Properties

Label 804.2.ba.a.749.1
Level 804
Weight 2
Character 804.749
Analytic conductor 6.420
Analytic rank 0
Dimension 20
CM discriminant -3
Inner twists 4

Related objects

Downloads

Learn more about

Newspace parameters

Level: \( N \) = \( 804 = 2^{2} \cdot 3 \cdot 67 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 804.ba (of order \(66\), degree \(20\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(6.41997232251\)
Analytic rank: \(0\)
Dimension: \(20\)
Coefficient field: \(\Q(\zeta_{33})\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{U}(1)[D_{66}]$

Embedding invariants

Embedding label 749.1
Root \(0.981929 + 0.189251i\)
Character \(\chi\) = 804.749
Dual form 804.2.ba.a.497.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.30900 - 1.13425i) q^{3} +(-1.35800 - 1.72684i) q^{7} +(0.426945 + 2.96946i) q^{9} +O(q^{10})\) \(q+(-1.30900 - 1.13425i) q^{3} +(-1.35800 - 1.72684i) q^{7} +(0.426945 + 2.96946i) q^{9} +(-3.42905 + 2.44182i) q^{13} +(-2.06016 - 1.62013i) q^{19} +(-0.181052 + 3.80075i) q^{21} +(-2.07708 + 4.54816i) q^{25} +(2.80925 - 4.37128i) q^{27} +(6.03124 + 4.29482i) q^{31} +(-5.22813 + 9.05539i) q^{37} +(7.25826 + 0.693079i) q^{39} +(-3.12884 + 10.6558i) q^{43} +(0.512504 - 2.11257i) q^{49} +(0.859110 + 4.45748i) q^{57} +(4.33139 + 8.40173i) q^{61} +(4.54800 - 4.76981i) q^{63} +(-7.79913 + 2.48466i) q^{67} +(-12.7250 + 6.56021i) q^{73} +(7.87764 - 3.59760i) q^{75} +(-0.645295 - 6.75784i) q^{79} +(-8.63544 + 2.53559i) q^{81} +(8.87330 + 2.60544i) q^{91} +(-3.02346 - 12.4629i) q^{93} +(7.53271 + 4.34901i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 20q + 6q^{7} + 6q^{9} + O(q^{10}) \) \( 20q + 6q^{7} + 6q^{9} + 9q^{13} - 8q^{19} + 6q^{21} + 10q^{25} - 3q^{31} + 10q^{37} - 9q^{39} - 5q^{49} + 141q^{57} + 27q^{61} + 147q^{63} + 11q^{67} - 180q^{73} - 166q^{79} - 18q^{81} - 36q^{91} - 3q^{93} + 33q^{97} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/804\mathbb{Z}\right)^\times\).

\(n\) \(269\) \(337\) \(403\)
\(\chi(n)\) \(-1\) \(e\left(\frac{41}{66}\right)\) \(1\)

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
\(3\) −1.30900 1.13425i −0.755750 0.654861i
\(4\) 0 0
\(5\) 0 0 −0.540641 0.841254i \(-0.681818\pi\)
0.540641 + 0.841254i \(0.318182\pi\)
\(6\) 0 0
\(7\) −1.35800 1.72684i −0.513277 0.652685i 0.458470 0.888710i \(-0.348398\pi\)
−0.971747 + 0.236025i \(0.924155\pi\)
\(8\) 0 0
\(9\) 0.426945 + 2.96946i 0.142315 + 0.989821i
\(10\) 0 0
\(11\) 0 0 0.458227 0.888835i \(-0.348485\pi\)
−0.458227 + 0.888835i \(0.651515\pi\)
\(12\) 0 0
\(13\) −3.42905 + 2.44182i −0.951048 + 0.677238i −0.946484 0.322751i \(-0.895392\pi\)
−0.00456441 + 0.999990i \(0.501453\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 0 0 0.723734 0.690079i \(-0.242424\pi\)
−0.723734 + 0.690079i \(0.757576\pi\)
\(18\) 0 0
\(19\) −2.06016 1.62013i −0.472633 0.371683i 0.353245 0.935531i \(-0.385078\pi\)
−0.825879 + 0.563848i \(0.809320\pi\)
\(20\) 0 0
\(21\) −0.181052 + 3.80075i −0.0395088 + 0.829391i
\(22\) 0 0
\(23\) 0 0 −0.327068 0.945001i \(-0.606061\pi\)
0.327068 + 0.945001i \(0.393939\pi\)
\(24\) 0 0
\(25\) −2.07708 + 4.54816i −0.415415 + 0.909632i
\(26\) 0 0
\(27\) 2.80925 4.37128i 0.540641 0.841254i
\(28\) 0 0
\(29\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(30\) 0 0
\(31\) 6.03124 + 4.29482i 1.08324 + 0.771373i 0.974878 0.222738i \(-0.0714995\pi\)
0.108364 + 0.994111i \(0.465439\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) −5.22813 + 9.05539i −0.859500 + 1.48870i 0.0129071 + 0.999917i \(0.495891\pi\)
−0.872407 + 0.488780i \(0.837442\pi\)
\(38\) 0 0
\(39\) 7.25826 + 0.693079i 1.16225 + 0.110982i
\(40\) 0 0
\(41\) 0 0 0.971812 0.235759i \(-0.0757576\pi\)
−0.971812 + 0.235759i \(0.924242\pi\)
\(42\) 0 0
\(43\) −3.12884 + 10.6558i −0.477143 + 1.62500i 0.271792 + 0.962356i \(0.412384\pi\)
−0.748935 + 0.662644i \(0.769434\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 0 0 −0.981929 0.189251i \(-0.939394\pi\)
0.981929 + 0.189251i \(0.0606061\pi\)
\(48\) 0 0
\(49\) 0.512504 2.11257i 0.0732148 0.301796i
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) 0 0 −0.281733 0.959493i \(-0.590909\pi\)
0.281733 + 0.959493i \(0.409091\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 0 0
\(57\) 0.859110 + 4.45748i 0.113792 + 0.590408i
\(58\) 0 0
\(59\) 0 0 −0.415415 0.909632i \(-0.636364\pi\)
0.415415 + 0.909632i \(0.363636\pi\)
\(60\) 0 0
\(61\) 4.33139 + 8.40173i 0.554578 + 1.07573i 0.984911 + 0.173061i \(0.0553659\pi\)
−0.430333 + 0.902670i \(0.641604\pi\)
\(62\) 0 0
\(63\) 4.54800 4.76981i 0.572994 0.600939i
\(64\) 0 0
\(65\) 0 0
\(66\) 0 0
\(67\) −7.79913 + 2.48466i −0.952816 + 0.303549i
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 0 0 −0.723734 0.690079i \(-0.757576\pi\)
0.723734 + 0.690079i \(0.242424\pi\)
\(72\) 0 0
\(73\) −12.7250 + 6.56021i −1.48935 + 0.767815i −0.994850 0.101361i \(-0.967680\pi\)
−0.494504 + 0.869176i \(0.664650\pi\)
\(74\) 0 0
\(75\) 7.87764 3.59760i 0.909632 0.415415i
\(76\) 0 0
\(77\) 0 0
\(78\) 0 0
\(79\) −0.645295 6.75784i −0.0726014 0.760316i −0.956325 0.292306i \(-0.905577\pi\)
0.883723 0.468010i \(-0.155029\pi\)
\(80\) 0 0
\(81\) −8.63544 + 2.53559i −0.959493 + 0.281733i
\(82\) 0 0
\(83\) 0 0 −0.0475819 0.998867i \(-0.515152\pi\)
0.0475819 + 0.998867i \(0.484848\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 0 0 −0.654861 0.755750i \(-0.727273\pi\)
0.654861 + 0.755750i \(0.272727\pi\)
\(90\) 0 0
\(91\) 8.87330 + 2.60544i 0.930174 + 0.273124i
\(92\) 0 0
\(93\) −3.02346 12.4629i −0.313518 1.29234i
\(94\) 0 0
\(95\) 0 0
\(96\) 0 0
\(97\) 7.53271 + 4.34901i 0.764831 + 0.441575i 0.831028 0.556231i \(-0.187753\pi\)
−0.0661967 + 0.997807i \(0.521086\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) 0 0 −0.371662 0.928368i \(-0.621212\pi\)
0.371662 + 0.928368i \(0.378788\pi\)
\(102\) 0 0
\(103\) 3.63994 5.11158i 0.358654 0.503659i −0.595345 0.803470i \(-0.702984\pi\)
0.953998 + 0.299812i \(0.0969239\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 0 0 −0.841254 0.540641i \(-0.818182\pi\)
0.841254 + 0.540641i \(0.181818\pi\)
\(108\) 0 0
\(109\) −2.71680 1.24072i −0.260223 0.118840i 0.281032 0.959698i \(-0.409323\pi\)
−0.541255 + 0.840859i \(0.682051\pi\)
\(110\) 0 0
\(111\) 17.1147 5.92346i 1.62446 0.562230i
\(112\) 0 0
\(113\) 0 0 −0.998867 0.0475819i \(-0.984848\pi\)
0.998867 + 0.0475819i \(0.0151515\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 0 0
\(117\) −8.71491 9.13993i −0.805693 0.844987i
\(118\) 0 0
\(119\) 0 0
\(120\) 0 0
\(121\) −6.38063 8.96034i −0.580057 0.814576i
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) 0 0
\(126\) 0 0
\(127\) −14.8734 + 11.6965i −1.31980 + 1.03790i −0.324026 + 0.946048i \(0.605036\pi\)
−0.995773 + 0.0918526i \(0.970721\pi\)
\(128\) 0 0
\(129\) 16.1820 10.3996i 1.42475 0.915631i
\(130\) 0 0
\(131\) 0 0 0.654861 0.755750i \(-0.272727\pi\)
−0.654861 + 0.755750i \(0.727273\pi\)
\(132\) 0 0
\(133\) 5.75771i 0.499257i
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 0 0 −0.755750 0.654861i \(-0.772727\pi\)
0.755750 + 0.654861i \(0.227273\pi\)
\(138\) 0 0
\(139\) −11.2372 17.4855i −0.953128 1.48310i −0.873822 0.486246i \(-0.838366\pi\)
−0.0793066 0.996850i \(-0.525271\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 0 0
\(144\) 0 0
\(145\) 0 0
\(146\) 0 0
\(147\) −3.06705 + 2.18404i −0.252966 + 0.180136i
\(148\) 0 0
\(149\) 0 0 0.142315 0.989821i \(-0.454545\pi\)
−0.142315 + 0.989821i \(0.545455\pi\)
\(150\) 0 0
\(151\) 10.6148 10.1212i 0.863822 0.823653i −0.121811 0.992553i \(-0.538870\pi\)
0.985633 + 0.168901i \(0.0540217\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 0 0
\(156\) 0 0
\(157\) −6.07713 17.5587i −0.485008 1.40134i −0.876609 0.481204i \(-0.840200\pi\)
0.391601 0.920135i \(-0.371921\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 0 0
\(162\) 0 0
\(163\) −11.2617 19.5058i −0.882084 1.52781i −0.849019 0.528362i \(-0.822806\pi\)
−0.0330650 0.999453i \(-0.510527\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 0 0 0.928368 0.371662i \(-0.121212\pi\)
−0.928368 + 0.371662i \(0.878788\pi\)
\(168\) 0 0
\(169\) 1.54405 4.46124i 0.118773 0.343172i
\(170\) 0 0
\(171\) 3.93134 6.80928i 0.300637 0.520719i
\(172\) 0 0
\(173\) 0 0 −0.995472 0.0950560i \(-0.969697\pi\)
0.995472 + 0.0950560i \(0.0303030\pi\)
\(174\) 0 0
\(175\) 10.6746 2.58964i 0.806926 0.195758i
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) 0 0 0.755750 0.654861i \(-0.227273\pi\)
−0.755750 + 0.654861i \(0.772727\pi\)
\(180\) 0 0
\(181\) −1.92125 0.370291i −0.142805 0.0275235i 0.117348 0.993091i \(-0.462561\pi\)
−0.260153 + 0.965567i \(0.583773\pi\)
\(182\) 0 0
\(183\) 3.85990 15.9107i 0.285332 1.17616i
\(184\) 0 0
\(185\) 0 0
\(186\) 0 0
\(187\) 0 0
\(188\) 0 0
\(189\) −11.3635 + 1.08508i −0.826572 + 0.0789280i
\(190\) 0 0
\(191\) 0 0 −0.189251 0.981929i \(-0.560606\pi\)
0.189251 + 0.981929i \(0.439394\pi\)
\(192\) 0 0
\(193\) −3.50738 7.68009i −0.252467 0.552825i 0.740384 0.672184i \(-0.234643\pi\)
−0.992851 + 0.119359i \(0.961916\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 0 0 0.690079 0.723734i \(-0.257576\pi\)
−0.690079 + 0.723734i \(0.742424\pi\)
\(198\) 0 0
\(199\) 9.25370 + 3.70462i 0.655977 + 0.262614i 0.675683 0.737192i \(-0.263849\pi\)
−0.0197060 + 0.999806i \(0.506273\pi\)
\(200\) 0 0
\(201\) 13.0273 + 5.59378i 0.918873 + 0.394555i
\(202\) 0 0
\(203\) 0 0
\(204\) 0 0
\(205\) 0 0
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) 0 0
\(210\) 0 0
\(211\) −23.0360 + 4.43982i −1.58586 + 0.305650i −0.904558 0.426350i \(-0.859799\pi\)
−0.681304 + 0.732000i \(0.738587\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) 0 0
\(216\) 0 0
\(217\) −0.773958 16.2474i −0.0525397 1.10294i
\(218\) 0 0
\(219\) 24.0980 + 5.84610i 1.62839 + 0.395043i
\(220\) 0 0
\(221\) 0 0
\(222\) 0 0
\(223\) −12.4284 14.3431i −0.832265 0.960485i 0.167412 0.985887i \(-0.446459\pi\)
−0.999677 + 0.0254020i \(0.991913\pi\)
\(224\) 0 0
\(225\) −14.3924 4.22599i −0.959493 0.281733i
\(226\) 0 0
\(227\) 0 0 −0.235759 0.971812i \(-0.575758\pi\)
0.235759 + 0.971812i \(0.424242\pi\)
\(228\) 0 0
\(229\) −2.84949 + 29.8412i −0.188299 + 1.97196i 0.0429870 + 0.999076i \(0.486313\pi\)
−0.231287 + 0.972886i \(0.574293\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 0 0 −0.945001 0.327068i \(-0.893939\pi\)
0.945001 + 0.327068i \(0.106061\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 0 0
\(237\) −6.82040 + 9.57791i −0.443033 + 0.622152i
\(238\) 0 0
\(239\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(240\) 0 0
\(241\) 25.8223 + 16.5950i 1.66336 + 1.06898i 0.913014 + 0.407929i \(0.133749\pi\)
0.750345 + 0.661047i \(0.229888\pi\)
\(242\) 0 0
\(243\) 14.1798 + 6.47568i 0.909632 + 0.415415i
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) 11.0205 + 0.524969i 0.701215 + 0.0334030i
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 0 0 −0.690079 0.723734i \(-0.742424\pi\)
0.690079 + 0.723734i \(0.257576\pi\)
\(252\) 0 0
\(253\) 0 0
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 0 0 −0.888835 0.458227i \(-0.848485\pi\)
0.888835 + 0.458227i \(0.151515\pi\)
\(258\) 0 0
\(259\) 22.7370 3.26909i 1.41281 0.203132i
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) 0 0 0.841254 0.540641i \(-0.181818\pi\)
−0.841254 + 0.540641i \(0.818182\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(270\) 0 0
\(271\) 20.0171 + 17.3449i 1.21595 + 1.05363i 0.996961 + 0.0778984i \(0.0248210\pi\)
0.218988 + 0.975728i \(0.429724\pi\)
\(272\) 0 0
\(273\) −8.65990 13.4751i −0.524121 0.815548i
\(274\) 0 0
\(275\) 0 0
\(276\) 0 0
\(277\) 4.71918 + 32.8226i 0.283548 + 1.97212i 0.227995 + 0.973662i \(0.426783\pi\)
0.0555527 + 0.998456i \(0.482308\pi\)
\(278\) 0 0
\(279\) −10.1783 + 19.7432i −0.609360 + 1.18199i
\(280\) 0 0
\(281\) 0 0 0.814576 0.580057i \(-0.196970\pi\)
−0.814576 + 0.580057i \(0.803030\pi\)
\(282\) 0 0
\(283\) −3.03154 + 21.0848i −0.180206 + 1.25336i 0.676068 + 0.736839i \(0.263682\pi\)
−0.856274 + 0.516522i \(0.827227\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 0 0
\(288\) 0 0
\(289\) 0.808893 16.9807i 0.0475819 0.998867i
\(290\) 0 0
\(291\) −4.92742 14.2368i −0.288850 0.834578i
\(292\) 0 0
\(293\) 0 0 0.415415 0.909632i \(-0.363636\pi\)
−0.415415 + 0.909632i \(0.636364\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 0 0
\(300\) 0 0
\(301\) 22.6499 9.06766i 1.30552 0.522651i
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) 0 0
\(306\) 0 0
\(307\) −26.4058 2.52145i −1.50706 0.143907i −0.691415 0.722458i \(-0.743012\pi\)
−0.815646 + 0.578551i \(0.803618\pi\)
\(308\) 0 0
\(309\) −10.5625 + 2.56243i −0.600879 + 0.145772i
\(310\) 0 0
\(311\) 0 0 0.281733 0.959493i \(-0.409091\pi\)
−0.281733 + 0.959493i \(0.590909\pi\)
\(312\) 0 0
\(313\) 13.4766 11.6776i 0.761744 0.660055i −0.184747 0.982786i \(-0.559147\pi\)
0.946491 + 0.322731i \(0.104601\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 0 0 0.235759 0.971812i \(-0.424242\pi\)
−0.235759 + 0.971812i \(0.575758\pi\)
\(318\) 0 0
\(319\) 0 0
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) 0 0
\(324\) 0 0
\(325\) −3.98338 20.6677i −0.220958 1.14644i
\(326\) 0 0
\(327\) 2.14899 + 4.70564i 0.118840 + 0.260223i
\(328\) 0 0
\(329\) 0 0
\(330\) 0 0
\(331\) 7.55738 7.92595i 0.415391 0.435649i −0.482481 0.875907i \(-0.660264\pi\)
0.897872 + 0.440257i \(0.145113\pi\)
\(332\) 0 0
\(333\) −29.1218 11.6586i −1.59586 0.638888i
\(334\) 0 0
\(335\) 0 0
\(336\) 0 0
\(337\) −3.92541 + 9.80520i −0.213831 + 0.534123i −0.996041 0.0888908i \(-0.971668\pi\)
0.782211 + 0.623014i \(0.214092\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) 0 0
\(342\) 0 0
\(343\) −18.3323 + 8.37210i −0.989853 + 0.452051i
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 0 0 −0.0950560 0.995472i \(-0.530303\pi\)
0.0950560 + 0.995472i \(0.469697\pi\)
\(348\) 0 0
\(349\) −31.1052 + 9.13332i −1.66502 + 0.488895i −0.972579 0.232574i \(-0.925285\pi\)
−0.692446 + 0.721470i \(0.743467\pi\)
\(350\) 0 0
\(351\) 1.04080 + 21.8490i 0.0555537 + 1.16622i
\(352\) 0 0
\(353\) 0 0 −0.971812 0.235759i \(-0.924242\pi\)
0.971812 + 0.235759i \(0.0757576\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 0 0 −0.959493 0.281733i \(-0.909091\pi\)
0.959493 + 0.281733i \(0.0909091\pi\)
\(360\) 0 0
\(361\) −2.85997 11.7890i −0.150525 0.620472i
\(362\) 0 0
\(363\) −1.81106 + 18.9663i −0.0950560 + 0.995472i
\(364\) 0 0
\(365\) 0 0
\(366\) 0 0
\(367\) 28.2494 + 9.77721i 1.47461 + 0.510366i 0.941888 0.335927i \(-0.109050\pi\)
0.532718 + 0.846293i \(0.321171\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) 0 0
\(372\) 0 0
\(373\) −17.8012 + 10.2775i −0.921713 + 0.532151i −0.884181 0.467144i \(-0.845283\pi\)
−0.0375318 + 0.999295i \(0.511950\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 0 0
\(378\) 0 0
\(379\) −36.2397 + 12.5427i −1.86151 + 0.644275i −0.874177 + 0.485608i \(0.838598\pi\)
−0.987332 + 0.158667i \(0.949280\pi\)
\(380\) 0 0
\(381\) 32.7360 + 1.55941i 1.67712 + 0.0798910i
\(382\) 0 0
\(383\) 0 0 0.618159 0.786053i \(-0.287879\pi\)
−0.618159 + 0.786053i \(0.712121\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) −32.9780 4.74152i −1.67636 0.241025i
\(388\) 0 0
\(389\) 0 0 −0.580057 0.814576i \(-0.696970\pi\)
0.580057 + 0.814576i \(0.303030\pi\)
\(390\) 0 0
\(391\) 0 0
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) 0 0
\(396\) 0 0
\(397\) 23.7356 15.2539i 1.19125 0.765573i 0.213832 0.976870i \(-0.431405\pi\)
0.977422 + 0.211298i \(0.0677690\pi\)
\(398\) 0 0
\(399\) 6.53069 7.53682i 0.326944 0.377313i
\(400\) 0 0
\(401\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(402\) 0 0
\(403\) −31.1686 −1.55262
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 0 0
\(408\) 0 0
\(409\) 5.49395 + 6.98613i 0.271658 + 0.345442i 0.902671 0.430331i \(-0.141603\pi\)
−0.631013 + 0.775772i \(0.717361\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) 0 0
\(414\) 0 0
\(415\) 0 0
\(416\) 0 0
\(417\) −5.12343 + 35.6342i −0.250895 + 1.74502i
\(418\) 0 0
\(419\) 0 0 0.723734 0.690079i \(-0.242424\pi\)
−0.723734 + 0.690079i \(0.757576\pi\)
\(420\) 0 0
\(421\) 14.6265 + 11.5024i 0.712853 + 0.560594i 0.907384 0.420303i \(-0.138076\pi\)
−0.194531 + 0.980896i \(0.562319\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) 0 0
\(426\) 0 0
\(427\) 8.62641 18.8892i 0.417461 0.914113i
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(432\) 0 0
\(433\) 15.5484 + 11.0720i 0.747209 + 0.532085i 0.889053 0.457804i \(-0.151364\pi\)
−0.141844 + 0.989889i \(0.545303\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 0 0
\(438\) 0 0
\(439\) 0.624991 1.08252i 0.0298292 0.0516656i −0.850725 0.525610i \(-0.823837\pi\)
0.880555 + 0.473945i \(0.157170\pi\)
\(440\) 0 0
\(441\) 6.49201 + 0.619912i 0.309143 + 0.0295196i
\(442\) 0 0
\(443\) 0 0 0.971812 0.235759i \(-0.0757576\pi\)
−0.971812 + 0.235759i \(0.924242\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) 0 0 −0.981929 0.189251i \(-0.939394\pi\)
0.981929 + 0.189251i \(0.0606061\pi\)
\(450\) 0 0
\(451\) 0 0
\(452\) 0 0
\(453\) −25.3748 + 1.20875i −1.19221 + 0.0567920i
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) 17.7551 1.69541i 0.830548 0.0793077i 0.328884 0.944370i \(-0.393327\pi\)
0.501664 + 0.865063i \(0.332721\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 0 0 −0.415415 0.909632i \(-0.636364\pi\)
0.415415 + 0.909632i \(0.363636\pi\)
\(462\) 0 0
\(463\) 11.5562 + 22.4159i 0.537061 + 1.04175i 0.988750 + 0.149578i \(0.0477914\pi\)
−0.451689 + 0.892175i \(0.649178\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 0 0 −0.928368 0.371662i \(-0.878788\pi\)
0.928368 + 0.371662i \(0.121212\pi\)
\(468\) 0 0
\(469\) 14.8819 + 10.0937i 0.687180 + 0.466084i
\(470\) 0 0
\(471\) −11.9611 + 29.8773i −0.551137 + 1.37667i
\(472\) 0 0
\(473\) 0 0
\(474\) 0 0
\(475\) 11.6477 6.00481i 0.534434 0.275520i
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) 0 0 0.981929 0.189251i \(-0.0606061\pi\)
−0.981929 + 0.189251i \(0.939394\pi\)
\(480\) 0 0
\(481\) −4.18407 43.8176i −0.190777 1.99791i
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 0 0
\(486\) 0 0
\(487\) 31.9440 + 7.74953i 1.44752 + 0.351165i 0.881092 0.472946i \(-0.156809\pi\)
0.566429 + 0.824110i \(0.308325\pi\)
\(488\) 0 0
\(489\) −7.38301 + 38.3067i −0.333871 + 1.73229i
\(490\) 0 0
\(491\) 0 0 −0.654861 0.755750i \(-0.727273\pi\)
0.654861 + 0.755750i \(0.272727\pi\)
\(492\) 0 0
\(493\) 0 0
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 0 0
\(498\) 0 0
\(499\) −13.9923 8.07843i −0.626379 0.361640i 0.152969 0.988231i \(-0.451116\pi\)
−0.779349 + 0.626591i \(0.784450\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) 0 0 −0.371662 0.928368i \(-0.621212\pi\)
0.371662 + 0.928368i \(0.378788\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) −7.08132 + 4.08840i −0.314492 + 0.181572i
\(508\) 0 0
\(509\) 0 0 −0.841254 0.540641i \(-0.818182\pi\)
0.841254 + 0.540641i \(0.181818\pi\)
\(510\) 0 0
\(511\) 28.6091 + 13.0653i 1.26559 + 0.577976i
\(512\) 0 0
\(513\) −12.8695 + 4.45419i −0.568204 + 0.196657i
\(514\) 0 0
\(515\) 0 0
\(516\) 0 0
\(517\) 0 0
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 0 0 −0.989821 0.142315i \(-0.954545\pi\)
0.989821 + 0.142315i \(0.0454545\pi\)
\(522\) 0 0
\(523\) −25.1956 35.3823i −1.10173 1.54716i −0.806028 0.591877i \(-0.798387\pi\)
−0.295699 0.955281i \(-0.595552\pi\)
\(524\) 0 0
\(525\) −16.9103 8.71789i −0.738028 0.380480i
\(526\) 0 0
\(527\) 0 0
\(528\) 0 0
\(529\) −18.0792 + 14.2177i −0.786053 + 0.618159i
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) 0 0
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) 0 0
\(540\) 0 0
\(541\) 14.4510 + 22.4863i 0.621299 + 0.966759i 0.999163 + 0.0408986i \(0.0130221\pi\)
−0.377865 + 0.925861i \(0.623342\pi\)
\(542\) 0 0
\(543\) 2.09491 + 2.66389i 0.0899011 + 0.114319i
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) −20.6902 + 40.1334i −0.884649 + 1.71598i −0.210200 + 0.977658i \(0.567412\pi\)
−0.674449 + 0.738321i \(0.735619\pi\)
\(548\) 0 0
\(549\) −23.0994 + 16.4490i −0.985858 + 0.702026i
\(550\) 0 0
\(551\) 0 0
\(552\) 0 0
\(553\) −10.7934 + 10.2915i −0.458982 + 0.437639i
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 0 0 0.0475819 0.998867i \(-0.484848\pi\)
−0.0475819 + 0.998867i \(0.515152\pi\)
\(558\) 0 0
\(559\) −15.2907 44.1795i −0.646726 1.86859i
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) 0 0 0.540641 0.841254i \(-0.318182\pi\)
−0.540641 + 0.841254i \(0.681818\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 0 0
\(567\) 16.1055 + 11.4687i 0.676368 + 0.481640i
\(568\) 0 0
\(569\) 0 0 0.928368 0.371662i \(-0.121212\pi\)
−0.928368 + 0.371662i \(0.878788\pi\)
\(570\) 0 0
\(571\) 2.35105 6.79290i 0.0983882 0.284274i −0.885056 0.465484i \(-0.845880\pi\)
0.983444 + 0.181210i \(0.0580014\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 0 0
\(576\) 0 0
\(577\) 45.2934 10.9881i 1.88559 0.457439i 0.885614 0.464421i \(-0.153738\pi\)
0.999976 + 0.00698200i \(0.00222246\pi\)
\(578\) 0 0
\(579\) −4.12001 + 14.0315i −0.171222 + 0.583128i
\(580\) 0 0
\(581\) 0 0
\(582\) 0 0
\(583\) 0 0
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 0 0 0.998867 0.0475819i \(-0.0151515\pi\)
−0.998867 + 0.0475819i \(0.984848\pi\)
\(588\) 0 0
\(589\) −5.46715 18.6194i −0.225270 0.767199i
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) 0 0 −0.189251 0.981929i \(-0.560606\pi\)
0.189251 + 0.981929i \(0.439394\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) −7.91108 15.3454i −0.323779 0.628044i
\(598\) 0 0
\(599\) 0 0 0.690079 0.723734i \(-0.257576\pi\)
−0.690079 + 0.723734i \(0.742424\pi\)
\(600\) 0 0
\(601\) 39.1380 + 15.6685i 1.59647 + 0.639131i 0.988001 0.154446i \(-0.0493591\pi\)
0.608471 + 0.793576i \(0.291783\pi\)
\(602\) 0 0
\(603\) −10.7079 22.0984i −0.436059 0.899918i
\(604\) 0 0
\(605\) 0 0
\(606\) 0 0
\(607\) 1.32455 + 1.26296i 0.0537619 + 0.0512619i 0.716484 0.697604i \(-0.245750\pi\)
−0.662722 + 0.748866i \(0.730599\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 0 0
\(612\) 0 0
\(613\) 43.9637 8.47330i 1.77568 0.342233i 0.806998 0.590554i \(-0.201091\pi\)
0.968678 + 0.248321i \(0.0798787\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 0 0 0.959493 0.281733i \(-0.0909091\pi\)
−0.959493 + 0.281733i \(0.909091\pi\)
\(618\) 0 0
\(619\) −0.522543 10.9695i −0.0210028 0.440902i −0.984738 0.174042i \(-0.944317\pi\)
0.963735 0.266860i \(-0.0859860\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 0 0
\(624\) 0 0
\(625\) −16.3715 18.8937i −0.654861 0.755750i
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 0 0
\(630\) 0 0
\(631\) 1.65145 17.2948i 0.0657433 0.688494i −0.901183 0.433439i \(-0.857300\pi\)
0.966926 0.255056i \(-0.0820939\pi\)
\(632\) 0 0
\(633\) 35.1899 + 20.3169i 1.39867 + 0.807524i
\(634\) 0 0
\(635\) 0 0
\(636\) 0 0
\(637\) 3.40111 + 8.49555i 0.134757 + 0.336606i
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(642\) 0 0
\(643\) −39.6763 25.4984i −1.56468 1.00556i −0.981100 0.193502i \(-0.938015\pi\)
−0.583579 0.812056i \(-0.698348\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 0 0 0.945001 0.327068i \(-0.106061\pi\)
−0.945001 + 0.327068i \(0.893939\pi\)
\(648\) 0 0
\(649\) 0 0
\(650\) 0 0
\(651\) −17.4155 + 22.1456i −0.682568 + 0.867955i
\(652\) 0 0
\(653\) 0 0 −0.690079 0.723734i \(-0.742424\pi\)
0.690079 + 0.723734i \(0.257576\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 0 0
\(657\) −24.9132 34.9857i −0.971957 1.36492i
\(658\) 0 0
\(659\) 0 0 −0.888835 0.458227i \(-0.848485\pi\)
0.888835 + 0.458227i \(0.151515\pi\)
\(660\) 0 0
\(661\) 50.7718 7.29988i 1.97479 0.283932i 0.977442 0.211205i \(-0.0677388\pi\)
0.997352 0.0727275i \(-0.0231703\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) 0 0
\(668\) 0 0
\(669\) 32.8720i 1.27090i
\(670\) 0 0
\(671\) 0 0
\(672\) 0 0
\(673\) −8.00736 6.93842i −0.308661 0.267456i 0.486731 0.873552i \(-0.338189\pi\)
−0.795392 + 0.606096i \(0.792735\pi\)
\(674\) 0 0
\(675\) 14.0463 + 21.8564i 0.540641 + 0.841254i
\(676\) 0 0
\(677\) 0 0 −0.618159 0.786053i \(-0.712121\pi\)
0.618159 + 0.786053i \(0.287879\pi\)
\(678\) 0 0
\(679\) −2.71939 18.9138i −0.104361 0.725844i
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 0 0 0.814576 0.580057i \(-0.196970\pi\)
−0.814576 + 0.580057i \(0.803030\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 0 0
\(687\) 37.5774 35.8300i 1.43367 1.36700i
\(688\) 0 0
\(689\) 0 0
\(690\) 0 0
\(691\) −2.40713 + 50.5319i −0.0915716 + 1.92232i 0.226067 + 0.974112i \(0.427413\pi\)
−0.317639 + 0.948212i \(0.602890\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 0 0
\(696\) 0 0
\(697\) 0 0
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) 0 0 −0.814576 0.580057i \(-0.803030\pi\)
0.814576 + 0.580057i \(0.196970\pi\)
\(702\) 0 0
\(703\) 25.4417 10.1853i 0.959551 0.384146i
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 0 0
\(708\) 0 0
\(709\) 50.8276 + 4.85345i 1.90887 + 0.182275i 0.981447 0.191733i \(-0.0614109\pi\)
0.927425 + 0.374009i \(0.122017\pi\)
\(710\) 0 0
\(711\) 19.7917 4.80140i 0.742245 0.180067i
\(712\) 0 0
\(713\) 0 0
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) 0 0 0.235759 0.971812i \(-0.424242\pi\)
−0.235759 + 0.971812i \(0.575758\pi\)
\(720\) 0 0
\(721\) −13.7699 + 0.655943i −0.512819 + 0.0244286i
\(722\) 0 0
\(723\) −14.9784 51.0117i −0.557052 1.89715i
\(724\) 0 0
\(725\) 0 0
\(726\) 0 0
\(727\) −6.70129 34.7696i −0.248537 1.28953i −0.864850 0.502031i \(-0.832586\pi\)
0.616313 0.787501i \(-0.288626\pi\)
\(728\) 0 0
\(729\) −11.2162 24.5601i −0.415415 0.909632i
\(730\) 0 0
\(731\) 0 0
\(732\) 0 0
\(733\) 32.1115 33.6776i 1.18607 1.24391i 0.222948 0.974830i \(-0.428432\pi\)
0.963118 0.269080i \(-0.0867197\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 0 0
\(738\) 0 0
\(739\) −10.3320 + 25.8081i −0.380068 + 0.949365i 0.607803 + 0.794088i \(0.292051\pi\)
−0.987871 + 0.155277i \(0.950373\pi\)
\(740\) 0 0
\(741\) −13.8303 13.1872i −0.508069 0.484442i
\(742\) 0 0
\(743\) 0 0 0.888835 0.458227i \(-0.151515\pi\)
−0.888835 + 0.458227i \(0.848485\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) 0 0
\(750\) 0 0
\(751\) −52.5547 + 15.4314i −1.91775 + 0.563101i −0.948753 + 0.316017i \(0.897654\pi\)
−0.968994 + 0.247084i \(0.920528\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 0 0
\(756\) 0 0
\(757\) 10.4126 54.0258i 0.378453 1.96360i 0.173400 0.984851i \(-0.444525\pi\)
0.205053 0.978751i \(-0.434263\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 0 0 −0.959493 0.281733i \(-0.909091\pi\)
0.959493 + 0.281733i \(0.0909091\pi\)
\(762\) 0 0
\(763\) 1.54690 + 6.37639i 0.0560014 + 0.230841i
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 0 0
\(768\) 0 0
\(769\) −51.9604 17.9837i −1.87374 0.648508i −0.979681 0.200561i \(-0.935723\pi\)
−0.894060 0.447947i \(-0.852155\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) 0 0 0.580057 0.814576i \(-0.303030\pi\)
−0.580057 + 0.814576i \(0.696970\pi\)
\(774\) 0 0
\(775\) −32.0609 + 18.5104i −1.15166 + 0.664912i
\(776\) 0 0
\(777\) −33.4707 21.5103i −1.20075 0.771678i
\(778\) 0 0
\(779\) 0 0
\(780\) 0 0
\(781\) 0 0
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) 0 0
\(786\) 0 0
\(787\) −36.1453 37.9081i −1.28844 1.35128i −0.903650 0.428272i \(-0.859123\pi\)
−0.384789 0.923004i \(-0.625726\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 0 0
\(792\) 0 0
\(793\) −35.3681 18.2335i −1.25596 0.647491i
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 0 0 0.786053 0.618159i \(-0.212121\pi\)
−0.786053 + 0.618159i \(0.787879\pi\)
\(798\) 0 0
\(799\) 0 0
\(800\) 0 0