Properties

Label 567.2.u.a.100.17
Level $567$
Weight $2$
Character 567.100
Analytic conductor $4.528$
Analytic rank $0$
Dimension $132$
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [567,2,Mod(100,567)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(567, base_ring=CyclotomicField(18))
 
chi = DirichletCharacter(H, H._module([16, 6]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("567.100");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 567 = 3^{4} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 567.u (of order \(9\), degree \(6\), not minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(4.52751779461\)
Analytic rank: \(0\)
Dimension: \(132\)
Relative dimension: \(22\) over \(\Q(\zeta_{9})\)
Twist minimal: no (minimal twist has level 189)
Sato-Tate group: $\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label 100.17
Character \(\chi\) \(=\) 567.100
Dual form 567.2.u.a.550.17

$q$-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 \(\left(\mathbb{Z}/567\mathbb{Z}\right)^\times\).

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

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.279530 1.58529i 0.197658 1.12097i −0.710925 0.703267i \(-0.751724\pi\)
0.908583 0.417704i \(-0.137165\pi\)
\(3\) 0 0
\(4\) −0.555633 0.202234i −0.277817 0.101117i
\(5\) −0.230811 0.0840085i −0.103222 0.0375697i 0.289893 0.957059i \(-0.406380\pi\)
−0.393115 + 0.919489i \(0.628603\pi\)
\(6\) 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 0.515828 0.856692i \(-0.327484\pi\)
0.945818 + 0.324696i \(0.105262\pi\)
\(12\) 0 0
\(13\) 4.55694 + 1.65859i 1.26387 + 0.460010i 0.885065 0.465467i \(-0.154114\pi\)
0.378803 + 0.925477i \(0.376336\pi\)
\(14\) 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 −0.752545 0.658541i \(-0.771174\pi\)
0.946586 + 0.322452i \(0.104507\pi\)
\(18\) 0 0
\(19\) −1.01489 1.75785i −0.232832 0.403278i 0.725808 0.687897i \(-0.241466\pi\)
−0.958641 + 0.284620i \(0.908133\pi\)
\(20\) 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 −0.955167 0.296068i \(-0.904324\pi\)
0.796302 0.604899i \(-0.206787\pi\)
\(24\) 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 −0.754575 0.656214i \(-0.772157\pi\)
−0.156232 + 0.987720i \(0.549935\pi\)
\(30\) 0 0
\(31\) 6.87843 + 2.50354i 1.23540 + 0.449650i 0.875444 0.483319i \(-0.160569\pi\)
0.359958 + 0.932969i \(0.382791\pi\)
\(32\) −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 0.710476 0.703721i \(-0.248480\pi\)
0.0919131 + 0.995767i \(0.470702\pi\)
\(42\) 0 0
\(43\) −1.25671 + 7.12716i −0.191646 + 1.08688i 0.725468 + 0.688256i \(0.241624\pi\)
−0.917114 + 0.398625i \(0.869488\pi\)
\(44\) −3.05039 −0.459863
\(45\) 0 0
\(46\) −7.06285 −1.04136
\(47\) −2.05603 + 0.748334i −0.299903 + 0.109156i −0.487589 0.873073i \(-0.662123\pi\)
0.187686 + 0.982229i \(0.439901\pi\)
\(48\) 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 0.536721 0.843760i \(-0.319663\pi\)
−0.999078 + 0.0429338i \(0.986330\pi\)
\(54\) 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 −0.243071 + 0.970009i \(0.578155\pi\)
−0.997481 + 0.0709378i \(0.977401\pi\)
\(60\) 0 0
\(61\) −3.15274 + 1.14750i −0.403667 + 0.146923i −0.535871 0.844300i \(-0.680017\pi\)
0.132204 + 0.991223i \(0.457795\pi\)
\(62\) 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 −0.955825 0.293936i \(-0.905035\pi\)
0.797649 0.603121i \(-0.206077\pi\)
\(68\) −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 0.894594 0.446879i \(-0.147465\pi\)
−0.834306 + 0.551302i \(0.814131\pi\)
\(72\) 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 0.788967 + 0.614436i \(0.210616\pi\)
−0.951536 + 0.307539i \(0.900495\pi\)
\(80\) 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 −0.677755 0.735288i \(-0.737047\pi\)
−0.0465569 + 0.998916i \(0.514825\pi\)
\(84\) 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 0.901827 + 0.432097i \(0.142226\pi\)
−0.0767068 + 0.997054i \(0.524441\pi\)
\(90\) 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 0.748730 + 0.662875i \(0.230664\pi\)
−0.930293 + 0.366818i \(0.880447\pi\)
\(98\) −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 −0.972148 0.234368i \(-0.924698\pi\)
0.993679 + 0.112261i \(0.0358092\pi\)
\(102\) 0 0
\(103\) −5.49218 1.99899i −0.541161 0.196966i 0.0569541 0.998377i \(-0.481861\pi\)
−0.598115 + 0.801410i \(0.704083\pi\)
\(104\) 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 −0.830359 0.557228i \(-0.811865\pi\)
0.897754 + 0.440498i \(0.145198\pi\)
\(108\) 0 0
\(109\) 7.71790 + 13.3678i 0.739241 + 1.28040i 0.952837 + 0.303481i \(0.0981489\pi\)
−0.213596 + 0.976922i \(0.568518\pi\)
\(110\) −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 −0.963720 0.266915i \(-0.913996\pi\)
0.814310 0.580430i \(-0.197115\pi\)
\(114\) 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 0.467779 + 0.883845i \(0.345054\pi\)
−0.999322 + 0.0368140i \(0.988279\pi\)
\(128\) −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 −0.840259 0.542185i \(-0.817597\pi\)
0.604147 0.796873i \(-0.293514\pi\)
\(132\) 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 −0.0822224 0.996614i \(-0.526202\pi\)
−0.995751 + 0.0920869i \(0.970646\pi\)
\(138\) 0 0
\(139\) −9.40916 + 7.89523i −0.798075 + 0.669664i −0.947730 0.319074i \(-0.896628\pi\)
0.149655 + 0.988738i \(0.452184\pi\)
\(140\) −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 −0.742069 0.670324i \(-0.766155\pi\)
0.531281 + 0.847196i \(0.321711\pi\)
\(150\) 0 0
\(151\) 9.11293 3.31683i 0.741600 0.269920i 0.0565331 0.998401i \(-0.481995\pi\)
0.685067 + 0.728481i \(0.259773\pi\)
\(152\) −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 −0.709140 0.705068i \(-0.750917\pi\)
0.571215 + 0.820800i \(0.306472\pi\)
\(158\) 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 −0.897163 0.441699i \(-0.854376\pi\)
0.831104 + 0.556117i \(0.187709\pi\)
\(164\) −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 0.914494 + 0.404598i \(0.132589\pi\)
−0.720963 + 0.692974i \(0.756300\pi\)
\(168\) 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 0.589910 0.807469i \(-0.299163\pi\)
−0.692765 + 0.721164i \(0.743607\pi\)
\(174\) 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 0.271763 + 0.962364i \(0.412393\pi\)
−0.969313 + 0.245829i \(0.920940\pi\)
\(180\) 0 0
\(181\) 3.45518 5.98454i 0.256821 0.444827i −0.708567 0.705643i \(-0.750658\pi\)
0.965389 + 0.260816i \(0.0839915\pi\)
\(182\) 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 −0.999769 0.0214718i \(-0.993165\pi\)
0.946820 + 0.321764i \(0.104276\pi\)
\(192\) 0 0
\(193\) −16.5826 6.03556i −1.19364 0.434449i −0.332639 0.943054i \(-0.607939\pi\)
−0.861000 + 0.508606i \(0.830161\pi\)
\(194\) 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 −0.716256 0.697838i \(-0.754146\pi\)
0.962473 + 0.271377i \(0.0874790\pi\)
\(198\) 0 0
\(199\) −2.90529 + 5.03211i −0.205950 + 0.356717i −0.950435 0.310923i \(-0.899362\pi\)
0.744485 + 0.667639i \(0.232695\pi\)
\(200\) −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 −0.991187 0.132466i \(-0.957710\pi\)
0.886105 0.463484i \(-0.153401\pi\)
\(212\) 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 0.350981 0.936383i \(-0.385848\pi\)
−0.861210 + 0.508250i \(0.830293\pi\)
\(224\) −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 −0.871616 0.490190i \(-0.836927\pi\)
−0.352608 + 0.935771i \(0.614705\pi\)
\(228\) 0 0
\(229\) 7.22389 6.06156i 0.477368 0.400559i −0.372106 0.928190i \(-0.621364\pi\)
0.849474 + 0.527631i \(0.176920\pi\)
\(230\) 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 −0.810760 0.585379i \(-0.800946\pi\)
0.435699 + 0.900093i \(0.356501\pi\)
\(240\) 0 0
\(241\) 7.18643 + 6.03013i 0.462919 + 0.388435i 0.844204 0.536023i \(-0.180074\pi\)
−0.381285 + 0.924458i \(0.624518\pi\)
\(242\) −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 0.316415 + 0.948621i \(0.397521\pi\)
−0.979737 + 0.200287i \(0.935813\pi\)
\(252\) 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 0.177176 0.984179i \(-0.443304\pi\)
0.999994 0.00358315i \(-0.00114055\pi\)
\(258\) 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 −0.975252 0.221097i \(-0.929036\pi\)
0.992057 + 0.125793i \(0.0401474\pi\)
\(264\) 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 0.760992 0.648761i \(-0.224712\pi\)
−0.942340 + 0.334658i \(0.891379\pi\)
\(270\) 0 0
\(271\) 5.09086 8.81763i 0.309248 0.535633i −0.668950 0.743307i \(-0.733256\pi\)
0.978198 + 0.207674i \(0.0665895\pi\)
\(272\) −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 −0.733488 0.679702i \(-0.762109\pi\)
0.921725 0.387843i \(-0.126780\pi\)
\(278\) 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 −0.932408 0.361408i \(-0.882296\pi\)
0.999786 0.0207105i \(-0.00659283\pi\)
\(282\) 0 0
\(283\) 2.14044 + 12.1391i 0.127236 + 0.721592i 0.979955 + 0.199221i \(0.0638412\pi\)
−0.852718 + 0.522371i \(0.825048\pi\)
\(284\) −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 −0.709804 0.704399i \(-0.751217\pi\)
0.570441 + 0.821338i \(0.306772\pi\)
\(294\) 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 0.503248 0.864142i \(-0.332138\pi\)
−0.999993 + 0.00375447i \(0.998805\pi\)
\(308\) 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 0.794325 + 0.607493i \(0.207825\pi\)
−0.538646 + 0.842532i \(0.681064\pi\)
\(312\) 0 0
\(313\) −20.1564 16.9132i −1.13931 0.955991i −0.139890 0.990167i \(-0.544675\pi\)
−0.999416 + 0.0341761i \(0.989119\pi\)
\(314\) 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 −0.411607 0.911362i \(-0.635032\pi\)
0.270503 + 0.962719i \(0.412810\pi\)
\(318\) 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 −0.813323 0.581813i \(-0.802344\pi\)
−0.249059 + 0.968488i \(0.580121\pi\)
\(332\) 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 −0.507982 0.861368i \(-0.669608\pi\)
−0.942813 + 0.333322i \(0.891830\pi\)
\(338\) 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 0.427649 0.903945i \(-0.359342\pi\)
−0.253446 + 0.967349i \(0.581564\pi\)
\(348\) 0 0
\(349\) 13.4023 4.87804i 0.717409 0.261116i 0.0425837 0.999093i \(-0.486441\pi\)
0.674826 + 0.737977i \(0.264219\pi\)
\(350\) −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 0.985471 0.169844i \(-0.0543264\pi\)
0.00386143 + 0.999993i \(0.498771\pi\)
\(354\) 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 0.919696 0.392630i \(-0.128435\pi\)
−0.799876 + 0.600165i \(0.795101\pi\)
\(360\) 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 −0.558764 0.829327i \(-0.688724\pi\)
0.105043 + 0.994468i \(0.466502\pi\)
\(368\) −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 0.983804 + 0.179249i \(0.0573667\pi\)
0.868856 + 0.495064i \(0.164855\pi\)
\(374\) −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 −0.996162 0.0875309i \(-0.972102\pi\)
−0.819368 0.573268i \(-0.805675\pi\)
\(384\) 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 0.703971 0.710229i \(-0.251409\pi\)
0.995799 + 0.0915636i \(0.0291865\pi\)
\(390\) 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 −0.875935 0.482429i \(-0.839755\pi\)
0.0201719 0.999797i \(-0.493579\pi\)
\(398\) 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 0.986067 0.166346i \(-0.0531970\pi\)
−0.983494 + 0.180940i \(0.942086\pi\)
\(402\) 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 0.908132 0.418685i \(-0.137509\pi\)
0.426544 + 0.904467i \(0.359731\pi\)
\(410\) −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 −0.187746 0.982218i \(-0.560118\pi\)
−0.775179 + 0.631742i \(0.782340\pi\)
\(420\) 0 0
\(421\) −4.09657 + 23.2328i −0.199655 + 1.13230i 0.705977 + 0.708234i \(0.250508\pi\)
−0.905632 + 0.424064i \(0.860603\pi\)
\(422\) −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 0.999934 0.0114729i \(-0.00365202\pi\)
−0.509903 + 0.860232i \(0.670319\pi\)
\(432\) 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 −0.320233 0.947339i \(-0.603761\pi\)
0.363625 + 0.931546i \(0.381539\pi\)
\(440\) −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 0.681163 0.732132i \(-0.261475\pi\)
−0.602727 + 0.797948i \(0.705919\pi\)
\(444\) 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 0.846480 0.532421i \(-0.178718\pi\)
−0.884330 + 0.466863i \(0.845384\pi\)
\(450\) 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 −0.572466 0.819929i \(-0.694013\pi\)
0.818374 0.574686i \(-0.194876\pi\)
\(458\) −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 −0.587421 0.809281i \(-0.699857\pi\)
0.0702054 + 0.997533i \(0.477635\pi\)
\(462\) 0 0
\(463\) 27.5236 23.0951i 1.27913 1.07332i 0.285768 0.958299i \(-0.407751\pi\)
0.993363 0.115019i \(-0.0366930\pi\)
\(464\) 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 0.897055 0.441920i \(-0.145702\pi\)
−0.831241 + 0.555912i \(0.812369\pi\)
\(468\) 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 −0.469303 0.883037i \(-0.655495\pi\)
0.743017 0.669272i \(-0.233394\pi\)
\(480\) 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 0.956106 0.293021i \(-0.0946605\pi\)
−0.731816 + 0.681502i \(0.761327\pi\)
\(488\) −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 −0.984760 0.173916i \(-0.944358\pi\)
0.865889 0.500236i \(-0.166753\pi\)
\(492\) 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 −0.921380 0.388662i \(-0.872937\pi\)
0.222761 + 0.974873i \(0.428493\pi\)
\(500\) −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 0.697343 0.716737i \(-0.254365\pi\)
−0.969384 + 0.245548i \(0.921032\pi\)
\(504\) 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 0.936251 + 0.351331i \(0.114271\pi\)
−0.759626 + 0.650360i \(0.774618\pi\)
\(510\) 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 −0.476947 0.878932i \(-0.658257\pi\)
0.999651 0.0264179i \(-0.00841006\pi\)
\(542\) −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 0.709041 0.705167i \(-0.249128\pi\)
−0.571331 + 0.820720i \(0.693573\pi\)
\(548\) 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 −0.690584 0.723252i \(-0.742647\pi\)
0.971647 + 0.236438i \(0.0759799\pi\)
\(558\) 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 0.676865 0.736107i \(-0.263338\pi\)
0.0453487 + 0.998971i \(0.485560\pi\)
\(564\) 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 0.684473 + 0.729038i \(0.260032\pi\)
−0.892540 + 0.450968i \(0.851079\pi\)
\(570\) 0 0
\(571\) −15.5965 5.67666i −0.652693 0.237561i −0.00561479 0.999984i \(-0.501787\pi\)
−0.647079 + 0.762423i \(0.724009\pi\)
\(572\) −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 −0.996821 0.0796698i \(-0.974613\pi\)
0.567407 + 0.823438i \(0.307947\pi\)
\(578\) 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 0.747747 0.663983i \(-0.231135\pi\)
−0.524051 + 0.851687i \(0.675580\pi\)
\(588\) 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 −0.918259 0.395981i \(-0.870405\pi\)
0.802059 + 0.597245i \(0.203738\pi\)
\(594\) 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 −0.420388 0.907345i \(-0.638106\pi\)
0.820560 + 0.571560i \(0.193661\pi\)
\(600\) 0 0
\(601\) −27.4619 23.0433i −1.12019 0.939954i −0.121580 0.992582i \(-0.538796\pi\)
−0.998614 + 0.0526274i \(0.983240\pi\)
\(602\) −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 −0.302519 + 0.953143i \(0.597828\pi\)
−0.991195 + 0.132412i \(0.957728\pi\)
\(608\) 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 −0.866296 0.499531i \(-0.833506\pi\)
0.341511 + 0.939878i \(0.389061\pi\)
\(618\) 0 0
\(619\) 8.97501 + 7.53093i 0.360736 + 0.302694i 0.805084 0.593161i \(-0.202120\pi\)
−0.444348 + 0.895854i \(0.646565\pi\)
\(620\) 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 0.794034 0.607873i \(-0.207977\pi\)
−0.923451 + 0.383717i \(0.874644\pi\)
\(632\) 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 0.931176 + 0.364569i \(0.118784\pi\)
−0.999710 + 0.0241022i \(0.992327\pi\)
\(642\) 0 0
\(643\) −2.03715 11.5532i −0.0803373 0.455615i −0.998266 0.0588693i \(-0.981250\pi\)
0.917928 0.396746i \(-0.129861\pi\)
\(644\) −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 0.999998 0.00183352i \(-0.000583627\pi\)
−0.501587 + 0.865107i \(0.667250\pi\)
\(648\) 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 0.771827 0.635832i \(-0.219343\pi\)
0.182549 + 0.983197i \(0.441565\pi\)
\(654\) 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 −0.997612 0.0690691i \(-0.977997\pi\)
0.961072 + 0.276300i \(0.0891082\pi\)
\(660\) 0 0
\(661\) −1.04141 5.90614i −0.0405062 0.229722i 0.957833 0.287324i \(-0.0927657\pi\)
−0.998340 + 0.0576020i \(0.981655\pi\)
\(662\) 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 −0.113447 0.993544i \(-0.536189\pi\)
0.551732 + 0.834021i \(0.313967\pi\)
\(674\) −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 −0.444125 0.895965i \(-0.646485\pi\)
0.723779 0.690032i \(-0.242403\pi\)
\(678\) 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 0.995250 0.0973475i \(-0.0310358\pi\)
0.0769548 + 0.997035i \(0.475480\pi\)
\(692\) 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 −0.183814 0.982961i \(-0.558844\pi\)
0.491026 + 0.871145i \(0.336622\pi\)
\(710\) −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 −0.575148 0.818049i \(-0.695056\pi\)
0.0852428 + 0.996360i \(0.472833\pi\)
\(728\) 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 −0.983853 0.178978i \(-0.942721\pi\)
0.863305 0.504682i \(-0.168390\pi\)
\(734\) 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 −0.670225 0.742158i \(-0.733802\pi\)
0.977840 + 0.209353i \(0.0671357\pi\)
\(740\) 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 0.460322 0.887752i \(-0.347734\pi\)
−0.218009 + 0.975947i \(0.569956\pi\)
\(744\) 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 0.497265 0.867599i \(-0.334338\pi\)
−0.176755 + 0.984255i \(0.556560\pi\)
\(752\) 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 0.103509 0.994629i \(-0.466993\pi\)
−0.560042 + 0.828464i \(0.689215\pi\)
\(762\) 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 0.895974 0.444106i \(-0.146479\pi\)
0.400890 + 0.916126i \(0.368701\pi\)
\(770\) −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 −0.785145 0.619312i \(-0.787412\pi\)
0.928912 + 0.370300i \(0.120745\pi\)
\(774\) 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