Properties

Label 6012.2.h.a.3005.16
Level 6012
Weight 2
Character 6012.3005
Analytic conductor 48.006
Analytic rank 0
Dimension 56
CM no
Inner twists 4

Related objects

Downloads

Learn more about

Newspace parameters

Level: \( N \) \(=\) \( 6012 = 2^{2} \cdot 3^{2} \cdot 167 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 6012.h (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(48.0060616952\)
Analytic rank: \(0\)
Dimension: \(56\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 3005.16
Character \(\chi\) \(=\) 6012.3005
Dual form 6012.2.h.a.3005.15

$q$-expansion

\(f(q)\) \(=\) \(q-2.08738 q^{5} +3.97701 q^{7} +O(q^{10})\) \(q-2.08738 q^{5} +3.97701 q^{7} +5.31004i q^{11} -4.83536i q^{13} +6.52168 q^{17} +7.92418 q^{19} -1.37306 q^{23} -0.642863 q^{25} -3.16157i q^{29} +5.86836 q^{31} -8.30151 q^{35} +8.85961i q^{37} -7.58734 q^{41} -1.05520i q^{43} -0.619938i q^{47} +8.81660 q^{49} -0.405697 q^{53} -11.0840i q^{55} +10.8869 q^{59} -1.50582 q^{61} +10.0932i q^{65} -14.1578i q^{67} -6.00226 q^{71} +3.66335i q^{73} +21.1181i q^{77} -6.01121i q^{79} +6.48181 q^{83} -13.6132 q^{85} -3.50411i q^{89} -19.2303i q^{91} -16.5407 q^{95} -16.1278 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 56q + O(q^{10}) \) \( 56q + 8q^{19} + 64q^{25} - 8q^{31} + 56q^{49} - 8q^{61} + 32q^{85} - 48q^{97} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/6012\mathbb{Z}\right)^\times\).

\(n\) \(3007\) \(3341\) \(4681\)
\(\chi(n)\) \(1\) \(-1\) \(-1\)

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
\(3\) 0 0
\(4\) 0 0
\(5\) −2.08738 −0.933503 −0.466751 0.884389i \(-0.654576\pi\)
−0.466751 + 0.884389i \(0.654576\pi\)
\(6\) 0 0
\(7\) 3.97701 1.50317 0.751584 0.659637i \(-0.229290\pi\)
0.751584 + 0.659637i \(0.229290\pi\)
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) 5.31004i 1.60104i 0.599308 + 0.800518i \(0.295442\pi\)
−0.599308 + 0.800518i \(0.704558\pi\)
\(12\) 0 0
\(13\) 4.83536i 1.34109i −0.741870 0.670544i \(-0.766061\pi\)
0.741870 0.670544i \(-0.233939\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 6.52168 1.58174 0.790870 0.611985i \(-0.209629\pi\)
0.790870 + 0.611985i \(0.209629\pi\)
\(18\) 0 0
\(19\) 7.92418 1.81793 0.908966 0.416870i \(-0.136873\pi\)
0.908966 + 0.416870i \(0.136873\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) −1.37306 −0.286303 −0.143152 0.989701i \(-0.545724\pi\)
−0.143152 + 0.989701i \(0.545724\pi\)
\(24\) 0 0
\(25\) −0.642863 −0.128573
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) 3.16157i 0.587088i −0.955945 0.293544i \(-0.905165\pi\)
0.955945 0.293544i \(-0.0948348\pi\)
\(30\) 0 0
\(31\) 5.86836 1.05399 0.526994 0.849869i \(-0.323319\pi\)
0.526994 + 0.849869i \(0.323319\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) −8.30151 −1.40321
\(36\) 0 0
\(37\) 8.85961i 1.45651i 0.685305 + 0.728256i \(0.259669\pi\)
−0.685305 + 0.728256i \(0.740331\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) −7.58734 −1.18494 −0.592471 0.805591i \(-0.701848\pi\)
−0.592471 + 0.805591i \(0.701848\pi\)
\(42\) 0 0
\(43\) 1.05520i 0.160917i −0.996758 0.0804583i \(-0.974362\pi\)
0.996758 0.0804583i \(-0.0256384\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 0.619938i 0.0904272i −0.998977 0.0452136i \(-0.985603\pi\)
0.998977 0.0452136i \(-0.0143969\pi\)
\(48\) 0 0
\(49\) 8.81660 1.25951
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) −0.405697 −0.0557267 −0.0278634 0.999612i \(-0.508870\pi\)
−0.0278634 + 0.999612i \(0.508870\pi\)
\(54\) 0 0
\(55\) 11.0840i 1.49457i
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) 10.8869 1.41736 0.708679 0.705531i \(-0.249292\pi\)
0.708679 + 0.705531i \(0.249292\pi\)
\(60\) 0 0
\(61\) −1.50582 −0.192801 −0.0964005 0.995343i \(-0.530733\pi\)
−0.0964005 + 0.995343i \(0.530733\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) 10.0932i 1.25191i
\(66\) 0 0
\(67\) 14.1578i 1.72965i −0.502075 0.864824i \(-0.667430\pi\)
0.502075 0.864824i \(-0.332570\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) −6.00226 −0.712337 −0.356169 0.934422i \(-0.615917\pi\)
−0.356169 + 0.934422i \(0.615917\pi\)
\(72\) 0 0
\(73\) 3.66335i 0.428763i 0.976750 + 0.214381i \(0.0687735\pi\)
−0.976750 + 0.214381i \(0.931226\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 21.1181i 2.40663i
\(78\) 0 0
\(79\) 6.01121i 0.676314i −0.941090 0.338157i \(-0.890196\pi\)
0.941090 0.338157i \(-0.109804\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) 6.48181 0.711471 0.355735 0.934587i \(-0.384230\pi\)
0.355735 + 0.934587i \(0.384230\pi\)
\(84\) 0 0
\(85\) −13.6132 −1.47656
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 3.50411i 0.371435i −0.982603 0.185718i \(-0.940539\pi\)
0.982603 0.185718i \(-0.0594610\pi\)
\(90\) 0 0
\(91\) 19.2303i 2.01588i
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) −16.5407 −1.69704
\(96\) 0 0
\(97\) −16.1278 −1.63753 −0.818765 0.574129i \(-0.805341\pi\)
−0.818765 + 0.574129i \(0.805341\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) −1.20758 −0.120159 −0.0600794 0.998194i \(-0.519135\pi\)
−0.0600794 + 0.998194i \(0.519135\pi\)
\(102\) 0 0
\(103\) 2.79454i 0.275354i −0.990477 0.137677i \(-0.956036\pi\)
0.990477 0.137677i \(-0.0439637\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 10.9620i 1.05974i 0.848079 + 0.529870i \(0.177759\pi\)
−0.848079 + 0.529870i \(0.822241\pi\)
\(108\) 0 0
\(109\) 0.681898i 0.0653140i −0.999467 0.0326570i \(-0.989603\pi\)
0.999467 0.0326570i \(-0.0103969\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) −15.5097 −1.45903 −0.729516 0.683964i \(-0.760255\pi\)
−0.729516 + 0.683964i \(0.760255\pi\)
\(114\) 0 0
\(115\) 2.86610 0.267265
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) 25.9368 2.37762
\(120\) 0 0
\(121\) −17.1965 −1.56332
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) 11.7788 1.05353
\(126\) 0 0
\(127\) 20.8656 1.85153 0.925763 0.378105i \(-0.123424\pi\)
0.925763 + 0.378105i \(0.123424\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) 4.87818 0.426208 0.213104 0.977029i \(-0.431643\pi\)
0.213104 + 0.977029i \(0.431643\pi\)
\(132\) 0 0
\(133\) 31.5145 2.73266
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 1.07973i 0.0922476i 0.998936 + 0.0461238i \(0.0146869\pi\)
−0.998936 + 0.0461238i \(0.985313\pi\)
\(138\) 0 0
\(139\) 11.8376i 1.00405i 0.864852 + 0.502027i \(0.167412\pi\)
−0.864852 + 0.502027i \(0.832588\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 25.6759 2.14713
\(144\) 0 0
\(145\) 6.59938i 0.548049i
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) 13.8597 1.13543 0.567714 0.823226i \(-0.307828\pi\)
0.567714 + 0.823226i \(0.307828\pi\)
\(150\) 0 0
\(151\) 18.1640i 1.47817i 0.673613 + 0.739084i \(0.264742\pi\)
−0.673613 + 0.739084i \(0.735258\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) −12.2495 −0.983901
\(156\) 0 0
\(157\) 6.90136 0.550789 0.275394 0.961331i \(-0.411192\pi\)
0.275394 + 0.961331i \(0.411192\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) −5.46068 −0.430362
\(162\) 0 0
\(163\) 3.64394i 0.285415i −0.989765 0.142708i \(-0.954419\pi\)
0.989765 0.142708i \(-0.0455808\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) −5.22495 + 11.8195i −0.404319 + 0.914618i
\(168\) 0 0
\(169\) −10.3807 −0.798515
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) 5.34258i 0.406189i 0.979159 + 0.203094i \(0.0650998\pi\)
−0.979159 + 0.203094i \(0.934900\pi\)
\(174\) 0 0
\(175\) −2.55667 −0.193266
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) 15.1556i 1.13279i 0.824135 + 0.566393i \(0.191662\pi\)
−0.824135 + 0.566393i \(0.808338\pi\)
\(180\) 0 0
\(181\) 13.0023 0.966455 0.483227 0.875495i \(-0.339464\pi\)
0.483227 + 0.875495i \(0.339464\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 18.4933i 1.35966i
\(186\) 0 0
\(187\) 34.6304i 2.53242i
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 22.0965i 1.59885i −0.600768 0.799423i \(-0.705139\pi\)
0.600768 0.799423i \(-0.294861\pi\)
\(192\) 0 0
\(193\) 18.9583i 1.36465i −0.731048 0.682326i \(-0.760969\pi\)
0.731048 0.682326i \(-0.239031\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 9.22603 0.657328 0.328664 0.944447i \(-0.393402\pi\)
0.328664 + 0.944447i \(0.393402\pi\)
\(198\) 0 0
\(199\) −12.7024 −0.900448 −0.450224 0.892916i \(-0.648656\pi\)
−0.450224 + 0.892916i \(0.648656\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) 12.5736i 0.882493i
\(204\) 0 0
\(205\) 15.8376 1.10615
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) 42.0777i 2.91058i
\(210\) 0 0
\(211\) −2.64849 −0.182330 −0.0911649 0.995836i \(-0.529059\pi\)
−0.0911649 + 0.995836i \(0.529059\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) 2.20260i 0.150216i
\(216\) 0 0
\(217\) 23.3385 1.58432
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) 31.5346i 2.12125i
\(222\) 0 0
\(223\) 14.0637 0.941772 0.470886 0.882194i \(-0.343934\pi\)
0.470886 + 0.882194i \(0.343934\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 27.1134 1.79958 0.899790 0.436323i \(-0.143720\pi\)
0.899790 + 0.436323i \(0.143720\pi\)
\(228\) 0 0
\(229\) −5.40537 −0.357197 −0.178599 0.983922i \(-0.557156\pi\)
−0.178599 + 0.983922i \(0.557156\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 20.2157i 1.32437i 0.749339 + 0.662187i \(0.230371\pi\)
−0.749339 + 0.662187i \(0.769629\pi\)
\(234\) 0 0
\(235\) 1.29404i 0.0844141i
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) 20.0580i 1.29744i −0.761026 0.648721i \(-0.775304\pi\)
0.761026 0.648721i \(-0.224696\pi\)
\(240\) 0 0
\(241\) 6.58002i 0.423857i −0.977285 0.211928i \(-0.932026\pi\)
0.977285 0.211928i \(-0.0679743\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) −18.4036 −1.17576
\(246\) 0 0
\(247\) 38.3163i 2.43801i
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 9.32718i 0.588726i −0.955694 0.294363i \(-0.904893\pi\)
0.955694 0.294363i \(-0.0951075\pi\)
\(252\) 0 0
\(253\) 7.29102i 0.458382i
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) −24.6036 −1.53473 −0.767367 0.641209i \(-0.778433\pi\)
−0.767367 + 0.641209i \(0.778433\pi\)
\(258\) 0 0
\(259\) 35.2348i 2.18938i
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) 20.2834i 1.25073i −0.780333 0.625364i \(-0.784950\pi\)
0.780333 0.625364i \(-0.215050\pi\)
\(264\) 0 0
\(265\) 0.846841 0.0520210
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) 10.1372 0.618077 0.309039 0.951049i \(-0.399993\pi\)
0.309039 + 0.951049i \(0.399993\pi\)
\(270\) 0 0
\(271\) 31.6624i 1.92335i 0.274183 + 0.961677i \(0.411592\pi\)
−0.274183 + 0.961677i \(0.588408\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 3.41363i 0.205850i
\(276\) 0 0
\(277\) 26.9874i 1.62151i −0.585382 0.810757i \(-0.699056\pi\)
0.585382 0.810757i \(-0.300944\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) 4.31730i 0.257549i 0.991674 + 0.128774i \(0.0411043\pi\)
−0.991674 + 0.128774i \(0.958896\pi\)
\(282\) 0 0
\(283\) 20.0419 1.19137 0.595683 0.803220i \(-0.296881\pi\)
0.595683 + 0.803220i \(0.296881\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) −30.1749 −1.78117
\(288\) 0 0
\(289\) 25.5323 1.50190
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) 18.6388i 1.08889i 0.838796 + 0.544446i \(0.183260\pi\)
−0.838796 + 0.544446i \(0.816740\pi\)
\(294\) 0 0
\(295\) −22.7251 −1.32311
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 6.63925i 0.383958i
\(300\) 0 0
\(301\) 4.19654i 0.241885i
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) 3.14322 0.179980
\(306\) 0 0
\(307\) 0.835081i 0.0476606i 0.999716 + 0.0238303i \(0.00758614\pi\)
−0.999716 + 0.0238303i \(0.992414\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 4.28717i 0.243103i 0.992585 + 0.121552i \(0.0387870\pi\)
−0.992585 + 0.121552i \(0.961213\pi\)
\(312\) 0 0
\(313\) 13.9566i 0.788872i −0.918923 0.394436i \(-0.870940\pi\)
0.918923 0.394436i \(-0.129060\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 28.9136i 1.62395i −0.583692 0.811975i \(-0.698392\pi\)
0.583692 0.811975i \(-0.301608\pi\)
\(318\) 0 0
\(319\) 16.7880 0.939950
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) 51.6790 2.87549
\(324\) 0 0
\(325\) 3.10848i 0.172427i
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) 2.46550i 0.135927i
\(330\) 0 0
\(331\) 30.6221i 1.68314i 0.540145 + 0.841572i \(0.318369\pi\)
−0.540145 + 0.841572i \(0.681631\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) 29.5526i 1.61463i
\(336\) 0 0
\(337\) −22.2130 −1.21002 −0.605011 0.796217i \(-0.706831\pi\)
−0.605011 + 0.796217i \(0.706831\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) 31.1612i 1.68747i
\(342\) 0 0
\(343\) 7.22464 0.390094
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) −8.23540 −0.442099 −0.221050 0.975263i \(-0.570948\pi\)
−0.221050 + 0.975263i \(0.570948\pi\)
\(348\) 0 0
\(349\) 20.8450i 1.11581i 0.829905 + 0.557904i \(0.188394\pi\)
−0.829905 + 0.557904i \(0.811606\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) 19.4771i 1.03666i 0.855179 + 0.518332i \(0.173447\pi\)
−0.855179 + 0.518332i \(0.826553\pi\)
\(354\) 0 0
\(355\) 12.5290 0.664969
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 8.74825i 0.461715i −0.972988 0.230857i \(-0.925847\pi\)
0.972988 0.230857i \(-0.0741531\pi\)
\(360\) 0 0
\(361\) 43.7926 2.30488
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) 7.64679i 0.400251i
\(366\) 0 0
\(367\) 26.2691 1.37123 0.685617 0.727962i \(-0.259532\pi\)
0.685617 + 0.727962i \(0.259532\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) −1.61346 −0.0837666
\(372\) 0 0
\(373\) 8.02553i 0.415546i −0.978177 0.207773i \(-0.933378\pi\)
0.978177 0.207773i \(-0.0666216\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) −15.2873 −0.787337
\(378\) 0 0
\(379\) 32.6197i 1.67556i −0.546007 0.837781i \(-0.683853\pi\)
0.546007 0.837781i \(-0.316147\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 26.8165i 1.37026i −0.728422 0.685129i \(-0.759746\pi\)
0.728422 0.685129i \(-0.240254\pi\)
\(384\) 0 0
\(385\) 44.0813i 2.24659i
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) 25.3033 1.28293 0.641463 0.767154i \(-0.278328\pi\)
0.641463 + 0.767154i \(0.278328\pi\)
\(390\) 0 0
\(391\) −8.95467 −0.452857
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) 12.5477i 0.631341i
\(396\) 0 0
\(397\) 2.37174 0.119034 0.0595172 0.998227i \(-0.481044\pi\)
0.0595172 + 0.998227i \(0.481044\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 17.9123 0.894495 0.447248 0.894410i \(-0.352404\pi\)
0.447248 + 0.894410i \(0.352404\pi\)
\(402\) 0 0
\(403\) 28.3756i 1.41349i
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) −47.0449 −2.33193
\(408\) 0 0
\(409\) 12.2284 0.604653 0.302327 0.953204i \(-0.402237\pi\)
0.302327 + 0.953204i \(0.402237\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) 43.2974 2.13053
\(414\) 0 0
\(415\) −13.5300 −0.664160
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 19.0883i 0.932523i 0.884647 + 0.466261i \(0.154399\pi\)
−0.884647 + 0.466261i \(0.845601\pi\)
\(420\) 0 0
\(421\) −14.5942 −0.711277 −0.355639 0.934624i \(-0.615737\pi\)
−0.355639 + 0.934624i \(0.615737\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) −4.19255 −0.203368
\(426\) 0 0
\(427\) −5.98867 −0.289812
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 27.1700i 1.30873i 0.756178 + 0.654366i \(0.227064\pi\)
−0.756178 + 0.654366i \(0.772936\pi\)
\(432\) 0 0
\(433\) 27.3677 1.31521 0.657603 0.753365i \(-0.271570\pi\)
0.657603 + 0.753365i \(0.271570\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) −10.8804 −0.520480
\(438\) 0 0
\(439\) 11.3349i 0.540984i −0.962722 0.270492i \(-0.912814\pi\)
0.962722 0.270492i \(-0.0871864\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 7.10877 0.337748 0.168874 0.985638i \(-0.445987\pi\)
0.168874 + 0.985638i \(0.445987\pi\)
\(444\) 0 0
\(445\) 7.31440i 0.346736i
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) 7.51446i 0.354629i 0.984154 + 0.177315i \(0.0567410\pi\)
−0.984154 + 0.177315i \(0.943259\pi\)
\(450\) 0 0
\(451\) 40.2890i 1.89714i
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) 40.1408i 1.88183i
\(456\) 0 0
\(457\) 12.3693i 0.578610i 0.957237 + 0.289305i \(0.0934241\pi\)
−0.957237 + 0.289305i \(0.906576\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 13.7961i 0.642549i −0.946986 0.321275i \(-0.895889\pi\)
0.946986 0.321275i \(-0.104111\pi\)
\(462\) 0 0
\(463\) 0.371515i 0.0172657i 0.999963 + 0.00863287i \(0.00274796\pi\)
−0.999963 + 0.00863287i \(0.997252\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 11.8305i 0.547450i 0.961808 + 0.273725i \(0.0882559\pi\)
−0.961808 + 0.273725i \(0.911744\pi\)
\(468\) 0 0
\(469\) 56.3056i 2.59995i
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) 5.60315 0.257633
\(474\) 0 0
\(475\) −5.09417 −0.233736
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) 31.1013 1.42105 0.710527 0.703670i \(-0.248457\pi\)
0.710527 + 0.703670i \(0.248457\pi\)
\(480\) 0 0
\(481\) 42.8394 1.95331
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 33.6648 1.52864
\(486\) 0 0
\(487\) 33.2095i 1.50486i 0.658670 + 0.752432i \(0.271119\pi\)
−0.658670 + 0.752432i \(0.728881\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) 32.8757i 1.48366i 0.670587 + 0.741831i \(0.266042\pi\)
−0.670587 + 0.741831i \(0.733958\pi\)
\(492\) 0 0
\(493\) 20.6187i 0.928621i
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) −23.8710 −1.07076
\(498\) 0 0
\(499\) 42.1052i 1.88489i 0.334364 + 0.942444i \(0.391479\pi\)
−0.334364 + 0.942444i \(0.608521\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) 31.5903i 1.40854i −0.709932 0.704270i \(-0.751274\pi\)
0.709932 0.704270i \(-0.248726\pi\)
\(504\) 0 0
\(505\) 2.52067 0.112169
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) 3.32671i 0.147454i 0.997278 + 0.0737270i \(0.0234894\pi\)
−0.997278 + 0.0737270i \(0.976511\pi\)
\(510\) 0 0
\(511\) 14.5692i 0.644502i
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) 5.83326i 0.257044i
\(516\) 0 0
\(517\) 3.29189 0.144777
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) −8.84464 −0.387491 −0.193745 0.981052i \(-0.562064\pi\)
−0.193745 + 0.981052i \(0.562064\pi\)
\(522\) 0 0
\(523\) −9.09660 −0.397767 −0.198883 0.980023i \(-0.563731\pi\)
−0.198883 + 0.980023i \(0.563731\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 38.2715 1.66713
\(528\) 0 0
\(529\) −21.1147 −0.918030
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) 36.6875i 1.58911i
\(534\) 0 0
\(535\) 22.8819i 0.989269i
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) 46.8165i 2.01653i
\(540\) 0 0
\(541\) 27.1309i 1.16645i 0.812312 + 0.583224i \(0.198209\pi\)
−0.812312 + 0.583224i \(0.801791\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) 1.42338i 0.0609708i
\(546\) 0 0
\(547\) 23.5346i 1.00627i 0.864209 + 0.503133i \(0.167819\pi\)
−0.864209 + 0.503133i \(0.832181\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) 25.0528i 1.06729i
\(552\) 0 0
\(553\) 23.9066i 1.01661i
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 11.1446i 0.472211i −0.971727 0.236106i \(-0.924129\pi\)
0.971727 0.236106i \(-0.0758711\pi\)
\(558\) 0 0
\(559\) −5.10227 −0.215803
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) 13.5797i 0.572318i −0.958182 0.286159i \(-0.907621\pi\)
0.958182 0.286159i \(-0.0923785\pi\)
\(564\) 0 0
\(565\) 32.3746 1.36201
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 12.2712 0.514437 0.257218 0.966353i \(-0.417194\pi\)
0.257218 + 0.966353i \(0.417194\pi\)
\(570\) 0 0
\(571\) 17.3601i 0.726498i −0.931692 0.363249i \(-0.881667\pi\)
0.931692 0.363249i \(-0.118333\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 0.882692 0.0368108
\(576\) 0 0
\(577\) −11.6366 −0.484440 −0.242220 0.970221i \(-0.577876\pi\)
−0.242220 + 0.970221i \(0.577876\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) 25.7782 1.06946
\(582\) 0 0
\(583\) 2.15426i 0.0892205i
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) −10.1689 −0.419714 −0.209857 0.977732i \(-0.567300\pi\)
−0.209857 + 0.977732i \(0.567300\pi\)
\(588\) 0 0
\(589\) 46.5019 1.91608
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) −30.7427 −1.26245 −0.631226 0.775599i \(-0.717448\pi\)
−0.631226 + 0.775599i \(0.717448\pi\)
\(594\) 0 0
\(595\) −54.1398 −2.21951
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) 0.884078i 0.0361225i 0.999837 + 0.0180612i \(0.00574938\pi\)
−0.999837 + 0.0180612i \(0.994251\pi\)
\(600\) 0 0
\(601\) 8.35635 0.340863 0.170431 0.985370i \(-0.445484\pi\)
0.170431 + 0.985370i \(0.445484\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) 35.8956 1.45936
\(606\) 0 0
\(607\) 35.0284i 1.42176i 0.703313 + 0.710880i \(0.251703\pi\)
−0.703313 + 0.710880i \(0.748297\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) −2.99762 −0.121271
\(612\) 0 0
\(613\) 27.7213 1.11965 0.559827 0.828610i \(-0.310868\pi\)
0.559827 + 0.828610i \(0.310868\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 19.4355i 0.782445i 0.920296 + 0.391223i \(0.127948\pi\)
−0.920296 + 0.391223i \(0.872052\pi\)
\(618\) 0 0
\(619\) 19.6060i 0.788030i −0.919104 0.394015i \(-0.871086\pi\)
0.919104 0.394015i \(-0.128914\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 13.9359i 0.558330i
\(624\) 0 0
\(625\) −21.3724 −0.854896
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 57.7795i 2.30382i
\(630\) 0 0
\(631\) 14.5937 0.580967 0.290483 0.956880i \(-0.406184\pi\)
0.290483 + 0.956880i \(0.406184\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) −43.5544 −1.72840
\(636\) 0 0
\(637\) 42.6314i 1.68912i
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) −42.9143 −1.69501 −0.847506 0.530786i \(-0.821897\pi\)
−0.847506 + 0.530786i \(0.821897\pi\)
\(642\) 0 0
\(643\) 24.5082i 0.966509i −0.875480 0.483255i \(-0.839455\pi\)
0.875480 0.483255i \(-0.160545\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) −18.7375 −0.736648 −0.368324 0.929698i \(-0.620068\pi\)
−0.368324 + 0.929698i \(0.620068\pi\)
\(648\) 0 0
\(649\) 57.8100i 2.26924i
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 27.0973i 1.06040i −0.847873 0.530200i \(-0.822117\pi\)
0.847873 0.530200i \(-0.177883\pi\)
\(654\) 0 0
\(655\) −10.1826 −0.397867
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) −20.6136 −0.802994 −0.401497 0.915860i \(-0.631510\pi\)
−0.401497 + 0.915860i \(0.631510\pi\)
\(660\) 0 0
\(661\) 33.9954i 1.32227i 0.750268 + 0.661134i \(0.229924\pi\)
−0.750268 + 0.661134i \(0.770076\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) −65.7827 −2.55094
\(666\) 0 0
\(667\) 4.34103i 0.168085i
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 7.99598i 0.308681i
\(672\) 0 0
\(673\) 35.7944i 1.37977i 0.723917 + 0.689887i \(0.242340\pi\)
−0.723917 + 0.689887i \(0.757660\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 25.8702i 0.994274i −0.867672 0.497137i \(-0.834385\pi\)
0.867672 0.497137i \(-0.165615\pi\)
\(678\) 0 0
\(679\) −64.1404 −2.46148
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) −8.26099 −0.316098 −0.158049 0.987431i \(-0.550520\pi\)
−0.158049 + 0.987431i \(0.550520\pi\)
\(684\) 0 0
\(685\) 2.25380i 0.0861134i
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) 1.96169i 0.0747344i
\(690\) 0 0
\(691\) 16.2248i 0.617220i −0.951189 0.308610i \(-0.900136\pi\)
0.951189 0.308610i \(-0.0998638\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 24.7096i 0.937287i
\(696\) 0 0
\(697\) −49.4822 −1.87427
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) 9.38880i 0.354610i −0.984156 0.177305i \(-0.943262\pi\)
0.984156 0.177305i \(-0.0567379\pi\)
\(702\) 0 0
\(703\) 70.2052i 2.64784i
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) −4.80256 −0.180619
\(708\) 0 0
\(709\) 23.9016i 0.897645i 0.893621 + 0.448822i \(0.148156\pi\)
−0.893621 + 0.448822i \(0.851844\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) −8.05762 −0.301760
\(714\) 0 0
\(715\) −53.5953 −2.00435
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) −13.8522 −0.516600 −0.258300 0.966065i \(-0.583162\pi\)
−0.258300 + 0.966065i \(0.583162\pi\)
\(720\) 0 0
\(721\) 11.1139i 0.413904i
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) 2.03246i 0.0754835i
\(726\) 0 0
\(727\) 29.0448i 1.07721i −0.842558 0.538606i \(-0.818951\pi\)
0.842558 0.538606i \(-0.181049\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) 6.88168i 0.254528i
\(732\) 0 0
\(733\) −17.0241 −0.628798 −0.314399 0.949291i \(-0.601803\pi\)
−0.314399 + 0.949291i \(0.601803\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 75.1784 2.76923
\(738\) 0 0
\(739\) 8.03430i 0.295547i −0.989021 0.147773i \(-0.952789\pi\)
0.989021 0.147773i \(-0.0472106\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 48.2156i 1.76886i −0.466674 0.884430i \(-0.654548\pi\)
0.466674 0.884430i \(-0.345452\pi\)
\(744\) 0 0
\(745\) −28.9303 −1.05992
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) 43.5961i 1.59297i
\(750\) 0 0
\(751\) 34.2525i 1.24989i 0.780668 + 0.624945i \(0.214879\pi\)
−0.780668 + 0.624945i \(0.785121\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 37.9152i 1.37987i
\(756\) 0 0
\(757\) 19.1088 0.694523 0.347261 0.937768i \(-0.387112\pi\)
0.347261 + 0.937768i \(0.387112\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 54.0783i 1.96034i −0.198163 0.980169i \(-0.563497\pi\)
0.198163 0.980169i \(-0.436503\pi\)
\(762\) 0 0
\(763\) 2.71192i 0.0981780i
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 52.6422i 1.90080i
\(768\) 0 0
\(769\) 49.4481i 1.78314i −0.452880 0.891571i \(-0.649604\pi\)
0.452880 0.891571i \(-0.350396\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) −35.6309 −1.28156 −0.640778 0.767726i \(-0.721388\pi\)
−0.640778 + 0.767726i \(0.721388\pi\)
\(774\) 0 0
\(775\) −3.77255 −0.135514
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) −60.1234 −2.15415
\(780\) 0 0
\(781\) 31.8722i 1.14048i
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) −14.4057 −0.514163
\(786\) 0 0
\(787\) 15.8163i 0.563790i −0.959445 0.281895i \(-0.909037\pi\)
0.959445 0.281895i \(-0.0909630\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) −61.6823 −2.19317
\(792\) 0 0
\(793\) 7.28120i 0.258563i
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) −15.5032 −0.549151 −0.274576 0.961566i \(-0.588537\pi\)
−0.274576 + 0.961566i \(0.588537\pi\)
\(798\) 0 0