Properties

Label 567.2.u.a.100.1
Level $567$
Weight $2$
Character 567.100
Analytic conductor $4.528$
Analytic rank $0$
Dimension $132$
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [567,2,Mod(100,567)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(567, base_ring=CyclotomicField(18))
 
chi = DirichletCharacter(H, H._module([16, 6]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("567.100");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 567 = 3^{4} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 567.u (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: \(4.52751779461\)
Analytic rank: \(0\)
Dimension: \(132\)
Relative dimension: \(22\) over \(\Q(\zeta_{9})\)
Twist minimal: no (minimal twist has level 189)
Sato-Tate group: $\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label 100.1
Character \(\chi\) \(=\) 567.100
Dual form 567.2.u.a.550.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.456041 + 2.58633i) q^{2} +(-4.60177 - 1.67491i) q^{4} +(-2.97048 - 1.08117i) q^{5} +(-2.55032 + 0.704184i) q^{7} +(3.80423 - 6.58912i) q^{8} +O(q^{10})\) \(q+(-0.456041 + 2.58633i) q^{2} +(-4.60177 - 1.67491i) q^{4} +(-2.97048 - 1.08117i) q^{5} +(-2.55032 + 0.704184i) q^{7} +(3.80423 - 6.58912i) q^{8} +(4.15092 - 7.18961i) q^{10} +(0.890208 - 0.324009i) q^{11} +(5.70296 + 2.07571i) q^{13} +(-0.658206 - 6.91711i) q^{14} +(7.80400 + 6.54833i) q^{16} +(0.304238 - 0.526956i) q^{17} +(-0.948584 - 1.64300i) q^{19} +(11.8586 + 9.95057i) q^{20} +(0.432025 + 2.45014i) q^{22} +(-0.715641 - 4.05860i) q^{23} +(3.82462 + 3.20924i) q^{25} +(-7.96926 + 13.8032i) q^{26} +(12.9154 + 1.03106i) q^{28} +(-0.760560 + 0.276821i) q^{29} +(1.80858 + 0.658271i) q^{31} +(-8.83827 + 7.41619i) q^{32} +(1.22414 + 1.02717i) q^{34} +(8.33702 + 0.665556i) q^{35} -2.07251 q^{37} +(4.68193 - 1.70408i) q^{38} +(-18.4243 + 15.4599i) q^{40} +(3.40353 + 1.23878i) q^{41} +(1.51736 - 8.60538i) q^{43} -4.63922 q^{44} +10.8233 q^{46} +(7.06911 - 2.57295i) q^{47} +(6.00825 - 3.59179i) q^{49} +(-10.0444 + 8.42821i) q^{50} +(-22.7671 - 19.1039i) q^{52} +(-0.902177 - 1.56262i) q^{53} -2.99466 q^{55} +(-5.06205 + 19.4832i) q^{56} +(-0.369106 - 2.09330i) q^{58} +(8.98391 - 7.53840i) q^{59} +(2.43545 - 0.886433i) q^{61} +(-2.52730 + 4.37741i) q^{62} +(-4.96275 - 8.59574i) q^{64} +(-14.6964 - 12.3317i) q^{65} +(-1.13472 - 6.43533i) q^{67} +(-2.28263 + 1.91536i) q^{68} +(-5.52337 + 21.2588i) q^{70} +(-5.39566 - 9.34556i) q^{71} -3.43163 q^{73} +(0.945149 - 5.36021i) q^{74} +(1.61330 + 9.14948i) q^{76} +(-2.04215 + 1.45320i) q^{77} +(-2.13746 + 12.1222i) q^{79} +(-16.1018 - 27.8891i) q^{80} +(-4.75606 + 8.23774i) q^{82} +(-2.14098 + 0.779253i) q^{83} +(-1.47346 + 1.23638i) q^{85} +(21.5644 + 7.84881i) q^{86} +(1.25162 - 7.09830i) q^{88} +(-2.69360 - 4.66546i) q^{89} +(-16.0060 - 1.27778i) q^{91} +(-3.50457 + 19.8754i) q^{92} +(3.43070 + 19.4565i) q^{94} +(1.04140 + 5.90607i) q^{95} +(1.05146 - 5.96314i) q^{97} +(6.54955 + 17.1773i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 132 q + 3 q^{2} - 3 q^{4} + 3 q^{5} - 6 q^{7} + 6 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 132 q + 3 q^{2} - 3 q^{4} + 3 q^{5} - 6 q^{7} + 6 q^{8} + 3 q^{10} + 15 q^{11} - 12 q^{13} + 30 q^{14} + 9 q^{16} - 27 q^{17} + 3 q^{19} + 18 q^{20} - 12 q^{22} + 36 q^{23} - 3 q^{25} - 30 q^{26} - 12 q^{28} + 30 q^{29} - 3 q^{31} + 75 q^{32} - 18 q^{34} - 15 q^{35} - 6 q^{37} - 69 q^{38} + 51 q^{40} - 12 q^{43} + 6 q^{44} - 6 q^{46} + 21 q^{47} - 42 q^{49} + 39 q^{50} + 9 q^{52} - 9 q^{53} - 24 q^{55} - 111 q^{56} - 3 q^{58} - 27 q^{59} - 21 q^{61} - 75 q^{62} - 30 q^{64} + 90 q^{65} - 3 q^{67} + 30 q^{68} + 39 q^{70} + 18 q^{71} - 42 q^{73} - 51 q^{74} - 24 q^{76} - 15 q^{77} + 15 q^{79} - 102 q^{80} - 6 q^{82} + 42 q^{83} - 63 q^{85} + 93 q^{86} - 51 q^{88} - 75 q^{89} - 21 q^{91} + 66 q^{92} + 33 q^{94} - 15 q^{95} - 12 q^{97} + 36 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/567\mathbb{Z}\right)^\times\).

\(n\) \(325\) \(407\)
\(\chi(n)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{8}{9}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.456041 + 2.58633i −0.322469 + 1.82881i 0.204423 + 0.978883i \(0.434468\pi\)
−0.526892 + 0.849932i \(0.676643\pi\)
\(3\) 0 0
\(4\) −4.60177 1.67491i −2.30088 0.837454i
\(5\) −2.97048 1.08117i −1.32844 0.483513i −0.422287 0.906462i \(-0.638773\pi\)
−0.906153 + 0.422949i \(0.860995\pi\)
\(6\) 0 0
\(7\) −2.55032 + 0.704184i −0.963930 + 0.266156i
\(8\) 3.80423 6.58912i 1.34500 2.32961i
\(9\) 0 0
\(10\) 4.15092 7.18961i 1.31264 2.27355i
\(11\) 0.890208 0.324009i 0.268408 0.0976925i −0.204310 0.978906i \(-0.565495\pi\)
0.472718 + 0.881214i \(0.343273\pi\)
\(12\) 0 0
\(13\) 5.70296 + 2.07571i 1.58172 + 0.575698i 0.975576 0.219660i \(-0.0704949\pi\)
0.606140 + 0.795358i \(0.292717\pi\)
\(14\) −0.658206 6.91711i −0.175913 1.84868i
\(15\) 0 0
\(16\) 7.80400 + 6.54833i 1.95100 + 1.63708i
\(17\) 0.304238 0.526956i 0.0737885 0.127806i −0.826770 0.562540i \(-0.809824\pi\)
0.900559 + 0.434734i \(0.143158\pi\)
\(18\) 0 0
\(19\) −0.948584 1.64300i −0.217620 0.376929i 0.736460 0.676481i \(-0.236496\pi\)
−0.954080 + 0.299552i \(0.903163\pi\)
\(20\) 11.8586 + 9.95057i 2.65167 + 2.22501i
\(21\) 0 0
\(22\) 0.432025 + 2.45014i 0.0921081 + 0.522371i
\(23\) −0.715641 4.05860i −0.149221 0.846277i −0.963880 0.266336i \(-0.914187\pi\)
0.814659 0.579941i \(-0.196924\pi\)
\(24\) 0 0
\(25\) 3.82462 + 3.20924i 0.764925 + 0.641848i
\(26\) −7.96926 + 13.8032i −1.56290 + 2.70702i
\(27\) 0 0
\(28\) 12.9154 + 1.03106i 2.44079 + 0.194851i
\(29\) −0.760560 + 0.276821i −0.141232 + 0.0514044i −0.411669 0.911333i \(-0.635054\pi\)
0.270437 + 0.962738i \(0.412832\pi\)
\(30\) 0 0
\(31\) 1.80858 + 0.658271i 0.324831 + 0.118229i 0.499288 0.866436i \(-0.333595\pi\)
−0.174457 + 0.984665i \(0.555817\pi\)
\(32\) −8.83827 + 7.41619i −1.56240 + 1.31101i
\(33\) 0 0
\(34\) 1.22414 + 1.02717i 0.209938 + 0.176159i
\(35\) 8.33702 + 0.665556i 1.40921 + 0.112499i
\(36\) 0 0
\(37\) −2.07251 −0.340719 −0.170359 0.985382i \(-0.554493\pi\)
−0.170359 + 0.985382i \(0.554493\pi\)
\(38\) 4.68193 1.70408i 0.759510 0.276439i
\(39\) 0 0
\(40\) −18.4243 + 15.4599i −2.91314 + 2.44442i
\(41\) 3.40353 + 1.23878i 0.531542 + 0.193466i 0.593827 0.804593i \(-0.297616\pi\)
−0.0622844 + 0.998058i \(0.519839\pi\)
\(42\) 0 0
\(43\) 1.51736 8.60538i 0.231395 1.31231i −0.618678 0.785644i \(-0.712332\pi\)
0.850074 0.526664i \(-0.176557\pi\)
\(44\) −4.63922 −0.699389
\(45\) 0 0
\(46\) 10.8233 1.59580
\(47\) 7.06911 2.57295i 1.03114 0.375303i 0.229623 0.973280i \(-0.426251\pi\)
0.801513 + 0.597977i \(0.204029\pi\)
\(48\) 0 0
\(49\) 6.00825 3.59179i 0.858322 0.513112i
\(50\) −10.0444 + 8.42821i −1.42049 + 1.19193i
\(51\) 0 0
\(52\) −22.7671 19.1039i −3.15723 2.64923i
\(53\) −0.902177 1.56262i −0.123924 0.214642i 0.797388 0.603467i \(-0.206214\pi\)
−0.921312 + 0.388825i \(0.872881\pi\)
\(54\) 0 0
\(55\) −2.99466 −0.403799
\(56\) −5.06205 + 19.4832i −0.676445 + 2.60356i
\(57\) 0 0
\(58\) −0.369106 2.09330i −0.0484660 0.274864i
\(59\) 8.98391 7.53840i 1.16961 0.981416i 0.169614 0.985510i \(-0.445748\pi\)
0.999992 + 0.00409447i \(0.00130331\pi\)
\(60\) 0 0
\(61\) 2.43545 0.886433i 0.311828 0.113496i −0.181366 0.983416i \(-0.558052\pi\)
0.493193 + 0.869920i \(0.335829\pi\)
\(62\) −2.52730 + 4.37741i −0.320967 + 0.555931i
\(63\) 0 0
\(64\) −4.96275 8.59574i −0.620344 1.07447i
\(65\) −14.6964 12.3317i −1.82286 1.52956i
\(66\) 0 0
\(67\) −1.13472 6.43533i −0.138628 0.786201i −0.972264 0.233886i \(-0.924856\pi\)
0.833636 0.552315i \(-0.186255\pi\)
\(68\) −2.28263 + 1.91536i −0.276810 + 0.232271i
\(69\) 0 0
\(70\) −5.52337 + 21.2588i −0.660169 + 2.54091i
\(71\) −5.39566 9.34556i −0.640347 1.10911i −0.985355 0.170514i \(-0.945457\pi\)
0.345008 0.938600i \(-0.387876\pi\)
\(72\) 0 0
\(73\) −3.43163 −0.401642 −0.200821 0.979628i \(-0.564361\pi\)
−0.200821 + 0.979628i \(0.564361\pi\)
\(74\) 0.945149 5.36021i 0.109871 0.623112i
\(75\) 0 0
\(76\) 1.61330 + 9.14948i 0.185058 + 1.04952i
\(77\) −2.04215 + 1.45320i −0.232725 + 0.165607i
\(78\) 0 0
\(79\) −2.13746 + 12.1222i −0.240484 + 1.36385i 0.590268 + 0.807207i \(0.299022\pi\)
−0.830752 + 0.556643i \(0.812089\pi\)
\(80\) −16.1018 27.8891i −1.80024 3.11810i
\(81\) 0 0
\(82\) −4.75606 + 8.23774i −0.525219 + 0.909706i
\(83\) −2.14098 + 0.779253i −0.235003 + 0.0855341i −0.456837 0.889550i \(-0.651018\pi\)
0.221834 + 0.975084i \(0.428796\pi\)
\(84\) 0 0
\(85\) −1.47346 + 1.23638i −0.159819 + 0.134104i
\(86\) 21.5644 + 7.84881i 2.32535 + 0.846359i
\(87\) 0 0
\(88\) 1.25162 7.09830i 0.133423 0.756681i
\(89\) −2.69360 4.66546i −0.285521 0.494537i 0.687214 0.726455i \(-0.258833\pi\)
−0.972735 + 0.231917i \(0.925500\pi\)
\(90\) 0 0
\(91\) −16.0060 1.27778i −1.67789 0.133948i
\(92\) −3.50457 + 19.8754i −0.365376 + 2.07215i
\(93\) 0 0
\(94\) 3.43070 + 19.4565i 0.353850 + 2.00678i
\(95\) 1.04140 + 5.90607i 0.106845 + 0.605950i
\(96\) 0 0
\(97\) 1.05146 5.96314i 0.106760 0.605465i −0.883743 0.467973i \(-0.844985\pi\)
0.990503 0.137493i \(-0.0439043\pi\)
\(98\) 6.54955 + 17.1773i 0.661605 + 1.73517i
\(99\) 0 0
\(100\) −12.2249 21.1741i −1.22249 2.11741i
\(101\) −2.02834 + 11.5033i −0.201828 + 1.14462i 0.700527 + 0.713626i \(0.252948\pi\)
−0.902354 + 0.430995i \(0.858163\pi\)
\(102\) 0 0
\(103\) 5.16256 + 1.87902i 0.508682 + 0.185145i 0.583595 0.812045i \(-0.301646\pi\)
−0.0749126 + 0.997190i \(0.523868\pi\)
\(104\) 35.3725 29.6810i 3.46856 2.91046i
\(105\) 0 0
\(106\) 4.45288 1.62072i 0.432502 0.157418i
\(107\) 5.26669 9.12217i 0.509150 0.881873i −0.490794 0.871276i \(-0.663293\pi\)
0.999944 0.0105978i \(-0.00337344\pi\)
\(108\) 0 0
\(109\) −6.32427 10.9540i −0.605755 1.04920i −0.991932 0.126774i \(-0.959538\pi\)
0.386176 0.922425i \(-0.373796\pi\)
\(110\) 1.36568 7.74518i 0.130213 0.738474i
\(111\) 0 0
\(112\) −24.5139 11.2049i −2.31635 1.05876i
\(113\) −2.30771 13.0877i −0.217091 1.23119i −0.877240 0.480052i \(-0.840618\pi\)
0.660149 0.751135i \(-0.270493\pi\)
\(114\) 0 0
\(115\) −2.26223 + 12.8297i −0.210954 + 1.19638i
\(116\) 3.96357 0.368008
\(117\) 0 0
\(118\) 15.3998 + 26.6732i 1.41767 + 2.45547i
\(119\) −0.404830 + 1.55814i −0.0371107 + 0.142835i
\(120\) 0 0
\(121\) −7.73900 + 6.49379i −0.703545 + 0.590345i
\(122\) 1.18195 + 6.70315i 0.107008 + 0.606874i
\(123\) 0 0
\(124\) −7.22014 6.05842i −0.648388 0.544062i
\(125\) 0.0115532 + 0.0200107i 0.00103335 + 0.00178981i
\(126\) 0 0
\(127\) 6.75138 11.6937i 0.599088 1.03765i −0.393867 0.919167i \(-0.628863\pi\)
0.992956 0.118484i \(-0.0378035\pi\)
\(128\) 2.81117 1.02318i 0.248475 0.0904374i
\(129\) 0 0
\(130\) 38.5961 32.3859i 3.38510 2.84043i
\(131\) 2.13216 + 12.0921i 0.186287 + 1.05649i 0.924290 + 0.381690i \(0.124658\pi\)
−0.738003 + 0.674797i \(0.764231\pi\)
\(132\) 0 0
\(133\) 3.57616 + 3.52219i 0.310093 + 0.305412i
\(134\) 17.1614 1.48252
\(135\) 0 0
\(136\) −2.31478 4.00932i −0.198491 0.343796i
\(137\) −4.38145 3.67647i −0.374332 0.314102i 0.436140 0.899879i \(-0.356345\pi\)
−0.810473 + 0.585777i \(0.800790\pi\)
\(138\) 0 0
\(139\) 5.32925 4.47177i 0.452021 0.379291i −0.388164 0.921590i \(-0.626891\pi\)
0.840185 + 0.542300i \(0.182446\pi\)
\(140\) −37.2503 17.0265i −3.14822 1.43900i
\(141\) 0 0
\(142\) 26.6314 9.69303i 2.23486 0.813421i
\(143\) 5.74937 0.480786
\(144\) 0 0
\(145\) 2.55852 0.212473
\(146\) 1.56496 8.87535i 0.129517 0.734529i
\(147\) 0 0
\(148\) 9.53722 + 3.47126i 0.783955 + 0.285336i
\(149\) 13.5112 11.3373i 1.10688 0.928784i 0.109013 0.994040i \(-0.465231\pi\)
0.997869 + 0.0652566i \(0.0207866\pi\)
\(150\) 0 0
\(151\) −2.27469 + 0.827918i −0.185111 + 0.0673750i −0.432913 0.901436i \(-0.642514\pi\)
0.247801 + 0.968811i \(0.420292\pi\)
\(152\) −14.4345 −1.17080
\(153\) 0 0
\(154\) −2.82715 5.94441i −0.227818 0.479014i
\(155\) −4.66067 3.91076i −0.374354 0.314120i
\(156\) 0 0
\(157\) 0.606979 0.509316i 0.0484422 0.0406478i −0.618245 0.785985i \(-0.712156\pi\)
0.666687 + 0.745338i \(0.267712\pi\)
\(158\) −30.3772 11.0564i −2.41668 0.879600i
\(159\) 0 0
\(160\) 34.2721 12.4740i 2.70945 0.986158i
\(161\) 4.68311 + 9.84678i 0.369081 + 0.776035i
\(162\) 0 0
\(163\) 9.42412 16.3231i 0.738154 1.27852i −0.215172 0.976576i \(-0.569031\pi\)
0.953326 0.301944i \(-0.0976355\pi\)
\(164\) −13.5874 11.4012i −1.06100 0.890284i
\(165\) 0 0
\(166\) −1.03904 5.89266i −0.0806448 0.457359i
\(167\) 3.61033 + 20.4752i 0.279376 + 1.58442i 0.724710 + 0.689053i \(0.241974\pi\)
−0.445335 + 0.895364i \(0.646915\pi\)
\(168\) 0 0
\(169\) 18.2566 + 15.3191i 1.40435 + 1.17839i
\(170\) −2.52574 4.37470i −0.193715 0.335524i
\(171\) 0 0
\(172\) −21.3958 + 37.0585i −1.63141 + 2.82569i
\(173\) 0.789302 + 0.662303i 0.0600095 + 0.0503540i 0.672299 0.740280i \(-0.265307\pi\)
−0.612290 + 0.790634i \(0.709751\pi\)
\(174\) 0 0
\(175\) −12.0139 5.49135i −0.908166 0.415107i
\(176\) 9.06890 + 3.30081i 0.683594 + 0.248808i
\(177\) 0 0
\(178\) 13.2948 4.83892i 0.996489 0.362692i
\(179\) −4.67764 + 8.10192i −0.349624 + 0.605566i −0.986183 0.165662i \(-0.947024\pi\)
0.636559 + 0.771228i \(0.280357\pi\)
\(180\) 0 0
\(181\) −7.15376 + 12.3907i −0.531735 + 0.920992i 0.467579 + 0.883951i \(0.345126\pi\)
−0.999314 + 0.0370404i \(0.988207\pi\)
\(182\) 10.6042 40.8143i 0.786034 3.02535i
\(183\) 0 0
\(184\) −29.4651 10.7244i −2.17219 0.790614i
\(185\) 6.15636 + 2.24073i 0.452625 + 0.164742i
\(186\) 0 0
\(187\) 0.100097 0.567676i 0.00731979 0.0415126i
\(188\) −36.8399 −2.68682
\(189\) 0 0
\(190\) −15.7500 −1.14262
\(191\) 0.860846 4.88210i 0.0622886 0.353256i −0.937695 0.347461i \(-0.887044\pi\)
0.999983 0.00579570i \(-0.00184484\pi\)
\(192\) 0 0
\(193\) −22.1383 8.05769i −1.59355 0.580006i −0.615458 0.788170i \(-0.711029\pi\)
−0.978094 + 0.208164i \(0.933251\pi\)
\(194\) 14.9432 + 5.43887i 1.07286 + 0.390488i
\(195\) 0 0
\(196\) −33.6645 + 6.46531i −2.40461 + 0.461808i
\(197\) −11.2274 + 19.4463i −0.799916 + 1.38549i 0.119754 + 0.992804i \(0.461789\pi\)
−0.919670 + 0.392691i \(0.871544\pi\)
\(198\) 0 0
\(199\) 4.93199 8.54246i 0.349620 0.605559i −0.636562 0.771225i \(-0.719644\pi\)
0.986182 + 0.165666i \(0.0529774\pi\)
\(200\) 35.6958 12.9922i 2.52408 0.918688i
\(201\) 0 0
\(202\) −28.8264 10.4919i −2.02822 0.738210i
\(203\) 1.74474 1.24156i 0.122456 0.0871401i
\(204\) 0 0
\(205\) −8.77080 7.35958i −0.612579 0.514015i
\(206\) −7.21411 + 12.4952i −0.502631 + 0.870582i
\(207\) 0 0
\(208\) 30.9135 + 53.5437i 2.14346 + 3.71259i
\(209\) −1.37678 1.15526i −0.0952341 0.0799109i
\(210\) 0 0
\(211\) 1.95127 + 11.0662i 0.134331 + 0.761828i 0.975323 + 0.220782i \(0.0708608\pi\)
−0.840992 + 0.541047i \(0.818028\pi\)
\(212\) 1.53437 + 8.70187i 0.105381 + 0.597647i
\(213\) 0 0
\(214\) 21.1912 + 17.7815i 1.44860 + 1.21552i
\(215\) −13.8112 + 23.9216i −0.941913 + 1.63144i
\(216\) 0 0
\(217\) −5.07601 0.405225i −0.344582 0.0275085i
\(218\) 31.2147 11.3612i 2.11413 0.769480i
\(219\) 0 0
\(220\) 13.7807 + 5.01577i 0.929096 + 0.338163i
\(221\) 2.82886 2.37370i 0.190290 0.159672i
\(222\) 0 0
\(223\) −20.0603 16.8326i −1.34334 1.12719i −0.980755 0.195242i \(-0.937451\pi\)
−0.362582 0.931952i \(-0.618105\pi\)
\(224\) 17.3181 25.1374i 1.15711 1.67956i
\(225\) 0 0
\(226\) 34.9016 2.32162
\(227\) −13.1205 + 4.77548i −0.870839 + 0.316959i −0.738507 0.674246i \(-0.764469\pi\)
−0.132332 + 0.991205i \(0.542247\pi\)
\(228\) 0 0
\(229\) 6.85549 5.75244i 0.453023 0.380132i −0.387533 0.921856i \(-0.626673\pi\)
0.840556 + 0.541724i \(0.182228\pi\)
\(230\) −32.1503 11.7018i −2.11993 0.771591i
\(231\) 0 0
\(232\) −1.06934 + 6.06451i −0.0702054 + 0.398155i
\(233\) 7.74614 0.507466 0.253733 0.967274i \(-0.418342\pi\)
0.253733 + 0.967274i \(0.418342\pi\)
\(234\) 0 0
\(235\) −23.7805 −1.55127
\(236\) −53.9680 + 19.6428i −3.51302 + 1.27863i
\(237\) 0 0
\(238\) −3.84526 1.75760i −0.249251 0.113929i
\(239\) 11.5961 9.73028i 0.750089 0.629400i −0.185437 0.982656i \(-0.559370\pi\)
0.935526 + 0.353257i \(0.114926\pi\)
\(240\) 0 0
\(241\) 11.4836 + 9.63587i 0.739723 + 0.620701i 0.932763 0.360490i \(-0.117390\pi\)
−0.193040 + 0.981191i \(0.561835\pi\)
\(242\) −13.2658 22.9771i −0.852759 1.47702i
\(243\) 0 0
\(244\) −12.6921 −0.812528
\(245\) −21.7307 + 4.17341i −1.38833 + 0.266630i
\(246\) 0 0
\(247\) −1.99936 11.3389i −0.127216 0.721479i
\(248\) 11.2177 9.41277i 0.712324 0.597711i
\(249\) 0 0
\(250\) −0.0570230 + 0.0207547i −0.00360645 + 0.00131264i
\(251\) 11.3387 19.6392i 0.715692 1.23961i −0.247001 0.969015i \(-0.579445\pi\)
0.962692 0.270599i \(-0.0872217\pi\)
\(252\) 0 0
\(253\) −1.95209 3.38113i −0.122727 0.212570i
\(254\) 27.1650 + 22.7942i 1.70448 + 1.43023i
\(255\) 0 0
\(256\) −2.08281 11.8122i −0.130175 0.738261i
\(257\) 11.5423 9.68514i 0.719989 0.604142i −0.207393 0.978258i \(-0.566498\pi\)
0.927382 + 0.374115i \(0.122054\pi\)
\(258\) 0 0
\(259\) 5.28556 1.45943i 0.328429 0.0906845i
\(260\) 46.9748 + 81.3627i 2.91325 + 5.04590i
\(261\) 0 0
\(262\) −32.2465 −1.99219
\(263\) −0.872812 + 4.94996i −0.0538199 + 0.305228i −0.999821 0.0189365i \(-0.993972\pi\)
0.946001 + 0.324164i \(0.105083\pi\)
\(264\) 0 0
\(265\) 0.990452 + 5.61713i 0.0608430 + 0.345058i
\(266\) −10.7404 + 7.64290i −0.658538 + 0.468616i
\(267\) 0 0
\(268\) −5.55685 + 31.5145i −0.339439 + 1.92505i
\(269\) 7.35597 + 12.7409i 0.448501 + 0.776827i 0.998289 0.0584776i \(-0.0186246\pi\)
−0.549787 + 0.835305i \(0.685291\pi\)
\(270\) 0 0
\(271\) 6.38218 11.0543i 0.387690 0.671498i −0.604449 0.796644i \(-0.706607\pi\)
0.992138 + 0.125146i \(0.0399399\pi\)
\(272\) 5.82495 2.12011i 0.353190 0.128550i
\(273\) 0 0
\(274\) 11.5067 9.65527i 0.695145 0.583296i
\(275\) 4.44453 + 1.61768i 0.268015 + 0.0975497i
\(276\) 0 0
\(277\) −3.77512 + 21.4098i −0.226825 + 1.28639i 0.632340 + 0.774691i \(0.282094\pi\)
−0.859165 + 0.511698i \(0.829017\pi\)
\(278\) 9.13515 + 15.8225i 0.547890 + 0.948973i
\(279\) 0 0
\(280\) 36.1014 52.4017i 2.15747 3.13160i
\(281\) −3.25313 + 18.4494i −0.194065 + 1.10060i 0.719678 + 0.694308i \(0.244289\pi\)
−0.913744 + 0.406291i \(0.866822\pi\)
\(282\) 0 0
\(283\) 0.478430 + 2.71331i 0.0284397 + 0.161290i 0.995720 0.0924202i \(-0.0294603\pi\)
−0.967280 + 0.253710i \(0.918349\pi\)
\(284\) 9.17665 + 52.0434i 0.544534 + 3.08820i
\(285\) 0 0
\(286\) −2.62195 + 14.8698i −0.155039 + 0.879269i
\(287\) −9.55242 0.762583i −0.563862 0.0450139i
\(288\) 0 0
\(289\) 8.31488 + 14.4018i 0.489111 + 0.847164i
\(290\) −1.16679 + 6.61719i −0.0685162 + 0.388575i
\(291\) 0 0
\(292\) 15.7916 + 5.74767i 0.924133 + 0.336357i
\(293\) −0.702665 + 0.589606i −0.0410502 + 0.0344452i −0.663082 0.748547i \(-0.730752\pi\)
0.622032 + 0.782992i \(0.286307\pi\)
\(294\) 0 0
\(295\) −34.8368 + 12.6796i −2.02828 + 0.738233i
\(296\) −7.88431 + 13.6560i −0.458266 + 0.793741i
\(297\) 0 0
\(298\) 23.1603 + 40.1148i 1.34164 + 2.32379i
\(299\) 4.34320 24.6315i 0.251174 1.42448i
\(300\) 0 0
\(301\) 2.19002 + 23.0150i 0.126230 + 1.32656i
\(302\) −1.10392 6.26066i −0.0635237 0.360261i
\(303\) 0 0
\(304\) 3.35613 19.0336i 0.192487 1.09165i
\(305\) −8.19285 −0.469121
\(306\) 0 0
\(307\) −14.3373 24.8329i −0.818271 1.41729i −0.906955 0.421228i \(-0.861599\pi\)
0.0886837 0.996060i \(-0.471734\pi\)
\(308\) 11.8315 3.26686i 0.674161 0.186147i
\(309\) 0 0
\(310\) 12.2400 10.2706i 0.695185 0.583330i
\(311\) −1.26093 7.15109i −0.0715008 0.405501i −0.999461 0.0328223i \(-0.989550\pi\)
0.927960 0.372679i \(-0.121561\pi\)
\(312\) 0 0
\(313\) −25.2359 21.1754i −1.42642 1.19691i −0.947793 0.318885i \(-0.896692\pi\)
−0.478623 0.878021i \(-0.658864\pi\)
\(314\) 1.04045 + 1.80212i 0.0587162 + 0.101699i
\(315\) 0 0
\(316\) 30.1396 52.2033i 1.69549 2.93667i
\(317\) −2.09299 + 0.761785i −0.117554 + 0.0427861i −0.400127 0.916460i \(-0.631034\pi\)
0.282574 + 0.959246i \(0.408812\pi\)
\(318\) 0 0
\(319\) −0.587364 + 0.492857i −0.0328861 + 0.0275947i
\(320\) 5.44834 + 30.8990i 0.304571 + 1.72731i
\(321\) 0 0
\(322\) −27.6028 + 7.62157i −1.53824 + 0.424733i
\(323\) −1.15438 −0.0642315
\(324\) 0 0
\(325\) 15.1502 + 26.2410i 0.840383 + 1.45559i
\(326\) 37.9191 + 31.8179i 2.10014 + 1.76223i
\(327\) 0 0
\(328\) 21.1103 17.7137i 1.16562 0.978074i
\(329\) −16.2167 + 11.5398i −0.894053 + 0.636209i
\(330\) 0 0
\(331\) 34.1051 12.4133i 1.87459 0.682294i 0.912871 0.408248i \(-0.133860\pi\)
0.961717 0.274046i \(-0.0883621\pi\)
\(332\) 11.1575 0.612346
\(333\) 0 0
\(334\) −54.6021 −2.98770
\(335\) −3.58700 + 20.3429i −0.195979 + 1.11145i
\(336\) 0 0
\(337\) 25.4920 + 9.27833i 1.38864 + 0.505423i 0.924785 0.380490i \(-0.124245\pi\)
0.463852 + 0.885913i \(0.346467\pi\)
\(338\) −47.9461 + 40.2316i −2.60792 + 2.18831i
\(339\) 0 0
\(340\) 8.85135 3.22163i 0.480032 0.174717i
\(341\) 1.82330 0.0987374
\(342\) 0 0
\(343\) −12.7937 + 13.3911i −0.690794 + 0.723052i
\(344\) −50.9295 42.7349i −2.74594 2.30411i
\(345\) 0 0
\(346\) −2.07289 + 1.73936i −0.111439 + 0.0935087i
\(347\) 8.07046 + 2.93741i 0.433245 + 0.157688i 0.549431 0.835539i \(-0.314845\pi\)
−0.116186 + 0.993227i \(0.537067\pi\)
\(348\) 0 0
\(349\) −2.20933 + 0.804130i −0.118263 + 0.0430441i −0.400474 0.916308i \(-0.631154\pi\)
0.282211 + 0.959352i \(0.408932\pi\)
\(350\) 19.6813 28.5677i 1.05201 1.52701i
\(351\) 0 0
\(352\) −5.46499 + 9.46564i −0.291285 + 0.504520i
\(353\) 7.82588 + 6.56669i 0.416530 + 0.349510i 0.826841 0.562436i \(-0.190136\pi\)
−0.410311 + 0.911945i \(0.634580\pi\)
\(354\) 0 0
\(355\) 5.92361 + 33.5944i 0.314392 + 1.78301i
\(356\) 4.58113 + 25.9809i 0.242800 + 1.37698i
\(357\) 0 0
\(358\) −18.8211 15.7928i −0.994725 0.834673i
\(359\) −0.801450 1.38815i −0.0422989 0.0732639i 0.844101 0.536184i \(-0.180135\pi\)
−0.886400 + 0.462921i \(0.846802\pi\)
\(360\) 0 0
\(361\) 7.70037 13.3374i 0.405283 0.701971i
\(362\) −28.7840 24.1527i −1.51286 1.26944i
\(363\) 0 0
\(364\) 71.5159 + 32.6887i 3.74845 + 1.71335i
\(365\) 10.1936 + 3.71017i 0.533558 + 0.194199i
\(366\) 0 0
\(367\) 15.7188 5.72116i 0.820513 0.298642i 0.102554 0.994727i \(-0.467299\pi\)
0.717959 + 0.696085i \(0.245076\pi\)
\(368\) 20.9922 36.3596i 1.09429 1.89537i
\(369\) 0 0
\(370\) −8.60283 + 14.9005i −0.447240 + 0.774642i
\(371\) 3.40121 + 3.34987i 0.176582 + 0.173917i
\(372\) 0 0
\(373\) −3.97055 1.44516i −0.205587 0.0748277i 0.237174 0.971467i \(-0.423779\pi\)
−0.442761 + 0.896639i \(0.646001\pi\)
\(374\) 1.42255 + 0.517767i 0.0735584 + 0.0267731i
\(375\) 0 0
\(376\) 9.93908 56.3673i 0.512569 2.90692i
\(377\) −4.91204 −0.252983
\(378\) 0 0
\(379\) −22.6376 −1.16282 −0.581408 0.813612i \(-0.697498\pi\)
−0.581408 + 0.813612i \(0.697498\pi\)
\(380\) 5.09984 28.9226i 0.261616 1.48370i
\(381\) 0 0
\(382\) 12.2342 + 4.45287i 0.625954 + 0.227829i
\(383\) −18.1487 6.60560i −0.927357 0.337530i −0.166195 0.986093i \(-0.553148\pi\)
−0.761161 + 0.648563i \(0.775370\pi\)
\(384\) 0 0
\(385\) 7.63733 2.10879i 0.389234 0.107474i
\(386\) 30.9359 53.5825i 1.57459 2.72728i
\(387\) 0 0
\(388\) −14.8263 + 25.6799i −0.752691 + 1.30370i
\(389\) −4.48151 + 1.63113i −0.227221 + 0.0827018i −0.453122 0.891449i \(-0.649690\pi\)
0.225901 + 0.974150i \(0.427468\pi\)
\(390\) 0 0
\(391\) −2.35643 0.857670i −0.119170 0.0433742i
\(392\) −0.809939 53.2531i −0.0409081 2.68969i
\(393\) 0 0
\(394\) −45.1746 37.9060i −2.27587 1.90968i
\(395\) 19.4554 33.6977i 0.978907 1.69552i
\(396\) 0 0
\(397\) 13.2756 + 22.9941i 0.666284 + 1.15404i 0.978935 + 0.204170i \(0.0654497\pi\)
−0.312651 + 0.949868i \(0.601217\pi\)
\(398\) 19.8445 + 16.6515i 0.994714 + 0.834664i
\(399\) 0 0
\(400\) 8.83218 + 50.0898i 0.441609 + 2.50449i
\(401\) −3.42460 19.4219i −0.171016 0.969882i −0.942642 0.333805i \(-0.891667\pi\)
0.771626 0.636077i \(-0.219444\pi\)
\(402\) 0 0
\(403\) 8.94790 + 7.50818i 0.445727 + 0.374009i
\(404\) 28.6009 49.5382i 1.42295 2.46462i
\(405\) 0 0
\(406\) 2.41541 + 5.07867i 0.119875 + 0.252050i
\(407\) −1.84497 + 0.671513i −0.0914516 + 0.0332857i
\(408\) 0 0
\(409\) −13.6377 4.96370i −0.674339 0.245439i −0.0179238 0.999839i \(-0.505706\pi\)
−0.656415 + 0.754400i \(0.727928\pi\)
\(410\) 23.0342 19.3280i 1.13758 0.954540i
\(411\) 0 0
\(412\) −20.6097 17.2936i −1.01537 0.851996i
\(413\) −17.6034 + 25.5516i −0.866208 + 1.25731i
\(414\) 0 0
\(415\) 7.20225 0.353544
\(416\) −65.7982 + 23.9486i −3.22602 + 1.17418i
\(417\) 0 0
\(418\) 3.61576 3.03398i 0.176852 0.148397i
\(419\) −31.3764 11.4201i −1.53284 0.557908i −0.568524 0.822666i \(-0.692485\pi\)
−0.964315 + 0.264759i \(0.914708\pi\)
\(420\) 0 0
\(421\) −0.561640 + 3.18522i −0.0273727 + 0.155238i −0.995430 0.0954889i \(-0.969559\pi\)
0.968058 + 0.250727i \(0.0806697\pi\)
\(422\) −29.5108 −1.43656
\(423\) 0 0
\(424\) −13.7284 −0.666708
\(425\) 2.85472 1.03903i 0.138474 0.0504005i
\(426\) 0 0
\(427\) −5.58697 + 3.97569i −0.270372 + 0.192397i
\(428\) −39.5149 + 33.1569i −1.91002 + 1.60270i
\(429\) 0 0
\(430\) −55.5709 46.6295i −2.67986 2.24867i
\(431\) −18.3492 31.7818i −0.883851 1.53087i −0.847025 0.531553i \(-0.821609\pi\)
−0.0368258 0.999322i \(-0.511725\pi\)
\(432\) 0 0
\(433\) 13.1621 0.632532 0.316266 0.948670i \(-0.397571\pi\)
0.316266 + 0.948670i \(0.397571\pi\)
\(434\) 3.36291 12.9435i 0.161425 0.621306i
\(435\) 0 0
\(436\) 10.7560 + 61.0001i 0.515118 + 2.92138i
\(437\) −5.98942 + 5.02572i −0.286513 + 0.240413i
\(438\) 0 0
\(439\) 32.9108 11.9785i 1.57075 0.571705i 0.597580 0.801810i \(-0.296129\pi\)
0.973166 + 0.230105i \(0.0739070\pi\)
\(440\) −11.3924 + 19.7322i −0.543110 + 0.940694i
\(441\) 0 0
\(442\) 4.84910 + 8.39889i 0.230648 + 0.399494i
\(443\) −9.70817 8.14612i −0.461249 0.387034i 0.382341 0.924021i \(-0.375118\pi\)
−0.843590 + 0.536987i \(0.819562\pi\)
\(444\) 0 0
\(445\) 2.95716 + 16.7709i 0.140183 + 0.795017i
\(446\) 52.6830 44.2063i 2.49461 2.09323i
\(447\) 0 0
\(448\) 18.7096 + 18.4272i 0.883944 + 0.870602i
\(449\) −13.1158 22.7172i −0.618971 1.07209i −0.989674 0.143338i \(-0.954217\pi\)
0.370703 0.928751i \(-0.379117\pi\)
\(450\) 0 0
\(451\) 3.43123 0.161570
\(452\) −11.3011 + 64.0917i −0.531559 + 3.01462i
\(453\) 0 0
\(454\) −6.36749 36.1118i −0.298841 1.69481i
\(455\) 46.1642 + 21.1008i 2.16421 + 0.989223i
\(456\) 0 0
\(457\) 5.13706 29.1337i 0.240301 1.36282i −0.590855 0.806778i \(-0.701209\pi\)
0.831156 0.556039i \(-0.187680\pi\)
\(458\) 11.7513 + 20.3539i 0.549104 + 0.951077i
\(459\) 0 0
\(460\) 31.8989 55.2505i 1.48729 2.57607i
\(461\) 14.5699 5.30303i 0.678590 0.246987i 0.0203479 0.999793i \(-0.493523\pi\)
0.658242 + 0.752806i \(0.271300\pi\)
\(462\) 0 0
\(463\) 5.28847 4.43756i 0.245776 0.206231i −0.511575 0.859239i \(-0.670938\pi\)
0.757351 + 0.653008i \(0.226493\pi\)
\(464\) −7.74812 2.82009i −0.359697 0.130919i
\(465\) 0 0
\(466\) −3.53255 + 20.0341i −0.163642 + 0.928062i
\(467\) −4.43296 7.67811i −0.205133 0.355300i 0.745042 0.667017i \(-0.232429\pi\)
−0.950175 + 0.311717i \(0.899096\pi\)
\(468\) 0 0
\(469\) 7.42556 + 15.6131i 0.342881 + 0.720946i
\(470\) 10.8449 61.5042i 0.500236 2.83698i
\(471\) 0 0
\(472\) −15.4945 87.8739i −0.713194 4.04472i
\(473\) −1.43746 8.15222i −0.0660943 0.374840i
\(474\) 0 0
\(475\) 1.64479 9.32808i 0.0754682 0.428002i
\(476\) 4.47268 6.49217i 0.205005 0.297568i
\(477\) 0 0
\(478\) 19.8775 + 34.4288i 0.909174 + 1.57474i
\(479\) −0.0218340 + 0.123827i −0.000997621 + 0.00565779i −0.985303 0.170819i \(-0.945359\pi\)
0.984305 + 0.176476i \(0.0564699\pi\)
\(480\) 0 0
\(481\) −11.8194 4.30193i −0.538921 0.196151i
\(482\) −30.1586 + 25.3061i −1.37369 + 1.15266i
\(483\) 0 0
\(484\) 46.4896 16.9208i 2.11316 0.769129i
\(485\) −9.57050 + 16.5766i −0.434574 + 0.752705i
\(486\) 0 0
\(487\) −9.35525 16.2038i −0.423927 0.734263i 0.572393 0.819980i \(-0.306015\pi\)
−0.996320 + 0.0857168i \(0.972682\pi\)
\(488\) 3.42422 19.4197i 0.155007 0.879088i
\(489\) 0 0
\(490\) −0.883751 58.1062i −0.0399238 2.62497i
\(491\) 0.257998 + 1.46318i 0.0116433 + 0.0660322i 0.990076 0.140534i \(-0.0448821\pi\)
−0.978433 + 0.206567i \(0.933771\pi\)
\(492\) 0 0
\(493\) −0.0855187 + 0.485001i −0.00385157 + 0.0218433i
\(494\) 30.2380 1.36047
\(495\) 0 0
\(496\) 9.80361 + 16.9803i 0.440195 + 0.762440i
\(497\) 20.3417 + 20.0346i 0.912448 + 0.898676i
\(498\) 0 0
\(499\) 6.67745 5.60305i 0.298924 0.250827i −0.480972 0.876736i \(-0.659716\pi\)
0.779896 + 0.625909i \(0.215272\pi\)
\(500\) −0.0196490 0.111435i −0.000878730 0.00498352i
\(501\) 0 0
\(502\) 45.6226 + 38.2819i 2.03624 + 1.70861i
\(503\) −3.55585 6.15890i −0.158547 0.274612i 0.775798 0.630982i \(-0.217348\pi\)
−0.934345 + 0.356370i \(0.884014\pi\)
\(504\) 0 0
\(505\) 18.4621 31.9774i 0.821555 1.42297i
\(506\) 9.63496 3.50684i 0.428326 0.155898i
\(507\) 0 0
\(508\) −50.6542 + 42.5040i −2.24742 + 1.88581i
\(509\) 6.95572 + 39.4478i 0.308307 + 1.74849i 0.607516 + 0.794307i \(0.292166\pi\)
−0.299209 + 0.954187i \(0.596723\pi\)
\(510\) 0 0
\(511\) 8.75176 2.41650i 0.387155 0.106900i
\(512\) 37.4833 1.65654
\(513\) 0 0
\(514\) 19.7853 + 34.2691i 0.872690 + 1.51154i
\(515\) −13.3038 11.1632i −0.586234 0.491909i
\(516\) 0 0
\(517\) 5.45932 4.58092i 0.240101 0.201468i
\(518\) 1.36414 + 14.3358i 0.0599368 + 0.629879i
\(519\) 0 0
\(520\) −137.163 + 49.9234i −6.01501 + 2.18929i
\(521\) 21.9149 0.960109 0.480055 0.877239i \(-0.340617\pi\)
0.480055 + 0.877239i \(0.340617\pi\)
\(522\) 0 0
\(523\) 8.49194 0.371327 0.185663 0.982613i \(-0.440557\pi\)
0.185663 + 0.982613i \(0.440557\pi\)
\(524\) 10.4414 59.2160i 0.456134 2.58686i
\(525\) 0 0
\(526\) −12.4042 4.51477i −0.540850 0.196853i
\(527\) 0.897119 0.752773i 0.0390791 0.0327913i
\(528\) 0 0
\(529\) 5.65283 2.05746i 0.245775 0.0894548i
\(530\) −14.9795 −0.650667
\(531\) 0 0
\(532\) −10.5573 22.1980i −0.457719 0.962407i
\(533\) 16.8389 + 14.1295i 0.729372 + 0.612016i
\(534\) 0 0
\(535\) −25.5072 + 21.4031i −1.10277 + 0.925336i
\(536\) −46.7199 17.0047i −2.01799 0.734490i
\(537\) 0 0
\(538\) −36.3069 + 13.2146i −1.56530 + 0.569723i
\(539\) 4.18482 5.14417i 0.180253 0.221575i
\(540\) 0 0
\(541\) −17.7266 + 30.7033i −0.762125 + 1.32004i 0.179629 + 0.983735i \(0.442510\pi\)
−0.941753 + 0.336304i \(0.890823\pi\)
\(542\) 25.6795 + 21.5476i 1.10303 + 0.925550i
\(543\) 0 0
\(544\) 1.21907 + 6.91366i 0.0522670 + 0.296421i
\(545\) 6.94307 + 39.3761i 0.297409 + 1.68669i
\(546\) 0 0
\(547\) 12.4441 + 10.4418i 0.532069 + 0.446459i 0.868815 0.495136i \(-0.164882\pi\)
−0.336746 + 0.941596i \(0.609326\pi\)
\(548\) 14.0047 + 24.2568i 0.598249 + 1.03620i
\(549\) 0 0
\(550\) −6.21075 + 10.7573i −0.264827 + 0.458694i
\(551\) 1.17627 + 0.987009i 0.0501108 + 0.0420480i
\(552\) 0 0
\(553\) −3.08501 32.4205i −0.131188 1.37866i
\(554\) −53.6512 19.5275i −2.27942 0.829642i
\(555\) 0 0
\(556\) −32.0138 + 11.6521i −1.35769 + 0.494158i
\(557\) −18.2394 + 31.5916i −0.772828 + 1.33858i 0.163179 + 0.986597i \(0.447825\pi\)
−0.936007 + 0.351981i \(0.885508\pi\)
\(558\) 0 0
\(559\) 26.5157 45.9265i 1.12149 1.94249i
\(560\) 60.7038 + 59.7875i 2.56520 + 2.52648i
\(561\) 0 0
\(562\) −46.2328 16.8274i −1.95021 0.709819i
\(563\) −1.16299 0.423294i −0.0490142 0.0178397i 0.317397 0.948293i \(-0.397191\pi\)
−0.366411 + 0.930453i \(0.619414\pi\)
\(564\) 0 0
\(565\) −7.29496 + 41.3718i −0.306901 + 1.74052i
\(566\) −7.23572 −0.304140
\(567\) 0 0
\(568\) −82.1054 −3.44507
\(569\) −6.91048 + 39.1913i −0.289702 + 1.64298i 0.398286 + 0.917261i \(0.369605\pi\)
−0.687988 + 0.725722i \(0.741506\pi\)
\(570\) 0 0
\(571\) 17.9874 + 6.54689i 0.752750 + 0.273979i 0.689763 0.724036i \(-0.257715\pi\)
0.0629876 + 0.998014i \(0.479937\pi\)
\(572\) −26.4573 9.62966i −1.10623 0.402636i
\(573\) 0 0
\(574\) 6.32859 24.3580i 0.264150 1.01668i
\(575\) 10.2880 17.8193i 0.429038 0.743115i
\(576\) 0 0
\(577\) 3.13865 5.43630i 0.130664 0.226316i −0.793269 0.608871i \(-0.791623\pi\)
0.923933 + 0.382555i \(0.124956\pi\)
\(578\) −41.0398 + 14.9373i −1.70703 + 0.621308i
\(579\) 0 0
\(580\) −11.7737 4.28528i −0.488877 0.177937i
\(581\) 4.91144 3.49499i 0.203761 0.144996i
\(582\) 0 0
\(583\) −1.30943 1.09874i −0.0542310 0.0455052i
\(584\) −13.0547 + 22.6114i −0.540208 + 0.935668i
\(585\) 0 0
\(586\) −1.20448 2.08621i −0.0497564 0.0861806i
\(587\) −16.4147 13.7736i −0.677509 0.568497i 0.237769 0.971322i \(-0.423584\pi\)
−0.915277 + 0.402825i \(0.868028\pi\)
\(588\) 0 0
\(589\) −0.634058 3.59592i −0.0261259 0.148167i
\(590\) −16.9066 95.8821i −0.696034 3.94740i
\(591\) 0 0
\(592\) −16.1739 13.5715i −0.664742 0.557785i
\(593\) 13.1642 22.8011i 0.540591 0.936331i −0.458279 0.888808i \(-0.651534\pi\)
0.998870 0.0475225i \(-0.0151326\pi\)
\(594\) 0 0
\(595\) 2.88716 4.19075i 0.118362 0.171804i
\(596\) −81.1643 + 29.5414i −3.32462 + 1.21006i
\(597\) 0 0
\(598\) 61.7246 + 22.4659i 2.52411 + 0.918700i
\(599\) −14.0230 + 11.7667i −0.572964 + 0.480774i −0.882628 0.470072i \(-0.844228\pi\)
0.309664 + 0.950846i \(0.399783\pi\)
\(600\) 0 0
\(601\) 22.8595 + 19.1814i 0.932458 + 0.782425i 0.976257 0.216615i \(-0.0695017\pi\)
−0.0437990 + 0.999040i \(0.513946\pi\)
\(602\) −60.5231 4.83165i −2.46674 0.196923i
\(603\) 0 0
\(604\) 11.8543 0.482343
\(605\) 30.0094 10.9225i 1.22006 0.444065i
\(606\) 0 0
\(607\) −10.5637 + 8.86396i −0.428766 + 0.359777i −0.831486 0.555546i \(-0.812509\pi\)
0.402720 + 0.915323i \(0.368065\pi\)
\(608\) 20.5686 + 7.48637i 0.834168 + 0.303612i
\(609\) 0 0
\(610\) 3.73627 21.1895i 0.151277 0.857936i
\(611\) 45.6555 1.84703
\(612\) 0 0
\(613\) 1.93233 0.0780459 0.0390229 0.999238i \(-0.487575\pi\)
0.0390229 + 0.999238i \(0.487575\pi\)
\(614\) 70.7645 25.7562i 2.85582 1.03943i
\(615\) 0 0
\(616\) 1.80647 + 18.9843i 0.0727848 + 0.764899i
\(617\) 4.89980 4.11142i 0.197258 0.165519i −0.538808 0.842428i \(-0.681125\pi\)
0.736067 + 0.676909i \(0.236681\pi\)
\(618\) 0 0
\(619\) 15.1565 + 12.7178i 0.609191 + 0.511172i 0.894385 0.447298i \(-0.147614\pi\)
−0.285194 + 0.958470i \(0.592058\pi\)
\(620\) 14.8971 + 25.8026i 0.598284 + 1.03626i
\(621\) 0 0
\(622\) 19.0701 0.764643
\(623\) 10.1549 + 10.0016i 0.406847 + 0.400706i
\(624\) 0 0
\(625\) −4.34754 24.6561i −0.173902 0.986245i
\(626\) 66.2753 55.6116i 2.64889 2.22269i
\(627\) 0 0
\(628\) −3.64623 + 1.32712i −0.145501 + 0.0529579i
\(629\) −0.630537 + 1.09212i −0.0251411 + 0.0435457i
\(630\) 0 0
\(631\) 11.5581 + 20.0192i 0.460121 + 0.796953i 0.998967 0.0454518i \(-0.0144727\pi\)
−0.538846 + 0.842405i \(0.681139\pi\)
\(632\) 71.7430 + 60.1995i 2.85378 + 2.39461i
\(633\) 0 0
\(634\) −1.01574 5.76057i −0.0403403 0.228781i
\(635\) −32.6978 + 27.4367i −1.29757 + 1.08879i
\(636\) 0 0
\(637\) 41.7203 8.01244i 1.65302 0.317464i
\(638\) −1.00683 1.74388i −0.0398608 0.0690410i
\(639\) 0 0
\(640\) −9.45677 −0.373812
\(641\) 7.59079 43.0495i 0.299818 1.70035i −0.347128 0.937818i \(-0.612843\pi\)
0.646946 0.762536i \(-0.276046\pi\)
\(642\) 0 0
\(643\) 4.25742 + 24.1450i 0.167896 + 0.952186i 0.946028 + 0.324085i \(0.105056\pi\)
−0.778132 + 0.628101i \(0.783832\pi\)
\(644\) −5.05816 53.1564i −0.199319 2.09466i
\(645\) 0 0
\(646\) 0.526445 2.98562i 0.0207127 0.117468i
\(647\) −11.8564 20.5358i −0.466122 0.807347i 0.533129 0.846034i \(-0.321016\pi\)
−0.999251 + 0.0386864i \(0.987683\pi\)
\(648\) 0 0
\(649\) 5.55504 9.62162i 0.218055 0.377682i
\(650\) −74.7770 + 27.2166i −2.93300 + 1.06752i
\(651\) 0 0
\(652\) −70.7072 + 59.3304i −2.76911 + 2.32356i
\(653\) −41.1103 14.9629i −1.60877 0.585545i −0.627576 0.778556i \(-0.715953\pi\)
−0.981197 + 0.193010i \(0.938175\pi\)
\(654\) 0 0
\(655\) 6.74000 38.2245i 0.263354 1.49355i
\(656\) 18.4492 + 31.9549i 0.720320 + 1.24763i
\(657\) 0 0
\(658\) −22.4503 47.2043i −0.875204 1.84022i
\(659\) 1.60924 9.12645i 0.0626870 0.355516i −0.937289 0.348554i \(-0.886673\pi\)
0.999976 0.00696195i \(-0.00221608\pi\)
\(660\) 0 0
\(661\) 5.24216 + 29.7298i 0.203896 + 1.15635i 0.899167 + 0.437606i \(0.144173\pi\)
−0.695270 + 0.718748i \(0.744715\pi\)
\(662\) 16.5515 + 93.8682i 0.643292 + 3.64829i
\(663\) 0 0
\(664\) −3.01019 + 17.0716i −0.116818 + 0.662508i
\(665\) −6.81486 14.3290i −0.264269 0.555656i
\(666\) 0 0
\(667\) 1.66779 + 2.88870i 0.0645772 + 0.111851i
\(668\) 17.6801 100.269i 0.684065 3.87953i
\(669\) 0 0
\(670\) −50.9777 18.5543i −1.96944 0.716817i
\(671\) 1.88085 1.57822i 0.0726093 0.0609265i
\(672\) 0 0
\(673\) −4.39081 + 1.59812i −0.169253 + 0.0616032i −0.425257 0.905073i \(-0.639816\pi\)
0.256004 + 0.966676i \(0.417594\pi\)
\(674\) −35.6222 + 61.6995i −1.37212 + 2.37658i
\(675\) 0 0
\(676\) −58.3546 101.073i −2.24441 3.88743i
\(677\) −7.45224 + 42.2637i −0.286413 + 1.62433i 0.413782 + 0.910376i \(0.364207\pi\)
−0.700195 + 0.713952i \(0.746904\pi\)
\(678\) 0 0
\(679\) 1.51758 + 15.9483i 0.0582394 + 0.612041i
\(680\) 2.54128 + 14.4123i 0.0974535 + 0.552686i
\(681\) 0 0
\(682\) −0.831500 + 4.71567i −0.0318398 + 0.180572i
\(683\) 12.6608 0.484453 0.242226 0.970220i \(-0.422122\pi\)
0.242226 + 0.970220i \(0.422122\pi\)
\(684\) 0 0
\(685\) 9.04013 + 15.6580i 0.345406 + 0.598260i
\(686\) −28.7995 39.1956i −1.09957 1.49650i
\(687\) 0 0
\(688\) 68.1924 57.2202i 2.59981 2.18150i
\(689\) −1.90155 10.7842i −0.0724431 0.410845i
\(690\) 0 0
\(691\) −13.5951 11.4076i −0.517182 0.433967i 0.346466 0.938063i \(-0.387382\pi\)
−0.863648 + 0.504095i \(0.831826\pi\)
\(692\) −2.52289 4.36977i −0.0959059 0.166114i
\(693\) 0 0
\(694\) −11.2776 + 19.5333i −0.428091 + 0.741475i
\(695\) −20.6652 + 7.52151i −0.783875 + 0.285307i
\(696\) 0 0
\(697\) 1.68827 1.41663i 0.0639477 0.0536585i
\(698\) −1.07221 6.08078i −0.0405836 0.230161i
\(699\) 0 0
\(700\) 46.0877 + 45.3921i 1.74195 + 1.71566i
\(701\) 24.8305 0.937836 0.468918 0.883242i \(-0.344644\pi\)
0.468918 + 0.883242i \(0.344644\pi\)
\(702\) 0 0
\(703\) 1.96595 + 3.40513i 0.0741473 + 0.128427i
\(704\) −7.20298 6.04402i −0.271473 0.227792i
\(705\) 0 0
\(706\) −20.5526 + 17.2457i −0.773507 + 0.649049i
\(707\) −2.92752 30.7654i −0.110101 1.15705i
\(708\) 0 0
\(709\) −14.6093 + 5.31734i −0.548663 + 0.199697i −0.601452 0.798909i \(-0.705411\pi\)
0.0527894 + 0.998606i \(0.483189\pi\)
\(710\) −89.5879 −3.36217
\(711\) 0 0
\(712\) −40.9884 −1.53610
\(713\) 1.37736 7.81141i 0.0515826 0.292540i
\(714\) 0 0
\(715\) −17.0784 6.21603i −0.638696 0.232466i
\(716\) 35.0954 29.4485i 1.31158 1.10054i
\(717\) 0 0
\(718\) 3.95572 1.43976i 0.147626 0.0537315i
\(719\) 19.7368 0.736058 0.368029 0.929814i \(-0.380033\pi\)
0.368029 + 0.929814i \(0.380033\pi\)
\(720\) 0 0
\(721\) −14.4894 1.15671i −0.539612 0.0430780i
\(722\) 30.9834 + 25.9982i 1.15308 + 0.967551i
\(723\) 0 0
\(724\) 53.6732 45.0371i 1.99475 1.67379i
\(725\) −3.79724 1.38208i −0.141026 0.0513292i
\(726\) 0 0
\(727\) −37.4857 + 13.6437i −1.39027 + 0.506016i −0.925275 0.379298i \(-0.876165\pi\)
−0.464993 + 0.885314i \(0.653943\pi\)
\(728\) −69.3102 + 100.605i −2.56881 + 3.72866i
\(729\) 0 0
\(730\) −14.2444 + 24.6721i −0.527210 + 0.913155i
\(731\) −4.07302 3.41767i −0.150646 0.126407i
\(732\) 0 0
\(733\) −6.01589 34.1178i −0.222202 1.26017i −0.867963 0.496630i \(-0.834571\pi\)
0.645761 0.763540i \(-0.276540\pi\)
\(734\) 7.62845 + 43.2631i 0.281571 + 1.59687i
\(735\) 0 0
\(736\) 36.4244 + 30.5637i 1.34262 + 1.12659i
\(737\) −3.09525 5.36113i −0.114015 0.197480i
\(738\) 0 0
\(739\) −25.8684 + 44.8053i −0.951583 + 1.64819i −0.209583 + 0.977791i \(0.567211\pi\)
−0.742000 + 0.670400i \(0.766123\pi\)
\(740\) −24.5771 20.6227i −0.903473 0.758104i
\(741\) 0 0
\(742\) −10.2150 + 7.26899i −0.375004 + 0.266853i
\(743\) 33.5147 + 12.1984i 1.22954 + 0.447514i 0.873438 0.486935i \(-0.161885\pi\)
0.356097 + 0.934449i \(0.384107\pi\)
\(744\) 0 0
\(745\) −52.3923 + 19.0692i −1.91950 + 0.698642i
\(746\) 5.54841 9.61013i 0.203142 0.351852i
\(747\) 0 0
\(748\) −1.41143 + 2.44466i −0.0516069 + 0.0893857i
\(749\) −7.00805 + 26.9732i −0.256068 + 0.985578i
\(750\) 0 0
\(751\) 1.35923 + 0.494719i 0.0495990 + 0.0180526i 0.366701 0.930339i \(-0.380487\pi\)
−0.317102 + 0.948392i \(0.602710\pi\)
\(752\) 72.0158 + 26.2116i 2.62615 + 0.955839i
\(753\) 0 0
\(754\) 2.24009 12.7042i 0.0815793 0.462659i
\(755\) 7.65203 0.278486
\(756\) 0 0
\(757\) 11.1234 0.404286 0.202143 0.979356i \(-0.435209\pi\)
0.202143 + 0.979356i \(0.435209\pi\)
\(758\) 10.3237 58.5484i 0.374973 2.12657i
\(759\) 0 0
\(760\) 42.8775 + 15.6061i 1.55533 + 0.566095i
\(761\) 7.49316 + 2.72729i 0.271627 + 0.0988641i 0.474243 0.880394i \(-0.342722\pi\)
−0.202616 + 0.979258i \(0.564944\pi\)
\(762\) 0 0
\(763\) 23.8425 + 23.4826i 0.863157 + 0.850128i
\(764\) −12.1385 + 21.0245i −0.439155 + 0.760638i
\(765\) 0 0
\(766\) 25.3608 43.9263i 0.916324 1.58712i
\(767\) 66.8824 24.3432i 2.41498 0.878982i
\(768\) 0 0
\(769\) −9.08130 3.30532i −0.327480 0.119193i 0.173048 0.984913i \(-0.444638\pi\)
−0.500528 + 0.865720i \(0.666861\pi\)
\(770\) 1.97110 + 20.7144i 0.0710335 + 0.746494i
\(771\) 0 0
\(772\) 88.3796 + 74.1593i 3.18085 + 2.66905i
\(773\) −7.95869 + 13.7848i −0.286254 + 0.495807i −0.972913 0.231174i \(-0.925743\pi\)
0.686658 + 0.726980i \(0.259077\pi\)
\(774\) 0 0
\(775\) 4.80460 + 8.32182i 0.172586 + 0.298928i
\(776\) −35.2919 29.6134i −1.26690 1.06306i
\(777\) 0 0
\(778\) −2.17491 12.3345i −0.0779744 0.442215i
\(779\) −1.19322 6.76708i −0.0427515 0.242456i
\(780\) 0 0
\(781\) −7.83131 6.57125i −0.280226 0.235138i
\(782\) 3.29285 5.70338i 0.117752 0.203952i
\(783\) 0 0