Properties

Label 475.2.l.c.351.2
Level $475$
Weight $2$
Character 475.351
Analytic conductor $3.793$
Analytic rank $0$
Dimension $18$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [475,2,Mod(101,475)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(475, base_ring=CyclotomicField(18))
 
chi = DirichletCharacter(H, H._module([0, 14]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("475.101");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 475 = 5^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 475.l (of order \(9\), degree \(6\), 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: \(3.79289409601\)
Analytic rank: \(0\)
Dimension: \(18\)
Relative dimension: \(3\) over \(\Q(\zeta_{9})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{18} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{18} - 3 x^{17} + 15 x^{16} - 14 x^{15} + 72 x^{14} - 51 x^{13} + 231 x^{12} - 93 x^{11} + 438 x^{10} - 156 x^{9} + 582 x^{8} - 138 x^{7} + 437 x^{6} - 132 x^{5} + 198 x^{4} - 16 x^{3} + \cdots + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 95)
Sato-Tate group: $\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label 351.2
Root \(0.394508 - 0.683308i\) of defining polynomial
Character \(\chi\) \(=\) 475.351
Dual form 475.2.l.c.226.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.0366369 - 0.207778i) q^{2} +(-0.0612035 + 0.0513559i) q^{3} +(1.83756 - 0.668816i) q^{4} +(0.0129129 + 0.0108352i) q^{6} +(-0.843614 + 1.46118i) q^{7} +(-0.417271 - 0.722735i) q^{8} +(-0.519836 + 2.94814i) q^{9} +O(q^{10})\) \(q+(-0.0366369 - 0.207778i) q^{2} +(-0.0612035 + 0.0513559i) q^{3} +(1.83756 - 0.668816i) q^{4} +(0.0129129 + 0.0108352i) q^{6} +(-0.843614 + 1.46118i) q^{7} +(-0.417271 - 0.722735i) q^{8} +(-0.519836 + 2.94814i) q^{9} +(1.44339 + 2.50003i) q^{11} +(-0.0781173 + 0.135303i) q^{12} +(4.95325 + 4.15627i) q^{13} +(0.334509 + 0.121751i) q^{14} +(2.86110 - 2.40075i) q^{16} +(-0.518598 - 2.94112i) q^{17} +0.631604 q^{18} +(-4.34933 - 0.288668i) q^{19} +(-0.0234081 - 0.132754i) q^{21} +(0.466570 - 0.391499i) q^{22} +(7.75955 - 2.82424i) q^{23} +(0.0626552 + 0.0228046i) q^{24} +(0.682111 - 1.18145i) q^{26} +(-0.239432 - 0.414708i) q^{27} +(-0.572926 + 3.24923i) q^{28} +(1.26021 - 7.14701i) q^{29} +(-2.02800 + 3.51260i) q^{31} +(-1.88224 - 1.57939i) q^{32} +(-0.216732 - 0.0788839i) q^{33} +(-0.592100 + 0.215507i) q^{34} +(1.01653 + 5.76504i) q^{36} -7.96989 q^{37} +(0.0993671 + 0.914272i) q^{38} -0.516605 q^{39} +(4.17950 - 3.50702i) q^{41} +(-0.0267258 + 0.00972740i) q^{42} +(-5.01011 - 1.82353i) q^{43} +(4.32437 + 3.62858i) q^{44} +(-0.871103 - 1.50879i) q^{46} +(-0.286452 + 1.62455i) q^{47} +(-0.0518169 + 0.293868i) q^{48} +(2.07663 + 3.59683i) q^{49} +(0.182783 + 0.153374i) q^{51} +(11.8817 + 4.32457i) q^{52} +(1.79663 - 0.653921i) q^{53} +(-0.0773952 + 0.0649423i) q^{54} +1.40806 q^{56} +(0.281019 - 0.205696i) q^{57} -1.53116 q^{58} +(0.616931 + 3.49879i) q^{59} +(7.42370 - 2.70201i) q^{61} +(0.804142 + 0.292684i) q^{62} +(-3.86922 - 3.24666i) q^{63} +(3.47569 - 6.02008i) q^{64} +(-0.00844998 + 0.0479222i) q^{66} +(-0.393370 + 2.23091i) q^{67} +(-2.92002 - 5.05762i) q^{68} +(-0.329870 + 0.571352i) q^{69} +(-9.79389 - 3.56469i) q^{71} +(2.34764 - 0.854469i) q^{72} +(-1.08155 + 0.907529i) q^{73} +(0.291992 + 1.65597i) q^{74} +(-8.18520 + 2.37846i) q^{76} -4.87066 q^{77} +(0.0189268 + 0.107339i) q^{78} +(-1.84675 + 1.54961i) q^{79} +(-8.40329 - 3.05855i) q^{81} +(-0.881806 - 0.739923i) q^{82} +(-5.70029 + 9.87319i) q^{83} +(-0.131802 - 0.228287i) q^{84} +(-0.195335 + 1.10780i) q^{86} +(0.289912 + 0.502142i) q^{87} +(1.20457 - 2.08638i) q^{88} +(-7.74938 - 6.50250i) q^{89} +(-10.2517 + 3.73131i) q^{91} +(12.3697 - 10.3794i) q^{92} +(-0.0562718 - 0.319133i) q^{93} +0.348041 q^{94} +0.196310 q^{96} +(1.71360 + 9.71828i) q^{97} +(0.671262 - 0.563256i) q^{98} +(-8.12075 + 2.95571i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 18 q + 3 q^{2} + 3 q^{3} - 3 q^{4} - 6 q^{6} + 6 q^{8} + 3 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 18 q + 3 q^{2} + 3 q^{3} - 3 q^{4} - 6 q^{6} + 6 q^{8} + 3 q^{9} + 18 q^{12} + 3 q^{13} - 12 q^{14} - 3 q^{16} - 24 q^{17} - 48 q^{18} - 21 q^{21} - 9 q^{22} + 9 q^{23} - 15 q^{24} + 3 q^{26} + 24 q^{27} + 12 q^{28} + 15 q^{29} - 18 q^{31} - 15 q^{32} + 33 q^{33} - 12 q^{34} + 75 q^{36} - 36 q^{37} + 33 q^{38} + 36 q^{39} - 30 q^{41} + 9 q^{42} + 36 q^{43} + 42 q^{44} + 9 q^{46} - 21 q^{47} - 33 q^{48} + 9 q^{49} - 45 q^{51} + 39 q^{52} + 12 q^{53} - 66 q^{54} - 72 q^{57} - 12 q^{58} + 18 q^{59} - 30 q^{61} + 24 q^{62} - 54 q^{63} + 36 q^{64} + 39 q^{66} - 51 q^{68} + 15 q^{69} - 12 q^{71} + 66 q^{72} - 24 q^{73} - 15 q^{74} - 33 q^{76} + 60 q^{77} + 48 q^{78} - 51 q^{79} + 27 q^{81} + 15 q^{82} + 48 q^{84} + 63 q^{86} + 15 q^{87} + 27 q^{88} - 54 q^{89} + 30 q^{91} + 42 q^{92} - 72 q^{93} + 30 q^{94} - 66 q^{96} - 27 q^{97} + 3 q^{98} - 93 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/475\mathbb{Z}\right)^\times\).

\(n\) \(77\) \(401\)
\(\chi(n)\) \(1\) \(e\left(\frac{4}{9}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.0366369 0.207778i −0.0259062 0.146921i 0.969111 0.246625i \(-0.0793216\pi\)
−0.995017 + 0.0997037i \(0.968211\pi\)
\(3\) −0.0612035 + 0.0513559i −0.0353359 + 0.0296503i −0.660285 0.751016i \(-0.729564\pi\)
0.624949 + 0.780666i \(0.285120\pi\)
\(4\) 1.83756 0.668816i 0.918778 0.334408i
\(5\) 0 0
\(6\) 0.0129129 + 0.0108352i 0.00527169 + 0.00442347i
\(7\) −0.843614 + 1.46118i −0.318856 + 0.552275i −0.980250 0.197764i \(-0.936632\pi\)
0.661394 + 0.750039i \(0.269965\pi\)
\(8\) −0.417271 0.722735i −0.147528 0.255526i
\(9\) −0.519836 + 2.94814i −0.173279 + 0.982712i
\(10\) 0 0
\(11\) 1.44339 + 2.50003i 0.435199 + 0.753787i 0.997312 0.0732738i \(-0.0233447\pi\)
−0.562113 + 0.827061i \(0.690011\pi\)
\(12\) −0.0781173 + 0.135303i −0.0225505 + 0.0390586i
\(13\) 4.95325 + 4.15627i 1.37378 + 1.15274i 0.971449 + 0.237250i \(0.0762461\pi\)
0.402336 + 0.915492i \(0.368198\pi\)
\(14\) 0.334509 + 0.121751i 0.0894014 + 0.0325394i
\(15\) 0 0
\(16\) 2.86110 2.40075i 0.715274 0.600186i
\(17\) −0.518598 2.94112i −0.125778 0.713325i −0.980842 0.194803i \(-0.937593\pi\)
0.855064 0.518523i \(-0.173518\pi\)
\(18\) 0.631604 0.148871
\(19\) −4.34933 0.288668i −0.997805 0.0662249i
\(20\) 0 0
\(21\) −0.0234081 0.132754i −0.00510807 0.0289693i
\(22\) 0.466570 0.391499i 0.0994731 0.0834678i
\(23\) 7.75955 2.82424i 1.61798 0.588896i 0.634982 0.772527i \(-0.281008\pi\)
0.982995 + 0.183631i \(0.0587853\pi\)
\(24\) 0.0626552 + 0.0228046i 0.0127894 + 0.00465497i
\(25\) 0 0
\(26\) 0.682111 1.18145i 0.133773 0.231702i
\(27\) −0.239432 0.414708i −0.0460786 0.0798105i
\(28\) −0.572926 + 3.24923i −0.108273 + 0.614046i
\(29\) 1.26021 7.14701i 0.234015 1.32717i −0.610662 0.791891i \(-0.709097\pi\)
0.844677 0.535276i \(-0.179792\pi\)
\(30\) 0 0
\(31\) −2.02800 + 3.51260i −0.364240 + 0.630882i −0.988654 0.150212i \(-0.952005\pi\)
0.624414 + 0.781094i \(0.285338\pi\)
\(32\) −1.88224 1.57939i −0.332736 0.279199i
\(33\) −0.216732 0.0788839i −0.0377281 0.0137319i
\(34\) −0.592100 + 0.215507i −0.101544 + 0.0369591i
\(35\) 0 0
\(36\) 1.01653 + 5.76504i 0.169422 + 0.960840i
\(37\) −7.96989 −1.31024 −0.655121 0.755524i \(-0.727382\pi\)
−0.655121 + 0.755524i \(0.727382\pi\)
\(38\) 0.0993671 + 0.914272i 0.0161195 + 0.148315i
\(39\) −0.516605 −0.0827230
\(40\) 0 0
\(41\) 4.17950 3.50702i 0.652728 0.547704i −0.255169 0.966896i \(-0.582131\pi\)
0.907897 + 0.419192i \(0.137687\pi\)
\(42\) −0.0267258 + 0.00972740i −0.00412388 + 0.00150097i
\(43\) −5.01011 1.82353i −0.764034 0.278086i −0.0695352 0.997580i \(-0.522152\pi\)
−0.694499 + 0.719494i \(0.744374\pi\)
\(44\) 4.32437 + 3.62858i 0.651923 + 0.547029i
\(45\) 0 0
\(46\) −0.871103 1.50879i −0.128437 0.222460i
\(47\) −0.286452 + 1.62455i −0.0417833 + 0.236965i −0.998546 0.0539044i \(-0.982833\pi\)
0.956763 + 0.290869i \(0.0939445\pi\)
\(48\) −0.0518169 + 0.293868i −0.00747912 + 0.0424162i
\(49\) 2.07663 + 3.59683i 0.296662 + 0.513833i
\(50\) 0 0
\(51\) 0.182783 + 0.153374i 0.0255948 + 0.0214766i
\(52\) 11.8817 + 4.32457i 1.64769 + 0.599710i
\(53\) 1.79663 0.653921i 0.246787 0.0898230i −0.215665 0.976467i \(-0.569192\pi\)
0.462452 + 0.886644i \(0.346970\pi\)
\(54\) −0.0773952 + 0.0649423i −0.0105322 + 0.00883753i
\(55\) 0 0
\(56\) 1.40806 0.188160
\(57\) 0.281019 0.205696i 0.0372219 0.0272451i
\(58\) −1.53116 −0.201052
\(59\) 0.616931 + 3.49879i 0.0803175 + 0.455503i 0.998269 + 0.0588110i \(0.0187309\pi\)
−0.917952 + 0.396692i \(0.870158\pi\)
\(60\) 0 0
\(61\) 7.42370 2.70201i 0.950508 0.345956i 0.180201 0.983630i \(-0.442325\pi\)
0.770307 + 0.637673i \(0.220103\pi\)
\(62\) 0.804142 + 0.292684i 0.102126 + 0.0371709i
\(63\) −3.86922 3.24666i −0.487476 0.409041i
\(64\) 3.47569 6.02008i 0.434462 0.752510i
\(65\) 0 0
\(66\) −0.00844998 + 0.0479222i −0.00104012 + 0.00589882i
\(67\) −0.393370 + 2.23091i −0.0480578 + 0.272550i −0.999362 0.0357028i \(-0.988633\pi\)
0.951305 + 0.308252i \(0.0997441\pi\)
\(68\) −2.92002 5.05762i −0.354104 0.613326i
\(69\) −0.329870 + 0.571352i −0.0397117 + 0.0687827i
\(70\) 0 0
\(71\) −9.79389 3.56469i −1.16232 0.423050i −0.312395 0.949952i \(-0.601131\pi\)
−0.849926 + 0.526902i \(0.823354\pi\)
\(72\) 2.34764 0.854469i 0.276671 0.100700i
\(73\) −1.08155 + 0.907529i −0.126586 + 0.106218i −0.703883 0.710316i \(-0.748552\pi\)
0.577297 + 0.816534i \(0.304108\pi\)
\(74\) 0.291992 + 1.65597i 0.0339434 + 0.192503i
\(75\) 0 0
\(76\) −8.18520 + 2.37846i −0.938907 + 0.272828i
\(77\) −4.87066 −0.555063
\(78\) 0.0189268 + 0.107339i 0.00214304 + 0.0121538i
\(79\) −1.84675 + 1.54961i −0.207776 + 0.174344i −0.740737 0.671795i \(-0.765524\pi\)
0.532961 + 0.846140i \(0.321079\pi\)
\(80\) 0 0
\(81\) −8.40329 3.05855i −0.933699 0.339838i
\(82\) −0.881806 0.739923i −0.0973792 0.0817108i
\(83\) −5.70029 + 9.87319i −0.625688 + 1.08372i 0.362719 + 0.931898i \(0.381848\pi\)
−0.988407 + 0.151825i \(0.951485\pi\)
\(84\) −0.131802 0.228287i −0.0143807 0.0249082i
\(85\) 0 0
\(86\) −0.195335 + 1.10780i −0.0210635 + 0.119457i
\(87\) 0.289912 + 0.502142i 0.0310818 + 0.0538352i
\(88\) 1.20457 2.08638i 0.128408 0.222409i
\(89\) −7.74938 6.50250i −0.821433 0.689264i 0.131874 0.991266i \(-0.457901\pi\)
−0.953307 + 0.302002i \(0.902345\pi\)
\(90\) 0 0
\(91\) −10.2517 + 3.73131i −1.07467 + 0.391148i
\(92\) 12.3697 10.3794i 1.28963 1.08213i
\(93\) −0.0562718 0.319133i −0.00583512 0.0330926i
\(94\) 0.348041 0.0358977
\(95\) 0 0
\(96\) 0.196310 0.0200358
\(97\) 1.71360 + 9.71828i 0.173989 + 0.986742i 0.939304 + 0.343086i \(0.111472\pi\)
−0.765315 + 0.643656i \(0.777417\pi\)
\(98\) 0.671262 0.563256i 0.0678077 0.0568974i
\(99\) −8.12075 + 2.95571i −0.816166 + 0.297060i
\(100\) 0 0
\(101\) 3.19421 + 2.68026i 0.317836 + 0.266696i 0.787722 0.616031i \(-0.211260\pi\)
−0.469886 + 0.882727i \(0.655705\pi\)
\(102\) 0.0251711 0.0435976i 0.00249231 0.00431680i
\(103\) −6.28180 10.8804i −0.618964 1.07208i −0.989675 0.143329i \(-0.954219\pi\)
0.370711 0.928748i \(-0.379114\pi\)
\(104\) 0.937034 5.31418i 0.0918837 0.521098i
\(105\) 0 0
\(106\) −0.201694 0.349344i −0.0195902 0.0339313i
\(107\) 7.47116 12.9404i 0.722264 1.25100i −0.237826 0.971308i \(-0.576435\pi\)
0.960090 0.279690i \(-0.0902318\pi\)
\(108\) −0.717332 0.601913i −0.0690253 0.0579191i
\(109\) −4.89106 1.78020i −0.468479 0.170512i 0.0969843 0.995286i \(-0.469080\pi\)
−0.565463 + 0.824774i \(0.691303\pi\)
\(110\) 0 0
\(111\) 0.487785 0.409301i 0.0462985 0.0388491i
\(112\) 1.09427 + 6.20589i 0.103398 + 0.586401i
\(113\) −8.57064 −0.806258 −0.403129 0.915143i \(-0.632077\pi\)
−0.403129 + 0.915143i \(0.632077\pi\)
\(114\) −0.0530349 0.0508536i −0.00496717 0.00476288i
\(115\) 0 0
\(116\) −2.46433 13.9759i −0.228807 1.29763i
\(117\) −14.8281 + 12.4423i −1.37086 + 1.15029i
\(118\) 0.704370 0.256370i 0.0648425 0.0236007i
\(119\) 4.73500 + 1.72340i 0.434057 + 0.157984i
\(120\) 0 0
\(121\) 1.33324 2.30924i 0.121204 0.209931i
\(122\) −0.833400 1.44349i −0.0754525 0.130688i
\(123\) −0.0756943 + 0.429284i −0.00682512 + 0.0387072i
\(124\) −1.37728 + 7.81096i −0.123684 + 0.701445i
\(125\) 0 0
\(126\) −0.532830 + 0.922889i −0.0474683 + 0.0822175i
\(127\) −9.98688 8.37999i −0.886192 0.743604i 0.0812503 0.996694i \(-0.474109\pi\)
−0.967443 + 0.253090i \(0.918553\pi\)
\(128\) −5.99600 2.18236i −0.529976 0.192896i
\(129\) 0.400285 0.145692i 0.0352431 0.0128274i
\(130\) 0 0
\(131\) 0.0324867 + 0.184241i 0.00283838 + 0.0160972i 0.986194 0.165594i \(-0.0529541\pi\)
−0.983356 + 0.181691i \(0.941843\pi\)
\(132\) −0.451015 −0.0392558
\(133\) 4.09095 6.11164i 0.354730 0.529946i
\(134\) 0.477948 0.0412884
\(135\) 0 0
\(136\) −1.90925 + 1.60205i −0.163717 + 0.137375i
\(137\) 2.02559 0.737254i 0.173058 0.0629879i −0.254038 0.967194i \(-0.581759\pi\)
0.427096 + 0.904206i \(0.359537\pi\)
\(138\) 0.130800 + 0.0476073i 0.0111344 + 0.00405260i
\(139\) −6.04955 5.07617i −0.513116 0.430555i 0.349108 0.937082i \(-0.386485\pi\)
−0.862224 + 0.506527i \(0.830929\pi\)
\(140\) 0 0
\(141\) −0.0658982 0.114139i −0.00554963 0.00961225i
\(142\) −0.381846 + 2.16556i −0.0320438 + 0.181730i
\(143\) −3.24131 + 18.3824i −0.271052 + 1.53721i
\(144\) 5.59042 + 9.68290i 0.465869 + 0.806908i
\(145\) 0 0
\(146\) 0.228189 + 0.191474i 0.0188851 + 0.0158465i
\(147\) −0.311815 0.113492i −0.0257181 0.00936063i
\(148\) −14.6451 + 5.33039i −1.20382 + 0.438155i
\(149\) 13.7096 11.5037i 1.12313 0.942421i 0.124375 0.992235i \(-0.460307\pi\)
0.998759 + 0.0498141i \(0.0158629\pi\)
\(150\) 0 0
\(151\) 2.93984 0.239241 0.119620 0.992820i \(-0.461832\pi\)
0.119620 + 0.992820i \(0.461832\pi\)
\(152\) 1.60622 + 3.26387i 0.130282 + 0.264735i
\(153\) 8.94040 0.722788
\(154\) 0.178446 + 1.01202i 0.0143796 + 0.0815507i
\(155\) 0 0
\(156\) −0.949291 + 0.345514i −0.0760041 + 0.0276632i
\(157\) 6.35878 + 2.31441i 0.507486 + 0.184710i 0.583058 0.812431i \(-0.301856\pi\)
−0.0755720 + 0.997140i \(0.524078\pi\)
\(158\) 0.389634 + 0.326942i 0.0309976 + 0.0260101i
\(159\) −0.0763776 + 0.132290i −0.00605714 + 0.0104913i
\(160\) 0 0
\(161\) −2.41933 + 13.7207i −0.190670 + 1.08134i
\(162\) −0.327629 + 1.85808i −0.0257410 + 0.145984i
\(163\) −0.453917 0.786207i −0.0355535 0.0615805i 0.847701 0.530474i \(-0.177986\pi\)
−0.883255 + 0.468894i \(0.844653\pi\)
\(164\) 5.33452 9.23965i 0.416556 0.721496i
\(165\) 0 0
\(166\) 2.26028 + 0.822673i 0.175431 + 0.0638518i
\(167\) 13.4109 4.88117i 1.03777 0.377716i 0.233733 0.972301i \(-0.424906\pi\)
0.804033 + 0.594585i \(0.202683\pi\)
\(168\) −0.0861785 + 0.0723123i −0.00664881 + 0.00557902i
\(169\) 5.00268 + 28.3716i 0.384822 + 2.18243i
\(170\) 0 0
\(171\) 3.11197 12.6724i 0.237978 0.969080i
\(172\) −10.4260 −0.794971
\(173\) −2.44452 13.8636i −0.185854 1.05403i −0.924854 0.380323i \(-0.875813\pi\)
0.739000 0.673705i \(-0.235298\pi\)
\(174\) 0.0937127 0.0786343i 0.00710434 0.00596125i
\(175\) 0 0
\(176\) 10.1316 + 3.68761i 0.763699 + 0.277964i
\(177\) −0.217442 0.182455i −0.0163439 0.0137142i
\(178\) −1.06717 + 1.84839i −0.0799875 + 0.138542i
\(179\) −7.87488 13.6397i −0.588596 1.01948i −0.994417 0.105525i \(-0.966348\pi\)
0.405821 0.913953i \(-0.366986\pi\)
\(180\) 0 0
\(181\) 0.791542 4.48906i 0.0588348 0.333669i −0.941156 0.337973i \(-0.890259\pi\)
0.999991 + 0.00430380i \(0.00136995\pi\)
\(182\) 1.15088 + 1.99338i 0.0853087 + 0.147759i
\(183\) −0.315593 + 0.546623i −0.0233293 + 0.0404075i
\(184\) −5.27902 4.42962i −0.389174 0.326556i
\(185\) 0 0
\(186\) −0.0642474 + 0.0233841i −0.00471085 + 0.00171461i
\(187\) 6.60433 5.54169i 0.482956 0.405249i
\(188\) 0.560153 + 3.17678i 0.0408533 + 0.231691i
\(189\) 0.807951 0.0587698
\(190\) 0 0
\(191\) −9.95887 −0.720599 −0.360299 0.932837i \(-0.617325\pi\)
−0.360299 + 0.932837i \(0.617325\pi\)
\(192\) 0.0964416 + 0.546947i 0.00696007 + 0.0394725i
\(193\) 16.3943 13.7564i 1.18009 0.990210i 0.180108 0.983647i \(-0.442355\pi\)
0.999978 0.00656365i \(-0.00208929\pi\)
\(194\) 1.95647 0.712096i 0.140466 0.0511255i
\(195\) 0 0
\(196\) 6.22154 + 5.22049i 0.444396 + 0.372892i
\(197\) 0.683372 1.18364i 0.0486883 0.0843305i −0.840654 0.541572i \(-0.817829\pi\)
0.889342 + 0.457242i \(0.151163\pi\)
\(198\) 0.911652 + 1.57903i 0.0647883 + 0.112217i
\(199\) −3.11454 + 17.6634i −0.220784 + 1.25213i 0.649799 + 0.760106i \(0.274853\pi\)
−0.870583 + 0.492022i \(0.836258\pi\)
\(200\) 0 0
\(201\) −0.0904949 0.156742i −0.00638302 0.0110557i
\(202\) 0.439874 0.761885i 0.0309495 0.0536060i
\(203\) 9.37996 + 7.87072i 0.658344 + 0.552416i
\(204\) 0.438453 + 0.159584i 0.0306979 + 0.0111731i
\(205\) 0 0
\(206\) −2.03057 + 1.70385i −0.141476 + 0.118713i
\(207\) 4.29257 + 24.3443i 0.298354 + 1.69205i
\(208\) 24.1499 1.67449
\(209\) −5.55611 11.2901i −0.384324 0.780953i
\(210\) 0 0
\(211\) 3.60629 + 20.4523i 0.248267 + 1.40799i 0.812781 + 0.582570i \(0.197953\pi\)
−0.564513 + 0.825424i \(0.690936\pi\)
\(212\) 2.86406 2.40323i 0.196705 0.165055i
\(213\) 0.782488 0.284802i 0.0536152 0.0195143i
\(214\) −2.96246 1.07825i −0.202510 0.0737075i
\(215\) 0 0
\(216\) −0.199816 + 0.346091i −0.0135957 + 0.0235485i
\(217\) −3.42170 5.92656i −0.232280 0.402321i
\(218\) −0.190694 + 1.08148i −0.0129154 + 0.0732469i
\(219\) 0.0195878 0.111088i 0.00132362 0.00750662i
\(220\) 0 0
\(221\) 9.65533 16.7235i 0.649488 1.12495i
\(222\) −0.102915 0.0863557i −0.00690719 0.00579582i
\(223\) 1.83236 + 0.666925i 0.122704 + 0.0446606i 0.402642 0.915357i \(-0.368092\pi\)
−0.279938 + 0.960018i \(0.590314\pi\)
\(224\) 3.89565 1.41790i 0.260289 0.0947375i
\(225\) 0 0
\(226\) 0.314002 + 1.78079i 0.0208871 + 0.118457i
\(227\) −12.6099 −0.836950 −0.418475 0.908228i \(-0.637435\pi\)
−0.418475 + 0.908228i \(0.637435\pi\)
\(228\) 0.378815 0.565928i 0.0250877 0.0374795i
\(229\) −6.12765 −0.404926 −0.202463 0.979290i \(-0.564895\pi\)
−0.202463 + 0.979290i \(0.564895\pi\)
\(230\) 0 0
\(231\) 0.298102 0.250137i 0.0196136 0.0164578i
\(232\) −5.69125 + 2.07145i −0.373649 + 0.135997i
\(233\) 6.20868 + 2.25977i 0.406744 + 0.148043i 0.537286 0.843400i \(-0.319450\pi\)
−0.130542 + 0.991443i \(0.541672\pi\)
\(234\) 3.12849 + 2.62512i 0.204516 + 0.171609i
\(235\) 0 0
\(236\) 3.47369 + 6.01660i 0.226118 + 0.391648i
\(237\) 0.0334462 0.189683i 0.00217256 0.0123212i
\(238\) 0.184609 1.04697i 0.0119664 0.0678650i
\(239\) 1.10191 + 1.90856i 0.0712766 + 0.123455i 0.899461 0.437001i \(-0.143959\pi\)
−0.828184 + 0.560456i \(0.810626\pi\)
\(240\) 0 0
\(241\) −0.0956409 0.0802523i −0.00616077 0.00516950i 0.639702 0.768623i \(-0.279058\pi\)
−0.645863 + 0.763453i \(0.723502\pi\)
\(242\) −0.528656 0.192415i −0.0339833 0.0123689i
\(243\) 2.02134 0.735707i 0.129669 0.0471956i
\(244\) 11.8343 9.93017i 0.757615 0.635714i
\(245\) 0 0
\(246\) 0.0919690 0.00586373
\(247\) −20.3435 19.5068i −1.29443 1.24119i
\(248\) 3.38491 0.214942
\(249\) −0.158168 0.897017i −0.0100235 0.0568462i
\(250\) 0 0
\(251\) −3.49264 + 1.27122i −0.220453 + 0.0802385i −0.449886 0.893086i \(-0.648535\pi\)
0.229432 + 0.973325i \(0.426313\pi\)
\(252\) −9.28133 3.37813i −0.584669 0.212802i
\(253\) 18.2608 + 15.3226i 1.14804 + 0.963323i
\(254\) −1.37529 + 2.38207i −0.0862935 + 0.149465i
\(255\) 0 0
\(256\) 2.18042 12.3658i 0.136276 0.772861i
\(257\) 4.68428 26.5659i 0.292198 1.65713i −0.386182 0.922423i \(-0.626206\pi\)
0.678379 0.734712i \(-0.262683\pi\)
\(258\) −0.0449368 0.0778328i −0.00279764 0.00484566i
\(259\) 6.72351 11.6455i 0.417779 0.723614i
\(260\) 0 0
\(261\) 20.4153 + 7.43055i 1.26367 + 0.459940i
\(262\) 0.0370911 0.0135001i 0.00229150 0.000834036i
\(263\) −15.8386 + 13.2902i −0.976652 + 0.819508i −0.983581 0.180468i \(-0.942239\pi\)
0.00692932 + 0.999976i \(0.497794\pi\)
\(264\) 0.0334238 + 0.189556i 0.00205709 + 0.0116663i
\(265\) 0 0
\(266\) −1.41975 0.626099i −0.0870502 0.0383886i
\(267\) 0.808231 0.0494629
\(268\) 0.769230 + 4.36252i 0.0469882 + 0.266483i
\(269\) −10.5139 + 8.82218i −0.641042 + 0.537898i −0.904338 0.426817i \(-0.859635\pi\)
0.263296 + 0.964715i \(0.415190\pi\)
\(270\) 0 0
\(271\) 5.05880 + 1.84125i 0.307300 + 0.111848i 0.491067 0.871122i \(-0.336607\pi\)
−0.183767 + 0.982970i \(0.558829\pi\)
\(272\) −8.54463 7.16979i −0.518094 0.434733i
\(273\) 0.435815 0.754854i 0.0263767 0.0456859i
\(274\) −0.227397 0.393863i −0.0137375 0.0237941i
\(275\) 0 0
\(276\) −0.224026 + 1.27051i −0.0134848 + 0.0764759i
\(277\) 11.3993 + 19.7441i 0.684916 + 1.18631i 0.973463 + 0.228843i \(0.0734944\pi\)
−0.288547 + 0.957466i \(0.593172\pi\)
\(278\) −0.833082 + 1.44294i −0.0499649 + 0.0865418i
\(279\) −9.30140 7.80481i −0.556861 0.467261i
\(280\) 0 0
\(281\) 16.1900 5.89267i 0.965814 0.351528i 0.189505 0.981880i \(-0.439312\pi\)
0.776309 + 0.630352i \(0.217090\pi\)
\(282\) −0.0213013 + 0.0178739i −0.00126848 + 0.00106438i
\(283\) −2.83026 16.0512i −0.168242 0.954146i −0.945659 0.325161i \(-0.894582\pi\)
0.777417 0.628986i \(-0.216530\pi\)
\(284\) −20.3809 −1.20939
\(285\) 0 0
\(286\) 3.93821 0.232871
\(287\) 1.59851 + 9.06558i 0.0943568 + 0.535124i
\(288\) 5.63470 4.72807i 0.332028 0.278604i
\(289\) 7.59356 2.76383i 0.446680 0.162578i
\(290\) 0 0
\(291\) −0.603969 0.506790i −0.0354053 0.0297086i
\(292\) −1.38044 + 2.39099i −0.0807841 + 0.139922i
\(293\) 12.6441 + 21.9002i 0.738675 + 1.27942i 0.953092 + 0.302681i \(0.0978817\pi\)
−0.214416 + 0.976742i \(0.568785\pi\)
\(294\) −0.0121571 + 0.0689465i −0.000709018 + 0.00402104i
\(295\) 0 0
\(296\) 3.32561 + 5.76012i 0.193297 + 0.334800i
\(297\) 0.691187 1.19717i 0.0401067 0.0694669i
\(298\) −2.89250 2.42710i −0.167558 0.140598i
\(299\) 50.1733 + 18.2616i 2.90160 + 1.05609i
\(300\) 0 0
\(301\) 6.89110 5.78232i 0.397197 0.333287i
\(302\) −0.107707 0.610834i −0.00619782 0.0351496i
\(303\) −0.333144 −0.0191386
\(304\) −13.1369 + 9.61573i −0.753451 + 0.551500i
\(305\) 0 0
\(306\) −0.327549 1.85762i −0.0187247 0.106193i
\(307\) −13.1982 + 11.0746i −0.753259 + 0.632059i −0.936362 0.351035i \(-0.885830\pi\)
0.183104 + 0.983094i \(0.441386\pi\)
\(308\) −8.95011 + 3.25757i −0.509980 + 0.185617i
\(309\) 0.943241 + 0.343312i 0.0536591 + 0.0195303i
\(310\) 0 0
\(311\) −12.4862 + 21.6267i −0.708028 + 1.22634i 0.257560 + 0.966262i \(0.417082\pi\)
−0.965588 + 0.260078i \(0.916252\pi\)
\(312\) 0.215565 + 0.373369i 0.0122039 + 0.0211378i
\(313\) 2.92827 16.6071i 0.165516 0.938687i −0.783015 0.622002i \(-0.786319\pi\)
0.948531 0.316684i \(-0.102570\pi\)
\(314\) 0.247917 1.40601i 0.0139908 0.0793457i
\(315\) 0 0
\(316\) −2.35710 + 4.08263i −0.132598 + 0.229666i
\(317\) −18.4779 15.5048i −1.03782 0.870834i −0.0460593 0.998939i \(-0.514666\pi\)
−0.991761 + 0.128104i \(0.959111\pi\)
\(318\) 0.0302852 + 0.0110229i 0.00169831 + 0.000618134i
\(319\) 19.6867 7.16538i 1.10224 0.401184i
\(320\) 0 0
\(321\) 0.207305 + 1.17569i 0.0115707 + 0.0656205i
\(322\) 2.93950 0.163812
\(323\) 1.40655 + 12.9416i 0.0782624 + 0.720089i
\(324\) −17.4871 −0.971506
\(325\) 0 0
\(326\) −0.146727 + 0.123118i −0.00812644 + 0.00681889i
\(327\) 0.390774 0.142230i 0.0216099 0.00786534i
\(328\) −4.27863 1.55729i −0.236248 0.0859872i
\(329\) −2.13211 1.78905i −0.117547 0.0986335i
\(330\) 0 0
\(331\) −7.77017 13.4583i −0.427087 0.739736i 0.569526 0.821973i \(-0.307127\pi\)
−0.996613 + 0.0822371i \(0.973794\pi\)
\(332\) −3.87126 + 21.9550i −0.212463 + 1.20494i
\(333\) 4.14304 23.4963i 0.227037 1.28759i
\(334\) −1.50553 2.60766i −0.0823792 0.142685i
\(335\) 0 0
\(336\) −0.385681 0.323625i −0.0210406 0.0176552i
\(337\) 10.3419 + 3.76416i 0.563361 + 0.205047i 0.607973 0.793958i \(-0.291983\pi\)
−0.0446119 + 0.999004i \(0.514205\pi\)
\(338\) 5.71172 2.07890i 0.310677 0.113077i
\(339\) 0.524554 0.440153i 0.0284898 0.0239058i
\(340\) 0 0
\(341\) −11.7088 −0.634067
\(342\) −2.74705 0.182324i −0.148544 0.00985894i
\(343\) −18.8181 −1.01608
\(344\) 0.772645 + 4.38189i 0.0416582 + 0.236255i
\(345\) 0 0
\(346\) −2.79099 + 1.01584i −0.150045 + 0.0546118i
\(347\) 28.6321 + 10.4212i 1.53705 + 0.559441i 0.965336 0.261010i \(-0.0840555\pi\)
0.571716 + 0.820451i \(0.306278\pi\)
\(348\) 0.868569 + 0.728816i 0.0465602 + 0.0390686i
\(349\) −2.80872 + 4.86485i −0.150347 + 0.260409i −0.931355 0.364112i \(-0.881373\pi\)
0.781008 + 0.624521i \(0.214706\pi\)
\(350\) 0 0
\(351\) 0.537673 3.04929i 0.0286988 0.162759i
\(352\) 1.23170 6.98532i 0.0656499 0.372319i
\(353\) −3.74308 6.48321i −0.199224 0.345067i 0.749053 0.662510i \(-0.230509\pi\)
−0.948277 + 0.317444i \(0.897176\pi\)
\(354\) −0.0299438 + 0.0518642i −0.00159150 + 0.00275655i
\(355\) 0 0
\(356\) −18.5889 6.76581i −0.985210 0.358587i
\(357\) −0.378305 + 0.137692i −0.0200220 + 0.00728743i
\(358\) −2.54552 + 2.13594i −0.134535 + 0.112888i
\(359\) −4.42550 25.0982i −0.233569 1.32463i −0.845607 0.533806i \(-0.820761\pi\)
0.612038 0.790828i \(-0.290350\pi\)
\(360\) 0 0
\(361\) 18.8333 + 2.51102i 0.991229 + 0.132159i
\(362\) −0.961728 −0.0505473
\(363\) 0.0369940 + 0.209803i 0.00194168 + 0.0110118i
\(364\) −16.3425 + 13.7130i −0.856580 + 0.718756i
\(365\) 0 0
\(366\) 0.125139 + 0.0455468i 0.00654111 + 0.00238077i
\(367\) 25.6366 + 21.5117i 1.33822 + 1.12290i 0.982079 + 0.188468i \(0.0603521\pi\)
0.356141 + 0.934432i \(0.384092\pi\)
\(368\) 15.4205 26.7091i 0.803850 1.39231i
\(369\) 8.16651 + 14.1448i 0.425132 + 0.736350i
\(370\) 0 0
\(371\) −0.560167 + 3.17686i −0.0290824 + 0.164935i
\(372\) −0.316844 0.548790i −0.0164276 0.0284534i
\(373\) −5.23935 + 9.07481i −0.271283 + 0.469876i −0.969191 0.246312i \(-0.920781\pi\)
0.697908 + 0.716188i \(0.254115\pi\)
\(374\) −1.39341 1.16921i −0.0720513 0.0604582i
\(375\) 0 0
\(376\) 1.29365 0.470849i 0.0667148 0.0242822i
\(377\) 35.9471 30.1632i 1.85137 1.55348i
\(378\) −0.0296008 0.167875i −0.00152250 0.00863454i
\(379\) −14.2962 −0.734344 −0.367172 0.930153i \(-0.619674\pi\)
−0.367172 + 0.930153i \(0.619674\pi\)
\(380\) 0 0
\(381\) 1.04159 0.0533625
\(382\) 0.364862 + 2.06924i 0.0186680 + 0.105871i
\(383\) −28.3295 + 23.7712i −1.44757 + 1.21465i −0.513238 + 0.858246i \(0.671554\pi\)
−0.934331 + 0.356408i \(0.884001\pi\)
\(384\) 0.479053 0.174361i 0.0244466 0.00889783i
\(385\) 0 0
\(386\) −3.45893 2.90238i −0.176055 0.147727i
\(387\) 7.98045 13.8225i 0.405669 0.702639i
\(388\) 9.64857 + 16.7118i 0.489832 + 0.848413i
\(389\) −2.88385 + 16.3551i −0.146217 + 0.829237i 0.820165 + 0.572127i \(0.193881\pi\)
−0.966382 + 0.257110i \(0.917230\pi\)
\(390\) 0 0
\(391\) −12.3305 21.3571i −0.623581 1.08007i
\(392\) 1.73304 3.00171i 0.0875316 0.151609i
\(393\) −0.0114502 0.00960783i −0.000577584 0.000484651i
\(394\) −0.270970 0.0986252i −0.0136513 0.00496866i
\(395\) 0 0
\(396\) −12.9455 + 10.8626i −0.650536 + 0.545865i
\(397\) 4.62570 + 26.2337i 0.232157 + 1.31663i 0.848518 + 0.529166i \(0.177495\pi\)
−0.616361 + 0.787464i \(0.711394\pi\)
\(398\) 3.78419 0.189684
\(399\) 0.0634878 + 0.584148i 0.00317836 + 0.0292440i
\(400\) 0 0
\(401\) 0.224832 + 1.27508i 0.0112276 + 0.0636747i 0.989907 0.141720i \(-0.0452633\pi\)
−0.978679 + 0.205395i \(0.934152\pi\)
\(402\) −0.0292521 + 0.0245454i −0.00145896 + 0.00122421i
\(403\) −24.6445 + 8.96988i −1.22763 + 0.446821i
\(404\) 7.66215 + 2.78879i 0.381206 + 0.138748i
\(405\) 0 0
\(406\) 1.29171 2.23731i 0.0641066 0.111036i
\(407\) −11.5037 19.9250i −0.570216 0.987643i
\(408\) 0.0345782 0.196102i 0.00171187 0.00970852i
\(409\) 4.69402 26.6211i 0.232104 1.31633i −0.616522 0.787337i \(-0.711459\pi\)
0.848627 0.528992i \(-0.177430\pi\)
\(410\) 0 0
\(411\) −0.0861109 + 0.149148i −0.00424754 + 0.00735695i
\(412\) −18.8201 15.7920i −0.927202 0.778015i
\(413\) −5.63282 2.05018i −0.277173 0.100883i
\(414\) 4.90096 1.78380i 0.240869 0.0876692i
\(415\) 0 0
\(416\) −2.75884 15.6462i −0.135263 0.767117i
\(417\) 0.630945 0.0308975
\(418\) −2.14228 + 1.56807i −0.104782 + 0.0766970i
\(419\) −4.15498 −0.202984 −0.101492 0.994836i \(-0.532362\pi\)
−0.101492 + 0.994836i \(0.532362\pi\)
\(420\) 0 0
\(421\) −20.2274 + 16.9728i −0.985822 + 0.827203i −0.984957 0.172797i \(-0.944720\pi\)
−0.000864321 1.00000i \(0.500275\pi\)
\(422\) 4.11742 1.49862i 0.200433 0.0729516i
\(423\) −4.64049 1.68900i −0.225628 0.0821219i
\(424\) −1.22230 1.02563i −0.0593599 0.0498089i
\(425\) 0 0
\(426\) −0.0878437 0.152150i −0.00425604 0.00737168i
\(427\) −2.31461 + 13.1268i −0.112012 + 0.635252i
\(428\) 5.07391 28.7756i 0.245257 1.39092i
\(429\) −0.745664 1.29153i −0.0360010 0.0623555i
\(430\) 0 0
\(431\) −7.44700 6.24878i −0.358710 0.300993i 0.445567 0.895249i \(-0.353002\pi\)
−0.804276 + 0.594256i \(0.797447\pi\)
\(432\) −1.68064 0.611705i −0.0808600 0.0294306i
\(433\) −0.620049 + 0.225679i −0.0297976 + 0.0108455i −0.356876 0.934152i \(-0.616158\pi\)
0.327078 + 0.944997i \(0.393936\pi\)
\(434\) −1.10605 + 0.928086i −0.0530921 + 0.0445496i
\(435\) 0 0
\(436\) −10.1782 −0.487449
\(437\) −34.5641 + 10.0436i −1.65342 + 0.480452i
\(438\) −0.0237993 −0.00113717
\(439\) 4.72146 + 26.7767i 0.225343 + 1.27798i 0.862029 + 0.506860i \(0.169194\pi\)
−0.636686 + 0.771123i \(0.719695\pi\)
\(440\) 0 0
\(441\) −11.6835 + 4.25243i −0.556355 + 0.202497i
\(442\) −3.82853 1.39347i −0.182104 0.0662806i
\(443\) −28.9473 24.2897i −1.37533 1.15404i −0.970905 0.239466i \(-0.923028\pi\)
−0.404424 0.914572i \(-0.632528\pi\)
\(444\) 0.622586 1.07835i 0.0295466 0.0511763i
\(445\) 0 0
\(446\) 0.0714405 0.405159i 0.00338280 0.0191848i
\(447\) −0.248292 + 1.40814i −0.0117438 + 0.0666025i
\(448\) 5.86429 + 10.1572i 0.277062 + 0.479885i
\(449\) 8.27496 14.3327i 0.390520 0.676400i −0.601998 0.798497i \(-0.705629\pi\)
0.992518 + 0.122097i \(0.0389620\pi\)
\(450\) 0 0
\(451\) 14.8003 + 5.38687i 0.696919 + 0.253658i
\(452\) −15.7490 + 5.73218i −0.740772 + 0.269619i
\(453\) −0.179928 + 0.150978i −0.00845377 + 0.00709356i
\(454\) 0.461989 + 2.62007i 0.0216822 + 0.122966i
\(455\) 0 0
\(456\) −0.265925 0.117271i −0.0124531 0.00549173i
\(457\) −11.4492 −0.535571 −0.267785 0.963479i \(-0.586292\pi\)
−0.267785 + 0.963479i \(0.586292\pi\)
\(458\) 0.224498 + 1.27319i 0.0104901 + 0.0594923i
\(459\) −1.09553 + 0.919262i −0.0511352 + 0.0429075i
\(460\) 0 0
\(461\) 10.1108 + 3.68002i 0.470905 + 0.171396i 0.566562 0.824019i \(-0.308273\pi\)
−0.0956571 + 0.995414i \(0.530495\pi\)
\(462\) −0.0628946 0.0527748i −0.00292612 0.00245531i
\(463\) 8.54409 14.7988i 0.397078 0.687758i −0.596286 0.802772i \(-0.703358\pi\)
0.993364 + 0.115013i \(0.0366911\pi\)
\(464\) −13.5526 23.4737i −0.629162 1.08974i
\(465\) 0 0
\(466\) 0.242065 1.37282i 0.0112134 0.0635946i
\(467\) 15.9280 + 27.5880i 0.737058 + 1.27662i 0.953815 + 0.300396i \(0.0971189\pi\)
−0.216756 + 0.976226i \(0.569548\pi\)
\(468\) −18.9259 + 32.7807i −0.874851 + 1.51529i
\(469\) −2.92792 2.45682i −0.135199 0.113445i
\(470\) 0 0
\(471\) −0.508038 + 0.184911i −0.0234092 + 0.00852024i
\(472\) 2.27127 1.90582i 0.104544 0.0877225i
\(473\) −2.67267 15.1575i −0.122890 0.696941i
\(474\) −0.0406374 −0.00186654
\(475\) 0 0
\(476\) 9.85346 0.451633
\(477\) 0.993894 + 5.63665i 0.0455073 + 0.258085i
\(478\) 0.356187 0.298877i 0.0162916 0.0136703i
\(479\) 3.61807 1.31687i 0.165314 0.0601693i −0.258038 0.966135i \(-0.583076\pi\)
0.423351 + 0.905966i \(0.360854\pi\)
\(480\) 0 0
\(481\) −39.4769 33.1250i −1.79999 1.51037i
\(482\) −0.0131707 + 0.0228123i −0.000599909 + 0.00103907i
\(483\) −0.556566 0.964000i −0.0253246 0.0438635i
\(484\) 0.905448 5.13505i 0.0411567 0.233411i
\(485\) 0 0
\(486\) −0.226919 0.393036i −0.0102933 0.0178285i
\(487\) 17.7037 30.6638i 0.802233 1.38951i −0.115910 0.993260i \(-0.536978\pi\)
0.918143 0.396249i \(-0.129688\pi\)
\(488\) −5.05053 4.23790i −0.228627 0.191841i
\(489\) 0.0681576 + 0.0248074i 0.00308220 + 0.00112183i
\(490\) 0 0
\(491\) 15.5179 13.0210i 0.700311 0.587631i −0.221551 0.975149i \(-0.571112\pi\)
0.921862 + 0.387518i \(0.126667\pi\)
\(492\) 0.148019 + 0.839458i 0.00667322 + 0.0378457i
\(493\) −21.6737 −0.976136
\(494\) −3.30777 + 4.94162i −0.148824 + 0.222334i
\(495\) 0 0
\(496\) 2.63055 + 14.9186i 0.118115 + 0.669866i
\(497\) 13.4709 11.3034i 0.604253 0.507029i
\(498\) −0.180586 + 0.0657279i −0.00809225 + 0.00294534i
\(499\) −0.553880 0.201596i −0.0247951 0.00902467i 0.329593 0.944123i \(-0.393089\pi\)
−0.354388 + 0.935099i \(0.615311\pi\)
\(500\) 0 0
\(501\) −0.570118 + 0.987473i −0.0254710 + 0.0441170i
\(502\) 0.392091 + 0.679121i 0.0174999 + 0.0303107i
\(503\) 1.97091 11.1776i 0.0878787 0.498385i −0.908820 0.417190i \(-0.863015\pi\)
0.996698 0.0811953i \(-0.0258738\pi\)
\(504\) −0.731962 + 4.15116i −0.0326042 + 0.184908i
\(505\) 0 0
\(506\) 2.51468 4.35556i 0.111791 0.193628i
\(507\) −1.76323 1.47953i −0.0783078 0.0657080i
\(508\) −23.9561 8.71931i −1.06288 0.386857i
\(509\) −11.1499 + 4.05822i −0.494209 + 0.179877i −0.577088 0.816682i \(-0.695811\pi\)
0.0828785 + 0.996560i \(0.473589\pi\)
\(510\) 0 0
\(511\) −0.413654 2.34595i −0.0182990 0.103779i
\(512\) −15.4108 −0.681069
\(513\) 0.921654 + 1.87282i 0.0406920 + 0.0826869i
\(514\) −5.69143 −0.251038
\(515\) 0 0
\(516\) 0.638105 0.535434i 0.0280910 0.0235712i
\(517\) −4.47488 + 1.62872i −0.196805 + 0.0716312i
\(518\) −2.66600 0.970346i −0.117137 0.0426346i
\(519\) 0.861589 + 0.722959i 0.0378196 + 0.0317344i
\(520\) 0 0
\(521\) 12.2611 + 21.2368i 0.537166 + 0.930400i 0.999055 + 0.0434617i \(0.0138386\pi\)
−0.461889 + 0.886938i \(0.652828\pi\)
\(522\) 0.795955 4.51408i 0.0348380 0.197576i
\(523\) −3.68721 + 20.9112i −0.161230 + 0.914382i 0.791636 + 0.610993i \(0.209230\pi\)
−0.952867 + 0.303390i \(0.901882\pi\)
\(524\) 0.182919 + 0.316826i 0.00799087 + 0.0138406i
\(525\) 0 0
\(526\) 3.34169 + 2.80401i 0.145705 + 0.122261i
\(527\) 11.3827 + 4.14296i 0.495838 + 0.180470i
\(528\) −0.809471 + 0.294623i −0.0352277 + 0.0128218i
\(529\) 34.6152 29.0456i 1.50501 1.26285i
\(530\) 0 0
\(531\) −10.6356 −0.461546
\(532\) 3.42979 13.9666i 0.148700 0.605528i
\(533\) 35.2782 1.52807
\(534\) −0.0296111 0.167933i −0.00128140 0.00726717i
\(535\) 0 0
\(536\) 1.77650 0.646594i 0.0767332 0.0279286i
\(537\) 1.18245 + 0.430376i 0.0510264 + 0.0185721i
\(538\) 2.21825 + 1.86134i 0.0956357 + 0.0802479i
\(539\) −5.99478 + 10.3833i −0.258214 + 0.447239i
\(540\) 0 0
\(541\) 2.57449 14.6006i 0.110686 0.627730i −0.878110 0.478458i \(-0.841196\pi\)
0.988796 0.149272i \(-0.0476930\pi\)
\(542\) 0.197233 1.11857i 0.00847190 0.0480465i
\(543\) 0.182094 + 0.315396i 0.00781441 + 0.0135350i
\(544\) −3.66903 + 6.35495i −0.157308 + 0.272466i
\(545\) 0 0
\(546\) −0.172809 0.0628974i −0.00739555 0.00269176i
\(547\) 7.48131 2.72298i 0.319878 0.116426i −0.177091 0.984195i \(-0.556669\pi\)
0.496969 + 0.867769i \(0.334446\pi\)
\(548\) 3.22905 2.70949i 0.137938 0.115744i
\(549\) 4.10678 + 23.2907i 0.175273 + 0.994022i
\(550\) 0 0
\(551\) −7.54419 + 30.7209i −0.321393 + 1.30876i
\(552\) 0.550581 0.0234343
\(553\) −0.706315 4.00571i −0.0300355 0.170340i
\(554\) 3.68476 3.09188i 0.156551 0.131362i
\(555\) 0 0
\(556\) −14.5114 5.28172i −0.615421 0.223995i
\(557\) 6.20896 + 5.20994i 0.263082 + 0.220752i 0.764781 0.644290i \(-0.222847\pi\)
−0.501699 + 0.865042i \(0.667292\pi\)
\(558\) −1.28089 + 2.21857i −0.0542246 + 0.0939197i
\(559\) −17.2372 29.8558i −0.729057 1.26276i
\(560\) 0 0
\(561\) −0.119610 + 0.678342i −0.00504994 + 0.0286396i
\(562\) −1.81752 3.14804i −0.0766675 0.132792i
\(563\) 4.14912 7.18648i 0.174864 0.302874i −0.765250 0.643733i \(-0.777385\pi\)
0.940114 + 0.340859i \(0.110718\pi\)
\(564\) −0.197430 0.165663i −0.00831329 0.00697568i
\(565\) 0 0
\(566\) −3.23141 + 1.17614i −0.135826 + 0.0494367i
\(567\) 11.5582 9.69850i 0.485400 0.407299i
\(568\) 1.51039 + 8.56583i 0.0633745 + 0.359414i
\(569\) −7.28643 −0.305463 −0.152732 0.988268i \(-0.548807\pi\)
−0.152732 + 0.988268i \(0.548807\pi\)
\(570\) 0 0
\(571\) −20.6974 −0.866159 −0.433080 0.901356i \(-0.642573\pi\)
−0.433080 + 0.901356i \(0.642573\pi\)
\(572\) 6.33834 + 35.9465i 0.265019 + 1.50300i
\(573\) 0.609518 0.511446i 0.0254630 0.0213660i
\(574\) 1.82507 0.664270i 0.0761768 0.0277261i
\(575\) 0 0
\(576\) 15.9412 + 13.3763i 0.664218 + 0.557345i
\(577\) 7.29547 12.6361i 0.303715 0.526049i −0.673260 0.739406i \(-0.735106\pi\)
0.976974 + 0.213357i \(0.0684398\pi\)
\(578\) −0.852469 1.47652i −0.0354580 0.0614151i
\(579\) −0.296914 + 1.68389i −0.0123393 + 0.0699799i
\(580\) 0 0
\(581\) −9.61769 16.6583i −0.399009 0.691104i
\(582\) −0.0831724 + 0.144059i −0.00344761 + 0.00597143i
\(583\) 4.22807 + 3.54777i 0.175109 + 0.146934i
\(584\) 1.10720 + 0.402989i 0.0458164 + 0.0166758i
\(585\) 0 0
\(586\) 4.08715 3.42952i 0.168838 0.141672i
\(587\) 1.82464 + 10.3481i 0.0753110 + 0.427110i 0.999030 + 0.0440388i \(0.0140225\pi\)
−0.923719 + 0.383071i \(0.874866\pi\)
\(588\) −0.648883 −0.0267595
\(589\) 9.83443 14.6920i 0.405220 0.605375i
\(590\) 0 0
\(591\) 0.0189618 + 0.107538i 0.000779985 + 0.00442352i
\(592\) −22.8026 + 19.1337i −0.937183 + 0.786389i
\(593\) 22.8495 8.31653i 0.938316 0.341519i 0.172815 0.984954i \(-0.444714\pi\)
0.765501 + 0.643435i \(0.222491\pi\)
\(594\) −0.274069 0.0997530i −0.0112452 0.00409292i
\(595\) 0 0
\(596\) 17.4983 30.3079i 0.716757 1.24146i
\(597\) −0.716500 1.24101i −0.0293244 0.0507913i
\(598\) 1.95617 11.0940i 0.0799936 0.453666i
\(599\) −6.58292 + 37.3336i −0.268971 + 1.52541i 0.488513 + 0.872557i \(0.337539\pi\)
−0.757484 + 0.652854i \(0.773572\pi\)
\(600\) 0 0
\(601\) −12.9738 + 22.4713i −0.529213 + 0.916623i 0.470207 + 0.882556i \(0.344179\pi\)
−0.999420 + 0.0340669i \(0.989154\pi\)
\(602\) −1.45391 1.21998i −0.0592569 0.0497225i
\(603\) −6.37255 2.31942i −0.259510 0.0944541i
\(604\) 5.40211 1.96621i 0.219809 0.0800039i
\(605\) 0 0
\(606\) 0.0122054 + 0.0692202i 0.000495810 + 0.00281188i
\(607\) 11.5300 0.467988 0.233994 0.972238i \(-0.424820\pi\)
0.233994 + 0.972238i \(0.424820\pi\)
\(608\) 7.73056 + 7.41261i 0.313516 + 0.300621i
\(609\) −0.978294 −0.0396425
\(610\) 0 0
\(611\) −8.17093 + 6.85623i −0.330561 + 0.277373i
\(612\) 16.4285 5.97948i 0.664082 0.241706i
\(613\) 21.2917 + 7.74954i 0.859963 + 0.313001i 0.734096 0.679046i \(-0.237606\pi\)
0.125868 + 0.992047i \(0.459829\pi\)
\(614\) 2.78459 + 2.33655i 0.112377 + 0.0942956i
\(615\) 0 0
\(616\) 2.03239 + 3.52020i 0.0818872 + 0.141833i
\(617\) −1.03785 + 5.88595i −0.0417823 + 0.236959i −0.998546 0.0539072i \(-0.982832\pi\)
0.956764 + 0.290867i \(0.0939436\pi\)
\(618\) 0.0367753 0.208563i 0.00147932 0.00838963i
\(619\) 17.1031 + 29.6234i 0.687431 + 1.19067i 0.972666 + 0.232208i \(0.0745951\pi\)
−0.285235 + 0.958458i \(0.592072\pi\)
\(620\) 0 0
\(621\) −3.02912 2.54173i −0.121554 0.101996i
\(622\) 4.95103 + 1.80203i 0.198518 + 0.0722547i
\(623\) 16.0388 5.83766i 0.642582 0.233881i
\(624\) −1.47806 + 1.24024i −0.0591697 + 0.0496492i
\(625\) 0 0
\(626\) −3.55787 −0.142201
\(627\) 0.919866 + 0.405656i 0.0367359 + 0.0162003i
\(628\) 13.2325 0.528035
\(629\) 4.13317 + 23.4404i 0.164800 + 0.934629i
\(630\) 0 0
\(631\) 13.3916 4.87414i 0.533111 0.194036i −0.0614161 0.998112i \(-0.519562\pi\)
0.594527 + 0.804076i \(0.297339\pi\)
\(632\) 1.89055 + 0.688105i 0.0752021 + 0.0273713i
\(633\) −1.27106 1.06655i −0.0505202 0.0423915i
\(634\) −2.54458 + 4.40735i −0.101058 + 0.175038i
\(635\) 0 0
\(636\) −0.0518706 + 0.294173i −0.00205680 + 0.0116647i
\(637\) −4.66333 + 26.4471i −0.184768 + 1.04787i
\(638\) −2.21007 3.82795i −0.0874975 0.151550i
\(639\) 15.6004 27.0207i 0.617142 1.06892i
\(640\) 0 0
\(641\) 37.3475 + 13.5934i 1.47514 + 0.536906i 0.949490 0.313797i \(-0.101601\pi\)
0.525647 + 0.850703i \(0.323823\pi\)
\(642\) 0.236687 0.0861471i 0.00934130 0.00339996i
\(643\) −12.1851 + 10.2245i −0.480532 + 0.403214i −0.850619 0.525783i \(-0.823772\pi\)
0.370087 + 0.928997i \(0.379328\pi\)
\(644\) 4.73096 + 26.8306i 0.186426 + 1.05727i
\(645\) 0 0
\(646\) 2.63745 0.766390i 0.103769 0.0301532i
\(647\) −18.8549 −0.741262 −0.370631 0.928780i \(-0.620858\pi\)
−0.370631 + 0.928780i \(0.620858\pi\)
\(648\) 1.29593 + 7.34960i 0.0509090 + 0.288719i
\(649\) −7.85659 + 6.59246i −0.308398 + 0.258777i
\(650\) 0 0
\(651\) 0.513784 + 0.187002i 0.0201368 + 0.00732919i
\(652\) −1.35993 1.14111i −0.0532588 0.0446894i
\(653\) −21.2626 + 36.8279i −0.832070 + 1.44119i 0.0643232 + 0.997929i \(0.479511\pi\)
−0.896394 + 0.443259i \(0.853822\pi\)
\(654\) −0.0438691 0.0759835i −0.00171542 0.00297119i
\(655\) 0 0
\(656\) 3.53850 20.0678i 0.138155 0.783517i
\(657\) −2.11329 3.66032i −0.0824473 0.142803i
\(658\) −0.293612 + 0.508551i −0.0114462 + 0.0198254i
\(659\) −35.1057 29.4572i −1.36752 1.14749i −0.973578 0.228354i \(-0.926666\pi\)
−0.393945 0.919134i \(-0.628890\pi\)
\(660\) 0 0
\(661\) 43.3834 15.7903i 1.68742 0.614170i 0.693121 0.720822i \(-0.256235\pi\)
0.994296 + 0.106652i \(0.0340131\pi\)
\(662\) −2.51167 + 2.10754i −0.0976189 + 0.0819120i
\(663\) 0.267910 + 1.51940i 0.0104048 + 0.0590084i
\(664\) 9.51427 0.369225
\(665\) 0 0
\(666\) −5.03382 −0.195056
\(667\) −10.4062 59.0167i −0.402931 2.28514i
\(668\) 21.3787 17.9388i 0.827166 0.694074i
\(669\) −0.146397 + 0.0532843i −0.00566005 + 0.00206009i
\(670\) 0 0
\(671\) 17.4704 + 14.6594i 0.674437 + 0.565920i
\(672\) −0.165610 + 0.286845i −0.00638855 + 0.0110653i
\(673\) 2.74410 + 4.75292i 0.105777 + 0.183212i 0.914056 0.405589i \(-0.132934\pi\)
−0.808278 + 0.588801i \(0.799600\pi\)
\(674\) 0.403213 2.28674i 0.0155312 0.0880818i
\(675\) 0 0
\(676\) 28.1681 + 48.7885i 1.08339 + 1.87648i
\(677\) −14.7154 + 25.4878i −0.565557 + 0.979574i 0.431440 + 0.902141i \(0.358006\pi\)
−0.996998 + 0.0774324i \(0.975328\pi\)
\(678\) −0.110672 0.0928650i −0.00425034 0.00356646i
\(679\) −15.6458 5.69460i −0.600430 0.218539i
\(680\) 0 0
\(681\) 0.771771 0.647593i 0.0295743 0.0248158i
\(682\) 0.428975 + 2.43284i 0.0164263 + 0.0931581i
\(683\) 27.4543 1.05051 0.525254 0.850945i \(-0.323970\pi\)
0.525254 + 0.850945i \(0.323970\pi\)
\(684\) −2.75705 25.3675i −0.105419 0.969951i
\(685\) 0 0
\(686\) 0.689437 + 3.90999i 0.0263228 + 0.149284i
\(687\) 0.375033 0.314690i 0.0143084 0.0120062i
\(688\) −18.7122 + 6.81069i −0.713397 + 0.259655i
\(689\) 11.6170 + 4.22826i 0.442574 + 0.161084i
\(690\) 0 0
\(691\) −1.71390 + 2.96856i −0.0651997 + 0.112929i −0.896783 0.442471i \(-0.854102\pi\)
0.831583 + 0.555401i \(0.187435\pi\)
\(692\) −13.7641 23.8402i −0.523233 0.906267i
\(693\) 2.53195 14.3594i 0.0961806 0.545468i
\(694\) 1.11631 6.33094i 0.0423747 0.240319i
\(695\) 0 0
\(696\) 0.241944 0.419059i 0.00917085 0.0158844i
\(697\) −12.4820 10.4737i −0.472790 0.396718i
\(698\) 1.11371 + 0.405358i 0.0421546 + 0.0153430i
\(699\) −0.496045 + 0.180546i −0.0187622 + 0.00682887i
\(700\) 0 0
\(701\) −0.566267 3.21146i −0.0213876 0.121295i 0.972245 0.233966i \(-0.0751705\pi\)
−0.993632 + 0.112671i \(0.964059\pi\)
\(702\) −0.653276 −0.0246563
\(703\) 34.6637 + 2.30065i 1.30737 + 0.0867707i
\(704\) 20.0672 0.756309
\(705\) 0 0
\(706\) −1.20994 + 1.01526i −0.0455365 + 0.0382097i
\(707\) −6.61103 + 2.40622i −0.248634 + 0.0904952i
\(708\) −0.521590 0.189843i −0.0196025 0.00713474i
\(709\) −13.1285 11.0161i −0.493052 0.413720i 0.362067 0.932152i \(-0.382071\pi\)
−0.855118 + 0.518433i \(0.826516\pi\)
\(710\) 0 0
\(711\) −3.60845 6.25001i −0.135327 0.234394i
\(712\) −1.46599 + 8.31406i −0.0549404 + 0.311583i
\(713\) −5.81593 + 32.9838i −0.217808 + 1.23525i
\(714\) 0.0424693 + 0.0735590i 0.00158937 + 0.00275288i
\(715\) 0 0
\(716\) −23.5930 19.7968i −0.881710 0.739843i
\(717\) −0.165457 0.0602213i −0.00617909 0.00224900i
\(718\) −5.05273 + 1.83904i −0.188566 + 0.0686325i
\(719\) 4.76900 4.00167i 0.177854 0.149237i −0.549515 0.835484i \(-0.685187\pi\)
0.727369 + 0.686247i \(0.240743\pi\)
\(720\) 0 0
\(721\) 21.1977 0.789442
\(722\) −0.168259 4.00516i −0.00626197 0.149056i
\(723\) 0.00997498 0.000370974
\(724\) −1.54785 8.77829i −0.0575253 0.326242i
\(725\) 0 0
\(726\) 0.0422373 0.0153731i 0.00156757 0.000570549i
\(727\) −39.7667 14.4739i −1.47487 0.536807i −0.525449 0.850825i \(-0.676103\pi\)
−0.949417 + 0.314017i \(0.898325\pi\)
\(728\) 6.97449 + 5.85229i 0.258492 + 0.216900i
\(729\) 13.3280 23.0847i 0.493628 0.854989i
\(730\) 0 0
\(731\) −2.76498 + 15.6810i −0.102266 + 0.579982i
\(732\) −0.214330 + 1.21552i −0.00792185 + 0.0449270i
\(733\) −11.3815 19.7134i −0.420386 0.728129i 0.575591 0.817737i \(-0.304772\pi\)
−0.995977 + 0.0896082i \(0.971439\pi\)
\(734\) 3.53041 6.11485i 0.130310 0.225703i
\(735\) 0 0
\(736\) −19.0659 6.93941i −0.702778 0.255790i
\(737\) −6.14514 + 2.23665i −0.226359 + 0.0823879i
\(738\) 2.63979 2.21505i 0.0971720 0.0815370i
\(739\) 3.11567 + 17.6698i 0.114612 + 0.649996i 0.986942 + 0.161078i \(0.0514971\pi\)
−0.872330 + 0.488918i \(0.837392\pi\)
\(740\) 0 0
\(741\) 2.24689 + 0.149127i 0.0825414 + 0.00547833i
\(742\) 0.680606 0.0249858
\(743\) 3.00948 + 17.0676i 0.110407 + 0.626150i 0.988922 + 0.148435i \(0.0474237\pi\)
−0.878515 + 0.477715i \(0.841465\pi\)
\(744\) −0.207168 + 0.173835i −0.00759516 + 0.00637310i
\(745\) 0 0
\(746\) 2.07750 + 0.756149i 0.0760628 + 0.0276846i
\(747\) −26.1443 21.9377i −0.956570 0.802658i
\(748\) 8.42945 14.6002i 0.308211 0.533838i
\(749\) 12.6055 + 21.8334i 0.460597 + 0.797777i
\(750\) 0 0
\(751\) −0.379642 + 2.15305i −0.0138533 + 0.0785661i −0.990951 0.134227i \(-0.957145\pi\)
0.977097 + 0.212793i \(0.0682560\pi\)
\(752\) 3.08056 + 5.33569i 0.112337 + 0.194573i
\(753\) 0.148477 0.257170i 0.00541081 0.00937181i
\(754\) −7.58424 6.36394i −0.276202 0.231761i
\(755\) 0 0
\(756\) 1.48466 0.540370i 0.0539964 0.0196531i
\(757\) 11.9799 10.0523i 0.435417 0.365358i −0.398574 0.917136i \(-0.630495\pi\)
0.833991 + 0.551778i \(0.186050\pi\)
\(758\) 0.523767 + 2.97043i 0.0190241 + 0.107891i
\(759\) −1.90453 −0.0691299
\(760\) 0 0
\(761\) 26.2993 0.953349 0.476675 0.879080i \(-0.341842\pi\)
0.476675 + 0.879080i \(0.341842\pi\)
\(762\) −0.0381608 0.216421i −0.00138242 0.00784009i
\(763\) 6.72737 5.64493i 0.243547 0.204360i
\(764\) −18.3000 + 6.66065i −0.662070 + 0.240974i
\(765\) 0 0
\(766\) 5.97705 + 5.01534i 0.215960 + 0.181212i
\(767\) −11.4861 + 19.8945i −0.414739 + 0.718349i
\(768\) 0.501605 + 0.868806i 0.0181001 + 0.0313503i
\(769\) 0.0147166 0.0834622i 0.000530695 0.00300972i −0.984541 0.175153i \(-0.943958\pi\)
0.985072 + 0.172143i \(0.0550692\pi\)
\(770\) 0 0
\(771\) 1.07762 + 1.86649i 0.0388095 + 0.0672200i
\(772\) 20.9249 36.2430i 0.753104 1.30441i
\(773\) 0.00879051 + 0.00737611i 0.000316173 + 0.000265300i 0.642946 0.765912i \(-0.277712\pi\)
−0.642630 + 0.766177i \(0.722157\pi\)
\(774\) −3.16440 1.15175i −0.113742 0.0413987i
\(775\) 0 0
\(776\) 6.30871 5.29364i 0.226470 0.190030i
\(777\) 0.186560 + 1.05803i 0.00669281 + 0.0379568i
\(778\) 3.50389 0.125621
\(779\) −19.1904 + 14.0467i −0.687567 + 0.503275i
\(780\) 0 0
\(781\) −5.22461 29.6302i −0.186951 1.06025i
\(782\) −3.98578 + 3.34447i −0.142531 + 0.119598i
\(783\) −3.26566 + 1.18860i −0.116705 + 0.0424771i
\(784\) 14.5765 + 5.30542i 0.520590 + 0.189479i
\(785\) 0 0
\(786\) −0.00157680 + 0.00273110i −5.62426e−5 + 9.74150e-5i
\(787\) 15.0534 + 26.0733i 0.536596 + 0.929411i 0.999084 + 0.0427861i \(0.0136234\pi\)
−0.462488 + 0.886625i \(0.653043\pi\)
\(788\) 0.464101 2.63205i 0.0165329 0.0937628i
\(789\) 0.286851 1.62681i 0.0102122 0.0579161i
\(790\) 0 0
\(791\) 7.23031 12.5233i 0.257080 0.445276i
\(792\) 5.52475 + 4.63582i 0.196314 + 0.164727i
\(793\) 48.0017 + 17.4712i 1.70459 + 0.620421i
\(794\) 5.28131 1.92224i 0.187427 0.0682178i
\(795\) 0 0
\(796\) 6.09044 + 34.5406i 0.215870 + 1.22426i
\(797\) −38.2339 −1.35432 −0.677158 0.735838i \(-0.736789\pi\)
−0.677158 + 0.735838i \(0.736789\pi\)
\(798\) 0.119047 0.0345928i 0.00421423 0.00122457i
\(799\) 4.92654 0.174288
\(800\) 0 0
\(801\) 23.1987 19.4660i 0.819685 0.687798i
\(802\) 0.256698 0.0934304i 0.00906431 0.00329914i
\(803\) −3.82995 1.39399i −0.135156 0.0491927i
\(804\) −0.271121 0.227497i −0.00956169 0.00802321i
\(805\) 0 0
\(806\) 2.76665 + 4.79197i 0.0974509 + 0.168790i
\(807\) 0.190415 1.07990i 0.00670292 0.0380142i
\(808\) 0.604267 3.42697i 0.0212580 0.120560i
\(809\) −1.85001 3.20432i −0.0650431 0.112658i 0.831670 0.555270i \(-0.187385\pi\)
−0.896713 + 0.442612i \(0.854052\pi\)
\(810\) 0 0
\(811\) 31.3508 + 26.3064i 1.10088 + 0.923744i 0.997484 0.0708964i \(-0.0225860\pi\)
0.103392 + 0.994641i \(0.467030\pi\)
\(812\) 22.5002 + 8.18942i 0.789604 + 0.287392i
\(813\) −0.404175 + 0.147108i −0.0141750 + 0.00515929i
\(814\) −3.71851 + 3.12020i −0.130334 + 0.109363i
\(815\) 0 0
\(816\) 0.891172 0.0311973
\(817\) 21.2642 + 9.37739i 0.743940 + 0.328073i
\(818\) −5.70327 −0.199410
\(819\) −5.67122 32.1631i −0.198168 1.12387i
\(820\) 0 0
\(821\) −16.3884 + 5.96489i −0.571959 + 0.208176i −0.611776 0.791031i \(-0.709545\pi\)
0.0398170 + 0.999207i \(0.487323\pi\)
\(822\) 0.0341447 + 0.0124276i 0.00119093 + 0.000433464i
\(823\) 4.98291 + 4.18116i 0.173693 + 0.145746i 0.725490 0.688233i \(-0.241613\pi\)
−0.551797 + 0.833979i \(0.686058\pi\)
\(824\) −5.24243 + 9.08016i −0.182629 + 0.316322i
\(825\) 0 0
\(826\) −0.219613 + 1.24549i −0.00764133 + 0.0433361i
\(827\) −0.281701 + 1.59761i −0.00979571 + 0.0555542i −0.989314 0.145802i \(-0.953424\pi\)
0.979518 + 0.201356i \(0.0645349\pi\)
\(828\) 24.1697 + 41.8632i 0.839955 + 1.45485i
\(829\) −16.3252 + 28.2760i −0.566996 + 0.982066i 0.429865 + 0.902893i \(0.358561\pi\)
−0.996861 + 0.0791727i \(0.974772\pi\)
\(830\) 0 0
\(831\) −1.71165 0.622990i −0.0593765 0.0216113i
\(832\) 42.2371 15.3730i 1.46431 0.532964i
\(833\) 9.50176 7.97292i 0.329216 0.276245i
\(834\) −0.0231159 0.131097i −0.000800437 0.00453951i
\(835\) 0 0
\(836\) −17.7607 17.0302i −0.614265 0.589001i
\(837\) 1.94227 0.0671347
\(838\) 0.152226 + 0.863314i 0.00525854 + 0.0298227i
\(839\) −8.85542 + 7.43058i −0.305723 + 0.256532i −0.782722 0.622372i \(-0.786169\pi\)
0.476999 + 0.878904i \(0.341725\pi\)
\(840\) 0 0
\(841\) −22.2406 8.09491i −0.766916 0.279135i
\(842\) 4.26764 + 3.58098i 0.147073 + 0.123409i
\(843\) −0.688261 + 1.19210i −0.0237050 + 0.0410582i
\(844\) 20.3056 + 35.1703i 0.698947 + 1.21061i
\(845\) 0 0
\(846\) −0.180924 + 1.02607i −0.00622030 + 0.0352771i
\(847\) 2.24948 + 3.89622i 0.0772931 + 0.133876i
\(848\) 3.57044 6.18419i 0.122610 0.212366i
\(849\) 0.997547 + 0.837041i 0.0342357 + 0.0287272i
\(850\) 0 0
\(851\) −61.8427 + 22.5089i −2.11994 + 0.771596i
\(852\) 1.24739 1.04668i 0.0427347 0.0358587i
\(853\) −8.28547 46.9892i −0.283689 1.60888i −0.709931 0.704271i \(-0.751274\pi\)
0.426242 0.904609i \(-0.359837\pi\)
\(854\) 2.81227 0.0962339
\(855\) 0 0
\(856\) −12.4700 −0.426216
\(857\) 6.69167 + 37.9503i 0.228583 + 1.29636i 0.855716 + 0.517447i \(0.173117\pi\)
−0.627132 + 0.778913i \(0.715772\pi\)
\(858\) −0.241033 + 0.202250i −0.00822872 + 0.00690471i
\(859\) −18.0347 + 6.56408i −0.615335 + 0.223964i −0.630836 0.775916i \(-0.717288\pi\)
0.0155009 + 0.999880i \(0.495066\pi\)
\(860\) 0 0
\(861\) −0.563405 0.472753i −0.0192008 0.0161114i
\(862\) −1.02553 + 1.77626i −0.0349295 + 0.0604997i
\(863\) −4.58397 7.93967i −0.156040 0.270269i 0.777397 0.629010i \(-0.216540\pi\)
−0.933437 + 0.358741i \(0.883206\pi\)
\(864\) −0.204316 + 1.15873i −0.00695097 + 0.0394209i
\(865\) 0 0
\(866\) 0.0696079 + 0.120564i 0.00236537 + 0.00409695i
\(867\) −0.322814 + 0.559130i −0.0109633 + 0.0189890i
\(868\) −10.2513 8.60190i −0.347953 0.291967i
\(869\) −6.53965 2.38024i −0.221842 0.0807440i
\(870\) 0 0
\(871\) −11.2207 + 9.41533i −0.380201 + 0.319026i
\(872\) 0.754286 + 4.27777i 0.0255434 + 0.144864i
\(873\) −29.5416 −0.999832
\(874\) 3.35317 + 6.81370i 0.113423 + 0.230477i
\(875\) 0 0
\(876\) −0.0383037 0.217231i −0.00129416 0.00733955i
\(877\) 2.78066 2.33325i 0.0938961 0.0787882i −0.594631 0.803999i \(-0.702702\pi\)
0.688527 + 0.725210i \(0.258257\pi\)
\(878\) 5.39064 1.96203i 0.181925 0.0662154i
\(879\) −1.89857 0.691022i −0.0640370 0.0233076i
\(880\) 0 0
\(881\) 4.17191 7.22596i 0.140555 0.243449i −0.787151 0.616761i \(-0.788445\pi\)
0.927706 + 0.373312i \(0.121778\pi\)
\(882\) 1.31161 + 2.27177i 0.0441642 + 0.0764946i
\(883\) −4.89899 + 27.7836i −0.164864 + 0.934991i 0.784340 + 0.620331i \(0.213002\pi\)
−0.949204 + 0.314660i \(0.898109\pi\)
\(884\) 6.55725 37.1880i 0.220544 1.25077i
\(885\) 0 0
\(886\) −3.98633 + 6.90452i −0.133923 + 0.231962i
\(887\) 6.77332 + 5.68349i 0.227426 + 0.190833i 0.749379 0.662141i \(-0.230352\pi\)
−0.521953 + 0.852974i \(0.674796\pi\)
\(888\) −0.499355 0.181750i −0.0167573 0.00609914i
\(889\) 20.6698 7.52318i 0.693242 0.252319i
\(890\) 0 0
\(891\) −4.48278 25.4231i −0.150179 0.851707i
\(892\) 3.81312 0.127673
\(893\) 1.71483 6.98301i 0.0573846 0.233678i
\(894\) 0.301677 0.0100896
\(895\) 0 0
\(896\) 8.24714 6.92017i 0.275517 0.231187i
\(897\) −4.00862 + 1.45902i −0.133844 + 0.0487152i
\(898\) −3.28118 1.19425i −0.109495 0.0398528i
\(899\) 22.5489 + 18.9208i 0.752048 + 0.631043i
\(900\) 0 0
\(901\) −2.85499 4.94498i −0.0951134 0.164741i
\(902\) 0.577037 3.27254i 0.0192132 0.108964i
\(903\) −0.124804 + 0.707797i −0.00415321 + 0.0235540i
\(904\) 3.57628 + 6.19431i 0.118945 + 0.206020i
\(905\) 0 0
\(906\) 0.0379619 + 0.0318539i 0.00126120 + 0.00105827i
\(907\) 3.97425 + 1.44651i 0.131963 + 0.0480305i 0.407157 0.913358i \(-0.366520\pi\)
−0.275195 + 0.961389i \(0.588742\pi\)
\(908\) −23.1714 + 8.43371i −0.768971 + 0.279882i
\(909\) −9.56225 + 8.02368i −0.317160 + 0.266129i
\(910\) 0 0
\(911\) 10.1182 0.335231 0.167616 0.985852i \(-0.446393\pi\)
0.167616 + 0.985852i \(0.446393\pi\)
\(912\) 0.310199 1.26317i 0.0102717 0.0418278i
\(913\) −32.9110 −1.08920
\(914\) 0.419463 + 2.37890i 0.0138746 + 0.0786869i
\(915\) 0 0
\(916\) −11.2599 + 4.09826i −0.372037 + 0.135410i
\(917\) −0.296616 0.107959i −0.00979513 0.00356513i
\(918\) 0.231140 + 0.193949i 0.00762875 + 0.00640128i
\(919\) 23.9378 41.4616i 0.789637 1.36769i −0.136553 0.990633i \(-0.543602\pi\)
0.926190 0.377058i \(-0.123064\pi\)
\(920\) 0 0
\(921\) 0.239030 1.35561i 0.00787630 0.0446687i
\(922\) 0.394201 2.23562i 0.0129823 0.0736263i
\(923\) −33.6958 58.3629i −1.10911 1.92104i
\(924\) 0.380483 0.659016i 0.0125170 0.0216800i
\(925\) 0 0
\(926\) −3.38790 1.23309i −0.111333 0.0405220i
\(927\) 35.3424 12.8636i 1.16080 0.422496i
\(928\) −13.6599 + 11.4620i −0.448408 + 0.376259i
\(929\) −3.75604 21.3015i −0.123232 0.698881i −0.982342 0.187092i \(-0.940094\pi\)
0.859111 0.511789i \(-0.171017\pi\)
\(930\) 0 0
\(931\) −7.99367 16.2433i −0.261982 0.532351i
\(932\) 12.9202 0.423214
\(933\) −0.346460 1.96487i −0.0113426 0.0643271i
\(934\) 5.14864 4.32023i 0.168469 0.141362i
\(935\) 0 0
\(936\) 15.1798 + 5.52501i 0.496168 + 0.180591i
\(937\) −27.6414 23.1939i −0.903006 0.757712i 0.0677696 0.997701i \(-0.478412\pi\)
−0.970776 + 0.239989i \(0.922856\pi\)
\(938\) −0.403203 + 0.698368i −0.0131651 + 0.0228025i
\(939\) 0.673649 + 1.16679i 0.0219837 + 0.0380769i
\(940\) 0 0
\(941\) −8.41858 + 47.7441i −0.274438 + 1.55641i 0.466305 + 0.884624i \(0.345585\pi\)
−0.740742 + 0.671789i \(0.765526\pi\)
\(942\) 0.0570334 + 0.0987847i 0.00185825 + 0.00321858i
\(943\) 22.5264 39.0168i 0.733559 1.27056i
\(944\) 10.1648 + 8.52928i 0.330836 + 0.277604i
\(945\) 0 0
\(946\) −3.05148 + 1.11065i −0.0992120 + 0.0361102i
\(947\) −26.9727 + 22.6328i −0.876495 + 0.735466i −0.965455 0.260569i \(-0.916090\pi\)
0.0889606 + 0.996035i \(0.471645\pi\)
\(948\) −0.0654036 0.370922i −0.00212421 0.0120470i
\(949\) −9.12913 −0.296344
\(950\) 0 0
\(951\) 1.92717 0.0624928
\(952\) −0.730219 4.14128i −0.0236665 0.134220i
\(953\) −34.1607 + 28.6643i −1.10657 + 0.928527i −0.997850 0.0655452i \(-0.979121\pi\)
−0.108725 + 0.994072i \(0.534677\pi\)
\(954\) 1.13476 0.413019i 0.0367392 0.0133720i
\(955\) 0 0
\(956\) 3.30130 + 2.77012i 0.106772 + 0.0895920i
\(957\) −0.836912 + 1.44957i −0.0270535 + 0.0468581i
\(958\) −0.406172 0.703510i −0.0131228 0.0227294i
\(959\) −0.631553 + 3.58171i −0.0203939 + 0.115660i
\(960\) 0 0
\(961\) 7.27442 + 12.5997i 0.234659 + 0.406441i
\(962\) −5.43635 + 9.41604i −0.175275 + 0.303585i
\(963\) 34.2664 + 28.7529i 1.10422 + 0.926549i
\(964\) −0.229419 0.0835019i −0.00738910 0.00268941i
\(965\) 0 0
\(966\) −0.179908 + 0.150960i −0.00578843 + 0.00485707i
\(967\) −0.469769 2.66419i −0.0151067 0.0856746i 0.976322 0.216321i \(-0.0694058\pi\)
−0.991429 + 0.130647i \(0.958295\pi\)
\(968\) −2.22529 −0.0715236
\(969\) −0.750712 0.719836i −0.0241163 0.0231245i
\(970\) 0 0
\(971\) −1.24026 7.03387i −0.0398019 0.225728i 0.958418 0.285368i \(-0.0921158\pi\)
−0.998220 + 0.0596403i \(0.981005\pi\)
\(972\) 3.22227 2.70380i 0.103354 0.0867246i
\(973\) 12.5207 4.55716i 0.401395 0.146096i
\(974\) −7.01988 2.55503i −0.224932 0.0818684i
\(975\) 0 0
\(976\) 14.7531 25.5531i 0.472235 0.817935i
\(977\) −14.4495 25.0272i −0.462280 0.800692i 0.536794 0.843713i \(-0.319635\pi\)
−0.999074 + 0.0430210i \(0.986302\pi\)
\(978\) 0.00265734 0.0150705i 8.49725e−5 0.000481903i
\(979\) 5.07105 28.7593i 0.162071 0.919152i
\(980\) 0 0
\(981\) 7.79083 13.4941i 0.248742 0.430834i
\(982\) −3.27402 2.74722i −0.104478 0.0876675i
\(983\) 9.71738 + 3.53684i 0.309936 + 0.112808i 0.492305 0.870423i \(-0.336154\pi\)
−0.182369 + 0.983230i \(0.558377\pi\)
\(984\) 0.341843 0.124421i 0.0108976 0.00396639i
\(985\) 0 0
\(986\) 0.794059 + 4.50333i 0.0252880 + 0.143415i
\(987\) 0.222371 0.00707814
\(988\) −50.4289 22.2388i −1.60436 0.707511i
\(989\) −44.0262 −1.39995
\(990\) 0 0
\(991\) 24.2226 20.3251i 0.769455 0.645650i −0.171114 0.985251i \(-0.554737\pi\)
0.940569 + 0.339602i \(0.110292\pi\)
\(992\) 9.36494 3.40856i 0.297337 0.108222i
\(993\) 1.16673 + 0.424653i 0.0370249 + 0.0134760i
\(994\) −2.84214 2.38484i −0.0901473 0.0756426i
\(995\) 0 0
\(996\) −0.890582 1.54253i −0.0282192 0.0488771i
\(997\) −1.36787 + 7.75758i −0.0433209 + 0.245685i −0.998777 0.0494495i \(-0.984253\pi\)
0.955456 + 0.295134i \(0.0953644\pi\)
\(998\) −0.0215948 + 0.122470i −0.000683571 + 0.00387672i
\(999\) 1.90824 + 3.30518i 0.0603742 + 0.104571i
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 475.2.l.c.351.2 18
5.2 odd 4 475.2.u.b.199.4 36
5.3 odd 4 475.2.u.b.199.3 36
5.4 even 2 95.2.k.a.66.2 yes 18
15.14 odd 2 855.2.bs.c.541.2 18
19.6 even 9 9025.2.a.cc.1.6 9
19.13 odd 18 9025.2.a.cf.1.4 9
19.17 even 9 inner 475.2.l.c.226.2 18
95.17 odd 36 475.2.u.b.74.3 36
95.44 even 18 1805.2.a.v.1.4 9
95.74 even 18 95.2.k.a.36.2 18
95.89 odd 18 1805.2.a.s.1.6 9
95.93 odd 36 475.2.u.b.74.4 36
285.74 odd 18 855.2.bs.c.226.2 18
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
95.2.k.a.36.2 18 95.74 even 18
95.2.k.a.66.2 yes 18 5.4 even 2
475.2.l.c.226.2 18 19.17 even 9 inner
475.2.l.c.351.2 18 1.1 even 1 trivial
475.2.u.b.74.3 36 95.17 odd 36
475.2.u.b.74.4 36 95.93 odd 36
475.2.u.b.199.3 36 5.3 odd 4
475.2.u.b.199.4 36 5.2 odd 4
855.2.bs.c.226.2 18 285.74 odd 18
855.2.bs.c.541.2 18 15.14 odd 2
1805.2.a.s.1.6 9 95.89 odd 18
1805.2.a.v.1.4 9 95.44 even 18
9025.2.a.cc.1.6 9 19.6 even 9
9025.2.a.cf.1.4 9 19.13 odd 18