Properties

Label 2268.2.x.j.1889.1
Level $2268$
Weight $2$
Character 2268.1889
Analytic conductor $18.110$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $8$

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Newspace parameters

Level: \( N \) \(=\) \( 2268 = 2^{2} \cdot 3^{4} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2268.x (of order \(6\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(18.1100711784\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(4\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\Q(\zeta_{24})\)
Defining polynomial: \(x^{8} - x^{4} + 1\)
Coefficient ring: \(\Z[a_1, \ldots, a_{13}]\)
Coefficient ring index: \( 2^{2}\cdot 3^{4} \)
Twist minimal: no (minimal twist has level 756)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 1889.1
Root \(-0.258819 - 0.965926i\) of defining polynomial
Character \(\chi\) \(=\) 2268.1889
Dual form 2268.2.x.j.377.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.866025 - 1.50000i) q^{5} +(-1.62132 - 2.09077i) q^{7} +O(q^{10})\) \(q+(-0.866025 - 1.50000i) q^{5} +(-1.62132 - 2.09077i) q^{7} +(-3.67423 - 2.12132i) q^{11} +(-2.12132 + 1.22474i) q^{13} +1.73205 q^{17} +2.44949i q^{19} +(7.34847 - 4.24264i) q^{23} +(1.00000 - 1.73205i) q^{25} +(-3.67423 - 2.12132i) q^{29} +(-6.36396 + 3.67423i) q^{31} +(-1.73205 + 4.24264i) q^{35} +1.00000 q^{37} +(0.866025 + 1.50000i) q^{41} +(-3.50000 + 6.06218i) q^{43} +(-6.06218 + 10.5000i) q^{47} +(-1.74264 + 6.77962i) q^{49} +7.34847i q^{55} +(-4.33013 - 7.50000i) q^{59} +(-2.12132 - 1.22474i) q^{61} +(3.67423 + 2.12132i) q^{65} +(5.00000 + 8.66025i) q^{67} +8.48528i q^{71} +9.79796i q^{73} +(1.52192 + 11.1213i) q^{77} +(-2.50000 + 4.33013i) q^{79} +(6.06218 - 10.5000i) q^{83} +(-1.50000 - 2.59808i) q^{85} +10.3923 q^{89} +(6.00000 + 2.44949i) q^{91} +(3.67423 - 2.12132i) q^{95} +(2.12132 + 1.22474i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8q + 4q^{7} + O(q^{10}) \) \( 8q + 4q^{7} + 8q^{25} + 8q^{37} - 28q^{43} + 20q^{49} + 40q^{67} - 20q^{79} - 12q^{85} + 48q^{91} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/2268\mathbb{Z}\right)^\times\).

\(n\) \(325\) \(1135\) \(1541\)
\(\chi(n)\) \(-1\) \(1\) \(e\left(\frac{1}{6}\right)\)

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
\(5\) −0.866025 1.50000i −0.387298 0.670820i 0.604787 0.796387i \(-0.293258\pi\)
−0.992085 + 0.125567i \(0.959925\pi\)
\(6\) 0 0
\(7\) −1.62132 2.09077i −0.612801 0.790237i
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) −3.67423 2.12132i −1.10782 0.639602i −0.169559 0.985520i \(-0.554234\pi\)
−0.938265 + 0.345918i \(0.887568\pi\)
\(12\) 0 0
\(13\) −2.12132 + 1.22474i −0.588348 + 0.339683i −0.764444 0.644690i \(-0.776986\pi\)
0.176096 + 0.984373i \(0.443653\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 1.73205 0.420084 0.210042 0.977692i \(-0.432640\pi\)
0.210042 + 0.977692i \(0.432640\pi\)
\(18\) 0 0
\(19\) 2.44949i 0.561951i 0.959715 + 0.280976i \(0.0906580\pi\)
−0.959715 + 0.280976i \(0.909342\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) 7.34847 4.24264i 1.53226 0.884652i 0.533005 0.846112i \(-0.321063\pi\)
0.999257 0.0385394i \(-0.0122705\pi\)
\(24\) 0 0
\(25\) 1.00000 1.73205i 0.200000 0.346410i
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) −3.67423 2.12132i −0.682288 0.393919i 0.118428 0.992963i \(-0.462214\pi\)
−0.800717 + 0.599043i \(0.795548\pi\)
\(30\) 0 0
\(31\) −6.36396 + 3.67423i −1.14300 + 0.659912i −0.947172 0.320726i \(-0.896073\pi\)
−0.195829 + 0.980638i \(0.562740\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) −1.73205 + 4.24264i −0.292770 + 0.717137i
\(36\) 0 0
\(37\) 1.00000 0.164399 0.0821995 0.996616i \(-0.473806\pi\)
0.0821995 + 0.996616i \(0.473806\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) 0.866025 + 1.50000i 0.135250 + 0.234261i 0.925693 0.378275i \(-0.123483\pi\)
−0.790443 + 0.612536i \(0.790149\pi\)
\(42\) 0 0
\(43\) −3.50000 + 6.06218i −0.533745 + 0.924473i 0.465478 + 0.885059i \(0.345882\pi\)
−0.999223 + 0.0394140i \(0.987451\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) −6.06218 + 10.5000i −0.884260 + 1.53158i −0.0376995 + 0.999289i \(0.512003\pi\)
−0.846560 + 0.532293i \(0.821330\pi\)
\(48\) 0 0
\(49\) −1.74264 + 6.77962i −0.248949 + 0.968517i
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(54\) 0 0
\(55\) 7.34847i 0.990867i
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) −4.33013 7.50000i −0.563735 0.976417i −0.997166 0.0752304i \(-0.976031\pi\)
0.433432 0.901186i \(-0.357303\pi\)
\(60\) 0 0
\(61\) −2.12132 1.22474i −0.271607 0.156813i 0.358011 0.933718i \(-0.383455\pi\)
−0.629618 + 0.776905i \(0.716789\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) 3.67423 + 2.12132i 0.455733 + 0.263117i
\(66\) 0 0
\(67\) 5.00000 + 8.66025i 0.610847 + 1.05802i 0.991098 + 0.133135i \(0.0425044\pi\)
−0.380251 + 0.924883i \(0.624162\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 8.48528i 1.00702i 0.863990 + 0.503509i \(0.167958\pi\)
−0.863990 + 0.503509i \(0.832042\pi\)
\(72\) 0 0
\(73\) 9.79796i 1.14676i 0.819288 + 0.573382i \(0.194369\pi\)
−0.819288 + 0.573382i \(0.805631\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 1.52192 + 11.1213i 0.173439 + 1.26739i
\(78\) 0 0
\(79\) −2.50000 + 4.33013i −0.281272 + 0.487177i −0.971698 0.236225i \(-0.924090\pi\)
0.690426 + 0.723403i \(0.257423\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) 6.06218 10.5000i 0.665410 1.15252i −0.313763 0.949501i \(-0.601590\pi\)
0.979174 0.203024i \(-0.0650768\pi\)
\(84\) 0 0
\(85\) −1.50000 2.59808i −0.162698 0.281801i
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 10.3923 1.10158 0.550791 0.834643i \(-0.314326\pi\)
0.550791 + 0.834643i \(0.314326\pi\)
\(90\) 0 0
\(91\) 6.00000 + 2.44949i 0.628971 + 0.256776i
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 3.67423 2.12132i 0.376969 0.217643i
\(96\) 0 0
\(97\) 2.12132 + 1.22474i 0.215387 + 0.124354i 0.603813 0.797126i \(-0.293647\pi\)
−0.388425 + 0.921480i \(0.626981\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) 5.19615 9.00000i 0.517036 0.895533i −0.482768 0.875748i \(-0.660368\pi\)
0.999804 0.0197851i \(-0.00629819\pi\)
\(102\) 0 0
\(103\) −16.9706 + 9.79796i −1.67216 + 0.965422i −0.705733 + 0.708478i \(0.749382\pi\)
−0.966426 + 0.256943i \(0.917285\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 8.48528i 0.820303i −0.912017 0.410152i \(-0.865476\pi\)
0.912017 0.410152i \(-0.134524\pi\)
\(108\) 0 0
\(109\) 13.0000 1.24517 0.622587 0.782551i \(-0.286082\pi\)
0.622587 + 0.782551i \(0.286082\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) −11.0227 + 6.36396i −1.03693 + 0.598671i −0.918962 0.394346i \(-0.870971\pi\)
−0.117967 + 0.993018i \(0.537638\pi\)
\(114\) 0 0
\(115\) −12.7279 7.34847i −1.18688 0.685248i
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) −2.80821 3.62132i −0.257428 0.331966i
\(120\) 0 0
\(121\) 3.50000 + 6.06218i 0.318182 + 0.551107i
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) −12.1244 −1.08444
\(126\) 0 0
\(127\) −13.0000 −1.15356 −0.576782 0.816898i \(-0.695692\pi\)
−0.576782 + 0.816898i \(0.695692\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) −5.19615 9.00000i −0.453990 0.786334i 0.544640 0.838670i \(-0.316666\pi\)
−0.998630 + 0.0523366i \(0.983333\pi\)
\(132\) 0 0
\(133\) 5.12132 3.97141i 0.444075 0.344365i
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 18.3712 + 10.6066i 1.56956 + 0.906183i 0.996220 + 0.0868620i \(0.0276839\pi\)
0.573335 + 0.819321i \(0.305649\pi\)
\(138\) 0 0
\(139\) −10.6066 + 6.12372i −0.899640 + 0.519408i −0.877083 0.480338i \(-0.840514\pi\)
−0.0225568 + 0.999746i \(0.507181\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 10.3923 0.869048
\(144\) 0 0
\(145\) 7.34847i 0.610257i
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) −11.0227 + 6.36396i −0.903015 + 0.521356i −0.878177 0.478335i \(-0.841240\pi\)
−0.0248379 + 0.999691i \(0.507907\pi\)
\(150\) 0 0
\(151\) 2.50000 4.33013i 0.203447 0.352381i −0.746190 0.665733i \(-0.768119\pi\)
0.949637 + 0.313353i \(0.101452\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 11.0227 + 6.36396i 0.885365 + 0.511166i
\(156\) 0 0
\(157\) −6.36396 + 3.67423i −0.507899 + 0.293236i −0.731970 0.681337i \(-0.761399\pi\)
0.224070 + 0.974573i \(0.428065\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) −20.7846 8.48528i −1.63806 0.668734i
\(162\) 0 0
\(163\) −1.00000 −0.0783260 −0.0391630 0.999233i \(-0.512469\pi\)
−0.0391630 + 0.999233i \(0.512469\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 9.52628 + 16.5000i 0.737166 + 1.27681i 0.953767 + 0.300548i \(0.0971696\pi\)
−0.216601 + 0.976260i \(0.569497\pi\)
\(168\) 0 0
\(169\) −3.50000 + 6.06218i −0.269231 + 0.466321i
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) −10.3923 + 18.0000i −0.790112 + 1.36851i 0.135785 + 0.990738i \(0.456644\pi\)
−0.925897 + 0.377776i \(0.876689\pi\)
\(174\) 0 0
\(175\) −5.24264 + 0.717439i −0.396306 + 0.0542333i
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) 4.24264i 0.317110i −0.987350 0.158555i \(-0.949317\pi\)
0.987350 0.158555i \(-0.0506835\pi\)
\(180\) 0 0
\(181\) 4.89898i 0.364138i 0.983286 + 0.182069i \(0.0582795\pi\)
−0.983286 + 0.182069i \(0.941721\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) −0.866025 1.50000i −0.0636715 0.110282i
\(186\) 0 0
\(187\) −6.36396 3.67423i −0.465379 0.268687i
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) −7.34847 4.24264i −0.531717 0.306987i 0.209999 0.977702i \(-0.432654\pi\)
−0.741715 + 0.670715i \(0.765987\pi\)
\(192\) 0 0
\(193\) −3.50000 6.06218i −0.251936 0.436365i 0.712123 0.702055i \(-0.247734\pi\)
−0.964059 + 0.265689i \(0.914400\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 21.2132i 1.51138i −0.654931 0.755689i \(-0.727302\pi\)
0.654931 0.755689i \(-0.272698\pi\)
\(198\) 0 0
\(199\) 9.79796i 0.694559i −0.937762 0.347279i \(-0.887106\pi\)
0.937762 0.347279i \(-0.112894\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) 1.52192 + 11.1213i 0.106818 + 0.780564i
\(204\) 0 0
\(205\) 1.50000 2.59808i 0.104765 0.181458i
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) 5.19615 9.00000i 0.359425 0.622543i
\(210\) 0 0
\(211\) 4.00000 + 6.92820i 0.275371 + 0.476957i 0.970229 0.242190i \(-0.0778659\pi\)
−0.694857 + 0.719148i \(0.744533\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) 12.1244 0.826874
\(216\) 0 0
\(217\) 18.0000 + 7.34847i 1.22192 + 0.498847i
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) −3.67423 + 2.12132i −0.247156 + 0.142695i
\(222\) 0 0
\(223\) −19.0919 11.0227i −1.27849 0.738135i −0.301917 0.953334i \(-0.597627\pi\)
−0.976570 + 0.215199i \(0.930960\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(228\) 0 0
\(229\) 12.7279 7.34847i 0.841085 0.485601i −0.0165480 0.999863i \(-0.505268\pi\)
0.857633 + 0.514263i \(0.171934\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 4.24264i 0.277945i 0.990296 + 0.138972i \(0.0443799\pi\)
−0.990296 + 0.138972i \(0.955620\pi\)
\(234\) 0 0
\(235\) 21.0000 1.36989
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) 18.3712 10.6066i 1.18833 0.686084i 0.230405 0.973095i \(-0.425995\pi\)
0.957927 + 0.287011i \(0.0926616\pi\)
\(240\) 0 0
\(241\) 23.3345 + 13.4722i 1.50311 + 0.867820i 0.999994 + 0.00360098i \(0.00114623\pi\)
0.503115 + 0.864219i \(0.332187\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) 11.6786 3.25736i 0.746118 0.208105i
\(246\) 0 0
\(247\) −3.00000 5.19615i −0.190885 0.330623i
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) −19.0526 −1.20259 −0.601293 0.799028i \(-0.705348\pi\)
−0.601293 + 0.799028i \(0.705348\pi\)
\(252\) 0 0
\(253\) −36.0000 −2.26330
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) −5.19615 9.00000i −0.324127 0.561405i 0.657208 0.753709i \(-0.271737\pi\)
−0.981335 + 0.192304i \(0.938404\pi\)
\(258\) 0 0
\(259\) −1.62132 2.09077i −0.100744 0.129914i
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) −18.3712 10.6066i −1.13282 0.654031i −0.188174 0.982136i \(-0.560257\pi\)
−0.944641 + 0.328105i \(0.893590\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) −1.73205 −0.105605 −0.0528025 0.998605i \(-0.516815\pi\)
−0.0528025 + 0.998605i \(0.516815\pi\)
\(270\) 0 0
\(271\) 4.89898i 0.297592i 0.988868 + 0.148796i \(0.0475397\pi\)
−0.988868 + 0.148796i \(0.952460\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) −7.34847 + 4.24264i −0.443129 + 0.255841i
\(276\) 0 0
\(277\) 3.50000 6.06218i 0.210295 0.364241i −0.741512 0.670940i \(-0.765891\pi\)
0.951807 + 0.306699i \(0.0992243\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) −7.34847 4.24264i −0.438373 0.253095i 0.264534 0.964376i \(-0.414782\pi\)
−0.702907 + 0.711282i \(0.748115\pi\)
\(282\) 0 0
\(283\) 6.36396 3.67423i 0.378298 0.218411i −0.298779 0.954322i \(-0.596579\pi\)
0.677078 + 0.735912i \(0.263246\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 1.73205 4.24264i 0.102240 0.250435i
\(288\) 0 0
\(289\) −14.0000 −0.823529
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) −4.33013 7.50000i −0.252969 0.438155i 0.711373 0.702815i \(-0.248074\pi\)
−0.964342 + 0.264660i \(0.914740\pi\)
\(294\) 0 0
\(295\) −7.50000 + 12.9904i −0.436667 + 0.756329i
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) −10.3923 + 18.0000i −0.601003 + 1.04097i
\(300\) 0 0
\(301\) 18.3492 2.51104i 1.05763 0.144734i
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) 4.24264i 0.242933i
\(306\) 0 0
\(307\) 29.3939i 1.67760i −0.544442 0.838799i \(-0.683259\pi\)
0.544442 0.838799i \(-0.316741\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) −11.2583 19.5000i −0.638401 1.10574i −0.985784 0.168020i \(-0.946263\pi\)
0.347382 0.937724i \(-0.387071\pi\)
\(312\) 0 0
\(313\) 21.2132 + 12.2474i 1.19904 + 0.692267i 0.960341 0.278827i \(-0.0899455\pi\)
0.238700 + 0.971093i \(0.423279\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(318\) 0 0
\(319\) 9.00000 + 15.5885i 0.503903 + 0.872786i
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) 4.24264i 0.236067i
\(324\) 0 0
\(325\) 4.89898i 0.271746i
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) 31.7818 4.34924i 1.75219 0.239781i
\(330\) 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
\(335\) 8.66025 15.0000i 0.473160 0.819538i
\(336\) 0 0
\(337\) −12.5000 21.6506i −0.680918 1.17939i −0.974701 0.223513i \(-0.928247\pi\)
0.293783 0.955872i \(-0.405086\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) 31.1769 1.68832
\(342\) 0 0
\(343\) 17.0000 7.34847i 0.917914 0.396780i
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) −18.3712 + 10.6066i −0.986216 + 0.569392i −0.904141 0.427234i \(-0.859488\pi\)
−0.0820751 + 0.996626i \(0.526155\pi\)
\(348\) 0 0
\(349\) 16.9706 + 9.79796i 0.908413 + 0.524473i 0.879920 0.475121i \(-0.157596\pi\)
0.0284931 + 0.999594i \(0.490929\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) −0.866025 + 1.50000i −0.0460939 + 0.0798369i −0.888152 0.459550i \(-0.848011\pi\)
0.842058 + 0.539387i \(0.181344\pi\)
\(354\) 0 0
\(355\) 12.7279 7.34847i 0.675528 0.390016i
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 33.9411i 1.79134i 0.444715 + 0.895672i \(0.353305\pi\)
−0.444715 + 0.895672i \(0.646695\pi\)
\(360\) 0 0
\(361\) 13.0000 0.684211
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) 14.6969 8.48528i 0.769273 0.444140i
\(366\) 0 0
\(367\) −4.24264 2.44949i −0.221464 0.127862i 0.385164 0.922848i \(-0.374145\pi\)
−0.606628 + 0.794986i \(0.707478\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) 0 0
\(372\) 0 0
\(373\) −5.50000 9.52628i −0.284779 0.493252i 0.687776 0.725923i \(-0.258587\pi\)
−0.972556 + 0.232671i \(0.925254\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 10.3923 0.535231
\(378\) 0 0
\(379\) −35.0000 −1.79783 −0.898915 0.438124i \(-0.855643\pi\)
−0.898915 + 0.438124i \(0.855643\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) −9.52628 16.5000i −0.486770 0.843111i 0.513114 0.858320i \(-0.328492\pi\)
−0.999884 + 0.0152097i \(0.995158\pi\)
\(384\) 0 0
\(385\) 15.3640 11.9142i 0.783020 0.607205i
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) −25.7196 14.8492i −1.30404 0.752886i −0.322944 0.946418i \(-0.604672\pi\)
−0.981094 + 0.193532i \(0.938006\pi\)
\(390\) 0 0
\(391\) 12.7279 7.34847i 0.643679 0.371628i
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) 8.66025 0.435745
\(396\) 0 0
\(397\) 29.3939i 1.47524i −0.675218 0.737618i \(-0.735950\pi\)
0.675218 0.737618i \(-0.264050\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 7.34847 4.24264i 0.366965 0.211867i −0.305167 0.952299i \(-0.598712\pi\)
0.672132 + 0.740432i \(0.265379\pi\)
\(402\) 0 0
\(403\) 9.00000 15.5885i 0.448322 0.776516i
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) −3.67423 2.12132i −0.182125 0.105150i
\(408\) 0 0
\(409\) 33.9411 19.5959i 1.67828 0.968956i 0.715523 0.698589i \(-0.246188\pi\)
0.962757 0.270367i \(-0.0871450\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) −8.66025 + 21.2132i −0.426143 + 1.04383i
\(414\) 0 0
\(415\) −21.0000 −1.03085
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 14.7224 + 25.5000i 0.719238 + 1.24576i 0.961302 + 0.275496i \(0.0888422\pi\)
−0.242064 + 0.970260i \(0.577824\pi\)
\(420\) 0 0
\(421\) −10.0000 + 17.3205i −0.487370 + 0.844150i −0.999895 0.0145228i \(-0.995377\pi\)
0.512524 + 0.858673i \(0.328710\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) 1.73205 3.00000i 0.0840168 0.145521i
\(426\) 0 0
\(427\) 0.878680 + 6.42090i 0.0425223 + 0.310729i
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 16.9706i 0.817443i 0.912659 + 0.408722i \(0.134025\pi\)
−0.912659 + 0.408722i \(0.865975\pi\)
\(432\) 0 0
\(433\) 22.0454i 1.05943i 0.848174 + 0.529717i \(0.177702\pi\)
−0.848174 + 0.529717i \(0.822298\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 10.3923 + 18.0000i 0.497131 + 0.861057i
\(438\) 0 0
\(439\) −25.4558 14.6969i −1.21494 0.701447i −0.251110 0.967959i \(-0.580795\pi\)
−0.963832 + 0.266512i \(0.914129\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 11.0227 + 6.36396i 0.523704 + 0.302361i 0.738449 0.674309i \(-0.235559\pi\)
−0.214745 + 0.976670i \(0.568892\pi\)
\(444\) 0 0
\(445\) −9.00000 15.5885i −0.426641 0.738964i
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) 21.2132i 1.00111i 0.865704 + 0.500556i \(0.166871\pi\)
−0.865704 + 0.500556i \(0.833129\pi\)
\(450\) 0 0
\(451\) 7.34847i 0.346026i
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) −1.52192 11.1213i −0.0713486 0.521376i
\(456\) 0 0
\(457\) 4.00000 6.92820i 0.187112 0.324088i −0.757174 0.653213i \(-0.773421\pi\)
0.944286 + 0.329125i \(0.106754\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) −14.7224 + 25.5000i −0.685692 + 1.18765i 0.287527 + 0.957773i \(0.407167\pi\)
−0.973219 + 0.229881i \(0.926166\pi\)
\(462\) 0 0
\(463\) −14.5000 25.1147i −0.673872 1.16718i −0.976797 0.214166i \(-0.931297\pi\)
0.302925 0.953014i \(-0.402037\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) −20.7846 −0.961797 −0.480899 0.876776i \(-0.659689\pi\)
−0.480899 + 0.876776i \(0.659689\pi\)
\(468\) 0 0
\(469\) 10.0000 24.4949i 0.461757 1.13107i
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) 25.7196 14.8492i 1.18259 0.682769i
\(474\) 0 0
\(475\) 4.24264 + 2.44949i 0.194666 + 0.112390i
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) −19.9186 + 34.5000i −0.910103 + 1.57635i −0.0961869 + 0.995363i \(0.530665\pi\)
−0.813916 + 0.580982i \(0.802669\pi\)
\(480\) 0 0
\(481\) −2.12132 + 1.22474i −0.0967239 + 0.0558436i
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 4.24264i 0.192648i
\(486\) 0 0
\(487\) 22.0000 0.996915 0.498458 0.866914i \(-0.333900\pi\)
0.498458 + 0.866914i \(0.333900\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) −11.0227 + 6.36396i −0.497448 + 0.287202i −0.727659 0.685939i \(-0.759392\pi\)
0.230211 + 0.973141i \(0.426058\pi\)
\(492\) 0 0
\(493\) −6.36396 3.67423i −0.286618 0.165479i
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 17.7408 13.7574i 0.795782 0.617102i
\(498\) 0 0
\(499\) −9.50000 16.4545i −0.425278 0.736604i 0.571168 0.820833i \(-0.306490\pi\)
−0.996446 + 0.0842294i \(0.973157\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) −1.73205 −0.0772283 −0.0386142 0.999254i \(-0.512294\pi\)
−0.0386142 + 0.999254i \(0.512294\pi\)
\(504\) 0 0
\(505\) −18.0000 −0.800989
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) −9.52628 16.5000i −0.422245 0.731350i 0.573914 0.818916i \(-0.305424\pi\)
−0.996159 + 0.0875661i \(0.972091\pi\)
\(510\) 0 0
\(511\) 20.4853 15.8856i 0.906215 0.702739i
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) 29.3939 + 16.9706i 1.29525 + 0.747812i
\(516\) 0 0
\(517\) 44.5477 25.7196i 1.95921 1.13115i
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) −1.73205 −0.0758825 −0.0379413 0.999280i \(-0.512080\pi\)
−0.0379413 + 0.999280i \(0.512080\pi\)
\(522\) 0 0
\(523\) 31.8434i 1.39241i −0.717841 0.696207i \(-0.754870\pi\)
0.717841 0.696207i \(-0.245130\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −11.0227 + 6.36396i −0.480157 + 0.277218i
\(528\) 0 0
\(529\) 24.5000 42.4352i 1.06522 1.84501i
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) −3.67423 2.12132i −0.159149 0.0918846i
\(534\) 0 0
\(535\) −12.7279 + 7.34847i −0.550276 + 0.317702i
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) 20.7846 21.2132i 0.895257 0.913717i
\(540\) 0 0
\(541\) 17.0000 0.730887 0.365444 0.930834i \(-0.380917\pi\)
0.365444 + 0.930834i \(0.380917\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) −11.2583 19.5000i −0.482254 0.835288i
\(546\) 0 0
\(547\) −20.5000 + 35.5070i −0.876517 + 1.51817i −0.0213785 + 0.999771i \(0.506805\pi\)
−0.855138 + 0.518400i \(0.826528\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) 5.19615 9.00000i 0.221364 0.383413i
\(552\) 0 0
\(553\) 13.1066 1.79360i 0.557349 0.0762715i
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 8.48528i 0.359533i −0.983709 0.179766i \(-0.942466\pi\)
0.983709 0.179766i \(-0.0575342\pi\)
\(558\) 0 0
\(559\) 17.1464i 0.725217i
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) 10.3923 + 18.0000i 0.437983 + 0.758610i 0.997534 0.0701867i \(-0.0223595\pi\)
−0.559550 + 0.828796i \(0.689026\pi\)
\(564\) 0 0
\(565\) 19.0919 + 11.0227i 0.803202 + 0.463729i
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) −29.3939 16.9706i −1.23226 0.711443i −0.264756 0.964315i \(-0.585291\pi\)
−0.967500 + 0.252872i \(0.918625\pi\)
\(570\) 0 0
\(571\) 12.5000 + 21.6506i 0.523109 + 0.906051i 0.999638 + 0.0268925i \(0.00856117\pi\)
−0.476530 + 0.879158i \(0.658105\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 16.9706i 0.707721i
\(576\) 0 0
\(577\) 19.5959i 0.815789i −0.913029 0.407894i \(-0.866263\pi\)
0.913029 0.407894i \(-0.133737\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) −31.7818 + 4.34924i −1.31853 + 0.180437i
\(582\) 0 0
\(583\) 0 0
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 20.7846 36.0000i 0.857873 1.48588i −0.0160815 0.999871i \(-0.505119\pi\)
0.873954 0.486008i \(-0.161548\pi\)
\(588\) 0 0
\(589\) −9.00000 15.5885i −0.370839 0.642311i
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) 8.66025 0.355634 0.177817 0.984064i \(-0.443096\pi\)
0.177817 + 0.984064i \(0.443096\pi\)
\(594\) 0 0
\(595\) −3.00000 + 7.34847i −0.122988 + 0.301258i
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) 3.67423 2.12132i 0.150125 0.0866748i −0.423056 0.906104i \(-0.639043\pi\)
0.573181 + 0.819429i \(0.305709\pi\)
\(600\) 0 0
\(601\) 19.0919 + 11.0227i 0.778774 + 0.449625i 0.835996 0.548736i \(-0.184891\pi\)
−0.0572215 + 0.998362i \(0.518224\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) 6.06218 10.5000i 0.246463 0.426886i
\(606\) 0 0
\(607\) 23.3345 13.4722i 0.947119 0.546819i 0.0549343 0.998490i \(-0.482505\pi\)
0.892185 + 0.451671i \(0.149172\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 29.6985i 1.20147i
\(612\) 0 0
\(613\) −4.00000 −0.161558 −0.0807792 0.996732i \(-0.525741\pi\)
−0.0807792 + 0.996732i \(0.525741\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) −22.0454 + 12.7279i −0.887515 + 0.512407i −0.873129 0.487490i \(-0.837913\pi\)
−0.0143859 + 0.999897i \(0.504579\pi\)
\(618\) 0 0
\(619\) 2.12132 + 1.22474i 0.0852631 + 0.0492267i 0.542025 0.840362i \(-0.317658\pi\)
−0.456762 + 0.889589i \(0.650991\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) −16.8493 21.7279i −0.675051 0.870511i
\(624\) 0 0
\(625\) 5.50000 + 9.52628i 0.220000 + 0.381051i
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 1.73205 0.0690614
\(630\) 0 0
\(631\) −37.0000 −1.47295 −0.736473 0.676467i \(-0.763510\pi\)
−0.736473 + 0.676467i \(0.763510\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) 11.2583 + 19.5000i 0.446773 + 0.773834i
\(636\) 0 0
\(637\) −4.60660 16.5160i −0.182520 0.654389i
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) 18.3712 + 10.6066i 0.725618 + 0.418936i 0.816817 0.576897i \(-0.195737\pi\)
−0.0911991 + 0.995833i \(0.529070\pi\)
\(642\) 0 0
\(643\) −12.7279 + 7.34847i −0.501940 + 0.289795i −0.729514 0.683965i \(-0.760254\pi\)
0.227574 + 0.973761i \(0.426921\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) −20.7846 −0.817127 −0.408564 0.912730i \(-0.633970\pi\)
−0.408564 + 0.912730i \(0.633970\pi\)
\(648\) 0 0
\(649\) 36.7423i 1.44226i
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 25.7196 14.8492i 1.00649 0.581096i 0.0963261 0.995350i \(-0.469291\pi\)
0.910161 + 0.414254i \(0.135958\pi\)
\(654\) 0 0
\(655\) −9.00000 + 15.5885i −0.351659 + 0.609091i
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) 14.6969 + 8.48528i 0.572511 + 0.330540i 0.758152 0.652078i \(-0.226103\pi\)
−0.185640 + 0.982618i \(0.559436\pi\)
\(660\) 0 0
\(661\) 10.6066 6.12372i 0.412549 0.238185i −0.279335 0.960194i \(-0.590114\pi\)
0.691884 + 0.722008i \(0.256781\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) −10.3923 4.24264i −0.402996 0.164523i
\(666\) 0 0
\(667\) −36.0000 −1.39393
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 5.19615 + 9.00000i 0.200595 + 0.347441i
\(672\) 0 0
\(673\) −8.00000 + 13.8564i −0.308377 + 0.534125i −0.978008 0.208569i \(-0.933119\pi\)
0.669630 + 0.742695i \(0.266453\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 15.5885 27.0000i 0.599113 1.03769i −0.393839 0.919179i \(-0.628853\pi\)
0.992952 0.118515i \(-0.0378134\pi\)
\(678\) 0 0
\(679\) −0.878680 6.42090i −0.0337206 0.246411i
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 38.1838i 1.46106i −0.682880 0.730531i \(-0.739273\pi\)
0.682880 0.730531i \(-0.260727\pi\)
\(684\) 0 0
\(685\) 36.7423i 1.40385i
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) 0 0
\(690\) 0 0
\(691\) 19.0919 + 11.0227i 0.726289 + 0.419323i 0.817063 0.576548i \(-0.195601\pi\)
−0.0907737 + 0.995872i \(0.528934\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 18.3712 + 10.6066i 0.696858 + 0.402331i
\(696\) 0 0
\(697\) 1.50000 + 2.59808i 0.0568166 + 0.0984092i
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) 12.7279i 0.480727i 0.970683 + 0.240363i \(0.0772666\pi\)
−0.970683 + 0.240363i \(0.922733\pi\)
\(702\) 0 0
\(703\) 2.44949i 0.0923843i
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) −27.2416 + 3.72792i −1.02452 + 0.140203i
\(708\) 0 0
\(709\) −24.5000 + 42.4352i −0.920117 + 1.59369i −0.120885 + 0.992667i \(0.538573\pi\)
−0.799232 + 0.601023i \(0.794760\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) −31.1769 + 54.0000i −1.16758 + 2.02232i
\(714\) 0 0
\(715\) −9.00000 15.5885i −0.336581 0.582975i
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) −32.9090 −1.22730 −0.613649 0.789579i \(-0.710299\pi\)
−0.613649 + 0.789579i \(0.710299\pi\)
\(720\) 0 0
\(721\) 48.0000 + 19.5959i 1.78761 + 0.729790i
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) −7.34847 + 4.24264i −0.272915 + 0.157568i
\(726\) 0 0
\(727\) 6.36396 + 3.67423i 0.236026 + 0.136270i 0.613349 0.789812i \(-0.289822\pi\)
−0.377323 + 0.926082i \(0.623155\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) −6.06218 + 10.5000i −0.224218 + 0.388357i
\(732\) 0 0
\(733\) 25.4558 14.6969i 0.940233 0.542844i 0.0501997 0.998739i \(-0.484014\pi\)
0.890033 + 0.455895i \(0.150681\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 42.4264i 1.56280i
\(738\) 0 0
\(739\) 38.0000 1.39785 0.698926 0.715194i \(-0.253662\pi\)
0.698926 + 0.715194i \(0.253662\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) −18.3712 + 10.6066i −0.673973 + 0.389118i −0.797580 0.603213i \(-0.793887\pi\)
0.123607 + 0.992331i \(0.460554\pi\)
\(744\) 0 0
\(745\) 19.0919 + 11.0227i 0.699472 + 0.403841i
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) −17.7408 + 13.7574i −0.648234 + 0.502683i
\(750\) 0 0
\(751\) −5.00000 8.66025i −0.182453 0.316017i 0.760263 0.649616i \(-0.225070\pi\)
−0.942715 + 0.333599i \(0.891737\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) −8.66025 −0.315179
\(756\) 0 0
\(757\) −53.0000 −1.92632 −0.963159 0.268933i \(-0.913329\pi\)
−0.963159 + 0.268933i \(0.913329\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 11.2583 + 19.5000i 0.408114 + 0.706874i 0.994678 0.103028i \(-0.0328532\pi\)
−0.586564 + 0.809903i \(0.699520\pi\)
\(762\) 0 0
\(763\) −21.0772 27.1800i −0.763045 0.983983i
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 18.3712 + 10.6066i 0.663345 + 0.382982i
\(768\) 0 0
\(769\) −4.24264 + 2.44949i −0.152994 + 0.0883309i −0.574542 0.818475i \(-0.694820\pi\)
0.421549 + 0.906806i \(0.361487\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) −39.8372 −1.43284 −0.716422 0.697668i \(-0.754221\pi\)
−0.716422 + 0.697668i \(0.754221\pi\)
\(774\) 0 0
\(775\) 14.6969i 0.527930i
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) −3.67423 + 2.12132i −0.131643 + 0.0760042i
\(780\) 0 0
\(781\) 18.0000 31.1769i 0.644091 1.11560i
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) 11.0227 + 6.36396i 0.393417 + 0.227140i
\(786\) 0 0
\(787\) 4.24264 2.44949i 0.151234 0.0873149i −0.422473 0.906375i \(-0.638838\pi\)
0.573707 + 0.819060i \(0.305505\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 31.1769 + 12.7279i 1.10852 + 0.452553i
\(792\) 0 0
\(793\) 6.00000 0.213066
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) −5.19615 9.00000i −0.184057 0.318796i 0.759201 0.650856i \(-0.225590\pi\)
−0.943258 + 0.332060i \(0.892256\pi\)
\(798\) 0 0
\(799\) −10.5000 + 18.1865i −0.371463 + 0.643393i
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) 20.7846 36.0000i 0.733473 1.27041i
\(804\) 0 0
\(805\) 5.27208 + 38.5254i 0.185816