Properties

Label 471.2.l.b.50.6
Level $471$
Weight $2$
Character 471.50
Analytic conductor $3.761$
Analytic rank $0$
Dimension $200$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [471,2,Mod(50,471)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(471, base_ring=CyclotomicField(12))
 
chi = DirichletCharacter(H, H._module([6, 11]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("471.50");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 471 = 3 \cdot 157 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 471.l (of order \(12\), 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: \(3.76095393520\)
Analytic rank: \(0\)
Dimension: \(200\)
Relative dimension: \(50\) over \(\Q(\zeta_{12})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label 50.6
Character \(\chi\) \(=\) 471.50
Dual form 471.2.l.b.179.6

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.59659 + 1.59659i) q^{2} +(-1.63950 - 0.558616i) q^{3} -3.09822i q^{4} +(0.704955 + 2.63093i) q^{5} +(3.50949 - 1.72573i) q^{6} +(-1.39752 + 1.39752i) q^{7} +(1.75342 + 1.75342i) q^{8} +(2.37590 + 1.83170i) q^{9} +O(q^{10})\) \(q+(-1.59659 + 1.59659i) q^{2} +(-1.63950 - 0.558616i) q^{3} -3.09822i q^{4} +(0.704955 + 2.63093i) q^{5} +(3.50949 - 1.72573i) q^{6} +(-1.39752 + 1.39752i) q^{7} +(1.75342 + 1.75342i) q^{8} +(2.37590 + 1.83170i) q^{9} +(-5.32605 - 3.07500i) q^{10} +(4.02694 + 2.32495i) q^{11} +(-1.73072 + 5.07952i) q^{12} +(4.50650 - 2.60183i) q^{13} -4.46255i q^{14} +(0.313908 - 4.70719i) q^{15} +0.597461 q^{16} +(-0.558662 - 0.322544i) q^{17} +(-6.71782 + 0.868862i) q^{18} +(-2.80533 + 4.85898i) q^{19} +(8.15120 - 2.18411i) q^{20} +(3.07191 - 1.51055i) q^{21} +(-10.1414 + 2.71738i) q^{22} +(2.97703 + 2.97703i) q^{23} +(-1.89523 - 3.85420i) q^{24} +(-2.09469 + 1.20937i) q^{25} +(-3.04098 + 11.3491i) q^{26} +(-2.87206 - 4.33028i) q^{27} +(4.32984 + 4.32984i) q^{28} +(-6.05852 + 6.05852i) q^{29} +(7.01429 + 8.01666i) q^{30} +(-2.30047 + 1.32818i) q^{31} +(-4.46073 + 4.46073i) q^{32} +(-5.30339 - 6.06127i) q^{33} +(1.40693 - 0.376985i) q^{34} +(-4.66197 - 2.69159i) q^{35} +(5.67501 - 7.36105i) q^{36} +(-3.88246 - 6.72463i) q^{37} +(-3.27884 - 12.2368i) q^{38} +(-8.84181 + 1.74828i) q^{39} +(-3.37703 + 5.84919i) q^{40} +(5.56610 - 5.56610i) q^{41} +(-2.49285 + 7.31634i) q^{42} +(0.280617 - 1.04728i) q^{43} +(7.20322 - 12.4764i) q^{44} +(-3.14417 + 7.54207i) q^{45} -9.50621 q^{46} +(-7.16378 + 4.13601i) q^{47} +(-0.979535 - 0.333751i) q^{48} +3.09386i q^{49} +(1.41350 - 5.27524i) q^{50} +(0.735747 + 0.840887i) q^{51} +(-8.06104 - 13.9621i) q^{52} +(-0.654755 + 2.44358i) q^{53} +(11.4992 + 2.32819i) q^{54} +(-3.27797 + 12.2336i) q^{55} -4.90088 q^{56} +(7.31363 - 6.39917i) q^{57} -19.3460i q^{58} +(-1.29552 + 1.29552i) q^{59} +(-14.5839 - 0.972557i) q^{60} +(13.3430 - 3.57525i) q^{61} +(1.55236 - 5.79349i) q^{62} +(-5.88021 + 0.760528i) q^{63} -13.0490i q^{64} +(10.0221 + 10.0221i) q^{65} +(18.1447 + 1.21002i) q^{66} -10.9325 q^{67} +(-0.999313 + 1.73086i) q^{68} +(-3.21781 - 6.54385i) q^{69} +(11.7407 - 3.14590i) q^{70} +(-6.71764 + 3.87843i) q^{71} +(0.954204 + 7.37766i) q^{72} +(-7.69676 + 2.06234i) q^{73} +(16.9352 + 4.53778i) q^{74} +(4.10981 - 0.812629i) q^{75} +(15.0542 + 8.69154i) q^{76} +(-8.87692 + 2.37856i) q^{77} +(11.3255 - 16.9081i) q^{78} +(4.80864 - 4.80864i) q^{79} +(0.421183 + 1.57188i) q^{80} +(2.28976 + 8.70385i) q^{81} +17.7736i q^{82} +(-1.07444 + 4.00986i) q^{83} +(-4.68004 - 9.51747i) q^{84} +(0.454758 - 1.69718i) q^{85} +(1.22404 + 2.12011i) q^{86} +(13.3173 - 6.54853i) q^{87} +(2.98429 + 11.1375i) q^{88} +(3.02683 + 1.74754i) q^{89} +(-7.02167 - 17.0616i) q^{90} +(-2.66182 + 9.93405i) q^{91} +(9.22350 - 9.22350i) q^{92} +(4.51356 - 0.892463i) q^{93} +(4.83412 - 18.0412i) q^{94} +(-14.7612 - 3.95526i) q^{95} +(9.80519 - 4.82152i) q^{96} +(9.04604 + 2.42388i) q^{97} +(-4.93963 - 4.93963i) q^{98} +(5.30897 + 12.9000i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 200 q - 6 q^{3} - 10 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 200 q - 6 q^{3} - 10 q^{9} - 36 q^{10} - 16 q^{12} - 24 q^{13} + 8 q^{15} - 208 q^{16} + 8 q^{18} - 12 q^{19} - 24 q^{22} - 20 q^{24} - 24 q^{25} + 64 q^{28} - 14 q^{30} - 48 q^{31} + 18 q^{33} + 32 q^{34} + 78 q^{36} + 44 q^{37} - 72 q^{39} + 60 q^{40} + 42 q^{42} - 24 q^{43} - 32 q^{45} - 32 q^{46} - 102 q^{48} - 54 q^{51} + 36 q^{52} + 48 q^{54} - 20 q^{55} - 6 q^{57} - 8 q^{61} - 8 q^{63} - 32 q^{66} - 16 q^{67} - 52 q^{69} + 60 q^{70} - 42 q^{72} - 64 q^{73} - 32 q^{75} + 132 q^{76} + 106 q^{78} + 40 q^{79} + 14 q^{81} + 172 q^{84} - 160 q^{85} - 88 q^{87} + 8 q^{88} + 84 q^{91} + 220 q^{93} + 128 q^{94} - 108 q^{96} - 36 q^{97} - 104 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/471\mathbb{Z}\right)^\times\).

\(n\) \(158\) \(319\)
\(\chi(n)\) \(-1\) \(e\left(\frac{11}{12}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.59659 + 1.59659i −1.12896 + 1.12896i −0.138616 + 0.990346i \(0.544265\pi\)
−0.990346 + 0.138616i \(0.955735\pi\)
\(3\) −1.63950 0.558616i −0.946564 0.322517i
\(4\) 3.09822i 1.54911i
\(5\) 0.704955 + 2.63093i 0.315265 + 1.17659i 0.923742 + 0.383015i \(0.125114\pi\)
−0.608477 + 0.793572i \(0.708219\pi\)
\(6\) 3.50949 1.72573i 1.43274 0.704525i
\(7\) −1.39752 + 1.39752i −0.528214 + 0.528214i −0.920040 0.391825i \(-0.871844\pi\)
0.391825 + 0.920040i \(0.371844\pi\)
\(8\) 1.75342 + 1.75342i 0.619926 + 0.619926i
\(9\) 2.37590 + 1.83170i 0.791965 + 0.610566i
\(10\) −5.32605 3.07500i −1.68424 0.972399i
\(11\) 4.02694 + 2.32495i 1.21417 + 0.701000i 0.963664 0.267116i \(-0.0860706\pi\)
0.250503 + 0.968116i \(0.419404\pi\)
\(12\) −1.73072 + 5.07952i −0.499615 + 1.46633i
\(13\) 4.50650 2.60183i 1.24988 0.721617i 0.278792 0.960351i \(-0.410066\pi\)
0.971085 + 0.238734i \(0.0767326\pi\)
\(14\) 4.46255i 1.19267i
\(15\) 0.313908 4.70719i 0.0810507 1.21539i
\(16\) 0.597461 0.149365
\(17\) −0.558662 0.322544i −0.135496 0.0782284i 0.430720 0.902486i \(-0.358260\pi\)
−0.566215 + 0.824257i \(0.691593\pi\)
\(18\) −6.71782 + 0.868862i −1.58340 + 0.204793i
\(19\) −2.80533 + 4.85898i −0.643587 + 1.11473i 0.341039 + 0.940049i \(0.389221\pi\)
−0.984626 + 0.174676i \(0.944112\pi\)
\(20\) 8.15120 2.18411i 1.82266 0.488381i
\(21\) 3.07191 1.51055i 0.670346 0.329630i
\(22\) −10.1414 + 2.71738i −2.16215 + 0.579347i
\(23\) 2.97703 + 2.97703i 0.620754 + 0.620754i 0.945724 0.324971i \(-0.105354\pi\)
−0.324971 + 0.945724i \(0.605354\pi\)
\(24\) −1.89523 3.85420i −0.386863 0.786736i
\(25\) −2.09469 + 1.20937i −0.418938 + 0.241874i
\(26\) −3.04098 + 11.3491i −0.596386 + 2.22574i
\(27\) −2.87206 4.33028i −0.552727 0.833362i
\(28\) 4.32984 + 4.32984i 0.818263 + 0.818263i
\(29\) −6.05852 + 6.05852i −1.12504 + 1.12504i −0.134067 + 0.990972i \(0.542804\pi\)
−0.990972 + 0.134067i \(0.957196\pi\)
\(30\) 7.01429 + 8.01666i 1.28063 + 1.46364i
\(31\) −2.30047 + 1.32818i −0.413177 + 0.238548i −0.692154 0.721750i \(-0.743338\pi\)
0.278977 + 0.960298i \(0.410005\pi\)
\(32\) −4.46073 + 4.46073i −0.788554 + 0.788554i
\(33\) −5.30339 6.06127i −0.923202 1.05513i
\(34\) 1.40693 0.376985i 0.241286 0.0646524i
\(35\) −4.66197 2.69159i −0.788017 0.454962i
\(36\) 5.67501 7.36105i 0.945835 1.22684i
\(37\) −3.88246 6.72463i −0.638273 1.10552i −0.985812 0.167856i \(-0.946316\pi\)
0.347538 0.937666i \(-0.387018\pi\)
\(38\) −3.27884 12.2368i −0.531898 1.98507i
\(39\) −8.84181 + 1.74828i −1.41582 + 0.279949i
\(40\) −3.37703 + 5.84919i −0.533955 + 0.924838i
\(41\) 5.56610 5.56610i 0.869279 0.869279i −0.123113 0.992393i \(-0.539288\pi\)
0.992393 + 0.123113i \(0.0392879\pi\)
\(42\) −2.49285 + 7.31634i −0.384656 + 1.12894i
\(43\) 0.280617 1.04728i 0.0427937 0.159708i −0.941223 0.337787i \(-0.890322\pi\)
0.984016 + 0.178079i \(0.0569883\pi\)
\(44\) 7.20322 12.4764i 1.08593 1.88088i
\(45\) −3.14417 + 7.54207i −0.468705 + 1.12431i
\(46\) −9.50621 −1.40161
\(47\) −7.16378 + 4.13601i −1.04494 + 0.603299i −0.921230 0.389019i \(-0.872814\pi\)
−0.123715 + 0.992318i \(0.539481\pi\)
\(48\) −0.979535 0.333751i −0.141384 0.0481729i
\(49\) 3.09386i 0.441980i
\(50\) 1.41350 5.27524i 0.199898 0.746031i
\(51\) 0.735747 + 0.840887i 0.103025 + 0.117748i
\(52\) −8.06104 13.9621i −1.11787 1.93620i
\(53\) −0.654755 + 2.44358i −0.0899376 + 0.335652i −0.996203 0.0870567i \(-0.972254\pi\)
0.906266 + 0.422708i \(0.138921\pi\)
\(54\) 11.4992 + 2.32819i 1.56484 + 0.316826i
\(55\) −3.27797 + 12.2336i −0.442002 + 1.64957i
\(56\) −4.90088 −0.654907
\(57\) 7.31363 6.39917i 0.968714 0.847591i
\(58\) 19.3460i 2.54025i
\(59\) −1.29552 + 1.29552i −0.168662 + 0.168662i −0.786391 0.617729i \(-0.788053\pi\)
0.617729 + 0.786391i \(0.288053\pi\)
\(60\) −14.5839 0.972557i −1.88278 0.125557i
\(61\) 13.3430 3.57525i 1.70840 0.457764i 0.733368 0.679832i \(-0.237947\pi\)
0.975031 + 0.222068i \(0.0712805\pi\)
\(62\) 1.55236 5.79349i 0.197150 0.735773i
\(63\) −5.88021 + 0.760528i −0.740837 + 0.0958176i
\(64\) 13.0490i 1.63113i
\(65\) 10.0221 + 10.0221i 1.24309 + 1.24309i
\(66\) 18.1447 + 1.21002i 2.23346 + 0.148943i
\(67\) −10.9325 −1.33562 −0.667811 0.744331i \(-0.732769\pi\)
−0.667811 + 0.744331i \(0.732769\pi\)
\(68\) −0.999313 + 1.73086i −0.121184 + 0.209898i
\(69\) −3.21781 6.54385i −0.387379 0.787787i
\(70\) 11.7407 3.14590i 1.40328 0.376007i
\(71\) −6.71764 + 3.87843i −0.797237 + 0.460285i −0.842504 0.538690i \(-0.818919\pi\)
0.0452671 + 0.998975i \(0.485586\pi\)
\(72\) 0.954204 + 7.37766i 0.112454 + 0.869466i
\(73\) −7.69676 + 2.06234i −0.900838 + 0.241379i −0.679376 0.733790i \(-0.737749\pi\)
−0.221462 + 0.975169i \(0.571083\pi\)
\(74\) 16.9352 + 4.53778i 1.96868 + 0.527506i
\(75\) 4.10981 0.812629i 0.474560 0.0938343i
\(76\) 15.0542 + 8.69154i 1.72683 + 0.996988i
\(77\) −8.87692 + 2.37856i −1.01162 + 0.271062i
\(78\) 11.3255 16.9081i 1.28236 1.91446i
\(79\) 4.80864 4.80864i 0.541014 0.541014i −0.382812 0.923826i \(-0.625044\pi\)
0.923826 + 0.382812i \(0.125044\pi\)
\(80\) 0.421183 + 1.57188i 0.0470897 + 0.175741i
\(81\) 2.28976 + 8.70385i 0.254418 + 0.967094i
\(82\) 17.7736i 1.96277i
\(83\) −1.07444 + 4.00986i −0.117935 + 0.440140i −0.999490 0.0319423i \(-0.989831\pi\)
0.881555 + 0.472082i \(0.156497\pi\)
\(84\) −4.68004 9.51747i −0.510634 1.03844i
\(85\) 0.454758 1.69718i 0.0493254 0.184085i
\(86\) 1.22404 + 2.12011i 0.131992 + 0.228617i
\(87\) 13.3173 6.54853i 1.42777 0.702077i
\(88\) 2.98429 + 11.1375i 0.318126 + 1.18726i
\(89\) 3.02683 + 1.74754i 0.320843 + 0.185239i 0.651768 0.758418i \(-0.274027\pi\)
−0.330925 + 0.943657i \(0.607361\pi\)
\(90\) −7.02167 17.0616i −0.740149 1.79845i
\(91\) −2.66182 + 9.93405i −0.279035 + 1.04137i
\(92\) 9.22350 9.22350i 0.961617 0.961617i
\(93\) 4.51356 0.892463i 0.468034 0.0925441i
\(94\) 4.83412 18.0412i 0.498601 1.86081i
\(95\) −14.7612 3.95526i −1.51447 0.405801i
\(96\) 9.80519 4.82152i 1.00074 0.492094i
\(97\) 9.04604 + 2.42388i 0.918486 + 0.246108i 0.686938 0.726716i \(-0.258954\pi\)
0.231548 + 0.972823i \(0.425621\pi\)
\(98\) −4.93963 4.93963i −0.498978 0.498978i
\(99\) 5.30897 + 12.9000i 0.533572 + 1.29650i
\(100\) 3.74689 + 6.48981i 0.374689 + 0.648981i
\(101\) 7.78595i 0.774731i −0.921926 0.387366i \(-0.873385\pi\)
0.921926 0.387366i \(-0.126615\pi\)
\(102\) −2.51724 0.167867i −0.249244 0.0166213i
\(103\) 10.1525 + 10.1525i 1.00035 + 1.00035i 1.00000 0.000352195i \(0.000112107\pi\)
0.000352195 1.00000i \(0.499888\pi\)
\(104\) 12.4638 + 3.33968i 1.22218 + 0.327482i
\(105\) 6.13972 + 7.01711i 0.599175 + 0.684799i
\(106\) −2.85603 4.94678i −0.277402 0.480474i
\(107\) −18.1296 4.85780i −1.75265 0.469621i −0.767462 0.641094i \(-0.778481\pi\)
−0.985189 + 0.171473i \(0.945147\pi\)
\(108\) −13.4162 + 8.89827i −1.29097 + 0.856236i
\(109\) −2.47834 + 4.29261i −0.237382 + 0.411157i −0.959962 0.280130i \(-0.909623\pi\)
0.722580 + 0.691287i \(0.242956\pi\)
\(110\) −14.2984 24.7656i −1.36330 2.36131i
\(111\) 2.60880 + 13.1938i 0.247616 + 1.25230i
\(112\) −0.834965 + 0.834965i −0.0788968 + 0.0788968i
\(113\) −2.91868 1.68510i −0.274567 0.158521i 0.356394 0.934336i \(-0.384006\pi\)
−0.630961 + 0.775814i \(0.717339\pi\)
\(114\) −1.46003 + 21.8938i −0.136744 + 2.05054i
\(115\) −5.73368 + 9.93102i −0.534668 + 0.926072i
\(116\) 18.7707 + 18.7707i 1.74281 + 1.74281i
\(117\) 15.4727 + 2.07287i 1.43045 + 0.191637i
\(118\) 4.13684i 0.380827i
\(119\) 1.23151 0.329981i 0.112892 0.0302493i
\(120\) 8.80408 7.70326i 0.803699 0.703208i
\(121\) 5.31082 + 9.19861i 0.482802 + 0.836237i
\(122\) −15.5952 + 27.0116i −1.41192 + 2.44552i
\(123\) −12.2349 + 6.01629i −1.10319 + 0.542471i
\(124\) 4.11500 + 7.12738i 0.369538 + 0.640058i
\(125\) 4.97144 + 4.97144i 0.444659 + 0.444659i
\(126\) 8.17405 10.6026i 0.728202 0.944551i
\(127\) 7.40524 4.27542i 0.657109 0.379382i −0.134066 0.990972i \(-0.542803\pi\)
0.791175 + 0.611590i \(0.209470\pi\)
\(128\) 11.9125 + 11.9125i 1.05293 + 1.05293i
\(129\) −1.04510 + 1.56025i −0.0920156 + 0.137372i
\(130\) −32.0024 −2.80680
\(131\) 8.62368 + 2.31071i 0.753454 + 0.201887i 0.615050 0.788488i \(-0.289136\pi\)
0.138404 + 0.990376i \(0.455803\pi\)
\(132\) −18.7792 + 16.4311i −1.63452 + 1.43014i
\(133\) −2.87002 10.7110i −0.248862 0.928766i
\(134\) 17.4548 17.4548i 1.50787 1.50787i
\(135\) 9.36797 10.6088i 0.806267 0.913062i
\(136\) −0.414014 1.54512i −0.0355014 0.132493i
\(137\) −1.82121 6.79686i −0.155597 0.580695i −0.999054 0.0434977i \(-0.986150\pi\)
0.843457 0.537197i \(-0.180517\pi\)
\(138\) 15.5854 + 5.31033i 1.32672 + 0.452045i
\(139\) 17.1953 + 4.60748i 1.45849 + 0.390801i 0.898968 0.438015i \(-0.144318\pi\)
0.559522 + 0.828816i \(0.310985\pi\)
\(140\) −8.33915 + 14.4438i −0.704787 + 1.22073i
\(141\) 14.0554 2.77917i 1.18368 0.234048i
\(142\) 4.53306 16.9176i 0.380406 1.41969i
\(143\) 24.1965 2.02341
\(144\) 1.41950 + 1.09437i 0.118292 + 0.0911973i
\(145\) −20.2105 11.6685i −1.67839 0.969020i
\(146\) 8.99588 15.5813i 0.744504 1.28952i
\(147\) 1.72828 5.07237i 0.142546 0.418362i
\(148\) −20.8344 + 12.0287i −1.71258 + 0.988756i
\(149\) −8.54583 + 8.54583i −0.700102 + 0.700102i −0.964432 0.264330i \(-0.914849\pi\)
0.264330 + 0.964432i \(0.414849\pi\)
\(150\) −5.26425 + 7.85913i −0.429825 + 0.641695i
\(151\) −2.57209 + 0.689189i −0.209314 + 0.0560854i −0.361952 0.932197i \(-0.617890\pi\)
0.152639 + 0.988282i \(0.451223\pi\)
\(152\) −13.4387 + 3.60089i −1.09002 + 0.292071i
\(153\) −0.736520 1.78963i −0.0595441 0.144683i
\(154\) 10.3752 17.9704i 0.836060 1.44810i
\(155\) −5.11607 5.11607i −0.410933 0.410933i
\(156\) 5.41657 + 27.3939i 0.433673 + 2.19327i
\(157\) 9.58346 + 8.07201i 0.764843 + 0.644217i
\(158\) 15.3549i 1.22157i
\(159\) 2.43849 3.64048i 0.193385 0.288709i
\(160\) −14.8805 8.59125i −1.17641 0.679198i
\(161\) −8.32094 −0.655782
\(162\) −17.5523 10.2407i −1.37904 0.804585i
\(163\) 1.70278 + 6.35486i 0.133372 + 0.497751i 0.999999 0.00120512i \(-0.000383600\pi\)
−0.866627 + 0.498956i \(0.833717\pi\)
\(164\) −17.2450 17.2450i −1.34661 1.34661i
\(165\) 12.2081 18.2258i 0.950399 1.41887i
\(166\) −4.68668 8.11757i −0.363757 0.630045i
\(167\) 2.49267 4.31744i 0.192889 0.334093i −0.753318 0.657657i \(-0.771548\pi\)
0.946206 + 0.323564i \(0.104881\pi\)
\(168\) 8.03497 + 2.73771i 0.619912 + 0.211219i
\(169\) 7.03901 12.1919i 0.541462 0.937840i
\(170\) 1.98364 + 3.43577i 0.152138 + 0.263511i
\(171\) −15.5654 + 6.40590i −1.19031 + 0.489871i
\(172\) −3.24470 0.869414i −0.247406 0.0662922i
\(173\) 22.9914i 1.74800i −0.485922 0.874002i \(-0.661516\pi\)
0.485922 0.874002i \(-0.338484\pi\)
\(174\) −10.8070 + 31.7177i −0.819276 + 2.40451i
\(175\) 1.23725 4.61750i 0.0935277 0.349050i
\(176\) 2.40594 + 1.38907i 0.181354 + 0.104705i
\(177\) 2.84770 1.40030i 0.214046 0.105253i
\(178\) −7.62273 + 2.04251i −0.571348 + 0.153092i
\(179\) −2.15621 8.04708i −0.161163 0.601467i −0.998499 0.0547784i \(-0.982555\pi\)
0.837336 0.546689i \(-0.184112\pi\)
\(180\) 23.3670 + 9.74133i 1.74168 + 0.726076i
\(181\) −23.6117 + 6.32673i −1.75504 + 0.470262i −0.985691 0.168563i \(-0.946087\pi\)
−0.769352 + 0.638825i \(0.779421\pi\)
\(182\) −11.6108 20.1105i −0.860649 1.49069i
\(183\) −23.8730 1.59202i −1.76475 0.117685i
\(184\) 10.4399i 0.769643i
\(185\) 14.9550 14.9550i 1.09952 1.09952i
\(186\) −5.78142 + 8.63122i −0.423914 + 0.632872i
\(187\) −1.49980 2.59773i −0.109676 0.189965i
\(188\) 12.8143 + 22.1950i 0.934578 + 1.61874i
\(189\) 10.0654 + 2.03790i 0.732152 + 0.148235i
\(190\) 29.8827 17.2528i 2.16792 1.25165i
\(191\) −2.41042 8.99582i −0.174412 0.650915i −0.996651 0.0817723i \(-0.973942\pi\)
0.822239 0.569142i \(-0.192725\pi\)
\(192\) −7.28940 + 21.3938i −0.526067 + 1.54397i
\(193\) 10.2193 5.90011i 0.735601 0.424700i −0.0848666 0.996392i \(-0.527046\pi\)
0.820468 + 0.571693i \(0.193713\pi\)
\(194\) −18.3128 + 10.5729i −1.31478 + 0.759090i
\(195\) −10.8327 22.0297i −0.775744 1.57758i
\(196\) 9.58546 0.684676
\(197\) 11.9259 + 6.88543i 0.849686 + 0.490566i 0.860545 0.509375i \(-0.170123\pi\)
−0.0108588 + 0.999941i \(0.503457\pi\)
\(198\) −29.0723 12.1198i −2.06608 0.861314i
\(199\) −19.2885 11.1362i −1.36733 0.789426i −0.376740 0.926319i \(-0.622955\pi\)
−0.990586 + 0.136894i \(0.956288\pi\)
\(200\) −5.79339 1.55233i −0.409654 0.109767i
\(201\) 17.9239 + 6.10709i 1.26425 + 0.430761i
\(202\) 12.4310 + 12.4310i 0.874642 + 0.874642i
\(203\) 16.9338i 1.18852i
\(204\) 2.60526 2.27951i 0.182404 0.159597i
\(205\) 18.5679 + 10.7202i 1.29684 + 0.748728i
\(206\) −32.4187 −2.25872
\(207\) 1.62009 + 12.5261i 0.112604 + 0.870626i
\(208\) 2.69245 1.55449i 0.186688 0.107784i
\(209\) −22.5938 + 13.0445i −1.56285 + 0.902309i
\(210\) −21.0061 1.40083i −1.44956 0.0966665i
\(211\) −8.99810 + 8.99810i −0.619455 + 0.619455i −0.945392 0.325937i \(-0.894320\pi\)
0.325937 + 0.945392i \(0.394320\pi\)
\(212\) 7.57076 + 2.02858i 0.519962 + 0.139323i
\(213\) 13.1801 2.60609i 0.903085 0.178566i
\(214\) 36.7015 21.1896i 2.50886 1.44849i
\(215\) 2.95313 0.201402
\(216\) 2.55687 12.6287i 0.173973 0.859273i
\(217\) 1.35880 5.07113i 0.0922417 0.344251i
\(218\) −2.89665 10.8105i −0.196186 0.732176i
\(219\) 13.7709 + 0.918336i 0.930549 + 0.0620554i
\(220\) 37.9023 + 10.1559i 2.55537 + 0.684710i
\(221\) −3.35681 −0.225804
\(222\) −25.2303 16.9000i −1.69335 1.13425i
\(223\) −15.1807 4.06765i −1.01657 0.272390i −0.288200 0.957570i \(-0.593057\pi\)
−0.728373 + 0.685180i \(0.759723\pi\)
\(224\) 12.4680i 0.833050i
\(225\) −7.19196 0.963503i −0.479464 0.0642335i
\(226\) 7.35038 1.96953i 0.488940 0.131011i
\(227\) 0.392404 + 1.46447i 0.0260448 + 0.0972005i 0.977725 0.209891i \(-0.0673109\pi\)
−0.951680 + 0.307091i \(0.900644\pi\)
\(228\) −19.8261 22.6593i −1.31301 1.50065i
\(229\) 6.44473 + 1.72686i 0.425879 + 0.114114i 0.465391 0.885105i \(-0.345914\pi\)
−0.0395118 + 0.999219i \(0.512580\pi\)
\(230\) −6.70145 25.0102i −0.441881 1.64912i
\(231\) 15.8824 + 1.05915i 1.04498 + 0.0696866i
\(232\) −21.2462 −1.39488
\(233\) −0.180566 + 0.312750i −0.0118293 + 0.0204889i −0.871879 0.489721i \(-0.837099\pi\)
0.860050 + 0.510209i \(0.170432\pi\)
\(234\) −28.0132 + 21.3941i −1.83128 + 1.39858i
\(235\) −15.9317 15.9317i −1.03927 1.03927i
\(236\) 4.01381 + 4.01381i 0.261277 + 0.261277i
\(237\) −10.5699 + 5.19756i −0.686591 + 0.337618i
\(238\) −1.43937 + 2.49306i −0.0933004 + 0.161601i
\(239\) −17.5188 −1.13320 −0.566599 0.823993i \(-0.691741\pi\)
−0.566599 + 0.823993i \(0.691741\pi\)
\(240\) 0.187548 2.81236i 0.0121061 0.181537i
\(241\) 2.04719 + 7.64023i 0.131871 + 0.492150i 0.999991 0.00420434i \(-0.00133829\pi\)
−0.868120 + 0.496355i \(0.834672\pi\)
\(242\) −23.1657 6.20722i −1.48915 0.399015i
\(243\) 1.10806 15.5490i 0.0710818 0.997470i
\(244\) −11.0769 41.3397i −0.709128 2.64650i
\(245\) −8.13971 + 2.18103i −0.520027 + 0.139341i
\(246\) 9.92863 29.1398i 0.633026 1.85788i
\(247\) 29.1959i 1.85769i
\(248\) −6.36254 1.70484i −0.404022 0.108257i
\(249\) 4.00152 5.97396i 0.253586 0.378584i
\(250\) −15.8747 −1.00401
\(251\) 22.5901 + 6.05299i 1.42587 + 0.382062i 0.887563 0.460685i \(-0.152396\pi\)
0.538310 + 0.842747i \(0.319063\pi\)
\(252\) 2.35629 + 18.2182i 0.148432 + 1.14764i
\(253\) 5.06686 + 18.9098i 0.318551 + 1.18885i
\(254\) −4.99706 + 18.6493i −0.313543 + 1.17016i
\(255\) −1.69365 + 2.52848i −0.106060 + 0.158340i
\(256\) −11.9409 −0.746307
\(257\) −5.78201 + 3.33825i −0.360672 + 0.208234i −0.669376 0.742924i \(-0.733438\pi\)
0.308703 + 0.951158i \(0.400105\pi\)
\(258\) −0.822490 4.15968i −0.0512060 0.258970i
\(259\) 14.8237 + 3.97199i 0.921097 + 0.246807i
\(260\) 31.0507 31.0507i 1.92568 1.92568i
\(261\) −25.4918 + 3.29703i −1.57790 + 0.204081i
\(262\) −17.4578 + 10.0792i −1.07854 + 0.622698i
\(263\) 19.5169 11.2681i 1.20346 0.694818i 0.242138 0.970242i \(-0.422151\pi\)
0.961323 + 0.275424i \(0.0888181\pi\)
\(264\) 1.32887 19.9270i 0.0817861 1.22642i
\(265\) −6.89045 −0.423277
\(266\) 21.6834 + 12.5189i 1.32950 + 0.767586i
\(267\) −3.98627 4.55592i −0.243956 0.278818i
\(268\) 33.8714i 2.06903i
\(269\) 6.81407 + 6.81407i 0.415461 + 0.415461i 0.883636 0.468175i \(-0.155088\pi\)
−0.468175 + 0.883636i \(0.655088\pi\)
\(270\) 1.98113 + 31.8948i 0.120567 + 1.94106i
\(271\) 8.70980 + 2.33378i 0.529082 + 0.141767i 0.513465 0.858111i \(-0.328362\pi\)
0.0156179 + 0.999878i \(0.495028\pi\)
\(272\) −0.333779 0.192707i −0.0202383 0.0116846i
\(273\) 9.91336 14.7999i 0.599984 0.895730i
\(274\) 13.7596 + 7.94408i 0.831245 + 0.479919i
\(275\) −11.2469 −0.678214
\(276\) −20.2743 + 9.96950i −1.22037 + 0.600093i
\(277\) 3.74046 2.15955i 0.224742 0.129755i −0.383402 0.923582i \(-0.625248\pi\)
0.608144 + 0.793827i \(0.291914\pi\)
\(278\) −34.8102 + 20.0977i −2.08778 + 1.20538i
\(279\) −7.89851 1.05816i −0.472871 0.0633503i
\(280\) −3.45490 12.8939i −0.206470 0.770555i
\(281\) 8.76932 5.06297i 0.523134 0.302031i −0.215082 0.976596i \(-0.569002\pi\)
0.738216 + 0.674565i \(0.235669\pi\)
\(282\) −18.0036 + 26.8780i −1.07210 + 1.60056i
\(283\) 9.48136 + 16.4222i 0.563609 + 0.976199i 0.997178 + 0.0750783i \(0.0239207\pi\)
−0.433569 + 0.901120i \(0.642746\pi\)
\(284\) 12.0162 + 20.8127i 0.713033 + 1.23501i
\(285\) 21.9915 + 14.7305i 1.30267 + 0.872560i
\(286\) −38.6320 + 38.6320i −2.28436 + 2.28436i
\(287\) 15.5575i 0.918331i
\(288\) −18.7690 + 2.42752i −1.10597 + 0.143043i
\(289\) −8.29193 14.3620i −0.487761 0.844826i
\(290\) 50.8979 13.6381i 2.98883 0.800854i
\(291\) −13.4769 9.02720i −0.790032 0.529184i
\(292\) 6.38959 + 23.8463i 0.373923 + 1.39550i
\(293\) −21.5111 + 5.76389i −1.25669 + 0.336730i −0.824918 0.565252i \(-0.808779\pi\)
−0.431774 + 0.901982i \(0.642112\pi\)
\(294\) 5.33915 + 10.8579i 0.311386 + 0.633244i
\(295\) −4.32170 2.49513i −0.251619 0.145272i
\(296\) 4.98349 18.5986i 0.289660 1.08102i
\(297\) −1.49790 24.1152i −0.0869168 1.39930i
\(298\) 27.2884i 1.58078i
\(299\) 21.1617 + 5.67026i 1.22381 + 0.327919i
\(300\) −2.51771 12.7331i −0.145360 0.735146i
\(301\) 1.07142 + 1.85576i 0.0617559 + 0.106964i
\(302\) 3.00623 5.20694i 0.172989 0.299626i
\(303\) −4.34936 + 12.7650i −0.249864 + 0.733332i
\(304\) −1.67608 + 2.90305i −0.0961295 + 0.166501i
\(305\) 18.8125 + 32.5841i 1.07720 + 1.86576i
\(306\) 4.03324 + 1.68139i 0.230565 + 0.0961187i
\(307\) 7.99553 + 7.99553i 0.456329 + 0.456329i 0.897448 0.441120i \(-0.145419\pi\)
−0.441120 + 0.897448i \(0.645419\pi\)
\(308\) 7.36932 + 27.5027i 0.419906 + 1.56711i
\(309\) −10.9736 22.3163i −0.624266 1.26953i
\(310\) 16.3366 0.927855
\(311\) −9.95010 5.74469i −0.564218 0.325751i 0.190619 0.981664i \(-0.438951\pi\)
−0.754837 + 0.655913i \(0.772284\pi\)
\(312\) −18.5688 12.4379i −1.05125 0.704157i
\(313\) 17.6463i 0.997427i 0.866767 + 0.498714i \(0.166194\pi\)
−0.866767 + 0.498714i \(0.833806\pi\)
\(314\) −28.1886 + 2.41316i −1.59078 + 0.136183i
\(315\) −6.14618 14.9343i −0.346298 0.841451i
\(316\) −14.8982 14.8982i −0.838091 0.838091i
\(317\) −14.0234 + 24.2892i −0.787631 + 1.36422i 0.139784 + 0.990182i \(0.455359\pi\)
−0.927415 + 0.374035i \(0.877974\pi\)
\(318\) 1.91909 + 9.70566i 0.107617 + 0.544266i
\(319\) −38.4831 + 10.3115i −2.15464 + 0.577334i
\(320\) 34.3311 9.19898i 1.91916 0.514239i
\(321\) 27.0097 + 18.0918i 1.50753 + 1.00979i
\(322\) 13.2852 13.2852i 0.740353 0.740353i
\(323\) 3.13447 1.80968i 0.174406 0.100694i
\(324\) 26.9665 7.09419i 1.49814 0.394122i
\(325\) −6.29314 + 10.9000i −0.349080 + 0.604625i
\(326\) −12.8648 7.42748i −0.712514 0.411370i
\(327\) 6.46115 5.65328i 0.357302 0.312627i
\(328\) 19.5194 1.07778
\(329\) 4.23138 15.7917i 0.233283 0.870626i
\(330\) 9.60776 + 48.5905i 0.528890 + 2.67482i
\(331\) 15.5519 26.9368i 0.854812 1.48058i −0.0220067 0.999758i \(-0.507006\pi\)
0.876819 0.480821i \(-0.159661\pi\)
\(332\) 12.4235 + 3.32885i 0.681826 + 0.182695i
\(333\) 3.09316 23.0885i 0.169504 1.26524i
\(334\) 2.91341 + 10.8730i 0.159415 + 0.594943i
\(335\) −7.70694 28.7627i −0.421075 1.57147i
\(336\) 1.83535 0.902497i 0.100126 0.0492353i
\(337\) 12.4344 12.4344i 0.677346 0.677346i −0.282053 0.959399i \(-0.591015\pi\)
0.959399 + 0.282053i \(0.0910154\pi\)
\(338\) 8.22710 + 30.7040i 0.447495 + 1.67008i
\(339\) 3.84385 + 4.39315i 0.208769 + 0.238603i
\(340\) −5.25824 1.40894i −0.285168 0.0764105i
\(341\) −12.3518 −0.668889
\(342\) 14.6239 35.0792i 0.790771 1.89686i
\(343\) −14.1064 14.1064i −0.761674 0.761674i
\(344\) 2.32835 1.34427i 0.125536 0.0724783i
\(345\) 14.9480 13.0789i 0.804772 0.704147i
\(346\) 36.7079 + 36.7079i 1.97343 + 1.97343i
\(347\) 7.80575 + 13.5200i 0.419035 + 0.725789i 0.995843 0.0910904i \(-0.0290352\pi\)
−0.576808 + 0.816880i \(0.695702\pi\)
\(348\) −20.2888 41.2600i −1.08759 2.21177i
\(349\) 0.997117 1.72706i 0.0533745 0.0924473i −0.838104 0.545511i \(-0.816336\pi\)
0.891478 + 0.453064i \(0.149669\pi\)
\(350\) 5.39687 + 9.34766i 0.288475 + 0.499653i
\(351\) −24.2095 12.0418i −1.29221 0.642743i
\(352\) −28.3341 + 7.59210i −1.51021 + 0.404660i
\(353\) 11.6157i 0.618244i −0.951022 0.309122i \(-0.899965\pi\)
0.951022 0.309122i \(-0.100035\pi\)
\(354\) −2.31090 + 6.78233i −0.122823 + 0.360477i
\(355\) −14.9395 14.9395i −0.792906 0.792906i
\(356\) 5.41427 9.37780i 0.286956 0.497022i
\(357\) −2.20338 0.146937i −0.116615 0.00777671i
\(358\) 16.2905 + 9.40533i 0.860980 + 0.497087i
\(359\) 15.0789 15.0789i 0.795835 0.795835i −0.186600 0.982436i \(-0.559747\pi\)
0.982436 + 0.186600i \(0.0597470\pi\)
\(360\) −18.7374 + 7.71136i −0.987549 + 0.406424i
\(361\) −6.23977 10.8076i −0.328409 0.568821i
\(362\) 27.5970 47.7995i 1.45047 2.51229i
\(363\) −3.56858 18.0478i −0.187302 0.947264i
\(364\) 30.7779 + 8.24691i 1.61320 + 0.432256i
\(365\) −10.8517 18.7958i −0.568006 0.983815i
\(366\) 40.6573 35.5737i 2.12519 1.85947i
\(367\) −4.91062 1.31580i −0.256332 0.0686840i 0.128364 0.991727i \(-0.459027\pi\)
−0.384697 + 0.923043i \(0.625694\pi\)
\(368\) 1.77866 + 1.77866i 0.0927190 + 0.0927190i
\(369\) 23.4199 3.02906i 1.21919 0.157686i
\(370\) 47.7542i 2.48262i
\(371\) −2.49992 4.33000i −0.129790 0.224802i
\(372\) −2.76505 13.9840i −0.143361 0.725038i
\(373\) 0.549281 + 0.549281i 0.0284407 + 0.0284407i 0.721184 0.692743i \(-0.243598\pi\)
−0.692743 + 0.721184i \(0.743598\pi\)
\(374\) 6.54209 + 1.75295i 0.338283 + 0.0906427i
\(375\) −5.37353 10.9278i −0.277488 0.564308i
\(376\) −19.8132 5.30894i −1.02179 0.273788i
\(377\) −11.5395 + 43.0659i −0.594314 + 2.21801i
\(378\) −19.3241 + 12.8167i −0.993924 + 0.659220i
\(379\) 9.97830 9.97830i 0.512551 0.512551i −0.402756 0.915307i \(-0.631948\pi\)
0.915307 + 0.402756i \(0.131948\pi\)
\(380\) −12.2543 + 45.7336i −0.628632 + 2.34609i
\(381\) −14.5292 + 2.87284i −0.744353 + 0.147180i
\(382\) 18.2111 + 10.5142i 0.931763 + 0.537953i
\(383\) 6.07272 + 22.6637i 0.310302 + 1.15806i 0.928285 + 0.371870i \(0.121283\pi\)
−0.617983 + 0.786191i \(0.712050\pi\)
\(384\) −12.8760 26.1851i −0.657077 1.33625i
\(385\) −12.5156 21.6777i −0.637857 1.10480i
\(386\) −6.89598 + 25.7362i −0.350996 + 1.30994i
\(387\) 2.58501 1.97421i 0.131403 0.100355i
\(388\) 7.50972 28.0266i 0.381248 1.42284i
\(389\) 17.4515i 0.884825i 0.896812 + 0.442412i \(0.145877\pi\)
−0.896812 + 0.442412i \(0.854123\pi\)
\(390\) 52.4678 + 17.8771i 2.65681 + 0.905241i
\(391\) −0.702932 2.62338i −0.0355488 0.132670i
\(392\) −5.42482 + 5.42482i −0.273995 + 0.273995i
\(393\) −12.8477 8.60572i −0.648080 0.434101i
\(394\) −30.0341 + 8.04760i −1.51309 + 0.405432i
\(395\) 16.0411 + 9.26131i 0.807113 + 0.465987i
\(396\) 39.9670 16.4484i 2.00842 0.826562i
\(397\) 23.9523 + 6.41799i 1.20213 + 0.322110i 0.803669 0.595076i \(-0.202878\pi\)
0.398460 + 0.917186i \(0.369545\pi\)
\(398\) 48.5759 13.0159i 2.43489 0.652427i
\(399\) −1.27798 + 19.1640i −0.0639792 + 0.959398i
\(400\) −1.25149 + 0.722550i −0.0625747 + 0.0361275i
\(401\) 12.2236 3.27530i 0.610416 0.163561i 0.0596489 0.998219i \(-0.481002\pi\)
0.550767 + 0.834659i \(0.314335\pi\)
\(402\) −38.3677 + 18.8666i −1.91360 + 0.940979i
\(403\) −6.91139 + 11.9709i −0.344281 + 0.596312i
\(404\) −24.1226 −1.20015
\(405\) −21.2850 + 12.1600i −1.05766 + 0.604236i
\(406\) 27.0365 + 27.0365i 1.34180 + 1.34180i
\(407\) 36.1062i 1.78972i
\(408\) −0.184355 + 2.76449i −0.00912695 + 0.136863i
\(409\) 6.62390 24.7207i 0.327531 1.22236i −0.584212 0.811601i \(-0.698596\pi\)
0.911743 0.410761i \(-0.134737\pi\)
\(410\) −46.7611 + 12.5296i −2.30936 + 0.618792i
\(411\) −0.810964 + 12.1608i −0.0400019 + 0.599847i
\(412\) 31.4546 31.4546i 1.54966 1.54966i
\(413\) 3.62104i 0.178180i
\(414\) −22.5858 17.4125i −1.11003 0.855779i
\(415\) −11.3071 −0.555043
\(416\) −8.49622 + 31.7083i −0.416562 + 1.55463i
\(417\) −25.6179 17.1595i −1.25451 0.840306i
\(418\) 15.2463 56.8999i 0.745720 2.78307i
\(419\) 0.636517 + 1.10248i 0.0310959 + 0.0538597i 0.881155 0.472828i \(-0.156767\pi\)
−0.850059 + 0.526688i \(0.823434\pi\)
\(420\) 21.7406 19.0222i 1.06083 0.928189i
\(421\) −5.51047 + 20.5654i −0.268564 + 1.00229i 0.691469 + 0.722406i \(0.256964\pi\)
−0.960033 + 0.279888i \(0.909703\pi\)
\(422\) 28.7326i 1.39868i
\(423\) −24.5963 3.29516i −1.19591 0.160216i
\(424\) −5.43267 + 3.13655i −0.263834 + 0.152325i
\(425\) 1.56030 0.0756856
\(426\) −16.8824 + 25.2041i −0.817955 + 1.22114i
\(427\) −13.6507 + 23.6437i −0.660603 + 1.14420i
\(428\) −15.0506 + 56.1694i −0.727496 + 2.71505i
\(429\) −39.6701 13.5166i −1.91529 0.652586i
\(430\) −4.71495 + 4.71495i −0.227375 + 0.227375i
\(431\) −10.0318 + 17.3755i −0.483212 + 0.836948i −0.999814 0.0192774i \(-0.993863\pi\)
0.516602 + 0.856226i \(0.327197\pi\)
\(432\) −1.71594 2.58717i −0.0825582 0.124475i
\(433\) 4.66270 + 17.4014i 0.224075 + 0.836260i 0.982773 + 0.184817i \(0.0591693\pi\)
−0.758698 + 0.651443i \(0.774164\pi\)
\(434\) 5.92707 + 10.2660i 0.284509 + 0.492783i
\(435\) 26.6168 + 30.4205i 1.27618 + 1.45855i
\(436\) 13.2995 + 7.67845i 0.636929 + 0.367731i
\(437\) −22.8169 + 6.11376i −1.09148 + 0.292461i
\(438\) −23.4527 + 20.5203i −1.12061 + 0.980496i
\(439\) 15.3273 15.3273i 0.731530 0.731530i −0.239393 0.970923i \(-0.576948\pi\)
0.970923 + 0.239393i \(0.0769483\pi\)
\(440\) −27.1982 + 15.7029i −1.29662 + 0.748605i
\(441\) −5.66701 + 7.35068i −0.269858 + 0.350033i
\(442\) 5.35947 5.35947i 0.254924 0.254924i
\(443\) −1.59972 1.59972i −0.0760049 0.0760049i 0.668082 0.744087i \(-0.267115\pi\)
−0.744087 + 0.668082i \(0.767115\pi\)
\(444\) 40.8774 8.08265i 1.93995 0.383585i
\(445\) −2.46388 + 9.19531i −0.116799 + 0.435899i
\(446\) 30.7318 17.7430i 1.45519 0.840155i
\(447\) 18.7847 9.23702i 0.888486 0.436896i
\(448\) 18.2363 + 18.2363i 0.861586 + 0.861586i
\(449\) 21.6345 5.79694i 1.02099 0.273574i 0.290777 0.956791i \(-0.406086\pi\)
0.730216 + 0.683216i \(0.239419\pi\)
\(450\) 13.0210 9.94432i 0.613814 0.468780i
\(451\) 35.3553 9.47342i 1.66482 0.446086i
\(452\) −5.22083 + 9.04274i −0.245567 + 0.425335i
\(453\) 4.60192 + 0.306888i 0.216217 + 0.0144188i
\(454\) −2.96468 1.71166i −0.139139 0.0803321i
\(455\) −28.0122 −1.31323
\(456\) 24.0442 + 1.60343i 1.12597 + 0.0750877i
\(457\) 21.9552i 1.02702i −0.858083 0.513511i \(-0.828344\pi\)
0.858083 0.513511i \(-0.171656\pi\)
\(458\) −13.0467 + 7.53252i −0.609632 + 0.351971i
\(459\) 0.207805 + 3.34553i 0.00969952 + 0.156156i
\(460\) 30.7685 + 17.7642i 1.43459 + 0.828260i
\(461\) 31.3522 + 18.1012i 1.46022 + 0.843056i 0.999021 0.0442431i \(-0.0140876\pi\)
0.461195 + 0.887299i \(0.347421\pi\)
\(462\) −27.0487 + 23.6667i −1.25842 + 1.10107i
\(463\) 27.9569 + 27.9569i 1.29927 + 1.29927i 0.928877 + 0.370388i \(0.120775\pi\)
0.370388 + 0.928877i \(0.379225\pi\)
\(464\) −3.61973 + 3.61973i −0.168042 + 0.168042i
\(465\) 5.52986 + 11.2457i 0.256441 + 0.521507i
\(466\) −0.211044 0.787626i −0.00977641 0.0364861i
\(467\) 27.2916i 1.26290i −0.775415 0.631452i \(-0.782459\pi\)
0.775415 0.631452i \(-0.217541\pi\)
\(468\) 6.42222 47.9380i 0.296867 2.21593i
\(469\) 15.2785 15.2785i 0.705494 0.705494i
\(470\) 50.8729 2.34659
\(471\) −11.2029 18.5875i −0.516202 0.856467i
\(472\) −4.54317 −0.209116
\(473\) 3.56490 3.56490i 0.163914 0.163914i
\(474\) 8.57749 25.1743i 0.393977 1.15629i
\(475\) 13.5707i 0.622667i
\(476\) −1.02235 3.81548i −0.0468596 0.174882i
\(477\) −6.03153 + 4.60638i −0.276165 + 0.210912i
\(478\) 27.9705 27.9705i 1.27934 1.27934i
\(479\) −9.50574 9.50574i −0.434328 0.434328i 0.455770 0.890098i \(-0.349364\pi\)
−0.890098 + 0.455770i \(0.849364\pi\)
\(480\) 19.5973 + 22.3978i 0.894489 + 1.02231i
\(481\) −34.9926 20.2030i −1.59553 0.921178i
\(482\) −15.4669 8.92980i −0.704497 0.406741i
\(483\) 13.6421 + 4.64821i 0.620739 + 0.211501i
\(484\) 28.4993 16.4541i 1.29542 0.747914i
\(485\) 25.5082i 1.15827i
\(486\) 23.0564 + 26.5946i 1.04586 + 1.20636i
\(487\) 14.1760 0.642376 0.321188 0.947015i \(-0.395918\pi\)
0.321188 + 0.947015i \(0.395918\pi\)
\(488\) 29.6648 + 17.1270i 1.34286 + 0.775301i
\(489\) 0.758227 11.3700i 0.0342882 0.514168i
\(490\) 9.51360 16.4780i 0.429781 0.744402i
\(491\) 30.4689 8.16411i 1.37504 0.368441i 0.505724 0.862695i \(-0.331226\pi\)
0.869317 + 0.494254i \(0.164559\pi\)
\(492\) 18.6398 + 37.9065i 0.840347 + 1.70896i
\(493\) 5.33881 1.43053i 0.240448 0.0644278i
\(494\) −46.6141 46.6141i −2.09727 2.09727i
\(495\) −30.1963 + 23.0614i −1.35722 + 1.03653i
\(496\) −1.37444 + 0.793535i −0.0617143 + 0.0356308i
\(497\) 3.96786 14.8083i 0.177983 0.664241i
\(498\) 3.14919 + 15.9268i 0.141119 + 0.713696i
\(499\) −26.4882 26.4882i −1.18578 1.18578i −0.978224 0.207552i \(-0.933450\pi\)
−0.207552 0.978224i \(-0.566550\pi\)
\(500\) 15.4026 15.4026i 0.688826 0.688826i
\(501\) −6.49852 + 5.68598i −0.290332 + 0.254031i
\(502\) −45.7314 + 26.4030i −2.04109 + 1.17842i
\(503\) 15.5095 15.5095i 0.691533 0.691533i −0.271036 0.962569i \(-0.587366\pi\)
0.962569 + 0.271036i \(0.0873664\pi\)
\(504\) −11.6440 8.97693i −0.518664 0.399864i
\(505\) 20.4843 5.48874i 0.911538 0.244246i
\(506\) −38.2809 22.1015i −1.70180 0.982532i
\(507\) −18.3510 + 16.0565i −0.814998 + 0.713094i
\(508\) −13.2462 22.9431i −0.587705 1.01794i
\(509\) 7.41134 + 27.6595i 0.328502 + 1.22599i 0.910745 + 0.412970i \(0.135509\pi\)
−0.582243 + 0.813015i \(0.697825\pi\)
\(510\) −1.33290 6.74102i −0.0590217 0.298498i
\(511\) 7.87423 13.6386i 0.348336 0.603335i
\(512\) −4.76031 + 4.76031i −0.210378 + 0.210378i
\(513\) 29.0978 1.80739i 1.28470 0.0797982i
\(514\) 3.90170 14.5614i 0.172097 0.642274i
\(515\) −19.5534 + 33.8674i −0.861624 + 1.49238i
\(516\) 4.83400 + 3.23794i 0.212805 + 0.142542i
\(517\) −38.4641 −1.69165
\(518\) −30.0090 + 17.3257i −1.31852 + 0.761248i
\(519\) −12.8434 + 37.6943i −0.563761 + 1.65460i
\(520\) 35.1458i 1.54124i
\(521\) 6.77129 25.2708i 0.296656 1.10713i −0.643238 0.765666i \(-0.722409\pi\)
0.939894 0.341468i \(-0.110924\pi\)
\(522\) 35.4360 45.9641i 1.55099 2.01179i
\(523\) 12.5095 + 21.6672i 0.547004 + 0.947439i 0.998478 + 0.0551546i \(0.0175652\pi\)
−0.451474 + 0.892284i \(0.649102\pi\)
\(524\) 7.15909 26.7181i 0.312746 1.16718i
\(525\) −4.60788 + 6.87922i −0.201104 + 0.300234i
\(526\) −13.1700 + 49.1510i −0.574238 + 2.14309i
\(527\) 1.71358 0.0746449
\(528\) −3.16857 3.62137i −0.137894 0.157600i
\(529\) 5.27459i 0.229330i
\(530\) 11.0013 11.0013i 0.477864 0.477864i
\(531\) −5.45102 + 0.705018i −0.236554 + 0.0305952i
\(532\) −33.1852 + 8.89195i −1.43876 + 0.385515i
\(533\) 10.6016 39.5657i 0.459206 1.71378i
\(534\) 13.6384 + 0.909503i 0.590192 + 0.0393580i
\(535\) 51.1221i 2.21020i
\(536\) −19.1693 19.1693i −0.827987 0.827987i
\(537\) −0.960134 + 14.3977i −0.0414328 + 0.621305i
\(538\) −21.7586 −0.938079
\(539\) −7.19308 + 12.4588i −0.309828 + 0.536637i
\(540\) −32.8685 29.0241i −1.41443 1.24900i
\(541\) −18.0563 + 4.83817i −0.776302 + 0.208009i −0.625154 0.780502i \(-0.714964\pi\)
−0.151148 + 0.988511i \(0.548297\pi\)
\(542\) −17.6321 + 10.1799i −0.757364 + 0.437264i
\(543\) 42.2455 + 2.81722i 1.81293 + 0.120898i
\(544\) 3.93083 1.05326i 0.168533 0.0451582i
\(545\) −13.0407 3.49423i −0.558600 0.149677i
\(546\) 7.80181 + 39.4570i 0.333887 + 1.68861i
\(547\) 23.3471 + 13.4794i 0.998248 + 0.576339i 0.907729 0.419556i \(-0.137814\pi\)
0.0905184 + 0.995895i \(0.471148\pi\)
\(548\) −21.0582 + 5.64252i −0.899561 + 0.241037i
\(549\) 38.2504 + 15.9460i 1.63249 + 0.680557i
\(550\) 17.9567 17.9567i 0.765678 0.765678i
\(551\) −12.4421 46.4344i −0.530049 1.97817i
\(552\) 5.83192 17.1162i 0.248223 0.728516i
\(553\) 13.4404i 0.571543i
\(554\) −2.52406 + 9.41992i −0.107237 + 0.400214i
\(555\) −32.8729 + 16.1646i −1.39538 + 0.686149i
\(556\) 14.2750 53.2750i 0.605394 2.25936i
\(557\) 8.41287 + 14.5715i 0.356465 + 0.617415i 0.987367 0.158447i \(-0.0506487\pi\)
−0.630903 + 0.775862i \(0.717315\pi\)
\(558\) 14.3002 10.9213i 0.605374 0.462334i
\(559\) −1.46023 5.44966i −0.0617613 0.230496i
\(560\) −2.78535 1.60812i −0.117702 0.0679555i
\(561\) 1.00778 + 5.09678i 0.0425486 + 0.215186i
\(562\) −5.91753 + 22.0845i −0.249616 + 0.931580i
\(563\) −1.19179 + 1.19179i −0.0502279 + 0.0502279i −0.731775 0.681547i \(-0.761308\pi\)
0.681547 + 0.731775i \(0.261308\pi\)
\(564\) −8.61049 43.5469i −0.362567 1.83365i
\(565\) 2.37584 8.86677i 0.0999525 0.373028i
\(566\) −41.3575 11.0817i −1.73838 0.465799i
\(567\) −15.3638 8.96384i −0.645220 0.376446i
\(568\) −18.5793 4.97831i −0.779571 0.208885i
\(569\) 9.89810 + 9.89810i 0.414950 + 0.414950i 0.883459 0.468509i \(-0.155209\pi\)
−0.468509 + 0.883459i \(0.655209\pi\)
\(570\) −58.6302 + 11.5929i −2.45575 + 0.485573i
\(571\) −3.11435 5.39422i −0.130332 0.225741i 0.793473 0.608606i \(-0.208271\pi\)
−0.923804 + 0.382865i \(0.874938\pi\)
\(572\) 74.9662i 3.13449i
\(573\) −1.07333 + 16.0951i −0.0448391 + 0.672383i
\(574\) −24.8390 24.8390i −1.03676 1.03676i
\(575\) −9.83628 2.63562i −0.410201 0.109913i
\(576\) 23.9019 31.0032i 0.995913 1.29180i
\(577\) 10.4715 + 18.1371i 0.435934 + 0.755059i 0.997371 0.0724597i \(-0.0230849\pi\)
−0.561438 + 0.827519i \(0.689752\pi\)
\(578\) 36.1692 + 9.69151i 1.50444 + 0.403114i
\(579\) −20.0504 + 3.96455i −0.833266 + 0.164761i
\(580\) −36.1518 + 62.6167i −1.50112 + 2.60002i
\(581\) −4.10232 7.10543i −0.170193 0.294783i
\(582\) 35.9300 7.10440i 1.48934 0.294487i
\(583\) −8.31787 + 8.31787i −0.344491 + 0.344491i
\(584\) −17.1118 9.87948i −0.708090 0.408816i
\(585\) 5.45400 + 42.1689i 0.225495 + 1.74347i
\(586\) 25.1419 43.5471i 1.03860 1.79891i
\(587\) 1.12613 + 1.12613i 0.0464804 + 0.0464804i 0.729965 0.683485i \(-0.239536\pi\)
−0.683485 + 0.729965i \(0.739536\pi\)
\(588\) −15.7153 5.35459i −0.648089 0.220820i
\(589\) 14.9039i 0.614106i
\(590\) 10.8837 2.91628i 0.448075 0.120061i
\(591\) −15.7062 17.9506i −0.646066 0.738391i
\(592\) −2.31962 4.01770i −0.0953358 0.165126i
\(593\) −4.00397 + 6.93507i −0.164423 + 0.284789i −0.936450 0.350800i \(-0.885910\pi\)
0.772027 + 0.635590i \(0.219243\pi\)
\(594\) 40.8936 + 36.1106i 1.67789 + 1.48163i
\(595\) 1.73631 + 3.00738i 0.0711819 + 0.123291i
\(596\) 26.4769 + 26.4769i 1.08454 + 1.08454i
\(597\) 25.4025 + 29.0327i 1.03966 + 1.18823i
\(598\) −42.8397 + 24.7335i −1.75185 + 1.01143i
\(599\) 14.6658 + 14.6658i 0.599229 + 0.599229i 0.940107 0.340878i \(-0.110724\pi\)
−0.340878 + 0.940107i \(0.610724\pi\)
\(600\) 8.63108 + 5.78132i 0.352362 + 0.236022i
\(601\) 19.8730 0.810635 0.405318 0.914176i \(-0.367161\pi\)
0.405318 + 0.914176i \(0.367161\pi\)
\(602\) −4.67353 1.25227i −0.190479 0.0510386i
\(603\) −25.9746 20.0251i −1.05777 0.815486i
\(604\) 2.13526 + 7.96891i 0.0868826 + 0.324250i
\(605\) −20.4570 + 20.4570i −0.831695 + 0.831695i
\(606\) −13.4364 27.3247i −0.545817 1.10999i
\(607\) −7.29536 27.2267i −0.296110 1.10510i −0.940332 0.340258i \(-0.889486\pi\)
0.644222 0.764838i \(-0.277181\pi\)
\(608\) −9.16076 34.1884i −0.371518 1.38652i
\(609\) −9.45952 + 27.7630i −0.383319 + 1.12501i
\(610\) −82.0595 21.9878i −3.32249 0.890259i
\(611\) −21.5224 + 37.2778i −0.870702 + 1.50810i
\(612\) −5.54468 + 2.28190i −0.224130 + 0.0922405i
\(613\) 1.36150 5.08118i 0.0549904 0.205227i −0.932965 0.359968i \(-0.882788\pi\)
0.987955 + 0.154741i \(0.0494543\pi\)
\(614\) −25.5312 −1.03036
\(615\) −24.4535 27.9480i −0.986060 1.12697i
\(616\) −19.7355 11.3943i −0.795167 0.459090i
\(617\) 10.9639 18.9900i 0.441390 0.764510i −0.556403 0.830913i \(-0.687819\pi\)
0.997793 + 0.0664029i \(0.0211523\pi\)
\(618\) 53.1504 + 18.1096i 2.13802 + 0.728476i
\(619\) −16.7777 + 9.68659i −0.674351 + 0.389337i −0.797723 0.603024i \(-0.793963\pi\)
0.123372 + 0.992360i \(0.460629\pi\)
\(620\) −15.8507 + 15.8507i −0.636581 + 0.636581i
\(621\) 4.34117 21.4416i 0.174205 0.860420i
\(622\) 25.0582 6.71432i 1.00474 0.269220i
\(623\) −6.67230 + 1.78784i −0.267320 + 0.0716282i
\(624\) −5.28263 + 1.04453i −0.211475 + 0.0418147i
\(625\) −15.6217 + 27.0576i −0.624868 + 1.08230i
\(626\) −28.1740 28.1740i −1.12606 1.12606i
\(627\) 44.3293 8.76520i 1.77034 0.350048i
\(628\) 25.0089 29.6917i 0.997963 1.18483i
\(629\) 5.00906i 0.199724i
\(630\) 33.6569 + 14.0310i 1.34092 + 0.559009i
\(631\) −32.8997 18.9947i −1.30972 0.756166i −0.327669 0.944792i \(-0.606263\pi\)
−0.982049 + 0.188626i \(0.939597\pi\)
\(632\) 16.8631 0.670778
\(633\) 19.7788 9.72586i 0.786138 0.386568i
\(634\) −16.3903 61.1696i −0.650944 2.42935i
\(635\) 16.4687 + 16.4687i 0.653539 + 0.653539i
\(636\) −11.2790 7.55499i −0.447243 0.299575i
\(637\) 8.04968 + 13.9425i 0.318940 + 0.552420i
\(638\) 44.9785 77.9051i 1.78072 3.08429i
\(639\) −23.0645 3.08994i −0.912419 0.122236i
\(640\) −22.9432 + 39.7388i −0.906911 + 1.57082i
\(641\) −20.4735 35.4611i −0.808654 1.40063i −0.913797 0.406172i \(-0.866863\pi\)
0.105143 0.994457i \(-0.466470\pi\)
\(642\) −72.0088 + 14.2382i −2.84196 + 0.561939i
\(643\) 19.4463 + 5.21061i 0.766886 + 0.205486i 0.620995 0.783814i \(-0.286729\pi\)
0.145890 + 0.989301i \(0.453395\pi\)
\(644\) 25.7801i 1.01588i
\(645\) −4.84165 1.64967i −0.190640 0.0649555i
\(646\) −2.11514 + 7.89380i −0.0832190 + 0.310577i
\(647\) 6.70450 + 3.87084i 0.263581 + 0.152179i 0.625967 0.779850i \(-0.284704\pi\)
−0.362386 + 0.932028i \(0.618038\pi\)
\(648\) −11.2466 + 19.2764i −0.441807 + 0.757247i
\(649\) −8.22900 + 2.20495i −0.323016 + 0.0865520i
\(650\) −7.35534 27.4505i −0.288500 1.07670i
\(651\) −5.06057 + 7.55504i −0.198339 + 0.296106i
\(652\) 19.6888 5.27559i 0.771072 0.206608i
\(653\) −11.5045 19.9264i −0.450207 0.779782i 0.548191 0.836353i \(-0.315317\pi\)
−0.998399 + 0.0565710i \(0.981983\pi\)
\(654\) −1.28984 + 19.3418i −0.0504369 + 0.756325i
\(655\) 24.3172i 0.950152i
\(656\) 3.32553 3.32553i 0.129840 0.129840i
\(657\) −22.0643 9.19824i −0.860810 0.358857i
\(658\) 18.4572 + 31.9688i 0.719535 + 1.24627i
\(659\) 3.07249 + 5.32170i 0.119687 + 0.207304i 0.919644 0.392754i \(-0.128478\pi\)
−0.799957 + 0.600058i \(0.795144\pi\)
\(660\) −56.4675 37.8234i −2.19799 1.47227i
\(661\) −0.618145 + 0.356886i −0.0240431 + 0.0138813i −0.511973 0.859001i \(-0.671085\pi\)
0.487930 + 0.872883i \(0.337752\pi\)
\(662\) 18.1769 + 67.8372i 0.706466 + 2.63657i
\(663\) 5.50348 + 1.87517i 0.213738 + 0.0728256i
\(664\) −8.91490 + 5.14702i −0.345965 + 0.199743i
\(665\) 26.1568 15.1016i 1.01432 0.585615i
\(666\) 31.9245 + 41.8015i 1.23705 + 1.61977i
\(667\) −36.0728 −1.39674
\(668\) −13.3764 7.72286i −0.517548 0.298806i
\(669\) 22.6164 + 15.1491i 0.874401 + 0.585697i
\(670\) 58.2272 + 33.6175i 2.24951 + 1.29876i
\(671\) 62.0438 + 16.6246i 2.39518 + 0.641785i
\(672\) −6.96480 + 20.4412i −0.268673 + 0.788535i
\(673\) 28.0872 + 28.0872i 1.08268 + 1.08268i 0.996258 + 0.0864251i \(0.0275443\pi\)
0.0864251 + 0.996258i \(0.472456\pi\)
\(674\) 39.7054i 1.52940i
\(675\) 11.2530 + 5.59721i 0.433127 + 0.215437i
\(676\) −37.7733 21.8084i −1.45282 0.838785i
\(677\) 41.5696 1.59765 0.798825 0.601563i \(-0.205455\pi\)
0.798825 + 0.601563i \(0.205455\pi\)
\(678\) −13.1511 0.877007i −0.505066 0.0336813i
\(679\) −16.0295 + 9.25462i −0.615155 + 0.355160i
\(680\) 3.77324 2.17848i 0.144697 0.0835409i
\(681\) 0.174733 2.62020i 0.00669578 0.100406i
\(682\) 19.7208 19.7208i 0.755150 0.755150i
\(683\) 39.3366 + 10.5402i 1.50517 + 0.403309i 0.914828 0.403843i \(-0.132326\pi\)
0.590343 + 0.807152i \(0.298992\pi\)
\(684\) 19.8469 + 48.2249i 0.758866 + 1.84393i
\(685\) 16.5982 9.58295i 0.634183 0.366146i
\(686\) 45.0444 1.71980
\(687\) −9.60145 6.43131i −0.366318 0.245370i
\(688\) 0.167658 0.625707i 0.00639189 0.0238548i
\(689\) 3.40712 + 12.7155i 0.129801 + 0.484424i
\(690\) −2.98408 + 44.7476i −0.113602 + 1.70351i
\(691\) 8.32595 + 2.23093i 0.316734 + 0.0848686i 0.413684 0.910421i \(-0.364242\pi\)
−0.0969497 + 0.995289i \(0.530909\pi\)
\(692\) −71.2325 −2.70785
\(693\) −25.4474 10.6086i −0.966668 0.402988i
\(694\) −34.0485 9.12327i −1.29246 0.346315i
\(695\) 48.4877i 1.83924i
\(696\) 34.8331 + 11.8685i 1.32034 + 0.449874i
\(697\) −4.90488 + 1.31426i −0.185786 + 0.0497811i
\(698\) 1.16542 + 4.34940i 0.0441117 + 0.164627i
\(699\) 0.470745 0.411885i 0.0178052 0.0155789i
\(700\) −14.3060 3.83329i −0.540717 0.144885i
\(701\) −11.0783 41.3447i −0.418421 1.56157i −0.777884 0.628408i \(-0.783707\pi\)
0.359463 0.933159i \(-0.382960\pi\)
\(702\) 57.8786 19.4270i 2.18449 0.733223i
\(703\) 43.5664 1.64314
\(704\) 30.3384 52.5477i 1.14342 1.98046i
\(705\) 17.2202 + 35.0196i 0.648552 + 1.31892i
\(706\) 18.5456 + 18.5456i 0.697974 + 0.697974i
\(707\) 10.8811 + 10.8811i 0.409224 + 0.409224i
\(708\) −4.33844 8.82280i −0.163049 0.331581i
\(709\) −22.3302 + 38.6770i −0.838628 + 1.45255i 0.0524136 + 0.998625i \(0.483309\pi\)
−0.891042 + 0.453921i \(0.850025\pi\)
\(710\) 47.7046 1.79032
\(711\) 20.2328 2.61685i 0.758789 0.0981395i
\(712\) 2.24313 + 8.37146i 0.0840647 + 0.313734i
\(713\) −10.8026 2.89455i −0.404561 0.108402i
\(714\) 3.75250 3.28331i 0.140434 0.122875i
\(715\) 17.0574 + 63.6592i 0.637912 + 2.38072i
\(716\) −24.9317 + 6.68042i −0.931740 + 0.249659i
\(717\) 28.7221 + 9.78630i 1.07264 + 0.365476i
\(718\) 48.1498i 1.79694i
\(719\) −30.4885 8.16938i −1.13703 0.304666i −0.359274 0.933232i \(-0.616976\pi\)
−0.777756 + 0.628566i \(0.783642\pi\)
\(720\) −1.87852 + 4.50609i −0.0700081 + 0.167932i
\(721\) −28.3766 −1.05680
\(722\) 27.2177 + 7.29297i 1.01294 + 0.271416i
\(723\) 0.911590 13.6697i 0.0339024 0.508382i
\(724\) 19.6016 + 73.1543i 0.728489 + 2.71876i
\(725\) 5.36373 20.0177i 0.199204 0.743439i
\(726\) 34.5126 + 23.1174i 1.28088 + 0.857968i
\(727\) 21.0439 0.780474 0.390237 0.920715i \(-0.372393\pi\)
0.390237 + 0.920715i \(0.372393\pi\)
\(728\) −22.0858 + 12.7512i −0.818554 + 0.472592i
\(729\) −10.5026 + 24.8736i −0.388985 + 0.921244i
\(730\) 47.3350 + 12.6834i 1.75195 + 0.469433i
\(731\) −0.494563 + 0.494563i −0.0182921 + 0.0182921i
\(732\) −4.93242 + 73.9640i −0.182308 + 2.73379i
\(733\) −42.0991 + 24.3059i −1.55496 + 0.897759i −0.557239 + 0.830352i \(0.688139\pi\)
−0.997726 + 0.0674065i \(0.978528\pi\)
\(734\) 9.94106 5.73947i 0.366931 0.211848i
\(735\) 14.5634 + 0.971186i 0.537179 + 0.0358227i
\(736\) −26.5595 −0.978995
\(737\) −44.0246 25.4176i −1.62167 0.936271i
\(738\) −32.5559 + 42.2282i −1.19840 + 1.55444i
\(739\) 6.89162i 0.253512i 0.991934 + 0.126756i \(0.0404566\pi\)
−0.991934 + 0.126756i \(0.959543\pi\)
\(740\) −46.3340 46.3340i −1.70327 1.70327i
\(741\) 16.3093 47.8666i 0.599138 1.75843i
\(742\) 10.9046 + 2.92188i 0.400321 + 0.107266i
\(743\) −20.1316 11.6230i −0.738557 0.426406i 0.0829874 0.996551i \(-0.473554\pi\)
−0.821544 + 0.570145i \(0.806887\pi\)
\(744\) 9.47901 + 6.34929i 0.347517 + 0.232776i
\(745\) −28.5079 16.4590i −1.04445 0.603012i
\(746\) −1.75396 −0.0642169
\(747\) −9.89762 + 7.55897i −0.362135 + 0.276568i
\(748\) −8.04834 + 4.64671i −0.294276 + 0.169901i
\(749\) 32.1254 18.5476i 1.17384 0.677714i
\(750\) 26.0266 + 8.86789i 0.950356 + 0.323809i
\(751\) −6.20651 23.1630i −0.226479 0.845230i −0.981807 0.189883i \(-0.939189\pi\)
0.755328 0.655347i \(-0.227478\pi\)
\(752\) −4.28008 + 2.47110i −0.156078 + 0.0901119i
\(753\) −33.6551 22.5430i −1.22646 0.821514i
\(754\) −50.3349 87.1827i −1.83309 3.17501i
\(755\) −3.62641 6.28113i −0.131979 0.228594i
\(756\) 6.31386 31.1849i 0.229633 1.13419i
\(757\) −33.2603 + 33.2603i −1.20887 + 1.20887i −0.237471 + 0.971395i \(0.576319\pi\)
−0.971395 + 0.237471i \(0.923681\pi\)
\(758\) 31.8626i 1.15730i
\(759\) 2.25621 33.8329i 0.0818953 1.22806i
\(760\) −18.9474 32.8178i −0.687294 1.19043i
\(761\) 11.4059 3.05620i 0.413464 0.110787i −0.0460899 0.998937i \(-0.514676\pi\)
0.459554 + 0.888150i \(0.348009\pi\)
\(762\) 18.6104 27.7840i 0.674185 1.00651i
\(763\) −2.53548 9.46256i −0.0917907 0.342568i
\(764\) −27.8711 + 7.46803i −1.00834 + 0.270184i
\(765\) 4.18918 3.19934i 0.151460 0.115672i
\(766\) −45.8804 26.4891i −1.65773 0.957089i
\(767\) −2.46754 + 9.20897i −0.0890976 + 0.332517i
\(768\) 19.5771 + 6.67038i 0.706427 + 0.240697i
\(769\) 24.9805i 0.900819i −0.892822 0.450410i \(-0.851278\pi\)
0.892822 0.450410i \(-0.148722\pi\)
\(770\) 54.5929 + 14.6281i 1.96739 + 0.527161i
\(771\) 11.3444 2.24312i 0.408558 0.0807839i
\(772\) −18.2799 31.6617i −0.657907 1.13953i
\(773\) 7.26402 12.5817i 0.261269 0.452531i −0.705311 0.708898i \(-0.749192\pi\)
0.966579 + 0.256368i \(0.0825258\pi\)
\(774\) −0.975194 + 7.27923i −0.0350526 + 0.261647i
\(775\) 3.21252 5.56424i 0.115397 0.199874i
\(776\) 11.6114 + 20.1115i 0.416825 + 0.721962i
\(777\) −22.0845 14.7928i −0.792277 0.530688i
\(778\) −27.8629 27.8629i −0.998934 0.998934i
\(779\) 11.4308 + 42.6603i 0.409551 + 1.52846i
\(780\) −68.2529 + 33.5621i −2.44385 + 1.20171i
\(781\) −36.0687 −1.29064
\(782\) 5.31076 + 3.06617i 0.189913 + 0.109646i
\(783\) 43.6355 + 8.83466i 1.55941 + 0.315725i
\(784\) 1.84846i 0.0660164i
\(785\) −14.4810 + 30.9038i −0.516848 + 1.10300i
\(786\) 34.2524 6.77270i 1.22174 0.241574i
\(787\) 1.77045 + 1.77045i 0.0631096 + 0.0631096i 0.737957 0.674848i \(-0.235791\pi\)
−0.674848 + 0.737957i \(0.735791\pi\)
\(788\) 21.3326 36.9491i 0.759942 1.31626i
\(789\) −38.2923 + 7.57151i −1.36324 + 0.269553i
\(790\) −40.3976 + 10.8245i −1.43728 + 0.385118i
\(791\) 6.43390 1.72396i 0.228763 0.0612969i
\(792\) −13.3102 + 31.9279i −0.472957 + 1.13451i
\(793\) 50.8281 50.8281i 1.80496 1.80496i
\(794\) −48.4889 + 27.9951i −1.72081 + 0.993509i
\(795\) 11.2969 + 3.84912i 0.400659 + 0.136514i
\(796\) −34.5025 + 59.7601i −1.22291 + 2.11814i
\(797\) −9.38140 5.41635i −0.332306 0.191857i 0.324558 0.945866i \(-0.394784\pi\)
−0.656864 + 0.754009i \(0.728118\pi\)
\(798\) −28.5566 32.6375i −1.01089 1.15535i
\(799\) 5.33618 0.188780
\(800\) 3.94917 14.7385i 0.139624 0.521085i
\(801\) 3.99047 + 9.69622i 0.140996 + 0.342599i
\(802\) −14.2868 + 24.7454i −0.504483 + 0.873790i
\(803\) −35.7892 9.58969i −1.26297 0.338413i
\(804\) 18.9211 55.5321i 0.667297 1.95847i
\(805\) −5.86588 21.8918i −0.206745 0.771584i
\(806\) −8.07794 30.1473i −0.284533 1.06189i
\(807\) −7.36519 14.9781i −0.259267 0.527253i
\(808\) 13.6520 13.6520i 0.480276 0.480276i
\(809\) −4.30614 16.0708i −0.151396 0.565018i −0.999387 0.0350070i \(-0.988855\pi\)
0.847991 0.530010i \(-0.177812\pi\)
\(810\) 14.5689 53.3981i 0.511899 1.87622i
\(811\) 15.1417 + 4.05721i 0.531697 + 0.142468i 0.514672 0.857387i \(-0.327914\pi\)
0.0170251 + 0.999855i \(0.494580\pi\)
\(812\) −52.4648 −1.84115
\(813\) −12.9760 8.69166i −0.455088 0.304830i
\(814\) 57.6469 + 57.6469i 2.02052 + 2.02052i
\(815\) −15.5188 + 8.95977i −0.543599 + 0.313847i
\(816\) 0.439580 + 0.502397i 0.0153884 + 0.0175874i
\(817\) 4.30147 + 4.30147i 0.150489 + 0.150489i
\(818\) 28.8933 + 50.0447i 1.01023 + 1.74977i
\(819\) −24.5204 + 18.7266i −0.856812 + 0.654361i
\(820\) 33.2134 57.5274i 1.15986 2.00894i
\(821\) −8.89171 15.4009i −0.310323 0.537495i 0.668110 0.744063i \(-0.267104\pi\)
−0.978432 + 0.206568i \(0.933770\pi\)
\(822\) −18.1210 20.7106i −0.632044 0.722365i
\(823\) −20.5528 + 5.50710i −0.716425 + 0.191966i −0.598576 0.801066i \(-0.704267\pi\)
−0.117849 + 0.993032i \(0.537600\pi\)
\(824\) 35.6030i 1.24029i
\(825\) 18.4393 + 6.28271i 0.641973 + 0.218736i
\(826\) 5.78132 + 5.78132i 0.201158 + 0.201158i
\(827\) −8.01702 + 13.8859i −0.278779 + 0.482860i −0.971082 0.238748i \(-0.923263\pi\)
0.692303 + 0.721607i \(0.256596\pi\)
\(828\) 38.8088 5.01941i 1.34870 0.174436i
\(829\) 34.8884 + 20.1428i 1.21172 + 0.699589i 0.963135 0.269020i \(-0.0866997\pi\)
0.248589 + 0.968609i \(0.420033\pi\)
\(830\) 18.0528 18.0528i 0.626623 0.626623i
\(831\) −7.33882 + 1.45110i −0.254581 + 0.0503381i
\(832\) −33.9513 58.8054i −1.17705 2.03871i
\(833\) 0.997905 1.72842i 0.0345754 0.0598863i
\(834\) 68.2981 13.5045i 2.36497 0.467624i
\(835\) 13.1161 + 3.51444i 0.453901 + 0.121622i
\(836\) 40.4149 + 70.0006i 1.39778 + 2.42102i
\(837\) 12.3585 + 6.14708i 0.427171 + 0.212474i
\(838\) −2.77647 0.743954i −0.0959117 0.0256995i
\(839\) 27.5389 + 27.5389i 0.950747 + 0.950747i 0.998843 0.0480957i \(-0.0153152\pi\)
−0.0480957 + 0.998843i \(0.515315\pi\)
\(840\) −1.53842 + 23.0694i −0.0530807 + 0.795969i
\(841\) 44.4114i 1.53143i
\(842\) −24.0365 41.6325i −0.828354 1.43475i
\(843\) −17.2055 + 3.40203i −0.592590 + 0.117172i
\(844\) 27.8781 + 27.8781i 0.959604 + 0.959604i
\(845\) 37.0382 + 9.92436i 1.27415 + 0.341408i
\(846\) 44.5314 34.0093i 1.53102 1.16926i
\(847\) −20.2773 5.43328i −0.696735 0.186690i
\(848\) −0.391191 + 1.45994i −0.0134335 + 0.0501347i
\(849\) −6.37095 32.2206i −0.218650 1.10581i
\(850\) −2.49116 + 2.49116i −0.0854462 + 0.0854462i
\(851\) 8.46120 31.5776i 0.290046 1.08247i
\(852\) −8.07425 40.8349i −0.276619 1.39898i
\(853\) −10.8141 6.24354i −0.370269 0.213775i 0.303307 0.952893i \(-0.401909\pi\)
−0.673576 + 0.739118i \(0.735243\pi\)
\(854\) −15.9548 59.5440i −0.545961 2.03755i
\(855\) −27.8263 36.4354i −0.951640 1.24607i
\(856\) −23.2709 40.3064i −0.795384 1.37764i
\(857\) 0.963180 3.59464i 0.0329016 0.122790i −0.947522 0.319691i \(-0.896421\pi\)
0.980423 + 0.196901i \(0.0630876\pi\)
\(858\) 84.9175 41.7565i 2.89903 1.42555i
\(859\) −4.32624 + 16.1457i −0.147609 + 0.550886i 0.852016 + 0.523516i \(0.175380\pi\)
−0.999625 + 0.0273698i \(0.991287\pi\)
\(860\) 9.14945i 0.311994i
\(861\) 8.69068 25.5065i 0.296178 0.869259i
\(862\) −11.7250 43.7582i −0.399355 1.49041i
\(863\) −11.2849 + 11.2849i −0.384142 + 0.384142i −0.872592 0.488450i \(-0.837563\pi\)
0.488450 + 0.872592i \(0.337563\pi\)
\(864\) 32.1277 + 6.50474i 1.09301 + 0.221296i
\(865\) 60.4887 16.2079i 2.05668 0.551085i
\(866\) −35.2275 20.3386i −1.19708 0.691134i
\(867\) 5.57172 + 28.1785i 0.189225 + 0.956993i
\(868\) −15.7115 4.20988i −0.533282 0.142893i
\(869\) 30.5440 8.18423i 1.03613 0.277631i
\(870\) −91.0654 6.07286i −3.08740 0.205889i
\(871\) −49.2674 + 28.4446i −1.66936 + 0.963807i
\(872\) −11.8723 + 3.18117i −0.402046 + 0.107728i
\(873\) 17.0526 + 22.3285i 0.577144 + 0.755705i
\(874\) 26.6681 46.1905i 0.902061 1.56242i
\(875\) −13.8954 −0.469750
\(876\) 2.84521 42.6652i 0.0961307 1.44152i
\(877\) 10.3191 + 10.3191i 0.348450 + 0.348450i 0.859532 0.511082i \(-0.170755\pi\)
−0.511082 + 0.859532i \(0.670755\pi\)
\(878\) 48.9428i 1.65174i
\(879\) 38.4872 + 2.56659i 1.29814 + 0.0865689i
\(880\) −1.95846 + 7.30908i −0.0660197 + 0.246389i
\(881\) 30.8493 8.26605i 1.03934 0.278490i 0.301500 0.953466i \(-0.402513\pi\)
0.737840 + 0.674976i \(0.235846\pi\)
\(882\) −2.68814 20.7840i −0.0905142 0.699833i
\(883\) 17.0985 17.0985i 0.575410 0.575410i −0.358225 0.933635i \(-0.616618\pi\)
0.933635 + 0.358225i \(0.116618\pi\)
\(884\) 10.4002i 0.349795i
\(885\) 5.69159 + 6.50493i 0.191321 + 0.218661i
\(886\) 5.10820 0.171613
\(887\) 14.7582 55.0782i 0.495530 1.84934i −0.0315097 0.999503i \(-0.510032\pi\)
0.527040 0.849841i \(-0.323302\pi\)
\(888\) −18.5599 + 27.7085i −0.622830 + 0.929838i
\(889\) −4.37400 + 16.3240i −0.146699 + 0.547489i
\(890\) −10.7474 18.6150i −0.360252 0.623976i
\(891\) −11.0153 + 40.3735i −0.369027 + 1.35256i
\(892\) −12.6025 + 47.0331i −0.421962 + 1.57479i
\(893\) 46.4115i 1.55310i
\(894\) −15.2438 + 44.7393i −0.509828 + 1.49631i
\(895\) 19.6513 11.3457i 0.656869 0.379244i
\(896\) −33.2961 −1.11234
\(897\) −31.5270 21.1176i −1.05266 0.705097i
\(898\) −25.2861 + 43.7968i −0.843808 + 1.46152i
\(899\) 5.89067 21.9843i 0.196465 0.733217i
\(900\) −2.98515 + 22.2823i −0.0995049 + 0.742743i
\(901\) 1.15395 1.15395i 0.0384436 0.0384436i
\(902\) −41.3228 + 71.5732i −1.37590 + 2.38313i
\(903\) −0.719938 3.64103i −0.0239580 0.121166i
\(904\) −2.16298 8.07235i −0.0719397 0.268483i
\(905\) −33.2903 57.6606i −1.10661 1.91670i
\(906\) −7.83738 + 6.85743i −0.260379 + 0.227823i
\(907\) −0.626017 0.361431i −0.0207866 0.0120011i 0.489571 0.871964i \(-0.337154\pi\)
−0.510357 + 0.859962i \(0.670487\pi\)
\(908\) 4.53727 1.21576i 0.150574 0.0403463i
\(909\) 14.2615 18.4986i 0.473025 0.613560i
\(910\) 44.7241 44.7241i 1.48259 1.48259i
\(911\) −7.51180 + 4.33694i −0.248877 + 0.143689i −0.619250 0.785194i \(-0.712563\pi\)
0.370373 + 0.928883i \(0.379230\pi\)
\(912\) 4.36961 3.82325i 0.144692 0.126601i
\(913\) −13.6495 + 13.6495i −0.451731 + 0.451731i
\(914\) 35.0536 + 35.0536i 1.15947 + 1.15947i
\(915\) −12.6409 63.9305i −0.417896 2.11348i
\(916\) 5.35019 19.9672i 0.176775 0.659735i
\(917\) −15.2811 + 8.82252i −0.504625 + 0.291345i
\(918\) −5.67323 5.00967i −0.187244 0.165344i
\(919\) 19.7424 + 19.7424i 0.651242 + 0.651242i 0.953292 0.302050i \(-0.0976710\pi\)
−0.302050 + 0.953292i \(0.597671\pi\)
\(920\) −27.4667 + 7.35969i −0.905551 + 0.242642i
\(921\) −8.64220 17.5751i −0.284770 0.579118i
\(922\) −78.9569 + 21.1564i −2.60031 + 0.696750i
\(923\) −20.1820 + 34.9563i −0.664299 + 1.15060i
\(924\) 3.28147 49.2071i 0.107952 1.61880i
\(925\) 16.2651 + 9.39066i 0.534793 + 0.308763i
\(926\) −89.2715 −2.93364
\(927\) 5.52494 + 42.7175i 0.181463 + 1.40303i
\(928\) 54.0509i 1.77431i
\(929\) −11.0821 + 6.39825i −0.363592 + 0.209920i −0.670655 0.741769i \(-0.733987\pi\)
0.307063 + 0.951689i \(0.400654\pi\)
\(930\) −26.7838 9.12588i −0.878274 0.299249i
\(931\) −15.0330 8.67930i −0.492686 0.284452i
\(932\) 0.968969 + 0.559435i 0.0317396 + 0.0183249i
\(933\) 13.1041 + 14.9767i 0.429008 + 0.490315i
\(934\) 43.5735 + 43.5735i 1.42577 + 1.42577i
\(935\) 5.77714 5.77714i 0.188933 0.188933i
\(936\) 23.4955 + 30.7647i 0.767975 + 1.00558i
\(937\) −6.82397 25.4674i −0.222929 0.831984i −0.983224 0.182405i \(-0.941612\pi\)
0.760294 0.649579i \(-0.225055\pi\)
\(938\) 48.7870i 1.59295i
\(939\) 9.85750 28.9310i 0.321687 0.944128i
\(940\) −49.3599 + 49.3599i −1.60994 + 1.60994i
\(941\) −41.5295 −1.35382 −0.676912 0.736064i \(-0.736682\pi\)
−0.676912 + 0.736064i \(0.736682\pi\)
\(942\) 47.5631 + 11.7902i 1.54969 + 0.384147i
\(943\) 33.1409 1.07922
\(944\) −0.774022 + 0.774022i −0.0251923 + 0.0251923i
\(945\) 1.73411 + 27.9180i 0.0564106 + 0.908174i
\(946\) 11.3834i 0.370106i
\(947\) −2.93395 10.9496i −0.0953404 0.355815i 0.901730 0.432299i \(-0.142297\pi\)
−0.997071 + 0.0764835i \(0.975631\pi\)
\(948\) 16.1032 + 32.7480i 0.523008 + 1.06361i
\(949\) −29.3196 + 29.3196i −0.951754 + 0.951754i
\(950\) 21.6669 + 21.6669i 0.702968 + 0.702968i
\(951\) 36.5596 31.9883i 1.18553 1.03729i
\(952\) 2.73794 + 1.58075i 0.0887370 + 0.0512323i
\(953\) 15.9146 + 9.18830i 0.515525 + 0.297638i 0.735102 0.677957i \(-0.237134\pi\)
−0.219577 + 0.975595i \(0.570468\pi\)
\(954\) 2.27539 16.9844i 0.0736686 0.549891i
\(955\) 21.9681 12.6833i 0.710871 0.410422i
\(956\) 54.2772i 1.75545i
\(957\) 68.8530 + 4.59159i 2.22570 + 0.148425i
\(958\) 30.3536 0.980680
\(959\) 12.0439 + 6.95358i 0.388919 + 0.224543i
\(960\) −61.4243 4.09620i −1.98246 0.132204i
\(961\) −11.9719 + 20.7359i −0.386190 + 0.668900i
\(962\) 88.1250 23.6130i 2.84126 0.761314i
\(963\) −34.1759 44.7495i −1.10130 1.44203i
\(964\) 23.6711 6.34266i 0.762395 0.204283i
\(965\) 22.7269 + 22.7269i 0.731605 + 0.731605i
\(966\) −29.2023 + 14.3597i −0.939567 + 0.462014i
\(967\) 33.9468 19.5992i 1.09166 0.630268i 0.157640 0.987497i \(-0.449612\pi\)
0.934017 + 0.357228i \(0.116278\pi\)
\(968\) −6.81691 + 25.4411i −0.219104 + 0.817707i
\(969\) −6.14986 + 1.21601i −0.197562 + 0.0390638i
\(970\) −40.7262 40.7262i −1.30764 1.30764i
\(971\) 2.75128 2.75128i 0.0882927 0.0882927i −0.661581 0.749874i \(-0.730114\pi\)
0.749874 + 0.661581i \(0.230114\pi\)
\(972\) −48.1743 3.43300i −1.54519 0.110114i
\(973\) −30.4699 + 17.5918i −0.976821 + 0.563968i
\(974\) −22.6333 + 22.6333i −0.725218 + 0.725218i
\(975\) 16.4065 14.3551i 0.525429 0.459732i
\(976\) 7.97193 2.13607i 0.255175 0.0683740i
\(977\) −24.9482 14.4038i −0.798164 0.460820i 0.0446650 0.999002i \(-0.485778\pi\)
−0.842829 + 0.538182i \(0.819111\pi\)
\(978\) 16.9426 + 19.3638i 0.541766 + 0.619186i
\(979\) 8.12591 + 14.0745i 0.259705 + 0.449822i
\(980\) 6.75732 + 25.2186i 0.215855 + 0.805580i
\(981\) −13.7510 + 5.65922i −0.439037 + 0.180685i
\(982\) −35.6116 + 61.6812i −1.13641 + 1.96833i
\(983\) 2.13967 2.13967i 0.0682448 0.0682448i −0.672161 0.740405i \(-0.734634\pi\)
0.740405 + 0.672161i \(0.234634\pi\)
\(984\) −32.0020 10.9038i −1.02019 0.347602i
\(985\) −9.70783 + 36.2301i −0.309317 + 1.15439i
\(986\) −6.23993 + 10.8079i −0.198720 + 0.344193i
\(987\) −15.7588 + 23.5268i −0.501609 + 0.748865i
\(988\) 90.4556 2.87777
\(989\) 3.95318 2.28237i 0.125704 0.0725751i
\(990\) 11.3916 85.0310i 0.362047 2.70246i
\(991\) 10.8201i 0.343711i 0.985122 + 0.171855i \(0.0549762\pi\)
−0.985122 + 0.171855i \(0.945024\pi\)
\(992\) 4.33715 16.1865i 0.137705 0.513921i
\(993\) −40.5447 + 35.4752i −1.28665 + 1.12577i
\(994\) 17.3077 + 29.9778i 0.548967 + 0.950839i
\(995\) 15.7011 58.5972i 0.497757 1.85765i
\(996\) −18.5087 12.3976i −0.586469 0.392833i
\(997\) −4.16012 + 15.5258i −0.131752 + 0.491706i −0.999990 0.00444189i \(-0.998586\pi\)
0.868238 + 0.496148i \(0.165253\pi\)
\(998\) 84.5819 2.67739
\(999\) −17.9688 + 36.1256i −0.568509 + 1.14296i
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 471.2.l.b.50.6 200
3.2 odd 2 inner 471.2.l.b.50.45 yes 200
157.22 odd 12 inner 471.2.l.b.179.45 yes 200
471.179 even 12 inner 471.2.l.b.179.6 yes 200
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
471.2.l.b.50.6 200 1.1 even 1 trivial
471.2.l.b.50.45 yes 200 3.2 odd 2 inner
471.2.l.b.179.6 yes 200 471.179 even 12 inner
471.2.l.b.179.45 yes 200 157.22 odd 12 inner