Properties

Label 9702.2.a.b.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 462)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

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

$q$-expansion

\(f(q)\) \(=\) \(q-1.00000 q^{2} +1.00000 q^{4} -4.00000 q^{5} -1.00000 q^{8} +O(q^{10})\) \(q-1.00000 q^{2} +1.00000 q^{4} -4.00000 q^{5} -1.00000 q^{8} +4.00000 q^{10} +1.00000 q^{11} +6.00000 q^{13} +1.00000 q^{16} -4.00000 q^{17} +2.00000 q^{19} -4.00000 q^{20} -1.00000 q^{22} +8.00000 q^{23} +11.0000 q^{25} -6.00000 q^{26} +6.00000 q^{29} -6.00000 q^{31} -1.00000 q^{32} +4.00000 q^{34} -6.00000 q^{37} -2.00000 q^{38} +4.00000 q^{40} +12.0000 q^{41} +4.00000 q^{43} +1.00000 q^{44} -8.00000 q^{46} +6.00000 q^{47} -11.0000 q^{50} +6.00000 q^{52} -2.00000 q^{53} -4.00000 q^{55} -6.00000 q^{58} -10.0000 q^{61} +6.00000 q^{62} +1.00000 q^{64} -24.0000 q^{65} +4.00000 q^{67} -4.00000 q^{68} +12.0000 q^{71} +6.00000 q^{74} +2.00000 q^{76} -16.0000 q^{79} -4.00000 q^{80} -12.0000 q^{82} -14.0000 q^{83} +16.0000 q^{85} -4.00000 q^{86} -1.00000 q^{88} -14.0000 q^{89} +8.00000 q^{92} -6.00000 q^{94} -8.00000 q^{95} +14.0000 q^{97} +O(q^{100})\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.00000 −0.707107
\(3\) 0 0
\(4\) 1.00000 0.500000
\(5\) −4.00000 −1.78885 −0.894427 0.447214i \(-0.852416\pi\)
−0.894427 + 0.447214i \(0.852416\pi\)
\(6\) 0 0
\(7\) 0 0
\(8\) −1.00000 −0.353553
\(9\) 0 0
\(10\) 4.00000 1.26491
\(11\) 1.00000 0.301511
\(12\) 0 0
\(13\) 6.00000 1.66410 0.832050 0.554700i \(-0.187167\pi\)
0.832050 + 0.554700i \(0.187167\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 1.00000 0.250000
\(17\) −4.00000 −0.970143 −0.485071 0.874475i \(-0.661206\pi\)
−0.485071 + 0.874475i \(0.661206\pi\)
\(18\) 0 0
\(19\) 2.00000 0.458831 0.229416 0.973329i \(-0.426318\pi\)
0.229416 + 0.973329i \(0.426318\pi\)
\(20\) −4.00000 −0.894427
\(21\) 0 0
\(22\) −1.00000 −0.213201
\(23\) 8.00000 1.66812 0.834058 0.551677i \(-0.186012\pi\)
0.834058 + 0.551677i \(0.186012\pi\)
\(24\) 0 0
\(25\) 11.0000 2.20000
\(26\) −6.00000 −1.17670
\(27\) 0 0
\(28\) 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 \(-0.681128\pi\)
−0.538816 + 0.842424i \(0.681128\pi\)
\(32\) −1.00000 −0.176777
\(33\) 0 0
\(34\) 4.00000 0.685994
\(35\) 0 0
\(36\) 0 0
\(37\) −6.00000 −0.986394 −0.493197 0.869918i \(-0.664172\pi\)
−0.493197 + 0.869918i \(0.664172\pi\)
\(38\) −2.00000 −0.324443
\(39\) 0 0
\(40\) 4.00000 0.632456
\(41\) 12.0000 1.87409 0.937043 0.349215i \(-0.113552\pi\)
0.937043 + 0.349215i \(0.113552\pi\)
\(42\) 0 0
\(43\) 4.00000 0.609994 0.304997 0.952353i \(-0.401344\pi\)
0.304997 + 0.952353i \(0.401344\pi\)
\(44\) 1.00000 0.150756
\(45\) 0 0
\(46\) −8.00000 −1.17954
\(47\) 6.00000 0.875190 0.437595 0.899172i \(-0.355830\pi\)
0.437595 + 0.899172i \(0.355830\pi\)
\(48\) 0 0
\(49\) 0 0
\(50\) −11.0000 −1.55563
\(51\) 0 0
\(52\) 6.00000 0.832050
\(53\) −2.00000 −0.274721 −0.137361 0.990521i \(-0.543862\pi\)
−0.137361 + 0.990521i \(0.543862\pi\)
\(54\) 0 0
\(55\) −4.00000 −0.539360
\(56\) 0 0
\(57\) 0 0
\(58\) −6.00000 −0.787839
\(59\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(60\) 0 0
\(61\) −10.0000 −1.28037 −0.640184 0.768221i \(-0.721142\pi\)
−0.640184 + 0.768221i \(0.721142\pi\)
\(62\) 6.00000 0.762001
\(63\) 0 0
\(64\) 1.00000 0.125000
\(65\) −24.0000 −2.97683
\(66\) 0 0
\(67\) 4.00000 0.488678 0.244339 0.969690i \(-0.421429\pi\)
0.244339 + 0.969690i \(0.421429\pi\)
\(68\) −4.00000 −0.485071
\(69\) 0 0
\(70\) 0 0
\(71\) 12.0000 1.42414 0.712069 0.702109i \(-0.247758\pi\)
0.712069 + 0.702109i \(0.247758\pi\)
\(72\) 0 0
\(73\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(74\) 6.00000 0.697486
\(75\) 0 0
\(76\) 2.00000 0.229416
\(77\) 0 0
\(78\) 0 0
\(79\) −16.0000 −1.80014 −0.900070 0.435745i \(-0.856485\pi\)
−0.900070 + 0.435745i \(0.856485\pi\)
\(80\) −4.00000 −0.447214
\(81\) 0 0
\(82\) −12.0000 −1.32518
\(83\) −14.0000 −1.53670 −0.768350 0.640030i \(-0.778922\pi\)
−0.768350 + 0.640030i \(0.778922\pi\)
\(84\) 0 0
\(85\) 16.0000 1.73544
\(86\) −4.00000 −0.431331
\(87\) 0 0
\(88\) −1.00000 −0.106600
\(89\) −14.0000 −1.48400 −0.741999 0.670402i \(-0.766122\pi\)
−0.741999 + 0.670402i \(0.766122\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 8.00000 0.834058
\(93\) 0 0
\(94\) −6.00000 −0.618853
\(95\) −8.00000 −0.820783
\(96\) 0 0
\(97\) 14.0000 1.42148 0.710742 0.703452i \(-0.248359\pi\)
0.710742 + 0.703452i \(0.248359\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 11.0000 1.10000
\(101\) 14.0000 1.39305 0.696526 0.717532i \(-0.254728\pi\)
0.696526 + 0.717532i \(0.254728\pi\)
\(102\) 0 0
\(103\) 6.00000 0.591198 0.295599 0.955312i \(-0.404481\pi\)
0.295599 + 0.955312i \(0.404481\pi\)
\(104\) −6.00000 −0.588348
\(105\) 0 0
\(106\) 2.00000 0.194257
\(107\) 8.00000 0.773389 0.386695 0.922208i \(-0.373617\pi\)
0.386695 + 0.922208i \(0.373617\pi\)
\(108\) 0 0
\(109\) 6.00000 0.574696 0.287348 0.957826i \(-0.407226\pi\)
0.287348 + 0.957826i \(0.407226\pi\)
\(110\) 4.00000 0.381385
\(111\) 0 0
\(112\) 0 0
\(113\) −14.0000 −1.31701 −0.658505 0.752577i \(-0.728811\pi\)
−0.658505 + 0.752577i \(0.728811\pi\)
\(114\) 0 0
\(115\) −32.0000 −2.98402
\(116\) 6.00000 0.557086
\(117\) 0 0
\(118\) 0 0
\(119\) 0 0
\(120\) 0 0
\(121\) 1.00000 0.0909091
\(122\) 10.0000 0.905357
\(123\) 0 0
\(124\) −6.00000 −0.538816
\(125\) −24.0000 −2.14663
\(126\) 0 0
\(127\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(128\) −1.00000 −0.0883883
\(129\) 0 0
\(130\) 24.0000 2.10494
\(131\) −2.00000 −0.174741 −0.0873704 0.996176i \(-0.527846\pi\)
−0.0873704 + 0.996176i \(0.527846\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) −4.00000 −0.345547
\(135\) 0 0
\(136\) 4.00000 0.342997
\(137\) −14.0000 −1.19610 −0.598050 0.801459i \(-0.704058\pi\)
−0.598050 + 0.801459i \(0.704058\pi\)
\(138\) 0 0
\(139\) −2.00000 −0.169638 −0.0848189 0.996396i \(-0.527031\pi\)
−0.0848189 + 0.996396i \(0.527031\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) −12.0000 −1.00702
\(143\) 6.00000 0.501745
\(144\) 0 0
\(145\) −24.0000 −1.99309
\(146\) 0 0
\(147\) 0 0
\(148\) −6.00000 −0.493197
\(149\) 10.0000 0.819232 0.409616 0.912258i \(-0.365663\pi\)
0.409616 + 0.912258i \(0.365663\pi\)
\(150\) 0 0
\(151\) −8.00000 −0.651031 −0.325515 0.945537i \(-0.605538\pi\)
−0.325515 + 0.945537i \(0.605538\pi\)
\(152\) −2.00000 −0.162221
\(153\) 0 0
\(154\) 0 0
\(155\) 24.0000 1.92773
\(156\) 0 0
\(157\) 4.00000 0.319235 0.159617 0.987179i \(-0.448974\pi\)
0.159617 + 0.987179i \(0.448974\pi\)
\(158\) 16.0000 1.27289
\(159\) 0 0
\(160\) 4.00000 0.316228
\(161\) 0 0
\(162\) 0 0
\(163\) 4.00000 0.313304 0.156652 0.987654i \(-0.449930\pi\)
0.156652 + 0.987654i \(0.449930\pi\)
\(164\) 12.0000 0.937043
\(165\) 0 0
\(166\) 14.0000 1.08661
\(167\) −12.0000 −0.928588 −0.464294 0.885681i \(-0.653692\pi\)
−0.464294 + 0.885681i \(0.653692\pi\)
\(168\) 0 0
\(169\) 23.0000 1.76923
\(170\) −16.0000 −1.22714
\(171\) 0 0
\(172\) 4.00000 0.304997
\(173\) 2.00000 0.152057 0.0760286 0.997106i \(-0.475776\pi\)
0.0760286 + 0.997106i \(0.475776\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 1.00000 0.0753778
\(177\) 0 0
\(178\) 14.0000 1.04934
\(179\) 4.00000 0.298974 0.149487 0.988764i \(-0.452238\pi\)
0.149487 + 0.988764i \(0.452238\pi\)
\(180\) 0 0
\(181\) 8.00000 0.594635 0.297318 0.954779i \(-0.403908\pi\)
0.297318 + 0.954779i \(0.403908\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) −8.00000 −0.589768
\(185\) 24.0000 1.76452
\(186\) 0 0
\(187\) −4.00000 −0.292509
\(188\) 6.00000 0.437595
\(189\) 0 0
\(190\) 8.00000 0.580381
\(191\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(192\) 0 0
\(193\) −14.0000 −1.00774 −0.503871 0.863779i \(-0.668091\pi\)
−0.503871 + 0.863779i \(0.668091\pi\)
\(194\) −14.0000 −1.00514
\(195\) 0 0
\(196\) 0 0
\(197\) −10.0000 −0.712470 −0.356235 0.934396i \(-0.615940\pi\)
−0.356235 + 0.934396i \(0.615940\pi\)
\(198\) 0 0
\(199\) −2.00000 −0.141776 −0.0708881 0.997484i \(-0.522583\pi\)
−0.0708881 + 0.997484i \(0.522583\pi\)
\(200\) −11.0000 −0.777817
\(201\) 0 0
\(202\) −14.0000 −0.985037
\(203\) 0 0
\(204\) 0 0
\(205\) −48.0000 −3.35247
\(206\) −6.00000 −0.418040
\(207\) 0 0
\(208\) 6.00000 0.416025
\(209\) 2.00000 0.138343
\(210\) 0 0
\(211\) −4.00000 −0.275371 −0.137686 0.990476i \(-0.543966\pi\)
−0.137686 + 0.990476i \(0.543966\pi\)
\(212\) −2.00000 −0.137361
\(213\) 0 0
\(214\) −8.00000 −0.546869
\(215\) −16.0000 −1.09119
\(216\) 0 0
\(217\) 0 0
\(218\) −6.00000 −0.406371
\(219\) 0 0
\(220\) −4.00000 −0.269680
\(221\) −24.0000 −1.61441
\(222\) 0 0
\(223\) −6.00000 −0.401790 −0.200895 0.979613i \(-0.564385\pi\)
−0.200895 + 0.979613i \(0.564385\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 14.0000 0.931266
\(227\) 6.00000 0.398234 0.199117 0.979976i \(-0.436193\pi\)
0.199117 + 0.979976i \(0.436193\pi\)
\(228\) 0 0
\(229\) −8.00000 −0.528655 −0.264327 0.964433i \(-0.585150\pi\)
−0.264327 + 0.964433i \(0.585150\pi\)
\(230\) 32.0000 2.11002
\(231\) 0 0
\(232\) −6.00000 −0.393919
\(233\) 14.0000 0.917170 0.458585 0.888650i \(-0.348356\pi\)
0.458585 + 0.888650i \(0.348356\pi\)
\(234\) 0 0
\(235\) −24.0000 −1.56559
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) 16.0000 1.03495 0.517477 0.855697i \(-0.326871\pi\)
0.517477 + 0.855697i \(0.326871\pi\)
\(240\) 0 0
\(241\) 8.00000 0.515325 0.257663 0.966235i \(-0.417048\pi\)
0.257663 + 0.966235i \(0.417048\pi\)
\(242\) −1.00000 −0.0642824
\(243\) 0 0
\(244\) −10.0000 −0.640184
\(245\) 0 0
\(246\) 0 0
\(247\) 12.0000 0.763542
\(248\) 6.00000 0.381000
\(249\) 0 0
\(250\) 24.0000 1.51789
\(251\) −16.0000 −1.00991 −0.504956 0.863145i \(-0.668491\pi\)
−0.504956 + 0.863145i \(0.668491\pi\)
\(252\) 0 0
\(253\) 8.00000 0.502956
\(254\) 0 0
\(255\) 0 0
\(256\) 1.00000 0.0625000
\(257\) 26.0000 1.62184 0.810918 0.585160i \(-0.198968\pi\)
0.810918 + 0.585160i \(0.198968\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) −24.0000 −1.48842
\(261\) 0 0
\(262\) 2.00000 0.123560
\(263\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(264\) 0 0
\(265\) 8.00000 0.491436
\(266\) 0 0
\(267\) 0 0
\(268\) 4.00000 0.244339
\(269\) −4.00000 −0.243884 −0.121942 0.992537i \(-0.538912\pi\)
−0.121942 + 0.992537i \(0.538912\pi\)
\(270\) 0 0
\(271\) 4.00000 0.242983 0.121491 0.992592i \(-0.461232\pi\)
0.121491 + 0.992592i \(0.461232\pi\)
\(272\) −4.00000 −0.242536
\(273\) 0 0
\(274\) 14.0000 0.845771
\(275\) 11.0000 0.663325
\(276\) 0 0
\(277\) −10.0000 −0.600842 −0.300421 0.953807i \(-0.597127\pi\)
−0.300421 + 0.953807i \(0.597127\pi\)
\(278\) 2.00000 0.119952
\(279\) 0 0
\(280\) 0 0
\(281\) −26.0000 −1.55103 −0.775515 0.631329i \(-0.782510\pi\)
−0.775515 + 0.631329i \(0.782510\pi\)
\(282\) 0 0
\(283\) 14.0000 0.832214 0.416107 0.909316i \(-0.363394\pi\)
0.416107 + 0.909316i \(0.363394\pi\)
\(284\) 12.0000 0.712069
\(285\) 0 0
\(286\) −6.00000 −0.354787
\(287\) 0 0
\(288\) 0 0
\(289\) −1.00000 −0.0588235
\(290\) 24.0000 1.40933
\(291\) 0 0
\(292\) 0 0
\(293\) −14.0000 −0.817889 −0.408944 0.912559i \(-0.634103\pi\)
−0.408944 + 0.912559i \(0.634103\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 6.00000 0.348743
\(297\) 0 0
\(298\) −10.0000 −0.579284
\(299\) 48.0000 2.77591
\(300\) 0 0
\(301\) 0 0
\(302\) 8.00000 0.460348
\(303\) 0 0
\(304\) 2.00000 0.114708
\(305\) 40.0000 2.29039
\(306\) 0 0
\(307\) 14.0000 0.799022 0.399511 0.916728i \(-0.369180\pi\)
0.399511 + 0.916728i \(0.369180\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) −24.0000 −1.36311
\(311\) 10.0000 0.567048 0.283524 0.958965i \(-0.408496\pi\)
0.283524 + 0.958965i \(0.408496\pi\)
\(312\) 0 0
\(313\) 34.0000 1.92179 0.960897 0.276907i \(-0.0893093\pi\)
0.960897 + 0.276907i \(0.0893093\pi\)
\(314\) −4.00000 −0.225733
\(315\) 0 0
\(316\) −16.0000 −0.900070
\(317\) 6.00000 0.336994 0.168497 0.985702i \(-0.446109\pi\)
0.168497 + 0.985702i \(0.446109\pi\)
\(318\) 0 0
\(319\) 6.00000 0.335936
\(320\) −4.00000 −0.223607
\(321\) 0 0
\(322\) 0 0
\(323\) −8.00000 −0.445132
\(324\) 0 0
\(325\) 66.0000 3.66102
\(326\) −4.00000 −0.221540
\(327\) 0 0
\(328\) −12.0000 −0.662589
\(329\) 0 0
\(330\) 0 0
\(331\) 20.0000 1.09930 0.549650 0.835395i \(-0.314761\pi\)
0.549650 + 0.835395i \(0.314761\pi\)
\(332\) −14.0000 −0.768350
\(333\) 0 0
\(334\) 12.0000 0.656611
\(335\) −16.0000 −0.874173
\(336\) 0 0
\(337\) 6.00000 0.326841 0.163420 0.986557i \(-0.447747\pi\)
0.163420 + 0.986557i \(0.447747\pi\)
\(338\) −23.0000 −1.25104
\(339\) 0 0
\(340\) 16.0000 0.867722
\(341\) −6.00000 −0.324918
\(342\) 0 0
\(343\) 0 0
\(344\) −4.00000 −0.215666
\(345\) 0 0
\(346\) −2.00000 −0.107521
\(347\) −8.00000 −0.429463 −0.214731 0.976673i \(-0.568888\pi\)
−0.214731 + 0.976673i \(0.568888\pi\)
\(348\) 0 0
\(349\) −6.00000 −0.321173 −0.160586 0.987022i \(-0.551338\pi\)
−0.160586 + 0.987022i \(0.551338\pi\)
\(350\) 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
\(355\) −48.0000 −2.54758
\(356\) −14.0000 −0.741999
\(357\) 0 0
\(358\) −4.00000 −0.211407
\(359\) −24.0000 −1.26667 −0.633336 0.773877i \(-0.718315\pi\)
−0.633336 + 0.773877i \(0.718315\pi\)
\(360\) 0 0
\(361\) −15.0000 −0.789474
\(362\) −8.00000 −0.420471
\(363\) 0 0
\(364\) 0 0
\(365\) 0 0
\(366\) 0 0
\(367\) 34.0000 1.77479 0.887393 0.461014i \(-0.152514\pi\)
0.887393 + 0.461014i \(0.152514\pi\)
\(368\) 8.00000 0.417029
\(369\) 0 0
\(370\) −24.0000 −1.24770
\(371\) 0 0
\(372\) 0 0
\(373\) −14.0000 −0.724893 −0.362446 0.932005i \(-0.618058\pi\)
−0.362446 + 0.932005i \(0.618058\pi\)
\(374\) 4.00000 0.206835
\(375\) 0 0
\(376\) −6.00000 −0.309426
\(377\) 36.0000 1.85409
\(378\) 0 0
\(379\) 20.0000 1.02733 0.513665 0.857991i \(-0.328287\pi\)
0.513665 + 0.857991i \(0.328287\pi\)
\(380\) −8.00000 −0.410391
\(381\) 0 0
\(382\) 0 0
\(383\) −22.0000 −1.12415 −0.562074 0.827087i \(-0.689996\pi\)
−0.562074 + 0.827087i \(0.689996\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 14.0000 0.712581
\(387\) 0 0
\(388\) 14.0000 0.710742
\(389\) −6.00000 −0.304212 −0.152106 0.988364i \(-0.548606\pi\)
−0.152106 + 0.988364i \(0.548606\pi\)
\(390\) 0 0
\(391\) −32.0000 −1.61831
\(392\) 0 0
\(393\) 0 0
\(394\) 10.0000 0.503793
\(395\) 64.0000 3.22019
\(396\) 0 0
\(397\) 20.0000 1.00377 0.501886 0.864934i \(-0.332640\pi\)
0.501886 + 0.864934i \(0.332640\pi\)
\(398\) 2.00000 0.100251
\(399\) 0 0
\(400\) 11.0000 0.550000
\(401\) 26.0000 1.29838 0.649189 0.760627i \(-0.275108\pi\)
0.649189 + 0.760627i \(0.275108\pi\)
\(402\) 0 0
\(403\) −36.0000 −1.79329
\(404\) 14.0000 0.696526
\(405\) 0 0
\(406\) 0 0
\(407\) −6.00000 −0.297409
\(408\) 0 0
\(409\) −4.00000 −0.197787 −0.0988936 0.995098i \(-0.531530\pi\)
−0.0988936 + 0.995098i \(0.531530\pi\)
\(410\) 48.0000 2.37055
\(411\) 0 0
\(412\) 6.00000 0.295599
\(413\) 0 0
\(414\) 0 0
\(415\) 56.0000 2.74893
\(416\) −6.00000 −0.294174
\(417\) 0 0
\(418\) −2.00000 −0.0978232
\(419\) 12.0000 0.586238 0.293119 0.956076i \(-0.405307\pi\)
0.293119 + 0.956076i \(0.405307\pi\)
\(420\) 0 0
\(421\) 38.0000 1.85201 0.926003 0.377515i \(-0.123221\pi\)
0.926003 + 0.377515i \(0.123221\pi\)
\(422\) 4.00000 0.194717
\(423\) 0 0
\(424\) 2.00000 0.0971286
\(425\) −44.0000 −2.13431
\(426\) 0 0
\(427\) 0 0
\(428\) 8.00000 0.386695
\(429\) 0 0
\(430\) 16.0000 0.771589
\(431\) 24.0000 1.15604 0.578020 0.816023i \(-0.303826\pi\)
0.578020 + 0.816023i \(0.303826\pi\)
\(432\) 0 0
\(433\) −26.0000 −1.24948 −0.624740 0.780833i \(-0.714795\pi\)
−0.624740 + 0.780833i \(0.714795\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 6.00000 0.287348
\(437\) 16.0000 0.765384
\(438\) 0 0
\(439\) 20.0000 0.954548 0.477274 0.878755i \(-0.341625\pi\)
0.477274 + 0.878755i \(0.341625\pi\)
\(440\) 4.00000 0.190693
\(441\) 0 0
\(442\) 24.0000 1.14156
\(443\) −28.0000 −1.33032 −0.665160 0.746701i \(-0.731637\pi\)
−0.665160 + 0.746701i \(0.731637\pi\)
\(444\) 0 0
\(445\) 56.0000 2.65465
\(446\) 6.00000 0.284108
\(447\) 0 0
\(448\) 0 0
\(449\) −14.0000 −0.660701 −0.330350 0.943858i \(-0.607167\pi\)
−0.330350 + 0.943858i \(0.607167\pi\)
\(450\) 0 0
\(451\) 12.0000 0.565058
\(452\) −14.0000 −0.658505
\(453\) 0 0
\(454\) −6.00000 −0.281594
\(455\) 0 0
\(456\) 0 0
\(457\) 10.0000 0.467780 0.233890 0.972263i \(-0.424854\pi\)
0.233890 + 0.972263i \(0.424854\pi\)
\(458\) 8.00000 0.373815
\(459\) 0 0
\(460\) −32.0000 −1.49201
\(461\) 14.0000 0.652045 0.326023 0.945362i \(-0.394291\pi\)
0.326023 + 0.945362i \(0.394291\pi\)
\(462\) 0 0
\(463\) −24.0000 −1.11537 −0.557687 0.830051i \(-0.688311\pi\)
−0.557687 + 0.830051i \(0.688311\pi\)
\(464\) 6.00000 0.278543
\(465\) 0 0
\(466\) −14.0000 −0.648537
\(467\) 36.0000 1.66588 0.832941 0.553362i \(-0.186655\pi\)
0.832941 + 0.553362i \(0.186655\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 24.0000 1.10704
\(471\) 0 0
\(472\) 0 0
\(473\) 4.00000 0.183920
\(474\) 0 0
\(475\) 22.0000 1.00943
\(476\) 0 0
\(477\) 0 0
\(478\) −16.0000 −0.731823
\(479\) 24.0000 1.09659 0.548294 0.836286i \(-0.315277\pi\)
0.548294 + 0.836286i \(0.315277\pi\)
\(480\) 0 0
\(481\) −36.0000 −1.64146
\(482\) −8.00000 −0.364390
\(483\) 0 0
\(484\) 1.00000 0.0454545
\(485\) −56.0000 −2.54283
\(486\) 0 0
\(487\) 20.0000 0.906287 0.453143 0.891438i \(-0.350303\pi\)
0.453143 + 0.891438i \(0.350303\pi\)
\(488\) 10.0000 0.452679
\(489\) 0 0
\(490\) 0 0
\(491\) 28.0000 1.26362 0.631811 0.775122i \(-0.282312\pi\)
0.631811 + 0.775122i \(0.282312\pi\)
\(492\) 0 0
\(493\) −24.0000 −1.08091
\(494\) −12.0000 −0.539906
\(495\) 0 0
\(496\) −6.00000 −0.269408
\(497\) 0 0
\(498\) 0 0
\(499\) −28.0000 −1.25345 −0.626726 0.779240i \(-0.715605\pi\)
−0.626726 + 0.779240i \(0.715605\pi\)
\(500\) −24.0000 −1.07331
\(501\) 0 0
\(502\) 16.0000 0.714115
\(503\) 20.0000 0.891756 0.445878 0.895094i \(-0.352892\pi\)
0.445878 + 0.895094i \(0.352892\pi\)
\(504\) 0 0
\(505\) −56.0000 −2.49197
\(506\) −8.00000 −0.355643
\(507\) 0 0
\(508\) 0 0
\(509\) 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
\(514\) −26.0000 −1.14681
\(515\) −24.0000 −1.05757
\(516\) 0 0
\(517\) 6.00000 0.263880
\(518\) 0 0
\(519\) 0 0
\(520\) 24.0000 1.05247
\(521\) 18.0000 0.788594 0.394297 0.918983i \(-0.370988\pi\)
0.394297 + 0.918983i \(0.370988\pi\)
\(522\) 0 0
\(523\) 22.0000 0.961993 0.480996 0.876723i \(-0.340275\pi\)
0.480996 + 0.876723i \(0.340275\pi\)
\(524\) −2.00000 −0.0873704
\(525\) 0 0
\(526\) 0 0
\(527\) 24.0000 1.04546
\(528\) 0 0
\(529\) 41.0000 1.78261
\(530\) −8.00000 −0.347498
\(531\) 0 0
\(532\) 0 0
\(533\) 72.0000 3.11867
\(534\) 0 0
\(535\) −32.0000 −1.38348
\(536\) −4.00000 −0.172774
\(537\) 0 0
\(538\) 4.00000 0.172452
\(539\) 0 0
\(540\) 0 0
\(541\) −14.0000 −0.601907 −0.300954 0.953639i \(-0.597305\pi\)
−0.300954 + 0.953639i \(0.597305\pi\)
\(542\) −4.00000 −0.171815
\(543\) 0 0
\(544\) 4.00000 0.171499
\(545\) −24.0000 −1.02805
\(546\) 0 0
\(547\) 8.00000 0.342055 0.171028 0.985266i \(-0.445291\pi\)
0.171028 + 0.985266i \(0.445291\pi\)
\(548\) −14.0000 −0.598050
\(549\) 0 0
\(550\) −11.0000 −0.469042
\(551\) 12.0000 0.511217
\(552\) 0 0
\(553\) 0 0
\(554\) 10.0000 0.424859
\(555\) 0 0
\(556\) −2.00000 −0.0848189
\(557\) 30.0000 1.27114 0.635570 0.772043i \(-0.280765\pi\)
0.635570 + 0.772043i \(0.280765\pi\)
\(558\) 0 0
\(559\) 24.0000 1.01509
\(560\) 0 0
\(561\) 0 0
\(562\) 26.0000 1.09674
\(563\) −26.0000 −1.09577 −0.547885 0.836554i \(-0.684567\pi\)
−0.547885 + 0.836554i \(0.684567\pi\)
\(564\) 0 0
\(565\) 56.0000 2.35594
\(566\) −14.0000 −0.588464
\(567\) 0 0
\(568\) −12.0000 −0.503509
\(569\) −10.0000 −0.419222 −0.209611 0.977785i \(-0.567220\pi\)
−0.209611 + 0.977785i \(0.567220\pi\)
\(570\) 0 0
\(571\) −32.0000 −1.33916 −0.669579 0.742741i \(-0.733526\pi\)
−0.669579 + 0.742741i \(0.733526\pi\)
\(572\) 6.00000 0.250873
\(573\) 0 0
\(574\) 0 0
\(575\) 88.0000 3.66985
\(576\) 0 0
\(577\) 34.0000 1.41544 0.707719 0.706494i \(-0.249724\pi\)
0.707719 + 0.706494i \(0.249724\pi\)
\(578\) 1.00000 0.0415945
\(579\) 0 0
\(580\) −24.0000 −0.996546
\(581\) 0 0
\(582\) 0 0
\(583\) −2.00000 −0.0828315
\(584\) 0 0
\(585\) 0 0
\(586\) 14.0000 0.578335
\(587\) 24.0000 0.990586 0.495293 0.868726i \(-0.335061\pi\)
0.495293 + 0.868726i \(0.335061\pi\)
\(588\) 0 0
\(589\) −12.0000 −0.494451
\(590\) 0 0
\(591\) 0 0
\(592\) −6.00000 −0.246598
\(593\) −12.0000 −0.492781 −0.246390 0.969171i \(-0.579245\pi\)
−0.246390 + 0.969171i \(0.579245\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 10.0000 0.409616
\(597\) 0 0
\(598\) −48.0000 −1.96287
\(599\) −12.0000 −0.490307 −0.245153 0.969484i \(-0.578838\pi\)
−0.245153 + 0.969484i \(0.578838\pi\)
\(600\) 0 0
\(601\) −4.00000 −0.163163 −0.0815817 0.996667i \(-0.525997\pi\)
−0.0815817 + 0.996667i \(0.525997\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) −8.00000 −0.325515
\(605\) −4.00000 −0.162623
\(606\) 0 0
\(607\) 8.00000 0.324710 0.162355 0.986732i \(-0.448091\pi\)
0.162355 + 0.986732i \(0.448091\pi\)
\(608\) −2.00000 −0.0811107
\(609\) 0 0
\(610\) −40.0000 −1.61955
\(611\) 36.0000 1.45640
\(612\) 0 0
\(613\) −6.00000 −0.242338 −0.121169 0.992632i \(-0.538664\pi\)
−0.121169 + 0.992632i \(0.538664\pi\)
\(614\) −14.0000 −0.564994
\(615\) 0 0
\(616\) 0 0
\(617\) −26.0000 −1.04672 −0.523360 0.852111i \(-0.675322\pi\)
−0.523360 + 0.852111i \(0.675322\pi\)
\(618\) 0 0
\(619\) 4.00000 0.160774 0.0803868 0.996764i \(-0.474384\pi\)
0.0803868 + 0.996764i \(0.474384\pi\)
\(620\) 24.0000 0.963863
\(621\) 0 0
\(622\) −10.0000 −0.400963
\(623\) 0 0
\(624\) 0 0
\(625\) 41.0000 1.64000
\(626\) −34.0000 −1.35891
\(627\) 0 0
\(628\) 4.00000 0.159617
\(629\) 24.0000 0.956943
\(630\) 0 0
\(631\) 28.0000 1.11466 0.557331 0.830290i \(-0.311825\pi\)
0.557331 + 0.830290i \(0.311825\pi\)
\(632\) 16.0000 0.636446
\(633\) 0 0
\(634\) −6.00000 −0.238290
\(635\) 0 0
\(636\) 0 0
\(637\) 0 0
\(638\) −6.00000 −0.237542
\(639\) 0 0
\(640\) 4.00000 0.158114
\(641\) −18.0000 −0.710957 −0.355479 0.934684i \(-0.615682\pi\)
−0.355479 + 0.934684i \(0.615682\pi\)
\(642\) 0 0
\(643\) −32.0000 −1.26196 −0.630978 0.775800i \(-0.717346\pi\)
−0.630978 + 0.775800i \(0.717346\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 8.00000 0.314756
\(647\) 26.0000 1.02217 0.511083 0.859532i \(-0.329245\pi\)
0.511083 + 0.859532i \(0.329245\pi\)
\(648\) 0 0
\(649\) 0 0
\(650\) −66.0000 −2.58873
\(651\) 0 0
\(652\) 4.00000 0.156652
\(653\) −30.0000 −1.17399 −0.586995 0.809590i \(-0.699689\pi\)
−0.586995 + 0.809590i \(0.699689\pi\)
\(654\) 0 0
\(655\) 8.00000 0.312586
\(656\) 12.0000 0.468521
\(657\) 0 0
\(658\) 0 0
\(659\) 24.0000 0.934907 0.467454 0.884018i \(-0.345171\pi\)
0.467454 + 0.884018i \(0.345171\pi\)
\(660\) 0 0
\(661\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(662\) −20.0000 −0.777322
\(663\) 0 0
\(664\) 14.0000 0.543305
\(665\) 0 0
\(666\) 0 0
\(667\) 48.0000 1.85857
\(668\) −12.0000 −0.464294
\(669\) 0 0
\(670\) 16.0000 0.618134
\(671\) −10.0000 −0.386046
\(672\) 0 0
\(673\) −10.0000 −0.385472 −0.192736 0.981251i \(-0.561736\pi\)
−0.192736 + 0.981251i \(0.561736\pi\)
\(674\) −6.00000 −0.231111
\(675\) 0 0
\(676\) 23.0000 0.884615
\(677\) 34.0000 1.30673 0.653363 0.757045i \(-0.273358\pi\)
0.653363 + 0.757045i \(0.273358\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) −16.0000 −0.613572
\(681\) 0 0
\(682\) 6.00000 0.229752
\(683\) 36.0000 1.37750 0.688751 0.724998i \(-0.258159\pi\)
0.688751 + 0.724998i \(0.258159\pi\)
\(684\) 0 0
\(685\) 56.0000 2.13965
\(686\) 0 0
\(687\) 0 0
\(688\) 4.00000 0.152499
\(689\) −12.0000 −0.457164
\(690\) 0 0
\(691\) −24.0000 −0.913003 −0.456502 0.889723i \(-0.650898\pi\)
−0.456502 + 0.889723i \(0.650898\pi\)
\(692\) 2.00000 0.0760286
\(693\) 0 0
\(694\) 8.00000 0.303676
\(695\) 8.00000 0.303457
\(696\) 0 0
\(697\) −48.0000 −1.81813
\(698\) 6.00000 0.227103
\(699\) 0 0
\(700\) 0 0
\(701\) 18.0000 0.679851 0.339925 0.940452i \(-0.389598\pi\)
0.339925 + 0.940452i \(0.389598\pi\)
\(702\) 0 0
\(703\) −12.0000 −0.452589
\(704\) 1.00000 0.0376889
\(705\) 0 0
\(706\) 6.00000 0.225813
\(707\) 0 0
\(708\) 0 0
\(709\) −30.0000 −1.12667 −0.563337 0.826227i \(-0.690483\pi\)
−0.563337 + 0.826227i \(0.690483\pi\)
\(710\) 48.0000 1.80141
\(711\) 0 0
\(712\) 14.0000 0.524672
\(713\) −48.0000 −1.79761
\(714\) 0 0
\(715\) −24.0000 −0.897549
\(716\) 4.00000 0.149487
\(717\) 0 0
\(718\) 24.0000 0.895672
\(719\) 18.0000 0.671287 0.335643 0.941989i \(-0.391046\pi\)
0.335643 + 0.941989i \(0.391046\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) 15.0000 0.558242
\(723\) 0 0
\(724\) 8.00000 0.297318
\(725\) 66.0000 2.45118
\(726\) 0 0
\(727\) 42.0000 1.55769 0.778847 0.627214i \(-0.215805\pi\)
0.778847 + 0.627214i \(0.215805\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) −16.0000 −0.591781
\(732\) 0 0
\(733\) −50.0000 −1.84679 −0.923396 0.383849i \(-0.874598\pi\)
−0.923396 + 0.383849i \(0.874598\pi\)
\(734\) −34.0000 −1.25496
\(735\) 0 0
\(736\) −8.00000 −0.294884
\(737\) 4.00000 0.147342
\(738\) 0 0
\(739\) −16.0000 −0.588570 −0.294285 0.955718i \(-0.595081\pi\)
−0.294285 + 0.955718i \(0.595081\pi\)
\(740\) 24.0000 0.882258
\(741\) 0 0
\(742\) 0 0
\(743\) −16.0000 −0.586983 −0.293492 0.955962i \(-0.594817\pi\)
−0.293492 + 0.955962i \(0.594817\pi\)
\(744\) 0 0
\(745\) −40.0000 −1.46549
\(746\) 14.0000 0.512576
\(747\) 0 0
\(748\) −4.00000 −0.146254
\(749\) 0 0
\(750\) 0 0
\(751\) −28.0000 −1.02173 −0.510867 0.859660i \(-0.670676\pi\)
−0.510867 + 0.859660i \(0.670676\pi\)
\(752\) 6.00000 0.218797
\(753\) 0 0
\(754\) −36.0000 −1.31104
\(755\) 32.0000 1.16460
\(756\) 0 0
\(757\) 2.00000 0.0726912 0.0363456 0.999339i \(-0.488428\pi\)
0.0363456 + 0.999339i \(0.488428\pi\)
\(758\) −20.0000 −0.726433
\(759\) 0 0
\(760\) 8.00000 0.290191
\(761\) 24.0000 0.869999 0.435000 0.900431i \(-0.356748\pi\)
0.435000 + 0.900431i \(0.356748\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 0 0
\(765\) 0 0
\(766\) 22.0000 0.794892
\(767\) 0 0
\(768\) 0 0
\(769\) −28.0000 −1.00971 −0.504853 0.863205i \(-0.668453\pi\)
−0.504853 + 0.863205i \(0.668453\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) −14.0000 −0.503871
\(773\) −24.0000 −0.863220 −0.431610 0.902060i \(-0.642054\pi\)
−0.431610 + 0.902060i \(0.642054\pi\)
\(774\) 0 0
\(775\) −66.0000 −2.37079
\(776\) −14.0000 −0.502571
\(777\) 0 0
\(778\) 6.00000 0.215110
\(779\) 24.0000 0.859889
\(780\) 0 0
\(781\) 12.0000 0.429394
\(782\) 32.0000 1.14432
\(783\) 0 0
\(784\) 0 0
\(785\) −16.0000 −0.571064
\(786\) 0 0
\(787\) 50.0000 1.78231 0.891154 0.453701i \(-0.149897\pi\)
0.891154 + 0.453701i \(0.149897\pi\)
\(788\) −10.0000 −0.356235
\(789\) 0 0
\(790\) −64.0000 −2.27702
\(791\) 0 0
\(792\) 0 0
\(793\) −60.0000 −2.13066
\(794\) −20.0000 −0.709773
\(795\) 0 0
\(796\) −2.00000 −0.0708881
\(797\) 24.0000 0.850124 0.425062 0.905164i \(-0.360252\pi\)
0.425062 + 0.905164i \(0.360252\pi\)
\(798\) 0 0
\(799\) −24.0000 −0.849059
\(800\) −11.0000 −0.388909
\(801\) 0 0
\(802\) −26.0000 −0.918092
\(803\) 0 0
\(804\) 0 0
\(805\) 0 0
\(806\) 36.0000 1.26805
\(807\) 0 0
\(808\) −14.0000 −0.492518
\(809\) 2.00000 0.0703163 0.0351581 0.999382i \(-0.488807\pi\)
0.0351581 + 0.999382i \(0.488807\pi\)
\(810\) 0 0
\(811\) −26.0000 −0.912983 −0.456492 0.889728i \(-0.650894\pi\)
−0.456492 + 0.889728i \(0.650894\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 6.00000 0.210300
\(815\) −16.0000 −0.560456
\(816\) 0 0
\(817\) 8.00000 0.279885
\(818\) 4.00000 0.139857
\(819\) 0 0
\(820\) −48.0000 −1.67623
\(821\) 26.0000 0.907406 0.453703 0.891153i \(-0.350103\pi\)
0.453703 + 0.891153i \(0.350103\pi\)
\(822\) 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
\(827\) 28.0000 0.973655 0.486828 0.873498i \(-0.338154\pi\)
0.486828 + 0.873498i \(0.338154\pi\)
\(828\) 0 0
\(829\) −16.0000 −0.555703 −0.277851 0.960624i \(-0.589622\pi\)
−0.277851 + 0.960624i \(0.589622\pi\)
\(830\) −56.0000 −1.94379
\(831\) 0 0
\(832\) 6.00000 0.208013
\(833\) 0 0
\(834\) 0 0
\(835\) 48.0000 1.66111
\(836\) 2.00000 0.0691714
\(837\) 0 0
\(838\) −12.0000 −0.414533
\(839\) −54.0000 −1.86429 −0.932144 0.362089i \(-0.882064\pi\)
−0.932144 + 0.362089i \(0.882064\pi\)
\(840\) 0 0
\(841\) 7.00000 0.241379
\(842\) −38.0000 −1.30957
\(843\) 0 0
\(844\) −4.00000 −0.137686
\(845\) −92.0000 −3.16490
\(846\) 0 0
\(847\) 0 0
\(848\) −2.00000 −0.0686803
\(849\) 0 0
\(850\) 44.0000 1.50919
\(851\) −48.0000 −1.64542
\(852\) 0 0
\(853\) 6.00000 0.205436 0.102718 0.994711i \(-0.467246\pi\)
0.102718 + 0.994711i \(0.467246\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) −8.00000 −0.273434
\(857\) −40.0000 −1.36637 −0.683187 0.730243i \(-0.739407\pi\)
−0.683187 + 0.730243i \(0.739407\pi\)
\(858\) 0 0
\(859\) −40.0000 −1.36478 −0.682391 0.730987i \(-0.739060\pi\)
−0.682391 + 0.730987i \(0.739060\pi\)
\(860\) −16.0000 −0.545595
\(861\) 0 0
\(862\) −24.0000 −0.817443
\(863\) 16.0000 0.544646 0.272323 0.962206i \(-0.412208\pi\)
0.272323 + 0.962206i \(0.412208\pi\)
\(864\) 0 0
\(865\) −8.00000 −0.272008
\(866\) 26.0000 0.883516
\(867\) 0 0
\(868\) 0 0
\(869\) −16.0000 −0.542763
\(870\) 0 0
\(871\) 24.0000 0.813209
\(872\) −6.00000 −0.203186
\(873\) 0 0
\(874\) −16.0000 −0.541208
\(875\) 0 0
\(876\) 0 0
\(877\) −18.0000 −0.607817 −0.303908 0.952701i \(-0.598292\pi\)
−0.303908 + 0.952701i \(0.598292\pi\)
\(878\) −20.0000 −0.674967
\(879\) 0 0
\(880\) −4.00000 −0.134840
\(881\) −50.0000 −1.68454 −0.842271 0.539054i \(-0.818782\pi\)
−0.842271 + 0.539054i \(0.818782\pi\)
\(882\) 0 0
\(883\) 28.0000 0.942275 0.471138 0.882060i \(-0.343844\pi\)
0.471138 + 0.882060i \(0.343844\pi\)
\(884\) −24.0000 −0.807207
\(885\) 0 0
\(886\) 28.0000 0.940678
\(887\) −24.0000 −0.805841 −0.402921 0.915235i \(-0.632005\pi\)
−0.402921 + 0.915235i \(0.632005\pi\)
\(888\) 0 0
\(889\) 0 0
\(890\) −56.0000 −1.87712
\(891\) 0 0
\(892\) −6.00000 −0.200895
\(893\) 12.0000 0.401565
\(894\) 0 0
\(895\) −16.0000 −0.534821
\(896\) 0 0
\(897\) 0 0
\(898\) 14.0000 0.467186
\(899\) −36.0000 −1.20067
\(900\) 0 0
\(901\) 8.00000 0.266519
\(902\) −12.0000 −0.399556
\(903\) 0 0
\(904\) 14.0000 0.465633
\(905\) −32.0000 −1.06372
\(906\) 0 0
\(907\) 52.0000 1.72663 0.863316 0.504664i \(-0.168384\pi\)
0.863316 + 0.504664i \(0.168384\pi\)
\(908\) 6.00000 0.199117
\(909\) 0 0
\(910\) 0 0
\(911\) −24.0000 −0.795155 −0.397578 0.917568i \(-0.630149\pi\)
−0.397578 + 0.917568i \(0.630149\pi\)
\(912\) 0 0
\(913\) −14.0000 −0.463332
\(914\) −10.0000 −0.330771
\(915\) 0 0
\(916\) −8.00000 −0.264327
\(917\) 0 0
\(918\) 0 0
\(919\) 32.0000 1.05558 0.527791 0.849374i \(-0.323020\pi\)
0.527791 + 0.849374i \(0.323020\pi\)
\(920\) 32.0000 1.05501
\(921\) 0 0
\(922\) −14.0000 −0.461065
\(923\) 72.0000 2.36991
\(924\) 0 0
\(925\) −66.0000 −2.17007
\(926\) 24.0000 0.788689
\(927\) 0 0
\(928\) −6.00000 −0.196960
\(929\) 18.0000 0.590561 0.295280 0.955411i \(-0.404587\pi\)
0.295280 + 0.955411i \(0.404587\pi\)
\(930\) 0 0
\(931\) 0 0
\(932\) 14.0000 0.458585
\(933\) 0 0
\(934\) −36.0000 −1.17796
\(935\) 16.0000 0.523256
\(936\) 0 0
\(937\) 32.0000 1.04539 0.522697 0.852518i \(-0.324926\pi\)
0.522697 + 0.852518i \(0.324926\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) −24.0000 −0.782794
\(941\) −30.0000 −0.977972 −0.488986 0.872292i \(-0.662633\pi\)
−0.488986 + 0.872292i \(0.662633\pi\)
\(942\) 0 0
\(943\) 96.0000 3.12619
\(944\) 0 0
\(945\) 0 0
\(946\) −4.00000 −0.130051
\(947\) −36.0000 −1.16984 −0.584921 0.811090i \(-0.698875\pi\)
−0.584921 + 0.811090i \(0.698875\pi\)
\(948\) 0 0
\(949\) 0 0
\(950\) −22.0000 −0.713774
\(951\) 0 0
\(952\) 0 0
\(953\) −30.0000 −0.971795 −0.485898 0.874016i \(-0.661507\pi\)
−0.485898 + 0.874016i \(0.661507\pi\)
\(954\) 0 0
\(955\) 0 0
\(956\) 16.0000 0.517477
\(957\) 0 0
\(958\) −24.0000 −0.775405
\(959\) 0 0
\(960\) 0 0
\(961\) 5.00000 0.161290
\(962\) 36.0000 1.16069
\(963\) 0 0
\(964\) 8.00000 0.257663
\(965\) 56.0000 1.80270
\(966\) 0 0
\(967\) −32.0000 −1.02905 −0.514525 0.857475i \(-0.672032\pi\)
−0.514525 + 0.857475i \(0.672032\pi\)
\(968\) −1.00000 −0.0321412
\(969\) 0 0
\(970\) 56.0000 1.79805
\(971\) −36.0000 −1.15529 −0.577647 0.816286i \(-0.696029\pi\)
−0.577647 + 0.816286i \(0.696029\pi\)
\(972\) 0 0
\(973\) 0 0
\(974\) −20.0000 −0.640841
\(975\) 0 0
\(976\) −10.0000 −0.320092
\(977\) −2.00000 −0.0639857 −0.0319928 0.999488i \(-0.510185\pi\)
−0.0319928 + 0.999488i \(0.510185\pi\)
\(978\) 0 0
\(979\) −14.0000 −0.447442
\(980\) 0 0
\(981\) 0 0
\(982\) −28.0000 −0.893516
\(983\) −42.0000 −1.33959 −0.669796 0.742545i \(-0.733618\pi\)
−0.669796 + 0.742545i \(0.733618\pi\)
\(984\) 0 0
\(985\) 40.0000 1.27451
\(986\) 24.0000 0.764316
\(987\) 0 0
\(988\) 12.0000 0.381771
\(989\) 32.0000 1.01754
\(990\) 0 0
\(991\) 8.00000 0.254128 0.127064 0.991894i \(-0.459445\pi\)
0.127064 + 0.991894i \(0.459445\pi\)
\(992\) 6.00000 0.190500
\(993\) 0 0
\(994\) 0 0
\(995\) 8.00000 0.253617
\(996\) 0 0
\(997\) 26.0000 0.823428 0.411714 0.911313i \(-0.364930\pi\)
0.411714 + 0.911313i \(0.364930\pi\)
\(998\) 28.0000 0.886325
\(999\) 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.b.1.1 1
3.2 odd 2 3234.2.a.v.1.1 1
7.6 odd 2 1386.2.a.e.1.1 1
21.20 even 2 462.2.a.e.1.1 1
84.83 odd 2 3696.2.a.p.1.1 1
231.230 odd 2 5082.2.a.a.1.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
462.2.a.e.1.1 1 21.20 even 2
1386.2.a.e.1.1 1 7.6 odd 2
3234.2.a.v.1.1 1 3.2 odd 2
3696.2.a.p.1.1 1 84.83 odd 2
5082.2.a.a.1.1 1 231.230 odd 2
9702.2.a.b.1.1 1 1.1 even 1 trivial