Properties

Label 4032.2.v.e.1583.6
Level 4032
Weight 2
Character 4032.1583
Analytic conductor 32.196
Analytic rank 0
Dimension 40
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.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 1583.6
Character \(\chi\) = 4032.1583
Dual form 4032.2.v.e.3599.6

$q$-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 0.392484 0.919759i \(-0.371616\pi\)
−0.919759 + 0.392484i \(0.871616\pi\)
\(6\) 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 \(0.671625\pi\)
−0.858133 + 0.513428i \(0.828375\pi\)
\(12\) 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 \(0.0800815\pi\)
−0.968519 + 0.248938i \(0.919918\pi\)
\(18\) 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 \(-0.923898\pi\)
0.971556 0.236810i \(-0.0761019\pi\)
\(24\) 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 −0.755887 0.654702i \(-0.772794\pi\)
0.654702 + 0.755887i \(0.272794\pi\)
\(30\) 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 \(-0.487879\pi\)
0.0380712 + 0.999275i \(0.487879\pi\)
\(42\) 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 \(-0.482157\pi\)
0.0560256 + 0.998429i \(0.482157\pi\)
\(48\) 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 0.725341 0.688389i \(-0.241682\pi\)
−0.688389 + 0.725341i \(0.741682\pi\)
\(54\) 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 −0.713454 0.700702i \(-0.752870\pi\)
0.700702 + 0.713454i \(0.252870\pi\)
\(60\) 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 \(0.171861\pi\)
−0.857752 + 0.514064i \(0.828139\pi\)
\(72\) 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 \(-0.976167\pi\)
−0.0748037 0.997198i \(1.47617\pi\)
\(84\) 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 \(-0.374030\pi\)
0.385497 + 0.922709i \(0.374030\pi\)
\(90\) 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 0.360581 0.932728i \(-0.382578\pi\)
−0.932728 + 0.360581i \(0.882578\pi\)
\(102\) 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 −0.938490 0.345307i \(-0.887775\pi\)
0.345307 + 0.938490i \(0.387775\pi\)
\(108\) 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 \(-0.771143\pi\)
0.752481 0.658614i \(-0.228857\pi\)
\(114\) 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 \(-0.938280\pi\)
−0.192685 0.981261i \(1.43828\pi\)
\(132\) 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 \(-0.643060\pi\)
−0.434457 + 0.900693i \(0.643060\pi\)
\(138\) 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 0.712578 0.701593i \(-0.247527\pi\)
−0.701593 + 0.712578i \(0.747527\pi\)
\(150\) 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 \(0.0542790\pi\)
−0.985496 + 0.169697i \(0.945721\pi\)
\(168\) 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 \(0.691197\pi\)
−0.824960 + 0.565191i \(0.808803\pi\)
\(174\) 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 0.815929 0.578152i \(-0.196226\pi\)
−0.578152 + 0.815929i \(0.696226\pi\)
\(180\) 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 \(-0.796784\pi\)
−0.803037 + 0.595929i \(0.796784\pi\)
\(192\) 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 0.456577 0.889684i \(-0.349075\pi\)
−0.889684 + 0.456577i \(0.849075\pi\)
\(198\) 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 \(-0.777961\pi\)
−0.642348 0.766413i \(1.27796\pi\)
\(228\) 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 \(-0.386621\pi\)
0.348707 + 0.937232i \(0.386621\pi\)
\(234\) 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 \(-0.392143\pi\)
0.332396 + 0.943140i \(0.392143\pi\)
\(240\) 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 −0.365611 0.930768i \(-0.619140\pi\)
0.930768 + 0.365611i \(0.119140\pi\)
\(252\) 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 \(-0.767483\pi\)
0.744858 0.667223i \(-0.232517\pi\)
\(258\) 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 \(-0.564746\pi\)
0.202006 0.979384i \(-0.435254\pi\)
\(264\) 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 −0.280541 0.959842i \(-0.590514\pi\)
0.959842 + 0.280541i \(0.0905140\pi\)
\(270\) 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 \(-0.454853\pi\)
0.141358 + 0.989959i \(0.454853\pi\)
\(282\) 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 0.560406 0.828218i \(-0.310645\pi\)
−0.828218 + 0.560406i \(0.810645\pi\)
\(294\) 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 \(0.0112682\pi\)
−0.999373 + 0.0353926i \(0.988732\pi\)
\(312\) 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 −0.485505 0.874234i \(-0.661364\pi\)
0.874234 + 0.485505i \(0.161364\pi\)
\(318\) 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 −0.321094 0.947047i \(-0.604050\pi\)
0.947047 + 0.321094i \(0.104050\pi\)
\(348\) 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 \(0.0395624\pi\)
−0.992286 + 0.123969i \(0.960438\pi\)
\(354\) 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 \(0.114862\pi\)
−0.935597 + 0.353070i \(0.885138\pi\)
\(360\) 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 \(-0.377355\pi\)
0.375839 + 0.926685i \(0.377355\pi\)
\(384\) 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 0.819634 0.572887i \(-0.194177\pi\)
−0.572887 + 0.819634i \(0.694177\pi\)
\(390\) 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 \(0.176280\pi\)
−0.850533 + 0.525922i \(0.823720\pi\)
\(402\) 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 0.575586 0.817741i \(-0.304774\pi\)
−0.817741 + 0.575586i \(0.804774\pi\)
\(420\) 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 \(-0.466062\pi\)
0.106416 + 0.994322i \(0.466062\pi\)
\(432\) 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 −0.760542 0.649289i \(-0.775067\pi\)
0.649289 + 0.760542i \(0.275067\pi\)
\(444\) 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 \(0.0671071\pi\)
−0.977859 + 0.209265i \(0.932893\pi\)
\(450\) 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 −0.156966 0.987604i \(-0.550171\pi\)
0.987604 + 0.156966i \(0.0501714\pi\)
\(462\) 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 0.947148 0.320797i \(-0.103951\pi\)
−0.320797 + 0.947148i \(0.603951\pi\)
\(468\) 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 \(-0.572313\pi\)
−0.225228 + 0.974306i \(0.572313\pi\)
\(480\) 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 −0.579564 0.814927i \(-0.696777\pi\)
0.814927 + 0.579564i \(0.196777\pi\)
\(492\) 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 \(0.0656119\pi\)
−0.978831 + 0.204669i \(0.934388\pi\)
\(504\) 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 −0.963958 0.266056i \(-0.914279\pi\)
0.266056 + 0.963958i \(0.414279\pi\)
\(510\) 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 \(-0.780887\pi\)
−0.772286 + 0.635275i \(0.780887\pi\)
\(522\) 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 −0.145459 0.989364i \(-0.546466\pi\)
0.989364 + 0.145459i \(0.0464658\pi\)
\(558\) 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 0.216533 0.976275i \(-0.430525\pi\)
−0.976275 + 0.216533i \(0.930525\pi\)
\(564\) 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 \(-0.705115\pi\)
−0.600708 + 0.799469i \(0.705115\pi\)
\(570\) 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 −0.168171 0.985758i \(-0.553786\pi\)
0.985758 + 0.168171i \(0.0537860\pi\)
\(588\) 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 \(-0.873643\pi\)
0.922239 0.386620i \(-0.126357\pi\)
\(594\) 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 \(0.163220\pi\)
−0.871388 + 0.490594i \(0.836780\pi\)
\(600\) 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 \(-0.291367\pi\)
0.609508 + 0.792780i \(0.291367\pi\)
\(618\) 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 \(-0.863958\pi\)
0.910051 0.414496i \(-0.136042\pi\)
\(642\) 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 \(-0.995947\pi\)
0.999919 0.0127319i \(-0.00405280\pi\)
\(648\) 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 \(0.502293\pi\)
−0.999974 + 0.00720262i \(0.997707\pi\)
\(654\) 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 0.956690 0.291108i \(-0.0940238\pi\)
−0.291108 + 0.956690i \(0.594024\pi\)
\(660\) 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 \(0.202835\pi\)
0.594968 + 0.803749i \(0.297165\pi\)
\(678\) 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 −0.395904 0.918292i \(-0.629569\pi\)
0.918292 + 0.395904i \(0.129569\pi\)
\(684\) 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 \(-0.485363\pi\)
0.998943 0.0459668i \(-0.0146369\pi\)
\(702\) 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 \(-0.610413\pi\)
−0.339957 + 0.940441i \(0.610413\pi\)
\(720\) 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 \(-0.745029\pi\)
0.695977 0.718064i \(-0.254971\pi\)
\(744\) 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 \(-0.829500\pi\)
−0.859941 + 0.510393i \(0.829500\pi\)
\(762\) 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 0.676623 0.736329i \(-0.263443\pi\)
−0.736329 + 0.676623i \(0.763443\pi\)
\(774\) 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