Properties

Label 1334.2.a.a.1.1
Level $1334$
Weight $2$
Character 1334.1
Self dual yes
Analytic conductor $10.652$
Analytic rank $0$
Dimension $1$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 1334 = 2 \cdot 23 \cdot 29 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1334.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(10.6520436296\)
Analytic rank: \(0\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Character \(\chi\) \(=\) 1334.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.00000 q^{2} +1.00000 q^{4} +4.00000 q^{7} -1.00000 q^{8} -3.00000 q^{9} +O(q^{10})\) \(q-1.00000 q^{2} +1.00000 q^{4} +4.00000 q^{7} -1.00000 q^{8} -3.00000 q^{9} +2.00000 q^{11} +6.00000 q^{13} -4.00000 q^{14} +1.00000 q^{16} +2.00000 q^{17} +3.00000 q^{18} -2.00000 q^{19} -2.00000 q^{22} +1.00000 q^{23} -5.00000 q^{25} -6.00000 q^{26} +4.00000 q^{28} -1.00000 q^{29} -1.00000 q^{32} -2.00000 q^{34} -3.00000 q^{36} +4.00000 q^{37} +2.00000 q^{38} -2.00000 q^{41} +10.0000 q^{43} +2.00000 q^{44} -1.00000 q^{46} +8.00000 q^{47} +9.00000 q^{49} +5.00000 q^{50} +6.00000 q^{52} -8.00000 q^{53} -4.00000 q^{56} +1.00000 q^{58} -4.00000 q^{59} -8.00000 q^{61} -12.0000 q^{63} +1.00000 q^{64} +2.00000 q^{67} +2.00000 q^{68} -8.00000 q^{71} +3.00000 q^{72} +6.00000 q^{73} -4.00000 q^{74} -2.00000 q^{76} +8.00000 q^{77} +8.00000 q^{79} +9.00000 q^{81} +2.00000 q^{82} -6.00000 q^{83} -10.0000 q^{86} -2.00000 q^{88} +6.00000 q^{89} +24.0000 q^{91} +1.00000 q^{92} -8.00000 q^{94} +18.0000 q^{97} -9.00000 q^{98} -6.00000 q^{99} +O(q^{100})\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.00000 −0.707107
\(3\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(4\) 1.00000 0.500000
\(5\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(6\) 0 0
\(7\) 4.00000 1.51186 0.755929 0.654654i \(-0.227186\pi\)
0.755929 + 0.654654i \(0.227186\pi\)
\(8\) −1.00000 −0.353553
\(9\) −3.00000 −1.00000
\(10\) 0 0
\(11\) 2.00000 0.603023 0.301511 0.953463i \(-0.402509\pi\)
0.301511 + 0.953463i \(0.402509\pi\)
\(12\) 0 0
\(13\) 6.00000 1.66410 0.832050 0.554700i \(-0.187167\pi\)
0.832050 + 0.554700i \(0.187167\pi\)
\(14\) −4.00000 −1.06904
\(15\) 0 0
\(16\) 1.00000 0.250000
\(17\) 2.00000 0.485071 0.242536 0.970143i \(-0.422021\pi\)
0.242536 + 0.970143i \(0.422021\pi\)
\(18\) 3.00000 0.707107
\(19\) −2.00000 −0.458831 −0.229416 0.973329i \(-0.573682\pi\)
−0.229416 + 0.973329i \(0.573682\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) −2.00000 −0.426401
\(23\) 1.00000 0.208514
\(24\) 0 0
\(25\) −5.00000 −1.00000
\(26\) −6.00000 −1.17670
\(27\) 0 0
\(28\) 4.00000 0.755929
\(29\) −1.00000 −0.185695
\(30\) 0 0
\(31\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(32\) −1.00000 −0.176777
\(33\) 0 0
\(34\) −2.00000 −0.342997
\(35\) 0 0
\(36\) −3.00000 −0.500000
\(37\) 4.00000 0.657596 0.328798 0.944400i \(-0.393356\pi\)
0.328798 + 0.944400i \(0.393356\pi\)
\(38\) 2.00000 0.324443
\(39\) 0 0
\(40\) 0 0
\(41\) −2.00000 −0.312348 −0.156174 0.987730i \(-0.549916\pi\)
−0.156174 + 0.987730i \(0.549916\pi\)
\(42\) 0 0
\(43\) 10.0000 1.52499 0.762493 0.646997i \(-0.223975\pi\)
0.762493 + 0.646997i \(0.223975\pi\)
\(44\) 2.00000 0.301511
\(45\) 0 0
\(46\) −1.00000 −0.147442
\(47\) 8.00000 1.16692 0.583460 0.812142i \(-0.301699\pi\)
0.583460 + 0.812142i \(0.301699\pi\)
\(48\) 0 0
\(49\) 9.00000 1.28571
\(50\) 5.00000 0.707107
\(51\) 0 0
\(52\) 6.00000 0.832050
\(53\) −8.00000 −1.09888 −0.549442 0.835532i \(-0.685160\pi\)
−0.549442 + 0.835532i \(0.685160\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) −4.00000 −0.534522
\(57\) 0 0
\(58\) 1.00000 0.131306
\(59\) −4.00000 −0.520756 −0.260378 0.965507i \(-0.583847\pi\)
−0.260378 + 0.965507i \(0.583847\pi\)
\(60\) 0 0
\(61\) −8.00000 −1.02430 −0.512148 0.858898i \(-0.671150\pi\)
−0.512148 + 0.858898i \(0.671150\pi\)
\(62\) 0 0
\(63\) −12.0000 −1.51186
\(64\) 1.00000 0.125000
\(65\) 0 0
\(66\) 0 0
\(67\) 2.00000 0.244339 0.122169 0.992509i \(-0.461015\pi\)
0.122169 + 0.992509i \(0.461015\pi\)
\(68\) 2.00000 0.242536
\(69\) 0 0
\(70\) 0 0
\(71\) −8.00000 −0.949425 −0.474713 0.880141i \(-0.657448\pi\)
−0.474713 + 0.880141i \(0.657448\pi\)
\(72\) 3.00000 0.353553
\(73\) 6.00000 0.702247 0.351123 0.936329i \(-0.385800\pi\)
0.351123 + 0.936329i \(0.385800\pi\)
\(74\) −4.00000 −0.464991
\(75\) 0 0
\(76\) −2.00000 −0.229416
\(77\) 8.00000 0.911685
\(78\) 0 0
\(79\) 8.00000 0.900070 0.450035 0.893011i \(-0.351411\pi\)
0.450035 + 0.893011i \(0.351411\pi\)
\(80\) 0 0
\(81\) 9.00000 1.00000
\(82\) 2.00000 0.220863
\(83\) −6.00000 −0.658586 −0.329293 0.944228i \(-0.606810\pi\)
−0.329293 + 0.944228i \(0.606810\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) −10.0000 −1.07833
\(87\) 0 0
\(88\) −2.00000 −0.213201
\(89\) 6.00000 0.635999 0.317999 0.948091i \(-0.396989\pi\)
0.317999 + 0.948091i \(0.396989\pi\)
\(90\) 0 0
\(91\) 24.0000 2.51588
\(92\) 1.00000 0.104257
\(93\) 0 0
\(94\) −8.00000 −0.825137
\(95\) 0 0
\(96\) 0 0
\(97\) 18.0000 1.82762 0.913812 0.406138i \(-0.133125\pi\)
0.913812 + 0.406138i \(0.133125\pi\)
\(98\) −9.00000 −0.909137
\(99\) −6.00000 −0.603023
\(100\) −5.00000 −0.500000
\(101\) −10.0000 −0.995037 −0.497519 0.867453i \(-0.665755\pi\)
−0.497519 + 0.867453i \(0.665755\pi\)
\(102\) 0 0
\(103\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(104\) −6.00000 −0.588348
\(105\) 0 0
\(106\) 8.00000 0.777029
\(107\) 10.0000 0.966736 0.483368 0.875417i \(-0.339413\pi\)
0.483368 + 0.875417i \(0.339413\pi\)
\(108\) 0 0
\(109\) 4.00000 0.383131 0.191565 0.981480i \(-0.438644\pi\)
0.191565 + 0.981480i \(0.438644\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 4.00000 0.377964
\(113\) 6.00000 0.564433 0.282216 0.959351i \(-0.408930\pi\)
0.282216 + 0.959351i \(0.408930\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) −1.00000 −0.0928477
\(117\) −18.0000 −1.66410
\(118\) 4.00000 0.368230
\(119\) 8.00000 0.733359
\(120\) 0 0
\(121\) −7.00000 −0.636364
\(122\) 8.00000 0.724286
\(123\) 0 0
\(124\) 0 0
\(125\) 0 0
\(126\) 12.0000 1.06904
\(127\) 16.0000 1.41977 0.709885 0.704317i \(-0.248747\pi\)
0.709885 + 0.704317i \(0.248747\pi\)
\(128\) −1.00000 −0.0883883
\(129\) 0 0
\(130\) 0 0
\(131\) 12.0000 1.04844 0.524222 0.851581i \(-0.324356\pi\)
0.524222 + 0.851581i \(0.324356\pi\)
\(132\) 0 0
\(133\) −8.00000 −0.693688
\(134\) −2.00000 −0.172774
\(135\) 0 0
\(136\) −2.00000 −0.171499
\(137\) 10.0000 0.854358 0.427179 0.904167i \(-0.359507\pi\)
0.427179 + 0.904167i \(0.359507\pi\)
\(138\) 0 0
\(139\) 12.0000 1.01783 0.508913 0.860818i \(-0.330047\pi\)
0.508913 + 0.860818i \(0.330047\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 8.00000 0.671345
\(143\) 12.0000 1.00349
\(144\) −3.00000 −0.250000
\(145\) 0 0
\(146\) −6.00000 −0.496564
\(147\) 0 0
\(148\) 4.00000 0.328798
\(149\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(150\) 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
\(153\) −6.00000 −0.485071
\(154\) −8.00000 −0.644658
\(155\) 0 0
\(156\) 0 0
\(157\) 4.00000 0.319235 0.159617 0.987179i \(-0.448974\pi\)
0.159617 + 0.987179i \(0.448974\pi\)
\(158\) −8.00000 −0.636446
\(159\) 0 0
\(160\) 0 0
\(161\) 4.00000 0.315244
\(162\) −9.00000 −0.707107
\(163\) −8.00000 −0.626608 −0.313304 0.949653i \(-0.601436\pi\)
−0.313304 + 0.949653i \(0.601436\pi\)
\(164\) −2.00000 −0.156174
\(165\) 0 0
\(166\) 6.00000 0.465690
\(167\) −16.0000 −1.23812 −0.619059 0.785345i \(-0.712486\pi\)
−0.619059 + 0.785345i \(0.712486\pi\)
\(168\) 0 0
\(169\) 23.0000 1.76923
\(170\) 0 0
\(171\) 6.00000 0.458831
\(172\) 10.0000 0.762493
\(173\) −14.0000 −1.06440 −0.532200 0.846619i \(-0.678635\pi\)
−0.532200 + 0.846619i \(0.678635\pi\)
\(174\) 0 0
\(175\) −20.0000 −1.51186
\(176\) 2.00000 0.150756
\(177\) 0 0
\(178\) −6.00000 −0.449719
\(179\) −8.00000 −0.597948 −0.298974 0.954261i \(-0.596644\pi\)
−0.298974 + 0.954261i \(0.596644\pi\)
\(180\) 0 0
\(181\) 20.0000 1.48659 0.743294 0.668965i \(-0.233262\pi\)
0.743294 + 0.668965i \(0.233262\pi\)
\(182\) −24.0000 −1.77900
\(183\) 0 0
\(184\) −1.00000 −0.0737210
\(185\) 0 0
\(186\) 0 0
\(187\) 4.00000 0.292509
\(188\) 8.00000 0.583460
\(189\) 0 0
\(190\) 0 0
\(191\) 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 \(0.668091\pi\)
\(194\) −18.0000 −1.29232
\(195\) 0 0
\(196\) 9.00000 0.642857
\(197\) 26.0000 1.85242 0.926212 0.377004i \(-0.123046\pi\)
0.926212 + 0.377004i \(0.123046\pi\)
\(198\) 6.00000 0.426401
\(199\) −20.0000 −1.41776 −0.708881 0.705328i \(-0.750800\pi\)
−0.708881 + 0.705328i \(0.750800\pi\)
\(200\) 5.00000 0.353553
\(201\) 0 0
\(202\) 10.0000 0.703598
\(203\) −4.00000 −0.280745
\(204\) 0 0
\(205\) 0 0
\(206\) 0 0
\(207\) −3.00000 −0.208514
\(208\) 6.00000 0.416025
\(209\) −4.00000 −0.276686
\(210\) 0 0
\(211\) −4.00000 −0.275371 −0.137686 0.990476i \(-0.543966\pi\)
−0.137686 + 0.990476i \(0.543966\pi\)
\(212\) −8.00000 −0.549442
\(213\) 0 0
\(214\) −10.0000 −0.683586
\(215\) 0 0
\(216\) 0 0
\(217\) 0 0
\(218\) −4.00000 −0.270914
\(219\) 0 0
\(220\) 0 0
\(221\) 12.0000 0.807207
\(222\) 0 0
\(223\) 8.00000 0.535720 0.267860 0.963458i \(-0.413684\pi\)
0.267860 + 0.963458i \(0.413684\pi\)
\(224\) −4.00000 −0.267261
\(225\) 15.0000 1.00000
\(226\) −6.00000 −0.399114
\(227\) −18.0000 −1.19470 −0.597351 0.801980i \(-0.703780\pi\)
−0.597351 + 0.801980i \(0.703780\pi\)
\(228\) 0 0
\(229\) −16.0000 −1.05731 −0.528655 0.848837i \(-0.677303\pi\)
−0.528655 + 0.848837i \(0.677303\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 1.00000 0.0656532
\(233\) −22.0000 −1.44127 −0.720634 0.693316i \(-0.756149\pi\)
−0.720634 + 0.693316i \(0.756149\pi\)
\(234\) 18.0000 1.17670
\(235\) 0 0
\(236\) −4.00000 −0.260378
\(237\) 0 0
\(238\) −8.00000 −0.518563
\(239\) −16.0000 −1.03495 −0.517477 0.855697i \(-0.673129\pi\)
−0.517477 + 0.855697i \(0.673129\pi\)
\(240\) 0 0
\(241\) −10.0000 −0.644157 −0.322078 0.946713i \(-0.604381\pi\)
−0.322078 + 0.946713i \(0.604381\pi\)
\(242\) 7.00000 0.449977
\(243\) 0 0
\(244\) −8.00000 −0.512148
\(245\) 0 0
\(246\) 0 0
\(247\) −12.0000 −0.763542
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) −10.0000 −0.631194 −0.315597 0.948893i \(-0.602205\pi\)
−0.315597 + 0.948893i \(0.602205\pi\)
\(252\) −12.0000 −0.755929
\(253\) 2.00000 0.125739
\(254\) −16.0000 −1.00393
\(255\) 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
\(259\) 16.0000 0.994192
\(260\) 0 0
\(261\) 3.00000 0.185695
\(262\) −12.0000 −0.741362
\(263\) 4.00000 0.246651 0.123325 0.992366i \(-0.460644\pi\)
0.123325 + 0.992366i \(0.460644\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 8.00000 0.490511
\(267\) 0 0
\(268\) 2.00000 0.122169
\(269\) 26.0000 1.58525 0.792624 0.609711i \(-0.208714\pi\)
0.792624 + 0.609711i \(0.208714\pi\)
\(270\) 0 0
\(271\) −8.00000 −0.485965 −0.242983 0.970031i \(-0.578126\pi\)
−0.242983 + 0.970031i \(0.578126\pi\)
\(272\) 2.00000 0.121268
\(273\) 0 0
\(274\) −10.0000 −0.604122
\(275\) −10.0000 −0.603023
\(276\) 0 0
\(277\) −22.0000 −1.32185 −0.660926 0.750451i \(-0.729836\pi\)
−0.660926 + 0.750451i \(0.729836\pi\)
\(278\) −12.0000 −0.719712
\(279\) 0 0
\(280\) 0 0
\(281\) 26.0000 1.55103 0.775515 0.631329i \(-0.217490\pi\)
0.775515 + 0.631329i \(0.217490\pi\)
\(282\) 0 0
\(283\) −18.0000 −1.06999 −0.534994 0.844856i \(-0.679686\pi\)
−0.534994 + 0.844856i \(0.679686\pi\)
\(284\) −8.00000 −0.474713
\(285\) 0 0
\(286\) −12.0000 −0.709575
\(287\) −8.00000 −0.472225
\(288\) 3.00000 0.176777
\(289\) −13.0000 −0.764706
\(290\) 0 0
\(291\) 0 0
\(292\) 6.00000 0.351123
\(293\) −4.00000 −0.233682 −0.116841 0.993151i \(-0.537277\pi\)
−0.116841 + 0.993151i \(0.537277\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) −4.00000 −0.232495
\(297\) 0 0
\(298\) 0 0
\(299\) 6.00000 0.346989
\(300\) 0 0
\(301\) 40.0000 2.30556
\(302\) 8.00000 0.460348
\(303\) 0 0
\(304\) −2.00000 −0.114708
\(305\) 0 0
\(306\) 6.00000 0.342997
\(307\) −32.0000 −1.82634 −0.913168 0.407583i \(-0.866372\pi\)
−0.913168 + 0.407583i \(0.866372\pi\)
\(308\) 8.00000 0.455842
\(309\) 0 0
\(310\) 0 0
\(311\) −24.0000 −1.36092 −0.680458 0.732787i \(-0.738219\pi\)
−0.680458 + 0.732787i \(0.738219\pi\)
\(312\) 0 0
\(313\) 22.0000 1.24351 0.621757 0.783210i \(-0.286419\pi\)
0.621757 + 0.783210i \(0.286419\pi\)
\(314\) −4.00000 −0.225733
\(315\) 0 0
\(316\) 8.00000 0.450035
\(317\) −6.00000 −0.336994 −0.168497 0.985702i \(-0.553891\pi\)
−0.168497 + 0.985702i \(0.553891\pi\)
\(318\) 0 0
\(319\) −2.00000 −0.111979
\(320\) 0 0
\(321\) 0 0
\(322\) −4.00000 −0.222911
\(323\) −4.00000 −0.222566
\(324\) 9.00000 0.500000
\(325\) −30.0000 −1.66410
\(326\) 8.00000 0.443079
\(327\) 0 0
\(328\) 2.00000 0.110432
\(329\) 32.0000 1.76422
\(330\) 0 0
\(331\) 12.0000 0.659580 0.329790 0.944054i \(-0.393022\pi\)
0.329790 + 0.944054i \(0.393022\pi\)
\(332\) −6.00000 −0.329293
\(333\) −12.0000 −0.657596
\(334\) 16.0000 0.875481
\(335\) 0 0
\(336\) 0 0
\(337\) −2.00000 −0.108947 −0.0544735 0.998515i \(-0.517348\pi\)
−0.0544735 + 0.998515i \(0.517348\pi\)
\(338\) −23.0000 −1.25104
\(339\) 0 0
\(340\) 0 0
\(341\) 0 0
\(342\) −6.00000 −0.324443
\(343\) 8.00000 0.431959
\(344\) −10.0000 −0.539164
\(345\) 0 0
\(346\) 14.0000 0.752645
\(347\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(348\) 0 0
\(349\) 2.00000 0.107058 0.0535288 0.998566i \(-0.482953\pi\)
0.0535288 + 0.998566i \(0.482953\pi\)
\(350\) 20.0000 1.06904
\(351\) 0 0
\(352\) −2.00000 −0.106600
\(353\) −14.0000 −0.745145 −0.372572 0.928003i \(-0.621524\pi\)
−0.372572 + 0.928003i \(0.621524\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 6.00000 0.317999
\(357\) 0 0
\(358\) 8.00000 0.422813
\(359\) −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
\(362\) −20.0000 −1.05118
\(363\) 0 0
\(364\) 24.0000 1.25794
\(365\) 0 0
\(366\) 0 0
\(367\) −16.0000 −0.835193 −0.417597 0.908633i \(-0.637127\pi\)
−0.417597 + 0.908633i \(0.637127\pi\)
\(368\) 1.00000 0.0521286
\(369\) 6.00000 0.312348
\(370\) 0 0
\(371\) −32.0000 −1.66136
\(372\) 0 0
\(373\) 32.0000 1.65690 0.828449 0.560065i \(-0.189224\pi\)
0.828449 + 0.560065i \(0.189224\pi\)
\(374\) −4.00000 −0.206835
\(375\) 0 0
\(376\) −8.00000 −0.412568
\(377\) −6.00000 −0.309016
\(378\) 0 0
\(379\) −10.0000 −0.513665 −0.256833 0.966456i \(-0.582679\pi\)
−0.256833 + 0.966456i \(0.582679\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) −16.0000 −0.817562 −0.408781 0.912633i \(-0.634046\pi\)
−0.408781 + 0.912633i \(0.634046\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 14.0000 0.712581
\(387\) −30.0000 −1.52499
\(388\) 18.0000 0.913812
\(389\) 16.0000 0.811232 0.405616 0.914044i \(-0.367057\pi\)
0.405616 + 0.914044i \(0.367057\pi\)
\(390\) 0 0
\(391\) 2.00000 0.101144
\(392\) −9.00000 −0.454569
\(393\) 0 0
\(394\) −26.0000 −1.30986
\(395\) 0 0
\(396\) −6.00000 −0.301511
\(397\) 22.0000 1.10415 0.552074 0.833795i \(-0.313837\pi\)
0.552074 + 0.833795i \(0.313837\pi\)
\(398\) 20.0000 1.00251
\(399\) 0 0
\(400\) −5.00000 −0.250000
\(401\) −26.0000 −1.29838 −0.649189 0.760627i \(-0.724892\pi\)
−0.649189 + 0.760627i \(0.724892\pi\)
\(402\) 0 0
\(403\) 0 0
\(404\) −10.0000 −0.497519
\(405\) 0 0
\(406\) 4.00000 0.198517
\(407\) 8.00000 0.396545
\(408\) 0 0
\(409\) −38.0000 −1.87898 −0.939490 0.342578i \(-0.888700\pi\)
−0.939490 + 0.342578i \(0.888700\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) −16.0000 −0.787309
\(414\) 3.00000 0.147442
\(415\) 0 0
\(416\) −6.00000 −0.294174
\(417\) 0 0
\(418\) 4.00000 0.195646
\(419\) 10.0000 0.488532 0.244266 0.969708i \(-0.421453\pi\)
0.244266 + 0.969708i \(0.421453\pi\)
\(420\) 0 0
\(421\) 20.0000 0.974740 0.487370 0.873195i \(-0.337956\pi\)
0.487370 + 0.873195i \(0.337956\pi\)
\(422\) 4.00000 0.194717
\(423\) −24.0000 −1.16692
\(424\) 8.00000 0.388514
\(425\) −10.0000 −0.485071
\(426\) 0 0
\(427\) −32.0000 −1.54859
\(428\) 10.0000 0.483368
\(429\) 0 0
\(430\) 0 0
\(431\) −20.0000 −0.963366 −0.481683 0.876346i \(-0.659974\pi\)
−0.481683 + 0.876346i \(0.659974\pi\)
\(432\) 0 0
\(433\) −22.0000 −1.05725 −0.528626 0.848855i \(-0.677293\pi\)
−0.528626 + 0.848855i \(0.677293\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 4.00000 0.191565
\(437\) −2.00000 −0.0956730
\(438\) 0 0
\(439\) −8.00000 −0.381819 −0.190910 0.981608i \(-0.561144\pi\)
−0.190910 + 0.981608i \(0.561144\pi\)
\(440\) 0 0
\(441\) −27.0000 −1.28571
\(442\) −12.0000 −0.570782
\(443\) −24.0000 −1.14027 −0.570137 0.821549i \(-0.693110\pi\)
−0.570137 + 0.821549i \(0.693110\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) −8.00000 −0.378811
\(447\) 0 0
\(448\) 4.00000 0.188982
\(449\) 22.0000 1.03824 0.519122 0.854700i \(-0.326259\pi\)
0.519122 + 0.854700i \(0.326259\pi\)
\(450\) −15.0000 −0.707107
\(451\) −4.00000 −0.188353
\(452\) 6.00000 0.282216
\(453\) 0 0
\(454\) 18.0000 0.844782
\(455\) 0 0
\(456\) 0 0
\(457\) 14.0000 0.654892 0.327446 0.944870i \(-0.393812\pi\)
0.327446 + 0.944870i \(0.393812\pi\)
\(458\) 16.0000 0.747631
\(459\) 0 0
\(460\) 0 0
\(461\) −6.00000 −0.279448 −0.139724 0.990190i \(-0.544622\pi\)
−0.139724 + 0.990190i \(0.544622\pi\)
\(462\) 0 0
\(463\) −16.0000 −0.743583 −0.371792 0.928316i \(-0.621256\pi\)
−0.371792 + 0.928316i \(0.621256\pi\)
\(464\) −1.00000 −0.0464238
\(465\) 0 0
\(466\) 22.0000 1.01913
\(467\) 14.0000 0.647843 0.323921 0.946084i \(-0.394999\pi\)
0.323921 + 0.946084i \(0.394999\pi\)
\(468\) −18.0000 −0.832050
\(469\) 8.00000 0.369406
\(470\) 0 0
\(471\) 0 0
\(472\) 4.00000 0.184115
\(473\) 20.0000 0.919601
\(474\) 0 0
\(475\) 10.0000 0.458831
\(476\) 8.00000 0.366679
\(477\) 24.0000 1.09888
\(478\) 16.0000 0.731823
\(479\) 4.00000 0.182765 0.0913823 0.995816i \(-0.470871\pi\)
0.0913823 + 0.995816i \(0.470871\pi\)
\(480\) 0 0
\(481\) 24.0000 1.09431
\(482\) 10.0000 0.455488
\(483\) 0 0
\(484\) −7.00000 −0.318182
\(485\) 0 0
\(486\) 0 0
\(487\) −16.0000 −0.725029 −0.362515 0.931978i \(-0.618082\pi\)
−0.362515 + 0.931978i \(0.618082\pi\)
\(488\) 8.00000 0.362143
\(489\) 0 0
\(490\) 0 0
\(491\) 8.00000 0.361035 0.180517 0.983572i \(-0.442223\pi\)
0.180517 + 0.983572i \(0.442223\pi\)
\(492\) 0 0
\(493\) −2.00000 −0.0900755
\(494\) 12.0000 0.539906
\(495\) 0 0
\(496\) 0 0
\(497\) −32.0000 −1.43540
\(498\) 0 0
\(499\) −8.00000 −0.358129 −0.179065 0.983837i \(-0.557307\pi\)
−0.179065 + 0.983837i \(0.557307\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 10.0000 0.446322
\(503\) −40.0000 −1.78351 −0.891756 0.452517i \(-0.850526\pi\)
−0.891756 + 0.452517i \(0.850526\pi\)
\(504\) 12.0000 0.534522
\(505\) 0 0
\(506\) −2.00000 −0.0889108
\(507\) 0 0
\(508\) 16.0000 0.709885
\(509\) −6.00000 −0.265945 −0.132973 0.991120i \(-0.542452\pi\)
−0.132973 + 0.991120i \(0.542452\pi\)
\(510\) 0 0
\(511\) 24.0000 1.06170
\(512\) −1.00000 −0.0441942
\(513\) 0 0
\(514\) −6.00000 −0.264649
\(515\) 0 0
\(516\) 0 0
\(517\) 16.0000 0.703679
\(518\) −16.0000 −0.703000
\(519\) 0 0
\(520\) 0 0
\(521\) 30.0000 1.31432 0.657162 0.753749i \(-0.271757\pi\)
0.657162 + 0.753749i \(0.271757\pi\)
\(522\) −3.00000 −0.131306
\(523\) 10.0000 0.437269 0.218635 0.975807i \(-0.429840\pi\)
0.218635 + 0.975807i \(0.429840\pi\)
\(524\) 12.0000 0.524222
\(525\) 0 0
\(526\) −4.00000 −0.174408
\(527\) 0 0
\(528\) 0 0
\(529\) 1.00000 0.0434783
\(530\) 0 0
\(531\) 12.0000 0.520756
\(532\) −8.00000 −0.346844
\(533\) −12.0000 −0.519778
\(534\) 0 0
\(535\) 0 0
\(536\) −2.00000 −0.0863868
\(537\) 0 0
\(538\) −26.0000 −1.12094
\(539\) 18.0000 0.775315
\(540\) 0 0
\(541\) 34.0000 1.46177 0.730887 0.682498i \(-0.239107\pi\)
0.730887 + 0.682498i \(0.239107\pi\)
\(542\) 8.00000 0.343629
\(543\) 0 0
\(544\) −2.00000 −0.0857493
\(545\) 0 0
\(546\) 0 0
\(547\) 28.0000 1.19719 0.598597 0.801050i \(-0.295725\pi\)
0.598597 + 0.801050i \(0.295725\pi\)
\(548\) 10.0000 0.427179
\(549\) 24.0000 1.02430
\(550\) 10.0000 0.426401
\(551\) 2.00000 0.0852029
\(552\) 0 0
\(553\) 32.0000 1.36078
\(554\) 22.0000 0.934690
\(555\) 0 0
\(556\) 12.0000 0.508913
\(557\) −12.0000 −0.508456 −0.254228 0.967144i \(-0.581821\pi\)
−0.254228 + 0.967144i \(0.581821\pi\)
\(558\) 0 0
\(559\) 60.0000 2.53773
\(560\) 0 0
\(561\) 0 0
\(562\) −26.0000 −1.09674
\(563\) −6.00000 −0.252870 −0.126435 0.991975i \(-0.540353\pi\)
−0.126435 + 0.991975i \(0.540353\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 18.0000 0.756596
\(567\) 36.0000 1.51186
\(568\) 8.00000 0.335673
\(569\) −6.00000 −0.251533 −0.125767 0.992060i \(-0.540139\pi\)
−0.125767 + 0.992060i \(0.540139\pi\)
\(570\) 0 0
\(571\) 18.0000 0.753277 0.376638 0.926360i \(-0.377080\pi\)
0.376638 + 0.926360i \(0.377080\pi\)
\(572\) 12.0000 0.501745
\(573\) 0 0
\(574\) 8.00000 0.333914
\(575\) −5.00000 −0.208514
\(576\) −3.00000 −0.125000
\(577\) −2.00000 −0.0832611 −0.0416305 0.999133i \(-0.513255\pi\)
−0.0416305 + 0.999133i \(0.513255\pi\)
\(578\) 13.0000 0.540729
\(579\) 0 0
\(580\) 0 0
\(581\) −24.0000 −0.995688
\(582\) 0 0
\(583\) −16.0000 −0.662652
\(584\) −6.00000 −0.248282
\(585\) 0 0
\(586\) 4.00000 0.165238
\(587\) 36.0000 1.48588 0.742940 0.669359i \(-0.233431\pi\)
0.742940 + 0.669359i \(0.233431\pi\)
\(588\) 0 0
\(589\) 0 0
\(590\) 0 0
\(591\) 0 0
\(592\) 4.00000 0.164399
\(593\) −26.0000 −1.06769 −0.533846 0.845582i \(-0.679254\pi\)
−0.533846 + 0.845582i \(0.679254\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) 0 0
\(598\) −6.00000 −0.245358
\(599\) 40.0000 1.63436 0.817178 0.576386i \(-0.195537\pi\)
0.817178 + 0.576386i \(0.195537\pi\)
\(600\) 0 0
\(601\) −10.0000 −0.407909 −0.203954 0.978980i \(-0.565379\pi\)
−0.203954 + 0.978980i \(0.565379\pi\)
\(602\) −40.0000 −1.63028
\(603\) −6.00000 −0.244339
\(604\) −8.00000 −0.325515
\(605\) 0 0
\(606\) 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
\(610\) 0 0
\(611\) 48.0000 1.94187
\(612\) −6.00000 −0.242536
\(613\) 36.0000 1.45403 0.727013 0.686624i \(-0.240908\pi\)
0.727013 + 0.686624i \(0.240908\pi\)
\(614\) 32.0000 1.29141
\(615\) 0 0
\(616\) −8.00000 −0.322329
\(617\) −42.0000 −1.69086 −0.845428 0.534089i \(-0.820655\pi\)
−0.845428 + 0.534089i \(0.820655\pi\)
\(618\) 0 0
\(619\) 10.0000 0.401934 0.200967 0.979598i \(-0.435592\pi\)
0.200967 + 0.979598i \(0.435592\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 24.0000 0.962312
\(623\) 24.0000 0.961540
\(624\) 0 0
\(625\) 25.0000 1.00000
\(626\) −22.0000 −0.879297
\(627\) 0 0
\(628\) 4.00000 0.159617
\(629\) 8.00000 0.318981
\(630\) 0 0
\(631\) −32.0000 −1.27390 −0.636950 0.770905i \(-0.719804\pi\)
−0.636950 + 0.770905i \(0.719804\pi\)
\(632\) −8.00000 −0.318223
\(633\) 0 0
\(634\) 6.00000 0.238290
\(635\) 0 0
\(636\) 0 0
\(637\) 54.0000 2.13956
\(638\) 2.00000 0.0791808
\(639\) 24.0000 0.949425
\(640\) 0 0
\(641\) 42.0000 1.65890 0.829450 0.558581i \(-0.188654\pi\)
0.829450 + 0.558581i \(0.188654\pi\)
\(642\) 0 0
\(643\) 14.0000 0.552106 0.276053 0.961142i \(-0.410973\pi\)
0.276053 + 0.961142i \(0.410973\pi\)
\(644\) 4.00000 0.157622
\(645\) 0 0
\(646\) 4.00000 0.157378
\(647\) −8.00000 −0.314512 −0.157256 0.987558i \(-0.550265\pi\)
−0.157256 + 0.987558i \(0.550265\pi\)
\(648\) −9.00000 −0.353553
\(649\) −8.00000 −0.314027
\(650\) 30.0000 1.17670
\(651\) 0 0
\(652\) −8.00000 −0.313304
\(653\) 46.0000 1.80012 0.900060 0.435767i \(-0.143523\pi\)
0.900060 + 0.435767i \(0.143523\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) −2.00000 −0.0780869
\(657\) −18.0000 −0.702247
\(658\) −32.0000 −1.24749
\(659\) −18.0000 −0.701180 −0.350590 0.936529i \(-0.614019\pi\)
−0.350590 + 0.936529i \(0.614019\pi\)
\(660\) 0 0
\(661\) −20.0000 −0.777910 −0.388955 0.921257i \(-0.627164\pi\)
−0.388955 + 0.921257i \(0.627164\pi\)
\(662\) −12.0000 −0.466393
\(663\) 0 0
\(664\) 6.00000 0.232845
\(665\) 0 0
\(666\) 12.0000 0.464991
\(667\) −1.00000 −0.0387202
\(668\) −16.0000 −0.619059
\(669\) 0 0
\(670\) 0 0
\(671\) −16.0000 −0.617673
\(672\) 0 0
\(673\) −50.0000 −1.92736 −0.963679 0.267063i \(-0.913947\pi\)
−0.963679 + 0.267063i \(0.913947\pi\)
\(674\) 2.00000 0.0770371
\(675\) 0 0
\(676\) 23.0000 0.884615
\(677\) −36.0000 −1.38359 −0.691796 0.722093i \(-0.743180\pi\)
−0.691796 + 0.722093i \(0.743180\pi\)
\(678\) 0 0
\(679\) 72.0000 2.76311
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) −4.00000 −0.153056 −0.0765279 0.997067i \(-0.524383\pi\)
−0.0765279 + 0.997067i \(0.524383\pi\)
\(684\) 6.00000 0.229416
\(685\) 0 0
\(686\) −8.00000 −0.305441
\(687\) 0 0
\(688\) 10.0000 0.381246
\(689\) −48.0000 −1.82865
\(690\) 0 0
\(691\) −20.0000 −0.760836 −0.380418 0.924815i \(-0.624220\pi\)
−0.380418 + 0.924815i \(0.624220\pi\)
\(692\) −14.0000 −0.532200
\(693\) −24.0000 −0.911685
\(694\) 0 0
\(695\) 0 0
\(696\) 0 0
\(697\) −4.00000 −0.151511
\(698\) −2.00000 −0.0757011
\(699\) 0 0
\(700\) −20.0000 −0.755929
\(701\) −20.0000 −0.755390 −0.377695 0.925930i \(-0.623283\pi\)
−0.377695 + 0.925930i \(0.623283\pi\)
\(702\) 0 0
\(703\) −8.00000 −0.301726
\(704\) 2.00000 0.0753778
\(705\) 0 0
\(706\) 14.0000 0.526897
\(707\) −40.0000 −1.50435
\(708\) 0 0
\(709\) −40.0000 −1.50223 −0.751116 0.660171i \(-0.770484\pi\)
−0.751116 + 0.660171i \(0.770484\pi\)
\(710\) 0 0
\(711\) −24.0000 −0.900070
\(712\) −6.00000 −0.224860
\(713\) 0 0
\(714\) 0 0
\(715\) 0 0
\(716\) −8.00000 −0.298974
\(717\) 0 0
\(718\) 24.0000 0.895672
\(719\) 24.0000 0.895049 0.447524 0.894272i \(-0.352306\pi\)
0.447524 + 0.894272i \(0.352306\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) 15.0000 0.558242
\(723\) 0 0
\(724\) 20.0000 0.743294
\(725\) 5.00000 0.185695
\(726\) 0 0
\(727\) 8.00000 0.296704 0.148352 0.988935i \(-0.452603\pi\)
0.148352 + 0.988935i \(0.452603\pi\)
\(728\) −24.0000 −0.889499
\(729\) −27.0000 −1.00000
\(730\) 0 0
\(731\) 20.0000 0.739727
\(732\) 0 0
\(733\) −12.0000 −0.443230 −0.221615 0.975134i \(-0.571133\pi\)
−0.221615 + 0.975134i \(0.571133\pi\)
\(734\) 16.0000 0.590571
\(735\) 0 0
\(736\) −1.00000 −0.0368605
\(737\) 4.00000 0.147342
\(738\) −6.00000 −0.220863
\(739\) −32.0000 −1.17714 −0.588570 0.808447i \(-0.700309\pi\)
−0.588570 + 0.808447i \(0.700309\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 32.0000 1.17476
\(743\) −4.00000 −0.146746 −0.0733729 0.997305i \(-0.523376\pi\)
−0.0733729 + 0.997305i \(0.523376\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) −32.0000 −1.17160
\(747\) 18.0000 0.658586
\(748\) 4.00000 0.146254
\(749\) 40.0000 1.46157
\(750\) 0 0
\(751\) −52.0000 −1.89751 −0.948753 0.316017i \(-0.897654\pi\)
−0.948753 + 0.316017i \(0.897654\pi\)
\(752\) 8.00000 0.291730
\(753\) 0 0
\(754\) 6.00000 0.218507
\(755\) 0 0
\(756\) 0 0
\(757\) 8.00000 0.290765 0.145382 0.989376i \(-0.453559\pi\)
0.145382 + 0.989376i \(0.453559\pi\)
\(758\) 10.0000 0.363216
\(759\) 0 0
\(760\) 0 0
\(761\) 34.0000 1.23250 0.616250 0.787551i \(-0.288651\pi\)
0.616250 + 0.787551i \(0.288651\pi\)
\(762\) 0 0
\(763\) 16.0000 0.579239
\(764\) 0 0
\(765\) 0 0
\(766\) 16.0000 0.578103
\(767\) −24.0000 −0.866590
\(768\) 0 0
\(769\) 42.0000 1.51456 0.757279 0.653091i \(-0.226528\pi\)
0.757279 + 0.653091i \(0.226528\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) −14.0000 −0.503871
\(773\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(774\) 30.0000 1.07833
\(775\) 0 0
\(776\) −18.0000 −0.646162
\(777\) 0 0
\(778\) −16.0000 −0.573628
\(779\) 4.00000 0.143315
\(780\) 0 0
\(781\) −16.0000 −0.572525
\(782\) −2.00000 −0.0715199
\(783\) 0 0
\(784\) 9.00000 0.321429
\(785\) 0 0
\(786\) 0 0
\(787\) −26.0000 −0.926800 −0.463400 0.886149i \(-0.653371\pi\)
−0.463400 + 0.886149i \(0.653371\pi\)
\(788\) 26.0000 0.926212
\(789\) 0 0
\(790\) 0 0
\(791\) 24.0000 0.853342
\(792\) 6.00000 0.213201
\(793\) −48.0000 −1.70453
\(794\) −22.0000 −0.780751
\(795\) 0 0
\(796\) −20.0000 −0.708881
\(797\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(798\) 0 0
\(799\) 16.0000 0.566039
\(800\) 5.00000 0.176777
\(801\) −18.0000 −0.635999
\(802\) 26.0000 0.918092
\(803\) 12.0000 0.423471
\(804\) 0 0
\(805\) 0 0
\(806\) 0 0
\(807\) 0 0
\(808\) 10.0000 0.351799
\(809\) −6.00000 −0.210949 −0.105474 0.994422i \(-0.533636\pi\)
−0.105474 + 0.994422i \(0.533636\pi\)
\(810\) 0 0
\(811\) 36.0000 1.26413 0.632065 0.774915i \(-0.282207\pi\)
0.632065 + 0.774915i \(0.282207\pi\)
\(812\) −4.00000 −0.140372
\(813\) 0 0
\(814\) −8.00000 −0.280400
\(815\) 0 0
\(816\) 0 0
\(817\) −20.0000 −0.699711
\(818\) 38.0000 1.32864
\(819\) −72.0000 −2.51588
\(820\) 0 0
\(821\) 38.0000 1.32621 0.663105 0.748527i \(-0.269238\pi\)
0.663105 + 0.748527i \(0.269238\pi\)
\(822\) 0 0
\(823\) 32.0000 1.11545 0.557725 0.830026i \(-0.311674\pi\)
0.557725 + 0.830026i \(0.311674\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 16.0000 0.556711
\(827\) 38.0000 1.32139 0.660695 0.750655i \(-0.270262\pi\)
0.660695 + 0.750655i \(0.270262\pi\)
\(828\) −3.00000 −0.104257
\(829\) 2.00000 0.0694629 0.0347314 0.999397i \(-0.488942\pi\)
0.0347314 + 0.999397i \(0.488942\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 6.00000 0.208013
\(833\) 18.0000 0.623663
\(834\) 0 0
\(835\) 0 0
\(836\) −4.00000 −0.138343
\(837\) 0 0
\(838\) −10.0000 −0.345444
\(839\) 36.0000 1.24286 0.621429 0.783470i \(-0.286552\pi\)
0.621429 + 0.783470i \(0.286552\pi\)
\(840\) 0 0
\(841\) 1.00000 0.0344828
\(842\) −20.0000 −0.689246
\(843\) 0 0
\(844\) −4.00000 −0.137686
\(845\) 0 0
\(846\) 24.0000 0.825137
\(847\) −28.0000 −0.962091
\(848\) −8.00000 −0.274721
\(849\) 0 0
\(850\) 10.0000 0.342997
\(851\) 4.00000 0.137118
\(852\) 0 0
\(853\) −42.0000 −1.43805 −0.719026 0.694983i \(-0.755412\pi\)
−0.719026 + 0.694983i \(0.755412\pi\)
\(854\) 32.0000 1.09502
\(855\) 0 0
\(856\) −10.0000 −0.341793
\(857\) 10.0000 0.341593 0.170797 0.985306i \(-0.445366\pi\)
0.170797 + 0.985306i \(0.445366\pi\)
\(858\) 0 0
\(859\) −24.0000 −0.818869 −0.409435 0.912339i \(-0.634274\pi\)
−0.409435 + 0.912339i \(0.634274\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 20.0000 0.681203
\(863\) −48.0000 −1.63394 −0.816970 0.576681i \(-0.804348\pi\)
−0.816970 + 0.576681i \(0.804348\pi\)
\(864\) 0 0
\(865\) 0 0
\(866\) 22.0000 0.747590
\(867\) 0 0
\(868\) 0 0
\(869\) 16.0000 0.542763
\(870\) 0 0
\(871\) 12.0000 0.406604
\(872\) −4.00000 −0.135457
\(873\) −54.0000 −1.82762
\(874\) 2.00000 0.0676510
\(875\) 0 0
\(876\) 0 0
\(877\) 34.0000 1.14810 0.574049 0.818821i \(-0.305372\pi\)
0.574049 + 0.818821i \(0.305372\pi\)
\(878\) 8.00000 0.269987
\(879\) 0 0
\(880\) 0 0
\(881\) −18.0000 −0.606435 −0.303218 0.952921i \(-0.598061\pi\)
−0.303218 + 0.952921i \(0.598061\pi\)
\(882\) 27.0000 0.909137
\(883\) 12.0000 0.403832 0.201916 0.979403i \(-0.435283\pi\)
0.201916 + 0.979403i \(0.435283\pi\)
\(884\) 12.0000 0.403604
\(885\) 0 0
\(886\) 24.0000 0.806296
\(887\) 8.00000 0.268614 0.134307 0.990940i \(-0.457119\pi\)
0.134307 + 0.990940i \(0.457119\pi\)
\(888\) 0 0
\(889\) 64.0000 2.14649
\(890\) 0 0
\(891\) 18.0000 0.603023
\(892\) 8.00000 0.267860
\(893\) −16.0000 −0.535420
\(894\) 0 0
\(895\) 0 0
\(896\) −4.00000 −0.133631
\(897\) 0 0
\(898\) −22.0000 −0.734150
\(899\) 0 0
\(900\) 15.0000 0.500000
\(901\) −16.0000 −0.533037
\(902\) 4.00000 0.133185
\(903\) 0 0
\(904\) −6.00000 −0.199557
\(905\) 0 0
\(906\) 0 0
\(907\) 26.0000 0.863316 0.431658 0.902037i \(-0.357929\pi\)
0.431658 + 0.902037i \(0.357929\pi\)
\(908\) −18.0000 −0.597351
\(909\) 30.0000 0.995037
\(910\) 0 0
\(911\) −48.0000 −1.59031 −0.795155 0.606406i \(-0.792611\pi\)
−0.795155 + 0.606406i \(0.792611\pi\)
\(912\) 0 0
\(913\) −12.0000 −0.397142
\(914\) −14.0000 −0.463079
\(915\) 0 0
\(916\) −16.0000 −0.528655
\(917\) 48.0000 1.58510
\(918\) 0 0
\(919\) −12.0000 −0.395843 −0.197922 0.980218i \(-0.563419\pi\)
−0.197922 + 0.980218i \(0.563419\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 6.00000 0.197599
\(923\) −48.0000 −1.57994
\(924\) 0 0
\(925\) −20.0000 −0.657596
\(926\) 16.0000 0.525793
\(927\) 0 0
\(928\) 1.00000 0.0328266
\(929\) −18.0000 −0.590561 −0.295280 0.955411i \(-0.595413\pi\)
−0.295280 + 0.955411i \(0.595413\pi\)
\(930\) 0 0
\(931\) −18.0000 −0.589926
\(932\) −22.0000 −0.720634
\(933\) 0 0
\(934\) −14.0000 −0.458094
\(935\) 0 0
\(936\) 18.0000 0.588348
\(937\) −22.0000 −0.718709 −0.359354 0.933201i \(-0.617003\pi\)
−0.359354 + 0.933201i \(0.617003\pi\)
\(938\) −8.00000 −0.261209
\(939\) 0 0
\(940\) 0 0
\(941\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(942\) 0 0
\(943\) −2.00000 −0.0651290
\(944\) −4.00000 −0.130189
\(945\) 0 0
\(946\) −20.0000 −0.650256
\(947\) −48.0000 −1.55979 −0.779895 0.625910i \(-0.784728\pi\)
−0.779895 + 0.625910i \(0.784728\pi\)
\(948\) 0 0
\(949\) 36.0000 1.16861
\(950\) −10.0000 −0.324443
\(951\) 0 0
\(952\) −8.00000 −0.259281
\(953\) 6.00000 0.194359 0.0971795 0.995267i \(-0.469018\pi\)
0.0971795 + 0.995267i \(0.469018\pi\)
\(954\) −24.0000 −0.777029
\(955\) 0 0
\(956\) −16.0000 −0.517477
\(957\) 0 0
\(958\) −4.00000 −0.129234
\(959\) 40.0000 1.29167
\(960\) 0 0
\(961\) −31.0000 −1.00000
\(962\) −24.0000 −0.773791
\(963\) −30.0000 −0.966736
\(964\) −10.0000 −0.322078
\(965\) 0 0
\(966\) 0 0
\(967\) −40.0000 −1.28631 −0.643157 0.765735i \(-0.722376\pi\)
−0.643157 + 0.765735i \(0.722376\pi\)
\(968\) 7.00000 0.224989
\(969\) 0 0
\(970\) 0 0
\(971\) 50.0000 1.60458 0.802288 0.596937i \(-0.203616\pi\)
0.802288 + 0.596937i \(0.203616\pi\)
\(972\) 0 0
\(973\) 48.0000 1.53881
\(974\) 16.0000 0.512673
\(975\) 0 0
\(976\) −8.00000 −0.256074
\(977\) 22.0000 0.703842 0.351921 0.936030i \(-0.385529\pi\)
0.351921 + 0.936030i \(0.385529\pi\)
\(978\) 0 0
\(979\) 12.0000 0.383522
\(980\) 0 0
\(981\) −12.0000 −0.383131
\(982\) −8.00000 −0.255290
\(983\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(984\) 0 0
\(985\) 0 0
\(986\) 2.00000 0.0636930
\(987\) 0 0
\(988\) −12.0000 −0.381771
\(989\) 10.0000 0.317982
\(990\) 0 0
\(991\) −16.0000 −0.508257 −0.254128 0.967170i \(-0.581789\pi\)
−0.254128 + 0.967170i \(0.581789\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 32.0000 1.01498
\(995\) 0 0
\(996\) 0 0
\(997\) 10.0000 0.316703 0.158352 0.987383i \(-0.449382\pi\)
0.158352 + 0.987383i \(0.449382\pi\)
\(998\) 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 1334.2.a.a.1.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1334.2.a.a.1.1 1 1.1 even 1 trivial