Properties

Label 1040.2.da.f.881.4
Level $1040$
Weight $2$
Character 1040.881
Analytic conductor $8.304$
Analytic rank $0$
Dimension $16$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [1040,2,Mod(641,1040)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1040, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([0, 0, 0, 1]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("1040.641");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1040 = 2^{4} \cdot 5 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1040.da (of order \(6\), 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: \(8.30444181021\)
Analytic rank: \(0\)
Dimension: \(16\)
Relative dimension: \(8\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} + \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{16} + 22x^{14} + 183x^{12} + 730x^{10} + 1485x^{8} + 1552x^{6} + 812x^{4} + 192x^{2} + 16 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{4} \)
Twist minimal: no (minimal twist has level 520)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 881.4
Root \(-1.44614i\) of defining polynomial
Character \(\chi\) \(=\) 1040.881
Dual form 1040.2.da.f.641.4

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.268727 - 0.465448i) q^{3} +1.00000i q^{5} +(0.331682 + 0.191497i) q^{7} +(1.35557 - 2.34792i) q^{9} +O(q^{10})\) \(q+(-0.268727 - 0.465448i) q^{3} +1.00000i q^{5} +(0.331682 + 0.191497i) q^{7} +(1.35557 - 2.34792i) q^{9} +(-5.66862 + 3.27278i) q^{11} +(-2.44183 + 2.65282i) q^{13} +(0.465448 - 0.268727i) q^{15} +(0.174340 - 0.301966i) q^{17} +(-3.55500 - 2.05248i) q^{19} -0.205841i q^{21} +(-3.36387 - 5.82639i) q^{23} -1.00000 q^{25} -3.06947 q^{27} +(1.91872 + 3.32331i) q^{29} -1.67765i q^{31} +(3.04662 + 1.75897i) q^{33} +(-0.191497 + 0.331682i) q^{35} +(0.963044 - 0.556014i) q^{37} +(1.89094 + 0.423660i) q^{39} +(-6.17915 + 3.56754i) q^{41} +(-2.87604 + 4.98145i) q^{43} +(2.34792 + 1.35557i) q^{45} +7.72357i q^{47} +(-3.42666 - 5.93515i) q^{49} -0.187399 q^{51} -7.18066 q^{53} +(-3.27278 - 5.66862i) q^{55} +2.20623i q^{57} +(3.85348 + 2.22481i) q^{59} +(5.19956 - 9.00590i) q^{61} +(0.899239 - 0.519176i) q^{63} +(-2.65282 - 2.44183i) q^{65} +(-3.01934 + 1.74322i) q^{67} +(-1.80792 + 3.13141i) q^{69} +(-2.93488 - 1.69446i) q^{71} +8.04467i q^{73} +(0.268727 + 0.465448i) q^{75} -2.50691 q^{77} -10.7375 q^{79} +(-3.24187 - 5.61508i) q^{81} -8.27761i q^{83} +(0.301966 + 0.174340i) q^{85} +(1.03122 - 1.78613i) q^{87} +(-15.5518 + 8.97885i) q^{89} +(-1.31792 + 0.412292i) q^{91} +(-0.780860 + 0.450830i) q^{93} +(2.05248 - 3.55500i) q^{95} +(1.14570 + 0.661472i) q^{97} +17.7460i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16 q + 4 q^{3} - 6 q^{7} - 16 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 16 q + 4 q^{3} - 6 q^{7} - 16 q^{9} + 6 q^{11} - 2 q^{13} + 4 q^{17} - 30 q^{19} - 6 q^{23} - 16 q^{25} - 44 q^{27} - 16 q^{29} + 24 q^{33} + 6 q^{35} - 24 q^{37} + 8 q^{39} - 24 q^{41} - 6 q^{43} + 12 q^{45} - 4 q^{49} + 40 q^{51} + 4 q^{53} + 6 q^{55} - 12 q^{59} - 2 q^{61} + 60 q^{63} - 10 q^{65} + 6 q^{67} + 52 q^{69} - 72 q^{71} - 4 q^{75} + 32 q^{77} - 36 q^{79} - 28 q^{81} + 22 q^{87} + 24 q^{89} + 22 q^{91} - 96 q^{93} - 10 q^{95} + 60 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1040\mathbb{Z}\right)^\times\).

\(n\) \(261\) \(417\) \(561\) \(911\)
\(\chi(n)\) \(1\) \(1\) \(e\left(\frac{5}{6}\right)\) \(1\)

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
\(3\) −0.268727 0.465448i −0.155149 0.268727i 0.777964 0.628309i \(-0.216253\pi\)
−0.933113 + 0.359582i \(0.882919\pi\)
\(4\) 0 0
\(5\) 1.00000i 0.447214i
\(6\) 0 0
\(7\) 0.331682 + 0.191497i 0.125364 + 0.0723790i 0.561371 0.827564i \(-0.310274\pi\)
−0.436007 + 0.899944i \(0.643608\pi\)
\(8\) 0 0
\(9\) 1.35557 2.34792i 0.451857 0.782640i
\(10\) 0 0
\(11\) −5.66862 + 3.27278i −1.70915 + 0.986780i −0.773545 + 0.633742i \(0.781518\pi\)
−0.935609 + 0.353039i \(0.885148\pi\)
\(12\) 0 0
\(13\) −2.44183 + 2.65282i −0.677241 + 0.735761i
\(14\) 0 0
\(15\) 0.465448 0.268727i 0.120178 0.0693849i
\(16\) 0 0
\(17\) 0.174340 0.301966i 0.0422837 0.0732376i −0.844109 0.536172i \(-0.819870\pi\)
0.886393 + 0.462934i \(0.153203\pi\)
\(18\) 0 0
\(19\) −3.55500 2.05248i −0.815574 0.470872i 0.0333141 0.999445i \(-0.489394\pi\)
−0.848888 + 0.528573i \(0.822727\pi\)
\(20\) 0 0
\(21\) 0.205841i 0.0449182i
\(22\) 0 0
\(23\) −3.36387 5.82639i −0.701415 1.21489i −0.967970 0.251067i \(-0.919219\pi\)
0.266555 0.963820i \(-0.414115\pi\)
\(24\) 0 0
\(25\) −1.00000 −0.200000
\(26\) 0 0
\(27\) −3.06947 −0.590720
\(28\) 0 0
\(29\) 1.91872 + 3.32331i 0.356297 + 0.617124i 0.987339 0.158624i \(-0.0507059\pi\)
−0.631042 + 0.775748i \(0.717373\pi\)
\(30\) 0 0
\(31\) 1.67765i 0.301315i −0.988586 0.150658i \(-0.951861\pi\)
0.988586 0.150658i \(-0.0481391\pi\)
\(32\) 0 0
\(33\) 3.04662 + 1.75897i 0.530348 + 0.306197i
\(34\) 0 0
\(35\) −0.191497 + 0.331682i −0.0323689 + 0.0560646i
\(36\) 0 0
\(37\) 0.963044 0.556014i 0.158324 0.0914081i −0.418745 0.908104i \(-0.637530\pi\)
0.577069 + 0.816696i \(0.304197\pi\)
\(38\) 0 0
\(39\) 1.89094 + 0.423660i 0.302792 + 0.0678399i
\(40\) 0 0
\(41\) −6.17915 + 3.56754i −0.965022 + 0.557155i −0.897715 0.440577i \(-0.854774\pi\)
−0.0673067 + 0.997732i \(0.521441\pi\)
\(42\) 0 0
\(43\) −2.87604 + 4.98145i −0.438592 + 0.759663i −0.997581 0.0695116i \(-0.977856\pi\)
0.558989 + 0.829175i \(0.311189\pi\)
\(44\) 0 0
\(45\) 2.34792 + 1.35557i 0.350007 + 0.202077i
\(46\) 0 0
\(47\) 7.72357i 1.12660i 0.826253 + 0.563299i \(0.190468\pi\)
−0.826253 + 0.563299i \(0.809532\pi\)
\(48\) 0 0
\(49\) −3.42666 5.93515i −0.489523 0.847878i
\(50\) 0 0
\(51\) −0.187399 −0.0262412
\(52\) 0 0
\(53\) −7.18066 −0.986339 −0.493169 0.869933i \(-0.664162\pi\)
−0.493169 + 0.869933i \(0.664162\pi\)
\(54\) 0 0
\(55\) −3.27278 5.66862i −0.441302 0.764357i
\(56\) 0 0
\(57\) 2.20623i 0.292222i
\(58\) 0 0
\(59\) 3.85348 + 2.22481i 0.501680 + 0.289645i 0.729407 0.684080i \(-0.239796\pi\)
−0.227727 + 0.973725i \(0.573129\pi\)
\(60\) 0 0
\(61\) 5.19956 9.00590i 0.665735 1.15309i −0.313350 0.949638i \(-0.601451\pi\)
0.979085 0.203450i \(-0.0652153\pi\)
\(62\) 0 0
\(63\) 0.899239 0.519176i 0.113293 0.0654100i
\(64\) 0 0
\(65\) −2.65282 2.44183i −0.329042 0.302872i
\(66\) 0 0
\(67\) −3.01934 + 1.74322i −0.368872 + 0.212968i −0.672965 0.739674i \(-0.734980\pi\)
0.304094 + 0.952642i \(0.401646\pi\)
\(68\) 0 0
\(69\) −1.80792 + 3.13141i −0.217648 + 0.376978i
\(70\) 0 0
\(71\) −2.93488 1.69446i −0.348307 0.201095i 0.315633 0.948881i \(-0.397783\pi\)
−0.663939 + 0.747787i \(0.731117\pi\)
\(72\) 0 0
\(73\) 8.04467i 0.941557i 0.882251 + 0.470779i \(0.156027\pi\)
−0.882251 + 0.470779i \(0.843973\pi\)
\(74\) 0 0
\(75\) 0.268727 + 0.465448i 0.0310299 + 0.0537453i
\(76\) 0 0
\(77\) −2.50691 −0.285689
\(78\) 0 0
\(79\) −10.7375 −1.20807 −0.604033 0.796959i \(-0.706441\pi\)
−0.604033 + 0.796959i \(0.706441\pi\)
\(80\) 0 0
\(81\) −3.24187 5.61508i −0.360208 0.623898i
\(82\) 0 0
\(83\) 8.27761i 0.908586i −0.890852 0.454293i \(-0.849892\pi\)
0.890852 0.454293i \(-0.150108\pi\)
\(84\) 0 0
\(85\) 0.301966 + 0.174340i 0.0327528 + 0.0189099i
\(86\) 0 0
\(87\) 1.03122 1.78613i 0.110558 0.191493i
\(88\) 0 0
\(89\) −15.5518 + 8.97885i −1.64849 + 0.951757i −0.670818 + 0.741622i \(0.734057\pi\)
−0.977672 + 0.210135i \(0.932610\pi\)
\(90\) 0 0
\(91\) −1.31792 + 0.412292i −0.138155 + 0.0432200i
\(92\) 0 0
\(93\) −0.780860 + 0.450830i −0.0809714 + 0.0467488i
\(94\) 0 0
\(95\) 2.05248 3.55500i 0.210580 0.364736i
\(96\) 0 0
\(97\) 1.14570 + 0.661472i 0.116329 + 0.0671623i 0.557035 0.830489i \(-0.311939\pi\)
−0.440707 + 0.897651i \(0.645272\pi\)
\(98\) 0 0
\(99\) 17.7460i 1.78354i
\(100\) 0 0
\(101\) −7.73517 13.3977i −0.769678 1.33312i −0.937737 0.347345i \(-0.887083\pi\)
0.168059 0.985777i \(-0.446250\pi\)
\(102\) 0 0
\(103\) 14.3730 1.41622 0.708109 0.706103i \(-0.249548\pi\)
0.708109 + 0.706103i \(0.249548\pi\)
\(104\) 0 0
\(105\) 0.205841 0.0200880
\(106\) 0 0
\(107\) 9.21819 + 15.9664i 0.891156 + 1.54353i 0.838491 + 0.544915i \(0.183438\pi\)
0.0526643 + 0.998612i \(0.483229\pi\)
\(108\) 0 0
\(109\) 3.91578i 0.375064i 0.982259 + 0.187532i \(0.0600488\pi\)
−0.982259 + 0.187532i \(0.939951\pi\)
\(110\) 0 0
\(111\) −0.517591 0.298831i −0.0491276 0.0283638i
\(112\) 0 0
\(113\) −10.1161 + 17.5215i −0.951640 + 1.64829i −0.209763 + 0.977752i \(0.567269\pi\)
−0.741877 + 0.670537i \(0.766064\pi\)
\(114\) 0 0
\(115\) 5.82639 3.36387i 0.543314 0.313682i
\(116\) 0 0
\(117\) 2.91854 + 9.32931i 0.269819 + 0.862495i
\(118\) 0 0
\(119\) 0.115651 0.0667713i 0.0106017 0.00612091i
\(120\) 0 0
\(121\) 15.9222 27.5780i 1.44747 2.50709i
\(122\) 0 0
\(123\) 3.32100 + 1.91738i 0.299445 + 0.172885i
\(124\) 0 0
\(125\) 1.00000i 0.0894427i
\(126\) 0 0
\(127\) 6.88887 + 11.9319i 0.611288 + 1.05878i 0.991024 + 0.133687i \(0.0426818\pi\)
−0.379735 + 0.925095i \(0.623985\pi\)
\(128\) 0 0
\(129\) 3.09147 0.272189
\(130\) 0 0
\(131\) 5.66818 0.495231 0.247616 0.968858i \(-0.420353\pi\)
0.247616 + 0.968858i \(0.420353\pi\)
\(132\) 0 0
\(133\) −0.786088 1.36154i −0.0681625 0.118061i
\(134\) 0 0
\(135\) 3.06947i 0.264178i
\(136\) 0 0
\(137\) 2.88380 + 1.66496i 0.246379 + 0.142247i 0.618105 0.786095i \(-0.287901\pi\)
−0.371726 + 0.928343i \(0.621234\pi\)
\(138\) 0 0
\(139\) 2.23569 3.87234i 0.189629 0.328447i −0.755497 0.655152i \(-0.772605\pi\)
0.945127 + 0.326704i \(0.105938\pi\)
\(140\) 0 0
\(141\) 3.59492 2.07553i 0.302747 0.174791i
\(142\) 0 0
\(143\) 5.15969 23.0294i 0.431475 1.92582i
\(144\) 0 0
\(145\) −3.32331 + 1.91872i −0.275986 + 0.159341i
\(146\) 0 0
\(147\) −1.84167 + 3.18986i −0.151898 + 0.263095i
\(148\) 0 0
\(149\) 11.1256 + 6.42338i 0.911446 + 0.526223i 0.880896 0.473310i \(-0.156941\pi\)
0.0305497 + 0.999533i \(0.490274\pi\)
\(150\) 0 0
\(151\) 7.20405i 0.586257i −0.956073 0.293129i \(-0.905304\pi\)
0.956073 0.293129i \(-0.0946964\pi\)
\(152\) 0 0
\(153\) −0.472662 0.818674i −0.0382124 0.0661859i
\(154\) 0 0
\(155\) 1.67765 0.134752
\(156\) 0 0
\(157\) 1.76129 0.140566 0.0702832 0.997527i \(-0.477610\pi\)
0.0702832 + 0.997527i \(0.477610\pi\)
\(158\) 0 0
\(159\) 1.92963 + 3.34222i 0.153030 + 0.265055i
\(160\) 0 0
\(161\) 2.57668i 0.203071i
\(162\) 0 0
\(163\) −3.01956 1.74334i −0.236510 0.136549i 0.377062 0.926188i \(-0.376934\pi\)
−0.613572 + 0.789639i \(0.710268\pi\)
\(164\) 0 0
\(165\) −1.75897 + 3.04662i −0.136935 + 0.237179i
\(166\) 0 0
\(167\) 11.0835 6.39909i 0.857671 0.495176i −0.00556090 0.999985i \(-0.501770\pi\)
0.863232 + 0.504808i \(0.168437\pi\)
\(168\) 0 0
\(169\) −1.07495 12.9555i −0.0826882 0.996575i
\(170\) 0 0
\(171\) −9.63812 + 5.56457i −0.737046 + 0.425534i
\(172\) 0 0
\(173\) 3.23046 5.59531i 0.245607 0.425404i −0.716695 0.697387i \(-0.754346\pi\)
0.962302 + 0.271983i \(0.0876794\pi\)
\(174\) 0 0
\(175\) −0.331682 0.191497i −0.0250728 0.0144758i
\(176\) 0 0
\(177\) 2.39146i 0.179753i
\(178\) 0 0
\(179\) 3.96078 + 6.86028i 0.296043 + 0.512761i 0.975227 0.221207i \(-0.0709995\pi\)
−0.679184 + 0.733968i \(0.737666\pi\)
\(180\) 0 0
\(181\) −22.0467 −1.63871 −0.819357 0.573283i \(-0.805670\pi\)
−0.819357 + 0.573283i \(0.805670\pi\)
\(182\) 0 0
\(183\) −5.58904 −0.413154
\(184\) 0 0
\(185\) 0.556014 + 0.963044i 0.0408790 + 0.0708044i
\(186\) 0 0
\(187\) 2.28231i 0.166899i
\(188\) 0 0
\(189\) −1.01809 0.587794i −0.0740551 0.0427558i
\(190\) 0 0
\(191\) 9.38199 16.2501i 0.678857 1.17582i −0.296468 0.955043i \(-0.595809\pi\)
0.975325 0.220773i \(-0.0708579\pi\)
\(192\) 0 0
\(193\) 10.7478 6.20526i 0.773646 0.446665i −0.0605279 0.998167i \(-0.519278\pi\)
0.834174 + 0.551502i \(0.185945\pi\)
\(194\) 0 0
\(195\) −0.423660 + 1.89094i −0.0303389 + 0.135413i
\(196\) 0 0
\(197\) −0.499279 + 0.288259i −0.0355721 + 0.0205376i −0.517681 0.855574i \(-0.673204\pi\)
0.482108 + 0.876112i \(0.339871\pi\)
\(198\) 0 0
\(199\) 5.96050 10.3239i 0.422529 0.731841i −0.573657 0.819095i \(-0.694476\pi\)
0.996186 + 0.0872543i \(0.0278093\pi\)
\(200\) 0 0
\(201\) 1.62276 + 0.936899i 0.114460 + 0.0660837i
\(202\) 0 0
\(203\) 1.46971i 0.103154i
\(204\) 0 0
\(205\) −3.56754 6.17915i −0.249167 0.431571i
\(206\) 0 0
\(207\) −18.2399 −1.26776
\(208\) 0 0
\(209\) 26.8693 1.85859
\(210\) 0 0
\(211\) 3.15018 + 5.45627i 0.216867 + 0.375625i 0.953849 0.300288i \(-0.0970827\pi\)
−0.736981 + 0.675913i \(0.763749\pi\)
\(212\) 0 0
\(213\) 1.82138i 0.124799i
\(214\) 0 0
\(215\) −4.98145 2.87604i −0.339732 0.196144i
\(216\) 0 0
\(217\) 0.321265 0.556448i 0.0218089 0.0377741i
\(218\) 0 0
\(219\) 3.74437 2.16182i 0.253021 0.146082i
\(220\) 0 0
\(221\) 0.375354 + 1.19984i 0.0252490 + 0.0807102i
\(222\) 0 0
\(223\) 9.93221 5.73436i 0.665110 0.384001i −0.129111 0.991630i \(-0.541212\pi\)
0.794221 + 0.607629i \(0.207879\pi\)
\(224\) 0 0
\(225\) −1.35557 + 2.34792i −0.0903715 + 0.156528i
\(226\) 0 0
\(227\) −16.6245 9.59817i −1.10341 0.637053i −0.166294 0.986076i \(-0.553180\pi\)
−0.937114 + 0.349024i \(0.886513\pi\)
\(228\) 0 0
\(229\) 6.23160i 0.411796i −0.978573 0.205898i \(-0.933989\pi\)
0.978573 0.205898i \(-0.0660115\pi\)
\(230\) 0 0
\(231\) 0.673673 + 1.16684i 0.0443244 + 0.0767722i
\(232\) 0 0
\(233\) 4.82258 0.315937 0.157969 0.987444i \(-0.449505\pi\)
0.157969 + 0.987444i \(0.449505\pi\)
\(234\) 0 0
\(235\) −7.72357 −0.503830
\(236\) 0 0
\(237\) 2.88546 + 4.99776i 0.187431 + 0.324640i
\(238\) 0 0
\(239\) 6.82214i 0.441288i −0.975354 0.220644i \(-0.929184\pi\)
0.975354 0.220644i \(-0.0708158\pi\)
\(240\) 0 0
\(241\) 8.92067 + 5.15035i 0.574631 + 0.331763i 0.758997 0.651094i \(-0.225690\pi\)
−0.184366 + 0.982858i \(0.559023\pi\)
\(242\) 0 0
\(243\) −6.34656 + 10.9926i −0.407132 + 0.705173i
\(244\) 0 0
\(245\) 5.93515 3.42666i 0.379183 0.218921i
\(246\) 0 0
\(247\) 14.1256 4.41899i 0.898789 0.281173i
\(248\) 0 0
\(249\) −3.85280 + 2.22441i −0.244161 + 0.140966i
\(250\) 0 0
\(251\) −2.40755 + 4.17001i −0.151963 + 0.263208i −0.931949 0.362589i \(-0.881893\pi\)
0.779986 + 0.625797i \(0.215226\pi\)
\(252\) 0 0
\(253\) 38.1370 + 22.0184i 2.39765 + 1.38428i
\(254\) 0 0
\(255\) 0.187399i 0.0117354i
\(256\) 0 0
\(257\) 14.1153 + 24.4484i 0.880487 + 1.52505i 0.850800 + 0.525489i \(0.176118\pi\)
0.0296867 + 0.999559i \(0.490549\pi\)
\(258\) 0 0
\(259\) 0.425900 0.0264641
\(260\) 0 0
\(261\) 10.4038 0.643981
\(262\) 0 0
\(263\) 11.2128 + 19.4211i 0.691410 + 1.19756i 0.971376 + 0.237547i \(0.0763433\pi\)
−0.279967 + 0.960010i \(0.590323\pi\)
\(264\) 0 0
\(265\) 7.18066i 0.441104i
\(266\) 0 0
\(267\) 8.35838 + 4.82571i 0.511524 + 0.295329i
\(268\) 0 0
\(269\) −1.25602 + 2.17550i −0.0765811 + 0.132642i −0.901773 0.432211i \(-0.857734\pi\)
0.825192 + 0.564853i \(0.191067\pi\)
\(270\) 0 0
\(271\) 6.68024 3.85684i 0.405796 0.234286i −0.283186 0.959065i \(-0.591391\pi\)
0.688982 + 0.724779i \(0.258058\pi\)
\(272\) 0 0
\(273\) 0.546060 + 0.502629i 0.0330491 + 0.0304205i
\(274\) 0 0
\(275\) 5.66862 3.27278i 0.341831 0.197356i
\(276\) 0 0
\(277\) 10.5166 18.2153i 0.631882 1.09445i −0.355284 0.934758i \(-0.615616\pi\)
0.987167 0.159694i \(-0.0510507\pi\)
\(278\) 0 0
\(279\) −3.93899 2.27418i −0.235821 0.136151i
\(280\) 0 0
\(281\) 10.4409i 0.622855i −0.950270 0.311427i \(-0.899193\pi\)
0.950270 0.311427i \(-0.100807\pi\)
\(282\) 0 0
\(283\) −7.93861 13.7501i −0.471901 0.817357i 0.527582 0.849504i \(-0.323099\pi\)
−0.999483 + 0.0321473i \(0.989765\pi\)
\(284\) 0 0
\(285\) −2.20623 −0.130685
\(286\) 0 0
\(287\) −2.73269 −0.161306
\(288\) 0 0
\(289\) 8.43921 + 14.6171i 0.496424 + 0.859832i
\(290\) 0 0
\(291\) 0.711020i 0.0416808i
\(292\) 0 0
\(293\) −16.0219 9.25024i −0.936009 0.540405i −0.0473019 0.998881i \(-0.515062\pi\)
−0.888707 + 0.458476i \(0.848396\pi\)
\(294\) 0 0
\(295\) −2.22481 + 3.85348i −0.129533 + 0.224358i
\(296\) 0 0
\(297\) 17.3997 10.0457i 1.00963 0.582911i
\(298\) 0 0
\(299\) 23.6704 + 5.30330i 1.36889 + 0.306698i
\(300\) 0 0
\(301\) −1.90786 + 1.10151i −0.109967 + 0.0634897i
\(302\) 0 0
\(303\) −4.15729 + 7.20064i −0.238830 + 0.413666i
\(304\) 0 0
\(305\) 9.00590 + 5.19956i 0.515676 + 0.297726i
\(306\) 0 0
\(307\) 27.4070i 1.56420i 0.623154 + 0.782099i \(0.285851\pi\)
−0.623154 + 0.782099i \(0.714149\pi\)
\(308\) 0 0
\(309\) −3.86242 6.68990i −0.219725 0.380575i
\(310\) 0 0
\(311\) −18.4956 −1.04879 −0.524395 0.851475i \(-0.675708\pi\)
−0.524395 + 0.851475i \(0.675708\pi\)
\(312\) 0 0
\(313\) −15.6117 −0.882425 −0.441212 0.897403i \(-0.645451\pi\)
−0.441212 + 0.897403i \(0.645451\pi\)
\(314\) 0 0
\(315\) 0.519176 + 0.899239i 0.0292522 + 0.0506664i
\(316\) 0 0
\(317\) 17.6446i 0.991019i 0.868602 + 0.495510i \(0.165019\pi\)
−0.868602 + 0.495510i \(0.834981\pi\)
\(318\) 0 0
\(319\) −21.7529 12.5591i −1.21793 0.703173i
\(320\) 0 0
\(321\) 4.95434 8.58117i 0.276524 0.478954i
\(322\) 0 0
\(323\) −1.23956 + 0.715661i −0.0689710 + 0.0398204i
\(324\) 0 0
\(325\) 2.44183 2.65282i 0.135448 0.147152i
\(326\) 0 0
\(327\) 1.82259 1.05227i 0.100790 0.0581909i
\(328\) 0 0
\(329\) −1.47904 + 2.56177i −0.0815421 + 0.141235i
\(330\) 0 0
\(331\) −25.2822 14.5967i −1.38963 0.802306i −0.396361 0.918095i \(-0.629727\pi\)
−0.993274 + 0.115789i \(0.963060\pi\)
\(332\) 0 0
\(333\) 3.01487i 0.165214i
\(334\) 0 0
\(335\) −1.74322 3.01934i −0.0952422 0.164964i
\(336\) 0 0
\(337\) −19.2691 −1.04966 −0.524828 0.851208i \(-0.675870\pi\)
−0.524828 + 0.851208i \(0.675870\pi\)
\(338\) 0 0
\(339\) 10.8738 0.590585
\(340\) 0 0
\(341\) 5.49058 + 9.50997i 0.297332 + 0.514994i
\(342\) 0 0
\(343\) 5.30574i 0.286483i
\(344\) 0 0
\(345\) −3.13141 1.80792i −0.168590 0.0973352i
\(346\) 0 0
\(347\) 6.63014 11.4837i 0.355925 0.616480i −0.631351 0.775497i \(-0.717499\pi\)
0.987276 + 0.159018i \(0.0508326\pi\)
\(348\) 0 0
\(349\) 21.6614 12.5062i 1.15951 0.669441i 0.208321 0.978061i \(-0.433200\pi\)
0.951186 + 0.308619i \(0.0998669\pi\)
\(350\) 0 0
\(351\) 7.49512 8.14277i 0.400060 0.434629i
\(352\) 0 0
\(353\) −23.6328 + 13.6444i −1.25785 + 0.726218i −0.972655 0.232253i \(-0.925390\pi\)
−0.285191 + 0.958471i \(0.592057\pi\)
\(354\) 0 0
\(355\) 1.69446 2.93488i 0.0899324 0.155767i
\(356\) 0 0
\(357\) −0.0621571 0.0358864i −0.00328970 0.00189931i
\(358\) 0 0
\(359\) 7.09226i 0.374315i 0.982330 + 0.187158i \(0.0599275\pi\)
−0.982330 + 0.187158i \(0.940072\pi\)
\(360\) 0 0
\(361\) −1.07464 1.86133i −0.0565599 0.0979646i
\(362\) 0 0
\(363\) −17.1148 −0.898296
\(364\) 0 0
\(365\) −8.04467 −0.421077
\(366\) 0 0
\(367\) −4.88298 8.45757i −0.254890 0.441482i 0.709976 0.704226i \(-0.248706\pi\)
−0.964866 + 0.262744i \(0.915372\pi\)
\(368\) 0 0
\(369\) 19.3442i 1.00702i
\(370\) 0 0
\(371\) −2.38170 1.37507i −0.123652 0.0713903i
\(372\) 0 0
\(373\) 3.51157 6.08222i 0.181822 0.314926i −0.760679 0.649128i \(-0.775134\pi\)
0.942501 + 0.334203i \(0.108467\pi\)
\(374\) 0 0
\(375\) −0.465448 + 0.268727i −0.0240356 + 0.0138770i
\(376\) 0 0
\(377\) −13.5013 3.02495i −0.695354 0.155793i
\(378\) 0 0
\(379\) −17.3393 + 10.0108i −0.890658 + 0.514222i −0.874158 0.485642i \(-0.838586\pi\)
−0.0165003 + 0.999864i \(0.505252\pi\)
\(380\) 0 0
\(381\) 3.70244 6.41282i 0.189682 0.328539i
\(382\) 0 0
\(383\) 8.67580 + 5.00898i 0.443313 + 0.255947i 0.705002 0.709206i \(-0.250946\pi\)
−0.261689 + 0.965152i \(0.584280\pi\)
\(384\) 0 0
\(385\) 2.50691i 0.127764i
\(386\) 0 0
\(387\) 7.79736 + 13.5054i 0.396362 + 0.686519i
\(388\) 0 0
\(389\) −29.0158 −1.47116 −0.735581 0.677437i \(-0.763091\pi\)
−0.735581 + 0.677437i \(0.763091\pi\)
\(390\) 0 0
\(391\) −2.34583 −0.118634
\(392\) 0 0
\(393\) −1.52319 2.63824i −0.0768348 0.133082i
\(394\) 0 0
\(395\) 10.7375i 0.540264i
\(396\) 0 0
\(397\) 4.27503 + 2.46819i 0.214557 + 0.123875i 0.603428 0.797418i \(-0.293801\pi\)
−0.388870 + 0.921293i \(0.627135\pi\)
\(398\) 0 0
\(399\) −0.422485 + 0.731766i −0.0211507 + 0.0366341i
\(400\) 0 0
\(401\) −21.6985 + 12.5276i −1.08357 + 0.625599i −0.931857 0.362825i \(-0.881812\pi\)
−0.151713 + 0.988425i \(0.548479\pi\)
\(402\) 0 0
\(403\) 4.45051 + 4.09654i 0.221696 + 0.204063i
\(404\) 0 0
\(405\) 5.61508 3.24187i 0.279016 0.161090i
\(406\) 0 0
\(407\) −3.63942 + 6.30366i −0.180399 + 0.312461i
\(408\) 0 0
\(409\) 2.88605 + 1.66626i 0.142706 + 0.0823912i 0.569653 0.821885i \(-0.307078\pi\)
−0.426947 + 0.904277i \(0.640411\pi\)
\(410\) 0 0
\(411\) 1.78968i 0.0882783i
\(412\) 0 0
\(413\) 0.852087 + 1.47586i 0.0419285 + 0.0726222i
\(414\) 0 0
\(415\) 8.27761 0.406332
\(416\) 0 0
\(417\) −2.40316 −0.117683
\(418\) 0 0
\(419\) 18.3877 + 31.8484i 0.898296 + 1.55589i 0.829672 + 0.558252i \(0.188528\pi\)
0.0686246 + 0.997643i \(0.478139\pi\)
\(420\) 0 0
\(421\) 9.58821i 0.467301i −0.972321 0.233650i \(-0.924933\pi\)
0.972321 0.233650i \(-0.0750671\pi\)
\(422\) 0 0
\(423\) 18.1343 + 10.4699i 0.881720 + 0.509062i
\(424\) 0 0
\(425\) −0.174340 + 0.301966i −0.00845675 + 0.0146475i
\(426\) 0 0
\(427\) 3.44920 1.99140i 0.166919 0.0963706i
\(428\) 0 0
\(429\) −12.1055 + 3.78705i −0.584461 + 0.182840i
\(430\) 0 0
\(431\) 27.8063 16.0540i 1.33938 0.773294i 0.352668 0.935748i \(-0.385274\pi\)
0.986716 + 0.162454i \(0.0519410\pi\)
\(432\) 0 0
\(433\) 16.6413 28.8235i 0.799728 1.38517i −0.120066 0.992766i \(-0.538310\pi\)
0.919793 0.392403i \(-0.128356\pi\)
\(434\) 0 0
\(435\) 1.78613 + 1.03122i 0.0856381 + 0.0494432i
\(436\) 0 0
\(437\) 27.6171i 1.32111i
\(438\) 0 0
\(439\) 0.866280 + 1.50044i 0.0413453 + 0.0716122i 0.885958 0.463766i \(-0.153502\pi\)
−0.844612 + 0.535379i \(0.820169\pi\)
\(440\) 0 0
\(441\) −18.5803 −0.884777
\(442\) 0 0
\(443\) −23.2056 −1.10253 −0.551265 0.834330i \(-0.685855\pi\)
−0.551265 + 0.834330i \(0.685855\pi\)
\(444\) 0 0
\(445\) −8.97885 15.5518i −0.425638 0.737227i
\(446\) 0 0
\(447\) 6.90453i 0.326573i
\(448\) 0 0
\(449\) 21.4815 + 12.4024i 1.01378 + 0.585304i 0.912295 0.409533i \(-0.134308\pi\)
0.101481 + 0.994837i \(0.467642\pi\)
\(450\) 0 0
\(451\) 23.3515 40.4460i 1.09958 1.90453i
\(452\) 0 0
\(453\) −3.35311 + 1.93592i −0.157543 + 0.0909574i
\(454\) 0 0
\(455\) −0.412292 1.31792i −0.0193286 0.0617850i
\(456\) 0 0
\(457\) −25.0074 + 14.4380i −1.16980 + 0.675383i −0.953632 0.300974i \(-0.902688\pi\)
−0.216165 + 0.976357i \(0.569355\pi\)
\(458\) 0 0
\(459\) −0.535133 + 0.926877i −0.0249779 + 0.0432629i
\(460\) 0 0
\(461\) −2.13975 1.23539i −0.0996583 0.0575377i 0.449343 0.893360i \(-0.351658\pi\)
−0.549001 + 0.835822i \(0.684992\pi\)
\(462\) 0 0
\(463\) 24.0731i 1.11877i 0.828908 + 0.559385i \(0.188963\pi\)
−0.828908 + 0.559385i \(0.811037\pi\)
\(464\) 0 0
\(465\) −0.450830 0.780860i −0.0209067 0.0362115i
\(466\) 0 0
\(467\) −20.4625 −0.946889 −0.473445 0.880824i \(-0.656990\pi\)
−0.473445 + 0.880824i \(0.656990\pi\)
\(468\) 0 0
\(469\) −1.33528 −0.0616577
\(470\) 0 0
\(471\) −0.473306 0.819790i −0.0218088 0.0377739i
\(472\) 0 0
\(473\) 37.6506i 1.73117i
\(474\) 0 0
\(475\) 3.55500 + 2.05248i 0.163115 + 0.0941743i
\(476\) 0 0
\(477\) −9.73390 + 16.8596i −0.445684 + 0.771948i
\(478\) 0 0
\(479\) −18.5360 + 10.7018i −0.846933 + 0.488977i −0.859615 0.510943i \(-0.829296\pi\)
0.0126818 + 0.999920i \(0.495963\pi\)
\(480\) 0 0
\(481\) −0.876582 + 3.91248i −0.0399687 + 0.178394i
\(482\) 0 0
\(483\) −1.19931 + 0.692423i −0.0545706 + 0.0315063i
\(484\) 0 0
\(485\) −0.661472 + 1.14570i −0.0300359 + 0.0520237i
\(486\) 0 0
\(487\) 14.8638 + 8.58161i 0.673543 + 0.388870i 0.797418 0.603428i \(-0.206199\pi\)
−0.123875 + 0.992298i \(0.539532\pi\)
\(488\) 0 0
\(489\) 1.87393i 0.0847420i
\(490\) 0 0
\(491\) −4.28967 7.42992i −0.193590 0.335308i 0.752847 0.658195i \(-0.228680\pi\)
−0.946437 + 0.322887i \(0.895346\pi\)
\(492\) 0 0
\(493\) 1.33804 0.0602622
\(494\) 0 0
\(495\) −17.7460 −0.797621
\(496\) 0 0
\(497\) −0.648966 1.12404i −0.0291101 0.0504202i
\(498\) 0 0
\(499\) 24.2361i 1.08496i −0.840070 0.542479i \(-0.817486\pi\)
0.840070 0.542479i \(-0.182514\pi\)
\(500\) 0 0
\(501\) −5.95689 3.43921i −0.266134 0.153653i
\(502\) 0 0
\(503\) −16.1531 + 27.9780i −0.720231 + 1.24748i 0.240676 + 0.970606i \(0.422631\pi\)
−0.960907 + 0.276871i \(0.910702\pi\)
\(504\) 0 0
\(505\) 13.3977 7.73517i 0.596190 0.344211i
\(506\) 0 0
\(507\) −5.74124 + 3.98181i −0.254977 + 0.176839i
\(508\) 0 0
\(509\) −15.3052 + 8.83646i −0.678391 + 0.391669i −0.799249 0.601001i \(-0.794769\pi\)
0.120857 + 0.992670i \(0.461436\pi\)
\(510\) 0 0
\(511\) −1.54053 + 2.66828i −0.0681490 + 0.118038i
\(512\) 0 0
\(513\) 10.9120 + 6.30003i 0.481776 + 0.278153i
\(514\) 0 0
\(515\) 14.3730i 0.633352i
\(516\) 0 0
\(517\) −25.2775 43.7820i −1.11170 1.92553i
\(518\) 0 0
\(519\) −3.47244 −0.152423
\(520\) 0 0
\(521\) −8.01036 −0.350940 −0.175470 0.984485i \(-0.556145\pi\)
−0.175470 + 0.984485i \(0.556145\pi\)
\(522\) 0 0
\(523\) −6.56245 11.3665i −0.286956 0.497022i 0.686126 0.727483i \(-0.259310\pi\)
−0.973082 + 0.230461i \(0.925977\pi\)
\(524\) 0 0
\(525\) 0.205841i 0.00898365i
\(526\) 0 0
\(527\) −0.506594 0.292482i −0.0220676 0.0127407i
\(528\) 0 0
\(529\) −11.1312 + 19.2798i −0.483966 + 0.838253i
\(530\) 0 0
\(531\) 10.4473 6.03177i 0.453376 0.261757i
\(532\) 0 0
\(533\) 5.62439 25.1035i 0.243619 1.08735i
\(534\) 0 0
\(535\) −15.9664 + 9.21819i −0.690286 + 0.398537i
\(536\) 0 0
\(537\) 2.12874 3.68708i 0.0918617 0.159109i
\(538\) 0 0
\(539\) 38.8488 + 22.4294i 1.67334 + 0.966102i
\(540\) 0 0
\(541\) 34.0136i 1.46236i 0.682186 + 0.731179i \(0.261029\pi\)
−0.682186 + 0.731179i \(0.738971\pi\)
\(542\) 0 0
\(543\) 5.92452 + 10.2616i 0.254246 + 0.440366i
\(544\) 0 0
\(545\) −3.91578 −0.167734
\(546\) 0 0
\(547\) 11.1875 0.478342 0.239171 0.970977i \(-0.423124\pi\)
0.239171 + 0.970977i \(0.423124\pi\)
\(548\) 0 0
\(549\) −14.0968 24.4163i −0.601635 1.04206i
\(550\) 0 0
\(551\) 15.7525i 0.671080i
\(552\) 0 0
\(553\) −3.56145 2.05620i −0.151448 0.0874387i
\(554\) 0 0
\(555\) 0.298831 0.517591i 0.0126847 0.0219705i
\(556\) 0 0
\(557\) −37.9254 + 21.8962i −1.60695 + 0.927773i −0.616903 + 0.787039i \(0.711613\pi\)
−0.990047 + 0.140734i \(0.955054\pi\)
\(558\) 0 0
\(559\) −6.19210 19.7935i −0.261898 0.837174i
\(560\) 0 0
\(561\) 1.06230 0.613317i 0.0448502 0.0258943i
\(562\) 0 0
\(563\) −16.7879 + 29.0774i −0.707524 + 1.22547i 0.258248 + 0.966079i \(0.416855\pi\)
−0.965773 + 0.259390i \(0.916479\pi\)
\(564\) 0 0
\(565\) −17.5215 10.1161i −0.737137 0.425586i
\(566\) 0 0
\(567\) 2.48323i 0.104286i
\(568\) 0 0
\(569\) −15.4982 26.8437i −0.649719 1.12535i −0.983190 0.182586i \(-0.941553\pi\)
0.333471 0.942760i \(-0.391780\pi\)
\(570\) 0 0
\(571\) −19.3467 −0.809636 −0.404818 0.914397i \(-0.632665\pi\)
−0.404818 + 0.914397i \(0.632665\pi\)
\(572\) 0 0
\(573\) −10.0848 −0.421297
\(574\) 0 0
\(575\) 3.36387 + 5.82639i 0.140283 + 0.242977i
\(576\) 0 0
\(577\) 9.69204i 0.403485i −0.979439 0.201742i \(-0.935340\pi\)
0.979439 0.201742i \(-0.0646604\pi\)
\(578\) 0 0
\(579\) −5.77645 3.33504i −0.240061 0.138599i
\(580\) 0 0
\(581\) 1.58514 2.74554i 0.0657626 0.113904i
\(582\) 0 0
\(583\) 40.7044 23.5007i 1.68580 0.973300i
\(584\) 0 0
\(585\) −9.32931 + 2.91854i −0.385720 + 0.120667i
\(586\) 0 0
\(587\) −0.329349 + 0.190150i −0.0135937 + 0.00784831i −0.506781 0.862075i \(-0.669165\pi\)
0.493188 + 0.869923i \(0.335832\pi\)
\(588\) 0 0
\(589\) −3.44335 + 5.96406i −0.141881 + 0.245745i
\(590\) 0 0
\(591\) 0.268339 + 0.154925i 0.0110380 + 0.00637278i
\(592\) 0 0
\(593\) 7.10741i 0.291866i −0.989294 0.145933i \(-0.953382\pi\)
0.989294 0.145933i \(-0.0466185\pi\)
\(594\) 0 0
\(595\) 0.0667713 + 0.115651i 0.00273736 + 0.00474124i
\(596\) 0 0
\(597\) −6.40698 −0.262220
\(598\) 0 0
\(599\) −34.6217 −1.41460 −0.707302 0.706912i \(-0.750088\pi\)
−0.707302 + 0.706912i \(0.750088\pi\)
\(600\) 0 0
\(601\) 3.12700 + 5.41613i 0.127553 + 0.220928i 0.922728 0.385452i \(-0.125954\pi\)
−0.795175 + 0.606380i \(0.792621\pi\)
\(602\) 0 0
\(603\) 9.45224i 0.384925i
\(604\) 0 0
\(605\) 27.5780 + 15.9222i 1.12121 + 0.647328i
\(606\) 0 0
\(607\) −6.81414 + 11.8024i −0.276577 + 0.479046i −0.970532 0.240973i \(-0.922534\pi\)
0.693955 + 0.720019i \(0.255867\pi\)
\(608\) 0 0
\(609\) 0.684075 0.394951i 0.0277201 0.0160042i
\(610\) 0 0
\(611\) −20.4893 18.8596i −0.828907 0.762979i
\(612\) 0 0
\(613\) −1.99544 + 1.15207i −0.0805949 + 0.0465315i −0.539756 0.841822i \(-0.681483\pi\)
0.459161 + 0.888353i \(0.348150\pi\)
\(614\) 0 0
\(615\) −1.91738 + 3.32100i −0.0773163 + 0.133916i
\(616\) 0 0
\(617\) 17.3637 + 10.0250i 0.699037 + 0.403589i 0.806989 0.590567i \(-0.201096\pi\)
−0.107952 + 0.994156i \(0.534429\pi\)
\(618\) 0 0
\(619\) 9.82852i 0.395042i −0.980299 0.197521i \(-0.936711\pi\)
0.980299 0.197521i \(-0.0632890\pi\)
\(620\) 0 0
\(621\) 10.3253 + 17.8839i 0.414340 + 0.717658i
\(622\) 0 0
\(623\) −6.87769 −0.275549
\(624\) 0 0
\(625\) 1.00000 0.0400000
\(626\) 0 0
\(627\) −7.22049 12.5063i −0.288359 0.499452i
\(628\) 0 0
\(629\) 0.387742i 0.0154603i
\(630\) 0 0
\(631\) 20.1654 + 11.6425i 0.802772 + 0.463480i 0.844439 0.535651i \(-0.179934\pi\)
−0.0416678 + 0.999132i \(0.513267\pi\)
\(632\) 0 0
\(633\) 1.69307 2.93249i 0.0672937 0.116556i
\(634\) 0 0
\(635\) −11.9319 + 6.88887i −0.473502 + 0.273376i
\(636\) 0 0
\(637\) 24.1122 + 5.40229i 0.955360 + 0.214046i
\(638\) 0 0
\(639\) −7.95689 + 4.59391i −0.314770 + 0.181732i
\(640\) 0 0
\(641\) −7.97269 + 13.8091i −0.314902 + 0.545427i −0.979417 0.201849i \(-0.935305\pi\)
0.664514 + 0.747276i \(0.268638\pi\)
\(642\) 0 0
\(643\) −25.7205 14.8497i −1.01432 0.585617i −0.101865 0.994798i \(-0.532481\pi\)
−0.912453 + 0.409181i \(0.865814\pi\)
\(644\) 0 0
\(645\) 3.09147i 0.121727i
\(646\) 0 0
\(647\) −17.8375 30.8954i −0.701263 1.21462i −0.968023 0.250861i \(-0.919286\pi\)
0.266760 0.963763i \(-0.414047\pi\)
\(648\) 0 0
\(649\) −29.1252 −1.14326
\(650\) 0 0
\(651\) −0.345330 −0.0135345
\(652\) 0 0
\(653\) 16.4768 + 28.5387i 0.644789 + 1.11681i 0.984350 + 0.176223i \(0.0563879\pi\)
−0.339562 + 0.940584i \(0.610279\pi\)
\(654\) 0 0
\(655\) 5.66818i 0.221474i
\(656\) 0 0
\(657\) 18.8882 + 10.9051i 0.736900 + 0.425450i
\(658\) 0 0
\(659\) 21.2848 36.8663i 0.829138 1.43611i −0.0695778 0.997577i \(-0.522165\pi\)
0.898716 0.438532i \(-0.144501\pi\)
\(660\) 0 0
\(661\) −38.5631 + 22.2644i −1.49993 + 0.865985i −1.00000 8.00698e-5i \(-0.999975\pi\)
−0.499931 + 0.866065i \(0.666641\pi\)
\(662\) 0 0
\(663\) 0.457597 0.497138i 0.0177716 0.0193072i
\(664\) 0 0
\(665\) 1.36154 0.786088i 0.0527984 0.0304832i
\(666\) 0 0
\(667\) 12.9086 22.3584i 0.499824 0.865720i
\(668\) 0 0
\(669\) −5.33809 3.08195i −0.206383 0.119155i
\(670\) 0 0
\(671\) 68.0680i 2.62774i
\(672\) 0 0
\(673\) −12.9568 22.4418i −0.499448 0.865069i 0.500552 0.865707i \(-0.333130\pi\)
−1.00000 0.000637339i \(0.999797\pi\)
\(674\) 0 0
\(675\) 3.06947 0.118144
\(676\) 0 0
\(677\) 33.4647 1.28615 0.643076 0.765803i \(-0.277658\pi\)
0.643076 + 0.765803i \(0.277658\pi\)
\(678\) 0 0
\(679\) 0.253340 + 0.438797i 0.00972229 + 0.0168395i
\(680\) 0 0
\(681\) 10.3171i 0.395353i
\(682\) 0 0
\(683\) 31.9754 + 18.4610i 1.22350 + 0.706391i 0.965663 0.259797i \(-0.0836555\pi\)
0.257841 + 0.966187i \(0.416989\pi\)
\(684\) 0 0
\(685\) −1.66496 + 2.88380i −0.0636149 + 0.110184i
\(686\) 0 0
\(687\) −2.90049 + 1.67460i −0.110660 + 0.0638898i
\(688\) 0 0
\(689\) 17.5339 19.0490i 0.667990 0.725710i
\(690\) 0 0
\(691\) −10.0947 + 5.82817i −0.384020 + 0.221714i −0.679566 0.733614i \(-0.737832\pi\)
0.295546 + 0.955329i \(0.404499\pi\)
\(692\) 0 0
\(693\) −3.39830 + 5.88602i −0.129091 + 0.223591i
\(694\) 0 0
\(695\) 3.87234 + 2.23569i 0.146886 + 0.0848047i
\(696\) 0 0
\(697\) 2.48786i 0.0942344i
\(698\) 0 0
\(699\) −1.29595 2.24466i −0.0490175 0.0849008i
\(700\) 0 0
\(701\) 34.2429 1.29334 0.646669 0.762771i \(-0.276162\pi\)
0.646669 + 0.762771i \(0.276162\pi\)
\(702\) 0 0
\(703\) −4.56483 −0.172166
\(704\) 0 0
\(705\) 2.07553 + 3.59492i 0.0781689 + 0.135392i
\(706\) 0 0
\(707\) 5.92505i 0.222834i
\(708\) 0 0
\(709\) 39.7122 + 22.9278i 1.49142 + 0.861073i 0.999952 0.00982181i \(-0.00312643\pi\)
0.491470 + 0.870895i \(0.336460\pi\)
\(710\) 0 0
\(711\) −14.5555 + 25.2109i −0.545874 + 0.945481i
\(712\) 0 0
\(713\) −9.77465 + 5.64340i −0.366064 + 0.211347i
\(714\) 0 0
\(715\) 23.0294 + 5.15969i 0.861251 + 0.192962i
\(716\) 0 0
\(717\) −3.17535 + 1.83329i −0.118586 + 0.0684655i
\(718\) 0 0
\(719\) −6.35463 + 11.0065i −0.236988 + 0.410475i −0.959849 0.280519i \(-0.909493\pi\)
0.722861 + 0.690994i \(0.242827\pi\)
\(720\) 0 0
\(721\) 4.76729 + 2.75239i 0.177543 + 0.102505i
\(722\) 0 0
\(723\) 5.53615i 0.205892i
\(724\) 0 0
\(725\) −1.91872 3.32331i −0.0712593 0.123425i
\(726\) 0 0
\(727\) 13.4712 0.499619 0.249809 0.968295i \(-0.419632\pi\)
0.249809 + 0.968295i \(0.419632\pi\)
\(728\) 0 0
\(729\) −12.6293 −0.467750
\(730\) 0 0
\(731\) 1.00282 + 1.73693i 0.0370906 + 0.0642428i
\(732\) 0 0
\(733\) 34.2367i 1.26456i −0.774739 0.632281i \(-0.782119\pi\)
0.774739 0.632281i \(-0.217881\pi\)
\(734\) 0 0
\(735\) −3.18986 1.84167i −0.117660 0.0679309i
\(736\) 0 0
\(737\) 11.4103 19.7633i 0.420306 0.727991i
\(738\) 0 0
\(739\) −25.5951 + 14.7774i −0.941532 + 0.543594i −0.890440 0.455100i \(-0.849604\pi\)
−0.0510921 + 0.998694i \(0.516270\pi\)
\(740\) 0 0
\(741\) −5.85273 5.38722i −0.215005 0.197905i
\(742\) 0 0
\(743\) −16.7730 + 9.68392i −0.615343 + 0.355269i −0.775054 0.631895i \(-0.782277\pi\)
0.159710 + 0.987164i \(0.448944\pi\)
\(744\) 0 0
\(745\) −6.42338 + 11.1256i −0.235334 + 0.407611i
\(746\) 0 0
\(747\) −19.4352 11.2209i −0.711096 0.410551i
\(748\) 0 0
\(749\) 7.06102i 0.258004i
\(750\) 0 0
\(751\) 3.64103 + 6.30645i 0.132863 + 0.230126i 0.924779 0.380504i \(-0.124250\pi\)
−0.791916 + 0.610630i \(0.790916\pi\)
\(752\) 0 0
\(753\) 2.58789 0.0943081
\(754\) 0 0
\(755\) 7.20405 0.262182
\(756\) 0 0
\(757\) −13.6265 23.6018i −0.495264 0.857822i 0.504721 0.863282i \(-0.331595\pi\)
−0.999985 + 0.00546016i \(0.998262\pi\)
\(758\) 0 0
\(759\) 23.6677i 0.859083i
\(760\) 0 0
\(761\) −2.07310 1.19690i −0.0751497 0.0433877i 0.461954 0.886904i \(-0.347148\pi\)
−0.537104 + 0.843516i \(0.680482\pi\)
\(762\) 0 0
\(763\) −0.749860 + 1.29880i −0.0271468 + 0.0470196i
\(764\) 0 0
\(765\) 0.818674 0.472662i 0.0295992 0.0170891i
\(766\) 0 0
\(767\) −15.3116 + 4.79000i −0.552868 + 0.172957i
\(768\) 0 0
\(769\) 27.4598 15.8539i 0.990225 0.571707i 0.0848835 0.996391i \(-0.472948\pi\)
0.905342 + 0.424684i \(0.139615\pi\)
\(770\) 0 0
\(771\) 7.58630 13.1399i 0.273214 0.473220i
\(772\) 0 0
\(773\) 5.51142 + 3.18202i 0.198232 + 0.114449i 0.595831 0.803110i \(-0.296823\pi\)
−0.397599 + 0.917559i \(0.630156\pi\)
\(774\) 0 0
\(775\) 1.67765i 0.0602630i
\(776\) 0 0
\(777\) −0.114451 0.198234i −0.00410589 0.00711161i
\(778\) 0 0
\(779\) 29.2892 1.04939
\(780\) 0 0
\(781\) 22.1823 0.793746
\(782\) 0 0
\(783\) −5.88945 10.2008i −0.210472 0.364548i
\(784\) 0 0
\(785\) 1.76129i 0.0628632i
\(786\) 0 0
\(787\) 4.95505 + 2.86080i 0.176629 + 0.101977i 0.585708 0.810522i \(-0.300817\pi\)
−0.409079 + 0.912499i \(0.634150\pi\)
\(788\) 0 0