Properties

Label 162.2.e.b.127.1
Level $162$
Weight $2$
Character 162.127
Analytic conductor $1.294$
Analytic rank $0$
Dimension $12$
Inner twists $2$

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [162,2,Mod(19,162)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(162, base_ring=CyclotomicField(18))
 
chi = DirichletCharacter(H, H._module([16]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("162.19");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 162 = 2 \cdot 3^{4} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 162.e (of order \(9\), degree \(6\), 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: \(1.29357651274\)
Analytic rank: \(0\)
Dimension: \(12\)
Relative dimension: \(2\) over \(\Q(\zeta_{9})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{12} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{12} - 6 x^{11} + 33 x^{10} - 110 x^{9} + 318 x^{8} - 678 x^{7} + 1225 x^{6} - 1698 x^{5} + 1905 x^{4} + \cdots + 57 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 3^{3} \)
Twist minimal: no (minimal twist has level 54)
Sato-Tate group: $\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label 127.1
Root \(0.500000 - 0.168222i\) of defining polynomial
Character \(\chi\) \(=\) 162.127
Dual form 162.2.e.b.37.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.766044 - 0.642788i) q^{2} +(0.173648 + 0.984808i) q^{4} +(-0.696050 - 0.253341i) q^{5} +(0.717657 - 4.07003i) q^{7} +(0.500000 - 0.866025i) q^{8} +(0.370360 + 0.641483i) q^{10} +(4.27215 - 1.55493i) q^{11} +(0.662744 - 0.556108i) q^{13} +(-3.16592 + 2.65653i) q^{14} +(-0.939693 + 0.342020i) q^{16} +(-2.17975 - 3.77544i) q^{17} +(-0.777964 + 1.34747i) q^{19} +(0.128625 - 0.729467i) q^{20} +(-4.27215 - 1.55493i) q^{22} +(0.608539 + 3.45119i) q^{23} +(-3.40992 - 2.86126i) q^{25} -0.865150 q^{26} +4.13282 q^{28} +(2.50318 + 2.10042i) q^{29} +(1.85778 + 10.5360i) q^{31} +(0.939693 + 0.342020i) q^{32} +(-0.757019 + 4.29327i) q^{34} +(-1.53063 + 2.65113i) q^{35} +(0.880842 + 1.52566i) q^{37} +(1.46209 - 0.532159i) q^{38} +(-0.567425 + 0.476126i) q^{40} +(1.97401 - 1.65639i) q^{41} +(2.58757 - 0.941797i) q^{43} +(2.27316 + 3.93723i) q^{44} +(1.75222 - 3.03493i) q^{46} +(-1.68378 + 9.54918i) q^{47} +(-9.47229 - 3.44763i) q^{49} +(0.772966 + 4.38371i) q^{50} +(0.662744 + 0.556108i) q^{52} -4.00839 q^{53} -3.36756 q^{55} +(-3.16592 - 2.65653i) q^{56} +(-0.567425 - 3.21803i) q^{58} +(1.34517 + 0.489601i) q^{59} +(-0.751711 + 4.26317i) q^{61} +(5.34926 - 9.26519i) q^{62} +(-0.500000 - 0.866025i) q^{64} +(-0.602188 + 0.219178i) q^{65} +(10.0444 - 8.42825i) q^{67} +(3.33957 - 2.80223i) q^{68} +(2.87665 - 1.04701i) q^{70} +(-2.54213 - 4.40310i) q^{71} +(0.286636 - 0.496469i) q^{73} +(0.305913 - 1.73492i) q^{74} +(-1.46209 - 0.532159i) q^{76} +(-3.26270 - 18.5037i) q^{77} +(5.17820 + 4.34502i) q^{79} +0.740720 q^{80} -2.57689 q^{82} +(-7.06556 - 5.92871i) q^{83} +(0.560740 + 3.18011i) q^{85} +(-2.58757 - 0.941797i) q^{86} +(0.789461 - 4.47725i) q^{88} +(-6.19947 + 10.7378i) q^{89} +(-1.78776 - 3.09648i) q^{91} +(-3.29309 + 1.19859i) q^{92} +(7.42794 - 6.23278i) q^{94} +(0.882872 - 0.740818i) q^{95} +(-5.40770 + 1.96824i) q^{97} +(5.04010 + 8.72971i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12 q + 3 q^{5} - 3 q^{7} + 6 q^{8} - 3 q^{10} + 12 q^{11} + 12 q^{13} + 3 q^{14} + 6 q^{17} - 9 q^{19} - 6 q^{20} - 12 q^{22} - 30 q^{23} - 9 q^{25} - 18 q^{26} + 12 q^{28} - 15 q^{29} - 15 q^{34} - 3 q^{35}+ \cdots + 12 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/162\mathbb{Z}\right)^\times\).

\(n\) \(83\)
\(\chi(n)\) \(e\left(\frac{2}{9}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.766044 0.642788i −0.541675 0.454519i
\(3\) 0 0
\(4\) 0.173648 + 0.984808i 0.0868241 + 0.492404i
\(5\) −0.696050 0.253341i −0.311283 0.113298i 0.181655 0.983362i \(-0.441855\pi\)
−0.492938 + 0.870065i \(0.664077\pi\)
\(6\) 0 0
\(7\) 0.717657 4.07003i 0.271249 1.53833i −0.479382 0.877606i \(-0.659139\pi\)
0.750631 0.660722i \(-0.229750\pi\)
\(8\) 0.500000 0.866025i 0.176777 0.306186i
\(9\) 0 0
\(10\) 0.370360 + 0.641483i 0.117118 + 0.202855i
\(11\) 4.27215 1.55493i 1.28810 0.468830i 0.394998 0.918682i \(-0.370745\pi\)
0.893103 + 0.449852i \(0.148523\pi\)
\(12\) 0 0
\(13\) 0.662744 0.556108i 0.183812 0.154237i −0.546239 0.837630i \(-0.683941\pi\)
0.730051 + 0.683393i \(0.239496\pi\)
\(14\) −3.16592 + 2.65653i −0.846129 + 0.709986i
\(15\) 0 0
\(16\) −0.939693 + 0.342020i −0.234923 + 0.0855050i
\(17\) −2.17975 3.77544i −0.528667 0.915678i −0.999441 0.0334246i \(-0.989359\pi\)
0.470774 0.882254i \(-0.343975\pi\)
\(18\) 0 0
\(19\) −0.777964 + 1.34747i −0.178477 + 0.309132i −0.941359 0.337406i \(-0.890450\pi\)
0.762882 + 0.646538i \(0.223784\pi\)
\(20\) 0.128625 0.729467i 0.0287614 0.163114i
\(21\) 0 0
\(22\) −4.27215 1.55493i −0.910825 0.331513i
\(23\) 0.608539 + 3.45119i 0.126889 + 0.719624i 0.980168 + 0.198169i \(0.0634994\pi\)
−0.853279 + 0.521455i \(0.825389\pi\)
\(24\) 0 0
\(25\) −3.40992 2.86126i −0.681984 0.572252i
\(26\) −0.865150 −0.169670
\(27\) 0 0
\(28\) 4.13282 0.781029
\(29\) 2.50318 + 2.10042i 0.464829 + 0.390038i 0.844904 0.534918i \(-0.179657\pi\)
−0.380075 + 0.924956i \(0.624102\pi\)
\(30\) 0 0
\(31\) 1.85778 + 10.5360i 0.333667 + 1.89232i 0.440016 + 0.897990i \(0.354973\pi\)
−0.106350 + 0.994329i \(0.533916\pi\)
\(32\) 0.939693 + 0.342020i 0.166116 + 0.0604612i
\(33\) 0 0
\(34\) −0.757019 + 4.29327i −0.129828 + 0.736290i
\(35\) −1.53063 + 2.65113i −0.258724 + 0.448123i
\(36\) 0 0
\(37\) 0.880842 + 1.52566i 0.144810 + 0.250817i 0.929302 0.369321i \(-0.120410\pi\)
−0.784492 + 0.620139i \(0.787076\pi\)
\(38\) 1.46209 0.532159i 0.237183 0.0863275i
\(39\) 0 0
\(40\) −0.567425 + 0.476126i −0.0897177 + 0.0752821i
\(41\) 1.97401 1.65639i 0.308289 0.258685i −0.475495 0.879718i \(-0.657731\pi\)
0.783784 + 0.621033i \(0.213287\pi\)
\(42\) 0 0
\(43\) 2.58757 0.941797i 0.394600 0.143623i −0.137096 0.990558i \(-0.543777\pi\)
0.531696 + 0.846935i \(0.321555\pi\)
\(44\) 2.27316 + 3.93723i 0.342692 + 0.593560i
\(45\) 0 0
\(46\) 1.75222 3.03493i 0.258350 0.447476i
\(47\) −1.68378 + 9.54918i −0.245604 + 1.39289i 0.573481 + 0.819219i \(0.305593\pi\)
−0.819085 + 0.573672i \(0.805519\pi\)
\(48\) 0 0
\(49\) −9.47229 3.44763i −1.35318 0.492519i
\(50\) 0.772966 + 4.38371i 0.109314 + 0.619950i
\(51\) 0 0
\(52\) 0.662744 + 0.556108i 0.0919060 + 0.0771183i
\(53\) −4.00839 −0.550595 −0.275297 0.961359i \(-0.588776\pi\)
−0.275297 + 0.961359i \(0.588776\pi\)
\(54\) 0 0
\(55\) −3.36756 −0.454081
\(56\) −3.16592 2.65653i −0.423064 0.354993i
\(57\) 0 0
\(58\) −0.567425 3.21803i −0.0745065 0.422548i
\(59\) 1.34517 + 0.489601i 0.175126 + 0.0637406i 0.428095 0.903734i \(-0.359185\pi\)
−0.252969 + 0.967474i \(0.581407\pi\)
\(60\) 0 0
\(61\) −0.751711 + 4.26317i −0.0962468 + 0.545843i 0.898111 + 0.439768i \(0.144939\pi\)
−0.994358 + 0.106075i \(0.966172\pi\)
\(62\) 5.34926 9.26519i 0.679357 1.17668i
\(63\) 0 0
\(64\) −0.500000 0.866025i −0.0625000 0.108253i
\(65\) −0.602188 + 0.219178i −0.0746922 + 0.0271857i
\(66\) 0 0
\(67\) 10.0444 8.42825i 1.22712 1.02967i 0.228697 0.973498i \(-0.426554\pi\)
0.998421 0.0561764i \(-0.0178909\pi\)
\(68\) 3.33957 2.80223i 0.404983 0.339821i
\(69\) 0 0
\(70\) 2.87665 1.04701i 0.343825 0.125142i
\(71\) −2.54213 4.40310i −0.301695 0.522551i 0.674825 0.737978i \(-0.264219\pi\)
−0.976520 + 0.215427i \(0.930886\pi\)
\(72\) 0 0
\(73\) 0.286636 0.496469i 0.0335483 0.0581073i −0.848764 0.528772i \(-0.822653\pi\)
0.882312 + 0.470665i \(0.155986\pi\)
\(74\) 0.305913 1.73492i 0.0355617 0.201680i
\(75\) 0 0
\(76\) −1.46209 0.532159i −0.167714 0.0610428i
\(77\) −3.26270 18.5037i −0.371819 2.10869i
\(78\) 0 0
\(79\) 5.17820 + 4.34502i 0.582593 + 0.488853i 0.885797 0.464072i \(-0.153612\pi\)
−0.303205 + 0.952925i \(0.598057\pi\)
\(80\) 0.740720 0.0828151
\(81\) 0 0
\(82\) −2.57689 −0.284570
\(83\) −7.06556 5.92871i −0.775546 0.650761i 0.166577 0.986029i \(-0.446729\pi\)
−0.942123 + 0.335268i \(0.891173\pi\)
\(84\) 0 0
\(85\) 0.560740 + 3.18011i 0.0608208 + 0.344932i
\(86\) −2.58757 0.941797i −0.279024 0.101557i
\(87\) 0 0
\(88\) 0.789461 4.47725i 0.0841568 0.477277i
\(89\) −6.19947 + 10.7378i −0.657142 + 1.13820i 0.324210 + 0.945985i \(0.394902\pi\)
−0.981352 + 0.192219i \(0.938432\pi\)
\(90\) 0 0
\(91\) −1.78776 3.09648i −0.187408 0.324600i
\(92\) −3.29309 + 1.19859i −0.343329 + 0.124961i
\(93\) 0 0
\(94\) 7.42794 6.23278i 0.766134 0.642862i
\(95\) 0.882872 0.740818i 0.0905808 0.0760063i
\(96\) 0 0
\(97\) −5.40770 + 1.96824i −0.549069 + 0.199845i −0.601633 0.798773i \(-0.705483\pi\)
0.0525637 + 0.998618i \(0.483261\pi\)
\(98\) 5.04010 + 8.72971i 0.509127 + 0.881834i
\(99\) 0 0
\(100\) 2.22567 3.85497i 0.222567 0.385497i
\(101\) 1.91700 10.8718i 0.190748 1.08179i −0.727596 0.686006i \(-0.759363\pi\)
0.918345 0.395782i \(-0.129526\pi\)
\(102\) 0 0
\(103\) 6.03419 + 2.19627i 0.594567 + 0.216405i 0.621737 0.783226i \(-0.286427\pi\)
−0.0271702 + 0.999631i \(0.508650\pi\)
\(104\) −0.150232 0.852007i −0.0147314 0.0835461i
\(105\) 0 0
\(106\) 3.07060 + 2.57654i 0.298243 + 0.250256i
\(107\) 17.2923 1.67171 0.835854 0.548952i \(-0.184973\pi\)
0.835854 + 0.548952i \(0.184973\pi\)
\(108\) 0 0
\(109\) −9.94570 −0.952626 −0.476313 0.879276i \(-0.658027\pi\)
−0.476313 + 0.879276i \(0.658027\pi\)
\(110\) 2.57970 + 2.16462i 0.245964 + 0.206389i
\(111\) 0 0
\(112\) 0.717657 + 4.07003i 0.0678122 + 0.384582i
\(113\) 2.30350 + 0.838405i 0.216695 + 0.0788705i 0.448087 0.893990i \(-0.352106\pi\)
−0.231392 + 0.972861i \(0.574328\pi\)
\(114\) 0 0
\(115\) 0.450757 2.55637i 0.0420333 0.238383i
\(116\) −1.63383 + 2.82988i −0.151698 + 0.262748i
\(117\) 0 0
\(118\) −0.715749 1.23971i −0.0658900 0.114125i
\(119\) −16.9305 + 6.16219i −1.55201 + 0.564887i
\(120\) 0 0
\(121\) 7.40693 6.21515i 0.673357 0.565014i
\(122\) 3.31616 2.78258i 0.300231 0.251923i
\(123\) 0 0
\(124\) −10.0533 + 3.65911i −0.902815 + 0.328598i
\(125\) 3.50040 + 6.06287i 0.313085 + 0.542279i
\(126\) 0 0
\(127\) −4.05136 + 7.01715i −0.359500 + 0.622672i −0.987877 0.155237i \(-0.950386\pi\)
0.628378 + 0.777908i \(0.283719\pi\)
\(128\) −0.173648 + 0.984808i −0.0153485 + 0.0870455i
\(129\) 0 0
\(130\) 0.602188 + 0.219178i 0.0528153 + 0.0192232i
\(131\) 2.76007 + 15.6532i 0.241149 + 1.36762i 0.829269 + 0.558849i \(0.188757\pi\)
−0.588120 + 0.808773i \(0.700132\pi\)
\(132\) 0 0
\(133\) 4.92595 + 4.13336i 0.427134 + 0.358408i
\(134\) −13.1120 −1.13271
\(135\) 0 0
\(136\) −4.35950 −0.373824
\(137\) 9.46551 + 7.94250i 0.808693 + 0.678574i 0.950295 0.311350i \(-0.100781\pi\)
−0.141603 + 0.989924i \(0.545225\pi\)
\(138\) 0 0
\(139\) −0.761169 4.31680i −0.0645615 0.366146i −0.999922 0.0124519i \(-0.996036\pi\)
0.935361 0.353695i \(-0.115075\pi\)
\(140\) −2.87665 1.04701i −0.243121 0.0884888i
\(141\) 0 0
\(142\) −0.882872 + 5.00702i −0.0740890 + 0.420179i
\(143\) 1.96663 3.40630i 0.164458 0.284849i
\(144\) 0 0
\(145\) −1.21021 2.09615i −0.100503 0.174076i
\(146\) −0.538700 + 0.196071i −0.0445832 + 0.0162269i
\(147\) 0 0
\(148\) −1.34953 + 1.13239i −0.110931 + 0.0930818i
\(149\) −5.23476 + 4.39248i −0.428848 + 0.359846i −0.831517 0.555499i \(-0.812527\pi\)
0.402669 + 0.915346i \(0.368083\pi\)
\(150\) 0 0
\(151\) 4.89254 1.78074i 0.398149 0.144915i −0.135182 0.990821i \(-0.543162\pi\)
0.533332 + 0.845906i \(0.320940\pi\)
\(152\) 0.777964 + 1.34747i 0.0631012 + 0.109295i
\(153\) 0 0
\(154\) −9.39457 + 16.2719i −0.757036 + 1.31122i
\(155\) 1.37609 7.80422i 0.110531 0.626850i
\(156\) 0 0
\(157\) −3.73260 1.35856i −0.297894 0.108424i 0.188749 0.982025i \(-0.439557\pi\)
−0.486643 + 0.873601i \(0.661779\pi\)
\(158\) −1.17380 6.65696i −0.0933826 0.529599i
\(159\) 0 0
\(160\) −0.567425 0.476126i −0.0448589 0.0376411i
\(161\) 14.4832 1.14144
\(162\) 0 0
\(163\) 2.34707 0.183837 0.0919184 0.995767i \(-0.470700\pi\)
0.0919184 + 0.995767i \(0.470700\pi\)
\(164\) 1.97401 + 1.65639i 0.154145 + 0.129343i
\(165\) 0 0
\(166\) 1.60163 + 9.08331i 0.124311 + 0.705002i
\(167\) −0.989141 0.360018i −0.0765420 0.0278590i 0.303465 0.952842i \(-0.401856\pi\)
−0.380007 + 0.924983i \(0.624079\pi\)
\(168\) 0 0
\(169\) −2.12745 + 12.0654i −0.163650 + 0.928107i
\(170\) 1.61459 2.79654i 0.123833 0.214485i
\(171\) 0 0
\(172\) 1.37682 + 2.38471i 0.104981 + 0.181833i
\(173\) 6.42081 2.33699i 0.488166 0.177678i −0.0861981 0.996278i \(-0.527472\pi\)
0.574364 + 0.818600i \(0.305250\pi\)
\(174\) 0 0
\(175\) −14.0926 + 11.8251i −1.06530 + 0.893892i
\(176\) −3.48269 + 2.92232i −0.262517 + 0.220278i
\(177\) 0 0
\(178\) 11.6512 4.24069i 0.873294 0.317853i
\(179\) −1.09877 1.90312i −0.0821258 0.142246i 0.822037 0.569434i \(-0.192838\pi\)
−0.904163 + 0.427188i \(0.859504\pi\)
\(180\) 0 0
\(181\) 7.86998 13.6312i 0.584971 1.01320i −0.409908 0.912127i \(-0.634439\pi\)
0.994879 0.101073i \(-0.0322275\pi\)
\(182\) −0.620881 + 3.52119i −0.0460228 + 0.261008i
\(183\) 0 0
\(184\) 3.29309 + 1.19859i 0.242770 + 0.0883610i
\(185\) −0.226596 1.28509i −0.0166597 0.0944818i
\(186\) 0 0
\(187\) −15.1828 12.7399i −1.11027 0.931631i
\(188\) −9.69649 −0.707189
\(189\) 0 0
\(190\) −1.15251 −0.0836117
\(191\) −6.00686 5.04036i −0.434641 0.364707i 0.399058 0.916926i \(-0.369337\pi\)
−0.833700 + 0.552218i \(0.813782\pi\)
\(192\) 0 0
\(193\) −2.87224 16.2893i −0.206748 1.17253i −0.894665 0.446738i \(-0.852586\pi\)
0.687916 0.725790i \(-0.258526\pi\)
\(194\) 5.40770 + 1.96824i 0.388251 + 0.141312i
\(195\) 0 0
\(196\) 1.75041 9.92706i 0.125029 0.709075i
\(197\) −5.68810 + 9.85208i −0.405260 + 0.701931i −0.994352 0.106135i \(-0.966152\pi\)
0.589091 + 0.808066i \(0.299486\pi\)
\(198\) 0 0
\(199\) −0.936258 1.62165i −0.0663696 0.114955i 0.830931 0.556375i \(-0.187808\pi\)
−0.897301 + 0.441420i \(0.854475\pi\)
\(200\) −4.18288 + 1.52245i −0.295775 + 0.107653i
\(201\) 0 0
\(202\) −8.45678 + 7.09608i −0.595017 + 0.499279i
\(203\) 10.3452 8.68065i 0.726090 0.609262i
\(204\) 0 0
\(205\) −1.79364 + 0.652833i −0.125274 + 0.0455958i
\(206\) −3.21073 5.56114i −0.223702 0.387463i
\(207\) 0 0
\(208\) −0.432575 + 0.749242i −0.0299937 + 0.0519506i
\(209\) −1.22834 + 6.96629i −0.0849663 + 0.481868i
\(210\) 0 0
\(211\) −5.14025 1.87090i −0.353870 0.128798i 0.158968 0.987284i \(-0.449183\pi\)
−0.512837 + 0.858486i \(0.671406\pi\)
\(212\) −0.696050 3.94749i −0.0478049 0.271115i
\(213\) 0 0
\(214\) −13.2467 11.1153i −0.905522 0.759824i
\(215\) −2.03967 −0.139104
\(216\) 0 0
\(217\) 44.2150 3.00151
\(218\) 7.61885 + 6.39297i 0.516014 + 0.432987i
\(219\) 0 0
\(220\) −0.584770 3.31639i −0.0394252 0.223591i
\(221\) −3.54417 1.28997i −0.238407 0.0867729i
\(222\) 0 0
\(223\) −0.219638 + 1.24563i −0.0147080 + 0.0834134i −0.991278 0.131786i \(-0.957929\pi\)
0.976570 + 0.215199i \(0.0690400\pi\)
\(224\) 2.06641 3.57913i 0.138068 0.239140i
\(225\) 0 0
\(226\) −1.22567 2.12292i −0.0815301 0.141214i
\(227\) 9.34189 3.40017i 0.620043 0.225677i −0.0128486 0.999917i \(-0.504090\pi\)
0.632892 + 0.774240i \(0.281868\pi\)
\(228\) 0 0
\(229\) −7.64692 + 6.41653i −0.505323 + 0.424016i −0.859480 0.511170i \(-0.829212\pi\)
0.354157 + 0.935186i \(0.384768\pi\)
\(230\) −1.98850 + 1.66855i −0.131118 + 0.110021i
\(231\) 0 0
\(232\) 3.07060 1.11761i 0.201595 0.0733746i
\(233\) −13.5765 23.5152i −0.889428 1.54053i −0.840553 0.541729i \(-0.817770\pi\)
−0.0488748 0.998805i \(-0.515564\pi\)
\(234\) 0 0
\(235\) 3.59119 6.22013i 0.234264 0.405757i
\(236\) −0.248577 + 1.40975i −0.0161810 + 0.0917669i
\(237\) 0 0
\(238\) 16.9305 + 6.16219i 1.09744 + 0.399435i
\(239\) 3.39241 + 19.2393i 0.219437 + 1.24449i 0.873039 + 0.487651i \(0.162146\pi\)
−0.653602 + 0.756839i \(0.726743\pi\)
\(240\) 0 0
\(241\) 12.4216 + 10.4229i 0.800144 + 0.671400i 0.948234 0.317573i \(-0.102868\pi\)
−0.148090 + 0.988974i \(0.547312\pi\)
\(242\) −9.66906 −0.621551
\(243\) 0 0
\(244\) −4.32893 −0.277132
\(245\) 5.71975 + 4.79944i 0.365422 + 0.306625i
\(246\) 0 0
\(247\) 0.233750 + 1.32566i 0.0148731 + 0.0843498i
\(248\) 10.0533 + 3.65911i 0.638386 + 0.232354i
\(249\) 0 0
\(250\) 1.21568 6.89444i 0.0768861 0.436043i
\(251\) 11.7303 20.3174i 0.740408 1.28242i −0.211902 0.977291i \(-0.567966\pi\)
0.952310 0.305133i \(-0.0987010\pi\)
\(252\) 0 0
\(253\) 7.96615 + 13.7978i 0.500827 + 0.867458i
\(254\) 7.61406 2.77129i 0.477749 0.173886i
\(255\) 0 0
\(256\) 0.766044 0.642788i 0.0478778 0.0401742i
\(257\) −16.8456 + 14.1352i −1.05080 + 0.881728i −0.993178 0.116611i \(-0.962797\pi\)
−0.0576244 + 0.998338i \(0.518353\pi\)
\(258\) 0 0
\(259\) 6.84164 2.49015i 0.425119 0.154731i
\(260\) −0.320417 0.554979i −0.0198714 0.0344183i
\(261\) 0 0
\(262\) 7.94732 13.7652i 0.490987 0.850414i
\(263\) 4.07773 23.1260i 0.251444 1.42601i −0.553595 0.832786i \(-0.686745\pi\)
0.805039 0.593222i \(-0.202144\pi\)
\(264\) 0 0
\(265\) 2.79004 + 1.01549i 0.171391 + 0.0623811i
\(266\) −1.11662 6.33268i −0.0684645 0.388281i
\(267\) 0 0
\(268\) 10.0444 + 8.42825i 0.613559 + 0.514837i
\(269\) −18.3001 −1.11578 −0.557888 0.829916i \(-0.688388\pi\)
−0.557888 + 0.829916i \(0.688388\pi\)
\(270\) 0 0
\(271\) −16.4825 −1.00124 −0.500620 0.865667i \(-0.666895\pi\)
−0.500620 + 0.865667i \(0.666895\pi\)
\(272\) 3.33957 + 2.80223i 0.202491 + 0.169910i
\(273\) 0 0
\(274\) −2.14566 12.1686i −0.129624 0.735133i
\(275\) −19.0167 6.92153i −1.14675 0.417384i
\(276\) 0 0
\(277\) 1.95736 11.1008i 0.117606 0.666980i −0.867820 0.496878i \(-0.834479\pi\)
0.985427 0.170101i \(-0.0544094\pi\)
\(278\) −2.19170 + 3.79613i −0.131449 + 0.227677i
\(279\) 0 0
\(280\) 1.53063 + 2.65113i 0.0914728 + 0.158435i
\(281\) −0.681601 + 0.248083i −0.0406609 + 0.0147994i −0.362271 0.932073i \(-0.617998\pi\)
0.321610 + 0.946872i \(0.395776\pi\)
\(282\) 0 0
\(283\) −16.9589 + 14.2302i −1.00810 + 0.845897i −0.988086 0.153903i \(-0.950816\pi\)
−0.0200144 + 0.999800i \(0.506371\pi\)
\(284\) 3.89477 3.26810i 0.231112 0.193926i
\(285\) 0 0
\(286\) −3.69605 + 1.34525i −0.218552 + 0.0795464i
\(287\) −5.32491 9.22302i −0.314320 0.544418i
\(288\) 0 0
\(289\) −1.00263 + 1.73660i −0.0589780 + 0.102153i
\(290\) −0.420303 + 2.38366i −0.0246811 + 0.139973i
\(291\) 0 0
\(292\) 0.538700 + 0.196071i 0.0315251 + 0.0114742i
\(293\) 1.13889 + 6.45895i 0.0665344 + 0.377336i 0.999834 + 0.0182360i \(0.00580504\pi\)
−0.933299 + 0.359100i \(0.883084\pi\)
\(294\) 0 0
\(295\) −0.812267 0.681573i −0.0472920 0.0396827i
\(296\) 1.76168 0.102396
\(297\) 0 0
\(298\) 6.83349 0.395854
\(299\) 2.32254 + 1.94884i 0.134316 + 0.112705i
\(300\) 0 0
\(301\) −1.97616 11.2074i −0.113904 0.645982i
\(302\) −4.89254 1.78074i −0.281534 0.102470i
\(303\) 0 0
\(304\) 0.270184 1.53229i 0.0154961 0.0878829i
\(305\) 1.60326 2.77694i 0.0918027 0.159007i
\(306\) 0 0
\(307\) −3.98740 6.90639i −0.227573 0.394168i 0.729515 0.683965i \(-0.239746\pi\)
−0.957088 + 0.289796i \(0.906412\pi\)
\(308\) 17.6560 6.42626i 1.00604 0.366170i
\(309\) 0 0
\(310\) −6.07060 + 5.09384i −0.344787 + 0.289311i
\(311\) −10.8380 + 9.09419i −0.614569 + 0.515684i −0.896091 0.443870i \(-0.853605\pi\)
0.281522 + 0.959555i \(0.409161\pi\)
\(312\) 0 0
\(313\) −22.5917 + 8.22270i −1.27696 + 0.464774i −0.889425 0.457082i \(-0.848895\pi\)
−0.387532 + 0.921856i \(0.626672\pi\)
\(314\) 1.98607 + 3.43998i 0.112081 + 0.194129i
\(315\) 0 0
\(316\) −3.37983 + 5.85403i −0.190130 + 0.329315i
\(317\) −3.15913 + 17.9163i −0.177435 + 1.00628i 0.757862 + 0.652415i \(0.226244\pi\)
−0.935296 + 0.353866i \(0.884867\pi\)
\(318\) 0 0
\(319\) 13.9600 + 5.08101i 0.781608 + 0.284482i
\(320\) 0.128625 + 0.729467i 0.00719034 + 0.0407785i
\(321\) 0 0
\(322\) −11.0948 9.30962i −0.618287 0.518805i
\(323\) 6.78307 0.377420
\(324\) 0 0
\(325\) −3.85107 −0.213619
\(326\) −1.79796 1.50867i −0.0995798 0.0835574i
\(327\) 0 0
\(328\) −0.447473 2.53774i −0.0247075 0.140123i
\(329\) 37.6571 + 13.7061i 2.07610 + 0.755640i
\(330\) 0 0
\(331\) 3.11884 17.6878i 0.171427 0.972212i −0.770760 0.637125i \(-0.780123\pi\)
0.942187 0.335086i \(-0.108766\pi\)
\(332\) 4.61172 7.98773i 0.253101 0.438384i
\(333\) 0 0
\(334\) 0.526311 + 0.911597i 0.0287985 + 0.0498804i
\(335\) −9.12662 + 3.32182i −0.498640 + 0.181490i
\(336\) 0 0
\(337\) −17.9989 + 15.1029i −0.980462 + 0.822705i −0.984159 0.177288i \(-0.943268\pi\)
0.00369714 + 0.999993i \(0.498823\pi\)
\(338\) 9.38520 7.87512i 0.510488 0.428350i
\(339\) 0 0
\(340\) −3.03443 + 1.10444i −0.164565 + 0.0598968i
\(341\) 24.3195 + 42.1225i 1.31697 + 2.28106i
\(342\) 0 0
\(343\) −6.36495 + 11.0244i −0.343675 + 0.595263i
\(344\) 0.478163 2.71180i 0.0257808 0.146210i
\(345\) 0 0
\(346\) −6.42081 2.33699i −0.345185 0.125637i
\(347\) −1.44691 8.20582i −0.0776741 0.440512i −0.998698 0.0510063i \(-0.983757\pi\)
0.921024 0.389505i \(-0.127354\pi\)
\(348\) 0 0
\(349\) −4.05619 3.40354i −0.217123 0.182188i 0.527739 0.849407i \(-0.323040\pi\)
−0.744861 + 0.667219i \(0.767484\pi\)
\(350\) 18.3966 0.983337
\(351\) 0 0
\(352\) 4.54632 0.242320
\(353\) −26.4759 22.2159i −1.40917 1.18243i −0.956852 0.290577i \(-0.906153\pi\)
−0.452318 0.891857i \(-0.649403\pi\)
\(354\) 0 0
\(355\) 0.653961 + 3.70880i 0.0347087 + 0.196843i
\(356\) −11.6512 4.24069i −0.617512 0.224756i
\(357\) 0 0
\(358\) −0.381598 + 2.16415i −0.0201681 + 0.114379i
\(359\) −12.8489 + 22.2549i −0.678138 + 1.17457i 0.297403 + 0.954752i \(0.403880\pi\)
−0.975541 + 0.219818i \(0.929454\pi\)
\(360\) 0 0
\(361\) 8.28954 + 14.3579i 0.436292 + 0.755680i
\(362\) −14.7907 + 5.38339i −0.777384 + 0.282944i
\(363\) 0 0
\(364\) 2.73900 2.29829i 0.143563 0.120463i
\(365\) −0.325289 + 0.272950i −0.0170264 + 0.0142869i
\(366\) 0 0
\(367\) −10.6739 + 3.88499i −0.557174 + 0.202795i −0.605231 0.796050i \(-0.706919\pi\)
0.0480573 + 0.998845i \(0.484697\pi\)
\(368\) −1.75222 3.03493i −0.0913406 0.158207i
\(369\) 0 0
\(370\) −0.652458 + 1.13009i −0.0339197 + 0.0587506i
\(371\) −2.87665 + 16.3143i −0.149348 + 0.846995i
\(372\) 0 0
\(373\) 26.9731 + 9.81739i 1.39661 + 0.508325i 0.927171 0.374639i \(-0.122233\pi\)
0.469441 + 0.882964i \(0.344455\pi\)
\(374\) 3.44166 + 19.5186i 0.177964 + 1.00928i
\(375\) 0 0
\(376\) 7.42794 + 6.23278i 0.383067 + 0.321431i
\(377\) 2.82703 0.145599
\(378\) 0 0
\(379\) −23.0493 −1.18396 −0.591981 0.805952i \(-0.701654\pi\)
−0.591981 + 0.805952i \(0.701654\pi\)
\(380\) 0.882872 + 0.740818i 0.0452904 + 0.0380031i
\(381\) 0 0
\(382\) 1.36165 + 7.72227i 0.0696678 + 0.395106i
\(383\) −23.1212 8.41541i −1.18144 0.430007i −0.324727 0.945808i \(-0.605272\pi\)
−0.856709 + 0.515800i \(0.827495\pi\)
\(384\) 0 0
\(385\) −2.41675 + 13.7061i −0.123169 + 0.698525i
\(386\) −8.27028 + 14.3246i −0.420946 + 0.729101i
\(387\) 0 0
\(388\) −2.87738 4.98377i −0.146077 0.253012i
\(389\) 34.8878 12.6981i 1.76888 0.643820i 0.768891 0.639380i \(-0.220809\pi\)
0.999990 0.00444021i \(-0.00141337\pi\)
\(390\) 0 0
\(391\) 11.7033 9.82024i 0.591862 0.496631i
\(392\) −7.72188 + 6.47943i −0.390014 + 0.327260i
\(393\) 0 0
\(394\) 10.6901 3.89089i 0.538561 0.196020i
\(395\) −2.50351 4.33620i −0.125965 0.218178i
\(396\) 0 0
\(397\) −3.19629 + 5.53614i −0.160417 + 0.277851i −0.935018 0.354599i \(-0.884617\pi\)
0.774601 + 0.632450i \(0.217951\pi\)
\(398\) −0.325159 + 1.84407i −0.0162987 + 0.0924348i
\(399\) 0 0
\(400\) 4.18288 + 1.52245i 0.209144 + 0.0761223i
\(401\) −5.67599 32.1901i −0.283445 1.60750i −0.710787 0.703407i \(-0.751661\pi\)
0.427342 0.904090i \(-0.359450\pi\)
\(402\) 0 0
\(403\) 7.09038 + 5.94953i 0.353197 + 0.296367i
\(404\) 11.0395 0.549238
\(405\) 0 0
\(406\) −13.5047 −0.670226
\(407\) 6.13539 + 5.14821i 0.304120 + 0.255187i
\(408\) 0 0
\(409\) −3.79522 21.5238i −0.187662 1.06428i −0.922488 0.386027i \(-0.873847\pi\)
0.734826 0.678256i \(-0.237264\pi\)
\(410\) 1.79364 + 0.652833i 0.0885818 + 0.0322411i
\(411\) 0 0
\(412\) −1.11507 + 6.32390i −0.0549357 + 0.311556i
\(413\) 2.95806 5.12351i 0.145557 0.252112i
\(414\) 0 0
\(415\) 3.41599 + 5.91668i 0.167685 + 0.290438i
\(416\) 0.812975 0.295899i 0.0398594 0.0145076i
\(417\) 0 0
\(418\) 5.41881 4.54692i 0.265043 0.222397i
\(419\) 20.0021 16.7838i 0.977168 0.819941i −0.00649160 0.999979i \(-0.502066\pi\)
0.983660 + 0.180037i \(0.0576219\pi\)
\(420\) 0 0
\(421\) 35.2362 12.8249i 1.71731 0.625049i 0.719707 0.694278i \(-0.244276\pi\)
0.997601 + 0.0692288i \(0.0220539\pi\)
\(422\) 2.73507 + 4.73728i 0.133141 + 0.230607i
\(423\) 0 0
\(424\) −2.00419 + 3.47137i −0.0973323 + 0.168584i
\(425\) −3.36975 + 19.1108i −0.163457 + 0.927009i
\(426\) 0 0
\(427\) 16.8118 + 6.11898i 0.813578 + 0.296118i
\(428\) 3.00277 + 17.0296i 0.145144 + 0.823155i
\(429\) 0 0
\(430\) 1.56248 + 1.31107i 0.0753494 + 0.0632256i
\(431\) −6.13162 −0.295350 −0.147675 0.989036i \(-0.547179\pi\)
−0.147675 + 0.989036i \(0.547179\pi\)
\(432\) 0 0
\(433\) −20.9401 −1.00632 −0.503158 0.864195i \(-0.667829\pi\)
−0.503158 + 0.864195i \(0.667829\pi\)
\(434\) −33.8707 28.4209i −1.62585 1.36425i
\(435\) 0 0
\(436\) −1.72705 9.79461i −0.0827109 0.469077i
\(437\) −5.12381 1.86492i −0.245105 0.0892110i
\(438\) 0 0
\(439\) −4.98629 + 28.2787i −0.237983 + 1.34967i 0.598258 + 0.801304i \(0.295860\pi\)
−0.836240 + 0.548363i \(0.815251\pi\)
\(440\) −1.68378 + 2.91639i −0.0802709 + 0.139033i
\(441\) 0 0
\(442\) 1.88581 + 3.26632i 0.0896989 + 0.155363i
\(443\) −14.2882 + 5.20050i −0.678855 + 0.247083i −0.658356 0.752707i \(-0.728748\pi\)
−0.0204992 + 0.999790i \(0.506526\pi\)
\(444\) 0 0
\(445\) 7.03547 5.90346i 0.333513 0.279851i
\(446\) 0.968926 0.813026i 0.0458800 0.0384979i
\(447\) 0 0
\(448\) −3.88358 + 1.41351i −0.183482 + 0.0667820i
\(449\) −6.21048 10.7569i −0.293091 0.507648i 0.681448 0.731866i \(-0.261351\pi\)
−0.974539 + 0.224218i \(0.928017\pi\)
\(450\) 0 0
\(451\) 5.85769 10.1458i 0.275828 0.477748i
\(452\) −0.425670 + 2.41409i −0.0200218 + 0.113549i
\(453\) 0 0
\(454\) −9.34189 3.40017i −0.438437 0.159578i
\(455\) 0.459899 + 2.60822i 0.0215604 + 0.122275i
\(456\) 0 0
\(457\) −8.30728 6.97064i −0.388598 0.326073i 0.427468 0.904030i \(-0.359405\pi\)
−0.816067 + 0.577957i \(0.803850\pi\)
\(458\) 9.98234 0.466444
\(459\) 0 0
\(460\) 2.59581 0.121030
\(461\) 6.28283 + 5.27192i 0.292621 + 0.245538i 0.777265 0.629173i \(-0.216606\pi\)
−0.484644 + 0.874711i \(0.661051\pi\)
\(462\) 0 0
\(463\) −5.84350 33.1401i −0.271571 1.54015i −0.749649 0.661836i \(-0.769778\pi\)
0.478078 0.878317i \(-0.341333\pi\)
\(464\) −3.07060 1.11761i −0.142549 0.0518837i
\(465\) 0 0
\(466\) −4.71508 + 26.7405i −0.218422 + 1.23873i
\(467\) 5.43426 9.41241i 0.251467 0.435554i −0.712463 0.701710i \(-0.752420\pi\)
0.963930 + 0.266156i \(0.0857535\pi\)
\(468\) 0 0
\(469\) −27.0948 46.9296i −1.25112 2.16701i
\(470\) −6.74924 + 2.45652i −0.311319 + 0.113311i
\(471\) 0 0
\(472\) 1.09659 0.920149i 0.0504747 0.0423533i
\(473\) 9.59003 8.04699i 0.440950 0.370001i
\(474\) 0 0
\(475\) 6.50827 2.36882i 0.298620 0.108689i
\(476\) −9.00852 15.6032i −0.412905 0.715172i
\(477\) 0 0
\(478\) 9.76807 16.9188i 0.446781 0.773847i
\(479\) 3.26943 18.5418i 0.149384 0.847198i −0.814358 0.580363i \(-0.802911\pi\)
0.963742 0.266836i \(-0.0859781\pi\)
\(480\) 0 0
\(481\) 1.43221 + 0.521280i 0.0653030 + 0.0237683i
\(482\) −2.81574 15.9689i −0.128254 0.727362i
\(483\) 0 0
\(484\) 7.40693 + 6.21515i 0.336679 + 0.282507i
\(485\) 4.26267 0.193558
\(486\) 0 0
\(487\) 32.9521 1.49320 0.746601 0.665272i \(-0.231685\pi\)
0.746601 + 0.665272i \(0.231685\pi\)
\(488\) 3.31616 + 2.78258i 0.150115 + 0.125962i
\(489\) 0 0
\(490\) −1.29656 7.35317i −0.0585727 0.332183i
\(491\) 32.5492 + 11.8469i 1.46892 + 0.534645i 0.947808 0.318841i \(-0.103294\pi\)
0.521116 + 0.853486i \(0.325516\pi\)
\(492\) 0 0
\(493\) 2.47369 14.0290i 0.111409 0.631834i
\(494\) 0.673056 1.16577i 0.0302822 0.0524503i
\(495\) 0 0
\(496\) −5.34926 9.26519i −0.240189 0.416019i
\(497\) −19.7451 + 7.18664i −0.885690 + 0.322365i
\(498\) 0 0
\(499\) 18.1706 15.2470i 0.813428 0.682547i −0.137995 0.990433i \(-0.544066\pi\)
0.951423 + 0.307886i \(0.0996214\pi\)
\(500\) −5.36292 + 4.50002i −0.239837 + 0.201247i
\(501\) 0 0
\(502\) −22.0457 + 8.02398i −0.983948 + 0.358128i
\(503\) 16.0067 + 27.7243i 0.713701 + 1.23617i 0.963458 + 0.267858i \(0.0863160\pi\)
−0.249757 + 0.968309i \(0.580351\pi\)
\(504\) 0 0
\(505\) −4.08861 + 7.08168i −0.181941 + 0.315131i
\(506\) 2.76661 15.6902i 0.122991 0.697517i
\(507\) 0 0
\(508\) −7.61406 2.77129i −0.337819 0.122956i
\(509\) −6.91488 39.2162i −0.306497 1.73823i −0.616376 0.787452i \(-0.711400\pi\)
0.309879 0.950776i \(-0.399711\pi\)
\(510\) 0 0
\(511\) −1.81494 1.52291i −0.0802881 0.0673697i
\(512\) −1.00000 −0.0441942
\(513\) 0 0
\(514\) 21.9904 0.969956
\(515\) −3.64369 3.05742i −0.160560 0.134726i
\(516\) 0 0
\(517\) 7.65500 + 43.4136i 0.336666 + 1.90933i
\(518\) −6.84164 2.49015i −0.300604 0.109411i
\(519\) 0 0
\(520\) −0.111280 + 0.631099i −0.00487994 + 0.0276755i
\(521\) 1.81609 3.14555i 0.0795642 0.137809i −0.823498 0.567319i \(-0.807980\pi\)
0.903062 + 0.429510i \(0.141314\pi\)
\(522\) 0 0
\(523\) −6.50104 11.2601i −0.284270 0.492371i 0.688162 0.725558i \(-0.258418\pi\)
−0.972432 + 0.233187i \(0.925085\pi\)
\(524\) −14.9361 + 5.43628i −0.652485 + 0.237485i
\(525\) 0 0
\(526\) −17.9888 + 15.0944i −0.784349 + 0.658147i
\(527\) 35.7285 29.9797i 1.55636 1.30594i
\(528\) 0 0
\(529\) 10.0725 3.66609i 0.437935 0.159395i
\(530\) −1.48455 2.57131i −0.0644847 0.111691i
\(531\) 0 0
\(532\) −3.21518 + 5.56886i −0.139396 + 0.241441i
\(533\) 0.387131 2.19553i 0.0167685 0.0950989i
\(534\) 0 0
\(535\) −12.0363 4.38085i −0.520374 0.189401i
\(536\) −2.27688 12.9128i −0.0983462 0.557749i
\(537\) 0 0
\(538\) 14.0187 + 11.7631i 0.604388 + 0.507142i
\(539\) −45.8278 −1.97394
\(540\) 0 0
\(541\) −31.1320 −1.33847 −0.669235 0.743051i \(-0.733378\pi\)
−0.669235 + 0.743051i \(0.733378\pi\)
\(542\) 12.6263 + 10.5947i 0.542347 + 0.455083i
\(543\) 0 0
\(544\) −0.757019 4.29327i −0.0324569 0.184072i
\(545\) 6.92270 + 2.51966i 0.296536 + 0.107930i
\(546\) 0 0
\(547\) 3.35773 19.0426i 0.143566 0.814204i −0.824941 0.565219i \(-0.808792\pi\)
0.968507 0.248985i \(-0.0800970\pi\)
\(548\) −6.17817 + 10.7009i −0.263918 + 0.457120i
\(549\) 0 0
\(550\) 10.1186 + 17.5259i 0.431459 + 0.747308i
\(551\) −4.77764 + 1.73892i −0.203534 + 0.0740804i
\(552\) 0 0
\(553\) 21.4005 17.9572i 0.910044 0.763617i
\(554\) −8.63485 + 7.24550i −0.366860 + 0.307832i
\(555\) 0 0
\(556\) 4.11905 1.49921i 0.174686 0.0635807i
\(557\) −0.618509 1.07129i −0.0262070 0.0453919i 0.852624 0.522524i \(-0.175010\pi\)
−0.878831 + 0.477132i \(0.841676\pi\)
\(558\) 0 0
\(559\) 1.19115 2.06314i 0.0503804 0.0872614i
\(560\) 0.531583 3.01476i 0.0224635 0.127397i
\(561\) 0 0
\(562\) 0.681601 + 0.248083i 0.0287516 + 0.0104647i
\(563\) 3.63180 + 20.5969i 0.153062 + 0.868057i 0.960536 + 0.278155i \(0.0897228\pi\)
−0.807474 + 0.589903i \(0.799166\pi\)
\(564\) 0 0
\(565\) −1.39095 1.16714i −0.0585176 0.0491021i
\(566\) 22.1382 0.930539
\(567\) 0 0
\(568\) −5.08426 −0.213331
\(569\) 4.70347 + 3.94668i 0.197180 + 0.165453i 0.736032 0.676947i \(-0.236697\pi\)
−0.538852 + 0.842400i \(0.681142\pi\)
\(570\) 0 0
\(571\) 2.98710 + 16.9407i 0.125006 + 0.708946i 0.981304 + 0.192464i \(0.0616478\pi\)
−0.856298 + 0.516483i \(0.827241\pi\)
\(572\) 3.69605 + 1.34525i 0.154540 + 0.0562478i
\(573\) 0 0
\(574\) −1.84932 + 10.4880i −0.0771893 + 0.437762i
\(575\) 7.79970 13.5095i 0.325270 0.563384i
\(576\) 0 0
\(577\) 7.08481 + 12.2713i 0.294945 + 0.510859i 0.974972 0.222328i \(-0.0713655\pi\)
−0.680027 + 0.733187i \(0.738032\pi\)
\(578\) 1.88432 0.685836i 0.0783773 0.0285270i
\(579\) 0 0
\(580\) 1.85416 1.55582i 0.0769897 0.0646020i
\(581\) −29.2007 + 24.5023i −1.21145 + 1.01653i
\(582\) 0 0
\(583\) −17.1244 + 6.23278i −0.709221 + 0.258135i
\(584\) −0.286636 0.496469i −0.0118611 0.0205440i
\(585\) 0 0
\(586\) 3.27929 5.67990i 0.135466 0.234635i
\(587\) −5.83795 + 33.1087i −0.240958 + 1.36654i 0.588737 + 0.808324i \(0.299625\pi\)
−0.829695 + 0.558217i \(0.811486\pi\)
\(588\) 0 0
\(589\) −15.6422 5.69331i −0.644527 0.234589i
\(590\) 0.184126 + 1.04423i 0.00758035 + 0.0429903i
\(591\) 0 0
\(592\) −1.34953 1.13239i −0.0554653 0.0465409i
\(593\) −6.82673 −0.280340 −0.140170 0.990127i \(-0.544765\pi\)
−0.140170 + 0.990127i \(0.544765\pi\)
\(594\) 0 0
\(595\) 13.3456 0.547116
\(596\) −5.23476 4.39248i −0.214424 0.179923i
\(597\) 0 0
\(598\) −0.526477 2.98580i −0.0215293 0.122099i
\(599\) −27.5399 10.0237i −1.12525 0.409557i −0.288684 0.957424i \(-0.593218\pi\)
−0.836565 + 0.547867i \(0.815440\pi\)
\(600\) 0 0
\(601\) −0.803257 + 4.55550i −0.0327655 + 0.185823i −0.996798 0.0799624i \(-0.974520\pi\)
0.964032 + 0.265785i \(0.0856311\pi\)
\(602\) −5.69013 + 9.85559i −0.231912 + 0.401684i
\(603\) 0 0
\(604\) 2.60327 + 4.50899i 0.105925 + 0.183468i
\(605\) −6.73014 + 2.44957i −0.273619 + 0.0995893i
\(606\) 0 0
\(607\) −10.3745 + 8.70526i −0.421089 + 0.353335i −0.828577 0.559875i \(-0.810849\pi\)
0.407488 + 0.913210i \(0.366405\pi\)
\(608\) −1.19191 + 1.00013i −0.0483383 + 0.0405607i
\(609\) 0 0
\(610\) −3.01315 + 1.09670i −0.121999 + 0.0444040i
\(611\) 4.19446 + 7.26502i 0.169690 + 0.293911i
\(612\) 0 0
\(613\) −14.9136 + 25.8311i −0.602354 + 1.04331i 0.390110 + 0.920768i \(0.372437\pi\)
−0.992464 + 0.122539i \(0.960896\pi\)
\(614\) −1.38481 + 7.85365i −0.0558864 + 0.316948i
\(615\) 0 0
\(616\) −17.6560 6.42626i −0.711381 0.258922i
\(617\) 5.84851 + 33.1685i 0.235452 + 1.33531i 0.841660 + 0.540008i \(0.181579\pi\)
−0.606208 + 0.795306i \(0.707310\pi\)
\(618\) 0 0
\(619\) 27.2839 + 22.8939i 1.09663 + 0.920182i 0.997194 0.0748615i \(-0.0238515\pi\)
0.0994367 + 0.995044i \(0.468296\pi\)
\(620\) 7.92461 0.318260
\(621\) 0 0
\(622\) 14.1480 0.567285
\(623\) 39.2541 + 32.9381i 1.57268 + 1.31964i
\(624\) 0 0
\(625\) 2.96435 + 16.8117i 0.118574 + 0.672467i
\(626\) 22.5917 + 8.22270i 0.902945 + 0.328645i
\(627\) 0 0
\(628\) 0.689756 3.91180i 0.0275243 0.156098i
\(629\) 3.84003 6.65113i 0.153112 0.265198i
\(630\) 0 0
\(631\) 19.6546 + 34.0427i 0.782436 + 1.35522i 0.930519 + 0.366243i \(0.119356\pi\)
−0.148083 + 0.988975i \(0.547310\pi\)
\(632\) 6.35200 2.31194i 0.252669 0.0919640i
\(633\) 0 0
\(634\) 13.9364 11.6941i 0.553486 0.464430i
\(635\) 4.59768 3.85791i 0.182453 0.153097i
\(636\) 0 0
\(637\) −8.19495 + 2.98272i −0.324696 + 0.118180i
\(638\) −7.42794 12.8656i −0.294075 0.509353i
\(639\) 0 0
\(640\) 0.370360 0.641483i 0.0146398 0.0253568i
\(641\) 4.79194 27.1764i 0.189270 1.07340i −0.731075 0.682297i \(-0.760981\pi\)
0.920345 0.391107i \(-0.127908\pi\)
\(642\) 0 0
\(643\) −30.6010 11.1378i −1.20678 0.439234i −0.341197 0.939992i \(-0.610832\pi\)
−0.865587 + 0.500758i \(0.833055\pi\)
\(644\) 2.51498 + 14.2632i 0.0991041 + 0.562047i
\(645\) 0 0
\(646\) −5.19613 4.36007i −0.204439 0.171545i
\(647\) 11.8337 0.465232 0.232616 0.972569i \(-0.425272\pi\)
0.232616 + 0.972569i \(0.425272\pi\)
\(648\) 0 0
\(649\) 6.50805 0.255463
\(650\) 2.95009 + 2.47542i 0.115712 + 0.0970940i
\(651\) 0 0
\(652\) 0.407565 + 2.31141i 0.0159615 + 0.0905219i
\(653\) −1.90882 0.694752i −0.0746978 0.0271878i 0.304401 0.952544i \(-0.401544\pi\)
−0.379099 + 0.925356i \(0.623766\pi\)
\(654\) 0 0
\(655\) 2.04444 11.5946i 0.0798830 0.453039i
\(656\) −1.28845 + 2.23165i −0.0503054 + 0.0871314i
\(657\) 0 0
\(658\) −20.0369 34.7050i −0.781120 1.35294i
\(659\) 45.4410 16.5392i 1.77013 0.644275i 0.770151 0.637861i \(-0.220181\pi\)
0.999979 0.00641394i \(-0.00204163\pi\)
\(660\) 0 0
\(661\) −13.0788 + 10.9744i −0.508706 + 0.426855i −0.860673 0.509157i \(-0.829957\pi\)
0.351968 + 0.936012i \(0.385513\pi\)
\(662\) −13.7587 + 11.5449i −0.534747 + 0.448706i
\(663\) 0 0
\(664\) −8.66720 + 3.15460i −0.336352 + 0.122422i
\(665\) −2.38155 4.12497i −0.0923527 0.159960i
\(666\) 0 0
\(667\) −5.72567 + 9.91715i −0.221699 + 0.383993i
\(668\) 0.182786 1.03663i 0.00707220 0.0401084i
\(669\) 0 0
\(670\) 9.12662 + 3.32182i 0.352592 + 0.128333i
\(671\) 3.41752 + 19.3817i 0.131932 + 0.748224i
\(672\) 0 0
\(673\) −22.8356 19.1613i −0.880247 0.738615i 0.0859825 0.996297i \(-0.472597\pi\)
−0.966230 + 0.257681i \(0.917042\pi\)
\(674\) 23.4959 0.905027
\(675\) 0 0
\(676\) −12.2515 −0.471212
\(677\) −6.10334 5.12131i −0.234570 0.196828i 0.517924 0.855427i \(-0.326705\pi\)
−0.752494 + 0.658599i \(0.771149\pi\)
\(678\) 0 0
\(679\) 4.12994 + 23.4221i 0.158493 + 0.898856i
\(680\) 3.03443 + 1.10444i 0.116365 + 0.0423534i
\(681\) 0 0
\(682\) 8.44606 47.9000i 0.323416 1.83419i
\(683\) −15.1593 + 26.2566i −0.580054 + 1.00468i 0.415419 + 0.909630i \(0.363635\pi\)
−0.995472 + 0.0950521i \(0.969698\pi\)
\(684\) 0 0
\(685\) −4.57630 7.92638i −0.174851 0.302851i
\(686\) 11.9622 4.35388i 0.456719 0.166232i
\(687\) 0 0
\(688\) −2.10940 + 1.77000i −0.0804202 + 0.0674806i
\(689\) −2.65653 + 2.22910i −0.101206 + 0.0849218i
\(690\) 0 0
\(691\) −24.9197 + 9.07005i −0.947992 + 0.345041i −0.769317 0.638867i \(-0.779403\pi\)
−0.178675 + 0.983908i \(0.557181\pi\)
\(692\) 3.41644 + 5.91745i 0.129874 + 0.224948i
\(693\) 0 0
\(694\) −4.16620 + 7.21608i −0.158147 + 0.273919i
\(695\) −0.563813 + 3.19754i −0.0213867 + 0.121290i
\(696\) 0 0
\(697\) −10.5565 3.84224i −0.399855 0.145535i
\(698\) 0.919463 + 5.21453i 0.0348022 + 0.197373i
\(699\) 0 0
\(700\) −14.0926 11.8251i −0.532649 0.446946i
\(701\) −46.2262 −1.74594 −0.872971 0.487773i \(-0.837809\pi\)
−0.872971 + 0.487773i \(0.837809\pi\)
\(702\) 0 0
\(703\) −2.74105 −0.103381
\(704\) −3.48269 2.92232i −0.131259 0.110139i
\(705\) 0 0
\(706\) 6.00160 + 34.0368i 0.225873 + 1.28099i
\(707\) −42.8730 15.6045i −1.61240 0.586867i
\(708\) 0 0
\(709\) 5.30328 30.0764i 0.199169 1.12954i −0.707186 0.707027i \(-0.750036\pi\)
0.906355 0.422516i \(-0.138853\pi\)
\(710\) 1.88301 3.26146i 0.0706680 0.122401i
\(711\) 0 0
\(712\) 6.19947 + 10.7378i 0.232335 + 0.402416i
\(713\) −35.2312 + 12.8231i −1.31942 + 0.480229i
\(714\) 0 0
\(715\) −2.23183 + 1.87272i −0.0834656 + 0.0700359i
\(716\) 1.68341 1.41255i 0.0629120 0.0527894i
\(717\) 0 0
\(718\) 24.1480 8.78915i 0.901195 0.328008i
\(719\) 3.46256 + 5.99733i 0.129132 + 0.223663i 0.923340 0.383982i \(-0.125448\pi\)
−0.794209 + 0.607645i \(0.792114\pi\)
\(720\) 0 0
\(721\) 13.2694 22.9832i 0.494177 0.855939i
\(722\) 2.87893 16.3272i 0.107143 0.607636i
\(723\) 0 0
\(724\) 14.7907 + 5.38339i 0.549693 + 0.200072i
\(725\) −2.52580 14.3245i −0.0938057 0.531999i
\(726\) 0 0
\(727\) −16.6231 13.9485i −0.616517 0.517319i 0.280189 0.959945i \(-0.409603\pi\)
−0.896707 + 0.442625i \(0.854047\pi\)
\(728\) −3.57551 −0.132517
\(729\) 0 0
\(730\) 0.424635 0.0157164
\(731\) −9.19595 7.71631i −0.340124 0.285398i
\(732\) 0 0
\(733\) 6.80782 + 38.6090i 0.251452 + 1.42606i 0.805017 + 0.593251i \(0.202156\pi\)
−0.553565 + 0.832806i \(0.686733\pi\)
\(734\) 10.6739 + 3.88499i 0.393981 + 0.143397i
\(735\) 0 0
\(736\) −0.608539 + 3.45119i −0.0224310 + 0.127213i
\(737\) 29.8057 51.6251i 1.09791 1.90163i
\(738\) 0 0
\(739\) 15.4039 + 26.6804i 0.566643 + 0.981454i 0.996895 + 0.0787451i \(0.0250913\pi\)
−0.430252 + 0.902709i \(0.641575\pi\)
\(740\) 1.22622 0.446307i 0.0450767 0.0164066i
\(741\) 0 0
\(742\) 12.6903 10.6484i 0.465874 0.390915i
\(743\) −24.4602 + 20.5245i −0.897357 + 0.752972i −0.969672 0.244410i \(-0.921406\pi\)
0.0723153 + 0.997382i \(0.476961\pi\)
\(744\) 0 0
\(745\) 4.75645 1.73121i 0.174263 0.0634265i
\(746\) −14.3521 24.8585i −0.525466 0.910134i
\(747\) 0 0
\(748\) 9.90985 17.1644i 0.362340 0.627591i
\(749\) 12.4099 70.3801i 0.453448 2.57163i
\(750\) 0 0
\(751\) −2.85191 1.03801i −0.104068 0.0378776i 0.289462 0.957190i \(-0.406524\pi\)
−0.393529 + 0.919312i \(0.628746\pi\)
\(752\) −1.68378 9.54918i −0.0614010 0.348223i
\(753\) 0 0
\(754\) −2.16563 1.81718i −0.0788675 0.0661777i
\(755\) −3.85659 −0.140356
\(756\) 0 0
\(757\) 10.7254 0.389823 0.194912 0.980821i \(-0.437558\pi\)
0.194912 + 0.980821i \(0.437558\pi\)
\(758\) 17.6568 + 14.8158i 0.641323 + 0.538134i
\(759\) 0 0
\(760\) −0.200131 1.13500i −0.00725951 0.0411707i
\(761\) 25.4656 + 9.26871i 0.923126 + 0.335990i 0.759481 0.650529i \(-0.225453\pi\)
0.163645 + 0.986519i \(0.447675\pi\)
\(762\) 0 0
\(763\) −7.13760 + 40.4793i −0.258398 + 1.46545i
\(764\) 3.92070 6.79085i 0.141846 0.245684i
\(765\) 0 0
\(766\) 12.3025 + 21.3086i 0.444508 + 0.769910i
\(767\) 1.16377 0.423579i 0.0420214 0.0152945i
\(768\) 0 0
\(769\) 20.6292 17.3100i 0.743910 0.624214i −0.189975 0.981789i \(-0.560841\pi\)
0.933885 + 0.357575i \(0.116396\pi\)
\(770\) 10.6614 8.94599i 0.384211 0.322391i
\(771\) 0 0
\(772\) 15.5431 5.65721i 0.559407 0.203607i
\(773\) −7.19832 12.4679i −0.258906 0.448438i 0.707043 0.707170i \(-0.250029\pi\)
−0.965949 + 0.258733i \(0.916695\pi\)
\(774\) 0 0
\(775\) 23.8113 41.2424i 0.855328 1.48147i
\(776\) −0.999303 + 5.66733i −0.0358729 + 0.203445i
\(777\) 0 0
\(778\) −34.8878 12.6981i −1.25079 0.455250i
\(779\) 0.696235 + 3.94855i 0.0249452 + 0.141471i
\(780\) 0 0
\(781\) −17.7069