Properties

Label 216.2.v.b.203.1
Level $216$
Weight $2$
Character 216.203
Analytic conductor $1.725$
Analytic rank $0$
Dimension $192$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [216,2,Mod(11,216)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(216, base_ring=CyclotomicField(18))
 
chi = DirichletCharacter(H, H._module([9, 9, 13]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("216.11");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 216 = 2^{3} \cdot 3^{3} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 216.v (of order \(18\), 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: \(1.72476868366\)
Analytic rank: \(0\)
Dimension: \(192\)
Relative dimension: \(32\) over \(\Q(\zeta_{18})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label 203.1
Character \(\chi\) \(=\) 216.203
Dual form 216.2.v.b.83.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.41378 - 0.0350966i) q^{2} +(1.62005 + 0.612720i) q^{3} +(1.99754 + 0.0992376i) q^{4} +(1.31649 + 1.10467i) q^{5} +(-2.26889 - 0.923108i) q^{6} +(1.63653 - 4.49634i) q^{7} +(-2.82059 - 0.210407i) q^{8} +(2.24915 + 1.98528i) q^{9} +O(q^{10})\) \(q+(-1.41378 - 0.0350966i) q^{2} +(1.62005 + 0.612720i) q^{3} +(1.99754 + 0.0992376i) q^{4} +(1.31649 + 1.10467i) q^{5} +(-2.26889 - 0.923108i) q^{6} +(1.63653 - 4.49634i) q^{7} +(-2.82059 - 0.210407i) q^{8} +(2.24915 + 1.98528i) q^{9} +(-1.82246 - 1.60796i) q^{10} +(0.757427 + 0.902667i) q^{11} +(3.17531 + 1.38470i) q^{12} +(-5.36812 - 0.946545i) q^{13} +(-2.47150 + 6.29938i) q^{14} +(1.45594 + 2.59627i) q^{15} +(3.98030 + 0.396461i) q^{16} +(-0.394582 - 0.227812i) q^{17} +(-3.11012 - 2.88568i) q^{18} +(1.73047 + 2.99726i) q^{19} +(2.52012 + 2.33726i) q^{20} +(5.40626 - 6.28157i) q^{21} +(-1.03915 - 1.30275i) q^{22} +(-1.07038 + 0.389588i) q^{23} +(-4.44059 - 2.06910i) q^{24} +(-0.355379 - 2.01545i) q^{25} +(7.55611 + 1.52661i) q^{26} +(2.42732 + 4.59435i) q^{27} +(3.71524 - 8.81919i) q^{28} +(0.152108 + 0.862650i) q^{29} +(-1.96725 - 3.72164i) q^{30} +(2.15993 + 5.93437i) q^{31} +(-5.61335 - 0.700203i) q^{32} +(0.673992 + 1.92646i) q^{33} +(0.549855 + 0.335924i) q^{34} +(7.12145 - 4.11157i) q^{35} +(4.29574 + 4.18886i) q^{36} +(5.49344 + 3.17164i) q^{37} +(-2.34131 - 4.29820i) q^{38} +(-8.11668 - 4.82261i) q^{39} +(-3.48086 - 3.39282i) q^{40} +(-11.4320 - 2.01577i) q^{41} +(-7.86372 + 8.69100i) q^{42} +(-1.41495 + 1.18728i) q^{43} +(1.42341 + 1.87827i) q^{44} +(0.767916 + 5.09817i) q^{45} +(1.52696 - 0.513224i) q^{46} +(-2.28362 - 0.831169i) q^{47} +(6.20539 + 3.08110i) q^{48} +(-12.1765 - 10.2173i) q^{49} +(0.431691 + 2.86188i) q^{50} +(-0.499659 - 0.610835i) q^{51} +(-10.6291 - 2.42348i) q^{52} -12.1387 q^{53} +(-3.27045 - 6.58059i) q^{54} +2.02506i q^{55} +(-5.56205 + 12.3380i) q^{56} +(0.966974 + 5.91602i) q^{57} +(-0.184772 - 1.22493i) q^{58} +(3.18940 - 3.80098i) q^{59} +(2.65064 + 5.33062i) q^{60} +(-2.41946 + 6.64740i) q^{61} +(-2.84539 - 8.46569i) q^{62} +(12.6073 - 6.86396i) q^{63} +(7.91146 + 1.18694i) q^{64} +(-6.02148 - 7.17612i) q^{65} +(-0.885262 - 2.74724i) q^{66} +(0.600205 - 3.40393i) q^{67} +(-0.765584 - 0.494220i) q^{68} +(-1.97279 - 0.0246918i) q^{69} +(-10.2125 + 5.56291i) q^{70} +(3.41347 - 5.91231i) q^{71} +(-5.92621 - 6.07289i) q^{72} +(-0.407067 - 0.705061i) q^{73} +(-7.65520 - 4.67680i) q^{74} +(0.659175 - 3.48289i) q^{75} +(3.15924 + 6.15887i) q^{76} +(5.29825 - 1.92840i) q^{77} +(11.3059 + 7.10296i) q^{78} +(-12.8555 + 2.26677i) q^{79} +(4.80209 + 4.91886i) q^{80} +(1.11735 + 8.93037i) q^{81} +(16.0916 + 3.25107i) q^{82} +(10.5557 - 1.86125i) q^{83} +(11.4226 - 12.0112i) q^{84} +(-0.267808 - 0.735795i) q^{85} +(2.04209 - 1.62889i) q^{86} +(-0.282139 + 1.49074i) q^{87} +(-1.94646 - 2.70542i) q^{88} +(7.03637 - 4.06245i) q^{89} +(-0.906734 - 7.23464i) q^{90} +(-13.0411 + 22.5878i) q^{91} +(-2.17679 + 0.671994i) q^{92} +(-0.136895 + 10.9374i) q^{93} +(3.19936 + 1.25524i) q^{94} +(-1.03283 + 5.85748i) q^{95} +(-8.66490 - 4.57378i) q^{96} +(-1.18161 + 0.991491i) q^{97} +(16.8563 + 14.8723i) q^{98} +(-0.0884767 + 3.53394i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 192 q - 6 q^{2} - 12 q^{3} - 6 q^{4} - 6 q^{6} - 9 q^{8} - 12 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 192 q - 6 q^{2} - 12 q^{3} - 6 q^{4} - 6 q^{6} - 9 q^{8} - 12 q^{9} - 3 q^{10} - 30 q^{11} - 3 q^{12} + 9 q^{14} - 6 q^{16} - 18 q^{17} + 63 q^{18} - 6 q^{19} - 27 q^{20} - 18 q^{22} - 30 q^{24} - 12 q^{25} + 18 q^{27} - 12 q^{28} - 21 q^{30} - 36 q^{32} - 30 q^{33} + 12 q^{34} - 18 q^{35} - 36 q^{36} - 102 q^{38} + 9 q^{40} + 18 q^{41} - 6 q^{42} - 42 q^{43} - 81 q^{44} - 3 q^{46} - 81 q^{48} - 12 q^{49} + 57 q^{50} - 18 q^{51} + 21 q^{52} + 78 q^{54} - 69 q^{56} - 36 q^{57} - 33 q^{58} - 84 q^{59} - 54 q^{60} + 90 q^{62} - 51 q^{64} - 12 q^{65} + 87 q^{66} + 30 q^{67} + 63 q^{68} - 33 q^{70} + 12 q^{72} - 6 q^{73} + 51 q^{74} - 96 q^{75} + 30 q^{76} + 90 q^{78} - 12 q^{81} - 12 q^{82} - 72 q^{83} - 48 q^{84} + 42 q^{86} - 78 q^{88} + 144 q^{89} + 120 q^{90} - 6 q^{91} - 3 q^{92} - 33 q^{94} - 78 q^{96} - 42 q^{97} + 162 q^{98} - 12 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/216\mathbb{Z}\right)^\times\).

\(n\) \(55\) \(109\) \(137\)
\(\chi(n)\) \(-1\) \(-1\) \(e\left(\frac{17}{18}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.41378 0.0350966i −0.999692 0.0248170i
\(3\) 1.62005 + 0.612720i 0.935339 + 0.353754i
\(4\) 1.99754 + 0.0992376i 0.998768 + 0.0496188i
\(5\) 1.31649 + 1.10467i 0.588754 + 0.494023i 0.887809 0.460213i \(-0.152227\pi\)
−0.299055 + 0.954236i \(0.596671\pi\)
\(6\) −2.26889 0.923108i −0.926271 0.376857i
\(7\) 1.63653 4.49634i 0.618551 1.69946i −0.0919543 0.995763i \(-0.529311\pi\)
0.710505 0.703692i \(-0.248466\pi\)
\(8\) −2.82059 0.210407i −0.997229 0.0743900i
\(9\) 2.24915 + 1.98528i 0.749716 + 0.661759i
\(10\) −1.82246 1.60796i −0.576313 0.508482i
\(11\) 0.757427 + 0.902667i 0.228373 + 0.272164i 0.868047 0.496482i \(-0.165375\pi\)
−0.639674 + 0.768646i \(0.720931\pi\)
\(12\) 3.17531 + 1.38470i 0.916634 + 0.399728i
\(13\) −5.36812 0.946545i −1.48885 0.262524i −0.630741 0.775993i \(-0.717249\pi\)
−0.858108 + 0.513469i \(0.828360\pi\)
\(14\) −2.47150 + 6.29938i −0.660536 + 1.68358i
\(15\) 1.45594 + 2.59627i 0.375922 + 0.670353i
\(16\) 3.98030 + 0.396461i 0.995076 + 0.0991153i
\(17\) −0.394582 0.227812i −0.0957001 0.0552525i 0.451386 0.892329i \(-0.350930\pi\)
−0.547086 + 0.837076i \(0.684263\pi\)
\(18\) −3.11012 2.88568i −0.733063 0.680161i
\(19\) 1.73047 + 2.99726i 0.396997 + 0.687619i 0.993354 0.115100i \(-0.0367189\pi\)
−0.596357 + 0.802720i \(0.703386\pi\)
\(20\) 2.52012 + 2.33726i 0.563516 + 0.522628i
\(21\) 5.40626 6.28157i 1.17974 1.37075i
\(22\) −1.03915 1.30275i −0.221548 0.277748i
\(23\) −1.07038 + 0.389588i −0.223191 + 0.0812347i −0.451195 0.892425i \(-0.649002\pi\)
0.228004 + 0.973660i \(0.426780\pi\)
\(24\) −4.44059 2.06910i −0.906431 0.422353i
\(25\) −0.355379 2.01545i −0.0710758 0.403091i
\(26\) 7.55611 + 1.52661i 1.48188 + 0.299392i
\(27\) 2.42732 + 4.59435i 0.467139 + 0.884184i
\(28\) 3.71524 8.81919i 0.702114 1.66667i
\(29\) 0.152108 + 0.862650i 0.0282458 + 0.160190i 0.995668 0.0929779i \(-0.0296386\pi\)
−0.967422 + 0.253168i \(0.918527\pi\)
\(30\) −1.96725 3.72164i −0.359170 0.679476i
\(31\) 2.15993 + 5.93437i 0.387935 + 1.06584i 0.967929 + 0.251223i \(0.0808328\pi\)
−0.579994 + 0.814621i \(0.696945\pi\)
\(32\) −5.61335 0.700203i −0.992310 0.123780i
\(33\) 0.673992 + 1.92646i 0.117327 + 0.335354i
\(34\) 0.549855 + 0.335924i 0.0942994 + 0.0576105i
\(35\) 7.12145 4.11157i 1.20375 0.694983i
\(36\) 4.29574 + 4.18886i 0.715957 + 0.698144i
\(37\) 5.49344 + 3.17164i 0.903117 + 0.521415i 0.878210 0.478275i \(-0.158738\pi\)
0.0249066 + 0.999690i \(0.492071\pi\)
\(38\) −2.34131 4.29820i −0.379810 0.697260i
\(39\) −8.11668 4.82261i −1.29971 0.772235i
\(40\) −3.48086 3.39282i −0.550373 0.536452i
\(41\) −11.4320 2.01577i −1.78538 0.314810i −0.819358 0.573282i \(-0.805670\pi\)
−0.966019 + 0.258472i \(0.916781\pi\)
\(42\) −7.86372 + 8.69100i −1.21340 + 1.34105i
\(43\) −1.41495 + 1.18728i −0.215777 + 0.181059i −0.744269 0.667880i \(-0.767202\pi\)
0.528492 + 0.848938i \(0.322758\pi\)
\(44\) 1.42341 + 1.87827i 0.214587 + 0.283161i
\(45\) 0.767916 + 5.09817i 0.114474 + 0.759991i
\(46\) 1.52696 0.513224i 0.225138 0.0756708i
\(47\) −2.28362 0.831169i −0.333100 0.121239i 0.170055 0.985435i \(-0.445605\pi\)
−0.503155 + 0.864196i \(0.667828\pi\)
\(48\) 6.20539 + 3.08110i 0.895670 + 0.444718i
\(49\) −12.1765 10.2173i −1.73950 1.45961i
\(50\) 0.431691 + 2.86188i 0.0610504 + 0.404731i
\(51\) −0.499659 0.610835i −0.0699662 0.0855340i
\(52\) −10.6291 2.42348i −1.47399 0.336076i
\(53\) −12.1387 −1.66737 −0.833687 0.552237i \(-0.813774\pi\)
−0.833687 + 0.552237i \(0.813774\pi\)
\(54\) −3.27045 6.58059i −0.445052 0.895505i
\(55\) 2.02506i 0.273059i
\(56\) −5.56205 + 12.3380i −0.743260 + 1.64873i
\(57\) 0.966974 + 5.91602i 0.128079 + 0.783596i
\(58\) −0.184772 1.22493i −0.0242617 0.160842i
\(59\) 3.18940 3.80098i 0.415225 0.494846i −0.517374 0.855759i \(-0.673091\pi\)
0.932599 + 0.360913i \(0.117535\pi\)
\(60\) 2.65064 + 5.33062i 0.342197 + 0.688180i
\(61\) −2.41946 + 6.64740i −0.309780 + 0.851112i 0.682919 + 0.730494i \(0.260710\pi\)
−0.992699 + 0.120619i \(0.961512\pi\)
\(62\) −2.84539 8.46569i −0.361365 1.07514i
\(63\) 12.6073 6.86396i 1.58837 0.864778i
\(64\) 7.91146 + 1.18694i 0.988932 + 0.148368i
\(65\) −6.02148 7.17612i −0.746873 0.890089i
\(66\) −0.885262 2.74724i −0.108968 0.338162i
\(67\) 0.600205 3.40393i 0.0733267 0.415856i −0.925944 0.377662i \(-0.876728\pi\)
0.999270 0.0381946i \(-0.0121607\pi\)
\(68\) −0.765584 0.494220i −0.0928407 0.0599329i
\(69\) −1.97279 0.0246918i −0.237496 0.00297255i
\(70\) −10.2125 + 5.56291i −1.22062 + 0.664895i
\(71\) 3.41347 5.91231i 0.405105 0.701662i −0.589229 0.807966i \(-0.700568\pi\)
0.994334 + 0.106304i \(0.0339017\pi\)
\(72\) −5.92621 6.07289i −0.698411 0.715697i
\(73\) −0.407067 0.705061i −0.0476436 0.0825211i 0.841220 0.540693i \(-0.181838\pi\)
−0.888864 + 0.458172i \(0.848505\pi\)
\(74\) −7.65520 4.67680i −0.889899 0.543667i
\(75\) 0.659175 3.48289i 0.0761150 0.402170i
\(76\) 3.15924 + 6.15887i 0.362389 + 0.706471i
\(77\) 5.29825 1.92840i 0.603791 0.219762i
\(78\) 11.3059 + 7.10296i 1.28014 + 0.804252i
\(79\) −12.8555 + 2.26677i −1.44636 + 0.255032i −0.841049 0.540959i \(-0.818061\pi\)
−0.605308 + 0.795991i \(0.706950\pi\)
\(80\) 4.80209 + 4.91886i 0.536890 + 0.549945i
\(81\) 1.11735 + 8.93037i 0.124150 + 0.992264i
\(82\) 16.0916 + 3.25107i 1.77701 + 0.359021i
\(83\) 10.5557 1.86125i 1.15864 0.204299i 0.438893 0.898539i \(-0.355371\pi\)
0.719743 + 0.694241i \(0.244260\pi\)
\(84\) 11.4226 12.0112i 1.24631 1.31053i
\(85\) −0.267808 0.735795i −0.0290478 0.0798082i
\(86\) 2.04209 1.62889i 0.220204 0.175648i
\(87\) −0.282139 + 1.49074i −0.0302484 + 0.159824i
\(88\) −1.94646 2.70542i −0.207494 0.288399i
\(89\) 7.03637 4.06245i 0.745853 0.430619i −0.0783403 0.996927i \(-0.524962\pi\)
0.824194 + 0.566308i \(0.191629\pi\)
\(90\) −0.906734 7.23464i −0.0955782 0.762598i
\(91\) −13.0411 + 22.5878i −1.36708 + 2.36785i
\(92\) −2.17679 + 0.671994i −0.226946 + 0.0700602i
\(93\) −0.136895 + 10.9374i −0.0141954 + 1.13416i
\(94\) 3.19936 + 1.25524i 0.329989 + 0.129468i
\(95\) −1.03283 + 5.85748i −0.105966 + 0.600965i
\(96\) −8.66490 4.57378i −0.884358 0.466809i
\(97\) −1.18161 + 0.991491i −0.119975 + 0.100671i −0.700801 0.713357i \(-0.747174\pi\)
0.580826 + 0.814027i \(0.302729\pi\)
\(98\) 16.8563 + 14.8723i 1.70274 + 1.50233i
\(99\) −0.0884767 + 3.53394i −0.00889225 + 0.355174i
\(100\) −0.509874 4.06121i −0.0509874 0.406121i
\(101\) 2.31957 + 0.844254i 0.230806 + 0.0840064i 0.454834 0.890576i \(-0.349699\pi\)
−0.224028 + 0.974583i \(0.571921\pi\)
\(102\) 0.684968 + 0.881122i 0.0678220 + 0.0872441i
\(103\) 1.22953 1.46530i 0.121149 0.144380i −0.702061 0.712117i \(-0.747736\pi\)
0.823210 + 0.567737i \(0.192181\pi\)
\(104\) 14.9421 + 3.79930i 1.46519 + 0.372552i
\(105\) 14.0564 2.29752i 1.37176 0.224215i
\(106\) 17.1614 + 0.426026i 1.66686 + 0.0413793i
\(107\) 16.8797i 1.63182i −0.578175 0.815912i \(-0.696235\pi\)
0.578175 0.815912i \(-0.303765\pi\)
\(108\) 4.39274 + 9.41827i 0.422691 + 0.906274i
\(109\) 11.1831i 1.07115i −0.844489 0.535573i \(-0.820095\pi\)
0.844489 0.535573i \(-0.179905\pi\)
\(110\) 0.0710728 2.86299i 0.00677653 0.272975i
\(111\) 6.95635 + 8.50417i 0.660267 + 0.807180i
\(112\) 8.29652 17.2480i 0.783947 1.62978i
\(113\) −11.3884 + 13.5722i −1.07133 + 1.27676i −0.112234 + 0.993682i \(0.535801\pi\)
−0.959096 + 0.283080i \(0.908644\pi\)
\(114\) −1.15945 8.39788i −0.108593 0.786534i
\(115\) −1.83952 0.669531i −0.171536 0.0624341i
\(116\) 0.218235 + 1.73827i 0.0202626 + 0.161394i
\(117\) −10.1946 12.7861i −0.942487 1.18208i
\(118\) −4.64251 + 5.26181i −0.427378 + 0.484389i
\(119\) −1.67006 + 1.40135i −0.153094 + 0.128462i
\(120\) −3.56034 7.62934i −0.325013 0.696461i
\(121\) 1.66902 9.46548i 0.151729 0.860498i
\(122\) 3.65387 9.31303i 0.330806 0.843162i
\(123\) −17.2853 10.2703i −1.55857 0.926038i
\(124\) 3.72563 + 12.0685i 0.334572 + 1.08378i
\(125\) 6.05496 10.4875i 0.541572 0.938031i
\(126\) −18.0648 + 9.26164i −1.60934 + 0.825093i
\(127\) 9.67865 5.58797i 0.858841 0.495852i −0.00478302 0.999989i \(-0.501522\pi\)
0.863624 + 0.504136i \(0.168189\pi\)
\(128\) −11.1434 1.95574i −0.984946 0.172864i
\(129\) −3.01976 + 1.05649i −0.265875 + 0.0930190i
\(130\) 8.26118 + 10.3568i 0.724554 + 0.908350i
\(131\) 3.76485 + 10.3438i 0.328936 + 0.903744i 0.988382 + 0.151992i \(0.0485689\pi\)
−0.659446 + 0.751752i \(0.729209\pi\)
\(132\) 1.15515 + 3.91506i 0.100543 + 0.340762i
\(133\) 16.3087 2.87566i 1.41414 0.249351i
\(134\) −0.968023 + 4.79134i −0.0836245 + 0.413909i
\(135\) −1.87969 + 8.72984i −0.161778 + 0.751345i
\(136\) 1.06502 + 0.725586i 0.0913247 + 0.0622185i
\(137\) 13.8815 2.44768i 1.18598 0.209119i 0.454348 0.890824i \(-0.349872\pi\)
0.731627 + 0.681705i \(0.238761\pi\)
\(138\) 2.78822 + 0.104147i 0.237349 + 0.00886557i
\(139\) −5.23084 + 1.90387i −0.443674 + 0.161484i −0.554190 0.832390i \(-0.686972\pi\)
0.110516 + 0.993874i \(0.464750\pi\)
\(140\) 14.6334 7.50630i 1.23675 0.634398i
\(141\) −3.19031 2.74576i −0.268673 0.231235i
\(142\) −5.03340 + 8.23889i −0.422393 + 0.691392i
\(143\) −3.21155 5.56256i −0.268563 0.465165i
\(144\) 8.16521 + 8.79371i 0.680434 + 0.732809i
\(145\) −0.752694 + 1.30370i −0.0625078 + 0.108267i
\(146\) 0.550757 + 1.01109i 0.0455810 + 0.0836781i
\(147\) −13.4662 24.0133i −1.11068 1.98059i
\(148\) 10.6586 + 6.88063i 0.876132 + 0.565584i
\(149\) −2.58539 + 14.6625i −0.211803 + 1.20120i 0.674565 + 0.738216i \(0.264331\pi\)
−0.886368 + 0.462981i \(0.846780\pi\)
\(150\) −1.05417 + 4.90090i −0.0860722 + 0.400157i
\(151\) 11.9983 + 14.2990i 0.976405 + 1.16363i 0.986513 + 0.163685i \(0.0523382\pi\)
−0.0101076 + 0.999949i \(0.503217\pi\)
\(152\) −4.25031 8.81816i −0.344745 0.715247i
\(153\) −0.435203 1.29574i −0.0351841 0.104754i
\(154\) −7.55822 + 2.54038i −0.609059 + 0.204710i
\(155\) −3.71198 + 10.1986i −0.298153 + 0.819169i
\(156\) −15.7348 10.4388i −1.25979 0.835774i
\(157\) −4.95279 + 5.90251i −0.395276 + 0.471071i −0.926573 0.376114i \(-0.877260\pi\)
0.531298 + 0.847185i \(0.321705\pi\)
\(158\) 18.2544 2.75353i 1.45224 0.219059i
\(159\) −19.6653 7.43760i −1.55956 0.589840i
\(160\) −6.61645 7.12272i −0.523077 0.563100i
\(161\) 5.45038i 0.429550i
\(162\) −1.26625 12.6648i −0.0994863 0.995039i
\(163\) −4.86594 −0.381130 −0.190565 0.981675i \(-0.561032\pi\)
−0.190565 + 0.981675i \(0.561032\pi\)
\(164\) −22.6358 5.16105i −1.76756 0.403011i
\(165\) −1.24080 + 3.28071i −0.0965958 + 0.255403i
\(166\) −14.9887 + 2.26093i −1.16335 + 0.175482i
\(167\) −5.93958 4.98390i −0.459619 0.385666i 0.383372 0.923594i \(-0.374763\pi\)
−0.842991 + 0.537928i \(0.819207\pi\)
\(168\) −16.5705 + 16.5802i −1.27844 + 1.27919i
\(169\) 15.7048 + 5.71607i 1.20806 + 0.439698i
\(170\) 0.352797 + 1.04965i 0.0270583 + 0.0805045i
\(171\) −2.05831 + 10.1768i −0.157403 + 0.778236i
\(172\) −2.94423 + 2.23122i −0.224495 + 0.170129i
\(173\) −2.39480 + 2.00948i −0.182073 + 0.152778i −0.729269 0.684227i \(-0.760140\pi\)
0.547196 + 0.837005i \(0.315695\pi\)
\(174\) 0.451201 2.09767i 0.0342055 0.159024i
\(175\) −9.64375 1.70045i −0.728999 0.128542i
\(176\) 2.65692 + 3.89318i 0.200273 + 0.293459i
\(177\) 7.49594 4.20359i 0.563429 0.315961i
\(178\) −10.0904 + 5.49645i −0.756310 + 0.411976i
\(179\) −9.72475 5.61459i −0.726862 0.419654i 0.0904110 0.995905i \(-0.471182\pi\)
−0.817273 + 0.576250i \(0.804515\pi\)
\(180\) 1.02801 + 10.2600i 0.0766234 + 0.764735i
\(181\) −12.9165 + 7.45734i −0.960075 + 0.554300i −0.896196 0.443658i \(-0.853680\pi\)
−0.0638789 + 0.997958i \(0.520347\pi\)
\(182\) 19.2300 31.4765i 1.42542 2.33319i
\(183\) −7.99264 + 9.28670i −0.590833 + 0.686493i
\(184\) 3.10109 0.873652i 0.228615 0.0644065i
\(185\) 3.72847 + 10.2439i 0.274123 + 0.753146i
\(186\) 0.577406 15.4583i 0.0423374 1.13346i
\(187\) −0.0932288 0.528727i −0.00681756 0.0386643i
\(188\) −4.47913 1.88691i −0.326674 0.137617i
\(189\) 24.6302 3.39526i 1.79158 0.246969i
\(190\) 1.66577 8.24493i 0.120848 0.598150i
\(191\) −1.67647 9.50775i −0.121305 0.687957i −0.983434 0.181267i \(-0.941980\pi\)
0.862129 0.506690i \(-0.169131\pi\)
\(192\) 12.0897 + 6.77041i 0.872501 + 0.488613i
\(193\) 5.42295 1.97379i 0.390352 0.142077i −0.139385 0.990238i \(-0.544513\pi\)
0.529738 + 0.848162i \(0.322290\pi\)
\(194\) 1.70534 1.36028i 0.122436 0.0976622i
\(195\) −5.35818 15.3152i −0.383707 1.09674i
\(196\) −23.3090 21.6178i −1.66493 1.54413i
\(197\) 7.24542 + 12.5494i 0.516215 + 0.894110i 0.999823 + 0.0188255i \(0.00599269\pi\)
−0.483608 + 0.875285i \(0.660674\pi\)
\(198\) 0.249116 4.99310i 0.0177039 0.354844i
\(199\) 12.3632 + 7.13788i 0.876402 + 0.505991i 0.869470 0.493985i \(-0.164460\pi\)
0.00693173 + 0.999976i \(0.497794\pi\)
\(200\) 0.578314 + 5.75955i 0.0408930 + 0.407261i
\(201\) 3.05802 5.14680i 0.215696 0.363027i
\(202\) −3.24973 1.27500i −0.228650 0.0897085i
\(203\) 4.12769 + 0.727824i 0.289707 + 0.0510832i
\(204\) −0.937469 1.26975i −0.0656359 0.0889003i
\(205\) −12.8234 15.2823i −0.895625 1.06736i
\(206\) −1.78971 + 2.02845i −0.124695 + 0.141329i
\(207\) −3.18089 1.24877i −0.221087 0.0867954i
\(208\) −20.9915 5.89579i −1.45550 0.408799i
\(209\) −1.39482 + 3.83225i −0.0964820 + 0.265082i
\(210\) −19.9532 + 2.75485i −1.37690 + 0.190102i
\(211\) 13.8816 + 11.6480i 0.955649 + 0.801885i 0.980240 0.197813i \(-0.0633838\pi\)
−0.0245907 + 0.999698i \(0.507828\pi\)
\(212\) −24.2474 1.20461i −1.66532 0.0827331i
\(213\) 9.15260 7.48676i 0.627126 0.512984i
\(214\) −0.592421 + 23.8642i −0.0404971 + 1.63132i
\(215\) −3.17432 −0.216487
\(216\) −5.87981 13.4695i −0.400070 0.916485i
\(217\) 30.2177 2.05131
\(218\) −0.392489 + 15.8104i −0.0265827 + 1.07082i
\(219\) −0.227466 1.39165i −0.0153707 0.0940393i
\(220\) −0.200962 + 4.04514i −0.0135489 + 0.272723i
\(221\) 1.90253 + 1.59641i 0.127978 + 0.107386i
\(222\) −9.53627 12.2672i −0.640032 0.823317i
\(223\) 3.12879 8.59628i 0.209519 0.575650i −0.789768 0.613406i \(-0.789799\pi\)
0.999287 + 0.0377565i \(0.0120211\pi\)
\(224\) −12.3348 + 24.0936i −0.824152 + 1.60982i
\(225\) 3.20194 5.23858i 0.213462 0.349239i
\(226\) 16.5770 18.7883i 1.10269 1.24978i
\(227\) 6.66470 + 7.94268i 0.442352 + 0.527174i 0.940443 0.339950i \(-0.110410\pi\)
−0.498092 + 0.867124i \(0.665966\pi\)
\(228\) 1.34447 + 11.9134i 0.0890400 + 0.788986i
\(229\) 5.01320 + 0.883963i 0.331282 + 0.0584139i 0.336815 0.941571i \(-0.390650\pi\)
−0.00553340 + 0.999985i \(0.501761\pi\)
\(230\) 2.57718 + 1.01113i 0.169934 + 0.0666719i
\(231\) 9.76502 + 0.122221i 0.642491 + 0.00804154i
\(232\) −0.247528 2.46519i −0.0162510 0.161847i
\(233\) 8.21403 + 4.74237i 0.538119 + 0.310683i 0.744316 0.667827i \(-0.232775\pi\)
−0.206197 + 0.978510i \(0.566109\pi\)
\(234\) 13.9641 + 18.4345i 0.912861 + 1.20510i
\(235\) −2.08820 3.61688i −0.136219 0.235939i
\(236\) 6.74815 7.27609i 0.439267 0.473633i
\(237\) −22.2155 4.20453i −1.44305 0.273113i
\(238\) 2.41028 1.92258i 0.156235 0.124623i
\(239\) 22.5356 8.20228i 1.45771 0.530561i 0.512973 0.858405i \(-0.328544\pi\)
0.944732 + 0.327843i \(0.106322\pi\)
\(240\) 4.76576 + 10.9112i 0.307629 + 0.704312i
\(241\) 3.02186 + 17.1378i 0.194655 + 1.10394i 0.912909 + 0.408162i \(0.133830\pi\)
−0.718255 + 0.695780i \(0.755059\pi\)
\(242\) −2.69183 + 13.3235i −0.173037 + 0.856467i
\(243\) −3.66165 + 15.1523i −0.234895 + 0.972021i
\(244\) −5.49262 + 13.0383i −0.351629 + 0.834693i
\(245\) −4.74355 26.9020i −0.303054 1.71871i
\(246\) 24.0772 + 15.1265i 1.53511 + 0.964432i
\(247\) −6.45233 17.7276i −0.410552 1.12798i
\(248\) −4.84366 17.1929i −0.307572 1.09175i
\(249\) 18.2412 + 3.45234i 1.15599 + 0.218783i
\(250\) −8.92845 + 14.6145i −0.564685 + 0.924302i
\(251\) −9.03981 + 5.21914i −0.570588 + 0.329429i −0.757384 0.652970i \(-0.773523\pi\)
0.186796 + 0.982399i \(0.440190\pi\)
\(252\) 25.8647 12.4599i 1.62932 0.784900i
\(253\) −1.16241 0.671116i −0.0730799 0.0421927i
\(254\) −13.8796 + 7.56046i −0.870882 + 0.474385i
\(255\) 0.0169735 1.35612i 0.00106292 0.0849235i
\(256\) 15.6856 + 3.15607i 0.980352 + 0.197255i
\(257\) −20.2320 3.56745i −1.26204 0.222532i −0.497702 0.867348i \(-0.665823\pi\)
−0.764338 + 0.644816i \(0.776934\pi\)
\(258\) 4.30635 1.38766i 0.268101 0.0863921i
\(259\) 23.2510 19.5099i 1.44474 1.21228i
\(260\) −11.3160 14.9321i −0.701788 0.926051i
\(261\) −1.37048 + 2.24221i −0.0848309 + 0.138789i
\(262\) −4.95962 14.7560i −0.306407 0.911629i
\(263\) 23.8393 + 8.67678i 1.46999 + 0.535033i 0.948098 0.317978i \(-0.103004\pi\)
0.521893 + 0.853011i \(0.325226\pi\)
\(264\) −1.49571 5.57556i −0.0920548 0.343152i
\(265\) −15.9805 13.4092i −0.981674 0.823722i
\(266\) −23.1578 + 3.49317i −1.41989 + 0.214180i
\(267\) 13.8884 2.27007i 0.849958 0.138926i
\(268\) 1.53673 6.73991i 0.0938707 0.411706i
\(269\) 19.8102 1.20785 0.603926 0.797040i \(-0.293602\pi\)
0.603926 + 0.797040i \(0.293602\pi\)
\(270\) 2.96385 12.2761i 0.180374 0.747098i
\(271\) 12.1420i 0.737573i −0.929514 0.368787i \(-0.879773\pi\)
0.929514 0.368787i \(-0.120227\pi\)
\(272\) −1.48024 1.06320i −0.0897525 0.0644658i
\(273\) −34.9673 + 28.6030i −2.11632 + 1.73113i
\(274\) −19.7112 + 2.97328i −1.19080 + 0.179623i
\(275\) 1.55011 1.84735i 0.0934752 0.111399i
\(276\) −3.93827 0.245098i −0.237056 0.0147531i
\(277\) 1.79216 4.92392i 0.107681 0.295850i −0.874136 0.485681i \(-0.838572\pi\)
0.981817 + 0.189831i \(0.0607940\pi\)
\(278\) 7.46206 2.50806i 0.447545 0.150424i
\(279\) −6.92335 + 17.6353i −0.414490 + 1.05580i
\(280\) −20.9518 + 10.0987i −1.25211 + 0.603510i
\(281\) −0.727805 0.867364i −0.0434172 0.0517426i 0.743899 0.668292i \(-0.232974\pi\)
−0.787316 + 0.616550i \(0.788530\pi\)
\(282\) 4.41403 + 3.99386i 0.262852 + 0.237831i
\(283\) 1.23962 7.03026i 0.0736880 0.417905i −0.925541 0.378647i \(-0.876389\pi\)
0.999229 0.0392582i \(-0.0124995\pi\)
\(284\) 7.40526 11.4713i 0.439421 0.680697i
\(285\) −5.26224 + 8.85660i −0.311708 + 0.524620i
\(286\) 4.34519 + 7.97694i 0.256936 + 0.471687i
\(287\) −27.7724 + 48.1032i −1.63935 + 2.83944i
\(288\) −11.2352 12.7189i −0.662039 0.749470i
\(289\) −8.39620 14.5427i −0.493894 0.855450i
\(290\) 1.10990 1.81673i 0.0651754 0.106682i
\(291\) −2.52178 + 0.882271i −0.147829 + 0.0517196i
\(292\) −0.743163 1.44878i −0.0434903 0.0847835i
\(293\) −2.36358 + 0.860272i −0.138082 + 0.0502576i −0.410137 0.912024i \(-0.634519\pi\)
0.272055 + 0.962282i \(0.412297\pi\)
\(294\) 18.1955 + 34.4221i 1.06118 + 2.00754i
\(295\) 8.39766 1.48073i 0.488931 0.0862117i
\(296\) −14.8274 10.1018i −0.861826 0.587153i
\(297\) −2.30865 + 5.67096i −0.133961 + 0.329062i
\(298\) 4.16977 20.6388i 0.241548 1.19557i
\(299\) 6.11472 1.07819i 0.353623 0.0623533i
\(300\) 1.66236 6.89179i 0.0959764 0.397898i
\(301\) 3.02281 + 8.30509i 0.174232 + 0.478697i
\(302\) −16.4610 20.6367i −0.947226 1.18751i
\(303\) 3.24054 + 2.78898i 0.186164 + 0.160223i
\(304\) 5.69950 + 12.6161i 0.326889 + 0.723582i
\(305\) −10.5284 + 6.07857i −0.602854 + 0.348058i
\(306\) 0.569805 + 1.84716i 0.0325736 + 0.105595i
\(307\) −5.71371 + 9.89644i −0.326099 + 0.564820i −0.981734 0.190258i \(-0.939068\pi\)
0.655635 + 0.755078i \(0.272401\pi\)
\(308\) 10.7748 3.32627i 0.613952 0.189532i
\(309\) 2.88972 1.62050i 0.164391 0.0921873i
\(310\) 5.60585 14.2882i 0.318391 0.811518i
\(311\) 1.99125 11.2930i 0.112914 0.640365i −0.874849 0.484397i \(-0.839039\pi\)
0.987762 0.155968i \(-0.0498497\pi\)
\(312\) 21.8791 + 15.3104i 1.23866 + 0.866781i
\(313\) 6.15688 5.16624i 0.348008 0.292013i −0.451982 0.892027i \(-0.649283\pi\)
0.799989 + 0.600014i \(0.204838\pi\)
\(314\) 7.20931 8.17101i 0.406845 0.461117i
\(315\) 24.1798 + 4.89052i 1.36238 + 0.275550i
\(316\) −25.9043 + 3.25221i −1.45723 + 0.182951i
\(317\) −10.7435 3.91031i −0.603415 0.219625i 0.0222044 0.999753i \(-0.492932\pi\)
−0.625620 + 0.780128i \(0.715154\pi\)
\(318\) 27.5413 + 11.2053i 1.54444 + 0.628362i
\(319\) −0.663474 + 0.790698i −0.0371474 + 0.0442706i
\(320\) 9.10421 + 10.3022i 0.508941 + 0.575908i
\(321\) 10.3425 27.3461i 0.577264 1.52631i
\(322\) 0.191290 7.70563i 0.0106602 0.429418i
\(323\) 1.57689i 0.0877403i
\(324\) 1.34571 + 17.9496i 0.0747618 + 0.997201i
\(325\) 11.1556i 0.618801i
\(326\) 6.87936 + 0.170778i 0.381012 + 0.00945851i
\(327\) 6.85211 18.1172i 0.378922 1.00189i
\(328\) 31.8208 + 8.09102i 1.75701 + 0.446752i
\(329\) −7.47443 + 8.90768i −0.412079 + 0.491096i
\(330\) 1.86935 4.59465i 0.102904 0.252927i
\(331\) 0.710903 + 0.258748i 0.0390748 + 0.0142221i 0.361484 0.932378i \(-0.382270\pi\)
−0.322409 + 0.946601i \(0.604493\pi\)
\(332\) 21.2700 2.67040i 1.16735 0.146557i
\(333\) 6.05899 + 18.0395i 0.332030 + 0.988559i
\(334\) 8.22233 + 7.25459i 0.449906 + 0.396953i
\(335\) 4.55039 3.81823i 0.248614 0.208612i
\(336\) 24.0090 22.8592i 1.30980 1.24707i
\(337\) −2.31594 + 13.1343i −0.126157 + 0.715473i 0.854457 + 0.519523i \(0.173890\pi\)
−0.980614 + 0.195950i \(0.937221\pi\)
\(338\) −22.0025 8.63244i −1.19678 0.469543i
\(339\) −26.7657 + 15.0097i −1.45372 + 0.815217i
\(340\) −0.461937 1.49635i −0.0250520 0.0811512i
\(341\) −3.72076 + 6.44455i −0.201491 + 0.348992i
\(342\) 3.26717 14.3154i 0.176668 0.774090i
\(343\) −36.8606 + 21.2815i −1.99029 + 1.14909i
\(344\) 4.24079 3.05112i 0.228648 0.164505i
\(345\) −2.56989 2.21179i −0.138358 0.119079i
\(346\) 3.45624 2.75690i 0.185809 0.148212i
\(347\) −6.31721 17.3564i −0.339126 0.931740i −0.985643 0.168841i \(-0.945998\pi\)
0.646518 0.762899i \(-0.276225\pi\)
\(348\) −0.711519 + 2.94981i −0.0381414 + 0.158126i
\(349\) −2.00043 + 0.352730i −0.107081 + 0.0188812i −0.226932 0.973911i \(-0.572869\pi\)
0.119851 + 0.992792i \(0.461758\pi\)
\(350\) 13.5744 + 2.74253i 0.725584 + 0.146594i
\(351\) −8.68141 26.9606i −0.463380 1.43905i
\(352\) −3.61966 5.59734i −0.192928 0.298339i
\(353\) 14.8073 2.61092i 0.788111 0.138965i 0.234914 0.972016i \(-0.424519\pi\)
0.553196 + 0.833051i \(0.313408\pi\)
\(354\) −10.7451 + 5.67986i −0.571097 + 0.301881i
\(355\) 11.0250 4.01276i 0.585145 0.212975i
\(356\) 14.4585 7.41662i 0.766301 0.393080i
\(357\) −3.56423 + 1.24698i −0.188639 + 0.0659973i
\(358\) 13.5516 + 8.27909i 0.716224 + 0.437563i
\(359\) −6.75445 11.6991i −0.356486 0.617453i 0.630885 0.775877i \(-0.282692\pi\)
−0.987371 + 0.158424i \(0.949359\pi\)
\(360\) −1.09329 14.5414i −0.0576213 0.766401i
\(361\) 3.51094 6.08113i 0.184786 0.320059i
\(362\) 18.5228 10.0897i 0.973535 0.530303i
\(363\) 8.50358 14.3119i 0.446322 0.751182i
\(364\) −28.2916 + 43.8258i −1.48288 + 2.29710i
\(365\) 0.242958 1.37788i 0.0127170 0.0721217i
\(366\) 11.6258 12.8488i 0.607688 0.671618i
\(367\) −19.2060 22.8888i −1.00254 1.19478i −0.980799 0.195021i \(-0.937523\pi\)
−0.0217439 0.999764i \(-0.506922\pi\)
\(368\) −4.41491 + 1.12631i −0.230143 + 0.0587131i
\(369\) −21.7104 27.2294i −1.13020 1.41751i
\(370\) −4.91171 14.6134i −0.255347 0.759717i
\(371\) −19.8653 + 54.5795i −1.03136 + 2.83363i
\(372\) −1.35886 + 21.8343i −0.0704534 + 1.13206i
\(373\) 1.28233 1.52822i 0.0663966 0.0791284i −0.731824 0.681494i \(-0.761331\pi\)
0.798220 + 0.602366i \(0.205775\pi\)
\(374\) 0.113248 + 0.750774i 0.00585593 + 0.0388216i
\(375\) 16.2353 13.2803i 0.838385 0.685793i
\(376\) 6.26627 + 2.82488i 0.323158 + 0.145682i
\(377\) 4.77479i 0.245914i
\(378\) −34.9407 + 3.93571i −1.79716 + 0.202431i
\(379\) −2.60318 −0.133716 −0.0668581 0.997762i \(-0.521297\pi\)
−0.0668581 + 0.997762i \(0.521297\pi\)
\(380\) −2.64440 + 11.5980i −0.135655 + 0.594967i
\(381\) 19.1038 3.12252i 0.978717 0.159971i
\(382\) 2.03647 + 13.5007i 0.104195 + 0.690755i
\(383\) 13.6082 + 11.4186i 0.695347 + 0.583465i 0.920446 0.390871i \(-0.127826\pi\)
−0.225099 + 0.974336i \(0.572271\pi\)
\(384\) −16.8546 9.99617i −0.860106 0.510115i
\(385\) 9.10536 + 3.31408i 0.464052 + 0.168901i
\(386\) −7.73612 + 2.60018i −0.393758 + 0.132345i
\(387\) −5.53950 0.138689i −0.281589 0.00704995i
\(388\) −2.45871 + 1.86328i −0.124822 + 0.0945936i
\(389\) −10.4996 + 8.81024i −0.532353 + 0.446697i −0.868913 0.494965i \(-0.835181\pi\)
0.336560 + 0.941662i \(0.390736\pi\)
\(390\) 7.03776 + 21.8403i 0.356371 + 1.10593i
\(391\) 0.511107 + 0.0901219i 0.0258478 + 0.00455766i
\(392\) 32.1951 + 31.3808i 1.62610 + 1.58497i
\(393\) −0.238613 + 19.0644i −0.0120364 + 0.961669i
\(394\) −9.80297 17.9964i −0.493867 0.906646i
\(395\) −19.4282 11.2169i −0.977541 0.564383i
\(396\) −0.527435 + 7.05039i −0.0265046 + 0.354295i
\(397\) 22.3133 12.8826i 1.11987 0.646560i 0.178505 0.983939i \(-0.442874\pi\)
0.941369 + 0.337379i \(0.109540\pi\)
\(398\) −17.2283 10.5253i −0.863575 0.527585i
\(399\) 28.1829 + 5.33392i 1.41091 + 0.267030i
\(400\) −0.615467 8.16302i −0.0307733 0.408151i
\(401\) −3.91465 10.7554i −0.195488 0.537100i 0.802757 0.596306i \(-0.203365\pi\)
−0.998246 + 0.0592057i \(0.981143\pi\)
\(402\) −4.50400 + 7.16910i −0.224639 + 0.357562i
\(403\) −5.97764 33.9009i −0.297767 1.68872i
\(404\) 4.54964 + 1.91662i 0.226353 + 0.0953553i
\(405\) −8.39413 + 12.9911i −0.417108 + 0.645532i
\(406\) −5.81010 1.17385i −0.288350 0.0582572i
\(407\) 1.29795 + 7.36104i 0.0643370 + 0.364873i
\(408\) 1.28081 + 1.82805i 0.0634095 + 0.0905018i
\(409\) −8.73375 + 3.17883i −0.431856 + 0.157183i −0.548796 0.835956i \(-0.684914\pi\)
0.116940 + 0.993139i \(0.462691\pi\)
\(410\) 17.5931 + 22.0559i 0.868860 + 1.08926i
\(411\) 23.9885 + 4.54008i 1.18327 + 0.223946i
\(412\) 2.60145 2.80497i 0.128164 0.138191i
\(413\) −11.8709 20.5611i −0.584130 1.01174i
\(414\) 4.45325 + 1.87712i 0.218865 + 0.0922554i
\(415\) 15.9526 + 9.21021i 0.783080 + 0.452111i
\(416\) 29.4704 + 9.07206i 1.44490 + 0.444795i
\(417\) −9.64078 0.120666i −0.472111 0.00590903i
\(418\) 2.10647 5.36899i 0.103031 0.262606i
\(419\) 13.8643 + 2.44465i 0.677314 + 0.119429i 0.501715 0.865033i \(-0.332703\pi\)
0.175599 + 0.984462i \(0.443814\pi\)
\(420\) 28.3061 3.19445i 1.38120 0.155873i
\(421\) −6.70587 7.99174i −0.326824 0.389494i 0.577464 0.816416i \(-0.304042\pi\)
−0.904288 + 0.426922i \(0.859598\pi\)
\(422\) −19.2167 16.9550i −0.935454 0.825354i
\(423\) −3.48610 6.40304i −0.169500 0.311327i
\(424\) 34.2382 + 2.55406i 1.66275 + 0.124036i
\(425\) −0.318918 + 0.876221i −0.0154698 + 0.0425030i
\(426\) −13.2025 + 10.2634i −0.639663 + 0.497263i
\(427\) 25.9294 + 21.7574i 1.25481 + 1.05291i
\(428\) 1.67510 33.7179i 0.0809692 1.62981i
\(429\) −1.79459 10.9794i −0.0866436 0.530092i
\(430\) 4.48778 + 0.111408i 0.216420 + 0.00537256i
\(431\) 16.0211 0.771709 0.385855 0.922560i \(-0.373907\pi\)
0.385855 + 0.922560i \(0.373907\pi\)
\(432\) 7.84001 + 19.2493i 0.377202 + 0.926131i
\(433\) −8.60544 −0.413551 −0.206775 0.978388i \(-0.566297\pi\)
−0.206775 + 0.978388i \(0.566297\pi\)
\(434\) −42.7211 1.06054i −2.05068 0.0509075i
\(435\) −2.01821 + 1.65088i −0.0967657 + 0.0791536i
\(436\) 1.10978 22.3387i 0.0531490 1.06983i
\(437\) −3.01997 2.53405i −0.144465 0.121220i
\(438\) 0.272744 + 1.97547i 0.0130322 + 0.0943918i
\(439\) −3.25240 + 8.93590i −0.155229 + 0.426487i −0.992792 0.119854i \(-0.961757\pi\)
0.837563 + 0.546341i \(0.183980\pi\)
\(440\) 0.426087 5.71187i 0.0203129 0.272303i
\(441\) −7.10259 47.1539i −0.338219 2.24542i
\(442\) −2.63372 2.32374i −0.125273 0.110529i
\(443\) −8.64715 10.3053i −0.410838 0.489618i 0.520454 0.853889i \(-0.325763\pi\)
−0.931293 + 0.364271i \(0.881318\pi\)
\(444\) 13.0516 + 17.6777i 0.619403 + 0.838948i
\(445\) 13.7510 + 2.42467i 0.651860 + 0.114941i
\(446\) −4.72512 + 12.0434i −0.223741 + 0.570273i
\(447\) −13.1725 + 22.1699i −0.623036 + 1.04860i
\(448\) 18.2842 33.6301i 0.863849 1.58887i
\(449\) 8.35608 + 4.82439i 0.394348 + 0.227677i 0.684042 0.729442i \(-0.260220\pi\)
−0.289694 + 0.957119i \(0.593554\pi\)
\(450\) −4.71068 + 7.29382i −0.222064 + 0.343834i
\(451\) −6.83934 11.8461i −0.322052 0.557810i
\(452\) −24.0956 + 25.9807i −1.13336 + 1.22203i
\(453\) 10.6766 + 30.5167i 0.501629 + 1.43380i
\(454\) −9.14364 11.4631i −0.429132 0.537990i
\(455\) −42.1206 + 15.3306i −1.97464 + 0.718712i
\(456\) −1.48267 16.8901i −0.0694323 0.790953i
\(457\) 2.34734 + 13.3124i 0.109804 + 0.622730i 0.989192 + 0.146624i \(0.0468409\pi\)
−0.879388 + 0.476106i \(0.842048\pi\)
\(458\) −7.05653 1.42567i −0.329730 0.0666174i
\(459\) 0.0888704 2.36582i 0.00414811 0.110427i
\(460\) −3.60807 1.51996i −0.168227 0.0708686i
\(461\) 7.09030 + 40.2111i 0.330228 + 1.87282i 0.470050 + 0.882640i \(0.344236\pi\)
−0.139822 + 0.990177i \(0.544653\pi\)
\(462\) −13.8013 0.515512i −0.642093 0.0239838i
\(463\) 7.18260 + 19.7340i 0.333804 + 0.917118i 0.987113 + 0.160027i \(0.0511581\pi\)
−0.653309 + 0.757091i \(0.726620\pi\)
\(464\) 0.263431 + 3.49391i 0.0122295 + 0.162201i
\(465\) −12.2625 + 14.2478i −0.568659 + 0.660728i
\(466\) −11.4464 6.99295i −0.530243 0.323942i
\(467\) −25.7460 + 14.8645i −1.19138 + 0.687846i −0.958620 0.284688i \(-0.908110\pi\)
−0.232763 + 0.972533i \(0.574777\pi\)
\(468\) −19.0951 26.5524i −0.882673 1.22739i
\(469\) −14.3230 8.26937i −0.661373 0.381844i
\(470\) 2.82532 + 5.18675i 0.130322 + 0.239247i
\(471\) −11.6404 + 6.52771i −0.536360 + 0.300781i
\(472\) −9.79575 + 10.0499i −0.450886 + 0.462586i
\(473\) −2.14344 0.377946i −0.0985553 0.0173780i
\(474\) 31.2602 + 6.72395i 1.43583 + 0.308841i
\(475\) 5.42588 4.55285i 0.248956 0.208899i
\(476\) −3.47508 + 2.63351i −0.159280 + 0.120707i
\(477\) −27.3017 24.0986i −1.25006 1.10340i
\(478\) −32.1482 + 10.8053i −1.47042 + 0.494222i
\(479\) −3.00899 1.09518i −0.137484 0.0500401i 0.272362 0.962195i \(-0.412195\pi\)
−0.409846 + 0.912155i \(0.634417\pi\)
\(480\) −6.35478 15.5932i −0.290055 0.711730i
\(481\) −26.4874 22.2255i −1.20772 1.01340i
\(482\) −3.67075 24.3351i −0.167198 1.10843i
\(483\) −3.33955 + 8.82991i −0.151955 + 0.401775i
\(484\) 4.27326 18.7420i 0.194239 0.851909i
\(485\) −2.65086 −0.120369
\(486\) 5.70856 21.2935i 0.258945 0.965892i
\(487\) 0.767571i 0.0347819i 0.999849 + 0.0173910i \(0.00553600\pi\)
−0.999849 + 0.0173910i \(0.994464\pi\)
\(488\) 8.22295 18.2405i 0.372235 0.825710i
\(489\) −7.88309 2.98146i −0.356485 0.134826i
\(490\) 5.76215 + 38.1999i 0.260308 + 1.72570i
\(491\) 10.2907 12.2639i 0.464411 0.553463i −0.482108 0.876112i \(-0.660129\pi\)
0.946519 + 0.322648i \(0.104573\pi\)
\(492\) −33.5089 22.2306i −1.51070 1.00223i
\(493\) 0.136503 0.375038i 0.00614777 0.0168909i
\(494\) 8.49999 + 25.2894i 0.382433 + 1.13782i
\(495\) −4.02031 + 4.55467i −0.180700 + 0.204717i
\(496\) 6.24444 + 24.4769i 0.280384 + 1.09905i
\(497\) −20.9975 25.0238i −0.941865 1.12247i
\(498\) −25.6678 5.52105i −1.15020 0.247404i
\(499\) 4.92918 27.9548i 0.220661 1.25143i −0.650148 0.759807i \(-0.725293\pi\)
0.870809 0.491621i \(-0.163596\pi\)
\(500\) 13.1358 20.3483i 0.587449 0.910003i
\(501\) −6.56871 11.7135i −0.293468 0.523320i
\(502\) 12.9635 7.06144i 0.578588 0.315167i
\(503\) 22.0465 38.1856i 0.983004 1.70261i 0.332515 0.943098i \(-0.392103\pi\)
0.650489 0.759516i \(-0.274564\pi\)
\(504\) −37.0042 + 16.7078i −1.64830 + 0.744223i
\(505\) 2.12108 + 3.67381i 0.0943867 + 0.163483i
\(506\) 1.61983 + 0.989605i 0.0720103 + 0.0439933i
\(507\) 21.9402 + 18.8830i 0.974400 + 0.838622i
\(508\) 19.8880 10.2017i 0.882387 0.452627i
\(509\) −18.6141 + 6.77499i −0.825057 + 0.300296i −0.719828 0.694152i \(-0.755780\pi\)
−0.105228 + 0.994448i \(0.533557\pi\)
\(510\) −0.0715919 + 1.91666i −0.00317014 + 0.0848709i
\(511\) −3.83637 + 0.676455i −0.169711 + 0.0299246i
\(512\) −22.0652 5.01250i −0.975155 0.221523i
\(513\) −9.57008 + 15.2257i −0.422529 + 0.672232i
\(514\) 28.4784 + 5.75366i 1.25613 + 0.253783i
\(515\) 3.23734 0.570831i 0.142654 0.0251538i
\(516\) −6.13692 + 1.81071i −0.270163 + 0.0797121i
\(517\) −0.979407 2.69090i −0.0430743 0.118346i
\(518\) −33.5564 + 26.7666i −1.47438 + 1.17606i
\(519\) −5.11095 + 1.78812i −0.224346 + 0.0784897i
\(520\) 15.4742 + 21.5079i 0.678590 + 0.943182i
\(521\) 21.7137 12.5364i 0.951292 0.549229i 0.0578103 0.998328i \(-0.481588\pi\)
0.893482 + 0.449099i \(0.148255\pi\)
\(522\) 2.01625 3.12188i 0.0882491 0.136641i
\(523\) −1.30383 + 2.25830i −0.0570126 + 0.0987487i −0.893123 0.449812i \(-0.851491\pi\)
0.836110 + 0.548561i \(0.184824\pi\)
\(524\) 6.49392 + 21.0358i 0.283688 + 0.918953i
\(525\) −14.5815 8.66374i −0.636389 0.378117i
\(526\) −33.3989 13.1037i −1.45626 0.571349i
\(527\) 0.499649 2.83365i 0.0217651 0.123436i
\(528\) 1.91892 + 7.93510i 0.0835105 + 0.345331i
\(529\) −16.6251 + 13.9501i −0.722829 + 0.606526i
\(530\) 22.1223 + 19.5185i 0.960929 + 0.847831i
\(531\) 14.7194 2.21713i 0.638770 0.0962151i
\(532\) 32.8625 4.12580i 1.42477 0.178876i
\(533\) 59.4603 + 21.6418i 2.57551 + 0.937410i
\(534\) −19.7148 + 2.72193i −0.853144 + 0.117790i
\(535\) 18.6465 22.2221i 0.806160 0.960744i
\(536\) −2.40914 + 9.47481i −0.104059 + 0.409249i
\(537\) −12.3145 15.0545i −0.531408 0.649649i
\(538\) −28.0073 0.695272i −1.20748 0.0299753i
\(539\) 18.7302i 0.806765i
\(540\) −4.62107 + 17.2516i −0.198859 + 0.742392i
\(541\) 5.42107i 0.233070i −0.993187 0.116535i \(-0.962821\pi\)
0.993187 0.116535i \(-0.0371787\pi\)
\(542\) −0.426142 + 17.1661i −0.0183044 + 0.737346i
\(543\) −25.4947 + 4.16710i −1.09408 + 0.178828i
\(544\) 2.05541 + 1.55508i 0.0881250 + 0.0666733i
\(545\) 12.3536 14.7225i 0.529172 0.630642i
\(546\) 50.4398 39.2110i 2.15862 1.67808i
\(547\) 6.73827 + 2.45253i 0.288107 + 0.104863i 0.482031 0.876154i \(-0.339899\pi\)
−0.193924 + 0.981017i \(0.562121\pi\)
\(548\) 27.9717 3.51177i 1.19489 0.150015i
\(549\) −18.6387 + 10.1477i −0.795478 + 0.433094i
\(550\) −2.25635 + 2.55734i −0.0962110 + 0.109045i
\(551\) −2.32237 + 1.94870i −0.0989363 + 0.0830174i
\(552\) 5.55923 + 0.484733i 0.236617 + 0.0206316i
\(553\) −10.8463 + 61.5123i −0.461231 + 2.61577i
\(554\) −2.70653 + 6.89843i −0.114989 + 0.293086i
\(555\) −0.236308 + 18.8802i −0.0100307 + 0.801418i
\(556\) −10.6377 + 3.28395i −0.451140 + 0.139271i
\(557\) −5.53410 + 9.58535i −0.234487 + 0.406144i −0.959124 0.282987i \(-0.908675\pi\)
0.724636 + 0.689132i \(0.242008\pi\)
\(558\) 10.4070 24.6895i 0.440565 1.04519i
\(559\) 8.71941 5.03415i 0.368792 0.212922i
\(560\) 29.9756 13.5419i 1.26670 0.572251i
\(561\) 0.172925 0.913689i 0.00730092 0.0385760i
\(562\) 0.998513 + 1.25180i 0.0421197 + 0.0528042i
\(563\) 5.06217 + 13.9082i 0.213345 + 0.586160i 0.999492 0.0318795i \(-0.0101493\pi\)
−0.786147 + 0.618040i \(0.787927\pi\)
\(564\) −6.10028 5.80135i −0.256868 0.244281i
\(565\) −29.9855 + 5.28726i −1.26150 + 0.222437i
\(566\) −1.99929 + 9.89572i −0.0840365 + 0.415948i
\(567\) 41.9825 + 9.59088i 1.76310 + 0.402779i
\(568\) −10.8720 + 15.9580i −0.456179 + 0.669582i
\(569\) 44.3139 7.81374i 1.85774 0.327569i 0.871176 0.490970i \(-0.163358\pi\)
0.986560 + 0.163401i \(0.0522466\pi\)
\(570\) 7.75047 12.3366i 0.324631 0.516722i
\(571\) −36.4607 + 13.2706i −1.52583 + 0.555357i −0.962596 0.270939i \(-0.912666\pi\)
−0.563235 + 0.826296i \(0.690444\pi\)
\(572\) −5.86317 11.4301i −0.245151 0.477918i
\(573\) 3.10961 16.4303i 0.129906 0.686385i
\(574\) 40.9523 67.0325i 1.70931 2.79788i
\(575\) 1.16559 + 2.01886i 0.0486084 + 0.0841923i
\(576\) 15.4376 + 18.3760i 0.643235 + 0.765669i
\(577\) −8.27041 + 14.3248i −0.344302 + 0.596348i −0.985227 0.171256i \(-0.945218\pi\)
0.640925 + 0.767603i \(0.278551\pi\)
\(578\) 11.3600 + 20.8548i 0.472512 + 0.867444i
\(579\) 9.99485 + 0.125097i 0.415372 + 0.00519887i
\(580\) −1.63291 + 2.52950i −0.0678029 + 0.105032i
\(581\) 8.90589 50.5078i 0.369479 2.09542i
\(582\) 3.59620 1.15883i 0.149067 0.0480350i
\(583\) −9.19416 10.9572i −0.380783 0.453800i
\(584\) 0.999820 + 2.07434i 0.0413728 + 0.0858367i
\(585\) 0.703383 28.0945i 0.0290813 1.16156i
\(586\) 3.37177 1.13328i 0.139286 0.0468154i
\(587\) −3.92702 + 10.7894i −0.162085 + 0.445326i −0.993974 0.109617i \(-0.965038\pi\)
0.831888 + 0.554943i \(0.187260\pi\)
\(588\) −24.5163 49.3038i −1.01103 2.03326i
\(589\) −14.0492 + 16.7431i −0.578886 + 0.689889i
\(590\) −11.9244 + 1.79870i −0.490920 + 0.0740513i
\(591\) 4.04869 + 24.7702i 0.166541 + 1.01891i
\(592\) 20.6081 + 14.8020i 0.846989 + 0.608360i
\(593\) 28.6932i 1.17829i 0.808028 + 0.589145i \(0.200535\pi\)
−0.808028 + 0.589145i \(0.799465\pi\)
\(594\) 3.46295 7.93645i 0.142086 0.325636i
\(595\) −3.74666 −0.153598
\(596\) −6.61948 + 29.0323i −0.271144 + 1.18921i
\(597\) 15.6555 + 19.1389i 0.640737 + 0.783304i
\(598\) −8.68269 + 1.30971i −0.355062 + 0.0535582i
\(599\) −10.2334 8.58682i −0.418124 0.350848i 0.409325 0.912389i \(-0.365764\pi\)
−0.827449 + 0.561541i \(0.810209\pi\)
\(600\) −2.59209 + 9.68512i −0.105822 + 0.395393i
\(601\) −18.0827 6.58157i −0.737610 0.268468i −0.0542273 0.998529i \(-0.517270\pi\)
−0.683382 + 0.730061i \(0.739492\pi\)
\(602\) −3.98210 11.8476i −0.162298 0.482874i
\(603\) 8.10770 6.46438i 0.330171 0.263250i
\(604\) 22.5480 + 29.7534i 0.917464 + 1.21065i
\(605\) 12.6535 10.6175i 0.514437 0.431664i
\(606\) −4.48351 4.05673i −0.182130 0.164794i
\(607\) 33.3808 + 5.88593i 1.35488 + 0.238903i 0.803478 0.595334i \(-0.202980\pi\)
0.551406 + 0.834237i \(0.314092\pi\)
\(608\) −7.61505 18.0364i −0.308831 0.731472i
\(609\) 6.24113 + 3.70823i 0.252904 + 0.150265i
\(610\) 15.0981 8.22423i 0.611306 0.332989i
\(611\) 11.4720 + 6.62337i 0.464108 + 0.267953i
\(612\) −0.740749 2.63147i −0.0299430 0.106371i
\(613\) −5.44638 + 3.14447i −0.219977 + 0.127004i −0.605940 0.795511i \(-0.707203\pi\)
0.385963 + 0.922514i \(0.373869\pi\)
\(614\) 8.42525 13.7908i 0.340016 0.556553i
\(615\) −11.4108 32.6153i −0.460128 1.31518i
\(616\) −15.3499 + 4.32445i −0.618466 + 0.174237i
\(617\) −9.83236 27.0142i −0.395836 1.08755i −0.964293 0.264838i \(-0.914682\pi\)
0.568457 0.822713i \(-0.307541\pi\)
\(618\) −4.14230 + 2.18961i −0.166628 + 0.0880792i
\(619\) −1.65721 9.39848i −0.0666087 0.377757i −0.999830 0.0184539i \(-0.994126\pi\)
0.933221 0.359303i \(-0.116986\pi\)
\(620\) −8.42689 + 20.0037i −0.338432 + 0.803366i
\(621\) −4.38808 3.97207i −0.176087 0.159394i
\(622\) −3.21153 + 15.8958i −0.128771 + 0.637365i
\(623\) −6.75089 38.2862i −0.270469 1.53390i
\(624\) −30.3949 22.4134i −1.21677 0.897254i
\(625\) 9.94093 3.61820i 0.397637 0.144728i
\(626\) −8.88578 + 7.08783i −0.355147 + 0.283287i
\(627\) −4.60778 + 5.35381i −0.184017 + 0.213811i
\(628\) −10.4791 + 11.2990i −0.418163 + 0.450878i
\(629\) −1.44507 2.50294i −0.0576189 0.0997989i
\(630\) −34.0133 7.76274i −1.35512 0.309275i
\(631\) −18.9384 10.9341i −0.753925 0.435279i 0.0731856 0.997318i \(-0.476683\pi\)
−0.827110 + 0.562040i \(0.810017\pi\)
\(632\) 36.7371 3.68875i 1.46132 0.146731i
\(633\) 15.3520 + 27.3760i 0.610186 + 1.08810i
\(634\) 15.0517 + 5.90538i 0.597779 + 0.234532i
\(635\) 18.9147 + 3.33518i 0.750609 + 0.132353i
\(636\) −38.5441 16.8084i −1.52837 0.666497i
\(637\) 55.6937 + 66.3732i 2.20667 + 2.62980i
\(638\) 0.965756 1.09459i 0.0382346 0.0433351i
\(639\) 19.4150 6.52097i 0.768045 0.257966i
\(640\) −12.5098 14.8845i −0.494492 0.588361i
\(641\) 5.37663 14.7722i 0.212364 0.583466i −0.787078 0.616853i \(-0.788407\pi\)
0.999442 + 0.0333872i \(0.0106295\pi\)
\(642\) −15.5818 + 38.2983i −0.614965 + 1.51151i
\(643\) 21.2643 + 17.8429i 0.838584 + 0.703655i 0.957245 0.289280i \(-0.0934157\pi\)
−0.118661 + 0.992935i \(0.537860\pi\)
\(644\) −0.540883 + 10.8873i −0.0213138 + 0.429021i
\(645\) −5.14257 1.94497i −0.202488 0.0765830i
\(646\) −0.0553434 + 2.22937i −0.00217746 + 0.0877133i
\(647\) −1.38696 −0.0545272 −0.0272636 0.999628i \(-0.508679\pi\)
−0.0272636 + 0.999628i \(0.508679\pi\)
\(648\) −1.27257 25.4240i −0.0499911 0.998750i
\(649\) 5.84676 0.229505
\(650\) 0.391523 15.7715i 0.0153568 0.618610i
\(651\) 48.9543 + 18.5150i 1.91867 + 0.725659i
\(652\) −9.71989 0.482884i −0.380660 0.0189112i
\(653\) 5.23172 + 4.38994i 0.204733 + 0.171792i 0.739389 0.673278i \(-0.235114\pi\)
−0.534656 + 0.845070i \(0.679559\pi\)
\(654\) −10.3232 + 25.3733i −0.403669 + 0.992173i
\(655\) −6.47012 + 17.7765i −0.252808 + 0.694586i
\(656\) −44.7036 12.5557i −1.74538 0.490218i
\(657\) 0.484187 2.39393i 0.0188899 0.0933960i
\(658\) 10.8798 12.3312i 0.424140 0.480719i
\(659\) −16.7924 20.0124i −0.654141 0.779574i 0.332392 0.943141i \(-0.392144\pi\)
−0.986532 + 0.163567i \(0.947700\pi\)
\(660\) −2.80410 + 6.43021i −0.109150 + 0.250295i
\(661\) 11.4759 + 2.02351i 0.446361 + 0.0787056i 0.392311 0.919833i \(-0.371676\pi\)
0.0540505 + 0.998538i \(0.482787\pi\)
\(662\) −0.995978 0.390762i −0.0387098 0.0151874i
\(663\) 2.10405 + 3.75199i 0.0817144 + 0.145715i
\(664\) −30.1648 + 3.02884i −1.17062 + 0.117542i
\(665\) 24.6469 + 14.2299i 0.955767 + 0.551812i
\(666\) −7.93294 25.7165i −0.307395 0.996494i
\(667\) −0.498893 0.864107i −0.0193172 0.0334584i
\(668\) −11.3699 10.5450i −0.439916 0.407996i
\(669\) 10.3359 12.0094i 0.399610 0.464309i
\(670\) −6.56725 + 5.23842i −0.253715 + 0.202378i
\(671\) −7.83295 + 2.85096i −0.302388 + 0.110060i
\(672\) −34.7456 + 31.4752i −1.34034 + 1.21418i
\(673\) 6.57735 + 37.3020i 0.253538 + 1.43789i 0.799797 + 0.600271i \(0.204940\pi\)
−0.546259 + 0.837617i \(0.683948\pi\)
\(674\) 3.73519 18.4878i 0.143874 0.712122i
\(675\) 8.39709 6.52490i 0.323204 0.251144i
\(676\) 30.8036 + 12.9766i 1.18475 + 0.499099i
\(677\) −7.47059 42.3678i −0.287118 1.62833i −0.697620 0.716468i \(-0.745758\pi\)
0.410502 0.911860i \(-0.365354\pi\)
\(678\) 38.3676 20.2811i 1.47350 0.778889i
\(679\) 2.52433 + 6.93553i 0.0968748 + 0.266161i
\(680\) 0.600559 + 2.13173i 0.0230304 + 0.0817480i
\(681\) 5.93054 + 16.9512i 0.227259 + 0.649570i
\(682\) 5.48652 8.98058i 0.210090 0.343884i
\(683\) 15.8827 9.16986i 0.607733 0.350875i −0.164345 0.986403i \(-0.552551\pi\)
0.772078 + 0.635528i \(0.219218\pi\)
\(684\) −5.12147 + 20.1242i −0.195824 + 0.769467i
\(685\) 20.9788 + 12.1121i 0.801558 + 0.462780i
\(686\) 52.8596 28.7936i 2.01819 1.09935i
\(687\) 7.58004 + 4.50376i 0.289197 + 0.171829i
\(688\) −6.10262 + 4.16476i −0.232660 + 0.158780i
\(689\) 65.1619 + 11.4898i 2.48247 + 0.437726i
\(690\) 3.55563 + 3.21717i 0.135360 + 0.122476i
\(691\) −14.5270 + 12.1896i −0.552634 + 0.463715i −0.875832 0.482617i \(-0.839686\pi\)
0.323198 + 0.946331i \(0.395242\pi\)
\(692\) −4.98312 + 3.77635i −0.189430 + 0.143555i
\(693\) 15.7450 + 6.18122i 0.598102 + 0.234805i
\(694\) 8.32198 + 24.7598i 0.315898 + 0.939869i
\(695\) −8.98952 3.27192i −0.340992 0.124111i
\(696\) 1.10946 4.14540i 0.0420539 0.157131i
\(697\) 4.05164 + 3.39973i 0.153467 + 0.128774i
\(698\) 2.84054 0.428473i 0.107516 0.0162179i
\(699\) 10.4014 + 12.7158i 0.393418 + 0.480956i
\(700\) −19.0950 4.35374i −0.721723 0.164556i
\(701\) −34.7772 −1.31352 −0.656759 0.754101i \(-0.728073\pi\)
−0.656759 + 0.754101i \(0.728073\pi\)
\(702\) 11.3274 + 38.4210i 0.427524 + 1.45011i
\(703\) 21.9537i 0.828001i
\(704\) 4.92094 + 8.04043i 0.185465 + 0.303035i
\(705\) −1.16687 7.13902i −0.0439470 0.268871i
\(706\) −21.0258 + 3.17158i −0.791317 + 0.119364i
\(707\) 7.59210 9.04791i 0.285530 0.340282i
\(708\) 15.3906 7.65294i 0.578413 0.287615i
\(709\) 9.57106 26.2963i 0.359449 0.987578i −0.619772 0.784782i \(-0.712775\pi\)
0.979221 0.202796i \(-0.0650028\pi\)
\(710\) −15.7277 + 5.28621i −0.590250 + 0.198388i
\(711\) −33.4141 20.4234i −1.25313 0.765939i
\(712\) −20.7015 + 9.97800i −0.775820 + 0.373941i
\(713\) −4.62392 5.51057i −0.173167 0.206372i
\(714\) 5.08279 1.63786i 0.190219 0.0612955i
\(715\) 1.91681 10.8708i 0.0716847 0.406544i
\(716\) −18.8684 12.1804i −0.705144 0.455203i
\(717\) 41.5346 + 0.519855i 1.55114 + 0.0194143i
\(718\) 9.13870 + 16.7769i 0.341053 + 0.626109i
\(719\) 7.82104 13.5464i 0.291676 0.505197i −0.682530 0.730857i \(-0.739121\pi\)
0.974206 + 0.225660i \(0.0724539\pi\)
\(720\) 1.03531 + 20.5967i 0.0385837 + 0.767595i
\(721\) −4.57631 7.92639i −0.170431 0.295194i
\(722\) −5.17712 + 8.47414i −0.192672 + 0.315375i
\(723\) −5.60509 + 29.6157i −0.208456 + 1.10142i
\(724\) −26.5412 + 13.6145i −0.986396 + 0.505979i
\(725\) 1.68458 0.613135i 0.0625636 0.0227713i
\(726\) −12.5245 + 19.9355i −0.464827 + 0.739874i
\(727\) 22.5584 3.97765i 0.836643 0.147523i 0.261118 0.965307i \(-0.415909\pi\)
0.575525 + 0.817784i \(0.304798\pi\)
\(728\) 41.5362 60.9671i 1.53943 2.25959i
\(729\) −15.2162 + 22.3040i −0.563562 + 0.826073i
\(730\) −0.391848 + 1.93949i −0.0145029 + 0.0717839i
\(731\) 0.828788 0.146138i 0.0306538 0.00540510i
\(732\) −16.8872 + 17.7574i −0.624168 + 0.656331i
\(733\) −14.5646 40.0158i −0.537954 1.47802i −0.849398 0.527753i \(-0.823035\pi\)
0.311444 0.950265i \(-0.399188\pi\)
\(734\) 26.3496 + 33.0337i 0.972583 + 1.21930i
\(735\) 8.79858 46.4891i 0.324540 1.71478i
\(736\) 6.28123 1.43741i 0.231529 0.0529836i
\(737\) 3.52723 2.03645i 0.129927 0.0750134i
\(738\) 29.7380 + 39.2583i 1.09467 + 1.44512i
\(739\) 16.7732 29.0520i 0.617011 1.06870i −0.373017 0.927825i \(-0.621677\pi\)
0.990028 0.140871i \(-0.0449901\pi\)
\(740\) 6.43118 + 20.8326i 0.236415 + 0.765820i
\(741\) 0.408944 32.6732i 0.0150229 1.20028i
\(742\) 30.0007 76.4661i 1.10136 2.80716i
\(743\) −3.95562 + 22.4334i −0.145118 + 0.823002i 0.822155 + 0.569263i \(0.192772\pi\)
−0.967273 + 0.253739i \(0.918340\pi\)
\(744\) 2.68743 30.8212i 0.0985260 1.12996i
\(745\) −19.6009 + 16.4471i −0.718120 + 0.602574i
\(746\) −1.86657 + 2.11556i −0.0683399 + 0.0774562i
\(747\) 27.4364 + 16.7697i 1.00384 + 0.613572i
\(748\) −0.133758 1.06540i −0.00489069 0.0389550i
\(749\) −75.8969 27.6242i −2.77321 1.00937i
\(750\) −23.4191 + 18.2056i −0.855146 + 0.664776i
\(751\) −25.7667 + 30.7076i −0.940242 + 1.12054i 0.0522997 + 0.998631i \(0.483345\pi\)
−0.992542 + 0.121905i \(0.961100\pi\)
\(752\) −8.75997 4.21367i −0.319443 0.153657i
\(753\) −17.8429 + 2.91642i −0.650230 + 0.106280i
\(754\) −0.167579 + 6.75049i −0.00610286 + 0.245838i
\(755\) 32.0786i 1.16746i
\(756\) 49.5366 4.33791i 1.80163 0.157768i
\(757\) 18.0630i 0.656512i −0.944589 0.328256i \(-0.893539\pi\)
0.944589 0.328256i \(-0.106461\pi\)
\(758\) 3.68031 + 0.0913626i 0.133675 + 0.00331844i
\(759\) −1.47196 1.79947i −0.0534286 0.0653167i
\(760\) 4.14565 16.3042i 0.150378 0.591417i
\(761\) 6.35846 7.57772i 0.230494 0.274692i −0.638384 0.769718i \(-0.720397\pi\)
0.868878 + 0.495026i \(0.164841\pi\)
\(762\) −27.1181 + 3.74407i −0.982385 + 0.135633i
\(763\) −50.2830 18.3015i −1.82037 0.662559i
\(764\) −2.40529 19.1585i −0.0870203 0.693128i
\(765\) 0.858419 2.18659i 0.0310362 0.0790562i
\(766\) −18.8382 16.6210i −0.680653 0.600542i
\(767\) −20.7189 + 17.3852i −0.748116 + 0.627744i
\(768\) 23.4778 + 14.7239i 0.847182 + 0.531303i
\(769\) −2.24867 + 12.7528i −0.0810890 + 0.459879i 0.917043 + 0.398788i \(0.130569\pi\)
−0.998132 + 0.0610908i \(0.980542\pi\)
\(770\) −12.7566 5.00494i −0.459718 0.180366i
\(771\) −30.5911 18.1760i −1.10171 0.654594i
\(772\) 11.0284 3.40456i 0.396921 0.122533i
\(773\) 11.3665 19.6874i 0.408825 0.708106i −0.585933 0.810359i \(-0.699272\pi\)
0.994758 + 0.102254i \(0.0326053\pi\)
\(774\) 7.82676 + 0.390493i 0.281327 + 0.0140360i
\(775\) 11.1929 6.46220i 0.402059 0.232129i
\(776\) 3.54146 2.54797i 0.127131 0.0914668i
\(777\) 49.6219 17.3607i 1.78018 0.622813i
\(778\) 15.1534 12.0872i 0.543274 0.433348i
\(779\) −13.7409 37.7529i −0.492320 1.35264i
\(780\) −9.18331 31.1244i −0.328815 1.11443i
\(781\) 7.92230 1.39692i 0.283482 0.0499856i
\(782\) −0.719428 0.145350i −0.0257267 0.00519772i
\(783\) −3.59410 + 2.79277i −0.128443 + 0.0998055i
\(784\) −44.4153 45.4954i −1.58626 1.62484i
\(785\) −13.0406 + 2.29942i −0.465441 + 0.0820697i
\(786\) 1.00644 26.9444i 0.0358985 0.961075i
\(787\) −19.7167 + 7.17628i −0.702823 + 0.255807i −0.668616 0.743608i \(-0.733113\pi\)
−0.0342072 + 0.999415i \(0.510891\pi\)
\(788\) 13.2276 + 25.7870i 0.471214 + 0.918623i
\(789\) 33.3044 + 28.6636i 1.18567 + 1.02045i
\(790\) 27.0735 + 16.5401i 0.963233 + 0.588469i
\(791\) 42.3875 + 73.4173i 1.50713 + 2.61042i
\(792\) 0.993120 9.94917i 0.0352890 0.353528i
\(793\) 19.2800 33.3939i 0.684653 1.18585i
\(794\) −31.9982 + 17.4300i −1.13558 + 0.618569i
\(795\) −17.6732 31.5152i −0.626803 1.11773i
\(796\) 23.9875 + 15.4851i 0.850216 + 0.548854i
\(797\) −5.29392 + 30.0233i −0.187520 + 1.06348i 0.735154 + 0.677900i \(0.237110\pi\)
−0.922674 + 0.385580i \(0.874001\pi\)
\(798\) −39.6572 8.53010i −1.40385 0.301962i
\(799\) 0.711724 + 0.848200i 0.0251790 + 0.0300071i
\(800\) 0.583639 + 11.5623i 0.0206348 + 0.408789i
\(801\) 23.8909 + 4.83209i 0.844144 + 0.170733i
\(802\) 5.15697 + 15.3432i 0.182099 + 0.541786i
\(803\) 0.328111 0.901478i 0.0115788 0.0318125i
\(804\) 6.61926 9.97744i 0.233443 0.351877i
\(805\) −6.02087 + 7.17540i −0.212208 + 0.252899i
\(806\) 7.26125 + 48.1381i 0.255767 + 1.69559i
\(807\) 32.0937 + 12.1381i 1.12975 + 0.427282i
\(808\) −6.36492 2.86935i −0.223917 0.100943i
\(809\) 12.1921i 0.428652i −0.976762 0.214326i \(-0.931244\pi\)
0.976762 0.214326i \(-0.0687555\pi\)
\(810\) 12.3234 18.0719i 0.433000 0.634982i
\(811\) −32.9198 −1.15597 −0.577985 0.816048i \(-0.696161\pi\)
−0.577985 + 0.816048i \(0.696161\pi\)
\(812\) 8.17299 + 1.86348i 0.286816 + 0.0653952i
\(813\) 7.43963 19.6707i 0.260919 0.689881i
\(814\) −1.57666 10.4524i −0.0552621 0.366357i
\(815\) −6.40598 5.37526i −0.224392 0.188287i
\(816\) −1.74662 2.62941i −0.0611440 0.0920476i
\(817\) −6.00711 2.18641i −0.210162 0.0764928i
\(818\) 12.4592 4.18763i 0.435624 0.146417i
\(819\) −74.1745 + 24.9132i −2.59187 + 0.870538i
\(820\) −24.0986 31.7996i −0.841560 1.11049i
\(821\) −23.5767 + 19.7832i −0.822832 + 0.690438i −0.953633 0.300971i \(-0.902689\pi\)
0.130802 + 0.991409i \(0.458245\pi\)
\(822\) −33.7551 7.26059i −1.17734 0.253242i
\(823\) −32.9923 5.81743i −1.15004 0.202783i −0.434046 0.900891i \(-0.642914\pi\)
−0.715992 + 0.698108i \(0.754026\pi\)
\(824\) −3.77631 + 3.87430i −0.131554 + 0.134968i
\(825\) 3.64317 2.04302i 0.126839 0.0711289i
\(826\) 16.0612 + 29.4854i 0.558842 + 1.02593i
\(827\) −45.1216 26.0510i −1.56903 0.905882i −0.996282 0.0861526i \(-0.972543\pi\)
−0.572751 0.819729i \(-0.694124\pi\)
\(828\) −6.23003 2.81012i −0.216508 0.0976586i
\(829\) −25.6067 + 14.7840i −0.889357 + 0.513471i −0.873732 0.486407i \(-0.838307\pi\)
−0.0156251 + 0.999878i \(0.504974\pi\)
\(830\) −22.2301 13.5811i −0.771619 0.471406i
\(831\) 5.92038 6.87893i 0.205376 0.238627i
\(832\) −41.3462 13.8602i −1.43342 0.480516i
\(833\) 2.47700 + 6.80550i 0.0858229 + 0.235797i
\(834\) 13.6257 + 0.508953i 0.471819 + 0.0176236i
\(835\) −2.31386 13.1226i −0.0800744 0.454125i
\(836\) −3.16652 + 7.51664i −0.109516 + 0.259968i
\(837\) −22.0217 + 24.3281i −0.761182 + 0.840903i
\(838\) −19.5152 3.94278i −0.674142 0.136201i
\(839\) 7.95080 + 45.0912i 0.274492 + 1.55672i 0.740571 + 0.671979i \(0.234555\pi\)
−0.466078 + 0.884743i \(0.654334\pi\)
\(840\) −40.1307 + 3.52280i −1.38464 + 0.121548i
\(841\) 26.5301 9.65615i 0.914830 0.332971i
\(842\) 9.20013 + 11.5339i 0.317057 + 0.397485i
\(843\) −0.647632 1.85112i −0.0223056 0.0637559i
\(844\) 26.5731 + 24.6450i 0.914683 + 0.848315i
\(845\) 14.3609 + 24.8738i 0.494029 + 0.855684i
\(846\) 4.70385 + 9.17483i 0.161722 + 0.315437i
\(847\) −39.8286 22.9950i −1.36853 0.790118i
\(848\) −48.3156 4.81251i −1.65916 0.165262i
\(849\) 6.31583 10.6299i 0.216759 0.364816i
\(850\) 0.481632 1.22759i 0.0165198 0.0421060i
\(851\) −7.11573 1.25470i −0.243924 0.0430104i
\(852\) 19.0256 14.0468i 0.651807 0.481235i
\(853\) 7.00400 + 8.34705i 0.239813 + 0.285797i 0.872504 0.488606i \(-0.162494\pi\)
−0.632692 + 0.774404i \(0.718050\pi\)
\(854\) −35.8948 31.6701i −1.22830 1.08373i
\(855\) −13.9517 + 11.1239i −0.477139 + 0.380429i
\(856\) −3.55161 + 47.6108i −0.121391 + 1.62730i
\(857\) −6.47755 + 17.7969i −0.221269 + 0.607931i −0.999807 0.0196666i \(-0.993740\pi\)
0.778538 + 0.627598i \(0.215962\pi\)
\(858\) 2.15181 + 15.5855i 0.0734616 + 0.532079i
\(859\) 30.2186 + 25.3564i 1.03105 + 0.865150i 0.990975 0.134047i \(-0.0427974\pi\)
0.0400702 + 0.999197i \(0.487242\pi\)
\(860\) −6.34082 0.315012i −0.216220 0.0107418i
\(861\) −74.4665 + 60.9131i −2.53781 + 2.07591i
\(862\) −22.6503 0.562286i −0.771472 0.0191515i
\(863\) −16.4124 −0.558684 −0.279342 0.960192i \(-0.590116\pi\)
−0.279342 + 0.960192i \(0.590116\pi\)
\(864\) −10.4084 27.4893i −0.354103 0.935207i
\(865\) −5.37255 −0.182672
\(866\) 12.1662 + 0.302022i 0.413424 + 0.0102631i
\(867\) −4.69174 28.7044i −0.159340 0.974852i
\(868\) 60.3610 + 2.99873i 2.04878 + 0.101784i
\(869\) −11.7833 9.88732i −0.399719 0.335404i
\(870\) 2.91124 2.26315i 0.0987003 0.0767278i
\(871\) −6.44395 + 17.7046i −0.218345 + 0.599897i
\(872\) −2.35300 + 31.5429i −0.0796826 + 1.06818i
\(873\) −4.62601 0.115818i −0.156567 0.00391985i
\(874\) 4.18063 + 3.68858i 0.141412 + 0.124768i
\(875\) −37.2462 44.3883i −1.25915 1.50060i
\(876\) −0.316267 2.80245i −0.0106857 0.0946861i
\(877\) −18.5740 3.27509i −0.627198 0.110592i −0.148990 0.988839i \(-0.547602\pi\)
−0.478208 + 0.878247i \(0.658713\pi\)
\(878\) 4.91179 12.5192i 0.165765 0.422503i
\(879\) −4.35623 0.0545234i −0.146932 0.00183903i
\(880\) −0.802859 + 8.06037i −0.0270644 + 0.271715i
\(881\) 10.7069 + 6.18163i 0.360725 + 0.208265i 0.669399 0.742903i \(-0.266552\pi\)
−0.308674 + 0.951168i \(0.599885\pi\)
\(882\) 8.38654 + 66.9144i 0.282390 + 2.25313i
\(883\) −11.5774 20.0526i −0.389610 0.674824i 0.602787 0.797902i \(-0.294057\pi\)
−0.992397 + 0.123078i \(0.960723\pi\)
\(884\) 3.64195 + 3.37769i 0.122492 + 0.113604i
\(885\) 14.5119 + 2.74654i 0.487814 + 0.0923240i
\(886\) 11.8635 + 14.8728i 0.398561 + 0.499663i
\(887\) 44.9592 16.3638i 1.50958 0.549443i 0.551061 0.834465i \(-0.314223\pi\)
0.958521 + 0.285022i \(0.0920010\pi\)
\(888\) −17.8317 25.4504i −0.598392 0.854061i
\(889\) −9.28597 52.6633i −0.311441 1.76627i
\(890\) −19.3558 3.91056i −0.648807 0.131082i
\(891\) −7.21484 + 7.77270i −0.241706 + 0.260395i
\(892\) 7.10295 16.8609i 0.237824 0.564544i
\(893\) −1.46050 8.28292i −0.0488739 0.277178i
\(894\) 19.4010 30.8810i 0.648867 1.03281i
\(895\) −6.60032 18.1342i −0.220624 0.606160i
\(896\) −27.0302 + 46.9038i −0.903014 + 1.56695i
\(897\) 10.5668 + 1.99988i 0.352815 + 0.0667741i
\(898\) −11.6443 7.11388i −0.388576 0.237393i
\(899\) −4.79074 + 2.76593i −0.159780 + 0.0922490i
\(900\) 6.91585 10.1465i 0.230528 0.338217i
\(901\) 4.78970 + 2.76533i 0.159568 + 0.0921266i
\(902\) 9.25355 + 16.9878i 0.308109 + 0.565631i
\(903\) −0.191583 + 15.3068i −0.00637549 + 0.509379i
\(904\) 34.9777 35.8853i 1.16334 1.19353i
\(905\) −25.2424 4.45091i −0.839085 0.147953i
\(906\) −14.0233 43.5185i −0.465892 1.44581i
\(907\) −45.8690 + 38.4887i −1.52306 + 1.27800i −0.691834 + 0.722057i \(0.743197\pi\)
−0.831223 + 0.555939i \(0.812359\pi\)
\(908\) 12.5248 + 16.5272i 0.415649 + 0.548474i
\(909\) 3.54098 + 6.50384i 0.117447 + 0.215719i
\(910\) 60.0872 20.1958i 1.99187 0.669486i
\(911\) 5.57494 + 2.02911i 0.184706 + 0.0672275i 0.432717 0.901530i \(-0.357555\pi\)
−0.248011 + 0.968757i \(0.579777\pi\)
\(912\) 1.50338 + 23.9309i 0.0497818 + 0.792432i
\(913\) 9.67524 + 8.11849i 0.320204 + 0.268683i
\(914\) −2.85140 18.9032i −0.0943160 0.625263i
\(915\) −20.7810 + 3.39666i −0.686999 + 0.112290i
\(916\) 9.92633 + 2.26325i 0.327975 + 0.0747798i
\(917\) 52.6706 1.73934
\(918\) −0.208675 + 3.34163i −0.00688731 + 0.110290i
\(919\) 16.2524i 0.536116i −0.963403 0.268058i \(-0.913618\pi\)
0.963403 0.268058i \(-0.0863819\pi\)
\(920\) 5.04766 + 2.27552i 0.166416 + 0.0750217i
\(921\) −15.3203 + 12.5319i −0.504820 + 0.412939i
\(922\) −8.61284 57.0984i −0.283649 1.88044i
\(923\) −23.9202 + 28.5070i −0.787343 + 0.938319i
\(924\) 19.4938 + 1.21320i 0.641300 + 0.0399113i
\(925\) 4.44004 12.1989i 0.145988 0.401098i
\(926\) −9.46201 28.1516i −0.310941 0.925120i
\(927\) 5.67442 0.854714i 0.186373 0.0280725i
\(928\) −0.249808 4.94886i −0.00820034 0.162454i
\(929\) −35.2810 42.0462i −1.15753 1.37949i −0.912044 0.410092i \(-0.865497\pi\)
−0.245486 0.969400i \(-0.578948\pi\)
\(930\) 17.8365 19.7129i 0.584881 0.646412i
\(931\) 9.55284 54.1768i 0.313082 1.77557i
\(932\) 15.9372 + 10.2882i 0.522041 + 0.337001i
\(933\) 10.1453 17.0751i 0.332144 0.559014i
\(934\) 36.9209 20.1115i 1.20809 0.658067i
\(935\) 0.461333 0.799053i 0.0150872 0.0261318i
\(936\) 26.0644 + 38.2094i 0.851941 + 1.24891i
\(937\) 17.4404 + 30.2077i 0.569753 + 0.986841i 0.996590 + 0.0825128i \(0.0262945\pi\)
−0.426837 + 0.904329i \(0.640372\pi\)
\(938\) 19.9593 + 12.1937i 0.651693 + 0.398140i
\(939\) 13.1399 4.59714i 0.428806 0.150022i
\(940\) −3.81233 7.43207i −0.124345 0.242407i
\(941\) 41.1785 14.9877i 1.34238 0.488586i 0.431818 0.901961i \(-0.357872\pi\)
0.910561 + 0.413374i \(0.135650\pi\)
\(942\) 16.6860 8.82019i 0.543659 0.287377i
\(943\) 13.0219 2.29612i 0.424053 0.0747720i
\(944\) 14.2017 13.8646i 0.462227 0.451254i
\(945\) 36.1761 + 22.7384i 1.17681 + 0.739679i
\(946\) 3.01708 + 0.609559i 0.0980937 + 0.0198185i
\(947\) −18.8196 + 3.31841i −0.611556 + 0.107834i −0.470844 0.882217i \(-0.656050\pi\)
−0.140713 + 0.990050i \(0.544939\pi\)
\(948\) −43.9590 10.6033i −1.42772 0.344379i
\(949\) 1.51781 + 4.17016i 0.0492703 + 0.135369i
\(950\) −7.83077 + 6.24629i −0.254064 + 0.202656i
\(951\) −15.0091 12.9177i −0.486704 0.418884i
\(952\) 5.00542 3.60124i 0.162227 0.116717i
\(953\) −12.5264 + 7.23211i −0.405769 + 0.234271i −0.688970 0.724790i \(-0.741937\pi\)
0.283201 + 0.959061i \(0.408604\pi\)
\(954\) 37.7527 + 35.0283i 1.22229 + 1.13408i
\(955\) 8.29586 14.3689i 0.268448 0.464965i
\(956\) 45.8296 14.1480i 1.48224 0.457578i
\(957\) −1.55934 + 0.874449i −0.0504063 + 0.0282669i
\(958\) 4.21560 + 1.65395i 0.136200 + 0.0534367i
\(959\) 11.7119 66.4215i 0.378197 2.14486i
\(960\) 8.43698 + 22.2684i 0.272302 + 0.718709i
\(961\) −6.80403 + 5.70926i −0.219485 + 0.184170i
\(962\) 36.6672 + 32.3516i 1.18220 + 1.04306i
\(963\) 33.5109 37.9650i 1.07988 1.22341i
\(964\) 4.33555 + 34.5332i 0.139639 + 1.11224i
\(965\) 9.31967 + 3.39208i 0.300011 + 0.109195i
\(966\) 5.03129 12.3663i 0.161879 0.397880i
\(967\) 8.91628 10.6260i 0.286728 0.341709i −0.603384 0.797451i \(-0.706181\pi\)
0.890112 + 0.455741i \(0.150626\pi\)
\(968\) −6.69922 + 26.3471i −0.215321 + 0.846826i
\(969\) 0.966189 2.55464i 0.0310385 0.0820669i
\(970\) 3.74772 + 0.0930360i 0.120332 + 0.00298721i
\(971\) 35.7599i 1.14759i 0.818999 + 0.573795i \(0.194530\pi\)
−0.818999 + 0.573795i \(0.805470\pi\)
\(972\) −8.81796 + 29.9039i −0.282836 + 0.959168i
\(973\) 26.6353i 0.853890i
\(974\) 0.0269391 1.08517i 0.000863185 0.0347712i
\(975\) −6.83525 + 18.0727i −0.218903 + 0.578788i
\(976\) −12.2656 + 25.4995i −0.392613 + 0.816218i
\(977\) −3.44365 + 4.10398i −0.110172 + 0.131298i −0.818312 0.574774i \(-0.805090\pi\)
0.708140 + 0.706072i \(0.249534\pi\)
\(978\) 11.0403 + 4.49179i 0.353030 + 0.143632i
\(979\) 8.99657 + 3.27448i 0.287532 + 0.104653i
\(980\) −6.80572 54.2084i −0.217401 1.73163i
\(981\) 22.2016 25.1525i 0.708841 0.803057i
\(982\) −14.9791 + 16.9773i −0.478003 + 0.541768i
\(983\) −20.2989 + 17.0328i −0.647436 + 0.543263i −0.906292 0.422653i \(-0.861099\pi\)
0.258856 + 0.965916i \(0.416655\pi\)
\(984\) 46.5939 + 32.6051i 1.48536 + 1.03941i
\(985\) −4.32443 + 24.5251i −0.137788 + 0.781433i
\(986\) −0.206147 + 0.525429i −0.00656506 + 0.0167331i
\(987\) −17.5669 + 9.85120i −0.559161 + 0.313567i
\(988\) −11.1295 36.0519i −0.354077 1.14696i
\(989\) 1.05199 1.82209i 0.0334512 0.0579391i
\(990\) 5.84368 6.29819i 0.185724 0.200170i
\(991\) 41.5804 24.0065i 1.32085 0.762590i 0.336982 0.941511i \(-0.390594\pi\)
0.983863 + 0.178921i \(0.0572606\pi\)
\(992\) −7.96920 34.8241i −0.253022 1.10567i
\(993\) 0.993162 + 0.854769i 0.0315170 + 0.0271253i
\(994\) 28.8075 + 36.1150i 0.913719 + 1.14550i
\(995\) 8.39105 + 23.0542i 0.266014 + 0.730868i
\(996\) 36.0948 + 8.70639i 1.14371 + 0.275873i
\(997\) −26.4974 + 4.67220i −0.839180 + 0.147970i −0.576689 0.816964i \(-0.695655\pi\)
−0.262492 + 0.964934i \(0.584544\pi\)
\(998\) −7.94989 + 39.3489i −0.251649 + 1.24557i
\(999\) −1.23727 + 32.9374i −0.0391455 + 1.04209i
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 216.2.v.b.203.1 yes 192
3.2 odd 2 648.2.v.b.395.32 192
4.3 odd 2 864.2.bh.b.527.4 192
8.3 odd 2 inner 216.2.v.b.203.4 yes 192
8.5 even 2 864.2.bh.b.527.3 192
24.11 even 2 648.2.v.b.395.29 192
27.2 odd 18 inner 216.2.v.b.83.4 yes 192
27.25 even 9 648.2.v.b.251.29 192
108.83 even 18 864.2.bh.b.623.3 192
216.29 odd 18 864.2.bh.b.623.4 192
216.83 even 18 inner 216.2.v.b.83.1 192
216.187 odd 18 648.2.v.b.251.32 192
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
216.2.v.b.83.1 192 216.83 even 18 inner
216.2.v.b.83.4 yes 192 27.2 odd 18 inner
216.2.v.b.203.1 yes 192 1.1 even 1 trivial
216.2.v.b.203.4 yes 192 8.3 odd 2 inner
648.2.v.b.251.29 192 27.25 even 9
648.2.v.b.251.32 192 216.187 odd 18
648.2.v.b.395.29 192 24.11 even 2
648.2.v.b.395.32 192 3.2 odd 2
864.2.bh.b.527.3 192 8.5 even 2
864.2.bh.b.527.4 192 4.3 odd 2
864.2.bh.b.623.3 192 108.83 even 18
864.2.bh.b.623.4 192 216.29 odd 18