Properties

Label 3240.2.q.be.1081.2
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 1081.2
Root \(2.13746 + 0.656712i\) of defining polynomial
Character \(\chi\) \(=\) 3240.1081
Dual form 3240.2.q.be.2161.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.500000 - 0.866025i) q^{5} +(1.63746 + 2.83616i) q^{7} +O(q^{10})\) \(q+(0.500000 - 0.866025i) q^{5} +(1.63746 + 2.83616i) q^{7} +(3.13746 + 5.43424i) q^{11} +(0.637459 - 1.10411i) q^{13} -2.00000 q^{17} +1.00000 q^{19} +(-3.63746 + 6.30026i) q^{23} +(-0.500000 - 0.866025i) q^{25} +(3.13746 + 5.43424i) q^{29} +(-3.13746 + 5.43424i) q^{31} +3.27492 q^{35} -10.5498 q^{37} +(3.77492 - 6.53835i) q^{41} +(-2.00000 - 3.46410i) q^{43} +(-0.637459 - 1.10411i) q^{47} +(-1.86254 + 3.22602i) q^{49} -0.725083 q^{53} +6.27492 q^{55} +(-6.50000 + 11.2583i) q^{59} +(-4.27492 - 7.40437i) q^{61} +(-0.637459 - 1.10411i) q^{65} +(-0.274917 + 0.476171i) q^{67} +8.27492 q^{71} +15.0997 q^{73} +(-10.2749 + 17.7967i) q^{77} +(-5.27492 - 9.13642i) q^{79} +(-1.27492 - 2.20822i) q^{83} +(-1.00000 + 1.73205i) q^{85} -12.8248 q^{89} +4.17525 q^{91} +(0.500000 - 0.866025i) q^{95} +(-8.00000 - 13.8564i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q + 2 q^{5} - q^{7}+O(q^{10}) \) 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
\(7\) 1.63746 + 2.83616i 0.618901 + 1.07197i 0.989687 + 0.143250i \(0.0457552\pi\)
−0.370785 + 0.928719i \(0.620911\pi\)
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) 3.13746 + 5.43424i 0.945979 + 1.63848i 0.753778 + 0.657129i \(0.228229\pi\)
0.192201 + 0.981356i \(0.438437\pi\)
\(12\) 0 0
\(13\) 0.637459 1.10411i 0.176799 0.306225i −0.763983 0.645236i \(-0.776759\pi\)
0.940782 + 0.339011i \(0.110092\pi\)
\(14\) 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
\(23\) −3.63746 + 6.30026i −0.758463 + 1.31370i 0.185172 + 0.982706i \(0.440716\pi\)
−0.943634 + 0.330990i \(0.892618\pi\)
\(24\) 0 0
\(25\) −0.500000 0.866025i −0.100000 0.173205i
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) 3.13746 + 5.43424i 0.582611 + 1.00911i 0.995169 + 0.0981809i \(0.0313024\pi\)
−0.412557 + 0.910932i \(0.635364\pi\)
\(30\) 0 0
\(31\) −3.13746 + 5.43424i −0.563504 + 0.976018i 0.433683 + 0.901066i \(0.357214\pi\)
−0.997187 + 0.0749524i \(0.976120\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) 3.27492 0.553562
\(36\) 0 0
\(37\) −10.5498 −1.73438 −0.867191 0.497976i \(-0.834077\pi\)
−0.867191 + 0.497976i \(0.834077\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) 3.77492 6.53835i 0.589543 1.02112i −0.404749 0.914428i \(-0.632641\pi\)
0.994292 0.106691i \(-0.0340255\pi\)
\(42\) 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
\(47\) −0.637459 1.10411i −0.0929829 0.161051i 0.815782 0.578359i \(-0.196307\pi\)
−0.908765 + 0.417308i \(0.862974\pi\)
\(48\) 0 0
\(49\) −1.86254 + 3.22602i −0.266077 + 0.460859i
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) −0.725083 −0.0995978 −0.0497989 0.998759i \(-0.515858\pi\)
−0.0497989 + 0.998759i \(0.515858\pi\)
\(54\) 0 0
\(55\) 6.27492 0.846110
\(56\) 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
\(61\) −4.27492 7.40437i −0.547347 0.948033i −0.998455 0.0555636i \(-0.982304\pi\)
0.451108 0.892469i \(-0.351029\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) −0.637459 1.10411i −0.0790670 0.136948i
\(66\) 0 0
\(67\) −0.274917 + 0.476171i −0.0335865 + 0.0581735i −0.882330 0.470631i \(-0.844026\pi\)
0.848744 + 0.528805i \(0.177360\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 8.27492 0.982052 0.491026 0.871145i \(-0.336622\pi\)
0.491026 + 0.871145i \(0.336622\pi\)
\(72\) 0 0
\(73\) 15.0997 1.76728 0.883641 0.468165i \(-0.155085\pi\)
0.883641 + 0.468165i \(0.155085\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) −10.2749 + 17.7967i −1.17094 + 2.02812i
\(78\) 0 0
\(79\) −5.27492 9.13642i −0.593475 1.02793i −0.993760 0.111538i \(-0.964422\pi\)
0.400286 0.916390i \(-0.368911\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) −1.27492 2.20822i −0.139940 0.242384i 0.787533 0.616272i \(-0.211358\pi\)
−0.927474 + 0.373888i \(0.878024\pi\)
\(84\) 0 0
\(85\) −1.00000 + 1.73205i −0.108465 + 0.187867i
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) −12.8248 −1.35942 −0.679710 0.733481i \(-0.737895\pi\)
−0.679710 + 0.733481i \(0.737895\pi\)
\(90\) 0 0
\(91\) 4.17525 0.437685
\(92\) 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
\(101\) 4.86254 + 8.42217i 0.483841 + 0.838037i 0.999828 0.0185594i \(-0.00590799\pi\)
−0.515987 + 0.856597i \(0.672575\pi\)
\(102\) 0 0
\(103\) 2.91238 5.04438i 0.286965 0.497038i −0.686119 0.727489i \(-0.740687\pi\)
0.973084 + 0.230452i \(0.0740204\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −15.0997 −1.45974 −0.729870 0.683586i \(-0.760419\pi\)
−0.729870 + 0.683586i \(0.760419\pi\)
\(108\) 0 0
\(109\) −6.27492 −0.601028 −0.300514 0.953777i \(-0.597158\pi\)
−0.300514 + 0.953777i \(0.597158\pi\)
\(110\) 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
\(115\) 3.63746 + 6.30026i 0.339195 + 0.587503i
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) −3.27492 5.67232i −0.300211 0.519981i
\(120\) 0 0
\(121\) −14.1873 + 24.5731i −1.28975 + 2.23392i
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) −1.00000 −0.0894427
\(126\) 0 0
\(127\) 11.2749 1.00049 0.500244 0.865885i \(-0.333244\pi\)
0.500244 + 0.865885i \(0.333244\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) 0.774917 1.34220i 0.0677048 0.117268i −0.830186 0.557487i \(-0.811766\pi\)
0.897891 + 0.440219i \(0.145099\pi\)
\(132\) 0 0
\(133\) 1.63746 + 2.83616i 0.141986 + 0.245926i
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 7.27492 + 12.6005i 0.621538 + 1.07654i 0.989199 + 0.146576i \(0.0468252\pi\)
−0.367661 + 0.929960i \(0.619841\pi\)
\(138\) 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
\(145\) 6.27492 0.521104
\(146\) 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
\(151\) 6.13746 + 10.6304i 0.499459 + 0.865089i 1.00000 0.000624236i \(-0.000198701\pi\)
−0.500541 + 0.865713i \(0.666865\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 3.13746 + 5.43424i 0.252007 + 0.436488i
\(156\) 0 0
\(157\) −5.36254 + 9.28819i −0.427977 + 0.741279i −0.996693 0.0812554i \(-0.974107\pi\)
0.568716 + 0.822534i \(0.307440\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) −23.8248 −1.87765
\(162\) 0 0
\(163\) 20.5498 1.60959 0.804794 0.593555i \(-0.202276\pi\)
0.804794 + 0.593555i \(0.202276\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) −3.72508 + 6.45203i −0.288256 + 0.499273i −0.973393 0.229140i \(-0.926409\pi\)
0.685138 + 0.728413i \(0.259742\pi\)
\(168\) 0 0
\(169\) 5.68729 + 9.85068i 0.437484 + 0.757745i
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) 4.36254 + 7.55614i 0.331678 + 0.574483i 0.982841 0.184455i \(-0.0590520\pi\)
−0.651163 + 0.758938i \(0.725719\pi\)
\(174\) 0 0
\(175\) 1.63746 2.83616i 0.123780 0.214394i
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) 11.5498 0.863275 0.431638 0.902047i \(-0.357936\pi\)
0.431638 + 0.902047i \(0.357936\pi\)
\(180\) 0 0
\(181\) 16.2749 1.20971 0.604853 0.796337i \(-0.293232\pi\)
0.604853 + 0.796337i \(0.293232\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) −5.27492 + 9.13642i −0.387820 + 0.671723i
\(186\) 0 0
\(187\) −6.27492 10.8685i −0.458867 0.794782i
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 9.68729 + 16.7789i 0.700948 + 1.21408i 0.968134 + 0.250432i \(0.0805728\pi\)
−0.267186 + 0.963645i \(0.586094\pi\)
\(192\) 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
\(197\) 22.3746 1.59412 0.797062 0.603898i \(-0.206387\pi\)
0.797062 + 0.603898i \(0.206387\pi\)
\(198\) 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
\(203\) −10.2749 + 17.7967i −0.721158 + 1.24908i
\(204\) 0 0
\(205\) −3.77492 6.53835i −0.263652 0.456658i
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) 3.13746 + 5.43424i 0.217023 + 0.375894i
\(210\) 0 0
\(211\) 8.04983 13.9427i 0.554173 0.959857i −0.443794 0.896129i \(-0.646368\pi\)
0.997967 0.0637277i \(-0.0202989\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) −4.00000 −0.272798
\(216\) 0 0
\(217\) −20.5498 −1.39501
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) −1.27492 + 2.20822i −0.0857602 + 0.148541i
\(222\) 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
\(227\) −3.72508 6.45203i −0.247242 0.428236i 0.715517 0.698595i \(-0.246191\pi\)
−0.962760 + 0.270359i \(0.912858\pi\)
\(228\) 0 0
\(229\) −4.27492 + 7.40437i −0.282494 + 0.489295i −0.971998 0.234987i \(-0.924495\pi\)
0.689504 + 0.724282i \(0.257829\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 9.09967 0.596139 0.298070 0.954544i \(-0.403657\pi\)
0.298070 + 0.954544i \(0.403657\pi\)
\(234\) 0 0
\(235\) −1.27492 −0.0831664
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) −6.72508 + 11.6482i −0.435009 + 0.753458i −0.997296 0.0734837i \(-0.976588\pi\)
0.562287 + 0.826942i \(0.309922\pi\)
\(240\) 0 0
\(241\) 12.1375 + 21.0227i 0.781842 + 1.35419i 0.930867 + 0.365357i \(0.119053\pi\)
−0.149025 + 0.988833i \(0.547613\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) 1.86254 + 3.22602i 0.118993 + 0.206103i
\(246\) 0 0
\(247\) 0.637459 1.10411i 0.0405605 0.0702529i
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) −18.7251 −1.18192 −0.590958 0.806702i \(-0.701250\pi\)
−0.590958 + 0.806702i \(0.701250\pi\)
\(252\) 0 0
\(253\) −45.6495 −2.86996
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 1.54983 2.68439i 0.0966760 0.167448i −0.813631 0.581382i \(-0.802512\pi\)
0.910307 + 0.413934i \(0.135846\pi\)
\(258\) 0 0
\(259\) −17.2749 29.9210i −1.07341 1.85920i
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) −0.362541 0.627940i −0.0223553 0.0387204i 0.854631 0.519235i \(-0.173783\pi\)
−0.876987 + 0.480515i \(0.840450\pi\)
\(264\) 0 0
\(265\) −0.362541 + 0.627940i −0.0222707 + 0.0385741i
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) 25.9244 1.58064 0.790320 0.612694i \(-0.209914\pi\)
0.790320 + 0.612694i \(0.209914\pi\)
\(270\) 0 0
\(271\) 13.4502 0.817039 0.408520 0.912750i \(-0.366045\pi\)
0.408520 + 0.912750i \(0.366045\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 3.13746 5.43424i 0.189196 0.327697i
\(276\) 0 0
\(277\) −12.6375 21.8887i −0.759311 1.31517i −0.943202 0.332219i \(-0.892203\pi\)
0.183891 0.982947i \(-0.441131\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) 3.08762 + 5.34792i 0.184192 + 0.319030i 0.943304 0.331930i \(-0.107700\pi\)
−0.759112 + 0.650960i \(0.774366\pi\)
\(282\) 0 0
\(283\) 5.72508 9.91613i 0.340321 0.589453i −0.644171 0.764881i \(-0.722798\pi\)
0.984492 + 0.175428i \(0.0561310\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 24.7251 1.45948
\(288\) 0 0
\(289\) −13.0000 −0.764706
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) 5.36254 9.28819i 0.313283 0.542622i −0.665788 0.746141i \(-0.731904\pi\)
0.979071 + 0.203519i \(0.0652378\pi\)
\(294\) 0 0
\(295\) 6.50000 + 11.2583i 0.378445 + 0.655485i
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 4.63746 + 8.03231i 0.268191 + 0.464521i
\(300\) 0 0
\(301\) 6.54983 11.3446i 0.377526 0.653895i
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) −8.54983 −0.489562
\(306\) 0 0
\(307\) 1.09967 0.0627614 0.0313807 0.999508i \(-0.490010\pi\)
0.0313807 + 0.999508i \(0.490010\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) −12.9622 + 22.4512i −0.735020 + 1.27309i 0.219695 + 0.975569i \(0.429494\pi\)
−0.954715 + 0.297523i \(0.903840\pi\)
\(312\) 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
\(317\) 2.63746 + 4.56821i 0.148134 + 0.256576i 0.930538 0.366195i \(-0.119340\pi\)
−0.782404 + 0.622772i \(0.786007\pi\)
\(318\) 0 0
\(319\) −19.6873 + 34.0994i −1.10228 + 1.90920i
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) −2.00000 −0.111283
\(324\) 0 0
\(325\) −1.27492 −0.0707197
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) 2.08762 3.61587i 0.115094 0.199349i
\(330\) 0 0
\(331\) 9.41238 + 16.3027i 0.517351 + 0.896078i 0.999797 + 0.0201524i \(0.00641515\pi\)
−0.482446 + 0.875926i \(0.660252\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) 0.274917 + 0.476171i 0.0150203 + 0.0260160i
\(336\) 0 0
\(337\) −2.72508 + 4.71998i −0.148445 + 0.257114i −0.930653 0.365903i \(-0.880760\pi\)
0.782208 + 0.623017i \(0.214093\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) −39.3746 −2.13225
\(342\) 0 0
\(343\) 10.7251 0.579100
\(344\) 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
\(349\) −6.41238 11.1066i −0.343247 0.594521i 0.641787 0.766883i \(-0.278193\pi\)
−0.985034 + 0.172362i \(0.944860\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) 3.27492 + 5.67232i 0.174306 + 0.301907i 0.939921 0.341392i \(-0.110898\pi\)
−0.765615 + 0.643299i \(0.777565\pi\)
\(354\) 0 0
\(355\) 4.13746 7.16629i 0.219594 0.380347i
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) −0.824752 −0.0435287 −0.0217644 0.999763i \(-0.506928\pi\)
−0.0217644 + 0.999763i \(0.506928\pi\)
\(360\) 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
\(367\) −6.27492 10.8685i −0.327548 0.567330i 0.654477 0.756082i \(-0.272889\pi\)
−0.982025 + 0.188752i \(0.939556\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) −1.18729 2.05645i −0.0616412 0.106766i
\(372\) 0 0
\(373\) −15.5498 + 26.9331i −0.805140 + 1.39454i 0.111057 + 0.993814i \(0.464576\pi\)
−0.916197 + 0.400729i \(0.868757\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 8.00000 0.412021
\(378\) 0 0
\(379\) 9.27492 0.476420 0.238210 0.971214i \(-0.423439\pi\)
0.238210 + 0.971214i \(0.423439\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 1.18729 2.05645i 0.0606678 0.105080i −0.834096 0.551619i \(-0.814010\pi\)
0.894764 + 0.446539i \(0.147344\pi\)
\(384\) 0 0
\(385\) 10.2749 + 17.7967i 0.523658 + 0.907003i
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) −8.27492 14.3326i −0.419555 0.726691i 0.576340 0.817210i \(-0.304481\pi\)
−0.995895 + 0.0905197i \(0.971147\pi\)
\(390\) 0 0
\(391\) 7.27492 12.6005i 0.367908 0.637236i
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) −10.5498 −0.530820
\(396\) 0 0
\(397\) 7.09967 0.356322 0.178161 0.984001i \(-0.442985\pi\)
0.178161 + 0.984001i \(0.442985\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 11.6375 20.1567i 0.581147 1.00658i −0.414197 0.910187i \(-0.635937\pi\)
0.995344 0.0963887i \(-0.0307292\pi\)
\(402\) 0 0
\(403\) 4.00000 + 6.92820i 0.199254 + 0.345118i
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) −33.0997 57.3303i −1.64069 2.84176i
\(408\) 0 0
\(409\) 14.9124 25.8290i 0.737370 1.27716i −0.216306 0.976326i \(-0.569401\pi\)
0.953676 0.300836i \(-0.0972657\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) −42.5739 −2.09493
\(414\) 0 0
\(415\) −2.54983 −0.125166
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) −4.54983 + 7.88054i −0.222274 + 0.384990i −0.955498 0.294997i \(-0.904681\pi\)
0.733224 + 0.679987i \(0.238015\pi\)
\(420\) 0 0
\(421\) 16.1375 + 27.9509i 0.786492 + 1.36224i 0.928104 + 0.372321i \(0.121438\pi\)
−0.141612 + 0.989922i \(0.545229\pi\)
\(422\) 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
\(431\) 6.27492 0.302252 0.151126 0.988514i \(-0.451710\pi\)
0.151126 + 0.988514i \(0.451710\pi\)
\(432\) 0 0
\(433\) 12.5498 0.603107 0.301553 0.953449i \(-0.402495\pi\)
0.301553 + 0.953449i \(0.402495\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) −3.63746 + 6.30026i −0.174003 + 0.301382i
\(438\) 0 0
\(439\) 12.6873 + 21.9750i 0.605531 + 1.04881i 0.991967 + 0.126495i \(0.0403727\pi\)
−0.386436 + 0.922316i \(0.626294\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 5.27492 + 9.13642i 0.250619 + 0.434085i 0.963696 0.267001i \(-0.0860326\pi\)
−0.713077 + 0.701085i \(0.752699\pi\)
\(444\) 0 0
\(445\) −6.41238 + 11.1066i −0.303976 + 0.526501i
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) −1.54983 −0.0731412 −0.0365706 0.999331i \(-0.511643\pi\)
−0.0365706 + 0.999331i \(0.511643\pi\)
\(450\) 0 0
\(451\) 47.3746 2.23078
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) 2.08762 3.61587i 0.0978693 0.169515i
\(456\) 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
\(461\) −11.6873 20.2430i −0.544332 0.942810i −0.998649 0.0519698i \(-0.983450\pi\)
0.454317 0.890840i \(-0.349883\pi\)
\(462\) 0 0
\(463\) −20.7371 + 35.9178i −0.963736 + 1.66924i −0.250763 + 0.968049i \(0.580681\pi\)
−0.712973 + 0.701191i \(0.752652\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 40.1993 1.86020 0.930102 0.367302i \(-0.119718\pi\)
0.930102 + 0.367302i \(0.119718\pi\)
\(468\) 0 0
\(469\) −1.80066 −0.0831469
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) 12.5498 21.7370i 0.577042 0.999466i
\(474\) 0 0
\(475\) −0.500000 0.866025i −0.0229416 0.0397360i
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) −2.13746 3.70219i −0.0976630 0.169157i 0.813054 0.582188i \(-0.197803\pi\)
−0.910717 + 0.413031i \(0.864470\pi\)
\(480\) 0 0
\(481\) −6.72508 + 11.6482i −0.306637 + 0.531112i
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) −16.0000 −0.726523
\(486\) 0 0
\(487\) −37.2749 −1.68909 −0.844544 0.535486i \(-0.820128\pi\)
−0.844544 + 0.535486i \(0.820128\pi\)
\(488\) 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
\(493\) −6.27492 10.8685i −0.282608 0.489492i
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 13.5498 + 23.4690i 0.607793 + 1.05273i
\(498\) 0 0
\(499\) 14.7749 25.5909i 0.661416 1.14561i −0.318828 0.947813i \(-0.603289\pi\)
0.980244 0.197794i \(-0.0633776\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(504\) 0 0
\(505\) 9.72508 0.432761
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) 14.0997 24.4213i 0.624957 1.08246i −0.363592 0.931558i \(-0.618450\pi\)
0.988549 0.150899i \(-0.0482168\pi\)
\(510\) 0 0
\(511\) 24.7251 + 42.8251i 1.09377 + 1.89447i
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) −2.91238 5.04438i −0.128335 0.222282i
\(516\) 0 0
\(517\) 4.00000 6.92820i 0.175920 0.304702i
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 26.9244 1.17958 0.589790 0.807557i \(-0.299210\pi\)
0.589790 + 0.807557i \(0.299210\pi\)
\(522\) 0 0
\(523\) −39.6495 −1.73375 −0.866876 0.498524i \(-0.833876\pi\)
−0.866876 + 0.498524i \(0.833876\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 6.27492 10.8685i 0.273340 0.473438i
\(528\) 0 0
\(529\) −14.9622 25.9153i −0.650531 1.12675i
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) −4.81271 8.33585i −0.208461 0.361066i
\(534\) 0 0
\(535\) −7.54983 + 13.0767i −0.326408 + 0.565355i
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) −23.3746 −1.00681
\(540\) 0 0
\(541\) 43.9244 1.88846 0.944229 0.329289i \(-0.106809\pi\)
0.944229 + 0.329289i \(0.106809\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) −3.13746 + 5.43424i −0.134394 + 0.232777i
\(546\) 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
\(551\) 3.13746 + 5.43424i 0.133660 + 0.231506i
\(552\) 0 0
\(553\) 17.2749 29.9210i 0.734604 1.27237i
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) −32.9244 −1.39505 −0.697526 0.716559i \(-0.745716\pi\)
−0.697526 + 0.716559i \(0.745716\pi\)
\(558\) 0 0
\(559\) −5.09967 −0.215693
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) 18.5498 32.1293i 0.781782 1.35409i −0.149120 0.988819i \(-0.547644\pi\)
0.930903 0.365268i \(-0.119023\pi\)
\(564\) 0 0
\(565\) 3.00000 + 5.19615i 0.126211 + 0.218604i
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) −13.2251 22.9065i −0.554424 0.960291i −0.997948 0.0640285i \(-0.979605\pi\)
0.443524 0.896263i \(-0.353728\pi\)
\(570\) 0 0
\(571\) 0.587624 1.01779i 0.0245913 0.0425934i −0.853468 0.521145i \(-0.825505\pi\)
0.878059 + 0.478552i \(0.158838\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 7.27492 0.303385
\(576\) 0 0
\(577\) −11.4502 −0.476677 −0.238338 0.971182i \(-0.576603\pi\)
−0.238338 + 0.971182i \(0.576603\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) 4.17525 7.23174i 0.173218 0.300023i
\(582\) 0 0
\(583\) −2.27492 3.94027i −0.0942174 0.163189i
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) −17.2749 29.9210i −0.713012 1.23497i −0.963721 0.266911i \(-0.913997\pi\)
0.250709 0.968062i \(-0.419336\pi\)
\(588\) 0 0
\(589\) −3.13746 + 5.43424i −0.129277 + 0.223914i
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) 48.1993 1.97931 0.989655 0.143469i \(-0.0458258\pi\)
0.989655 + 0.143469i \(0.0458258\pi\)
\(594\) 0 0
\(595\) −6.54983 −0.268517
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) −7.86254 + 13.6183i −0.321255 + 0.556430i −0.980747 0.195282i \(-0.937438\pi\)
0.659492 + 0.751711i \(0.270771\pi\)
\(600\) 0 0
\(601\) 0.950166 + 1.64574i 0.0387581 + 0.0671309i 0.884754 0.466059i \(-0.154327\pi\)
−0.845996 + 0.533190i \(0.820993\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) 14.1873 + 24.5731i 0.576795 + 0.999039i
\(606\) 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
\(611\) −1.62541 −0.0657572
\(612\) 0 0
\(613\) −46.0241 −1.85890 −0.929448 0.368954i \(-0.879716\pi\)
−0.929448 + 0.368954i \(0.879716\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) −21.8248 + 37.8016i −0.878631 + 1.52183i −0.0257881 + 0.999667i \(0.508210\pi\)
−0.852843 + 0.522167i \(0.825124\pi\)
\(618\) 0 0
\(619\) 9.18729 + 15.9129i 0.369268 + 0.639592i 0.989451 0.144865i \(-0.0462749\pi\)
−0.620183 + 0.784457i \(0.712942\pi\)
\(620\) 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
\(629\) 21.0997 0.841299
\(630\) 0 0
\(631\) 24.4743 0.974305 0.487152 0.873317i \(-0.338036\pi\)
0.487152 + 0.873317i \(0.338036\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) 5.63746 9.76436i 0.223716 0.387487i
\(636\) 0 0
\(637\) 2.37459 + 4.11290i 0.0940845 + 0.162959i
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) 16.9622 + 29.3794i 0.669967 + 1.16042i 0.977913 + 0.209013i \(0.0670251\pi\)
−0.307946 + 0.951404i \(0.599642\pi\)
\(642\) 0 0
\(643\) 16.5498 28.6652i 0.652662 1.13044i −0.329813 0.944046i \(-0.606986\pi\)
0.982475 0.186397i \(-0.0596811\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 28.5498 1.12241 0.561205 0.827677i \(-0.310338\pi\)
0.561205 + 0.827677i \(0.310338\pi\)
\(648\) 0 0
\(649\) −81.5739 −3.20206
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 4.72508 8.18408i 0.184907 0.320268i −0.758638 0.651512i \(-0.774135\pi\)
0.943545 + 0.331244i \(0.107468\pi\)
\(654\) 0 0
\(655\) −0.774917 1.34220i −0.0302785 0.0524439i
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) −8.63746 14.9605i −0.336468 0.582779i 0.647298 0.762237i \(-0.275899\pi\)
−0.983766 + 0.179458i \(0.942566\pi\)
\(660\) 0 0
\(661\) 19.9622 34.5756i 0.776440 1.34483i −0.157542 0.987512i \(-0.550357\pi\)
0.933982 0.357321i \(-0.116310\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 3.27492 0.126996
\(666\) 0 0
\(667\) −45.6495 −1.76756
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 26.8248 46.4618i 1.03556 1.79364i
\(672\) 0 0
\(673\) 4.45017 + 7.70791i 0.171541 + 0.297118i 0.938959 0.344029i \(-0.111792\pi\)
−0.767418 + 0.641148i \(0.778459\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) −13.4622 23.3172i −0.517395 0.896154i −0.999796 0.0202036i \(-0.993569\pi\)
0.482401 0.875950i \(-0.339765\pi\)
\(678\) 0 0
\(679\) 26.1993 45.3786i 1.00544 1.74147i
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 1.45017 0.0554890 0.0277445 0.999615i \(-0.491168\pi\)
0.0277445 + 0.999615i \(0.491168\pi\)
\(684\) 0 0
\(685\) 14.5498 0.555921
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) −0.462210 + 0.800572i −0.0176088 + 0.0304994i
\(690\) 0 0
\(691\) 3.91238 + 6.77643i 0.148834 + 0.257788i 0.930797 0.365537i \(-0.119115\pi\)
−0.781963 + 0.623325i \(0.785781\pi\)
\(692\) 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
\(701\) 33.3746 1.26054 0.630270 0.776376i \(-0.282944\pi\)
0.630270 + 0.776376i \(0.282944\pi\)
\(702\) 0 0
\(703\) −10.5498 −0.397895
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) −15.9244 + 27.5819i −0.598899 + 1.03732i
\(708\) 0 0
\(709\) 0.450166 + 0.779710i 0.0169063 + 0.0292826i 0.874355 0.485287i \(-0.161285\pi\)
−0.857448 + 0.514570i \(0.827952\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) −22.8248 39.5336i −0.854794 1.48055i
\(714\) 0 0
\(715\) 4.00000 6.92820i 0.149592 0.259100i
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) 44.8248 1.67168 0.835841 0.548972i \(-0.184981\pi\)
0.835841 + 0.548972i \(0.184981\pi\)
\(720\) 0 0
\(721\) 19.0756 0.710412
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) 3.13746 5.43424i 0.116522 0.201823i
\(726\) 0 0
\(727\) 15.1873 + 26.3052i 0.563266 + 0.975604i 0.997209 + 0.0746643i \(0.0237885\pi\)
−0.433943 + 0.900940i \(0.642878\pi\)
\(728\) 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
\(737\) −3.45017 −0.127088
\(738\) 0 0
\(739\) 15.9244 0.585789 0.292895 0.956145i \(-0.405381\pi\)
0.292895 + 0.956145i \(0.405381\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) −14.2749 + 24.7249i −0.523696 + 0.907068i 0.475924 + 0.879487i \(0.342114\pi\)
−0.999620 + 0.0275813i \(0.991219\pi\)
\(744\) 0 0
\(745\) −1.00000 1.73205i −0.0366372 0.0634574i
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) −24.7251 42.8251i −0.903435 1.56480i
\(750\) 0 0
\(751\) −17.2749 + 29.9210i −0.630371 + 1.09183i 0.357105 + 0.934064i \(0.383764\pi\)
−0.987476 + 0.157770i \(0.949570\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 12.2749 0.446730
\(756\) 0 0
\(757\) 34.3746 1.24937 0.624683 0.780879i \(-0.285228\pi\)
0.624683 + 0.780879i \(0.285228\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 24.7749 42.9114i 0.898090 1.55554i 0.0681570 0.997675i \(-0.478288\pi\)
0.829933 0.557863i \(-0.188379\pi\)
\(762\) 0 0
\(763\) −10.2749 17.7967i −0.371977 0.644283i
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 8.28696 + 14.3534i 0.299225 + 0.518273i
\(768\) 0 0
\(769\) 8.13746 14.0945i 0.293444 0.508260i −0.681178 0.732118i \(-0.738532\pi\)
0.974622 + 0.223858i \(0.0718652\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) −31.6495 −1.13835 −0.569177 0.822215i \(-0.692738\pi\)
−0.569177 + 0.822215i \(0.692738\pi\)
\(774\) 0 0
\(775\) 6.27492 0.225402
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 3.77492 6.53835i 0.135250 0.234261i
\(780\) 0 0
\(781\) 25.9622 + 44.9679i 0.929001 + 1.60908i
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) 5.36254 + 9.28819i 0.191397 + 0.331510i
\(786\) 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
\(791\) −19.6495 −0.698656
\(792\) 0 0
\(793\) −10.9003 −0.387082
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) −12.7251 + 22.0405i −0.450746 + 0.780714i −0.998432 0.0559691i \(-0.982175\pi\)
0.547687 + 0.836683i