Properties

Label 1400.2.x.b.993.8
Level $1400$
Weight $2$
Character 1400.993
Analytic conductor $11.179$
Analytic rank $0$
Dimension $24$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 1400 = 2^{3} \cdot 5^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1400.x (of order \(4\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(11.1790562830\)
Analytic rank: \(0\)
Dimension: \(24\)
Relative dimension: \(12\) over \(\Q(i)\)
Twist minimal: no (minimal twist has level 280)
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 993.8
Character \(\chi\) \(=\) 1400.993
Dual form 1400.2.x.b.657.8

$q$-expansion

\(f(q)\) \(=\) \(q+(0.730185 - 0.730185i) q^{3} +(-2.41329 - 1.08445i) q^{7} +1.93366i q^{9} +O(q^{10})\) \(q+(0.730185 - 0.730185i) q^{3} +(-2.41329 - 1.08445i) q^{7} +1.93366i q^{9} +5.95977 q^{11} +(0.921623 - 0.921623i) q^{13} +(-2.02728 - 2.02728i) q^{17} +3.29475 q^{19} +(-2.55400 + 0.970294i) q^{21} +(-0.0544054 - 0.0544054i) q^{23} +(3.60248 + 3.60248i) q^{27} -3.78901i q^{29} +4.88150i q^{31} +(4.35174 - 4.35174i) q^{33} +(3.20809 - 3.20809i) q^{37} -1.34591i q^{39} -10.6672i q^{41} +(1.60483 + 1.60483i) q^{43} +(-2.64854 - 2.64854i) q^{47} +(4.64792 + 5.23420i) q^{49} -2.96059 q^{51} +(9.16786 + 9.16786i) q^{53} +(2.40577 - 2.40577i) q^{57} +13.3231 q^{59} -11.2091i q^{61} +(2.09697 - 4.66648i) q^{63} +(6.43325 - 6.43325i) q^{67} -0.0794520 q^{69} -8.51221 q^{71} +(8.66633 - 8.66633i) q^{73} +(-14.3826 - 6.46310i) q^{77} -1.76209i q^{79} -0.540019 q^{81} +(2.36897 - 2.36897i) q^{83} +(-2.76668 - 2.76668i) q^{87} -9.73989 q^{89} +(-3.22360 + 1.22468i) q^{91} +(3.56440 + 3.56440i) q^{93} +(2.05040 + 2.05040i) q^{97} +11.5242i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 24q - 4q^{7} + O(q^{10}) \) \( 24q - 4q^{7} + 8q^{11} + 16q^{21} + 32q^{23} + 8q^{37} - 16q^{43} - 24q^{51} + 16q^{53} - 20q^{63} + 32q^{67} - 32q^{71} + 40q^{77} - 72q^{81} - 64q^{91} - 72q^{93} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1400\mathbb{Z}\right)^\times\).

\(n\) \(351\) \(701\) \(801\) \(1177\)
\(\chi(n)\) \(1\) \(1\) \(-1\) \(e\left(\frac{3}{4}\right)\)

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
\(3\) 0.730185 0.730185i 0.421573 0.421573i −0.464172 0.885745i \(-0.653648\pi\)
0.885745 + 0.464172i \(0.153648\pi\)
\(4\) 0 0
\(5\) 0 0
\(6\) 0 0
\(7\) −2.41329 1.08445i −0.912137 0.409885i
\(8\) 0 0
\(9\) 1.93366i 0.644553i
\(10\) 0 0
\(11\) 5.95977 1.79694 0.898470 0.439036i \(-0.144680\pi\)
0.898470 + 0.439036i \(0.144680\pi\)
\(12\) 0 0
\(13\) 0.921623 0.921623i 0.255612 0.255612i −0.567655 0.823267i \(-0.692149\pi\)
0.823267 + 0.567655i \(0.192149\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) −2.02728 2.02728i −0.491689 0.491689i 0.417149 0.908838i \(-0.363029\pi\)
−0.908838 + 0.417149i \(0.863029\pi\)
\(18\) 0 0
\(19\) 3.29475 0.755867 0.377933 0.925833i \(-0.376635\pi\)
0.377933 + 0.925833i \(0.376635\pi\)
\(20\) 0 0
\(21\) −2.55400 + 0.970294i −0.557328 + 0.211736i
\(22\) 0 0
\(23\) −0.0544054 0.0544054i −0.0113443 0.0113443i 0.701412 0.712756i \(-0.252553\pi\)
−0.712756 + 0.701412i \(0.752553\pi\)
\(24\) 0 0
\(25\) 0 0
\(26\) 0 0
\(27\) 3.60248 + 3.60248i 0.693298 + 0.693298i
\(28\) 0 0
\(29\) 3.78901i 0.703602i −0.936075 0.351801i \(-0.885569\pi\)
0.936075 0.351801i \(-0.114431\pi\)
\(30\) 0 0
\(31\) 4.88150i 0.876744i 0.898794 + 0.438372i \(0.144445\pi\)
−0.898794 + 0.438372i \(0.855555\pi\)
\(32\) 0 0
\(33\) 4.35174 4.35174i 0.757540 0.757540i
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) 3.20809 3.20809i 0.527406 0.527406i −0.392392 0.919798i \(-0.628352\pi\)
0.919798 + 0.392392i \(0.128352\pi\)
\(38\) 0 0
\(39\) 1.34591i 0.215518i
\(40\) 0 0
\(41\) 10.6672i 1.66593i −0.553323 0.832967i \(-0.686641\pi\)
0.553323 0.832967i \(-0.313359\pi\)
\(42\) 0 0
\(43\) 1.60483 + 1.60483i 0.244734 + 0.244734i 0.818805 0.574071i \(-0.194637\pi\)
−0.574071 + 0.818805i \(0.694637\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) −2.64854 2.64854i −0.386329 0.386329i 0.487047 0.873376i \(-0.338074\pi\)
−0.873376 + 0.487047i \(0.838074\pi\)
\(48\) 0 0
\(49\) 4.64792 + 5.23420i 0.663988 + 0.747743i
\(50\) 0 0
\(51\) −2.96059 −0.414565
\(52\) 0 0
\(53\) 9.16786 + 9.16786i 1.25930 + 1.25930i 0.951426 + 0.307876i \(0.0996182\pi\)
0.307876 + 0.951426i \(0.400382\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 0 0
\(57\) 2.40577 2.40577i 0.318653 0.318653i
\(58\) 0 0
\(59\) 13.3231 1.73452 0.867261 0.497854i \(-0.165879\pi\)
0.867261 + 0.497854i \(0.165879\pi\)
\(60\) 0 0
\(61\) 11.2091i 1.43518i −0.696465 0.717591i \(-0.745245\pi\)
0.696465 0.717591i \(-0.254755\pi\)
\(62\) 0 0
\(63\) 2.09697 4.66648i 0.264193 0.587921i
\(64\) 0 0
\(65\) 0 0
\(66\) 0 0
\(67\) 6.43325 6.43325i 0.785947 0.785947i −0.194880 0.980827i \(-0.562432\pi\)
0.980827 + 0.194880i \(0.0624318\pi\)
\(68\) 0 0
\(69\) −0.0794520 −0.00956489
\(70\) 0 0
\(71\) −8.51221 −1.01021 −0.505107 0.863057i \(-0.668547\pi\)
−0.505107 + 0.863057i \(0.668547\pi\)
\(72\) 0 0
\(73\) 8.66633 8.66633i 1.01432 1.01432i 0.0144206 0.999896i \(-0.495410\pi\)
0.999896 0.0144206i \(-0.00459039\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) −14.3826 6.46310i −1.63905 0.736539i
\(78\) 0 0
\(79\) 1.76209i 0.198250i −0.995075 0.0991251i \(-0.968396\pi\)
0.995075 0.0991251i \(-0.0316044\pi\)
\(80\) 0 0
\(81\) −0.540019 −0.0600021
\(82\) 0 0
\(83\) 2.36897 2.36897i 0.260028 0.260028i −0.565037 0.825065i \(-0.691138\pi\)
0.825065 + 0.565037i \(0.191138\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 0 0
\(87\) −2.76668 2.76668i −0.296619 0.296619i
\(88\) 0 0
\(89\) −9.73989 −1.03243 −0.516213 0.856460i \(-0.672659\pi\)
−0.516213 + 0.856460i \(0.672659\pi\)
\(90\) 0 0
\(91\) −3.22360 + 1.22468i −0.337925 + 0.128382i
\(92\) 0 0
\(93\) 3.56440 + 3.56440i 0.369611 + 0.369611i
\(94\) 0 0
\(95\) 0 0
\(96\) 0 0
\(97\) 2.05040 + 2.05040i 0.208187 + 0.208187i 0.803496 0.595310i \(-0.202971\pi\)
−0.595310 + 0.803496i \(0.702971\pi\)
\(98\) 0 0
\(99\) 11.5242i 1.15822i
\(100\) 0 0
\(101\) 5.96787i 0.593825i 0.954905 + 0.296912i \(0.0959570\pi\)
−0.954905 + 0.296912i \(0.904043\pi\)
\(102\) 0 0
\(103\) −8.07151 + 8.07151i −0.795309 + 0.795309i −0.982352 0.187043i \(-0.940110\pi\)
0.187043 + 0.982352i \(0.440110\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −3.43407 + 3.43407i −0.331984 + 0.331984i −0.853339 0.521356i \(-0.825426\pi\)
0.521356 + 0.853339i \(0.325426\pi\)
\(108\) 0 0
\(109\) 2.47368i 0.236935i 0.992958 + 0.118468i \(0.0377982\pi\)
−0.992958 + 0.118468i \(0.962202\pi\)
\(110\) 0 0
\(111\) 4.68500i 0.444680i
\(112\) 0 0
\(113\) −6.51377 6.51377i −0.612764 0.612764i 0.330901 0.943665i \(-0.392647\pi\)
−0.943665 + 0.330901i \(0.892647\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 0 0
\(117\) 1.78211 + 1.78211i 0.164756 + 0.164756i
\(118\) 0 0
\(119\) 2.69392 + 7.09092i 0.246952 + 0.650024i
\(120\) 0 0
\(121\) 24.5189 2.22899
\(122\) 0 0
\(123\) −7.78901 7.78901i −0.702312 0.702312i
\(124\) 0 0
\(125\) 0 0
\(126\) 0 0
\(127\) −4.97529 + 4.97529i −0.441485 + 0.441485i −0.892511 0.451026i \(-0.851058\pi\)
0.451026 + 0.892511i \(0.351058\pi\)
\(128\) 0 0
\(129\) 2.34364 0.206346
\(130\) 0 0
\(131\) 7.19072i 0.628256i 0.949381 + 0.314128i \(0.101712\pi\)
−0.949381 + 0.314128i \(0.898288\pi\)
\(132\) 0 0
\(133\) −7.95117 3.57300i −0.689454 0.309819i
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) −10.9598 + 10.9598i −0.936357 + 0.936357i −0.998093 0.0617359i \(-0.980336\pi\)
0.0617359 + 0.998093i \(0.480336\pi\)
\(138\) 0 0
\(139\) −16.0473 −1.36112 −0.680559 0.732693i \(-0.738263\pi\)
−0.680559 + 0.732693i \(0.738263\pi\)
\(140\) 0 0
\(141\) −3.86784 −0.325731
\(142\) 0 0
\(143\) 5.49267 5.49267i 0.459320 0.459320i
\(144\) 0 0
\(145\) 0 0
\(146\) 0 0
\(147\) 7.21577 + 0.428096i 0.595147 + 0.0353088i
\(148\) 0 0
\(149\) 18.0802i 1.48119i −0.671954 0.740593i \(-0.734545\pi\)
0.671954 0.740593i \(-0.265455\pi\)
\(150\) 0 0
\(151\) −4.72625 −0.384617 −0.192308 0.981335i \(-0.561597\pi\)
−0.192308 + 0.981335i \(0.561597\pi\)
\(152\) 0 0
\(153\) 3.92008 3.92008i 0.316920 0.316920i
\(154\) 0 0
\(155\) 0 0
\(156\) 0 0
\(157\) −4.46067 4.46067i −0.356000 0.356000i 0.506336 0.862336i \(-0.331000\pi\)
−0.862336 + 0.506336i \(0.831000\pi\)
\(158\) 0 0
\(159\) 13.3885 1.06177
\(160\) 0 0
\(161\) 0.0722957 + 0.190296i 0.00569770 + 0.0149974i
\(162\) 0 0
\(163\) 12.2914 + 12.2914i 0.962735 + 0.962735i 0.999330 0.0365956i \(-0.0116513\pi\)
−0.0365956 + 0.999330i \(0.511651\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 13.3128 + 13.3128i 1.03017 + 1.03017i 0.999530 + 0.0306429i \(0.00975545\pi\)
0.0306429 + 0.999530i \(0.490245\pi\)
\(168\) 0 0
\(169\) 11.3012i 0.869325i
\(170\) 0 0
\(171\) 6.37092i 0.487196i
\(172\) 0 0
\(173\) 6.42769 6.42769i 0.488688 0.488688i −0.419204 0.907892i \(-0.637691\pi\)
0.907892 + 0.419204i \(0.137691\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) 9.72834 9.72834i 0.731227 0.731227i
\(178\) 0 0
\(179\) 1.34949i 0.100866i 0.998727 + 0.0504328i \(0.0160601\pi\)
−0.998727 + 0.0504328i \(0.983940\pi\)
\(180\) 0 0
\(181\) 0.167463i 0.0124474i −0.999981 0.00622371i \(-0.998019\pi\)
0.999981 0.00622371i \(-0.00198108\pi\)
\(182\) 0 0
\(183\) −8.18474 8.18474i −0.605033 0.605033i
\(184\) 0 0
\(185\) 0 0
\(186\) 0 0
\(187\) −12.0822 12.0822i −0.883535 0.883535i
\(188\) 0 0
\(189\) −4.78710 12.6006i −0.348210 0.916556i
\(190\) 0 0
\(191\) 16.1288 1.16704 0.583521 0.812098i \(-0.301675\pi\)
0.583521 + 0.812098i \(0.301675\pi\)
\(192\) 0 0
\(193\) −8.46997 8.46997i −0.609682 0.609682i 0.333181 0.942863i \(-0.391878\pi\)
−0.942863 + 0.333181i \(0.891878\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) −2.23062 + 2.23062i −0.158925 + 0.158925i −0.782090 0.623165i \(-0.785846\pi\)
0.623165 + 0.782090i \(0.285846\pi\)
\(198\) 0 0
\(199\) 5.47878 0.388380 0.194190 0.980964i \(-0.437792\pi\)
0.194190 + 0.980964i \(0.437792\pi\)
\(200\) 0 0
\(201\) 9.39493i 0.662667i
\(202\) 0 0
\(203\) −4.10901 + 9.14398i −0.288396 + 0.641782i
\(204\) 0 0
\(205\) 0 0
\(206\) 0 0
\(207\) 0.105201 0.105201i 0.00731201 0.00731201i
\(208\) 0 0
\(209\) 19.6359 1.35825
\(210\) 0 0
\(211\) −7.22125 −0.497132 −0.248566 0.968615i \(-0.579959\pi\)
−0.248566 + 0.968615i \(0.579959\pi\)
\(212\) 0 0
\(213\) −6.21549 + 6.21549i −0.425878 + 0.425878i
\(214\) 0 0
\(215\) 0 0
\(216\) 0 0
\(217\) 5.29377 11.7805i 0.359364 0.799711i
\(218\) 0 0
\(219\) 12.6560i 0.855216i
\(220\) 0 0
\(221\) −3.73679 −0.251363
\(222\) 0 0
\(223\) −12.2709 + 12.2709i −0.821721 + 0.821721i −0.986355 0.164634i \(-0.947356\pi\)
0.164634 + 0.986355i \(0.447356\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 13.9412 + 13.9412i 0.925307 + 0.925307i 0.997398 0.0720910i \(-0.0229672\pi\)
−0.0720910 + 0.997398i \(0.522967\pi\)
\(228\) 0 0
\(229\) −24.5615 −1.62307 −0.811535 0.584304i \(-0.801368\pi\)
−0.811535 + 0.584304i \(0.801368\pi\)
\(230\) 0 0
\(231\) −15.2213 + 5.78273i −1.00149 + 0.380476i
\(232\) 0 0
\(233\) 14.4981 + 14.4981i 0.949802 + 0.949802i 0.998799 0.0489972i \(-0.0156025\pi\)
−0.0489972 + 0.998799i \(0.515603\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 0 0
\(237\) −1.28665 1.28665i −0.0835769 0.0835769i
\(238\) 0 0
\(239\) 2.70102i 0.174715i −0.996177 0.0873573i \(-0.972158\pi\)
0.996177 0.0873573i \(-0.0278422\pi\)
\(240\) 0 0
\(241\) 6.19167i 0.398840i −0.979914 0.199420i \(-0.936094\pi\)
0.979914 0.199420i \(-0.0639059\pi\)
\(242\) 0 0
\(243\) −11.2018 + 11.2018i −0.718594 + 0.718594i
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) 3.03652 3.03652i 0.193209 0.193209i
\(248\) 0 0
\(249\) 3.45957i 0.219241i
\(250\) 0 0
\(251\) 21.2989i 1.34437i 0.740381 + 0.672187i \(0.234645\pi\)
−0.740381 + 0.672187i \(0.765355\pi\)
\(252\) 0 0
\(253\) −0.324244 0.324244i −0.0203850 0.0203850i
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 13.5045 + 13.5045i 0.842390 + 0.842390i 0.989169 0.146779i \(-0.0468907\pi\)
−0.146779 + 0.989169i \(0.546891\pi\)
\(258\) 0 0
\(259\) −11.2211 + 4.26301i −0.697243 + 0.264891i
\(260\) 0 0
\(261\) 7.32666 0.453509
\(262\) 0 0
\(263\) 3.28861 + 3.28861i 0.202784 + 0.202784i 0.801192 0.598408i \(-0.204200\pi\)
−0.598408 + 0.801192i \(0.704200\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) −7.11192 + 7.11192i −0.435243 + 0.435243i
\(268\) 0 0
\(269\) −27.9298 −1.70291 −0.851454 0.524429i \(-0.824279\pi\)
−0.851454 + 0.524429i \(0.824279\pi\)
\(270\) 0 0
\(271\) 6.55143i 0.397971i −0.980002 0.198985i \(-0.936235\pi\)
0.980002 0.198985i \(-0.0637647\pi\)
\(272\) 0 0
\(273\) −1.45958 + 3.24807i −0.0883377 + 0.196582i
\(274\) 0 0
\(275\) 0 0
\(276\) 0 0
\(277\) 10.6137 10.6137i 0.637717 0.637717i −0.312275 0.949992i \(-0.601091\pi\)
0.949992 + 0.312275i \(0.101091\pi\)
\(278\) 0 0
\(279\) −9.43917 −0.565108
\(280\) 0 0
\(281\) −23.3116 −1.39065 −0.695326 0.718695i \(-0.744740\pi\)
−0.695326 + 0.718695i \(0.744740\pi\)
\(282\) 0 0
\(283\) −18.9859 + 18.9859i −1.12860 + 1.12860i −0.138190 + 0.990406i \(0.544128\pi\)
−0.990406 + 0.138190i \(0.955872\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) −11.5681 + 25.7430i −0.682841 + 1.51956i
\(288\) 0 0
\(289\) 8.78023i 0.516484i
\(290\) 0 0
\(291\) 2.99434 0.175531
\(292\) 0 0
\(293\) −11.5947 + 11.5947i −0.677371 + 0.677371i −0.959405 0.282033i \(-0.908991\pi\)
0.282033 + 0.959405i \(0.408991\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 0 0
\(297\) 21.4700 + 21.4700i 1.24582 + 1.24582i
\(298\) 0 0
\(299\) −0.100282 −0.00579949
\(300\) 0 0
\(301\) −2.13255 5.61327i −0.122918 0.323543i
\(302\) 0 0
\(303\) 4.35765 + 4.35765i 0.250340 + 0.250340i
\(304\) 0 0
\(305\) 0 0
\(306\) 0 0
\(307\) −16.8061 16.8061i −0.959174 0.959174i 0.0400244 0.999199i \(-0.487256\pi\)
−0.999199 + 0.0400244i \(0.987256\pi\)
\(308\) 0 0
\(309\) 11.7874i 0.670561i
\(310\) 0 0
\(311\) 15.1113i 0.856881i 0.903570 + 0.428440i \(0.140937\pi\)
−0.903570 + 0.428440i \(0.859063\pi\)
\(312\) 0 0
\(313\) −13.1100 + 13.1100i −0.741023 + 0.741023i −0.972775 0.231752i \(-0.925554\pi\)
0.231752 + 0.972775i \(0.425554\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 12.6159 12.6159i 0.708578 0.708578i −0.257658 0.966236i \(-0.582951\pi\)
0.966236 + 0.257658i \(0.0829508\pi\)
\(318\) 0 0
\(319\) 22.5817i 1.26433i
\(320\) 0 0
\(321\) 5.01501i 0.279910i
\(322\) 0 0
\(323\) −6.67939 6.67939i −0.371651 0.371651i
\(324\) 0 0
\(325\) 0 0
\(326\) 0 0
\(327\) 1.80624 + 1.80624i 0.0998855 + 0.0998855i
\(328\) 0 0
\(329\) 3.51946 + 9.26389i 0.194034 + 0.510735i
\(330\) 0 0
\(331\) 16.8901 0.928364 0.464182 0.885740i \(-0.346348\pi\)
0.464182 + 0.885740i \(0.346348\pi\)
\(332\) 0 0
\(333\) 6.20335 + 6.20335i 0.339942 + 0.339942i
\(334\) 0 0
\(335\) 0 0
\(336\) 0 0
\(337\) −20.8552 + 20.8552i −1.13606 + 1.13606i −0.146906 + 0.989150i \(0.546931\pi\)
−0.989150 + 0.146906i \(0.953069\pi\)
\(338\) 0 0
\(339\) −9.51252 −0.516649
\(340\) 0 0
\(341\) 29.0927i 1.57546i
\(342\) 0 0
\(343\) −5.54051 17.6721i −0.299159 0.954203i
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 3.75386 3.75386i 0.201518 0.201518i −0.599132 0.800650i \(-0.704488\pi\)
0.800650 + 0.599132i \(0.204488\pi\)
\(348\) 0 0
\(349\) 1.12253 0.0600874 0.0300437 0.999549i \(-0.490435\pi\)
0.0300437 + 0.999549i \(0.490435\pi\)
\(350\) 0 0
\(351\) 6.64027 0.354431
\(352\) 0 0
\(353\) −2.71896 + 2.71896i −0.144716 + 0.144716i −0.775753 0.631037i \(-0.782630\pi\)
0.631037 + 0.775753i \(0.282630\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 0 0
\(357\) 7.14475 + 3.21062i 0.378140 + 0.169924i
\(358\) 0 0
\(359\) 5.21128i 0.275041i 0.990499 + 0.137520i \(0.0439133\pi\)
−0.990499 + 0.137520i \(0.956087\pi\)
\(360\) 0 0
\(361\) −8.14465 −0.428666
\(362\) 0 0
\(363\) 17.9033 17.9033i 0.939681 0.939681i
\(364\) 0 0
\(365\) 0 0
\(366\) 0 0
\(367\) −0.978681 0.978681i −0.0510867 0.0510867i 0.681102 0.732189i \(-0.261501\pi\)
−0.732189 + 0.681102i \(0.761501\pi\)
\(368\) 0 0
\(369\) 20.6267 1.07378
\(370\) 0 0
\(371\) −12.1826 32.0668i −0.632487 1.66483i
\(372\) 0 0
\(373\) −18.7892 18.7892i −0.972870 0.972870i 0.0267714 0.999642i \(-0.491477\pi\)
−0.999642 + 0.0267714i \(0.991477\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) −3.49204 3.49204i −0.179849 0.179849i
\(378\) 0 0
\(379\) 0.517830i 0.0265992i −0.999912 0.0132996i \(-0.995766\pi\)
0.999912 0.0132996i \(-0.00423351\pi\)
\(380\) 0 0
\(381\) 7.26576i 0.372236i
\(382\) 0 0
\(383\) 13.1105 13.1105i 0.669917 0.669917i −0.287779 0.957697i \(-0.592917\pi\)
0.957697 + 0.287779i \(0.0929170\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) −3.10319 + 3.10319i −0.157744 + 0.157744i
\(388\) 0 0
\(389\) 14.3932i 0.729766i 0.931053 + 0.364883i \(0.118891\pi\)
−0.931053 + 0.364883i \(0.881109\pi\)
\(390\) 0 0
\(391\) 0.220590i 0.0111557i
\(392\) 0 0
\(393\) 5.25056 + 5.25056i 0.264856 + 0.264856i
\(394\) 0 0
\(395\) 0 0
\(396\) 0 0
\(397\) −9.94079 9.94079i −0.498914 0.498914i 0.412186 0.911100i \(-0.364765\pi\)
−0.911100 + 0.412186i \(0.864765\pi\)
\(398\) 0 0
\(399\) −8.41478 + 3.19687i −0.421266 + 0.160044i
\(400\) 0 0
\(401\) 16.7962 0.838763 0.419382 0.907810i \(-0.362247\pi\)
0.419382 + 0.907810i \(0.362247\pi\)
\(402\) 0 0
\(403\) 4.49891 + 4.49891i 0.224107 + 0.224107i
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 19.1195 19.1195i 0.947717 0.947717i
\(408\) 0 0
\(409\) −1.41163 −0.0698008 −0.0349004 0.999391i \(-0.511111\pi\)
−0.0349004 + 0.999391i \(0.511111\pi\)
\(410\) 0 0
\(411\) 16.0053i 0.789484i
\(412\) 0 0
\(413\) −32.1525 14.4483i −1.58212 0.710955i
\(414\) 0 0
\(415\) 0 0
\(416\) 0 0
\(417\) −11.7175 + 11.7175i −0.573810 + 0.573810i
\(418\) 0 0
\(419\) 5.68831 0.277892 0.138946 0.990300i \(-0.455629\pi\)
0.138946 + 0.990300i \(0.455629\pi\)
\(420\) 0 0
\(421\) −12.1346 −0.591402 −0.295701 0.955280i \(-0.595553\pi\)
−0.295701 + 0.955280i \(0.595553\pi\)
\(422\) 0 0
\(423\) 5.12137 5.12137i 0.249009 0.249009i
\(424\) 0 0
\(425\) 0 0
\(426\) 0 0
\(427\) −12.1558 + 27.0509i −0.588260 + 1.30908i
\(428\) 0 0
\(429\) 8.02132i 0.387273i
\(430\) 0 0
\(431\) 32.9391 1.58662 0.793311 0.608817i \(-0.208356\pi\)
0.793311 + 0.608817i \(0.208356\pi\)
\(432\) 0 0
\(433\) 0.964365 0.964365i 0.0463444 0.0463444i −0.683555 0.729899i \(-0.739567\pi\)
0.729899 + 0.683555i \(0.239567\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) −0.179252 0.179252i −0.00857478 0.00857478i
\(438\) 0 0
\(439\) −8.75634 −0.417917 −0.208959 0.977924i \(-0.567007\pi\)
−0.208959 + 0.977924i \(0.567007\pi\)
\(440\) 0 0
\(441\) −10.1212 + 8.98749i −0.481960 + 0.427976i
\(442\) 0 0
\(443\) −4.24169 4.24169i −0.201529 0.201529i 0.599126 0.800655i \(-0.295515\pi\)
−0.800655 + 0.599126i \(0.795515\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 0 0
\(447\) −13.2019 13.2019i −0.624428 0.624428i
\(448\) 0 0
\(449\) 2.36447i 0.111586i 0.998442 + 0.0557931i \(0.0177687\pi\)
−0.998442 + 0.0557931i \(0.982231\pi\)
\(450\) 0 0
\(451\) 63.5740i 2.99358i
\(452\) 0 0
\(453\) −3.45104 + 3.45104i −0.162144 + 0.162144i
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) −9.06926 + 9.06926i −0.424242 + 0.424242i −0.886661 0.462419i \(-0.846982\pi\)
0.462419 + 0.886661i \(0.346982\pi\)
\(458\) 0 0
\(459\) 14.6065i 0.681774i
\(460\) 0 0
\(461\) 32.6249i 1.51949i 0.650219 + 0.759747i \(0.274677\pi\)
−0.650219 + 0.759747i \(0.725323\pi\)
\(462\) 0 0
\(463\) −25.9003 25.9003i −1.20369 1.20369i −0.973036 0.230654i \(-0.925913\pi\)
−0.230654 0.973036i \(-0.574087\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 10.7966 + 10.7966i 0.499608 + 0.499608i 0.911316 0.411708i \(-0.135068\pi\)
−0.411708 + 0.911316i \(0.635068\pi\)
\(468\) 0 0
\(469\) −22.5019 + 8.54872i −1.03904 + 0.394743i
\(470\) 0 0
\(471\) −6.51423 −0.300160
\(472\) 0 0
\(473\) 9.56440 + 9.56440i 0.439772 + 0.439772i
\(474\) 0 0
\(475\) 0 0
\(476\) 0 0
\(477\) −17.7275 + 17.7275i −0.811688 + 0.811688i
\(478\) 0 0
\(479\) −14.8255 −0.677395 −0.338697 0.940895i \(-0.609986\pi\)
−0.338697 + 0.940895i \(0.609986\pi\)
\(480\) 0 0
\(481\) 5.91330i 0.269623i
\(482\) 0 0
\(483\) 0.191740 + 0.0861620i 0.00872449 + 0.00392051i
\(484\) 0 0
\(485\) 0 0
\(486\) 0 0
\(487\) 19.4866 19.4866i 0.883024 0.883024i −0.110817 0.993841i \(-0.535347\pi\)
0.993841 + 0.110817i \(0.0353466\pi\)
\(488\) 0 0
\(489\) 17.9500 0.811725
\(490\) 0 0
\(491\) −18.7117 −0.844446 −0.422223 0.906492i \(-0.638750\pi\)
−0.422223 + 0.906492i \(0.638750\pi\)
\(492\) 0 0
\(493\) −7.68141 + 7.68141i −0.345953 + 0.345953i
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 20.5424 + 9.23110i 0.921453 + 0.414071i
\(498\) 0 0
\(499\) 3.85409i 0.172533i 0.996272 + 0.0862664i \(0.0274936\pi\)
−0.996272 + 0.0862664i \(0.972506\pi\)
\(500\) 0 0
\(501\) 19.4416 0.868585
\(502\) 0 0
\(503\) −17.3619 + 17.3619i −0.774129 + 0.774129i −0.978825 0.204697i \(-0.934379\pi\)
0.204697 + 0.978825i \(0.434379\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) 8.25198 + 8.25198i 0.366483 + 0.366483i
\(508\) 0 0
\(509\) −6.19089 −0.274406 −0.137203 0.990543i \(-0.543811\pi\)
−0.137203 + 0.990543i \(0.543811\pi\)
\(510\) 0 0
\(511\) −30.3126 + 11.5161i −1.34095 + 0.509442i
\(512\) 0 0
\(513\) 11.8693 + 11.8693i 0.524041 + 0.524041i
\(514\) 0 0
\(515\) 0 0
\(516\) 0 0
\(517\) −15.7847 15.7847i −0.694209 0.694209i
\(518\) 0 0
\(519\) 9.38681i 0.412035i
\(520\) 0 0
\(521\) 23.4163i 1.02589i −0.858422 0.512943i \(-0.828555\pi\)
0.858422 0.512943i \(-0.171445\pi\)
\(522\) 0 0
\(523\) 4.35649 4.35649i 0.190496 0.190496i −0.605414 0.795910i \(-0.706993\pi\)
0.795910 + 0.605414i \(0.206993\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 9.89620 9.89620i 0.431085 0.431085i
\(528\) 0 0
\(529\) 22.9941i 0.999743i
\(530\) 0 0
\(531\) 25.7624i 1.11799i
\(532\) 0 0
\(533\) −9.83112 9.83112i −0.425833 0.425833i
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) 0.985377 + 0.985377i 0.0425221 + 0.0425221i
\(538\) 0 0
\(539\) 27.7005 + 31.1947i 1.19315 + 1.34365i
\(540\) 0 0
\(541\) 8.06640 0.346801 0.173401 0.984851i \(-0.444524\pi\)
0.173401 + 0.984851i \(0.444524\pi\)
\(542\) 0 0
\(543\) −0.122279 0.122279i −0.00524749 0.00524749i
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) 19.3200 19.3200i 0.826063 0.826063i −0.160907 0.986970i \(-0.551442\pi\)
0.986970 + 0.160907i \(0.0514419\pi\)
\(548\) 0 0
\(549\) 21.6746 0.925051
\(550\) 0 0
\(551\) 12.4838i 0.531829i
\(552\) 0 0
\(553\) −1.91090 + 4.25242i −0.0812599 + 0.180831i
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) −12.4346 + 12.4346i −0.526872 + 0.526872i −0.919638 0.392767i \(-0.871518\pi\)
0.392767 + 0.919638i \(0.371518\pi\)
\(558\) 0 0
\(559\) 2.95809 0.125114
\(560\) 0 0
\(561\) −17.6444 −0.744948
\(562\) 0 0
\(563\) 19.6018 19.6018i 0.826118 0.826118i −0.160859 0.986977i \(-0.551427\pi\)
0.986977 + 0.160859i \(0.0514265\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 0 0
\(567\) 1.30322 + 0.585626i 0.0547302 + 0.0245940i
\(568\) 0 0
\(569\) 17.4875i 0.733115i −0.930395 0.366558i \(-0.880536\pi\)
0.930395 0.366558i \(-0.119464\pi\)
\(570\) 0 0
\(571\) 31.0074 1.29762 0.648810 0.760950i \(-0.275267\pi\)
0.648810 + 0.760950i \(0.275267\pi\)
\(572\) 0 0
\(573\) 11.7770 11.7770i 0.491993 0.491993i
\(574\) 0 0
\(575\) 0 0
\(576\) 0 0
\(577\) −19.6961 19.6961i −0.819957 0.819957i 0.166144 0.986101i \(-0.446868\pi\)
−0.986101 + 0.166144i \(0.946868\pi\)
\(578\) 0 0
\(579\) −12.3693 −0.514050
\(580\) 0 0
\(581\) −8.28603 + 3.14796i −0.343762 + 0.130599i
\(582\) 0 0
\(583\) 54.6384 + 54.6384i 2.26289 + 2.26289i
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) −18.6924 18.6924i −0.771519 0.771519i 0.206853 0.978372i \(-0.433678\pi\)
−0.978372 + 0.206853i \(0.933678\pi\)
\(588\) 0 0
\(589\) 16.0833i 0.662701i
\(590\) 0 0
\(591\) 3.25754i 0.133997i
\(592\) 0 0
\(593\) 24.8700 24.8700i 1.02129 1.02129i 0.0215185 0.999768i \(-0.493150\pi\)
0.999768 0.0215185i \(-0.00685007\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) 4.00052 4.00052i 0.163730 0.163730i
\(598\) 0 0
\(599\) 32.1708i 1.31446i 0.753688 + 0.657232i \(0.228273\pi\)
−0.753688 + 0.657232i \(0.771727\pi\)
\(600\) 0 0
\(601\) 11.8081i 0.481664i −0.970567 0.240832i \(-0.922580\pi\)
0.970567 0.240832i \(-0.0774204\pi\)
\(602\) 0 0
\(603\) 12.4397 + 12.4397i 0.506585 + 0.506585i
\(604\) 0 0
\(605\) 0 0
\(606\) 0 0
\(607\) −6.50201 6.50201i −0.263908 0.263908i 0.562731 0.826640i \(-0.309751\pi\)
−0.826640 + 0.562731i \(0.809751\pi\)
\(608\) 0 0
\(609\) 3.67646 + 9.67714i 0.148978 + 0.392137i
\(610\) 0 0
\(611\) −4.88190 −0.197501
\(612\) 0 0
\(613\) 18.1899 + 18.1899i 0.734682 + 0.734682i 0.971543 0.236861i \(-0.0761187\pi\)
−0.236861 + 0.971543i \(0.576119\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 4.68616 4.68616i 0.188658 0.188658i −0.606458 0.795116i \(-0.707410\pi\)
0.795116 + 0.606458i \(0.207410\pi\)
\(618\) 0 0
\(619\) −6.78552 −0.272733 −0.136366 0.990658i \(-0.543542\pi\)
−0.136366 + 0.990658i \(0.543542\pi\)
\(620\) 0 0
\(621\) 0.391989i 0.0157300i
\(622\) 0 0
\(623\) 23.5052 + 10.5625i 0.941714 + 0.423176i
\(624\) 0 0
\(625\) 0 0
\(626\) 0 0
\(627\) 14.3379 14.3379i 0.572599 0.572599i
\(628\) 0 0
\(629\) −13.0074 −0.518640
\(630\) 0 0
\(631\) −0.0455199 −0.00181212 −0.000906059 1.00000i \(-0.500288\pi\)
−0.000906059 1.00000i \(0.500288\pi\)
\(632\) 0 0
\(633\) −5.27285 + 5.27285i −0.209577 + 0.209577i
\(634\) 0 0
\(635\) 0 0
\(636\) 0 0
\(637\) 9.10759 + 0.540333i 0.360856 + 0.0214088i
\(638\) 0 0
\(639\) 16.4597i 0.651136i
\(640\) 0 0
\(641\) −14.9331 −0.589823 −0.294912 0.955524i \(-0.595290\pi\)
−0.294912 + 0.955524i \(0.595290\pi\)
\(642\) 0 0
\(643\) 14.2308 14.2308i 0.561208 0.561208i −0.368443 0.929650i \(-0.620109\pi\)
0.929650 + 0.368443i \(0.120109\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) −10.4339 10.4339i −0.410201 0.410201i 0.471608 0.881809i \(-0.343674\pi\)
−0.881809 + 0.471608i \(0.843674\pi\)
\(648\) 0 0
\(649\) 79.4027 3.11683
\(650\) 0 0
\(651\) −4.73649 12.4674i −0.185638 0.488634i
\(652\) 0 0
\(653\) −2.78826 2.78826i −0.109113 0.109113i 0.650442 0.759556i \(-0.274584\pi\)
−0.759556 + 0.650442i \(0.774584\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 0 0
\(657\) 16.7577 + 16.7577i 0.653781 + 0.653781i
\(658\) 0 0
\(659\) 7.73193i 0.301193i 0.988595 + 0.150597i \(0.0481195\pi\)
−0.988595 + 0.150597i \(0.951881\pi\)
\(660\) 0 0
\(661\) 35.3366i 1.37443i 0.726453 + 0.687217i \(0.241168\pi\)
−0.726453 + 0.687217i \(0.758832\pi\)
\(662\) 0 0
\(663\) −2.72855 + 2.72855i −0.105968 + 0.105968i
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) −0.206143 + 0.206143i −0.00798187 + 0.00798187i
\(668\) 0 0
\(669\) 17.9201i 0.692830i
\(670\) 0 0
\(671\) 66.8039i 2.57894i
\(672\) 0 0
\(673\) 3.30292 + 3.30292i 0.127318 + 0.127318i 0.767895 0.640576i \(-0.221304\pi\)
−0.640576 + 0.767895i \(0.721304\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) −11.8424 11.8424i −0.455138 0.455138i 0.441917 0.897056i \(-0.354298\pi\)
−0.897056 + 0.441917i \(0.854298\pi\)
\(678\) 0 0
\(679\) −2.72464 7.17177i −0.104562 0.275227i
\(680\) 0 0
\(681\) 20.3592 0.780168
\(682\) 0 0
\(683\) −9.37696 9.37696i −0.358799 0.358799i 0.504571 0.863370i \(-0.331651\pi\)
−0.863370 + 0.504571i \(0.831651\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 0 0
\(687\) −17.9344 + 17.9344i −0.684242 + 0.684242i
\(688\) 0 0
\(689\) 16.8986 0.643787
\(690\) 0 0
\(691\) 13.1758i 0.501233i −0.968086 0.250616i \(-0.919367\pi\)
0.968086 0.250616i \(-0.0806333\pi\)
\(692\) 0 0
\(693\) 12.4974 27.8111i 0.474739 1.05646i
\(694\) 0 0
\(695\) 0 0
\(696\) 0 0
\(697\) −21.6254 + 21.6254i −0.819121 + 0.819121i
\(698\) 0 0
\(699\) 21.1726 0.800821
\(700\) 0 0
\(701\) −19.5277 −0.737550 −0.368775 0.929519i \(-0.620223\pi\)
−0.368775 + 0.929519i \(0.620223\pi\)
\(702\) 0 0
\(703\) 10.5698 10.5698i 0.398649 0.398649i
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 6.47188 14.4022i 0.243400 0.541650i
\(708\) 0 0
\(709\) 24.3216i 0.913415i −0.889617 0.456708i \(-0.849029\pi\)
0.889617 0.456708i \(-0.150971\pi\)
\(710\) 0 0
\(711\) 3.40728 0.127783
\(712\) 0 0
\(713\) 0.265580 0.265580i 0.00994605 0.00994605i
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) −1.97225 1.97225i −0.0736549 0.0736549i
\(718\) 0 0
\(719\) −30.5952 −1.14101 −0.570505 0.821294i \(-0.693252\pi\)
−0.570505 + 0.821294i \(0.693252\pi\)
\(720\) 0 0
\(721\) 28.2321 10.7257i 1.05142 0.399446i
\(722\) 0 0
\(723\) −4.52106 4.52106i −0.168140 0.168140i
\(724\) 0 0
\(725\) 0 0
\(726\) 0 0
\(727\) 2.97003 + 2.97003i 0.110152 + 0.110152i 0.760035 0.649882i \(-0.225182\pi\)
−0.649882 + 0.760035i \(0.725182\pi\)
\(728\) 0 0
\(729\) 14.7387i 0.545877i
\(730\) 0 0
\(731\) 6.50688i 0.240666i
\(732\) 0 0
\(733\) −26.7197 + 26.7197i −0.986914 + 0.986914i −0.999915 0.0130016i \(-0.995861\pi\)
0.0130016 + 0.999915i \(0.495861\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 38.3407 38.3407i 1.41230 1.41230i
\(738\) 0 0
\(739\) 41.5880i 1.52984i −0.644126 0.764920i \(-0.722779\pi\)
0.644126 0.764920i \(-0.277221\pi\)
\(740\) 0 0
\(741\) 4.43444i 0.162903i
\(742\) 0 0
\(743\) −3.50770 3.50770i −0.128685 0.128685i 0.639831 0.768516i \(-0.279004\pi\)
−0.768516 + 0.639831i \(0.779004\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0 0
\(747\) 4.58077 + 4.58077i 0.167602 + 0.167602i
\(748\) 0 0
\(749\) 12.0115 4.56330i 0.438890 0.166739i
\(750\) 0 0
\(751\) 49.1334 1.79290 0.896451 0.443142i \(-0.146136\pi\)
0.896451 + 0.443142i \(0.146136\pi\)
\(752\) 0 0
\(753\) 15.5521 + 15.5521i 0.566751 + 0.566751i
\(754\) 0 0
\(755\) 0 0
\(756\) 0 0
\(757\) 34.8748 34.8748i 1.26755 1.26755i 0.320194 0.947352i \(-0.396252\pi\)
0.947352 0.320194i \(-0.103748\pi\)
\(758\) 0 0
\(759\) −0.473516 −0.0171875
\(760\) 0 0
\(761\) 42.8325i 1.55268i 0.630317 + 0.776338i \(0.282925\pi\)
−0.630317 + 0.776338i \(0.717075\pi\)
\(762\) 0 0
\(763\) 2.68259 5.96970i 0.0971164 0.216118i
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 12.2789 12.2789i 0.443365 0.443365i
\(768\) 0 0
\(769\) −10.4385 −0.376422 −0.188211 0.982129i \(-0.560269\pi\)
−0.188211 + 0.982129i \(0.560269\pi\)
\(770\) 0 0
\(771\) 19.7216 0.710257
\(772\) 0 0
\(773\) −11.9124 + 11.9124i −0.428459 + 0.428459i −0.888103 0.459644i \(-0.847977\pi\)
0.459644 + 0.888103i \(0.347977\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 0 0
\(777\) −5.08066 + 11.3062i −0.182268 + 0.405609i
\(778\) 0 0
\(779\) 35.1456i 1.25922i
\(780\) 0 0
\(781\) −50.7308 −1.81529
\(782\) 0 0
\(783\) 13.6499 13.6499i 0.487806 0.487806i
\(784\) 0 0
\(785\) 0 0
\(786\) 0 0
\(787\) −29.0925 29.0925i −1.03704 1.03704i −0.999287 0.0377482i \(-0.987982\pi\)
−0.0377482 0.999287i \(-0.512018\pi\)
\(788\) 0 0
\(789\) 4.80258 0.170976
\(790\) 0 0
\(791\) 8.65572 + 22.7835i 0.307762 + 0.810088i
\(792\) 0 0
\(793\) −10.3306 10.3306i −0.366850 0.366850i
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 14.9404 + 14.9404i 0.529215 + 0.529215i 0.920338 0.391123i \(-0.127913\pi\)
−0.391123 + 0.920338i \(0.627913\pi\)
\(798\) 0 0
\(799\) 10.7387i 0.379907i
\(800\) 0 0
\(801\) 18.8336i 0.665454i
\(802\) 0 0
\(803\) 51.6493 51.6493i 1.82267 1.82267i
\(804\)