Properties

Label 504.2.cs.a.85.3
Level $504$
Weight $2$
Character 504.85
Analytic conductor $4.024$
Analytic rank $0$
Dimension $72$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [504,2,Mod(85,504)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(504, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([0, 3, 2, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("504.85");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 504 = 2^{3} \cdot 3^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 504.cs (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: \(4.02446026187\)
Analytic rank: \(0\)
Dimension: \(72\)
Relative dimension: \(36\) over \(\Q(\zeta_{6})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 85.3
Character \(\chi\) \(=\) 504.85
Dual form 504.2.cs.a.421.3

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.38589 - 0.281624i) q^{2} +(1.31821 - 1.12353i) q^{3} +(1.84138 + 0.780600i) q^{4} +(2.74638 + 1.58562i) q^{5} +(-2.14331 + 1.18585i) q^{6} +(0.500000 + 0.866025i) q^{7} +(-2.33211 - 1.60040i) q^{8} +(0.475349 - 2.96210i) q^{9} +O(q^{10})\) \(q+(-1.38589 - 0.281624i) q^{2} +(1.31821 - 1.12353i) q^{3} +(1.84138 + 0.780600i) q^{4} +(2.74638 + 1.58562i) q^{5} +(-2.14331 + 1.18585i) q^{6} +(0.500000 + 0.866025i) q^{7} +(-2.33211 - 1.60040i) q^{8} +(0.475349 - 2.96210i) q^{9} +(-3.35962 - 2.97094i) q^{10} +(3.01620 - 1.74141i) q^{11} +(3.30435 - 1.03985i) q^{12} +(-6.16846 - 3.56136i) q^{13} +(-0.449051 - 1.34103i) q^{14} +(5.40179 - 0.995463i) q^{15} +(2.78133 + 2.87476i) q^{16} +5.78991 q^{17} +(-1.49298 + 3.97127i) q^{18} +1.23567i q^{19} +(3.81937 + 5.06355i) q^{20} +(1.63211 + 0.579836i) q^{21} +(-4.67054 + 1.56396i) q^{22} +(-3.95802 + 6.85549i) q^{23} +(-4.87230 + 0.510533i) q^{24} +(2.52839 + 4.37930i) q^{25} +(7.54583 + 6.67284i) q^{26} +(-2.70141 - 4.43874i) q^{27} +(0.244668 + 1.98498i) q^{28} +(6.94356 - 4.00887i) q^{29} +(-7.76663 - 0.141675i) q^{30} +(-1.16438 + 2.01677i) q^{31} +(-3.04501 - 4.76738i) q^{32} +(2.01946 - 5.68434i) q^{33} +(-8.02417 - 1.63058i) q^{34} +3.17124i q^{35} +(3.18751 - 5.08328i) q^{36} +1.06276i q^{37} +(0.347995 - 1.71250i) q^{38} +(-12.1326 + 2.23585i) q^{39} +(-3.86721 - 8.09314i) q^{40} +(0.170503 - 0.295320i) q^{41} +(-2.09863 - 1.26323i) q^{42} +(-2.22471 + 1.28444i) q^{43} +(6.91330 - 0.852133i) q^{44} +(6.00226 - 7.38132i) q^{45} +(7.41604 - 8.38627i) q^{46} +(2.42471 + 4.19972i) q^{47} +(6.89625 + 0.664617i) q^{48} +(-0.500000 + 0.866025i) q^{49} +(-2.27075 - 6.78127i) q^{50} +(7.63231 - 6.50515i) q^{51} +(-8.57845 - 11.3729i) q^{52} +2.97668i q^{53} +(2.49379 + 6.91238i) q^{54} +11.0448 q^{55} +(0.219935 - 2.81986i) q^{56} +(1.38831 + 1.62887i) q^{57} +(-10.7520 + 3.60037i) q^{58} +(-5.05088 - 2.91612i) q^{59} +(10.7238 + 2.38362i) q^{60} +(4.86161 - 2.80685i) q^{61} +(2.18167 - 2.46709i) q^{62} +(2.80293 - 1.06939i) q^{63} +(2.87743 + 7.46461i) q^{64} +(-11.2939 - 19.5617i) q^{65} +(-4.39959 + 7.30913i) q^{66} +(-6.92522 - 3.99828i) q^{67} +(10.6614 + 4.51961i) q^{68} +(2.48487 + 13.4839i) q^{69} +(0.893099 - 4.39499i) q^{70} -4.79832 q^{71} +(-5.84911 + 6.14718i) q^{72} -9.24923 q^{73} +(0.299300 - 1.47287i) q^{74} +(8.25323 + 2.93210i) q^{75} +(-0.964564 + 2.27533i) q^{76} +(3.01620 + 1.74141i) q^{77} +(17.4441 + 0.318208i) q^{78} +(0.117791 + 0.204020i) q^{79} +(3.08030 + 12.3053i) q^{80} +(-8.54809 - 2.81607i) q^{81} +(-0.319468 + 0.361263i) q^{82} +(8.77989 - 5.06907i) q^{83} +(2.55271 + 2.34172i) q^{84} +(15.9013 + 9.18061i) q^{85} +(3.44493 - 1.15355i) q^{86} +(4.64897 - 13.0858i) q^{87} +(-9.82105 - 0.765993i) q^{88} +2.91474 q^{89} +(-10.3972 + 8.53931i) q^{90} -7.12272i q^{91} +(-12.6396 + 9.53390i) q^{92} +(0.731005 + 3.96674i) q^{93} +(-2.17764 - 6.50321i) q^{94} +(-1.95930 + 3.39361i) q^{95} +(-9.37027 - 2.86324i) q^{96} +(2.31751 + 4.01404i) q^{97} +(0.936838 - 1.05940i) q^{98} +(-3.72447 - 9.76207i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 72 q - 8 q^{6} + 36 q^{7} + 6 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 72 q - 8 q^{6} + 36 q^{7} + 6 q^{8} + 20 q^{12} + 40 q^{17} - q^{18} + 2 q^{20} - 12 q^{22} + 12 q^{23} + 10 q^{24} + 36 q^{25} - 42 q^{26} + 4 q^{30} + 5 q^{32} + 8 q^{33} + 6 q^{34} - 18 q^{36} - 25 q^{38} - 4 q^{39} - 9 q^{40} + 24 q^{41} - 7 q^{42} + 12 q^{46} - 53 q^{48} - 36 q^{49} + 41 q^{50} - 9 q^{52} + 12 q^{54} + 3 q^{56} + 4 q^{57} + 9 q^{58} - 50 q^{60} + 60 q^{62} - 6 q^{64} - 40 q^{65} - 2 q^{66} + 23 q^{68} - 56 q^{71} + 19 q^{72} + 22 q^{74} - 24 q^{76} - 54 q^{78} - 6 q^{80} - 4 q^{81} - 48 q^{82} + 10 q^{84} - 39 q^{86} - 76 q^{87} - 12 q^{88} - 88 q^{89} - 77 q^{90} + 11 q^{92} + 24 q^{94} - 24 q^{95} + 59 q^{96}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/504\mathbb{Z}\right)^\times\).

\(n\) \(73\) \(127\) \(253\) \(281\)
\(\chi(n)\) \(1\) \(1\) \(-1\) \(e\left(\frac{1}{3}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.38589 0.281624i −0.979971 0.199139i
\(3\) 1.31821 1.12353i 0.761068 0.648672i
\(4\) 1.84138 + 0.780600i 0.920688 + 0.390300i
\(5\) 2.74638 + 1.58562i 1.22822 + 0.709111i 0.966657 0.256076i \(-0.0824297\pi\)
0.261560 + 0.965187i \(0.415763\pi\)
\(6\) −2.14331 + 1.18585i −0.875001 + 0.484122i
\(7\) 0.500000 + 0.866025i 0.188982 + 0.327327i
\(8\) −2.33211 1.60040i −0.824524 0.565827i
\(9\) 0.475349 2.96210i 0.158450 0.987367i
\(10\) −3.35962 2.97094i −1.06241 0.939494i
\(11\) 3.01620 1.74141i 0.909419 0.525053i 0.0291749 0.999574i \(-0.490712\pi\)
0.880244 + 0.474521i \(0.157379\pi\)
\(12\) 3.30435 1.03985i 0.953883 0.300179i
\(13\) −6.16846 3.56136i −1.71082 0.987744i −0.933454 0.358698i \(-0.883221\pi\)
−0.777368 0.629046i \(-0.783446\pi\)
\(14\) −0.449051 1.34103i −0.120014 0.358405i
\(15\) 5.40179 0.995463i 1.39474 0.257028i
\(16\) 2.78133 + 2.87476i 0.695332 + 0.718689i
\(17\) 5.78991 1.40426 0.702130 0.712049i \(-0.252233\pi\)
0.702130 + 0.712049i \(0.252233\pi\)
\(18\) −1.49298 + 3.97127i −0.351899 + 0.936038i
\(19\) 1.23567i 0.283482i 0.989904 + 0.141741i \(0.0452700\pi\)
−0.989904 + 0.141741i \(0.954730\pi\)
\(20\) 3.81937 + 5.06355i 0.854038 + 1.13224i
\(21\) 1.63211 + 0.579836i 0.356156 + 0.126531i
\(22\) −4.67054 + 1.56396i −0.995763 + 0.333437i
\(23\) −3.95802 + 6.85549i −0.825304 + 1.42947i 0.0763834 + 0.997079i \(0.475663\pi\)
−0.901687 + 0.432389i \(0.857671\pi\)
\(24\) −4.87230 + 0.510533i −0.994555 + 0.104212i
\(25\) 2.52839 + 4.37930i 0.505678 + 0.875859i
\(26\) 7.54583 + 6.67284i 1.47986 + 1.30865i
\(27\) −2.70141 4.43874i −0.519886 0.854236i
\(28\) 0.244668 + 1.98498i 0.0462379 + 0.375126i
\(29\) 6.94356 4.00887i 1.28939 0.744428i 0.310842 0.950461i \(-0.399389\pi\)
0.978545 + 0.206033i \(0.0660555\pi\)
\(30\) −7.76663 0.141675i −1.41799 0.0258663i
\(31\) −1.16438 + 2.01677i −0.209129 + 0.362222i −0.951440 0.307833i \(-0.900396\pi\)
0.742312 + 0.670055i \(0.233729\pi\)
\(32\) −3.04501 4.76738i −0.538287 0.842762i
\(33\) 2.01946 5.68434i 0.351543 0.989516i
\(34\) −8.02417 1.63058i −1.37613 0.279642i
\(35\) 3.17124i 0.536038i
\(36\) 3.18751 5.08328i 0.531252 0.847214i
\(37\) 1.06276i 0.174717i 0.996177 + 0.0873585i \(0.0278426\pi\)
−0.996177 + 0.0873585i \(0.972157\pi\)
\(38\) 0.347995 1.71250i 0.0564522 0.277804i
\(39\) −12.1326 + 2.23585i −1.94277 + 0.358022i
\(40\) −3.86721 8.09314i −0.611460 1.27964i
\(41\) 0.170503 0.295320i 0.0266281 0.0461213i −0.852404 0.522883i \(-0.824856\pi\)
0.879032 + 0.476762i \(0.158190\pi\)
\(42\) −2.09863 1.26323i −0.323826 0.194921i
\(43\) −2.22471 + 1.28444i −0.339265 + 0.195875i −0.659947 0.751312i \(-0.729421\pi\)
0.320682 + 0.947187i \(0.396088\pi\)
\(44\) 6.91330 0.852133i 1.04222 0.128464i
\(45\) 6.00226 7.38132i 0.894764 1.10034i
\(46\) 7.41604 8.38627i 1.09344 1.23649i
\(47\) 2.42471 + 4.19972i 0.353680 + 0.612592i 0.986891 0.161387i \(-0.0515967\pi\)
−0.633211 + 0.773979i \(0.718263\pi\)
\(48\) 6.89625 + 0.664617i 0.995388 + 0.0959292i
\(49\) −0.500000 + 0.866025i −0.0714286 + 0.123718i
\(50\) −2.27075 6.78127i −0.321132 0.959017i
\(51\) 7.63231 6.50515i 1.06874 0.910904i
\(52\) −8.57845 11.3729i −1.18962 1.57714i
\(53\) 2.97668i 0.408878i 0.978879 + 0.204439i \(0.0655370\pi\)
−0.978879 + 0.204439i \(0.934463\pi\)
\(54\) 2.49379 + 6.91238i 0.339362 + 0.940656i
\(55\) 11.0448 1.48929
\(56\) 0.219935 2.81986i 0.0293901 0.376820i
\(57\) 1.38831 + 1.62887i 0.183887 + 0.215749i
\(58\) −10.7520 + 3.60037i −1.41181 + 0.472752i
\(59\) −5.05088 2.91612i −0.657568 0.379647i 0.133782 0.991011i \(-0.457288\pi\)
−0.791350 + 0.611364i \(0.790621\pi\)
\(60\) 10.7238 + 2.38362i 1.38444 + 0.307724i
\(61\) 4.86161 2.80685i 0.622466 0.359381i −0.155362 0.987858i \(-0.549655\pi\)
0.777828 + 0.628477i \(0.216321\pi\)
\(62\) 2.18167 2.46709i 0.277073 0.313321i
\(63\) 2.80293 1.06939i 0.353136 0.134730i
\(64\) 2.87743 + 7.46461i 0.359679 + 0.933076i
\(65\) −11.2939 19.5617i −1.40084 2.42633i
\(66\) −4.39959 + 7.30913i −0.541553 + 0.899692i
\(67\) −6.92522 3.99828i −0.846050 0.488467i 0.0132660 0.999912i \(-0.495777\pi\)
−0.859316 + 0.511445i \(0.829111\pi\)
\(68\) 10.6614 + 4.51961i 1.29288 + 0.548083i
\(69\) 2.48487 + 13.4839i 0.299143 + 1.62327i
\(70\) 0.893099 4.39499i 0.106746 0.525302i
\(71\) −4.79832 −0.569456 −0.284728 0.958608i \(-0.591903\pi\)
−0.284728 + 0.958608i \(0.591903\pi\)
\(72\) −5.84911 + 6.14718i −0.689325 + 0.724452i
\(73\) −9.24923 −1.08254 −0.541270 0.840849i \(-0.682056\pi\)
−0.541270 + 0.840849i \(0.682056\pi\)
\(74\) 0.299300 1.47287i 0.0347929 0.171218i
\(75\) 8.25323 + 2.93210i 0.953001 + 0.338570i
\(76\) −0.964564 + 2.27533i −0.110643 + 0.260998i
\(77\) 3.01620 + 1.74141i 0.343728 + 0.198452i
\(78\) 17.4441 + 0.318208i 1.97516 + 0.0360300i
\(79\) 0.117791 + 0.204020i 0.0132525 + 0.0229540i 0.872576 0.488479i \(-0.162448\pi\)
−0.859323 + 0.511433i \(0.829115\pi\)
\(80\) 3.08030 + 12.3053i 0.344388 + 1.37577i
\(81\) −8.54809 2.81607i −0.949787 0.312896i
\(82\) −0.319468 + 0.361263i −0.0352793 + 0.0398948i
\(83\) 8.77989 5.06907i 0.963718 0.556403i 0.0664027 0.997793i \(-0.478848\pi\)
0.897315 + 0.441390i \(0.145514\pi\)
\(84\) 2.55271 + 2.34172i 0.278524 + 0.255503i
\(85\) 15.9013 + 9.18061i 1.72474 + 0.995777i
\(86\) 3.44493 1.15355i 0.371476 0.124391i
\(87\) 4.64897 13.0858i 0.498422 1.40295i
\(88\) −9.82105 0.765993i −1.04693 0.0816551i
\(89\) 2.91474 0.308961 0.154481 0.987996i \(-0.450630\pi\)
0.154481 + 0.987996i \(0.450630\pi\)
\(90\) −10.3972 + 8.53931i −1.09596 + 0.900122i
\(91\) 7.12272i 0.746664i
\(92\) −12.6396 + 9.53390i −1.31777 + 0.993977i
\(93\) 0.731005 + 3.96674i 0.0758017 + 0.411331i
\(94\) −2.17764 6.50321i −0.224606 0.670754i
\(95\) −1.95930 + 3.39361i −0.201020 + 0.348177i
\(96\) −9.37027 2.86324i −0.956349 0.292228i
\(97\) 2.31751 + 4.01404i 0.235307 + 0.407564i 0.959362 0.282178i \(-0.0910570\pi\)
−0.724055 + 0.689743i \(0.757724\pi\)
\(98\) 0.936838 1.05940i 0.0946350 0.107016i
\(99\) −3.72447 9.76207i −0.374323 0.981125i
\(100\) 1.23723 + 10.0376i 0.123723 + 1.00376i
\(101\) −11.3205 + 6.53589i −1.12643 + 0.650345i −0.943035 0.332694i \(-0.892042\pi\)
−0.183396 + 0.983039i \(0.558709\pi\)
\(102\) −12.4095 + 6.86598i −1.22873 + 0.679833i
\(103\) −7.57149 + 13.1142i −0.746041 + 1.29218i 0.203665 + 0.979041i \(0.434715\pi\)
−0.949707 + 0.313141i \(0.898619\pi\)
\(104\) 8.68589 + 18.1775i 0.851721 + 1.78245i
\(105\) 3.56299 + 4.18036i 0.347713 + 0.407961i
\(106\) 0.838305 4.12534i 0.0814234 0.400689i
\(107\) 8.59891i 0.831288i 0.909527 + 0.415644i \(0.136444\pi\)
−0.909527 + 0.415644i \(0.863556\pi\)
\(108\) −1.50943 10.2821i −0.145245 0.989396i
\(109\) 17.9715i 1.72136i −0.509146 0.860680i \(-0.670039\pi\)
0.509146 0.860680i \(-0.329961\pi\)
\(110\) −15.3069 3.11049i −1.45946 0.296574i
\(111\) 1.19405 + 1.40094i 0.113334 + 0.132972i
\(112\) −1.09895 + 3.84608i −0.103841 + 0.363420i
\(113\) −0.177327 + 0.307140i −0.0166816 + 0.0288933i −0.874246 0.485484i \(-0.838643\pi\)
0.857564 + 0.514377i \(0.171977\pi\)
\(114\) −1.46532 2.64842i −0.137240 0.248047i
\(115\) −21.7404 + 12.5518i −2.02730 + 1.17046i
\(116\) 15.9150 1.96169i 1.47767 0.182138i
\(117\) −13.4813 + 16.5787i −1.24634 + 1.53270i
\(118\) 6.17870 + 5.46387i 0.568796 + 0.502990i
\(119\) 2.89496 + 5.01421i 0.265380 + 0.459652i
\(120\) −14.1907 6.32351i −1.29543 0.577255i
\(121\) 0.564983 0.978580i 0.0513621 0.0889618i
\(122\) −7.52814 + 2.52084i −0.681565 + 0.228226i
\(123\) −0.107043 0.580860i −0.00965175 0.0523744i
\(124\) −3.71835 + 2.80471i −0.333918 + 0.251870i
\(125\) 0.180053i 0.0161045i
\(126\) −4.18571 + 0.692677i −0.372893 + 0.0617086i
\(127\) −11.6211 −1.03120 −0.515601 0.856829i \(-0.672431\pi\)
−0.515601 + 0.856829i \(0.672431\pi\)
\(128\) −1.88559 11.1555i −0.166664 0.986014i
\(129\) −1.48953 + 4.19269i −0.131145 + 0.369146i
\(130\) 10.1431 + 30.2909i 0.889608 + 2.65669i
\(131\) −15.0603 8.69508i −1.31583 0.759692i −0.332771 0.943008i \(-0.607984\pi\)
−0.983054 + 0.183315i \(0.941317\pi\)
\(132\) 8.15578 8.89061i 0.709869 0.773828i
\(133\) −1.07012 + 0.617835i −0.0927913 + 0.0535731i
\(134\) 8.47157 + 7.49148i 0.731832 + 0.647165i
\(135\) −0.380924 16.4739i −0.0327847 1.41784i
\(136\) −13.5027 9.26618i −1.15785 0.794569i
\(137\) 1.80895 + 3.13320i 0.154549 + 0.267687i 0.932895 0.360149i \(-0.117274\pi\)
−0.778345 + 0.627836i \(0.783941\pi\)
\(138\) 0.353649 19.3870i 0.0301046 1.65033i
\(139\) −3.04116 1.75581i −0.257948 0.148926i 0.365450 0.930831i \(-0.380915\pi\)
−0.623398 + 0.781905i \(0.714248\pi\)
\(140\) −2.47547 + 5.83945i −0.209216 + 0.493523i
\(141\) 7.91480 + 2.81187i 0.666546 + 0.236802i
\(142\) 6.64994 + 1.35133i 0.558051 + 0.113401i
\(143\) −24.8071 −2.07447
\(144\) 9.83742 6.87206i 0.819785 0.572672i
\(145\) 25.4262 2.11153
\(146\) 12.8184 + 2.60481i 1.06086 + 0.215575i
\(147\) 0.313903 + 1.70337i 0.0258903 + 0.140491i
\(148\) −0.829593 + 1.95694i −0.0681921 + 0.160860i
\(149\) 6.45180 + 3.72495i 0.528552 + 0.305159i 0.740426 0.672137i \(-0.234624\pi\)
−0.211875 + 0.977297i \(0.567957\pi\)
\(150\) −10.6123 6.38788i −0.866491 0.521568i
\(151\) 0.677921 + 1.17419i 0.0551685 + 0.0955546i 0.892291 0.451461i \(-0.149097\pi\)
−0.837122 + 0.547016i \(0.815764\pi\)
\(152\) 1.97757 2.88171i 0.160402 0.233738i
\(153\) 2.75223 17.1503i 0.222505 1.38652i
\(154\) −3.68970 3.26283i −0.297324 0.262926i
\(155\) −6.39565 + 3.69253i −0.513711 + 0.296591i
\(156\) −24.0860 5.35369i −1.92842 0.428638i
\(157\) 7.03486 + 4.06158i 0.561443 + 0.324149i 0.753724 0.657191i \(-0.228255\pi\)
−0.192282 + 0.981340i \(0.561589\pi\)
\(158\) −0.105788 0.315921i −0.00841604 0.0251333i
\(159\) 3.34439 + 3.92388i 0.265228 + 0.311184i
\(160\) −0.803479 17.9213i −0.0635206 1.41680i
\(161\) −7.91603 −0.623871
\(162\) 11.0536 + 6.31010i 0.868455 + 0.495768i
\(163\) 13.0772i 1.02429i 0.858900 + 0.512143i \(0.171148\pi\)
−0.858900 + 0.512143i \(0.828852\pi\)
\(164\) 0.544487 0.410701i 0.0425173 0.0320703i
\(165\) 14.5594 12.4092i 1.13345 0.966057i
\(166\) −13.5955 + 4.55254i −1.05522 + 0.353345i
\(167\) −2.25135 + 3.89945i −0.174215 + 0.301749i −0.939889 0.341480i \(-0.889072\pi\)
0.765675 + 0.643228i \(0.222405\pi\)
\(168\) −2.87829 3.96427i −0.222065 0.305850i
\(169\) 18.8666 + 32.6779i 1.45127 + 2.51368i
\(170\) −19.4519 17.2015i −1.49189 1.31929i
\(171\) 3.66018 + 0.587374i 0.279901 + 0.0449176i
\(172\) −5.09916 + 0.628522i −0.388807 + 0.0479243i
\(173\) −12.7987 + 7.38932i −0.973065 + 0.561799i −0.900169 0.435540i \(-0.856557\pi\)
−0.0728957 + 0.997340i \(0.523224\pi\)
\(174\) −10.1283 + 16.8263i −0.767821 + 1.27560i
\(175\) −2.52839 + 4.37930i −0.191128 + 0.331044i
\(176\) 13.3952 + 3.82743i 1.00970 + 0.288503i
\(177\) −9.93447 + 1.83076i −0.746721 + 0.137609i
\(178\) −4.03950 0.820861i −0.302773 0.0615261i
\(179\) 20.7869i 1.55369i 0.629695 + 0.776843i \(0.283180\pi\)
−0.629695 + 0.776843i \(0.716820\pi\)
\(180\) 16.8143 8.90642i 1.25326 0.663845i
\(181\) 9.54710i 0.709631i −0.934936 0.354815i \(-0.884544\pi\)
0.934936 0.354815i \(-0.115456\pi\)
\(182\) −2.00593 + 9.87130i −0.148690 + 0.731709i
\(183\) 3.25503 9.16220i 0.240619 0.677290i
\(184\) 20.2020 9.65330i 1.48931 0.711651i
\(185\) −1.68514 + 2.91875i −0.123894 + 0.214590i
\(186\) 0.104038 5.70332i 0.00762840 0.418188i
\(187\) 17.4635 10.0826i 1.27706 0.737311i
\(188\) 1.18650 + 9.62599i 0.0865343 + 0.702048i
\(189\) 2.49336 4.55886i 0.181365 0.331608i
\(190\) 3.67110 4.15138i 0.266330 0.301173i
\(191\) −2.45074 4.24480i −0.177329 0.307143i 0.763636 0.645647i \(-0.223412\pi\)
−0.940965 + 0.338504i \(0.890079\pi\)
\(192\) 12.1798 + 6.60702i 0.879000 + 0.476821i
\(193\) 2.74903 4.76146i 0.197880 0.342737i −0.749961 0.661482i \(-0.769928\pi\)
0.947841 + 0.318744i \(0.103261\pi\)
\(194\) −2.08136 6.21569i −0.149433 0.446260i
\(195\) −36.8659 13.0973i −2.64002 0.937914i
\(196\) −1.59671 + 1.20438i −0.114051 + 0.0860270i
\(197\) 16.3525i 1.16507i −0.812807 0.582533i \(-0.802062\pi\)
0.812807 0.582533i \(-0.197938\pi\)
\(198\) 2.41246 + 14.5780i 0.171446 + 1.03602i
\(199\) 9.98715 0.707970 0.353985 0.935251i \(-0.384826\pi\)
0.353985 + 0.935251i \(0.384826\pi\)
\(200\) 1.11216 14.2594i 0.0786418 1.00829i
\(201\) −13.6211 + 2.51014i −0.960757 + 0.177052i
\(202\) 17.5296 5.86989i 1.23338 0.413004i
\(203\) 6.94356 + 4.00887i 0.487343 + 0.281367i
\(204\) 19.1319 6.02065i 1.33950 0.421530i
\(205\) 0.936532 0.540707i 0.0654102 0.0377646i
\(206\) 14.1865 16.0425i 0.988422 1.11774i
\(207\) 18.4252 + 14.9828i 1.28064 + 1.04138i
\(208\) −6.91845 27.6381i −0.479708 1.91636i
\(209\) 2.15180 + 3.72703i 0.148843 + 0.257804i
\(210\) −3.76062 6.79694i −0.259508 0.469033i
\(211\) 10.0796 + 5.81945i 0.693907 + 0.400627i 0.805074 0.593174i \(-0.202126\pi\)
−0.111167 + 0.993802i \(0.535459\pi\)
\(212\) −2.32359 + 5.48118i −0.159585 + 0.376449i
\(213\) −6.32519 + 5.39107i −0.433395 + 0.369390i
\(214\) 2.42166 11.9171i 0.165541 0.814638i
\(215\) −8.14652 −0.555588
\(216\) −0.803795 + 14.6749i −0.0546913 + 0.998503i
\(217\) −2.32876 −0.158087
\(218\) −5.06122 + 24.9065i −0.342789 + 1.68688i
\(219\) −12.1924 + 10.3918i −0.823887 + 0.702213i
\(220\) 20.3377 + 8.62160i 1.37117 + 0.581268i
\(221\) −35.7148 20.6200i −2.40244 1.38705i
\(222\) −1.26028 2.27782i −0.0845843 0.152878i
\(223\) −10.4817 18.1548i −0.701904 1.21573i −0.967797 0.251731i \(-0.919000\pi\)
0.265893 0.964003i \(-0.414333\pi\)
\(224\) 2.60617 5.02075i 0.174132 0.335463i
\(225\) 14.1738 5.40765i 0.944919 0.360510i
\(226\) 0.332254 0.375722i 0.0221012 0.0249927i
\(227\) −1.01782 + 0.587641i −0.0675554 + 0.0390031i −0.533397 0.845865i \(-0.679085\pi\)
0.465842 + 0.884868i \(0.345752\pi\)
\(228\) 1.28491 + 4.08308i 0.0850954 + 0.270409i
\(229\) 11.1077 + 6.41302i 0.734016 + 0.423784i 0.819890 0.572522i \(-0.194035\pi\)
−0.0858737 + 0.996306i \(0.527368\pi\)
\(230\) 33.6647 11.2728i 2.21978 0.743307i
\(231\) 5.93251 1.09327i 0.390330 0.0719316i
\(232\) −22.6089 1.76338i −1.48435 0.115772i
\(233\) 4.19252 0.274661 0.137331 0.990525i \(-0.456148\pi\)
0.137331 + 0.990525i \(0.456148\pi\)
\(234\) 23.3525 19.1796i 1.52660 1.25381i
\(235\) 15.3787i 1.00320i
\(236\) −7.02423 9.31240i −0.457239 0.606185i
\(237\) 0.384495 + 0.136599i 0.0249757 + 0.00887303i
\(238\) −2.59996 7.76443i −0.168531 0.503293i
\(239\) 1.18170 2.04677i 0.0764379 0.132394i −0.825273 0.564734i \(-0.808979\pi\)
0.901711 + 0.432340i \(0.142312\pi\)
\(240\) 17.8859 + 12.7601i 1.15453 + 0.823663i
\(241\) −2.18309 3.78122i −0.140625 0.243570i 0.787107 0.616816i \(-0.211578\pi\)
−0.927732 + 0.373246i \(0.878245\pi\)
\(242\) −1.05860 + 1.19709i −0.0680491 + 0.0769518i
\(243\) −14.4321 + 5.89189i −0.925820 + 0.377965i
\(244\) 11.1431 1.37350i 0.713363 0.0879291i
\(245\) −2.74638 + 1.58562i −0.175460 + 0.101302i
\(246\) −0.0152345 + 0.835153i −0.000971315 + 0.0532474i
\(247\) 4.40066 7.62217i 0.280008 0.484987i
\(248\) 5.94309 2.83983i 0.377387 0.180330i
\(249\) 5.87846 16.5466i 0.372532 1.04860i
\(250\) 0.0507074 0.249534i 0.00320702 0.0157819i
\(251\) 16.6989i 1.05402i −0.849858 0.527012i \(-0.823312\pi\)
0.849858 0.527012i \(-0.176688\pi\)
\(252\) 5.99601 + 0.218826i 0.377713 + 0.0137847i
\(253\) 27.5700i 1.73331i
\(254\) 16.1055 + 3.27277i 1.01055 + 0.205352i
\(255\) 31.2759 5.76365i 1.95857 0.360933i
\(256\) −0.528441 + 15.9913i −0.0330276 + 0.999454i
\(257\) 5.04875 8.74470i 0.314933 0.545479i −0.664491 0.747297i \(-0.731351\pi\)
0.979423 + 0.201817i \(0.0646847\pi\)
\(258\) 3.24508 5.39112i 0.202030 0.335636i
\(259\) −0.920379 + 0.531381i −0.0571896 + 0.0330184i
\(260\) −5.52653 44.8364i −0.342741 2.78064i
\(261\) −8.57406 22.4732i −0.530721 1.39105i
\(262\) 18.4232 + 16.2918i 1.13819 + 1.00651i
\(263\) 14.7794 + 25.5987i 0.911337 + 1.57848i 0.812178 + 0.583410i \(0.198282\pi\)
0.0991587 + 0.995072i \(0.468385\pi\)
\(264\) −13.8068 + 10.0245i −0.849750 + 0.616967i
\(265\) −4.71988 + 8.17507i −0.289940 + 0.502191i
\(266\) 1.65707 0.554878i 0.101601 0.0340218i
\(267\) 3.84223 3.27480i 0.235141 0.200415i
\(268\) −9.63087 12.7682i −0.588299 0.779939i
\(269\) 14.9064i 0.908859i 0.890783 + 0.454429i \(0.150157\pi\)
−0.890783 + 0.454429i \(0.849843\pi\)
\(270\) −4.11152 + 22.9382i −0.250219 + 1.39597i
\(271\) −11.2654 −0.684324 −0.342162 0.939641i \(-0.611159\pi\)
−0.342162 + 0.939641i \(0.611159\pi\)
\(272\) 16.1036 + 16.6446i 0.976427 + 1.00923i
\(273\) −8.00261 9.38923i −0.484340 0.568262i
\(274\) −1.62462 4.85171i −0.0981471 0.293103i
\(275\) 15.2523 + 8.80590i 0.919746 + 0.531016i
\(276\) −5.94998 + 26.7687i −0.358146 + 1.61128i
\(277\) −19.7137 + 11.3817i −1.18448 + 0.683862i −0.957047 0.289931i \(-0.906368\pi\)
−0.227436 + 0.973793i \(0.573034\pi\)
\(278\) 3.72022 + 3.28982i 0.223124 + 0.197311i
\(279\) 5.42038 + 4.40768i 0.324509 + 0.263881i
\(280\) 5.07526 7.39567i 0.303305 0.441976i
\(281\) −5.22469 9.04942i −0.311679 0.539843i 0.667047 0.745015i \(-0.267558\pi\)
−0.978726 + 0.205172i \(0.934225\pi\)
\(282\) −10.1771 6.12594i −0.606040 0.364794i
\(283\) −17.6479 10.1890i −1.04906 0.605674i −0.126672 0.991945i \(-0.540430\pi\)
−0.922385 + 0.386271i \(0.873763\pi\)
\(284\) −8.83552 3.74557i −0.524292 0.222259i
\(285\) 1.23006 + 6.67483i 0.0728627 + 0.395383i
\(286\) 34.3799 + 6.98628i 2.03292 + 0.413107i
\(287\) 0.341006 0.0201290
\(288\) −15.5689 + 6.75345i −0.917407 + 0.397951i
\(289\) 16.5231 0.971946
\(290\) −35.2379 7.16063i −2.06924 0.420487i
\(291\) 7.56487 + 2.68755i 0.443461 + 0.157547i
\(292\) −17.0313 7.21995i −0.996681 0.422515i
\(293\) −17.4466 10.0728i −1.01924 0.588460i −0.105358 0.994434i \(-0.533599\pi\)
−0.913885 + 0.405974i \(0.866932\pi\)
\(294\) 0.0446751 2.44908i 0.00260550 0.142833i
\(295\) −9.24774 16.0176i −0.538424 0.932578i
\(296\) 1.70085 2.47847i 0.0988597 0.144058i
\(297\) −15.8776 8.68389i −0.921314 0.503890i
\(298\) −7.89244 6.97934i −0.457196 0.404302i
\(299\) 48.8297 28.1918i 2.82390 1.63038i
\(300\) 12.9085 + 11.8416i 0.745272 + 0.683673i
\(301\) −2.22471 1.28444i −0.128230 0.0740337i
\(302\) −0.608842 1.81822i −0.0350349 0.104627i
\(303\) −7.57949 + 21.3346i −0.435430 + 1.22564i
\(304\) −3.55225 + 3.43680i −0.203735 + 0.197114i
\(305\) 17.8024 1.01936
\(306\) −8.64423 + 22.9933i −0.494158 + 1.31444i
\(307\) 1.80261i 0.102880i −0.998676 0.0514401i \(-0.983619\pi\)
0.998676 0.0514401i \(-0.0163811\pi\)
\(308\) 4.19462 + 5.56103i 0.239011 + 0.316869i
\(309\) 4.75343 + 25.7941i 0.270413 + 1.46737i
\(310\) 9.90357 3.31627i 0.562485 0.188351i
\(311\) 3.94517 6.83323i 0.223710 0.387477i −0.732222 0.681066i \(-0.761516\pi\)
0.955932 + 0.293589i \(0.0948498\pi\)
\(312\) 31.8728 + 14.2028i 1.80444 + 0.804077i
\(313\) −11.0478 19.1353i −0.624456 1.08159i −0.988646 0.150265i \(-0.951987\pi\)
0.364190 0.931325i \(-0.381346\pi\)
\(314\) −8.60569 7.61008i −0.485647 0.429462i
\(315\) 9.39354 + 1.50745i 0.529266 + 0.0849350i
\(316\) 0.0576393 + 0.467624i 0.00324246 + 0.0263059i
\(317\) 26.9005 15.5310i 1.51088 0.872307i 0.510961 0.859604i \(-0.329290\pi\)
0.999919 0.0127032i \(-0.00404365\pi\)
\(318\) −3.52990 6.37993i −0.197947 0.357769i
\(319\) 13.9621 24.1831i 0.781729 1.35399i
\(320\) −3.93353 + 25.0631i −0.219891 + 1.40107i
\(321\) 9.66115 + 11.3352i 0.539233 + 0.632667i
\(322\) 10.9707 + 2.22935i 0.611376 + 0.124237i
\(323\) 7.15442i 0.398082i
\(324\) −13.5420 11.8581i −0.752334 0.658782i
\(325\) 36.0180i 1.99792i
\(326\) 3.68286 18.1236i 0.203975 1.00377i
\(327\) −20.1916 23.6902i −1.11660 1.31007i
\(328\) −0.870262 + 0.415844i −0.0480522 + 0.0229612i
\(329\) −2.42471 + 4.19972i −0.133679 + 0.231538i
\(330\) −23.6724 + 13.0975i −1.30313 + 0.720995i
\(331\) −8.04996 + 4.64764i −0.442466 + 0.255458i −0.704643 0.709562i \(-0.748893\pi\)
0.262177 + 0.965020i \(0.415559\pi\)
\(332\) 20.1240 2.48048i 1.10445 0.136134i
\(333\) 3.14801 + 0.505183i 0.172510 + 0.0276839i
\(334\) 4.21830 4.77017i 0.230815 0.261012i
\(335\) −12.6795 21.9615i −0.692755 1.19989i
\(336\) 2.87255 + 6.30464i 0.156710 + 0.343946i
\(337\) −1.25420 + 2.17233i −0.0683204 + 0.118334i −0.898162 0.439665i \(-0.855097\pi\)
0.829842 + 0.557999i \(0.188431\pi\)
\(338\) −16.9441 50.6012i −0.921637 2.75234i
\(339\) 0.111327 + 0.604108i 0.00604647 + 0.0328106i
\(340\) 22.1138 + 29.3175i 1.19929 + 1.58996i
\(341\) 8.11063i 0.439215i
\(342\) −4.90718 1.84483i −0.265350 0.0997570i
\(343\) −1.00000 −0.0539949
\(344\) 7.24387 + 0.564986i 0.390563 + 0.0304620i
\(345\) −14.5560 + 40.9720i −0.783669 + 2.20586i
\(346\) 19.8185 6.63635i 1.06545 0.356773i
\(347\) 14.2952 + 8.25336i 0.767408 + 0.443063i 0.831949 0.554852i \(-0.187225\pi\)
−0.0645410 + 0.997915i \(0.520558\pi\)
\(348\) 18.7753 20.4670i 1.00646 1.09714i
\(349\) −14.2736 + 8.24085i −0.764047 + 0.441123i −0.830747 0.556650i \(-0.812086\pi\)
0.0666998 + 0.997773i \(0.478753\pi\)
\(350\) 4.73738 5.35716i 0.253224 0.286352i
\(351\) 0.855569 + 37.0008i 0.0456669 + 1.97496i
\(352\) −17.4863 9.07679i −0.932023 0.483795i
\(353\) −11.4198 19.7797i −0.607814 1.05276i −0.991600 0.129343i \(-0.958713\pi\)
0.383786 0.923422i \(-0.374620\pi\)
\(354\) 14.2837 + 0.260556i 0.759168 + 0.0138484i
\(355\) −13.1780 7.60833i −0.699416 0.403808i
\(356\) 5.36712 + 2.27524i 0.284457 + 0.120588i
\(357\) 9.44979 + 3.35720i 0.500136 + 0.177682i
\(358\) 5.85410 28.8083i 0.309399 1.52257i
\(359\) 14.8943 0.786089 0.393044 0.919519i \(-0.371422\pi\)
0.393044 + 0.919519i \(0.371422\pi\)
\(360\) −25.8110 + 7.60800i −1.36036 + 0.400977i
\(361\) 17.4731 0.919638
\(362\) −2.68870 + 13.2312i −0.141315 + 0.695418i
\(363\) −0.354700 1.92475i −0.0186169 0.101023i
\(364\) 5.56000 13.1156i 0.291423 0.687444i
\(365\) −25.4019 14.6658i −1.32959 0.767641i
\(366\) −7.09141 + 11.7811i −0.370674 + 0.615808i
\(367\) −3.79574 6.57441i −0.198136 0.343182i 0.749788 0.661678i \(-0.230155\pi\)
−0.947924 + 0.318496i \(0.896822\pi\)
\(368\) −30.7164 + 7.68902i −1.60120 + 0.400818i
\(369\) −0.793720 0.645428i −0.0413194 0.0335996i
\(370\) 3.15740 3.57048i 0.164146 0.185620i
\(371\) −2.57788 + 1.48834i −0.133837 + 0.0772707i
\(372\) −1.75038 + 7.87487i −0.0907530 + 0.408293i
\(373\) 3.87691 + 2.23834i 0.200739 + 0.115897i 0.597000 0.802241i \(-0.296359\pi\)
−0.396261 + 0.918138i \(0.629693\pi\)
\(374\) −27.0420 + 9.05518i −1.39831 + 0.468232i
\(375\) 0.202296 + 0.237348i 0.0104465 + 0.0122566i
\(376\) 1.06656 13.6747i 0.0550036 0.705219i
\(377\) −57.1081 −2.94122
\(378\) −4.73940 + 5.61588i −0.243768 + 0.288850i
\(379\) 7.08778i 0.364075i 0.983292 + 0.182037i \(0.0582692\pi\)
−0.983292 + 0.182037i \(0.941731\pi\)
\(380\) −6.25687 + 4.71948i −0.320971 + 0.242104i
\(381\) −15.3190 + 13.0566i −0.784815 + 0.668911i
\(382\) 2.20101 + 6.57301i 0.112613 + 0.336305i
\(383\) −13.6263 + 23.6014i −0.696270 + 1.20597i 0.273481 + 0.961877i \(0.411825\pi\)
−0.969751 + 0.244097i \(0.921508\pi\)
\(384\) −15.0191 12.5867i −0.766442 0.642314i
\(385\) 5.52242 + 9.56511i 0.281448 + 0.487483i
\(386\) −5.15079 + 5.82466i −0.262169 + 0.296467i
\(387\) 2.74712 + 7.20037i 0.139644 + 0.366016i
\(388\) 1.13404 + 9.20041i 0.0575722 + 0.467080i
\(389\) 2.39842 1.38473i 0.121605 0.0702085i −0.437964 0.898993i \(-0.644300\pi\)
0.559568 + 0.828784i \(0.310967\pi\)
\(390\) 47.4036 + 28.5337i 2.40037 + 1.44486i
\(391\) −22.9166 + 39.6927i −1.15894 + 2.00734i
\(392\) 2.55204 1.21946i 0.128898 0.0615921i
\(393\) −29.6218 + 5.45883i −1.49422 + 0.275361i
\(394\) −4.60526 + 22.6627i −0.232010 + 1.14173i
\(395\) 0.747086i 0.0375900i
\(396\) 0.762129 20.8830i 0.0382984 1.04941i
\(397\) 1.76707i 0.0886867i −0.999016 0.0443433i \(-0.985880\pi\)
0.999016 0.0443433i \(-0.0141196\pi\)
\(398\) −13.8411 2.81262i −0.693790 0.140984i
\(399\) −0.716486 + 2.01675i −0.0358691 + 0.100964i
\(400\) −5.55714 + 19.4488i −0.277857 + 0.972438i
\(401\) −4.96674 + 8.60264i −0.248027 + 0.429595i −0.962978 0.269579i \(-0.913116\pi\)
0.714951 + 0.699174i \(0.246449\pi\)
\(402\) 19.5842 + 0.357247i 0.976772 + 0.0178178i
\(403\) 14.3649 8.29355i 0.715564 0.413131i
\(404\) −25.9472 + 3.19825i −1.29092 + 0.159119i
\(405\) −19.0110 21.2880i −0.944667 1.05781i
\(406\) −8.49401 7.51132i −0.421551 0.372781i
\(407\) 1.85070 + 3.20551i 0.0917358 + 0.158891i
\(408\) −28.2102 + 2.95594i −1.39661 + 0.146341i
\(409\) −13.3854 + 23.1841i −0.661864 + 1.14638i 0.318262 + 0.948003i \(0.396901\pi\)
−0.980125 + 0.198379i \(0.936432\pi\)
\(410\) −1.45021 + 0.485610i −0.0716205 + 0.0239825i
\(411\) 5.90483 + 2.09779i 0.291264 + 0.103477i
\(412\) −24.1789 + 18.2379i −1.19121 + 0.898516i
\(413\) 5.83225i 0.286986i
\(414\) −21.3158 25.9535i −1.04761 1.27554i
\(415\) 32.1505 1.57821
\(416\) 1.80464 + 40.2518i 0.0884799 + 1.97350i
\(417\) −5.98159 + 1.10231i −0.292920 + 0.0539804i
\(418\) −1.93253 5.77125i −0.0945234 0.282281i
\(419\) −10.8419 6.25958i −0.529662 0.305800i 0.211217 0.977439i \(-0.432257\pi\)
−0.740879 + 0.671639i \(0.765591\pi\)
\(420\) 3.29762 + 10.4789i 0.160907 + 0.511317i
\(421\) 0.524677 0.302922i 0.0255712 0.0147635i −0.487160 0.873313i \(-0.661967\pi\)
0.512731 + 0.858549i \(0.328634\pi\)
\(422\) −12.3303 10.9038i −0.600229 0.530787i
\(423\) 13.5926 5.18590i 0.660894 0.252147i
\(424\) 4.76388 6.94192i 0.231354 0.337130i
\(425\) 14.6391 + 25.3557i 0.710103 + 1.22993i
\(426\) 10.2843 5.69010i 0.498275 0.275686i
\(427\) 4.86161 + 2.80685i 0.235270 + 0.135833i
\(428\) −6.71231 + 15.8338i −0.324452 + 0.765356i
\(429\) −32.7009 + 27.8716i −1.57882 + 1.34565i
\(430\) 11.2902 + 2.29426i 0.544461 + 0.110639i
\(431\) 11.4034 0.549285 0.274642 0.961546i \(-0.411441\pi\)
0.274642 + 0.961546i \(0.411441\pi\)
\(432\) 5.24679 20.1115i 0.252436 0.967614i
\(433\) 9.08671 0.436680 0.218340 0.975873i \(-0.429936\pi\)
0.218340 + 0.975873i \(0.429936\pi\)
\(434\) 3.22740 + 0.655836i 0.154920 + 0.0314811i
\(435\) 33.5170 28.5671i 1.60702 1.36969i
\(436\) 14.0286 33.0923i 0.671847 1.58483i
\(437\) −8.47111 4.89080i −0.405228 0.233959i
\(438\) 19.8239 10.9682i 0.947223 0.524081i
\(439\) −12.4362 21.5401i −0.593545 1.02805i −0.993750 0.111625i \(-0.964394\pi\)
0.400205 0.916426i \(-0.368939\pi\)
\(440\) −25.7577 17.6762i −1.22795 0.842678i
\(441\) 2.32758 + 1.89272i 0.110837 + 0.0901293i
\(442\) 43.6897 + 38.6351i 2.07811 + 1.83769i
\(443\) 29.6382 17.1116i 1.40815 0.812997i 0.412942 0.910757i \(-0.364501\pi\)
0.995210 + 0.0977603i \(0.0311679\pi\)
\(444\) 1.10511 + 3.51174i 0.0524464 + 0.166660i
\(445\) 8.00496 + 4.62167i 0.379472 + 0.219088i
\(446\) 9.41359 + 28.1124i 0.445747 + 1.33116i
\(447\) 12.6899 2.33855i 0.600212 0.110609i
\(448\) −5.02582 + 6.22423i −0.237448 + 0.294067i
\(449\) −0.0273929 −0.00129275 −0.000646375 1.00000i \(-0.500206\pi\)
−0.000646375 1.00000i \(0.500206\pi\)
\(450\) −21.1662 + 3.50271i −0.997785 + 0.165119i
\(451\) 1.18766i 0.0559248i
\(452\) −0.566280 + 0.427138i −0.0266356 + 0.0200909i
\(453\) 2.21289 + 0.786167i 0.103971 + 0.0369373i
\(454\) 1.57609 0.527761i 0.0739693 0.0247691i
\(455\) 11.2939 19.5617i 0.529468 0.917065i
\(456\) −0.630851 6.02056i −0.0295423 0.281938i
\(457\) −9.23823 16.0011i −0.432146 0.748499i 0.564912 0.825151i \(-0.308910\pi\)
−0.997058 + 0.0766522i \(0.975577\pi\)
\(458\) −13.5879 12.0159i −0.634923 0.561467i
\(459\) −15.6409 25.6999i −0.730055 1.19957i
\(460\) −49.8302 + 6.14207i −2.32335 + 0.286375i
\(461\) 13.7709 7.95065i 0.641376 0.370299i −0.143768 0.989611i \(-0.545922\pi\)
0.785145 + 0.619313i \(0.212589\pi\)
\(462\) −8.52969 0.155595i −0.396837 0.00723892i
\(463\) 14.0391 24.3164i 0.652450 1.13008i −0.330076 0.943954i \(-0.607075\pi\)
0.982527 0.186123i \(-0.0595922\pi\)
\(464\) 30.8368 + 8.81108i 1.43156 + 0.409044i
\(465\) −4.28213 + 12.0532i −0.198579 + 0.558956i
\(466\) −5.81037 1.18072i −0.269160 0.0546956i
\(467\) 28.0375i 1.29742i 0.761035 + 0.648711i \(0.224691\pi\)
−0.761035 + 0.648711i \(0.775309\pi\)
\(468\) −37.7654 + 20.0041i −1.74571 + 0.924691i
\(469\) 7.99656i 0.369247i
\(470\) 4.33101 21.3132i 0.199775 0.983102i
\(471\) 13.8367 2.54988i 0.637563 0.117492i
\(472\) 7.11221 + 14.8841i 0.327366 + 0.685098i
\(473\) −4.47345 + 7.74824i −0.205689 + 0.356265i
\(474\) −0.494398 0.297594i −0.0227085 0.0136689i
\(475\) −5.41136 + 3.12425i −0.248290 + 0.143351i
\(476\) 1.41661 + 11.4928i 0.0649301 + 0.526774i
\(477\) 8.81722 + 1.41496i 0.403713 + 0.0647866i
\(478\) −2.21413 + 2.50380i −0.101272 + 0.114521i
\(479\) 0.426833 + 0.739297i 0.0195025 + 0.0337794i 0.875612 0.483015i \(-0.160458\pi\)
−0.856109 + 0.516795i \(0.827125\pi\)
\(480\) −21.1943 22.7212i −0.967381 1.03708i
\(481\) 3.78488 6.55560i 0.172576 0.298910i
\(482\) 1.96064 + 5.85517i 0.0893045 + 0.266696i
\(483\) −10.4350 + 8.89392i −0.474808 + 0.404687i
\(484\) 1.80423 1.36091i 0.0820103 0.0618594i
\(485\) 14.6988i 0.667437i
\(486\) 21.6606 4.10107i 0.982544 0.186028i
\(487\) −11.0383 −0.500191 −0.250096 0.968221i \(-0.580462\pi\)
−0.250096 + 0.968221i \(0.580462\pi\)
\(488\) −15.8299 1.23465i −0.716586 0.0558901i
\(489\) 14.6927 + 17.2385i 0.664426 + 0.779552i
\(490\) 4.25272 1.42405i 0.192118 0.0643319i
\(491\) 15.0542 + 8.69155i 0.679386 + 0.392244i 0.799624 0.600501i \(-0.205032\pi\)
−0.120237 + 0.992745i \(0.538366\pi\)
\(492\) 0.256313 1.15314i 0.0115555 0.0519875i
\(493\) 40.2026 23.2110i 1.81064 1.04537i
\(494\) −8.24542 + 9.32415i −0.370979 + 0.419513i
\(495\) 5.25015 32.7159i 0.235977 1.47047i
\(496\) −9.03623 + 2.26198i −0.405739 + 0.101566i
\(497\) −2.39916 4.15547i −0.107617 0.186398i
\(498\) −12.8068 + 21.2762i −0.573887 + 0.953410i
\(499\) 29.3496 + 16.9450i 1.31387 + 0.758562i 0.982735 0.185021i \(-0.0592354\pi\)
0.331134 + 0.943584i \(0.392569\pi\)
\(500\) −0.140550 + 0.331546i −0.00628558 + 0.0148272i
\(501\) 1.41341 + 7.66975i 0.0631466 + 0.342659i
\(502\) −4.70281 + 23.1428i −0.209897 + 1.03291i
\(503\) 20.2562 0.903178 0.451589 0.892226i \(-0.350857\pi\)
0.451589 + 0.892226i \(0.350857\pi\)
\(504\) −8.24817 1.99189i −0.367403 0.0887258i
\(505\) −41.4538 −1.84467
\(506\) 7.76440 38.2090i 0.345170 1.69860i
\(507\) 61.5847 + 21.8790i 2.73507 + 0.971682i
\(508\) −21.3987 9.07139i −0.949415 0.402478i
\(509\) 11.1979 + 6.46509i 0.496337 + 0.286560i 0.727199 0.686426i \(-0.240822\pi\)
−0.230863 + 0.972986i \(0.574155\pi\)
\(510\) −44.9681 0.820289i −1.99122 0.0363230i
\(511\) −4.62461 8.01006i −0.204581 0.354344i
\(512\) 5.23589 22.0133i 0.231396 0.972860i
\(513\) 5.48481 3.33805i 0.242160 0.147378i
\(514\) −9.45973 + 10.6973i −0.417251 + 0.471839i
\(515\) −41.5883 + 24.0110i −1.83260 + 1.05805i
\(516\) −6.01559 + 6.55759i −0.264822 + 0.288682i
\(517\) 14.6268 + 8.44481i 0.643287 + 0.371402i
\(518\) 1.42519 0.477234i 0.0626194 0.0209685i
\(519\) −8.56918 + 24.1204i −0.376145 + 1.05877i
\(520\) −4.96787 + 63.6947i −0.217855 + 2.79320i
\(521\) 35.1139 1.53837 0.769184 0.639028i \(-0.220663\pi\)
0.769184 + 0.639028i \(0.220663\pi\)
\(522\) 5.55370 + 33.5600i 0.243079 + 1.46888i
\(523\) 1.54778i 0.0676797i 0.999427 + 0.0338398i \(0.0107736\pi\)
−0.999427 + 0.0338398i \(0.989226\pi\)
\(524\) −20.9443 27.7670i −0.914957 1.21301i
\(525\) 1.58734 + 8.61356i 0.0692772 + 0.375926i
\(526\) −13.2734 39.6391i −0.578747 1.72835i
\(527\) −6.74166 + 11.6769i −0.293671 + 0.508654i
\(528\) 21.9579 10.0045i 0.955593 0.435392i
\(529\) −19.8318 34.3497i −0.862252 1.49346i
\(530\) 8.84353 10.0005i 0.384138 0.434394i
\(531\) −11.0388 + 13.5750i −0.479043 + 0.589106i
\(532\) −2.45278 + 0.302329i −0.106341 + 0.0131076i
\(533\) −2.10348 + 1.21445i −0.0911120 + 0.0526035i
\(534\) −6.24717 + 3.45644i −0.270341 + 0.149575i
\(535\) −13.6346 + 23.6158i −0.589475 + 1.02100i
\(536\) 9.75150 + 20.4075i 0.421200 + 0.881471i
\(537\) 23.3548 + 27.4015i 1.00783 + 1.18246i
\(538\) 4.19800 20.6586i 0.180989 0.890656i
\(539\) 3.48281i 0.150015i
\(540\) 12.1581 30.6319i 0.523200 1.31819i
\(541\) 15.0247i 0.645964i −0.946405 0.322982i \(-0.895315\pi\)
0.946405 0.322982i \(-0.104685\pi\)
\(542\) 15.6126 + 3.17261i 0.670618 + 0.136275i
\(543\) −10.7265 12.5851i −0.460317 0.540077i
\(544\) −17.6303 27.6027i −0.755894 1.18346i
\(545\) 28.4960 49.3566i 1.22064 2.11420i
\(546\) 8.44649 + 15.2662i 0.361476 + 0.653331i
\(547\) 28.1945 16.2781i 1.20551 0.696002i 0.243736 0.969842i \(-0.421627\pi\)
0.961775 + 0.273840i \(0.0882937\pi\)
\(548\) 0.885187 + 7.18147i 0.0378133 + 0.306777i
\(549\) −6.00322 15.7348i −0.256211 0.671546i
\(550\) −18.6580 16.4994i −0.795579 0.703537i
\(551\) 4.95364 + 8.57995i 0.211032 + 0.365518i
\(552\) 15.7847 35.4227i 0.671842 1.50769i
\(553\) −0.117791 + 0.204020i −0.00500897 + 0.00867579i
\(554\) 30.5264 10.2219i 1.29694 0.434289i
\(555\) 1.05794 + 5.74082i 0.0449071 + 0.243684i
\(556\) −4.22932 5.60704i −0.179363 0.237791i
\(557\) 29.1719i 1.23605i −0.786157 0.618026i \(-0.787932\pi\)
0.786157 0.618026i \(-0.212068\pi\)
\(558\) −6.27073 7.63506i −0.265461 0.323218i
\(559\) 18.2974 0.773896
\(560\) −9.11655 + 8.82026i −0.385244 + 0.372724i
\(561\) 11.6925 32.9118i 0.493657 1.38954i
\(562\) 4.69230 + 14.0129i 0.197933 + 0.591098i
\(563\) −6.05943 3.49842i −0.255375 0.147441i 0.366848 0.930281i \(-0.380437\pi\)
−0.622223 + 0.782840i \(0.713770\pi\)
\(564\) 12.3792 + 11.3560i 0.521257 + 0.478174i
\(565\) −0.974016 + 0.562348i −0.0409771 + 0.0236582i
\(566\) 21.5885 + 19.0909i 0.907434 + 0.802451i
\(567\) −1.83526 8.81089i −0.0770736 0.370023i
\(568\) 11.1902 + 7.67924i 0.469530 + 0.322214i
\(569\) 22.4539 + 38.8913i 0.941316 + 1.63041i 0.762965 + 0.646439i \(0.223743\pi\)
0.178350 + 0.983967i \(0.442924\pi\)
\(570\) 0.175064 9.59699i 0.00733263 0.401974i
\(571\) −1.78032 1.02787i −0.0745039 0.0430149i 0.462285 0.886731i \(-0.347030\pi\)
−0.536789 + 0.843716i \(0.680363\pi\)
\(572\) −45.6792 19.3644i −1.90994 0.809667i
\(573\) −7.99976 2.84205i −0.334195 0.118728i
\(574\) −0.472597 0.0960357i −0.0197258 0.00400845i
\(575\) −40.0296 −1.66935
\(576\) 23.4787 4.97495i 0.978280 0.207290i
\(577\) −29.8221 −1.24151 −0.620755 0.784005i \(-0.713174\pi\)
−0.620755 + 0.784005i \(0.713174\pi\)
\(578\) −22.8992 4.65330i −0.952479 0.193552i
\(579\) −1.72586 9.36522i −0.0717243 0.389205i
\(580\) 46.8192 + 19.8477i 1.94406 + 0.824130i
\(581\) 8.77989 + 5.06907i 0.364251 + 0.210301i
\(582\) −9.72719 5.85510i −0.403205 0.242702i
\(583\) 5.18360 + 8.97826i 0.214683 + 0.371841i
\(584\) 21.5702 + 14.8025i 0.892580 + 0.612531i
\(585\) −63.3122 + 24.1552i −2.61764 + 0.998693i
\(586\) 21.3423 + 18.8732i 0.881644 + 0.779644i
\(587\) −16.9034 + 9.75916i −0.697677 + 0.402804i −0.806481 0.591259i \(-0.798631\pi\)
0.108805 + 0.994063i \(0.465298\pi\)
\(588\) −0.751636 + 3.38157i −0.0309969 + 0.139454i
\(589\) −2.49206 1.43879i −0.102683 0.0592843i
\(590\) 8.30540 + 24.8029i 0.341928 + 1.02112i
\(591\) −18.3726 21.5560i −0.755746 0.886695i
\(592\) −3.05518 + 2.95589i −0.125567 + 0.121486i
\(593\) 40.5312 1.66442 0.832209 0.554462i \(-0.187076\pi\)
0.832209 + 0.554462i \(0.187076\pi\)
\(594\) 19.5590 + 16.5064i 0.802517 + 0.677267i
\(595\) 18.3612i 0.752736i
\(596\) 8.97248 + 11.8953i 0.367527 + 0.487250i
\(597\) 13.1651 11.2209i 0.538813 0.459240i
\(598\) −75.6121 + 25.3191i −3.09201 + 1.03538i
\(599\) 5.59058 9.68316i 0.228425 0.395643i −0.728917 0.684602i \(-0.759976\pi\)
0.957341 + 0.288959i \(0.0933092\pi\)
\(600\) −14.5549 20.0464i −0.594200 0.818393i
\(601\) 22.6284 + 39.1935i 0.923030 + 1.59873i 0.794700 + 0.607003i \(0.207628\pi\)
0.128330 + 0.991732i \(0.459038\pi\)
\(602\) 2.72147 + 2.40662i 0.110919 + 0.0980865i
\(603\) −15.1352 + 18.6126i −0.616353 + 0.757965i
\(604\) 0.331732 + 2.69132i 0.0134980 + 0.109508i
\(605\) 3.10331 1.79170i 0.126168 0.0728429i
\(606\) 16.5127 27.4328i 0.670781 1.11438i
\(607\) 10.9071 18.8917i 0.442707 0.766790i −0.555183 0.831728i \(-0.687352\pi\)
0.997889 + 0.0649381i \(0.0206850\pi\)
\(608\) 5.89091 3.76262i 0.238908 0.152595i
\(609\) 13.6572 2.51679i 0.553416 0.101986i
\(610\) −24.6722 5.01360i −0.998948 0.202995i
\(611\) 34.5411i 1.39738i
\(612\) 18.4554 29.4318i 0.746016 1.18971i
\(613\) 38.6709i 1.56190i −0.624592 0.780951i \(-0.714735\pi\)
0.624592 0.780951i \(-0.285265\pi\)
\(614\) −0.507658 + 2.49821i −0.0204874 + 0.100820i
\(615\) 0.627043 1.76499i 0.0252848 0.0711712i
\(616\) −4.24715 8.88827i −0.171123 0.358119i
\(617\) 23.5343 40.7626i 0.947456 1.64104i 0.196698 0.980464i \(-0.436978\pi\)
0.750758 0.660577i \(-0.229688\pi\)
\(618\) 0.676514 37.0864i 0.0272134 1.49183i
\(619\) −7.44781 + 4.30000i −0.299353 + 0.172831i −0.642152 0.766577i \(-0.721958\pi\)
0.342799 + 0.939409i \(0.388625\pi\)
\(620\) −14.6592 + 1.80689i −0.588727 + 0.0725664i
\(621\) 41.1219 0.950861i 1.65017 0.0381567i
\(622\) −7.39197 + 8.35904i −0.296391 + 0.335167i
\(623\) 1.45737 + 2.52423i 0.0583882 + 0.101131i
\(624\) −40.1723 28.6597i −1.60818 1.14731i
\(625\) 12.3564 21.4020i 0.494258 0.856080i
\(626\) 9.92200 + 29.6307i 0.396563 + 1.18428i
\(627\) 7.02396 + 2.49538i 0.280510 + 0.0996560i
\(628\) 9.78335 + 12.9703i 0.390398 + 0.517571i
\(629\) 6.15330i 0.245348i
\(630\) −12.5939 4.73460i −0.501752 0.188631i
\(631\) 1.54659 0.0615686 0.0307843 0.999526i \(-0.490200\pi\)
0.0307843 + 0.999526i \(0.490200\pi\)
\(632\) 0.0518127 0.664307i 0.00206100 0.0264247i
\(633\) 19.8253 3.65349i 0.787986 0.145213i
\(634\) −41.6549 + 13.9484i −1.65433 + 0.553962i
\(635\) −31.9158 18.4266i −1.26654 0.731237i
\(636\) 3.09530 + 9.83597i 0.122737 + 0.390022i
\(637\) 6.16846 3.56136i 0.244403 0.141106i
\(638\) −26.1605 + 29.5830i −1.03570 + 1.17120i
\(639\) −2.28088 + 14.2131i −0.0902302 + 0.562262i
\(640\) 12.5098 33.6269i 0.494494 1.32922i
\(641\) 11.7787 + 20.4014i 0.465233 + 0.805806i 0.999212 0.0396911i \(-0.0126374\pi\)
−0.533979 + 0.845497i \(0.679304\pi\)
\(642\) −10.1970 18.4301i −0.402444 0.727377i
\(643\) 9.54889 + 5.51305i 0.376571 + 0.217414i 0.676325 0.736603i \(-0.263571\pi\)
−0.299754 + 0.954016i \(0.596905\pi\)
\(644\) −14.5764 6.17926i −0.574390 0.243497i
\(645\) −10.7388 + 9.15288i −0.422841 + 0.360394i
\(646\) 2.01486 9.91523i 0.0792735 0.390109i
\(647\) 18.9187 0.743769 0.371885 0.928279i \(-0.378712\pi\)
0.371885 + 0.928279i \(0.378712\pi\)
\(648\) 15.4282 + 20.2477i 0.606077 + 0.795406i
\(649\) −20.3126 −0.797340
\(650\) −10.1435 + 49.9170i −0.397863 + 1.95790i
\(651\) −3.06979 + 2.61644i −0.120315 + 0.102546i
\(652\) −10.2081 + 24.0801i −0.399779 + 0.943048i
\(653\) −5.83422 3.36839i −0.228311 0.131815i 0.381482 0.924376i \(-0.375414\pi\)
−0.609792 + 0.792561i \(0.708747\pi\)
\(654\) 21.3116 + 38.5185i 0.833348 + 1.50619i
\(655\) −27.5742 47.7599i −1.07741 1.86613i
\(656\) 1.32320 0.331227i 0.0516622 0.0129322i
\(657\) −4.39661 + 27.3971i −0.171528 + 1.06886i
\(658\) 4.54312 5.13749i 0.177109 0.200280i
\(659\) 37.4410 21.6166i 1.45849 0.842062i 0.459557 0.888148i \(-0.348008\pi\)
0.998937 + 0.0460857i \(0.0146747\pi\)
\(660\) 36.4960 11.4850i 1.42060 0.447052i
\(661\) −19.4670 11.2393i −0.757180 0.437158i 0.0711024 0.997469i \(-0.477348\pi\)
−0.828282 + 0.560311i \(0.810682\pi\)
\(662\) 12.4652 4.17405i 0.484475 0.162229i
\(663\) −70.2468 + 12.9453i −2.72816 + 0.502756i
\(664\) −28.5882 2.22974i −1.10944 0.0865305i
\(665\) −3.91861 −0.151957
\(666\) −4.22052 1.58668i −0.163542 0.0614828i
\(667\) 63.4687i 2.45752i
\(668\) −7.18949 + 5.42295i −0.278170 + 0.209820i
\(669\) −34.2145 12.1553i −1.32281 0.469951i
\(670\) 11.3875 + 34.0071i 0.439937 + 1.31381i
\(671\) 9.77574 16.9321i 0.377388 0.653656i
\(672\) −2.20550 9.54651i −0.0850788 0.368264i
\(673\) 17.8779 + 30.9655i 0.689144 + 1.19363i 0.972115 + 0.234504i \(0.0753464\pi\)
−0.282972 + 0.959128i \(0.591320\pi\)
\(674\) 2.34996 2.65740i 0.0905169 0.102359i
\(675\) 12.6083 23.0531i 0.485296 0.887315i
\(676\) 9.23210 + 74.8995i 0.355081 + 2.88075i
\(677\) −1.48425 + 0.856932i −0.0570444 + 0.0329346i −0.528251 0.849088i \(-0.677152\pi\)
0.471207 + 0.882023i \(0.343819\pi\)
\(678\) 0.0158442 0.868579i 0.000608494 0.0333576i
\(679\) −2.31751 + 4.01404i −0.0889379 + 0.154045i
\(680\) −22.3908 46.8586i −0.858648 1.79694i
\(681\) −0.681471 + 1.91819i −0.0261140 + 0.0735053i
\(682\) 2.28415 11.2404i 0.0874647 0.430418i
\(683\) 6.51249i 0.249194i 0.992207 + 0.124597i \(0.0397637\pi\)
−0.992207 + 0.124597i \(0.960236\pi\)
\(684\) 6.28126 + 3.93871i 0.240170 + 0.150600i
\(685\) 11.4733i 0.438371i
\(686\) 1.38589 + 0.281624i 0.0529135 + 0.0107525i
\(687\) 21.8475 4.02614i 0.833533 0.153607i
\(688\) −9.88009 2.82306i −0.376675 0.107628i
\(689\) 10.6010 18.3615i 0.403867 0.699517i
\(690\) 31.7117 52.6833i 1.20724 2.00562i
\(691\) 18.4092 10.6285i 0.700318 0.404329i −0.107148 0.994243i \(-0.534172\pi\)
0.807466 + 0.589914i \(0.200838\pi\)
\(692\) −29.3353 + 3.61586i −1.11516 + 0.137454i
\(693\) 6.59197 8.10652i 0.250408 0.307941i
\(694\) −17.4873 15.4641i −0.663807 0.587010i
\(695\) −5.56811 9.64424i −0.211210 0.365827i
\(696\) −31.7845 + 23.0774i −1.20479 + 0.874745i
\(697\) 0.987199 1.70988i 0.0373928 0.0647663i
\(698\) 22.1024 7.40112i 0.836589 0.280137i
\(699\) 5.52662 4.71043i 0.209036 0.178165i
\(700\) −8.07419 + 6.09027i −0.305176 + 0.230191i
\(701\) 30.5912i 1.15541i 0.816245 + 0.577706i \(0.196052\pi\)
−0.816245 + 0.577706i \(0.803948\pi\)
\(702\) 9.23462 51.5200i 0.348538 1.94450i
\(703\) −1.31322 −0.0495291
\(704\) 21.6778 + 17.5040i 0.817014 + 0.659707i
\(705\) 17.2785 + 20.2723i 0.650744 + 0.763500i
\(706\) 10.2561 + 30.6285i 0.385994 + 1.15272i
\(707\) −11.3205 6.53589i −0.425751 0.245807i
\(708\) −19.7222 4.38373i −0.741205 0.164751i
\(709\) 14.9773 8.64716i 0.562485 0.324751i −0.191657 0.981462i \(-0.561386\pi\)
0.754142 + 0.656711i \(0.228053\pi\)
\(710\) 16.1206 + 14.2555i 0.604994 + 0.535001i
\(711\) 0.660318 0.251927i 0.0247639 0.00944802i
\(712\) −6.79747 4.66475i −0.254746 0.174819i
\(713\) −9.21727 15.9648i −0.345190 0.597886i
\(714\) −12.1509 7.31400i −0.454735 0.273719i
\(715\) −68.1296 39.3346i −2.54790 1.47103i
\(716\) −16.2263 + 38.2765i −0.606404 + 1.43046i
\(717\) −0.741880 4.02575i −0.0277060 0.150344i
\(718\) −20.6418 4.19459i −0.770345 0.156541i
\(719\) 21.5609 0.804087 0.402044 0.915621i \(-0.368300\pi\)
0.402044 + 0.915621i \(0.368300\pi\)
\(720\) 37.9137 3.27484i 1.41296 0.122046i
\(721\) −15.1430 −0.563954
\(722\) −24.2158 4.92086i −0.901219 0.183135i
\(723\) −7.12610 2.53167i −0.265022 0.0941538i
\(724\) 7.45247 17.5798i 0.276969 0.653348i
\(725\) 35.1121 + 20.2720i 1.30403 + 0.752881i
\(726\) −0.0504813 + 2.76738i −0.00187354 + 0.102707i
\(727\) −10.5280 18.2351i −0.390463 0.676302i 0.602048 0.798460i \(-0.294352\pi\)
−0.992511 + 0.122158i \(0.961018\pi\)
\(728\) −11.3992 + 16.6109i −0.422483 + 0.615642i
\(729\) −12.4048 + 23.9817i −0.459437 + 0.888210i
\(730\) 31.0739 + 27.4789i 1.15010 + 1.01704i
\(731\) −12.8809 + 7.43678i −0.476416 + 0.275059i
\(732\) 13.1458 14.3302i 0.485881 0.529659i
\(733\) −36.7419 21.2129i −1.35709 0.783518i −0.367861 0.929881i \(-0.619910\pi\)
−0.989231 + 0.146363i \(0.953243\pi\)
\(734\) 3.40896 + 10.1804i 0.125827 + 0.375765i
\(735\) −1.83880 + 5.17582i −0.0678252 + 0.190913i
\(736\) 44.7349 2.00564i 1.64895 0.0739288i
\(737\) −27.8505 −1.02589
\(738\) 0.918239 + 1.11802i 0.0338008 + 0.0411550i
\(739\) 8.05062i 0.296147i −0.988976 0.148073i \(-0.952693\pi\)
0.988976 0.148073i \(-0.0473072\pi\)
\(740\) −5.38135 + 4.05909i −0.197822 + 0.149215i
\(741\) −2.76277 14.9919i −0.101493 0.550741i
\(742\) 3.99180 1.33668i 0.146544 0.0490710i
\(743\) 4.90467 8.49514i 0.179935 0.311657i −0.761923 0.647668i \(-0.775745\pi\)
0.941858 + 0.336011i \(0.109078\pi\)
\(744\) 4.64359 10.4208i 0.170242 0.382043i
\(745\) 11.8127 + 20.4602i 0.432784 + 0.749604i
\(746\) −4.74260 4.19392i −0.173639 0.153550i
\(747\) −10.8416 28.4165i −0.396673 1.03971i
\(748\) 40.0274 4.93377i 1.46355 0.180397i
\(749\) −7.44687 + 4.29945i −0.272103 + 0.157099i
\(750\) −0.213517 0.385910i −0.00779653 0.0140914i
\(751\) −5.17081 + 8.95610i −0.188685 + 0.326813i −0.944812 0.327612i \(-0.893756\pi\)
0.756127 + 0.654425i \(0.227089\pi\)
\(752\) −5.32926 + 18.6513i −0.194338 + 0.680141i
\(753\) −18.7617 22.0126i −0.683716 0.802184i
\(754\) 79.1455 + 16.0830i 2.88231 + 0.585709i
\(755\) 4.29971i 0.156482i
\(756\) 8.14985 6.44825i 0.296407 0.234521i
\(757\) 0.226816i 0.00824378i −0.999992 0.00412189i \(-0.998688\pi\)
0.999992 0.00412189i \(-0.00131204\pi\)
\(758\) 1.99609 9.82288i 0.0725013 0.356783i
\(759\) 30.9758 + 36.3431i 1.12435 + 1.31917i
\(760\) 10.0004 4.77859i 0.362754 0.173338i
\(761\) −15.3462 + 26.5804i −0.556300 + 0.963540i 0.441501 + 0.897261i \(0.354446\pi\)
−0.997801 + 0.0662792i \(0.978887\pi\)
\(762\) 24.9075 13.7808i 0.902302 0.499227i
\(763\) 15.5638 8.98576i 0.563447 0.325306i
\(764\) −1.19924 9.72932i −0.0433868 0.351995i
\(765\) 34.7525 42.7372i 1.25648 1.54517i
\(766\) 25.5312 28.8714i 0.922480 1.04317i
\(767\) 20.7707 + 35.9760i 0.749988 + 1.29902i
\(768\) 17.2701 + 21.6736i 0.623182 + 0.782077i
\(769\) 6.21620 10.7668i 0.224162 0.388260i −0.731906 0.681406i \(-0.761369\pi\)
0.956068 + 0.293146i \(0.0947022\pi\)
\(770\) −4.95969 14.8114i −0.178735 0.533767i
\(771\) −3.16964 17.1998i −0.114152 0.619435i
\(772\) 8.77879 6.62174i 0.315956 0.238322i
\(773\) 24.7073i 0.888660i −0.895863 0.444330i \(-0.853442\pi\)
0.895863 0.444330i \(-0.146558\pi\)
\(774\) −1.77940 10.7526i −0.0639592 0.386493i
\(775\) −11.7760 −0.423007
\(776\) 1.01940 13.0701i 0.0365945 0.469190i
\(777\) −0.616228 + 1.73455i −0.0221071 + 0.0622265i
\(778\) −3.71391 + 1.24362i −0.133150 + 0.0445861i
\(779\) 0.364918 + 0.210686i 0.0130746 + 0.00754859i
\(780\) −57.6603 52.8945i −2.06457 1.89393i
\(781\) −14.4727 + 8.35583i −0.517875 + 0.298995i
\(782\) 42.9382 48.5558i 1.53547 1.73635i
\(783\) −36.5517 19.9911i −1.30625 0.714423i
\(784\) −3.88027 + 0.971322i −0.138581 + 0.0346901i
\(785\) 12.8802 + 22.3092i 0.459716 + 0.796251i
\(786\) 42.5899 + 0.776906i 1.51913 + 0.0277113i
\(787\) 32.7240 + 18.8932i 1.16649 + 0.673471i 0.952850 0.303442i \(-0.0981360\pi\)
0.213636 + 0.976913i \(0.431469\pi\)
\(788\) 12.7648 30.1111i 0.454726 1.07266i
\(789\) 48.2433 + 17.1393i 1.71751 + 0.610174i
\(790\) 0.210398 1.03538i 0.00748561 0.0368371i
\(791\) −0.354655 −0.0126101
\(792\) −6.93738 + 28.7268i −0.246509 + 1.02076i
\(793\) −39.9849 −1.41990
\(794\) −0.497650 + 2.44896i −0.0176609 + 0.0869104i
\(795\) 2.96317 + 16.0794i 0.105093 + 0.570277i
\(796\) 18.3901 + 7.79597i 0.651819 + 0.276321i
\(797\) 12.5617 + 7.25248i 0.444957 + 0.256896i 0.705698 0.708513i \(-0.250634\pi\)
−0.260741 + 0.965409i \(0.583967\pi\)
\(798\) 1.56094 2.59321i 0.0552565 0.0917987i
\(799\) 14.0389 + 24.3160i 0.496659 + 0.860239i
\(800\) 13.1788 25.3888i 0.465941 0.897629i
\(801\) 1.38552 8.63374i 0.0489548 0.305058i
\(802\) 9.30606 10.5235i 0.328608 0.371599i
\(803\) −27.8975 + 16.1066i −0.984483 + 0.568391i
\(804\) −27.0409 6.01050i −0.953661 0.211974i
\(805\) −21.7404 12.5518i −0.766249 0.442394i
\(806\) −22.2438 + 7.44845i −0.783503 + 0.262360i
\(807\) 16.7478 + 19.6497i 0.589551 + 0.691704i
\(808\) 36.8606 + 2.87494i 1.29675 + 0.101140i
\(809\) −42.3650 −1.48947 −0.744737 0.667358i \(-0.767425\pi\)
−0.744737 + 0.667358i \(0.767425\pi\)
\(810\) 20.3520 + 34.8568i 0.715096 + 1.22474i
\(811\) 41.6068i 1.46101i −0.682907 0.730505i \(-0.739285\pi\)
0.682907 0.730505i \(-0.260715\pi\)
\(812\) 9.65638 + 12.8020i 0.338873 + 0.449261i
\(813\) −14.8501 + 12.6570i −0.520817 + 0.443901i
\(814\) −1.66212 4.96368i −0.0582571 0.173977i
\(815\) −20.7355 + 35.9149i −0.726333 + 1.25805i
\(816\) 39.9287 + 3.84808i 1.39778 + 0.134710i
\(817\) −1.58714 2.74901i −0.0555270 0.0961756i
\(818\) 25.0798 28.3610i 0.876896 0.991619i
\(819\) −21.0982 3.38578i −0.737231 0.118309i
\(820\) 2.14658 0.264588i 0.0749619 0.00923980i
\(821\) −11.3021 + 6.52525i −0.394444 + 0.227733i −0.684084 0.729403i \(-0.739798\pi\)
0.289640 + 0.957136i \(0.406465\pi\)
\(822\) −7.59265 4.57025i −0.264824 0.159406i
\(823\) 24.5256 42.4795i 0.854907 1.48074i −0.0218240 0.999762i \(-0.506947\pi\)
0.876731 0.480981i \(-0.159719\pi\)
\(824\) 38.6455 18.4663i 1.34628 0.643304i
\(825\) 29.9994 5.52840i 1.04444 0.192474i
\(826\) −1.64250 + 8.08285i −0.0571500 + 0.281238i
\(827\) 32.7515i 1.13888i 0.822033 + 0.569440i \(0.192840\pi\)
−0.822033 + 0.569440i \(0.807160\pi\)
\(828\) 22.2321 + 41.9717i 0.772620 + 1.45862i
\(829\) 42.1327i 1.46333i 0.681664 + 0.731665i \(0.261257\pi\)
−0.681664 + 0.731665i \(0.738743\pi\)
\(830\) −44.5570 9.05437i −1.54660 0.314282i
\(831\) −13.1991 + 37.1525i −0.457871 + 1.28881i
\(832\) 8.83484 56.2927i 0.306293 1.95160i
\(833\) −2.89496 + 5.01421i −0.100304 + 0.173732i
\(834\) 8.60026 + 0.156882i 0.297803 + 0.00543238i
\(835\) −12.3661 + 7.13957i −0.427947 + 0.247075i
\(836\) 1.05295 + 8.54255i 0.0364172 + 0.295450i
\(837\) 12.0974 0.279727i 0.418146 0.00966877i
\(838\) 13.2628 + 11.7284i 0.458157 + 0.405152i
\(839\) −6.95180 12.0409i −0.240003 0.415697i 0.720712 0.693235i \(-0.243815\pi\)
−0.960715 + 0.277538i \(0.910482\pi\)
\(840\) −1.61903 15.4513i −0.0558617 0.533119i
\(841\) 17.6421 30.5569i 0.608347 1.05369i
\(842\) −0.812454 + 0.272055i −0.0279990 + 0.00937563i
\(843\) −17.0545 6.05892i −0.587390 0.208680i
\(844\) 14.0176 + 18.5839i 0.482507 + 0.639685i
\(845\) 119.661i 4.11646i
\(846\) −20.2983 + 3.35908i −0.697870 + 0.115488i
\(847\) 1.12997 0.0388261
\(848\) −8.55722 + 8.27911i −0.293856 + 0.284306i
\(849\) −34.7113 + 6.39673i −1.19129 + 0.219535i
\(850\) −13.1474 39.2630i −0.450953 1.34671i
\(851\) −7.28575 4.20643i −0.249752 0.144195i
\(852\) −15.8553 + 4.98954i −0.543195 + 0.170939i
\(853\) −46.5067 + 26.8506i −1.59236 + 0.919348i −0.599456 + 0.800408i \(0.704616\pi\)
−0.992901 + 0.118941i \(0.962050\pi\)
\(854\) −5.94718 5.25914i −0.203508 0.179964i
\(855\) 9.12087 + 7.41681i 0.311927 + 0.253649i
\(856\) 13.7617 20.0536i 0.470365 0.685416i
\(857\) −3.36558 5.82935i −0.114966 0.199127i 0.802800 0.596248i \(-0.203343\pi\)
−0.917766 + 0.397121i \(0.870009\pi\)
\(858\) 53.1691 29.4175i 1.81516 1.00430i
\(859\) −24.4912 14.1400i −0.835628 0.482450i 0.0201475 0.999797i \(-0.493586\pi\)
−0.855776 + 0.517347i \(0.826920\pi\)
\(860\) −15.0008 6.35918i −0.511523 0.216846i
\(861\) 0.449518 0.383132i 0.0153195 0.0130571i
\(862\) −15.8039 3.21149i −0.538283 0.109384i
\(863\) 33.6320 1.14485 0.572424 0.819958i \(-0.306003\pi\)
0.572424 + 0.819958i \(0.306003\pi\)
\(864\) −12.9353 + 26.3946i −0.440070 + 0.897964i
\(865\) −46.8666 −1.59351
\(866\) −12.5932 2.55904i −0.427933 0.0869597i
\(867\) 21.7809 18.5642i 0.739717 0.630474i
\(868\) −4.28812 1.81783i −0.145548 0.0617012i
\(869\) 0.710561 + 0.410243i 0.0241041 + 0.0139165i
\(870\) −54.4961 + 30.1517i −1.84759 + 1.02224i
\(871\) 28.4786 + 49.3264i 0.964961 + 1.67136i
\(872\) −28.7617 + 41.9115i −0.973992 + 1.41930i
\(873\) 12.9916 4.95662i 0.439700 0.167756i
\(874\) 10.3627 + 9.16378i 0.350522 + 0.309969i
\(875\) −0.155931 + 0.0900267i −0.00527143 + 0.00304346i
\(876\) −30.5627 + 9.61782i −1.03262 + 0.324956i
\(877\) 21.4238 + 12.3690i 0.723430 + 0.417672i 0.816014 0.578032i \(-0.196179\pi\)
−0.0925839 + 0.995705i \(0.529513\pi\)
\(878\) 11.1689 + 33.3544i 0.376933 + 1.12566i
\(879\) −34.3154 + 6.32378i −1.15743 + 0.213296i
\(880\) 30.7193 + 31.7512i 1.03555 + 1.07033i
\(881\) 19.8982 0.670387 0.335194 0.942149i \(-0.391198\pi\)
0.335194 + 0.942149i \(0.391198\pi\)
\(882\) −2.69273 3.27860i −0.0906690 0.110396i
\(883\) 11.1586i 0.375516i −0.982215 0.187758i \(-0.939878\pi\)
0.982215 0.187758i \(-0.0601220\pi\)
\(884\) −49.6685 65.8481i −1.67053 2.21471i
\(885\) −30.1867 10.7243i −1.01471 0.360495i
\(886\) −45.8943 + 15.3680i −1.54185 + 0.516296i
\(887\) 21.5110 37.2582i 0.722269 1.25101i −0.237819 0.971309i \(-0.576433\pi\)
0.960088 0.279697i \(-0.0902341\pi\)
\(888\) −0.542576 5.17810i −0.0182077 0.173766i
\(889\) −5.81053 10.0641i −0.194879 0.337540i
\(890\) −9.79241 8.65951i −0.328242 0.290267i
\(891\) −30.6867 + 6.39186i −1.02804 + 0.214135i
\(892\) −5.12906 41.6117i −0.171734 1.39326i
\(893\) −5.18947 + 2.99614i −0.173659 + 0.100262i
\(894\) −18.2454 0.332824i −0.610217 0.0111313i
\(895\) −32.9601 + 57.0886i −1.10174 + 1.90826i
\(896\) 8.71813 7.21070i 0.291252 0.240893i
\(897\) 32.6933 92.0245i 1.09160 3.07261i
\(898\) 0.0379635 + 0.00771451i 0.00126686 + 0.000257436i
\(899\) 18.6714i 0.622726i
\(900\) 30.3205 + 1.10655i 1.01068 + 0.0368851i
\(901\) 17.2347i 0.574171i
\(902\) −0.334474 + 1.64597i −0.0111368 + 0.0548047i
\(903\) −4.37574 + 0.806378i −0.145615 + 0.0268346i
\(904\) 0.905094 0.432488i 0.0301030 0.0143843i
\(905\) 15.1381 26.2199i 0.503207 0.871580i
\(906\) −2.84541 1.71274i −0.0945325 0.0569021i
\(907\) −13.6280 + 7.86813i −0.452510 + 0.261257i −0.708890 0.705319i \(-0.750804\pi\)
0.256379 + 0.966576i \(0.417470\pi\)
\(908\) −2.33291 + 0.287554i −0.0774203 + 0.00954282i
\(909\) 13.9788 + 36.6393i 0.463647 + 1.21525i
\(910\) −21.1612 + 23.9297i −0.701486 + 0.793260i
\(911\) −9.51357 16.4780i −0.315198 0.545940i 0.664281 0.747483i \(-0.268738\pi\)
−0.979480 + 0.201543i \(0.935404\pi\)
\(912\) −0.821247 + 8.52149i −0.0271942 + 0.282175i
\(913\) 17.6546 30.5787i 0.584282 1.01201i
\(914\) 8.29687 + 24.7774i 0.274436 + 0.819565i
\(915\) 23.4673 20.0016i 0.775806 0.661233i
\(916\) 15.4474 + 20.4794i 0.510396 + 0.676659i
\(917\) 17.3902i 0.574273i
\(918\) 14.4388 + 40.0221i 0.476553 + 1.32093i
\(919\) −29.6782 −0.978992 −0.489496 0.872005i \(-0.662819\pi\)
−0.489496 + 0.872005i \(0.662819\pi\)
\(920\) 70.7889 + 5.52118i 2.33384 + 0.182028i
\(921\) −2.02529 2.37621i −0.0667355 0.0782989i
\(922\) −21.3241 + 7.14049i −0.702271 + 0.235160i
\(923\) 29.5983 + 17.0886i 0.974239 + 0.562477i
\(924\) 11.7774 + 2.61781i 0.387447 + 0.0861195i
\(925\) −4.65415 + 2.68708i −0.153028 + 0.0883505i
\(926\) −26.3046 + 29.7460i −0.864424 + 0.977515i
\(927\) 35.2465 + 28.6614i 1.15765 + 0.941363i
\(928\) −40.2550 20.8956i −1.32144 0.685931i
\(929\) −16.4321 28.4613i −0.539121 0.933785i −0.998952 0.0457785i \(-0.985423\pi\)
0.459830 0.888007i \(-0.347910\pi\)
\(930\) 9.32904 15.4985i 0.305911 0.508216i
\(931\) −1.07012 0.617835i −0.0350718 0.0202487i
\(932\) 7.72001 + 3.27268i 0.252877 + 0.107200i
\(933\) −2.47680 13.4402i −0.0810869 0.440011i
\(934\) 7.89605 38.8569i 0.258367 1.27144i
\(935\) 63.9486 2.09134
\(936\) 57.9723 17.0878i 1.89489 0.558533i
\(937\) 47.3964 1.54837 0.774186 0.632959i \(-0.218160\pi\)
0.774186 + 0.632959i \(0.218160\pi\)
\(938\) −2.25202 + 11.0823i −0.0735312 + 0.361851i
\(939\) −36.0624 12.8118i −1.17685 0.418097i
\(940\) −12.0046 + 28.3179i −0.391547 + 0.923629i
\(941\) −3.77876 2.18167i −0.123184 0.0711203i 0.437142 0.899393i \(-0.355991\pi\)
−0.560326 + 0.828272i \(0.689324\pi\)
\(942\) −19.8943 0.362902i −0.648190 0.0118240i
\(943\) 1.34971 + 2.33777i 0.0439526 + 0.0761281i
\(944\) −5.66499 22.6307i −0.184380 0.736568i
\(945\) 14.0763 8.56682i 0.457903 0.278679i
\(946\) 8.38180 9.47837i 0.272516 0.308168i
\(947\) −43.7474 + 25.2576i −1.42160 + 0.820761i −0.996436 0.0843556i \(-0.973117\pi\)
−0.425164 + 0.905116i \(0.639783\pi\)
\(948\) 0.601371 + 0.551666i 0.0195316 + 0.0179173i
\(949\) 57.0534 + 32.9398i 1.85203 + 1.06927i
\(950\) 8.37941 2.80589i 0.271864 0.0910352i
\(951\) 18.0109 50.6966i 0.584042 1.64395i
\(952\) 1.27341 16.3268i 0.0412713 0.529153i
\(953\) 39.0711 1.26564 0.632818 0.774301i \(-0.281898\pi\)
0.632818 + 0.774301i \(0.281898\pi\)
\(954\) −11.8212 4.44412i −0.382725 0.143884i
\(955\) 15.5438i 0.502984i
\(956\) 3.77366 2.84643i 0.122049 0.0920601i
\(957\) −8.76552 47.5653i −0.283349 1.53757i
\(958\) −0.383340 1.14479i −0.0123851 0.0369865i
\(959\) −1.80895 + 3.13320i −0.0584142 + 0.101176i
\(960\) 22.9740 + 37.4579i 0.741484 + 1.20895i
\(961\) 12.7884 + 22.1502i 0.412530 + 0.714523i
\(962\) −7.09164 + 8.01942i −0.228644 + 0.258557i
\(963\) 25.4708 + 4.08748i 0.820786 + 0.131717i
\(964\) −1.06827 8.66677i −0.0344065 0.279138i
\(965\) 15.0997 8.71784i 0.486078 0.280637i
\(966\) 16.9665 9.38724i 0.545887 0.302030i
\(967\) −5.36971 + 9.30061i −0.172678 + 0.299088i −0.939355 0.342945i \(-0.888575\pi\)
0.766677 + 0.642033i \(0.221909\pi\)
\(968\) −2.88372 + 1.37795i −0.0926863 + 0.0442890i
\(969\) 8.03822 + 9.43102i 0.258225 + 0.302968i
\(970\) 4.13953 20.3709i 0.132912 0.654069i
\(971\) 27.0182i 0.867054i −0.901141 0.433527i \(-0.857269\pi\)
0.901141 0.433527i \(-0.142731\pi\)
\(972\) −31.1741 0.416518i −0.999911 0.0133598i
\(973\) 3.51162i 0.112578i
\(974\) 15.2978 + 3.10864i 0.490173 + 0.0996073i
\(975\) −40.4674 47.4793i −1.29599 1.52055i
\(976\) 21.5908 + 6.16917i 0.691103 + 0.197470i
\(977\) −11.5514 + 20.0076i −0.369562 + 0.640101i −0.989497 0.144552i \(-0.953826\pi\)
0.619935 + 0.784653i \(0.287159\pi\)
\(978\) −15.5076 28.0285i −0.495879 0.896251i
\(979\) 8.79143 5.07574i 0.280975 0.162221i
\(980\) −6.29485 + 0.775902i −0.201081 + 0.0247853i
\(981\) −53.2335 8.54275i −1.69961 0.272749i
\(982\) −18.4157 16.2851i −0.587668 0.519680i
\(983\) −19.3217 33.4661i −0.616265 1.06740i −0.990161 0.139932i \(-0.955312\pi\)
0.373896 0.927471i \(-0.378022\pi\)
\(984\) −0.679973 + 1.52594i −0.0216767 + 0.0486451i
\(985\) 25.9289 44.9101i 0.826162 1.43095i
\(986\) −62.2532 + 20.8458i −1.98254 + 0.663866i
\(987\) 1.52225 + 8.26035i 0.0484537 + 0.262930i
\(988\) 14.0531 10.6001i 0.447090 0.337235i
\(989\) 20.3353i 0.646625i
\(990\) −16.4897 + 43.8621i −0.524078 + 1.39403i
\(991\) 23.6882 0.752479 0.376240 0.926522i \(-0.377217\pi\)
0.376240 + 0.926522i \(0.377217\pi\)
\(992\) 13.1602 0.590024i 0.417838 0.0187333i
\(993\) −5.38974 + 15.1710i −0.171038 + 0.481436i
\(994\) 2.15469 + 6.43468i 0.0683426 + 0.204096i
\(995\) 27.4285 + 15.8358i 0.869541 + 0.502030i
\(996\) 23.7407 25.8797i 0.752254 0.820031i
\(997\) −18.8111 + 10.8606i −0.595755 + 0.343959i −0.767370 0.641205i \(-0.778435\pi\)
0.171615 + 0.985164i \(0.445101\pi\)
\(998\) −35.9032 31.7494i −1.13649 1.00501i
\(999\) 4.71732 2.87095i 0.149250 0.0908330i
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 504.2.cs.a.85.3 72
8.5 even 2 inner 504.2.cs.a.85.22 yes 72
9.7 even 3 inner 504.2.cs.a.421.22 yes 72
72.61 even 6 inner 504.2.cs.a.421.3 yes 72
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
504.2.cs.a.85.3 72 1.1 even 1 trivial
504.2.cs.a.85.22 yes 72 8.5 even 2 inner
504.2.cs.a.421.3 yes 72 72.61 even 6 inner
504.2.cs.a.421.22 yes 72 9.7 even 3 inner