Properties

Label 1400.2.x.b.993.5
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 993.5
Character \(\chi\) \(=\) 1400.993
Dual form 1400.2.x.b.657.5

$q$-expansion

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

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 −0.885745 0.464172i \(-0.846352\pi\)
0.464172 + 0.885745i \(0.346352\pi\)
\(4\) 0 0
\(5\) 0 0
\(6\) 0 0
\(7\) 1.08445 + 2.41329i 0.409885 + 0.912137i
\(8\) 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 −0.823267 0.567655i \(-0.807851\pi\)
0.567655 + 0.823267i \(0.307851\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 2.02728 + 2.02728i 0.491689 + 0.491689i 0.908838 0.417149i \(-0.136971\pi\)
−0.417149 + 0.908838i \(0.636971\pi\)
\(18\) 0 0
\(19\) −3.29475 −0.755867 −0.377933 0.925833i \(-0.623365\pi\)
−0.377933 + 0.925833i \(0.623365\pi\)
\(20\) 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 \(-0.855555\pi\)
0.898794 0.438372i \(-0.144445\pi\)
\(32\) 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 \(0.313359\pi\)
−0.553323 + 0.832967i \(0.686641\pi\)
\(42\) 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 0.873376 0.487047i \(-0.161926\pi\)
−0.487047 + 0.873376i \(0.661926\pi\)
\(48\) 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 \(-0.834121\pi\)
−0.867261 + 0.497854i \(0.834121\pi\)
\(60\) 0 0
\(61\) 11.2091i 1.43518i 0.696465 + 0.717591i \(0.254755\pi\)
−0.696465 + 0.717591i \(0.745245\pi\)
\(62\) 0 0
\(63\) −4.66648 + 2.09697i −0.587921 + 0.264193i
\(64\) 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 \(0.504590\pi\)
−0.999896 + 0.0144206i \(0.995410\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 6.46310 + 14.3826i 0.736539 + 1.63905i
\(78\) 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 −0.825065 0.565037i \(-0.808862\pi\)
0.565037 + 0.825065i \(0.308862\pi\)
\(84\) 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 \(-0.327341\pi\)
0.516213 + 0.856460i \(0.327341\pi\)
\(90\) 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 0.595310 0.803496i \(-0.297029\pi\)
−0.803496 + 0.595310i \(0.797029\pi\)
\(98\) 0 0
\(99\) 11.5242i 1.15822i
\(100\) 0 0
\(101\) 5.96787i 0.593825i −0.954905 0.296912i \(-0.904043\pi\)
0.954905 0.296912i \(-0.0959570\pi\)
\(102\) 0 0
\(103\) 8.07151 8.07151i 0.795309 0.795309i −0.187043 0.982352i \(-0.559890\pi\)
0.982352 + 0.187043i \(0.0598902\pi\)
\(104\) 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 \(-0.898288\pi\)
0.949381 0.314128i \(-0.101712\pi\)
\(132\) 0 0
\(133\) −3.57300 7.95117i −0.309819 0.689454i
\(134\) 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 \(-0.261737\pi\)
0.680559 + 0.732693i \(0.261737\pi\)
\(140\) 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
\(147\) −0.428096 7.21577i −0.0353088 0.595147i
\(148\) 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 0.862336 0.506336i \(-0.169000\pi\)
−0.506336 + 0.862336i \(0.669000\pi\)
\(158\) 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 \(-0.990245\pi\)
−0.0306429 0.999530i \(-0.509755\pi\)
\(168\) 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 −0.907892 0.419204i \(-0.862309\pi\)
0.419204 + 0.907892i \(0.362309\pi\)
\(174\) 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 \(0.00198108\pi\)
−0.999981 + 0.00622371i \(0.998019\pi\)
\(182\) 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 \(-0.562208\pi\)
−0.194190 + 0.980964i \(0.562208\pi\)
\(200\) 0 0
\(201\) 9.39493i 0.662667i
\(202\) 0 0
\(203\) 9.14398 4.10901i 0.641782 0.288396i
\(204\) 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
\(217\) 11.7805 5.29377i 0.799711 0.359364i
\(218\) 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 −0.164634 0.986355i \(-0.552644\pi\)
0.986355 + 0.164634i \(0.0526443\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) −13.9412 13.9412i −0.925307 0.925307i 0.0720910 0.997398i \(-0.477033\pi\)
−0.997398 + 0.0720910i \(0.977033\pi\)
\(228\) 0 0
\(229\) 24.5615 1.62307 0.811535 0.584304i \(-0.198632\pi\)
0.811535 + 0.584304i \(0.198632\pi\)
\(230\) 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 \(0.0639059\pi\)
−0.979914 + 0.199420i \(0.936094\pi\)
\(242\) 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 \(-0.765355\pi\)
0.740381 0.672187i \(-0.234645\pi\)
\(252\) 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 0.146779 0.989169i \(-0.453109\pi\)
−0.989169 + 0.146779i \(0.953109\pi\)
\(258\) 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 \(-0.175721\pi\)
0.851454 + 0.524429i \(0.175721\pi\)
\(270\) 0 0
\(271\) 6.55143i 0.397971i 0.980002 + 0.198985i \(0.0637647\pi\)
−0.980002 + 0.198985i \(0.936235\pi\)
\(272\) 0 0
\(273\) 3.24807 1.45958i 0.196582 0.0883377i
\(274\) 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 \(-0.455872\pi\)
0.990406 0.138190i \(-0.0441283\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) −25.7430 + 11.5681i −1.51956 + 0.682841i
\(288\) 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 −0.282033 0.959405i \(-0.591009\pi\)
0.959405 + 0.282033i \(0.0910088\pi\)
\(294\) 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 0.999199 0.0400244i \(-0.0127436\pi\)
−0.0400244 + 0.999199i \(0.512744\pi\)
\(308\) 0 0
\(309\) 11.7874i 0.670561i
\(310\) 0 0
\(311\) 15.1113i 0.856881i −0.903570 0.428440i \(-0.859063\pi\)
0.903570 0.428440i \(-0.140937\pi\)
\(312\) 0 0
\(313\) 13.1100 13.1100i 0.741023 0.741023i −0.231752 0.972775i \(-0.574446\pi\)
0.972775 + 0.231752i \(0.0744458\pi\)
\(314\) 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
\(343\) −17.6721 5.54051i −0.954203 0.299159i
\(344\) 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 \(-0.509565\pi\)
−0.0300437 + 0.999549i \(0.509565\pi\)
\(350\) 0 0
\(351\) 6.64027 0.354431
\(352\) 0 0
\(353\) 2.71896 2.71896i 0.144716 0.144716i −0.631037 0.775753i \(-0.717370\pi\)
0.775753 + 0.631037i \(0.217370\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 0 0
\(357\) −3.21062 7.14475i −0.169924 0.378140i
\(358\) 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 0.732189 0.681102i \(-0.238499\pi\)
−0.681102 + 0.732189i \(0.738499\pi\)
\(368\) 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 −0.957697 0.287779i \(-0.907083\pi\)
0.287779 + 0.957697i \(0.407083\pi\)
\(384\) 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 0.911100 0.412186i \(-0.135235\pi\)
−0.412186 + 0.911100i \(0.635235\pi\)
\(398\) 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 \(-0.488889\pi\)
0.0349004 + 0.999391i \(0.488889\pi\)
\(410\) 0 0
\(411\) 16.0053i 0.789484i
\(412\) 0 0
\(413\) −14.4483 32.1525i −0.710955 1.58212i
\(414\) 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 \(-0.544371\pi\)
−0.138946 + 0.990300i \(0.544371\pi\)
\(420\) 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
\(427\) −27.0509 + 12.1558i −1.30908 + 0.588260i
\(428\) 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 −0.729899 0.683555i \(-0.760433\pi\)
0.683555 + 0.729899i \(0.260433\pi\)
\(434\) 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 \(-0.432993\pi\)
0.208959 + 0.977924i \(0.432993\pi\)
\(440\) 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 \(-0.725323\pi\)
0.650219 0.759747i \(-0.274677\pi\)
\(462\) 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 0.411708 0.911316i \(-0.364932\pi\)
−0.911316 + 0.411708i \(0.864932\pi\)
\(468\) 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 \(-0.390014\pi\)
0.338697 + 0.940895i \(0.390014\pi\)
\(480\) 0 0
\(481\) 5.91330i 0.269623i
\(482\) 0 0
\(483\) 0.0861620 + 0.191740i 0.00392051 + 0.00872449i
\(484\) 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
\(497\) −9.23110 20.5424i −0.414071 0.921453i
\(498\) 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 −0.204697 0.978825i \(-0.565621\pi\)
0.978825 + 0.204697i \(0.0656208\pi\)
\(504\) 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 \(-0.456189\pi\)
0.137203 + 0.990543i \(0.456189\pi\)
\(510\) 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 \(0.171445\pi\)
−0.858422 + 0.512943i \(0.828555\pi\)
\(522\) 0 0
\(523\) −4.35649 + 4.35649i −0.190496 + 0.190496i −0.795910 0.605414i \(-0.793007\pi\)
0.605414 + 0.795910i \(0.293007\pi\)
\(524\) 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
\(553\) 4.25242 1.91090i 0.180831 0.0812599i
\(554\) 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 −0.986977 0.160859i \(-0.948573\pi\)
0.160859 + 0.986977i \(0.448573\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 0 0
\(567\) −0.585626 1.30322i −0.0245940 0.0547302i
\(568\) 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 0.986101 0.166144i \(-0.0531317\pi\)
−0.166144 + 0.986101i \(0.553132\pi\)
\(578\) 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 0.978372 0.206853i \(-0.0663223\pi\)
−0.206853 + 0.978372i \(0.566322\pi\)
\(588\) 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 \(0.506850\pi\)
−0.999768 + 0.0215185i \(0.993150\pi\)
\(594\) 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 \(0.0774204\pi\)
−0.970567 + 0.240832i \(0.922580\pi\)
\(602\) 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 0.826640 0.562731i \(-0.190249\pi\)
−0.562731 + 0.826640i \(0.690249\pi\)
\(608\) 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 \(-0.456458\pi\)
0.136366 + 0.990658i \(0.456458\pi\)
\(620\) 0 0
\(621\) 0.391989i 0.0157300i
\(622\) 0 0
\(623\) 10.5625 + 23.5052i 0.423176 + 0.941714i
\(624\) 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
\(637\) −0.540333 9.10759i −0.0214088 0.360856i
\(638\) 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 −0.929650 0.368443i \(-0.879891\pi\)
0.368443 + 0.929650i \(0.379891\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 10.4339 + 10.4339i 0.410201 + 0.410201i 0.881809 0.471608i \(-0.156326\pi\)
−0.471608 + 0.881809i \(0.656326\pi\)
\(648\) 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 \(-0.758832\pi\)
0.726453 0.687217i \(-0.241168\pi\)
\(662\) 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 0.897056 0.441917i \(-0.145702\pi\)
−0.441917 + 0.897056i \(0.645702\pi\)
\(678\) 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 \(0.0806333\pi\)
−0.968086 + 0.250616i \(0.919367\pi\)
\(692\) 0 0
\(693\) −27.8111 + 12.4974i −1.05646 + 0.474739i
\(694\) 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
\(707\) 14.4022 6.47188i 0.541650 0.243400i
\(708\) 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 \(-0.306748\pi\)
0.570505 + 0.821294i \(0.306748\pi\)
\(720\) 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 0.649882 0.760035i \(-0.274818\pi\)
−0.760035 + 0.649882i \(0.774818\pi\)
\(728\) 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 −0.0130016 0.999915i \(-0.504139\pi\)
0.999915 + 0.0130016i \(0.00413865\pi\)
\(734\) 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 \(-0.717075\pi\)
0.630317 0.776338i \(-0.282925\pi\)
\(762\) 0 0
\(763\) −5.96970 + 2.68259i −0.216118 + 0.0971164i
\(764\) 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 \(-0.439731\pi\)
0.188211 + 0.982129i \(0.439731\pi\)
\(770\) 0 0
\(771\) 19.7216 0.710257
\(772\) 0 0
\(773\) 11.9124 11.9124i 0.428459 0.428459i −0.459644 0.888103i \(-0.652023\pi\)
0.888103 + 0.459644i \(0.152023\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 0 0
\(777\) −11.3062 + 5.08066i −0.405609 + 0.182268i
\(778\) 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 \(0.0120185\pi\)
0.0377482 + 0.999287i \(0.487982\pi\)
\(788\) 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 0.391123 0.920338i \(-0.372087\pi\)
−0.920338 + 0.391123i \(0.872087\pi\)
\(798\) 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
\(804\) 0