Properties

Label 546.2.l.j.211.2
Level $546$
Weight $2$
Character 546.211
Analytic conductor $4.360$
Analytic rank $0$
Dimension $4$
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [546,2,Mod(211,546)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(546, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([0, 0, 2]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("546.211");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 546 = 2 \cdot 3 \cdot 7 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 546.l (of order \(3\), 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: \(4.35983195036\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\Q(\sqrt{-3}, \sqrt{-19})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{4} - x^{3} - 4x^{2} - 5x + 25 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 3 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 211.2
Root \(2.13746 - 0.656712i\) of defining polynomial
Character \(\chi\) \(=\) 546.211
Dual form 546.2.l.j.295.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} +4.27492 q^{5} +(-0.500000 + 0.866025i) q^{6} +(-0.500000 + 0.866025i) q^{7} +1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +(-2.13746 - 3.70219i) q^{10} +(2.00000 + 3.46410i) q^{11} +1.00000 q^{12} +(3.50000 - 0.866025i) q^{13} +1.00000 q^{14} +(-2.13746 - 3.70219i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(-1.50000 + 2.59808i) q^{17} +1.00000 q^{18} +(-3.27492 + 5.67232i) q^{19} +(-2.13746 + 3.70219i) q^{20} +1.00000 q^{21} +(2.00000 - 3.46410i) q^{22} +(2.63746 + 4.56821i) q^{23} +(-0.500000 - 0.866025i) q^{24} +13.2749 q^{25} +(-2.50000 - 2.59808i) q^{26} +1.00000 q^{27} +(-0.500000 - 0.866025i) q^{28} +(-4.13746 - 7.16629i) q^{29} +(-2.13746 + 3.70219i) q^{30} -1.27492 q^{31} +(-0.500000 + 0.866025i) q^{32} +(2.00000 - 3.46410i) q^{33} +3.00000 q^{34} +(-2.13746 + 3.70219i) q^{35} +(-0.500000 - 0.866025i) q^{36} +(-0.137459 - 0.238085i) q^{37} +6.54983 q^{38} +(-2.50000 - 2.59808i) q^{39} +4.27492 q^{40} +(-4.13746 - 7.16629i) q^{41} +(-0.500000 - 0.866025i) q^{42} +(5.91238 - 10.2405i) q^{43} -4.00000 q^{44} +(-2.13746 + 3.70219i) q^{45} +(2.63746 - 4.56821i) q^{46} -6.54983 q^{47} +(-0.500000 + 0.866025i) q^{48} +(-0.500000 - 0.866025i) q^{49} +(-6.63746 - 11.4964i) q^{50} +3.00000 q^{51} +(-1.00000 + 3.46410i) q^{52} -3.54983 q^{53} +(-0.500000 - 0.866025i) q^{54} +(8.54983 + 14.8087i) q^{55} +(-0.500000 + 0.866025i) q^{56} +6.54983 q^{57} +(-4.13746 + 7.16629i) q^{58} +(5.91238 - 10.2405i) q^{59} +4.27492 q^{60} +(4.50000 - 7.79423i) q^{61} +(0.637459 + 1.10411i) q^{62} +(-0.500000 - 0.866025i) q^{63} +1.00000 q^{64} +(14.9622 - 3.70219i) q^{65} -4.00000 q^{66} +(1.36254 + 2.35999i) q^{67} +(-1.50000 - 2.59808i) q^{68} +(2.63746 - 4.56821i) q^{69} +4.27492 q^{70} +(-2.63746 + 4.56821i) q^{71} +(-0.500000 + 0.866025i) q^{72} +5.72508 q^{73} +(-0.137459 + 0.238085i) q^{74} +(-6.63746 - 11.4964i) q^{75} +(-3.27492 - 5.67232i) q^{76} -4.00000 q^{77} +(-1.00000 + 3.46410i) q^{78} -8.00000 q^{79} +(-2.13746 - 3.70219i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-4.13746 + 7.16629i) q^{82} -11.8248 q^{83} +(-0.500000 + 0.866025i) q^{84} +(-6.41238 + 11.1066i) q^{85} -11.8248 q^{86} +(-4.13746 + 7.16629i) q^{87} +(2.00000 + 3.46410i) q^{88} +(-0.362541 - 0.627940i) q^{89} +4.27492 q^{90} +(-1.00000 + 3.46410i) q^{91} -5.27492 q^{92} +(0.637459 + 1.10411i) q^{93} +(3.27492 + 5.67232i) q^{94} +(-14.0000 + 24.2487i) q^{95} +1.00000 q^{96} +(0.274917 - 0.476171i) q^{97} +(-0.500000 + 0.866025i) q^{98} -4.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q - 2 q^{2} - 2 q^{3} - 2 q^{4} + 2 q^{5} - 2 q^{6} - 2 q^{7} + 4 q^{8} - 2 q^{9} - q^{10} + 8 q^{11} + 4 q^{12} + 14 q^{13} + 4 q^{14} - q^{15} - 2 q^{16} - 6 q^{17} + 4 q^{18} + 2 q^{19} - q^{20}+ \cdots - 16 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/546\mathbb{Z}\right)^\times\).

\(n\) \(157\) \(365\) \(379\)
\(\chi(n)\) \(1\) \(1\) \(e\left(\frac{1}{3}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.500000 0.866025i −0.353553 0.612372i
\(3\) −0.500000 0.866025i −0.288675 0.500000i
\(4\) −0.500000 + 0.866025i −0.250000 + 0.433013i
\(5\) 4.27492 1.91180 0.955901 0.293691i \(-0.0948835\pi\)
0.955901 + 0.293691i \(0.0948835\pi\)
\(6\) −0.500000 + 0.866025i −0.204124 + 0.353553i
\(7\) −0.500000 + 0.866025i −0.188982 + 0.327327i
\(8\) 1.00000 0.353553
\(9\) −0.500000 + 0.866025i −0.166667 + 0.288675i
\(10\) −2.13746 3.70219i −0.675924 1.17073i
\(11\) 2.00000 + 3.46410i 0.603023 + 1.04447i 0.992361 + 0.123371i \(0.0393705\pi\)
−0.389338 + 0.921095i \(0.627296\pi\)
\(12\) 1.00000 0.288675
\(13\) 3.50000 0.866025i 0.970725 0.240192i
\(14\) 1.00000 0.267261
\(15\) −2.13746 3.70219i −0.551889 0.955901i
\(16\) −0.500000 0.866025i −0.125000 0.216506i
\(17\) −1.50000 + 2.59808i −0.363803 + 0.630126i −0.988583 0.150675i \(-0.951855\pi\)
0.624780 + 0.780801i \(0.285189\pi\)
\(18\) 1.00000 0.235702
\(19\) −3.27492 + 5.67232i −0.751318 + 1.30132i 0.195867 + 0.980631i \(0.437248\pi\)
−0.947184 + 0.320690i \(0.896085\pi\)
\(20\) −2.13746 + 3.70219i −0.477950 + 0.827834i
\(21\) 1.00000 0.218218
\(22\) 2.00000 3.46410i 0.426401 0.738549i
\(23\) 2.63746 + 4.56821i 0.549948 + 0.952538i 0.998277 + 0.0586697i \(0.0186859\pi\)
−0.448329 + 0.893868i \(0.647981\pi\)
\(24\) −0.500000 0.866025i −0.102062 0.176777i
\(25\) 13.2749 2.65498
\(26\) −2.50000 2.59808i −0.490290 0.509525i
\(27\) 1.00000 0.192450
\(28\) −0.500000 0.866025i −0.0944911 0.163663i
\(29\) −4.13746 7.16629i −0.768307 1.33075i −0.938480 0.345332i \(-0.887766\pi\)
0.170174 0.985414i \(-0.445567\pi\)
\(30\) −2.13746 + 3.70219i −0.390245 + 0.675924i
\(31\) −1.27492 −0.228982 −0.114491 0.993424i \(-0.536524\pi\)
−0.114491 + 0.993424i \(0.536524\pi\)
\(32\) −0.500000 + 0.866025i −0.0883883 + 0.153093i
\(33\) 2.00000 3.46410i 0.348155 0.603023i
\(34\) 3.00000 0.514496
\(35\) −2.13746 + 3.70219i −0.361296 + 0.625784i
\(36\) −0.500000 0.866025i −0.0833333 0.144338i
\(37\) −0.137459 0.238085i −0.0225981 0.0391410i 0.854505 0.519443i \(-0.173860\pi\)
−0.877103 + 0.480302i \(0.840527\pi\)
\(38\) 6.54983 1.06252
\(39\) −2.50000 2.59808i −0.400320 0.416025i
\(40\) 4.27492 0.675924
\(41\) −4.13746 7.16629i −0.646162 1.11919i −0.984032 0.177993i \(-0.943040\pi\)
0.337869 0.941193i \(-0.390294\pi\)
\(42\) −0.500000 0.866025i −0.0771517 0.133631i
\(43\) 5.91238 10.2405i 0.901629 1.56167i 0.0762493 0.997089i \(-0.475706\pi\)
0.825380 0.564578i \(-0.190961\pi\)
\(44\) −4.00000 −0.603023
\(45\) −2.13746 + 3.70219i −0.318634 + 0.551889i
\(46\) 2.63746 4.56821i 0.388872 0.673546i
\(47\) −6.54983 −0.955392 −0.477696 0.878525i \(-0.658528\pi\)
−0.477696 + 0.878525i \(0.658528\pi\)
\(48\) −0.500000 + 0.866025i −0.0721688 + 0.125000i
\(49\) −0.500000 0.866025i −0.0714286 0.123718i
\(50\) −6.63746 11.4964i −0.938678 1.62584i
\(51\) 3.00000 0.420084
\(52\) −1.00000 + 3.46410i −0.138675 + 0.480384i
\(53\) −3.54983 −0.487607 −0.243804 0.969825i \(-0.578395\pi\)
−0.243804 + 0.969825i \(0.578395\pi\)
\(54\) −0.500000 0.866025i −0.0680414 0.117851i
\(55\) 8.54983 + 14.8087i 1.15286 + 1.99681i
\(56\) −0.500000 + 0.866025i −0.0668153 + 0.115728i
\(57\) 6.54983 0.867547
\(58\) −4.13746 + 7.16629i −0.543275 + 0.940980i
\(59\) 5.91238 10.2405i 0.769726 1.33320i −0.167986 0.985789i \(-0.553726\pi\)
0.937712 0.347415i \(-0.112940\pi\)
\(60\) 4.27492 0.551889
\(61\) 4.50000 7.79423i 0.576166 0.997949i −0.419748 0.907641i \(-0.637882\pi\)
0.995914 0.0903080i \(-0.0287851\pi\)
\(62\) 0.637459 + 1.10411i 0.0809573 + 0.140222i
\(63\) −0.500000 0.866025i −0.0629941 0.109109i
\(64\) 1.00000 0.125000
\(65\) 14.9622 3.70219i 1.85583 0.459200i
\(66\) −4.00000 −0.492366
\(67\) 1.36254 + 2.35999i 0.166461 + 0.288319i 0.937173 0.348865i \(-0.113433\pi\)
−0.770712 + 0.637183i \(0.780099\pi\)
\(68\) −1.50000 2.59808i −0.181902 0.315063i
\(69\) 2.63746 4.56821i 0.317513 0.549948i
\(70\) 4.27492 0.510950
\(71\) −2.63746 + 4.56821i −0.313009 + 0.542147i −0.979012 0.203802i \(-0.934670\pi\)
0.666003 + 0.745949i \(0.268004\pi\)
\(72\) −0.500000 + 0.866025i −0.0589256 + 0.102062i
\(73\) 5.72508 0.670070 0.335035 0.942206i \(-0.391252\pi\)
0.335035 + 0.942206i \(0.391252\pi\)
\(74\) −0.137459 + 0.238085i −0.0159792 + 0.0276769i
\(75\) −6.63746 11.4964i −0.766428 1.32749i
\(76\) −3.27492 5.67232i −0.375659 0.650660i
\(77\) −4.00000 −0.455842
\(78\) −1.00000 + 3.46410i −0.113228 + 0.392232i
\(79\) −8.00000 −0.900070 −0.450035 0.893011i \(-0.648589\pi\)
−0.450035 + 0.893011i \(0.648589\pi\)
\(80\) −2.13746 3.70219i −0.238975 0.413917i
\(81\) −0.500000 0.866025i −0.0555556 0.0962250i
\(82\) −4.13746 + 7.16629i −0.456906 + 0.791384i
\(83\) −11.8248 −1.29794 −0.648968 0.760816i \(-0.724799\pi\)
−0.648968 + 0.760816i \(0.724799\pi\)
\(84\) −0.500000 + 0.866025i −0.0545545 + 0.0944911i
\(85\) −6.41238 + 11.1066i −0.695520 + 1.20468i
\(86\) −11.8248 −1.27510
\(87\) −4.13746 + 7.16629i −0.443582 + 0.768307i
\(88\) 2.00000 + 3.46410i 0.213201 + 0.369274i
\(89\) −0.362541 0.627940i −0.0384293 0.0665615i 0.846171 0.532911i \(-0.178902\pi\)
−0.884600 + 0.466350i \(0.845569\pi\)
\(90\) 4.27492 0.450616
\(91\) −1.00000 + 3.46410i −0.104828 + 0.363137i
\(92\) −5.27492 −0.549948
\(93\) 0.637459 + 1.10411i 0.0661014 + 0.114491i
\(94\) 3.27492 + 5.67232i 0.337782 + 0.585055i
\(95\) −14.0000 + 24.2487i −1.43637 + 2.48787i
\(96\) 1.00000 0.102062
\(97\) 0.274917 0.476171i 0.0279136 0.0483478i −0.851731 0.523979i \(-0.824447\pi\)
0.879645 + 0.475631i \(0.157780\pi\)
\(98\) −0.500000 + 0.866025i −0.0505076 + 0.0874818i
\(99\) −4.00000 −0.402015
\(100\) −6.63746 + 11.4964i −0.663746 + 1.14964i
\(101\) −0.862541 1.49397i −0.0858261 0.148655i 0.819917 0.572483i \(-0.194020\pi\)
−0.905743 + 0.423828i \(0.860686\pi\)
\(102\) −1.50000 2.59808i −0.148522 0.257248i
\(103\) 5.27492 0.519753 0.259877 0.965642i \(-0.416318\pi\)
0.259877 + 0.965642i \(0.416318\pi\)
\(104\) 3.50000 0.866025i 0.343203 0.0849208i
\(105\) 4.27492 0.417189
\(106\) 1.77492 + 3.07425i 0.172395 + 0.298597i
\(107\) −1.27492 2.20822i −0.123251 0.213477i 0.797797 0.602926i \(-0.205999\pi\)
−0.921048 + 0.389449i \(0.872665\pi\)
\(108\) −0.500000 + 0.866025i −0.0481125 + 0.0833333i
\(109\) −4.54983 −0.435795 −0.217898 0.975972i \(-0.569920\pi\)
−0.217898 + 0.975972i \(0.569920\pi\)
\(110\) 8.54983 14.8087i 0.815195 1.41196i
\(111\) −0.137459 + 0.238085i −0.0130470 + 0.0225981i
\(112\) 1.00000 0.0944911
\(113\) −7.41238 + 12.8386i −0.697298 + 1.20775i 0.272102 + 0.962268i \(0.412281\pi\)
−0.969400 + 0.245487i \(0.921052\pi\)
\(114\) −3.27492 5.67232i −0.306724 0.531262i
\(115\) 11.2749 + 19.5287i 1.05139 + 1.82106i
\(116\) 8.27492 0.768307
\(117\) −1.00000 + 3.46410i −0.0924500 + 0.320256i
\(118\) −11.8248 −1.08856
\(119\) −1.50000 2.59808i −0.137505 0.238165i
\(120\) −2.13746 3.70219i −0.195122 0.337962i
\(121\) −2.50000 + 4.33013i −0.227273 + 0.393648i
\(122\) −9.00000 −0.814822
\(123\) −4.13746 + 7.16629i −0.373062 + 0.646162i
\(124\) 0.637459 1.10411i 0.0572455 0.0991521i
\(125\) 35.3746 3.16400
\(126\) −0.500000 + 0.866025i −0.0445435 + 0.0771517i
\(127\) −4.00000 6.92820i −0.354943 0.614779i 0.632166 0.774833i \(-0.282166\pi\)
−0.987108 + 0.160055i \(0.948833\pi\)
\(128\) −0.500000 0.866025i −0.0441942 0.0765466i
\(129\) −11.8248 −1.04111
\(130\) −10.6873 11.1066i −0.937338 0.974110i
\(131\) −2.72508 −0.238092 −0.119046 0.992889i \(-0.537984\pi\)
−0.119046 + 0.992889i \(0.537984\pi\)
\(132\) 2.00000 + 3.46410i 0.174078 + 0.301511i
\(133\) −3.27492 5.67232i −0.283971 0.491853i
\(134\) 1.36254 2.35999i 0.117706 0.203872i
\(135\) 4.27492 0.367926
\(136\) −1.50000 + 2.59808i −0.128624 + 0.222783i
\(137\) −11.4124 + 19.7668i −0.975025 + 1.68879i −0.295173 + 0.955444i \(0.595377\pi\)
−0.679852 + 0.733349i \(0.737956\pi\)
\(138\) −5.27492 −0.449031
\(139\) 4.54983 7.88054i 0.385912 0.668419i −0.605983 0.795477i \(-0.707220\pi\)
0.991895 + 0.127058i \(0.0405535\pi\)
\(140\) −2.13746 3.70219i −0.180648 0.312892i
\(141\) 3.27492 + 5.67232i 0.275798 + 0.477696i
\(142\) 5.27492 0.442661
\(143\) 10.0000 + 10.3923i 0.836242 + 0.869048i
\(144\) 1.00000 0.0833333
\(145\) −17.6873 30.6353i −1.46885 2.54412i
\(146\) −2.86254 4.95807i −0.236906 0.410333i
\(147\) −0.500000 + 0.866025i −0.0412393 + 0.0714286i
\(148\) 0.274917 0.0225981
\(149\) 0.500000 0.866025i 0.0409616 0.0709476i −0.844818 0.535054i \(-0.820291\pi\)
0.885779 + 0.464107i \(0.153625\pi\)
\(150\) −6.63746 + 11.4964i −0.541946 + 0.938678i
\(151\) 13.0997 1.06604 0.533018 0.846104i \(-0.321058\pi\)
0.533018 + 0.846104i \(0.321058\pi\)
\(152\) −3.27492 + 5.67232i −0.265631 + 0.460086i
\(153\) −1.50000 2.59808i −0.121268 0.210042i
\(154\) 2.00000 + 3.46410i 0.161165 + 0.279145i
\(155\) −5.45017 −0.437768
\(156\) 3.50000 0.866025i 0.280224 0.0693375i
\(157\) −3.72508 −0.297294 −0.148647 0.988890i \(-0.547492\pi\)
−0.148647 + 0.988890i \(0.547492\pi\)
\(158\) 4.00000 + 6.92820i 0.318223 + 0.551178i
\(159\) 1.77492 + 3.07425i 0.140760 + 0.243804i
\(160\) −2.13746 + 3.70219i −0.168981 + 0.292684i
\(161\) −5.27492 −0.415722
\(162\) −0.500000 + 0.866025i −0.0392837 + 0.0680414i
\(163\) 6.63746 11.4964i 0.519886 0.900469i −0.479847 0.877352i \(-0.659308\pi\)
0.999733 0.0231165i \(-0.00735887\pi\)
\(164\) 8.27492 0.646162
\(165\) 8.54983 14.8087i 0.665604 1.15286i
\(166\) 5.91238 + 10.2405i 0.458889 + 0.794820i
\(167\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(168\) 1.00000 0.0771517
\(169\) 11.5000 6.06218i 0.884615 0.466321i
\(170\) 12.8248 0.983614
\(171\) −3.27492 5.67232i −0.250439 0.433773i
\(172\) 5.91238 + 10.2405i 0.450814 + 0.780833i
\(173\) 2.27492 3.94027i 0.172959 0.299573i −0.766494 0.642251i \(-0.778001\pi\)
0.939453 + 0.342678i \(0.111334\pi\)
\(174\) 8.27492 0.627320
\(175\) −6.63746 + 11.4964i −0.501745 + 0.869047i
\(176\) 2.00000 3.46410i 0.150756 0.261116i
\(177\) −11.8248 −0.888803
\(178\) −0.362541 + 0.627940i −0.0271736 + 0.0470661i
\(179\) −0.725083 1.25588i −0.0541952 0.0938689i 0.837655 0.546200i \(-0.183926\pi\)
−0.891850 + 0.452331i \(0.850593\pi\)
\(180\) −2.13746 3.70219i −0.159317 0.275945i
\(181\) −16.8248 −1.25057 −0.625287 0.780395i \(-0.715018\pi\)
−0.625287 + 0.780395i \(0.715018\pi\)
\(182\) 3.50000 0.866025i 0.259437 0.0641941i
\(183\) −9.00000 −0.665299
\(184\) 2.63746 + 4.56821i 0.194436 + 0.336773i
\(185\) −0.587624 1.01779i −0.0432030 0.0748298i
\(186\) 0.637459 1.10411i 0.0467407 0.0809573i
\(187\) −12.0000 −0.877527
\(188\) 3.27492 5.67232i 0.238848 0.413697i
\(189\) −0.500000 + 0.866025i −0.0363696 + 0.0629941i
\(190\) 28.0000 2.03133
\(191\) −3.36254 + 5.82409i −0.243305 + 0.421417i −0.961654 0.274267i \(-0.911565\pi\)
0.718349 + 0.695683i \(0.244898\pi\)
\(192\) −0.500000 0.866025i −0.0360844 0.0625000i
\(193\) 12.4124 + 21.4989i 0.893462 + 1.54752i 0.835696 + 0.549192i \(0.185064\pi\)
0.0577662 + 0.998330i \(0.481602\pi\)
\(194\) −0.549834 −0.0394758
\(195\) −10.6873 11.1066i −0.765333 0.795357i
\(196\) 1.00000 0.0714286
\(197\) 10.9124 + 18.9008i 0.777475 + 1.34663i 0.933393 + 0.358856i \(0.116833\pi\)
−0.155919 + 0.987770i \(0.549834\pi\)
\(198\) 2.00000 + 3.46410i 0.142134 + 0.246183i
\(199\) −5.91238 + 10.2405i −0.419117 + 0.725932i −0.995851 0.0909999i \(-0.970994\pi\)
0.576734 + 0.816932i \(0.304327\pi\)
\(200\) 13.2749 0.938678
\(201\) 1.36254 2.35999i 0.0961063 0.166461i
\(202\) −0.862541 + 1.49397i −0.0606882 + 0.105115i
\(203\) 8.27492 0.580785
\(204\) −1.50000 + 2.59808i −0.105021 + 0.181902i
\(205\) −17.6873 30.6353i −1.23533 2.13966i
\(206\) −2.63746 4.56821i −0.183760 0.318282i
\(207\) −5.27492 −0.366632
\(208\) −2.50000 2.59808i −0.173344 0.180144i
\(209\) −26.1993 −1.81225
\(210\) −2.13746 3.70219i −0.147499 0.255475i
\(211\) −10.5498 18.2728i −0.726281 1.25795i −0.958445 0.285278i \(-0.907914\pi\)
0.232164 0.972677i \(-0.425419\pi\)
\(212\) 1.77492 3.07425i 0.121902 0.211140i
\(213\) 5.27492 0.361431
\(214\) −1.27492 + 2.20822i −0.0871515 + 0.150951i
\(215\) 25.2749 43.7774i 1.72374 2.98560i
\(216\) 1.00000 0.0680414
\(217\) 0.637459 1.10411i 0.0432735 0.0749519i
\(218\) 2.27492 + 3.94027i 0.154077 + 0.266869i
\(219\) −2.86254 4.95807i −0.193433 0.335035i
\(220\) −17.0997 −1.15286
\(221\) −3.00000 + 10.3923i −0.201802 + 0.699062i
\(222\) 0.274917 0.0184512
\(223\) −5.36254 9.28819i −0.359102 0.621983i 0.628709 0.777641i \(-0.283584\pi\)
−0.987811 + 0.155657i \(0.950250\pi\)
\(224\) −0.500000 0.866025i −0.0334077 0.0578638i
\(225\) −6.63746 + 11.4964i −0.442497 + 0.766428i
\(226\) 14.8248 0.986128
\(227\) 10.5498 18.2728i 0.700217 1.21281i −0.268173 0.963371i \(-0.586420\pi\)
0.968390 0.249441i \(-0.0802468\pi\)
\(228\) −3.27492 + 5.67232i −0.216887 + 0.375659i
\(229\) 12.7251 0.840897 0.420449 0.907316i \(-0.361873\pi\)
0.420449 + 0.907316i \(0.361873\pi\)
\(230\) 11.2749 19.5287i 0.743446 1.28769i
\(231\) 2.00000 + 3.46410i 0.131590 + 0.227921i
\(232\) −4.13746 7.16629i −0.271637 0.470490i
\(233\) 7.45017 0.488077 0.244038 0.969766i \(-0.421528\pi\)
0.244038 + 0.969766i \(0.421528\pi\)
\(234\) 3.50000 0.866025i 0.228802 0.0566139i
\(235\) −28.0000 −1.82652
\(236\) 5.91238 + 10.2405i 0.384863 + 0.666602i
\(237\) 4.00000 + 6.92820i 0.259828 + 0.450035i
\(238\) −1.50000 + 2.59808i −0.0972306 + 0.168408i
\(239\) −5.27492 −0.341206 −0.170603 0.985340i \(-0.554572\pi\)
−0.170603 + 0.985340i \(0.554572\pi\)
\(240\) −2.13746 + 3.70219i −0.137972 + 0.238975i
\(241\) 7.86254 13.6183i 0.506471 0.877233i −0.493501 0.869745i \(-0.664283\pi\)
0.999972 0.00748804i \(-0.00238354\pi\)
\(242\) 5.00000 0.321412
\(243\) −0.500000 + 0.866025i −0.0320750 + 0.0555556i
\(244\) 4.50000 + 7.79423i 0.288083 + 0.498974i
\(245\) −2.13746 3.70219i −0.136557 0.236524i
\(246\) 8.27492 0.527589
\(247\) −6.54983 + 22.6893i −0.416756 + 1.44369i
\(248\) −1.27492 −0.0809573
\(249\) 5.91238 + 10.2405i 0.374682 + 0.648968i
\(250\) −17.6873 30.6353i −1.11864 1.93755i
\(251\) −6.63746 + 11.4964i −0.418953 + 0.725647i −0.995834 0.0911804i \(-0.970936\pi\)
0.576882 + 0.816828i \(0.304269\pi\)
\(252\) 1.00000 0.0629941
\(253\) −10.5498 + 18.2728i −0.663262 + 1.14880i
\(254\) −4.00000 + 6.92820i −0.250982 + 0.434714i
\(255\) 12.8248 0.803117
\(256\) −0.500000 + 0.866025i −0.0312500 + 0.0541266i
\(257\) −7.50000 12.9904i −0.467837 0.810318i 0.531487 0.847066i \(-0.321633\pi\)
−0.999325 + 0.0367485i \(0.988300\pi\)
\(258\) 5.91238 + 10.2405i 0.368088 + 0.637548i
\(259\) 0.274917 0.0170825
\(260\) −4.27492 + 14.8087i −0.265119 + 0.918400i
\(261\) 8.27492 0.512205
\(262\) 1.36254 + 2.35999i 0.0841781 + 0.145801i
\(263\) −10.5498 18.2728i −0.650531 1.12675i −0.982994 0.183636i \(-0.941213\pi\)
0.332464 0.943116i \(-0.392120\pi\)
\(264\) 2.00000 3.46410i 0.123091 0.213201i
\(265\) −15.1752 −0.932208
\(266\) −3.27492 + 5.67232i −0.200798 + 0.347792i
\(267\) −0.362541 + 0.627940i −0.0221872 + 0.0384293i
\(268\) −2.72508 −0.166461
\(269\) 9.00000 15.5885i 0.548740 0.950445i −0.449622 0.893219i \(-0.648441\pi\)
0.998361 0.0572259i \(-0.0182255\pi\)
\(270\) −2.13746 3.70219i −0.130082 0.225308i
\(271\) −12.6375 21.8887i −0.767671 1.32965i −0.938823 0.344400i \(-0.888082\pi\)
0.171152 0.985245i \(-0.445251\pi\)
\(272\) 3.00000 0.181902
\(273\) 3.50000 0.866025i 0.211830 0.0524142i
\(274\) 22.8248 1.37889
\(275\) 26.5498 + 45.9857i 1.60102 + 2.77304i
\(276\) 2.63746 + 4.56821i 0.158756 + 0.274974i
\(277\) −7.41238 + 12.8386i −0.445366 + 0.771397i −0.998078 0.0619755i \(-0.980260\pi\)
0.552711 + 0.833373i \(0.313593\pi\)
\(278\) −9.09967 −0.545762
\(279\) 0.637459 1.10411i 0.0381636 0.0661014i
\(280\) −2.13746 + 3.70219i −0.127738 + 0.221248i
\(281\) −20.8248 −1.24230 −0.621150 0.783691i \(-0.713334\pi\)
−0.621150 + 0.783691i \(0.713334\pi\)
\(282\) 3.27492 5.67232i 0.195018 0.337782i
\(283\) 4.72508 + 8.18408i 0.280877 + 0.486493i 0.971601 0.236625i \(-0.0760414\pi\)
−0.690724 + 0.723119i \(0.742708\pi\)
\(284\) −2.63746 4.56821i −0.156504 0.271074i
\(285\) 28.0000 1.65858
\(286\) 4.00000 13.8564i 0.236525 0.819346i
\(287\) 8.27492 0.488453
\(288\) −0.500000 0.866025i −0.0294628 0.0510310i
\(289\) 4.00000 + 6.92820i 0.235294 + 0.407541i
\(290\) −17.6873 + 30.6353i −1.03863 + 1.79897i
\(291\) −0.549834 −0.0322319
\(292\) −2.86254 + 4.95807i −0.167518 + 0.290149i
\(293\) 9.13746 15.8265i 0.533816 0.924596i −0.465404 0.885099i \(-0.654091\pi\)
0.999220 0.0394979i \(-0.0125759\pi\)
\(294\) 1.00000 0.0583212
\(295\) 25.2749 43.7774i 1.47156 2.54882i
\(296\) −0.137459 0.238085i −0.00798962 0.0138384i
\(297\) 2.00000 + 3.46410i 0.116052 + 0.201008i
\(298\) −1.00000 −0.0579284
\(299\) 13.1873 + 13.7046i 0.762641 + 0.792560i
\(300\) 13.2749 0.766428
\(301\) 5.91238 + 10.2405i 0.340784 + 0.590255i
\(302\) −6.54983 11.3446i −0.376901 0.652811i
\(303\) −0.862541 + 1.49397i −0.0495517 + 0.0858261i
\(304\) 6.54983 0.375659
\(305\) 19.2371 33.3197i 1.10151 1.90788i
\(306\) −1.50000 + 2.59808i −0.0857493 + 0.148522i
\(307\) −1.45017 −0.0827653 −0.0413827 0.999143i \(-0.513176\pi\)
−0.0413827 + 0.999143i \(0.513176\pi\)
\(308\) 2.00000 3.46410i 0.113961 0.197386i
\(309\) −2.63746 4.56821i −0.150040 0.259877i
\(310\) 2.72508 + 4.71998i 0.154774 + 0.268077i
\(311\) −2.54983 −0.144588 −0.0722939 0.997383i \(-0.523032\pi\)
−0.0722939 + 0.997383i \(0.523032\pi\)
\(312\) −2.50000 2.59808i −0.141535 0.147087i
\(313\) 17.6495 0.997609 0.498804 0.866715i \(-0.333773\pi\)
0.498804 + 0.866715i \(0.333773\pi\)
\(314\) 1.86254 + 3.22602i 0.105109 + 0.182055i
\(315\) −2.13746 3.70219i −0.120432 0.208595i
\(316\) 4.00000 6.92820i 0.225018 0.389742i
\(317\) −7.54983 −0.424041 −0.212020 0.977265i \(-0.568004\pi\)
−0.212020 + 0.977265i \(0.568004\pi\)
\(318\) 1.77492 3.07425i 0.0995324 0.172395i
\(319\) 16.5498 28.6652i 0.926613 1.60494i
\(320\) 4.27492 0.238975
\(321\) −1.27492 + 2.20822i −0.0711589 + 0.123251i
\(322\) 2.63746 + 4.56821i 0.146980 + 0.254577i
\(323\) −9.82475 17.0170i −0.546664 0.946849i
\(324\) 1.00000 0.0555556
\(325\) 46.4622 11.4964i 2.57726 0.637706i
\(326\) −13.2749 −0.735230
\(327\) 2.27492 + 3.94027i 0.125803 + 0.217898i
\(328\) −4.13746 7.16629i −0.228453 0.395692i
\(329\) 3.27492 5.67232i 0.180552 0.312725i
\(330\) −17.0997 −0.941306
\(331\) −2.00000 + 3.46410i −0.109930 + 0.190404i −0.915742 0.401768i \(-0.868396\pi\)
0.805812 + 0.592172i \(0.201729\pi\)
\(332\) 5.91238 10.2405i 0.324484 0.562022i
\(333\) 0.274917 0.0150654
\(334\) 0 0
\(335\) 5.82475 + 10.0888i 0.318240 + 0.551208i
\(336\) −0.500000 0.866025i −0.0272772 0.0472456i
\(337\) 0.274917 0.0149757 0.00748785 0.999972i \(-0.497617\pi\)
0.00748785 + 0.999972i \(0.497617\pi\)
\(338\) −11.0000 6.92820i −0.598321 0.376845i
\(339\) 14.8248 0.805170
\(340\) −6.41238 11.1066i −0.347760 0.602338i
\(341\) −2.54983 4.41644i −0.138081 0.239164i
\(342\) −3.27492 + 5.67232i −0.177087 + 0.306724i
\(343\) 1.00000 0.0539949
\(344\) 5.91238 10.2405i 0.318774 0.552133i
\(345\) 11.2749 19.5287i 0.607021 1.05139i
\(346\) −4.54983 −0.244601
\(347\) −15.2749 + 26.4569i −0.820001 + 1.42028i 0.0856804 + 0.996323i \(0.472694\pi\)
−0.905681 + 0.423960i \(0.860640\pi\)
\(348\) −4.13746 7.16629i −0.221791 0.384153i
\(349\) 17.4622 + 30.2454i 0.934731 + 1.61900i 0.775113 + 0.631822i \(0.217693\pi\)
0.159617 + 0.987179i \(0.448974\pi\)
\(350\) 13.2749 0.709574
\(351\) 3.50000 0.866025i 0.186816 0.0462250i
\(352\) −4.00000 −0.213201
\(353\) 9.77492 + 16.9307i 0.520266 + 0.901128i 0.999722 + 0.0235618i \(0.00750066\pi\)
−0.479456 + 0.877566i \(0.659166\pi\)
\(354\) 5.91238 + 10.2405i 0.314239 + 0.544278i
\(355\) −11.2749 + 19.5287i −0.598410 + 1.03648i
\(356\) 0.725083 0.0384293
\(357\) −1.50000 + 2.59808i −0.0793884 + 0.137505i
\(358\) −0.725083 + 1.25588i −0.0383218 + 0.0663753i
\(359\) −1.09967 −0.0580383 −0.0290192 0.999579i \(-0.509238\pi\)
−0.0290192 + 0.999579i \(0.509238\pi\)
\(360\) −2.13746 + 3.70219i −0.112654 + 0.195122i
\(361\) −11.9502 20.6983i −0.628956 1.08938i
\(362\) 8.41238 + 14.5707i 0.442145 + 0.765817i
\(363\) 5.00000 0.262432
\(364\) −2.50000 2.59808i −0.131036 0.136176i
\(365\) 24.4743 1.28104
\(366\) 4.50000 + 7.79423i 0.235219 + 0.407411i
\(367\) −6.63746 11.4964i −0.346473 0.600108i 0.639148 0.769084i \(-0.279287\pi\)
−0.985620 + 0.168976i \(0.945954\pi\)
\(368\) 2.63746 4.56821i 0.137487 0.238135i
\(369\) 8.27492 0.430775
\(370\) −0.587624 + 1.01779i −0.0305491 + 0.0529126i
\(371\) 1.77492 3.07425i 0.0921491 0.159607i
\(372\) −1.27492 −0.0661014
\(373\) −13.4124 + 23.2309i −0.694466 + 1.20285i 0.275894 + 0.961188i \(0.411026\pi\)
−0.970360 + 0.241663i \(0.922307\pi\)
\(374\) 6.00000 + 10.3923i 0.310253 + 0.537373i
\(375\) −17.6873 30.6353i −0.913368 1.58200i
\(376\) −6.54983 −0.337782
\(377\) −20.6873 21.4989i −1.06545 1.10725i
\(378\) 1.00000 0.0514344
\(379\) 10.0000 + 17.3205i 0.513665 + 0.889695i 0.999874 + 0.0158521i \(0.00504609\pi\)
−0.486209 + 0.873843i \(0.661621\pi\)
\(380\) −14.0000 24.2487i −0.718185 1.24393i
\(381\) −4.00000 + 6.92820i −0.204926 + 0.354943i
\(382\) 6.72508 0.344085
\(383\) −11.0997 + 19.2252i −0.567167 + 0.982361i 0.429678 + 0.902982i \(0.358627\pi\)
−0.996844 + 0.0793791i \(0.974706\pi\)
\(384\) −0.500000 + 0.866025i −0.0255155 + 0.0441942i
\(385\) −17.0997 −0.871480
\(386\) 12.4124 21.4989i 0.631773 1.09426i
\(387\) 5.91238 + 10.2405i 0.300543 + 0.520556i
\(388\) 0.274917 + 0.476171i 0.0139568 + 0.0241739i
\(389\) −24.6495 −1.24978 −0.624890 0.780713i \(-0.714856\pi\)
−0.624890 + 0.780713i \(0.714856\pi\)
\(390\) −4.27492 + 14.8087i −0.216469 + 0.749870i
\(391\) −15.8248 −0.800292
\(392\) −0.500000 0.866025i −0.0252538 0.0437409i
\(393\) 1.36254 + 2.35999i 0.0687311 + 0.119046i
\(394\) 10.9124 18.9008i 0.549758 0.952208i
\(395\) −34.1993 −1.72076
\(396\) 2.00000 3.46410i 0.100504 0.174078i
\(397\) −11.6375 + 20.1567i −0.584067 + 1.01163i 0.410924 + 0.911670i \(0.365206\pi\)
−0.994991 + 0.0999645i \(0.968127\pi\)
\(398\) 11.8248 0.592721
\(399\) −3.27492 + 5.67232i −0.163951 + 0.283971i
\(400\) −6.63746 11.4964i −0.331873 0.574821i
\(401\) 1.13746 + 1.97014i 0.0568020 + 0.0983839i 0.893028 0.450001i \(-0.148576\pi\)
−0.836226 + 0.548385i \(0.815243\pi\)
\(402\) −2.72508 −0.135915
\(403\) −4.46221 + 1.10411i −0.222279 + 0.0549997i
\(404\) 1.72508 0.0858261
\(405\) −2.13746 3.70219i −0.106211 0.183963i
\(406\) −4.13746 7.16629i −0.205339 0.355657i
\(407\) 0.549834 0.952341i 0.0272543 0.0472058i
\(408\) 3.00000 0.148522
\(409\) 14.9622 25.9153i 0.739834 1.28143i −0.212736 0.977110i \(-0.568238\pi\)
0.952570 0.304320i \(-0.0984292\pi\)
\(410\) −17.6873 + 30.6353i −0.873513 + 1.51297i
\(411\) 22.8248 1.12586
\(412\) −2.63746 + 4.56821i −0.129938 + 0.225060i
\(413\) 5.91238 + 10.2405i 0.290929 + 0.503904i
\(414\) 2.63746 + 4.56821i 0.129624 + 0.224515i
\(415\) −50.5498 −2.48139
\(416\) −1.00000 + 3.46410i −0.0490290 + 0.169842i
\(417\) −9.09967 −0.445613
\(418\) 13.0997 + 22.6893i 0.640726 + 1.10977i
\(419\) 11.1873 + 19.3770i 0.546535 + 0.946626i 0.998509 + 0.0545951i \(0.0173868\pi\)
−0.451974 + 0.892031i \(0.649280\pi\)
\(420\) −2.13746 + 3.70219i −0.104297 + 0.180648i
\(421\) 8.27492 0.403295 0.201647 0.979458i \(-0.435370\pi\)
0.201647 + 0.979458i \(0.435370\pi\)
\(422\) −10.5498 + 18.2728i −0.513558 + 0.889508i
\(423\) 3.27492 5.67232i 0.159232 0.275798i
\(424\) −3.54983 −0.172395
\(425\) −19.9124 + 34.4892i −0.965892 + 1.67297i
\(426\) −2.63746 4.56821i −0.127785 0.221331i
\(427\) 4.50000 + 7.79423i 0.217770 + 0.377189i
\(428\) 2.54983 0.123251
\(429\) 4.00000 13.8564i 0.193122 0.668994i
\(430\) −50.5498 −2.43773
\(431\) 6.63746 + 11.4964i 0.319715 + 0.553763i 0.980429 0.196875i \(-0.0630795\pi\)
−0.660713 + 0.750638i \(0.729746\pi\)
\(432\) −0.500000 0.866025i −0.0240563 0.0416667i
\(433\) 5.13746 8.89834i 0.246891 0.427627i −0.715771 0.698335i \(-0.753925\pi\)
0.962661 + 0.270708i \(0.0872579\pi\)
\(434\) −1.27492 −0.0611980
\(435\) −17.6873 + 30.6353i −0.848041 + 1.46885i
\(436\) 2.27492 3.94027i 0.108949 0.188705i
\(437\) −34.5498 −1.65274
\(438\) −2.86254 + 4.95807i −0.136778 + 0.236906i
\(439\) −6.54983 11.3446i −0.312607 0.541450i 0.666319 0.745667i \(-0.267869\pi\)
−0.978926 + 0.204216i \(0.934535\pi\)
\(440\) 8.54983 + 14.8087i 0.407597 + 0.705979i
\(441\) 1.00000 0.0476190
\(442\) 10.5000 2.59808i 0.499434 0.123578i
\(443\) 34.5498 1.64151 0.820756 0.571279i \(-0.193552\pi\)
0.820756 + 0.571279i \(0.193552\pi\)
\(444\) −0.137459 0.238085i −0.00652350 0.0112990i
\(445\) −1.54983 2.68439i −0.0734692 0.127252i
\(446\) −5.36254 + 9.28819i −0.253924 + 0.439809i
\(447\) −1.00000 −0.0472984
\(448\) −0.500000 + 0.866025i −0.0236228 + 0.0409159i
\(449\) 9.54983 16.5408i 0.450685 0.780609i −0.547744 0.836646i \(-0.684513\pi\)
0.998429 + 0.0560374i \(0.0178466\pi\)
\(450\) 13.2749 0.625786
\(451\) 16.5498 28.6652i 0.779301 1.34979i
\(452\) −7.41238 12.8386i −0.348649 0.603877i
\(453\) −6.54983 11.3446i −0.307738 0.533018i
\(454\) −21.0997 −0.990257
\(455\) −4.27492 + 14.8087i −0.200411 + 0.694245i
\(456\) 6.54983 0.306724
\(457\) 8.50000 + 14.7224i 0.397613 + 0.688686i 0.993431 0.114433i \(-0.0365053\pi\)
−0.595818 + 0.803120i \(0.703172\pi\)
\(458\) −6.36254 11.0202i −0.297302 0.514942i
\(459\) −1.50000 + 2.59808i −0.0700140 + 0.121268i
\(460\) −22.5498 −1.05139
\(461\) 9.68729 16.7789i 0.451182 0.781471i −0.547278 0.836951i \(-0.684336\pi\)
0.998460 + 0.0554807i \(0.0176691\pi\)
\(462\) 2.00000 3.46410i 0.0930484 0.161165i
\(463\) −10.5498 −0.490292 −0.245146 0.969486i \(-0.578836\pi\)
−0.245146 + 0.969486i \(0.578836\pi\)
\(464\) −4.13746 + 7.16629i −0.192077 + 0.332687i
\(465\) 2.72508 + 4.71998i 0.126373 + 0.218884i
\(466\) −3.72508 6.45203i −0.172561 0.298885i
\(467\) −8.17525 −0.378305 −0.189153 0.981948i \(-0.560574\pi\)
−0.189153 + 0.981948i \(0.560574\pi\)
\(468\) −2.50000 2.59808i −0.115563 0.120096i
\(469\) −2.72508 −0.125833
\(470\) 14.0000 + 24.2487i 0.645772 + 1.11851i
\(471\) 1.86254 + 3.22602i 0.0858214 + 0.148647i
\(472\) 5.91238 10.2405i 0.272139 0.471359i
\(473\) 47.2990 2.17481
\(474\) 4.00000 6.92820i 0.183726 0.318223i
\(475\) −43.4743 + 75.2996i −1.99474 + 3.45498i
\(476\) 3.00000 0.137505
\(477\) 1.77492 3.07425i 0.0812679 0.140760i
\(478\) 2.63746 + 4.56821i 0.120635 + 0.208945i
\(479\) −10.0000 17.3205i −0.456912 0.791394i 0.541884 0.840453i \(-0.317711\pi\)
−0.998796 + 0.0490589i \(0.984378\pi\)
\(480\) 4.27492 0.195122
\(481\) −0.687293 0.714256i −0.0313379 0.0325673i
\(482\) −15.7251 −0.716258
\(483\) 2.63746 + 4.56821i 0.120009 + 0.207861i
\(484\) −2.50000 4.33013i −0.113636 0.196824i
\(485\) 1.17525 2.03559i 0.0533653 0.0924314i
\(486\) 1.00000 0.0453609
\(487\) 0.549834 0.952341i 0.0249154 0.0431547i −0.853299 0.521422i \(-0.825402\pi\)
0.878214 + 0.478267i \(0.158735\pi\)
\(488\) 4.50000 7.79423i 0.203705 0.352828i
\(489\) −13.2749 −0.600313
\(490\) −2.13746 + 3.70219i −0.0965605 + 0.167248i
\(491\) −12.5498 21.7370i −0.566366 0.980975i −0.996921 0.0784105i \(-0.975016\pi\)
0.430555 0.902564i \(-0.358318\pi\)
\(492\) −4.13746 7.16629i −0.186531 0.323081i
\(493\) 24.8248 1.11805
\(494\) 22.9244 5.67232i 1.03142 0.255210i
\(495\) −17.0997 −0.768573
\(496\) 0.637459 + 1.10411i 0.0286227 + 0.0495760i
\(497\) −2.63746 4.56821i −0.118306 0.204912i
\(498\) 5.91238 10.2405i 0.264940 0.458889i
\(499\) −31.8248 −1.42467 −0.712336 0.701839i \(-0.752363\pi\)
−0.712336 + 0.701839i \(0.752363\pi\)
\(500\) −17.6873 + 30.6353i −0.791000 + 1.37005i
\(501\) 0 0
\(502\) 13.2749 0.592489
\(503\) 10.5498 18.2728i 0.470394 0.814746i −0.529033 0.848601i \(-0.677445\pi\)
0.999427 + 0.0338552i \(0.0107785\pi\)
\(504\) −0.500000 0.866025i −0.0222718 0.0385758i
\(505\) −3.68729 6.38658i −0.164082 0.284199i
\(506\) 21.0997 0.937995
\(507\) −11.0000 6.92820i −0.488527 0.307692i
\(508\) 8.00000 0.354943
\(509\) 6.58762 + 11.4101i 0.291991 + 0.505744i 0.974281 0.225339i \(-0.0723488\pi\)
−0.682289 + 0.731082i \(0.739015\pi\)
\(510\) −6.41238 11.1066i −0.283945 0.491807i
\(511\) −2.86254 + 4.95807i −0.126631 + 0.219332i
\(512\) 1.00000 0.0441942
\(513\) −3.27492 + 5.67232i −0.144591 + 0.250439i
\(514\) −7.50000 + 12.9904i −0.330811 + 0.572981i
\(515\) 22.5498 0.993664
\(516\) 5.91238 10.2405i 0.260278 0.450814i
\(517\) −13.0997 22.6893i −0.576123 0.997874i
\(518\) −0.137459 0.238085i −0.00603958 0.0104609i
\(519\) −4.54983 −0.199716
\(520\) 14.9622 3.70219i 0.656136 0.162352i
\(521\) −20.8248 −0.912349 −0.456174 0.889890i \(-0.650781\pi\)
−0.456174 + 0.889890i \(0.650781\pi\)
\(522\) −4.13746 7.16629i −0.181092 0.313660i
\(523\) 13.0997 + 22.6893i 0.572809 + 0.992133i 0.996276 + 0.0862221i \(0.0274795\pi\)
−0.423467 + 0.905911i \(0.639187\pi\)
\(524\) 1.36254 2.35999i 0.0595229 0.103097i
\(525\) 13.2749 0.579365
\(526\) −10.5498 + 18.2728i −0.459995 + 0.796734i
\(527\) 1.91238 3.31233i 0.0833044 0.144287i
\(528\) −4.00000 −0.174078
\(529\) −2.41238 + 4.17836i −0.104886 + 0.181668i
\(530\) 7.58762 + 13.1422i 0.329585 + 0.570859i
\(531\) 5.91238 + 10.2405i 0.256575 + 0.444401i
\(532\) 6.54983 0.283971
\(533\) −20.6873 21.4989i −0.896066 0.931219i
\(534\) 0.725083 0.0313774
\(535\) −5.45017 9.43996i −0.235631 0.408125i
\(536\) 1.36254 + 2.35999i 0.0588528 + 0.101936i
\(537\) −0.725083 + 1.25588i −0.0312896 + 0.0541952i
\(538\) −18.0000 −0.776035
\(539\) 2.00000 3.46410i 0.0861461 0.149209i
\(540\) −2.13746 + 3.70219i −0.0919816 + 0.159317i
\(541\) 25.3746 1.09094 0.545469 0.838131i \(-0.316351\pi\)
0.545469 + 0.838131i \(0.316351\pi\)
\(542\) −12.6375 + 21.8887i −0.542825 + 0.940201i
\(543\) 8.41238 + 14.5707i 0.361010 + 0.625287i
\(544\) −1.50000 2.59808i −0.0643120 0.111392i
\(545\) −19.4502 −0.833154
\(546\) −2.50000 2.59808i −0.106990 0.111187i
\(547\) 2.90033 0.124009 0.0620046 0.998076i \(-0.480251\pi\)
0.0620046 + 0.998076i \(0.480251\pi\)
\(548\) −11.4124 19.7668i −0.487513 0.844396i
\(549\) 4.50000 + 7.79423i 0.192055 + 0.332650i
\(550\) 26.5498 45.9857i 1.13209 1.96084i
\(551\) 54.1993 2.30897
\(552\) 2.63746 4.56821i 0.112258 0.194436i
\(553\) 4.00000 6.92820i 0.170097 0.294617i
\(554\) 14.8248 0.629843
\(555\) −0.587624 + 1.01779i −0.0249433 + 0.0432030i
\(556\) 4.54983 + 7.88054i 0.192956 + 0.334210i
\(557\) 17.5997 + 30.4835i 0.745722 + 1.29163i 0.949857 + 0.312685i \(0.101229\pi\)
−0.204135 + 0.978943i \(0.565438\pi\)
\(558\) −1.27492 −0.0539715
\(559\) 11.8248 40.9621i 0.500134 1.73251i
\(560\) 4.27492 0.180648
\(561\) 6.00000 + 10.3923i 0.253320 + 0.438763i
\(562\) 10.4124 + 18.0348i 0.439220 + 0.760751i
\(563\) −12.0000 + 20.7846i −0.505740 + 0.875967i 0.494238 + 0.869326i \(0.335447\pi\)
−0.999978 + 0.00664037i \(0.997886\pi\)
\(564\) −6.54983 −0.275798
\(565\) −31.6873 + 54.8840i −1.33309 + 2.30899i
\(566\) 4.72508 8.18408i 0.198610 0.344003i
\(567\) 1.00000 0.0419961
\(568\) −2.63746 + 4.56821i −0.110665 + 0.191678i
\(569\) −2.45017 4.24381i −0.102716 0.177910i 0.810087 0.586310i \(-0.199420\pi\)
−0.912803 + 0.408400i \(0.866087\pi\)
\(570\) −14.0000 24.2487i −0.586395 1.01567i
\(571\) −14.7251 −0.616226 −0.308113 0.951350i \(-0.599697\pi\)
−0.308113 + 0.951350i \(0.599697\pi\)
\(572\) −14.0000 + 3.46410i −0.585369 + 0.144841i
\(573\) 6.72508 0.280944
\(574\) −4.13746 7.16629i −0.172694 0.299115i
\(575\) 35.0120 + 60.6426i 1.46010 + 2.52897i
\(576\) −0.500000 + 0.866025i −0.0208333 + 0.0360844i
\(577\) 9.37459 0.390269 0.195135 0.980776i \(-0.437486\pi\)
0.195135 + 0.980776i \(0.437486\pi\)
\(578\) 4.00000 6.92820i 0.166378 0.288175i
\(579\) 12.4124 21.4989i 0.515841 0.893462i
\(580\) 35.3746 1.46885
\(581\) 5.91238 10.2405i 0.245287 0.424849i
\(582\) 0.274917 + 0.476171i 0.0113957 + 0.0197379i
\(583\) −7.09967 12.2970i −0.294038 0.509289i
\(584\) 5.72508 0.236906
\(585\) −4.27492 + 14.8087i −0.176746 + 0.612266i
\(586\) −18.2749 −0.754930
\(587\) −4.46221 7.72877i −0.184175 0.319001i 0.759123 0.650947i \(-0.225628\pi\)
−0.943298 + 0.331946i \(0.892295\pi\)
\(588\) −0.500000 0.866025i −0.0206197 0.0357143i
\(589\) 4.17525 7.23174i 0.172038 0.297979i
\(590\) −50.5498 −2.08110
\(591\) 10.9124 18.9008i 0.448875 0.777475i
\(592\) −0.137459 + 0.238085i −0.00564951 + 0.00978525i
\(593\) 4.45017 0.182746 0.0913732 0.995817i \(-0.470874\pi\)
0.0913732 + 0.995817i \(0.470874\pi\)
\(594\) 2.00000 3.46410i 0.0820610 0.142134i
\(595\) −6.41238 11.1066i −0.262882 0.455325i
\(596\) 0.500000 + 0.866025i 0.0204808 + 0.0354738i
\(597\) 11.8248 0.483955
\(598\) 5.27492 18.2728i 0.215707 0.747232i
\(599\) −10.7251 −0.438215 −0.219108 0.975701i \(-0.570315\pi\)
−0.219108 + 0.975701i \(0.570315\pi\)
\(600\) −6.63746 11.4964i −0.270973 0.469339i
\(601\) 3.86254 + 6.69012i 0.157556 + 0.272896i 0.933987 0.357307i \(-0.116305\pi\)
−0.776431 + 0.630203i \(0.782972\pi\)
\(602\) 5.91238 10.2405i 0.240970 0.417373i
\(603\) −2.72508 −0.110974
\(604\) −6.54983 + 11.3446i −0.266509 + 0.461607i
\(605\) −10.6873 + 18.5109i −0.434500 + 0.752577i
\(606\) 1.72508 0.0700767
\(607\) −7.36254 + 12.7523i −0.298836 + 0.517600i −0.975870 0.218352i \(-0.929932\pi\)
0.677034 + 0.735952i \(0.263265\pi\)
\(608\) −3.27492 5.67232i −0.132815 0.230043i
\(609\) −4.13746 7.16629i −0.167658 0.290393i
\(610\) −38.4743 −1.55778
\(611\) −22.9244 + 5.67232i −0.927423 + 0.229478i
\(612\) 3.00000 0.121268
\(613\) −14.6873 25.4391i −0.593214 1.02748i −0.993796 0.111216i \(-0.964525\pi\)
0.400582 0.916261i \(-0.368808\pi\)
\(614\) 0.725083 + 1.25588i 0.0292620 + 0.0506832i
\(615\) −17.6873 + 30.6353i −0.713220 + 1.23533i
\(616\) −4.00000 −0.161165
\(617\) −19.9622 + 34.5756i −0.803648 + 1.39196i 0.113551 + 0.993532i \(0.463777\pi\)
−0.917200 + 0.398428i \(0.869556\pi\)
\(618\) −2.63746 + 4.56821i −0.106094 + 0.183760i
\(619\) −15.6495 −0.629007 −0.314503 0.949256i \(-0.601838\pi\)
−0.314503 + 0.949256i \(0.601838\pi\)
\(620\) 2.72508 4.71998i 0.109442 0.189559i
\(621\) 2.63746 + 4.56821i 0.105838 + 0.183316i
\(622\) 1.27492 + 2.20822i 0.0511195 + 0.0885416i
\(623\) 0.725083 0.0290498
\(624\) −1.00000 + 3.46410i −0.0400320 + 0.138675i
\(625\) 84.8488 3.39395
\(626\) −8.82475 15.2849i −0.352708 0.610908i
\(627\) 13.0997 + 22.6893i 0.523150 + 0.906123i
\(628\) 1.86254 3.22602i 0.0743235 0.128732i
\(629\) 0.824752 0.0328850
\(630\) −2.13746 + 3.70219i −0.0851584 + 0.147499i
\(631\) 14.5498 25.2011i 0.579220 1.00324i −0.416349 0.909205i \(-0.636691\pi\)
0.995569 0.0940333i \(-0.0299760\pi\)
\(632\) −8.00000 −0.318223
\(633\) −10.5498 + 18.2728i −0.419318 + 0.726281i
\(634\) 3.77492 + 6.53835i 0.149921 + 0.259671i
\(635\) −17.0997 29.6175i −0.678580 1.17533i
\(636\) −3.54983 −0.140760
\(637\) −2.50000 2.59808i −0.0990536 0.102940i
\(638\) −33.0997 −1.31043
\(639\) −2.63746 4.56821i −0.104336 0.180716i
\(640\) −2.13746 3.70219i −0.0844905 0.146342i
\(641\) −9.41238 + 16.3027i −0.371766 + 0.643918i −0.989837 0.142204i \(-0.954581\pi\)
0.618071 + 0.786122i \(0.287914\pi\)
\(642\) 2.54983 0.100634
\(643\) 16.3746 28.3616i 0.645751 1.11847i −0.338377 0.941011i \(-0.609878\pi\)
0.984128 0.177462i \(-0.0567888\pi\)
\(644\) 2.63746 4.56821i 0.103930 0.180013i
\(645\) −50.5498 −1.99040
\(646\) −9.82475 + 17.0170i −0.386550 + 0.669524i
\(647\) −4.72508 8.18408i −0.185762 0.321750i 0.758071 0.652172i \(-0.226142\pi\)
−0.943833 + 0.330423i \(0.892809\pi\)
\(648\) −0.500000 0.866025i −0.0196419 0.0340207i
\(649\) 47.2990 1.85665
\(650\) −33.1873 34.4892i −1.30171 1.35278i
\(651\) −1.27492 −0.0499679
\(652\) 6.63746 + 11.4964i 0.259943 + 0.450234i
\(653\) −16.7371 28.9896i −0.654974 1.13445i −0.981900 0.189399i \(-0.939346\pi\)
0.326926 0.945050i \(-0.393987\pi\)
\(654\) 2.27492 3.94027i 0.0889563 0.154077i
\(655\) −11.6495 −0.455184
\(656\) −4.13746 + 7.16629i −0.161541 + 0.279797i
\(657\) −2.86254 + 4.95807i −0.111678 + 0.193433i
\(658\) −6.54983 −0.255339
\(659\) 6.72508 11.6482i 0.261972 0.453749i −0.704794 0.709412i \(-0.748961\pi\)
0.966766 + 0.255663i \(0.0822938\pi\)
\(660\) 8.54983 + 14.8087i 0.332802 + 0.576430i
\(661\) −4.95017 8.57394i −0.192539 0.333488i 0.753552 0.657388i \(-0.228339\pi\)
−0.946091 + 0.323901i \(0.895006\pi\)
\(662\) 4.00000 0.155464
\(663\) 10.5000 2.59808i 0.407786 0.100901i
\(664\) −11.8248 −0.458889
\(665\) −14.0000 24.2487i −0.542897 0.940325i
\(666\) −0.137459 0.238085i −0.00532641 0.00922562i
\(667\) 21.8248 37.8016i 0.845058 1.46368i
\(668\) 0 0
\(669\) −5.36254 + 9.28819i −0.207328 + 0.359102i
\(670\) 5.82475 10.0888i 0.225030 0.389763i
\(671\) 36.0000 1.38976
\(672\) −0.500000 + 0.866025i −0.0192879 + 0.0334077i
\(673\) 9.04983 + 15.6748i 0.348845 + 0.604218i 0.986045 0.166481i \(-0.0532405\pi\)
−0.637199 + 0.770699i \(0.719907\pi\)
\(674\) −0.137459 0.238085i −0.00529471 0.00917070i
\(675\) 13.2749 0.510952
\(676\) −0.500000 + 12.9904i −0.0192308 + 0.499630i
\(677\) −33.6495 −1.29326 −0.646628 0.762806i \(-0.723821\pi\)
−0.646628 + 0.762806i \(0.723821\pi\)
\(678\) −7.41238 12.8386i −0.284671 0.493064i
\(679\) 0.274917 + 0.476171i 0.0105504 + 0.0182738i
\(680\) −6.41238 + 11.1066i −0.245903 + 0.425917i
\(681\) −21.0997 −0.808541
\(682\) −2.54983 + 4.41644i −0.0976382 + 0.169114i
\(683\) 2.17525 3.76764i 0.0832336 0.144165i −0.821404 0.570347i \(-0.806809\pi\)
0.904637 + 0.426183i \(0.140142\pi\)
\(684\) 6.54983 0.250439
\(685\) −48.7870 + 84.5015i −1.86405 + 3.22864i
\(686\) −0.500000 0.866025i −0.0190901 0.0330650i
\(687\) −6.36254 11.0202i −0.242746 0.420449i
\(688\) −11.8248 −0.450814
\(689\) −12.4244 + 3.07425i −0.473333 + 0.117119i
\(690\) −22.5498 −0.858458
\(691\) −4.00000 6.92820i −0.152167 0.263561i 0.779857 0.625958i \(-0.215292\pi\)
−0.932024 + 0.362397i \(0.881959\pi\)
\(692\) 2.27492 + 3.94027i 0.0864794 + 0.149787i
\(693\) 2.00000 3.46410i 0.0759737 0.131590i
\(694\) 30.5498 1.15966
\(695\) 19.4502 33.6887i 0.737787 1.27788i
\(696\) −4.13746 + 7.16629i −0.156830 + 0.271637i
\(697\) 24.8248 0.940305
\(698\) 17.4622 30.2454i 0.660954 1.14481i
\(699\) −3.72508 6.45203i −0.140896 0.244038i
\(700\) −6.63746 11.4964i −0.250872 0.434524i
\(701\) 14.9244 0.563688 0.281844 0.959460i \(-0.409054\pi\)
0.281844 + 0.959460i \(0.409054\pi\)
\(702\) −2.50000 2.59808i −0.0943564 0.0980581i
\(703\) 1.80066 0.0679133
\(704\) 2.00000 + 3.46410i 0.0753778 + 0.130558i
\(705\) 14.0000 + 24.2487i 0.527271 + 0.913259i
\(706\) 9.77492 16.9307i 0.367884 0.637194i
\(707\) 1.72508 0.0648784
\(708\) 5.91238 10.2405i 0.222201 0.384863i
\(709\) 23.6873 41.0276i 0.889595 1.54082i 0.0492402 0.998787i \(-0.484320\pi\)
0.840355 0.542037i \(-0.182347\pi\)
\(710\) 22.5498 0.846280
\(711\) 4.00000 6.92820i 0.150012 0.259828i
\(712\) −0.362541 0.627940i −0.0135868 0.0235331i
\(713\) −3.36254 5.82409i −0.125928 0.218114i
\(714\) 3.00000 0.112272
\(715\) 42.7492 + 44.4262i 1.59873 + 1.66145i
\(716\) 1.45017 0.0541952
\(717\) 2.63746 + 4.56821i 0.0984977 + 0.170603i
\(718\) 0.549834 + 0.952341i 0.0205196 + 0.0355411i
\(719\) 4.00000 6.92820i 0.149175 0.258378i −0.781748 0.623595i \(-0.785672\pi\)
0.930923 + 0.365216i \(0.119005\pi\)
\(720\) 4.27492 0.159317
\(721\) −2.63746 + 4.56821i −0.0982241 + 0.170129i
\(722\) −11.9502 + 20.6983i −0.444739 + 0.770311i
\(723\) −15.7251 −0.584822
\(724\) 8.41238 14.5707i 0.312643 0.541514i
\(725\) −54.9244 95.1319i −2.03984 3.53311i
\(726\) −2.50000 4.33013i −0.0927837 0.160706i
\(727\) 19.8248 0.735259 0.367630 0.929972i \(-0.380169\pi\)
0.367630 + 0.929972i \(0.380169\pi\)
\(728\) −1.00000 + 3.46410i −0.0370625 + 0.128388i
\(729\) 1.00000 0.0370370
\(730\) −12.2371 21.1953i −0.452916 0.784474i
\(731\) 17.7371 + 30.7216i 0.656031 + 1.13628i
\(732\) 4.50000 7.79423i 0.166325 0.288083i
\(733\) −32.6495 −1.20594 −0.602968 0.797765i \(-0.706016\pi\)
−0.602968 + 0.797765i \(0.706016\pi\)
\(734\) −6.63746 + 11.4964i −0.244993 + 0.424340i
\(735\) −2.13746 + 3.70219i −0.0788413 + 0.136557i
\(736\) −5.27492 −0.194436
\(737\) −5.45017 + 9.43996i −0.200759 + 0.347726i
\(738\) −4.13746 7.16629i −0.152302 0.263795i
\(739\) 24.6375 + 42.6733i 0.906304 + 1.56976i 0.819158 + 0.573568i \(0.194441\pi\)
0.0871458 + 0.996196i \(0.472225\pi\)
\(740\) 1.17525 0.0432030
\(741\) 22.9244 5.67232i 0.842150 0.208378i
\(742\) −3.54983 −0.130319
\(743\) 2.08762 + 3.61587i 0.0765875 + 0.132653i 0.901776 0.432205i \(-0.142264\pi\)
−0.825188 + 0.564858i \(0.808931\pi\)
\(744\) 0.637459 + 1.10411i 0.0233704 + 0.0404787i
\(745\) 2.13746 3.70219i 0.0783104 0.135638i
\(746\) 26.8248 0.982124
\(747\) 5.91238 10.2405i 0.216323 0.374682i
\(748\) 6.00000 10.3923i 0.219382 0.379980i
\(749\) 2.54983 0.0931689
\(750\) −17.6873 + 30.6353i −0.645849 + 1.11864i
\(751\) 9.27492 + 16.0646i 0.338447 + 0.586207i 0.984141 0.177390i \(-0.0567652\pi\)
−0.645694 + 0.763596i \(0.723432\pi\)
\(752\) 3.27492 + 5.67232i 0.119424 + 0.206848i
\(753\) 13.2749 0.483765
\(754\) −8.27492 + 28.6652i −0.301355 + 1.04392i
\(755\) 56.0000 2.03805
\(756\) −0.500000 0.866025i −0.0181848 0.0314970i
\(757\) 13.0000 + 22.5167i 0.472493 + 0.818382i 0.999505 0.0314762i \(-0.0100208\pi\)
−0.527011 + 0.849858i \(0.676688\pi\)
\(758\) 10.0000 17.3205i 0.363216 0.629109i
\(759\) 21.0997 0.765869
\(760\) −14.0000 + 24.2487i −0.507833 + 0.879593i
\(761\) −10.0997 + 17.4931i −0.366113 + 0.634126i −0.988954 0.148222i \(-0.952645\pi\)
0.622841 + 0.782348i \(0.285978\pi\)
\(762\) 8.00000 0.289809
\(763\) 2.27492 3.94027i 0.0823575 0.142647i
\(764\) −3.36254 5.82409i −0.121652 0.210708i
\(765\) −6.41238 11.1066i −0.231840 0.401559i
\(766\) 22.1993 0.802095
\(767\) 11.8248 40.9621i 0.426967 1.47906i
\(768\) 1.00000 0.0360844
\(769\) −20.8248 36.0695i −0.750960 1.30070i −0.947358 0.320176i \(-0.896258\pi\)
0.196398 0.980524i \(-0.437075\pi\)
\(770\) 8.54983 + 14.8087i 0.308115 + 0.533670i
\(771\) −7.50000 + 12.9904i −0.270106 + 0.467837i
\(772\) −24.8248 −0.893462
\(773\) 10.4502 18.1002i 0.375866 0.651020i −0.614590 0.788847i \(-0.710679\pi\)
0.990456 + 0.137827i \(0.0440118\pi\)
\(774\) 5.91238 10.2405i 0.212516 0.368088i
\(775\) −16.9244 −0.607943
\(776\) 0.274917 0.476171i 0.00986895 0.0170935i
\(777\) −0.137459 0.238085i −0.00493130 0.00854126i
\(778\) 12.3248 + 21.3471i 0.441864 + 0.765330i
\(779\) 54.1993 1.94189
\(780\) 14.9622 3.70219i 0.535733 0.132560i
\(781\) −21.0997 −0.755006
\(782\) 7.91238 + 13.7046i 0.282946 + 0.490077i
\(783\) −4.13746 7.16629i −0.147861 0.256102i
\(784\) −0.500000 + 0.866025i −0.0178571 + 0.0309295i
\(785\) −15.9244 −0.568367
\(786\) 1.36254 2.35999i 0.0486002 0.0841781i
\(787\) −10.5498 + 18.2728i −0.376061 + 0.651357i −0.990485 0.137619i \(-0.956055\pi\)
0.614424 + 0.788976i \(0.289388\pi\)
\(788\) −21.8248 −0.777475
\(789\) −10.5498 + 18.2728i −0.375584 + 0.650531i
\(790\) 17.0997 + 29.6175i 0.608379 + 1.05374i
\(791\) −7.41238 12.8386i −0.263554 0.456488i
\(792\) −4.00000 −0.142134
\(793\) 9.00000 31.1769i 0.319599 1.10712i
\(794\) 23.2749 0.825996
\(795\) 7.58762 + 13.1422i 0.269105 + 0.466104i
\(796\) −5.91238 10.2405i −0.209559 0.362966i
\(797\) −8.27492 + 14.3326i −0.293113 + 0.507686i −0.974544 0.224196i \(-0.928024\pi\)
0.681431 + 0.731882i \(0.261358\pi\)
\(798\) 6.54983 0.231862
\(799\) 9.82475 17.0170i 0.347575 0.602017i
\(800\) −6.63746 + 11.4964i −0.234670 + 0.406460i
\(801\) 0.725083 0.0256195
\(802\) 1.13746 1.97014i 0.0401651 0.0695679i
\(803\) 11.4502 + 19.8323i 0.404068 + 0.699866i
\(804\) 1.36254 + 2.35999i 0.0480531 + 0.0832305i
\(805\) −22.5498 −0.794777
\(806\) 3.18729 + 3.31233i 0.112268 + 0.116672i
\(807\) −18.0000 −0.633630
\(808\) −0.862541 1.49397i −0.0303441 0.0525575i
\(809\) −4.86254 8.42217i −0.170958 0.296108i 0.767797 0.640693i \(-0.221353\pi\)
−0.938755 + 0.344585i \(0.888020\pi\)
\(810\) −2.13746 + 3.70219i −0.0751026 + 0.130082i
\(811\) 5.09967 0.179074 0.0895368 0.995984i \(-0.471461\pi\)
0.0895368 + 0.995984i \(0.471461\pi\)
\(812\) −4.13746 + 7.16629i −0.145196 + 0.251487i
\(813\) −12.6375 + 21.8887i −0.443215 + 0.767671i
\(814\) −1.09967 −0.0385434
\(815\) 28.3746 49.1462i 0.993918 1.72152i
\(816\) −1.50000 2.59808i −0.0525105 0.0909509i
\(817\) 38.7251 + 67.0738i 1.35482 + 2.34662i
\(818\) −29.9244 −1.04628
\(819\) −2.50000 2.59808i −0.0873571 0.0907841i
\(820\) 35.3746 1.23533
\(821\) −7.63746 13.2285i −0.266549 0.461677i 0.701419 0.712749i \(-0.252550\pi\)
−0.967968 + 0.251072i \(0.919217\pi\)
\(822\) −11.4124 19.7668i −0.398052 0.689447i
\(823\) 3.45017 5.97586i 0.120265 0.208305i −0.799607 0.600524i \(-0.794959\pi\)
0.919872 + 0.392218i \(0.128292\pi\)
\(824\) 5.27492 0.183760
\(825\) 26.5498 45.9857i 0.924347 1.60102i
\(826\) 5.91238 10.2405i 0.205718 0.356314i
\(827\) 5.09967 0.177333 0.0886664 0.996061i \(-0.471739\pi\)
0.0886664 + 0.996061i \(0.471739\pi\)
\(828\) 2.63746 4.56821i 0.0916580 0.158756i
\(829\) 22.4124 + 38.8194i 0.778414 + 1.34825i 0.932856 + 0.360251i \(0.117309\pi\)
−0.154442 + 0.988002i \(0.549358\pi\)
\(830\) 25.2749 + 43.7774i 0.877305 + 1.51954i
\(831\) 14.8248 0.514265
\(832\) 3.50000 0.866025i 0.121341 0.0300240i
\(833\) 3.00000 0.103944
\(834\) 4.54983 + 7.88054i 0.157548 + 0.272881i
\(835\) 0 0
\(836\) 13.0997 22.6893i 0.453062 0.784726i
\(837\) −1.27492 −0.0440676
\(838\) 11.1873 19.3770i 0.386459 0.669366i
\(839\) 10.3746 17.9693i 0.358170 0.620369i −0.629485 0.777013i \(-0.716734\pi\)
0.987655 + 0.156643i \(0.0500673\pi\)
\(840\) 4.27492 0.147499
\(841\) −19.7371 + 34.1857i −0.680591 + 1.17882i
\(842\) −4.13746 7.16629i −0.142586 0.246967i
\(843\) 10.4124 + 18.0348i 0.358621 + 0.621150i
\(844\) 21.0997 0.726281
\(845\) 49.1615 25.9153i 1.69121 0.891514i
\(846\) −6.54983 −0.225188
\(847\) −2.50000 4.33013i −0.0859010 0.148785i
\(848\) 1.77492 + 3.07425i 0.0609509 + 0.105570i
\(849\) 4.72508 8.18408i 0.162164 0.280877i
\(850\) 39.8248 1.36598
\(851\) 0.725083 1.25588i 0.0248555 0.0430510i
\(852\) −2.63746 + 4.56821i −0.0903578 + 0.156504i
\(853\) −14.4502 −0.494764 −0.247382 0.968918i \(-0.579570\pi\)
−0.247382 + 0.968918i \(0.579570\pi\)
\(854\) 4.50000 7.79423i 0.153987 0.266713i
\(855\) −14.0000 24.2487i −0.478790 0.829288i
\(856\) −1.27492 2.20822i −0.0435758 0.0754755i
\(857\) −36.8248 −1.25791 −0.628955 0.777442i \(-0.716517\pi\)
−0.628955 + 0.777442i \(0.716517\pi\)
\(858\) −14.0000 + 3.46410i −0.477952 + 0.118262i
\(859\) −27.6495 −0.943389 −0.471694 0.881762i \(-0.656357\pi\)
−0.471694 + 0.881762i \(0.656357\pi\)
\(860\) 25.2749 + 43.7774i 0.861868 + 1.49280i
\(861\) −4.13746 7.16629i −0.141004 0.244226i
\(862\) 6.63746 11.4964i 0.226073 0.391569i
\(863\) 35.2990 1.20159 0.600796 0.799402i \(-0.294850\pi\)
0.600796 + 0.799402i \(0.294850\pi\)
\(864\) −0.500000 + 0.866025i −0.0170103 + 0.0294628i
\(865\) 9.72508 16.8443i 0.330663 0.572725i
\(866\) −10.2749 −0.349156
\(867\) 4.00000 6.92820i 0.135847 0.235294i
\(868\) 0.637459 + 1.10411i 0.0216368 + 0.0374760i
\(869\) −16.0000 27.7128i −0.542763 0.940093i
\(870\) 35.3746 1.19931
\(871\) 6.81271 + 7.07997i 0.230840 + 0.239896i
\(872\) −4.54983 −0.154077
\(873\) 0.274917 + 0.476171i 0.00930454 + 0.0161159i
\(874\) 17.2749 + 29.9210i 0.584333 + 1.01209i
\(875\) −17.6873 + 30.6353i −0.597940 + 1.03566i
\(876\) 5.72508 0.193433
\(877\) 1.86254 3.22602i 0.0628936 0.108935i −0.832864 0.553478i \(-0.813300\pi\)
0.895758 + 0.444543i \(0.146634\pi\)
\(878\) −6.54983 + 11.3446i −0.221046 + 0.382863i
\(879\) −18.2749 −0.616398
\(880\) 8.54983 14.8087i 0.288215 0.499203i
\(881\) −0.774917 1.34220i −0.0261076 0.0452197i 0.852676 0.522439i \(-0.174978\pi\)
−0.878784 + 0.477220i \(0.841645\pi\)
\(882\) −0.500000 0.866025i −0.0168359 0.0291606i
\(883\) 58.0241 1.95267 0.976333 0.216273i \(-0.0693900\pi\)
0.976333 + 0.216273i \(0.0693900\pi\)
\(884\) −7.50000 7.79423i −0.252252 0.262148i
\(885\) −50.5498 −1.69921
\(886\) −17.2749 29.9210i −0.580362 1.00522i
\(887\) −23.2749 40.3133i −0.781495 1.35359i −0.931071 0.364839i \(-0.881124\pi\)
0.149575 0.988750i \(-0.452209\pi\)
\(888\) −0.137459 + 0.238085i −0.00461281 + 0.00798962i
\(889\) 8.00000 0.268311
\(890\) −1.54983 + 2.68439i −0.0519506 + 0.0899810i
\(891\) 2.00000 3.46410i 0.0670025 0.116052i
\(892\) 10.7251 0.359102
\(893\) 21.4502 37.1528i 0.717802 1.24327i
\(894\) 0.500000 + 0.866025i 0.0167225 + 0.0289642i
\(895\) −3.09967 5.36878i −0.103611 0.179459i
\(896\) 1.00000 0.0334077
\(897\) 5.27492 18.2728i 0.176124 0.610113i
\(898\) −19.0997 −0.637364
\(899\) 5.27492 + 9.13642i 0.175928 + 0.304717i
\(900\) −6.63746 11.4964i −0.221249 0.383214i
\(901\) 5.32475 9.22274i 0.177393 0.307254i
\(902\) −33.0997 −1.10210
\(903\) 5.91238 10.2405i 0.196752 0.340784i
\(904\) −7.41238 + 12.8386i −0.246532 + 0.427006i
\(905\) −71.9244 −2.39085
\(906\) −6.54983 + 11.3446i −0.217604 + 0.376901i
\(907\) 19.9124 + 34.4892i 0.661180 + 1.14520i 0.980306 + 0.197484i \(0.0632772\pi\)
−0.319126 + 0.947712i \(0.603389\pi\)
\(908\) 10.5498 + 18.2728i 0.350109 + 0.606406i
\(909\) 1.72508 0.0572174
\(910\) 14.9622 3.70219i 0.495992 0.122726i
\(911\) −25.0997 −0.831589 −0.415795 0.909459i \(-0.636496\pi\)
−0.415795 + 0.909459i \(0.636496\pi\)
\(912\) −3.27492 5.67232i −0.108443 0.187829i
\(913\) −23.6495 40.9621i −0.782684 1.35565i
\(914\) 8.50000 14.7224i 0.281155 0.486975i
\(915\) −38.4743 −1.27192
\(916\) −6.36254 + 11.0202i −0.210224 + 0.364119i
\(917\) 1.36254 2.35999i 0.0449951 0.0779338i
\(918\) 3.00000 0.0990148
\(919\) −19.8248 + 34.3375i −0.653958 + 1.13269i 0.328196 + 0.944610i \(0.393559\pi\)
−0.982154 + 0.188079i \(0.939774\pi\)
\(920\) 11.2749 + 19.5287i 0.371723 + 0.643843i
\(921\) 0.725083 + 1.25588i 0.0238923 + 0.0413827i
\(922\) −19.3746 −0.638068
\(923\) −5.27492 + 18.2728i −0.173626 + 0.601458i
\(924\) −4.00000 −0.131590
\(925\) −1.82475 3.16056i −0.0599975 0.103919i
\(926\) 5.27492 + 9.13642i 0.173345 + 0.300242i
\(927\) −2.63746 + 4.56821i −0.0866255 + 0.150040i
\(928\) 8.27492 0.271637
\(929\) −26.7749 + 46.3755i −0.878457 + 1.52153i −0.0254221 + 0.999677i \(0.508093\pi\)
−0.853034 + 0.521855i \(0.825240\pi\)
\(930\) 2.72508 4.71998i 0.0893590 0.154774i
\(931\) 6.54983 0.214662
\(932\) −3.72508 + 6.45203i −0.122019 + 0.211343i
\(933\) 1.27492 + 2.20822i 0.0417389 + 0.0722939i
\(934\) 4.08762 + 7.07997i 0.133751 + 0.231664i
\(935\) −51.2990 −1.67766
\(936\) −1.00000 + 3.46410i −0.0326860 + 0.113228i
\(937\) 19.1752 0.626428 0.313214 0.949683i \(-0.398594\pi\)
0.313214 + 0.949683i \(0.398594\pi\)
\(938\) 1.36254 + 2.35999i 0.0444886 + 0.0770564i
\(939\) −8.82475 15.2849i −0.287985 0.498804i
\(940\) 14.0000 24.2487i 0.456630 0.790906i
\(941\) 37.6495 1.22734 0.613669 0.789563i \(-0.289693\pi\)
0.613669 + 0.789563i \(0.289693\pi\)
\(942\) 1.86254 3.22602i 0.0606849 0.105109i
\(943\) 21.8248 37.8016i 0.710712 1.23099i
\(944\) −11.8248 −0.384863
\(945\) −2.13746 + 3.70219i −0.0695315 + 0.120432i
\(946\) −23.6495 40.9621i −0.768912 1.33179i
\(947\) 4.54983 + 7.88054i 0.147850 + 0.256083i 0.930433 0.366463i \(-0.119431\pi\)
−0.782583 + 0.622547i \(0.786098\pi\)
\(948\) −8.00000 −0.259828
\(949\) 20.0378 4.95807i 0.650454 0.160946i
\(950\) 86.9485 2.82098
\(951\) 3.77492 + 6.53835i 0.122410 + 0.212020i
\(952\) −1.50000 2.59808i −0.0486153 0.0842041i
\(953\) 5.54983 9.61260i 0.179777 0.311383i −0.762027 0.647545i \(-0.775796\pi\)
0.941804 + 0.336162i \(0.109129\pi\)
\(954\) −3.54983 −0.114930
\(955\) −14.3746 + 24.8975i −0.465151 + 0.805665i
\(956\) 2.63746 4.56821i 0.0853015 0.147747i
\(957\) −33.0997 −1.06996
\(958\) −10.0000 + 17.3205i −0.323085 + 0.559600i
\(959\) −11.4124 19.7668i −0.368525 0.638304i
\(960\) −2.13746 3.70219i −0.0689862 0.119488i
\(961\) −29.3746 −0.947567
\(962\) −0.274917 + 0.952341i −0.00886369 + 0.0307047i
\(963\) 2.54983 0.0821673
\(964\) 7.86254 + 13.6183i 0.253235 + 0.438617i
\(965\) 53.0619 + 91.9059i 1.70812 + 2.95855i
\(966\) 2.63746 4.56821i 0.0848588 0.146980i
\(967\) −18.5498 −0.596522 −0.298261 0.954484i \(-0.596407\pi\)
−0.298261 + 0.954484i \(0.596407\pi\)
\(968\) −2.50000 + 4.33013i −0.0803530 + 0.139176i
\(969\) −9.82475 + 17.0170i −0.315616 + 0.546664i
\(970\) −2.35050 −0.0754699
\(971\) −24.2870 + 42.0663i −0.779406 + 1.34997i 0.152879 + 0.988245i \(0.451146\pi\)
−0.932285 + 0.361725i \(0.882188\pi\)
\(972\) −0.500000 0.866025i −0.0160375 0.0277778i
\(973\) 4.54983 + 7.88054i 0.145861 + 0.252639i
\(974\) −1.09967 −0.0352357
\(975\) −33.1873 34.4892i −1.06284 1.10454i
\(976\) −9.00000 −0.288083
\(977\) −12.3127 21.3262i −0.393918 0.682287i 0.599044 0.800716i \(-0.295547\pi\)
−0.992962 + 0.118429i \(0.962214\pi\)
\(978\) 6.63746 + 11.4964i 0.212243 + 0.367615i
\(979\) 1.45017 2.51176i 0.0463475 0.0802762i
\(980\) 4.27492 0.136557
\(981\) 2.27492 3.94027i 0.0726325 0.125803i
\(982\) −12.5498 + 21.7370i −0.400481 + 0.693654i
\(983\) 53.8488 1.71751 0.858756 0.512385i \(-0.171238\pi\)
0.858756 + 0.512385i \(0.171238\pi\)
\(984\) −4.13746 + 7.16629i −0.131897 + 0.228453i
\(985\) 46.6495 + 80.7993i 1.48638 + 2.57448i
\(986\) −12.4124 21.4989i −0.395291 0.684663i
\(987\) −6.54983 −0.208484
\(988\) −16.3746 17.0170i −0.520945 0.541382i
\(989\) 62.3746 1.98340
\(990\) 8.54983 + 14.8087i 0.271732 + 0.470653i
\(991\) 18.3746 + 31.8257i 0.583688 + 1.01098i 0.995038 + 0.0994996i \(0.0317242\pi\)
−0.411350 + 0.911478i \(0.634942\pi\)
\(992\) 0.637459 1.10411i 0.0202393 0.0350555i
\(993\) 4.00000 0.126936
\(994\) −2.63746 + 4.56821i −0.0836551 + 0.144895i
\(995\) −25.2749 + 43.7774i −0.801269 + 1.38784i
\(996\) −11.8248 −0.374682
\(997\) 1.95017 3.37779i 0.0617624 0.106976i −0.833491 0.552533i \(-0.813661\pi\)
0.895253 + 0.445558i \(0.146995\pi\)
\(998\) 15.9124 + 27.5610i 0.503697 + 0.872430i
\(999\) −0.137459 0.238085i −0.00434900 0.00753269i
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 546.2.l.j.211.2 4
3.2 odd 2 1638.2.r.x.757.1 4
13.3 even 3 7098.2.a.ca.1.2 2
13.9 even 3 inner 546.2.l.j.295.2 yes 4
13.10 even 6 7098.2.a.bm.1.1 2
39.35 odd 6 1638.2.r.x.1387.1 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
546.2.l.j.211.2 4 1.1 even 1 trivial
546.2.l.j.295.2 yes 4 13.9 even 3 inner
1638.2.r.x.757.1 4 3.2 odd 2
1638.2.r.x.1387.1 4 39.35 odd 6
7098.2.a.bm.1.1 2 13.10 even 6
7098.2.a.ca.1.2 2 13.3 even 3