Properties

Label 546.2.k.c.445.4
Level $546$
Weight $2$
Character 546.445
Analytic conductor $4.360$
Analytic rank $0$
Dimension $8$
CM no
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(373,546)]
 
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, 2, 4]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("546.373");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 546 = 2 \cdot 3 \cdot 7 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 546.k (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: \(8\)
Relative dimension: \(4\) over \(\Q(\zeta_{3})\)
Coefficient field: 8.0.447703281.1
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{8} - x^{7} - 2x^{6} + 2x^{5} + 3x^{4} + 4x^{3} - 8x^{2} - 8x + 16 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 3 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 445.4
Root \(-1.38232 + 0.298668i\) of defining polynomial
Character \(\chi\) \(=\) 546.445
Dual form 546.2.k.c.373.4

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.500000 + 0.866025i) q^{2} +1.00000 q^{3} +(-0.500000 - 0.866025i) q^{4} +(1.75410 + 3.03819i) q^{5} +(-0.500000 + 0.866025i) q^{6} +(1.12588 + 2.39424i) q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q+(-0.500000 + 0.866025i) q^{2} +1.00000 q^{3} +(-0.500000 - 0.866025i) q^{4} +(1.75410 + 3.03819i) q^{5} +(-0.500000 + 0.866025i) q^{6} +(1.12588 + 2.39424i) q^{7} +1.00000 q^{8} +1.00000 q^{9} -3.50820 q^{10} -6.40782 q^{11} +(-0.500000 - 0.866025i) q^{12} +(-0.213022 + 3.59925i) q^{13} +(-2.63641 - 0.222079i) q^{14} +(1.75410 + 3.03819i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(-2.33890 - 4.05110i) q^{17} +(-0.500000 + 0.866025i) q^{18} +5.23821 q^{19} +(1.75410 - 3.03819i) q^{20} +(1.12588 + 2.39424i) q^{21} +(3.20391 - 5.54934i) q^{22} +(1.08480 - 1.87894i) q^{23} +1.00000 q^{24} +(-3.65372 + 6.32843i) q^{25} +(-3.01053 - 1.98411i) q^{26} +1.00000 q^{27} +(1.51053 - 2.17216i) q^{28} +(-1.23033 - 2.13099i) q^{29} -3.50820 q^{30} +(4.46035 - 7.72555i) q^{31} +(-0.500000 - 0.866025i) q^{32} -6.40782 q^{33} +4.67781 q^{34} +(-5.29925 + 7.62037i) q^{35} +(-0.500000 - 0.866025i) q^{36} +(-1.94981 + 3.37717i) q^{37} +(-2.61911 + 4.53642i) q^{38} +(-0.213022 + 3.59925i) q^{39} +(1.75410 + 3.03819i) q^{40} +(5.09300 + 8.82134i) q^{41} +(-2.63641 - 0.222079i) q^{42} +(-1.19338 + 2.06699i) q^{43} +(3.20391 + 5.54934i) q^{44} +(1.75410 + 3.03819i) q^{45} +(1.08480 + 1.87894i) q^{46} +(-2.44070 - 4.22742i) q^{47} +(-0.500000 + 0.866025i) q^{48} +(-4.46478 + 5.39126i) q^{49} +(-3.65372 - 6.32843i) q^{50} +(-2.33890 - 4.05110i) q^{51} +(3.22356 - 1.61514i) q^{52} +(-1.05395 + 1.82549i) q^{53} +(-0.500000 + 0.866025i) q^{54} +(-11.2399 - 19.4682i) q^{55} +(1.12588 + 2.39424i) q^{56} +5.23821 q^{57} +2.46066 q^{58} +(5.89729 + 10.2144i) q^{59} +(1.75410 - 3.03819i) q^{60} +9.35561 q^{61} +(4.46035 + 7.72555i) q^{62} +(1.12588 + 2.39424i) q^{63} +1.00000 q^{64} +(-11.3089 + 5.66624i) q^{65} +(3.20391 - 5.54934i) q^{66} +7.28922 q^{67} +(-2.33890 + 4.05110i) q^{68} +(1.08480 - 1.87894i) q^{69} +(-3.94981 - 8.39947i) q^{70} +(2.79339 - 4.83829i) q^{71} +1.00000 q^{72} +(4.23175 - 7.32961i) q^{73} +(-1.94981 - 3.37717i) q^{74} +(-3.65372 + 6.32843i) q^{75} +(-2.61911 - 4.53642i) q^{76} +(-7.21444 - 15.3419i) q^{77} +(-3.01053 - 1.98411i) q^{78} +(0.893764 + 1.54804i) q^{79} -3.50820 q^{80} +1.00000 q^{81} -10.1860 q^{82} -2.59218 q^{83} +(1.51053 - 2.17216i) q^{84} +(8.20533 - 14.2121i) q^{85} +(-1.19338 - 2.06699i) q^{86} +(-1.23033 - 2.13099i) q^{87} -6.40782 q^{88} +(-3.50376 + 6.06869i) q^{89} -3.50820 q^{90} +(-8.85732 + 3.54230i) q^{91} -2.16961 q^{92} +(4.46035 - 7.72555i) q^{93} +4.88140 q^{94} +(9.18834 + 15.9147i) q^{95} +(-0.500000 - 0.866025i) q^{96} +(-4.92513 + 8.53057i) q^{97} +(-2.43658 - 6.56225i) q^{98} -6.40782 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q - 4 q^{2} + 8 q^{3} - 4 q^{4} + 2 q^{5} - 4 q^{6} - 3 q^{7} + 8 q^{8} + 8 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 8 q - 4 q^{2} + 8 q^{3} - 4 q^{4} + 2 q^{5} - 4 q^{6} - 3 q^{7} + 8 q^{8} + 8 q^{9} - 4 q^{10} - 8 q^{11} - 4 q^{12} + 3 q^{13} + 3 q^{14} + 2 q^{15} - 4 q^{16} - 2 q^{17} - 4 q^{18} + 8 q^{19} + 2 q^{20} - 3 q^{21} + 4 q^{22} + 4 q^{23} + 8 q^{24} + 2 q^{25} - 12 q^{26} + 8 q^{27} + 2 q^{29} - 4 q^{30} + 14 q^{31} - 4 q^{32} - 8 q^{33} + 4 q^{34} - 4 q^{35} - 4 q^{36} - 6 q^{37} - 4 q^{38} + 3 q^{39} + 2 q^{40} + 12 q^{41} + 3 q^{42} + 4 q^{44} + 2 q^{45} + 4 q^{46} + 7 q^{47} - 4 q^{48} - 7 q^{49} + 2 q^{50} - 2 q^{51} + 9 q^{52} - q^{53} - 4 q^{54} - 25 q^{55} - 3 q^{56} + 8 q^{57} - 4 q^{58} + 16 q^{59} + 2 q^{60} + 8 q^{61} + 14 q^{62} - 3 q^{63} + 8 q^{64} + q^{65} + 4 q^{66} - 38 q^{67} - 2 q^{68} + 4 q^{69} - 22 q^{70} + 20 q^{71} + 8 q^{72} - 7 q^{73} - 6 q^{74} + 2 q^{75} - 4 q^{76} - 24 q^{77} - 12 q^{78} + 24 q^{79} - 4 q^{80} + 8 q^{81} - 24 q^{82} - 64 q^{83} + 15 q^{85} + 2 q^{87} - 8 q^{88} - 11 q^{89} - 4 q^{90} - 20 q^{91} - 8 q^{92} + 14 q^{93} - 14 q^{94} + 28 q^{95} - 4 q^{96} + 11 q^{97} + 2 q^{98} - 8 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

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

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

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
\(3\) 1.00000 0.577350
\(4\) −0.500000 0.866025i −0.250000 0.433013i
\(5\) 1.75410 + 3.03819i 0.784457 + 1.35872i 0.929323 + 0.369268i \(0.120391\pi\)
−0.144866 + 0.989451i \(0.546275\pi\)
\(6\) −0.500000 + 0.866025i −0.204124 + 0.353553i
\(7\) 1.12588 + 2.39424i 0.425543 + 0.904938i
\(8\) 1.00000 0.353553
\(9\) 1.00000 0.333333
\(10\) −3.50820 −1.10939
\(11\) −6.40782 −1.93203 −0.966015 0.258485i \(-0.916777\pi\)
−0.966015 + 0.258485i \(0.916777\pi\)
\(12\) −0.500000 0.866025i −0.144338 0.250000i
\(13\) −0.213022 + 3.59925i −0.0590817 + 0.998253i
\(14\) −2.63641 0.222079i −0.704611 0.0593532i
\(15\) 1.75410 + 3.03819i 0.452906 + 0.784457i
\(16\) −0.500000 + 0.866025i −0.125000 + 0.216506i
\(17\) −2.33890 4.05110i −0.567267 0.982536i −0.996835 0.0795010i \(-0.974667\pi\)
0.429567 0.903035i \(-0.358666\pi\)
\(18\) −0.500000 + 0.866025i −0.117851 + 0.204124i
\(19\) 5.23821 1.20173 0.600864 0.799351i \(-0.294823\pi\)
0.600864 + 0.799351i \(0.294823\pi\)
\(20\) 1.75410 3.03819i 0.392228 0.679359i
\(21\) 1.12588 + 2.39424i 0.245687 + 0.522466i
\(22\) 3.20391 5.54934i 0.683076 1.18312i
\(23\) 1.08480 1.87894i 0.226197 0.391785i −0.730481 0.682933i \(-0.760704\pi\)
0.956678 + 0.291148i \(0.0940372\pi\)
\(24\) 1.00000 0.204124
\(25\) −3.65372 + 6.32843i −0.730745 + 1.26569i
\(26\) −3.01053 1.98411i −0.590414 0.389116i
\(27\) 1.00000 0.192450
\(28\) 1.51053 2.17216i 0.285464 0.410500i
\(29\) −1.23033 2.13099i −0.228467 0.395716i 0.728887 0.684634i \(-0.240038\pi\)
−0.957354 + 0.288918i \(0.906705\pi\)
\(30\) −3.50820 −0.640506
\(31\) 4.46035 7.72555i 0.801102 1.38755i −0.117790 0.993039i \(-0.537581\pi\)
0.918892 0.394510i \(-0.129086\pi\)
\(32\) −0.500000 0.866025i −0.0883883 0.153093i
\(33\) −6.40782 −1.11546
\(34\) 4.67781 0.802237
\(35\) −5.29925 + 7.62037i −0.895737 + 1.28808i
\(36\) −0.500000 0.866025i −0.0833333 0.144338i
\(37\) −1.94981 + 3.37717i −0.320547 + 0.555204i −0.980601 0.196014i \(-0.937200\pi\)
0.660054 + 0.751218i \(0.270533\pi\)
\(38\) −2.61911 + 4.53642i −0.424875 + 0.735905i
\(39\) −0.213022 + 3.59925i −0.0341108 + 0.576342i
\(40\) 1.75410 + 3.03819i 0.277347 + 0.480380i
\(41\) 5.09300 + 8.82134i 0.795393 + 1.37766i 0.922589 + 0.385784i \(0.126069\pi\)
−0.127196 + 0.991878i \(0.540598\pi\)
\(42\) −2.63641 0.222079i −0.406808 0.0342676i
\(43\) −1.19338 + 2.06699i −0.181988 + 0.315213i −0.942558 0.334044i \(-0.891587\pi\)
0.760569 + 0.649257i \(0.224920\pi\)
\(44\) 3.20391 + 5.54934i 0.483008 + 0.836594i
\(45\) 1.75410 + 3.03819i 0.261486 + 0.452906i
\(46\) 1.08480 + 1.87894i 0.159946 + 0.277034i
\(47\) −2.44070 4.22742i −0.356013 0.616632i 0.631278 0.775557i \(-0.282531\pi\)
−0.987291 + 0.158924i \(0.949197\pi\)
\(48\) −0.500000 + 0.866025i −0.0721688 + 0.125000i
\(49\) −4.46478 + 5.39126i −0.637826 + 0.770180i
\(50\) −3.65372 6.32843i −0.516714 0.894976i
\(51\) −2.33890 4.05110i −0.327512 0.567267i
\(52\) 3.22356 1.61514i 0.447027 0.223980i
\(53\) −1.05395 + 1.82549i −0.144771 + 0.250750i −0.929287 0.369358i \(-0.879578\pi\)
0.784517 + 0.620108i \(0.212911\pi\)
\(54\) −0.500000 + 0.866025i −0.0680414 + 0.117851i
\(55\) −11.2399 19.4682i −1.51559 2.62509i
\(56\) 1.12588 + 2.39424i 0.150452 + 0.319944i
\(57\) 5.23821 0.693818
\(58\) 2.46066 0.323101
\(59\) 5.89729 + 10.2144i 0.767761 + 1.32980i 0.938774 + 0.344533i \(0.111963\pi\)
−0.171013 + 0.985269i \(0.554704\pi\)
\(60\) 1.75410 3.03819i 0.226453 0.392228i
\(61\) 9.35561 1.19786 0.598932 0.800800i \(-0.295592\pi\)
0.598932 + 0.800800i \(0.295592\pi\)
\(62\) 4.46035 + 7.72555i 0.566464 + 0.981145i
\(63\) 1.12588 + 2.39424i 0.141848 + 0.301646i
\(64\) 1.00000 0.125000
\(65\) −11.3089 + 5.66624i −1.40269 + 0.702811i
\(66\) 3.20391 5.54934i 0.394374 0.683076i
\(67\) 7.28922 0.890520 0.445260 0.895401i \(-0.353111\pi\)
0.445260 + 0.895401i \(0.353111\pi\)
\(68\) −2.33890 + 4.05110i −0.283634 + 0.491268i
\(69\) 1.08480 1.87894i 0.130595 0.226197i
\(70\) −3.94981 8.39947i −0.472093 1.00393i
\(71\) 2.79339 4.83829i 0.331514 0.574199i −0.651295 0.758825i \(-0.725774\pi\)
0.982809 + 0.184625i \(0.0591072\pi\)
\(72\) 1.00000 0.117851
\(73\) 4.23175 7.32961i 0.495289 0.857866i −0.504696 0.863297i \(-0.668395\pi\)
0.999985 + 0.00543110i \(0.00172878\pi\)
\(74\) −1.94981 3.37717i −0.226661 0.392588i
\(75\) −3.65372 + 6.32843i −0.421896 + 0.730745i
\(76\) −2.61911 4.53642i −0.300432 0.520364i
\(77\) −7.21444 15.3419i −0.822162 1.74837i
\(78\) −3.01053 1.98411i −0.340876 0.224656i
\(79\) 0.893764 + 1.54804i 0.100556 + 0.174169i 0.911914 0.410381i \(-0.134604\pi\)
−0.811358 + 0.584550i \(0.801271\pi\)
\(80\) −3.50820 −0.392228
\(81\) 1.00000 0.111111
\(82\) −10.1860 −1.12486
\(83\) −2.59218 −0.284529 −0.142264 0.989829i \(-0.545438\pi\)
−0.142264 + 0.989829i \(0.545438\pi\)
\(84\) 1.51053 2.17216i 0.164813 0.237002i
\(85\) 8.20533 14.2121i 0.889993 1.54151i
\(86\) −1.19338 2.06699i −0.128685 0.222889i
\(87\) −1.23033 2.13099i −0.131905 0.228467i
\(88\) −6.40782 −0.683076
\(89\) −3.50376 + 6.06869i −0.371398 + 0.643280i −0.989781 0.142597i \(-0.954455\pi\)
0.618383 + 0.785877i \(0.287788\pi\)
\(90\) −3.50820 −0.369796
\(91\) −8.85732 + 3.54230i −0.928499 + 0.371334i
\(92\) −2.16961 −0.226197
\(93\) 4.46035 7.72555i 0.462516 0.801102i
\(94\) 4.88140 0.503478
\(95\) 9.18834 + 15.9147i 0.942704 + 1.63281i
\(96\) −0.500000 0.866025i −0.0510310 0.0883883i
\(97\) −4.92513 + 8.53057i −0.500071 + 0.866149i 0.499929 + 0.866066i \(0.333359\pi\)
−1.00000 8.21569e-5i \(0.999974\pi\)
\(98\) −2.43658 6.56225i −0.246132 0.662887i
\(99\) −6.40782 −0.644010
\(100\) 7.30745 0.730745
\(101\) 13.8203 1.37517 0.687586 0.726103i \(-0.258670\pi\)
0.687586 + 0.726103i \(0.258670\pi\)
\(102\) 4.67781 0.463172
\(103\) −6.56658 11.3737i −0.647025 1.12068i −0.983830 0.179105i \(-0.942680\pi\)
0.336805 0.941574i \(-0.390654\pi\)
\(104\) −0.213022 + 3.59925i −0.0208885 + 0.352936i
\(105\) −5.29925 + 7.62037i −0.517154 + 0.743672i
\(106\) −1.05395 1.82549i −0.102368 0.177307i
\(107\) 4.88232 8.45642i 0.471991 0.817513i −0.527495 0.849558i \(-0.676869\pi\)
0.999486 + 0.0320452i \(0.0102020\pi\)
\(108\) −0.500000 0.866025i −0.0481125 0.0833333i
\(109\) 1.14786 1.98816i 0.109945 0.190431i −0.805803 0.592184i \(-0.798266\pi\)
0.915748 + 0.401753i \(0.131599\pi\)
\(110\) 22.4799 2.14337
\(111\) −1.94981 + 3.37717i −0.185068 + 0.320547i
\(112\) −2.63641 0.222079i −0.249118 0.0209845i
\(113\) 1.96268 3.39947i 0.184634 0.319795i −0.758819 0.651301i \(-0.774223\pi\)
0.943453 + 0.331506i \(0.107557\pi\)
\(114\) −2.61911 + 4.53642i −0.245302 + 0.424875i
\(115\) 7.61142 0.709768
\(116\) −1.23033 + 2.13099i −0.114233 + 0.197858i
\(117\) −0.213022 + 3.59925i −0.0196939 + 0.332751i
\(118\) −11.7946 −1.08578
\(119\) 7.06598 10.1610i 0.647738 0.931453i
\(120\) 1.75410 + 3.03819i 0.160127 + 0.277347i
\(121\) 30.0602 2.73274
\(122\) −4.67781 + 8.10220i −0.423509 + 0.733539i
\(123\) 5.09300 + 8.82134i 0.459220 + 0.795393i
\(124\) −8.92069 −0.801102
\(125\) −8.09497 −0.724036
\(126\) −2.63641 0.222079i −0.234870 0.0197844i
\(127\) 3.51196 + 6.08289i 0.311636 + 0.539769i 0.978717 0.205216i \(-0.0657898\pi\)
−0.667081 + 0.744985i \(0.732457\pi\)
\(128\) −0.500000 + 0.866025i −0.0441942 + 0.0765466i
\(129\) −1.19338 + 2.06699i −0.105071 + 0.181988i
\(130\) 0.747323 12.6269i 0.0655446 1.10745i
\(131\) −4.56251 7.90250i −0.398628 0.690444i 0.594929 0.803778i \(-0.297180\pi\)
−0.993557 + 0.113334i \(0.963847\pi\)
\(132\) 3.20391 + 5.54934i 0.278865 + 0.483008i
\(133\) 5.89760 + 12.5415i 0.511387 + 1.08749i
\(134\) −3.64461 + 6.31265i −0.314846 + 0.545330i
\(135\) 1.75410 + 3.03819i 0.150969 + 0.261486i
\(136\) −2.33890 4.05110i −0.200559 0.347379i
\(137\) −7.53370 13.0488i −0.643648 1.11483i −0.984612 0.174754i \(-0.944087\pi\)
0.340964 0.940076i \(-0.389246\pi\)
\(138\) 1.08480 + 1.87894i 0.0923447 + 0.159946i
\(139\) 7.02519 12.1680i 0.595869 1.03208i −0.397555 0.917578i \(-0.630141\pi\)
0.993424 0.114497i \(-0.0365255\pi\)
\(140\) 9.24906 + 0.779098i 0.781688 + 0.0658458i
\(141\) −2.44070 4.22742i −0.205544 0.356013i
\(142\) 2.79339 + 4.83829i 0.234416 + 0.406020i
\(143\) 1.36501 23.0634i 0.114148 1.92866i
\(144\) −0.500000 + 0.866025i −0.0416667 + 0.0721688i
\(145\) 4.31624 7.47595i 0.358444 0.620844i
\(146\) 4.23175 + 7.32961i 0.350222 + 0.606603i
\(147\) −4.46478 + 5.39126i −0.368249 + 0.444664i
\(148\) 3.89962 0.320547
\(149\) 1.22934 0.100711 0.0503555 0.998731i \(-0.483965\pi\)
0.0503555 + 0.998731i \(0.483965\pi\)
\(150\) −3.65372 6.32843i −0.298325 0.516714i
\(151\) 8.17245 14.1551i 0.665065 1.15193i −0.314203 0.949356i \(-0.601737\pi\)
0.979268 0.202570i \(-0.0649294\pi\)
\(152\) 5.23821 0.424875
\(153\) −2.33890 4.05110i −0.189089 0.327512i
\(154\) 16.8937 + 1.42304i 1.36133 + 0.114672i
\(155\) 31.2955 2.51372
\(156\) 3.22356 1.61514i 0.258091 0.129315i
\(157\) −7.98494 + 13.8303i −0.637267 + 1.10378i 0.348763 + 0.937211i \(0.386602\pi\)
−0.986030 + 0.166568i \(0.946731\pi\)
\(158\) −1.78753 −0.142208
\(159\) −1.05395 + 1.82549i −0.0835834 + 0.144771i
\(160\) 1.75410 3.03819i 0.138674 0.240190i
\(161\) 5.71999 + 0.481825i 0.450798 + 0.0379731i
\(162\) −0.500000 + 0.866025i −0.0392837 + 0.0680414i
\(163\) 7.78633 0.609872 0.304936 0.952373i \(-0.401365\pi\)
0.304936 + 0.952373i \(0.401365\pi\)
\(164\) 5.09300 8.82134i 0.397697 0.688831i
\(165\) −11.2399 19.4682i −0.875029 1.51559i
\(166\) 1.29609 2.24489i 0.100596 0.174237i
\(167\) 3.32333 + 5.75618i 0.257167 + 0.445427i 0.965482 0.260470i \(-0.0838776\pi\)
−0.708315 + 0.705897i \(0.750544\pi\)
\(168\) 1.12588 + 2.39424i 0.0868636 + 0.184720i
\(169\) −12.9092 1.53344i −0.993019 0.117957i
\(170\) 8.20533 + 14.2121i 0.629320 + 1.09001i
\(171\) 5.23821 0.400576
\(172\) 2.38675 0.181988
\(173\) −14.6067 −1.11053 −0.555265 0.831673i \(-0.687383\pi\)
−0.555265 + 0.831673i \(0.687383\pi\)
\(174\) 2.46066 0.186542
\(175\) −19.2655 1.62283i −1.45633 0.122675i
\(176\) 3.20391 5.54934i 0.241504 0.418297i
\(177\) 5.89729 + 10.2144i 0.443267 + 0.767761i
\(178\) −3.50376 6.06869i −0.262618 0.454867i
\(179\) −14.1285 −1.05601 −0.528006 0.849240i \(-0.677060\pi\)
−0.528006 + 0.849240i \(0.677060\pi\)
\(180\) 1.75410 3.03819i 0.130743 0.226453i
\(181\) −13.6453 −1.01425 −0.507124 0.861873i \(-0.669291\pi\)
−0.507124 + 0.861873i \(0.669291\pi\)
\(182\) 1.36093 9.44181i 0.100879 0.699874i
\(183\) 9.35561 0.691587
\(184\) 1.08480 1.87894i 0.0799729 0.138517i
\(185\) −13.6807 −1.00582
\(186\) 4.46035 + 7.72555i 0.327048 + 0.566464i
\(187\) 14.9873 + 25.9587i 1.09598 + 1.89829i
\(188\) −2.44070 + 4.22742i −0.178006 + 0.308316i
\(189\) 1.12588 + 2.39424i 0.0818958 + 0.174155i
\(190\) −18.3767 −1.33318
\(191\) −2.43145 −0.175933 −0.0879666 0.996123i \(-0.528037\pi\)
−0.0879666 + 0.996123i \(0.528037\pi\)
\(192\) 1.00000 0.0721688
\(193\) 3.51754 0.253198 0.126599 0.991954i \(-0.459594\pi\)
0.126599 + 0.991954i \(0.459594\pi\)
\(194\) −4.92513 8.53057i −0.353604 0.612460i
\(195\) −11.3089 + 5.66624i −0.809845 + 0.405768i
\(196\) 6.90136 + 1.17099i 0.492954 + 0.0836418i
\(197\) 1.15702 + 2.00402i 0.0824345 + 0.142781i 0.904295 0.426908i \(-0.140397\pi\)
−0.821861 + 0.569689i \(0.807064\pi\)
\(198\) 3.20391 5.54934i 0.227692 0.394374i
\(199\) −2.84733 4.93173i −0.201842 0.349601i 0.747280 0.664509i \(-0.231359\pi\)
−0.949122 + 0.314909i \(0.898026\pi\)
\(200\) −3.65372 + 6.32843i −0.258357 + 0.447488i
\(201\) 7.28922 0.514142
\(202\) −6.91016 + 11.9687i −0.486197 + 0.842118i
\(203\) 3.71691 5.34495i 0.260876 0.375142i
\(204\) −2.33890 + 4.05110i −0.163756 + 0.283634i
\(205\) −17.8673 + 30.9470i −1.24790 + 2.16143i
\(206\) 13.1332 0.915031
\(207\) 1.08480 1.87894i 0.0753991 0.130595i
\(208\) −3.01053 1.98411i −0.208743 0.137573i
\(209\) −33.5655 −2.32178
\(210\) −3.94981 8.39947i −0.272563 0.579619i
\(211\) 0.291966 + 0.505700i 0.0200998 + 0.0348139i 0.875900 0.482492i \(-0.160268\pi\)
−0.855801 + 0.517306i \(0.826935\pi\)
\(212\) 2.10789 0.144771
\(213\) 2.79339 4.83829i 0.191400 0.331514i
\(214\) 4.88232 + 8.45642i 0.333748 + 0.578069i
\(215\) −8.37320 −0.571048
\(216\) 1.00000 0.0680414
\(217\) 23.5186 + 1.98110i 1.59655 + 0.134486i
\(218\) 1.14786 + 1.98816i 0.0777430 + 0.134655i
\(219\) 4.23175 7.32961i 0.285955 0.495289i
\(220\) −11.2399 + 19.4682i −0.757797 + 1.31254i
\(221\) 15.0792 7.55533i 1.01433 0.508227i
\(222\) −1.94981 3.37717i −0.130863 0.226661i
\(223\) −7.25749 12.5703i −0.485998 0.841773i 0.513873 0.857866i \(-0.328210\pi\)
−0.999870 + 0.0160938i \(0.994877\pi\)
\(224\) 1.51053 2.17216i 0.100927 0.145134i
\(225\) −3.65372 + 6.32843i −0.243582 + 0.421896i
\(226\) 1.96268 + 3.39947i 0.130556 + 0.226129i
\(227\) −10.1232 17.5339i −0.671899 1.16376i −0.977365 0.211560i \(-0.932146\pi\)
0.305466 0.952203i \(-0.401188\pi\)
\(228\) −2.61911 4.53642i −0.173455 0.300432i
\(229\) −0.668929 1.15862i −0.0442041 0.0765637i 0.843077 0.537793i \(-0.180742\pi\)
−0.887281 + 0.461229i \(0.847409\pi\)
\(230\) −3.80571 + 6.59168i −0.250941 + 0.434643i
\(231\) −7.21444 15.3419i −0.474676 1.00942i
\(232\) −1.23033 2.13099i −0.0807752 0.139907i
\(233\) 6.97568 + 12.0822i 0.456992 + 0.791534i 0.998800 0.0489686i \(-0.0155934\pi\)
−0.541808 + 0.840502i \(0.682260\pi\)
\(234\) −3.01053 1.98411i −0.196805 0.129705i
\(235\) 8.56246 14.8306i 0.558553 0.967443i
\(236\) 5.89729 10.2144i 0.383881 0.664901i
\(237\) 0.893764 + 1.54804i 0.0580562 + 0.100556i
\(238\) 5.26665 + 11.1998i 0.341386 + 0.725975i
\(239\) 9.05495 0.585716 0.292858 0.956156i \(-0.405394\pi\)
0.292858 + 0.956156i \(0.405394\pi\)
\(240\) −3.50820 −0.226453
\(241\) −10.0551 17.4159i −0.647705 1.12186i −0.983670 0.179983i \(-0.942396\pi\)
0.335965 0.941875i \(-0.390938\pi\)
\(242\) −15.0301 + 26.0329i −0.966171 + 1.67346i
\(243\) 1.00000 0.0641500
\(244\) −4.67781 8.10220i −0.299466 0.518690i
\(245\) −24.2113 4.10805i −1.54681 0.262454i
\(246\) −10.1860 −0.649436
\(247\) −1.11585 + 18.8536i −0.0710001 + 1.19963i
\(248\) 4.46035 7.72555i 0.283232 0.490573i
\(249\) −2.59218 −0.164273
\(250\) 4.04749 7.01045i 0.255986 0.443380i
\(251\) 4.09035 7.08469i 0.258181 0.447182i −0.707574 0.706639i \(-0.750210\pi\)
0.965755 + 0.259457i \(0.0835437\pi\)
\(252\) 1.51053 2.17216i 0.0951547 0.136833i
\(253\) −6.95123 + 12.0399i −0.437020 + 0.756941i
\(254\) −7.02391 −0.440719
\(255\) 8.20533 14.2121i 0.513838 0.889993i
\(256\) −0.500000 0.866025i −0.0312500 0.0541266i
\(257\) −4.87696 + 8.44715i −0.304217 + 0.526919i −0.977087 0.212842i \(-0.931728\pi\)
0.672870 + 0.739761i \(0.265061\pi\)
\(258\) −1.19338 2.06699i −0.0742964 0.128685i
\(259\) −10.2810 0.866025i −0.638832 0.0538122i
\(260\) 10.5615 + 6.96065i 0.654999 + 0.431681i
\(261\) −1.23033 2.13099i −0.0761555 0.131905i
\(262\) 9.12502 0.563745
\(263\) −2.94716 −0.181730 −0.0908648 0.995863i \(-0.528963\pi\)
−0.0908648 + 0.995863i \(0.528963\pi\)
\(264\) −6.40782 −0.394374
\(265\) −7.39490 −0.454265
\(266\) −13.8101 1.16330i −0.846751 0.0713264i
\(267\) −3.50376 + 6.06869i −0.214427 + 0.371398i
\(268\) −3.64461 6.31265i −0.222630 0.385607i
\(269\) 11.9676 + 20.7285i 0.729679 + 1.26384i 0.957019 + 0.290026i \(0.0936639\pi\)
−0.227340 + 0.973816i \(0.573003\pi\)
\(270\) −3.50820 −0.213502
\(271\) −9.68335 + 16.7721i −0.588222 + 1.01883i 0.406244 + 0.913765i \(0.366838\pi\)
−0.994465 + 0.105065i \(0.966495\pi\)
\(272\) 4.67781 0.283634
\(273\) −8.85732 + 3.54230i −0.536069 + 0.214390i
\(274\) 15.0674 0.910255
\(275\) 23.4124 40.5515i 1.41182 2.44535i
\(276\) −2.16961 −0.130595
\(277\) −1.21710 2.10807i −0.0731282 0.126662i 0.827143 0.561992i \(-0.189965\pi\)
−0.900271 + 0.435330i \(0.856632\pi\)
\(278\) 7.02519 + 12.1680i 0.421343 + 0.729787i
\(279\) 4.46035 7.72555i 0.267034 0.462516i
\(280\) −5.29925 + 7.62037i −0.316691 + 0.455404i
\(281\) −2.80329 −0.167230 −0.0836152 0.996498i \(-0.526647\pi\)
−0.0836152 + 0.996498i \(0.526647\pi\)
\(282\) 4.88140 0.290683
\(283\) −16.9541 −1.00782 −0.503909 0.863757i \(-0.668105\pi\)
−0.503909 + 0.863757i \(0.668105\pi\)
\(284\) −5.58678 −0.331514
\(285\) 9.18834 + 15.9147i 0.544270 + 0.942704i
\(286\) 19.2910 + 12.7138i 1.14070 + 0.751784i
\(287\) −15.3863 + 22.1257i −0.908224 + 1.30604i
\(288\) −0.500000 0.866025i −0.0294628 0.0510310i
\(289\) −2.44094 + 4.22782i −0.143584 + 0.248696i
\(290\) 4.31624 + 7.47595i 0.253458 + 0.439003i
\(291\) −4.92513 + 8.53057i −0.288716 + 0.500071i
\(292\) −8.46350 −0.495289
\(293\) 2.84568 4.92886i 0.166246 0.287947i −0.770851 0.637016i \(-0.780169\pi\)
0.937097 + 0.349069i \(0.113502\pi\)
\(294\) −2.43658 6.56225i −0.142104 0.382718i
\(295\) −20.6888 + 35.8341i −1.20455 + 2.08634i
\(296\) −1.94981 + 3.37717i −0.113331 + 0.196294i
\(297\) −6.40782 −0.371820
\(298\) −0.614668 + 1.06464i −0.0356067 + 0.0616727i
\(299\) 6.53168 + 4.30474i 0.377737 + 0.248950i
\(300\) 7.30745 0.421896
\(301\) −6.29247 0.530048i −0.362692 0.0305515i
\(302\) 8.17245 + 14.1551i 0.470272 + 0.814535i
\(303\) 13.8203 0.793956
\(304\) −2.61911 + 4.53642i −0.150216 + 0.260182i
\(305\) 16.4107 + 28.4241i 0.939672 + 1.62756i
\(306\) 4.67781 0.267412
\(307\) 3.48603 0.198958 0.0994791 0.995040i \(-0.468282\pi\)
0.0994791 + 0.995040i \(0.468282\pi\)
\(308\) −9.67923 + 13.9188i −0.551525 + 0.793099i
\(309\) −6.56658 11.3737i −0.373560 0.647025i
\(310\) −15.6478 + 27.1027i −0.888734 + 1.53933i
\(311\) 12.0016 20.7873i 0.680546 1.17874i −0.294268 0.955723i \(-0.595076\pi\)
0.974814 0.223018i \(-0.0715908\pi\)
\(312\) −0.213022 + 3.59925i −0.0120600 + 0.203768i
\(313\) −8.77758 15.2032i −0.496138 0.859337i 0.503852 0.863790i \(-0.331916\pi\)
−0.999990 + 0.00445337i \(0.998582\pi\)
\(314\) −7.98494 13.8303i −0.450616 0.780490i
\(315\) −5.29925 + 7.62037i −0.298579 + 0.429359i
\(316\) 0.893764 1.54804i 0.0502781 0.0870843i
\(317\) −1.42018 2.45983i −0.0797655 0.138158i 0.823383 0.567486i \(-0.192084\pi\)
−0.903149 + 0.429328i \(0.858750\pi\)
\(318\) −1.05395 1.82549i −0.0591024 0.102368i
\(319\) 7.88374 + 13.6550i 0.441405 + 0.764535i
\(320\) 1.75410 + 3.03819i 0.0980571 + 0.169840i
\(321\) 4.88232 8.45642i 0.272504 0.471991i
\(322\) −3.27727 + 4.71274i −0.182635 + 0.262631i
\(323\) −12.2517 21.2205i −0.681701 1.18074i
\(324\) −0.500000 0.866025i −0.0277778 0.0481125i
\(325\) −21.9993 14.4988i −1.22030 0.804247i
\(326\) −3.89316 + 6.74316i −0.215622 + 0.373469i
\(327\) 1.14786 1.98816i 0.0634769 0.109945i
\(328\) 5.09300 + 8.82134i 0.281214 + 0.487077i
\(329\) 7.37352 10.6032i 0.406515 0.584573i
\(330\) 22.4799 1.23748
\(331\) −18.8749 −1.03746 −0.518729 0.854939i \(-0.673595\pi\)
−0.518729 + 0.854939i \(0.673595\pi\)
\(332\) 1.29609 + 2.24489i 0.0711321 + 0.123204i
\(333\) −1.94981 + 3.37717i −0.106849 + 0.185068i
\(334\) −6.64666 −0.363689
\(335\) 12.7860 + 22.1460i 0.698575 + 1.20997i
\(336\) −2.63641 0.222079i −0.143828 0.0121154i
\(337\) 10.9560 0.596813 0.298407 0.954439i \(-0.403545\pi\)
0.298407 + 0.954439i \(0.403545\pi\)
\(338\) 7.78262 10.4130i 0.423319 0.566393i
\(339\) 1.96268 3.39947i 0.106598 0.184634i
\(340\) −16.4107 −0.889993
\(341\) −28.5811 + 49.5039i −1.54775 + 2.68079i
\(342\) −2.61911 + 4.53642i −0.141625 + 0.245302i
\(343\) −17.9348 4.61985i −0.968388 0.249449i
\(344\) −1.19338 + 2.06699i −0.0643426 + 0.111445i
\(345\) 7.61142 0.409785
\(346\) 7.30337 12.6498i 0.392632 0.680058i
\(347\) 16.0515 + 27.8020i 0.861688 + 1.49249i 0.870299 + 0.492524i \(0.163926\pi\)
−0.00861062 + 0.999963i \(0.502741\pi\)
\(348\) −1.23033 + 2.13099i −0.0659526 + 0.114233i
\(349\) −9.04373 15.6642i −0.484100 0.838485i 0.515734 0.856749i \(-0.327519\pi\)
−0.999833 + 0.0182638i \(0.994186\pi\)
\(350\) 11.0381 15.8730i 0.590013 0.848445i
\(351\) −0.213022 + 3.59925i −0.0113703 + 0.192114i
\(352\) 3.20391 + 5.54934i 0.170769 + 0.295781i
\(353\) −27.4645 −1.46179 −0.730894 0.682491i \(-0.760897\pi\)
−0.730894 + 0.682491i \(0.760897\pi\)
\(354\) −11.7946 −0.626875
\(355\) 19.5995 1.04023
\(356\) 7.00752 0.371398
\(357\) 7.06598 10.1610i 0.373971 0.537775i
\(358\) 7.06425 12.2356i 0.373357 0.646673i
\(359\) −10.8390 18.7738i −0.572063 0.990842i −0.996354 0.0853162i \(-0.972810\pi\)
0.424291 0.905526i \(-0.360523\pi\)
\(360\) 1.75410 + 3.03819i 0.0924491 + 0.160127i
\(361\) 8.43886 0.444151
\(362\) 6.82265 11.8172i 0.358591 0.621097i
\(363\) 30.0602 1.57775
\(364\) 7.49638 + 5.89951i 0.392917 + 0.309218i
\(365\) 29.6916 1.55413
\(366\) −4.67781 + 8.10220i −0.244513 + 0.423509i
\(367\) 15.3217 0.799788 0.399894 0.916561i \(-0.369047\pi\)
0.399894 + 0.916561i \(0.369047\pi\)
\(368\) 1.08480 + 1.87894i 0.0565494 + 0.0979463i
\(369\) 5.09300 + 8.82134i 0.265131 + 0.459220i
\(370\) 6.84033 11.8478i 0.355612 0.615937i
\(371\) −5.55728 0.468119i −0.288520 0.0243035i
\(372\) −8.92069 −0.462516
\(373\) −33.3585 −1.72724 −0.863618 0.504147i \(-0.831807\pi\)
−0.863618 + 0.504147i \(0.831807\pi\)
\(374\) −29.9745 −1.54995
\(375\) −8.09497 −0.418023
\(376\) −2.44070 4.22742i −0.125870 0.218012i
\(377\) 7.93208 3.97432i 0.408523 0.204688i
\(378\) −2.63641 0.222079i −0.135603 0.0114225i
\(379\) 8.43868 + 14.6162i 0.433466 + 0.750785i 0.997169 0.0751926i \(-0.0239571\pi\)
−0.563703 + 0.825977i \(0.690624\pi\)
\(380\) 9.18834 15.9147i 0.471352 0.816405i
\(381\) 3.51196 + 6.08289i 0.179923 + 0.311636i
\(382\) 1.21572 2.10569i 0.0622018 0.107737i
\(383\) 21.5866 1.10302 0.551512 0.834167i \(-0.314051\pi\)
0.551512 + 0.834167i \(0.314051\pi\)
\(384\) −0.500000 + 0.866025i −0.0255155 + 0.0441942i
\(385\) 33.9566 48.8300i 1.73059 2.48861i
\(386\) −1.75877 + 3.04628i −0.0895191 + 0.155052i
\(387\) −1.19338 + 2.06699i −0.0606628 + 0.105071i
\(388\) 9.85026 0.500071
\(389\) 8.68908 15.0499i 0.440554 0.763062i −0.557177 0.830394i \(-0.688115\pi\)
0.997731 + 0.0673322i \(0.0214487\pi\)
\(390\) 0.747323 12.6269i 0.0378422 0.639387i
\(391\) −10.1490 −0.513258
\(392\) −4.46478 + 5.39126i −0.225506 + 0.272300i
\(393\) −4.56251 7.90250i −0.230148 0.398628i
\(394\) −2.31405 −0.116580
\(395\) −3.13550 + 5.43084i −0.157764 + 0.273255i
\(396\) 3.20391 + 5.54934i 0.161003 + 0.278865i
\(397\) 5.87435 0.294825 0.147413 0.989075i \(-0.452905\pi\)
0.147413 + 0.989075i \(0.452905\pi\)
\(398\) 5.69467 0.285448
\(399\) 5.89760 + 12.5415i 0.295249 + 0.627863i
\(400\) −3.65372 6.32843i −0.182686 0.316422i
\(401\) 6.98855 12.1045i 0.348992 0.604471i −0.637079 0.770799i \(-0.719857\pi\)
0.986071 + 0.166327i \(0.0531908\pi\)
\(402\) −3.64461 + 6.31265i −0.181777 + 0.314846i
\(403\) 26.8560 + 17.6996i 1.33779 + 0.881681i
\(404\) −6.91016 11.9687i −0.343793 0.595467i
\(405\) 1.75410 + 3.03819i 0.0871619 + 0.150969i
\(406\) 2.77041 + 5.89142i 0.137493 + 0.292386i
\(407\) 12.4940 21.6403i 0.619307 1.07267i
\(408\) −2.33890 4.05110i −0.115793 0.200559i
\(409\) 18.7448 + 32.4670i 0.926873 + 1.60539i 0.788521 + 0.615008i \(0.210847\pi\)
0.138352 + 0.990383i \(0.455819\pi\)
\(410\) −17.8673 30.9470i −0.882401 1.52836i
\(411\) −7.53370 13.0488i −0.371610 0.643648i
\(412\) −6.56658 + 11.3737i −0.323512 + 0.560340i
\(413\) −17.8161 + 25.6197i −0.876673 + 1.26066i
\(414\) 1.08480 + 1.87894i 0.0533152 + 0.0923447i
\(415\) −4.54694 7.87553i −0.223200 0.386594i
\(416\) 3.22356 1.61514i 0.158048 0.0791889i
\(417\) 7.02519 12.1680i 0.344025 0.595869i
\(418\) 16.7828 29.0686i 0.820872 1.42179i
\(419\) −16.9548 29.3665i −0.828294 1.43465i −0.899375 0.437177i \(-0.855978\pi\)
0.0710814 0.997471i \(-0.477355\pi\)
\(420\) 9.24906 + 0.779098i 0.451308 + 0.0380161i
\(421\) −10.5503 −0.514192 −0.257096 0.966386i \(-0.582766\pi\)
−0.257096 + 0.966386i \(0.582766\pi\)
\(422\) −0.583933 −0.0284254
\(423\) −2.44070 4.22742i −0.118671 0.205544i
\(424\) −1.05395 + 1.82549i −0.0511842 + 0.0886536i
\(425\) 34.1828 1.65811
\(426\) 2.79339 + 4.83829i 0.135340 + 0.234416i
\(427\) 10.5333 + 22.3996i 0.509742 + 1.08399i
\(428\) −9.76463 −0.471991
\(429\) 1.36501 23.0634i 0.0659032 1.11351i
\(430\) 4.18660 7.25141i 0.201896 0.349694i
\(431\) −25.6086 −1.23352 −0.616761 0.787151i \(-0.711555\pi\)
−0.616761 + 0.787151i \(0.711555\pi\)
\(432\) −0.500000 + 0.866025i −0.0240563 + 0.0416667i
\(433\) 3.68968 6.39071i 0.177315 0.307118i −0.763645 0.645636i \(-0.776592\pi\)
0.940960 + 0.338518i \(0.109926\pi\)
\(434\) −13.4750 + 19.3772i −0.646821 + 0.930135i
\(435\) 4.31624 7.47595i 0.206948 0.358444i
\(436\) −2.29572 −0.109945
\(437\) 5.68244 9.84227i 0.271828 0.470820i
\(438\) 4.23175 + 7.32961i 0.202201 + 0.350222i
\(439\) 11.5255 19.9628i 0.550082 0.952771i −0.448186 0.893941i \(-0.647930\pi\)
0.998268 0.0588301i \(-0.0187370\pi\)
\(440\) −11.2399 19.4682i −0.535844 0.928108i
\(441\) −4.46478 + 5.39126i −0.212609 + 0.256727i
\(442\) −0.996476 + 16.8366i −0.0473975 + 0.800836i
\(443\) 9.05605 + 15.6855i 0.430266 + 0.745242i 0.996896 0.0787300i \(-0.0250865\pi\)
−0.566630 + 0.823972i \(0.691753\pi\)
\(444\) 3.89962 0.185068
\(445\) −24.5837 −1.16538
\(446\) 14.5150 0.687304
\(447\) 1.22934 0.0581456
\(448\) 1.12588 + 2.39424i 0.0531929 + 0.113117i
\(449\) −9.23084 + 15.9883i −0.435630 + 0.754534i −0.997347 0.0727961i \(-0.976808\pi\)
0.561717 + 0.827330i \(0.310141\pi\)
\(450\) −3.65372 6.32843i −0.172238 0.298325i
\(451\) −32.6350 56.5256i −1.53672 2.66168i
\(452\) −3.92536 −0.184634
\(453\) 8.17245 14.1551i 0.383975 0.665065i
\(454\) 20.2464 0.950209
\(455\) −26.2988 20.6966i −1.23291 0.970274i
\(456\) 5.23821 0.245302
\(457\) 8.90233 15.4193i 0.416433 0.721283i −0.579145 0.815225i \(-0.696613\pi\)
0.995578 + 0.0939414i \(0.0299466\pi\)
\(458\) 1.33786 0.0625140
\(459\) −2.33890 4.05110i −0.109171 0.189089i
\(460\) −3.80571 6.59168i −0.177442 0.307339i
\(461\) −2.51030 + 4.34797i −0.116916 + 0.202505i −0.918544 0.395318i \(-0.870634\pi\)
0.801628 + 0.597823i \(0.203968\pi\)
\(462\) 16.8937 + 1.42304i 0.785965 + 0.0662060i
\(463\) −25.0075 −1.16220 −0.581099 0.813833i \(-0.697377\pi\)
−0.581099 + 0.813833i \(0.697377\pi\)
\(464\) 2.46066 0.114233
\(465\) 31.2955 1.45130
\(466\) −13.9514 −0.646284
\(467\) 12.9128 + 22.3656i 0.597532 + 1.03496i 0.993184 + 0.116555i \(0.0371851\pi\)
−0.395653 + 0.918400i \(0.629482\pi\)
\(468\) 3.22356 1.61514i 0.149009 0.0746601i
\(469\) 8.20680 + 17.4522i 0.378955 + 0.805866i
\(470\) 8.56246 + 14.8306i 0.394957 + 0.684085i
\(471\) −7.98494 + 13.8303i −0.367926 + 0.637267i
\(472\) 5.89729 + 10.2144i 0.271445 + 0.470156i
\(473\) 7.64695 13.2449i 0.351607 0.609001i
\(474\) −1.78753 −0.0821039
\(475\) −19.1390 + 33.1497i −0.878156 + 1.52101i
\(476\) −12.3326 1.03884i −0.565265 0.0476153i
\(477\) −1.05395 + 1.82549i −0.0482569 + 0.0835834i
\(478\) −4.52748 + 7.84182i −0.207082 + 0.358677i
\(479\) 23.1137 1.05609 0.528047 0.849215i \(-0.322925\pi\)
0.528047 + 0.849215i \(0.322925\pi\)
\(480\) 1.75410 3.03819i 0.0800633 0.138674i
\(481\) −11.7399 7.73728i −0.535296 0.352790i
\(482\) 20.1102 0.915993
\(483\) 5.71999 + 0.481825i 0.260269 + 0.0219238i
\(484\) −15.0301 26.0329i −0.683186 1.18331i
\(485\) −34.5566 −1.56914
\(486\) −0.500000 + 0.866025i −0.0226805 + 0.0392837i
\(487\) 8.13701 + 14.0937i 0.368723 + 0.638647i 0.989366 0.145446i \(-0.0464617\pi\)
−0.620643 + 0.784093i \(0.713128\pi\)
\(488\) 9.35561 0.423509
\(489\) 7.78633 0.352110
\(490\) 15.6633 18.9136i 0.707598 0.854430i
\(491\) −19.0299 32.9608i −0.858809 1.48750i −0.873065 0.487603i \(-0.837871\pi\)
0.0142561 0.999898i \(-0.495462\pi\)
\(492\) 5.09300 8.82134i 0.229610 0.397697i
\(493\) −5.75525 + 9.96838i −0.259203 + 0.448953i
\(494\) −15.7698 10.3932i −0.709517 0.467611i
\(495\) −11.2399 19.4682i −0.505198 0.875029i
\(496\) 4.46035 + 7.72555i 0.200275 + 0.346887i
\(497\) 14.7291 + 1.24071i 0.660689 + 0.0556533i
\(498\) 1.29609 2.24489i 0.0580792 0.100596i
\(499\) 17.1178 + 29.6489i 0.766297 + 1.32727i 0.939558 + 0.342389i \(0.111236\pi\)
−0.173261 + 0.984876i \(0.555430\pi\)
\(500\) 4.04749 + 7.01045i 0.181009 + 0.313517i
\(501\) 3.32333 + 5.75618i 0.148476 + 0.257167i
\(502\) 4.09035 + 7.08469i 0.182561 + 0.316205i
\(503\) −1.12053 + 1.94081i −0.0499619 + 0.0865365i −0.889925 0.456107i \(-0.849243\pi\)
0.839963 + 0.542644i \(0.182577\pi\)
\(504\) 1.12588 + 2.39424i 0.0501507 + 0.106648i
\(505\) 24.2422 + 41.9887i 1.07876 + 1.86847i
\(506\) −6.95123 12.0399i −0.309020 0.535238i
\(507\) −12.9092 1.53344i −0.573320 0.0681025i
\(508\) 3.51196 6.08289i 0.155818 0.269884i
\(509\) 12.9164 22.3718i 0.572509 0.991614i −0.423799 0.905756i \(-0.639304\pi\)
0.996307 0.0858576i \(-0.0273630\pi\)
\(510\) 8.20533 + 14.2121i 0.363338 + 0.629320i
\(511\) 22.3133 + 1.87957i 0.987083 + 0.0831472i
\(512\) 1.00000 0.0441942
\(513\) 5.23821 0.231273
\(514\) −4.87696 8.44715i −0.215114 0.372588i
\(515\) 23.0369 39.9010i 1.01513 1.75825i
\(516\) 2.38675 0.105071
\(517\) 15.6396 + 27.0885i 0.687828 + 1.19135i
\(518\) 5.89051 8.47062i 0.258814 0.372178i
\(519\) −14.6067 −0.641165
\(520\) −11.3089 + 5.66624i −0.495927 + 0.248481i
\(521\) −12.1715 + 21.0817i −0.533245 + 0.923607i 0.466001 + 0.884784i \(0.345694\pi\)
−0.999246 + 0.0388230i \(0.987639\pi\)
\(522\) 2.46066 0.107700
\(523\) −4.44354 + 7.69644i −0.194303 + 0.336542i −0.946672 0.322200i \(-0.895578\pi\)
0.752369 + 0.658742i \(0.228911\pi\)
\(524\) −4.56251 + 7.90250i −0.199314 + 0.345222i
\(525\) −19.2655 1.62283i −0.840813 0.0708262i
\(526\) 1.47358 2.55232i 0.0642511 0.111286i
\(527\) −41.7293 −1.81776
\(528\) 3.20391 5.54934i 0.139432 0.241504i
\(529\) 9.14640 + 15.8420i 0.397669 + 0.688784i
\(530\) 3.69745 6.40417i 0.160607 0.278180i
\(531\) 5.89729 + 10.2144i 0.255920 + 0.443267i
\(532\) 7.91249 11.3782i 0.343050 0.493310i
\(533\) −32.8351 + 16.4519i −1.42225 + 0.712609i
\(534\) −3.50376 6.06869i −0.151622 0.262618i
\(535\) 34.2563 1.48103
\(536\) 7.28922 0.314846
\(537\) −14.1285 −0.609689
\(538\) −23.9353 −1.03192
\(539\) 28.6095 34.5462i 1.23230 1.48801i
\(540\) 1.75410 3.03819i 0.0754844 0.130743i
\(541\) 8.01702 + 13.8859i 0.344679 + 0.597001i 0.985295 0.170860i \(-0.0546545\pi\)
−0.640617 + 0.767861i \(0.721321\pi\)
\(542\) −9.68335 16.7721i −0.415936 0.720422i
\(543\) −13.6453 −0.585576
\(544\) −2.33890 + 4.05110i −0.100280 + 0.173689i
\(545\) 8.05385 0.344989
\(546\) 1.36093 9.44181i 0.0582426 0.404072i
\(547\) −10.3955 −0.444481 −0.222240 0.974992i \(-0.571337\pi\)
−0.222240 + 0.974992i \(0.571337\pi\)
\(548\) −7.53370 + 13.0488i −0.321824 + 0.557415i
\(549\) 9.35561 0.399288
\(550\) 23.4124 + 40.5515i 0.998308 + 1.72912i
\(551\) −6.44473 11.1626i −0.274555 0.475543i
\(552\) 1.08480 1.87894i 0.0461724 0.0799729i
\(553\) −2.70012 + 3.88280i −0.114821 + 0.165113i
\(554\) 2.43419 0.103419
\(555\) −13.6807 −0.580711
\(556\) −14.0504 −0.595869
\(557\) 32.3902 1.37242 0.686209 0.727404i \(-0.259274\pi\)
0.686209 + 0.727404i \(0.259274\pi\)
\(558\) 4.46035 + 7.72555i 0.188821 + 0.327048i
\(559\) −7.18540 4.73558i −0.303910 0.200294i
\(560\) −3.94981 8.39947i −0.166910 0.354942i
\(561\) 14.9873 + 25.9587i 0.632763 + 1.09598i
\(562\) 1.40165 2.42772i 0.0591248 0.102407i
\(563\) 1.21655 + 2.10712i 0.0512713 + 0.0888045i 0.890522 0.454940i \(-0.150339\pi\)
−0.839251 + 0.543745i \(0.817006\pi\)
\(564\) −2.44070 + 4.22742i −0.102772 + 0.178006i
\(565\) 13.7710 0.579348
\(566\) 8.47705 14.6827i 0.356317 0.617159i
\(567\) 1.12588 + 2.39424i 0.0472826 + 0.100549i
\(568\) 2.79339 4.83829i 0.117208 0.203010i
\(569\) 3.97033 6.87681i 0.166445 0.288291i −0.770723 0.637171i \(-0.780105\pi\)
0.937167 + 0.348880i \(0.113438\pi\)
\(570\) −18.3767 −0.769714
\(571\) 18.0463 31.2571i 0.755214 1.30807i −0.190054 0.981774i \(-0.560866\pi\)
0.945268 0.326295i \(-0.105800\pi\)
\(572\) −20.6560 + 10.3496i −0.863669 + 0.432737i
\(573\) −2.43145 −0.101575
\(574\) −11.4682 24.3878i −0.478675 1.01793i
\(575\) 7.92715 + 13.7302i 0.330585 + 0.572590i
\(576\) 1.00000 0.0416667
\(577\) −16.3980 + 28.4021i −0.682657 + 1.18240i 0.291510 + 0.956568i \(0.405842\pi\)
−0.974167 + 0.225829i \(0.927491\pi\)
\(578\) −2.44094 4.22782i −0.101530 0.175854i
\(579\) 3.51754 0.146184
\(580\) −8.63248 −0.358444
\(581\) −2.91848 6.20630i −0.121079 0.257481i
\(582\) −4.92513 8.53057i −0.204153 0.353604i
\(583\) 6.75350 11.6974i 0.279701 0.484457i
\(584\) 4.23175 7.32961i 0.175111 0.303301i
\(585\) −11.3089 + 5.66624i −0.467564 + 0.234270i
\(586\) 2.84568 + 4.92886i 0.117554 + 0.203609i
\(587\) 10.9482 + 18.9629i 0.451881 + 0.782681i 0.998503 0.0546984i \(-0.0174197\pi\)
−0.546622 + 0.837380i \(0.684086\pi\)
\(588\) 6.90136 + 1.17099i 0.284607 + 0.0482906i
\(589\) 23.3642 40.4680i 0.962707 1.66746i
\(590\) −20.6888 35.8341i −0.851746 1.47527i
\(591\) 1.15702 + 2.00402i 0.0475936 + 0.0824345i
\(592\) −1.94981 3.37717i −0.0801368 0.138801i
\(593\) 3.25002 + 5.62921i 0.133463 + 0.231164i 0.925009 0.379945i \(-0.124057\pi\)
−0.791547 + 0.611109i \(0.790724\pi\)
\(594\) 3.20391 5.54934i 0.131458 0.227692i
\(595\) 43.2653 + 3.64447i 1.77370 + 0.149409i
\(596\) −0.614668 1.06464i −0.0251778 0.0436092i
\(597\) −2.84733 4.93173i −0.116534 0.201842i
\(598\) −6.99386 + 3.50423i −0.286000 + 0.143299i
\(599\) 1.40105 2.42668i 0.0572452 0.0991516i −0.835983 0.548756i \(-0.815102\pi\)
0.893228 + 0.449604i \(0.148435\pi\)
\(600\) −3.65372 + 6.32843i −0.149163 + 0.258357i
\(601\) −11.8591 20.5405i −0.483741 0.837864i 0.516085 0.856538i \(-0.327389\pi\)
−0.999826 + 0.0186737i \(0.994056\pi\)
\(602\) 3.60527 5.18442i 0.146940 0.211301i
\(603\) 7.28922 0.296840
\(604\) −16.3449 −0.665065
\(605\) 52.7285 + 91.3284i 2.14372 + 3.71303i
\(606\) −6.91016 + 11.9687i −0.280706 + 0.486197i
\(607\) −11.8430 −0.480694 −0.240347 0.970687i \(-0.577261\pi\)
−0.240347 + 0.970687i \(0.577261\pi\)
\(608\) −2.61911 4.53642i −0.106219 0.183976i
\(609\) 3.71691 5.34495i 0.150617 0.216589i
\(610\) −32.8213 −1.32890
\(611\) 15.7355 7.88417i 0.636589 0.318959i
\(612\) −2.33890 + 4.05110i −0.0945446 + 0.163756i
\(613\) −16.1979 −0.654227 −0.327114 0.944985i \(-0.606076\pi\)
−0.327114 + 0.944985i \(0.606076\pi\)
\(614\) −1.74302 + 3.01899i −0.0703424 + 0.121837i
\(615\) −17.8673 + 30.9470i −0.720477 + 1.24790i
\(616\) −7.21444 15.3419i −0.290678 0.618142i
\(617\) −22.0973 + 38.2737i −0.889606 + 1.54084i −0.0492637 + 0.998786i \(0.515687\pi\)
−0.840342 + 0.542057i \(0.817646\pi\)
\(618\) 13.1332 0.528293
\(619\) −17.0272 + 29.4920i −0.684383 + 1.18539i 0.289248 + 0.957254i \(0.406595\pi\)
−0.973630 + 0.228131i \(0.926738\pi\)
\(620\) −15.6478 27.1027i −0.628430 1.08847i
\(621\) 1.08480 1.87894i 0.0435317 0.0753991i
\(622\) 12.0016 + 20.7873i 0.481219 + 0.833496i
\(623\) −18.4747 1.55622i −0.740174 0.0623488i
\(624\) −3.01053 1.98411i −0.120518 0.0794279i
\(625\) 4.06923 + 7.04812i 0.162769 + 0.281925i
\(626\) 17.5552 0.701646
\(627\) −33.5655 −1.34048
\(628\) 15.9699 0.637267
\(629\) 18.2417 0.727344
\(630\) −3.94981 8.39947i −0.157364 0.334643i
\(631\) −0.712707 + 1.23444i −0.0283724 + 0.0491424i −0.879863 0.475227i \(-0.842366\pi\)
0.851491 + 0.524370i \(0.175699\pi\)
\(632\) 0.893764 + 1.54804i 0.0355520 + 0.0615779i
\(633\) 0.291966 + 0.505700i 0.0116046 + 0.0200998i
\(634\) 2.84037 0.112805
\(635\) −12.3206 + 21.3400i −0.488929 + 0.846850i
\(636\) 2.10789 0.0835834
\(637\) −18.4534 17.2183i −0.731151 0.682216i
\(638\) −15.7675 −0.624240
\(639\) 2.79339 4.83829i 0.110505 0.191400i
\(640\) −3.50820 −0.138674
\(641\) 11.6001 + 20.0919i 0.458175 + 0.793582i 0.998865 0.0476400i \(-0.0151700\pi\)
−0.540690 + 0.841222i \(0.681837\pi\)
\(642\) 4.88232 + 8.45642i 0.192690 + 0.333748i
\(643\) 3.41821 5.92052i 0.134801 0.233482i −0.790720 0.612178i \(-0.790294\pi\)
0.925521 + 0.378695i \(0.123627\pi\)
\(644\) −2.44272 5.19457i −0.0962567 0.204695i
\(645\) −8.37320 −0.329695
\(646\) 24.5033 0.964071
\(647\) −42.5965 −1.67464 −0.837320 0.546713i \(-0.815879\pi\)
−0.837320 + 0.546713i \(0.815879\pi\)
\(648\) 1.00000 0.0392837
\(649\) −37.7888 65.4521i −1.48334 2.56922i
\(650\) 23.5560 11.8026i 0.923941 0.462935i
\(651\) 23.5186 + 1.98110i 0.921768 + 0.0776454i
\(652\) −3.89316 6.74316i −0.152468 0.264082i
\(653\) 19.7223 34.1601i 0.771794 1.33679i −0.164784 0.986330i \(-0.552693\pi\)
0.936579 0.350457i \(-0.113974\pi\)
\(654\) 1.14786 + 1.98816i 0.0448850 + 0.0777430i
\(655\) 16.0062 27.7235i 0.625413 1.08325i
\(656\) −10.1860 −0.397697
\(657\) 4.23175 7.32961i 0.165096 0.285955i
\(658\) 5.49588 + 11.6873i 0.214252 + 0.455617i
\(659\) 0.667872 1.15679i 0.0260166 0.0450621i −0.852724 0.522362i \(-0.825051\pi\)
0.878741 + 0.477300i \(0.158384\pi\)
\(660\) −11.2399 + 19.4682i −0.437514 + 0.757797i
\(661\) −12.8932 −0.501488 −0.250744 0.968053i \(-0.580675\pi\)
−0.250744 + 0.968053i \(0.580675\pi\)
\(662\) 9.43745 16.3461i 0.366797 0.635311i
\(663\) 15.0792 7.55533i 0.585626 0.293425i
\(664\) −2.59218 −0.100596
\(665\) −27.7586 + 39.9171i −1.07643 + 1.54792i
\(666\) −1.94981 3.37717i −0.0755537 0.130863i
\(667\) −5.33867 −0.206714
\(668\) 3.32333 5.75618i 0.128584 0.222713i
\(669\) −7.25749 12.5703i −0.280591 0.485998i
\(670\) −25.5720 −0.987934
\(671\) −59.9491 −2.31431
\(672\) 1.51053 2.17216i 0.0582701 0.0837930i
\(673\) −13.8759 24.0338i −0.534877 0.926434i −0.999169 0.0407519i \(-0.987025\pi\)
0.464292 0.885682i \(-0.346309\pi\)
\(674\) −5.47802 + 9.48821i −0.211005 + 0.365472i
\(675\) −3.65372 + 6.32843i −0.140632 + 0.243582i
\(676\) 5.12662 + 11.9465i 0.197178 + 0.459479i
\(677\) −1.50219 2.60188i −0.0577340 0.0999982i 0.835714 0.549165i \(-0.185054\pi\)
−0.893448 + 0.449167i \(0.851721\pi\)
\(678\) 1.96268 + 3.39947i 0.0753764 + 0.130556i
\(679\) −25.9694 2.18754i −0.996613 0.0839500i
\(680\) 8.20533 14.2121i 0.314660 0.545007i
\(681\) −10.1232 17.5339i −0.387921 0.671899i
\(682\) −28.5811 49.5039i −1.09443 1.89560i
\(683\) 7.43467 + 12.8772i 0.284480 + 0.492733i 0.972483 0.232974i \(-0.0748458\pi\)
−0.688003 + 0.725708i \(0.741513\pi\)
\(684\) −2.61911 4.53642i −0.100144 0.173455i
\(685\) 26.4297 45.7776i 1.00983 1.74907i
\(686\) 12.9683 13.2221i 0.495132 0.504821i
\(687\) −0.668929 1.15862i −0.0255212 0.0442041i
\(688\) −1.19338 2.06699i −0.0454971 0.0788033i
\(689\) −6.34588 4.18229i −0.241759 0.159333i
\(690\) −3.80571 + 6.59168i −0.144881 + 0.250941i
\(691\) −4.19053 + 7.25822i −0.159415 + 0.276116i −0.934658 0.355548i \(-0.884294\pi\)
0.775243 + 0.631664i \(0.217628\pi\)
\(692\) 7.30337 + 12.6498i 0.277633 + 0.480874i
\(693\) −7.21444 15.3419i −0.274054 0.582789i
\(694\) −32.1029 −1.21861
\(695\) 49.2915 1.86973
\(696\) −1.23033 2.13099i −0.0466356 0.0807752i
\(697\) 23.8241 41.2645i 0.902401 1.56300i
\(698\) 18.0875 0.684620
\(699\) 6.97568 + 12.0822i 0.263845 + 0.456992i
\(700\) 8.22731 + 17.4958i 0.310963 + 0.661279i
\(701\) 39.2809 1.48362 0.741809 0.670611i \(-0.233968\pi\)
0.741809 + 0.670611i \(0.233968\pi\)
\(702\) −3.01053 1.98411i −0.113625 0.0748854i
\(703\) −10.2135 + 17.6904i −0.385211 + 0.667204i
\(704\) −6.40782 −0.241504
\(705\) 8.56246 14.8306i 0.322481 0.558553i
\(706\) 13.7323 23.7850i 0.516820 0.895159i
\(707\) 15.5600 + 33.0892i 0.585195 + 1.24445i
\(708\) 5.89729 10.2144i 0.221634 0.383881i
\(709\) 19.3204 0.725592 0.362796 0.931869i \(-0.381822\pi\)
0.362796 + 0.931869i \(0.381822\pi\)
\(710\) −9.79976 + 16.9737i −0.367778 + 0.637011i
\(711\) 0.893764 + 1.54804i 0.0335188 + 0.0580562i
\(712\) −3.50376 + 6.06869i −0.131309 + 0.227434i
\(713\) −9.67721 16.7614i −0.362414 0.627720i
\(714\) 5.26665 + 11.1998i 0.197100 + 0.419142i
\(715\) 72.4652 36.3083i 2.71004 1.35785i
\(716\) 7.06425 + 12.2356i 0.264003 + 0.457267i
\(717\) 9.05495 0.338163
\(718\) 21.6781 0.809019
\(719\) −28.4410 −1.06067 −0.530335 0.847788i \(-0.677934\pi\)
−0.530335 + 0.847788i \(0.677934\pi\)
\(720\) −3.50820 −0.130743
\(721\) 19.8381 28.5274i 0.738809 1.06241i
\(722\) −4.21943 + 7.30827i −0.157031 + 0.271986i
\(723\) −10.0551 17.4159i −0.373953 0.647705i
\(724\) 6.82265 + 11.8172i 0.253562 + 0.439182i
\(725\) 17.9811 0.667803
\(726\) −15.0301 + 26.0329i −0.557819 + 0.966171i
\(727\) −48.4057 −1.79527 −0.897634 0.440741i \(-0.854716\pi\)
−0.897634 + 0.440741i \(0.854716\pi\)
\(728\) −8.85732 + 3.54230i −0.328274 + 0.131287i
\(729\) 1.00000 0.0370370
\(730\) −14.8458 + 25.7137i −0.549468 + 0.951707i
\(731\) 11.1648 0.412944
\(732\) −4.67781 8.10220i −0.172897 0.299466i
\(733\) −3.69118 6.39332i −0.136337 0.236143i 0.789770 0.613403i \(-0.210200\pi\)
−0.926107 + 0.377260i \(0.876866\pi\)
\(734\) −7.66086 + 13.2690i −0.282768 + 0.489768i
\(735\) −24.2113 4.10805i −0.893049 0.151528i
\(736\) −2.16961 −0.0799729
\(737\) −46.7080 −1.72051
\(738\) −10.1860 −0.374952
\(739\) 4.82426 0.177463 0.0887316 0.996056i \(-0.471719\pi\)
0.0887316 + 0.996056i \(0.471719\pi\)
\(740\) 6.84033 + 11.8478i 0.251455 + 0.435533i
\(741\) −1.11585 + 18.8536i −0.0409920 + 0.692606i
\(742\) 3.18404 4.57868i 0.116890 0.168089i
\(743\) 17.8556 + 30.9268i 0.655059 + 1.13460i 0.981879 + 0.189509i \(0.0606895\pi\)
−0.326820 + 0.945087i \(0.605977\pi\)
\(744\) 4.46035 7.72555i 0.163524 0.283232i
\(745\) 2.15637 + 3.73495i 0.0790035 + 0.136838i
\(746\) 16.6792 28.8893i 0.610670 1.05771i
\(747\) −2.59218 −0.0948429
\(748\) 14.9873 25.9587i 0.547989 0.949145i
\(749\) 25.7436 + 2.16852i 0.940651 + 0.0792361i
\(750\) 4.04749 7.01045i 0.147793 0.255986i
\(751\) −6.54845 + 11.3422i −0.238956 + 0.413885i −0.960415 0.278573i \(-0.910139\pi\)
0.721459 + 0.692457i \(0.243472\pi\)
\(752\) 4.88140 0.178006
\(753\) 4.09035 7.08469i 0.149061 0.258181i
\(754\) −0.524175 + 8.85654i −0.0190893 + 0.322536i
\(755\) 57.3411 2.08686
\(756\) 1.51053 2.17216i 0.0549376 0.0790008i
\(757\) −22.0344 38.1646i −0.800852 1.38712i −0.919056 0.394127i \(-0.871047\pi\)
0.118204 0.992989i \(-0.462286\pi\)
\(758\) −16.8774 −0.613013
\(759\) −6.95123 + 12.0399i −0.252314 + 0.437020i
\(760\) 9.18834 + 15.9147i 0.333296 + 0.577286i
\(761\) −8.61142 −0.312164 −0.156082 0.987744i \(-0.549886\pi\)
−0.156082 + 0.987744i \(0.549886\pi\)
\(762\) −7.02391 −0.254449
\(763\) 6.05248 + 0.509833i 0.219115 + 0.0184572i
\(764\) 1.21572 + 2.10569i 0.0439833 + 0.0761814i
\(765\) 8.20533 14.2121i 0.296664 0.513838i
\(766\) −10.7933 + 18.6945i −0.389978 + 0.675461i
\(767\) −38.0205 + 19.0499i −1.37284 + 0.687853i
\(768\) −0.500000 0.866025i −0.0180422 0.0312500i
\(769\) −3.20391 5.54934i −0.115536 0.200114i 0.802458 0.596709i \(-0.203525\pi\)
−0.917994 + 0.396595i \(0.870192\pi\)
\(770\) 25.3097 + 53.8223i 0.912098 + 1.93962i
\(771\) −4.87696 + 8.44715i −0.175640 + 0.304217i
\(772\) −1.75877 3.04628i −0.0632996 0.109638i
\(773\) −6.29082 10.8960i −0.226265 0.391902i 0.730433 0.682984i \(-0.239318\pi\)
−0.956698 + 0.291082i \(0.905985\pi\)
\(774\) −1.19338 2.06699i −0.0428951 0.0742964i
\(775\) 32.5937 + 56.4540i 1.17080 + 2.02789i
\(776\) −4.92513 + 8.53057i −0.176802 + 0.306230i
\(777\) −10.2810 0.866025i −0.368830 0.0310685i
\(778\) 8.68908 + 15.0499i 0.311519 + 0.539566i
\(779\) 26.6782 + 46.2080i 0.955846 + 1.65557i
\(780\) 10.5615 + 6.96065i 0.378164 + 0.249231i
\(781\) −17.8995 + 31.0029i −0.640496 + 1.10937i
\(782\) 5.07451 8.78930i 0.181464 0.314305i
\(783\) −1.23033 2.13099i −0.0439684 0.0761555i
\(784\) −2.43658 6.56225i −0.0870206 0.234366i
\(785\) −56.0255 −1.99963
\(786\) 9.12502 0.325479
\(787\) 9.60693 + 16.6397i 0.342450 + 0.593141i 0.984887 0.173198i \(-0.0554099\pi\)
−0.642437 + 0.766338i \(0.722077\pi\)
\(788\) 1.15702 2.00402i 0.0412172 0.0713904i
\(789\) −2.94716 −0.104922
\(790\) −3.13550 5.43084i −0.111556 0.193221i
\(791\) 10.3489 + 0.871742i 0.367964 + 0.0309956i
\(792\) −6.40782 −0.227692
\(793\) −1.99295 + 33.6732i −0.0707718 + 1.19577i
\(794\) −2.93718 + 5.08734i −0.104237 + 0.180543i
\(795\) −7.39490 −0.262270
\(796\) −2.84733 + 4.93173i −0.100921 + 0.174800i
\(797\) −8.43333 + 14.6070i −0.298724 + 0.517405i −0.975844 0.218467i \(-0.929894\pi\)
0.677120 + 0.735872i \(0.263228\pi\)
\(798\) −13.8101 1.16330i −0.488872 0.0411803i
\(799\) −11.4171 + 19.7750i −0.403909 + 0.699591i
\(800\) 7.30745 0.258357
\(801\) −3.50376 + 6.06869i −0.123799 + 0.214427i
\(802\) 6.98855 + 12.1045i 0.246774 + 0.427426i
\(803\) −27.1163 + 46.9668i −0.956914 + 1.65742i
\(804\) −3.64461 6.31265i −0.128536 0.222630i
\(805\) 8.56955 + 18.2236i 0.302037 + 0.642296i
\(806\) −28.7563 + 14.4082i −1.01290 + 0.507507i
\(807\) 11.9676 + 20.7285i 0.421280 + 0.729679i
\(808\) 13.8203 0.486197
\(809\) 8.76049 0.308002 0.154001 0.988071i \(-0.450784\pi\)
0.154001 + 0.988071i \(0.450784\pi\)
\(810\) −3.50820 −0.123265
\(811\) −32.7259 −1.14916 −0.574581 0.818448i \(-0.694835\pi\)
−0.574581 + 0.818448i \(0.694835\pi\)
\(812\) −6.48732 0.546462i −0.227660 0.0191770i
\(813\) −9.68335 + 16.7721i −0.339610 + 0.588222i
\(814\) 12.4940 + 21.6403i 0.437916 + 0.758493i
\(815\) 13.6580 + 23.6563i 0.478418 + 0.828645i
\(816\) 4.67781 0.163756
\(817\) −6.25116 + 10.8273i −0.218701 + 0.378800i
\(818\) −37.4897 −1.31080
\(819\) −8.85732 + 3.54230i −0.309500 + 0.123778i
\(820\) 35.7345 1.24790
\(821\) −7.34756 + 12.7263i −0.256432 + 0.444152i −0.965283 0.261205i \(-0.915880\pi\)
0.708852 + 0.705357i \(0.249213\pi\)
\(822\) 15.0674 0.525536
\(823\) −20.6994 35.8525i −0.721537 1.24974i −0.960384 0.278682i \(-0.910103\pi\)
0.238846 0.971057i \(-0.423231\pi\)
\(824\) −6.56658 11.3737i −0.228758 0.396220i
\(825\) 23.4124 40.5515i 0.815115 1.41182i
\(826\) −13.2793 28.2391i −0.462046 0.982563i
\(827\) 37.8157 1.31498 0.657491 0.753462i \(-0.271618\pi\)
0.657491 + 0.753462i \(0.271618\pi\)
\(828\) −2.16961 −0.0753991
\(829\) 34.4239 1.19559 0.597796 0.801648i \(-0.296043\pi\)
0.597796 + 0.801648i \(0.296043\pi\)
\(830\) 9.09387 0.315653
\(831\) −1.21710 2.10807i −0.0422206 0.0731282i
\(832\) −0.213022 + 3.59925i −0.00738521 + 0.124782i
\(833\) 32.2832 + 5.47764i 1.11855 + 0.189789i
\(834\) 7.02519 + 12.1680i 0.243262 + 0.421343i
\(835\) −11.6589 + 20.1938i −0.403473 + 0.698836i
\(836\) 16.7828 + 29.0686i 0.580444 + 1.00536i
\(837\) 4.46035 7.72555i 0.154172 0.267034i
\(838\) 33.9095 1.17138
\(839\) −0.709771 + 1.22936i −0.0245040 + 0.0424422i −0.878017 0.478629i \(-0.841134\pi\)
0.853513 + 0.521071i \(0.174467\pi\)
\(840\) −5.29925 + 7.62037i −0.182841 + 0.262928i
\(841\) 11.4726 19.8711i 0.395606 0.685210i
\(842\) 5.27517 9.13685i 0.181794 0.314877i
\(843\) −2.80329 −0.0965505
\(844\) 0.291966 0.505700i 0.0100499 0.0174069i
\(845\) −17.9852 41.9105i −0.618710 1.44177i
\(846\) 4.88140 0.167826
\(847\) 33.8442 + 71.9713i 1.16290 + 2.47296i
\(848\) −1.05395 1.82549i −0.0361927 0.0626875i
\(849\) −16.9541 −0.581864
\(850\) −17.0914 + 29.6032i −0.586230 + 1.01538i
\(851\) 4.23033 + 7.32715i 0.145014 + 0.251171i
\(852\) −5.58678 −0.191400
\(853\) 36.8892 1.26306 0.631531 0.775351i \(-0.282427\pi\)
0.631531 + 0.775351i \(0.282427\pi\)
\(854\) −24.6653 2.07769i −0.844028 0.0710970i
\(855\) 9.18834 + 15.9147i 0.314235 + 0.544270i
\(856\) 4.88232 8.45642i 0.166874 0.289034i
\(857\) 13.9245 24.1180i 0.475653 0.823855i −0.523958 0.851744i \(-0.675545\pi\)
0.999611 + 0.0278890i \(0.00887851\pi\)
\(858\) 19.2910 + 12.7138i 0.658583 + 0.434043i
\(859\) −25.2862 43.7970i −0.862754 1.49433i −0.869260 0.494355i \(-0.835404\pi\)
0.00650572 0.999979i \(-0.497929\pi\)
\(860\) 4.18660 + 7.25141i 0.142762 + 0.247271i
\(861\) −15.3863 + 22.1257i −0.524364 + 0.754040i
\(862\) 12.8043 22.1777i 0.436116 0.755375i
\(863\) 14.5501 + 25.2016i 0.495293 + 0.857872i 0.999985 0.00542701i \(-0.00172748\pi\)
−0.504693 + 0.863299i \(0.668394\pi\)
\(864\) −0.500000 0.866025i −0.0170103 0.0294628i
\(865\) −25.6217 44.3780i −0.871163 1.50890i
\(866\) 3.68968 + 6.39071i 0.125380 + 0.217165i
\(867\) −2.44094 + 4.22782i −0.0828985 + 0.143584i
\(868\) −10.0436 21.3583i −0.340903 0.724948i
\(869\) −5.72708 9.91959i −0.194278 0.336499i
\(870\) 4.31624 + 7.47595i 0.146334 + 0.253458i
\(871\) −1.55277 + 26.2358i −0.0526135 + 0.888965i
\(872\) 1.14786 1.98816i 0.0388715 0.0673275i
\(873\) −4.92513 + 8.53057i −0.166690 + 0.288716i
\(874\) 5.68244 + 9.84227i 0.192211 + 0.332920i
\(875\) −9.11398 19.3813i −0.308109 0.655208i
\(876\) −8.46350 −0.285955
\(877\) 1.11266 0.0375720 0.0187860 0.999824i \(-0.494020\pi\)
0.0187860 + 0.999824i \(0.494020\pi\)
\(878\) 11.5255 + 19.9628i 0.388967 + 0.673711i
\(879\) 2.84568 4.92886i 0.0959823 0.166246i
\(880\) 22.4799 0.757797
\(881\) −8.14254 14.1033i −0.274329 0.475152i 0.695636 0.718394i \(-0.255122\pi\)
−0.969966 + 0.243242i \(0.921789\pi\)
\(882\) −2.43658 6.56225i −0.0820438 0.220962i
\(883\) −37.0876 −1.24810 −0.624048 0.781386i \(-0.714513\pi\)
−0.624048 + 0.781386i \(0.714513\pi\)
\(884\) −14.0827 9.28128i −0.473652 0.312163i
\(885\) −20.6888 + 35.8341i −0.695448 + 1.20455i
\(886\) −18.1121 −0.608488
\(887\) 10.8028 18.7110i 0.362722 0.628252i −0.625686 0.780075i \(-0.715181\pi\)
0.988408 + 0.151823i \(0.0485143\pi\)
\(888\) −1.94981 + 3.37717i −0.0654314 + 0.113331i
\(889\) −10.6099 + 15.2571i −0.355843 + 0.511706i
\(890\) 12.2919 21.2902i 0.412025 0.713647i
\(891\) −6.40782 −0.214670
\(892\) −7.25749 + 12.5703i −0.242999 + 0.420886i
\(893\) −12.7849 22.1441i −0.427831 0.741024i
\(894\) −0.614668 + 1.06464i −0.0205576 + 0.0356067i
\(895\) −24.7828 42.9250i −0.828396 1.43482i
\(896\) −2.63641 0.222079i −0.0880764 0.00741914i
\(897\) 6.53168 + 4.30474i 0.218086 + 0.143731i
\(898\) −9.23084 15.9883i −0.308037 0.533536i
\(899\) −21.9508 −0.732100
\(900\) 7.30745 0.243582
\(901\) 9.86031 0.328495
\(902\) 65.2701 2.17326
\(903\) −6.29247 0.530048i −0.209400 0.0176389i
\(904\) 1.96268 3.39947i 0.0652778 0.113065i
\(905\) −23.9352 41.4570i −0.795633 1.37808i
\(906\) 8.17245 + 14.1551i 0.271512 + 0.470272i
\(907\) −29.0539 −0.964720 −0.482360 0.875973i \(-0.660220\pi\)
−0.482360 + 0.875973i \(0.660220\pi\)
\(908\) −10.1232 + 17.5339i −0.335950 + 0.581882i
\(909\) 13.8203 0.458391
\(910\) 31.0732 12.4271i 1.03007 0.411954i
\(911\) −22.2791 −0.738141 −0.369071 0.929401i \(-0.620324\pi\)
−0.369071 + 0.929401i \(0.620324\pi\)
\(912\) −2.61911 + 4.53642i −0.0867273 + 0.150216i
\(913\) 16.6102 0.549718
\(914\) 8.90233 + 15.4193i 0.294463 + 0.510024i
\(915\) 16.4107 + 28.4241i 0.542520 + 0.939672i
\(916\) −0.668929 + 1.15862i −0.0221020 + 0.0382819i
\(917\) 13.7836 19.8210i 0.455176 0.654548i
\(918\) 4.67781 0.154391
\(919\) −35.1435 −1.15928 −0.579639 0.814873i \(-0.696806\pi\)
−0.579639 + 0.814873i \(0.696806\pi\)
\(920\) 7.61142 0.250941
\(921\) 3.48603 0.114869
\(922\) −2.51030 4.34797i −0.0826723 0.143193i
\(923\) 16.8192 + 11.0848i 0.553610 + 0.364860i
\(924\) −9.67923 + 13.9188i −0.318423 + 0.457896i
\(925\) −14.2481 24.6785i −0.468476 0.811425i
\(926\) 12.5038 21.6571i 0.410899 0.711698i
\(927\) −6.56658 11.3737i −0.215675 0.373560i
\(928\) −1.23033 + 2.13099i −0.0403876 + 0.0699533i
\(929\) −36.7445 −1.20555 −0.602774 0.797912i \(-0.705938\pi\)
−0.602774 + 0.797912i \(0.705938\pi\)
\(930\) −15.6478 + 27.1027i −0.513111 + 0.888734i
\(931\) −23.3875 + 28.2406i −0.766494 + 0.925547i
\(932\) 6.97568 12.0822i 0.228496 0.395767i
\(933\) 12.0016 20.7873i 0.392914 0.680546i
\(934\) −25.8255 −0.845037
\(935\) −52.5783 + 91.0683i −1.71949 + 2.97825i
\(936\) −0.213022 + 3.59925i −0.00696285 + 0.117645i
\(937\) 18.5284 0.605295 0.302647 0.953103i \(-0.402130\pi\)
0.302647 + 0.953103i \(0.402130\pi\)
\(938\) −19.2174 1.61878i −0.627471 0.0528552i
\(939\) −8.77758 15.2032i −0.286446 0.496138i
\(940\) −17.1249 −0.558553
\(941\) 22.5985 39.1417i 0.736689 1.27598i −0.217290 0.976107i \(-0.569722\pi\)
0.953979 0.299875i \(-0.0969450\pi\)
\(942\) −7.98494 13.8303i −0.260163 0.450616i
\(943\) 22.0996 0.719664
\(944\) −11.7946 −0.383881
\(945\) −5.29925 + 7.62037i −0.172385 + 0.247891i
\(946\) 7.64695 + 13.2449i 0.248624 + 0.430629i
\(947\) −14.4333 + 24.9993i −0.469020 + 0.812367i −0.999373 0.0354104i \(-0.988726\pi\)
0.530353 + 0.847777i \(0.322059\pi\)
\(948\) 0.893764 1.54804i 0.0290281 0.0502781i
\(949\) 25.4797 + 16.7925i 0.827105 + 0.545108i
\(950\) −19.1390 33.1497i −0.620950 1.07552i
\(951\) −1.42018 2.45983i −0.0460526 0.0797655i
\(952\) 7.06598 10.1610i 0.229010 0.329318i
\(953\) 8.36687 14.4919i 0.271030 0.469437i −0.698096 0.716004i \(-0.745969\pi\)
0.969126 + 0.246567i \(0.0793025\pi\)
\(954\) −1.05395 1.82549i −0.0341228 0.0591024i
\(955\) −4.26500 7.38719i −0.138012 0.239044i
\(956\) −4.52748 7.84182i −0.146429 0.253623i
\(957\) 7.88374 + 13.6550i 0.254845 + 0.441405i
\(958\) −11.5569 + 20.0171i −0.373386 + 0.646723i
\(959\) 22.7598 32.7288i 0.734953 1.05687i
\(960\) 1.75410 + 3.03819i 0.0566133 + 0.0980571i
\(961\) −24.2894 42.0704i −0.783528 1.35711i
\(962\) 12.5707 6.29845i 0.405294 0.203070i
\(963\) 4.88232 8.45642i 0.157330 0.272504i
\(964\) −10.0551 + 17.4159i −0.323852 + 0.560929i
\(965\) 6.17012 + 10.6870i 0.198623 + 0.344025i
\(966\) −3.27727 + 4.71274i −0.105444 + 0.151630i
\(967\) −3.01759 −0.0970392 −0.0485196 0.998822i \(-0.515450\pi\)
−0.0485196 + 0.998822i \(0.515450\pi\)
\(968\) 30.0602 0.966171
\(969\) −12.2517 21.2205i −0.393580 0.681701i
\(970\) 17.2783 29.9269i 0.554774 0.960896i
\(971\) 25.6802 0.824116 0.412058 0.911158i \(-0.364810\pi\)
0.412058 + 0.911158i \(0.364810\pi\)
\(972\) −0.500000 0.866025i −0.0160375 0.0277778i
\(973\) 37.0426 + 3.12030i 1.18753 + 0.100032i
\(974\) −16.2740 −0.521453
\(975\) −21.9993 14.4988i −0.704542 0.464332i
\(976\) −4.67781 + 8.10220i −0.149733 + 0.259345i
\(977\) −40.6502 −1.30052 −0.650258 0.759713i \(-0.725339\pi\)
−0.650258 + 0.759713i \(0.725339\pi\)
\(978\) −3.89316 + 6.74316i −0.124490 + 0.215622i
\(979\) 22.4515 38.8871i 0.717552 1.24284i
\(980\) 8.54799 + 23.0217i 0.273056 + 0.735400i
\(981\) 1.14786 1.98816i 0.0366484 0.0634769i
\(982\) 38.0599 1.21454
\(983\) −2.39794 + 4.15335i −0.0764823 + 0.132471i −0.901730 0.432300i \(-0.857702\pi\)
0.825248 + 0.564771i \(0.191036\pi\)
\(984\) 5.09300 + 8.82134i 0.162359 + 0.281214i
\(985\) −4.05906 + 7.03051i −0.129333 + 0.224011i
\(986\) −5.75525 9.96838i −0.183284 0.317458i
\(987\) 7.37352 10.6032i 0.234702 0.337503i
\(988\) 16.8857 8.46047i 0.537205 0.269163i
\(989\) 2.58916 + 4.48456i 0.0823306 + 0.142601i
\(990\) 22.4799 0.714458
\(991\) −39.1431 −1.24342 −0.621710 0.783247i \(-0.713562\pi\)
−0.621710 + 0.783247i \(0.713562\pi\)
\(992\) −8.92069 −0.283232
\(993\) −18.8749 −0.598977
\(994\) −8.43901 + 12.1354i −0.267669 + 0.384911i
\(995\) 9.98901 17.3015i 0.316673 0.548494i
\(996\) 1.29609 + 2.24489i 0.0410682 + 0.0711321i
\(997\) 28.7246 + 49.7524i 0.909716 + 1.57567i 0.814459 + 0.580221i \(0.197034\pi\)
0.0952567 + 0.995453i \(0.469633\pi\)
\(998\) −34.2356 −1.08371
\(999\) −1.94981 + 3.37717i −0.0616893 + 0.106849i
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.k.c.445.4 yes 8
3.2 odd 2 1638.2.p.h.991.1 8
7.2 even 3 546.2.j.c.289.4 8
13.9 even 3 546.2.j.c.529.4 yes 8
21.2 odd 6 1638.2.m.h.289.1 8
39.35 odd 6 1638.2.m.h.1621.1 8
91.9 even 3 inner 546.2.k.c.373.4 yes 8
273.191 odd 6 1638.2.p.h.919.1 8
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
546.2.j.c.289.4 8 7.2 even 3
546.2.j.c.529.4 yes 8 13.9 even 3
546.2.k.c.373.4 yes 8 91.9 even 3 inner
546.2.k.c.445.4 yes 8 1.1 even 1 trivial
1638.2.m.h.289.1 8 21.2 odd 6
1638.2.m.h.1621.1 8 39.35 odd 6
1638.2.p.h.919.1 8 273.191 odd 6
1638.2.p.h.991.1 8 3.2 odd 2