Properties

Label 440.2.y.a.81.2
Level $440$
Weight $2$
Character 440.81
Analytic conductor $3.513$
Analytic rank $0$
Dimension $8$
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] = [440,2,Mod(81,440)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(440, base_ring=CyclotomicField(10))
 
chi = DirichletCharacter(H, H._module([0, 0, 0, 2]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("440.81");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 440 = 2^{3} \cdot 5 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 440.y (of order \(5\), degree \(4\), 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: \(3.51341768894\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(2\) over \(\Q(\zeta_{5})\)
Coefficient field: 8.0.13140625.1
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{8} - 3x^{7} + 5x^{6} - 3x^{5} + 4x^{4} + 3x^{3} + 5x^{2} + 3x + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label 81.2
Root \(-0.386111 - 0.280526i\) of defining polynomial
Character \(\chi\) \(=\) 440.81
Dual form 440.2.y.a.201.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.0911485 - 0.280526i) q^{3} +(-0.809017 + 0.587785i) q^{5} +(-1.35666 - 4.17538i) q^{7} +(2.35666 + 1.71222i) q^{9} +O(q^{10})\) \(q+(0.0911485 - 0.280526i) q^{3} +(-0.809017 + 0.587785i) q^{5} +(-1.35666 - 4.17538i) q^{7} +(2.35666 + 1.71222i) q^{9} +(3.31118 + 0.189896i) q^{11} +(-4.82402 - 3.50485i) q^{13} +(0.0911485 + 0.280526i) q^{15} +(1.34932 - 0.980336i) q^{17} +(2.37743 - 7.31696i) q^{19} -1.29496 q^{21} -0.904706 q^{23} +(0.309017 - 0.951057i) q^{25} +(1.41102 - 1.02516i) q^{27} +(-1.46443 - 4.50705i) q^{29} +(4.14709 + 3.01303i) q^{31} +(0.355081 - 0.911566i) q^{33} +(3.55179 + 2.58053i) q^{35} +(-0.0571606 - 0.175922i) q^{37} +(-1.42291 + 1.03380i) q^{39} +(-0.810356 + 2.49402i) q^{41} +3.59822 q^{43} -2.91300 q^{45} +(-0.239853 + 0.738191i) q^{47} +(-9.93016 + 7.21469i) q^{49} +(-0.152022 - 0.467875i) q^{51} +(7.76295 + 5.64012i) q^{53} +(-2.79042 + 1.79264i) q^{55} +(-1.83590 - 1.33386i) q^{57} +(-3.47762 - 10.7030i) q^{59} +(-10.6708 + 7.75277i) q^{61} +(3.95196 - 12.1629i) q^{63} +5.96281 q^{65} -7.79954 q^{67} +(-0.0824626 + 0.253794i) q^{69} +(5.63943 - 4.09729i) q^{71} +(3.94122 + 12.1298i) q^{73} +(-0.238630 - 0.173375i) q^{75} +(-3.69927 - 14.0831i) q^{77} +(8.11547 + 5.89624i) q^{79} +(2.54152 + 7.82200i) q^{81} +(-3.31316 + 2.40715i) q^{83} +(-0.515393 + 1.58622i) q^{85} -1.39783 q^{87} -0.466291 q^{89} +(-8.08953 + 24.8970i) q^{91} +(1.22324 - 0.888733i) q^{93} +(2.37743 + 7.31696i) q^{95} +(-5.74372 - 4.17306i) q^{97} +(7.47820 + 6.11699i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q + q^{3} - 2 q^{5} + q^{7} + 7 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 8 q + q^{3} - 2 q^{5} + q^{7} + 7 q^{9} + 3 q^{11} - 4 q^{13} + q^{15} - 3 q^{17} + 9 q^{19} - 4 q^{21} - 22 q^{23} - 2 q^{25} - 8 q^{27} - 17 q^{29} - 4 q^{31} + 21 q^{33} + 6 q^{35} + 24 q^{37} - 13 q^{39} - 4 q^{41} - 14 q^{43} - 8 q^{45} - 12 q^{47} - 15 q^{49} - 17 q^{51} + 35 q^{53} + 3 q^{55} - q^{57} + 21 q^{59} - 22 q^{61} + 5 q^{63} + 6 q^{65} + 14 q^{67} + 3 q^{69} + 40 q^{71} + 9 q^{73} + q^{75} - 4 q^{77} + 41 q^{79} + 24 q^{81} - 7 q^{83} - 8 q^{85} - 46 q^{87} - 24 q^{89} - 18 q^{91} + 3 q^{93} + 9 q^{95} + 4 q^{97} + 22 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/440\mathbb{Z}\right)^\times\).

\(n\) \(111\) \(177\) \(221\) \(321\)
\(\chi(n)\) \(1\) \(1\) \(1\) \(e\left(\frac{1}{5}\right)\)

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
\(3\) 0.0911485 0.280526i 0.0526246 0.161962i −0.921290 0.388876i \(-0.872864\pi\)
0.973915 + 0.226914i \(0.0728635\pi\)
\(4\) 0 0
\(5\) −0.809017 + 0.587785i −0.361803 + 0.262866i
\(6\) 0 0
\(7\) −1.35666 4.17538i −0.512771 1.57815i −0.787302 0.616568i \(-0.788523\pi\)
0.274531 0.961578i \(-0.411477\pi\)
\(8\) 0 0
\(9\) 2.35666 + 1.71222i 0.785555 + 0.570739i
\(10\) 0 0
\(11\) 3.31118 + 0.189896i 0.998360 + 0.0572559i
\(12\) 0 0
\(13\) −4.82402 3.50485i −1.33794 0.972071i −0.999517 0.0310775i \(-0.990106\pi\)
−0.338424 0.940994i \(-0.609894\pi\)
\(14\) 0 0
\(15\) 0.0911485 + 0.280526i 0.0235345 + 0.0724316i
\(16\) 0 0
\(17\) 1.34932 0.980336i 0.327258 0.237767i −0.412009 0.911180i \(-0.635173\pi\)
0.739266 + 0.673413i \(0.235173\pi\)
\(18\) 0 0
\(19\) 2.37743 7.31696i 0.545419 1.67863i −0.174573 0.984644i \(-0.555855\pi\)
0.719992 0.693982i \(-0.244145\pi\)
\(20\) 0 0
\(21\) −1.29496 −0.282584
\(22\) 0 0
\(23\) −0.904706 −0.188644 −0.0943221 0.995542i \(-0.530068\pi\)
−0.0943221 + 0.995542i \(0.530068\pi\)
\(24\) 0 0
\(25\) 0.309017 0.951057i 0.0618034 0.190211i
\(26\) 0 0
\(27\) 1.41102 1.02516i 0.271551 0.197293i
\(28\) 0 0
\(29\) −1.46443 4.50705i −0.271938 0.836938i −0.990013 0.140973i \(-0.954977\pi\)
0.718076 0.695965i \(-0.245023\pi\)
\(30\) 0 0
\(31\) 4.14709 + 3.01303i 0.744839 + 0.541157i 0.894223 0.447622i \(-0.147729\pi\)
−0.149384 + 0.988779i \(0.547729\pi\)
\(32\) 0 0
\(33\) 0.355081 0.911566i 0.0618116 0.158683i
\(34\) 0 0
\(35\) 3.55179 + 2.58053i 0.600362 + 0.436189i
\(36\) 0 0
\(37\) −0.0571606 0.175922i −0.00939715 0.0289214i 0.946248 0.323442i \(-0.104840\pi\)
−0.955645 + 0.294521i \(0.904840\pi\)
\(38\) 0 0
\(39\) −1.42291 + 1.03380i −0.227847 + 0.165541i
\(40\) 0 0
\(41\) −0.810356 + 2.49402i −0.126556 + 0.389501i −0.994181 0.107719i \(-0.965645\pi\)
0.867625 + 0.497219i \(0.165645\pi\)
\(42\) 0 0
\(43\) 3.59822 0.548723 0.274361 0.961627i \(-0.411534\pi\)
0.274361 + 0.961627i \(0.411534\pi\)
\(44\) 0 0
\(45\) −2.91300 −0.434244
\(46\) 0 0
\(47\) −0.239853 + 0.738191i −0.0349861 + 0.107676i −0.967024 0.254683i \(-0.918029\pi\)
0.932038 + 0.362360i \(0.118029\pi\)
\(48\) 0 0
\(49\) −9.93016 + 7.21469i −1.41859 + 1.03067i
\(50\) 0 0
\(51\) −0.152022 0.467875i −0.0212873 0.0655157i
\(52\) 0 0
\(53\) 7.76295 + 5.64012i 1.06632 + 0.774729i 0.975248 0.221114i \(-0.0709694\pi\)
0.0910758 + 0.995844i \(0.470969\pi\)
\(54\) 0 0
\(55\) −2.79042 + 1.79264i −0.376260 + 0.241719i
\(56\) 0 0
\(57\) −1.83590 1.33386i −0.243171 0.176674i
\(58\) 0 0
\(59\) −3.47762 10.7030i −0.452748 1.39341i −0.873759 0.486359i \(-0.838325\pi\)
0.421012 0.907055i \(-0.361675\pi\)
\(60\) 0 0
\(61\) −10.6708 + 7.75277i −1.36625 + 0.992640i −0.368233 + 0.929734i \(0.620037\pi\)
−0.998019 + 0.0629067i \(0.979963\pi\)
\(62\) 0 0
\(63\) 3.95196 12.1629i 0.497900 1.53238i
\(64\) 0 0
\(65\) 5.96281 0.739596
\(66\) 0 0
\(67\) −7.79954 −0.952866 −0.476433 0.879211i \(-0.658070\pi\)
−0.476433 + 0.879211i \(0.658070\pi\)
\(68\) 0 0
\(69\) −0.0824626 + 0.253794i −0.00992734 + 0.0305532i
\(70\) 0 0
\(71\) 5.63943 4.09729i 0.669278 0.486259i −0.200506 0.979693i \(-0.564258\pi\)
0.869783 + 0.493434i \(0.164258\pi\)
\(72\) 0 0
\(73\) 3.94122 + 12.1298i 0.461285 + 1.41969i 0.863595 + 0.504186i \(0.168207\pi\)
−0.402310 + 0.915504i \(0.631793\pi\)
\(74\) 0 0
\(75\) −0.238630 0.173375i −0.0275546 0.0200196i
\(76\) 0 0
\(77\) −3.69927 14.0831i −0.421571 1.60492i
\(78\) 0 0
\(79\) 8.11547 + 5.89624i 0.913062 + 0.663378i 0.941787 0.336209i \(-0.109145\pi\)
−0.0287255 + 0.999587i \(0.509145\pi\)
\(80\) 0 0
\(81\) 2.54152 + 7.82200i 0.282391 + 0.869112i
\(82\) 0 0
\(83\) −3.31316 + 2.40715i −0.363667 + 0.264219i −0.754580 0.656208i \(-0.772159\pi\)
0.390913 + 0.920428i \(0.372159\pi\)
\(84\) 0 0
\(85\) −0.515393 + 1.58622i −0.0559023 + 0.172049i
\(86\) 0 0
\(87\) −1.39783 −0.149863
\(88\) 0 0
\(89\) −0.466291 −0.0494267 −0.0247134 0.999695i \(-0.507867\pi\)
−0.0247134 + 0.999695i \(0.507867\pi\)
\(90\) 0 0
\(91\) −8.08953 + 24.8970i −0.848013 + 2.60992i
\(92\) 0 0
\(93\) 1.22324 0.888733i 0.126844 0.0921574i
\(94\) 0 0
\(95\) 2.37743 + 7.31696i 0.243919 + 0.750705i
\(96\) 0 0
\(97\) −5.74372 4.17306i −0.583186 0.423710i 0.256685 0.966495i \(-0.417370\pi\)
−0.839871 + 0.542785i \(0.817370\pi\)
\(98\) 0 0
\(99\) 7.47820 + 6.11699i 0.751588 + 0.614780i
\(100\) 0 0
\(101\) 13.1749 + 9.57214i 1.31095 + 0.952463i 0.999998 + 0.00203865i \(0.000648924\pi\)
0.310955 + 0.950425i \(0.399351\pi\)
\(102\) 0 0
\(103\) 0.985946 + 3.03443i 0.0971481 + 0.298991i 0.987808 0.155680i \(-0.0497568\pi\)
−0.890659 + 0.454671i \(0.849757\pi\)
\(104\) 0 0
\(105\) 1.04765 0.761160i 0.102240 0.0742816i
\(106\) 0 0
\(107\) −4.06801 + 12.5201i −0.393270 + 1.21036i 0.537031 + 0.843562i \(0.319546\pi\)
−0.930301 + 0.366797i \(0.880454\pi\)
\(108\) 0 0
\(109\) 1.33532 0.127900 0.0639502 0.997953i \(-0.479630\pi\)
0.0639502 + 0.997953i \(0.479630\pi\)
\(110\) 0 0
\(111\) −0.0545610 −0.00517870
\(112\) 0 0
\(113\) −0.517444 + 1.59253i −0.0486770 + 0.149812i −0.972441 0.233151i \(-0.925096\pi\)
0.923764 + 0.382963i \(0.125096\pi\)
\(114\) 0 0
\(115\) 0.731923 0.531773i 0.0682521 0.0495881i
\(116\) 0 0
\(117\) −5.36752 16.5195i −0.496227 1.52723i
\(118\) 0 0
\(119\) −5.92385 4.30393i −0.543038 0.394541i
\(120\) 0 0
\(121\) 10.9279 + 1.25756i 0.993444 + 0.114324i
\(122\) 0 0
\(123\) 0.625776 + 0.454653i 0.0564243 + 0.0409946i
\(124\) 0 0
\(125\) 0.309017 + 0.951057i 0.0276393 + 0.0850651i
\(126\) 0 0
\(127\) −0.729305 + 0.529871i −0.0647153 + 0.0470185i −0.619673 0.784860i \(-0.712735\pi\)
0.554957 + 0.831879i \(0.312735\pi\)
\(128\) 0 0
\(129\) 0.327972 1.00939i 0.0288763 0.0888722i
\(130\) 0 0
\(131\) −14.5527 −1.27148 −0.635739 0.771904i \(-0.719305\pi\)
−0.635739 + 0.771904i \(0.719305\pi\)
\(132\) 0 0
\(133\) −33.7765 −2.92879
\(134\) 0 0
\(135\) −0.538961 + 1.65875i −0.0463864 + 0.142763i
\(136\) 0 0
\(137\) 16.6573 12.1022i 1.42313 1.03396i 0.431881 0.901931i \(-0.357850\pi\)
0.991246 0.132031i \(-0.0421498\pi\)
\(138\) 0 0
\(139\) −4.63035 14.2508i −0.392741 1.20873i −0.930707 0.365767i \(-0.880807\pi\)
0.537965 0.842967i \(-0.319193\pi\)
\(140\) 0 0
\(141\) 0.185220 + 0.134570i 0.0155983 + 0.0113328i
\(142\) 0 0
\(143\) −15.3076 12.5213i −1.28009 1.04708i
\(144\) 0 0
\(145\) 3.83392 + 2.78551i 0.318390 + 0.231324i
\(146\) 0 0
\(147\) 1.11879 + 3.44328i 0.0922762 + 0.283997i
\(148\) 0 0
\(149\) −8.86891 + 6.44364i −0.726570 + 0.527884i −0.888476 0.458922i \(-0.848236\pi\)
0.161907 + 0.986806i \(0.448236\pi\)
\(150\) 0 0
\(151\) −1.82682 + 5.62238i −0.148665 + 0.457543i −0.997464 0.0711723i \(-0.977326\pi\)
0.848799 + 0.528715i \(0.177326\pi\)
\(152\) 0 0
\(153\) 4.85844 0.392781
\(154\) 0 0
\(155\) −5.12608 −0.411737
\(156\) 0 0
\(157\) −1.36780 + 4.20964i −0.109162 + 0.335966i −0.990685 0.136176i \(-0.956519\pi\)
0.881523 + 0.472142i \(0.156519\pi\)
\(158\) 0 0
\(159\) 2.28978 1.66362i 0.181592 0.131934i
\(160\) 0 0
\(161\) 1.22738 + 3.77749i 0.0967313 + 0.297708i
\(162\) 0 0
\(163\) 5.97430 + 4.34059i 0.467944 + 0.339981i 0.796639 0.604455i \(-0.206609\pi\)
−0.328696 + 0.944436i \(0.606609\pi\)
\(164\) 0 0
\(165\) 0.248539 + 0.946183i 0.0193487 + 0.0736603i
\(166\) 0 0
\(167\) 15.7658 + 11.4545i 1.21999 + 0.886375i 0.996099 0.0882386i \(-0.0281238\pi\)
0.223892 + 0.974614i \(0.428124\pi\)
\(168\) 0 0
\(169\) 6.96991 + 21.4512i 0.536147 + 1.65009i
\(170\) 0 0
\(171\) 18.1310 13.1730i 1.38651 1.00736i
\(172\) 0 0
\(173\) 2.93815 9.04269i 0.223383 0.687503i −0.775068 0.631877i \(-0.782285\pi\)
0.998452 0.0556257i \(-0.0177153\pi\)
\(174\) 0 0
\(175\) −4.39026 −0.331872
\(176\) 0 0
\(177\) −3.31946 −0.249506
\(178\) 0 0
\(179\) 2.22879 6.85952i 0.166588 0.512705i −0.832562 0.553932i \(-0.813127\pi\)
0.999150 + 0.0412273i \(0.0131268\pi\)
\(180\) 0 0
\(181\) 18.9225 13.7480i 1.40650 1.02188i 0.412676 0.910878i \(-0.364594\pi\)
0.993820 0.111002i \(-0.0354060\pi\)
\(182\) 0 0
\(183\) 1.20223 + 3.70009i 0.0888715 + 0.273518i
\(184\) 0 0
\(185\) 0.149648 + 0.108726i 0.0110024 + 0.00799369i
\(186\) 0 0
\(187\) 4.65400 2.98984i 0.340334 0.218639i
\(188\) 0 0
\(189\) −6.19473 4.50074i −0.450601 0.327380i
\(190\) 0 0
\(191\) −1.28728 3.96183i −0.0931441 0.286668i 0.893621 0.448821i \(-0.148156\pi\)
−0.986766 + 0.162153i \(0.948156\pi\)
\(192\) 0 0
\(193\) 18.7417 13.6166i 1.34906 0.980148i 0.350000 0.936750i \(-0.386182\pi\)
0.999058 0.0433979i \(-0.0138183\pi\)
\(194\) 0 0
\(195\) 0.543502 1.67273i 0.0389210 0.119786i
\(196\) 0 0
\(197\) 10.1507 0.723209 0.361604 0.932332i \(-0.382229\pi\)
0.361604 + 0.932332i \(0.382229\pi\)
\(198\) 0 0
\(199\) −17.0131 −1.20603 −0.603014 0.797731i \(-0.706034\pi\)
−0.603014 + 0.797731i \(0.706034\pi\)
\(200\) 0 0
\(201\) −0.710917 + 2.18798i −0.0501442 + 0.154328i
\(202\) 0 0
\(203\) −16.8319 + 12.2291i −1.18137 + 0.858315i
\(204\) 0 0
\(205\) −0.810356 2.49402i −0.0565977 0.174190i
\(206\) 0 0
\(207\) −2.13209 1.54905i −0.148190 0.107667i
\(208\) 0 0
\(209\) 9.26156 23.7763i 0.640635 1.64464i
\(210\) 0 0
\(211\) 4.86721 + 3.53624i 0.335073 + 0.243445i 0.742580 0.669757i \(-0.233602\pi\)
−0.407507 + 0.913202i \(0.633602\pi\)
\(212\) 0 0
\(213\) −0.635371 1.95547i −0.0435349 0.133987i
\(214\) 0 0
\(215\) −2.91102 + 2.11498i −0.198530 + 0.144240i
\(216\) 0 0
\(217\) 6.95437 21.4033i 0.472093 1.45295i
\(218\) 0 0
\(219\) 3.76197 0.254211
\(220\) 0 0
\(221\) −9.94506 −0.668977
\(222\) 0 0
\(223\) 0.770711 2.37201i 0.0516107 0.158841i −0.921929 0.387358i \(-0.873388\pi\)
0.973540 + 0.228517i \(0.0733876\pi\)
\(224\) 0 0
\(225\) 2.35666 1.71222i 0.157111 0.114148i
\(226\) 0 0
\(227\) −7.72396 23.7719i −0.512657 1.57780i −0.787505 0.616309i \(-0.788627\pi\)
0.274848 0.961488i \(-0.411373\pi\)
\(228\) 0 0
\(229\) 2.24164 + 1.62865i 0.148132 + 0.107624i 0.659383 0.751807i \(-0.270818\pi\)
−0.511251 + 0.859432i \(0.670818\pi\)
\(230\) 0 0
\(231\) −4.28786 0.245909i −0.282121 0.0161796i
\(232\) 0 0
\(233\) 7.76676 + 5.64288i 0.508818 + 0.369678i 0.812375 0.583136i \(-0.198174\pi\)
−0.303557 + 0.952813i \(0.598174\pi\)
\(234\) 0 0
\(235\) −0.239853 0.738191i −0.0156463 0.0481543i
\(236\) 0 0
\(237\) 2.39376 1.73917i 0.155492 0.112971i
\(238\) 0 0
\(239\) 4.56394 14.0464i 0.295217 0.908584i −0.687932 0.725775i \(-0.741481\pi\)
0.983149 0.182808i \(-0.0585188\pi\)
\(240\) 0 0
\(241\) −10.4338 −0.672099 −0.336049 0.941844i \(-0.609091\pi\)
−0.336049 + 0.941844i \(0.609091\pi\)
\(242\) 0 0
\(243\) 7.65828 0.491279
\(244\) 0 0
\(245\) 3.79298 11.6736i 0.242325 0.745799i
\(246\) 0 0
\(247\) −37.1136 + 26.9646i −2.36148 + 1.71572i
\(248\) 0 0
\(249\) 0.373280 + 1.14884i 0.0236557 + 0.0728047i
\(250\) 0 0
\(251\) 5.44787 + 3.95811i 0.343866 + 0.249834i 0.746291 0.665619i \(-0.231833\pi\)
−0.402425 + 0.915453i \(0.631833\pi\)
\(252\) 0 0
\(253\) −2.99565 0.171800i −0.188335 0.0108010i
\(254\) 0 0
\(255\) 0.397999 + 0.289163i 0.0249236 + 0.0181081i
\(256\) 0 0
\(257\) 2.39239 + 7.36301i 0.149233 + 0.459292i 0.997531 0.0702272i \(-0.0223724\pi\)
−0.848298 + 0.529519i \(0.822372\pi\)
\(258\) 0 0
\(259\) −0.656995 + 0.477335i −0.0408237 + 0.0296601i
\(260\) 0 0
\(261\) 4.26588 13.1290i 0.264051 0.812666i
\(262\) 0 0
\(263\) 18.1618 1.11990 0.559952 0.828525i \(-0.310819\pi\)
0.559952 + 0.828525i \(0.310819\pi\)
\(264\) 0 0
\(265\) −9.59554 −0.589449
\(266\) 0 0
\(267\) −0.0425017 + 0.130807i −0.00260106 + 0.00800525i
\(268\) 0 0
\(269\) 8.67812 6.30502i 0.529114 0.384424i −0.290912 0.956750i \(-0.593959\pi\)
0.820026 + 0.572326i \(0.193959\pi\)
\(270\) 0 0
\(271\) −5.80566 17.8680i −0.352669 1.08540i −0.957349 0.288935i \(-0.906699\pi\)
0.604680 0.796469i \(-0.293301\pi\)
\(272\) 0 0
\(273\) 6.24692 + 4.53865i 0.378081 + 0.274692i
\(274\) 0 0
\(275\) 1.20381 3.09044i 0.0725927 0.186361i
\(276\) 0 0
\(277\) −23.3375 16.9557i −1.40221 1.01877i −0.994398 0.105701i \(-0.966291\pi\)
−0.407814 0.913065i \(-0.633709\pi\)
\(278\) 0 0
\(279\) 4.61432 + 14.2014i 0.276252 + 0.850217i
\(280\) 0 0
\(281\) −21.8873 + 15.9021i −1.30569 + 0.948637i −0.999994 0.00349313i \(-0.998888\pi\)
−0.305693 + 0.952130i \(0.598888\pi\)
\(282\) 0 0
\(283\) 3.97802 12.2431i 0.236468 0.727775i −0.760455 0.649391i \(-0.775024\pi\)
0.996923 0.0783842i \(-0.0249761\pi\)
\(284\) 0 0
\(285\) 2.26930 0.134422
\(286\) 0 0
\(287\) 11.5129 0.679583
\(288\) 0 0
\(289\) −4.39369 + 13.5224i −0.258452 + 0.795435i
\(290\) 0 0
\(291\) −1.69418 + 1.23090i −0.0993148 + 0.0721565i
\(292\) 0 0
\(293\) 1.81972 + 5.60052i 0.106309 + 0.327186i 0.990035 0.140818i \(-0.0449733\pi\)
−0.883726 + 0.468004i \(0.844973\pi\)
\(294\) 0 0
\(295\) 9.10453 + 6.61483i 0.530086 + 0.385130i
\(296\) 0 0
\(297\) 4.86682 3.12656i 0.282401 0.181422i
\(298\) 0 0
\(299\) 4.36432 + 3.17086i 0.252395 + 0.183376i
\(300\) 0 0
\(301\) −4.88157 15.0239i −0.281369 0.865965i
\(302\) 0 0
\(303\) 3.88611 2.82343i 0.223251 0.162202i
\(304\) 0 0
\(305\) 4.07587 12.5442i 0.233384 0.718281i
\(306\) 0 0
\(307\) 6.85844 0.391432 0.195716 0.980661i \(-0.437297\pi\)
0.195716 + 0.980661i \(0.437297\pi\)
\(308\) 0 0
\(309\) 0.941105 0.0535376
\(310\) 0 0
\(311\) −4.40946 + 13.5709i −0.250037 + 0.769536i 0.744730 + 0.667366i \(0.232578\pi\)
−0.994767 + 0.102170i \(0.967422\pi\)
\(312\) 0 0
\(313\) −1.29421 + 0.940297i −0.0731529 + 0.0531487i −0.623761 0.781615i \(-0.714396\pi\)
0.550608 + 0.834764i \(0.314396\pi\)
\(314\) 0 0
\(315\) 3.95196 + 12.1629i 0.222668 + 0.685300i
\(316\) 0 0
\(317\) 24.9627 + 18.1365i 1.40204 + 1.01864i 0.994420 + 0.105495i \(0.0336427\pi\)
0.407624 + 0.913150i \(0.366357\pi\)
\(318\) 0 0
\(319\) −3.99312 15.2018i −0.223572 0.851135i
\(320\) 0 0
\(321\) 3.14141 + 2.28237i 0.175337 + 0.127389i
\(322\) 0 0
\(323\) −3.96518 12.2036i −0.220629 0.679025i
\(324\) 0 0
\(325\) −4.82402 + 3.50485i −0.267588 + 0.194414i
\(326\) 0 0
\(327\) 0.121712 0.374592i 0.00673071 0.0207150i
\(328\) 0 0
\(329\) 3.40763 0.187869
\(330\) 0 0
\(331\) −1.16816 −0.0642079 −0.0321040 0.999485i \(-0.510221\pi\)
−0.0321040 + 0.999485i \(0.510221\pi\)
\(332\) 0 0
\(333\) 0.166509 0.512461i 0.00912462 0.0280827i
\(334\) 0 0
\(335\) 6.30996 4.58446i 0.344750 0.250476i
\(336\) 0 0
\(337\) 4.33522 + 13.3424i 0.236154 + 0.726809i 0.996966 + 0.0778359i \(0.0248010\pi\)
−0.760812 + 0.648973i \(0.775199\pi\)
\(338\) 0 0
\(339\) 0.399582 + 0.290313i 0.0217023 + 0.0157677i
\(340\) 0 0
\(341\) 13.1596 + 10.7642i 0.712632 + 0.582916i
\(342\) 0 0
\(343\) 18.7334 + 13.6106i 1.01151 + 0.734905i
\(344\) 0 0
\(345\) −0.0824626 0.253794i −0.00443964 0.0136638i
\(346\) 0 0
\(347\) −26.9818 + 19.6034i −1.44846 + 1.05237i −0.462273 + 0.886738i \(0.652966\pi\)
−0.986188 + 0.165630i \(0.947034\pi\)
\(348\) 0 0
\(349\) −10.9166 + 33.5978i −0.584351 + 1.79845i 0.0175108 + 0.999847i \(0.494426\pi\)
−0.601862 + 0.798600i \(0.705574\pi\)
\(350\) 0 0
\(351\) −10.3998 −0.555102
\(352\) 0 0
\(353\) 11.7558 0.625698 0.312849 0.949803i \(-0.398717\pi\)
0.312849 + 0.949803i \(0.398717\pi\)
\(354\) 0 0
\(355\) −2.15407 + 6.62955i −0.114326 + 0.351860i
\(356\) 0 0
\(357\) −1.74732 + 1.26950i −0.0924778 + 0.0671890i
\(358\) 0 0
\(359\) −0.840838 2.58783i −0.0443777 0.136581i 0.926413 0.376510i \(-0.122876\pi\)
−0.970790 + 0.239929i \(0.922876\pi\)
\(360\) 0 0
\(361\) −32.5145 23.6232i −1.71129 1.24332i
\(362\) 0 0
\(363\) 1.34884 2.95093i 0.0707957 0.154884i
\(364\) 0 0
\(365\) −10.3183 7.49665i −0.540082 0.392393i
\(366\) 0 0
\(367\) 0.959060 + 2.95168i 0.0500625 + 0.154077i 0.972962 0.230963i \(-0.0741877\pi\)
−0.922900 + 0.385040i \(0.874188\pi\)
\(368\) 0 0
\(369\) −6.18004 + 4.49006i −0.321720 + 0.233743i
\(370\) 0 0
\(371\) 13.0179 40.0650i 0.675857 2.08007i
\(372\) 0 0
\(373\) −27.4604 −1.42185 −0.710924 0.703269i \(-0.751723\pi\)
−0.710924 + 0.703269i \(0.751723\pi\)
\(374\) 0 0
\(375\) 0.294963 0.0152318
\(376\) 0 0
\(377\) −8.73211 + 26.8747i −0.449727 + 1.38412i
\(378\) 0 0
\(379\) −11.2805 + 8.19577i −0.579441 + 0.420989i −0.838523 0.544867i \(-0.816580\pi\)
0.259081 + 0.965855i \(0.416580\pi\)
\(380\) 0 0
\(381\) 0.0821677 + 0.252886i 0.00420958 + 0.0129558i
\(382\) 0 0
\(383\) −6.59841 4.79402i −0.337163 0.244963i 0.406301 0.913739i \(-0.366818\pi\)
−0.743464 + 0.668776i \(0.766818\pi\)
\(384\) 0 0
\(385\) 11.2706 + 9.21908i 0.574403 + 0.469848i
\(386\) 0 0
\(387\) 8.47979 + 6.16093i 0.431052 + 0.313177i
\(388\) 0 0
\(389\) −0.958326 2.94942i −0.0485891 0.149542i 0.923818 0.382831i \(-0.125051\pi\)
−0.972407 + 0.233290i \(0.925051\pi\)
\(390\) 0 0
\(391\) −1.22074 + 0.886916i −0.0617352 + 0.0448533i
\(392\) 0 0
\(393\) −1.32646 + 4.08243i −0.0669111 + 0.205931i
\(394\) 0 0
\(395\) −10.0313 −0.504728
\(396\) 0 0
\(397\) 23.1546 1.16209 0.581047 0.813870i \(-0.302643\pi\)
0.581047 + 0.813870i \(0.302643\pi\)
\(398\) 0 0
\(399\) −3.07868 + 9.47520i −0.154127 + 0.474353i
\(400\) 0 0
\(401\) 6.66933 4.84555i 0.333051 0.241975i −0.408673 0.912681i \(-0.634008\pi\)
0.741724 + 0.670705i \(0.234008\pi\)
\(402\) 0 0
\(403\) −9.44537 29.0699i −0.470507 1.44807i
\(404\) 0 0
\(405\) −6.65379 4.83426i −0.330630 0.240217i
\(406\) 0 0
\(407\) −0.155862 0.593366i −0.00772581 0.0294120i
\(408\) 0 0
\(409\) −1.76891 1.28518i −0.0874667 0.0635483i 0.543192 0.839608i \(-0.317215\pi\)
−0.630659 + 0.776060i \(0.717215\pi\)
\(410\) 0 0
\(411\) −1.87670 5.77590i −0.0925710 0.284904i
\(412\) 0 0
\(413\) −39.9712 + 29.0408i −1.96686 + 1.42900i
\(414\) 0 0
\(415\) 1.26552 3.89486i 0.0621217 0.191191i
\(416\) 0 0
\(417\) −4.41977 −0.216437
\(418\) 0 0
\(419\) 10.7348 0.524429 0.262215 0.965010i \(-0.415547\pi\)
0.262215 + 0.965010i \(0.415547\pi\)
\(420\) 0 0
\(421\) 5.80597 17.8689i 0.282966 0.870878i −0.704036 0.710165i \(-0.748620\pi\)
0.987001 0.160714i \(-0.0513795\pi\)
\(422\) 0 0
\(423\) −1.82919 + 1.32899i −0.0889385 + 0.0646176i
\(424\) 0 0
\(425\) −0.515393 1.58622i −0.0250003 0.0769429i
\(426\) 0 0
\(427\) 46.8474 + 34.0366i 2.26711 + 1.64715i
\(428\) 0 0
\(429\) −4.90782 + 3.15290i −0.236952 + 0.152224i
\(430\) 0 0
\(431\) 7.26399 + 5.27760i 0.349894 + 0.254213i 0.748825 0.662768i \(-0.230619\pi\)
−0.398931 + 0.916981i \(0.630619\pi\)
\(432\) 0 0
\(433\) 9.73586 + 29.9639i 0.467876 + 1.43997i 0.855330 + 0.518084i \(0.173355\pi\)
−0.387454 + 0.921889i \(0.626645\pi\)
\(434\) 0 0
\(435\) 1.13087 0.821622i 0.0542208 0.0393937i
\(436\) 0 0
\(437\) −2.15087 + 6.61970i −0.102890 + 0.316663i
\(438\) 0 0
\(439\) 27.4750 1.31131 0.655655 0.755060i \(-0.272393\pi\)
0.655655 + 0.755060i \(0.272393\pi\)
\(440\) 0 0
\(441\) −35.7552 −1.70263
\(442\) 0 0
\(443\) −9.33108 + 28.7181i −0.443333 + 1.36444i 0.440968 + 0.897523i \(0.354635\pi\)
−0.884301 + 0.466916i \(0.845365\pi\)
\(444\) 0 0
\(445\) 0.377237 0.274079i 0.0178827 0.0129926i
\(446\) 0 0
\(447\) 0.999223 + 3.07529i 0.0472616 + 0.145456i
\(448\) 0 0
\(449\) 22.1525 + 16.0947i 1.04544 + 0.759558i 0.971340 0.237693i \(-0.0763912\pi\)
0.0741012 + 0.997251i \(0.476391\pi\)
\(450\) 0 0
\(451\) −3.15684 + 8.10428i −0.148650 + 0.381615i
\(452\) 0 0
\(453\) 1.41071 + 1.02494i 0.0662811 + 0.0481560i
\(454\) 0 0
\(455\) −8.08953 24.8970i −0.379243 1.16719i
\(456\) 0 0
\(457\) −11.5596 + 8.39854i −0.540735 + 0.392867i −0.824358 0.566069i \(-0.808464\pi\)
0.283623 + 0.958936i \(0.408464\pi\)
\(458\) 0 0
\(459\) 0.898905 2.76655i 0.0419573 0.129131i
\(460\) 0 0
\(461\) 8.78738 0.409269 0.204635 0.978838i \(-0.434399\pi\)
0.204635 + 0.978838i \(0.434399\pi\)
\(462\) 0 0
\(463\) −13.8394 −0.643172 −0.321586 0.946880i \(-0.604216\pi\)
−0.321586 + 0.946880i \(0.604216\pi\)
\(464\) 0 0
\(465\) −0.467235 + 1.43800i −0.0216675 + 0.0666857i
\(466\) 0 0
\(467\) −20.1359 + 14.6296i −0.931778 + 0.676976i −0.946428 0.322916i \(-0.895337\pi\)
0.0146495 + 0.999893i \(0.495337\pi\)
\(468\) 0 0
\(469\) 10.5814 + 32.5661i 0.488602 + 1.50376i
\(470\) 0 0
\(471\) 1.05624 + 0.767405i 0.0486691 + 0.0353602i
\(472\) 0 0
\(473\) 11.9144 + 0.683288i 0.547823 + 0.0314176i
\(474\) 0 0
\(475\) −6.22418 4.52213i −0.285585 0.207490i
\(476\) 0 0
\(477\) 8.63757 + 26.5837i 0.395487 + 1.21718i
\(478\) 0 0
\(479\) 23.1303 16.8051i 1.05685 0.767846i 0.0833469 0.996521i \(-0.473439\pi\)
0.973503 + 0.228674i \(0.0734390\pi\)
\(480\) 0 0
\(481\) −0.340838 + 1.04899i −0.0155409 + 0.0478299i
\(482\) 0 0
\(483\) 1.17156 0.0533079
\(484\) 0 0
\(485\) 7.09963 0.322377
\(486\) 0 0
\(487\) 1.43808 4.42594i 0.0651654 0.200559i −0.913172 0.407574i \(-0.866375\pi\)
0.978338 + 0.207015i \(0.0663749\pi\)
\(488\) 0 0
\(489\) 1.76220 1.28031i 0.0796893 0.0578977i
\(490\) 0 0
\(491\) 7.70564 + 23.7155i 0.347751 + 1.07027i 0.960095 + 0.279675i \(0.0902268\pi\)
−0.612344 + 0.790592i \(0.709773\pi\)
\(492\) 0 0
\(493\) −6.39440 4.64581i −0.287989 0.209237i
\(494\) 0 0
\(495\) −9.64547 0.553168i −0.433532 0.0248630i
\(496\) 0 0
\(497\) −24.7586 17.9882i −1.11057 0.806879i
\(498\) 0 0
\(499\) 4.75417 + 14.6318i 0.212826 + 0.655010i 0.999301 + 0.0373883i \(0.0119038\pi\)
−0.786475 + 0.617622i \(0.788096\pi\)
\(500\) 0 0
\(501\) 4.65031 3.37865i 0.207761 0.150947i
\(502\) 0 0
\(503\) −10.1206 + 31.1481i −0.451257 + 1.38883i 0.424217 + 0.905560i \(0.360549\pi\)
−0.875474 + 0.483265i \(0.839451\pi\)
\(504\) 0 0
\(505\) −16.2851 −0.724677
\(506\) 0 0
\(507\) 6.65292 0.295467
\(508\) 0 0
\(509\) 4.85208 14.9332i 0.215065 0.661901i −0.784084 0.620654i \(-0.786867\pi\)
0.999149 0.0412466i \(-0.0131329\pi\)
\(510\) 0 0
\(511\) 45.2998 32.9122i 2.00394 1.45595i
\(512\) 0 0
\(513\) −4.14650 12.7616i −0.183073 0.563439i
\(514\) 0 0
\(515\) −2.58124 1.87538i −0.113743 0.0826391i
\(516\) 0 0
\(517\) −0.934376 + 2.39874i −0.0410938 + 0.105496i
\(518\) 0 0
\(519\) −2.26891 1.64846i −0.0995939 0.0723592i
\(520\) 0 0
\(521\) −10.3905 31.9786i −0.455215 1.40101i −0.870883 0.491490i \(-0.836452\pi\)
0.415668 0.909516i \(-0.363548\pi\)
\(522\) 0 0
\(523\) 18.5729 13.4940i 0.812136 0.590051i −0.102313 0.994752i \(-0.532624\pi\)
0.914449 + 0.404701i \(0.132624\pi\)
\(524\) 0 0
\(525\) −0.400166 + 1.23158i −0.0174647 + 0.0537507i
\(526\) 0 0
\(527\) 8.54952 0.372423
\(528\) 0 0
\(529\) −22.1815 −0.964413
\(530\) 0 0
\(531\) 10.1303 31.1779i 0.439617 1.35300i
\(532\) 0 0
\(533\) 12.6503 9.19101i 0.547947 0.398107i
\(534\) 0 0
\(535\) −4.06801 12.5201i −0.175876 0.541289i
\(536\) 0 0
\(537\) −1.72113 1.25047i −0.0742720 0.0539618i
\(538\) 0 0
\(539\) −34.2506 + 22.0034i −1.47528 + 0.947756i
\(540\) 0 0
\(541\) 15.1914 + 11.0372i 0.653131 + 0.474528i 0.864336 0.502914i \(-0.167739\pi\)
−0.211205 + 0.977442i \(0.567739\pi\)
\(542\) 0 0
\(543\) −2.13192 6.56136i −0.0914893 0.281575i
\(544\) 0 0
\(545\) −1.08030 + 0.784881i −0.0462748 + 0.0336206i
\(546\) 0 0
\(547\) 5.95740 18.3350i 0.254720 0.783947i −0.739165 0.673525i \(-0.764780\pi\)
0.993885 0.110423i \(-0.0352205\pi\)
\(548\) 0 0
\(549\) −38.4218 −1.63980
\(550\) 0 0
\(551\) −36.4595 −1.55323
\(552\) 0 0
\(553\) 13.6091 41.8844i 0.578717 1.78111i
\(554\) 0 0
\(555\) 0.0441407 0.0320701i 0.00187367 0.00136130i
\(556\) 0 0
\(557\) −5.54314 17.0600i −0.234870 0.722857i −0.997139 0.0755955i \(-0.975914\pi\)
0.762268 0.647261i \(-0.224086\pi\)
\(558\) 0 0
\(559\) −17.3579 12.6112i −0.734159 0.533398i
\(560\) 0 0
\(561\) −0.414525 1.57809i −0.0175012 0.0666270i
\(562\) 0 0
\(563\) 1.46665 + 1.06558i 0.0618120 + 0.0449090i 0.618262 0.785972i \(-0.287837\pi\)
−0.556450 + 0.830881i \(0.687837\pi\)
\(564\) 0 0
\(565\) −0.517444 1.59253i −0.0217690 0.0669982i
\(566\) 0 0
\(567\) 29.2119 21.2237i 1.22678 0.891310i
\(568\) 0 0
\(569\) 2.63761 8.11773i 0.110574 0.340313i −0.880424 0.474187i \(-0.842742\pi\)
0.990998 + 0.133874i \(0.0427419\pi\)
\(570\) 0 0
\(571\) −32.2491 −1.34958 −0.674792 0.738008i \(-0.735767\pi\)
−0.674792 + 0.738008i \(0.735767\pi\)
\(572\) 0 0
\(573\) −1.22873 −0.0513310
\(574\) 0 0
\(575\) −0.279570 + 0.860427i −0.0116589 + 0.0358823i
\(576\) 0 0
\(577\) −24.2423 + 17.6131i −1.00922 + 0.733243i −0.964046 0.265736i \(-0.914385\pi\)
−0.0451763 + 0.998979i \(0.514385\pi\)
\(578\) 0 0
\(579\) −2.11155 6.49868i −0.0877530 0.270076i
\(580\) 0 0
\(581\) 14.5456 + 10.5680i 0.603455 + 0.438435i
\(582\) 0 0
\(583\) 24.6335 + 20.1496i 1.02022 + 0.834512i
\(584\) 0 0
\(585\) 14.0523 + 10.2096i 0.580993 + 0.422116i
\(586\) 0 0
\(587\) 3.02941 + 9.32357i 0.125037 + 0.384825i 0.993908 0.110214i \(-0.0351537\pi\)
−0.868871 + 0.495039i \(0.835154\pi\)
\(588\) 0 0
\(589\) 31.9057 23.1808i 1.31465 0.955149i
\(590\) 0 0
\(591\) 0.925223 2.84754i 0.0380586 0.117132i
\(592\) 0 0
\(593\) 15.4666 0.635136 0.317568 0.948235i \(-0.397134\pi\)
0.317568 + 0.948235i \(0.397134\pi\)
\(594\) 0 0
\(595\) 7.32228 0.300184
\(596\) 0 0
\(597\) −1.55072 + 4.77263i −0.0634668 + 0.195331i
\(598\) 0 0
\(599\) 0.225061 0.163516i 0.00919574 0.00668110i −0.583178 0.812344i \(-0.698191\pi\)
0.592374 + 0.805663i \(0.298191\pi\)
\(600\) 0 0
\(601\) 9.27220 + 28.5369i 0.378221 + 1.16404i 0.941280 + 0.337628i \(0.109624\pi\)
−0.563059 + 0.826417i \(0.690376\pi\)
\(602\) 0 0
\(603\) −18.3809 13.3545i −0.748528 0.543837i
\(604\) 0 0
\(605\) −9.58002 + 5.40586i −0.389483 + 0.219779i
\(606\) 0 0
\(607\) 18.0387 + 13.1059i 0.732169 + 0.531952i 0.890249 0.455474i \(-0.150530\pi\)
−0.158080 + 0.987426i \(0.550530\pi\)
\(608\) 0 0
\(609\) 1.89638 + 5.83646i 0.0768452 + 0.236505i
\(610\) 0 0
\(611\) 3.74430 2.72040i 0.151478 0.110055i
\(612\) 0 0
\(613\) −8.76829 + 26.9860i −0.354148 + 1.08996i 0.602354 + 0.798229i \(0.294230\pi\)
−0.956502 + 0.291726i \(0.905770\pi\)
\(614\) 0 0
\(615\) −0.773501 −0.0311906
\(616\) 0 0
\(617\) −15.1603 −0.610332 −0.305166 0.952299i \(-0.598712\pi\)
−0.305166 + 0.952299i \(0.598712\pi\)
\(618\) 0 0
\(619\) −9.12336 + 28.0788i −0.366699 + 1.12858i 0.582212 + 0.813037i \(0.302187\pi\)
−0.948910 + 0.315545i \(0.897813\pi\)
\(620\) 0 0
\(621\) −1.27656 + 0.927473i −0.0512265 + 0.0372182i
\(622\) 0 0
\(623\) 0.632600 + 1.94694i 0.0253446 + 0.0780026i
\(624\) 0 0
\(625\) −0.809017 0.587785i −0.0323607 0.0235114i
\(626\) 0 0
\(627\) −5.82572 4.76529i −0.232657 0.190307i
\(628\) 0 0
\(629\) −0.249591 0.181338i −0.00995184 0.00723043i
\(630\) 0 0
\(631\) −14.1188 43.4532i −0.562061 1.72985i −0.676527 0.736418i \(-0.736516\pi\)
0.114466 0.993427i \(-0.463484\pi\)
\(632\) 0 0
\(633\) 1.43565 1.04306i 0.0570618 0.0414579i
\(634\) 0 0
\(635\) 0.278570 0.857349i 0.0110547 0.0340229i
\(636\) 0 0
\(637\) 73.1897 2.89988
\(638\) 0 0
\(639\) 20.3057 0.803281
\(640\) 0 0
\(641\) 11.1602 34.3475i 0.440801 1.35665i −0.446223 0.894922i \(-0.647231\pi\)
0.887024 0.461724i \(-0.152769\pi\)
\(642\) 0 0
\(643\) 27.0998 19.6892i 1.06871 0.776465i 0.0930318 0.995663i \(-0.470344\pi\)
0.975680 + 0.219198i \(0.0703442\pi\)
\(644\) 0 0
\(645\) 0.327972 + 1.00939i 0.0129139 + 0.0397449i
\(646\) 0 0
\(647\) −31.7188 23.0451i −1.24700 0.905996i −0.248953 0.968516i \(-0.580086\pi\)
−0.998044 + 0.0625198i \(0.980086\pi\)
\(648\) 0 0
\(649\) −9.48258 36.1000i −0.372224 1.41705i
\(650\) 0 0
\(651\) −5.37032 3.90177i −0.210480 0.152922i
\(652\) 0 0
\(653\) 7.65109 + 23.5476i 0.299410 + 0.921491i 0.981704 + 0.190412i \(0.0609825\pi\)
−0.682294 + 0.731078i \(0.739017\pi\)
\(654\) 0 0
\(655\) 11.7734 8.55388i 0.460025 0.334228i
\(656\) 0 0
\(657\) −11.4808 + 35.3342i −0.447907 + 1.37852i
\(658\) 0 0
\(659\) 24.8813 0.969238 0.484619 0.874725i \(-0.338958\pi\)
0.484619 + 0.874725i \(0.338958\pi\)
\(660\) 0 0
\(661\) −5.94396 −0.231193 −0.115597 0.993296i \(-0.536878\pi\)
−0.115597 + 0.993296i \(0.536878\pi\)
\(662\) 0 0
\(663\) −0.906478 + 2.78985i −0.0352047 + 0.108349i
\(664\) 0 0
\(665\) 27.3258 19.8533i 1.05965 0.769879i
\(666\) 0 0
\(667\) 1.32488 + 4.07755i 0.0512995 + 0.157883i
\(668\) 0 0
\(669\) −0.595161 0.432410i −0.0230103 0.0167179i
\(670\) 0 0
\(671\) −36.8051 + 23.6445i −1.42085 + 0.912786i
\(672\) 0 0
\(673\) −30.6213 22.2477i −1.18036 0.857585i −0.188152 0.982140i \(-0.560250\pi\)
−0.992213 + 0.124555i \(0.960250\pi\)
\(674\) 0 0
\(675\) −0.538961 1.65875i −0.0207446 0.0638454i
\(676\) 0 0
\(677\) −0.153794 + 0.111738i −0.00591078 + 0.00429443i −0.590737 0.806864i \(-0.701163\pi\)
0.584826 + 0.811159i \(0.301163\pi\)
\(678\) 0 0
\(679\) −9.63181 + 29.6437i −0.369635 + 1.13762i
\(680\) 0 0
\(681\) −7.37267 −0.282521
\(682\) 0 0
\(683\) 23.0773 0.883030 0.441515 0.897254i \(-0.354441\pi\)
0.441515 + 0.897254i \(0.354441\pi\)
\(684\) 0 0
\(685\) −6.36251 + 19.5818i −0.243099 + 0.748182i
\(686\) 0 0
\(687\) 0.661201 0.480391i 0.0252264 0.0183281i
\(688\) 0 0
\(689\) −17.6808 54.4160i −0.673586 2.07308i
\(690\) 0 0
\(691\) −37.7877 27.4544i −1.43751 1.04441i −0.988555 0.150862i \(-0.951795\pi\)
−0.448958 0.893553i \(-0.648205\pi\)
\(692\) 0 0
\(693\) 15.3953 39.5231i 0.584821 1.50136i
\(694\) 0 0
\(695\) 12.1224 + 8.80746i 0.459830 + 0.334086i
\(696\) 0 0
\(697\) 1.35155 + 4.15965i 0.0511936 + 0.157558i
\(698\) 0 0
\(699\) 2.29091 1.66444i 0.0866501 0.0629550i
\(700\) 0 0
\(701\) 1.28934 3.96818i 0.0486977 0.149876i −0.923751 0.382994i \(-0.874893\pi\)
0.972448 + 0.233118i \(0.0748929\pi\)
\(702\) 0 0
\(703\) −1.42311 −0.0536737
\(704\) 0 0
\(705\) −0.228944 −0.00862254
\(706\) 0 0
\(707\) 22.0934 67.9965i 0.830908 2.55727i
\(708\) 0 0
\(709\) 7.07305 5.13887i 0.265634 0.192994i −0.446993 0.894537i \(-0.647505\pi\)
0.712627 + 0.701543i \(0.247505\pi\)
\(710\) 0 0
\(711\) 9.02981 + 27.7909i 0.338644 + 1.04224i
\(712\) 0 0
\(713\) −3.75189 2.72591i −0.140510 0.102086i
\(714\) 0 0
\(715\) 19.7440 + 1.13232i 0.738382 + 0.0423462i
\(716\) 0 0
\(717\) −3.52438 2.56061i −0.131620 0.0956278i
\(718\) 0 0
\(719\) −2.28722 7.03934i −0.0852990 0.262523i 0.899305 0.437321i \(-0.144073\pi\)
−0.984604 + 0.174798i \(0.944073\pi\)
\(720\) 0 0
\(721\) 11.3323 8.23340i 0.422037 0.306628i
\(722\) 0 0
\(723\) −0.951024 + 2.92695i −0.0353690 + 0.108854i
\(724\) 0 0
\(725\) −4.73899 −0.176002
\(726\) 0 0
\(727\) 18.0187 0.668275 0.334137 0.942524i \(-0.391555\pi\)
0.334137 + 0.942524i \(0.391555\pi\)
\(728\) 0 0
\(729\) −6.92653 + 21.3177i −0.256538 + 0.789543i
\(730\) 0 0
\(731\) 4.85514 3.52746i 0.179574 0.130468i
\(732\) 0 0
\(733\) −11.2463 34.6127i −0.415393 1.27845i −0.911899 0.410415i \(-0.865384\pi\)
0.496506 0.868033i \(-0.334616\pi\)
\(734\) 0 0
\(735\) −2.92903 2.12806i −0.108039 0.0784948i
\(736\) 0 0
\(737\) −25.8257 1.48110i −0.951302 0.0545572i
\(738\) 0 0
\(739\) 10.0576 + 7.30726i 0.369974 + 0.268802i 0.757200 0.653183i \(-0.226567\pi\)
−0.387226 + 0.921985i \(0.626567\pi\)
\(740\) 0 0
\(741\) 4.18144 + 12.8691i 0.153609 + 0.472759i
\(742\) 0 0
\(743\) −30.2327 + 21.9653i −1.10913 + 0.805829i −0.982526 0.186125i \(-0.940407\pi\)
−0.126602 + 0.991954i \(0.540407\pi\)
\(744\) 0 0
\(745\) 3.38762 10.4260i 0.124113 0.381980i
\(746\) 0 0
\(747\) −11.9296 −0.436480
\(748\) 0 0
\(749\) 57.7950 2.11178
\(750\) 0 0
\(751\) −2.44111 + 7.51295i −0.0890772 + 0.274151i −0.985665 0.168715i \(-0.946038\pi\)
0.896588 + 0.442866i \(0.146038\pi\)
\(752\) 0 0
\(753\) 1.60692 1.16749i 0.0585594 0.0425459i
\(754\) 0 0
\(755\) −1.82682 5.62238i −0.0664848 0.204619i
\(756\) 0 0
\(757\) 2.56487 + 1.86349i 0.0932219 + 0.0677297i 0.633420 0.773808i \(-0.281651\pi\)
−0.540198 + 0.841538i \(0.681651\pi\)
\(758\) 0 0
\(759\) −0.321244 + 0.824699i −0.0116604 + 0.0299347i
\(760\) 0 0
\(761\) −37.8368 27.4901i −1.37158 0.996514i −0.997612 0.0690739i \(-0.977996\pi\)
−0.373972 0.927440i \(-0.622004\pi\)
\(762\) 0 0
\(763\) −1.81158 5.57547i −0.0655836 0.201845i
\(764\) 0 0
\(765\) −3.93056 + 2.85572i −0.142110 + 0.103249i
\(766\) 0 0
\(767\) −20.7364 + 63.8201i −0.748748 + 2.30441i
\(768\) 0 0
\(769\) −1.95610 −0.0705388 −0.0352694 0.999378i \(-0.511229\pi\)
−0.0352694 + 0.999378i \(0.511229\pi\)
\(770\) 0 0
\(771\) 2.28358 0.0822411
\(772\) 0 0
\(773\) −6.31718 + 19.4423i −0.227213 + 0.699290i 0.770846 + 0.637021i \(0.219834\pi\)
−0.998059 + 0.0622690i \(0.980166\pi\)
\(774\) 0 0
\(775\) 4.14709 3.01303i 0.148968 0.108231i
\(776\) 0 0
\(777\) 0.0740209 + 0.227813i 0.00265548 + 0.00817274i
\(778\) 0 0
\(779\) 16.3221 + 11.8587i 0.584800 + 0.424882i
\(780\) 0 0
\(781\) 19.4513 12.4960i 0.696021 0.447141i
\(782\) 0 0
\(783\) −6.68680 4.85825i −0.238967 0.173620i
\(784\) 0 0
\(785\) −1.36780 4.20964i −0.0488187 0.150249i
\(786\) 0 0
\(787\) 2.09694 1.52351i 0.0747478 0.0543074i −0.549784 0.835307i \(-0.685290\pi\)
0.624532 + 0.781000i \(0.285290\pi\)
\(788\) 0 0