Properties

Label 400.2.q.f.149.3
Level $400$
Weight $2$
Character 400.149
Analytic conductor $3.194$
Analytic rank $0$
Dimension $12$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [400,2,Mod(149,400)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(400, base_ring=CyclotomicField(4))
 
chi = DirichletCharacter(H, H._module([0, 1, 2]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("400.149");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 400 = 2^{4} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 400.q (of order \(4\), degree \(2\), not 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: \(3.19401608085\)
Analytic rank: \(0\)
Dimension: \(12\)
Relative dimension: \(6\) over \(\Q(i)\)
Coefficient field: 12.0.4767670494822400.1
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{12} - 4 x^{11} + 7 x^{10} - 4 x^{9} - 8 x^{8} + 24 x^{7} - 38 x^{6} + 48 x^{5} - 32 x^{4} - 32 x^{3} + 112 x^{2} - 128 x + 64 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{2} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 149.3
Root \(-1.41313 + 0.0554252i\) of defining polynomial
Character \(\chi\) \(=\) 400.149
Dual form 400.2.q.f.349.3

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.0554252 - 1.41313i) q^{2} +(-0.488516 - 0.488516i) q^{3} +(-1.99386 - 0.156646i) q^{4} +(-0.717411 + 0.663259i) q^{6} +4.71540 q^{7} +(-0.331870 + 2.80889i) q^{8} -2.52270i q^{9} +O(q^{10})\) \(q+(0.0554252 - 1.41313i) q^{2} +(-0.488516 - 0.488516i) q^{3} +(-1.99386 - 0.156646i) q^{4} +(-0.717411 + 0.663259i) q^{6} +4.71540 q^{7} +(-0.331870 + 2.80889i) q^{8} -2.52270i q^{9} +(-3.91360 - 3.91360i) q^{11} +(0.897506 + 1.05055i) q^{12} +(-0.0878822 - 0.0878822i) q^{13} +(0.261352 - 6.66346i) q^{14} +(3.95092 + 0.624658i) q^{16} -4.67442i q^{17} +(-3.56490 - 0.139821i) q^{18} +(-1.81249 + 1.81249i) q^{19} +(-2.30355 - 2.30355i) q^{21} +(-5.74732 + 5.31350i) q^{22} +1.63007 q^{23} +(1.53431 - 1.21006i) q^{24} +(-0.129060 + 0.119318i) q^{26} +(-2.69793 + 2.69793i) q^{27} +(-9.40184 - 0.738648i) q^{28} +(-3.26362 + 3.26362i) q^{29} -2.12875 q^{31} +(1.10170 - 5.54854i) q^{32} +3.82371i q^{33} +(-6.60555 - 0.259081i) q^{34} +(-0.395171 + 5.02991i) q^{36} +(3.97797 - 3.97797i) q^{37} +(2.46082 + 2.66173i) q^{38} +0.0858637i q^{39} -8.25504i q^{41} +(-3.38288 + 3.12753i) q^{42} +(-2.27336 + 2.27336i) q^{43} +(7.19010 + 8.41620i) q^{44} +(0.0903468 - 2.30349i) q^{46} +4.06129i q^{47} +(-1.62493 - 2.23524i) q^{48} +15.2350 q^{49} +(-2.28353 + 2.28353i) q^{51} +(0.161458 + 0.188991i) q^{52} +(5.03938 - 5.03938i) q^{53} +(3.66298 + 3.96205i) q^{54} +(-1.56490 + 13.2450i) q^{56} +1.77086 q^{57} +(4.43103 + 4.79280i) q^{58} +(5.16453 + 5.16453i) q^{59} +(7.12726 - 7.12726i) q^{61} +(-0.117986 + 3.00819i) q^{62} -11.8956i q^{63} +(-7.77972 - 1.86437i) q^{64} +(5.40339 + 0.211930i) q^{66} +(7.49920 + 7.49920i) q^{67} +(-0.732228 + 9.32012i) q^{68} +(-0.796314 - 0.796314i) q^{69} +4.54072i q^{71} +(7.08600 + 0.837210i) q^{72} +8.30557 q^{73} +(-5.40090 - 5.84186i) q^{74} +(3.89776 - 3.32992i) q^{76} +(-18.4542 - 18.4542i) q^{77} +(0.121336 + 0.00475901i) q^{78} -11.5317 q^{79} -4.93215 q^{81} +(-11.6654 - 0.457537i) q^{82} +(-1.16919 - 1.16919i) q^{83} +(4.23211 + 4.95379i) q^{84} +(3.08655 + 3.33855i) q^{86} +3.18866 q^{87} +(12.2917 - 9.69406i) q^{88} -3.24572i q^{89} +(-0.414400 - 0.414400i) q^{91} +(-3.25012 - 0.255343i) q^{92} +(1.03993 + 1.03993i) q^{93} +(5.73912 + 0.225098i) q^{94} +(-3.24875 + 2.17235i) q^{96} +13.9581i q^{97} +(0.844405 - 21.5290i) q^{98} +(-9.87285 + 9.87285i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12 q + 2 q^{2} - 2 q^{3} - 2 q^{4} + 6 q^{6} + 12 q^{7} + 2 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 12 q + 2 q^{2} - 2 q^{3} - 2 q^{4} + 6 q^{6} + 12 q^{7} + 2 q^{8} - 2 q^{11} - 6 q^{12} + 4 q^{13} - 14 q^{14} + 2 q^{16} - 18 q^{18} + 14 q^{19} - 20 q^{21} - 20 q^{22} + 12 q^{23} + 14 q^{24} - 16 q^{26} + 10 q^{27} - 10 q^{28} - 4 q^{31} + 2 q^{32} + 6 q^{34} + 2 q^{36} - 8 q^{37} + 28 q^{38} + 10 q^{42} + 44 q^{44} - 10 q^{46} - 58 q^{48} - 4 q^{49} + 10 q^{51} - 16 q^{53} - 10 q^{54} + 6 q^{56} - 16 q^{57} + 4 q^{58} - 20 q^{59} + 4 q^{61} + 22 q^{62} - 38 q^{64} + 32 q^{66} + 50 q^{67} + 50 q^{68} - 54 q^{72} + 40 q^{73} - 10 q^{74} + 60 q^{76} - 8 q^{77} - 48 q^{78} - 12 q^{79} - 8 q^{81} - 12 q^{82} + 2 q^{83} - 34 q^{84} + 6 q^{86} - 64 q^{87} + 56 q^{88} + 50 q^{92} + 44 q^{93} - 32 q^{94} - 34 q^{96} - 30 q^{98} - 12 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/400\mathbb{Z}\right)^\times\).

\(n\) \(101\) \(177\) \(351\)
\(\chi(n)\) \(e\left(\frac{1}{4}\right)\) \(-1\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.0554252 1.41313i 0.0391915 0.999232i
\(3\) −0.488516 0.488516i −0.282045 0.282045i 0.551879 0.833924i \(-0.313911\pi\)
−0.833924 + 0.551879i \(0.813911\pi\)
\(4\) −1.99386 0.156646i −0.996928 0.0783229i
\(5\) 0 0
\(6\) −0.717411 + 0.663259i −0.292882 + 0.270774i
\(7\) 4.71540 1.78226 0.891128 0.453753i \(-0.149915\pi\)
0.891128 + 0.453753i \(0.149915\pi\)
\(8\) −0.331870 + 2.80889i −0.117334 + 0.993093i
\(9\) 2.52270i 0.840901i
\(10\) 0 0
\(11\) −3.91360 3.91360i −1.17999 1.17999i −0.979745 0.200249i \(-0.935825\pi\)
−0.200249 0.979745i \(-0.564175\pi\)
\(12\) 0.897506 + 1.05055i 0.259088 + 0.303269i
\(13\) −0.0878822 0.0878822i −0.0243741 0.0243741i 0.694815 0.719189i \(-0.255486\pi\)
−0.719189 + 0.694815i \(0.755486\pi\)
\(14\) 0.261352 6.66346i 0.0698493 1.78089i
\(15\) 0 0
\(16\) 3.95092 + 0.624658i 0.987731 + 0.156165i
\(17\) 4.67442i 1.13371i −0.823816 0.566857i \(-0.808159\pi\)
0.823816 0.566857i \(-0.191841\pi\)
\(18\) −3.56490 0.139821i −0.840255 0.0329562i
\(19\) −1.81249 + 1.81249i −0.415813 + 0.415813i −0.883758 0.467945i \(-0.844995\pi\)
0.467945 + 0.883758i \(0.344995\pi\)
\(20\) 0 0
\(21\) −2.30355 2.30355i −0.502676 0.502676i
\(22\) −5.74732 + 5.31350i −1.22533 + 1.13284i
\(23\) 1.63007 0.339893 0.169946 0.985453i \(-0.445641\pi\)
0.169946 + 0.985453i \(0.445641\pi\)
\(24\) 1.53431 1.21006i 0.313190 0.247003i
\(25\) 0 0
\(26\) −0.129060 + 0.119318i −0.0253107 + 0.0234002i
\(27\) −2.69793 + 2.69793i −0.519217 + 0.519217i
\(28\) −9.40184 0.738648i −1.77678 0.139591i
\(29\) −3.26362 + 3.26362i −0.606039 + 0.606039i −0.941909 0.335869i \(-0.890970\pi\)
0.335869 + 0.941909i \(0.390970\pi\)
\(30\) 0 0
\(31\) −2.12875 −0.382334 −0.191167 0.981557i \(-0.561227\pi\)
−0.191167 + 0.981557i \(0.561227\pi\)
\(32\) 1.10170 5.54854i 0.194755 0.980852i
\(33\) 3.82371i 0.665622i
\(34\) −6.60555 0.259081i −1.13284 0.0444320i
\(35\) 0 0
\(36\) −0.395171 + 5.02991i −0.0658618 + 0.838318i
\(37\) 3.97797 3.97797i 0.653974 0.653974i −0.299973 0.953948i \(-0.596978\pi\)
0.953948 + 0.299973i \(0.0969778\pi\)
\(38\) 2.46082 + 2.66173i 0.399197 + 0.431790i
\(39\) 0.0858637i 0.0137492i
\(40\) 0 0
\(41\) 8.25504i 1.28922i −0.764511 0.644611i \(-0.777020\pi\)
0.764511 0.644611i \(-0.222980\pi\)
\(42\) −3.38288 + 3.12753i −0.521990 + 0.482589i
\(43\) −2.27336 + 2.27336i −0.346685 + 0.346685i −0.858873 0.512188i \(-0.828835\pi\)
0.512188 + 0.858873i \(0.328835\pi\)
\(44\) 7.19010 + 8.41620i 1.08395 + 1.26879i
\(45\) 0 0
\(46\) 0.0903468 2.30349i 0.0133209 0.339631i
\(47\) 4.06129i 0.592400i 0.955126 + 0.296200i \(0.0957195\pi\)
−0.955126 + 0.296200i \(0.904281\pi\)
\(48\) −1.62493 2.23524i −0.234539 0.322630i
\(49\) 15.2350 2.17643
\(50\) 0 0
\(51\) −2.28353 + 2.28353i −0.319758 + 0.319758i
\(52\) 0.161458 + 0.188991i 0.0223902 + 0.0262083i
\(53\) 5.03938 5.03938i 0.692211 0.692211i −0.270507 0.962718i \(-0.587191\pi\)
0.962718 + 0.270507i \(0.0871912\pi\)
\(54\) 3.66298 + 3.96205i 0.498469 + 0.539167i
\(55\) 0 0
\(56\) −1.56490 + 13.2450i −0.209119 + 1.76994i
\(57\) 1.77086 0.234556
\(58\) 4.43103 + 4.79280i 0.581822 + 0.629325i
\(59\) 5.16453 + 5.16453i 0.672365 + 0.672365i 0.958261 0.285896i \(-0.0922911\pi\)
−0.285896 + 0.958261i \(0.592291\pi\)
\(60\) 0 0
\(61\) 7.12726 7.12726i 0.912552 0.912552i −0.0839206 0.996472i \(-0.526744\pi\)
0.996472 + 0.0839206i \(0.0267442\pi\)
\(62\) −0.117986 + 3.00819i −0.0149843 + 0.382041i
\(63\) 11.8956i 1.49870i
\(64\) −7.77972 1.86437i −0.972466 0.233047i
\(65\) 0 0
\(66\) 5.40339 + 0.211930i 0.665111 + 0.0260868i
\(67\) 7.49920 + 7.49920i 0.916173 + 0.916173i 0.996748 0.0805758i \(-0.0256759\pi\)
−0.0805758 + 0.996748i \(0.525676\pi\)
\(68\) −0.732228 + 9.32012i −0.0887957 + 1.13023i
\(69\) −0.796314 0.796314i −0.0958649 0.0958649i
\(70\) 0 0
\(71\) 4.54072i 0.538884i 0.963017 + 0.269442i \(0.0868393\pi\)
−0.963017 + 0.269442i \(0.913161\pi\)
\(72\) 7.08600 + 0.837210i 0.835093 + 0.0986662i
\(73\) 8.30557 0.972093 0.486047 0.873933i \(-0.338439\pi\)
0.486047 + 0.873933i \(0.338439\pi\)
\(74\) −5.40090 5.84186i −0.627842 0.679102i
\(75\) 0 0
\(76\) 3.89776 3.32992i 0.447104 0.381968i
\(77\) −18.4542 18.4542i −2.10305 2.10305i
\(78\) 0.121336 + 0.00475901i 0.0137386 + 0.000538852i
\(79\) −11.5317 −1.29742 −0.648709 0.761037i \(-0.724691\pi\)
−0.648709 + 0.761037i \(0.724691\pi\)
\(80\) 0 0
\(81\) −4.93215 −0.548017
\(82\) −11.6654 0.457537i −1.28823 0.0505266i
\(83\) −1.16919 1.16919i −0.128335 0.128335i 0.640022 0.768357i \(-0.278925\pi\)
−0.768357 + 0.640022i \(0.778925\pi\)
\(84\) 4.23211 + 4.95379i 0.461761 + 0.540503i
\(85\) 0 0
\(86\) 3.08655 + 3.33855i 0.332831 + 0.360006i
\(87\) 3.18866 0.341861
\(88\) 12.2917 9.69406i 1.31030 1.03339i
\(89\) 3.24572i 0.344046i −0.985093 0.172023i \(-0.944970\pi\)
0.985093 0.172023i \(-0.0550304\pi\)
\(90\) 0 0
\(91\) −0.414400 0.414400i −0.0434409 0.0434409i
\(92\) −3.25012 0.255343i −0.338848 0.0266214i
\(93\) 1.03993 + 1.03993i 0.107835 + 0.107835i
\(94\) 5.73912 + 0.225098i 0.591945 + 0.0232171i
\(95\) 0 0
\(96\) −3.24875 + 2.17235i −0.331574 + 0.221714i
\(97\) 13.9581i 1.41723i 0.705598 + 0.708613i \(0.250679\pi\)
−0.705598 + 0.708613i \(0.749321\pi\)
\(98\) 0.844405 21.5290i 0.0852978 2.17476i
\(99\) −9.87285 + 9.87285i −0.992258 + 0.992258i
\(100\) 0 0
\(101\) 13.4088 + 13.4088i 1.33422 + 1.33422i 0.901552 + 0.432672i \(0.142429\pi\)
0.432672 + 0.901552i \(0.357571\pi\)
\(102\) 3.10035 + 3.35348i 0.306981 + 0.332044i
\(103\) 13.7638 1.35618 0.678092 0.734977i \(-0.262807\pi\)
0.678092 + 0.734977i \(0.262807\pi\)
\(104\) 0.276017 0.217686i 0.0270657 0.0213459i
\(105\) 0 0
\(106\) −6.84197 7.40059i −0.664551 0.718808i
\(107\) −0.327996 + 0.327996i −0.0317086 + 0.0317086i −0.722783 0.691075i \(-0.757138\pi\)
0.691075 + 0.722783i \(0.257138\pi\)
\(108\) 5.80190 4.95666i 0.558288 0.476955i
\(109\) 0.149698 0.149698i 0.0143385 0.0143385i −0.699901 0.714240i \(-0.746773\pi\)
0.714240 + 0.699901i \(0.246773\pi\)
\(110\) 0 0
\(111\) −3.88660 −0.368900
\(112\) 18.6302 + 2.94551i 1.76039 + 0.278325i
\(113\) 5.97999i 0.562550i 0.959627 + 0.281275i \(0.0907573\pi\)
−0.959627 + 0.281275i \(0.909243\pi\)
\(114\) 0.0981502 2.50245i 0.00919261 0.234376i
\(115\) 0 0
\(116\) 7.01843 5.99596i 0.651644 0.556711i
\(117\) −0.221701 + 0.221701i −0.0204962 + 0.0204962i
\(118\) 7.58439 7.01189i 0.698199 0.645497i
\(119\) 22.0418i 2.02057i
\(120\) 0 0
\(121\) 19.6325i 1.78477i
\(122\) −9.67669 10.4668i −0.876086 0.947615i
\(123\) −4.03272 + 4.03272i −0.363618 + 0.363618i
\(124\) 4.24442 + 0.333459i 0.381160 + 0.0299455i
\(125\) 0 0
\(126\) −16.8100 0.659314i −1.49755 0.0587364i
\(127\) 2.73076i 0.242315i 0.992633 + 0.121158i \(0.0386607\pi\)
−0.992633 + 0.121158i \(0.961339\pi\)
\(128\) −3.06579 + 10.8904i −0.270980 + 0.962585i
\(129\) 2.22115 0.195561
\(130\) 0 0
\(131\) −0.813555 + 0.813555i −0.0710806 + 0.0710806i −0.741753 0.670673i \(-0.766006\pi\)
0.670673 + 0.741753i \(0.266006\pi\)
\(132\) 0.598967 7.62392i 0.0521334 0.663577i
\(133\) −8.54661 + 8.54661i −0.741085 + 0.741085i
\(134\) 11.0130 10.1817i 0.951375 0.879563i
\(135\) 0 0
\(136\) 13.1299 + 1.55130i 1.12588 + 0.133023i
\(137\) 0.199812 0.0170711 0.00853557 0.999964i \(-0.497283\pi\)
0.00853557 + 0.999964i \(0.497283\pi\)
\(138\) −1.16943 + 1.08116i −0.0995484 + 0.0920342i
\(139\) 11.6301 + 11.6301i 0.986448 + 0.986448i 0.999909 0.0134610i \(-0.00428488\pi\)
−0.0134610 + 0.999909i \(0.504285\pi\)
\(140\) 0 0
\(141\) 1.98400 1.98400i 0.167083 0.167083i
\(142\) 6.41661 + 0.251670i 0.538470 + 0.0211197i
\(143\) 0.687871i 0.0575227i
\(144\) 1.57583 9.96701i 0.131319 0.830585i
\(145\) 0 0
\(146\) 0.460338 11.7368i 0.0380978 0.971346i
\(147\) −7.44256 7.44256i −0.613852 0.613852i
\(148\) −8.55463 + 7.30837i −0.703186 + 0.600744i
\(149\) 1.13384 + 1.13384i 0.0928880 + 0.0928880i 0.752024 0.659136i \(-0.229078\pi\)
−0.659136 + 0.752024i \(0.729078\pi\)
\(150\) 0 0
\(151\) 7.12216i 0.579593i 0.957088 + 0.289797i \(0.0935877\pi\)
−0.957088 + 0.289797i \(0.906412\pi\)
\(152\) −4.48957 5.69259i −0.364152 0.461730i
\(153\) −11.7922 −0.953341
\(154\) −27.1009 + 25.0553i −2.18386 + 2.01901i
\(155\) 0 0
\(156\) 0.0134502 0.171200i 0.00107688 0.0137070i
\(157\) 5.32145 + 5.32145i 0.424698 + 0.424698i 0.886818 0.462120i \(-0.152911\pi\)
−0.462120 + 0.886818i \(0.652911\pi\)
\(158\) −0.639147 + 16.2957i −0.0508478 + 1.29642i
\(159\) −4.92363 −0.390469
\(160\) 0 0
\(161\) 7.68643 0.605775
\(162\) −0.273365 + 6.96976i −0.0214776 + 0.547596i
\(163\) −12.3010 12.3010i −0.963488 0.963488i 0.0358685 0.999357i \(-0.488580\pi\)
−0.999357 + 0.0358685i \(0.988580\pi\)
\(164\) −1.29312 + 16.4594i −0.100975 + 1.28526i
\(165\) 0 0
\(166\) −1.71702 + 1.58741i −0.133266 + 0.123207i
\(167\) 9.86820 0.763624 0.381812 0.924240i \(-0.375300\pi\)
0.381812 + 0.924240i \(0.375300\pi\)
\(168\) 7.23490 5.70594i 0.558184 0.440223i
\(169\) 12.9846i 0.998812i
\(170\) 0 0
\(171\) 4.57237 + 4.57237i 0.349658 + 0.349658i
\(172\) 4.88887 4.17665i 0.372773 0.318466i
\(173\) −13.4089 13.4089i −1.01946 1.01946i −0.999807 0.0196525i \(-0.993744\pi\)
−0.0196525 0.999807i \(-0.506256\pi\)
\(174\) 0.176732 4.50599i 0.0133980 0.341598i
\(175\) 0 0
\(176\) −13.0177 17.9070i −0.981243 1.34979i
\(177\) 5.04591i 0.379274i
\(178\) −4.58662 0.179895i −0.343782 0.0134837i
\(179\) −0.419587 + 0.419587i −0.0313614 + 0.0313614i −0.722614 0.691252i \(-0.757059\pi\)
0.691252 + 0.722614i \(0.257059\pi\)
\(180\) 0 0
\(181\) −14.2605 14.2605i −1.05998 1.05998i −0.998083 0.0618956i \(-0.980285\pi\)
−0.0618956 0.998083i \(-0.519715\pi\)
\(182\) −0.608568 + 0.562632i −0.0451101 + 0.0417050i
\(183\) −6.96356 −0.514761
\(184\) −0.540971 + 4.57868i −0.0398809 + 0.337545i
\(185\) 0 0
\(186\) 1.52719 1.41191i 0.111979 0.103526i
\(187\) −18.2938 + 18.2938i −1.33777 + 1.33777i
\(188\) 0.636183 8.09762i 0.0463984 0.590580i
\(189\) −12.7218 + 12.7218i −0.925377 + 0.925377i
\(190\) 0 0
\(191\) 17.3304 1.25399 0.626993 0.779025i \(-0.284285\pi\)
0.626993 + 0.779025i \(0.284285\pi\)
\(192\) 2.88974 + 4.71130i 0.208549 + 0.340008i
\(193\) 16.8667i 1.21409i 0.794667 + 0.607045i \(0.207645\pi\)
−0.794667 + 0.607045i \(0.792355\pi\)
\(194\) 19.7245 + 0.773628i 1.41614 + 0.0555432i
\(195\) 0 0
\(196\) −30.3765 2.38650i −2.16975 0.170464i
\(197\) −3.58908 + 3.58908i −0.255712 + 0.255712i −0.823307 0.567596i \(-0.807874\pi\)
0.567596 + 0.823307i \(0.307874\pi\)
\(198\) 13.4044 + 14.4988i 0.952608 + 1.03038i
\(199\) 6.64501i 0.471052i −0.971868 0.235526i \(-0.924319\pi\)
0.971868 0.235526i \(-0.0756813\pi\)
\(200\) 0 0
\(201\) 7.32695i 0.516803i
\(202\) 19.6915 18.2051i 1.38549 1.28091i
\(203\) −15.3893 + 15.3893i −1.08012 + 1.08012i
\(204\) 4.91073 4.19532i 0.343820 0.293731i
\(205\) 0 0
\(206\) 0.762860 19.4500i 0.0531510 1.35514i
\(207\) 4.11218i 0.285816i
\(208\) −0.292320 0.402112i −0.0202687 0.0278815i
\(209\) 14.1867 0.981314
\(210\) 0 0
\(211\) 1.90906 1.90906i 0.131425 0.131425i −0.638334 0.769759i \(-0.720376\pi\)
0.769759 + 0.638334i \(0.220376\pi\)
\(212\) −10.8372 + 9.25839i −0.744301 + 0.635869i
\(213\) 2.21821 2.21821i 0.151989 0.151989i
\(214\) 0.445321 + 0.481680i 0.0304415 + 0.0329270i
\(215\) 0 0
\(216\) −6.68282 8.47355i −0.454709 0.576552i
\(217\) −10.0379 −0.681418
\(218\) −0.203245 0.219839i −0.0137655 0.0148894i
\(219\) −4.05740 4.05740i −0.274174 0.274174i
\(220\) 0 0
\(221\) −0.410798 + 0.410798i −0.0276333 + 0.0276333i
\(222\) −0.215416 + 5.49226i −0.0144578 + 0.368617i
\(223\) 24.1071i 1.61433i 0.590326 + 0.807165i \(0.298999\pi\)
−0.590326 + 0.807165i \(0.701001\pi\)
\(224\) 5.19497 26.1636i 0.347103 1.74813i
\(225\) 0 0
\(226\) 8.45048 + 0.331442i 0.562118 + 0.0220472i
\(227\) −6.67411 6.67411i −0.442977 0.442977i 0.450035 0.893011i \(-0.351412\pi\)
−0.893011 + 0.450035i \(0.851412\pi\)
\(228\) −3.53084 0.277397i −0.233835 0.0183711i
\(229\) −16.0807 16.0807i −1.06264 1.06264i −0.997902 0.0647388i \(-0.979379\pi\)
−0.0647388 0.997902i \(-0.520621\pi\)
\(230\) 0 0
\(231\) 18.0303i 1.18631i
\(232\) −8.08406 10.2503i −0.530744 0.672962i
\(233\) 16.4976 1.08079 0.540396 0.841411i \(-0.318274\pi\)
0.540396 + 0.841411i \(0.318274\pi\)
\(234\) 0.301004 + 0.325579i 0.0196772 + 0.0212838i
\(235\) 0 0
\(236\) −9.48833 11.1063i −0.617638 0.722961i
\(237\) 5.63342 + 5.63342i 0.365930 + 0.365930i
\(238\) −31.1478 1.22167i −2.01901 0.0791891i
\(239\) −5.25917 −0.340188 −0.170094 0.985428i \(-0.554407\pi\)
−0.170094 + 0.985428i \(0.554407\pi\)
\(240\) 0 0
\(241\) −14.1126 −0.909075 −0.454538 0.890728i \(-0.650196\pi\)
−0.454538 + 0.890728i \(0.650196\pi\)
\(242\) 27.7432 + 1.08813i 1.78340 + 0.0699479i
\(243\) 10.5032 + 10.5032i 0.673782 + 0.673782i
\(244\) −15.3272 + 13.0943i −0.981222 + 0.838275i
\(245\) 0 0
\(246\) 5.47523 + 5.92226i 0.349088 + 0.377589i
\(247\) 0.318571 0.0202702
\(248\) 0.706468 5.97942i 0.0448608 0.379693i
\(249\) 1.14234i 0.0723927i
\(250\) 0 0
\(251\) −9.98825 9.98825i −0.630453 0.630453i 0.317729 0.948182i \(-0.397080\pi\)
−0.948182 + 0.317729i \(0.897080\pi\)
\(252\) −1.86339 + 23.7181i −0.117383 + 1.49410i
\(253\) −6.37943 6.37943i −0.401071 0.401071i
\(254\) 3.85890 + 0.151353i 0.242129 + 0.00949671i
\(255\) 0 0
\(256\) 15.2196 + 4.93595i 0.951225 + 0.308497i
\(257\) 8.44760i 0.526947i 0.964667 + 0.263474i \(0.0848682\pi\)
−0.964667 + 0.263474i \(0.915132\pi\)
\(258\) 0.123108 3.13877i 0.00766435 0.195411i
\(259\) 18.7577 18.7577i 1.16555 1.16555i
\(260\) 0 0
\(261\) 8.23315 + 8.23315i 0.509619 + 0.509619i
\(262\) 1.10457 + 1.19475i 0.0682403 + 0.0738118i
\(263\) −18.3064 −1.12882 −0.564410 0.825494i \(-0.690896\pi\)
−0.564410 + 0.825494i \(0.690896\pi\)
\(264\) −10.7404 1.26897i −0.661024 0.0781000i
\(265\) 0 0
\(266\) 11.6037 + 12.5511i 0.711472 + 0.769560i
\(267\) −1.58559 + 1.58559i −0.0970364 + 0.0970364i
\(268\) −13.7776 16.1270i −0.841601 0.985115i
\(269\) −13.5631 + 13.5631i −0.826955 + 0.826955i −0.987094 0.160140i \(-0.948806\pi\)
0.160140 + 0.987094i \(0.448806\pi\)
\(270\) 0 0
\(271\) −2.24520 −0.136386 −0.0681930 0.997672i \(-0.521723\pi\)
−0.0681930 + 0.997672i \(0.521723\pi\)
\(272\) 2.91991 18.4683i 0.177046 1.11980i
\(273\) 0.404882i 0.0245046i
\(274\) 0.0110746 0.282360i 0.000669044 0.0170580i
\(275\) 0 0
\(276\) 1.46300 + 1.71247i 0.0880620 + 0.103079i
\(277\) 7.28255 7.28255i 0.437566 0.437566i −0.453626 0.891192i \(-0.649870\pi\)
0.891192 + 0.453626i \(0.149870\pi\)
\(278\) 17.0793 15.7901i 1.02435 0.947030i
\(279\) 5.37020i 0.321506i
\(280\) 0 0
\(281\) 6.04084i 0.360367i 0.983633 + 0.180183i \(0.0576691\pi\)
−0.983633 + 0.180183i \(0.942331\pi\)
\(282\) −2.69369 2.91361i −0.160407 0.173503i
\(283\) 15.1350 15.1350i 0.899682 0.899682i −0.0957259 0.995408i \(-0.530517\pi\)
0.995408 + 0.0957259i \(0.0305172\pi\)
\(284\) 0.711284 9.05354i 0.0422070 0.537229i
\(285\) 0 0
\(286\) 0.972049 + 0.0381254i 0.0574785 + 0.00225440i
\(287\) 38.9259i 2.29772i
\(288\) −13.9973 2.77927i −0.824800 0.163770i
\(289\) −4.85021 −0.285306
\(290\) 0 0
\(291\) 6.81873 6.81873i 0.399721 0.399721i
\(292\) −16.5601 1.30103i −0.969107 0.0761371i
\(293\) 10.7777 10.7777i 0.629637 0.629637i −0.318339 0.947977i \(-0.603125\pi\)
0.947977 + 0.318339i \(0.103125\pi\)
\(294\) −10.9298 + 10.1048i −0.637438 + 0.589322i
\(295\) 0 0
\(296\) 9.85351 + 12.4939i 0.572724 + 0.726190i
\(297\) 21.1172 1.22534
\(298\) 1.66511 1.53942i 0.0964571 0.0891762i
\(299\) −0.143254 0.143254i −0.00828459 0.00828459i
\(300\) 0 0
\(301\) −10.7198 + 10.7198i −0.617881 + 0.617881i
\(302\) 10.0645 + 0.394747i 0.579148 + 0.0227152i
\(303\) 13.1008i 0.752621i
\(304\) −8.29319 + 6.02882i −0.475647 + 0.345776i
\(305\) 0 0
\(306\) −0.653584 + 16.6639i −0.0373629 + 0.952609i
\(307\) −7.94378 7.94378i −0.453376 0.453376i 0.443098 0.896473i \(-0.353880\pi\)
−0.896473 + 0.443098i \(0.853880\pi\)
\(308\) 33.9042 + 39.6858i 1.93187 + 2.26131i
\(309\) −6.72382 6.72382i −0.382505 0.382505i
\(310\) 0 0
\(311\) 31.1649i 1.76720i −0.468244 0.883599i \(-0.655113\pi\)
0.468244 0.883599i \(-0.344887\pi\)
\(312\) −0.241182 0.0284956i −0.0136542 0.00161325i
\(313\) −5.35842 −0.302876 −0.151438 0.988467i \(-0.548390\pi\)
−0.151438 + 0.988467i \(0.548390\pi\)
\(314\) 7.81482 7.22494i 0.441016 0.407727i
\(315\) 0 0
\(316\) 22.9925 + 1.80639i 1.29343 + 0.101617i
\(317\) 8.88165 + 8.88165i 0.498843 + 0.498843i 0.911078 0.412235i \(-0.135252\pi\)
−0.412235 + 0.911078i \(0.635252\pi\)
\(318\) −0.272893 + 6.95771i −0.0153031 + 0.390169i
\(319\) 25.5450 1.43025
\(320\) 0 0
\(321\) 0.320463 0.0178865
\(322\) 0.426022 10.8619i 0.0237413 0.605310i
\(323\) 8.47233 + 8.47233i 0.471413 + 0.471413i
\(324\) 9.83400 + 0.772600i 0.546333 + 0.0429222i
\(325\) 0 0
\(326\) −18.0646 + 16.7011i −1.00051 + 0.924987i
\(327\) −0.146260 −0.00808817
\(328\) 23.1875 + 2.73960i 1.28032 + 0.151269i
\(329\) 19.1506i 1.05581i
\(330\) 0 0
\(331\) 6.07281 + 6.07281i 0.333792 + 0.333792i 0.854025 0.520233i \(-0.174155\pi\)
−0.520233 + 0.854025i \(0.674155\pi\)
\(332\) 2.14805 + 2.51435i 0.117890 + 0.137993i
\(333\) −10.0352 10.0352i −0.549928 0.549928i
\(334\) 0.546947 13.9450i 0.0299276 0.763038i
\(335\) 0 0
\(336\) −7.66222 10.5401i −0.418008 0.575009i
\(337\) 22.0227i 1.19965i 0.800130 + 0.599827i \(0.204764\pi\)
−0.800130 + 0.599827i \(0.795236\pi\)
\(338\) −18.3488 0.719672i −0.998044 0.0391450i
\(339\) 2.92132 2.92132i 0.158664 0.158664i
\(340\) 0 0
\(341\) 8.33106 + 8.33106i 0.451152 + 0.451152i
\(342\) 6.71477 6.20792i 0.363093 0.335686i
\(343\) 38.8315 2.09670
\(344\) −5.63117 7.14009i −0.303612 0.384968i
\(345\) 0 0
\(346\) −19.6917 + 18.2053i −1.05863 + 0.978722i
\(347\) 11.8920 11.8920i 0.638395 0.638395i −0.311765 0.950159i \(-0.600920\pi\)
0.950159 + 0.311765i \(0.100920\pi\)
\(348\) −6.35773 0.499490i −0.340810 0.0267755i
\(349\) 8.65696 8.65696i 0.463396 0.463396i −0.436371 0.899767i \(-0.643736\pi\)
0.899767 + 0.436371i \(0.143736\pi\)
\(350\) 0 0
\(351\) 0.474200 0.0253109
\(352\) −26.0263 + 17.4031i −1.38721 + 0.927589i
\(353\) 26.6153i 1.41659i −0.705916 0.708296i \(-0.749464\pi\)
0.705916 0.708296i \(-0.250536\pi\)
\(354\) −7.13051 0.279671i −0.378983 0.0148643i
\(355\) 0 0
\(356\) −0.508429 + 6.47151i −0.0269467 + 0.342989i
\(357\) −10.7678 + 10.7678i −0.569890 + 0.569890i
\(358\) 0.569674 + 0.616185i 0.0301082 + 0.0325664i
\(359\) 4.85032i 0.255990i 0.991775 + 0.127995i \(0.0408542\pi\)
−0.991775 + 0.127995i \(0.959146\pi\)
\(360\) 0 0
\(361\) 12.4298i 0.654199i
\(362\) −20.9424 + 19.3616i −1.10071 + 1.01762i
\(363\) 9.59078 9.59078i 0.503385 0.503385i
\(364\) 0.761340 + 0.891168i 0.0399051 + 0.0467099i
\(365\) 0 0
\(366\) −0.385957 + 9.84039i −0.0201743 + 0.514365i
\(367\) 15.6741i 0.818182i 0.912494 + 0.409091i \(0.134154\pi\)
−0.912494 + 0.409091i \(0.865846\pi\)
\(368\) 6.44027 + 1.01823i 0.335722 + 0.0530792i
\(369\) −20.8250 −1.08411
\(370\) 0 0
\(371\) 23.7627 23.7627i 1.23370 1.23370i
\(372\) −1.91057 2.23637i −0.0990582 0.115950i
\(373\) −5.44481 + 5.44481i −0.281922 + 0.281922i −0.833875 0.551953i \(-0.813883\pi\)
0.551953 + 0.833875i \(0.313883\pi\)
\(374\) 24.8375 + 26.8654i 1.28432 + 1.38918i
\(375\) 0 0
\(376\) −11.4077 1.34782i −0.588308 0.0695085i
\(377\) 0.573629 0.0295434
\(378\) 17.2724 + 18.6827i 0.888399 + 0.960933i
\(379\) 17.4103 + 17.4103i 0.894309 + 0.894309i 0.994925 0.100616i \(-0.0320814\pi\)
−0.100616 + 0.994925i \(0.532081\pi\)
\(380\) 0 0
\(381\) 1.33402 1.33402i 0.0683438 0.0683438i
\(382\) 0.960543 24.4901i 0.0491457 1.25302i
\(383\) 9.04928i 0.462396i −0.972907 0.231198i \(-0.925735\pi\)
0.972907 0.231198i \(-0.0742646\pi\)
\(384\) 6.81782 3.82245i 0.347921 0.195064i
\(385\) 0 0
\(386\) 23.8348 + 0.934839i 1.21316 + 0.0475821i
\(387\) 5.73503 + 5.73503i 0.291528 + 0.291528i
\(388\) 2.18647 27.8303i 0.111001 1.41287i
\(389\) 15.3617 + 15.3617i 0.778871 + 0.778871i 0.979639 0.200768i \(-0.0643437\pi\)
−0.200768 + 0.979639i \(0.564344\pi\)
\(390\) 0 0
\(391\) 7.61962i 0.385341i
\(392\) −5.05605 + 42.7935i −0.255369 + 2.16140i
\(393\) 0.794869 0.0400959
\(394\) 4.87291 + 5.27076i 0.245493 + 0.265537i
\(395\) 0 0
\(396\) 21.2316 18.1385i 1.06693 0.911494i
\(397\) 9.44519 + 9.44519i 0.474041 + 0.474041i 0.903220 0.429179i \(-0.141197\pi\)
−0.429179 + 0.903220i \(0.641197\pi\)
\(398\) −9.39024 0.368301i −0.470690 0.0184613i
\(399\) 8.35031 0.418038
\(400\) 0 0
\(401\) −21.5765 −1.07748 −0.538739 0.842473i \(-0.681099\pi\)
−0.538739 + 0.842473i \(0.681099\pi\)
\(402\) −10.3539 0.406098i −0.516406 0.0202543i
\(403\) 0.187079 + 0.187079i 0.00931907 + 0.00931907i
\(404\) −24.6347 28.8356i −1.22562 1.43462i
\(405\) 0 0
\(406\) 20.8941 + 22.6000i 1.03696 + 1.12162i
\(407\) −31.1363 −1.54337
\(408\) −5.65635 7.17202i −0.280031 0.355068i
\(409\) 4.17336i 0.206359i 0.994663 + 0.103180i \(0.0329017\pi\)
−0.994663 + 0.103180i \(0.967098\pi\)
\(410\) 0 0
\(411\) −0.0976116 0.0976116i −0.00481482 0.00481482i
\(412\) −27.4430 2.15604i −1.35202 0.106220i
\(413\) 24.3529 + 24.3529i 1.19833 + 1.19833i
\(414\) −5.81103 0.227918i −0.285597 0.0112016i
\(415\) 0 0
\(416\) −0.584438 + 0.390798i −0.0286544 + 0.0191604i
\(417\) 11.3629i 0.556445i
\(418\) 0.786300 20.0476i 0.0384592 0.980560i
\(419\) −27.1191 + 27.1191i −1.32485 + 1.32485i −0.415060 + 0.909794i \(0.636239\pi\)
−0.909794 + 0.415060i \(0.863761\pi\)
\(420\) 0 0
\(421\) −26.9594 26.9594i −1.31392 1.31392i −0.918500 0.395421i \(-0.870599\pi\)
−0.395421 0.918500i \(-0.629401\pi\)
\(422\) −2.59193 2.80355i −0.126173 0.136475i
\(423\) 10.2454 0.498150
\(424\) 12.4826 + 15.8275i 0.606210 + 0.768650i
\(425\) 0 0
\(426\) −3.01167 3.25756i −0.145916 0.157829i
\(427\) 33.6079 33.6079i 1.62640 1.62640i
\(428\) 0.705357 0.602598i 0.0340947 0.0291277i
\(429\) 0.336036 0.336036i 0.0162240 0.0162240i
\(430\) 0 0
\(431\) −22.4059 −1.07925 −0.539626 0.841905i \(-0.681434\pi\)
−0.539626 + 0.841905i \(0.681434\pi\)
\(432\) −12.3446 + 8.97403i −0.593930 + 0.431763i
\(433\) 16.8061i 0.807649i −0.914837 0.403824i \(-0.867681\pi\)
0.914837 0.403824i \(-0.132319\pi\)
\(434\) −0.556353 + 14.1848i −0.0267058 + 0.680894i
\(435\) 0 0
\(436\) −0.321925 + 0.275026i −0.0154174 + 0.0131714i
\(437\) −2.95448 + 2.95448i −0.141332 + 0.141332i
\(438\) −5.95851 + 5.50874i −0.284708 + 0.263218i
\(439\) 9.08322i 0.433519i −0.976225 0.216759i \(-0.930451\pi\)
0.976225 0.216759i \(-0.0695487\pi\)
\(440\) 0 0
\(441\) 38.4335i 1.83017i
\(442\) 0.557742 + 0.603279i 0.0265291 + 0.0286951i
\(443\) −12.5397 + 12.5397i −0.595781 + 0.595781i −0.939187 0.343406i \(-0.888419\pi\)
0.343406 + 0.939187i \(0.388419\pi\)
\(444\) 7.74933 + 0.608820i 0.367767 + 0.0288933i
\(445\) 0 0
\(446\) 34.0664 + 1.33614i 1.61309 + 0.0632681i
\(447\) 1.10780i 0.0523972i
\(448\) −36.6845 8.79127i −1.73318 0.415349i
\(449\) −18.0707 −0.852811 −0.426406 0.904532i \(-0.640220\pi\)
−0.426406 + 0.904532i \(0.640220\pi\)
\(450\) 0 0
\(451\) −32.3069 + 32.3069i −1.52127 + 1.52127i
\(452\) 0.936740 11.9232i 0.0440605 0.560822i
\(453\) 3.47929 3.47929i 0.163471 0.163471i
\(454\) −9.80129 + 9.06146i −0.459997 + 0.425275i
\(455\) 0 0
\(456\) −0.587695 + 4.97415i −0.0275213 + 0.232936i
\(457\) 18.6637 0.873052 0.436526 0.899692i \(-0.356209\pi\)
0.436526 + 0.899692i \(0.356209\pi\)
\(458\) −23.6153 + 21.8328i −1.10347 + 1.02018i
\(459\) 12.6113 + 12.6113i 0.588643 + 0.588643i
\(460\) 0 0
\(461\) −0.831229 + 0.831229i −0.0387142 + 0.0387142i −0.726199 0.687485i \(-0.758715\pi\)
0.687485 + 0.726199i \(0.258715\pi\)
\(462\) 25.4791 + 0.999335i 1.18540 + 0.0464933i
\(463\) 7.82533i 0.363674i 0.983329 + 0.181837i \(0.0582043\pi\)
−0.983329 + 0.181837i \(0.941796\pi\)
\(464\) −14.9330 + 10.8557i −0.693246 + 0.503962i
\(465\) 0 0
\(466\) 0.914382 23.3132i 0.0423579 1.07996i
\(467\) −8.75068 8.75068i −0.404933 0.404933i 0.475034 0.879967i \(-0.342436\pi\)
−0.879967 + 0.475034i \(0.842436\pi\)
\(468\) 0.476768 0.407311i 0.0220386 0.0188280i
\(469\) 35.3617 + 35.3617i 1.63285 + 1.63285i
\(470\) 0 0
\(471\) 5.19922i 0.239568i
\(472\) −16.2206 + 12.7926i −0.746612 + 0.588829i
\(473\) 17.7941 0.818172
\(474\) 8.27297 7.64850i 0.379990 0.351307i
\(475\) 0 0
\(476\) −3.45275 + 43.9481i −0.158257 + 2.01436i
\(477\) −12.7129 12.7129i −0.582082 0.582082i
\(478\) −0.291491 + 7.43188i −0.0133325 + 0.339926i
\(479\) −2.10417 −0.0961421 −0.0480710 0.998844i \(-0.515307\pi\)
−0.0480710 + 0.998844i \(0.515307\pi\)
\(480\) 0 0
\(481\) −0.699186 −0.0318801
\(482\) −0.782196 + 19.9430i −0.0356281 + 0.908377i
\(483\) −3.75494 3.75494i −0.170856 0.170856i
\(484\) 3.07534 39.1443i 0.139788 1.77929i
\(485\) 0 0
\(486\) 15.4245 14.2602i 0.699671 0.646858i
\(487\) 4.87183 0.220764 0.110382 0.993889i \(-0.464793\pi\)
0.110382 + 0.993889i \(0.464793\pi\)
\(488\) 17.6544 + 22.3850i 0.799175 + 1.01332i
\(489\) 12.0185i 0.543494i
\(490\) 0 0
\(491\) 14.3582 + 14.3582i 0.647975 + 0.647975i 0.952503 0.304528i \(-0.0984987\pi\)
−0.304528 + 0.952503i \(0.598499\pi\)
\(492\) 8.67237 7.40895i 0.390981 0.334021i
\(493\) 15.2555 + 15.2555i 0.687075 + 0.687075i
\(494\) 0.0176569 0.450181i 0.000794419 0.0202546i
\(495\) 0 0
\(496\) −8.41052 1.32974i −0.377644 0.0597071i
\(497\) 21.4113i 0.960429i
\(498\) 1.61427 + 0.0633143i 0.0723370 + 0.00283718i
\(499\) 25.1060 25.1060i 1.12390 1.12390i 0.132748 0.991150i \(-0.457620\pi\)
0.991150 0.132748i \(-0.0423801\pi\)
\(500\) 0 0
\(501\) −4.82077 4.82077i −0.215376 0.215376i
\(502\) −14.6683 + 13.5611i −0.654677 + 0.605260i
\(503\) −18.8868 −0.842120 −0.421060 0.907033i \(-0.638342\pi\)
−0.421060 + 0.907033i \(0.638342\pi\)
\(504\) 33.4133 + 3.94778i 1.48835 + 0.175848i
\(505\) 0 0
\(506\) −9.36852 + 8.66136i −0.416482 + 0.385044i
\(507\) −6.34316 + 6.34316i −0.281710 + 0.281710i
\(508\) 0.427761 5.44473i 0.0189788 0.241571i
\(509\) 22.9756 22.9756i 1.01837 1.01837i 0.0185459 0.999828i \(-0.494096\pi\)
0.999828 0.0185459i \(-0.00590369\pi\)
\(510\) 0 0
\(511\) 39.1641 1.73252
\(512\) 7.81868 21.2337i 0.345540 0.938404i
\(513\) 9.77993i 0.431794i
\(514\) 11.9375 + 0.468210i 0.526542 + 0.0206519i
\(515\) 0 0
\(516\) −4.42865 0.347933i −0.194961 0.0153169i
\(517\) 15.8942 15.8942i 0.699028 0.699028i
\(518\) −25.4674 27.5467i −1.11897 1.21033i
\(519\) 13.1009i 0.575066i
\(520\) 0 0
\(521\) 20.2089i 0.885367i 0.896678 + 0.442683i \(0.145973\pi\)
−0.896678 + 0.442683i \(0.854027\pi\)
\(522\) 12.0908 11.1782i 0.529201 0.489255i
\(523\) 3.93445 3.93445i 0.172042 0.172042i −0.615834 0.787876i \(-0.711181\pi\)
0.787876 + 0.615834i \(0.211181\pi\)
\(524\) 1.74955 1.49467i 0.0764295 0.0652951i
\(525\) 0 0
\(526\) −1.01464 + 25.8693i −0.0442402 + 1.12795i
\(527\) 9.95066i 0.433458i
\(528\) −2.38851 + 15.1072i −0.103947 + 0.657456i
\(529\) −20.3429 −0.884473
\(530\) 0 0
\(531\) 13.0286 13.0286i 0.565393 0.565393i
\(532\) 18.3795 15.7019i 0.796853 0.680765i
\(533\) −0.725471 + 0.725471i −0.0314237 + 0.0314237i
\(534\) 2.15276 + 2.32852i 0.0931589 + 0.100765i
\(535\) 0 0
\(536\) −23.5532 + 18.5757i −1.01734 + 0.802346i
\(537\) 0.409950 0.0176906
\(538\) 18.4146 + 19.9181i 0.793910 + 0.858729i
\(539\) −59.6238 59.6238i −2.56818 2.56818i
\(540\) 0 0
\(541\) −3.17895 + 3.17895i −0.136674 + 0.136674i −0.772134 0.635460i \(-0.780811\pi\)
0.635460 + 0.772134i \(0.280811\pi\)
\(542\) −0.124440 + 3.17275i −0.00534518 + 0.136281i
\(543\) 13.9330i 0.597923i
\(544\) −25.9362 5.14982i −1.11201 0.220797i
\(545\) 0 0
\(546\) 0.572150 + 0.0224407i 0.0244857 + 0.000960372i
\(547\) 1.32918 + 1.32918i 0.0568317 + 0.0568317i 0.734951 0.678120i \(-0.237205\pi\)
−0.678120 + 0.734951i \(0.737205\pi\)
\(548\) −0.398397 0.0312998i −0.0170187 0.00133706i
\(549\) −17.9800 17.9800i −0.767366 0.767366i
\(550\) 0 0
\(551\) 11.8306i 0.503998i
\(552\) 2.50103 1.97249i 0.106451 0.0839545i
\(553\) −54.3766 −2.31233
\(554\) −9.88754 10.6948i −0.420081 0.454379i
\(555\) 0 0
\(556\) −21.3669 25.0105i −0.906157 1.06068i
\(557\) 24.9082 + 24.9082i 1.05539 + 1.05539i 0.998373 + 0.0570196i \(0.0181598\pi\)
0.0570196 + 0.998373i \(0.481840\pi\)
\(558\) 7.58878 + 0.297645i 0.321259 + 0.0126003i
\(559\) 0.399576 0.0169003
\(560\) 0 0
\(561\) 17.8736 0.754625
\(562\) 8.53648 + 0.334815i 0.360090 + 0.0141233i
\(563\) −3.80804 3.80804i −0.160490 0.160490i 0.622294 0.782784i \(-0.286201\pi\)
−0.782784 + 0.622294i \(0.786201\pi\)
\(564\) −4.26660 + 3.64503i −0.179656 + 0.153484i
\(565\) 0 0
\(566\) −20.5488 22.2265i −0.863731 0.934251i
\(567\) −23.2571 −0.976706
\(568\) −12.7544 1.50693i −0.535162 0.0632293i
\(569\) 8.43971i 0.353811i 0.984228 + 0.176905i \(0.0566087\pi\)
−0.984228 + 0.176905i \(0.943391\pi\)
\(570\) 0 0
\(571\) −21.2821 21.2821i −0.890629 0.890629i 0.103953 0.994582i \(-0.466851\pi\)
−0.994582 + 0.103953i \(0.966851\pi\)
\(572\) 0.107752 1.37152i 0.00450534 0.0573460i
\(573\) −8.46619 8.46619i −0.353680 0.353680i
\(574\) −55.0072 2.15747i −2.29596 0.0900512i
\(575\) 0 0
\(576\) −4.70326 + 19.6259i −0.195969 + 0.817748i
\(577\) 36.3491i 1.51323i −0.653860 0.756615i \(-0.726852\pi\)
0.653860 0.756615i \(-0.273148\pi\)
\(578\) −0.268824 + 6.85396i −0.0111816 + 0.285087i
\(579\) 8.23964 8.23964i 0.342428 0.342428i
\(580\) 0 0
\(581\) −5.51321 5.51321i −0.228726 0.228726i
\(582\) −9.25780 10.0137i −0.383748 0.415080i
\(583\) −39.4442 −1.63361
\(584\) −2.75637 + 23.3294i −0.114059 + 0.965379i
\(585\) 0 0
\(586\) −14.6328 15.8275i −0.604477 0.653830i
\(587\) 6.55994 6.55994i 0.270758 0.270758i −0.558647 0.829405i \(-0.688679\pi\)
0.829405 + 0.558647i \(0.188679\pi\)
\(588\) 13.6735 + 16.0052i 0.563887 + 0.660044i
\(589\) 3.85833 3.85833i 0.158980 0.158980i
\(590\) 0 0
\(591\) 3.50665 0.144244
\(592\) 18.2015 13.2318i 0.748078 0.543823i
\(593\) 1.40974i 0.0578911i 0.999581 + 0.0289455i \(0.00921494\pi\)
−0.999581 + 0.0289455i \(0.990785\pi\)
\(594\) 1.17043 29.8413i 0.0480231 1.22440i
\(595\) 0 0
\(596\) −2.08311 2.43833i −0.0853274 0.0998779i
\(597\) −3.24619 + 3.24619i −0.132858 + 0.132858i
\(598\) −0.210376 + 0.194496i −0.00860291 + 0.00795354i
\(599\) 23.3593i 0.954435i 0.878785 + 0.477218i \(0.158355\pi\)
−0.878785 + 0.477218i \(0.841645\pi\)
\(600\) 0 0
\(601\) 20.4138i 0.832695i −0.909206 0.416347i \(-0.863310\pi\)
0.909206 0.416347i \(-0.136690\pi\)
\(602\) 14.5543 + 15.7426i 0.593190 + 0.641622i
\(603\) 18.9183 18.9183i 0.770411 0.770411i
\(604\) 1.11566 14.2006i 0.0453954 0.577813i
\(605\) 0 0
\(606\) −18.5131 0.726115i −0.752043 0.0294964i
\(607\) 0.758240i 0.0307760i 0.999882 + 0.0153880i \(0.00489835\pi\)
−0.999882 + 0.0153880i \(0.995102\pi\)
\(608\) 8.05983 + 12.0535i 0.326869 + 0.488833i
\(609\) 15.0358 0.609283
\(610\) 0 0
\(611\) 0.356915 0.356915i 0.0144392 0.0144392i
\(612\) 23.5119 + 1.84719i 0.950413 + 0.0746684i
\(613\) 12.0341 12.0341i 0.486052 0.486052i −0.421006 0.907058i \(-0.638323\pi\)
0.907058 + 0.421006i \(0.138323\pi\)
\(614\) −11.6659 + 10.7853i −0.470796 + 0.435259i
\(615\) 0 0
\(616\) 57.9602 45.7114i 2.33528 1.84176i
\(617\) −32.6899 −1.31605 −0.658023 0.752998i \(-0.728607\pi\)
−0.658023 + 0.752998i \(0.728607\pi\)
\(618\) −9.87428 + 9.12894i −0.397202 + 0.367220i
\(619\) −26.3836 26.3836i −1.06045 1.06045i −0.998052 0.0623934i \(-0.980127\pi\)
−0.0623934 0.998052i \(-0.519873\pi\)
\(620\) 0 0
\(621\) −4.39781 + 4.39781i −0.176478 + 0.176478i
\(622\) −44.0399 1.72732i −1.76584 0.0692592i
\(623\) 15.3049i 0.613178i
\(624\) −0.0536355 + 0.339241i −0.00214714 + 0.0135805i
\(625\) 0 0
\(626\) −0.296991 + 7.57213i −0.0118702 + 0.302643i
\(627\) −6.93042 6.93042i −0.276774 0.276774i
\(628\) −9.77662 11.4438i −0.390130 0.456657i
\(629\) −18.5947 18.5947i −0.741420 0.741420i
\(630\) 0 0
\(631\) 6.08765i 0.242345i −0.992631 0.121173i \(-0.961335\pi\)
0.992631 0.121173i \(-0.0386655\pi\)
\(632\) 3.82703 32.3913i 0.152231 1.28846i
\(633\) −1.86521 −0.0741354
\(634\) 13.0432 12.0586i 0.518010 0.478909i
\(635\) 0 0
\(636\) 9.81701 + 0.771266i 0.389270 + 0.0305827i
\(637\) −1.33889 1.33889i −0.0530487 0.0530487i
\(638\) 1.41584 36.0983i 0.0560535 1.42915i
\(639\) 11.4549 0.453149
\(640\) 0 0
\(641\) 11.1680 0.441111 0.220555 0.975374i \(-0.429213\pi\)
0.220555 + 0.975374i \(0.429213\pi\)
\(642\) 0.0177617 0.452855i 0.000700999 0.0178728i
\(643\) 21.9585 + 21.9585i 0.865957 + 0.865957i 0.992022 0.126065i \(-0.0402348\pi\)
−0.126065 + 0.992022i \(0.540235\pi\)
\(644\) −15.3256 1.20405i −0.603914 0.0474460i
\(645\) 0 0
\(646\) 12.4421 11.5029i 0.489526 0.452575i
\(647\) 36.9848 1.45402 0.727011 0.686625i \(-0.240909\pi\)
0.727011 + 0.686625i \(0.240909\pi\)
\(648\) 1.63683 13.8539i 0.0643009 0.544231i
\(649\) 40.4238i 1.58677i
\(650\) 0 0
\(651\) 4.90368 + 4.90368i 0.192190 + 0.192190i
\(652\) 22.5995 + 26.4533i 0.885065 + 1.03599i
\(653\) 18.4157 + 18.4157i 0.720663 + 0.720663i 0.968740 0.248077i \(-0.0797986\pi\)
−0.248077 + 0.968740i \(0.579799\pi\)
\(654\) −0.00810646 + 0.206683i −0.000316988 + 0.00808196i
\(655\) 0 0
\(656\) 5.15658 32.6150i 0.201331 1.27340i
\(657\) 20.9525i 0.817435i
\(658\) 27.0622 + 1.06143i 1.05500 + 0.0413787i
\(659\) 15.5421 15.5421i 0.605434 0.605434i −0.336316 0.941749i \(-0.609181\pi\)
0.941749 + 0.336316i \(0.109181\pi\)
\(660\) 0 0
\(661\) 29.6677 + 29.6677i 1.15394 + 1.15394i 0.985755 + 0.168185i \(0.0537906\pi\)
0.168185 + 0.985755i \(0.446209\pi\)
\(662\) 8.91825 8.24507i 0.346617 0.320454i
\(663\) 0.401363 0.0155877
\(664\) 3.67215 2.89611i 0.142507 0.112391i
\(665\) 0 0
\(666\) −14.7373 + 13.6249i −0.571058 + 0.527953i
\(667\) −5.31992 + 5.31992i −0.205988 + 0.205988i
\(668\) −19.6758 1.54581i −0.761278 0.0598092i
\(669\) 11.7767 11.7767i 0.455313 0.455313i
\(670\) 0 0
\(671\) −55.7864 −2.15361
\(672\) −15.3192 + 10.2435i −0.590949 + 0.395152i
\(673\) 29.2198i 1.12634i 0.826340 + 0.563171i \(0.190419\pi\)
−0.826340 + 0.563171i \(0.809581\pi\)
\(674\) 31.1209 + 1.22061i 1.19873 + 0.0470163i
\(675\) 0 0
\(676\) −2.03397 + 25.8893i −0.0782298 + 0.995743i
\(677\) −17.2591 + 17.2591i −0.663320 + 0.663320i −0.956161 0.292841i \(-0.905399\pi\)
0.292841 + 0.956161i \(0.405399\pi\)
\(678\) −3.96628 4.29011i −0.152324 0.164761i
\(679\) 65.8179i 2.52586i
\(680\) 0 0
\(681\) 6.52082i 0.249878i
\(682\) 12.2346 11.3111i 0.468487 0.433124i
\(683\) 1.10407 1.10407i 0.0422459 0.0422459i −0.685668 0.727914i \(-0.740490\pi\)
0.727914 + 0.685668i \(0.240490\pi\)
\(684\) −8.40041 9.83289i −0.321198 0.375970i
\(685\) 0 0
\(686\) 2.15224 54.8738i 0.0821731 2.09509i
\(687\) 15.7113i 0.599425i
\(688\) −10.4020 + 7.56181i −0.396571 + 0.288291i
\(689\) −0.885743 −0.0337441
\(690\) 0 0
\(691\) −28.4233 + 28.4233i −1.08127 + 1.08127i −0.0848830 + 0.996391i \(0.527052\pi\)
−0.996391 + 0.0848830i \(0.972948\pi\)
\(692\) 24.6350 + 28.8359i 0.936481 + 1.09617i
\(693\) −46.5545 + 46.5545i −1.76846 + 1.76846i
\(694\) −16.1458 17.4640i −0.612885 0.662924i
\(695\) 0 0
\(696\) −1.05822 + 8.95660i −0.0401118 + 0.339499i
\(697\) −38.5875 −1.46161
\(698\) −11.7536 12.7132i −0.444879 0.481201i
\(699\) −8.05933 8.05933i −0.304832 0.304832i
\(700\) 0 0
\(701\) −23.7991 + 23.7991i −0.898880 + 0.898880i −0.995337 0.0964573i \(-0.969249\pi\)
0.0964573 + 0.995337i \(0.469249\pi\)
\(702\) 0.0262826 0.670105i 0.000991974 0.0252915i
\(703\) 14.4200i 0.543862i
\(704\) 23.1503 + 37.7431i 0.872510 + 1.42250i
\(705\) 0 0
\(706\) −37.6109 1.47516i −1.41550 0.0555184i
\(707\) 63.2278 + 63.2278i 2.37793 + 2.37793i
\(708\) −0.790421 + 10.0608i −0.0297058 + 0.378109i
\(709\) −1.49921 1.49921i −0.0563039 0.0563039i 0.678394 0.734698i \(-0.262676\pi\)
−0.734698 + 0.678394i \(0.762676\pi\)
\(710\) 0 0
\(711\) 29.0911i 1.09100i
\(712\) 9.11688 + 1.07716i 0.341670 + 0.0403682i
\(713\) −3.47000 −0.129953
\(714\) 14.6194 + 15.8130i 0.547118 + 0.591787i
\(715\) 0 0
\(716\) 0.902323 0.770870i 0.0337214 0.0288088i
\(717\) 2.56919 + 2.56919i 0.0959482 + 0.0959482i
\(718\) 6.85412 + 0.268830i 0.255794 + 0.0100327i
\(719\) −7.37612 −0.275083 −0.137541 0.990496i \(-0.543920\pi\)
−0.137541 + 0.990496i \(0.543920\pi\)
\(720\) 0 0
\(721\) 64.9017 2.41707
\(722\) 17.5649 + 0.688923i 0.653696 + 0.0256391i
\(723\) 6.89425 + 6.89425i 0.256400 + 0.256400i
\(724\) 26.1996 + 30.6673i 0.973702 + 1.13974i
\(725\) 0 0
\(726\) −13.0214 14.0846i −0.483270 0.522727i
\(727\) −30.1470 −1.11809 −0.559045 0.829137i \(-0.688832\pi\)
−0.559045 + 0.829137i \(0.688832\pi\)
\(728\) 1.30153 1.02648i 0.0482380 0.0380438i
\(729\) 4.53447i 0.167943i
\(730\) 0 0
\(731\) 10.6267 + 10.6267i 0.393041 + 0.393041i
\(732\) 13.8843 + 1.09081i 0.513180 + 0.0403176i
\(733\) 1.43297 + 1.43297i 0.0529279 + 0.0529279i 0.733075 0.680147i \(-0.238084\pi\)
−0.680147 + 0.733075i \(0.738084\pi\)
\(734\) 22.1495 + 0.868740i 0.817553 + 0.0320658i
\(735\) 0 0
\(736\) 1.79585 9.04449i 0.0661959 0.333384i
\(737\) 58.6977i 2.16216i
\(738\) −1.15423 + 29.4284i −0.0424879 + 1.08328i
\(739\) −31.0001 + 31.0001i −1.14036 + 1.14036i −0.151973 + 0.988385i \(0.548563\pi\)
−0.988385 + 0.151973i \(0.951437\pi\)
\(740\) 0 0
\(741\) −0.155627 0.155627i −0.00571710 0.00571710i
\(742\) −32.2626 34.8968i −1.18440 1.28110i
\(743\) −38.5395 −1.41388 −0.706938 0.707276i \(-0.749924\pi\)
−0.706938 + 0.707276i \(0.749924\pi\)
\(744\) −3.26616 + 2.57592i −0.119743 + 0.0944378i
\(745\) 0 0
\(746\) 7.39243 + 7.99599i 0.270656 + 0.292754i
\(747\) −2.94952 + 2.94952i −0.107917 + 0.107917i
\(748\) 39.3408 33.6096i 1.43844 1.22889i
\(749\) −1.54664 + 1.54664i −0.0565128 + 0.0565128i
\(750\) 0 0
\(751\) 26.9523 0.983503 0.491751 0.870736i \(-0.336357\pi\)
0.491751 + 0.870736i \(0.336357\pi\)
\(752\) −2.53692 + 16.0458i −0.0925118 + 0.585132i
\(753\) 9.75884i 0.355632i
\(754\) 0.0317935 0.810610i 0.00115785 0.0295207i
\(755\) 0 0
\(756\) 27.3583 23.3727i 0.995012 0.850056i
\(757\) −17.0688 + 17.0688i −0.620377 + 0.620377i −0.945628 0.325251i \(-0.894551\pi\)
0.325251 + 0.945628i \(0.394551\pi\)
\(758\) 25.5680 23.6380i 0.928671 0.858573i
\(759\) 6.23290i 0.226240i
\(760\) 0 0
\(761\) 6.89608i 0.249983i −0.992158 0.124991i \(-0.960110\pi\)
0.992158 0.124991i \(-0.0398903\pi\)
\(762\) −1.81120 1.95907i −0.0656128 0.0709698i
\(763\) 0.705886 0.705886i 0.0255548 0.0255548i
\(764\) −34.5544 2.71474i −1.25013 0.0982158i
\(765\) 0 0
\(766\) −12.7878 0.501558i −0.462041 0.0181220i
\(767\) 0.907741i 0.0327766i
\(768\) −5.02373 9.84631i −0.181278 0.355298i
\(769\) −11.8443 −0.427117 −0.213558 0.976930i \(-0.568505\pi\)
−0.213558 + 0.976930i \(0.568505\pi\)
\(770\) 0 0
\(771\) 4.12679 4.12679i 0.148623 0.148623i
\(772\) 2.64209 33.6297i 0.0950910 1.21036i
\(773\) −3.58865 + 3.58865i −0.129075 + 0.129075i −0.768693 0.639618i \(-0.779093\pi\)
0.639618 + 0.768693i \(0.279093\pi\)
\(774\) 8.42219 7.78646i 0.302729 0.279878i
\(775\) 0 0
\(776\) −39.2066 4.63226i −1.40744 0.166288i
\(777\) −18.3269 −0.657474
\(778\) 22.5595 20.8567i 0.808798 0.747748i
\(779\) 14.9622 + 14.9622i 0.536075 + 0.536075i
\(780\) 0 0
\(781\) 17.7705 17.7705i 0.635880 0.635880i
\(782\) −10.7675 0.422319i −0.385045 0.0151021i
\(783\) 17.6100i 0.629332i
\(784\) 60.1925 + 9.51668i 2.14973 + 0.339882i
\(785\) 0 0
\(786\) 0.0440558 1.12325i 0.00157142 0.0400650i
\(787\) −22.4800 22.4800i −0.801326 0.801326i 0.181977 0.983303i \(-0.441750\pi\)
−0.983303 + 0.181977i \(0.941750\pi\)
\(788\) 7.71833 6.59390i 0.274954 0.234898i
\(789\) 8.94296 + 8.94296i 0.318378 + 0.318378i
\(790\) 0 0
\(791\) 28.1981i 1.00261i
\(792\) −24.4552 31.0082i −0.868979 1.10183i
\(793\) −1.25272 −0.0444853
\(794\) 13.8708 12.8238i 0.492255 0.455098i
\(795\) 0 0
\(796\) −1.04091 + 13.2492i −0.0368941 + 0.469605i
\(797\) −8.67589 8.67589i −0.307316 0.307316i 0.536552 0.843867i \(-0.319727\pi\)
−0.843867 + 0.536552i \(0.819727\pi\)
\(798\) 0.462818 11.8001i 0.0163836 0.417717i
\(799\) 18.9842 0.671612
\(800\) 0 0
\(801\) −8.18800 −0.289309
\(802\) −1.19588 + 30.4903i −0.0422280 + 1.07665i
\(803\) −32.5046 32.5046i −1.14706 1.14706i
\(804\) −1.14774 + 14.6089i −0.0404775 + 0.515216i
\(805\) 0 0
\(806\) 0.274735 0.253998i 0.00967714 0.00894668i
\(807\) 13.2515 0.466476
\(808\) −42.1138 + 33.2138i −1.48156 + 1.16846i
\(809\) 27.9066i 0.981143i 0.871401 + 0.490571i \(0.163212\pi\)
−0.871401 + 0.490571i \(0.836788\pi\)
\(810\) 0 0
\(811\) 15.2635 + 15.2635i 0.535974 + 0.535974i 0.922344 0.386370i \(-0.126271\pi\)
−0.386370 + 0.922344i \(0.626271\pi\)
\(812\) 33.0947 28.2734i 1.16140 0.992201i
\(813\) 1.09681 + 1.09681i 0.0384670 + 0.0384670i
\(814\) −1.72574 + 43.9996i −0.0604871 + 1.54219i
\(815\) 0 0
\(816\) −10.4485 + 7.59562i −0.365770 + 0.265900i
\(817\) 8.24089i 0.288312i
\(818\) 5.89749 + 0.231309i 0.206201 + 0.00808754i
\(819\) −1.04541 + 1.04541i −0.0365295 + 0.0365295i
\(820\) 0 0
\(821\) 25.2883 + 25.2883i 0.882567 + 0.882567i 0.993795 0.111228i \(-0.0354782\pi\)
−0.111228 + 0.993795i \(0.535478\pi\)
\(822\) −0.143348 + 0.132527i −0.00499983 + 0.00462242i
\(823\) −7.12228 −0.248267 −0.124133 0.992266i \(-0.539615\pi\)
−0.124133 + 0.992266i \(0.539615\pi\)
\(824\) −4.56778 + 38.6609i −0.159126 + 1.34682i
\(825\) 0 0
\(826\) 35.7634 33.0639i 1.24437 1.15044i
\(827\) −32.1618 + 32.1618i −1.11837 + 1.11837i −0.126394 + 0.991980i \(0.540340\pi\)
−0.991980 + 0.126394i \(0.959660\pi\)
\(828\) −0.644155 + 8.19909i −0.0223859 + 0.284938i
\(829\) 34.9802 34.9802i 1.21491 1.21491i 0.245522 0.969391i \(-0.421041\pi\)
0.969391 0.245522i \(-0.0789594\pi\)
\(830\) 0 0
\(831\) −7.11529 −0.246827
\(832\) 0.519854 + 0.847545i 0.0180227 + 0.0293833i
\(833\) 71.2149i 2.46745i
\(834\) −16.0573 0.629793i −0.556018 0.0218079i
\(835\) 0 0
\(836\) −28.2862 2.22228i −0.978299 0.0768593i
\(837\) 5.74321 5.74321i 0.198514 0.198514i
\(838\) 36.8196 + 39.8258i 1.27191 + 1.37576i
\(839\) 11.1147i 0.383721i −0.981422 0.191861i \(-0.938548\pi\)
0.981422 0.191861i \(-0.0614521\pi\)
\(840\) 0 0
\(841\) 7.69754i 0.265432i
\(842\) −39.5913 + 36.6028i −1.36441 + 1.26142i
\(843\) 2.95105 2.95105i 0.101640 0.101640i
\(844\) −4.10543 + 3.50734i −0.141315 + 0.120728i
\(845\) 0 0
\(846\) 0.567855 14.4781i 0.0195233 0.497767i
\(847\) 92.5750i 3.18092i
\(848\) 23.0581 16.7623i 0.791818 0.575620i
\(849\) −14.7874 −0.507501
\(850\) 0 0
\(851\) 6.48436 6.48436i 0.222281 0.222281i
\(852\) −4.77027 + 4.07532i −0.163427 + 0.139618i
\(853\) 28.9107 28.9107i 0.989884 0.989884i −0.0100656 0.999949i \(-0.503204\pi\)
0.999949 + 0.0100656i \(0.00320402\pi\)
\(854\) −45.6295 49.3550i −1.56141 1.68889i
\(855\) 0 0
\(856\) −0.812454 1.03016i −0.0277691 0.0352101i
\(857\) 34.1485 1.16649 0.583245 0.812296i \(-0.301783\pi\)
0.583245 + 0.812296i \(0.301783\pi\)
\(858\) −0.456237 0.493486i −0.0155757 0.0168473i
\(859\) −20.4589 20.4589i −0.698047 0.698047i 0.265942 0.963989i \(-0.414317\pi\)
−0.963989 + 0.265942i \(0.914317\pi\)
\(860\) 0 0
\(861\) −19.0159 + 19.0159i −0.648060 + 0.648060i
\(862\) −1.24185 + 31.6623i −0.0422976 + 1.07842i
\(863\) 35.3591i 1.20364i 0.798633 + 0.601818i \(0.205557\pi\)
−0.798633 + 0.601818i \(0.794443\pi\)
\(864\) 11.9972 + 17.9419i 0.408154 + 0.610395i
\(865\) 0 0
\(866\) −23.7491 0.931480i −0.807028 0.0316530i
\(867\) 2.36940 + 2.36940i 0.0804692 + 0.0804692i
\(868\) 20.0141 + 1.57240i 0.679324 + 0.0533706i
\(869\) 45.1304 + 45.1304i 1.53094 + 1.53094i
\(870\) 0 0
\(871\) 1.31809i 0.0446618i
\(872\) 0.370804 + 0.470165i 0.0125570 + 0.0159218i
\(873\) 35.2120 1.19175
\(874\) 4.01130 + 4.33880i 0.135684 + 0.146762i
\(875\) 0 0
\(876\) 7.45430 + 8.72545i 0.251857 + 0.294806i
\(877\) −3.15415 3.15415i −0.106508 0.106508i 0.651845 0.758353i \(-0.273995\pi\)
−0.758353 + 0.651845i \(0.773995\pi\)
\(878\) −12.8358 0.503440i −0.433186 0.0169903i
\(879\) −10.5301 −0.355172
\(880\) 0 0
\(881\) 20.3066 0.684146 0.342073 0.939673i \(-0.388871\pi\)
0.342073 + 0.939673i \(0.388871\pi\)
\(882\) −54.3114 2.13018i −1.82876 0.0717270i
\(883\) −0.523303 0.523303i −0.0176105 0.0176105i 0.698247 0.715857i \(-0.253964\pi\)
−0.715857 + 0.698247i \(0.753964\pi\)
\(884\) 0.883423 0.754723i 0.0297127 0.0253841i
\(885\) 0 0
\(886\) 17.0252 + 18.4153i 0.571973 + 0.618673i
\(887\) −34.8129 −1.16890 −0.584452 0.811429i \(-0.698690\pi\)
−0.584452 + 0.811429i \(0.698690\pi\)
\(888\) 1.28985 10.9170i 0.0432845 0.366352i
\(889\) 12.8766i 0.431868i
\(890\) 0 0
\(891\) 19.3024 + 19.3024i 0.646656 + 0.646656i
\(892\) 3.77627 48.0661i 0.126439 1.60937i
\(893\) −7.36103 7.36103i −0.246328 0.246328i
\(894\) −1.56546 0.0614001i −0.0523569 0.00205353i
\(895\) 0 0
\(896\) −14.4564 + 51.3527i −0.482956 + 1.71557i
\(897\) 0.139964i 0.00467325i
\(898\) −1.00157 + 25.5363i −0.0334230 + 0.852156i
\(899\) 6.94743 6.94743i 0.231710 0.231710i
\(900\) 0 0
\(901\) −23.5562 23.5562i −0.784770 0.784770i
\(902\) 43.8631 + 47.4444i 1.46048 + 1.57973i
\(903\) 10.4736 0.348540
\(904\) −16.7971 1.98458i −0.558664 0.0660061i
\(905\) 0 0
\(906\) −4.72384 5.10952i −0.156939 0.169752i
\(907\) 13.3188 13.3188i 0.442244 0.442244i −0.450521 0.892766i \(-0.648762\pi\)
0.892766 + 0.450521i \(0.148762\pi\)
\(908\) 12.2618 + 14.3527i 0.406921 + 0.476311i
\(909\) 33.8264 33.8264i 1.12195 1.12195i
\(910\) 0 0
\(911\) −47.0117 −1.55757 −0.778783 0.627294i \(-0.784163\pi\)
−0.778783 + 0.627294i \(0.784163\pi\)
\(912\) 6.99653 + 1.10618i 0.231678 + 0.0366293i
\(913\) 9.15148i 0.302870i
\(914\) 1.03444 26.3742i 0.0342163 0.872382i
\(915\) 0 0
\(916\) 29.5436 + 34.5815i 0.976148 + 1.14261i
\(917\) −3.83624 + 3.83624i −0.126684 + 0.126684i
\(918\) 18.5203 17.1223i 0.611261 0.565121i
\(919\) 31.3426i 1.03390i −0.856016 0.516949i \(-0.827068\pi\)
0.856016 0.516949i \(-0.172932\pi\)
\(920\) 0 0
\(921\) 7.76133i 0.255745i
\(922\) 1.12856 + 1.22070i 0.0371672 + 0.0402017i
\(923\) 0.399048 0.399048i 0.0131348 0.0131348i
\(924\) 2.82437 35.9499i 0.0929151 1.18266i
\(925\) 0 0
\(926\) 11.0582 + 0.433721i 0.363395 + 0.0142529i
\(927\) 34.7219i 1.14042i
\(928\) 14.5128 + 21.7039i 0.476406 + 0.712464i
\(929\) −30.3384 −0.995369 −0.497685 0.867358i \(-0.665816\pi\)
−0.497685 + 0.867358i \(0.665816\pi\)
\(930\) 0 0
\(931\) −27.6133 + 27.6133i −0.904990 + 0.904990i
\(932\) −32.8938 2.58427i −1.07747 0.0846507i
\(933\) −15.2245 + 15.2245i −0.498429 + 0.498429i
\(934\) −12.8508 + 11.8808i −0.420492 + 0.388752i
\(935\) 0 0
\(936\) −0.549157 0.696309i −0.0179498 0.0227596i
\(937\) −14.5267 −0.474565 −0.237283 0.971441i \(-0.576257\pi\)
−0.237283 + 0.971441i \(0.576257\pi\)
\(938\) 51.9306 48.0107i 1.69559 1.56760i
\(939\) 2.61767 + 2.61767i 0.0854245 + 0.0854245i
\(940\) 0 0
\(941\) 37.2863 37.2863i 1.21550 1.21550i 0.246307 0.969192i \(-0.420783\pi\)
0.969192 0.246307i \(-0.0792172\pi\)
\(942\) −7.34716 0.288168i −0.239384 0.00938902i
\(943\) 13.4563i 0.438197i
\(944\) 17.1786 + 23.6307i 0.559116 + 0.769115i
\(945\) 0 0
\(946\) 0.986239 25.1453i 0.0320654 0.817543i
\(947\) 15.8961 + 15.8961i 0.516553 + 0.516553i 0.916527 0.399973i \(-0.130981\pi\)
−0.399973 + 0.916527i \(0.630981\pi\)
\(948\) −10.3498 12.1147i −0.336145 0.393466i
\(949\) −0.729912 0.729912i −0.0236939 0.0236939i
\(950\) 0 0
\(951\) 8.67765i 0.281392i
\(952\) 61.9129 + 7.31501i 2.00661 + 0.237081i
\(953\) 33.2248 1.07626 0.538129 0.842862i \(-0.319131\pi\)
0.538129 + 0.842862i \(0.319131\pi\)
\(954\) −18.6695 + 17.2603i −0.604447 + 0.558822i
\(955\) 0 0
\(956\) 10.4860 + 0.823827i 0.339143 + 0.0266445i
\(957\) −12.4791 12.4791i −0.403393 0.403393i
\(958\) −0.116624 + 2.97346i −0.00376796 + 0.0960682i
\(959\) 0.942197 0.0304251
\(960\) 0 0
\(961\) −26.4684 −0.853820
\(962\) −0.0387525 + 0.988038i −0.00124943 + 0.0318556i
\(963\) 0.827438 + 0.827438i 0.0266638 + 0.0266638i
\(964\) 28.1386 + 2.21069i 0.906283 + 0.0712014i
\(965\) 0 0
\(966\) −5.51433 + 5.09809i −0.177421 + 0.164028i
\(967\) 1.79116 0.0576000 0.0288000 0.999585i \(-0.490831\pi\)
0.0288000 + 0.999585i \(0.490831\pi\)
\(968\) −55.1455 6.51543i −1.77244 0.209414i
\(969\) 8.27774i 0.265919i
\(970\) 0 0
\(971\) 5.31278 + 5.31278i 0.170495 + 0.170495i 0.787197 0.616702i \(-0.211531\pi\)
−0.616702 + 0.787197i \(0.711531\pi\)
\(972\) −19.2966 22.5872i −0.618940 0.724485i
\(973\) 54.8404 + 54.8404i 1.75810 + 1.75810i
\(974\) 0.270022 6.88451i 0.00865207 0.220594i
\(975\) 0 0
\(976\) 32.6114 23.7072i 1.04386 0.758848i
\(977\) 6.81676i 0.218088i 0.994037 + 0.109044i \(0.0347789\pi\)
−0.994037 + 0.109044i \(0.965221\pi\)
\(978\) 16.9836 + 0.666126i 0.543076 + 0.0213003i
\(979\) −12.7025 + 12.7025i −0.405972 + 0.405972i
\(980\) 0 0
\(981\) −0.377643 0.377643i −0.0120572 0.0120572i
\(982\) 21.0857 19.4941i 0.672873 0.622082i
\(983\) 5.49468 0.175253 0.0876265 0.996153i \(-0.472072\pi\)
0.0876265 + 0.996153i \(0.472072\pi\)
\(984\) −9.98913 12.6658i −0.318442 0.403771i
\(985\) 0 0
\(986\) 22.4036 20.7125i 0.713475 0.659620i
\(987\) 9.35538 9.35538i 0.297785 0.297785i
\(988\) −0.635184 0.0499028i −0.0202079 0.00158762i
\(989\) −3.70574 + 3.70574i −0.117836 + 0.117836i
\(990\) 0 0
\(991\) 48.7524 1.54867 0.774335 0.632775i \(-0.218084\pi\)
0.774335 + 0.632775i \(0.218084\pi\)
\(992\) −2.34525 + 11.8114i −0.0744616 + 0.375013i
\(993\) 5.93333i 0.188289i
\(994\) 30.2569 + 1.18673i 0.959691 + 0.0376407i
\(995\) 0 0
\(996\) 0.178942 2.27766i 0.00567000 0.0721703i
\(997\) 42.5246 42.5246i 1.34677 1.34677i 0.457618 0.889149i \(-0.348703\pi\)
0.889149 0.457618i \(-0.151297\pi\)
\(998\) −34.0864 36.8694i −1.07899 1.16708i
\(999\) 21.4646i 0.679109i
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 400.2.q.f.149.3 12
4.3 odd 2 1600.2.q.f.49.4 12
5.2 odd 4 400.2.l.f.101.6 12
5.3 odd 4 400.2.l.g.101.1 yes 12
5.4 even 2 400.2.q.e.149.4 12
16.3 odd 4 1600.2.q.e.849.3 12
16.13 even 4 400.2.q.e.349.4 12
20.3 even 4 1600.2.l.f.1201.3 12
20.7 even 4 1600.2.l.g.1201.4 12
20.19 odd 2 1600.2.q.e.49.3 12
80.3 even 4 1600.2.l.f.401.3 12
80.13 odd 4 400.2.l.g.301.1 yes 12
80.19 odd 4 1600.2.q.f.849.4 12
80.29 even 4 inner 400.2.q.f.349.3 12
80.67 even 4 1600.2.l.g.401.4 12
80.77 odd 4 400.2.l.f.301.6 yes 12
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
400.2.l.f.101.6 12 5.2 odd 4
400.2.l.f.301.6 yes 12 80.77 odd 4
400.2.l.g.101.1 yes 12 5.3 odd 4
400.2.l.g.301.1 yes 12 80.13 odd 4
400.2.q.e.149.4 12 5.4 even 2
400.2.q.e.349.4 12 16.13 even 4
400.2.q.f.149.3 12 1.1 even 1 trivial
400.2.q.f.349.3 12 80.29 even 4 inner
1600.2.l.f.401.3 12 80.3 even 4
1600.2.l.f.1201.3 12 20.3 even 4
1600.2.l.g.401.4 12 80.67 even 4
1600.2.l.g.1201.4 12 20.7 even 4
1600.2.q.e.49.3 12 20.19 odd 2
1600.2.q.e.849.3 12 16.3 odd 4
1600.2.q.f.49.4 12 4.3 odd 2
1600.2.q.f.849.4 12 80.19 odd 4