Properties

Label 320.2.c.b.129.1
Level $320$
Weight $2$
Character 320.129
Analytic conductor $2.555$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 320 = 2^{6} \cdot 5 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 320.c (of order \(2\), degree \(1\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(2.55521286468\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(i)\)
Defining polynomial: \(x^{2} + 1\)
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 2 \)
Twist minimal: no (minimal twist has level 40)
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 129.1
Root \(-1.00000i\) of defining polynomial
Character \(\chi\) \(=\) 320.129
Dual form 320.2.c.b.129.2

$q$-expansion

\(f(q)\) \(=\) \(q-2.00000i q^{3} +(1.00000 - 2.00000i) q^{5} -2.00000i q^{7} -1.00000 q^{9} +O(q^{10})\) \(q-2.00000i q^{3} +(1.00000 - 2.00000i) q^{5} -2.00000i q^{7} -1.00000 q^{9} -4.00000 q^{11} +4.00000i q^{13} +(-4.00000 - 2.00000i) q^{15} +4.00000 q^{19} -4.00000 q^{21} -2.00000i q^{23} +(-3.00000 - 4.00000i) q^{25} -4.00000i q^{27} +2.00000 q^{29} +8.00000i q^{33} +(-4.00000 - 2.00000i) q^{35} -4.00000i q^{37} +8.00000 q^{39} +2.00000 q^{41} +6.00000i q^{43} +(-1.00000 + 2.00000i) q^{45} +6.00000i q^{47} +3.00000 q^{49} -4.00000i q^{53} +(-4.00000 + 8.00000i) q^{55} -8.00000i q^{57} +12.0000 q^{59} +10.0000 q^{61} +2.00000i q^{63} +(8.00000 + 4.00000i) q^{65} +14.0000i q^{67} -4.00000 q^{69} -8.00000 q^{71} -8.00000i q^{73} +(-8.00000 + 6.00000i) q^{75} +8.00000i q^{77} +16.0000 q^{79} -11.0000 q^{81} -2.00000i q^{83} -4.00000i q^{87} -6.00000 q^{89} +8.00000 q^{91} +(4.00000 - 8.00000i) q^{95} +16.0000i q^{97} +4.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2q + 2q^{5} - 2q^{9} + O(q^{10}) \) \( 2q + 2q^{5} - 2q^{9} - 8q^{11} - 8q^{15} + 8q^{19} - 8q^{21} - 6q^{25} + 4q^{29} - 8q^{35} + 16q^{39} + 4q^{41} - 2q^{45} + 6q^{49} - 8q^{55} + 24q^{59} + 20q^{61} + 16q^{65} - 8q^{69} - 16q^{71} - 16q^{75} + 32q^{79} - 22q^{81} - 12q^{89} + 16q^{91} + 8q^{95} + 8q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/320\mathbb{Z}\right)^\times\).

\(n\) \(191\) \(257\) \(261\)
\(\chi(n)\) \(1\) \(-1\) \(1\)

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
\(3\) 2.00000i 1.15470i −0.816497 0.577350i \(-0.804087\pi\)
0.816497 0.577350i \(-0.195913\pi\)
\(4\) 0 0
\(5\) 1.00000 2.00000i 0.447214 0.894427i
\(6\) 0 0
\(7\) 2.00000i 0.755929i −0.925820 0.377964i \(-0.876624\pi\)
0.925820 0.377964i \(-0.123376\pi\)
\(8\) 0 0
\(9\) −1.00000 −0.333333
\(10\) 0 0
\(11\) −4.00000 −1.20605 −0.603023 0.797724i \(-0.706037\pi\)
−0.603023 + 0.797724i \(0.706037\pi\)
\(12\) 0 0
\(13\) 4.00000i 1.10940i 0.832050 + 0.554700i \(0.187167\pi\)
−0.832050 + 0.554700i \(0.812833\pi\)
\(14\) 0 0
\(15\) −4.00000 2.00000i −1.03280 0.516398i
\(16\) 0 0
\(17\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(18\) 0 0
\(19\) 4.00000 0.917663 0.458831 0.888523i \(-0.348268\pi\)
0.458831 + 0.888523i \(0.348268\pi\)
\(20\) 0 0
\(21\) −4.00000 −0.872872
\(22\) 0 0
\(23\) 2.00000i 0.417029i −0.978019 0.208514i \(-0.933137\pi\)
0.978019 0.208514i \(-0.0668628\pi\)
\(24\) 0 0
\(25\) −3.00000 4.00000i −0.600000 0.800000i
\(26\) 0 0
\(27\) 4.00000i 0.769800i
\(28\) 0 0
\(29\) 2.00000 0.371391 0.185695 0.982607i \(-0.440546\pi\)
0.185695 + 0.982607i \(0.440546\pi\)
\(30\) 0 0
\(31\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(32\) 0 0
\(33\) 8.00000i 1.39262i
\(34\) 0 0
\(35\) −4.00000 2.00000i −0.676123 0.338062i
\(36\) 0 0
\(37\) 4.00000i 0.657596i −0.944400 0.328798i \(-0.893356\pi\)
0.944400 0.328798i \(-0.106644\pi\)
\(38\) 0 0
\(39\) 8.00000 1.28103
\(40\) 0 0
\(41\) 2.00000 0.312348 0.156174 0.987730i \(-0.450084\pi\)
0.156174 + 0.987730i \(0.450084\pi\)
\(42\) 0 0
\(43\) 6.00000i 0.914991i 0.889212 + 0.457496i \(0.151253\pi\)
−0.889212 + 0.457496i \(0.848747\pi\)
\(44\) 0 0
\(45\) −1.00000 + 2.00000i −0.149071 + 0.298142i
\(46\) 0 0
\(47\) 6.00000i 0.875190i 0.899172 + 0.437595i \(0.144170\pi\)
−0.899172 + 0.437595i \(0.855830\pi\)
\(48\) 0 0
\(49\) 3.00000 0.428571
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) 4.00000i 0.549442i −0.961524 0.274721i \(-0.911414\pi\)
0.961524 0.274721i \(-0.0885855\pi\)
\(54\) 0 0
\(55\) −4.00000 + 8.00000i −0.539360 + 1.07872i
\(56\) 0 0
\(57\) 8.00000i 1.05963i
\(58\) 0 0
\(59\) 12.0000 1.56227 0.781133 0.624364i \(-0.214642\pi\)
0.781133 + 0.624364i \(0.214642\pi\)
\(60\) 0 0
\(61\) 10.0000 1.28037 0.640184 0.768221i \(-0.278858\pi\)
0.640184 + 0.768221i \(0.278858\pi\)
\(62\) 0 0
\(63\) 2.00000i 0.251976i
\(64\) 0 0
\(65\) 8.00000 + 4.00000i 0.992278 + 0.496139i
\(66\) 0 0
\(67\) 14.0000i 1.71037i 0.518321 + 0.855186i \(0.326557\pi\)
−0.518321 + 0.855186i \(0.673443\pi\)
\(68\) 0 0
\(69\) −4.00000 −0.481543
\(70\) 0 0
\(71\) −8.00000 −0.949425 −0.474713 0.880141i \(-0.657448\pi\)
−0.474713 + 0.880141i \(0.657448\pi\)
\(72\) 0 0
\(73\) 8.00000i 0.936329i −0.883641 0.468165i \(-0.844915\pi\)
0.883641 0.468165i \(-0.155085\pi\)
\(74\) 0 0
\(75\) −8.00000 + 6.00000i −0.923760 + 0.692820i
\(76\) 0 0
\(77\) 8.00000i 0.911685i
\(78\) 0 0
\(79\) 16.0000 1.80014 0.900070 0.435745i \(-0.143515\pi\)
0.900070 + 0.435745i \(0.143515\pi\)
\(80\) 0 0
\(81\) −11.0000 −1.22222
\(82\) 0 0
\(83\) 2.00000i 0.219529i −0.993958 0.109764i \(-0.964990\pi\)
0.993958 0.109764i \(-0.0350096\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 0 0
\(87\) 4.00000i 0.428845i
\(88\) 0 0
\(89\) −6.00000 −0.635999 −0.317999 0.948091i \(-0.603011\pi\)
−0.317999 + 0.948091i \(0.603011\pi\)
\(90\) 0 0
\(91\) 8.00000 0.838628
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 4.00000 8.00000i 0.410391 0.820783i
\(96\) 0 0
\(97\) 16.0000i 1.62455i 0.583272 + 0.812277i \(0.301772\pi\)
−0.583272 + 0.812277i \(0.698228\pi\)
\(98\) 0 0
\(99\) 4.00000 0.402015
\(100\) 0 0
\(101\) −6.00000 −0.597022 −0.298511 0.954406i \(-0.596490\pi\)
−0.298511 + 0.954406i \(0.596490\pi\)
\(102\) 0 0
\(103\) 14.0000i 1.37946i 0.724066 + 0.689730i \(0.242271\pi\)
−0.724066 + 0.689730i \(0.757729\pi\)
\(104\) 0 0
\(105\) −4.00000 + 8.00000i −0.390360 + 0.780720i
\(106\) 0 0
\(107\) 10.0000i 0.966736i −0.875417 0.483368i \(-0.839413\pi\)
0.875417 0.483368i \(-0.160587\pi\)
\(108\) 0 0
\(109\) −6.00000 −0.574696 −0.287348 0.957826i \(-0.592774\pi\)
−0.287348 + 0.957826i \(0.592774\pi\)
\(110\) 0 0
\(111\) −8.00000 −0.759326
\(112\) 0 0
\(113\) 16.0000i 1.50515i −0.658505 0.752577i \(-0.728811\pi\)
0.658505 0.752577i \(-0.271189\pi\)
\(114\) 0 0
\(115\) −4.00000 2.00000i −0.373002 0.186501i
\(116\) 0 0
\(117\) 4.00000i 0.369800i
\(118\) 0 0
\(119\) 0 0
\(120\) 0 0
\(121\) 5.00000 0.454545
\(122\) 0 0
\(123\) 4.00000i 0.360668i
\(124\) 0 0
\(125\) −11.0000 + 2.00000i −0.983870 + 0.178885i
\(126\) 0 0
\(127\) 6.00000i 0.532414i 0.963916 + 0.266207i \(0.0857705\pi\)
−0.963916 + 0.266207i \(0.914230\pi\)
\(128\) 0 0
\(129\) 12.0000 1.05654
\(130\) 0 0
\(131\) −12.0000 −1.04844 −0.524222 0.851581i \(-0.675644\pi\)
−0.524222 + 0.851581i \(0.675644\pi\)
\(132\) 0 0
\(133\) 8.00000i 0.693688i
\(134\) 0 0
\(135\) −8.00000 4.00000i −0.688530 0.344265i
\(136\) 0 0
\(137\) 8.00000i 0.683486i 0.939793 + 0.341743i \(0.111017\pi\)
−0.939793 + 0.341743i \(0.888983\pi\)
\(138\) 0 0
\(139\) −4.00000 −0.339276 −0.169638 0.985506i \(-0.554260\pi\)
−0.169638 + 0.985506i \(0.554260\pi\)
\(140\) 0 0
\(141\) 12.0000 1.01058
\(142\) 0 0
\(143\) 16.0000i 1.33799i
\(144\) 0 0
\(145\) 2.00000 4.00000i 0.166091 0.332182i
\(146\) 0 0
\(147\) 6.00000i 0.494872i
\(148\) 0 0
\(149\) 18.0000 1.47462 0.737309 0.675556i \(-0.236096\pi\)
0.737309 + 0.675556i \(0.236096\pi\)
\(150\) 0 0
\(151\) 8.00000 0.651031 0.325515 0.945537i \(-0.394462\pi\)
0.325515 + 0.945537i \(0.394462\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 0 0
\(156\) 0 0
\(157\) 4.00000i 0.319235i 0.987179 + 0.159617i \(0.0510260\pi\)
−0.987179 + 0.159617i \(0.948974\pi\)
\(158\) 0 0
\(159\) −8.00000 −0.634441
\(160\) 0 0
\(161\) −4.00000 −0.315244
\(162\) 0 0
\(163\) 2.00000i 0.156652i −0.996928 0.0783260i \(-0.975042\pi\)
0.996928 0.0783260i \(-0.0249575\pi\)
\(164\) 0 0
\(165\) 16.0000 + 8.00000i 1.24560 + 0.622799i
\(166\) 0 0
\(167\) 18.0000i 1.39288i −0.717614 0.696441i \(-0.754766\pi\)
0.717614 0.696441i \(-0.245234\pi\)
\(168\) 0 0
\(169\) −3.00000 −0.230769
\(170\) 0 0
\(171\) −4.00000 −0.305888
\(172\) 0 0
\(173\) 12.0000i 0.912343i −0.889892 0.456172i \(-0.849220\pi\)
0.889892 0.456172i \(-0.150780\pi\)
\(174\) 0 0
\(175\) −8.00000 + 6.00000i −0.604743 + 0.453557i
\(176\) 0 0
\(177\) 24.0000i 1.80395i
\(178\) 0 0
\(179\) 4.00000 0.298974 0.149487 0.988764i \(-0.452238\pi\)
0.149487 + 0.988764i \(0.452238\pi\)
\(180\) 0 0
\(181\) −22.0000 −1.63525 −0.817624 0.575753i \(-0.804709\pi\)
−0.817624 + 0.575753i \(0.804709\pi\)
\(182\) 0 0
\(183\) 20.0000i 1.47844i
\(184\) 0 0
\(185\) −8.00000 4.00000i −0.588172 0.294086i
\(186\) 0 0
\(187\) 0 0
\(188\) 0 0
\(189\) −8.00000 −0.581914
\(190\) 0 0
\(191\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(192\) 0 0
\(193\) 16.0000i 1.15171i 0.817554 + 0.575853i \(0.195330\pi\)
−0.817554 + 0.575853i \(0.804670\pi\)
\(194\) 0 0
\(195\) 8.00000 16.0000i 0.572892 1.14578i
\(196\) 0 0
\(197\) 12.0000i 0.854965i 0.904024 + 0.427482i \(0.140599\pi\)
−0.904024 + 0.427482i \(0.859401\pi\)
\(198\) 0 0
\(199\) −8.00000 −0.567105 −0.283552 0.958957i \(-0.591513\pi\)
−0.283552 + 0.958957i \(0.591513\pi\)
\(200\) 0 0
\(201\) 28.0000 1.97497
\(202\) 0 0
\(203\) 4.00000i 0.280745i
\(204\) 0 0
\(205\) 2.00000 4.00000i 0.139686 0.279372i
\(206\) 0 0
\(207\) 2.00000i 0.139010i
\(208\) 0 0
\(209\) −16.0000 −1.10674
\(210\) 0 0
\(211\) 4.00000 0.275371 0.137686 0.990476i \(-0.456034\pi\)
0.137686 + 0.990476i \(0.456034\pi\)
\(212\) 0 0
\(213\) 16.0000i 1.09630i
\(214\) 0 0
\(215\) 12.0000 + 6.00000i 0.818393 + 0.409197i
\(216\) 0 0
\(217\) 0 0
\(218\) 0 0
\(219\) −16.0000 −1.08118
\(220\) 0 0
\(221\) 0 0
\(222\) 0 0
\(223\) 6.00000i 0.401790i 0.979613 + 0.200895i \(0.0643850\pi\)
−0.979613 + 0.200895i \(0.935615\pi\)
\(224\) 0 0
\(225\) 3.00000 + 4.00000i 0.200000 + 0.266667i
\(226\) 0 0
\(227\) 2.00000i 0.132745i −0.997795 0.0663723i \(-0.978857\pi\)
0.997795 0.0663723i \(-0.0211425\pi\)
\(228\) 0 0
\(229\) −6.00000 −0.396491 −0.198246 0.980152i \(-0.563524\pi\)
−0.198246 + 0.980152i \(0.563524\pi\)
\(230\) 0 0
\(231\) 16.0000 1.05272
\(232\) 0 0
\(233\) 24.0000i 1.57229i 0.618041 + 0.786146i \(0.287927\pi\)
−0.618041 + 0.786146i \(0.712073\pi\)
\(234\) 0 0
\(235\) 12.0000 + 6.00000i 0.782794 + 0.391397i
\(236\) 0 0
\(237\) 32.0000i 2.07862i
\(238\) 0 0
\(239\) −16.0000 −1.03495 −0.517477 0.855697i \(-0.673129\pi\)
−0.517477 + 0.855697i \(0.673129\pi\)
\(240\) 0 0
\(241\) −22.0000 −1.41714 −0.708572 0.705638i \(-0.750660\pi\)
−0.708572 + 0.705638i \(0.750660\pi\)
\(242\) 0 0
\(243\) 10.0000i 0.641500i
\(244\) 0 0
\(245\) 3.00000 6.00000i 0.191663 0.383326i
\(246\) 0 0
\(247\) 16.0000i 1.01806i
\(248\) 0 0
\(249\) −4.00000 −0.253490
\(250\) 0 0
\(251\) −20.0000 −1.26239 −0.631194 0.775625i \(-0.717435\pi\)
−0.631194 + 0.775625i \(0.717435\pi\)
\(252\) 0 0
\(253\) 8.00000i 0.502956i
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(258\) 0 0
\(259\) −8.00000 −0.497096
\(260\) 0 0
\(261\) −2.00000 −0.123797
\(262\) 0 0
\(263\) 30.0000i 1.84988i 0.380114 + 0.924940i \(0.375885\pi\)
−0.380114 + 0.924940i \(0.624115\pi\)
\(264\) 0 0
\(265\) −8.00000 4.00000i −0.491436 0.245718i
\(266\) 0 0
\(267\) 12.0000i 0.734388i
\(268\) 0 0
\(269\) −6.00000 −0.365826 −0.182913 0.983129i \(-0.558553\pi\)
−0.182913 + 0.983129i \(0.558553\pi\)
\(270\) 0 0
\(271\) 16.0000 0.971931 0.485965 0.873978i \(-0.338468\pi\)
0.485965 + 0.873978i \(0.338468\pi\)
\(272\) 0 0
\(273\) 16.0000i 0.968364i
\(274\) 0 0
\(275\) 12.0000 + 16.0000i 0.723627 + 0.964836i
\(276\) 0 0
\(277\) 12.0000i 0.721010i 0.932757 + 0.360505i \(0.117396\pi\)
−0.932757 + 0.360505i \(0.882604\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) 18.0000 1.07379 0.536895 0.843649i \(-0.319597\pi\)
0.536895 + 0.843649i \(0.319597\pi\)
\(282\) 0 0
\(283\) 6.00000i 0.356663i 0.983970 + 0.178331i \(0.0570699\pi\)
−0.983970 + 0.178331i \(0.942930\pi\)
\(284\) 0 0
\(285\) −16.0000 8.00000i −0.947758 0.473879i
\(286\) 0 0
\(287\) 4.00000i 0.236113i
\(288\) 0 0
\(289\) 17.0000 1.00000
\(290\) 0 0
\(291\) 32.0000 1.87587
\(292\) 0 0
\(293\) 28.0000i 1.63578i 0.575376 + 0.817889i \(0.304856\pi\)
−0.575376 + 0.817889i \(0.695144\pi\)
\(294\) 0 0
\(295\) 12.0000 24.0000i 0.698667 1.39733i
\(296\) 0 0
\(297\) 16.0000i 0.928414i
\(298\) 0 0
\(299\) 8.00000 0.462652
\(300\) 0 0
\(301\) 12.0000 0.691669
\(302\) 0 0
\(303\) 12.0000i 0.689382i
\(304\) 0 0
\(305\) 10.0000 20.0000i 0.572598 1.14520i
\(306\) 0 0
\(307\) 2.00000i 0.114146i −0.998370 0.0570730i \(-0.981823\pi\)
0.998370 0.0570730i \(-0.0181768\pi\)
\(308\) 0 0
\(309\) 28.0000 1.59286
\(310\) 0 0
\(311\) −24.0000 −1.36092 −0.680458 0.732787i \(-0.738219\pi\)
−0.680458 + 0.732787i \(0.738219\pi\)
\(312\) 0 0
\(313\) 8.00000i 0.452187i −0.974106 0.226093i \(-0.927405\pi\)
0.974106 0.226093i \(-0.0725954\pi\)
\(314\) 0 0
\(315\) 4.00000 + 2.00000i 0.225374 + 0.112687i
\(316\) 0 0
\(317\) 12.0000i 0.673987i −0.941507 0.336994i \(-0.890590\pi\)
0.941507 0.336994i \(-0.109410\pi\)
\(318\) 0 0
\(319\) −8.00000 −0.447914
\(320\) 0 0
\(321\) −20.0000 −1.11629
\(322\) 0 0
\(323\) 0 0
\(324\) 0 0
\(325\) 16.0000 12.0000i 0.887520 0.665640i
\(326\) 0 0
\(327\) 12.0000i 0.663602i
\(328\) 0 0
\(329\) 12.0000 0.661581
\(330\) 0 0
\(331\) 28.0000 1.53902 0.769510 0.638635i \(-0.220501\pi\)
0.769510 + 0.638635i \(0.220501\pi\)
\(332\) 0 0
\(333\) 4.00000i 0.219199i
\(334\) 0 0
\(335\) 28.0000 + 14.0000i 1.52980 + 0.764902i
\(336\) 0 0
\(337\) 16.0000i 0.871576i −0.900049 0.435788i \(-0.856470\pi\)
0.900049 0.435788i \(-0.143530\pi\)
\(338\) 0 0
\(339\) −32.0000 −1.73800
\(340\) 0 0
\(341\) 0 0
\(342\) 0 0
\(343\) 20.0000i 1.07990i
\(344\) 0 0
\(345\) −4.00000 + 8.00000i −0.215353 + 0.430706i
\(346\) 0 0
\(347\) 22.0000i 1.18102i 0.807030 + 0.590511i \(0.201074\pi\)
−0.807030 + 0.590511i \(0.798926\pi\)
\(348\) 0 0
\(349\) 2.00000 0.107058 0.0535288 0.998566i \(-0.482953\pi\)
0.0535288 + 0.998566i \(0.482953\pi\)
\(350\) 0 0
\(351\) 16.0000 0.854017
\(352\) 0 0
\(353\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(354\) 0 0
\(355\) −8.00000 + 16.0000i −0.424596 + 0.849192i
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) −8.00000 −0.422224 −0.211112 0.977462i \(-0.567708\pi\)
−0.211112 + 0.977462i \(0.567708\pi\)
\(360\) 0 0
\(361\) −3.00000 −0.157895
\(362\) 0 0
\(363\) 10.0000i 0.524864i
\(364\) 0 0
\(365\) −16.0000 8.00000i −0.837478 0.418739i
\(366\) 0 0
\(367\) 10.0000i 0.521996i −0.965339 0.260998i \(-0.915948\pi\)
0.965339 0.260998i \(-0.0840516\pi\)
\(368\) 0 0
\(369\) −2.00000 −0.104116
\(370\) 0 0
\(371\) −8.00000 −0.415339
\(372\) 0 0
\(373\) 20.0000i 1.03556i −0.855514 0.517780i \(-0.826758\pi\)
0.855514 0.517780i \(-0.173242\pi\)
\(374\) 0 0
\(375\) 4.00000 + 22.0000i 0.206559 + 1.13608i
\(376\) 0 0
\(377\) 8.00000i 0.412021i
\(378\) 0 0
\(379\) −20.0000 −1.02733 −0.513665 0.857991i \(-0.671713\pi\)
−0.513665 + 0.857991i \(0.671713\pi\)
\(380\) 0 0
\(381\) 12.0000 0.614779
\(382\) 0 0
\(383\) 6.00000i 0.306586i 0.988181 + 0.153293i \(0.0489878\pi\)
−0.988181 + 0.153293i \(0.951012\pi\)
\(384\) 0 0
\(385\) 16.0000 + 8.00000i 0.815436 + 0.407718i
\(386\) 0 0
\(387\) 6.00000i 0.304997i
\(388\) 0 0
\(389\) −30.0000 −1.52106 −0.760530 0.649303i \(-0.775061\pi\)
−0.760530 + 0.649303i \(0.775061\pi\)
\(390\) 0 0
\(391\) 0 0
\(392\) 0 0
\(393\) 24.0000i 1.21064i
\(394\) 0 0
\(395\) 16.0000 32.0000i 0.805047 1.61009i
\(396\) 0 0
\(397\) 36.0000i 1.80679i 0.428811 + 0.903394i \(0.358933\pi\)
−0.428811 + 0.903394i \(0.641067\pi\)
\(398\) 0 0
\(399\) −16.0000 −0.801002
\(400\) 0 0
\(401\) −14.0000 −0.699127 −0.349563 0.936913i \(-0.613670\pi\)
−0.349563 + 0.936913i \(0.613670\pi\)
\(402\) 0 0
\(403\) 0 0
\(404\) 0 0
\(405\) −11.0000 + 22.0000i −0.546594 + 1.09319i
\(406\) 0 0
\(407\) 16.0000i 0.793091i
\(408\) 0 0
\(409\) −14.0000 −0.692255 −0.346128 0.938187i \(-0.612504\pi\)
−0.346128 + 0.938187i \(0.612504\pi\)
\(410\) 0 0
\(411\) 16.0000 0.789222
\(412\) 0 0
\(413\) 24.0000i 1.18096i
\(414\) 0 0
\(415\) −4.00000 2.00000i −0.196352 0.0981761i
\(416\) 0 0
\(417\) 8.00000i 0.391762i
\(418\) 0 0
\(419\) −12.0000 −0.586238 −0.293119 0.956076i \(-0.594693\pi\)
−0.293119 + 0.956076i \(0.594693\pi\)
\(420\) 0 0
\(421\) 2.00000 0.0974740 0.0487370 0.998812i \(-0.484480\pi\)
0.0487370 + 0.998812i \(0.484480\pi\)
\(422\) 0 0
\(423\) 6.00000i 0.291730i
\(424\) 0 0
\(425\) 0 0
\(426\) 0 0
\(427\) 20.0000i 0.967868i
\(428\) 0 0
\(429\) −32.0000 −1.54497
\(430\) 0 0
\(431\) −16.0000 −0.770693 −0.385346 0.922772i \(-0.625918\pi\)
−0.385346 + 0.922772i \(0.625918\pi\)
\(432\) 0 0
\(433\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(434\) 0 0
\(435\) −8.00000 4.00000i −0.383571 0.191785i
\(436\) 0 0
\(437\) 8.00000i 0.382692i
\(438\) 0 0
\(439\) −24.0000 −1.14546 −0.572729 0.819745i \(-0.694115\pi\)
−0.572729 + 0.819745i \(0.694115\pi\)
\(440\) 0 0
\(441\) −3.00000 −0.142857
\(442\) 0 0
\(443\) 6.00000i 0.285069i 0.989790 + 0.142534i \(0.0455251\pi\)
−0.989790 + 0.142534i \(0.954475\pi\)
\(444\) 0 0
\(445\) −6.00000 + 12.0000i −0.284427 + 0.568855i
\(446\) 0 0
\(447\) 36.0000i 1.70274i
\(448\) 0 0
\(449\) −6.00000 −0.283158 −0.141579 0.989927i \(-0.545218\pi\)
−0.141579 + 0.989927i \(0.545218\pi\)
\(450\) 0 0
\(451\) −8.00000 −0.376705
\(452\) 0 0
\(453\) 16.0000i 0.751746i
\(454\) 0 0
\(455\) 8.00000 16.0000i 0.375046 0.750092i
\(456\) 0 0
\(457\) 24.0000i 1.12267i −0.827588 0.561336i \(-0.810287\pi\)
0.827588 0.561336i \(-0.189713\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 18.0000 0.838344 0.419172 0.907907i \(-0.362320\pi\)
0.419172 + 0.907907i \(0.362320\pi\)
\(462\) 0 0
\(463\) 26.0000i 1.20832i −0.796862 0.604161i \(-0.793508\pi\)
0.796862 0.604161i \(-0.206492\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 18.0000i 0.832941i −0.909149 0.416470i \(-0.863267\pi\)
0.909149 0.416470i \(-0.136733\pi\)
\(468\) 0 0
\(469\) 28.0000 1.29292
\(470\) 0 0
\(471\) 8.00000 0.368621
\(472\) 0 0
\(473\) 24.0000i 1.10352i
\(474\) 0 0
\(475\) −12.0000 16.0000i −0.550598 0.734130i
\(476\) 0 0
\(477\) 4.00000i 0.183147i
\(478\) 0 0
\(479\) 32.0000 1.46212 0.731059 0.682315i \(-0.239027\pi\)
0.731059 + 0.682315i \(0.239027\pi\)
\(480\) 0 0
\(481\) 16.0000 0.729537
\(482\) 0 0
\(483\) 8.00000i 0.364013i
\(484\) 0 0
\(485\) 32.0000 + 16.0000i 1.45305 + 0.726523i
\(486\) 0 0
\(487\) 2.00000i 0.0906287i −0.998973 0.0453143i \(-0.985571\pi\)
0.998973 0.0453143i \(-0.0144289\pi\)
\(488\) 0 0
\(489\) −4.00000 −0.180886
\(490\) 0 0
\(491\) −4.00000 −0.180517 −0.0902587 0.995918i \(-0.528769\pi\)
−0.0902587 + 0.995918i \(0.528769\pi\)
\(492\) 0 0
\(493\) 0 0
\(494\) 0 0
\(495\) 4.00000 8.00000i 0.179787 0.359573i
\(496\) 0 0
\(497\) 16.0000i 0.717698i
\(498\) 0 0
\(499\) 4.00000 0.179065 0.0895323 0.995984i \(-0.471463\pi\)
0.0895323 + 0.995984i \(0.471463\pi\)
\(500\) 0 0
\(501\) −36.0000 −1.60836
\(502\) 0 0
\(503\) 34.0000i 1.51599i −0.652263 0.757993i \(-0.726180\pi\)
0.652263 0.757993i \(-0.273820\pi\)
\(504\) 0 0
\(505\) −6.00000 + 12.0000i −0.266996 + 0.533993i
\(506\) 0 0
\(507\) 6.00000i 0.266469i
\(508\) 0 0
\(509\) 34.0000 1.50702 0.753512 0.657434i \(-0.228358\pi\)
0.753512 + 0.657434i \(0.228358\pi\)
\(510\) 0 0
\(511\) −16.0000 −0.707798
\(512\) 0 0
\(513\) 16.0000i 0.706417i
\(514\) 0 0
\(515\) 28.0000 + 14.0000i 1.23383 + 0.616914i
\(516\) 0 0
\(517\) 24.0000i 1.05552i
\(518\) 0 0
\(519\) −24.0000 −1.05348
\(520\) 0 0
\(521\) 10.0000 0.438108 0.219054 0.975713i \(-0.429703\pi\)
0.219054 + 0.975713i \(0.429703\pi\)
\(522\) 0 0
\(523\) 10.0000i 0.437269i −0.975807 0.218635i \(-0.929840\pi\)
0.975807 0.218635i \(-0.0701603\pi\)
\(524\) 0 0
\(525\) 12.0000 + 16.0000i 0.523723 + 0.698297i
\(526\) 0 0
\(527\) 0 0
\(528\) 0 0
\(529\) 19.0000 0.826087
\(530\) 0 0
\(531\) −12.0000 −0.520756
\(532\) 0 0
\(533\) 8.00000i 0.346518i
\(534\) 0 0
\(535\) −20.0000 10.0000i −0.864675 0.432338i
\(536\) 0 0
\(537\) 8.00000i 0.345225i
\(538\) 0 0
\(539\) −12.0000 −0.516877
\(540\) 0 0
\(541\) 2.00000 0.0859867 0.0429934 0.999075i \(-0.486311\pi\)
0.0429934 + 0.999075i \(0.486311\pi\)
\(542\) 0 0
\(543\) 44.0000i 1.88822i
\(544\) 0 0
\(545\) −6.00000 + 12.0000i −0.257012 + 0.514024i
\(546\) 0 0
\(547\) 34.0000i 1.45374i −0.686778 0.726868i \(-0.740975\pi\)
0.686778 0.726868i \(-0.259025\pi\)
\(548\) 0 0
\(549\) −10.0000 −0.426790
\(550\) 0 0
\(551\) 8.00000 0.340811
\(552\) 0 0
\(553\) 32.0000i 1.36078i
\(554\) 0 0
\(555\) −8.00000 + 16.0000i −0.339581 + 0.679162i
\(556\) 0 0
\(557\) 12.0000i 0.508456i −0.967144 0.254228i \(-0.918179\pi\)
0.967144 0.254228i \(-0.0818214\pi\)
\(558\) 0 0
\(559\) −24.0000 −1.01509
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) 18.0000i 0.758610i −0.925272 0.379305i \(-0.876163\pi\)
0.925272 0.379305i \(-0.123837\pi\)
\(564\) 0 0
\(565\) −32.0000 16.0000i −1.34625 0.673125i
\(566\) 0 0
\(567\) 22.0000i 0.923913i
\(568\) 0 0
\(569\) 18.0000 0.754599 0.377300 0.926091i \(-0.376853\pi\)
0.377300 + 0.926091i \(0.376853\pi\)
\(570\) 0 0
\(571\) −20.0000 −0.836974 −0.418487 0.908223i \(-0.637439\pi\)
−0.418487 + 0.908223i \(0.637439\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) −8.00000 + 6.00000i −0.333623 + 0.250217i
\(576\) 0 0
\(577\) 32.0000i 1.33218i 0.745873 + 0.666089i \(0.232033\pi\)
−0.745873 + 0.666089i \(0.767967\pi\)
\(578\) 0 0
\(579\) 32.0000 1.32987
\(580\) 0 0
\(581\) −4.00000 −0.165948
\(582\) 0 0
\(583\) 16.0000i 0.662652i
\(584\) 0 0
\(585\) −8.00000 4.00000i −0.330759 0.165380i
\(586\) 0 0
\(587\) 38.0000i 1.56843i 0.620491 + 0.784214i \(0.286934\pi\)
−0.620491 + 0.784214i \(0.713066\pi\)
\(588\) 0 0
\(589\) 0 0
\(590\) 0 0
\(591\) 24.0000 0.987228
\(592\) 0 0
\(593\) 16.0000i 0.657041i 0.944497 + 0.328521i \(0.106550\pi\)
−0.944497 + 0.328521i \(0.893450\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) 16.0000i 0.654836i
\(598\) 0 0
\(599\) 40.0000 1.63436 0.817178 0.576386i \(-0.195537\pi\)
0.817178 + 0.576386i \(0.195537\pi\)
\(600\) 0 0
\(601\) 18.0000 0.734235 0.367118 0.930175i \(-0.380345\pi\)
0.367118 + 0.930175i \(0.380345\pi\)
\(602\) 0 0
\(603\) 14.0000i 0.570124i
\(604\) 0 0
\(605\) 5.00000 10.0000i 0.203279 0.406558i
\(606\) 0 0
\(607\) 10.0000i 0.405887i −0.979190 0.202944i \(-0.934949\pi\)
0.979190 0.202944i \(-0.0650509\pi\)
\(608\) 0 0
\(609\) −8.00000 −0.324176
\(610\) 0 0
\(611\) −24.0000 −0.970936
\(612\) 0 0
\(613\) 20.0000i 0.807792i −0.914805 0.403896i \(-0.867656\pi\)
0.914805 0.403896i \(-0.132344\pi\)
\(614\) 0 0
\(615\) −8.00000 4.00000i −0.322591 0.161296i
\(616\) 0 0
\(617\) 8.00000i 0.322068i −0.986949 0.161034i \(-0.948517\pi\)
0.986949 0.161034i \(-0.0514829\pi\)
\(618\) 0 0
\(619\) −4.00000 −0.160774 −0.0803868 0.996764i \(-0.525616\pi\)
−0.0803868 + 0.996764i \(0.525616\pi\)
\(620\) 0 0
\(621\) −8.00000 −0.321029
\(622\) 0 0
\(623\) 12.0000i 0.480770i
\(624\) 0 0
\(625\) −7.00000 + 24.0000i −0.280000 + 0.960000i
\(626\) 0 0
\(627\) 32.0000i 1.27796i
\(628\) 0 0
\(629\) 0 0
\(630\) 0 0
\(631\) 40.0000 1.59237 0.796187 0.605050i \(-0.206847\pi\)
0.796187 + 0.605050i \(0.206847\pi\)
\(632\) 0 0
\(633\) 8.00000i 0.317971i
\(634\) 0 0
\(635\) 12.0000 + 6.00000i 0.476205 + 0.238103i
\(636\) 0 0
\(637\) 12.0000i 0.475457i
\(638\) 0 0
\(639\) 8.00000 0.316475
\(640\) 0 0
\(641\) −6.00000 −0.236986 −0.118493 0.992955i \(-0.537806\pi\)
−0.118493 + 0.992955i \(0.537806\pi\)
\(642\) 0 0
\(643\) 18.0000i 0.709851i −0.934895 0.354925i \(-0.884506\pi\)
0.934895 0.354925i \(-0.115494\pi\)
\(644\) 0 0
\(645\) 12.0000 24.0000i 0.472500 0.944999i
\(646\) 0 0
\(647\) 2.00000i 0.0786281i −0.999227 0.0393141i \(-0.987483\pi\)
0.999227 0.0393141i \(-0.0125173\pi\)
\(648\) 0 0
\(649\) −48.0000 −1.88416
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 36.0000i 1.40879i 0.709809 + 0.704394i \(0.248781\pi\)
−0.709809 + 0.704394i \(0.751219\pi\)
\(654\) 0 0
\(655\) −12.0000 + 24.0000i −0.468879 + 0.937758i
\(656\) 0 0
\(657\) 8.00000i 0.312110i
\(658\) 0 0
\(659\) 36.0000 1.40236 0.701180 0.712984i \(-0.252657\pi\)
0.701180 + 0.712984i \(0.252657\pi\)
\(660\) 0 0
\(661\) −14.0000 −0.544537 −0.272268 0.962221i \(-0.587774\pi\)
−0.272268 + 0.962221i \(0.587774\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) −16.0000 8.00000i −0.620453 0.310227i
\(666\) 0 0
\(667\) 4.00000i 0.154881i
\(668\) 0 0
\(669\) 12.0000 0.463947
\(670\) 0 0
\(671\) −40.0000 −1.54418
\(672\) 0 0
\(673\) 16.0000i 0.616755i 0.951264 + 0.308377i \(0.0997859\pi\)
−0.951264 + 0.308377i \(0.900214\pi\)
\(674\) 0 0
\(675\) −16.0000 + 12.0000i −0.615840 + 0.461880i
\(676\) 0 0
\(677\) 12.0000i 0.461197i 0.973049 + 0.230599i \(0.0740685\pi\)
−0.973049 + 0.230599i \(0.925932\pi\)
\(678\) 0 0
\(679\) 32.0000 1.22805
\(680\) 0 0
\(681\) −4.00000 −0.153280
\(682\) 0 0
\(683\) 38.0000i 1.45403i 0.686622 + 0.727015i \(0.259093\pi\)
−0.686622 + 0.727015i \(0.740907\pi\)
\(684\) 0 0
\(685\) 16.0000 + 8.00000i 0.611329 + 0.305664i
\(686\) 0 0
\(687\) 12.0000i 0.457829i
\(688\) 0 0
\(689\) 16.0000 0.609551
\(690\) 0 0
\(691\) 36.0000 1.36950 0.684752 0.728776i \(-0.259910\pi\)
0.684752 + 0.728776i \(0.259910\pi\)
\(692\) 0 0
\(693\) 8.00000i 0.303895i
\(694\) 0 0
\(695\) −4.00000 + 8.00000i −0.151729 + 0.303457i
\(696\) 0 0
\(697\) 0 0
\(698\) 0 0
\(699\) 48.0000 1.81553
\(700\) 0 0
\(701\) −22.0000 −0.830929 −0.415464 0.909610i \(-0.636381\pi\)
−0.415464 + 0.909610i \(0.636381\pi\)
\(702\) 0 0
\(703\) 16.0000i 0.603451i
\(704\) 0 0
\(705\) 12.0000 24.0000i 0.451946 0.903892i
\(706\) 0 0
\(707\) 12.0000i 0.451306i
\(708\) 0 0
\(709\) −38.0000 −1.42712 −0.713560 0.700594i \(-0.752918\pi\)
−0.713560 + 0.700594i \(0.752918\pi\)
\(710\) 0 0
\(711\) −16.0000 −0.600047
\(712\) 0 0
\(713\) 0 0
\(714\) 0 0
\(715\) −32.0000 16.0000i −1.19673 0.598366i
\(716\) 0 0
\(717\) 32.0000i 1.19506i
\(718\) 0 0
\(719\) 16.0000 0.596699 0.298350 0.954457i \(-0.403564\pi\)
0.298350 + 0.954457i \(0.403564\pi\)
\(720\) 0 0
\(721\) 28.0000 1.04277
\(722\) 0 0
\(723\) 44.0000i 1.63638i
\(724\) 0 0
\(725\) −6.00000 8.00000i −0.222834 0.297113i
\(726\) 0 0
\(727\) 18.0000i 0.667583i −0.942647 0.333792i \(-0.891672\pi\)
0.942647 0.333792i \(-0.108328\pi\)
\(728\) 0 0
\(729\) −13.0000 −0.481481
\(730\) 0 0
\(731\) 0 0
\(732\) 0 0
\(733\) 36.0000i 1.32969i 0.746981 + 0.664845i \(0.231502\pi\)
−0.746981 + 0.664845i \(0.768498\pi\)
\(734\) 0 0
\(735\) −12.0000 6.00000i −0.442627 0.221313i
\(736\) 0 0
\(737\) 56.0000i 2.06279i
\(738\) 0 0
\(739\) −12.0000 −0.441427 −0.220714 0.975339i \(-0.570839\pi\)
−0.220714 + 0.975339i \(0.570839\pi\)
\(740\) 0 0
\(741\) 32.0000 1.17555
\(742\) 0 0
\(743\) 30.0000i 1.10059i 0.834969 + 0.550297i \(0.185485\pi\)
−0.834969 + 0.550297i \(0.814515\pi\)
\(744\) 0 0
\(745\) 18.0000 36.0000i 0.659469 1.31894i
\(746\) 0 0
\(747\) 2.00000i 0.0731762i
\(748\) 0 0
\(749\) −20.0000 −0.730784
\(750\) 0 0
\(751\) 16.0000 0.583848 0.291924 0.956441i \(-0.405705\pi\)
0.291924 + 0.956441i \(0.405705\pi\)
\(752\) 0 0
\(753\) 40.0000i 1.45768i
\(754\) 0 0
\(755\) 8.00000 16.0000i 0.291150 0.582300i
\(756\) 0 0
\(757\) 52.0000i 1.88997i −0.327111 0.944986i \(-0.606075\pi\)
0.327111 0.944986i \(-0.393925\pi\)
\(758\) 0 0
\(759\) 16.0000 0.580763
\(760\) 0 0
\(761\) −38.0000 −1.37750 −0.688749 0.724999i \(-0.741840\pi\)
−0.688749 + 0.724999i \(0.741840\pi\)
\(762\) 0 0
\(763\) 12.0000i 0.434429i
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 48.0000i 1.73318i
\(768\) 0 0
\(769\) 2.00000 0.0721218 0.0360609 0.999350i \(-0.488519\pi\)
0.0360609 + 0.999350i \(0.488519\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) 20.0000i 0.719350i −0.933078 0.359675i \(-0.882888\pi\)
0.933078 0.359675i \(-0.117112\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 0 0
\(777\) 16.0000i 0.573997i
\(778\) 0 0
\(779\) 8.00000 0.286630
\(780\) 0 0
\(781\) 32.0000 1.14505
\(782\) 0 0
\(783\) 8.00000i 0.285897i
\(784\) 0 0
\(785\) 8.00000 + 4.00000i 0.285532 + 0.142766i
\(786\) 0 0
\(787\) 2.00000i 0.0712923i −0.999364 0.0356462i \(-0.988651\pi\)
0.999364 0.0356462i \(-0.0113489\pi\)
\(788\) 0 0
\(789\) 60.0000 2.13606
\(790\) 0 0
\(791\) −32.0000 −1.13779
\(792\) 0 0
\(793\) 40.0000i 1.42044i
\(794\) 0 0
\(795\) −8.00000 + 16.0000i −0.283731 + 0.567462i
\(796\) 0 0
\(797\) 12.0000i 0.425062i −0.977154 0.212531i \(-0.931829\pi\)
0.977154 0.212531i \(-0.0681706\pi\)
\(798\) 0 0
\(799\) 0 0
\(800\) 0 0
\(801\) 6.00000 0.212000
\(802\) 0 0
\(803\)