Properties

Label 560.2.t.a.43.16
Level $560$
Weight $2$
Character 560.43
Analytic conductor $4.472$
Analytic rank $0$
Dimension $144$
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] = [560,2,Mod(43,560)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(560, base_ring=CyclotomicField(4))
 
chi = DirichletCharacter(H, H._module([2, 1, 3, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("560.43");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 560 = 2^{4} \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 560.t (of order \(4\), 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: \(4.47162251319\)
Analytic rank: \(0\)
Dimension: \(144\)
Relative dimension: \(72\) over \(\Q(i)\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 43.16
Character \(\chi\) \(=\) 560.43
Dual form 560.2.t.a.547.16

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.09978 - 0.889090i) q^{2} +2.37538i q^{3} +(0.419039 + 1.95561i) q^{4} +(-0.533053 - 2.17160i) q^{5} +(2.11192 - 2.61239i) q^{6} +(-0.707107 + 0.707107i) q^{7} +(1.27786 - 2.52331i) q^{8} -2.64241 q^{9} +O(q^{10})\) \(q+(-1.09978 - 0.889090i) q^{2} +2.37538i q^{3} +(0.419039 + 1.95561i) q^{4} +(-0.533053 - 2.17160i) q^{5} +(2.11192 - 2.61239i) q^{6} +(-0.707107 + 0.707107i) q^{7} +(1.27786 - 2.52331i) q^{8} -2.64241 q^{9} +(-1.34451 + 2.86222i) q^{10} +(0.687717 - 0.687717i) q^{11} +(-4.64531 + 0.995374i) q^{12} +6.05133 q^{13} +(1.40634 - 0.148981i) q^{14} +(5.15837 - 1.26620i) q^{15} +(-3.64881 + 1.63895i) q^{16} +(4.07805 - 4.07805i) q^{17} +(2.90608 + 2.34934i) q^{18} +(-2.38574 + 2.38574i) q^{19} +(4.02343 - 1.95243i) q^{20} +(-1.67964 - 1.67964i) q^{21} +(-1.36778 + 0.144896i) q^{22} +(2.83792 + 2.83792i) q^{23} +(5.99380 + 3.03540i) q^{24} +(-4.43171 + 2.31516i) q^{25} +(-6.65514 - 5.38018i) q^{26} +0.849404i q^{27} +(-1.67913 - 1.08652i) q^{28} +(-1.13639 - 1.13639i) q^{29} +(-6.79885 - 3.19371i) q^{30} +5.40683i q^{31} +(5.47007 + 1.44164i) q^{32} +(1.63359 + 1.63359i) q^{33} +(-8.11071 + 0.859210i) q^{34} +(1.91248 + 1.15863i) q^{35} +(-1.10727 - 5.16753i) q^{36} +6.98696 q^{37} +(4.74492 - 0.502655i) q^{38} +14.3742i q^{39} +(-6.16078 - 1.42995i) q^{40} +5.40855i q^{41} +(0.353887 + 3.34060i) q^{42} -0.891002 q^{43} +(1.63309 + 1.05673i) q^{44} +(1.40855 + 5.73827i) q^{45} +(-0.597925 - 5.64425i) q^{46} +(3.87464 + 3.87464i) q^{47} +(-3.89313 - 8.66731i) q^{48} -1.00000i q^{49} +(6.93229 + 1.39402i) q^{50} +(9.68690 + 9.68690i) q^{51} +(2.53574 + 11.8340i) q^{52} +7.55987i q^{53} +(0.755197 - 0.934159i) q^{54} +(-1.86004 - 1.12686i) q^{55} +(0.880662 + 2.68783i) q^{56} +(-5.66702 - 5.66702i) q^{57} +(0.239427 + 2.26013i) q^{58} +(-4.82059 - 4.82059i) q^{59} +(4.63775 + 9.55717i) q^{60} +(1.88117 - 1.88117i) q^{61} +(4.80716 - 5.94633i) q^{62} +(1.86847 - 1.86847i) q^{63} +(-4.73414 - 6.44887i) q^{64} +(-3.22568 - 13.1411i) q^{65} +(-0.344183 - 3.24900i) q^{66} -0.887380 q^{67} +(9.68392 + 6.26621i) q^{68} +(-6.74112 + 6.74112i) q^{69} +(-1.07318 - 2.97460i) q^{70} +14.3596 q^{71} +(-3.37664 + 6.66761i) q^{72} +(7.54908 - 7.54908i) q^{73} +(-7.68412 - 6.21203i) q^{74} +(-5.49937 - 10.5270i) q^{75} +(-5.66528 - 3.66585i) q^{76} +0.972579i q^{77} +(12.7799 - 15.8085i) q^{78} +5.68501 q^{79} +(5.50416 + 7.05012i) q^{80} -9.94489 q^{81} +(4.80869 - 5.94823i) q^{82} -13.1028i q^{83} +(2.58089 - 3.98856i) q^{84} +(-11.0297 - 6.68208i) q^{85} +(0.979908 + 0.792181i) q^{86} +(2.69935 - 2.69935i) q^{87} +(-0.856513 - 2.61413i) q^{88} +1.50123 q^{89} +(3.55274 - 7.56317i) q^{90} +(-4.27894 + 4.27894i) q^{91} +(-4.36066 + 6.73905i) q^{92} -12.8433 q^{93} +(-0.816355 - 7.70617i) q^{94} +(6.45260 + 3.90915i) q^{95} +(-3.42443 + 12.9935i) q^{96} +(-8.99779 + 8.99779i) q^{97} +(-0.889090 + 1.09978i) q^{98} +(-1.81723 + 1.81723i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 144 q + 8 q^{4} - 144 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 144 q + 8 q^{4} - 144 q^{9} - 16 q^{12} + 8 q^{16} - 28 q^{18} - 16 q^{19} + 4 q^{22} + 32 q^{26} - 36 q^{30} + 32 q^{34} - 32 q^{36} - 56 q^{38} + 8 q^{40} - 20 q^{42} + 64 q^{43} - 56 q^{44} - 32 q^{46} - 80 q^{48} - 48 q^{50} - 16 q^{51} - 16 q^{52} + 32 q^{54} - 24 q^{56} + 52 q^{58} + 72 q^{60} - 32 q^{61} - 40 q^{62} + 32 q^{64} + 32 q^{66} - 24 q^{68} - 32 q^{69} + 80 q^{72} - 16 q^{73} - 32 q^{74} - 88 q^{75} + 76 q^{78} + 128 q^{80} + 144 q^{81} + 56 q^{82} + 32 q^{86} - 112 q^{87} + 88 q^{88} + 88 q^{90} - 136 q^{92} - 8 q^{94} + 80 q^{95} + 32 q^{96} + 64 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/560\mathbb{Z}\right)^\times\).

\(n\) \(241\) \(337\) \(351\) \(421\)
\(\chi(n)\) \(1\) \(e\left(\frac{3}{4}\right)\) \(-1\) \(e\left(\frac{1}{4}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.09978 0.889090i −0.777663 0.628681i
\(3\) 2.37538i 1.37142i 0.727873 + 0.685712i \(0.240509\pi\)
−0.727873 + 0.685712i \(0.759491\pi\)
\(4\) 0.419039 + 1.95561i 0.209519 + 0.977805i
\(5\) −0.533053 2.17160i −0.238389 0.971170i
\(6\) 2.11192 2.61239i 0.862189 1.06651i
\(7\) −0.707107 + 0.707107i −0.267261 + 0.267261i
\(8\) 1.27786 2.52331i 0.451792 0.892123i
\(9\) −2.64241 −0.880804
\(10\) −1.34451 + 2.86222i −0.425170 + 0.905113i
\(11\) 0.687717 0.687717i 0.207355 0.207355i −0.595788 0.803142i \(-0.703160\pi\)
0.803142 + 0.595788i \(0.203160\pi\)
\(12\) −4.64531 + 0.995374i −1.34098 + 0.287340i
\(13\) 6.05133 1.67834 0.839169 0.543871i \(-0.183042\pi\)
0.839169 + 0.543871i \(0.183042\pi\)
\(14\) 1.40634 0.148981i 0.375861 0.0398170i
\(15\) 5.15837 1.26620i 1.33189 0.326932i
\(16\) −3.64881 + 1.63895i −0.912203 + 0.409738i
\(17\) 4.07805 4.07805i 0.989072 0.989072i −0.0108692 0.999941i \(-0.503460\pi\)
0.999941 + 0.0108692i \(0.00345984\pi\)
\(18\) 2.90608 + 2.34934i 0.684969 + 0.553745i
\(19\) −2.38574 + 2.38574i −0.547326 + 0.547326i −0.925666 0.378341i \(-0.876495\pi\)
0.378341 + 0.925666i \(0.376495\pi\)
\(20\) 4.02343 1.95243i 0.899667 0.436576i
\(21\) −1.67964 1.67964i −0.366529 0.366529i
\(22\) −1.36778 + 0.144896i −0.291612 + 0.0308920i
\(23\) 2.83792 + 2.83792i 0.591747 + 0.591747i 0.938103 0.346356i \(-0.112581\pi\)
−0.346356 + 0.938103i \(0.612581\pi\)
\(24\) 5.99380 + 3.03540i 1.22348 + 0.619599i
\(25\) −4.43171 + 2.31516i −0.886342 + 0.463032i
\(26\) −6.65514 5.38018i −1.30518 1.05514i
\(27\) 0.849404i 0.163468i
\(28\) −1.67913 1.08652i −0.317326 0.205333i
\(29\) −1.13639 1.13639i −0.211022 0.211022i 0.593680 0.804702i \(-0.297675\pi\)
−0.804702 + 0.593680i \(0.797675\pi\)
\(30\) −6.79885 3.19371i −1.24129 0.583089i
\(31\) 5.40683i 0.971095i 0.874210 + 0.485548i \(0.161380\pi\)
−0.874210 + 0.485548i \(0.838620\pi\)
\(32\) 5.47007 + 1.44164i 0.966981 + 0.254847i
\(33\) 1.63359 + 1.63359i 0.284371 + 0.284371i
\(34\) −8.11071 + 0.859210i −1.39098 + 0.147353i
\(35\) 1.91248 + 1.15863i 0.323268 + 0.195844i
\(36\) −1.10727 5.16753i −0.184545 0.861254i
\(37\) 6.98696 1.14865 0.574324 0.818628i \(-0.305265\pi\)
0.574324 + 0.818628i \(0.305265\pi\)
\(38\) 4.74492 0.502655i 0.769728 0.0815414i
\(39\) 14.3742i 2.30171i
\(40\) −6.16078 1.42995i −0.974105 0.226095i
\(41\) 5.40855i 0.844674i 0.906439 + 0.422337i \(0.138790\pi\)
−0.906439 + 0.422337i \(0.861210\pi\)
\(42\) 0.353887 + 3.34060i 0.0546060 + 0.515465i
\(43\) −0.891002 −0.135877 −0.0679383 0.997690i \(-0.521642\pi\)
−0.0679383 + 0.997690i \(0.521642\pi\)
\(44\) 1.63309 + 1.05673i 0.246197 + 0.159307i
\(45\) 1.40855 + 5.73827i 0.209974 + 0.855411i
\(46\) −0.597925 5.64425i −0.0881593 0.832200i
\(47\) 3.87464 + 3.87464i 0.565175 + 0.565175i 0.930773 0.365598i \(-0.119135\pi\)
−0.365598 + 0.930773i \(0.619135\pi\)
\(48\) −3.89313 8.66731i −0.561924 1.25102i
\(49\) 1.00000i 0.142857i
\(50\) 6.93229 + 1.39402i 0.980375 + 0.197144i
\(51\) 9.68690 + 9.68690i 1.35644 + 1.35644i
\(52\) 2.53574 + 11.8340i 0.351644 + 1.64109i
\(53\) 7.55987i 1.03843i 0.854644 + 0.519214i \(0.173775\pi\)
−0.854644 + 0.519214i \(0.826225\pi\)
\(54\) 0.755197 0.934159i 0.102769 0.127123i
\(55\) −1.86004 1.12686i −0.250807 0.151946i
\(56\) 0.880662 + 2.68783i 0.117683 + 0.359177i
\(57\) −5.66702 5.66702i −0.750616 0.750616i
\(58\) 0.239427 + 2.26013i 0.0314384 + 0.296770i
\(59\) −4.82059 4.82059i −0.627587 0.627587i 0.319873 0.947460i \(-0.396360\pi\)
−0.947460 + 0.319873i \(0.896360\pi\)
\(60\) 4.63775 + 9.55717i 0.598731 + 1.23383i
\(61\) 1.88117 1.88117i 0.240859 0.240859i −0.576347 0.817205i \(-0.695522\pi\)
0.817205 + 0.576347i \(0.195522\pi\)
\(62\) 4.80716 5.94633i 0.610510 0.755185i
\(63\) 1.86847 1.86847i 0.235405 0.235405i
\(64\) −4.73414 6.44887i −0.591768 0.806109i
\(65\) −3.22568 13.1411i −0.400097 1.62995i
\(66\) −0.344183 3.24900i −0.0423660 0.399924i
\(67\) −0.887380 −0.108411 −0.0542054 0.998530i \(-0.517263\pi\)
−0.0542054 + 0.998530i \(0.517263\pi\)
\(68\) 9.68392 + 6.26621i 1.17435 + 0.759889i
\(69\) −6.74112 + 6.74112i −0.811536 + 0.811536i
\(70\) −1.07318 2.97460i −0.128270 0.355533i
\(71\) 14.3596 1.70417 0.852086 0.523401i \(-0.175337\pi\)
0.852086 + 0.523401i \(0.175337\pi\)
\(72\) −3.37664 + 6.66761i −0.397941 + 0.785786i
\(73\) 7.54908 7.54908i 0.883553 0.883553i −0.110341 0.993894i \(-0.535194\pi\)
0.993894 + 0.110341i \(0.0351942\pi\)
\(74\) −7.68412 6.21203i −0.893261 0.722134i
\(75\) −5.49937 10.5270i −0.635013 1.21555i
\(76\) −5.66528 3.66585i −0.649853 0.420502i
\(77\) 0.972579i 0.110836i
\(78\) 12.7799 15.8085i 1.44704 1.78996i
\(79\) 5.68501 0.639614 0.319807 0.947483i \(-0.396382\pi\)
0.319807 + 0.947483i \(0.396382\pi\)
\(80\) 5.50416 + 7.05012i 0.615384 + 0.788228i
\(81\) −9.94489 −1.10499
\(82\) 4.80869 5.94823i 0.531031 0.656872i
\(83\) 13.1028i 1.43822i −0.694898 0.719108i \(-0.744551\pi\)
0.694898 0.719108i \(-0.255449\pi\)
\(84\) 2.58089 3.98856i 0.281598 0.435188i
\(85\) −11.0297 6.68208i −1.19634 0.724773i
\(86\) 0.979908 + 0.792181i 0.105666 + 0.0854231i
\(87\) 2.69935 2.69935i 0.289401 0.289401i
\(88\) −0.856513 2.61413i −0.0913046 0.278667i
\(89\) 1.50123 0.159130 0.0795648 0.996830i \(-0.474647\pi\)
0.0795648 + 0.996830i \(0.474647\pi\)
\(90\) 3.55274 7.56317i 0.374492 0.797228i
\(91\) −4.27894 + 4.27894i −0.448555 + 0.448555i
\(92\) −4.36066 + 6.73905i −0.454630 + 0.702595i
\(93\) −12.8433 −1.33178
\(94\) −0.816355 7.70617i −0.0842006 0.794831i
\(95\) 6.45260 + 3.90915i 0.662022 + 0.401070i
\(96\) −3.42443 + 12.9935i −0.349504 + 1.32614i
\(97\) −8.99779 + 8.99779i −0.913587 + 0.913587i −0.996552 0.0829655i \(-0.973561\pi\)
0.0829655 + 0.996552i \(0.473561\pi\)
\(98\) −0.889090 + 1.09978i −0.0898116 + 0.111095i
\(99\) −1.81723 + 1.81723i −0.182639 + 0.182639i
\(100\) −6.38460 7.69655i −0.638460 0.769655i
\(101\) −9.56999 9.56999i −0.952250 0.952250i 0.0466610 0.998911i \(-0.485142\pi\)
−0.998911 + 0.0466610i \(0.985142\pi\)
\(102\) −2.04095 19.2660i −0.202084 1.90762i
\(103\) −1.44935 1.44935i −0.142809 0.142809i 0.632088 0.774897i \(-0.282198\pi\)
−0.774897 + 0.632088i \(0.782198\pi\)
\(104\) 7.73276 15.2694i 0.758260 1.49728i
\(105\) −2.75218 + 4.54286i −0.268585 + 0.443338i
\(106\) 6.72141 8.31421i 0.652841 0.807547i
\(107\) 15.3451i 1.48346i −0.670696 0.741732i \(-0.734004\pi\)
0.670696 0.741732i \(-0.265996\pi\)
\(108\) −1.66110 + 0.355933i −0.159840 + 0.0342497i
\(109\) 10.2375 + 10.2375i 0.980579 + 0.980579i 0.999815 0.0192360i \(-0.00612338\pi\)
−0.0192360 + 0.999815i \(0.506123\pi\)
\(110\) 1.04376 + 2.89304i 0.0995183 + 0.275840i
\(111\) 16.5967i 1.57528i
\(112\) 1.42119 3.73901i 0.134290 0.353304i
\(113\) 13.0337 + 13.0337i 1.22611 + 1.22611i 0.965424 + 0.260683i \(0.0839477\pi\)
0.260683 + 0.965424i \(0.416052\pi\)
\(114\) 1.19399 + 11.2710i 0.111828 + 1.05562i
\(115\) 4.65007 7.67559i 0.433621 0.715752i
\(116\) 1.74614 2.69852i 0.162125 0.250551i
\(117\) −15.9901 −1.47829
\(118\) 1.01566 + 9.58753i 0.0934988 + 0.882603i
\(119\) 5.76723i 0.528681i
\(120\) 3.39667 14.6342i 0.310072 1.33591i
\(121\) 10.0541i 0.914008i
\(122\) −3.74140 + 0.396346i −0.338730 + 0.0358835i
\(123\) −12.8474 −1.15841
\(124\) −10.5736 + 2.26567i −0.949541 + 0.203463i
\(125\) 7.38994 + 8.38980i 0.660976 + 0.750407i
\(126\) −3.71614 + 0.393671i −0.331060 + 0.0350710i
\(127\) 1.33831 + 1.33831i 0.118756 + 0.118756i 0.763987 0.645231i \(-0.223239\pi\)
−0.645231 + 0.763987i \(0.723239\pi\)
\(128\) −0.527104 + 11.3014i −0.0465898 + 0.998914i
\(129\) 2.11647i 0.186344i
\(130\) −8.13606 + 17.3202i −0.713580 + 1.51909i
\(131\) −3.85010 3.85010i −0.336385 0.336385i 0.518620 0.855005i \(-0.326446\pi\)
−0.855005 + 0.518620i \(0.826446\pi\)
\(132\) −2.51012 + 3.87919i −0.218478 + 0.337641i
\(133\) 3.37394i 0.292558i
\(134\) 0.975924 + 0.788961i 0.0843070 + 0.0681558i
\(135\) 1.84457 0.452778i 0.158755 0.0389689i
\(136\) −5.07898 15.5013i −0.435519 1.32923i
\(137\) −4.79678 4.79678i −0.409816 0.409816i 0.471858 0.881674i \(-0.343583\pi\)
−0.881674 + 0.471858i \(0.843583\pi\)
\(138\) 13.4072 1.42030i 1.14130 0.120904i
\(139\) −14.1926 14.1926i −1.20380 1.20380i −0.973001 0.230802i \(-0.925865\pi\)
−0.230802 0.973001i \(-0.574135\pi\)
\(140\) −1.46442 + 4.22557i −0.123766 + 0.357126i
\(141\) −9.20374 + 9.20374i −0.775095 + 0.775095i
\(142\) −15.7924 12.7670i −1.32527 1.07138i
\(143\) 4.16161 4.16161i 0.348011 0.348011i
\(144\) 9.64167 4.33078i 0.803473 0.360899i
\(145\) −1.86203 + 3.07354i −0.154633 + 0.255243i
\(146\) −15.0141 + 1.59053i −1.24258 + 0.131633i
\(147\) 2.37538 0.195918
\(148\) 2.92780 + 13.6638i 0.240664 + 1.12315i
\(149\) 1.48023 1.48023i 0.121266 0.121266i −0.643870 0.765135i \(-0.722672\pi\)
0.765135 + 0.643870i \(0.222672\pi\)
\(150\) −3.31132 + 16.4668i −0.270368 + 1.34451i
\(151\) −3.51235 −0.285831 −0.142915 0.989735i \(-0.545648\pi\)
−0.142915 + 0.989735i \(0.545648\pi\)
\(152\) 2.97130 + 9.06858i 0.241004 + 0.735559i
\(153\) −10.7759 + 10.7759i −0.871179 + 0.871179i
\(154\) 0.864710 1.06962i 0.0696803 0.0861928i
\(155\) 11.7415 2.88213i 0.943099 0.231498i
\(156\) −28.1103 + 6.02334i −2.25063 + 0.482253i
\(157\) 13.1146i 1.04666i −0.852131 0.523329i \(-0.824690\pi\)
0.852131 0.523329i \(-0.175310\pi\)
\(158\) −6.25227 5.05448i −0.497404 0.402113i
\(159\) −17.9575 −1.42413
\(160\) 0.214818 12.6473i 0.0169829 0.999856i
\(161\) −4.01342 −0.316302
\(162\) 10.9372 + 8.84190i 0.859308 + 0.694686i
\(163\) 12.5244i 0.980987i 0.871445 + 0.490493i \(0.163183\pi\)
−0.871445 + 0.490493i \(0.836817\pi\)
\(164\) −10.5770 + 2.26639i −0.825926 + 0.176976i
\(165\) 2.67671 4.41829i 0.208382 0.343963i
\(166\) −11.6495 + 14.4102i −0.904180 + 1.11845i
\(167\) 7.52389 7.52389i 0.582216 0.582216i −0.353296 0.935512i \(-0.614939\pi\)
0.935512 + 0.353296i \(0.114939\pi\)
\(168\) −6.38461 + 2.09190i −0.492583 + 0.161394i
\(169\) 23.6186 1.81682
\(170\) 6.18930 + 17.1552i 0.474698 + 1.31575i
\(171\) 6.30410 6.30410i 0.482087 0.482087i
\(172\) −0.373364 1.74245i −0.0284687 0.132861i
\(173\) −23.7672 −1.80699 −0.903494 0.428601i \(-0.859007\pi\)
−0.903494 + 0.428601i \(0.859007\pi\)
\(174\) −5.36866 + 0.568730i −0.406997 + 0.0431153i
\(175\) 1.49663 4.77076i 0.113134 0.360635i
\(176\) −1.38222 + 3.63649i −0.104189 + 0.274111i
\(177\) 11.4507 11.4507i 0.860688 0.860688i
\(178\) −1.65102 1.33472i −0.123749 0.100042i
\(179\) −15.0765 + 15.0765i −1.12687 + 1.12687i −0.136189 + 0.990683i \(0.543485\pi\)
−0.990683 + 0.136189i \(0.956515\pi\)
\(180\) −10.6316 + 5.15912i −0.792431 + 0.384538i
\(181\) −17.3931 17.3931i −1.29282 1.29282i −0.933035 0.359785i \(-0.882850\pi\)
−0.359785 0.933035i \(-0.617150\pi\)
\(182\) 8.51026 0.901536i 0.630822 0.0668263i
\(183\) 4.46848 + 4.46848i 0.330319 + 0.330319i
\(184\) 10.7874 3.53447i 0.795258 0.260564i
\(185\) −3.72442 15.1729i −0.273825 1.11553i
\(186\) 14.1248 + 11.4188i 1.03568 + 0.837268i
\(187\) 5.60909i 0.410177i
\(188\) −5.95366 + 9.20091i −0.434216 + 0.671046i
\(189\) −0.600619 0.600619i −0.0436886 0.0436886i
\(190\) −3.62086 10.0361i −0.262685 0.728098i
\(191\) 11.9441i 0.864247i 0.901814 + 0.432124i \(0.142236\pi\)
−0.901814 + 0.432124i \(0.857764\pi\)
\(192\) 15.3185 11.2454i 1.10552 0.811564i
\(193\) −2.94923 2.94923i −0.212290 0.212290i 0.592949 0.805240i \(-0.297963\pi\)
−0.805240 + 0.592949i \(0.797963\pi\)
\(194\) 17.8954 1.89576i 1.28482 0.136108i
\(195\) 31.2150 7.66221i 2.23535 0.548702i
\(196\) 1.95561 0.419039i 0.139686 0.0299313i
\(197\) −3.06506 −0.218377 −0.109188 0.994021i \(-0.534825\pi\)
−0.109188 + 0.994021i \(0.534825\pi\)
\(198\) 3.61424 0.382876i 0.256853 0.0272098i
\(199\) 23.5139i 1.66686i −0.552625 0.833430i \(-0.686374\pi\)
0.552625 0.833430i \(-0.313626\pi\)
\(200\) 0.178742 + 14.1410i 0.0126390 + 0.999920i
\(201\) 2.10786i 0.148677i
\(202\) 2.01632 + 19.0335i 0.141868 + 1.33919i
\(203\) 1.60710 0.112796
\(204\) −14.8846 + 23.0030i −1.04213 + 1.61053i
\(205\) 11.7452 2.88305i 0.820322 0.201361i
\(206\) 0.305366 + 2.88257i 0.0212759 + 0.200838i
\(207\) −7.49895 7.49895i −0.521213 0.521213i
\(208\) −22.0802 + 9.91784i −1.53099 + 0.687678i
\(209\) 3.28143i 0.226981i
\(210\) 7.06581 2.54922i 0.487587 0.175913i
\(211\) −3.49115 3.49115i −0.240341 0.240341i 0.576650 0.816991i \(-0.304359\pi\)
−0.816991 + 0.576650i \(0.804359\pi\)
\(212\) −14.7842 + 3.16788i −1.01538 + 0.217571i
\(213\) 34.1095i 2.33714i
\(214\) −13.6432 + 16.8762i −0.932627 + 1.15364i
\(215\) 0.474951 + 1.93490i 0.0323914 + 0.131959i
\(216\) 2.14331 + 1.08542i 0.145834 + 0.0738535i
\(217\) −3.82321 3.82321i −0.259536 0.259536i
\(218\) −2.15696 20.3612i −0.146088 1.37903i
\(219\) 17.9319 + 17.9319i 1.21173 + 1.21173i
\(220\) 1.42427 4.10970i 0.0960240 0.277076i
\(221\) 24.6776 24.6776i 1.66000 1.66000i
\(222\) 14.7559 18.2527i 0.990352 1.22504i
\(223\) −0.585016 + 0.585016i −0.0391756 + 0.0391756i −0.726423 0.687248i \(-0.758819\pi\)
0.687248 + 0.726423i \(0.258819\pi\)
\(224\) −4.88731 + 2.84854i −0.326547 + 0.190326i
\(225\) 11.7104 6.11760i 0.780694 0.407840i
\(226\) −2.74609 25.9224i −0.182667 1.72433i
\(227\) 12.7085 0.843492 0.421746 0.906714i \(-0.361417\pi\)
0.421746 + 0.906714i \(0.361417\pi\)
\(228\) 8.70778 13.4572i 0.576687 0.891224i
\(229\) 11.0321 11.0321i 0.729019 0.729019i −0.241406 0.970424i \(-0.577608\pi\)
0.970424 + 0.241406i \(0.0776084\pi\)
\(230\) −11.9383 + 4.30714i −0.787191 + 0.284005i
\(231\) −2.31024 −0.152003
\(232\) −4.31960 + 1.41531i −0.283596 + 0.0929195i
\(233\) 0.175592 0.175592i 0.0115034 0.0115034i −0.701332 0.712835i \(-0.747411\pi\)
0.712835 + 0.701332i \(0.247411\pi\)
\(234\) 17.5856 + 14.2167i 1.14961 + 0.929372i
\(235\) 6.34879 10.4796i 0.414150 0.683612i
\(236\) 7.40717 11.4472i 0.482166 0.745149i
\(237\) 13.5040i 0.877181i
\(238\) 5.12759 6.34269i 0.332372 0.411136i
\(239\) 19.0313 1.23103 0.615517 0.788123i \(-0.288947\pi\)
0.615517 + 0.788123i \(0.288947\pi\)
\(240\) −16.7467 + 13.0745i −1.08099 + 0.843952i
\(241\) −21.7789 −1.40290 −0.701451 0.712718i \(-0.747464\pi\)
−0.701451 + 0.712718i \(0.747464\pi\)
\(242\) 8.93899 11.0573i 0.574620 0.710790i
\(243\) 21.0747i 1.35194i
\(244\) 4.46711 + 2.89055i 0.285977 + 0.185048i
\(245\) −2.17160 + 0.533053i −0.138739 + 0.0340555i
\(246\) 14.1293 + 11.4224i 0.900850 + 0.728269i
\(247\) −14.4369 + 14.4369i −0.918597 + 0.918597i
\(248\) 13.6431 + 6.90918i 0.866337 + 0.438733i
\(249\) 31.1240 1.97240
\(250\) −0.668027 15.7973i −0.0422497 0.999107i
\(251\) −4.74684 + 4.74684i −0.299618 + 0.299618i −0.840864 0.541246i \(-0.817953\pi\)
0.541246 + 0.840864i \(0.317953\pi\)
\(252\) 4.43695 + 2.87103i 0.279502 + 0.180858i
\(253\) 3.90337 0.245403
\(254\) −0.281971 2.66173i −0.0176925 0.167012i
\(255\) 15.8725 26.1997i 0.993971 1.64069i
\(256\) 10.6277 11.9605i 0.664230 0.747528i
\(257\) 7.93030 7.93030i 0.494678 0.494678i −0.415098 0.909777i \(-0.636253\pi\)
0.909777 + 0.415098i \(0.136253\pi\)
\(258\) −1.88173 + 2.32765i −0.117151 + 0.144913i
\(259\) −4.94052 + 4.94052i −0.306989 + 0.306989i
\(260\) 24.3471 11.8148i 1.50995 0.732722i
\(261\) 3.00281 + 3.00281i 0.185869 + 0.185869i
\(262\) 0.811184 + 7.65736i 0.0501151 + 0.473073i
\(263\) −11.8724 11.8724i −0.732085 0.732085i 0.238948 0.971032i \(-0.423198\pi\)
−0.971032 + 0.238948i \(0.923198\pi\)
\(264\) 6.20954 2.03454i 0.382171 0.125217i
\(265\) 16.4170 4.02981i 1.00849 0.247549i
\(266\) −2.99974 + 3.71060i −0.183926 + 0.227511i
\(267\) 3.56598i 0.218234i
\(268\) −0.371846 1.73537i −0.0227141 0.106005i
\(269\) −3.89222 3.89222i −0.237313 0.237313i 0.578423 0.815737i \(-0.303668\pi\)
−0.815737 + 0.578423i \(0.803668\pi\)
\(270\) −2.43118 1.14203i −0.147957 0.0695017i
\(271\) 31.7298i 1.92745i 0.266902 + 0.963724i \(0.414000\pi\)
−0.266902 + 0.963724i \(0.586000\pi\)
\(272\) −8.19631 + 21.5638i −0.496975 + 1.30749i
\(273\) −10.1641 10.1641i −0.615159 0.615159i
\(274\) 1.01064 + 9.54017i 0.0610550 + 0.576343i
\(275\) −1.45559 + 4.63994i −0.0877753 + 0.279799i
\(276\) −16.0078 10.3582i −0.963556 0.623491i
\(277\) −9.51177 −0.571507 −0.285753 0.958303i \(-0.592244\pi\)
−0.285753 + 0.958303i \(0.592244\pi\)
\(278\) 2.99027 + 28.2273i 0.179344 + 1.69296i
\(279\) 14.2871i 0.855345i
\(280\) 5.36746 3.34520i 0.320767 0.199914i
\(281\) 5.40996i 0.322731i 0.986895 + 0.161365i \(0.0515898\pi\)
−0.986895 + 0.161365i \(0.948410\pi\)
\(282\) 18.3050 1.93915i 1.09005 0.115475i
\(283\) 23.1613 1.37680 0.688399 0.725332i \(-0.258314\pi\)
0.688399 + 0.725332i \(0.258314\pi\)
\(284\) 6.01723 + 28.0818i 0.357057 + 1.66635i
\(285\) −9.28569 + 15.3273i −0.550037 + 0.907913i
\(286\) −8.27690 + 0.876816i −0.489423 + 0.0518472i
\(287\) −3.82443 3.82443i −0.225749 0.225749i
\(288\) −14.4542 3.80940i −0.851721 0.224471i
\(289\) 16.2609i 0.956526i
\(290\) 4.78047 1.72471i 0.280719 0.101278i
\(291\) −21.3731 21.3731i −1.25292 1.25292i
\(292\) 17.9264 + 11.5997i 1.04906 + 0.678821i
\(293\) 21.0839i 1.23173i 0.787850 + 0.615867i \(0.211194\pi\)
−0.787850 + 0.615867i \(0.788806\pi\)
\(294\) −2.61239 2.11192i −0.152358 0.123170i
\(295\) −7.89877 + 13.0380i −0.459884 + 0.759103i
\(296\) 8.92836 17.6302i 0.518950 1.02474i
\(297\) 0.584150 + 0.584150i 0.0338958 + 0.0338958i
\(298\) −2.94400 + 0.311873i −0.170541 + 0.0180663i
\(299\) 17.1732 + 17.1732i 0.993151 + 0.993151i
\(300\) 18.2822 15.1658i 1.05552 0.875600i
\(301\) 0.630034 0.630034i 0.0363145 0.0363145i
\(302\) 3.86282 + 3.12279i 0.222280 + 0.179697i
\(303\) 22.7323 22.7323i 1.30594 1.30594i
\(304\) 4.79500 12.6152i 0.275012 0.723532i
\(305\) −5.08791 3.08238i −0.291333 0.176497i
\(306\) 21.4318 2.27039i 1.22518 0.129789i
\(307\) −13.8446 −0.790151 −0.395075 0.918649i \(-0.629282\pi\)
−0.395075 + 0.918649i \(0.629282\pi\)
\(308\) −1.90198 + 0.407548i −0.108376 + 0.0232222i
\(309\) 3.44275 3.44275i 0.195851 0.195851i
\(310\) −15.4755 7.26952i −0.878951 0.412881i
\(311\) −25.9420 −1.47103 −0.735517 0.677506i \(-0.763061\pi\)
−0.735517 + 0.677506i \(0.763061\pi\)
\(312\) 36.2705 + 18.3682i 2.05341 + 1.03990i
\(313\) 15.5163 15.5163i 0.877035 0.877035i −0.116192 0.993227i \(-0.537069\pi\)
0.993227 + 0.116192i \(0.0370688\pi\)
\(314\) −11.6601 + 14.4232i −0.658015 + 0.813947i
\(315\) −5.05356 3.06158i −0.284736 0.172500i
\(316\) 2.38224 + 11.1177i 0.134011 + 0.625417i
\(317\) 14.2709i 0.801534i −0.916180 0.400767i \(-0.868744\pi\)
0.916180 0.400767i \(-0.131256\pi\)
\(318\) 19.7494 + 15.9659i 1.10749 + 0.895321i
\(319\) −1.56303 −0.0875127
\(320\) −11.4808 + 13.7183i −0.641798 + 0.766874i
\(321\) 36.4503 2.03446
\(322\) 4.41389 + 3.56829i 0.245976 + 0.198853i
\(323\) 19.4583i 1.08269i
\(324\) −4.16729 19.4483i −0.231516 1.08046i
\(325\) −26.8177 + 14.0098i −1.48758 + 0.777124i
\(326\) 11.1353 13.7741i 0.616728 0.762877i
\(327\) −24.3180 + 24.3180i −1.34479 + 1.34479i
\(328\) 13.6474 + 6.91138i 0.753553 + 0.381617i
\(329\) −5.47957 −0.302099
\(330\) −6.87206 + 2.47932i −0.378294 + 0.136482i
\(331\) −11.6211 + 11.6211i −0.638751 + 0.638751i −0.950247 0.311496i \(-0.899170\pi\)
0.311496 + 0.950247i \(0.399170\pi\)
\(332\) 25.6239 5.49057i 1.40629 0.301334i
\(333\) −18.4624 −1.01173
\(334\) −14.9641 + 1.58522i −0.818797 + 0.0867394i
\(335\) 0.473021 + 1.92704i 0.0258439 + 0.105285i
\(336\) 8.88157 + 3.37585i 0.484529 + 0.184168i
\(337\) −7.26088 + 7.26088i −0.395525 + 0.395525i −0.876651 0.481126i \(-0.840228\pi\)
0.481126 + 0.876651i \(0.340228\pi\)
\(338\) −25.9753 20.9991i −1.41287 1.14220i
\(339\) −30.9599 + 30.9599i −1.68151 + 1.68151i
\(340\) 8.44566 24.3698i 0.458030 1.32164i
\(341\) 3.71837 + 3.71837i 0.201361 + 0.201361i
\(342\) −12.5380 + 1.32822i −0.677980 + 0.0718220i
\(343\) 0.707107 + 0.707107i 0.0381802 + 0.0381802i
\(344\) −1.13858 + 2.24827i −0.0613880 + 0.121219i
\(345\) 18.2324 + 11.0457i 0.981600 + 0.594678i
\(346\) 26.1387 + 21.1312i 1.40523 + 1.13602i
\(347\) 6.84211i 0.367304i −0.982991 0.183652i \(-0.941208\pi\)
0.982991 0.183652i \(-0.0587919\pi\)
\(348\) 6.41000 + 4.14774i 0.343612 + 0.222342i
\(349\) 6.65746 + 6.65746i 0.356366 + 0.356366i 0.862472 0.506106i \(-0.168915\pi\)
−0.506106 + 0.862472i \(0.668915\pi\)
\(350\) −5.88759 + 3.91615i −0.314705 + 0.209327i
\(351\) 5.14003i 0.274354i
\(352\) 4.75330 2.77043i 0.253352 0.147664i
\(353\) −7.85475 7.85475i −0.418066 0.418066i 0.466471 0.884537i \(-0.345525\pi\)
−0.884537 + 0.466471i \(0.845525\pi\)
\(354\) −22.7740 + 2.41257i −1.21042 + 0.128227i
\(355\) −7.65444 31.1834i −0.406255 1.65504i
\(356\) 0.629071 + 2.93581i 0.0333407 + 0.155598i
\(357\) −13.6993 −0.725046
\(358\) 29.9853 3.17650i 1.58477 0.167883i
\(359\) 13.1496i 0.694008i −0.937864 0.347004i \(-0.887199\pi\)
0.937864 0.347004i \(-0.112801\pi\)
\(360\) 16.2793 + 3.77852i 0.857996 + 0.199145i
\(361\) 7.61652i 0.400869i
\(362\) 3.66458 + 34.5927i 0.192606 + 1.81815i
\(363\) −23.8822 −1.25349
\(364\) −10.1610 6.57489i −0.532580 0.344618i
\(365\) −20.4177 12.3695i −1.06871 0.647451i
\(366\) −0.941471 8.88723i −0.0492115 0.464543i
\(367\) 2.92500 + 2.92500i 0.152684 + 0.152684i 0.779316 0.626632i \(-0.215567\pi\)
−0.626632 + 0.779316i \(0.715567\pi\)
\(368\) −15.0062 5.70382i −0.782254 0.297332i
\(369\) 14.2916i 0.743993i
\(370\) −9.39401 + 19.9982i −0.488371 + 1.03966i
\(371\) −5.34564 5.34564i −0.277532 0.277532i
\(372\) −5.38182 25.1164i −0.279034 1.30222i
\(373\) 18.9965i 0.983600i 0.870708 + 0.491800i \(0.163661\pi\)
−0.870708 + 0.491800i \(0.836339\pi\)
\(374\) −4.98698 + 6.16877i −0.257871 + 0.318980i
\(375\) −19.9289 + 17.5539i −1.02913 + 0.906479i
\(376\) 14.7282 4.82565i 0.759547 0.248864i
\(377\) −6.87666 6.87666i −0.354166 0.354166i
\(378\) 0.126545 + 1.19455i 0.00650880 + 0.0614413i
\(379\) −0.317238 0.317238i −0.0162954 0.0162954i 0.698912 0.715208i \(-0.253668\pi\)
−0.715208 + 0.698912i \(0.753668\pi\)
\(380\) −4.94088 + 14.2568i −0.253462 + 0.731360i
\(381\) −3.17900 + 3.17900i −0.162865 + 0.162865i
\(382\) 10.6194 13.1359i 0.543336 0.672093i
\(383\) −9.84614 + 9.84614i −0.503114 + 0.503114i −0.912404 0.409290i \(-0.865776\pi\)
0.409290 + 0.912404i \(0.365776\pi\)
\(384\) −26.8451 1.25207i −1.36993 0.0638944i
\(385\) 2.11205 0.518436i 0.107640 0.0264220i
\(386\) 0.621378 + 5.86564i 0.0316273 + 0.298553i
\(387\) 2.35440 0.119681
\(388\) −21.3666 13.8257i −1.08472 0.701895i
\(389\) 27.4925 27.4925i 1.39392 1.39392i 0.577609 0.816314i \(-0.303986\pi\)
0.816314 0.577609i \(-0.196014\pi\)
\(390\) −41.1421 19.3262i −2.08331 0.978620i
\(391\) 23.1463 1.17056
\(392\) −2.52331 1.27786i −0.127446 0.0645417i
\(393\) 9.14544 9.14544i 0.461327 0.461327i
\(394\) 3.37090 + 2.72512i 0.169823 + 0.137289i
\(395\) −3.03041 12.3456i −0.152477 0.621173i
\(396\) −4.31529 2.79231i −0.216851 0.140319i
\(397\) 28.9497i 1.45294i 0.687197 + 0.726471i \(0.258841\pi\)
−0.687197 + 0.726471i \(0.741159\pi\)
\(398\) −20.9060 + 25.8602i −1.04792 + 1.29625i
\(399\) 8.01438 0.401221
\(400\) 12.3760 15.7109i 0.618802 0.785547i
\(401\) −26.5646 −1.32657 −0.663287 0.748365i \(-0.730839\pi\)
−0.663287 + 0.748365i \(0.730839\pi\)
\(402\) −1.87408 + 2.31819i −0.0934705 + 0.115621i
\(403\) 32.7185i 1.62983i
\(404\) 14.7050 22.7254i 0.731599 1.13063i
\(405\) 5.30116 + 21.5963i 0.263417 + 1.07313i
\(406\) −1.76745 1.42885i −0.0877173 0.0709127i
\(407\) 4.80505 4.80505i 0.238178 0.238178i
\(408\) 36.8215 12.0645i 1.82294 0.597281i
\(409\) 21.2762 1.05204 0.526021 0.850472i \(-0.323683\pi\)
0.526021 + 0.850472i \(0.323683\pi\)
\(410\) −15.4805 7.27184i −0.764526 0.359131i
\(411\) 11.3942 11.3942i 0.562032 0.562032i
\(412\) 2.22703 3.44170i 0.109718 0.169560i
\(413\) 6.81734 0.335459
\(414\) 1.57997 + 14.9144i 0.0776511 + 0.733005i
\(415\) −28.4540 + 6.98447i −1.39675 + 0.342854i
\(416\) 33.1012 + 8.72381i 1.62292 + 0.427720i
\(417\) 33.7128 33.7128i 1.65092 1.65092i
\(418\) 2.91748 3.60885i 0.142699 0.176515i
\(419\) 11.9419 11.9419i 0.583402 0.583402i −0.352435 0.935836i \(-0.614646\pi\)
0.935836 + 0.352435i \(0.114646\pi\)
\(420\) −10.0373 3.47855i −0.489771 0.169736i
\(421\) −10.7729 10.7729i −0.525039 0.525039i 0.394050 0.919089i \(-0.371074\pi\)
−0.919089 + 0.394050i \(0.871074\pi\)
\(422\) 0.735556 + 6.94344i 0.0358063 + 0.338002i
\(423\) −10.2384 10.2384i −0.497808 0.497808i
\(424\) 19.0759 + 9.66047i 0.926406 + 0.469154i
\(425\) −8.63139 + 27.5140i −0.418684 + 1.33463i
\(426\) 30.3264 37.5130i 1.46932 1.81751i
\(427\) 2.66037i 0.128744i
\(428\) 30.0090 6.43018i 1.45054 0.310814i
\(429\) 9.88538 + 9.88538i 0.477271 + 0.477271i
\(430\) 1.19796 2.55024i 0.0577707 0.122984i
\(431\) 33.2454i 1.60137i −0.599083 0.800687i \(-0.704468\pi\)
0.599083 0.800687i \(-0.295532\pi\)
\(432\) −1.39213 3.09932i −0.0669790 0.149116i
\(433\) 16.9146 + 16.9146i 0.812862 + 0.812862i 0.985062 0.172200i \(-0.0550875\pi\)
−0.172200 + 0.985062i \(0.555087\pi\)
\(434\) 0.805518 + 7.60387i 0.0386661 + 0.364997i
\(435\) −7.30081 4.42301i −0.350047 0.212067i
\(436\) −15.7307 + 24.3106i −0.753364 + 1.16426i
\(437\) −13.5411 −0.647756
\(438\) −3.77810 35.6643i −0.180525 1.70410i
\(439\) 27.0959i 1.29322i 0.762822 + 0.646609i \(0.223813\pi\)
−0.762822 + 0.646609i \(0.776187\pi\)
\(440\) −5.22028 + 3.25348i −0.248867 + 0.155103i
\(441\) 2.64241i 0.125829i
\(442\) −49.0806 + 5.19937i −2.33453 + 0.247309i
\(443\) −32.4500 −1.54175 −0.770874 0.636987i \(-0.780180\pi\)
−0.770874 + 0.636987i \(0.780180\pi\)
\(444\) −32.4566 + 6.95464i −1.54032 + 0.330052i
\(445\) −0.800233 3.26006i −0.0379347 0.154542i
\(446\) 1.16352 0.123258i 0.0550943 0.00583643i
\(447\) 3.51611 + 3.51611i 0.166306 + 0.166306i
\(448\) 7.90758 + 1.21250i 0.373598 + 0.0572851i
\(449\) 11.4827i 0.541901i −0.962593 0.270951i \(-0.912662\pi\)
0.962593 0.270951i \(-0.0873380\pi\)
\(450\) −18.3180 3.68357i −0.863518 0.173645i
\(451\) 3.71956 + 3.71956i 0.175147 + 0.175147i
\(452\) −20.0272 + 30.9504i −0.942000 + 1.45579i
\(453\) 8.34315i 0.391995i
\(454\) −13.9766 11.2990i −0.655953 0.530288i
\(455\) 11.5731 + 7.01125i 0.542553 + 0.328692i
\(456\) −21.5413 + 7.05796i −1.00876 + 0.330519i
\(457\) −7.83252 7.83252i −0.366390 0.366390i 0.499769 0.866159i \(-0.333418\pi\)
−0.866159 + 0.499769i \(0.833418\pi\)
\(458\) −21.9413 + 2.32436i −1.02525 + 0.108610i
\(459\) 3.46391 + 3.46391i 0.161681 + 0.161681i
\(460\) 16.9590 + 5.87734i 0.790718 + 0.274033i
\(461\) 12.0472 12.0472i 0.561096 0.561096i −0.368523 0.929619i \(-0.620136\pi\)
0.929619 + 0.368523i \(0.120136\pi\)
\(462\) 2.54076 + 2.05401i 0.118207 + 0.0955613i
\(463\) −14.2822 + 14.2822i −0.663751 + 0.663751i −0.956262 0.292511i \(-0.905509\pi\)
0.292511 + 0.956262i \(0.405509\pi\)
\(464\) 6.00895 + 2.28398i 0.278959 + 0.106031i
\(465\) 6.84614 + 27.8904i 0.317482 + 1.29339i
\(466\) −0.349230 + 0.0369958i −0.0161778 + 0.00171380i
\(467\) −38.2989 −1.77226 −0.886131 0.463435i \(-0.846617\pi\)
−0.886131 + 0.463435i \(0.846617\pi\)
\(468\) −6.70048 31.2704i −0.309730 1.44548i
\(469\) 0.627473 0.627473i 0.0289740 0.0289740i
\(470\) −16.2996 + 5.88059i −0.751843 + 0.271252i
\(471\) 31.1521 1.43541
\(472\) −18.3239 + 6.00377i −0.843424 + 0.276346i
\(473\) −0.612758 + 0.612758i −0.0281746 + 0.0281746i
\(474\) 12.0063 14.8515i 0.551468 0.682151i
\(475\) 5.04953 16.0963i 0.231688 0.738547i
\(476\) −11.2784 + 2.41669i −0.516947 + 0.110769i
\(477\) 19.9763i 0.914652i
\(478\) −20.9303 16.9206i −0.957330 0.773929i
\(479\) −3.87202 −0.176917 −0.0884586 0.996080i \(-0.528194\pi\)
−0.0884586 + 0.996080i \(0.528194\pi\)
\(480\) 30.0421 + 0.510274i 1.37123 + 0.0232907i
\(481\) 42.2804 1.92782
\(482\) 23.9520 + 19.3634i 1.09098 + 0.881978i
\(483\) 9.53339i 0.433784i
\(484\) −19.6619 + 4.21305i −0.893721 + 0.191502i
\(485\) 24.3359 + 14.7433i 1.10504 + 0.669459i
\(486\) −18.7373 + 23.1775i −0.849939 + 1.05135i
\(487\) 7.57181 7.57181i 0.343112 0.343112i −0.514424 0.857536i \(-0.671994\pi\)
0.857536 + 0.514424i \(0.171994\pi\)
\(488\) −2.34289 7.15063i −0.106058 0.323694i
\(489\) −29.7502 −1.34535
\(490\) 2.86222 + 1.34451i 0.129302 + 0.0607386i
\(491\) 12.8182 12.8182i 0.578477 0.578477i −0.356006 0.934484i \(-0.615862\pi\)
0.934484 + 0.356006i \(0.115862\pi\)
\(492\) −5.38353 25.1244i −0.242708 1.13270i
\(493\) −9.26849 −0.417432
\(494\) 28.7131 3.04173i 1.29186 0.136854i
\(495\) 4.91499 + 2.97762i 0.220912 + 0.133834i
\(496\) −8.86153 19.7285i −0.397894 0.885836i
\(497\) −10.1538 + 10.1538i −0.455459 + 0.455459i
\(498\) −34.2296 27.6720i −1.53387 1.24001i
\(499\) −7.77963 + 7.77963i −0.348264 + 0.348264i −0.859463 0.511199i \(-0.829202\pi\)
0.511199 + 0.859463i \(0.329202\pi\)
\(500\) −13.3105 + 17.9675i −0.595264 + 0.803530i
\(501\) 17.8721 + 17.8721i 0.798465 + 0.798465i
\(502\) 9.44085 1.00012i 0.421366 0.0446375i
\(503\) −12.4545 12.4545i −0.555320 0.555320i 0.372652 0.927971i \(-0.378449\pi\)
−0.927971 + 0.372652i \(0.878449\pi\)
\(504\) −2.32707 7.10236i −0.103656 0.316364i
\(505\) −15.6809 + 25.8835i −0.697791 + 1.15180i
\(506\) −4.29285 3.47045i −0.190841 0.154280i
\(507\) 56.1031i 2.49163i
\(508\) −2.05641 + 3.17802i −0.0912385 + 0.141002i
\(509\) −3.71209 3.71209i −0.164535 0.164535i 0.620037 0.784572i \(-0.287118\pi\)
−0.784572 + 0.620037i \(0.787118\pi\)
\(510\) −40.7501 + 14.7019i −1.80445 + 0.651012i
\(511\) 10.6760i 0.472279i
\(512\) −22.3220 + 3.70492i −0.986504 + 0.163736i
\(513\) −2.02646 2.02646i −0.0894702 0.0894702i
\(514\) −15.7723 + 1.67085i −0.695688 + 0.0736979i
\(515\) −2.37483 + 3.91999i −0.104648 + 0.172736i
\(516\) 4.13898 0.886880i 0.182208 0.0390427i
\(517\) 5.32932 0.234383
\(518\) 9.82607 1.04093i 0.431733 0.0457357i
\(519\) 56.4561i 2.47815i
\(520\) −37.2809 8.65310i −1.63488 0.379464i
\(521\) 12.7618i 0.559103i 0.960131 + 0.279551i \(0.0901857\pi\)
−0.960131 + 0.279551i \(0.909814\pi\)
\(522\) −0.632666 5.97219i −0.0276910 0.261396i
\(523\) 16.9371 0.740610 0.370305 0.928910i \(-0.379253\pi\)
0.370305 + 0.928910i \(0.379253\pi\)
\(524\) 5.91595 9.14264i 0.258440 0.399398i
\(525\) 11.3323 + 3.55505i 0.494584 + 0.155155i
\(526\) 2.50142 + 23.6127i 0.109067 + 1.02956i
\(527\) 22.0493 + 22.0493i 0.960483 + 0.960483i
\(528\) −8.63803 3.28329i −0.375922 0.142887i
\(529\) 6.89245i 0.299672i
\(530\) −21.6380 10.1643i −0.939895 0.441509i
\(531\) 12.7380 + 12.7380i 0.552781 + 0.552781i
\(532\) 6.59811 1.41381i 0.286064 0.0612965i
\(533\) 32.7290i 1.41765i
\(534\) 3.17047 3.92179i 0.137200 0.169713i
\(535\) −33.3234 + 8.17974i −1.44070 + 0.353641i
\(536\) −1.13395 + 2.23913i −0.0489791 + 0.0967157i
\(537\) −35.8124 35.8124i −1.54542 1.54542i
\(538\) 0.820059 + 7.74113i 0.0353553 + 0.333744i
\(539\) −0.687717 0.687717i −0.0296221 0.0296221i
\(540\) 1.65840 + 3.41752i 0.0713662 + 0.147067i
\(541\) 8.30783 8.30783i 0.357182 0.357182i −0.505591 0.862773i \(-0.668726\pi\)
0.862773 + 0.505591i \(0.168726\pi\)
\(542\) 28.2106 34.8958i 1.21175 1.49890i
\(543\) 41.3152 41.3152i 1.77300 1.77300i
\(544\) 28.1863 16.4282i 1.20848 0.704351i
\(545\) 16.7747 27.6890i 0.718550 1.18607i
\(546\) 2.14149 + 20.2151i 0.0916472 + 0.865125i
\(547\) 5.57600 0.238413 0.119206 0.992870i \(-0.461965\pi\)
0.119206 + 0.992870i \(0.461965\pi\)
\(548\) 7.37059 11.3907i 0.314856 0.486585i
\(549\) −4.97082 + 4.97082i −0.212149 + 0.212149i
\(550\) 5.72615 3.80877i 0.244164 0.162406i
\(551\) 5.42225 0.230995
\(552\) 8.39569 + 25.6241i 0.357344 + 1.09064i
\(553\) −4.01991 + 4.01991i −0.170944 + 0.170944i
\(554\) 10.4609 + 8.45681i 0.444439 + 0.359296i
\(555\) 36.0413 8.84690i 1.52987 0.375530i
\(556\) 21.8080 33.7025i 0.924864 1.42930i
\(557\) 0.469590i 0.0198972i 0.999951 + 0.00994859i \(0.00316679\pi\)
−0.999951 + 0.00994859i \(0.996833\pi\)
\(558\) −12.7025 + 15.7127i −0.537740 + 0.665170i
\(559\) −5.39175 −0.228047
\(560\) −8.87722 1.09316i −0.375131 0.0461944i
\(561\) 13.3237 0.562527
\(562\) 4.80994 5.94977i 0.202895 0.250976i
\(563\) 23.1326i 0.974922i 0.873145 + 0.487461i \(0.162077\pi\)
−0.873145 + 0.487461i \(0.837923\pi\)
\(564\) −21.8556 14.1422i −0.920288 0.595494i
\(565\) 21.3564 35.2517i 0.898469 1.48305i
\(566\) −25.4724 20.5925i −1.07069 0.865568i
\(567\) 7.03210 7.03210i 0.295320 0.295320i
\(568\) 18.3496 36.2337i 0.769932 1.52033i
\(569\) 2.97599 0.124760 0.0623800 0.998052i \(-0.480131\pi\)
0.0623800 + 0.998052i \(0.480131\pi\)
\(570\) 23.8396 8.60091i 0.998532 0.360253i
\(571\) −26.5433 + 26.5433i −1.11080 + 1.11080i −0.117758 + 0.993042i \(0.537571\pi\)
−0.993042 + 0.117758i \(0.962429\pi\)
\(572\) 9.88235 + 6.39460i 0.413202 + 0.267372i
\(573\) −28.3718 −1.18525
\(574\) 0.805774 + 7.60629i 0.0336324 + 0.317480i
\(575\) −19.1471 6.00660i −0.798487 0.250492i
\(576\) 12.5096 + 17.0406i 0.521231 + 0.710024i
\(577\) −24.4050 + 24.4050i −1.01599 + 1.01599i −0.0161238 + 0.999870i \(0.505133\pi\)
−0.999870 + 0.0161238i \(0.994867\pi\)
\(578\) −14.4574 + 17.8835i −0.601350 + 0.743855i
\(579\) 7.00554 7.00554i 0.291140 0.291140i
\(580\) −6.79090 2.35347i −0.281977 0.0977224i
\(581\) 9.26506 + 9.26506i 0.384379 + 0.384379i
\(582\) 4.50314 + 42.5084i 0.186661 + 1.76203i
\(583\) 5.19905 + 5.19905i 0.215323 + 0.215323i
\(584\) −9.40196 28.6953i −0.389056 1.18742i
\(585\) 8.52358 + 34.7242i 0.352407 + 1.43567i
\(586\) 18.7455 23.1877i 0.774369 0.957874i
\(587\) 1.84258i 0.0760514i 0.999277 + 0.0380257i \(0.0121069\pi\)
−0.999277 + 0.0380257i \(0.987893\pi\)
\(588\) 0.995374 + 4.64531i 0.0410485 + 0.191569i
\(589\) −12.8993 12.8993i −0.531505 0.531505i
\(590\) 20.2789 7.31626i 0.834869 0.301206i
\(591\) 7.28068i 0.299487i
\(592\) −25.4941 + 11.4513i −1.04780 + 0.470645i
\(593\) −21.1030 21.1030i −0.866597 0.866597i 0.125497 0.992094i \(-0.459948\pi\)
−0.992094 + 0.125497i \(0.959948\pi\)
\(594\) −0.123076 1.16180i −0.00504985 0.0476692i
\(595\) 12.5241 3.07424i 0.513439 0.126032i
\(596\) 3.51504 + 2.27448i 0.143981 + 0.0931665i
\(597\) 55.8545 2.28597
\(598\) −3.61825 34.1553i −0.147961 1.39671i
\(599\) 13.4830i 0.550902i −0.961315 0.275451i \(-0.911173\pi\)
0.961315 0.275451i \(-0.0888272\pi\)
\(600\) −33.5902 + 0.424580i −1.37131 + 0.0173334i
\(601\) 12.3353i 0.503168i −0.967835 0.251584i \(-0.919048\pi\)
0.967835 0.251584i \(-0.0809515\pi\)
\(602\) −1.25306 + 0.132743i −0.0510707 + 0.00541019i
\(603\) 2.34482 0.0954886
\(604\) −1.47181 6.86878i −0.0598871 0.279487i
\(605\) 21.8335 5.35936i 0.887657 0.217889i
\(606\) −45.2117 + 4.78951i −1.83660 + 0.194561i
\(607\) −24.7714 24.7714i −1.00544 1.00544i −0.999985 0.00545670i \(-0.998263\pi\)
−0.00545670 0.999985i \(-0.501737\pi\)
\(608\) −16.4895 + 9.61079i −0.668738 + 0.389769i
\(609\) 3.81746i 0.154691i
\(610\) 2.85507 + 7.91355i 0.115598 + 0.320410i
\(611\) 23.4468 + 23.4468i 0.948554 + 0.948554i
\(612\) −25.5889 16.5579i −1.03437 0.669314i
\(613\) 5.69015i 0.229823i 0.993376 + 0.114912i \(0.0366585\pi\)
−0.993376 + 0.114912i \(0.963342\pi\)
\(614\) 15.2260 + 12.3091i 0.614471 + 0.496753i
\(615\) 6.84832 + 27.8993i 0.276151 + 1.12501i
\(616\) 2.45411 + 1.24282i 0.0988791 + 0.0500747i
\(617\) −8.01452 8.01452i −0.322652 0.322652i 0.527131 0.849784i \(-0.323268\pi\)
−0.849784 + 0.527131i \(0.823268\pi\)
\(618\) −6.84719 + 0.725359i −0.275434 + 0.0291782i
\(619\) −28.4303 28.4303i −1.14271 1.14271i −0.987952 0.154759i \(-0.950540\pi\)
−0.154759 0.987952i \(-0.549460\pi\)
\(620\) 10.5564 + 21.7540i 0.423957 + 0.873663i
\(621\) −2.41054 + 2.41054i −0.0967316 + 0.0967316i
\(622\) 28.5305 + 23.0647i 1.14397 + 0.924812i
\(623\) −1.06153 + 1.06153i −0.0425292 + 0.0425292i
\(624\) −23.5586 52.4487i −0.943099 2.09963i
\(625\) 14.2801 20.5202i 0.571203 0.820809i
\(626\) −30.8600 + 3.26916i −1.23341 + 0.130662i
\(627\) −7.79462 −0.311287
\(628\) 25.6470 5.49552i 1.02343 0.219295i
\(629\) 28.4931 28.4931i 1.13610 1.13610i
\(630\) 2.83580 + 7.86013i 0.112981 + 0.313155i
\(631\) −15.1390 −0.602672 −0.301336 0.953518i \(-0.597433\pi\)
−0.301336 + 0.953518i \(0.597433\pi\)
\(632\) 7.26465 14.3450i 0.288972 0.570614i
\(633\) 8.29279 8.29279i 0.329609 0.329609i
\(634\) −12.6881 + 15.6949i −0.503910 + 0.623324i
\(635\) 2.19289 3.61967i 0.0870222 0.143642i
\(636\) −7.52490 35.1179i −0.298382 1.39252i
\(637\) 6.05133i 0.239763i
\(638\) 1.71899 + 1.38967i 0.0680554 + 0.0550176i
\(639\) −37.9440 −1.50104
\(640\) 24.8232 4.87960i 0.981222 0.192883i
\(641\) −19.9351 −0.787390 −0.393695 0.919241i \(-0.628803\pi\)
−0.393695 + 0.919241i \(0.628803\pi\)
\(642\) −40.0874 32.4076i −1.58212 1.27903i
\(643\) 36.8071i 1.45153i −0.687943 0.725764i \(-0.741486\pi\)
0.687943 0.725764i \(-0.258514\pi\)
\(644\) −1.68178 7.84868i −0.0662713 0.309281i
\(645\) −4.59612 + 1.12819i −0.180972 + 0.0444224i
\(646\) 17.3002 21.3999i 0.680666 0.841967i
\(647\) 24.2753 24.2753i 0.954362 0.954362i −0.0446409 0.999003i \(-0.514214\pi\)
0.999003 + 0.0446409i \(0.0142144\pi\)
\(648\) −12.7082 + 25.0940i −0.499225 + 0.985786i
\(649\) −6.63040 −0.260266
\(650\) 41.9496 + 8.43567i 1.64540 + 0.330874i
\(651\) 9.08155 9.08155i 0.355934 0.355934i
\(652\) −24.4928 + 5.24821i −0.959213 + 0.205536i
\(653\) 35.7958 1.40080 0.700400 0.713751i \(-0.253005\pi\)
0.700400 + 0.713751i \(0.253005\pi\)
\(654\) 48.3654 5.12360i 1.89124 0.200349i
\(655\) −6.30858 + 10.4132i −0.246497 + 0.406877i
\(656\) −8.86435 19.7348i −0.346095 0.770515i
\(657\) −19.9478 + 19.9478i −0.778237 + 0.778237i
\(658\) 6.02633 + 4.87183i 0.234931 + 0.189924i
\(659\) 5.29572 5.29572i 0.206292 0.206292i −0.596397 0.802689i \(-0.703402\pi\)
0.802689 + 0.596397i \(0.203402\pi\)
\(660\) 9.76209 + 3.38317i 0.379989 + 0.131690i
\(661\) 21.2538 + 21.2538i 0.826678 + 0.826678i 0.987056 0.160378i \(-0.0512714\pi\)
−0.160378 + 0.987056i \(0.551271\pi\)
\(662\) 23.1128 2.44846i 0.898304 0.0951621i
\(663\) 58.6186 + 58.6186i 2.27656 + 2.27656i
\(664\) −33.0623 16.7435i −1.28307 0.649775i
\(665\) −7.32686 + 1.79849i −0.284123 + 0.0697425i
\(666\) 20.3046 + 16.4148i 0.786788 + 0.636059i
\(667\) 6.44995i 0.249743i
\(668\) 17.8666 + 11.5610i 0.691279 + 0.447308i
\(669\) −1.38963 1.38963i −0.0537263 0.0537263i
\(670\) 1.19309 2.53988i 0.0460930 0.0981240i
\(671\) 2.58742i 0.0998863i
\(672\) −6.76634 11.6092i −0.261017 0.447835i
\(673\) 23.1172 + 23.1172i 0.891103 + 0.891103i 0.994627 0.103524i \(-0.0330117\pi\)
−0.103524 + 0.994627i \(0.533012\pi\)
\(674\) 14.4410 1.52981i 0.556245 0.0589259i
\(675\) −1.96651 3.76431i −0.0756908 0.144888i
\(676\) 9.89712 + 46.1888i 0.380658 + 1.77649i
\(677\) −33.0151 −1.26887 −0.634437 0.772974i \(-0.718768\pi\)
−0.634437 + 0.772974i \(0.718768\pi\)
\(678\) 61.5753 6.52300i 2.36479 0.250514i
\(679\) 12.7248i 0.488333i
\(680\) −30.9554 + 19.2926i −1.18708 + 0.739836i
\(681\) 30.1875i 1.15679i
\(682\) −0.783430 7.39536i −0.0299991 0.283183i
\(683\) −35.3615 −1.35307 −0.676536 0.736410i \(-0.736520\pi\)
−0.676536 + 0.736410i \(0.736520\pi\)
\(684\) 14.9700 + 9.68670i 0.572393 + 0.370380i
\(685\) −7.85975 + 12.9736i −0.300306 + 0.495697i
\(686\) −0.148981 1.40634i −0.00568814 0.0536945i
\(687\) 26.2053 + 26.2053i 0.999794 + 0.999794i
\(688\) 3.25110 1.46031i 0.123947 0.0556737i
\(689\) 45.7473i 1.74283i
\(690\) −10.2311 28.3581i −0.389491 1.07957i
\(691\) −22.6208 22.6208i −0.860537 0.860537i 0.130864 0.991400i \(-0.458225\pi\)
−0.991400 + 0.130864i \(0.958225\pi\)
\(692\) −9.95938 46.4794i −0.378599 1.76688i
\(693\) 2.56996i 0.0976245i
\(694\) −6.08325 + 7.52483i −0.230917 + 0.285639i
\(695\) −23.2553 + 38.3862i −0.882124 + 1.45607i
\(696\) −3.36189 10.2607i −0.127432 0.388930i
\(697\) 22.0563 + 22.0563i 0.835443 + 0.835443i
\(698\) −1.40267 13.2408i −0.0530919 0.501173i
\(699\) 0.417097 + 0.417097i 0.0157761 + 0.0157761i
\(700\) 9.95688 + 0.927687i 0.376335 + 0.0350633i
\(701\) 5.34711 5.34711i 0.201957 0.201957i −0.598881 0.800838i \(-0.704388\pi\)
0.800838 + 0.598881i \(0.204388\pi\)
\(702\) 4.56995 5.65291i 0.172482 0.213355i
\(703\) −16.6690 + 16.6690i −0.628685 + 0.628685i
\(704\) −7.69075 1.17925i −0.289856 0.0444446i
\(705\) 24.8929 + 15.0808i 0.937522 + 0.567975i
\(706\) 1.65493 + 15.6221i 0.0622841 + 0.587945i
\(707\) 13.5340 0.508999
\(708\) 27.1914 + 17.5948i 1.02192 + 0.661254i
\(709\) −35.3011 + 35.3011i −1.32576 + 1.32576i −0.416732 + 0.909029i \(0.636825\pi\)
−0.909029 + 0.416732i \(0.863175\pi\)
\(710\) −19.3066 + 41.1004i −0.724564 + 1.54247i
\(711\) −15.0221 −0.563374
\(712\) 1.91836 3.78805i 0.0718935 0.141963i
\(713\) −15.3441 + 15.3441i −0.574643 + 0.574643i
\(714\) 15.0663 + 12.1799i 0.563841 + 0.455823i
\(715\) −11.2557 6.81899i −0.420940 0.255016i
\(716\) −35.8014 23.1661i −1.33796 0.865759i
\(717\) 45.2066i 1.68827i
\(718\) −11.6912 + 14.4617i −0.436310 + 0.539705i
\(719\) −44.1493 −1.64649 −0.823245 0.567686i \(-0.807839\pi\)
−0.823245 + 0.567686i \(0.807839\pi\)
\(720\) −14.5443 18.6293i −0.542033 0.694274i
\(721\) 2.04969 0.0763345
\(722\) 6.77177 8.37651i 0.252019 0.311741i
\(723\) 51.7330i 1.92397i
\(724\) 26.7258 41.3025i 0.993255 1.53500i
\(725\) 7.66706 + 2.40522i 0.284747 + 0.0893277i
\(726\) 26.2653 + 21.2335i 0.974795 + 0.788048i
\(727\) 5.76306 5.76306i 0.213740 0.213740i −0.592114 0.805854i \(-0.701706\pi\)
0.805854 + 0.592114i \(0.201706\pi\)
\(728\) 5.32918 + 16.2650i 0.197513 + 0.602819i
\(729\) 20.2255 0.749094
\(730\) 11.4573 + 31.7569i 0.424055 + 1.17538i
\(731\) −3.63355 + 3.63355i −0.134392 + 0.134392i
\(732\) −6.86613 + 10.6111i −0.253780 + 0.392196i
\(733\) 37.3735 1.38042 0.690210 0.723609i \(-0.257518\pi\)
0.690210 + 0.723609i \(0.257518\pi\)
\(734\) −0.616273 5.81745i −0.0227471 0.214726i
\(735\) −1.26620 5.15837i −0.0467046 0.190269i
\(736\) 11.4324 + 19.6149i 0.421403 + 0.723013i
\(737\) −0.610267 + 0.610267i −0.0224795 + 0.0224795i
\(738\) −12.7065 + 15.7177i −0.467734 + 0.578575i
\(739\) −10.4981 + 10.4981i −0.386180 + 0.386180i −0.873323 0.487142i \(-0.838039\pi\)
0.487142 + 0.873323i \(0.338039\pi\)
\(740\) 28.1116 13.6415i 1.03340 0.501473i
\(741\) −34.2930 34.2930i −1.25979 1.25979i
\(742\) 1.12628 + 10.6318i 0.0413471 + 0.390305i
\(743\) −2.49020 2.49020i −0.0913564 0.0913564i 0.659952 0.751308i \(-0.270577\pi\)
−0.751308 + 0.659952i \(0.770577\pi\)
\(744\) −16.4119 + 32.4075i −0.601689 + 1.18812i
\(745\) −4.00352 2.42544i −0.146678 0.0888611i
\(746\) 16.8896 20.8920i 0.618371 0.764909i
\(747\) 34.6229i 1.26679i
\(748\) 10.9692 2.35042i 0.401073 0.0859400i
\(749\) 10.8506 + 10.8506i 0.396473 + 0.396473i
\(750\) 37.5245 1.58682i 1.37020 0.0579423i
\(751\) 13.1729i 0.480685i 0.970688 + 0.240343i \(0.0772598\pi\)
−0.970688 + 0.240343i \(0.922740\pi\)
\(752\) −20.4882 7.78750i −0.747128 0.283981i
\(753\) −11.2755 11.2755i −0.410903 0.410903i
\(754\) 1.44886 + 13.6768i 0.0527642 + 0.498080i
\(755\) 1.87227 + 7.62742i 0.0681388 + 0.277590i
\(756\) 0.922894 1.42626i 0.0335653 0.0518726i
\(757\) 36.0838 1.31149 0.655743 0.754984i \(-0.272355\pi\)
0.655743 + 0.754984i \(0.272355\pi\)
\(758\) 0.0668394 + 0.630945i 0.00242771 + 0.0229170i
\(759\) 9.27197i 0.336551i
\(760\) 18.1095 11.2865i 0.656900 0.409405i
\(761\) 22.3147i 0.808908i 0.914558 + 0.404454i \(0.132538\pi\)
−0.914558 + 0.404454i \(0.867462\pi\)
\(762\) 6.32262 0.669788i 0.229044 0.0242639i
\(763\) −14.4781 −0.524142
\(764\) −23.3581 + 5.00505i −0.845065 + 0.181076i
\(765\) 29.1450 + 17.6568i 1.05374 + 0.638383i
\(766\) 19.5827 2.07450i 0.707552 0.0749547i
\(767\) −29.1710 29.1710i −1.05330 1.05330i
\(768\) 28.4106 + 25.2447i 1.02518 + 0.910941i
\(769\) 37.4991i 1.35225i 0.736786 + 0.676126i \(0.236342\pi\)
−0.736786 + 0.676126i \(0.763658\pi\)
\(770\) −2.78374 1.30764i −0.100319 0.0471241i
\(771\) 18.8374 + 18.8374i 0.678414 + 0.678414i
\(772\) 4.53170 7.00339i 0.163100 0.252057i
\(773\) 47.4421i 1.70637i −0.521607 0.853186i \(-0.674667\pi\)
0.521607 0.853186i \(-0.325333\pi\)
\(774\) −2.58932 2.09327i −0.0930712 0.0752410i
\(775\) −12.5177 23.9615i −0.449648 0.860722i
\(776\) 11.2062 + 34.2021i 0.402281 + 1.22778i
\(777\) −11.7356 11.7356i −0.421012 0.421012i
\(778\) −54.6789 + 5.79243i −1.96034 + 0.207669i
\(779\) −12.9034 12.9034i −0.462312 0.462312i
\(780\) 28.0646 + 57.8336i 1.00487 + 2.07078i
\(781\) 9.87536 9.87536i 0.353368 0.353368i
\(782\) −25.4559 20.5792i −0.910301 0.735909i
\(783\) 0.965253 0.965253i 0.0344953 0.0344953i
\(784\) 1.63895 + 3.64881i 0.0585340 + 0.130315i
\(785\) −28.4797 + 6.99077i −1.01648 + 0.249511i
\(786\) −18.1891 + 1.92687i −0.648784 + 0.0687291i
\(787\) 21.6223 0.770752 0.385376 0.922760i \(-0.374072\pi\)
0.385376 + 0.922760i \(0.374072\pi\)
\(788\) −1.28438 5.99406i −0.0457541 0.213530i
\(789\) 28.2015 28.2015i 1.00400 1.00400i
\(790\) −7.64354 + 16.2717i −0.271945 + 0.578923i
\(791\) −18.4324 −0.655382
\(792\) 2.26326 + 6.90761i 0.0804215 + 0.245451i
\(793\) 11.3836 11.3836i 0.404242 0.404242i
\(794\) 25.7389 31.8383i 0.913438 1.12990i
\(795\) 9.57232 + 38.9966i 0.339495 + 1.38307i
\(796\) 45.9841 9.85325i 1.62986 0.349239i
\(797\) 5.43553i 0.192536i −0.995355 0.0962682i \(-0.969309\pi\)
0.995355 0.0962682i \(-0.0306907\pi\)
\(798\) −8.81407 7.12550i −0.312015 0.252240i
\(799\) 31.6020 1.11800
\(800\) −27.5794 + 6.27518i −0.975078 + 0.221861i
\(801\) −3.96686 −0.140162
\(802\) 29.2153 + 23.6183i 1.03163 + 0.833992i
\(803\) 10.3833i 0.366418i
\(804\) 4.12215 0.883275i 0.145377 0.0311507i
\(805\) 2.13937 + 8.71555i 0.0754028 + 0.307183i
\(806\) 29.0897 35.9832i 1.02464 1.26746i
\(807\) 9.24550 9.24550i 0.325457 0.325457i
\(808\) −36.3771 + 11.9189i −1.27974 + 0.419305i
\(809\) −37.6093 −1.32227 −0.661137 0.750265i \(-0.729926\pi\)
−0.661137 + 0.750265i \(0.729926\pi\)
\(810\) 13.3710 28.4645i 0.469808 1.00014i
\(811\) 12.6490 12.6490i 0.444166 0.444166i −0.449243 0.893409i \(-0.648306\pi\)
0.893409 + 0.449243i \(0.148306\pi\)
\(812\) 0.673435 + 3.14285i 0.0236329 + 0.110292i
\(813\) −75.3702 −2.64335
\(814\) −9.55663 + 1.01238i −0.334960 + 0.0354840i
\(815\) 27.1980 6.67617i 0.952705 0.233856i
\(816\) −51.2220 19.4693i −1.79313 0.681563i
\(817\) 2.12570 2.12570i 0.0743687 0.0743687i
\(818\) −23.3992 18.9165i −0.818134 0.661399i
\(819\) 11.3067 11.3067i 0.395089 0.395089i
\(820\) 10.5598 + 21.7610i 0.368765 + 0.759926i
\(821\) −18.6856 18.6856i −0.652134 0.652134i 0.301373 0.953506i \(-0.402555\pi\)
−0.953506 + 0.301373i \(0.902555\pi\)
\(822\) −22.6615 + 2.40065i −0.790411 + 0.0837324i
\(823\) 21.4388 + 21.4388i 0.747311 + 0.747311i 0.973973 0.226662i \(-0.0727814\pi\)
−0.226662 + 0.973973i \(0.572781\pi\)
\(824\) −5.50922 + 1.80509i −0.191923 + 0.0628831i
\(825\) −11.0216 3.45757i −0.383723 0.120377i
\(826\) −7.49758 6.06123i −0.260874 0.210897i
\(827\) 2.57326i 0.0894810i 0.998999 + 0.0447405i \(0.0142461\pi\)
−0.998999 + 0.0447405i \(0.985754\pi\)
\(828\) 11.5227 17.8074i 0.400440 0.618849i
\(829\) −13.4129 13.4129i −0.465849 0.465849i 0.434718 0.900567i \(-0.356848\pi\)
−0.900567 + 0.434718i \(0.856848\pi\)
\(830\) 37.5030 + 17.6168i 1.30175 + 0.611487i
\(831\) 22.5940i 0.783778i
\(832\) −28.6479 39.0243i −0.993186 1.35292i
\(833\) −4.07805 4.07805i −0.141296 0.141296i
\(834\) −67.0505 + 7.10301i −2.32177 + 0.245957i
\(835\) −20.3495 12.3283i −0.704225 0.426637i
\(836\) −6.41719 + 1.37504i −0.221943 + 0.0475569i
\(837\) −4.59258 −0.158743
\(838\) −23.7510 + 2.51606i −0.820463 + 0.0869160i
\(839\) 50.9789i 1.75999i 0.474986 + 0.879993i \(0.342453\pi\)
−0.474986 + 0.879993i \(0.657547\pi\)
\(840\) 7.94612 + 12.7497i 0.274167 + 0.439908i
\(841\) 26.4172i 0.910939i
\(842\) 2.26976 + 21.4259i 0.0782210 + 0.738385i
\(843\) −12.8507 −0.442601
\(844\) 5.36439 8.29025i 0.184650 0.285362i
\(845\) −12.5900 51.2903i −0.433109 1.76444i
\(846\) 2.15715 + 20.3629i 0.0741642 + 0.700090i
\(847\) −7.10932 7.10932i −0.244279 0.244279i
\(848\) −12.3903 27.5846i −0.425483 0.947258i
\(849\) 55.0169i 1.88818i
\(850\) 33.9551 22.5853i 1.16465 0.774671i
\(851\) 19.8284 + 19.8284i 0.679709 + 0.679709i
\(852\) −66.7048 + 14.2932i −2.28527 + 0.489677i
\(853\) 3.66787i 0.125585i 0.998027 + 0.0627927i \(0.0200007\pi\)
−0.998027 + 0.0627927i \(0.979999\pi\)
\(854\) 2.36531 2.92583i 0.0809392 0.100120i
\(855\) −17.0504 10.3296i −0.583112 0.353264i
\(856\) −38.7203 19.6089i −1.32343 0.670218i
\(857\) −27.4350 27.4350i −0.937162 0.937162i 0.0609774 0.998139i \(-0.480578\pi\)
−0.998139 + 0.0609774i \(0.980578\pi\)
\(858\) −2.08277 19.6608i −0.0711045 0.671207i
\(859\) −4.98573 4.98573i −0.170111 0.170111i 0.616917 0.787028i \(-0.288381\pi\)
−0.787028 + 0.616917i \(0.788381\pi\)
\(860\) −3.58489 + 1.73962i −0.122244 + 0.0593205i
\(861\) 9.08445 9.08445i 0.309597 0.309597i
\(862\) −29.5581 + 36.5627i −1.00675 + 1.24533i
\(863\) 25.4596 25.4596i 0.866653 0.866653i −0.125447 0.992100i \(-0.540037\pi\)
0.992100 + 0.125447i \(0.0400365\pi\)
\(864\) −1.22453 + 4.64630i −0.0416594 + 0.158070i
\(865\) 12.6692 + 51.6129i 0.430765 + 1.75489i
\(866\) −3.56376 33.6409i −0.121101 1.14316i
\(867\) 38.6258 1.31180
\(868\) 5.87463 9.07877i 0.199398 0.308153i
\(869\) 3.90968 3.90968i 0.132627 0.132627i
\(870\) 4.09684 + 11.3554i 0.138896 + 0.384985i
\(871\) −5.36983 −0.181950
\(872\) 38.9146 12.7503i 1.31782 0.431779i
\(873\) 23.7759 23.7759i 0.804691 0.804691i
\(874\) 14.8922 + 12.0392i 0.503736 + 0.407232i
\(875\) −11.1580 0.707012i −0.377208 0.0239014i
\(876\) −27.5536 + 42.5820i −0.930951 + 1.43871i
\(877\) 25.7942i 0.871008i 0.900187 + 0.435504i \(0.143430\pi\)
−0.900187 + 0.435504i \(0.856570\pi\)
\(878\) 24.0907 29.7996i 0.813022 1.00569i
\(879\) −50.0822 −1.68923
\(880\) 8.63380 + 1.06318i 0.291045 + 0.0358399i
\(881\) −40.4674 −1.36338 −0.681690 0.731641i \(-0.738755\pi\)
−0.681690 + 0.731641i \(0.738755\pi\)
\(882\) 2.34934 2.90608i 0.0791065 0.0978527i
\(883\) 11.0792i 0.372845i −0.982470 0.186423i \(-0.940311\pi\)
0.982470 0.186423i \(-0.0596893\pi\)
\(884\) 58.6007 + 37.9189i 1.97095 + 1.27535i
\(885\) −30.9702 18.7625i −1.04105 0.630696i
\(886\) 35.6880 + 28.8510i 1.19896 + 0.969269i
\(887\) 6.91864 6.91864i 0.232305 0.232305i −0.581349 0.813654i \(-0.697475\pi\)
0.813654 + 0.581349i \(0.197475\pi\)
\(888\) 41.8784 + 21.2082i 1.40535 + 0.711701i
\(889\) −1.89266 −0.0634778
\(890\) −2.01841 + 4.29684i −0.0676572 + 0.144030i
\(891\) −6.83928 + 6.83928i −0.229124 + 0.229124i
\(892\) −1.38921 0.898918i −0.0465141 0.0300980i
\(893\) −18.4878 −0.618669
\(894\) −0.740816 6.99310i −0.0247766 0.233884i
\(895\) 40.7768 + 24.7036i 1.36302 + 0.825751i
\(896\) −7.61859 8.36403i −0.254519 0.279423i
\(897\) −40.7928 + 40.7928i −1.36203 + 1.36203i
\(898\) −10.2091 + 12.6284i −0.340683 + 0.421416i
\(899\) 6.14426 6.14426i 0.204922 0.204922i
\(900\) 16.8708 + 20.3375i 0.562358 + 0.677915i
\(901\) 30.8295 + 30.8295i 1.02708 + 1.02708i
\(902\) −0.783679 7.39772i −0.0260937 0.246317i
\(903\) 1.49657 + 1.49657i 0.0498026 + 0.0498026i
\(904\) 49.5433 16.2327i 1.64778 0.539893i
\(905\) −28.4995 + 47.0424i −0.947354 + 1.56374i
\(906\) −7.41781 + 9.17564i −0.246440 + 0.304840i
\(907\) 1.13295i 0.0376191i 0.999823 + 0.0188095i \(0.00598762\pi\)
−0.999823 + 0.0188095i \(0.994012\pi\)
\(908\) 5.32535 + 24.8528i 0.176728 + 0.824771i
\(909\) 25.2879 + 25.2879i 0.838746 + 0.838746i
\(910\) −6.49420 18.0003i −0.215281 0.596705i
\(911\) 2.67816i 0.0887313i −0.999015 0.0443657i \(-0.985873\pi\)
0.999015 0.0443657i \(-0.0141267\pi\)
\(912\) 29.9659 + 11.3899i 0.992270 + 0.377159i
\(913\) −9.01100 9.01100i −0.298221 0.298221i
\(914\) 1.65025 + 15.5779i 0.0545853 + 0.515270i
\(915\) 7.32182 12.0857i 0.242052 0.399541i
\(916\) 26.1972 + 16.9515i 0.865581 + 0.560094i
\(917\) 5.44487 0.179805
\(918\) −0.729817 6.88927i −0.0240875 0.227380i
\(919\) 16.1154i 0.531597i −0.964029 0.265798i \(-0.914364\pi\)
0.964029 0.265798i \(-0.0856355\pi\)
\(920\) −13.4257 21.5419i −0.442633 0.710215i
\(921\) 32.8860i 1.08363i
\(922\) −23.9604 + 2.53825i −0.789094 + 0.0835929i
\(923\) 86.8948 2.86018
\(924\) −0.968080 4.51793i −0.0318475 0.148629i
\(925\) −30.9642 + 16.1759i −1.01810 + 0.531861i
\(926\) 28.4055 3.00914i 0.933462 0.0988866i
\(927\) 3.82978 + 3.82978i 0.125787 + 0.125787i
\(928\) −4.57787 7.85438i −0.150276 0.257833i
\(929\) 22.7868i 0.747611i 0.927507 + 0.373806i \(0.121947\pi\)
−0.927507 + 0.373806i \(0.878053\pi\)
\(930\) 17.2679 36.7602i 0.566235 1.20542i
\(931\) 2.38574 + 2.38574i 0.0781894 + 0.0781894i
\(932\) 0.416969 + 0.269810i 0.0136583 + 0.00883791i
\(933\) 61.6219i 2.01741i
\(934\) 42.1204 + 34.0512i 1.37822 + 1.11419i
\(935\) −12.1807 + 2.98994i −0.398352 + 0.0977815i
\(936\) −20.4332 + 40.3480i −0.667879 + 1.31881i
\(937\) −15.2719 15.2719i −0.498911 0.498911i 0.412188 0.911099i \(-0.364765\pi\)
−0.911099 + 0.412188i \(0.864765\pi\)
\(938\) −1.24796 + 0.132203i −0.0407474 + 0.00431659i
\(939\) 36.8571 + 36.8571i 1.20279 + 1.20279i
\(940\) 23.1543 + 8.02441i 0.755211 + 0.261727i
\(941\) 19.4676 19.4676i 0.634627 0.634627i −0.314598 0.949225i \(-0.601870\pi\)
0.949225 + 0.314598i \(0.101870\pi\)
\(942\) −34.2605 27.6970i −1.11627 0.902417i
\(943\) −15.3490 + 15.3490i −0.499833 + 0.499833i
\(944\) 25.4901 + 9.68872i 0.829633 + 0.315341i
\(945\) −0.984144 + 1.62447i −0.0320142 + 0.0528440i
\(946\) 1.21870 0.129103i 0.0396232 0.00419750i
\(947\) 29.0481 0.943938 0.471969 0.881615i \(-0.343543\pi\)
0.471969 + 0.881615i \(0.343543\pi\)
\(948\) −26.4086 + 5.65871i −0.857712 + 0.183786i
\(949\) 45.6820 45.6820i 1.48290 1.48290i
\(950\) −19.8644 + 13.2129i −0.644486 + 0.428682i
\(951\) 33.8988 1.09924
\(952\) 14.5525 + 7.36972i 0.471649 + 0.238854i
\(953\) 8.99401 8.99401i 0.291345 0.291345i −0.546267 0.837611i \(-0.683951\pi\)
0.837611 + 0.546267i \(0.183951\pi\)
\(954\) −17.7607 + 21.9696i −0.575025 + 0.711291i
\(955\) 25.9379 6.36686i 0.839331 0.206027i
\(956\) 7.97486 + 37.2179i 0.257925 + 1.20371i
\(957\) 3.71278i 0.120017i
\(958\) 4.25838 + 3.44258i 0.137582 + 0.111225i
\(959\) 6.78367 0.219056
\(960\) −32.5860 27.2713i −1.05171 0.880177i
\(961\) 1.76619 0.0569738
\(962\) −46.4992 37.5911i −1.49919 1.21198i
\(963\) 40.5480i 1.30664i
\(964\) −9.12619 42.5910i −0.293935 1.37176i
\(965\) −4.83246 + 7.97666i −0.155562 + 0.256778i
\(966\) −8.47604 + 10.4846i −0.272712 + 0.337338i
\(967\) 41.8479 41.8479i 1.34574 1.34574i 0.455501 0.890235i \(-0.349460\pi\)
0.890235 0.455501i \(-0.150540\pi\)
\(968\) 25.3695 + 12.8477i 0.815408 + 0.412942i
\(969\) −46.2208 −1.48483
\(970\) −13.6561 37.8512i −0.438469 1.21533i
\(971\) −5.67731 + 5.67731i −0.182194 + 0.182194i −0.792311 0.610117i \(-0.791122\pi\)
0.610117 + 0.792311i \(0.291122\pi\)
\(972\) 41.2138 8.83109i 1.32193 0.283257i
\(973\) 20.0714 0.643460
\(974\) −15.0594 + 1.59532i −0.482533 + 0.0511173i
\(975\) −33.2785 63.7022i −1.06577 2.04010i
\(976\) −3.78089 + 9.94717i −0.121023 + 0.318401i
\(977\) 24.9118 24.9118i 0.796998 0.796998i −0.185623 0.982621i \(-0.559430\pi\)
0.982621 + 0.185623i \(0.0594302\pi\)
\(978\) 32.7187 + 26.4506i 1.04623 + 0.845796i
\(979\) 1.03242 1.03242i 0.0329963 0.0329963i
\(980\) −1.95243 4.02343i −0.0623680 0.128524i
\(981\) −27.0518 27.0518i −0.863698 0.863698i
\(982\) −25.4937 + 2.70069i −0.813538 + 0.0861824i
\(983\) 10.4506 + 10.4506i 0.333323 + 0.333323i 0.853847 0.520524i \(-0.174263\pi\)
−0.520524 + 0.853847i \(0.674263\pi\)
\(984\) −16.4171 + 32.4178i −0.523359 + 1.03344i
\(985\) 1.63384 + 6.65609i 0.0520585 + 0.212081i
\(986\) 10.1933 + 8.24052i 0.324621 + 0.262432i
\(987\) 13.0161i 0.414305i
\(988\) −34.2825 22.1833i −1.09067 0.705745i
\(989\) −2.52859 2.52859i −0.0804045 0.0804045i
\(990\) −2.75804 7.64460i −0.0876562 0.242961i
\(991\) 2.78388i 0.0884328i 0.999022 + 0.0442164i \(0.0140791\pi\)
−0.999022 + 0.0442164i \(0.985921\pi\)
\(992\) −7.79468 + 29.5758i −0.247481 + 0.939031i
\(993\) −27.6044 27.6044i −0.875999 0.875999i
\(994\) 20.1946 2.13932i 0.640533 0.0678550i
\(995\) −51.0629 + 12.5342i −1.61880 + 0.397360i
\(996\) 13.0422 + 60.8664i 0.413257 + 1.92863i
\(997\) 42.6862 1.35189 0.675944 0.736953i \(-0.263736\pi\)
0.675944 + 0.736953i \(0.263736\pi\)
\(998\) 15.4727 1.63910i 0.489779 0.0518849i
\(999\) 5.93475i 0.187767i
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 560.2.t.a.43.16 144
5.2 odd 4 560.2.bl.a.267.54 yes 144
16.3 odd 4 560.2.bl.a.323.54 yes 144
80.67 even 4 inner 560.2.t.a.547.16 yes 144
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
560.2.t.a.43.16 144 1.1 even 1 trivial
560.2.t.a.547.16 yes 144 80.67 even 4 inner
560.2.bl.a.267.54 yes 144 5.2 odd 4
560.2.bl.a.323.54 yes 144 16.3 odd 4