Properties

Label 1512.2.s.h.865.1
Level $1512$
Weight $2$
Character 1512.865
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 865.1
Root \(0.500000 + 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 1512.865
Dual form 1512.2.s.h.1297.1

$q$-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 \(\left(\mathbb{Z}/1512\mathbb{Z}\right)^\times\).

\(n\) \(757\) \(785\) \(1081\) \(1135\)
\(\chi(n)\) \(1\) \(1\) \(e\left(\frac{2}{3}\right)\) \(1\)

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 0.998203 0.0599153i \(-0.0190830\pi\)
−0.550990 + 0.834512i \(0.685750\pi\)
\(6\) 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 0.389338 + 0.921095i \(0.372704\pi\)
−0.992361 + 0.123371i \(0.960630\pi\)
\(12\) 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 \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(18\) 0 0
\(19\) 2.00000 + 3.46410i 0.458831 + 0.794719i 0.998899 0.0469020i \(-0.0149348\pi\)
−0.540068 + 0.841621i \(0.681602\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) 3.00000 + 5.19615i 0.625543 + 1.08347i 0.988436 + 0.151642i \(0.0484560\pi\)
−0.362892 + 0.931831i \(0.618211\pi\)
\(24\) 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 −0.998322 0.0579057i \(-0.981558\pi\)
0.549309 + 0.835619i \(0.314891\pi\)
\(32\) 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 0.821995 0.569495i \(-0.192861\pi\)
−0.904194 + 0.427121i \(0.859528\pi\)
\(38\) 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 0.974219 0.225605i \(-0.0724358\pi\)
−0.682489 + 0.730896i \(0.739102\pi\)
\(48\) 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 −0.995117 0.0987002i \(-0.968532\pi\)
0.583036 + 0.812447i \(0.301865\pi\)
\(54\) 0 0
\(55\) −8.00000 −1.07872
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(60\) 0 0
\(61\) 1.50000 + 2.59808i 0.192055 + 0.332650i 0.945931 0.324367i \(-0.105151\pi\)
−0.753876 + 0.657017i \(0.771818\pi\)
\(62\) 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 0.305424 + 0.952217i \(0.401202\pi\)
−0.977356 + 0.211604i \(0.932131\pi\)
\(68\) 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 −0.0869195 0.996215i \(-0.527702\pi\)
0.906208 0.422833i \(-0.138964\pi\)
\(74\) 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 −0.956325 0.292306i \(-0.905577\pi\)
0.225018 0.974355i \(-0.427756\pi\)
\(80\) 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 0.980071 0.198650i \(-0.0636557\pi\)
−0.662071 + 0.749441i \(0.730322\pi\)
\(90\) 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 −0.999996 0.00286291i \(-0.999089\pi\)
0.502477 + 0.864590i \(0.332422\pi\)
\(102\) 0 0
\(103\) 6.50000 + 11.2583i 0.640464 + 1.10932i 0.985329 + 0.170664i \(0.0545913\pi\)
−0.344865 + 0.938652i \(0.612075\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 9.00000 + 15.5885i 0.870063 + 1.50699i 0.861931 + 0.507026i \(0.169255\pi\)
0.00813215 + 0.999967i \(0.497411\pi\)
\(108\) 0 0
\(109\) 0.500000 0.866025i 0.0478913 0.0829502i −0.841086 0.540901i \(-0.818083\pi\)
0.888977 + 0.457951i \(0.151417\pi\)
\(110\) 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 −0.968826 0.247741i \(-0.920312\pi\)
0.269863 0.962899i \(-0.413022\pi\)
\(132\) 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 0.169226 + 0.985577i \(0.445873\pi\)
−0.938148 + 0.346235i \(0.887460\pi\)
\(138\) 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 0.716578 0.697507i \(-0.245707\pi\)
−0.962348 + 0.271821i \(0.912374\pi\)
\(150\) 0 0
\(151\) −1.50000 + 2.59808i −0.122068 + 0.211428i −0.920583 0.390547i \(-0.872286\pi\)
0.798515 + 0.601975i \(0.205619\pi\)
\(152\) 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 −0.243403 0.969925i \(-0.578264\pi\)
0.961681 0.274169i \(-0.0884028\pi\)
\(158\) 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 0.903873 + 0.427802i \(0.140712\pi\)
−0.0814491 + 0.996678i \(0.525955\pi\)
\(164\) 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 −0.810745 0.585399i \(-0.800938\pi\)
−0.101598 0.994826i \(-0.532395\pi\)
\(174\) 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 −0.826231 0.563331i \(-0.809520\pi\)
0.900975 + 0.433872i \(0.142853\pi\)
\(180\) 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 −0.922246 0.386604i \(-0.873648\pi\)
0.126314 0.991990i \(-0.459685\pi\)
\(192\) 0 0
\(193\) 8.50000 14.7224i 0.611843 1.05974i −0.379086 0.925361i \(-0.623762\pi\)
0.990930 0.134382i \(-0.0429051\pi\)
\(194\) 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 −0.467656 0.883911i \(-0.654901\pi\)
0.999317 0.0369532i \(-0.0117652\pi\)
\(200\) 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 −0.226746 0.973954i \(-0.572809\pi\)
0.956842 0.290609i \(-0.0938578\pi\)
\(228\) 0 0
\(229\) −9.50000 16.4545i −0.627778 1.08734i −0.987997 0.154475i \(-0.950631\pi\)
0.360219 0.932868i \(-0.382702\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) −8.00000 13.8564i −0.524097 0.907763i −0.999606 0.0280525i \(-0.991069\pi\)
0.475509 0.879711i \(-0.342264\pi\)
\(234\) 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 −0.881680 0.471848i \(-0.843587\pi\)
0.849472 + 0.527633i \(0.176921\pi\)
\(242\) 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 −0.973070 0.230508i \(-0.925961\pi\)
0.286909 0.957958i \(-0.407372\pi\)
\(258\) 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 0.212565 + 0.977147i \(0.431818\pi\)
−0.952517 + 0.304487i \(0.901515\pi\)
\(264\) 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 −0.512132 0.858906i \(-0.671144\pi\)
0.999901 + 0.0140665i \(0.00447764\pi\)
\(270\) 0 0
\(271\) −7.50000 12.9904i −0.455593 0.789109i 0.543130 0.839649i \(-0.317239\pi\)
−0.998722 + 0.0505395i \(0.983906\pi\)
\(272\) 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 −0.781094 0.624413i \(-0.785338\pi\)
0.931305 + 0.364241i \(0.118672\pi\)
\(278\) 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 −0.124096 + 0.992270i \(0.539603\pi\)
−0.797283 + 0.603606i \(0.793730\pi\)
\(284\) 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 −0.836280 0.548303i \(-0.815274\pi\)
0.892984 + 0.450088i \(0.148607\pi\)
\(312\) 0 0
\(313\) 1.00000 + 1.73205i 0.0565233 + 0.0979013i 0.892903 0.450250i \(-0.148665\pi\)
−0.836379 + 0.548151i \(0.815332\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −6.00000 10.3923i −0.336994 0.583690i 0.646872 0.762598i \(-0.276077\pi\)
−0.983866 + 0.178908i \(0.942743\pi\)
\(318\) 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 0.734905 0.678170i \(-0.237227\pi\)
−0.954765 + 0.297361i \(0.903893\pi\)
\(332\) 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 −0.980921 0.194409i \(-0.937721\pi\)
0.658824 + 0.752297i \(0.271054\pi\)
\(348\) 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 −0.570697 0.821160i \(-0.693327\pi\)
0.996495 + 0.0836583i \(0.0266604\pi\)
\(354\) 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 0.524588 0.851356i \(-0.324219\pi\)
−0.999590 + 0.0286287i \(0.990886\pi\)
\(360\) 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 −0.742538 0.669804i \(-0.766378\pi\)
0.951336 + 0.308155i \(0.0997115\pi\)
\(368\) 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 0.707055 0.707159i \(-0.250023\pi\)
−0.965945 + 0.258748i \(0.916690\pi\)
\(374\) 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 −0.939469 0.342634i \(-0.888681\pi\)
0.173005 0.984921i \(-0.444652\pi\)
\(384\) 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 −0.810859 0.585241i \(-0.801000\pi\)
0.912263 + 0.409604i \(0.134333\pi\)
\(390\) 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 −0.988080 0.153941i \(-0.950803\pi\)
0.360723 0.932673i \(-0.382530\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) −6.00000 10.3923i −0.299626 0.518967i 0.676425 0.736512i \(-0.263528\pi\)
−0.976050 + 0.217545i \(0.930195\pi\)
\(402\) 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 −0.878122 0.478436i \(-0.841204\pi\)
0.853399 + 0.521258i \(0.174537\pi\)
\(410\) 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 −0.999779 0.0210230i \(-0.993308\pi\)
0.518096 + 0.855323i \(0.326641\pi\)
\(432\) 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 −0.996284 0.0861252i \(-0.972552\pi\)
0.423556 0.905870i \(-0.360782\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) −12.0000 20.7846i −0.570137 0.987507i −0.996551 0.0829786i \(-0.973557\pi\)
0.426414 0.904528i \(-0.359777\pi\)
\(444\) 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 0.999014 + 0.0443868i \(0.0141334\pi\)
−0.461067 + 0.887365i \(0.652533\pi\)
\(458\) 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 −0.992584 0.121563i \(-0.961209\pi\)
0.391015 0.920384i \(-0.372124\pi\)
\(468\) 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 −0.583803 0.811895i \(-0.698436\pi\)
0.995023 + 0.0996406i \(0.0317693\pi\)
\(480\) 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 −0.625859 0.779936i \(-0.715252\pi\)
0.988374 + 0.152042i \(0.0485850\pi\)
\(488\) 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 0.877000 0.480490i \(-0.159541\pi\)
−0.854617 + 0.519259i \(0.826208\pi\)
\(500\) 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 −0.888065 0.459718i \(-0.847950\pi\)
0.0459045 0.998946i \(-0.485383\pi\)
\(510\) 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 −0.792797 0.609486i \(-0.791376\pi\)
0.924229 + 0.381839i \(0.124709\pi\)
\(522\) 0 0
\(523\) 8.50000 + 14.7224i 0.371679 + 0.643767i 0.989824 0.142297i \(-0.0454489\pi\)
−0.618145 + 0.786064i \(0.712116\pi\)
\(524\) 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 0.843728 0.536771i \(-0.180356\pi\)
−0.886721 + 0.462304i \(0.847023\pi\)
\(542\) 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 0.240561 + 0.970634i \(0.422669\pi\)
−0.960874 + 0.276985i \(0.910665\pi\)
\(558\) 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 −0.951942 0.306280i \(-0.900916\pi\)
0.741217 + 0.671266i \(0.234249\pi\)
\(564\) 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 0.921869 + 0.387503i \(0.126662\pi\)
−0.125347 + 0.992113i \(0.540004\pi\)
\(570\) 0 0
\(571\) −2.00000 + 3.46410i −0.0836974 + 0.144968i −0.904835 0.425762i \(-0.860006\pi\)
0.821138 + 0.570730i \(0.193340\pi\)
\(572\) 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 −0.993164 0.116731i \(-0.962759\pi\)
0.597673 + 0.801740i \(0.296092\pi\)
\(578\) 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 0.950236 0.311530i \(-0.100841\pi\)
−0.744911 + 0.667164i \(0.767508\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(600\) 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 −0.983262 0.182199i \(-0.941678\pi\)
0.333842 0.942629i \(-0.391655\pi\)
\(608\) 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 −0.834142 0.551549i \(-0.814037\pi\)
0.894727 + 0.446614i \(0.147370\pi\)
\(614\) 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 −0.811400 0.584491i \(-0.801294\pi\)
0.911884 + 0.410448i \(0.134628\pi\)
\(620\) 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 0.253541 + 0.967325i \(0.418405\pi\)
−0.964498 + 0.264089i \(0.914929\pi\)
\(642\) 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 0.358723 + 0.933444i \(0.383212\pi\)
−0.987748 + 0.156059i \(0.950121\pi\)
\(648\) 0 0
\(649\) 0 0
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 17.0000 + 29.4449i 0.665261 + 1.15227i 0.979214 + 0.202828i \(0.0650132\pi\)
−0.313953 + 0.949439i \(0.601653\pi\)
\(654\) 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 −0.568831 0.822454i \(-0.692604\pi\)
0.996682 + 0.0813955i \(0.0259377\pi\)
\(662\) 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 0.971249 + 0.238067i \(0.0765137\pi\)
−0.279453 + 0.960159i \(0.590153\pi\)
\(678\) 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 −0.985240 0.171178i \(-0.945243\pi\)
0.640865 + 0.767654i \(0.278576\pi\)
\(684\) 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 0.856358 0.516382i \(-0.172722\pi\)
−0.875379 + 0.483437i \(0.839388\pi\)
\(692\) 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 0.885617 + 0.464417i \(0.153736\pi\)
−0.0406114 + 0.999175i \(0.512931\pi\)
\(710\) 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 0.999848 0.0174426i \(-0.00555244\pi\)
−0.515030 + 0.857172i \(0.672219\pi\)
\(720\) 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 −0.983982 0.178270i \(-0.942950\pi\)
0.337604 0.941288i \(-0.390383\pi\)
\(734\) 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 −0.816373 0.577524i \(-0.804019\pi\)
0.908337 + 0.418238i \(0.137352\pi\)
\(740\) 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 −0.999921 0.0125942i \(-0.995991\pi\)
0.489053 0.872254i \(-0.337342\pi\)
\(752\) 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 \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(762\) 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 −0.899749 0.436407i \(-0.856251\pi\)
0.827814 + 0.561002i \(0.189584\pi\)
\(774\) 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 −0.907137 0.420834i \(-0.861737\pi\)
0.818022 + 0.575187i \(0.195071\pi\)
\(788\) 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 −0.992009 0.126168i \(-0.959732\pi\)
0.605269 + 0.796021i \(0.293065\pi\)
\(810\) 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