Properties

Label 4032.2.v.e.1583.15
Level 4032
Weight 2
Character 4032.1583
Analytic conductor 32.196
Analytic rank 0
Dimension 40
CM no
Inner twists 4

Related objects

Downloads

Learn more about

Newspace parameters

Level: \( N \) = \( 4032 = 2^{6} \cdot 3^{2} \cdot 7 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 4032.v (of order \(4\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(32.1956820950\)
Analytic rank: \(0\)
Dimension: \(40\)
Relative dimension: \(20\) over \(\Q(i)\)
Coefficient ring index: multiple of None
Twist minimal: no (minimal twist has level 1008)
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 1583.15
Character \(\chi\) = 4032.1583
Dual form 4032.2.v.e.3599.15

$q$-expansion

\(f(q)\) \(=\) \(q+(1.17902 + 1.17902i) q^{5} -1.00000 q^{7} +O(q^{10})\) \(q+(1.17902 + 1.17902i) q^{5} -1.00000 q^{7} +(4.54895 - 4.54895i) q^{11} +(2.56073 + 2.56073i) q^{13} -2.05280i q^{17} +(3.64422 - 3.64422i) q^{19} +2.27140i q^{23} -2.21982i q^{25} +(0.544898 - 0.544898i) q^{29} +10.1006i q^{31} +(-1.17902 - 1.17902i) q^{35} +(4.71698 - 4.71698i) q^{37} -0.487549 q^{41} +(-7.56607 - 7.56607i) q^{43} -0.768184 q^{47} +1.00000 q^{49} +(-0.269015 - 0.269015i) q^{53} +10.7266 q^{55} +(0.0979540 - 0.0979540i) q^{59} +(-7.41725 - 7.41725i) q^{61} +6.03831i q^{65} +(-6.83972 + 6.83972i) q^{67} -8.66316i q^{71} -13.6358i q^{73} +(-4.54895 + 4.54895i) q^{77} -9.29142i q^{79} +(9.76640 + 9.76640i) q^{83} +(2.42029 - 2.42029i) q^{85} -7.27355 q^{89} +(-2.56073 - 2.56073i) q^{91} +8.59324 q^{95} +10.4508 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 40q - 40q^{7} + O(q^{10}) \) \( 40q - 40q^{7} - 24q^{13} + 32q^{19} - 8q^{37} - 32q^{43} + 40q^{49} - 48q^{55} - 24q^{61} + 64q^{85} + 24q^{91} + 64q^{97} + O(q^{100}) \)

Character values

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

\(n\) \(127\) \(577\) \(1793\) \(3781\)
\(\chi(n)\) \(-1\) \(1\) \(-1\) \(e\left(\frac{3}{4}\right)\)

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
\(5\) 1.17902 + 1.17902i 0.527275 + 0.527275i 0.919759 0.392484i \(-0.128384\pi\)
−0.392484 + 0.919759i \(0.628384\pi\)
\(6\) 0 0
\(7\) −1.00000 −0.377964
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) 4.54895 4.54895i 1.37156 1.37156i 0.513428 0.858133i \(-0.328375\pi\)
0.858133 0.513428i \(-0.171625\pi\)
\(12\) 0 0
\(13\) 2.56073 + 2.56073i 0.710218 + 0.710218i 0.966581 0.256363i \(-0.0825241\pi\)
−0.256363 + 0.966581i \(0.582524\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 2.05280i 0.497876i −0.968519 0.248938i \(-0.919918\pi\)
0.968519 0.248938i \(-0.0800815\pi\)
\(18\) 0 0
\(19\) 3.64422 3.64422i 0.836042 0.836042i −0.152293 0.988335i \(-0.548666\pi\)
0.988335 + 0.152293i \(0.0486657\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) 2.27140i 0.473620i 0.971556 + 0.236810i \(0.0761019\pi\)
−0.971556 + 0.236810i \(0.923898\pi\)
\(24\) 0 0
\(25\) 2.21982i 0.443963i
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) 0.544898 0.544898i 0.101185 0.101185i −0.654702 0.755887i \(-0.727206\pi\)
0.755887 + 0.654702i \(0.227206\pi\)
\(30\) 0 0
\(31\) 10.1006i 1.81412i 0.421004 + 0.907059i \(0.361678\pi\)
−0.421004 + 0.907059i \(0.638322\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) −1.17902 1.17902i −0.199291 0.199291i
\(36\) 0 0
\(37\) 4.71698 4.71698i 0.775467 0.775467i −0.203590 0.979056i \(-0.565261\pi\)
0.979056 + 0.203590i \(0.0652608\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) −0.487549 −0.0761424 −0.0380712 0.999275i \(-0.512121\pi\)
−0.0380712 + 0.999275i \(0.512121\pi\)
\(42\) 0 0
\(43\) −7.56607 7.56607i −1.15381 1.15381i −0.985781 0.168033i \(-0.946258\pi\)
−0.168033 0.985781i \(-0.553742\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) −0.768184 −0.112051 −0.0560256 0.998429i \(-0.517843\pi\)
−0.0560256 + 0.998429i \(0.517843\pi\)
\(48\) 0 0
\(49\) 1.00000 0.142857
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) −0.269015 0.269015i −0.0369520 0.0369520i 0.688389 0.725341i \(-0.258318\pi\)
−0.725341 + 0.688389i \(0.758318\pi\)
\(54\) 0 0
\(55\) 10.7266 1.44638
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) 0.0979540 0.0979540i 0.0127525 0.0127525i −0.700702 0.713454i \(-0.747130\pi\)
0.713454 + 0.700702i \(0.247130\pi\)
\(60\) 0 0
\(61\) −7.41725 7.41725i −0.949682 0.949682i 0.0491117 0.998793i \(-0.484361\pi\)
−0.998793 + 0.0491117i \(0.984361\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) 6.03831i 0.748960i
\(66\) 0 0
\(67\) −6.83972 + 6.83972i −0.835604 + 0.835604i −0.988277 0.152672i \(-0.951212\pi\)
0.152672 + 0.988277i \(0.451212\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 8.66316i 1.02813i −0.857752 0.514064i \(-0.828139\pi\)
0.857752 0.514064i \(-0.171861\pi\)
\(72\) 0 0
\(73\) 13.6358i 1.59594i −0.602694 0.797972i \(-0.705906\pi\)
0.602694 0.797972i \(-0.294094\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) −4.54895 + 4.54895i −0.518401 + 0.518401i
\(78\) 0 0
\(79\) 9.29142i 1.04537i −0.852527 0.522683i \(-0.824931\pi\)
0.852527 0.522683i \(-0.175069\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) 9.76640 + 9.76640i 1.07200 + 1.07200i 0.997198 + 0.0748037i \(0.0238330\pi\)
0.0748037 + 0.997198i \(0.476167\pi\)
\(84\) 0 0
\(85\) 2.42029 2.42029i 0.262517 0.262517i
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) −7.27355 −0.770995 −0.385497 0.922709i \(-0.625970\pi\)
−0.385497 + 0.922709i \(0.625970\pi\)
\(90\) 0 0
\(91\) −2.56073 2.56073i −0.268437 0.268437i
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 8.59324 0.881648
\(96\) 0 0
\(97\) 10.4508 1.06112 0.530561 0.847647i \(-0.321981\pi\)
0.530561 + 0.847647i \(0.321981\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) 5.75000 + 5.75000i 0.572147 + 0.572147i 0.932728 0.360581i \(-0.117422\pi\)
−0.360581 + 0.932728i \(0.617422\pi\)
\(102\) 0 0
\(103\) −7.11905 −0.701460 −0.350730 0.936477i \(-0.614067\pi\)
−0.350730 + 0.936477i \(0.614067\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 6.13593 6.13593i 0.593182 0.593182i −0.345307 0.938490i \(-0.612225\pi\)
0.938490 + 0.345307i \(0.112225\pi\)
\(108\) 0 0
\(109\) 1.54344 + 1.54344i 0.147835 + 0.147835i 0.777150 0.629315i \(-0.216665\pi\)
−0.629315 + 0.777150i \(0.716665\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) 14.0023i 1.31723i 0.752481 + 0.658614i \(0.228857\pi\)
−0.752481 + 0.658614i \(0.771143\pi\)
\(114\) 0 0
\(115\) −2.67803 + 2.67803i −0.249728 + 0.249728i
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) 2.05280i 0.188179i
\(120\) 0 0
\(121\) 30.3859i 2.76236i
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) 8.51232 8.51232i 0.761365 0.761365i
\(126\) 0 0
\(127\) 5.32939i 0.472906i 0.971643 + 0.236453i \(0.0759850\pi\)
−0.971643 + 0.236453i \(0.924015\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) 13.4364 + 13.4364i 1.17395 + 1.17395i 0.981261 + 0.192685i \(0.0617196\pi\)
0.192685 + 0.981261i \(0.438280\pi\)
\(132\) 0 0
\(133\) −3.64422 + 3.64422i −0.315994 + 0.315994i
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 10.1704 0.868914 0.434457 0.900693i \(-0.356940\pi\)
0.434457 + 0.900693i \(0.356940\pi\)
\(138\) 0 0
\(139\) 6.90089 + 6.90089i 0.585326 + 0.585326i 0.936362 0.351036i \(-0.114171\pi\)
−0.351036 + 0.936362i \(0.614171\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 23.2973 1.94821
\(144\) 0 0
\(145\) 1.28489 0.106705
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) −0.134093 0.134093i −0.0109853 0.0109853i 0.701593 0.712578i \(-0.252473\pi\)
−0.712578 + 0.701593i \(0.752473\pi\)
\(150\) 0 0
\(151\) 13.7321 1.11750 0.558750 0.829336i \(-0.311281\pi\)
0.558750 + 0.829336i \(0.311281\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) −11.9088 + 11.9088i −0.956538 + 0.956538i
\(156\) 0 0
\(157\) −2.49258 2.49258i −0.198929 0.198929i 0.600612 0.799541i \(-0.294924\pi\)
−0.799541 + 0.600612i \(0.794924\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 2.27140i 0.179012i
\(162\) 0 0
\(163\) −6.43203 + 6.43203i −0.503796 + 0.503796i −0.912615 0.408820i \(-0.865941\pi\)
0.408820 + 0.912615i \(0.365941\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 4.38595i 0.339395i −0.985496 0.169697i \(-0.945721\pi\)
0.985496 0.169697i \(-0.0542790\pi\)
\(168\) 0 0
\(169\) 0.114651i 0.00881930i
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) 18.2846 18.2846i 1.39015 1.39015i 0.565191 0.824960i \(-0.308803\pi\)
0.824960 0.565191i \(-0.191197\pi\)
\(174\) 0 0
\(175\) 2.21982i 0.167802i
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) −3.18124 3.18124i −0.237777 0.237777i 0.578152 0.815929i \(-0.303774\pi\)
−0.815929 + 0.578152i \(0.803774\pi\)
\(180\) 0 0
\(181\) −18.4064 + 18.4064i −1.36813 + 1.36813i −0.505036 + 0.863098i \(0.668521\pi\)
−0.863098 + 0.505036i \(0.831479\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 11.1228 0.817768
\(186\) 0 0
\(187\) −9.33807 9.33807i −0.682867 0.682867i
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 22.1964 1.60607 0.803037 0.595929i \(-0.203216\pi\)
0.803037 + 0.595929i \(0.203216\pi\)
\(192\) 0 0
\(193\) −6.93243 −0.499007 −0.249503 0.968374i \(-0.580267\pi\)
−0.249503 + 0.968374i \(0.580267\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 6.07895 + 6.07895i 0.433107 + 0.433107i 0.889684 0.456577i \(-0.150925\pi\)
−0.456577 + 0.889684i \(0.650925\pi\)
\(198\) 0 0
\(199\) 10.9223 0.774265 0.387132 0.922024i \(-0.373466\pi\)
0.387132 + 0.922024i \(0.373466\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) −0.544898 + 0.544898i −0.0382444 + 0.0382444i
\(204\) 0 0
\(205\) −0.574831 0.574831i −0.0401480 0.0401480i
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) 33.1548i 2.29337i
\(210\) 0 0
\(211\) 9.67612 9.67612i 0.666131 0.666131i −0.290687 0.956818i \(-0.593884\pi\)
0.956818 + 0.290687i \(0.0938838\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) 17.8411i 1.21675i
\(216\) 0 0
\(217\) 10.1006i 0.685672i
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) 5.25665 5.25665i 0.353601 0.353601i
\(222\) 0 0
\(223\) 4.17535i 0.279602i −0.990180 0.139801i \(-0.955354\pi\)
0.990180 0.139801i \(-0.0446463\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 21.2251 + 21.2251i 1.40876 + 1.40876i 0.766413 + 0.642348i \(0.222039\pi\)
0.642348 + 0.766413i \(0.277961\pi\)
\(228\) 0 0
\(229\) −6.46169 + 6.46169i −0.427000 + 0.427000i −0.887605 0.460605i \(-0.847633\pi\)
0.460605 + 0.887605i \(0.347633\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) −10.6456 −0.697413 −0.348707 0.937232i \(-0.613379\pi\)
−0.348707 + 0.937232i \(0.613379\pi\)
\(234\) 0 0
\(235\) −0.905705 0.905705i −0.0590817 0.0590817i
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) −10.2774 −0.664792 −0.332396 0.943140i \(-0.607857\pi\)
−0.332396 + 0.943140i \(0.607857\pi\)
\(240\) 0 0
\(241\) −0.195675 −0.0126045 −0.00630227 0.999980i \(-0.502006\pi\)
−0.00630227 + 0.999980i \(0.502006\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) 1.17902 + 1.17902i 0.0753249 + 0.0753249i
\(246\) 0 0
\(247\) 18.6637 1.18754
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) −8.95377 + 8.95377i −0.565157 + 0.565157i −0.930768 0.365611i \(-0.880860\pi\)
0.365611 + 0.930768i \(0.380860\pi\)
\(252\) 0 0
\(253\) 10.3325 + 10.3325i 0.649599 + 0.649599i
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 21.3928i 1.33445i 0.744858 + 0.667223i \(0.232517\pi\)
−0.744858 + 0.667223i \(0.767483\pi\)
\(258\) 0 0
\(259\) −4.71698 + 4.71698i −0.293099 + 0.293099i
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) 31.7659i 1.95877i 0.202006 + 0.979384i \(0.435254\pi\)
−0.202006 + 0.979384i \(0.564746\pi\)
\(264\) 0 0
\(265\) 0.634348i 0.0389677i
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) −11.1414 + 11.1414i −0.679301 + 0.679301i −0.959842 0.280541i \(-0.909486\pi\)
0.280541 + 0.959842i \(0.409486\pi\)
\(270\) 0 0
\(271\) 19.1289i 1.16200i −0.813904 0.580999i \(-0.802662\pi\)
0.813904 0.580999i \(-0.197338\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) −10.0978 10.0978i −0.608922 0.608922i
\(276\) 0 0
\(277\) −1.64734 + 1.64734i −0.0989791 + 0.0989791i −0.754862 0.655883i \(-0.772296\pi\)
0.655883 + 0.754862i \(0.272296\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) −4.73918 −0.282716 −0.141358 0.989959i \(-0.545147\pi\)
−0.141358 + 0.989959i \(0.545147\pi\)
\(282\) 0 0
\(283\) −9.70607 9.70607i −0.576966 0.576966i 0.357100 0.934066i \(-0.383766\pi\)
−0.934066 + 0.357100i \(0.883766\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 0.487549 0.0287791
\(288\) 0 0
\(289\) 12.7860 0.752119
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) 4.58419 + 4.58419i 0.267811 + 0.267811i 0.828218 0.560406i \(-0.189355\pi\)
−0.560406 + 0.828218i \(0.689355\pi\)
\(294\) 0 0
\(295\) 0.230980 0.0134482
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) −5.81644 + 5.81644i −0.336373 + 0.336373i
\(300\) 0 0
\(301\) 7.56607 + 7.56607i 0.436101 + 0.436101i
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) 17.4902i 1.00149i
\(306\) 0 0
\(307\) 12.3272 12.3272i 0.703552 0.703552i −0.261619 0.965171i \(-0.584256\pi\)
0.965171 + 0.261619i \(0.0842565\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 1.24831i 0.0707852i −0.999373 0.0353926i \(-0.988732\pi\)
0.999373 0.0353926i \(-0.0112682\pi\)
\(312\) 0 0
\(313\) 23.1106i 1.30629i 0.757234 + 0.653144i \(0.226550\pi\)
−0.757234 + 0.653144i \(0.773450\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −6.92113 + 6.92113i −0.388729 + 0.388729i −0.874234 0.485505i \(-0.838636\pi\)
0.485505 + 0.874234i \(0.338636\pi\)
\(318\) 0 0
\(319\) 4.95743i 0.277563i
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) −7.48085 7.48085i −0.416245 0.416245i
\(324\) 0 0
\(325\) 5.68434 5.68434i 0.315311 0.315311i
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) 0.768184 0.0423513
\(330\) 0 0
\(331\) −14.3780 14.3780i −0.790288 0.790288i 0.191253 0.981541i \(-0.438745\pi\)
−0.981541 + 0.191253i \(0.938745\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) −16.1283 −0.881186
\(336\) 0 0
\(337\) −5.99526 −0.326583 −0.163291 0.986578i \(-0.552211\pi\)
−0.163291 + 0.986578i \(0.552211\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) 45.9471 + 45.9471i 2.48817 + 2.48817i
\(342\) 0 0
\(343\) −1.00000 −0.0539949
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) −11.6602 + 11.6602i −0.625954 + 0.625954i −0.947047 0.321094i \(-0.895950\pi\)
0.321094 + 0.947047i \(0.395950\pi\)
\(348\) 0 0
\(349\) −18.7098 18.7098i −1.00151 1.00151i −0.999999 0.00151266i \(-0.999519\pi\)
−0.00151266 0.999999i \(-0.500481\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) 4.65833i 0.247938i −0.992286 0.123969i \(-0.960438\pi\)
0.992286 0.123969i \(-0.0395624\pi\)
\(354\) 0 0
\(355\) 10.2141 10.2141i 0.542106 0.542106i
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 13.3794i 0.706140i −0.935597 0.353070i \(-0.885138\pi\)
0.935597 0.353070i \(-0.114862\pi\)
\(360\) 0 0
\(361\) 7.56074i 0.397934i
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) 16.0769 16.0769i 0.841501 0.841501i
\(366\) 0 0
\(367\) 20.7376i 1.08249i −0.840864 0.541247i \(-0.817953\pi\)
0.840864 0.541247i \(-0.182047\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) 0.269015 + 0.269015i 0.0139665 + 0.0139665i
\(372\) 0 0
\(373\) 6.84888 6.84888i 0.354622 0.354622i −0.507204 0.861826i \(-0.669321\pi\)
0.861826 + 0.507204i \(0.169321\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 2.79067 0.143727
\(378\) 0 0
\(379\) −17.1046 17.1046i −0.878602 0.878602i 0.114788 0.993390i \(-0.463381\pi\)
−0.993390 + 0.114788i \(0.963381\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) −14.7106 −0.751678 −0.375839 0.926685i \(-0.622645\pi\)
−0.375839 + 0.926685i \(0.622645\pi\)
\(384\) 0 0
\(385\) −10.7266 −0.546680
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) −4.86662 4.86662i −0.246747 0.246747i 0.572887 0.819634i \(-0.305823\pi\)
−0.819634 + 0.572887i \(0.805823\pi\)
\(390\) 0 0
\(391\) 4.66272 0.235804
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) 10.9548 10.9548i 0.551195 0.551195i
\(396\) 0 0
\(397\) 25.4535 + 25.4535i 1.27747 + 1.27747i 0.942077 + 0.335396i \(0.108870\pi\)
0.335396 + 0.942077i \(0.391130\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 21.0632i 1.05184i −0.850533 0.525922i \(-0.823720\pi\)
0.850533 0.525922i \(-0.176280\pi\)
\(402\) 0 0
\(403\) −25.8648 + 25.8648i −1.28842 + 1.28842i
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 42.9146i 2.12720i
\(408\) 0 0
\(409\) 36.0796i 1.78402i −0.452016 0.892010i \(-0.649295\pi\)
0.452016 0.892010i \(-0.350705\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) −0.0979540 + 0.0979540i −0.00482000 + 0.00482000i
\(414\) 0 0
\(415\) 23.0296i 1.13048i
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 4.95680 + 4.95680i 0.242155 + 0.242155i 0.817741 0.575586i \(-0.195226\pi\)
−0.575586 + 0.817741i \(0.695226\pi\)
\(420\) 0 0
\(421\) −7.80250 + 7.80250i −0.380271 + 0.380271i −0.871200 0.490929i \(-0.836657\pi\)
0.490929 + 0.871200i \(0.336657\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) −4.55683 −0.221039
\(426\) 0 0
\(427\) 7.41725 + 7.41725i 0.358946 + 0.358946i
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) −4.41852 −0.212832 −0.106416 0.994322i \(-0.533938\pi\)
−0.106416 + 0.994322i \(0.533938\pi\)
\(432\) 0 0
\(433\) −3.06712 −0.147396 −0.0736981 0.997281i \(-0.523480\pi\)
−0.0736981 + 0.997281i \(0.523480\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 8.27750 + 8.27750i 0.395966 + 0.395966i
\(438\) 0 0
\(439\) 4.24215 0.202467 0.101233 0.994863i \(-0.467721\pi\)
0.101233 + 0.994863i \(0.467721\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 2.34161 2.34161i 0.111253 0.111253i −0.649289 0.760542i \(-0.724933\pi\)
0.760542 + 0.649289i \(0.224933\pi\)
\(444\) 0 0
\(445\) −8.57567 8.57567i −0.406526 0.406526i
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) 8.86849i 0.418530i −0.977859 0.209265i \(-0.932893\pi\)
0.977859 0.209265i \(-0.0671071\pi\)
\(450\) 0 0
\(451\) −2.21784 + 2.21784i −0.104434 + 0.104434i
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) 6.03831i 0.283080i
\(456\) 0 0
\(457\) 7.14847i 0.334392i 0.985924 + 0.167196i \(0.0534712\pi\)
−0.985924 + 0.167196i \(0.946529\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) −17.8346 + 17.8346i −0.830638 + 0.830638i −0.987604 0.156966i \(-0.949829\pi\)
0.156966 + 0.987604i \(0.449829\pi\)
\(462\) 0 0
\(463\) 16.1618i 0.751102i 0.926802 + 0.375551i \(0.122547\pi\)
−0.926802 + 0.375551i \(0.877453\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) −13.5356 13.5356i −0.626352 0.626352i 0.320797 0.947148i \(-0.396049\pi\)
−0.947148 + 0.320797i \(0.896049\pi\)
\(468\) 0 0
\(469\) 6.83972 6.83972i 0.315829 0.315829i
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) −68.8354 −3.16505
\(474\) 0 0
\(475\) −8.08951 8.08951i −0.371172 0.371172i
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) 9.85872 0.450456 0.225228 0.974306i \(-0.427687\pi\)
0.225228 + 0.974306i \(0.427687\pi\)
\(480\) 0 0
\(481\) 24.1578 1.10150
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 12.3218 + 12.3218i 0.559503 + 0.559503i
\(486\) 0 0
\(487\) 29.4055 1.33249 0.666245 0.745733i \(-0.267900\pi\)
0.666245 + 0.745733i \(0.267900\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) −5.21529 + 5.21529i −0.235363 + 0.235363i −0.814927 0.579564i \(-0.803223\pi\)
0.579564 + 0.814927i \(0.303223\pi\)
\(492\) 0 0
\(493\) −1.11856 1.11856i −0.0503776 0.0503776i
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 8.66316i 0.388596i
\(498\) 0 0
\(499\) 11.8610 11.8610i 0.530973 0.530973i −0.389889 0.920862i \(-0.627487\pi\)
0.920862 + 0.389889i \(0.127487\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) 9.18051i 0.409339i −0.978831 0.204669i \(-0.934388\pi\)
0.978831 0.204669i \(-0.0656119\pi\)
\(504\) 0 0
\(505\) 13.5588i 0.603357i
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) 15.7454 15.7454i 0.697902 0.697902i −0.266056 0.963958i \(-0.585721\pi\)
0.963958 + 0.266056i \(0.0857206\pi\)
\(510\) 0 0
\(511\) 13.6358i 0.603210i
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) −8.39351 8.39351i −0.369862 0.369862i
\(516\) 0 0
\(517\) −3.49443 + 3.49443i −0.153685 + 0.153685i
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 35.2555 1.54457 0.772286 0.635275i \(-0.219113\pi\)
0.772286 + 0.635275i \(0.219113\pi\)
\(522\) 0 0
\(523\) −13.3455 13.3455i −0.583559 0.583559i 0.352320 0.935880i \(-0.385393\pi\)
−0.935880 + 0.352320i \(0.885393\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 20.7344 0.903206
\(528\) 0 0
\(529\) 17.8407 0.775684
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) −1.24848 1.24848i −0.0540777 0.0540777i
\(534\) 0 0
\(535\) 14.4688 0.625540
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) 4.54895 4.54895i 0.195937 0.195937i
\(540\) 0 0
\(541\) 22.4225 + 22.4225i 0.964020 + 0.964020i 0.999375 0.0353552i \(-0.0112563\pi\)
−0.0353552 + 0.999375i \(0.511256\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) 3.63950i 0.155899i
\(546\) 0 0
\(547\) 6.02624 6.02624i 0.257664 0.257664i −0.566440 0.824103i \(-0.691680\pi\)
0.824103 + 0.566440i \(0.191680\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) 3.97146i 0.169190i
\(552\) 0 0
\(553\) 9.29142i 0.395111i
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) −19.9169 + 19.9169i −0.843905 + 0.843905i −0.989364 0.145459i \(-0.953534\pi\)
0.145459 + 0.989364i \(0.453534\pi\)
\(558\) 0 0
\(559\) 38.7493i 1.63892i
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) 18.0269 + 18.0269i 0.759743 + 0.759743i 0.976275 0.216533i \(-0.0694748\pi\)
−0.216533 + 0.976275i \(0.569475\pi\)
\(564\) 0 0
\(565\) −16.5090 + 16.5090i −0.694541 + 0.694541i
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 28.6582 1.20142 0.600708 0.799469i \(-0.294885\pi\)
0.600708 + 0.799469i \(0.294885\pi\)
\(570\) 0 0
\(571\) 4.74392 + 4.74392i 0.198527 + 0.198527i 0.799368 0.600841i \(-0.205168\pi\)
−0.600841 + 0.799368i \(0.705168\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 5.04209 0.210270
\(576\) 0 0
\(577\) −27.7361 −1.15467 −0.577335 0.816507i \(-0.695907\pi\)
−0.577335 + 0.816507i \(0.695907\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) −9.76640 9.76640i −0.405179 0.405179i
\(582\) 0 0
\(583\) −2.44747 −0.101364
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) −19.8086 + 19.8086i −0.817587 + 0.817587i −0.985758 0.168171i \(-0.946214\pi\)
0.168171 + 0.985758i \(0.446214\pi\)
\(588\) 0 0
\(589\) 36.8088 + 36.8088i 1.51668 + 1.51668i
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) 18.8296i 0.773239i 0.922239 + 0.386620i \(0.126357\pi\)
−0.922239 + 0.386620i \(0.873643\pi\)
\(594\) 0 0
\(595\) −2.42029 + 2.42029i −0.0992222 + 0.0992222i
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) 24.0141i 0.981188i −0.871388 0.490594i \(-0.836780\pi\)
0.871388 0.490594i \(-0.163220\pi\)
\(600\) 0 0
\(601\) 14.3602i 0.585766i −0.956148 0.292883i \(-0.905385\pi\)
0.956148 0.292883i \(-0.0946147\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) 35.8257 35.8257i 1.45652 1.45652i
\(606\) 0 0
\(607\) 6.44642i 0.261652i 0.991405 + 0.130826i \(0.0417629\pi\)
−0.991405 + 0.130826i \(0.958237\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) −1.96711 1.96711i −0.0795807 0.0795807i
\(612\) 0 0
\(613\) −31.4106 + 31.4106i −1.26866 + 1.26866i −0.321884 + 0.946779i \(0.604316\pi\)
−0.946779 + 0.321884i \(0.895684\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) −30.2797 −1.21902 −0.609508 0.792780i \(-0.708633\pi\)
−0.609508 + 0.792780i \(0.708633\pi\)
\(618\) 0 0
\(619\) −6.97556 6.97556i −0.280372 0.280372i 0.552886 0.833257i \(-0.313527\pi\)
−0.833257 + 0.552886i \(0.813527\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 7.27355 0.291409
\(624\) 0 0
\(625\) 8.97334 0.358934
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) −9.68300 9.68300i −0.386086 0.386086i
\(630\) 0 0
\(631\) −14.0268 −0.558398 −0.279199 0.960233i \(-0.590069\pi\)
−0.279199 + 0.960233i \(0.590069\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) −6.28346 + 6.28346i −0.249352 + 0.249352i
\(636\) 0 0
\(637\) 2.56073 + 2.56073i 0.101460 + 0.101460i
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) 20.9884i 0.828992i 0.910051 + 0.414496i \(0.136042\pi\)
−0.910051 + 0.414496i \(0.863958\pi\)
\(642\) 0 0
\(643\) −32.1818 + 32.1818i −1.26913 + 1.26913i −0.322589 + 0.946539i \(0.604553\pi\)
−0.946539 + 0.322589i \(0.895447\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 0.647703i 0.0254638i 0.999919 + 0.0127319i \(0.00405280\pi\)
−0.999919 + 0.0127319i \(0.995947\pi\)
\(648\) 0 0
\(649\) 0.891176i 0.0349817i
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 25.7373 25.7373i 1.00718 1.00718i 0.00720262 0.999974i \(-0.497707\pi\)
0.999974 0.00720262i \(-0.00229269\pi\)
\(654\) 0 0
\(655\) 31.6837i 1.23798i
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) −17.0862 17.0862i −0.665583 0.665583i 0.291108 0.956690i \(-0.405976\pi\)
−0.956690 + 0.291108i \(0.905976\pi\)
\(660\) 0 0
\(661\) −8.34196 + 8.34196i −0.324465 + 0.324465i −0.850477 0.526012i \(-0.823687\pi\)
0.526012 + 0.850477i \(0.323687\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) −8.59324 −0.333232
\(666\) 0 0
\(667\) 1.23768 + 1.23768i 0.0479233 + 0.0479233i
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) −67.4814 −2.60509
\(672\) 0 0
\(673\) −1.69237 −0.0652361 −0.0326180 0.999468i \(-0.510384\pi\)
−0.0326180 + 0.999468i \(0.510384\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) −36.3935 36.3935i −1.39872 1.39872i −0.803749 0.594968i \(-0.797165\pi\)
−0.594968 0.803749i \(1.29716\pi\)
\(678\) 0 0
\(679\) −10.4508 −0.401066
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) −13.6522 + 13.6522i −0.522388 + 0.522388i −0.918292 0.395904i \(-0.870431\pi\)
0.395904 + 0.918292i \(0.370431\pi\)
\(684\) 0 0
\(685\) 11.9911 + 11.9911i 0.458156 + 0.458156i
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) 1.37775i 0.0524880i
\(690\) 0 0
\(691\) 2.36989 2.36989i 0.0901550 0.0901550i −0.660591 0.750746i \(-0.729694\pi\)
0.750746 + 0.660591i \(0.229694\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 16.2726i 0.617254i
\(696\) 0 0
\(697\) 1.00084i 0.0379095i
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) −27.6655 + 27.6655i −1.04491 + 1.04491i −0.0459668 + 0.998943i \(0.514637\pi\)
−0.998943 + 0.0459668i \(0.985363\pi\)
\(702\) 0 0
\(703\) 34.3795i 1.29665i
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) −5.75000 5.75000i −0.216251 0.216251i
\(708\) 0 0
\(709\) 4.38704 4.38704i 0.164759 0.164759i −0.619912 0.784671i \(-0.712832\pi\)
0.784671 + 0.619912i \(0.212832\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) −22.9425 −0.859202
\(714\) 0 0
\(715\) 27.4680 + 27.4680i 1.02724 + 1.02724i
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) 18.2313 0.679915 0.339957 0.940441i \(-0.389587\pi\)
0.339957 + 0.940441i \(0.389587\pi\)
\(720\) 0 0
\(721\) 7.11905 0.265127
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) −1.20957 1.20957i −0.0449224 0.0449224i
\(726\) 0 0
\(727\) −17.1985 −0.637857 −0.318928 0.947779i \(-0.603323\pi\)
−0.318928 + 0.947779i \(0.603323\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) −15.5316 + 15.5316i −0.574457 + 0.574457i
\(732\) 0 0
\(733\) 1.76630 + 1.76630i 0.0652396 + 0.0652396i 0.738974 0.673734i \(-0.235311\pi\)
−0.673734 + 0.738974i \(0.735311\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 62.2271i 2.29216i
\(738\) 0 0
\(739\) −20.8217 + 20.8217i −0.765939 + 0.765939i −0.977389 0.211450i \(-0.932182\pi\)
0.211450 + 0.977389i \(0.432182\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 39.1460i 1.43613i 0.695977 + 0.718064i \(0.254971\pi\)
−0.695977 + 0.718064i \(0.745029\pi\)
\(744\) 0 0
\(745\) 0.316196i 0.0115845i
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) −6.13593 + 6.13593i −0.224202 + 0.224202i
\(750\) 0 0
\(751\) 44.9147i 1.63896i 0.573106 + 0.819481i \(0.305738\pi\)
−0.573106 + 0.819481i \(0.694262\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 16.1904 + 16.1904i 0.589229 + 0.589229i
\(756\) 0 0
\(757\) −35.8730 + 35.8730i −1.30383 + 1.30383i −0.378036 + 0.925791i \(0.623400\pi\)
−0.925791 + 0.378036i \(0.876600\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 47.4451 1.71988 0.859941 0.510393i \(-0.170500\pi\)
0.859941 + 0.510393i \(0.170500\pi\)
\(762\) 0 0
\(763\) −1.54344 1.54344i −0.0558764 0.0558764i
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 0.501667 0.0181141
\(768\) 0 0
\(769\) 4.59306 0.165630 0.0828150 0.996565i \(-0.473609\pi\)
0.0828150 + 0.996565i \(0.473609\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) 1.66000 + 1.66000i 0.0597062 + 0.0597062i 0.736329 0.676623i \(-0.236557\pi\)
−0.676623 + 0.736329i \(0.736557\pi\)
\(774\) 0 0
\(775\) 22.4214 0.805401
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) −1.77674 + 1.77674i −0.0636583 + 0.0636583i
\(780\) 0 0
\(781\) −39.4083 39.4083i −1.41014 1.41014i
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) 5.87761i 0.209781i
\(786\) 0 0
\(787\) 16.7673 16.7673i 0.597688 0.597688i −0.342009 0.939697i \(-0.611107\pi\)
0.939697 + 0.342009i \(0.111107\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 14.0023i 0.497865i
\(792\) 0 0
\(793\) 37.9871i 1.34896i
\(794\) 0 0