Properties

Label 2880.2.o.f.2879.5
Level $2880$
Weight $2$
Character 2880.2879
Analytic conductor $22.997$
Analytic rank $0$
Dimension $12$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 2880 = 2^{6} \cdot 3^{2} \cdot 5 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2880.o (of order \(2\), degree \(1\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(22.9969157821\)
Analytic rank: \(0\)
Dimension: \(12\)
Coefficient field: 12.0.426337261060096.1
Defining polynomial: \(x^{12} - 4 x^{9} - 3 x^{8} + 4 x^{7} + 8 x^{6} + 8 x^{5} - 12 x^{4} - 32 x^{3} + 64\)
Coefficient ring: \(\Z[a_1, \ldots, a_{13}]\)
Coefficient ring index: \( 2^{10} \)
Twist minimal: no (minimal twist has level 1440)
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 2879.5
Root \(-0.394157 - 1.35818i\) of defining polynomial
Character \(\chi\) \(=\) 2880.2879
Dual form 2880.2.o.f.2879.6

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.256912 - 2.22126i) q^{5} -3.50466 q^{7} +O(q^{10})\) \(q+(-0.256912 - 2.22126i) q^{5} -3.50466 q^{7} -1.92804 q^{11} -5.50466i q^{13} -4.44252 q^{17} +7.00933i q^{19} -1.10027i q^{23} +(-4.86799 + 1.14134i) q^{25} +5.47017i q^{29} +8.28267i q^{31} +(0.900390 + 7.78477i) q^{35} -0.778008i q^{37} -2.44186i q^{41} +9.55602 q^{43} -11.7135i q^{47} +5.28267 q^{49} +11.5268 q^{53} +(0.495336 + 4.28267i) q^{55} +9.78543 q^{59} +3.45331 q^{61} +(-12.2273 + 1.41421i) q^{65} -5.45331 q^{67} +4.25583 q^{71} +7.27334i q^{73} +6.75712 q^{77} +2.82936i q^{79} +4.25583i q^{83} +(1.14134 + 9.86799i) q^{85} +0.386566i q^{89} +19.2920i q^{91} +(15.5695 - 1.80078i) q^{95} +9.29200i q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12q + O(q^{10}) \) \( 12q - 8q^{25} + 64q^{43} - 4q^{49} + 48q^{55} + 8q^{61} - 32q^{67} - 20q^{85} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/2880\mathbb{Z}\right)^\times\).

\(n\) \(577\) \(641\) \(901\) \(2431\)
\(\chi(n)\) \(-1\) \(-1\) \(1\) \(-1\)

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
\(5\) −0.256912 2.22126i −0.114894 0.993378i
\(6\) 0 0
\(7\) −3.50466 −1.32464 −0.662319 0.749222i \(-0.730428\pi\)
−0.662319 + 0.749222i \(0.730428\pi\)
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) −1.92804 −0.581325 −0.290663 0.956826i \(-0.593876\pi\)
−0.290663 + 0.956826i \(0.593876\pi\)
\(12\) 0 0
\(13\) 5.50466i 1.52672i −0.645974 0.763360i \(-0.723548\pi\)
0.645974 0.763360i \(-0.276452\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) −4.44252 −1.07747 −0.538735 0.842475i \(-0.681097\pi\)
−0.538735 + 0.842475i \(0.681097\pi\)
\(18\) 0 0
\(19\) 7.00933i 1.60805i 0.594595 + 0.804025i \(0.297312\pi\)
−0.594595 + 0.804025i \(0.702688\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) 1.10027i 0.229422i −0.993399 0.114711i \(-0.963406\pi\)
0.993399 0.114711i \(-0.0365942\pi\)
\(24\) 0 0
\(25\) −4.86799 + 1.14134i −0.973599 + 0.228267i
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) 5.47017i 1.01578i 0.861421 + 0.507892i \(0.169575\pi\)
−0.861421 + 0.507892i \(0.830425\pi\)
\(30\) 0 0
\(31\) 8.28267i 1.48761i 0.668396 + 0.743806i \(0.266981\pi\)
−0.668396 + 0.743806i \(0.733019\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) 0.900390 + 7.78477i 0.152194 + 1.31587i
\(36\) 0 0
\(37\) 0.778008i 0.127904i −0.997953 0.0639519i \(-0.979630\pi\)
0.997953 0.0639519i \(-0.0203704\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) 2.44186i 0.381355i −0.981653 0.190677i \(-0.938932\pi\)
0.981653 0.190677i \(-0.0610684\pi\)
\(42\) 0 0
\(43\) 9.55602 1.45728 0.728639 0.684898i \(-0.240153\pi\)
0.728639 + 0.684898i \(0.240153\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 11.7135i 1.70858i −0.519793 0.854292i \(-0.673991\pi\)
0.519793 0.854292i \(-0.326009\pi\)
\(48\) 0 0
\(49\) 5.28267 0.754667
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) 11.5268 1.58333 0.791663 0.610959i \(-0.209216\pi\)
0.791663 + 0.610959i \(0.209216\pi\)
\(54\) 0 0
\(55\) 0.495336 + 4.28267i 0.0667910 + 0.577475i
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) 9.78543 1.27395 0.636977 0.770883i \(-0.280185\pi\)
0.636977 + 0.770883i \(0.280185\pi\)
\(60\) 0 0
\(61\) 3.45331 0.442151 0.221076 0.975257i \(-0.429043\pi\)
0.221076 + 0.975257i \(0.429043\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) −12.2273 + 1.41421i −1.51661 + 0.175412i
\(66\) 0 0
\(67\) −5.45331 −0.666228 −0.333114 0.942887i \(-0.608099\pi\)
−0.333114 + 0.942887i \(0.608099\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 4.25583 0.505075 0.252537 0.967587i \(-0.418735\pi\)
0.252537 + 0.967587i \(0.418735\pi\)
\(72\) 0 0
\(73\) 7.27334i 0.851280i 0.904892 + 0.425640i \(0.139951\pi\)
−0.904892 + 0.425640i \(0.860049\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 6.75712 0.770046
\(78\) 0 0
\(79\) 2.82936i 0.318328i 0.987252 + 0.159164i \(0.0508798\pi\)
−0.987252 + 0.159164i \(0.949120\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) 4.25583i 0.467138i 0.972340 + 0.233569i \(0.0750405\pi\)
−0.972340 + 0.233569i \(0.924959\pi\)
\(84\) 0 0
\(85\) 1.14134 + 9.86799i 0.123795 + 1.07033i
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 0.386566i 0.0409759i 0.999790 + 0.0204880i \(0.00652198\pi\)
−0.999790 + 0.0204880i \(0.993478\pi\)
\(90\) 0 0
\(91\) 19.2920i 2.02235i
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 15.5695 1.80078i 1.59740 0.184756i
\(96\) 0 0
\(97\) 9.29200i 0.943460i 0.881743 + 0.471730i \(0.156370\pi\)
−0.881743 + 0.471730i \(0.843630\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) 7.27095i 0.723486i −0.932278 0.361743i \(-0.882182\pi\)
0.932278 0.361743i \(-0.117818\pi\)
\(102\) 0 0
\(103\) −16.9580 −1.67092 −0.835460 0.549552i \(-0.814798\pi\)
−0.835460 + 0.549552i \(0.814798\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 9.91269i 0.958296i 0.877734 + 0.479148i \(0.159054\pi\)
−0.877734 + 0.479148i \(0.840946\pi\)
\(108\) 0 0
\(109\) −8.28267 −0.793336 −0.396668 0.917962i \(-0.629834\pi\)
−0.396668 + 0.917962i \(0.629834\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) 17.8115 1.67557 0.837784 0.546002i \(-0.183851\pi\)
0.837784 + 0.546002i \(0.183851\pi\)
\(114\) 0 0
\(115\) −2.44398 + 0.282672i −0.227903 + 0.0263593i
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) 15.5695 1.42726
\(120\) 0 0
\(121\) −7.28267 −0.662061
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) 3.78585 + 10.5199i 0.338617 + 0.940924i
\(126\) 0 0
\(127\) −0.957977 −0.0850067 −0.0425034 0.999096i \(-0.513533\pi\)
−0.0425034 + 0.999096i \(0.513533\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) 8.38441 0.732549 0.366275 0.930507i \(-0.380633\pi\)
0.366275 + 0.930507i \(0.380633\pi\)
\(132\) 0 0
\(133\) 24.5653i 2.13009i
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) −11.1270 −0.950646 −0.475323 0.879811i \(-0.657669\pi\)
−0.475323 + 0.879811i \(0.657669\pi\)
\(138\) 0 0
\(139\) 1.17064i 0.0992924i −0.998767 0.0496462i \(-0.984191\pi\)
0.998767 0.0496462i \(-0.0158094\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 10.6132i 0.887520i
\(144\) 0 0
\(145\) 12.1507 1.40535i 1.00906 0.116708i
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) 11.5268i 0.944311i −0.881515 0.472155i \(-0.843476\pi\)
0.881515 0.472155i \(-0.156524\pi\)
\(150\) 0 0
\(151\) 10.8294i 0.881281i 0.897684 + 0.440640i \(0.145249\pi\)
−0.897684 + 0.440640i \(0.854751\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 18.3980 2.12792i 1.47776 0.170918i
\(156\) 0 0
\(157\) 10.3340i 0.824745i 0.911015 + 0.412372i \(0.135300\pi\)
−0.911015 + 0.412372i \(0.864700\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 3.85607i 0.303901i
\(162\) 0 0
\(163\) 8.99067 0.704204 0.352102 0.935962i \(-0.385467\pi\)
0.352102 + 0.935962i \(0.385467\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 13.0683i 1.01125i 0.862753 + 0.505626i \(0.168738\pi\)
−0.862753 + 0.505626i \(0.831262\pi\)
\(168\) 0 0
\(169\) −17.3013 −1.33087
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) −19.6123 −1.49110 −0.745548 0.666452i \(-0.767812\pi\)
−0.745548 + 0.666452i \(0.767812\pi\)
\(174\) 0 0
\(175\) 17.0607 4.00000i 1.28967 0.302372i
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) 7.58489 0.566921 0.283461 0.958984i \(-0.408517\pi\)
0.283461 + 0.958984i \(0.408517\pi\)
\(180\) 0 0
\(181\) 2.82936 0.210305 0.105152 0.994456i \(-0.466467\pi\)
0.105152 + 0.994456i \(0.466467\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) −1.72816 + 0.199879i −0.127057 + 0.0146954i
\(186\) 0 0
\(187\) 8.56534 0.626360
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) −15.1698 −1.09765 −0.548823 0.835938i \(-0.684924\pi\)
−0.548823 + 0.835938i \(0.684924\pi\)
\(192\) 0 0
\(193\) 0.565344i 0.0406944i −0.999793 0.0203472i \(-0.993523\pi\)
0.999793 0.0203472i \(-0.00647716\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) −8.37122 −0.596424 −0.298212 0.954500i \(-0.596390\pi\)
−0.298212 + 0.954500i \(0.596390\pi\)
\(198\) 0 0
\(199\) 19.7546i 1.40037i 0.713962 + 0.700185i \(0.246899\pi\)
−0.713962 + 0.700185i \(0.753101\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) 19.1711i 1.34555i
\(204\) 0 0
\(205\) −5.42401 + 0.627343i −0.378829 + 0.0438155i
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) 13.5142i 0.934800i
\(210\) 0 0
\(211\) 14.8294i 1.02090i 0.859909 + 0.510448i \(0.170520\pi\)
−0.859909 + 0.510448i \(0.829480\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) −2.45505 21.2264i −0.167433 1.44763i
\(216\) 0 0
\(217\) 29.0280i 1.97055i
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) 24.4546i 1.64499i
\(222\) 0 0
\(223\) −19.5047 −1.30613 −0.653064 0.757302i \(-0.726517\pi\)
−0.653064 + 0.757302i \(0.726517\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 6.45637i 0.428524i −0.976776 0.214262i \(-0.931265\pi\)
0.976776 0.214262i \(-0.0687347\pi\)
\(228\) 0 0
\(229\) 24.8480 1.64200 0.821002 0.570926i \(-0.193416\pi\)
0.821002 + 0.570926i \(0.193416\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 8.04408 0.526985 0.263493 0.964661i \(-0.415126\pi\)
0.263493 + 0.964661i \(0.415126\pi\)
\(234\) 0 0
\(235\) −26.0187 + 3.00933i −1.69727 + 0.196307i
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) 19.5709 1.26593 0.632967 0.774179i \(-0.281837\pi\)
0.632967 + 0.774179i \(0.281837\pi\)
\(240\) 0 0
\(241\) 25.1307 1.61881 0.809405 0.587251i \(-0.199790\pi\)
0.809405 + 0.587251i \(0.199790\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) −1.35718 11.7342i −0.0867071 0.749670i
\(246\) 0 0
\(247\) 38.5840 2.45504
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) −26.7560 −1.68882 −0.844412 0.535695i \(-0.820050\pi\)
−0.844412 + 0.535695i \(0.820050\pi\)
\(252\) 0 0
\(253\) 2.12136i 0.133369i
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 8.69835 0.542588 0.271294 0.962496i \(-0.412548\pi\)
0.271294 + 0.962496i \(0.412548\pi\)
\(258\) 0 0
\(259\) 2.72666i 0.169426i
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) 18.0708i 1.11430i 0.830413 + 0.557148i \(0.188104\pi\)
−0.830413 + 0.557148i \(0.811896\pi\)
\(264\) 0 0
\(265\) −2.96137 25.6040i −0.181915 1.57284i
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) 9.95413i 0.606914i −0.952845 0.303457i \(-0.901859\pi\)
0.952845 0.303457i \(-0.0981409\pi\)
\(270\) 0 0
\(271\) 27.1893i 1.65163i 0.563939 + 0.825816i \(0.309285\pi\)
−0.563939 + 0.825816i \(0.690715\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 9.38567 2.20054i 0.565977 0.132697i
\(276\) 0 0
\(277\) 9.40196i 0.564909i 0.959281 + 0.282455i \(0.0911486\pi\)
−0.959281 + 0.282455i \(0.908851\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) 9.52612i 0.568281i 0.958783 + 0.284140i \(0.0917082\pi\)
−0.958783 + 0.284140i \(0.908292\pi\)
\(282\) 0 0
\(283\) −14.5840 −0.866929 −0.433464 0.901171i \(-0.642709\pi\)
−0.433464 + 0.901171i \(0.642709\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 8.55790i 0.505157i
\(288\) 0 0
\(289\) 2.73599 0.160940
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) −21.8855 −1.27856 −0.639281 0.768973i \(-0.720768\pi\)
−0.639281 + 0.768973i \(0.720768\pi\)
\(294\) 0 0
\(295\) −2.51399 21.7360i −0.146370 1.26552i
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) −6.05661 −0.350263
\(300\) 0 0
\(301\) −33.4906 −1.93037
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) −0.887197 7.67071i −0.0508008 0.439223i
\(306\) 0 0
\(307\) −25.1307 −1.43428 −0.717142 0.696927i \(-0.754550\pi\)
−0.717142 + 0.696927i \(0.754550\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) −22.8819 −1.29752 −0.648758 0.760995i \(-0.724711\pi\)
−0.648758 + 0.760995i \(0.724711\pi\)
\(312\) 0 0
\(313\) 32.5653i 1.84070i 0.391093 + 0.920351i \(0.372097\pi\)
−0.391093 + 0.920351i \(0.627903\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 1.91484 0.107548 0.0537742 0.998553i \(-0.482875\pi\)
0.0537742 + 0.998553i \(0.482875\pi\)
\(318\) 0 0
\(319\) 10.5467i 0.590501i
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) 31.1391i 1.73262i
\(324\) 0 0
\(325\) 6.28267 + 26.7967i 0.348500 + 1.48641i
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) 41.0518i 2.26326i
\(330\) 0 0
\(331\) 6.44398i 0.354193i 0.984193 + 0.177097i \(0.0566705\pi\)
−0.984193 + 0.177097i \(0.943329\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) 1.40102 + 12.1132i 0.0765459 + 0.661816i
\(336\) 0 0
\(337\) 8.93206i 0.486560i −0.969956 0.243280i \(-0.921777\pi\)
0.969956 0.243280i \(-0.0782235\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) 15.9693i 0.864786i
\(342\) 0 0
\(343\) 6.01866 0.324977
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 23.2817i 1.24983i 0.780694 + 0.624913i \(0.214866\pi\)
−0.780694 + 0.624913i \(0.785134\pi\)
\(348\) 0 0
\(349\) −17.1120 −0.915986 −0.457993 0.888956i \(-0.651432\pi\)
−0.457993 + 0.888956i \(0.651432\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) 14.7286 0.783923 0.391962 0.919982i \(-0.371797\pi\)
0.391962 + 0.919982i \(0.371797\pi\)
\(354\) 0 0
\(355\) −1.09337 9.45331i −0.0580303 0.501730i
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) −20.2251 −1.06744 −0.533721 0.845661i \(-0.679207\pi\)
−0.533721 + 0.845661i \(0.679207\pi\)
\(360\) 0 0
\(361\) −30.1307 −1.58583
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) 16.1560 1.86861i 0.845643 0.0978074i
\(366\) 0 0
\(367\) −12.0700 −0.630049 −0.315025 0.949083i \(-0.602013\pi\)
−0.315025 + 0.949083i \(0.602013\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) −40.3975 −2.09733
\(372\) 0 0
\(373\) 12.8153i 0.663552i 0.943358 + 0.331776i \(0.107648\pi\)
−0.943358 + 0.331776i \(0.892352\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 30.1114 1.55082
\(378\) 0 0
\(379\) 17.7360i 0.911036i −0.890226 0.455518i \(-0.849454\pi\)
0.890226 0.455518i \(-0.150546\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 25.0825i 1.28165i 0.767685 + 0.640827i \(0.221408\pi\)
−0.767685 + 0.640827i \(0.778592\pi\)
\(384\) 0 0
\(385\) −1.73599 15.0093i −0.0884740 0.764946i
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) 23.4684i 1.18989i 0.803765 + 0.594947i \(0.202827\pi\)
−0.803765 + 0.594947i \(0.797173\pi\)
\(390\) 0 0
\(391\) 4.88797i 0.247195i
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) 6.28474 0.726896i 0.316220 0.0365741i
\(396\) 0 0
\(397\) 2.69396i 0.135206i −0.997712 0.0676031i \(-0.978465\pi\)
0.997712 0.0676031i \(-0.0215351\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 32.3252i 1.61424i −0.590386 0.807121i \(-0.701025\pi\)
0.590386 0.807121i \(-0.298975\pi\)
\(402\) 0 0
\(403\) 45.5933 2.27117
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 1.50003i 0.0743536i
\(408\) 0 0
\(409\) 20.6426 1.02071 0.510356 0.859963i \(-0.329514\pi\)
0.510356 + 0.859963i \(0.329514\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) −34.2946 −1.68753
\(414\) 0 0
\(415\) 9.45331 1.09337i 0.464045 0.0536716i
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 23.1544 1.13117 0.565584 0.824691i \(-0.308651\pi\)
0.565584 + 0.824691i \(0.308651\pi\)
\(420\) 0 0
\(421\) 28.3200 1.38023 0.690116 0.723699i \(-0.257560\pi\)
0.690116 + 0.723699i \(0.257560\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) 21.6262 5.07041i 1.04902 0.245951i
\(426\) 0 0
\(427\) −12.1027 −0.585691
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) −26.6287 −1.28266 −0.641331 0.767265i \(-0.721617\pi\)
−0.641331 + 0.767265i \(0.721617\pi\)
\(432\) 0 0
\(433\) 23.3693i 1.12306i 0.827458 + 0.561528i \(0.189786\pi\)
−0.827458 + 0.561528i \(0.810214\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 7.71215 0.368922
\(438\) 0 0
\(439\) 28.3200i 1.35164i −0.737067 0.675820i \(-0.763790\pi\)
0.737067 0.675820i \(-0.236210\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 23.2817i 1.10615i −0.833133 0.553073i \(-0.813455\pi\)
0.833133 0.553073i \(-0.186545\pi\)
\(444\) 0 0
\(445\) 0.858664 0.0993134i 0.0407046 0.00470791i
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) 29.3251i 1.38394i −0.721927 0.691969i \(-0.756744\pi\)
0.721927 0.691969i \(-0.243256\pi\)
\(450\) 0 0
\(451\) 4.70800i 0.221691i
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) 42.8526 4.95634i 2.00896 0.232357i
\(456\) 0 0
\(457\) 18.9507i 0.886477i 0.896404 + 0.443239i \(0.146171\pi\)
−0.896404 + 0.443239i \(0.853829\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 10.3539i 0.482229i −0.970497 0.241114i \(-0.922487\pi\)
0.970497 0.241114i \(-0.0775129\pi\)
\(462\) 0 0
\(463\) 3.07934 0.143109 0.0715545 0.997437i \(-0.477204\pi\)
0.0715545 + 0.997437i \(0.477204\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 40.9065i 1.89293i −0.322809 0.946464i \(-0.604627\pi\)
0.322809 0.946464i \(-0.395373\pi\)
\(468\) 0 0
\(469\) 19.1120 0.882512
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) −18.4244 −0.847153
\(474\) 0 0
\(475\) −8.00000 34.1214i −0.367065 1.56560i
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) −16.3691 −0.747921 −0.373961 0.927445i \(-0.622001\pi\)
−0.373961 + 0.927445i \(0.622001\pi\)
\(480\) 0 0
\(481\) −4.28267 −0.195273
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 20.6400 2.38723i 0.937212 0.108398i
\(486\) 0 0
\(487\) 0.957977 0.0434101 0.0217050 0.999764i \(-0.493091\pi\)
0.0217050 + 0.999764i \(0.493091\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) 10.8395 0.489178 0.244589 0.969627i \(-0.421347\pi\)
0.244589 + 0.969627i \(0.421347\pi\)
\(492\) 0 0
\(493\) 24.3013i 1.09448i
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) −14.9153 −0.669041
\(498\) 0 0
\(499\) 31.5747i 1.41348i −0.707475 0.706738i \(-0.750166\pi\)
0.707475 0.706738i \(-0.249834\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) 15.8241i 0.705560i −0.935706 0.352780i \(-0.885236\pi\)
0.935706 0.352780i \(-0.114764\pi\)
\(504\) 0 0
\(505\) −16.1507 + 1.86799i −0.718695 + 0.0831246i
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) 10.1258i 0.448816i 0.974495 + 0.224408i \(0.0720449\pi\)
−0.974495 + 0.224408i \(0.927955\pi\)
\(510\) 0 0
\(511\) 25.4906i 1.12764i
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) 4.35671 + 37.6681i 0.191979 + 1.65985i
\(516\) 0 0
\(517\) 22.5840i 0.993243i
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 33.3528i 1.46121i 0.682799 + 0.730607i \(0.260763\pi\)
−0.682799 + 0.730607i \(0.739237\pi\)
\(522\) 0 0
\(523\) 25.9160 1.13323 0.566613 0.823984i \(-0.308254\pi\)
0.566613 + 0.823984i \(0.308254\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 36.7959i 1.60286i
\(528\) 0 0
\(529\) 21.7894 0.947366
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) −13.4416 −0.582221
\(534\) 0 0
\(535\) 22.0187 2.54669i 0.951950 0.110103i
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) −10.1852 −0.438707
\(540\) 0 0
\(541\) −3.39470 −0.145950 −0.0729749 0.997334i \(-0.523249\pi\)
−0.0729749 + 0.997334i \(0.523249\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) 2.12792 + 18.3980i 0.0911499 + 0.788082i
\(546\) 0 0
\(547\) 7.57467 0.323870 0.161935 0.986801i \(-0.448227\pi\)
0.161935 + 0.986801i \(0.448227\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) −38.3422 −1.63343
\(552\) 0 0
\(553\) 9.91595i 0.421669i
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 1.38596 0.0587252 0.0293626 0.999569i \(-0.490652\pi\)
0.0293626 + 0.999569i \(0.490652\pi\)
\(558\) 0 0
\(559\) 52.6027i 2.22486i
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) 31.7934i 1.33993i 0.742393 + 0.669965i \(0.233691\pi\)
−0.742393 + 0.669965i \(0.766309\pi\)
\(564\) 0 0
\(565\) −4.57599 39.5640i −0.192513 1.66447i
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 11.3005i 0.473742i 0.971541 + 0.236871i \(0.0761219\pi\)
−0.971541 + 0.236871i \(0.923878\pi\)
\(570\) 0 0
\(571\) 13.5933i 0.568863i −0.958696 0.284432i \(-0.908195\pi\)
0.958696 0.284432i \(-0.0918049\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 1.25578 + 5.35610i 0.0523695 + 0.223365i
\(576\) 0 0
\(577\) 43.0466i 1.79206i −0.443998 0.896028i \(-0.646440\pi\)
0.443998 0.896028i \(-0.353560\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) 14.9153i 0.618790i
\(582\) 0 0
\(583\) −22.2241 −0.920427
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 5.80210i 0.239478i 0.992805 + 0.119739i \(0.0382058\pi\)
−0.992805 + 0.119739i \(0.961794\pi\)
\(588\) 0 0
\(589\) −58.0560 −2.39215
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) −15.9015 −0.652995 −0.326498 0.945198i \(-0.605869\pi\)
−0.326498 + 0.945198i \(0.605869\pi\)
\(594\) 0 0
\(595\) −4.00000 34.5840i −0.163984 1.41781i
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) 39.2510 1.60375 0.801876 0.597490i \(-0.203835\pi\)
0.801876 + 0.597490i \(0.203835\pi\)
\(600\) 0 0
\(601\) −7.73599 −0.315557 −0.157779 0.987474i \(-0.550433\pi\)
−0.157779 + 0.987474i \(0.550433\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) 1.87100 + 16.1767i 0.0760672 + 0.657677i
\(606\) 0 0
\(607\) −7.60737 −0.308774 −0.154387 0.988010i \(-0.549340\pi\)
−0.154387 + 0.988010i \(0.549340\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) −64.4787 −2.60853
\(612\) 0 0
\(613\) 0.418069i 0.0168856i −0.999964 0.00844282i \(-0.997313\pi\)
0.999964 0.00844282i \(-0.00268747\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) −44.3214 −1.78431 −0.892156 0.451727i \(-0.850808\pi\)
−0.892156 + 0.451727i \(0.850808\pi\)
\(618\) 0 0
\(619\) 4.07727i 0.163879i 0.996637 + 0.0819396i \(0.0261115\pi\)
−0.996637 + 0.0819396i \(0.973889\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 1.35478i 0.0542783i
\(624\) 0 0
\(625\) 22.3947 11.1120i 0.895788 0.444481i
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 3.45632i 0.137812i
\(630\) 0 0
\(631\) 7.71733i 0.307222i 0.988131 + 0.153611i \(0.0490903\pi\)
−0.988131 + 0.153611i \(0.950910\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) 0.246116 + 2.12792i 0.00976680 + 0.0844438i
\(636\) 0 0
\(637\) 29.0793i 1.15217i
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) 6.18866i 0.244438i 0.992503 + 0.122219i \(0.0390010\pi\)
−0.992503 + 0.122219i \(0.960999\pi\)
\(642\) 0 0
\(643\) −26.1214 −1.03013 −0.515063 0.857152i \(-0.672231\pi\)
−0.515063 + 0.857152i \(0.672231\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 3.20180i 0.125876i 0.998017 + 0.0629379i \(0.0200470\pi\)
−0.998017 + 0.0629379i \(0.979953\pi\)
\(648\) 0 0
\(649\) −18.8667 −0.740582
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 19.4568 0.761403 0.380702 0.924698i \(-0.375683\pi\)
0.380702 + 0.924698i \(0.375683\pi\)
\(654\) 0 0
\(655\) −2.15405 18.6240i −0.0841659 0.727698i
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) −2.32780 −0.0906781 −0.0453390 0.998972i \(-0.514437\pi\)
−0.0453390 + 0.998972i \(0.514437\pi\)
\(660\) 0 0
\(661\) 38.0373 1.47948 0.739740 0.672893i \(-0.234948\pi\)
0.739740 + 0.672893i \(0.234948\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) −54.5660 + 6.31113i −2.11598 + 0.244735i
\(666\) 0 0
\(667\) 6.01866 0.233043
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) −6.65812 −0.257034
\(672\) 0 0
\(673\) 34.6867i 1.33707i 0.743679 + 0.668537i \(0.233079\pi\)
−0.743679 + 0.668537i \(0.766921\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 45.1672 1.73591 0.867957 0.496639i \(-0.165433\pi\)
0.867957 + 0.496639i \(0.165433\pi\)
\(678\) 0 0
\(679\) 32.5653i 1.24974i
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 44.7986i 1.71417i 0.515175 + 0.857085i \(0.327727\pi\)
−0.515175 + 0.857085i \(0.672273\pi\)
\(684\) 0 0
\(685\) 2.85866 + 24.7160i 0.109224 + 0.944350i
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) 63.4511i 2.41729i
\(690\) 0 0
\(691\) 6.80392i 0.258833i 0.991590 + 0.129417i \(0.0413105\pi\)
−0.991590 + 0.129417i \(0.958690\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) −2.60030 + 0.300751i −0.0986349 + 0.0114082i
\(696\) 0 0
\(697\) 10.8480i 0.410898i
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) 29.5250i 1.11514i 0.830129 + 0.557572i \(0.188267\pi\)
−0.830129 + 0.557572i \(0.811733\pi\)
\(702\) 0 0
\(703\) 5.45331 0.205676
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 25.4822i 0.958358i
\(708\) 0 0
\(709\) 27.1893 1.02112 0.510558 0.859843i \(-0.329439\pi\)
0.510558 + 0.859843i \(0.329439\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) 9.11317 0.341291
\(714\) 0 0
\(715\) 23.5747 2.72666i 0.881643 0.101971i
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) −16.1145 −0.600971 −0.300486 0.953786i \(-0.597149\pi\)
−0.300486 + 0.953786i \(0.597149\pi\)
\(720\) 0 0
\(721\) 59.4320 2.21336
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) −6.24330 26.6287i −0.231870 0.988966i
\(726\) 0 0
\(727\) −31.1820 −1.15648 −0.578239 0.815867i \(-0.696260\pi\)
−0.578239 + 0.815867i \(0.696260\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) −42.4528 −1.57017
\(732\) 0 0
\(733\) 4.41129i 0.162935i −0.996676 0.0814674i \(-0.974039\pi\)
0.996676 0.0814674i \(-0.0259606\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 10.5142 0.387295
\(738\) 0 0
\(739\) 17.5560i 0.645808i −0.946432 0.322904i \(-0.895341\pi\)
0.946432 0.322904i \(-0.104659\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 9.65817i 0.354324i −0.984182 0.177162i \(-0.943308\pi\)
0.984182 0.177162i \(-0.0566917\pi\)
\(744\) 0 0
\(745\) −25.6040 + 2.96137i −0.938057 + 0.108496i
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) 34.7406i 1.26940i
\(750\) 0 0
\(751\) 12.6053i 0.459974i 0.973194 + 0.229987i \(0.0738683\pi\)
−0.973194 + 0.229987i \(0.926132\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 24.0548 2.78219i 0.875445 0.101254i
\(756\) 0 0
\(757\) 36.0887i 1.31166i −0.754906 0.655832i \(-0.772318\pi\)
0.754906 0.655832i \(-0.227682\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 16.8385i 0.610396i −0.952289 0.305198i \(-0.901277\pi\)
0.952289 0.305198i \(-0.0987226\pi\)
\(762\) 0 0
\(763\) 29.0280 1.05088
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 53.8655i 1.94497i
\(768\) 0 0
\(769\) −54.3200 −1.95883 −0.979414 0.201860i \(-0.935301\pi\)
−0.979414 + 0.201860i \(0.935301\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) 6.17068 0.221944 0.110972 0.993824i \(-0.464604\pi\)
0.110972 + 0.993824i \(0.464604\pi\)
\(774\) 0 0
\(775\) −9.45331 40.3200i −0.339573 1.44834i
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 17.1158 0.613237
\(780\) 0 0
\(781\) −8.20541 −0.293612
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) 22.9546 2.65493i 0.819283 0.0947586i
\(786\) 0 0
\(787\) −2.12136 −0.0756183 −0.0378092 0.999285i \(-0.512038\pi\)
−0.0378092 + 0.999285i \(0.512038\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) −62.4234 −2.21952
\(792\) 0 0
\(793\) 19.0093i 0.675041i
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) −7.92522 −0.280726 −0.140363 0.990100i \(-0.544827\pi\)
−0.140363 + 0.990100i \(0.544827\pi\)
\(798\) 0 0
\(799\) 52.0373i 1.84095i
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) 14.0233i 0.494871i
\(804\) 0 0
\(805\) 8.56534 0.990671i 0.301889 0.0349166i
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) 29.2158i 1.02717i 0.858037 + 0.513587i