Properties

Label 567.2.u.a.550.17
Level $567$
Weight $2$
Character 567.550
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 550.17
Character \(\chi\) \(=\) 567.550
Dual form 567.2.u.a.100.17

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.279530 + 1.58529i) q^{2} +(-0.555633 + 0.202234i) q^{4} +(-0.230811 + 0.0840085i) q^{5} +(-1.31413 - 2.29631i) q^{7} +(1.13383 + 1.96386i) q^{8} +O(q^{10})\) \(q+(0.279530 + 1.58529i) q^{2} +(-0.555633 + 0.202234i) q^{4} +(-0.230811 + 0.0840085i) q^{5} +(-1.31413 - 2.29631i) q^{7} +(1.13383 + 1.96386i) q^{8} +(-0.197697 - 0.342421i) q^{10} +(4.84773 + 1.76443i) q^{11} +(4.55694 - 1.65859i) q^{13} +(3.27299 - 2.72518i) q^{14} +(-3.70226 + 3.10657i) q^{16} +(0.800052 + 1.38573i) q^{17} +(-1.01489 + 1.75785i) q^{19} +(0.111257 - 0.0933558i) q^{20} +(-1.44205 + 8.17829i) q^{22} +(-0.761889 + 4.32089i) q^{23} +(-3.78401 + 3.17516i) q^{25} +(3.90315 + 6.76046i) q^{26} +(1.19457 + 1.01014i) q^{28} +(-4.90485 - 1.78522i) q^{29} +(6.87843 - 2.50354i) q^{31} +(-2.48544 - 2.08554i) q^{32} +(-1.97315 + 1.65567i) q^{34} +(0.496227 + 0.419617i) q^{35} +7.97175 q^{37} +(-3.07039 - 1.11753i) q^{38} +(-0.426682 - 0.358029i) q^{40} +(5.13780 - 1.87001i) q^{41} +(-1.25671 - 7.12716i) q^{43} -3.05039 q^{44} -7.06285 q^{46} +(-2.05603 - 0.748334i) q^{47} +(-3.54610 + 6.03533i) q^{49} +(-6.09130 - 5.11121i) q^{50} +(-2.19656 + 1.84314i) q^{52} +(-3.36601 + 5.83010i) q^{53} -1.26714 q^{55} +(3.01962 - 5.18441i) q^{56} +(1.45904 - 8.27464i) q^{58} +(-9.52886 - 7.99566i) q^{59} +(-3.15274 - 1.14750i) q^{61} +(5.89158 + 10.2045i) q^{62} +(-2.22153 + 3.84780i) q^{64} +(-0.912458 + 0.765644i) q^{65} +(-1.29472 + 7.34273i) q^{67} +(-0.724777 - 0.608160i) q^{68} +(-0.526505 + 0.903961i) q^{70} +(0.508002 - 0.879885i) q^{71} +5.79634 q^{73} +(2.22834 + 12.6376i) q^{74} +(0.208412 - 1.18196i) q^{76} +(-2.31889 - 13.4506i) q^{77} +(-1.44495 - 8.19469i) q^{79} +(0.593546 - 1.02805i) q^{80} +(4.40068 + 7.62220i) q^{82} +(-6.59880 - 2.40177i) q^{83} +(-0.301074 - 0.252631i) q^{85} +(10.9473 - 3.98451i) q^{86} +(2.03143 + 11.5208i) q^{88} +(7.78417 - 13.4826i) q^{89} +(-9.79707 - 8.28455i) q^{91} +(-0.450499 - 2.55491i) q^{92} +(0.611607 - 3.46859i) q^{94} +(0.0865749 - 0.490991i) q^{95} +(-1.78818 - 10.1413i) q^{97} +(-10.5590 - 3.93456i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 132 q + 3 q^{2} - 3 q^{4} + 3 q^{5} - 6 q^{7} + 6 q^{8}+O(q^{10}) \) 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 \(\left(\mathbb{Z}/567\mathbb{Z}\right)^\times\).

\(n\) \(325\) \(407\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{9}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.279530 + 1.58529i 0.197658 + 1.12097i 0.908583 + 0.417704i \(0.137165\pi\)
−0.710925 + 0.703267i \(0.751724\pi\)
\(3\) 0 0
\(4\) −0.555633 + 0.202234i −0.277817 + 0.101117i
\(5\) −0.230811 + 0.0840085i −0.103222 + 0.0375697i −0.393115 0.919489i \(-0.628603\pi\)
0.289893 + 0.957059i \(0.406380\pi\)
\(6\) 0 0
\(7\) −1.31413 2.29631i −0.496696 0.867924i
\(8\) 1.13383 + 1.96386i 0.400871 + 0.694328i
\(9\) 0 0
\(10\) −0.197697 0.342421i −0.0625172 0.108283i
\(11\) 4.84773 + 1.76443i 1.46165 + 0.531996i 0.945818 0.324696i \(-0.105262\pi\)
0.515828 + 0.856692i \(0.327484\pi\)
\(12\) 0 0
\(13\) 4.55694 1.65859i 1.26387 0.460010i 0.378803 0.925477i \(-0.376336\pi\)
0.885065 + 0.465467i \(0.154114\pi\)
\(14\) 3.27299 2.72518i 0.874743 0.728334i
\(15\) 0 0
\(16\) −3.70226 + 3.10657i −0.925565 + 0.776641i
\(17\) 0.800052 + 1.38573i 0.194041 + 0.336089i 0.946586 0.322452i \(-0.104507\pi\)
−0.752545 + 0.658541i \(0.771174\pi\)
\(18\) 0 0
\(19\) −1.01489 + 1.75785i −0.232832 + 0.403278i −0.958641 0.284620i \(-0.908133\pi\)
0.725808 + 0.687897i \(0.241466\pi\)
\(20\) 0.111257 0.0933558i 0.0248778 0.0208750i
\(21\) 0 0
\(22\) −1.44205 + 8.17829i −0.307447 + 1.74362i
\(23\) −0.761889 + 4.32089i −0.158865 + 0.900967i 0.796302 + 0.604899i \(0.206787\pi\)
−0.955167 + 0.296068i \(0.904324\pi\)
\(24\) 0 0
\(25\) −3.78401 + 3.17516i −0.756801 + 0.635032i
\(26\) 3.90315 + 6.76046i 0.765472 + 1.32584i
\(27\) 0 0
\(28\) 1.19457 + 1.01014i 0.225752 + 0.190899i
\(29\) −4.90485 1.78522i −0.910807 0.331507i −0.156232 0.987720i \(-0.549935\pi\)
−0.754575 + 0.656214i \(0.772157\pi\)
\(30\) 0 0
\(31\) 6.87843 2.50354i 1.23540 0.449650i 0.359958 0.932969i \(-0.382791\pi\)
0.875444 + 0.483319i \(0.160569\pi\)
\(32\) −2.48544 2.08554i −0.439369 0.368674i
\(33\) 0 0
\(34\) −1.97315 + 1.65567i −0.338393 + 0.283945i
\(35\) 0.496227 + 0.419617i 0.0838777 + 0.0709282i
\(36\) 0 0
\(37\) 7.97175 1.31055 0.655273 0.755392i \(-0.272553\pi\)
0.655273 + 0.755392i \(0.272553\pi\)
\(38\) −3.07039 1.11753i −0.498084 0.181288i
\(39\) 0 0
\(40\) −0.426682 0.358029i −0.0674644 0.0566094i
\(41\) 5.13780 1.87001i 0.802389 0.292046i 0.0919131 0.995767i \(-0.470702\pi\)
0.710476 + 0.703721i \(0.248480\pi\)
\(42\) 0 0
\(43\) −1.25671 7.12716i −0.191646 1.08688i −0.917114 0.398625i \(-0.869488\pi\)
0.725468 0.688256i \(-0.241624\pi\)
\(44\) −3.05039 −0.459863
\(45\) 0 0
\(46\) −7.06285 −1.04136
\(47\) −2.05603 0.748334i −0.299903 0.109156i 0.187686 0.982229i \(-0.439901\pi\)
−0.487589 + 0.873073i \(0.662123\pi\)
\(48\) 0 0
\(49\) −3.54610 + 6.03533i −0.506586 + 0.862190i
\(50\) −6.09130 5.11121i −0.861440 0.722834i
\(51\) 0 0
\(52\) −2.19656 + 1.84314i −0.304609 + 0.255597i
\(53\) −3.36601 + 5.83010i −0.462357 + 0.800826i −0.999078 0.0429338i \(-0.986330\pi\)
0.536721 + 0.843760i \(0.319663\pi\)
\(54\) 0 0
\(55\) −1.26714 −0.170861
\(56\) 3.01962 5.18441i 0.403514 0.692795i
\(57\) 0 0
\(58\) 1.45904 8.27464i 0.191582 1.08651i
\(59\) −9.52886 7.99566i −1.24055 1.04095i −0.997481 0.0709378i \(-0.977401\pi\)
−0.243071 0.970009i \(-0.578155\pi\)
\(60\) 0 0
\(61\) −3.15274 1.14750i −0.403667 0.146923i 0.132204 0.991223i \(-0.457795\pi\)
−0.535871 + 0.844300i \(0.680017\pi\)
\(62\) 5.89158 + 10.2045i 0.748231 + 1.29597i
\(63\) 0 0
\(64\) −2.22153 + 3.84780i −0.277691 + 0.480975i
\(65\) −0.912458 + 0.765644i −0.113177 + 0.0949664i
\(66\) 0 0
\(67\) −1.29472 + 7.34273i −0.158175 + 0.897058i 0.797649 + 0.603121i \(0.206077\pi\)
−0.955825 + 0.293936i \(0.905035\pi\)
\(68\) −0.724777 0.608160i −0.0878922 0.0737503i
\(69\) 0 0
\(70\) −0.526505 + 0.903961i −0.0629294 + 0.108044i
\(71\) 0.508002 0.879885i 0.0602887 0.104423i −0.834306 0.551302i \(-0.814131\pi\)
0.894594 + 0.446879i \(0.147465\pi\)
\(72\) 0 0
\(73\) 5.79634 0.678410 0.339205 0.940712i \(-0.389842\pi\)
0.339205 + 0.940712i \(0.389842\pi\)
\(74\) 2.22834 + 12.6376i 0.259040 + 1.46909i
\(75\) 0 0
\(76\) 0.208412 1.18196i 0.0239065 0.135580i
\(77\) −2.31889 13.4506i −0.264262 1.53284i
\(78\) 0 0
\(79\) −1.44495 8.19469i −0.162569 0.921975i −0.951536 0.307539i \(-0.900495\pi\)
0.788967 0.614436i \(-0.210616\pi\)
\(80\) 0.593546 1.02805i 0.0663605 0.114940i
\(81\) 0 0
\(82\) 4.40068 + 7.62220i 0.485973 + 0.841731i
\(83\) −6.59880 2.40177i −0.724312 0.263628i −0.0465569 0.998916i \(-0.514825\pi\)
−0.677755 + 0.735288i \(0.737047\pi\)
\(84\) 0 0
\(85\) −0.301074 0.252631i −0.0326561 0.0274017i
\(86\) 10.9473 3.98451i 1.18048 0.429661i
\(87\) 0 0
\(88\) 2.03143 + 11.5208i 0.216551 + 1.22812i
\(89\) 7.78417 13.4826i 0.825120 1.42915i −0.0767068 0.997054i \(-0.524441\pi\)
0.901827 0.432097i \(-0.142226\pi\)
\(90\) 0 0
\(91\) −9.79707 8.28455i −1.02701 0.868457i
\(92\) −0.450499 2.55491i −0.0469678 0.266368i
\(93\) 0 0
\(94\) 0.611607 3.46859i 0.0630824 0.357758i
\(95\) 0.0865749 0.490991i 0.00888240 0.0503746i
\(96\) 0 0
\(97\) −1.78818 10.1413i −0.181563 1.02969i −0.930293 0.366818i \(-0.880447\pi\)
0.748730 0.662875i \(-0.230664\pi\)
\(98\) −10.5590 3.93456i −1.06662 0.397450i
\(99\) 0 0
\(100\) 1.46039 2.52948i 0.146039 0.252948i
\(101\) 0.216381 + 1.22716i 0.0215307 + 0.122107i 0.993679 0.112261i \(-0.0358092\pi\)
−0.972148 + 0.234368i \(0.924698\pi\)
\(102\) 0 0
\(103\) −5.49218 + 1.99899i −0.541161 + 0.196966i −0.598115 0.801410i \(-0.704083\pi\)
0.0569541 + 0.998377i \(0.481861\pi\)
\(104\) 8.42404 + 7.06861i 0.826045 + 0.693134i
\(105\) 0 0
\(106\) −10.1833 3.70643i −0.989092 0.360000i
\(107\) 0.697132 + 1.20747i 0.0673943 + 0.116730i 0.897754 0.440498i \(-0.145198\pi\)
−0.830359 + 0.557228i \(0.811865\pi\)
\(108\) 0 0
\(109\) 7.71790 13.3678i 0.739241 1.28040i −0.213596 0.976922i \(-0.568518\pi\)
0.952837 0.303481i \(-0.0981489\pi\)
\(110\) −0.354204 2.00879i −0.0337720 0.191530i
\(111\) 0 0
\(112\) 11.9989 + 4.41910i 1.13379 + 0.417566i
\(113\) −1.58825 + 9.00739i −0.149410 + 0.847344i 0.814310 + 0.580430i \(0.197115\pi\)
−0.963720 + 0.266915i \(0.913996\pi\)
\(114\) 0 0
\(115\) −0.187139 1.06132i −0.0174508 0.0989682i
\(116\) 3.08633 0.286558
\(117\) 0 0
\(118\) 10.0119 17.3411i 0.921667 1.59637i
\(119\) 2.13070 3.65821i 0.195321 0.335347i
\(120\) 0 0
\(121\) 11.9608 + 10.0363i 1.08735 + 0.912393i
\(122\) 0.937845 5.31878i 0.0849085 0.481540i
\(123\) 0 0
\(124\) −3.31558 + 2.78210i −0.297748 + 0.249840i
\(125\) 1.22071 2.11434i 0.109184 0.189112i
\(126\) 0 0
\(127\) −5.99018 10.3753i −0.531543 0.920659i −0.999322 0.0368140i \(-0.988279\pi\)
0.467779 0.883845i \(-0.345054\pi\)
\(128\) −12.8186 4.66558i −1.13301 0.412383i
\(129\) 0 0
\(130\) −1.46883 1.23249i −0.128825 0.108097i
\(131\) −2.70243 + 15.3262i −0.236112 + 1.33906i 0.604147 + 0.796873i \(0.293514\pi\)
−0.840259 + 0.542185i \(0.817597\pi\)
\(132\) 0 0
\(133\) 5.37027 + 0.0204650i 0.465661 + 0.00177454i
\(134\) −12.0023 −1.03684
\(135\) 0 0
\(136\) −1.81425 + 3.14238i −0.155571 + 0.269456i
\(137\) −12.6174 + 10.5872i −1.07797 + 0.904527i −0.995751 0.0920869i \(-0.970646\pi\)
−0.0822224 + 0.996614i \(0.526202\pi\)
\(138\) 0 0
\(139\) −9.40916 7.89523i −0.798075 0.669664i 0.149655 0.988738i \(-0.452184\pi\)
−0.947730 + 0.319074i \(0.896628\pi\)
\(140\) −0.360581 0.132799i −0.0304746 0.0112236i
\(141\) 0 0
\(142\) 1.53688 + 0.559377i 0.128972 + 0.0469419i
\(143\) 25.0173 2.09205
\(144\) 0 0
\(145\) 1.28207 0.106470
\(146\) 1.62025 + 9.18890i 0.134093 + 0.760479i
\(147\) 0 0
\(148\) −4.42936 + 1.61216i −0.364092 + 0.132518i
\(149\) −2.57300 2.15900i −0.210788 0.176872i 0.531281 0.847196i \(-0.321711\pi\)
−0.742069 + 0.670324i \(0.766155\pi\)
\(150\) 0 0
\(151\) 9.11293 + 3.31683i 0.741600 + 0.269920i 0.685067 0.728481i \(-0.259773\pi\)
0.0565331 + 0.998401i \(0.481995\pi\)
\(152\) −4.60288 −0.373343
\(153\) 0 0
\(154\) 20.6750 7.43597i 1.66604 0.599208i
\(155\) −1.37730 + 1.15569i −0.110628 + 0.0928275i
\(156\) 0 0
\(157\) −1.72819 1.45013i −0.137925 0.115733i 0.571215 0.820800i \(-0.306472\pi\)
−0.709140 + 0.705068i \(0.750917\pi\)
\(158\) 12.5871 4.58132i 1.00137 0.364471i
\(159\) 0 0
\(160\) 0.748872 + 0.272567i 0.0592035 + 0.0215483i
\(161\) 10.9233 3.92869i 0.860879 0.309624i
\(162\) 0 0
\(163\) −0.843390 1.46079i −0.0660594 0.114418i 0.831104 0.556117i \(-0.187709\pi\)
−0.897163 + 0.441699i \(0.854376\pi\)
\(164\) −2.47655 + 2.07807i −0.193386 + 0.162270i
\(165\) 0 0
\(166\) 1.96294 11.1324i 0.152354 0.864041i
\(167\) 2.50098 14.1838i 0.193532 1.09757i −0.720963 0.692974i \(-0.756300\pi\)
0.914494 0.404598i \(-0.132589\pi\)
\(168\) 0 0
\(169\) 8.05621 6.75996i 0.619708 0.519997i
\(170\) 0.316336 0.547909i 0.0242618 0.0420227i
\(171\) 0 0
\(172\) 2.13962 + 3.70593i 0.163145 + 0.282575i
\(173\) −1.35283 + 1.13516i −0.102854 + 0.0863048i −0.692765 0.721164i \(-0.743607\pi\)
0.589910 + 0.807469i \(0.299163\pi\)
\(174\) 0 0
\(175\) 12.2638 + 4.51667i 0.927060 + 0.341429i
\(176\) −23.4289 + 8.52742i −1.76602 + 0.642779i
\(177\) 0 0
\(178\) 23.5498 + 8.57141i 1.76513 + 0.642454i
\(179\) −9.33259 16.1645i −0.697550 1.20819i −0.969313 0.245829i \(-0.920940\pi\)
0.271763 0.962364i \(-0.412393\pi\)
\(180\) 0 0
\(181\) 3.45518 + 5.98454i 0.256821 + 0.444827i 0.965389 0.260816i \(-0.0839915\pi\)
−0.708567 + 0.705643i \(0.750658\pi\)
\(182\) 10.3949 17.8470i 0.770518 1.32291i
\(183\) 0 0
\(184\) −9.34946 + 3.40292i −0.689251 + 0.250867i
\(185\) −1.83997 + 0.669694i −0.135277 + 0.0492369i
\(186\) 0 0
\(187\) 1.43341 + 8.12929i 0.104822 + 0.594473i
\(188\) 1.29374 0.0943555
\(189\) 0 0
\(190\) 0.802565 0.0582242
\(191\) −0.731779 4.15013i −0.0529497 0.300293i 0.946820 0.321764i \(-0.104276\pi\)
−0.999769 + 0.0214718i \(0.993165\pi\)
\(192\) 0 0
\(193\) −16.5826 + 6.03556i −1.19364 + 0.434449i −0.861000 0.508606i \(-0.830161\pi\)
−0.332639 + 0.943054i \(0.607939\pi\)
\(194\) 15.5771 5.66959i 1.11837 0.407053i
\(195\) 0 0
\(196\) 0.749783 4.07057i 0.0535560 0.290755i
\(197\) 3.45583 + 5.98566i 0.246217 + 0.426461i 0.962473 0.271377i \(-0.0874790\pi\)
−0.716256 + 0.697838i \(0.754146\pi\)
\(198\) 0 0
\(199\) −2.90529 5.03211i −0.205950 0.356717i 0.744485 0.667639i \(-0.232695\pi\)
−0.950435 + 0.310923i \(0.899362\pi\)
\(200\) −10.5260 3.83115i −0.744299 0.270903i
\(201\) 0 0
\(202\) −1.88492 + 0.686055i −0.132622 + 0.0482706i
\(203\) 2.34621 + 13.6091i 0.164672 + 0.955170i
\(204\) 0 0
\(205\) −1.02877 + 0.863238i −0.0718522 + 0.0602911i
\(206\) −4.70422 8.14794i −0.327758 0.567694i
\(207\) 0 0
\(208\) −11.7185 + 20.2970i −0.812529 + 1.40734i
\(209\) −8.02153 + 6.73086i −0.554861 + 0.465583i
\(210\) 0 0
\(211\) −1.52641 + 8.65668i −0.105082 + 0.595950i 0.886105 + 0.463484i \(0.153401\pi\)
−0.991187 + 0.132466i \(0.957710\pi\)
\(212\) 0.691223 3.92012i 0.0474734 0.269235i
\(213\) 0 0
\(214\) −1.71932 + 1.44268i −0.117530 + 0.0986197i
\(215\) 0.888805 + 1.53946i 0.0606160 + 0.104990i
\(216\) 0 0
\(217\) −14.7881 12.5050i −1.00388 0.848897i
\(218\) 23.3493 + 8.49844i 1.58141 + 0.575587i
\(219\) 0 0
\(220\) 0.704065 0.256259i 0.0474680 0.0172770i
\(221\) 5.94415 + 4.98774i 0.399847 + 0.335511i
\(222\) 0 0
\(223\) −7.61933 + 6.39338i −0.510228 + 0.428132i −0.861210 0.508250i \(-0.830293\pi\)
0.350981 + 0.936383i \(0.385848\pi\)
\(224\) −1.52283 + 8.44803i −0.101749 + 0.564458i
\(225\) 0 0
\(226\) −14.7233 −0.979381
\(227\) −18.4448 6.71335i −1.22422 0.445581i −0.352608 0.935771i \(-0.614705\pi\)
−0.871616 + 0.490190i \(0.836927\pi\)
\(228\) 0 0
\(229\) 7.22389 + 6.06156i 0.477368 + 0.400559i 0.849474 0.527631i \(-0.176920\pi\)
−0.372106 + 0.928190i \(0.621364\pi\)
\(230\) 1.63019 0.593339i 0.107491 0.0391236i
\(231\) 0 0
\(232\) −2.05536 11.6566i −0.134941 0.765290i
\(233\) −10.4888 −0.687145 −0.343572 0.939126i \(-0.611637\pi\)
−0.343572 + 0.939126i \(0.611637\pi\)
\(234\) 0 0
\(235\) 0.537422 0.0350575
\(236\) 6.91154 + 2.51560i 0.449903 + 0.163751i
\(237\) 0 0
\(238\) 6.39493 + 2.35520i 0.414521 + 0.152665i
\(239\) −5.79830 4.86535i −0.375061 0.314714i 0.435699 0.900093i \(-0.356501\pi\)
−0.810760 + 0.585379i \(0.800946\pi\)
\(240\) 0 0
\(241\) 7.18643 6.03013i 0.462919 0.388435i −0.381285 0.924458i \(-0.624518\pi\)
0.844204 + 0.536023i \(0.180074\pi\)
\(242\) −12.5671 + 21.7669i −0.807844 + 1.39923i
\(243\) 0 0
\(244\) 1.98383 0.127002
\(245\) 0.311462 1.69093i 0.0198986 0.108029i
\(246\) 0 0
\(247\) −1.70926 + 9.69369i −0.108758 + 0.616795i
\(248\) 12.7156 + 10.6696i 0.807441 + 0.677523i
\(249\) 0 0
\(250\) 3.69307 + 1.34417i 0.233570 + 0.0850126i
\(251\) −10.5090 18.2021i −0.663322 1.14891i −0.979737 0.200287i \(-0.935813\pi\)
0.316415 0.948621i \(-0.397521\pi\)
\(252\) 0 0
\(253\) −11.3173 + 19.6022i −0.711515 + 1.23238i
\(254\) 14.7735 12.3964i 0.926970 0.777820i
\(255\) 0 0
\(256\) 2.27008 12.8743i 0.141880 0.804641i
\(257\) 18.8715 + 15.8350i 1.17717 + 0.987762i 0.999994 + 0.00358315i \(0.00114055\pi\)
0.177176 + 0.984179i \(0.443304\pi\)
\(258\) 0 0
\(259\) −10.4759 18.3056i −0.650944 1.13746i
\(260\) 0.352153 0.609947i 0.0218396 0.0378273i
\(261\) 0 0
\(262\) −25.0520 −1.54772
\(263\) 0.272526 + 1.54557i 0.0168047 + 0.0953042i 0.992057 0.125793i \(-0.0401474\pi\)
−0.975252 + 0.221097i \(0.929036\pi\)
\(264\) 0 0
\(265\) 0.287136 1.62843i 0.0176386 0.100034i
\(266\) 1.46871 + 8.51917i 0.0900523 + 0.522344i
\(267\) 0 0
\(268\) −0.765559 4.34170i −0.0467640 0.265212i
\(269\) −2.97432 + 5.15166i −0.181347 + 0.314103i −0.942340 0.334658i \(-0.891379\pi\)
0.760992 + 0.648761i \(0.224712\pi\)
\(270\) 0 0
\(271\) 5.09086 + 8.81763i 0.309248 + 0.535633i 0.978198 0.207674i \(-0.0665895\pi\)
−0.668950 + 0.743307i \(0.733256\pi\)
\(272\) −7.26687 2.64492i −0.440619 0.160372i
\(273\) 0 0
\(274\) −20.3108 17.0428i −1.22702 1.02959i
\(275\) −23.9462 + 8.71570i −1.44401 + 0.525577i
\(276\) 0 0
\(277\) 3.13289 + 17.7675i 0.188237 + 1.06755i 0.921725 + 0.387843i \(0.126780\pi\)
−0.733488 + 0.679702i \(0.762109\pi\)
\(278\) 9.88611 17.1232i 0.592929 1.02698i
\(279\) 0 0
\(280\) −0.261428 + 1.45029i −0.0156233 + 0.0866717i
\(281\) 1.12946 + 6.40548i 0.0673779 + 0.382119i 0.999786 + 0.0207105i \(0.00659283\pi\)
−0.932408 + 0.361408i \(0.882296\pi\)
\(282\) 0 0
\(283\) 2.14044 12.1391i 0.127236 0.721592i −0.852718 0.522371i \(-0.825048\pi\)
0.979955 0.199221i \(-0.0638412\pi\)
\(284\) −0.104320 + 0.591628i −0.00619025 + 0.0351067i
\(285\) 0 0
\(286\) 6.99309 + 39.6598i 0.413510 + 2.34513i
\(287\) −11.0459 9.34055i −0.652017 0.551355i
\(288\) 0 0
\(289\) 7.21983 12.5051i 0.424696 0.735595i
\(290\) 0.358377 + 2.03245i 0.0210446 + 0.119350i
\(291\) 0 0
\(292\) −3.22064 + 1.17222i −0.188474 + 0.0685988i
\(293\) −2.38551 2.00168i −0.139363 0.116939i 0.570441 0.821338i \(-0.306772\pi\)
−0.709804 + 0.704399i \(0.751217\pi\)
\(294\) 0 0
\(295\) 2.87107 + 1.04499i 0.167160 + 0.0608414i
\(296\) 9.03863 + 15.6554i 0.525360 + 0.909950i
\(297\) 0 0
\(298\) 2.70342 4.68246i 0.156605 0.271248i
\(299\) 3.69470 + 20.9537i 0.213670 + 1.21178i
\(300\) 0 0
\(301\) −14.7147 + 12.2518i −0.848141 + 0.706184i
\(302\) −2.71082 + 15.3738i −0.155990 + 0.884664i
\(303\) 0 0
\(304\) −1.70347 9.66084i −0.0977005 0.554087i
\(305\) 0.824089 0.0471872
\(306\) 0 0
\(307\) −8.70368 + 15.0752i −0.496745 + 0.860388i −0.999993 0.00375447i \(-0.998805\pi\)
0.503248 + 0.864142i \(0.332138\pi\)
\(308\) 4.00862 + 7.00465i 0.228412 + 0.399127i
\(309\) 0 0
\(310\) −2.21711 1.86038i −0.125923 0.105662i
\(311\) 4.50894 25.5715i 0.255679 1.45003i −0.538646 0.842532i \(-0.681064\pi\)
0.794325 0.607493i \(-0.207825\pi\)
\(312\) 0 0
\(313\) −20.1564 + 16.9132i −1.13931 + 0.955991i −0.999416 0.0341761i \(-0.989119\pi\)
−0.139890 + 0.990167i \(0.544675\pi\)
\(314\) 1.81580 3.14505i 0.102471 0.177485i
\(315\) 0 0
\(316\) 2.46010 + 4.26102i 0.138392 + 0.239701i
\(317\) −2.51228 0.914394i −0.141104 0.0513575i 0.270503 0.962719i \(-0.412810\pi\)
−0.411607 + 0.911362i \(0.635032\pi\)
\(318\) 0 0
\(319\) −20.6275 17.3085i −1.15492 0.969091i
\(320\) 0.189506 1.07474i 0.0105937 0.0600800i
\(321\) 0 0
\(322\) 9.28153 + 16.2185i 0.517239 + 0.903822i
\(323\) −3.24787 −0.180716
\(324\) 0 0
\(325\) −11.9772 + 20.7451i −0.664376 + 1.15073i
\(326\) 2.08003 1.74536i 0.115202 0.0966663i
\(327\) 0 0
\(328\) 9.49783 + 7.96962i 0.524430 + 0.440049i
\(329\) 0.983492 + 5.70470i 0.0542217 + 0.314510i
\(330\) 0 0
\(331\) −19.3284 7.03494i −1.06238 0.386676i −0.249059 0.968488i \(-0.580121\pi\)
−0.813323 + 0.581813i \(0.802344\pi\)
\(332\) 4.15223 0.227883
\(333\) 0 0
\(334\) 23.1845 1.26860
\(335\) −0.318015 1.80356i −0.0173750 0.0985387i
\(336\) 0 0
\(337\) −26.6331 + 9.69364i −1.45079 + 0.528046i −0.942813 0.333322i \(-0.891830\pi\)
−0.507982 + 0.861368i \(0.669608\pi\)
\(338\) 12.9685 + 10.8818i 0.705392 + 0.591894i
\(339\) 0 0
\(340\) 0.218378 + 0.0794829i 0.0118432 + 0.00431057i
\(341\) 37.7621 2.04493
\(342\) 0 0
\(343\) 18.5190 + 0.211725i 0.999935 + 0.0114321i
\(344\) 12.5718 10.5490i 0.677827 0.568764i
\(345\) 0 0
\(346\) −2.17772 1.82733i −0.117075 0.0982377i
\(347\) 3.24503 1.18110i 0.174203 0.0634045i −0.253446 0.967349i \(-0.581564\pi\)
0.427649 + 0.903945i \(0.359342\pi\)
\(348\) 0 0
\(349\) 13.4023 + 4.87804i 0.717409 + 0.261116i 0.674826 0.737977i \(-0.264219\pi\)
0.0425837 + 0.999093i \(0.486441\pi\)
\(350\) −3.73214 + 20.7043i −0.199491 + 1.10669i
\(351\) 0 0
\(352\) −8.36899 14.4955i −0.446069 0.772614i
\(353\) 18.5879 15.5971i 0.989332 0.830148i 0.00386143 0.999993i \(-0.498771\pi\)
0.985471 + 0.169844i \(0.0543264\pi\)
\(354\) 0 0
\(355\) −0.0433348 + 0.245764i −0.00229997 + 0.0130438i
\(356\) −1.59851 + 9.06559i −0.0847208 + 0.480475i
\(357\) 0 0
\(358\) 23.0168 19.3134i 1.21647 1.02074i
\(359\) 2.27027 3.93223i 0.119820 0.207535i −0.799876 0.600165i \(-0.795101\pi\)
0.919696 + 0.392630i \(0.128435\pi\)
\(360\) 0 0
\(361\) 7.43998 + 12.8864i 0.391578 + 0.678233i
\(362\) −8.52143 + 7.15033i −0.447876 + 0.375813i
\(363\) 0 0
\(364\) 7.11899 + 2.62187i 0.373137 + 0.137423i
\(365\) −1.33786 + 0.486942i −0.0700269 + 0.0254877i
\(366\) 0 0
\(367\) −8.69204 3.16364i −0.453721 0.165141i 0.105043 0.994468i \(-0.466502\pi\)
−0.558764 + 0.829327i \(0.688724\pi\)
\(368\) −10.6024 18.3639i −0.552689 0.957285i
\(369\) 0 0
\(370\) −1.57599 2.72969i −0.0819318 0.141910i
\(371\) 17.8111 + 0.0678745i 0.924708 + 0.00352387i
\(372\) 0 0
\(373\) 35.7808 13.0231i 1.85266 0.674313i 0.868856 0.495064i \(-0.164855\pi\)
0.983804 0.179249i \(-0.0573667\pi\)
\(374\) −12.4866 + 4.54476i −0.645668 + 0.235004i
\(375\) 0 0
\(376\) −0.861575 4.88623i −0.0444323 0.251988i
\(377\) −25.3120 −1.30364
\(378\) 0 0
\(379\) 31.7811 1.63248 0.816242 0.577710i \(-0.196054\pi\)
0.816242 + 0.577710i \(0.196054\pi\)
\(380\) 0.0511911 + 0.290319i 0.00262605 + 0.0148931i
\(381\) 0 0
\(382\) 6.37461 2.32017i 0.326154 0.118710i
\(383\) −35.5306 + 12.9321i −1.81553 + 0.660799i −0.819368 + 0.573268i \(0.805675\pi\)
−0.996162 + 0.0875309i \(0.972102\pi\)
\(384\) 0 0
\(385\) 1.66519 + 2.90975i 0.0848661 + 0.148295i
\(386\) −14.2034 24.6011i −0.722936 1.25216i
\(387\) 0 0
\(388\) 3.04449 + 5.27321i 0.154560 + 0.267707i
\(389\) 33.5247 + 12.2020i 1.69977 + 0.618666i 0.995799 0.0915636i \(-0.0291865\pi\)
0.703971 + 0.710229i \(0.251409\pi\)
\(390\) 0 0
\(391\) −6.59714 + 2.40116i −0.333632 + 0.121432i
\(392\) −15.8732 0.120981i −0.801718 0.00611045i
\(393\) 0 0
\(394\) −8.52303 + 7.15167i −0.429384 + 0.360296i
\(395\) 1.02193 + 1.77004i 0.0514191 + 0.0890604i
\(396\) 0 0
\(397\) −17.0510 + 29.5331i −0.855763 + 1.48223i 0.0201719 + 0.999797i \(0.493579\pi\)
−0.875935 + 0.482429i \(0.839755\pi\)
\(398\) 7.16525 6.01236i 0.359161 0.301372i
\(399\) 0 0
\(400\) 4.14554 23.5105i 0.207277 1.17553i
\(401\) 0.0515308 0.292246i 0.00257333 0.0145941i −0.983494 0.180940i \(-0.942086\pi\)
0.986067 + 0.166346i \(0.0531970\pi\)
\(402\) 0 0
\(403\) 27.1922 22.8170i 1.35454 1.13660i
\(404\) −0.368401 0.638090i −0.0183286 0.0317461i
\(405\) 0 0
\(406\) −20.9185 + 7.52358i −1.03817 + 0.373389i
\(407\) 38.6449 + 14.0656i 1.91556 + 0.697206i
\(408\) 0 0
\(409\) 26.9921 9.82433i 1.33468 0.485782i 0.426544 0.904467i \(-0.359731\pi\)
0.908132 + 0.418685i \(0.137509\pi\)
\(410\) −1.65606 1.38960i −0.0817868 0.0686273i
\(411\) 0 0
\(412\) 2.64737 2.22141i 0.130427 0.109441i
\(413\) −5.83833 + 32.3886i −0.287286 + 1.59374i
\(414\) 0 0
\(415\) 1.72485 0.0846694
\(416\) −14.7851 5.38133i −0.724898 0.263841i
\(417\) 0 0
\(418\) −12.9126 10.8350i −0.631578 0.529957i
\(419\) −19.7106 + 7.17406i −0.962925 + 0.350476i −0.775179 0.631742i \(-0.782340\pi\)
−0.187746 + 0.982218i \(0.560118\pi\)
\(420\) 0 0
\(421\) −4.09657 23.2328i −0.199655 1.13230i −0.905632 0.424064i \(-0.860603\pi\)
0.705977 0.708234i \(-0.250508\pi\)
\(422\) −14.1500 −0.688814
\(423\) 0 0
\(424\) −15.2660 −0.741381
\(425\) −7.42732 2.70332i −0.360278 0.131130i
\(426\) 0 0
\(427\) 1.50810 + 8.74765i 0.0729820 + 0.423329i
\(428\) −0.631540 0.529925i −0.0305266 0.0256149i
\(429\) 0 0
\(430\) −2.19204 + 1.83934i −0.105710 + 0.0887009i
\(431\) 10.1733 17.6207i 0.490031 0.848759i −0.509903 0.860232i \(-0.670319\pi\)
0.999934 + 0.0114729i \(0.00365202\pi\)
\(432\) 0 0
\(433\) −29.6631 −1.42552 −0.712758 0.701410i \(-0.752554\pi\)
−0.712758 + 0.701410i \(0.752554\pi\)
\(434\) 15.6904 26.9390i 0.753164 1.29311i
\(435\) 0 0
\(436\) −1.58490 + 8.98841i −0.0759029 + 0.430467i
\(437\) −6.82222 5.72452i −0.326351 0.273841i
\(438\) 0 0
\(439\) 0.909155 + 0.330905i 0.0433916 + 0.0157933i 0.363625 0.931546i \(-0.381539\pi\)
−0.320233 + 0.947339i \(0.603761\pi\)
\(440\) −1.43673 2.48848i −0.0684932 0.118634i
\(441\) 0 0
\(442\) −6.24546 + 10.8174i −0.297066 + 0.514533i
\(443\) 1.65088 1.38526i 0.0784358 0.0658155i −0.602727 0.797948i \(-0.705919\pi\)
0.681163 + 0.732132i \(0.261475\pi\)
\(444\) 0 0
\(445\) −0.664025 + 3.76587i −0.0314778 + 0.178519i
\(446\) −12.2652 10.2917i −0.580775 0.487328i
\(447\) 0 0
\(448\) 11.7551 + 0.0447964i 0.555378 + 0.00211643i
\(449\) −0.802022 + 1.38914i −0.0378498 + 0.0655577i −0.884330 0.466863i \(-0.845384\pi\)
0.846480 + 0.532421i \(0.178718\pi\)
\(450\) 0 0
\(451\) 28.2062 1.32818
\(452\) −0.939118 5.32600i −0.0441724 0.250514i
\(453\) 0 0
\(454\) 5.48676 31.1170i 0.257507 1.46039i
\(455\) 2.95725 + 1.08913i 0.138638 + 0.0510593i
\(456\) 0 0
\(457\) 5.25692 + 29.8135i 0.245908 + 1.39461i 0.818374 + 0.574686i \(0.194876\pi\)
−0.572466 + 0.819929i \(0.694013\pi\)
\(458\) −7.59006 + 13.1464i −0.354660 + 0.614289i
\(459\) 0 0
\(460\) 0.318614 + 0.551856i 0.0148555 + 0.0257304i
\(461\) −11.1051 4.04192i −0.517216 0.188251i 0.0702054 0.997533i \(-0.477635\pi\)
−0.587421 + 0.809281i \(0.699857\pi\)
\(462\) 0 0
\(463\) 27.5236 + 23.0951i 1.27913 + 1.07332i 0.993363 + 0.115019i \(0.0366930\pi\)
0.285768 + 0.958299i \(0.407751\pi\)
\(464\) 23.7049 8.62788i 1.10047 0.400539i
\(465\) 0 0
\(466\) −2.93194 16.6278i −0.135819 0.770270i
\(467\) 1.42224 2.46339i 0.0658134 0.113992i −0.831241 0.555912i \(-0.812369\pi\)
0.897055 + 0.441920i \(0.145702\pi\)
\(468\) 0 0
\(469\) 18.5627 6.67625i 0.857144 0.308281i
\(470\) 0.150226 + 0.851971i 0.00692939 + 0.0392985i
\(471\) 0 0
\(472\) 4.89820 27.7791i 0.225458 1.27863i
\(473\) 6.48318 36.7679i 0.298097 1.69059i
\(474\) 0 0
\(475\) −1.74108 9.87414i −0.0798861 0.453057i
\(476\) −0.444071 + 2.46352i −0.0203540 + 0.112915i
\(477\) 0 0
\(478\) 6.09221 10.5520i 0.278651 0.482638i
\(479\) 5.99052 + 33.9740i 0.273714 + 1.55231i 0.743017 + 0.669272i \(0.233394\pi\)
−0.469303 + 0.883037i \(0.655495\pi\)
\(480\) 0 0
\(481\) 36.3268 13.2219i 1.65636 0.602865i
\(482\) 11.5684 + 9.70700i 0.526924 + 0.442142i
\(483\) 0 0
\(484\) −8.67551 3.15763i −0.394341 0.143529i
\(485\) 1.26469 + 2.19051i 0.0574266 + 0.0994657i
\(486\) 0 0
\(487\) 4.94964 8.57303i 0.224290 0.388481i −0.731816 0.681502i \(-0.761327\pi\)
0.956106 + 0.293021i \(0.0946605\pi\)
\(488\) −1.32115 7.49261i −0.0598056 0.339174i
\(489\) 0 0
\(490\) 2.76768 + 0.0210944i 0.125031 + 0.000952948i
\(491\) −2.63401 + 14.9382i −0.118871 + 0.674152i 0.865889 + 0.500236i \(0.166753\pi\)
−0.984760 + 0.173916i \(0.944358\pi\)
\(492\) 0 0
\(493\) −1.45030 8.22507i −0.0653183 0.370438i
\(494\) −15.8451 −0.712906
\(495\) 0 0
\(496\) −17.6883 + 30.6371i −0.794229 + 1.37564i
\(497\) −2.68807 0.0102437i −0.120577 0.000459492i
\(498\) 0 0
\(499\) −15.6060 13.0950i −0.698619 0.586211i 0.222761 0.974873i \(-0.428493\pi\)
−0.921380 + 0.388662i \(0.872937\pi\)
\(500\) −0.250678 + 1.42166i −0.0112107 + 0.0635788i
\(501\) 0 0
\(502\) 25.9181 21.7479i 1.15678 0.970655i
\(503\) −6.10125 + 10.5677i −0.272041 + 0.471189i −0.969384 0.245548i \(-0.921032\pi\)
0.697343 + 0.716737i \(0.254365\pi\)
\(504\) 0 0
\(505\) −0.153035 0.265064i −0.00680996 0.0117952i
\(506\) −34.2388 12.4619i −1.52210 0.553999i
\(507\) 0 0
\(508\) 5.42658 + 4.55344i 0.240766 + 0.202026i
\(509\) 3.98485 22.5992i 0.176625 1.00169i −0.759626 0.650360i \(-0.774618\pi\)
0.936251 0.351331i \(-0.114271\pi\)
\(510\) 0 0
\(511\) −7.61717 13.3102i −0.336964 0.588809i
\(512\) −6.23845 −0.275703
\(513\) 0 0
\(514\) −19.8280 + 34.3432i −0.874577 + 1.51481i
\(515\) 1.09973 0.922780i 0.0484597 0.0406625i
\(516\) 0 0
\(517\) −8.64671 7.25545i −0.380282 0.319094i
\(518\) 26.0914 21.7244i 1.14639 0.954516i
\(519\) 0 0
\(520\) −2.53819 0.923825i −0.111307 0.0405124i
\(521\) 29.0781 1.27393 0.636967 0.770891i \(-0.280189\pi\)
0.636967 + 0.770891i \(0.280189\pi\)
\(522\) 0 0
\(523\) 27.7925 1.21528 0.607641 0.794212i \(-0.292116\pi\)
0.607641 + 0.794212i \(0.292116\pi\)
\(524\) −1.59792 9.06228i −0.0698056 0.395887i
\(525\) 0 0
\(526\) −2.37401 + 0.864068i −0.103512 + 0.0376752i
\(527\) 8.97234 + 7.52869i 0.390841 + 0.327955i
\(528\) 0 0
\(529\) 3.52333 + 1.28239i 0.153188 + 0.0557560i
\(530\) 2.66180 0.115621
\(531\) 0 0
\(532\) −2.98804 + 1.07468i −0.129548 + 0.0465933i
\(533\) 20.3111 17.0430i 0.879770 0.738215i
\(534\) 0 0
\(535\) −0.262344 0.220132i −0.0113421 0.00951715i
\(536\) −15.8881 + 5.78279i −0.686260 + 0.249778i
\(537\) 0 0
\(538\) −8.99831 3.27512i −0.387945 0.141200i
\(539\) −27.8395 + 23.0008i −1.19913 + 0.990715i
\(540\) 0 0
\(541\) 12.1578 + 21.0579i 0.522704 + 0.905350i 0.999651 + 0.0264179i \(0.00841006\pi\)
−0.476947 + 0.878932i \(0.658257\pi\)
\(542\) −12.5555 + 10.5353i −0.539304 + 0.452530i
\(543\) 0 0
\(544\) 0.901506 5.11270i 0.0386518 0.219205i
\(545\) −0.658372 + 3.73381i −0.0282015 + 0.159939i
\(546\) 0 0
\(547\) 3.22077 2.70254i 0.137710 0.115552i −0.571331 0.820720i \(-0.693573\pi\)
0.709041 + 0.705167i \(0.249128\pi\)
\(548\) 4.86952 8.43426i 0.208016 0.360294i
\(549\) 0 0
\(550\) −20.5106 35.5255i −0.874576 1.51481i
\(551\) 8.11603 6.81016i 0.345755 0.290123i
\(552\) 0 0
\(553\) −16.9187 + 14.0870i −0.719457 + 0.599039i
\(554\) −27.2910 + 9.93310i −1.15948 + 0.422017i
\(555\) 0 0
\(556\) 6.82472 + 2.48400i 0.289433 + 0.105345i
\(557\) 6.63331 + 11.4892i 0.281062 + 0.486814i 0.971647 0.236438i \(-0.0759799\pi\)
−0.690584 + 0.723252i \(0.742647\pi\)
\(558\) 0 0
\(559\) −17.5478 30.3937i −0.742192 1.28551i
\(560\) −3.14073 0.0119687i −0.132720 0.000505769i
\(561\) 0 0
\(562\) −9.83885 + 3.58105i −0.415027 + 0.151057i
\(563\) 17.1364 6.23715i 0.722214 0.262864i 0.0453487 0.998971i \(-0.485560\pi\)
0.676865 + 0.736107i \(0.263338\pi\)
\(564\) 0 0
\(565\) −0.390112 2.21244i −0.0164121 0.0930779i
\(566\) 19.8423 0.834033
\(567\) 0 0
\(568\) 2.30396 0.0966718
\(569\) −4.96317 28.1475i −0.208067 1.18001i −0.892540 0.450968i \(-0.851079\pi\)
0.684473 0.729038i \(-0.260032\pi\)
\(570\) 0 0
\(571\) −15.5965 + 5.67666i −0.652693 + 0.237561i −0.647079 0.762423i \(-0.724009\pi\)
−0.00561479 + 0.999984i \(0.501787\pi\)
\(572\) −13.9004 + 5.05935i −0.581207 + 0.211542i
\(573\) 0 0
\(574\) 11.7199 20.1219i 0.489178 0.839873i
\(575\) −10.8365 18.7694i −0.451914 0.782737i
\(576\) 0 0
\(577\) −10.3149 17.8659i −0.429415 0.743768i 0.567407 0.823438i \(-0.307947\pi\)
−0.996821 + 0.0796698i \(0.974613\pi\)
\(578\) 21.8424 + 7.95000i 0.908526 + 0.330676i
\(579\) 0 0
\(580\) −0.712359 + 0.259278i −0.0295791 + 0.0107659i
\(581\) 3.15650 + 18.3091i 0.130954 + 0.759591i
\(582\) 0 0
\(583\) −26.6043 + 22.3237i −1.10184 + 0.924553i
\(584\) 6.57208 + 11.3832i 0.271955 + 0.471039i
\(585\) 0 0
\(586\) 2.50642 4.34125i 0.103539 0.179336i
\(587\) 5.41973 4.54769i 0.223696 0.187703i −0.524051 0.851687i \(-0.675580\pi\)
0.747747 + 0.663983i \(0.231135\pi\)
\(588\) 0 0
\(589\) −2.58002 + 14.6320i −0.106308 + 0.602903i
\(590\) −0.854057 + 4.84360i −0.0351610 + 0.199408i
\(591\) 0 0
\(592\) −29.5135 + 24.7647i −1.21300 + 1.01782i
\(593\) −2.82966 4.90111i −0.116200 0.201265i 0.802059 0.597245i \(-0.203738\pi\)
−0.918259 + 0.395981i \(0.870405\pi\)
\(594\) 0 0
\(595\) −0.184468 + 1.02335i −0.00756247 + 0.0419534i
\(596\) 1.86626 + 0.679265i 0.0764452 + 0.0278238i
\(597\) 0 0
\(598\) −32.1850 + 11.7144i −1.31614 + 0.479036i
\(599\) 9.79402 + 8.21816i 0.400173 + 0.335785i 0.820560 0.571560i \(-0.193661\pi\)
−0.420388 + 0.907345i \(0.638106\pi\)
\(600\) 0 0
\(601\) −27.4619 + 23.0433i −1.12019 + 0.939954i −0.998614 0.0526274i \(-0.983240\pi\)
−0.121580 + 0.992582i \(0.538796\pi\)
\(602\) −23.5360 19.9023i −0.959254 0.811159i
\(603\) 0 0
\(604\) −5.73422 −0.233322
\(605\) −3.60383 1.31169i −0.146517 0.0533277i
\(606\) 0 0
\(607\) −31.8737 26.7452i −1.29371 1.08556i −0.991195 0.132412i \(-0.957728\pi\)
−0.302519 0.953143i \(-0.597828\pi\)
\(608\) 6.18851 2.25243i 0.250977 0.0913483i
\(609\) 0 0
\(610\) 0.230358 + 1.30642i 0.00932690 + 0.0528955i
\(611\) −10.6104 −0.429250
\(612\) 0 0
\(613\) 16.6078 0.670782 0.335391 0.942079i \(-0.391132\pi\)
0.335391 + 0.942079i \(0.391132\pi\)
\(614\) −26.3316 9.58391i −1.06266 0.386775i
\(615\) 0 0
\(616\) 23.7858 19.8047i 0.958359 0.797955i
\(617\) −13.0354 10.9380i −0.524785 0.440347i 0.341511 0.939878i \(-0.389061\pi\)
−0.866296 + 0.499531i \(0.833506\pi\)
\(618\) 0 0
\(619\) 8.97501 7.53093i 0.360736 0.302694i −0.444348 0.895854i \(-0.646565\pi\)
0.805084 + 0.593161i \(0.202120\pi\)
\(620\) 0.531554 0.920678i 0.0213477 0.0369753i
\(621\) 0 0
\(622\) 41.7987 1.67597
\(623\) −41.1897 0.156965i −1.65023 0.00628868i
\(624\) 0 0
\(625\) 4.18469 23.7326i 0.167388 0.949302i
\(626\) −32.4467 27.2260i −1.29683 1.08817i
\(627\) 0 0
\(628\) 1.25351 + 0.456239i 0.0500204 + 0.0182059i
\(629\) 6.37781 + 11.0467i 0.254300 + 0.440461i
\(630\) 0 0
\(631\) −3.25090 + 5.63073i −0.129416 + 0.224156i −0.923451 0.383717i \(-0.874644\pi\)
0.794034 + 0.607873i \(0.207977\pi\)
\(632\) 14.4549 12.1291i 0.574984 0.482469i
\(633\) 0 0
\(634\) 0.747326 4.23830i 0.0296801 0.168324i
\(635\) 2.25422 + 1.89151i 0.0894559 + 0.0750624i
\(636\) 0 0
\(637\) −6.14924 + 33.3842i −0.243642 + 1.32273i
\(638\) 21.6731 37.5389i 0.858046 1.48618i
\(639\) 0 0
\(640\) 3.35062 0.132445
\(641\) −1.73512 9.84038i −0.0685333 0.388672i −0.999710 0.0241022i \(-0.992327\pi\)
0.931176 0.364569i \(-0.118784\pi\)
\(642\) 0 0
\(643\) −2.03715 + 11.5532i −0.0803373 + 0.455615i 0.917928 + 0.396746i \(0.129861\pi\)
−0.998266 + 0.0588693i \(0.981250\pi\)
\(644\) −5.27485 + 4.39198i −0.207858 + 0.173068i
\(645\) 0 0
\(646\) −0.907877 5.14883i −0.0357199 0.202578i
\(647\) 12.6777 21.9584i 0.498411 0.863274i −0.501587 0.865107i \(-0.667250\pi\)
0.999998 + 0.00183352i \(0.000583627\pi\)
\(648\) 0 0
\(649\) −32.0856 55.5738i −1.25947 2.18146i
\(650\) −36.2351 13.1885i −1.42126 0.517295i
\(651\) 0 0
\(652\) 0.764037 + 0.641103i 0.0299220 + 0.0251075i
\(653\) 24.3880 8.87651i 0.954376 0.347365i 0.182549 0.983197i \(-0.441565\pi\)
0.771827 + 0.635832i \(0.219343\pi\)
\(654\) 0 0
\(655\) −0.663782 3.76450i −0.0259361 0.147091i
\(656\) −13.2122 + 22.8842i −0.515849 + 0.893476i
\(657\) 0 0
\(658\) −8.76871 + 3.15376i −0.341840 + 0.122946i
\(659\) −0.938027 5.31981i −0.0365403 0.207230i 0.961072 0.276300i \(-0.0891082\pi\)
−0.997612 + 0.0690691i \(0.977997\pi\)
\(660\) 0 0
\(661\) −1.04141 + 5.90614i −0.0405062 + 0.229722i −0.998340 0.0576020i \(-0.981655\pi\)
0.957833 + 0.287324i \(0.0927657\pi\)
\(662\) 5.74960 32.6076i 0.223464 1.26733i
\(663\) 0 0
\(664\) −2.76521 15.6823i −0.107311 0.608591i
\(665\) −1.24124 + 0.446425i −0.0481332 + 0.0173116i
\(666\) 0 0
\(667\) 11.4507 19.8332i 0.443372 0.767943i
\(668\) 1.47881 + 8.38675i 0.0572169 + 0.324493i
\(669\) 0 0
\(670\) 2.77027 1.00830i 0.107025 0.0389539i
\(671\) −13.2590 11.1256i −0.511856 0.429498i
\(672\) 0 0
\(673\) 11.3701 + 4.13838i 0.438285 + 0.159523i 0.551732 0.834021i \(-0.313967\pi\)
−0.113447 + 0.993544i \(0.536189\pi\)
\(674\) −22.8120 39.5115i −0.878685 1.52193i
\(675\) 0 0
\(676\) −3.10920 + 5.38529i −0.119585 + 0.207127i
\(677\) 7.27638 + 41.2664i 0.279654 + 1.58600i 0.723779 + 0.690032i \(0.242403\pi\)
−0.444125 + 0.895965i \(0.646485\pi\)
\(678\) 0 0
\(679\) −20.9377 + 17.4333i −0.803514 + 0.669027i
\(680\) 0.154764 0.877709i 0.00593492 0.0336586i
\(681\) 0 0
\(682\) 10.5556 + 59.8640i 0.404197 + 2.29231i
\(683\) 8.33047 0.318757 0.159378 0.987218i \(-0.449051\pi\)
0.159378 + 0.987218i \(0.449051\pi\)
\(684\) 0 0
\(685\) 2.02281 3.50362i 0.0772878 0.133866i
\(686\) 4.84098 + 29.4173i 0.184830 + 1.12316i
\(687\) 0 0
\(688\) 26.7936 + 22.4825i 1.02150 + 0.857139i
\(689\) −5.66896 + 32.1503i −0.215970 + 1.22483i
\(690\) 0 0
\(691\) 28.1849 23.6500i 1.07221 0.899687i 0.0769548 0.997035i \(-0.475480\pi\)
0.995250 + 0.0973475i \(0.0310358\pi\)
\(692\) 0.522111 0.904323i 0.0198477 0.0343772i
\(693\) 0 0
\(694\) 2.77947 + 4.81418i 0.105507 + 0.182744i
\(695\) 2.83501 + 1.03186i 0.107538 + 0.0391406i
\(696\) 0 0
\(697\) 6.70183 + 5.62351i 0.253850 + 0.213005i
\(698\) −3.98678 + 22.6102i −0.150902 + 0.855807i
\(699\) 0 0
\(700\) −7.72762 0.0294484i −0.292077 0.00111304i
\(701\) 51.6323 1.95013 0.975063 0.221930i \(-0.0712355\pi\)
0.975063 + 0.221930i \(0.0712355\pi\)
\(702\) 0 0
\(703\) −8.09047 + 14.0131i −0.305138 + 0.528514i
\(704\) −17.5586 + 14.7334i −0.661763 + 0.555285i
\(705\) 0 0
\(706\) 29.9218 + 25.1074i 1.12612 + 0.944929i
\(707\) 2.53358 2.10953i 0.0952852 0.0793370i
\(708\) 0 0
\(709\) 8.18015 + 2.97733i 0.307212 + 0.111816i 0.491026 0.871145i \(-0.336622\pi\)
−0.183814 + 0.982961i \(0.558844\pi\)
\(710\) −0.401721 −0.0150763
\(711\) 0 0
\(712\) 35.3038 1.32307
\(713\) 5.57693 + 31.6283i 0.208858 + 1.18449i
\(714\) 0 0
\(715\) −5.77428 + 2.10167i −0.215946 + 0.0785979i
\(716\) 8.45451 + 7.09417i 0.315960 + 0.265122i
\(717\) 0 0
\(718\) 6.86835 + 2.49987i 0.256324 + 0.0932945i
\(719\) −37.2254 −1.38827 −0.694137 0.719843i \(-0.744214\pi\)
−0.694137 + 0.719843i \(0.744214\pi\)
\(720\) 0 0
\(721\) 11.8078 + 9.98482i 0.439744 + 0.371854i
\(722\) −18.3491 + 15.3967i −0.682882 + 0.573006i
\(723\) 0 0
\(724\) −3.13009 2.62645i −0.116329 0.0976114i
\(725\) 24.2283 8.81839i 0.899817 0.327507i
\(726\) 0 0
\(727\) −13.2093 4.80779i −0.489905 0.178311i 0.0852428 0.996360i \(-0.472833\pi\)
−0.575148 + 0.818049i \(0.695056\pi\)
\(728\) 5.16141 28.6333i 0.191295 1.06122i
\(729\) 0 0
\(730\) −1.14592 1.98479i −0.0424123 0.0734603i
\(731\) 8.87089 7.44356i 0.328102 0.275310i
\(732\) 0 0
\(733\) −3.26371 + 18.5094i −0.120548 + 0.683661i 0.863305 + 0.504682i \(0.168390\pi\)
−0.983853 + 0.178978i \(0.942721\pi\)
\(734\) 2.58562 14.6638i 0.0954369 0.541250i
\(735\) 0 0
\(736\) 10.9050 9.15038i 0.401964 0.337288i
\(737\) −19.2322 + 33.3112i −0.708428 + 1.22703i
\(738\) 0 0
\(739\) 8.36238 + 14.4841i 0.307615 + 0.532805i 0.977840 0.209353i \(-0.0671357\pi\)
−0.670225 + 0.742158i \(0.733802\pi\)
\(740\) 0.886913 0.744209i 0.0326036 0.0273577i
\(741\) 0 0
\(742\) 4.87114 + 28.2548i 0.178825 + 1.03727i
\(743\) 6.60496 2.40401i 0.242313 0.0881945i −0.218009 0.975947i \(-0.569956\pi\)
0.460322 + 0.887752i \(0.347734\pi\)
\(744\) 0 0
\(745\) 0.775251 + 0.282168i 0.0284030 + 0.0103379i
\(746\) 30.6473 + 53.0827i 1.12208 + 1.94350i
\(747\) 0 0
\(748\) −2.44047 4.22702i −0.0892324 0.154555i
\(749\) 1.85660 3.18761i 0.0678386 0.116473i
\(750\) 0 0
\(751\) 8.78339 3.19689i 0.320510 0.116656i −0.176755 0.984255i \(-0.556560\pi\)
0.497265 + 0.867599i \(0.334338\pi\)
\(752\) 9.93671 3.61667i 0.362355 0.131886i
\(753\) 0 0
\(754\) −7.07547 40.1270i −0.257674 1.46134i
\(755\) −2.38201 −0.0866903
\(756\) 0 0
\(757\) 34.6375 1.25892 0.629461 0.777032i \(-0.283276\pi\)
0.629461 + 0.777032i \(0.283276\pi\)
\(758\) 8.88376 + 50.3823i 0.322673 + 1.82997i
\(759\) 0 0
\(760\) 1.06240 0.386681i 0.0385372 0.0140264i
\(761\) −12.5940 + 4.58385i −0.456533 + 0.166165i −0.560042 0.828464i \(-0.689215\pi\)
0.103509 + 0.994629i \(0.466993\pi\)
\(762\) 0 0
\(763\) −40.8390 0.155629i −1.47847 0.00563415i
\(764\) 1.24590 + 2.15796i 0.0450750 + 0.0780721i
\(765\) 0 0
\(766\) −30.4330 52.7115i −1.09959 1.90455i
\(767\) −56.6840 20.6313i −2.04674 0.744952i
\(768\) 0 0
\(769\) 35.9631 13.0895i 1.29686 0.472020i 0.400890 0.916126i \(-0.368701\pi\)
0.895974 + 0.444106i \(0.146479\pi\)
\(770\) −4.14734 + 3.45318i −0.149460 + 0.124444i
\(771\) 0 0
\(772\) 7.99322 6.70711i 0.287682 0.241394i
\(773\) 3.99713 + 6.92324i 0.143767 + 0.249012i 0.928912 0.370300i \(-0.120745\pi\)
−0.785145 + 0.619312i \(0.787412\pi\)
\(774\) 0 0
\(775\) −18.0789 + 31.3135i −0.649412 + 1.12481i
\(776\) 17.8885 15.0103i 0.642161 0.538837i
\(777\) 0 0
\(778\) −9.97258 + 56.5573i −0.357534 + 2.02768i
\(779\) −1.92713 + 10.9293i −0.0690467 + 0.391583i
\(780\) 0 0
\(781\) 4.01515 3.36911i 0.143673 0.120556i
\(782\) −5.65065 9.78721i −0.202067 0.349990i
\(783\) 0