Properties

Label 1008.2.cs.b.271.1
Level 1008
Weight 2
Character 1008.271
Analytic conductor 8.049
Analytic rank 0
Dimension 2
CM no
Inner twists 2

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Newspace parameters

Level: \( N \) \(=\) \( 1008 = 2^{4} \cdot 3^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1008.cs (of order \(6\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(8.04892052375\)
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: no (minimal twist has level 336)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 271.1
Root \(0.500000 - 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 1008.271
Dual form 1008.2.cs.b.703.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-3.00000 - 1.73205i) q^{5} +(0.500000 + 2.59808i) q^{7} +O(q^{10})\) \(q+(-3.00000 - 1.73205i) q^{5} +(0.500000 + 2.59808i) q^{7} +(3.00000 - 1.73205i) q^{11} +1.73205i q^{13} +(2.50000 - 4.33013i) q^{19} +(-6.00000 - 3.46410i) q^{23} +(3.50000 + 6.06218i) q^{25} +(-2.50000 - 4.33013i) q^{31} +(3.00000 - 8.66025i) q^{35} +(5.50000 - 9.52628i) q^{37} -3.46410i q^{41} -8.66025i q^{43} +(3.00000 - 5.19615i) q^{47} +(-6.50000 + 2.59808i) q^{49} +(6.00000 + 10.3923i) q^{53} -12.0000 q^{55} +(-6.00000 - 10.3923i) q^{59} +(-12.0000 - 6.92820i) q^{61} +(3.00000 - 5.19615i) q^{65} +(7.50000 - 4.33013i) q^{67} +3.46410i q^{71} +(-4.50000 + 2.59808i) q^{73} +(6.00000 + 6.92820i) q^{77} +(10.5000 + 6.06218i) q^{79} +18.0000 q^{83} +(-6.00000 - 3.46410i) q^{89} +(-4.50000 + 0.866025i) q^{91} +(-15.0000 + 8.66025i) q^{95} -6.92820i q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2q - 6q^{5} + q^{7} + O(q^{10}) \) \( 2q - 6q^{5} + q^{7} + 6q^{11} + 5q^{19} - 12q^{23} + 7q^{25} - 5q^{31} + 6q^{35} + 11q^{37} + 6q^{47} - 13q^{49} + 12q^{53} - 24q^{55} - 12q^{59} - 24q^{61} + 6q^{65} + 15q^{67} - 9q^{73} + 12q^{77} + 21q^{79} + 36q^{83} - 12q^{89} - 9q^{91} - 30q^{95} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1008\mathbb{Z}\right)^\times\).

\(n\) \(127\) \(577\) \(757\) \(785\)
\(\chi(n)\) \(-1\) \(e\left(\frac{5}{6}\right)\) \(1\) \(1\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) 0 0
\(4\) 0 0
\(5\) −3.00000 1.73205i −1.34164 0.774597i −0.354593 0.935021i \(-0.615380\pi\)
−0.987048 + 0.160424i \(0.948714\pi\)
\(6\) 0 0
\(7\) 0.500000 + 2.59808i 0.188982 + 0.981981i
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) 3.00000 1.73205i 0.904534 0.522233i 0.0258656 0.999665i \(-0.491766\pi\)
0.878668 + 0.477432i \(0.158432\pi\)
\(12\) 0 0
\(13\) 1.73205i 0.480384i 0.970725 + 0.240192i \(0.0772105\pi\)
−0.970725 + 0.240192i \(0.922790\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(18\) 0 0
\(19\) 2.50000 4.33013i 0.573539 0.993399i −0.422659 0.906289i \(-0.638903\pi\)
0.996199 0.0871106i \(-0.0277634\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) −6.00000 3.46410i −1.25109 0.722315i −0.279761 0.960070i \(-0.590255\pi\)
−0.971325 + 0.237754i \(0.923589\pi\)
\(24\) 0 0
\(25\) 3.50000 + 6.06218i 0.700000 + 1.21244i
\(26\) 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
\(35\) 3.00000 8.66025i 0.507093 1.46385i
\(36\) 0 0
\(37\) 5.50000 9.52628i 0.904194 1.56611i 0.0821995 0.996616i \(-0.473806\pi\)
0.821995 0.569495i \(-0.192861\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) 3.46410i 0.541002i −0.962720 0.270501i \(-0.912811\pi\)
0.962720 0.270501i \(-0.0871893\pi\)
\(42\) 0 0
\(43\) 8.66025i 1.32068i −0.750968 0.660338i \(-0.770413\pi\)
0.750968 0.660338i \(-0.229587\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 3.00000 5.19615i 0.437595 0.757937i −0.559908 0.828554i \(-0.689164\pi\)
0.997503 + 0.0706177i \(0.0224970\pi\)
\(48\) 0 0
\(49\) −6.50000 + 2.59808i −0.928571 + 0.371154i
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) 6.00000 + 10.3923i 0.824163 + 1.42749i 0.902557 + 0.430570i \(0.141688\pi\)
−0.0783936 + 0.996922i \(0.524979\pi\)
\(54\) 0 0
\(55\) −12.0000 −1.61808
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) −6.00000 10.3923i −0.781133 1.35296i −0.931282 0.364299i \(-0.881308\pi\)
0.150148 0.988663i \(1.54798\pi\)
\(60\) 0 0
\(61\) −12.0000 6.92820i −1.53644 0.887066i −0.999043 0.0437377i \(-0.986073\pi\)
−0.537400 0.843328i \(-0.680593\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) 3.00000 5.19615i 0.372104 0.644503i
\(66\) 0 0
\(67\) 7.50000 4.33013i 0.916271 0.529009i 0.0338274 0.999428i \(-0.489230\pi\)
0.882443 + 0.470418i \(0.155897\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 3.46410i 0.411113i 0.978645 + 0.205557i \(0.0659005\pi\)
−0.978645 + 0.205557i \(0.934100\pi\)
\(72\) 0 0
\(73\) −4.50000 + 2.59808i −0.526685 + 0.304082i −0.739666 0.672975i \(-0.765016\pi\)
0.212980 + 0.977056i \(0.431683\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 6.00000 + 6.92820i 0.683763 + 0.789542i
\(78\) 0 0
\(79\) 10.5000 + 6.06218i 1.18134 + 0.682048i 0.956325 0.292306i \(-0.0944227\pi\)
0.225018 + 0.974355i \(0.427756\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) 18.0000 1.97576 0.987878 0.155230i \(-0.0496119\pi\)
0.987878 + 0.155230i \(0.0496119\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) −6.00000 3.46410i −0.635999 0.367194i 0.147073 0.989126i \(-0.453015\pi\)
−0.783072 + 0.621932i \(0.786348\pi\)
\(90\) 0 0
\(91\) −4.50000 + 0.866025i −0.471728 + 0.0907841i
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) −15.0000 + 8.66025i −1.53897 + 0.888523i
\(96\) 0 0
\(97\) 6.92820i 0.703452i −0.936103 0.351726i \(-0.885595\pi\)
0.936103 0.351726i \(-0.114405\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) −9.00000 + 5.19615i −0.895533 + 0.517036i −0.875748 0.482768i \(-0.839632\pi\)
−0.0197851 + 0.999804i \(0.506298\pi\)
\(102\) 0 0
\(103\) −2.50000 + 4.33013i −0.246332 + 0.426660i −0.962505 0.271263i \(-0.912559\pi\)
0.716173 + 0.697923i \(0.245892\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(108\) 0 0
\(109\) 3.50000 + 6.06218i 0.335239 + 0.580651i 0.983531 0.180741i \(-0.0578495\pi\)
−0.648292 + 0.761392i \(0.724516\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) 6.00000 0.564433 0.282216 0.959351i \(-0.408930\pi\)
0.282216 + 0.959351i \(0.408930\pi\)
\(114\) 0 0
\(115\) 12.0000 + 20.7846i 1.11901 + 1.93817i
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) 0 0
\(120\) 0 0
\(121\) 0.500000 0.866025i 0.0454545 0.0787296i
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) 6.92820i 0.619677i
\(126\) 0 0
\(127\) 12.1244i 1.07586i −0.842989 0.537931i \(-0.819206\pi\)
0.842989 0.537931i \(-0.180794\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) −3.00000 + 5.19615i −0.262111 + 0.453990i −0.966803 0.255524i \(-0.917752\pi\)
0.704692 + 0.709514i \(0.251085\pi\)
\(132\) 0 0
\(133\) 12.5000 + 4.33013i 1.08389 + 0.375470i
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 6.00000 + 10.3923i 0.512615 + 0.887875i 0.999893 + 0.0146279i \(0.00465636\pi\)
−0.487278 + 0.873247i \(0.662010\pi\)
\(138\) 0 0
\(139\) −7.00000 −0.593732 −0.296866 0.954919i \(-0.595942\pi\)
−0.296866 + 0.954919i \(0.595942\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 3.00000 + 5.19615i 0.250873 + 0.434524i
\(144\) 0 0
\(145\) 0 0
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) 6.00000 10.3923i 0.491539 0.851371i −0.508413 0.861113i \(-0.669768\pi\)
0.999953 + 0.00974235i \(0.00310113\pi\)
\(150\) 0 0
\(151\) 3.00000 1.73205i 0.244137 0.140952i −0.372940 0.927855i \(-0.621650\pi\)
0.617076 + 0.786903i \(0.288317\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 17.3205i 1.39122i
\(156\) 0 0
\(157\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 6.00000 17.3205i 0.472866 1.36505i
\(162\) 0 0
\(163\) −3.00000 1.73205i −0.234978 0.135665i 0.377888 0.925851i \(-0.376650\pi\)
−0.612866 + 0.790186i \(0.709984\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 6.00000 0.464294 0.232147 0.972681i \(-0.425425\pi\)
0.232147 + 0.972681i \(0.425425\pi\)
\(168\) 0 0
\(169\) 10.0000 0.769231
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) −6.00000 3.46410i −0.456172 0.263371i 0.254262 0.967135i \(-0.418168\pi\)
−0.710433 + 0.703765i \(0.751501\pi\)
\(174\) 0 0
\(175\) −14.0000 + 12.1244i −1.05830 + 0.916515i
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) 9.00000 5.19615i 0.672692 0.388379i −0.124404 0.992232i \(-0.539702\pi\)
0.797096 + 0.603853i \(0.206369\pi\)
\(180\) 0 0
\(181\) 5.19615i 0.386227i 0.981176 + 0.193113i \(0.0618586\pi\)
−0.981176 + 0.193113i \(0.938141\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) −33.0000 + 19.0526i −2.42621 + 1.40077i
\(186\) 0 0
\(187\) 0 0
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) −15.0000 8.66025i −1.08536 0.626634i −0.153024 0.988222i \(-0.548901\pi\)
−0.932338 + 0.361588i \(0.882235\pi\)
\(192\) 0 0
\(193\) 5.50000 + 9.52628i 0.395899 + 0.685717i 0.993215 0.116289i \(-0.0370998\pi\)
−0.597317 + 0.802005i \(0.703766\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) −24.0000 −1.70993 −0.854965 0.518686i \(-0.826421\pi\)
−0.854965 + 0.518686i \(0.826421\pi\)
\(198\) 0 0
\(199\) −8.00000 13.8564i −0.567105 0.982255i −0.996850 0.0793045i \(-0.974730\pi\)
0.429745 0.902950i \(1.64140\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) 0 0
\(204\) 0 0
\(205\) −6.00000 + 10.3923i −0.419058 + 0.725830i
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) 17.3205i 1.19808i
\(210\) 0 0
\(211\) 3.46410i 0.238479i −0.992866 0.119239i \(-0.961954\pi\)
0.992866 0.119239i \(-0.0380456\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) −15.0000 + 25.9808i −1.02299 + 1.77187i
\(216\) 0 0
\(217\) 10.0000 8.66025i 0.678844 0.587896i
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) 0 0
\(222\) 0 0
\(223\) 16.0000 1.07144 0.535720 0.844396i \(-0.320040\pi\)
0.535720 + 0.844396i \(0.320040\pi\)
\(224\) 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
\(229\) 7.50000 + 4.33013i 0.495614 + 0.286143i 0.726900 0.686743i \(-0.240960\pi\)
−0.231287 + 0.972886i \(0.574293\pi\)
\(230\) 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
\(235\) −18.0000 + 10.3923i −1.17419 + 0.677919i
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) 10.3923i 0.672222i 0.941822 + 0.336111i \(0.109112\pi\)
−0.941822 + 0.336111i \(0.890888\pi\)
\(240\) 0 0
\(241\) −12.0000 + 6.92820i −0.772988 + 0.446285i −0.833939 0.551856i \(-0.813920\pi\)
0.0609515 + 0.998141i \(0.480586\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) 24.0000 + 3.46410i 1.53330 + 0.221313i
\(246\) 0 0
\(247\) 7.50000 + 4.33013i 0.477214 + 0.275519i
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) −12.0000 −0.757433 −0.378717 0.925513i \(-0.623635\pi\)
−0.378717 + 0.925513i \(0.623635\pi\)
\(252\) 0 0
\(253\) −24.0000 −1.50887
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 15.0000 + 8.66025i 0.935674 + 0.540212i 0.888602 0.458680i \(-0.151677\pi\)
0.0470726 + 0.998891i \(0.485011\pi\)
\(258\) 0 0
\(259\) 27.5000 + 9.52628i 1.70877 + 0.591934i
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) −12.0000 + 6.92820i −0.739952 + 0.427211i −0.822052 0.569413i \(-0.807171\pi\)
0.0821001 + 0.996624i \(0.473837\pi\)
\(264\) 0 0
\(265\) 41.5692i 2.55358i
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) 15.0000 8.66025i 0.914566 0.528025i 0.0326687 0.999466i \(-0.489599\pi\)
0.881897 + 0.471441i \(0.156266\pi\)
\(270\) 0 0
\(271\) −4.00000 + 6.92820i −0.242983 + 0.420858i −0.961563 0.274586i \(-0.911459\pi\)
0.718580 + 0.695444i \(0.244792\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 21.0000 + 12.1244i 1.26635 + 0.731126i
\(276\) 0 0
\(277\) −9.50000 16.4545i −0.570800 0.988654i −0.996484 0.0837823i \(-0.973300\pi\)
0.425684 0.904872i \(-0.360033\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(282\) 0 0
\(283\) −3.50000 6.06218i −0.208053 0.360359i 0.743048 0.669238i \(-0.233379\pi\)
−0.951101 + 0.308879i \(0.900046\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 9.00000 1.73205i 0.531253 0.102240i
\(288\) 0 0
\(289\) −8.50000 + 14.7224i −0.500000 + 0.866025i
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) 20.7846i 1.21425i −0.794606 0.607125i \(-0.792323\pi\)
0.794606 0.607125i \(-0.207677\pi\)
\(294\) 0 0
\(295\) 41.5692i 2.42025i
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 6.00000 10.3923i 0.346989 0.601003i
\(300\) 0 0
\(301\) 22.5000 4.33013i 1.29688 0.249584i
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) 24.0000 + 41.5692i 1.37424 + 2.38025i
\(306\) 0 0
\(307\) −11.0000 −0.627803 −0.313902 0.949456i \(-0.601636\pi\)
−0.313902 + 0.949456i \(0.601636\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 9.00000 + 15.5885i 0.510343 + 0.883940i 0.999928 + 0.0119847i \(0.00381495\pi\)
−0.489585 + 0.871956i \(0.662852\pi\)
\(312\) 0 0
\(313\) 13.5000 + 7.79423i 0.763065 + 0.440556i 0.830395 0.557175i \(-0.188115\pi\)
−0.0673300 + 0.997731i \(0.521448\pi\)
\(314\) 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
\(325\) −10.5000 + 6.06218i −0.582435 + 0.336269i
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) 15.0000 + 5.19615i 0.826977 + 0.286473i
\(330\) 0 0
\(331\) 13.5000 + 7.79423i 0.742027 + 0.428410i 0.822806 0.568323i \(-0.192407\pi\)
−0.0807788 + 0.996732i \(0.525741\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) −30.0000 −1.63908
\(336\) 0 0
\(337\) −19.0000 −1.03500 −0.517498 0.855684i \(-0.673136\pi\)
−0.517498 + 0.855684i \(0.673136\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) −15.0000 8.66025i −0.812296 0.468979i
\(342\) 0 0
\(343\) −10.0000 15.5885i −0.539949 0.841698i
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 24.0000 13.8564i 1.28839 0.743851i 0.310021 0.950730i \(-0.399664\pi\)
0.978367 + 0.206879i \(0.0663306\pi\)
\(348\) 0 0
\(349\) 13.8564i 0.741716i 0.928689 + 0.370858i \(0.120936\pi\)
−0.928689 + 0.370858i \(0.879064\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) −21.0000 + 12.1244i −1.11772 + 0.645314i −0.940817 0.338914i \(-0.889940\pi\)
−0.176900 + 0.984229i \(0.556607\pi\)
\(354\) 0 0
\(355\) 6.00000 10.3923i 0.318447 0.551566i
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 18.0000 + 10.3923i 0.950004 + 0.548485i 0.893082 0.449894i \(-0.148538\pi\)
0.0569216 + 0.998379i \(0.481871\pi\)
\(360\) 0 0
\(361\) −3.00000 5.19615i −0.157895 0.273482i
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) 18.0000 0.942163
\(366\) 0 0
\(367\) 5.50000 + 9.52628i 0.287098 + 0.497268i 0.973116 0.230317i \(-0.0739762\pi\)
−0.686018 + 0.727585i \(0.740643\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) −24.0000 + 20.7846i −1.24602 + 1.07908i
\(372\) 0 0
\(373\) 0.500000 0.866025i 0.0258890 0.0448411i −0.852791 0.522253i \(-0.825092\pi\)
0.878680 + 0.477412i \(0.158425\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 0 0
\(378\) 0 0
\(379\) 8.66025i 0.444847i −0.974950 0.222424i \(-0.928603\pi\)
0.974950 0.222424i \(-0.0713968\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 12.0000 20.7846i 0.613171 1.06204i −0.377531 0.925997i \(-0.623227\pi\)
0.990702 0.136047i \(-0.0434398\pi\)
\(384\) 0 0
\(385\) −6.00000 31.1769i −0.305788 1.58892i
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) −3.00000 5.19615i −0.152106 0.263455i 0.779895 0.625910i \(-0.215272\pi\)
−0.932002 + 0.362454i \(0.881939\pi\)
\(390\) 0 0
\(391\) 0 0
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) −21.0000 36.3731i −1.05662 1.83013i
\(396\) 0 0
\(397\) −1.50000 0.866025i −0.0752828 0.0434646i 0.461886 0.886939i \(-0.347173\pi\)
−0.537169 + 0.843475i \(0.680506\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 6.00000 10.3923i 0.299626 0.518967i −0.676425 0.736512i \(-0.736472\pi\)
0.976050 + 0.217545i \(0.0698049\pi\)
\(402\) 0 0
\(403\) 7.50000 4.33013i 0.373602 0.215699i
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 38.1051i 1.88880i
\(408\) 0 0
\(409\) −19.5000 + 11.2583i −0.964213 + 0.556689i −0.897467 0.441081i \(-0.854595\pi\)
−0.0667458 + 0.997770i \(0.521262\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) 24.0000 20.7846i 1.18096 1.02274i
\(414\) 0 0
\(415\) −54.0000 31.1769i −2.65076 1.53041i
\(416\) 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
\(421\) 7.00000 0.341159 0.170580 0.985344i \(-0.445436\pi\)
0.170580 + 0.985344i \(0.445436\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) 0 0
\(426\) 0 0
\(427\) 12.0000 34.6410i 0.580721 1.67640i
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) −21.0000 + 12.1244i −1.01153 + 0.584010i −0.911641 0.410988i \(-0.865184\pi\)
−0.0998939 + 0.994998i \(0.531850\pi\)
\(432\) 0 0
\(433\) 1.73205i 0.0832370i 0.999134 + 0.0416185i \(0.0132514\pi\)
−0.999134 + 0.0416185i \(0.986749\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) −30.0000 + 17.3205i −1.43509 + 0.828552i
\(438\) 0 0
\(439\) 4.00000 6.92820i 0.190910 0.330665i −0.754642 0.656136i \(-0.772190\pi\)
0.945552 + 0.325471i \(0.105523\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) −12.0000 6.92820i −0.570137 0.329169i 0.187067 0.982347i \(-0.440102\pi\)
−0.757204 + 0.653178i \(0.773435\pi\)
\(444\) 0 0
\(445\) 12.0000 + 20.7846i 0.568855 + 0.985285i
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) −30.0000 −1.41579 −0.707894 0.706319i \(-0.750354\pi\)
−0.707894 + 0.706319i \(0.750354\pi\)
\(450\) 0 0
\(451\) −6.00000 10.3923i −0.282529 0.489355i
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) 15.0000 + 5.19615i 0.703211 + 0.243599i
\(456\) 0 0
\(457\) 9.50000 16.4545i 0.444391 0.769708i −0.553618 0.832771i \(-0.686753\pi\)
0.998010 + 0.0630623i \(0.0200867\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 13.8564i 0.645357i −0.946509 0.322679i \(-0.895417\pi\)
0.946509 0.322679i \(-0.104583\pi\)
\(462\) 0 0
\(463\) 15.5885i 0.724457i 0.932089 + 0.362229i \(0.117984\pi\)
−0.932089 + 0.362229i \(0.882016\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 15.0000 25.9808i 0.694117 1.20225i −0.276360 0.961054i \(-0.589128\pi\)
0.970477 0.241192i \(-0.0775384\pi\)
\(468\) 0 0
\(469\) 15.0000 + 17.3205i 0.692636 + 0.799787i
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) −15.0000 25.9808i −0.689701 1.19460i
\(474\) 0 0
\(475\) 35.0000 1.60591
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) −6.00000 10.3923i −0.274147 0.474837i 0.695773 0.718262i \(-0.255062\pi\)
−0.969920 + 0.243426i \(0.921729\pi\)
\(480\) 0 0
\(481\) 16.5000 + 9.52628i 0.752335 + 0.434361i
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) −12.0000 + 20.7846i −0.544892 + 0.943781i
\(486\) 0 0
\(487\) 22.5000 12.9904i 1.01957 0.588650i 0.105592 0.994410i \(-0.466326\pi\)
0.913980 + 0.405759i \(0.132993\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) 34.6410i 1.56333i −0.623700 0.781664i \(-0.714371\pi\)
0.623700 0.781664i \(-0.285629\pi\)
\(492\) 0 0
\(493\) 0 0
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) −9.00000 + 1.73205i −0.403705 + 0.0776931i
\(498\) 0 0
\(499\) −28.5000 16.4545i −1.27584 0.736604i −0.299755 0.954016i \(-0.596905\pi\)
−0.976080 + 0.217412i \(0.930238\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) 6.00000 0.267527 0.133763 0.991013i \(-0.457294\pi\)
0.133763 + 0.991013i \(0.457294\pi\)
\(504\) 0 0
\(505\) 36.0000 1.60198
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) −27.0000 15.5885i −1.19675 0.690946i −0.236924 0.971528i \(-0.576139\pi\)
−0.959830 + 0.280582i \(0.909473\pi\)
\(510\) 0 0
\(511\) −9.00000 10.3923i −0.398137 0.459728i
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) 15.0000 8.66025i 0.660979 0.381616i
\(516\) 0 0
\(517\) 20.7846i 0.914106i
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 12.0000 6.92820i 0.525730 0.303530i −0.213546 0.976933i \(-0.568501\pi\)
0.739276 + 0.673403i \(0.235168\pi\)
\(522\) 0 0
\(523\) −5.50000 + 9.52628i −0.240498 + 0.416555i −0.960856 0.277047i \(-0.910644\pi\)
0.720358 + 0.693602i \(0.243977\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 0 0
\(528\) 0 0
\(529\) 12.5000 + 21.6506i 0.543478 + 0.941332i
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) 6.00000 0.259889
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) −15.0000 + 19.0526i −0.646096 + 0.820652i
\(540\) 0 0
\(541\) 2.50000 4.33013i 0.107483 0.186167i −0.807267 0.590187i \(-0.799054\pi\)
0.914750 + 0.404020i \(0.132387\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) 24.2487i 1.03870i
\(546\) 0 0
\(547\) 3.46410i 0.148114i 0.997254 + 0.0740571i \(0.0235947\pi\)
−0.997254 + 0.0740571i \(0.976405\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) 0 0
\(552\) 0 0
\(553\) −10.5000 + 30.3109i −0.446505 + 1.28895i
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 21.0000 + 36.3731i 0.889799 + 1.54118i 0.840113 + 0.542411i \(0.182489\pi\)
0.0496855 + 0.998765i \(0.484178\pi\)
\(558\) 0 0
\(559\) 15.0000 0.634432
\(560\) 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
\(565\) −18.0000 10.3923i −0.757266 0.437208i
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 21.0000 36.3731i 0.880366 1.52484i 0.0294311 0.999567i \(-0.490630\pi\)
0.850935 0.525271i \(-0.176036\pi\)
\(570\) 0 0
\(571\) −40.5000 + 23.3827i −1.69487 + 0.978535i −0.744396 + 0.667739i \(0.767262\pi\)
−0.950477 + 0.310796i \(0.899404\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 48.4974i 2.02248i
\(576\) 0 0
\(577\) 10.5000 6.06218i 0.437121 0.252372i −0.265255 0.964178i \(-0.585456\pi\)
0.702376 + 0.711807i \(0.252123\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) 9.00000 + 46.7654i 0.373383 + 1.94015i
\(582\) 0 0
\(583\) 36.0000 + 20.7846i 1.49097 + 0.860811i
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) −12.0000 −0.495293 −0.247647 0.968850i \(-0.579657\pi\)
−0.247647 + 0.968850i \(0.579657\pi\)
\(588\) 0 0
\(589\) −25.0000 −1.03011
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) −3.00000 1.73205i −0.123195 0.0711268i 0.437136 0.899395i \(-0.355993\pi\)
−0.560331 + 0.828269i \(0.689326\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) 42.0000 24.2487i 1.71607 0.990775i 0.790280 0.612746i \(-0.209935\pi\)
0.925794 0.378030i \(-0.123398\pi\)
\(600\) 0 0
\(601\) 39.8372i 1.62499i 0.582967 + 0.812496i \(0.301892\pi\)
−0.582967 + 0.812496i \(0.698108\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) −3.00000 + 1.73205i −0.121967 + 0.0704179i
\(606\) 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
\(611\) 9.00000 + 5.19615i 0.364101 + 0.210214i
\(612\) 0 0
\(613\) −1.00000 1.73205i −0.0403896 0.0699569i 0.845124 0.534570i \(-0.179527\pi\)
−0.885514 + 0.464614i \(0.846193\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 18.0000 0.724653 0.362326 0.932051i \(-0.381983\pi\)
0.362326 + 0.932051i \(0.381983\pi\)
\(618\) 0 0
\(619\) 0.500000 + 0.866025i 0.0200967 + 0.0348085i 0.875899 0.482495i \(-0.160269\pi\)
−0.855802 + 0.517303i \(0.826936\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 6.00000 17.3205i 0.240385 0.693932i
\(624\) 0 0
\(625\) 5.50000 9.52628i 0.220000 0.381051i
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 0 0
\(630\) 0 0
\(631\) 3.46410i 0.137904i −0.997620 0.0689519i \(-0.978035\pi\)
0.997620 0.0689519i \(-0.0219655\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) −21.0000 + 36.3731i −0.833360 + 1.44342i
\(636\) 0 0
\(637\) −4.50000 11.2583i −0.178296 0.446071i
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) 12.0000 + 20.7846i 0.473972 + 0.820943i 0.999556 0.0297987i \(-0.00948663\pi\)
−0.525584 + 0.850741i \(0.676153\pi\)
\(642\) 0 0
\(643\) 31.0000 1.22252 0.611260 0.791430i \(-0.290663\pi\)
0.611260 + 0.791430i \(0.290663\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 15.0000 + 25.9808i 0.589711 + 1.02141i 0.994270 + 0.106897i \(0.0340916\pi\)
−0.404559 + 0.914512i \(0.632575\pi\)
\(648\) 0 0
\(649\) −36.0000 20.7846i −1.41312 0.815867i
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 3.00000 5.19615i 0.117399 0.203341i −0.801337 0.598213i \(-0.795878\pi\)
0.918736 + 0.394872i \(0.129211\pi\)
\(654\) 0 0
\(655\) 18.0000 10.3923i 0.703318 0.406061i
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) 13.8564i 0.539769i 0.962893 + 0.269884i \(0.0869855\pi\)
−0.962893 + 0.269884i \(0.913014\pi\)
\(660\) 0 0
\(661\) 22.5000 12.9904i 0.875149 0.505267i 0.00609283 0.999981i \(-0.498061\pi\)
0.869056 + 0.494714i \(0.164727\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) −30.0000 34.6410i −1.16335 1.34332i
\(666\) 0 0
\(667\) 0 0
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) −48.0000 −1.85302
\(672\) 0 0
\(673\) 1.00000 0.0385472 0.0192736 0.999814i \(-0.493865\pi\)
0.0192736 + 0.999814i \(0.493865\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 6.00000 + 3.46410i 0.230599 + 0.133136i 0.610848 0.791748i \(-0.290829\pi\)
−0.380250 + 0.924884i \(0.624162\pi\)
\(678\) 0 0
\(679\) 18.0000 3.46410i 0.690777 0.132940i
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) −6.00000 + 3.46410i −0.229584 + 0.132550i −0.610380 0.792109i \(-0.708983\pi\)
0.380796 + 0.924659i \(0.375650\pi\)
\(684\) 0 0
\(685\) 41.5692i 1.58828i
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) −18.0000 + 10.3923i −0.685745 + 0.395915i
\(690\) 0 0
\(691\) −11.5000 + 19.9186i −0.437481 + 0.757739i −0.997494 0.0707446i \(-0.977462\pi\)
0.560014 + 0.828483i \(0.310796\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 21.0000 + 12.1244i 0.796575 + 0.459903i
\(696\) 0 0
\(697\) 0 0
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) −12.0000 −0.453234 −0.226617 0.973984i \(-0.572767\pi\)
−0.226617 + 0.973984i \(0.572767\pi\)
\(702\) 0 0
\(703\) −27.5000 47.6314i −1.03718 1.79645i
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) −18.0000 20.7846i −0.676960 0.781686i
\(708\) 0 0
\(709\) 5.00000 8.66025i 0.187779 0.325243i −0.756730 0.653727i \(-0.773204\pi\)
0.944509 + 0.328484i \(0.106538\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) 34.6410i 1.29732i
\(714\) 0 0
\(715\) 20.7846i 0.777300i
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) 15.0000 25.9808i 0.559406 0.968919i −0.438141 0.898906i \(-0.644363\pi\)
0.997546 0.0700124i \(-0.0223039\pi\)
\(720\) 0 0
\(721\) −12.5000 4.33013i −0.465524 0.161262i
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) 0 0
\(726\) 0 0
\(727\) 23.0000 0.853023 0.426511 0.904482i \(-0.359742\pi\)
0.426511 + 0.904482i \(0.359742\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) 0 0
\(732\) 0 0
\(733\) −25.5000 14.7224i −0.941864 0.543785i −0.0513199 0.998682i \(-0.516343\pi\)
−0.890544 + 0.454897i \(0.849676\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 15.0000 25.9808i 0.552532 0.957014i
\(738\) 0 0
\(739\) −46.5000 + 26.8468i −1.71053 + 0.987575i −0.776691 + 0.629882i \(0.783103\pi\)
−0.933839 + 0.357693i \(0.883563\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 3.46410i 0.127086i 0.997979 + 0.0635428i \(0.0202399\pi\)
−0.997979 + 0.0635428i \(0.979760\pi\)
\(744\) 0 0
\(745\) −36.0000 + 20.7846i −1.31894 + 0.761489i
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) 0 0
\(750\) 0 0
\(751\) −4.50000 2.59808i −0.164207 0.0948051i 0.415644 0.909527i \(-0.363556\pi\)
−0.579852 + 0.814722i \(0.696889\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) −12.0000 −0.436725
\(756\) 0 0
\(757\) 26.0000 0.944986 0.472493 0.881334i \(-0.343354\pi\)
0.472493 + 0.881334i \(0.343354\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 36.0000 + 20.7846i 1.30500 + 0.753442i 0.981257 0.192704i \(-0.0617257\pi\)
0.323742 + 0.946145i \(0.395059\pi\)
\(762\) 0 0
\(763\) −14.0000 + 12.1244i −0.506834 + 0.438931i
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 18.0000 10.3923i 0.649942 0.375244i
\(768\) 0 0
\(769\) 15.5885i 0.562134i 0.959688 + 0.281067i \(0.0906883\pi\)
−0.959688 + 0.281067i \(0.909312\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) 39.0000 22.5167i 1.40273 0.809868i 0.408060 0.912955i \(-0.366205\pi\)
0.994672 + 0.103087i \(0.0328720\pi\)
\(774\) 0 0
\(775\) 17.5000 30.3109i 0.628619 1.08880i
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) −15.0000 8.66025i −0.537431 0.310286i
\(780\) 0 0
\(781\) 6.00000 + 10.3923i 0.214697 + 0.371866i
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) 0 0
\(786\) 0 0
\(787\) 8.00000 + 13.8564i 0.285169 + 0.493928i 0.972650 0.232275i \(-0.0746169\pi\)
−0.687481 + 0.726202i \(0.741284\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 3.00000 + 15.5885i 0.106668 + 0.554262i
\(792\) 0 0
\(793\) 12.0000 20.7846i 0.426132 0.738083i
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 34.6410i 1.22705i 0.789676 + 0.613524i \(0.210249\pi\)
−0.789676 + 0.613524i \(0.789751\pi\)
\(798\) 0 0
\(799\) 0 0
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) −9.00000 + 15.5885i −0.317603 + 0.550105i
\(804\) 0 0
\(805\) −48.0000 + 41.5692i −1.69178 + 1.46512i
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) 9.00000 + 15.5885i 0.316423 + 0.548061i 0.979739 0.200279i \(-0.0641847\pi\)
−0.663316 + 0.748340i \(0.730851\pi\)
\(810\) 0 0
\(811\) −40.0000 −1.40459 −0.702295 0.711886i \(-0.747841\pi\)
−0.702295 + 0.711886i \(0.747841\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) 6.00000 + 10.3923i 0.210171 + 0.364027i
\(816\) 0 <