Properties

Label 675.2.l.f.76.7
Level $675$
Weight $2$
Character 675.76
Analytic conductor $5.390$
Analytic rank $0$
Dimension $66$
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [675,2,Mod(76,675)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(675, base_ring=CyclotomicField(18))
 
chi = DirichletCharacter(H, H._module([14, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("675.76");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 675 = 3^{3} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 675.l (of order \(9\), degree \(6\), 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: \(5.38990213644\)
Analytic rank: \(0\)
Dimension: \(66\)
Relative dimension: \(11\) over \(\Q(\zeta_{9})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label 76.7
Character \(\chi\) \(=\) 675.76
Dual form 675.2.l.f.151.7

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.211903 - 0.177808i) q^{2} +(-0.483303 - 1.66326i) q^{3} +(-0.334009 + 1.89426i) q^{4} +(-0.398153 - 0.266514i) q^{6} +(0.293371 + 1.66379i) q^{7} +(0.542656 + 0.939908i) q^{8} +(-2.53284 + 1.60771i) q^{9} +O(q^{10})\) \(q+(0.211903 - 0.177808i) q^{2} +(-0.483303 - 1.66326i) q^{3} +(-0.334009 + 1.89426i) q^{4} +(-0.398153 - 0.266514i) q^{6} +(0.293371 + 1.66379i) q^{7} +(0.542656 + 0.939908i) q^{8} +(-2.53284 + 1.60771i) q^{9} +(-4.65944 - 1.69590i) q^{11} +(3.31206 - 0.359958i) q^{12} +(-2.87084 - 2.40892i) q^{13} +(0.358001 + 0.300398i) q^{14} +(-3.33285 - 1.21306i) q^{16} +(3.15798 - 5.46979i) q^{17} +(-0.250852 + 0.791037i) q^{18} +(-3.42671 - 5.93524i) q^{19} +(2.62552 - 1.29206i) q^{21} +(-1.28889 + 0.469119i) q^{22} +(1.12343 - 6.37131i) q^{23} +(1.30104 - 1.35684i) q^{24} -1.03667 q^{26} +(3.89816 + 3.43574i) q^{27} -3.24964 q^{28} +(-0.115261 + 0.0967151i) q^{29} +(-1.06440 + 6.03653i) q^{31} +(-2.96165 + 1.07795i) q^{32} +(-0.568791 + 8.56948i) q^{33} +(-0.303384 - 1.72058i) q^{34} +(-2.19943 - 5.33484i) q^{36} +(-1.23541 + 2.13979i) q^{37} +(-1.78146 - 0.648400i) q^{38} +(-2.61917 + 5.93918i) q^{39} +(-3.02499 - 2.53826i) q^{41} +(0.326617 - 0.740630i) q^{42} +(-6.57849 - 2.39437i) q^{43} +(4.76877 - 8.25975i) q^{44} +(-0.894809 - 1.54985i) q^{46} +(1.07632 + 6.10414i) q^{47} +(-0.406850 + 6.12965i) q^{48} +(3.89572 - 1.41793i) q^{49} +(-10.6239 - 2.60897i) q^{51} +(5.52201 - 4.63352i) q^{52} -0.373453 q^{53} +(1.43693 + 0.0349210i) q^{54} +(-1.40461 + 1.17861i) q^{56} +(-8.21568 + 8.56802i) q^{57} +(-0.00722737 + 0.0409885i) q^{58} +(0.342887 - 0.124801i) q^{59} +(1.07271 + 6.08365i) q^{61} +(0.847791 + 1.46842i) q^{62} +(-3.41795 - 3.74245i) q^{63} +(3.11083 - 5.38811i) q^{64} +(1.40319 + 1.91703i) q^{66} +(0.475424 + 0.398928i) q^{67} +(9.30640 + 7.80900i) q^{68} +(-11.1401 + 1.21071i) q^{69} +(-3.39814 + 5.88576i) q^{71} +(-2.88556 - 1.50820i) q^{72} +(-2.27683 - 3.94359i) q^{73} +(0.118685 + 0.673094i) q^{74} +(12.3874 - 4.50866i) q^{76} +(1.45467 - 8.24986i) q^{77} +(0.501023 + 1.72424i) q^{78} +(-12.4889 + 10.4794i) q^{79} +(3.83053 - 8.14414i) q^{81} -1.09233 q^{82} +(8.56544 - 7.18726i) q^{83} +(1.57056 + 5.40498i) q^{84} +(-1.81974 + 0.662331i) q^{86} +(0.216568 + 0.144965i) q^{87} +(-0.934487 - 5.29974i) q^{88} +(4.58274 + 7.93753i) q^{89} +(3.16572 - 5.48319i) q^{91} +(11.6937 + 4.25615i) q^{92} +(10.5547 - 1.14710i) q^{93} +(1.31344 + 1.10211i) q^{94} +(3.22429 + 4.40501i) q^{96} +(-12.9391 - 4.70945i) q^{97} +(0.573397 - 0.993152i) q^{98} +(14.5281 - 3.19561i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 66 q - 6 q^{2} - 6 q^{6} - 6 q^{7} - 12 q^{8} - 6 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 66 q - 6 q^{2} - 6 q^{6} - 6 q^{7} - 12 q^{8} - 6 q^{9} + 15 q^{11} - 18 q^{12} + 15 q^{14} + 18 q^{16} - 30 q^{17} + 12 q^{18} + 12 q^{19} + 12 q^{21} + 45 q^{22} - 36 q^{23} - 39 q^{24} + 6 q^{26} - 51 q^{27} + 36 q^{28} - 15 q^{29} + 3 q^{31} - 27 q^{32} + 3 q^{33} + 30 q^{36} - 6 q^{37} + 12 q^{38} - 15 q^{39} + 39 q^{41} - 48 q^{42} - 12 q^{43} + 51 q^{44} + 9 q^{46} - 30 q^{47} + 132 q^{48} - 6 q^{49} - 9 q^{52} + 24 q^{53} + 75 q^{54} + 144 q^{56} - 33 q^{57} - 27 q^{58} + 45 q^{59} - 54 q^{61} - 66 q^{62} + 120 q^{63} - 24 q^{64} + 48 q^{66} - 9 q^{67} + 69 q^{68} + 51 q^{69} - 15 q^{71} - 9 q^{72} + 15 q^{73} + 96 q^{74} - 48 q^{76} + 36 q^{77} + 18 q^{78} + 48 q^{79} - 54 q^{81} + 36 q^{82} - 30 q^{83} + 57 q^{84} - 111 q^{86} + 33 q^{87} - 36 q^{88} - 12 q^{89} + 9 q^{91} + 219 q^{92} - 63 q^{93} + 36 q^{94} - 249 q^{96} - 57 q^{97} - 75 q^{98} - 48 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/675\mathbb{Z}\right)^\times\).

\(n\) \(326\) \(352\)
\(\chi(n)\) \(e\left(\frac{7}{9}\right)\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.211903 0.177808i 0.149838 0.125729i −0.564787 0.825237i \(-0.691042\pi\)
0.714625 + 0.699508i \(0.246597\pi\)
\(3\) −0.483303 1.66326i −0.279035 0.960281i
\(4\) −0.334009 + 1.89426i −0.167005 + 0.947130i
\(5\) 0 0
\(6\) −0.398153 0.266514i −0.162545 0.108804i
\(7\) 0.293371 + 1.66379i 0.110884 + 0.628853i 0.988706 + 0.149867i \(0.0478846\pi\)
−0.877822 + 0.478986i \(0.841004\pi\)
\(8\) 0.542656 + 0.939908i 0.191858 + 0.332308i
\(9\) −2.53284 + 1.60771i −0.844279 + 0.535904i
\(10\) 0 0
\(11\) −4.65944 1.69590i −1.40488 0.511333i −0.475254 0.879849i \(-0.657644\pi\)
−0.929621 + 0.368516i \(0.879866\pi\)
\(12\) 3.31206 0.359958i 0.956111 0.103911i
\(13\) −2.87084 2.40892i −0.796229 0.668115i 0.151050 0.988526i \(-0.451735\pi\)
−0.947279 + 0.320411i \(0.896179\pi\)
\(14\) 0.358001 + 0.300398i 0.0956798 + 0.0802849i
\(15\) 0 0
\(16\) −3.33285 1.21306i −0.833212 0.303264i
\(17\) 3.15798 5.46979i 0.765923 1.32662i −0.173834 0.984775i \(-0.555615\pi\)
0.939757 0.341843i \(-0.111051\pi\)
\(18\) −0.250852 + 0.791037i −0.0591265 + 0.186449i
\(19\) −3.42671 5.93524i −0.786142 1.36164i −0.928314 0.371796i \(-0.878742\pi\)
0.142172 0.989842i \(-0.454591\pi\)
\(20\) 0 0
\(21\) 2.62552 1.29206i 0.572935 0.281952i
\(22\) −1.28889 + 0.469119i −0.274793 + 0.100017i
\(23\) 1.12343 6.37131i 0.234252 1.32851i −0.609931 0.792454i \(-0.708803\pi\)
0.844183 0.536055i \(-0.180086\pi\)
\(24\) 1.30104 1.35684i 0.265574 0.276963i
\(25\) 0 0
\(26\) −1.03667 −0.203307
\(27\) 3.89816 + 3.43574i 0.750202 + 0.661209i
\(28\) −3.24964 −0.614124
\(29\) −0.115261 + 0.0967151i −0.0214034 + 0.0179596i −0.653427 0.756990i \(-0.726669\pi\)
0.632023 + 0.774949i \(0.282225\pi\)
\(30\) 0 0
\(31\) −1.06440 + 6.03653i −0.191172 + 1.08419i 0.726593 + 0.687068i \(0.241103\pi\)
−0.917765 + 0.397124i \(0.870008\pi\)
\(32\) −2.96165 + 1.07795i −0.523551 + 0.190557i
\(33\) −0.568791 + 8.56948i −0.0990138 + 1.49175i
\(34\) −0.303384 1.72058i −0.0520300 0.295077i
\(35\) 0 0
\(36\) −2.19943 5.33484i −0.366572 0.889140i
\(37\) −1.23541 + 2.13979i −0.203100 + 0.351780i −0.949526 0.313689i \(-0.898435\pi\)
0.746426 + 0.665469i \(0.231768\pi\)
\(38\) −1.78146 0.648400i −0.288992 0.105184i
\(39\) −2.61917 + 5.93918i −0.419403 + 0.951031i
\(40\) 0 0
\(41\) −3.02499 2.53826i −0.472423 0.396410i 0.375254 0.926922i \(-0.377555\pi\)
−0.847678 + 0.530512i \(0.822000\pi\)
\(42\) 0.326617 0.740630i 0.0503980 0.114282i
\(43\) −6.57849 2.39437i −1.00321 0.365139i −0.212388 0.977185i \(-0.568124\pi\)
−0.790822 + 0.612047i \(0.790346\pi\)
\(44\) 4.76877 8.25975i 0.718919 1.24520i
\(45\) 0 0
\(46\) −0.894809 1.54985i −0.131932 0.228514i
\(47\) 1.07632 + 6.10414i 0.156998 + 0.890380i 0.956936 + 0.290298i \(0.0937544\pi\)
−0.799938 + 0.600082i \(0.795135\pi\)
\(48\) −0.406850 + 6.12965i −0.0587238 + 0.884739i
\(49\) 3.89572 1.41793i 0.556531 0.202561i
\(50\) 0 0
\(51\) −10.6239 2.60897i −1.48765 0.365329i
\(52\) 5.52201 4.63352i 0.765766 0.642554i
\(53\) −0.373453 −0.0512977 −0.0256488 0.999671i \(-0.508165\pi\)
−0.0256488 + 0.999671i \(0.508165\pi\)
\(54\) 1.43693 + 0.0349210i 0.195542 + 0.00475215i
\(55\) 0 0
\(56\) −1.40461 + 1.17861i −0.187699 + 0.157498i
\(57\) −8.21568 + 8.56802i −1.08819 + 1.13486i
\(58\) −0.00722737 + 0.0409885i −0.000949001 + 0.00538205i
\(59\) 0.342887 0.124801i 0.0446401 0.0162477i −0.319604 0.947551i \(-0.603550\pi\)
0.364244 + 0.931304i \(0.381328\pi\)
\(60\) 0 0
\(61\) 1.07271 + 6.08365i 0.137347 + 0.778931i 0.973197 + 0.229974i \(0.0738640\pi\)
−0.835850 + 0.548958i \(0.815025\pi\)
\(62\) 0.847791 + 1.46842i 0.107670 + 0.186489i
\(63\) −3.41795 3.74245i −0.430622 0.471505i
\(64\) 3.11083 5.38811i 0.388854 0.673514i
\(65\) 0 0
\(66\) 1.40319 + 1.91703i 0.172721 + 0.235971i
\(67\) 0.475424 + 0.398928i 0.0580823 + 0.0487369i 0.671367 0.741125i \(-0.265708\pi\)
−0.613284 + 0.789862i \(0.710152\pi\)
\(68\) 9.30640 + 7.80900i 1.12857 + 0.946980i
\(69\) −11.1401 + 1.21071i −1.34111 + 0.145753i
\(70\) 0 0
\(71\) −3.39814 + 5.88576i −0.403285 + 0.698511i −0.994120 0.108282i \(-0.965465\pi\)
0.590835 + 0.806793i \(0.298799\pi\)
\(72\) −2.88556 1.50820i −0.340067 0.177743i
\(73\) −2.27683 3.94359i −0.266483 0.461563i 0.701468 0.712701i \(-0.252528\pi\)
−0.967951 + 0.251138i \(0.919195\pi\)
\(74\) 0.118685 + 0.673094i 0.0137968 + 0.0782456i
\(75\) 0 0
\(76\) 12.3874 4.50866i 1.42094 0.517179i
\(77\) 1.45467 8.24986i 0.165775 0.940159i
\(78\) 0.501023 + 1.72424i 0.0567297 + 0.195232i
\(79\) −12.4889 + 10.4794i −1.40511 + 1.17903i −0.446338 + 0.894864i \(0.647272\pi\)
−0.958775 + 0.284166i \(0.908283\pi\)
\(80\) 0 0
\(81\) 3.83053 8.14414i 0.425614 0.904905i
\(82\) −1.09233 −0.120627
\(83\) 8.56544 7.18726i 0.940179 0.788904i −0.0374374 0.999299i \(-0.511919\pi\)
0.977616 + 0.210395i \(0.0674750\pi\)
\(84\) 1.57056 + 5.40498i 0.171362 + 0.589731i
\(85\) 0 0
\(86\) −1.81974 + 0.662331i −0.196228 + 0.0714210i
\(87\) 0.216568 + 0.144965i 0.0232185 + 0.0155419i
\(88\) −0.934487 5.29974i −0.0996167 0.564954i
\(89\) 4.58274 + 7.93753i 0.485769 + 0.841377i 0.999866 0.0163553i \(-0.00520627\pi\)
−0.514097 + 0.857732i \(0.671873\pi\)
\(90\) 0 0
\(91\) 3.16572 5.48319i 0.331858 0.574794i
\(92\) 11.6937 + 4.25615i 1.21915 + 0.443734i
\(93\) 10.5547 1.14710i 1.09447 0.118948i
\(94\) 1.31344 + 1.10211i 0.135471 + 0.113674i
\(95\) 0 0
\(96\) 3.22429 + 4.40501i 0.329077 + 0.449584i
\(97\) −12.9391 4.70945i −1.31377 0.478172i −0.412312 0.911043i \(-0.635279\pi\)
−0.901456 + 0.432871i \(0.857501\pi\)
\(98\) 0.573397 0.993152i 0.0579218 0.100324i
\(99\) 14.5281 3.19561i 1.46013 0.321171i
\(100\) 0 0
\(101\) 1.98385 + 11.2510i 0.197400 + 1.11951i 0.908959 + 0.416886i \(0.136879\pi\)
−0.711558 + 0.702627i \(0.752010\pi\)
\(102\) −2.71514 + 1.33617i −0.268838 + 0.132300i
\(103\) −8.62703 + 3.13998i −0.850046 + 0.309392i −0.730059 0.683384i \(-0.760508\pi\)
−0.119987 + 0.992775i \(0.538285\pi\)
\(104\) 0.706286 4.00555i 0.0692571 0.392776i
\(105\) 0 0
\(106\) −0.0791358 + 0.0664028i −0.00768635 + 0.00644961i
\(107\) −1.09015 −0.105389 −0.0526946 0.998611i \(-0.516781\pi\)
−0.0526946 + 0.998611i \(0.516781\pi\)
\(108\) −7.81021 + 6.23656i −0.751538 + 0.600113i
\(109\) −0.574982 −0.0550733 −0.0275366 0.999621i \(-0.508766\pi\)
−0.0275366 + 0.999621i \(0.508766\pi\)
\(110\) 0 0
\(111\) 4.15610 + 1.02063i 0.394480 + 0.0968744i
\(112\) 1.04051 5.90104i 0.0983191 0.557595i
\(113\) 16.5549 6.02550i 1.55736 0.566832i 0.587228 0.809421i \(-0.300219\pi\)
0.970129 + 0.242590i \(0.0779968\pi\)
\(114\) −0.217468 + 3.27640i −0.0203678 + 0.306863i
\(115\) 0 0
\(116\) −0.144705 0.250637i −0.0134356 0.0232711i
\(117\) 11.1442 + 1.48592i 1.03028 + 0.137374i
\(118\) 0.0504683 0.0874136i 0.00464598 0.00804708i
\(119\) 10.0270 + 3.64954i 0.919177 + 0.334553i
\(120\) 0 0
\(121\) 10.4079 + 8.73323i 0.946169 + 0.793930i
\(122\) 1.30903 + 1.09841i 0.118514 + 0.0994451i
\(123\) −2.75980 + 6.25807i −0.248843 + 0.564272i
\(124\) −11.0792 4.03251i −0.994944 0.362130i
\(125\) 0 0
\(126\) −1.38971 0.185298i −0.123805 0.0165077i
\(127\) −3.97850 6.89096i −0.353035 0.611474i 0.633745 0.773542i \(-0.281517\pi\)
−0.986780 + 0.162068i \(0.948184\pi\)
\(128\) −1.39344 7.90257i −0.123164 0.698496i
\(129\) −0.803054 + 12.0989i −0.0707050 + 1.06525i
\(130\) 0 0
\(131\) 1.46844 8.32796i 0.128298 0.727617i −0.850995 0.525173i \(-0.824001\pi\)
0.979294 0.202444i \(-0.0648883\pi\)
\(132\) −16.0428 3.93972i −1.39635 0.342909i
\(133\) 8.86970 7.44256i 0.769100 0.645352i
\(134\) 0.171676 0.0148306
\(135\) 0 0
\(136\) 6.85480 0.587794
\(137\) 0.303815 0.254931i 0.0259567 0.0217802i −0.629717 0.776825i \(-0.716829\pi\)
0.655674 + 0.755044i \(0.272385\pi\)
\(138\) −2.14534 + 2.23734i −0.182624 + 0.190455i
\(139\) −0.813377 + 4.61289i −0.0689897 + 0.391260i 0.930687 + 0.365818i \(0.119211\pi\)
−0.999676 + 0.0254426i \(0.991901\pi\)
\(140\) 0 0
\(141\) 9.63255 4.74035i 0.811207 0.399209i
\(142\) 0.326456 + 1.85143i 0.0273956 + 0.155368i
\(143\) 9.29124 + 16.0929i 0.776973 + 1.34576i
\(144\) 10.3918 2.28578i 0.865984 0.190482i
\(145\) 0 0
\(146\) −1.18367 0.430821i −0.0979612 0.0356550i
\(147\) −4.24118 5.79429i −0.349807 0.477905i
\(148\) −3.64069 3.05490i −0.299263 0.251111i
\(149\) −17.6585 14.8172i −1.44664 1.21387i −0.934987 0.354682i \(-0.884589\pi\)
−0.511653 0.859192i \(-0.670967\pi\)
\(150\) 0 0
\(151\) −4.86203 1.76963i −0.395666 0.144011i 0.136522 0.990637i \(-0.456408\pi\)
−0.532188 + 0.846626i \(0.678630\pi\)
\(152\) 3.71906 6.44159i 0.301655 0.522482i
\(153\) 0.795184 + 18.9312i 0.0642868 + 1.53050i
\(154\) −1.15864 2.00682i −0.0933659 0.161714i
\(155\) 0 0
\(156\) −10.3755 6.94513i −0.830707 0.556055i
\(157\) 13.0179 4.73812i 1.03894 0.378143i 0.234462 0.972125i \(-0.424667\pi\)
0.804478 + 0.593982i \(0.202445\pi\)
\(158\) −0.783113 + 4.44125i −0.0623011 + 0.353327i
\(159\) 0.180491 + 0.621147i 0.0143138 + 0.0492602i
\(160\) 0 0
\(161\) 10.9301 0.861412
\(162\) −0.636392 2.40687i −0.0499997 0.189101i
\(163\) 2.98083 0.233477 0.116738 0.993163i \(-0.462756\pi\)
0.116738 + 0.993163i \(0.462756\pi\)
\(164\) 5.81850 4.88231i 0.454349 0.381244i
\(165\) 0 0
\(166\) 0.537093 3.04600i 0.0416865 0.236416i
\(167\) −17.6335 + 6.41805i −1.36452 + 0.496644i −0.917448 0.397855i \(-0.869755\pi\)
−0.447070 + 0.894499i \(0.647532\pi\)
\(168\) 2.63918 + 1.76660i 0.203617 + 0.136296i
\(169\) 0.181402 + 1.02878i 0.0139540 + 0.0791371i
\(170\) 0 0
\(171\) 18.2215 + 9.52383i 1.39343 + 0.728306i
\(172\) 6.73284 11.6616i 0.513374 0.889190i
\(173\) −7.89065 2.87196i −0.599915 0.218351i 0.0241697 0.999708i \(-0.492306\pi\)
−0.624085 + 0.781357i \(0.714528\pi\)
\(174\) 0.0716673 0.00778887i 0.00543308 0.000590473i
\(175\) 0 0
\(176\) 13.4720 + 11.3043i 1.01549 + 0.852097i
\(177\) −0.373294 0.509992i −0.0280585 0.0383334i
\(178\) 2.38245 + 0.867141i 0.178572 + 0.0649950i
\(179\) 11.7123 20.2863i 0.875420 1.51627i 0.0191052 0.999817i \(-0.493918\pi\)
0.856315 0.516454i \(-0.172748\pi\)
\(180\) 0 0
\(181\) 4.02049 + 6.96369i 0.298841 + 0.517607i 0.975871 0.218348i \(-0.0700667\pi\)
−0.677030 + 0.735955i \(0.736733\pi\)
\(182\) −0.304128 1.72479i −0.0225434 0.127850i
\(183\) 9.60022 4.72444i 0.709668 0.349240i
\(184\) 6.59808 2.40151i 0.486417 0.177041i
\(185\) 0 0
\(186\) 2.03261 2.11978i 0.149038 0.155430i
\(187\) −23.9906 + 20.1305i −1.75437 + 1.47209i
\(188\) −11.9223 −0.869525
\(189\) −4.57275 + 7.49367i −0.332618 + 0.545084i
\(190\) 0 0
\(191\) 2.02875 1.70232i 0.146795 0.123176i −0.566433 0.824108i \(-0.691677\pi\)
0.713228 + 0.700932i \(0.247232\pi\)
\(192\) −10.4653 2.57001i −0.755267 0.185475i
\(193\) 2.39096 13.5598i 0.172105 0.976055i −0.769328 0.638854i \(-0.779409\pi\)
0.941433 0.337201i \(-0.109480\pi\)
\(194\) −3.57921 + 1.30273i −0.256973 + 0.0935304i
\(195\) 0 0
\(196\) 1.38471 + 7.85310i 0.0989081 + 0.560936i
\(197\) −5.44000 9.42236i −0.387584 0.671315i 0.604540 0.796575i \(-0.293357\pi\)
−0.992124 + 0.125260i \(0.960024\pi\)
\(198\) 2.51035 3.26037i 0.178403 0.231705i
\(199\) 9.58456 16.6009i 0.679431 1.17681i −0.295721 0.955274i \(-0.595560\pi\)
0.975152 0.221535i \(-0.0711068\pi\)
\(200\) 0 0
\(201\) 0.433746 0.983555i 0.0305941 0.0693747i
\(202\) 2.42089 + 2.03137i 0.170334 + 0.142927i
\(203\) −0.194728 0.163396i −0.0136672 0.0114682i
\(204\) 8.49055 19.2530i 0.594457 1.34798i
\(205\) 0 0
\(206\) −1.26978 + 2.19932i −0.0884698 + 0.153234i
\(207\) 7.39775 + 17.9436i 0.514179 + 1.24717i
\(208\) 6.64592 + 11.5111i 0.460812 + 0.798150i
\(209\) 5.90101 + 33.4663i 0.408181 + 2.31491i
\(210\) 0 0
\(211\) −14.2097 + 5.17190i −0.978235 + 0.356048i −0.781154 0.624339i \(-0.785369\pi\)
−0.197081 + 0.980387i \(0.563146\pi\)
\(212\) 0.124737 0.707417i 0.00856695 0.0485856i
\(213\) 11.4319 + 2.80738i 0.783297 + 0.192358i
\(214\) −0.231007 + 0.193838i −0.0157913 + 0.0132505i
\(215\) 0 0
\(216\) −1.11392 + 5.52834i −0.0757928 + 0.376156i
\(217\) −10.3558 −0.702996
\(218\) −0.121840 + 0.102236i −0.00825207 + 0.00692431i
\(219\) −5.45880 + 5.69291i −0.368872 + 0.384691i
\(220\) 0 0
\(221\) −22.2424 + 8.09556i −1.49618 + 0.544566i
\(222\) 1.06217 0.522711i 0.0712880 0.0350821i
\(223\) 0.809497 + 4.59088i 0.0542079 + 0.307428i 0.999841 0.0178057i \(-0.00566802\pi\)
−0.945634 + 0.325234i \(0.894557\pi\)
\(224\) −2.66235 4.61133i −0.177886 0.308107i
\(225\) 0 0
\(226\) 2.43666 4.22042i 0.162084 0.280738i
\(227\) 0.187481 + 0.0682374i 0.0124435 + 0.00452908i 0.348234 0.937407i \(-0.386781\pi\)
−0.335791 + 0.941937i \(0.609004\pi\)
\(228\) −13.4859 18.4244i −0.893128 1.22019i
\(229\) 13.3044 + 11.1637i 0.879179 + 0.737719i 0.966010 0.258504i \(-0.0832296\pi\)
−0.0868311 + 0.996223i \(0.527674\pi\)
\(230\) 0 0
\(231\) −14.4247 + 1.56769i −0.949074 + 0.103146i
\(232\) −0.153450 0.0558513i −0.0100745 0.00366682i
\(233\) 7.90504 13.6919i 0.517876 0.896988i −0.481908 0.876222i \(-0.660056\pi\)
0.999784 0.0207662i \(-0.00661058\pi\)
\(234\) 2.62571 1.66666i 0.171648 0.108953i
\(235\) 0 0
\(236\) 0.121877 + 0.691202i 0.00793355 + 0.0449934i
\(237\) 23.4659 + 15.7075i 1.52428 + 1.02031i
\(238\) 2.77368 1.00954i 0.179791 0.0654385i
\(239\) −5.21235 + 29.5607i −0.337159 + 1.91212i 0.0676249 + 0.997711i \(0.478458\pi\)
−0.404784 + 0.914412i \(0.632653\pi\)
\(240\) 0 0
\(241\) −2.74958 + 2.30717i −0.177116 + 0.148618i −0.727036 0.686600i \(-0.759103\pi\)
0.549920 + 0.835217i \(0.314658\pi\)
\(242\) 3.75829 0.241592
\(243\) −15.3971 2.43506i −0.987724 0.156209i
\(244\) −11.8823 −0.760686
\(245\) 0 0
\(246\) 0.527925 + 1.81682i 0.0336592 + 0.115836i
\(247\) −4.45999 + 25.2938i −0.283782 + 1.60941i
\(248\) −6.25139 + 2.27532i −0.396964 + 0.144483i
\(249\) −16.0939 10.7729i −1.01991 0.682704i
\(250\) 0 0
\(251\) −12.8233 22.2107i −0.809401 1.40192i −0.913279 0.407334i \(-0.866458\pi\)
0.103878 0.994590i \(-0.466875\pi\)
\(252\) 8.23080 5.22448i 0.518492 0.329111i
\(253\) −16.0397 + 27.7815i −1.00841 + 1.74661i
\(254\) −2.06832 0.752808i −0.129778 0.0472354i
\(255\) 0 0
\(256\) 7.83172 + 6.57159i 0.489483 + 0.410725i
\(257\) 6.42079 + 5.38768i 0.400518 + 0.336075i 0.820694 0.571368i \(-0.193587\pi\)
−0.420176 + 0.907443i \(0.638032\pi\)
\(258\) 1.98111 + 2.70659i 0.123339 + 0.168505i
\(259\) −3.92260 1.42771i −0.243738 0.0887135i
\(260\) 0 0
\(261\) 0.136446 0.430270i 0.00844581 0.0266330i
\(262\) −1.16961 2.02582i −0.0722586 0.125156i
\(263\) −0.883720 5.01183i −0.0544925 0.309043i 0.945363 0.326019i \(-0.105707\pi\)
−0.999856 + 0.0169761i \(0.994596\pi\)
\(264\) −8.36318 + 4.11567i −0.514718 + 0.253302i
\(265\) 0 0
\(266\) 0.556171 3.15420i 0.0341010 0.193397i
\(267\) 10.9873 11.4585i 0.672411 0.701248i
\(268\) −0.914470 + 0.767331i −0.0558601 + 0.0468722i
\(269\) 28.2625 1.72320 0.861599 0.507590i \(-0.169464\pi\)
0.861599 + 0.507590i \(0.169464\pi\)
\(270\) 0 0
\(271\) −17.2893 −1.05025 −0.525125 0.851025i \(-0.675982\pi\)
−0.525125 + 0.851025i \(0.675982\pi\)
\(272\) −17.1602 + 14.3992i −1.04049 + 0.873077i
\(273\) −10.6499 2.61536i −0.644564 0.158289i
\(274\) 0.0190506 0.108041i 0.00115089 0.00652702i
\(275\) 0 0
\(276\) 1.42748 21.5066i 0.0859241 1.29454i
\(277\) −0.718943 4.07733i −0.0431971 0.244983i 0.955562 0.294791i \(-0.0952501\pi\)
−0.998759 + 0.0498083i \(0.984139\pi\)
\(278\) 0.647851 + 1.12211i 0.0388555 + 0.0672997i
\(279\) −7.00904 17.0008i −0.419620 1.01781i
\(280\) 0 0
\(281\) 18.0380 + 6.56528i 1.07605 + 0.391652i 0.818438 0.574595i \(-0.194840\pi\)
0.257617 + 0.966247i \(0.417063\pi\)
\(282\) 1.19830 2.71724i 0.0713575 0.161809i
\(283\) −7.31199 6.13548i −0.434652 0.364717i 0.399051 0.916929i \(-0.369339\pi\)
−0.833704 + 0.552212i \(0.813784\pi\)
\(284\) −10.0141 8.40286i −0.594230 0.498618i
\(285\) 0 0
\(286\) 4.83029 + 1.75808i 0.285621 + 0.103957i
\(287\) 3.33570 5.77759i 0.196900 0.341041i
\(288\) 5.76835 7.49176i 0.339903 0.441456i
\(289\) −11.4457 19.8246i −0.673277 1.16615i
\(290\) 0 0
\(291\) −1.57951 + 23.7971i −0.0925927 + 1.39501i
\(292\) 8.23067 2.99572i 0.481664 0.175311i
\(293\) 1.10363 6.25900i 0.0644748 0.365655i −0.935451 0.353457i \(-0.885006\pi\)
0.999926 0.0121977i \(-0.00388276\pi\)
\(294\) −1.92899 0.473712i −0.112501 0.0276274i
\(295\) 0 0
\(296\) −2.68161 −0.155866
\(297\) −12.3366 22.6195i −0.715842 1.31252i
\(298\) −6.37651 −0.369381
\(299\) −18.5732 + 15.5848i −1.07412 + 0.901290i
\(300\) 0 0
\(301\) 2.05380 11.6477i 0.118379 0.671360i
\(302\) −1.34493 + 0.489516i −0.0773922 + 0.0281685i
\(303\) 17.7544 8.73727i 1.01997 0.501943i
\(304\) 4.22093 + 23.9381i 0.242087 + 1.37294i
\(305\) 0 0
\(306\) 3.53462 + 3.87019i 0.202061 + 0.221244i
\(307\) 4.29280 7.43535i 0.245003 0.424358i −0.717129 0.696940i \(-0.754544\pi\)
0.962133 + 0.272582i \(0.0878777\pi\)
\(308\) 15.1415 + 5.51106i 0.862767 + 0.314022i
\(309\) 9.39206 + 12.8314i 0.534295 + 0.729952i
\(310\) 0 0
\(311\) −8.78608 7.37239i −0.498213 0.418050i 0.358746 0.933435i \(-0.383204\pi\)
−0.856959 + 0.515385i \(0.827649\pi\)
\(312\) −7.00360 + 0.761158i −0.396501 + 0.0430921i
\(313\) 23.4476 + 8.53424i 1.32534 + 0.482384i 0.905165 0.425060i \(-0.139747\pi\)
0.420173 + 0.907444i \(0.361969\pi\)
\(314\) 1.91605 3.31870i 0.108129 0.187285i
\(315\) 0 0
\(316\) −15.6794 27.1575i −0.882034 1.52773i
\(317\) 0.110144 + 0.624658i 0.00618630 + 0.0350843i 0.987745 0.156078i \(-0.0498853\pi\)
−0.981558 + 0.191163i \(0.938774\pi\)
\(318\) 0.148691 + 0.0995304i 0.00833820 + 0.00558139i
\(319\) 0.701069 0.255168i 0.0392524 0.0142867i
\(320\) 0 0
\(321\) 0.526875 + 1.81321i 0.0294073 + 0.101203i
\(322\) 2.31612 1.94346i 0.129072 0.108305i
\(323\) −43.2860 −2.40850
\(324\) 14.1477 + 9.97623i 0.785983 + 0.554235i
\(325\) 0 0
\(326\) 0.631648 0.530015i 0.0349837 0.0293548i
\(327\) 0.277890 + 0.956342i 0.0153674 + 0.0528858i
\(328\) 0.744208 4.22062i 0.0410920 0.233045i
\(329\) −9.84024 + 3.58155i −0.542510 + 0.197457i
\(330\) 0 0
\(331\) −3.50296 19.8662i −0.192540 1.09195i −0.915879 0.401455i \(-0.868505\pi\)
0.723339 0.690493i \(-0.242606\pi\)
\(332\) 10.7536 + 18.6258i 0.590180 + 1.02222i
\(333\) −0.311078 7.40593i −0.0170470 0.405843i
\(334\) −2.59540 + 4.49537i −0.142014 + 0.245976i
\(335\) 0 0
\(336\) −10.3178 + 1.12135i −0.562883 + 0.0611746i
\(337\) 23.2996 + 19.5507i 1.26921 + 1.06499i 0.994637 + 0.103428i \(0.0329812\pi\)
0.274574 + 0.961566i \(0.411463\pi\)
\(338\) 0.221365 + 0.185747i 0.0120407 + 0.0101033i
\(339\) −18.0230 24.6229i −0.978875 1.33733i
\(340\) 0 0
\(341\) 15.1969 26.3217i 0.822956 1.42540i
\(342\) 5.55460 1.22179i 0.300358 0.0660668i
\(343\) 9.41512 + 16.3075i 0.508369 + 0.880520i
\(344\) −1.31937 7.48250i −0.0711355 0.403429i
\(345\) 0 0
\(346\) −2.18271 + 0.794442i −0.117343 + 0.0427094i
\(347\) 6.41781 36.3972i 0.344526 1.95391i 0.0481276 0.998841i \(-0.484675\pi\)
0.296399 0.955064i \(-0.404214\pi\)
\(348\) −0.346937 + 0.361816i −0.0185978 + 0.0193954i
\(349\) 5.58600 4.68721i 0.299012 0.250901i −0.480921 0.876764i \(-0.659698\pi\)
0.779933 + 0.625863i \(0.215253\pi\)
\(350\) 0 0
\(351\) −2.91457 19.2539i −0.155568 1.02769i
\(352\) 15.6278 0.832962
\(353\) −8.72291 + 7.31939i −0.464273 + 0.389572i −0.844700 0.535239i \(-0.820221\pi\)
0.380427 + 0.924811i \(0.375777\pi\)
\(354\) −0.169783 0.0416944i −0.00902385 0.00221603i
\(355\) 0 0
\(356\) −16.5664 + 6.02968i −0.878018 + 0.319573i
\(357\) 1.22403 18.4414i 0.0647824 0.976020i
\(358\) −1.12519 6.38128i −0.0594682 0.337261i
\(359\) −12.4562 21.5748i −0.657414 1.13867i −0.981283 0.192573i \(-0.938317\pi\)
0.323869 0.946102i \(-0.395016\pi\)
\(360\) 0 0
\(361\) −13.9847 + 24.2223i −0.736039 + 1.27486i
\(362\) 2.09015 + 0.760754i 0.109856 + 0.0399843i
\(363\) 9.49544 21.5317i 0.498381 1.13012i
\(364\) 9.32920 + 7.82813i 0.488983 + 0.410305i
\(365\) 0 0
\(366\) 1.19427 2.70812i 0.0624257 0.141555i
\(367\) 27.0081 + 9.83014i 1.40981 + 0.513129i 0.931074 0.364830i \(-0.118873\pi\)
0.478736 + 0.877959i \(0.341095\pi\)
\(368\) −11.4730 + 19.8718i −0.598071 + 1.03589i
\(369\) 11.7426 + 1.56571i 0.611295 + 0.0815074i
\(370\) 0 0
\(371\) −0.109560 0.621347i −0.00568808 0.0322587i
\(372\) −1.35247 + 20.3765i −0.0701224 + 1.05647i
\(373\) −17.4252 + 6.34227i −0.902245 + 0.328390i −0.751152 0.660129i \(-0.770501\pi\)
−0.151093 + 0.988520i \(0.548279\pi\)
\(374\) −1.50432 + 8.53145i −0.0777868 + 0.441151i
\(375\) 0 0
\(376\) −5.15326 + 4.32410i −0.265759 + 0.222998i
\(377\) 0.563875 0.0290410
\(378\) 0.363454 + 2.40100i 0.0186940 + 0.123494i
\(379\) 23.8701 1.22613 0.613063 0.790034i \(-0.289937\pi\)
0.613063 + 0.790034i \(0.289937\pi\)
\(380\) 0 0
\(381\) −9.53861 + 9.94768i −0.488678 + 0.509635i
\(382\) 0.127212 0.721455i 0.00650873 0.0369129i
\(383\) −28.7180 + 10.4525i −1.46742 + 0.534097i −0.947398 0.320057i \(-0.896298\pi\)
−0.520021 + 0.854154i \(0.674076\pi\)
\(384\) −12.4705 + 6.13698i −0.636385 + 0.313176i
\(385\) 0 0
\(386\) −1.90439 3.29849i −0.0969307 0.167889i
\(387\) 20.5117 4.51175i 1.04267 0.229345i
\(388\) 13.2427 22.9370i 0.672296 1.16445i
\(389\) 7.60180 + 2.76683i 0.385427 + 0.140284i 0.527464 0.849578i \(-0.323143\pi\)
−0.142037 + 0.989861i \(0.545365\pi\)
\(390\) 0 0
\(391\) −31.3019 26.2654i −1.58301 1.32830i
\(392\) 3.44676 + 2.89217i 0.174088 + 0.146077i
\(393\) −14.5612 + 1.58253i −0.734516 + 0.0798279i
\(394\) −2.82812 1.02935i −0.142479 0.0518580i
\(395\) 0 0
\(396\) 1.20078 + 28.5874i 0.0603416 + 1.43657i
\(397\) −9.75843 16.9021i −0.489762 0.848292i 0.510169 0.860074i \(-0.329583\pi\)
−0.999931 + 0.0117821i \(0.996250\pi\)
\(398\) −0.920780 5.22200i −0.0461545 0.261755i
\(399\) −16.6656 11.1556i −0.834325 0.558477i
\(400\) 0 0
\(401\) 2.44572 13.8704i 0.122134 0.692654i −0.860835 0.508883i \(-0.830058\pi\)
0.982969 0.183771i \(-0.0588305\pi\)
\(402\) −0.0829717 0.285542i −0.00413825 0.0142415i
\(403\) 17.5973 14.7659i 0.876582 0.735540i
\(404\) −21.9749 −1.09329
\(405\) 0 0
\(406\) −0.0703165 −0.00348975
\(407\) 9.38520 7.87512i 0.465207 0.390355i
\(408\) −3.31294 11.4013i −0.164015 0.564448i
\(409\) 0.282399 1.60156i 0.0139637 0.0791923i −0.977030 0.213104i \(-0.931643\pi\)
0.990993 + 0.133912i \(0.0427538\pi\)
\(410\) 0 0
\(411\) −0.570850 0.382113i −0.0281580 0.0188482i
\(412\) −3.06643 17.3906i −0.151072 0.856774i
\(413\) 0.308235 + 0.533879i 0.0151673 + 0.0262705i
\(414\) 4.75812 + 2.48693i 0.233849 + 0.122226i
\(415\) 0 0
\(416\) 11.0991 + 4.03976i 0.544181 + 0.198066i
\(417\) 8.06552 0.876569i 0.394970 0.0429257i
\(418\) 7.20101 + 6.04236i 0.352213 + 0.295542i
\(419\) −24.5436 20.5945i −1.19903 1.00611i −0.999657 0.0261853i \(-0.991664\pi\)
−0.199376 0.979923i \(-0.563892\pi\)
\(420\) 0 0
\(421\) −3.21532 1.17028i −0.156705 0.0570360i 0.262477 0.964938i \(-0.415461\pi\)
−0.419182 + 0.907902i \(0.637683\pi\)
\(422\) −2.09147 + 3.62254i −0.101811 + 0.176342i
\(423\) −12.5398 13.7304i −0.609708 0.667593i
\(424\) −0.202657 0.351011i −0.00984187 0.0170466i
\(425\) 0 0
\(426\) 2.92162 1.43778i 0.141553 0.0696607i
\(427\) −9.80721 + 3.56953i −0.474604 + 0.172742i
\(428\) 0.364121 2.06504i 0.0176005 0.0998173i
\(429\) 22.2761 23.2315i 1.07550 1.12163i
\(430\) 0 0
\(431\) 33.8955 1.63269 0.816344 0.577565i \(-0.195997\pi\)
0.816344 + 0.577565i \(0.195997\pi\)
\(432\) −8.82423 16.1795i −0.424556 0.778437i
\(433\) 17.6676 0.849049 0.424524 0.905417i \(-0.360441\pi\)
0.424524 + 0.905417i \(0.360441\pi\)
\(434\) −2.19442 + 1.84134i −0.105336 + 0.0883870i
\(435\) 0 0
\(436\) 0.192049 1.08916i 0.00919748 0.0521615i
\(437\) −41.6649 + 15.1648i −1.99310 + 0.725430i
\(438\) −0.144494 + 2.17696i −0.00690418 + 0.104019i
\(439\) 1.25144 + 7.09728i 0.0597281 + 0.338735i 0.999999 0.00169354i \(-0.000539072\pi\)
−0.940270 + 0.340428i \(0.889428\pi\)
\(440\) 0 0
\(441\) −7.58761 + 9.85457i −0.361315 + 0.469265i
\(442\) −3.27377 + 5.67034i −0.155718 + 0.269711i
\(443\) −32.5861 11.8604i −1.54821 0.563504i −0.580216 0.814463i \(-0.697032\pi\)
−0.967998 + 0.250959i \(0.919254\pi\)
\(444\) −3.32152 + 7.53183i −0.157632 + 0.357445i
\(445\) 0 0
\(446\) 0.987830 + 0.828888i 0.0467751 + 0.0392490i
\(447\) −16.1104 + 36.5318i −0.761998 + 1.72789i
\(448\) 9.87731 + 3.59505i 0.466659 + 0.169850i
\(449\) −4.87046 + 8.43589i −0.229851 + 0.398114i −0.957764 0.287556i \(-0.907157\pi\)
0.727913 + 0.685670i \(0.240491\pi\)
\(450\) 0 0
\(451\) 9.79011 + 16.9570i 0.460998 + 0.798473i
\(452\) 5.88437 + 33.3719i 0.276777 + 1.56968i
\(453\) −0.593521 + 8.94206i −0.0278861 + 0.420135i
\(454\) 0.0518609 0.0188758i 0.00243395 0.000885886i
\(455\) 0 0
\(456\) −12.5114 3.07250i −0.585902 0.143883i
\(457\) −24.2137 + 20.3177i −1.13267 + 0.950421i −0.999174 0.0406289i \(-0.987064\pi\)
−0.133493 + 0.991050i \(0.542619\pi\)
\(458\) 4.80424 0.224487
\(459\) 31.1031 10.4721i 1.45177 0.488796i
\(460\) 0 0
\(461\) −13.9469 + 11.7028i −0.649572 + 0.545056i −0.906941 0.421258i \(-0.861589\pi\)
0.257369 + 0.966313i \(0.417144\pi\)
\(462\) −2.77789 + 2.89702i −0.129239 + 0.134781i
\(463\) −4.90983 + 27.8450i −0.228179 + 1.29407i 0.628334 + 0.777943i \(0.283737\pi\)
−0.856513 + 0.516125i \(0.827374\pi\)
\(464\) 0.501467 0.182519i 0.0232800 0.00847324i
\(465\) 0 0
\(466\) −0.759430 4.30694i −0.0351799 0.199515i
\(467\) −7.02539 12.1683i −0.325096 0.563083i 0.656435 0.754382i \(-0.272063\pi\)
−0.981532 + 0.191299i \(0.938730\pi\)
\(468\) −6.53700 + 20.6138i −0.302173 + 0.952871i
\(469\) −0.524257 + 0.908040i −0.0242080 + 0.0419294i
\(470\) 0 0
\(471\) −14.1723 19.3621i −0.653024 0.892159i
\(472\) 0.303371 + 0.254559i 0.0139638 + 0.0117170i
\(473\) 26.5915 + 22.3129i 1.22268 + 1.02595i
\(474\) 7.76542 0.843953i 0.356678 0.0387641i
\(475\) 0 0
\(476\) −10.2623 + 17.7748i −0.470372 + 0.814708i
\(477\) 0.945895 0.600404i 0.0433096 0.0274906i
\(478\) 4.15161 + 7.19080i 0.189890 + 0.328900i
\(479\) 1.21657 + 6.89953i 0.0555867 + 0.315248i 0.999905 0.0137857i \(-0.00438826\pi\)
−0.944318 + 0.329033i \(0.893277\pi\)
\(480\) 0 0
\(481\) 8.70127 3.16700i 0.396744 0.144403i
\(482\) −0.172411 + 0.977792i −0.00785311 + 0.0445372i
\(483\) −5.28254 18.1795i −0.240364 0.827198i
\(484\) −20.0193 + 16.7982i −0.909969 + 0.763555i
\(485\) 0 0
\(486\) −3.69566 + 2.22173i −0.167639 + 0.100780i
\(487\) 20.2826 0.919093 0.459547 0.888154i \(-0.348012\pi\)
0.459547 + 0.888154i \(0.348012\pi\)
\(488\) −5.13596 + 4.30958i −0.232494 + 0.195086i
\(489\) −1.44064 4.95789i −0.0651482 0.224203i
\(490\) 0 0
\(491\) 4.72637 1.72026i 0.213298 0.0776342i −0.233161 0.972438i \(-0.574907\pi\)
0.446459 + 0.894804i \(0.352685\pi\)
\(492\) −10.9326 7.31803i −0.492881 0.329922i
\(493\) 0.165020 + 0.935876i 0.00743213 + 0.0421497i
\(494\) 3.55236 + 6.15286i 0.159828 + 0.276830i
\(495\) 0 0
\(496\) 10.8701 18.8277i 0.488084 0.845387i
\(497\) −10.7896 3.92709i −0.483979 0.176154i
\(498\) −5.32586 + 0.578820i −0.238658 + 0.0259375i
\(499\) 18.3084 + 15.3625i 0.819595 + 0.687722i 0.952877 0.303356i \(-0.0981072\pi\)
−0.133282 + 0.991078i \(0.542552\pi\)
\(500\) 0 0
\(501\) 19.1972 + 26.2271i 0.857666 + 1.17174i
\(502\) −6.66653 2.42642i −0.297542 0.108296i
\(503\) −4.04017 + 6.99778i −0.180142 + 0.312015i −0.941929 0.335813i \(-0.890989\pi\)
0.761787 + 0.647828i \(0.224322\pi\)
\(504\) 1.66279 5.24343i 0.0740664 0.233561i
\(505\) 0 0
\(506\) 1.54092 + 8.73897i 0.0685020 + 0.388494i
\(507\) 1.62346 0.798931i 0.0721002 0.0354818i
\(508\) 14.3821 5.23467i 0.638104 0.232251i
\(509\) 2.73491 15.5104i 0.121223 0.687487i −0.862257 0.506470i \(-0.830950\pi\)
0.983480 0.181017i \(-0.0579389\pi\)
\(510\) 0 0
\(511\) 5.89335 4.94511i 0.260707 0.218759i
\(512\) 18.8770 0.834254
\(513\) 7.03408 34.9098i 0.310562 1.54131i
\(514\) 2.31856 0.102267
\(515\) 0 0
\(516\) −22.6503 5.56234i −0.997122 0.244868i
\(517\) 5.33693 30.2672i 0.234718 1.33115i
\(518\) −1.08507 + 0.394933i −0.0476752 + 0.0173523i
\(519\) −0.963233 + 14.5122i −0.0422813 + 0.637015i
\(520\) 0 0
\(521\) 6.71663 + 11.6335i 0.294261 + 0.509675i 0.974813 0.223025i \(-0.0715932\pi\)
−0.680552 + 0.732700i \(0.738260\pi\)
\(522\) −0.0475919 0.115437i −0.00208304 0.00505253i
\(523\) −9.04762 + 15.6709i −0.395625 + 0.685242i −0.993181 0.116585i \(-0.962805\pi\)
0.597556 + 0.801827i \(0.296139\pi\)
\(524\) 15.2848 + 5.56323i 0.667721 + 0.243031i
\(525\) 0 0
\(526\) −1.07841 0.904889i −0.0470207 0.0394551i
\(527\) 29.6572 + 24.8853i 1.29189 + 1.08402i
\(528\) 12.2910 27.8708i 0.534896 1.21292i
\(529\) −17.7185 6.44901i −0.770370 0.280392i
\(530\) 0 0
\(531\) −0.667833 + 0.867363i −0.0289815 + 0.0376404i
\(532\) 11.1356 + 19.2874i 0.482789 + 0.836214i
\(533\) 2.56978 + 14.5739i 0.111309 + 0.631267i
\(534\) 0.290832 4.38172i 0.0125855 0.189615i
\(535\) 0 0
\(536\) −0.116964 + 0.663337i −0.00505208 + 0.0286518i
\(537\) −39.4020 9.67614i −1.70032 0.417556i
\(538\) 5.98892 5.02530i 0.258201 0.216656i
\(539\) −20.5565 −0.885433
\(540\) 0 0
\(541\) 10.6112 0.456211 0.228106 0.973636i \(-0.426747\pi\)
0.228106 + 0.973636i \(0.426747\pi\)
\(542\) −3.66366 + 3.07417i −0.157368 + 0.132047i
\(543\) 9.63929 10.0527i 0.413661 0.431402i
\(544\) −3.45667 + 19.6038i −0.148204 + 0.840505i
\(545\) 0 0
\(546\) −2.72179 + 1.33944i −0.116482 + 0.0573227i
\(547\) 2.92380 + 16.5817i 0.125013 + 0.708983i 0.981300 + 0.192483i \(0.0616541\pi\)
−0.856287 + 0.516500i \(0.827235\pi\)
\(548\) 0.381429 + 0.660654i 0.0162938 + 0.0282217i
\(549\) −12.4978 13.6843i −0.533391 0.584031i
\(550\) 0 0
\(551\) 0.968993 + 0.352685i 0.0412805 + 0.0150249i
\(552\) −7.18319 9.81364i −0.305737 0.417696i
\(553\) −21.0995 17.7046i −0.897241 0.752875i
\(554\) −0.877326 0.736164i −0.0372740 0.0312766i
\(555\) 0 0
\(556\) −8.46634 3.08149i −0.359053 0.130684i
\(557\) −2.30112 + 3.98565i −0.0975015 + 0.168877i −0.910650 0.413179i \(-0.864418\pi\)
0.813148 + 0.582056i \(0.197752\pi\)
\(558\) −4.50811 2.35626i −0.190844 0.0997484i
\(559\) 13.1179 + 22.7209i 0.554830 + 0.960994i
\(560\) 0 0
\(561\) 45.0770 + 30.1734i 1.90315 + 1.27392i
\(562\) 4.98966 1.81609i 0.210476 0.0766070i
\(563\) 1.86442 10.5736i 0.0785758 0.445626i −0.919983 0.391958i \(-0.871798\pi\)
0.998559 0.0536674i \(-0.0170911\pi\)
\(564\) 5.76209 + 19.8299i 0.242628 + 0.834988i
\(565\) 0 0
\(566\) −2.64037 −0.110983
\(567\) 14.6739 + 3.98393i 0.616246 + 0.167310i
\(568\) −7.37610 −0.309494
\(569\) 10.4618 8.77850i 0.438582 0.368014i −0.396597 0.917993i \(-0.629809\pi\)
0.835178 + 0.549979i \(0.185364\pi\)
\(570\) 0 0
\(571\) −2.92720 + 16.6010i −0.122499 + 0.694729i 0.860262 + 0.509852i \(0.170300\pi\)
−0.982762 + 0.184877i \(0.940811\pi\)
\(572\) −33.5875 + 12.2248i −1.40436 + 0.511147i
\(573\) −3.81190 2.55159i −0.159244 0.106594i
\(574\) −0.320457 1.81740i −0.0133756 0.0758569i
\(575\) 0 0
\(576\) 0.783310 + 18.6485i 0.0326379 + 0.777022i
\(577\) 7.71289 13.3591i 0.321092 0.556147i −0.659622 0.751598i \(-0.729284\pi\)
0.980714 + 0.195450i \(0.0626168\pi\)
\(578\) −5.95034 2.16575i −0.247502 0.0900832i
\(579\) −23.7090 + 2.57671i −0.985311 + 0.107085i
\(580\) 0 0
\(581\) 14.4709 + 12.1426i 0.600355 + 0.503758i
\(582\) 3.89661 + 5.32354i 0.161520 + 0.220668i
\(583\) 1.74008 + 0.633338i 0.0720668 + 0.0262302i
\(584\) 2.47108 4.28003i 0.102254 0.177109i
\(585\) 0 0
\(586\) −0.879036 1.52254i −0.0363126 0.0628953i
\(587\) −2.05906 11.6775i −0.0849866 0.481983i −0.997359 0.0726229i \(-0.976863\pi\)
0.912373 0.409360i \(-0.134248\pi\)
\(588\) 12.3925 6.09856i 0.511057 0.251500i
\(589\) 39.4757 14.3680i 1.62657 0.592022i
\(590\) 0 0
\(591\) −13.0426 + 13.6020i −0.536502 + 0.559510i
\(592\) 6.71313 5.63298i 0.275908 0.231514i
\(593\) 34.8582 1.43146 0.715728 0.698379i \(-0.246095\pi\)
0.715728 + 0.698379i \(0.246095\pi\)
\(594\) −6.63609 2.59961i −0.272282 0.106663i
\(595\) 0 0
\(596\) 33.9658 28.5007i 1.39129 1.16743i
\(597\) −32.2439 7.91829i −1.31965 0.324074i
\(598\) −1.16462 + 6.60492i −0.0476251 + 0.270095i
\(599\) 11.2279 4.08662i 0.458759 0.166975i −0.102294 0.994754i \(-0.532618\pi\)
0.561054 + 0.827779i \(0.310396\pi\)
\(600\) 0 0
\(601\) 3.39336 + 19.2447i 0.138418 + 0.785007i 0.972418 + 0.233243i \(0.0749338\pi\)
−0.834001 + 0.551764i \(0.813955\pi\)
\(602\) −1.63584 2.83336i −0.0666718 0.115479i
\(603\) −1.84553 0.246075i −0.0751560 0.0100210i
\(604\) 4.97611 8.61887i 0.202475 0.350697i
\(605\) 0 0
\(606\) 2.20867 5.00833i 0.0897209 0.203450i
\(607\) −7.81863 6.56061i −0.317348 0.266287i 0.470173 0.882574i \(-0.344192\pi\)
−0.787521 + 0.616287i \(0.788636\pi\)
\(608\) 16.5467 + 13.8843i 0.671055 + 0.563082i
\(609\) −0.177657 + 0.402852i −0.00719902 + 0.0163244i
\(610\) 0 0
\(611\) 11.6144 20.1168i 0.469870 0.813839i
\(612\) −36.1262 4.81691i −1.46032 0.194712i
\(613\) 7.38192 + 12.7859i 0.298153 + 0.516416i 0.975713 0.219051i \(-0.0702961\pi\)
−0.677560 + 0.735467i \(0.736963\pi\)
\(614\) −0.412406 2.33887i −0.0166433 0.0943890i
\(615\) 0 0
\(616\) 8.54350 3.10958i 0.344228 0.125289i
\(617\) 5.66996 32.1559i 0.228264 1.29455i −0.628082 0.778147i \(-0.716160\pi\)
0.856346 0.516402i \(-0.172729\pi\)
\(618\) 4.27173 + 1.04903i 0.171834 + 0.0421982i
\(619\) 11.2792 9.46438i 0.453350 0.380406i −0.387327 0.921942i \(-0.626602\pi\)
0.840677 + 0.541537i \(0.182157\pi\)
\(620\) 0 0
\(621\) 26.2695 20.9766i 1.05416 0.841760i
\(622\) −3.17267 −0.127212
\(623\) −11.8619 + 9.95335i −0.475239 + 0.398773i
\(624\) 15.9339 16.6172i 0.637865 0.665220i
\(625\) 0 0
\(626\) 6.48608 2.36074i 0.259236 0.0943541i
\(627\) 52.8110 25.9892i 2.10907 1.03791i
\(628\) 4.62714 + 26.2418i 0.184643 + 1.04716i
\(629\) 7.80281 + 13.5149i 0.311118 + 0.538873i
\(630\) 0 0
\(631\) 12.9621 22.4511i 0.516014 0.893762i −0.483813 0.875171i \(-0.660749\pi\)
0.999827 0.0185911i \(-0.00591806\pi\)
\(632\) −16.6269 6.05170i −0.661383 0.240724i
\(633\) 15.4698 + 21.1347i 0.614868 + 0.840031i
\(634\) 0.134409 + 0.112782i 0.00533806 + 0.00447916i
\(635\) 0 0
\(636\) −1.23690 + 0.134427i −0.0490463 + 0.00533040i
\(637\) −14.5997 5.31385i −0.578460 0.210542i
\(638\) 0.103188 0.178727i 0.00408525 0.00707585i
\(639\) −0.855657 20.3709i −0.0338493 0.805860i
\(640\) 0 0
\(641\) −3.45147 19.5742i −0.136325 0.773136i −0.973928 0.226857i \(-0.927155\pi\)
0.837603 0.546279i \(-0.183956\pi\)
\(642\) 0.434048 + 0.290541i 0.0171305 + 0.0114668i
\(643\) 31.1702 11.3450i 1.22923 0.447404i 0.355897 0.934525i \(-0.384175\pi\)
0.873334 + 0.487121i \(0.161953\pi\)
\(644\) −3.65075 + 20.7044i −0.143860 + 0.815869i
\(645\) 0 0
\(646\) −9.17244 + 7.69659i −0.360885 + 0.302818i
\(647\) −18.8740 −0.742014 −0.371007 0.928630i \(-0.620987\pi\)
−0.371007 + 0.928630i \(0.620987\pi\)
\(648\) 9.73341 0.819127i 0.382364 0.0321783i
\(649\) −1.80931 −0.0710217
\(650\) 0 0
\(651\) 5.00497 + 17.2243i 0.196160 + 0.675074i
\(652\) −0.995625 + 5.64647i −0.0389917 + 0.221133i
\(653\) −25.7663 + 9.37817i −1.00831 + 0.366996i −0.792785 0.609502i \(-0.791370\pi\)
−0.215528 + 0.976498i \(0.569147\pi\)
\(654\) 0.228931 + 0.153241i 0.00895190 + 0.00599218i
\(655\) 0 0
\(656\) 7.00276 + 12.1291i 0.273412 + 0.473563i
\(657\) 12.1070 + 6.32798i 0.472339 + 0.246878i
\(658\) −1.44835 + 2.50861i −0.0564625 + 0.0977959i
\(659\) −4.90832 1.78648i −0.191201 0.0695915i 0.244645 0.969613i \(-0.421329\pi\)
−0.435846 + 0.900021i \(0.643551\pi\)
\(660\) 0 0
\(661\) 17.4652 + 14.6551i 0.679319 + 0.570017i 0.915807 0.401618i \(-0.131552\pi\)
−0.236488 + 0.971634i \(0.575996\pi\)
\(662\) −4.27466 3.58687i −0.166139 0.139408i
\(663\) 24.2148 + 33.0821i 0.940424 + 1.28480i
\(664\) 11.4035 + 4.15052i 0.442540 + 0.161071i
\(665\) 0 0
\(666\) −1.38275 1.51403i −0.0535805 0.0586674i
\(667\) 0.486714 + 0.843014i 0.0188456 + 0.0326416i
\(668\) −6.26772 35.5460i −0.242505 1.37532i
\(669\) 7.24458 3.56519i 0.280092 0.137838i
\(670\) 0 0
\(671\) 5.31901 30.1656i 0.205338 1.16453i
\(672\) −6.38309 + 6.65684i −0.246233 + 0.256793i
\(673\) −13.3460 + 11.1986i −0.514450 + 0.431675i −0.862692 0.505730i \(-0.831223\pi\)
0.348242 + 0.937405i \(0.386779\pi\)
\(674\) 8.41353 0.324077
\(675\) 0 0
\(676\) −2.00937 −0.0772835
\(677\) 24.5750 20.6209i 0.944495 0.792526i −0.0338665 0.999426i \(-0.510782\pi\)
0.978362 + 0.206901i \(0.0663377\pi\)
\(678\) −8.19728 2.01305i −0.314815 0.0773107i
\(679\) 4.03958 22.9096i 0.155025 0.879189i
\(680\) 0 0
\(681\) 0.0228863 0.344808i 0.000877005 0.0132131i
\(682\) −1.45995 8.27978i −0.0559043 0.317049i
\(683\) −10.6001 18.3599i −0.405600 0.702520i 0.588791 0.808285i \(-0.299604\pi\)
−0.994391 + 0.105765i \(0.966271\pi\)
\(684\) −24.1267 + 31.3351i −0.922509 + 1.19813i
\(685\) 0 0
\(686\) 4.89469 + 1.78152i 0.186880 + 0.0680188i
\(687\) 12.1381 27.5241i 0.463096 1.05011i
\(688\) 19.0206 + 15.9602i 0.725153 + 0.608476i
\(689\) 1.07212 + 0.899619i 0.0408447 + 0.0342728i
\(690\) 0 0
\(691\) −10.2500 3.73069i −0.389928 0.141922i 0.139614 0.990206i \(-0.455414\pi\)
−0.529542 + 0.848284i \(0.677636\pi\)
\(692\) 8.07579 13.9877i 0.306995 0.531732i
\(693\) 9.57895 + 23.2342i 0.363874 + 0.882596i
\(694\) −5.11176 8.85382i −0.194040 0.336086i
\(695\) 0 0
\(696\) −0.0187321 + 0.282220i −0.000710038 + 0.0106975i
\(697\) −23.4366 + 8.53023i −0.887725 + 0.323106i
\(698\) 0.350268 1.98647i 0.0132578 0.0751889i
\(699\) −26.5937 6.53075i −1.00587 0.247016i
\(700\) 0 0
\(701\) −16.5817 −0.626282 −0.313141 0.949707i \(-0.601381\pi\)
−0.313141 + 0.949707i \(0.601381\pi\)
\(702\) −4.04109 3.56172i −0.152521 0.134428i
\(703\) 16.9336 0.638662
\(704\) −23.6324 + 19.8300i −0.890681 + 0.747370i
\(705\) 0 0
\(706\) −0.546967 + 3.10200i −0.0205854 + 0.116745i
\(707\) −18.1372 + 6.60142i −0.682121 + 0.248272i
\(708\) 1.09074 0.536773i 0.0409926 0.0201732i
\(709\) −0.653972 3.70886i −0.0245604 0.139289i 0.970062 0.242858i \(-0.0780849\pi\)
−0.994622 + 0.103569i \(0.966974\pi\)
\(710\) 0 0
\(711\) 14.7845 46.6213i 0.554461 1.74844i
\(712\) −4.97370 + 8.61470i −0.186397 + 0.322850i
\(713\) 37.2648 + 13.5633i 1.39558 + 0.507948i
\(714\) −3.01964 4.12542i −0.113007 0.154390i
\(715\) 0 0
\(716\) 34.5156 + 28.9620i 1.28991 + 1.08236i
\(717\) 51.6861 5.61730i 1.93025 0.209782i
\(718\) −6.47568 2.35695i −0.241670 0.0879608i
\(719\) 0.0341167 0.0590919i 0.00127234 0.00220375i −0.865389 0.501101i \(-0.832928\pi\)
0.866661 + 0.498898i \(0.166262\pi\)
\(720\) 0 0
\(721\) −7.75519 13.4324i −0.288818 0.500248i
\(722\) 1.34350 + 7.61937i 0.0499999 + 0.283564i
\(723\) 5.16629 + 3.45819i 0.192136 + 0.128611i
\(724\) −14.5339 + 5.28992i −0.540149 + 0.196598i
\(725\) 0 0
\(726\) −1.81639 6.25100i −0.0674127 0.231996i
\(727\) 33.5717 28.1700i 1.24511 1.04477i 0.247998 0.968760i \(-0.420227\pi\)
0.997107 0.0760072i \(-0.0242172\pi\)
\(728\) 6.87159 0.254678
\(729\) 3.39133 + 26.7862i 0.125605 + 0.992080i
\(730\) 0 0
\(731\) −33.8715 + 28.4215i −1.25278 + 1.05121i
\(732\) 5.74275 + 19.7633i 0.212258 + 0.730473i
\(733\) 0.894591 5.07348i 0.0330425 0.187393i −0.963819 0.266557i \(-0.914114\pi\)
0.996862 + 0.0791639i \(0.0252250\pi\)
\(734\) 7.47097 2.71921i 0.275759 0.100368i
\(735\) 0 0
\(736\) 3.54075 + 20.0806i 0.130514 + 0.740181i
\(737\) −1.53867 2.66506i −0.0566777 0.0981686i
\(738\) 2.76669 1.75615i 0.101843 0.0646447i
\(739\) −0.515367 + 0.892642i −0.0189581 + 0.0328364i −0.875349 0.483492i \(-0.839368\pi\)
0.856391 + 0.516328i \(0.172702\pi\)
\(740\) 0 0
\(741\) 44.2256 4.80648i 1.62467 0.176571i
\(742\) −0.133696 0.112185i −0.00490815 0.00411843i
\(743\) −32.5316 27.2972i −1.19347 1.00144i −0.999792 0.0203733i \(-0.993515\pi\)
−0.193676 0.981066i \(-0.562041\pi\)
\(744\) 6.80575 + 9.29799i 0.249511 + 0.340881i
\(745\) 0 0
\(746\) −2.56476 + 4.44229i −0.0939025 + 0.162644i
\(747\) −10.1398 + 31.9749i −0.370997 + 1.16990i
\(748\) −30.1194 52.1683i −1.10127 1.90746i
\(749\) −0.319820 1.81379i −0.0116860 0.0662744i
\(750\) 0 0
\(751\) 2.32349 0.845681i 0.0847853 0.0308593i −0.299279 0.954166i \(-0.596746\pi\)
0.384065 + 0.923306i \(0.374524\pi\)
\(752\) 3.81745 21.6498i 0.139208 0.789487i
\(753\) −30.7444 + 32.0629i −1.12039 + 1.16844i
\(754\) 0.119487 0.100261i 0.00435145 0.00365130i
\(755\) 0 0
\(756\) −12.6676 11.1649i −0.460717 0.406064i
\(757\) −52.6699 −1.91432 −0.957160 0.289559i \(-0.906491\pi\)
−0.957160 + 0.289559i \(0.906491\pi\)
\(758\) 5.05816 4.24430i 0.183721 0.154160i
\(759\) 53.9598 + 13.2512i 1.95862 + 0.480987i
\(760\) 0 0
\(761\) −28.1597 + 10.2493i −1.02079 + 0.371537i −0.797567 0.603231i \(-0.793880\pi\)
−0.223222 + 0.974768i \(0.571658\pi\)
\(762\) −0.252486 + 3.80398i −0.00914660 + 0.137804i
\(763\) −0.168683 0.956649i −0.00610673 0.0346330i
\(764\) 2.54702 + 4.41157i 0.0921480 + 0.159605i
\(765\) 0 0
\(766\) −4.22689 + 7.32119i −0.152724 + 0.264525i
\(767\) −1.28501 0.467705i −0.0463990 0.0168879i
\(768\) 7.14515 16.2022i 0.257828 0.584647i
\(769\) −33.0529 27.7347i −1.19192 1.00014i −0.999824 0.0187613i \(-0.994028\pi\)
−0.192094 0.981377i \(-0.561528\pi\)
\(770\) 0 0
\(771\) 5.85791 13.2833i 0.210967 0.478386i
\(772\) 24.8872 + 9.05819i 0.895709 + 0.326011i
\(773\) −19.4784 + 33.7376i −0.700590 + 1.21346i 0.267669 + 0.963511i \(0.413746\pi\)
−0.968260 + 0.249947i \(0.919587\pi\)
\(774\) 3.54427 4.60319i 0.127396 0.165458i
\(775\) 0 0