Properties

Label 2268.2.x.j.377.2
Level $2268$
Weight $2$
Character 2268.377
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 377.2
Root \(0.258819 - 0.965926i\) of defining polynomial
Character \(\chi\) \(=\) 2268.377
Dual form 2268.2.x.j.1889.2

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.866025 + 1.50000i) q^{5} +(2.62132 - 0.358719i) q^{7} +O(q^{10})\) \(q+(-0.866025 + 1.50000i) q^{5} +(2.62132 - 0.358719i) q^{7} +(3.67423 - 2.12132i) q^{11} +(2.12132 + 1.22474i) q^{13} +1.73205 q^{17} +2.44949i q^{19} +(-7.34847 - 4.24264i) q^{23} +(1.00000 + 1.73205i) q^{25} +(3.67423 - 2.12132i) q^{29} +(6.36396 + 3.67423i) q^{31} +(-1.73205 + 4.24264i) q^{35} +1.00000 q^{37} +(0.866025 - 1.50000i) q^{41} +(-3.50000 - 6.06218i) q^{43} +(-6.06218 - 10.5000i) q^{47} +(6.74264 - 1.88064i) q^{49} +7.34847i q^{55} +(-4.33013 + 7.50000i) q^{59} +(2.12132 - 1.22474i) q^{61} +(-3.67423 + 2.12132i) q^{65} +(5.00000 - 8.66025i) q^{67} +8.48528i q^{71} +9.79796i q^{73} +(8.87039 - 6.87868i) q^{77} +(-2.50000 - 4.33013i) q^{79} +(6.06218 + 10.5000i) q^{83} +(-1.50000 + 2.59808i) q^{85} +10.3923 q^{89} +(6.00000 + 2.44949i) q^{91} +(-3.67423 - 2.12132i) q^{95} +(-2.12132 + 1.22474i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8q + 4q^{7} + O(q^{10}) \) \( 8q + 4q^{7} + 8q^{25} + 8q^{37} - 28q^{43} + 20q^{49} + 40q^{67} - 20q^{79} - 12q^{85} + 48q^{91} + O(q^{100}) \)

Character values

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

\(n\) \(325\) \(1135\) \(1541\)
\(\chi(n)\) \(-1\) \(1\) \(e\left(\frac{5}{6}\right)\)

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 −0.992085 0.125567i \(-0.959925\pi\)
0.604787 + 0.796387i \(0.293258\pi\)
\(6\) 0 0
\(7\) 2.62132 0.358719i 0.990766 0.135583i
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) 3.67423 2.12132i 1.10782 0.639602i 0.169559 0.985520i \(-0.445766\pi\)
0.938265 + 0.345918i \(0.112432\pi\)
\(12\) 0 0
\(13\) 2.12132 + 1.22474i 0.588348 + 0.339683i 0.764444 0.644690i \(-0.223014\pi\)
−0.176096 + 0.984373i \(0.556347\pi\)
\(14\) 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 −0.999257 0.0385394i \(-0.987729\pi\)
−0.533005 0.846112i \(-0.678937\pi\)
\(24\) 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 \(-0.537786\pi\)
0.800717 + 0.599043i \(0.204452\pi\)
\(30\) 0 0
\(31\) 6.36396 + 3.67423i 1.14300 + 0.659912i 0.947172 0.320726i \(-0.103927\pi\)
0.195829 + 0.980638i \(0.437260\pi\)
\(32\) 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 −0.790443 0.612536i \(-0.790149\pi\)
0.925693 + 0.378275i \(0.123483\pi\)
\(42\) 0 0
\(43\) −3.50000 6.06218i −0.533745 0.924473i −0.999223 0.0394140i \(-0.987451\pi\)
0.465478 0.885059i \(-0.345882\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) −6.06218 10.5000i −0.884260 1.53158i −0.846560 0.532293i \(-0.821330\pi\)
−0.0376995 0.999289i \(-0.512003\pi\)
\(48\) 0 0
\(49\) 6.74264 1.88064i 0.963234 0.268662i
\(50\) 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 0.433432 + 0.901186i \(0.357303\pi\)
−0.997166 + 0.0752304i \(0.976031\pi\)
\(60\) 0 0
\(61\) 2.12132 1.22474i 0.271607 0.156813i −0.358011 0.933718i \(-0.616545\pi\)
0.629618 + 0.776905i \(0.283211\pi\)
\(62\) 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 −0.380251 0.924883i \(-0.624162\pi\)
0.991098 0.133135i \(-0.0425044\pi\)
\(68\) 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
\(77\) 8.87039 6.87868i 1.01087 0.783898i
\(78\) 0 0
\(79\) −2.50000 4.33013i −0.281272 0.487177i 0.690426 0.723403i \(-0.257423\pi\)
−0.971698 + 0.236225i \(0.924090\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) 6.06218 + 10.5000i 0.665410 + 1.15252i 0.979174 + 0.203024i \(0.0650768\pi\)
−0.313763 + 0.949501i \(0.601590\pi\)
\(84\) 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 \(-0.706353\pi\)
0.388425 + 0.921480i \(0.373019\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) 5.19615 + 9.00000i 0.517036 + 0.895533i 0.999804 + 0.0197851i \(0.00629819\pi\)
−0.482768 + 0.875748i \(0.660368\pi\)
\(102\) 0 0
\(103\) 16.9706 + 9.79796i 1.67216 + 0.965422i 0.966426 + 0.256943i \(0.0827154\pi\)
0.705733 + 0.708478i \(0.250618\pi\)
\(104\) 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 \(-0.129029\pi\)
0.117967 + 0.993018i \(0.462362\pi\)
\(114\) 0 0
\(115\) 12.7279 7.34847i 1.18688 0.685248i
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) 4.54026 0.621320i 0.416205 0.0569563i
\(120\) 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 −0.998630 0.0523366i \(-0.983333\pi\)
0.544640 + 0.838670i \(0.316666\pi\)
\(132\) 0 0
\(133\) 0.878680 + 6.42090i 0.0761912 + 0.556762i
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) −18.3712 + 10.6066i −1.56956 + 0.906183i −0.573335 + 0.819321i \(0.694351\pi\)
−0.996220 + 0.0868620i \(0.972316\pi\)
\(138\) 0 0
\(139\) 10.6066 + 6.12372i 0.899640 + 0.519408i 0.877083 0.480338i \(-0.159486\pi\)
0.0225568 + 0.999746i \(0.492819\pi\)
\(140\) 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 \(-0.158760\pi\)
0.0248379 + 0.999691i \(0.492093\pi\)
\(150\) 0 0
\(151\) 2.50000 + 4.33013i 0.203447 + 0.352381i 0.949637 0.313353i \(-0.101452\pi\)
−0.746190 + 0.665733i \(0.768119\pi\)
\(152\) 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 \(-0.238601\pi\)
−0.224070 + 0.974573i \(0.571935\pi\)
\(158\) 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 −0.216601 0.976260i \(-0.569497\pi\)
0.953767 0.300548i \(-0.0971696\pi\)
\(168\) 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 −0.925897 0.377776i \(-0.876689\pi\)
0.135785 0.990738i \(-0.456644\pi\)
\(174\) 0 0
\(175\) 3.24264 + 4.18154i 0.245121 + 0.316095i
\(176\) 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 \(-0.567346\pi\)
0.741715 + 0.670715i \(0.234013\pi\)
\(192\) 0 0
\(193\) −3.50000 + 6.06218i −0.251936 + 0.436365i −0.964059 0.265689i \(-0.914400\pi\)
0.712123 + 0.702055i \(0.247734\pi\)
\(194\) 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
\(203\) 8.87039 6.87868i 0.622579 0.482789i
\(204\) 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 −0.694857 0.719148i \(-0.744533\pi\)
0.970229 + 0.242190i \(0.0778659\pi\)
\(212\) 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 \(-0.402373\pi\)
0.976570 + 0.215199i \(0.0690401\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(228\) 0 0
\(229\) −12.7279 7.34847i −0.841085 0.485601i 0.0165480 0.999863i \(-0.494732\pi\)
−0.857633 + 0.514263i \(0.828066\pi\)
\(230\) 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 \(-0.574005\pi\)
−0.957927 + 0.287011i \(0.907338\pi\)
\(240\) 0 0
\(241\) −23.3345 + 13.4722i −1.50311 + 0.867820i −0.503115 + 0.864219i \(0.667813\pi\)
−0.999994 + 0.00360098i \(0.998854\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) −3.01834 + 11.7426i −0.192835 + 0.750210i
\(246\) 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 −0.981335 0.192304i \(-0.938404\pi\)
0.657208 + 0.753709i \(0.271737\pi\)
\(258\) 0 0
\(259\) 2.62132 0.358719i 0.162881 0.0222897i
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) 18.3712 10.6066i 1.13282 0.654031i 0.188174 0.982136i \(-0.439743\pi\)
0.944641 + 0.328105i \(0.106410\pi\)
\(264\) 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 0.951807 0.306699i \(-0.0992243\pi\)
−0.741512 + 0.670940i \(0.765891\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) 7.34847 4.24264i 0.438373 0.253095i −0.264534 0.964376i \(-0.585218\pi\)
0.702907 + 0.711282i \(0.251885\pi\)
\(282\) 0 0
\(283\) −6.36396 3.67423i −0.378298 0.218411i 0.298779 0.954322i \(-0.403421\pi\)
−0.677078 + 0.735912i \(0.736754\pi\)
\(284\) 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 −0.964342 0.264660i \(-0.914740\pi\)
0.711373 + 0.702815i \(0.248074\pi\)
\(294\) 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
\(301\) −11.3492 14.6354i −0.654159 0.843570i
\(302\) 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 0.347382 + 0.937724i \(0.387071\pi\)
−0.985784 + 0.168020i \(0.946263\pi\)
\(312\) 0 0
\(313\) −21.2132 + 12.2474i −1.19904 + 0.692267i −0.960341 0.278827i \(-0.910054\pi\)
−0.238700 + 0.971093i \(0.576721\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(318\) 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
\(329\) −19.6575 25.3492i −1.08375 1.39755i
\(330\) 0 0
\(331\) −6.50000 11.2583i −0.357272 0.618814i 0.630232 0.776407i \(-0.282960\pi\)
−0.987504 + 0.157593i \(0.949627\pi\)
\(332\) 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 0.293783 + 0.955872i \(0.405086\pi\)
−0.974701 + 0.223513i \(0.928247\pi\)
\(338\) 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 \(-0.140512\pi\)
0.0820751 + 0.996626i \(0.473845\pi\)
\(348\) 0 0
\(349\) −16.9706 + 9.79796i −0.908413 + 0.524473i −0.879920 0.475121i \(-0.842404\pi\)
−0.0284931 + 0.999594i \(0.509071\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) −0.866025 1.50000i −0.0460939 0.0798369i 0.842058 0.539387i \(-0.181344\pi\)
−0.888152 + 0.459550i \(0.848011\pi\)
\(354\) 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 \(-0.625855\pi\)
0.606628 + 0.794986i \(0.292522\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) 0 0
\(372\) 0 0
\(373\) −5.50000 + 9.52628i −0.284779 + 0.493252i −0.972556 0.232671i \(-0.925254\pi\)
0.687776 + 0.725923i \(0.258587\pi\)
\(374\) 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 −0.999884 0.0152097i \(-0.995158\pi\)
0.513114 + 0.858320i \(0.328492\pi\)
\(384\) 0 0
\(385\) 2.63604 + 19.2627i 0.134345 + 0.981718i
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) 25.7196 14.8492i 1.30404 0.752886i 0.322944 0.946418i \(-0.395328\pi\)
0.981094 + 0.193532i \(0.0619942\pi\)
\(390\) 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 \(-0.401288\pi\)
−0.672132 + 0.740432i \(0.734621\pi\)
\(402\) 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 −0.962757 0.270367i \(-0.912855\pi\)
−0.715523 0.698589i \(-0.753812\pi\)
\(410\) 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 −0.242064 0.970260i \(-0.577824\pi\)
0.961302 0.275496i \(-0.0888422\pi\)
\(420\) 0 0
\(421\) −10.0000 17.3205i −0.487370 0.844150i 0.512524 0.858673i \(-0.328710\pi\)
−0.999895 + 0.0145228i \(0.995377\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) 1.73205 + 3.00000i 0.0840168 + 0.145521i
\(426\) 0 0
\(427\) 5.12132 3.97141i 0.247838 0.192190i
\(428\) 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 \(-0.419205\pi\)
0.963832 + 0.266512i \(0.0858712\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) −11.0227 + 6.36396i −0.523704 + 0.302361i −0.738449 0.674309i \(-0.764441\pi\)
0.214745 + 0.976670i \(0.431108\pi\)
\(444\) 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
\(455\) −8.87039 + 6.87868i −0.415850 + 0.322477i
\(456\) 0 0
\(457\) 4.00000 + 6.92820i 0.187112 + 0.324088i 0.944286 0.329125i \(-0.106754\pi\)
−0.757174 + 0.653213i \(0.773421\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) −14.7224 25.5000i −0.685692 1.18765i −0.973219 0.229881i \(-0.926166\pi\)
0.287527 0.957773i \(-0.407167\pi\)
\(462\) 0 0
\(463\) −14.5000 + 25.1147i −0.673872 + 1.16718i 0.302925 + 0.953014i \(0.402037\pi\)
−0.976797 + 0.214166i \(0.931297\pi\)
\(464\) 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 −0.813916 0.580982i \(-0.802669\pi\)
−0.0961869 0.995363i \(-0.530665\pi\)
\(480\) 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 \(-0.240608\pi\)
−0.230211 + 0.973141i \(0.573942\pi\)
\(492\) 0 0
\(493\) 6.36396 3.67423i 0.286618 0.165479i
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 3.04384 + 22.2426i 0.136535 + 0.997719i
\(498\) 0 0
\(499\) −9.50000 + 16.4545i −0.425278 + 0.736604i −0.996446 0.0842294i \(-0.973157\pi\)
0.571168 + 0.820833i \(0.306490\pi\)
\(500\) 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 −0.996159 0.0875661i \(-0.972091\pi\)
0.573914 + 0.818916i \(0.305424\pi\)
\(510\) 0 0
\(511\) 3.51472 + 25.6836i 0.155482 + 1.13618i
\(512\) 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 −0.855138 0.518400i \(-0.826528\pi\)
−0.0213785 0.999771i \(-0.506805\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) 5.19615 + 9.00000i 0.221364 + 0.383413i
\(552\) 0 0
\(553\) −8.10660 10.4539i −0.344728 0.444543i
\(554\) 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 −0.559550 0.828796i \(-0.689026\pi\)
0.997534 + 0.0701867i \(0.0223595\pi\)
\(564\) 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 \(-0.414709\pi\)
0.967500 + 0.252872i \(0.0813753\pi\)
\(570\) 0 0
\(571\) 12.5000 21.6506i 0.523109 0.906051i −0.476530 0.879158i \(-0.658105\pi\)
0.999638 0.0268925i \(-0.00856117\pi\)
\(572\) 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
\(581\) 19.6575 + 25.3492i 0.815529 + 1.05166i
\(582\) 0 0
\(583\) 0 0
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 20.7846 + 36.0000i 0.857873 + 1.48588i 0.873954 + 0.486008i \(0.161548\pi\)
−0.0160815 + 0.999871i \(0.505119\pi\)
\(588\) 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 \(-0.360957\pi\)
−0.573181 + 0.819429i \(0.694291\pi\)
\(600\) 0 0
\(601\) −19.0919 + 11.0227i −0.778774 + 0.449625i −0.835996 0.548736i \(-0.815109\pi\)
0.0572215 + 0.998362i \(0.481776\pi\)
\(602\) 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 \(-0.517495\pi\)
−0.892185 + 0.451671i \(0.850828\pi\)
\(608\) 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 \(-0.162087\pi\)
0.0143859 + 0.999897i \(0.495421\pi\)
\(618\) 0 0
\(619\) −2.12132 + 1.22474i −0.0852631 + 0.0492267i −0.542025 0.840362i \(-0.682342\pi\)
0.456762 + 0.889589i \(0.349009\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 27.2416 3.72792i 1.09141 0.149356i
\(624\) 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
\(637\) 16.6066 + 4.26858i 0.657978 + 0.169127i
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) −18.3712 + 10.6066i −0.725618 + 0.418936i −0.816817 0.576897i \(-0.804263\pi\)
0.0911991 + 0.995833i \(0.470930\pi\)
\(642\) 0 0
\(643\) 12.7279 + 7.34847i 0.501940 + 0.289795i 0.729514 0.683965i \(-0.239746\pi\)
−0.227574 + 0.973761i \(0.573079\pi\)
\(644\) 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 \(-0.530709\pi\)
−0.910161 + 0.414254i \(0.864042\pi\)
\(654\) 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 \(-0.773897\pi\)
0.185640 + 0.982618i \(0.440564\pi\)
\(660\) 0 0
\(661\) −10.6066 6.12372i −0.412549 0.238185i 0.279335 0.960194i \(-0.409886\pi\)
−0.691884 + 0.722008i \(0.743219\pi\)
\(662\) 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 0.669630 0.742695i \(-0.266453\pi\)
−0.978008 + 0.208569i \(0.933119\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 15.5885 + 27.0000i 0.599113 + 1.03769i 0.992952 + 0.118515i \(0.0378134\pi\)
−0.393839 + 0.919179i \(0.628853\pi\)
\(678\) 0 0
\(679\) −5.12132 + 3.97141i −0.196538 + 0.152409i
\(680\) 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 \(-0.804399\pi\)
0.0907737 + 0.995872i \(0.471066\pi\)
\(692\) 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
\(707\) 16.8493 + 21.7279i 0.633681 + 0.817163i
\(708\) 0 0
\(709\) −24.5000 42.4352i −0.920117 1.59369i −0.799232 0.601023i \(-0.794760\pi\)
−0.120885 0.992667i \(-0.538573\pi\)
\(710\) 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 \(-0.710178\pi\)
0.377323 + 0.926082i \(0.376845\pi\)
\(728\) 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 \(-0.515986\pi\)
−0.890033 + 0.455895i \(0.849319\pi\)
\(734\) 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 \(-0.206113\pi\)
−0.123607 + 0.992331i \(0.539446\pi\)
\(744\) 0 0
\(745\) −19.0919 + 11.0227i −0.699472 + 0.403841i
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) −3.04384 22.2426i −0.111219 0.812728i
\(750\) 0 0
\(751\) −5.00000 + 8.66025i −0.182453 + 0.316017i −0.942715 0.333599i \(-0.891737\pi\)
0.760263 + 0.649616i \(0.225070\pi\)
\(752\) 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 −0.586564 0.809903i \(-0.699520\pi\)
0.994678 + 0.103028i \(0.0328532\pi\)
\(762\) 0 0
\(763\) 34.0772 4.66335i 1.23368 0.168825i
\(764\) 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 \(-0.305180\pi\)
−0.421549 + 0.906806i \(0.638513\pi\)
\(770\) 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 \(-0.361162\pi\)
−0.573707 + 0.819060i \(0.694495\pi\)
\(788\) 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 −0.943258 0.332060i \(-0.892256\pi\)
0.759201 + 0.650856i \(0.225590\pi\)
\(798\) 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
\(805\) 30.7279 23.8284i 1.08302