Properties

Label 567.2.w.a.37.20
Level $567$
Weight $2$
Character 567.37
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(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 37.20
Character \(\chi\) \(=\) 567.37
Dual form 567.2.w.a.46.20

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.402178 + 2.28086i) q^{2} +(-3.16120 + 1.15058i) q^{4} +(-0.125418 + 0.711279i) q^{5} +(-2.42560 + 1.05663i) q^{7} +(-1.57964 - 2.73601i) q^{8} +O(q^{10})\) \(q+(0.402178 + 2.28086i) q^{2} +(-3.16120 + 1.15058i) q^{4} +(-0.125418 + 0.711279i) q^{5} +(-2.42560 + 1.05663i) q^{7} +(-1.57964 - 2.73601i) q^{8} -1.67277 q^{10} +(0.324200 + 1.83863i) q^{11} +(-1.90566 - 1.59904i) q^{13} +(-3.38556 - 5.10750i) q^{14} +(0.451103 - 0.378521i) q^{16} -6.86741 q^{17} +5.07851 q^{19} +(-0.421915 - 2.39280i) q^{20} +(-4.06328 + 1.47891i) q^{22} +(-2.68373 - 2.25192i) q^{23} +(4.20827 + 1.53169i) q^{25} +(2.88077 - 4.98963i) q^{26} +(6.45205 - 6.13109i) q^{28} +(0.282637 - 0.237160i) q^{29} +(-7.40251 + 2.69429i) q^{31} +(-3.79551 - 3.18481i) q^{32} +(-2.76192 - 15.6636i) q^{34} +(-0.447350 - 1.85780i) q^{35} +(1.35324 + 2.34388i) q^{37} +(2.04246 + 11.5834i) q^{38} +(2.14418 - 0.780419i) q^{40} +(0.493140 + 0.413793i) q^{41} +(4.01947 + 1.46297i) q^{43} +(-3.14036 - 5.43926i) q^{44} +(4.05697 - 7.02688i) q^{46} +(-2.67992 - 0.975411i) q^{47} +(4.76705 - 5.12594i) q^{49} +(-1.80109 + 10.2145i) q^{50} +(7.86398 + 2.86226i) q^{52} +(4.24901 + 7.35949i) q^{53} -1.34844 q^{55} +(6.72253 + 4.96736i) q^{56} +(0.654600 + 0.549275i) q^{58} +(6.47288 + 5.43139i) q^{59} +(-4.38206 - 1.59494i) q^{61} +(-9.12243 - 15.8005i) q^{62} +(6.32652 - 10.9579i) q^{64} +(1.37636 - 1.15491i) q^{65} +(-2.00941 + 11.3959i) q^{67} +(21.7093 - 7.90153i) q^{68} +(4.05747 - 1.76751i) q^{70} +(-4.04136 + 6.99984i) q^{71} +(-7.29326 + 12.6323i) q^{73} +(-4.80183 + 4.02922i) q^{74} +(-16.0542 + 5.84324i) q^{76} +(-2.72914 - 4.11722i) q^{77} +(2.88040 + 16.3356i) q^{79} +(0.212658 + 0.368334i) q^{80} +(-0.745476 + 1.29120i) q^{82} +(12.8518 - 10.7839i) q^{83} +(0.861296 - 4.88465i) q^{85} +(-1.72029 + 9.75622i) q^{86} +(4.51840 - 3.79138i) q^{88} +1.40964 q^{89} +(6.31195 + 1.86503i) q^{91} +(11.0748 + 4.03090i) q^{92} +(1.14697 - 6.50482i) q^{94} +(-0.636935 + 3.61224i) q^{95} +(-1.25952 - 0.458428i) q^{97} +(13.6088 + 8.81143i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 132 q + 3 q^{2} - 3 q^{4} + 3 q^{5} - 6 q^{7} + 6 q^{8}+O(q^{10}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.402178 + 2.28086i 0.284382 + 1.61281i 0.707483 + 0.706730i \(0.249831\pi\)
−0.423100 + 0.906083i \(0.639058\pi\)
\(3\) 0 0
\(4\) −3.16120 + 1.15058i −1.58060 + 0.575292i
\(5\) −0.125418 + 0.711279i −0.0560885 + 0.318094i −0.999924 0.0123217i \(-0.996078\pi\)
0.943836 + 0.330416i \(0.107189\pi\)
\(6\) 0 0
\(7\) −2.42560 + 1.05663i −0.916790 + 0.399370i
\(8\) −1.57964 2.73601i −0.558486 0.967326i
\(9\) 0 0
\(10\) −1.67277 −0.528977
\(11\) 0.324200 + 1.83863i 0.0977500 + 0.554368i 0.993870 + 0.110556i \(0.0352631\pi\)
−0.896120 + 0.443812i \(0.853626\pi\)
\(12\) 0 0
\(13\) −1.90566 1.59904i −0.528534 0.443493i 0.339061 0.940764i \(-0.389891\pi\)
−0.867595 + 0.497272i \(0.834335\pi\)
\(14\) −3.38556 5.10750i −0.904829 1.36504i
\(15\) 0 0
\(16\) 0.451103 0.378521i 0.112776 0.0946302i
\(17\) −6.86741 −1.66559 −0.832796 0.553580i \(-0.813261\pi\)
−0.832796 + 0.553580i \(0.813261\pi\)
\(18\) 0 0
\(19\) 5.07851 1.16509 0.582545 0.812799i \(-0.302057\pi\)
0.582545 + 0.812799i \(0.302057\pi\)
\(20\) −0.421915 2.39280i −0.0943431 0.535047i
\(21\) 0 0
\(22\) −4.06328 + 1.47891i −0.866293 + 0.315305i
\(23\) −2.68373 2.25192i −0.559596 0.469557i 0.318579 0.947896i \(-0.396794\pi\)
−0.878175 + 0.478340i \(0.841239\pi\)
\(24\) 0 0
\(25\) 4.20827 + 1.53169i 0.841655 + 0.306337i
\(26\) 2.88077 4.98963i 0.564965 0.978548i
\(27\) 0 0
\(28\) 6.45205 6.13109i 1.21932 1.15867i
\(29\) 0.282637 0.237160i 0.0524843 0.0440396i −0.616168 0.787615i \(-0.711316\pi\)
0.668652 + 0.743575i \(0.266871\pi\)
\(30\) 0 0
\(31\) −7.40251 + 2.69429i −1.32953 + 0.483909i −0.906500 0.422207i \(-0.861256\pi\)
−0.423030 + 0.906116i \(0.639033\pi\)
\(32\) −3.79551 3.18481i −0.670958 0.563001i
\(33\) 0 0
\(34\) −2.76192 15.6636i −0.473665 2.68629i
\(35\) −0.447350 1.85780i −0.0756159 0.314025i
\(36\) 0 0
\(37\) 1.35324 + 2.34388i 0.222472 + 0.385332i 0.955558 0.294804i \(-0.0952542\pi\)
−0.733086 + 0.680136i \(0.761921\pi\)
\(38\) 2.04246 + 11.5834i 0.331331 + 1.87907i
\(39\) 0 0
\(40\) 2.14418 0.780419i 0.339025 0.123395i
\(41\) 0.493140 + 0.413793i 0.0770155 + 0.0646237i 0.680483 0.732764i \(-0.261770\pi\)
−0.603467 + 0.797388i \(0.706215\pi\)
\(42\) 0 0
\(43\) 4.01947 + 1.46297i 0.612963 + 0.223100i 0.629799 0.776758i \(-0.283137\pi\)
−0.0168362 + 0.999858i \(0.505359\pi\)
\(44\) −3.14036 5.43926i −0.473427 0.819999i
\(45\) 0 0
\(46\) 4.05697 7.02688i 0.598168 1.03606i
\(47\) −2.67992 0.975411i −0.390907 0.142278i 0.139087 0.990280i \(-0.455583\pi\)
−0.529993 + 0.848002i \(0.677806\pi\)
\(48\) 0 0
\(49\) 4.76705 5.12594i 0.681006 0.732277i
\(50\) −1.80109 + 10.2145i −0.254713 + 1.44455i
\(51\) 0 0
\(52\) 7.86398 + 2.86226i 1.09054 + 0.396923i
\(53\) 4.24901 + 7.35949i 0.583646 + 1.01090i 0.995043 + 0.0994480i \(0.0317077\pi\)
−0.411397 + 0.911456i \(0.634959\pi\)
\(54\) 0 0
\(55\) −1.34844 −0.181824
\(56\) 6.72253 + 4.96736i 0.898336 + 0.663792i
\(57\) 0 0
\(58\) 0.654600 + 0.549275i 0.0859532 + 0.0721233i
\(59\) 6.47288 + 5.43139i 0.842698 + 0.707107i 0.958169 0.286204i \(-0.0923934\pi\)
−0.115471 + 0.993311i \(0.536838\pi\)
\(60\) 0 0
\(61\) −4.38206 1.59494i −0.561066 0.204211i 0.0458906 0.998946i \(-0.485387\pi\)
−0.606956 + 0.794735i \(0.707610\pi\)
\(62\) −9.12243 15.8005i −1.15855 2.00667i
\(63\) 0 0
\(64\) 6.32652 10.9579i 0.790816 1.36973i
\(65\) 1.37636 1.15491i 0.170717 0.143249i
\(66\) 0 0
\(67\) −2.00941 + 11.3959i −0.245489 + 1.39223i 0.573867 + 0.818949i \(0.305443\pi\)
−0.819355 + 0.573286i \(0.805668\pi\)
\(68\) 21.7093 7.90153i 2.63264 0.958201i
\(69\) 0 0
\(70\) 4.05747 1.76751i 0.484960 0.211258i
\(71\) −4.04136 + 6.99984i −0.479621 + 0.830728i −0.999727 0.0233741i \(-0.992559\pi\)
0.520106 + 0.854102i \(0.325892\pi\)
\(72\) 0 0
\(73\) −7.29326 + 12.6323i −0.853612 + 1.47850i 0.0243146 + 0.999704i \(0.492260\pi\)
−0.877927 + 0.478795i \(0.841074\pi\)
\(74\) −4.80183 + 4.02922i −0.558202 + 0.468387i
\(75\) 0 0
\(76\) −16.0542 + 5.84324i −1.84154 + 0.670266i
\(77\) −2.72914 4.11722i −0.311014 0.469200i
\(78\) 0 0
\(79\) 2.88040 + 16.3356i 0.324070 + 1.83789i 0.516130 + 0.856510i \(0.327372\pi\)
−0.192059 + 0.981383i \(0.561517\pi\)
\(80\) 0.212658 + 0.368334i 0.0237758 + 0.0411810i
\(81\) 0 0
\(82\) −0.745476 + 1.29120i −0.0823241 + 0.142589i
\(83\) 12.8518 10.7839i 1.41067 1.18369i 0.454544 0.890724i \(-0.349802\pi\)
0.956123 0.292966i \(-0.0946422\pi\)
\(84\) 0 0
\(85\) 0.861296 4.88465i 0.0934206 0.529815i
\(86\) −1.72029 + 9.75622i −0.185503 + 1.05204i
\(87\) 0 0
\(88\) 4.51840 3.79138i 0.481663 0.404163i
\(89\) 1.40964 0.149422 0.0747109 0.997205i \(-0.476197\pi\)
0.0747109 + 0.997205i \(0.476197\pi\)
\(90\) 0 0
\(91\) 6.31195 + 1.86503i 0.661672 + 0.195509i
\(92\) 11.0748 + 4.03090i 1.15463 + 0.420251i
\(93\) 0 0
\(94\) 1.14697 6.50482i 0.118301 0.670921i
\(95\) −0.636935 + 3.61224i −0.0653481 + 0.370608i
\(96\) 0 0
\(97\) −1.25952 0.458428i −0.127885 0.0465463i 0.277285 0.960788i \(-0.410565\pi\)
−0.405170 + 0.914241i \(0.632788\pi\)
\(98\) 13.6088 + 8.81143i 1.37469 + 0.890089i
\(99\) 0 0
\(100\) −15.0655 −1.50655
\(101\) 1.30110 1.09175i 0.129464 0.108634i −0.575756 0.817621i \(-0.695292\pi\)
0.705221 + 0.708988i \(0.250848\pi\)
\(102\) 0 0
\(103\) 1.69162 9.59363i 0.166680 0.945288i −0.780636 0.624986i \(-0.785105\pi\)
0.947316 0.320302i \(-0.103784\pi\)
\(104\) −1.36473 + 7.73979i −0.133823 + 0.758949i
\(105\) 0 0
\(106\) −15.0771 + 12.6512i −1.46442 + 1.22880i
\(107\) 2.52070 4.36597i 0.243685 0.422075i −0.718076 0.695965i \(-0.754977\pi\)
0.961761 + 0.273890i \(0.0883104\pi\)
\(108\) 0 0
\(109\) −1.44108 2.49602i −0.138030 0.239076i 0.788721 0.614752i \(-0.210744\pi\)
−0.926751 + 0.375676i \(0.877411\pi\)
\(110\) −0.542312 3.07561i −0.0517075 0.293248i
\(111\) 0 0
\(112\) −0.694237 + 1.39479i −0.0655992 + 0.131795i
\(113\) −10.2167 + 3.71858i −0.961108 + 0.349815i −0.774467 0.632614i \(-0.781982\pi\)
−0.186640 + 0.982428i \(0.559760\pi\)
\(114\) 0 0
\(115\) 1.93833 1.62645i 0.180750 0.151667i
\(116\) −0.620599 + 1.07491i −0.0576212 + 0.0998028i
\(117\) 0 0
\(118\) −9.78501 + 16.9481i −0.900783 + 1.56020i
\(119\) 16.6576 7.25635i 1.52700 0.665189i
\(120\) 0 0
\(121\) 7.06116 2.57005i 0.641924 0.233641i
\(122\) 1.87547 10.6363i 0.169797 0.962968i
\(123\) 0 0
\(124\) 20.3008 17.0344i 1.82307 1.52973i
\(125\) −3.42288 + 5.92860i −0.306152 + 0.530270i
\(126\) 0 0
\(127\) 7.92097 + 13.7195i 0.702873 + 1.21741i 0.967454 + 0.253048i \(0.0814330\pi\)
−0.264581 + 0.964363i \(0.585234\pi\)
\(128\) 18.2260 + 6.63372i 1.61097 + 0.586343i
\(129\) 0 0
\(130\) 3.18773 + 2.67482i 0.279582 + 0.234597i
\(131\) 6.27502 + 5.26537i 0.548251 + 0.460038i 0.874348 0.485299i \(-0.161289\pi\)
−0.326097 + 0.945336i \(0.605734\pi\)
\(132\) 0 0
\(133\) −12.3184 + 5.36613i −1.06814 + 0.465302i
\(134\) −26.8007 −2.31523
\(135\) 0 0
\(136\) 10.8480 + 18.7893i 0.930210 + 1.61117i
\(137\) −20.8951 7.60520i −1.78519 0.649756i −0.999516 0.0311161i \(-0.990094\pi\)
−0.785675 0.618640i \(-0.787684\pi\)
\(138\) 0 0
\(139\) −0.705370 + 4.00035i −0.0598287 + 0.339306i −0.999999 0.00139934i \(-0.999555\pi\)
0.940170 + 0.340705i \(0.110666\pi\)
\(140\) 3.55171 + 5.35816i 0.300175 + 0.452847i
\(141\) 0 0
\(142\) −17.5910 6.40260i −1.47620 0.537294i
\(143\) 2.32222 4.02220i 0.194194 0.336354i
\(144\) 0 0
\(145\) 0.133240 + 0.230778i 0.0110649 + 0.0191651i
\(146\) −31.7457 11.5545i −2.62730 0.956257i
\(147\) 0 0
\(148\) −6.97470 5.85247i −0.573317 0.481070i
\(149\) −14.5402 + 5.29221i −1.19118 + 0.433555i −0.860139 0.510060i \(-0.829623\pi\)
−0.331044 + 0.943615i \(0.607401\pi\)
\(150\) 0 0
\(151\) −1.59428 9.04160i −0.129741 0.735795i −0.978379 0.206821i \(-0.933688\pi\)
0.848638 0.528974i \(-0.177423\pi\)
\(152\) −8.02220 13.8949i −0.650686 1.12702i
\(153\) 0 0
\(154\) 8.29320 7.88064i 0.668285 0.635040i
\(155\) −0.987989 5.60316i −0.0793572 0.450057i
\(156\) 0 0
\(157\) −4.76831 4.00109i −0.380553 0.319321i 0.432367 0.901698i \(-0.357679\pi\)
−0.812919 + 0.582376i \(0.802123\pi\)
\(158\) −36.1007 + 13.1396i −2.87202 + 1.04533i
\(159\) 0 0
\(160\) 2.74132 2.30024i 0.216720 0.181850i
\(161\) 8.88910 + 2.62652i 0.700559 + 0.206999i
\(162\) 0 0
\(163\) −8.74022 + 15.1385i −0.684587 + 1.18574i 0.288980 + 0.957335i \(0.406684\pi\)
−0.973566 + 0.228404i \(0.926649\pi\)
\(164\) −2.03502 0.740686i −0.158908 0.0578378i
\(165\) 0 0
\(166\) 29.7654 + 24.9761i 2.31024 + 1.93852i
\(167\) 5.53091 2.01309i 0.427995 0.155777i −0.119036 0.992890i \(-0.537980\pi\)
0.547031 + 0.837113i \(0.315758\pi\)
\(168\) 0 0
\(169\) −1.18282 6.70808i −0.0909858 0.516006i
\(170\) 11.4876 0.881059
\(171\) 0 0
\(172\) −14.3896 −1.09720
\(173\) 4.46564 3.74712i 0.339517 0.284888i −0.457048 0.889442i \(-0.651093\pi\)
0.796564 + 0.604554i \(0.206649\pi\)
\(174\) 0 0
\(175\) −11.8260 + 0.731355i −0.893963 + 0.0552852i
\(176\) 0.842207 + 0.706696i 0.0634838 + 0.0532692i
\(177\) 0 0
\(178\) 0.566926 + 3.21520i 0.0424929 + 0.240989i
\(179\) 23.7123 1.77234 0.886172 0.463357i \(-0.153355\pi\)
0.886172 + 0.463357i \(0.153355\pi\)
\(180\) 0 0
\(181\) 0.0286987 + 0.0497077i 0.00213316 + 0.00369474i 0.867090 0.498151i \(-0.165988\pi\)
−0.864957 + 0.501846i \(0.832654\pi\)
\(182\) −1.71536 + 15.1468i −0.127151 + 1.12275i
\(183\) 0 0
\(184\) −1.92195 + 10.8999i −0.141688 + 0.803553i
\(185\) −1.83688 + 0.668568i −0.135050 + 0.0491541i
\(186\) 0 0
\(187\) −2.22642 12.6266i −0.162812 0.923351i
\(188\) 9.59406 0.699719
\(189\) 0 0
\(190\) −8.49518 −0.616305
\(191\) 2.15810 + 12.2392i 0.156155 + 0.885598i 0.957722 + 0.287694i \(0.0928886\pi\)
−0.801568 + 0.597904i \(0.796000\pi\)
\(192\) 0 0
\(193\) 3.92287 1.42781i 0.282374 0.102776i −0.196950 0.980413i \(-0.563104\pi\)
0.479325 + 0.877638i \(0.340882\pi\)
\(194\) 0.539060 3.05716i 0.0387023 0.219492i
\(195\) 0 0
\(196\) −9.17177 + 21.6890i −0.655126 + 1.54922i
\(197\) 2.25971 + 3.91394i 0.160998 + 0.278857i 0.935227 0.354049i \(-0.115195\pi\)
−0.774229 + 0.632906i \(0.781862\pi\)
\(198\) 0 0
\(199\) 14.1358 1.00206 0.501032 0.865429i \(-0.332954\pi\)
0.501032 + 0.865429i \(0.332954\pi\)
\(200\) −2.45683 13.9334i −0.173724 0.985240i
\(201\) 0 0
\(202\) 3.01341 + 2.52855i 0.212023 + 0.177908i
\(203\) −0.434971 + 0.873899i −0.0305290 + 0.0613357i
\(204\) 0 0
\(205\) −0.356171 + 0.298863i −0.0248761 + 0.0208735i
\(206\) 22.5621 1.57197
\(207\) 0 0
\(208\) −1.46492 −0.101574
\(209\) 1.64645 + 9.33750i 0.113888 + 0.645888i
\(210\) 0 0
\(211\) 0.0245695 0.00894256i 0.00169143 0.000615631i −0.341174 0.940000i \(-0.610825\pi\)
0.342866 + 0.939384i \(0.388602\pi\)
\(212\) −21.8997 18.3760i −1.50408 1.26207i
\(213\) 0 0
\(214\) 10.9720 + 3.99346i 0.750027 + 0.272988i
\(215\) −1.54469 + 2.67548i −0.105347 + 0.182466i
\(216\) 0 0
\(217\) 15.1086 14.3570i 1.02564 0.974618i
\(218\) 5.11352 4.29075i 0.346331 0.290606i
\(219\) 0 0
\(220\) 4.26269 1.55149i 0.287391 0.104602i
\(221\) 13.0869 + 10.9812i 0.880322 + 0.738678i
\(222\) 0 0
\(223\) −2.69670 15.2937i −0.180584 1.02414i −0.931499 0.363745i \(-0.881498\pi\)
0.750914 0.660400i \(-0.229613\pi\)
\(224\) 12.5716 + 3.71460i 0.839973 + 0.248192i
\(225\) 0 0
\(226\) −12.5905 21.8074i −0.837508 1.45061i
\(227\) −2.75656 15.6332i −0.182959 1.03761i −0.928550 0.371208i \(-0.878944\pi\)
0.745591 0.666404i \(-0.232167\pi\)
\(228\) 0 0
\(229\) 9.95731 3.62417i 0.657998 0.239492i 0.00862615 0.999963i \(-0.497254\pi\)
0.649372 + 0.760471i \(0.275032\pi\)
\(230\) 4.48926 + 3.76694i 0.296013 + 0.248385i
\(231\) 0 0
\(232\) −1.09534 0.398670i −0.0719124 0.0261740i
\(233\) −6.61075 11.4502i −0.433085 0.750125i 0.564052 0.825739i \(-0.309242\pi\)
−0.997137 + 0.0756140i \(0.975908\pi\)
\(234\) 0 0
\(235\) 1.02990 1.78384i 0.0671832 0.116365i
\(236\) −26.7114 9.72214i −1.73876 0.632857i
\(237\) 0 0
\(238\) 23.2500 + 35.0753i 1.50708 + 2.27359i
\(239\) 2.71665 15.4069i 0.175725 0.996589i −0.761578 0.648074i \(-0.775575\pi\)
0.937303 0.348515i \(-0.113314\pi\)
\(240\) 0 0
\(241\) −5.55204 2.02078i −0.357638 0.130170i 0.156951 0.987606i \(-0.449833\pi\)
−0.514590 + 0.857437i \(0.672056\pi\)
\(242\) 8.70178 + 15.0719i 0.559372 + 0.968860i
\(243\) 0 0
\(244\) 15.6877 1.00430
\(245\) 3.04810 + 4.03359i 0.194736 + 0.257696i
\(246\) 0 0
\(247\) −9.67789 8.12071i −0.615789 0.516708i
\(248\) 19.0649 + 15.9973i 1.21062 + 1.01583i
\(249\) 0 0
\(250\) −14.8989 5.42277i −0.942291 0.342966i
\(251\) 15.2062 + 26.3379i 0.959807 + 1.66243i 0.722963 + 0.690887i \(0.242780\pi\)
0.236844 + 0.971548i \(0.423887\pi\)
\(252\) 0 0
\(253\) 3.27037 5.66445i 0.205607 0.356121i
\(254\) −28.1067 + 23.5843i −1.76357 + 1.47981i
\(255\) 0 0
\(256\) −3.40615 + 19.3173i −0.212885 + 1.20733i
\(257\) −5.62221 + 2.04632i −0.350704 + 0.127646i −0.511364 0.859364i \(-0.670860\pi\)
0.160661 + 0.987010i \(0.448638\pi\)
\(258\) 0 0
\(259\) −5.75905 4.25544i −0.357850 0.264420i
\(260\) −3.02215 + 5.23451i −0.187426 + 0.324631i
\(261\) 0 0
\(262\) −9.48591 + 16.4301i −0.586042 + 1.01505i
\(263\) 23.9036 20.0575i 1.47396 1.23680i 0.561596 0.827411i \(-0.310187\pi\)
0.912361 0.409386i \(-0.134257\pi\)
\(264\) 0 0
\(265\) −5.76756 + 2.09922i −0.354298 + 0.128954i
\(266\) −17.1936 25.9385i −1.05421 1.59039i
\(267\) 0 0
\(268\) −6.75982 38.3368i −0.412922 2.34179i
\(269\) −4.99123 8.64507i −0.304321 0.527099i 0.672789 0.739834i \(-0.265096\pi\)
−0.977110 + 0.212735i \(0.931763\pi\)
\(270\) 0 0
\(271\) −10.1417 + 17.5660i −0.616065 + 1.06706i 0.374131 + 0.927376i \(0.377941\pi\)
−0.990197 + 0.139680i \(0.955392\pi\)
\(272\) −3.09791 + 2.59946i −0.187839 + 0.157615i
\(273\) 0 0
\(274\) 8.94287 50.7175i 0.540258 3.06396i
\(275\) −1.45188 + 8.23403i −0.0875518 + 0.496531i
\(276\) 0 0
\(277\) 1.56000 1.30900i 0.0937314 0.0786500i −0.594718 0.803935i \(-0.702736\pi\)
0.688449 + 0.725285i \(0.258292\pi\)
\(278\) −9.40794 −0.564251
\(279\) 0 0
\(280\) −4.37631 + 4.15860i −0.261534 + 0.248524i
\(281\) 21.0206 + 7.65087i 1.25398 + 0.456413i 0.881746 0.471725i \(-0.156368\pi\)
0.372238 + 0.928137i \(0.378591\pi\)
\(282\) 0 0
\(283\) 4.76342 27.0147i 0.283156 1.60586i −0.428642 0.903474i \(-0.641008\pi\)
0.711798 0.702384i \(-0.247881\pi\)
\(284\) 4.72165 26.7778i 0.280178 1.58897i
\(285\) 0 0
\(286\) 10.1080 + 3.67902i 0.597701 + 0.217545i
\(287\) −1.63339 0.482627i −0.0964158 0.0284886i
\(288\) 0 0
\(289\) 30.1614 1.77420
\(290\) −0.472786 + 0.396715i −0.0277630 + 0.0232959i
\(291\) 0 0
\(292\) 8.52096 48.3248i 0.498651 2.82799i
\(293\) −1.10723 + 6.27940i −0.0646849 + 0.366846i 0.935233 + 0.354033i \(0.115190\pi\)
−0.999918 + 0.0128134i \(0.995921\pi\)
\(294\) 0 0
\(295\) −4.67505 + 3.92283i −0.272192 + 0.228396i
\(296\) 4.27526 7.40497i 0.248495 0.430405i
\(297\) 0 0
\(298\) −17.9186 31.0359i −1.03799 1.79786i
\(299\) 1.51337 + 8.58275i 0.0875205 + 0.496353i
\(300\) 0 0
\(301\) −11.2954 + 0.698542i −0.651058 + 0.0402633i
\(302\) 19.9815 7.27266i 1.14980 0.418494i
\(303\) 0 0
\(304\) 2.29093 1.92232i 0.131394 0.110253i
\(305\) 1.68404 2.91684i 0.0964277 0.167018i
\(306\) 0 0
\(307\) 5.96849 10.3377i 0.340640 0.590005i −0.643912 0.765100i \(-0.722690\pi\)
0.984552 + 0.175094i \(0.0560230\pi\)
\(308\) 13.3646 + 9.87524i 0.761516 + 0.562694i
\(309\) 0 0
\(310\) 12.3827 4.50693i 0.703290 0.255977i
\(311\) 2.86628 16.2555i 0.162532 0.921763i −0.789041 0.614340i \(-0.789422\pi\)
0.951573 0.307423i \(-0.0994666\pi\)
\(312\) 0 0
\(313\) 2.42452 2.03442i 0.137042 0.114992i −0.571690 0.820470i \(-0.693712\pi\)
0.708732 + 0.705478i \(0.249268\pi\)
\(314\) 7.20822 12.4850i 0.406783 0.704570i
\(315\) 0 0
\(316\) −27.9009 48.3258i −1.56955 2.71854i
\(317\) −0.962531 0.350333i −0.0540611 0.0196766i 0.314848 0.949142i \(-0.398046\pi\)
−0.368909 + 0.929465i \(0.620269\pi\)
\(318\) 0 0
\(319\) 0.527681 + 0.442777i 0.0295445 + 0.0247908i
\(320\) 7.00064 + 5.87424i 0.391348 + 0.328380i
\(321\) 0 0
\(322\) −2.41573 + 21.3311i −0.134624 + 1.18874i
\(323\) −34.8762 −1.94056
\(324\) 0 0
\(325\) −5.57030 9.64805i −0.308985 0.535177i
\(326\) −38.0440 13.8469i −2.10706 0.766907i
\(327\) 0 0
\(328\) 0.353162 2.00288i 0.0195001 0.110591i
\(329\) 7.53106 0.465743i 0.415201 0.0256772i
\(330\) 0 0
\(331\) 24.6665 + 8.97788i 1.35579 + 0.493469i 0.914752 0.404017i \(-0.132386\pi\)
0.441043 + 0.897486i \(0.354609\pi\)
\(332\) −28.2193 + 48.8772i −1.54873 + 2.68249i
\(333\) 0 0
\(334\) 6.81599 + 11.8056i 0.372954 + 0.645976i
\(335\) −7.85368 2.85850i −0.429092 0.156177i
\(336\) 0 0
\(337\) 7.99671 + 6.71003i 0.435608 + 0.365519i 0.834063 0.551669i \(-0.186009\pi\)
−0.398455 + 0.917188i \(0.630453\pi\)
\(338\) 14.8245 5.39568i 0.806347 0.293486i
\(339\) 0 0
\(340\) 2.89747 + 16.4324i 0.157137 + 0.891170i
\(341\) −7.35370 12.7370i −0.398225 0.689746i
\(342\) 0 0
\(343\) −6.14668 + 17.4705i −0.331890 + 0.943318i
\(344\) −2.34661 13.3083i −0.126521 0.717534i
\(345\) 0 0
\(346\) 10.3426 + 8.67851i 0.556024 + 0.466560i
\(347\) 1.76021 0.640664i 0.0944930 0.0343926i −0.294341 0.955700i \(-0.595100\pi\)
0.388834 + 0.921308i \(0.372878\pi\)
\(348\) 0 0
\(349\) 10.7190 8.99431i 0.573775 0.481455i −0.309121 0.951023i \(-0.600035\pi\)
0.882896 + 0.469568i \(0.155590\pi\)
\(350\) −6.42428 26.6794i −0.343392 1.42607i
\(351\) 0 0
\(352\) 4.62519 8.01106i 0.246523 0.426991i
\(353\) 4.45890 + 1.62291i 0.237324 + 0.0863787i 0.457944 0.888981i \(-0.348586\pi\)
−0.220620 + 0.975360i \(0.570808\pi\)
\(354\) 0 0
\(355\) −4.47198 3.75244i −0.237348 0.199159i
\(356\) −4.45616 + 1.62191i −0.236176 + 0.0859611i
\(357\) 0 0
\(358\) 9.53657 + 54.0846i 0.504023 + 2.85846i
\(359\) −8.12436 −0.428787 −0.214394 0.976747i \(-0.568778\pi\)
−0.214394 + 0.976747i \(0.568778\pi\)
\(360\) 0 0
\(361\) 6.79124 0.357433
\(362\) −0.101834 + 0.0854492i −0.00535230 + 0.00449111i
\(363\) 0 0
\(364\) −22.0992 + 1.36668i −1.15831 + 0.0716335i
\(365\) −8.07039 6.77186i −0.422424 0.354456i
\(366\) 0 0
\(367\) 1.24204 + 7.04395i 0.0648338 + 0.367691i 0.999912 + 0.0132499i \(0.00421771\pi\)
−0.935078 + 0.354441i \(0.884671\pi\)
\(368\) −2.06304 −0.107543
\(369\) 0 0
\(370\) −2.26366 3.92078i −0.117682 0.203832i
\(371\) −18.0827 13.3615i −0.938806 0.693696i
\(372\) 0 0
\(373\) 0.150877 0.855666i 0.00781212 0.0443047i −0.980653 0.195757i \(-0.937284\pi\)
0.988465 + 0.151452i \(0.0483949\pi\)
\(374\) 27.9042 10.1563i 1.44289 0.525170i
\(375\) 0 0
\(376\) 1.56457 + 8.87309i 0.0806863 + 0.457595i
\(377\) −0.917836 −0.0472710
\(378\) 0 0
\(379\) −22.2215 −1.14144 −0.570720 0.821145i \(-0.693336\pi\)
−0.570720 + 0.821145i \(0.693336\pi\)
\(380\) −2.14270 12.1519i −0.109918 0.623377i
\(381\) 0 0
\(382\) −27.0480 + 9.84467i −1.38390 + 0.503697i
\(383\) −2.14113 + 12.1429i −0.109406 + 0.620475i 0.879962 + 0.475044i \(0.157568\pi\)
−0.989368 + 0.145431i \(0.953543\pi\)
\(384\) 0 0
\(385\) 3.27077 1.42481i 0.166694 0.0726150i
\(386\) 4.83432 + 8.37329i 0.246061 + 0.426189i
\(387\) 0 0
\(388\) 4.50906 0.228913
\(389\) −3.70034 20.9857i −0.187615 1.06402i −0.922549 0.385879i \(-0.873898\pi\)
0.734935 0.678138i \(-0.237213\pi\)
\(390\) 0 0
\(391\) 18.4303 + 15.4648i 0.932059 + 0.782090i
\(392\) −21.5548 4.94556i −1.08868 0.249789i
\(393\) 0 0
\(394\) −8.01835 + 6.72819i −0.403959 + 0.338961i
\(395\) −11.9804 −0.602799
\(396\) 0 0
\(397\) −24.6872 −1.23902 −0.619508 0.784990i \(-0.712668\pi\)
−0.619508 + 0.784990i \(0.712668\pi\)
\(398\) 5.68512 + 32.2419i 0.284969 + 1.61614i
\(399\) 0 0
\(400\) 2.47814 0.901970i 0.123907 0.0450985i
\(401\) 24.2424 + 20.3418i 1.21061 + 1.01582i 0.999262 + 0.0384088i \(0.0122289\pi\)
0.211345 + 0.977411i \(0.432216\pi\)
\(402\) 0 0
\(403\) 18.4149 + 6.70247i 0.917311 + 0.333874i
\(404\) −2.85689 + 4.94828i −0.142136 + 0.246186i
\(405\) 0 0
\(406\) −2.16818 0.640646i −0.107605 0.0317947i
\(407\) −3.87081 + 3.24800i −0.191869 + 0.160997i
\(408\) 0 0
\(409\) −30.0555 + 10.9393i −1.48615 + 0.540914i −0.952432 0.304750i \(-0.901427\pi\)
−0.533716 + 0.845664i \(0.679205\pi\)
\(410\) −0.824910 0.692181i −0.0407394 0.0341844i
\(411\) 0 0
\(412\) 5.69073 + 32.2737i 0.280362 + 1.59001i
\(413\) −21.4396 6.33490i −1.05497 0.311720i
\(414\) 0 0
\(415\) 6.05854 + 10.4937i 0.297402 + 0.515116i
\(416\) 2.14031 + 12.1383i 0.104937 + 0.595130i
\(417\) 0 0
\(418\) −20.6354 + 7.51066i −1.00931 + 0.367359i
\(419\) 5.06260 + 4.24803i 0.247324 + 0.207530i 0.758019 0.652232i \(-0.226167\pi\)
−0.510695 + 0.859762i \(0.670612\pi\)
\(420\) 0 0
\(421\) −23.7462 8.64291i −1.15732 0.421230i −0.309180 0.951004i \(-0.600055\pi\)
−0.848139 + 0.529774i \(0.822277\pi\)
\(422\) 0.0302781 + 0.0524431i 0.00147391 + 0.00255289i
\(423\) 0 0
\(424\) 13.4238 23.2507i 0.651916 1.12915i
\(425\) −28.9000 10.5187i −1.40185 0.510233i
\(426\) 0 0
\(427\) 12.3144 0.761557i 0.595935 0.0368543i
\(428\) −2.94501 + 16.7020i −0.142353 + 0.807321i
\(429\) 0 0
\(430\) −6.72365 2.44721i −0.324243 0.118015i
\(431\) −0.0626025 0.108431i −0.00301546 0.00522292i 0.864514 0.502609i \(-0.167627\pi\)
−0.867529 + 0.497386i \(0.834293\pi\)
\(432\) 0 0
\(433\) −30.5722 −1.46920 −0.734602 0.678498i \(-0.762631\pi\)
−0.734602 + 0.678498i \(0.762631\pi\)
\(434\) 38.8227 + 28.6866i 1.86355 + 1.37700i
\(435\) 0 0
\(436\) 7.42743 + 6.23235i 0.355709 + 0.298475i
\(437\) −13.6293 11.4364i −0.651979 0.547076i
\(438\) 0 0
\(439\) 23.1461 + 8.42451i 1.10471 + 0.402080i 0.829049 0.559176i \(-0.188883\pi\)
0.275657 + 0.961256i \(0.411105\pi\)
\(440\) 2.13005 + 3.68935i 0.101546 + 0.175883i
\(441\) 0 0
\(442\) −19.7834 + 34.2659i −0.941001 + 1.62986i
\(443\) −14.7799 + 12.4018i −0.702216 + 0.589229i −0.922403 0.386229i \(-0.873778\pi\)
0.220187 + 0.975458i \(0.429333\pi\)
\(444\) 0 0
\(445\) −0.176794 + 1.00265i −0.00838084 + 0.0475301i
\(446\) 33.7984 12.3016i 1.60040 0.582497i
\(447\) 0 0
\(448\) −3.76714 + 33.2642i −0.177981 + 1.57159i
\(449\) −0.445937 + 0.772386i −0.0210451 + 0.0364511i −0.876356 0.481664i \(-0.840033\pi\)
0.855311 + 0.518115i \(0.173366\pi\)
\(450\) 0 0
\(451\) −0.600937 + 1.04085i −0.0282970 + 0.0490119i
\(452\) 28.0186 23.5104i 1.31788 1.10583i
\(453\) 0 0
\(454\) 34.5486 12.5746i 1.62144 0.590158i
\(455\) −2.11819 + 4.25565i −0.0993023 + 0.199508i
\(456\) 0 0
\(457\) 1.94609 + 11.0368i 0.0910342 + 0.516281i 0.995891 + 0.0905639i \(0.0288669\pi\)
−0.904856 + 0.425717i \(0.860022\pi\)
\(458\) 12.2708 + 21.2537i 0.573378 + 0.993120i
\(459\) 0 0
\(460\) −4.25608 + 7.37174i −0.198441 + 0.343709i
\(461\) −15.4375 + 12.9536i −0.718996 + 0.603309i −0.927107 0.374796i \(-0.877713\pi\)
0.208112 + 0.978105i \(0.433268\pi\)
\(462\) 0 0
\(463\) 0.782554 4.43809i 0.0363684 0.206255i −0.961209 0.275821i \(-0.911050\pi\)
0.997577 + 0.0695658i \(0.0221614\pi\)
\(464\) 0.0377283 0.213968i 0.00175149 0.00993320i
\(465\) 0 0
\(466\) 23.4575 19.6832i 1.08665 0.911808i
\(467\) −5.98885 −0.277131 −0.138566 0.990353i \(-0.544249\pi\)
−0.138566 + 0.990353i \(0.544249\pi\)
\(468\) 0 0
\(469\) −7.16732 29.7652i −0.330956 1.37443i
\(470\) 4.48289 + 1.63164i 0.206780 + 0.0752619i
\(471\) 0 0
\(472\) 4.63555 26.2895i 0.213369 1.21007i
\(473\) −1.38674 + 7.86461i −0.0637625 + 0.361615i
\(474\) 0 0
\(475\) 21.3718 + 7.77868i 0.980603 + 0.356910i
\(476\) −44.3089 + 42.1047i −2.03090 + 1.92987i
\(477\) 0 0
\(478\) 36.2336 1.65728
\(479\) −10.4902 + 8.80236i −0.479312 + 0.402190i −0.850177 0.526496i \(-0.823505\pi\)
0.370866 + 0.928686i \(0.379061\pi\)
\(480\) 0 0
\(481\) 1.16914 6.63052i 0.0533081 0.302326i
\(482\) 2.37621 13.4762i 0.108233 0.613822i
\(483\) 0 0
\(484\) −19.3647 + 16.2489i −0.880214 + 0.738587i
\(485\) 0.484037 0.838376i 0.0219790 0.0380687i
\(486\) 0 0
\(487\) 1.04894 + 1.81682i 0.0475320 + 0.0823279i 0.888813 0.458271i \(-0.151531\pi\)
−0.841281 + 0.540599i \(0.818198\pi\)
\(488\) 2.55829 + 14.5088i 0.115809 + 0.656783i
\(489\) 0 0
\(490\) −7.97417 + 8.57453i −0.360236 + 0.387358i
\(491\) 0.889790 0.323857i 0.0401556 0.0146155i −0.321864 0.946786i \(-0.604309\pi\)
0.362020 + 0.932170i \(0.382087\pi\)
\(492\) 0 0
\(493\) −1.94098 + 1.62868i −0.0874175 + 0.0733520i
\(494\) 14.6300 25.3399i 0.658235 1.14010i
\(495\) 0 0
\(496\) −2.31945 + 4.01741i −0.104146 + 0.180387i
\(497\) 2.40643 21.2490i 0.107943 0.953149i
\(498\) 0 0
\(499\) −25.5527 + 9.30041i −1.14389 + 0.416344i −0.843318 0.537414i \(-0.819401\pi\)
−0.300576 + 0.953758i \(0.597179\pi\)
\(500\) 3.99906 22.6798i 0.178843 1.01427i
\(501\) 0 0
\(502\) −53.9576 + 45.2758i −2.40824 + 2.02076i
\(503\) −6.89642 + 11.9450i −0.307496 + 0.532599i −0.977814 0.209475i \(-0.932825\pi\)
0.670318 + 0.742074i \(0.266158\pi\)
\(504\) 0 0
\(505\) 0.613361 + 1.06237i 0.0272942 + 0.0472749i
\(506\) 14.2351 + 5.18116i 0.632828 + 0.230331i
\(507\) 0 0
\(508\) −40.8252 34.2564i −1.81133 1.51988i
\(509\) −18.2888 15.3461i −0.810636 0.680204i 0.140124 0.990134i \(-0.455250\pi\)
−0.950759 + 0.309930i \(0.899694\pi\)
\(510\) 0 0
\(511\) 4.34279 38.3472i 0.192114 1.69638i
\(512\) −6.63851 −0.293384
\(513\) 0 0
\(514\) −6.92849 12.0005i −0.305603 0.529319i
\(515\) 6.61159 + 2.40642i 0.291341 + 0.106040i
\(516\) 0 0
\(517\) 0.924590 5.24361i 0.0406634 0.230614i
\(518\) 7.38990 14.8470i 0.324694 0.652341i
\(519\) 0 0
\(520\) −5.33399 1.94141i −0.233911 0.0851367i
\(521\) −10.4111 + 18.0326i −0.456120 + 0.790023i −0.998752 0.0499476i \(-0.984095\pi\)
0.542632 + 0.839971i \(0.317428\pi\)
\(522\) 0 0
\(523\) 4.62970 + 8.01887i 0.202443 + 0.350641i 0.949315 0.314327i \(-0.101779\pi\)
−0.746872 + 0.664967i \(0.768445\pi\)
\(524\) −25.8949 9.42496i −1.13122 0.411731i
\(525\) 0 0
\(526\) 55.3618 + 46.4541i 2.41389 + 2.02549i
\(527\) 50.8361 18.5028i 2.21445 0.805995i
\(528\) 0 0
\(529\) −1.86263 10.5635i −0.0809841 0.459284i
\(530\) −7.10761 12.3107i −0.308735 0.534745i
\(531\) 0 0
\(532\) 32.7668 31.1368i 1.42062 1.34995i
\(533\) −0.278085 1.57710i −0.0120452 0.0683116i
\(534\) 0 0
\(535\) 2.78929 + 2.34049i 0.120591 + 0.101188i
\(536\) 34.3536 12.5037i 1.48385 0.540076i
\(537\) 0 0
\(538\) 17.7108 14.8612i 0.763569 0.640710i
\(539\) 10.9702 + 7.10300i 0.472519 + 0.305948i
\(540\) 0 0
\(541\) 10.6424 18.4331i 0.457551 0.792501i −0.541280 0.840842i \(-0.682060\pi\)
0.998831 + 0.0483412i \(0.0153935\pi\)
\(542\) −44.1443 16.0672i −1.89616 0.690146i
\(543\) 0 0
\(544\) 26.0654 + 21.8714i 1.11754 + 0.937730i
\(545\) 1.95611 0.711965i 0.0837904 0.0304972i
\(546\) 0 0
\(547\) 2.16825 + 12.2968i 0.0927078 + 0.525772i 0.995426 + 0.0955390i \(0.0304575\pi\)
−0.902718 + 0.430233i \(0.858431\pi\)
\(548\) 74.8041 3.19547
\(549\) 0 0
\(550\) −19.3646 −0.825710
\(551\) 1.43537 1.20442i 0.0611489 0.0513100i
\(552\) 0 0
\(553\) −24.2474 36.5800i −1.03110 1.55554i
\(554\) 3.61304 + 3.03170i 0.153503 + 0.128805i
\(555\) 0 0
\(556\) −2.37292 13.4575i −0.100634 0.570725i
\(557\) −29.3181 −1.24225 −0.621124 0.783712i \(-0.713324\pi\)
−0.621124 + 0.783712i \(0.713324\pi\)
\(558\) 0 0
\(559\) −5.32039 9.21518i −0.225028 0.389761i
\(560\) −0.905016 0.668728i −0.0382439 0.0282589i
\(561\) 0 0
\(562\) −8.99657 + 51.0221i −0.379497 + 2.15224i
\(563\) −1.16127 + 0.422668i −0.0489418 + 0.0178133i −0.366375 0.930467i \(-0.619401\pi\)
0.317433 + 0.948281i \(0.397179\pi\)
\(564\) 0 0
\(565\) −1.36359 7.73331i −0.0573667 0.325343i
\(566\) 63.5326 2.67047
\(567\) 0 0
\(568\) 25.5355 1.07145
\(569\) 2.60292 + 14.7619i 0.109120 + 0.618851i 0.989494 + 0.144571i \(0.0461803\pi\)
−0.880374 + 0.474280i \(0.842709\pi\)
\(570\) 0 0
\(571\) 40.0045 14.5605i 1.67414 0.609336i 0.681650 0.731678i \(-0.261263\pi\)
0.992488 + 0.122342i \(0.0390404\pi\)
\(572\) −2.71313 + 15.3869i −0.113441 + 0.643359i
\(573\) 0 0
\(574\) 0.443895 3.91963i 0.0185278 0.163602i
\(575\) −7.84464 13.5873i −0.327144 0.566630i
\(576\) 0 0
\(577\) −1.84922 −0.0769842 −0.0384921 0.999259i \(-0.512255\pi\)
−0.0384921 + 0.999259i \(0.512255\pi\)
\(578\) 12.1302 + 68.7940i 0.504551 + 2.86145i
\(579\) 0 0
\(580\) −0.686726 0.576232i −0.0285148 0.0239267i
\(581\) −19.7786 + 39.7371i −0.820554 + 1.64857i
\(582\) 0 0
\(583\) −12.1539 + 10.1983i −0.503361 + 0.422370i
\(584\) 46.0829 1.90692
\(585\) 0 0
\(586\) −14.7677 −0.610050
\(587\) 5.36637 + 30.4342i 0.221494 + 1.25615i 0.869276 + 0.494327i \(0.164586\pi\)
−0.647782 + 0.761826i \(0.724303\pi\)
\(588\) 0 0
\(589\) −37.5937 + 13.6830i −1.54902 + 0.563797i
\(590\) −10.8276 9.08548i −0.445767 0.374043i
\(591\) 0 0
\(592\) 1.49766 + 0.545104i 0.0615535 + 0.0224036i
\(593\) 13.3896 23.1914i 0.549844 0.952357i −0.448441 0.893812i \(-0.648021\pi\)
0.998285 0.0585448i \(-0.0186461\pi\)
\(594\) 0 0
\(595\) 3.07214 + 12.7583i 0.125945 + 0.523038i
\(596\) 39.8755 33.4595i 1.63336 1.37055i
\(597\) 0 0
\(598\) −18.9674 + 6.90358i −0.775636 + 0.282308i
\(599\) 0.893093 + 0.749394i 0.0364908 + 0.0306194i 0.660851 0.750517i \(-0.270196\pi\)
−0.624360 + 0.781137i \(0.714640\pi\)
\(600\) 0 0
\(601\) 1.77160 + 10.0473i 0.0722652 + 0.409836i 0.999385 + 0.0350707i \(0.0111656\pi\)
−0.927120 + 0.374765i \(0.877723\pi\)
\(602\) −6.13605 25.4824i −0.250087 1.03858i
\(603\) 0 0
\(604\) 15.4429 + 26.7480i 0.628365 + 1.08836i
\(605\) 0.942431 + 5.34479i 0.0383153 + 0.217297i
\(606\) 0 0
\(607\) −30.2305 + 11.0030i −1.22702 + 0.446599i −0.872576 0.488479i \(-0.837552\pi\)
−0.354444 + 0.935077i \(0.615330\pi\)
\(608\) −19.2755 16.1741i −0.781726 0.655946i
\(609\) 0 0
\(610\) 7.33019 + 2.66797i 0.296791 + 0.108023i
\(611\) 3.54729 + 6.14408i 0.143508 + 0.248563i
\(612\) 0 0
\(613\) −8.12274 + 14.0690i −0.328074 + 0.568241i −0.982130 0.188205i \(-0.939733\pi\)
0.654055 + 0.756447i \(0.273066\pi\)
\(614\) 25.9793 + 9.45570i 1.04844 + 0.381601i
\(615\) 0 0
\(616\) −6.95370 + 13.9707i −0.280173 + 0.562894i
\(617\) −0.147224 + 0.834951i −0.00592703 + 0.0336139i −0.987628 0.156816i \(-0.949877\pi\)
0.981701 + 0.190430i \(0.0609882\pi\)
\(618\) 0 0
\(619\) 7.21056 + 2.62443i 0.289817 + 0.105485i 0.482837 0.875710i \(-0.339606\pi\)
−0.193021 + 0.981195i \(0.561828\pi\)
\(620\) 9.57013 + 16.5760i 0.384346 + 0.665707i
\(621\) 0 0
\(622\) 38.2292 1.53285
\(623\) −3.41922 + 1.48948i −0.136988 + 0.0596746i
\(624\) 0 0
\(625\) 13.3655 + 11.2150i 0.534619 + 0.448599i
\(626\) 5.61531 + 4.71181i 0.224433 + 0.188322i
\(627\) 0 0
\(628\) 19.6772 + 7.16190i 0.785204 + 0.285791i
\(629\) −9.29327 16.0964i −0.370547 0.641806i
\(630\) 0 0
\(631\) 19.1932 33.2436i 0.764069 1.32341i −0.176668 0.984271i \(-0.556532\pi\)
0.940737 0.339136i \(-0.110135\pi\)
\(632\) 40.1443 33.6851i 1.59685 1.33992i
\(633\) 0 0
\(634\) 0.411952 2.33630i 0.0163607 0.0927862i
\(635\) −10.7518 + 3.91335i −0.426674 + 0.155297i
\(636\) 0 0
\(637\) −17.2809 + 2.14561i −0.684695 + 0.0850121i
\(638\) −0.797692 + 1.38164i −0.0315809 + 0.0546998i
\(639\) 0 0
\(640\) −7.00429 + 12.1318i −0.276869 + 0.479551i
\(641\) 17.3262 14.5384i 0.684342 0.574231i −0.232929 0.972494i \(-0.574831\pi\)
0.917271 + 0.398263i \(0.130387\pi\)
\(642\) 0 0
\(643\) −2.28504 + 0.831686i −0.0901131 + 0.0327985i −0.386683 0.922213i \(-0.626379\pi\)
0.296570 + 0.955011i \(0.404157\pi\)
\(644\) −31.1222 + 1.92469i −1.22639 + 0.0758434i
\(645\) 0 0
\(646\) −14.0264 79.5478i −0.551863 3.12977i
\(647\) −11.4140 19.7696i −0.448729 0.777222i 0.549574 0.835445i \(-0.314790\pi\)
−0.998304 + 0.0582230i \(0.981457\pi\)
\(648\) 0 0
\(649\) −7.88781 + 13.6621i −0.309624 + 0.536284i
\(650\) 19.7656 16.5853i 0.775271 0.650530i
\(651\) 0 0
\(652\) 10.2115 57.9122i 0.399913 2.26802i
\(653\) 3.15325 17.8830i 0.123396 0.699815i −0.858851 0.512225i \(-0.828821\pi\)
0.982247 0.187590i \(-0.0600675\pi\)
\(654\) 0 0
\(655\) −4.53215 + 3.80292i −0.177086 + 0.148593i
\(656\) 0.379086 0.0148008
\(657\) 0 0
\(658\) 4.09112 + 16.9900i 0.159488 + 0.662339i
\(659\) −2.87917 1.04793i −0.112156 0.0408216i 0.285332 0.958429i \(-0.407896\pi\)
−0.397489 + 0.917607i \(0.630118\pi\)
\(660\) 0 0
\(661\) −5.25948 + 29.8280i −0.204570 + 1.16017i 0.693545 + 0.720413i \(0.256048\pi\)
−0.898115 + 0.439761i \(0.855063\pi\)
\(662\) −10.5570 + 59.8716i −0.410309 + 2.32698i
\(663\) 0 0
\(664\) −49.8061 18.1279i −1.93285 0.703501i
\(665\) −2.27187 9.43484i −0.0880993 0.365867i
\(666\) 0 0
\(667\) −1.29259 −0.0500491
\(668\) −15.1681 + 12.7276i −0.586872 + 0.492444i
\(669\) 0 0
\(670\) 3.36128 19.0628i 0.129858 0.736459i
\(671\) 1.51184 8.57407i 0.0583639 0.330998i
\(672\) 0 0
\(673\) 10.6644 8.94848i 0.411082 0.344939i −0.413677 0.910424i \(-0.635756\pi\)
0.824758 + 0.565485i \(0.191311\pi\)
\(674\) −12.0886 + 20.9380i −0.465634 + 0.806502i
\(675\) 0 0
\(676\) 11.4573 + 19.8447i 0.440666 + 0.763256i
\(677\) 8.57044 + 48.6054i 0.329389 + 1.86806i 0.476843 + 0.878988i \(0.341781\pi\)
−0.147454 + 0.989069i \(0.547108\pi\)
\(678\) 0 0
\(679\) 3.53948 0.218892i 0.135833 0.00840030i
\(680\) −14.7250 + 5.35946i −0.564678 + 0.205526i
\(681\) 0 0
\(682\) 26.0938 21.8953i 0.999184 0.838415i
\(683\) −5.15894 + 8.93555i −0.197401 + 0.341909i −0.947685 0.319207i \(-0.896584\pi\)
0.750284 + 0.661116i \(0.229917\pi\)
\(684\) 0 0
\(685\) 8.03004 13.9084i 0.306812 0.531414i
\(686\) −42.3199 6.99349i −1.61578 0.267013i
\(687\) 0 0
\(688\) 2.36696 0.861502i 0.0902394 0.0328445i
\(689\) 3.67095 20.8190i 0.139852 0.793140i
\(690\) 0 0
\(691\) 19.7323 16.5574i 0.750654 0.629873i −0.185022 0.982734i \(-0.559236\pi\)
0.935676 + 0.352861i \(0.114791\pi\)
\(692\) −9.80542 + 16.9835i −0.372746 + 0.645616i
\(693\) 0 0
\(694\) 2.16918 + 3.75713i 0.0823411 + 0.142619i
\(695\) −2.75690 1.00343i −0.104575 0.0380623i
\(696\) 0 0
\(697\) −3.38660 2.84169i −0.128276 0.107637i
\(698\) 24.8257 + 20.8313i 0.939668 + 0.788475i
\(699\) 0 0
\(700\) 36.5429 15.9188i 1.38119 0.601673i
\(701\) 37.7435 1.42555 0.712776 0.701392i \(-0.247438\pi\)
0.712776 + 0.701392i \(0.247438\pi\)
\(702\) 0 0
\(703\) 6.87245 + 11.9034i 0.259199 + 0.448946i
\(704\) 22.1985 + 8.07960i 0.836638 + 0.304511i
\(705\) 0 0
\(706\) −1.90836 + 10.8228i −0.0718221 + 0.407323i
\(707\) −2.00236 + 4.02294i −0.0753066 + 0.151298i
\(708\) 0 0
\(709\) −41.0034 14.9240i −1.53991 0.560483i −0.573890 0.818933i \(-0.694566\pi\)
−0.966025 + 0.258450i \(0.916788\pi\)
\(710\) 6.76026 11.7091i 0.253708 0.439435i
\(711\) 0 0
\(712\) −2.22672 3.85680i −0.0834500 0.144540i
\(713\) 25.9336 + 9.43907i 0.971222 + 0.353496i
\(714\) 0 0
\(715\) 2.56966 + 2.15620i 0.0960999 + 0.0806374i
\(716\) −74.9595 + 27.2830i −2.80137 + 1.01961i
\(717\) 0 0
\(718\) −3.26743 18.5305i −0.121940 0.691554i
\(719\) 8.96074 + 15.5205i 0.334179 + 0.578815i 0.983327 0.181847i \(-0.0582076\pi\)
−0.649148 + 0.760663i \(0.724874\pi\)
\(720\) 0 0
\(721\) 6.03378 + 25.0577i 0.224710 + 0.933197i
\(722\) 2.73128 + 15.4899i 0.101648 + 0.576473i
\(723\) 0 0
\(724\) −0.147915 0.124116i −0.00549723 0.00461272i
\(725\) 1.55267 0.565125i 0.0576647 0.0209882i
\(726\) 0 0
\(727\) −18.2453 + 15.3097i −0.676682 + 0.567804i −0.915035 0.403375i \(-0.867837\pi\)
0.238353 + 0.971179i \(0.423393\pi\)
\(728\) −4.86784 20.2156i −0.180414 0.749242i
\(729\) 0 0
\(730\) 12.2000 21.1309i 0.451541 0.782091i
\(731\) −27.6033 10.0468i −1.02095 0.371594i
\(732\) 0 0
\(733\) 24.7611 + 20.7770i 0.914572 + 0.767417i 0.972983 0.230875i \(-0.0741589\pi\)
−0.0584109 + 0.998293i \(0.518603\pi\)
\(734\) −15.5667 + 5.66583i −0.574579 + 0.209130i
\(735\) 0 0
\(736\) 3.01419 + 17.0943i 0.111105 + 0.630106i
\(737\) −21.6044 −0.795807
\(738\) 0 0
\(739\) 13.5866 0.499791 0.249896 0.968273i \(-0.419604\pi\)
0.249896 + 0.968273i \(0.419604\pi\)
\(740\) 5.03749 4.22696i 0.185182 0.155386i
\(741\) 0 0
\(742\) 23.2033 46.6178i 0.851822 1.71139i
\(743\) 18.9955 + 15.9391i 0.696876 + 0.584749i 0.920883 0.389839i \(-0.127469\pi\)
−0.224007 + 0.974588i \(0.571914\pi\)
\(744\) 0 0
\(745\) −1.94064 11.0059i −0.0710995 0.403225i
\(746\) 2.01234 0.0736769
\(747\) 0 0
\(748\) 21.5661 + 37.3537i 0.788536 + 1.36578i
\(749\) −1.50095 + 13.2536i −0.0548436 + 0.484274i
\(750\) 0 0
\(751\) −2.53191 + 14.3592i −0.0923909 + 0.523975i 0.903125 + 0.429378i \(0.141267\pi\)
−0.995516 + 0.0945966i \(0.969844\pi\)
\(752\) −1.57813 + 0.574394i −0.0575486 + 0.0209460i
\(753\) 0 0
\(754\) −0.369133 2.09346i −0.0134430 0.0762392i
\(755\) 6.63106 0.241329
\(756\) 0 0
\(757\) 7.78642 0.283002 0.141501 0.989938i \(-0.454807\pi\)
0.141501 + 0.989938i \(0.454807\pi\)
\(758\) −8.93698 50.6841i −0.324606 1.84093i
\(759\) 0 0
\(760\) 10.8893 3.96336i 0.394995 0.143766i
\(761\) 3.51730 19.9476i 0.127502 0.723099i −0.852288 0.523072i \(-0.824786\pi\)
0.979790 0.200027i \(-0.0641030\pi\)
\(762\) 0 0
\(763\) 6.13287 + 4.53165i 0.222025 + 0.164057i
\(764\) −20.9044 36.2075i −0.756296 1.30994i
\(765\) 0 0
\(766\) −28.5575 −1.03182
\(767\) −3.65010 20.7007i −0.131797 0.747460i
\(768\) 0 0
\(769\) 12.3416 + 10.3559i 0.445051 + 0.373442i 0.837595 0.546291i \(-0.183961\pi\)
−0.392545 + 0.919733i \(0.628405\pi\)
\(770\) 4.56522 + 6.88716i 0.164519 + 0.248196i
\(771\) 0 0
\(772\) −10.7582 + 9.02717i −0.387195 + 0.324895i
\(773\) 8.76026 0.315084 0.157542 0.987512i \(-0.449643\pi\)
0.157542 + 0.987512i \(0.449643\pi\)
\(774\) 0 0
\(775\) −35.2786 −1.26724
\(776\) 0.735321 + 4.17022i 0.0263965 + 0.149702i
\(777\) 0 0
\(778\) 46.3773 16.8799i 1.66271 0.605176i
\(779\) 2.50441 + 2.10145i 0.0897299 + 0.0752924i
\(780\) 0 0
\(781\) −14.1803 5.16121i −0.507412 0.184683i
\(782\) −27.8609 + 48.2565i −0.996304 + 1.72565i
\(783\) 0 0