Properties

Label 418.2.f.g.191.4
Level $418$
Weight $2$
Character 418.191
Analytic conductor $3.338$
Analytic rank $0$
Dimension $16$
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] = [418,2,Mod(115,418)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(418, base_ring=CyclotomicField(10))
 
chi = DirichletCharacter(H, H._module([4, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("418.115");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 418 = 2 \cdot 11 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 418.f (of order \(5\), degree \(4\), 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: \(3.33774680449\)
Analytic rank: \(0\)
Dimension: \(16\)
Relative dimension: \(4\) over \(\Q(\zeta_{5})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{16} - x^{15} + 7 x^{14} - 13 x^{13} + 51 x^{12} - 74 x^{11} + 332 x^{10} - 614 x^{9} + 1832 x^{8} - 2960 x^{7} + 5348 x^{6} - 6872 x^{5} + 8232 x^{4} - 6344 x^{3} + 3984 x^{2} + \cdots + 16 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label 191.4
Root \(0.540846 - 1.66455i\) of defining polynomial
Character \(\chi\) \(=\) 418.191
Dual form 418.2.f.g.267.4

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.809017 + 0.587785i) q^{2} +(0.540846 - 1.66455i) q^{3} +(0.309017 + 0.951057i) q^{4} +(2.42502 - 1.76188i) q^{5} +(1.41595 - 1.02875i) q^{6} +(0.0678059 + 0.208685i) q^{7} +(-0.309017 + 0.951057i) q^{8} +(-0.0511674 - 0.0371753i) q^{9} +O(q^{10})\) \(q+(0.809017 + 0.587785i) q^{2} +(0.540846 - 1.66455i) q^{3} +(0.309017 + 0.951057i) q^{4} +(2.42502 - 1.76188i) q^{5} +(1.41595 - 1.02875i) q^{6} +(0.0678059 + 0.208685i) q^{7} +(-0.309017 + 0.951057i) q^{8} +(-0.0511674 - 0.0371753i) q^{9} +2.99749 q^{10} +(-2.87157 - 1.65954i) q^{11} +1.75021 q^{12} +(1.17773 + 0.855668i) q^{13} +(-0.0678059 + 0.208685i) q^{14} +(-1.62118 - 4.98947i) q^{15} +(-0.809017 + 0.587785i) q^{16} +(-2.45198 + 1.78147i) q^{17} +(-0.0195442 - 0.0601509i) q^{18} +(0.309017 - 0.951057i) q^{19} +(2.42502 + 1.76188i) q^{20} +0.384040 q^{21} +(-1.34770 - 3.03046i) q^{22} -1.59420 q^{23} +(1.41595 + 1.02875i) q^{24} +(1.23141 - 3.78988i) q^{25} +(0.449851 + 1.38450i) q^{26} +(4.15830 - 3.02118i) q^{27} +(-0.177518 + 0.128975i) q^{28} +(1.09211 + 3.36117i) q^{29} +(1.62118 - 4.98947i) q^{30} +(-2.58312 - 1.87675i) q^{31} -1.00000 q^{32} +(-4.31546 + 3.88233i) q^{33} -3.03081 q^{34} +(0.532108 + 0.386599i) q^{35} +(0.0195442 - 0.0601509i) q^{36} +(0.324198 + 0.997779i) q^{37} +(0.809017 - 0.587785i) q^{38} +(2.06127 - 1.49760i) q^{39} +(0.926274 + 2.85078i) q^{40} +(-1.77266 + 5.45570i) q^{41} +(0.310695 + 0.225733i) q^{42} +5.67401 q^{43} +(0.690949 - 3.24385i) q^{44} -0.189580 q^{45} +(-1.28973 - 0.937045i) q^{46} +(-2.13949 + 6.58466i) q^{47} +(0.540846 + 1.66455i) q^{48} +(5.62417 - 4.08620i) q^{49} +(3.22387 - 2.34228i) q^{50} +(1.63920 + 5.04495i) q^{51} +(-0.449851 + 1.38450i) q^{52} +(-1.20992 - 0.879062i) q^{53} +5.13995 q^{54} +(-9.88752 + 1.03495i) q^{55} -0.219425 q^{56} +(-1.41595 - 1.02875i) q^{57} +(-1.09211 + 3.36117i) q^{58} +(-0.0621808 - 0.191373i) q^{59} +(4.24430 - 3.08366i) q^{60} +(-9.14270 + 6.64256i) q^{61} +(-0.986664 - 3.03664i) q^{62} +(0.00428848 - 0.0131986i) q^{63} +(-0.809017 - 0.587785i) q^{64} +4.36359 q^{65} +(-5.77326 + 0.604303i) q^{66} -5.87830 q^{67} +(-2.45198 - 1.78147i) q^{68} +(-0.862214 + 2.65362i) q^{69} +(0.203247 + 0.625531i) q^{70} +(-2.77129 + 2.01346i) q^{71} +(0.0511674 - 0.0371753i) q^{72} +(2.83389 + 8.72182i) q^{73} +(-0.324198 + 0.997779i) q^{74} +(-5.64246 - 4.09948i) q^{75} +1.00000 q^{76} +(0.151611 - 0.711781i) q^{77} +2.54787 q^{78} +(-4.19903 - 3.05077i) q^{79} +(-0.926274 + 2.85078i) q^{80} +(-2.83855 - 8.73616i) q^{81} +(-4.64089 + 3.37181i) q^{82} +(-4.18186 + 3.03830i) q^{83} +(0.118675 + 0.365244i) q^{84} +(-2.80736 + 8.64018i) q^{85} +(4.59037 + 3.33510i) q^{86} +6.18551 q^{87} +(2.46568 - 2.21820i) q^{88} -6.32025 q^{89} +(-0.153374 - 0.111432i) q^{90} +(-0.0987085 + 0.303793i) q^{91} +(-0.492634 - 1.51617i) q^{92} +(-4.52101 + 3.28471i) q^{93} +(-5.60125 + 4.06955i) q^{94} +(-0.926274 - 2.85078i) q^{95} +(-0.540846 + 1.66455i) q^{96} +(-3.41795 - 2.48329i) q^{97} +6.95185 q^{98} +(0.0852371 + 0.191666i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16 q + 4 q^{2} + q^{3} - 4 q^{4} + q^{5} - q^{6} - 12 q^{7} + 4 q^{8} - q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 16 q + 4 q^{2} + q^{3} - 4 q^{4} + q^{5} - q^{6} - 12 q^{7} + 4 q^{8} - q^{9} + 4 q^{10} + 4 q^{11} - 4 q^{12} - 12 q^{13} + 12 q^{14} - 10 q^{15} - 4 q^{16} + 6 q^{17} + q^{18} - 4 q^{19} + q^{20} + 14 q^{21} - 9 q^{22} - 26 q^{23} - q^{24} + 33 q^{25} - 3 q^{26} + 13 q^{27} - 2 q^{28} + 10 q^{30} + 11 q^{31} - 16 q^{32} - 31 q^{33} - 6 q^{34} - 4 q^{35} - q^{36} + 4 q^{38} + 12 q^{39} - q^{40} - 7 q^{41} + 6 q^{42} + 66 q^{43} - 11 q^{44} - 42 q^{45} - 24 q^{46} + 47 q^{47} + q^{48} + 24 q^{49} + 37 q^{50} - 41 q^{51} + 3 q^{52} + 15 q^{53} - 8 q^{54} - 9 q^{55} - 28 q^{56} + q^{57} - 18 q^{59} + 5 q^{60} - 43 q^{61} + 9 q^{62} - 37 q^{63} - 4 q^{64} + 52 q^{65} - 39 q^{66} - 50 q^{67} + 6 q^{68} + 81 q^{69} - 11 q^{70} - 5 q^{71} + q^{72} - 13 q^{73} + 39 q^{75} + 16 q^{76} - 10 q^{77} - 22 q^{78} + 5 q^{79} + q^{80} + 2 q^{82} + 7 q^{83} - q^{84} - 29 q^{85} + 29 q^{86} + 4 q^{87} - 4 q^{88} - 28 q^{89} - 18 q^{90} - 11 q^{92} - 5 q^{93} + 28 q^{94} + q^{95} - q^{96} - 11 q^{97} - 24 q^{98} + 43 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/418\mathbb{Z}\right)^\times\).

\(n\) \(287\) \(343\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{5}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.809017 + 0.587785i 0.572061 + 0.415627i
\(3\) 0.540846 1.66455i 0.312257 0.961029i −0.664611 0.747189i \(-0.731403\pi\)
0.976869 0.213840i \(-0.0685972\pi\)
\(4\) 0.309017 + 0.951057i 0.154508 + 0.475528i
\(5\) 2.42502 1.76188i 1.08450 0.787936i 0.106038 0.994362i \(-0.466183\pi\)
0.978462 + 0.206426i \(0.0661834\pi\)
\(6\) 1.41595 1.02875i 0.578060 0.419985i
\(7\) 0.0678059 + 0.208685i 0.0256282 + 0.0788756i 0.963053 0.269313i \(-0.0867967\pi\)
−0.937424 + 0.348189i \(0.886797\pi\)
\(8\) −0.309017 + 0.951057i −0.109254 + 0.336249i
\(9\) −0.0511674 0.0371753i −0.0170558 0.0123918i
\(10\) 2.99749 0.947888
\(11\) −2.87157 1.65954i −0.865812 0.500369i
\(12\) 1.75021 0.505243
\(13\) 1.17773 + 0.855668i 0.326643 + 0.237320i 0.739005 0.673700i \(-0.235296\pi\)
−0.412362 + 0.911020i \(0.635296\pi\)
\(14\) −0.0678059 + 0.208685i −0.0181219 + 0.0557735i
\(15\) −1.62118 4.98947i −0.418586 1.28828i
\(16\) −0.809017 + 0.587785i −0.202254 + 0.146946i
\(17\) −2.45198 + 1.78147i −0.594693 + 0.432069i −0.843991 0.536357i \(-0.819800\pi\)
0.249298 + 0.968427i \(0.419800\pi\)
\(18\) −0.0195442 0.0601509i −0.00460661 0.0141777i
\(19\) 0.309017 0.951057i 0.0708934 0.218187i
\(20\) 2.42502 + 1.76188i 0.542250 + 0.393968i
\(21\) 0.384040 0.0838044
\(22\) −1.34770 3.03046i −0.287331 0.646097i
\(23\) −1.59420 −0.332413 −0.166206 0.986091i \(-0.553152\pi\)
−0.166206 + 0.986091i \(0.553152\pi\)
\(24\) 1.41595 + 1.02875i 0.289030 + 0.209993i
\(25\) 1.23141 3.78988i 0.246282 0.757977i
\(26\) 0.449851 + 1.38450i 0.0882231 + 0.271523i
\(27\) 4.15830 3.02118i 0.800266 0.581427i
\(28\) −0.177518 + 0.128975i −0.0335478 + 0.0243739i
\(29\) 1.09211 + 3.36117i 0.202800 + 0.624154i 0.999797 + 0.0201701i \(0.00642078\pi\)
−0.796997 + 0.603984i \(0.793579\pi\)
\(30\) 1.62118 4.98947i 0.295985 0.910948i
\(31\) −2.58312 1.87675i −0.463942 0.337074i 0.331134 0.943584i \(-0.392569\pi\)
−0.795076 + 0.606510i \(0.792569\pi\)
\(32\) −1.00000 −0.176777
\(33\) −4.31546 + 3.88233i −0.751226 + 0.675827i
\(34\) −3.03081 −0.519780
\(35\) 0.532108 + 0.386599i 0.0899427 + 0.0653472i
\(36\) 0.0195442 0.0601509i 0.00325737 0.0100251i
\(37\) 0.324198 + 0.997779i 0.0532978 + 0.164034i 0.974162 0.225849i \(-0.0725155\pi\)
−0.920865 + 0.389883i \(0.872516\pi\)
\(38\) 0.809017 0.587785i 0.131240 0.0953514i
\(39\) 2.06127 1.49760i 0.330068 0.239808i
\(40\) 0.926274 + 2.85078i 0.146457 + 0.450748i
\(41\) −1.77266 + 5.45570i −0.276843 + 0.852037i 0.711882 + 0.702299i \(0.247843\pi\)
−0.988726 + 0.149738i \(0.952157\pi\)
\(42\) 0.310695 + 0.225733i 0.0479412 + 0.0348313i
\(43\) 5.67401 0.865278 0.432639 0.901567i \(-0.357582\pi\)
0.432639 + 0.901567i \(0.357582\pi\)
\(44\) 0.690949 3.24385i 0.104165 0.489029i
\(45\) −0.189580 −0.0282609
\(46\) −1.28973 0.937045i −0.190161 0.138160i
\(47\) −2.13949 + 6.58466i −0.312076 + 0.960472i 0.664865 + 0.746964i \(0.268489\pi\)
−0.976941 + 0.213508i \(0.931511\pi\)
\(48\) 0.540846 + 1.66455i 0.0780643 + 0.240257i
\(49\) 5.62417 4.08620i 0.803452 0.583742i
\(50\) 3.22387 2.34228i 0.455924 0.331248i
\(51\) 1.63920 + 5.04495i 0.229534 + 0.706434i
\(52\) −0.449851 + 1.38450i −0.0623832 + 0.191996i
\(53\) −1.20992 0.879062i −0.166196 0.120748i 0.501578 0.865112i \(-0.332753\pi\)
−0.667774 + 0.744364i \(0.732753\pi\)
\(54\) 5.13995 0.699458
\(55\) −9.88752 + 1.03495i −1.33323 + 0.139553i
\(56\) −0.219425 −0.0293218
\(57\) −1.41595 1.02875i −0.187547 0.136261i
\(58\) −1.09211 + 3.36117i −0.143401 + 0.441343i
\(59\) −0.0621808 0.191373i −0.00809525 0.0249146i 0.946927 0.321448i \(-0.104169\pi\)
−0.955023 + 0.296533i \(0.904169\pi\)
\(60\) 4.24430 3.08366i 0.547936 0.398099i
\(61\) −9.14270 + 6.64256i −1.17060 + 0.850493i −0.991081 0.133261i \(-0.957455\pi\)
−0.179522 + 0.983754i \(0.557455\pi\)
\(62\) −0.986664 3.03664i −0.125306 0.385654i
\(63\) 0.00428848 0.0131986i 0.000540298 0.00166286i
\(64\) −0.809017 0.587785i −0.101127 0.0734732i
\(65\) 4.36359 0.541237
\(66\) −5.77326 + 0.604303i −0.710639 + 0.0743846i
\(67\) −5.87830 −0.718148 −0.359074 0.933309i \(-0.616907\pi\)
−0.359074 + 0.933309i \(0.616907\pi\)
\(68\) −2.45198 1.78147i −0.297346 0.216035i
\(69\) −0.862214 + 2.65362i −0.103798 + 0.319459i
\(70\) 0.203247 + 0.625531i 0.0242927 + 0.0747652i
\(71\) −2.77129 + 2.01346i −0.328892 + 0.238954i −0.739960 0.672650i \(-0.765156\pi\)
0.411068 + 0.911605i \(0.365156\pi\)
\(72\) 0.0511674 0.0371753i 0.00603013 0.00438115i
\(73\) 2.83389 + 8.72182i 0.331682 + 1.02081i 0.968333 + 0.249660i \(0.0803190\pi\)
−0.636652 + 0.771152i \(0.719681\pi\)
\(74\) −0.324198 + 0.997779i −0.0376873 + 0.115989i
\(75\) −5.64246 4.09948i −0.651535 0.473368i
\(76\) 1.00000 0.114708
\(77\) 0.151611 0.711781i 0.0172777 0.0811150i
\(78\) 2.54787 0.288490
\(79\) −4.19903 3.05077i −0.472427 0.343239i 0.325959 0.945384i \(-0.394313\pi\)
−0.798387 + 0.602145i \(0.794313\pi\)
\(80\) −0.926274 + 2.85078i −0.103561 + 0.318727i
\(81\) −2.83855 8.73616i −0.315394 0.970684i
\(82\) −4.64089 + 3.37181i −0.512501 + 0.372354i
\(83\) −4.18186 + 3.03830i −0.459019 + 0.333497i −0.793146 0.609031i \(-0.791559\pi\)
0.334127 + 0.942528i \(0.391559\pi\)
\(84\) 0.118675 + 0.365244i 0.0129485 + 0.0398513i
\(85\) −2.80736 + 8.64018i −0.304501 + 0.937159i
\(86\) 4.59037 + 3.33510i 0.494992 + 0.359633i
\(87\) 6.18551 0.663156
\(88\) 2.46568 2.21820i 0.262842 0.236461i
\(89\) −6.32025 −0.669945 −0.334972 0.942228i \(-0.608727\pi\)
−0.334972 + 0.942228i \(0.608727\pi\)
\(90\) −0.153374 0.111432i −0.0161670 0.0117460i
\(91\) −0.0987085 + 0.303793i −0.0103475 + 0.0318462i
\(92\) −0.492634 1.51617i −0.0513606 0.158072i
\(93\) −4.52101 + 3.28471i −0.468807 + 0.340608i
\(94\) −5.60125 + 4.06955i −0.577725 + 0.419742i
\(95\) −0.926274 2.85078i −0.0950337 0.292484i
\(96\) −0.540846 + 1.66455i −0.0551998 + 0.169888i
\(97\) −3.41795 2.48329i −0.347041 0.252140i 0.400586 0.916259i \(-0.368807\pi\)
−0.747626 + 0.664120i \(0.768807\pi\)
\(98\) 6.95185 0.702243
\(99\) 0.0852371 + 0.191666i 0.00856665 + 0.0192631i
\(100\) 3.98492 0.398492
\(101\) 1.94336 + 1.41193i 0.193372 + 0.140493i 0.680258 0.732972i \(-0.261868\pi\)
−0.486887 + 0.873465i \(0.661868\pi\)
\(102\) −1.63920 + 5.04495i −0.162305 + 0.499524i
\(103\) −2.43717 7.50085i −0.240142 0.739081i −0.996398 0.0848046i \(-0.972973\pi\)
0.756256 0.654276i \(-0.227027\pi\)
\(104\) −1.17773 + 0.855668i −0.115486 + 0.0839052i
\(105\) 0.931303 0.676631i 0.0908859 0.0660324i
\(106\) −0.462150 1.42235i −0.0448880 0.138151i
\(107\) 0.996913 3.06818i 0.0963752 0.296612i −0.891234 0.453543i \(-0.850160\pi\)
0.987610 + 0.156931i \(0.0501599\pi\)
\(108\) 4.15830 + 3.02118i 0.400133 + 0.290714i
\(109\) 18.6233 1.78379 0.891896 0.452241i \(-0.149375\pi\)
0.891896 + 0.452241i \(0.149375\pi\)
\(110\) −8.60750 4.97444i −0.820693 0.474294i
\(111\) 1.83620 0.174284
\(112\) −0.177518 0.128975i −0.0167739 0.0121869i
\(113\) 5.32725 16.3956i 0.501145 1.54237i −0.306011 0.952028i \(-0.598994\pi\)
0.807156 0.590338i \(-0.201006\pi\)
\(114\) −0.540846 1.66455i −0.0506548 0.155900i
\(115\) −3.86595 + 2.80878i −0.360502 + 0.261920i
\(116\) −2.85918 + 2.07732i −0.265468 + 0.192874i
\(117\) −0.0284515 0.0875646i −0.00263034 0.00809535i
\(118\) 0.0621808 0.191373i 0.00572420 0.0176173i
\(119\) −0.538025 0.390898i −0.0493206 0.0358335i
\(120\) 5.24624 0.478914
\(121\) 5.49187 + 9.53097i 0.499261 + 0.866452i
\(122\) −11.3010 −1.02314
\(123\) 8.12255 + 5.90138i 0.732386 + 0.532109i
\(124\) 0.986664 3.03664i 0.0886050 0.272698i
\(125\) 0.940242 + 2.89377i 0.0840978 + 0.258826i
\(126\) 0.0112274 0.00815717i 0.00100021 0.000726699i
\(127\) −4.40557 + 3.20083i −0.390931 + 0.284028i −0.765837 0.643035i \(-0.777675\pi\)
0.374906 + 0.927063i \(0.377675\pi\)
\(128\) −0.309017 0.951057i −0.0273135 0.0840623i
\(129\) 3.06876 9.44468i 0.270189 0.831558i
\(130\) 3.53022 + 2.56485i 0.309621 + 0.224953i
\(131\) −17.5416 −1.53261 −0.766307 0.642475i \(-0.777908\pi\)
−0.766307 + 0.642475i \(0.777908\pi\)
\(132\) −5.02587 2.90455i −0.437445 0.252808i
\(133\) 0.219425 0.0190265
\(134\) −4.75564 3.45518i −0.410825 0.298482i
\(135\) 4.76100 14.6528i 0.409761 1.26112i
\(136\) −0.936573 2.88248i −0.0803105 0.247170i
\(137\) −9.89559 + 7.18957i −0.845437 + 0.614246i −0.923884 0.382672i \(-0.875004\pi\)
0.0784470 + 0.996918i \(0.475004\pi\)
\(138\) −2.25731 + 1.64003i −0.192155 + 0.139608i
\(139\) 3.56764 + 10.9801i 0.302603 + 0.931316i 0.980561 + 0.196216i \(0.0628652\pi\)
−0.677958 + 0.735101i \(0.737135\pi\)
\(140\) −0.203247 + 0.625531i −0.0171775 + 0.0528670i
\(141\) 9.80338 + 7.12257i 0.825594 + 0.599829i
\(142\) −3.42551 −0.287462
\(143\) −1.96191 4.41160i −0.164063 0.368916i
\(144\) 0.0632464 0.00527053
\(145\) 8.57036 + 6.22673i 0.711730 + 0.517102i
\(146\) −2.83389 + 8.72182i −0.234535 + 0.721823i
\(147\) −3.75988 11.5717i −0.310110 0.954419i
\(148\) −0.848762 + 0.616661i −0.0697678 + 0.0506893i
\(149\) 8.82362 6.41074i 0.722859 0.525188i −0.164437 0.986388i \(-0.552581\pi\)
0.887296 + 0.461200i \(0.152581\pi\)
\(150\) −2.15523 6.63311i −0.175974 0.541591i
\(151\) 5.14721 15.8415i 0.418874 1.28916i −0.489865 0.871798i \(-0.662954\pi\)
0.908739 0.417364i \(-0.137046\pi\)
\(152\) 0.809017 + 0.587785i 0.0656199 + 0.0476757i
\(153\) 0.191688 0.0154971
\(154\) 0.541031 0.486728i 0.0435975 0.0392217i
\(155\) −9.57071 −0.768738
\(156\) 2.06127 + 1.49760i 0.165034 + 0.119904i
\(157\) 6.81490 20.9741i 0.543888 1.67392i −0.179731 0.983716i \(-0.557523\pi\)
0.723619 0.690200i \(-0.242477\pi\)
\(158\) −1.60388 4.93625i −0.127598 0.392707i
\(159\) −2.11763 + 1.53855i −0.167939 + 0.122015i
\(160\) −2.42502 + 1.76188i −0.191714 + 0.139289i
\(161\) −0.108096 0.332685i −0.00851915 0.0262193i
\(162\) 2.83855 8.73616i 0.223018 0.686377i
\(163\) 14.3702 + 10.4405i 1.12556 + 0.817766i 0.985042 0.172312i \(-0.0551238\pi\)
0.140516 + 0.990078i \(0.455124\pi\)
\(164\) −5.73646 −0.447942
\(165\) −3.62489 + 17.0180i −0.282197 + 1.32485i
\(166\) −5.16907 −0.401198
\(167\) −15.6347 11.3593i −1.20985 0.879006i −0.214632 0.976695i \(-0.568855\pi\)
−0.995217 + 0.0976887i \(0.968855\pi\)
\(168\) −0.118675 + 0.365244i −0.00915596 + 0.0281792i
\(169\) −3.36235 10.3482i −0.258642 0.796019i
\(170\) −7.34978 + 5.33993i −0.563702 + 0.409554i
\(171\) −0.0511674 + 0.0371753i −0.00391287 + 0.00284287i
\(172\) 1.75337 + 5.39630i 0.133693 + 0.411464i
\(173\) −2.79424 + 8.59979i −0.212442 + 0.653830i 0.786883 + 0.617102i \(0.211694\pi\)
−0.999325 + 0.0367280i \(0.988306\pi\)
\(174\) 5.00418 + 3.63575i 0.379366 + 0.275625i
\(175\) 0.874389 0.0660976
\(176\) 3.29860 0.345274i 0.248642 0.0260260i
\(177\) −0.352180 −0.0264715
\(178\) −5.11319 3.71495i −0.383249 0.278447i
\(179\) 6.18932 19.0488i 0.462611 1.42377i −0.399350 0.916798i \(-0.630764\pi\)
0.861962 0.506973i \(-0.169236\pi\)
\(180\) −0.0585835 0.180301i −0.00436655 0.0134389i
\(181\) −6.56097 + 4.76682i −0.487673 + 0.354315i −0.804289 0.594239i \(-0.797453\pi\)
0.316616 + 0.948554i \(0.397453\pi\)
\(182\) −0.258422 + 0.187755i −0.0191555 + 0.0139173i
\(183\) 6.11210 + 18.8111i 0.451819 + 1.39056i
\(184\) 0.492634 1.51617i 0.0363174 0.111774i
\(185\) 2.54415 + 1.84843i 0.187050 + 0.135900i
\(186\) −5.58828 −0.409752
\(187\) 9.99746 1.04646i 0.731086 0.0765249i
\(188\) −6.92353 −0.504950
\(189\) 0.912434 + 0.662922i 0.0663698 + 0.0482205i
\(190\) 0.926274 2.85078i 0.0671990 0.206817i
\(191\) 5.09818 + 15.6906i 0.368891 + 1.13533i 0.947508 + 0.319731i \(0.103592\pi\)
−0.578617 + 0.815599i \(0.696408\pi\)
\(192\) −1.41595 + 1.02875i −0.102188 + 0.0742436i
\(193\) −14.5637 + 10.5811i −1.04832 + 0.761646i −0.971891 0.235430i \(-0.924350\pi\)
−0.0764240 + 0.997075i \(0.524350\pi\)
\(194\) −1.30554 4.01804i −0.0937324 0.288479i
\(195\) 2.36003 7.26342i 0.169005 0.520144i
\(196\) 5.62417 + 4.08620i 0.401726 + 0.291871i
\(197\) 12.4047 0.883799 0.441899 0.897065i \(-0.354305\pi\)
0.441899 + 0.897065i \(0.354305\pi\)
\(198\) −0.0437000 + 0.205162i −0.00310563 + 0.0145802i
\(199\) 22.3028 1.58100 0.790502 0.612460i \(-0.209820\pi\)
0.790502 + 0.612460i \(0.209820\pi\)
\(200\) 3.22387 + 2.34228i 0.227962 + 0.165624i
\(201\) −3.17925 + 9.78473i −0.224247 + 0.690161i
\(202\) 0.742298 + 2.28456i 0.0522279 + 0.160741i
\(203\) −0.627375 + 0.455815i −0.0440331 + 0.0319919i
\(204\) −4.29149 + 3.11795i −0.300464 + 0.218300i
\(205\) 5.31353 + 16.3534i 0.371113 + 1.14217i
\(206\) 2.43717 7.50085i 0.169806 0.522609i
\(207\) 0.0815709 + 0.0592647i 0.00566957 + 0.00411918i
\(208\) −1.45575 −0.100938
\(209\) −2.46568 + 2.21820i −0.170555 + 0.153436i
\(210\) 1.15115 0.0794372
\(211\) 16.9867 + 12.3416i 1.16941 + 0.849628i 0.990938 0.134317i \(-0.0428840\pi\)
0.178474 + 0.983945i \(0.442884\pi\)
\(212\) 0.462150 1.42235i 0.0317406 0.0976875i
\(213\) 1.85267 + 5.70193i 0.126943 + 0.390690i
\(214\) 2.60995 1.89624i 0.178413 0.129624i
\(215\) 13.7596 9.99691i 0.938395 0.681784i
\(216\) 1.58833 + 4.88838i 0.108072 + 0.332612i
\(217\) 0.216498 0.666313i 0.0146969 0.0452323i
\(218\) 15.0666 + 10.9465i 1.02044 + 0.741392i
\(219\) 16.0506 1.08460
\(220\) −4.03971 9.08377i −0.272357 0.612428i
\(221\) −4.41211 −0.296790
\(222\) 1.48551 + 1.07929i 0.0997012 + 0.0724371i
\(223\) 7.24940 22.3114i 0.485456 1.49408i −0.345864 0.938285i \(-0.612414\pi\)
0.831320 0.555795i \(-0.187586\pi\)
\(224\) −0.0678059 0.208685i −0.00453047 0.0139434i
\(225\) −0.203898 + 0.148141i −0.0135932 + 0.00987604i
\(226\) 13.9469 10.1330i 0.927735 0.674039i
\(227\) −4.95867 15.2612i −0.329119 1.01292i −0.969547 0.244905i \(-0.921243\pi\)
0.640428 0.768018i \(-0.278757\pi\)
\(228\) 0.540846 1.66455i 0.0358184 0.110238i
\(229\) 20.3598 + 14.7923i 1.34542 + 0.977501i 0.999226 + 0.0393367i \(0.0125245\pi\)
0.346189 + 0.938165i \(0.387476\pi\)
\(230\) −4.77858 −0.315090
\(231\) −1.10280 0.637329i −0.0725588 0.0419331i
\(232\) −3.53414 −0.232028
\(233\) −14.8887 10.8173i −0.975389 0.708662i −0.0187157 0.999825i \(-0.505958\pi\)
−0.956673 + 0.291163i \(0.905958\pi\)
\(234\) 0.0284515 0.0875646i 0.00185993 0.00572428i
\(235\) 6.41308 + 19.7374i 0.418343 + 1.28753i
\(236\) 0.162791 0.118275i 0.0105968 0.00769904i
\(237\) −7.34919 + 5.33950i −0.477381 + 0.346838i
\(238\) −0.205507 0.632486i −0.0133211 0.0409980i
\(239\) 1.77504 5.46302i 0.114818 0.353373i −0.877091 0.480324i \(-0.840519\pi\)
0.991909 + 0.126951i \(0.0405191\pi\)
\(240\) 4.24430 + 3.08366i 0.273968 + 0.199050i
\(241\) 15.2741 0.983889 0.491945 0.870626i \(-0.336286\pi\)
0.491945 + 0.870626i \(0.336286\pi\)
\(242\) −1.15915 + 10.9388i −0.0745129 + 0.703170i
\(243\) −0.657167 −0.0421573
\(244\) −9.14270 6.64256i −0.585301 0.425246i
\(245\) 6.43932 19.8182i 0.411393 1.26614i
\(246\) 3.10254 + 9.54863i 0.197811 + 0.608799i
\(247\) 1.17773 0.855668i 0.0749369 0.0544449i
\(248\) 2.58312 1.87675i 0.164028 0.119174i
\(249\) 2.79567 + 8.60418i 0.177168 + 0.545268i
\(250\) −0.940242 + 2.89377i −0.0594661 + 0.183018i
\(251\) −14.7199 10.6946i −0.929109 0.675037i 0.0166656 0.999861i \(-0.494695\pi\)
−0.945774 + 0.324824i \(0.894695\pi\)
\(252\) 0.0138778 0.000874220
\(253\) 4.57785 + 2.64563i 0.287807 + 0.166329i
\(254\) −5.44558 −0.341686
\(255\) 12.8637 + 9.34601i 0.805555 + 0.585270i
\(256\) 0.309017 0.951057i 0.0193136 0.0594410i
\(257\) −6.44755 19.8435i −0.402187 1.23781i −0.923221 0.384269i \(-0.874453\pi\)
0.521034 0.853536i \(-0.325547\pi\)
\(258\) 8.03413 5.83713i 0.500183 0.363404i
\(259\) −0.186239 + 0.135311i −0.0115723 + 0.00840780i
\(260\) 1.34842 + 4.15002i 0.0836257 + 0.257373i
\(261\) 0.0690720 0.212582i 0.00427545 0.0131585i
\(262\) −14.1914 10.3107i −0.876749 0.636995i
\(263\) 0.446416 0.0275272 0.0137636 0.999905i \(-0.495619\pi\)
0.0137636 + 0.999905i \(0.495619\pi\)
\(264\) −2.35876 5.30396i −0.145172 0.326436i
\(265\) −4.48289 −0.275382
\(266\) 0.177518 + 0.128975i 0.0108843 + 0.00790794i
\(267\) −3.41828 + 10.5204i −0.209195 + 0.643836i
\(268\) −1.81649 5.59059i −0.110960 0.341500i
\(269\) −4.94104 + 3.58988i −0.301261 + 0.218879i −0.728138 0.685431i \(-0.759614\pi\)
0.426877 + 0.904310i \(0.359614\pi\)
\(270\) 12.4645 9.05596i 0.758562 0.551128i
\(271\) 1.84693 + 5.68428i 0.112193 + 0.345295i 0.991351 0.131235i \(-0.0418943\pi\)
−0.879158 + 0.476530i \(0.841894\pi\)
\(272\) 0.936573 2.88248i 0.0567881 0.174776i
\(273\) 0.452294 + 0.328611i 0.0273741 + 0.0198884i
\(274\) −12.2316 −0.738939
\(275\) −9.82554 + 8.83936i −0.592502 + 0.533034i
\(276\) −2.79018 −0.167949
\(277\) −12.2503 8.90037i −0.736050 0.534771i 0.155422 0.987848i \(-0.450326\pi\)
−0.891471 + 0.453077i \(0.850326\pi\)
\(278\) −3.56764 + 10.9801i −0.213973 + 0.658540i
\(279\) 0.0624029 + 0.192056i 0.00373596 + 0.0114981i
\(280\) −0.532108 + 0.386599i −0.0317996 + 0.0231037i
\(281\) 14.2585 10.3594i 0.850592 0.617991i −0.0747174 0.997205i \(-0.523805\pi\)
0.925309 + 0.379214i \(0.123805\pi\)
\(282\) 3.74456 + 11.5246i 0.222985 + 0.686278i
\(283\) 8.97231 27.6139i 0.533348 1.64148i −0.213842 0.976868i \(-0.568598\pi\)
0.747191 0.664610i \(-0.231402\pi\)
\(284\) −2.77129 2.01346i −0.164446 0.119477i
\(285\) −5.24624 −0.310760
\(286\) 1.00585 4.72224i 0.0594771 0.279232i
\(287\) −1.25872 −0.0742999
\(288\) 0.0511674 + 0.0371753i 0.00301507 + 0.00219057i
\(289\) −2.41471 + 7.43171i −0.142042 + 0.437159i
\(290\) 3.27359 + 10.0751i 0.192232 + 0.591628i
\(291\) −5.98215 + 4.34628i −0.350680 + 0.254784i
\(292\) −7.41922 + 5.39038i −0.434177 + 0.315448i
\(293\) −5.62139 17.3009i −0.328405 1.01073i −0.969880 0.243583i \(-0.921677\pi\)
0.641475 0.767144i \(-0.278323\pi\)
\(294\) 3.75988 11.5717i 0.219281 0.674876i
\(295\) −0.487965 0.354527i −0.0284104 0.0206414i
\(296\) −1.04913 −0.0609793
\(297\) −16.9546 + 1.77469i −0.983808 + 0.102978i
\(298\) 10.9066 0.631802
\(299\) −1.87753 1.36410i −0.108580 0.0788881i
\(300\) 2.15523 6.63311i 0.124432 0.382963i
\(301\) 0.384731 + 1.18408i 0.0221755 + 0.0682493i
\(302\) 13.4756 9.79058i 0.775432 0.563385i
\(303\) 3.40130 2.47119i 0.195399 0.141966i
\(304\) 0.309017 + 0.951057i 0.0177233 + 0.0545468i
\(305\) −10.4678 + 32.2166i −0.599386 + 1.84472i
\(306\) 0.155079 + 0.112671i 0.00886527 + 0.00644100i
\(307\) −21.0281 −1.20014 −0.600068 0.799949i \(-0.704860\pi\)
−0.600068 + 0.799949i \(0.704860\pi\)
\(308\) 0.723795 0.0757616i 0.0412420 0.00431692i
\(309\) −13.8037 −0.785264
\(310\) −7.74286 5.62552i −0.439765 0.319508i
\(311\) 5.56241 17.1193i 0.315415 0.970748i −0.660168 0.751118i \(-0.729515\pi\)
0.975583 0.219630i \(-0.0704850\pi\)
\(312\) 0.787336 + 2.42317i 0.0445741 + 0.137185i
\(313\) 0.185227 0.134575i 0.0104696 0.00760665i −0.582538 0.812803i \(-0.697940\pi\)
0.593008 + 0.805197i \(0.297940\pi\)
\(314\) 17.8416 12.9627i 1.00686 0.731528i
\(315\) −0.0128547 0.0395626i −0.000724278 0.00222910i
\(316\) 1.60388 4.93625i 0.0902256 0.277686i
\(317\) 12.1522 + 8.82910i 0.682536 + 0.495891i 0.874198 0.485570i \(-0.161388\pi\)
−0.191662 + 0.981461i \(0.561388\pi\)
\(318\) −2.61753 −0.146784
\(319\) 2.44191 11.4642i 0.136721 0.641875i
\(320\) −2.99749 −0.167565
\(321\) −4.56797 3.31883i −0.254959 0.185239i
\(322\) 0.108096 0.332685i 0.00602395 0.0185398i
\(323\) 0.936573 + 2.88248i 0.0521123 + 0.160385i
\(324\) 7.43142 5.39924i 0.412857 0.299958i
\(325\) 4.69315 3.40977i 0.260329 0.189140i
\(326\) 5.48892 + 16.8931i 0.304003 + 0.935625i
\(327\) 10.0723 30.9995i 0.557002 1.71428i
\(328\) −4.64089 3.37181i −0.256250 0.186177i
\(329\) −1.51919 −0.0837557
\(330\) −12.9355 + 11.6372i −0.712078 + 0.640608i
\(331\) −16.0202 −0.880549 −0.440274 0.897863i \(-0.645119\pi\)
−0.440274 + 0.897863i \(0.645119\pi\)
\(332\) −4.18186 3.03830i −0.229510 0.166749i
\(333\) 0.0205044 0.0631059i 0.00112363 0.00345818i
\(334\) −5.97192 18.3797i −0.326769 1.00569i
\(335\) −14.2550 + 10.3568i −0.778832 + 0.565855i
\(336\) −0.310695 + 0.225733i −0.0169498 + 0.0123147i
\(337\) −8.25977 25.4210i −0.449938 1.38477i −0.876976 0.480534i \(-0.840443\pi\)
0.427038 0.904234i \(-0.359557\pi\)
\(338\) 3.36235 10.3482i 0.182888 0.562871i
\(339\) −24.4101 17.7350i −1.32577 0.963231i
\(340\) −9.08482 −0.492694
\(341\) 4.30309 + 9.67600i 0.233025 + 0.523985i
\(342\) −0.0632464 −0.00341997
\(343\) 2.47671 + 1.79943i 0.133730 + 0.0971603i
\(344\) −1.75337 + 5.39630i −0.0945351 + 0.290949i
\(345\) 2.58447 + 7.95419i 0.139143 + 0.428239i
\(346\) −7.31542 + 5.31497i −0.393280 + 0.285734i
\(347\) −7.23210 + 5.25443i −0.388239 + 0.282072i −0.764734 0.644346i \(-0.777129\pi\)
0.376494 + 0.926419i \(0.377129\pi\)
\(348\) 1.91143 + 5.88277i 0.102463 + 0.315349i
\(349\) −4.13638 + 12.7305i −0.221415 + 0.681446i 0.777221 + 0.629228i \(0.216629\pi\)
−0.998636 + 0.0522176i \(0.983371\pi\)
\(350\) 0.707396 + 0.513953i 0.0378119 + 0.0274720i
\(351\) 7.48247 0.399385
\(352\) 2.87157 + 1.65954i 0.153055 + 0.0884537i
\(353\) −18.5323 −0.986375 −0.493188 0.869923i \(-0.664168\pi\)
−0.493188 + 0.869923i \(0.664168\pi\)
\(354\) −0.284920 0.207006i −0.0151433 0.0110023i
\(355\) −3.17296 + 9.76536i −0.168403 + 0.518292i
\(356\) −1.95306 6.01091i −0.103512 0.318578i
\(357\) −0.941658 + 0.684155i −0.0498378 + 0.0362093i
\(358\) 16.2038 11.7728i 0.856400 0.622211i
\(359\) −1.24924 3.84476i −0.0659323 0.202919i 0.912663 0.408713i \(-0.134022\pi\)
−0.978595 + 0.205794i \(0.934022\pi\)
\(360\) 0.0585835 0.180301i 0.00308762 0.00950272i
\(361\) −0.809017 0.587785i −0.0425798 0.0309361i
\(362\) −8.10980 −0.426242
\(363\) 18.8350 3.98672i 0.988583 0.209248i
\(364\) −0.319427 −0.0167425
\(365\) 22.2390 + 16.1576i 1.16404 + 0.845727i
\(366\) −6.11210 + 18.8111i −0.319484 + 0.983272i
\(367\) 6.12685 + 18.8565i 0.319819 + 0.984302i 0.973725 + 0.227726i \(0.0731291\pi\)
−0.653906 + 0.756576i \(0.726871\pi\)
\(368\) 1.28973 0.937045i 0.0672319 0.0488468i
\(369\) 0.293520 0.213254i 0.0152800 0.0111016i
\(370\) 0.971779 + 2.99083i 0.0505204 + 0.155486i
\(371\) 0.101407 0.312099i 0.00526479 0.0162034i
\(372\) −4.52101 3.28471i −0.234403 0.170304i
\(373\) 0.375806 0.0194585 0.00972924 0.999953i \(-0.496903\pi\)
0.00972924 + 0.999953i \(0.496903\pi\)
\(374\) 8.70321 + 5.02975i 0.450032 + 0.260082i
\(375\) 5.32535 0.275000
\(376\) −5.60125 4.06955i −0.288862 0.209871i
\(377\) −1.58984 + 4.89302i −0.0818809 + 0.252004i
\(378\) 0.348519 + 1.07263i 0.0179259 + 0.0551701i
\(379\) −20.7352 + 15.0650i −1.06510 + 0.773838i −0.975025 0.222097i \(-0.928710\pi\)
−0.0900724 + 0.995935i \(0.528710\pi\)
\(380\) 2.42502 1.76188i 0.124401 0.0903824i
\(381\) 2.94522 + 9.06445i 0.150888 + 0.464386i
\(382\) −5.09818 + 15.6906i −0.260845 + 0.802799i
\(383\) 22.1779 + 16.1132i 1.13324 + 0.823346i 0.986163 0.165779i \(-0.0530138\pi\)
0.147076 + 0.989125i \(0.453014\pi\)
\(384\) −1.75021 −0.0893152
\(385\) −0.886412 1.99320i −0.0451757 0.101583i
\(386\) −18.0017 −0.916261
\(387\) −0.290324 0.210933i −0.0147580 0.0107223i
\(388\) 1.30554 4.01804i 0.0662788 0.203985i
\(389\) −3.58817 11.0433i −0.181928 0.559916i 0.817954 0.575283i \(-0.195108\pi\)
−0.999882 + 0.0153674i \(0.995108\pi\)
\(390\) 6.17863 4.48904i 0.312867 0.227311i
\(391\) 3.90894 2.84001i 0.197683 0.143625i
\(392\) 2.14824 + 6.61160i 0.108503 + 0.333936i
\(393\) −9.48728 + 29.1988i −0.478570 + 1.47289i
\(394\) 10.0356 + 7.29130i 0.505587 + 0.367331i
\(395\) −15.5578 −0.782797
\(396\) −0.155945 + 0.140293i −0.00783655 + 0.00705000i
\(397\) 12.8213 0.643481 0.321741 0.946828i \(-0.395732\pi\)
0.321741 + 0.946828i \(0.395732\pi\)
\(398\) 18.0433 + 13.1093i 0.904431 + 0.657107i
\(399\) 0.118675 0.365244i 0.00594117 0.0182850i
\(400\) 1.23141 + 3.78988i 0.0615704 + 0.189494i
\(401\) −16.2994 + 11.8422i −0.813955 + 0.591373i −0.914975 0.403511i \(-0.867790\pi\)
0.101019 + 0.994884i \(0.467790\pi\)
\(402\) −8.32339 + 6.04729i −0.415133 + 0.301612i
\(403\) −1.43634 4.42059i −0.0715490 0.220205i
\(404\) −0.742298 + 2.28456i −0.0369307 + 0.113661i
\(405\) −22.2756 16.1842i −1.10688 0.804197i
\(406\) −0.775478 −0.0384863
\(407\) 0.724894 3.40322i 0.0359316 0.168691i
\(408\) −5.30457 −0.262615
\(409\) −4.01623 2.91796i −0.198590 0.144284i 0.484046 0.875042i \(-0.339167\pi\)
−0.682636 + 0.730759i \(0.739167\pi\)
\(410\) −5.31353 + 16.3534i −0.262417 + 0.807635i
\(411\) 6.61542 + 20.3602i 0.326315 + 1.00429i
\(412\) 6.38060 4.63578i 0.314350 0.228388i
\(413\) 0.0357204 0.0259524i 0.00175769 0.00127703i
\(414\) 0.0311573 + 0.0958923i 0.00153130 + 0.00471285i
\(415\) −4.78797 + 14.7359i −0.235032 + 0.723355i
\(416\) −1.17773 0.855668i −0.0577428 0.0419526i
\(417\) 20.2064 0.989513
\(418\) −3.29860 + 0.345274i −0.161340 + 0.0168879i
\(419\) −37.3432 −1.82433 −0.912167 0.409818i \(-0.865592\pi\)
−0.912167 + 0.409818i \(0.865592\pi\)
\(420\) 0.931303 + 0.676631i 0.0454429 + 0.0330162i
\(421\) 6.67781 20.5522i 0.325457 1.00165i −0.645778 0.763526i \(-0.723467\pi\)
0.971234 0.238127i \(-0.0765334\pi\)
\(422\) 6.48834 + 19.9691i 0.315847 + 0.972079i
\(423\) 0.354259 0.257384i 0.0172246 0.0125144i
\(424\) 1.20992 0.879062i 0.0587591 0.0426910i
\(425\) 3.73217 + 11.4864i 0.181037 + 0.557174i
\(426\) −1.85267 + 5.70193i −0.0897622 + 0.276260i
\(427\) −2.00613 1.45754i −0.0970836 0.0705354i
\(428\) 3.22608 0.155938
\(429\) −8.40442 + 0.879715i −0.405769 + 0.0424730i
\(430\) 17.0078 0.820187
\(431\) −1.69339 1.23032i −0.0815678 0.0592625i 0.546254 0.837620i \(-0.316053\pi\)
−0.627822 + 0.778357i \(0.716053\pi\)
\(432\) −1.58833 + 4.88838i −0.0764186 + 0.235192i
\(433\) 2.11269 + 6.50218i 0.101529 + 0.312475i 0.988900 0.148581i \(-0.0474706\pi\)
−0.887371 + 0.461056i \(0.847471\pi\)
\(434\) 0.566800 0.411804i 0.0272073 0.0197672i
\(435\) 15.0000 10.8981i 0.719193 0.522524i
\(436\) 5.75492 + 17.7118i 0.275611 + 0.848243i
\(437\) −0.492634 + 1.51617i −0.0235659 + 0.0725283i
\(438\) 12.9852 + 9.43432i 0.620458 + 0.450789i
\(439\) −8.17083 −0.389972 −0.194986 0.980806i \(-0.562466\pi\)
−0.194986 + 0.980806i \(0.562466\pi\)
\(440\) 2.07111 9.72341i 0.0987363 0.463545i
\(441\) −0.439679 −0.0209371
\(442\) −3.56947 2.59337i −0.169782 0.123354i
\(443\) −1.09010 + 3.35498i −0.0517922 + 0.159400i −0.973607 0.228230i \(-0.926706\pi\)
0.921815 + 0.387630i \(0.126706\pi\)
\(444\) 0.567416 + 1.74633i 0.0269284 + 0.0828770i
\(445\) −15.3267 + 11.1355i −0.726555 + 0.527873i
\(446\) 18.9792 13.7892i 0.898690 0.652937i
\(447\) −5.89878 18.1546i −0.279003 0.858683i
\(448\) 0.0678059 0.208685i 0.00320353 0.00985945i
\(449\) 8.39921 + 6.10238i 0.396383 + 0.287989i 0.768066 0.640370i \(-0.221219\pi\)
−0.371683 + 0.928360i \(0.621219\pi\)
\(450\) −0.252032 −0.0118809
\(451\) 14.1443 12.7246i 0.666028 0.599179i
\(452\) 17.2393 0.810870
\(453\) −23.5851 17.1356i −1.10813 0.805101i
\(454\) 4.95867 15.2612i 0.232722 0.716245i
\(455\) 0.295877 + 0.910616i 0.0138709 + 0.0426904i
\(456\) 1.41595 1.02875i 0.0663080 0.0481756i
\(457\) 11.5069 8.36022i 0.538268 0.391075i −0.285173 0.958476i \(-0.592051\pi\)
0.823441 + 0.567401i \(0.192051\pi\)
\(458\) 7.77676 + 23.9344i 0.363384 + 1.11838i
\(459\) −4.81393 + 14.8158i −0.224695 + 0.691541i
\(460\) −3.86595 2.80878i −0.180251 0.130960i
\(461\) −8.90046 −0.414536 −0.207268 0.978284i \(-0.566457\pi\)
−0.207268 + 0.978284i \(0.566457\pi\)
\(462\) −0.517570 1.16382i −0.0240796 0.0541457i
\(463\) −4.58762 −0.213205 −0.106602 0.994302i \(-0.533997\pi\)
−0.106602 + 0.994302i \(0.533997\pi\)
\(464\) −2.85918 2.07732i −0.132734 0.0964371i
\(465\) −5.17627 + 15.9309i −0.240044 + 0.738779i
\(466\) −5.68697 17.5027i −0.263444 0.810796i
\(467\) −9.63966 + 7.00363i −0.446070 + 0.324089i −0.788042 0.615621i \(-0.788905\pi\)
0.341972 + 0.939710i \(0.388905\pi\)
\(468\) 0.0744869 0.0541179i 0.00344316 0.00250160i
\(469\) −0.398583 1.22671i −0.0184049 0.0566443i
\(470\) −6.41308 + 19.7374i −0.295813 + 0.910420i
\(471\) −31.2267 22.6875i −1.43885 1.04538i
\(472\) 0.201221 0.00926196
\(473\) −16.2933 9.41623i −0.749168 0.432959i
\(474\) −9.08410 −0.417246
\(475\) −3.22387 2.34228i −0.147921 0.107471i
\(476\) 0.205507 0.632486i 0.00941941 0.0289900i
\(477\) 0.0292293 + 0.0899586i 0.00133832 + 0.00411892i
\(478\) 4.64712 3.37633i 0.212554 0.154430i
\(479\) 16.8066 12.2107i 0.767915 0.557923i −0.133413 0.991061i \(-0.542594\pi\)
0.901328 + 0.433138i \(0.142594\pi\)
\(480\) 1.62118 + 4.98947i 0.0739963 + 0.227737i
\(481\) −0.471951 + 1.45252i −0.0215191 + 0.0662291i
\(482\) 12.3570 + 8.97787i 0.562845 + 0.408931i
\(483\) −0.612235 −0.0278576
\(484\) −7.36741 + 8.16831i −0.334882 + 0.371287i
\(485\) −12.6638 −0.575035
\(486\) −0.531659 0.386273i −0.0241165 0.0175217i
\(487\) 2.81501 8.66370i 0.127560 0.392589i −0.866799 0.498658i \(-0.833826\pi\)
0.994359 + 0.106069i \(0.0338263\pi\)
\(488\) −3.49220 10.7479i −0.158085 0.486534i
\(489\) 25.1509 18.2732i 1.13736 0.826341i
\(490\) 16.8584 12.2483i 0.761583 0.553323i
\(491\) 4.33395 + 13.3385i 0.195588 + 0.601959i 0.999969 + 0.00784485i \(0.00249712\pi\)
−0.804381 + 0.594114i \(0.797503\pi\)
\(492\) −3.10254 + 9.54863i −0.139873 + 0.430486i
\(493\) −8.66565 6.29597i −0.390281 0.283556i
\(494\) 1.45575 0.0654973
\(495\) 0.544393 + 0.314615i 0.0244687 + 0.0141409i
\(496\) 3.19291 0.143366
\(497\) −0.608090 0.441803i −0.0272766 0.0198176i
\(498\) −2.79567 + 8.60418i −0.125277 + 0.385563i
\(499\) 10.7148 + 32.9767i 0.479659 + 1.47624i 0.839569 + 0.543253i \(0.182807\pi\)
−0.359910 + 0.932987i \(0.617193\pi\)
\(500\) −2.46159 + 1.78845i −0.110085 + 0.0799818i
\(501\) −27.3640 + 19.8811i −1.22254 + 0.888224i
\(502\) −5.62248 17.3042i −0.250944 0.772325i
\(503\) −9.57192 + 29.4594i −0.426791 + 1.31353i 0.474478 + 0.880267i \(0.342637\pi\)
−0.901269 + 0.433260i \(0.857363\pi\)
\(504\) 0.0112274 + 0.00815717i 0.000500107 + 0.000363349i
\(505\) 7.20034 0.320411
\(506\) 2.14850 + 4.83115i 0.0955124 + 0.214771i
\(507\) −19.0437 −0.845761
\(508\) −4.40557 3.20083i −0.195465 0.142014i
\(509\) −0.221942 + 0.683067i −0.00983741 + 0.0302764i −0.955855 0.293840i \(-0.905067\pi\)
0.946017 + 0.324116i \(0.105067\pi\)
\(510\) 4.91349 + 15.1222i 0.217573 + 0.669620i
\(511\) −1.62796 + 1.18278i −0.0720167 + 0.0523232i
\(512\) 0.809017 0.587785i 0.0357538 0.0259767i
\(513\) −1.58833 4.88838i −0.0701265 0.215827i
\(514\) 6.44755 19.8435i 0.284389 0.875260i
\(515\) −19.1258 13.8957i −0.842782 0.612317i
\(516\) 9.93072 0.437176
\(517\) 17.0712 15.3578i 0.750790 0.675435i
\(518\) −0.230204 −0.0101146
\(519\) 12.8035 + 9.30232i 0.562013 + 0.408327i
\(520\) −1.34842 + 4.15002i −0.0591323 + 0.181990i
\(521\) −2.93162 9.02259i −0.128436 0.395287i 0.866075 0.499914i \(-0.166635\pi\)
−0.994512 + 0.104627i \(0.966635\pi\)
\(522\) 0.180833 0.131383i 0.00791484 0.00575047i
\(523\) −35.7352 + 25.9631i −1.56259 + 1.13529i −0.628745 + 0.777612i \(0.716431\pi\)
−0.933845 + 0.357677i \(0.883569\pi\)
\(524\) −5.42064 16.6830i −0.236802 0.728801i
\(525\) 0.472910 1.45547i 0.0206395 0.0635218i
\(526\) 0.361158 + 0.262397i 0.0157473 + 0.0114411i
\(527\) 9.67712 0.421542
\(528\) 1.20931 5.67744i 0.0526284 0.247079i
\(529\) −20.4585 −0.889502
\(530\) −3.62673 2.63497i −0.157535 0.114456i
\(531\) −0.00393271 + 0.0121036i −0.000170665 + 0.000525253i
\(532\) 0.0678059 + 0.208685i 0.00293976 + 0.00904765i
\(533\) −6.75598 + 4.90851i −0.292634 + 0.212611i
\(534\) −8.94917 + 6.50195i −0.387268 + 0.281367i
\(535\) −2.98823 9.19683i −0.129193 0.397614i
\(536\) 1.81649 5.59059i 0.0784606 0.241477i
\(537\) −28.3602 20.6049i −1.22383 0.889166i
\(538\) −6.10747 −0.263312
\(539\) −22.9314 + 2.40030i −0.987726 + 0.103388i
\(540\) 15.4069 0.663008
\(541\) 20.0191 + 14.5447i 0.860687 + 0.625325i 0.928072 0.372402i \(-0.121466\pi\)
−0.0673851 + 0.997727i \(0.521466\pi\)
\(542\) −1.84693 + 5.68428i −0.0793326 + 0.244161i
\(543\) 4.38615 + 13.4992i 0.188228 + 0.579306i
\(544\) 2.45198 1.78147i 0.105128 0.0763798i
\(545\) 45.1619 32.8120i 1.93452 1.40551i
\(546\) 0.172761 + 0.531703i 0.00739348 + 0.0227548i
\(547\) 10.3536 31.8652i 0.442690 1.36246i −0.442308 0.896863i \(-0.645840\pi\)
0.884998 0.465595i \(-0.154160\pi\)
\(548\) −9.89559 7.18957i −0.422719 0.307123i
\(549\) 0.714747 0.0305047
\(550\) −13.1447 + 1.37589i −0.560491 + 0.0586682i
\(551\) 3.53414 0.150560
\(552\) −2.25731 1.64003i −0.0960773 0.0698042i
\(553\) 0.351932 1.08313i 0.0149657 0.0460596i
\(554\) −4.67920 14.4011i −0.198800 0.611844i
\(555\) 4.45281 3.23515i 0.189011 0.137325i
\(556\) −9.34020 + 6.78605i −0.396113 + 0.287793i
\(557\) −8.74395 26.9111i −0.370493 1.14026i −0.946469 0.322794i \(-0.895378\pi\)
0.575976 0.817466i \(-0.304622\pi\)
\(558\) −0.0624029 + 0.192056i −0.00264173 + 0.00813040i
\(559\) 6.68243 + 4.85507i 0.282637 + 0.205348i
\(560\) −0.657722 −0.0277938
\(561\) 3.66519 17.2073i 0.154744 0.726491i
\(562\) 17.6245 0.743444
\(563\) 12.2817 + 8.92317i 0.517611 + 0.376067i 0.815703 0.578471i \(-0.196350\pi\)
−0.298092 + 0.954537i \(0.596350\pi\)
\(564\) −3.74456 + 11.5246i −0.157674 + 0.485272i
\(565\) −15.9683 49.1455i −0.671793 2.06757i
\(566\) 23.4898 17.0663i 0.987351 0.717352i
\(567\) 1.63064 1.18473i 0.0684803 0.0497538i
\(568\) −1.05854 3.25785i −0.0444154 0.136696i
\(569\) 6.79777 20.9214i 0.284977 0.877070i −0.701428 0.712740i \(-0.747454\pi\)
0.986405 0.164330i \(-0.0525462\pi\)
\(570\) −4.24430 3.08366i −0.177774 0.129160i
\(571\) −16.0273 −0.670724 −0.335362 0.942089i \(-0.608859\pi\)
−0.335362 + 0.942089i \(0.608859\pi\)
\(572\) 3.58941 3.22915i 0.150081 0.135018i
\(573\) 28.8751 1.20627
\(574\) −1.01833 0.739857i −0.0425041 0.0308810i
\(575\) −1.96311 + 6.04182i −0.0818672 + 0.251961i
\(576\) 0.0195442 + 0.0601509i 0.000814342 + 0.00250629i
\(577\) 37.3881 27.1640i 1.55649 1.13085i 0.617669 0.786438i \(-0.288077\pi\)
0.938818 0.344415i \(-0.111923\pi\)
\(578\) −6.32179 + 4.59305i −0.262952 + 0.191046i
\(579\) 9.73613 + 29.9647i 0.404620 + 1.24529i
\(580\) −3.27359 + 10.0751i −0.135928 + 0.418344i
\(581\) −0.917604 0.666678i −0.0380686 0.0276585i
\(582\) −7.39434 −0.306505
\(583\) 2.01555 + 4.53221i 0.0834756 + 0.187705i
\(584\) −9.17067 −0.379485
\(585\) −0.223273 0.162218i −0.00923122 0.00670688i
\(586\) 5.62139 17.3009i 0.232218 0.714692i
\(587\) 2.48129 + 7.63663i 0.102414 + 0.315197i 0.989115 0.147146i \(-0.0470087\pi\)
−0.886701 + 0.462343i \(0.847009\pi\)
\(588\) 9.84349 7.15172i 0.405939 0.294932i
\(589\) −2.58312 + 1.87675i −0.106436 + 0.0773300i
\(590\) −0.186386 0.573637i −0.00767339 0.0236163i
\(591\) 6.70903 20.6483i 0.275973 0.849357i
\(592\) −0.848762 0.616661i −0.0348839 0.0253446i
\(593\) 15.3857 0.631813 0.315907 0.948790i \(-0.397691\pi\)
0.315907 + 0.948790i \(0.397691\pi\)
\(594\) −14.7597 8.52993i −0.605599 0.349987i
\(595\) −1.99343 −0.0817228
\(596\) 8.82362 + 6.41074i 0.361430 + 0.262594i
\(597\) 12.0624 37.1242i 0.493680 1.51939i
\(598\) −0.717151 2.20716i −0.0293265 0.0902577i
\(599\) 6.98936 5.07806i 0.285577 0.207484i −0.435769 0.900058i \(-0.643524\pi\)
0.721346 + 0.692574i \(0.243524\pi\)
\(600\) 5.64246 4.09948i 0.230352 0.167361i
\(601\) 6.05009 + 18.6203i 0.246788 + 0.759537i 0.995337 + 0.0964569i \(0.0307510\pi\)
−0.748549 + 0.663080i \(0.769249\pi\)
\(602\) −0.384731 + 1.18408i −0.0156805 + 0.0482596i
\(603\) 0.300777 + 0.218527i 0.0122486 + 0.00889912i
\(604\) 16.6567 0.677753
\(605\) 30.1103 + 13.4368i 1.22416 + 0.546282i
\(606\) 4.20423 0.170785
\(607\) 25.6557 + 18.6399i 1.04133 + 0.756571i 0.970545 0.240920i \(-0.0774492\pi\)
0.0707863 + 0.997492i \(0.477449\pi\)
\(608\) −0.309017 + 0.951057i −0.0125323 + 0.0385704i
\(609\) 0.419414 + 1.29082i 0.0169955 + 0.0523068i
\(610\) −27.4051 + 19.9110i −1.10960 + 0.806172i
\(611\) −8.15402 + 5.92424i −0.329876 + 0.239669i
\(612\) 0.0592349 + 0.182306i 0.00239443 + 0.00736929i
\(613\) 11.6976 36.0016i 0.472463 1.45409i −0.376886 0.926260i \(-0.623005\pi\)
0.849349 0.527832i \(-0.176995\pi\)
\(614\) −17.0121 12.3600i −0.686552 0.498809i
\(615\) 30.0948 1.21354
\(616\) 0.630094 + 0.364143i 0.0253872 + 0.0146718i
\(617\) 21.5474 0.867465 0.433733 0.901042i \(-0.357196\pi\)
0.433733 + 0.901042i \(0.357196\pi\)
\(618\) −11.1674 8.11360i −0.449219 0.326377i
\(619\) −7.44437 + 22.9114i −0.299215 + 0.920888i 0.682559 + 0.730831i \(0.260867\pi\)
−0.981773 + 0.190057i \(0.939133\pi\)
\(620\) −2.95751 9.10228i −0.118776 0.365556i
\(621\) −6.62915 + 4.81636i −0.266019 + 0.193274i
\(622\) 14.5626 10.5803i 0.583906 0.424232i
\(623\) −0.428550 1.31894i −0.0171695 0.0528423i
\(624\) −0.787336 + 2.42317i −0.0315187 + 0.0970045i
\(625\) 23.4979 + 17.0722i 0.939916 + 0.682889i
\(626\) 0.228953 0.00915081
\(627\) 2.35876 + 5.30396i 0.0941999 + 0.211820i
\(628\) 22.0535 0.880029
\(629\) −2.57244 1.86899i −0.102570 0.0745214i
\(630\) 0.0128547 0.0395626i 0.000512142 0.00157621i
\(631\) 14.6854 + 45.1970i 0.584616 + 1.79926i 0.600807 + 0.799394i \(0.294846\pi\)
−0.0161906 + 0.999869i \(0.505154\pi\)
\(632\) 4.19903 3.05077i 0.167028 0.121353i
\(633\) 29.7303 21.6004i 1.18167 0.858537i
\(634\) 4.64173 + 14.2858i 0.184347 + 0.567361i
\(635\) −5.04410 + 15.5241i −0.200169 + 0.616057i
\(636\) −2.11763 1.53855i −0.0839693 0.0610073i
\(637\) 10.1202 0.400975
\(638\) 8.71407 7.83945i 0.344993 0.310367i
\(639\) 0.216651 0.00857058
\(640\) −2.42502 1.76188i −0.0958572 0.0696443i
\(641\) −10.9912 + 33.8275i −0.434127 + 1.33610i 0.459852 + 0.887995i \(0.347902\pi\)
−0.893979 + 0.448109i \(0.852098\pi\)
\(642\) −1.74481 5.36997i −0.0688621 0.211936i
\(643\) −18.5467 + 13.4750i −0.731411 + 0.531401i −0.890010 0.455942i \(-0.849303\pi\)
0.158598 + 0.987343i \(0.449303\pi\)
\(644\) 0.282999 0.205611i 0.0111517 0.00810220i
\(645\) −9.19857 28.3103i −0.362193 1.11472i
\(646\) −0.936573 + 2.88248i −0.0368490 + 0.113410i
\(647\) 2.81107 + 2.04236i 0.110515 + 0.0802935i 0.641670 0.766981i \(-0.278242\pi\)
−0.531155 + 0.847274i \(0.678242\pi\)
\(648\) 9.18574 0.360850
\(649\) −0.139034 + 0.652732i −0.00545755 + 0.0256220i
\(650\) 5.80105 0.227536
\(651\) −0.992021 0.720745i −0.0388804 0.0282482i
\(652\) −5.48892 + 16.8931i −0.214963 + 0.661587i
\(653\) 11.2709 + 34.6883i 0.441065 + 1.35746i 0.886742 + 0.462265i \(0.152963\pi\)
−0.445677 + 0.895194i \(0.647037\pi\)
\(654\) 26.3697 19.1587i 1.03114 0.749166i
\(655\) −42.5386 + 30.9061i −1.66212 + 1.20760i
\(656\) −1.77266 5.45570i −0.0692109 0.213009i
\(657\) 0.179233 0.551624i 0.00699256 0.0215209i
\(658\) −1.22905 0.892958i −0.0479134 0.0348111i
\(659\) 40.0640 1.56067 0.780335 0.625361i \(-0.215048\pi\)
0.780335 + 0.625361i \(0.215048\pi\)
\(660\) −17.3053 + 1.81139i −0.673606 + 0.0705083i
\(661\) 42.6426 1.65861 0.829303 0.558799i \(-0.188738\pi\)
0.829303 + 0.558799i \(0.188738\pi\)
\(662\) −12.9606 9.41642i −0.503728 0.365980i
\(663\) −2.38627 + 7.34418i −0.0926750 + 0.285224i
\(664\) −1.59733 4.91608i −0.0619884 0.190781i
\(665\) 0.532108 0.386599i 0.0206343 0.0149917i
\(666\) 0.0536811 0.0390016i 0.00208010 0.00151128i
\(667\) −1.74104 5.35837i −0.0674133 0.207477i
\(668\) 5.97192 18.3797i 0.231061 0.711131i
\(669\) −33.2176 24.1340i −1.28427 0.933075i
\(670\) −17.6201 −0.680724
\(671\) 37.2775 3.90194i 1.43908 0.150633i
\(672\) −0.384040 −0.0148147
\(673\) −13.3643 9.70974i −0.515156 0.374283i 0.299620 0.954059i \(-0.403140\pi\)
−0.814776 + 0.579776i \(0.803140\pi\)
\(674\) 8.25977 25.4210i 0.318154 0.979178i
\(675\) −6.32937 19.4798i −0.243618 0.749778i
\(676\) 8.80275 6.39557i 0.338567 0.245983i
\(677\) 5.41342 3.93308i 0.208055 0.151161i −0.478878 0.877881i \(-0.658957\pi\)
0.686933 + 0.726721i \(0.258957\pi\)
\(678\) −9.32382 28.6958i −0.358079 1.10205i
\(679\) 0.286468 0.881658i 0.0109936 0.0338349i
\(680\) −7.34978 5.33993i −0.281851 0.204777i
\(681\) −28.0850 −1.07622
\(682\) −2.20614 + 10.3573i −0.0844775 + 0.396603i
\(683\) −16.9752 −0.649536 −0.324768 0.945794i \(-0.605286\pi\)
−0.324768 + 0.945794i \(0.605286\pi\)
\(684\) −0.0511674 0.0371753i −0.00195643 0.00142143i
\(685\) −11.3298 + 34.8696i −0.432891 + 1.33230i
\(686\) 0.946018 + 2.91154i 0.0361191 + 0.111163i
\(687\) 35.6340 25.8896i 1.35952 0.987752i
\(688\) −4.59037 + 3.33510i −0.175006 + 0.127149i
\(689\) −0.672775 2.07059i −0.0256307 0.0788831i
\(690\) −2.58447 + 7.95419i −0.0983892 + 0.302811i
\(691\) 21.5236 + 15.6378i 0.818796 + 0.594890i 0.916367 0.400338i \(-0.131107\pi\)
−0.0975713 + 0.995229i \(0.531107\pi\)
\(692\) −9.04236 −0.343739
\(693\) −0.0342182 + 0.0307838i −0.00129984 + 0.00116938i
\(694\) −8.93937 −0.339334
\(695\) 27.9971 + 20.3411i 1.06199 + 0.771581i
\(696\) −1.91143 + 5.88277i −0.0724524 + 0.222986i
\(697\) −5.37261 16.5352i −0.203502 0.626315i
\(698\) −10.8292 + 7.86786i −0.409890 + 0.297803i
\(699\) −26.0583 + 18.9325i −0.985617 + 0.716093i
\(700\) 0.270201 + 0.831594i 0.0102126 + 0.0314313i
\(701\) −1.98897 + 6.12142i −0.0751224 + 0.231203i −0.981566 0.191124i \(-0.938787\pi\)
0.906443 + 0.422327i \(0.138787\pi\)
\(702\) 6.05345 + 4.39809i 0.228473 + 0.165995i
\(703\) 1.04913 0.0395686
\(704\) 1.34770 + 3.03046i 0.0507933 + 0.114215i
\(705\) 36.3225 1.36798
\(706\) −14.9930 10.8930i −0.564267 0.409964i
\(707\) −0.162878 + 0.501288i −0.00612567 + 0.0188529i
\(708\) −0.108830 0.334943i −0.00409007 0.0125879i
\(709\) −18.2733 + 13.2763i −0.686267 + 0.498602i −0.875431 0.483343i \(-0.839422\pi\)
0.189164 + 0.981946i \(0.439422\pi\)
\(710\) −8.30691 + 6.03533i −0.311753 + 0.226502i
\(711\) 0.101440 + 0.312200i 0.00380429 + 0.0117084i
\(712\) 1.95306 6.01091i 0.0731941 0.225268i
\(713\) 4.11800 + 2.99190i 0.154220 + 0.112048i
\(714\) −1.16395 −0.0435599
\(715\) −12.5304 7.24154i −0.468609 0.270818i
\(716\) 20.0291 0.748521
\(717\) −8.13345 5.90930i −0.303749 0.220687i
\(718\) 1.24924 3.84476i 0.0466212 0.143485i
\(719\) 8.06688 + 24.8273i 0.300844 + 0.925902i 0.981196 + 0.193016i \(0.0618270\pi\)
−0.680352 + 0.732886i \(0.738173\pi\)
\(720\) 0.153374 0.111432i 0.00571589 0.00415284i
\(721\) 1.40006 1.01720i 0.0521410 0.0378827i
\(722\) −0.309017 0.951057i −0.0115004 0.0353947i
\(723\) 8.26092 25.4245i 0.307227 0.945547i
\(724\) −6.56097 4.76682i −0.243836 0.177158i
\(725\) 14.0833 0.523040
\(726\) 17.5812 + 7.84564i 0.652500 + 0.291179i
\(727\) 41.2022 1.52810 0.764052 0.645155i \(-0.223207\pi\)
0.764052 + 0.645155i \(0.223207\pi\)
\(728\) −0.258422 0.187755i −0.00957776 0.00695865i
\(729\) 8.16022 25.1146i 0.302230 0.930170i
\(730\) 8.49455 + 26.1435i 0.314397 + 0.967616i
\(731\) −13.9126 + 10.1081i −0.514575 + 0.373860i
\(732\) −16.0017 + 11.6259i −0.591439 + 0.429706i
\(733\) 1.83470 + 5.64662i 0.0677661 + 0.208563i 0.979205 0.202872i \(-0.0650277\pi\)
−0.911439 + 0.411435i \(0.865028\pi\)
\(734\) −6.12685 + 18.8565i −0.226146 + 0.696007i
\(735\) −29.5057 21.4372i −1.08834 0.790722i
\(736\) 1.59420 0.0587628
\(737\) 16.8800 + 9.75525i 0.621781 + 0.359339i
\(738\) 0.362810 0.0133552
\(739\) 21.6501 + 15.7297i 0.796412 + 0.578627i 0.909859 0.414917i \(-0.136189\pi\)
−0.113448 + 0.993544i \(0.536189\pi\)
\(740\) −0.971779 + 2.99083i −0.0357233 + 0.109945i
\(741\) −0.787336 2.42317i −0.0289235 0.0890174i
\(742\) 0.265487 0.192888i 0.00974634 0.00708113i
\(743\) 15.0272 10.9179i 0.551295 0.400539i −0.276968 0.960879i \(-0.589330\pi\)
0.828263 + 0.560340i \(0.189330\pi\)
\(744\) −1.72687 5.31477i −0.0633102 0.194849i
\(745\) 10.1025 31.0923i 0.370127 1.13913i
\(746\) 0.304033 + 0.220893i 0.0111314 + 0.00808747i
\(747\) 0.326925 0.0119616
\(748\) 4.08463 + 9.18477i 0.149349 + 0.335828i
\(749\) 0.707881 0.0258654
\(750\) 4.30830 + 3.13016i 0.157317 + 0.114297i
\(751\) −3.50991 + 10.8024i −0.128078 + 0.394185i −0.994449 0.105216i \(-0.966447\pi\)
0.866371 + 0.499401i \(0.166447\pi\)
\(752\) −2.13949 6.58466i −0.0780191 0.240118i
\(753\) −25.7629 + 18.7178i −0.938852 + 0.682116i
\(754\) −4.16225 + 3.02406i −0.151580 + 0.110130i
\(755\) −15.4287 47.4846i −0.561508 1.72814i
\(756\) −0.348519 + 1.07263i −0.0126755 + 0.0390112i
\(757\) −24.0382 17.4647i −0.873681 0.634767i 0.0578908 0.998323i \(-0.481562\pi\)
−0.931572 + 0.363556i \(0.881562\pi\)
\(758\) −25.6301 −0.930929
\(759\) 6.87970 6.18919i 0.249717 0.224653i
\(760\) 2.99749 0.108730
\(761\) 21.9856 + 15.9735i 0.796977 + 0.579038i 0.910026 0.414552i \(-0.136062\pi\)
−0.113049 + 0.993589i \(0.536062\pi\)
\(762\) −2.94522 + 9.06445i −0.106694 + 0.328370i
\(763\) 1.26277 + 3.88641i 0.0457154 + 0.140698i
\(764\) −13.3472 + 9.69731i −0.482885 + 0.350836i
\(765\) 0.464847 0.337731i 0.0168066 0.0122107i
\(766\) 8.47121 + 26.0717i 0.306077 + 0.942009i
\(767\) 0.0905196 0.278591i 0.00326847 0.0100593i
\(768\) −1.41595 1.02875i −0.0510938 0.0371218i
\(769\) −14.8422 −0.535222 −0.267611 0.963527i \(-0.586234\pi\)
−0.267611 + 0.963527i \(0.586234\pi\)
\(770\) 0.454453 2.13355i 0.0163773 0.0768880i
\(771\) −36.5177 −1.31515
\(772\) −14.5637 10.5811i −0.524158 0.380823i
\(773\) 5.25711 16.1797i 0.189085 0.581945i −0.810910 0.585172i \(-0.801027\pi\)
0.999995 + 0.00322699i \(0.00102719\pi\)
\(774\) −0.110894 0.341297i −0.00398600 0.0122677i
\(775\) −10.2935 + 7.47868i −0.369754 + 0.268642i
\(776\) 3.41795 2.48329i 0.122697 0.0891448i
\(777\) 0.124505 + 0.383187i 0.00446659 + 0.0137468i
\(778\) 3.58817 11.0433i 0.128642 0.395920i
\(779\) 4.64089 + 3.37181i 0.166277 + 0.120807i
\(780\) 7.63721 0.273456
\(781\) 11.2994 1.18274i 0.404324 0.0423217i
\(782\) 4.83171 0.172782
\(783\) 14.6960 + 10.6773i 0.525194 + 0.381576i
\(784\) −2.14824 + 6.61160i −0.0767229 + 0.236129i
\(785\) −20.4276 62.8696i −0.729091 2.24391i
\(786\) −24.8380 + 18.0459i −0.885942 + 0.643675i
\(787\) −36.2184 + 26.3142i −1.29105 + 0.938001i −0.999826 0.0186550i \(-0.994062\pi\)
−0.291221 + 0.956656i \(0.594062\pi\)
\(788\) 3.83327 + 11.7976i 0.136554 + 0.420271i
\(789\) 0.241442 0.743083i 0.00859558 0.0264545i
\(790\) −12.5865 9.14464i −0.447808 0.325352i
\(791\) 3.78273 0.134499
\(792\) −0.208625 + 0.0218373i −0.00741316 + 0.000775956i
\(793\) −16.4514 −0.584207
\(794\) 10.3726 + 7.53616i 0.368111 + 0.267448i
\(795\) −2.42455 + 7.46200i −0.0859899 + 0.264650i
\(796\) 6.89194 + 21.2112i 0.244278 + 0.751812i
\(797\) 33.5931 24.4068i 1.18993 0.864533i 0.196671 0.980470i \(-0.436987\pi\)
0.993257 + 0.115937i \(0.0369869\pi\)
\(798\) 0.310695 0.225733i 0.0109985 0.00799086i
\(799\) −6.48439 19.9569i −0.229401 0.706024i
\(800\) −1.23141 + 3.78988i −0.0435369 + 0.133993i
\(801\) 0.323390 + 0.234957i 0.0114264 + 0.00830179i
\(802\) −20.1472 −0.711423
\(803\) 6.33647 29.7483i 0.223609 1.04979i
\(804\) −10.2883 −0.362839
\(805\) −0.848285 0.616315i −0.0298981 0.0217223i
\(806\) 1.43634 4.42059i 0.0505928 0.155709i
\(807\) 3.30320 + 10.1662i 0.116278 + 0.357867i
\(808\) −1.94336 + 1.41193i −0.0683672 + 0.0496717i
\(809\) −45.7238 + 33.2203i −1.60756 + 1.16796i −0.737015 + 0.675877i \(0.763765\pi\)
−0.870547 + 0.492085i \(0.836235\pi\)
\(810\) −8.50851 26.1865i −0.298959 0.920100i
\(811\) −6.14937 + 18.9258i −0.215934 + 0.664576i 0.783152 + 0.621830i \(0.213610\pi\)
−0.999086 + 0.0427456i \(0.986390\pi\)
\(812\) −0.627375 0.455815i −0.0220165 0.0159960i
\(813\) 10.4607 0.366872
\(814\) 2.58681 2.32718i 0.0906677 0.0815675i
\(815\) 53.2429 1.86502
\(816\) −4.29149 3.11795i −0.150232 0.109150i
\(817\) 1.75337 5.39630i 0.0613425 0.188793i
\(818\) −1.53406 4.72136i −0.0536372 0.165078i
\(819\) 0.0163443 0.0118748i 0.000571115 0.000414939i
\(820\) −13.9110 + 10.1069i −0.485793 + 0.352950i
\(821\) 13.0671 + 40.2163i 0.456044 + 1.40356i 0.869906 + 0.493218i \(0.164180\pi\)
−0.413862 + 0.910340i \(0.635820\pi\)
\(822\) −6.61542 + 20.3602i −0.230739 + 0.710142i
\(823\) 9.56358 + 6.94835i 0.333366 + 0.242204i 0.741857 0.670558i \(-0.233945\pi\)
−0.408492 + 0.912762i \(0.633945\pi\)
\(824\) 7.88686 0.274752
\(825\) 9.39948 + 21.1358i 0.327248 + 0.735856i
\(826\) 0.0441529 0.00153627
\(827\) −1.80096 1.30848i −0.0626256 0.0455001i 0.556032 0.831161i \(-0.312323\pi\)
−0.618658 + 0.785661i \(0.712323\pi\)
\(828\) −0.0311573 + 0.0958923i −0.00108279 + 0.00333249i
\(829\) −5.83372 17.9544i −0.202614 0.623581i −0.999803 0.0198512i \(-0.993681\pi\)
0.797189 0.603729i \(-0.206319\pi\)
\(830\) −12.5351 + 9.10727i −0.435099 + 0.316118i
\(831\) −21.4406 + 15.5775i −0.743768 + 0.540379i
\(832\) −0.449851 1.38450i −0.0155958 0.0479989i
\(833\) −6.51092 + 20.0385i −0.225590 + 0.694295i
\(834\) 16.3473 + 11.8770i 0.566062 + 0.411268i
\(835\) −57.9280 −2.00468
\(836\) −2.87157 1.65954i −0.0993154 0.0573963i
\(837\) −16.4114 −0.567261
\(838\) −30.2113 21.9498i −1.04363 0.758243i
\(839\) 5.55633 17.1006i 0.191826 0.590379i −0.808173 0.588945i \(-0.799544\pi\)
0.999999 0.00143402i \(-0.000456462\pi\)
\(840\) 0.355726 + 1.09481i 0.0122737 + 0.0377746i
\(841\) 13.3567 9.70423i 0.460577 0.334629i
\(842\) 17.4827 12.7020i 0.602495 0.437738i
\(843\) −9.53213 29.3369i −0.328304 1.01042i
\(844\) −6.48834 + 19.9691i −0.223338 + 0.687363i
\(845\) −26.3861 19.1706i −0.907710 0.659490i
\(846\) 0.437888 0.0150549
\(847\) −1.61659 + 1.79233i −0.0555467 + 0.0615851i
\(848\) 1.49555 0.0513574
\(849\) −41.1122 29.8697i −1.41097 1.02513i
\(850\) −3.73217 + 11.4864i −0.128012 + 0.393982i
\(851\) −0.516835 1.59066i −0.0177169 0.0545270i
\(852\) −4.85036 + 3.52399i −0.166170 + 0.120730i
\(853\) −43.3231 + 31.4761i −1.48336 + 1.07772i −0.506899 + 0.862005i \(0.669208\pi\)
−0.976456 + 0.215715i \(0.930792\pi\)
\(854\) −0.766275 2.35835i −0.0262214 0.0807011i
\(855\) −0.0585835 + 0.180301i −0.00200351 + 0.00616618i
\(856\) 2.60995 + 1.89624i 0.0892063 + 0.0648122i
\(857\) −6.51232 −0.222457 −0.111228 0.993795i \(-0.535478\pi\)
−0.111228 + 0.993795i \(0.535478\pi\)
\(858\) −7.31640 4.22829i −0.249778 0.144351i
\(859\) −23.9426 −0.816912 −0.408456 0.912778i \(-0.633933\pi\)
−0.408456 + 0.912778i \(0.633933\pi\)
\(860\) 13.7596 + 9.99691i 0.469197 + 0.340892i
\(861\) −0.680773 + 2.09520i −0.0232007 + 0.0714044i
\(862\) −0.646818 1.99070i −0.0220307 0.0678035i
\(863\) −0.336499 + 0.244481i −0.0114545 + 0.00832222i −0.593498 0.804836i \(-0.702253\pi\)
0.582043 + 0.813158i \(0.302253\pi\)
\(864\) −4.15830 + 3.02118i −0.141468 + 0.102783i
\(865\) 8.37570 + 25.7778i 0.284782 + 0.876470i
\(866\) −2.11269 + 6.50218i −0.0717920 + 0.220953i
\(867\) 11.0645 + 8.03882i 0.375769 + 0.273013i
\(868\) 0.700603 0.0237800
\(869\) 6.99494 + 15.7290i 0.237287 + 0.533568i
\(870\) 18.5410 0.628598
\(871\) −6.92302 5.02987i −0.234578 0.170431i
\(872\) −5.75492 + 17.7118i −0.194886 + 0.599799i
\(873\) 0.0825708 + 0.254127i 0.00279460 + 0.00860089i
\(874\) −1.28973 + 0.937045i −0.0436258 + 0.0316960i
\(875\) −0.540132 + 0.392429i −0.0182598 + 0.0132665i
\(876\) 4.95991 + 15.2650i 0.167580 + 0.515758i
\(877\) 4.44931 13.6936i 0.150242 0.462399i −0.847405 0.530946i \(-0.821837\pi\)
0.997648 + 0.0685477i \(0.0218365\pi\)
\(878\) −6.61034 4.80269i −0.223088 0.162083i
\(879\) −31.8385 −1.07389
\(880\) 7.39084 6.64903i 0.249145 0.224139i
\(881\) 28.5670 0.962447 0.481223 0.876598i \(-0.340193\pi\)
0.481223 + 0.876598i \(0.340193\pi\)
\(882\) −0.355708 0.258437i −0.0119773 0.00870203i
\(883\) −10.2561 + 31.5651i −0.345146 + 1.06225i 0.616360 + 0.787464i \(0.288607\pi\)
−0.961506 + 0.274785i \(0.911393\pi\)
\(884\) −1.36342 4.19616i −0.0458567 0.141132i
\(885\) −0.854042 + 0.620498i −0.0287083 + 0.0208578i
\(886\) −2.85392 + 2.07349i −0.0958792 + 0.0696603i
\(887\) 6.63500 + 20.4204i 0.222781 + 0.685650i 0.998509 + 0.0545829i \(0.0173829\pi\)
−0.775728 + 0.631068i \(0.782617\pi\)
\(888\) −0.567416 + 1.74633i −0.0190412 + 0.0586029i
\(889\) −0.966689 0.702341i −0.0324217 0.0235558i
\(890\) −18.9448 −0.635033
\(891\) −6.34688 + 29.7972i −0.212628 + 0.998244i
\(892\) 23.4596 0.785484
\(893\) 5.60125 + 4.06955i 0.187439 + 0.136182i
\(894\) 5.89878 18.1546i 0.197285 0.607180i
\(895\) −18.5524 57.0984i −0.620138 1.90859i
\(896\) 0.177518 0.128975i 0.00593047 0.00430874i
\(897\) −3.28607 + 2.38747i −0.109719 + 0.0797153i
\(898\) 3.20821 + 9.87386i 0.107059 + 0.329495i
\(899\) 3.48701 10.7319i 0.116298 0.357930i
\(900\) −0.203898 0.148141i −0.00679660 0.00493802i
\(901\) 4.53273 0.151007
\(902\) 18.9223 1.98065i 0.630044 0.0659485i
\(903\) 2.17905 0.0725141
\(904\) 13.9469 + 10.1330i 0.463867 + 0.337019i
\(905\) −7.51190 + 23.1193i −0.249704 + 0.768510i
\(906\) −9.00872 27.7260i −0.299295 0.921134i
\(907\) 35.6368 25.8917i 1.18330 0.859719i 0.190762 0.981636i \(-0.438904\pi\)
0.992540 + 0.121917i \(0.0389042\pi\)
\(908\) 12.9820 9.43196i 0.430822 0.313011i
\(909\) −0.0469476 0.144490i −0.00155715 0.00479243i
\(910\) −0.295877 + 0.910616i −0.00980823 + 0.0301866i
\(911\) 32.6393 + 23.7139i 1.08139 + 0.785676i 0.977925 0.208958i \(-0.0670071\pi\)
0.103465 + 0.994633i \(0.467007\pi\)
\(912\) 1.75021 0.0579554
\(913\) 17.0507 1.78475i 0.564296 0.0590665i
\(914\) 14.2233 0.470464
\(915\) 47.9648 + 34.8485i 1.58567 + 1.15205i
\(916\) −7.77676 + 23.9344i −0.256951 + 0.790815i
\(917\) −1.18942 3.66066i −0.0392782 0.120886i
\(918\) −12.6030 + 9.15665i −0.415962 + 0.302214i
\(919\) −10.2495 + 7.44667i −0.338098 + 0.245643i −0.743859 0.668337i \(-0.767007\pi\)
0.405761 + 0.913979i \(0.367007\pi\)
\(920\) −1.47666 4.54470i −0.0486841 0.149834i
\(921\) −11.3729 + 35.0023i −0.374751 + 1.15337i
\(922\) −7.20062 5.23156i −0.237140 0.172292i
\(923\) −4.98668 −0.164139
\(924\) 0.265352 1.24577i 0.00872944 0.0409828i
\(925\) 4.18069 0.137460
\(926\) −3.71146 2.69653i −0.121966 0.0886136i
\(927\) −0.154142 + 0.474402i −0.00506270 + 0.0155814i
\(928\) −1.09211 3.36117i −0.0358503 0.110336i
\(929\) 8.85034 6.43015i 0.290370 0.210966i −0.433058 0.901366i \(-0.642565\pi\)
0.723428 + 0.690400i \(0.242565\pi\)
\(930\) −13.5517 + 9.84586i −0.444377 + 0.322858i
\(931\) −2.14824 6.61160i −0.0704057 0.216687i
\(932\) 5.68697 17.5027i 0.186283 0.573319i
\(933\) −25.4876 18.5178i −0.834427 0.606246i
\(934\) −11.9153 −0.389880
\(935\) 22.4003 20.1520i 0.732567 0.659040i
\(936\) 0.0920709 0.00300943
\(937\) −29.9216 21.7393i −0.977497 0.710193i −0.0203492 0.999793i \(-0.506478\pi\)
−0.957148 + 0.289600i \(0.906478\pi\)
\(938\) 0.398583 1.22671i 0.0130142 0.0400536i
\(939\) −0.123828 0.381104i −0.00404098 0.0124369i
\(940\) −16.7897 + 12.1984i −0.547619 + 0.397868i
\(941\) −42.7770 + 31.0793i −1.39449 + 1.01316i −0.399135 + 0.916892i \(0.630690\pi\)
−0.995356 + 0.0962648i \(0.969310\pi\)
\(942\) −11.9275 36.7092i −0.388620 1.19605i
\(943\) 2.82597 8.69745i 0.0920263 0.283228i
\(944\) 0.162791 + 0.118275i 0.00529841 + 0.00384952i
\(945\) 3.38065 0.109973
\(946\) −7.64686 17.1949i −0.248621 0.559054i
\(947\) 21.5968 0.701803 0.350902 0.936412i \(-0.385875\pi\)
0.350902 + 0.936412i \(0.385875\pi\)
\(948\) −7.34919 5.33950i −0.238691 0.173419i
\(949\) −4.12544 + 12.6968i −0.133917 + 0.412155i
\(950\) −1.23141 3.78988i −0.0399522 0.122960i
\(951\) 21.2690 15.4528i 0.689693 0.501091i
\(952\) 0.538025 0.390898i 0.0174375 0.0126691i
\(953\) −8.23761 25.3528i −0.266842 0.821256i −0.991263 0.131898i \(-0.957893\pi\)
0.724421 0.689358i \(-0.242107\pi\)
\(954\) −0.0292293 + 0.0899586i −0.000946334 + 0.00291252i
\(955\) 40.0080 + 29.0675i 1.29463 + 0.940603i
\(956\) 5.74415 0.185779
\(957\) −17.7621 10.2651i −0.574168 0.331823i
\(958\) 20.7742 0.671182
\(959\) −2.17134 1.57757i −0.0701161 0.0509423i
\(960\) −1.62118 + 4.98947i −0.0523233 + 0.161034i
\(961\) −6.42920 19.7870i −0.207393 0.638291i
\(962\) −1.23558 + 0.897705i −0.0398368 + 0.0289432i
\(963\) −0.165070 + 0.119930i −0.00531930 + 0.00386470i
\(964\) 4.71995 + 14.5265i 0.152019 + 0.467867i
\(965\) −16.6745 + 51.3188i −0.536771 + 1.65201i
\(966\) −0.495308 0.359863i −0.0159363 0.0115784i
\(967\) −32.4852 −1.04465 −0.522326 0.852746i \(-0.674936\pi\)
−0.522326 + 0.852746i \(0.674936\pi\)
\(968\) −10.7616 + 2.27785i −0.345890 + 0.0732127i
\(969\) 5.30457 0.170407
\(970\) −10.2453 7.44362i −0.328956 0.239000i
\(971\) −9.66085 + 29.7330i −0.310031 + 0.954178i 0.667720 + 0.744412i \(0.267270\pi\)
−0.977752 + 0.209766i \(0.932730\pi\)
\(972\) −0.203076 0.625003i −0.00651366 0.0200470i
\(973\) −2.04947 + 1.48903i −0.0657029 + 0.0477360i
\(974\) 7.36978 5.35446i 0.236143 0.171568i
\(975\) −3.13747 9.65614i −0.100479 0.309244i
\(976\) 3.49220 10.7479i 0.111783 0.344032i
\(977\) 11.2967 + 8.20752i 0.361413 + 0.262582i 0.753641 0.657286i \(-0.228296\pi\)
−0.392228 + 0.919868i \(0.628296\pi\)
\(978\) 31.0882 0.994090
\(979\) 18.1490 + 10.4887i 0.580046 + 0.335220i
\(980\) 20.8381 0.665648
\(981\) −0.952907 0.692328i −0.0304240 0.0221043i
\(982\) −4.33395 + 13.3385i −0.138302 + 0.425649i
\(983\) −15.5996 48.0105i −0.497549 1.53130i −0.812947 0.582338i \(-0.802138\pi\)
0.315398 0.948959i \(-0.397862\pi\)
\(984\) −8.12255 + 5.90138i −0.258937 + 0.188129i
\(985\) 30.0816 21.8556i 0.958480 0.696377i
\(986\) −3.30998 10.1871i −0.105411 0.324423i
\(987\) −0.821648 + 2.52877i −0.0261533 + 0.0804917i
\(988\) 1.17773 + 0.855668i 0.0374685 + 0.0272224i
\(989\) −9.04548 −0.287630
\(990\) 0.255497 + 0.574515i 0.00812023 + 0.0182593i
\(991\) −17.5153 −0.556392 −0.278196 0.960524i \(-0.589736\pi\)
−0.278196 + 0.960524i \(0.589736\pi\)
\(992\) 2.58312 + 1.87675i 0.0820141 + 0.0595868i
\(993\) −8.66444 + 26.6664i −0.274958 + 0.846233i
\(994\) −0.232270 0.714853i −0.00736715 0.0226737i
\(995\) 54.0846 39.2948i 1.71460 1.24573i
\(996\) −7.31915 + 5.31768i −0.231916 + 0.168497i
\(997\) −12.1545 37.4076i −0.384936 1.18471i −0.936527 0.350596i \(-0.885979\pi\)
0.551591 0.834115i \(-0.314021\pi\)
\(998\) −10.7148 + 32.9767i −0.339170 + 1.04386i
\(999\) 4.36259 + 3.16961i 0.138026 + 0.100282i
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 418.2.f.g.191.4 16
11.3 even 5 inner 418.2.f.g.267.4 yes 16
11.5 even 5 4598.2.a.bw.1.7 8
11.6 odd 10 4598.2.a.bz.1.7 8
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
418.2.f.g.191.4 16 1.1 even 1 trivial
418.2.f.g.267.4 yes 16 11.3 even 5 inner
4598.2.a.bw.1.7 8 11.5 even 5
4598.2.a.bz.1.7 8 11.6 odd 10