Properties

Label 273.2.bf.b.152.10
Level $273$
Weight $2$
Character 273.152
Analytic conductor $2.180$
Analytic rank $0$
Dimension $64$
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] = [273,2,Mod(152,273)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(273, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([3, 5, 4]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("273.152");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 273 = 3 \cdot 7 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 273.bf (of order \(6\), degree \(2\), 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: \(2.17991597518\)
Analytic rank: \(0\)
Dimension: \(64\)
Relative dimension: \(32\) over \(\Q(\zeta_{6})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 152.10
Character \(\chi\) \(=\) 273.152
Dual form 273.2.bf.b.185.10

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.21710 + 0.702692i) q^{2} +(1.65544 - 0.509428i) q^{3} +(-0.0124468 + 0.0215586i) q^{4} +(1.48377 - 2.56997i) q^{5} +(-1.65686 + 1.78329i) q^{6} +(-2.30005 - 1.30759i) q^{7} -2.84575i q^{8} +(2.48097 - 1.68666i) q^{9} +O(q^{10})\) \(q+(-1.21710 + 0.702692i) q^{2} +(1.65544 - 0.509428i) q^{3} +(-0.0124468 + 0.0215586i) q^{4} +(1.48377 - 2.56997i) q^{5} +(-1.65686 + 1.78329i) q^{6} +(-2.30005 - 1.30759i) q^{7} -2.84575i q^{8} +(2.48097 - 1.68666i) q^{9} +4.17054i q^{10} -2.71980i q^{11} +(-0.00962246 + 0.0420297i) q^{12} +(-3.51855 - 0.787262i) q^{13} +(3.71822 - 0.0247658i) q^{14} +(1.14708 - 5.01031i) q^{15} +(1.97480 + 3.42045i) q^{16} +(0.233104 - 0.403748i) q^{17} +(-1.83438 + 3.79618i) q^{18} +2.58817i q^{19} +(0.0369366 + 0.0639760i) q^{20} +(-4.47371 - 0.992919i) q^{21} +(1.91119 + 3.31027i) q^{22} +(-2.09876 + 1.21172i) q^{23} +(-1.44971 - 4.71098i) q^{24} +(-1.90316 - 3.29638i) q^{25} +(4.83563 - 1.51429i) q^{26} +(3.24786 - 4.05603i) q^{27} +(0.0568180 - 0.0333104i) q^{28} +(7.22253 + 4.16993i) q^{29} +(2.12459 + 6.90409i) q^{30} +(5.80759 - 3.35302i) q^{31} +(0.121947 + 0.0704059i) q^{32} +(-1.38555 - 4.50247i) q^{33} +0.655201i q^{34} +(-6.77320 + 3.97090i) q^{35} +(0.00548172 + 0.0744796i) q^{36} +(5.67682 + 9.83255i) q^{37} +(-1.81869 - 3.15006i) q^{38} +(-6.22581 + 0.489186i) q^{39} +(-7.31350 - 4.22245i) q^{40} +(4.19212 - 7.26096i) q^{41} +(6.14267 - 1.93516i) q^{42} +(-2.24397 - 3.88666i) q^{43} +(0.0586351 + 0.0338530i) q^{44} +(-0.653469 - 8.87862i) q^{45} +(1.70293 - 2.94956i) q^{46} +(-4.26729 + 7.39117i) q^{47} +(5.01163 + 4.65633i) q^{48} +(3.58044 + 6.01502i) q^{49} +(4.63268 + 2.67468i) q^{50} +(0.180209 - 0.787130i) q^{51} +(0.0607671 - 0.0660560i) q^{52} +(-0.995744 + 0.574893i) q^{53} +(-1.10282 + 7.21884i) q^{54} +(-6.98981 - 4.03557i) q^{55} +(-3.72107 + 6.54537i) q^{56} +(1.31849 + 4.28456i) q^{57} -11.7207 q^{58} +(5.19062 - 8.99042i) q^{59} +(0.0937375 + 0.0870919i) q^{60} +9.12590i q^{61} +(-4.71228 + 8.16190i) q^{62} +(-7.91179 + 0.635319i) q^{63} -8.09708 q^{64} +(-7.24397 + 7.87446i) q^{65} +(4.85020 + 4.50634i) q^{66} +4.45771 q^{67} +(0.00580281 + 0.0100508i) q^{68} +(-2.85708 + 3.07509i) q^{69} +(5.45334 - 9.59245i) q^{70} +(-7.31046 + 4.22070i) q^{71} +(-4.79981 - 7.06022i) q^{72} +(-6.75653 + 3.90088i) q^{73} +(-13.8185 - 7.97812i) q^{74} +(-4.82984 - 4.48743i) q^{75} +(-0.0557973 - 0.0322146i) q^{76} +(-3.55638 + 6.25568i) q^{77} +(7.23368 - 4.97022i) q^{78} +(-1.45705 + 2.52368i) q^{79} +11.7206 q^{80} +(3.31038 - 8.36907i) q^{81} +11.7831i q^{82} -10.6532 q^{83} +(0.0770895 - 0.0840881i) q^{84} +(-0.691746 - 1.19814i) q^{85} +(5.46226 + 3.15364i) q^{86} +(14.0807 + 3.22371i) q^{87} -7.73990 q^{88} +(-3.44068 - 5.95943i) q^{89} +(7.03428 + 10.3470i) q^{90} +(7.06343 + 6.41155i) q^{91} -0.0603282i q^{92} +(7.90600 - 8.50927i) q^{93} -11.9944i q^{94} +(6.65152 + 3.84026i) q^{95} +(0.237742 + 0.0544297i) q^{96} +(8.95629 - 5.17091i) q^{97} +(-8.58446 - 4.80492i) q^{98} +(-4.58738 - 6.74774i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 64 q + 32 q^{4} - 12 q^{6} - 4 q^{7} + 8 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 64 q + 32 q^{4} - 12 q^{6} - 4 q^{7} + 8 q^{9} + 6 q^{12} - 12 q^{13} - 9 q^{15} - 16 q^{16} + 2 q^{18} + 10 q^{21} + 10 q^{22} - 24 q^{25} - 50 q^{28} - 16 q^{30} - 24 q^{31} - 33 q^{39} + 90 q^{40} - 48 q^{42} - 20 q^{43} - 3 q^{45} + 6 q^{48} - 10 q^{51} + 30 q^{52} - 27 q^{54} + 18 q^{55} + 4 q^{57} - 60 q^{58} + 55 q^{60} - 74 q^{63} - 84 q^{64} + 75 q^{66} - 88 q^{67} - 33 q^{69} + 20 q^{70} - 34 q^{72} + 84 q^{73} + 33 q^{75} + 18 q^{76} - 71 q^{78} + 20 q^{79} - 32 q^{81} - 6 q^{84} - 2 q^{85} + 3 q^{87} + 92 q^{88} - 76 q^{91} + 28 q^{93} + 30 q^{96} + 24 q^{97} + 22 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/273\mathbb{Z}\right)^\times\).

\(n\) \(92\) \(106\) \(157\)
\(\chi(n)\) \(-1\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{5}{6}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.21710 + 0.702692i −0.860619 + 0.496879i −0.864219 0.503115i \(-0.832187\pi\)
0.00360060 + 0.999994i \(0.498854\pi\)
\(3\) 1.65544 0.509428i 0.955769 0.294119i
\(4\) −0.0124468 + 0.0215586i −0.00622342 + 0.0107793i
\(5\) 1.48377 2.56997i 0.663563 1.14933i −0.316109 0.948723i \(-0.602377\pi\)
0.979673 0.200603i \(-0.0642900\pi\)
\(6\) −1.65686 + 1.78329i −0.676412 + 0.728025i
\(7\) −2.30005 1.30759i −0.869336 0.494221i
\(8\) 2.84575i 1.00613i
\(9\) 2.48097 1.68666i 0.826988 0.562219i
\(10\) 4.17054i 1.31884i
\(11\) 2.71980i 0.820052i −0.912074 0.410026i \(-0.865520\pi\)
0.912074 0.410026i \(-0.134480\pi\)
\(12\) −0.00962246 + 0.0420297i −0.00277776 + 0.0121329i
\(13\) −3.51855 0.787262i −0.975871 0.218347i
\(14\) 3.71822 0.0247658i 0.993735 0.00661894i
\(15\) 1.14708 5.01031i 0.296175 1.29366i
\(16\) 1.97480 + 3.42045i 0.493699 + 0.855112i
\(17\) 0.233104 0.403748i 0.0565360 0.0979232i −0.836372 0.548162i \(-0.815328\pi\)
0.892908 + 0.450239i \(0.148661\pi\)
\(18\) −1.83438 + 3.79618i −0.432367 + 0.894769i
\(19\) 2.58817i 0.593767i 0.954914 + 0.296884i \(0.0959473\pi\)
−0.954914 + 0.296884i \(0.904053\pi\)
\(20\) 0.0369366 + 0.0639760i 0.00825927 + 0.0143055i
\(21\) −4.47371 0.992919i −0.976244 0.216673i
\(22\) 1.91119 + 3.31027i 0.407466 + 0.705752i
\(23\) −2.09876 + 1.21172i −0.437621 + 0.252661i −0.702588 0.711597i \(-0.747972\pi\)
0.264967 + 0.964257i \(0.414639\pi\)
\(24\) −1.44971 4.71098i −0.295921 0.961624i
\(25\) −1.90316 3.29638i −0.380633 0.659275i
\(26\) 4.83563 1.51429i 0.948345 0.296976i
\(27\) 3.24786 4.05603i 0.625051 0.780584i
\(28\) 0.0568180 0.0333104i 0.0107376 0.00629508i
\(29\) 7.22253 + 4.16993i 1.34119 + 0.774336i 0.986982 0.160830i \(-0.0514172\pi\)
0.354208 + 0.935167i \(0.384751\pi\)
\(30\) 2.12459 + 6.90409i 0.387896 + 1.26051i
\(31\) 5.80759 3.35302i 1.04307 0.602219i 0.122372 0.992484i \(-0.460950\pi\)
0.920703 + 0.390265i \(0.127617\pi\)
\(32\) 0.121947 + 0.0704059i 0.0215573 + 0.0124461i
\(33\) −1.38555 4.50247i −0.241193 0.783780i
\(34\) 0.655201i 0.112366i
\(35\) −6.77320 + 3.97090i −1.14488 + 0.671204i
\(36\) 0.00548172 + 0.0744796i 0.000913620 + 0.0124133i
\(37\) 5.67682 + 9.83255i 0.933264 + 1.61646i 0.777701 + 0.628635i \(0.216386\pi\)
0.155563 + 0.987826i \(0.450281\pi\)
\(38\) −1.81869 3.15006i −0.295030 0.511007i
\(39\) −6.22581 + 0.489186i −0.996927 + 0.0783325i
\(40\) −7.31350 4.22245i −1.15637 0.667629i
\(41\) 4.19212 7.26096i 0.654699 1.13397i −0.327270 0.944931i \(-0.606129\pi\)
0.981969 0.189041i \(-0.0605379\pi\)
\(42\) 6.14267 1.93516i 0.947834 0.298602i
\(43\) −2.24397 3.88666i −0.342202 0.592711i 0.642640 0.766169i \(-0.277839\pi\)
−0.984841 + 0.173458i \(0.944506\pi\)
\(44\) 0.0586351 + 0.0338530i 0.00883957 + 0.00510353i
\(45\) −0.653469 8.87862i −0.0974134 1.32355i
\(46\) 1.70293 2.94956i 0.251083 0.434889i
\(47\) −4.26729 + 7.39117i −0.622448 + 1.07811i 0.366580 + 0.930387i \(0.380529\pi\)
−0.989028 + 0.147726i \(0.952805\pi\)
\(48\) 5.01163 + 4.65633i 0.723367 + 0.672083i
\(49\) 3.58044 + 6.01502i 0.511492 + 0.859288i
\(50\) 4.63268 + 2.67468i 0.655160 + 0.378257i
\(51\) 0.180209 0.787130i 0.0252343 0.110220i
\(52\) 0.0607671 0.0660560i 0.00842688 0.00916032i
\(53\) −0.995744 + 0.574893i −0.136776 + 0.0789676i −0.566827 0.823837i \(-0.691829\pi\)
0.430051 + 0.902805i \(0.358496\pi\)
\(54\) −1.10282 + 7.21884i −0.150075 + 0.982360i
\(55\) −6.98981 4.03557i −0.942506 0.544156i
\(56\) −3.72107 + 6.54537i −0.497248 + 0.874662i
\(57\) 1.31849 + 4.28456i 0.174638 + 0.567504i
\(58\) −11.7207 −1.53900
\(59\) 5.19062 8.99042i 0.675761 1.17045i −0.300485 0.953787i \(-0.597148\pi\)
0.976246 0.216666i \(-0.0695182\pi\)
\(60\) 0.0937375 + 0.0870919i 0.0121015 + 0.0112435i
\(61\) 9.12590i 1.16845i 0.811591 + 0.584226i \(0.198602\pi\)
−0.811591 + 0.584226i \(0.801398\pi\)
\(62\) −4.71228 + 8.16190i −0.598460 + 1.03656i
\(63\) −7.91179 + 0.635319i −0.996791 + 0.0800426i
\(64\) −8.09708 −1.01214
\(65\) −7.24397 + 7.87446i −0.898504 + 0.976706i
\(66\) 4.85020 + 4.50634i 0.597018 + 0.554692i
\(67\) 4.45771 0.544596 0.272298 0.962213i \(-0.412216\pi\)
0.272298 + 0.962213i \(0.412216\pi\)
\(68\) 0.00580281 + 0.0100508i 0.000703695 + 0.00121883i
\(69\) −2.85708 + 3.07509i −0.343952 + 0.370198i
\(70\) 5.45334 9.59245i 0.651799 1.14652i
\(71\) −7.31046 + 4.22070i −0.867593 + 0.500905i −0.866547 0.499095i \(-0.833666\pi\)
−0.00104506 + 0.999999i \(0.500333\pi\)
\(72\) −4.79981 7.06022i −0.565663 0.832055i
\(73\) −6.75653 + 3.90088i −0.790792 + 0.456564i −0.840241 0.542213i \(-0.817587\pi\)
0.0494495 + 0.998777i \(0.484253\pi\)
\(74\) −13.8185 7.97812i −1.60637 0.927438i
\(75\) −4.82984 4.48743i −0.557702 0.518164i
\(76\) −0.0557973 0.0322146i −0.00640038 0.00369526i
\(77\) −3.55638 + 6.25568i −0.405287 + 0.712901i
\(78\) 7.23368 4.97022i 0.819053 0.562766i
\(79\) −1.45705 + 2.52368i −0.163931 + 0.283936i −0.936275 0.351268i \(-0.885751\pi\)
0.772344 + 0.635204i \(0.219084\pi\)
\(80\) 11.7206 1.31040
\(81\) 3.31038 8.36907i 0.367820 0.929897i
\(82\) 11.7831i 1.30122i
\(83\) −10.6532 −1.16934 −0.584671 0.811271i \(-0.698776\pi\)
−0.584671 + 0.811271i \(0.698776\pi\)
\(84\) 0.0770895 0.0840881i 0.00841116 0.00917477i
\(85\) −0.691746 1.19814i −0.0750304 0.129957i
\(86\) 5.46226 + 3.15364i 0.589011 + 0.340065i
\(87\) 14.0807 + 3.22371i 1.50961 + 0.345618i
\(88\) −7.73990 −0.825076
\(89\) −3.44068 5.95943i −0.364711 0.631699i 0.624018 0.781410i \(-0.285499\pi\)
−0.988730 + 0.149711i \(0.952166\pi\)
\(90\) 7.03428 + 10.3470i 0.741478 + 1.09067i
\(91\) 7.06343 + 6.41155i 0.740449 + 0.672113i
\(92\) 0.0603282i 0.00628965i
\(93\) 7.90600 8.50927i 0.819814 0.882370i
\(94\) 11.9944i 1.23713i
\(95\) 6.65152 + 3.84026i 0.682432 + 0.394002i
\(96\) 0.237742 + 0.0544297i 0.0242644 + 0.00555521i
\(97\) 8.95629 5.17091i 0.909373 0.525027i 0.0291437 0.999575i \(-0.490722\pi\)
0.880229 + 0.474548i \(0.157389\pi\)
\(98\) −8.58446 4.80492i −0.867161 0.485370i
\(99\) −4.58738 6.74774i −0.461049 0.678173i
\(100\) 0.0947535 0.00947535
\(101\) −6.64640 −0.661341 −0.330671 0.943746i \(-0.607275\pi\)
−0.330671 + 0.943746i \(0.607275\pi\)
\(102\) 0.333778 + 1.08465i 0.0330490 + 0.107396i
\(103\) 7.72448 + 4.45973i 0.761116 + 0.439431i 0.829696 0.558215i \(-0.188514\pi\)
−0.0685803 + 0.997646i \(0.521847\pi\)
\(104\) −2.24035 + 10.0129i −0.219685 + 0.981850i
\(105\) −9.18975 + 10.0240i −0.896827 + 0.978246i
\(106\) 0.807946 1.39940i 0.0784746 0.135922i
\(107\) −0.100989 + 0.0583060i −0.00976297 + 0.00563666i −0.504874 0.863193i \(-0.668461\pi\)
0.495111 + 0.868830i \(0.335128\pi\)
\(108\) 0.0470167 + 0.120504i 0.00452418 + 0.0115955i
\(109\) −2.10015 3.63757i −0.201158 0.348416i 0.747744 0.663987i \(-0.231137\pi\)
−0.948902 + 0.315572i \(0.897804\pi\)
\(110\) 11.3431 1.08152
\(111\) 14.4066 + 13.3853i 1.36742 + 1.27047i
\(112\) −0.0696000 10.4494i −0.00657659 0.987376i
\(113\) 11.1270 6.42418i 1.04674 0.604336i 0.125005 0.992156i \(-0.460105\pi\)
0.921735 + 0.387820i \(0.126772\pi\)
\(114\) −4.61546 4.28825i −0.432277 0.401631i
\(115\) 7.19165i 0.670625i
\(116\) −0.179795 + 0.103805i −0.0166936 + 0.00963804i
\(117\) −10.0572 + 3.98142i −0.929793 + 0.368083i
\(118\) 14.5896i 1.34308i
\(119\) −1.06408 + 0.623836i −0.0975445 + 0.0571870i
\(120\) −14.2581 3.26431i −1.30158 0.297990i
\(121\) 3.60267 0.327515
\(122\) −6.41270 11.1071i −0.580578 1.00559i
\(123\) 3.24086 14.1557i 0.292219 1.27637i
\(124\) 0.166938i 0.0149915i
\(125\) 3.54228 0.316831
\(126\) 9.18299 6.33280i 0.818086 0.564170i
\(127\) −0.679843 + 1.17752i −0.0603263 + 0.104488i −0.894611 0.446845i \(-0.852547\pi\)
0.834285 + 0.551333i \(0.185881\pi\)
\(128\) 9.61105 5.54895i 0.849505 0.490462i
\(129\) −5.69473 5.29100i −0.501393 0.465847i
\(130\) 3.28331 14.6743i 0.287965 1.28702i
\(131\) 5.82910 10.0963i 0.509291 0.882118i −0.490651 0.871356i \(-0.663241\pi\)
0.999942 0.0107620i \(-0.00342571\pi\)
\(132\) 0.114313 + 0.0261712i 0.00994963 + 0.00227791i
\(133\) 3.38425 5.95292i 0.293452 0.516184i
\(134\) −5.42548 + 3.13240i −0.468690 + 0.270598i
\(135\) −5.60480 14.3651i −0.482385 1.23635i
\(136\) −1.14897 0.663356i −0.0985231 0.0568823i
\(137\) 1.10479 + 0.637851i 0.0943887 + 0.0544953i 0.546451 0.837491i \(-0.315978\pi\)
−0.452063 + 0.891986i \(0.649312\pi\)
\(138\) 1.31651 5.75034i 0.112069 0.489502i
\(139\) 3.59002 2.07270i 0.304501 0.175804i −0.339962 0.940439i \(-0.610414\pi\)
0.644463 + 0.764635i \(0.277081\pi\)
\(140\) −0.00130180 0.195446i −0.000110022 0.0165182i
\(141\) −3.29898 + 14.4095i −0.277824 + 1.21350i
\(142\) 5.93171 10.2740i 0.497778 0.862176i
\(143\) −2.14120 + 9.56978i −0.179056 + 0.800265i
\(144\) 10.6685 + 5.15521i 0.889044 + 0.429601i
\(145\) 21.4332 12.3745i 1.77993 1.02764i
\(146\) 5.48224 9.49552i 0.453714 0.785855i
\(147\) 8.99143 + 8.13352i 0.741601 + 0.670842i
\(148\) −0.282634 −0.0232324
\(149\) 12.4970i 1.02380i 0.859046 + 0.511899i \(0.171058\pi\)
−0.859046 + 0.511899i \(0.828942\pi\)
\(150\) 9.03168 + 2.06775i 0.737433 + 0.168831i
\(151\) 2.63468 + 4.56339i 0.214407 + 0.371364i 0.953089 0.302690i \(-0.0978848\pi\)
−0.738682 + 0.674054i \(0.764552\pi\)
\(152\) 7.36530 0.597405
\(153\) −0.102661 1.39485i −0.00829968 0.112767i
\(154\) −0.0673581 10.1128i −0.00542787 0.814914i
\(155\) 19.9005i 1.59844i
\(156\) 0.0669455 0.140308i 0.00535993 0.0112337i
\(157\) −0.305705 + 0.176499i −0.0243979 + 0.0140861i −0.512149 0.858896i \(-0.671151\pi\)
0.487751 + 0.872983i \(0.337817\pi\)
\(158\) 4.09542i 0.325814i
\(159\) −1.35553 + 1.45896i −0.107500 + 0.115703i
\(160\) 0.361882 0.208933i 0.0286093 0.0165176i
\(161\) 6.41166 0.0427060i 0.505310 0.00336570i
\(162\) 1.85183 + 12.5122i 0.145493 + 0.983049i
\(163\) −23.7010 −1.85641 −0.928205 0.372070i \(-0.878648\pi\)
−0.928205 + 0.372070i \(0.878648\pi\)
\(164\) 0.104357 + 0.180752i 0.00814894 + 0.0141144i
\(165\) −13.6271 3.11984i −1.06086 0.242879i
\(166\) 12.9660 7.48593i 1.00636 0.581021i
\(167\) 1.87878 3.25415i 0.145385 0.251814i −0.784132 0.620594i \(-0.786891\pi\)
0.929516 + 0.368781i \(0.120225\pi\)
\(168\) −2.82560 + 12.7311i −0.218000 + 0.982225i
\(169\) 11.7604 + 5.54005i 0.904649 + 0.426157i
\(170\) 1.68385 + 0.972170i 0.129145 + 0.0745620i
\(171\) 4.36536 + 6.42116i 0.333827 + 0.491039i
\(172\) 0.111721 0.00851866
\(173\) 4.23157 0.321720 0.160860 0.986977i \(-0.448573\pi\)
0.160860 + 0.986977i \(0.448573\pi\)
\(174\) −19.4029 + 5.97086i −1.47093 + 0.452650i
\(175\) 0.0670754 + 10.0704i 0.00507042 + 0.761249i
\(176\) 9.30295 5.37106i 0.701236 0.404859i
\(177\) 4.01279 17.5273i 0.301619 1.31744i
\(178\) 8.37530 + 4.83548i 0.627755 + 0.362435i
\(179\) 1.00129i 0.0748401i −0.999300 0.0374201i \(-0.988086\pi\)
0.999300 0.0374201i \(-0.0119140\pi\)
\(180\) 0.199544 + 0.0964230i 0.0148731 + 0.00718694i
\(181\) 4.63844i 0.344773i −0.985029 0.172386i \(-0.944852\pi\)
0.985029 0.172386i \(-0.0551477\pi\)
\(182\) −13.1022 2.84007i −0.971203 0.210520i
\(183\) 4.64899 + 15.1074i 0.343663 + 1.11677i
\(184\) 3.44825 + 5.97255i 0.254208 + 0.440302i
\(185\) 33.6925 2.47712
\(186\) −3.64299 + 15.9121i −0.267117 + 1.16673i
\(187\) −1.09811 0.633997i −0.0803021 0.0463624i
\(188\) −0.106229 0.183993i −0.00774752 0.0134191i
\(189\) −12.7738 + 5.08222i −0.929160 + 0.369677i
\(190\) −10.7941 −0.783085
\(191\) 2.70485i 0.195716i 0.995200 + 0.0978581i \(0.0311991\pi\)
−0.995200 + 0.0978581i \(0.968801\pi\)
\(192\) −13.4042 + 4.12488i −0.967367 + 0.297688i
\(193\) −24.2731 −1.74722 −0.873608 0.486631i \(-0.838226\pi\)
−0.873608 + 0.486631i \(0.838226\pi\)
\(194\) −7.26712 + 12.5870i −0.521749 + 0.903696i
\(195\) −7.98049 + 16.7260i −0.571495 + 1.19777i
\(196\) −0.174240 + 0.00232122i −0.0124457 + 0.000165801i
\(197\) −6.13256 3.54064i −0.436927 0.252260i 0.265366 0.964148i \(-0.414507\pi\)
−0.702293 + 0.711888i \(0.747840\pi\)
\(198\) 10.3249 + 4.98915i 0.733757 + 0.354564i
\(199\) −16.6686 9.62360i −1.18160 0.682199i −0.225218 0.974308i \(-0.572310\pi\)
−0.956385 + 0.292109i \(0.905643\pi\)
\(200\) −9.38068 + 5.41594i −0.663314 + 0.382965i
\(201\) 7.37948 2.27089i 0.520508 0.160176i
\(202\) 8.08932 4.67037i 0.569163 0.328606i
\(203\) −11.1596 19.0351i −0.783252 1.33600i
\(204\) 0.0147264 + 0.0136823i 0.00103105 + 0.000957955i
\(205\) −12.4403 21.5472i −0.868869 1.50492i
\(206\) −12.5353 −0.873374
\(207\) −3.16319 + 6.54611i −0.219857 + 0.454986i
\(208\) −4.25564 13.5897i −0.295075 0.942277i
\(209\) 7.03932 0.486920
\(210\) 4.14101 18.6578i 0.285757 1.28751i
\(211\) −11.6667 + 20.2073i −0.803169 + 1.39113i 0.114351 + 0.993440i \(0.463521\pi\)
−0.917520 + 0.397690i \(0.869812\pi\)
\(212\) 0.0286224i 0.00196580i
\(213\) −9.95189 + 10.7113i −0.681893 + 0.733924i
\(214\) 0.0819424 0.141928i 0.00560147 0.00970203i
\(215\) −13.3181 −0.908290
\(216\) −11.5425 9.24261i −0.785366 0.628880i
\(217\) −17.7421 + 0.118174i −1.20441 + 0.00802219i
\(218\) 5.11218 + 2.95152i 0.346240 + 0.199902i
\(219\) −9.19781 + 9.89965i −0.621530 + 0.668956i
\(220\) 0.174002 0.100460i 0.0117312 0.00677303i
\(221\) −1.13804 + 1.23709i −0.0765531 + 0.0832160i
\(222\) −26.9400 6.16776i −1.80809 0.413953i
\(223\) 4.43230 + 2.55899i 0.296809 + 0.171363i 0.641008 0.767534i \(-0.278516\pi\)
−0.344200 + 0.938897i \(0.611850\pi\)
\(224\) −0.188421 0.321392i −0.0125894 0.0214739i
\(225\) −10.2815 4.96821i −0.685436 0.331214i
\(226\) −9.02844 + 15.6377i −0.600563 + 1.04021i
\(227\) −11.5535 + 20.0112i −0.766832 + 1.32819i 0.172441 + 0.985020i \(0.444835\pi\)
−0.939273 + 0.343172i \(0.888499\pi\)
\(228\) −0.108780 0.0249046i −0.00720413 0.00164935i
\(229\) 21.6165 + 12.4803i 1.42846 + 0.824720i 0.996999 0.0774125i \(-0.0246658\pi\)
0.431458 + 0.902133i \(0.357999\pi\)
\(230\) −5.05352 8.75295i −0.333219 0.577153i
\(231\) −2.70055 + 12.1676i −0.177683 + 0.800571i
\(232\) 11.8666 20.5535i 0.779080 1.34941i
\(233\) 10.3307 + 5.96443i 0.676787 + 0.390743i 0.798643 0.601805i \(-0.205551\pi\)
−0.121857 + 0.992548i \(0.538885\pi\)
\(234\) 9.44295 11.9129i 0.617305 0.778773i
\(235\) 12.6634 + 21.9336i 0.826068 + 1.43079i
\(236\) 0.129214 + 0.223805i 0.00841109 + 0.0145684i
\(237\) −1.12642 + 4.92006i −0.0731689 + 0.319592i
\(238\) 0.856731 1.50699i 0.0555336 0.0976839i
\(239\) 10.2941i 0.665868i −0.942950 0.332934i \(-0.891961\pi\)
0.942950 0.332934i \(-0.108039\pi\)
\(240\) 19.4027 5.97081i 1.25244 0.385414i
\(241\) 13.7616 + 7.94527i 0.886464 + 0.511800i 0.872784 0.488106i \(-0.162312\pi\)
0.0136795 + 0.999906i \(0.495646\pi\)
\(242\) −4.38480 + 2.53157i −0.281866 + 0.162735i
\(243\) 1.21669 15.5409i 0.0780505 0.996949i
\(244\) −0.196741 0.113589i −0.0125951 0.00727177i
\(245\) 20.7710 0.276709i 1.32701 0.0176783i
\(246\) 6.00264 + 19.5062i 0.382714 + 1.24367i
\(247\) 2.03757 9.10662i 0.129647 0.579440i
\(248\) −9.54186 16.5270i −0.605909 1.04946i
\(249\) −17.6358 + 5.42705i −1.11762 + 0.343925i
\(250\) −4.31130 + 2.48913i −0.272671 + 0.157426i
\(251\) 8.02838 + 13.9056i 0.506747 + 0.877712i 0.999970 + 0.00780844i \(0.00248553\pi\)
−0.493222 + 0.869903i \(0.664181\pi\)
\(252\) 0.0847802 0.178474i 0.00534065 0.0112428i
\(253\) 3.29563 + 5.70821i 0.207195 + 0.358872i
\(254\) 1.91088i 0.119899i
\(255\) −1.75551 1.63105i −0.109934 0.102141i
\(256\) 0.298678 0.517325i 0.0186674 0.0323328i
\(257\) 5.49333 + 9.51472i 0.342664 + 0.593512i 0.984927 0.172973i \(-0.0553373\pi\)
−0.642262 + 0.766485i \(0.722004\pi\)
\(258\) 10.6490 + 2.43803i 0.662978 + 0.151785i
\(259\) −0.200075 30.0383i −0.0124320 1.86649i
\(260\) −0.0795974 0.254182i −0.00493642 0.0157637i
\(261\) 24.9521 1.83648i 1.54450 0.113675i
\(262\) 16.3843i 1.01222i
\(263\) 6.93143i 0.427410i 0.976898 + 0.213705i \(0.0685532\pi\)
−0.976898 + 0.213705i \(0.931447\pi\)
\(264\) −12.8129 + 3.94292i −0.788582 + 0.242670i
\(265\) 3.41204i 0.209600i
\(266\) 0.0640981 + 9.62338i 0.00393011 + 0.590047i
\(267\) −8.73175 8.11271i −0.534374 0.496490i
\(268\) −0.0554844 + 0.0961019i −0.00338925 + 0.00587036i
\(269\) −3.57872 + 6.19852i −0.218198 + 0.377931i −0.954257 0.298987i \(-0.903351\pi\)
0.736059 + 0.676918i \(0.236685\pi\)
\(270\) 16.9159 + 13.5453i 1.02947 + 0.824343i
\(271\) 12.1343 7.00577i 0.737109 0.425570i −0.0839081 0.996473i \(-0.526740\pi\)
0.821017 + 0.570903i \(0.193407\pi\)
\(272\) 1.84133 0.111647
\(273\) 14.9593 + 7.01562i 0.905379 + 0.424605i
\(274\) −1.79285 −0.108310
\(275\) −8.96550 + 5.17623i −0.540640 + 0.312139i
\(276\) −0.0307329 0.0998698i −0.00184990 0.00601145i
\(277\) 11.8084 20.4527i 0.709497 1.22888i −0.255547 0.966797i \(-0.582256\pi\)
0.965044 0.262088i \(-0.0844111\pi\)
\(278\) −2.91294 + 5.04536i −0.174706 + 0.302600i
\(279\) 8.75305 18.1141i 0.524031 1.08446i
\(280\) 11.3002 + 19.2749i 0.675316 + 1.15189i
\(281\) 16.8039i 1.00244i 0.865320 + 0.501219i \(0.167115\pi\)
−0.865320 + 0.501219i \(0.832885\pi\)
\(282\) −6.11027 19.8560i −0.363862 1.18241i
\(283\) 8.94217i 0.531557i −0.964034 0.265778i \(-0.914371\pi\)
0.964034 0.265778i \(-0.0856289\pi\)
\(284\) 0.210137i 0.0124694i
\(285\) 12.9675 + 2.96884i 0.768131 + 0.175859i
\(286\) −4.11856 13.1520i −0.243536 0.777692i
\(287\) −19.1364 + 11.2190i −1.12959 + 0.662237i
\(288\) 0.421296 0.0310075i 0.0248251 0.00182713i
\(289\) 8.39133 + 14.5342i 0.493607 + 0.854953i
\(290\) −17.3909 + 30.1219i −1.02123 + 1.76882i
\(291\) 12.1924 13.1227i 0.714730 0.769268i
\(292\) 0.194215i 0.0113656i
\(293\) −8.37506 14.5060i −0.489277 0.847452i 0.510647 0.859790i \(-0.329406\pi\)
−0.999924 + 0.0123385i \(0.996072\pi\)
\(294\) −16.6588 3.58109i −0.971562 0.208854i
\(295\) −15.4034 26.6795i −0.896821 1.55334i
\(296\) 27.9810 16.1548i 1.62636 0.938981i
\(297\) −11.0316 8.83354i −0.640119 0.512574i
\(298\) −8.78157 15.2101i −0.508703 0.881099i
\(299\) 8.33853 2.61122i 0.482229 0.151011i
\(300\) 0.156859 0.0482701i 0.00905625 0.00278688i
\(301\) 0.0790867 + 11.8737i 0.00455848 + 0.684388i
\(302\) −6.41332 3.70273i −0.369045 0.213068i
\(303\) −11.0027 + 3.38586i −0.632089 + 0.194513i
\(304\) −8.85271 + 5.11111i −0.507737 + 0.293142i
\(305\) 23.4533 + 13.5408i 1.34293 + 0.775342i
\(306\) 1.10510 + 1.62553i 0.0631743 + 0.0929254i
\(307\) 2.98509i 0.170368i −0.996365 0.0851842i \(-0.972852\pi\)
0.996365 0.0851842i \(-0.0271479\pi\)
\(308\) −0.0905978 0.154534i −0.00516229 0.00880538i
\(309\) 15.0593 + 3.44775i 0.856696 + 0.196136i
\(310\) 13.9839 + 24.2208i 0.794232 + 1.37565i
\(311\) −1.42109 2.46141i −0.0805828 0.139574i 0.822918 0.568161i \(-0.192345\pi\)
−0.903500 + 0.428587i \(0.859011\pi\)
\(312\) 1.39210 + 17.7171i 0.0788124 + 1.00303i
\(313\) −7.32752 4.23055i −0.414176 0.239125i 0.278406 0.960463i \(-0.410194\pi\)
−0.692582 + 0.721339i \(0.743527\pi\)
\(314\) 0.248049 0.429633i 0.0139982 0.0242456i
\(315\) −10.1065 + 21.2757i −0.569439 + 1.19875i
\(316\) −0.0362713 0.0628237i −0.00204042 0.00353411i
\(317\) −24.6025 14.2043i −1.38182 0.797792i −0.389442 0.921051i \(-0.627332\pi\)
−0.992375 + 0.123259i \(0.960666\pi\)
\(318\) 0.624610 2.72822i 0.0350264 0.152991i
\(319\) 11.3414 19.6439i 0.634996 1.09985i
\(320\) −12.0142 + 20.8093i −0.671616 + 1.16327i
\(321\) −0.137479 + 0.147969i −0.00767330 + 0.00825881i
\(322\) −7.77362 + 4.55741i −0.433207 + 0.253974i
\(323\) 1.04497 + 0.603313i 0.0581436 + 0.0335692i
\(324\) 0.139221 + 0.175536i 0.00773453 + 0.00975197i
\(325\) 4.10127 + 13.0968i 0.227498 + 0.726478i
\(326\) 28.8465 16.6545i 1.59766 0.922410i
\(327\) −5.32975 4.95190i −0.294736 0.273841i
\(328\) −20.6629 11.9297i −1.14092 0.658710i
\(329\) 19.4796 11.4202i 1.07394 0.629615i
\(330\) 18.7778 5.77848i 1.03368 0.318095i
\(331\) −24.7098 −1.35817 −0.679086 0.734059i \(-0.737624\pi\)
−0.679086 + 0.734059i \(0.737624\pi\)
\(332\) 0.132599 0.229668i 0.00727731 0.0126047i
\(333\) 30.6681 + 14.8194i 1.68060 + 0.812095i
\(334\) 5.28083i 0.288954i
\(335\) 6.61423 11.4562i 0.361374 0.625918i
\(336\) −5.43845 17.2629i −0.296692 0.941769i
\(337\) −4.13151 −0.225057 −0.112529 0.993648i \(-0.535895\pi\)
−0.112529 + 0.993648i \(0.535895\pi\)
\(338\) −18.2066 + 1.52119i −0.990307 + 0.0827416i
\(339\) 15.1474 16.3033i 0.822695 0.885471i
\(340\) 0.0344402 0.00186778
\(341\) −9.11954 15.7955i −0.493851 0.855375i
\(342\) −9.82517 4.74769i −0.531285 0.256726i
\(343\) −0.370042 18.5166i −0.0199804 0.999800i
\(344\) −11.0605 + 6.38578i −0.596342 + 0.344298i
\(345\) 3.66363 + 11.9054i 0.197243 + 0.640963i
\(346\) −5.15024 + 2.97349i −0.276878 + 0.159856i
\(347\) −8.01426 4.62703i −0.430228 0.248392i 0.269216 0.963080i \(-0.413236\pi\)
−0.699444 + 0.714688i \(0.746569\pi\)
\(348\) −0.244759 + 0.263436i −0.0131205 + 0.0141216i
\(349\) 7.84315 + 4.52825i 0.419834 + 0.242391i 0.695006 0.719004i \(-0.255402\pi\)
−0.275172 + 0.961395i \(0.588735\pi\)
\(350\) −7.15801 12.2095i −0.382612 0.652626i
\(351\) −14.6209 + 11.7145i −0.780407 + 0.625272i
\(352\) 0.191490 0.331671i 0.0102065 0.0176781i
\(353\) 11.7797 0.626968 0.313484 0.949593i \(-0.398504\pi\)
0.313484 + 0.949593i \(0.398504\pi\)
\(354\) 7.43238 + 24.1523i 0.395026 + 1.28368i
\(355\) 25.0502i 1.32953i
\(356\) 0.171302 0.00907901
\(357\) −1.44373 + 1.57480i −0.0764102 + 0.0833472i
\(358\) 0.703600 + 1.21867i 0.0371864 + 0.0644088i
\(359\) −1.14560 0.661413i −0.0604625 0.0349080i 0.469464 0.882952i \(-0.344447\pi\)
−0.529927 + 0.848044i \(0.677780\pi\)
\(360\) −25.2664 + 1.85961i −1.33166 + 0.0980102i
\(361\) 12.3014 0.647440
\(362\) 3.25940 + 5.64544i 0.171310 + 0.296718i
\(363\) 5.96400 1.83530i 0.313029 0.0963283i
\(364\) −0.226141 + 0.0724739i −0.0118530 + 0.00379866i
\(365\) 23.1521i 1.21184i
\(366\) −16.2741 15.1204i −0.850662 0.790354i
\(367\) 5.82994i 0.304320i −0.988356 0.152160i \(-0.951377\pi\)
0.988356 0.152160i \(-0.0486230\pi\)
\(368\) −8.28923 4.78579i −0.432106 0.249477i
\(369\) −1.84625 25.0849i −0.0961120 1.30587i
\(370\) −41.0071 + 23.6754i −2.13186 + 1.23083i
\(371\) 3.04198 0.0202616i 0.157932 0.00105193i
\(372\) 0.0850429 + 0.276356i 0.00440927 + 0.0143284i
\(373\) 3.23740 0.167626 0.0838130 0.996482i \(-0.473290\pi\)
0.0838130 + 0.996482i \(0.473290\pi\)
\(374\) 1.78202 0.0921460
\(375\) 5.86403 1.80454i 0.302817 0.0931859i
\(376\) 21.0334 + 12.1437i 1.08472 + 0.626262i
\(377\) −22.1300 20.3581i −1.13975 1.04850i
\(378\) 11.9758 15.1616i 0.615968 0.779831i
\(379\) −11.8507 + 20.5261i −0.608731 + 1.05435i 0.382719 + 0.923865i \(0.374988\pi\)
−0.991450 + 0.130488i \(0.958346\pi\)
\(380\) −0.165581 + 0.0955982i −0.00849412 + 0.00490408i
\(381\) −0.525576 + 2.29565i −0.0269261 + 0.117610i
\(382\) −1.90068 3.29207i −0.0972472 0.168437i
\(383\) −35.5991 −1.81903 −0.909515 0.415671i \(-0.863547\pi\)
−0.909515 + 0.415671i \(0.863547\pi\)
\(384\) 13.0837 14.0821i 0.667677 0.718624i
\(385\) 10.8001 + 18.4218i 0.550422 + 0.938861i
\(386\) 29.5428 17.0565i 1.50369 0.868154i
\(387\) −12.1227 5.85788i −0.616230 0.297773i
\(388\) 0.257446i 0.0130699i
\(389\) −0.288306 + 0.166454i −0.0146177 + 0.00843954i −0.507291 0.861775i \(-0.669353\pi\)
0.492673 + 0.870214i \(0.336020\pi\)
\(390\) −2.04017 25.9650i −0.103308 1.31479i
\(391\) 1.12982i 0.0571377i
\(392\) 17.1173 10.1891i 0.864552 0.514625i
\(393\) 4.50639 19.6833i 0.227317 0.992893i
\(394\) 9.95192 0.501370
\(395\) 4.32385 + 7.48913i 0.217557 + 0.376819i
\(396\) 0.202570 0.0149092i 0.0101795 0.000749215i
\(397\) 29.6338i 1.48728i 0.668581 + 0.743639i \(0.266902\pi\)
−0.668581 + 0.743639i \(0.733098\pi\)
\(398\) 27.0497 1.35588
\(399\) 2.56984 11.5787i 0.128653 0.579662i
\(400\) 7.51672 13.0193i 0.375836 0.650967i
\(401\) −8.55524 + 4.93937i −0.427228 + 0.246660i −0.698165 0.715937i \(-0.746000\pi\)
0.270937 + 0.962597i \(0.412667\pi\)
\(402\) −7.38582 + 7.94939i −0.368371 + 0.396480i
\(403\) −23.0740 + 7.22567i −1.14940 + 0.359936i
\(404\) 0.0827267 0.143287i 0.00411581 0.00712878i
\(405\) −16.5964 20.9254i −0.824683 1.03979i
\(406\) 26.9582 + 15.3258i 1.33791 + 0.760608i
\(407\) 26.7426 15.4398i 1.32558 0.765325i
\(408\) −2.23998 0.512830i −0.110895 0.0253889i
\(409\) 2.89726 + 1.67273i 0.143260 + 0.0827113i 0.569917 0.821702i \(-0.306975\pi\)
−0.426657 + 0.904414i \(0.640309\pi\)
\(410\) 30.2822 + 17.4834i 1.49553 + 0.863444i
\(411\) 2.15385 + 0.493113i 0.106242 + 0.0243235i
\(412\) −0.192291 + 0.111019i −0.00947349 + 0.00546952i
\(413\) −23.6944 + 13.8912i −1.16593 + 0.683542i
\(414\) −0.749988 10.1900i −0.0368599 0.500812i
\(415\) −15.8069 + 27.3784i −0.775932 + 1.34395i
\(416\) −0.373648 0.343731i −0.0183196 0.0168528i
\(417\) 4.88717 5.26009i 0.239326 0.257588i
\(418\) −8.56755 + 4.94648i −0.419052 + 0.241940i
\(419\) 7.87912 13.6470i 0.384920 0.666702i −0.606838 0.794826i \(-0.707562\pi\)
0.991758 + 0.128124i \(0.0408956\pi\)
\(420\) −0.101721 0.322885i −0.00496346 0.0157552i
\(421\) −1.57179 −0.0766041 −0.0383021 0.999266i \(-0.512195\pi\)
−0.0383021 + 0.999266i \(0.512195\pi\)
\(422\) 32.7924i 1.59631i
\(423\) 1.87936 + 25.5347i 0.0913776 + 1.24154i
\(424\) 1.63600 + 2.83364i 0.0794514 + 0.137614i
\(425\) −1.77454 −0.0860778
\(426\) 4.58571 20.0298i 0.222178 0.970447i
\(427\) 11.9329 20.9900i 0.577473 1.01578i
\(428\) 0.00290290i 0.000140317i
\(429\) 1.33049 + 16.9330i 0.0642367 + 0.817532i
\(430\) 16.2095 9.35856i 0.781692 0.451310i
\(431\) 35.3995i 1.70514i 0.522617 + 0.852568i \(0.324956\pi\)
−0.522617 + 0.852568i \(0.675044\pi\)
\(432\) 20.2873 + 3.09929i 0.976074 + 0.149115i
\(433\) 31.5305 18.2041i 1.51526 0.874834i 0.515417 0.856939i \(-0.327637\pi\)
0.999840 0.0178948i \(-0.00569638\pi\)
\(434\) 21.5108 12.6111i 1.03255 0.605350i
\(435\) 29.1775 31.4038i 1.39895 1.50570i
\(436\) 0.104561 0.00500756
\(437\) −3.13613 5.43194i −0.150022 0.259845i
\(438\) 4.23823 18.5121i 0.202511 0.884541i
\(439\) −28.2871 + 16.3316i −1.35007 + 0.779464i −0.988259 0.152786i \(-0.951175\pi\)
−0.361813 + 0.932251i \(0.617842\pi\)
\(440\) −11.4842 + 19.8913i −0.547490 + 0.948280i
\(441\) 19.0282 + 8.88407i 0.906106 + 0.423051i
\(442\) 0.515815 2.30536i 0.0245348 0.109655i
\(443\) −4.64059 2.67925i −0.220481 0.127295i 0.385692 0.922628i \(-0.373963\pi\)
−0.606173 + 0.795333i \(0.707296\pi\)
\(444\) −0.467884 + 0.143982i −0.0222048 + 0.00683308i
\(445\) −20.4208 −0.968037
\(446\) −7.19273 −0.340586
\(447\) 6.36635 + 20.6881i 0.301118 + 0.978514i
\(448\) 18.6237 + 10.5876i 0.879886 + 0.500218i
\(449\) −25.3524 + 14.6372i −1.19645 + 0.690774i −0.959763 0.280811i \(-0.909397\pi\)
−0.236692 + 0.971585i \(0.576063\pi\)
\(450\) 16.0048 1.17796i 0.754472 0.0555294i
\(451\) −19.7484 11.4017i −0.929916 0.536887i
\(452\) 0.319843i 0.0150441i
\(453\) 6.68627 + 6.21224i 0.314148 + 0.291877i
\(454\) 32.4742i 1.52409i
\(455\) 26.9580 8.63952i 1.26381 0.405027i
\(456\) 12.1928 3.75209i 0.570981 0.175708i
\(457\) 15.6657 + 27.1338i 0.732812 + 1.26927i 0.955677 + 0.294418i \(0.0951257\pi\)
−0.222865 + 0.974849i \(0.571541\pi\)
\(458\) −35.0792 −1.63914
\(459\) −0.880526 2.25679i −0.0410994 0.105338i
\(460\) −0.155042 0.0895134i −0.00722886 0.00417358i
\(461\) −2.74375 4.75231i −0.127789 0.221337i 0.795031 0.606569i \(-0.207455\pi\)
−0.922820 + 0.385232i \(0.874121\pi\)
\(462\) −5.26327 16.7069i −0.244869 0.777273i
\(463\) 10.4977 0.487870 0.243935 0.969792i \(-0.421562\pi\)
0.243935 + 0.969792i \(0.421562\pi\)
\(464\) 32.9390i 1.52916i
\(465\) −10.1379 32.9440i −0.470132 1.52774i
\(466\) −16.7646 −0.776607
\(467\) 6.11729 10.5955i 0.283075 0.490299i −0.689066 0.724699i \(-0.741979\pi\)
0.972140 + 0.234399i \(0.0753123\pi\)
\(468\) 0.0393472 0.266376i 0.00181883 0.0123132i
\(469\) −10.2530 5.82884i −0.473437 0.269151i
\(470\) −30.8252 17.7969i −1.42186 0.820911i
\(471\) −0.416162 + 0.447918i −0.0191758 + 0.0206390i
\(472\) −25.5845 14.7712i −1.17762 0.679901i
\(473\) −10.5710 + 6.10315i −0.486054 + 0.280623i
\(474\) −2.08633 6.77973i −0.0958281 0.311403i
\(475\) 8.53159 4.92571i 0.391456 0.226007i
\(476\) −0.000204515 0.0307049i −9.37394e−6 0.00140736i
\(477\) −1.50076 + 3.10577i −0.0687150 + 0.142203i
\(478\) 7.23357 + 12.5289i 0.330856 + 0.573059i
\(479\) 15.7699 0.720544 0.360272 0.932847i \(-0.382684\pi\)
0.360272 + 0.932847i \(0.382684\pi\)
\(480\) 0.492638 0.530228i 0.0224857 0.0242015i
\(481\) −12.2334 39.0655i −0.557796 1.78123i
\(482\) −22.3323 −1.01721
\(483\) 10.5924 3.33698i 0.481970 0.151838i
\(484\) −0.0448418 + 0.0776683i −0.00203826 + 0.00353038i
\(485\) 30.6899i 1.39355i
\(486\) 9.43965 + 19.7698i 0.428191 + 0.896775i
\(487\) −12.4868 + 21.6278i −0.565833 + 0.980051i 0.431139 + 0.902285i \(0.358112\pi\)
−0.996972 + 0.0777654i \(0.975221\pi\)
\(488\) 25.9701 1.17561
\(489\) −39.2357 + 12.0740i −1.77430 + 0.546005i
\(490\) −25.0859 + 14.9324i −1.13327 + 0.674577i
\(491\) −36.6633 21.1676i −1.65459 0.955280i −0.975148 0.221552i \(-0.928888\pi\)
−0.679444 0.733727i \(-0.737779\pi\)
\(492\) 0.264838 + 0.246062i 0.0119398 + 0.0110933i
\(493\) 3.36720 1.94405i 0.151651 0.0875557i
\(494\) 3.91923 + 12.5154i 0.176334 + 0.563096i
\(495\) −24.1481 + 1.77731i −1.08538 + 0.0798840i
\(496\) 22.9376 + 13.2430i 1.02993 + 0.594630i
\(497\) 22.3333 0.148755i 1.00179 0.00667257i
\(498\) 17.6509 18.9978i 0.790956 0.851310i
\(499\) 4.70714 8.15301i 0.210721 0.364979i −0.741220 0.671263i \(-0.765752\pi\)
0.951940 + 0.306284i \(0.0990856\pi\)
\(500\) −0.0440902 + 0.0763664i −0.00197177 + 0.00341521i
\(501\) 1.45246 6.34415i 0.0648910 0.283436i
\(502\) −19.5427 11.2830i −0.872232 0.503583i
\(503\) 4.94844 + 8.57095i 0.220640 + 0.382160i 0.955003 0.296598i \(-0.0958520\pi\)
−0.734362 + 0.678758i \(0.762519\pi\)
\(504\) 1.80796 + 22.5150i 0.0805330 + 1.00290i
\(505\) −9.86174 + 17.0810i −0.438842 + 0.760096i
\(506\) −8.02223 4.63163i −0.356631 0.205901i
\(507\) 22.2910 + 3.18011i 0.989976 + 0.141234i
\(508\) −0.0169238 0.0293129i −0.000750872 0.00130055i
\(509\) −15.9736 27.6670i −0.708015 1.22632i −0.965592 0.260061i \(-0.916257\pi\)
0.257577 0.966258i \(-0.417076\pi\)
\(510\) 3.28276 + 0.751569i 0.145363 + 0.0332800i
\(511\) 20.6411 0.137483i 0.913107 0.00608190i
\(512\) 23.0353i 1.01803i
\(513\) 10.4977 + 8.40602i 0.463485 + 0.371135i
\(514\) −13.3718 7.72024i −0.589807 0.340525i
\(515\) 22.9228 13.2345i 1.01010 0.583180i
\(516\) 0.184948 0.0569140i 0.00814187 0.00250550i
\(517\) 20.1025 + 11.6062i 0.884108 + 0.510440i
\(518\) 21.3512 + 36.4189i 0.938116 + 1.60016i
\(519\) 7.00511 2.15568i 0.307490 0.0946239i
\(520\) 22.4088 + 20.6146i 0.982690 + 0.904009i
\(521\) 1.58017 + 2.73693i 0.0692283 + 0.119907i 0.898562 0.438847i \(-0.144613\pi\)
−0.829333 + 0.558754i \(0.811280\pi\)
\(522\) −29.0787 + 19.7688i −1.27274 + 0.865257i
\(523\) −9.19469 + 5.30855i −0.402056 + 0.232127i −0.687371 0.726307i \(-0.741235\pi\)
0.285315 + 0.958434i \(0.407902\pi\)
\(524\) 0.145108 + 0.251334i 0.00633907 + 0.0109796i
\(525\) 5.24117 + 16.6367i 0.228744 + 0.726087i
\(526\) −4.87066 8.43624i −0.212371 0.367837i
\(527\) 3.12640i 0.136188i
\(528\) 12.6643 13.6307i 0.551143 0.593198i
\(529\) −8.56348 + 14.8324i −0.372325 + 0.644886i
\(530\) −2.39762 4.15279i −0.104146 0.180386i
\(531\) −2.28600 31.0597i −0.0992040 1.34788i
\(532\) 0.0862131 + 0.147055i 0.00373781 + 0.00637563i
\(533\) −20.4665 + 22.2478i −0.886501 + 0.963659i
\(534\) 16.3281 + 3.73823i 0.706588 + 0.161769i
\(535\) 0.346052i 0.0149611i
\(536\) 12.6856i 0.547933i
\(537\) −0.510087 1.65758i −0.0220119 0.0715298i
\(538\) 10.0590i 0.433672i
\(539\) 16.3597 9.73810i 0.704661 0.419450i
\(540\) 0.379454 + 0.0579691i 0.0163291 + 0.00249459i
\(541\) 10.0471 17.4021i 0.431958 0.748173i −0.565084 0.825034i \(-0.691156\pi\)
0.997042 + 0.0768601i \(0.0244895\pi\)
\(542\) −9.84580 + 17.0534i −0.422913 + 0.732507i
\(543\) −2.36295 7.67866i −0.101404 0.329523i
\(544\) 0.0568524 0.0328238i 0.00243753 0.00140731i
\(545\) −12.4646 −0.533924
\(546\) −23.1368 + 1.97309i −0.990163 + 0.0844404i
\(547\) 18.0920 0.773556 0.386778 0.922173i \(-0.373588\pi\)
0.386778 + 0.922173i \(0.373588\pi\)
\(548\) −0.0275023 + 0.0158785i −0.00117484 + 0.000678295i
\(549\) 15.3923 + 22.6410i 0.656926 + 0.966296i
\(550\) 7.27460 12.6000i 0.310190 0.537265i
\(551\) −10.7925 + 18.6931i −0.459776 + 0.796355i
\(552\) 8.75096 + 8.13056i 0.372466 + 0.346059i
\(553\) 6.65120 3.89937i 0.282838 0.165818i
\(554\) 33.1906i 1.41014i
\(555\) 55.7759 17.1639i 2.36755 0.728567i
\(556\) 0.103194i 0.00437641i
\(557\) 32.7781i 1.38885i −0.719563 0.694427i \(-0.755658\pi\)
0.719563 0.694427i \(-0.244342\pi\)
\(558\) 2.07533 + 28.1974i 0.0878559 + 1.19369i
\(559\) 4.83569 + 15.4420i 0.204528 + 0.653128i
\(560\) −26.9579 15.3257i −1.13918 0.647628i
\(561\) −2.14084 0.490133i −0.0903863 0.0206934i
\(562\) −11.8080 20.4521i −0.498090 0.862718i
\(563\) 9.35180 16.1978i 0.394131 0.682656i −0.598859 0.800855i \(-0.704379\pi\)
0.992990 + 0.118199i \(0.0377122\pi\)
\(564\) −0.269587 0.250474i −0.0113516 0.0105469i
\(565\) 38.1281i 1.60406i
\(566\) 6.28359 + 10.8835i 0.264119 + 0.457468i
\(567\) −18.5573 + 14.9207i −0.779333 + 0.626609i
\(568\) 12.0111 + 20.8038i 0.503973 + 0.872908i
\(569\) 2.94338 1.69936i 0.123393 0.0712408i −0.437033 0.899445i \(-0.643971\pi\)
0.560426 + 0.828205i \(0.310637\pi\)
\(570\) −17.8690 + 5.49881i −0.748448 + 0.230320i
\(571\) 4.29368 + 7.43687i 0.179685 + 0.311224i 0.941773 0.336250i \(-0.109159\pi\)
−0.762088 + 0.647474i \(0.775825\pi\)
\(572\) −0.179659 0.165275i −0.00751194 0.00691048i
\(573\) 1.37793 + 4.47772i 0.0575638 + 0.187060i
\(574\) 15.4074 27.1017i 0.643092 1.13120i
\(575\) 7.98855 + 4.61219i 0.333146 + 0.192342i
\(576\) −20.0886 + 13.6570i −0.837024 + 0.569042i
\(577\) −19.0273 + 10.9854i −0.792117 + 0.457329i −0.840707 0.541490i \(-0.817860\pi\)
0.0485903 + 0.998819i \(0.484527\pi\)
\(578\) −20.4261 11.7930i −0.849616 0.490526i
\(579\) −40.1827 + 12.3654i −1.66993 + 0.513889i
\(580\) 0.616092i 0.0255818i
\(581\) 24.5029 + 13.9300i 1.01655 + 0.577913i
\(582\) −5.61810 + 24.5392i −0.232878 + 1.01718i
\(583\) 1.56360 + 2.70823i 0.0647575 + 0.112163i
\(584\) 11.1010 + 19.2274i 0.459361 + 0.795636i
\(585\) −4.69054 + 31.7544i −0.193930 + 1.31288i
\(586\) 20.3866 + 11.7702i 0.842161 + 0.486222i
\(587\) −21.5356 + 37.3007i −0.888868 + 1.53956i −0.0476531 + 0.998864i \(0.515174\pi\)
−0.841215 + 0.540701i \(0.818159\pi\)
\(588\) −0.287262 + 0.0926056i −0.0118465 + 0.00381899i
\(589\) 8.67818 + 15.0310i 0.357578 + 0.619343i
\(590\) 37.4949 + 21.6477i 1.54364 + 0.891222i
\(591\) −11.9558 2.73721i −0.491796 0.112594i
\(592\) −22.4211 + 38.8346i −0.921503 + 1.59609i
\(593\) 15.2562 26.4245i 0.626498 1.08513i −0.361752 0.932274i \(-0.617821\pi\)
0.988249 0.152851i \(-0.0488455\pi\)
\(594\) 19.6338 + 2.99946i 0.805586 + 0.123069i
\(595\) 0.0243800 + 3.66030i 0.000999483 + 0.150058i
\(596\) −0.269418 0.155549i −0.0110358 0.00637152i
\(597\) −32.4964 7.43985i −1.32999 0.304493i
\(598\) −8.31392 + 9.03753i −0.339982 + 0.369572i
\(599\) −22.8836 + 13.2118i −0.934998 + 0.539821i −0.888389 0.459092i \(-0.848175\pi\)
−0.0466090 + 0.998913i \(0.514841\pi\)
\(600\) −12.7701 + 13.7445i −0.521338 + 0.561119i
\(601\) −32.5373 18.7854i −1.32722 0.766272i −0.342353 0.939571i \(-0.611224\pi\)
−0.984869 + 0.173299i \(0.944557\pi\)
\(602\) −8.43981 14.3959i −0.343981 0.586732i
\(603\) 11.0594 7.51863i 0.450375 0.306182i
\(604\) −0.131174 −0.00533738
\(605\) 5.34554 9.25874i 0.217327 0.376421i
\(606\) 11.0122 11.8525i 0.447339 0.481473i
\(607\) 0.974616i 0.0395585i 0.999804 + 0.0197792i \(0.00629633\pi\)
−0.999804 + 0.0197792i \(0.993704\pi\)
\(608\) −0.182222 + 0.315619i −0.00739010 + 0.0128000i
\(609\) −28.1711 25.8265i −1.14155 1.04654i
\(610\) −38.0599 −1.54100
\(611\) 20.8335 22.6467i 0.842832 0.916189i
\(612\) 0.0313488 + 0.0151483i 0.00126720 + 0.000612332i
\(613\) 0.0794798 0.00321016 0.00160508 0.999999i \(-0.499489\pi\)
0.00160508 + 0.999999i \(0.499489\pi\)
\(614\) 2.09760 + 3.63316i 0.0846524 + 0.146622i
\(615\) −31.5710 29.3327i −1.27306 1.18281i
\(616\) 17.8021 + 10.1206i 0.717268 + 0.407769i
\(617\) −8.99665 + 5.19422i −0.362192 + 0.209111i −0.670042 0.742323i \(-0.733724\pi\)
0.307850 + 0.951435i \(0.400390\pi\)
\(618\) −20.7514 + 6.38583i −0.834744 + 0.256876i
\(619\) 34.3765 19.8473i 1.38171 0.797729i 0.389346 0.921092i \(-0.372701\pi\)
0.992362 + 0.123362i \(0.0393678\pi\)
\(620\) 0.429025 + 0.247698i 0.0172301 + 0.00994778i
\(621\) −1.90170 + 12.4481i −0.0763124 + 0.499526i
\(622\) 3.45922 + 1.99718i 0.138702 + 0.0800797i
\(623\) 0.121264 + 18.2060i 0.00485834 + 0.729407i
\(624\) −13.9679 20.3290i −0.559165 0.813812i
\(625\) 14.7718 25.5854i 0.590870 1.02342i
\(626\) 11.8911 0.475263
\(627\) 11.6532 3.58603i 0.465383 0.143212i
\(628\) 0.00878741i 0.000350656i
\(629\) 5.29316 0.211052
\(630\) −2.64962 32.9965i −0.105564 1.31461i
\(631\) −22.2297 38.5030i −0.884952 1.53278i −0.845769 0.533550i \(-0.820858\pi\)
−0.0391833 0.999232i \(-0.512476\pi\)
\(632\) 7.18177 + 4.14640i 0.285676 + 0.164935i
\(633\) −9.01935 + 39.3954i −0.358487 + 1.56583i
\(634\) 39.9250 1.58562
\(635\) 2.01746 + 3.49435i 0.0800606 + 0.138669i
\(636\) −0.0145811 0.0473827i −0.000578177 0.00187885i
\(637\) −7.86258 23.9829i −0.311527 0.950237i
\(638\) 31.8780i 1.26206i
\(639\) −11.0181 + 22.8017i −0.435871 + 0.902019i
\(640\) 32.9335i 1.30181i
\(641\) −22.5064 12.9941i −0.888950 0.513235i −0.0153508 0.999882i \(-0.504887\pi\)
−0.873599 + 0.486647i \(0.838220\pi\)
\(642\) 0.0633484 0.276698i 0.00250016 0.0109204i
\(643\) 6.96396 4.02064i 0.274632 0.158559i −0.356359 0.934349i \(-0.615982\pi\)
0.630991 + 0.775790i \(0.282649\pi\)
\(644\) −0.0788843 + 0.138758i −0.00310848 + 0.00546782i
\(645\) −22.0474 + 6.78464i −0.868116 + 0.267145i
\(646\) −1.69577 −0.0667193
\(647\) 19.5481 0.768516 0.384258 0.923226i \(-0.374457\pi\)
0.384258 + 0.923226i \(0.374457\pi\)
\(648\) −23.8163 9.42052i −0.935594 0.370073i
\(649\) −24.4522 14.1175i −0.959832 0.554159i
\(650\) −14.1947 13.0581i −0.556760 0.512182i
\(651\) −29.3108 + 9.23396i −1.14878 + 0.361907i
\(652\) 0.295003 0.510961i 0.0115532 0.0200108i
\(653\) −31.6753 + 18.2877i −1.23955 + 0.715654i −0.969002 0.247053i \(-0.920538\pi\)
−0.270547 + 0.962707i \(0.587205\pi\)
\(654\) 9.96650 + 2.28177i 0.389721 + 0.0892244i
\(655\) −17.2981 29.9612i −0.675894 1.17068i
\(656\) 33.1143 1.29290
\(657\) −10.1833 + 21.0739i −0.397287 + 0.822171i
\(658\) −15.6837 + 27.5876i −0.611413 + 1.07548i
\(659\) 24.3137 14.0375i 0.947126 0.546824i 0.0549393 0.998490i \(-0.482503\pi\)
0.892187 + 0.451666i \(0.149170\pi\)
\(660\) 0.236873 0.254948i 0.00922027 0.00992382i
\(661\) 0.894387i 0.0347876i −0.999849 0.0173938i \(-0.994463\pi\)
0.999849 0.0173938i \(-0.00553690\pi\)
\(662\) 30.0742 17.3634i 1.16887 0.674847i
\(663\) −1.25375 + 2.62769i −0.0486917 + 0.102051i
\(664\) 30.3164i 1.17651i
\(665\) −10.2774 17.5302i −0.398539 0.679792i
\(666\) −47.7396 + 3.51365i −1.84987 + 0.136151i
\(667\) −20.2111 −0.782577
\(668\) 0.0467698 + 0.0810077i 0.00180958 + 0.00313428i
\(669\) 8.64103 + 1.97832i 0.334082 + 0.0764861i
\(670\) 18.5911i 0.718236i
\(671\) 24.8207 0.958191
\(672\) −0.475647 0.436059i −0.0183485 0.0168213i
\(673\) −14.0268 + 24.2951i −0.540692 + 0.936506i 0.458172 + 0.888863i \(0.348504\pi\)
−0.998864 + 0.0476430i \(0.984829\pi\)
\(674\) 5.02845 2.90318i 0.193689 0.111826i
\(675\) −19.5514 2.98687i −0.752535 0.114965i
\(676\) −0.265816 + 0.184582i −0.0102237 + 0.00709931i
\(677\) 16.0687 27.8319i 0.617572 1.06967i −0.372356 0.928090i \(-0.621450\pi\)
0.989927 0.141575i \(-0.0452168\pi\)
\(678\) −6.97974 + 30.4867i −0.268055 + 1.17083i
\(679\) −27.3613 + 0.182245i −1.05003 + 0.00699390i
\(680\) −3.40961 + 1.96854i −0.130753 + 0.0754901i
\(681\) −8.93182 + 39.0131i −0.342268 + 1.49498i
\(682\) 22.1988 + 12.8165i 0.850035 + 0.490768i
\(683\) 20.7123 + 11.9583i 0.792535 + 0.457570i 0.840854 0.541262i \(-0.182053\pi\)
−0.0483193 + 0.998832i \(0.515387\pi\)
\(684\) −0.192766 + 0.0141876i −0.00737059 + 0.000542477i
\(685\) 3.27852 1.89285i 0.125266 0.0723222i
\(686\) 13.4618 + 22.2765i 0.513975 + 0.850519i
\(687\) 42.1426 + 9.64831i 1.60784 + 0.368106i
\(688\) 8.86276 15.3507i 0.337889 0.585242i
\(689\) 3.95617 1.23888i 0.150718 0.0471976i
\(690\) −12.8248 11.9156i −0.488232 0.453619i
\(691\) 41.3896 23.8963i 1.57454 0.909059i 0.578934 0.815375i \(-0.303469\pi\)
0.995602 0.0936839i \(-0.0298643\pi\)
\(692\) −0.0526697 + 0.0912265i −0.00200220 + 0.00346791i
\(693\) 1.72794 + 21.5185i 0.0656391 + 0.817421i
\(694\) 13.0055 0.493683
\(695\) 12.3017i 0.466628i
\(696\) 9.17388 40.0703i 0.347735 1.51886i
\(697\) −1.95440 3.38512i −0.0740281 0.128220i
\(698\) −12.7279 −0.481756
\(699\) 20.1403 + 4.61101i 0.761776 + 0.174404i
\(700\) −0.217938 0.123898i −0.00823727 0.00468292i
\(701\) 6.73334i 0.254315i 0.991883 + 0.127157i \(0.0405853\pi\)
−0.991883 + 0.127157i \(0.959415\pi\)
\(702\) 9.56345 24.5317i 0.360949 0.925888i
\(703\) −25.4483 + 14.6926i −0.959801 + 0.554142i
\(704\) 22.0225i 0.830003i
\(705\) 32.1371 + 29.8587i 1.21035 + 1.12454i
\(706\) −14.3370 + 8.27748i −0.539581 + 0.311527i
\(707\) 15.2870 + 8.69073i 0.574928 + 0.326849i
\(708\) 0.327918 + 0.304670i 0.0123239 + 0.0114502i
\(709\) −38.0202 −1.42788 −0.713939 0.700208i \(-0.753091\pi\)
−0.713939 + 0.700208i \(0.753091\pi\)
\(710\) −17.6026 30.4886i −0.660614 1.14422i
\(711\) 0.641698 + 8.71870i 0.0240656 + 0.326977i
\(712\) −16.9591 + 9.79133i −0.635569 + 0.366946i
\(713\) −8.12581 + 14.0743i −0.304314 + 0.527088i
\(714\) 0.650562 2.93118i 0.0243467 0.109697i
\(715\) 21.4170 + 19.7022i 0.800950 + 0.736820i
\(716\) 0.0215864 + 0.0124629i 0.000806723 + 0.000465762i
\(717\) −5.24409 17.0412i −0.195844 0.636416i
\(718\) 1.85908 0.0693802
\(719\) −24.6301 −0.918549 −0.459275 0.888294i \(-0.651891\pi\)
−0.459275 + 0.888294i \(0.651891\pi\)
\(720\) 29.0784 19.7686i 1.08369 0.736733i
\(721\) −11.9352 20.3580i −0.444490 0.758172i
\(722\) −14.9720 + 8.64408i −0.557199 + 0.321699i
\(723\) 26.8291 + 6.14237i 0.997784 + 0.228437i
\(724\) 0.0999981 + 0.0577340i 0.00371640 + 0.00214567i
\(725\) 31.7442i 1.17895i
\(726\) −5.96912 + 6.42460i −0.221535 + 0.238439i
\(727\) 6.39426i 0.237150i 0.992945 + 0.118575i \(0.0378326\pi\)
−0.992945 + 0.118575i \(0.962167\pi\)
\(728\) 18.2457 20.1008i 0.676230 0.744985i
\(729\) −5.90283 26.3469i −0.218623 0.975809i
\(730\) −16.2688 28.1784i −0.602135 1.04293i
\(731\) −2.09231 −0.0773869
\(732\) −0.383559 0.0878136i −0.0141767 0.00324568i
\(733\) 19.2593 + 11.1194i 0.711359 + 0.410703i 0.811564 0.584263i \(-0.198616\pi\)
−0.100205 + 0.994967i \(0.531950\pi\)
\(734\) 4.09665 + 7.09561i 0.151210 + 0.261904i
\(735\) 34.2441 11.0394i 1.26311 0.407195i
\(736\) −0.341248 −0.0125786
\(737\) 12.1241i 0.446597i
\(738\) 19.8740 + 29.2334i 0.731573 + 1.07610i
\(739\) 23.2140 0.853940 0.426970 0.904266i \(-0.359581\pi\)
0.426970 + 0.904266i \(0.359581\pi\)
\(740\) −0.419365 + 0.726361i −0.0154162 + 0.0267016i
\(741\) −1.26610 16.1135i −0.0465113 0.591943i
\(742\) −3.68815 + 2.16224i −0.135396 + 0.0793782i
\(743\) −13.9525 8.05548i −0.511867 0.295527i 0.221734 0.975107i \(-0.428828\pi\)
−0.733601 + 0.679581i \(0.762162\pi\)
\(744\) −24.2153 22.4985i −0.887776 0.824837i
\(745\) 32.1170 + 18.5428i 1.17668 + 0.679354i
\(746\) −3.94023 + 2.27489i −0.144262 + 0.0832897i
\(747\) −26.4302 + 17.9683i −0.967032 + 0.657426i
\(748\) 0.0273361 0.0157825i 0.000999508 0.000577066i
\(749\) 0.308520 0.00205495i 0.0112731 7.50861e-5i
\(750\) −5.86907 + 6.31691i −0.214308 + 0.230661i
\(751\) 3.91086 + 6.77381i 0.142709 + 0.247180i 0.928516 0.371292i \(-0.121085\pi\)
−0.785807 + 0.618472i \(0.787752\pi\)
\(752\) −33.7081 −1.22921
\(753\) 20.3744 + 18.9300i 0.742484 + 0.689846i
\(754\) 41.2399 + 9.22727i 1.50187 + 0.336037i
\(755\) 15.6370 0.569090
\(756\) 0.0494286 0.338643i 0.00179770 0.0123163i
\(757\) 25.1290 43.5247i 0.913329 1.58193i 0.104001 0.994577i \(-0.466836\pi\)
0.809329 0.587356i \(-0.199831\pi\)
\(758\) 33.3097i 1.20986i
\(759\) 8.36365 + 7.77070i 0.303581 + 0.282059i
\(760\) 10.9284 18.9286i 0.396416 0.686613i
\(761\) −14.4623 −0.524258 −0.262129 0.965033i \(-0.584425\pi\)
−0.262129 + 0.965033i \(0.584425\pi\)
\(762\) −0.973457 3.16335i −0.0352646 0.114596i
\(763\) 0.0740180 + 11.1127i 0.00267963 + 0.402307i
\(764\) −0.0583127 0.0336669i −0.00210968 0.00121802i
\(765\) −3.73705 1.80580i −0.135113 0.0652890i
\(766\) 43.3277 25.0152i 1.56549 0.903837i
\(767\) −25.3413 + 27.5469i −0.915021 + 0.994660i
\(768\) 0.230903 1.00856i 0.00833200 0.0363931i
\(769\) −17.5980 10.1602i −0.634602 0.366388i 0.147930 0.988998i \(-0.452739\pi\)
−0.782532 + 0.622610i \(0.786072\pi\)
\(770\) −26.0896 14.8320i −0.940203 0.534509i
\(771\) 13.9409 + 12.9526i 0.502071 + 0.466476i
\(772\) 0.302123 0.523293i 0.0108737 0.0188337i
\(773\) 19.9457 34.5469i 0.717397 1.24257i −0.244631 0.969616i \(-0.578667\pi\)
0.962028 0.272951i \(-0.0879998\pi\)
\(774\) 18.8708 1.38889i 0.678296 0.0499228i
\(775\) −22.1056 12.7627i −0.794057 0.458449i
\(776\) −14.7152 25.4874i −0.528243 0.914944i
\(777\) −15.6336 49.6246i −0.560851 1.78027i
\(778\) 0.233931 0.405181i 0.00838685 0.0145265i
\(779\) 18.7926 + 10.8499i 0.673315 + 0.388739i
\(780\) −0.261256 0.380234i −0.00935447 0.0136145i
\(781\) 11.4795 + 19.8830i 0.410768 + 0.711471i
\(782\) −0.793919 1.37511i −0.0283905 0.0491738i
\(783\) 40.3711 15.7515i 1.44275 0.562912i
\(784\) −13.5034 + 24.1252i −0.482265 + 0.861613i
\(785\) 1.04754i 0.0373882i
\(786\) 8.34661 + 27.1232i 0.297714 + 0.967452i
\(787\) −4.19300 2.42083i −0.149464 0.0862933i 0.423403 0.905942i \(-0.360836\pi\)
−0.572867 + 0.819648i \(0.694169\pi\)
\(788\) 0.152662 0.0881395i 0.00543836 0.00313984i
\(789\) 3.53107 + 11.4746i 0.125709 + 0.408506i
\(790\) −10.5251 6.07668i −0.374467 0.216199i
\(791\) −33.9928 + 0.226415i −1.20864 + 0.00805038i
\(792\) −19.2024 + 13.0545i −0.682328 + 0.463873i
\(793\) 7.18447 32.1100i 0.255128 1.14026i
\(794\) −20.8234 36.0673i −0.738996 1.27998i
\(795\) 1.73819 + 5.64843i 0.0616473 + 0.200329i
\(796\) 0.414942 0.239567i 0.0147072 0.00849122i
\(797\) 22.9572 + 39.7631i 0.813187 + 1.40848i 0.910623 + 0.413239i \(0.135603\pi\)
−0.0974358 + 0.995242i \(0.531064\pi\)
\(798\) 5.00853 + 15.8983i 0.177300 + 0.562793i
\(799\) 1.98944 + 3.44582i 0.0703815 + 0.121904i
\(800\) 0.535976i 0.0189496i
\(801\) −18.5877 8.98190i −0.656765 0.317360i
\(802\) 6.94172 12.0234i 0.245120 0.424561i
\(803\) 10.6096 + 18.3764i 0.374406 + 0.648490i
\(804\) −0.0428941 + 0.187356i −0.00151276 + 0.00660755i
\(805\) 9.40370 16.5412i 0.331437 0.582999i
\(806\) 23.0060 25.0083i 0.810350 0.880880i
\(807\) −2.76665 + 12.0844i −0.0973908 + 0.425391i
\(808\) 18.9140i 0.665393i
\(809\) 33.0727i 1.16278i 0.813627 + 0.581388i \(0.197490\pi\)
−0.813627 + 0.581388i \(0.802510\pi\)
\(810\) 34.9036 + 13.8061i 1.22639 + 0.485096i
\(811\) 26.0753i 0.915629i 0.889048 + 0.457815i \(0.151368\pi\)
−0.889048 + 0.457815i \(0.848632\pi\)
\(812\) 0.549272 0.00365852i 0.0192757 0.000128389i
\(813\) 16.5188 17.7792i 0.579338 0.623544i
\(814\) −21.6989 + 37.5836i −0.760547 + 1.31731i
\(815\) −35.1670 + 60.9110i −1.23185 + 2.13362i
\(816\) 3.04821 0.938026i 0.106709 0.0328375i
\(817\) 10.0594 5.80777i 0.351932 0.203188i
\(818\) −4.70166 −0.164390
\(819\) 28.3382 + 3.99325i 0.990217 + 0.139535i
\(820\) 0.619370 0.0216293
\(821\) −36.8176 + 21.2566i −1.28494 + 0.741862i −0.977747 0.209785i \(-0.932723\pi\)
−0.307194 + 0.951647i \(0.599390\pi\)
\(822\) −2.96796 + 0.913330i −0.103520 + 0.0318561i
\(823\) 13.4898 23.3651i 0.470226 0.814455i −0.529194 0.848501i \(-0.677506\pi\)
0.999420 + 0.0340454i \(0.0108391\pi\)
\(824\) 12.6913 21.9820i 0.442123 0.765779i
\(825\) −12.2049 + 13.1362i −0.424921 + 0.457345i
\(826\) 19.0772 33.5569i 0.663780 1.16759i
\(827\) 25.9887i 0.903716i −0.892090 0.451858i \(-0.850761\pi\)
0.892090 0.451858i \(-0.149239\pi\)
\(828\) −0.101753 0.149672i −0.00353616 0.00520147i
\(829\) 7.73524i 0.268656i −0.990937 0.134328i \(-0.957112\pi\)
0.990937 0.134328i \(-0.0428876\pi\)
\(830\) 44.4297i 1.54218i
\(831\) 9.12888 39.8738i 0.316677 1.38321i
\(832\) 28.4900 + 6.37452i 0.987713 + 0.220997i
\(833\) 3.26316 0.0434716i 0.113062 0.00150620i
\(834\) −2.25195 + 9.83622i −0.0779785 + 0.340601i
\(835\) −5.57538 9.65683i −0.192944 0.334189i
\(836\) −0.0876173 + 0.151758i −0.00303031 + 0.00524865i
\(837\) 5.26230 34.4459i 0.181892 1.19062i
\(838\) 22.1464i 0.765035i
\(839\) −0.385592 0.667865i −0.0133121 0.0230573i 0.859293 0.511484i \(-0.170904\pi\)
−0.872605 + 0.488427i \(0.837571\pi\)
\(840\) 28.5260 + 26.1518i 0.984239 + 0.902322i
\(841\) 20.2766 + 35.1201i 0.699193 + 1.21104i
\(842\) 1.91302 1.10448i 0.0659270 0.0380630i
\(843\) 8.56040 + 27.8179i 0.294836 + 0.958100i
\(844\) −0.290427 0.503035i −0.00999692 0.0173152i
\(845\) 31.6876 22.0038i 1.09009 0.756954i
\(846\) −20.2304 29.7576i −0.695535 1.02309i
\(847\) −8.28630 4.71079i −0.284721 0.161865i
\(848\) −3.93278 2.27059i −0.135052 0.0779725i
\(849\) −4.55539 14.8032i −0.156341 0.508045i
\(850\) 2.15979 1.24696i 0.0740802 0.0427702i
\(851\) −23.8285 13.7574i −0.816832 0.471598i
\(852\) −0.107050 0.347870i −0.00366747 0.0119178i
\(853\) 8.91797i 0.305346i −0.988277 0.152673i \(-0.951212\pi\)
0.988277 0.152673i \(-0.0487881\pi\)
\(854\) 0.226010 + 33.9321i 0.00773391 + 1.16113i
\(855\) 22.9794 1.69129i 0.785879 0.0578409i
\(856\) 0.165925 + 0.287390i 0.00567119 + 0.00982278i
\(857\) −10.6106 18.3781i −0.362451 0.627783i 0.625913 0.779893i \(-0.284727\pi\)
−0.988364 + 0.152110i \(0.951393\pi\)
\(858\) −13.5180 19.6742i −0.461497 0.671666i
\(859\) −19.4014 11.2014i −0.661967 0.382187i 0.131059 0.991375i \(-0.458162\pi\)
−0.793026 + 0.609188i \(0.791496\pi\)
\(860\) 0.165769 0.287120i 0.00565267 0.00979072i
\(861\) −25.9639 + 28.3210i −0.884847 + 0.965178i
\(862\) −24.8750 43.0847i −0.847245 1.46747i
\(863\) 21.5282 + 12.4293i 0.732830 + 0.423099i 0.819456 0.573141i \(-0.194275\pi\)
−0.0866268 + 0.996241i \(0.527609\pi\)
\(864\) 0.681634 0.265951i 0.0231897 0.00904784i
\(865\) 6.27869 10.8750i 0.213482 0.369761i
\(866\) −25.5838 + 44.3124i −0.869373 + 1.50580i
\(867\) 21.2955 + 19.7857i 0.723232 + 0.671958i
\(868\) 0.218285 0.383965i 0.00740909 0.0130326i
\(869\) 6.86391 + 3.96288i 0.232842 + 0.134432i
\(870\) −13.4446 + 58.7244i −0.455815 + 1.99094i
\(871\) −15.6847 3.50939i −0.531456 0.118911i
\(872\) −10.3516 + 5.97651i −0.350550 + 0.202390i
\(873\) 13.4987 27.9350i 0.456861 0.945458i
\(874\) 7.63397 + 4.40747i 0.258223 + 0.149085i
\(875\) −8.14741 4.63183i −0.275433 0.156584i
\(876\) −0.0989385 0.321511i −0.00334282 0.0108628i
\(877\) −13.5131 −0.456304 −0.228152 0.973625i \(-0.573268\pi\)
−0.228152 + 0.973625i \(0.573268\pi\)
\(878\) 22.9522 39.7543i 0.774598 1.34164i
\(879\) −21.2542 19.7474i −0.716887 0.666063i
\(880\) 31.8777i 1.07460i
\(881\) −12.9595 + 22.4465i −0.436616 + 0.756240i −0.997426 0.0717039i \(-0.977156\pi\)
0.560810 + 0.827944i \(0.310490\pi\)
\(882\) −29.4020 + 2.55819i −0.990017 + 0.0861389i
\(883\) 18.4111 0.619582 0.309791 0.950805i \(-0.399741\pi\)
0.309791 + 0.950805i \(0.399741\pi\)
\(884\) −0.0125049 0.0399325i −0.000420586 0.00134308i
\(885\) −39.0907 36.3193i −1.31402 1.22086i
\(886\) 7.53075 0.253001
\(887\) 16.2068 + 28.0711i 0.544173 + 0.942535i 0.998658 + 0.0517808i \(0.0164897\pi\)
−0.454486 + 0.890754i \(0.650177\pi\)
\(888\) 38.0912 40.9977i 1.27826 1.37579i
\(889\) 3.10338 1.81940i 0.104084 0.0610209i
\(890\) 24.8541 14.3495i 0.833111 0.480997i
\(891\) −22.7622 9.00358i −0.762564 0.301631i
\(892\) −0.110336 + 0.0637027i −0.00369433 + 0.00213292i
\(893\) −19.1296 11.0445i −0.640148 0.369589i
\(894\) −22.2858 20.7059i −0.745350 0.692508i
\(895\) −2.57329 1.48569i −0.0860156 0.0496612i
\(896\) −29.3616 + 0.195568i −0.980902 + 0.00653346i
\(897\) 12.4737 8.57061i 0.416485 0.286164i
\(898\) 20.5709 35.6299i 0.686461 1.18899i
\(899\) 55.9273 1.86528
\(900\) 0.235080 0.159817i 0.00783601 0.00532722i
\(901\) 0.536039i 0.0178581i
\(902\) 32.0477 1.06707
\(903\) 6.17972 + 19.6159i 0.205648 + 0.652776i
\(904\) −18.2816 31.6647i −0.608038 1.05315i
\(905\) −11.9207 6.88239i −0.396256 0.228779i
\(906\) −12.5031 2.86252i −0.415389 0.0951010i
\(907\) 13.4248 0.445763 0.222881 0.974846i \(-0.428454\pi\)
0.222881 + 0.974846i \(0.428454\pi\)
\(908\) −0.287609 0.498153i −0.00954464 0.0165318i
\(909\) −16.4895 + 11.2102i −0.546922 + 0.371819i
\(910\) −26.7396 + 29.4583i −0.886411 + 0.976535i
\(911\) 14.3638i 0.475892i 0.971278 + 0.237946i \(0.0764742\pi\)
−0.971278 + 0.237946i \(0.923526\pi\)
\(912\) −12.0514 + 12.9710i −0.399061 + 0.429511i
\(913\) 28.9746i 0.958921i
\(914\) −38.1335 22.0164i −1.26134 0.728237i
\(915\) 45.7236 + 10.4681i 1.51157 + 0.346066i
\(916\) −0.538114 + 0.310680i −0.0177798 + 0.0102652i
\(917\) −26.6090 + 15.5999i −0.878707 + 0.515155i
\(918\) 2.65752 + 2.12800i 0.0877112 + 0.0702345i
\(919\) 0.613513 0.0202379 0.0101190 0.999949i \(-0.496779\pi\)
0.0101190 + 0.999949i \(0.496779\pi\)
\(920\) 20.4657 0.674734
\(921\) −1.52069 4.94165i −0.0501085 0.162833i
\(922\) 6.67883 + 3.85602i 0.219955 + 0.126991i
\(923\) 29.0451 9.09550i 0.956030 0.299382i
\(924\) −0.228703 0.209668i −0.00752378 0.00689758i
\(925\) 21.6078 37.4259i 0.710462 1.23056i
\(926\) −12.7767 + 7.37666i −0.419870 + 0.242412i
\(927\) 26.6862 1.96411i 0.876490 0.0645099i
\(928\) 0.587175 + 1.01702i 0.0192750 + 0.0333852i
\(929\) 1.25806 0.0412755 0.0206378 0.999787i \(-0.493430\pi\)
0.0206378 + 0.999787i \(0.493430\pi\)
\(930\) 35.4883 + 32.9723i 1.16371 + 1.08121i
\(931\) −15.5679 + 9.26680i −0.510217 + 0.303707i
\(932\) −0.257169 + 0.148477i −0.00842386 + 0.00486352i
\(933\) −3.60645 3.35077i −0.118070 0.109699i
\(934\) 17.1943i 0.562615i
\(935\) −3.25871 + 1.88141i −0.106571 + 0.0615288i
\(936\) 11.3302 + 28.6205i 0.370338 + 0.935489i
\(937\) 13.4531i 0.439494i −0.975557 0.219747i \(-0.929477\pi\)
0.975557 0.219747i \(-0.0705232\pi\)
\(938\) 16.5747 0.110399i 0.541184 0.00360465i
\(939\) −14.2854 3.27057i −0.466187 0.106731i
\(940\) −0.630477 −0.0205639
\(941\) 10.6364 + 18.4228i 0.346736 + 0.600565i 0.985668 0.168699i \(-0.0539566\pi\)
−0.638931 + 0.769264i \(0.720623\pi\)
\(942\) 0.191762 0.837594i 0.00624796 0.0272903i
\(943\) 20.3187i 0.661666i
\(944\) 41.0017 1.33449
\(945\) −5.89232 + 40.3693i −0.191677 + 1.31321i
\(946\) 8.57727 14.8563i 0.278871 0.483019i
\(947\) 6.58584 3.80234i 0.214011 0.123559i −0.389163 0.921169i \(-0.627236\pi\)
0.603174 + 0.797609i \(0.293902\pi\)
\(948\) −0.0920491 0.0855232i −0.00298962 0.00277767i
\(949\) 26.8442 8.40631i 0.871400 0.272880i
\(950\) −6.92252 + 11.9902i −0.224596 + 0.389012i
\(951\) −47.9641 10.9811i −1.55534 0.356087i
\(952\) 1.77528 + 3.02812i 0.0575373 + 0.0981421i
\(953\) 11.5075 6.64386i 0.372765 0.215216i −0.301901 0.953339i \(-0.597621\pi\)
0.674666 + 0.738123i \(0.264288\pi\)
\(954\) −0.355828 4.83460i −0.0115203 0.156526i
\(955\) 6.95139 + 4.01339i 0.224942 + 0.129870i
\(956\) 0.221925 + 0.128129i 0.00717758 + 0.00414398i
\(957\) 8.76785 38.2969i 0.283424 1.23796i
\(958\) −19.1935 + 11.0814i −0.620113 + 0.358023i
\(959\) −1.70703 2.91170i −0.0551228 0.0940236i
\(960\) −9.28801 + 40.5689i −0.299769 + 1.30935i
\(961\) 6.98542 12.0991i 0.225336 0.390294i
\(962\) 42.3403 + 38.9502i 1.36511 + 1.25581i
\(963\) −0.152208 + 0.314989i −0.00490483 + 0.0101504i
\(964\) −0.342577 + 0.197787i −0.0110337 + 0.00637029i
\(965\) −36.0158 + 62.3811i −1.15939 + 2.00812i
\(966\) −10.5471 + 11.5046i −0.339347 + 0.370155i
\(967\) 41.8154 1.34469 0.672346 0.740237i \(-0.265287\pi\)
0.672346 + 0.740237i \(0.265287\pi\)
\(968\) 10.2523i 0.329522i
\(969\) 2.03723 + 0.466412i 0.0654452 + 0.0149833i
\(970\) 21.5655 + 37.3526i 0.692427 + 1.19932i
\(971\) 20.3903 0.654354 0.327177 0.944963i \(-0.393903\pi\)
0.327177 + 0.944963i \(0.393903\pi\)
\(972\) 0.319896 + 0.219665i 0.0102607 + 0.00704576i
\(973\) −10.9674 + 0.0730505i −0.351600 + 0.00234189i
\(974\) 35.0976i 1.12460i
\(975\) 13.4613 + 19.5916i 0.431106 + 0.627434i
\(976\) −31.2147 + 18.0218i −0.999157 + 0.576863i
\(977\) 8.77937i 0.280877i −0.990089 0.140438i \(-0.955149\pi\)
0.990089 0.140438i \(-0.0448512\pi\)
\(978\) 39.2694 42.2658i 1.25570 1.35151i
\(979\) −16.2085 + 9.35798i −0.518026 + 0.299082i
\(980\) −0.252568 + 0.451237i −0.00806798 + 0.0144142i
\(981\) −11.3457 5.48244i −0.362241 0.175041i
\(982\) 59.4972 1.89863
\(983\) −11.5468 19.9996i −0.368285 0.637888i 0.621013 0.783800i \(-0.286721\pi\)
−0.989297 + 0.145913i \(0.953388\pi\)
\(984\) −40.2836 9.22270i −1.28419 0.294009i
\(985\) −18.1987 + 10.5070i −0.579858 + 0.334781i
\(986\) −2.73214 + 4.73221i −0.0870091 + 0.150704i
\(987\) 26.4295 28.8289i 0.841259 0.917633i
\(988\) 0.170964 + 0.157276i 0.00543910 + 0.00500361i
\(989\) 9.41908 + 5.43811i 0.299509 + 0.172922i
\(990\) 28.1417 19.1319i 0.894403 0.608050i
\(991\) −6.00941 −0.190895 −0.0954477 0.995434i \(-0.530428\pi\)
−0.0954477 + 0.995434i \(0.530428\pi\)
\(992\) 0.944288 0.0299812
\(993\) −40.9056 + 12.5879i −1.29810 + 0.399464i
\(994\) −27.0774 + 15.8745i −0.858842 + 0.503509i
\(995\) −49.4647 + 28.5585i −1.56814 + 0.905365i
\(996\) 0.102510 0.447751i 0.00324816 0.0141875i
\(997\) −10.6404 6.14323i −0.336985 0.194558i 0.321953 0.946756i \(-0.395661\pi\)
−0.658938 + 0.752197i \(0.728994\pi\)
\(998\) 13.2307i 0.418810i
\(999\) 58.3187 + 8.90933i 1.84512 + 0.281879i
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 273.2.bf.b.152.10 yes 64
3.2 odd 2 inner 273.2.bf.b.152.23 yes 64
7.3 odd 6 273.2.r.b.269.10 yes 64
13.3 even 3 273.2.r.b.68.10 64
21.17 even 6 273.2.r.b.269.23 yes 64
39.29 odd 6 273.2.r.b.68.23 yes 64
91.3 odd 6 inner 273.2.bf.b.185.23 yes 64
273.185 even 6 inner 273.2.bf.b.185.10 yes 64
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
273.2.r.b.68.10 64 13.3 even 3
273.2.r.b.68.23 yes 64 39.29 odd 6
273.2.r.b.269.10 yes 64 7.3 odd 6
273.2.r.b.269.23 yes 64 21.17 even 6
273.2.bf.b.152.10 yes 64 1.1 even 1 trivial
273.2.bf.b.152.23 yes 64 3.2 odd 2 inner
273.2.bf.b.185.10 yes 64 273.185 even 6 inner
273.2.bf.b.185.23 yes 64 91.3 odd 6 inner