Properties

Label 3240.2.q.be.1081.1
Level $3240$
Weight $2$
Character 3240.1081
Analytic conductor $25.872$
Analytic rank $0$
Dimension $4$
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [3240,2,Mod(1081,3240)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(3240, 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("3240.1081");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 3240 = 2^{3} \cdot 3^{4} \cdot 5 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 3240.q (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: \(25.8715302549\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\Q(\sqrt{-3}, \sqrt{-19})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{4} - x^{3} - 4x^{2} - 5x + 25 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 3 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 1081.1
Root \(-1.63746 - 1.52274i\) of defining polynomial
Character \(\chi\) \(=\) 3240.1081
Dual form 3240.2.q.be.2161.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.500000 - 0.866025i) q^{5} +(-2.13746 - 3.70219i) q^{7} +O(q^{10})\) \(q+(0.500000 - 0.866025i) q^{5} +(-2.13746 - 3.70219i) q^{7} +(-0.637459 - 1.10411i) q^{11} +(-3.13746 + 5.43424i) q^{13} -2.00000 q^{17} +1.00000 q^{19} +(0.137459 - 0.238085i) q^{23} +(-0.500000 - 0.866025i) q^{25} +(-0.637459 - 1.10411i) q^{29} +(0.637459 - 1.10411i) q^{31} -4.27492 q^{35} +4.54983 q^{37} +(-3.77492 + 6.53835i) q^{41} +(-2.00000 - 3.46410i) q^{43} +(3.13746 + 5.43424i) q^{47} +(-5.63746 + 9.76436i) q^{49} -8.27492 q^{53} -1.27492 q^{55} +(-6.50000 + 11.2583i) q^{59} +(3.27492 + 5.67232i) q^{61} +(3.13746 + 5.43424i) q^{65} +(7.27492 - 12.6005i) q^{67} +0.725083 q^{71} -15.0997 q^{73} +(-2.72508 + 4.71998i) q^{77} +(2.27492 + 3.94027i) q^{79} +(6.27492 + 10.8685i) q^{83} +(-1.00000 + 1.73205i) q^{85} +9.82475 q^{89} +26.8248 q^{91} +(0.500000 - 0.866025i) q^{95} +(-8.00000 - 13.8564i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q + 2 q^{5} - q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 4 q + 2 q^{5} - q^{7} + 5 q^{11} - 5 q^{13} - 8 q^{17} + 4 q^{19} - 7 q^{23} - 2 q^{25} + 5 q^{29} - 5 q^{31} - 2 q^{35} - 12 q^{37} - 8 q^{43} + 5 q^{47} - 15 q^{49} - 18 q^{53} + 10 q^{55} - 26 q^{59} - 2 q^{61} + 5 q^{65} + 14 q^{67} + 18 q^{71} - 26 q^{77} - 6 q^{79} + 10 q^{83} - 4 q^{85} - 6 q^{89} + 62 q^{91} + 2 q^{95} - 32 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/3240\mathbb{Z}\right)^\times\).

\(n\) \(1297\) \(1621\) \(2431\) \(3161\)
\(\chi(n)\) \(1\) \(1\) \(1\) \(e\left(\frac{1}{3}\right)\)

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 0
\(4\) 0 0
\(5\) 0.500000 0.866025i 0.223607 0.387298i
\(6\) 0 0
\(7\) −2.13746 3.70219i −0.807883 1.39930i −0.914327 0.404976i \(-0.867280\pi\)
0.106444 0.994319i \(-0.466054\pi\)
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) −0.637459 1.10411i −0.192201 0.332902i 0.753778 0.657129i \(-0.228229\pi\)
−0.945979 + 0.324227i \(0.894896\pi\)
\(12\) 0 0
\(13\) −3.13746 + 5.43424i −0.870174 + 1.50719i −0.00835861 + 0.999965i \(0.502661\pi\)
−0.861816 + 0.507221i \(0.830673\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) −2.00000 −0.485071 −0.242536 0.970143i \(-0.577979\pi\)
−0.242536 + 0.970143i \(0.577979\pi\)
\(18\) 0 0
\(19\) 1.00000 0.229416 0.114708 0.993399i \(-0.463407\pi\)
0.114708 + 0.993399i \(0.463407\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) 0.137459 0.238085i 0.0286621 0.0496442i −0.851339 0.524617i \(-0.824209\pi\)
0.880001 + 0.474972i \(0.157542\pi\)
\(24\) 0 0
\(25\) −0.500000 0.866025i −0.100000 0.173205i
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) −0.637459 1.10411i −0.118373 0.205028i 0.800750 0.598999i \(-0.204435\pi\)
−0.919123 + 0.393970i \(0.871101\pi\)
\(30\) 0 0
\(31\) 0.637459 1.10411i 0.114491 0.198304i −0.803085 0.595864i \(-0.796810\pi\)
0.917576 + 0.397560i \(0.130143\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) −4.27492 −0.722593
\(36\) 0 0
\(37\) 4.54983 0.747988 0.373994 0.927431i \(-0.377988\pi\)
0.373994 + 0.927431i \(0.377988\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) −3.77492 + 6.53835i −0.589543 + 1.02112i 0.404749 + 0.914428i \(0.367359\pi\)
−0.994292 + 0.106691i \(0.965975\pi\)
\(42\) 0 0
\(43\) −2.00000 3.46410i −0.304997 0.528271i 0.672264 0.740312i \(-0.265322\pi\)
−0.977261 + 0.212041i \(0.931989\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 3.13746 + 5.43424i 0.457645 + 0.792665i 0.998836 0.0482349i \(-0.0153596\pi\)
−0.541191 + 0.840900i \(0.682026\pi\)
\(48\) 0 0
\(49\) −5.63746 + 9.76436i −0.805351 + 1.39491i
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) −8.27492 −1.13665 −0.568324 0.822805i \(-0.692408\pi\)
−0.568324 + 0.822805i \(0.692408\pi\)
\(54\) 0 0
\(55\) −1.27492 −0.171910
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) −6.50000 + 11.2583i −0.846228 + 1.46571i 0.0383226 + 0.999265i \(0.487799\pi\)
−0.884551 + 0.466444i \(0.845535\pi\)
\(60\) 0 0
\(61\) 3.27492 + 5.67232i 0.419310 + 0.726267i 0.995870 0.0907882i \(-0.0289386\pi\)
−0.576560 + 0.817055i \(0.695605\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) 3.13746 + 5.43424i 0.389154 + 0.674034i
\(66\) 0 0
\(67\) 7.27492 12.6005i 0.888773 1.53940i 0.0474449 0.998874i \(-0.484892\pi\)
0.841328 0.540525i \(-0.181775\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 0.725083 0.0860515 0.0430257 0.999074i \(-0.486300\pi\)
0.0430257 + 0.999074i \(0.486300\pi\)
\(72\) 0 0
\(73\) −15.0997 −1.76728 −0.883641 0.468165i \(-0.844915\pi\)
−0.883641 + 0.468165i \(0.844915\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) −2.72508 + 4.71998i −0.310552 + 0.537892i
\(78\) 0 0
\(79\) 2.27492 + 3.94027i 0.255948 + 0.443315i 0.965153 0.261688i \(-0.0842790\pi\)
−0.709204 + 0.705003i \(0.750946\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) 6.27492 + 10.8685i 0.688762 + 1.19297i 0.972239 + 0.233991i \(0.0751787\pi\)
−0.283477 + 0.958979i \(0.591488\pi\)
\(84\) 0 0
\(85\) −1.00000 + 1.73205i −0.108465 + 0.187867i
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 9.82475 1.04142 0.520711 0.853733i \(-0.325667\pi\)
0.520711 + 0.853733i \(0.325667\pi\)
\(90\) 0 0
\(91\) 26.8248 2.81200
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 0.500000 0.866025i 0.0512989 0.0888523i
\(96\) 0 0
\(97\) −8.00000 13.8564i −0.812277 1.40690i −0.911267 0.411816i \(-0.864894\pi\)
0.0989899 0.995088i \(-0.468439\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) 8.63746 + 14.9605i 0.859459 + 1.48863i 0.872445 + 0.488711i \(0.162533\pi\)
−0.0129862 + 0.999916i \(0.504134\pi\)
\(102\) 0 0
\(103\) −8.41238 + 14.5707i −0.828896 + 1.43569i 0.0700089 + 0.997546i \(0.477697\pi\)
−0.898905 + 0.438144i \(0.855636\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 15.0997 1.45974 0.729870 0.683586i \(-0.239581\pi\)
0.729870 + 0.683586i \(0.239581\pi\)
\(108\) 0 0
\(109\) 1.27492 0.122115 0.0610575 0.998134i \(-0.480553\pi\)
0.0610575 + 0.998134i \(0.480553\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) −3.00000 + 5.19615i −0.282216 + 0.488813i −0.971930 0.235269i \(-0.924403\pi\)
0.689714 + 0.724082i \(0.257736\pi\)
\(114\) 0 0
\(115\) −0.137459 0.238085i −0.0128181 0.0222016i
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) 4.27492 + 7.40437i 0.391881 + 0.678758i
\(120\) 0 0
\(121\) 4.68729 8.11863i 0.426118 0.738057i
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) −1.00000 −0.0894427
\(126\) 0 0
\(127\) 3.72508 0.330548 0.165274 0.986248i \(-0.447149\pi\)
0.165274 + 0.986248i \(0.447149\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) −6.77492 + 11.7345i −0.591927 + 1.02525i 0.402045 + 0.915620i \(0.368299\pi\)
−0.993973 + 0.109628i \(0.965034\pi\)
\(132\) 0 0
\(133\) −2.13746 3.70219i −0.185341 0.321020i
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) −0.274917 0.476171i −0.0234878 0.0406820i 0.854043 0.520203i \(-0.174144\pi\)
−0.877530 + 0.479521i \(0.840810\pi\)
\(138\) 0 0
\(139\) 4.50000 7.79423i 0.381685 0.661098i −0.609618 0.792695i \(-0.708677\pi\)
0.991303 + 0.131597i \(0.0420106\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 8.00000 0.668994
\(144\) 0 0
\(145\) −1.27492 −0.105876
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) 1.00000 1.73205i 0.0819232 0.141895i −0.822153 0.569267i \(-0.807227\pi\)
0.904076 + 0.427372i \(0.140560\pi\)
\(150\) 0 0
\(151\) 2.36254 + 4.09204i 0.192261 + 0.333006i 0.945999 0.324169i \(-0.105085\pi\)
−0.753738 + 0.657175i \(0.771751\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) −0.637459 1.10411i −0.0512019 0.0886843i
\(156\) 0 0
\(157\) −9.13746 + 15.8265i −0.729249 + 1.26310i 0.227953 + 0.973672i \(0.426797\pi\)
−0.957201 + 0.289423i \(0.906536\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) −1.17525 −0.0926225
\(162\) 0 0
\(163\) 5.45017 0.426890 0.213445 0.976955i \(-0.431532\pi\)
0.213445 + 0.976955i \(0.431532\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) −11.2749 + 19.5287i −0.872479 + 1.51118i −0.0130554 + 0.999915i \(0.504156\pi\)
−0.859424 + 0.511264i \(0.829178\pi\)
\(168\) 0 0
\(169\) −13.1873 22.8411i −1.01441 1.75700i
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) 8.13746 + 14.0945i 0.618680 + 1.07158i 0.989727 + 0.142970i \(0.0456654\pi\)
−0.371047 + 0.928614i \(0.621001\pi\)
\(174\) 0 0
\(175\) −2.13746 + 3.70219i −0.161577 + 0.279859i
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) −3.54983 −0.265327 −0.132664 0.991161i \(-0.542353\pi\)
−0.132664 + 0.991161i \(0.542353\pi\)
\(180\) 0 0
\(181\) 8.72508 0.648530 0.324265 0.945966i \(-0.394883\pi\)
0.324265 + 0.945966i \(0.394883\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 2.27492 3.94027i 0.167255 0.289695i
\(186\) 0 0
\(187\) 1.27492 + 2.20822i 0.0932312 + 0.161481i
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) −9.18729 15.9129i −0.664769 1.15141i −0.979348 0.202183i \(-0.935197\pi\)
0.314579 0.949231i \(-0.398137\pi\)
\(192\) 0 0
\(193\) −2.00000 + 3.46410i −0.143963 + 0.249351i −0.928986 0.370116i \(-0.879318\pi\)
0.785022 + 0.619467i \(0.212651\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) −15.3746 −1.09539 −0.547697 0.836677i \(-0.684495\pi\)
−0.547697 + 0.836677i \(0.684495\pi\)
\(198\) 0 0
\(199\) 8.00000 0.567105 0.283552 0.958957i \(-0.408487\pi\)
0.283552 + 0.958957i \(0.408487\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) −2.72508 + 4.71998i −0.191263 + 0.331278i
\(204\) 0 0
\(205\) 3.77492 + 6.53835i 0.263652 + 0.456658i
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) −0.637459 1.10411i −0.0440939 0.0763729i
\(210\) 0 0
\(211\) −7.04983 + 12.2107i −0.485331 + 0.840617i −0.999858 0.0168567i \(-0.994634\pi\)
0.514527 + 0.857474i \(0.327967\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) −4.00000 −0.272798
\(216\) 0 0
\(217\) −5.45017 −0.369981
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) 6.27492 10.8685i 0.422097 0.731093i
\(222\) 0 0
\(223\) −4.00000 6.92820i −0.267860 0.463947i 0.700449 0.713702i \(-0.252983\pi\)
−0.968309 + 0.249756i \(0.919650\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) −11.2749 19.5287i −0.748343 1.29617i −0.948617 0.316427i \(-0.897517\pi\)
0.200274 0.979740i \(-0.435817\pi\)
\(228\) 0 0
\(229\) 3.27492 5.67232i 0.216413 0.374838i −0.737296 0.675570i \(-0.763898\pi\)
0.953709 + 0.300732i \(0.0972310\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) −21.0997 −1.38229 −0.691143 0.722718i \(-0.742892\pi\)
−0.691143 + 0.722718i \(0.742892\pi\)
\(234\) 0 0
\(235\) 6.27492 0.409330
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) −14.2749 + 24.7249i −0.923368 + 1.59932i −0.129202 + 0.991618i \(0.541242\pi\)
−0.794166 + 0.607701i \(0.792092\pi\)
\(240\) 0 0
\(241\) 8.36254 + 14.4843i 0.538679 + 0.933019i 0.998976 + 0.0452537i \(0.0144096\pi\)
−0.460297 + 0.887765i \(0.652257\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) 5.63746 + 9.76436i 0.360164 + 0.623822i
\(246\) 0 0
\(247\) −3.13746 + 5.43424i −0.199632 + 0.345772i
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) −26.2749 −1.65846 −0.829229 0.558909i \(-0.811220\pi\)
−0.829229 + 0.558909i \(0.811220\pi\)
\(252\) 0 0
\(253\) −0.350497 −0.0220355
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) −13.5498 + 23.4690i −0.845215 + 1.46396i 0.0402185 + 0.999191i \(0.487195\pi\)
−0.885434 + 0.464765i \(0.846139\pi\)
\(258\) 0 0
\(259\) −9.72508 16.8443i −0.604287 1.04666i
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) −4.13746 7.16629i −0.255127 0.441892i 0.709803 0.704400i \(-0.248784\pi\)
−0.964930 + 0.262508i \(0.915450\pi\)
\(264\) 0 0
\(265\) −4.13746 + 7.16629i −0.254162 + 0.440222i
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) −26.9244 −1.64161 −0.820805 0.571208i \(-0.806475\pi\)
−0.820805 + 0.571208i \(0.806475\pi\)
\(270\) 0 0
\(271\) 28.5498 1.73428 0.867139 0.498065i \(-0.165956\pi\)
0.867139 + 0.498065i \(0.165956\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) −0.637459 + 1.10411i −0.0384402 + 0.0665804i
\(276\) 0 0
\(277\) −8.86254 15.3504i −0.532499 0.922314i −0.999280 0.0379418i \(-0.987920\pi\)
0.466781 0.884373i \(-0.345413\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) 14.4124 + 24.9630i 0.859770 + 1.48917i 0.872148 + 0.489242i \(0.162727\pi\)
−0.0123776 + 0.999923i \(0.503940\pi\)
\(282\) 0 0
\(283\) 13.2749 22.9928i 0.789112 1.36678i −0.137400 0.990516i \(-0.543874\pi\)
0.926512 0.376266i \(-0.122792\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 32.2749 1.90513
\(288\) 0 0
\(289\) −13.0000 −0.764706
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) 9.13746 15.8265i 0.533816 0.924596i −0.465404 0.885099i \(-0.654091\pi\)
0.999220 0.0394979i \(-0.0125759\pi\)
\(294\) 0 0
\(295\) 6.50000 + 11.2583i 0.378445 + 0.655485i
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 0.862541 + 1.49397i 0.0498821 + 0.0863983i
\(300\) 0 0
\(301\) −8.54983 + 14.8087i −0.492804 + 0.853562i
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) 6.54983 0.375042
\(306\) 0 0
\(307\) −29.0997 −1.66081 −0.830403 0.557163i \(-0.811890\pi\)
−0.830403 + 0.557163i \(0.811890\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 13.4622 23.3172i 0.763372 1.32220i −0.177731 0.984079i \(-0.556876\pi\)
0.941103 0.338120i \(-0.109791\pi\)
\(312\) 0 0
\(313\) −4.00000 6.92820i −0.226093 0.391605i 0.730554 0.682855i \(-0.239262\pi\)
−0.956647 + 0.291250i \(0.905929\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −1.13746 1.97014i −0.0638860 0.110654i 0.832313 0.554306i \(-0.187016\pi\)
−0.896199 + 0.443652i \(0.853683\pi\)
\(318\) 0 0
\(319\) −0.812707 + 1.40765i −0.0455029 + 0.0788133i
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) −2.00000 −0.111283
\(324\) 0 0
\(325\) 6.27492 0.348070
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) 13.4124 23.2309i 0.739448 1.28076i
\(330\) 0 0
\(331\) −1.91238 3.31233i −0.105114 0.182062i 0.808671 0.588261i \(-0.200187\pi\)
−0.913785 + 0.406199i \(0.866854\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) −7.27492 12.6005i −0.397471 0.688440i
\(336\) 0 0
\(337\) −10.2749 + 17.7967i −0.559710 + 0.969447i 0.437810 + 0.899068i \(0.355754\pi\)
−0.997520 + 0.0703793i \(0.977579\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) −1.62541 −0.0880211
\(342\) 0 0
\(343\) 18.2749 0.986753
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 7.00000 12.1244i 0.375780 0.650870i −0.614664 0.788789i \(-0.710708\pi\)
0.990443 + 0.137920i \(0.0440416\pi\)
\(348\) 0 0
\(349\) 4.91238 + 8.50848i 0.262953 + 0.455449i 0.967025 0.254680i \(-0.0819701\pi\)
−0.704072 + 0.710129i \(0.748637\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) −4.27492 7.40437i −0.227531 0.394095i 0.729545 0.683933i \(-0.239732\pi\)
−0.957076 + 0.289838i \(0.906399\pi\)
\(354\) 0 0
\(355\) 0.362541 0.627940i 0.0192417 0.0333276i
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 21.8248 1.15187 0.575933 0.817497i \(-0.304639\pi\)
0.575933 + 0.817497i \(0.304639\pi\)
\(360\) 0 0
\(361\) −18.0000 −0.947368
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) −7.54983 + 13.0767i −0.395176 + 0.684466i
\(366\) 0 0
\(367\) 1.27492 + 2.20822i 0.0665501 + 0.115268i 0.897381 0.441257i \(-0.145467\pi\)
−0.830830 + 0.556526i \(0.812134\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) 17.6873 + 30.6353i 0.918279 + 1.59051i
\(372\) 0 0
\(373\) −0.450166 + 0.779710i −0.0233087 + 0.0403718i −0.877444 0.479678i \(-0.840753\pi\)
0.854136 + 0.520050i \(0.174087\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 8.00000 0.412021
\(378\) 0 0
\(379\) 1.72508 0.0886116 0.0443058 0.999018i \(-0.485892\pi\)
0.0443058 + 0.999018i \(0.485892\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) −17.6873 + 30.6353i −0.903778 + 1.56539i −0.0812298 + 0.996695i \(0.525885\pi\)
−0.822549 + 0.568695i \(0.807449\pi\)
\(384\) 0 0
\(385\) 2.72508 + 4.71998i 0.138883 + 0.240553i
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) −0.725083 1.25588i −0.0367632 0.0636757i 0.847058 0.531500i \(-0.178371\pi\)
−0.883822 + 0.467824i \(0.845038\pi\)
\(390\) 0 0
\(391\) −0.274917 + 0.476171i −0.0139032 + 0.0240810i
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) 4.54983 0.228927
\(396\) 0 0
\(397\) −23.0997 −1.15934 −0.579670 0.814852i \(-0.696818\pi\)
−0.579670 + 0.814852i \(0.696818\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 7.86254 13.6183i 0.392637 0.680067i −0.600160 0.799880i \(-0.704896\pi\)
0.992796 + 0.119814i \(0.0382297\pi\)
\(402\) 0 0
\(403\) 4.00000 + 6.92820i 0.199254 + 0.345118i
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) −2.90033 5.02352i −0.143764 0.249007i
\(408\) 0 0
\(409\) 3.58762 6.21395i 0.177397 0.307260i −0.763591 0.645700i \(-0.776566\pi\)
0.940988 + 0.338440i \(0.109899\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) 55.5739 2.73461
\(414\) 0 0
\(415\) 12.5498 0.616047
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 10.5498 18.2728i 0.515393 0.892687i −0.484447 0.874820i \(-0.660979\pi\)
0.999840 0.0178666i \(-0.00568743\pi\)
\(420\) 0 0
\(421\) 12.3625 + 21.4125i 0.602513 + 1.04358i 0.992439 + 0.122738i \(0.0391673\pi\)
−0.389926 + 0.920846i \(0.627499\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) 1.00000 + 1.73205i 0.0485071 + 0.0840168i
\(426\) 0 0
\(427\) 14.0000 24.2487i 0.677507 1.17348i
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) −1.27492 −0.0614106 −0.0307053 0.999528i \(-0.509775\pi\)
−0.0307053 + 0.999528i \(0.509775\pi\)
\(432\) 0 0
\(433\) −2.54983 −0.122537 −0.0612686 0.998121i \(-0.519515\pi\)
−0.0612686 + 0.998121i \(0.519515\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 0.137459 0.238085i 0.00657554 0.0113892i
\(438\) 0 0
\(439\) −6.18729 10.7167i −0.295303 0.511480i 0.679752 0.733442i \(-0.262087\pi\)
−0.975055 + 0.221962i \(0.928754\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) −2.27492 3.94027i −0.108085 0.187208i 0.806910 0.590675i \(-0.201138\pi\)
−0.914994 + 0.403467i \(0.867805\pi\)
\(444\) 0 0
\(445\) 4.91238 8.50848i 0.232869 0.403341i
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) 13.5498 0.639456 0.319728 0.947509i \(-0.396408\pi\)
0.319728 + 0.947509i \(0.396408\pi\)
\(450\) 0 0
\(451\) 9.62541 0.453243
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) 13.4124 23.2309i 0.628782 1.08908i
\(456\) 0 0
\(457\) −8.00000 13.8564i −0.374224 0.648175i 0.615986 0.787757i \(-0.288758\pi\)
−0.990211 + 0.139581i \(0.955424\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 7.18729 + 12.4488i 0.334746 + 0.579796i 0.983436 0.181256i \(-0.0580163\pi\)
−0.648690 + 0.761052i \(0.724683\pi\)
\(462\) 0 0
\(463\) 13.2371 22.9274i 0.615181 1.06553i −0.375171 0.926956i \(-0.622416\pi\)
0.990353 0.138570i \(-0.0442506\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) −20.1993 −0.934714 −0.467357 0.884069i \(-0.654794\pi\)
−0.467357 + 0.884069i \(0.654794\pi\)
\(468\) 0 0
\(469\) −62.1993 −2.87210
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) −2.54983 + 4.41644i −0.117242 + 0.203068i
\(474\) 0 0
\(475\) −0.500000 0.866025i −0.0229416 0.0397360i
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) 1.63746 + 2.83616i 0.0748174 + 0.129588i 0.901007 0.433805i \(-0.142829\pi\)
−0.826189 + 0.563392i \(0.809496\pi\)
\(480\) 0 0
\(481\) −14.2749 + 24.7249i −0.650880 + 1.12736i
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) −16.0000 −0.726523
\(486\) 0 0
\(487\) −29.7251 −1.34697 −0.673486 0.739200i \(-0.735204\pi\)
−0.673486 + 0.739200i \(0.735204\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) 7.50000 12.9904i 0.338470 0.586248i −0.645675 0.763612i \(-0.723424\pi\)
0.984145 + 0.177365i \(0.0567572\pi\)
\(492\) 0 0
\(493\) 1.27492 + 2.20822i 0.0574194 + 0.0994533i
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) −1.54983 2.68439i −0.0695196 0.120411i
\(498\) 0 0
\(499\) 7.22508 12.5142i 0.323439 0.560213i −0.657756 0.753231i \(-0.728494\pi\)
0.981195 + 0.193018i \(0.0618276\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(504\) 0 0
\(505\) 17.2749 0.768724
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) −16.0997 + 27.8854i −0.713605 + 1.23600i 0.249890 + 0.968274i \(0.419606\pi\)
−0.963495 + 0.267726i \(0.913728\pi\)
\(510\) 0 0
\(511\) 32.2749 + 55.9018i 1.42776 + 2.47295i
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) 8.41238 + 14.5707i 0.370694 + 0.642060i
\(516\) 0 0
\(517\) 4.00000 6.92820i 0.175920 0.304702i
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) −25.9244 −1.13577 −0.567885 0.823108i \(-0.692238\pi\)
−0.567885 + 0.823108i \(0.692238\pi\)
\(522\) 0 0
\(523\) 5.64950 0.247036 0.123518 0.992342i \(-0.460582\pi\)
0.123518 + 0.992342i \(0.460582\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −1.27492 + 2.20822i −0.0555363 + 0.0961916i
\(528\) 0 0
\(529\) 11.4622 + 19.8531i 0.498357 + 0.863180i
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) −23.6873 41.0276i −1.02601 1.77710i
\(534\) 0 0
\(535\) 7.54983 13.0767i 0.326408 0.565355i
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) 14.3746 0.619157
\(540\) 0 0
\(541\) −8.92442 −0.383691 −0.191845 0.981425i \(-0.561447\pi\)
−0.191845 + 0.981425i \(0.561447\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) 0.637459 1.10411i 0.0273057 0.0472949i
\(546\) 0 0
\(547\) −10.0000 17.3205i −0.427569 0.740571i 0.569087 0.822277i \(-0.307297\pi\)
−0.996657 + 0.0817056i \(0.973963\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) −0.637459 1.10411i −0.0271566 0.0470367i
\(552\) 0 0
\(553\) 9.72508 16.8443i 0.413553 0.716294i
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 19.9244 0.844225 0.422112 0.906544i \(-0.361289\pi\)
0.422112 + 0.906544i \(0.361289\pi\)
\(558\) 0 0
\(559\) 25.0997 1.06160
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) 3.45017 5.97586i 0.145407 0.251853i −0.784118 0.620612i \(-0.786884\pi\)
0.929525 + 0.368760i \(0.120217\pi\)
\(564\) 0 0
\(565\) 3.00000 + 5.19615i 0.126211 + 0.218604i
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) −20.7749 35.9832i −0.870930 1.50849i −0.861036 0.508544i \(-0.830184\pi\)
−0.00989364 0.999951i \(-0.503149\pi\)
\(570\) 0 0
\(571\) 11.9124 20.6328i 0.498517 0.863457i −0.501481 0.865169i \(-0.667211\pi\)
0.999999 + 0.00171110i \(0.000544660\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) −0.274917 −0.0114648
\(576\) 0 0
\(577\) −26.5498 −1.10528 −0.552642 0.833419i \(-0.686380\pi\)
−0.552642 + 0.833419i \(0.686380\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) 26.8248 46.4618i 1.11288 1.92756i
\(582\) 0 0
\(583\) 5.27492 + 9.13642i 0.218465 + 0.378392i
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) −9.72508 16.8443i −0.401397 0.695240i 0.592498 0.805572i \(-0.298142\pi\)
−0.993895 + 0.110332i \(0.964809\pi\)
\(588\) 0 0
\(589\) 0.637459 1.10411i 0.0262660 0.0454941i
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) −12.1993 −0.500967 −0.250483 0.968121i \(-0.580590\pi\)
−0.250483 + 0.968121i \(0.580590\pi\)
\(594\) 0 0
\(595\) 8.54983 0.350509
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) −11.6375 + 20.1567i −0.475494 + 0.823579i −0.999606 0.0280700i \(-0.991064\pi\)
0.524112 + 0.851649i \(0.324397\pi\)
\(600\) 0 0
\(601\) 16.0498 + 27.7991i 0.654686 + 1.13395i 0.981972 + 0.189025i \(0.0605326\pi\)
−0.327286 + 0.944925i \(0.606134\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) −4.68729 8.11863i −0.190566 0.330069i
\(606\) 0 0
\(607\) 12.0000 20.7846i 0.487065 0.843621i −0.512824 0.858494i \(-0.671401\pi\)
0.999889 + 0.0148722i \(0.00473415\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) −39.3746 −1.59293
\(612\) 0 0
\(613\) 37.0241 1.49539 0.747694 0.664043i \(-0.231161\pi\)
0.747694 + 0.664043i \(0.231161\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 0.824752 1.42851i 0.0332033 0.0575097i −0.848946 0.528479i \(-0.822762\pi\)
0.882150 + 0.470969i \(0.156096\pi\)
\(618\) 0 0
\(619\) −9.68729 16.7789i −0.389365 0.674400i 0.602999 0.797742i \(-0.293972\pi\)
−0.992364 + 0.123342i \(0.960639\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) −21.0000 36.3731i −0.841347 1.45726i
\(624\) 0 0
\(625\) −0.500000 + 0.866025i −0.0200000 + 0.0346410i
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) −9.09967 −0.362828
\(630\) 0 0
\(631\) −43.4743 −1.73068 −0.865341 0.501183i \(-0.832898\pi\)
−0.865341 + 0.501183i \(0.832898\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) 1.86254 3.22602i 0.0739127 0.128021i
\(636\) 0 0
\(637\) −35.3746 61.2706i −1.40159 2.42763i
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) −9.46221 16.3890i −0.373735 0.647328i 0.616402 0.787432i \(-0.288590\pi\)
−0.990137 + 0.140104i \(0.955256\pi\)
\(642\) 0 0
\(643\) 1.45017 2.51176i 0.0571889 0.0990542i −0.836014 0.548709i \(-0.815120\pi\)
0.893203 + 0.449655i \(0.148453\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 13.4502 0.528781 0.264390 0.964416i \(-0.414829\pi\)
0.264390 + 0.964416i \(0.414829\pi\)
\(648\) 0 0
\(649\) 16.5739 0.650583
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 12.2749 21.2608i 0.480355 0.831999i −0.519391 0.854536i \(-0.673841\pi\)
0.999746 + 0.0225379i \(0.00717463\pi\)
\(654\) 0 0
\(655\) 6.77492 + 11.7345i 0.264718 + 0.458505i
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) −4.86254 8.42217i −0.189418 0.328081i 0.755639 0.654989i \(-0.227327\pi\)
−0.945056 + 0.326908i \(0.893993\pi\)
\(660\) 0 0
\(661\) −6.46221 + 11.1929i −0.251351 + 0.435352i −0.963898 0.266272i \(-0.914208\pi\)
0.712547 + 0.701624i \(0.247541\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) −4.27492 −0.165774
\(666\) 0 0
\(667\) −0.350497 −0.0135713
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 4.17525 7.23174i 0.161184 0.279178i
\(672\) 0 0
\(673\) 19.5498 + 33.8613i 0.753591 + 1.30526i 0.946072 + 0.323957i \(0.105013\pi\)
−0.192481 + 0.981301i \(0.561653\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 12.9622 + 22.4512i 0.498178 + 0.862870i 0.999998 0.00210235i \(-0.000669198\pi\)
−0.501820 + 0.864972i \(0.667336\pi\)
\(678\) 0 0
\(679\) −34.1993 + 59.2350i −1.31245 + 2.27323i
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 16.5498 0.633262 0.316631 0.948549i \(-0.397448\pi\)
0.316631 + 0.948549i \(0.397448\pi\)
\(684\) 0 0
\(685\) −0.549834 −0.0210081
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) 25.9622 44.9679i 0.989081 1.71314i
\(690\) 0 0
\(691\) −7.41238 12.8386i −0.281980 0.488404i 0.689892 0.723912i \(-0.257658\pi\)
−0.971872 + 0.235508i \(0.924325\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) −4.50000 7.79423i −0.170695 0.295652i
\(696\) 0 0
\(697\) 7.54983 13.0767i 0.285970 0.495315i
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) −4.37459 −0.165226 −0.0826129 0.996582i \(-0.526327\pi\)
−0.0826129 + 0.996582i \(0.526327\pi\)
\(702\) 0 0
\(703\) 4.54983 0.171600
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 36.9244 63.9550i 1.38869 2.40527i
\(708\) 0 0
\(709\) 15.5498 + 26.9331i 0.583986 + 1.01149i 0.995001 + 0.0998652i \(0.0318412\pi\)
−0.411015 + 0.911629i \(0.634826\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) −0.175248 0.303539i −0.00656310 0.0113676i
\(714\) 0 0
\(715\) 4.00000 6.92820i 0.149592 0.259100i
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) 22.1752 0.826997 0.413499 0.910505i \(-0.364307\pi\)
0.413499 + 0.910505i \(0.364307\pi\)
\(720\) 0 0
\(721\) 71.9244 2.67861
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) −0.637459 + 1.10411i −0.0236746 + 0.0410056i
\(726\) 0 0
\(727\) −3.68729 6.38658i −0.136754 0.236865i 0.789512 0.613735i \(-0.210334\pi\)
−0.926266 + 0.376870i \(0.877000\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) 4.00000 + 6.92820i 0.147945 + 0.256249i
\(732\) 0 0
\(733\) 3.00000 5.19615i 0.110808 0.191924i −0.805289 0.592883i \(-0.797990\pi\)
0.916096 + 0.400959i \(0.131323\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) −18.5498 −0.683292
\(738\) 0 0
\(739\) −36.9244 −1.35829 −0.679143 0.734006i \(-0.737649\pi\)
−0.679143 + 0.734006i \(0.737649\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) −6.72508 + 11.6482i −0.246719 + 0.427330i −0.962614 0.270878i \(-0.912686\pi\)
0.715894 + 0.698209i \(0.246019\pi\)
\(744\) 0 0
\(745\) −1.00000 1.73205i −0.0366372 0.0634574i
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) −32.2749 55.9018i −1.17930 2.04261i
\(750\) 0 0
\(751\) −9.72508 + 16.8443i −0.354873 + 0.614659i −0.987096 0.160128i \(-0.948809\pi\)
0.632223 + 0.774787i \(0.282143\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 4.72508 0.171963
\(756\) 0 0
\(757\) −3.37459 −0.122651 −0.0613257 0.998118i \(-0.519533\pi\)
−0.0613257 + 0.998118i \(0.519533\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 17.2251 29.8347i 0.624409 1.08151i −0.364246 0.931303i \(-0.618673\pi\)
0.988655 0.150205i \(-0.0479934\pi\)
\(762\) 0 0
\(763\) −2.72508 4.71998i −0.0986546 0.170875i
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) −40.7870 70.6451i −1.47273 2.55085i
\(768\) 0 0
\(769\) 4.36254 7.55614i 0.157317 0.272481i −0.776583 0.630015i \(-0.783049\pi\)
0.933900 + 0.357533i \(0.116382\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) 13.6495 0.490939 0.245469 0.969404i \(-0.421058\pi\)
0.245469 + 0.969404i \(0.421058\pi\)
\(774\) 0 0
\(775\) −1.27492 −0.0457964
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) −3.77492 + 6.53835i −0.135250 + 0.234261i
\(780\) 0 0
\(781\) −0.462210 0.800572i −0.0165392 0.0286467i
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) 9.13746 + 15.8265i 0.326130 + 0.564874i
\(786\) 0 0
\(787\) 17.0000 29.4449i 0.605985 1.04960i −0.385911 0.922536i \(-0.626113\pi\)
0.991895 0.127060i \(-0.0405540\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 25.6495 0.911991
\(792\) 0 0
\(793\) −41.0997 −1.45949
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) −20.2749 + 35.1172i −0.718174 + 1.24391i 0.243548 + 0.969889i \(0.421689\pi\)