−0.570484 + 0.821309i \(0.693244\pi\)
\(942\) 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 \(-0.830245\pi\)
−0.861134 + 0.508378i \(0.830245\pi\)
\(948\) 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 \(-0.638360\pi\)
−0.421111 + 0.907009i \(0.638360\pi\)
\(954\) 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 \(-0.520444\pi\)
−0.0641831 + 0.997938i \(0.520444\pi\)
\(972\) 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 \(-0.352172\pi\)
0.447900 + 0.894084i \(0.352172\pi\)
\(978\) 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 \(-0.713661\pi\)
−0.621953 + 0.783054i \(0.713661\pi\)
\(984\) 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.ca.1.1 1
3.2 odd 2 9702.2.a.f.1.1 1
7.3 odd 6 1386.2.k.h.793.1 2
7.5 odd 6 1386.2.k.h.991.1 yes 2
7.6 odd 2 9702.2.a.bi.1.1 1
21.5 even 6 1386.2.k.l.991.1 yes 2
21.17 even 6 1386.2.k.l.793.1 yes 2
21.20 even 2 9702.2.a.s.1.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1386.2.k.h.793.1 2 7.3 odd 6
1386.2.k.h.991.1 yes 2 7.5 odd 6
1386.2.k.l.793.1 yes 2 21.17 even 6
1386.2.k.l.991.1 yes 2 21.5 even 6
9702.2.a.f.1.1 1 3.2 odd 2
9702.2.a.s.1.1 1 21.20 even 2
9702.2.a.bi.1.1 1 7.6 odd 2
9702.2.a.ca.1.1 1 1.1 even 1 trivial