Properties

Label 1512.2.s.o.865.1
Level $1512$
Weight $2$
Character 1512.865
Analytic conductor $12.073$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 1512 = 2^{3} \cdot 3^{3} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1512.s (of order \(3\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(12.0733807856\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(4\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{8} - \cdots)\)
Defining polynomial: \(x^{8} - 3 x^{7} + 4 x^{6} + 28 x^{5} + 14 x^{4} - 52 x^{3} + 306 x^{2} + 1052 x + 1051\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 865.1
Root \(-1.54823 - 0.711712i\) of defining polynomial
Character \(\chi\) \(=\) 1512.865
Dual form 1512.2.s.o.1297.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.99232 - 3.45080i) q^{5} +(-0.657753 - 2.56269i) q^{7} +O(q^{10})\) \(q+(-1.99232 - 3.45080i) q^{5} +(-0.657753 - 2.56269i) q^{7} +(0.444095 - 0.769196i) q^{11} -6.98465 q^{13} +(0.342247 - 0.592789i) q^{17} +(1.73272 + 3.00116i) q^{19} +(-2.94638 - 5.10328i) q^{23} +(-5.43870 + 9.42011i) q^{25} +5.87741 q^{29} +(-0.604133 + 1.04639i) q^{31} +(-7.53287 + 7.37548i) q^{35} +(4.32689 + 7.49440i) q^{37} +6.30015 q^{41} +0.888190 q^{43} +(-1.59417 - 2.76119i) q^{47} +(-6.13472 + 3.37123i) q^{49} +(0.890475 - 1.54235i) q^{53} -3.53912 q^{55} +(-5.11552 + 8.86034i) q^{59} +(0.882798 + 1.52905i) q^{61} +(13.9157 + 24.1027i) q^{65} +(-5.83457 + 10.1058i) q^{67} +8.50385 q^{71} +(5.14240 - 8.90690i) q^{73} +(-2.26331 - 0.632136i) q^{77} +(-2.64011 - 4.57281i) q^{79} -11.4120 q^{83} -2.72747 q^{85} +(-5.77099 - 9.99565i) q^{89} +(4.59417 + 17.8995i) q^{91} +(6.90428 - 11.9586i) q^{95} -10.6003 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8q + 2q^{5} - 4q^{7} + O(q^{10}) \) \( 8q + 2q^{5} - 4q^{7} + q^{11} - 20q^{13} + 4q^{17} + q^{19} - 12q^{23} - 14q^{25} - 12q^{29} + 8q^{31} - 9q^{35} + 12q^{41} + 2q^{43} + 9q^{47} + 6q^{49} - 7q^{53} - 36q^{55} + 4q^{59} - 25q^{61} + 28q^{65} - 30q^{67} + 22q^{71} + 4q^{73} + 37q^{77} + 7q^{79} - 58q^{83} + 14q^{85} - 9q^{89} + 15q^{91} + 4q^{95} - 8q^{97} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1512\mathbb{Z}\right)^\times\).

\(n\) \(757\) \(785\) \(1081\) \(1135\)
\(\chi(n)\) \(1\) \(1\) \(e\left(\frac{2}{3}\right)\) \(1\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) 0 0
\(4\) 0 0
\(5\) −1.99232 3.45080i −0.890994 1.54325i −0.838686 0.544616i \(-0.816675\pi\)
−0.0523084 0.998631i \(-0.516658\pi\)
\(6\) 0 0
\(7\) −0.657753 2.56269i −0.248607 0.968604i
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) 0.444095 0.769196i 0.133900 0.231921i −0.791277 0.611458i \(-0.790583\pi\)
0.925177 + 0.379537i \(0.123917\pi\)
\(12\) 0 0
\(13\) −6.98465 −1.93719 −0.968596 0.248639i \(-0.920017\pi\)
−0.968596 + 0.248639i \(0.920017\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 0.342247 0.592789i 0.0830071 0.143773i −0.821533 0.570161i \(-0.806881\pi\)
0.904540 + 0.426388i \(0.140214\pi\)
\(18\) 0 0
\(19\) 1.73272 + 3.00116i 0.397514 + 0.688514i 0.993419 0.114541i \(-0.0365398\pi\)
−0.595905 + 0.803055i \(0.703206\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) −2.94638 5.10328i −0.614363 1.06411i −0.990496 0.137542i \(-0.956080\pi\)
0.376133 0.926566i \(-0.377253\pi\)
\(24\) 0 0
\(25\) −5.43870 + 9.42011i −1.08774 + 1.88402i
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) 5.87741 1.09141 0.545703 0.837978i \(-0.316263\pi\)
0.545703 + 0.837978i \(0.316263\pi\)
\(30\) 0 0
\(31\) −0.604133 + 1.04639i −0.108505 + 0.187937i −0.915165 0.403079i \(-0.867940\pi\)
0.806660 + 0.591016i \(0.201273\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) −7.53287 + 7.37548i −1.27329 + 1.24668i
\(36\) 0 0
\(37\) 4.32689 + 7.49440i 0.711337 + 1.23207i 0.964355 + 0.264610i \(0.0852433\pi\)
−0.253019 + 0.967461i \(0.581423\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) 6.30015 0.983918 0.491959 0.870618i \(-0.336281\pi\)
0.491959 + 0.870618i \(0.336281\pi\)
\(42\) 0 0
\(43\) 0.888190 0.135448 0.0677239 0.997704i \(-0.478426\pi\)
0.0677239 + 0.997704i \(0.478426\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) −1.59417 2.76119i −0.232534 0.402760i 0.726019 0.687674i \(-0.241368\pi\)
−0.958553 + 0.284914i \(0.908035\pi\)
\(48\) 0 0
\(49\) −6.13472 + 3.37123i −0.876389 + 0.481604i
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) 0.890475 1.54235i 0.122316 0.211858i −0.798365 0.602174i \(-0.794301\pi\)
0.920681 + 0.390317i \(0.127634\pi\)
\(54\) 0 0
\(55\) −3.53912 −0.477215
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) −5.11552 + 8.86034i −0.665984 + 1.15352i 0.313034 + 0.949742i \(0.398655\pi\)
−0.979018 + 0.203776i \(0.934679\pi\)
\(60\) 0 0
\(61\) 0.882798 + 1.52905i 0.113031 + 0.195775i 0.916991 0.398908i \(-0.130611\pi\)
−0.803960 + 0.594683i \(0.797277\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) 13.9157 + 24.1027i 1.72603 + 2.98957i
\(66\) 0 0
\(67\) −5.83457 + 10.1058i −0.712806 + 1.23462i 0.250993 + 0.967989i \(0.419243\pi\)
−0.963800 + 0.266628i \(0.914091\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 8.50385 1.00922 0.504611 0.863347i \(-0.331636\pi\)
0.504611 + 0.863347i \(0.331636\pi\)
\(72\) 0 0
\(73\) 5.14240 8.90690i 0.601872 1.04247i −0.390665 0.920533i \(-0.627755\pi\)
0.992537 0.121941i \(-0.0389117\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) −2.26331 0.632136i −0.257928 0.0720386i
\(78\) 0 0
\(79\) −2.64011 4.57281i −0.297036 0.514482i 0.678420 0.734674i \(-0.262665\pi\)
−0.975456 + 0.220192i \(0.929332\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) −11.4120 −1.25263 −0.626313 0.779572i \(-0.715437\pi\)
−0.626313 + 0.779572i \(0.715437\pi\)
\(84\) 0 0
\(85\) −2.72747 −0.295835
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) −5.77099 9.99565i −0.611724 1.05954i −0.990950 0.134232i \(-0.957143\pi\)
0.379226 0.925304i \(-0.376190\pi\)
\(90\) 0 0
\(91\) 4.59417 + 17.8995i 0.481600 + 1.87637i
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 6.90428 11.9586i 0.708365 1.22692i
\(96\) 0 0
\(97\) −10.6003 −1.07630 −0.538149 0.842850i \(-0.680876\pi\)
−0.538149 + 0.842850i \(0.680876\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) −7.29248 + 12.6309i −0.725628 + 1.25683i 0.233086 + 0.972456i \(0.425117\pi\)
−0.958715 + 0.284369i \(0.908216\pi\)
\(102\) 0 0
\(103\) −7.88280 13.6534i −0.776715 1.34531i −0.933825 0.357729i \(-0.883551\pi\)
0.157110 0.987581i \(-0.449782\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −0.869126 1.50537i −0.0840216 0.145530i 0.820952 0.570997i \(-0.193443\pi\)
−0.904974 + 0.425467i \(0.860110\pi\)
\(108\) 0 0
\(109\) −3.31551 + 5.74262i −0.317568 + 0.550044i −0.979980 0.199096i \(-0.936199\pi\)
0.662412 + 0.749140i \(0.269533\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) 2.17299 0.204418 0.102209 0.994763i \(-0.467409\pi\)
0.102209 + 0.994763i \(0.467409\pi\)
\(114\) 0 0
\(115\) −11.7403 + 20.3348i −1.09479 + 1.89623i
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) −1.74425 0.487163i −0.159895 0.0446582i
\(120\) 0 0
\(121\) 5.10556 + 8.84309i 0.464142 + 0.803917i
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) 23.4194 2.09469
\(126\) 0 0
\(127\) −19.2387 −1.70716 −0.853581 0.520960i \(-0.825574\pi\)
−0.853581 + 0.520960i \(0.825574\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) −10.5198 18.2208i −0.919120 1.59196i −0.800755 0.598992i \(-0.795568\pi\)
−0.118364 0.992970i \(-0.537765\pi\)
\(132\) 0 0
\(133\) 6.55134 6.41445i 0.568073 0.556203i
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 3.66914 6.35514i 0.313476 0.542956i −0.665637 0.746276i \(-0.731840\pi\)
0.979112 + 0.203320i \(0.0651732\pi\)
\(138\) 0 0
\(139\) 9.17756 0.778430 0.389215 0.921147i \(-0.372746\pi\)
0.389215 + 0.921147i \(0.372746\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) −3.10185 + 5.37256i −0.259390 + 0.449276i
\(144\) 0 0
\(145\) −11.7097 20.2818i −0.972437 1.68431i
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) −11.1002 19.2261i −0.909361 1.57506i −0.814954 0.579526i \(-0.803238\pi\)
−0.0944073 0.995534i \(-0.530096\pi\)
\(150\) 0 0
\(151\) 0.326893 0.566196i 0.0266022 0.0460764i −0.852418 0.522861i \(-0.824865\pi\)
0.879020 + 0.476785i \(0.158198\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 4.81451 0.386711
\(156\) 0 0
\(157\) 2.48236 4.29958i 0.198114 0.343144i −0.749803 0.661661i \(-0.769852\pi\)
0.947917 + 0.318518i \(0.103185\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) −11.1401 + 10.9073i −0.877964 + 0.859619i
\(162\) 0 0
\(163\) −6.93642 12.0142i −0.543302 0.941027i −0.998712 0.0507449i \(-0.983840\pi\)
0.455409 0.890282i \(-0.349493\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) −20.1084 −1.55604 −0.778019 0.628241i \(-0.783775\pi\)
−0.778019 + 0.628241i \(0.783775\pi\)
\(168\) 0 0
\(169\) 35.7853 2.75271
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) −0.730438 1.26516i −0.0555341 0.0961880i 0.836922 0.547322i \(-0.184353\pi\)
−0.892456 + 0.451134i \(0.851019\pi\)
\(174\) 0 0
\(175\) 27.7181 + 7.74159i 2.09529 + 0.585209i
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) −4.88508 + 8.46121i −0.365128 + 0.632421i −0.988797 0.149268i \(-0.952308\pi\)
0.623669 + 0.781689i \(0.285642\pi\)
\(180\) 0 0
\(181\) 1.83928 0.136712 0.0683562 0.997661i \(-0.478225\pi\)
0.0683562 + 0.997661i \(0.478225\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 17.2411 29.8625i 1.26759 2.19554i
\(186\) 0 0
\(187\) −0.303981 0.526510i −0.0222293 0.0385022i
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) −1.44410 2.50125i −0.104491 0.180984i 0.809039 0.587755i \(-0.199988\pi\)
−0.913530 + 0.406771i \(0.866655\pi\)
\(192\) 0 0
\(193\) −0.849924 + 1.47211i −0.0611789 + 0.105965i −0.894993 0.446081i \(-0.852819\pi\)
0.833814 + 0.552046i \(0.186153\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 15.5465 1.10765 0.553823 0.832635i \(-0.313169\pi\)
0.553823 + 0.832635i \(0.313169\pi\)
\(198\) 0 0
\(199\) −5.59646 + 9.69335i −0.396722 + 0.687143i −0.993319 0.115398i \(-0.963186\pi\)
0.596597 + 0.802541i \(0.296519\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) −3.86588 15.0619i −0.271332 1.05714i
\(204\) 0 0
\(205\) −12.5519 21.7406i −0.876665 1.51843i
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) 3.07797 0.212908
\(210\) 0 0
\(211\) 17.3155 1.19205 0.596024 0.802966i \(-0.296746\pi\)
0.596024 + 0.802966i \(0.296746\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) −1.76956 3.06497i −0.120683 0.209029i
\(216\) 0 0
\(217\) 3.07894 + 0.859937i 0.209012 + 0.0583764i
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) −2.39048 + 4.14042i −0.160801 + 0.278515i
\(222\) 0 0
\(223\) 0.595735 0.0398934 0.0199467 0.999801i \(-0.493650\pi\)
0.0199467 + 0.999801i \(0.493650\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) −11.4310 + 19.7991i −0.758704 + 1.31411i 0.184808 + 0.982775i \(0.440834\pi\)
−0.943512 + 0.331339i \(0.892500\pi\)
\(228\) 0 0
\(229\) 11.4830 + 19.8891i 0.758816 + 1.31431i 0.943455 + 0.331501i \(0.107555\pi\)
−0.184639 + 0.982806i \(0.559112\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 5.41735 + 9.38313i 0.354903 + 0.614709i 0.987101 0.160097i \(-0.0511807\pi\)
−0.632199 + 0.774806i \(0.717847\pi\)
\(234\) 0 0
\(235\) −6.35221 + 11.0023i −0.414372 + 0.717714i
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) −4.60003 −0.297551 −0.148776 0.988871i \(-0.547533\pi\)
−0.148776 + 0.988871i \(0.547533\pi\)
\(240\) 0 0
\(241\) −4.68834 + 8.12045i −0.302003 + 0.523084i −0.976589 0.215112i \(-0.930988\pi\)
0.674587 + 0.738196i \(0.264322\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) 23.8558 + 14.4532i 1.52409 + 0.923378i
\(246\) 0 0
\(247\) −12.1025 20.9621i −0.770061 1.33378i
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) −1.88819 −0.119182 −0.0595908 0.998223i \(-0.518980\pi\)
−0.0595908 + 0.998223i \(0.518980\pi\)
\(252\) 0 0
\(253\) −5.23389 −0.329052
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 10.9747 + 19.0087i 0.684582 + 1.18573i 0.973568 + 0.228398i \(0.0733486\pi\)
−0.288986 + 0.957333i \(0.593318\pi\)
\(258\) 0 0
\(259\) 16.3598 16.0179i 1.01655 0.995306i
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) −9.92106 + 17.1838i −0.611759 + 1.05960i 0.379185 + 0.925321i \(0.376204\pi\)
−0.990944 + 0.134277i \(0.957129\pi\)
\(264\) 0 0
\(265\) −7.09646 −0.435932
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) −6.51139 + 11.2781i −0.397006 + 0.687635i −0.993355 0.115090i \(-0.963284\pi\)
0.596349 + 0.802725i \(0.296618\pi\)
\(270\) 0 0
\(271\) −14.4211 24.9780i −0.876017 1.51731i −0.855675 0.517513i \(-0.826858\pi\)
−0.0203422 0.999793i \(-0.506476\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 4.83060 + 8.36685i 0.291296 + 0.504540i
\(276\) 0 0
\(277\) −11.2051 + 19.4078i −0.673251 + 1.16610i 0.303726 + 0.952759i \(0.401769\pi\)
−0.976977 + 0.213345i \(0.931564\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) −16.0965 −0.960234 −0.480117 0.877204i \(-0.659406\pi\)
−0.480117 + 0.877204i \(0.659406\pi\)
\(282\) 0 0
\(283\) 15.4279 26.7219i 0.917095 1.58845i 0.113289 0.993562i \(-0.463861\pi\)
0.803805 0.594892i \(-0.202805\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) −4.14394 16.1453i −0.244609 0.953028i
\(288\) 0 0
\(289\) 8.26573 + 14.3167i 0.486220 + 0.842157i
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) 0.154783 0.00904250 0.00452125 0.999990i \(-0.498561\pi\)
0.00452125 + 0.999990i \(0.498561\pi\)
\(294\) 0 0
\(295\) 40.7671 2.37355
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 20.5794 + 35.6446i 1.19014 + 2.06138i
\(300\) 0 0
\(301\) −0.584210 2.27615i −0.0336733 0.131195i
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) 3.51764 6.09273i 0.201419 0.348869i
\(306\) 0 0
\(307\) 14.6430 0.835720 0.417860 0.908511i \(-0.362780\pi\)
0.417860 + 0.908511i \(0.362780\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 12.7702 22.1186i 0.724130 1.25423i −0.235202 0.971947i \(-0.575575\pi\)
0.959331 0.282283i \(-0.0910916\pi\)
\(312\) 0 0
\(313\) −9.48465 16.4279i −0.536104 0.928559i −0.999109 0.0422036i \(-0.986562\pi\)
0.463005 0.886356i \(-0.346771\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −0.395867 0.685662i −0.0222341 0.0385106i 0.854694 0.519132i \(-0.173745\pi\)
−0.876928 + 0.480621i \(0.840411\pi\)
\(318\) 0 0
\(319\) 2.61013 4.52087i 0.146139 0.253120i
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) 2.37208 0.131986
\(324\) 0 0
\(325\) 37.9874 65.7961i 2.10716 3.64971i
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) −6.02748 + 5.90154i −0.332306 + 0.325362i
\(330\) 0 0
\(331\) −9.25253 16.0258i −0.508565 0.880860i −0.999951 0.00991827i \(-0.996843\pi\)
0.491386 0.870942i \(-0.336490\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) 46.4974 2.54042
\(336\) 0 0
\(337\) −2.41169 −0.131373 −0.0656865 0.997840i \(-0.520924\pi\)
−0.0656865 + 0.997840i \(0.520924\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) 0.536585 + 0.929392i 0.0290577 + 0.0503294i
\(342\) 0 0
\(343\) 12.6745 + 13.5039i 0.684360 + 0.729144i
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) −6.60185 + 11.4347i −0.354406 + 0.613849i −0.987016 0.160621i \(-0.948650\pi\)
0.632610 + 0.774470i \(0.281984\pi\)
\(348\) 0 0
\(349\) −24.0885 −1.28943 −0.644715 0.764423i \(-0.723024\pi\)
−0.644715 + 0.764423i \(0.723024\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) 10.0550 17.4159i 0.535176 0.926952i −0.463979 0.885846i \(-0.653579\pi\)
0.999155 0.0411059i \(-0.0130881\pi\)
\(354\) 0 0
\(355\) −16.9424 29.3451i −0.899210 1.55748i
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) −9.67514 16.7578i −0.510634 0.884444i −0.999924 0.0123231i \(-0.996077\pi\)
0.489290 0.872121i \(-0.337256\pi\)
\(360\) 0 0
\(361\) 3.49535 6.05412i 0.183966 0.318638i
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) −40.9813 −2.14506
\(366\) 0 0
\(367\) 12.3982 21.4742i 0.647178 1.12095i −0.336616 0.941642i \(-0.609282\pi\)
0.983794 0.179303i \(-0.0573844\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) −4.53827 1.26752i −0.235615 0.0658066i
\(372\) 0 0
\(373\) 9.19291 + 15.9226i 0.475991 + 0.824440i 0.999622 0.0275049i \(-0.00875618\pi\)
−0.523631 + 0.851945i \(0.675423\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) −41.0516 −2.11426
\(378\) 0 0
\(379\) −8.23588 −0.423049 −0.211524 0.977373i \(-0.567843\pi\)
−0.211524 + 0.977373i \(0.567843\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 8.47554 + 14.6801i 0.433080 + 0.750117i 0.997137 0.0756194i \(-0.0240934\pi\)
−0.564057 + 0.825736i \(0.690760\pi\)
\(384\) 0 0
\(385\) 2.32787 + 9.06967i 0.118639 + 0.462233i
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) 6.00371 10.3987i 0.304400 0.527237i −0.672727 0.739890i \(-0.734877\pi\)
0.977128 + 0.212654i \(0.0682106\pi\)
\(390\) 0 0
\(391\) −4.03356 −0.203986
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) −10.5199 + 18.2210i −0.529315 + 0.916800i
\(396\) 0 0
\(397\) −3.77939 6.54609i −0.189682 0.328539i 0.755462 0.655192i \(-0.227412\pi\)
−0.945144 + 0.326653i \(0.894079\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) −5.32306 9.21982i −0.265821 0.460416i 0.701957 0.712219i \(-0.252310\pi\)
−0.967778 + 0.251803i \(0.918976\pi\)
\(402\) 0 0
\(403\) 4.21965 7.30865i 0.210196 0.364070i
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 7.68621 0.380991
\(408\) 0 0
\(409\) 3.45177 5.97864i 0.170679 0.295625i −0.767978 0.640476i \(-0.778737\pi\)
0.938657 + 0.344851i \(0.112071\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) 26.0710 + 7.28156i 1.28287 + 0.358302i
\(414\) 0 0
\(415\) 22.7363 + 39.3805i 1.11608 + 1.93311i
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) −21.2205 −1.03669 −0.518345 0.855171i \(-0.673452\pi\)
−0.518345 + 0.855171i \(0.673452\pi\)
\(420\) 0 0
\(421\) 19.8529 0.967572 0.483786 0.875186i \(-0.339261\pi\)
0.483786 + 0.875186i \(0.339261\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) 3.72276 + 6.44801i 0.180580 + 0.312774i
\(426\) 0 0
\(427\) 3.33782 3.26807i 0.161528 0.158153i
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 13.7923 23.8890i 0.664354 1.15069i −0.315107 0.949056i \(-0.602040\pi\)
0.979460 0.201638i \(-0.0646264\pi\)
\(432\) 0 0
\(433\) 1.90046 0.0913301 0.0456650 0.998957i \(-0.485459\pi\)
0.0456650 + 0.998957i \(0.485459\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 10.2105 17.6851i 0.488435 0.845995i
\(438\) 0 0
\(439\) 15.0604 + 26.0853i 0.718792 + 1.24498i 0.961479 + 0.274879i \(0.0886378\pi\)
−0.242687 + 0.970105i \(0.578029\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) −17.3154 29.9911i −0.822679 1.42492i −0.903680 0.428208i \(-0.859145\pi\)
0.0810014 0.996714i \(-0.474188\pi\)
\(444\) 0 0
\(445\) −22.9953 + 39.8291i −1.09008 + 1.88808i
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) −23.2342 −1.09649 −0.548244 0.836318i \(-0.684704\pi\)
−0.548244 + 0.836318i \(0.684704\pi\)
\(450\) 0 0
\(451\) 2.79787 4.84605i 0.131746 0.228192i
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) 52.6145 51.5151i 2.46660 2.41506i
\(456\) 0 0
\(457\) 1.01367 + 1.75573i 0.0474176 + 0.0821297i 0.888760 0.458373i \(-0.151568\pi\)
−0.841342 + 0.540502i \(0.818234\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) −35.2371 −1.64115 −0.820577 0.571535i \(-0.806348\pi\)
−0.820577 + 0.571535i \(0.806348\pi\)
\(462\) 0 0
\(463\) 6.28195 0.291947 0.145973 0.989289i \(-0.453369\pi\)
0.145973 + 0.989289i \(0.453369\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) −7.74579 13.4161i −0.358432 0.620823i 0.629267 0.777189i \(-0.283355\pi\)
−0.987699 + 0.156366i \(0.950022\pi\)
\(468\) 0 0
\(469\) 29.7356 + 8.30507i 1.37306 + 0.383493i
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) 0.394441 0.683192i 0.0181364 0.0314132i
\(474\) 0 0
\(475\) −37.6950 −1.72957
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) 18.2119 31.5439i 0.832121 1.44128i −0.0642320 0.997935i \(-0.520460\pi\)
0.896353 0.443341i \(-0.146207\pi\)
\(480\) 0 0
\(481\) −30.2218 52.3457i −1.37800 2.38676i
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 21.1192 + 36.5796i 0.958975 + 1.66099i
\(486\) 0 0
\(487\) −12.6178 + 21.8547i −0.571767 + 0.990330i 0.424617 + 0.905373i \(0.360409\pi\)
−0.996385 + 0.0849571i \(0.972925\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) −30.0305 −1.35526 −0.677628 0.735405i \(-0.736992\pi\)
−0.677628 + 0.735405i \(0.736992\pi\)
\(492\) 0 0
\(493\) 2.01153 3.48406i 0.0905945 0.156914i
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) −5.59343 21.7927i −0.250900 0.977536i
\(498\) 0 0
\(499\) 4.96247 + 8.59526i 0.222151 + 0.384777i 0.955461 0.295118i \(-0.0953589\pi\)
−0.733310 + 0.679894i \(0.762026\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) 5.12095 0.228332 0.114166 0.993462i \(-0.463580\pi\)
0.114166 + 0.993462i \(0.463580\pi\)
\(504\) 0 0
\(505\) 58.1159 2.58612
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) −2.14851 3.72133i −0.0952311 0.164945i 0.814474 0.580200i \(-0.197026\pi\)
−0.909705 + 0.415255i \(0.863692\pi\)
\(510\) 0 0
\(511\) −26.2080 7.31982i −1.15937 0.323810i
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) −31.4102 + 54.4040i −1.38410 + 2.39733i
\(516\) 0 0
\(517\) −2.83186 −0.124545
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 6.52520 11.3020i 0.285874 0.495148i −0.686947 0.726708i \(-0.741049\pi\)
0.972821 + 0.231559i \(0.0743828\pi\)
\(522\) 0 0
\(523\) −3.16543 5.48269i −0.138415 0.239741i 0.788482 0.615058i \(-0.210867\pi\)
−0.926897 + 0.375317i \(0.877534\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 0.413525 + 0.716247i 0.0180134 + 0.0312002i
\(528\) 0 0
\(529\) −5.86231 + 10.1538i −0.254883 + 0.441470i
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) −44.0043 −1.90604
\(534\) 0 0
\(535\) −3.46316 + 5.99837i −0.149725 + 0.259332i
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) −0.131267 + 6.21595i −0.00565407 + 0.267740i
\(540\) 0 0
\(541\) −10.2043 17.6744i −0.438717 0.759880i 0.558874 0.829253i \(-0.311234\pi\)
−0.997591 + 0.0693725i \(0.977900\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) 26.4222 1.13180
\(546\) 0 0
\(547\) 8.08732 0.345789 0.172894 0.984940i \(-0.444688\pi\)
0.172894 + 0.984940i \(0.444688\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) 10.1839 + 17.6391i 0.433849 + 0.751449i
\(552\) 0 0
\(553\) −9.98214 + 9.77357i −0.424484 + 0.415614i
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 2.99018 5.17914i 0.126698 0.219447i −0.795698 0.605694i \(-0.792895\pi\)
0.922395 + 0.386247i \(0.126229\pi\)
\(558\) 0 0
\(559\) −6.20370 −0.262388
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) −7.20059 + 12.4718i −0.303469 + 0.525623i −0.976919 0.213609i \(-0.931478\pi\)
0.673451 + 0.739232i \(0.264811\pi\)
\(564\) 0 0
\(565\) −4.32930 7.49856i −0.182135 0.315467i
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) −4.36830 7.56612i −0.183129 0.317188i 0.759816 0.650139i \(-0.225289\pi\)
−0.942944 + 0.332950i \(0.891956\pi\)
\(570\) 0 0
\(571\) 0.123197 0.213384i 0.00515564 0.00892983i −0.863436 0.504458i \(-0.831692\pi\)
0.868592 + 0.495528i \(0.165026\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 64.0979 2.67307
\(576\) 0 0
\(577\) −3.74257 + 6.48231i −0.155805 + 0.269862i −0.933352 0.358963i \(-0.883130\pi\)
0.777547 + 0.628825i \(0.216464\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) 7.50625 + 29.2453i 0.311412 + 1.21330i
\(582\) 0 0
\(583\) −0.790911 1.36990i −0.0327562 0.0567354i
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 11.2800 0.465574 0.232787 0.972528i \(-0.425216\pi\)
0.232787 + 0.972528i \(0.425216\pi\)
\(588\) 0 0
\(589\) −4.18718 −0.172530
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) −1.51846 2.63005i −0.0623557 0.108003i 0.833162 0.553029i \(-0.186528\pi\)
−0.895518 + 0.445025i \(0.853195\pi\)
\(594\) 0 0
\(595\) 1.79400 + 6.98964i 0.0735468 + 0.286547i
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) −3.22901 + 5.59281i −0.131934 + 0.228516i −0.924422 0.381371i \(-0.875452\pi\)
0.792488 + 0.609887i \(0.208785\pi\)
\(600\) 0 0
\(601\) 35.0578 1.43004 0.715019 0.699105i \(-0.246418\pi\)
0.715019 + 0.699105i \(0.246418\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) 20.3438 35.2366i 0.827095 1.43257i
\(606\) 0 0
\(607\) 7.04055 + 12.1946i 0.285767 + 0.494963i 0.972795 0.231668i \(-0.0744183\pi\)
−0.687028 + 0.726631i \(0.741085\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 11.1347 + 19.2859i 0.450463 + 0.780224i
\(612\) 0 0
\(613\) 0.160037 0.277193i 0.00646385 0.0111957i −0.862775 0.505587i \(-0.831276\pi\)
0.869239 + 0.494392i \(0.164609\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) −22.2145 −0.894321 −0.447161 0.894454i \(-0.647565\pi\)
−0.447161 + 0.894454i \(0.647565\pi\)
\(618\) 0 0
\(619\) 0.754894 1.30752i 0.0303418 0.0525535i −0.850456 0.526047i \(-0.823674\pi\)
0.880798 + 0.473493i \(0.157007\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) −21.8198 + 21.3639i −0.874193 + 0.855927i
\(624\) 0 0
\(625\) −19.4655 33.7152i −0.778619 1.34861i
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 5.92347 0.236184
\(630\) 0 0
\(631\) −2.55733 −0.101806 −0.0509029 0.998704i \(-0.516210\pi\)
−0.0509029 + 0.998704i \(0.516210\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) 38.3298 + 66.3891i 1.52107 + 2.63457i
\(636\) 0 0
\(637\) 42.8489 23.5468i 1.69773 0.932960i
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) −12.3160 + 21.3319i −0.486452 + 0.842559i −0.999879 0.0155743i \(-0.995042\pi\)
0.513427 + 0.858133i \(0.328376\pi\)
\(642\) 0 0
\(643\) −30.7486 −1.21261 −0.606303 0.795234i \(-0.707348\pi\)
−0.606303 + 0.795234i \(0.707348\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) −14.2787 + 24.7314i −0.561352 + 0.972291i 0.436027 + 0.899934i \(0.356385\pi\)
−0.997379 + 0.0723568i \(0.976948\pi\)
\(648\) 0 0
\(649\) 4.54356 + 7.86967i 0.178350 + 0.308912i
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) −13.8545 23.9967i −0.542169 0.939064i −0.998779 0.0493974i \(-0.984270\pi\)
0.456610 0.889667i \(-0.349063\pi\)
\(654\) 0 0
\(655\) −41.9177 + 72.6036i −1.63786 + 2.83686i
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) 34.7244 1.35267 0.676335 0.736594i \(-0.263567\pi\)
0.676335 + 0.736594i \(0.263567\pi\)
\(660\) 0 0
\(661\) −20.1254 + 34.8582i −0.782786 + 1.35582i 0.147527 + 0.989058i \(0.452869\pi\)
−0.930313 + 0.366767i \(0.880465\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) −35.1874 9.82773i −1.36451 0.381103i
\(666\) 0 0
\(667\) −17.3171 29.9940i −0.670520 1.16137i
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 1.56819 0.0605391
\(672\) 0 0
\(673\) −19.6202 −0.756304 −0.378152 0.925743i \(-0.623440\pi\)
−0.378152 + 0.925743i \(0.623440\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) −6.22290 10.7784i −0.239165 0.414247i 0.721310 0.692613i \(-0.243540\pi\)
−0.960475 + 0.278366i \(0.910207\pi\)
\(678\) 0 0
\(679\) 6.97238 + 27.1653i 0.267575 + 1.04251i
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 3.36602 5.83011i 0.128797 0.223083i −0.794414 0.607377i \(-0.792222\pi\)
0.923211 + 0.384294i \(0.125555\pi\)
\(684\) 0 0
\(685\) −29.2405 −1.11722
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) −6.21965 + 10.7728i −0.236950 + 0.410409i
\(690\) 0 0
\(691\) −24.1891 41.8967i −0.920196 1.59383i −0.799110 0.601184i \(-0.794696\pi\)
−0.121086 0.992642i \(-0.538638\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) −18.2847 31.6700i −0.693577 1.20131i
\(696\) 0 0
\(697\) 2.15621 3.73466i 0.0816722 0.141460i
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) −20.6903 −0.781461 −0.390730 0.920505i \(-0.627778\pi\)
−0.390730 + 0.920505i \(0.627778\pi\)
\(702\) 0 0
\(703\) −14.9946 + 25.9714i −0.565532 + 0.979531i
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 37.1658 + 10.3803i 1.39776 + 0.390391i
\(708\) 0 0
\(709\) −13.4717 23.3337i −0.505941 0.876315i −0.999976 0.00687356i \(-0.997812\pi\)
0.494036 0.869442i \(-0.335521\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) 7.12002 0.266647
\(714\) 0 0
\(715\) 24.7195 0.924458
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) −4.48080 7.76097i −0.167106 0.289435i 0.770295 0.637687i \(-0.220109\pi\)
−0.937401 + 0.348252i \(0.886775\pi\)
\(720\) 0 0
\(721\) −29.8045 + 29.1817i −1.10998 + 1.08678i
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) −31.9655 + 55.3658i −1.18717 + 2.05623i
\(726\) 0 0
\(727\) −1.86854 −0.0693004 −0.0346502 0.999400i \(-0.511032\pi\)
−0.0346502 + 0.999400i \(0.511032\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) 0.303981 0.526510i 0.0112431 0.0194737i
\(732\) 0 0
\(733\) 16.2585 + 28.1606i 0.600522 + 1.04014i 0.992742 + 0.120263i \(0.0383739\pi\)
−0.392220 + 0.919872i \(0.628293\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 5.18221 + 8.97585i 0.190889 + 0.330630i
\(738\) 0 0
\(739\) −18.8522 + 32.6530i −0.693490 + 1.20116i 0.277197 + 0.960813i \(0.410595\pi\)
−0.970687 + 0.240347i \(0.922739\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 21.3073 0.781689 0.390844 0.920457i \(-0.372183\pi\)
0.390844 + 0.920457i \(0.372183\pi\)
\(744\) 0 0
\(745\) −44.2302 + 76.6090i −1.62047 + 2.80674i
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) −3.28612 + 3.21746i −0.120072 + 0.117563i
\(750\) 0 0
\(751\) 2.24028 + 3.88028i 0.0817490 + 0.141593i 0.904001 0.427530i \(-0.140616\pi\)
−0.822252 + 0.569123i \(0.807283\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) −2.60511 −0.0948096
\(756\) 0 0
\(757\) −42.1970 −1.53367 −0.766837 0.641841i \(-0.778171\pi\)
−0.766837 + 0.641841i \(0.778171\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 15.9791 + 27.6766i 0.579243 + 1.00328i 0.995566 + 0.0940611i \(0.0299849\pi\)
−0.416324 + 0.909216i \(0.636682\pi\)
\(762\) 0 0
\(763\) 16.8973 + 4.71937i 0.611724 + 0.170853i
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 35.7301 61.8863i 1.29014 2.23459i
\(768\) 0 0
\(769\) −2.12716 −0.0767075 −0.0383537 0.999264i \(-0.512211\pi\)
−0.0383537 + 0.999264i \(0.512211\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) 4.11167 7.12162i 0.147887 0.256147i −0.782560 0.622576i \(-0.786086\pi\)
0.930446 + 0.366429i \(0.119420\pi\)
\(774\) 0 0
\(775\) −6.57140 11.3820i −0.236052 0.408853i
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 10.9164 + 18.9078i 0.391121 + 0.677442i
\(780\) 0 0
\(781\) 3.77652 6.54112i 0.135134 0.234060i
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) −19.7827 −0.706074
\(786\) 0 0
\(787\) 5.86744 10.1627i 0.209152 0.362262i −0.742296 0.670072i \(-0.766263\pi\)
0.951448 + 0.307811i \(0.0995964\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) −1.42929 5.56869i −0.0508197 0.198000i
\(792\) 0 0
\(793\) −6.16603 10.6799i −0.218962 0.379254i
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 21.3167 0.755077 0.377538 0.925994i \(-0.376771\pi\)
0.377538 + 0.925994i \(0.376771\pi\)
\(798\) 0 0
\(799\) −2.18240 −0.0772078
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) −4.56743 7.91102i −0.161181 0.279174i
\(804\) 0 0
\(805\) 59.8338 + 16.7114i 2.10887 + 0.589000i