Properties

Label 920.2.bb.a.251.2
Level $920$
Weight $2$
Character 920.251
Analytic conductor $7.346$
Analytic rank $0$
Dimension $480$
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [920,2,Mod(11,920)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(920, base_ring=CyclotomicField(22))
 
chi = DirichletCharacter(H, H._module([11, 11, 0, 9]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("920.11");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 920 = 2^{3} \cdot 5 \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 920.bb (of order \(22\), degree \(10\), 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: \(7.34623698596\)
Analytic rank: \(0\)
Dimension: \(480\)
Relative dimension: \(48\) over \(\Q(\zeta_{22})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{22}]$

Embedding invariants

Embedding label 251.2
Character \(\chi\) \(=\) 920.251
Dual form 920.2.bb.a.11.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.41405 + 0.0214454i) q^{2} +(-0.417492 - 2.90372i) q^{3} +(1.99908 - 0.0606497i) q^{4} +(-0.959493 - 0.281733i) q^{5} +(0.652627 + 4.09706i) q^{6} +(2.59694 - 2.99703i) q^{7} +(-2.82550 + 0.128633i) q^{8} +(-5.37883 + 1.57937i) q^{9} +(1.36281 + 0.377808i) q^{10} +(1.45984 + 2.27156i) q^{11} +(-1.01071 - 5.77946i) q^{12} +(1.80368 - 1.56290i) q^{13} +(-3.60793 + 4.29364i) q^{14} +(-0.417492 + 2.90372i) q^{15} +(3.99264 - 0.242487i) q^{16} +(-6.50839 - 2.97228i) q^{17} +(7.57208 - 2.34866i) q^{18} +(4.78524 - 2.18535i) q^{19} +(-1.93519 - 0.505013i) q^{20} +(-9.78674 - 6.28955i) q^{21} +(-2.11301 - 3.18079i) q^{22} +(-2.91434 - 3.80876i) q^{23} +(1.55314 + 8.15077i) q^{24} +(0.841254 + 0.540641i) q^{25} +(-2.51698 + 2.24870i) q^{26} +(3.17571 + 6.95383i) q^{27} +(5.00972 - 6.14880i) q^{28} +(-3.38405 - 1.54544i) q^{29} +(0.528084 - 4.11497i) q^{30} +(-8.17242 - 1.17502i) q^{31} +(-5.64060 + 0.428513i) q^{32} +(5.98650 - 5.18734i) q^{33} +(9.26694 + 4.06338i) q^{34} +(-3.33610 + 2.14398i) q^{35} +(-10.6569 + 3.48351i) q^{36} +(-2.31872 + 0.680838i) q^{37} +(-6.71971 + 3.19281i) q^{38} +(-5.29125 - 4.58489i) q^{39} +(2.74729 + 0.672613i) q^{40} +(7.76984 + 2.28143i) q^{41} +(13.9738 + 8.68387i) q^{42} +(4.51454 - 0.649093i) q^{43} +(3.05611 + 4.45249i) q^{44} +5.60591 q^{45} +(4.20270 + 5.32328i) q^{46} +2.82882i q^{47} +(-2.37101 - 11.4923i) q^{48} +(-1.24187 - 8.63743i) q^{49} +(-1.20117 - 0.746453i) q^{50} +(-5.91348 + 20.1395i) q^{51} +(3.51091 - 3.23375i) q^{52} +(6.73907 - 7.77731i) q^{53} +(-4.63974 - 9.76497i) q^{54} +(-0.760736 - 2.59083i) q^{55} +(-6.95213 + 8.80215i) q^{56} +(-8.34345 - 12.9827i) q^{57} +(4.81836 + 2.11276i) q^{58} +(0.524253 + 0.605020i) q^{59} +(-0.658491 + 5.83010i) q^{60} +(-0.543398 + 3.77942i) q^{61} +(11.5814 + 1.48627i) q^{62} +(-9.23509 + 20.2220i) q^{63} +(7.96691 - 0.726904i) q^{64} +(-2.17094 + 0.991434i) q^{65} +(-8.35398 + 7.46354i) q^{66} +(-8.78544 + 13.6704i) q^{67} +(-13.1911 - 5.54710i) q^{68} +(-9.84286 + 10.0526i) q^{69} +(4.67144 - 3.10325i) q^{70} +(5.47514 - 8.51948i) q^{71} +(14.9947 - 5.15440i) q^{72} +(1.80492 + 3.95221i) q^{73} +(3.26419 - 1.01247i) q^{74} +(1.21865 - 2.66848i) q^{75} +(9.43354 - 4.65891i) q^{76} +(10.5990 + 1.52391i) q^{77} +(7.58042 + 6.36980i) q^{78} +(-5.70803 - 6.58742i) q^{79} +(-3.89923 - 0.892193i) q^{80} +(4.71819 - 3.03220i) q^{81} +(-11.0359 - 3.05943i) q^{82} +(3.96423 + 13.5009i) q^{83} +(-19.9459 - 11.9798i) q^{84} +(5.40737 + 4.68551i) q^{85} +(-6.36987 + 1.01467i) q^{86} +(-3.07472 + 10.4716i) q^{87} +(-4.41698 - 6.23051i) q^{88} +(-17.0823 + 2.45607i) q^{89} +(-7.92705 + 0.120221i) q^{90} -9.46443i q^{91} +(-6.05700 - 7.43726i) q^{92} +24.2210i q^{93} +(-0.0606650 - 4.00009i) q^{94} +(-5.20709 + 0.748667i) q^{95} +(3.59919 + 16.1998i) q^{96} +(-2.42670 + 8.26459i) q^{97} +(1.94131 + 12.1871i) q^{98} +(-11.4399 - 9.91271i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 480 q + 2 q^{2} - 4 q^{4} - 48 q^{5} + 5 q^{6} - q^{8} - 48 q^{9} + 2 q^{10} + 3 q^{12} + 32 q^{16} + 7 q^{18} - 4 q^{20} + 8 q^{21} + 4 q^{23} + 2 q^{24} - 48 q^{25} + 7 q^{26} + 12 q^{27} + 5 q^{30}+ \cdots - 98 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/920\mathbb{Z}\right)^\times\).

\(n\) \(231\) \(281\) \(461\) \(737\)
\(\chi(n)\) \(-1\) \(e\left(\frac{13}{22}\right)\) \(-1\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.41405 + 0.0214454i −0.999885 + 0.0151642i
\(3\) −0.417492 2.90372i −0.241039 1.67647i −0.646934 0.762546i \(-0.723949\pi\)
0.405895 0.913920i \(-0.366960\pi\)
\(4\) 1.99908 0.0606497i 0.999540 0.0303249i
\(5\) −0.959493 0.281733i −0.429098 0.125995i
\(6\) 0.652627 + 4.09706i 0.266434 + 1.67262i
\(7\) 2.59694 2.99703i 0.981550 1.13277i −0.00959057 0.999954i \(-0.503053\pi\)
0.991141 0.132815i \(-0.0424017\pi\)
\(8\) −2.82550 + 0.128633i −0.998965 + 0.0454786i
\(9\) −5.37883 + 1.57937i −1.79294 + 0.526456i
\(10\) 1.36281 + 0.377808i 0.430960 + 0.119473i
\(11\) 1.45984 + 2.27156i 0.440159 + 0.684901i 0.988477 0.151369i \(-0.0483682\pi\)
−0.548318 + 0.836270i \(0.684732\pi\)
\(12\) −1.01071 5.77946i −0.291767 1.66839i
\(13\) 1.80368 1.56290i 0.500251 0.433470i −0.367830 0.929893i \(-0.619899\pi\)
0.868081 + 0.496423i \(0.165354\pi\)
\(14\) −3.60793 + 4.29364i −0.964260 + 1.14752i
\(15\) −0.417492 + 2.90372i −0.107796 + 0.749738i
\(16\) 3.99264 0.242487i 0.998161 0.0606218i
\(17\) −6.50839 2.97228i −1.57852 0.720884i −0.582737 0.812661i \(-0.698018\pi\)
−0.995780 + 0.0917766i \(0.970745\pi\)
\(18\) 7.57208 2.34866i 1.78476 0.553584i
\(19\) 4.78524 2.18535i 1.09781 0.501353i 0.217648 0.976027i \(-0.430161\pi\)
0.880162 + 0.474674i \(0.157434\pi\)
\(20\) −1.93519 0.505013i −0.432722 0.112924i
\(21\) −9.78674 6.28955i −2.13564 1.37249i
\(22\) −2.11301 3.18079i −0.450494 0.678147i
\(23\) −2.91434 3.80876i −0.607682 0.794181i
\(24\) 1.55314 + 8.15077i 0.317033 + 1.66377i
\(25\) 0.841254 + 0.540641i 0.168251 + 0.108128i
\(26\) −2.51698 + 2.24870i −0.493620 + 0.441006i
\(27\) 3.17571 + 6.95383i 0.611165 + 1.33827i
\(28\) 5.00972 6.14880i 0.946748 1.16201i
\(29\) −3.38405 1.54544i −0.628402 0.286982i 0.0756452 0.997135i \(-0.475898\pi\)
−0.704047 + 0.710153i \(0.748626\pi\)
\(30\) 0.528084 4.11497i 0.0964145 0.751287i
\(31\) −8.17242 1.17502i −1.46781 0.211039i −0.638411 0.769696i \(-0.720408\pi\)
−0.829399 + 0.558656i \(0.811317\pi\)
\(32\) −5.64060 + 0.428513i −0.997127 + 0.0757511i
\(33\) 5.98650 5.18734i 1.04212 0.902999i
\(34\) 9.26694 + 4.06338i 1.58927 + 0.696865i
\(35\) −3.33610 + 2.14398i −0.563904 + 0.362399i
\(36\) −10.6569 + 3.48351i −1.77616 + 0.580585i
\(37\) −2.31872 + 0.680838i −0.381195 + 0.111929i −0.466716 0.884407i \(-0.654563\pi\)
0.0855203 + 0.996336i \(0.472745\pi\)
\(38\) −6.71971 + 3.19281i −1.09008 + 0.517943i
\(39\) −5.29125 4.58489i −0.847278 0.734170i
\(40\) 2.74729 + 0.672613i 0.434384 + 0.106349i
\(41\) 7.76984 + 2.28143i 1.21344 + 0.356299i 0.824979 0.565164i \(-0.191187\pi\)
0.388466 + 0.921463i \(0.373005\pi\)
\(42\) 13.9738 + 8.68387i 2.15621 + 1.33995i
\(43\) 4.51454 0.649093i 0.688461 0.0989858i 0.210799 0.977529i \(-0.432393\pi\)
0.477662 + 0.878544i \(0.341484\pi\)
\(44\) 3.05611 + 4.45249i 0.460726 + 0.671238i
\(45\) 5.60591 0.835680
\(46\) 4.20270 + 5.32328i 0.619655 + 0.784874i
\(47\) 2.82882i 0.412625i 0.978486 + 0.206313i \(0.0661464\pi\)
−0.978486 + 0.206313i \(0.933854\pi\)
\(48\) −2.37101 11.4923i −0.342226 1.65877i
\(49\) −1.24187 8.63743i −0.177411 1.23392i
\(50\) −1.20117 0.746453i −0.169871 0.105564i
\(51\) −5.91348 + 20.1395i −0.828053 + 2.82009i
\(52\) 3.51091 3.23375i 0.486876 0.448441i
\(53\) 6.73907 7.77731i 0.925683 1.06830i −0.0718021 0.997419i \(-0.522875\pi\)
0.997485 0.0708763i \(-0.0225796\pi\)
\(54\) −4.63974 9.76497i −0.631389 1.32884i
\(55\) −0.760736 2.59083i −0.102578 0.349347i
\(56\) −6.95213 + 8.80215i −0.929018 + 1.17624i
\(57\) −8.34345 12.9827i −1.10512 1.71960i
\(58\) 4.81836 + 2.11276i 0.632681 + 0.277419i
\(59\) 0.524253 + 0.605020i 0.0682519 + 0.0787669i 0.788849 0.614587i \(-0.210678\pi\)
−0.720597 + 0.693354i \(0.756132\pi\)
\(60\) −0.658491 + 5.83010i −0.0850108 + 0.752662i
\(61\) −0.543398 + 3.77942i −0.0695750 + 0.483905i 0.925007 + 0.379950i \(0.124059\pi\)
−0.994582 + 0.103955i \(0.966850\pi\)
\(62\) 11.5814 + 1.48627i 1.47084 + 0.188757i
\(63\) −9.23509 + 20.2220i −1.16351 + 2.54774i
\(64\) 7.96691 0.726904i 0.995863 0.0908630i
\(65\) −2.17094 + 0.991434i −0.269272 + 0.122972i
\(66\) −8.35398 + 7.46354i −1.02830 + 0.918698i
\(67\) −8.78544 + 13.6704i −1.07331 + 1.67011i −0.434705 + 0.900573i \(0.643148\pi\)
−0.638607 + 0.769533i \(0.720489\pi\)
\(68\) −13.1911 5.54710i −1.59965 0.672685i
\(69\) −9.84286 + 10.0526i −1.18494 + 1.21019i
\(70\) 4.67144 3.10325i 0.558344 0.370909i
\(71\) 5.47514 8.51948i 0.649779 1.01108i −0.347523 0.937671i \(-0.612977\pi\)
0.997302 0.0734047i \(-0.0233865\pi\)
\(72\) 14.9947 5.15440i 1.76715 0.607452i
\(73\) 1.80492 + 3.95221i 0.211249 + 0.462572i 0.985362 0.170477i \(-0.0545308\pi\)
−0.774112 + 0.633048i \(0.781803\pi\)
\(74\) 3.26419 1.01247i 0.379454 0.117697i
\(75\) 1.21865 2.66848i 0.140718 0.308130i
\(76\) 9.43354 4.65891i 1.08210 0.534413i
\(77\) 10.5990 + 1.52391i 1.20787 + 0.173666i
\(78\) 7.58042 + 6.36980i 0.858313 + 0.721238i
\(79\) −5.70803 6.58742i −0.642204 0.741143i 0.337559 0.941304i \(-0.390399\pi\)
−0.979763 + 0.200161i \(0.935853\pi\)
\(80\) −3.89923 0.892193i −0.435947 0.0997502i
\(81\) 4.71819 3.03220i 0.524243 0.336911i
\(82\) −11.0359 3.05943i −1.21871 0.337858i
\(83\) 3.96423 + 13.5009i 0.435131 + 1.48192i 0.827160 + 0.561967i \(0.189955\pi\)
−0.392029 + 0.919953i \(0.628227\pi\)
\(84\) −19.9459 11.9798i −2.17628 1.30710i
\(85\) 5.40737 + 4.68551i 0.586511 + 0.508215i
\(86\) −6.36987 + 1.01467i −0.686881 + 0.109414i
\(87\) −3.07472 + 10.4716i −0.329645 + 1.12267i
\(88\) −4.41698 6.23051i −0.470852 0.664174i
\(89\) −17.0823 + 2.45607i −1.81072 + 0.260343i −0.962885 0.269913i \(-0.913005\pi\)
−0.847838 + 0.530256i \(0.822096\pi\)
\(90\) −7.92705 + 0.120221i −0.835584 + 0.0126724i
\(91\) 9.46443i 0.992141i
\(92\) −6.05700 7.43726i −0.631486 0.775388i
\(93\) 24.2210i 2.51160i
\(94\) −0.0606650 4.00009i −0.00625712 0.412578i
\(95\) −5.20709 + 0.748667i −0.534236 + 0.0768116i
\(96\) 3.59919 + 16.1998i 0.367341 + 1.65339i
\(97\) −2.42670 + 8.26459i −0.246394 + 0.839142i 0.739697 + 0.672940i \(0.234969\pi\)
−0.986092 + 0.166202i \(0.946850\pi\)
\(98\) 1.94131 + 12.1871i 0.196102 + 1.23109i
\(99\) −11.4399 9.91271i −1.14975 0.996265i
\(100\) 1.71452 + 1.02976i 0.171452 + 0.102976i
\(101\) 0.816787 + 2.78172i 0.0812733 + 0.276792i 0.990096 0.140391i \(-0.0448359\pi\)
−0.908823 + 0.417182i \(0.863018\pi\)
\(102\) 7.93007 28.6051i 0.785194 2.83232i
\(103\) −9.50954 + 6.11141i −0.937003 + 0.602175i −0.917544 0.397635i \(-0.869831\pi\)
−0.0194595 + 0.999811i \(0.506195\pi\)
\(104\) −4.89526 + 4.64798i −0.480020 + 0.455772i
\(105\) 7.61833 + 8.79203i 0.743473 + 0.858014i
\(106\) −9.36261 + 11.1420i −0.909377 + 1.08221i
\(107\) 7.97864 + 1.14716i 0.771324 + 0.110900i 0.516730 0.856148i \(-0.327149\pi\)
0.254594 + 0.967048i \(0.418058\pi\)
\(108\) 6.77024 + 13.7087i 0.651467 + 1.31912i
\(109\) 0.538879 1.17998i 0.0516153 0.113022i −0.882067 0.471123i \(-0.843849\pi\)
0.933683 + 0.358102i \(0.116576\pi\)
\(110\) 1.13128 + 3.64725i 0.107863 + 0.347752i
\(111\) 2.94501 + 6.44868i 0.279528 + 0.612082i
\(112\) 9.64191 12.5958i 0.911074 1.19019i
\(113\) 9.28256 14.4440i 0.873230 1.35877i −0.0595116 0.998228i \(-0.518954\pi\)
0.932742 0.360545i \(-0.117409\pi\)
\(114\) 12.0765 + 18.1792i 1.13107 + 1.70264i
\(115\) 1.72324 + 4.47554i 0.160693 + 0.417346i
\(116\) −6.85871 2.88422i −0.636816 0.267793i
\(117\) −7.23331 + 11.2552i −0.668719 + 1.04055i
\(118\) −0.754295 0.844286i −0.0694385 0.0777229i
\(119\) −25.8099 + 11.7870i −2.36599 + 1.08051i
\(120\) 0.806111 8.25818i 0.0735875 0.753865i
\(121\) 1.54073 3.37372i 0.140066 0.306702i
\(122\) 0.687341 5.35594i 0.0622290 0.484904i
\(123\) 3.38079 23.5139i 0.304836 2.12018i
\(124\) −16.4086 1.85330i −1.47353 0.166431i
\(125\) −0.654861 0.755750i −0.0585725 0.0675963i
\(126\) 12.6252 28.7930i 1.12474 2.56509i
\(127\) −2.14629 3.33970i −0.190453 0.296350i 0.732875 0.680363i \(-0.238178\pi\)
−0.923328 + 0.384013i \(0.874542\pi\)
\(128\) −11.2500 + 1.19873i −0.994371 + 0.105954i
\(129\) −3.76957 12.8380i −0.331893 1.13032i
\(130\) 3.04856 1.44850i 0.267376 0.127041i
\(131\) −2.91737 + 3.36682i −0.254892 + 0.294161i −0.868745 0.495259i \(-0.835073\pi\)
0.613854 + 0.789420i \(0.289619\pi\)
\(132\) 11.6529 10.7330i 1.01425 0.934186i
\(133\) 5.87744 20.0167i 0.509638 1.73567i
\(134\) 12.1299 19.5191i 1.04786 1.68619i
\(135\) −1.08795 7.56685i −0.0936358 0.651251i
\(136\) 18.7718 + 7.56099i 1.60967 + 0.648350i
\(137\) 0.380632i 0.0325196i −0.999868 0.0162598i \(-0.994824\pi\)
0.999868 0.0162598i \(-0.00517588\pi\)
\(138\) 13.7027 14.4259i 1.16645 1.22802i
\(139\) 7.59377 0.644095 0.322048 0.946723i \(-0.395629\pi\)
0.322048 + 0.946723i \(0.395629\pi\)
\(140\) −6.53911 + 4.48833i −0.552655 + 0.379333i
\(141\) 8.21410 1.18101i 0.691752 0.0994590i
\(142\) −7.55942 + 12.1644i −0.634372 + 1.02081i
\(143\) 6.18330 + 1.81558i 0.517074 + 0.151827i
\(144\) −21.0928 + 7.61015i −1.75773 + 0.634179i
\(145\) 2.81157 + 2.43624i 0.233488 + 0.202319i
\(146\) −2.63700 5.54992i −0.218240 0.459315i
\(147\) −24.5622 + 7.21212i −2.02586 + 0.594846i
\(148\) −4.59402 + 1.50168i −0.377626 + 0.123437i
\(149\) 12.5592 8.07132i 1.02889 0.661228i 0.0866762 0.996237i \(-0.472375\pi\)
0.942215 + 0.335008i \(0.108739\pi\)
\(150\) −1.66601 + 3.79950i −0.136029 + 0.310228i
\(151\) 11.8155 10.2382i 0.961529 0.833169i −0.0245076 0.999700i \(-0.507802\pi\)
0.986036 + 0.166530i \(0.0532563\pi\)
\(152\) −13.2396 + 6.79024i −1.07387 + 0.550761i
\(153\) 39.7019 + 5.70827i 3.20971 + 0.461486i
\(154\) −15.0203 1.92759i −1.21037 0.155329i
\(155\) 7.51034 + 3.42986i 0.603245 + 0.275493i
\(156\) −10.8557 8.84465i −0.869152 0.708139i
\(157\) −8.62870 18.8942i −0.688645 1.50792i −0.853216 0.521557i \(-0.825351\pi\)
0.164571 0.986365i \(-0.447376\pi\)
\(158\) 8.21272 + 9.19254i 0.653369 + 0.731319i
\(159\) −25.3967 16.3214i −2.01409 1.29437i
\(160\) 5.53284 + 1.17799i 0.437410 + 0.0931279i
\(161\) −18.9833 1.15676i −1.49609 0.0911651i
\(162\) −6.60673 + 4.38886i −0.519074 + 0.344822i
\(163\) −5.21835 3.35363i −0.408733 0.262677i 0.320079 0.947391i \(-0.396291\pi\)
−0.728812 + 0.684714i \(0.759927\pi\)
\(164\) 15.6709 + 4.08952i 1.22369 + 0.319338i
\(165\) −7.20545 + 3.29062i −0.560944 + 0.256174i
\(166\) −5.89516 19.0060i −0.457553 1.47515i
\(167\) 0.149124 + 0.0681026i 0.0115396 + 0.00526994i 0.421176 0.906979i \(-0.361617\pi\)
−0.409637 + 0.912249i \(0.634345\pi\)
\(168\) 28.4615 + 16.5122i 2.19585 + 1.27395i
\(169\) −1.03948 + 7.22974i −0.0799600 + 0.556134i
\(170\) −7.74677 6.50959i −0.594150 0.499262i
\(171\) −22.2876 + 19.3123i −1.70437 + 1.47685i
\(172\) 8.98556 1.57139i 0.685143 0.119818i
\(173\) 0.159051 + 0.247488i 0.0120924 + 0.0188161i 0.847247 0.531199i \(-0.178258\pi\)
−0.835155 + 0.550015i \(0.814622\pi\)
\(174\) 4.12325 14.8732i 0.312583 1.12754i
\(175\) 3.80500 1.11725i 0.287631 0.0844560i
\(176\) 6.37945 + 8.71553i 0.480869 + 0.656958i
\(177\) 1.53794 1.77488i 0.115599 0.133408i
\(178\) 24.1026 3.83934i 1.80657 0.287771i
\(179\) 15.1020 + 4.43435i 1.12878 + 0.331439i 0.792227 0.610227i \(-0.208922\pi\)
0.336550 + 0.941666i \(0.390740\pi\)
\(180\) 11.2067 0.339997i 0.835296 0.0253419i
\(181\) 1.10560 + 7.68959i 0.0821783 + 0.571562i 0.988758 + 0.149527i \(0.0477751\pi\)
−0.906579 + 0.422035i \(0.861316\pi\)
\(182\) 0.202968 + 13.3832i 0.0150450 + 0.992027i
\(183\) 11.2012 0.828020
\(184\) 8.72440 + 10.3868i 0.643171 + 0.765723i
\(185\) 2.41661 0.177673
\(186\) −0.519429 34.2498i −0.0380864 2.51131i
\(187\) −2.74951 19.1232i −0.201064 1.39843i
\(188\) 0.171567 + 5.65503i 0.0125128 + 0.412436i
\(189\) 29.0879 + 8.54099i 2.11584 + 0.621265i
\(190\) 7.34704 1.17032i 0.533010 0.0849040i
\(191\) −1.79097 + 2.06689i −0.129590 + 0.149555i −0.816836 0.576870i \(-0.804274\pi\)
0.687246 + 0.726425i \(0.258819\pi\)
\(192\) −5.43685 22.8302i −0.392371 1.64763i
\(193\) 1.96732 0.577657i 0.141611 0.0415806i −0.210159 0.977667i \(-0.567398\pi\)
0.351770 + 0.936087i \(0.385580\pi\)
\(194\) 3.25424 11.7386i 0.233641 0.842782i
\(195\) 3.78520 + 5.88989i 0.271064 + 0.421784i
\(196\) −3.00647 17.1916i −0.214748 1.22797i
\(197\) −0.118757 + 0.102904i −0.00846109 + 0.00733158i −0.659081 0.752072i \(-0.729055\pi\)
0.650620 + 0.759404i \(0.274509\pi\)
\(198\) 16.3891 + 13.7717i 1.16473 + 0.978715i
\(199\) 2.62241 18.2392i 0.185898 1.29295i −0.656597 0.754241i \(-0.728005\pi\)
0.842495 0.538704i \(-0.181086\pi\)
\(200\) −2.44651 1.41937i −0.172994 0.100364i
\(201\) 43.3629 + 19.8032i 3.05859 + 1.39681i
\(202\) −1.21463 3.91598i −0.0854613 0.275527i
\(203\) −13.4199 + 6.12866i −0.941892 + 0.430148i
\(204\) −10.6001 + 40.6191i −0.742154 + 2.84390i
\(205\) −6.81235 4.37803i −0.475795 0.305775i
\(206\) 13.3159 8.84578i 0.927764 0.616315i
\(207\) 21.6912 + 15.8839i 1.50764 + 1.10400i
\(208\) 6.82247 6.67746i 0.473053 0.462999i
\(209\) 11.9498 + 7.67970i 0.826588 + 0.531216i
\(210\) −10.9613 12.2690i −0.756399 0.846641i
\(211\) −4.89813 10.7254i −0.337201 0.738367i 0.662744 0.748846i \(-0.269392\pi\)
−0.999945 + 0.0104787i \(0.996664\pi\)
\(212\) 13.0003 15.9562i 0.892861 1.09588i
\(213\) −27.0240 12.3415i −1.85166 0.845623i
\(214\) −11.3068 1.45103i −0.772917 0.0991904i
\(215\) −4.51454 0.649093i −0.307889 0.0442678i
\(216\) −9.86746 19.2396i −0.671395 1.30909i
\(217\) −24.7448 + 21.4415i −1.67979 + 1.45554i
\(218\) −0.736698 + 1.68011i −0.0498955 + 0.113791i
\(219\) 10.7226 6.89099i 0.724566 0.465650i
\(220\) −1.67791 5.13314i −0.113124 0.346076i
\(221\) −16.3844 + 4.81090i −1.10214 + 0.323616i
\(222\) −4.30270 9.05561i −0.288778 0.607773i
\(223\) 11.8047 + 10.2288i 0.790500 + 0.684972i 0.953413 0.301668i \(-0.0975435\pi\)
−0.162913 + 0.986640i \(0.552089\pi\)
\(224\) −13.3640 + 18.0178i −0.892921 + 1.20387i
\(225\) −5.37883 1.57937i −0.358589 0.105291i
\(226\) −12.8163 + 20.6236i −0.852525 + 1.37186i
\(227\) −6.86109 + 0.986475i −0.455386 + 0.0654747i −0.366191 0.930540i \(-0.619338\pi\)
−0.0891948 + 0.996014i \(0.528429\pi\)
\(228\) −17.4666 25.4473i −1.15675 1.68529i
\(229\) 13.4293 0.887433 0.443717 0.896167i \(-0.353660\pi\)
0.443717 + 0.896167i \(0.353660\pi\)
\(230\) −2.53272 6.29169i −0.167003 0.414861i
\(231\) 31.4129i 2.06682i
\(232\) 9.76042 + 3.93135i 0.640803 + 0.258106i
\(233\) −3.44109 23.9333i −0.225433 1.56792i −0.716993 0.697080i \(-0.754482\pi\)
0.491560 0.870844i \(-0.336427\pi\)
\(234\) 9.98689 16.0706i 0.652864 1.05057i
\(235\) 0.796970 2.71423i 0.0519886 0.177057i
\(236\) 1.08472 + 1.17769i 0.0706091 + 0.0766609i
\(237\) −16.7450 + 19.3248i −1.08770 + 1.25528i
\(238\) 36.2437 17.2209i 2.34933 1.11626i
\(239\) 3.66216 + 12.4722i 0.236886 + 0.806759i 0.989024 + 0.147754i \(0.0472043\pi\)
−0.752138 + 0.659005i \(0.770978\pi\)
\(240\) −0.962783 + 11.6948i −0.0621473 + 0.754894i
\(241\) −7.57875 11.7928i −0.488190 0.759639i 0.506534 0.862220i \(-0.330926\pi\)
−0.994725 + 0.102581i \(0.967290\pi\)
\(242\) −2.10632 + 4.80366i −0.135399 + 0.308791i
\(243\) 4.24410 + 4.89795i 0.272259 + 0.314204i
\(244\) −0.857075 + 7.58831i −0.0548686 + 0.485792i
\(245\) −1.24187 + 8.63743i −0.0793405 + 0.551825i
\(246\) −4.27635 + 33.3224i −0.272650 + 2.12456i
\(247\) 5.21557 11.4205i 0.331859 0.726670i
\(248\) 23.2423 + 2.26877i 1.47589 + 0.144067i
\(249\) 37.5479 17.1476i 2.37950 1.08668i
\(250\) 0.942214 + 1.05462i 0.0595908 + 0.0667003i
\(251\) 7.24186 11.2686i 0.457102 0.711265i −0.533835 0.845588i \(-0.679250\pi\)
0.990938 + 0.134324i \(0.0428862\pi\)
\(252\) −17.2352 + 40.9856i −1.08572 + 2.58185i
\(253\) 4.39734 12.1803i 0.276458 0.765767i
\(254\) 3.10659 + 4.67647i 0.194925 + 0.293428i
\(255\) 11.3479 17.6577i 0.710633 1.10577i
\(256\) 15.8824 1.93633i 0.992650 0.121021i
\(257\) −5.88964 12.8965i −0.367386 0.804463i −0.999561 0.0296371i \(-0.990565\pi\)
0.632175 0.774826i \(-0.282162\pi\)
\(258\) 5.60569 + 18.0727i 0.348995 + 1.12516i
\(259\) −3.98109 + 8.71736i −0.247373 + 0.541671i
\(260\) −4.27975 + 2.11362i −0.265419 + 0.131081i
\(261\) 20.6431 + 2.96802i 1.27777 + 0.183716i
\(262\) 4.05310 4.82342i 0.250402 0.297992i
\(263\) −1.14086 1.31662i −0.0703485 0.0811865i 0.719484 0.694509i \(-0.244378\pi\)
−0.789833 + 0.613322i \(0.789833\pi\)
\(264\) −16.2476 + 15.4269i −0.999971 + 0.949459i
\(265\) −8.65721 + 5.56365i −0.531808 + 0.341773i
\(266\) −7.88173 + 28.4307i −0.483260 + 1.74320i
\(267\) 14.2635 + 48.5770i 0.872911 + 2.97286i
\(268\) −16.7337 + 27.8611i −1.02217 + 1.70189i
\(269\) −4.89624 4.24261i −0.298529 0.258677i 0.492697 0.870201i \(-0.336011\pi\)
−0.791226 + 0.611524i \(0.790557\pi\)
\(270\) 1.70069 + 10.6766i 0.103501 + 0.649756i
\(271\) −5.41170 + 18.4306i −0.328737 + 1.11958i 0.614903 + 0.788603i \(0.289195\pi\)
−0.943640 + 0.330974i \(0.892623\pi\)
\(272\) −26.7064 10.2891i −1.61931 0.623866i
\(273\) −27.4821 + 3.95133i −1.66329 + 0.239145i
\(274\) 0.00816280 + 0.538233i 0.000493133 + 0.0325159i
\(275\) 2.70021i 0.162829i
\(276\) −19.0670 + 20.6928i −1.14770 + 1.24556i
\(277\) 24.1858i 1.45319i −0.687068 0.726593i \(-0.741103\pi\)
0.687068 0.726593i \(-0.258897\pi\)
\(278\) −10.7380 + 0.162851i −0.644021 + 0.00976717i
\(279\) 45.8139 6.58704i 2.74281 0.394356i
\(280\) 9.15038 6.48696i 0.546840 0.387670i
\(281\) 1.99525 6.79520i 0.119027 0.405368i −0.878328 0.478059i \(-0.841341\pi\)
0.997354 + 0.0726912i \(0.0231587\pi\)
\(282\) −11.5898 + 1.84616i −0.690164 + 0.109937i
\(283\) 9.33245 + 8.08661i 0.554756 + 0.480699i 0.886537 0.462657i \(-0.153104\pi\)
−0.331781 + 0.943356i \(0.607649\pi\)
\(284\) 10.4285 17.3632i 0.618820 1.03032i
\(285\) 4.34784 + 14.8074i 0.257544 + 0.877114i
\(286\) −8.78244 2.43472i −0.519317 0.143968i
\(287\) 27.0153 17.3617i 1.59466 1.02483i
\(288\) 29.6631 11.2135i 1.74791 0.660761i
\(289\) 22.3920 + 25.8418i 1.31718 + 1.52011i
\(290\) −4.02795 3.38467i −0.236529 0.198755i
\(291\) 25.0112 + 3.59607i 1.46618 + 0.210805i
\(292\) 3.84787 + 7.79132i 0.225180 + 0.455953i
\(293\) −1.27492 + 2.79168i −0.0744815 + 0.163092i −0.943210 0.332197i \(-0.892210\pi\)
0.868729 + 0.495288i \(0.164938\pi\)
\(294\) 34.5776 10.7251i 2.01661 0.625498i
\(295\) −0.332563 0.728212i −0.0193626 0.0423981i
\(296\) 6.46397 2.22197i 0.375711 0.129150i
\(297\) −11.1600 + 17.3653i −0.647569 + 1.00764i
\(298\) −17.5863 + 11.6826i −1.01875 + 0.676755i
\(299\) −11.2092 2.31497i −0.648247 0.133878i
\(300\) 2.27435 5.40842i 0.131309 0.312255i
\(301\) 9.77864 15.2159i 0.563631 0.877027i
\(302\) −16.4881 + 14.7307i −0.948784 + 0.847654i
\(303\) 7.73635 3.53307i 0.444442 0.202970i
\(304\) 18.5758 9.88567i 1.06540 0.566982i
\(305\) 1.58617 3.47323i 0.0908239 0.198877i
\(306\) −56.2629 7.22036i −3.21634 0.412761i
\(307\) 3.35843 23.3584i 0.191676 1.33313i −0.635896 0.771775i \(-0.719369\pi\)
0.827572 0.561360i \(-0.189722\pi\)
\(308\) 21.2807 + 2.40359i 1.21258 + 0.136957i
\(309\) 21.7160 + 25.0616i 1.23538 + 1.42571i
\(310\) −10.6936 4.68893i −0.607353 0.266313i
\(311\) −0.336387 0.523428i −0.0190748 0.0296809i 0.831585 0.555397i \(-0.187434\pi\)
−0.850660 + 0.525716i \(0.823797\pi\)
\(312\) 15.5402 + 12.2740i 0.879790 + 0.694878i
\(313\) −0.772329 2.63031i −0.0436546 0.148674i 0.934782 0.355223i \(-0.115595\pi\)
−0.978436 + 0.206549i \(0.933777\pi\)
\(314\) 12.6066 + 26.5323i 0.711432 + 1.49731i
\(315\) 14.5582 16.8011i 0.820262 0.946633i
\(316\) −11.8103 12.8226i −0.664384 0.721327i
\(317\) −0.192504 + 0.655608i −0.0108121 + 0.0368226i −0.964722 0.263269i \(-0.915199\pi\)
0.953910 + 0.300092i \(0.0970174\pi\)
\(318\) 36.2622 + 22.5347i 2.03348 + 1.26368i
\(319\) −1.42961 9.94316i −0.0800428 0.556710i
\(320\) −7.84898 1.54708i −0.438772 0.0864843i
\(321\) 23.6467i 1.31983i
\(322\) 26.8682 + 1.22861i 1.49730 + 0.0684676i
\(323\) −37.6397 −2.09433
\(324\) 9.24814 6.34776i 0.513785 0.352653i
\(325\) 2.36232 0.339650i 0.131038 0.0188404i
\(326\) 7.45094 + 4.63030i 0.412669 + 0.256448i
\(327\) −3.65132 1.07212i −0.201918 0.0592886i
\(328\) −22.2471 5.44672i −1.22839 0.300745i
\(329\) 8.47804 + 7.34626i 0.467409 + 0.405012i
\(330\) 10.1183 4.80763i 0.556994 0.264651i
\(331\) 1.28006 0.375858i 0.0703582 0.0206590i −0.246364 0.969177i \(-0.579236\pi\)
0.316722 + 0.948518i \(0.397418\pi\)
\(332\) 8.74364 + 26.7490i 0.479870 + 1.46804i
\(333\) 11.3967 7.32423i 0.624537 0.401365i
\(334\) −0.212329 0.0931026i −0.0116181 0.00509435i
\(335\) 12.2810 10.6415i 0.670981 0.581408i
\(336\) −40.6001 22.7388i −2.21492 1.24050i
\(337\) 10.7118 + 1.54012i 0.583507 + 0.0838957i 0.427746 0.903899i \(-0.359308\pi\)
0.155761 + 0.987795i \(0.450217\pi\)
\(338\) 1.31483 10.2455i 0.0715175 0.557283i
\(339\) −45.8167 20.9238i −2.48842 1.13642i
\(340\) 11.0939 + 9.03875i 0.601653 + 0.490195i
\(341\) −9.26132 20.2795i −0.501529 1.09819i
\(342\) 31.1016 27.7865i 1.68178 1.50252i
\(343\) −5.75895 3.70105i −0.310954 0.199838i
\(344\) −12.6723 + 2.41473i −0.683247 + 0.130194i
\(345\) 12.2763 6.87231i 0.660933 0.369993i
\(346\) −0.230213 0.346549i −0.0123763 0.0186306i
\(347\) −27.1339 17.4379i −1.45662 0.936116i −0.998894 0.0470255i \(-0.985026\pi\)
−0.457731 0.889091i \(-0.651338\pi\)
\(348\) −5.51153 + 21.1200i −0.295449 + 1.13215i
\(349\) −8.97024 + 4.09657i −0.480166 + 0.219285i −0.640768 0.767735i \(-0.721384\pi\)
0.160602 + 0.987019i \(0.448657\pi\)
\(350\) −5.35650 + 1.66145i −0.286317 + 0.0888080i
\(351\) 16.5961 + 7.57918i 0.885834 + 0.404547i
\(352\) −9.20778 12.1874i −0.490776 0.649590i
\(353\) 2.39019 16.6241i 0.127217 0.884813i −0.821842 0.569715i \(-0.807054\pi\)
0.949059 0.315098i \(-0.102037\pi\)
\(354\) −2.13666 + 2.54275i −0.113562 + 0.135146i
\(355\) −7.65357 + 6.63186i −0.406209 + 0.351982i
\(356\) −34.0000 + 5.94591i −1.80199 + 0.315133i
\(357\) 45.0016 + 70.0238i 2.38174 + 3.70605i
\(358\) −21.4501 5.94653i −1.13367 0.314284i
\(359\) 13.0464 3.83076i 0.688561 0.202180i 0.0813088 0.996689i \(-0.474090\pi\)
0.607252 + 0.794509i \(0.292272\pi\)
\(360\) −15.8395 + 0.721104i −0.834816 + 0.0380055i
\(361\) 5.68045 6.55559i 0.298971 0.345031i
\(362\) −1.72827 10.8498i −0.0908361 0.570251i
\(363\) −10.4396 3.06534i −0.547937 0.160889i
\(364\) −0.574015 18.9201i −0.0300865 0.991685i
\(365\) −0.618336 4.30062i −0.0323652 0.225105i
\(366\) −15.8391 + 0.240215i −0.827924 + 0.0125562i
\(367\) −28.7128 −1.49880 −0.749398 0.662119i \(-0.769657\pi\)
−0.749398 + 0.662119i \(0.769657\pi\)
\(368\) −12.5595 14.5003i −0.654709 0.755881i
\(369\) −45.3959 −2.36321
\(370\) −3.41721 + 0.0518251i −0.177652 + 0.00269426i
\(371\) −5.80783 40.3944i −0.301528 2.09717i
\(372\) 1.46900 + 48.4198i 0.0761640 + 2.51045i
\(373\) −16.5850 4.86979i −0.858738 0.252148i −0.177419 0.984135i \(-0.556775\pi\)
−0.681318 + 0.731987i \(0.738593\pi\)
\(374\) 4.29805 + 26.9823i 0.222247 + 1.39522i
\(375\) −1.92109 + 2.21705i −0.0992046 + 0.114488i
\(376\) −0.363879 7.99282i −0.0187656 0.412198i
\(377\) −8.51911 + 2.50144i −0.438757 + 0.128831i
\(378\) −41.3150 11.4536i −2.12501 0.589109i
\(379\) 2.38394 + 3.70949i 0.122455 + 0.190543i 0.897069 0.441891i \(-0.145692\pi\)
−0.774614 + 0.632434i \(0.782056\pi\)
\(380\) −10.3640 + 1.81245i −0.531661 + 0.0929769i
\(381\) −8.80150 + 7.62654i −0.450914 + 0.390719i
\(382\) 2.48820 2.96110i 0.127307 0.151503i
\(383\) −0.634390 + 4.41228i −0.0324158 + 0.225457i −0.999589 0.0286605i \(-0.990876\pi\)
0.967173 + 0.254117i \(0.0817849\pi\)
\(384\) 8.17759 + 32.1665i 0.417311 + 1.64149i
\(385\) −9.74037 4.44828i −0.496415 0.226705i
\(386\) −2.76950 + 0.859026i −0.140964 + 0.0437233i
\(387\) −23.2578 + 10.6215i −1.18226 + 0.539921i
\(388\) −4.34993 + 16.6688i −0.220834 + 0.846228i
\(389\) −4.01908 2.58291i −0.203775 0.130959i 0.434773 0.900540i \(-0.356829\pi\)
−0.638549 + 0.769581i \(0.720465\pi\)
\(390\) −5.47878 8.24743i −0.277429 0.417625i
\(391\) 7.64695 + 33.4511i 0.386723 + 1.69170i
\(392\) 4.61998 + 24.2453i 0.233344 + 1.22457i
\(393\) 10.9943 + 7.06561i 0.554589 + 0.356413i
\(394\) 0.165722 0.148058i 0.00834894 0.00745904i
\(395\) 3.62093 + 7.92872i 0.182189 + 0.398937i
\(396\) −23.4704 19.1225i −1.17943 0.960940i
\(397\) −14.1911 6.48085i −0.712230 0.325264i 0.0261421 0.999658i \(-0.491678\pi\)
−0.738372 + 0.674394i \(0.764405\pi\)
\(398\) −3.31707 + 25.8475i −0.166270 + 1.29562i
\(399\) −60.5768 8.70963i −3.03263 0.436027i
\(400\) 3.48992 + 1.95459i 0.174496 + 0.0977296i
\(401\) 11.5198 9.98198i 0.575272 0.498476i −0.317940 0.948111i \(-0.602991\pi\)
0.893213 + 0.449634i \(0.148446\pi\)
\(402\) −61.7421 27.0728i −3.07942 1.35027i
\(403\) −16.5769 + 10.6533i −0.825753 + 0.530679i
\(404\) 1.80153 + 5.51134i 0.0896296 + 0.274200i
\(405\) −5.38134 + 1.58010i −0.267401 + 0.0785160i
\(406\) 18.8450 8.95403i 0.935261 0.444381i
\(407\) −4.93153 4.27320i −0.244447 0.211814i
\(408\) 14.1180 57.6648i 0.698943 2.85483i
\(409\) −29.2118 8.57736i −1.44443 0.424123i −0.536735 0.843751i \(-0.680342\pi\)
−0.907696 + 0.419628i \(0.862161\pi\)
\(410\) 9.72690 + 6.04467i 0.480377 + 0.298525i
\(411\) −1.10525 + 0.158911i −0.0545180 + 0.00783850i
\(412\) −18.6397 + 12.7940i −0.918311 + 0.630313i
\(413\) 3.17471 0.156217
\(414\) −31.0131 21.9954i −1.52421 1.08102i
\(415\) 14.0709i 0.690713i
\(416\) −9.50412 + 9.58858i −0.465978 + 0.470119i
\(417\) −3.17034 22.0502i −0.155252 1.07980i
\(418\) −17.0624 10.6032i −0.834548 0.518620i
\(419\) −3.44656 + 11.7379i −0.168375 + 0.573434i 0.831465 + 0.555577i \(0.187503\pi\)
−0.999841 + 0.0178571i \(0.994316\pi\)
\(420\) 15.7629 + 17.1139i 0.769151 + 0.835074i
\(421\) 23.9730 27.6663i 1.16837 1.34837i 0.242676 0.970107i \(-0.421975\pi\)
0.925697 0.378267i \(-0.123480\pi\)
\(422\) 7.15621 + 15.0612i 0.348359 + 0.733169i
\(423\) −4.46774 15.2157i −0.217229 0.739814i
\(424\) −18.0408 + 22.8416i −0.876141 + 1.10929i
\(425\) −3.86827 6.01914i −0.187639 0.291971i
\(426\) 38.4780 + 16.8719i 1.86427 + 0.817447i
\(427\) 9.91583 + 11.4435i 0.479861 + 0.553789i
\(428\) 16.0195 + 1.80935i 0.774333 + 0.0874584i
\(429\) 2.69046 18.7126i 0.129897 0.903453i
\(430\) 6.39771 + 0.821035i 0.308525 + 0.0395938i
\(431\) 9.06396 19.8473i 0.436596 0.956011i −0.555615 0.831440i \(-0.687517\pi\)
0.992211 0.124571i \(-0.0397556\pi\)
\(432\) 14.3657 + 26.9941i 0.691169 + 1.29875i
\(433\) 10.9007 4.97819i 0.523854 0.239236i −0.135893 0.990723i \(-0.543390\pi\)
0.659748 + 0.751487i \(0.270663\pi\)
\(434\) 34.5306 30.8501i 1.65752 1.48085i
\(435\) 5.90035 9.18113i 0.282900 0.440201i
\(436\) 1.00570 2.39156i 0.0481642 0.114535i
\(437\) −22.2693 11.8570i −1.06528 0.567196i
\(438\) −15.0145 + 9.97417i −0.717421 + 0.476584i
\(439\) −16.7995 + 26.1406i −0.801799 + 1.24762i 0.163518 + 0.986540i \(0.447716\pi\)
−0.965316 + 0.261083i \(0.915921\pi\)
\(440\) 2.48273 + 7.22253i 0.118359 + 0.344321i
\(441\) 20.3215 + 44.4979i 0.967692 + 2.11895i
\(442\) 23.0652 7.15423i 1.09710 0.340292i
\(443\) 13.2235 28.9555i 0.628269 1.37572i −0.281081 0.959684i \(-0.590693\pi\)
0.909350 0.416033i \(-0.136580\pi\)
\(444\) 6.27843 + 12.7128i 0.297961 + 0.603324i
\(445\) 17.0823 + 2.45607i 0.809780 + 0.116429i
\(446\) −16.9118 14.2109i −0.800796 0.672906i
\(447\) −28.6803 33.0988i −1.35653 1.56552i
\(448\) 18.5110 25.7648i 0.874563 1.21727i
\(449\) −24.2593 + 15.5905i −1.14487 + 0.735761i −0.968611 0.248583i \(-0.920035\pi\)
−0.176256 + 0.984344i \(0.556399\pi\)
\(450\) 7.63982 + 2.11796i 0.360144 + 0.0998414i
\(451\) 6.16033 + 20.9802i 0.290079 + 0.987917i
\(452\) 17.6806 29.4376i 0.831624 1.38463i
\(453\) −34.6617 30.0345i −1.62855 1.41114i
\(454\) 9.68077 1.54206i 0.454341 0.0723727i
\(455\) −2.66644 + 9.08105i −0.125004 + 0.425726i
\(456\) 25.2444 + 35.6093i 1.18218 + 1.66756i
\(457\) 12.7643 1.83523i 0.597089 0.0858485i 0.162857 0.986650i \(-0.447929\pi\)
0.434232 + 0.900801i \(0.357020\pi\)
\(458\) −18.9897 + 0.287996i −0.887331 + 0.0134572i
\(459\) 54.6973i 2.55305i
\(460\) 3.71633 + 8.84245i 0.173275 + 0.412281i
\(461\) 15.8262i 0.737100i −0.929608 0.368550i \(-0.879854\pi\)
0.929608 0.368550i \(-0.120146\pi\)
\(462\) 0.673661 + 44.4194i 0.0313416 + 2.06658i
\(463\) 9.06780 1.30375i 0.421417 0.0605905i 0.0716554 0.997429i \(-0.477172\pi\)
0.349761 + 0.936839i \(0.386263\pi\)
\(464\) −13.8860 5.34981i −0.644643 0.248359i
\(465\) 6.82385 23.2399i 0.316448 1.07772i
\(466\) 5.37914 + 33.7691i 0.249184 + 1.56433i
\(467\) 14.1975 + 12.3022i 0.656982 + 0.569278i 0.918256 0.395986i \(-0.129597\pi\)
−0.261274 + 0.965265i \(0.584143\pi\)
\(468\) −13.7773 + 22.9388i −0.636857 + 1.06035i
\(469\) 18.1553 + 61.8314i 0.838335 + 2.85511i
\(470\) −1.06875 + 3.85515i −0.0492977 + 0.177825i
\(471\) −51.2612 + 32.9435i −2.36199 + 1.51796i
\(472\) −1.55910 1.64205i −0.0717635 0.0755814i
\(473\) 8.06497 + 9.30747i 0.370828 + 0.427958i
\(474\) 23.2639 27.6853i 1.06854 1.27163i
\(475\) 5.20709 + 0.748667i 0.238918 + 0.0343512i
\(476\) −50.8812 + 25.1285i −2.33213 + 1.15176i
\(477\) −23.9651 + 52.4763i −1.09729 + 2.40273i
\(478\) −5.44596 17.5578i −0.249092 0.803074i
\(479\) 13.5771 + 29.7298i 0.620355 + 1.35839i 0.915261 + 0.402861i \(0.131984\pi\)
−0.294906 + 0.955526i \(0.595288\pi\)
\(480\) 1.11062 16.5576i 0.0506929 0.755750i
\(481\) −3.11815 + 4.85194i −0.142176 + 0.221229i
\(482\) 10.9696 + 16.5130i 0.499653 + 0.752148i
\(483\) 4.56648 + 55.6052i 0.207782 + 2.53012i
\(484\) 2.87542 6.83778i 0.130701 0.310808i
\(485\) 4.65681 7.24613i 0.211455 0.329030i
\(486\) −6.10641 6.83494i −0.276993 0.310039i
\(487\) −10.9200 + 4.98701i −0.494833 + 0.225983i −0.647170 0.762346i \(-0.724048\pi\)
0.152336 + 0.988329i \(0.451320\pi\)
\(488\) 1.04921 10.7486i 0.0474957 0.486568i
\(489\) −7.55940 + 16.5528i −0.341848 + 0.748542i
\(490\) 1.57084 12.2404i 0.0709634 0.552965i
\(491\) −1.19567 + 8.31607i −0.0539598 + 0.375299i 0.944892 + 0.327383i \(0.106167\pi\)
−0.998851 + 0.0479154i \(0.984742\pi\)
\(492\) 5.33236 47.2113i 0.240402 2.12845i
\(493\) 17.4312 + 20.1167i 0.785062 + 0.906010i
\(494\) −7.13017 + 16.2610i −0.320802 + 0.731619i
\(495\) 8.18375 + 12.7342i 0.367832 + 0.572358i
\(496\) −32.9145 2.70972i −1.47790 0.121670i
\(497\) −11.3145 38.5337i −0.507525 1.72847i
\(498\) −52.7270 + 25.0528i −2.36275 + 1.12264i
\(499\) 9.34048 10.7795i 0.418137 0.482556i −0.507131 0.861869i \(-0.669294\pi\)
0.925269 + 0.379313i \(0.123840\pi\)
\(500\) −1.35496 1.47109i −0.0605954 0.0657890i
\(501\) 0.135493 0.461447i 0.00605339 0.0206159i
\(502\) −9.99870 + 16.0896i −0.446264 + 0.718115i
\(503\) 0.453070 + 3.15117i 0.0202014 + 0.140504i 0.997426 0.0717040i \(-0.0228437\pi\)
−0.977225 + 0.212208i \(0.931935\pi\)
\(504\) 23.4925 58.3253i 1.04644 2.59801i
\(505\) 2.89916i 0.129011i
\(506\) −5.95685 + 17.3178i −0.264814 + 0.769871i
\(507\) 21.4271 0.951613
\(508\) −4.49316 6.54615i −0.199352 0.290438i
\(509\) 22.4461 3.22727i 0.994908 0.143046i 0.374418 0.927260i \(-0.377843\pi\)
0.620490 + 0.784214i \(0.286934\pi\)
\(510\) −15.6678 + 25.2122i −0.693783 + 1.11641i
\(511\) 16.5321 + 4.85427i 0.731339 + 0.214740i
\(512\) −22.4170 + 3.07867i −0.990701 + 0.136059i
\(513\) 30.3931 + 26.3357i 1.34189 + 1.16275i
\(514\) 8.60483 + 18.1100i 0.379543 + 0.798799i
\(515\) 10.8461 3.18471i 0.477937 0.140335i
\(516\) −8.31430 25.4356i −0.366017 1.11974i
\(517\) −6.42582 + 4.12962i −0.282607 + 0.181621i
\(518\) 5.44251 12.4122i 0.239130 0.545360i
\(519\) 0.652233 0.565163i 0.0286299 0.0248079i
\(520\) 6.00646 3.08055i 0.263401 0.135091i
\(521\) 18.1624 + 2.61136i 0.795710 + 0.114406i 0.528167 0.849140i \(-0.322879\pi\)
0.267543 + 0.963546i \(0.413788\pi\)
\(522\) −29.2540 3.75424i −1.28041 0.164319i
\(523\) 28.2381 + 12.8959i 1.23477 + 0.563899i 0.922464 0.386083i \(-0.126172\pi\)
0.312304 + 0.949982i \(0.398899\pi\)
\(524\) −5.62786 + 6.90749i −0.245854 + 0.301755i
\(525\) −4.83274 10.5822i −0.210918 0.461846i
\(526\) 1.64147 + 1.83731i 0.0715716 + 0.0801104i
\(527\) 49.6968 + 31.9382i 2.16483 + 1.39125i
\(528\) 22.6441 22.1628i 0.985459 0.964513i
\(529\) −6.01326 + 22.2000i −0.261446 + 0.965218i
\(530\) 12.1224 8.05295i 0.526565 0.349798i
\(531\) −3.77542 2.42631i −0.163839 0.105293i
\(532\) 10.5355 40.3715i 0.456770 1.75033i
\(533\) 17.5799 8.02849i 0.761472 0.347753i
\(534\) −21.2110 68.3844i −0.917892 2.95928i
\(535\) −7.33226 3.34853i −0.317001 0.144770i
\(536\) 23.0648 39.7558i 0.996247 1.71719i
\(537\) 6.57115 45.7034i 0.283566 1.97225i
\(538\) 7.01451 + 5.89427i 0.302417 + 0.254120i
\(539\) 17.8075 15.4303i 0.767023 0.664629i
\(540\) −2.63382 15.0608i −0.113342 0.648112i
\(541\) −22.0135 34.2536i −0.946433 1.47268i −0.880048 0.474884i \(-0.842490\pi\)
−0.0663844 0.997794i \(-0.521146\pi\)
\(542\) 7.25717 26.1778i 0.311722 1.12443i
\(543\) 21.8669 6.42069i 0.938397 0.275538i
\(544\) 37.9849 + 13.9765i 1.62859 + 0.599239i
\(545\) −0.849490 + 0.980364i −0.0363881 + 0.0419942i
\(546\) 38.7763 6.17674i 1.65947 0.264340i
\(547\) −21.8908 6.42773i −0.935985 0.274830i −0.222044 0.975037i \(-0.571273\pi\)
−0.713940 + 0.700207i \(0.753091\pi\)
\(548\) −0.0230852 0.760914i −0.000986152 0.0325046i
\(549\) −3.04624 21.1871i −0.130010 0.904242i
\(550\) −0.0579069 3.81823i −0.00246916 0.162810i
\(551\) −19.5708 −0.833745
\(552\) 26.5179 29.6696i 1.12868 1.26282i
\(553\) −34.5661 −1.46990
\(554\) 0.518674 + 34.2000i 0.0220364 + 1.45302i
\(555\) −1.00892 7.01717i −0.0428261 0.297862i
\(556\) 15.1806 0.460560i 0.643799 0.0195321i
\(557\) 35.3582 + 10.3821i 1.49818 + 0.439904i 0.925140 0.379626i \(-0.123947\pi\)
0.573036 + 0.819530i \(0.305765\pi\)
\(558\) −64.6419 + 10.2969i −2.73651 + 0.435903i
\(559\) 7.12832 8.22653i 0.301496 0.347945i
\(560\) −12.8000 + 9.36912i −0.540898 + 0.395918i
\(561\) −54.3807 + 15.9676i −2.29596 + 0.674154i
\(562\) −2.67566 + 9.65155i −0.112866 + 0.407126i
\(563\) 15.6775 + 24.3947i 0.660728 + 1.02811i 0.996287 + 0.0860933i \(0.0274383\pi\)
−0.335559 + 0.942019i \(0.608925\pi\)
\(564\) 16.3490 2.85912i 0.688418 0.120390i
\(565\) −12.9759 + 11.2437i −0.545900 + 0.473025i
\(566\) −13.3700 11.2347i −0.561982 0.472231i
\(567\) 3.16527 22.0150i 0.132929 0.924542i
\(568\) −14.3741 + 24.7761i −0.603125 + 1.03958i
\(569\) −1.81120 0.827150i −0.0759297 0.0346759i 0.377088 0.926177i \(-0.376925\pi\)
−0.453018 + 0.891501i \(0.649653\pi\)
\(570\) −6.46562 20.8452i −0.270815 0.873108i
\(571\) 33.2637 15.1910i 1.39204 0.635725i 0.428565 0.903511i \(-0.359019\pi\)
0.963479 + 0.267786i \(0.0862919\pi\)
\(572\) 12.4710 + 3.25448i 0.521440 + 0.136077i
\(573\) 6.74940 + 4.33758i 0.281960 + 0.181205i
\(574\) −37.8287 + 25.1296i −1.57894 + 1.04889i
\(575\) −0.392528 4.77974i −0.0163696 0.199329i
\(576\) −41.7046 + 16.4926i −1.73769 + 0.687191i
\(577\) 22.7831 + 14.6418i 0.948471 + 0.609545i 0.920785 0.390071i \(-0.127550\pi\)
0.0276862 + 0.999617i \(0.491186\pi\)
\(578\) −32.2177 36.0614i −1.34008 1.49996i
\(579\) −2.49870 5.47138i −0.103842 0.227383i
\(580\) 5.76831 + 4.69971i 0.239516 + 0.195145i
\(581\) 50.7575 + 23.1802i 2.10578 + 0.961676i
\(582\) −35.4443 4.54865i −1.46921 0.188548i
\(583\) 27.5046 + 3.95456i 1.13912 + 0.163781i
\(584\) −5.60817 10.9348i −0.232068 0.452486i
\(585\) 10.1113 8.76147i 0.418050 0.362242i
\(586\) 1.74293 3.97492i 0.0719998 0.164202i
\(587\) 9.32193 5.99084i 0.384757 0.247268i −0.333936 0.942596i \(-0.608377\pi\)
0.718693 + 0.695327i \(0.244741\pi\)
\(588\) −48.6645 + 15.9073i −2.00689 + 0.656006i
\(589\) −41.6748 + 12.2368i −1.71718 + 0.504210i
\(590\) 0.485878 + 1.02260i 0.0200033 + 0.0420996i
\(591\) 0.348384 + 0.301876i 0.0143306 + 0.0124175i
\(592\) −9.09273 + 3.28060i −0.373709 + 0.134832i
\(593\) −11.2692 3.30894i −0.462772 0.135882i 0.0420319 0.999116i \(-0.486617\pi\)
−0.504804 + 0.863234i \(0.668435\pi\)
\(594\) 15.4084 24.7947i 0.632214 1.01734i
\(595\) 28.0852 4.03804i 1.15138 0.165544i
\(596\) 24.6174 16.8969i 1.00837 0.692125i
\(597\) −54.0566 −2.21239
\(598\) 15.9001 + 3.03309i 0.650202 + 0.124032i
\(599\) 7.73638i 0.316100i 0.987431 + 0.158050i \(0.0505207\pi\)
−0.987431 + 0.158050i \(0.949479\pi\)
\(600\) −3.10006 + 7.69656i −0.126559 + 0.314211i
\(601\) 0.791496 + 5.50498i 0.0322858 + 0.224553i 0.999576 0.0291200i \(-0.00927048\pi\)
−0.967290 + 0.253673i \(0.918361\pi\)
\(602\) −13.5012 + 21.7257i −0.550267 + 0.885473i
\(603\) 25.6648 87.4063i 1.04515 3.55946i
\(604\) 22.9991 21.1835i 0.935821 0.861944i
\(605\) −2.42880 + 2.80299i −0.0987449 + 0.113958i
\(606\) −10.8638 + 5.16185i −0.441313 + 0.209686i
\(607\) 4.00465 + 13.6386i 0.162544 + 0.553573i 0.999975 + 0.00703109i \(0.00223808\pi\)
−0.837431 + 0.546542i \(0.815944\pi\)
\(608\) −26.0552 + 14.3772i −1.05668 + 0.583073i
\(609\) 23.3986 + 36.4090i 0.948161 + 1.47537i
\(610\) −2.16844 + 4.94534i −0.0877976 + 0.200231i
\(611\) 4.42115 + 5.10228i 0.178861 + 0.206416i
\(612\) 79.7134 + 9.00338i 3.22223 + 0.363940i
\(613\) 4.44807 30.9370i 0.179656 1.24953i −0.677905 0.735150i \(-0.737112\pi\)
0.857560 0.514383i \(-0.171979\pi\)
\(614\) −4.24806 + 33.1020i −0.171438 + 1.33589i
\(615\) −9.86849 + 21.6090i −0.397936 + 0.871358i
\(616\) −30.1436 2.94243i −1.21452 0.118554i
\(617\) 6.32033 2.88640i 0.254447 0.116202i −0.284108 0.958792i \(-0.591698\pi\)
0.538555 + 0.842590i \(0.318970\pi\)
\(618\) −31.2450 34.9727i −1.25686 1.40681i
\(619\) 4.44057 6.90965i 0.178481 0.277722i −0.740473 0.672086i \(-0.765399\pi\)
0.918955 + 0.394363i \(0.129035\pi\)
\(620\) 15.2218 + 6.40106i 0.611322 + 0.257073i
\(621\) 17.2304 32.3613i 0.691431 1.29862i
\(622\) 0.486893 + 0.732940i 0.0195226 + 0.0293882i
\(623\) −37.0008 + 57.5744i −1.48241 + 2.30667i
\(624\) −22.2378 17.0228i −0.890226 0.681457i
\(625\) 0.415415 + 0.909632i 0.0166166 + 0.0363853i
\(626\) 1.14852 + 3.70283i 0.0459041 + 0.147995i
\(627\) 17.3107 37.9053i 0.691325 1.51379i
\(628\) −18.3954 37.2477i −0.734056 1.48635i
\(629\) 17.1148 + 2.46074i 0.682411 + 0.0981159i
\(630\) −20.2257 + 24.0698i −0.805813 + 0.958963i
\(631\) −1.95427 2.25535i −0.0777983 0.0897840i 0.715516 0.698596i \(-0.246192\pi\)
−0.793314 + 0.608812i \(0.791646\pi\)
\(632\) 16.9754 + 17.8785i 0.675246 + 0.711170i
\(633\) −29.0987 + 18.7006i −1.15657 + 0.743282i
\(634\) 0.258151 0.931192i 0.0102525 0.0369823i
\(635\) 1.11845 + 3.80910i 0.0443844 + 0.151159i
\(636\) −51.7599 31.0876i −2.05241 1.23270i
\(637\) −15.7394 13.6382i −0.623616 0.540367i
\(638\) 2.23478 + 14.0295i 0.0884757 + 0.555432i
\(639\) −15.9945 + 54.4721i −0.632731 + 2.15488i
\(640\) 11.1320 + 2.01932i 0.440033 + 0.0798207i
\(641\) −21.3177 + 3.06502i −0.841998 + 0.121061i −0.549799 0.835297i \(-0.685296\pi\)
−0.292198 + 0.956358i \(0.594387\pi\)
\(642\) 0.507112 + 33.4376i 0.0200141 + 1.31968i
\(643\) 13.8501i 0.546194i −0.961987 0.273097i \(-0.911952\pi\)
0.961987 0.273097i \(-0.0880480\pi\)
\(644\) −38.0193 1.16112i −1.49817 0.0457544i
\(645\) 13.3800i 0.526836i
\(646\) 53.2244 0.807197i 2.09409 0.0317588i
\(647\) 36.7399 5.28240i 1.44439 0.207673i 0.624875 0.780725i \(-0.285150\pi\)
0.819519 + 0.573052i \(0.194241\pi\)
\(648\) −12.9412 + 9.17439i −0.508379 + 0.360404i
\(649\) −0.609012 + 2.07410i −0.0239058 + 0.0814157i
\(650\) −3.33316 + 0.530944i −0.130737 + 0.0208253i
\(651\) 72.5910 + 62.9005i 2.84507 + 2.46526i
\(652\) −10.6353 6.38769i −0.416511 0.250161i
\(653\) 6.47854 + 22.0639i 0.253525 + 0.863426i 0.983647 + 0.180109i \(0.0576450\pi\)
−0.730122 + 0.683317i \(0.760537\pi\)
\(654\) 5.18614 + 1.43773i 0.202794 + 0.0562198i
\(655\) 3.74774 2.40852i 0.146436 0.0941089i
\(656\) 31.5754 + 7.22485i 1.23281 + 0.282083i
\(657\) −15.9503 18.4077i −0.622282 0.718152i
\(658\) −12.1459 10.2062i −0.473497 0.397878i
\(659\) −3.08735 0.443894i −0.120266 0.0172917i 0.0819189 0.996639i \(-0.473895\pi\)
−0.202185 + 0.979347i \(0.564804\pi\)
\(660\) −14.2047 + 7.01522i −0.552917 + 0.273067i
\(661\) 8.05791 17.6444i 0.313416 0.686286i −0.685719 0.727867i \(-0.740512\pi\)
0.999135 + 0.0415805i \(0.0132393\pi\)
\(662\) −1.80200 + 0.558934i −0.0700368 + 0.0217236i
\(663\) 20.8099 + 45.5673i 0.808190 + 1.76969i
\(664\) −12.9376 37.6370i −0.502076 1.46060i
\(665\) −11.2787 + 17.5500i −0.437370 + 0.680561i
\(666\) −15.9585 + 10.6012i −0.618379 + 0.410790i
\(667\) 3.97605 + 17.3930i 0.153953 + 0.673458i
\(668\) 0.302241 + 0.127098i 0.0116941 + 0.00491758i
\(669\) 24.7733 38.5480i 0.957791 1.49035i
\(670\) −17.1377 + 15.3110i −0.662087 + 0.591516i
\(671\) −9.37844 + 4.28299i −0.362050 + 0.165343i
\(672\) 57.8982 + 31.2831i 2.23347 + 1.20677i
\(673\) −2.15050 + 4.70894i −0.0828958 + 0.181516i −0.946541 0.322584i \(-0.895449\pi\)
0.863645 + 0.504100i \(0.168176\pi\)
\(674\) −15.1800 1.94809i −0.584712 0.0750376i
\(675\) −1.08795 + 7.56685i −0.0418752 + 0.291248i
\(676\) −1.63952 + 14.5159i −0.0630585 + 0.558303i
\(677\) −23.8746 27.5527i −0.917575 1.05894i −0.998065 0.0621825i \(-0.980194\pi\)
0.0804899 0.996755i \(-0.474352\pi\)
\(678\) 65.2358 + 28.6047i 2.50537 + 1.09856i
\(679\) 18.4672 + 28.7355i 0.708706 + 1.10277i
\(680\) −15.8812 12.5433i −0.609017 0.481015i
\(681\) 5.72890 + 19.5109i 0.219532 + 0.747657i
\(682\) 13.5309 + 28.4776i 0.518124 + 1.09046i
\(683\) −28.1117 + 32.4426i −1.07566 + 1.24138i −0.106670 + 0.994294i \(0.534019\pi\)
−0.968993 + 0.247087i \(0.920527\pi\)
\(684\) −43.3833 + 39.9585i −1.65880 + 1.52785i
\(685\) −0.107236 + 0.365214i −0.00409729 + 0.0139541i
\(686\) 8.22282 + 5.10997i 0.313949 + 0.195100i
\(687\) −5.60663 38.9950i −0.213906 1.48775i
\(688\) 17.8676 3.68632i 0.681194 0.140539i
\(689\) 24.5603i 0.935671i
\(690\) −17.2119 + 9.98106i −0.655247 + 0.379973i
\(691\) 41.1915 1.56700 0.783499 0.621394i \(-0.213433\pi\)
0.783499 + 0.621394i \(0.213433\pi\)
\(692\) 0.332965 + 0.485101i 0.0126574 + 0.0184408i
\(693\) −59.4173 + 8.54292i −2.25708 + 0.324519i
\(694\) 38.7427 + 24.0762i 1.47065 + 0.913920i
\(695\) −7.28617 2.13941i −0.276380 0.0811526i
\(696\) 7.34065 29.9829i 0.278247 1.13650i
\(697\) −43.7881 37.9426i −1.65859 1.43718i
\(698\) 12.5965 5.98513i 0.476786 0.226541i
\(699\) −68.0591 + 19.9840i −2.57423 + 0.755863i
\(700\) 7.53873 2.46424i 0.284937 0.0931395i
\(701\) −33.5137 + 21.5380i −1.26580 + 0.813477i −0.989066 0.147471i \(-0.952887\pi\)
−0.276729 + 0.960948i \(0.589250\pi\)
\(702\) −23.6303 10.3614i −0.891867 0.391067i
\(703\) −9.60778 + 8.32519i −0.362364 + 0.313990i
\(704\) 13.2816 + 17.0361i 0.500570 + 0.642073i
\(705\) −8.21410 1.18101i −0.309361 0.0444794i
\(706\) −3.02334 + 23.5586i −0.113785 + 0.886640i
\(707\) 10.4580 + 4.77602i 0.393315 + 0.179621i
\(708\) 2.96682 3.64140i 0.111500 0.136852i
\(709\) −2.59606 5.68457i −0.0974969 0.213488i 0.854599 0.519289i \(-0.173803\pi\)
−0.952096 + 0.305801i \(0.901076\pi\)
\(710\) 10.6803 9.54192i 0.400825 0.358102i
\(711\) 41.1065 + 26.4176i 1.54162 + 0.990736i
\(712\) 47.9502 9.13697i 1.79701 0.342422i
\(713\) 19.3419 + 34.5512i 0.724358 + 1.29395i
\(714\) −65.1362 98.0522i −2.43766 3.66951i
\(715\) −5.42133 3.48407i −0.202746 0.130297i
\(716\) 30.4591 + 7.94869i 1.13831 + 0.297056i
\(717\) 34.6869 15.8410i 1.29540 0.591591i
\(718\) −18.3661 + 5.69667i −0.685416 + 0.212598i
\(719\) −20.9320 9.55935i −0.780634 0.356503i −0.0150889 0.999886i \(-0.504803\pi\)
−0.765545 + 0.643383i \(0.777530\pi\)
\(720\) 22.3824 1.35936i 0.834143 0.0506604i
\(721\) −6.37963 + 44.3713i −0.237590 + 1.65247i
\(722\) −7.89186 + 9.39176i −0.293705 + 0.349525i
\(723\) −31.0789 + 26.9300i −1.15584 + 1.00154i
\(724\) 2.67655 + 15.3050i 0.0994730 + 0.568808i
\(725\) −2.01131 3.12966i −0.0746983 0.116233i
\(726\) 14.8279 + 4.11067i 0.550314 + 0.152561i
\(727\) 39.0875 11.4771i 1.44968 0.425663i 0.540242 0.841510i \(-0.318333\pi\)
0.909435 + 0.415847i \(0.136515\pi\)
\(728\) 1.21744 + 26.7417i 0.0451212 + 0.991115i
\(729\) 23.4688 27.0845i 0.869216 1.00313i
\(730\) 0.966588 + 6.06804i 0.0357750 + 0.224588i
\(731\) −31.3117 9.19394i −1.15810 0.340050i
\(732\) 22.3922 0.679352i 0.827639 0.0251096i
\(733\) 5.37159 + 37.3602i 0.198404 + 1.37993i 0.808916 + 0.587924i \(0.200055\pi\)
−0.610512 + 0.792007i \(0.709036\pi\)
\(734\) 40.6014 0.615757i 1.49862 0.0227280i
\(735\) 25.5992 0.944240
\(736\) 18.0707 + 20.2348i 0.666096 + 0.745866i
\(737\) −43.8785 −1.61628
\(738\) 64.1921 0.973531i 2.36294 0.0358362i
\(739\) 3.49281 + 24.2930i 0.128485 + 0.893633i 0.947476 + 0.319827i \(0.103625\pi\)
−0.818991 + 0.573806i \(0.805466\pi\)
\(740\) 4.83100 0.146567i 0.177591 0.00538790i
\(741\) −35.3395 10.3766i −1.29823 0.381194i
\(742\) 9.07884 + 56.9951i 0.333295 + 2.09236i
\(743\) −4.37107 + 5.04448i −0.160359 + 0.185064i −0.830243 0.557402i \(-0.811798\pi\)
0.669884 + 0.742466i \(0.266344\pi\)
\(744\) −3.11562 68.4365i −0.114224 2.50900i
\(745\) −14.3244 + 4.20603i −0.524807 + 0.154097i
\(746\) 23.5564 + 6.53046i 0.862463 + 0.239097i
\(747\) −42.6459 66.3583i −1.56033 2.42792i
\(748\) −6.65631 38.0621i −0.243379 1.39169i
\(749\) 24.1581 20.9331i 0.882717 0.764879i
\(750\) 2.66897 3.17623i 0.0974571 0.115979i
\(751\) 3.13224 21.7852i 0.114297 0.794954i −0.849360 0.527813i \(-0.823012\pi\)
0.963658 0.267141i \(-0.0860789\pi\)
\(752\) 0.685952 + 11.2945i 0.0250141 + 0.411866i
\(753\) −35.7442 16.3238i −1.30259 0.594873i
\(754\) 11.9928 3.71985i 0.436752 0.135469i
\(755\) −14.2213 + 6.49464i −0.517565 + 0.236364i
\(756\) 58.6671 + 15.3099i 2.13370 + 0.556817i
\(757\) 6.11457 + 3.92959i 0.222238 + 0.142823i 0.647023 0.762471i \(-0.276014\pi\)
−0.424785 + 0.905294i \(0.639650\pi\)
\(758\) −3.45057 5.19428i −0.125330 0.188665i
\(759\) −37.2040 7.68349i −1.35042 0.278893i
\(760\) 14.6163 2.78516i 0.530190 0.101028i
\(761\) −25.1922 16.1901i −0.913218 0.586890i −0.00253575 0.999997i \(-0.500807\pi\)
−0.910682 + 0.413107i \(0.864444\pi\)
\(762\) 12.2822 10.9731i 0.444938 0.397512i
\(763\) −2.13700 4.67937i −0.0773645 0.169405i
\(764\) −3.45494 + 4.24051i −0.124995 + 0.153416i
\(765\) −36.4855 16.6624i −1.31913 0.602429i
\(766\) 0.802436 6.25279i 0.0289932 0.225922i
\(767\) 1.89117 + 0.271909i 0.0682862 + 0.00981807i
\(768\) −12.2534 45.3097i −0.442155 1.63497i
\(769\) −11.8041 + 10.2283i −0.425665 + 0.368841i −0.841189 0.540741i \(-0.818144\pi\)
0.415524 + 0.909582i \(0.363598\pi\)
\(770\) 13.8688 + 6.08120i 0.499796 + 0.219151i
\(771\) −34.9891 + 22.4861i −1.26010 + 0.809817i
\(772\) 3.89779 1.27410i 0.140285 0.0458558i
\(773\) 5.77655 1.69615i 0.207768 0.0610062i −0.176192 0.984356i \(-0.556378\pi\)
0.383960 + 0.923350i \(0.374560\pi\)
\(774\) 32.6600 15.5181i 1.17394 0.557787i
\(775\) −6.23982 5.40683i −0.224141 0.194219i
\(776\) 5.79355 23.6638i 0.207976 0.849479i
\(777\) 26.9749 + 7.92054i 0.967719 + 0.284148i
\(778\) 5.73858 + 3.56617i 0.205738 + 0.127853i
\(779\) 42.1663 6.06259i 1.51076 0.217215i
\(780\) 7.92414 + 11.5448i 0.283730 + 0.413370i
\(781\) 27.3453 0.978493
\(782\) −11.5306 47.1376i −0.412332 1.68564i
\(783\) 28.4400i 1.01636i
\(784\) −7.05283 34.1850i −0.251887 1.22089i
\(785\) 2.95606 + 20.5598i 0.105506 + 0.733812i
\(786\) −15.6980 9.75535i −0.559930 0.347962i
\(787\) −3.50001 + 11.9200i −0.124762 + 0.424900i −0.998058 0.0622894i \(-0.980160\pi\)
0.873296 + 0.487190i \(0.161978\pi\)
\(788\) −0.231164 + 0.212915i −0.00823487 + 0.00758479i
\(789\) −3.34681 + 3.86243i −0.119150 + 0.137506i
\(790\) −5.29021 11.1340i −0.188217 0.396129i
\(791\) −19.1827 65.3301i −0.682057 2.32287i
\(792\) 33.5985 + 26.5368i 1.19387 + 0.942945i
\(793\) 4.92672 + 7.66613i 0.174953 + 0.272232i
\(794\) 20.2059 + 8.85992i 0.717080 + 0.314427i
\(795\) 19.7696 + 22.8154i 0.701157 + 0.809178i
\(796\) 4.13620 36.6208i 0.146604 1.29799i
\(797\) −4.27810 + 29.7548i −0.151538 + 1.05397i 0.762105 + 0.647453i \(0.224166\pi\)
−0.913643 + 0.406517i \(0.866743\pi\)
\(798\) 85.8454 + 11.0168i 3.03890 + 0.389989i
\(799\) 8.40804 18.4110i 0.297455 0.651336i
\(800\) −4.97685 2.68905i −0.175958 0.0950723i
\(801\) 88.0039 40.1901i 3.10947 1.42005i
\(802\) −16.0755 + 14.3621i −0.567647 + 0.507143i
\(803\) −6.34279 + 9.86957i −0.223832 + 0.348290i
\(804\) 87.8871 + 36.9582i 3.09954 + 1.30342i
\(805\) 17.8884 + 6.45811i 0.630485 + 0.227619i
\(806\) 23.2121 15.4198i 0.817610 0.543140i
\(807\) −10.2752 + 15.9886i −0.361705 + 0.562825i
\(808\) −2.66565 7.75469i −0.0937773 0.272809i
\(809\) −12.6170 27.6274i −0.443591 0.971328i −0.990925 0.134414i \(-0.957085\pi\)
0.547334 0.836914i \(-0.315643\pi\)
\(810\) 7.57560 2.34975i 0.266179 0.0825619i
\(811\) 14.7235 32.2401i 0.517014 1.13210i −0.453544 0.891234i \(-0.649841\pi\)
0.970558 0.240868i \(-0.0774322\pi\)
\(812\) −26.4557 + 13.0656i −0.928415 + 0.458513i
\(813\) 55.7766 + 8.01947i 1.95617 + 0.281255i
\(814\) 7.06508 + 5.93676i 0.247631 + 0.208083i
\(815\) 4.06214 + 4.68797i 0.142291 + 0.164212i
\(816\) −18.7269 + 81.8437i −0.655571 + 2.86510i
\(817\) 20.1847 12.9719i 0.706173 0.453830i
\(818\) 41.4909 + 11.5024i 1.45070 + 0.402171i
\(819\) 14.9478 + 50.9076i 0.522319 + 1.77885i
\(820\) −13.8840 8.33887i −0.484849 0.291206i
\(821\) 31.6509 + 27.4257i 1.10463 + 0.957163i 0.999305 0.0372753i \(-0.0118678\pi\)
0.105320 + 0.994438i \(0.466413\pi\)
\(822\) 1.55947 0.248411i 0.0543929 0.00866432i
\(823\) −3.29630 + 11.2262i −0.114902 + 0.391320i −0.996783 0.0801528i \(-0.974459\pi\)
0.881881 + 0.471473i \(0.156277\pi\)
\(824\) 26.0831 18.4910i 0.908647 0.644166i
\(825\) 7.84065 1.12732i 0.272977 0.0392481i
\(826\) −4.48921 + 0.0680829i −0.156199 + 0.00236891i
\(827\) 8.57638i 0.298230i 0.988820 + 0.149115i \(0.0476425\pi\)
−0.988820 + 0.149115i \(0.952358\pi\)
\(828\) 44.3257 + 30.4375i 1.54043 + 1.05778i
\(829\) 33.8755i 1.17654i −0.808663 0.588272i \(-0.799808\pi\)
0.808663 0.588272i \(-0.200192\pi\)
\(830\) 0.301756 + 19.8970i 0.0104741 + 0.690634i
\(831\) −70.2290 + 10.0974i −2.43622 + 0.350275i
\(832\) 13.2337 13.7626i 0.458795 0.477131i
\(833\) −17.5903 + 59.9070i −0.609467 + 2.07565i
\(834\) 4.95590 + 31.1121i 0.171609 + 1.07733i
\(835\) −0.123897 0.107357i −0.00428762 0.00371525i
\(836\) 24.3545 + 14.6276i 0.842317 + 0.505905i
\(837\) −17.7824 60.5612i −0.614648 2.09330i
\(838\) 4.62189 16.6719i 0.159660 0.575921i
\(839\) 24.5724 15.7917i 0.848334 0.545191i −0.0427205 0.999087i \(-0.513603\pi\)
0.891055 + 0.453896i \(0.149966\pi\)
\(840\) −22.6566 23.8619i −0.781725 0.823314i
\(841\) −9.92758 11.4570i −0.342330 0.395070i
\(842\) −33.3057 + 39.6357i −1.14779 + 1.36594i
\(843\) −20.5644 2.95671i −0.708275 0.101835i
\(844\) −10.4422 21.1439i −0.359437 0.727802i
\(845\) 3.03423 6.64403i 0.104381 0.228562i
\(846\) 6.64392 + 21.4200i 0.228423 + 0.736435i
\(847\) −6.10996 13.3789i −0.209941 0.459706i
\(848\) 25.0208 32.6861i 0.859219 1.12245i
\(849\) 19.5851 30.4749i 0.672157 1.04590i
\(850\) 5.59901 + 8.42842i 0.192045 + 0.289092i
\(851\) 9.35069 + 6.84725i 0.320537 + 0.234721i
\(852\) −54.7717 23.0326i −1.87645 0.789083i
\(853\) −0.546803 + 0.850842i −0.0187222 + 0.0291323i −0.850489 0.525994i \(-0.823694\pi\)
0.831766 + 0.555126i \(0.187330\pi\)
\(854\) −14.2669 15.9690i −0.488203 0.546449i
\(855\) 26.8257 12.2509i 0.917418 0.418971i
\(856\) −22.6912 2.21497i −0.775570 0.0757062i
\(857\) 0.0750635 0.164366i 0.00256412 0.00561464i −0.908346 0.418220i \(-0.862654\pi\)
0.910910 + 0.412606i \(0.135381\pi\)
\(858\) −3.40316 + 26.5183i −0.116182 + 0.905318i
\(859\) −6.23836 + 43.3888i −0.212850 + 1.48041i 0.550725 + 0.834687i \(0.314351\pi\)
−0.763575 + 0.645719i \(0.776558\pi\)
\(860\) −9.06430 1.02378i −0.309090 0.0349107i
\(861\) −61.6922 71.1966i −2.10246 2.42637i
\(862\) −12.3913 + 28.2595i −0.422048 + 0.962522i
\(863\) −24.1786 37.6227i −0.823050 1.28069i −0.957112 0.289718i \(-0.906439\pi\)
0.134062 0.990973i \(-0.457198\pi\)
\(864\) −20.8927 37.8630i −0.710784 1.28812i
\(865\) −0.0828827 0.282272i −0.00281809 0.00959755i
\(866\) −15.3074 + 7.27318i −0.520166 + 0.247153i
\(867\) 65.6889 75.8091i 2.23091 2.57461i
\(868\) −48.1665 + 44.3641i −1.63488 + 1.50581i
\(869\) 6.63089 22.5827i 0.224937 0.766067i
\(870\) −8.14651 + 13.1091i −0.276192 + 0.444441i
\(871\) 5.51933 + 38.3878i 0.187015 + 1.30072i
\(872\) −1.37082 + 3.40335i −0.0464218 + 0.115252i
\(873\) 48.2865i 1.63425i
\(874\) 31.7442 + 16.2888i 1.07376 + 0.550977i
\(875\) −3.96563 −0.134063
\(876\) 21.0174 14.4260i 0.710112 0.487408i
\(877\) −47.1899 + 6.78489i −1.59349 + 0.229109i −0.881189 0.472764i \(-0.843256\pi\)
−0.712302 + 0.701873i \(0.752347\pi\)
\(878\) 23.1948 37.3244i 0.782787 1.25964i
\(879\) 8.63854 + 2.53650i 0.291371 + 0.0855542i
\(880\) −3.66559 10.1598i −0.123567 0.342486i
\(881\) 11.3449 + 9.83038i 0.382218 + 0.331194i 0.824686 0.565590i \(-0.191352\pi\)
−0.442468 + 0.896784i \(0.645897\pi\)
\(882\) −29.6899 62.4865i −0.999712 2.10403i
\(883\) 7.36183 2.16163i 0.247745 0.0727446i −0.155502 0.987836i \(-0.549700\pi\)
0.403248 + 0.915091i \(0.367881\pi\)
\(884\) −32.4620 + 10.6111i −1.09182 + 0.356890i
\(885\) −1.97568 + 1.26969i −0.0664118 + 0.0426803i
\(886\) −18.0778 + 41.2281i −0.607335 + 1.38509i
\(887\) −36.4077 + 31.5475i −1.22245 + 1.05926i −0.226084 + 0.974108i \(0.572592\pi\)
−0.996368 + 0.0851529i \(0.972862\pi\)
\(888\) −9.15065 17.8419i −0.307076 0.598736i
\(889\) −15.5829 2.24049i −0.522635 0.0751436i
\(890\) −24.2079 3.10667i −0.811452 0.104136i
\(891\) 13.7756 + 6.29111i 0.461501 + 0.210760i
\(892\) 24.2189 + 19.7323i 0.810908 + 0.660685i
\(893\) 6.18195 + 13.5366i 0.206871 + 0.452984i
\(894\) 41.2652 + 46.1883i 1.38011 + 1.54477i
\(895\) −13.2410 8.50945i −0.442597 0.284440i
\(896\) −25.6230 + 36.8296i −0.856004 + 1.23039i
\(897\) −2.04225 + 33.5150i −0.0681888 + 1.11903i
\(898\) 33.9695 22.5660i 1.13358 0.753038i
\(899\) 25.8399 + 16.6063i 0.861810 + 0.553852i
\(900\) −10.8485 2.83106i −0.361617 0.0943686i
\(901\) −66.9769 + 30.5873i −2.23132 + 1.01901i
\(902\) −9.16095 29.5349i −0.305026 0.983405i
\(903\) −48.2651 22.0420i −1.60616 0.733510i
\(904\) −24.3699 + 42.0054i −0.810532 + 1.39708i
\(905\) 1.10560 7.68959i 0.0367512 0.255610i
\(906\) 49.6574 + 41.7270i 1.64976 + 1.38629i
\(907\) 21.8716 18.9518i 0.726234 0.629286i −0.211202 0.977442i \(-0.567738\pi\)
0.937436 + 0.348157i \(0.113192\pi\)
\(908\) −13.6560 + 2.38817i −0.453191 + 0.0792541i
\(909\) −8.78672 13.6724i −0.291437 0.453485i
\(910\) 3.57573 12.8983i 0.118534 0.427573i
\(911\) 53.3662 15.6697i 1.76810 0.519161i 0.774546 0.632517i \(-0.217978\pi\)
0.993554 + 0.113356i \(0.0361600\pi\)
\(912\) −36.4605 49.8119i −1.20733 1.64944i
\(913\) −24.8810 + 28.7142i −0.823441 + 0.950301i
\(914\) −18.0100 + 2.86884i −0.595719 + 0.0948930i
\(915\) −10.7475 3.15575i −0.355302 0.104326i
\(916\) 26.8463 0.814483i 0.887025 0.0269113i
\(917\) 2.51423 + 17.4869i 0.0830272 + 0.577467i
\(918\) 1.17301 + 77.3448i 0.0387149 + 2.55276i
\(919\) 43.0788 1.42104 0.710519 0.703678i \(-0.248460\pi\)
0.710519 + 0.703678i \(0.248460\pi\)
\(920\) −5.44471 12.4240i −0.179507 0.409606i
\(921\) −69.2285 −2.28116
\(922\) 0.339399 + 22.3791i 0.0111775 + 0.737016i
\(923\) −3.43968 23.9235i −0.113218 0.787452i
\(924\) −1.90518 62.7969i −0.0626759 2.06587i
\(925\) −2.31872 0.680838i −0.0762391 0.0223858i
\(926\) −12.7944 + 2.03804i −0.420449 + 0.0669740i
\(927\) 41.4981 47.8913i 1.36298 1.57296i
\(928\) 19.7503 + 7.26712i 0.648335 + 0.238555i
\(929\) 29.9973 8.80800i 0.984179 0.288981i 0.250231 0.968186i \(-0.419494\pi\)
0.733948 + 0.679205i \(0.237675\pi\)
\(930\) −9.15088 + 33.0087i −0.300069 + 1.08240i
\(931\) −24.8185 38.6183i −0.813392 1.26566i
\(932\) −8.33057 47.6359i −0.272877 1.56037i
\(933\) −1.37945 + 1.19530i −0.0451612 + 0.0391324i
\(934\) −20.3398 17.0915i −0.665539 0.559250i
\(935\) −2.74951 + 19.1232i −0.0899185 + 0.625397i
\(936\) 18.9899 32.7321i 0.620705 1.06988i
\(937\) 19.8820 + 9.07979i 0.649515 + 0.296624i 0.712795 0.701372i \(-0.247429\pi\)
−0.0632799 + 0.997996i \(0.520156\pi\)
\(938\) −26.9986 87.0434i −0.881534 2.84207i
\(939\) −7.31525 + 3.34076i −0.238724 + 0.109022i
\(940\) 1.42859 5.47430i 0.0465954 0.178552i
\(941\) 24.7214 + 15.8875i 0.805894 + 0.517916i 0.877534 0.479514i \(-0.159187\pi\)
−0.0716404 + 0.997431i \(0.522823\pi\)
\(942\) 71.7794 47.6832i 2.33870 1.55360i
\(943\) −13.9545 36.2423i −0.454422 1.18021i
\(944\) 2.23986 + 2.28850i 0.0729014 + 0.0744845i
\(945\) −25.5034 16.3900i −0.829625 0.533168i
\(946\) −11.6039 12.9883i −0.377275 0.422285i
\(947\) 10.5359 + 23.0703i 0.342369 + 0.749685i 0.999993 0.00366193i \(-0.00116563\pi\)
−0.657624 + 0.753346i \(0.728438\pi\)
\(948\) −32.3025 + 39.6473i −1.04914 + 1.28768i
\(949\) 9.43240 + 4.30763i 0.306189 + 0.139832i
\(950\) −7.37915 0.946985i −0.239411 0.0307242i
\(951\) 1.98407 + 0.285267i 0.0643380 + 0.00925041i
\(952\) 71.4097 36.6241i 2.31440 1.18699i
\(953\) 42.1276 36.5038i 1.36465 1.18247i 0.400752 0.916187i \(-0.368749\pi\)
0.963894 0.266286i \(-0.0857965\pi\)
\(954\) 32.7625 74.7181i 1.06073 2.41909i
\(955\) 2.30074 1.47859i 0.0744501 0.0478462i
\(956\) 8.07740 + 24.7108i 0.261242 + 0.799204i
\(957\) −28.2753 + 8.30239i −0.914012 + 0.268378i
\(958\) −19.8363 41.7482i −0.640882 1.34882i
\(959\) −1.14076 0.988478i −0.0368372 0.0319196i
\(960\) −1.21540 + 23.4372i −0.0392267 + 0.756432i
\(961\) 35.6635 + 10.4718i 1.15044 + 0.337799i
\(962\) 4.30517 6.92776i 0.138804 0.223360i
\(963\) −44.7276 + 6.43085i −1.44133 + 0.207231i
\(964\) −15.8658 23.1150i −0.511002 0.744485i
\(965\) −2.05037 −0.0660038
\(966\) −7.64972 78.5307i −0.246126 2.52668i
\(967\) 10.2475i 0.329537i 0.986332 + 0.164768i \(0.0526877\pi\)
−0.986332 + 0.164768i \(0.947312\pi\)
\(968\) −3.91935 + 9.73064i −0.125973 + 0.312755i
\(969\) 15.7143 + 109.295i 0.504816 + 3.51107i
\(970\) −6.42957 + 10.3463i −0.206441 + 0.332199i
\(971\) −12.4872 + 42.5275i −0.400734 + 1.36477i 0.474151 + 0.880443i \(0.342755\pi\)
−0.874885 + 0.484330i \(0.839063\pi\)
\(972\) 8.78136 + 9.53400i 0.281662 + 0.305803i
\(973\) 19.7206 22.7587i 0.632212 0.729611i
\(974\) 15.3345 7.28607i 0.491350 0.233461i
\(975\) −1.97250 6.71772i −0.0631706 0.215139i
\(976\) −1.25313 + 15.2216i −0.0401118 + 0.487232i
\(977\) −10.8231 16.8411i −0.346262 0.538794i 0.623821 0.781567i \(-0.285579\pi\)
−0.970083 + 0.242773i \(0.921943\pi\)
\(978\) 10.3344 23.5686i 0.330457 0.753640i
\(979\) −30.5166 35.2180i −0.975314 1.12557i
\(980\) −1.95875 + 17.3422i −0.0625700 + 0.553977i
\(981\) −1.03492 + 7.19801i −0.0330424 + 0.229815i
\(982\) 1.51240 11.7850i 0.0482625 0.376074i
\(983\) 23.9740 52.4956i 0.764650 1.67435i 0.0265612 0.999647i \(-0.491544\pi\)
0.738089 0.674703i \(-0.235728\pi\)
\(984\) −6.52777 + 66.8735i −0.208098 + 2.13185i
\(985\) 0.142938 0.0652776i 0.00455438 0.00207992i
\(986\) −25.0800 28.0722i −0.798711 0.894001i
\(987\) 17.7920 27.6849i 0.566325 0.881220i
\(988\) 9.73370 23.1468i 0.309670 0.736399i
\(989\) −15.6291 15.3031i −0.496978 0.486611i
\(990\) −11.8453 17.8312i −0.376469 0.566714i
\(991\) −2.19995 + 3.42319i −0.0698837 + 0.108741i −0.874437 0.485140i \(-0.838769\pi\)
0.804553 + 0.593881i \(0.202405\pi\)
\(992\) 46.6009 + 3.12581i 1.47958 + 0.0992446i
\(993\) −1.62580 3.56001i −0.0515933 0.112973i
\(994\) 16.8257 + 54.2459i 0.533678 + 1.72058i
\(995\) −7.65477 + 16.7616i −0.242673 + 0.531379i
\(996\) 74.0213 36.5566i 2.34546 1.15834i
\(997\) −31.8879 4.58478i −1.00990 0.145202i −0.382546 0.923936i \(-0.624953\pi\)
−0.627353 + 0.778735i \(0.715862\pi\)
\(998\) −12.9767 + 15.4431i −0.410772 + 0.488841i
\(999\) −12.0980 13.9619i −0.382764 0.441734i
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 \(a_p\))

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 920.2.bb.a.251.2 yes 480
8.3 odd 2 920.2.bb.b.251.20 yes 480
23.11 odd 22 920.2.bb.b.11.20 yes 480
184.11 even 22 inner 920.2.bb.a.11.2 480
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
920.2.bb.a.11.2 480 184.11 even 22 inner
920.2.bb.a.251.2 yes 480 1.1 even 1 trivial
920.2.bb.b.11.20 yes 480 23.11 odd 22
920.2.bb.b.251.20 yes 480 8.3 odd 2