Properties

Label 2520.2.bi.k.1801.2
Level $2520$
Weight $2$
Character 2520.1801
Analytic conductor $20.122$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 2520 = 2^{3} \cdot 3^{2} \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2520.bi (of order \(3\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(20.1223013094\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\Q(\sqrt{2}, \sqrt{-3})\)
Defining polynomial: \(x^{4} + 2 x^{2} + 4\)
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 280)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 1801.2
Root \(0.707107 + 1.22474i\) of defining polynomial
Character \(\chi\) \(=\) 2520.1801
Dual form 2520.2.bi.k.361.2

$q$-expansion

\(f(q)\) \(=\) \(q+(0.500000 - 0.866025i) q^{5} +(1.62132 - 2.09077i) q^{7} +O(q^{10})\) \(q+(0.500000 - 0.866025i) q^{5} +(1.62132 - 2.09077i) q^{7} +(0.414214 + 0.717439i) q^{11} +2.00000 q^{13} +(-3.82843 - 6.63103i) q^{17} +(2.82843 - 4.89898i) q^{19} +(-2.79289 + 4.83743i) q^{23} +(-0.500000 - 0.866025i) q^{25} +7.82843 q^{29} +(-0.414214 - 0.717439i) q^{31} +(-1.00000 - 2.44949i) q^{35} +(-2.82843 + 4.89898i) q^{37} -5.82843 q^{41} -6.89949 q^{43} +(5.82843 - 10.0951i) q^{47} +(-1.74264 - 6.77962i) q^{49} +(-2.82843 - 4.89898i) q^{53} +0.828427 q^{55} +(-2.00000 - 3.46410i) q^{59} +(-3.32843 + 5.76500i) q^{61} +(1.00000 - 1.73205i) q^{65} +(6.44975 + 11.1713i) q^{67} +12.0000 q^{71} +(-1.82843 - 3.16693i) q^{73} +(2.17157 + 0.297173i) q^{77} +(2.00000 - 3.46410i) q^{79} +4.75736 q^{83} -7.65685 q^{85} +(-2.67157 + 4.62730i) q^{89} +(3.24264 - 4.18154i) q^{91} +(-2.82843 - 4.89898i) q^{95} +6.00000 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4q + 2q^{5} - 2q^{7} + O(q^{10}) \) \( 4q + 2q^{5} - 2q^{7} - 4q^{11} + 8q^{13} - 4q^{17} - 14q^{23} - 2q^{25} + 20q^{29} + 4q^{31} - 4q^{35} - 12q^{41} + 12q^{43} + 12q^{47} + 10q^{49} - 8q^{55} - 8q^{59} - 2q^{61} + 4q^{65} + 6q^{67} + 48q^{71} + 4q^{73} + 20q^{77} + 8q^{79} + 36q^{83} - 8q^{85} - 22q^{89} - 4q^{91} + 24q^{97} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/2520\mathbb{Z}\right)^\times\).

\(n\) \(281\) \(631\) \(1081\) \(1261\) \(2017\)
\(\chi(n)\) \(1\) \(1\) \(e\left(\frac{1}{3}\right)\) \(1\) \(1\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) 0 0
\(4\) 0 0
\(5\) 0.500000 0.866025i 0.223607 0.387298i
\(6\) 0 0
\(7\) 1.62132 2.09077i 0.612801 0.790237i
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) 0.414214 + 0.717439i 0.124890 + 0.216316i 0.921690 0.387927i \(-0.126809\pi\)
−0.796800 + 0.604243i \(0.793476\pi\)
\(12\) 0 0
\(13\) 2.00000 0.554700 0.277350 0.960769i \(-0.410544\pi\)
0.277350 + 0.960769i \(0.410544\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) −3.82843 6.63103i −0.928530 1.60826i −0.785783 0.618502i \(-0.787740\pi\)
−0.142747 0.989759i \(-0.545593\pi\)
\(18\) 0 0
\(19\) 2.82843 4.89898i 0.648886 1.12390i −0.334504 0.942394i \(-0.608569\pi\)
0.983389 0.181509i \(-0.0580980\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) −2.79289 + 4.83743i −0.582358 + 1.00867i 0.412841 + 0.910803i \(0.364537\pi\)
−0.995199 + 0.0978712i \(0.968797\pi\)
\(24\) 0 0
\(25\) −0.500000 0.866025i −0.100000 0.173205i
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) 7.82843 1.45370 0.726851 0.686795i \(-0.240983\pi\)
0.726851 + 0.686795i \(0.240983\pi\)
\(30\) 0 0
\(31\) −0.414214 0.717439i −0.0743950 0.128856i 0.826428 0.563042i \(-0.190369\pi\)
−0.900823 + 0.434187i \(0.857036\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) −1.00000 2.44949i −0.169031 0.414039i
\(36\) 0 0
\(37\) −2.82843 + 4.89898i −0.464991 + 0.805387i −0.999201 0.0399642i \(-0.987276\pi\)
0.534211 + 0.845351i \(0.320609\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) −5.82843 −0.910247 −0.455124 0.890428i \(-0.650405\pi\)
−0.455124 + 0.890428i \(0.650405\pi\)
\(42\) 0 0
\(43\) −6.89949 −1.05216 −0.526082 0.850434i \(-0.676339\pi\)
−0.526082 + 0.850434i \(0.676339\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 5.82843 10.0951i 0.850163 1.47253i −0.0308969 0.999523i \(-0.509836\pi\)
0.881060 0.473004i \(-0.156830\pi\)
\(48\) 0 0
\(49\) −1.74264 6.77962i −0.248949 0.968517i
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) −2.82843 4.89898i −0.388514 0.672927i 0.603736 0.797185i \(-0.293678\pi\)
−0.992250 + 0.124258i \(0.960345\pi\)
\(54\) 0 0
\(55\) 0.828427 0.111705
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) −2.00000 3.46410i −0.260378 0.450988i 0.705965 0.708247i \(-0.250514\pi\)
−0.966342 + 0.257260i \(0.917180\pi\)
\(60\) 0 0
\(61\) −3.32843 + 5.76500i −0.426161 + 0.738133i −0.996528 0.0832569i \(-0.973468\pi\)
0.570367 + 0.821390i \(0.306801\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) 1.00000 1.73205i 0.124035 0.214834i
\(66\) 0 0
\(67\) 6.44975 + 11.1713i 0.787962 + 1.36479i 0.927213 + 0.374533i \(0.122197\pi\)
−0.139251 + 0.990257i \(0.544470\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 12.0000 1.42414 0.712069 0.702109i \(-0.247758\pi\)
0.712069 + 0.702109i \(0.247758\pi\)
\(72\) 0 0
\(73\) −1.82843 3.16693i −0.214001 0.370661i 0.738962 0.673747i \(-0.235316\pi\)
−0.952963 + 0.303086i \(0.901983\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 2.17157 + 0.297173i 0.247474 + 0.0338660i
\(78\) 0 0
\(79\) 2.00000 3.46410i 0.225018 0.389742i −0.731307 0.682048i \(-0.761089\pi\)
0.956325 + 0.292306i \(0.0944227\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) 4.75736 0.522188 0.261094 0.965313i \(-0.415917\pi\)
0.261094 + 0.965313i \(0.415917\pi\)
\(84\) 0 0
\(85\) −7.65685 −0.830502
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) −2.67157 + 4.62730i −0.283186 + 0.490493i −0.972168 0.234286i \(-0.924725\pi\)
0.688982 + 0.724779i \(0.258058\pi\)
\(90\) 0 0
\(91\) 3.24264 4.18154i 0.339921 0.438345i
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) −2.82843 4.89898i −0.290191 0.502625i
\(96\) 0 0
\(97\) 6.00000 0.609208 0.304604 0.952479i \(-0.401476\pi\)
0.304604 + 0.952479i \(0.401476\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) −5.74264 9.94655i −0.571414 0.989718i −0.996421 0.0845282i \(-0.973062\pi\)
0.425007 0.905190i \(-0.360272\pi\)
\(102\) 0 0
\(103\) −3.79289 + 6.56948i −0.373725 + 0.647310i −0.990135 0.140115i \(-0.955253\pi\)
0.616410 + 0.787425i \(0.288586\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −2.79289 + 4.83743i −0.269999 + 0.467652i −0.968861 0.247604i \(-0.920357\pi\)
0.698862 + 0.715256i \(0.253690\pi\)
\(108\) 0 0
\(109\) −9.15685 15.8601i −0.877068 1.51913i −0.854544 0.519379i \(-0.826163\pi\)
−0.0225237 0.999746i \(-0.507170\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) −11.3137 −1.06430 −0.532152 0.846649i \(-0.678617\pi\)
−0.532152 + 0.846649i \(0.678617\pi\)
\(114\) 0 0
\(115\) 2.79289 + 4.83743i 0.260439 + 0.451093i
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) −20.0711 2.74666i −1.83991 0.251786i
\(120\) 0 0
\(121\) 5.15685 8.93193i 0.468805 0.811994i
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) −1.00000 −0.0894427
\(126\) 0 0
\(127\) −4.34315 −0.385392 −0.192696 0.981259i \(-0.561723\pi\)
−0.192696 + 0.981259i \(0.561723\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) 6.82843 11.8272i 0.596602 1.03335i −0.396716 0.917941i \(-0.629850\pi\)
0.993319 0.115404i \(-0.0368164\pi\)
\(132\) 0 0
\(133\) −5.65685 13.8564i −0.490511 1.20150i
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) −2.00000 3.46410i −0.170872 0.295958i 0.767853 0.640626i \(-0.221325\pi\)
−0.938725 + 0.344668i \(0.887992\pi\)
\(138\) 0 0
\(139\) 2.48528 0.210799 0.105399 0.994430i \(-0.466388\pi\)
0.105399 + 0.994430i \(0.466388\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 0.828427 + 1.43488i 0.0692766 + 0.119991i
\(144\) 0 0
\(145\) 3.91421 6.77962i 0.325058 0.563017i
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) 2.32843 4.03295i 0.190752 0.330392i −0.754748 0.656015i \(-0.772241\pi\)
0.945500 + 0.325623i \(0.105574\pi\)
\(150\) 0 0
\(151\) 5.58579 + 9.67487i 0.454565 + 0.787329i 0.998663 0.0516921i \(-0.0164614\pi\)
−0.544098 + 0.839022i \(0.683128\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) −0.828427 −0.0665409
\(156\) 0 0
\(157\) −0.656854 1.13770i −0.0524227 0.0907987i 0.838623 0.544712i \(-0.183361\pi\)
−0.891046 + 0.453913i \(0.850028\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 5.58579 + 13.6823i 0.440222 + 1.07832i
\(162\) 0 0
\(163\) 7.82843 13.5592i 0.613170 1.06204i −0.377533 0.925996i \(-0.623227\pi\)
0.990703 0.136045i \(-0.0434392\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) −2.07107 −0.160264 −0.0801320 0.996784i \(-0.525534\pi\)
−0.0801320 + 0.996784i \(0.525534\pi\)
\(168\) 0 0
\(169\) −9.00000 −0.692308
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) 5.17157 8.95743i 0.393187 0.681021i −0.599681 0.800239i \(-0.704706\pi\)
0.992868 + 0.119219i \(0.0380390\pi\)
\(174\) 0 0
\(175\) −2.62132 0.358719i −0.198153 0.0271166i
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) −3.24264 5.61642i −0.242366 0.419791i 0.719022 0.694988i \(-0.244590\pi\)
−0.961388 + 0.275197i \(0.911257\pi\)
\(180\) 0 0
\(181\) −4.17157 −0.310071 −0.155035 0.987909i \(-0.549549\pi\)
−0.155035 + 0.987909i \(0.549549\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 2.82843 + 4.89898i 0.207950 + 0.360180i
\(186\) 0 0
\(187\) 3.17157 5.49333i 0.231928 0.401712i
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) −2.75736 + 4.77589i −0.199516 + 0.345571i −0.948371 0.317162i \(-0.897270\pi\)
0.748856 + 0.662733i \(0.230603\pi\)
\(192\) 0 0
\(193\) 2.65685 + 4.60181i 0.191245 + 0.331245i 0.945663 0.325149i \(-0.105414\pi\)
−0.754418 + 0.656394i \(0.772081\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) −0.343146 −0.0244481 −0.0122241 0.999925i \(-0.503891\pi\)
−0.0122241 + 0.999925i \(0.503891\pi\)
\(198\) 0 0
\(199\) 11.6569 + 20.1903i 0.826332 + 1.43125i 0.900897 + 0.434034i \(0.142910\pi\)
−0.0745642 + 0.997216i \(0.523757\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) 12.6924 16.3674i 0.890831 1.14877i
\(204\) 0 0
\(205\) −2.91421 + 5.04757i −0.203538 + 0.352537i
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) 4.68629 0.324158
\(210\) 0 0
\(211\) 26.6274 1.83311 0.916553 0.399912i \(-0.130959\pi\)
0.916553 + 0.399912i \(0.130959\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) −3.44975 + 5.97514i −0.235271 + 0.407501i
\(216\) 0 0
\(217\) −2.17157 0.297173i −0.147416 0.0201734i
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) −7.65685 13.2621i −0.515056 0.892103i
\(222\) 0 0
\(223\) −14.9706 −1.00250 −0.501252 0.865302i \(-0.667127\pi\)
−0.501252 + 0.865302i \(0.667127\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 7.00000 + 12.1244i 0.464606 + 0.804722i 0.999184 0.0403978i \(-0.0128625\pi\)
−0.534577 + 0.845120i \(0.679529\pi\)
\(228\) 0 0
\(229\) 7.00000 12.1244i 0.462573 0.801200i −0.536515 0.843891i \(-0.680260\pi\)
0.999088 + 0.0426906i \(0.0135930\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 5.82843 10.0951i 0.381833 0.661354i −0.609491 0.792793i \(-0.708626\pi\)
0.991324 + 0.131439i \(0.0419596\pi\)
\(234\) 0 0
\(235\) −5.82843 10.0951i −0.380205 0.658534i
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) 30.4853 1.97193 0.985964 0.166955i \(-0.0533936\pi\)
0.985964 + 0.166955i \(0.0533936\pi\)
\(240\) 0 0
\(241\) 5.00000 + 8.66025i 0.322078 + 0.557856i 0.980917 0.194429i \(-0.0622852\pi\)
−0.658838 + 0.752285i \(0.728952\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) −6.74264 1.88064i −0.430772 0.120150i
\(246\) 0 0
\(247\) 5.65685 9.79796i 0.359937 0.623429i
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 27.4558 1.73300 0.866499 0.499179i \(-0.166365\pi\)
0.866499 + 0.499179i \(0.166365\pi\)
\(252\) 0 0
\(253\) −4.62742 −0.290923
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 7.65685 13.2621i 0.477621 0.827265i −0.522050 0.852915i \(-0.674832\pi\)
0.999671 + 0.0256506i \(0.00816572\pi\)
\(258\) 0 0
\(259\) 5.65685 + 13.8564i 0.351500 + 0.860995i
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) −7.86396 13.6208i −0.484913 0.839893i 0.514937 0.857228i \(-0.327815\pi\)
−0.999850 + 0.0173347i \(0.994482\pi\)
\(264\) 0 0
\(265\) −5.65685 −0.347498
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) −3.32843 5.76500i −0.202938 0.351499i 0.746536 0.665345i \(-0.231716\pi\)
−0.949474 + 0.313847i \(0.898382\pi\)
\(270\) 0 0
\(271\) 1.65685 2.86976i 0.100647 0.174325i −0.811305 0.584624i \(-0.801242\pi\)
0.911951 + 0.410298i \(0.134575\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 0.414214 0.717439i 0.0249780 0.0432632i
\(276\) 0 0
\(277\) −14.3137 24.7921i −0.860027 1.48961i −0.871901 0.489682i \(-0.837113\pi\)
0.0118739 0.999930i \(-0.496220\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) −2.68629 −0.160251 −0.0801254 0.996785i \(-0.525532\pi\)
−0.0801254 + 0.996785i \(0.525532\pi\)
\(282\) 0 0
\(283\) −9.00000 15.5885i −0.534994 0.926638i −0.999164 0.0408910i \(-0.986980\pi\)
0.464169 0.885747i \(-0.346353\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) −9.44975 + 12.1859i −0.557801 + 0.719311i
\(288\) 0 0
\(289\) −20.8137 + 36.0504i −1.22434 + 2.12061i
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) −16.9706 −0.991431 −0.495715 0.868485i \(-0.665094\pi\)
−0.495715 + 0.868485i \(0.665094\pi\)
\(294\) 0 0
\(295\) −4.00000 −0.232889
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) −5.58579 + 9.67487i −0.323034 + 0.559512i
\(300\) 0 0
\(301\) −11.1863 + 14.4253i −0.644767 + 0.831458i
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) 3.32843 + 5.76500i 0.190585 + 0.330103i
\(306\) 0 0
\(307\) 4.75736 0.271517 0.135758 0.990742i \(-0.456653\pi\)
0.135758 + 0.990742i \(0.456653\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 10.8284 + 18.7554i 0.614024 + 1.06352i 0.990555 + 0.137116i \(0.0437834\pi\)
−0.376531 + 0.926404i \(0.622883\pi\)
\(312\) 0 0
\(313\) −10.4853 + 18.1610i −0.592663 + 1.02652i 0.401209 + 0.915987i \(0.368590\pi\)
−0.993872 + 0.110536i \(0.964743\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −11.0000 + 19.0526i −0.617822 + 1.07010i 0.372061 + 0.928208i \(0.378651\pi\)
−0.989882 + 0.141890i \(0.954682\pi\)
\(318\) 0 0
\(319\) 3.24264 + 5.61642i 0.181553 + 0.314459i
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) −43.3137 −2.41004
\(324\) 0 0
\(325\) −1.00000 1.73205i −0.0554700 0.0960769i
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) −11.6569 28.5533i −0.642663 1.57420i
\(330\) 0 0
\(331\) −13.2426 + 22.9369i −0.727881 + 1.26073i 0.229896 + 0.973215i \(0.426162\pi\)
−0.957777 + 0.287512i \(0.907172\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) 12.8995 0.704775
\(336\) 0 0
\(337\) 24.9706 1.36023 0.680117 0.733104i \(-0.261929\pi\)
0.680117 + 0.733104i \(0.261929\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) 0.343146 0.594346i 0.0185824 0.0321856i
\(342\) 0 0
\(343\) −17.0000 7.34847i −0.917914 0.396780i
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 5.69239 + 9.85951i 0.305583 + 0.529286i 0.977391 0.211440i \(-0.0678152\pi\)
−0.671808 + 0.740726i \(0.734482\pi\)
\(348\) 0 0
\(349\) 9.82843 0.526104 0.263052 0.964782i \(-0.415271\pi\)
0.263052 + 0.964782i \(0.415271\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) 16.8284 + 29.1477i 0.895687 + 1.55138i 0.832952 + 0.553345i \(0.186649\pi\)
0.0627345 + 0.998030i \(0.480018\pi\)
\(354\) 0 0
\(355\) 6.00000 10.3923i 0.318447 0.551566i
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) −3.24264 + 5.61642i −0.171140 + 0.296423i −0.938819 0.344412i \(-0.888078\pi\)
0.767679 + 0.640835i \(0.221412\pi\)
\(360\) 0 0
\(361\) −6.50000 11.2583i −0.342105 0.592544i
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) −3.65685 −0.191408
\(366\) 0 0
\(367\) −10.7929 18.6938i −0.563384 0.975810i −0.997198 0.0748078i \(-0.976166\pi\)
0.433814 0.901003i \(-0.357168\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) −14.8284 2.02922i −0.769854 0.105352i
\(372\) 0 0
\(373\) −6.00000 + 10.3923i −0.310668 + 0.538093i −0.978507 0.206213i \(-0.933886\pi\)
0.667839 + 0.744306i \(0.267219\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 15.6569 0.806369
\(378\) 0 0
\(379\) 4.68629 0.240719 0.120359 0.992730i \(-0.461595\pi\)
0.120359 + 0.992730i \(0.461595\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) −0.449747 + 0.778985i −0.0229810 + 0.0398043i −0.877287 0.479966i \(-0.840649\pi\)
0.854306 + 0.519770i \(0.173982\pi\)
\(384\) 0 0
\(385\) 1.34315 1.73205i 0.0684530 0.0882735i
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) 2.65685 + 4.60181i 0.134708 + 0.233321i 0.925486 0.378782i \(-0.123657\pi\)
−0.790778 + 0.612103i \(0.790324\pi\)
\(390\) 0 0
\(391\) 42.7696 2.16295
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) −2.00000 3.46410i −0.100631 0.174298i
\(396\) 0 0
\(397\) 12.3137 21.3280i 0.618007 1.07042i −0.371842 0.928296i \(-0.621274\pi\)
0.989849 0.142124i \(-0.0453931\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) −16.1569 + 27.9845i −0.806835 + 1.39748i 0.108211 + 0.994128i \(0.465488\pi\)
−0.915045 + 0.403351i \(0.867845\pi\)
\(402\) 0 0
\(403\) −0.828427 1.43488i −0.0412669 0.0714764i
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) −4.68629 −0.232291
\(408\) 0 0
\(409\) 12.5711 + 21.7737i 0.621599 + 1.07664i 0.989188 + 0.146653i \(0.0468501\pi\)
−0.367589 + 0.929988i \(0.619817\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) −10.4853 1.43488i −0.515947 0.0706057i
\(414\) 0 0
\(415\) 2.37868 4.11999i 0.116765 0.202243i
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 15.3137 0.748124 0.374062 0.927404i \(-0.377965\pi\)
0.374062 + 0.927404i \(0.377965\pi\)
\(420\) 0 0
\(421\) 27.3431 1.33262 0.666312 0.745673i \(-0.267872\pi\)
0.666312 + 0.745673i \(0.267872\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) −3.82843 + 6.63103i −0.185706 + 0.321652i
\(426\) 0 0
\(427\) 6.65685 + 16.3059i 0.322148 + 0.789098i
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) −0.414214 0.717439i −0.0199520 0.0345578i 0.855877 0.517179i \(-0.173018\pi\)
−0.875829 + 0.482622i \(0.839685\pi\)
\(432\) 0 0
\(433\) −19.3137 −0.928158 −0.464079 0.885794i \(-0.653615\pi\)
−0.464079 + 0.885794i \(0.653615\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 15.7990 + 27.3647i 0.755768 + 1.30903i
\(438\) 0 0
\(439\) 9.17157 15.8856i 0.437735 0.758180i −0.559779 0.828642i \(-0.689114\pi\)
0.997514 + 0.0704621i \(0.0224474\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) −7.79289 + 13.4977i −0.370252 + 0.641294i −0.989604 0.143819i \(-0.954062\pi\)
0.619353 + 0.785113i \(0.287395\pi\)
\(444\) 0 0
\(445\) 2.67157 + 4.62730i 0.126645 + 0.219355i
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) 7.48528 0.353252 0.176626 0.984278i \(-0.443482\pi\)
0.176626 + 0.984278i \(0.443482\pi\)
\(450\) 0 0
\(451\) −2.41421 4.18154i −0.113681 0.196901i
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) −2.00000 4.89898i −0.0937614 0.229668i
\(456\) 0 0
\(457\) −14.4853 + 25.0892i −0.677593 + 1.17363i 0.298111 + 0.954531i \(0.403643\pi\)
−0.975704 + 0.219094i \(0.929690\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) −1.31371 −0.0611855 −0.0305928 0.999532i \(-0.509739\pi\)
−0.0305928 + 0.999532i \(0.509739\pi\)
\(462\) 0 0
\(463\) 14.8995 0.692438 0.346219 0.938154i \(-0.387465\pi\)
0.346219 + 0.938154i \(0.387465\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) −18.9350 + 32.7964i −0.876209 + 1.51764i −0.0207390 + 0.999785i \(0.506602\pi\)
−0.855470 + 0.517853i \(0.826731\pi\)
\(468\) 0 0
\(469\) 33.8137 + 4.62730i 1.56137 + 0.213669i
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) −2.85786 4.94997i −0.131405 0.227600i
\(474\) 0 0
\(475\) −5.65685 −0.259554
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) −0.757359 1.31178i −0.0346046 0.0599370i 0.848204 0.529669i \(-0.177684\pi\)
−0.882809 + 0.469732i \(0.844351\pi\)
\(480\) 0 0
\(481\) −5.65685 + 9.79796i −0.257930 + 0.446748i
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 3.00000 5.19615i 0.136223 0.235945i
\(486\) 0 0
\(487\) 19.1421 + 33.1552i 0.867413 + 1.50240i 0.864631 + 0.502407i \(0.167552\pi\)
0.00278182 + 0.999996i \(0.499115\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) −1.51472 −0.0683583 −0.0341791 0.999416i \(-0.510882\pi\)
−0.0341791 + 0.999416i \(0.510882\pi\)
\(492\) 0 0
\(493\) −29.9706 51.9105i −1.34981 2.33793i
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 19.4558 25.0892i 0.872714 1.12541i
\(498\) 0 0
\(499\) −22.0711 + 38.2282i −0.988037 + 1.71133i −0.360461 + 0.932774i \(0.617381\pi\)
−0.627576 + 0.778555i \(0.715953\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) 3.92893 0.175182 0.0875912 0.996157i \(-0.472083\pi\)
0.0875912 + 0.996157i \(0.472083\pi\)
\(504\) 0 0
\(505\) −11.4853 −0.511088
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) −16.7426 + 28.9991i −0.742105 + 1.28536i 0.209431 + 0.977823i \(0.432839\pi\)
−0.951535 + 0.307539i \(0.900494\pi\)
\(510\) 0 0
\(511\) −9.58579 1.31178i −0.424050 0.0580299i
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) 3.79289 + 6.56948i 0.167135 + 0.289486i
\(516\) 0 0
\(517\) 9.65685 0.424708
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 18.3137 + 31.7203i 0.802338 + 1.38969i 0.918073 + 0.396410i \(0.129744\pi\)
−0.115735 + 0.993280i \(0.536922\pi\)
\(522\) 0 0
\(523\) −13.9706 + 24.1977i −0.610890 + 1.05809i 0.380201 + 0.924904i \(0.375855\pi\)
−0.991091 + 0.133189i \(0.957478\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −3.17157 + 5.49333i −0.138156 + 0.239293i
\(528\) 0 0
\(529\) −4.10051 7.10228i −0.178283 0.308795i
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) −11.6569 −0.504914
\(534\) 0 0
\(535\) 2.79289 + 4.83743i 0.120747 + 0.209140i
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) 4.14214 4.05845i 0.178414 0.174810i
\(540\) 0 0
\(541\) 11.7426 20.3389i 0.504856 0.874435i −0.495129 0.868820i \(-0.664879\pi\)
0.999984 0.00561582i \(-0.00178758\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) −18.3137 −0.784473
\(546\) 0 0
\(547\) −2.27208 −0.0971470 −0.0485735 0.998820i \(-0.515468\pi\)
−0.0485735 + 0.998820i \(0.515468\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) 22.1421 38.3513i 0.943287 1.63382i
\(552\) 0 0
\(553\) −4.00000 9.79796i −0.170097 0.416652i
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) −8.65685 14.9941i −0.366803 0.635321i 0.622261 0.782810i \(-0.286214\pi\)
−0.989064 + 0.147489i \(0.952881\pi\)
\(558\) 0 0
\(559\) −13.7990 −0.583635
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) −2.03553 3.52565i −0.0857875 0.148588i 0.819939 0.572451i \(-0.194007\pi\)
−0.905727 + 0.423863i \(0.860674\pi\)
\(564\) 0 0
\(565\) −5.65685 + 9.79796i −0.237986 + 0.412203i
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) −18.3137 + 31.7203i −0.767751 + 1.32978i 0.171029 + 0.985266i \(0.445291\pi\)
−0.938780 + 0.344517i \(0.888043\pi\)
\(570\) 0 0
\(571\) 10.4853 + 18.1610i 0.438795 + 0.760016i 0.997597 0.0692856i \(-0.0220720\pi\)
−0.558801 + 0.829301i \(0.688739\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 5.58579 0.232943
\(576\) 0 0
\(577\) 11.1421 + 19.2987i 0.463853 + 0.803417i 0.999149 0.0412474i \(-0.0131332\pi\)
−0.535296 + 0.844665i \(0.679800\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) 7.71320 9.94655i 0.319998 0.412652i
\(582\) 0 0
\(583\) 2.34315 4.05845i 0.0970432 0.168084i
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 22.6863 0.936363 0.468182 0.883632i \(-0.344909\pi\)
0.468182 + 0.883632i \(0.344909\pi\)
\(588\) 0 0
\(589\) −4.68629 −0.193095
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) 14.9706 25.9298i 0.614767 1.06481i −0.375658 0.926758i \(-0.622583\pi\)
0.990425 0.138050i \(-0.0440834\pi\)
\(594\) 0 0
\(595\) −12.4142 + 16.0087i −0.508933 + 0.656294i
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) 21.3137 + 36.9164i 0.870855 + 1.50836i 0.861114 + 0.508412i \(0.169767\pi\)
0.00974040 + 0.999953i \(0.496899\pi\)
\(600\) 0 0
\(601\) −34.0000 −1.38689 −0.693444 0.720510i \(-0.743908\pi\)
−0.693444 + 0.720510i \(0.743908\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) −5.15685 8.93193i −0.209656 0.363135i
\(606\) 0 0
\(607\) −13.6213 + 23.5928i −0.552872 + 0.957603i 0.445193 + 0.895434i \(0.353135\pi\)
−0.998066 + 0.0621685i \(0.980198\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 11.6569 20.1903i 0.471586 0.816811i
\(612\) 0 0
\(613\) −19.4853 33.7495i −0.787003 1.36313i −0.927795 0.373090i \(-0.878298\pi\)
0.140792 0.990039i \(-0.455035\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 12.6863 0.510731 0.255365 0.966845i \(-0.417804\pi\)
0.255365 + 0.966845i \(0.417804\pi\)
\(618\) 0 0
\(619\) −19.7279 34.1698i −0.792932 1.37340i −0.924144 0.382044i \(-0.875220\pi\)
0.131212 0.991354i \(-0.458113\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 5.34315 + 13.0880i 0.214069 + 0.524359i
\(624\) 0 0
\(625\) −0.500000 + 0.866025i −0.0200000 + 0.0346410i
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 43.3137 1.72703
\(630\) 0 0
\(631\) −1.51472 −0.0603000 −0.0301500 0.999545i \(-0.509598\pi\)
−0.0301500 + 0.999545i \(0.509598\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) −2.17157 + 3.76127i −0.0861762 + 0.149262i
\(636\) 0 0
\(637\) −3.48528 13.5592i −0.138092 0.537236i
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) 7.05635 + 12.2220i 0.278709 + 0.482738i 0.971064 0.238819i \(-0.0767602\pi\)
−0.692355 + 0.721557i \(0.743427\pi\)
\(642\) 0 0
\(643\) 26.0000 1.02534 0.512670 0.858586i \(-0.328656\pi\)
0.512670 + 0.858586i \(0.328656\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) −10.3787 17.9764i −0.408028 0.706725i 0.586641 0.809847i \(-0.300450\pi\)
−0.994669 + 0.103122i \(0.967117\pi\)
\(648\) 0 0
\(649\) 1.65685 2.86976i 0.0650372 0.112648i
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) −7.82843 + 13.5592i −0.306350 + 0.530614i −0.977561 0.210653i \(-0.932441\pi\)
0.671211 + 0.741266i \(0.265774\pi\)
\(654\) 0 0
\(655\) −6.82843 11.8272i −0.266809 0.462126i
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) −12.6863 −0.494188 −0.247094 0.968992i \(-0.579476\pi\)
−0.247094 + 0.968992i \(0.579476\pi\)
\(660\) 0 0
\(661\) 25.1569 + 43.5729i 0.978488 + 1.69479i 0.667907 + 0.744244i \(0.267190\pi\)
0.310581 + 0.950547i \(0.399476\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) −14.8284 2.02922i −0.575022 0.0786899i
\(666\) 0 0
\(667\) −21.8640 + 37.8695i −0.846576 + 1.46631i
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) −5.51472 −0.212893
\(672\) 0 0
\(673\) −5.65685 −0.218056 −0.109028 0.994039i \(-0.534774\pi\)
−0.109028 + 0.994039i \(0.534774\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 11.4853 19.8931i 0.441415 0.764554i −0.556380 0.830928i \(-0.687810\pi\)
0.997795 + 0.0663747i \(0.0211433\pi\)
\(678\) 0 0
\(679\) 9.72792 12.5446i 0.373323 0.481418i
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) −0.964466 1.67050i −0.0369043 0.0639201i 0.846983 0.531619i \(-0.178416\pi\)
−0.883888 + 0.467699i \(0.845083\pi\)
\(684\) 0 0
\(685\) −4.00000 −0.152832
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) −5.65685 9.79796i −0.215509 0.373273i
\(690\) 0 0
\(691\) 21.3848 37.0395i 0.813515 1.40905i −0.0968739 0.995297i \(-0.530884\pi\)
0.910389 0.413753i \(-0.135782\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 1.24264 2.15232i 0.0471360 0.0816420i
\(696\) 0 0
\(697\) 22.3137 + 38.6485i 0.845192 + 1.46392i
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) 11.0000 0.415464 0.207732 0.978186i \(-0.433392\pi\)
0.207732 + 0.978186i \(0.433392\pi\)
\(702\) 0 0
\(703\) 16.0000 + 27.7128i 0.603451 + 1.04521i
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) −30.1066 4.11999i −1.13228 0.154948i
\(708\) 0 0
\(709\) 17.7132 30.6802i 0.665233 1.15222i −0.313989 0.949427i \(-0.601665\pi\)
0.979222 0.202791i \(-0.0650013\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) 4.62742 0.173298
\(714\) 0 0
\(715\) 1.65685 0.0619628
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) −12.8995 + 22.3426i −0.481070 + 0.833238i −0.999764 0.0217223i \(-0.993085\pi\)
0.518694 + 0.854960i \(0.326418\pi\)
\(720\) 0 0
\(721\) 7.58579 + 18.5813i 0.282509 + 0.692004i
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) −3.91421 6.77962i −0.145370 0.251789i
\(726\) 0 0
\(727\) 38.0711 1.41198 0.705989 0.708223i \(-0.250503\pi\)
0.705989 + 0.708223i \(0.250503\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) 26.4142 + 45.7508i 0.976965 + 1.69215i
\(732\) 0 0
\(733\) −3.82843 + 6.63103i −0.141406 + 0.244923i −0.928026 0.372514i \(-0.878496\pi\)
0.786620 + 0.617437i \(0.211829\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) −5.34315 + 9.25460i −0.196817 + 0.340898i
\(738\) 0 0
\(739\) −8.41421 14.5738i −0.309522 0.536108i 0.668736 0.743500i \(-0.266836\pi\)
−0.978258 + 0.207392i \(0.933502\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 10.7574 0.394649 0.197325 0.980338i \(-0.436775\pi\)
0.197325 + 0.980338i \(0.436775\pi\)
\(744\) 0 0
\(745\) −2.32843 4.03295i −0.0853070 0.147756i
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) 5.58579 + 13.6823i 0.204100 + 0.499941i
\(750\) 0 0
\(751\) 6.00000 10.3923i 0.218943 0.379221i −0.735542 0.677479i \(-0.763072\pi\)
0.954485 + 0.298259i \(0.0964058\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 11.1716 0.406575
\(756\) 0 0
\(757\) 6.00000 0.218074 0.109037 0.994038i \(-0.465223\pi\)
0.109037 + 0.994038i \(0.465223\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) −21.9706 + 38.0541i −0.796432 + 1.37946i 0.125493 + 0.992094i \(0.459949\pi\)
−0.921926 + 0.387367i \(0.873385\pi\)
\(762\) 0 0
\(763\) −48.0061 6.56948i −1.73794 0.237831i
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) −4.00000 6.92820i −0.144432 0.250163i
\(768\) 0 0
\(769\) 43.2548 1.55981 0.779905 0.625898i \(-0.215268\pi\)
0.779905 + 0.625898i \(0.215268\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) 12.1716 + 21.0818i 0.437781 + 0.758259i 0.997518 0.0704113i \(-0.0224312\pi\)
−0.559737 + 0.828670i \(0.689098\pi\)
\(774\) 0 0
\(775\) −0.414214 + 0.717439i −0.0148790 + 0.0257712i
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) −16.4853 + 28.5533i −0.590647 + 1.02303i
\(780\) 0 0
\(781\) 4.97056 + 8.60927i 0.177861 + 0.308064i
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) −1.31371 −0.0468883
\(786\) 0 0
\(787\) 0.792893 + 1.37333i 0.0282636 + 0.0489540i 0.879811 0.475323i \(-0.157669\pi\)
−0.851548 + 0.524277i \(0.824336\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) −18.3431 + 23.6544i −0.652207 + 0.841052i
\(792\) 0 0
\(793\) −6.65685 + 11.5300i −0.236392 + 0.409443i
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 35.3137 1.25088 0.625438 0.780274i \(-0.284920\pi\)
0.625438 + 0.780274i \(0.284920\pi\)
\(798\) 0 0
\(799\) −89.2548 −3.15761
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) 1.51472 2.62357i 0.0534533 0.0925838i