Properties

Label 240.3.c.c.209.1
Level $240$
Weight $3$
Character 240.209
Analytic conductor $6.540$
Analytic rank $0$
Dimension $4$
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [240,3,Mod(209,240)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(240, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 0, 1, 1]))
 
N = Newforms(chi, 3, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("240.209");
 
S:= CuspForms(chi, 3);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 240 = 2^{4} \cdot 3 \cdot 5 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 240.c (of order \(2\), degree \(1\), 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: \(6.53952634465\)
Analytic rank: \(0\)
Dimension: \(4\)
Coefficient field: \(\Q(\sqrt{2}, \sqrt{-17})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{4} + 16x^{2} + 81 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 30)
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 209.1
Root \(-0.707107 - 2.91548i\) of defining polynomial
Character \(\chi\) \(=\) 240.209
Dual form 240.3.c.c.209.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.707107 - 2.91548i) q^{3} +(2.82843 + 4.12311i) q^{5} +5.83095i q^{7} +(-8.00000 + 4.12311i) q^{9} +O(q^{10})\) \(q+(-0.707107 - 2.91548i) q^{3} +(2.82843 + 4.12311i) q^{5} +5.83095i q^{7} +(-8.00000 + 4.12311i) q^{9} +16.4924i q^{11} +(10.0208 - 11.1617i) q^{15} +11.3137 q^{17} -12.0000 q^{19} +(17.0000 - 4.12311i) q^{21} +24.0416 q^{23} +(-9.00000 + 23.3238i) q^{25} +(17.6777 + 20.4083i) q^{27} +32.0000 q^{31} +(48.0833 - 11.6619i) q^{33} +(-24.0416 + 16.4924i) q^{35} -23.3238i q^{37} +57.7235i q^{41} -40.8167i q^{43} +(-39.6274 - 21.3229i) q^{45} -35.3553 q^{47} +15.0000 q^{49} +(-8.00000 - 32.9848i) q^{51} -67.8823 q^{53} +(-68.0000 + 46.6476i) q^{55} +(8.48528 + 34.9857i) q^{57} +16.4924i q^{59} -16.0000 q^{61} +(-24.0416 - 46.6476i) q^{63} -5.83095i q^{67} +(-17.0000 - 70.0928i) q^{69} -116.619i q^{73} +(74.3640 + 9.74686i) q^{75} -96.1665 q^{77} +72.0000 q^{79} +(47.0000 - 65.9697i) q^{81} -43.8406 q^{83} +(32.0000 + 46.6476i) q^{85} +65.9697i q^{89} +(-22.6274 - 93.2952i) q^{93} +(-33.9411 - 49.4773i) q^{95} +163.267i q^{97} +(-68.0000 - 131.939i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q - 32 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 4 q - 32 q^{9} - 8 q^{15} - 48 q^{19} + 68 q^{21} - 36 q^{25} + 128 q^{31} - 68 q^{45} + 60 q^{49} - 32 q^{51} - 272 q^{55} - 64 q^{61} - 68 q^{69} + 272 q^{75} + 288 q^{79} + 188 q^{81} + 128 q^{85} - 272 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/240\mathbb{Z}\right)^\times\).

\(n\) \(31\) \(97\) \(161\) \(181\)
\(\chi(n)\) \(1\) \(-1\) \(-1\) \(1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) −0.707107 2.91548i −0.235702 0.971825i
\(4\) 0 0
\(5\) 2.82843 + 4.12311i 0.565685 + 0.824621i
\(6\) 0 0
\(7\) 5.83095i 0.832993i 0.909137 + 0.416497i \(0.136742\pi\)
−0.909137 + 0.416497i \(0.863258\pi\)
\(8\) 0 0
\(9\) −8.00000 + 4.12311i −0.888889 + 0.458123i
\(10\) 0 0
\(11\) 16.4924i 1.49931i 0.661828 + 0.749656i \(0.269781\pi\)
−0.661828 + 0.749656i \(0.730219\pi\)
\(12\) 0 0
\(13\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(14\) 0 0
\(15\) 10.0208 11.1617i 0.668054 0.744112i
\(16\) 0 0
\(17\) 11.3137 0.665512 0.332756 0.943013i \(-0.392021\pi\)
0.332756 + 0.943013i \(0.392021\pi\)
\(18\) 0 0
\(19\) −12.0000 −0.631579 −0.315789 0.948829i \(-0.602269\pi\)
−0.315789 + 0.948829i \(0.602269\pi\)
\(20\) 0 0
\(21\) 17.0000 4.12311i 0.809524 0.196338i
\(22\) 0 0
\(23\) 24.0416 1.04529 0.522644 0.852551i \(-0.324946\pi\)
0.522644 + 0.852551i \(0.324946\pi\)
\(24\) 0 0
\(25\) −9.00000 + 23.3238i −0.360000 + 0.932952i
\(26\) 0 0
\(27\) 17.6777 + 20.4083i 0.654729 + 0.755864i
\(28\) 0 0
\(29\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(30\) 0 0
\(31\) 32.0000 1.03226 0.516129 0.856511i \(-0.327372\pi\)
0.516129 + 0.856511i \(0.327372\pi\)
\(32\) 0 0
\(33\) 48.0833 11.6619i 1.45707 0.353391i
\(34\) 0 0
\(35\) −24.0416 + 16.4924i −0.686904 + 0.471212i
\(36\) 0 0
\(37\) 23.3238i 0.630373i −0.949030 0.315187i \(-0.897933\pi\)
0.949030 0.315187i \(-0.102067\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) 57.7235i 1.40789i 0.710255 + 0.703945i \(0.248580\pi\)
−0.710255 + 0.703945i \(0.751420\pi\)
\(42\) 0 0
\(43\) 40.8167i 0.949225i −0.880195 0.474612i \(-0.842588\pi\)
0.880195 0.474612i \(-0.157412\pi\)
\(44\) 0 0
\(45\) −39.6274 21.3229i −0.880609 0.473843i
\(46\) 0 0
\(47\) −35.3553 −0.752241 −0.376121 0.926571i \(-0.622742\pi\)
−0.376121 + 0.926571i \(0.622742\pi\)
\(48\) 0 0
\(49\) 15.0000 0.306122
\(50\) 0 0
\(51\) −8.00000 32.9848i −0.156863 0.646762i
\(52\) 0 0
\(53\) −67.8823 −1.28080 −0.640399 0.768043i \(-0.721231\pi\)
−0.640399 + 0.768043i \(0.721231\pi\)
\(54\) 0 0
\(55\) −68.0000 + 46.6476i −1.23636 + 0.848138i
\(56\) 0 0
\(57\) 8.48528 + 34.9857i 0.148865 + 0.613784i
\(58\) 0 0
\(59\) 16.4924i 0.279533i 0.990185 + 0.139766i \(0.0446351\pi\)
−0.990185 + 0.139766i \(0.955365\pi\)
\(60\) 0 0
\(61\) −16.0000 −0.262295 −0.131148 0.991363i \(-0.541866\pi\)
−0.131148 + 0.991363i \(0.541866\pi\)
\(62\) 0 0
\(63\) −24.0416 46.6476i −0.381613 0.740438i
\(64\) 0 0
\(65\) 0 0
\(66\) 0 0
\(67\) 5.83095i 0.0870291i −0.999053 0.0435146i \(-0.986145\pi\)
0.999053 0.0435146i \(-0.0138555\pi\)
\(68\) 0 0
\(69\) −17.0000 70.0928i −0.246377 1.01584i
\(70\) 0 0
\(71\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(72\) 0 0
\(73\) 116.619i 1.59752i −0.601649 0.798761i \(-0.705489\pi\)
0.601649 0.798761i \(-0.294511\pi\)
\(74\) 0 0
\(75\) 74.3640 + 9.74686i 0.991519 + 0.129958i
\(76\) 0 0
\(77\) −96.1665 −1.24892
\(78\) 0 0
\(79\) 72.0000 0.911392 0.455696 0.890135i \(-0.349390\pi\)
0.455696 + 0.890135i \(0.349390\pi\)
\(80\) 0 0
\(81\) 47.0000 65.9697i 0.580247 0.814441i
\(82\) 0 0
\(83\) −43.8406 −0.528200 −0.264100 0.964495i \(-0.585075\pi\)
−0.264100 + 0.964495i \(0.585075\pi\)
\(84\) 0 0
\(85\) 32.0000 + 46.6476i 0.376471 + 0.548795i
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 65.9697i 0.741232i 0.928786 + 0.370616i \(0.120853\pi\)
−0.928786 + 0.370616i \(0.879147\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 0 0
\(93\) −22.6274 93.2952i −0.243306 1.00317i
\(94\) 0 0
\(95\) −33.9411 49.4773i −0.357275 0.520813i
\(96\) 0 0
\(97\) 163.267i 1.68316i 0.540131 + 0.841581i \(0.318375\pi\)
−0.540131 + 0.841581i \(0.681625\pi\)
\(98\) 0 0
\(99\) −68.0000 131.939i −0.686869 1.33272i
\(100\) 0 0
\(101\) 131.939i 1.30633i −0.757215 0.653165i \(-0.773441\pi\)
0.757215 0.653165i \(-0.226559\pi\)
\(102\) 0 0
\(103\) 99.1262i 0.962390i −0.876614 0.481195i \(-0.840203\pi\)
0.876614 0.481195i \(-0.159797\pi\)
\(104\) 0 0
\(105\) 65.0833 + 58.4309i 0.619841 + 0.556485i
\(106\) 0 0
\(107\) −55.1543 −0.515461 −0.257731 0.966217i \(-0.582975\pi\)
−0.257731 + 0.966217i \(0.582975\pi\)
\(108\) 0 0
\(109\) 80.0000 0.733945 0.366972 0.930232i \(-0.380394\pi\)
0.366972 + 0.930232i \(0.380394\pi\)
\(110\) 0 0
\(111\) −68.0000 + 16.4924i −0.612613 + 0.148580i
\(112\) 0 0
\(113\) 152.735 1.35164 0.675819 0.737068i \(-0.263790\pi\)
0.675819 + 0.737068i \(0.263790\pi\)
\(114\) 0 0
\(115\) 68.0000 + 99.1262i 0.591304 + 0.861967i
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) 65.9697i 0.554367i
\(120\) 0 0
\(121\) −151.000 −1.24793
\(122\) 0 0
\(123\) 168.291 40.8167i 1.36822 0.331843i
\(124\) 0 0
\(125\) −121.622 + 28.8617i −0.972979 + 0.230894i
\(126\) 0 0
\(127\) 40.8167i 0.321391i 0.987004 + 0.160696i \(0.0513737\pi\)
−0.987004 + 0.160696i \(0.948626\pi\)
\(128\) 0 0
\(129\) −119.000 + 28.8617i −0.922481 + 0.223734i
\(130\) 0 0
\(131\) 49.4773i 0.377689i 0.982007 + 0.188845i \(0.0604742\pi\)
−0.982007 + 0.188845i \(0.939526\pi\)
\(132\) 0 0
\(133\) 69.9714i 0.526101i
\(134\) 0 0
\(135\) −34.1457 + 130.610i −0.252931 + 0.967484i
\(136\) 0 0
\(137\) 50.9117 0.371618 0.185809 0.982586i \(-0.440509\pi\)
0.185809 + 0.982586i \(0.440509\pi\)
\(138\) 0 0
\(139\) −44.0000 −0.316547 −0.158273 0.987395i \(-0.550593\pi\)
−0.158273 + 0.987395i \(0.550593\pi\)
\(140\) 0 0
\(141\) 25.0000 + 103.078i 0.177305 + 0.731047i
\(142\) 0 0
\(143\) 0 0
\(144\) 0 0
\(145\) 0 0
\(146\) 0 0
\(147\) −10.6066 43.7321i −0.0721538 0.297498i
\(148\) 0 0
\(149\) 8.24621i 0.0553437i 0.999617 + 0.0276718i \(0.00880935\pi\)
−0.999617 + 0.0276718i \(0.991191\pi\)
\(150\) 0 0
\(151\) −136.000 −0.900662 −0.450331 0.892862i \(-0.648694\pi\)
−0.450331 + 0.892862i \(0.648694\pi\)
\(152\) 0 0
\(153\) −90.5097 + 46.6476i −0.591566 + 0.304886i
\(154\) 0 0
\(155\) 90.5097 + 131.939i 0.583933 + 0.851222i
\(156\) 0 0
\(157\) 116.619i 0.742796i −0.928474 0.371398i \(-0.878878\pi\)
0.928474 0.371398i \(-0.121122\pi\)
\(158\) 0 0
\(159\) 48.0000 + 197.909i 0.301887 + 1.24471i
\(160\) 0 0
\(161\) 140.186i 0.870718i
\(162\) 0 0
\(163\) 99.1262i 0.608136i −0.952650 0.304068i \(-0.901655\pi\)
0.952650 0.304068i \(-0.0983450\pi\)
\(164\) 0 0
\(165\) 184.083 + 165.268i 1.11566 + 1.00162i
\(166\) 0 0
\(167\) 292.742 1.75295 0.876474 0.481450i \(-0.159890\pi\)
0.876474 + 0.481450i \(0.159890\pi\)
\(168\) 0 0
\(169\) 169.000 1.00000
\(170\) 0 0
\(171\) 96.0000 49.4773i 0.561404 0.289341i
\(172\) 0 0
\(173\) 164.049 0.948259 0.474129 0.880455i \(-0.342763\pi\)
0.474129 + 0.880455i \(0.342763\pi\)
\(174\) 0 0
\(175\) −136.000 52.4786i −0.777143 0.299878i
\(176\) 0 0
\(177\) 48.0833 11.6619i 0.271657 0.0658865i
\(178\) 0 0
\(179\) 16.4924i 0.0921364i 0.998938 + 0.0460682i \(0.0146692\pi\)
−0.998938 + 0.0460682i \(0.985331\pi\)
\(180\) 0 0
\(181\) −82.0000 −0.453039 −0.226519 0.974007i \(-0.572735\pi\)
−0.226519 + 0.974007i \(0.572735\pi\)
\(182\) 0 0
\(183\) 11.3137 + 46.6476i 0.0618235 + 0.254905i
\(184\) 0 0
\(185\) 96.1665 65.9697i 0.519819 0.356593i
\(186\) 0 0
\(187\) 186.590i 0.997810i
\(188\) 0 0
\(189\) −119.000 + 103.078i −0.629630 + 0.545384i
\(190\) 0 0
\(191\) 296.864i 1.55426i −0.629340 0.777130i \(-0.716675\pi\)
0.629340 0.777130i \(-0.283325\pi\)
\(192\) 0 0
\(193\) 116.619i 0.604244i −0.953269 0.302122i \(-0.902305\pi\)
0.953269 0.302122i \(-0.0976950\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 192.333 0.976310 0.488155 0.872757i \(-0.337670\pi\)
0.488155 + 0.872757i \(0.337670\pi\)
\(198\) 0 0
\(199\) 312.000 1.56784 0.783920 0.620862i \(-0.213217\pi\)
0.783920 + 0.620862i \(0.213217\pi\)
\(200\) 0 0
\(201\) −17.0000 + 4.12311i −0.0845771 + 0.0205130i
\(202\) 0 0
\(203\) 0 0
\(204\) 0 0
\(205\) −238.000 + 163.267i −1.16098 + 0.796423i
\(206\) 0 0
\(207\) −192.333 + 99.1262i −0.929145 + 0.478870i
\(208\) 0 0
\(209\) 197.909i 0.946933i
\(210\) 0 0
\(211\) 12.0000 0.0568720 0.0284360 0.999596i \(-0.490947\pi\)
0.0284360 + 0.999596i \(0.490947\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) 168.291 115.447i 0.782751 0.536963i
\(216\) 0 0
\(217\) 186.590i 0.859864i
\(218\) 0 0
\(219\) −340.000 + 82.4621i −1.55251 + 0.376539i
\(220\) 0 0
\(221\) 0 0
\(222\) 0 0
\(223\) 40.8167i 0.183034i −0.995803 0.0915172i \(-0.970828\pi\)
0.995803 0.0915172i \(-0.0291716\pi\)
\(224\) 0 0
\(225\) −24.1665 223.698i −0.107407 0.994215i
\(226\) 0 0
\(227\) −159.806 −0.703992 −0.351996 0.936002i \(-0.614497\pi\)
−0.351996 + 0.936002i \(0.614497\pi\)
\(228\) 0 0
\(229\) 82.0000 0.358079 0.179039 0.983842i \(-0.442701\pi\)
0.179039 + 0.983842i \(0.442701\pi\)
\(230\) 0 0
\(231\) 68.0000 + 280.371i 0.294372 + 1.21373i
\(232\) 0 0
\(233\) −192.333 −0.825464 −0.412732 0.910853i \(-0.635425\pi\)
−0.412732 + 0.910853i \(0.635425\pi\)
\(234\) 0 0
\(235\) −100.000 145.774i −0.425532 0.620314i
\(236\) 0 0
\(237\) −50.9117 209.914i −0.214817 0.885714i
\(238\) 0 0
\(239\) 461.788i 1.93217i −0.258231 0.966083i \(-0.583139\pi\)
0.258231 0.966083i \(-0.416861\pi\)
\(240\) 0 0
\(241\) 304.000 1.26141 0.630705 0.776022i \(-0.282766\pi\)
0.630705 + 0.776022i \(0.282766\pi\)
\(242\) 0 0
\(243\) −225.567 90.3798i −0.928260 0.371933i
\(244\) 0 0
\(245\) 42.4264 + 61.8466i 0.173169 + 0.252435i
\(246\) 0 0
\(247\) 0 0
\(248\) 0 0
\(249\) 31.0000 + 127.816i 0.124498 + 0.513318i
\(250\) 0 0
\(251\) 346.341i 1.37984i 0.723884 + 0.689922i \(0.242355\pi\)
−0.723884 + 0.689922i \(0.757645\pi\)
\(252\) 0 0
\(253\) 396.505i 1.56721i
\(254\) 0 0
\(255\) 113.373 126.280i 0.444598 0.495216i
\(256\) 0 0
\(257\) −390.323 −1.51877 −0.759383 0.650644i \(-0.774499\pi\)
−0.759383 + 0.650644i \(0.774499\pi\)
\(258\) 0 0
\(259\) 136.000 0.525097
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) 295.571 1.12384 0.561921 0.827191i \(-0.310062\pi\)
0.561921 + 0.827191i \(0.310062\pi\)
\(264\) 0 0
\(265\) −192.000 279.886i −0.724528 1.05617i
\(266\) 0 0
\(267\) 192.333 46.6476i 0.720348 0.174710i
\(268\) 0 0
\(269\) 74.2159i 0.275896i −0.990440 0.137948i \(-0.955949\pi\)
0.990440 0.137948i \(-0.0440506\pi\)
\(270\) 0 0
\(271\) −40.0000 −0.147601 −0.0738007 0.997273i \(-0.523513\pi\)
−0.0738007 + 0.997273i \(0.523513\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) −384.666 148.432i −1.39879 0.539752i
\(276\) 0 0
\(277\) 443.152i 1.59983i −0.600115 0.799914i \(-0.704878\pi\)
0.600115 0.799914i \(-0.295122\pi\)
\(278\) 0 0
\(279\) −256.000 + 131.939i −0.917563 + 0.472901i
\(280\) 0 0
\(281\) 519.511i 1.84879i −0.381431 0.924397i \(-0.624569\pi\)
0.381431 0.924397i \(-0.375431\pi\)
\(282\) 0 0
\(283\) 320.702i 1.13322i 0.823985 + 0.566612i \(0.191746\pi\)
−0.823985 + 0.566612i \(0.808254\pi\)
\(284\) 0 0
\(285\) −120.250 + 133.940i −0.421929 + 0.469966i
\(286\) 0 0
\(287\) −336.583 −1.17276
\(288\) 0 0
\(289\) −161.000 −0.557093
\(290\) 0 0
\(291\) 476.000 115.447i 1.63574 0.396725i
\(292\) 0 0
\(293\) −84.8528 −0.289600 −0.144800 0.989461i \(-0.546254\pi\)
−0.144800 + 0.989461i \(0.546254\pi\)
\(294\) 0 0
\(295\) −68.0000 + 46.6476i −0.230508 + 0.158128i
\(296\) 0 0
\(297\) −336.583 + 291.548i −1.13328 + 0.981642i
\(298\) 0 0
\(299\) 0 0
\(300\) 0 0
\(301\) 238.000 0.790698
\(302\) 0 0
\(303\) −384.666 + 93.2952i −1.26953 + 0.307905i
\(304\) 0 0
\(305\) −45.2548 65.9697i −0.148377 0.216294i
\(306\) 0 0
\(307\) 367.350i 1.19658i −0.801280 0.598290i \(-0.795847\pi\)
0.801280 0.598290i \(-0.204153\pi\)
\(308\) 0 0
\(309\) −289.000 + 70.0928i −0.935275 + 0.226838i
\(310\) 0 0
\(311\) 98.9545i 0.318182i −0.987264 0.159091i \(-0.949144\pi\)
0.987264 0.159091i \(-0.0508563\pi\)
\(312\) 0 0
\(313\) 186.590i 0.596136i −0.954545 0.298068i \(-0.903658\pi\)
0.954545 0.298068i \(-0.0963422\pi\)
\(314\) 0 0
\(315\) 124.333 231.066i 0.394708 0.733541i
\(316\) 0 0
\(317\) 520.431 1.64174 0.820868 0.571117i \(-0.193490\pi\)
0.820868 + 0.571117i \(0.193490\pi\)
\(318\) 0 0
\(319\) 0 0
\(320\) 0 0
\(321\) 39.0000 + 160.801i 0.121495 + 0.500938i
\(322\) 0 0
\(323\) −135.765 −0.420324
\(324\) 0 0
\(325\) 0 0
\(326\) 0 0
\(327\) −56.5685 233.238i −0.172992 0.713266i
\(328\) 0 0
\(329\) 206.155i 0.626612i
\(330\) 0 0
\(331\) −292.000 −0.882175 −0.441088 0.897464i \(-0.645407\pi\)
−0.441088 + 0.897464i \(0.645407\pi\)
\(332\) 0 0
\(333\) 96.1665 + 186.590i 0.288788 + 0.560332i
\(334\) 0 0
\(335\) 24.0416 16.4924i 0.0717661 0.0492311i
\(336\) 0 0
\(337\) 326.533i 0.968942i 0.874807 + 0.484471i \(0.160988\pi\)
−0.874807 + 0.484471i \(0.839012\pi\)
\(338\) 0 0
\(339\) −108.000 445.295i −0.318584 1.31356i
\(340\) 0 0
\(341\) 527.758i 1.54768i
\(342\) 0 0
\(343\) 373.181i 1.08799i
\(344\) 0 0
\(345\) 240.917 268.345i 0.698309 0.777812i
\(346\) 0 0
\(347\) 394.566 1.13708 0.568538 0.822657i \(-0.307509\pi\)
0.568538 + 0.822657i \(0.307509\pi\)
\(348\) 0 0
\(349\) 254.000 0.727794 0.363897 0.931439i \(-0.381446\pi\)
0.363897 + 0.931439i \(0.381446\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) −345.068 −0.977530 −0.488765 0.872415i \(-0.662552\pi\)
−0.488765 + 0.872415i \(0.662552\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 0 0
\(357\) 192.333 46.6476i 0.538748 0.130666i
\(358\) 0 0
\(359\) 395.818i 1.10256i 0.834321 + 0.551279i \(0.185860\pi\)
−0.834321 + 0.551279i \(0.814140\pi\)
\(360\) 0 0
\(361\) −217.000 −0.601108
\(362\) 0 0
\(363\) 106.773 + 440.237i 0.294141 + 1.21277i
\(364\) 0 0
\(365\) 480.833 329.848i 1.31735 0.903694i
\(366\) 0 0
\(367\) 413.998i 1.12806i −0.825755 0.564029i \(-0.809250\pi\)
0.825755 0.564029i \(-0.190750\pi\)
\(368\) 0 0
\(369\) −238.000 461.788i −0.644986 1.25146i
\(370\) 0 0
\(371\) 395.818i 1.06690i
\(372\) 0 0
\(373\) 629.743i 1.68832i 0.536092 + 0.844159i \(0.319900\pi\)
−0.536092 + 0.844159i \(0.680100\pi\)
\(374\) 0 0
\(375\) 170.146 + 334.179i 0.453722 + 0.891143i
\(376\) 0 0
\(377\) 0 0
\(378\) 0 0
\(379\) 572.000 1.50923 0.754617 0.656165i \(-0.227822\pi\)
0.754617 + 0.656165i \(0.227822\pi\)
\(380\) 0 0
\(381\) 119.000 28.8617i 0.312336 0.0757526i
\(382\) 0 0
\(383\) −193.747 −0.505868 −0.252934 0.967484i \(-0.581395\pi\)
−0.252934 + 0.967484i \(0.581395\pi\)
\(384\) 0 0
\(385\) −272.000 396.505i −0.706494 1.02988i
\(386\) 0 0
\(387\) 168.291 + 326.533i 0.434862 + 0.843755i
\(388\) 0 0
\(389\) 387.572i 0.996329i 0.867083 + 0.498164i \(0.165992\pi\)
−0.867083 + 0.498164i \(0.834008\pi\)
\(390\) 0 0
\(391\) 272.000 0.695652
\(392\) 0 0
\(393\) 144.250 34.9857i 0.367048 0.0890222i
\(394\) 0 0
\(395\) 203.647 + 296.864i 0.515561 + 0.751553i
\(396\) 0 0
\(397\) 513.124i 1.29250i −0.763124 0.646252i \(-0.776336\pi\)
0.763124 0.646252i \(-0.223664\pi\)
\(398\) 0 0
\(399\) −204.000 + 49.4773i −0.511278 + 0.124003i
\(400\) 0 0
\(401\) 65.9697i 0.164513i 0.996611 + 0.0822565i \(0.0262127\pi\)
−0.996611 + 0.0822565i \(0.973787\pi\)
\(402\) 0 0
\(403\) 0 0
\(404\) 0 0
\(405\) 404.936 + 7.19550i 0.999842 + 0.0177667i
\(406\) 0 0
\(407\) 384.666 0.945126
\(408\) 0 0
\(409\) 640.000 1.56479 0.782396 0.622781i \(-0.213997\pi\)
0.782396 + 0.622781i \(0.213997\pi\)
\(410\) 0 0
\(411\) −36.0000 148.432i −0.0875912 0.361148i
\(412\) 0 0
\(413\) −96.1665 −0.232849
\(414\) 0 0
\(415\) −124.000 180.760i −0.298795 0.435565i
\(416\) 0 0
\(417\) 31.1127 + 128.281i 0.0746108 + 0.307628i
\(418\) 0 0
\(419\) 577.235i 1.37765i 0.724928 + 0.688824i \(0.241873\pi\)
−0.724928 + 0.688824i \(0.758127\pi\)
\(420\) 0 0
\(421\) −656.000 −1.55819 −0.779097 0.626903i \(-0.784322\pi\)
−0.779097 + 0.626903i \(0.784322\pi\)
\(422\) 0 0
\(423\) 282.843 145.774i 0.668659 0.344619i
\(424\) 0 0
\(425\) −101.823 + 263.879i −0.239584 + 0.620891i
\(426\) 0 0
\(427\) 93.2952i 0.218490i
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 362.833i 0.841841i 0.907098 + 0.420920i \(0.138293\pi\)
−0.907098 + 0.420920i \(0.861707\pi\)
\(432\) 0 0
\(433\) 163.267i 0.377059i 0.982068 + 0.188530i \(0.0603722\pi\)
−0.982068 + 0.188530i \(0.939628\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) −288.500 −0.660182
\(438\) 0 0
\(439\) −432.000 −0.984055 −0.492027 0.870580i \(-0.663744\pi\)
−0.492027 + 0.870580i \(0.663744\pi\)
\(440\) 0 0
\(441\) −120.000 + 61.8466i −0.272109 + 0.140242i
\(442\) 0 0
\(443\) 123.037 0.277735 0.138867 0.990311i \(-0.455654\pi\)
0.138867 + 0.990311i \(0.455654\pi\)
\(444\) 0 0
\(445\) −272.000 + 186.590i −0.611236 + 0.419304i
\(446\) 0 0
\(447\) 24.0416 5.83095i 0.0537844 0.0130446i
\(448\) 0 0
\(449\) 865.852i 1.92840i 0.265174 + 0.964201i \(0.414571\pi\)
−0.265174 + 0.964201i \(0.585429\pi\)
\(450\) 0 0
\(451\) −952.000 −2.11086
\(452\) 0 0
\(453\) 96.1665 + 396.505i 0.212288 + 0.875286i
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) 466.476i 1.02074i 0.859956 + 0.510368i \(0.170491\pi\)
−0.859956 + 0.510368i \(0.829509\pi\)
\(458\) 0 0
\(459\) 200.000 + 230.894i 0.435730 + 0.503037i
\(460\) 0 0
\(461\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(462\) 0 0
\(463\) 612.250i 1.32235i 0.750230 + 0.661177i \(0.229943\pi\)
−0.750230 + 0.661177i \(0.770057\pi\)
\(464\) 0 0
\(465\) 320.666 357.174i 0.689604 0.768116i
\(466\) 0 0
\(467\) −767.918 −1.64436 −0.822182 0.569225i \(-0.807243\pi\)
−0.822182 + 0.569225i \(0.807243\pi\)
\(468\) 0 0
\(469\) 34.0000 0.0724947
\(470\) 0 0
\(471\) −340.000 + 82.4621i −0.721868 + 0.175079i
\(472\) 0 0
\(473\) 673.166 1.42318
\(474\) 0 0
\(475\) 108.000 279.886i 0.227368 0.589233i
\(476\) 0 0
\(477\) 543.058 279.886i 1.13849 0.586762i
\(478\) 0 0
\(479\) 560.742i 1.17065i −0.810798 0.585326i \(-0.800967\pi\)
0.810798 0.585326i \(-0.199033\pi\)
\(480\) 0 0
\(481\) 0 0
\(482\) 0 0
\(483\) 408.708 99.1262i 0.846186 0.205230i
\(484\) 0 0
\(485\) −673.166 + 461.788i −1.38797 + 0.952140i
\(486\) 0 0
\(487\) 647.236i 1.32903i 0.747277 + 0.664513i \(0.231361\pi\)
−0.747277 + 0.664513i \(0.768639\pi\)
\(488\) 0 0
\(489\) −289.000 + 70.0928i −0.591002 + 0.143339i
\(490\) 0 0
\(491\) 346.341i 0.705379i 0.935740 + 0.352689i \(0.114733\pi\)
−0.935740 + 0.352689i \(0.885267\pi\)
\(492\) 0 0
\(493\) 0 0
\(494\) 0 0
\(495\) 351.667 653.552i 0.710438 1.32031i
\(496\) 0 0
\(497\) 0 0
\(498\) 0 0
\(499\) 660.000 1.32265 0.661323 0.750102i \(-0.269995\pi\)
0.661323 + 0.750102i \(0.269995\pi\)
\(500\) 0 0
\(501\) −207.000 853.483i −0.413174 1.70356i
\(502\) 0 0
\(503\) −182.434 −0.362691 −0.181345 0.983419i \(-0.558045\pi\)
−0.181345 + 0.983419i \(0.558045\pi\)
\(504\) 0 0
\(505\) 544.000 373.181i 1.07723 0.738972i
\(506\) 0 0
\(507\) −119.501 492.715i −0.235702 0.971825i
\(508\) 0 0
\(509\) 395.818i 0.777639i −0.921314 0.388819i \(-0.872883\pi\)
0.921314 0.388819i \(-0.127117\pi\)
\(510\) 0 0
\(511\) 680.000 1.33072
\(512\) 0 0
\(513\) −212.132 244.900i −0.413513 0.477388i
\(514\) 0 0
\(515\) 408.708 280.371i 0.793607 0.544410i
\(516\) 0 0
\(517\) 583.095i 1.12784i
\(518\) 0 0
\(519\) −116.000 478.280i −0.223507 0.921542i
\(520\) 0 0
\(521\) 131.939i 0.253243i −0.991951 0.126621i \(-0.959587\pi\)
0.991951 0.126621i \(-0.0404133\pi\)
\(522\) 0 0
\(523\) 145.774i 0.278726i 0.990241 + 0.139363i \(0.0445055\pi\)
−0.990241 + 0.139363i \(0.955494\pi\)
\(524\) 0 0
\(525\) −56.8335 + 433.613i −0.108254 + 0.825929i
\(526\) 0 0
\(527\) 362.039 0.686980
\(528\) 0 0
\(529\) 49.0000 0.0926276
\(530\) 0 0
\(531\) −68.0000 131.939i −0.128060 0.248473i
\(532\) 0 0
\(533\) 0 0
\(534\) 0 0
\(535\) −156.000 227.407i −0.291589 0.425060i
\(536\) 0 0
\(537\) 48.0833 11.6619i 0.0895405 0.0217168i
\(538\) 0 0
\(539\) 247.386i 0.458973i
\(540\) 0 0
\(541\) 418.000 0.772643 0.386322 0.922364i \(-0.373745\pi\)
0.386322 + 0.922364i \(0.373745\pi\)
\(542\) 0 0
\(543\) 57.9828 + 239.069i 0.106782 + 0.440274i
\(544\) 0 0
\(545\) 226.274 + 329.848i 0.415182 + 0.605227i
\(546\) 0 0
\(547\) 285.717i 0.522334i 0.965294 + 0.261167i \(0.0841073\pi\)
−0.965294 + 0.261167i \(0.915893\pi\)
\(548\) 0 0
\(549\) 128.000 65.9697i 0.233151 0.120163i
\(550\) 0 0
\(551\) 0 0
\(552\) 0 0
\(553\) 419.829i 0.759184i
\(554\) 0 0
\(555\) −260.333 233.724i −0.469069 0.421124i
\(556\) 0 0
\(557\) −424.264 −0.761695 −0.380847 0.924638i \(-0.624368\pi\)
−0.380847 + 0.924638i \(0.624368\pi\)
\(558\) 0 0
\(559\) 0 0
\(560\) 0 0
\(561\) 544.000 131.939i 0.969697 0.235186i
\(562\) 0 0
\(563\) −813.173 −1.44436 −0.722178 0.691707i \(-0.756859\pi\)
−0.722178 + 0.691707i \(0.756859\pi\)
\(564\) 0 0
\(565\) 432.000 + 629.743i 0.764602 + 1.11459i
\(566\) 0 0
\(567\) 384.666 + 274.055i 0.678423 + 0.483342i
\(568\) 0 0
\(569\) 453.542i 0.797085i −0.917150 0.398543i \(-0.869516\pi\)
0.917150 0.398543i \(-0.130484\pi\)
\(570\) 0 0
\(571\) −220.000 −0.385289 −0.192644 0.981269i \(-0.561706\pi\)
−0.192644 + 0.981269i \(0.561706\pi\)
\(572\) 0 0
\(573\) −865.499 + 209.914i −1.51047 + 0.366343i
\(574\) 0 0
\(575\) −216.375 + 560.742i −0.376304 + 0.975204i
\(576\) 0 0
\(577\) 46.6476i 0.0808451i 0.999183 + 0.0404225i \(0.0128704\pi\)
−0.999183 + 0.0404225i \(0.987130\pi\)
\(578\) 0 0
\(579\) −340.000 + 82.4621i −0.587219 + 0.142422i
\(580\) 0 0
\(581\) 255.633i 0.439987i
\(582\) 0 0
\(583\) 1119.54i 1.92031i
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 55.1543 0.0939597 0.0469798 0.998896i \(-0.485040\pi\)
0.0469798 + 0.998896i \(0.485040\pi\)
\(588\) 0 0
\(589\) −384.000 −0.651952
\(590\) 0 0
\(591\) −136.000 560.742i −0.230118 0.948803i
\(592\) 0 0
\(593\) −390.323 −0.658217 −0.329109 0.944292i \(-0.606748\pi\)
−0.329109 + 0.944292i \(0.606748\pi\)
\(594\) 0 0
\(595\) −272.000 + 186.590i −0.457143 + 0.313597i
\(596\) 0 0
\(597\) −220.617 909.628i −0.369543 1.52367i
\(598\) 0 0
\(599\) 98.9545i 0.165200i −0.996583 0.0825998i \(-0.973678\pi\)
0.996583 0.0825998i \(-0.0263223\pi\)
\(600\) 0 0
\(601\) −880.000 −1.46423 −0.732113 0.681183i \(-0.761466\pi\)
−0.732113 + 0.681183i \(0.761466\pi\)
\(602\) 0 0
\(603\) 24.0416 + 46.6476i 0.0398700 + 0.0773592i
\(604\) 0 0
\(605\) −427.092 622.589i −0.705938 1.02907i
\(606\) 0 0
\(607\) 425.659i 0.701251i −0.936516 0.350626i \(-0.885969\pi\)
0.936516 0.350626i \(-0.114031\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 0 0
\(612\) 0 0
\(613\) 606.419i 0.989264i −0.869102 0.494632i \(-0.835303\pi\)
0.869102 0.494632i \(-0.164697\pi\)
\(614\) 0 0
\(615\) 644.291 + 578.436i 1.04763 + 0.940547i
\(616\) 0 0
\(617\) 113.137 0.183366 0.0916832 0.995788i \(-0.470775\pi\)
0.0916832 + 0.995788i \(0.470775\pi\)
\(618\) 0 0
\(619\) −52.0000 −0.0840065 −0.0420032 0.999117i \(-0.513374\pi\)
−0.0420032 + 0.999117i \(0.513374\pi\)
\(620\) 0 0
\(621\) 425.000 + 490.650i 0.684380 + 0.790096i
\(622\) 0 0
\(623\) −384.666 −0.617442
\(624\) 0 0
\(625\) −463.000 419.829i −0.740800 0.671726i
\(626\) 0 0
\(627\) −576.999 + 139.943i −0.920254 + 0.223194i
\(628\) 0 0
\(629\) 263.879i 0.419521i
\(630\) 0 0
\(631\) 544.000 0.862124 0.431062 0.902322i \(-0.358139\pi\)
0.431062 + 0.902322i \(0.358139\pi\)
\(632\) 0 0
\(633\) −8.48528 34.9857i −0.0134049 0.0552697i
\(634\) 0 0
\(635\) −168.291 + 115.447i −0.265026 + 0.181806i
\(636\) 0 0
\(637\) 0 0
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) 849.360i 1.32505i 0.749038 + 0.662527i \(0.230516\pi\)
−0.749038 + 0.662527i \(0.769484\pi\)
\(642\) 0 0
\(643\) 367.350i 0.571306i −0.958333 0.285653i \(-0.907789\pi\)
0.958333 0.285653i \(-0.0922105\pi\)
\(644\) 0 0
\(645\) −455.583 409.016i −0.706330 0.634134i
\(646\) 0 0
\(647\) −971.565 −1.50165 −0.750823 0.660504i \(-0.770343\pi\)
−0.750823 + 0.660504i \(0.770343\pi\)
\(648\) 0 0
\(649\) −272.000 −0.419106
\(650\) 0 0
\(651\) 544.000 131.939i 0.835637 0.202672i
\(652\) 0 0
\(653\) −350.725 −0.537098 −0.268549 0.963266i \(-0.586544\pi\)
−0.268549 + 0.963266i \(0.586544\pi\)
\(654\) 0 0
\(655\) −204.000 + 139.943i −0.311450 + 0.213653i
\(656\) 0 0
\(657\) 480.833 + 932.952i 0.731861 + 1.42002i
\(658\) 0 0
\(659\) 577.235i 0.875925i −0.898993 0.437963i \(-0.855700\pi\)
0.898993 0.437963i \(-0.144300\pi\)
\(660\) 0 0
\(661\) 80.0000 0.121029 0.0605144 0.998167i \(-0.480726\pi\)
0.0605144 + 0.998167i \(0.480726\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 288.500 197.909i 0.433834 0.297608i
\(666\) 0 0
\(667\) 0 0
\(668\) 0 0
\(669\) −119.000 + 28.8617i −0.177877 + 0.0431416i
\(670\) 0 0
\(671\) 263.879i 0.393262i
\(672\) 0 0
\(673\) 489.800i 0.727786i −0.931441 0.363893i \(-0.881447\pi\)
0.931441 0.363893i \(-0.118553\pi\)
\(674\) 0 0
\(675\) −635.099 + 228.636i −0.940887 + 0.338719i
\(676\) 0 0
\(677\) −192.333 −0.284096 −0.142048 0.989860i \(-0.545369\pi\)
−0.142048 + 0.989860i \(0.545369\pi\)
\(678\) 0 0
\(679\) −952.000 −1.40206
\(680\) 0 0
\(681\) 113.000 + 465.911i 0.165932 + 0.684157i
\(682\) 0 0
\(683\) 236.174 0.345789 0.172894 0.984940i \(-0.444688\pi\)
0.172894 + 0.984940i \(0.444688\pi\)
\(684\) 0 0
\(685\) 144.000 + 209.914i 0.210219 + 0.306444i
\(686\) 0 0
\(687\) −57.9828 239.069i −0.0843999 0.347990i
\(688\) 0 0
\(689\) 0 0
\(690\) 0 0
\(691\) 548.000 0.793054 0.396527 0.918023i \(-0.370215\pi\)
0.396527 + 0.918023i \(0.370215\pi\)
\(692\) 0 0
\(693\) 769.332 396.505i 1.11015 0.572157i
\(694\) 0 0
\(695\) −124.451 181.417i −0.179066 0.261031i
\(696\) 0 0
\(697\) 653.067i 0.936968i
\(698\) 0 0
\(699\) 136.000 + 560.742i 0.194564 + 0.802207i
\(700\) 0 0
\(701\) 57.7235i 0.0823445i 0.999152 + 0.0411722i \(0.0131092\pi\)
−0.999152 + 0.0411722i \(0.986891\pi\)
\(702\) 0 0
\(703\) 279.886i 0.398130i
\(704\) 0 0
\(705\) −354.289 + 394.625i −0.502538 + 0.559752i
\(706\) 0 0
\(707\) 769.332 1.08816
\(708\) 0 0
\(709\) 1230.00 1.73484 0.867419 0.497579i \(-0.165777\pi\)
0.867419 + 0.497579i \(0.165777\pi\)
\(710\) 0 0
\(711\) −576.000 + 296.864i −0.810127 + 0.417530i
\(712\) 0 0
\(713\) 769.332 1.07901
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) −1346.33 + 326.533i −1.87773 + 0.455416i
\(718\) 0 0
\(719\) 626.712i 0.871644i 0.900033 + 0.435822i \(0.143542\pi\)
−0.900033 + 0.435822i \(0.856458\pi\)
\(720\) 0 0
\(721\) 578.000 0.801664
\(722\) 0 0
\(723\) −214.960 886.305i −0.297317 1.22587i
\(724\) 0 0
\(725\) 0 0
\(726\) 0 0
\(727\) 367.350i 0.505296i 0.967558 + 0.252648i \(0.0813014\pi\)
−0.967558 + 0.252648i \(0.918699\pi\)
\(728\) 0 0
\(729\) −104.000 + 721.543i −0.142661 + 0.989772i
\(730\) 0 0
\(731\) 461.788i 0.631721i
\(732\) 0 0
\(733\) 1002.92i 1.36825i −0.729367 0.684123i \(-0.760185\pi\)
0.729367 0.684123i \(-0.239815\pi\)
\(734\) 0 0
\(735\) 150.312 167.425i 0.204506 0.227790i
\(736\) 0 0
\(737\) 96.1665 0.130484
\(738\) 0 0
\(739\) 340.000 0.460081 0.230041 0.973181i \(-0.426114\pi\)
0.230041 + 0.973181i \(0.426114\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 1243.09 1.67307 0.836537 0.547911i \(-0.184577\pi\)
0.836537 + 0.547911i \(0.184577\pi\)
\(744\) 0 0
\(745\) −34.0000 + 23.3238i −0.0456376 + 0.0313071i
\(746\) 0 0
\(747\) 350.725 180.760i 0.469511 0.241981i
\(748\) 0 0
\(749\) 321.602i 0.429375i
\(750\) 0 0
\(751\) 520.000 0.692410 0.346205 0.938159i \(-0.387470\pi\)
0.346205 + 0.938159i \(0.387470\pi\)
\(752\) 0 0
\(753\) 1009.75 244.900i 1.34097 0.325232i
\(754\) 0 0
\(755\) −384.666 560.742i −0.509492 0.742705i
\(756\) 0 0
\(757\) 816.333i 1.07838i 0.842184 + 0.539190i \(0.181269\pi\)
−0.842184 + 0.539190i \(0.818731\pi\)
\(758\) 0 0
\(759\) 1156.00 280.371i 1.52306 0.369395i
\(760\) 0 0
\(761\) 395.818i 0.520129i −0.965591 0.260064i \(-0.916256\pi\)
0.965591 0.260064i \(-0.0837438\pi\)
\(762\) 0 0
\(763\) 466.476i 0.611371i
\(764\) 0 0
\(765\) −448.333 241.242i −0.586056 0.315348i
\(766\) 0 0
\(767\) 0 0
\(768\) 0 0
\(769\) −306.000 −0.397919 −0.198960 0.980008i \(-0.563756\pi\)
−0.198960 + 0.980008i \(0.563756\pi\)
\(770\) 0 0
\(771\) 276.000 + 1137.98i 0.357977 + 1.47598i
\(772\) 0 0
\(773\) −305.470 −0.395175 −0.197587 0.980285i \(-0.563311\pi\)
−0.197587 + 0.980285i \(0.563311\pi\)
\(774\) 0 0
\(775\) −288.000 + 746.362i −0.371613 + 0.963048i
\(776\) 0 0
\(777\) −96.1665 396.505i −0.123766 0.510302i
\(778\) 0 0
\(779\) 692.682i 0.889194i
\(780\) 0 0
\(781\) 0 0
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) 480.833 329.848i 0.612526 0.420189i
\(786\) 0 0
\(787\) 565.602i 0.718681i 0.933206 + 0.359341i \(0.116998\pi\)
−0.933206 + 0.359341i \(0.883002\pi\)
\(788\) 0 0
\(789\) −209.000 861.729i −0.264892 1.09218i
\(790\) 0 0
\(791\) 890.591i 1.12590i
\(792\) 0 0
\(793\)