Properties

Label 546.2.bn.f.101.17
Level $546$
Weight $2$
Character 546.101
Analytic conductor $4.360$
Analytic rank $0$
Dimension $34$
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(101,546)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(546, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([3, 1, 5]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("546.101");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 546 = 2 \cdot 3 \cdot 7 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 546.bn (of order \(6\), degree \(2\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(4.35983195036\)
Analytic rank: \(0\)
Dimension: \(34\)
Relative dimension: \(17\) over \(\Q(\zeta_{6})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 101.17
Character \(\chi\) \(=\) 546.101
Dual form 546.2.bn.f.173.17

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.500000 - 0.866025i) q^{2} +(1.73183 - 0.0276700i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(2.84717 - 1.64381i) q^{5} +(0.841952 - 1.51364i) q^{6} +(-0.683149 + 2.55603i) q^{7} -1.00000 q^{8} +(2.99847 - 0.0958395i) q^{9} +O(q^{10})\) \(q+(0.500000 - 0.866025i) q^{2} +(1.73183 - 0.0276700i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(2.84717 - 1.64381i) q^{5} +(0.841952 - 1.51364i) q^{6} +(-0.683149 + 2.55603i) q^{7} -1.00000 q^{8} +(2.99847 - 0.0958395i) q^{9} -3.28763i q^{10} +2.07020 q^{11} +(-0.889878 - 1.48597i) q^{12} +(-3.53365 + 0.716460i) q^{13} +(1.87202 + 1.86964i) q^{14} +(4.88532 - 2.92558i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(0.561810 + 0.973084i) q^{17} +(1.41623 - 2.64467i) q^{18} -1.01086 q^{19} +(-2.84717 - 1.64381i) q^{20} +(-1.11237 + 4.44552i) q^{21} +(1.03510 - 1.79285i) q^{22} +(-3.03183 - 1.75043i) q^{23} +(-1.73183 + 0.0276700i) q^{24} +(2.90424 - 5.03029i) q^{25} +(-1.14635 + 3.41846i) q^{26} +(5.19019 - 0.248945i) q^{27} +(2.55516 - 0.686393i) q^{28} +(-7.97573 + 4.60479i) q^{29} +(-0.0909687 - 5.69361i) q^{30} +(1.86666 - 3.23315i) q^{31} +(0.500000 + 0.866025i) q^{32} +(3.58524 - 0.0572825i) q^{33} +1.12362 q^{34} +(2.25660 + 8.40042i) q^{35} +(-1.58223 - 2.54883i) q^{36} +(-6.03816 - 3.48613i) q^{37} +(-0.505430 + 0.875431i) q^{38} +(-6.09986 + 1.33856i) q^{39} +(-2.84717 + 1.64381i) q^{40} +(-8.52566 + 4.92229i) q^{41} +(3.29375 + 3.18610i) q^{42} +(3.35600 - 5.81276i) q^{43} +(-1.03510 - 1.79285i) q^{44} +(8.37960 - 5.20179i) q^{45} +(-3.03183 + 1.75043i) q^{46} +(1.05515 - 0.609193i) q^{47} +(-0.841952 + 1.51364i) q^{48} +(-6.06662 - 3.49230i) q^{49} +(-2.90424 - 5.03029i) q^{50} +(0.999885 + 1.66967i) q^{51} +(2.38730 + 2.70200i) q^{52} +(5.05843 + 2.92049i) q^{53} +(2.37950 - 4.61931i) q^{54} +(5.89421 - 3.40302i) q^{55} +(0.683149 - 2.55603i) q^{56} +(-1.75064 + 0.0279705i) q^{57} +9.20958i q^{58} +(8.49492 - 4.90455i) q^{59} +(-4.97629 - 2.76802i) q^{60} +0.241991i q^{61} +(-1.86666 - 3.23315i) q^{62} +(-1.80343 + 7.72966i) q^{63} +1.00000 q^{64} +(-8.88317 + 7.84854i) q^{65} +(1.74301 - 3.13355i) q^{66} +11.8144i q^{67} +(0.561810 - 0.973084i) q^{68} +(-5.29905 - 2.94755i) q^{69} +(8.40328 + 2.24594i) q^{70} +(3.94585 - 6.83441i) q^{71} +(-2.99847 + 0.0958395i) q^{72} +(-0.878160 + 1.52102i) q^{73} +(-6.03816 + 3.48613i) q^{74} +(4.89046 - 8.79197i) q^{75} +(0.505430 + 0.875431i) q^{76} +(-1.41426 + 5.29150i) q^{77} +(-1.89070 + 5.95191i) q^{78} +(-2.48977 - 4.31240i) q^{79} +3.28763i q^{80} +(8.98163 - 0.574744i) q^{81} +9.84458i q^{82} +0.999900i q^{83} +(4.40612 - 1.25942i) q^{84} +(3.19914 + 1.84702i) q^{85} +(-3.35600 - 5.81276i) q^{86} +(-13.6852 + 8.19540i) q^{87} -2.07020 q^{88} +(6.59807 + 3.80940i) q^{89} +(-0.315084 - 9.85784i) q^{90} +(0.582714 - 9.52158i) q^{91} +3.50085i q^{92} +(3.14328 - 5.65092i) q^{93} -1.21839i q^{94} +(-2.87809 + 1.66167i) q^{95} +(0.889878 + 1.48597i) q^{96} +(3.21628 - 5.57077i) q^{97} +(-6.05773 + 3.50769i) q^{98} +(6.20743 - 0.198407i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 34 q + 17 q^{2} - 3 q^{3} - 17 q^{4} - 9 q^{5} + 3 q^{6} + 5 q^{7} - 34 q^{8} + 7 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 34 q + 17 q^{2} - 3 q^{3} - 17 q^{4} - 9 q^{5} + 3 q^{6} + 5 q^{7} - 34 q^{8} + 7 q^{9} + 18 q^{11} + 6 q^{12} - 8 q^{13} + 4 q^{14} - 4 q^{15} - 17 q^{16} - 6 q^{17} - 4 q^{18} - 10 q^{19} + 9 q^{20} + 7 q^{21} + 9 q^{22} - 6 q^{23} + 3 q^{24} + 16 q^{25} - 13 q^{26} - 18 q^{27} - q^{28} - 27 q^{29} + 13 q^{30} + q^{31} + 17 q^{32} + 21 q^{33} - 12 q^{34} + 3 q^{35} - 11 q^{36} + 6 q^{37} - 5 q^{38} - 2 q^{39} + 9 q^{40} - 3 q^{41} + 8 q^{42} - 3 q^{43} - 9 q^{44} + 9 q^{45} - 6 q^{46} + 27 q^{47} - 3 q^{48} - 5 q^{49} - 16 q^{50} - 36 q^{51} - 5 q^{52} - 21 q^{53} + 57 q^{55} - 5 q^{56} + 17 q^{57} + 6 q^{59} + 17 q^{60} - q^{62} + 34 q^{64} - 33 q^{65} - 6 q^{68} - 42 q^{69} + 3 q^{70} + 15 q^{71} - 7 q^{72} + 19 q^{73} + 6 q^{74} - 9 q^{75} + 5 q^{76} + 9 q^{77} - 7 q^{78} - 9 q^{79} - 5 q^{81} + q^{84} - 42 q^{85} + 3 q^{86} + 6 q^{87} - 18 q^{88} + 18 q^{89} + 9 q^{90} - 27 q^{91} + 8 q^{93} + 3 q^{95} - 6 q^{96} - 19 q^{97} - 7 q^{98} + 27 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

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

\(n\) \(157\) \(365\) \(379\)
\(\chi(n)\) \(e\left(\frac{1}{6}\right)\) \(-1\) \(e\left(\frac{5}{6}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.500000 0.866025i 0.353553 0.612372i
\(3\) 1.73183 0.0276700i 0.999872 0.0159753i
\(4\) −0.500000 0.866025i −0.250000 0.433013i
\(5\) 2.84717 1.64381i 1.27329 0.735135i 0.297686 0.954664i \(-0.403785\pi\)
0.975606 + 0.219529i \(0.0704519\pi\)
\(6\) 0.841952 1.51364i 0.343725 0.617942i
\(7\) −0.683149 + 2.55603i −0.258206 + 0.966090i
\(8\) −1.00000 −0.353553
\(9\) 2.99847 0.0958395i 0.999490 0.0319465i
\(10\) 3.28763i 1.03964i
\(11\) 2.07020 0.624189 0.312095 0.950051i \(-0.398969\pi\)
0.312095 + 0.950051i \(0.398969\pi\)
\(12\) −0.889878 1.48597i −0.256886 0.428964i
\(13\) −3.53365 + 0.716460i −0.980058 + 0.198710i
\(14\) 1.87202 + 1.86964i 0.500317 + 0.499683i
\(15\) 4.88532 2.92558i 1.26139 0.755383i
\(16\) −0.500000 + 0.866025i −0.125000 + 0.216506i
\(17\) 0.561810 + 0.973084i 0.136259 + 0.236008i 0.926078 0.377333i \(-0.123159\pi\)
−0.789819 + 0.613340i \(0.789825\pi\)
\(18\) 1.41623 2.64467i 0.333810 0.623355i
\(19\) −1.01086 −0.231907 −0.115954 0.993255i \(-0.536992\pi\)
−0.115954 + 0.993255i \(0.536992\pi\)
\(20\) −2.84717 1.64381i −0.636646 0.367568i
\(21\) −1.11237 + 4.44552i −0.242739 + 0.970092i
\(22\) 1.03510 1.79285i 0.220684 0.382236i
\(23\) −3.03183 1.75043i −0.632180 0.364989i 0.149416 0.988774i \(-0.452261\pi\)
−0.781596 + 0.623785i \(0.785594\pi\)
\(24\) −1.73183 + 0.0276700i −0.353508 + 0.00564812i
\(25\) 2.90424 5.03029i 0.580848 1.00606i
\(26\) −1.14635 + 3.41846i −0.224818 + 0.670415i
\(27\) 5.19019 0.248945i 0.998852 0.0479096i
\(28\) 2.55516 0.686393i 0.482881 0.129716i
\(29\) −7.97573 + 4.60479i −1.48106 + 0.855088i −0.999769 0.0214746i \(-0.993164\pi\)
−0.481287 + 0.876563i \(0.659831\pi\)
\(30\) −0.0909687 5.69361i −0.0166085 1.03951i
\(31\) 1.86666 3.23315i 0.335262 0.580691i −0.648273 0.761408i \(-0.724508\pi\)
0.983535 + 0.180717i \(0.0578418\pi\)
\(32\) 0.500000 + 0.866025i 0.0883883 + 0.153093i
\(33\) 3.58524 0.0572825i 0.624109 0.00997160i
\(34\) 1.12362 0.192699
\(35\) 2.25660 + 8.40042i 0.381435 + 1.41993i
\(36\) −1.58223 2.54883i −0.263706 0.424805i
\(37\) −6.03816 3.48613i −0.992667 0.573116i −0.0865963 0.996243i \(-0.527599\pi\)
−0.906070 + 0.423127i \(0.860932\pi\)
\(38\) −0.505430 + 0.875431i −0.0819916 + 0.142014i
\(39\) −6.09986 + 1.33856i −0.976759 + 0.214342i
\(40\) −2.84717 + 1.64381i −0.450177 + 0.259910i
\(41\) −8.52566 + 4.92229i −1.33148 + 0.768733i −0.985527 0.169517i \(-0.945779\pi\)
−0.345957 + 0.938250i \(0.612446\pi\)
\(42\) 3.29375 + 3.18610i 0.508236 + 0.491626i
\(43\) 3.35600 5.81276i 0.511785 0.886438i −0.488122 0.872776i \(-0.662318\pi\)
0.999907 0.0136621i \(-0.00434890\pi\)
\(44\) −1.03510 1.79285i −0.156047 0.270282i
\(45\) 8.37960 5.20179i 1.24916 0.775437i
\(46\) −3.03183 + 1.75043i −0.447019 + 0.258086i
\(47\) 1.05515 0.609193i 0.153910 0.0888599i −0.421067 0.907029i \(-0.638344\pi\)
0.574977 + 0.818170i \(0.305011\pi\)
\(48\) −0.841952 + 1.51364i −0.121525 + 0.218476i
\(49\) −6.06662 3.49230i −0.866659 0.498900i
\(50\) −2.90424 5.03029i −0.410722 0.711391i
\(51\) 0.999885 + 1.66967i 0.140012 + 0.233801i
\(52\) 2.38730 + 2.70200i 0.331059 + 0.374700i
\(53\) 5.05843 + 2.92049i 0.694829 + 0.401160i 0.805419 0.592706i \(-0.201941\pi\)
−0.110589 + 0.993866i \(0.535274\pi\)
\(54\) 2.37950 4.61931i 0.323809 0.628608i
\(55\) 5.89421 3.40302i 0.794775 0.458863i
\(56\) 0.683149 2.55603i 0.0912896 0.341564i
\(57\) −1.75064 + 0.0279705i −0.231878 + 0.00370479i
\(58\) 9.20958i 1.20928i
\(59\) 8.49492 4.90455i 1.10594 0.638517i 0.168169 0.985758i \(-0.446215\pi\)
0.937776 + 0.347241i \(0.112881\pi\)
\(60\) −4.97629 2.76802i −0.642437 0.357350i
\(61\) 0.241991i 0.0309838i 0.999880 + 0.0154919i \(0.00493142\pi\)
−0.999880 + 0.0154919i \(0.995069\pi\)
\(62\) −1.86666 3.23315i −0.237066 0.410611i
\(63\) −1.80343 + 7.72966i −0.227211 + 0.973846i
\(64\) 1.00000 0.125000
\(65\) −8.88317 + 7.84854i −1.10182 + 0.973492i
\(66\) 1.74301 3.13355i 0.214550 0.385713i
\(67\) 11.8144i 1.44336i 0.692226 + 0.721680i \(0.256630\pi\)
−0.692226 + 0.721680i \(0.743370\pi\)
\(68\) 0.561810 0.973084i 0.0681295 0.118004i
\(69\) −5.29905 2.94755i −0.637930 0.354843i
\(70\) 8.40328 + 2.24594i 1.00438 + 0.268441i
\(71\) 3.94585 6.83441i 0.468286 0.811096i −0.531057 0.847336i \(-0.678205\pi\)
0.999343 + 0.0362405i \(0.0115383\pi\)
\(72\) −2.99847 + 0.0958395i −0.353373 + 0.0112948i
\(73\) −0.878160 + 1.52102i −0.102781 + 0.178022i −0.912829 0.408341i \(-0.866107\pi\)
0.810049 + 0.586363i \(0.199441\pi\)
\(74\) −6.03816 + 3.48613i −0.701921 + 0.405254i
\(75\) 4.89046 8.79197i 0.564702 1.01521i
\(76\) 0.505430 + 0.875431i 0.0579768 + 0.100419i
\(77\) −1.41426 + 5.29150i −0.161169 + 0.603023i
\(78\) −1.89070 + 5.95191i −0.214079 + 0.673921i
\(79\) −2.48977 4.31240i −0.280121 0.485183i 0.691294 0.722574i \(-0.257041\pi\)
−0.971414 + 0.237391i \(0.923708\pi\)
\(80\) 3.28763i 0.367568i
\(81\) 8.98163 0.574744i 0.997959 0.0638604i
\(82\) 9.84458i 1.08715i
\(83\) 0.999900i 0.109753i 0.998493 + 0.0548767i \(0.0174766\pi\)
−0.998493 + 0.0548767i \(0.982523\pi\)
\(84\) 4.40612 1.25942i 0.480747 0.137414i
\(85\) 3.19914 + 1.84702i 0.346995 + 0.200338i
\(86\) −3.35600 5.81276i −0.361887 0.626806i
\(87\) −13.6852 + 8.19540i −1.46721 + 0.878640i
\(88\) −2.07020 −0.220684
\(89\) 6.59807 + 3.80940i 0.699394 + 0.403795i 0.807122 0.590385i \(-0.201024\pi\)
−0.107728 + 0.994180i \(0.534358\pi\)
\(90\) −0.315084 9.85784i −0.0332128 1.03911i
\(91\) 0.582714 9.52158i 0.0610850 0.998133i
\(92\) 3.50085i 0.364989i
\(93\) 3.14328 5.65092i 0.325943 0.585973i
\(94\) 1.21839i 0.125667i
\(95\) −2.87809 + 1.66167i −0.295286 + 0.170483i
\(96\) 0.889878 + 1.48597i 0.0908228 + 0.151662i
\(97\) 3.21628 5.57077i 0.326564 0.565626i −0.655264 0.755400i \(-0.727442\pi\)
0.981828 + 0.189775i \(0.0607757\pi\)
\(98\) −6.05773 + 3.50769i −0.611923 + 0.354330i
\(99\) 6.20743 0.198407i 0.623870 0.0199407i
\(100\) −5.80848 −0.580848
\(101\) −19.3241 −1.92282 −0.961409 0.275123i \(-0.911281\pi\)
−0.961409 + 0.275123i \(0.911281\pi\)
\(102\) 1.94592 0.0310906i 0.192675 0.00307843i
\(103\) −7.86720 + 4.54213i −0.775178 + 0.447549i −0.834719 0.550677i \(-0.814370\pi\)
0.0595405 + 0.998226i \(0.481036\pi\)
\(104\) 3.53365 0.716460i 0.346503 0.0702547i
\(105\) 4.14049 + 14.4857i 0.404070 + 1.41366i
\(106\) 5.05843 2.92049i 0.491318 0.283663i
\(107\) 3.25929 + 1.88175i 0.315088 + 0.181916i 0.649201 0.760617i \(-0.275103\pi\)
−0.334113 + 0.942533i \(0.608437\pi\)
\(108\) −2.81069 4.37036i −0.270458 0.420538i
\(109\) 2.43945 + 1.40841i 0.233657 + 0.134902i 0.612258 0.790658i \(-0.290261\pi\)
−0.378601 + 0.925560i \(0.623595\pi\)
\(110\) 6.80604i 0.648931i
\(111\) −10.5535 5.87031i −1.00170 0.557185i
\(112\) −1.87202 1.86964i −0.176889 0.176664i
\(113\) 4.57774 + 2.64296i 0.430637 + 0.248629i 0.699618 0.714517i \(-0.253354\pi\)
−0.268981 + 0.963146i \(0.586687\pi\)
\(114\) −0.851096 + 1.53008i −0.0797124 + 0.143305i
\(115\) −11.5095 −1.07327
\(116\) 7.97573 + 4.60479i 0.740528 + 0.427544i
\(117\) −10.5269 + 2.48695i −0.973210 + 0.229918i
\(118\) 9.80909i 0.903000i
\(119\) −2.87104 + 0.771245i −0.263187 + 0.0706999i
\(120\) −4.88532 + 2.92558i −0.445967 + 0.267068i
\(121\) −6.71427 −0.610388
\(122\) 0.209571 + 0.120996i 0.0189736 + 0.0109544i
\(123\) −14.6288 + 8.76048i −1.31903 + 0.789906i
\(124\) −3.73332 −0.335262
\(125\) 2.65798i 0.237737i
\(126\) 5.79237 + 5.42665i 0.516025 + 0.483444i
\(127\) 9.40084 + 16.2827i 0.834190 + 1.44486i 0.894688 + 0.446691i \(0.147398\pi\)
−0.0604988 + 0.998168i \(0.519269\pi\)
\(128\) 0.500000 0.866025i 0.0441942 0.0765466i
\(129\) 5.65118 10.1596i 0.497559 0.894500i
\(130\) 2.35545 + 11.6173i 0.206587 + 1.01891i
\(131\) 1.45204 + 2.51500i 0.126865 + 0.219737i 0.922460 0.386092i \(-0.126175\pi\)
−0.795595 + 0.605828i \(0.792842\pi\)
\(132\) −1.84223 3.07626i −0.160345 0.267754i
\(133\) 0.690568 2.58379i 0.0598799 0.224043i
\(134\) 10.2316 + 5.90721i 0.883874 + 0.510305i
\(135\) 14.3681 9.24048i 1.23661 0.795294i
\(136\) −0.561810 0.973084i −0.0481748 0.0834413i
\(137\) 10.5895 + 18.3416i 0.904724 + 1.56703i 0.821288 + 0.570515i \(0.193256\pi\)
0.0834363 + 0.996513i \(0.473410\pi\)
\(138\) −5.20218 + 3.11533i −0.442839 + 0.265195i
\(139\) −17.6205 10.1732i −1.49455 0.862878i −0.494568 0.869139i \(-0.664674\pi\)
−0.999980 + 0.00626156i \(0.998007\pi\)
\(140\) 6.14668 6.15449i 0.519489 0.520149i
\(141\) 1.81049 1.08421i 0.152471 0.0913073i
\(142\) −3.94585 6.83441i −0.331128 0.573531i
\(143\) −7.31537 + 1.48322i −0.611742 + 0.124033i
\(144\) −1.41623 + 2.64467i −0.118020 + 0.220389i
\(145\) −15.1388 + 26.2212i −1.25721 + 2.17755i
\(146\) 0.878160 + 1.52102i 0.0726770 + 0.125880i
\(147\) −10.6030 5.88021i −0.874519 0.484992i
\(148\) 6.97226i 0.573116i
\(149\) 13.2500 1.08549 0.542743 0.839899i \(-0.317386\pi\)
0.542743 + 0.839899i \(0.317386\pi\)
\(150\) −5.16884 8.63125i −0.422034 0.704738i
\(151\) 15.0137 + 8.66818i 1.22180 + 0.705407i 0.965301 0.261138i \(-0.0840978\pi\)
0.256499 + 0.966545i \(0.417431\pi\)
\(152\) 1.01086 0.0819916
\(153\) 1.77783 + 2.86392i 0.143729 + 0.231534i
\(154\) 3.87545 + 3.87053i 0.312293 + 0.311896i
\(155\) 12.2738i 0.985852i
\(156\) 4.20916 + 4.61335i 0.337002 + 0.369364i
\(157\) 12.2223 + 7.05652i 0.975442 + 0.563172i 0.900891 0.434045i \(-0.142914\pi\)
0.0745511 + 0.997217i \(0.476248\pi\)
\(158\) −4.97953 −0.396150
\(159\) 8.84115 + 4.91782i 0.701149 + 0.390008i
\(160\) 2.84717 + 1.64381i 0.225088 + 0.129955i
\(161\) 6.54534 6.55365i 0.515845 0.516500i
\(162\) 3.99307 8.06569i 0.313725 0.633701i
\(163\) 10.3152i 0.807947i −0.914771 0.403974i \(-0.867629\pi\)
0.914771 0.403974i \(-0.132371\pi\)
\(164\) 8.52566 + 4.92229i 0.665742 + 0.384366i
\(165\) 10.1136 6.05655i 0.787343 0.471502i
\(166\) 0.865939 + 0.499950i 0.0672099 + 0.0388037i
\(167\) 12.1099 6.99167i 0.937094 0.541032i 0.0480461 0.998845i \(-0.484701\pi\)
0.889048 + 0.457813i \(0.151367\pi\)
\(168\) 1.11237 4.44552i 0.0858214 0.342979i
\(169\) 11.9734 5.06344i 0.921028 0.389495i
\(170\) 3.19914 1.84702i 0.245363 0.141660i
\(171\) −3.03103 + 0.0968804i −0.231789 + 0.00740863i
\(172\) −6.71200 −0.511785
\(173\) −5.07795 −0.386069 −0.193035 0.981192i \(-0.561833\pi\)
−0.193035 + 0.981192i \(0.561833\pi\)
\(174\) 0.254829 + 15.9494i 0.0193186 + 1.20912i
\(175\) 10.8736 + 10.8598i 0.821964 + 0.820922i
\(176\) −1.03510 + 1.79285i −0.0780236 + 0.135141i
\(177\) 14.5760 8.72889i 1.09560 0.656104i
\(178\) 6.59807 3.80940i 0.494546 0.285526i
\(179\) 11.7132i 0.875486i 0.899100 + 0.437743i \(0.144222\pi\)
−0.899100 + 0.437743i \(0.855778\pi\)
\(180\) −8.69468 4.65605i −0.648063 0.347041i
\(181\) 22.6731i 1.68528i −0.538480 0.842638i \(-0.681001\pi\)
0.538480 0.842638i \(-0.318999\pi\)
\(182\) −7.95457 5.26543i −0.589632 0.390300i
\(183\) 0.00669590 + 0.419088i 0.000494975 + 0.0309798i
\(184\) 3.03183 + 1.75043i 0.223509 + 0.129043i
\(185\) −22.9222 −1.68527
\(186\) −3.32220 5.54762i −0.243596 0.406771i
\(187\) 1.16306 + 2.01448i 0.0850514 + 0.147313i
\(188\) −1.05515 0.609193i −0.0769549 0.0444299i
\(189\) −2.90936 + 13.4364i −0.211625 + 0.977351i
\(190\) 3.32333i 0.241100i
\(191\) 25.8552i 1.87082i 0.353570 + 0.935408i \(0.384968\pi\)
−0.353570 + 0.935408i \(0.615032\pi\)
\(192\) 1.73183 0.0276700i 0.124984 0.00199691i
\(193\) 21.8098i 1.56990i −0.619558 0.784951i \(-0.712688\pi\)
0.619558 0.784951i \(-0.287312\pi\)
\(194\) −3.21628 5.57077i −0.230916 0.399958i
\(195\) −15.1670 + 13.8381i −1.08613 + 0.990969i
\(196\) 0.00888497 + 6.99999i 0.000634641 + 0.500000i
\(197\) −3.51025 6.07993i −0.250095 0.433177i 0.713457 0.700699i \(-0.247128\pi\)
−0.963552 + 0.267522i \(0.913795\pi\)
\(198\) 2.93189 5.47500i 0.208360 0.389091i
\(199\) −13.0589 + 7.53954i −0.925719 + 0.534464i −0.885455 0.464725i \(-0.846153\pi\)
−0.0402638 + 0.999189i \(0.512820\pi\)
\(200\) −2.90424 + 5.03029i −0.205361 + 0.355695i
\(201\) 0.326905 + 20.4606i 0.0230581 + 1.44318i
\(202\) −9.66204 + 16.7351i −0.679819 + 1.17748i
\(203\) −6.32139 23.5320i −0.443675 1.65162i
\(204\) 0.946035 1.70076i 0.0662357 0.119077i
\(205\) −16.1827 + 28.0292i −1.13025 + 1.95764i
\(206\) 9.08426i 0.632930i
\(207\) −9.25860 4.95803i −0.643517 0.344607i
\(208\) 1.14635 3.41846i 0.0794853 0.237028i
\(209\) −2.09268 −0.144754
\(210\) 14.6152 + 3.65706i 1.00854 + 0.252361i
\(211\) −10.2101 17.6845i −0.702895 1.21745i −0.967446 0.253079i \(-0.918557\pi\)
0.264550 0.964372i \(-0.414776\pi\)
\(212\) 5.84097i 0.401160i
\(213\) 6.64443 11.9452i 0.455269 0.818473i
\(214\) 3.25929 1.88175i 0.222801 0.128634i
\(215\) 22.0665i 1.50493i
\(216\) −5.19019 + 0.248945i −0.353147 + 0.0169386i
\(217\) 6.98884 + 6.97997i 0.474433 + 0.473831i
\(218\) 2.43945 1.40841i 0.165220 0.0953899i
\(219\) −1.47874 + 2.65844i −0.0999238 + 0.179641i
\(220\) −5.89421 3.40302i −0.397387 0.229432i
\(221\) −2.68242 3.03602i −0.180439 0.204225i
\(222\) −10.3606 + 6.20446i −0.695358 + 0.416416i
\(223\) −1.37326 2.37855i −0.0919602 0.159280i 0.816376 0.577521i \(-0.195980\pi\)
−0.908336 + 0.418241i \(0.862647\pi\)
\(224\) −2.55516 + 0.686393i −0.170724 + 0.0458615i
\(225\) 8.22617 15.3615i 0.548411 1.02410i
\(226\) 4.57774 2.64296i 0.304507 0.175807i
\(227\) 7.77691 4.49000i 0.516172 0.298012i −0.219195 0.975681i \(-0.570343\pi\)
0.735367 + 0.677669i \(0.237010\pi\)
\(228\) 0.899542 + 1.50211i 0.0595736 + 0.0994798i
\(229\) −8.23500 14.2634i −0.544184 0.942554i −0.998658 0.0517940i \(-0.983506\pi\)
0.454474 0.890760i \(-0.349827\pi\)
\(230\) −5.75475 + 9.96752i −0.379457 + 0.657239i
\(231\) −2.30283 + 9.20311i −0.151515 + 0.605521i
\(232\) 7.97573 4.60479i 0.523633 0.302319i
\(233\) −4.79194 + 2.76663i −0.313931 + 0.181248i −0.648684 0.761058i \(-0.724680\pi\)
0.334753 + 0.942306i \(0.391347\pi\)
\(234\) −3.10968 + 10.3600i −0.203286 + 0.677255i
\(235\) 2.00280 3.46895i 0.130648 0.226289i
\(236\) −8.49492 4.90455i −0.552972 0.319259i
\(237\) −4.43118 7.39946i −0.287836 0.480646i
\(238\) −0.767600 + 2.87201i −0.0497561 + 0.186165i
\(239\) −4.33497 −0.280406 −0.140203 0.990123i \(-0.544776\pi\)
−0.140203 + 0.990123i \(0.544776\pi\)
\(240\) 0.0909687 + 5.69361i 0.00587200 + 0.367521i
\(241\) 2.10349 + 3.64335i 0.135498 + 0.234689i 0.925787 0.378044i \(-0.123403\pi\)
−0.790290 + 0.612733i \(0.790070\pi\)
\(242\) −3.35713 + 5.81473i −0.215805 + 0.373785i
\(243\) 15.5388 1.24388i 0.996811 0.0797949i
\(244\) 0.209571 0.120996i 0.0134164 0.00774595i
\(245\) −23.0134 + 0.0292105i −1.47027 + 0.00186619i
\(246\) 0.272400 + 17.0491i 0.0173676 + 1.08701i
\(247\) 3.57203 0.724241i 0.227283 0.0460824i
\(248\) −1.86666 + 3.23315i −0.118533 + 0.205305i
\(249\) 0.0276673 + 1.73166i 0.00175334 + 0.109739i
\(250\) −2.30188 1.32899i −0.145583 0.0840526i
\(251\) 9.79168 16.9597i 0.618045 1.07049i −0.371797 0.928314i \(-0.621258\pi\)
0.989842 0.142172i \(-0.0454086\pi\)
\(252\) 7.59580 2.30301i 0.478490 0.145076i
\(253\) −6.27649 3.62374i −0.394600 0.227822i
\(254\) 18.8017 1.17972
\(255\) 5.59147 + 3.11021i 0.350151 + 0.194769i
\(256\) −0.500000 0.866025i −0.0312500 0.0541266i
\(257\) −8.97486 + 15.5449i −0.559837 + 0.969665i 0.437673 + 0.899134i \(0.355803\pi\)
−0.997510 + 0.0705311i \(0.977531\pi\)
\(258\) −5.97286 9.97385i −0.371854 0.620945i
\(259\) 13.0356 13.0522i 0.809994 0.811023i
\(260\) 11.2386 + 3.76878i 0.696990 + 0.233730i
\(261\) −23.4737 + 14.5717i −1.45298 + 0.901967i
\(262\) 2.90408 0.179414
\(263\) 27.8469i 1.71711i −0.512717 0.858557i \(-0.671361\pi\)
0.512717 0.858557i \(-0.328639\pi\)
\(264\) −3.58524 + 0.0572825i −0.220656 + 0.00352549i
\(265\) 19.2029 1.17963
\(266\) −1.89235 1.88995i −0.116027 0.115880i
\(267\) 11.5321 + 6.41466i 0.705755 + 0.392571i
\(268\) 10.2316 5.90721i 0.624994 0.360840i
\(269\) −14.1534 24.5145i −0.862951 1.49467i −0.869068 0.494693i \(-0.835280\pi\)
0.00611690 0.999981i \(-0.498053\pi\)
\(270\) −0.818439 17.0634i −0.0498086 1.03844i
\(271\) 12.6519 21.9137i 0.768546 1.33116i −0.169806 0.985478i \(-0.554314\pi\)
0.938352 0.345682i \(-0.112353\pi\)
\(272\) −1.12362 −0.0681295
\(273\) 0.745698 16.5059i 0.0451317 0.998981i
\(274\) 21.1790 1.27947
\(275\) 6.01236 10.4137i 0.362559 0.627970i
\(276\) 0.0968687 + 6.06288i 0.00583081 + 0.364943i
\(277\) 6.54676 + 11.3393i 0.393356 + 0.681313i 0.992890 0.119036i \(-0.0379805\pi\)
−0.599533 + 0.800350i \(0.704647\pi\)
\(278\) −17.6205 + 10.1732i −1.05680 + 0.610147i
\(279\) 5.28726 9.87340i 0.316540 0.591105i
\(280\) −2.25660 8.40042i −0.134858 0.502021i
\(281\) 16.5616 0.987980 0.493990 0.869468i \(-0.335538\pi\)
0.493990 + 0.869468i \(0.335538\pi\)
\(282\) −0.0337127 2.11004i −0.00200756 0.125651i
\(283\) 18.3919i 1.09328i −0.837367 0.546642i \(-0.815906\pi\)
0.837367 0.546642i \(-0.184094\pi\)
\(284\) −7.89170 −0.468286
\(285\) −4.93838 + 2.95736i −0.292524 + 0.175179i
\(286\) −2.37318 + 7.07690i −0.140329 + 0.418466i
\(287\) −6.75725 25.1545i −0.398868 1.48483i
\(288\) 1.58223 + 2.54883i 0.0932340 + 0.150191i
\(289\) 7.86874 13.6291i 0.462867 0.801709i
\(290\) 15.1388 + 26.2212i 0.888983 + 1.53976i
\(291\) 5.41591 9.73662i 0.317486 0.570771i
\(292\) 1.75632 0.102781
\(293\) −7.37759 4.25945i −0.431003 0.248840i 0.268771 0.963204i \(-0.413383\pi\)
−0.699774 + 0.714364i \(0.746716\pi\)
\(294\) −10.3939 + 6.24234i −0.606185 + 0.364061i
\(295\) 16.1243 27.9281i 0.938793 1.62604i
\(296\) 6.03816 + 3.48613i 0.350961 + 0.202627i
\(297\) 10.7447 0.515367i 0.623472 0.0299046i
\(298\) 6.62502 11.4749i 0.383777 0.664721i
\(299\) 11.9675 + 4.01321i 0.692100 + 0.232090i
\(300\) −10.0593 + 0.160721i −0.580774 + 0.00927922i
\(301\) 12.5650 + 12.5490i 0.724233 + 0.723314i
\(302\) 15.0137 8.66818i 0.863943 0.498798i
\(303\) −33.4660 + 0.534698i −1.92257 + 0.0307176i
\(304\) 0.505430 0.875431i 0.0289884 0.0502094i
\(305\) 0.397788 + 0.688989i 0.0227773 + 0.0394514i
\(306\) 3.36914 0.107687i 0.192601 0.00615607i
\(307\) 21.3161 1.21658 0.608288 0.793716i \(-0.291857\pi\)
0.608288 + 0.793716i \(0.291857\pi\)
\(308\) 5.28970 1.42097i 0.301409 0.0809673i
\(309\) −13.4990 + 8.08388i −0.767930 + 0.459876i
\(310\) −10.6294 6.13688i −0.603709 0.348551i
\(311\) 7.40693 12.8292i 0.420008 0.727476i −0.575931 0.817498i \(-0.695361\pi\)
0.995940 + 0.0900223i \(0.0286938\pi\)
\(312\) 6.09986 1.33856i 0.345336 0.0757812i
\(313\) −22.7031 + 13.1077i −1.28326 + 0.740889i −0.977442 0.211203i \(-0.932262\pi\)
−0.305814 + 0.952091i \(0.598929\pi\)
\(314\) 12.2223 7.05652i 0.689742 0.398223i
\(315\) 7.57144 + 24.9721i 0.426602 + 1.40702i
\(316\) −2.48977 + 4.31240i −0.140060 + 0.242592i
\(317\) 9.80532 + 16.9833i 0.550722 + 0.953878i 0.998223 + 0.0595945i \(0.0189808\pi\)
−0.447501 + 0.894283i \(0.647686\pi\)
\(318\) 8.67953 5.19775i 0.486724 0.291476i
\(319\) −16.5114 + 9.53284i −0.924459 + 0.533737i
\(320\) 2.84717 1.64381i 0.159161 0.0918919i
\(321\) 5.69661 + 3.16869i 0.317954 + 0.176859i
\(322\) −2.40296 8.94526i −0.133912 0.498500i
\(323\) −0.567912 0.983652i −0.0315995 0.0547319i
\(324\) −4.98856 7.49095i −0.277142 0.416164i
\(325\) −6.65857 + 19.8561i −0.369351 + 1.10142i
\(326\) −8.93321 5.15759i −0.494765 0.285652i
\(327\) 4.26368 + 2.37163i 0.235782 + 0.131152i
\(328\) 8.52566 4.92229i 0.470751 0.271788i
\(329\) 0.836291 + 3.11317i 0.0461062 + 0.171635i
\(330\) −0.188323 11.7869i −0.0103669 0.648848i
\(331\) 26.0774i 1.43334i 0.697412 + 0.716671i \(0.254335\pi\)
−0.697412 + 0.716671i \(0.745665\pi\)
\(332\) 0.865939 0.499950i 0.0475246 0.0274383i
\(333\) −18.4393 9.87436i −1.01047 0.541112i
\(334\) 13.9833i 0.765134i
\(335\) 19.4207 + 33.6376i 1.06107 + 1.83782i
\(336\) −3.29375 3.18610i −0.179689 0.173816i
\(337\) −13.5184 −0.736394 −0.368197 0.929748i \(-0.620025\pi\)
−0.368197 + 0.929748i \(0.620025\pi\)
\(338\) 1.60162 12.9010i 0.0871166 0.701720i
\(339\) 8.00099 + 4.45049i 0.434554 + 0.241717i
\(340\) 3.69404i 0.200338i
\(341\) 3.86436 6.69327i 0.209267 0.362461i
\(342\) −1.43162 + 2.67339i −0.0774129 + 0.144561i
\(343\) 13.0708 13.1207i 0.705759 0.708452i
\(344\) −3.35600 + 5.81276i −0.180943 + 0.313403i
\(345\) −19.9325 + 0.318468i −1.07313 + 0.0171457i
\(346\) −2.53897 + 4.39763i −0.136496 + 0.236418i
\(347\) 29.0781 16.7882i 1.56099 0.901239i 0.563835 0.825887i \(-0.309325\pi\)
0.997157 0.0753519i \(-0.0240080\pi\)
\(348\) 13.9400 + 7.75403i 0.747264 + 0.415659i
\(349\) −11.8845 20.5845i −0.636161 1.10186i −0.986268 0.165153i \(-0.947188\pi\)
0.350107 0.936710i \(-0.386145\pi\)
\(350\) 14.8416 3.98690i 0.793318 0.213109i
\(351\) −18.1619 + 4.59825i −0.969413 + 0.245436i
\(352\) 1.03510 + 1.79285i 0.0551710 + 0.0955590i
\(353\) 10.7207i 0.570608i 0.958437 + 0.285304i \(0.0920945\pi\)
−0.958437 + 0.285304i \(0.907905\pi\)
\(354\) −0.271418 16.9877i −0.0144257 0.902885i
\(355\) 25.9450i 1.37702i
\(356\) 7.61879i 0.403795i
\(357\) −4.95081 + 1.41511i −0.262024 + 0.0748954i
\(358\) 10.1439 + 5.85660i 0.536123 + 0.309531i
\(359\) 7.26878 + 12.5899i 0.383632 + 0.664469i 0.991578 0.129508i \(-0.0413399\pi\)
−0.607947 + 0.793978i \(0.708007\pi\)
\(360\) −8.37960 + 5.20179i −0.441644 + 0.274159i
\(361\) −17.9782 −0.946219
\(362\) −19.6355 11.3365i −1.03202 0.595835i
\(363\) −11.6280 + 0.185784i −0.610310 + 0.00975113i
\(364\) −8.53729 + 4.25614i −0.447475 + 0.223083i
\(365\) 5.77412i 0.302231i
\(366\) 0.366288 + 0.203745i 0.0191462 + 0.0106499i
\(367\) 17.4965i 0.913308i −0.889644 0.456654i \(-0.849048\pi\)
0.889644 0.456654i \(-0.150952\pi\)
\(368\) 3.03183 1.75043i 0.158045 0.0912473i
\(369\) −25.0922 + 15.5764i −1.30625 + 0.810877i
\(370\) −11.4611 + 19.8512i −0.595834 + 1.03201i
\(371\) −10.9205 + 10.9344i −0.566965 + 0.567686i
\(372\) −6.46548 + 0.103301i −0.335219 + 0.00535591i
\(373\) −11.8665 −0.614423 −0.307211 0.951641i \(-0.599396\pi\)
−0.307211 + 0.951641i \(0.599396\pi\)
\(374\) 2.32612 0.120281
\(375\) −0.0735463 4.60316i −0.00379791 0.237706i
\(376\) −1.05515 + 0.609193i −0.0544153 + 0.0314167i
\(377\) 24.8843 21.9860i 1.28161 1.13234i
\(378\) 10.1815 + 9.23775i 0.523682 + 0.475139i
\(379\) 10.9141 6.30127i 0.560620 0.323674i −0.192774 0.981243i \(-0.561748\pi\)
0.753394 + 0.657569i \(0.228415\pi\)
\(380\) 2.87809 + 1.66167i 0.147643 + 0.0852416i
\(381\) 16.7312 + 27.9388i 0.857165 + 1.43135i
\(382\) 22.3913 + 12.9276i 1.14564 + 0.661433i
\(383\) 1.06335i 0.0543345i 0.999631 + 0.0271672i \(0.00864866\pi\)
−0.999631 + 0.0271672i \(0.991351\pi\)
\(384\) 0.841952 1.51364i 0.0429657 0.0772428i
\(385\) 4.67162 + 17.3906i 0.238088 + 0.886305i
\(386\) −18.8878 10.9049i −0.961364 0.555044i
\(387\) 9.50577 17.7510i 0.483205 0.902335i
\(388\) −6.43257 −0.326564
\(389\) 2.28039 + 1.31658i 0.115620 + 0.0667534i 0.556695 0.830717i \(-0.312069\pi\)
−0.441075 + 0.897470i \(0.645403\pi\)
\(390\) 4.40069 + 20.0540i 0.222838 + 1.01548i
\(391\) 3.93363i 0.198932i
\(392\) 6.06662 + 3.49230i 0.306410 + 0.176388i
\(393\) 2.58427 + 4.31538i 0.130359 + 0.217682i
\(394\) −7.02050 −0.353688
\(395\) −14.1776 8.18542i −0.713351 0.411853i
\(396\) −3.27554 5.27659i −0.164602 0.265159i
\(397\) −8.54714 −0.428969 −0.214484 0.976727i \(-0.568807\pi\)
−0.214484 + 0.976727i \(0.568807\pi\)
\(398\) 15.0791i 0.755846i
\(399\) 1.12445 4.49380i 0.0562931 0.224971i
\(400\) 2.90424 + 5.03029i 0.145212 + 0.251515i
\(401\) 7.78768 13.4887i 0.388898 0.673592i −0.603403 0.797436i \(-0.706189\pi\)
0.992302 + 0.123845i \(0.0395224\pi\)
\(402\) 17.8828 + 9.94717i 0.891914 + 0.496120i
\(403\) −4.27970 + 12.7622i −0.213187 + 0.635731i
\(404\) 9.66204 + 16.7351i 0.480705 + 0.832605i
\(405\) 24.6274 16.4005i 1.22375 0.814948i
\(406\) −23.5400 6.29152i −1.16827 0.312243i
\(407\) −12.5002 7.21699i −0.619612 0.357733i
\(408\) −0.999885 1.66967i −0.0495017 0.0826610i
\(409\) 5.40484 + 9.36145i 0.267252 + 0.462894i 0.968151 0.250366i \(-0.0805511\pi\)
−0.700899 + 0.713260i \(0.747218\pi\)
\(410\) 16.1827 + 28.0292i 0.799204 + 1.38426i
\(411\) 18.8468 + 31.4715i 0.929642 + 1.55237i
\(412\) 7.86720 + 4.54213i 0.387589 + 0.223775i
\(413\) 6.73289 + 25.0638i 0.331304 + 1.23331i
\(414\) −8.92308 + 5.53917i −0.438546 + 0.272235i
\(415\) 1.64365 + 2.84688i 0.0806836 + 0.139748i
\(416\) −2.38730 2.70200i −0.117047 0.132477i
\(417\) −30.7971 17.1307i −1.50814 0.838892i
\(418\) −1.04634 + 1.81232i −0.0511783 + 0.0886434i
\(419\) 7.13932 + 12.3657i 0.348779 + 0.604102i 0.986033 0.166551i \(-0.0532632\pi\)
−0.637254 + 0.770654i \(0.719930\pi\)
\(420\) 10.4747 10.8286i 0.511113 0.528382i
\(421\) 31.1553i 1.51842i 0.650848 + 0.759208i \(0.274414\pi\)
−0.650848 + 0.759208i \(0.725586\pi\)
\(422\) −20.4203 −0.994044
\(423\) 3.10546 1.92777i 0.150993 0.0937314i
\(424\) −5.05843 2.92049i −0.245659 0.141831i
\(425\) 6.52653 0.316583
\(426\) −7.02265 11.7269i −0.340249 0.568168i
\(427\) −0.618538 0.165316i −0.0299331 0.00800020i
\(428\) 3.76351i 0.181916i
\(429\) −12.6279 + 2.77109i −0.609682 + 0.133790i
\(430\) −19.1102 11.0333i −0.921575 0.532071i
\(431\) −21.5902 −1.03996 −0.519981 0.854178i \(-0.674061\pi\)
−0.519981 + 0.854178i \(0.674061\pi\)
\(432\) −2.37950 + 4.61931i −0.114484 + 0.222246i
\(433\) −16.2009 9.35358i −0.778565 0.449505i 0.0573567 0.998354i \(-0.481733\pi\)
−0.835921 + 0.548849i \(0.815066\pi\)
\(434\) 9.53925 2.56252i 0.457899 0.123005i
\(435\) −25.4923 + 45.8296i −1.22226 + 2.19736i
\(436\) 2.81683i 0.134902i
\(437\) 3.06476 + 1.76944i 0.146607 + 0.0846437i
\(438\) 1.56291 + 2.60985i 0.0746787 + 0.124703i
\(439\) −12.4456 7.18545i −0.593994 0.342943i 0.172681 0.984978i \(-0.444757\pi\)
−0.766675 + 0.642035i \(0.778090\pi\)
\(440\) −5.89421 + 3.40302i −0.280995 + 0.162233i
\(441\) −18.5253 9.89014i −0.882155 0.470959i
\(442\) −3.97048 + 0.805029i −0.188857 + 0.0382913i
\(443\) −1.21594 + 0.702023i −0.0577711 + 0.0333541i −0.528607 0.848866i \(-0.677286\pi\)
0.470836 + 0.882221i \(0.343952\pi\)
\(444\) 0.192923 + 12.0748i 0.00915570 + 0.573043i
\(445\) 25.0477 1.18738
\(446\) −2.74652 −0.130051
\(447\) 22.9468 0.366629i 1.08535 0.0173409i
\(448\) −0.683149 + 2.55603i −0.0322757 + 0.120761i
\(449\) 11.0266 19.0987i 0.520379 0.901323i −0.479340 0.877629i \(-0.659124\pi\)
0.999719 0.0236937i \(-0.00754264\pi\)
\(450\) −9.19037 14.8048i −0.433238 0.697906i
\(451\) −17.6498 + 10.1901i −0.831098 + 0.479835i
\(452\) 5.28591i 0.248629i
\(453\) 26.2411 + 14.5964i 1.23291 + 0.685798i
\(454\) 8.98000i 0.421453i
\(455\) −13.9926 28.0674i −0.655984 1.31582i
\(456\) 1.75064 0.0279705i 0.0819812 0.00130984i
\(457\) 36.6548 + 21.1627i 1.71464 + 0.989948i 0.928036 + 0.372491i \(0.121496\pi\)
0.786604 + 0.617457i \(0.211837\pi\)
\(458\) −16.4700 −0.769592
\(459\) 3.15815 + 4.91063i 0.147410 + 0.229208i
\(460\) 5.75475 + 9.96752i 0.268317 + 0.464738i
\(461\) −10.2913 5.94166i −0.479312 0.276731i 0.240818 0.970570i \(-0.422584\pi\)
−0.720130 + 0.693839i \(0.755918\pi\)
\(462\) 6.81871 + 6.59587i 0.317235 + 0.306868i
\(463\) 3.56440i 0.165652i 0.996564 + 0.0828258i \(0.0263945\pi\)
−0.996564 + 0.0828258i \(0.973605\pi\)
\(464\) 9.20958i 0.427544i
\(465\) −0.339615 21.2561i −0.0157493 0.985727i
\(466\) 5.53326i 0.256323i
\(467\) 3.56143 + 6.16858i 0.164803 + 0.285448i 0.936585 0.350439i \(-0.113968\pi\)
−0.771782 + 0.635887i \(0.780634\pi\)
\(468\) 7.41720 + 7.87307i 0.342860 + 0.363933i
\(469\) −30.1981 8.07101i −1.39442 0.372684i
\(470\) −2.00280 3.46895i −0.0923821 0.160011i
\(471\) 21.3621 + 11.8825i 0.984314 + 0.547517i
\(472\) −8.49492 + 4.90455i −0.391010 + 0.225750i
\(473\) 6.94759 12.0336i 0.319451 0.553305i
\(474\) −8.62370 + 0.137784i −0.396100 + 0.00632862i
\(475\) −2.93578 + 5.08492i −0.134703 + 0.233312i
\(476\) 2.10344 + 2.10077i 0.0964108 + 0.0962885i
\(477\) 15.4474 + 8.27219i 0.707290 + 0.378758i
\(478\) −2.16749 + 3.75420i −0.0991386 + 0.171713i
\(479\) 30.5472i 1.39574i 0.716225 + 0.697870i \(0.245868\pi\)
−0.716225 + 0.697870i \(0.754132\pi\)
\(480\) 4.97629 + 2.76802i 0.227136 + 0.126342i
\(481\) 23.8344 + 7.99267i 1.08676 + 0.364434i
\(482\) 4.20698 0.191623
\(483\) 11.1541 11.5309i 0.507528 0.524675i
\(484\) 3.35713 + 5.81473i 0.152597 + 0.264306i
\(485\) 21.1479i 0.960275i
\(486\) 6.69214 14.0789i 0.303562 0.638632i
\(487\) −27.7303 + 16.0101i −1.25658 + 0.725488i −0.972408 0.233285i \(-0.925052\pi\)
−0.284173 + 0.958773i \(0.591719\pi\)
\(488\) 0.241991i 0.0109544i
\(489\) −0.285421 17.8641i −0.0129072 0.807844i
\(490\) −11.4814 + 19.9448i −0.518676 + 0.901012i
\(491\) 13.0865 7.55549i 0.590585 0.340975i −0.174744 0.984614i \(-0.555910\pi\)
0.765329 + 0.643639i \(0.222576\pi\)
\(492\) 14.9012 + 8.28867i 0.671798 + 0.373682i
\(493\) −8.96170 5.17404i −0.403615 0.233027i
\(494\) 1.15880 3.45559i 0.0521370 0.155474i
\(495\) 17.3475 10.7688i 0.779710 0.484019i
\(496\) 1.86666 + 3.23315i 0.0838156 + 0.145173i
\(497\) 14.7734 + 14.7546i 0.662677 + 0.661836i
\(498\) 1.51349 + 0.841868i 0.0678212 + 0.0377250i
\(499\) 4.18606 2.41682i 0.187394 0.108192i −0.403368 0.915038i \(-0.632161\pi\)
0.590762 + 0.806846i \(0.298827\pi\)
\(500\) −2.30188 + 1.32899i −0.102943 + 0.0594342i
\(501\) 20.7789 12.4435i 0.928332 0.555933i
\(502\) −9.79168 16.9597i −0.437024 0.756948i
\(503\) −13.7946 + 23.8930i −0.615073 + 1.06534i 0.375299 + 0.926904i \(0.377540\pi\)
−0.990372 + 0.138433i \(0.955793\pi\)
\(504\) 1.80343 7.72966i 0.0803312 0.344306i
\(505\) −55.0189 + 31.7652i −2.44831 + 1.41353i
\(506\) −6.27649 + 3.62374i −0.279024 + 0.161095i
\(507\) 20.5957 9.10032i 0.914689 0.404159i
\(508\) 9.40084 16.2827i 0.417095 0.722429i
\(509\) −27.1836 15.6945i −1.20489 0.695645i −0.243253 0.969963i \(-0.578214\pi\)
−0.961639 + 0.274318i \(0.911548\pi\)
\(510\) 5.48925 3.28725i 0.243068 0.145562i
\(511\) −3.28786 3.28369i −0.145446 0.145262i
\(512\) −1.00000 −0.0441942
\(513\) −5.24655 + 0.251649i −0.231641 + 0.0111106i
\(514\) 8.97486 + 15.5449i 0.395864 + 0.685657i
\(515\) −14.9328 + 25.8644i −0.658019 + 1.13972i
\(516\) −11.6240 + 0.185721i −0.511720 + 0.00817592i
\(517\) 2.18438 1.26115i 0.0960688 0.0554654i
\(518\) −4.78571 17.8153i −0.210272 0.782758i
\(519\) −8.79414 + 0.140507i −0.386020 + 0.00616757i
\(520\) 8.88317 7.84854i 0.389553 0.344181i
\(521\) −0.178115 + 0.308505i −0.00780338 + 0.0135159i −0.869901 0.493227i \(-0.835817\pi\)
0.862097 + 0.506743i \(0.169151\pi\)
\(522\) 0.882642 + 27.6146i 0.0386322 + 1.20866i
\(523\) 21.5730 + 12.4552i 0.943320 + 0.544626i 0.891000 0.454004i \(-0.150005\pi\)
0.0523207 + 0.998630i \(0.483338\pi\)
\(524\) 1.45204 2.51500i 0.0634326 0.109868i
\(525\) 19.1317 + 18.5064i 0.834974 + 0.807686i
\(526\) −24.1161 13.9235i −1.05151 0.607092i
\(527\) 4.19484 0.182730
\(528\) −1.74301 + 3.13355i −0.0758548 + 0.136370i
\(529\) −5.37201 9.30459i −0.233566 0.404548i
\(530\) 9.60147 16.6302i 0.417061 0.722371i
\(531\) 25.0017 15.5203i 1.08498 0.673523i
\(532\) −2.58291 + 0.693847i −0.111984 + 0.0300821i
\(533\) 26.6001 23.5020i 1.15218 1.01798i
\(534\) 11.3213 6.77979i 0.489922 0.293390i
\(535\) 12.3730 0.534931
\(536\) 11.8144i 0.510305i
\(537\) 0.324105 + 20.2853i 0.0139861 + 0.875374i
\(538\) −28.3069 −1.22040
\(539\) −12.5591 7.22977i −0.540959 0.311408i
\(540\) −15.1865 7.82290i −0.653525 0.336644i
\(541\) −17.5713 + 10.1448i −0.755447 + 0.436158i −0.827659 0.561232i \(-0.810328\pi\)
0.0722115 + 0.997389i \(0.476994\pi\)
\(542\) −12.6519 21.9137i −0.543444 0.941272i
\(543\) −0.627364 39.2659i −0.0269228 1.68506i
\(544\) −0.561810 + 0.973084i −0.0240874 + 0.0417206i
\(545\) 9.26068 0.396684
\(546\) −13.9217 8.89873i −0.595792 0.380831i
\(547\) −18.3443 −0.784344 −0.392172 0.919892i \(-0.628276\pi\)
−0.392172 + 0.919892i \(0.628276\pi\)
\(548\) 10.5895 18.3416i 0.452362 0.783514i
\(549\) 0.0231923 + 0.725603i 0.000989824 + 0.0309680i
\(550\) −6.01236 10.4137i −0.256368 0.444042i
\(551\) 8.06235 4.65480i 0.343468 0.198301i
\(552\) 5.29905 + 2.94755i 0.225542 + 0.125456i
\(553\) 12.7235 3.41791i 0.541059 0.145345i
\(554\) 13.0935 0.556290
\(555\) −39.6973 + 0.634257i −1.68506 + 0.0269227i
\(556\) 20.3464i 0.862878i
\(557\) 12.1781 0.516004 0.258002 0.966144i \(-0.416936\pi\)
0.258002 + 0.966144i \(0.416936\pi\)
\(558\) −5.90699 9.51560i −0.250063 0.402828i
\(559\) −7.69432 + 22.9447i −0.325435 + 0.970457i
\(560\) −8.40328 2.24594i −0.355103 0.0949082i
\(561\) 2.06996 + 3.45655i 0.0873939 + 0.145936i
\(562\) 8.28078 14.3427i 0.349304 0.605012i
\(563\) 5.68587 + 9.84822i 0.239631 + 0.415053i 0.960608 0.277906i \(-0.0896403\pi\)
−0.720978 + 0.692958i \(0.756307\pi\)
\(564\) −1.84420 1.02582i −0.0776549 0.0431949i
\(565\) 17.3781 0.731102
\(566\) −15.9278 9.19594i −0.669497 0.386534i
\(567\) −4.66673 + 23.3500i −0.195984 + 0.980607i
\(568\) −3.94585 + 6.83441i −0.165564 + 0.286766i
\(569\) 20.8276 + 12.0248i 0.873140 + 0.504108i 0.868391 0.495881i \(-0.165155\pi\)
0.00474984 + 0.999989i \(0.498488\pi\)
\(570\) 0.0919566 + 5.75544i 0.00385164 + 0.241069i
\(571\) 3.64194 6.30802i 0.152410 0.263983i −0.779703 0.626150i \(-0.784630\pi\)
0.932113 + 0.362167i \(0.117963\pi\)
\(572\) 4.94219 + 5.59369i 0.206643 + 0.233884i
\(573\) 0.715414 + 44.7768i 0.0298868 + 1.87058i
\(574\) −25.1631 6.72532i −1.05029 0.280709i
\(575\) −17.6103 + 10.1673i −0.734401 + 0.424007i
\(576\) 2.99847 0.0958395i 0.124936 0.00399331i
\(577\) 2.11186 3.65785i 0.0879179 0.152278i −0.818713 0.574203i \(-0.805312\pi\)
0.906631 + 0.421925i \(0.138645\pi\)
\(578\) −7.86874 13.6291i −0.327296 0.566894i
\(579\) −0.603477 37.7708i −0.0250796 1.56970i
\(580\) 30.2777 1.25721
\(581\) −2.55578 0.683081i −0.106032 0.0283390i
\(582\) −5.72420 9.55863i −0.237276 0.396218i
\(583\) 10.4720 + 6.04600i 0.433705 + 0.250400i
\(584\) 0.878160 1.52102i 0.0363385 0.0629402i
\(585\) −25.8837 + 24.3850i −1.07016 + 1.00819i
\(586\) −7.37759 + 4.25945i −0.304765 + 0.175956i
\(587\) −39.5103 + 22.8113i −1.63077 + 0.941523i −0.646908 + 0.762568i \(0.723938\pi\)
−0.983857 + 0.178954i \(0.942729\pi\)
\(588\) 0.209077 + 12.1226i 0.00862220 + 0.499926i
\(589\) −1.88693 + 3.26827i −0.0777498 + 0.134667i
\(590\) −16.1243 27.9281i −0.663827 1.14978i
\(591\) −6.24738 10.4323i −0.256983 0.429126i
\(592\) 6.03816 3.48613i 0.248167 0.143279i
\(593\) 21.1653 12.2198i 0.869154 0.501807i 0.00208732 0.999998i \(-0.499336\pi\)
0.867067 + 0.498191i \(0.166002\pi\)
\(594\) 4.92604 9.56289i 0.202118 0.392370i
\(595\) −6.90654 + 6.91531i −0.283140 + 0.283500i
\(596\) −6.62502 11.4749i −0.271371 0.470029i
\(597\) −22.4071 + 13.4185i −0.917062 + 0.549184i
\(598\) 9.45931 8.35758i 0.386820 0.341767i
\(599\) 11.4214 + 6.59416i 0.466667 + 0.269430i 0.714843 0.699285i \(-0.246498\pi\)
−0.248177 + 0.968715i \(0.579831\pi\)
\(600\) −4.89046 + 8.79197i −0.199652 + 0.358931i
\(601\) −34.6176 + 19.9865i −1.41208 + 0.815266i −0.995584 0.0938714i \(-0.970076\pi\)
−0.416497 + 0.909137i \(0.636742\pi\)
\(602\) 17.1503 4.60707i 0.698992 0.187770i
\(603\) 1.13229 + 35.4252i 0.0461103 + 1.44262i
\(604\) 17.3364i 0.705407i
\(605\) −19.1166 + 11.0370i −0.777202 + 0.448718i
\(606\) −16.2699 + 29.2498i −0.660922 + 1.18819i
\(607\) 20.1780i 0.819000i 0.912310 + 0.409500i \(0.134297\pi\)
−0.912310 + 0.409500i \(0.865703\pi\)
\(608\) −0.505430 0.875431i −0.0204979 0.0355034i
\(609\) −11.5987 40.5785i −0.470003 1.64432i
\(610\) 0.795576 0.0322119
\(611\) −3.29208 + 2.90865i −0.133183 + 0.117671i
\(612\) 1.59131 2.97161i 0.0643249 0.120120i
\(613\) 24.9422i 1.00741i −0.863877 0.503703i \(-0.831970\pi\)
0.863877 0.503703i \(-0.168030\pi\)
\(614\) 10.6581 18.4603i 0.430124 0.744997i
\(615\) −27.2500 + 48.9895i −1.09883 + 1.97545i
\(616\) 1.41426 5.29150i 0.0569820 0.213201i
\(617\) −1.22499 + 2.12175i −0.0493164 + 0.0854185i −0.889630 0.456682i \(-0.849038\pi\)
0.840313 + 0.542101i \(0.182371\pi\)
\(618\) 0.251362 + 15.7324i 0.0101112 + 0.632850i
\(619\) 11.9145 20.6365i 0.478883 0.829449i −0.520824 0.853664i \(-0.674375\pi\)
0.999707 + 0.0242147i \(0.00770853\pi\)
\(620\) −10.6294 + 6.13688i −0.426887 + 0.246463i
\(621\) −16.1715 8.33028i −0.648941 0.334283i
\(622\) −7.40693 12.8292i −0.296991 0.514403i
\(623\) −14.2444 + 14.2625i −0.570690 + 0.571415i
\(624\) 1.89070 5.95191i 0.0756885 0.238267i
\(625\) 10.1520 + 17.5837i 0.406079 + 0.703350i
\(626\) 26.2153i 1.04777i
\(627\) −3.62417 + 0.0579046i −0.144736 + 0.00231249i
\(628\) 14.1130i 0.563172i
\(629\) 7.83418i 0.312369i
\(630\) 25.4122 + 5.92901i 1.01245 + 0.236217i
\(631\) −17.5516 10.1334i −0.698718 0.403405i 0.108152 0.994134i \(-0.465507\pi\)
−0.806870 + 0.590729i \(0.798840\pi\)
\(632\) 2.48977 + 4.31240i 0.0990376 + 0.171538i
\(633\) −18.1716 30.3440i −0.722255 1.20607i
\(634\) 19.6106 0.778838
\(635\) 53.5315 + 30.9064i 2.12433 + 1.22648i
\(636\) −0.161620 10.1156i −0.00640865 0.401109i
\(637\) 23.9394 + 7.99409i 0.948513 + 0.316737i
\(638\) 19.0657i 0.754818i
\(639\) 11.1765 20.8709i 0.442136 0.825642i
\(640\) 3.28763i 0.129955i
\(641\) −28.8080 + 16.6323i −1.13785 + 0.656938i −0.945897 0.324467i \(-0.894815\pi\)
−0.191952 + 0.981404i \(0.561482\pi\)
\(642\) 5.59247 3.34906i 0.220717 0.132177i
\(643\) 3.65734 6.33469i 0.144231 0.249816i −0.784855 0.619680i \(-0.787262\pi\)
0.929086 + 0.369864i \(0.120596\pi\)
\(644\) −8.94830 2.39160i −0.352612 0.0942424i
\(645\) −0.610581 38.2155i −0.0240416 1.50473i
\(646\) −1.13582 −0.0446884
\(647\) −32.0372 −1.25951 −0.629757 0.776792i \(-0.716846\pi\)
−0.629757 + 0.776792i \(0.716846\pi\)
\(648\) −8.98163 + 0.574744i −0.352832 + 0.0225781i
\(649\) 17.5862 10.1534i 0.690319 0.398556i
\(650\) 13.8666 + 15.6945i 0.543892 + 0.615590i
\(651\) 12.2966 + 11.8947i 0.481942 + 0.466192i
\(652\) −8.93321 + 5.15759i −0.349851 + 0.201987i
\(653\) 29.1377 + 16.8227i 1.14025 + 0.658321i 0.946491 0.322729i \(-0.104600\pi\)
0.193754 + 0.981050i \(0.437934\pi\)
\(654\) 4.18573 2.50663i 0.163675 0.0980171i
\(655\) 8.26839 + 4.77376i 0.323073 + 0.186526i
\(656\) 9.84458i 0.384366i
\(657\) −2.48736 + 4.64489i −0.0970412 + 0.181214i
\(658\) 3.11423 + 0.832338i 0.121405 + 0.0324479i
\(659\) −21.1966 12.2379i −0.825704 0.476720i 0.0266755 0.999644i \(-0.491508\pi\)
−0.852379 + 0.522924i \(0.824841\pi\)
\(660\) −10.3019 5.73036i −0.401002 0.223054i
\(661\) 5.55570 0.216092 0.108046 0.994146i \(-0.465541\pi\)
0.108046 + 0.994146i \(0.465541\pi\)
\(662\) 22.5837 + 13.0387i 0.877739 + 0.506763i
\(663\) −4.72950 5.18366i −0.183678 0.201317i
\(664\) 0.999900i 0.0388037i
\(665\) −2.28111 8.49166i −0.0884576 0.329292i
\(666\) −17.7711 + 11.0317i −0.688617 + 0.427472i
\(667\) 32.2414 1.24839
\(668\) −12.1099 6.99167i −0.468547 0.270516i
\(669\) −2.44407 4.08125i −0.0944930 0.157790i
\(670\) 38.8414 1.50057
\(671\) 0.500970i 0.0193397i
\(672\) −4.40612 + 1.25942i −0.169970 + 0.0485830i
\(673\) 9.31475 + 16.1336i 0.359057 + 0.621905i 0.987804 0.155705i \(-0.0497649\pi\)
−0.628746 + 0.777610i \(0.716432\pi\)
\(674\) −6.75920 + 11.7073i −0.260355 + 0.450947i
\(675\) 13.8213 26.8311i 0.531981 1.03273i
\(676\) −10.3718 7.83752i −0.398913 0.301443i
\(677\) 13.4512 + 23.2982i 0.516972 + 0.895422i 0.999806 + 0.0197102i \(0.00627434\pi\)
−0.482833 + 0.875712i \(0.660392\pi\)
\(678\) 7.85473 4.70382i 0.301659 0.180649i
\(679\) 12.0419 + 12.0266i 0.462124 + 0.461538i
\(680\) −3.19914 1.84702i −0.122681 0.0708301i
\(681\) 13.3440 7.99111i 0.511345 0.306220i
\(682\) −3.86436 6.69327i −0.147974 0.256299i
\(683\) 20.3836 + 35.3055i 0.779958 + 1.35093i 0.931965 + 0.362548i \(0.118093\pi\)
−0.152007 + 0.988379i \(0.548574\pi\)
\(684\) 1.59942 + 2.57651i 0.0611553 + 0.0985154i
\(685\) 60.3003 + 34.8144i 2.30395 + 1.33019i
\(686\) −4.82745 17.8800i −0.184313 0.682663i
\(687\) −14.6563 24.4740i −0.559172 0.933740i
\(688\) 3.35600 + 5.81276i 0.127946 + 0.221609i
\(689\) −19.9671 6.69582i −0.760688 0.255090i
\(690\) −9.69044 + 17.4213i −0.368909 + 0.663217i
\(691\) 6.89853 11.9486i 0.262432 0.454546i −0.704455 0.709748i \(-0.748809\pi\)
0.966888 + 0.255202i \(0.0821420\pi\)
\(692\) 2.53897 + 4.39763i 0.0965173 + 0.167173i
\(693\) −3.73347 + 16.0019i −0.141823 + 0.607864i
\(694\) 33.5765i 1.27454i
\(695\) −66.8912 −2.53733
\(696\) 13.6852 8.19540i 0.518736 0.310646i
\(697\) −9.57961 5.53079i −0.362854 0.209494i
\(698\) −23.7689 −0.899667
\(699\) −8.22228 + 4.92393i −0.310995 + 0.186240i
\(700\) 3.96806 14.8467i 0.149978 0.561151i
\(701\) 9.30649i 0.351501i −0.984435 0.175751i \(-0.943765\pi\)
0.984435 0.175751i \(-0.0562352\pi\)
\(702\) −5.09877 + 18.0278i −0.192441 + 0.680416i
\(703\) 6.10373 + 3.52399i 0.230207 + 0.132910i
\(704\) 2.07020 0.0780236
\(705\) 3.37252 6.06304i 0.127016 0.228347i
\(706\) 9.28444 + 5.36037i 0.349425 + 0.201740i
\(707\) 13.2012 49.3930i 0.496483 1.85762i
\(708\) −14.8475 8.25878i −0.558002 0.310384i
\(709\) 3.09917i 0.116392i −0.998305 0.0581958i \(-0.981465\pi\)
0.998305 0.0581958i \(-0.0185348\pi\)
\(710\) −22.4690 12.9725i −0.843246 0.486848i
\(711\) −7.87879 12.6920i −0.295478 0.475987i
\(712\) −6.59807 3.80940i −0.247273 0.142763i
\(713\) −11.3188 + 6.53491i −0.423892 + 0.244734i
\(714\) −1.24988 + 4.99508i −0.0467757 + 0.186936i
\(715\) −18.3899 + 16.2481i −0.687745 + 0.607643i
\(716\) 10.1439 5.85660i 0.379097 0.218871i
\(717\) −7.50744 + 0.119949i −0.280370 + 0.00447957i
\(718\) 14.5376 0.542537
\(719\) −11.7740 −0.439098 −0.219549 0.975602i \(-0.570459\pi\)
−0.219549 + 0.975602i \(0.570459\pi\)
\(720\) 0.315084 + 9.85784i 0.0117425 + 0.367380i
\(721\) −6.23537 23.2118i −0.232217 0.864452i
\(722\) −8.98908 + 15.5695i −0.334539 + 0.579438i
\(723\) 3.74370 + 6.25146i 0.139230 + 0.232494i
\(724\) −19.6355 + 11.3365i −0.729746 + 0.421319i
\(725\) 53.4937i 1.98671i
\(726\) −5.65309 + 10.1630i −0.209806 + 0.377185i
\(727\) 13.8729i 0.514518i 0.966342 + 0.257259i \(0.0828194\pi\)
−0.966342 + 0.257259i \(0.917181\pi\)
\(728\) −0.582714 + 9.52158i −0.0215968 + 0.352893i
\(729\) 26.8761 2.58415i 0.995409 0.0957091i
\(730\) 5.00054 + 2.88706i 0.185078 + 0.106855i
\(731\) 7.54174 0.278941
\(732\) 0.359592 0.215343i 0.0132909 0.00795929i
\(733\) −21.6003 37.4129i −0.797827 1.38188i −0.921029 0.389495i \(-0.872650\pi\)
0.123202 0.992382i \(-0.460684\pi\)
\(734\) −15.1524 8.74823i −0.559284 0.322903i
\(735\) −39.8544 + 0.687368i −1.47005 + 0.0253539i
\(736\) 3.50085i 0.129043i
\(737\) 24.4582i 0.900930i
\(738\) 0.943500 + 29.5187i 0.0347307 + 1.08660i
\(739\) 34.1756i 1.25717i 0.777741 + 0.628585i \(0.216365\pi\)
−0.777741 + 0.628585i \(0.783635\pi\)
\(740\) 11.4611 + 19.8512i 0.421318 + 0.729744i
\(741\) 6.16610 1.35310i 0.226517 0.0497074i
\(742\) 4.00920 + 14.9247i 0.147182 + 0.547901i
\(743\) 15.6321 + 27.0755i 0.573484 + 0.993304i 0.996204 + 0.0870439i \(0.0277420\pi\)
−0.422720 + 0.906260i \(0.638925\pi\)
\(744\) −3.14328 + 5.65092i −0.115238 + 0.207173i
\(745\) 37.7251 21.7806i 1.38214 0.797978i
\(746\) −5.93324 + 10.2767i −0.217231 + 0.376256i
\(747\) 0.0958300 + 2.99817i 0.00350624 + 0.109697i
\(748\) 1.16306 2.01448i 0.0425257 0.0736567i
\(749\) −7.03641 + 7.04534i −0.257105 + 0.257431i
\(750\) −4.02323 2.23789i −0.146908 0.0817162i
\(751\) −1.05163 + 1.82147i −0.0383744 + 0.0664664i −0.884575 0.466398i \(-0.845551\pi\)
0.846200 + 0.532865i \(0.178885\pi\)
\(752\) 1.21839i 0.0444299i
\(753\) 16.4883 29.6422i 0.600865 1.08022i
\(754\) −6.59830 32.5434i −0.240296 1.18516i
\(755\) 56.9955 2.07428
\(756\) 13.0909 4.19860i 0.476112 0.152702i
\(757\) 16.8638 + 29.2089i 0.612924 + 1.06162i 0.990745 + 0.135737i \(0.0433402\pi\)
−0.377821 + 0.925879i \(0.623326\pi\)
\(758\) 12.6025i 0.457745i
\(759\) −10.9701 6.10202i −0.398189 0.221489i
\(760\) 2.87809 1.66167i 0.104399 0.0602749i
\(761\) 19.2154i 0.696556i −0.937391 0.348278i \(-0.886767\pi\)
0.937391 0.348278i \(-0.113233\pi\)
\(762\) 32.5613 0.520243i 1.17957 0.0188464i
\(763\) −5.26646 + 5.27315i −0.190659 + 0.190901i
\(764\) 22.3913 12.9276i 0.810087 0.467704i
\(765\) 9.76953 + 5.23163i 0.353218 + 0.189150i
\(766\) 0.920885 + 0.531673i 0.0332729 + 0.0192101i
\(767\) −26.5042 + 23.4172i −0.957010 + 0.845547i
\(768\) −0.889878 1.48597i −0.0321107 0.0536205i
\(769\) −19.1381 33.1482i −0.690139 1.19536i −0.971792 0.235840i \(-0.924216\pi\)
0.281653 0.959516i \(-0.409117\pi\)
\(770\) 17.3965 + 4.64954i 0.626926 + 0.167558i
\(771\) −15.1128 + 27.1695i −0.544274 + 0.978485i
\(772\) −18.8878 + 10.9049i −0.679787 + 0.392475i
\(773\) 2.18604 1.26211i 0.0786263 0.0453949i −0.460171 0.887830i \(-0.652212\pi\)
0.538798 + 0.842435i \(0.318879\pi\)
\(774\) −10.6199 17.1077i −0.381726 0.614925i
\(775\) −10.8425 18.7797i −0.389473 0.674587i
\(776\) −3.21628 + 5.57077i −0.115458 + 0.199979i
\(777\) 22.2143 22.9649i 0.796935 0.823860i
\(778\) 2.28039 1.31658i 0.0817558 0.0472018i
\(779\) 8.61825 4.97575i 0.308781 0.178275i
\(780\) 19.5677 + 6.21591i 0.700634 + 0.222565i
\(781\) 8.16870 14.1486i 0.292299 0.506277i
\(782\) −3.40663 1.96682i −0.121821 0.0703332i
\(783\) −40.2492 + 25.8852i −1.43839 + 0.925063i
\(784\) 6.05773 3.50769i 0.216348 0.125275i
\(785\) 46.3984 1.65603
\(786\) 5.02937 0.0803559i 0.179392 0.00286620i
\(787\) −0.882459 1.52846i −0.0314563 0.0544839i 0.849869 0.526995i \(-0.176681\pi\)
−0.881325 + 0.472511i \(0.843348\pi\)
\(788\) −3.51025 + 6.07993i −0.125047 + 0.216588i
\(789\) −0.770525 48.2261i −0.0274314 1.71690i
\(790\) −14.1776 + 8.18542i −0.504415 + 0.291224i
\(791\) −9.88276 + 9.89532i −0.351391 + 0.351837i
\(792\) −6.20743 + 0.198407i −0.220572 + 0.00705009i
\(793\) −0.173377 0.855112i −0.00615680 0.0303659i
\(794\) −4.27357 + 7.40204i −0.151663 + 0.262689i
\(795\) 33.2562 0.531346i 1.17948 0.0188449i
\(796\) 13.0589 + 7.53954i 0.462859 + 0.267232i
\(797\) 5.40206 9.35664i 0.191351 0.331429i −0.754347 0.656476i \(-0.772047\pi\)
0.945698 + 0.325046i \(0.105380\pi\)
\(798\) −3.32952 3.22070i −0.117864 0.114012i
\(799\) 1.18559 + 0.684502i 0.0419432 + 0.0242159i
\(800\) 5.80848 0.205361
\(801\) 20.1492 + 10.7900i 0.711937 + 0.381246i
\(802\) −7.78768 13.4887i −0.274993 0.476301i
\(803\) −1.81797 + 3.14881i −0.0641547 + 0.111119i
\(804\) 17.5559 10.5134i 0.619149 0.370779i
\(805\) 7.86270 29.4187i 0.277124 1.03687i
\(806\) 8.91255 + 10.0874i 0.313931 + 0.355315i
\(807\) −25.1897 42.0633i −0.886718 1.48070i
\(808\) 19.3241 0.679819
\(809\) 16.6138i 0.584110i −0.956402 0.292055i \(-0.905661\pi\)
0.956402 0.292055i \(-0.0943390\pi\)
\(810\) −1.88954 29.5282i −0.0663917 1.03752i
\(811\) 7.44633 0.261476 0.130738 0.991417i \(-0.458265\pi\)
0.130738 + 0.991417i \(0.458265\pi\)
\(812\) −17.2186 + 17.2405i −0.604255 + 0.605022i
\(813\) 21.3045 38.3008i 0.747182 1.34327i
\(814\) −12.5002 + 7.21699i −0.438132 + 0.252955i
\(815\) −16.9562 29.3690i −0.593951 1.02875i
\(816\) −1.94592 + 0.0310906i −0.0681208 + 0.00108839i
\(817\) −3.39245 + 5.87589i −0.118687 + 0.205571i
\(818\) 10.8097 0.377951
\(819\) 0.834705 28.6060i 0.0291669 0.999575i
\(820\) 32.3653 1.13025
\(821\) −1.71387 + 2.96850i −0.0598143 + 0.103601i −0.894382 0.447304i \(-0.852384\pi\)
0.834568 + 0.550905i \(0.185718\pi\)
\(822\) 36.6785 0.586025i 1.27931 0.0204400i
\(823\) −19.8190 34.3275i −0.690847 1.19658i −0.971561 0.236791i \(-0.923904\pi\)
0.280713 0.959792i \(-0.409429\pi\)
\(824\) 7.86720 4.54213i 0.274067 0.158233i
\(825\) 10.1242 18.2011i 0.352481 0.633682i
\(826\) 25.0724 + 6.70107i 0.872379 + 0.233160i
\(827\) −0.211856 −0.00736695 −0.00368347 0.999993i \(-0.501172\pi\)
−0.00368347 + 0.999993i \(0.501172\pi\)
\(828\) 0.335520 + 10.4972i 0.0116601 + 0.364803i
\(829\) 31.5116i 1.09444i 0.836988 + 0.547221i \(0.184314\pi\)
−0.836988 + 0.547221i \(0.815686\pi\)
\(830\) 3.28730 0.114104
\(831\) 11.6516 + 19.4566i 0.404190 + 0.674942i
\(832\) −3.53365 + 0.716460i −0.122507 + 0.0248388i
\(833\) −0.00998334 7.86534i −0.000345902 0.272518i
\(834\) −30.2341 + 18.1058i −1.04692 + 0.626952i
\(835\) 22.9860 39.8129i 0.795463 1.37778i
\(836\) 1.04634 + 1.81232i 0.0361885 + 0.0626803i
\(837\) 8.88344 17.2454i 0.307057 0.596087i
\(838\) 14.2786 0.493248
\(839\) −13.7645 7.94694i −0.475204 0.274359i 0.243212 0.969973i \(-0.421799\pi\)
−0.718416 + 0.695614i \(0.755132\pi\)
\(840\) −4.14049 14.4857i −0.142860 0.499803i
\(841\) 27.9082 48.3384i 0.962352 1.66684i
\(842\) 26.9813 + 15.5776i 0.929836 + 0.536841i
\(843\) 28.6818 0.458259i 0.987854 0.0157833i
\(844\) −10.2101 + 17.6845i −0.351448 + 0.608725i
\(845\) 25.7668 34.0984i 0.886406 1.17302i
\(846\) −0.116769 3.65329i −0.00401462 0.125603i
\(847\) 4.58684 17.1619i 0.157606 0.589690i
\(848\) −5.05843 + 2.92049i −0.173707 + 0.100290i
\(849\) −0.508904 31.8516i −0.0174655 1.09314i
\(850\) 3.26326 5.65214i 0.111929 0.193867i
\(851\) 12.2044 + 21.1387i 0.418363 + 0.724625i
\(852\) −13.6671 + 0.218364i −0.468227 + 0.00748101i
\(853\) 8.80214 0.301379 0.150690 0.988581i \(-0.451851\pi\)
0.150690 + 0.988581i \(0.451851\pi\)
\(854\) −0.452437 + 0.453011i −0.0154821 + 0.0155017i
\(855\) −8.47061 + 5.25829i −0.289689 + 0.179830i
\(856\) −3.25929 1.88175i −0.111400 0.0643170i
\(857\) −2.96296 + 5.13199i −0.101213 + 0.175305i −0.912185 0.409780i \(-0.865606\pi\)
0.810972 + 0.585085i \(0.198939\pi\)
\(858\) −3.91413 + 12.3217i −0.133626 + 0.420654i
\(859\) 21.0079 12.1289i 0.716781 0.413834i −0.0967860 0.995305i \(-0.530856\pi\)
0.813567 + 0.581472i \(0.197523\pi\)
\(860\) −19.1102 + 11.0333i −0.651652 + 0.376231i
\(861\) −12.3984 43.3764i −0.422537 1.47826i
\(862\) −10.7951 + 18.6976i −0.367682 + 0.636844i
\(863\) −9.92236 17.1860i −0.337761 0.585019i 0.646250 0.763126i \(-0.276336\pi\)
−0.984011 + 0.178106i \(0.943003\pi\)
\(864\) 2.81069 + 4.37036i 0.0956215 + 0.148683i
\(865\) −14.4578 + 8.34719i −0.491579 + 0.283813i
\(866\) −16.2009 + 9.35358i −0.550528 + 0.317848i
\(867\) 13.2502 23.8209i 0.450000 0.809001i
\(868\) 2.55041 9.54250i 0.0865667 0.323893i
\(869\) −5.15432 8.92754i −0.174848 0.302846i
\(870\) 26.9434 + 44.9918i 0.913467 + 1.52536i
\(871\) −8.46456 41.7480i −0.286811 1.41458i
\(872\) −2.43945 1.40841i −0.0826101 0.0476949i
\(873\) 9.11003 17.0120i 0.308328 0.575770i
\(874\) 3.06476 1.76944i 0.103667 0.0598521i
\(875\) 6.79388 + 1.81579i 0.229675 + 0.0613850i
\(876\) 3.04165 0.0485974i 0.102768 0.00164195i
\(877\) 8.82826i 0.298109i −0.988829 0.149055i \(-0.952377\pi\)
0.988829 0.149055i \(-0.0476230\pi\)
\(878\) −12.4456 + 7.18545i −0.420017 + 0.242497i
\(879\) −12.8946 7.17251i −0.434923 0.241923i
\(880\) 6.80604i 0.229432i
\(881\) −9.51336 16.4776i −0.320513 0.555145i 0.660081 0.751195i \(-0.270522\pi\)
−0.980594 + 0.196049i \(0.937189\pi\)
\(882\) −17.8277 + 11.0983i −0.600291 + 0.373698i
\(883\) −30.8587 −1.03848 −0.519239 0.854629i \(-0.673785\pi\)
−0.519239 + 0.854629i \(0.673785\pi\)
\(884\) −1.28807 + 3.84105i −0.0433223 + 0.129189i
\(885\) 27.1518 48.8129i 0.912697 1.64083i
\(886\) 1.40405i 0.0471699i
\(887\) 6.57095 11.3812i 0.220631 0.382144i −0.734369 0.678751i \(-0.762522\pi\)
0.955000 + 0.296607i \(0.0958551\pi\)
\(888\) 10.5535 + 5.87031i 0.354153 + 0.196995i
\(889\) −48.0414 + 12.9053i −1.61126 + 0.432831i
\(890\) 12.5239 21.6920i 0.419801 0.727116i
\(891\) 18.5938 1.18983i 0.622915 0.0398610i
\(892\) −1.37326 + 2.37855i −0.0459801 + 0.0796399i
\(893\) −1.06661 + 0.615809i −0.0356928 + 0.0206073i
\(894\) 11.1559 20.0558i 0.373109 0.670767i
\(895\) 19.2543 + 33.3494i 0.643601 + 1.11475i
\(896\) 1.87202 + 1.86964i 0.0625397 + 0.0624603i
\(897\) 20.8368 + 6.61906i 0.695720 + 0.221004i
\(898\) −11.0266 19.0987i −0.367963 0.637331i
\(899\) 34.3823i 1.14672i
\(900\) −17.4165 + 0.556682i −0.580551 + 0.0185561i
\(901\) 6.56304i 0.218647i
\(902\) 20.3803i 0.678589i
\(903\) 22.1076 + 21.3851i 0.735695 + 0.711652i
\(904\) −4.57774 2.64296i −0.152253 0.0879035i
\(905\) −37.2703 64.5540i −1.23891 2.14585i
\(906\) 25.7614 15.4272i 0.855864 0.512536i
\(907\) 48.7067 1.61728 0.808640 0.588303i \(-0.200204\pi\)
0.808640 + 0.588303i \(0.200204\pi\)
\(908\) −7.77691 4.49000i −0.258086 0.149006i
\(909\) −57.9427 + 1.85201i −1.92184 + 0.0614273i
\(910\) −31.3034 1.91574i −1.03770 0.0635063i
\(911\) 7.94598i 0.263262i −0.991299 0.131631i \(-0.957979\pi\)
0.991299 0.131631i \(-0.0420214\pi\)
\(912\) 0.851096 1.53008i 0.0281826 0.0506661i
\(913\) 2.06999i 0.0685068i
\(914\) 36.6548 21.1627i 1.21243 0.699999i
\(915\) 0.707966 + 1.18221i 0.0234046 + 0.0390825i
\(916\) −8.23500 + 14.2634i −0.272092 + 0.471277i
\(917\) −7.42039 + 1.99334i −0.245043 + 0.0658258i
\(918\) 5.83180 0.279720i 0.192478 0.00923215i
\(919\) −27.1660 −0.896124 −0.448062 0.894002i \(-0.647886\pi\)
−0.448062 + 0.894002i \(0.647886\pi\)
\(920\) 11.5095 0.379457
\(921\) 36.9159 0.589818i 1.21642 0.0194352i
\(922\) −10.2913 + 5.94166i −0.338925 + 0.195678i
\(923\) −9.04667 + 26.9775i −0.297775 + 0.887974i
\(924\) 9.12155 2.60725i 0.300077 0.0857721i
\(925\) −35.0725 + 20.2491i −1.15318 + 0.665787i
\(926\) 3.08686 + 1.78220i 0.101441 + 0.0585667i
\(927\) −23.1542 + 14.3734i −0.760485 + 0.472085i
\(928\) −7.97573 4.60479i −0.261816 0.151160i
\(929\) 23.7500i 0.779211i 0.920982 + 0.389605i \(0.127389\pi\)
−0.920982 + 0.389605i \(0.872611\pi\)
\(930\) −18.5781 10.3339i −0.609200 0.338863i
\(931\) 6.13250 + 3.53023i 0.200985 + 0.115699i
\(932\) 4.79194 + 2.76663i 0.156965 + 0.0906240i
\(933\) 12.4726 22.4229i 0.408333 0.734093i
\(934\) 7.12287 0.233067
\(935\) 6.62285 + 3.82371i 0.216591 + 0.125049i
\(936\) 10.5269 2.48695i 0.344082 0.0812884i
\(937\) 44.8244i 1.46435i 0.681116 + 0.732175i \(0.261495\pi\)
−0.681116 + 0.732175i \(0.738505\pi\)
\(938\) −22.0887 + 22.1168i −0.721222 + 0.722138i
\(939\) −38.9553 + 23.3284i −1.27126 + 0.761294i
\(940\) −4.00559 −0.130648
\(941\) 26.3318 + 15.2027i 0.858393 + 0.495593i 0.863474 0.504394i \(-0.168284\pi\)
−0.00508113 + 0.999987i \(0.501617\pi\)
\(942\) 20.9716 12.5589i 0.683292 0.409191i
\(943\) 34.4645 1.12232
\(944\) 9.80909i 0.319259i
\(945\) 13.8034 + 43.0380i 0.449026 + 1.40003i
\(946\) −6.94759 12.0336i −0.225886 0.391245i
\(947\) 4.00703 6.94038i 0.130211 0.225532i −0.793547 0.608509i \(-0.791768\pi\)
0.923758 + 0.382977i \(0.125101\pi\)
\(948\) −4.19253 + 7.53724i −0.136167 + 0.244798i
\(949\) 2.01336 6.00391i 0.0653565 0.194895i
\(950\) 2.93578 + 5.08492i 0.0952493 + 0.164977i
\(951\) 17.4511 + 29.1409i 0.565890 + 0.944958i
\(952\) 2.87104 0.771245i 0.0930508 0.0249962i
\(953\) −4.48194 2.58765i −0.145184 0.0838222i 0.425648 0.904889i \(-0.360046\pi\)
−0.570833 + 0.821067i \(0.693379\pi\)
\(954\) 14.8877 9.24179i 0.482006 0.299214i
\(955\) 42.5011 + 73.6140i 1.37530 + 2.38209i
\(956\) 2.16749 + 3.75420i 0.0701016 + 0.121419i
\(957\) −28.3311 + 16.9661i −0.915815 + 0.548437i
\(958\) 26.4547 + 15.2736i 0.854712 + 0.493468i
\(959\) −54.1159 + 14.5371i −1.74749 + 0.469429i
\(960\) 4.88532 2.92558i 0.157673 0.0944228i
\(961\) 8.53115 + 14.7764i 0.275199 + 0.476658i
\(962\) 18.8391 16.6449i 0.607396 0.536652i
\(963\) 9.95323 + 5.33001i 0.320738 + 0.171757i
\(964\) 2.10349 3.64335i 0.0677488 0.117344i
\(965\) −35.8512 62.0960i −1.15409 1.99894i
\(966\) −4.40903 15.4252i −0.141858 0.496297i
\(967\) 14.4231i 0.463816i −0.972738 0.231908i \(-0.925503\pi\)
0.972738 0.231908i \(-0.0744968\pi\)
\(968\) 6.71427 0.215805
\(969\) −1.01074 1.68780i −0.0324698 0.0542201i
\(970\) −18.3146 10.5739i −0.588046 0.339509i
\(971\) −1.42967 −0.0458802 −0.0229401 0.999737i \(-0.507303\pi\)
−0.0229401 + 0.999737i \(0.507303\pi\)
\(972\) −8.84661 12.8350i −0.283755 0.411683i
\(973\) 38.0404 38.0887i 1.21952 1.22107i
\(974\) 32.0202i 1.02599i
\(975\) −10.9821 + 34.5716i −0.351708 + 1.10718i
\(976\) −0.209571 0.120996i −0.00670819 0.00387297i
\(977\) −14.9269 −0.477552 −0.238776 0.971075i \(-0.576746\pi\)
−0.238776 + 0.971075i \(0.576746\pi\)
\(978\) −15.6135 8.68489i −0.499265 0.277712i
\(979\) 13.6593 + 7.88621i 0.436554 + 0.252044i
\(980\) 11.5320 + 19.9155i 0.368375 + 0.636179i
\(981\) 7.44958 + 3.98929i 0.237847 + 0.127368i
\(982\) 15.1110i 0.482211i
\(983\) −2.34938 1.35641i −0.0749334 0.0432628i 0.462065 0.886846i \(-0.347109\pi\)
−0.536999 + 0.843583i \(0.680442\pi\)
\(984\) 14.6288 8.76048i 0.466349 0.279274i
\(985\) −19.9885 11.5404i −0.636887 0.367707i
\(986\) −8.96170 + 5.17404i −0.285399 + 0.164775i
\(987\) 1.53445 + 5.36835i 0.0488422 + 0.170876i
\(988\) −2.41322 2.73135i −0.0767749 0.0868957i
\(989\) −20.3496 + 11.7489i −0.647080 + 0.373592i
\(990\) −0.652288 20.4077i −0.0207311 0.648600i
\(991\) −6.57676 −0.208918 −0.104459 0.994529i \(-0.533311\pi\)
−0.104459 + 0.994529i \(0.533311\pi\)
\(992\) 3.73332 0.118533
\(993\) 0.721561 + 45.1615i 0.0228980 + 1.43316i
\(994\) 20.1646 5.41681i 0.639582 0.171811i
\(995\) −24.7872 + 42.9327i −0.785807 + 1.36106i
\(996\) 1.48583 0.889789i 0.0470802 0.0281941i
\(997\) 19.9103 11.4952i 0.630565 0.364057i −0.150406 0.988624i \(-0.548058\pi\)
0.780971 + 0.624568i \(0.214725\pi\)
\(998\) 4.83365i 0.153007i
\(999\) −32.2070 16.5905i −1.01898 0.524900i
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.bn.f.101.17 yes 34
3.2 odd 2 546.2.bn.e.101.1 yes 34
7.5 odd 6 546.2.bi.e.257.12 yes 34
13.4 even 6 546.2.bi.f.17.6 yes 34
21.5 even 6 546.2.bi.f.257.6 yes 34
39.17 odd 6 546.2.bi.e.17.12 34
91.82 odd 6 546.2.bn.e.173.1 yes 34
273.173 even 6 inner 546.2.bn.f.173.17 yes 34
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
546.2.bi.e.17.12 34 39.17 odd 6
546.2.bi.e.257.12 yes 34 7.5 odd 6
546.2.bi.f.17.6 yes 34 13.4 even 6
546.2.bi.f.257.6 yes 34 21.5 even 6
546.2.bn.e.101.1 yes 34 3.2 odd 2
546.2.bn.e.173.1 yes 34 91.82 odd 6
546.2.bn.f.101.17 yes 34 1.1 even 1 trivial
546.2.bn.f.173.17 yes 34 273.173 even 6 inner