Properties

Label 567.2.w.a.37.4
Level $567$
Weight $2$
Character 567.37
Analytic conductor $4.528$
Analytic rank $0$
Dimension $132$
Inner twists $2$

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [567,2,Mod(37,567)]
 
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([14, 6]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("567.37");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 567 = 3^{4} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 567.w (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 37.4
Character \(\chi\) \(=\) 567.37
Dual form 567.2.w.a.46.4

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.351787 - 1.99508i) q^{2} +(-1.97722 + 0.719650i) q^{4} +(-0.155052 + 0.879341i) q^{5} +(-1.72949 + 2.00222i) q^{7} +(0.105462 + 0.182666i) q^{8} +O(q^{10})\) \(q+(-0.351787 - 1.99508i) q^{2} +(-1.97722 + 0.719650i) q^{4} +(-0.155052 + 0.879341i) q^{5} +(-1.72949 + 2.00222i) q^{7} +(0.105462 + 0.182666i) q^{8} +1.80890 q^{10} +(0.545772 + 3.09523i) q^{11} +(3.46133 + 2.90440i) q^{13} +(4.60300 + 2.74612i) q^{14} +(-2.89636 + 2.43033i) q^{16} -5.74615 q^{17} +1.22738 q^{19} +(-0.326246 - 1.85024i) q^{20} +(5.98324 - 2.17772i) q^{22} +(4.25634 + 3.57150i) q^{23} +(3.94926 + 1.43741i) q^{25} +(4.57688 - 7.92738i) q^{26} +(1.97869 - 5.20345i) q^{28} +(0.0345809 - 0.0290169i) q^{29} +(0.226384 - 0.0823972i) q^{31} +(6.19078 + 5.19468i) q^{32} +(2.02142 + 11.4640i) q^{34} +(-1.49247 - 1.83126i) q^{35} +(5.13755 + 8.89849i) q^{37} +(-0.431777 - 2.44873i) q^{38} +(-0.176978 + 0.0644148i) q^{40} +(-3.74834 - 3.14523i) q^{41} +(-6.92531 - 2.52060i) q^{43} +(-3.30659 - 5.72718i) q^{44} +(5.62811 - 9.74817i) q^{46} +(-5.21418 - 1.89781i) q^{47} +(-1.01774 - 6.92562i) q^{49} +(1.47846 - 8.38478i) q^{50} +(-8.93398 - 3.25170i) q^{52} +(3.82297 + 6.62158i) q^{53} -2.80638 q^{55} +(-0.548134 - 0.104761i) q^{56} +(-0.0700562 - 0.0587841i) q^{58} +(2.88652 + 2.42208i) q^{59} +(-0.765603 - 0.278657i) q^{61} +(-0.244029 - 0.422670i) q^{62} +(4.40506 - 7.62979i) q^{64} +(-3.09065 + 2.59336i) q^{65} +(0.114256 - 0.647980i) q^{67} +(11.3614 - 4.13522i) q^{68} +(-3.12848 + 3.62182i) q^{70} +(-3.75882 + 6.51047i) q^{71} +(4.87293 - 8.44017i) q^{73} +(15.9459 - 13.3802i) q^{74} +(-2.42681 + 0.883285i) q^{76} +(-7.14122 - 4.26040i) q^{77} +(-2.29784 - 13.0317i) q^{79} +(-1.68801 - 2.92371i) q^{80} +(-4.95638 + 8.58471i) q^{82} +(-4.92372 + 4.13150i) q^{83} +(0.890949 - 5.05282i) q^{85} +(-2.59259 + 14.7033i) q^{86} +(-0.507835 + 0.426124i) q^{88} +12.6111 q^{89} +(-11.8016 + 1.90720i) q^{91} +(-10.9860 - 3.99856i) q^{92} +(-1.95200 + 11.0704i) q^{94} +(-0.190307 + 1.07929i) q^{95} +(-11.8862 - 4.32622i) q^{97} +(-13.4592 + 4.46682i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 132 q + 3 q^{2} - 3 q^{4} + 3 q^{5} - 6 q^{7} + 6 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 132 q + 3 q^{2} - 3 q^{4} + 3 q^{5} - 6 q^{7} + 6 q^{8} - 6 q^{10} - 3 q^{11} - 12 q^{13} - 15 q^{14} - 9 q^{16} + 54 q^{17} - 6 q^{19} + 18 q^{20} - 12 q^{22} - 3 q^{25} - 30 q^{26} - 12 q^{28} + 30 q^{29} - 3 q^{31} - 51 q^{32} - 18 q^{34} + 12 q^{35} + 3 q^{37} + 57 q^{38} - 66 q^{40} - 12 q^{43} - 3 q^{44} + 3 q^{46} + 21 q^{47} + 12 q^{49} + 39 q^{50} + 9 q^{52} - 9 q^{53} - 24 q^{55} - 57 q^{56} - 3 q^{58} + 18 q^{59} + 33 q^{61} - 75 q^{62} - 30 q^{64} - 81 q^{65} - 3 q^{67} - 6 q^{68} - 42 q^{70} + 18 q^{71} + 21 q^{73} + 93 q^{74} - 24 q^{76} - 87 q^{77} + 15 q^{79} - 102 q^{80} - 6 q^{82} + 42 q^{83} - 63 q^{85} - 159 q^{86} + 57 q^{88} + 150 q^{89} + 6 q^{91} + 66 q^{92} + 33 q^{94} + 147 q^{95} - 12 q^{97} - 99 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

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

\(n\) \(325\) \(407\)
\(\chi(n)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{7}{9}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.351787 1.99508i −0.248751 1.41074i −0.811617 0.584190i \(-0.801412\pi\)
0.562866 0.826548i \(-0.309699\pi\)
\(3\) 0 0
\(4\) −1.97722 + 0.719650i −0.988611 + 0.359825i
\(5\) −0.155052 + 0.879341i −0.0693412 + 0.393253i 0.930308 + 0.366778i \(0.119539\pi\)
−0.999649 + 0.0264748i \(0.991572\pi\)
\(6\) 0 0
\(7\) −1.72949 + 2.00222i −0.653685 + 0.756767i
\(8\) 0.105462 + 0.182666i 0.0372866 + 0.0645823i
\(9\) 0 0
\(10\) 1.80890 0.572026
\(11\) 0.545772 + 3.09523i 0.164556 + 0.933245i 0.949521 + 0.313704i \(0.101570\pi\)
−0.784964 + 0.619541i \(0.787319\pi\)
\(12\) 0 0
\(13\) 3.46133 + 2.90440i 0.960001 + 0.805536i 0.980953 0.194244i \(-0.0622253\pi\)
−0.0209522 + 0.999780i \(0.506670\pi\)
\(14\) 4.60300 + 2.74612i 1.23020 + 0.733932i
\(15\) 0 0
\(16\) −2.89636 + 2.43033i −0.724090 + 0.607583i
\(17\) −5.74615 −1.39365 −0.696823 0.717243i \(-0.745404\pi\)
−0.696823 + 0.717243i \(0.745404\pi\)
\(18\) 0 0
\(19\) 1.22738 0.281581 0.140790 0.990039i \(-0.455036\pi\)
0.140790 + 0.990039i \(0.455036\pi\)
\(20\) −0.326246 1.85024i −0.0729509 0.413725i
\(21\) 0 0
\(22\) 5.98324 2.17772i 1.27563 0.464292i
\(23\) 4.25634 + 3.57150i 0.887509 + 0.744709i 0.967709 0.252070i \(-0.0811114\pi\)
−0.0801999 + 0.996779i \(0.525556\pi\)
\(24\) 0 0
\(25\) 3.94926 + 1.43741i 0.789853 + 0.287483i
\(26\) 4.57688 7.92738i 0.897599 1.55469i
\(27\) 0 0
\(28\) 1.97869 5.20345i 0.373937 0.983360i
\(29\) 0.0345809 0.0290169i 0.00642152 0.00538829i −0.639571 0.768732i \(-0.720888\pi\)
0.645993 + 0.763344i \(0.276444\pi\)
\(30\) 0 0
\(31\) 0.226384 0.0823972i 0.0406599 0.0147990i −0.321610 0.946872i \(-0.604224\pi\)
0.362270 + 0.932073i \(0.382002\pi\)
\(32\) 6.19078 + 5.19468i 1.09439 + 0.918298i
\(33\) 0 0
\(34\) 2.02142 + 11.4640i 0.346671 + 1.96607i
\(35\) −1.49247 1.83126i −0.252274 0.309539i
\(36\) 0 0
\(37\) 5.13755 + 8.89849i 0.844607 + 1.46290i 0.885962 + 0.463758i \(0.153499\pi\)
−0.0413547 + 0.999145i \(0.513167\pi\)
\(38\) −0.431777 2.44873i −0.0700435 0.397236i
\(39\) 0 0
\(40\) −0.176978 + 0.0644148i −0.0279827 + 0.0101849i
\(41\) −3.74834 3.14523i −0.585392 0.491203i 0.301321 0.953523i \(-0.402573\pi\)
−0.886713 + 0.462320i \(0.847017\pi\)
\(42\) 0 0
\(43\) −6.92531 2.52060i −1.05610 0.384389i −0.245138 0.969488i \(-0.578833\pi\)
−0.810961 + 0.585100i \(0.801055\pi\)
\(44\) −3.30659 5.72718i −0.498487 0.863405i
\(45\) 0 0
\(46\) 5.62811 9.74817i 0.829820 1.43729i
\(47\) −5.21418 1.89781i −0.760567 0.276824i −0.0675215 0.997718i \(-0.521509\pi\)
−0.693045 + 0.720894i \(0.743731\pi\)
\(48\) 0 0
\(49\) −1.01774 6.92562i −0.145391 0.989374i
\(50\) 1.47846 8.38478i 0.209086 1.18579i
\(51\) 0 0
\(52\) −8.93398 3.25170i −1.23892 0.450930i
\(53\) 3.82297 + 6.62158i 0.525126 + 0.909545i 0.999572 + 0.0292600i \(0.00931508\pi\)
−0.474446 + 0.880285i \(0.657352\pi\)
\(54\) 0 0
\(55\) −2.80638 −0.378412
\(56\) −0.548134 0.104761i −0.0732475 0.0139992i
\(57\) 0 0
\(58\) −0.0700562 0.0587841i −0.00919883 0.00771874i
\(59\) 2.88652 + 2.42208i 0.375793 + 0.315328i 0.811048 0.584979i \(-0.198897\pi\)
−0.435255 + 0.900307i \(0.643342\pi\)
\(60\) 0 0
\(61\) −0.765603 0.278657i −0.0980254 0.0356783i 0.292542 0.956253i \(-0.405499\pi\)
−0.390567 + 0.920574i \(0.627721\pi\)
\(62\) −0.244029 0.422670i −0.0309917 0.0536791i
\(63\) 0 0
\(64\) 4.40506 7.62979i 0.550633 0.953724i
\(65\) −3.09065 + 2.59336i −0.383347 + 0.321667i
\(66\) 0 0
\(67\) 0.114256 0.647980i 0.0139586 0.0791633i −0.977033 0.213090i \(-0.931647\pi\)
0.990991 + 0.133926i \(0.0427585\pi\)
\(68\) 11.3614 4.13522i 1.37777 0.501469i
\(69\) 0 0
\(70\) −3.12848 + 3.62182i −0.373925 + 0.432890i
\(71\) −3.75882 + 6.51047i −0.446090 + 0.772650i −0.998127 0.0611691i \(-0.980517\pi\)
0.552038 + 0.833819i \(0.313850\pi\)
\(72\) 0 0
\(73\) 4.87293 8.44017i 0.570334 0.987847i −0.426198 0.904630i \(-0.640147\pi\)
0.996531 0.0832170i \(-0.0265195\pi\)
\(74\) 15.9459 13.3802i 1.85367 1.55542i
\(75\) 0 0
\(76\) −2.42681 + 0.883285i −0.278374 + 0.101320i
\(77\) −7.14122 4.26040i −0.813817 0.485518i
\(78\) 0 0
\(79\) −2.29784 13.0317i −0.258527 1.46618i −0.786854 0.617139i \(-0.788292\pi\)
0.528327 0.849041i \(-0.322820\pi\)
\(80\) −1.68801 2.92371i −0.188725 0.326881i
\(81\) 0 0
\(82\) −4.95638 + 8.58471i −0.547341 + 0.948022i
\(83\) −4.92372 + 4.13150i −0.540449 + 0.453490i −0.871691 0.490055i \(-0.836977\pi\)
0.331242 + 0.943546i \(0.392532\pi\)
\(84\) 0 0
\(85\) 0.890949 5.05282i 0.0966370 0.548055i
\(86\) −2.59259 + 14.7033i −0.279566 + 1.58550i
\(87\) 0 0
\(88\) −0.507835 + 0.426124i −0.0541354 + 0.0454250i
\(89\) 12.6111 1.33678 0.668388 0.743812i \(-0.266984\pi\)
0.668388 + 0.743812i \(0.266984\pi\)
\(90\) 0 0
\(91\) −11.8016 + 1.90720i −1.23714 + 0.199929i
\(92\) −10.9860 3.99856i −1.14537 0.416879i
\(93\) 0 0
\(94\) −1.95200 + 11.0704i −0.201334 + 1.14182i
\(95\) −0.190307 + 1.07929i −0.0195251 + 0.110732i
\(96\) 0 0
\(97\) −11.8862 4.32622i −1.20686 0.439261i −0.341246 0.939974i \(-0.610849\pi\)
−0.865613 + 0.500713i \(0.833071\pi\)
\(98\) −13.4592 + 4.46682i −1.35958 + 0.451217i
\(99\) 0 0
\(100\) −8.84301 −0.884301
\(101\) −7.78093 + 6.52898i −0.774232 + 0.649658i −0.941789 0.336205i \(-0.890857\pi\)
0.167557 + 0.985862i \(0.446412\pi\)
\(102\) 0 0
\(103\) −2.60057 + 14.7486i −0.256242 + 1.45322i 0.536622 + 0.843823i \(0.319700\pi\)
−0.792864 + 0.609399i \(0.791411\pi\)
\(104\) −0.165496 + 0.938575i −0.0162282 + 0.0920348i
\(105\) 0 0
\(106\) 11.8657 9.95654i 1.15250 0.967065i
\(107\) −7.28317 + 12.6148i −0.704090 + 1.21952i 0.262929 + 0.964815i \(0.415312\pi\)
−0.967019 + 0.254705i \(0.918022\pi\)
\(108\) 0 0
\(109\) −1.69401 2.93411i −0.162257 0.281037i 0.773421 0.633893i \(-0.218544\pi\)
−0.935678 + 0.352856i \(0.885211\pi\)
\(110\) 0.987249 + 5.59897i 0.0941305 + 0.533841i
\(111\) 0 0
\(112\) 0.143166 10.0024i 0.0135279 0.945135i
\(113\) 12.6640 4.60933i 1.19133 0.433609i 0.331140 0.943582i \(-0.392567\pi\)
0.860191 + 0.509973i \(0.170344\pi\)
\(114\) 0 0
\(115\) −3.80052 + 3.18901i −0.354400 + 0.297377i
\(116\) −0.0474922 + 0.0822590i −0.00440954 + 0.00763755i
\(117\) 0 0
\(118\) 3.81681 6.61092i 0.351366 0.608584i
\(119\) 9.93789 11.5050i 0.911005 1.05466i
\(120\) 0 0
\(121\) 1.05407 0.383649i 0.0958243 0.0348772i
\(122\) −0.286614 + 1.62547i −0.0259488 + 0.147163i
\(123\) 0 0
\(124\) −0.388315 + 0.325835i −0.0348717 + 0.0292609i
\(125\) −4.10858 + 7.11627i −0.367483 + 0.636499i
\(126\) 0 0
\(127\) 5.56469 + 9.63833i 0.493786 + 0.855263i 0.999974 0.00716008i \(-0.00227914\pi\)
−0.506188 + 0.862423i \(0.668946\pi\)
\(128\) −1.58349 0.576343i −0.139962 0.0509420i
\(129\) 0 0
\(130\) 6.26122 + 5.25379i 0.549145 + 0.460788i
\(131\) −6.02780 5.05793i −0.526651 0.441913i 0.340292 0.940320i \(-0.389474\pi\)
−0.866943 + 0.498407i \(0.833919\pi\)
\(132\) 0 0
\(133\) −2.12274 + 2.45748i −0.184065 + 0.213091i
\(134\) −1.33297 −0.115151
\(135\) 0 0
\(136\) −0.606003 1.04963i −0.0519643 0.0900048i
\(137\) 1.64156 + 0.597477i 0.140248 + 0.0510459i 0.411190 0.911550i \(-0.365113\pi\)
−0.270943 + 0.962595i \(0.587335\pi\)
\(138\) 0 0
\(139\) −2.01511 + 11.4282i −0.170919 + 0.969330i 0.771830 + 0.635828i \(0.219341\pi\)
−0.942749 + 0.333502i \(0.891770\pi\)
\(140\) 4.26881 + 2.54674i 0.360780 + 0.215239i
\(141\) 0 0
\(142\) 14.3112 + 5.20886i 1.20097 + 0.437118i
\(143\) −7.10068 + 12.2987i −0.593789 + 1.02847i
\(144\) 0 0
\(145\) 0.0201539 + 0.0349075i 0.00167369 + 0.00289891i
\(146\) −18.5531 6.75277i −1.53546 0.558863i
\(147\) 0 0
\(148\) −16.5619 13.8971i −1.36138 1.14233i
\(149\) 8.57674 3.12168i 0.702634 0.255738i 0.0340988 0.999418i \(-0.489144\pi\)
0.668535 + 0.743681i \(0.266922\pi\)
\(150\) 0 0
\(151\) 1.62003 + 9.18763i 0.131836 + 0.747678i 0.977011 + 0.213189i \(0.0683850\pi\)
−0.845175 + 0.534490i \(0.820504\pi\)
\(152\) 0.129443 + 0.224201i 0.0104992 + 0.0181851i
\(153\) 0 0
\(154\) −5.98768 + 15.7461i −0.482501 + 1.26886i
\(155\) 0.0373540 + 0.211845i 0.00300034 + 0.0170158i
\(156\) 0 0
\(157\) 10.0221 + 8.40952i 0.799849 + 0.671153i 0.948162 0.317787i \(-0.102940\pi\)
−0.148313 + 0.988940i \(0.547384\pi\)
\(158\) −25.1910 + 9.16877i −2.00409 + 0.729428i
\(159\) 0 0
\(160\) −5.52778 + 4.63836i −0.437010 + 0.366695i
\(161\) −14.5122 + 2.34526i −1.14372 + 0.184832i
\(162\) 0 0
\(163\) 2.67921 4.64053i 0.209852 0.363474i −0.741816 0.670604i \(-0.766035\pi\)
0.951668 + 0.307129i \(0.0993684\pi\)
\(164\) 9.67477 + 3.52133i 0.755472 + 0.274969i
\(165\) 0 0
\(166\) 9.97478 + 8.36984i 0.774193 + 0.649625i
\(167\) −6.66051 + 2.42423i −0.515406 + 0.187592i −0.586610 0.809869i \(-0.699538\pi\)
0.0712043 + 0.997462i \(0.477316\pi\)
\(168\) 0 0
\(169\) 1.28784 + 7.30371i 0.0990647 + 0.561824i
\(170\) −10.3942 −0.797201
\(171\) 0 0
\(172\) 15.5068 1.18238
\(173\) 13.8890 11.6542i 1.05596 0.886054i 0.0622501 0.998061i \(-0.480172\pi\)
0.993707 + 0.112007i \(0.0357279\pi\)
\(174\) 0 0
\(175\) −9.70822 + 5.42129i −0.733872 + 0.409811i
\(176\) −9.10318 7.63847i −0.686178 0.575772i
\(177\) 0 0
\(178\) −4.43643 25.1603i −0.332525 1.88584i
\(179\) 15.9280 1.19052 0.595259 0.803534i \(-0.297049\pi\)
0.595259 + 0.803534i \(0.297049\pi\)
\(180\) 0 0
\(181\) −11.7915 20.4235i −0.876456 1.51807i −0.855203 0.518293i \(-0.826568\pi\)
−0.0212529 0.999774i \(-0.506766\pi\)
\(182\) 7.95668 + 22.8742i 0.589788 + 1.69555i
\(183\) 0 0
\(184\) −0.203508 + 1.15415i −0.0150028 + 0.0850851i
\(185\) −8.62139 + 3.13793i −0.633857 + 0.230705i
\(186\) 0 0
\(187\) −3.13608 17.7856i −0.229333 1.30061i
\(188\) 11.6754 0.851513
\(189\) 0 0
\(190\) 2.22022 0.161071
\(191\) −3.73858 21.2025i −0.270514 1.53416i −0.752860 0.658181i \(-0.771326\pi\)
0.482345 0.875981i \(-0.339785\pi\)
\(192\) 0 0
\(193\) −8.25517 + 3.00464i −0.594220 + 0.216278i −0.621584 0.783347i \(-0.713511\pi\)
0.0273645 + 0.999626i \(0.491289\pi\)
\(194\) −4.44976 + 25.2359i −0.319474 + 1.81183i
\(195\) 0 0
\(196\) 6.99632 + 12.9611i 0.499737 + 0.925791i
\(197\) −1.67466 2.90060i −0.119315 0.206659i 0.800182 0.599758i \(-0.204736\pi\)
−0.919496 + 0.393099i \(0.871403\pi\)
\(198\) 0 0
\(199\) −11.4381 −0.810825 −0.405413 0.914134i \(-0.632872\pi\)
−0.405413 + 0.914134i \(0.632872\pi\)
\(200\) 0.153932 + 0.872991i 0.0108846 + 0.0617298i
\(201\) 0 0
\(202\) 15.7631 + 13.2268i 1.10909 + 0.930635i
\(203\) −0.00170932 + 0.119423i −0.000119971 + 0.00838184i
\(204\) 0 0
\(205\) 3.34692 2.80840i 0.233759 0.196147i
\(206\) 30.3395 2.11386
\(207\) 0 0
\(208\) −17.0839 −1.18456
\(209\) 0.669870 + 3.79902i 0.0463359 + 0.262784i
\(210\) 0 0
\(211\) 16.9946 6.18552i 1.16995 0.425829i 0.317311 0.948322i \(-0.397220\pi\)
0.852644 + 0.522493i \(0.174998\pi\)
\(212\) −12.3241 10.3411i −0.846422 0.710233i
\(213\) 0 0
\(214\) 27.7297 + 10.0928i 1.89557 + 0.689930i
\(215\) 3.29025 5.69888i 0.224393 0.388660i
\(216\) 0 0
\(217\) −0.226552 + 0.595776i −0.0153794 + 0.0404439i
\(218\) −5.25786 + 4.41187i −0.356107 + 0.298810i
\(219\) 0 0
\(220\) 5.54884 2.01961i 0.374103 0.136162i
\(221\) −19.8893 16.6891i −1.33790 1.12263i
\(222\) 0 0
\(223\) −2.13914 12.1316i −0.143247 0.812395i −0.968758 0.248008i \(-0.920224\pi\)
0.825511 0.564386i \(-0.190887\pi\)
\(224\) −21.1078 + 3.41114i −1.41032 + 0.227916i
\(225\) 0 0
\(226\) −13.6510 23.6443i −0.908053 1.57279i
\(227\) 4.13532 + 23.4526i 0.274471 + 1.55660i 0.740638 + 0.671904i \(0.234523\pi\)
−0.466168 + 0.884696i \(0.654366\pi\)
\(228\) 0 0
\(229\) 21.2430 7.73183i 1.40378 0.510933i 0.474481 0.880266i \(-0.342636\pi\)
0.929297 + 0.369333i \(0.120414\pi\)
\(230\) 7.69932 + 6.46050i 0.507678 + 0.425993i
\(231\) 0 0
\(232\) 0.00894740 + 0.00325659i 0.000587425 + 0.000213805i
\(233\) 0.152366 + 0.263905i 0.00998180 + 0.0172890i 0.870973 0.491331i \(-0.163489\pi\)
−0.860991 + 0.508620i \(0.830156\pi\)
\(234\) 0 0
\(235\) 2.47729 4.29079i 0.161600 0.279900i
\(236\) −7.45035 2.71171i −0.484977 0.176517i
\(237\) 0 0
\(238\) −26.4495 15.7796i −1.71447 1.02284i
\(239\) 4.19570 23.7950i 0.271397 1.53917i −0.478780 0.877935i \(-0.658921\pi\)
0.750178 0.661236i \(-0.229968\pi\)
\(240\) 0 0
\(241\) −13.4282 4.88748i −0.864989 0.314830i −0.128853 0.991664i \(-0.541129\pi\)
−0.736136 + 0.676834i \(0.763352\pi\)
\(242\) −1.13622 1.96799i −0.0730390 0.126507i
\(243\) 0 0
\(244\) 1.71430 0.109747
\(245\) 6.24778 + 0.178888i 0.399156 + 0.0114287i
\(246\) 0 0
\(247\) 4.24838 + 3.56481i 0.270318 + 0.226823i
\(248\) 0.0389263 + 0.0326630i 0.00247182 + 0.00207410i
\(249\) 0 0
\(250\) 15.6429 + 5.69355i 0.989345 + 0.360092i
\(251\) −1.67494 2.90107i −0.105721 0.183114i 0.808312 0.588755i \(-0.200382\pi\)
−0.914033 + 0.405641i \(0.867048\pi\)
\(252\) 0 0
\(253\) −8.73159 + 15.1236i −0.548951 + 0.950810i
\(254\) 17.2717 14.4927i 1.08372 0.909351i
\(255\) 0 0
\(256\) 2.46692 13.9906i 0.154183 0.874413i
\(257\) 16.9888 6.18343i 1.05973 0.385711i 0.247405 0.968912i \(-0.420422\pi\)
0.812328 + 0.583201i \(0.198200\pi\)
\(258\) 0 0
\(259\) −26.7020 5.10336i −1.65918 0.317107i
\(260\) 4.24458 7.35183i 0.263238 0.455941i
\(261\) 0 0
\(262\) −7.97049 + 13.8053i −0.492418 + 0.852893i
\(263\) 18.5162 15.5369i 1.14176 0.958049i 0.142263 0.989829i \(-0.454562\pi\)
0.999495 + 0.0317800i \(0.0101176\pi\)
\(264\) 0 0
\(265\) −6.41539 + 2.33501i −0.394094 + 0.143439i
\(266\) 5.64964 + 3.37054i 0.346402 + 0.206661i
\(267\) 0 0
\(268\) 0.240409 + 1.36342i 0.0146853 + 0.0832844i
\(269\) −7.45250 12.9081i −0.454387 0.787022i 0.544266 0.838913i \(-0.316808\pi\)
−0.998653 + 0.0518912i \(0.983475\pi\)
\(270\) 0 0
\(271\) −2.69114 + 4.66119i −0.163475 + 0.283147i −0.936113 0.351700i \(-0.885604\pi\)
0.772638 + 0.634847i \(0.218937\pi\)
\(272\) 16.6429 13.9651i 1.00912 0.846756i
\(273\) 0 0
\(274\) 0.614540 3.48523i 0.0371257 0.210550i
\(275\) −2.29372 + 13.0084i −0.138317 + 0.784434i
\(276\) 0 0
\(277\) −0.775246 + 0.650509i −0.0465800 + 0.0390853i −0.665780 0.746148i \(-0.731901\pi\)
0.619200 + 0.785233i \(0.287457\pi\)
\(278\) 23.5092 1.40999
\(279\) 0 0
\(280\) 0.177109 0.465753i 0.0105843 0.0278341i
\(281\) 12.2222 + 4.44851i 0.729114 + 0.265376i 0.679790 0.733407i \(-0.262071\pi\)
0.0493245 + 0.998783i \(0.484293\pi\)
\(282\) 0 0
\(283\) −3.28461 + 18.6280i −0.195250 + 1.10732i 0.716812 + 0.697266i \(0.245600\pi\)
−0.912062 + 0.410052i \(0.865511\pi\)
\(284\) 2.74676 15.5777i 0.162990 0.924365i
\(285\) 0 0
\(286\) 27.0350 + 9.83992i 1.59861 + 0.581847i
\(287\) 12.7801 2.06535i 0.754388 0.121914i
\(288\) 0 0
\(289\) 16.0182 0.942247
\(290\) 0.0625536 0.0524887i 0.00367328 0.00308224i
\(291\) 0 0
\(292\) −3.56091 + 20.1949i −0.208386 + 1.18182i
\(293\) 0.436945 2.47804i 0.0255266 0.144769i −0.969381 0.245563i \(-0.921027\pi\)
0.994907 + 0.100794i \(0.0321384\pi\)
\(294\) 0 0
\(295\) −2.57739 + 2.16269i −0.150062 + 0.125917i
\(296\) −1.08364 + 1.87691i −0.0629851 + 0.109093i
\(297\) 0 0
\(298\) −9.24520 16.0132i −0.535560 0.927617i
\(299\) 4.35956 + 24.7243i 0.252120 + 1.42984i
\(300\) 0 0
\(301\) 17.0240 9.50660i 0.981249 0.547951i
\(302\) 17.7602 6.46418i 1.02198 0.371972i
\(303\) 0 0
\(304\) −3.55494 + 2.98295i −0.203890 + 0.171084i
\(305\) 0.363742 0.630020i 0.0208278 0.0360748i
\(306\) 0 0
\(307\) 3.33310 5.77311i 0.190230 0.329489i −0.755096 0.655614i \(-0.772410\pi\)
0.945326 + 0.326125i \(0.105743\pi\)
\(308\) 17.1858 + 3.28459i 0.979250 + 0.187157i
\(309\) 0 0
\(310\) 0.409508 0.149049i 0.0232585 0.00846540i
\(311\) 2.53672 14.3865i 0.143844 0.815782i −0.824444 0.565944i \(-0.808512\pi\)
0.968288 0.249837i \(-0.0803772\pi\)
\(312\) 0 0
\(313\) 16.7927 14.0907i 0.949177 0.796454i −0.0299819 0.999550i \(-0.509545\pi\)
0.979159 + 0.203097i \(0.0651005\pi\)
\(314\) 13.2521 22.9533i 0.747858 1.29533i
\(315\) 0 0
\(316\) 13.9216 + 24.1129i 0.783151 + 1.35646i
\(317\) −8.74471 3.18282i −0.491152 0.178765i 0.0845581 0.996419i \(-0.473052\pi\)
−0.575710 + 0.817654i \(0.695274\pi\)
\(318\) 0 0
\(319\) 0.108687 + 0.0911992i 0.00608530 + 0.00510618i
\(320\) 6.02617 + 5.05656i 0.336873 + 0.282670i
\(321\) 0 0
\(322\) 9.78420 + 28.1280i 0.545252 + 1.56751i
\(323\) −7.05271 −0.392423
\(324\) 0 0
\(325\) 9.49489 + 16.4456i 0.526681 + 0.912239i
\(326\) −10.2008 3.71277i −0.564968 0.205631i
\(327\) 0 0
\(328\) 0.179219 1.01640i 0.00989570 0.0561213i
\(329\) 12.8177 7.15768i 0.706662 0.394616i
\(330\) 0 0
\(331\) −12.7757 4.64997i −0.702215 0.255585i −0.0338587 0.999427i \(-0.510780\pi\)
−0.668356 + 0.743841i \(0.733002\pi\)
\(332\) 6.76207 11.7122i 0.371117 0.642793i
\(333\) 0 0
\(334\) 7.17963 + 12.4355i 0.392852 + 0.680439i
\(335\) 0.552080 + 0.200941i 0.0301633 + 0.0109786i
\(336\) 0 0
\(337\) −18.7794 15.7578i −1.02298 0.858382i −0.0329809 0.999456i \(-0.510500\pi\)
−0.989999 + 0.141074i \(0.954944\pi\)
\(338\) 14.1185 5.13870i 0.767944 0.279509i
\(339\) 0 0
\(340\) 1.87466 + 10.6317i 0.101668 + 0.576586i
\(341\) 0.378592 + 0.655741i 0.0205019 + 0.0355104i
\(342\) 0 0
\(343\) 15.6268 + 9.94005i 0.843766 + 0.536712i
\(344\) −0.269930 1.53085i −0.0145537 0.0825379i
\(345\) 0 0
\(346\) −28.1371 23.6098i −1.51266 1.26927i
\(347\) −11.7888 + 4.29078i −0.632858 + 0.230341i −0.638475 0.769643i \(-0.720434\pi\)
0.00561693 + 0.999984i \(0.498212\pi\)
\(348\) 0 0
\(349\) 19.9884 16.7723i 1.06996 0.897800i 0.0749083 0.997190i \(-0.476134\pi\)
0.995049 + 0.0993900i \(0.0316891\pi\)
\(350\) 14.2312 + 17.4616i 0.760687 + 0.933361i
\(351\) 0 0
\(352\) −12.7000 + 21.9970i −0.676910 + 1.17244i
\(353\) −22.3840 8.14711i −1.19138 0.433627i −0.331172 0.943570i \(-0.607444\pi\)
−0.860208 + 0.509944i \(0.829666\pi\)
\(354\) 0 0
\(355\) −5.14211 4.31474i −0.272915 0.229003i
\(356\) −24.9350 + 9.07560i −1.32155 + 0.481006i
\(357\) 0 0
\(358\) −5.60328 31.7778i −0.296143 1.67951i
\(359\) 18.6890 0.986366 0.493183 0.869926i \(-0.335833\pi\)
0.493183 + 0.869926i \(0.335833\pi\)
\(360\) 0 0
\(361\) −17.4935 −0.920712
\(362\) −36.5985 + 30.7098i −1.92357 + 1.61407i
\(363\) 0 0
\(364\) 21.9618 12.2640i 1.15111 0.642807i
\(365\) 6.66623 + 5.59363i 0.348926 + 0.292784i
\(366\) 0 0
\(367\) 4.28546 + 24.3040i 0.223699 + 1.26866i 0.865157 + 0.501501i \(0.167219\pi\)
−0.641458 + 0.767158i \(0.721670\pi\)
\(368\) −21.0078 −1.09511
\(369\) 0 0
\(370\) 9.29333 + 16.0965i 0.483137 + 0.836818i
\(371\) −19.8696 3.79753i −1.03158 0.197158i
\(372\) 0 0
\(373\) 5.21360 29.5678i 0.269950 1.53096i −0.484610 0.874730i \(-0.661038\pi\)
0.754560 0.656231i \(-0.227850\pi\)
\(374\) −34.3806 + 12.5135i −1.77778 + 0.647058i
\(375\) 0 0
\(376\) −0.203235 1.15260i −0.0104810 0.0594410i
\(377\) 0.203973 0.0105051
\(378\) 0 0
\(379\) 29.6444 1.52273 0.761365 0.648324i \(-0.224530\pi\)
0.761365 + 0.648324i \(0.224530\pi\)
\(380\) −0.400429 2.27094i −0.0205416 0.116497i
\(381\) 0 0
\(382\) −40.9857 + 14.9176i −2.09701 + 0.763249i
\(383\) −0.542179 + 3.07485i −0.0277040 + 0.157117i −0.995521 0.0945361i \(-0.969863\pi\)
0.967817 + 0.251654i \(0.0809743\pi\)
\(384\) 0 0
\(385\) 4.85360 5.61898i 0.247363 0.286370i
\(386\) 8.89856 + 15.4128i 0.452925 + 0.784489i
\(387\) 0 0
\(388\) 26.6150 1.35117
\(389\) 1.24377 + 7.05376i 0.0630615 + 0.357640i 0.999968 + 0.00805830i \(0.00256506\pi\)
−0.936906 + 0.349581i \(0.886324\pi\)
\(390\) 0 0
\(391\) −24.4576 20.5223i −1.23687 1.03786i
\(392\) 1.15774 0.916300i 0.0584749 0.0462801i
\(393\) 0 0
\(394\) −5.19781 + 4.36148i −0.261862 + 0.219728i
\(395\) 11.8156 0.594507
\(396\) 0 0
\(397\) 18.4934 0.928157 0.464079 0.885794i \(-0.346386\pi\)
0.464079 + 0.885794i \(0.346386\pi\)
\(398\) 4.02378 + 22.8200i 0.201694 + 1.14386i
\(399\) 0 0
\(400\) −14.9319 + 5.43476i −0.746594 + 0.271738i
\(401\) 14.0554 + 11.7939i 0.701896 + 0.588960i 0.922312 0.386445i \(-0.126297\pi\)
−0.220417 + 0.975406i \(0.570742\pi\)
\(402\) 0 0
\(403\) 1.02291 + 0.372308i 0.0509546 + 0.0185460i
\(404\) 10.6861 18.5088i 0.531651 0.920847i
\(405\) 0 0
\(406\) 0.238860 0.0386012i 0.0118544 0.00191574i
\(407\) −24.7389 + 20.7584i −1.22626 + 1.02896i
\(408\) 0 0
\(409\) 0.100901 0.0367251i 0.00498925 0.00181594i −0.339524 0.940597i \(-0.610266\pi\)
0.344514 + 0.938781i \(0.388044\pi\)
\(410\) −6.78039 5.68942i −0.334860 0.280981i
\(411\) 0 0
\(412\) −5.47191 31.0328i −0.269582 1.52887i
\(413\) −9.84174 + 1.59048i −0.484280 + 0.0782626i
\(414\) 0 0
\(415\) −2.86956 4.97023i −0.140861 0.243979i
\(416\) 6.34090 + 35.9610i 0.310888 + 1.76313i
\(417\) 0 0
\(418\) 7.34372 2.67289i 0.359193 0.130736i
\(419\) −1.12657 0.945301i −0.0550364 0.0461810i 0.614855 0.788641i \(-0.289215\pi\)
−0.669891 + 0.742460i \(0.733659\pi\)
\(420\) 0 0
\(421\) 29.7174 + 10.8162i 1.44834 + 0.527152i 0.942126 0.335258i \(-0.108823\pi\)
0.506211 + 0.862410i \(0.331046\pi\)
\(422\) −18.3191 31.7296i −0.891760 1.54457i
\(423\) 0 0
\(424\) −0.806361 + 1.39666i −0.0391603 + 0.0678277i
\(425\) −22.6930 8.25959i −1.10077 0.400649i
\(426\) 0 0
\(427\) 1.88203 1.05097i 0.0910779 0.0508600i
\(428\) 5.32219 30.1836i 0.257258 1.45898i
\(429\) 0 0
\(430\) −12.5272 4.55953i −0.604116 0.219880i
\(431\) 13.4216 + 23.2470i 0.646498 + 1.11977i 0.983953 + 0.178425i \(0.0571003\pi\)
−0.337456 + 0.941341i \(0.609566\pi\)
\(432\) 0 0
\(433\) 4.77702 0.229569 0.114785 0.993390i \(-0.463382\pi\)
0.114785 + 0.993390i \(0.463382\pi\)
\(434\) 1.26832 + 0.242405i 0.0608814 + 0.0116358i
\(435\) 0 0
\(436\) 5.46096 + 4.58229i 0.261533 + 0.219452i
\(437\) 5.22416 + 4.38359i 0.249905 + 0.209695i
\(438\) 0 0
\(439\) −18.9217 6.88695i −0.903086 0.328696i −0.151597 0.988442i \(-0.548442\pi\)
−0.751489 + 0.659746i \(0.770664\pi\)
\(440\) −0.295968 0.512631i −0.0141097 0.0244387i
\(441\) 0 0
\(442\) −26.2994 + 45.5519i −1.25094 + 2.16668i
\(443\) −20.6066 + 17.2910i −0.979048 + 0.821518i −0.983945 0.178470i \(-0.942885\pi\)
0.00489783 + 0.999988i \(0.498441\pi\)
\(444\) 0 0
\(445\) −1.95537 + 11.0895i −0.0926936 + 0.525692i
\(446\) −23.4511 + 8.53551i −1.11044 + 0.404168i
\(447\) 0 0
\(448\) 7.65798 + 22.0155i 0.361806 + 1.04014i
\(449\) −7.02501 + 12.1677i −0.331531 + 0.574228i −0.982812 0.184608i \(-0.940898\pi\)
0.651281 + 0.758836i \(0.274232\pi\)
\(450\) 0 0
\(451\) 7.68946 13.3185i 0.362083 0.627145i
\(452\) −21.7225 + 18.2273i −1.02174 + 0.857341i
\(453\) 0 0
\(454\) 45.3351 16.5006i 2.12768 0.774412i
\(455\) 0.152769 10.6733i 0.00716194 0.500373i
\(456\) 0 0
\(457\) 6.37787 + 36.1707i 0.298344 + 1.69199i 0.653291 + 0.757107i \(0.273388\pi\)
−0.354947 + 0.934886i \(0.615501\pi\)
\(458\) −22.8987 39.6617i −1.06998 1.85327i
\(459\) 0 0
\(460\) 5.21949 9.04043i 0.243360 0.421512i
\(461\) 32.4211 27.2046i 1.51000 1.26704i 0.646251 0.763125i \(-0.276336\pi\)
0.863752 0.503917i \(-0.168108\pi\)
\(462\) 0 0
\(463\) −3.29439 + 18.6834i −0.153103 + 0.868293i 0.807396 + 0.590010i \(0.200876\pi\)
−0.960499 + 0.278283i \(0.910235\pi\)
\(464\) −0.0296382 + 0.168086i −0.00137592 + 0.00780322i
\(465\) 0 0
\(466\) 0.472912 0.396820i 0.0219072 0.0183824i
\(467\) −14.9158 −0.690219 −0.345110 0.938562i \(-0.612158\pi\)
−0.345110 + 0.938562i \(0.612158\pi\)
\(468\) 0 0
\(469\) 1.09979 + 1.34944i 0.0507836 + 0.0623113i
\(470\) −9.43196 3.43295i −0.435064 0.158350i
\(471\) 0 0
\(472\) −0.138013 + 0.782710i −0.00635255 + 0.0360271i
\(473\) 4.02220 22.8111i 0.184941 1.04885i
\(474\) 0 0
\(475\) 4.84725 + 1.76426i 0.222407 + 0.0809496i
\(476\) −11.3698 + 29.8998i −0.521135 + 1.37046i
\(477\) 0 0
\(478\) −48.9490 −2.23888
\(479\) −10.1870 + 8.54789i −0.465455 + 0.390563i −0.845133 0.534555i \(-0.820479\pi\)
0.379678 + 0.925119i \(0.376035\pi\)
\(480\) 0 0
\(481\) −8.06205 + 45.7221i −0.367598 + 2.08475i
\(482\) −5.02705 + 28.5098i −0.228976 + 1.29859i
\(483\) 0 0
\(484\) −1.80803 + 1.51712i −0.0821833 + 0.0689600i
\(485\) 5.64719 9.78122i 0.256426 0.444143i
\(486\) 0 0
\(487\) 6.60006 + 11.4316i 0.299077 + 0.518017i 0.975925 0.218106i \(-0.0699878\pi\)
−0.676848 + 0.736123i \(0.736654\pi\)
\(488\) −0.0298412 0.169238i −0.00135085 0.00766103i
\(489\) 0 0
\(490\) −1.84099 12.5278i −0.0831676 0.565948i
\(491\) −15.3102 + 5.57245i −0.690939 + 0.251481i −0.663537 0.748143i \(-0.730946\pi\)
−0.0274020 + 0.999624i \(0.508723\pi\)
\(492\) 0 0
\(493\) −0.198707 + 0.166735i −0.00894932 + 0.00750937i
\(494\) 5.61757 9.72992i 0.252747 0.437770i
\(495\) 0 0
\(496\) −0.455438 + 0.788842i −0.0204498 + 0.0354200i
\(497\) −6.53452 18.7857i −0.293113 0.842656i
\(498\) 0 0
\(499\) −0.207754 + 0.0756161i −0.00930033 + 0.00338504i −0.346666 0.937989i \(-0.612686\pi\)
0.337366 + 0.941374i \(0.390464\pi\)
\(500\) 3.00235 17.0272i 0.134269 0.761479i
\(501\) 0 0
\(502\) −5.19867 + 4.36220i −0.232028 + 0.194695i
\(503\) −0.112688 + 0.195182i −0.00502452 + 0.00870272i −0.868527 0.495642i \(-0.834933\pi\)
0.863502 + 0.504345i \(0.168266\pi\)
\(504\) 0 0
\(505\) −4.53475 7.85442i −0.201794 0.349517i
\(506\) 33.2445 + 12.1000i 1.47790 + 0.537910i
\(507\) 0 0
\(508\) −17.9389 15.0525i −0.795908 0.667846i
\(509\) 24.8793 + 20.8762i 1.10275 + 0.925320i 0.997607 0.0691366i \(-0.0220244\pi\)
0.105146 + 0.994457i \(0.466469\pi\)
\(510\) 0 0
\(511\) 8.47136 + 24.3538i 0.374751 + 1.07735i
\(512\) −32.1505 −1.42086
\(513\) 0 0
\(514\) −18.3129 31.7189i −0.807748 1.39906i
\(515\) −12.5658 4.57358i −0.553716 0.201536i
\(516\) 0 0
\(517\) 3.02839 17.1748i 0.133188 0.755348i
\(518\) −0.788200 + 55.0681i −0.0346315 + 2.41955i
\(519\) 0 0
\(520\) −0.799667 0.291055i −0.0350677 0.0127636i
\(521\) 11.7781 20.4003i 0.516009 0.893754i −0.483818 0.875169i \(-0.660750\pi\)
0.999827 0.0185855i \(-0.00591630\pi\)
\(522\) 0 0
\(523\) 6.29514 + 10.9035i 0.275267 + 0.476777i 0.970202 0.242296i \(-0.0779004\pi\)
−0.694935 + 0.719072i \(0.744567\pi\)
\(524\) 15.5582 + 5.66274i 0.679665 + 0.247378i
\(525\) 0 0
\(526\) −37.5113 31.4757i −1.63557 1.37241i
\(527\) −1.30084 + 0.473466i −0.0566654 + 0.0206245i
\(528\) 0 0
\(529\) 1.36697 + 7.75246i 0.0594334 + 0.337063i
\(530\) 6.91539 + 11.9778i 0.300386 + 0.520283i
\(531\) 0 0
\(532\) 2.42860 6.38662i 0.105293 0.276895i
\(533\) −3.83923 21.7734i −0.166296 0.943110i
\(534\) 0 0
\(535\) −9.96346 8.36033i −0.430758 0.361449i
\(536\) 0.130414 0.0474668i 0.00563302 0.00205025i
\(537\) 0 0
\(538\) −23.1311 + 19.4093i −0.997252 + 0.836794i
\(539\) 20.8809 6.92994i 0.899404 0.298494i
\(540\) 0 0
\(541\) 5.81252 10.0676i 0.249900 0.432839i −0.713598 0.700555i \(-0.752936\pi\)
0.963498 + 0.267716i \(0.0862690\pi\)
\(542\) 10.2462 + 3.72930i 0.440111 + 0.160187i
\(543\) 0 0
\(544\) −35.5731 29.8494i −1.52518 1.27978i
\(545\) 2.84274 1.03467i 0.121770 0.0443205i
\(546\) 0 0
\(547\) −5.74175 32.5631i −0.245500 1.39230i −0.819330 0.573323i \(-0.805654\pi\)
0.573830 0.818974i \(-0.305457\pi\)
\(548\) −3.67570 −0.157018
\(549\) 0 0
\(550\) 26.7597 1.14104
\(551\) 0.0424440 0.0356147i 0.00180818 0.00151724i
\(552\) 0 0
\(553\) 30.0664 + 17.9374i 1.27855 + 0.762776i
\(554\) 1.57054 + 1.31784i 0.0667259 + 0.0559897i
\(555\) 0 0
\(556\) −4.24002 24.0463i −0.179817 1.01979i
\(557\) 31.4617 1.33307 0.666537 0.745472i \(-0.267776\pi\)
0.666537 + 0.745472i \(0.267776\pi\)
\(558\) 0 0
\(559\) −16.6499 28.8385i −0.704217 1.21974i
\(560\) 8.77329 + 1.67677i 0.370739 + 0.0708566i
\(561\) 0 0
\(562\) 4.57555 25.9492i 0.193008 1.09460i
\(563\) 11.7079 4.26132i 0.493428 0.179593i −0.0833076 0.996524i \(-0.526548\pi\)
0.576736 + 0.816931i \(0.304326\pi\)
\(564\) 0 0
\(565\) 2.08959 + 11.8507i 0.0879099 + 0.498562i
\(566\) 38.3198 1.61070
\(567\) 0 0
\(568\) −1.58566 −0.0665327
\(569\) 5.48364 + 31.0993i 0.229886 + 1.30375i 0.853121 + 0.521714i \(0.174707\pi\)
−0.623234 + 0.782035i \(0.714182\pi\)
\(570\) 0 0
\(571\) −11.7658 + 4.28241i −0.492384 + 0.179213i −0.576266 0.817263i \(-0.695491\pi\)
0.0838813 + 0.996476i \(0.473268\pi\)
\(572\) 5.18884 29.4274i 0.216956 1.23042i
\(573\) 0 0
\(574\) −8.61643 24.7709i −0.359643 1.03392i
\(575\) 11.6757 + 20.2229i 0.486911 + 0.843354i
\(576\) 0 0
\(577\) 12.4119 0.516713 0.258357 0.966050i \(-0.416819\pi\)
0.258357 + 0.966050i \(0.416819\pi\)
\(578\) −5.63500 31.9577i −0.234385 1.32926i
\(579\) 0 0
\(580\) −0.0649699 0.0545162i −0.00269773 0.00226366i
\(581\) 0.243378 17.0037i 0.0100970 0.705434i
\(582\) 0 0
\(583\) −18.4088 + 15.4468i −0.762416 + 0.639743i
\(584\) 2.05565 0.0850633
\(585\) 0 0
\(586\) −5.09761 −0.210580
\(587\) 0.730292 + 4.14169i 0.0301424 + 0.170946i 0.996163 0.0875200i \(-0.0278942\pi\)
−0.966020 + 0.258466i \(0.916783\pi\)
\(588\) 0 0
\(589\) 0.277860 0.101133i 0.0114490 0.00416710i
\(590\) 5.22145 + 4.38131i 0.214964 + 0.180376i
\(591\) 0 0
\(592\) −36.5065 13.2873i −1.50041 0.546103i
\(593\) −11.3399 + 19.6412i −0.465673 + 0.806569i −0.999232 0.0391942i \(-0.987521\pi\)
0.533559 + 0.845763i \(0.320854\pi\)
\(594\) 0 0
\(595\) 8.57596 + 10.5227i 0.351580 + 0.431387i
\(596\) −14.7116 + 12.3445i −0.602611 + 0.505651i
\(597\) 0 0
\(598\) 47.7934 17.3954i 1.95442 0.711350i
\(599\) 4.77957 + 4.01053i 0.195288 + 0.163866i 0.735188 0.677863i \(-0.237094\pi\)
−0.539901 + 0.841729i \(0.681538\pi\)
\(600\) 0 0
\(601\) 4.34521 + 24.6429i 0.177245 + 1.00520i 0.935521 + 0.353271i \(0.114931\pi\)
−0.758276 + 0.651933i \(0.773958\pi\)
\(602\) −24.9553 30.6201i −1.01710 1.24798i
\(603\) 0 0
\(604\) −9.81503 17.0001i −0.399368 0.691725i
\(605\) 0.173924 + 0.986370i 0.00707100 + 0.0401016i
\(606\) 0 0
\(607\) 11.3906 4.14582i 0.462328 0.168274i −0.100346 0.994953i \(-0.531995\pi\)
0.562674 + 0.826679i \(0.309773\pi\)
\(608\) 7.59844 + 6.37585i 0.308158 + 0.258575i
\(609\) 0 0
\(610\) −1.38490 0.504063i −0.0560731 0.0204089i
\(611\) −12.5360 21.7130i −0.507153 0.878415i
\(612\) 0 0
\(613\) 2.16690 3.75318i 0.0875202 0.151589i −0.818942 0.573876i \(-0.805439\pi\)
0.906462 + 0.422287i \(0.138772\pi\)
\(614\) −12.6904 4.61892i −0.512142 0.186404i
\(615\) 0 0
\(616\) 0.0251021 1.75377i 0.00101139 0.0706615i
\(617\) −4.00429 + 22.7095i −0.161207 + 0.914249i 0.791683 + 0.610932i \(0.209205\pi\)
−0.952890 + 0.303317i \(0.901906\pi\)
\(618\) 0 0
\(619\) −5.53714 2.01536i −0.222557 0.0810040i 0.228335 0.973583i \(-0.426672\pi\)
−0.450892 + 0.892579i \(0.648894\pi\)
\(620\) −0.226311 0.391983i −0.00908888 0.0157424i
\(621\) 0 0
\(622\) −29.5946 −1.18664
\(623\) −21.8108 + 25.2502i −0.873831 + 1.01163i
\(624\) 0 0
\(625\) 10.4768 + 8.79104i 0.419070 + 0.351642i
\(626\) −34.0196 28.5458i −1.35970 1.14092i
\(627\) 0 0
\(628\) −25.8678 9.41511i −1.03224 0.375704i
\(629\) −29.5211 51.1320i −1.17708 2.03877i
\(630\) 0 0
\(631\) 13.0197 22.5509i 0.518308 0.897735i −0.481466 0.876465i \(-0.659895\pi\)
0.999774 0.0212707i \(-0.00677118\pi\)
\(632\) 2.13812 1.79409i 0.0850497 0.0713652i
\(633\) 0 0
\(634\) −3.27371 + 18.5661i −0.130016 + 0.737355i
\(635\) −9.33819 + 3.39882i −0.370575 + 0.134878i
\(636\) 0 0
\(637\) 16.5921 26.9278i 0.657401 1.06692i
\(638\) 0.143715 0.248922i 0.00568975 0.00985493i
\(639\) 0 0
\(640\) 0.752324 1.30306i 0.0297382 0.0515081i
\(641\) 16.4390 13.7940i 0.649301 0.544829i −0.257557 0.966263i \(-0.582918\pi\)
0.906859 + 0.421434i \(0.138473\pi\)
\(642\) 0 0
\(643\) −36.9983 + 13.4663i −1.45907 + 0.531058i −0.945109 0.326756i \(-0.894044\pi\)
−0.513961 + 0.857814i \(0.671822\pi\)
\(644\) 27.0061 15.0808i 1.06419 0.594267i
\(645\) 0 0
\(646\) 2.48105 + 14.0708i 0.0976158 + 0.553607i
\(647\) 0.110173 + 0.190824i 0.00433133 + 0.00750208i 0.868183 0.496244i \(-0.165288\pi\)
−0.863852 + 0.503746i \(0.831955\pi\)
\(648\) 0 0
\(649\) −5.92150 + 10.2563i −0.232439 + 0.402597i
\(650\) 29.4702 24.7285i 1.15592 0.969930i
\(651\) 0 0
\(652\) −1.95784 + 11.1035i −0.0766749 + 0.434845i
\(653\) −4.32225 + 24.5127i −0.169143 + 0.959256i 0.775547 + 0.631290i \(0.217474\pi\)
−0.944690 + 0.327966i \(0.893637\pi\)
\(654\) 0 0
\(655\) 5.38226 4.51625i 0.210302 0.176465i
\(656\) 18.5005 0.722323
\(657\) 0 0
\(658\) −18.7893 23.0544i −0.732483 0.898754i
\(659\) 0.718602 + 0.261550i 0.0279928 + 0.0101885i 0.355979 0.934494i \(-0.384148\pi\)
−0.327986 + 0.944683i \(0.606370\pi\)
\(660\) 0 0
\(661\) −3.69556 + 20.9586i −0.143741 + 0.815193i 0.824629 + 0.565674i \(0.191384\pi\)
−0.968370 + 0.249520i \(0.919727\pi\)
\(662\) −4.78276 + 27.1244i −0.185887 + 1.05422i
\(663\) 0 0
\(664\) −1.27395 0.463681i −0.0494390 0.0179943i
\(665\) −1.83183 2.24765i −0.0710353 0.0871601i
\(666\) 0 0
\(667\) 0.250822 0.00971187
\(668\) 11.4247 9.58648i 0.442036 0.370912i
\(669\) 0 0
\(670\) 0.206679 1.17213i 0.00798470 0.0452835i
\(671\) 0.444661 2.52180i 0.0171659 0.0973529i
\(672\) 0 0
\(673\) −18.7235 + 15.7109i −0.721737 + 0.605609i −0.927865 0.372916i \(-0.878358\pi\)
0.206128 + 0.978525i \(0.433914\pi\)
\(674\) −24.8318 + 43.0099i −0.956485 + 1.65668i
\(675\) 0 0
\(676\) −7.80247 13.5143i −0.300095 0.519779i
\(677\) −4.91971 27.9011i −0.189080 1.07233i −0.920600 0.390506i \(-0.872300\pi\)
0.731520 0.681820i \(-0.238811\pi\)
\(678\) 0 0
\(679\) 29.2190 16.3166i 1.12132 0.626173i
\(680\) 1.01694 0.370137i 0.0389980 0.0141941i
\(681\) 0 0
\(682\) 1.17507 0.986005i 0.0449959 0.0377561i
\(683\) −1.72661 + 2.99057i −0.0660668 + 0.114431i −0.897167 0.441692i \(-0.854378\pi\)
0.831100 + 0.556123i \(0.187712\pi\)
\(684\) 0 0
\(685\) −0.779912 + 1.35085i −0.0297989 + 0.0516132i
\(686\) 14.3339 34.6735i 0.547272 1.32384i
\(687\) 0 0
\(688\) 26.1841 9.53022i 0.998259 0.363336i
\(689\) −5.99917 + 34.0230i −0.228550 + 1.29617i
\(690\) 0 0
\(691\) 37.7308 31.6599i 1.43535 1.20440i 0.492884 0.870095i \(-0.335943\pi\)
0.942465 0.334306i \(-0.108502\pi\)
\(692\) −19.0746 + 33.0382i −0.725107 + 1.25592i
\(693\) 0 0
\(694\) 12.7076 + 22.0103i 0.482375 + 0.835499i
\(695\) −9.73687 3.54393i −0.369340 0.134429i
\(696\) 0 0
\(697\) 21.5385 + 18.0730i 0.815829 + 0.684562i
\(698\) −40.4938 33.9784i −1.53271 1.28610i
\(699\) 0 0
\(700\) 15.2939 17.7056i 0.578054 0.669209i
\(701\) 26.2546 0.991624 0.495812 0.868430i \(-0.334870\pi\)
0.495812 + 0.868430i \(0.334870\pi\)
\(702\) 0 0
\(703\) 6.30573 + 10.9218i 0.237825 + 0.411925i
\(704\) 26.0201 + 9.47053i 0.980668 + 0.356934i
\(705\) 0 0
\(706\) −8.37976 + 47.5240i −0.315377 + 1.78859i
\(707\) 0.384608 26.8709i 0.0144647 1.01058i
\(708\) 0 0
\(709\) 7.39480 + 2.69149i 0.277718 + 0.101081i 0.477124 0.878836i \(-0.341679\pi\)
−0.199407 + 0.979917i \(0.563901\pi\)
\(710\) −6.79934 + 11.7768i −0.255175 + 0.441976i
\(711\) 0 0
\(712\) 1.33000 + 2.30363i 0.0498439 + 0.0863321i
\(713\) 1.25785 + 0.457821i 0.0471069 + 0.0171455i
\(714\) 0 0
\(715\) −9.71382 8.15086i −0.363276 0.304825i
\(716\) −31.4933 + 11.4626i −1.17696 + 0.428378i
\(717\) 0 0
\(718\) −6.57454 37.2861i −0.245360 1.39150i
\(719\) −5.36852 9.29854i −0.200212 0.346777i 0.748385 0.663265i \(-0.230830\pi\)
−0.948597 + 0.316488i \(0.897496\pi\)
\(720\) 0 0
\(721\) −25.0322 30.7144i −0.932248 1.14387i
\(722\) 6.15400 + 34.9011i 0.229028 + 1.29888i
\(723\) 0 0
\(724\) 38.0122 + 31.8960i 1.41271 + 1.18541i
\(725\) 0.178279 0.0648881i 0.00662110 0.00240988i
\(726\) 0 0
\(727\) −3.16208 + 2.65330i −0.117275 + 0.0984056i −0.699539 0.714594i \(-0.746611\pi\)
0.582264 + 0.813000i \(0.302167\pi\)
\(728\) −1.59301 1.95461i −0.0590407 0.0724428i
\(729\) 0 0
\(730\) 8.81467 15.2675i 0.326246 0.565074i
\(731\) 39.7938 + 14.4838i 1.47183 + 0.535701i
\(732\) 0 0
\(733\) −15.0457 12.6249i −0.555726 0.466310i 0.321148 0.947029i \(-0.395931\pi\)
−0.876875 + 0.480719i \(0.840376\pi\)
\(734\) 46.9810 17.0997i 1.73410 0.631161i
\(735\) 0 0
\(736\) 7.79730 + 44.2207i 0.287412 + 1.63000i
\(737\) 2.06800 0.0761758
\(738\) 0 0
\(739\) −25.9618 −0.955019 −0.477509 0.878627i \(-0.658460\pi\)
−0.477509 + 0.878627i \(0.658460\pi\)
\(740\) 14.7882 12.4088i 0.543625 0.456155i
\(741\) 0 0
\(742\) −0.586519 + 40.9775i −0.0215318 + 1.50433i
\(743\) 11.7874 + 9.89080i 0.432438 + 0.362858i 0.832871 0.553468i \(-0.186696\pi\)
−0.400433 + 0.916326i \(0.631140\pi\)
\(744\) 0 0
\(745\) 1.41518 + 8.02590i 0.0518483 + 0.294046i
\(746\) −60.8243 −2.22694
\(747\) 0 0
\(748\) 19.0002 + 32.9092i 0.694715 + 1.20328i
\(749\) −12.6614 36.3996i −0.462639 1.33001i
\(750\) 0 0
\(751\) −2.84804 + 16.1520i −0.103927 + 0.589396i 0.887717 + 0.460389i \(0.152290\pi\)
−0.991644 + 0.129007i \(0.958821\pi\)
\(752\) 19.7144 7.17547i 0.718912 0.261662i
\(753\) 0 0
\(754\) −0.0717550 0.406943i −0.00261316 0.0148200i
\(755\) −8.33024 −0.303169
\(756\) 0 0
\(757\) −15.8693 −0.576779 −0.288389 0.957513i \(-0.593120\pi\)
−0.288389 + 0.957513i \(0.593120\pi\)
\(758\) −10.4285 59.1430i −0.378781 2.14817i
\(759\) 0 0
\(760\) −0.217220 + 0.0790615i −0.00787939 + 0.00286786i
\(761\) 4.30253 24.4009i 0.155967 0.884531i −0.801930 0.597418i \(-0.796193\pi\)
0.957897 0.287113i \(-0.0926956\pi\)
\(762\) 0 0
\(763\) 8.80448 + 1.68274i 0.318744 + 0.0609191i
\(764\) 22.6504 + 39.2317i 0.819463 + 1.41935i
\(765\) 0 0
\(766\) 6.32531 0.228543
\(767\) 2.95652 + 16.7673i 0.106754 + 0.605431i
\(768\) 0 0
\(769\) −18.0600 15.1541i −0.651261 0.546473i 0.256193 0.966626i \(-0.417532\pi\)
−0.907453 + 0.420153i \(0.861976\pi\)
\(770\) −12.9178 7.70666i −0.465524 0.277729i
\(771\) 0 0
\(772\) 14.1600 11.8817i 0.509630 0.427630i
\(773\) −6.30291 −0.226700 −0.113350 0.993555i \(-0.536158\pi\)
−0.113350 + 0.993555i \(0.536158\pi\)
\(774\) 0 0
\(775\) 1.01249 0.0363697
\(776\) −0.463292 2.62746i −0.0166312 0.0943203i
\(777\) 0 0
\(778\) 13.6353 4.96284i 0.488849 0.177927i
\(779\) −4.60064 3.86040i −0.164835 0.138313i
\(780\) 0 0
\(781\) −22.2028 8.08116i −0.794479 0.289167i
\(782\) −32.3399 + 56.0144i −1.15647 + 2.00307i
\(783\) 0 0