Properties

Label 360.2.bd.b.59.20
Level $360$
Weight $2$
Character 360.59
Analytic conductor $2.875$
Analytic rank $0$
Dimension $128$
CM no
Inner twists $8$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [360,2,Mod(59,360)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(360, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([3, 3, 5, 3]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("360.59");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 360 = 2^{3} \cdot 3^{2} \cdot 5 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 360.bd (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: \(2.87461447277\)
Analytic rank: \(0\)
Dimension: \(128\)
Relative dimension: \(64\) over \(\Q(\zeta_{6})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 59.20
Character \(\chi\) \(=\) 360.59
Dual form 360.2.bd.b.299.20

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.784848 + 1.17644i) q^{2} +(-1.32971 - 1.10989i) q^{3} +(-0.768027 - 1.84665i) q^{4} +(0.451766 - 2.18996i) q^{5} +(2.34935 - 0.693233i) q^{6} +(-2.22153 - 3.84780i) q^{7} +(2.77527 + 0.545804i) q^{8} +(0.536278 + 2.95168i) q^{9} +O(q^{10})\) \(q+(-0.784848 + 1.17644i) q^{2} +(-1.32971 - 1.10989i) q^{3} +(-0.768027 - 1.84665i) q^{4} +(0.451766 - 2.18996i) q^{5} +(2.34935 - 0.693233i) q^{6} +(-2.22153 - 3.84780i) q^{7} +(2.77527 + 0.545804i) q^{8} +(0.536278 + 2.95168i) q^{9} +(2.22179 + 2.25026i) q^{10} +(-2.97913 + 1.72000i) q^{11} +(-1.02833 + 3.30795i) q^{12} +(-3.22299 + 5.58238i) q^{13} +(6.27027 + 0.406441i) q^{14} +(-3.03134 + 2.41060i) q^{15} +(-2.82027 + 2.83656i) q^{16} +2.90120 q^{17} +(-3.89337 - 1.68572i) q^{18} -1.72505 q^{19} +(-4.39106 + 0.847690i) q^{20} +(-1.31665 + 7.58213i) q^{21} +(0.314684 - 4.85471i) q^{22} +(4.32408 + 2.49651i) q^{23} +(-3.08452 - 3.80601i) q^{24} +(-4.59181 - 1.97870i) q^{25} +(-4.03778 - 8.17297i) q^{26} +(2.56295 - 4.52010i) q^{27} +(-5.39936 + 7.05761i) q^{28} +(-0.523887 - 0.907399i) q^{29} +(-0.456795 - 5.45814i) q^{30} +(-1.88690 - 1.08940i) q^{31} +(-1.12357 - 5.54415i) q^{32} +(5.87041 + 1.01940i) q^{33} +(-2.27700 + 3.41309i) q^{34} +(-9.43013 + 3.12674i) q^{35} +(5.03886 - 3.25729i) q^{36} -3.02322 q^{37} +(1.35390 - 2.02942i) q^{38} +(10.4815 - 3.84579i) q^{39} +(2.44906 - 5.83113i) q^{40} +(-1.94134 - 1.12084i) q^{41} +(-7.88656 - 7.49978i) q^{42} +(-2.07856 + 1.20006i) q^{43} +(5.46430 + 4.18042i) q^{44} +(6.70632 + 0.159044i) q^{45} +(-6.33074 + 3.12764i) q^{46} +(-0.453489 + 0.261822i) q^{47} +(6.89843 - 0.641623i) q^{48} +(-6.37038 + 11.0338i) q^{49} +(5.93170 - 3.84902i) q^{50} +(-3.85777 - 3.22002i) q^{51} +(12.7841 + 1.66433i) q^{52} -1.38655i q^{53} +(3.30610 + 6.56275i) q^{54} +(2.42086 + 7.30120i) q^{55} +(-4.06519 - 11.8912i) q^{56} +(2.29382 + 1.91462i) q^{57} +(1.47867 + 0.0958480i) q^{58} +(-5.53954 - 3.19826i) q^{59} +(6.77970 + 3.74642i) q^{60} +(-3.04912 + 1.76041i) q^{61} +(2.76254 - 1.36481i) q^{62} +(10.1661 - 8.62073i) q^{63} +(7.40420 + 3.02950i) q^{64} +(10.7691 + 9.58013i) q^{65} +(-5.80665 + 6.10611i) q^{66} +(-12.5787 - 7.26229i) q^{67} +(-2.22820 - 5.35752i) q^{68} +(-2.97893 - 8.11890i) q^{69} +(3.72278 - 13.5480i) q^{70} +0.671509 q^{71} +(-0.122726 + 8.48439i) q^{72} -11.5525i q^{73} +(2.37277 - 3.55664i) q^{74} +(3.90966 + 7.72752i) q^{75} +(1.32489 + 3.18557i) q^{76} +(13.2364 + 7.64207i) q^{77} +(-3.70202 + 15.3492i) q^{78} +(-9.41493 + 5.43572i) q^{79} +(4.93785 + 7.45773i) q^{80} +(-8.42481 + 3.16584i) q^{81} +(2.84226 - 1.40419i) q^{82} +(0.978245 + 1.69437i) q^{83} +(15.0128 - 3.39189i) q^{84} +(1.31066 - 6.35350i) q^{85} +(0.219557 - 3.38717i) q^{86} +(-0.310496 + 1.78804i) q^{87} +(-9.20666 + 3.14744i) q^{88} -2.43279i q^{89} +(-5.45055 + 7.76476i) q^{90} +28.6398 q^{91} +(1.28918 - 9.90247i) q^{92} +(1.29992 + 3.54284i) q^{93} +(0.0479018 - 0.738994i) q^{94} +(-0.779319 + 3.77779i) q^{95} +(-4.65939 + 8.61917i) q^{96} +(9.65294 - 5.57313i) q^{97} +(-7.98086 - 16.1542i) q^{98} +(-6.67453 - 7.87104i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 128 q - 10 q^{4} + 4 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 128 q - 10 q^{4} + 4 q^{9} - 48 q^{11} - 30 q^{14} + 14 q^{16} + 24 q^{19} - 24 q^{20} - 10 q^{24} + 14 q^{25} + 26 q^{30} + 8 q^{36} + 12 q^{40} - 24 q^{41} - 36 q^{46} - 52 q^{49} - 42 q^{50} - 68 q^{51} - 62 q^{54} - 54 q^{56} - 24 q^{60} + 68 q^{64} - 18 q^{65} + 44 q^{66} - 60 q^{74} + 10 q^{75} + 24 q^{76} + 36 q^{81} + 94 q^{84} - 74 q^{90} + 88 q^{91} - 26 q^{94} - 22 q^{96} - 76 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/360\mathbb{Z}\right)^\times\).

\(n\) \(181\) \(217\) \(271\) \(281\)
\(\chi(n)\) \(-1\) \(-1\) \(-1\) \(e\left(\frac{5}{6}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.784848 + 1.17644i −0.554971 + 0.831869i
\(3\) −1.32971 1.10989i −0.767711 0.640797i
\(4\) −0.768027 1.84665i −0.384014 0.923327i
\(5\) 0.451766 2.18996i 0.202036 0.979378i
\(6\) 2.34935 0.693233i 0.959117 0.283011i
\(7\) −2.22153 3.84780i −0.839659 1.45433i −0.890180 0.455609i \(-0.849422\pi\)
0.0505211 0.998723i \(-0.483912\pi\)
\(8\) 2.77527 + 0.545804i 0.981204 + 0.192971i
\(9\) 0.536278 + 2.95168i 0.178759 + 0.983893i
\(10\) 2.22179 + 2.25026i 0.702591 + 0.711594i
\(11\) −2.97913 + 1.72000i −0.898242 + 0.518600i −0.876629 0.481166i \(-0.840213\pi\)
−0.0216123 + 0.999766i \(0.506880\pi\)
\(12\) −1.02833 + 3.30795i −0.296854 + 0.954923i
\(13\) −3.22299 + 5.58238i −0.893896 + 1.54827i −0.0587299 + 0.998274i \(0.518705\pi\)
−0.835166 + 0.549999i \(0.814628\pi\)
\(14\) 6.27027 + 0.406441i 1.67580 + 0.108626i
\(15\) −3.03134 + 2.41060i −0.782687 + 0.622415i
\(16\) −2.82027 + 2.83656i −0.705067 + 0.709141i
\(17\) 2.90120 0.703645 0.351822 0.936067i \(-0.385562\pi\)
0.351822 + 0.936067i \(0.385562\pi\)
\(18\) −3.89337 1.68572i −0.917677 0.397328i
\(19\) −1.72505 −0.395754 −0.197877 0.980227i \(-0.563405\pi\)
−0.197877 + 0.980227i \(0.563405\pi\)
\(20\) −4.39106 + 0.847690i −0.981871 + 0.189549i
\(21\) −1.31665 + 7.58213i −0.287316 + 1.65456i
\(22\) 0.314684 4.85471i 0.0670908 1.03503i
\(23\) 4.32408 + 2.49651i 0.901633 + 0.520558i 0.877730 0.479156i \(-0.159057\pi\)
0.0239032 + 0.999714i \(0.492391\pi\)
\(24\) −3.08452 3.80601i −0.629626 0.776898i
\(25\) −4.59181 1.97870i −0.918363 0.395739i
\(26\) −4.03778 8.17297i −0.791874 1.60285i
\(27\) 2.56295 4.52010i 0.493240 0.869893i
\(28\) −5.39936 + 7.05761i −1.02038 + 1.33376i
\(29\) −0.523887 0.907399i −0.0972834 0.168500i 0.813276 0.581878i \(-0.197682\pi\)
−0.910559 + 0.413378i \(0.864349\pi\)
\(30\) −0.456795 5.45814i −0.0833990 0.996516i
\(31\) −1.88690 1.08940i −0.338897 0.195662i 0.320887 0.947117i \(-0.396019\pi\)
−0.659784 + 0.751455i \(0.729352\pi\)
\(32\) −1.12357 5.54415i −0.198621 0.980076i
\(33\) 5.87041 + 1.01940i 1.02191 + 0.177455i
\(34\) −2.27700 + 3.41309i −0.390503 + 0.585341i
\(35\) −9.43013 + 3.12674i −1.59398 + 0.528516i
\(36\) 5.03886 3.25729i 0.839809 0.542882i
\(37\) −3.02322 −0.497015 −0.248507 0.968630i \(-0.579940\pi\)
−0.248507 + 0.968630i \(0.579940\pi\)
\(38\) 1.35390 2.02942i 0.219632 0.329215i
\(39\) 10.4815 3.84579i 1.67838 0.615820i
\(40\) 2.44906 5.83113i 0.387230 0.921983i
\(41\) −1.94134 1.12084i −0.303187 0.175045i 0.340687 0.940177i \(-0.389340\pi\)
−0.643874 + 0.765132i \(0.722674\pi\)
\(42\) −7.88656 7.49978i −1.21692 1.15724i
\(43\) −2.07856 + 1.20006i −0.316978 + 0.183007i −0.650045 0.759896i \(-0.725250\pi\)
0.333067 + 0.942903i \(0.391916\pi\)
\(44\) 5.46430 + 4.18042i 0.823775 + 0.630222i
\(45\) 6.70632 + 0.159044i 0.999719 + 0.0237089i
\(46\) −6.33074 + 3.12764i −0.933417 + 0.461146i
\(47\) −0.453489 + 0.261822i −0.0661482 + 0.0381907i −0.532709 0.846298i \(-0.678826\pi\)
0.466561 + 0.884489i \(0.345493\pi\)
\(48\) 6.89843 0.641623i 0.995702 0.0926103i
\(49\) −6.37038 + 11.0338i −0.910054 + 1.57626i
\(50\) 5.93170 3.84902i 0.838868 0.544334i
\(51\) −3.85777 3.22002i −0.540196 0.450893i
\(52\) 12.7841 + 1.66433i 1.77283 + 0.230800i
\(53\) 1.38655i 0.190458i −0.995455 0.0952288i \(-0.969642\pi\)
0.995455 0.0952288i \(-0.0303583\pi\)
\(54\) 3.30610 + 6.56275i 0.449904 + 0.893077i
\(55\) 2.42086 + 7.30120i 0.326428 + 0.984494i
\(56\) −4.06519 11.8912i −0.543233 1.58903i
\(57\) 2.29382 + 1.91462i 0.303824 + 0.253598i
\(58\) 1.47867 + 0.0958480i 0.194159 + 0.0125855i
\(59\) −5.53954 3.19826i −0.721187 0.416377i 0.0940025 0.995572i \(-0.470034\pi\)
−0.815189 + 0.579195i \(0.803367\pi\)
\(60\) 6.77970 + 3.74642i 0.875256 + 0.483661i
\(61\) −3.04912 + 1.76041i −0.390400 + 0.225398i −0.682333 0.731041i \(-0.739035\pi\)
0.291933 + 0.956439i \(0.405701\pi\)
\(62\) 2.76254 1.36481i 0.350843 0.173331i
\(63\) 10.1661 8.62073i 1.28081 1.08611i
\(64\) 7.40420 + 3.02950i 0.925524 + 0.378688i
\(65\) 10.7691 + 9.58013i 1.33575 + 1.18827i
\(66\) −5.80665 + 6.10611i −0.714749 + 0.751610i
\(67\) −12.5787 7.26229i −1.53673 0.887230i −0.999027 0.0440942i \(-0.985960\pi\)
−0.537700 0.843136i \(-0.680707\pi\)
\(68\) −2.22820 5.35752i −0.270209 0.649695i
\(69\) −2.97893 8.11890i −0.358621 0.977401i
\(70\) 3.72278 13.5480i 0.444958 1.61930i
\(71\) 0.671509 0.0796934 0.0398467 0.999206i \(-0.487313\pi\)
0.0398467 + 0.999206i \(0.487313\pi\)
\(72\) −0.122726 + 8.48439i −0.0144634 + 0.999895i
\(73\) 11.5525i 1.35212i −0.736848 0.676058i \(-0.763687\pi\)
0.736848 0.676058i \(-0.236313\pi\)
\(74\) 2.37277 3.55664i 0.275829 0.413451i
\(75\) 3.90966 + 7.72752i 0.451449 + 0.892297i
\(76\) 1.32489 + 3.18557i 0.151975 + 0.365410i
\(77\) 13.2364 + 7.64207i 1.50843 + 0.870894i
\(78\) −3.70202 + 15.3492i −0.419171 + 1.73796i
\(79\) −9.41493 + 5.43572i −1.05926 + 0.611566i −0.925228 0.379411i \(-0.876127\pi\)
−0.134035 + 0.990977i \(0.542793\pi\)
\(80\) 4.93785 + 7.45773i 0.552068 + 0.833799i
\(81\) −8.42481 + 3.16584i −0.936090 + 0.351760i
\(82\) 2.84226 1.40419i 0.313875 0.155067i
\(83\) 0.978245 + 1.69437i 0.107376 + 0.185981i 0.914707 0.404119i \(-0.132422\pi\)
−0.807330 + 0.590100i \(0.799088\pi\)
\(84\) 15.0128 3.39189i 1.63803 0.370086i
\(85\) 1.31066 6.35350i 0.142162 0.689134i
\(86\) 0.219557 3.38717i 0.0236755 0.365248i
\(87\) −0.310496 + 1.78804i −0.0332886 + 0.191698i
\(88\) −9.20666 + 3.14744i −0.981433 + 0.335518i
\(89\) 2.43279i 0.257876i −0.991653 0.128938i \(-0.958843\pi\)
0.991653 0.128938i \(-0.0411568\pi\)
\(90\) −5.45055 + 7.76476i −0.574538 + 0.818478i
\(91\) 28.6398 3.00227
\(92\) 1.28918 9.90247i 0.134406 1.03240i
\(93\) 1.29992 + 3.54284i 0.134795 + 0.367376i
\(94\) 0.0479018 0.738994i 0.00494069 0.0762214i
\(95\) −0.779319 + 3.77779i −0.0799565 + 0.387593i
\(96\) −4.65939 + 8.61917i −0.475547 + 0.879691i
\(97\) 9.65294 5.57313i 0.980107 0.565865i 0.0778047 0.996969i \(-0.475209\pi\)
0.902303 + 0.431103i \(0.141876\pi\)
\(98\) −7.98086 16.1542i −0.806189 1.63183i
\(99\) −6.67453 7.87104i −0.670816 0.791069i
\(100\) −0.127329 + 9.99919i −0.0127329 + 0.999919i
\(101\) 4.16927 + 7.22139i 0.414858 + 0.718556i 0.995414 0.0956652i \(-0.0304978\pi\)
−0.580555 + 0.814221i \(0.697164\pi\)
\(102\) 6.81593 2.01121i 0.674877 0.199139i
\(103\) −2.60688 + 4.51525i −0.256863 + 0.444900i −0.965400 0.260774i \(-0.916022\pi\)
0.708537 + 0.705674i \(0.249356\pi\)
\(104\) −11.9915 + 13.7335i −1.17587 + 1.34668i
\(105\) 16.0097 + 6.30875i 1.56239 + 0.615671i
\(106\) 1.63120 + 1.08823i 0.158436 + 0.105699i
\(107\) −7.15717 −0.691909 −0.345955 0.938251i \(-0.612445\pi\)
−0.345955 + 0.938251i \(0.612445\pi\)
\(108\) −10.3155 1.26132i −0.992607 0.121371i
\(109\) 10.9196i 1.04591i −0.852360 0.522956i \(-0.824829\pi\)
0.852360 0.522956i \(-0.175171\pi\)
\(110\) −10.4894 2.88234i −1.00013 0.274820i
\(111\) 4.02002 + 3.35545i 0.381563 + 0.318485i
\(112\) 17.1798 + 4.55032i 1.62334 + 0.429965i
\(113\) −6.71874 + 11.6372i −0.632046 + 1.09473i 0.355087 + 0.934833i \(0.384451\pi\)
−0.987133 + 0.159902i \(0.948882\pi\)
\(114\) −4.05274 + 1.19586i −0.379574 + 0.112003i
\(115\) 7.42072 8.34170i 0.691985 0.777868i
\(116\) −1.27329 + 1.66435i −0.118222 + 0.154531i
\(117\) −18.2058 6.51952i −1.68313 0.602729i
\(118\) 8.11026 4.00680i 0.746610 0.368856i
\(119\) −6.44510 11.1632i −0.590822 1.02333i
\(120\) −9.72848 + 5.03555i −0.888084 + 0.459680i
\(121\) 0.416811 0.721937i 0.0378919 0.0656307i
\(122\) 0.322077 4.96877i 0.0291595 0.449851i
\(123\) 1.33742 + 3.64507i 0.120592 + 0.328665i
\(124\) −0.562558 + 4.32114i −0.0505192 + 0.388050i
\(125\) −6.40768 + 9.16196i −0.573121 + 0.819471i
\(126\) 2.16292 + 18.7258i 0.192689 + 1.66823i
\(127\) −8.48173 −0.752632 −0.376316 0.926491i \(-0.622809\pi\)
−0.376316 + 0.926491i \(0.622809\pi\)
\(128\) −9.37520 + 6.33290i −0.828658 + 0.559755i
\(129\) 4.09583 + 0.711246i 0.360618 + 0.0626217i
\(130\) −19.7226 + 5.15029i −1.72978 + 0.451711i
\(131\) 3.96031 + 2.28648i 0.346014 + 0.199771i 0.662928 0.748683i \(-0.269313\pi\)
−0.316914 + 0.948454i \(0.602647\pi\)
\(132\) −2.62615 11.6235i −0.228577 1.01170i
\(133\) 3.83225 + 6.63765i 0.332298 + 0.575557i
\(134\) 18.4160 9.09826i 1.59090 0.785970i
\(135\) −8.74096 7.65477i −0.752302 0.658818i
\(136\) 8.05160 + 1.58349i 0.690419 + 0.135783i
\(137\) −8.47943 14.6868i −0.724446 1.25478i −0.959202 0.282723i \(-0.908762\pi\)
0.234755 0.972054i \(-0.424571\pi\)
\(138\) 11.8894 + 2.86757i 1.01209 + 0.244103i
\(139\) 6.53326 11.3159i 0.554144 0.959806i −0.443825 0.896113i \(-0.646379\pi\)
0.997970 0.0636926i \(-0.0202877\pi\)
\(140\) 13.0166 + 15.0128i 1.10010 + 1.26881i
\(141\) 0.893606 + 0.155176i 0.0752552 + 0.0130682i
\(142\) −0.527032 + 0.789991i −0.0442276 + 0.0662945i
\(143\) 22.1742i 1.85430i
\(144\) −9.88507 6.80334i −0.823756 0.566945i
\(145\) −2.22384 + 0.737358i −0.184680 + 0.0612342i
\(146\) 13.5908 + 9.06695i 1.12478 + 0.750386i
\(147\) 20.7171 7.60139i 1.70872 0.626952i
\(148\) 2.32192 + 5.58285i 0.190860 + 0.458907i
\(149\) 4.42309 7.66101i 0.362353 0.627615i −0.625994 0.779828i \(-0.715307\pi\)
0.988348 + 0.152213i \(0.0486400\pi\)
\(150\) −12.1595 1.46544i −0.992816 0.119653i
\(151\) 11.2985 6.52318i 0.919458 0.530849i 0.0359957 0.999352i \(-0.488540\pi\)
0.883462 + 0.468503i \(0.155206\pi\)
\(152\) −4.78747 0.941540i −0.388315 0.0763690i
\(153\) 1.55585 + 8.56342i 0.125783 + 0.692311i
\(154\) −19.3790 + 9.57404i −1.56161 + 0.771498i
\(155\) −3.23818 + 3.64007i −0.260097 + 0.292377i
\(156\) −15.1519 16.4020i −1.21312 1.31321i
\(157\) 3.00104 5.19795i 0.239509 0.414842i −0.721065 0.692868i \(-0.756347\pi\)
0.960573 + 0.278026i \(0.0896802\pi\)
\(158\) 0.994493 15.3423i 0.0791177 1.22057i
\(159\) −1.53892 + 1.84372i −0.122045 + 0.146216i
\(160\) −12.6490 0.0440948i −0.999994 0.00348600i
\(161\) 22.1843i 1.74836i
\(162\) 2.88777 12.3960i 0.226885 0.973922i
\(163\) 1.53671i 0.120365i 0.998187 + 0.0601823i \(0.0191682\pi\)
−0.998187 + 0.0601823i \(0.980832\pi\)
\(164\) −0.578791 + 4.44582i −0.0451960 + 0.347160i
\(165\) 4.88450 12.3954i 0.380258 0.964981i
\(166\) −2.76110 0.178975i −0.214303 0.0138912i
\(167\) 9.36196 + 5.40513i 0.724450 + 0.418262i 0.816388 0.577503i \(-0.195973\pi\)
−0.0919381 + 0.995765i \(0.529306\pi\)
\(168\) −7.79241 + 20.3238i −0.601197 + 1.56801i
\(169\) −14.2753 24.7255i −1.09810 1.90196i
\(170\) 6.44585 + 6.52845i 0.494374 + 0.500710i
\(171\) −0.925106 5.09180i −0.0707446 0.389379i
\(172\) 3.81249 + 2.91671i 0.290699 + 0.222397i
\(173\) −19.2525 + 11.1154i −1.46374 + 0.845091i −0.999182 0.0404512i \(-0.987120\pi\)
−0.464559 + 0.885542i \(0.653787\pi\)
\(174\) −1.85983 1.76862i −0.140994 0.134079i
\(175\) 2.58722 + 22.0641i 0.195576 + 1.66789i
\(176\) 3.52305 13.3014i 0.265560 1.00263i
\(177\) 3.81628 + 10.4011i 0.286850 + 0.781792i
\(178\) 2.86204 + 1.90937i 0.214519 + 0.143114i
\(179\) 19.6132i 1.46596i 0.680252 + 0.732979i \(0.261870\pi\)
−0.680252 + 0.732979i \(0.738130\pi\)
\(180\) −4.85694 12.5064i −0.362015 0.932172i
\(181\) 14.2901i 1.06217i −0.847318 0.531086i \(-0.821784\pi\)
0.847318 0.531086i \(-0.178216\pi\)
\(182\) −22.4779 + 33.6931i −1.66617 + 2.49750i
\(183\) 6.00833 + 1.04335i 0.444148 + 0.0771270i
\(184\) 10.6379 + 9.28857i 0.784234 + 0.684763i
\(185\) −1.36579 + 6.62072i −0.100415 + 0.486765i
\(186\) −5.18818 1.25132i −0.380416 0.0917512i
\(187\) −8.64306 + 4.99007i −0.632043 + 0.364910i
\(188\) 0.831788 + 0.636352i 0.0606643 + 0.0464107i
\(189\) −23.0861 + 0.179807i −1.67927 + 0.0130791i
\(190\) −3.83269 3.88181i −0.278053 0.281616i
\(191\) −5.73266 9.92925i −0.414800 0.718455i 0.580607 0.814184i \(-0.302815\pi\)
−0.995407 + 0.0957285i \(0.969482\pi\)
\(192\) −6.48304 12.2462i −0.467873 0.883796i
\(193\) −7.67383 4.43049i −0.552374 0.318913i 0.197705 0.980262i \(-0.436651\pi\)
−0.750079 + 0.661348i \(0.769985\pi\)
\(194\) −1.01963 + 15.7302i −0.0732054 + 1.12936i
\(195\) −3.68694 24.6914i −0.264027 1.76819i
\(196\) 25.2683 + 3.28962i 1.80488 + 0.234973i
\(197\) 11.7577i 0.837703i −0.908055 0.418851i \(-0.862433\pi\)
0.908055 0.418851i \(-0.137567\pi\)
\(198\) 14.4983 1.67463i 1.03035 0.119011i
\(199\) 24.6295i 1.74594i −0.487772 0.872971i \(-0.662190\pi\)
0.487772 0.872971i \(-0.337810\pi\)
\(200\) −11.6635 7.99764i −0.824736 0.565518i
\(201\) 8.66565 + 23.6177i 0.611228 + 1.66587i
\(202\) −11.7678 0.762791i −0.827979 0.0536698i
\(203\) −2.32766 + 4.03163i −0.163370 + 0.282965i
\(204\) −2.98340 + 9.59703i −0.208880 + 0.671927i
\(205\) −3.33161 + 3.74510i −0.232690 + 0.261569i
\(206\) −3.26592 6.61062i −0.227547 0.460584i
\(207\) −5.04998 + 14.1021i −0.350998 + 0.980165i
\(208\) −6.74508 24.8860i −0.467687 1.72553i
\(209\) 5.13915 2.96709i 0.355482 0.205238i
\(210\) −19.9871 + 13.8831i −1.37924 + 0.958024i
\(211\) −9.12269 + 15.8010i −0.628032 + 1.08778i 0.359914 + 0.932985i \(0.382806\pi\)
−0.987946 + 0.154798i \(0.950527\pi\)
\(212\) −2.56048 + 1.06491i −0.175855 + 0.0731383i
\(213\) −0.892915 0.745303i −0.0611815 0.0510673i
\(214\) 5.61729 8.41999i 0.383990 0.575578i
\(215\) 1.68905 + 5.09411i 0.115192 + 0.347415i
\(216\) 9.57995 11.1456i 0.651833 0.758362i
\(217\) 9.68054i 0.657158i
\(218\) 12.8463 + 8.57026i 0.870062 + 0.580451i
\(219\) −12.8220 + 15.3615i −0.866432 + 1.03803i
\(220\) 11.6235 10.0780i 0.783657 0.679459i
\(221\) −9.35053 + 16.1956i −0.628985 + 1.08943i
\(222\) −7.10259 + 2.09580i −0.476695 + 0.140661i
\(223\) 0.488331 + 0.845814i 0.0327011 + 0.0566399i 0.881913 0.471413i \(-0.156256\pi\)
−0.849212 + 0.528053i \(0.822922\pi\)
\(224\) −18.8367 + 16.6398i −1.25858 + 1.11179i
\(225\) 3.37799 14.6147i 0.225199 0.974313i
\(226\) −8.41729 17.0376i −0.559909 1.13333i
\(227\) 6.74202 + 11.6775i 0.447484 + 0.775064i 0.998222 0.0596138i \(-0.0189869\pi\)
−0.550738 + 0.834678i \(0.685654\pi\)
\(228\) 1.77392 5.70638i 0.117481 0.377914i
\(229\) 8.09471 + 4.67348i 0.534913 + 0.308832i 0.743015 0.669275i \(-0.233395\pi\)
−0.208102 + 0.978107i \(0.566728\pi\)
\(230\) 3.98939 + 15.2770i 0.263053 + 1.00734i
\(231\) −9.11881 24.8528i −0.599974 1.63519i
\(232\) −0.958664 2.80421i −0.0629394 0.184106i
\(233\) 17.3072 1.13383 0.566916 0.823776i \(-0.308136\pi\)
0.566916 + 0.823776i \(0.308136\pi\)
\(234\) 21.9586 16.3012i 1.43548 1.06564i
\(235\) 0.368508 + 1.11140i 0.0240388 + 0.0725000i
\(236\) −1.65155 + 12.6860i −0.107507 + 0.825786i
\(237\) 18.5522 + 3.22162i 1.20510 + 0.209267i
\(238\) 18.1913 + 1.17917i 1.17917 + 0.0764340i
\(239\) −11.2185 + 19.4311i −0.725666 + 1.25689i 0.233033 + 0.972469i \(0.425135\pi\)
−0.958699 + 0.284422i \(0.908198\pi\)
\(240\) 1.71135 15.3971i 0.110467 0.993880i
\(241\) 6.28764 + 10.8905i 0.405023 + 0.701520i 0.994324 0.106393i \(-0.0339303\pi\)
−0.589301 + 0.807913i \(0.700597\pi\)
\(242\) 0.522184 + 1.05696i 0.0335672 + 0.0679442i
\(243\) 14.7163 + 5.14098i 0.944053 + 0.329794i
\(244\) 5.59268 + 4.27863i 0.358035 + 0.273911i
\(245\) 21.2857 + 18.9356i 1.35989 + 1.20975i
\(246\) −5.33789 1.28743i −0.340331 0.0820833i
\(247\) 5.55981 9.62988i 0.353763 0.612735i
\(248\) −4.64204 4.05325i −0.294770 0.257382i
\(249\) 0.579782 3.33877i 0.0367422 0.211586i
\(250\) −5.74945 14.7290i −0.363627 0.931544i
\(251\) 17.4293i 1.10013i −0.835122 0.550064i \(-0.814603\pi\)
0.835122 0.550064i \(-0.185397\pi\)
\(252\) −23.7274 12.1523i −1.49468 0.765526i
\(253\) −17.1760 −1.07985
\(254\) 6.65687 9.97826i 0.417689 0.626092i
\(255\) −8.79452 + 6.99365i −0.550734 + 0.437959i
\(256\) −0.0921787 15.9997i −0.00576117 0.999983i
\(257\) 0.662264 1.14708i 0.0413109 0.0715526i −0.844631 0.535349i \(-0.820180\pi\)
0.885942 + 0.463797i \(0.153513\pi\)
\(258\) −4.05134 + 4.26028i −0.252226 + 0.265234i
\(259\) 6.71617 + 11.6328i 0.417323 + 0.722824i
\(260\) 9.42021 27.2446i 0.584216 1.68964i
\(261\) 2.39740 2.03296i 0.148395 0.125837i
\(262\) −5.79815 + 2.86453i −0.358211 + 0.176971i
\(263\) −2.22865 + 1.28671i −0.137424 + 0.0793420i −0.567136 0.823624i \(-0.691949\pi\)
0.429712 + 0.902966i \(0.358615\pi\)
\(264\) 15.7355 + 6.03321i 0.968456 + 0.371318i
\(265\) −3.03649 0.626397i −0.186530 0.0384793i
\(266\) −10.8165 0.701131i −0.663205 0.0429891i
\(267\) −2.70014 + 3.23492i −0.165246 + 0.197974i
\(268\) −3.75019 + 28.8061i −0.229079 + 1.75961i
\(269\) 25.2205 1.53772 0.768861 0.639416i \(-0.220824\pi\)
0.768861 + 0.639416i \(0.220824\pi\)
\(270\) 15.8657 4.27539i 0.965557 0.260192i
\(271\) 23.6914i 1.43915i 0.694413 + 0.719576i \(0.255664\pi\)
−0.694413 + 0.719576i \(0.744336\pi\)
\(272\) −8.18217 + 8.22944i −0.496117 + 0.498983i
\(273\) −38.0828 31.7871i −2.30487 1.92384i
\(274\) 23.9332 + 1.55136i 1.44586 + 0.0937209i
\(275\) 17.0830 2.00314i 1.03014 0.120794i
\(276\) −12.7049 + 11.7366i −0.764746 + 0.706460i
\(277\) −5.43107 9.40689i −0.326321 0.565205i 0.655458 0.755232i \(-0.272476\pi\)
−0.981779 + 0.190027i \(0.939142\pi\)
\(278\) 8.18492 + 16.5673i 0.490899 + 0.993640i
\(279\) 2.20366 6.15374i 0.131930 0.368414i
\(280\) −27.8777 + 3.53054i −1.66601 + 0.210990i
\(281\) 21.6886 12.5219i 1.29383 0.746996i 0.314503 0.949257i \(-0.398162\pi\)
0.979332 + 0.202261i \(0.0648290\pi\)
\(282\) −0.883900 + 0.929485i −0.0526355 + 0.0553500i
\(283\) 23.1480 + 13.3645i 1.37601 + 0.794437i 0.991676 0.128759i \(-0.0410993\pi\)
0.384330 + 0.923196i \(0.374433\pi\)
\(284\) −0.515737 1.24005i −0.0306034 0.0735831i
\(285\) 5.22921 4.15841i 0.309751 0.246323i
\(286\) 26.0866 + 17.4033i 1.54253 + 1.02908i
\(287\) 9.95987i 0.587912i
\(288\) 15.7620 6.28961i 0.928785 0.370619i
\(289\) −8.58303 −0.504884
\(290\) 0.877918 3.19493i 0.0515531 0.187613i
\(291\) −19.0212 3.30306i −1.11504 0.193629i
\(292\) −21.3335 + 8.87263i −1.24845 + 0.519231i
\(293\) −15.1704 8.75861i −0.886262 0.511683i −0.0135438 0.999908i \(-0.504311\pi\)
−0.872718 + 0.488225i \(0.837645\pi\)
\(294\) −7.31722 + 30.3384i −0.426749 + 1.76937i
\(295\) −9.50662 + 10.6865i −0.553497 + 0.622191i
\(296\) −8.39024 1.65009i −0.487673 0.0959094i
\(297\) 0.139214 + 17.8742i 0.00807804 + 1.03717i
\(298\) 5.54128 + 11.2162i 0.320998 + 0.649739i
\(299\) −27.8729 + 16.0924i −1.61193 + 0.930649i
\(300\) 11.2673 13.1547i 0.650520 0.759489i
\(301\) 9.23517 + 5.33193i 0.532306 + 0.307327i
\(302\) −1.19345 + 18.4117i −0.0686754 + 1.05947i
\(303\) 2.47103 14.2298i 0.141957 0.817483i
\(304\) 4.86510 4.89321i 0.279033 0.280645i
\(305\) 2.47773 + 7.47274i 0.141875 + 0.427888i
\(306\) −11.2955 4.89061i −0.645718 0.279578i
\(307\) 21.8552i 1.24734i 0.781686 + 0.623672i \(0.214360\pi\)
−0.781686 + 0.623672i \(0.785640\pi\)
\(308\) 3.94630 30.3125i 0.224862 1.72721i
\(309\) 8.47784 3.11063i 0.482287 0.176958i
\(310\) −1.74085 6.66642i −0.0988736 0.378627i
\(311\) −0.374893 + 0.649334i −0.0212583 + 0.0368204i −0.876459 0.481477i \(-0.840101\pi\)
0.855201 + 0.518297i \(0.173434\pi\)
\(312\) 31.1880 4.95226i 1.76567 0.280367i
\(313\) −13.8003 + 7.96758i −0.780037 + 0.450354i −0.836443 0.548053i \(-0.815369\pi\)
0.0564066 + 0.998408i \(0.482036\pi\)
\(314\) 3.75972 + 7.61015i 0.212174 + 0.429465i
\(315\) −14.2863 26.1579i −0.804942 1.47383i
\(316\) 17.2688 + 13.2114i 0.971447 + 0.743197i
\(317\) 23.4404 13.5333i 1.31654 0.760107i 0.333373 0.942795i \(-0.391813\pi\)
0.983171 + 0.182688i \(0.0584799\pi\)
\(318\) −0.961204 3.25749i −0.0539017 0.182671i
\(319\) 3.12146 + 1.80217i 0.174768 + 0.100902i
\(320\) 9.97944 14.8462i 0.557868 0.829930i
\(321\) 9.51698 + 7.94369i 0.531186 + 0.443373i
\(322\) 26.0985 + 17.4113i 1.45441 + 0.970292i
\(323\) −5.00472 −0.278470
\(324\) 12.3167 + 13.1263i 0.684261 + 0.729237i
\(325\) 25.8452 19.2559i 1.43363 1.06813i
\(326\) −1.80785 1.20609i −0.100128 0.0667990i
\(327\) −12.1196 + 14.5200i −0.670217 + 0.802958i
\(328\) −4.77599 4.17021i −0.263710 0.230261i
\(329\) 2.01488 + 1.16329i 0.111084 + 0.0641343i
\(330\) 10.7489 + 15.4748i 0.591706 + 0.851862i
\(331\) −5.52615 9.57158i −0.303745 0.526102i 0.673236 0.739427i \(-0.264904\pi\)
−0.976981 + 0.213326i \(0.931570\pi\)
\(332\) 2.37760 3.10780i 0.130488 0.170563i
\(333\) −1.62129 8.92358i −0.0888459 0.489009i
\(334\) −13.7065 + 6.77159i −0.749988 + 0.370525i
\(335\) −21.5867 + 24.2659i −1.17941 + 1.32579i
\(336\) −17.7939 25.1184i −0.970737 1.37032i
\(337\) −16.4588 9.50249i −0.896568 0.517634i −0.0204827 0.999790i \(-0.506520\pi\)
−0.876085 + 0.482157i \(0.839854\pi\)
\(338\) 40.2920 + 2.61174i 2.19160 + 0.142060i
\(339\) 21.8500 8.01706i 1.18673 0.435427i
\(340\) −12.7394 + 2.45932i −0.690889 + 0.133375i
\(341\) 7.49508 0.405881
\(342\) 6.71626 + 2.90795i 0.363174 + 0.157244i
\(343\) 25.5065 1.37722
\(344\) −6.42356 + 2.19599i −0.346335 + 0.118400i
\(345\) −19.1258 + 2.85588i −1.02970 + 0.153756i
\(346\) 2.03363 31.3734i 0.109329 1.68664i
\(347\) 18.0715 31.3007i 0.970128 1.68031i 0.274970 0.961453i \(-0.411332\pi\)
0.695157 0.718858i \(-0.255335\pi\)
\(348\) 3.54036 0.799886i 0.189783 0.0428784i
\(349\) 9.80141 5.65885i 0.524658 0.302911i −0.214181 0.976794i \(-0.568708\pi\)
0.738838 + 0.673883i \(0.235375\pi\)
\(350\) −27.9877 14.2733i −1.49601 0.762938i
\(351\) 16.9725 + 28.8756i 0.905927 + 1.54126i
\(352\) 12.8832 + 14.5842i 0.686677 + 0.777341i
\(353\) −11.2508 19.4870i −0.598821 1.03719i −0.992995 0.118152i \(-0.962303\pi\)
0.394175 0.919035i \(-0.371030\pi\)
\(354\) −15.2314 3.67362i −0.809542 0.195250i
\(355\) 0.303365 1.47057i 0.0161009 0.0780500i
\(356\) −4.49253 + 1.86845i −0.238104 + 0.0990278i
\(357\) −3.81986 + 21.9973i −0.202168 + 1.16422i
\(358\) −23.0737 15.3934i −1.21948 0.813564i
\(359\) −8.28323 −0.437172 −0.218586 0.975818i \(-0.570144\pi\)
−0.218586 + 0.975818i \(0.570144\pi\)
\(360\) 18.5250 + 4.10173i 0.976354 + 0.216180i
\(361\) −16.0242 −0.843379
\(362\) 16.8114 + 11.2155i 0.883588 + 0.589475i
\(363\) −1.35551 + 0.497355i −0.0711459 + 0.0261044i
\(364\) −21.9962 52.8879i −1.15291 2.77208i
\(365\) −25.2994 5.21902i −1.32423 0.273176i
\(366\) −5.94307 + 6.24957i −0.310649 + 0.326670i
\(367\) −6.11970 10.5996i −0.319446 0.553296i 0.660927 0.750450i \(-0.270163\pi\)
−0.980373 + 0.197154i \(0.936830\pi\)
\(368\) −19.2766 + 5.22470i −1.00486 + 0.272356i
\(369\) 2.26725 6.33130i 0.118028 0.329594i
\(370\) −6.71695 6.80303i −0.349198 0.353673i
\(371\) −5.33518 + 3.08027i −0.276989 + 0.159919i
\(372\) 5.54404 5.12150i 0.287445 0.265537i
\(373\) −4.19378 + 7.26385i −0.217146 + 0.376108i −0.953934 0.300016i \(-0.903008\pi\)
0.736788 + 0.676123i \(0.236341\pi\)
\(374\) 0.912961 14.0845i 0.0472081 0.728292i
\(375\) 18.6892 5.07095i 0.965105 0.261863i
\(376\) −1.40146 + 0.479110i −0.0722746 + 0.0247082i
\(377\) 6.75393 0.347845
\(378\) 17.9075 27.3006i 0.921065 1.40419i
\(379\) 4.09156 0.210169 0.105085 0.994463i \(-0.466489\pi\)
0.105085 + 0.994463i \(0.466489\pi\)
\(380\) 7.57480 1.46231i 0.388579 0.0750148i
\(381\) 11.2783 + 9.41381i 0.577804 + 0.482284i
\(382\) 16.1804 + 1.04882i 0.827863 + 0.0536623i
\(383\) 8.65205 + 4.99526i 0.442099 + 0.255246i 0.704488 0.709716i \(-0.251177\pi\)
−0.262389 + 0.964962i \(0.584510\pi\)
\(384\) 19.4952 + 1.98452i 0.994859 + 0.101272i
\(385\) 22.7156 25.5348i 1.15769 1.30137i
\(386\) 11.2350 5.55055i 0.571846 0.282516i
\(387\) −4.65687 5.49168i −0.236722 0.279158i
\(388\) −17.7054 13.5453i −0.898853 0.687660i
\(389\) −15.5346 26.9067i −0.787636 1.36423i −0.927412 0.374042i \(-0.877971\pi\)
0.139776 0.990183i \(-0.455362\pi\)
\(390\) 31.9417 + 15.0415i 1.61743 + 0.761657i
\(391\) 12.5450 + 7.24287i 0.634429 + 0.366288i
\(392\) −23.7018 + 27.1448i −1.19712 + 1.37102i
\(393\) −2.72832 7.43589i −0.137626 0.375091i
\(394\) 13.8323 + 9.22802i 0.696859 + 0.464901i
\(395\) 7.65063 + 23.0740i 0.384945 + 1.16098i
\(396\) −9.40886 + 18.3707i −0.472813 + 0.923164i
\(397\) 19.0643 0.956811 0.478406 0.878139i \(-0.341215\pi\)
0.478406 + 0.878139i \(0.341215\pi\)
\(398\) 28.9752 + 19.3304i 1.45240 + 0.968948i
\(399\) 2.27128 13.0796i 0.113706 0.654797i
\(400\) 18.5628 7.44452i 0.928142 0.372226i
\(401\) −10.4688 6.04419i −0.522789 0.301832i 0.215286 0.976551i \(-0.430932\pi\)
−0.738075 + 0.674719i \(0.764265\pi\)
\(402\) −34.5861 8.34169i −1.72500 0.416046i
\(403\) 12.1629 7.02225i 0.605877 0.349803i
\(404\) 10.1333 13.2454i 0.504151 0.658985i
\(405\) 3.12700 + 19.8802i 0.155382 + 0.987854i
\(406\) −2.91611 5.90257i −0.144724 0.292940i
\(407\) 9.00657 5.19995i 0.446439 0.257752i
\(408\) −8.94883 11.0420i −0.443033 0.546661i
\(409\) −17.0935 + 29.6068i −0.845218 + 1.46396i 0.0402130 + 0.999191i \(0.487196\pi\)
−0.885431 + 0.464770i \(0.846137\pi\)
\(410\) −1.79108 6.85878i −0.0884552 0.338731i
\(411\) −5.02555 + 28.9405i −0.247892 + 1.42753i
\(412\) 10.3403 + 1.34617i 0.509428 + 0.0663211i
\(413\) 28.4201i 1.39846i
\(414\) −12.6268 17.0090i −0.620575 0.835948i
\(415\) 4.15253 1.37685i 0.203840 0.0675871i
\(416\) 34.5708 + 11.5965i 1.69497 + 0.568567i
\(417\) −21.2469 + 7.79575i −1.04046 + 0.381759i
\(418\) −0.542845 + 8.37462i −0.0265514 + 0.409616i
\(419\) −3.57511 2.06409i −0.174656 0.100838i 0.410124 0.912030i \(-0.365486\pi\)
−0.584779 + 0.811192i \(0.698819\pi\)
\(420\) −0.645819 34.4097i −0.0315127 1.67902i
\(421\) −8.50677 + 4.91139i −0.414595 + 0.239366i −0.692762 0.721166i \(-0.743606\pi\)
0.278167 + 0.960533i \(0.410273\pi\)
\(422\) −11.4290 23.1337i −0.556354 1.12613i
\(423\) −1.01601 1.19815i −0.0494002 0.0582558i
\(424\) 0.756786 3.84805i 0.0367528 0.186878i
\(425\) −13.3218 5.74060i −0.646201 0.278460i
\(426\) 1.57761 0.465512i 0.0764353 0.0225541i
\(427\) 13.5474 + 7.82161i 0.655606 + 0.378514i
\(428\) 5.49690 + 13.2168i 0.265703 + 0.638859i
\(429\) −24.6109 + 29.4853i −1.18823 + 1.42356i
\(430\) −7.31856 2.01103i −0.352932 0.0969804i
\(431\) −6.50175 −0.313178 −0.156589 0.987664i \(-0.550050\pi\)
−0.156589 + 0.987664i \(0.550050\pi\)
\(432\) 5.59334 + 20.0179i 0.269110 + 0.963110i
\(433\) 4.89817i 0.235391i −0.993050 0.117695i \(-0.962449\pi\)
0.993050 0.117695i \(-0.0375506\pi\)
\(434\) −11.3886 7.59775i −0.546670 0.364704i
\(435\) 3.77546 + 1.48775i 0.181019 + 0.0713320i
\(436\) −20.1648 + 8.38658i −0.965719 + 0.401644i
\(437\) −7.45925 4.30660i −0.356825 0.206013i
\(438\) −8.00857 27.1408i −0.382664 1.29684i
\(439\) 5.41005 3.12349i 0.258208 0.149076i −0.365309 0.930886i \(-0.619037\pi\)
0.623517 + 0.781810i \(0.285703\pi\)
\(440\) 2.73350 + 21.5841i 0.130314 + 1.02898i
\(441\) −35.9846 12.8861i −1.71355 0.613625i
\(442\) −11.7144 23.7114i −0.557198 1.12784i
\(443\) 7.00848 + 12.1390i 0.332983 + 0.576743i 0.983095 0.183095i \(-0.0586115\pi\)
−0.650112 + 0.759838i \(0.725278\pi\)
\(444\) 3.10887 10.0007i 0.147541 0.474611i
\(445\) −5.32771 1.09905i −0.252558 0.0521002i
\(446\) −1.37832 0.0893428i −0.0652651 0.00423050i
\(447\) −14.3843 + 5.27780i −0.680356 + 0.249631i
\(448\) −4.79171 35.2200i −0.226387 1.66399i
\(449\) 27.5050i 1.29804i 0.760771 + 0.649020i \(0.224821\pi\)
−0.760771 + 0.649020i \(0.775179\pi\)
\(450\) 14.5421 + 15.4443i 0.685522 + 0.728052i
\(451\) 7.71135 0.363113
\(452\) 26.6501 + 3.46950i 1.25351 + 0.163192i
\(453\) −22.2638 3.86614i −1.04604 0.181647i
\(454\) −19.0294 1.23349i −0.893093 0.0578905i
\(455\) 12.9385 62.7200i 0.606566 2.94036i
\(456\) 5.32096 + 6.56556i 0.249177 + 0.307460i
\(457\) −24.6195 + 14.2141i −1.15165 + 0.664905i −0.949289 0.314406i \(-0.898195\pi\)
−0.202361 + 0.979311i \(0.564861\pi\)
\(458\) −11.8512 + 5.85497i −0.553770 + 0.273585i
\(459\) 7.43564 13.1137i 0.347066 0.612096i
\(460\) −21.1036 7.29684i −0.983959 0.340217i
\(461\) −14.7518 25.5509i −0.687060 1.19002i −0.972785 0.231711i \(-0.925567\pi\)
0.285724 0.958312i \(-0.407766\pi\)
\(462\) 36.3947 + 8.77791i 1.69324 + 0.408386i
\(463\) 14.2019 24.5984i 0.660019 1.14319i −0.320592 0.947217i \(-0.603882\pi\)
0.980610 0.195968i \(-0.0627849\pi\)
\(464\) 4.05140 + 1.07307i 0.188081 + 0.0498160i
\(465\) 8.34593 1.24622i 0.387033 0.0577921i
\(466\) −13.5835 + 20.3609i −0.629244 + 0.943200i
\(467\) −18.8199 −0.870881 −0.435441 0.900217i \(-0.643407\pi\)
−0.435441 + 0.900217i \(0.643407\pi\)
\(468\) 1.94325 + 38.6270i 0.0898269 + 1.78553i
\(469\) 64.5336i 2.97988i
\(470\) −1.59672 0.438755i −0.0736514 0.0202383i
\(471\) −9.75969 + 3.58096i −0.449703 + 0.165002i
\(472\) −13.6281 11.8995i −0.627283 0.547720i
\(473\) 4.12820 7.15026i 0.189815 0.328769i
\(474\) −18.3507 + 19.2971i −0.842877 + 0.886346i
\(475\) 7.92111 + 3.41335i 0.363446 + 0.156615i
\(476\) −15.6646 + 20.4756i −0.717988 + 0.938496i
\(477\) 4.09266 0.743577i 0.187390 0.0340461i
\(478\) −14.0547 28.4484i −0.642845 1.30120i
\(479\) 15.7865 + 27.3430i 0.721302 + 1.24933i 0.960478 + 0.278356i \(0.0897895\pi\)
−0.239176 + 0.970976i \(0.576877\pi\)
\(480\) 16.7707 + 14.0977i 0.765472 + 0.643469i
\(481\) 9.74380 16.8768i 0.444279 0.769514i
\(482\) −17.7469 1.15036i −0.808349 0.0523974i
\(483\) −24.6221 + 29.4987i −1.12035 + 1.34224i
\(484\) −1.65329 0.215238i −0.0751496 0.00978354i
\(485\) −7.84403 23.6573i −0.356179 1.07422i
\(486\) −17.5981 + 13.2780i −0.798268 + 0.602303i
\(487\) −26.0524 −1.18055 −0.590273 0.807204i \(-0.700980\pi\)
−0.590273 + 0.807204i \(0.700980\pi\)
\(488\) −9.42296 + 3.22139i −0.426558 + 0.145825i
\(489\) 1.70559 2.04339i 0.0771293 0.0924053i
\(490\) −38.9826 + 10.1798i −1.76105 + 0.459876i
\(491\) 15.9676 + 9.21888i 0.720606 + 0.416042i 0.814976 0.579495i \(-0.196750\pi\)
−0.0943697 + 0.995537i \(0.530084\pi\)
\(492\) 5.70401 5.26928i 0.257157 0.237557i
\(493\) −1.51990 2.63255i −0.0684530 0.118564i
\(494\) 6.96538 + 14.0988i 0.313387 + 0.634334i
\(495\) −20.2526 + 11.0611i −0.910284 + 0.497158i
\(496\) 8.41171 2.27990i 0.377697 0.102371i
\(497\) −1.49178 2.58383i −0.0669153 0.115901i
\(498\) 3.47283 + 3.30251i 0.155621 + 0.147989i
\(499\) 4.26300 7.38373i 0.190838 0.330541i −0.754690 0.656081i \(-0.772213\pi\)
0.945528 + 0.325540i \(0.105546\pi\)
\(500\) 21.8403 + 4.79614i 0.976726 + 0.214490i
\(501\) −6.44962 17.5780i −0.288148 0.785329i
\(502\) 20.5046 + 13.6794i 0.915163 + 0.610540i
\(503\) 8.43519i 0.376107i −0.982159 0.188053i \(-0.939782\pi\)
0.982159 0.188053i \(-0.0602178\pi\)
\(504\) 32.9189 18.3761i 1.46632 0.818537i
\(505\) 17.6981 5.86815i 0.787554 0.261129i
\(506\) 13.4805 20.2065i 0.599283 0.898290i
\(507\) −8.46062 + 48.7219i −0.375749 + 2.16381i
\(508\) 6.51420 + 15.6628i 0.289021 + 0.694926i
\(509\) 10.7797 18.6710i 0.477801 0.827576i −0.521875 0.853022i \(-0.674767\pi\)
0.999676 + 0.0254459i \(0.00810057\pi\)
\(510\) −1.32525 15.8352i −0.0586833 0.701193i
\(511\) −44.4517 + 25.6642i −1.96643 + 1.13532i
\(512\) 18.8951 + 12.4489i 0.835053 + 0.550170i
\(513\) −4.42122 + 7.79740i −0.195202 + 0.344264i
\(514\) 0.829690 + 1.67939i 0.0365961 + 0.0740749i
\(515\) 8.71049 + 7.74878i 0.383830 + 0.341452i
\(516\) −1.83228 8.10984i −0.0806617 0.357016i
\(517\) 0.900669 1.56000i 0.0396114 0.0686089i
\(518\) −18.9564 1.22876i −0.832897 0.0539886i
\(519\) 37.9373 + 6.58786i 1.66526 + 0.289175i
\(520\) 24.6583 + 32.4652i 1.08134 + 1.42369i
\(521\) 0.782710i 0.0342912i 0.999853 + 0.0171456i \(0.00545788\pi\)
−0.999853 + 0.0171456i \(0.994542\pi\)
\(522\) 0.510067 + 4.41597i 0.0223250 + 0.193282i
\(523\) 17.8348i 0.779862i −0.920844 0.389931i \(-0.872499\pi\)
0.920844 0.389931i \(-0.127501\pi\)
\(524\) 1.18072 9.06940i 0.0515801 0.396199i
\(525\) 21.0485 32.2105i 0.918633 1.40578i
\(526\) 0.235411 3.63175i 0.0102644 0.158352i
\(527\) −5.47427 3.16057i −0.238463 0.137677i
\(528\) −19.4477 + 13.7768i −0.846354 + 0.599558i
\(529\) 0.965104 + 1.67161i 0.0419611 + 0.0726787i
\(530\) 3.12010 3.08062i 0.135529 0.133814i
\(531\) 6.46949 18.0661i 0.280752 0.784002i
\(532\) 9.31418 12.1747i 0.403821 0.527842i
\(533\) 12.5138 7.22487i 0.542035 0.312944i
\(534\) −1.68649 5.71548i −0.0729817 0.247333i
\(535\) −3.23337 + 15.6739i −0.139791 + 0.677641i
\(536\) −30.9453 27.0203i −1.33663 1.16710i
\(537\) 21.7685 26.0799i 0.939380 1.12543i
\(538\) −19.7943 + 29.6704i −0.853391 + 1.27918i
\(539\) 43.8283i 1.88782i
\(540\) −7.42243 + 22.0206i −0.319410 + 0.947616i
\(541\) 30.1985i 1.29834i −0.760645 0.649168i \(-0.775117\pi\)
0.760645 0.649168i \(-0.224883\pi\)
\(542\) −27.8716 18.5942i −1.19719 0.798688i
\(543\) −15.8604 + 19.0017i −0.680636 + 0.815440i
\(544\) −3.25970 16.0847i −0.139758 0.689626i
\(545\) −23.9135 4.93312i −1.02434 0.211312i
\(546\) 67.2849 19.8541i 2.87953 0.849676i
\(547\) −13.0967 + 7.56137i −0.559973 + 0.323301i −0.753135 0.657866i \(-0.771459\pi\)
0.193161 + 0.981167i \(0.438126\pi\)
\(548\) −20.6090 + 26.9384i −0.880373 + 1.15075i
\(549\) −6.83135 8.05596i −0.291555 0.343820i
\(550\) −11.0510 + 21.6693i −0.471215 + 0.923981i
\(551\) 0.903732 + 1.56531i 0.0385003 + 0.0666844i
\(552\) −3.83599 24.1580i −0.163271 1.02823i
\(553\) 41.8311 + 24.1512i 1.77884 + 1.02701i
\(554\) 15.3292 + 0.993643i 0.651276 + 0.0422159i
\(555\) 9.16440 7.28779i 0.389007 0.309349i
\(556\) −25.9144 3.37373i −1.09901 0.143078i
\(557\) 33.5757i 1.42265i 0.702865 + 0.711323i \(0.251904\pi\)
−0.702865 + 0.711323i \(0.748096\pi\)
\(558\) 5.50997 + 7.42222i 0.233256 + 0.314208i
\(559\) 15.4711i 0.654357i
\(560\) 17.7263 35.5674i 0.749072 1.50300i
\(561\) 17.0312 + 2.95750i 0.719059 + 0.124866i
\(562\) −2.29095 + 35.3432i −0.0966381 + 1.49086i
\(563\) 7.95097 13.7715i 0.335094 0.580399i −0.648409 0.761292i \(-0.724565\pi\)
0.983503 + 0.180893i \(0.0578987\pi\)
\(564\) −0.399757 1.76936i −0.0168328 0.0745035i
\(565\) 22.4496 + 19.9710i 0.944464 + 0.840187i
\(566\) −33.8902 + 16.7432i −1.42451 + 0.703767i
\(567\) 30.8975 + 25.3840i 1.29757 + 1.06603i
\(568\) 1.86362 + 0.366512i 0.0781956 + 0.0153785i
\(569\) 30.6625 17.7030i 1.28544 0.742148i 0.307601 0.951515i \(-0.400474\pi\)
0.977837 + 0.209368i \(0.0671405\pi\)
\(570\) 0.787995 + 9.41558i 0.0330055 + 0.394375i
\(571\) −13.5162 + 23.4107i −0.565634 + 0.979706i 0.431357 + 0.902181i \(0.358035\pi\)
−0.996990 + 0.0775247i \(0.975298\pi\)
\(572\) −40.9480 + 17.0304i −1.71212 + 0.712075i
\(573\) −3.39761 + 19.5657i −0.141937 + 0.817369i
\(574\) −11.7172 7.81698i −0.489066 0.326275i
\(575\) −14.9155 20.0195i −0.622021 0.834872i
\(576\) −4.97142 + 23.4795i −0.207142 + 0.978311i
\(577\) 39.6149i 1.64919i 0.565723 + 0.824596i \(0.308597\pi\)
−0.565723 + 0.824596i \(0.691403\pi\)
\(578\) 6.73637 10.0974i 0.280196 0.419998i
\(579\) 5.28663 + 14.4084i 0.219705 + 0.598793i
\(580\) 3.06961 + 3.54035i 0.127459 + 0.147005i
\(581\) 4.34640 7.52818i 0.180319 0.312322i
\(582\) 18.8146 19.7849i 0.779891 0.820112i
\(583\) 2.38487 + 4.13072i 0.0987713 + 0.171077i
\(584\) 6.30540 32.0612i 0.260919 1.32670i
\(585\) −22.5022 + 36.9246i −0.930352 + 1.52664i
\(586\) 22.2104 10.9729i 0.917504 0.453284i
\(587\) −16.4029 28.4107i −0.677020 1.17263i −0.975874 0.218335i \(-0.929938\pi\)
0.298854 0.954299i \(-0.403396\pi\)
\(588\) −29.9485 32.4193i −1.23505 1.33695i
\(589\) 3.25499 + 1.87927i 0.134120 + 0.0774340i
\(590\) −5.11078 19.5712i −0.210407 0.805735i
\(591\) −13.0498 + 15.6344i −0.536797 + 0.643113i
\(592\) 8.52629 8.57556i 0.350429 0.352453i
\(593\) −3.01321 −0.123738 −0.0618689 0.998084i \(-0.519706\pi\)
−0.0618689 + 0.998084i \(0.519706\pi\)
\(594\) −21.1373 13.8648i −0.867272 0.568879i
\(595\) −27.3587 + 9.07132i −1.12160 + 0.371888i
\(596\) −17.5443 2.28405i −0.718642 0.0935583i
\(597\) −27.3361 + 32.7502i −1.11879 + 1.34038i
\(598\) 2.94420 45.4209i 0.120397 1.85740i
\(599\) −6.12099 + 10.6019i −0.250097 + 0.433180i −0.963552 0.267520i \(-0.913796\pi\)
0.713455 + 0.700701i \(0.247129\pi\)
\(600\) 6.63263 + 23.5798i 0.270776 + 0.962642i
\(601\) 13.5824 + 23.5254i 0.554038 + 0.959622i 0.997978 + 0.0635651i \(0.0202470\pi\)
−0.443940 + 0.896057i \(0.646420\pi\)
\(602\) −13.5209 + 6.67988i −0.551071 + 0.272252i
\(603\) 14.6903 41.0228i 0.598235 1.67058i
\(604\) −20.7236 15.8544i −0.843232 0.645107i
\(605\) −1.39271 1.23894i −0.0566217 0.0503702i
\(606\) 14.8012 + 14.0753i 0.601257 + 0.571769i
\(607\) 2.87905 4.98666i 0.116857 0.202402i −0.801663 0.597776i \(-0.796051\pi\)
0.918521 + 0.395373i \(0.129385\pi\)
\(608\) 1.93821 + 9.56394i 0.0786049 + 0.387869i
\(609\) 7.56980 2.77746i 0.306744 0.112548i
\(610\) −10.7359 2.95006i −0.434683 0.119444i
\(611\) 3.37540i 0.136554i
\(612\) 14.6187 9.45005i 0.590927 0.381996i
\(613\) 31.0299 1.25329 0.626643 0.779307i \(-0.284428\pi\)
0.626643 + 0.779307i \(0.284428\pi\)
\(614\) −25.7114 17.1530i −1.03763 0.692240i
\(615\) 8.58675 1.28218i 0.346251 0.0517025i
\(616\) 32.5636 + 28.4333i 1.31202 + 1.14561i
\(617\) −5.20064 + 9.00778i −0.209370 + 0.362640i −0.951516 0.307598i \(-0.900475\pi\)
0.742146 + 0.670238i \(0.233808\pi\)
\(618\) −2.99434 + 12.4150i −0.120450 + 0.499406i
\(619\) −10.9667 18.9949i −0.440790 0.763471i 0.556958 0.830541i \(-0.311968\pi\)
−0.997748 + 0.0670697i \(0.978635\pi\)
\(620\) 9.20896 + 3.18412i 0.369841 + 0.127877i
\(621\) 22.3669 13.1468i 0.897551 0.527564i
\(622\) −0.469669 0.950669i −0.0188320 0.0381183i
\(623\) −9.36091 + 5.40452i −0.375037 + 0.216528i
\(624\) −18.6518 + 40.5776i −0.746668 + 1.62440i
\(625\) 17.1695 + 18.1716i 0.686781 + 0.726864i
\(626\) 1.45771 22.4885i 0.0582619 0.898823i
\(627\) −10.1267 1.75852i −0.404423 0.0702287i
\(628\) −11.9037 1.54971i −0.475009 0.0618403i
\(629\) −8.77098 −0.349722
\(630\) 41.9858 + 3.72297i 1.67275 + 0.148327i
\(631\) 21.1882i 0.843487i −0.906715 0.421744i \(-0.861418\pi\)
0.906715 0.421744i \(-0.138582\pi\)
\(632\) −29.0958 + 9.94684i −1.15737 + 0.395664i
\(633\) 29.6679 10.8856i 1.17919 0.432662i
\(634\) −2.47599 + 38.1978i −0.0983343 + 1.51703i
\(635\) −3.83176 + 18.5746i −0.152059 + 0.737111i
\(636\) 4.58665 + 1.42584i 0.181872 + 0.0565381i
\(637\) −41.0633 71.1237i −1.62699 2.81802i
\(638\) −4.57002 + 2.25778i −0.180929 + 0.0893863i
\(639\) 0.360115 + 1.98208i 0.0142459 + 0.0784098i
\(640\) 9.63338 + 23.3923i 0.380793 + 0.924660i
\(641\) −32.1022 + 18.5342i −1.26796 + 0.732058i −0.974602 0.223944i \(-0.928107\pi\)
−0.293360 + 0.956002i \(0.594773\pi\)
\(642\) −16.8147 + 4.96159i −0.663622 + 0.195818i
\(643\) 1.11222 + 0.642142i 0.0438618 + 0.0253236i 0.521771 0.853086i \(-0.325272\pi\)
−0.477909 + 0.878409i \(0.658605\pi\)
\(644\) −40.9667 + 17.0381i −1.61431 + 0.671396i
\(645\) 3.40795 8.64837i 0.134188 0.340529i
\(646\) 3.92794 5.88776i 0.154543 0.231651i
\(647\) 20.7519i 0.815840i −0.913018 0.407920i \(-0.866254\pi\)
0.913018 0.407920i \(-0.133746\pi\)
\(648\) −25.1090 + 4.18774i −0.986375 + 0.164510i
\(649\) 22.0040 0.863733
\(650\) 2.36893 + 45.5183i 0.0929170 + 1.78537i
\(651\) 10.7444 12.8723i 0.421105 0.504507i
\(652\) 2.83778 1.18024i 0.111136 0.0462217i
\(653\) −0.660974 0.381613i −0.0258659 0.0149337i 0.487011 0.873396i \(-0.338087\pi\)
−0.512877 + 0.858462i \(0.671420\pi\)
\(654\) −7.56986 25.6540i −0.296005 1.00315i
\(655\) 6.79643 7.63994i 0.265559 0.298517i
\(656\) 8.65443 2.34569i 0.337899 0.0915837i
\(657\) 34.0992 6.19534i 1.33034 0.241703i
\(658\) −2.94992 + 1.45738i −0.115000 + 0.0568146i
\(659\) 36.1360 20.8631i 1.40766 0.812711i 0.412496 0.910960i \(-0.364657\pi\)
0.995162 + 0.0982481i \(0.0313239\pi\)
\(660\) −26.6415 + 0.500020i −1.03702 + 0.0194633i
\(661\) −6.19796 3.57839i −0.241073 0.139183i 0.374597 0.927188i \(-0.377781\pi\)
−0.615670 + 0.788004i \(0.711114\pi\)
\(662\) 15.5976 + 1.01104i 0.606218 + 0.0392952i
\(663\) 30.4089 11.1574i 1.18098 0.433318i
\(664\) 1.79009 + 5.23625i 0.0694691 + 0.203206i
\(665\) 16.2674 5.39379i 0.630824 0.209162i
\(666\) 11.7705 + 5.09630i 0.456099 + 0.197478i
\(667\) 5.23156i 0.202567i
\(668\) 2.79117 21.4396i 0.107994 0.829523i
\(669\) 0.289422 1.66669i 0.0111897 0.0644378i
\(670\) −11.6051 44.4405i −0.448343 1.71689i
\(671\) 6.05582 10.4890i 0.233782 0.404923i
\(672\) 43.5158 1.21935i 1.67866 0.0470374i
\(673\) 16.9451 9.78327i 0.653187 0.377117i −0.136489 0.990642i \(-0.543582\pi\)
0.789676 + 0.613524i \(0.210249\pi\)
\(674\) 24.0968 11.9048i 0.928173 0.458556i
\(675\) −20.7125 + 15.6842i −0.797224 + 0.603683i
\(676\) −34.6957 + 45.3514i −1.33445 + 1.74428i
\(677\) 10.7409 6.20128i 0.412807 0.238334i −0.279188 0.960236i \(-0.590065\pi\)
0.691995 + 0.721902i \(0.256732\pi\)
\(678\) −7.71735 + 31.9974i −0.296383 + 1.22885i
\(679\) −42.8886 24.7617i −1.64591 0.950268i
\(680\) 7.10521 16.9173i 0.272472 0.648749i
\(681\) 3.99584 23.0107i 0.153121 0.881771i
\(682\) −5.88250 + 8.81752i −0.225253 + 0.337640i
\(683\) 3.77134 0.144306 0.0721531 0.997394i \(-0.477013\pi\)
0.0721531 + 0.997394i \(0.477013\pi\)
\(684\) −8.69228 + 5.61899i −0.332358 + 0.214847i
\(685\) −35.9942 + 11.9346i −1.37527 + 0.455997i
\(686\) −20.0187 + 30.0069i −0.764319 + 1.14567i
\(687\) −5.57658 15.1986i −0.212760 0.579865i
\(688\) 2.45806 9.28046i 0.0937127 0.353814i
\(689\) 7.74026 + 4.46884i 0.294880 + 0.170249i
\(690\) 11.6511 24.7418i 0.443549 0.941906i
\(691\) −12.2697 21.2518i −0.466763 0.808457i 0.532516 0.846420i \(-0.321246\pi\)
−0.999279 + 0.0379629i \(0.987913\pi\)
\(692\) 35.3128 + 27.0158i 1.34239 + 1.02699i
\(693\) −15.4585 + 43.1680i −0.587220 + 1.63982i
\(694\) 22.6401 + 45.8263i 0.859406 + 1.73954i
\(695\) −21.8299 19.4197i −0.828056 0.736632i
\(696\) −1.83763 + 4.79282i −0.0696551 + 0.181671i
\(697\) −5.63223 3.25177i −0.213336 0.123170i
\(698\) −1.03532 + 15.9721i −0.0391873 + 0.604554i
\(699\) −23.0136 19.2091i −0.870455 0.726556i
\(700\) 38.7578 21.7236i 1.46491 0.821073i
\(701\) −9.59102 −0.362248 −0.181124 0.983460i \(-0.557973\pi\)
−0.181124 + 0.983460i \(0.557973\pi\)
\(702\) −47.2913 2.69574i −1.78489 0.101744i
\(703\) 5.21521 0.196695
\(704\) −27.2688 + 3.70994i −1.02773 + 0.139824i
\(705\) 0.743529 1.88685i 0.0280029 0.0710630i
\(706\) 31.7555 + 2.05840i 1.19513 + 0.0774688i
\(707\) 18.5243 32.0851i 0.696679 1.20668i
\(708\) 16.2762 15.0357i 0.611695 0.565075i
\(709\) −28.1065 + 16.2273i −1.05556 + 0.609428i −0.924201 0.381906i \(-0.875268\pi\)
−0.131360 + 0.991335i \(0.541934\pi\)
\(710\) 1.49195 + 1.51107i 0.0559919 + 0.0567094i
\(711\) −21.0935 24.8748i −0.791068 0.932878i
\(712\) 1.32783 6.75165i 0.0497625 0.253029i
\(713\) −5.43939 9.42131i −0.203707 0.352831i
\(714\) −22.8805 21.7584i −0.856282 0.814287i
\(715\) −48.5604 10.0175i −1.81606 0.374635i
\(716\) 36.2188 15.0635i 1.35356 0.562948i
\(717\) 36.4838 13.3864i 1.36251 0.499924i
\(718\) 6.50107 9.74473i 0.242618 0.363670i
\(719\) −3.09937 −0.115587 −0.0577935 0.998329i \(-0.518407\pi\)
−0.0577935 + 0.998329i \(0.518407\pi\)
\(720\) −19.3648 + 18.5743i −0.721682 + 0.692225i
\(721\) 23.1650 0.862710
\(722\) 12.5766 18.8515i 0.468051 0.701581i
\(723\) 3.72654 21.4599i 0.138591 0.798102i
\(724\) −26.3888 + 10.9752i −0.980732 + 0.407888i
\(725\) 0.610126 + 5.20322i 0.0226595 + 0.193243i
\(726\) 0.478762 1.98503i 0.0177685 0.0736713i
\(727\) 14.2922 + 24.7548i 0.530069 + 0.918106i 0.999385 + 0.0350755i \(0.0111672\pi\)
−0.469316 + 0.883030i \(0.655500\pi\)
\(728\) 79.4831 + 15.6317i 2.94584 + 0.579351i
\(729\) −13.8626 23.1696i −0.513429 0.858132i
\(730\) 25.9961 25.6672i 0.962158 0.949984i
\(731\) −6.03033 + 3.48161i −0.223040 + 0.128772i
\(732\) −2.68785 11.8966i −0.0993456 0.439712i
\(733\) 7.45704 12.9160i 0.275432 0.477062i −0.694812 0.719191i \(-0.744512\pi\)
0.970244 + 0.242129i \(0.0778458\pi\)
\(734\) 17.2729 + 1.11963i 0.637554 + 0.0413264i
\(735\) −7.28741 48.8037i −0.268800 1.80015i
\(736\) 8.98262 26.7783i 0.331104 0.987063i
\(737\) 49.9646 1.84047
\(738\) 5.66896 + 7.63639i 0.208677 + 0.281099i
\(739\) 34.3294 1.26283 0.631415 0.775445i \(-0.282475\pi\)
0.631415 + 0.775445i \(0.282475\pi\)
\(740\) 13.2752 2.56276i 0.488004 0.0942087i
\(741\) −18.0811 + 6.63419i −0.664226 + 0.243713i
\(742\) 0.563551 8.69406i 0.0206886 0.319169i
\(743\) −3.91484 2.26023i −0.143621 0.0829199i 0.426467 0.904503i \(-0.359758\pi\)
−0.570089 + 0.821583i \(0.693091\pi\)
\(744\) 1.67391 + 10.5418i 0.0613686 + 0.386482i
\(745\) −14.7791 13.1474i −0.541464 0.481682i
\(746\) −5.25401 10.6348i −0.192363 0.389366i
\(747\) −4.47662 + 3.79612i −0.163791 + 0.138893i
\(748\) 15.8530 + 12.1282i 0.579645 + 0.443452i
\(749\) 15.8999 + 27.5394i 0.580968 + 1.00627i
\(750\) −8.70249 + 25.9666i −0.317770 + 0.948168i
\(751\) 10.3164 + 5.95615i 0.376449 + 0.217343i 0.676272 0.736652i \(-0.263594\pi\)
−0.299823 + 0.953995i \(0.596928\pi\)
\(752\) 0.536286 2.02476i 0.0195564 0.0738354i
\(753\) −19.3447 + 23.1760i −0.704959 + 0.844580i
\(754\) −5.30080 + 7.94560i −0.193044 + 0.289362i
\(755\) −9.18121 27.6901i −0.334139 1.00775i
\(756\) 18.0628 + 42.4940i 0.656938 + 1.54549i
\(757\) 9.35259 0.339926 0.169963 0.985450i \(-0.445635\pi\)
0.169963 + 0.985450i \(0.445635\pi\)
\(758\) −3.21125 + 4.81348i −0.116638 + 0.174834i
\(759\) 22.8392 + 19.0635i 0.829009 + 0.691961i
\(760\) −4.22475 + 10.0590i −0.153248 + 0.364878i
\(761\) 24.6852 + 14.2520i 0.894838 + 0.516635i 0.875522 0.483178i \(-0.160518\pi\)
0.0193163 + 0.999813i \(0.493851\pi\)
\(762\) −19.9265 + 5.87982i −0.721862 + 0.213003i
\(763\) −42.0166 + 24.2583i −1.52110 + 0.878209i
\(764\) −13.9331 + 18.2122i −0.504080 + 0.658893i
\(765\) 19.4564 + 0.461419i 0.703447 + 0.0166826i
\(766\) −12.6672 + 6.25810i −0.457684 + 0.226114i
\(767\) 35.7077 20.6159i 1.28933 0.744396i
\(768\) −17.6354 + 21.3774i −0.636363 + 0.771390i
\(769\) 10.8746 18.8354i 0.392149 0.679221i −0.600584 0.799562i \(-0.705065\pi\)
0.992733 + 0.120340i \(0.0383986\pi\)
\(770\) 12.2119 + 46.7645i 0.440088 + 1.68527i
\(771\) −2.15375 + 0.790240i −0.0775655 + 0.0284598i
\(772\) −2.28787 + 17.5737i −0.0823422 + 0.632490i
\(773\) 6.91973i 0.248885i 0.992227 + 0.124443i \(0.0397143\pi\)
−0.992227 + 0.124443i \(0.960286\pi\)
\(774\) 10.1156 1.16840i 0.363597 0.0419973i
\(775\) 6.50869 + 8.73592i 0.233799 + 0.313804i
\(776\) 29.8313 10.1983i 1.07088 0.366097i
\(777\) 3.98052 22.9225i 0.142800 0.822339i
\(778\) 43.8465 + 2.84214i 1.57197 + 0.101896i
\(779\) 3.34892 + 1.93350i 0.119987 + 0.0692747i
\(780\) −42.7648 + 25.7722i −1.53123 + 0.922792i
\(781\) −2.00051 + 1.15500i −0.0715840 + 0.0413290i
\(782\) −18.3668 + 9.07393i −0.656794 + 0.324483i
\(783\) −5.44423 + 0.0424027i −0.194561 + 0.00151535i
\(784\) −13.3320 49.1883i −0.476141 1.75673i
\(785\) −10.0275 8.92040i −0.357897 0.318383i
\(786\) 10.8892 + 2.62633i 0.388405 + 0.0936780i
\(787\) −8.18337 4.72467i −0.291706 0.168416i 0.347005 0.937863i \(-0.387199\pi\)
−0.638711 + 0.769447i \(0.720532\pi\)
\(788\) −21.7124 + 9.03025i −0.773474 + 0.321689i
\(789\) 4.39158 + 0.762603i 0.156344 + 0.0271494i
\(790\) −33.1497 9.10904i −1.17941 0.324085i
\(791\) 59.7035 2.12281
\(792\) −14.2276 25.4872i −0.505554 0.905648i
\(793\) 22.6951i 0.805928i
\(794\) −14.9626 + 22.4281i −0.531003 + 0.795942i
\(795\) 3.34243 + 4.20311i 0.118544 + 0.149069i
\(796\) −45.4823 + 18.9162i −1.61208 + 0.670466i
\(797\) −7.63414 4.40757i −0.270415 0.156124i 0.358661 0.933468i \(-0.383233\pi\)
−0.629076 + 0.777344i \(0.716567\pi\)
\(798\) 13.6047 + 12.9375i 0.481602 + 0.457982i
\(799\) −1.31566 + 0.759599i −0.0465449 + 0.0268727i
\(800\) −5.81097 + 27.6809i −0.205449 + 0.978668i
\(801\) 7.18083 1.30465i 0.253722 0.0460976i
\(802\) 15.3271 7.57221i 0.541218 0.267384i
\(803\) 19.8703 + 34.4164i 0.701208 + 1.21453i
\(804\) 36.9583 34.1415i 1.30342 1.20408i
\(805\) −48.5825 10.0221i −1.71231 0.353232i
\(806\) −1.28476 + 19.8203i −0.0452537 + 0.698141i
\(807\) −33.5361 27.9921i −1.18053 0.985367i
\(808\) 7.62937 + 22.3169i 0.268400 + 0.785106i
\(809\) 36.7458i 1.29191i 0.763375 + 0.645956i \(0.223541\pi\)
−0.763375 + 0.645956i \(0.776459\pi\)
\(810\) −25.8421 11.9242i −0.907999 0.418973i
\(811\) −40.2672 −1.41397 −0.706986 0.707228i \(-0.749946\pi\)
−0.706986 + 0.707228i \(0.749946\pi\)
\(812\) 9.23273 + 1.20199i 0.324005 + 0.0421815i
\(813\) 26.2950 31.5028i 0.922204 1.10485i
\(814\) −0.951358 + 14.6769i −0.0333451 + 0.514424i
\(815\) 3.36534 + 0.694235i 0.117883 + 0.0243180i
\(816\) 20.0137 1.86148i 0.700621 0.0651648i
\(817\) 3.58563 2.07016i 0.125445 0.0724258i
\(818\) −21.4149 43.3463i −0.748753 1.51557i
\(819\) 15.3589 + 84.5356i 0.536683 + 2.95391i
\(820\) 9.47468 + 3.27600i 0.330870 + 0.114403i
\(821\) 13.0871 + 22.6675i 0.456743 + 0.791102i 0.998787 0.0492486i \(-0.0156827\pi\)
−0.542044 + 0.840350i \(0.682349\pi\)
\(822\) −30.1025 28.6261i −1.04994 0.998452i
\(823\) 11.6368 20.1555i 0.405633 0.702577i −0.588762 0.808306i \(-0.700385\pi\)
0.994395 + 0.105730i \(0.0337179\pi\)
\(824\) −9.69922 + 11.1082i −0.337888 + 0.386971i
\(825\) −24.9387 16.2967i −0.868255 0.567377i
\(826\) −33.4345 22.3054i −1.16334 0.776105i
\(827\) −24.4553 −0.850393 −0.425197 0.905101i \(-0.639795\pi\)
−0.425197 + 0.905101i \(0.639795\pi\)
\(828\) 29.9203 1.50523i 1.03980 0.0523105i
\(829\) 17.8015i 0.618271i 0.951018 + 0.309136i \(0.100040\pi\)
−0.951018 + 0.309136i \(0.899960\pi\)
\(830\) −1.63932 + 5.96583i −0.0569016 + 0.207077i
\(831\) −3.21887 + 18.5364i −0.111661 + 0.643020i
\(832\) −40.7754 + 31.5690i −1.41363 + 1.09446i
\(833\) −18.4818 + 32.0113i −0.640355 + 1.10913i
\(834\) 7.50431 31.1141i 0.259853 1.07739i
\(835\) 16.0664 18.0604i 0.556001 0.625007i
\(836\) −9.42620 7.21143i −0.326012 0.249413i
\(837\) −9.76022 + 5.73688i −0.337363 + 0.198296i
\(838\) 5.23420 2.58591i 0.180813 0.0893288i
\(839\) 6.54732 + 11.3403i 0.226039 + 0.391511i 0.956631 0.291304i \(-0.0940891\pi\)
−0.730592 + 0.682814i \(0.760756\pi\)
\(840\) 40.9879 + 26.2466i 1.41422 + 0.905595i
\(841\) 13.9511 24.1640i 0.481072 0.833241i
\(842\) 0.898565 13.8624i 0.0309666 0.477730i
\(843\) −42.7376 7.42145i −1.47196 0.255608i
\(844\) 36.1854 + 4.71089i 1.24555 + 0.162155i
\(845\) −60.5969 + 20.0921i −2.08460 + 0.691189i
\(846\) 2.20696 0.254915i 0.0758769 0.00876417i
\(847\) −3.70383 −0.127265
\(848\) 3.93304 + 3.91045i 0.135061 + 0.134285i
\(849\) −15.9470 43.4627i −0.547301 1.49164i
\(850\) 17.2090 11.1668i 0.590265 0.383018i
\(851\) −13.0726 7.54750i −0.448125 0.258725i
\(852\) −0.690534 + 2.22132i −0.0236573 + 0.0761011i
\(853\) 23.8247 + 41.2656i 0.815743 + 1.41291i 0.908793 + 0.417246i \(0.137005\pi\)
−0.0930509 + 0.995661i \(0.529662\pi\)
\(854\) −19.8343 + 9.79898i −0.678717 + 0.335314i
\(855\) −11.5687 0.274359i −0.395643 0.00938288i
\(856\) −19.8630 3.90641i −0.678905 0.133518i
\(857\) −0.880471 1.52502i −0.0300763 0.0520937i 0.850595 0.525821i \(-0.176242\pi\)
−0.880672 + 0.473727i \(0.842908\pi\)
\(858\) −15.3719 52.0948i −0.524787 1.77849i
\(859\) −4.91608 + 8.51489i −0.167734 + 0.290524i −0.937623 0.347654i \(-0.886978\pi\)
0.769889 + 0.638178i \(0.220312\pi\)
\(860\) 8.10982 7.03151i 0.276542 0.239772i
\(861\) 11.0544 13.2438i 0.376732 0.451347i
\(862\) 5.10289 7.64893i 0.173805 0.260524i
\(863\) 51.8077i 1.76355i 0.471667 + 0.881777i \(0.343652\pi\)
−0.471667 + 0.881777i \(0.656348\pi\)
\(864\) −27.9397 9.13074i −0.950530 0.310634i
\(865\) 15.6447 + 47.1837i 0.531935 + 1.60429i
\(866\) 5.76240 + 3.84431i 0.195814 + 0.130635i
\(867\) 11.4130 + 9.52624i 0.387605 + 0.323528i
\(868\) 17.8766 7.43492i 0.606772 0.252358i
\(869\) 18.6989 32.3874i 0.634316 1.09867i
\(870\) −4.71341 + 3.27395i −0.159799 + 0.110997i
\(871\) 81.0817 46.8125i 2.74735 1.58618i
\(872\) 5.95999 30.3049i 0.201831 1.02625i
\(873\) 21.6267 + 25.5036i 0.731954 + 0.863167i
\(874\) 10.9208 5.39535i 0.369403 0.182500i
\(875\) 49.4883 + 4.30192i 1.67301 + 0.145431i
\(876\) 38.2151 + 11.8798i 1.29117 + 0.401381i
\(877\) −16.5425 + 28.6524i −0.558600 + 0.967523i 0.439014 + 0.898480i \(0.355328\pi\)
−0.997614 + 0.0690427i \(0.978006\pi\)
\(878\) −0.571460 + 8.81607i −0.0192858 + 0.297528i
\(879\) 10.4511 + 28.4839i 0.352507 + 0.960738i
\(880\) −27.5378 13.7244i −0.928299 0.462650i
\(881\) 41.2175i 1.38865i 0.719660 + 0.694327i \(0.244298\pi\)
−0.719660 + 0.694327i \(0.755702\pi\)
\(882\) 43.4022 32.2201i 1.46143 1.08491i
\(883\) 11.3770i 0.382867i 0.981506 + 0.191433i \(0.0613136\pi\)
−0.981506 + 0.191433i \(0.938686\pi\)
\(884\) 37.0891 + 4.82854i 1.24744 + 0.162401i
\(885\) 24.5019 3.65865i 0.823623 0.122984i
\(886\) −19.7815 1.28224i −0.664571 0.0430777i
\(887\) 33.1810 + 19.1571i 1.11411 + 0.643232i 0.939891 0.341475i \(-0.110926\pi\)
0.174220 + 0.984707i \(0.444260\pi\)
\(888\) 9.32520 + 11.5064i 0.312933 + 0.386130i
\(889\) 18.8424 + 32.6360i 0.631954 + 1.09458i
\(890\) 5.47442 5.40515i 0.183503 0.181181i
\(891\) 19.6534 23.9221i 0.658413 0.801422i
\(892\) 1.18687 1.55139i 0.0397395 0.0519443i
\(893\) 0.782292 0.451657i 0.0261784 0.0151141i
\(894\) 5.08050 21.0646i 0.169917 0.704506i
\(895\) 42.9520 + 8.86056i 1.43573 + 0.296176i
\(896\) 45.1950 + 22.0052i 1.50986 + 0.735141i
\(897\) 54.9238 + 9.53760i 1.83385 + 0.318451i
\(898\) −32.3580 21.5872i −1.07980 0.720375i
\(899\) 2.28289i 0.0761387i
\(900\) −29.5827 + 4.98651i −0.986089 + 0.166217i
\(901\) 4.02267i 0.134015i
\(902\) −6.05224 + 9.07195i −0.201518 + 0.302063i
\(903\) −6.36227 17.3400i −0.211723 0.577039i
\(904\) −24.9979 + 28.6292i −0.831418 + 0.952192i
\(905\) −31.2946 6.45576i −1.04027 0.214597i
\(906\) 22.0220 23.1577i 0.731631 0.769363i
\(907\) 38.5617 22.2636i 1.28042 0.739251i 0.303496 0.952833i \(-0.401846\pi\)
0.976925 + 0.213581i \(0.0685128\pi\)
\(908\) 16.3863 21.4188i 0.543798 0.710809i
\(909\) −19.0793 + 16.1790i −0.632822 + 0.536625i
\(910\) 63.6316 + 64.4470i 2.10937 + 2.13640i
\(911\) −22.2854 38.5995i −0.738349 1.27886i −0.953238 0.302220i \(-0.902272\pi\)
0.214889 0.976639i \(-0.431061\pi\)
\(912\) −11.9001 + 1.10683i −0.394053 + 0.0366509i
\(913\) −5.82864 3.36516i −0.192900 0.111371i
\(914\) 2.60054 40.1192i 0.0860181 1.32703i
\(915\) 4.99926 12.6866i 0.165270 0.419407i
\(916\) 2.41335 18.5375i 0.0797393 0.612496i
\(917\) 20.3180i 0.670958i
\(918\) 9.59167 + 19.0399i 0.316572 + 0.628409i
\(919\) 6.48928i 0.214062i 0.994256 + 0.107031i \(0.0341344\pi\)
−0.994256 + 0.107031i \(0.965866\pi\)
\(920\) 25.1474 19.1002i 0.829085 0.629714i
\(921\) 24.2570 29.0612i 0.799294 0.957600i
\(922\) 41.6370 + 2.69892i 1.37124 + 0.0888843i
\(923\) −2.16426 + 3.74861i −0.0712376 + 0.123387i
\(924\) −38.8910 + 35.9269i −1.27942 + 1.18191i
\(925\) 13.8821 + 5.98204i 0.456440 + 0.196688i
\(926\) 17.7923 + 36.0137i 0.584690 + 1.18348i
\(927\) −14.7256 5.27324i −0.483651 0.173196i
\(928\) −4.44214 + 3.92403i −0.145820 + 0.128813i
\(929\) −1.60961 + 0.929307i −0.0528095 + 0.0304896i −0.526172 0.850378i \(-0.676373\pi\)
0.473363 + 0.880868i \(0.343040\pi\)
\(930\) −5.08418 + 10.7966i −0.166717 + 0.354034i
\(931\) 10.9892 19.0339i 0.360157 0.623811i
\(932\) −13.2924 31.9604i −0.435407 1.04690i
\(933\) 1.21919 0.447338i 0.0399146 0.0146452i
\(934\) 14.7708 22.1405i 0.483314 0.724460i
\(935\) 7.02340 + 21.1823i 0.229690 + 0.692734i
\(936\) −46.9675 28.0302i −1.53518 0.916195i
\(937\) 16.0395i 0.523987i −0.965070 0.261993i \(-0.915620\pi\)
0.965070 0.261993i \(-0.0843799\pi\)
\(938\) −75.9199 50.6490i −2.47887 1.65375i
\(939\) 27.1936 + 4.72220i 0.887428 + 0.154103i
\(940\) 1.76936 1.53410i 0.0577100 0.0500367i
\(941\) −6.86599 + 11.8922i −0.223825 + 0.387676i −0.955966 0.293477i \(-0.905188\pi\)
0.732141 + 0.681153i \(0.238521\pi\)
\(942\) 3.44709 14.2922i 0.112312 0.465665i
\(943\) −5.59635 9.69316i −0.182242 0.315653i
\(944\) 24.6950 6.69332i 0.803755 0.217849i
\(945\) −10.0357 + 50.6388i −0.326463 + 1.64728i
\(946\) 5.17185 + 10.4685i 0.168151 + 0.340359i
\(947\) 2.83989 + 4.91884i 0.0922841 + 0.159841i 0.908472 0.417946i \(-0.137250\pi\)
−0.816188 + 0.577787i \(0.803917\pi\)
\(948\) −8.29940 36.7339i −0.269552 1.19306i
\(949\) 64.4903 + 37.2335i 2.09344 + 1.20865i
\(950\) −10.2325 + 6.63976i −0.331985 + 0.215422i
\(951\) −46.1895 8.02088i −1.49780 0.260095i
\(952\) −11.7939 34.4987i −0.382243 1.11811i
\(953\) −2.21764 −0.0718365 −0.0359183 0.999355i \(-0.511436\pi\)
−0.0359183 + 0.999355i \(0.511436\pi\)
\(954\) −2.33734 + 5.39837i −0.0756741 + 0.174779i
\(955\) −24.3344 + 8.06856i −0.787444 + 0.261093i
\(956\) 44.4986 + 5.79316i 1.43919 + 0.187364i
\(957\) −2.15042 5.86086i −0.0695134 0.189455i
\(958\) −44.5574 2.88822i −1.43958 0.0933142i
\(959\) −37.6746 + 65.2543i −1.21658 + 2.10717i
\(960\) −29.7475 + 8.66514i −0.960097 + 0.279666i
\(961\) −13.1264 22.7356i −0.423433 0.733407i
\(962\) 12.2071 + 24.7087i 0.393573 + 0.796640i
\(963\) −3.83823 21.1257i −0.123685 0.680765i
\(964\) 15.2819 19.9753i 0.492198 0.643362i
\(965\) −13.1693 + 14.8038i −0.423936 + 0.476551i
\(966\) −15.3789 52.1185i −0.494807 1.67689i
\(967\) 5.83420 10.1051i 0.187615 0.324959i −0.756840 0.653601i \(-0.773258\pi\)
0.944455 + 0.328642i \(0.106591\pi\)
\(968\) 1.55080 1.77607i 0.0498445 0.0570851i
\(969\) 6.65485 + 5.55470i 0.213784 + 0.178443i
\(970\) 33.9877 + 9.33931i 1.09128 + 0.299867i
\(971\) 7.63561i 0.245038i 0.992466 + 0.122519i \(0.0390973\pi\)
−0.992466 + 0.122519i \(0.960903\pi\)
\(972\) −1.80893 31.1244i −0.0580216 0.998315i
\(973\) −58.0553 −1.86117
\(974\) 20.4472 30.6491i 0.655169 0.982060i
\(975\) −55.7387 3.08050i −1.78507 0.0986549i
\(976\) 3.60582 13.6139i 0.115420 0.435769i
\(977\) 4.06102 7.03389i 0.129923 0.225034i −0.793723 0.608279i \(-0.791860\pi\)
0.923647 + 0.383245i \(0.125193\pi\)
\(978\) 1.06530 + 3.61027i 0.0340646 + 0.115444i
\(979\) 4.18441 + 7.24761i 0.133734 + 0.231635i
\(980\) 18.6195 53.8503i 0.594777 1.72018i
\(981\) 32.2313 5.85596i 1.02907 0.186966i
\(982\) −23.3776 + 11.5495i −0.746008 + 0.368559i
\(983\) 21.3682 12.3369i 0.681540 0.393487i −0.118895 0.992907i \(-0.537935\pi\)
0.800435 + 0.599420i \(0.204602\pi\)
\(984\) 1.72221 + 10.8460i 0.0549021 + 0.345758i
\(985\) −25.7489 5.31174i −0.820428 0.169246i
\(986\) 4.28993 + 0.278074i 0.136619 + 0.00885569i
\(987\) −1.38808 3.78314i −0.0441832 0.120419i
\(988\) −22.0532 2.87105i −0.701604 0.0913401i
\(989\) −11.9838 −0.381063
\(990\) 2.88248 32.5072i 0.0916113 1.03315i
\(991\) 2.72058i 0.0864221i 0.999066 + 0.0432111i \(0.0137588\pi\)
−0.999066 + 0.0432111i \(0.986241\pi\)
\(992\) −3.91974 + 11.6853i −0.124452 + 0.371007i
\(993\) −3.27522 + 18.8609i −0.103936 + 0.598532i
\(994\) 4.21054 + 0.272929i 0.133550 + 0.00865677i
\(995\) −53.9376 11.1268i −1.70994 0.352743i
\(996\) −6.61085 + 1.49361i −0.209473 + 0.0473269i
\(997\) 20.7291 + 35.9039i 0.656497 + 1.13709i 0.981516 + 0.191379i \(0.0612961\pi\)
−0.325019 + 0.945708i \(0.605371\pi\)
\(998\) 5.34072 + 10.8103i 0.169057 + 0.342193i
\(999\) −7.74837 + 13.6653i −0.245147 + 0.432350i
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 360.2.bd.b.59.20 yes 128
5.4 even 2 inner 360.2.bd.b.59.45 yes 128
8.3 odd 2 inner 360.2.bd.b.59.64 yes 128
9.2 odd 6 inner 360.2.bd.b.299.1 yes 128
40.19 odd 2 inner 360.2.bd.b.59.1 128
45.29 odd 6 inner 360.2.bd.b.299.64 yes 128
72.11 even 6 inner 360.2.bd.b.299.45 yes 128
360.299 even 6 inner 360.2.bd.b.299.20 yes 128
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
360.2.bd.b.59.1 128 40.19 odd 2 inner
360.2.bd.b.59.20 yes 128 1.1 even 1 trivial
360.2.bd.b.59.45 yes 128 5.4 even 2 inner
360.2.bd.b.59.64 yes 128 8.3 odd 2 inner
360.2.bd.b.299.1 yes 128 9.2 odd 6 inner
360.2.bd.b.299.20 yes 128 360.299 even 6 inner
360.2.bd.b.299.45 yes 128 72.11 even 6 inner
360.2.bd.b.299.64 yes 128 45.29 odd 6 inner