Properties

Label 1512.2.s.g.1297.1
Level $1512$
Weight $2$
Character 1512.1297
Analytic conductor $12.073$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 1512 = 2^{3} \cdot 3^{3} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1512.s (of order \(3\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(12.0733807856\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\zeta_{6})\)
Defining polynomial: \(x^{2} - x + 1\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 1297.1
Root \(0.500000 - 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 1512.1297
Dual form 1512.2.s.g.865.1

$q$-expansion

\(f(q)\) \(=\) \(q+(1.00000 - 1.73205i) q^{5} +(0.500000 - 2.59808i) q^{7} +O(q^{10})\) \(q+(1.00000 - 1.73205i) q^{5} +(0.500000 - 2.59808i) q^{7} -2.00000 q^{13} +(-3.00000 - 5.19615i) q^{17} +(0.500000 - 0.866025i) q^{19} +(1.00000 - 1.73205i) q^{23} +(0.500000 + 0.866025i) q^{25} -6.00000 q^{29} +(-0.500000 - 0.866025i) q^{31} +(-4.00000 - 3.46410i) q^{35} +(-1.00000 + 1.73205i) q^{37} -2.00000 q^{41} +9.00000 q^{43} +(-1.00000 + 1.73205i) q^{47} +(-6.50000 - 2.59808i) q^{49} +(-3.00000 - 5.19615i) q^{53} +(-4.00000 - 6.92820i) q^{59} +(-5.50000 + 9.52628i) q^{61} +(-2.00000 + 3.46410i) q^{65} +(6.00000 + 10.3923i) q^{67} -4.00000 q^{71} +(-2.50000 - 4.33013i) q^{73} +(2.00000 - 3.46410i) q^{79} -4.00000 q^{83} -12.0000 q^{85} +(9.00000 - 15.5885i) q^{89} +(-1.00000 + 5.19615i) q^{91} +(-1.00000 - 1.73205i) q^{95} +1.00000 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2q + 2q^{5} + q^{7} + O(q^{10}) \) \( 2q + 2q^{5} + q^{7} - 4q^{13} - 6q^{17} + q^{19} + 2q^{23} + q^{25} - 12q^{29} - q^{31} - 8q^{35} - 2q^{37} - 4q^{41} + 18q^{43} - 2q^{47} - 13q^{49} - 6q^{53} - 8q^{59} - 11q^{61} - 4q^{65} + 12q^{67} - 8q^{71} - 5q^{73} + 4q^{79} - 8q^{83} - 24q^{85} + 18q^{89} - 2q^{91} - 2q^{95} + 2q^{97} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1512\mathbb{Z}\right)^\times\).

\(n\) \(757\) \(785\) \(1081\) \(1135\)
\(\chi(n)\) \(1\) \(1\) \(e\left(\frac{1}{3}\right)\) \(1\)

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
\(3\) 0 0
\(4\) 0 0
\(5\) 1.00000 1.73205i 0.447214 0.774597i −0.550990 0.834512i \(-0.685750\pi\)
0.998203 + 0.0599153i \(0.0190830\pi\)
\(6\) 0 0
\(7\) 0.500000 2.59808i 0.188982 0.981981i
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(12\) 0 0
\(13\) −2.00000 −0.554700 −0.277350 0.960769i \(-0.589456\pi\)
−0.277350 + 0.960769i \(0.589456\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) −3.00000 5.19615i −0.727607 1.26025i −0.957892 0.287129i \(-0.907299\pi\)
0.230285 0.973123i \(-0.426034\pi\)
\(18\) 0 0
\(19\) 0.500000 0.866025i 0.114708 0.198680i −0.802955 0.596040i \(-0.796740\pi\)
0.917663 + 0.397360i \(0.130073\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) 1.00000 1.73205i 0.208514 0.361158i −0.742732 0.669588i \(-0.766471\pi\)
0.951247 + 0.308431i \(0.0998038\pi\)
\(24\) 0 0
\(25\) 0.500000 + 0.866025i 0.100000 + 0.173205i
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) −6.00000 −1.11417 −0.557086 0.830455i \(-0.688081\pi\)
−0.557086 + 0.830455i \(0.688081\pi\)
\(30\) 0 0
\(31\) −0.500000 0.866025i −0.0898027 0.155543i 0.817625 0.575751i \(-0.195290\pi\)
−0.907428 + 0.420208i \(0.861957\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) −4.00000 3.46410i −0.676123 0.585540i
\(36\) 0 0
\(37\) −1.00000 + 1.73205i −0.164399 + 0.284747i −0.936442 0.350823i \(-0.885902\pi\)
0.772043 + 0.635571i \(0.219235\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) −2.00000 −0.312348 −0.156174 0.987730i \(-0.549916\pi\)
−0.156174 + 0.987730i \(0.549916\pi\)
\(42\) 0 0
\(43\) 9.00000 1.37249 0.686244 0.727372i \(-0.259258\pi\)
0.686244 + 0.727372i \(0.259258\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) −1.00000 + 1.73205i −0.145865 + 0.252646i −0.929695 0.368329i \(-0.879930\pi\)
0.783830 + 0.620975i \(0.213263\pi\)
\(48\) 0 0
\(49\) −6.50000 2.59808i −0.928571 0.371154i
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) −3.00000 5.19615i −0.412082 0.713746i 0.583036 0.812447i \(-0.301865\pi\)
−0.995117 + 0.0987002i \(0.968532\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) −4.00000 6.92820i −0.520756 0.901975i −0.999709 0.0241347i \(-0.992317\pi\)
0.478953 0.877841i \(-0.341016\pi\)
\(60\) 0 0
\(61\) −5.50000 + 9.52628i −0.704203 + 1.21972i 0.262776 + 0.964857i \(0.415362\pi\)
−0.966978 + 0.254858i \(0.917971\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) −2.00000 + 3.46410i −0.248069 + 0.429669i
\(66\) 0 0
\(67\) 6.00000 + 10.3923i 0.733017 + 1.26962i 0.955588 + 0.294706i \(0.0952216\pi\)
−0.222571 + 0.974916i \(0.571445\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) −4.00000 −0.474713 −0.237356 0.971423i \(-0.576281\pi\)
−0.237356 + 0.971423i \(0.576281\pi\)
\(72\) 0 0
\(73\) −2.50000 4.33013i −0.292603 0.506803i 0.681822 0.731519i \(-0.261188\pi\)
−0.974424 + 0.224716i \(0.927855\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 0 0
\(78\) 0 0
\(79\) 2.00000 3.46410i 0.225018 0.389742i −0.731307 0.682048i \(-0.761089\pi\)
0.956325 + 0.292306i \(0.0944227\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) −4.00000 −0.439057 −0.219529 0.975606i \(-0.570452\pi\)
−0.219529 + 0.975606i \(0.570452\pi\)
\(84\) 0 0
\(85\) −12.0000 −1.30158
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 9.00000 15.5885i 0.953998 1.65237i 0.217354 0.976093i \(-0.430258\pi\)
0.736644 0.676280i \(-0.236409\pi\)
\(90\) 0 0
\(91\) −1.00000 + 5.19615i −0.104828 + 0.544705i
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) −1.00000 1.73205i −0.102598 0.177705i
\(96\) 0 0
\(97\) 1.00000 0.101535 0.0507673 0.998711i \(-0.483833\pi\)
0.0507673 + 0.998711i \(0.483833\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) −4.00000 6.92820i −0.398015 0.689382i 0.595466 0.803380i \(-0.296967\pi\)
−0.993481 + 0.113998i \(0.963634\pi\)
\(102\) 0 0
\(103\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 8.00000 13.8564i 0.773389 1.33955i −0.162306 0.986740i \(-0.551893\pi\)
0.935695 0.352809i \(-0.114773\pi\)
\(108\) 0 0
\(109\) −2.50000 4.33013i −0.239457 0.414751i 0.721102 0.692829i \(-0.243636\pi\)
−0.960558 + 0.278078i \(0.910303\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) −16.0000 −1.50515 −0.752577 0.658505i \(-0.771189\pi\)
−0.752577 + 0.658505i \(0.771189\pi\)
\(114\) 0 0
\(115\) −2.00000 3.46410i −0.186501 0.323029i
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) −15.0000 + 5.19615i −1.37505 + 0.476331i
\(120\) 0 0
\(121\) 5.50000 9.52628i 0.500000 0.866025i
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) 12.0000 1.07331
\(126\) 0 0
\(127\) 17.0000 1.50851 0.754253 0.656584i \(-0.227999\pi\)
0.754253 + 0.656584i \(0.227999\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) 9.00000 15.5885i 0.786334 1.36197i −0.141865 0.989886i \(-0.545310\pi\)
0.928199 0.372084i \(-0.121357\pi\)
\(132\) 0 0
\(133\) −2.00000 1.73205i −0.173422 0.150188i
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 11.0000 + 19.0526i 0.939793 + 1.62777i 0.765855 + 0.643013i \(0.222316\pi\)
0.173939 + 0.984757i \(0.444351\pi\)
\(138\) 0 0
\(139\) 20.0000 1.69638 0.848189 0.529694i \(-0.177693\pi\)
0.848189 + 0.529694i \(0.177693\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 0 0
\(144\) 0 0
\(145\) −6.00000 + 10.3923i −0.498273 + 0.863034i
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) 3.00000 5.19615i 0.245770 0.425685i −0.716578 0.697507i \(-0.754293\pi\)
0.962348 + 0.271821i \(0.0876260\pi\)
\(150\) 0 0
\(151\) −6.50000 11.2583i −0.528962 0.916190i −0.999430 0.0337724i \(-0.989248\pi\)
0.470467 0.882418i \(-0.344085\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) −2.00000 −0.160644
\(156\) 0 0
\(157\) −1.00000 1.73205i −0.0798087 0.138233i 0.823359 0.567521i \(-0.192098\pi\)
−0.903167 + 0.429289i \(0.858764\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) −4.00000 3.46410i −0.315244 0.273009i
\(162\) 0 0
\(163\) 0.500000 0.866025i 0.0391630 0.0678323i −0.845780 0.533533i \(-0.820864\pi\)
0.884943 + 0.465700i \(0.154198\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) −4.00000 −0.309529 −0.154765 0.987951i \(-0.549462\pi\)
−0.154765 + 0.987951i \(0.549462\pi\)
\(168\) 0 0
\(169\) −9.00000 −0.692308
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) −11.0000 + 19.0526i −0.836315 + 1.44854i 0.0566411 + 0.998395i \(0.481961\pi\)
−0.892956 + 0.450145i \(0.851372\pi\)
\(174\) 0 0
\(175\) 2.50000 0.866025i 0.188982 0.0654654i
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) 3.00000 + 5.19615i 0.224231 + 0.388379i 0.956088 0.293079i \(-0.0946798\pi\)
−0.731858 + 0.681457i \(0.761346\pi\)
\(180\) 0 0
\(181\) −3.00000 −0.222988 −0.111494 0.993765i \(-0.535564\pi\)
−0.111494 + 0.993765i \(0.535564\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 2.00000 + 3.46410i 0.147043 + 0.254686i
\(186\) 0 0
\(187\) 0 0
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) −5.00000 + 8.66025i −0.361787 + 0.626634i −0.988255 0.152813i \(-0.951167\pi\)
0.626468 + 0.779447i \(0.284500\pi\)
\(192\) 0 0
\(193\) −3.00000 5.19615i −0.215945 0.374027i 0.737620 0.675216i \(-0.235950\pi\)
−0.953564 + 0.301189i \(0.902616\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 8.00000 0.569976 0.284988 0.958531i \(-0.408010\pi\)
0.284988 + 0.958531i \(0.408010\pi\)
\(198\) 0 0
\(199\) −7.50000 12.9904i −0.531661 0.920864i −0.999317 0.0369532i \(-0.988235\pi\)
0.467656 0.883911i \(-0.345099\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) −3.00000 + 15.5885i −0.210559 + 1.09410i
\(204\) 0 0
\(205\) −2.00000 + 3.46410i −0.139686 + 0.241943i
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) 0 0
\(210\) 0 0
\(211\) 15.0000 1.03264 0.516321 0.856395i \(-0.327301\pi\)
0.516321 + 0.856395i \(0.327301\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) 9.00000 15.5885i 0.613795 1.06312i
\(216\) 0 0
\(217\) −2.50000 + 0.866025i −0.169711 + 0.0587896i
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) 6.00000 + 10.3923i 0.403604 + 0.699062i
\(222\) 0 0
\(223\) −8.00000 −0.535720 −0.267860 0.963458i \(-0.586316\pi\)
−0.267860 + 0.963458i \(0.586316\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 9.00000 + 15.5885i 0.597351 + 1.03464i 0.993210 + 0.116331i \(0.0371134\pi\)
−0.395860 + 0.918311i \(0.629553\pi\)
\(228\) 0 0
\(229\) −4.50000 + 7.79423i −0.297368 + 0.515057i −0.975533 0.219853i \(-0.929442\pi\)
0.678165 + 0.734910i \(0.262776\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) −3.00000 + 5.19615i −0.196537 + 0.340411i −0.947403 0.320043i \(-0.896303\pi\)
0.750867 + 0.660454i \(0.229636\pi\)
\(234\) 0 0
\(235\) 2.00000 + 3.46410i 0.130466 + 0.225973i
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) −6.00000 −0.388108 −0.194054 0.980991i \(-0.562164\pi\)
−0.194054 + 0.980991i \(0.562164\pi\)
\(240\) 0 0
\(241\) 9.50000 + 16.4545i 0.611949 + 1.05993i 0.990912 + 0.134515i \(0.0429475\pi\)
−0.378963 + 0.925412i \(0.623719\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) −11.0000 + 8.66025i −0.702764 + 0.553283i
\(246\) 0 0
\(247\) −1.00000 + 1.73205i −0.0636285 + 0.110208i
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 10.0000 0.631194 0.315597 0.948893i \(-0.397795\pi\)
0.315597 + 0.948893i \(0.397795\pi\)
\(252\) 0 0
\(253\) 0 0
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 10.0000 17.3205i 0.623783 1.08042i −0.364992 0.931011i \(-0.618928\pi\)
0.988775 0.149413i \(-0.0477384\pi\)
\(258\) 0 0
\(259\) 4.00000 + 3.46410i 0.248548 + 0.215249i
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) 14.0000 + 24.2487i 0.863277 + 1.49524i 0.868748 + 0.495255i \(0.164925\pi\)
−0.00547092 + 0.999985i \(0.501741\pi\)
\(264\) 0 0
\(265\) −12.0000 −0.737154
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) −10.0000 17.3205i −0.609711 1.05605i −0.991288 0.131713i \(-0.957952\pi\)
0.381577 0.924337i \(-0.375381\pi\)
\(270\) 0 0
\(271\) 11.5000 19.9186i 0.698575 1.20997i −0.270385 0.962752i \(-0.587151\pi\)
0.968960 0.247216i \(-0.0795156\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 0 0
\(276\) 0 0
\(277\) 9.50000 + 16.4545i 0.570800 + 0.988654i 0.996484 + 0.0837823i \(0.0267000\pi\)
−0.425684 + 0.904872i \(0.639967\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(282\) 0 0
\(283\) 13.5000 + 23.3827i 0.802492 + 1.38996i 0.917971 + 0.396647i \(0.129826\pi\)
−0.115480 + 0.993310i \(0.536841\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) −1.00000 + 5.19615i −0.0590281 + 0.306719i
\(288\) 0 0
\(289\) −9.50000 + 16.4545i −0.558824 + 0.967911i
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) 28.0000 1.63578 0.817889 0.575376i \(-0.195144\pi\)
0.817889 + 0.575376i \(0.195144\pi\)
\(294\) 0 0
\(295\) −16.0000 −0.931556
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) −2.00000 + 3.46410i −0.115663 + 0.200334i
\(300\) 0 0
\(301\) 4.50000 23.3827i 0.259376 1.34776i
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) 11.0000 + 19.0526i 0.629858 + 1.09095i
\(306\) 0 0
\(307\) −13.0000 −0.741949 −0.370975 0.928643i \(-0.620976\pi\)
−0.370975 + 0.928643i \(0.620976\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 12.0000 + 20.7846i 0.680458 + 1.17859i 0.974841 + 0.222900i \(0.0715523\pi\)
−0.294384 + 0.955687i \(0.595114\pi\)
\(312\) 0 0
\(313\) 10.5000 18.1865i 0.593495 1.02796i −0.400262 0.916401i \(-0.631081\pi\)
0.993757 0.111563i \(-0.0355857\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 2.00000 3.46410i 0.112331 0.194563i −0.804379 0.594117i \(-0.797502\pi\)
0.916710 + 0.399554i \(0.130835\pi\)
\(318\) 0 0
\(319\) 0 0
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) −6.00000 −0.333849
\(324\) 0 0
\(325\) −1.00000 1.73205i −0.0554700 0.0960769i
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) 4.00000 + 3.46410i 0.220527 + 0.190982i
\(330\) 0 0
\(331\) −6.50000 + 11.2583i −0.357272 + 0.618814i −0.987504 0.157593i \(-0.949627\pi\)
0.630232 + 0.776407i \(0.282960\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) 24.0000 1.31126
\(336\) 0 0
\(337\) −27.0000 −1.47078 −0.735392 0.677642i \(-0.763002\pi\)
−0.735392 + 0.677642i \(0.763002\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) 0 0
\(342\) 0 0
\(343\) −10.0000 + 15.5885i −0.539949 + 0.841698i
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 14.0000 + 24.2487i 0.751559 + 1.30174i 0.947067 + 0.321037i \(0.104031\pi\)
−0.195507 + 0.980702i \(0.562635\pi\)
\(348\) 0 0
\(349\) 11.0000 0.588817 0.294408 0.955680i \(-0.404877\pi\)
0.294408 + 0.955680i \(0.404877\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) −2.00000 3.46410i −0.106449 0.184376i 0.807880 0.589347i \(-0.200615\pi\)
−0.914329 + 0.404971i \(0.867282\pi\)
\(354\) 0 0
\(355\) −4.00000 + 6.92820i −0.212298 + 0.367711i
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 12.0000 20.7846i 0.633336 1.09697i −0.353529 0.935423i \(-0.615019\pi\)
0.986865 0.161546i \(-0.0516481\pi\)
\(360\) 0 0
\(361\) 9.00000 + 15.5885i 0.473684 + 0.820445i
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) −10.0000 −0.523424
\(366\) 0 0
\(367\) −14.5000 25.1147i −0.756894 1.31098i −0.944427 0.328720i \(-0.893383\pi\)
0.187533 0.982258i \(-0.439951\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) −15.0000 + 5.19615i −0.778761 + 0.269771i
\(372\) 0 0
\(373\) 8.50000 14.7224i 0.440113 0.762299i −0.557584 0.830120i \(-0.688272\pi\)
0.997697 + 0.0678218i \(0.0216049\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 12.0000 0.618031
\(378\) 0 0
\(379\) 20.0000 1.02733 0.513665 0.857991i \(-0.328287\pi\)
0.513665 + 0.857991i \(0.328287\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 10.0000 17.3205i 0.510976 0.885037i −0.488943 0.872316i \(-0.662617\pi\)
0.999919 0.0127209i \(-0.00404928\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) 19.0000 + 32.9090i 0.963338 + 1.66855i 0.714015 + 0.700130i \(0.246875\pi\)
0.249323 + 0.968420i \(0.419792\pi\)
\(390\) 0 0
\(391\) −12.0000 −0.606866
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) −4.00000 6.92820i −0.201262 0.348596i
\(396\) 0 0
\(397\) 8.50000 14.7224i 0.426603 0.738898i −0.569966 0.821668i \(-0.693044\pi\)
0.996569 + 0.0827707i \(0.0263769\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) −10.0000 + 17.3205i −0.499376 + 0.864945i −1.00000 0.000720188i \(-0.999771\pi\)
0.500624 + 0.865665i \(0.333104\pi\)
\(402\) 0 0
\(403\) 1.00000 + 1.73205i 0.0498135 + 0.0862796i
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 0 0
\(408\) 0 0
\(409\) 7.00000 + 12.1244i 0.346128 + 0.599511i 0.985558 0.169338i \(-0.0541630\pi\)
−0.639430 + 0.768849i \(0.720830\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) −20.0000 + 6.92820i −0.984136 + 0.340915i
\(414\) 0 0
\(415\) −4.00000 + 6.92820i −0.196352 + 0.340092i
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 6.00000 0.293119 0.146560 0.989202i \(-0.453180\pi\)
0.146560 + 0.989202i \(0.453180\pi\)
\(420\) 0 0
\(421\) −3.00000 −0.146211 −0.0731055 0.997324i \(-0.523291\pi\)
−0.0731055 + 0.997324i \(0.523291\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) 3.00000 5.19615i 0.145521 0.252050i
\(426\) 0 0
\(427\) 22.0000 + 19.0526i 1.06465 + 0.922018i
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 12.0000 + 20.7846i 0.578020 + 1.00116i 0.995706 + 0.0925683i \(0.0295076\pi\)
−0.417687 + 0.908591i \(0.637159\pi\)
\(432\) 0 0
\(433\) 7.00000 0.336399 0.168199 0.985753i \(-0.446205\pi\)
0.168199 + 0.985753i \(0.446205\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) −1.00000 1.73205i −0.0478365 0.0828552i
\(438\) 0 0
\(439\) 12.0000 20.7846i 0.572729 0.991995i −0.423556 0.905870i \(-0.639218\pi\)
0.996284 0.0861252i \(-0.0274485\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) −11.0000 + 19.0526i −0.522626 + 0.905214i 0.477028 + 0.878888i \(0.341714\pi\)
−0.999653 + 0.0263261i \(0.991619\pi\)
\(444\) 0 0
\(445\) −18.0000 31.1769i −0.853282 1.47793i
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) −10.0000 −0.471929 −0.235965 0.971762i \(-0.575825\pi\)
−0.235965 + 0.971762i \(0.575825\pi\)
\(450\) 0 0
\(451\) 0 0
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) 8.00000 + 6.92820i 0.375046 + 0.324799i
\(456\) 0 0
\(457\) 17.5000 30.3109i 0.818615 1.41788i −0.0880870 0.996113i \(-0.528075\pi\)
0.906702 0.421771i \(-0.138591\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(462\) 0 0
\(463\) −7.00000 −0.325318 −0.162659 0.986682i \(-0.552007\pi\)
−0.162659 + 0.986682i \(0.552007\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) −2.00000 + 3.46410i −0.0925490 + 0.160300i −0.908583 0.417704i \(-0.862835\pi\)
0.816034 + 0.578004i \(0.196168\pi\)
\(468\) 0 0
\(469\) 30.0000 10.3923i 1.38527 0.479872i
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) 0 0
\(474\) 0 0
\(475\) 1.00000 0.0458831
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) −15.0000 25.9808i −0.685367 1.18709i −0.973321 0.229447i \(-0.926308\pi\)
0.287954 0.957644i \(-0.407025\pi\)
\(480\) 0 0
\(481\) 2.00000 3.46410i 0.0911922 0.157949i
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 1.00000 1.73205i 0.0454077 0.0786484i
\(486\) 0 0
\(487\) −18.5000 32.0429i −0.838315 1.45200i −0.891303 0.453409i \(-0.850208\pi\)
0.0529875 0.998595i \(-0.483126\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) −36.0000 −1.62466 −0.812329 0.583200i \(-0.801800\pi\)
−0.812329 + 0.583200i \(0.801800\pi\)
\(492\) 0 0
\(493\) 18.0000 + 31.1769i 0.810679 + 1.40414i
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) −2.00000 + 10.3923i −0.0897123 + 0.466159i
\(498\) 0 0
\(499\) −18.5000 + 32.0429i −0.828174 + 1.43444i 0.0712957 + 0.997455i \(0.477287\pi\)
−0.899469 + 0.436984i \(0.856047\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) −6.00000 −0.267527 −0.133763 0.991013i \(-0.542706\pi\)
−0.133763 + 0.991013i \(0.542706\pi\)
\(504\) 0 0
\(505\) −16.0000 −0.711991
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) 18.0000 31.1769i 0.797836 1.38189i −0.123187 0.992384i \(-0.539311\pi\)
0.921023 0.389509i \(-0.127355\pi\)
\(510\) 0 0
\(511\) −12.5000 + 4.33013i −0.552967 + 0.191554i
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) 0 0
\(516\) 0 0
\(517\) 0 0
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 12.0000 + 20.7846i 0.525730 + 0.910590i 0.999551 + 0.0299693i \(0.00954094\pi\)
−0.473821 + 0.880621i \(0.657126\pi\)
\(522\) 0 0
\(523\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −3.00000 + 5.19615i −0.130682 + 0.226348i
\(528\) 0 0
\(529\) 9.50000 + 16.4545i 0.413043 + 0.715412i
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) 4.00000 0.173259
\(534\) 0 0
\(535\) −16.0000 27.7128i −0.691740 1.19813i
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) 0 0
\(540\) 0 0
\(541\) 5.50000 9.52628i 0.236463 0.409567i −0.723234 0.690604i \(-0.757345\pi\)
0.959697 + 0.281037i \(0.0906783\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) −10.0000 −0.428353
\(546\) 0 0
\(547\) 7.00000 0.299298 0.149649 0.988739i \(-0.452186\pi\)
0.149649 + 0.988739i \(0.452186\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) −3.00000 + 5.19615i −0.127804 + 0.221364i
\(552\) 0 0
\(553\) −8.00000 6.92820i −0.340195 0.294617i
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 9.00000 + 15.5885i 0.381342 + 0.660504i 0.991254 0.131965i \(-0.0421286\pi\)
−0.609912 + 0.792469i \(0.708795\pi\)
\(558\) 0 0
\(559\) −18.0000 −0.761319
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) 3.00000 + 5.19615i 0.126435 + 0.218992i 0.922293 0.386492i \(-0.126313\pi\)
−0.795858 + 0.605483i \(0.792980\pi\)
\(564\) 0 0
\(565\) −16.0000 + 27.7128i −0.673125 + 1.16589i
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 18.0000 31.1769i 0.754599 1.30700i −0.190974 0.981595i \(-0.561165\pi\)
0.945573 0.325409i \(-0.105502\pi\)
\(570\) 0 0
\(571\) 2.50000 + 4.33013i 0.104622 + 0.181210i 0.913584 0.406651i \(-0.133303\pi\)
−0.808962 + 0.587861i \(0.799970\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 2.00000 0.0834058
\(576\) 0 0
\(577\) 9.00000 + 15.5885i 0.374675 + 0.648956i 0.990278 0.139100i \(-0.0444210\pi\)
−0.615603 + 0.788056i \(0.711088\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) −2.00000 + 10.3923i −0.0829740 + 0.431145i
\(582\) 0 0
\(583\) 0 0
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 18.0000 0.742940 0.371470 0.928445i \(-0.378854\pi\)
0.371470 + 0.928445i \(0.378854\pi\)
\(588\) 0 0
\(589\) −1.00000 −0.0412043
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) 6.00000 10.3923i 0.246390 0.426761i −0.716131 0.697966i \(-0.754089\pi\)
0.962522 + 0.271205i \(0.0874221\pi\)
\(594\) 0 0
\(595\) −6.00000 + 31.1769i −0.245976 + 1.27813i
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) −15.0000 25.9808i −0.612883 1.06155i −0.990752 0.135686i \(-0.956676\pi\)
0.377869 0.925859i \(-0.376657\pi\)
\(600\) 0 0
\(601\) 35.0000 1.42768 0.713840 0.700309i \(-0.246954\pi\)
0.713840 + 0.700309i \(0.246954\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) −11.0000 19.0526i −0.447214 0.774597i
\(606\) 0 0
\(607\) −6.50000 + 11.2583i −0.263827 + 0.456962i −0.967256 0.253804i \(-0.918318\pi\)
0.703429 + 0.710766i \(0.251651\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 2.00000 3.46410i 0.0809113 0.140143i
\(612\) 0 0
\(613\) −5.50000 9.52628i −0.222143 0.384763i 0.733316 0.679888i \(-0.237972\pi\)
−0.955458 + 0.295126i \(0.904638\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) −36.0000 −1.44931 −0.724653 0.689114i \(-0.758000\pi\)
−0.724653 + 0.689114i \(0.758000\pi\)
\(618\) 0 0
\(619\) −6.00000 10.3923i −0.241160 0.417702i 0.719885 0.694094i \(-0.244195\pi\)
−0.961045 + 0.276392i \(0.910861\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) −36.0000 31.1769i −1.44231 1.24908i
\(624\) 0 0
\(625\) 9.50000 16.4545i 0.380000 0.658179i
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 12.0000 0.478471
\(630\) 0 0
\(631\) −23.0000 −0.915616 −0.457808 0.889051i \(-0.651365\pi\)
−0.457808 + 0.889051i \(0.651365\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) 17.0000 29.4449i 0.674624 1.16848i
\(636\) 0 0
\(637\) 13.0000 + 5.19615i 0.515079 + 0.205879i
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) −5.00000 8.66025i −0.197488 0.342059i 0.750225 0.661182i \(-0.229945\pi\)
−0.947713 + 0.319123i \(0.896612\pi\)
\(642\) 0 0
\(643\) 1.00000 0.0394362 0.0197181 0.999806i \(-0.493723\pi\)
0.0197181 + 0.999806i \(0.493723\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) −22.0000 38.1051i −0.864909 1.49807i −0.867137 0.498069i \(-0.834043\pi\)
0.00222801 0.999998i \(-0.499291\pi\)
\(648\) 0 0
\(649\) 0 0
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) −3.00000 + 5.19615i −0.117399 + 0.203341i −0.918736 0.394872i \(-0.870789\pi\)
0.801337 + 0.598213i \(0.204122\pi\)
\(654\) 0 0
\(655\) −18.0000 31.1769i −0.703318 1.21818i
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) 30.0000 1.16863 0.584317 0.811525i \(-0.301362\pi\)
0.584317 + 0.811525i \(0.301362\pi\)
\(660\) 0 0
\(661\) 18.5000 + 32.0429i 0.719567 + 1.24633i 0.961172 + 0.275951i \(0.0889928\pi\)
−0.241605 + 0.970375i \(0.577674\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) −5.00000 + 1.73205i −0.193892 + 0.0671660i
\(666\) 0 0
\(667\) −6.00000 + 10.3923i −0.232321 + 0.402392i
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 0 0
\(672\) 0 0
\(673\) −1.00000 −0.0385472 −0.0192736 0.999814i \(-0.506135\pi\)
−0.0192736 + 0.999814i \(0.506135\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 2.00000 3.46410i 0.0768662 0.133136i −0.825030 0.565089i \(-0.808842\pi\)
0.901896 + 0.431953i \(0.142175\pi\)
\(678\) 0 0
\(679\) 0.500000 2.59808i 0.0191882 0.0997050i
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 16.0000 + 27.7128i 0.612223 + 1.06040i 0.990865 + 0.134858i \(0.0430579\pi\)
−0.378642 + 0.925543i \(0.623609\pi\)
\(684\) 0 0
\(685\) 44.0000 1.68115
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) 6.00000 + 10.3923i 0.228582 + 0.395915i
\(690\) 0 0
\(691\) −1.50000 + 2.59808i −0.0570627 + 0.0988355i −0.893146 0.449768i \(-0.851507\pi\)
0.836083 + 0.548603i \(0.184840\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 20.0000 34.6410i 0.758643 1.31401i
\(696\) 0 0
\(697\) 6.00000 + 10.3923i 0.227266 + 0.393637i
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) −26.0000 −0.982006 −0.491003 0.871158i \(-0.663370\pi\)
−0.491003 + 0.871158i \(0.663370\pi\)
\(702\) 0 0
\(703\) 1.00000 + 1.73205i 0.0377157 + 0.0653255i
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) −20.0000 + 6.92820i −0.752177 + 0.260562i
\(708\) 0 0
\(709\) −16.5000 + 28.5788i −0.619671 + 1.07330i 0.369875 + 0.929081i \(0.379400\pi\)
−0.989546 + 0.144219i \(0.953933\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) −2.00000 −0.0749006
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) 4.00000 6.92820i 0.149175 0.258378i −0.781748 0.623595i \(-0.785672\pi\)
0.930923 + 0.365216i \(0.119005\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) −3.00000 5.19615i −0.111417 0.192980i
\(726\) 0 0
\(727\) −37.0000 −1.37225 −0.686127 0.727482i \(-0.740691\pi\)
−0.686127 + 0.727482i \(0.740691\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) −27.0000 46.7654i −0.998631 1.72968i
\(732\) 0 0
\(733\) 9.50000 16.4545i 0.350891 0.607760i −0.635515 0.772088i \(-0.719212\pi\)
0.986406 + 0.164328i \(0.0525456\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 0 0
\(738\) 0 0
\(739\) 5.50000 + 9.52628i 0.202321 + 0.350430i 0.949276 0.314445i \(-0.101818\pi\)
−0.746955 + 0.664875i \(0.768485\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) −34.0000 −1.24734 −0.623670 0.781688i \(-0.714359\pi\)
−0.623670 + 0.781688i \(0.714359\pi\)
\(744\) 0 0
\(745\) −6.00000 10.3923i −0.219823 0.380745i
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) −32.0000 27.7128i −1.16925 1.01260i
\(750\) 0 0
\(751\) −7.50000 + 12.9904i −0.273679 + 0.474026i −0.969801 0.243898i \(-0.921574\pi\)
0.696122 + 0.717923i \(0.254907\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) −26.0000 −0.946237
\(756\) 0 0
\(757\) −7.00000 −0.254419 −0.127210 0.991876i \(-0.540602\pi\)
−0.127210 + 0.991876i \(0.540602\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 24.0000 41.5692i 0.869999 1.50688i 0.00800331 0.999968i \(-0.497452\pi\)
0.861996 0.506915i \(-0.169214\pi\)
\(762\) 0 0
\(763\) −12.5000 + 4.33013i −0.452530 + 0.156761i
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 8.00000 + 13.8564i 0.288863 + 0.500326i
\(768\) 0 0
\(769\) 19.0000 0.685158 0.342579 0.939489i \(-0.388700\pi\)
0.342579 + 0.939489i \(0.388700\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) 5.00000 + 8.66025i 0.179838 + 0.311488i 0.941825 0.336104i \(-0.109109\pi\)
−0.761987 + 0.647592i \(0.775776\pi\)
\(774\) 0 0
\(775\) 0.500000 0.866025i 0.0179605 0.0311086i
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) −1.00000 + 1.73205i −0.0358287 + 0.0620572i
\(780\) 0 0
\(781\) 0 0
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) −4.00000 −0.142766
\(786\) 0 0
\(787\) −8.50000 14.7224i −0.302992 0.524798i 0.673820 0.738896i \(-0.264652\pi\)
−0.976812 + 0.214097i \(0.931319\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) −8.00000 + 41.5692i −0.284447 + 1.47803i
\(792\) 0 0
\(793\) 11.0000 19.0526i 0.390621 0.676576i
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) −36.0000 −1.27519 −0.637593 0.770374i \(-0.720070\pi\)
−0.637593 + 0.770374i \(0.720070\pi\)
\(798\) 0 0
\(799\) 12.0000 0.424529
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) 0 0
\(804\) 0 0
\(805\) −10.0000 + 3.46410i −0.352454 + 0.122094i
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) −20.0000 34.6410i −0.703163 1.21791i −0.967351 0.253442i \(-0.918437\pi\)
0.264188 0.964471i \(-0.414896\pi\)
\(810\) 0 0
\(811\) −28.0000 −0.983213 −0.491606 0.870817i \(-0.663590\pi\)
−0.491606 + 0.870817i \(0.663590\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) −1.00000 1.73205i −0.0350285 0.0606711i
\(816\) 0 0
\(817\) 4.50000 7.79423i 0.157435 0.272686i
\(818\) 0 0