Properties

Label 1840.2.e.h.369.7
Level $1840$
Weight $2$
Character 1840.369
Analytic conductor $14.692$
Analytic rank $0$
Dimension $16$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 1840 = 2^{4} \cdot 5 \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1840.e (of order \(2\), degree \(1\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(14.6924739719\)
Analytic rank: \(0\)
Dimension: \(16\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} - \cdots)\)
Defining polynomial: \(x^{16} - 2 x^{15} + 2 x^{14} + 6 x^{13} + 100 x^{12} - 196 x^{11} + 210 x^{10} + 702 x^{9} + 1572 x^{8} - 1594 x^{7} + 2464 x^{6} + 9568 x^{5} + 15457 x^{4} + 4336 x^{3} + 128 x^{2} - 512 x + 1024\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 2^{2} \)
Twist minimal: no (minimal twist has level 920)
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 369.7
Root \(1.95202 - 1.95202i\) of defining polynomial
Character \(\chi\) \(=\) 1840.369
Dual form 1840.2.e.h.369.10

$q$-expansion

\(f(q)\) \(=\) \(q-0.493532i q^{3} +(1.09069 + 1.95202i) q^{5} +4.54439i q^{7} +2.75643 q^{9} +O(q^{10})\) \(q-0.493532i q^{3} +(1.09069 + 1.95202i) q^{5} +4.54439i q^{7} +2.75643 q^{9} +4.61297 q^{11} -5.54274i q^{13} +(0.963386 - 0.538289i) q^{15} -7.16998i q^{17} +1.35966 q^{19} +2.24280 q^{21} +1.00000i q^{23} +(-2.62080 + 4.25810i) q^{25} -2.84098i q^{27} +3.66351 q^{29} +4.46616 q^{31} -2.27665i q^{33} +(-8.87075 + 4.95651i) q^{35} -3.32432i q^{37} -2.73552 q^{39} +8.95216 q^{41} -8.68458i q^{43} +(3.00640 + 5.38061i) q^{45} +9.59028i q^{47} -13.6515 q^{49} -3.53861 q^{51} +10.4676i q^{53} +(5.03131 + 9.00463i) q^{55} -0.671035i q^{57} -2.08543 q^{59} -0.686197 q^{61} +12.5263i q^{63} +(10.8196 - 6.04540i) q^{65} +8.84324i q^{67} +0.493532 q^{69} -15.9040 q^{71} +4.44647i q^{73} +(2.10151 + 1.29345i) q^{75} +20.9631i q^{77} -8.65227 q^{79} +6.86717 q^{81} +4.43591i q^{83} +(13.9960 - 7.82021i) q^{85} -1.80806i q^{87} -13.2284 q^{89} +25.1884 q^{91} -2.20419i q^{93} +(1.48297 + 2.65409i) q^{95} +1.21785i q^{97} +12.7153 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16q - 2q^{5} - 22q^{9} + O(q^{10}) \) \( 16q - 2q^{5} - 22q^{9} - 14q^{11} - 6q^{15} + 22q^{19} + 12q^{25} - 44q^{29} - 18q^{31} - 20q^{35} + 14q^{41} + 14q^{45} - 78q^{49} + 38q^{51} - 30q^{55} + 64q^{59} + 34q^{61} + 6q^{65} + 6q^{69} - 30q^{71} - 56q^{75} - 4q^{79} + 48q^{81} + 52q^{85} - 92q^{89} + 70q^{91} - 38q^{95} + 122q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1840\mathbb{Z}\right)^\times\).

\(n\) \(737\) \(1151\) \(1201\) \(1381\)
\(\chi(n)\) \(-1\) \(1\) \(1\) \(1\)

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
\(3\) 0.493532i 0.284941i −0.989799 0.142470i \(-0.954495\pi\)
0.989799 0.142470i \(-0.0455045\pi\)
\(4\) 0 0
\(5\) 1.09069 + 1.95202i 0.487771 + 0.872972i
\(6\) 0 0
\(7\) 4.54439i 1.71762i 0.512297 + 0.858809i \(0.328795\pi\)
−0.512297 + 0.858809i \(0.671205\pi\)
\(8\) 0 0
\(9\) 2.75643 0.918809
\(10\) 0 0
\(11\) 4.61297 1.39086 0.695431 0.718593i \(-0.255213\pi\)
0.695431 + 0.718593i \(0.255213\pi\)
\(12\) 0 0
\(13\) 5.54274i 1.53728i −0.639682 0.768640i \(-0.720934\pi\)
0.639682 0.768640i \(-0.279066\pi\)
\(14\) 0 0
\(15\) 0.963386 0.538289i 0.248745 0.138986i
\(16\) 0 0
\(17\) 7.16998i 1.73897i −0.493955 0.869487i \(-0.664449\pi\)
0.493955 0.869487i \(-0.335551\pi\)
\(18\) 0 0
\(19\) 1.35966 0.311928 0.155964 0.987763i \(-0.450152\pi\)
0.155964 + 0.987763i \(0.450152\pi\)
\(20\) 0 0
\(21\) 2.24280 0.489419
\(22\) 0 0
\(23\) 1.00000i 0.208514i
\(24\) 0 0
\(25\) −2.62080 + 4.25810i −0.524159 + 0.851620i
\(26\) 0 0
\(27\) 2.84098i 0.546747i
\(28\) 0 0
\(29\) 3.66351 0.680297 0.340148 0.940372i \(-0.389523\pi\)
0.340148 + 0.940372i \(0.389523\pi\)
\(30\) 0 0
\(31\) 4.46616 0.802146 0.401073 0.916046i \(-0.368637\pi\)
0.401073 + 0.916046i \(0.368637\pi\)
\(32\) 0 0
\(33\) 2.27665i 0.396313i
\(34\) 0 0
\(35\) −8.87075 + 4.95651i −1.49943 + 0.837804i
\(36\) 0 0
\(37\) 3.32432i 0.546514i −0.961941 0.273257i \(-0.911899\pi\)
0.961941 0.273257i \(-0.0881010\pi\)
\(38\) 0 0
\(39\) −2.73552 −0.438033
\(40\) 0 0
\(41\) 8.95216 1.39809 0.699046 0.715076i \(-0.253608\pi\)
0.699046 + 0.715076i \(0.253608\pi\)
\(42\) 0 0
\(43\) 8.68458i 1.32439i −0.749333 0.662193i \(-0.769626\pi\)
0.749333 0.662193i \(-0.230374\pi\)
\(44\) 0 0
\(45\) 3.00640 + 5.38061i 0.448168 + 0.802094i
\(46\) 0 0
\(47\) 9.59028i 1.39889i 0.714688 + 0.699443i \(0.246569\pi\)
−0.714688 + 0.699443i \(0.753431\pi\)
\(48\) 0 0
\(49\) −13.6515 −1.95021
\(50\) 0 0
\(51\) −3.53861 −0.495505
\(52\) 0 0
\(53\) 10.4676i 1.43784i 0.695095 + 0.718918i \(0.255362\pi\)
−0.695095 + 0.718918i \(0.744638\pi\)
\(54\) 0 0
\(55\) 5.03131 + 9.00463i 0.678422 + 1.21418i
\(56\) 0 0
\(57\) 0.671035i 0.0888808i
\(58\) 0 0
\(59\) −2.08543 −0.271499 −0.135750 0.990743i \(-0.543344\pi\)
−0.135750 + 0.990743i \(0.543344\pi\)
\(60\) 0 0
\(61\) −0.686197 −0.0878586 −0.0439293 0.999035i \(-0.513988\pi\)
−0.0439293 + 0.999035i \(0.513988\pi\)
\(62\) 0 0
\(63\) 12.5263i 1.57816i
\(64\) 0 0
\(65\) 10.8196 6.04540i 1.34200 0.749840i
\(66\) 0 0
\(67\) 8.84324i 1.08037i 0.841545 + 0.540187i \(0.181646\pi\)
−0.841545 + 0.540187i \(0.818354\pi\)
\(68\) 0 0
\(69\) 0.493532 0.0594142
\(70\) 0 0
\(71\) −15.9040 −1.88746 −0.943729 0.330721i \(-0.892708\pi\)
−0.943729 + 0.330721i \(0.892708\pi\)
\(72\) 0 0
\(73\) 4.44647i 0.520420i 0.965552 + 0.260210i \(0.0837918\pi\)
−0.965552 + 0.260210i \(0.916208\pi\)
\(74\) 0 0
\(75\) 2.10151 + 1.29345i 0.242661 + 0.149354i
\(76\) 0 0
\(77\) 20.9631i 2.38897i
\(78\) 0 0
\(79\) −8.65227 −0.973457 −0.486728 0.873553i \(-0.661810\pi\)
−0.486728 + 0.873553i \(0.661810\pi\)
\(80\) 0 0
\(81\) 6.86717 0.763019
\(82\) 0 0
\(83\) 4.43591i 0.486904i 0.969913 + 0.243452i \(0.0782798\pi\)
−0.969913 + 0.243452i \(0.921720\pi\)
\(84\) 0 0
\(85\) 13.9960 7.82021i 1.51808 0.848221i
\(86\) 0 0
\(87\) 1.80806i 0.193844i
\(88\) 0 0
\(89\) −13.2284 −1.40220 −0.701102 0.713061i \(-0.747308\pi\)
−0.701102 + 0.713061i \(0.747308\pi\)
\(90\) 0 0
\(91\) 25.1884 2.64046
\(92\) 0 0
\(93\) 2.20419i 0.228564i
\(94\) 0 0
\(95\) 1.48297 + 2.65409i 0.152149 + 0.272304i
\(96\) 0 0
\(97\) 1.21785i 0.123654i 0.998087 + 0.0618270i \(0.0196927\pi\)
−0.998087 + 0.0618270i \(0.980307\pi\)
\(98\) 0 0
\(99\) 12.7153 1.27794
\(100\) 0 0
\(101\) 10.4999 1.04478 0.522390 0.852706i \(-0.325040\pi\)
0.522390 + 0.852706i \(0.325040\pi\)
\(102\) 0 0
\(103\) 8.32614i 0.820399i −0.911996 0.410200i \(-0.865459\pi\)
0.911996 0.410200i \(-0.134541\pi\)
\(104\) 0 0
\(105\) 2.44620 + 4.37800i 0.238724 + 0.427249i
\(106\) 0 0
\(107\) 9.60096i 0.928160i −0.885793 0.464080i \(-0.846385\pi\)
0.885793 0.464080i \(-0.153615\pi\)
\(108\) 0 0
\(109\) −10.2997 −0.986534 −0.493267 0.869878i \(-0.664197\pi\)
−0.493267 + 0.869878i \(0.664197\pi\)
\(110\) 0 0
\(111\) −1.64066 −0.155724
\(112\) 0 0
\(113\) 16.2479i 1.52848i −0.644933 0.764239i \(-0.723115\pi\)
0.644933 0.764239i \(-0.276885\pi\)
\(114\) 0 0
\(115\) −1.95202 + 1.09069i −0.182027 + 0.101707i
\(116\) 0 0
\(117\) 15.2782i 1.41247i
\(118\) 0 0
\(119\) 32.5832 2.98689
\(120\) 0 0
\(121\) 10.2795 0.934498
\(122\) 0 0
\(123\) 4.41817i 0.398373i
\(124\) 0 0
\(125\) −11.1704 0.471594i −0.999110 0.0421806i
\(126\) 0 0
\(127\) 1.58555i 0.140695i −0.997523 0.0703473i \(-0.977589\pi\)
0.997523 0.0703473i \(-0.0224108\pi\)
\(128\) 0 0
\(129\) −4.28612 −0.377371
\(130\) 0 0
\(131\) −4.69595 −0.410287 −0.205143 0.978732i \(-0.565766\pi\)
−0.205143 + 0.978732i \(0.565766\pi\)
\(132\) 0 0
\(133\) 6.17882i 0.535772i
\(134\) 0 0
\(135\) 5.54566 3.09862i 0.477294 0.266687i
\(136\) 0 0
\(137\) 10.3059i 0.880494i 0.897877 + 0.440247i \(0.145109\pi\)
−0.897877 + 0.440247i \(0.854891\pi\)
\(138\) 0 0
\(139\) 0.673372 0.0571147 0.0285573 0.999592i \(-0.490909\pi\)
0.0285573 + 0.999592i \(0.490909\pi\)
\(140\) 0 0
\(141\) 4.73311 0.398599
\(142\) 0 0
\(143\) 25.5685i 2.13814i
\(144\) 0 0
\(145\) 3.99575 + 7.15126i 0.331829 + 0.593880i
\(146\) 0 0
\(147\) 6.73743i 0.555694i
\(148\) 0 0
\(149\) 4.74118 0.388413 0.194206 0.980961i \(-0.437787\pi\)
0.194206 + 0.980961i \(0.437787\pi\)
\(150\) 0 0
\(151\) −3.16664 −0.257698 −0.128849 0.991664i \(-0.541128\pi\)
−0.128849 + 0.991664i \(0.541128\pi\)
\(152\) 0 0
\(153\) 19.7635i 1.59779i
\(154\) 0 0
\(155\) 4.87119 + 8.71805i 0.391263 + 0.700251i
\(156\) 0 0
\(157\) 8.07863i 0.644745i 0.946613 + 0.322373i \(0.104480\pi\)
−0.946613 + 0.322373i \(0.895520\pi\)
\(158\) 0 0
\(159\) 5.16609 0.409698
\(160\) 0 0
\(161\) −4.54439 −0.358148
\(162\) 0 0
\(163\) 2.25691i 0.176775i 0.996086 + 0.0883876i \(0.0281714\pi\)
−0.996086 + 0.0883876i \(0.971829\pi\)
\(164\) 0 0
\(165\) 4.44407 2.48311i 0.345970 0.193310i
\(166\) 0 0
\(167\) 2.01566i 0.155976i −0.996954 0.0779881i \(-0.975150\pi\)
0.996954 0.0779881i \(-0.0248496\pi\)
\(168\) 0 0
\(169\) −17.7220 −1.36323
\(170\) 0 0
\(171\) 3.74780 0.286602
\(172\) 0 0
\(173\) 8.17720i 0.621701i 0.950459 + 0.310850i \(0.100614\pi\)
−0.950459 + 0.310850i \(0.899386\pi\)
\(174\) 0 0
\(175\) −19.3505 11.9099i −1.46276 0.900305i
\(176\) 0 0
\(177\) 1.02922i 0.0773612i
\(178\) 0 0
\(179\) −1.48152 −0.110734 −0.0553670 0.998466i \(-0.517633\pi\)
−0.0553670 + 0.998466i \(0.517633\pi\)
\(180\) 0 0
\(181\) −7.93951 −0.590139 −0.295069 0.955476i \(-0.595343\pi\)
−0.295069 + 0.955476i \(0.595343\pi\)
\(182\) 0 0
\(183\) 0.338660i 0.0250345i
\(184\) 0 0
\(185\) 6.48915 3.62579i 0.477091 0.266574i
\(186\) 0 0
\(187\) 33.0749i 2.41867i
\(188\) 0 0
\(189\) 12.9105 0.939101
\(190\) 0 0
\(191\) −18.2987 −1.32405 −0.662023 0.749484i \(-0.730302\pi\)
−0.662023 + 0.749484i \(0.730302\pi\)
\(192\) 0 0
\(193\) 3.65357i 0.262990i 0.991317 + 0.131495i \(0.0419777\pi\)
−0.991317 + 0.131495i \(0.958022\pi\)
\(194\) 0 0
\(195\) −2.98360 5.33979i −0.213660 0.382391i
\(196\) 0 0
\(197\) 9.14216i 0.651352i 0.945481 + 0.325676i \(0.105592\pi\)
−0.945481 + 0.325676i \(0.894408\pi\)
\(198\) 0 0
\(199\) −0.0416302 −0.00295109 −0.00147554 0.999999i \(-0.500470\pi\)
−0.00147554 + 0.999999i \(0.500470\pi\)
\(200\) 0 0
\(201\) 4.36442 0.307842
\(202\) 0 0
\(203\) 16.6484i 1.16849i
\(204\) 0 0
\(205\) 9.76402 + 17.4748i 0.681949 + 1.22050i
\(206\) 0 0
\(207\) 2.75643i 0.191585i
\(208\) 0 0
\(209\) 6.27207 0.433848
\(210\) 0 0
\(211\) 1.08537 0.0747202 0.0373601 0.999302i \(-0.488105\pi\)
0.0373601 + 0.999302i \(0.488105\pi\)
\(212\) 0 0
\(213\) 7.84912i 0.537813i
\(214\) 0 0
\(215\) 16.9525 9.47218i 1.15615 0.645997i
\(216\) 0 0
\(217\) 20.2960i 1.37778i
\(218\) 0 0
\(219\) 2.19447 0.148289
\(220\) 0 0
\(221\) −39.7413 −2.67329
\(222\) 0 0
\(223\) 12.2417i 0.819766i 0.912138 + 0.409883i \(0.134430\pi\)
−0.912138 + 0.409883i \(0.865570\pi\)
\(224\) 0 0
\(225\) −7.22403 + 11.7371i −0.481602 + 0.782476i
\(226\) 0 0
\(227\) 6.60662i 0.438497i −0.975669 0.219248i \(-0.929639\pi\)
0.975669 0.219248i \(-0.0703605\pi\)
\(228\) 0 0
\(229\) 25.5008 1.68514 0.842571 0.538585i \(-0.181041\pi\)
0.842571 + 0.538585i \(0.181041\pi\)
\(230\) 0 0
\(231\) 10.3460 0.680714
\(232\) 0 0
\(233\) 5.15810i 0.337918i −0.985623 0.168959i \(-0.945959\pi\)
0.985623 0.168959i \(-0.0540406\pi\)
\(234\) 0 0
\(235\) −18.7205 + 10.4600i −1.22119 + 0.682336i
\(236\) 0 0
\(237\) 4.27017i 0.277377i
\(238\) 0 0
\(239\) 13.8196 0.893917 0.446959 0.894555i \(-0.352507\pi\)
0.446959 + 0.894555i \(0.352507\pi\)
\(240\) 0 0
\(241\) −14.9170 −0.960890 −0.480445 0.877025i \(-0.659525\pi\)
−0.480445 + 0.877025i \(0.659525\pi\)
\(242\) 0 0
\(243\) 11.9121i 0.764161i
\(244\) 0 0
\(245\) −14.8895 26.6480i −0.951255 1.70248i
\(246\) 0 0
\(247\) 7.53624i 0.479520i
\(248\) 0 0
\(249\) 2.18926 0.138739
\(250\) 0 0
\(251\) −12.8472 −0.810905 −0.405453 0.914116i \(-0.632886\pi\)
−0.405453 + 0.914116i \(0.632886\pi\)
\(252\) 0 0
\(253\) 4.61297i 0.290015i
\(254\) 0 0
\(255\) −3.85952 6.90745i −0.241693 0.432561i
\(256\) 0 0
\(257\) 12.2196i 0.762235i −0.924527 0.381118i \(-0.875539\pi\)
0.924527 0.381118i \(-0.124461\pi\)
\(258\) 0 0
\(259\) 15.1070 0.938702
\(260\) 0 0
\(261\) 10.0982 0.625062
\(262\) 0 0
\(263\) 25.2134i 1.55472i −0.629054 0.777361i \(-0.716558\pi\)
0.629054 0.777361i \(-0.283442\pi\)
\(264\) 0 0
\(265\) −20.4330 + 11.4169i −1.25519 + 0.701335i
\(266\) 0 0
\(267\) 6.52862i 0.399545i
\(268\) 0 0
\(269\) 5.85220 0.356815 0.178407 0.983957i \(-0.442906\pi\)
0.178407 + 0.983957i \(0.442906\pi\)
\(270\) 0 0
\(271\) 12.8405 0.780008 0.390004 0.920813i \(-0.372474\pi\)
0.390004 + 0.920813i \(0.372474\pi\)
\(272\) 0 0
\(273\) 12.4312i 0.752373i
\(274\) 0 0
\(275\) −12.0896 + 19.6425i −0.729033 + 1.18449i
\(276\) 0 0
\(277\) 31.6190i 1.89980i 0.312547 + 0.949902i \(0.398818\pi\)
−0.312547 + 0.949902i \(0.601182\pi\)
\(278\) 0 0
\(279\) 12.3106 0.737019
\(280\) 0 0
\(281\) −22.4411 −1.33873 −0.669363 0.742935i \(-0.733433\pi\)
−0.669363 + 0.742935i \(0.733433\pi\)
\(282\) 0 0
\(283\) 1.10282i 0.0655559i −0.999463 0.0327779i \(-0.989565\pi\)
0.999463 0.0327779i \(-0.0104354\pi\)
\(284\) 0 0
\(285\) 1.30988 0.731891i 0.0775904 0.0433535i
\(286\) 0 0
\(287\) 40.6821i 2.40139i
\(288\) 0 0
\(289\) −34.4086 −2.02403
\(290\) 0 0
\(291\) 0.601048 0.0352340
\(292\) 0 0
\(293\) 24.5092i 1.43185i −0.698180 0.715923i \(-0.746006\pi\)
0.698180 0.715923i \(-0.253994\pi\)
\(294\) 0 0
\(295\) −2.27455 4.07080i −0.132429 0.237011i
\(296\) 0 0
\(297\) 13.1053i 0.760449i
\(298\) 0 0
\(299\) 5.54274 0.320545
\(300\) 0 0
\(301\) 39.4661 2.27479
\(302\) 0 0
\(303\) 5.18204i 0.297700i
\(304\) 0 0
\(305\) −0.748428 1.33947i −0.0428548 0.0766980i
\(306\) 0 0
\(307\) 34.3319i 1.95943i 0.200401 + 0.979714i \(0.435775\pi\)
−0.200401 + 0.979714i \(0.564225\pi\)
\(308\) 0 0
\(309\) −4.10921 −0.233765
\(310\) 0 0
\(311\) −13.6914 −0.776369 −0.388185 0.921582i \(-0.626898\pi\)
−0.388185 + 0.921582i \(0.626898\pi\)
\(312\) 0 0
\(313\) 4.65568i 0.263155i 0.991306 + 0.131577i \(0.0420041\pi\)
−0.991306 + 0.131577i \(0.957996\pi\)
\(314\) 0 0
\(315\) −24.4516 + 13.6623i −1.37769 + 0.769781i
\(316\) 0 0
\(317\) 1.44552i 0.0811884i −0.999176 0.0405942i \(-0.987075\pi\)
0.999176 0.0405942i \(-0.0129251\pi\)
\(318\) 0 0
\(319\) 16.8997 0.946199
\(320\) 0 0
\(321\) −4.73838 −0.264470
\(322\) 0 0
\(323\) 9.74873i 0.542434i
\(324\) 0 0
\(325\) 23.6015 + 14.5264i 1.30918 + 0.805779i
\(326\) 0 0
\(327\) 5.08324i 0.281104i
\(328\) 0 0
\(329\) −43.5820 −2.40275
\(330\) 0 0
\(331\) 17.9258 0.985292 0.492646 0.870230i \(-0.336030\pi\)
0.492646 + 0.870230i \(0.336030\pi\)
\(332\) 0 0
\(333\) 9.16323i 0.502142i
\(334\) 0 0
\(335\) −17.2622 + 9.64522i −0.943135 + 0.526975i
\(336\) 0 0
\(337\) 11.2720i 0.614026i −0.951705 0.307013i \(-0.900670\pi\)
0.951705 0.307013i \(-0.0993295\pi\)
\(338\) 0 0
\(339\) −8.01887 −0.435525
\(340\) 0 0
\(341\) 20.6023 1.11567
\(342\) 0 0
\(343\) 30.2268i 1.63209i
\(344\) 0 0
\(345\) 0.538289 + 0.963386i 0.0289805 + 0.0518669i
\(346\) 0 0
\(347\) 20.8228i 1.11783i 0.829226 + 0.558914i \(0.188782\pi\)
−0.829226 + 0.558914i \(0.811218\pi\)
\(348\) 0 0
\(349\) 8.58121 0.459342 0.229671 0.973268i \(-0.426235\pi\)
0.229671 + 0.973268i \(0.426235\pi\)
\(350\) 0 0
\(351\) −15.7468 −0.840502
\(352\) 0 0
\(353\) 7.31628i 0.389406i 0.980862 + 0.194703i \(0.0623744\pi\)
−0.980862 + 0.194703i \(0.937626\pi\)
\(354\) 0 0
\(355\) −17.3463 31.0450i −0.920647 1.64770i
\(356\) 0 0
\(357\) 16.0808i 0.851087i
\(358\) 0 0
\(359\) −33.9028 −1.78932 −0.894660 0.446747i \(-0.852582\pi\)
−0.894660 + 0.446747i \(0.852582\pi\)
\(360\) 0 0
\(361\) −17.1513 −0.902701
\(362\) 0 0
\(363\) 5.07325i 0.266276i
\(364\) 0 0
\(365\) −8.67962 + 4.84972i −0.454312 + 0.253846i
\(366\) 0 0
\(367\) 11.3121i 0.590488i −0.955422 0.295244i \(-0.904599\pi\)
0.955422 0.295244i \(-0.0954009\pi\)
\(368\) 0 0
\(369\) 24.6760 1.28458
\(370\) 0 0
\(371\) −47.5689 −2.46965
\(372\) 0 0
\(373\) 22.1518i 1.14697i −0.819214 0.573487i \(-0.805590\pi\)
0.819214 0.573487i \(-0.194410\pi\)
\(374\) 0 0
\(375\) −0.232746 + 5.51294i −0.0120190 + 0.284687i
\(376\) 0 0
\(377\) 20.3059i 1.04581i
\(378\) 0 0
\(379\) −8.82898 −0.453514 −0.226757 0.973951i \(-0.572812\pi\)
−0.226757 + 0.973951i \(0.572812\pi\)
\(380\) 0 0
\(381\) −0.782518 −0.0400896
\(382\) 0 0
\(383\) 21.2152i 1.08405i −0.840364 0.542023i \(-0.817659\pi\)
0.840364 0.542023i \(-0.182341\pi\)
\(384\) 0 0
\(385\) −40.9205 + 22.8642i −2.08550 + 1.16527i
\(386\) 0 0
\(387\) 23.9384i 1.21686i
\(388\) 0 0
\(389\) −27.8793 −1.41354 −0.706768 0.707445i \(-0.749848\pi\)
−0.706768 + 0.707445i \(0.749848\pi\)
\(390\) 0 0
\(391\) 7.16998 0.362601
\(392\) 0 0
\(393\) 2.31760i 0.116907i
\(394\) 0 0
\(395\) −9.43694 16.8894i −0.474824 0.849800i
\(396\) 0 0
\(397\) 22.8676i 1.14769i −0.818964 0.573845i \(-0.805451\pi\)
0.818964 0.573845i \(-0.194549\pi\)
\(398\) 0 0
\(399\) 3.04944 0.152663
\(400\) 0 0
\(401\) −2.37194 −0.118449 −0.0592246 0.998245i \(-0.518863\pi\)
−0.0592246 + 0.998245i \(0.518863\pi\)
\(402\) 0 0
\(403\) 24.7548i 1.23312i
\(404\) 0 0
\(405\) 7.48994 + 13.4049i 0.372178 + 0.666094i
\(406\) 0 0
\(407\) 15.3350i 0.760126i
\(408\) 0 0
\(409\) 18.3125 0.905494 0.452747 0.891639i \(-0.350444\pi\)
0.452747 + 0.891639i \(0.350444\pi\)
\(410\) 0 0
\(411\) 5.08630 0.250888
\(412\) 0 0
\(413\) 9.47698i 0.466332i
\(414\) 0 0
\(415\) −8.65900 + 4.83819i −0.425053 + 0.237498i
\(416\) 0 0
\(417\) 0.332331i 0.0162743i
\(418\) 0 0
\(419\) 22.0541 1.07741 0.538706 0.842494i \(-0.318913\pi\)
0.538706 + 0.842494i \(0.318913\pi\)
\(420\) 0 0
\(421\) 37.9042 1.84734 0.923670 0.383190i \(-0.125174\pi\)
0.923670 + 0.383190i \(0.125174\pi\)
\(422\) 0 0
\(423\) 26.4349i 1.28531i
\(424\) 0 0
\(425\) 30.5305 + 18.7910i 1.48095 + 0.911500i
\(426\) 0 0
\(427\) 3.11835i 0.150907i
\(428\) 0 0
\(429\) −12.6189 −0.609244
\(430\) 0 0
\(431\) −33.8877 −1.63231 −0.816156 0.577831i \(-0.803899\pi\)
−0.816156 + 0.577831i \(0.803899\pi\)
\(432\) 0 0
\(433\) 5.57737i 0.268031i −0.990979 0.134016i \(-0.957213\pi\)
0.990979 0.134016i \(-0.0427872\pi\)
\(434\) 0 0
\(435\) 3.52937 1.97203i 0.169220 0.0945515i
\(436\) 0 0
\(437\) 1.35966i 0.0650414i
\(438\) 0 0
\(439\) −15.2124 −0.726046 −0.363023 0.931780i \(-0.618255\pi\)
−0.363023 + 0.931780i \(0.618255\pi\)
\(440\) 0 0
\(441\) −37.6292 −1.79187
\(442\) 0 0
\(443\) 11.7086i 0.556291i −0.960539 0.278145i \(-0.910280\pi\)
0.960539 0.278145i \(-0.0897197\pi\)
\(444\) 0 0
\(445\) −14.4280 25.8221i −0.683954 1.22408i
\(446\) 0 0
\(447\) 2.33992i 0.110675i
\(448\) 0 0
\(449\) 14.1523 0.667889 0.333945 0.942593i \(-0.391620\pi\)
0.333945 + 0.942593i \(0.391620\pi\)
\(450\) 0 0
\(451\) 41.2960 1.94455
\(452\) 0 0
\(453\) 1.56284i 0.0734285i
\(454\) 0 0
\(455\) 27.4727 + 49.1683i 1.28794 + 2.30504i
\(456\) 0 0
\(457\) 10.4278i 0.487793i −0.969801 0.243896i \(-0.921574\pi\)
0.969801 0.243896i \(-0.0784257\pi\)
\(458\) 0 0
\(459\) −20.3697 −0.950778
\(460\) 0 0
\(461\) 39.5905 1.84391 0.921957 0.387291i \(-0.126589\pi\)
0.921957 + 0.387291i \(0.126589\pi\)
\(462\) 0 0
\(463\) 10.5954i 0.492408i 0.969218 + 0.246204i \(0.0791834\pi\)
−0.969218 + 0.246204i \(0.920817\pi\)
\(464\) 0 0
\(465\) 4.30263 2.40409i 0.199530 0.111487i
\(466\) 0 0
\(467\) 34.0553i 1.57589i 0.615746 + 0.787945i \(0.288855\pi\)
−0.615746 + 0.787945i \(0.711145\pi\)
\(468\) 0 0
\(469\) −40.1871 −1.85567
\(470\) 0 0
\(471\) 3.98706 0.183714
\(472\) 0 0
\(473\) 40.0617i 1.84204i
\(474\) 0 0
\(475\) −3.56339 + 5.78957i −0.163500 + 0.265644i
\(476\) 0 0
\(477\) 28.8532i 1.32110i
\(478\) 0 0
\(479\) 11.8776 0.542702 0.271351 0.962480i \(-0.412530\pi\)
0.271351 + 0.962480i \(0.412530\pi\)
\(480\) 0 0
\(481\) −18.4258 −0.840145
\(482\) 0 0
\(483\) 2.24280i 0.102051i
\(484\) 0 0
\(485\) −2.37727 + 1.32830i −0.107946 + 0.0603148i
\(486\) 0 0
\(487\) 24.7980i 1.12371i 0.827237 + 0.561853i \(0.189911\pi\)
−0.827237 + 0.561853i \(0.810089\pi\)
\(488\) 0 0
\(489\) 1.11386 0.0503704
\(490\) 0 0
\(491\) −25.6220 −1.15630 −0.578152 0.815929i \(-0.696226\pi\)
−0.578152 + 0.815929i \(0.696226\pi\)
\(492\) 0 0
\(493\) 26.2673i 1.18302i
\(494\) 0 0
\(495\) 13.8684 + 24.8206i 0.623340 + 1.11560i
\(496\) 0 0
\(497\) 72.2739i 3.24193i
\(498\) 0 0
\(499\) 28.7020 1.28488 0.642438 0.766337i \(-0.277923\pi\)
0.642438 + 0.766337i \(0.277923\pi\)
\(500\) 0 0
\(501\) −0.994790 −0.0444439
\(502\) 0 0
\(503\) 14.8193i 0.660760i 0.943848 + 0.330380i \(0.107177\pi\)
−0.943848 + 0.330380i \(0.892823\pi\)
\(504\) 0 0
\(505\) 11.4521 + 20.4961i 0.509614 + 0.912064i
\(506\) 0 0
\(507\) 8.74635i 0.388439i
\(508\) 0 0
\(509\) 22.5059 0.997555 0.498777 0.866730i \(-0.333783\pi\)
0.498777 + 0.866730i \(0.333783\pi\)
\(510\) 0 0
\(511\) −20.2065 −0.893883
\(512\) 0 0
\(513\) 3.86277i 0.170545i
\(514\) 0 0
\(515\) 16.2528 9.08123i 0.716185 0.400167i
\(516\) 0 0
\(517\) 44.2397i 1.94566i
\(518\) 0 0
\(519\) 4.03570 0.177148
\(520\) 0 0
\(521\) −21.1227 −0.925404 −0.462702 0.886514i \(-0.653120\pi\)
−0.462702 + 0.886514i \(0.653120\pi\)
\(522\) 0 0
\(523\) 0.617011i 0.0269800i −0.999909 0.0134900i \(-0.995706\pi\)
0.999909 0.0134900i \(-0.00429413\pi\)
\(524\) 0 0
\(525\) −5.87792 + 9.55006i −0.256533 + 0.416799i
\(526\) 0 0
\(527\) 32.0223i 1.39491i
\(528\) 0 0
\(529\) −1.00000 −0.0434783
\(530\) 0 0
\(531\) −5.74832 −0.249456
\(532\) 0 0
\(533\) 49.6195i 2.14926i
\(534\) 0 0
\(535\) 18.7413 10.4717i 0.810257 0.452729i
\(536\) 0 0
\(537\) 0.731177i 0.0315526i
\(538\) 0 0
\(539\) −62.9738 −2.71247
\(540\) 0 0
\(541\) 13.5801 0.583856 0.291928 0.956440i \(-0.405703\pi\)
0.291928 + 0.956440i \(0.405703\pi\)
\(542\) 0 0
\(543\) 3.91840i 0.168154i
\(544\) 0 0
\(545\) −11.2338 20.1053i −0.481203 0.861216i
\(546\) 0 0
\(547\) 25.4825i 1.08955i −0.838581 0.544777i \(-0.816614\pi\)
0.838581 0.544777i \(-0.183386\pi\)
\(548\) 0 0
\(549\) −1.89145 −0.0807252
\(550\) 0 0
\(551\) 4.98113 0.212203
\(552\) 0 0
\(553\) 39.3193i 1.67203i
\(554\) 0 0
\(555\) −1.78944 3.20260i −0.0759577 0.135943i
\(556\) 0 0
\(557\) 14.2051i 0.601891i 0.953641 + 0.300945i \(0.0973022\pi\)
−0.953641 + 0.300945i \(0.902698\pi\)
\(558\) 0 0
\(559\) −48.1364 −2.03595
\(560\) 0 0
\(561\) −16.3235 −0.689179
\(562\) 0 0
\(563\) 6.10564i 0.257322i −0.991689 0.128661i \(-0.958932\pi\)
0.991689 0.128661i \(-0.0410679\pi\)
\(564\) 0 0
\(565\) 31.7164 17.7214i 1.33432 0.745547i
\(566\) 0 0
\(567\) 31.2071i 1.31057i
\(568\) 0 0
\(569\) −9.28182 −0.389114 −0.194557 0.980891i \(-0.562327\pi\)
−0.194557 + 0.980891i \(0.562327\pi\)
\(570\) 0 0
\(571\) 6.76185 0.282975 0.141487 0.989940i \(-0.454812\pi\)
0.141487 + 0.989940i \(0.454812\pi\)
\(572\) 0 0
\(573\) 9.03097i 0.377274i
\(574\) 0 0
\(575\) −4.25810 2.62080i −0.177575 0.109295i
\(576\) 0 0
\(577\) 31.2132i 1.29942i 0.760182 + 0.649711i \(0.225110\pi\)
−0.760182 + 0.649711i \(0.774890\pi\)
\(578\) 0 0
\(579\) 1.80315 0.0749365
\(580\) 0 0
\(581\) −20.1585 −0.836315
\(582\) 0 0
\(583\) 48.2867i 1.99983i
\(584\) 0 0
\(585\) 29.8233 16.6637i 1.23304 0.688960i
\(586\) 0 0
\(587\) 24.7138i 1.02005i −0.860161 0.510023i \(-0.829637\pi\)
0.860161 0.510023i \(-0.170363\pi\)
\(588\) 0 0
\(589\) 6.07246 0.250211
\(590\) 0 0
\(591\) 4.51195 0.185597
\(592\) 0 0
\(593\) 20.3119i 0.834109i 0.908882 + 0.417054i \(0.136938\pi\)
−0.908882 + 0.417054i \(0.863062\pi\)
\(594\) 0 0
\(595\) 35.5381 + 63.6031i 1.45692 + 2.60747i
\(596\) 0 0
\(597\) 0.0205458i 0.000840885i
\(598\) 0 0
\(599\) 17.2979 0.706772 0.353386 0.935478i \(-0.385030\pi\)
0.353386 + 0.935478i \(0.385030\pi\)
\(600\) 0 0
\(601\) 32.9939 1.34585 0.672924 0.739711i \(-0.265038\pi\)
0.672924 + 0.739711i \(0.265038\pi\)
\(602\) 0 0
\(603\) 24.3757i 0.992657i
\(604\) 0 0
\(605\) 11.2117 + 20.0658i 0.455821 + 0.815790i
\(606\) 0 0
\(607\) 35.8434i 1.45484i −0.686193 0.727419i \(-0.740719\pi\)
0.686193 0.727419i \(-0.259281\pi\)
\(608\) 0 0
\(609\) 8.21651 0.332950
\(610\) 0 0
\(611\) 53.1564 2.15048
\(612\) 0 0
\(613\) 30.1971i 1.21965i 0.792536 + 0.609825i \(0.208760\pi\)
−0.792536 + 0.609825i \(0.791240\pi\)
\(614\) 0 0
\(615\) 8.62438 4.81885i 0.347769 0.194315i
\(616\) 0 0
\(617\) 5.34282i 0.215094i −0.994200 0.107547i \(-0.965700\pi\)
0.994200 0.107547i \(-0.0342996\pi\)
\(618\) 0 0
\(619\) 2.48462 0.0998652 0.0499326 0.998753i \(-0.484099\pi\)
0.0499326 + 0.998753i \(0.484099\pi\)
\(620\) 0 0
\(621\) 2.84098 0.114005
\(622\) 0 0
\(623\) 60.1148i 2.40845i
\(624\) 0 0
\(625\) −11.2629 22.3192i −0.450514 0.892769i
\(626\) 0 0
\(627\) 3.09546i 0.123621i
\(628\) 0 0
\(629\) −23.8353 −0.950375
\(630\) 0 0
\(631\) −0.724918 −0.0288585 −0.0144293 0.999896i \(-0.504593\pi\)
−0.0144293 + 0.999896i \(0.504593\pi\)
\(632\) 0 0
\(633\) 0.535666i 0.0212908i
\(634\) 0 0
\(635\) 3.09503 1.72934i 0.122822 0.0686268i
\(636\) 0 0
\(637\) 75.6665i 2.99802i
\(638\) 0 0
\(639\) −43.8382 −1.73421
\(640\) 0 0
\(641\) 26.8404 1.06013 0.530067 0.847956i \(-0.322167\pi\)
0.530067 + 0.847956i \(0.322167\pi\)
\(642\) 0 0
\(643\) 2.47661i 0.0976679i −0.998807 0.0488340i \(-0.984449\pi\)
0.998807 0.0488340i \(-0.0155505\pi\)
\(644\) 0 0
\(645\) −4.67482 8.36660i −0.184071 0.329435i
\(646\) 0 0
\(647\) 35.7731i 1.40639i −0.710999 0.703193i \(-0.751757\pi\)
0.710999 0.703193i \(-0.248243\pi\)
\(648\) 0 0
\(649\) −9.62000 −0.377618
\(650\) 0 0
\(651\) 10.0167 0.392585
\(652\) 0 0
\(653\) 14.5123i 0.567909i −0.958838 0.283955i \(-0.908354\pi\)
0.958838 0.283955i \(-0.0916465\pi\)
\(654\) 0 0
\(655\) −5.12182 9.16661i −0.200126 0.358169i
\(656\) 0 0
\(657\) 12.2564i 0.478167i
\(658\) 0 0
\(659\) 8.05918 0.313941 0.156970 0.987603i \(-0.449827\pi\)
0.156970 + 0.987603i \(0.449827\pi\)
\(660\) 0 0
\(661\) −27.0801 −1.05329 −0.526647 0.850084i \(-0.676551\pi\)
−0.526647 + 0.850084i \(0.676551\pi\)
\(662\) 0 0
\(663\) 19.6136i 0.761729i
\(664\) 0 0
\(665\) −12.0612 + 6.73917i −0.467714 + 0.261334i
\(666\) 0 0
\(667\) 3.66351i 0.141852i
\(668\) 0 0
\(669\) 6.04167 0.233585
\(670\) 0 0
\(671\) −3.16541 −0.122199
\(672\) 0 0
\(673\) 20.1388i 0.776292i 0.921598 + 0.388146i \(0.126884\pi\)
−0.921598 + 0.388146i \(0.873116\pi\)
\(674\) 0 0
\(675\) 12.0972 + 7.44562i 0.465620 + 0.286582i
\(676\) 0 0
\(677\) 26.8739i 1.03285i −0.856333 0.516424i \(-0.827263\pi\)
0.856333 0.516424i \(-0.172737\pi\)
\(678\) 0 0
\(679\) −5.53439 −0.212390
\(680\) 0 0
\(681\) −3.26058 −0.124946
\(682\) 0 0
\(683\) 40.0529i 1.53258i −0.642495 0.766290i \(-0.722100\pi\)
0.642495 0.766290i \(-0.277900\pi\)
\(684\) 0 0
\(685\) −20.1174 + 11.2405i −0.768646 + 0.429479i
\(686\) 0 0
\(687\) 12.5855i 0.480166i
\(688\) 0 0
\(689\) 58.0192 2.21036
\(690\) 0 0
\(691\) −25.1106 −0.955254 −0.477627 0.878563i \(-0.658503\pi\)
−0.477627 + 0.878563i \(0.658503\pi\)
\(692\) 0 0
\(693\) 57.7833i 2.19501i
\(694\) 0 0
\(695\) 0.734440 + 1.31444i 0.0278589 + 0.0498595i
\(696\) 0 0
\(697\) 64.1868i 2.43125i
\(698\) 0 0
\(699\) −2.54568 −0.0962866
\(700\) 0 0
\(701\) −33.6355 −1.27039 −0.635197 0.772350i \(-0.719081\pi\)
−0.635197 + 0.772350i \(0.719081\pi\)
\(702\) 0 0
\(703\) 4.51994i 0.170473i
\(704\) 0 0
\(705\) 5.16235 + 9.23914i 0.194425 + 0.347966i
\(706\) 0 0
\(707\) 47.7157i 1.79453i
\(708\) 0 0
\(709\) −6.25559 −0.234934 −0.117467 0.993077i \(-0.537477\pi\)
−0.117467 + 0.993077i \(0.537477\pi\)
\(710\) 0 0
\(711\) −23.8494 −0.894421
\(712\) 0 0
\(713\) 4.46616i 0.167259i
\(714\) 0 0
\(715\) 49.9103 27.8873i 1.86654 1.04292i
\(716\) 0 0
\(717\) 6.82042i 0.254713i
\(718\) 0 0
\(719\) −45.8585 −1.71024 −0.855118 0.518434i \(-0.826515\pi\)
−0.855118 + 0.518434i \(0.826515\pi\)
\(720\) 0 0
\(721\) 37.8372 1.40913
\(722\) 0 0
\(723\) 7.36202i 0.273797i
\(724\) 0 0
\(725\) −9.60131 + 15.5996i −0.356584 + 0.579354i
\(726\) 0 0
\(727\) 15.5296i 0.575961i −0.957636 0.287981i \(-0.907016\pi\)
0.957636 0.287981i \(-0.0929839\pi\)
\(728\) 0 0
\(729\) 14.7225 0.545278
\(730\) 0 0
\(731\) −62.2683 −2.30307
\(732\) 0 0
\(733\) 43.1452i 1.59360i −0.604240 0.796802i \(-0.706523\pi\)
0.604240 0.796802i \(-0.293477\pi\)
\(734\) 0 0
\(735\) −13.1516 + 7.34844i −0.485105 + 0.271051i
\(736\) 0 0
\(737\) 40.7936i 1.50265i
\(738\) 0 0
\(739\) −33.5882 −1.23556 −0.617781 0.786350i \(-0.711968\pi\)
−0.617781 + 0.786350i \(0.711968\pi\)
\(740\) 0 0
\(741\) −3.71937 −0.136635
\(742\) 0 0
\(743\) 13.8916i 0.509632i −0.966990 0.254816i \(-0.917985\pi\)
0.966990 0.254816i \(-0.0820149\pi\)
\(744\) 0 0
\(745\) 5.17115 + 9.25490i 0.189456 + 0.339073i
\(746\) 0 0
\(747\) 12.2273i 0.447372i
\(748\) 0 0
\(749\) 43.6305 1.59422
\(750\) 0 0
\(751\) 38.4863 1.40439 0.702193 0.711987i \(-0.252204\pi\)
0.702193 + 0.711987i \(0.252204\pi\)
\(752\) 0 0
\(753\) 6.34048i 0.231060i
\(754\) 0 0
\(755\) −3.45382 6.18136i −0.125697 0.224963i
\(756\) 0 0
\(757\) 4.03386i 0.146613i 0.997309 + 0.0733066i \(0.0233552\pi\)
−0.997309 + 0.0733066i \(0.976645\pi\)
\(758\) 0 0
\(759\) 2.27665 0.0826370
\(760\) 0 0
\(761\) −2.28005 −0.0826518 −0.0413259 0.999146i \(-0.513158\pi\)
−0.0413259 + 0.999146i \(0.513158\pi\)
\(762\) 0 0
\(763\) 46.8059i 1.69449i
\(764\) 0 0
\(765\) 38.5789 21.5558i 1.39482 0.779353i
\(766\) 0 0
\(767\) 11.5590i 0.417370i
\(768\) 0 0
\(769\) 48.0050 1.73111 0.865553 0.500818i \(-0.166967\pi\)
0.865553 + 0.500818i \(0.166967\pi\)
\(770\) 0 0
\(771\) −6.03074 −0.217192
\(772\) 0 0
\(773\) 3.67822i 0.132297i 0.997810 + 0.0661483i \(0.0210710\pi\)
−0.997810 + 0.0661483i \(0.978929\pi\)
\(774\) 0 0
\(775\) −11.7049 + 19.0174i −0.420452 + 0.683124i
\(776\) 0 0
\(777\) 7.45577i 0.267474i
\(778\) 0 0
\(779\) 12.1719 0.436104
\(780\) 0 0
\(781\) −73.3646 −2.62519
\(782\) 0 0
\(783\) 10.4079i 0.371950i
\(784\) 0 0
\(785\) −15.7697 + 8.81128i −0.562844 + 0.314488i
\(786\) 0 0
\(787\) 13.9078i 0.495761i 0.968791 + 0.247881i \(0.0797341\pi\)
−0.968791 + 0.247881i \(0.920266\pi\)
\(788\) 0 0
\(789\) −12.4436 −0.443004
\(790\) 0 0
\(791\) 73.8369 2.62534
\(792\) 0 0
\(793\) 3.80341i 0.135063i
\(794\) 0 0
\(795\) 5.63460 + 10.0843i 0.199839 + 0.357655i
\(796\) 0 0
\(797\) 13.8982i 0.492301i 0.969232 + 0.246150i \(0.0791657\pi\)
−0.969232 + 0.246150i \(0.920834\pi\)
\(798\) 0 0
\(799\) 68.7621 2.43263
\(800\) 0 0
\(801\) −36.4630 −1.28836
\(802\) 0 0