Properties

Label 3024.2.r.g.2017.1
Level $3024$
Weight $2$
Character 3024.2017
Analytic conductor $24.147$
Analytic rank $0$
Dimension $6$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [3024,2,Mod(1009,3024)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(3024, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([0, 0, 2, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("3024.1009");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 3024 = 2^{4} \cdot 3^{3} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 3024.r (of order \(3\), degree \(2\), not minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(24.1467615712\)
Analytic rank: \(0\)
Dimension: \(6\)
Relative dimension: \(3\) over \(\Q(\zeta_{3})\)
Coefficient field: 6.0.309123.1
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{6} - 3x^{5} + 10x^{4} - 15x^{3} + 19x^{2} - 12x + 3 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 3 \)
Twist minimal: no (minimal twist has level 63)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 2017.1
Root \(0.500000 - 0.224437i\) of defining polynomial
Character \(\chi\) \(=\) 3024.2017
Dual form 3024.2.r.g.1009.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.79418 - 3.10761i) q^{5} +(-0.500000 + 0.866025i) q^{7} +O(q^{10})\) \(q+(-1.79418 - 3.10761i) q^{5} +(-0.500000 + 0.866025i) q^{7} +(1.40545 - 2.43430i) q^{11} +(-0.500000 - 0.866025i) q^{13} +4.11126 q^{17} +0.888736 q^{19} +(-2.93818 - 5.08907i) q^{23} +(-3.93818 + 6.82112i) q^{25} +(-0.849814 + 1.47192i) q^{29} +(-3.49381 - 6.05146i) q^{31} +3.58836 q^{35} +4.76509 q^{37} +(-2.70582 - 4.68661i) q^{41} +(2.60507 - 4.51212i) q^{43} +(1.33310 - 2.30900i) q^{47} +(-0.500000 - 0.866025i) q^{49} +0.123644 q^{53} -10.0865 q^{55} +(4.43818 + 7.68715i) q^{59} +(-1.93818 + 3.35702i) q^{61} +(-1.79418 + 3.10761i) q^{65} +(6.15452 + 10.6599i) q^{67} -2.87636 q^{71} -10.6414 q^{73} +(1.40545 + 2.43430i) q^{77} +(-3.54325 + 6.13709i) q^{79} +(2.05563 - 3.56046i) q^{83} +(-7.37636 - 12.7762i) q^{85} -9.60940 q^{89} +1.00000 q^{91} +(-1.59455 - 2.76185i) q^{95} +(-3.66071 + 6.34053i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6 q - 5 q^{5} - 3 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 6 q - 5 q^{5} - 3 q^{7} + 2 q^{11} - 3 q^{13} + 24 q^{17} + 6 q^{19} - 6 q^{25} + q^{29} - 3 q^{31} + 10 q^{35} - 6 q^{37} - 22 q^{41} - 3 q^{43} + 9 q^{47} - 3 q^{49} + 36 q^{53} + 12 q^{55} + 9 q^{59} + 6 q^{61} - 5 q^{65} + 18 q^{71} + 6 q^{73} + 2 q^{77} + 15 q^{79} + 12 q^{83} - 9 q^{85} + 4 q^{89} + 6 q^{91} - 16 q^{95} - 3 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/3024\mathbb{Z}\right)^\times\).

\(n\) \(757\) \(785\) \(1135\) \(2593\)
\(\chi(n)\) \(1\) \(e\left(\frac{2}{3}\right)\) \(1\) \(1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) 0 0
\(4\) 0 0
\(5\) −1.79418 3.10761i −0.802383 1.38977i −0.918044 0.396479i \(-0.870232\pi\)
0.115661 0.993289i \(-0.463101\pi\)
\(6\) 0 0
\(7\) −0.500000 + 0.866025i −0.188982 + 0.327327i
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) 1.40545 2.43430i 0.423758 0.733970i −0.572546 0.819873i \(-0.694044\pi\)
0.996304 + 0.0859026i \(0.0273774\pi\)
\(12\) 0 0
\(13\) −0.500000 0.866025i −0.138675 0.240192i 0.788320 0.615265i \(-0.210951\pi\)
−0.926995 + 0.375073i \(0.877618\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 4.11126 0.997128 0.498564 0.866853i \(-0.333861\pi\)
0.498564 + 0.866853i \(0.333861\pi\)
\(18\) 0 0
\(19\) 0.888736 0.203890 0.101945 0.994790i \(-0.467493\pi\)
0.101945 + 0.994790i \(0.467493\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) −2.93818 5.08907i −0.612652 1.06115i −0.990792 0.135396i \(-0.956769\pi\)
0.378139 0.925749i \(-0.376564\pi\)
\(24\) 0 0
\(25\) −3.93818 + 6.82112i −0.787636 + 1.36422i
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) −0.849814 + 1.47192i −0.157807 + 0.273329i −0.934077 0.357071i \(-0.883776\pi\)
0.776271 + 0.630399i \(0.217109\pi\)
\(30\) 0 0
\(31\) −3.49381 6.05146i −0.627507 1.08687i −0.988050 0.154131i \(-0.950742\pi\)
0.360544 0.932742i \(-0.382591\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) 3.58836 0.606544
\(36\) 0 0
\(37\) 4.76509 0.783376 0.391688 0.920098i \(-0.371891\pi\)
0.391688 + 0.920098i \(0.371891\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) −2.70582 4.68661i −0.422578 0.731926i 0.573613 0.819126i \(-0.305541\pi\)
−0.996191 + 0.0872002i \(0.972208\pi\)
\(42\) 0 0
\(43\) 2.60507 4.51212i 0.397270 0.688092i −0.596118 0.802897i \(-0.703291\pi\)
0.993388 + 0.114805i \(0.0366243\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 1.33310 2.30900i 0.194453 0.336803i −0.752268 0.658857i \(-0.771040\pi\)
0.946721 + 0.322055i \(0.104373\pi\)
\(48\) 0 0
\(49\) −0.500000 0.866025i −0.0714286 0.123718i
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) 0.123644 0.0169838 0.00849190 0.999964i \(-0.497297\pi\)
0.00849190 + 0.999964i \(0.497297\pi\)
\(54\) 0 0
\(55\) −10.0865 −1.36006
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) 4.43818 + 7.68715i 0.577802 + 1.00078i 0.995731 + 0.0923022i \(0.0294226\pi\)
−0.417929 + 0.908479i \(0.637244\pi\)
\(60\) 0 0
\(61\) −1.93818 + 3.35702i −0.248158 + 0.429823i −0.963015 0.269448i \(-0.913159\pi\)
0.714857 + 0.699271i \(0.246492\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) −1.79418 + 3.10761i −0.222541 + 0.385452i
\(66\) 0 0
\(67\) 6.15452 + 10.6599i 0.751894 + 1.30232i 0.946904 + 0.321517i \(0.104193\pi\)
−0.195010 + 0.980801i \(0.562474\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) −2.87636 −0.341361 −0.170680 0.985326i \(-0.554597\pi\)
−0.170680 + 0.985326i \(0.554597\pi\)
\(72\) 0 0
\(73\) −10.6414 −1.24549 −0.622744 0.782426i \(-0.713982\pi\)
−0.622744 + 0.782426i \(0.713982\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 1.40545 + 2.43430i 0.160165 + 0.277415i
\(78\) 0 0
\(79\) −3.54325 + 6.13709i −0.398647 + 0.690477i −0.993559 0.113314i \(-0.963853\pi\)
0.594912 + 0.803791i \(0.297187\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) 2.05563 3.56046i 0.225635 0.390811i −0.730875 0.682512i \(-0.760888\pi\)
0.956510 + 0.291700i \(0.0942210\pi\)
\(84\) 0 0
\(85\) −7.37636 12.7762i −0.800078 1.38578i
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) −9.60940 −1.01859 −0.509297 0.860591i \(-0.670095\pi\)
−0.509297 + 0.860591i \(0.670095\pi\)
\(90\) 0 0
\(91\) 1.00000 0.104828
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) −1.59455 2.76185i −0.163598 0.283360i
\(96\) 0 0
\(97\) −3.66071 + 6.34053i −0.371688 + 0.643783i −0.989825 0.142287i \(-0.954554\pi\)
0.618137 + 0.786070i \(0.287888\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) 1.73236 3.00054i 0.172376 0.298564i −0.766874 0.641798i \(-0.778189\pi\)
0.939250 + 0.343233i \(0.111522\pi\)
\(102\) 0 0
\(103\) −7.93818 13.7493i −0.782172 1.35476i −0.930674 0.365849i \(-0.880779\pi\)
0.148502 0.988912i \(-0.452555\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −5.35346 −0.517538 −0.258769 0.965939i \(-0.583317\pi\)
−0.258769 + 0.965939i \(0.583317\pi\)
\(108\) 0 0
\(109\) −18.8640 −1.80684 −0.903421 0.428755i \(-0.858952\pi\)
−0.903421 + 0.428755i \(0.858952\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) −9.27561 16.0658i −0.872576 1.51135i −0.859322 0.511434i \(-0.829114\pi\)
−0.0132538 0.999912i \(-0.504219\pi\)
\(114\) 0 0
\(115\) −10.5433 + 18.2614i −0.983163 + 1.70289i
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) −2.05563 + 3.56046i −0.188439 + 0.326387i
\(120\) 0 0
\(121\) 1.54944 + 2.68371i 0.140858 + 0.243974i
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) 10.3214 0.923175
\(126\) 0 0
\(127\) −9.98762 −0.886258 −0.443129 0.896458i \(-0.646132\pi\)
−0.443129 + 0.896458i \(0.646132\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) −8.02654 13.9024i −0.701282 1.21466i −0.968017 0.250886i \(-0.919278\pi\)
0.266734 0.963770i \(-0.414055\pi\)
\(132\) 0 0
\(133\) −0.444368 + 0.769668i −0.0385316 + 0.0667387i
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) −6.49381 + 11.2476i −0.554804 + 0.960948i 0.443115 + 0.896465i \(0.353873\pi\)
−0.997919 + 0.0644834i \(0.979460\pi\)
\(138\) 0 0
\(139\) 0.555632 + 0.962383i 0.0471281 + 0.0816283i 0.888627 0.458630i \(-0.151660\pi\)
−0.841499 + 0.540259i \(0.818326\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) −2.81089 −0.235059
\(144\) 0 0
\(145\) 6.09888 0.506485
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) 4.21634 + 7.30291i 0.345416 + 0.598278i 0.985429 0.170086i \(-0.0544045\pi\)
−0.640013 + 0.768364i \(0.721071\pi\)
\(150\) 0 0
\(151\) −7.42580 + 12.8619i −0.604303 + 1.04668i 0.387858 + 0.921719i \(0.373215\pi\)
−0.992161 + 0.124964i \(0.960118\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) −12.5371 + 21.7148i −1.00700 + 1.74418i
\(156\) 0 0
\(157\) −1.44437 2.50172i −0.115273 0.199659i 0.802616 0.596496i \(-0.203441\pi\)
−0.917889 + 0.396837i \(0.870108\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 5.87636 0.463122
\(162\) 0 0
\(163\) 10.3090 0.807466 0.403733 0.914877i \(-0.367713\pi\)
0.403733 + 0.914877i \(0.367713\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) −6.07598 10.5239i −0.470174 0.814365i 0.529244 0.848469i \(-0.322475\pi\)
−0.999418 + 0.0341045i \(0.989142\pi\)
\(168\) 0 0
\(169\) 6.00000 10.3923i 0.461538 0.799408i
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) −3.30470 + 5.72391i −0.251252 + 0.435181i −0.963871 0.266370i \(-0.914176\pi\)
0.712619 + 0.701551i \(0.247509\pi\)
\(174\) 0 0
\(175\) −3.93818 6.82112i −0.297698 0.515629i
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) −3.84294 −0.287234 −0.143617 0.989633i \(-0.545873\pi\)
−0.143617 + 0.989633i \(0.545873\pi\)
\(180\) 0 0
\(181\) 18.5426 1.37826 0.689129 0.724639i \(-0.257993\pi\)
0.689129 + 0.724639i \(0.257993\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) −8.54944 14.8081i −0.628567 1.08871i
\(186\) 0 0
\(187\) 5.77816 10.0081i 0.422541 0.731862i
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) −2.31708 + 4.01330i −0.167658 + 0.290392i −0.937596 0.347726i \(-0.886954\pi\)
0.769938 + 0.638119i \(0.220287\pi\)
\(192\) 0 0
\(193\) 12.6483 + 21.9075i 0.910446 + 1.57694i 0.813435 + 0.581656i \(0.197595\pi\)
0.0970118 + 0.995283i \(0.469072\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) −10.7207 −0.763816 −0.381908 0.924200i \(-0.624733\pi\)
−0.381908 + 0.924200i \(0.624733\pi\)
\(198\) 0 0
\(199\) 8.76647 0.621439 0.310719 0.950502i \(-0.399430\pi\)
0.310719 + 0.950502i \(0.399430\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) −0.849814 1.47192i −0.0596453 0.103309i
\(204\) 0 0
\(205\) −9.70946 + 16.8173i −0.678138 + 1.17457i
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) 1.24907 2.16345i 0.0864000 0.149649i
\(210\) 0 0
\(211\) 5.26509 + 9.11941i 0.362464 + 0.627806i 0.988366 0.152096i \(-0.0486023\pi\)
−0.625902 + 0.779902i \(0.715269\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) −18.6959 −1.27505
\(216\) 0 0
\(217\) 6.98762 0.474351
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) −2.05563 3.56046i −0.138277 0.239502i
\(222\) 0 0
\(223\) −2.83379 + 4.90827i −0.189765 + 0.328682i −0.945172 0.326574i \(-0.894106\pi\)
0.755407 + 0.655256i \(0.227439\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 5.54944 9.61192i 0.368329 0.637965i −0.620975 0.783830i \(-0.713263\pi\)
0.989304 + 0.145865i \(0.0465965\pi\)
\(228\) 0 0
\(229\) −9.82141 17.0112i −0.649017 1.12413i −0.983358 0.181679i \(-0.941847\pi\)
0.334341 0.942452i \(-0.391486\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) −8.96286 −0.587177 −0.293588 0.955932i \(-0.594849\pi\)
−0.293588 + 0.955932i \(0.594849\pi\)
\(234\) 0 0
\(235\) −9.56732 −0.624103
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) −5.61126 9.71899i −0.362963 0.628670i 0.625484 0.780237i \(-0.284901\pi\)
−0.988447 + 0.151567i \(0.951568\pi\)
\(240\) 0 0
\(241\) 3.49312 6.05026i 0.225012 0.389732i −0.731311 0.682044i \(-0.761091\pi\)
0.956323 + 0.292312i \(0.0944246\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) −1.79418 + 3.10761i −0.114626 + 0.198538i
\(246\) 0 0
\(247\) −0.444368 0.769668i −0.0282745 0.0489728i
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 4.62041 0.291638 0.145819 0.989311i \(-0.453418\pi\)
0.145819 + 0.989311i \(0.453418\pi\)
\(252\) 0 0
\(253\) −16.5178 −1.03847
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) −0.712008 1.23323i −0.0444138 0.0769270i 0.842964 0.537970i \(-0.180809\pi\)
−0.887378 + 0.461043i \(0.847475\pi\)
\(258\) 0 0
\(259\) −2.38255 + 4.12669i −0.148044 + 0.256420i
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) −8.13162 + 14.0844i −0.501417 + 0.868480i 0.498582 + 0.866843i \(0.333854\pi\)
−0.999999 + 0.00163692i \(0.999479\pi\)
\(264\) 0 0
\(265\) −0.221840 0.384237i −0.0136275 0.0236035i
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) 18.6538 1.13734 0.568672 0.822564i \(-0.307457\pi\)
0.568672 + 0.822564i \(0.307457\pi\)
\(270\) 0 0
\(271\) −3.96286 −0.240727 −0.120363 0.992730i \(-0.538406\pi\)
−0.120363 + 0.992730i \(0.538406\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 11.0698 + 19.1734i 0.667534 + 1.15620i
\(276\) 0 0
\(277\) 1.16690 2.02112i 0.0701120 0.121438i −0.828838 0.559488i \(-0.810998\pi\)
0.898950 + 0.438051i \(0.144331\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) 13.9975 24.2443i 0.835018 1.44629i −0.0589978 0.998258i \(-0.518790\pi\)
0.894016 0.448035i \(-0.147876\pi\)
\(282\) 0 0
\(283\) 5.16002 + 8.93741i 0.306731 + 0.531274i 0.977645 0.210261i \(-0.0674314\pi\)
−0.670914 + 0.741535i \(0.734098\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 5.41164 0.319439
\(288\) 0 0
\(289\) −0.0975070 −0.00573571
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) −15.3480 26.5834i −0.896637 1.55302i −0.831765 0.555127i \(-0.812670\pi\)
−0.0648718 0.997894i \(-0.520664\pi\)
\(294\) 0 0
\(295\) 15.9258 27.5843i 0.927236 1.60602i
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) −2.93818 + 5.08907i −0.169919 + 0.294309i
\(300\) 0 0
\(301\) 2.60507 + 4.51212i 0.150154 + 0.260074i
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) 13.9098 0.796471
\(306\) 0 0
\(307\) 11.4437 0.653125 0.326563 0.945176i \(-0.394110\pi\)
0.326563 + 0.945176i \(0.394110\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) −5.98143 10.3601i −0.339176 0.587470i 0.645102 0.764096i \(-0.276815\pi\)
−0.984278 + 0.176627i \(0.943481\pi\)
\(312\) 0 0
\(313\) 6.77197 11.7294i 0.382774 0.662985i −0.608683 0.793413i \(-0.708302\pi\)
0.991458 + 0.130429i \(0.0416353\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −14.9814 + 25.9486i −0.841441 + 1.45742i 0.0472355 + 0.998884i \(0.484959\pi\)
−0.888676 + 0.458535i \(0.848374\pi\)
\(318\) 0 0
\(319\) 2.38874 + 4.13741i 0.133744 + 0.231651i
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) 3.65383 0.203304
\(324\) 0 0
\(325\) 7.87636 0.436902
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) 1.33310 + 2.30900i 0.0734964 + 0.127299i
\(330\) 0 0
\(331\) 1.04325 1.80697i 0.0573423 0.0993198i −0.835929 0.548837i \(-0.815071\pi\)
0.893272 + 0.449517i \(0.148404\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) 22.0846 38.2517i 1.20661 2.08992i
\(336\) 0 0
\(337\) 8.10439 + 14.0372i 0.441474 + 0.764655i 0.997799 0.0663093i \(-0.0211224\pi\)
−0.556325 + 0.830965i \(0.687789\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) −19.6414 −1.06364
\(342\) 0 0
\(343\) 1.00000 0.0539949
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) −5.63348 9.75747i −0.302421 0.523808i 0.674263 0.738491i \(-0.264461\pi\)
−0.976684 + 0.214683i \(0.931128\pi\)
\(348\) 0 0
\(349\) 0.0988844 0.171273i 0.00529316 0.00916803i −0.863367 0.504577i \(-0.831648\pi\)
0.868660 + 0.495409i \(0.164982\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) −6.25093 + 10.8269i −0.332703 + 0.576259i −0.983041 0.183386i \(-0.941294\pi\)
0.650338 + 0.759645i \(0.274627\pi\)
\(354\) 0 0
\(355\) 5.16071 + 8.93861i 0.273902 + 0.474412i
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 20.0197 1.05660 0.528299 0.849059i \(-0.322830\pi\)
0.528299 + 0.849059i \(0.322830\pi\)
\(360\) 0 0
\(361\) −18.2101 −0.958429
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) 19.0927 + 33.0695i 0.999357 + 1.73094i
\(366\) 0 0
\(367\) 15.0364 26.0438i 0.784892 1.35947i −0.144171 0.989553i \(-0.546052\pi\)
0.929063 0.369921i \(-0.120615\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) −0.0618219 + 0.107079i −0.00320963 + 0.00555925i
\(372\) 0 0
\(373\) −3.50619 6.07290i −0.181544 0.314443i 0.760863 0.648913i \(-0.224776\pi\)
−0.942406 + 0.334470i \(0.891443\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 1.69963 0.0875353
\(378\) 0 0
\(379\) 19.0741 0.979772 0.489886 0.871787i \(-0.337038\pi\)
0.489886 + 0.871787i \(0.337038\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) −1.60507 2.78007i −0.0820155 0.142055i 0.822100 0.569343i \(-0.192802\pi\)
−0.904116 + 0.427288i \(0.859469\pi\)
\(384\) 0 0
\(385\) 5.04325 8.73517i 0.257028 0.445185i
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) 2.56801 4.44793i 0.130203 0.225519i −0.793552 0.608503i \(-0.791770\pi\)
0.923755 + 0.382984i \(0.125104\pi\)
\(390\) 0 0
\(391\) −12.0796 20.9225i −0.610893 1.05810i
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) 25.4290 1.27947
\(396\) 0 0
\(397\) 22.9381 1.15123 0.575615 0.817721i \(-0.304763\pi\)
0.575615 + 0.817721i \(0.304763\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) −9.10507 15.7705i −0.454686 0.787539i 0.543984 0.839095i \(-0.316915\pi\)
−0.998670 + 0.0515566i \(0.983582\pi\)
\(402\) 0 0
\(403\) −3.49381 + 6.05146i −0.174039 + 0.301445i
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 6.69708 11.5997i 0.331962 0.574975i
\(408\) 0 0
\(409\) 7.66621 + 13.2783i 0.379070 + 0.656568i 0.990927 0.134400i \(-0.0429108\pi\)
−0.611858 + 0.790968i \(0.709577\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) −8.87636 −0.436777
\(414\) 0 0
\(415\) −14.7527 −0.724182
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) −5.28435 9.15276i −0.258157 0.447142i 0.707591 0.706622i \(-0.249782\pi\)
−0.965748 + 0.259481i \(0.916449\pi\)
\(420\) 0 0
\(421\) 18.0858 31.3256i 0.881449 1.52671i 0.0317181 0.999497i \(-0.489902\pi\)
0.849731 0.527217i \(-0.176765\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) −16.1909 + 28.0434i −0.785374 + 1.36031i
\(426\) 0 0
\(427\) −1.93818 3.35702i −0.0937950 0.162458i
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 35.0989 1.69065 0.845327 0.534249i \(-0.179406\pi\)
0.845327 + 0.534249i \(0.179406\pi\)
\(432\) 0 0
\(433\) −41.1730 −1.97865 −0.989324 0.145731i \(-0.953447\pi\)
−0.989324 + 0.145731i \(0.953447\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) −2.61126 4.52284i −0.124914 0.216357i
\(438\) 0 0
\(439\) −2.33929 + 4.05178i −0.111648 + 0.193381i −0.916435 0.400184i \(-0.868946\pi\)
0.804787 + 0.593564i \(0.202280\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) −15.0865 + 26.1306i −0.716781 + 1.24150i 0.245487 + 0.969400i \(0.421052\pi\)
−0.962268 + 0.272102i \(0.912281\pi\)
\(444\) 0 0
\(445\) 17.2410 + 29.8623i 0.817303 + 1.41561i
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) −0.333792 −0.0157526 −0.00787632 0.999969i \(-0.502507\pi\)
−0.00787632 + 0.999969i \(0.502507\pi\)
\(450\) 0 0
\(451\) −15.2115 −0.716283
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) −1.79418 3.10761i −0.0841125 0.145687i
\(456\) 0 0
\(457\) 9.65452 16.7221i 0.451619 0.782227i −0.546868 0.837219i \(-0.684180\pi\)
0.998487 + 0.0549917i \(0.0175132\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 19.5538 33.8681i 0.910710 1.57740i 0.0976463 0.995221i \(-0.468869\pi\)
0.813064 0.582175i \(-0.197798\pi\)
\(462\) 0 0
\(463\) 10.9382 + 18.9455i 0.508340 + 0.880471i 0.999953 + 0.00965741i \(0.00307410\pi\)
−0.491613 + 0.870814i \(0.663593\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) −12.3200 −0.570103 −0.285052 0.958512i \(-0.592011\pi\)
−0.285052 + 0.958512i \(0.592011\pi\)
\(468\) 0 0
\(469\) −12.3090 −0.568378
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) −7.32258 12.6831i −0.336693 0.583169i
\(474\) 0 0
\(475\) −3.50000 + 6.06218i −0.160591 + 0.278152i
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) −6.74474 + 11.6822i −0.308175 + 0.533775i −0.977963 0.208777i \(-0.933052\pi\)
0.669788 + 0.742552i \(0.266385\pi\)
\(480\) 0 0
\(481\) −2.38255 4.12669i −0.108635 0.188161i
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 26.2719 1.19295
\(486\) 0 0
\(487\) −7.54394 −0.341849 −0.170924 0.985284i \(-0.554675\pi\)
−0.170924 + 0.985284i \(0.554675\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) 8.06979 + 13.9773i 0.364185 + 0.630786i 0.988645 0.150270i \(-0.0480143\pi\)
−0.624460 + 0.781057i \(0.714681\pi\)
\(492\) 0 0
\(493\) −3.49381 + 6.05146i −0.157353 + 0.272544i
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 1.43818 2.49100i 0.0645111 0.111737i
\(498\) 0 0
\(499\) −15.4327 26.7302i −0.690862 1.19661i −0.971556 0.236810i \(-0.923898\pi\)
0.280694 0.959797i \(-0.409435\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) 24.6304 1.09822 0.549109 0.835751i \(-0.314967\pi\)
0.549109 + 0.835751i \(0.314967\pi\)
\(504\) 0 0
\(505\) −12.4327 −0.553247
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) 6.79487 + 11.7691i 0.301177 + 0.521654i 0.976403 0.215957i \(-0.0692870\pi\)
−0.675226 + 0.737611i \(0.735954\pi\)
\(510\) 0 0
\(511\) 5.32072 9.21576i 0.235375 0.407681i
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) −28.4851 + 49.3376i −1.25520 + 2.17407i
\(516\) 0 0
\(517\) −3.74721 6.49036i −0.164802 0.285446i
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 39.1730 1.71620 0.858100 0.513482i \(-0.171645\pi\)
0.858100 + 0.513482i \(0.171645\pi\)
\(522\) 0 0
\(523\) −19.1236 −0.836219 −0.418109 0.908397i \(-0.637307\pi\)
−0.418109 + 0.908397i \(0.637307\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −14.3640 24.8791i −0.625705 1.08375i
\(528\) 0 0
\(529\) −5.76578 + 9.98663i −0.250686 + 0.434201i
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) −2.70582 + 4.68661i −0.117202 + 0.203000i
\(534\) 0 0
\(535\) 9.60507 + 16.6365i 0.415264 + 0.719258i
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) −2.81089 −0.121074
\(540\) 0 0
\(541\) 2.53018 0.108781 0.0543906 0.998520i \(-0.482678\pi\)
0.0543906 + 0.998520i \(0.482678\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) 33.8454 + 58.6220i 1.44978 + 2.51109i
\(546\) 0 0
\(547\) 8.92580 15.4599i 0.381640 0.661019i −0.609657 0.792665i \(-0.708693\pi\)
0.991297 + 0.131646i \(0.0420262\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) −0.755260 + 1.30815i −0.0321752 + 0.0557290i
\(552\) 0 0
\(553\) −3.54325 6.13709i −0.150674 0.260976i
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) −41.3607 −1.75251 −0.876255 0.481847i \(-0.839966\pi\)
−0.876255 + 0.481847i \(0.839966\pi\)
\(558\) 0 0
\(559\) −5.21015 −0.220366
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) 10.3683 + 17.9584i 0.436972 + 0.756858i 0.997454 0.0713087i \(-0.0227175\pi\)
−0.560482 + 0.828166i \(0.689384\pi\)
\(564\) 0 0
\(565\) −33.2843 + 57.6501i −1.40028 + 2.42536i
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) −0.134164 + 0.232379i −0.00562446 + 0.00974185i −0.868824 0.495121i \(-0.835124\pi\)
0.863199 + 0.504863i \(0.168457\pi\)
\(570\) 0 0
\(571\) 17.9684 + 31.1221i 0.751953 + 1.30242i 0.946875 + 0.321601i \(0.104221\pi\)
−0.194923 + 0.980819i \(0.562446\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 46.2843 1.93019
\(576\) 0 0
\(577\) 5.43130 0.226108 0.113054 0.993589i \(-0.463937\pi\)
0.113054 + 0.993589i \(0.463937\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) 2.05563 + 3.56046i 0.0852820 + 0.147713i
\(582\) 0 0
\(583\) 0.173775 0.300987i 0.00719702 0.0124656i
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) −17.5822 + 30.4532i −0.725694 + 1.25694i 0.232994 + 0.972478i \(0.425148\pi\)
−0.958688 + 0.284461i \(0.908185\pi\)
\(588\) 0 0
\(589\) −3.10507 5.37815i −0.127942 0.221603i
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) 33.5068 1.37596 0.687980 0.725730i \(-0.258498\pi\)
0.687980 + 0.725730i \(0.258498\pi\)
\(594\) 0 0
\(595\) 14.7527 0.604802
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) −3.12364 5.41031i −0.127629 0.221059i 0.795129 0.606441i \(-0.207403\pi\)
−0.922757 + 0.385381i \(0.874070\pi\)
\(600\) 0 0
\(601\) −11.2040 + 19.4058i −0.457019 + 0.791580i −0.998802 0.0489384i \(-0.984416\pi\)
0.541783 + 0.840519i \(0.317750\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) 5.55996 9.63014i 0.226045 0.391521i
\(606\) 0 0
\(607\) 7.47524 + 12.9475i 0.303411 + 0.525523i 0.976906 0.213669i \(-0.0685413\pi\)
−0.673496 + 0.739191i \(0.735208\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) −2.66621 −0.107863
\(612\) 0 0
\(613\) 35.1978 1.42162 0.710812 0.703382i \(-0.248328\pi\)
0.710812 + 0.703382i \(0.248328\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) −1.00619 1.74277i −0.0405077 0.0701614i 0.845061 0.534670i \(-0.179564\pi\)
−0.885568 + 0.464509i \(0.846231\pi\)
\(618\) 0 0
\(619\) 19.6909 34.1056i 0.791444 1.37082i −0.133629 0.991031i \(-0.542663\pi\)
0.925073 0.379789i \(-0.124004\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 4.80470 8.32199i 0.192496 0.333413i
\(624\) 0 0
\(625\) 1.17240 + 2.03065i 0.0468959 + 0.0812261i
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 19.5906 0.781126
\(630\) 0 0
\(631\) −44.3832 −1.76687 −0.883433 0.468558i \(-0.844774\pi\)
−0.883433 + 0.468558i \(0.844774\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) 17.9196 + 31.0377i 0.711118 + 1.23169i
\(636\) 0 0
\(637\) −0.500000 + 0.866025i −0.0198107 + 0.0343132i
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) −7.49312 + 12.9785i −0.295961 + 0.512619i −0.975208 0.221291i \(-0.928973\pi\)
0.679247 + 0.733909i \(0.262306\pi\)
\(642\) 0 0
\(643\) −5.32691 9.22649i −0.210073 0.363857i 0.741664 0.670771i \(-0.234037\pi\)
−0.951737 + 0.306914i \(0.900703\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 2.12955 0.0837213 0.0418606 0.999123i \(-0.486671\pi\)
0.0418606 + 0.999123i \(0.486671\pi\)
\(648\) 0 0
\(649\) 24.9505 0.979392
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 5.58582 + 9.67492i 0.218590 + 0.378609i 0.954377 0.298604i \(-0.0965210\pi\)
−0.735787 + 0.677213i \(0.763188\pi\)
\(654\) 0 0
\(655\) −28.8022 + 49.8868i −1.12539 + 1.94924i
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) 5.65452 9.79391i 0.220269 0.381517i −0.734621 0.678478i \(-0.762640\pi\)
0.954890 + 0.296961i \(0.0959733\pi\)
\(660\) 0 0
\(661\) −16.1785 28.0220i −0.629271 1.08993i −0.987698 0.156372i \(-0.950020\pi\)
0.358427 0.933558i \(-0.383313\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 3.18911 0.123668
\(666\) 0 0
\(667\) 9.98762 0.386722
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 5.44801 + 9.43623i 0.210318 + 0.364282i
\(672\) 0 0
\(673\) 12.0803 20.9237i 0.465662 0.806550i −0.533569 0.845756i \(-0.679150\pi\)
0.999231 + 0.0392063i \(0.0124830\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 12.5371 21.7148i 0.481838 0.834569i −0.517944 0.855414i \(-0.673303\pi\)
0.999783 + 0.0208457i \(0.00663587\pi\)
\(678\) 0 0
\(679\) −3.66071 6.34053i −0.140485 0.243327i
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) −47.6784 −1.82436 −0.912182 0.409785i \(-0.865604\pi\)
−0.912182 + 0.409785i \(0.865604\pi\)
\(684\) 0 0
\(685\) 46.6043 1.78066
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) −0.0618219 0.107079i −0.00235523 0.00407937i
\(690\) 0 0
\(691\) −12.3400 + 21.3735i −0.469435 + 0.813085i −0.999389 0.0349408i \(-0.988876\pi\)
0.529954 + 0.848026i \(0.322209\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 1.99381 3.45338i 0.0756295 0.130994i
\(696\) 0 0
\(697\) −11.1243 19.2679i −0.421364 0.729824i
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) 29.6784 1.12094 0.560469 0.828175i \(-0.310621\pi\)
0.560469 + 0.828175i \(0.310621\pi\)
\(702\) 0 0
\(703\) 4.23491 0.159723
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 1.73236 + 3.00054i 0.0651521 + 0.112847i
\(708\) 0 0
\(709\) 14.6291 25.3383i 0.549406 0.951599i −0.448909 0.893577i \(-0.648187\pi\)
0.998315 0.0580220i \(-0.0184794\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) −20.5309 + 35.5605i −0.768887 + 1.33175i
\(714\) 0 0
\(715\) 5.04325 + 8.73517i 0.188607 + 0.326677i
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) 1.07413 0.0400581 0.0200291 0.999799i \(-0.493624\pi\)
0.0200291 + 0.999799i \(0.493624\pi\)
\(720\) 0 0
\(721\) 15.8764 0.591266
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) −6.69344 11.5934i −0.248588 0.430567i
\(726\) 0 0
\(727\) 12.7163 22.0253i 0.471623 0.816875i −0.527850 0.849338i \(-0.677002\pi\)
0.999473 + 0.0324628i \(0.0103350\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) 10.7101 18.5505i 0.396129 0.686116i
\(732\) 0 0
\(733\) 5.69777 + 9.86883i 0.210452 + 0.364513i 0.951856 0.306545i \(-0.0991731\pi\)
−0.741404 + 0.671059i \(0.765840\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 34.5994 1.27448
\(738\) 0 0
\(739\) 29.9395 1.10134 0.550671 0.834723i \(-0.314372\pi\)
0.550671 + 0.834723i \(0.314372\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 9.50069 + 16.4557i 0.348546 + 0.603700i 0.985991 0.166796i \(-0.0533420\pi\)
−0.637445 + 0.770496i \(0.720009\pi\)
\(744\) 0 0
\(745\) 15.1298 26.2055i 0.554311 0.960096i
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) 2.67673 4.63623i 0.0978055 0.169404i
\(750\) 0 0
\(751\) 0.0130684 + 0.0226352i 0.000476873 + 0.000825969i 0.866264 0.499587i \(-0.166515\pi\)
−0.865787 + 0.500413i \(0.833182\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 53.2929 1.93953
\(756\) 0 0
\(757\) −13.6910 −0.497607 −0.248803 0.968554i \(-0.580037\pi\)
−0.248803 + 0.968554i \(0.580037\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) −7.32141 12.6811i −0.265401 0.459688i 0.702268 0.711913i \(-0.252171\pi\)
−0.967669 + 0.252225i \(0.918838\pi\)
\(762\) 0 0
\(763\) 9.43199 16.3367i 0.341461 0.591428i
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 4.43818 7.68715i 0.160253 0.277567i
\(768\) 0 0
\(769\) −24.5672 42.5517i −0.885918 1.53445i −0.844658 0.535306i \(-0.820196\pi\)
−0.0412592 0.999148i \(-0.513137\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) −12.4413 −0.447484 −0.223742 0.974648i \(-0.571827\pi\)
−0.223742 + 0.974648i \(0.571827\pi\)
\(774\) 0 0
\(775\) 55.0370 1.97699
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) −2.40476 4.16516i −0.0861594 0.149232i
\(780\) 0 0
\(781\) −4.04256 + 7.00193i −0.144654 + 0.250549i
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) −5.18292 + 8.97708i −0.184986 + 0.320406i
\(786\) 0 0
\(787\) −16.4567 28.5038i −0.586617 1.01605i −0.994672 0.103093i \(-0.967126\pi\)
0.408055 0.912957i \(-0.366207\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 18.5512 0.659606
\(792\) 0 0
\(793\) 3.87636 0.137653
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 13.1989 <