Properties

Label 546.2.bb.a.269.29
Level $546$
Weight $2$
Character 546.269
Analytic conductor $4.360$
Analytic rank $0$
Dimension $76$
CM no
Inner twists $4$

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [546,2,Mod(269,546)]
 
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([3, 1, 4]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("546.269");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 546 = 2 \cdot 3 \cdot 7 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 546.bb (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: \(4.35983195036\)
Analytic rank: \(0\)
Dimension: \(76\)
Relative dimension: \(38\) over \(\Q(\zeta_{6})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 269.29
Character \(\chi\) \(=\) 546.269
Dual form 546.2.bb.a.341.10

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+1.00000i q^{2} +(0.0345880 + 1.73171i) q^{3} -1.00000 q^{4} +(-0.699535 - 1.21163i) q^{5} +(-1.73171 + 0.0345880i) q^{6} +(-2.51159 + 0.831830i) q^{7} -1.00000i q^{8} +(-2.99761 + 0.119792i) q^{9} +O(q^{10})\) \(q+1.00000i q^{2} +(0.0345880 + 1.73171i) q^{3} -1.00000 q^{4} +(-0.699535 - 1.21163i) q^{5} +(-1.73171 + 0.0345880i) q^{6} +(-2.51159 + 0.831830i) q^{7} -1.00000i q^{8} +(-2.99761 + 0.119792i) q^{9} +(1.21163 - 0.699535i) q^{10} +(-1.09604 + 0.632798i) q^{11} +(-0.0345880 - 1.73171i) q^{12} +(3.58555 - 0.379286i) q^{13} +(-0.831830 - 2.51159i) q^{14} +(2.07399 - 1.25330i) q^{15} +1.00000 q^{16} -6.86805 q^{17} +(-0.119792 - 2.99761i) q^{18} +(-3.99411 - 2.30600i) q^{19} +(0.699535 + 1.21163i) q^{20} +(-1.52735 - 4.32055i) q^{21} +(-0.632798 - 1.09604i) q^{22} -2.51705i q^{23} +(1.73171 - 0.0345880i) q^{24} +(1.52130 - 2.63497i) q^{25} +(0.379286 + 3.58555i) q^{26} +(-0.311127 - 5.18683i) q^{27} +(2.51159 - 0.831830i) q^{28} +(-4.55247 - 2.62837i) q^{29} +(1.25330 + 2.07399i) q^{30} +(4.41277 + 2.54772i) q^{31} +1.00000i q^{32} +(-1.13373 - 1.87613i) q^{33} -6.86805i q^{34} +(2.76481 + 2.46122i) q^{35} +(2.99761 - 0.119792i) q^{36} -6.91395 q^{37} +(2.30600 - 3.99411i) q^{38} +(0.780828 + 6.19599i) q^{39} +(-1.21163 + 0.699535i) q^{40} +(-3.22591 + 5.58745i) q^{41} +(4.32055 - 1.52735i) q^{42} +(6.08396 + 10.5377i) q^{43} +(1.09604 - 0.632798i) q^{44} +(2.24208 + 3.54819i) q^{45} +2.51705 q^{46} +(1.58414 + 2.74382i) q^{47} +(0.0345880 + 1.73171i) q^{48} +(5.61612 - 4.17842i) q^{49} +(2.63497 + 1.52130i) q^{50} +(-0.237552 - 11.8934i) q^{51} +(-3.58555 + 0.379286i) q^{52} +(0.444106 + 0.256405i) q^{53} +(5.18683 - 0.311127i) q^{54} +(1.53343 + 0.885329i) q^{55} +(0.831830 + 2.51159i) q^{56} +(3.85517 - 6.99639i) q^{57} +(2.62837 - 4.55247i) q^{58} -14.3744 q^{59} +(-2.07399 + 1.25330i) q^{60} +(-2.66263 - 1.53727i) q^{61} +(-2.54772 + 4.41277i) q^{62} +(7.42910 - 2.79437i) q^{63} -1.00000 q^{64} +(-2.96777 - 4.07903i) q^{65} +(1.87613 - 1.13373i) q^{66} +(0.312240 + 0.540816i) q^{67} +6.86805 q^{68} +(4.35878 - 0.0870596i) q^{69} +(-2.46122 + 2.76481i) q^{70} +(-3.78894 + 2.18755i) q^{71} +(0.119792 + 2.99761i) q^{72} +(-7.24349 - 4.18203i) q^{73} -6.91395i q^{74} +(4.61561 + 2.54331i) q^{75} +(3.99411 + 2.30600i) q^{76} +(2.22641 - 2.50104i) q^{77} +(-6.19599 + 0.780828i) q^{78} +(7.13902 + 12.3651i) q^{79} +(-0.699535 - 1.21163i) q^{80} +(8.97130 - 0.718182i) q^{81} +(-5.58745 - 3.22591i) q^{82} +3.52068 q^{83} +(1.52735 + 4.32055i) q^{84} +(4.80444 + 8.32154i) q^{85} +(-10.5377 + 6.08396i) q^{86} +(4.39410 - 7.97445i) q^{87} +(0.632798 + 1.09604i) q^{88} -15.8874 q^{89} +(-3.54819 + 2.24208i) q^{90} +(-8.68990 + 3.93517i) q^{91} +2.51705i q^{92} +(-4.25927 + 7.72975i) q^{93} +(-2.74382 + 1.58414i) q^{94} +6.45252i q^{95} +(-1.73171 + 0.0345880i) q^{96} +(2.18746 - 1.26293i) q^{97} +(4.17842 + 5.61612i) q^{98} +(3.20969 - 2.02818i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 76 q - 76 q^{4} + 10 q^{7} + 4 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 76 q - 76 q^{4} + 10 q^{7} + 4 q^{9} - 2 q^{13} + 12 q^{15} + 76 q^{16} + 18 q^{19} - 8 q^{21} - 42 q^{25} - 10 q^{28} - 10 q^{30} + 12 q^{31} + 72 q^{33} - 4 q^{36} + 12 q^{37} - 42 q^{39} + 2 q^{42} - 2 q^{43} + 8 q^{46} - 10 q^{49} + 10 q^{51} + 2 q^{52} - 24 q^{55} + 8 q^{57} - 8 q^{58} - 12 q^{60} + 78 q^{61} + 2 q^{63} - 76 q^{64} - 24 q^{66} - 48 q^{67} + 30 q^{69} - 54 q^{73} - 18 q^{76} - 12 q^{78} - 60 q^{79} - 4 q^{81} - 24 q^{82} + 8 q^{84} + 8 q^{85} - 8 q^{91} - 32 q^{93} - 24 q^{94} + 66 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

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

\(n\) \(157\) \(365\) \(379\)
\(\chi(n)\) \(e\left(\frac{1}{6}\right)\) \(-1\) \(e\left(\frac{2}{3}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000i 0.707107i
\(3\) 0.0345880 + 1.73171i 0.0199694 + 0.999801i
\(4\) −1.00000 −0.500000
\(5\) −0.699535 1.21163i −0.312842 0.541858i 0.666135 0.745831i \(-0.267948\pi\)
−0.978976 + 0.203974i \(0.934614\pi\)
\(6\) −1.73171 + 0.0345880i −0.706966 + 0.0141205i
\(7\) −2.51159 + 0.831830i −0.949290 + 0.314402i
\(8\) 1.00000i 0.353553i
\(9\) −2.99761 + 0.119792i −0.999202 + 0.0399308i
\(10\) 1.21163 0.699535i 0.383151 0.221212i
\(11\) −1.09604 + 0.632798i −0.330468 + 0.190796i −0.656049 0.754718i \(-0.727773\pi\)
0.325581 + 0.945514i \(0.394440\pi\)
\(12\) −0.0345880 1.73171i −0.00998470 0.499900i
\(13\) 3.58555 0.379286i 0.994452 0.105195i
\(14\) −0.831830 2.51159i −0.222316 0.671249i
\(15\) 2.07399 1.25330i 0.535502 0.323600i
\(16\) 1.00000 0.250000
\(17\) −6.86805 −1.66575 −0.832873 0.553464i \(-0.813306\pi\)
−0.832873 + 0.553464i \(0.813306\pi\)
\(18\) −0.119792 2.99761i −0.0282354 0.706543i
\(19\) −3.99411 2.30600i −0.916312 0.529033i −0.0338555 0.999427i \(-0.510779\pi\)
−0.882457 + 0.470394i \(0.844112\pi\)
\(20\) 0.699535 + 1.21163i 0.156421 + 0.270929i
\(21\) −1.52735 4.32055i −0.333296 0.942822i
\(22\) −0.632798 1.09604i −0.134913 0.233676i
\(23\) 2.51705i 0.524840i −0.964954 0.262420i \(-0.915479\pi\)
0.964954 0.262420i \(-0.0845206\pi\)
\(24\) 1.73171 0.0345880i 0.353483 0.00706025i
\(25\) 1.52130 2.63497i 0.304260 0.526994i
\(26\) 0.379286 + 3.58555i 0.0743840 + 0.703183i
\(27\) −0.311127 5.18683i −0.0598763 0.998206i
\(28\) 2.51159 0.831830i 0.474645 0.157201i
\(29\) −4.55247 2.62837i −0.845372 0.488076i 0.0137143 0.999906i \(-0.495634\pi\)
−0.859087 + 0.511830i \(0.828968\pi\)
\(30\) 1.25330 + 2.07399i 0.228820 + 0.378657i
\(31\) 4.41277 + 2.54772i 0.792558 + 0.457583i 0.840862 0.541249i \(-0.182048\pi\)
−0.0483045 + 0.998833i \(0.515382\pi\)
\(32\) 1.00000i 0.176777i
\(33\) −1.13373 1.87613i −0.197357 0.326592i
\(34\) 6.86805i 1.17786i
\(35\) 2.76481 + 2.46122i 0.467339 + 0.416022i
\(36\) 2.99761 0.119792i 0.499601 0.0199654i
\(37\) −6.91395 −1.13665 −0.568323 0.822805i \(-0.692408\pi\)
−0.568323 + 0.822805i \(0.692408\pi\)
\(38\) 2.30600 3.99411i 0.374083 0.647931i
\(39\) 0.780828 + 6.19599i 0.125032 + 0.992153i
\(40\) −1.21163 + 0.699535i −0.191576 + 0.110606i
\(41\) −3.22591 + 5.58745i −0.503803 + 0.872613i 0.496187 + 0.868216i \(0.334733\pi\)
−0.999990 + 0.00439709i \(0.998600\pi\)
\(42\) 4.32055 1.52735i 0.666676 0.235676i
\(43\) 6.08396 + 10.5377i 0.927796 + 1.60699i 0.787002 + 0.616951i \(0.211632\pi\)
0.140794 + 0.990039i \(0.455034\pi\)
\(44\) 1.09604 0.632798i 0.165234 0.0953979i
\(45\) 2.24208 + 3.54819i 0.334229 + 0.528933i
\(46\) 2.51705 0.371118
\(47\) 1.58414 + 2.74382i 0.231071 + 0.400227i 0.958124 0.286355i \(-0.0924437\pi\)
−0.727053 + 0.686582i \(0.759110\pi\)
\(48\) 0.0345880 + 1.73171i 0.00499235 + 0.249950i
\(49\) 5.61612 4.17842i 0.802303 0.596917i
\(50\) 2.63497 + 1.52130i 0.372641 + 0.215144i
\(51\) −0.237552 11.8934i −0.0332639 1.66541i
\(52\) −3.58555 + 0.379286i −0.497226 + 0.0525974i
\(53\) 0.444106 + 0.256405i 0.0610026 + 0.0352199i 0.530191 0.847878i \(-0.322120\pi\)
−0.469188 + 0.883098i \(0.655454\pi\)
\(54\) 5.18683 0.311127i 0.705838 0.0423390i
\(55\) 1.53343 + 0.885329i 0.206768 + 0.119378i
\(56\) 0.831830 + 2.51159i 0.111158 + 0.335625i
\(57\) 3.85517 6.99639i 0.510629 0.926694i
\(58\) 2.62837 4.55247i 0.345122 0.597769i
\(59\) −14.3744 −1.87139 −0.935693 0.352815i \(-0.885224\pi\)
−0.935693 + 0.352815i \(0.885224\pi\)
\(60\) −2.07399 + 1.25330i −0.267751 + 0.161800i
\(61\) −2.66263 1.53727i −0.340915 0.196827i 0.319762 0.947498i \(-0.396397\pi\)
−0.660676 + 0.750671i \(0.729730\pi\)
\(62\) −2.54772 + 4.41277i −0.323560 + 0.560423i
\(63\) 7.42910 2.79437i 0.935978 0.352057i
\(64\) −1.00000 −0.125000
\(65\) −2.96777 4.07903i −0.368107 0.505942i
\(66\) 1.87613 1.13373i 0.230935 0.139552i
\(67\) 0.312240 + 0.540816i 0.0381462 + 0.0660711i 0.884468 0.466601i \(-0.154521\pi\)
−0.846322 + 0.532672i \(0.821188\pi\)
\(68\) 6.86805 0.832873
\(69\) 4.35878 0.0870596i 0.524736 0.0104807i
\(70\) −2.46122 + 2.76481i −0.294172 + 0.330458i
\(71\) −3.78894 + 2.18755i −0.449665 + 0.259614i −0.707689 0.706524i \(-0.750262\pi\)
0.258024 + 0.966139i \(0.416929\pi\)
\(72\) 0.119792 + 2.99761i 0.0141177 + 0.353271i
\(73\) −7.24349 4.18203i −0.847786 0.489470i 0.0121171 0.999927i \(-0.496143\pi\)
−0.859903 + 0.510457i \(0.829476\pi\)
\(74\) 6.91395i 0.803730i
\(75\) 4.61561 + 2.54331i 0.532965 + 0.293676i
\(76\) 3.99411 + 2.30600i 0.458156 + 0.264517i
\(77\) 2.22641 2.50104i 0.253723 0.285020i
\(78\) −6.19599 + 0.780828i −0.701558 + 0.0884113i
\(79\) 7.13902 + 12.3651i 0.803203 + 1.39119i 0.917498 + 0.397741i \(0.130206\pi\)
−0.114295 + 0.993447i \(0.536461\pi\)
\(80\) −0.699535 1.21163i −0.0782104 0.135464i
\(81\) 8.97130 0.718182i 0.996811 0.0797980i
\(82\) −5.58745 3.22591i −0.617030 0.356243i
\(83\) 3.52068 0.386444 0.193222 0.981155i \(-0.438106\pi\)
0.193222 + 0.981155i \(0.438106\pi\)
\(84\) 1.52735 + 4.32055i 0.166648 + 0.471411i
\(85\) 4.80444 + 8.32154i 0.521115 + 0.902597i
\(86\) −10.5377 + 6.08396i −1.13631 + 0.656051i
\(87\) 4.39410 7.97445i 0.471097 0.854950i
\(88\) 0.632798 + 1.09604i 0.0674565 + 0.116838i
\(89\) −15.8874 −1.68406 −0.842028 0.539434i \(-0.818638\pi\)
−0.842028 + 0.539434i \(0.818638\pi\)
\(90\) −3.54819 + 2.24208i −0.374012 + 0.236336i
\(91\) −8.68990 + 3.93517i −0.910949 + 0.412518i
\(92\) 2.51705i 0.262420i
\(93\) −4.25927 + 7.72975i −0.441665 + 0.801537i
\(94\) −2.74382 + 1.58414i −0.283003 + 0.163392i
\(95\) 6.45252i 0.662014i
\(96\) −1.73171 + 0.0345880i −0.176741 + 0.00353012i
\(97\) 2.18746 1.26293i 0.222102 0.128231i −0.384821 0.922991i \(-0.625737\pi\)
0.606923 + 0.794760i \(0.292403\pi\)
\(98\) 4.17842 + 5.61612i 0.422084 + 0.567314i
\(99\) 3.20969 2.02818i 0.322586 0.203839i
\(100\) −1.52130 + 2.63497i −0.152130 + 0.263497i
\(101\) −4.21730 7.30458i −0.419637 0.726833i 0.576266 0.817262i \(-0.304509\pi\)
−0.995903 + 0.0904297i \(0.971176\pi\)
\(102\) 11.8934 0.237552i 1.17763 0.0235212i
\(103\) −10.2521 + 5.91907i −1.01017 + 0.583224i −0.911242 0.411871i \(-0.864876\pi\)
−0.0989308 + 0.995094i \(0.531542\pi\)
\(104\) −0.379286 3.58555i −0.0371920 0.351592i
\(105\) −4.16648 + 4.87297i −0.406606 + 0.475553i
\(106\) −0.256405 + 0.444106i −0.0249042 + 0.0431354i
\(107\) 2.08622i 0.201683i −0.994903 0.100841i \(-0.967847\pi\)
0.994903 0.100841i \(-0.0321535\pi\)
\(108\) 0.311127 + 5.18683i 0.0299382 + 0.499103i
\(109\) −7.90043 + 13.6840i −0.756724 + 1.31068i 0.187788 + 0.982210i \(0.439868\pi\)
−0.944513 + 0.328475i \(0.893465\pi\)
\(110\) −0.885329 + 1.53343i −0.0844128 + 0.146207i
\(111\) −0.239140 11.9729i −0.0226981 1.13642i
\(112\) −2.51159 + 0.831830i −0.237322 + 0.0786005i
\(113\) 10.6760 6.16378i 1.00431 0.579840i 0.0947910 0.995497i \(-0.469782\pi\)
0.909521 + 0.415657i \(0.136448\pi\)
\(114\) 6.99639 + 3.85517i 0.655272 + 0.361069i
\(115\) −3.04973 + 1.76076i −0.284389 + 0.164192i
\(116\) 4.55247 + 2.62837i 0.422686 + 0.244038i
\(117\) −10.7026 + 1.56647i −0.989458 + 0.144820i
\(118\) 14.3744i 1.32327i
\(119\) 17.2497 5.71305i 1.58128 0.523714i
\(120\) −1.25330 2.07399i −0.114410 0.189329i
\(121\) −4.69913 + 8.13914i −0.427194 + 0.739922i
\(122\) 1.53727 2.66263i 0.139178 0.241063i
\(123\) −9.78739 5.39307i −0.882499 0.486277i
\(124\) −4.41277 2.54772i −0.396279 0.228792i
\(125\) −11.2522 −1.00642
\(126\) 2.79437 + 7.42910i 0.248942 + 0.661837i
\(127\) 4.41803 7.65224i 0.392036 0.679027i −0.600682 0.799488i \(-0.705104\pi\)
0.992718 + 0.120461i \(0.0384374\pi\)
\(128\) 1.00000i 0.0883883i
\(129\) −18.0378 + 10.9001i −1.58814 + 0.959701i
\(130\) 4.07903 2.96777i 0.357755 0.260291i
\(131\) 8.68707 + 15.0464i 0.758993 + 1.31461i 0.943365 + 0.331757i \(0.107642\pi\)
−0.184372 + 0.982857i \(0.559025\pi\)
\(132\) 1.13373 + 1.87613i 0.0986785 + 0.163296i
\(133\) 11.9498 + 2.46930i 1.03617 + 0.214115i
\(134\) −0.540816 + 0.312240i −0.0467194 + 0.0269734i
\(135\) −6.06688 + 4.00534i −0.522154 + 0.344725i
\(136\) 6.86805i 0.588930i
\(137\) 7.08381i 0.605210i −0.953116 0.302605i \(-0.902144\pi\)
0.953116 0.302605i \(-0.0978564\pi\)
\(138\) 0.0870596 + 4.35878i 0.00741101 + 0.371044i
\(139\) −1.93885 + 1.11939i −0.164451 + 0.0949457i −0.579967 0.814640i \(-0.696934\pi\)
0.415516 + 0.909586i \(0.363601\pi\)
\(140\) −2.76481 2.46122i −0.233669 0.208011i
\(141\) −4.69669 + 2.83817i −0.395533 + 0.239017i
\(142\) −2.18755 3.78894i −0.183575 0.317961i
\(143\) −3.68989 + 2.68464i −0.308564 + 0.224501i
\(144\) −2.99761 + 0.119792i −0.249801 + 0.00998271i
\(145\) 7.35455i 0.610762i
\(146\) 4.18203 7.24349i 0.346107 0.599475i
\(147\) 7.43005 + 9.58094i 0.612820 + 0.790223i
\(148\) 6.91395 0.568323
\(149\) 8.65889 + 4.99921i 0.709364 + 0.409552i 0.810826 0.585288i \(-0.199019\pi\)
−0.101461 + 0.994839i \(0.532352\pi\)
\(150\) −2.54331 + 4.61561i −0.207660 + 0.376863i
\(151\) 3.60495 6.24397i 0.293367 0.508127i −0.681237 0.732063i \(-0.738558\pi\)
0.974604 + 0.223937i \(0.0718909\pi\)
\(152\) −2.30600 + 3.99411i −0.187041 + 0.323965i
\(153\) 20.5877 0.822741i 1.66442 0.0665146i
\(154\) 2.50104 + 2.22641i 0.201540 + 0.179409i
\(155\) 7.12887i 0.572605i
\(156\) −0.780828 6.19599i −0.0625162 0.496076i
\(157\) −5.32283 3.07314i −0.424808 0.245263i 0.272324 0.962206i \(-0.412208\pi\)
−0.697132 + 0.716942i \(0.745541\pi\)
\(158\) −12.3651 + 7.13902i −0.983718 + 0.567950i
\(159\) −0.428656 + 0.777929i −0.0339947 + 0.0616938i
\(160\) 1.21163 0.699535i 0.0957878 0.0553031i
\(161\) 2.09375 + 6.32178i 0.165011 + 0.498226i
\(162\) 0.718182 + 8.97130i 0.0564257 + 0.704852i
\(163\) 6.89482 11.9422i 0.540044 0.935384i −0.458857 0.888510i \(-0.651741\pi\)
0.998901 0.0468738i \(-0.0149259\pi\)
\(164\) 3.22591 5.58745i 0.251902 0.436306i
\(165\) −1.48009 + 2.68608i −0.115225 + 0.209111i
\(166\) 3.52068i 0.273258i
\(167\) −7.46828 + 12.9354i −0.577913 + 1.00097i 0.417805 + 0.908537i \(0.362799\pi\)
−0.995718 + 0.0924384i \(0.970534\pi\)
\(168\) −4.32055 + 1.52735i −0.333338 + 0.117838i
\(169\) 12.7123 2.71989i 0.977868 0.209222i
\(170\) −8.32154 + 4.80444i −0.638233 + 0.368484i
\(171\) 12.2490 + 6.43402i 0.936706 + 0.492022i
\(172\) −6.08396 10.5377i −0.463898 0.803495i
\(173\) −2.74366 + 4.75216i −0.208597 + 0.361300i −0.951273 0.308351i \(-0.900223\pi\)
0.742676 + 0.669651i \(0.233556\pi\)
\(174\) 7.97445 + 4.39410i 0.604541 + 0.333116i
\(175\) −1.62903 + 7.88342i −0.123143 + 0.595930i
\(176\) −1.09604 + 0.632798i −0.0826170 + 0.0476989i
\(177\) −0.497181 24.8922i −0.0373704 1.87101i
\(178\) 15.8874i 1.19081i
\(179\) 5.38969 3.11174i 0.402844 0.232582i −0.284866 0.958567i \(-0.591949\pi\)
0.687710 + 0.725985i \(0.258616\pi\)
\(180\) −2.24208 3.54819i −0.167114 0.264467i
\(181\) 10.2706i 0.763407i −0.924285 0.381704i \(-0.875337\pi\)
0.924285 0.381704i \(-0.124663\pi\)
\(182\) −3.93517 8.68990i −0.291694 0.644138i
\(183\) 2.57000 4.66406i 0.189980 0.344777i
\(184\) −2.51705 −0.185559
\(185\) 4.83655 + 8.37715i 0.355590 + 0.615900i
\(186\) −7.72975 4.25927i −0.566773 0.312305i
\(187\) 7.52764 4.34609i 0.550476 0.317817i
\(188\) −1.58414 2.74382i −0.115536 0.200113i
\(189\) 5.09598 + 12.7684i 0.370678 + 0.928761i
\(190\) −6.45252 −0.468115
\(191\) −8.41156 4.85641i −0.608639 0.351398i 0.163794 0.986495i \(-0.447627\pi\)
−0.772433 + 0.635097i \(0.780960\pi\)
\(192\) −0.0345880 1.73171i −0.00249617 0.124975i
\(193\) −2.73242 4.73270i −0.196684 0.340667i 0.750767 0.660567i \(-0.229684\pi\)
−0.947451 + 0.319900i \(0.896351\pi\)
\(194\) 1.26293 + 2.18746i 0.0906729 + 0.157050i
\(195\) 6.96104 5.28039i 0.498490 0.378136i
\(196\) −5.61612 + 4.17842i −0.401151 + 0.298459i
\(197\) 22.5837 + 13.0387i 1.60902 + 0.928971i 0.989589 + 0.143923i \(0.0459718\pi\)
0.619435 + 0.785048i \(0.287362\pi\)
\(198\) 2.02818 + 3.20969i 0.144136 + 0.228103i
\(199\) 13.7069i 0.971655i 0.874055 + 0.485828i \(0.161482\pi\)
−0.874055 + 0.485828i \(0.838518\pi\)
\(200\) −2.63497 1.52130i −0.186321 0.107572i
\(201\) −0.925734 + 0.559414i −0.0652962 + 0.0394580i
\(202\) 7.30458 4.21730i 0.513948 0.296728i
\(203\) 13.6203 + 2.81449i 0.955956 + 0.197539i
\(204\) 0.237552 + 11.8934i 0.0166320 + 0.832707i
\(205\) 9.02656 0.630442
\(206\) −5.91907 10.2521i −0.412401 0.714300i
\(207\) 0.301523 + 7.54512i 0.0209573 + 0.524422i
\(208\) 3.58555 0.379286i 0.248613 0.0262987i
\(209\) 5.83693 0.403749
\(210\) −4.87297 4.16648i −0.336267 0.287514i
\(211\) 6.43745 11.1500i 0.443172 0.767597i −0.554751 0.832017i \(-0.687186\pi\)
0.997923 + 0.0644199i \(0.0205197\pi\)
\(212\) −0.444106 0.256405i −0.0305013 0.0176099i
\(213\) −3.91924 6.48567i −0.268542 0.444391i
\(214\) 2.08622 0.142611
\(215\) 8.51189 14.7430i 0.580506 1.00547i
\(216\) −5.18683 + 0.311127i −0.352919 + 0.0211695i
\(217\) −13.2023 2.72813i −0.896232 0.185198i
\(218\) −13.6840 7.90043i −0.926794 0.535085i
\(219\) 6.99151 12.6882i 0.472442 0.857392i
\(220\) −1.53343 0.885329i −0.103384 0.0596889i
\(221\) −24.6257 + 2.60495i −1.65650 + 0.175228i
\(222\) 11.9729 0.239140i 0.803570 0.0160500i
\(223\) −17.8707 10.3176i −1.19671 0.690919i −0.236888 0.971537i \(-0.576127\pi\)
−0.959820 + 0.280618i \(0.909461\pi\)
\(224\) −0.831830 2.51159i −0.0555790 0.167812i
\(225\) −4.24461 + 8.08085i −0.282974 + 0.538723i
\(226\) 6.16378 + 10.6760i 0.410009 + 0.710156i
\(227\) 18.2051 1.20831 0.604157 0.796865i \(-0.293510\pi\)
0.604157 + 0.796865i \(0.293510\pi\)
\(228\) −3.85517 + 6.99639i −0.255315 + 0.463347i
\(229\) −16.0335 + 9.25697i −1.05953 + 0.611717i −0.925301 0.379233i \(-0.876188\pi\)
−0.134225 + 0.990951i \(0.542854\pi\)
\(230\) −1.76076 3.04973i −0.116101 0.201093i
\(231\) 4.40808 + 3.76899i 0.290030 + 0.247981i
\(232\) −2.62837 + 4.55247i −0.172561 + 0.298884i
\(233\) 9.27681 5.35597i 0.607744 0.350881i −0.164338 0.986404i \(-0.552549\pi\)
0.772082 + 0.635523i \(0.219215\pi\)
\(234\) −1.56647 10.7026i −0.102403 0.699652i
\(235\) 2.21633 3.83879i 0.144577 0.250415i
\(236\) 14.3744 0.935693
\(237\) −21.1659 + 12.7904i −1.37487 + 0.830824i
\(238\) 5.71305 + 17.2497i 0.370322 + 1.11813i
\(239\) 3.88709i 0.251435i −0.992066 0.125718i \(-0.959877\pi\)
0.992066 0.125718i \(-0.0401233\pi\)
\(240\) 2.07399 1.25330i 0.133876 0.0809000i
\(241\) 6.18514i 0.398420i −0.979957 0.199210i \(-0.936162\pi\)
0.979957 0.199210i \(-0.0638376\pi\)
\(242\) −8.13914 4.69913i −0.523204 0.302072i
\(243\) 1.55398 + 15.5108i 0.0996878 + 0.995019i
\(244\) 2.66263 + 1.53727i 0.170457 + 0.0984136i
\(245\) −8.99138 3.88171i −0.574438 0.247993i
\(246\) 5.39307 9.78739i 0.343850 0.624021i
\(247\) −15.1957 6.75337i −0.966880 0.429706i
\(248\) 2.54772 4.41277i 0.161780 0.280211i
\(249\) 0.121773 + 6.09678i 0.00771706 + 0.386367i
\(250\) 11.2522i 0.711649i
\(251\) −0.889061 1.53990i −0.0561171 0.0971976i 0.836602 0.547811i \(-0.184539\pi\)
−0.892719 + 0.450613i \(0.851205\pi\)
\(252\) −7.42910 + 2.79437i −0.467989 + 0.176029i
\(253\) 1.59278 + 2.75878i 0.100137 + 0.173443i
\(254\) 7.65224 + 4.41803i 0.480145 + 0.277212i
\(255\) −14.2443 + 8.60770i −0.892011 + 0.539035i
\(256\) 1.00000 0.0625000
\(257\) −12.0249 −0.750094 −0.375047 0.927006i \(-0.622373\pi\)
−0.375047 + 0.927006i \(0.622373\pi\)
\(258\) −10.9001 18.0378i −0.678611 1.12299i
\(259\) 17.3650 5.75123i 1.07901 0.357364i
\(260\) 2.96777 + 4.07903i 0.184053 + 0.252971i
\(261\) 13.9614 + 7.33347i 0.864188 + 0.453930i
\(262\) −15.0464 + 8.68707i −0.929572 + 0.536689i
\(263\) −1.64102 + 0.947444i −0.101190 + 0.0584219i −0.549741 0.835335i \(-0.685274\pi\)
0.448551 + 0.893757i \(0.351940\pi\)
\(264\) −1.87613 + 1.13373i −0.115468 + 0.0697762i
\(265\) 0.717456i 0.0440730i
\(266\) −2.46930 + 11.9498i −0.151402 + 0.732686i
\(267\) −0.549512 27.5122i −0.0336296 1.68372i
\(268\) −0.312240 0.540816i −0.0190731 0.0330356i
\(269\) 24.9727 1.52261 0.761306 0.648392i \(-0.224558\pi\)
0.761306 + 0.648392i \(0.224558\pi\)
\(270\) −4.00534 6.06688i −0.243757 0.369218i
\(271\) 7.99045i 0.485385i −0.970103 0.242693i \(-0.921969\pi\)
0.970103 0.242693i \(-0.0780306\pi\)
\(272\) −6.86805 −0.416437
\(273\) −7.11512 14.9122i −0.430627 0.902530i
\(274\) 7.08381 0.427948
\(275\) 3.85071i 0.232206i
\(276\) −4.35878 + 0.0870596i −0.262368 + 0.00524037i
\(277\) −16.5670 −0.995416 −0.497708 0.867345i \(-0.665825\pi\)
−0.497708 + 0.867345i \(0.665825\pi\)
\(278\) −1.11939 1.93885i −0.0671367 0.116284i
\(279\) −13.5330 7.10844i −0.810197 0.425571i
\(280\) 2.46122 2.76481i 0.147086 0.165229i
\(281\) 1.18198i 0.0705110i −0.999378 0.0352555i \(-0.988776\pi\)
0.999378 0.0352555i \(-0.0112245\pi\)
\(282\) −2.83817 4.69669i −0.169011 0.279684i
\(283\) 28.4527 16.4272i 1.69134 0.976495i 0.737898 0.674912i \(-0.235818\pi\)
0.953440 0.301583i \(-0.0975149\pi\)
\(284\) 3.78894 2.18755i 0.224832 0.129807i
\(285\) −11.1739 + 0.223180i −0.661882 + 0.0132200i
\(286\) −2.68464 3.68989i −0.158746 0.218187i
\(287\) 3.45435 16.7168i 0.203904 0.986759i
\(288\) −0.119792 2.99761i −0.00705884 0.176636i
\(289\) 30.1701 1.77471
\(290\) −7.35455 −0.431874
\(291\) 2.26268 + 3.74435i 0.132641 + 0.219497i
\(292\) 7.24349 + 4.18203i 0.423893 + 0.244735i
\(293\) −2.82022 4.88477i −0.164759 0.285371i 0.771811 0.635852i \(-0.219351\pi\)
−0.936570 + 0.350481i \(0.886018\pi\)
\(294\) −9.58094 + 7.43005i −0.558772 + 0.433329i
\(295\) 10.0554 + 17.4164i 0.585447 + 1.01402i
\(296\) 6.91395i 0.401865i
\(297\) 3.62322 + 5.48808i 0.210241 + 0.318451i
\(298\) −4.99921 + 8.65889i −0.289597 + 0.501596i
\(299\) −0.954679 9.02499i −0.0552105 0.521928i
\(300\) −4.61561 2.54331i −0.266482 0.146838i
\(301\) −24.0460 21.4056i −1.38599 1.23380i
\(302\) 6.24397 + 3.60495i 0.359300 + 0.207442i
\(303\) 12.5035 7.55577i 0.718308 0.434068i
\(304\) −3.99411 2.30600i −0.229078 0.132258i
\(305\) 4.30150i 0.246303i
\(306\) 0.822741 + 20.5877i 0.0470329 + 1.17692i
\(307\) 25.4559i 1.45284i −0.687249 0.726422i \(-0.741182\pi\)
0.687249 0.726422i \(-0.258818\pi\)
\(308\) −2.22641 + 2.50104i −0.126862 + 0.142510i
\(309\) −10.6047 17.5490i −0.603280 0.998325i
\(310\) 7.12887 0.404893
\(311\) −7.30444 + 12.6517i −0.414197 + 0.717410i −0.995344 0.0963890i \(-0.969271\pi\)
0.581147 + 0.813798i \(0.302604\pi\)
\(312\) 6.19599 0.780828i 0.350779 0.0442057i
\(313\) −9.58723 + 5.53519i −0.541902 + 0.312868i −0.745850 0.666114i \(-0.767956\pi\)
0.203947 + 0.978982i \(0.434623\pi\)
\(314\) 3.07314 5.32283i 0.173427 0.300385i
\(315\) −8.58266 7.04656i −0.483578 0.397029i
\(316\) −7.13902 12.3651i −0.401601 0.695594i
\(317\) 13.3841 7.72732i 0.751727 0.434010i −0.0745906 0.997214i \(-0.523765\pi\)
0.826318 + 0.563205i \(0.190432\pi\)
\(318\) −0.777929 0.428656i −0.0436241 0.0240379i
\(319\) 6.65291 0.372491
\(320\) 0.699535 + 1.21163i 0.0391052 + 0.0677322i
\(321\) 3.61273 0.0721583i 0.201643 0.00402749i
\(322\) −6.32178 + 2.09375i −0.352299 + 0.116680i
\(323\) 27.4318 + 15.8377i 1.52634 + 0.881235i
\(324\) −8.97130 + 0.718182i −0.498406 + 0.0398990i
\(325\) 4.45529 10.0248i 0.247135 0.556077i
\(326\) 11.9422 + 6.89482i 0.661417 + 0.381869i
\(327\) −23.9698 13.2079i −1.32553 0.730400i
\(328\) 5.58745 + 3.22591i 0.308515 + 0.178121i
\(329\) −6.26110 5.57359i −0.345186 0.307282i
\(330\) −2.68608 1.48009i −0.147864 0.0814763i
\(331\) 0.496658 0.860237i 0.0272988 0.0472829i −0.852053 0.523455i \(-0.824643\pi\)
0.879352 + 0.476172i \(0.157976\pi\)
\(332\) −3.52068 −0.193222
\(333\) 20.7253 0.828239i 1.13574 0.0453872i
\(334\) −12.9354 7.46828i −0.707796 0.408646i
\(335\) 0.436846 0.756639i 0.0238674 0.0413396i
\(336\) −1.52735 4.32055i −0.0833240 0.235706i
\(337\) 16.8178 0.916123 0.458061 0.888921i \(-0.348544\pi\)
0.458061 + 0.888921i \(0.348544\pi\)
\(338\) 2.71989 + 12.7123i 0.147943 + 0.691457i
\(339\) 11.0431 + 18.2745i 0.599780 + 0.992533i
\(340\) −4.80444 8.32154i −0.260557 0.451299i
\(341\) −6.44876 −0.349220
\(342\) −6.43402 + 12.2490i −0.347912 + 0.662351i
\(343\) −10.6296 + 15.1661i −0.573946 + 0.818893i
\(344\) 10.5377 6.08396i 0.568157 0.328025i
\(345\) −3.15461 5.22033i −0.169838 0.281053i
\(346\) −4.75216 2.74366i −0.255478 0.147500i
\(347\) 8.81697i 0.473320i −0.971593 0.236660i \(-0.923947\pi\)
0.971593 0.236660i \(-0.0760527\pi\)
\(348\) −4.39410 + 7.97445i −0.235549 + 0.427475i
\(349\) 11.1058 + 6.41193i 0.594479 + 0.343223i 0.766866 0.641807i \(-0.221815\pi\)
−0.172388 + 0.985029i \(0.555148\pi\)
\(350\) −7.88342 1.62903i −0.421386 0.0870753i
\(351\) −3.08285 18.4796i −0.164550 0.986369i
\(352\) −0.632798 1.09604i −0.0337282 0.0584190i
\(353\) −17.2343 29.8507i −0.917289 1.58879i −0.803515 0.595285i \(-0.797039\pi\)
−0.113774 0.993507i \(-0.536294\pi\)
\(354\) 24.8922 0.497181i 1.32301 0.0264249i
\(355\) 5.30100 + 3.06053i 0.281348 + 0.162436i
\(356\) 15.8874 0.842028
\(357\) 10.4899 + 29.6738i 0.555187 + 1.57050i
\(358\) 3.11174 + 5.38969i 0.164460 + 0.284854i
\(359\) −24.1704 + 13.9548i −1.27567 + 0.736506i −0.976048 0.217554i \(-0.930192\pi\)
−0.299617 + 0.954060i \(0.596859\pi\)
\(360\) 3.54819 2.24208i 0.187006 0.118168i
\(361\) 1.13529 + 1.96637i 0.0597519 + 0.103493i
\(362\) 10.2706 0.539811
\(363\) −14.2571 7.85600i −0.748305 0.412333i
\(364\) 8.68990 3.93517i 0.455475 0.206259i
\(365\) 11.7019i 0.612506i
\(366\) 4.66406 + 2.57000i 0.243794 + 0.134336i
\(367\) −2.94391 + 1.69967i −0.153671 + 0.0887219i −0.574864 0.818249i \(-0.694945\pi\)
0.421193 + 0.906971i \(0.361612\pi\)
\(368\) 2.51705i 0.131210i
\(369\) 9.00069 17.1354i 0.468557 0.892034i
\(370\) −8.37715 + 4.83655i −0.435507 + 0.251440i
\(371\) −1.32869 0.274561i −0.0689824 0.0142545i
\(372\) 4.25927 7.72975i 0.220833 0.400769i
\(373\) −4.22173 + 7.31225i −0.218593 + 0.378614i −0.954378 0.298601i \(-0.903480\pi\)
0.735785 + 0.677215i \(0.236813\pi\)
\(374\) 4.34609 + 7.52764i 0.224731 + 0.389245i
\(375\) −0.389190 19.4854i −0.0200977 1.00622i
\(376\) 2.74382 1.58414i 0.141502 0.0816960i
\(377\) −17.3200 7.69746i −0.892025 0.396439i
\(378\) −12.7684 + 5.09598i −0.656734 + 0.262109i
\(379\) −12.2942 + 21.2942i −0.631512 + 1.09381i 0.355730 + 0.934589i \(0.384232\pi\)
−0.987243 + 0.159223i \(0.949101\pi\)
\(380\) 6.45252i 0.331007i
\(381\) 13.4042 + 7.38604i 0.686720 + 0.378398i
\(382\) 4.85641 8.41156i 0.248476 0.430373i
\(383\) 12.3294 21.3552i 0.630003 1.09120i −0.357547 0.933895i \(-0.616387\pi\)
0.987550 0.157303i \(-0.0502798\pi\)
\(384\) 1.73171 0.0345880i 0.0883707 0.00176506i
\(385\) −4.58779 0.948022i −0.233816 0.0483157i
\(386\) 4.73270 2.73242i 0.240888 0.139077i
\(387\) −19.4997 30.8592i −0.991224 1.56866i
\(388\) −2.18746 + 1.26293i −0.111051 + 0.0641155i
\(389\) 3.13636 + 1.81078i 0.159020 + 0.0918101i 0.577398 0.816463i \(-0.304068\pi\)
−0.418378 + 0.908273i \(0.637401\pi\)
\(390\) 5.28039 + 6.96104i 0.267383 + 0.352486i
\(391\) 17.2872i 0.874251i
\(392\) −4.17842 5.61612i −0.211042 0.283657i
\(393\) −25.7555 + 15.5639i −1.29920 + 0.785093i
\(394\) −13.0387 + 22.5837i −0.656881 + 1.13775i
\(395\) 9.98799 17.2997i 0.502550 0.870443i
\(396\) −3.20969 + 2.02818i −0.161293 + 0.101920i
\(397\) −12.1481 7.01373i −0.609698 0.352009i 0.163149 0.986601i \(-0.447835\pi\)
−0.772847 + 0.634592i \(0.781168\pi\)
\(398\) −13.7069 −0.687064
\(399\) −3.86278 + 20.7789i −0.193381 + 1.04024i
\(400\) 1.52130 2.63497i 0.0760651 0.131749i
\(401\) 31.9750i 1.59675i 0.602159 + 0.798376i \(0.294307\pi\)
−0.602159 + 0.798376i \(0.705693\pi\)
\(402\) −0.559414 0.925734i −0.0279010 0.0461714i
\(403\) 16.7885 + 7.46125i 0.836296 + 0.371672i
\(404\) 4.21730 + 7.30458i 0.209819 + 0.363416i
\(405\) −7.14591 10.3675i −0.355083 0.515166i
\(406\) −2.81449 + 13.6203i −0.139681 + 0.675963i
\(407\) 7.57795 4.37513i 0.375625 0.216867i
\(408\) −11.8934 + 0.237552i −0.588813 + 0.0117606i
\(409\) 0.556454i 0.0275149i −0.999905 0.0137574i \(-0.995621\pi\)
0.999905 0.0137574i \(-0.00437926\pi\)
\(410\) 9.02656i 0.445790i
\(411\) 12.2671 0.245015i 0.605090 0.0120857i
\(412\) 10.2521 5.91907i 0.505087 0.291612i
\(413\) 36.1025 11.9570i 1.77649 0.588368i
\(414\) −7.54512 + 0.301523i −0.370822 + 0.0148191i
\(415\) −2.46284 4.26576i −0.120896 0.209398i
\(416\) 0.379286 + 3.58555i 0.0185960 + 0.175796i
\(417\) −2.00552 3.31879i −0.0982107 0.162522i
\(418\) 5.83693i 0.285494i
\(419\) −7.69809 + 13.3335i −0.376076 + 0.651383i −0.990488 0.137603i \(-0.956060\pi\)
0.614411 + 0.788986i \(0.289394\pi\)
\(420\) 4.16648 4.87297i 0.203303 0.237777i
\(421\) 5.44197 0.265225 0.132613 0.991168i \(-0.457663\pi\)
0.132613 + 0.991168i \(0.457663\pi\)
\(422\) 11.1500 + 6.43745i 0.542773 + 0.313370i
\(423\) −5.07733 8.03512i −0.246868 0.390681i
\(424\) 0.256405 0.444106i 0.0124521 0.0215677i
\(425\) −10.4484 + 18.0971i −0.506820 + 0.877839i
\(426\) 6.48567 3.91924i 0.314232 0.189888i
\(427\) 7.96616 + 1.64613i 0.385510 + 0.0796618i
\(428\) 2.08622i 0.100841i
\(429\) −4.77663 6.29694i −0.230618 0.304019i
\(430\) 14.7430 + 8.51189i 0.710972 + 0.410480i
\(431\) −19.7911 + 11.4264i −0.953305 + 0.550391i −0.894106 0.447855i \(-0.852188\pi\)
−0.0591992 + 0.998246i \(0.518855\pi\)
\(432\) −0.311127 5.18683i −0.0149691 0.249551i
\(433\) 6.71928 3.87938i 0.322908 0.186431i −0.329780 0.944058i \(-0.606975\pi\)
0.652688 + 0.757627i \(0.273641\pi\)
\(434\) 2.72813 13.2023i 0.130954 0.633732i
\(435\) −12.7359 + 0.254379i −0.610640 + 0.0121965i
\(436\) 7.90043 13.6840i 0.378362 0.655342i
\(437\) −5.80431 + 10.0534i −0.277658 + 0.480918i
\(438\) 12.6882 + 6.99151i 0.606267 + 0.334067i
\(439\) 41.6588i 1.98827i 0.108159 + 0.994134i \(0.465504\pi\)
−0.108159 + 0.994134i \(0.534496\pi\)
\(440\) 0.885329 1.53343i 0.0422064 0.0731036i
\(441\) −16.3344 + 13.1980i −0.777827 + 0.628478i
\(442\) −2.60495 24.6257i −0.123905 1.17133i
\(443\) 22.4612 12.9680i 1.06716 0.616127i 0.139758 0.990186i \(-0.455368\pi\)
0.927405 + 0.374059i \(0.122034\pi\)
\(444\) 0.239140 + 11.9729i 0.0113491 + 0.568210i
\(445\) 11.1138 + 19.2496i 0.526843 + 0.912518i
\(446\) 10.3176 17.8707i 0.488554 0.846200i
\(447\) −8.35767 + 15.1676i −0.395304 + 0.717401i
\(448\) 2.51159 0.831830i 0.118661 0.0393003i
\(449\) 5.20037 3.00244i 0.245421 0.141694i −0.372245 0.928135i \(-0.621412\pi\)
0.617666 + 0.786441i \(0.288079\pi\)
\(450\) −8.08085 4.24461i −0.380935 0.200093i
\(451\) 8.16541i 0.384494i
\(452\) −10.6760 + 6.16378i −0.502156 + 0.289920i
\(453\) 10.9374 + 6.02675i 0.513884 + 0.283162i
\(454\) 18.2051i 0.854407i
\(455\) 10.8469 + 7.77616i 0.508509 + 0.364552i
\(456\) −6.99639 3.85517i −0.327636 0.180535i
\(457\) −29.6490 −1.38692 −0.693460 0.720495i \(-0.743915\pi\)
−0.693460 + 0.720495i \(0.743915\pi\)
\(458\) −9.25697 16.0335i −0.432550 0.749198i
\(459\) 2.13683 + 35.6234i 0.0997388 + 1.66276i
\(460\) 3.04973 1.76076i 0.142194 0.0820960i
\(461\) 3.80284 + 6.58672i 0.177116 + 0.306774i 0.940892 0.338708i \(-0.109990\pi\)
−0.763775 + 0.645482i \(0.776657\pi\)
\(462\) −3.76899 + 4.40808i −0.175349 + 0.205082i
\(463\) −13.7605 −0.639506 −0.319753 0.947501i \(-0.603600\pi\)
−0.319753 + 0.947501i \(0.603600\pi\)
\(464\) −4.55247 2.62837i −0.211343 0.122019i
\(465\) 12.3451 0.246573i 0.572490 0.0114346i
\(466\) 5.35597 + 9.27681i 0.248111 + 0.429740i
\(467\) 8.10576 + 14.0396i 0.375090 + 0.649675i 0.990341 0.138657i \(-0.0442785\pi\)
−0.615250 + 0.788332i \(0.710945\pi\)
\(468\) 10.7026 1.56647i 0.494729 0.0724101i
\(469\) −1.23408 1.09857i −0.0569847 0.0507274i
\(470\) 3.83879 + 2.21633i 0.177070 + 0.102232i
\(471\) 5.13766 9.32387i 0.236731 0.429621i
\(472\) 14.3744i 0.661635i
\(473\) −13.3365 7.69984i −0.613214 0.354039i
\(474\) −12.7904 21.1659i −0.587481 0.972180i
\(475\) −12.1525 + 7.01625i −0.557595 + 0.321927i
\(476\) −17.2497 + 5.71305i −0.790638 + 0.261857i
\(477\) −1.36197 0.715400i −0.0623603 0.0327559i
\(478\) 3.88709 0.177792
\(479\) −3.83449 6.64153i −0.175202 0.303459i 0.765029 0.643996i \(-0.222725\pi\)
−0.940231 + 0.340537i \(0.889391\pi\)
\(480\) 1.25330 + 2.07399i 0.0572049 + 0.0946643i
\(481\) −24.7903 + 2.62236i −1.13034 + 0.119569i
\(482\) 6.18514 0.281725
\(483\) −10.8750 + 3.84442i −0.494831 + 0.174927i
\(484\) 4.69913 8.13914i 0.213597 0.369961i
\(485\) −3.06040 1.76692i −0.138966 0.0802319i
\(486\) −15.5108 + 1.55398i −0.703585 + 0.0704899i
\(487\) 1.25273 0.0567668 0.0283834 0.999597i \(-0.490964\pi\)
0.0283834 + 0.999597i \(0.490964\pi\)
\(488\) −1.53727 + 2.66263i −0.0695889 + 0.120532i
\(489\) 20.9188 + 11.5267i 0.945982 + 0.521258i
\(490\) 3.88171 8.99138i 0.175358 0.406189i
\(491\) 1.78584 + 1.03105i 0.0805938 + 0.0465308i 0.539755 0.841822i \(-0.318517\pi\)
−0.459162 + 0.888353i \(0.651850\pi\)
\(492\) 9.78739 + 5.39307i 0.441250 + 0.243139i
\(493\) 31.2666 + 18.0518i 1.40818 + 0.813011i
\(494\) 6.75337 15.1957i 0.303848 0.683687i
\(495\) −4.70269 2.47017i −0.211370 0.111026i
\(496\) 4.41277 + 2.54772i 0.198139 + 0.114396i
\(497\) 7.69659 8.64597i 0.345239 0.387825i
\(498\) −6.09678 + 0.121773i −0.273203 + 0.00545679i
\(499\) −6.12234 10.6042i −0.274074 0.474710i 0.695827 0.718209i \(-0.255038\pi\)
−0.969901 + 0.243500i \(0.921705\pi\)
\(500\) 11.2522 0.503212
\(501\) −22.6587 12.4855i −1.01232 0.557809i
\(502\) 1.53990 0.889061i 0.0687291 0.0396808i
\(503\) −19.8446 34.3719i −0.884828 1.53257i −0.845911 0.533324i \(-0.820943\pi\)
−0.0389171 0.999242i \(-0.512391\pi\)
\(504\) −2.79437 7.42910i −0.124471 0.330918i
\(505\) −5.90030 + 10.2196i −0.262560 + 0.454767i
\(506\) −2.75878 + 1.59278i −0.122643 + 0.0708078i
\(507\) 5.14974 + 21.9199i 0.228708 + 0.973495i
\(508\) −4.41803 + 7.65224i −0.196018 + 0.339513i
\(509\) 22.8013 1.01065 0.505325 0.862929i \(-0.331373\pi\)
0.505325 + 0.862929i \(0.331373\pi\)
\(510\) −8.60770 14.2443i −0.381155 0.630747i
\(511\) 21.6714 + 4.47817i 0.958685 + 0.198103i
\(512\) 1.00000i 0.0441942i
\(513\) −10.7182 + 21.4342i −0.473218 + 0.946345i
\(514\) 12.0249i 0.530396i
\(515\) 14.3435 + 8.28120i 0.632048 + 0.364913i
\(516\) 18.0378 10.9001i 0.794071 0.479851i
\(517\) −3.47256 2.00489i −0.152723 0.0881748i
\(518\) 5.75123 + 17.3650i 0.252695 + 0.762973i
\(519\) −8.32424 4.58684i −0.365393 0.201340i
\(520\) −4.07903 + 2.96777i −0.178877 + 0.130145i
\(521\) −1.95101 + 3.37925i −0.0854752 + 0.148047i −0.905594 0.424146i \(-0.860574\pi\)
0.820118 + 0.572194i \(0.193908\pi\)
\(522\) −7.33347 + 13.9614i −0.320977 + 0.611073i
\(523\) 7.78077i 0.340229i 0.985424 + 0.170115i \(0.0544138\pi\)
−0.985424 + 0.170115i \(0.945586\pi\)
\(524\) −8.68707 15.0464i −0.379496 0.657307i
\(525\) −13.7081 2.54833i −0.598271 0.111218i
\(526\) −0.947444 1.64102i −0.0413105 0.0715520i
\(527\) −30.3072 17.4978i −1.32020 0.762218i
\(528\) −1.13373 1.87613i −0.0493392 0.0816480i
\(529\) 16.6645 0.724543
\(530\) 0.717456 0.0311643
\(531\) 43.0888 1.72194i 1.86989 0.0747260i
\(532\) −11.9498 2.46930i −0.518087 0.107058i
\(533\) −9.44743 + 21.2576i −0.409213 + 0.920769i
\(534\) 27.5122 0.549512i 1.19057 0.0237797i
\(535\) −2.52773 + 1.45939i −0.109283 + 0.0630948i
\(536\) 0.540816 0.312240i 0.0233597 0.0134867i
\(537\) 5.57503 + 9.22572i 0.240580 + 0.398119i
\(538\) 24.9727i 1.07665i
\(539\) −3.51138 + 8.13358i −0.151246 + 0.350338i
\(540\) 6.06688 4.00534i 0.261077 0.172362i
\(541\) −2.23765 3.87573i −0.0962042 0.166631i 0.813906 0.580996i \(-0.197337\pi\)
−0.910111 + 0.414366i \(0.864004\pi\)
\(542\) 7.99045 0.343219
\(543\) 17.7856 0.355239i 0.763255 0.0152448i
\(544\) 6.86805i 0.294465i
\(545\) 22.1065 0.946939
\(546\) 14.9122 7.11512i 0.638185 0.304499i
\(547\) −35.3736 −1.51246 −0.756232 0.654304i \(-0.772962\pi\)
−0.756232 + 0.654304i \(0.772962\pi\)
\(548\) 7.08381i 0.302605i
\(549\) 8.16567 + 4.28917i 0.348502 + 0.183057i
\(550\) −3.85071 −0.164195
\(551\) 12.1221 + 20.9960i 0.516417 + 0.894460i
\(552\) −0.0870596 4.35878i −0.00370550 0.185522i
\(553\) −28.2160 25.1177i −1.19986 1.06811i
\(554\) 16.5670i 0.703866i
\(555\) −14.3395 + 8.66523i −0.608677 + 0.367819i
\(556\) 1.93885 1.11939i 0.0822254 0.0474728i
\(557\) −18.0142 + 10.4005i −0.763287 + 0.440684i −0.830475 0.557056i \(-0.811931\pi\)
0.0671876 + 0.997740i \(0.478597\pi\)
\(558\) 7.10844 13.5330i 0.300924 0.572896i
\(559\) 25.8111 + 35.4760i 1.09170 + 1.50047i
\(560\) 2.76481 + 2.46122i 0.116835 + 0.104005i
\(561\) 7.78651 + 12.8853i 0.328747 + 0.544020i
\(562\) 1.18198 0.0498588
\(563\) 24.1919 1.01957 0.509784 0.860302i \(-0.329725\pi\)
0.509784 + 0.860302i \(0.329725\pi\)
\(564\) 4.69669 2.83817i 0.197766 0.119509i
\(565\) −14.9365 8.62357i −0.628381 0.362796i
\(566\) 16.4272 + 28.4527i 0.690486 + 1.19596i
\(567\) −21.9348 + 9.26637i −0.921174 + 0.389151i
\(568\) 2.18755 + 3.78894i 0.0917875 + 0.158981i
\(569\) 35.0754i 1.47044i −0.677829 0.735219i \(-0.737079\pi\)
0.677829 0.735219i \(-0.262921\pi\)
\(570\) −0.223180 11.1739i −0.00934797 0.468021i
\(571\) 10.1633 17.6034i 0.425321 0.736678i −0.571129 0.820860i \(-0.693494\pi\)
0.996450 + 0.0841821i \(0.0268277\pi\)
\(572\) 3.68989 2.68464i 0.154282 0.112250i
\(573\) 8.11894 14.7343i 0.339174 0.615535i
\(574\) 16.7168 + 3.45435i 0.697744 + 0.144182i
\(575\) −6.63234 3.82919i −0.276588 0.159688i
\(576\) 2.99761 0.119792i 0.124900 0.00499135i
\(577\) −12.8575 7.42329i −0.535266 0.309036i 0.207892 0.978152i \(-0.433340\pi\)
−0.743158 + 0.669116i \(0.766673\pi\)
\(578\) 30.1701i 1.25491i
\(579\) 8.10113 4.89545i 0.336671 0.203448i
\(580\) 7.35455i 0.305381i
\(581\) −8.84248 + 2.92860i −0.366848 + 0.121499i
\(582\) −3.74435 + 2.26268i −0.155208 + 0.0937911i
\(583\) −0.649009 −0.0268792
\(584\) −4.18203 + 7.24349i −0.173054 + 0.299738i
\(585\) 9.38485 + 11.8718i 0.388016 + 0.490840i
\(586\) 4.88477 2.82022i 0.201788 0.116502i
\(587\) −10.5944 + 18.3500i −0.437276 + 0.757384i −0.997478 0.0709716i \(-0.977390\pi\)
0.560202 + 0.828356i \(0.310723\pi\)
\(588\) −7.43005 9.58094i −0.306410 0.395111i
\(589\) −11.7501 20.3517i −0.484154 0.838578i
\(590\) −17.4164 + 10.0554i −0.717024 + 0.413974i
\(591\) −21.7981 + 39.5594i −0.896654 + 1.62725i
\(592\) −6.91395 −0.284162
\(593\) −12.5747 21.7800i −0.516381 0.894397i −0.999819 0.0190190i \(-0.993946\pi\)
0.483439 0.875378i \(-0.339388\pi\)
\(594\) −5.48808 + 3.62322i −0.225179 + 0.148663i
\(595\) −18.9889 16.9038i −0.778468 0.692987i
\(596\) −8.65889 4.99921i −0.354682 0.204776i
\(597\) −23.7363 + 0.474094i −0.971461 + 0.0194034i
\(598\) 9.02499 0.954679i 0.369059 0.0390397i
\(599\) −27.8317 16.0687i −1.13717 0.656547i −0.191444 0.981503i \(-0.561317\pi\)
−0.945729 + 0.324956i \(0.894650\pi\)
\(600\) 2.54331 4.61561i 0.103830 0.188432i
\(601\) −15.0678 8.69938i −0.614627 0.354855i 0.160147 0.987093i \(-0.448803\pi\)
−0.774774 + 0.632238i \(0.782136\pi\)
\(602\) 21.4056 24.0460i 0.872427 0.980042i
\(603\) −1.00076 1.58375i −0.0407540 0.0644952i
\(604\) −3.60495 + 6.24397i −0.146684 + 0.254063i
\(605\) 13.1488 0.534576
\(606\) 7.55577 + 12.5035i 0.306932 + 0.507920i
\(607\) 25.4203 + 14.6764i 1.03178 + 0.595698i 0.917494 0.397750i \(-0.130209\pi\)
0.114286 + 0.993448i \(0.463542\pi\)
\(608\) 2.30600 3.99411i 0.0935207 0.161983i
\(609\) −4.40278 + 23.6836i −0.178410 + 0.959710i
\(610\) −4.30150 −0.174162
\(611\) 6.72071 + 9.23724i 0.271891 + 0.373699i
\(612\) −20.5877 + 0.822741i −0.832209 + 0.0332573i
\(613\) 17.4142 + 30.1624i 0.703355 + 1.21825i 0.967282 + 0.253704i \(0.0816489\pi\)
−0.263927 + 0.964543i \(0.585018\pi\)
\(614\) 25.4559 1.02732
\(615\) 0.312211 + 15.6313i 0.0125896 + 0.630317i
\(616\) −2.50104 2.22641i −0.100770 0.0897047i
\(617\) −15.1344 + 8.73785i −0.609288 + 0.351773i −0.772687 0.634787i \(-0.781088\pi\)
0.163399 + 0.986560i \(0.447754\pi\)
\(618\) 17.5490 10.6047i 0.705922 0.426583i
\(619\) −20.5117 11.8425i −0.824436 0.475989i 0.0275075 0.999622i \(-0.491243\pi\)
−0.851944 + 0.523633i \(0.824576\pi\)
\(620\) 7.12887i 0.286302i
\(621\) −13.0555 + 0.783120i −0.523899 + 0.0314255i
\(622\) −12.6517 7.30444i −0.507285 0.292881i
\(623\) 39.9024 13.2156i 1.59866 0.529471i
\(624\) 0.780828 + 6.19599i 0.0312581 + 0.248038i
\(625\) 0.264780 + 0.458612i 0.0105912 + 0.0183445i
\(626\) −5.53519 9.58723i −0.221231 0.383183i
\(627\) 0.201888 + 10.1078i 0.00806263 + 0.403669i
\(628\) 5.32283 + 3.07314i 0.212404 + 0.122632i
\(629\) 47.4853 1.89336
\(630\) 7.04656 8.58266i 0.280742 0.341941i
\(631\) 3.58972 + 6.21757i 0.142904 + 0.247518i 0.928589 0.371109i \(-0.121023\pi\)
−0.785685 + 0.618627i \(0.787689\pi\)
\(632\) 12.3651 7.13902i 0.491859 0.283975i
\(633\) 19.5311 + 10.7621i 0.776294 + 0.427755i
\(634\) 7.72732 + 13.3841i 0.306891 + 0.531551i
\(635\) −12.3623 −0.490581
\(636\) 0.428656 0.777929i 0.0169973 0.0308469i
\(637\) 18.5520 17.1120i 0.735059 0.678004i
\(638\) 6.65291i 0.263391i
\(639\) 11.0957 7.01130i 0.438940 0.277363i
\(640\) −1.21163 + 0.699535i −0.0478939 + 0.0276516i
\(641\) 28.5103i 1.12609i −0.826427 0.563044i \(-0.809630\pi\)
0.826427 0.563044i \(-0.190370\pi\)
\(642\) 0.0721583 + 3.61273i 0.00284786 + 0.142583i
\(643\) −39.1207 + 22.5863i −1.54277 + 0.890718i −0.544106 + 0.839016i \(0.683131\pi\)
−0.998663 + 0.0517020i \(0.983535\pi\)
\(644\) −2.09375 6.32178i −0.0825055 0.249113i
\(645\) 25.8250 + 14.2302i 1.01686 + 0.560312i
\(646\) −15.8377 + 27.4318i −0.623127 + 1.07929i
\(647\) 8.96906 + 15.5349i 0.352610 + 0.610739i 0.986706 0.162516i \(-0.0519608\pi\)
−0.634096 + 0.773255i \(0.718627\pi\)
\(648\) −0.718182 8.97130i −0.0282128 0.352426i
\(649\) 15.7549 9.09609i 0.618433 0.357053i
\(650\) 10.0248 + 4.45529i 0.393206 + 0.174751i
\(651\) 4.26767 22.9569i 0.167263 0.899752i
\(652\) −6.89482 + 11.9422i −0.270022 + 0.467692i
\(653\) 28.3261i 1.10849i 0.832355 + 0.554243i \(0.186992\pi\)
−0.832355 + 0.554243i \(0.813008\pi\)
\(654\) 13.2079 23.9698i 0.516471 0.937295i
\(655\) 12.1538 21.0510i 0.474889 0.822532i
\(656\) −3.22591 + 5.58745i −0.125951 + 0.218153i
\(657\) 22.2141 + 11.6684i 0.866655 + 0.455226i
\(658\) 5.57359 6.26110i 0.217281 0.244083i
\(659\) −33.6960 + 19.4544i −1.31261 + 0.757836i −0.982528 0.186116i \(-0.940410\pi\)
−0.330082 + 0.943952i \(0.607076\pi\)
\(660\) 1.48009 2.68608i 0.0576124 0.104555i
\(661\) −12.2971 + 7.09975i −0.478303 + 0.276148i −0.719709 0.694276i \(-0.755725\pi\)
0.241406 + 0.970424i \(0.422391\pi\)
\(662\) 0.860237 + 0.496658i 0.0334340 + 0.0193032i
\(663\) −5.36276 42.5544i −0.208272 1.65267i
\(664\) 3.52068i 0.136629i
\(665\) −5.36740 16.2060i −0.208139 0.628443i
\(666\) 0.828239 + 20.7253i 0.0320936 + 0.803089i
\(667\) −6.61573 + 11.4588i −0.256162 + 0.443686i
\(668\) 7.46828 12.9354i 0.288957 0.500487i
\(669\) 17.2490 31.3036i 0.666884 1.21027i
\(670\) 0.756639 + 0.436846i 0.0292315 + 0.0168768i
\(671\) 3.89112 0.150215
\(672\) 4.32055 1.52735i 0.166669 0.0589190i
\(673\) 10.7809 18.6731i 0.415574 0.719795i −0.579915 0.814677i \(-0.696914\pi\)
0.995489 + 0.0948822i \(0.0302475\pi\)
\(674\) 16.8178i 0.647797i
\(675\) −14.1405 7.07092i −0.544267 0.272160i
\(676\) −12.7123 + 2.71989i −0.488934 + 0.104611i
\(677\) −20.3440 35.2368i −0.781883 1.35426i −0.930844 0.365418i \(-0.880926\pi\)
0.148960 0.988843i \(-0.452407\pi\)
\(678\) −18.2745 + 11.0431i −0.701827 + 0.424108i
\(679\) −4.44344 + 4.99154i −0.170524 + 0.191558i
\(680\) 8.32154 4.80444i 0.319116 0.184242i
\(681\) 0.629678 + 31.5258i 0.0241293 + 1.20807i
\(682\) 6.44876i 0.246936i
\(683\) 36.2054i 1.38536i 0.721244 + 0.692681i \(0.243571\pi\)
−0.721244 + 0.692681i \(0.756429\pi\)
\(684\) −12.2490 6.43402i −0.468353 0.246011i
\(685\) −8.58296 + 4.95537i −0.327938 + 0.189335i
\(686\) −15.1661 10.6296i −0.579045 0.405841i
\(687\) −16.5849 27.4452i −0.632754 1.04710i
\(688\) 6.08396 + 10.5377i 0.231949 + 0.401747i
\(689\) 1.68961 + 0.750907i 0.0643691 + 0.0286073i
\(690\) 5.22033 3.15461i 0.198735 0.120094i
\(691\) 8.30431i 0.315911i 0.987446 + 0.157955i \(0.0504902\pi\)
−0.987446 + 0.157955i \(0.949510\pi\)
\(692\) 2.74366 4.75216i 0.104298 0.180650i
\(693\) −6.37431 + 7.76385i −0.242140 + 0.294924i
\(694\) 8.81697 0.334688
\(695\) 2.71258 + 1.56611i 0.102894 + 0.0594059i
\(696\) −7.97445 4.39410i −0.302271 0.166558i
\(697\) 22.1557 38.3749i 0.839208 1.45355i
\(698\) −6.41193 + 11.1058i −0.242695 + 0.420360i
\(699\) 9.59583 + 15.8795i 0.362948 + 0.600616i
\(700\) 1.62903 7.88342i 0.0615715 0.297965i
\(701\) 48.0958i 1.81655i 0.418371 + 0.908276i \(0.362601\pi\)
−0.418371 + 0.908276i \(0.637399\pi\)
\(702\) 18.4796 3.08285i 0.697468 0.116355i
\(703\) 27.6151 + 15.9436i 1.04152 + 0.601323i
\(704\) 1.09604 0.632798i 0.0413085 0.0238495i
\(705\) 6.72432 + 3.70525i 0.253252 + 0.139548i
\(706\) 29.8507 17.2343i 1.12345 0.648621i
\(707\) 16.6683 + 14.8380i 0.626875 + 0.558040i
\(708\) 0.497181 + 24.8922i 0.0186852 + 0.935506i
\(709\) 15.7103 27.2110i 0.590013 1.02193i −0.404217 0.914663i \(-0.632456\pi\)
0.994230 0.107269i \(-0.0342107\pi\)
\(710\) −3.06053 + 5.30100i −0.114860 + 0.198943i
\(711\) −22.8812 36.2107i −0.858113 1.35801i
\(712\) 15.8874i 0.595404i
\(713\) 6.41272 11.1072i 0.240158 0.415966i
\(714\) −29.6738 + 10.4899i −1.11051 + 0.392576i
\(715\) 5.83399 + 2.59278i 0.218179 + 0.0969644i
\(716\) −5.38969 + 3.11174i −0.201422 + 0.116291i
\(717\) 6.73130 0.134447i 0.251385 0.00502101i
\(718\) −13.9548 24.1704i −0.520788 0.902032i
\(719\) −12.6822 + 21.9662i −0.472965 + 0.819200i −0.999521 0.0309406i \(-0.990150\pi\)
0.526556 + 0.850140i \(0.323483\pi\)
\(720\) 2.24208 + 3.54819i 0.0835572 + 0.132233i
\(721\) 20.8255 23.3943i 0.775580 0.871249i
\(722\) −1.96637 + 1.13529i −0.0731809 + 0.0422510i
\(723\) 10.7108 0.213932i 0.398341 0.00795621i
\(724\) 10.2706i 0.381704i
\(725\) −13.8514 + 7.99708i −0.514426 + 0.297004i
\(726\) 7.85600 14.2571i 0.291563 0.529131i
\(727\) 2.55940i 0.0949230i 0.998873 + 0.0474615i \(0.0151132\pi\)
−0.998873 + 0.0474615i \(0.984887\pi\)
\(728\) 3.93517 + 8.68990i 0.145847 + 0.322069i
\(729\) −26.8064 + 3.22752i −0.992830 + 0.119538i
\(730\) −11.7019 −0.433107
\(731\) −41.7850 72.3737i −1.54547 2.67684i
\(732\) −2.57000 + 4.66406i −0.0949900 + 0.172389i
\(733\) 41.4839 23.9507i 1.53224 0.884641i 0.532985 0.846125i \(-0.321070\pi\)
0.999258 0.0385160i \(-0.0122631\pi\)
\(734\) −1.69967 2.94391i −0.0627359 0.108662i
\(735\) 6.41098 15.7047i 0.236473 0.579276i
\(736\) 2.51705 0.0927795
\(737\) −0.684454 0.395170i −0.0252122 0.0145563i
\(738\) 17.1354 + 9.00069i 0.630763 + 0.331320i
\(739\) −0.652666 1.13045i −0.0240087 0.0415843i 0.853771 0.520648i \(-0.174310\pi\)
−0.877780 + 0.479064i \(0.840976\pi\)
\(740\) −4.83655 8.37715i −0.177795 0.307950i
\(741\) 11.1693 26.5481i 0.410313 0.975268i
\(742\) 0.274561 1.32869i 0.0100795 0.0487779i
\(743\) 4.26349 + 2.46153i 0.156412 + 0.0903046i 0.576163 0.817335i \(-0.304549\pi\)
−0.419751 + 0.907639i \(0.637883\pi\)
\(744\) 7.72975 + 4.25927i 0.283386 + 0.156152i
\(745\) 13.9885i 0.512499i
\(746\) −7.31225 4.22173i −0.267721 0.154569i
\(747\) −10.5536 + 0.421751i −0.386136 + 0.0154310i
\(748\) −7.52764 + 4.34609i −0.275238 + 0.158909i
\(749\) 1.73538 + 5.23973i 0.0634095 + 0.191456i
\(750\) 19.4854 0.389190i 0.711508 0.0142112i
\(751\) −46.7878 −1.70731 −0.853656 0.520838i \(-0.825620\pi\)
−0.853656 + 0.520838i \(0.825620\pi\)
\(752\) 1.58414 + 2.74382i 0.0577678 + 0.100057i
\(753\) 2.63590 1.59285i 0.0960576 0.0580468i
\(754\) 7.69746 17.3200i 0.280325 0.630757i
\(755\) −10.0872 −0.367110
\(756\) −5.09598 12.7684i −0.185339 0.464381i
\(757\) −2.63180 + 4.55840i −0.0956542 + 0.165678i −0.909881 0.414868i \(-0.863828\pi\)
0.814227 + 0.580546i \(0.197161\pi\)
\(758\) −21.2942 12.2942i −0.773441 0.446547i
\(759\) −4.72230 + 2.85365i −0.171409 + 0.103581i
\(760\) 6.45252 0.234057
\(761\) 6.36638 11.0269i 0.230781 0.399724i −0.727257 0.686365i \(-0.759205\pi\)
0.958038 + 0.286641i \(0.0925386\pi\)
\(762\) −7.38604 + 13.4042i −0.267568 + 0.485585i
\(763\) 8.45989 40.9402i 0.306269 1.48214i
\(764\) 8.41156 + 4.85641i 0.304319 + 0.175699i
\(765\) −15.3987 24.3692i −0.556741 0.881069i
\(766\) 21.3552 + 12.3294i 0.771593 + 0.445480i
\(767\) −51.5400 + 5.45200i −1.86100 + 0.196860i
\(768\) 0.0345880 + 1.73171i 0.00124809 + 0.0624875i
\(769\) −28.1406 16.2470i −1.01478 0.585881i −0.102189 0.994765i \(-0.532585\pi\)
−0.912586 + 0.408884i \(0.865918\pi\)
\(770\) 0.948022 4.58779i 0.0341644 0.165333i
\(771\) −0.415918 20.8236i −0.0149789 0.749944i
\(772\) 2.73242 + 4.73270i 0.0983421 + 0.170334i
\(773\) 12.3187 0.443073 0.221537 0.975152i \(-0.428893\pi\)
0.221537 + 0.975152i \(0.428893\pi\)
\(774\) 30.8592 19.4997i 1.10921 0.700901i
\(775\) 13.4263 7.75169i 0.482288 0.278449i
\(776\) −1.26293 2.18746i −0.0453365 0.0785251i
\(777\) 10.5601 + 29.8721i 0.378840 + 1.07166i
\(778\) −1.81078 + 3.13636i −0.0649195 + 0.112444i
\(779\) 25.7693 14.8779i 0.923282 0.533057i
\(780\) −6.96104 + 5.28039i −0.249245 + 0.189068i
\(781\) 2.76855 4.79527i 0.0990666 0.171588i
\(782\) −17.2872 −0.618189
\(783\) −12.2165 + 24.4306i −0.436583 + 0.873080i
\(784\) 5.61612 4.17842i 0.200576 0.149229i
\(785\) 8.59907i 0.306914i
\(786\) −15.5639 25.7555i −0.555145 0.918670i
\(787\) 32.1160i 1.14481i 0.819970 + 0.572407i \(0.193990\pi\)
−0.819970 + 0.572407i \(0.806010\pi\)
\(788\) −22.5837 13.0387i −0.804512 0.464485i
\(789\) −1.69745 2.80900i −0.0604310 0.100003i
\(790\) 17.2997 + 9.98799i 0.615496 + 0.355357i
\(791\) −21.6864 + 24.3615i −0.771081 + 0.866194i
\(792\) −2.02818 3.20969i −0.0720681 0.114051i
\(793\) −10.1300 4.50205i −0.359728 0.159873i
\(794\) 7.01373 12.1481i 0.248908 0.431121i
\(795\) 1.24242 0.0248154i 0.0440642 0.000880110i
\(796\) 13.7069i 0.485828i
\(797\) −8.26661 14.3182i −0.292819 0.507177i 0.681657 0.731672i \(-0.261260\pi\)
−0.974475 + 0.224496i \(0.927927\pi\)
\(798\) −20.7789 3.86278i −0.735564 0.136741i
\(799\) −10.8800 18.8447i −0.384906 0.666676i
\(800\) 2.63497 + 1.52130i 0.0931603 + 0.0537861i
\(801\) 47.6240 1.90319i 1.68271 0.0672457i
\(802\) −31.9750 −1.12907
\(803\) 10.5855 0.373555
\(804\) 0.925734 0.559414i 0.0326481 0.0197290i
\(805\) 6.19500 6.95916i 0.218345 0.245278i
\(806\) −7.46125 + 16.7885i −0.262811 + 0.591350i
\(807\) 0.863756 + 43.2454i 0.0304057 + 1.52231i
\(808\) −7.30458 + 4.21730i −0.256974 + 0.148364i
\(809\) −7.01097 + 4.04779i −0.246493 + 0.142313i −0.618157 0.786054i \(-0.712120\pi\)
0.371665 + 0.928367i \(0.378787\pi\)
\(810\) 10.3675 7.14591i 0.364277 0.251082i
\(811\) 19.7787i 0.694525i 0.937768 + 0.347263i \(0.112889\pi\)
−0.937768 + 0.347263i \(0.887111\pi\)
\(812\) −13.6203 2.81449i −0.477978 0.0987694i
\(813\) 13.8371 0.276374i 0.485288 0.00969285i
\(814\) 4.37513 + 7.57795i 0.153348 + 0.265607i
\(815\) −19.2927 −0.675793
\(816\) −0.237552 11.8934i −0.00831599 0.416354i
\(817\) 56.1185i 1.96334i
\(818\) 0.556454 0.0194559
\(819\) 25.5775 12.8371i 0.893751 0.448564i
\(820\) −9.02656 −0.315221
\(821\) 22.5545i 0.787157i −0.919291 0.393579i \(-0.871237\pi\)
0.919291 0.393579i \(-0.128763\pi\)
\(822\) 0.245015 + 12.2671i 0.00854587 + 0.427863i
\(823\) −37.7875 −1.31719 −0.658595 0.752498i \(-0.728849\pi\)
−0.658595 + 0.752498i \(0.728849\pi\)
\(824\) 5.91907 + 10.2521i 0.206201 + 0.357150i
\(825\) −6.66829 + 0.133188i −0.232160 + 0.00463702i
\(826\) 11.9570 + 36.1025i 0.416039 + 1.25617i
\(827\) 6.55062i 0.227788i −0.993493 0.113894i \(-0.963668\pi\)
0.993493 0.113894i \(-0.0363323\pi\)
\(828\) −0.301523 7.54512i −0.0104787 0.262211i
\(829\) 7.89232 4.55664i 0.274112 0.158258i −0.356643 0.934241i \(-0.616079\pi\)
0.630755 + 0.775982i \(0.282745\pi\)
\(830\) 4.26576 2.46284i 0.148067 0.0854863i
\(831\) −0.573021 28.6892i −0.0198779 0.995218i
\(832\) −3.58555 + 0.379286i −0.124306 + 0.0131494i
\(833\) −38.5718 + 28.6976i −1.33643 + 0.994313i
\(834\) 3.31879 2.00552i 0.114920 0.0694455i
\(835\) 20.8973 0.723181
\(836\) −5.83693 −0.201875
\(837\) 11.8416 23.6810i 0.409307 0.818534i
\(838\) −13.3335 7.69809i −0.460598 0.265926i
\(839\) −9.49359 16.4434i −0.327755 0.567688i 0.654311 0.756226i \(-0.272959\pi\)
−0.982066 + 0.188537i \(0.939625\pi\)
\(840\) 4.87297 + 4.16648i 0.168133 + 0.143757i
\(841\) −0.683344 1.18359i −0.0235636 0.0408133i
\(842\) 5.44197i 0.187543i
\(843\) 2.04684 0.0408823i 0.0704969 0.00140806i
\(844\) −6.43745 + 11.1500i −0.221586 + 0.383798i
\(845\) −12.1882 13.4999i −0.419287 0.464412i
\(846\) 8.03512 5.07733i 0.276253 0.174562i
\(847\) 5.03190 24.3510i 0.172898 0.836711i
\(848\) 0.444106 + 0.256405i 0.0152506 + 0.00880497i
\(849\) 29.4312 + 48.7035i 1.01007 + 1.67150i
\(850\) −18.0971 10.4484i −0.620726 0.358376i
\(851\) 17.4027i 0.596558i
\(852\) 3.91924 + 6.48567i 0.134271 + 0.222195i
\(853\) 46.7396i 1.60033i 0.599779 + 0.800166i \(0.295255\pi\)
−0.599779 + 0.800166i \(0.704745\pi\)
\(854\) −1.64613 + 7.96616i −0.0563294 + 0.272597i
\(855\) −0.772963 19.3421i −0.0264348 0.661486i
\(856\) −2.08622 −0.0713057
\(857\) 1.41497 2.45080i 0.0483345 0.0837177i −0.840846 0.541274i \(-0.817942\pi\)
0.889180 + 0.457557i \(0.151275\pi\)
\(858\) 6.29694 4.77663i 0.214974 0.163071i
\(859\) 19.7715 11.4151i 0.674595 0.389478i −0.123221 0.992379i \(-0.539322\pi\)
0.797815 + 0.602902i \(0.205989\pi\)
\(860\) −8.51189 + 14.7430i −0.290253 + 0.502733i
\(861\) 29.0680 + 5.40372i 0.990634 + 0.184158i
\(862\) −11.4264 19.7911i −0.389185 0.674089i
\(863\) −40.5300 + 23.4000i −1.37966 + 0.796546i −0.992118 0.125307i \(-0.960008\pi\)
−0.387540 + 0.921853i \(0.626675\pi\)
\(864\) 5.18683 0.311127i 0.176460 0.0105847i
\(865\) 7.67715 0.261031
\(866\) 3.87938 + 6.71928i 0.131827 + 0.228330i
\(867\) 1.04352 + 52.2457i 0.0354399 + 1.77436i
\(868\) 13.2023 + 2.72813i 0.448116 + 0.0925988i
\(869\) −15.6493 9.03512i −0.530865 0.306495i
\(870\) −0.254379 12.7359i −0.00862426 0.431788i
\(871\) 1.32467 + 1.82069i 0.0448849 + 0.0616918i
\(872\) 13.6840 + 7.90043i 0.463397 + 0.267542i
\(873\) −6.40584 + 4.04780i −0.216805 + 0.136997i
\(874\) −10.0534 5.80431i −0.340060 0.196334i
\(875\) 28.2608 9.35989i 0.955388 0.316422i
\(876\) −6.99151 + 12.6882i −0.236221 + 0.428696i
\(877\) 9.58136 16.5954i 0.323540 0.560387i −0.657676 0.753301i \(-0.728460\pi\)
0.981216 + 0.192914i \(0.0617938\pi\)
\(878\) −41.6588 −1.40592
\(879\) 8.36143 5.05275i 0.282024 0.170425i
\(880\) 1.53343 + 0.885329i 0.0516921 + 0.0298444i
\(881\) −22.6060 + 39.1548i −0.761616 + 1.31916i 0.180401 + 0.983593i \(0.442260\pi\)
−0.942017 + 0.335564i \(0.891073\pi\)
\(882\) −13.1980 16.3344i −0.444401 0.550007i
\(883\) −29.3707 −0.988402 −0.494201 0.869348i \(-0.664539\pi\)
−0.494201 + 0.869348i \(0.664539\pi\)
\(884\) 24.6257 2.60495i 0.828252 0.0876140i
\(885\) −29.8124 + 18.0154i −1.00213 + 0.605580i
\(886\) 12.9680 + 22.4612i 0.435667 + 0.754598i
\(887\) −9.65593 −0.324214 −0.162107 0.986773i \(-0.551829\pi\)
−0.162107 + 0.986773i \(0.551829\pi\)
\(888\) −11.9729 + 0.239140i −0.401785 + 0.00802500i
\(889\) −4.73088 + 22.8943i −0.158669 + 0.767850i
\(890\) −19.2496 + 11.1138i −0.645248 + 0.372534i
\(891\) −9.37842 + 6.46418i −0.314189 + 0.216558i
\(892\) 17.8707 + 10.3176i 0.598354 + 0.345460i
\(893\) 14.6122i 0.488977i
\(894\) −15.1676 8.35767i −0.507279 0.279522i
\(895\) −7.54055 4.35354i −0.252053 0.145523i
\(896\) 0.831830 + 2.51159i 0.0277895 + 0.0839062i
\(897\) 15.5956 1.96538i 0.520722 0.0656221i
\(898\) 3.00244 + 5.20037i 0.100193 + 0.173539i
\(899\) −13.3927 23.1968i −0.446671 0.773657i
\(900\) 4.24461 8.08085i 0.141487 0.269362i
\(901\) −3.05014 1.76100i −0.101615 0.0586674i
\(902\) 8.16541 0.271878
\(903\) 36.2365 42.3810i 1.20587 1.41035i
\(904\) −6.16378 10.6760i −0.205004 0.355078i
\(905\) −12.4442 + 7.18464i −0.413658 + 0.238826i
\(906\) −6.02675 + 10.9374i −0.200225 + 0.363371i
\(907\) −8.64496 14.9735i −0.287051 0.497187i 0.686053 0.727551i \(-0.259342\pi\)
−0.973105 + 0.230364i \(0.926008\pi\)
\(908\) −18.2051 −0.604157
\(909\) 13.5168 + 21.3911i 0.448325 + 0.709496i
\(910\) −7.77616 + 10.8469i −0.257777 + 0.359570i
\(911\) 27.9182i 0.924970i −0.886627 0.462485i \(-0.846958\pi\)
0.886627 0.462485i \(-0.153042\pi\)
\(912\) 3.85517 6.99639i 0.127657 0.231673i
\(913\) −3.85880 + 2.22788i −0.127708 + 0.0737320i
\(914\) 29.6490i 0.980700i
\(915\) −7.44892 + 0.148780i −0.246254 + 0.00491852i
\(916\) 16.0335 9.25697i 0.529763 0.305859i
\(917\) −34.3344 30.5643i −1.13382 1.00932i
\(918\) −35.6234 + 2.13683i −1.17575 + 0.0705260i
\(919\) 6.32253 10.9509i 0.208561 0.361238i −0.742700 0.669624i \(-0.766455\pi\)
0.951261 + 0.308385i \(0.0997886\pi\)
\(920\) 1.76076 + 3.04973i 0.0580506 + 0.100547i
\(921\) 44.0821 0.880468i 1.45255 0.0290124i
\(922\) −6.58672 + 3.80284i −0.216922 + 0.125240i
\(923\) −12.7557 + 9.28065i −0.419860 + 0.305476i
\(924\) −4.40808 3.76899i −0.145015 0.123991i
\(925\) −10.5182 + 18.2181i −0.345836 + 0.599006i
\(926\) 13.7605i 0.452199i
\(927\) 30.0228 18.9712i 0.986079 0.623096i
\(928\) 2.62837 4.55247i 0.0862805 0.149442i
\(929\) 10.6030 18.3649i 0.347873 0.602534i −0.637998 0.770038i \(-0.720237\pi\)
0.985871 + 0.167504i \(0.0535707\pi\)
\(930\) 0.246573 + 12.3451i 0.00808546 + 0.404812i
\(931\) −32.0669 + 3.73831i −1.05095 + 0.122518i
\(932\) −9.27681 + 5.35597i −0.303872 + 0.175441i
\(933\) −22.1616 12.2115i −0.725538 0.399788i
\(934\) −14.0396 + 8.10576i −0.459390 + 0.265229i
\(935\) −10.5317 6.08048i −0.344424 0.198853i
\(936\) 1.56647 + 10.7026i 0.0512017 + 0.349826i
\(937\) 44.9305i 1.46782i −0.679249 0.733908i \(-0.737694\pi\)
0.679249 0.733908i \(-0.262306\pi\)
\(938\) 1.09857 1.23408i 0.0358697 0.0402943i
\(939\) −9.91692 16.4108i −0.323627 0.535547i
\(940\) −2.21633 + 3.83879i −0.0722887 + 0.125208i
\(941\) 12.0246 20.8273i 0.391992 0.678950i −0.600720 0.799459i \(-0.705120\pi\)
0.992712 + 0.120510i \(0.0384529\pi\)
\(942\) 9.32387 + 5.13766i 0.303788 + 0.167394i
\(943\) 14.0639 + 8.11977i 0.457982 + 0.264416i
\(944\) −14.3744 −0.467847
\(945\) 11.9057 15.1064i 0.387293 0.491410i
\(946\) 7.69984 13.3365i 0.250343 0.433608i
\(947\) 7.20515i 0.234136i 0.993124 + 0.117068i \(0.0373495\pi\)
−0.993124 + 0.117068i \(0.962650\pi\)
\(948\) 21.1659 12.7904i 0.687435 0.415412i
\(949\) −27.5580 12.2475i −0.894572 0.397571i
\(950\) −7.01625 12.1525i −0.227637 0.394279i
\(951\) 13.8444 + 22.9101i 0.448935 + 0.742910i
\(952\) −5.71305 17.2497i −0.185161 0.559066i
\(953\) −50.9766 + 29.4313i −1.65129 + 0.953374i −0.674751 + 0.738046i \(0.735749\pi\)
−0.976542 + 0.215329i \(0.930918\pi\)
\(954\) 0.715400 1.36197i 0.0231619 0.0440954i
\(955\) 13.5889i 0.439727i
\(956\) 3.88709i 0.125718i
\(957\) 0.230111 + 11.5209i 0.00743843 + 0.372417i
\(958\) 6.64153 3.83449i 0.214578 0.123887i
\(959\) 5.89252 + 17.7916i 0.190279 + 0.574520i
\(960\) −2.07399 + 1.25330i −0.0669378 + 0.0404500i
\(961\) −2.51828 4.36179i −0.0812348 0.140703i
\(962\) −2.62236 24.7903i −0.0845483 0.799271i
\(963\) 0.249914 + 6.25368i 0.00805337 + 0.201522i
\(964\) 6.18514i 0.199210i
\(965\) −3.82285 + 6.62138i −0.123062 + 0.213150i
\(966\) −3.84442 10.8750i −0.123692 0.349898i
\(967\) −8.84170 −0.284330 −0.142165 0.989843i \(-0.545406\pi\)
−0.142165 + 0.989843i \(0.545406\pi\)
\(968\) 8.13914 + 4.69913i 0.261602 + 0.151036i
\(969\) −26.4775 + 48.0515i −0.850579 + 1.54364i
\(970\) 1.76692 3.06040i 0.0567325 0.0982636i
\(971\) 3.61560 6.26240i 0.116030 0.200970i −0.802161 0.597108i \(-0.796316\pi\)
0.918191 + 0.396138i \(0.129650\pi\)
\(972\) −1.55398 15.5108i −0.0498439 0.497509i
\(973\) 3.93843 4.42424i 0.126260 0.141835i
\(974\) 1.25273i 0.0401402i
\(975\) 17.5141 + 7.36851i 0.560901 + 0.235981i
\(976\) −2.66263 1.53727i −0.0852287 0.0492068i
\(977\) 46.8604 27.0549i 1.49920 0.865562i 0.499198 0.866488i \(-0.333628\pi\)
1.00000 0.000926109i \(0.000294790\pi\)
\(978\) −11.5267 + 20.9188i −0.368585 + 0.668910i
\(979\) 17.4131 10.0535i 0.556527 0.321311i
\(980\) 8.99138 + 3.88171i 0.287219 + 0.123997i
\(981\) 22.0432 41.9655i 0.703784 1.33986i
\(982\) −1.03105 + 1.78584i −0.0329023 + 0.0569884i
\(983\) −9.49650 + 16.4484i −0.302891 + 0.524623i −0.976790 0.214201i \(-0.931285\pi\)
0.673898 + 0.738824i \(0.264619\pi\)
\(984\) −5.39307 + 9.78739i −0.171925 + 0.312011i
\(985\) 36.4842i 1.16248i
\(986\) −18.0518 + 31.2666i −0.574886 + 0.995731i
\(987\) 9.43526 11.0352i 0.300328 0.351253i
\(988\) 15.1957 + 6.75337i 0.483440 + 0.214853i
\(989\) 26.5240 15.3136i 0.843413 0.486945i
\(990\) 2.47017 4.70269i 0.0785073 0.149461i
\(991\) 4.42404 + 7.66266i 0.140534 + 0.243412i 0.927698 0.373332i \(-0.121785\pi\)
−0.787164 + 0.616744i \(0.788451\pi\)
\(992\) −2.54772 + 4.41277i −0.0808901 + 0.140106i
\(993\) 1.50685 + 0.830311i 0.0478186 + 0.0263491i
\(994\) 8.64597 + 7.69659i 0.274233 + 0.244121i
\(995\) 16.6077 9.58845i 0.526499 0.303974i
\(996\) −0.121773 6.09678i −0.00385853 0.193184i
\(997\) 31.9533i 1.01197i −0.862542 0.505986i \(-0.831129\pi\)
0.862542 0.505986i \(-0.168871\pi\)
\(998\) 10.6042 6.12234i 0.335670 0.193799i
\(999\) 2.15111 + 35.8615i 0.0680582 + 1.13461i
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.bb.a.269.29 yes 76
3.2 odd 2 inner 546.2.bb.a.269.4 yes 76
7.5 odd 6 546.2.u.a.425.35 yes 76
13.3 even 3 546.2.u.a.185.4 76
21.5 even 6 546.2.u.a.425.4 yes 76
39.29 odd 6 546.2.u.a.185.35 yes 76
91.68 odd 6 inner 546.2.bb.a.341.23 yes 76
273.68 even 6 inner 546.2.bb.a.341.10 yes 76
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
546.2.u.a.185.4 76 13.3 even 3
546.2.u.a.185.35 yes 76 39.29 odd 6
546.2.u.a.425.4 yes 76 21.5 even 6
546.2.u.a.425.35 yes 76 7.5 odd 6
546.2.bb.a.269.4 yes 76 3.2 odd 2 inner
546.2.bb.a.269.29 yes 76 1.1 even 1 trivial
546.2.bb.a.341.10 yes 76 273.68 even 6 inner
546.2.bb.a.341.23 yes 76 91.68 odd 6 inner