Properties

Label 1512.2.s.h.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: \(\Z[a_1, \ldots, a_{25}]\)
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.h.865.1

$q$-expansion

\(f(q)\) \(=\) \(q+(1.00000 - 1.73205i) q^{5} +(2.00000 + 1.73205i) q^{7} +O(q^{10})\) \(q+(1.00000 - 1.73205i) q^{5} +(2.00000 + 1.73205i) q^{7} +(-2.00000 - 3.46410i) q^{11} -1.00000 q^{13} +(2.00000 - 3.46410i) q^{19} +(3.00000 - 5.19615i) q^{23} +(0.500000 + 0.866025i) q^{25} +(-2.50000 - 4.33013i) q^{31} +(5.00000 - 1.73205i) q^{35} +(-0.500000 + 0.866025i) q^{37} +4.00000 q^{41} -1.00000 q^{43} +(2.00000 - 3.46410i) q^{47} +(1.00000 + 6.92820i) q^{49} +(-3.00000 - 5.19615i) q^{53} -8.00000 q^{55} +(1.50000 - 2.59808i) q^{61} +(-1.00000 + 1.73205i) q^{65} +(-5.50000 - 9.52628i) q^{67} +14.0000 q^{71} +(7.00000 + 12.1244i) q^{73} +(2.00000 - 10.3923i) q^{77} +(-6.50000 + 11.2583i) q^{79} -14.0000 q^{83} +(3.00000 - 5.19615i) q^{89} +(-2.00000 - 1.73205i) q^{91} +(-4.00000 - 6.92820i) q^{95} +9.00000 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2q + 2q^{5} + 4q^{7} + O(q^{10}) \) \( 2q + 2q^{5} + 4q^{7} - 4q^{11} - 2q^{13} + 4q^{19} + 6q^{23} + q^{25} - 5q^{31} + 10q^{35} - q^{37} + 8q^{41} - 2q^{43} + 4q^{47} + 2q^{49} - 6q^{53} - 16q^{55} + 3q^{61} - 2q^{65} - 11q^{67} + 28q^{71} + 14q^{73} + 4q^{77} - 13q^{79} - 28q^{83} + 6q^{89} - 4q^{91} - 8q^{95} + 18q^{97} + O(q^{100}) \)

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
\(7\) 2.00000 + 1.73205i 0.755929 + 0.654654i
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) −2.00000 3.46410i −0.603023 1.04447i −0.992361 0.123371i \(-0.960630\pi\)
0.389338 0.921095i \(-0.372704\pi\)
\(12\) 0 0
\(13\) −1.00000 −0.277350 −0.138675 0.990338i \(-0.544284\pi\)
−0.138675 + 0.990338i \(0.544284\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(18\) 0 0
\(19\) 2.00000 3.46410i 0.458831 0.794719i −0.540068 0.841621i \(-0.681602\pi\)
0.998899 + 0.0469020i \(0.0149348\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) 3.00000 5.19615i 0.625543 1.08347i −0.362892 0.931831i \(-0.618211\pi\)
0.988436 0.151642i \(-0.0484560\pi\)
\(24\) 0 0
\(25\) 0.500000 + 0.866025i 0.100000 + 0.173205i
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(30\) 0 0
\(31\) −2.50000 4.33013i −0.449013 0.777714i 0.549309 0.835619i \(-0.314891\pi\)
−0.998322 + 0.0579057i \(0.981558\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) 5.00000 1.73205i 0.845154 0.292770i
\(36\) 0 0
\(37\) −0.500000 + 0.866025i −0.0821995 + 0.142374i −0.904194 0.427121i \(-0.859528\pi\)
0.821995 + 0.569495i \(0.192861\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) 4.00000 0.624695 0.312348 0.949968i \(-0.398885\pi\)
0.312348 + 0.949968i \(0.398885\pi\)
\(42\) 0 0
\(43\) −1.00000 −0.152499 −0.0762493 0.997089i \(-0.524294\pi\)
−0.0762493 + 0.997089i \(0.524294\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 2.00000 3.46410i 0.291730 0.505291i −0.682489 0.730896i \(-0.739102\pi\)
0.974219 + 0.225605i \(0.0724358\pi\)
\(48\) 0 0
\(49\) 1.00000 + 6.92820i 0.142857 + 0.989743i
\(50\) 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
\(55\) −8.00000 −1.07872
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(60\) 0 0
\(61\) 1.50000 2.59808i 0.192055 0.332650i −0.753876 0.657017i \(-0.771818\pi\)
0.945931 + 0.324367i \(0.105151\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) −1.00000 + 1.73205i −0.124035 + 0.214834i
\(66\) 0 0
\(67\) −5.50000 9.52628i −0.671932 1.16382i −0.977356 0.211604i \(-0.932131\pi\)
0.305424 0.952217i \(-0.401202\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 14.0000 1.66149 0.830747 0.556650i \(-0.187914\pi\)
0.830747 + 0.556650i \(0.187914\pi\)
\(72\) 0 0
\(73\) 7.00000 + 12.1244i 0.819288 + 1.41905i 0.906208 + 0.422833i \(0.138964\pi\)
−0.0869195 + 0.996215i \(0.527702\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 2.00000 10.3923i 0.227921 1.18431i
\(78\) 0 0
\(79\) −6.50000 + 11.2583i −0.731307 + 1.26666i 0.225018 + 0.974355i \(0.427756\pi\)
−0.956325 + 0.292306i \(0.905577\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) −14.0000 −1.53670 −0.768350 0.640030i \(-0.778922\pi\)
−0.768350 + 0.640030i \(0.778922\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 3.00000 5.19615i 0.317999 0.550791i −0.662071 0.749441i \(-0.730322\pi\)
0.980071 + 0.198650i \(0.0636557\pi\)
\(90\) 0 0
\(91\) −2.00000 1.73205i −0.209657 0.181568i
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) −4.00000 6.92820i −0.410391 0.710819i
\(96\) 0 0
\(97\) 9.00000 0.913812 0.456906 0.889515i \(-0.348958\pi\)
0.456906 + 0.889515i \(0.348958\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) −5.00000 8.66025i −0.497519 0.861727i 0.502477 0.864590i \(-0.332422\pi\)
−0.999996 + 0.00286291i \(0.999089\pi\)
\(102\) 0 0
\(103\) 6.50000 11.2583i 0.640464 1.10932i −0.344865 0.938652i \(-0.612075\pi\)
0.985329 0.170664i \(-0.0545913\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 9.00000 15.5885i 0.870063 1.50699i 0.00813215 0.999967i \(-0.497411\pi\)
0.861931 0.507026i \(-0.169255\pi\)
\(108\) 0 0
\(109\) 0.500000 + 0.866025i 0.0478913 + 0.0829502i 0.888977 0.457951i \(-0.151417\pi\)
−0.841086 + 0.540901i \(0.818083\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) 10.0000 0.940721 0.470360 0.882474i \(-0.344124\pi\)
0.470360 + 0.882474i \(0.344124\pi\)
\(114\) 0 0
\(115\) −6.00000 10.3923i −0.559503 0.969087i
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) 0 0
\(120\) 0 0
\(121\) −2.50000 + 4.33013i −0.227273 + 0.393648i
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) 12.0000 1.07331
\(126\) 0 0
\(127\) −11.0000 −0.976092 −0.488046 0.872818i \(-0.662290\pi\)
−0.488046 + 0.872818i \(0.662290\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) −8.00000 + 13.8564i −0.698963 + 1.21064i 0.269863 + 0.962899i \(0.413022\pi\)
−0.968826 + 0.247741i \(0.920312\pi\)
\(132\) 0 0
\(133\) 10.0000 3.46410i 0.867110 0.300376i
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) −9.00000 15.5885i −0.768922 1.33181i −0.938148 0.346235i \(-0.887460\pi\)
0.169226 0.985577i \(-0.445873\pi\)
\(138\) 0 0
\(139\) 1.00000 0.0848189 0.0424094 0.999100i \(-0.486497\pi\)
0.0424094 + 0.999100i \(0.486497\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 2.00000 + 3.46410i 0.167248 + 0.289683i
\(144\) 0 0
\(145\) 0 0
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) −3.00000 + 5.19615i −0.245770 + 0.425685i −0.962348 0.271821i \(-0.912374\pi\)
0.716578 + 0.697507i \(0.245707\pi\)
\(150\) 0 0
\(151\) −1.50000 2.59808i −0.122068 0.211428i 0.798515 0.601975i \(-0.205619\pi\)
−0.920583 + 0.390547i \(0.872286\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) −10.0000 −0.803219
\(156\) 0 0
\(157\) 9.00000 + 15.5885i 0.718278 + 1.24409i 0.961681 + 0.274169i \(0.0884028\pi\)
−0.243403 + 0.969925i \(0.578264\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 15.0000 5.19615i 1.18217 0.409514i
\(162\) 0 0
\(163\) 10.5000 18.1865i 0.822423 1.42448i −0.0814491 0.996678i \(-0.525955\pi\)
0.903873 0.427802i \(-0.140712\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 2.00000 0.154765 0.0773823 0.997001i \(-0.475344\pi\)
0.0773823 + 0.997001i \(0.475344\pi\)
\(168\) 0 0
\(169\) −12.0000 −0.923077
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) −12.0000 + 20.7846i −0.912343 + 1.58022i −0.101598 + 0.994826i \(0.532395\pi\)
−0.810745 + 0.585399i \(0.800938\pi\)
\(174\) 0 0
\(175\) −0.500000 + 2.59808i −0.0377964 + 0.196396i
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) 1.00000 + 1.73205i 0.0747435 + 0.129460i 0.900975 0.433872i \(-0.142853\pi\)
−0.826231 + 0.563331i \(0.809520\pi\)
\(180\) 0 0
\(181\) 10.0000 0.743294 0.371647 0.928374i \(-0.378793\pi\)
0.371647 + 0.928374i \(0.378793\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 1.00000 + 1.73205i 0.0735215 + 0.127343i
\(186\) 0 0
\(187\) 0 0
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) −11.0000 + 19.0526i −0.795932 + 1.37859i 0.126314 + 0.991990i \(0.459685\pi\)
−0.922246 + 0.386604i \(0.873648\pi\)
\(192\) 0 0
\(193\) 8.50000 + 14.7224i 0.611843 + 1.05974i 0.990930 + 0.134382i \(0.0429051\pi\)
−0.379086 + 0.925361i \(0.623762\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 12.0000 0.854965 0.427482 0.904024i \(-0.359401\pi\)
0.427482 + 0.904024i \(0.359401\pi\)
\(198\) 0 0
\(199\) 7.50000 + 12.9904i 0.531661 + 0.920864i 0.999317 + 0.0369532i \(0.0117652\pi\)
−0.467656 + 0.883911i \(0.654901\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) 0 0
\(204\) 0 0
\(205\) 4.00000 6.92820i 0.279372 0.483887i
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) −16.0000 −1.10674
\(210\) 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
\(215\) −1.00000 + 1.73205i −0.0681994 + 0.118125i
\(216\) 0 0
\(217\) 2.50000 12.9904i 0.169711 0.881845i
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) 0 0
\(222\) 0 0
\(223\) −12.0000 −0.803579 −0.401790 0.915732i \(-0.631612\pi\)
−0.401790 + 0.915732i \(0.631612\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 11.0000 + 19.0526i 0.730096 + 1.26456i 0.956842 + 0.290609i \(0.0938578\pi\)
−0.226746 + 0.973954i \(0.572809\pi\)
\(228\) 0 0
\(229\) −9.50000 + 16.4545i −0.627778 + 1.08734i 0.360219 + 0.932868i \(0.382702\pi\)
−0.987997 + 0.154475i \(0.950631\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) −8.00000 + 13.8564i −0.524097 + 0.907763i 0.475509 + 0.879711i \(0.342264\pi\)
−0.999606 + 0.0280525i \(0.991069\pi\)
\(234\) 0 0
\(235\) −4.00000 6.92820i −0.260931 0.451946i
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) 22.0000 1.42306 0.711531 0.702655i \(-0.248002\pi\)
0.711531 + 0.702655i \(0.248002\pi\)
\(240\) 0 0
\(241\) −0.500000 0.866025i −0.0322078 0.0557856i 0.849472 0.527633i \(-0.176921\pi\)
−0.881680 + 0.471848i \(0.843587\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) 13.0000 + 5.19615i 0.830540 + 0.331970i
\(246\) 0 0
\(247\) −2.00000 + 3.46410i −0.127257 + 0.220416i
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) −6.00000 −0.378717 −0.189358 0.981908i \(-0.560641\pi\)
−0.189358 + 0.981908i \(0.560641\pi\)
\(252\) 0 0
\(253\) −24.0000 −1.50887
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) −11.0000 + 19.0526i −0.686161 + 1.18847i 0.286909 + 0.957958i \(0.407372\pi\)
−0.973070 + 0.230508i \(0.925961\pi\)
\(258\) 0 0
\(259\) −2.50000 + 0.866025i −0.155342 + 0.0538122i
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) −12.0000 20.7846i −0.739952 1.28163i −0.952517 0.304487i \(-0.901515\pi\)
0.212565 0.977147i \(-0.431818\pi\)
\(264\) 0 0
\(265\) −12.0000 −0.737154
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) 8.00000 + 13.8564i 0.487769 + 0.844840i 0.999901 0.0140665i \(-0.00447764\pi\)
−0.512132 + 0.858906i \(0.671144\pi\)
\(270\) 0 0
\(271\) −7.50000 + 12.9904i −0.455593 + 0.789109i −0.998722 0.0505395i \(-0.983906\pi\)
0.543130 + 0.839649i \(0.317239\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 2.00000 3.46410i 0.120605 0.208893i
\(276\) 0 0
\(277\) 2.50000 + 4.33013i 0.150210 + 0.260172i 0.931305 0.364241i \(-0.118672\pi\)
−0.781094 + 0.624413i \(0.785338\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) −30.0000 −1.78965 −0.894825 0.446417i \(-0.852700\pi\)
−0.894825 + 0.446417i \(0.852700\pi\)
\(282\) 0 0
\(283\) −15.5000 26.8468i −0.921379 1.59588i −0.797283 0.603606i \(-0.793730\pi\)
−0.124096 0.992270i \(-0.539603\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 8.00000 + 6.92820i 0.472225 + 0.408959i
\(288\) 0 0
\(289\) 8.50000 14.7224i 0.500000 0.866025i
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) −24.0000 −1.40209 −0.701047 0.713115i \(-0.747284\pi\)
−0.701047 + 0.713115i \(0.747284\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) −3.00000 + 5.19615i −0.173494 + 0.300501i
\(300\) 0 0
\(301\) −2.00000 1.73205i −0.115278 0.0998337i
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) −3.00000 5.19615i −0.171780 0.297531i
\(306\) 0 0
\(307\) 1.00000 0.0570730 0.0285365 0.999593i \(-0.490915\pi\)
0.0285365 + 0.999593i \(0.490915\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 1.00000 + 1.73205i 0.0567048 + 0.0982156i 0.892984 0.450088i \(-0.148607\pi\)
−0.836280 + 0.548303i \(0.815274\pi\)
\(312\) 0 0
\(313\) 1.00000 1.73205i 0.0565233 0.0979013i −0.836379 0.548151i \(-0.815332\pi\)
0.892903 + 0.450250i \(0.148665\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −6.00000 + 10.3923i −0.336994 + 0.583690i −0.983866 0.178908i \(-0.942743\pi\)
0.646872 + 0.762598i \(0.276077\pi\)
\(318\) 0 0
\(319\) 0 0
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) 0 0
\(324\) 0 0
\(325\) −0.500000 0.866025i −0.0277350 0.0480384i
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) 10.0000 3.46410i 0.551318 0.190982i
\(330\) 0 0
\(331\) −4.00000 + 6.92820i −0.219860 + 0.380808i −0.954765 0.297361i \(-0.903893\pi\)
0.734905 + 0.678170i \(0.237227\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) −22.0000 −1.20199
\(336\) 0 0
\(337\) 2.00000 0.108947 0.0544735 0.998515i \(-0.482652\pi\)
0.0544735 + 0.998515i \(0.482652\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) −10.0000 + 17.3205i −0.541530 + 0.937958i
\(342\) 0 0
\(343\) −10.0000 + 15.5885i −0.539949 + 0.841698i
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) −6.00000 10.3923i −0.322097 0.557888i 0.658824 0.752297i \(-0.271054\pi\)
−0.980921 + 0.194409i \(0.937721\pi\)
\(348\) 0 0
\(349\) 9.00000 0.481759 0.240879 0.970555i \(-0.422564\pi\)
0.240879 + 0.970555i \(0.422564\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) 8.00000 + 13.8564i 0.425797 + 0.737502i 0.996495 0.0836583i \(-0.0266604\pi\)
−0.570697 + 0.821160i \(0.693327\pi\)
\(354\) 0 0
\(355\) 14.0000 24.2487i 0.743043 1.28699i
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) −9.00000 + 15.5885i −0.475002 + 0.822727i −0.999590 0.0286287i \(-0.990886\pi\)
0.524588 + 0.851356i \(0.324219\pi\)
\(360\) 0 0
\(361\) 1.50000 + 2.59808i 0.0789474 + 0.136741i
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) 28.0000 1.46559
\(366\) 0 0
\(367\) 4.00000 + 6.92820i 0.208798 + 0.361649i 0.951336 0.308155i \(-0.0997115\pi\)
−0.742538 + 0.669804i \(0.766378\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) 3.00000 15.5885i 0.155752 0.809312i
\(372\) 0 0
\(373\) −5.00000 + 8.66025i −0.258890 + 0.448411i −0.965945 0.258748i \(-0.916690\pi\)
0.707055 + 0.707159i \(0.250023\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 0 0
\(378\) 0 0
\(379\) 23.0000 1.18143 0.590715 0.806880i \(-0.298846\pi\)
0.590715 + 0.806880i \(0.298846\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) −15.0000 + 25.9808i −0.766464 + 1.32755i 0.173005 + 0.984921i \(0.444652\pi\)
−0.939469 + 0.342634i \(0.888681\pi\)
\(384\) 0 0
\(385\) −16.0000 13.8564i −0.815436 0.706188i
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) 2.00000 + 3.46410i 0.101404 + 0.175637i 0.912263 0.409604i \(-0.134333\pi\)
−0.810859 + 0.585241i \(0.801000\pi\)
\(390\) 0 0
\(391\) 0 0
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) 13.0000 + 22.5167i 0.654101 + 1.13294i
\(396\) 0 0
\(397\) −12.5000 + 21.6506i −0.627357 + 1.08661i 0.360723 + 0.932673i \(0.382530\pi\)
−0.988080 + 0.153941i \(0.950803\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) −6.00000 + 10.3923i −0.299626 + 0.518967i −0.976050 0.217545i \(-0.930195\pi\)
0.676425 + 0.736512i \(0.263528\pi\)
\(402\) 0 0
\(403\) 2.50000 + 4.33013i 0.124534 + 0.215699i
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 4.00000 0.198273
\(408\) 0 0
\(409\) −0.500000 0.866025i −0.0247234 0.0428222i 0.853399 0.521258i \(-0.174537\pi\)
−0.878122 + 0.478436i \(0.841204\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) 0 0
\(414\) 0 0
\(415\) −14.0000 + 24.2487i −0.687233 + 1.19032i
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 10.0000 0.488532 0.244266 0.969708i \(-0.421453\pi\)
0.244266 + 0.969708i \(0.421453\pi\)
\(420\) 0 0
\(421\) 34.0000 1.65706 0.828529 0.559946i \(-0.189178\pi\)
0.828529 + 0.559946i \(0.189178\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) 0 0
\(426\) 0 0
\(427\) 7.50000 2.59808i 0.362950 0.125730i
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) −10.0000 17.3205i −0.481683 0.834300i 0.518096 0.855323i \(-0.326641\pi\)
−0.999779 + 0.0210230i \(0.993308\pi\)
\(432\) 0 0
\(433\) 31.0000 1.48976 0.744882 0.667196i \(-0.232506\pi\)
0.744882 + 0.667196i \(0.232506\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) −12.0000 20.7846i −0.574038 0.994263i
\(438\) 0 0
\(439\) −12.0000 + 20.7846i −0.572729 + 0.991995i 0.423556 + 0.905870i \(0.360782\pi\)
−0.996284 + 0.0861252i \(0.972552\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) −12.0000 + 20.7846i −0.570137 + 0.987507i 0.426414 + 0.904528i \(0.359777\pi\)
−0.996551 + 0.0829786i \(0.973557\pi\)
\(444\) 0 0
\(445\) −6.00000 10.3923i −0.284427 0.492642i
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) 14.0000 0.660701 0.330350 0.943858i \(-0.392833\pi\)
0.330350 + 0.943858i \(0.392833\pi\)
\(450\) 0 0
\(451\) −8.00000 13.8564i −0.376705 0.652473i
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) −5.00000 + 1.73205i −0.234404 + 0.0811998i
\(456\) 0 0
\(457\) 11.5000 19.9186i 0.537947 0.931752i −0.461067 0.887365i \(-0.652533\pi\)
0.999014 0.0443868i \(-0.0141334\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) −12.0000 −0.558896 −0.279448 0.960161i \(-0.590151\pi\)
−0.279448 + 0.960161i \(0.590151\pi\)
\(462\) 0 0
\(463\) 32.0000 1.48717 0.743583 0.668644i \(-0.233125\pi\)
0.743583 + 0.668644i \(0.233125\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) −13.0000 + 22.5167i −0.601568 + 1.04195i 0.391015 + 0.920384i \(0.372124\pi\)
−0.992584 + 0.121563i \(0.961209\pi\)
\(468\) 0 0
\(469\) 5.50000 28.5788i 0.253966 1.31965i
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) 2.00000 + 3.46410i 0.0919601 + 0.159280i
\(474\) 0 0
\(475\) 4.00000 0.183533
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) 9.00000 + 15.5885i 0.411220 + 0.712255i 0.995023 0.0996406i \(-0.0317693\pi\)
−0.583803 + 0.811895i \(0.698436\pi\)
\(480\) 0 0
\(481\) 0.500000 0.866025i 0.0227980 0.0394874i
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 9.00000 15.5885i 0.408669 0.707835i
\(486\) 0 0
\(487\) 8.00000 + 13.8564i 0.362515 + 0.627894i 0.988374 0.152042i \(-0.0485850\pi\)
−0.625859 + 0.779936i \(0.715252\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) 30.0000 1.35388 0.676941 0.736038i \(-0.263305\pi\)
0.676941 + 0.736038i \(0.263305\pi\)
\(492\) 0 0
\(493\) 0 0
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 28.0000 + 24.2487i 1.25597 + 1.08770i
\(498\) 0 0
\(499\) 0.500000 0.866025i 0.0223831 0.0387686i −0.854617 0.519259i \(-0.826208\pi\)
0.877000 + 0.480490i \(0.159541\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) −22.0000 −0.980932 −0.490466 0.871460i \(-0.663173\pi\)
−0.490466 + 0.871460i \(0.663173\pi\)
\(504\) 0 0
\(505\) −20.0000 −0.889988
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) −19.0000 + 32.9090i −0.842160 + 1.45866i 0.0459045 + 0.998946i \(0.485383\pi\)
−0.888065 + 0.459718i \(0.847950\pi\)
\(510\) 0 0
\(511\) −7.00000 + 36.3731i −0.309662 + 1.60905i
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) −13.0000 22.5167i −0.572848 0.992203i
\(516\) 0 0
\(517\) −16.0000 −0.703679
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 3.00000 + 5.19615i 0.131432 + 0.227648i 0.924229 0.381839i \(-0.124709\pi\)
−0.792797 + 0.609486i \(0.791376\pi\)
\(522\) 0 0
\(523\) 8.50000 14.7224i 0.371679 0.643767i −0.618145 0.786064i \(-0.712116\pi\)
0.989824 + 0.142297i \(0.0454489\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 0 0
\(528\) 0 0
\(529\) −6.50000 11.2583i −0.282609 0.489493i
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) −4.00000 −0.173259
\(534\) 0 0
\(535\) −18.0000 31.1769i −0.778208 1.34790i
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) 22.0000 17.3205i 0.947607 0.746047i
\(540\) 0 0
\(541\) −1.00000 + 1.73205i −0.0429934 + 0.0744667i −0.886721 0.462304i \(-0.847023\pi\)
0.843728 + 0.536771i \(0.180356\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) 2.00000 0.0856706
\(546\) 0 0
\(547\) 39.0000 1.66752 0.833760 0.552127i \(-0.186184\pi\)
0.833760 + 0.552127i \(0.186184\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) 0 0
\(552\) 0 0
\(553\) −32.5000 + 11.2583i −1.38204 + 0.478753i
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) −17.0000 29.4449i −0.720313 1.24762i −0.960874 0.276985i \(-0.910665\pi\)
0.240561 0.970634i \(-0.422669\pi\)
\(558\) 0 0
\(559\) 1.00000 0.0422955
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) −5.00000 8.66025i −0.210725 0.364986i 0.741217 0.671266i \(-0.234249\pi\)
−0.951942 + 0.306280i \(0.900916\pi\)
\(564\) 0 0
\(565\) 10.0000 17.3205i 0.420703 0.728679i
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 19.0000 32.9090i 0.796521 1.37962i −0.125347 0.992113i \(-0.540004\pi\)
0.921869 0.387503i \(-0.126662\pi\)
\(570\) 0 0
\(571\) −2.00000 3.46410i −0.0836974 0.144968i 0.821138 0.570730i \(-0.193340\pi\)
−0.904835 + 0.425762i \(0.860006\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 6.00000 0.250217
\(576\) 0 0
\(577\) −9.50000 16.4545i −0.395490 0.685009i 0.597673 0.801740i \(-0.296092\pi\)
−0.993164 + 0.116731i \(0.962759\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) −28.0000 24.2487i −1.16164 1.00601i
\(582\) 0 0
\(583\) −12.0000 + 20.7846i −0.496989 + 0.860811i
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 30.0000 1.23823 0.619116 0.785299i \(-0.287491\pi\)
0.619116 + 0.785299i \(0.287491\pi\)
\(588\) 0 0
\(589\) −20.0000 −0.824086
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) 5.00000 8.66025i 0.205325 0.355634i −0.744911 0.667164i \(-0.767508\pi\)
0.950236 + 0.311530i \(0.100841\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(600\) 0 0
\(601\) −37.0000 −1.50926 −0.754631 0.656150i \(-0.772184\pi\)
−0.754631 + 0.656150i \(0.772184\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) 5.00000 + 8.66025i 0.203279 + 0.352089i
\(606\) 0 0
\(607\) −16.0000 + 27.7128i −0.649420 + 1.12483i 0.333842 + 0.942629i \(0.391655\pi\)
−0.983262 + 0.182199i \(0.941678\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) −2.00000 + 3.46410i −0.0809113 + 0.140143i
\(612\) 0 0
\(613\) 1.50000 + 2.59808i 0.0605844 + 0.104935i 0.894727 0.446614i \(-0.147370\pi\)
−0.834142 + 0.551549i \(0.814037\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 8.00000 0.322068 0.161034 0.986949i \(-0.448517\pi\)
0.161034 + 0.986949i \(0.448517\pi\)
\(618\) 0 0
\(619\) 2.50000 + 4.33013i 0.100483 + 0.174042i 0.911884 0.410448i \(-0.134628\pi\)
−0.811400 + 0.584491i \(0.801294\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 15.0000 5.19615i 0.600962 0.208179i
\(624\) 0 0
\(625\) 9.50000 16.4545i 0.380000 0.658179i
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 0 0
\(630\) 0 0
\(631\) 27.0000 1.07485 0.537427 0.843311i \(-0.319397\pi\)
0.537427 + 0.843311i \(0.319397\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) −11.0000 + 19.0526i −0.436522 + 0.756078i
\(636\) 0 0
\(637\) −1.00000 6.92820i −0.0396214 0.274505i
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) −18.0000 31.1769i −0.710957 1.23141i −0.964498 0.264089i \(-0.914929\pi\)
0.253541 0.967325i \(-0.418405\pi\)
\(642\) 0 0
\(643\) 19.0000 0.749287 0.374643 0.927169i \(-0.377765\pi\)
0.374643 + 0.927169i \(0.377765\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) −16.0000 27.7128i −0.629025 1.08950i −0.987748 0.156059i \(-0.950121\pi\)
0.358723 0.933444i \(-0.383212\pi\)
\(648\) 0 0
\(649\) 0 0
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 17.0000 29.4449i 0.665261 1.15227i −0.313953 0.949439i \(-0.601653\pi\)
0.979214 0.202828i \(-0.0650132\pi\)
\(654\) 0 0
\(655\) 16.0000 + 27.7128i 0.625172 + 1.08283i
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) 18.0000 0.701180 0.350590 0.936529i \(-0.385981\pi\)
0.350590 + 0.936529i \(0.385981\pi\)
\(660\) 0 0
\(661\) 11.0000 + 19.0526i 0.427850 + 0.741059i 0.996682 0.0813955i \(-0.0259377\pi\)
−0.568831 + 0.822454i \(0.692604\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 4.00000 20.7846i 0.155113 0.805993i
\(666\) 0 0
\(667\) 0 0
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) −12.0000 −0.463255
\(672\) 0 0
\(673\) −50.0000 −1.92736 −0.963679 0.267063i \(-0.913947\pi\)
−0.963679 + 0.267063i \(0.913947\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 18.0000 31.1769i 0.691796 1.19823i −0.279453 0.960159i \(-0.590153\pi\)
0.971249 0.238067i \(-0.0765137\pi\)
\(678\) 0 0
\(679\) 18.0000 + 15.5885i 0.690777 + 0.598230i
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) −9.00000 15.5885i −0.344375 0.596476i 0.640865 0.767654i \(-0.278576\pi\)
−0.985240 + 0.171178i \(0.945243\pi\)
\(684\) 0 0
\(685\) −36.0000 −1.37549
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) 3.00000 + 5.19615i 0.114291 + 0.197958i
\(690\) 0 0
\(691\) −0.500000 + 0.866025i −0.0190209 + 0.0329452i −0.875379 0.483437i \(-0.839388\pi\)
0.856358 + 0.516382i \(0.172722\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 1.00000 1.73205i 0.0379322 0.0657004i
\(696\) 0 0
\(697\) 0 0
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) 12.0000 0.453234 0.226617 0.973984i \(-0.427233\pi\)
0.226617 + 0.973984i \(0.427233\pi\)
\(702\) 0 0
\(703\) 2.00000 + 3.46410i 0.0754314 + 0.130651i
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 5.00000 25.9808i 0.188044 0.977107i
\(708\) 0 0
\(709\) 22.5000 38.9711i 0.845005 1.46359i −0.0406114 0.999175i \(-0.512931\pi\)
0.885617 0.464417i \(-0.153736\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) −30.0000 −1.12351
\(714\) 0 0
\(715\) 8.00000 0.299183
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) 13.0000 22.5167i 0.484818 0.839730i −0.515030 0.857172i \(-0.672219\pi\)
0.999848 + 0.0174426i \(0.00555244\pi\)
\(720\) 0 0
\(721\) 32.5000 11.2583i 1.21036 0.419282i
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) 0 0
\(726\) 0 0
\(727\) −5.00000 −0.185440 −0.0927199 0.995692i \(-0.529556\pi\)
−0.0927199 + 0.995692i \(0.529556\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) 0 0
\(732\) 0 0
\(733\) −17.5000 + 30.3109i −0.646377 + 1.11956i 0.337604 + 0.941288i \(0.390383\pi\)
−0.983982 + 0.178270i \(0.942950\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) −22.0000 + 38.1051i −0.810380 + 1.40362i
\(738\) 0 0
\(739\) 2.50000 + 4.33013i 0.0919640 + 0.159286i 0.908337 0.418238i \(-0.137352\pi\)
−0.816373 + 0.577524i \(0.804019\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) −8.00000 −0.293492 −0.146746 0.989174i \(-0.546880\pi\)
−0.146746 + 0.989174i \(0.546880\pi\)
\(744\) 0 0
\(745\) 6.00000 + 10.3923i 0.219823 + 0.380745i
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) 45.0000 15.5885i 1.64426 0.569590i
\(750\) 0 0
\(751\) −14.0000 + 24.2487i −0.510867 + 0.884848i 0.489053 + 0.872254i \(0.337342\pi\)
−0.999921 + 0.0125942i \(0.995991\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) −6.00000 −0.218362
\(756\) 0 0
\(757\) −29.0000 −1.05402 −0.527011 0.849858i \(-0.676688\pi\)
−0.527011 + 0.849858i \(0.676688\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(762\) 0 0
\(763\) −0.500000 + 2.59808i −0.0181012 + 0.0940567i
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 0 0
\(768\) 0 0
\(769\) 38.0000 1.37032 0.685158 0.728395i \(-0.259733\pi\)
0.685158 + 0.728395i \(0.259733\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) −2.00000 3.46410i −0.0719350 0.124595i 0.827814 0.561002i \(-0.189584\pi\)
−0.899749 + 0.436407i \(0.856251\pi\)
\(774\) 0 0
\(775\) 2.50000 4.33013i 0.0898027 0.155543i
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 8.00000 13.8564i 0.286630 0.496457i
\(780\) 0 0
\(781\) −28.0000 48.4974i −1.00192 1.73537i
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) 36.0000 1.28490
\(786\) 0 0
\(787\) −2.50000 4.33013i −0.0891154 0.154352i 0.818022 0.575187i \(-0.195071\pi\)
−0.907137 + 0.420834i \(0.861737\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 20.0000 + 17.3205i 0.711118 + 0.615846i
\(792\) 0 0
\(793\) −1.50000 + 2.59808i −0.0532666 + 0.0922604i
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 12.0000 0.425062 0.212531 0.977154i \(-0.431829\pi\)
0.212531 + 0.977154i \(0.431829\pi\)
\(798\) 0 0
\(799\) 0 0
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) 28.0000 48.4974i 0.988099 1.71144i
\(804\) 0 0
\(805\) 6.00000 31.1769i 0.211472 1.09884i
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) −11.0000 19.0526i −0.386739 0.669852i 0.605269 0.796021i \(-0.293065\pi\)
−0.992009 + 0.126168i \(0.959732\pi\)
\(810\) 0 0
\(811\) −20.0000 −0.702295 −0.351147 0.936320i \(-0.614208\pi\)
−0.351147 + 0.936320i \(0.614208\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) −21.0000 36.3731i −0.735598 1.27409i
\(816\) 0 0
\(817\) −2.00000 + 3.46410i −0.0699711 + 0.121194i
\(818\) 0