Properties

Label 4032.2.h.h.575.7
Level 4032
Weight 2
Character 4032.575
Analytic conductor 32.196
Analytic rank 0
Dimension 12
CM no
Inner twists 4

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Newspace parameters

Level: \( N \) = \( 4032 = 2^{6} \cdot 3^{2} \cdot 7 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 4032.h (of order \(2\), degree \(1\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(32.1956820950\)
Analytic rank: \(0\)
Dimension: \(12\)
Coefficient field: 12.0.653473922154496.1
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 2^{13} \)
Twist minimal: no (minimal twist has level 252)
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 575.7
Root \(1.16947 + 0.795191i\)
Character \(\chi\) = 4032.575
Dual form 4032.2.h.h.575.6

$q$-expansion

\(f(q)\) \(=\) \(q+0.665647i q^{5} -1.00000i q^{7} +O(q^{10})\) \(q+0.665647i q^{5} -1.00000i q^{7} +2.07986 q^{11} -5.55691 q^{13} +2.16278i q^{17} -4.49828i q^{19} -4.28167 q^{23} +4.55691 q^{25} +1.41421i q^{29} +6.61555i q^{31} +0.665647 q^{35} +5.43965 q^{37} +5.69588i q^{41} +2.11727i q^{43} +10.5213 q^{47} -1.00000 q^{49} -10.6042i q^{53} +1.38445i q^{55} +13.5155 q^{59} +0.615547 q^{61} -3.69894i q^{65} +14.0552i q^{67} +15.5954 q^{71} -11.9379 q^{73} -2.07986i q^{77} -0.824101i q^{79} -6.36153 q^{83} -1.43965 q^{85} -12.6840i q^{89} +5.55691i q^{91} +2.99427 q^{95} +0.824101 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12q + O(q^{10}) \) \( 12q - 12q^{25} - 8q^{37} - 12q^{49} - 56q^{61} + 56q^{85} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/4032\mathbb{Z}\right)^\times\).

\(n\) \(127\) \(577\) \(1793\) \(3781\)
\(\chi(n)\) \(-1\) \(1\) \(-1\) \(1\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) 0 0
\(4\) 0 0
\(5\) 0.665647i 0.297686i 0.988861 + 0.148843i \(0.0475550\pi\)
−0.988861 + 0.148843i \(0.952445\pi\)
\(6\) 0 0
\(7\) − 1.00000i − 0.377964i
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) 2.07986 0.627102 0.313551 0.949571i \(-0.398481\pi\)
0.313551 + 0.949571i \(0.398481\pi\)
\(12\) 0 0
\(13\) −5.55691 −1.54121 −0.770605 0.637313i \(-0.780046\pi\)
−0.770605 + 0.637313i \(0.780046\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 2.16278i 0.524551i 0.964993 + 0.262276i \(0.0844730\pi\)
−0.964993 + 0.262276i \(0.915527\pi\)
\(18\) 0 0
\(19\) − 4.49828i − 1.03198i −0.856596 0.515988i \(-0.827425\pi\)
0.856596 0.515988i \(-0.172575\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) −4.28167 −0.892790 −0.446395 0.894836i \(-0.647292\pi\)
−0.446395 + 0.894836i \(0.647292\pi\)
\(24\) 0 0
\(25\) 4.55691 0.911383
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) 1.41421i 0.262613i 0.991342 + 0.131306i \(0.0419172\pi\)
−0.991342 + 0.131306i \(0.958083\pi\)
\(30\) 0 0
\(31\) 6.61555i 1.18819i 0.804396 + 0.594094i \(0.202489\pi\)
−0.804396 + 0.594094i \(0.797511\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) 0.665647 0.112515
\(36\) 0 0
\(37\) 5.43965 0.894273 0.447136 0.894466i \(-0.352444\pi\)
0.447136 + 0.894466i \(0.352444\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) 5.69588i 0.889548i 0.895643 + 0.444774i \(0.146716\pi\)
−0.895643 + 0.444774i \(0.853284\pi\)
\(42\) 0 0
\(43\) 2.11727i 0.322880i 0.986883 + 0.161440i \(0.0516138\pi\)
−0.986883 + 0.161440i \(0.948386\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 10.5213 1.53468 0.767341 0.641239i \(-0.221579\pi\)
0.767341 + 0.641239i \(0.221579\pi\)
\(48\) 0 0
\(49\) −1.00000 −0.142857
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) − 10.6042i − 1.45659i −0.685261 0.728297i \(-0.740312\pi\)
0.685261 0.728297i \(-0.259688\pi\)
\(54\) 0 0
\(55\) 1.38445i 0.186680i
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) 13.5155 1.75957 0.879785 0.475371i \(-0.157686\pi\)
0.879785 + 0.475371i \(0.157686\pi\)
\(60\) 0 0
\(61\) 0.615547 0.0788128 0.0394064 0.999223i \(-0.487453\pi\)
0.0394064 + 0.999223i \(0.487453\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) − 3.69894i − 0.458797i
\(66\) 0 0
\(67\) 14.0552i 1.71712i 0.512717 + 0.858558i \(0.328639\pi\)
−0.512717 + 0.858558i \(0.671361\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 15.5954 1.85083 0.925415 0.378954i \(-0.123716\pi\)
0.925415 + 0.378954i \(0.123716\pi\)
\(72\) 0 0
\(73\) −11.9379 −1.39723 −0.698614 0.715498i \(-0.746200\pi\)
−0.698614 + 0.715498i \(0.746200\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) − 2.07986i − 0.237022i
\(78\) 0 0
\(79\) − 0.824101i − 0.0927186i −0.998925 0.0463593i \(-0.985238\pi\)
0.998925 0.0463593i \(-0.0147619\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) −6.36153 −0.698269 −0.349134 0.937073i \(-0.613524\pi\)
−0.349134 + 0.937073i \(0.613524\pi\)
\(84\) 0 0
\(85\) −1.43965 −0.156152
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) − 12.6840i − 1.34450i −0.740322 0.672252i \(-0.765327\pi\)
0.740322 0.672252i \(-0.234673\pi\)
\(90\) 0 0
\(91\) 5.55691i 0.582523i
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 2.99427 0.307205
\(96\) 0 0
\(97\) 0.824101 0.0836747 0.0418374 0.999124i \(-0.486679\pi\)
0.0418374 + 0.999124i \(0.486679\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) 17.8801i 1.77914i 0.456802 + 0.889569i \(0.348995\pi\)
−0.456802 + 0.889569i \(0.651005\pi\)
\(102\) 0 0
\(103\) 12.4983i 1.23149i 0.787945 + 0.615746i \(0.211145\pi\)
−0.787945 + 0.615746i \(0.788855\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 13.3936 1.29481 0.647403 0.762148i \(-0.275855\pi\)
0.647403 + 0.762148i \(0.275855\pi\)
\(108\) 0 0
\(109\) 6.11727 0.585928 0.292964 0.956123i \(-0.405358\pi\)
0.292964 + 0.956123i \(0.405358\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) 3.61602i 0.340167i 0.985430 + 0.170083i \(0.0544037\pi\)
−0.985430 + 0.170083i \(0.945596\pi\)
\(114\) 0 0
\(115\) − 2.85008i − 0.265771i
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) 2.16278 0.198262
\(120\) 0 0
\(121\) −6.67418 −0.606744
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) 6.36153i 0.568993i
\(126\) 0 0
\(127\) − 8.17246i − 0.725189i −0.931947 0.362594i \(-0.881891\pi\)
0.931947 0.362594i \(-0.118109\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) 2.99427 0.261610 0.130805 0.991408i \(-0.458244\pi\)
0.130805 + 0.991408i \(0.458244\pi\)
\(132\) 0 0
\(133\) −4.49828 −0.390050
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) − 10.7700i − 0.920144i −0.887882 0.460072i \(-0.847824\pi\)
0.887882 0.460072i \(-0.152176\pi\)
\(138\) 0 0
\(139\) 16.0000i 1.35710i 0.734553 + 0.678551i \(0.237392\pi\)
−0.734553 + 0.678551i \(0.762608\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) −11.5576 −0.966496
\(144\) 0 0
\(145\) −0.941367 −0.0781763
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) 2.57967i 0.211335i 0.994402 + 0.105667i \(0.0336979\pi\)
−0.994402 + 0.105667i \(0.966302\pi\)
\(150\) 0 0
\(151\) − 5.23109i − 0.425700i −0.977085 0.212850i \(-0.931725\pi\)
0.977085 0.212850i \(-0.0682746\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) −4.40362 −0.353707
\(156\) 0 0
\(157\) 5.61211 0.447895 0.223948 0.974601i \(-0.428106\pi\)
0.223948 + 0.974601i \(0.428106\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 4.28167i 0.337443i
\(162\) 0 0
\(163\) − 8.17246i − 0.640117i −0.947398 0.320058i \(-0.896297\pi\)
0.947398 0.320058i \(-0.103703\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 16.5098 1.27757 0.638783 0.769387i \(-0.279438\pi\)
0.638783 + 0.769387i \(0.279438\pi\)
\(168\) 0 0
\(169\) 17.8793 1.37533
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) − 4.19875i − 0.319225i −0.987180 0.159613i \(-0.948976\pi\)
0.987180 0.159613i \(-0.0510245\pi\)
\(174\) 0 0
\(175\) − 4.55691i − 0.344470i
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) 2.07986 0.155456 0.0777280 0.996975i \(-0.475233\pi\)
0.0777280 + 0.996975i \(0.475233\pi\)
\(180\) 0 0
\(181\) 11.4396 0.850302 0.425151 0.905122i \(-0.360221\pi\)
0.425151 + 0.905122i \(0.360221\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 3.62088i 0.266213i
\(186\) 0 0
\(187\) 4.49828i 0.328947i
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 8.44139 0.610798 0.305399 0.952225i \(-0.401210\pi\)
0.305399 + 0.952225i \(0.401210\pi\)
\(192\) 0 0
\(193\) 9.67418 0.696363 0.348181 0.937427i \(-0.386799\pi\)
0.348181 + 0.937427i \(0.386799\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) − 13.4326i − 0.957033i −0.878079 0.478516i \(-0.841175\pi\)
0.878079 0.478516i \(-0.158825\pi\)
\(198\) 0 0
\(199\) 27.1138i 1.92205i 0.276464 + 0.961024i \(0.410837\pi\)
−0.276464 + 0.961024i \(0.589163\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) 1.41421 0.0992583
\(204\) 0 0
\(205\) −3.79145 −0.264806
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) − 9.35580i − 0.647154i
\(210\) 0 0
\(211\) 11.1138i 0.765108i 0.923933 + 0.382554i \(0.124955\pi\)
−0.923933 + 0.382554i \(0.875045\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) −1.40935 −0.0961170
\(216\) 0 0
\(217\) 6.61555 0.449093
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) − 12.0184i − 0.808444i
\(222\) 0 0
\(223\) 6.87930i 0.460672i 0.973111 + 0.230336i \(0.0739825\pi\)
−0.973111 + 0.230336i \(0.926018\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 5.19608 0.344876 0.172438 0.985020i \(-0.444836\pi\)
0.172438 + 0.985020i \(0.444836\pi\)
\(228\) 0 0
\(229\) −5.55691 −0.367211 −0.183606 0.983000i \(-0.558777\pi\)
−0.183606 + 0.983000i \(0.558777\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 24.1197i 1.58013i 0.613021 + 0.790067i \(0.289954\pi\)
−0.613021 + 0.790067i \(0.710046\pi\)
\(234\) 0 0
\(235\) 7.00344i 0.456854i
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) −8.44139 −0.546028 −0.273014 0.962010i \(-0.588021\pi\)
−0.273014 + 0.962010i \(0.588021\pi\)
\(240\) 0 0
\(241\) −25.8207 −1.66326 −0.831628 0.555334i \(-0.812591\pi\)
−0.831628 + 0.555334i \(0.812591\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) − 0.665647i − 0.0425266i
\(246\) 0 0
\(247\) 24.9966i 1.59049i
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 19.8770 1.25463 0.627314 0.778766i \(-0.284154\pi\)
0.627314 + 0.778766i \(0.284154\pi\)
\(252\) 0 0
\(253\) −8.90528 −0.559870
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 21.3352i 1.33085i 0.746465 + 0.665425i \(0.231750\pi\)
−0.746465 + 0.665425i \(0.768250\pi\)
\(258\) 0 0
\(259\) − 5.43965i − 0.338003i
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) 19.7551 1.21815 0.609076 0.793112i \(-0.291541\pi\)
0.609076 + 0.793112i \(0.291541\pi\)
\(264\) 0 0
\(265\) 7.05863 0.433608
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) 2.62356i 0.159961i 0.996796 + 0.0799806i \(0.0254858\pi\)
−0.996796 + 0.0799806i \(0.974514\pi\)
\(270\) 0 0
\(271\) 0.732814i 0.0445153i 0.999752 + 0.0222576i \(0.00708541\pi\)
−0.999752 + 0.0222576i \(0.992915\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 9.47775 0.571530
\(276\) 0 0
\(277\) −11.4396 −0.687342 −0.343671 0.939090i \(-0.611670\pi\)
−0.343671 + 0.939090i \(0.611670\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) − 0.875377i − 0.0522206i −0.999659 0.0261103i \(-0.991688\pi\)
0.999659 0.0261103i \(-0.00831212\pi\)
\(282\) 0 0
\(283\) − 22.4914i − 1.33698i −0.743723 0.668488i \(-0.766942\pi\)
0.743723 0.668488i \(-0.233058\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 5.69588 0.336217
\(288\) 0 0
\(289\) 12.3224 0.724846
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) − 24.2416i − 1.41621i −0.706106 0.708106i \(-0.749550\pi\)
0.706106 0.708106i \(-0.250450\pi\)
\(294\) 0 0
\(295\) 8.99656i 0.523800i
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 23.7929 1.37598
\(300\) 0 0
\(301\) 2.11727 0.122037
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) 0.409737i 0.0234615i
\(306\) 0 0
\(307\) 7.61211i 0.434446i 0.976122 + 0.217223i \(0.0696999\pi\)
−0.976122 + 0.217223i \(0.930300\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 13.5155 0.766395 0.383197 0.923666i \(-0.374823\pi\)
0.383197 + 0.923666i \(0.374823\pi\)
\(312\) 0 0
\(313\) −7.64820 −0.432302 −0.216151 0.976360i \(-0.569350\pi\)
−0.216151 + 0.976360i \(0.569350\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 29.7765i 1.67242i 0.548411 + 0.836209i \(0.315233\pi\)
−0.548411 + 0.836209i \(0.684767\pi\)
\(318\) 0 0
\(319\) 2.94137i 0.164685i
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) 9.72879 0.541325
\(324\) 0 0
\(325\) −25.3224 −1.40463
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) − 10.5213i − 0.580055i
\(330\) 0 0
\(331\) 11.1138i 0.610871i 0.952213 + 0.305436i \(0.0988021\pi\)
−0.952213 + 0.305436i \(0.901198\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) −9.35580 −0.511162
\(336\) 0 0
\(337\) −5.88273 −0.320453 −0.160226 0.987080i \(-0.551222\pi\)
−0.160226 + 0.987080i \(0.551222\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) 13.7594i 0.745114i
\(342\) 0 0
\(343\) 1.00000i 0.0539949i
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) −10.6432 −0.571357 −0.285678 0.958326i \(-0.592219\pi\)
−0.285678 + 0.958326i \(0.592219\pi\)
\(348\) 0 0
\(349\) −2.49828 −0.133730 −0.0668650 0.997762i \(-0.521300\pi\)
−0.0668650 + 0.997762i \(0.521300\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) 0.126811i 0.00674945i 0.999994 + 0.00337472i \(0.00107421\pi\)
−0.999994 + 0.00337472i \(0.998926\pi\)
\(354\) 0 0
\(355\) 10.3810i 0.550967i
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 19.7551 1.04263 0.521317 0.853363i \(-0.325441\pi\)
0.521317 + 0.853363i \(0.325441\pi\)
\(360\) 0 0
\(361\) −1.23453 −0.0649754
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) − 7.94645i − 0.415936i
\(366\) 0 0
\(367\) − 28.7620i − 1.50137i −0.660663 0.750683i \(-0.729725\pi\)
0.660663 0.750683i \(-0.270275\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) −10.6042 −0.550541
\(372\) 0 0
\(373\) 0.879296 0.0455282 0.0227641 0.999741i \(-0.492753\pi\)
0.0227641 + 0.999741i \(0.492753\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) − 7.85866i − 0.404742i
\(378\) 0 0
\(379\) 22.8793i 1.17523i 0.809140 + 0.587615i \(0.199933\pi\)
−0.809140 + 0.587615i \(0.800067\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) −32.3562 −1.65333 −0.826663 0.562698i \(-0.809763\pi\)
−0.826663 + 0.562698i \(0.809763\pi\)
\(384\) 0 0
\(385\) 1.38445 0.0705582
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) 16.3391i 0.828424i 0.910180 + 0.414212i \(0.135943\pi\)
−0.910180 + 0.414212i \(0.864057\pi\)
\(390\) 0 0
\(391\) − 9.26031i − 0.468314i
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) 0.548560 0.0276010
\(396\) 0 0
\(397\) 4.85008 0.243419 0.121709 0.992566i \(-0.461162\pi\)
0.121709 + 0.992566i \(0.461162\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) − 20.8305i − 1.04022i −0.854098 0.520112i \(-0.825890\pi\)
0.854098 0.520112i \(-0.174110\pi\)
\(402\) 0 0
\(403\) − 36.7620i − 1.83125i
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 11.3137 0.560800
\(408\) 0 0
\(409\) 12.9345 0.639569 0.319785 0.947490i \(-0.396389\pi\)
0.319785 + 0.947490i \(0.396389\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) − 13.5155i − 0.665055i
\(414\) 0 0
\(415\) − 4.23453i − 0.207865i
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) −14.5519 −0.710906 −0.355453 0.934694i \(-0.615673\pi\)
−0.355453 + 0.934694i \(0.615673\pi\)
\(420\) 0 0
\(421\) 29.9018 1.45733 0.728663 0.684872i \(-0.240142\pi\)
0.728663 + 0.684872i \(0.240142\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) 9.85560i 0.478067i
\(426\) 0 0
\(427\) − 0.615547i − 0.0297884i
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) −5.86658 −0.282583 −0.141292 0.989968i \(-0.545126\pi\)
−0.141292 + 0.989968i \(0.545126\pi\)
\(432\) 0 0
\(433\) 26.1104 1.25479 0.627393 0.778703i \(-0.284122\pi\)
0.627393 + 0.778703i \(0.284122\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 19.2602i 0.921338i
\(438\) 0 0
\(439\) − 25.9931i − 1.24058i −0.784371 0.620292i \(-0.787014\pi\)
0.784371 0.620292i \(-0.212986\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) −9.23385 −0.438713 −0.219357 0.975645i \(-0.570396\pi\)
−0.219357 + 0.975645i \(0.570396\pi\)
\(444\) 0 0
\(445\) 8.44309 0.400241
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) − 33.4755i − 1.57981i −0.613232 0.789903i \(-0.710131\pi\)
0.613232 0.789903i \(-0.289869\pi\)
\(450\) 0 0
\(451\) 11.8466i 0.557837i
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) −3.69894 −0.173409
\(456\) 0 0
\(457\) −30.2277 −1.41399 −0.706995 0.707218i \(-0.749950\pi\)
−0.706995 + 0.707218i \(0.749950\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) − 10.4822i − 0.488206i −0.969749 0.244103i \(-0.921507\pi\)
0.969749 0.244103i \(-0.0784935\pi\)
\(462\) 0 0
\(463\) − 9.82066i − 0.456405i −0.973614 0.228202i \(-0.926715\pi\)
0.973614 0.228202i \(-0.0732848\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) −21.4620 −0.993141 −0.496571 0.867996i \(-0.665408\pi\)
−0.496571 + 0.867996i \(0.665408\pi\)
\(468\) 0 0
\(469\) 14.0552 0.649009
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) 4.40362i 0.202479i
\(474\) 0 0
\(475\) − 20.4983i − 0.940526i
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) 8.56334 0.391269 0.195634 0.980677i \(-0.437323\pi\)
0.195634 + 0.980677i \(0.437323\pi\)
\(480\) 0 0
\(481\) −30.2277 −1.37826
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 0.548560i 0.0249088i
\(486\) 0 0
\(487\) 9.46563i 0.428929i 0.976732 + 0.214464i \(0.0688005\pi\)
−0.976732 + 0.214464i \(0.931199\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) 19.6260 0.885709 0.442854 0.896593i \(-0.353966\pi\)
0.442854 + 0.896593i \(0.353966\pi\)
\(492\) 0 0
\(493\) −3.05863 −0.137754
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) − 15.5954i − 0.699548i
\(498\) 0 0
\(499\) 2.11727i 0.0947819i 0.998876 + 0.0473909i \(0.0150907\pi\)
−0.998876 + 0.0473909i \(0.984909\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) −4.03062 −0.179717 −0.0898583 0.995955i \(-0.528641\pi\)
−0.0898583 + 0.995955i \(0.528641\pi\)
\(504\) 0 0
\(505\) −11.9018 −0.529625
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) 13.6423i 0.604686i 0.953199 + 0.302343i \(0.0977687\pi\)
−0.953199 + 0.302343i \(0.902231\pi\)
\(510\) 0 0
\(511\) 11.9379i 0.528103i
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) −8.31944 −0.366598
\(516\) 0 0
\(517\) 21.8827 0.962402
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 24.4585i 1.07155i 0.844362 + 0.535774i \(0.179980\pi\)
−0.844362 + 0.535774i \(0.820020\pi\)
\(522\) 0 0
\(523\) 16.0000i 0.699631i 0.936819 + 0.349816i \(0.113756\pi\)
−0.936819 + 0.349816i \(0.886244\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −14.3080 −0.623265
\(528\) 0 0
\(529\) −4.66730 −0.202926
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) − 31.6515i − 1.37098i
\(534\) 0 0
\(535\) 8.91539i 0.385446i
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) −2.07986 −0.0895859
\(540\) 0 0
\(541\) −7.20512 −0.309772 −0.154886 0.987932i \(-0.549501\pi\)
−0.154886 + 0.987932i \(0.549501\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) 4.07194i 0.174423i
\(546\) 0 0
\(547\) − 39.0518i − 1.66973i −0.550453 0.834866i \(-0.685545\pi\)
0.550453 0.834866i \(-0.314455\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) 6.36153 0.271010
\(552\) 0 0
\(553\) −0.824101 −0.0350443
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) − 3.99874i − 0.169432i −0.996405 0.0847161i \(-0.973002\pi\)
0.996405 0.0847161i \(-0.0269983\pi\)
\(558\) 0 0
\(559\) − 11.7655i − 0.497626i
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) −39.1372 −1.64944 −0.824718 0.565544i \(-0.808666\pi\)
−0.824718 + 0.565544i \(0.808666\pi\)
\(564\) 0 0
\(565\) −2.40699 −0.101263
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 32.7708i 1.37382i 0.726741 + 0.686912i \(0.241034\pi\)
−0.726741 + 0.686912i \(0.758966\pi\)
\(570\) 0 0
\(571\) 18.8172i 0.787476i 0.919223 + 0.393738i \(0.128818\pi\)
−0.919223 + 0.393738i \(0.871182\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) −19.5112 −0.813673
\(576\) 0 0
\(577\) −5.00344 −0.208296 −0.104148 0.994562i \(-0.533212\pi\)
−0.104148 + 0.994562i \(0.533212\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) 6.36153i 0.263921i
\(582\) 0 0
\(583\) − 22.0552i − 0.913433i
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 24.8292 1.02481 0.512406 0.858743i \(-0.328754\pi\)
0.512406 + 0.858743i \(0.328754\pi\)
\(588\) 0 0
\(589\) 29.7586 1.22618
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) 16.1391i 0.662752i 0.943499 + 0.331376i \(0.107513\pi\)
−0.943499 + 0.331376i \(0.892487\pi\)
\(594\) 0 0
\(595\) 1.43965i 0.0590198i
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) 7.03204 0.287321 0.143661 0.989627i \(-0.454113\pi\)
0.143661 + 0.989627i \(0.454113\pi\)
\(600\) 0 0
\(601\) −2.99656 −0.122232 −0.0611162 0.998131i \(-0.519466\pi\)
−0.0611162 + 0.998131i \(0.519466\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) − 4.44265i − 0.180619i
\(606\) 0 0
\(607\) − 9.46563i − 0.384198i −0.981376 0.192099i \(-0.938471\pi\)
0.981376 0.192099i \(-0.0615295\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) −58.4657 −2.36527
\(612\) 0 0
\(613\) −11.2311 −0.453620 −0.226810 0.973939i \(-0.572830\pi\)
−0.226810 + 0.973939i \(0.572830\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) − 37.6352i − 1.51514i −0.652756 0.757568i \(-0.726387\pi\)
0.652756 0.757568i \(-0.273613\pi\)
\(618\) 0 0
\(619\) 43.3346i 1.74177i 0.491491 + 0.870883i \(0.336452\pi\)
−0.491491 + 0.870883i \(0.663548\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) −12.6840 −0.508175
\(624\) 0 0
\(625\) 18.5500 0.742002
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 11.7648i 0.469092i
\(630\) 0 0
\(631\) 18.2897i 0.728103i 0.931379 + 0.364051i \(0.118607\pi\)
−0.931379 + 0.364051i \(0.881393\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) 5.43997 0.215879
\(636\) 0 0
\(637\) 5.55691 0.220173
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) − 14.2251i − 0.561856i −0.959729 0.280928i \(-0.909358\pi\)
0.959729 0.280928i \(-0.0906422\pi\)
\(642\) 0 0
\(643\) − 38.4914i − 1.51795i −0.651118 0.758976i \(-0.725700\pi\)
0.651118 0.758976i \(-0.274300\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 0.792458 0.0311547 0.0155774 0.999879i \(-0.495041\pi\)
0.0155774 + 0.999879i \(0.495041\pi\)
\(648\) 0 0
\(649\) 28.1104 1.10343
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 7.85380i 0.307343i 0.988122 + 0.153672i \(0.0491098\pi\)
−0.988122 + 0.153672i \(0.950890\pi\)
\(654\) 0 0
\(655\) 1.99312i 0.0778778i
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) −13.3936 −0.521739 −0.260870 0.965374i \(-0.584009\pi\)
−0.260870 + 0.965374i \(0.584009\pi\)
\(660\) 0 0
\(661\) −35.2603 −1.37147 −0.685734 0.727853i \(-0.740518\pi\)
−0.685734 + 0.727853i \(0.740518\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) − 2.99427i − 0.116113i
\(666\) 0 0
\(667\) − 6.05520i − 0.234458i
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 1.28025 0.0494236
\(672\) 0 0
\(673\) 40.1364 1.54714 0.773572 0.633709i \(-0.218468\pi\)
0.773572 + 0.633709i \(0.218468\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) − 20.2478i − 0.778184i −0.921199 0.389092i \(-0.872789\pi\)
0.921199 0.389092i \(-0.127211\pi\)
\(678\) 0 0
\(679\) − 0.824101i − 0.0316261i
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 40.6685 1.55614 0.778068 0.628179i \(-0.216200\pi\)
0.778068 + 0.628179i \(0.216200\pi\)
\(684\) 0 0
\(685\) 7.16902 0.273914
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) 58.9265i 2.24492i
\(690\) 0 0
\(691\) − 35.1138i − 1.33579i −0.744254 0.667896i \(-0.767195\pi\)
0.744254 0.667896i \(-0.232805\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) −10.6504 −0.403991
\(696\) 0 0
\(697\) −12.3189 −0.466613
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) 6.73939i 0.254543i 0.991868 + 0.127272i \(0.0406220\pi\)
−0.991868 + 0.127272i \(0.959378\pi\)
\(702\) 0 0
\(703\) − 24.4691i − 0.922868i
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 17.8801 0.672451
\(708\) 0 0
\(709\) −24.1104 −0.905485 −0.452742 0.891641i \(-0.649554\pi\)
−0.452742 + 0.891641i \(0.649554\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) − 28.3256i − 1.06080i
\(714\) 0 0
\(715\) − 7.69328i − 0.287713i
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) 17.1267 0.638717 0.319359 0.947634i \(-0.396533\pi\)
0.319359 + 0.947634i \(0.396533\pi\)
\(720\) 0 0
\(721\) 12.4983 0.465460
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) 6.44445i 0.239341i
\(726\) 0 0
\(727\) 2.72594i 0.101099i 0.998722 + 0.0505497i \(0.0160973\pi\)
−0.998722 + 0.0505497i \(0.983903\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) −4.57918 −0.169367
\(732\) 0 0
\(733\) −46.5535 −1.71949 −0.859746 0.510722i \(-0.829378\pi\)
−0.859746 + 0.510722i \(0.829378\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 29.2328i 1.07681i
\(738\) 0 0
\(739\) − 18.2897i − 0.672799i −0.941719 0.336399i \(-0.890791\pi\)
0.941719 0.336399i \(-0.109209\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) −37.3012 −1.36845 −0.684225 0.729271i \(-0.739859\pi\)
−0.684225 + 0.729271i \(0.739859\pi\)
\(744\) 0 0
\(745\) −1.71715 −0.0629114
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) − 13.3936i − 0.489390i
\(750\) 0 0
\(751\) − 12.2345i − 0.446444i −0.974768 0.223222i \(-0.928342\pi\)
0.974768 0.223222i \(-0.0716576\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 3.48206 0.126725
\(756\) 0 0
\(757\) −3.87586 −0.140870 −0.0704352 0.997516i \(-0.522439\pi\)
−0.0704352 + 0.997516i \(0.522439\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) − 33.0219i − 1.19704i −0.801107 0.598521i \(-0.795755\pi\)
0.801107 0.598521i \(-0.204245\pi\)
\(762\) 0 0
\(763\) − 6.11727i − 0.221460i
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) −75.1046 −2.71187
\(768\) 0 0
\(769\) −23.3415 −0.841715 −0.420858 0.907127i \(-0.638271\pi\)
−0.420858 + 0.907127i \(0.638271\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) 31.7783i 1.14299i 0.820606 + 0.571494i \(0.193636\pi\)
−0.820606 + 0.571494i \(0.806364\pi\)
\(774\) 0 0
\(775\) 30.1465i 1.08289i
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 25.6217 0.917992
\(780\) 0 0
\(781\) 32.4362 1.16066
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) 3.73568i 0.133332i
\(786\) 0 0
\(787\) − 1.64820i − 0.0587520i −0.999568 0.0293760i \(-0.990648\pi\)
0.999568 0.0293760i \(-0.00935202\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 3.61602 0.128571
\(792\) 0 0
\(793\) −3.42054 −0.121467
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) − 20.8376i − 0.738107i −0.929408 0.369053i \(-0.879682\pi\)
0.929408 0.369053i \(-0.120318\pi\)
\(798\) 0 0
\(799\) 22.7552i 0.805019i
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) −24.8292 −0.876204
\(804\) 0 0
\(805\) −2.85008 −0.100452
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) − 27.0262i − 0.950190i −0.879935 0.475095i \(-0.842414\pi\)
0.879935 0.475095i \(-0.157586\pi\)
\(810\) 0 0
\(811\) 8.65164i 0.303800i 0.988396 + 0.151900i \(0.0485392\pi\)
−0.988396 + 0.151900i \(0.951461\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) 5.43997 0.190554
\(816\) 0 0
\(817\) 9.52406 0.333205
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) − 19.2456i − 0.671675i −0.941920 0.335837i \(-0.890981\pi\)
0.941920 0.335837i \(-0.109019\pi\)
\(822\) 0 0
\(823\) 21.4036i 0.746081i 0.927815 + 0.373041i \(0.121685\pi\)
−0.927815 + 0.373041i \(0.878315\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) −37.4303 −1.30158 −0.650790 0.759258i \(-0.725562\pi\)
−0.650790 + 0.759258i \(0.725562\pi\)
\(828\) 0 0
\(829\) −49.0157 −1.70238 −0.851192 0.524854i \(-0.824120\pi\)
−0.851192 + 0.524854i \(0.824120\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) − 2.16278i − 0.0749359i
\(834\) 0 0
\(835\) 10.9897i 0.380314i
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) −15.9612 −0.551043 −0.275521 0.961295i \(-0.588850\pi\)
−0.275521 + 0.961295i \(0.588850\pi\)
\(840\) 0 0
\(841\) 27.0000 0.931034
\(842\) 0 0
\(843\) 0 0
\(844\) 0 0
\(845\) 11.9013i 0.409417i
\(846\) 0 0
\(847\) 6.67418i 0.229328i
\(848\) 0 0
\(849\) 0 0
\(850\) 0 0
\(851\) −23.2908 −0.798398
\(852\) 0 0
\(853\) −5.50172 −0.188375 −0.0941876 0.995554i \(-0.530025\pi\)
−0.0941876 + 0.995554i \(0.530025\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) 38.6007i 1.31857i 0.751892 + 0.659287i \(0.229142\pi\)
−0.751892 + 0.659287i \(0.770858\pi\)
\(858\) 0 0
\(859\) − 6.14648i − 0.209715i −0.994487 0.104858i \(-0.966561\pi\)
0.994487 0.104858i \(-0.0334387\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) −41.9631 −1.42844 −0.714220 0.699922i \(-0.753218\pi\)
−0.714220 + 0.699922i \(0.753218\pi\)
\(864\) 0 0
\(865\) 2.79488 0.0950289
\(866\) 0 0
\(867\) 0 0
\(868\) 0 0
\(869\) − 1.71401i − 0.0581439i
\(870\) 0 0
\(871\) − 78.1035i − 2.64644i
\(872\) 0 0
\(873\) 0 0
\(874\) 0 0
\(875\) 6.36153 0.215059
\(876\) 0 0
\(877\) −45.8759 −1.54912 −0.774559 0.632502i \(-0.782028\pi\)
−0.774559 + 0.632502i \(0.782028\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) − 39.3323i − 1.32514i −0.749000 0.662570i \(-0.769466\pi\)
0.749000 0.662570i \(-0.230534\pi\)
\(882\) 0 0
\(883\) − 34.1173i − 1.14814i −0.818807 0.574069i \(-0.805364\pi\)
0.818807 0.574069i \(-0.194636\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) 35.9674 1.20767 0.603833 0.797111i \(-0.293639\pi\)
0.603833 + 0.797111i \(0.293639\pi\)
\(888\) 0 0
\(889\) −8.17246 −0.274096
\(890\) 0 0
\(891\) 0 0
\(892\) 0 0
\(893\) − 47.3275i − 1.58376i
\(894\) 0 0
\(895\) 1.38445i 0.0462771i
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) −9.35580 −0.312033
\(900\) 0 0
\(901\) 22.9345 0.764059
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) 7.61477i 0.253123i
\(906\) 0 0
\(907\) − 24.3449i − 0.808360i −0.914679 0.404180i \(-0.867557\pi\)
0.914679 0.404180i \(-0.132443\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) −17.4242 −0.577289 −0.288645 0.957436i \(-0.593205\pi\)
−0.288645 + 0.957436i \(0.593205\pi\)
\(912\) 0 0
\(913\) −13.2311 −0.437885
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) − 2.99427i − 0.0988794i
\(918\) 0 0
\(919\) − 7.22422i − 0.238305i −0.992876 0.119152i \(-0.961982\pi\)
0.992876 0.119152i \(-0.0380177\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 0 0
\(923\) −86.6622 −2.85252
\(924\) 0 0
\(925\) 24.7880 0.815025
\(926\) 0 0
\(927\) 0 0
\(928\) 0 0
\(929\) 36.7208i 1.20477i 0.798206 + 0.602385i \(0.205783\pi\)
−0.798206 + 0.602385i \(0.794217\pi\)
\(930\) 0 0
\(931\) 4.49828i 0.147425i
\(932\) 0 0
\(933\) 0 0
\(934\) 0 0
\(935\) −2.99427 −0.0979230
\(936\) 0 0
\(937\) −20.6448 −0.674435 −0.337218 0.941427i \(-0.609486\pi\)
−0.337218 + 0.941427i \(0.609486\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0 0
\(941\) 39.9687i 1.30294i 0.758674 + 0.651471i \(0.225848\pi\)
−0.758674 + 0.651471i \(0.774152\pi\)
\(942\) 0 0
\(943\) − 24.3879i − 0.794179i
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) −16.1439 −0.524607 −0.262304 0.964985i \(-0.584482\pi\)
−0.262304 + 0.964985i \(0.584482\pi\)
\(948\) 0 0
\(949\) 66.3380 2.15342
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) 23.2394i 0.752800i 0.926457 + 0.376400i \(0.122838\pi\)
−0.926457 + 0.376400i \(0.877162\pi\)
\(954\) 0 0
\(955\) 5.61899i 0.181826i
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) −10.7700 −0.347782
\(960\) 0 0
\(961\) −12.7655 −0.411789
\(962\) 0 0
\(963\) 0 0
\(964\) 0 0
\(965\) 6.43959i 0.207298i
\(966\) 0 0
\(967\) − 16.0483i − 0.516079i −0.966134 0.258040i \(-0.916924\pi\)
0.966134 0.258040i \(-0.0830765\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) −28.8134 −0.924665 −0.462333 0.886707i \(-0.652987\pi\)
−0.462333 + 0.886707i \(0.652987\pi\)
\(972\) 0 0
\(973\) 16.0000 0.512936
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) − 35.3043i − 1.12948i −0.825267 0.564742i \(-0.808976\pi\)
0.825267 0.564742i \(-0.191024\pi\)
\(978\) 0 0
\(979\) − 26.3810i − 0.843141i
\(980\) 0 0
\(981\) 0 0
\(982\) 0 0
\(983\) −10.2774 −0.327797 −0.163898 0.986477i \(-0.552407\pi\)
−0.163898 + 0.986477i \(0.552407\pi\)
\(984\) 0 0
\(985\) 8.94137 0.284896
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) − 9.06543i − 0.288264i
\(990\) 0 0
\(991\) − 57.2173i − 1.81757i −0.417266 0.908784i \(-0.637012\pi\)
0.417266 0.908784i \(-0.362988\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0 0
\(995\) −18.0482 −0.572168
\(996\) 0 0
\(997\) −5.73625 −0.181669 −0.0908345 0.995866i \(-0.528953\pi\)
−0.0908345 + 0.995866i \(0.528953\pi\)
\(998\) 0 0
\(999\) 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 4032.2.h.h.575.7 12
3.2 odd 2 inner 4032.2.h.h.575.5 12
4.3 odd 2 inner 4032.2.h.h.575.8 12
8.3 odd 2 252.2.e.a.71.3 12
8.5 even 2 252.2.e.a.71.9 yes 12
12.11 even 2 inner 4032.2.h.h.575.6 12
24.5 odd 2 252.2.e.a.71.4 yes 12
24.11 even 2 252.2.e.a.71.10 yes 12
56.13 odd 2 1764.2.e.g.1079.9 12
56.27 even 2 1764.2.e.g.1079.3 12
168.83 odd 2 1764.2.e.g.1079.10 12
168.125 even 2 1764.2.e.g.1079.4 12
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
252.2.e.a.71.3 12 8.3 odd 2
252.2.e.a.71.4 yes 12 24.5 odd 2
252.2.e.a.71.9 yes 12 8.5 even 2
252.2.e.a.71.10 yes 12 24.11 even 2
1764.2.e.g.1079.3 12 56.27 even 2
1764.2.e.g.1079.4 12 168.125 even 2
1764.2.e.g.1079.9 12 56.13 odd 2
1764.2.e.g.1079.10 12 168.83 odd 2
4032.2.h.h.575.5 12 3.2 odd 2 inner
4032.2.h.h.575.6 12 12.11 even 2 inner
4032.2.h.h.575.7 12 1.1 even 1 trivial
4032.2.h.h.575.8 12 4.3 odd 2 inner