Properties

Label 1368.2.s.j.505.1
Level $1368$
Weight $2$
Character 1368.505
Analytic conductor $10.924$
Analytic rank $0$
Dimension $6$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 1368 = 2^{3} \cdot 3^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1368.s (of order \(3\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(10.9235349965\)
Analytic rank: \(0\)
Dimension: \(6\)
Relative dimension: \(3\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\Q(\zeta_{18})\)
Defining polynomial: \( x^{6} - x^{3} + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{19}]\)
Coefficient ring index: \( 2^{6} \)
Twist minimal: no (minimal twist has level 456)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 505.1
Root \(-0.766044 - 0.642788i\) of defining polynomial
Character \(\chi\) \(=\) 1368.505
Dual form 1368.2.s.j.577.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.87939 + 3.25519i) q^{5} +4.75877 q^{7} +O(q^{10})\) \(q+(-1.87939 + 3.25519i) q^{5} +4.75877 q^{7} +4.36959 q^{11} +(-0.500000 - 0.866025i) q^{13} +(3.06418 - 5.30731i) q^{17} +(0.694593 + 4.30320i) q^{19} +(-1.87939 - 3.25519i) q^{23} +(-4.56418 - 7.90539i) q^{25} +(2.69459 + 4.66717i) q^{29} +7.36959 q^{31} +(-8.94356 + 15.4907i) q^{35} -7.12836 q^{37} +(-1.75877 + 3.04628i) q^{41} +(0.379385 - 0.657115i) q^{43} +(-3.00000 - 5.19615i) q^{47} +15.6459 q^{49} +(2.57398 + 4.45826i) q^{53} +(-8.21213 + 14.2238i) q^{55} +(4.63816 - 8.03352i) q^{59} +(4.25877 + 7.37641i) q^{61} +3.75877 q^{65} +(-0.684793 - 1.18610i) q^{67} +(-5.82295 + 10.0856i) q^{71} +(-2.25877 + 3.91231i) q^{73} +20.7939 q^{77} +(-7.07398 + 12.2525i) q^{79} -4.90673 q^{83} +(11.5175 + 19.9490i) q^{85} +(4.18479 + 7.24827i) q^{89} +(-2.37939 - 4.12122i) q^{91} +(-15.3131 - 5.82634i) q^{95} +(5.82295 - 10.0856i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6 q + 6 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 6 q + 6 q^{7} + 12 q^{11} - 3 q^{13} - 9 q^{25} + 12 q^{29} + 30 q^{31} - 24 q^{35} - 6 q^{37} + 12 q^{41} - 9 q^{43} - 18 q^{47} + 12 q^{49} - 6 q^{59} + 3 q^{61} + 3 q^{67} + 6 q^{71} + 9 q^{73} + 12 q^{77} - 27 q^{79} + 24 q^{83} + 24 q^{85} + 18 q^{89} - 3 q^{91} - 48 q^{95} - 6 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1368\mathbb{Z}\right)^\times\).

\(n\) \(343\) \(685\) \(1009\) \(1217\)
\(\chi(n)\) \(1\) \(1\) \(e\left(\frac{2}{3}\right)\) \(1\)

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
\(5\) −1.87939 + 3.25519i −0.840487 + 1.45577i 0.0489972 + 0.998799i \(0.484397\pi\)
−0.889484 + 0.456967i \(0.848936\pi\)
\(6\) 0 0
\(7\) 4.75877 1.79865 0.899323 0.437285i \(-0.144060\pi\)
0.899323 + 0.437285i \(0.144060\pi\)
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) 4.36959 1.31748 0.658740 0.752371i \(-0.271090\pi\)
0.658740 + 0.752371i \(0.271090\pi\)
\(12\) 0 0
\(13\) −0.500000 0.866025i −0.138675 0.240192i 0.788320 0.615265i \(-0.210951\pi\)
−0.926995 + 0.375073i \(0.877618\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 3.06418 5.30731i 0.743172 1.28721i −0.207872 0.978156i \(-0.566654\pi\)
0.951044 0.309056i \(-0.100013\pi\)
\(18\) 0 0
\(19\) 0.694593 + 4.30320i 0.159350 + 0.987222i
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) −1.87939 3.25519i −0.391879 0.678754i 0.600818 0.799385i \(-0.294841\pi\)
−0.992697 + 0.120631i \(0.961508\pi\)
\(24\) 0 0
\(25\) −4.56418 7.90539i −0.912836 1.58108i
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) 2.69459 + 4.66717i 0.500373 + 0.866672i 1.00000 0.000431109i \(0.000137226\pi\)
−0.499627 + 0.866241i \(0.666529\pi\)
\(30\) 0 0
\(31\) 7.36959 1.32362 0.661808 0.749673i \(-0.269789\pi\)
0.661808 + 0.749673i \(0.269789\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) −8.94356 + 15.4907i −1.51174 + 2.61841i
\(36\) 0 0
\(37\) −7.12836 −1.17189 −0.585947 0.810349i \(-0.699277\pi\)
−0.585947 + 0.810349i \(0.699277\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) −1.75877 + 3.04628i −0.274674 + 0.475749i −0.970053 0.242894i \(-0.921903\pi\)
0.695379 + 0.718643i \(0.255237\pi\)
\(42\) 0 0
\(43\) 0.379385 0.657115i 0.0578557 0.100209i −0.835647 0.549267i \(-0.814907\pi\)
0.893503 + 0.449058i \(0.148240\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) −3.00000 5.19615i −0.437595 0.757937i 0.559908 0.828554i \(-0.310836\pi\)
−0.997503 + 0.0706177i \(0.977503\pi\)
\(48\) 0 0
\(49\) 15.6459 2.23513
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) 2.57398 + 4.45826i 0.353563 + 0.612389i 0.986871 0.161511i \(-0.0516366\pi\)
−0.633308 + 0.773900i \(0.718303\pi\)
\(54\) 0 0
\(55\) −8.21213 + 14.2238i −1.10732 + 1.91794i
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) 4.63816 8.03352i 0.603836 1.04588i −0.388398 0.921492i \(-0.626971\pi\)
0.992234 0.124384i \(-0.0396953\pi\)
\(60\) 0 0
\(61\) 4.25877 + 7.37641i 0.545280 + 0.944452i 0.998589 + 0.0530990i \(0.0169099\pi\)
−0.453310 + 0.891353i \(0.649757\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) 3.75877 0.466218
\(66\) 0 0
\(67\) −0.684793 1.18610i −0.0836607 0.144905i 0.821159 0.570699i \(-0.193328\pi\)
−0.904820 + 0.425795i \(0.859995\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) −5.82295 + 10.0856i −0.691057 + 1.19695i 0.280435 + 0.959873i \(0.409521\pi\)
−0.971492 + 0.237073i \(0.923812\pi\)
\(72\) 0 0
\(73\) −2.25877 + 3.91231i −0.264369 + 0.457901i −0.967398 0.253260i \(-0.918497\pi\)
0.703029 + 0.711161i \(0.251830\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 20.7939 2.36968
\(78\) 0 0
\(79\) −7.07398 + 12.2525i −0.795885 + 1.37851i 0.126391 + 0.991980i \(0.459661\pi\)
−0.922276 + 0.386532i \(0.873673\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) −4.90673 −0.538583 −0.269292 0.963059i \(-0.586790\pi\)
−0.269292 + 0.963059i \(0.586790\pi\)
\(84\) 0 0
\(85\) 11.5175 + 19.9490i 1.24925 + 2.16377i
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 4.18479 + 7.24827i 0.443587 + 0.768315i 0.997953 0.0639579i \(-0.0203723\pi\)
−0.554365 + 0.832273i \(0.687039\pi\)
\(90\) 0 0
\(91\) −2.37939 4.12122i −0.249427 0.432021i
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) −15.3131 5.82634i −1.57110 0.597770i
\(96\) 0 0
\(97\) 5.82295 10.0856i 0.591231 1.02404i −0.402836 0.915272i \(-0.631976\pi\)
0.994067 0.108770i \(-0.0346911\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) −2.06418 3.57526i −0.205393 0.355752i 0.744865 0.667216i \(-0.232514\pi\)
−0.950258 + 0.311464i \(0.899181\pi\)
\(102\) 0 0
\(103\) −6.75877 −0.665961 −0.332981 0.942934i \(-0.608054\pi\)
−0.332981 + 0.942934i \(0.608054\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 4.12836 0.399103 0.199552 0.979887i \(-0.436051\pi\)
0.199552 + 0.979887i \(0.436051\pi\)
\(108\) 0 0
\(109\) 0.0641778 0.111159i 0.00614712 0.0106471i −0.862935 0.505314i \(-0.831377\pi\)
0.869083 + 0.494667i \(0.164710\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) 2.40879 0.226600 0.113300 0.993561i \(-0.463858\pi\)
0.113300 + 0.993561i \(0.463858\pi\)
\(114\) 0 0
\(115\) 14.1284 1.31748
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) 14.5817 25.2563i 1.33670 2.31524i
\(120\) 0 0
\(121\) 8.09327 0.735752
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) 15.5175 1.38793
\(126\) 0 0
\(127\) −0.241230 0.417822i −0.0214057 0.0370757i 0.855124 0.518423i \(-0.173481\pi\)
−0.876530 + 0.481348i \(0.840147\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) −1.69459 + 2.93512i −0.148057 + 0.256443i −0.930509 0.366268i \(-0.880635\pi\)
0.782452 + 0.622711i \(0.213969\pi\)
\(132\) 0 0
\(133\) 3.30541 + 20.4779i 0.286615 + 1.77566i
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) −9.21213 15.9559i −0.787046 1.36320i −0.927769 0.373154i \(-0.878276\pi\)
0.140724 0.990049i \(-0.455057\pi\)
\(138\) 0 0
\(139\) −0.00980018 0.0169744i −0.000831240 0.00143975i 0.865609 0.500720i \(-0.166931\pi\)
−0.866441 + 0.499280i \(0.833598\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) −2.18479 3.78417i −0.182702 0.316448i
\(144\) 0 0
\(145\) −20.2567 −1.68223
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) 3.12061 5.40506i 0.255651 0.442800i −0.709421 0.704785i \(-0.751044\pi\)
0.965072 + 0.261985i \(0.0843770\pi\)
\(150\) 0 0
\(151\) 0.739170 0.0601528 0.0300764 0.999548i \(-0.490425\pi\)
0.0300764 + 0.999548i \(0.490425\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) −13.8503 + 23.9894i −1.11248 + 1.92688i
\(156\) 0 0
\(157\) 3.32295 5.75552i 0.265200 0.459340i −0.702416 0.711767i \(-0.747895\pi\)
0.967616 + 0.252427i \(0.0812286\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) −8.94356 15.4907i −0.704852 1.22084i
\(162\) 0 0
\(163\) −11.3696 −0.890535 −0.445267 0.895398i \(-0.646891\pi\)
−0.445267 + 0.895398i \(0.646891\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 1.49020 + 2.58110i 0.115315 + 0.199732i 0.917906 0.396799i \(-0.129879\pi\)
−0.802591 + 0.596530i \(0.796546\pi\)
\(168\) 0 0
\(169\) 6.00000 10.3923i 0.461538 0.799408i
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) −2.69459 + 4.66717i −0.204866 + 0.354838i −0.950090 0.311976i \(-0.899009\pi\)
0.745224 + 0.666814i \(0.232343\pi\)
\(174\) 0 0
\(175\) −21.7199 37.6199i −1.64187 2.84380i
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) −4.24123 −0.317004 −0.158502 0.987359i \(-0.550666\pi\)
−0.158502 + 0.987359i \(0.550666\pi\)
\(180\) 0 0
\(181\) −6.30541 10.9213i −0.468677 0.811773i 0.530682 0.847571i \(-0.321936\pi\)
−0.999359 + 0.0357984i \(0.988603\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 13.3969 23.2042i 0.984962 1.70600i
\(186\) 0 0
\(187\) 13.3892 23.1907i 0.979114 1.69588i
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 22.6263 1.63718 0.818591 0.574377i \(-0.194756\pi\)
0.818591 + 0.574377i \(0.194756\pi\)
\(192\) 0 0
\(193\) −12.3229 + 21.3440i −0.887025 + 1.53637i −0.0436505 + 0.999047i \(0.513899\pi\)
−0.843375 + 0.537326i \(0.819435\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) −22.6655 −1.61485 −0.807425 0.589970i \(-0.799139\pi\)
−0.807425 + 0.589970i \(0.799139\pi\)
\(198\) 0 0
\(199\) −6.96110 12.0570i −0.493460 0.854697i 0.506512 0.862233i \(-0.330935\pi\)
−0.999972 + 0.00753584i \(0.997601\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) 12.8229 + 22.2100i 0.899995 + 1.55884i
\(204\) 0 0
\(205\) −6.61081 11.4503i −0.461719 0.799721i
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) 3.03508 + 18.8032i 0.209941 + 1.30064i
\(210\) 0 0
\(211\) 1.00980 1.74903i 0.0695175 0.120408i −0.829172 0.558994i \(-0.811187\pi\)
0.898689 + 0.438586i \(0.144521\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) 1.42602 + 2.46994i 0.0972539 + 0.168449i
\(216\) 0 0
\(217\) 35.0702 2.38072
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) −6.12836 −0.412238
\(222\) 0 0
\(223\) −14.1827 + 24.5652i −0.949746 + 1.64501i −0.203789 + 0.979015i \(0.565325\pi\)
−0.745958 + 0.665993i \(0.768008\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) −20.1830 −1.33960 −0.669798 0.742544i \(-0.733619\pi\)
−0.669798 + 0.742544i \(0.733619\pi\)
\(228\) 0 0
\(229\) 11.7784 0.778337 0.389168 0.921167i \(-0.372762\pi\)
0.389168 + 0.921167i \(0.372762\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) −0.0641778 + 0.111159i −0.00420443 + 0.00728228i −0.868120 0.496354i \(-0.834672\pi\)
0.863916 + 0.503637i \(0.168005\pi\)
\(234\) 0 0
\(235\) 22.5526 1.47117
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) −3.10876 −0.201089 −0.100544 0.994933i \(-0.532058\pi\)
−0.100544 + 0.994933i \(0.532058\pi\)
\(240\) 0 0
\(241\) −5.64796 9.78255i −0.363817 0.630149i 0.624769 0.780810i \(-0.285193\pi\)
−0.988586 + 0.150661i \(0.951860\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) −29.4047 + 50.9304i −1.87860 + 3.25382i
\(246\) 0 0
\(247\) 3.37939 2.75314i 0.215025 0.175178i
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) −0.758770 1.31423i −0.0478932 0.0829534i 0.841085 0.540903i \(-0.181917\pi\)
−0.888978 + 0.457950i \(0.848584\pi\)
\(252\) 0 0
\(253\) −8.21213 14.2238i −0.516292 0.894245i
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) −6.09152 10.5508i −0.379979 0.658142i 0.611080 0.791569i \(-0.290735\pi\)
−0.991059 + 0.133427i \(0.957402\pi\)
\(258\) 0 0
\(259\) −33.9222 −2.10782
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) −9.69459 + 16.7915i −0.597794 + 1.03541i 0.395352 + 0.918530i \(0.370623\pi\)
−0.993146 + 0.116880i \(0.962711\pi\)
\(264\) 0 0
\(265\) −19.3500 −1.18866
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) 11.7023 20.2690i 0.713504 1.23582i −0.250030 0.968238i \(-0.580440\pi\)
0.963534 0.267587i \(-0.0862262\pi\)
\(270\) 0 0
\(271\) −0.482459 + 0.835644i −0.0293073 + 0.0507617i −0.880307 0.474404i \(-0.842663\pi\)
0.851000 + 0.525166i \(0.175997\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) −19.9436 34.5433i −1.20264 2.08304i
\(276\) 0 0
\(277\) 15.3892 0.924647 0.462323 0.886711i \(-0.347016\pi\)
0.462323 + 0.886711i \(0.347016\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) 4.24897 + 7.35943i 0.253472 + 0.439027i 0.964479 0.264158i \(-0.0850940\pi\)
−0.711007 + 0.703185i \(0.751761\pi\)
\(282\) 0 0
\(283\) 5.51754 9.55666i 0.327984 0.568085i −0.654128 0.756384i \(-0.726964\pi\)
0.982112 + 0.188299i \(0.0602975\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) −8.36959 + 14.4965i −0.494041 + 0.855704i
\(288\) 0 0
\(289\) −10.2784 17.8027i −0.604610 1.04722i
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) 1.03508 0.0604701 0.0302351 0.999543i \(-0.490374\pi\)
0.0302351 + 0.999543i \(0.490374\pi\)
\(294\) 0 0
\(295\) 17.4338 + 30.1962i 1.01503 + 1.75809i
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) −1.87939 + 3.25519i −0.108688 + 0.188253i
\(300\) 0 0
\(301\) 1.80541 3.12706i 0.104062 0.180241i
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) −32.0155 −1.83320
\(306\) 0 0
\(307\) −7.43376 + 12.8757i −0.424267 + 0.734852i −0.996352 0.0853423i \(-0.972802\pi\)
0.572084 + 0.820195i \(0.306135\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 16.0547 0.910378 0.455189 0.890395i \(-0.349572\pi\)
0.455189 + 0.890395i \(0.349572\pi\)
\(312\) 0 0
\(313\) −17.5817 30.4524i −0.993777 1.72127i −0.593350 0.804945i \(-0.702195\pi\)
−0.400428 0.916328i \(-0.631138\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 9.26857 + 16.0536i 0.520575 + 0.901662i 0.999714 + 0.0239230i \(0.00761564\pi\)
−0.479139 + 0.877739i \(0.659051\pi\)
\(318\) 0 0
\(319\) 11.7743 + 20.3936i 0.659232 + 1.14182i
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) 24.9668 + 9.49935i 1.38919 + 0.528558i
\(324\) 0 0
\(325\) −4.56418 + 7.90539i −0.253175 + 0.438512i
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) −14.2763 24.7273i −0.787079 1.36326i
\(330\) 0 0
\(331\) −8.75877 −0.481426 −0.240713 0.970596i \(-0.577381\pi\)
−0.240713 + 0.970596i \(0.577381\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) 5.14796 0.281263
\(336\) 0 0
\(337\) 10.6925 18.5200i 0.582459 1.00885i −0.412728 0.910855i \(-0.635424\pi\)
0.995187 0.0979947i \(-0.0312428\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) 32.2020 1.74384
\(342\) 0 0
\(343\) 41.1438 2.22156
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 11.9632 20.7208i 0.642216 1.11235i −0.342721 0.939437i \(-0.611348\pi\)
0.984937 0.172914i \(-0.0553182\pi\)
\(348\) 0 0
\(349\) −23.0702 −1.23492 −0.617459 0.786603i \(-0.711838\pi\)
−0.617459 + 0.786603i \(0.711838\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) 28.4979 1.51679 0.758396 0.651794i \(-0.225983\pi\)
0.758396 + 0.651794i \(0.225983\pi\)
\(354\) 0 0
\(355\) −21.8871 37.9096i −1.16165 2.01203i
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 2.48246 4.29975i 0.131019 0.226932i −0.793051 0.609156i \(-0.791508\pi\)
0.924070 + 0.382224i \(0.124842\pi\)
\(360\) 0 0
\(361\) −18.0351 + 5.97794i −0.949215 + 0.314629i
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) −8.49020 14.7055i −0.444397 0.769719i
\(366\) 0 0
\(367\) −9.42396 16.3228i −0.491927 0.852042i 0.508030 0.861339i \(-0.330374\pi\)
−0.999957 + 0.00929712i \(0.997041\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) 12.2490 + 21.2158i 0.635935 + 1.10147i
\(372\) 0 0
\(373\) 35.9026 1.85897 0.929483 0.368864i \(-0.120253\pi\)
0.929483 + 0.368864i \(0.120253\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 2.69459 4.66717i 0.138779 0.240372i
\(378\) 0 0
\(379\) −12.2763 −0.630592 −0.315296 0.948993i \(-0.602104\pi\)
−0.315296 + 0.948993i \(0.602104\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 7.20439 12.4784i 0.368127 0.637615i −0.621145 0.783695i \(-0.713332\pi\)
0.989273 + 0.146080i \(0.0466657\pi\)
\(384\) 0 0
\(385\) −39.0797 + 67.6880i −1.99168 + 3.44970i
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) 3.18479 + 5.51622i 0.161475 + 0.279684i 0.935398 0.353597i \(-0.115041\pi\)
−0.773923 + 0.633280i \(0.781708\pi\)
\(390\) 0 0
\(391\) −23.0351 −1.16493
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) −26.5895 46.0543i −1.33786 2.31724i
\(396\) 0 0
\(397\) 5.27837 9.14241i 0.264914 0.458844i −0.702627 0.711558i \(-0.747990\pi\)
0.967541 + 0.252714i \(0.0813231\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 10.7219 18.5709i 0.535428 0.927388i −0.463715 0.885985i \(-0.653484\pi\)
0.999143 0.0414036i \(-0.0131829\pi\)
\(402\) 0 0
\(403\) −3.68479 6.38225i −0.183553 0.317922i
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) −31.1480 −1.54395
\(408\) 0 0
\(409\) −3.32501 5.75908i −0.164411 0.284768i 0.772035 0.635580i \(-0.219239\pi\)
−0.936446 + 0.350812i \(0.885906\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) 22.0719 38.2297i 1.08609 1.88116i
\(414\) 0 0
\(415\) 9.22163 15.9723i 0.452672 0.784051i
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) −5.84793 −0.285690 −0.142845 0.989745i \(-0.545625\pi\)
−0.142845 + 0.989745i \(0.545625\pi\)
\(420\) 0 0
\(421\) −0.714193 + 1.23702i −0.0348076 + 0.0602886i −0.882904 0.469553i \(-0.844415\pi\)
0.848097 + 0.529841i \(0.177749\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) −55.9418 −2.71358
\(426\) 0 0
\(427\) 20.2665 + 35.1026i 0.980765 + 1.69874i
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 0.389185 + 0.674089i 0.0187464 + 0.0324697i 0.875246 0.483677i \(-0.160699\pi\)
−0.856500 + 0.516147i \(0.827366\pi\)
\(432\) 0 0
\(433\) −13.3425 23.1100i −0.641202 1.11059i −0.985165 0.171611i \(-0.945103\pi\)
0.343963 0.938983i \(-0.388231\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 12.7023 10.3484i 0.607635 0.495031i
\(438\) 0 0
\(439\) 14.2665 24.7103i 0.680903 1.17936i −0.293802 0.955866i \(-0.594921\pi\)
0.974706 0.223493i \(-0.0717460\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) −8.82295 15.2818i −0.419191 0.726060i 0.576667 0.816979i \(-0.304353\pi\)
−0.995858 + 0.0909191i \(0.971020\pi\)
\(444\) 0 0
\(445\) −31.4593 −1.49132
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) 1.38919 0.0655597 0.0327799 0.999463i \(-0.489564\pi\)
0.0327799 + 0.999463i \(0.489564\pi\)
\(450\) 0 0
\(451\) −7.68510 + 13.3110i −0.361877 + 0.626790i
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) 17.8871 0.838561
\(456\) 0 0
\(457\) 24.6851 1.15472 0.577360 0.816490i \(-0.304083\pi\)
0.577360 + 0.816490i \(0.304083\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 0.795607 1.37803i 0.0370551 0.0641813i −0.846903 0.531747i \(-0.821536\pi\)
0.883958 + 0.467566i \(0.154869\pi\)
\(462\) 0 0
\(463\) −21.7547 −1.01102 −0.505512 0.862819i \(-0.668696\pi\)
−0.505512 + 0.862819i \(0.668696\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) −15.5175 −0.718066 −0.359033 0.933325i \(-0.616893\pi\)
−0.359033 + 0.933325i \(0.616893\pi\)
\(468\) 0 0
\(469\) −3.25877 5.64436i −0.150476 0.260632i
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) 1.65776 2.87132i 0.0762237 0.132023i
\(474\) 0 0
\(475\) 30.8482 25.1316i 1.41541 1.15312i
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) −5.82295 10.0856i −0.266057 0.460825i 0.701783 0.712391i \(-0.252388\pi\)
−0.967840 + 0.251566i \(0.919054\pi\)
\(480\) 0 0
\(481\) 3.56418 + 6.17334i 0.162513 + 0.281480i
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 21.8871 + 37.9096i 0.993843 + 1.72139i
\(486\) 0 0
\(487\) 38.5526 1.74699 0.873493 0.486837i \(-0.161849\pi\)
0.873493 + 0.486837i \(0.161849\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) 3.82295 6.62154i 0.172527 0.298826i −0.766776 0.641915i \(-0.778140\pi\)
0.939303 + 0.343089i \(0.111473\pi\)
\(492\) 0 0
\(493\) 33.0268 1.48745
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) −27.7101 + 47.9953i −1.24297 + 2.15288i
\(498\) 0 0
\(499\) −15.3152 + 26.5267i −0.685603 + 1.18750i 0.287644 + 0.957737i \(0.407128\pi\)
−0.973247 + 0.229762i \(0.926205\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) −2.69459 4.66717i −0.120146 0.208099i 0.799679 0.600428i \(-0.205003\pi\)
−0.919825 + 0.392329i \(0.871670\pi\)
\(504\) 0 0
\(505\) 15.5175 0.690522
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) −1.12836 1.95437i −0.0500135 0.0866259i 0.839935 0.542687i \(-0.182593\pi\)
−0.889948 + 0.456061i \(0.849260\pi\)
\(510\) 0 0
\(511\) −10.7490 + 18.6178i −0.475506 + 0.823601i
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) 12.7023 22.0011i 0.559732 0.969484i
\(516\) 0 0
\(517\) −13.1088 22.7050i −0.576522 0.998566i
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) −37.2763 −1.63310 −0.816552 0.577271i \(-0.804118\pi\)
−0.816552 + 0.577271i \(0.804118\pi\)
\(522\) 0 0
\(523\) 0.186852 + 0.323637i 0.00817046 + 0.0141517i 0.870082 0.492907i \(-0.164066\pi\)
−0.861911 + 0.507059i \(0.830733\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 22.5817 39.1127i 0.983675 1.70378i
\(528\) 0 0
\(529\) 4.43582 7.68307i 0.192862 0.334046i
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) 3.51754 0.152362
\(534\) 0 0
\(535\) −7.75877 + 13.4386i −0.335441 + 0.581001i
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) 68.3661 2.94474
\(540\) 0 0
\(541\) 9.54458 + 16.5317i 0.410353 + 0.710753i 0.994928 0.100587i \(-0.0320720\pi\)
−0.584575 + 0.811340i \(0.698739\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) 0.241230 + 0.417822i 0.0103331 + 0.0178975i
\(546\) 0 0
\(547\) −21.8773 37.8926i −0.935407 1.62017i −0.773907 0.633300i \(-0.781700\pi\)
−0.161500 0.986873i \(-0.551633\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) −18.2121 + 14.8372i −0.775863 + 0.632084i
\(552\) 0 0
\(553\) −33.6634 + 58.3068i −1.43151 + 2.47946i
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 15.9513 + 27.6285i 0.675878 + 1.17066i 0.976211 + 0.216821i \(0.0695689\pi\)
−0.300333 + 0.953834i \(0.597098\pi\)
\(558\) 0 0
\(559\) −0.758770 −0.0320926
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) 3.87164 0.163170 0.0815852 0.996666i \(-0.474002\pi\)
0.0815852 + 0.996666i \(0.474002\pi\)
\(564\) 0 0
\(565\) −4.52704 + 7.84106i −0.190454 + 0.329876i
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 32.9959 1.38326 0.691630 0.722252i \(-0.256893\pi\)
0.691630 + 0.722252i \(0.256893\pi\)
\(570\) 0 0
\(571\) −24.1789 −1.01186 −0.505928 0.862576i \(-0.668850\pi\)
−0.505928 + 0.862576i \(0.668850\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) −17.1557 + 29.7145i −0.715442 + 1.23918i
\(576\) 0 0
\(577\) −3.16344 −0.131696 −0.0658478 0.997830i \(-0.520975\pi\)
−0.0658478 + 0.997830i \(0.520975\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) −23.3500 −0.968721
\(582\) 0 0
\(583\) 11.2472 + 19.4807i 0.465812 + 0.806810i
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) −3.00774 + 5.20956i −0.124143 + 0.215022i −0.921398 0.388621i \(-0.872951\pi\)
0.797255 + 0.603643i \(0.206285\pi\)
\(588\) 0 0
\(589\) 5.11886 + 31.7128i 0.210919 + 1.30670i
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) 11.4611 + 19.8512i 0.470651 + 0.815192i 0.999437 0.0335639i \(-0.0106857\pi\)
−0.528785 + 0.848756i \(0.677352\pi\)
\(594\) 0 0
\(595\) 54.8093 + 94.9326i 2.24696 + 3.89186i
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) 17.2199 + 29.8257i 0.703585 + 1.21864i 0.967200 + 0.254017i \(0.0817519\pi\)
−0.263615 + 0.964628i \(0.584915\pi\)
\(600\) 0 0
\(601\) 24.1634 0.985647 0.492824 0.870129i \(-0.335965\pi\)
0.492824 + 0.870129i \(0.335965\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) −15.2104 + 26.3451i −0.618390 + 1.07108i
\(606\) 0 0
\(607\) −6.84793 −0.277949 −0.138974 0.990296i \(-0.544381\pi\)
−0.138974 + 0.990296i \(0.544381\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) −3.00000 + 5.19615i −0.121367 + 0.210214i
\(612\) 0 0
\(613\) −8.47296 + 14.6756i −0.342220 + 0.592742i −0.984845 0.173439i \(-0.944512\pi\)
0.642625 + 0.766181i \(0.277845\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 21.1361 + 36.6088i 0.850907 + 1.47381i 0.880391 + 0.474249i \(0.157280\pi\)
−0.0294834 + 0.999565i \(0.509386\pi\)
\(618\) 0 0
\(619\) 4.59121 0.184536 0.0922682 0.995734i \(-0.470588\pi\)
0.0922682 + 0.995734i \(0.470588\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 19.9145 + 34.4929i 0.797856 + 1.38193i
\(624\) 0 0
\(625\) −6.34255 + 10.9856i −0.253702 + 0.439425i
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) −21.8425 + 37.8324i −0.870919 + 1.50848i
\(630\) 0 0
\(631\) 18.7841 + 32.5349i 0.747781 + 1.29520i 0.948884 + 0.315625i \(0.102214\pi\)
−0.201103 + 0.979570i \(0.564452\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) 1.81345 0.0719647
\(636\) 0 0
\(637\) −7.82295 13.5497i −0.309956 0.536860i
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) −2.75877 + 4.77833i −0.108965 + 0.188733i −0.915351 0.402656i \(-0.868087\pi\)
0.806386 + 0.591389i \(0.201420\pi\)
\(642\) 0 0
\(643\) 17.5915 30.4694i 0.693742 1.20160i −0.276861 0.960910i \(-0.589294\pi\)
0.970603 0.240686i \(-0.0773724\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 3.57573 0.140577 0.0702883 0.997527i \(-0.477608\pi\)
0.0702883 + 0.997527i \(0.477608\pi\)
\(648\) 0 0
\(649\) 20.2668 35.1032i 0.795542 1.37792i
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) −32.6418 −1.27737 −0.638686 0.769468i \(-0.720522\pi\)
−0.638686 + 0.769468i \(0.720522\pi\)
\(654\) 0 0
\(655\) −6.36959 11.0324i −0.248880 0.431073i
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) 24.4807 + 42.4018i 0.953633 + 1.65174i 0.737466 + 0.675384i \(0.236022\pi\)
0.216167 + 0.976356i \(0.430645\pi\)
\(660\) 0 0
\(661\) −17.7392 30.7251i −0.689974 1.19507i −0.971846 0.235618i \(-0.924289\pi\)
0.281872 0.959452i \(-0.409045\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) −72.8718 27.7262i −2.82585 1.07518i
\(666\) 0 0
\(667\) 10.1284 17.5428i 0.392171 0.679261i
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 18.6091 + 32.2318i 0.718395 + 1.24430i
\(672\) 0 0
\(673\) 2.68510 0.103503 0.0517514 0.998660i \(-0.483520\pi\)
0.0517514 + 0.998660i \(0.483520\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) −18.3351 −0.704676 −0.352338 0.935873i \(-0.614613\pi\)
−0.352338 + 0.935873i \(0.614613\pi\)
\(678\) 0 0
\(679\) 27.7101 47.9953i 1.06342 1.84189i
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) −4.07367 −0.155875 −0.0779374 0.996958i \(-0.524833\pi\)
−0.0779374 + 0.996958i \(0.524833\pi\)
\(684\) 0 0
\(685\) 69.2526 2.64601
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) 2.57398 4.45826i 0.0980608 0.169846i
\(690\) 0 0
\(691\) 43.5485 1.65666 0.828332 0.560238i \(-0.189290\pi\)
0.828332 + 0.560238i \(0.189290\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 0.0736733 0.00279459
\(696\) 0 0
\(697\) 10.7784 + 18.6687i 0.408260 + 0.707127i
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) 15.6536 27.1129i 0.591230 1.02404i −0.402837 0.915272i \(-0.631976\pi\)
0.994067 0.108768i \(-0.0346907\pi\)
\(702\) 0 0
\(703\) −4.95130 30.6747i −0.186742 1.15692i
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) −9.82295 17.0138i −0.369430 0.639872i
\(708\) 0 0
\(709\) −11.9047 20.6195i −0.447089 0.774381i 0.551106 0.834435i \(-0.314206\pi\)
−0.998195 + 0.0600541i \(0.980873\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) −13.8503 23.9894i −0.518697 0.898410i
\(714\) 0 0
\(715\) 16.4243 0.614233
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) 15.8949 27.5307i 0.592779 1.02672i −0.401078 0.916044i \(-0.631364\pi\)
0.993856 0.110678i \(-0.0353024\pi\)
\(720\) 0 0
\(721\) −32.1634 −1.19783
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) 24.5972 42.6036i 0.913517 1.58226i
\(726\) 0 0
\(727\) 3.22193 5.58055i 0.119495 0.206971i −0.800073 0.599903i \(-0.795206\pi\)
0.919568 + 0.392932i \(0.128539\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) −2.32501 4.02703i −0.0859935 0.148945i
\(732\) 0 0
\(733\) −33.9728 −1.25481 −0.627406 0.778692i \(-0.715884\pi\)
−0.627406 + 0.778692i \(0.715884\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) −2.99226 5.18274i −0.110221 0.190909i
\(738\) 0 0
\(739\) −11.4632 + 19.8548i −0.421679 + 0.730370i −0.996104 0.0881876i \(-0.971893\pi\)
0.574425 + 0.818557i \(0.305226\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) −3.98276 + 6.89835i −0.146113 + 0.253076i −0.929788 0.368096i \(-0.880010\pi\)
0.783674 + 0.621172i \(0.213343\pi\)
\(744\) 0 0
\(745\) 11.7297 + 20.3164i 0.429742 + 0.744335i
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) 19.6459 0.717845
\(750\) 0 0
\(751\) 11.3794 + 19.7097i 0.415240 + 0.719216i 0.995454 0.0952479i \(-0.0303644\pi\)
−0.580214 + 0.814464i \(0.697031\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) −1.38919 + 2.40614i −0.0505576 + 0.0875684i
\(756\) 0 0
\(757\) −2.38713 + 4.13462i −0.0867616 + 0.150275i −0.906140 0.422977i \(-0.860985\pi\)
0.819379 + 0.573252i \(0.194318\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) −28.2222 −1.02306 −0.511528 0.859267i \(-0.670920\pi\)
−0.511528 + 0.859267i \(0.670920\pi\)
\(762\) 0 0
\(763\) 0.305407 0.528981i 0.0110565 0.0191504i
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) −9.27631 −0.334948
\(768\) 0 0
\(769\) −12.1108 20.9765i −0.436727 0.756434i 0.560708 0.828014i \(-0.310529\pi\)
−0.997435 + 0.0715802i \(0.977196\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) 11.9804 + 20.7507i 0.430905 + 0.746349i 0.996951 0.0780239i \(-0.0248611\pi\)
−0.566046 + 0.824373i \(0.691528\pi\)
\(774\) 0 0
\(775\) −33.6361 58.2594i −1.20824 2.09274i
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) −14.3304 5.45242i −0.513439 0.195353i
\(780\) 0 0
\(781\) −25.4439 + 44.0701i −0.910453 + 1.57695i
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) 12.4902 + 21.6337i 0.445794 + 0.772138i
\(786\) 0 0
\(787\) −28.8871 −1.02971 −0.514857 0.857276i \(-0.672155\pi\)
−0.514857 + 0.857276i \(0.672155\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 11.4629 0.407572
\(792\) 0 0
\(793\) 4.25877 7.37641i 0.151233 0.261944i
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 7.61493 0.269735 0.134867 0.990864i \(-0.456939\pi\)
0.134867 + 0.990864i \(0.456939\pi\)
\(798\) 0 0
\(799\) −36.7701 −1.30083
\(800\) 0 0
\(801\) 0 0
\(802\) 0