Properties

Label 3240.2.q.y.2161.2
Level $3240$
Weight $2$
Character 3240.2161
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 2161.2
Root \(2.13746 - 0.656712i\) of defining polynomial
Character \(\chi\) \(=\) 3240.2161
Dual form 3240.2.q.y.1081.2

$q$-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 \(\left(\mathbb{Z}/3240\mathbb{Z}\right)^\times\).

\(n\) \(1297\) \(1621\) \(2431\) \(3161\)
\(\chi(n)\) \(1\) \(1\) \(1\) \(e\left(\frac{2}{3}\right)\)

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 −0.370785 0.928719i \(-0.620911\pi\)
0.989687 0.143250i \(-0.0457552\pi\)
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) −3.13746 + 5.43424i −0.945979 + 1.63848i −0.192201 + 0.981356i \(0.561563\pi\)
−0.753778 + 0.657129i \(0.771771\pi\)
\(12\) 0 0
\(13\) 0.637459 + 1.10411i 0.176799 + 0.306225i 0.940782 0.339011i \(-0.110092\pi\)
−0.763983 + 0.645236i \(0.776759\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 2.00000 0.485071 0.242536 0.970143i \(-0.422021\pi\)
0.242536 + 0.970143i \(0.422021\pi\)
\(18\) 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 0.943634 + 0.330990i \(0.107382\pi\)
−0.185172 + 0.982706i \(0.559284\pi\)
\(24\) 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 0.412557 + 0.910932i \(0.364636\pi\)
−0.995169 + 0.0981809i \(0.968698\pi\)
\(30\) 0 0
\(31\) −3.13746 5.43424i −0.563504 0.976018i −0.997187 0.0749524i \(-0.976120\pi\)
0.433683 0.901066i \(-0.357214\pi\)
\(32\) 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 −0.994292 0.106691i \(-0.965975\pi\)
0.404749 0.914428i \(-0.367359\pi\)
\(42\) 0 0
\(43\) −2.00000 + 3.46410i −0.304997 + 0.528271i −0.977261 0.212041i \(-0.931989\pi\)
0.672264 + 0.740312i \(0.265322\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 0.637459 1.10411i 0.0929829 0.161051i −0.815782 0.578359i \(-0.803693\pi\)
0.908765 + 0.417308i \(0.137026\pi\)
\(48\) 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 \(-0.484142\pi\)
0.0497989 + 0.998759i \(0.484142\pi\)
\(54\) 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 0.884551 + 0.466444i \(0.154465\pi\)
−0.0383226 + 0.999265i \(0.512201\pi\)
\(60\) 0 0
\(61\) −4.27492 + 7.40437i −0.547347 + 0.948033i 0.451108 + 0.892469i \(0.351029\pi\)
−0.998455 + 0.0555636i \(0.982304\pi\)
\(62\) 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 0.848744 0.528805i \(-0.177360\pi\)
−0.882330 + 0.470631i \(0.844026\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) −8.27492 −0.982052 −0.491026 0.871145i \(-0.663378\pi\)
−0.491026 + 0.871145i \(0.663378\pi\)
\(72\) 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 0.400286 + 0.916390i \(0.368911\pi\)
−0.993760 + 0.111538i \(0.964422\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) 1.27492 2.20822i 0.139940 0.242384i −0.787533 0.616272i \(-0.788642\pi\)
0.927474 + 0.373888i \(0.121976\pi\)
\(84\) 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 \(-0.262105\pi\)
0.679710 + 0.733481i \(0.262105\pi\)
\(90\) 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 0.0989899 + 0.995088i \(0.468439\pi\)
−0.911267 + 0.411816i \(0.864894\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) −4.86254 + 8.42217i −0.483841 + 0.838037i −0.999828 0.0185594i \(-0.994092\pi\)
0.515987 + 0.856597i \(0.327425\pi\)
\(102\) 0 0
\(103\) 2.91238 + 5.04438i 0.286965 + 0.497038i 0.973084 0.230452i \(-0.0740204\pi\)
−0.686119 + 0.727489i \(0.740687\pi\)
\(104\) 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
\(109\) −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 \(-0.0755971\pi\)
−0.689714 + 0.724082i \(0.742264\pi\)
\(114\) 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 \(-0.188234\pi\)
−0.897891 + 0.440219i \(0.854901\pi\)
\(132\) 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 0.367661 + 0.929960i \(0.380159\pi\)
−0.989199 + 0.146576i \(0.953175\pi\)
\(138\) 0 0
\(139\) 4.50000 + 7.79423i 0.381685 + 0.661098i 0.991303 0.131597i \(-0.0420106\pi\)
−0.609618 + 0.792695i \(0.708677\pi\)
\(140\) 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 \(-0.192773\pi\)
−0.904076 + 0.427372i \(0.859440\pi\)
\(150\) 0 0
\(151\) 6.13746 10.6304i 0.499459 0.865089i −0.500541 0.865713i \(-0.666865\pi\)
1.00000 0.000624236i \(0.000198701\pi\)
\(152\) 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 0.568716 0.822534i \(-0.307440\pi\)
−0.996693 + 0.0812554i \(0.974107\pi\)
\(158\) 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 \(-0.0735914\pi\)
−0.685138 + 0.728413i \(0.740258\pi\)
\(168\) 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 \(-0.940948\pi\)
0.651163 + 0.758938i \(0.274281\pi\)
\(174\) 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 \(-0.642064\pi\)
−0.431638 + 0.902047i \(0.642064\pi\)
\(180\) 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 0.267186 + 0.963645i \(0.413906\pi\)
−0.968134 + 0.250432i \(0.919427\pi\)
\(192\) 0 0
\(193\) −2.00000 3.46410i −0.143963 0.249351i 0.785022 0.619467i \(-0.212651\pi\)
−0.928986 + 0.370116i \(0.879318\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) −22.3746 −1.59412 −0.797062 0.603898i \(-0.793613\pi\)
−0.797062 + 0.603898i \(0.793613\pi\)
\(198\) 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 0.997967 + 0.0637277i \(0.0202989\pi\)
−0.443794 + 0.896129i \(0.646368\pi\)
\(212\) 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 −0.968309 0.249756i \(-0.919650\pi\)
0.700449 + 0.713702i \(0.252983\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 3.72508 6.45203i 0.247242 0.428236i −0.715517 0.698595i \(-0.753809\pi\)
0.962760 + 0.270359i \(0.0871423\pi\)
\(228\) 0 0
\(229\) −4.27492 7.40437i −0.282494 0.489295i 0.689504 0.724282i \(-0.257829\pi\)
−0.971998 + 0.234987i \(0.924495\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) −9.09967 −0.596139 −0.298070 0.954544i \(-0.596343\pi\)
−0.298070 + 0.954544i \(0.596343\pi\)
\(234\) 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 \(-0.0234117\pi\)
−0.562287 + 0.826942i \(0.690078\pi\)
\(240\) 0 0
\(241\) 12.1375 21.0227i 0.781842 1.35419i −0.149025 0.988833i \(-0.547613\pi\)
0.930867 0.365357i \(-0.119053\pi\)
\(242\) 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 \(-0.298750\pi\)
0.590958 + 0.806702i \(0.298750\pi\)
\(252\) 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 \(-0.197488\pi\)
−0.910307 + 0.413934i \(0.864154\pi\)
\(258\) 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 \(-0.826217\pi\)
0.876987 + 0.480515i \(0.159550\pi\)
\(264\) 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 \(-0.790086\pi\)
−0.790320 + 0.612694i \(0.790086\pi\)
\(270\) 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 0.183891 + 0.982947i \(0.441131\pi\)
−0.943202 + 0.332219i \(0.892203\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) −3.08762 + 5.34792i −0.184192 + 0.319030i −0.943304 0.331930i \(-0.892300\pi\)
0.759112 + 0.650960i \(0.225634\pi\)
\(282\) 0 0
\(283\) 5.72508 + 9.91613i 0.340321 + 0.589453i 0.984492 0.175428i \(-0.0561310\pi\)
−0.644171 + 0.764881i \(0.722798\pi\)
\(284\) 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 \(-0.268096\pi\)
−0.979071 + 0.203519i \(0.934762\pi\)
\(294\) 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 0.954715 + 0.297523i \(0.0961604\pi\)
−0.219695 + 0.975569i \(0.570506\pi\)
\(312\) 0 0
\(313\) −4.00000 + 6.92820i −0.226093 + 0.391605i −0.956647 0.291250i \(-0.905929\pi\)
0.730554 + 0.682855i \(0.239262\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −2.63746 + 4.56821i −0.148134 + 0.256576i −0.930538 0.366195i \(-0.880660\pi\)
0.782404 + 0.622772i \(0.213993\pi\)
\(318\) 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 −0.482446 0.875926i \(-0.660252\pi\)
0.999797 0.0201524i \(-0.00641515\pi\)
\(332\) 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 0.782208 0.623017i \(-0.214093\pi\)
−0.930653 + 0.365903i \(0.880760\pi\)
\(338\) 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 \(-0.289292\pi\)
−0.990443 + 0.137920i \(0.955958\pi\)
\(348\) 0 0
\(349\) −6.41238 + 11.1066i −0.343247 + 0.594521i −0.985034 0.172362i \(-0.944860\pi\)
0.641787 + 0.766883i \(0.278193\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) −3.27492 + 5.67232i −0.174306 + 0.301907i −0.939921 0.341392i \(-0.889102\pi\)
0.765615 + 0.643299i \(0.222435\pi\)
\(354\) 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 \(-0.493072\pi\)
0.0217644 + 0.999763i \(0.493072\pi\)
\(360\) 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 −0.982025 0.188752i \(-0.939556\pi\)
0.654477 + 0.756082i \(0.272889\pi\)
\(368\) 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 −0.916197 0.400729i \(-0.868757\pi\)
0.111057 0.993814i \(-0.464576\pi\)
\(374\) 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 \(-0.185990\pi\)
−0.894764 + 0.446539i \(0.852656\pi\)
\(384\) 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 \(-0.695519\pi\)
0.995895 + 0.0905197i \(0.0288528\pi\)
\(390\) 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 −0.995344 0.0963887i \(-0.969271\pi\)
0.414197 0.910187i \(-0.364063\pi\)
\(402\) 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 0.953676 + 0.300836i \(0.0972657\pi\)
−0.216306 + 0.976326i \(0.569401\pi\)
\(410\) 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 \(-0.0953187\pi\)
−0.733224 + 0.679987i \(0.761985\pi\)
\(420\) 0 0
\(421\) 16.1375 27.9509i 0.786492 1.36224i −0.141612 0.989922i \(-0.545229\pi\)
0.928104 0.372321i \(-0.121438\pi\)
\(422\) 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 \(-0.548290\pi\)
−0.151126 + 0.988514i \(0.548290\pi\)
\(432\) 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 −0.386436 0.922316i \(-0.626294\pi\)
0.991967 0.126495i \(-0.0403727\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) −5.27492 + 9.13642i −0.250619 + 0.434085i −0.963696 0.267001i \(-0.913967\pi\)
0.713077 + 0.701085i \(0.247301\pi\)
\(444\) 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 \(-0.488357\pi\)
0.0365706 + 0.999331i \(0.488357\pi\)
\(450\) 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 −0.990211 0.139581i \(-0.955424\pi\)
0.615986 + 0.787757i \(0.288758\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 11.6873 20.2430i 0.544332 0.942810i −0.454317 0.890840i \(-0.650117\pi\)
0.998649 0.0519698i \(-0.0165500\pi\)
\(462\) 0 0
\(463\) −20.7371 35.9178i −0.963736 1.66924i −0.712973 0.701191i \(-0.752652\pi\)
−0.250763 0.968049i \(-0.580681\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) −40.1993 −1.86020 −0.930102 0.367302i \(-0.880282\pi\)
−0.930102 + 0.367302i \(0.880282\pi\)
\(468\) 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 \(-0.802197\pi\)
0.910717 + 0.413031i \(0.135530\pi\)
\(480\) 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 \(-0.276576\pi\)
−0.984145 + 0.177365i \(0.943243\pi\)
\(492\) 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 0.980244 + 0.197794i \(0.0633776\pi\)
−0.318828 + 0.947813i \(0.603289\pi\)
\(500\) 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 −0.988549 0.150899i \(-0.951783\pi\)
0.363592 0.931558i \(-0.381550\pi\)
\(510\) 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 \(-0.700790\pi\)
−0.589790 + 0.807557i \(0.700790\pi\)
\(522\) 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 −0.996657 0.0817056i \(-0.973963\pi\)
0.569087 + 0.822277i \(0.307297\pi\)
\(548\) 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 \(-0.254284\pi\)
0.697526 + 0.716559i \(0.254284\pi\)
\(558\) 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 −0.930903 0.365268i \(-0.880977\pi\)
0.149120 0.988819i \(-0.452356\pi\)
\(564\) 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 −0.443524 0.896263i \(-0.646272\pi\)
0.997948 0.0640285i \(-0.0203948\pi\)
\(570\) 0 0
\(571\) 0.587624 + 1.01779i 0.0245913 + 0.0425934i 0.878059 0.478552i \(-0.158838\pi\)
−0.853468 + 0.521145i \(0.825505\pi\)
\(572\) 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 −0.250709 0.968062i \(-0.580664\pi\)
0.963721 0.266911i \(-0.0860029\pi\)
\(588\) 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 \(-0.954174\pi\)
−0.989655 + 0.143469i \(0.954174\pi\)
\(594\) 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 \(-0.0625621\pi\)
−0.659492 + 0.751711i \(0.729229\pi\)
\(600\) 0 0
\(601\) 0.950166 1.64574i 0.0387581 0.0671309i −0.845996 0.533190i \(-0.820993\pi\)
0.884754 + 0.466059i \(0.154327\pi\)
\(602\) 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 0.999889 0.0148722i \(-0.00473415\pi\)
−0.512824 + 0.858494i \(0.671401\pi\)
\(608\) 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 0.852843 + 0.522167i \(0.174876\pi\)
0.0257881 + 0.999667i \(0.491790\pi\)
\(618\) 0 0
\(619\) 9.18729 15.9129i 0.369268 0.639592i −0.620183 0.784457i \(-0.712942\pi\)
0.989451 + 0.144865i \(0.0462749\pi\)
\(620\) 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 0.307946 + 0.951404i \(0.400358\pi\)
−0.977913 + 0.209013i \(0.932975\pi\)
\(642\) 0 0
\(643\) 16.5498 + 28.6652i 0.652662 + 1.13044i 0.982475 + 0.186397i \(0.0596811\pi\)
−0.329813 + 0.944046i \(0.606986\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) −28.5498 −1.12241 −0.561205 0.827677i \(-0.689662\pi\)
−0.561205 + 0.827677i \(0.689662\pi\)
\(648\) 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 \(-0.225865\pi\)
−0.943545 + 0.331244i \(0.892532\pi\)
\(654\) 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 \(-0.724101\pi\)
0.983766 + 0.179458i \(0.0574344\pi\)
\(660\) 0 0
\(661\) 19.9622 + 34.5756i 0.776440 + 1.34483i 0.933982 + 0.357321i \(0.116310\pi\)
−0.157542 + 0.987512i \(0.550357\pi\)
\(662\) 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 −0.767418 0.641148i \(-0.778459\pi\)
0.938959 + 0.344029i \(0.111792\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 13.4622 23.3172i 0.517395 0.896154i −0.482401 0.875950i \(-0.660235\pi\)
0.999796 0.0202036i \(-0.00643144\pi\)
\(678\) 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 \(-0.508832\pi\)
−0.0277445 + 0.999615i \(0.508832\pi\)
\(684\) 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 −0.781963 0.623325i \(-0.785781\pi\)
0.930797 + 0.365537i \(0.119115\pi\)
\(692\) 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 \(-0.717056\pi\)
−0.630270 + 0.776376i \(0.717056\pi\)
\(702\) 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 −0.857448 0.514570i \(-0.827952\pi\)
0.874355 + 0.485287i \(0.161285\pi\)
\(710\) 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 \(-0.815019\pi\)
−0.835841 + 0.548972i \(0.815019\pi\)
\(720\) 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 −0.433943 0.900940i \(-0.642878\pi\)
0.997209 0.0746643i \(-0.0237885\pi\)
\(728\) 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 0.916096 0.400959i \(-0.131323\pi\)
−0.805289 + 0.592883i \(0.797990\pi\)
\(734\) 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 0.999620 + 0.0275813i \(0.00878053\pi\)
−0.475924 + 0.879487i \(0.657886\pi\)
\(744\) 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 −0.987476 0.157770i \(-0.949570\pi\)
0.357105 0.934064i \(-0.383764\pi\)
\(752\) 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 −0.829933 0.557863i \(-0.811621\pi\)
−0.0681570 0.997675i \(-0.521712\pi\)
\(762\) 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 0.974622 0.223858i \(-0.0718652\pi\)
−0.681178 + 0.732118i \(0.738532\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) 31.6495 1.13835 0.569177 0.822215i \(-0.307262\pi\)
0.569177 + 0.822215i \(0.307262\pi\)
\(774\) 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 0.991895 + 0.127060i \(0.0405540\pi\)
−0.385911 + 0.922536i \(0.626113\pi\)
\(788\) 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