Properties

Label 336.2.y.a.125.16
Level $336$
Weight $2$
Character 336.125
Analytic conductor $2.683$
Analytic rank $0$
Dimension $120$
CM no
Inner twists $8$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [336,2,Mod(125,336)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(336, base_ring=CyclotomicField(4))
 
chi = DirichletCharacter(H, H._module([0, 3, 2, 2]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("336.125");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 336 = 2^{4} \cdot 3 \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 336.y (of order \(4\), degree \(2\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(2.68297350792\)
Analytic rank: \(0\)
Dimension: \(120\)
Relative dimension: \(60\) over \(\Q(i)\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 125.16
Character \(\chi\) \(=\) 336.125
Dual form 336.2.y.a.293.16

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.957005 + 1.04122i) q^{2} +(1.52023 + 0.830004i) q^{3} +(-0.168282 - 1.99291i) q^{4} +(1.24321 - 1.24321i) q^{5} +(-2.31908 + 0.788576i) q^{6} +(-1.10620 - 2.40340i) q^{7} +(2.23610 + 1.73200i) q^{8} +(1.62219 + 2.52359i) q^{9} +O(q^{10})\) \(q+(-0.957005 + 1.04122i) q^{2} +(1.52023 + 0.830004i) q^{3} +(-0.168282 - 1.99291i) q^{4} +(1.24321 - 1.24321i) q^{5} +(-2.31908 + 0.788576i) q^{6} +(-1.10620 - 2.40340i) q^{7} +(2.23610 + 1.73200i) q^{8} +(1.62219 + 2.52359i) q^{9} +(0.104698 + 2.48421i) q^{10} +(0.0609709 + 0.0609709i) q^{11} +(1.39829 - 3.16935i) q^{12} +(1.21487 - 1.21487i) q^{13} +(3.56111 + 1.14827i) q^{14} +(2.92183 - 0.858093i) q^{15} +(-3.94336 + 0.670742i) q^{16} +5.01681 q^{17} +(-4.18006 - 0.726033i) q^{18} +(3.53049 - 3.53049i) q^{19} +(-2.68681 - 2.26839i) q^{20} +(0.313152 - 4.57186i) q^{21} +(-0.121834 + 0.00513471i) q^{22} +0.280155 q^{23} +(1.96182 + 4.48902i) q^{24} +1.90886i q^{25} +(0.102311 + 2.42758i) q^{26} +(0.371506 + 5.18285i) q^{27} +(-4.60360 + 2.60900i) q^{28} +(-6.89820 + 6.89820i) q^{29} +(-1.90274 + 3.86347i) q^{30} -5.91625i q^{31} +(3.07543 - 4.74782i) q^{32} +(0.0420836 + 0.143296i) q^{33} +(-4.80111 + 5.22360i) q^{34} +(-4.36316 - 1.61269i) q^{35} +(4.75630 - 3.65755i) q^{36} +(0.0123848 - 0.0123848i) q^{37} +(0.297323 + 7.05472i) q^{38} +(2.85522 - 0.838531i) q^{39} +(4.93319 - 0.626702i) q^{40} +3.16937i q^{41} +(4.46063 + 4.70136i) q^{42} +(-3.09016 + 3.09016i) q^{43} +(0.111249 - 0.131770i) q^{44} +(5.15407 + 1.12063i) q^{45} +(-0.268110 + 0.291703i) q^{46} -4.07120 q^{47} +(-6.55153 - 2.25332i) q^{48} +(-4.55264 + 5.31728i) q^{49} +(-1.98755 - 1.82679i) q^{50} +(7.62669 + 4.16397i) q^{51} +(-2.62556 - 2.21668i) q^{52} +(2.89054 + 2.89054i) q^{53} +(-5.75203 - 4.57320i) q^{54} +0.151599 q^{55} +(1.68912 - 7.29019i) q^{56} +(8.29747 - 2.43683i) q^{57} +(-0.580938 - 13.7842i) q^{58} +(-7.03973 + 7.03973i) q^{59} +(-2.20179 - 5.67853i) q^{60} +(9.52586 - 9.52586i) q^{61} +(6.16013 + 5.66188i) q^{62} +(4.27073 - 6.69036i) q^{63} +(2.00032 + 7.74588i) q^{64} -3.02067i q^{65} +(-0.189477 - 0.0933164i) q^{66} +(-5.50592 - 5.50592i) q^{67} +(-0.844240 - 9.99803i) q^{68} +(0.425900 + 0.232530i) q^{69} +(5.85473 - 2.99967i) q^{70} -8.84887 q^{71} +(-0.743487 + 8.45265i) q^{72} -7.61652 q^{73} +(0.00104299 + 0.0247476i) q^{74} +(-1.58436 + 2.90191i) q^{75} +(-7.63006 - 6.44182i) q^{76} +(0.0790913 - 0.213983i) q^{77} +(-1.85936 + 3.77539i) q^{78} +1.98466 q^{79} +(-4.06855 + 5.73630i) q^{80} +(-3.73701 + 8.18747i) q^{81} +(-3.30002 - 3.03311i) q^{82} +(-4.67832 - 4.67832i) q^{83} +(-9.16400 + 0.145280i) q^{84} +(6.23694 - 6.23694i) q^{85} +(-0.260240 - 6.17483i) q^{86} +(-16.2124 + 4.76131i) q^{87} +(0.0307354 + 0.241939i) q^{88} -14.9865i q^{89} +(-6.09929 + 4.29407i) q^{90} +(-4.26369 - 1.57592i) q^{91} +(-0.0471451 - 0.558323i) q^{92} +(4.91051 - 8.99405i) q^{93} +(3.89616 - 4.23902i) q^{94} -8.77827i q^{95} +(8.61606 - 4.66515i) q^{96} +14.3790i q^{97} +(-1.17956 - 9.82897i) q^{98} +(-0.0549593 + 0.252772i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 120 q - 8 q^{4}+O(q^{10}) \) Copy content Toggle raw display \( 120 q - 8 q^{4} - 8 q^{15} + 8 q^{16} - 32 q^{18} - 8 q^{21} + 16 q^{22} - 16 q^{30} - 8 q^{36} - 8 q^{37} - 24 q^{42} - 8 q^{43} - 24 q^{46} - 8 q^{49} - 56 q^{51} + 40 q^{58} - 96 q^{60} + 24 q^{63} - 56 q^{64} + 24 q^{67} - 80 q^{70} - 8 q^{72} + 64 q^{78} - 16 q^{79} - 8 q^{81} - 48 q^{84} - 48 q^{85} - 24 q^{88} - 8 q^{91} + 8 q^{93} - 40 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/336\mathbb{Z}\right)^\times\).

\(n\) \(85\) \(113\) \(127\) \(241\)
\(\chi(n)\) \(e\left(\frac{3}{4}\right)\) \(-1\) \(1\) \(-1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.957005 + 1.04122i −0.676705 + 0.736254i
\(3\) 1.52023 + 0.830004i 0.877704 + 0.479203i
\(4\) −0.168282 1.99291i −0.0841411 0.996454i
\(5\) 1.24321 1.24321i 0.555980 0.555980i −0.372180 0.928160i \(-0.621390\pi\)
0.928160 + 0.372180i \(0.121390\pi\)
\(6\) −2.31908 + 0.788576i −0.946762 + 0.321935i
\(7\) −1.10620 2.40340i −0.418104 0.908399i
\(8\) 2.23610 + 1.73200i 0.790582 + 0.612356i
\(9\) 1.62219 + 2.52359i 0.540729 + 0.841197i
\(10\) 0.104698 + 2.48421i 0.0331084 + 0.785577i
\(11\) 0.0609709 + 0.0609709i 0.0183834 + 0.0183834i 0.716239 0.697855i \(-0.245862\pi\)
−0.697855 + 0.716239i \(0.745862\pi\)
\(12\) 1.39829 3.16935i 0.403653 0.914912i
\(13\) 1.21487 1.21487i 0.336943 0.336943i −0.518272 0.855216i \(-0.673425\pi\)
0.855216 + 0.518272i \(0.173425\pi\)
\(14\) 3.56111 + 1.14827i 0.951746 + 0.306887i
\(15\) 2.92183 0.858093i 0.754413 0.221559i
\(16\) −3.94336 + 0.670742i −0.985841 + 0.167686i
\(17\) 5.01681 1.21675 0.608377 0.793648i \(-0.291821\pi\)
0.608377 + 0.793648i \(0.291821\pi\)
\(18\) −4.18006 0.726033i −0.985249 0.171128i
\(19\) 3.53049 3.53049i 0.809950 0.809950i −0.174676 0.984626i \(-0.555888\pi\)
0.984626 + 0.174676i \(0.0558878\pi\)
\(20\) −2.68681 2.26839i −0.600789 0.507228i
\(21\) 0.313152 4.57186i 0.0683355 0.997662i
\(22\) −0.121834 + 0.00513471i −0.0259750 + 0.00109472i
\(23\) 0.280155 0.0584164 0.0292082 0.999573i \(-0.490701\pi\)
0.0292082 + 0.999573i \(0.490701\pi\)
\(24\) 1.96182 + 4.48902i 0.400455 + 0.916317i
\(25\) 1.90886i 0.381773i
\(26\) 0.102311 + 2.42758i 0.0200648 + 0.476087i
\(27\) 0.371506 + 5.18285i 0.0714965 + 0.997441i
\(28\) −4.60360 + 2.60900i −0.869998 + 0.493055i
\(29\) −6.89820 + 6.89820i −1.28096 + 1.28096i −0.340844 + 0.940120i \(0.610713\pi\)
−0.940120 + 0.340844i \(0.889287\pi\)
\(30\) −1.90274 + 3.86347i −0.347391 + 0.705370i
\(31\) 5.91625i 1.06259i −0.847187 0.531295i \(-0.821706\pi\)
0.847187 0.531295i \(-0.178294\pi\)
\(32\) 3.07543 4.74782i 0.543664 0.839303i
\(33\) 0.0420836 + 0.143296i 0.00732581 + 0.0249446i
\(34\) −4.80111 + 5.22360i −0.823384 + 0.895841i
\(35\) −4.36316 1.61269i −0.737509 0.272594i
\(36\) 4.75630 3.65755i 0.792716 0.609591i
\(37\) 0.0123848 0.0123848i 0.00203605 0.00203605i −0.706088 0.708124i \(-0.749542\pi\)
0.708124 + 0.706088i \(0.249542\pi\)
\(38\) 0.297323 + 7.05472i 0.0482322 + 1.14443i
\(39\) 2.85522 0.838531i 0.457201 0.134272i
\(40\) 4.93319 0.626702i 0.780005 0.0990903i
\(41\) 3.16937i 0.494973i 0.968891 + 0.247486i \(0.0796046\pi\)
−0.968891 + 0.247486i \(0.920395\pi\)
\(42\) 4.46063 + 4.70136i 0.688290 + 0.725435i
\(43\) −3.09016 + 3.09016i −0.471245 + 0.471245i −0.902317 0.431073i \(-0.858135\pi\)
0.431073 + 0.902317i \(0.358135\pi\)
\(44\) 0.111249 0.131770i 0.0167714 0.0198650i
\(45\) 5.15407 + 1.12063i 0.768323 + 0.167054i
\(46\) −0.268110 + 0.291703i −0.0395306 + 0.0430093i
\(47\) −4.07120 −0.593846 −0.296923 0.954901i \(-0.595960\pi\)
−0.296923 + 0.954901i \(0.595960\pi\)
\(48\) −6.55153 2.25332i −0.945632 0.325239i
\(49\) −4.55264 + 5.31728i −0.650378 + 0.759611i
\(50\) −1.98755 1.82679i −0.281082 0.258347i
\(51\) 7.62669 + 4.16397i 1.06795 + 0.583072i
\(52\) −2.62556 2.21668i −0.364099 0.307398i
\(53\) 2.89054 + 2.89054i 0.397046 + 0.397046i 0.877190 0.480144i \(-0.159415\pi\)
−0.480144 + 0.877190i \(0.659415\pi\)
\(54\) −5.75203 4.57320i −0.782752 0.622333i
\(55\) 0.151599 0.0204416
\(56\) 1.68912 7.29019i 0.225718 0.974193i
\(57\) 8.29747 2.43683i 1.09903 0.322766i
\(58\) −0.580938 13.7842i −0.0762809 1.80995i
\(59\) −7.03973 + 7.03973i −0.916495 + 0.916495i −0.996773 0.0802776i \(-0.974419\pi\)
0.0802776 + 0.996773i \(0.474419\pi\)
\(60\) −2.20179 5.67853i −0.284250 0.733096i
\(61\) 9.52586 9.52586i 1.21966 1.21966i 0.251912 0.967750i \(-0.418941\pi\)
0.967750 0.251912i \(-0.0810592\pi\)
\(62\) 6.16013 + 5.66188i 0.782337 + 0.719060i
\(63\) 4.27073 6.69036i 0.538061 0.842906i
\(64\) 2.00032 + 7.74588i 0.250041 + 0.968235i
\(65\) 3.02067i 0.374667i
\(66\) −0.189477 0.0933164i −0.0233230 0.0114865i
\(67\) −5.50592 5.50592i −0.672655 0.672655i 0.285672 0.958327i \(-0.407783\pi\)
−0.958327 + 0.285672i \(0.907783\pi\)
\(68\) −0.844240 9.99803i −0.102379 1.21244i
\(69\) 0.425900 + 0.232530i 0.0512723 + 0.0279933i
\(70\) 5.85473 2.99967i 0.699775 0.358529i
\(71\) −8.84887 −1.05017 −0.525084 0.851050i \(-0.675966\pi\)
−0.525084 + 0.851050i \(0.675966\pi\)
\(72\) −0.743487 + 8.45265i −0.0876208 + 0.996154i
\(73\) −7.61652 −0.891446 −0.445723 0.895171i \(-0.647053\pi\)
−0.445723 + 0.895171i \(0.647053\pi\)
\(74\) 0.00104299 + 0.0247476i 0.000121246 + 0.00287685i
\(75\) −1.58436 + 2.90191i −0.182947 + 0.335083i
\(76\) −7.63006 6.44182i −0.875228 0.738928i
\(77\) 0.0790913 0.213983i 0.00901329 0.0243857i
\(78\) −1.85936 + 3.77539i −0.210531 + 0.427479i
\(79\) 1.98466 0.223292 0.111646 0.993748i \(-0.464388\pi\)
0.111646 + 0.993748i \(0.464388\pi\)
\(80\) −4.06855 + 5.73630i −0.454878 + 0.641337i
\(81\) −3.73701 + 8.18747i −0.415224 + 0.909719i
\(82\) −3.30002 3.03311i −0.364426 0.334951i
\(83\) −4.67832 4.67832i −0.513512 0.513512i 0.402089 0.915601i \(-0.368284\pi\)
−0.915601 + 0.402089i \(0.868284\pi\)
\(84\) −9.16400 + 0.145280i −0.999874 + 0.0158513i
\(85\) 6.23694 6.23694i 0.676491 0.676491i
\(86\) −0.260240 6.17483i −0.0280624 0.665850i
\(87\) −16.2124 + 4.76131i −1.73815 + 0.510466i
\(88\) 0.0307354 + 0.241939i 0.00327641 + 0.0257908i
\(89\) 14.9865i 1.58856i −0.607550 0.794282i \(-0.707847\pi\)
0.607550 0.794282i \(-0.292153\pi\)
\(90\) −6.09929 + 4.29407i −0.642922 + 0.452635i
\(91\) −4.26369 1.57592i −0.446956 0.165202i
\(92\) −0.0471451 0.558323i −0.00491522 0.0582092i
\(93\) 4.91051 8.99405i 0.509196 0.932640i
\(94\) 3.89616 4.23902i 0.401858 0.437222i
\(95\) 8.77827i 0.900632i
\(96\) 8.61606 4.66515i 0.879372 0.476135i
\(97\) 14.3790i 1.45997i 0.683464 + 0.729984i \(0.260473\pi\)
−0.683464 + 0.729984i \(0.739527\pi\)
\(98\) −1.17956 9.82897i −0.119153 0.992876i
\(99\) −0.0549593 + 0.252772i −0.00552362 + 0.0254045i
\(100\) 3.80419 0.321228i 0.380419 0.0321228i
\(101\) 1.20675 1.20675i 0.120076 0.120076i −0.644516 0.764591i \(-0.722941\pi\)
0.764591 + 0.644516i \(0.222941\pi\)
\(102\) −11.6344 + 3.95613i −1.15198 + 0.391715i
\(103\) −3.50422 −0.345281 −0.172640 0.984985i \(-0.555230\pi\)
−0.172640 + 0.984985i \(0.555230\pi\)
\(104\) 4.82072 0.612415i 0.472711 0.0600522i
\(105\) −5.29447 6.07310i −0.516687 0.592673i
\(106\) −5.77595 + 0.243429i −0.561010 + 0.0236439i
\(107\) −3.97643 3.97643i −0.384416 0.384416i 0.488274 0.872690i \(-0.337627\pi\)
−0.872690 + 0.488274i \(0.837627\pi\)
\(108\) 10.2664 1.61256i 0.987888 0.155169i
\(109\) 13.8058 + 13.8058i 1.32236 + 1.32236i 0.911861 + 0.410500i \(0.134646\pi\)
0.410500 + 0.911861i \(0.365354\pi\)
\(110\) −0.145081 + 0.157848i −0.0138329 + 0.0150502i
\(111\) 0.0291071 0.00854828i 0.00276273 0.000811367i
\(112\) 5.97421 + 8.73549i 0.564510 + 0.825427i
\(113\) 5.90456i 0.555454i −0.960660 0.277727i \(-0.910419\pi\)
0.960660 0.277727i \(-0.0895811\pi\)
\(114\) −5.40344 + 10.9716i −0.506079 + 1.02758i
\(115\) 0.348291 0.348291i 0.0324783 0.0324783i
\(116\) 14.9083 + 12.5866i 1.38420 + 1.16864i
\(117\) 5.03657 + 1.09508i 0.465631 + 0.101241i
\(118\) −0.592857 14.0670i −0.0545769 1.29497i
\(119\) −5.54959 12.0574i −0.508730 1.10530i
\(120\) 8.01974 + 3.14183i 0.732098 + 0.286809i
\(121\) 10.9926i 0.999324i
\(122\) 0.802229 + 19.0348i 0.0726304 + 1.72333i
\(123\) −2.63059 + 4.81817i −0.237192 + 0.434440i
\(124\) −11.7905 + 0.995601i −1.05882 + 0.0894076i
\(125\) 8.58916 + 8.58916i 0.768238 + 0.768238i
\(126\) 2.87903 + 10.8495i 0.256485 + 0.966548i
\(127\) −16.1466 −1.43278 −0.716392 0.697698i \(-0.754208\pi\)
−0.716392 + 0.697698i \(0.754208\pi\)
\(128\) −9.97950 5.33007i −0.882071 0.471116i
\(129\) −7.26259 + 2.13290i −0.639435 + 0.187792i
\(130\) 3.14518 + 2.89079i 0.275851 + 0.253539i
\(131\) 10.6544 + 10.6544i 0.930877 + 0.930877i 0.997761 0.0668840i \(-0.0213057\pi\)
−0.0668840 + 0.997761i \(0.521306\pi\)
\(132\) 0.278493 0.107983i 0.0242397 0.00939870i
\(133\) −12.3906 4.57974i −1.07440 0.397114i
\(134\) 11.0021 0.463686i 0.950435 0.0400563i
\(135\) 6.90523 + 5.98151i 0.594308 + 0.514806i
\(136\) 11.2181 + 8.68913i 0.961944 + 0.745087i
\(137\) −13.8010 −1.17910 −0.589551 0.807731i \(-0.700695\pi\)
−0.589551 + 0.807731i \(0.700695\pi\)
\(138\) −0.649703 + 0.220923i −0.0553064 + 0.0188063i
\(139\) 15.9294 + 15.9294i 1.35111 + 1.35111i 0.884417 + 0.466697i \(0.154556\pi\)
0.466697 + 0.884417i \(0.345444\pi\)
\(140\) −2.47969 + 8.96677i −0.209572 + 0.757830i
\(141\) −6.18916 3.37911i −0.521221 0.284573i
\(142\) 8.46842 9.21363i 0.710654 0.773191i
\(143\) 0.148143 0.0123883
\(144\) −8.08955 8.86336i −0.674129 0.738613i
\(145\) 17.1518i 1.42438i
\(146\) 7.28905 7.93048i 0.603246 0.656331i
\(147\) −11.3344 + 4.30477i −0.934847 + 0.355051i
\(148\) −0.0267659 0.0225976i −0.00220014 0.00185751i
\(149\) 9.64384 + 9.64384i 0.790054 + 0.790054i 0.981503 0.191449i \(-0.0613185\pi\)
−0.191449 + 0.981503i \(0.561319\pi\)
\(150\) −1.50528 4.42681i −0.122906 0.361448i
\(151\) 13.9337i 1.13391i −0.823749 0.566955i \(-0.808121\pi\)
0.823749 0.566955i \(-0.191879\pi\)
\(152\) 14.0094 1.77972i 1.13631 0.144354i
\(153\) 8.13820 + 12.6604i 0.657935 + 1.02353i
\(154\) 0.147113 + 0.287135i 0.0118547 + 0.0231380i
\(155\) −7.35514 7.35514i −0.590779 0.590779i
\(156\) −2.15160 5.54908i −0.172266 0.444282i
\(157\) −9.86847 + 9.86847i −0.787590 + 0.787590i −0.981099 0.193509i \(-0.938013\pi\)
0.193509 + 0.981099i \(0.438013\pi\)
\(158\) −1.89933 + 2.06647i −0.151103 + 0.164399i
\(159\) 1.99512 + 6.79344i 0.158223 + 0.538755i
\(160\) −2.07913 9.72592i −0.164369 0.768902i
\(161\) −0.309908 0.673324i −0.0244241 0.0530654i
\(162\) −4.94863 11.7265i −0.388801 0.921322i
\(163\) −1.16411 1.16411i −0.0911802 0.0911802i 0.660045 0.751226i \(-0.270537\pi\)
−0.751226 + 0.660045i \(0.770537\pi\)
\(164\) 6.31627 0.533349i 0.493218 0.0416476i
\(165\) 0.230465 + 0.125828i 0.0179417 + 0.00979568i
\(166\) 9.34834 0.393989i 0.725572 0.0305794i
\(167\) 4.59666i 0.355700i −0.984058 0.177850i \(-0.943086\pi\)
0.984058 0.177850i \(-0.0569142\pi\)
\(168\) 8.61873 9.68078i 0.664949 0.746889i
\(169\) 10.0482i 0.772938i
\(170\) 0.525249 + 12.4628i 0.0402848 + 0.955854i
\(171\) 14.6366 + 3.18239i 1.11929 + 0.243364i
\(172\) 6.67842 + 5.63838i 0.509225 + 0.429922i
\(173\) −9.61704 9.61704i −0.731170 0.731170i 0.239682 0.970851i \(-0.422957\pi\)
−0.970851 + 0.239682i \(0.922957\pi\)
\(174\) 10.5578 21.4373i 0.800381 1.62515i
\(175\) 4.58776 2.11158i 0.346802 0.159621i
\(176\) −0.281326 0.199534i −0.0212057 0.0150405i
\(177\) −16.5450 + 4.85900i −1.24360 + 0.365224i
\(178\) 15.6042 + 14.3421i 1.16959 + 1.07499i
\(179\) 10.4081 10.4081i 0.777939 0.777939i −0.201541 0.979480i \(-0.564595\pi\)
0.979480 + 0.201541i \(0.0645948\pi\)
\(180\) 1.36598 10.4602i 0.101814 0.779655i
\(181\) 6.73426 + 6.73426i 0.500554 + 0.500554i 0.911610 0.411056i \(-0.134840\pi\)
−0.411056 + 0.911610i \(0.634840\pi\)
\(182\) 5.72126 2.93128i 0.424088 0.217281i
\(183\) 22.3880 6.57498i 1.65497 0.486037i
\(184\) 0.626456 + 0.485230i 0.0461829 + 0.0357716i
\(185\) 0.0307937i 0.00226400i
\(186\) 4.66541 + 13.7203i 0.342085 + 1.00602i
\(187\) 0.305879 + 0.305879i 0.0223681 + 0.0223681i
\(188\) 0.685111 + 8.11353i 0.0499669 + 0.591740i
\(189\) 12.0455 6.62615i 0.876181 0.481982i
\(190\) 9.14012 + 8.40085i 0.663094 + 0.609462i
\(191\) 26.7283i 1.93400i 0.254785 + 0.966998i \(0.417995\pi\)
−0.254785 + 0.966998i \(0.582005\pi\)
\(192\) −3.38816 + 13.4358i −0.244519 + 0.969644i
\(193\) 8.08244 0.581787 0.290893 0.956755i \(-0.406047\pi\)
0.290893 + 0.956755i \(0.406047\pi\)
\(194\) −14.9717 13.7608i −1.07491 0.987968i
\(195\) 2.50716 4.59210i 0.179542 0.328847i
\(196\) 11.3630 + 8.17819i 0.811641 + 0.584157i
\(197\) −7.07498 7.07498i −0.504072 0.504072i 0.408629 0.912701i \(-0.366007\pi\)
−0.912701 + 0.408629i \(0.866007\pi\)
\(198\) −0.210595 0.299129i −0.0149663 0.0212581i
\(199\) −20.1790 −1.43045 −0.715226 0.698893i \(-0.753676\pi\)
−0.715226 + 0.698893i \(0.753676\pi\)
\(200\) −3.30616 + 4.26842i −0.233781 + 0.301823i
\(201\) −3.80032 12.9402i −0.268054 0.912731i
\(202\) 0.101627 + 2.41135i 0.00715046 + 0.169662i
\(203\) 24.2099 + 8.94833i 1.69920 + 0.628050i
\(204\) 7.01497 15.9000i 0.491146 1.11322i
\(205\) 3.94019 + 3.94019i 0.275195 + 0.275195i
\(206\) 3.35355 3.64867i 0.233653 0.254215i
\(207\) 0.454464 + 0.706996i 0.0315874 + 0.0491397i
\(208\) −3.97580 + 5.60552i −0.275672 + 0.388673i
\(209\) 0.430514 0.0297793
\(210\) 11.3903 + 0.299273i 0.786003 + 0.0206518i
\(211\) 2.09005 + 2.09005i 0.143885 + 0.143885i 0.775380 0.631495i \(-0.217558\pi\)
−0.631495 + 0.775380i \(0.717558\pi\)
\(212\) 5.27415 6.24700i 0.362230 0.429046i
\(213\) −13.4523 7.34460i −0.921737 0.503244i
\(214\) 7.94581 0.334878i 0.543164 0.0228918i
\(215\) 7.68342i 0.524005i
\(216\) −8.14600 + 12.2329i −0.554265 + 0.832340i
\(217\) −14.2191 + 6.54456i −0.965256 + 0.444274i
\(218\) −27.5872 + 1.16267i −1.86844 + 0.0787460i
\(219\) −11.5789 6.32174i −0.782426 0.427184i
\(220\) −0.0255114 0.302123i −0.00171998 0.0203691i
\(221\) 6.09475 6.09475i 0.409977 0.409977i
\(222\) −0.0189550 + 0.0384877i −0.00127218 + 0.00258312i
\(223\) 6.04615i 0.404880i −0.979295 0.202440i \(-0.935113\pi\)
0.979295 0.202440i \(-0.0648871\pi\)
\(224\) −14.8129 2.13944i −0.989730 0.142947i
\(225\) −4.81719 + 3.09653i −0.321146 + 0.206436i
\(226\) 6.14795 + 5.65069i 0.408955 + 0.375878i
\(227\) 13.1223 + 13.1223i 0.870960 + 0.870960i 0.992577 0.121617i \(-0.0388079\pi\)
−0.121617 + 0.992577i \(0.538808\pi\)
\(228\) −6.25270 16.1260i −0.414095 1.06797i
\(229\) −1.28246 1.28246i −0.0847474 0.0847474i 0.663462 0.748210i \(-0.269086\pi\)
−0.748210 + 0.663462i \(0.769086\pi\)
\(230\) 0.0293316 + 0.695965i 0.00193407 + 0.0458905i
\(231\) 0.297844 0.259657i 0.0195967 0.0170842i
\(232\) −27.3728 + 3.47739i −1.79711 + 0.228302i
\(233\) −11.4914 −0.752829 −0.376414 0.926451i \(-0.622843\pi\)
−0.376414 + 0.926451i \(0.622843\pi\)
\(234\) −5.96024 + 4.19618i −0.389633 + 0.274313i
\(235\) −5.06136 + 5.06136i −0.330166 + 0.330166i
\(236\) 15.2142 + 12.8449i 0.990360 + 0.836130i
\(237\) 3.01714 + 1.64727i 0.195984 + 0.107002i
\(238\) 17.8654 + 5.76063i 1.15804 + 0.373406i
\(239\) 14.8760i 0.962250i 0.876652 + 0.481125i \(0.159772\pi\)
−0.876652 + 0.481125i \(0.840228\pi\)
\(240\) −10.9463 + 5.34357i −0.706579 + 0.344926i
\(241\) 28.2283i 1.81834i −0.416421 0.909172i \(-0.636716\pi\)
0.416421 0.909172i \(-0.363284\pi\)
\(242\) 11.4457 + 10.5199i 0.735757 + 0.676247i
\(243\) −12.4767 + 9.34509i −0.800384 + 0.599488i
\(244\) −20.5872 17.3811i −1.31796 1.11271i
\(245\) 0.950602 + 12.2704i 0.0607317 + 0.783925i
\(246\) −2.49929 7.35004i −0.159349 0.468622i
\(247\) 8.57815i 0.545815i
\(248\) 10.2470 13.2294i 0.650683 0.840065i
\(249\) −3.22909 10.9951i −0.204635 0.696788i
\(250\) −17.1631 + 0.723343i −1.08549 + 0.0457482i
\(251\) −2.14171 + 2.14171i −0.135184 + 0.135184i −0.771461 0.636277i \(-0.780474\pi\)
0.636277 + 0.771461i \(0.280474\pi\)
\(252\) −14.0520 7.38530i −0.885190 0.465230i
\(253\) 0.0170813 + 0.0170813i 0.00107389 + 0.00107389i
\(254\) 15.4524 16.8122i 0.969571 1.05489i
\(255\) 14.6583 4.30489i 0.917935 0.269583i
\(256\) 15.1002 5.28996i 0.943763 0.330622i
\(257\) −22.0909 −1.37799 −0.688997 0.724764i \(-0.741949\pi\)
−0.688997 + 0.724764i \(0.741949\pi\)
\(258\) 4.72951 9.60316i 0.294446 0.597866i
\(259\) −0.0434656 0.0160655i −0.00270082 0.000998262i
\(260\) −6.01991 + 0.508325i −0.373339 + 0.0315249i
\(261\) −28.5984 6.21805i −1.77020 0.384888i
\(262\) −21.2898 + 0.897267i −1.31529 + 0.0554333i
\(263\) −10.5382 −0.649813 −0.324906 0.945746i \(-0.605333\pi\)
−0.324906 + 0.945746i \(0.605333\pi\)
\(264\) −0.154085 + 0.393313i −0.00948330 + 0.0242067i
\(265\) 7.18709 0.441499
\(266\) 16.6264 8.51852i 1.01943 0.522304i
\(267\) 12.4388 22.7829i 0.761244 1.39429i
\(268\) −10.0462 + 11.8993i −0.613672 + 0.726868i
\(269\) −7.58942 7.58942i −0.462735 0.462735i 0.436816 0.899551i \(-0.356106\pi\)
−0.899551 + 0.436816i \(0.856106\pi\)
\(270\) −12.8364 + 1.46553i −0.781199 + 0.0891896i
\(271\) 3.70554i 0.225096i 0.993646 + 0.112548i \(0.0359012\pi\)
−0.993646 + 0.112548i \(0.964099\pi\)
\(272\) −19.7831 + 3.36498i −1.19953 + 0.204032i
\(273\) −5.17377 5.93464i −0.313131 0.359181i
\(274\) 13.2077 14.3699i 0.797904 0.868119i
\(275\) −0.116385 + 0.116385i −0.00701828 + 0.00701828i
\(276\) 0.391739 0.887909i 0.0235799 0.0534459i
\(277\) −1.42855 + 1.42855i −0.0858331 + 0.0858331i −0.748720 0.662887i \(-0.769331\pi\)
0.662887 + 0.748720i \(0.269331\pi\)
\(278\) −31.8305 + 1.34151i −1.90907 + 0.0804583i
\(279\) 14.9302 9.59727i 0.893848 0.574574i
\(280\) −6.96331 11.1632i −0.416137 0.667126i
\(281\) 17.2560 1.02941 0.514703 0.857369i \(-0.327902\pi\)
0.514703 + 0.857369i \(0.327902\pi\)
\(282\) 9.44146 3.21045i 0.562231 0.191180i
\(283\) 2.79408 + 2.79408i 0.166091 + 0.166091i 0.785259 0.619168i \(-0.212530\pi\)
−0.619168 + 0.785259i \(0.712530\pi\)
\(284\) 1.48911 + 17.6350i 0.0883623 + 1.04644i
\(285\) 7.28600 13.3450i 0.431585 0.790488i
\(286\) −0.141774 + 0.154250i −0.00838325 + 0.00912097i
\(287\) 7.61727 3.50596i 0.449633 0.206950i
\(288\) 16.9705 + 0.0592703i 0.999994 + 0.00349253i
\(289\) 8.16835 0.480491
\(290\) −17.8588 16.4144i −1.04871 0.963885i
\(291\) −11.9346 + 21.8594i −0.699621 + 1.28142i
\(292\) 1.28173 + 15.1790i 0.0750073 + 0.888285i
\(293\) −15.3314 + 15.3314i −0.895673 + 0.895673i −0.995050 0.0993770i \(-0.968315\pi\)
0.0993770 + 0.995050i \(0.468315\pi\)
\(294\) 6.36488 15.9213i 0.371207 0.928550i
\(295\) 17.5037i 1.01911i
\(296\) 0.0491442 0.00624317i 0.00285645 0.000362877i
\(297\) −0.293352 + 0.338654i −0.0170220 + 0.0196507i
\(298\) −19.2706 + 0.812164i −1.11631 + 0.0470474i
\(299\) 0.340351 0.340351i 0.0196830 0.0196830i
\(300\) 6.04985 + 2.66915i 0.349289 + 0.154103i
\(301\) 10.8452 + 4.00855i 0.625108 + 0.231049i
\(302\) 14.5081 + 13.3346i 0.834846 + 0.767322i
\(303\) 2.83613 0.832926i 0.162932 0.0478503i
\(304\) −11.5540 + 16.2901i −0.662665 + 0.934299i
\(305\) 23.6853i 1.35622i
\(306\) −20.9705 3.64237i −1.19881 0.208220i
\(307\) 15.7216 15.7216i 0.897279 0.897279i −0.0979153 0.995195i \(-0.531217\pi\)
0.995195 + 0.0979153i \(0.0312174\pi\)
\(308\) −0.439759 0.121612i −0.0250576 0.00692949i
\(309\) −5.32721 2.90851i −0.303054 0.165460i
\(310\) 14.6972 0.619419i 0.834747 0.0351806i
\(311\) 15.6433i 0.887049i −0.896262 0.443524i \(-0.853728\pi\)
0.896262 0.443524i \(-0.146272\pi\)
\(312\) 7.83690 + 3.07021i 0.443677 + 0.173816i
\(313\) 0.512480 0.0289671 0.0144836 0.999895i \(-0.495390\pi\)
0.0144836 + 0.999895i \(0.495390\pi\)
\(314\) −0.831082 19.7194i −0.0469007 1.11283i
\(315\) −3.00811 13.6269i −0.169488 0.767790i
\(316\) −0.333983 3.95524i −0.0187880 0.222500i
\(317\) −6.60807 + 6.60807i −0.371146 + 0.371146i −0.867895 0.496748i \(-0.834527\pi\)
0.496748 + 0.867895i \(0.334527\pi\)
\(318\) −8.98281 4.42399i −0.503731 0.248085i
\(319\) −0.841179 −0.0470970
\(320\) 12.1166 + 7.14293i 0.677337 + 0.399302i
\(321\) −2.74463 9.34554i −0.153190 0.521617i
\(322\) 0.997662 + 0.321692i 0.0555975 + 0.0179272i
\(323\) 17.7118 17.7118i 0.985510 0.985510i
\(324\) 16.9458 + 6.06972i 0.941431 + 0.337207i
\(325\) 2.31901 + 2.31901i 0.128636 + 0.128636i
\(326\) 2.32616 0.0980366i 0.128834 0.00542975i
\(327\) 9.52913 + 32.4469i 0.526962 + 1.79432i
\(328\) −5.48937 + 7.08705i −0.303100 + 0.391317i
\(329\) 4.50356 + 9.78472i 0.248290 + 0.539449i
\(330\) −0.351571 + 0.119547i −0.0193533 + 0.00658086i
\(331\) 11.7674 11.7674i 0.646797 0.646797i −0.305421 0.952218i \(-0.598797\pi\)
0.952218 + 0.305421i \(0.0987970\pi\)
\(332\) −8.53618 + 10.1107i −0.468484 + 0.554899i
\(333\) 0.0513446 + 0.0111637i 0.00281366 + 0.000611766i
\(334\) 4.78614 + 4.39902i 0.261886 + 0.240704i
\(335\) −13.6900 −0.747966
\(336\) 1.83167 + 18.2386i 0.0999257 + 0.994995i
\(337\) 17.1936 0.936597 0.468298 0.883570i \(-0.344867\pi\)
0.468298 + 0.883570i \(0.344867\pi\)
\(338\) −10.4624 9.61618i −0.569079 0.523051i
\(339\) 4.90080 8.97628i 0.266175 0.487524i
\(340\) −13.4792 11.3801i −0.731013 0.617171i
\(341\) 0.360719 0.360719i 0.0195340 0.0195340i
\(342\) −17.3209 + 12.1944i −0.936607 + 0.659398i
\(343\) 17.8157 + 5.05984i 0.961956 + 0.273206i
\(344\) −12.2621 + 1.55775i −0.661127 + 0.0839882i
\(345\) 0.818565 0.240399i 0.0440701 0.0129427i
\(346\) 19.2170 0.809907i 1.03311 0.0435409i
\(347\) 5.17637 + 5.17637i 0.277882 + 0.277882i 0.832263 0.554381i \(-0.187045\pi\)
−0.554381 + 0.832263i \(0.687045\pi\)
\(348\) 12.2171 + 31.5085i 0.654905 + 1.68903i
\(349\) 0.888537 0.888537i 0.0475623 0.0475623i −0.682926 0.730488i \(-0.739293\pi\)
0.730488 + 0.682926i \(0.239293\pi\)
\(350\) −2.19188 + 6.79767i −0.117161 + 0.363351i
\(351\) 6.74781 + 5.84515i 0.360171 + 0.311991i
\(352\) 0.476990 0.101967i 0.0254236 0.00543486i
\(353\) 12.7956 0.681039 0.340520 0.940237i \(-0.389397\pi\)
0.340520 + 0.940237i \(0.389397\pi\)
\(354\) 10.7744 21.8771i 0.572651 1.16275i
\(355\) −11.0010 + 11.0010i −0.583872 + 0.583872i
\(356\) −29.8667 + 2.52196i −1.58293 + 0.133664i
\(357\) 1.57103 22.9362i 0.0831475 1.21391i
\(358\) 0.876528 + 20.7978i 0.0463260 + 1.09920i
\(359\) −2.98237 −0.157404 −0.0787018 0.996898i \(-0.525078\pi\)
−0.0787018 + 0.996898i \(0.525078\pi\)
\(360\) 9.58410 + 11.4327i 0.505126 + 0.602557i
\(361\) 5.92873i 0.312038i
\(362\) −13.4566 + 0.567131i −0.707262 + 0.0298078i
\(363\) 9.12387 16.7112i 0.478879 0.877111i
\(364\) −2.42316 + 8.76235i −0.127008 + 0.459272i
\(365\) −9.46893 + 9.46893i −0.495626 + 0.495626i
\(366\) −14.5794 + 29.6031i −0.762078 + 1.54738i
\(367\) 9.07525i 0.473724i −0.971543 0.236862i \(-0.923881\pi\)
0.971543 0.236862i \(-0.0761190\pi\)
\(368\) −1.10475 + 0.187912i −0.0575892 + 0.00979558i
\(369\) −7.99820 + 5.14132i −0.416370 + 0.267646i
\(370\) 0.0320631 + 0.0294698i 0.00166688 + 0.00153206i
\(371\) 3.74960 10.1446i 0.194670 0.526683i
\(372\) −18.7507 8.27266i −0.972177 0.428917i
\(373\) 23.0196 23.0196i 1.19191 1.19191i 0.215381 0.976530i \(-0.430901\pi\)
0.976530 0.215381i \(-0.0690993\pi\)
\(374\) −0.611216 + 0.0257599i −0.0316052 + 0.00133201i
\(375\) 5.92845 + 20.1865i 0.306144 + 1.04243i
\(376\) −9.10363 7.05134i −0.469484 0.363645i
\(377\) 16.7608i 0.863224i
\(378\) −4.62832 + 18.8833i −0.238055 + 0.971252i
\(379\) −8.03549 + 8.03549i −0.412755 + 0.412755i −0.882697 0.469942i \(-0.844275\pi\)
0.469942 + 0.882697i \(0.344275\pi\)
\(380\) −17.4943 + 1.47723i −0.897438 + 0.0757802i
\(381\) −24.5466 13.4018i −1.25756 0.686594i
\(382\) −27.8301 25.5792i −1.42391 1.30874i
\(383\) 30.3101 1.54877 0.774386 0.632714i \(-0.218059\pi\)
0.774386 + 0.632714i \(0.218059\pi\)
\(384\) −10.7471 16.3859i −0.548437 0.836192i
\(385\) −0.167699 0.364353i −0.00854673 0.0185691i
\(386\) −7.73494 + 8.41561i −0.393698 + 0.428343i
\(387\) −12.8111 2.78548i −0.651225 0.141594i
\(388\) 28.6561 2.41973i 1.45479 0.122843i
\(389\) 4.63160 + 4.63160i 0.234831 + 0.234831i 0.814706 0.579874i \(-0.196898\pi\)
−0.579874 + 0.814706i \(0.696898\pi\)
\(390\) 2.38202 + 7.00518i 0.120618 + 0.354721i
\(391\) 1.40548 0.0710784
\(392\) −19.3897 + 4.00479i −0.979329 + 0.202273i
\(393\) 7.35391 + 25.0402i 0.370956 + 1.26311i
\(394\) 14.1374 0.595825i 0.712233 0.0300173i
\(395\) 2.46735 2.46735i 0.124146 0.124146i
\(396\) 0.512999 + 0.0669918i 0.0257792 + 0.00336646i
\(397\) 4.50105 4.50105i 0.225901 0.225901i −0.585077 0.810978i \(-0.698936\pi\)
0.810978 + 0.585077i \(0.198936\pi\)
\(398\) 19.3114 21.0108i 0.967994 1.05318i
\(399\) −15.0353 17.2465i −0.752708 0.863405i
\(400\) −1.28035 7.52734i −0.0640177 0.376367i
\(401\) 15.5305i 0.775558i −0.921752 0.387779i \(-0.873242\pi\)
0.921752 0.387779i \(-0.126758\pi\)
\(402\) 17.1105 + 8.42686i 0.853396 + 0.420293i
\(403\) −7.18746 7.18746i −0.358033 0.358033i
\(404\) −2.60801 2.20186i −0.129753 0.109547i
\(405\) 5.53285 + 14.8246i 0.274930 + 0.736642i
\(406\) −32.4862 + 16.6443i −1.61226 + 0.826041i
\(407\) 0.00151022 7.48589e−5
\(408\) 9.84207 + 22.5205i 0.487255 + 1.11493i
\(409\) 33.3505 1.64907 0.824537 0.565808i \(-0.191436\pi\)
0.824537 + 0.565808i \(0.191436\pi\)
\(410\) −7.87340 + 0.331827i −0.388839 + 0.0163877i
\(411\) −20.9807 11.4549i −1.03490 0.565029i
\(412\) 0.589698 + 6.98358i 0.0290523 + 0.344056i
\(413\) 24.7066 + 9.13192i 1.21573 + 0.449353i
\(414\) −1.17106 0.203402i −0.0575547 0.00999665i
\(415\) −11.6323 −0.571005
\(416\) −2.03173 9.50420i −0.0996137 0.465982i
\(417\) 10.9949 + 37.4378i 0.538421 + 1.83334i
\(418\) −0.412004 + 0.448260i −0.0201518 + 0.0219251i
\(419\) 2.47502 + 2.47502i 0.120913 + 0.120913i 0.764974 0.644061i \(-0.222752\pi\)
−0.644061 + 0.764974i \(0.722752\pi\)
\(420\) −11.2122 + 11.5734i −0.547097 + 0.564723i
\(421\) −8.16871 + 8.16871i −0.398118 + 0.398118i −0.877569 0.479450i \(-0.840836\pi\)
0.479450 + 0.877569i \(0.340836\pi\)
\(422\) −4.17639 + 0.176015i −0.203304 + 0.00856829i
\(423\) −6.60426 10.2740i −0.321110 0.499541i
\(424\) 1.45712 + 11.4700i 0.0707641 + 0.557031i
\(425\) 9.57640i 0.464524i
\(426\) 20.5213 6.97801i 0.994259 0.338086i
\(427\) −33.4320 12.3569i −1.61789 0.597994i
\(428\) −7.25550 + 8.59382i −0.350708 + 0.415398i
\(429\) 0.225211 + 0.122959i 0.0108733 + 0.00593653i
\(430\) −8.00014 7.35308i −0.385801 0.354597i
\(431\) 21.6958i 1.04505i −0.852624 0.522525i \(-0.824990\pi\)
0.852624 0.522525i \(-0.175010\pi\)
\(432\) −4.94134 20.1887i −0.237740 0.971329i
\(433\) 15.3846i 0.739337i −0.929164 0.369668i \(-0.879471\pi\)
0.929164 0.369668i \(-0.120529\pi\)
\(434\) 6.79343 21.0684i 0.326095 1.01132i
\(435\) −14.2361 + 26.0747i −0.682567 + 1.25018i
\(436\) 25.1905 29.8371i 1.20641 1.42894i
\(437\) 0.989085 0.989085i 0.0473143 0.0473143i
\(438\) 17.6633 6.00620i 0.843987 0.286988i
\(439\) 29.0912 1.38845 0.694224 0.719759i \(-0.255748\pi\)
0.694224 + 0.719759i \(0.255748\pi\)
\(440\) 0.338991 + 0.262570i 0.0161608 + 0.0125175i
\(441\) −20.8039 2.86338i −0.990661 0.136351i
\(442\) 0.513274 + 12.1787i 0.0244140 + 0.579281i
\(443\) 10.8476 + 10.8476i 0.515386 + 0.515386i 0.916172 0.400786i \(-0.131263\pi\)
−0.400786 + 0.916172i \(0.631263\pi\)
\(444\) −0.0219341 0.0565693i −0.00104095 0.00268466i
\(445\) −18.6313 18.6313i −0.883209 0.883209i
\(446\) 6.29538 + 5.78620i 0.298095 + 0.273984i
\(447\) 6.65641 + 22.6653i 0.314838 + 1.07203i
\(448\) 16.4037 13.3761i 0.775001 0.631960i
\(449\) 17.2559i 0.814355i −0.913349 0.407178i \(-0.866513\pi\)
0.913349 0.407178i \(-0.133487\pi\)
\(450\) 1.38590 7.97916i 0.0653318 0.376141i
\(451\) −0.193239 + 0.193239i −0.00909929 + 0.00909929i
\(452\) −11.7672 + 0.993632i −0.553484 + 0.0467365i
\(453\) 11.5650 21.1824i 0.543373 0.995238i
\(454\) −26.2214 + 1.10511i −1.23063 + 0.0518653i
\(455\) −7.25986 + 3.34146i −0.340348 + 0.156650i
\(456\) 22.7746 + 8.92224i 1.06652 + 0.417822i
\(457\) 17.1678i 0.803078i 0.915842 + 0.401539i \(0.131525\pi\)
−0.915842 + 0.401539i \(0.868475\pi\)
\(458\) 2.56265 0.108004i 0.119745 0.00504667i
\(459\) 1.86378 + 26.0014i 0.0869936 + 1.21364i
\(460\) −0.752724 0.635501i −0.0350959 0.0296304i
\(461\) −1.19220 1.19220i −0.0555261 0.0555261i 0.678798 0.734325i \(-0.262501\pi\)
−0.734325 + 0.678798i \(0.762501\pi\)
\(462\) −0.0146773 + 0.558614i −0.000682849 + 0.0259891i
\(463\) 1.80130 0.0837133 0.0418567 0.999124i \(-0.486673\pi\)
0.0418567 + 0.999124i \(0.486673\pi\)
\(464\) 22.5752 31.8290i 1.04803 1.47763i
\(465\) −5.07670 17.2863i −0.235426 0.801632i
\(466\) 10.9974 11.9651i 0.509443 0.554273i
\(467\) 16.0619 + 16.0619i 0.743255 + 0.743255i 0.973203 0.229948i \(-0.0738556\pi\)
−0.229948 + 0.973203i \(0.573856\pi\)
\(468\) 1.33484 10.2217i 0.0617028 0.472498i
\(469\) −7.14227 + 19.3236i −0.329799 + 0.892280i
\(470\) −0.426246 10.1137i −0.0196613 0.466512i
\(471\) −23.1932 + 6.81146i −1.06869 + 0.313856i
\(472\) −27.9344 + 3.54873i −1.28579 + 0.163344i
\(473\) −0.376819 −0.0173262
\(474\) −4.60259 + 1.56505i −0.211404 + 0.0718853i
\(475\) 6.73922 + 6.73922i 0.309217 + 0.309217i
\(476\) −23.0954 + 13.0889i −1.05857 + 0.599927i
\(477\) −2.60554 + 11.9835i −0.119299 + 0.548688i
\(478\) −15.4892 14.2364i −0.708461 0.651160i
\(479\) −3.84880 −0.175856 −0.0879282 0.996127i \(-0.528025\pi\)
−0.0879282 + 0.996127i \(0.528025\pi\)
\(480\) 4.91180 16.5113i 0.224192 0.753635i
\(481\) 0.0300917i 0.00137206i
\(482\) 29.3919 + 27.0146i 1.33876 + 1.23048i
\(483\) 0.0877312 1.28083i 0.00399191 0.0582798i
\(484\) −21.9072 + 1.84985i −0.995780 + 0.0840843i
\(485\) 17.8761 + 17.8761i 0.811713 + 0.811713i
\(486\) 2.21000 21.9344i 0.100248 0.994962i
\(487\) 4.94704i 0.224172i −0.993699 0.112086i \(-0.964247\pi\)
0.993699 0.112086i \(-0.0357532\pi\)
\(488\) 37.7997 4.80199i 1.71111 0.217376i
\(489\) −0.803498 2.73593i −0.0363354 0.123723i
\(490\) −13.6859 10.7530i −0.618266 0.485772i
\(491\) 16.4925 + 16.4925i 0.744295 + 0.744295i 0.973401 0.229106i \(-0.0735804\pi\)
−0.229106 + 0.973401i \(0.573580\pi\)
\(492\) 10.0449 + 4.43171i 0.452857 + 0.199797i
\(493\) −34.6069 + 34.6069i −1.55862 + 1.55862i
\(494\) 8.93175 + 8.20933i 0.401858 + 0.369355i
\(495\) 0.245922 + 0.382574i 0.0110534 + 0.0171954i
\(496\) 3.96828 + 23.3299i 0.178181 + 1.04754i
\(497\) 9.78863 + 21.2674i 0.439080 + 0.953972i
\(498\) 14.5386 + 7.16020i 0.651491 + 0.320856i
\(499\) 3.03089 + 3.03089i 0.135681 + 0.135681i 0.771685 0.636004i \(-0.219414\pi\)
−0.636004 + 0.771685i \(0.719414\pi\)
\(500\) 15.6720 18.5628i 0.700873 0.830154i
\(501\) 3.81524 6.98797i 0.170452 0.312199i
\(502\) −0.180366 4.27962i −0.00805013 0.191009i
\(503\) 34.6875i 1.54664i −0.634017 0.773319i \(-0.718595\pi\)
0.634017 0.773319i \(-0.281405\pi\)
\(504\) 21.1375 7.56342i 0.941540 0.336902i
\(505\) 3.00047i 0.133519i
\(506\) −0.0341323 + 0.00143852i −0.00151737 + 6.39498e-5i
\(507\) −8.34004 + 15.2756i −0.370394 + 0.678411i
\(508\) 2.71719 + 32.1788i 0.120556 + 1.42770i
\(509\) −13.1540 13.1540i −0.583042 0.583042i 0.352696 0.935738i \(-0.385265\pi\)
−0.935738 + 0.352696i \(0.885265\pi\)
\(510\) −9.54568 + 19.3823i −0.422690 + 0.858262i
\(511\) 8.42540 + 18.3055i 0.372718 + 0.809789i
\(512\) −8.94296 + 20.7852i −0.395227 + 0.918584i
\(513\) 19.6096 + 16.9864i 0.865786 + 0.749969i
\(514\) 21.1411 23.0015i 0.932495 1.01455i
\(515\) −4.35648 + 4.35648i −0.191969 + 0.191969i
\(516\) 5.47284 + 14.1147i 0.240928 + 0.621367i
\(517\) −0.248225 0.248225i −0.0109169 0.0109169i
\(518\) 0.0583246 0.0298825i 0.00256263 0.00131296i
\(519\) −6.63791 22.6023i −0.291372 0.992129i
\(520\) 5.23180 6.75452i 0.229430 0.296205i
\(521\) 26.5867i 1.16478i −0.812908 0.582392i \(-0.802117\pi\)
0.812908 0.582392i \(-0.197883\pi\)
\(522\) 33.8432 23.8266i 1.48128 1.04286i
\(523\) −28.0334 28.0334i −1.22582 1.22582i −0.965532 0.260283i \(-0.916184\pi\)
−0.260283 0.965532i \(-0.583816\pi\)
\(524\) 19.4402 23.0261i 0.849251 1.00590i
\(525\) 8.72706 + 0.597765i 0.380880 + 0.0260886i
\(526\) 10.0851 10.9726i 0.439731 0.478428i
\(527\) 29.6807i 1.29291i
\(528\) −0.262065 0.536840i −0.0114049 0.0233629i
\(529\) −22.9215 −0.996588
\(530\) −6.87808 + 7.48335i −0.298765 + 0.325056i
\(531\) −29.1852 6.34563i −1.26653 0.275377i
\(532\) −7.04189 + 25.4640i −0.305305 + 1.10401i
\(533\) 3.85037 + 3.85037i 0.166778 + 0.166778i
\(534\) 11.8180 + 34.7549i 0.511414 + 1.50399i
\(535\) −9.88707 −0.427455
\(536\) −2.77554 21.8481i −0.119885 0.943694i
\(537\) 24.4615 7.18394i 1.05559 0.310010i
\(538\) 15.1654 0.639149i 0.653826 0.0275557i
\(539\) −0.601778 + 0.0466205i −0.0259204 + 0.00200809i
\(540\) 10.7586 14.7681i 0.462975 0.635517i
\(541\) −22.8763 22.8763i −0.983528 0.983528i 0.0163386 0.999867i \(-0.494799\pi\)
−0.999867 + 0.0163386i \(0.994799\pi\)
\(542\) −3.85829 3.54622i −0.165728 0.152323i
\(543\) 4.64815 + 15.8271i 0.199471 + 0.679205i
\(544\) 15.4288 23.8189i 0.661505 1.02123i
\(545\) 34.3271 1.47041
\(546\) 11.1306 + 0.292450i 0.476345 + 0.0125157i
\(547\) −1.70364 1.70364i −0.0728425 0.0728425i 0.669747 0.742589i \(-0.266403\pi\)
−0.742589 + 0.669747i \(0.766403\pi\)
\(548\) 2.32247 + 27.5042i 0.0992110 + 1.17492i
\(549\) 39.4921 + 8.58664i 1.68548 + 0.366469i
\(550\) −0.00980146 0.232564i −0.000417936 0.00991655i
\(551\) 48.7081i 2.07503i
\(552\) 0.549614 + 1.25762i 0.0233931 + 0.0535279i
\(553\) −2.19543 4.76993i −0.0933592 0.202838i
\(554\) −0.120306 2.85456i −0.00511132 0.121279i
\(555\) 0.0255589 0.0468135i 0.00108492 0.00198712i
\(556\) 29.0652 34.4265i 1.23264 1.46001i
\(557\) 10.9552 10.9552i 0.464185 0.464185i −0.435840 0.900024i \(-0.643549\pi\)
0.900024 + 0.435840i \(0.143549\pi\)
\(558\) −4.29539 + 24.7303i −0.181839 + 1.04692i
\(559\) 7.50826i 0.317566i
\(560\) 18.2872 + 3.43285i 0.772777 + 0.145065i
\(561\) 0.211125 + 0.718887i 0.00891371 + 0.0303514i
\(562\) −16.5141 + 17.9673i −0.696604 + 0.757904i
\(563\) −25.3249 25.3249i −1.06732 1.06732i −0.997564 0.0697547i \(-0.977778\pi\)
−0.0697547 0.997564i \(-0.522222\pi\)
\(564\) −5.69274 + 12.9031i −0.239707 + 0.543317i
\(565\) −7.34060 7.34060i −0.308821 0.308821i
\(566\) −5.58320 + 0.235306i −0.234679 + 0.00989063i
\(567\) 23.8116 0.0754531i 0.999995 0.00316873i
\(568\) −19.7870 15.3263i −0.830244 0.643077i
\(569\) 12.4225 0.520777 0.260388 0.965504i \(-0.416149\pi\)
0.260388 + 0.965504i \(0.416149\pi\)
\(570\) 6.92233 + 20.3576i 0.289945 + 0.852684i
\(571\) 21.1840 21.1840i 0.886521 0.886521i −0.107666 0.994187i \(-0.534338\pi\)
0.994187 + 0.107666i \(0.0343378\pi\)
\(572\) −0.0249298 0.295235i −0.00104237 0.0123444i
\(573\) −22.1846 + 40.6332i −0.926776 + 1.69748i
\(574\) −3.63928 + 11.2865i −0.151901 + 0.471089i
\(575\) 0.534778i 0.0223018i
\(576\) −16.3025 + 17.6133i −0.679272 + 0.733887i
\(577\) 41.0640i 1.70952i −0.519025 0.854759i \(-0.673705\pi\)
0.519025 0.854759i \(-0.326295\pi\)
\(578\) −7.81715 + 8.50505i −0.325151 + 0.353764i
\(579\) 12.2872 + 6.70846i 0.510637 + 0.278794i
\(580\) 34.1820 2.88635i 1.41933 0.119849i
\(581\) −6.06870 + 16.4190i −0.251772 + 0.681176i
\(582\) −11.3389 33.3462i −0.470015 1.38224i
\(583\) 0.352477i 0.0145981i
\(584\) −17.0313 13.1918i −0.704762 0.545882i
\(585\) 7.62292 4.90009i 0.315169 0.202594i
\(586\) −1.29115 30.6357i −0.0533369 1.26555i
\(587\) 7.77641 7.77641i 0.320967 0.320967i −0.528171 0.849138i \(-0.677122\pi\)
0.849138 + 0.528171i \(0.177122\pi\)
\(588\) 10.4864 + 21.8640i 0.432451 + 0.901657i
\(589\) −20.8873 20.8873i −0.860645 0.860645i
\(590\) −18.2252 16.7511i −0.750321 0.689634i
\(591\) −4.88333 16.6278i −0.200873 0.683978i
\(592\) −0.0405307 + 0.0571447i −0.00166580 + 0.00234863i
\(593\) 24.5194 1.00689 0.503445 0.864027i \(-0.332066\pi\)
0.503445 + 0.864027i \(0.332066\pi\)
\(594\) −0.0718744 0.629538i −0.00294904 0.0258303i
\(595\) −21.8891 8.09054i −0.897368 0.331680i
\(596\) 17.5964 20.8422i 0.720776 0.853728i
\(597\) −30.6767 16.7487i −1.25551 0.685477i
\(598\) 0.0286629 + 0.680098i 0.00117211 + 0.0278113i
\(599\) −13.6610 −0.558174 −0.279087 0.960266i \(-0.590032\pi\)
−0.279087 + 0.960266i \(0.590032\pi\)
\(600\) −8.56892 + 3.74484i −0.349825 + 0.152883i
\(601\) −23.1095 −0.942655 −0.471327 0.881958i \(-0.656225\pi\)
−0.471327 + 0.881958i \(0.656225\pi\)
\(602\) −14.5527 + 7.45606i −0.593124 + 0.303886i
\(603\) 4.96305 22.8263i 0.202111 0.929560i
\(604\) −27.7686 + 2.34480i −1.12989 + 0.0954085i
\(605\) −13.6661 13.6661i −0.555604 0.555604i
\(606\) −1.84693 + 3.75016i −0.0750266 + 0.152340i
\(607\) 21.7085i 0.881122i 0.897723 + 0.440561i \(0.145220\pi\)
−0.897723 + 0.440561i \(0.854780\pi\)
\(608\) −5.90435 27.6199i −0.239453 1.12013i
\(609\) 29.3774 + 33.6978i 1.19043 + 1.36550i
\(610\) 24.6616 + 22.6669i 0.998519 + 0.917757i
\(611\) −4.94597 + 4.94597i −0.200092 + 0.200092i
\(612\) 23.8614 18.3492i 0.964541 0.741722i
\(613\) −15.3709 + 15.3709i −0.620827 + 0.620827i −0.945743 0.324916i \(-0.894664\pi\)
0.324916 + 0.945743i \(0.394664\pi\)
\(614\) 1.32401 + 31.4153i 0.0534326 + 1.26782i
\(615\) 2.71962 + 9.26037i 0.109666 + 0.373414i
\(616\) 0.547476 0.341502i 0.0220584 0.0137595i
\(617\) 1.96274 0.0790169 0.0395085 0.999219i \(-0.487421\pi\)
0.0395085 + 0.999219i \(0.487421\pi\)
\(618\) 8.12657 2.76334i 0.326899 0.111158i
\(619\) 19.0295 + 19.0295i 0.764859 + 0.764859i 0.977196 0.212338i \(-0.0681077\pi\)
−0.212338 + 0.977196i \(0.568108\pi\)
\(620\) −13.4204 + 15.8959i −0.538975 + 0.638393i
\(621\) 0.104079 + 1.45200i 0.00417656 + 0.0582669i
\(622\) 16.2881 + 14.9707i 0.653094 + 0.600270i
\(623\) −36.0185 + 16.5780i −1.44305 + 0.664185i
\(624\) −10.6967 + 5.22175i −0.428212 + 0.209037i
\(625\) 11.8119 0.472477
\(626\) −0.490446 + 0.533605i −0.0196022 + 0.0213272i
\(627\) 0.654480 + 0.357328i 0.0261374 + 0.0142703i
\(628\) 21.3276 + 18.0063i 0.851066 + 0.718528i
\(629\) 0.0621321 0.0621321i 0.00247737 0.00247737i
\(630\) 17.0674 + 9.90893i 0.679982 + 0.394781i
\(631\) 16.7405i 0.666430i 0.942851 + 0.333215i \(0.108134\pi\)
−0.942851 + 0.333215i \(0.891866\pi\)
\(632\) 4.43791 + 3.43744i 0.176530 + 0.136734i
\(633\) 1.44260 + 4.91210i 0.0573384 + 0.195239i
\(634\) −0.556504 13.2044i −0.0221016 0.524414i
\(635\) −20.0737 + 20.0737i −0.796599 + 0.796599i
\(636\) 13.2030 5.11931i 0.523531 0.202994i
\(637\) 0.928930 + 11.9906i 0.0368055 + 0.475086i
\(638\) 0.805012 0.875853i 0.0318707 0.0346753i
\(639\) −14.3545 22.3309i −0.567857 0.883398i
\(640\) −19.0330 + 5.78021i −0.752345 + 0.228483i
\(641\) 20.5613i 0.812122i −0.913846 0.406061i \(-0.866902\pi\)
0.913846 0.406061i \(-0.133098\pi\)
\(642\) 12.3574 + 6.08596i 0.487707 + 0.240194i
\(643\) −6.03940 + 6.03940i −0.238171 + 0.238171i −0.816092 0.577922i \(-0.803864\pi\)
0.577922 + 0.816092i \(0.303864\pi\)
\(644\) −1.28972 + 0.730926i −0.0508221 + 0.0288025i
\(645\) −6.37727 + 11.6806i −0.251105 + 0.459922i
\(646\) 1.49161 + 35.3922i 0.0586867 + 1.39249i
\(647\) 23.4634i 0.922441i 0.887286 + 0.461220i \(0.152588\pi\)
−0.887286 + 0.461220i \(0.847412\pi\)
\(648\) −22.5371 + 11.8355i −0.885340 + 0.464943i
\(649\) −0.858437 −0.0336966
\(650\) −4.63391 + 0.195298i −0.181757 + 0.00766021i
\(651\) −27.0483 1.85269i −1.06011 0.0726126i
\(652\) −2.12407 + 2.51587i −0.0831849 + 0.0985289i
\(653\) −24.6322 + 24.6322i −0.963931 + 0.963931i −0.999372 0.0354410i \(-0.988716\pi\)
0.0354410 + 0.999372i \(0.488716\pi\)
\(654\) −42.9039 21.1300i −1.67767 0.826247i
\(655\) 26.4912 1.03510
\(656\) −2.12583 12.4980i −0.0829998 0.487964i
\(657\) −12.3554 19.2210i −0.482031 0.749882i
\(658\) −14.4980 4.67482i −0.565191 0.182243i
\(659\) 26.0375 26.0375i 1.01428 1.01428i 0.0143800 0.999897i \(-0.495423\pi\)
0.999897 0.0143800i \(-0.00457745\pi\)
\(660\) 0.211980 0.480470i 0.00825131 0.0187023i
\(661\) 24.4645 + 24.4645i 0.951560 + 0.951560i 0.998880 0.0473202i \(-0.0150681\pi\)
−0.0473202 + 0.998880i \(0.515068\pi\)
\(662\) 0.991005 + 23.5140i 0.0385165 + 0.913898i
\(663\) 14.3241 4.20675i 0.556301 0.163376i
\(664\) −2.35834 18.5641i −0.0915214 0.720426i
\(665\) −21.0977 + 9.71053i −0.818133 + 0.376558i
\(666\) −0.0607609 + 0.0427773i −0.00235444 + 0.00165759i
\(667\) −1.93257 + 1.93257i −0.0748292 + 0.0748292i
\(668\) −9.16071 + 0.773536i −0.354439 + 0.0299290i
\(669\) 5.01833 9.19153i 0.194020 0.355365i
\(670\) 13.1014 14.2543i 0.506152 0.550693i
\(671\) 1.16160 0.0448431
\(672\) −20.7433 15.5472i −0.800190 0.599747i
\(673\) −22.4919 −0.867001 −0.433500 0.901153i \(-0.642722\pi\)
−0.433500 + 0.901153i \(0.642722\pi\)
\(674\) −16.4544 + 17.9024i −0.633799 + 0.689573i
\(675\) −9.89336 + 0.709155i −0.380796 + 0.0272954i
\(676\) 20.0251 1.69093i 0.770197 0.0650359i
\(677\) 8.84883 8.84883i 0.340088 0.340088i −0.516312 0.856400i \(-0.672696\pi\)
0.856400 + 0.516312i \(0.172696\pi\)
\(678\) 4.65619 + 13.6932i 0.178820 + 0.525883i
\(679\) 34.5585 15.9061i 1.32623 0.610419i
\(680\) 24.7488 3.14404i 0.949075 0.120569i
\(681\) 9.05736 + 30.8405i 0.347079 + 1.18181i
\(682\) 0.0303783 + 0.720798i 0.00116324 + 0.0276008i
\(683\) −19.9603 19.9603i −0.763761 0.763761i 0.213239 0.977000i \(-0.431599\pi\)
−0.977000 + 0.213239i \(0.931599\pi\)
\(684\) 3.87913 29.7050i 0.148322 1.13580i
\(685\) −17.1576 + 17.1576i −0.655557 + 0.655557i
\(686\) −22.3181 + 13.7078i −0.852109 + 0.523365i
\(687\) −0.885186 3.01408i −0.0337720 0.114994i
\(688\) 10.1129 14.2583i 0.385551 0.543593i
\(689\) 7.02324 0.267564
\(690\) −0.533062 + 1.08237i −0.0202933 + 0.0412051i
\(691\) −28.0214 + 28.0214i −1.06599 + 1.06599i −0.0683228 + 0.997663i \(0.521765\pi\)
−0.997663 + 0.0683228i \(0.978235\pi\)
\(692\) −17.5475 + 20.7842i −0.667055 + 0.790098i
\(693\) 0.668307 0.147527i 0.0253869 0.00560409i
\(694\) −10.3436 + 0.435932i −0.392636 + 0.0165478i
\(695\) 39.6071 1.50238
\(696\) −44.4992 17.4331i −1.68674 0.660800i
\(697\) 15.9001i 0.602260i
\(698\) 0.0748289 + 1.77550i 0.00283231 + 0.0672036i
\(699\) −17.4696 9.53793i −0.660761 0.360758i
\(700\) −4.98023 8.78764i −0.188235 0.332141i
\(701\) 20.6251 20.6251i 0.779000 0.779000i −0.200661 0.979661i \(-0.564309\pi\)
0.979661 + 0.200661i \(0.0643089\pi\)
\(702\) −12.5438 + 1.43212i −0.473434 + 0.0540520i
\(703\) 0.0874487i 0.00329819i
\(704\) −0.350312 + 0.594235i −0.0132029 + 0.0223961i
\(705\) −11.8954 + 3.49347i −0.448005 + 0.131572i
\(706\) −12.2454 + 13.3230i −0.460863 + 0.501418i
\(707\) −4.23519 1.56539i −0.159281 0.0588725i
\(708\) 12.4678 + 32.1550i 0.468567 + 1.20846i
\(709\) −19.8254 + 19.8254i −0.744558 + 0.744558i −0.973451 0.228893i \(-0.926489\pi\)
0.228893 + 0.973451i \(0.426489\pi\)
\(710\) −0.926458 21.9825i −0.0347694 0.824988i
\(711\) 3.21949 + 5.00847i 0.120740 + 0.187832i
\(712\) 25.9566 33.5113i 0.972766 1.25589i
\(713\) 1.65747i 0.0620727i
\(714\) 22.3781 + 23.5858i 0.837480 + 0.882676i
\(715\) 0.184173 0.184173i 0.00688767 0.00688767i
\(716\) −22.4939 18.9909i −0.840637 0.709724i
\(717\) −12.3472 + 22.6150i −0.461113 + 0.844571i
\(718\) 2.85415 3.10531i 0.106516 0.115889i
\(719\) −36.6002 −1.36496 −0.682478 0.730906i \(-0.739098\pi\)
−0.682478 + 0.730906i \(0.739098\pi\)
\(720\) −21.0760 0.962005i −0.785457 0.0358518i
\(721\) 3.87637 + 8.42203i 0.144363 + 0.313653i
\(722\) 6.17311 + 5.67382i 0.229740 + 0.211158i
\(723\) 23.4296 42.9134i 0.871355 1.59597i
\(724\) 12.2875 14.5540i 0.456661 0.540896i
\(725\) −13.1677 13.1677i −0.489037 0.489037i
\(726\) 8.66847 + 25.4927i 0.321717 + 0.946122i
\(727\) −15.4698 −0.573743 −0.286871 0.957969i \(-0.592615\pi\)
−0.286871 + 0.957969i \(0.592615\pi\)
\(728\) −6.80456 10.9087i −0.252194 0.404302i
\(729\) −26.7240 + 3.85093i −0.989777 + 0.142627i
\(730\) −0.797434 18.9211i −0.0295143 0.700300i
\(731\) −15.5027 + 15.5027i −0.573389 + 0.573389i
\(732\) −16.8708 43.5107i −0.623564 1.60820i
\(733\) 17.4996 17.4996i 0.646363 0.646363i −0.305749 0.952112i \(-0.598907\pi\)
0.952112 + 0.305749i \(0.0989068\pi\)
\(734\) 9.44934 + 8.68506i 0.348782 + 0.320571i
\(735\) −8.73932 + 19.4428i −0.322355 + 0.717157i
\(736\) 0.861596 1.33012i 0.0317589 0.0490290i
\(737\) 0.671402i 0.0247314i
\(738\) 2.30107 13.2482i 0.0847035 0.487672i
\(739\) 27.4155 + 27.4155i 1.00850 + 1.00850i 0.999964 + 0.00853203i \(0.00271586\pi\)
0.00853203 + 0.999964i \(0.497284\pi\)
\(740\) −0.0613691 + 0.00518204i −0.00225597 + 0.000190496i
\(741\) 7.11990 13.0407i 0.261556 0.479064i
\(742\) 6.97441 + 13.6126i 0.256039 + 0.499735i
\(743\) −26.5108 −0.972589 −0.486294 0.873795i \(-0.661652\pi\)
−0.486294 + 0.873795i \(0.661652\pi\)
\(744\) 26.5582 11.6066i 0.973669 0.425519i
\(745\) 23.9786 0.878508
\(746\) 1.93862 + 45.9984i 0.0709778 + 1.68412i
\(747\) 4.21705 19.3953i 0.154294 0.709636i
\(748\) 0.558115 0.661063i 0.0204067 0.0241708i
\(749\) −5.15822 + 13.9557i −0.188477 + 0.509929i
\(750\) −26.6922 13.1458i −0.974661 0.480016i
\(751\) 3.53220 0.128892 0.0644458 0.997921i \(-0.479472\pi\)
0.0644458 + 0.997921i \(0.479472\pi\)
\(752\) 16.0542 2.73073i 0.585437 0.0995794i
\(753\) −5.03352 + 1.47826i −0.183432 + 0.0538708i
\(754\) −17.4517 16.0402i −0.635553 0.584148i
\(755\) −17.3225 17.3225i −0.630431 0.630431i
\(756\) −15.2324 22.8905i −0.553995 0.832520i
\(757\) 23.4555 23.4555i 0.852506 0.852506i −0.137936 0.990441i \(-0.544047\pi\)
0.990441 + 0.137936i \(0.0440467\pi\)
\(758\) −0.676716 16.0567i −0.0245794 0.583207i
\(759\) 0.0117899 + 0.0401450i 0.000427947 + 0.00145717i
\(760\) 15.2040 19.6291i 0.551507 0.712024i
\(761\) 45.1029i 1.63498i −0.575943 0.817490i \(-0.695365\pi\)
0.575943 0.817490i \(-0.304635\pi\)
\(762\) 37.4454 12.7329i 1.35650 0.461263i
\(763\) 17.9089 48.4530i 0.648346 1.75412i
\(764\) 53.2671 4.49791i 1.92714 0.162729i
\(765\) 25.8570 + 5.62199i 0.934860 + 0.203264i
\(766\) −29.0069 + 31.5595i −1.04806 + 1.14029i
\(767\) 17.1047i 0.617614i
\(768\) 27.3465 + 4.49129i 0.986780 + 0.162065i
\(769\) 4.03224i 0.145406i −0.997354 0.0727032i \(-0.976837\pi\)
0.997354 0.0727032i \(-0.0231626\pi\)
\(770\) 0.539861 + 0.174076i 0.0194552 + 0.00627326i
\(771\) −33.5832 18.3355i −1.20947 0.660339i
\(772\) −1.36013 16.1076i −0.0489522 0.579724i
\(773\) 2.31299 2.31299i 0.0831926 0.0831926i −0.664286 0.747479i \(-0.731264\pi\)
0.747479 + 0.664286i \(0.231264\pi\)
\(774\) 15.1606 10.6735i 0.544936 0.383650i
\(775\) 11.2933 0.405668
\(776\) −24.9045 + 32.1530i −0.894020 + 1.15423i
\(777\) −0.0527432 0.0604999i −0.00189215 0.00217042i
\(778\) −9.25498 + 0.390054i −0.331807 + 0.0139841i
\(779\) 11.1894 + 11.1894i 0.400903 + 0.400903i
\(780\) −9.57355 4.22378i −0.342788 0.151235i
\(781\) −0.539524 0.539524i −0.0193057 0.0193057i
\(782\) −1.34506 + 1.46342i −0.0480991 + 0.0523318i
\(783\) −38.3151 33.1896i −1.36927 1.18610i
\(784\) 14.3862 24.0216i 0.513793 0.857914i
\(785\) 24.5371i 0.875768i
\(786\) −33.1102 16.3066i −1.18100 0.581637i
\(787\) 20.2942 20.2942i 0.723410 0.723410i −0.245888 0.969298i \(-0.579080\pi\)
0.969298 + 0.245888i \(0.0790797\pi\)
\(788\) −12.9092 + 15.2904i −0.459871 + 0.544697i
\(789\) −16.0205 8.74674i −0.570343 0.311392i
\(790\) 0.207790 + 4.93032i 0.00739282 + 0.175413i
\(791\) −14.1910 + 6.53162i −0.504574 + 0.232238i
\(792\) −0.560696 + 0.470034i −0.0199235 + 0.0167019i
\(793\) 23.1453i 0.821914i
\(794\) 0.379060 + 8.99412i 0.0134523 + 0.319189i
\(795\) 10.9260 + 5.96531i 0.387506 + 0.211568i
\(796\) 3.39577 + 40.2149i 0.120360 + 1.42538i
\(797\) −5.34160 5.34160i −0.189209 0.189209i 0.606145 0.795354i \(-0.292715\pi\)
−0.795354 + 0.606145i \(0.792715\pi\)
\(798\) 32.3463 + 0.849881i 1.14505 + 0.0300855i
\(799\) −20.4244 −0.722565
\(800\) 9.06293 + 5.87057i 0.320423 + 0.207556i
\(801\) 37.8197 24.3109i 1.33629 0.858983i
\(802\) 16.1707 + 14.8628i 0.571008 + 0.524824i
\(803\) −0.464386 0.464386i −0.0163878 0.0163878i
\(804\) −25.1491 + 9.75130i −0.886940 + 0.343902i
\(805\) −1.22236 0.451803i −0.0430826 0.0159239i
\(806\) 14.3622 0.605298i 0.505886 0.0213207i
\(807\) −5.23840 17.8369i −0.184401 0.627889i
\(808\) 4.78850 0.608321i 0.168459 0.0214007i
\(809\) −8.10987 −0.285128 −0.142564 0.989786i \(-0.545535\pi\)
−0.142564 + 0.989786i \(0.545535\pi\)
\(810\) −20.7307 8.42633i −0.728402 0.296071i
\(811\) −16.1361 16.1361i −0.566615 0.566615i 0.364564 0.931179i \(-0.381218\pi\)
−0.931179 + 0.364564i \(0.881218\pi\)
\(812\) 13.7591 49.7540i 0.482850 1.74602i
\(813\) −3.07561 + 5.63327i −0.107866 + 0.197567i
\(814\) −0.00144529 + 0.00157248i −5.06574e−5 + 5.51152e-5i
\(815\) −2.89447 −0.101389
\(816\) −32.8678 11.3045i −1.15060 0.395736i
\(817\) 21.8195i 0.763369i
\(818\) −31.9166 + 34.7252i −1.11594 + 1.21414i
\(819\) −2.93953 13.3163i −0.102715 0.465308i
\(820\) 7.18938 8.51551i 0.251064 0.297374i
\(821\) 29.4715 + 29.4715i 1.02856 + 1.02856i 0.999580 + 0.0289824i \(0.00922668\pi\)
0.0289824 + 0.999580i \(0.490773\pi\)
\(822\) 32.0058 10.8832i 1.11633 0.379594i
\(823\) 32.5659i 1.13517i 0.823313 + 0.567587i \(0.192123\pi\)
−0.823313 + 0.567587i \(0.807877\pi\)
\(824\) −7.83580 6.06932i −0.272973 0.211435i
\(825\) −0.273532 + 0.0803318i −0.00952316 + 0.00279680i
\(826\) −33.1527 + 16.9858i −1.15353 + 0.591010i
\(827\) −30.3017 30.3017i −1.05369 1.05369i −0.998474 0.0552178i \(-0.982415\pi\)
−0.0552178 0.998474i \(-0.517585\pi\)
\(828\) 1.33250 1.02468i 0.0463076 0.0356101i
\(829\) −5.98502 + 5.98502i −0.207868 + 0.207868i −0.803361 0.595492i \(-0.796957\pi\)
0.595492 + 0.803361i \(0.296957\pi\)
\(830\) 11.1321 12.1117i 0.386402 0.420405i
\(831\) −3.35742 + 0.986018i −0.116467 + 0.0342046i
\(832\) 11.8403 + 6.98009i 0.410490 + 0.241991i
\(833\) −22.8397 + 26.6758i −0.791350 + 0.924260i
\(834\) −49.5032 24.3801i −1.71415 0.844213i
\(835\) −5.71460 5.71460i −0.197762 0.197762i
\(836\) −0.0724479 0.857975i −0.00250566 0.0296737i
\(837\) 30.6631 2.19793i 1.05987 0.0759714i
\(838\) −4.94565 + 0.208436i −0.170845 + 0.00720030i
\(839\) 0.539555i 0.0186275i 0.999957 + 0.00931375i \(0.00296470\pi\)
−0.999957 + 0.00931375i \(0.997035\pi\)
\(840\) −1.32036 22.7501i −0.0455566 0.784953i
\(841\) 66.1704i 2.28174i
\(842\) −0.687935 16.3229i −0.0237078 0.562525i
\(843\) 26.2330 + 14.3225i 0.903513 + 0.493294i
\(844\) 3.81356 4.51700i 0.131268 0.155481i
\(845\) 12.4920 + 12.4920i 0.429738 + 0.429738i
\(846\) 17.0179 + 2.95583i 0.585086 + 0.101623i
\(847\) −26.4195 + 12.1600i −0.907785 + 0.417822i
\(848\) −13.3372 9.45964i −0.458003 0.324845i
\(849\) 1.92854 + 6.56673i 0.0661874 + 0.225370i
\(850\) −9.97115 9.16466i −0.342007 0.314345i
\(851\) 0.00346966 0.00346966i 0.000118938 0.000118938i
\(852\) −12.3733 + 28.0452i −0.423903 + 0.960812i
\(853\) −21.6730 21.6730i −0.742070 0.742070i 0.230906 0.972976i \(-0.425831\pi\)
−0.972976 + 0.230906i \(0.925831\pi\)
\(854\) 44.8608 22.9844i 1.53511 0.786510i
\(855\) 22.1528 14.2400i 0.757609 0.486998i
\(856\) −2.00452 15.7789i −0.0685131 0.539312i
\(857\) 22.6194i 0.772664i 0.922360 + 0.386332i \(0.126258\pi\)
−0.922360 + 0.386332i \(0.873742\pi\)
\(858\) −0.343556 + 0.116822i −0.0117288 + 0.00398823i
\(859\) −28.5727 28.5727i −0.974889 0.974889i 0.0248032 0.999692i \(-0.492104\pi\)
−0.999692 + 0.0248032i \(0.992104\pi\)
\(860\) 15.3124 1.29298i 0.522147 0.0440904i
\(861\) 14.4899 + 0.992497i 0.493816 + 0.0338242i
\(862\) 22.5901 + 20.7630i 0.769423 + 0.707191i
\(863\) 1.11141i 0.0378330i −0.999821 0.0189165i \(-0.993978\pi\)
0.999821 0.0189165i \(-0.00602166\pi\)
\(864\) 25.7498 + 14.1756i 0.876025 + 0.482265i
\(865\) −23.9120 −0.813031
\(866\) 16.0188 + 14.7231i 0.544340 + 0.500313i
\(867\) 12.4178 + 6.77976i 0.421729 + 0.230253i
\(868\) 15.4355 + 27.2360i 0.523916 + 0.924451i
\(869\) 0.121006 + 0.121006i 0.00410486 + 0.00410486i
\(870\) −13.5255 39.7765i −0.458557 1.34855i
\(871\) −13.3779 −0.453294
\(872\) 6.95953 + 54.7831i 0.235680 + 1.85519i
\(873\) −36.2868 + 23.3255i −1.22812 + 0.789448i
\(874\) 0.0832966 + 1.97641i 0.00281755 + 0.0668532i
\(875\) 11.1418 30.1445i 0.376663 1.01907i
\(876\) −10.6501 + 24.1394i −0.359835 + 0.815595i
\(877\) 28.2181 + 28.2181i 0.952859 + 0.952859i 0.998938 0.0460791i \(-0.0146726\pi\)
−0.0460791 + 0.998938i \(0.514673\pi\)
\(878\) −27.8404 + 30.2904i −0.939569 + 1.02225i
\(879\) −36.0325 + 10.5821i −1.21534 + 0.356927i
\(880\) −0.597810 + 0.101684i −0.0201522 + 0.00342776i
\(881\) 5.09258 0.171573 0.0857867 0.996314i \(-0.472660\pi\)
0.0857867 + 0.996314i \(0.472660\pi\)
\(882\) 22.8908 18.9212i 0.770774 0.637109i
\(883\) 30.4047 + 30.4047i 1.02320 + 1.02320i 0.999724 + 0.0234738i \(0.00747263\pi\)
0.0234738 + 0.999724i \(0.492527\pi\)
\(884\) −13.1719 11.1206i −0.443019 0.374027i
\(885\) −14.5281 + 26.6096i −0.488358 + 0.894473i
\(886\) −21.6760 + 0.913541i −0.728219 + 0.0306910i
\(887\) 1.96980i 0.0661395i −0.999453 0.0330698i \(-0.989472\pi\)
0.999453 0.0330698i \(-0.0105284\pi\)
\(888\) 0.0798922 + 0.0312988i 0.00268101 + 0.00105032i
\(889\) 17.8614 + 38.8068i 0.599053 + 1.30154i
\(890\) 37.2296 1.56905i 1.24794 0.0525947i
\(891\) −0.727046 + 0.271348i −0.0243570 + 0.00909051i
\(892\) −12.0494 + 1.01746i −0.403444 + 0.0340671i
\(893\) −14.3733 + 14.3733i −0.480986 + 0.480986i
\(894\) −29.9698 14.7600i −1.00234 0.493647i
\(895\) 25.8789i 0.865037i
\(896\) −1.77096 + 29.8808i −0.0591635 + 0.998248i
\(897\) 0.799904 0.234919i 0.0267080 0.00784370i
\(898\) 17.9672 + 16.5140i 0.599573 + 0.551078i
\(899\) 40.8115 + 40.8115i 1.36114 + 1.36114i
\(900\) 6.98176 + 9.07912i 0.232725 + 0.302637i
\(901\) 14.5013 + 14.5013i 0.483108 + 0.483108i
\(902\) −0.0162738 0.386136i −0.000541859 0.0128569i
\(903\) 13.1601 + 15.0955i 0.437940 + 0.502346i
\(904\) 10.2267 13.2032i 0.340136 0.439132i
\(905\) 16.7442 0.556595
\(906\) 10.9878 + 32.3135i 0.365045 + 1.07354i
\(907\) 22.0232 22.0232i 0.731268 0.731268i −0.239603 0.970871i \(-0.577017\pi\)
0.970871 + 0.239603i \(0.0770171\pi\)
\(908\) 23.9434 28.3599i 0.794588 0.941156i
\(909\) 5.00290 + 1.08776i 0.165936 + 0.0360788i
\(910\) 3.46853 10.7569i 0.114981 0.356588i
\(911\) 13.5474i 0.448845i 0.974492 + 0.224422i \(0.0720495\pi\)
−0.974492 + 0.224422i \(0.927950\pi\)
\(912\) −31.0854 + 15.1748i −1.02934 + 0.502487i
\(913\) 0.570482i 0.0188802i
\(914\) −17.8755 16.4297i −0.591269 0.543446i
\(915\) 19.6589 36.0070i 0.649902 1.19036i
\(916\) −2.34001 + 2.77164i −0.0773161 + 0.0915776i
\(917\) 13.8208 37.3926i 0.456404 1.23481i
\(918\) −28.8568 22.9429i −0.952417 0.757227i
\(919\) 30.7662i 1.01488i 0.861686 + 0.507441i \(0.169408\pi\)
−0.861686 + 0.507441i \(0.830592\pi\)
\(920\) 1.38206 0.175574i 0.0455651 0.00578850i
\(921\) 36.9494 10.8514i 1.21752 0.357567i
\(922\) 2.38228 0.100402i 0.0784561 0.00330656i
\(923\) −10.7502 + 10.7502i −0.353847 + 0.353847i
\(924\) −0.567595 0.549879i −0.0186725 0.0180897i
\(925\) 0.0236409 + 0.0236409i 0.000777307 + 0.000777307i
\(926\) −1.72385 + 1.87555i −0.0566492 + 0.0616343i
\(927\) −5.68450 8.84321i −0.186703 0.290449i
\(928\) 11.5365 + 53.9663i 0.378703 + 1.77153i
\(929\) −17.4067 −0.571094 −0.285547 0.958365i \(-0.592175\pi\)
−0.285547 + 0.958365i \(0.592175\pi\)
\(930\) 22.8573 + 11.2571i 0.749519 + 0.369135i
\(931\) 2.69954 + 34.8457i 0.0884738 + 1.14202i
\(932\) 1.93380 + 22.9014i 0.0633438 + 0.750159i
\(933\) 12.9840 23.7814i 0.425076 0.778567i
\(934\) −32.0953 + 1.35266i −1.05019 + 0.0442605i
\(935\) 0.760543 0.0248724
\(936\) 9.36560 + 11.1721i 0.306124 + 0.365171i
\(937\) 19.0002 0.620711 0.310356 0.950621i \(-0.399552\pi\)
0.310356 + 0.950621i \(0.399552\pi\)
\(938\) −13.2849 25.9294i −0.433768 0.846626i
\(939\) 0.779087 + 0.425361i 0.0254245 + 0.0138811i
\(940\) 10.9386 + 9.23508i 0.356776 + 0.301215i
\(941\) 1.02822 + 1.02822i 0.0335189 + 0.0335189i 0.723668 0.690149i \(-0.242455\pi\)
−0.690149 + 0.723668i \(0.742455\pi\)
\(942\) 15.1038 30.6679i 0.492108 0.999213i
\(943\) 0.887916i 0.0289145i
\(944\) 23.0384 32.4821i 0.749835 1.05720i
\(945\) 6.73738 23.2128i 0.219167 0.755111i
\(946\) 0.360618 0.392352i 0.0117247 0.0127565i
\(947\) −25.3941 + 25.3941i −0.825199 + 0.825199i −0.986848 0.161650i \(-0.948319\pi\)
0.161650 + 0.986848i \(0.448319\pi\)
\(948\) 2.77514 6.29008i 0.0901322 0.204292i
\(949\) −9.25306 + 9.25306i −0.300367 + 0.300367i
\(950\) −13.4665 + 0.567549i −0.436911 + 0.0184137i
\(951\) −15.5305 + 4.56105i −0.503611 + 0.147902i
\(952\) 8.47397 36.5735i 0.274643 1.18535i
\(953\) −34.3999 −1.11432 −0.557161 0.830405i \(-0.688109\pi\)
−0.557161 + 0.830405i \(0.688109\pi\)
\(954\) −9.98399 14.1812i −0.323244 0.459135i
\(955\) 33.2289 + 33.2289i 1.07526 + 1.07526i
\(956\) 29.6466 2.50337i 0.958838 0.0809648i
\(957\) −1.27878 0.698181i −0.0413372 0.0225690i
\(958\) 3.68333 4.00746i 0.119003 0.129475i
\(959\) 15.2667 + 33.1694i 0.492988 + 1.07110i
\(960\) 12.4913 + 20.9157i 0.403155 + 0.675051i
\(961\) −4.00205 −0.129098
\(962\) 0.0313321 + 0.0287979i 0.00101019 + 0.000928483i
\(963\) 3.58436 16.4854i 0.115505 0.531235i
\(964\) −56.2564 + 4.75032i −1.81190 + 0.152998i
\(965\) 10.0482 10.0482i 0.323462 0.323462i
\(966\) 1.24967 + 1.31711i 0.0402074 + 0.0423773i
\(967\) 51.8029i 1.66587i 0.553373 + 0.832934i \(0.313341\pi\)
−0.553373 + 0.832934i \(0.686659\pi\)
\(968\) 19.0392 24.5805i 0.611942 0.790048i
\(969\) 41.6268 12.2251i 1.33725 0.392727i
\(970\) −35.7205 + 1.50545i −1.14692 + 0.0483372i
\(971\) 27.2829 27.2829i 0.875551 0.875551i −0.117520 0.993071i \(-0.537494\pi\)
0.993071 + 0.117520i \(0.0374943\pi\)
\(972\) 20.7235 + 23.2924i 0.664707 + 0.747104i
\(973\) 20.6636 55.9058i 0.662444 1.79226i
\(974\) 5.15096 + 4.73434i 0.165047 + 0.151698i
\(975\) 1.60064 + 5.45022i 0.0512615 + 0.174547i
\(976\) −31.1745 + 43.9533i −0.997872 + 1.40691i
\(977\) 22.3034i 0.713550i −0.934190 0.356775i \(-0.883876\pi\)
0.934190 0.356775i \(-0.116124\pi\)
\(978\) 3.61766 + 1.78168i 0.115680 + 0.0569719i
\(979\) 0.913739 0.913739i 0.0292032 0.0292032i
\(980\) 24.2938 3.95935i 0.776035 0.126477i
\(981\) −12.4446 + 57.2360i −0.397326 + 1.82740i
\(982\) −32.9557 + 1.38893i −1.05166 + 0.0443225i
\(983\) 41.5873i 1.32643i −0.748429 0.663214i \(-0.769192\pi\)
0.748429 0.663214i \(-0.230808\pi\)
\(984\) −14.2274 + 6.21774i −0.453552 + 0.198214i
\(985\) −17.5914 −0.560507
\(986\) −2.91445 69.1525i −0.0928151 2.20226i
\(987\) −1.27491 + 18.6130i −0.0405807 + 0.592458i
\(988\) −17.0955 + 1.44355i −0.543879 + 0.0459255i
\(989\) −0.865723 + 0.865723i −0.0275284 + 0.0275284i
\(990\) −0.633693 0.110066i −0.0201401 0.00349812i
\(991\) 44.9577 1.42813 0.714065 0.700080i \(-0.246852\pi\)
0.714065 + 0.700080i \(0.246852\pi\)
\(992\) −28.0893 18.1950i −0.891835 0.577692i
\(993\) 27.6562 8.12218i 0.877643 0.257749i
\(994\) −31.5118 10.1609i −0.999493 0.322283i
\(995\) −25.0867 + 25.0867i −0.795303 + 0.795303i
\(996\) −21.3689 + 8.28557i −0.677099 + 0.262538i
\(997\) −8.88328 8.88328i −0.281336 0.281336i 0.552305 0.833642i \(-0.313748\pi\)
−0.833642 + 0.552305i \(0.813748\pi\)
\(998\) −6.05640 + 0.255249i −0.191712 + 0.00807976i
\(999\) 0.0687896 + 0.0595875i 0.00217641 + 0.00188527i
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 336.2.y.a.125.16 yes 120
3.2 odd 2 inner 336.2.y.a.125.45 yes 120
7.6 odd 2 inner 336.2.y.a.125.15 120
16.5 even 4 inner 336.2.y.a.293.46 yes 120
21.20 even 2 inner 336.2.y.a.125.46 yes 120
48.5 odd 4 inner 336.2.y.a.293.15 yes 120
112.69 odd 4 inner 336.2.y.a.293.45 yes 120
336.293 even 4 inner 336.2.y.a.293.16 yes 120
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
336.2.y.a.125.15 120 7.6 odd 2 inner
336.2.y.a.125.16 yes 120 1.1 even 1 trivial
336.2.y.a.125.45 yes 120 3.2 odd 2 inner
336.2.y.a.125.46 yes 120 21.20 even 2 inner
336.2.y.a.293.15 yes 120 48.5 odd 4 inner
336.2.y.a.293.16 yes 120 336.293 even 4 inner
336.2.y.a.293.45 yes 120 112.69 odd 4 inner
336.2.y.a.293.46 yes 120 16.5 even 4 inner