Properties

Label 950.2.l.i.651.3
Level $950$
Weight $2$
Character 950.651
Analytic conductor $7.586$
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] = [950,2,Mod(101,950)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(950, 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("950.101");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 950 = 2 \cdot 5^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 950.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: \(7.58578819202\)
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: \( x^{18} + 24 x^{16} - 12 x^{15} + 393 x^{14} - 222 x^{13} + 3518 x^{12} - 2478 x^{11} + 22809 x^{10} - 12862 x^{9} + 77397 x^{8} - 24822 x^{7} + 178501 x^{6} - 39408 x^{5} + \cdots + 64 \) 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 190)
Sato-Tate group: $\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label 651.3
Root \(1.60792 - 2.78500i\) of defining polynomial
Character \(\chi\) \(=\) 950.651
Dual form 950.2.l.i.251.3

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.939693 + 0.342020i) q^{2} +(0.558424 - 3.16698i) q^{3} +(0.766044 - 0.642788i) q^{4} +(0.558424 + 3.16698i) q^{6} +(-0.0116976 - 0.0202608i) q^{7} +(-0.500000 + 0.866025i) q^{8} +(-6.89886 - 2.51098i) q^{9} +O(q^{10})\) \(q+(-0.939693 + 0.342020i) q^{2} +(0.558424 - 3.16698i) q^{3} +(0.766044 - 0.642788i) q^{4} +(0.558424 + 3.16698i) q^{6} +(-0.0116976 - 0.0202608i) q^{7} +(-0.500000 + 0.866025i) q^{8} +(-6.89886 - 2.51098i) q^{9} +(-1.08041 + 1.87132i) q^{11} +(-1.60792 - 2.78500i) q^{12} +(0.276152 + 1.56613i) q^{13} +(0.0179217 + 0.0150381i) q^{14} +(0.173648 - 0.984808i) q^{16} +(-7.49847 + 2.72922i) q^{17} +7.34161 q^{18} +(1.06458 + 4.22690i) q^{19} +(-0.0706976 + 0.0257318i) q^{21} +(0.375222 - 2.12799i) q^{22} +(-3.43239 + 2.88011i) q^{23} +(2.46347 + 2.06710i) q^{24} +(-0.795147 - 1.37724i) q^{26} +(-6.98095 + 12.0914i) q^{27} +(-0.0219842 - 0.00800160i) q^{28} +(-7.09702 - 2.58310i) q^{29} +(-2.22993 - 3.86236i) q^{31} +(0.173648 + 0.984808i) q^{32} +(5.32312 + 4.46663i) q^{33} +(6.11281 - 5.12925i) q^{34} +(-6.89886 + 2.51098i) q^{36} +0.389132 q^{37} +(-2.44606 - 3.60788i) q^{38} +5.11413 q^{39} +(0.972920 - 5.51771i) q^{41} +(0.0576332 - 0.0483600i) q^{42} +(-7.43337 - 6.23734i) q^{43} +(0.375222 + 2.12799i) q^{44} +(2.24033 - 3.88037i) q^{46} +(4.01711 + 1.46211i) q^{47} +(-3.02190 - 1.09988i) q^{48} +(3.49973 - 6.06170i) q^{49} +(4.45606 + 25.2716i) q^{51} +(1.21824 + 1.02222i) q^{52} +(2.89731 - 2.43113i) q^{53} +(2.42446 - 13.7498i) q^{54} +0.0233951 q^{56} +(13.9810 - 1.01111i) q^{57} +7.55249 q^{58} +(3.41426 - 1.24269i) q^{59} +(-8.84152 + 7.41891i) q^{61} +(3.41646 + 2.86675i) q^{62} +(0.0298254 + 0.169148i) q^{63} +(-0.500000 - 0.866025i) q^{64} +(-6.52977 - 2.37664i) q^{66} +(3.62429 + 1.31913i) q^{67} +(-3.98985 + 6.91062i) q^{68} +(7.20454 + 12.4786i) q^{69} +(-9.85813 - 8.27195i) q^{71} +(5.62400 - 4.71909i) q^{72} +(0.330206 - 1.87269i) q^{73} +(-0.365664 + 0.133091i) q^{74} +(3.53251 + 2.55369i) q^{76} +0.0505526 q^{77} +(-4.80571 + 1.74914i) q^{78} +(-1.65165 + 9.36698i) q^{79} +(17.5228 + 14.7034i) q^{81} +(0.972920 + 5.51771i) q^{82} +(-1.31417 - 2.27622i) q^{83} +(-0.0376174 + 0.0651553i) q^{84} +(9.11838 + 3.31882i) q^{86} +(-12.1438 + 21.0337i) q^{87} +(-1.08041 - 1.87132i) q^{88} +(1.54115 + 8.74032i) q^{89} +(0.0285008 - 0.0239150i) q^{91} +(-0.778059 + 4.41259i) q^{92} +(-13.4773 + 4.90532i) q^{93} -4.27492 q^{94} +3.21584 q^{96} +(10.4812 - 3.81486i) q^{97} +(-1.21544 + 6.89312i) q^{98} +(12.1524 - 10.1971i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 18 q - 9 q^{8} - 18 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 18 q - 9 q^{8} - 18 q^{9} - 12 q^{11} + 6 q^{13} + 6 q^{14} + 42 q^{18} + 12 q^{21} + 3 q^{22} - 9 q^{23} - 9 q^{26} + 18 q^{27} - 3 q^{28} - 6 q^{29} - 6 q^{31} - 66 q^{33} + 18 q^{34} - 18 q^{36} + 12 q^{37} + 6 q^{38} + 48 q^{39} - 21 q^{41} - 42 q^{42} - 18 q^{43} + 3 q^{44} + 18 q^{46} + 54 q^{47} - 39 q^{49} + 42 q^{51} - 12 q^{52} + 24 q^{53} - 54 q^{54} + 18 q^{57} - 30 q^{59} + 48 q^{61} + 30 q^{62} + 57 q^{63} - 9 q^{64} + 24 q^{66} + 6 q^{67} + 6 q^{68} - 30 q^{69} + 30 q^{71} - 6 q^{73} - 3 q^{74} - 21 q^{76} - 30 q^{77} + 24 q^{78} + 30 q^{79} + 18 q^{81} - 21 q^{82} - 6 q^{83} + 6 q^{84} + 36 q^{86} - 24 q^{87} - 12 q^{88} + 30 q^{89} - 60 q^{91} + 18 q^{92} + 12 q^{93} + 6 q^{94} + 12 q^{97} + 18 q^{98} + 171 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/950\mathbb{Z}\right)^\times\).

\(n\) \(77\) \(401\)
\(\chi(n)\) \(1\) \(e\left(\frac{8}{9}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.939693 + 0.342020i −0.664463 + 0.241845i
\(3\) 0.558424 3.16698i 0.322406 1.82846i −0.204901 0.978783i \(-0.565687\pi\)
0.527307 0.849675i \(-0.323202\pi\)
\(4\) 0.766044 0.642788i 0.383022 0.321394i
\(5\) 0 0
\(6\) 0.558424 + 3.16698i 0.227976 + 1.29291i
\(7\) −0.0116976 0.0202608i −0.00442126 0.00765785i 0.863806 0.503824i \(-0.168074\pi\)
−0.868228 + 0.496166i \(0.834741\pi\)
\(8\) −0.500000 + 0.866025i −0.176777 + 0.306186i
\(9\) −6.89886 2.51098i −2.29962 0.836993i
\(10\) 0 0
\(11\) −1.08041 + 1.87132i −0.325755 + 0.564225i −0.981665 0.190615i \(-0.938952\pi\)
0.655910 + 0.754839i \(0.272285\pi\)
\(12\) −1.60792 2.78500i −0.464166 0.803959i
\(13\) 0.276152 + 1.56613i 0.0765907 + 0.434368i 0.998856 + 0.0478110i \(0.0152245\pi\)
−0.922266 + 0.386557i \(0.873664\pi\)
\(14\) 0.0179217 + 0.0150381i 0.00478977 + 0.00401910i
\(15\) 0 0
\(16\) 0.173648 0.984808i 0.0434120 0.246202i
\(17\) −7.49847 + 2.72922i −1.81865 + 0.661933i −0.823073 + 0.567936i \(0.807742\pi\)
−0.995573 + 0.0939966i \(0.970036\pi\)
\(18\) 7.34161 1.73043
\(19\) 1.06458 + 4.22690i 0.244232 + 0.969717i
\(20\) 0 0
\(21\) −0.0706976 + 0.0257318i −0.0154275 + 0.00561515i
\(22\) 0.375222 2.12799i 0.0799976 0.453689i
\(23\) −3.43239 + 2.88011i −0.715702 + 0.600545i −0.926193 0.377050i \(-0.876938\pi\)
0.210491 + 0.977596i \(0.432494\pi\)
\(24\) 2.46347 + 2.06710i 0.502855 + 0.421945i
\(25\) 0 0
\(26\) −0.795147 1.37724i −0.155941 0.270098i
\(27\) −6.98095 + 12.0914i −1.34348 + 2.32698i
\(28\) −0.0219842 0.00800160i −0.00415463 0.00151216i
\(29\) −7.09702 2.58310i −1.31788 0.479670i −0.415104 0.909774i \(-0.636255\pi\)
−0.902780 + 0.430104i \(0.858477\pi\)
\(30\) 0 0
\(31\) −2.22993 3.86236i −0.400508 0.693700i 0.593279 0.804997i \(-0.297833\pi\)
−0.993787 + 0.111297i \(0.964500\pi\)
\(32\) 0.173648 + 0.984808i 0.0306970 + 0.174091i
\(33\) 5.32312 + 4.46663i 0.926636 + 0.777540i
\(34\) 6.11281 5.12925i 1.04834 0.879660i
\(35\) 0 0
\(36\) −6.89886 + 2.51098i −1.14981 + 0.418496i
\(37\) 0.389132 0.0639729 0.0319864 0.999488i \(-0.489817\pi\)
0.0319864 + 0.999488i \(0.489817\pi\)
\(38\) −2.44606 3.60788i −0.396804 0.585275i
\(39\) 5.11413 0.818916
\(40\) 0 0
\(41\) 0.972920 5.51771i 0.151945 0.861721i −0.809582 0.587007i \(-0.800306\pi\)
0.961526 0.274713i \(-0.0885830\pi\)
\(42\) 0.0576332 0.0483600i 0.00889300 0.00746212i
\(43\) −7.43337 6.23734i −1.13358 0.951185i −0.134369 0.990931i \(-0.542901\pi\)
−0.999210 + 0.0397459i \(0.987345\pi\)
\(44\) 0.375222 + 2.12799i 0.0565668 + 0.320806i
\(45\) 0 0
\(46\) 2.24033 3.88037i 0.330319 0.572129i
\(47\) 4.01711 + 1.46211i 0.585956 + 0.213271i 0.617950 0.786218i \(-0.287963\pi\)
−0.0319938 + 0.999488i \(0.510186\pi\)
\(48\) −3.02190 1.09988i −0.436173 0.158754i
\(49\) 3.49973 6.06170i 0.499961 0.865958i
\(50\) 0 0
\(51\) 4.45606 + 25.2716i 0.623973 + 3.53873i
\(52\) 1.21824 + 1.02222i 0.168939 + 0.141757i
\(53\) 2.89731 2.43113i 0.397976 0.333941i −0.421735 0.906719i \(-0.638579\pi\)
0.819711 + 0.572778i \(0.194134\pi\)
\(54\) 2.42446 13.7498i 0.329927 1.87111i
\(55\) 0 0
\(56\) 0.0233951 0.00312630
\(57\) 13.9810 1.01111i 1.85183 0.133925i
\(58\) 7.55249 0.991691
\(59\) 3.41426 1.24269i 0.444499 0.161784i −0.110067 0.993924i \(-0.535107\pi\)
0.554566 + 0.832140i \(0.312884\pi\)
\(60\) 0 0
\(61\) −8.84152 + 7.41891i −1.13204 + 0.949894i −0.999149 0.0412364i \(-0.986870\pi\)
−0.132891 + 0.991131i \(0.542426\pi\)
\(62\) 3.41646 + 2.86675i 0.433890 + 0.364077i
\(63\) 0.0298254 + 0.169148i 0.00375765 + 0.0213107i
\(64\) −0.500000 0.866025i −0.0625000 0.108253i
\(65\) 0 0
\(66\) −6.52977 2.37664i −0.803759 0.292544i
\(67\) 3.62429 + 1.31913i 0.442778 + 0.161158i 0.553781 0.832662i \(-0.313184\pi\)
−0.111004 + 0.993820i \(0.535407\pi\)
\(68\) −3.98985 + 6.91062i −0.483840 + 0.838036i
\(69\) 7.20454 + 12.4786i 0.867325 + 1.50225i
\(70\) 0 0
\(71\) −9.85813 8.27195i −1.16994 0.981700i −0.169952 0.985452i \(-0.554361\pi\)
−0.999993 + 0.00375214i \(0.998806\pi\)
\(72\) 5.62400 4.71909i 0.662795 0.556151i
\(73\) 0.330206 1.87269i 0.0386477 0.219182i −0.959367 0.282161i \(-0.908949\pi\)
0.998015 + 0.0629785i \(0.0200600\pi\)
\(74\) −0.365664 + 0.133091i −0.0425076 + 0.0154715i
\(75\) 0 0
\(76\) 3.53251 + 2.55369i 0.405207 + 0.292928i
\(77\) 0.0505526 0.00576100
\(78\) −4.80571 + 1.74914i −0.544139 + 0.198051i
\(79\) −1.65165 + 9.36698i −0.185825 + 1.05387i 0.739065 + 0.673634i \(0.235267\pi\)
−0.924891 + 0.380233i \(0.875844\pi\)
\(80\) 0 0
\(81\) 17.5228 + 14.7034i 1.94698 + 1.63371i
\(82\) 0.972920 + 5.51771i 0.107441 + 0.609329i
\(83\) −1.31417 2.27622i −0.144249 0.249847i 0.784843 0.619694i \(-0.212743\pi\)
−0.929093 + 0.369847i \(0.879410\pi\)
\(84\) −0.0376174 + 0.0651553i −0.00410440 + 0.00710903i
\(85\) 0 0
\(86\) 9.11838 + 3.31882i 0.983260 + 0.357877i
\(87\) −12.1438 + 21.0337i −1.30195 + 2.25505i
\(88\) −1.08041 1.87132i −0.115172 0.199484i
\(89\) 1.54115 + 8.74032i 0.163362 + 0.926472i 0.950737 + 0.309998i \(0.100328\pi\)
−0.787375 + 0.616474i \(0.788561\pi\)
\(90\) 0 0
\(91\) 0.0285008 0.0239150i 0.00298769 0.00250697i
\(92\) −0.778059 + 4.41259i −0.0811183 + 0.460045i
\(93\) −13.4773 + 4.90532i −1.39753 + 0.508658i
\(94\) −4.27492 −0.440924
\(95\) 0 0
\(96\) 3.21584 0.328215
\(97\) 10.4812 3.81486i 1.06421 0.387340i 0.250201 0.968194i \(-0.419503\pi\)
0.814008 + 0.580854i \(0.197281\pi\)
\(98\) −1.21544 + 6.89312i −0.122778 + 0.696310i
\(99\) 12.1524 10.1971i 1.22137 1.02485i
\(100\) 0 0
\(101\) −3.23809 18.3641i −0.322202 1.82730i −0.528651 0.848840i \(-0.677302\pi\)
0.206449 0.978457i \(-0.433809\pi\)
\(102\) −12.8307 22.2234i −1.27043 2.20045i
\(103\) 1.76795 3.06218i 0.174201 0.301726i −0.765683 0.643218i \(-0.777599\pi\)
0.939885 + 0.341492i \(0.110932\pi\)
\(104\) −1.49439 0.543913i −0.146537 0.0533350i
\(105\) 0 0
\(106\) −1.89108 + 3.27545i −0.183678 + 0.318140i
\(107\) 2.79632 + 4.84336i 0.270330 + 0.468226i 0.968946 0.247271i \(-0.0795338\pi\)
−0.698616 + 0.715497i \(0.746200\pi\)
\(108\) 2.42446 + 13.7498i 0.233294 + 1.32307i
\(109\) 7.21936 + 6.05777i 0.691490 + 0.580229i 0.919338 0.393468i \(-0.128725\pi\)
−0.227849 + 0.973697i \(0.573169\pi\)
\(110\) 0 0
\(111\) 0.217301 1.23237i 0.0206253 0.116972i
\(112\) −0.0219842 + 0.00800160i −0.00207731 + 0.000756080i
\(113\) 5.69339 0.535589 0.267795 0.963476i \(-0.413705\pi\)
0.267795 + 0.963476i \(0.413705\pi\)
\(114\) −12.7920 + 5.73191i −1.19808 + 0.536843i
\(115\) 0 0
\(116\) −7.09702 + 2.58310i −0.658942 + 0.239835i
\(117\) 2.02740 11.4979i 0.187433 1.06299i
\(118\) −2.78333 + 2.33549i −0.256226 + 0.214999i
\(119\) 0.143010 + 0.119999i 0.0131097 + 0.0110003i
\(120\) 0 0
\(121\) 3.16544 + 5.48269i 0.287767 + 0.498427i
\(122\) 5.77089 9.99547i 0.522472 0.904948i
\(123\) −16.9312 6.16244i −1.52663 0.555649i
\(124\) −4.19091 1.52536i −0.376354 0.136982i
\(125\) 0 0
\(126\) −0.0858789 0.148747i −0.00765070 0.0132514i
\(127\) −1.50642 8.54334i −0.133673 0.758099i −0.975774 0.218779i \(-0.929793\pi\)
0.842101 0.539320i \(-0.181319\pi\)
\(128\) 0.766044 + 0.642788i 0.0677094 + 0.0568149i
\(129\) −23.9045 + 20.0583i −2.10468 + 1.76603i
\(130\) 0 0
\(131\) −19.4945 + 7.09542i −1.70324 + 0.619930i −0.996188 0.0872292i \(-0.972199\pi\)
−0.707055 + 0.707159i \(0.749977\pi\)
\(132\) 6.94884 0.604818
\(133\) 0.0731872 0.0710136i 0.00634613 0.00615766i
\(134\) −3.85689 −0.333185
\(135\) 0 0
\(136\) 1.38566 7.85847i 0.118819 0.673858i
\(137\) −4.57200 + 3.83636i −0.390612 + 0.327762i −0.816852 0.576848i \(-0.804283\pi\)
0.426240 + 0.904610i \(0.359838\pi\)
\(138\) −11.0380 9.26198i −0.939617 0.788432i
\(139\) −2.44517 13.8672i −0.207397 1.17620i −0.893624 0.448817i \(-0.851845\pi\)
0.686227 0.727387i \(-0.259266\pi\)
\(140\) 0 0
\(141\) 6.87373 11.9056i 0.578872 1.00264i
\(142\) 12.0928 + 4.40141i 1.01480 + 0.369358i
\(143\) −3.22910 1.17530i −0.270031 0.0982832i
\(144\) −3.67080 + 6.35802i −0.305900 + 0.529835i
\(145\) 0 0
\(146\) 0.330206 + 1.87269i 0.0273281 + 0.154985i
\(147\) −17.2430 14.4686i −1.42218 1.19335i
\(148\) 0.298092 0.250129i 0.0245030 0.0205605i
\(149\) 1.22145 6.92721i 0.100065 0.567499i −0.893012 0.450034i \(-0.851412\pi\)
0.993077 0.117465i \(-0.0374769\pi\)
\(150\) 0 0
\(151\) −14.0840 −1.14614 −0.573070 0.819507i \(-0.694248\pi\)
−0.573070 + 0.819507i \(0.694248\pi\)
\(152\) −4.19289 1.19149i −0.340088 0.0966429i
\(153\) 58.5838 4.73622
\(154\) −0.0475039 + 0.0172900i −0.00382797 + 0.00139327i
\(155\) 0 0
\(156\) 3.91765 3.28730i 0.313663 0.263195i
\(157\) −2.07466 1.74085i −0.165576 0.138935i 0.556235 0.831025i \(-0.312245\pi\)
−0.721811 + 0.692090i \(0.756690\pi\)
\(158\) −1.65165 9.36698i −0.131398 0.745197i
\(159\) −6.08141 10.5333i −0.482288 0.835346i
\(160\) 0 0
\(161\) 0.0985039 + 0.0358525i 0.00776319 + 0.00282557i
\(162\) −21.4949 7.82350i −1.68880 0.614672i
\(163\) 6.89810 11.9479i 0.540301 0.935829i −0.458585 0.888650i \(-0.651644\pi\)
0.998886 0.0471785i \(-0.0150229\pi\)
\(164\) −2.80141 4.85219i −0.218754 0.378892i
\(165\) 0 0
\(166\) 2.01343 + 1.68947i 0.156273 + 0.131128i
\(167\) −18.5877 + 15.5969i −1.43836 + 1.20692i −0.497798 + 0.867293i \(0.665858\pi\)
−0.940558 + 0.339632i \(0.889698\pi\)
\(168\) 0.0130644 0.0740919i 0.00100794 0.00571631i
\(169\) 9.83949 3.58128i 0.756884 0.275483i
\(170\) 0 0
\(171\) 3.26925 31.8339i 0.250006 2.43440i
\(172\) −9.70358 −0.739891
\(173\) −18.1956 + 6.62267i −1.38339 + 0.503512i −0.923204 0.384311i \(-0.874439\pi\)
−0.460184 + 0.887823i \(0.652217\pi\)
\(174\) 4.21749 23.9186i 0.319727 1.81326i
\(175\) 0 0
\(176\) 1.65528 + 1.38895i 0.124772 + 0.104696i
\(177\) −2.02897 11.5068i −0.152506 0.864907i
\(178\) −4.43758 7.68611i −0.332610 0.576098i
\(179\) −4.29621 + 7.44125i −0.321114 + 0.556185i −0.980718 0.195428i \(-0.937391\pi\)
0.659604 + 0.751613i \(0.270724\pi\)
\(180\) 0 0
\(181\) 3.94197 + 1.43476i 0.293005 + 0.106645i 0.484340 0.874880i \(-0.339060\pi\)
−0.191336 + 0.981525i \(0.561282\pi\)
\(182\) −0.0186026 + 0.0322206i −0.00137891 + 0.00238835i
\(183\) 18.5582 + 32.1438i 1.37186 + 2.37614i
\(184\) −0.778059 4.41259i −0.0573593 0.325301i
\(185\) 0 0
\(186\) 10.9868 9.21899i 0.805589 0.675969i
\(187\) 2.99416 16.9807i 0.218955 1.24175i
\(188\) 4.01711 1.46211i 0.292978 0.106635i
\(189\) 0.326640 0.0237596
\(190\) 0 0
\(191\) 18.8620 1.36481 0.682403 0.730976i \(-0.260935\pi\)
0.682403 + 0.730976i \(0.260935\pi\)
\(192\) −3.02190 + 1.09988i −0.218087 + 0.0793771i
\(193\) 3.08999 17.5242i 0.222422 1.26142i −0.645130 0.764073i \(-0.723197\pi\)
0.867552 0.497346i \(-0.165692\pi\)
\(194\) −8.54438 + 7.16959i −0.613451 + 0.514747i
\(195\) 0 0
\(196\) −1.21544 6.89312i −0.0868173 0.492365i
\(197\) 6.75642 + 11.7025i 0.481375 + 0.833766i 0.999772 0.0213742i \(-0.00680412\pi\)
−0.518396 + 0.855140i \(0.673471\pi\)
\(198\) −7.93194 + 13.7385i −0.563698 + 0.976354i
\(199\) −6.59301 2.39966i −0.467366 0.170107i 0.0975926 0.995226i \(-0.468886\pi\)
−0.564959 + 0.825119i \(0.691108\pi\)
\(200\) 0 0
\(201\) 6.20156 10.7414i 0.437425 0.757642i
\(202\) 9.32370 + 16.1491i 0.656013 + 1.13625i
\(203\) 0.0306821 + 0.174007i 0.00215346 + 0.0122129i
\(204\) 19.6578 + 16.4948i 1.37632 + 1.15487i
\(205\) 0 0
\(206\) −0.614003 + 3.48218i −0.0427796 + 0.242615i
\(207\) 30.9114 11.2508i 2.14849 0.781988i
\(208\) 1.59029 0.110267
\(209\) −9.06007 2.57460i −0.626698 0.178089i
\(210\) 0 0
\(211\) −6.68827 + 2.43433i −0.460440 + 0.167586i −0.561817 0.827262i \(-0.689897\pi\)
0.101377 + 0.994848i \(0.467675\pi\)
\(212\) 0.656766 3.72471i 0.0451069 0.255814i
\(213\) −31.7021 + 26.6013i −2.17219 + 1.82269i
\(214\) −4.28421 3.59488i −0.292862 0.245741i
\(215\) 0 0
\(216\) −6.98095 12.0914i −0.474994 0.822713i
\(217\) −0.0521696 + 0.0903603i −0.00354150 + 0.00613406i
\(218\) −8.85586 3.22327i −0.599795 0.218307i
\(219\) −5.74639 2.09151i −0.388305 0.141331i
\(220\) 0 0
\(221\) −6.34504 10.9899i −0.426813 0.739263i
\(222\) 0.217301 + 1.23237i 0.0145843 + 0.0827115i
\(223\) 3.34000 + 2.80259i 0.223663 + 0.187675i 0.747733 0.664000i \(-0.231142\pi\)
−0.524070 + 0.851675i \(0.675587\pi\)
\(224\) 0.0179217 0.0150381i 0.00119744 0.00100477i
\(225\) 0 0
\(226\) −5.35004 + 1.94725i −0.355879 + 0.129529i
\(227\) −9.44623 −0.626969 −0.313484 0.949593i \(-0.601496\pi\)
−0.313484 + 0.949593i \(0.601496\pi\)
\(228\) 10.0601 9.76136i 0.666249 0.646462i
\(229\) 22.8675 1.51112 0.755562 0.655077i \(-0.227364\pi\)
0.755562 + 0.655077i \(0.227364\pi\)
\(230\) 0 0
\(231\) 0.0282298 0.160099i 0.00185738 0.0105337i
\(232\) 5.78554 4.85465i 0.379840 0.318723i
\(233\) 8.10215 + 6.79851i 0.530790 + 0.445385i 0.868374 0.495910i \(-0.165165\pi\)
−0.337584 + 0.941295i \(0.609610\pi\)
\(234\) 2.02740 + 11.4979i 0.132535 + 0.751644i
\(235\) 0 0
\(236\) 1.81669 3.14660i 0.118256 0.204826i
\(237\) 28.7427 + 10.4615i 1.86704 + 0.679547i
\(238\) −0.175427 0.0638504i −0.0113713 0.00413880i
\(239\) −8.67636 + 15.0279i −0.561227 + 0.972074i 0.436163 + 0.899868i \(0.356337\pi\)
−0.997390 + 0.0722058i \(0.976996\pi\)
\(240\) 0 0
\(241\) −0.0833347 0.472614i −0.00536806 0.0304438i 0.982006 0.188849i \(-0.0604758\pi\)
−0.987374 + 0.158406i \(0.949365\pi\)
\(242\) −4.84973 4.06940i −0.311752 0.261591i
\(243\) 24.2641 20.3600i 1.55655 1.30610i
\(244\) −2.00421 + 11.3664i −0.128306 + 0.727661i
\(245\) 0 0
\(246\) 18.0178 1.14877
\(247\) −6.32590 + 2.83454i −0.402508 + 0.180358i
\(248\) 4.45987 0.283202
\(249\) −7.94260 + 2.89087i −0.503342 + 0.183202i
\(250\) 0 0
\(251\) 4.56913 3.83396i 0.288401 0.241997i −0.487096 0.873348i \(-0.661944\pi\)
0.775497 + 0.631351i \(0.217499\pi\)
\(252\) 0.131574 + 0.110404i 0.00828839 + 0.00695478i
\(253\) −1.68124 9.53480i −0.105699 0.599448i
\(254\) 4.33757 + 7.51289i 0.272163 + 0.471400i
\(255\) 0 0
\(256\) −0.939693 0.342020i −0.0587308 0.0213763i
\(257\) −12.7121 4.62683i −0.792959 0.288614i −0.0863936 0.996261i \(-0.527534\pi\)
−0.706566 + 0.707648i \(0.749756\pi\)
\(258\) 15.6026 27.0244i 0.971373 1.68247i
\(259\) −0.00455189 0.00788411i −0.000282841 0.000489895i
\(260\) 0 0
\(261\) 42.4752 + 35.6409i 2.62915 + 2.20612i
\(262\) 15.8921 13.3350i 0.981815 0.823841i
\(263\) 3.05915 17.3493i 0.188635 1.06980i −0.732560 0.680703i \(-0.761674\pi\)
0.921195 0.389101i \(-0.127214\pi\)
\(264\) −6.52977 + 2.37664i −0.401880 + 0.146272i
\(265\) 0 0
\(266\) −0.0444853 + 0.0917624i −0.00272757 + 0.00562632i
\(267\) 28.5410 1.74668
\(268\) 3.62429 1.31913i 0.221389 0.0805789i
\(269\) −0.447725 + 2.53918i −0.0272983 + 0.154816i −0.995410 0.0957028i \(-0.969490\pi\)
0.968112 + 0.250519i \(0.0806013\pi\)
\(270\) 0 0
\(271\) −8.49966 7.13206i −0.516318 0.433242i 0.347028 0.937855i \(-0.387191\pi\)
−0.863346 + 0.504613i \(0.831635\pi\)
\(272\) 1.38566 + 7.85847i 0.0840180 + 0.476490i
\(273\) −0.0598228 0.103616i −0.00362064 0.00627113i
\(274\) 2.98416 5.16871i 0.180280 0.312253i
\(275\) 0 0
\(276\) 13.5401 + 4.92820i 0.815019 + 0.296643i
\(277\) −1.47762 + 2.55932i −0.0887817 + 0.153774i −0.906996 0.421138i \(-0.861631\pi\)
0.818215 + 0.574913i \(0.194964\pi\)
\(278\) 7.04059 + 12.1947i 0.422266 + 0.731387i
\(279\) 5.68569 + 32.2452i 0.340394 + 1.93047i
\(280\) 0 0
\(281\) 10.6181 8.90966i 0.633424 0.531506i −0.268567 0.963261i \(-0.586550\pi\)
0.901991 + 0.431755i \(0.142106\pi\)
\(282\) −2.38722 + 13.5386i −0.142157 + 0.806212i
\(283\) −4.36045 + 1.58707i −0.259202 + 0.0943418i −0.468353 0.883542i \(-0.655152\pi\)
0.209151 + 0.977883i \(0.432930\pi\)
\(284\) −12.8689 −0.763627
\(285\) 0 0
\(286\) 3.43634 0.203195
\(287\) −0.123174 + 0.0448316i −0.00727071 + 0.00264632i
\(288\) 1.27486 7.23007i 0.0751217 0.426036i
\(289\) 35.7556 30.0025i 2.10327 1.76485i
\(290\) 0 0
\(291\) −6.22861 35.3242i −0.365128 2.07074i
\(292\) −0.950791 1.64682i −0.0556409 0.0963728i
\(293\) 5.93313 10.2765i 0.346617 0.600358i −0.639029 0.769182i \(-0.720664\pi\)
0.985646 + 0.168824i \(0.0539971\pi\)
\(294\) 21.1516 + 7.69857i 1.23359 + 0.448989i
\(295\) 0 0
\(296\) −0.194566 + 0.336998i −0.0113089 + 0.0195876i
\(297\) −15.0846 26.1272i −0.875295 1.51606i
\(298\) 1.22145 + 6.92721i 0.0707569 + 0.401282i
\(299\) −5.45851 4.58023i −0.315674 0.264882i
\(300\) 0 0
\(301\) −0.0394210 + 0.223567i −0.00227219 + 0.0128862i
\(302\) 13.2346 4.81701i 0.761567 0.277188i
\(303\) −59.9670 −3.44501
\(304\) 4.34754 0.314416i 0.249349 0.0180330i
\(305\) 0 0
\(306\) −55.0508 + 20.0369i −3.14704 + 1.14543i
\(307\) −1.81328 + 10.2836i −0.103489 + 0.586918i 0.888323 + 0.459218i \(0.151870\pi\)
−0.991813 + 0.127699i \(0.959241\pi\)
\(308\) 0.0387255 0.0324946i 0.00220659 0.00185155i
\(309\) −8.71060 7.30906i −0.495529 0.415798i
\(310\) 0 0
\(311\) 7.33307 + 12.7012i 0.415820 + 0.720222i 0.995514 0.0946125i \(-0.0301612\pi\)
−0.579694 + 0.814834i \(0.696828\pi\)
\(312\) −2.55706 + 4.42897i −0.144765 + 0.250741i
\(313\) −20.1826 7.34588i −1.14079 0.415214i −0.298592 0.954381i \(-0.596517\pi\)
−0.842199 + 0.539167i \(0.818739\pi\)
\(314\) 2.54495 + 0.926285i 0.143620 + 0.0522733i
\(315\) 0 0
\(316\) 4.75574 + 8.23718i 0.267531 + 0.463378i
\(317\) −2.05192 11.6370i −0.115247 0.653599i −0.986628 0.162991i \(-0.947886\pi\)
0.871381 0.490608i \(-0.163225\pi\)
\(318\) 9.31727 + 7.81812i 0.522486 + 0.438418i
\(319\) 12.5015 10.4900i 0.699950 0.587327i
\(320\) 0 0
\(321\) 16.9004 6.15123i 0.943287 0.343328i
\(322\) −0.104826 −0.00584170
\(323\) −19.5189 28.7898i −1.08606 1.60191i
\(324\) 22.8744 1.27080
\(325\) 0 0
\(326\) −2.39569 + 13.5866i −0.132685 + 0.752493i
\(327\) 23.2163 19.4808i 1.28386 1.07729i
\(328\) 4.29201 + 3.60143i 0.236987 + 0.198856i
\(329\) −0.0173669 0.0984928i −0.000957471 0.00543009i
\(330\) 0 0
\(331\) −8.88073 + 15.3819i −0.488129 + 0.845464i −0.999907 0.0136535i \(-0.995654\pi\)
0.511778 + 0.859118i \(0.328987\pi\)
\(332\) −2.46984 0.898948i −0.135550 0.0493362i
\(333\) −2.68456 0.977102i −0.147113 0.0535448i
\(334\) 12.1322 21.0137i 0.663847 1.14982i
\(335\) 0 0
\(336\) 0.0130644 + 0.0740919i 0.000712721 + 0.00404204i
\(337\) −1.82756 1.53351i −0.0995537 0.0835354i 0.591652 0.806193i \(-0.298476\pi\)
−0.691206 + 0.722658i \(0.742920\pi\)
\(338\) −8.02122 + 6.73060i −0.436297 + 0.366097i
\(339\) 3.17933 18.0309i 0.172677 0.979302i
\(340\) 0 0
\(341\) 9.63696 0.521871
\(342\) 7.81574 + 31.0322i 0.422627 + 1.67803i
\(343\) −0.327519 −0.0176843
\(344\) 9.11838 3.31882i 0.491630 0.178939i
\(345\) 0 0
\(346\) 14.8332 12.4465i 0.797438 0.669130i
\(347\) −11.7982 9.89984i −0.633359 0.531451i 0.268612 0.963249i \(-0.413435\pi\)
−0.901971 + 0.431797i \(0.857880\pi\)
\(348\) 4.21749 + 23.9186i 0.226081 + 1.28217i
\(349\) −4.92259 8.52618i −0.263500 0.456396i 0.703669 0.710528i \(-0.251544\pi\)
−0.967170 + 0.254132i \(0.918210\pi\)
\(350\) 0 0
\(351\) −20.8645 7.59406i −1.11366 0.405341i
\(352\) −2.03050 0.739043i −0.108226 0.0393911i
\(353\) −4.25682 + 7.37302i −0.226567 + 0.392426i −0.956789 0.290785i \(-0.906084\pi\)
0.730221 + 0.683211i \(0.239417\pi\)
\(354\) 5.84218 + 10.1189i 0.310508 + 0.537816i
\(355\) 0 0
\(356\) 6.79876 + 5.70484i 0.360334 + 0.302356i
\(357\) 0.459896 0.385899i 0.0243403 0.0204239i
\(358\) 1.49206 8.46188i 0.0788577 0.447224i
\(359\) −29.6177 + 10.7800i −1.56317 + 0.568946i −0.971459 0.237208i \(-0.923768\pi\)
−0.591706 + 0.806154i \(0.701545\pi\)
\(360\) 0 0
\(361\) −16.7333 + 8.99976i −0.880702 + 0.473672i
\(362\) −4.19496 −0.220482
\(363\) 19.1312 6.96320i 1.00413 0.365473i
\(364\) 0.00646060 0.0366399i 0.000338628 0.00192045i
\(365\) 0 0
\(366\) −28.4329 23.8580i −1.48621 1.24708i
\(367\) −1.21117 6.86889i −0.0632226 0.358553i −0.999964 0.00853004i \(-0.997285\pi\)
0.936741 0.350023i \(-0.113826\pi\)
\(368\) 2.24033 + 3.88037i 0.116785 + 0.202278i
\(369\) −20.5669 + 35.6229i −1.07067 + 1.85445i
\(370\) 0 0
\(371\) −0.0831479 0.0302634i −0.00431683 0.00157120i
\(372\) −7.17110 + 12.4207i −0.371804 + 0.643984i
\(373\) 6.02737 + 10.4397i 0.312085 + 0.540548i 0.978814 0.204753i \(-0.0656392\pi\)
−0.666728 + 0.745301i \(0.732306\pi\)
\(374\) 2.99416 + 16.9807i 0.154824 + 0.878052i
\(375\) 0 0
\(376\) −3.27478 + 2.74787i −0.168884 + 0.141710i
\(377\) 2.08563 11.8282i 0.107416 0.609184i
\(378\) −0.306941 + 0.111718i −0.0157874 + 0.00574613i
\(379\) −6.82285 −0.350466 −0.175233 0.984527i \(-0.556068\pi\)
−0.175233 + 0.984527i \(0.556068\pi\)
\(380\) 0 0
\(381\) −27.8978 −1.42925
\(382\) −17.7245 + 6.45118i −0.906863 + 0.330071i
\(383\) −1.88011 + 10.6626i −0.0960690 + 0.544834i 0.898346 + 0.439290i \(0.144770\pi\)
−0.994415 + 0.105545i \(0.966341\pi\)
\(384\) 2.46347 2.06710i 0.125714 0.105486i
\(385\) 0 0
\(386\) 3.08999 + 17.5242i 0.157276 + 0.891958i
\(387\) 35.6199 + 61.6955i 1.81066 + 3.13616i
\(388\) 5.57695 9.65956i 0.283127 0.490390i
\(389\) 7.07236 + 2.57413i 0.358583 + 0.130513i 0.515028 0.857173i \(-0.327781\pi\)
−0.156446 + 0.987687i \(0.550004\pi\)
\(390\) 0 0
\(391\) 17.8772 30.9642i 0.904088 1.56593i
\(392\) 3.49973 + 6.06170i 0.176763 + 0.306162i
\(393\) 11.5849 + 65.7010i 0.584379 + 3.31418i
\(394\) −10.3514 8.68589i −0.521498 0.437589i
\(395\) 0 0
\(396\) 2.75473 15.6229i 0.138431 0.785078i
\(397\) −4.65031 + 1.69258i −0.233393 + 0.0849479i −0.456069 0.889944i \(-0.650743\pi\)
0.222676 + 0.974892i \(0.428521\pi\)
\(398\) 7.01614 0.351687
\(399\) −0.184029 0.271438i −0.00921299 0.0135889i
\(400\) 0 0
\(401\) −18.6833 + 6.80015i −0.932998 + 0.339583i −0.763397 0.645929i \(-0.776470\pi\)
−0.169601 + 0.985513i \(0.554248\pi\)
\(402\) −2.15378 + 12.2147i −0.107421 + 0.609214i
\(403\) 5.43317 4.55897i 0.270646 0.227099i
\(404\) −14.2847 11.9863i −0.710692 0.596342i
\(405\) 0 0
\(406\) −0.0883457 0.153019i −0.00438452 0.00759422i
\(407\) −0.420421 + 0.728191i −0.0208395 + 0.0360951i
\(408\) −24.1138 8.77672i −1.19381 0.434512i
\(409\) −12.1132 4.40884i −0.598958 0.218003i 0.0247068 0.999695i \(-0.492135\pi\)
−0.623665 + 0.781692i \(0.714357\pi\)
\(410\) 0 0
\(411\) 9.59657 + 16.6217i 0.473364 + 0.819890i
\(412\) −0.614003 3.48218i −0.0302497 0.171555i
\(413\) −0.0651163 0.0546391i −0.00320416 0.00268861i
\(414\) −25.1992 + 21.1447i −1.23848 + 1.03920i
\(415\) 0 0
\(416\) −1.49439 + 0.543913i −0.0732684 + 0.0266675i
\(417\) −45.2828 −2.21751
\(418\) 9.39425 0.679394i 0.459488 0.0332303i
\(419\) 4.48425 0.219070 0.109535 0.993983i \(-0.465064\pi\)
0.109535 + 0.993983i \(0.465064\pi\)
\(420\) 0 0
\(421\) −3.74698 + 21.2502i −0.182616 + 1.03567i 0.746363 + 0.665539i \(0.231798\pi\)
−0.928980 + 0.370131i \(0.879313\pi\)
\(422\) 5.45233 4.57505i 0.265415 0.222710i
\(423\) −24.0421 20.1738i −1.16897 0.980882i
\(424\) 0.656766 + 3.72471i 0.0318954 + 0.180888i
\(425\) 0 0
\(426\) 20.6921 35.8398i 1.00254 1.73644i
\(427\) 0.253737 + 0.0923527i 0.0122792 + 0.00446926i
\(428\) 5.25536 + 1.91279i 0.254027 + 0.0924584i
\(429\) −5.52535 + 9.57018i −0.266766 + 0.462053i
\(430\) 0 0
\(431\) 2.06827 + 11.7298i 0.0996252 + 0.565003i 0.993232 + 0.116151i \(0.0370557\pi\)
−0.893606 + 0.448852i \(0.851833\pi\)
\(432\) 10.6954 + 8.97454i 0.514585 + 0.431788i
\(433\) −16.9528 + 14.2251i −0.814701 + 0.683615i −0.951725 0.306952i \(-0.900691\pi\)
0.137024 + 0.990568i \(0.456246\pi\)
\(434\) 0.0181183 0.102754i 0.000869706 0.00493235i
\(435\) 0 0
\(436\) 9.42421 0.451338
\(437\) −15.8280 11.4422i −0.757156 0.547356i
\(438\) 6.11518 0.292195
\(439\) 6.47904 2.35818i 0.309228 0.112550i −0.182745 0.983160i \(-0.558498\pi\)
0.491973 + 0.870611i \(0.336276\pi\)
\(440\) 0 0
\(441\) −39.3649 + 33.0311i −1.87452 + 1.57291i
\(442\) 9.72116 + 8.15702i 0.462389 + 0.387990i
\(443\) 0.268390 + 1.52212i 0.0127516 + 0.0723180i 0.990520 0.137372i \(-0.0438656\pi\)
−0.977768 + 0.209690i \(0.932754\pi\)
\(444\) −0.625692 1.08373i −0.0296940 0.0514316i
\(445\) 0 0
\(446\) −4.09711 1.49123i −0.194004 0.0706117i
\(447\) −21.2562 7.73664i −1.00539 0.365931i
\(448\) −0.0116976 + 0.0202608i −0.000552658 + 0.000957231i
\(449\) −2.95993 5.12674i −0.139688 0.241946i 0.787691 0.616071i \(-0.211276\pi\)
−0.927378 + 0.374125i \(0.877943\pi\)
\(450\) 0 0
\(451\) 9.27425 + 7.78202i 0.436708 + 0.366441i
\(452\) 4.36139 3.65964i 0.205143 0.172135i
\(453\) −7.86485 + 44.6038i −0.369523 + 2.09567i
\(454\) 8.87656 3.23080i 0.416597 0.151629i
\(455\) 0 0
\(456\) −6.11485 + 12.6135i −0.286354 + 0.590679i
\(457\) −29.5382 −1.38174 −0.690870 0.722979i \(-0.742772\pi\)
−0.690870 + 0.722979i \(0.742772\pi\)
\(458\) −21.4884 + 7.82113i −1.00409 + 0.365458i
\(459\) 19.3465 109.719i 0.903015 5.12125i
\(460\) 0 0
\(461\) 23.3287 + 19.5751i 1.08652 + 0.911702i 0.996446 0.0842331i \(-0.0268440\pi\)
0.0900776 + 0.995935i \(0.471288\pi\)
\(462\) 0.0282298 + 0.160099i 0.00131337 + 0.00744848i
\(463\) 19.4309 + 33.6554i 0.903033 + 1.56410i 0.823536 + 0.567263i \(0.191998\pi\)
0.0794963 + 0.996835i \(0.474669\pi\)
\(464\) −3.77625 + 6.54065i −0.175308 + 0.303642i
\(465\) 0 0
\(466\) −9.93876 3.61741i −0.460404 0.167573i
\(467\) 14.3141 24.7927i 0.662377 1.14727i −0.317612 0.948221i \(-0.602881\pi\)
0.979989 0.199050i \(-0.0637857\pi\)
\(468\) −5.83766 10.1111i −0.269846 0.467387i
\(469\) −0.0156687 0.0888615i −0.000723513 0.00410324i
\(470\) 0 0
\(471\) −6.67177 + 5.59828i −0.307419 + 0.257955i
\(472\) −0.630930 + 3.57818i −0.0290409 + 0.164699i
\(473\) 19.7032 7.17136i 0.905952 0.329740i
\(474\) −30.5874 −1.40492
\(475\) 0 0
\(476\) 0.186686 0.00855674
\(477\) −26.0926 + 9.49693i −1.19470 + 0.434835i
\(478\) 3.01327 17.0891i 0.137824 0.781637i
\(479\) −12.7889 + 10.7312i −0.584340 + 0.490320i −0.886369 0.462979i \(-0.846781\pi\)
0.302029 + 0.953299i \(0.402336\pi\)
\(480\) 0 0
\(481\) 0.107459 + 0.609433i 0.00489973 + 0.0277877i
\(482\) 0.239953 + 0.415610i 0.0109295 + 0.0189305i
\(483\) 0.168551 0.291939i 0.00766934 0.0132837i
\(484\) 5.94907 + 2.16529i 0.270412 + 0.0984221i
\(485\) 0 0
\(486\) −15.8373 + 27.4310i −0.718394 + 1.24430i
\(487\) 9.69165 + 16.7864i 0.439171 + 0.760666i 0.997626 0.0688690i \(-0.0219390\pi\)
−0.558455 + 0.829535i \(0.688606\pi\)
\(488\) −2.00421 11.3664i −0.0907263 0.514534i
\(489\) −33.9866 28.5181i −1.53693 1.28963i
\(490\) 0 0
\(491\) 6.30923 35.7814i 0.284731 1.61479i −0.421511 0.906823i \(-0.638500\pi\)
0.706243 0.707970i \(-0.250389\pi\)
\(492\) −16.9312 + 6.16244i −0.763316 + 0.277824i
\(493\) 60.2666 2.71427
\(494\) 4.97493 4.82719i 0.223833 0.217185i
\(495\) 0 0
\(496\) −4.19091 + 1.52536i −0.188177 + 0.0684909i
\(497\) −0.0522800 + 0.296495i −0.00234508 + 0.0132996i
\(498\) 6.47487 5.43306i 0.290146 0.243461i
\(499\) −5.94585 4.98916i −0.266173 0.223346i 0.499926 0.866068i \(-0.333360\pi\)
−0.766099 + 0.642722i \(0.777805\pi\)
\(500\) 0 0
\(501\) 39.0153 + 67.5765i 1.74308 + 3.01909i
\(502\) −2.98229 + 5.16548i −0.133106 + 0.230546i
\(503\) 0.597098 + 0.217326i 0.0266233 + 0.00969008i 0.355297 0.934753i \(-0.384380\pi\)
−0.328674 + 0.944443i \(0.606602\pi\)
\(504\) −0.161399 0.0587446i −0.00718930 0.00261669i
\(505\) 0 0
\(506\) 4.84095 + 8.38477i 0.215206 + 0.372748i
\(507\) −5.84724 33.1613i −0.259685 1.47275i
\(508\) −6.64554 5.57627i −0.294848 0.247407i
\(509\) 20.1192 16.8820i 0.891767 0.748282i −0.0767966 0.997047i \(-0.524469\pi\)
0.968564 + 0.248765i \(0.0800248\pi\)
\(510\) 0 0
\(511\) −0.0418048 + 0.0152157i −0.00184934 + 0.000673103i
\(512\) 1.00000 0.0441942
\(513\) −58.5408 16.6355i −2.58464 0.734476i
\(514\) 13.5279 0.596692
\(515\) 0 0
\(516\) −5.41871 + 30.7311i −0.238546 + 1.35286i
\(517\) −7.07620 + 5.93764i −0.311211 + 0.261137i
\(518\) 0.00697390 + 0.00585180i 0.000306416 + 0.000257113i
\(519\) 10.8130 + 61.3235i 0.474637 + 2.69180i
\(520\) 0 0
\(521\) −20.1453 + 34.8927i −0.882583 + 1.52868i −0.0341245 + 0.999418i \(0.510864\pi\)
−0.848459 + 0.529262i \(0.822469\pi\)
\(522\) −52.1035 18.9641i −2.28051 0.830038i
\(523\) 15.7402 + 5.72897i 0.688271 + 0.250510i 0.662395 0.749155i \(-0.269540\pi\)
0.0258764 + 0.999665i \(0.491762\pi\)
\(524\) −10.3728 + 17.9662i −0.453138 + 0.784859i
\(525\) 0 0
\(526\) 3.05915 + 17.3493i 0.133385 + 0.756466i
\(527\) 27.2623 + 22.8758i 1.18756 + 0.996485i
\(528\) 5.32312 4.46663i 0.231659 0.194385i
\(529\) −0.507688 + 2.87924i −0.0220734 + 0.125184i
\(530\) 0 0
\(531\) −26.6748 −1.15759
\(532\) 0.0104179 0.101443i 0.000451675 0.00439813i
\(533\) 8.91014 0.385941
\(534\) −26.8198 + 9.76161i −1.16061 + 0.422426i
\(535\) 0 0
\(536\) −2.95455 + 2.47916i −0.127617 + 0.107083i
\(537\) 21.1672 + 17.7614i 0.913432 + 0.766461i
\(538\) −0.447725 2.53918i −0.0193028 0.109472i
\(539\) 7.56227 + 13.0982i 0.325730 + 0.564181i
\(540\) 0 0
\(541\) −28.7784 10.4745i −1.23728 0.450334i −0.361196 0.932490i \(-0.617632\pi\)
−0.876085 + 0.482156i \(0.839854\pi\)
\(542\) 10.4264 + 3.79489i 0.447851 + 0.163005i
\(543\) 6.74515 11.6830i 0.289462 0.501363i
\(544\) −3.98985 6.91062i −0.171063 0.296291i
\(545\) 0 0
\(546\) 0.0916539 + 0.0769067i 0.00392242 + 0.00329130i
\(547\) 0.00614318 0.00515474i 0.000262663 0.000220401i −0.642656 0.766155i \(-0.722168\pi\)
0.642919 + 0.765934i \(0.277723\pi\)
\(548\) −1.03639 + 5.87764i −0.0442723 + 0.251081i
\(549\) 79.6251 28.9812i 3.39831 1.23689i
\(550\) 0 0
\(551\) 3.36316 32.7483i 0.143275 1.39512i
\(552\) −14.4091 −0.613291
\(553\) 0.209102 0.0761070i 0.00889194 0.00323640i
\(554\) 0.513173 2.91035i 0.0218026 0.123649i
\(555\) 0 0
\(556\) −10.7868 9.05120i −0.457462 0.383856i
\(557\) −1.16220 6.59116i −0.0492440 0.279276i 0.950236 0.311532i \(-0.100842\pi\)
−0.999480 + 0.0322555i \(0.989731\pi\)
\(558\) −16.3713 28.3559i −0.693052 1.20040i
\(559\) 7.71578 13.3641i 0.326343 0.565242i
\(560\) 0 0
\(561\) −52.1056 18.9649i −2.19990 0.800698i
\(562\) −6.93049 + 12.0040i −0.292345 + 0.506356i
\(563\) 3.30354 + 5.72191i 0.139228 + 0.241150i 0.927205 0.374555i \(-0.122205\pi\)
−0.787977 + 0.615705i \(0.788871\pi\)
\(564\) −2.38722 13.5386i −0.100520 0.570078i
\(565\) 0 0
\(566\) 3.55467 2.98272i 0.149414 0.125373i
\(567\) 0.0929276 0.527019i 0.00390259 0.0221327i
\(568\) 12.0928 4.40141i 0.507402 0.184679i
\(569\) −18.2452 −0.764879 −0.382440 0.923980i \(-0.624916\pi\)
−0.382440 + 0.923980i \(0.624916\pi\)
\(570\) 0 0
\(571\) −4.61851 −0.193279 −0.0966393 0.995319i \(-0.530809\pi\)
−0.0966393 + 0.995319i \(0.530809\pi\)
\(572\) −3.22910 + 1.17530i −0.135015 + 0.0491416i
\(573\) 10.5330 59.7356i 0.440022 2.49549i
\(574\) 0.100412 0.0842558i 0.00419112 0.00351677i
\(575\) 0 0
\(576\) 1.27486 + 7.23007i 0.0531190 + 0.301253i
\(577\) −20.1637 34.9245i −0.839424 1.45393i −0.890377 0.455224i \(-0.849559\pi\)
0.0509529 0.998701i \(-0.483774\pi\)
\(578\) −23.3378 + 40.4223i −0.970725 + 1.68135i
\(579\) −53.7733 19.5719i −2.23474 0.813379i
\(580\) 0 0
\(581\) −0.0307453 + 0.0532524i −0.00127553 + 0.00220928i
\(582\) 17.9346 + 31.0636i 0.743412 + 1.28763i
\(583\) 1.41915 + 8.04841i 0.0587752 + 0.333331i
\(584\) 1.45670 + 1.22231i 0.0602785 + 0.0505797i
\(585\) 0 0
\(586\) −2.06055 + 11.6860i −0.0851207 + 0.482743i
\(587\) 14.3315 5.21623i 0.591523 0.215297i −0.0288761 0.999583i \(-0.509193\pi\)
0.620399 + 0.784286i \(0.286971\pi\)
\(588\) −22.5091 −0.928260
\(589\) 13.9518 13.5375i 0.574876 0.557803i
\(590\) 0 0
\(591\) 40.8344 14.8625i 1.67970 0.611363i
\(592\) 0.0675720 0.383220i 0.00277719 0.0157502i
\(593\) 30.6860 25.7487i 1.26012 1.05737i 0.264456 0.964398i \(-0.414808\pi\)
0.995669 0.0929726i \(-0.0296369\pi\)
\(594\) 23.1109 + 19.3923i 0.948251 + 0.795677i
\(595\) 0 0
\(596\) −3.51704 6.09168i −0.144063 0.249525i
\(597\) −11.2814 + 19.5399i −0.461716 + 0.799716i
\(598\) 6.69585 + 2.43709i 0.273814 + 0.0996600i
\(599\) 25.5138 + 9.28628i 1.04247 + 0.379427i 0.805815 0.592167i \(-0.201728\pi\)
0.236652 + 0.971594i \(0.423950\pi\)
\(600\) 0 0
\(601\) 12.9663 + 22.4583i 0.528907 + 0.916094i 0.999432 + 0.0337070i \(0.0107313\pi\)
−0.470525 + 0.882387i \(0.655935\pi\)
\(602\) −0.0394210 0.223567i −0.00160668 0.00911193i
\(603\) −21.6911 18.2010i −0.883332 0.741203i
\(604\) −10.7890 + 9.05302i −0.438997 + 0.368362i
\(605\) 0 0
\(606\) 56.3506 20.5099i 2.28908 0.833159i
\(607\) 15.2583 0.619316 0.309658 0.950848i \(-0.399785\pi\)
0.309658 + 0.950848i \(0.399785\pi\)
\(608\) −3.97782 + 1.78240i −0.161322 + 0.0722859i
\(609\) 0.568211 0.0230251
\(610\) 0 0
\(611\) −1.18053 + 6.69510i −0.0477590 + 0.270855i
\(612\) 44.8778 37.6570i 1.81408 1.52219i
\(613\) 3.61626 + 3.03440i 0.146059 + 0.122558i 0.712890 0.701276i \(-0.247386\pi\)
−0.566830 + 0.823835i \(0.691831\pi\)
\(614\) −1.81328 10.2836i −0.0731781 0.415013i
\(615\) 0 0
\(616\) −0.0252763 + 0.0437798i −0.00101841 + 0.00176394i
\(617\) 28.4553 + 10.3569i 1.14557 + 0.416953i 0.843922 0.536467i \(-0.180241\pi\)
0.301647 + 0.953420i \(0.402463\pi\)
\(618\) 10.6851 + 3.88907i 0.429819 + 0.156441i
\(619\) 2.84795 4.93279i 0.114469 0.198266i −0.803099 0.595846i \(-0.796817\pi\)
0.917567 + 0.397581i \(0.130150\pi\)
\(620\) 0 0
\(621\) −10.8632 61.6082i −0.435925 2.47225i
\(622\) −11.2349 9.42721i −0.450479 0.377997i
\(623\) 0.159058 0.133465i 0.00637252 0.00534718i
\(624\) 0.888059 5.03643i 0.0355508 0.201619i
\(625\) 0 0
\(626\) 21.4779 0.858430
\(627\) −13.2131 + 27.2554i −0.527679 + 1.08847i
\(628\) −2.70828 −0.108072
\(629\) −2.91789 + 1.06203i −0.116344 + 0.0423457i
\(630\) 0 0
\(631\) −32.4485 + 27.2275i −1.29175 + 1.08391i −0.300246 + 0.953862i \(0.597069\pi\)
−0.991508 + 0.130048i \(0.958487\pi\)
\(632\) −7.28621 6.11386i −0.289830 0.243196i
\(633\) 3.97459 + 22.5410i 0.157976 + 0.895925i
\(634\) 5.90826 + 10.2334i 0.234647 + 0.406420i
\(635\) 0 0
\(636\) −11.4293 4.15993i −0.453202 0.164952i
\(637\) 10.4599 + 3.80709i 0.414436 + 0.150842i
\(638\) −8.15977 + 14.1331i −0.323049 + 0.559537i
\(639\) 47.2391 + 81.8206i 1.86875 + 3.23677i
\(640\) 0 0
\(641\) −20.8636 17.5066i −0.824062 0.691470i 0.129858 0.991533i \(-0.458548\pi\)
−0.953920 + 0.300063i \(0.902992\pi\)
\(642\) −13.7773 + 11.5605i −0.543747 + 0.456258i
\(643\) 0.608700 3.45211i 0.0240048 0.136138i −0.970450 0.241302i \(-0.922426\pi\)
0.994455 + 0.105164i \(0.0335367\pi\)
\(644\) 0.0985039 0.0358525i 0.00388160 0.00141279i
\(645\) 0 0
\(646\) 28.1884 + 20.3777i 1.10906 + 0.801750i
\(647\) −44.9855 −1.76856 −0.884280 0.466956i \(-0.845351\pi\)
−0.884280 + 0.466956i \(0.845351\pi\)
\(648\) −21.4949 + 7.82350i −0.844399 + 0.307336i
\(649\) −1.36332 + 7.73179i −0.0535151 + 0.303499i
\(650\) 0 0
\(651\) 0.257037 + 0.215679i 0.0100741 + 0.00845314i
\(652\) −2.39569 13.5866i −0.0938223 0.532093i
\(653\) 7.96033 + 13.7877i 0.311512 + 0.539555i 0.978690 0.205344i \(-0.0658313\pi\)
−0.667178 + 0.744898i \(0.732498\pi\)
\(654\) −15.1534 + 26.2464i −0.592543 + 1.02632i
\(655\) 0 0
\(656\) −5.26493 1.91628i −0.205561 0.0748181i
\(657\) −6.98034 + 12.0903i −0.272329 + 0.471687i
\(658\) 0.0500061 + 0.0866132i 0.00194944 + 0.00337653i
\(659\) 3.30453 + 18.7409i 0.128726 + 0.730042i 0.979025 + 0.203741i \(0.0653102\pi\)
−0.850299 + 0.526301i \(0.823579\pi\)
\(660\) 0 0
\(661\) 17.6520 14.8118i 0.686583 0.576111i −0.231339 0.972873i \(-0.574311\pi\)
0.917922 + 0.396762i \(0.129866\pi\)
\(662\) 3.08425 17.4916i 0.119873 0.679831i
\(663\) −38.3481 + 13.9576i −1.48932 + 0.542067i
\(664\) 2.62835 0.102000
\(665\) 0 0
\(666\) 2.85685 0.110701
\(667\) 31.7994 11.5740i 1.23128 0.448148i
\(668\) −4.21348 + 23.8958i −0.163025 + 0.924558i
\(669\) 10.7409 9.01268i 0.415267 0.348450i
\(670\) 0 0
\(671\) −4.33073 24.5608i −0.167186 0.948158i
\(672\) −0.0376174 0.0651553i −0.00145112 0.00251342i
\(673\) 5.68840 9.85260i 0.219272 0.379790i −0.735314 0.677727i \(-0.762965\pi\)
0.954586 + 0.297937i \(0.0962985\pi\)
\(674\) 2.24184 + 0.815962i 0.0863523 + 0.0314297i
\(675\) 0 0
\(676\) 5.23548 9.06812i 0.201365 0.348774i
\(677\) 20.8875 + 36.1782i 0.802771 + 1.39044i 0.917786 + 0.397076i \(0.129975\pi\)
−0.115015 + 0.993364i \(0.536692\pi\)
\(678\) 3.17933 + 18.0309i 0.122101 + 0.692471i
\(679\) −0.199897 0.167733i −0.00767134 0.00643701i
\(680\) 0 0
\(681\) −5.27501 + 29.9160i −0.202139 + 1.14639i
\(682\) −9.05578 + 3.29603i −0.346764 + 0.126212i
\(683\) −9.65205 −0.369325 −0.184663 0.982802i \(-0.559119\pi\)
−0.184663 + 0.982802i \(0.559119\pi\)
\(684\) −17.9580 26.4876i −0.686643 1.01278i
\(685\) 0 0
\(686\) 0.307767 0.112018i 0.0117506 0.00427687i
\(687\) 12.7697 72.4208i 0.487196 2.76303i
\(688\) −7.43337 + 6.23734i −0.283395 + 0.237796i
\(689\) 4.60757 + 3.86621i 0.175535 + 0.147291i
\(690\) 0 0
\(691\) 3.58223 + 6.20461i 0.136275 + 0.236034i 0.926084 0.377318i \(-0.123154\pi\)
−0.789809 + 0.613353i \(0.789820\pi\)
\(692\) −9.68169 + 16.7692i −0.368043 + 0.637469i
\(693\) −0.348755 0.126936i −0.0132481 0.00482191i
\(694\) 14.4726 + 5.26759i 0.549372 + 0.199955i
\(695\) 0 0
\(696\) −12.1438 21.0337i −0.460309 0.797279i
\(697\) 7.76361 + 44.0296i 0.294068 + 1.66774i
\(698\) 7.54185 + 6.32836i 0.285463 + 0.239532i
\(699\) 26.0552 21.8629i 0.985498 0.826931i
\(700\) 0 0
\(701\) −5.58820 + 2.03394i −0.211063 + 0.0768208i −0.445388 0.895338i \(-0.646934\pi\)
0.234325 + 0.972158i \(0.424712\pi\)
\(702\) 22.2035 0.838019
\(703\) 0.414263 + 1.64482i 0.0156242 + 0.0620356i
\(704\) 2.16082 0.0814389
\(705\) 0 0
\(706\) 1.47838 8.38429i 0.0556394 0.315547i
\(707\) −0.334193 + 0.280421i −0.0125686 + 0.0105463i
\(708\) −8.95073 7.51056i −0.336389 0.282264i
\(709\) 6.60131 + 37.4379i 0.247918 + 1.40601i 0.813618 + 0.581400i \(0.197495\pi\)
−0.565701 + 0.824611i \(0.691394\pi\)
\(710\) 0 0
\(711\) 34.9148 60.4742i 1.30941 2.26796i
\(712\) −8.33992 3.03548i −0.312552 0.113759i
\(713\) 18.7780 + 6.83465i 0.703243 + 0.255959i
\(714\) −0.300176 + 0.519920i −0.0112338 + 0.0194575i
\(715\) 0 0
\(716\) 1.49206 + 8.46188i 0.0557608 + 0.316235i
\(717\) 42.7480 + 35.8698i 1.59645 + 1.33958i
\(718\) 24.1446 20.2597i 0.901069 0.756087i
\(719\) 1.48425 8.41760i 0.0553532 0.313923i −0.944542 0.328390i \(-0.893494\pi\)
0.999895 + 0.0144667i \(0.00460506\pi\)
\(720\) 0 0
\(721\) −0.0827228 −0.00308076
\(722\) 12.6461 14.1801i 0.470639 0.527730i
\(723\) −1.54330 −0.0573958
\(724\) 3.94197 1.43476i 0.146502 0.0533225i
\(725\) 0 0
\(726\) −15.5959 + 13.0865i −0.578819 + 0.485687i
\(727\) −6.42127 5.38809i −0.238152 0.199833i 0.515899 0.856650i \(-0.327458\pi\)
−0.754050 + 0.656817i \(0.771903\pi\)
\(728\) 0.00646060 + 0.0366399i 0.000239446 + 0.00135796i
\(729\) −16.6186 28.7842i −0.615503 1.06608i
\(730\) 0 0
\(731\) 72.7620 + 26.4832i 2.69120 + 0.979516i
\(732\) 34.8781 + 12.6946i 1.28913 + 0.469205i
\(733\) −5.96195 + 10.3264i −0.220210 + 0.381414i −0.954872 0.297019i \(-0.904007\pi\)
0.734662 + 0.678433i \(0.237341\pi\)
\(734\) 3.48743 + 6.04040i 0.128723 + 0.222955i
\(735\) 0 0
\(736\) −3.43239 2.88011i −0.126519 0.106162i
\(737\) −6.38424 + 5.35701i −0.235166 + 0.197328i
\(738\) 7.14280 40.5088i 0.262930 1.49115i
\(739\) −23.9241 + 8.70767i −0.880063 + 0.320317i −0.742235 0.670140i \(-0.766234\pi\)
−0.137828 + 0.990456i \(0.544012\pi\)
\(740\) 0 0
\(741\) 5.44441 + 21.6169i 0.200005 + 0.794117i
\(742\) 0.0884842 0.00324836
\(743\) 14.9949 5.45769i 0.550109 0.200223i −0.0519860 0.998648i \(-0.516555\pi\)
0.602095 + 0.798425i \(0.294333\pi\)
\(744\) 2.49050 14.1243i 0.0913061 0.517823i
\(745\) 0 0
\(746\) −9.23447 7.74864i −0.338098 0.283698i
\(747\) 3.35077 + 19.0032i 0.122598 + 0.695289i
\(748\) −8.62134 14.9326i −0.315227 0.545990i
\(749\) 0.0654201 0.113311i 0.00239040 0.00414029i
\(750\) 0 0
\(751\) 1.48505 + 0.540514i 0.0541903 + 0.0197237i 0.368973 0.929440i \(-0.379709\pi\)
−0.314783 + 0.949164i \(0.601932\pi\)
\(752\) 2.13746 3.70219i 0.0779452 0.135005i
\(753\) −9.59055 16.6113i −0.349499 0.605350i
\(754\) 2.08563 + 11.8282i 0.0759543 + 0.430758i
\(755\) 0 0
\(756\) 0.250221 0.209960i 0.00910045 0.00763618i
\(757\) 3.33882 18.9354i 0.121351 0.688217i −0.862057 0.506811i \(-0.830824\pi\)
0.983408 0.181406i \(-0.0580648\pi\)
\(758\) 6.41138 2.33355i 0.232872 0.0847584i
\(759\) −31.1354 −1.13014
\(760\) 0 0
\(761\) 12.6228 0.457576 0.228788 0.973476i \(-0.426524\pi\)
0.228788 + 0.973476i \(0.426524\pi\)
\(762\) 26.2154 9.54161i 0.949683 0.345656i
\(763\) 0.0382860 0.217131i 0.00138605 0.00786067i
\(764\) 14.4491 12.1243i 0.522751 0.438640i
\(765\) 0 0
\(766\) −1.88011 10.6626i −0.0679310 0.385256i
\(767\) 2.88907 + 5.00402i 0.104318 + 0.180685i
\(768\) −1.60792 + 2.78500i −0.0580208 + 0.100495i
\(769\) 37.7534 + 13.7411i 1.36142 + 0.495518i 0.916494 0.400048i \(-0.131007\pi\)
0.444929 + 0.895566i \(0.353229\pi\)
\(770\) 0 0
\(771\) −21.7518 + 37.6753i −0.783373 + 1.35684i
\(772\) −8.89727 15.4105i −0.320220 0.554637i
\(773\) −4.48376 25.4287i −0.161270 0.914606i −0.952828 0.303512i \(-0.901841\pi\)
0.791558 0.611094i \(-0.209270\pi\)
\(774\) −54.5729 45.7921i −1.96158 1.64596i
\(775\) 0 0
\(776\) −1.93685 + 10.9844i −0.0695290 + 0.394319i
\(777\) −0.0275107 + 0.0100131i −0.000986941 + 0.000359217i
\(778\) −7.52625 −0.269829
\(779\) 24.3585 1.76162i 0.872735 0.0631164i
\(780\) 0 0
\(781\) 26.1303 9.51065i 0.935016 0.340318i
\(782\) −6.20868 + 35.2112i −0.222022 + 1.25915i
\(783\) 80.7772 67.7801i 2.88674 2.42226i
\(784\) −5.36189 4.49916i −0.191496 0.160684i
\(785\) 0 0
\(786\) −33.3573 57.7765i −1.18981 2.06082i
\(787\) −12.3413 + 21.3757i −0.439919 + 0.761963i −0.997683 0.0680373i \(-0.978326\pi\)
0.557763 + 0.830000i \(0.311660\pi\)
\(788\) 12.6979 + 4.62167i 0.452345 + 0.164640i
\(789\) −53.2366 19.3766i −1.89527 0.689823i
\(790\) 0 0
\(791\) −0.0665987 0.115352i −0.00236798 0.00410146i
\(792\) 2.75473 + 15.6229i 0.0978852 + 0.555134i
\(793\) −14.0606 11.7983i −0.499307 0.418968i
\(794\) 3.79097 3.18100i 0.134537 0.112890i
\(795\) 0 0
\(796\) −6.59301 + 2.39966i −0.233683 + 0.0850537i
\(797\) −20.6723 −0.732249 −0.366124 0.930566i \(-0.619316\pi\)
−0.366124 + 0.930566i \(0.619316\pi\)
\(798\) 0.265768 + 0.192127i 0.00940809 + 0.00680121i
\(799\) −34.1126 −1.20682
\(800\) 0 0
\(801\) 11.3145 64.1680i 0.399780 2.26726i
\(802\) 15.2307 12.7801i 0.537816 0.451281i
\(803\) 3.14766 + 2.64120i 0.111078 + 0.0932058i
\(804\) −2.15378 12.2147i −0.0759580 0.430779i
\(805\) 0 0
\(806\) −3.54625 + 6.14229i −0.124911 + 0.216353i
\(807\) 7.79150 + 2.83587i 0.274274 + 0.0998275i
\(808\) 17.5228 + 6.37779i 0.616451 + 0.224370i
\(809\) 14.2987 24.7661i 0.502716 0.870729i −0.497279 0.867590i \(-0.665668\pi\)
0.999995 0.00313869i \(-0.000999078\pi\)
\(810\) 0 0
\(811\) −2.71497 15.3973i −0.0953353 0.540674i −0.994644 0.103359i \(-0.967041\pi\)
0.899309 0.437314i \(-0.144070\pi\)
\(812\) 0.135353 + 0.113575i 0.00474997 + 0.00398570i
\(813\) −27.3335 + 22.9355i −0.958628 + 0.804385i
\(814\) 0.146011 0.828068i 0.00511768 0.0290238i
\(815\) 0 0
\(816\) 25.6614 0.898329
\(817\) 18.4512 38.0603i 0.645525 1.33156i
\(818\) 12.8906 0.450708
\(819\) −0.256673 + 0.0934212i −0.00896887 + 0.00326440i
\(820\) 0 0
\(821\) 19.8911 16.6906i 0.694204 0.582506i −0.225914 0.974147i \(-0.572537\pi\)
0.920118 + 0.391641i \(0.128092\pi\)
\(822\) −14.7028 12.3371i −0.512819 0.430306i
\(823\) 6.29176 + 35.6823i 0.219317 + 1.24381i 0.873256 + 0.487261i \(0.162004\pi\)
−0.653939 + 0.756547i \(0.726885\pi\)
\(824\) 1.76795 + 3.06218i 0.0615895 + 0.106676i
\(825\) 0 0
\(826\) 0.0798770 + 0.0290728i 0.00277928 + 0.00101157i
\(827\) −16.9142 6.15626i −0.588164 0.214074i 0.0307580 0.999527i \(-0.490208\pi\)
−0.618921 + 0.785453i \(0.712430\pi\)
\(828\) 16.4476 28.4881i 0.571595 0.990031i
\(829\) 13.0982 + 22.6867i 0.454919 + 0.787943i 0.998684 0.0512947i \(-0.0163348\pi\)
−0.543764 + 0.839238i \(0.683001\pi\)
\(830\) 0 0
\(831\) 7.28016 + 6.10878i 0.252546 + 0.211911i
\(832\) 1.21824 1.02222i 0.0422348 0.0354392i
\(833\) −9.69887 + 55.0050i −0.336046 + 1.90581i
\(834\) 42.5519 15.4876i 1.47345 0.536292i
\(835\) 0 0
\(836\) −8.59534 + 3.85144i −0.297276 + 0.133205i
\(837\) 62.2683 2.15231
\(838\) −4.21382 + 1.53371i −0.145564 + 0.0529810i
\(839\) 0.609122 3.45450i 0.0210292 0.119263i −0.972486 0.232961i \(-0.925159\pi\)
0.993515 + 0.113698i \(0.0362697\pi\)
\(840\) 0 0
\(841\) 21.4800 + 18.0238i 0.740689 + 0.621512i
\(842\) −3.74698 21.2502i −0.129129 0.732329i
\(843\) −22.2873 38.6028i −0.767616 1.32955i
\(844\) −3.55876 + 6.16395i −0.122497 + 0.212172i
\(845\) 0 0
\(846\) 29.4921 + 10.7342i 1.01396 + 0.369051i
\(847\) 0.0740557 0.128268i 0.00254458 0.00440735i
\(848\) −1.89108 3.27545i −0.0649400 0.112479i
\(849\) 2.59125 + 14.6957i 0.0889316 + 0.504356i
\(850\) 0 0
\(851\) −1.33565 + 1.12074i −0.0457855 + 0.0384186i
\(852\) −7.18629 + 40.7555i −0.246198 + 1.39626i
\(853\) 37.9556 13.8147i 1.29958 0.473007i 0.402717 0.915325i \(-0.368066\pi\)
0.896858 + 0.442318i \(0.145844\pi\)
\(854\) −0.270021 −0.00923993
\(855\) 0 0
\(856\) −5.59263 −0.191152
\(857\) −15.9081 + 5.79009i −0.543412 + 0.197786i −0.599117 0.800662i \(-0.704482\pi\)
0.0557051 + 0.998447i \(0.482259\pi\)
\(858\) 1.91893 10.8828i 0.0655113 0.371533i
\(859\) 8.61145 7.22586i 0.293819 0.246543i −0.483947 0.875097i \(-0.660797\pi\)
0.777766 + 0.628554i \(0.216353\pi\)
\(860\) 0 0
\(861\) 0.0731975 + 0.415124i 0.00249457 + 0.0141474i
\(862\) −5.95535 10.3150i −0.202840 0.351329i
\(863\) −27.5361 + 47.6939i −0.937340 + 1.62352i −0.166932 + 0.985968i \(0.553386\pi\)
−0.770407 + 0.637552i \(0.779947\pi\)
\(864\) −13.1199 4.77525i −0.446348 0.162457i
\(865\) 0 0
\(866\) 11.0652 19.1654i 0.376010 0.651268i
\(867\) −75.0506 129.991i −2.54885 4.41474i
\(868\) 0.0181183 + 0.102754i 0.000614975 + 0.00348770i
\(869\) −15.7442 13.2109i −0.534085 0.448150i
\(870\) 0 0
\(871\) −1.06509 + 6.04041i −0.0360891 + 0.204671i
\(872\) −8.85586 + 3.22327i −0.299897 + 0.109154i
\(873\) −81.8876 −2.77147
\(874\) 18.7869 + 5.33868i 0.635478 + 0.180584i
\(875\) 0 0
\(876\) −5.74639 + 2.09151i −0.194153 + 0.0706657i
\(877\) 3.25617 18.4667i 0.109953 0.623575i −0.879173 0.476503i \(-0.841904\pi\)
0.989126 0.147072i \(-0.0469848\pi\)
\(878\) −5.28176 + 4.43192i −0.178251 + 0.149570i
\(879\) −29.2322 24.5287i −0.985978 0.827334i
\(880\) 0 0
\(881\) −25.3287 43.8706i −0.853345 1.47804i −0.878172 0.478345i \(-0.841237\pi\)
0.0248271 0.999692i \(-0.492096\pi\)
\(882\) 25.6936 44.5027i 0.865149 1.49848i
\(883\) −32.0818 11.6768i −1.07964 0.392956i −0.259866 0.965645i \(-0.583678\pi\)
−0.819773 + 0.572688i \(0.805901\pi\)
\(884\) −11.9248 4.34026i −0.401073 0.145979i
\(885\) 0 0
\(886\) −0.772800 1.33853i −0.0259627 0.0449687i
\(887\) 6.11812 + 34.6976i 0.205426 + 1.16503i 0.896767 + 0.442502i \(0.145909\pi\)
−0.691341 + 0.722529i \(0.742980\pi\)
\(888\) 0.958616 + 0.804375i 0.0321691 + 0.0269930i
\(889\) −0.155473 + 0.130457i −0.00521440 + 0.00437540i
\(890\) 0 0
\(891\) −46.4465 + 16.9052i −1.55602 + 0.566344i
\(892\) 4.36006 0.145986
\(893\) −1.90364 + 18.5365i −0.0637029 + 0.620299i
\(894\) 22.6204 0.756540
\(895\) 0 0
\(896\) 0.00406252 0.0230397i 0.000135719 0.000769702i
\(897\) −17.5537 + 14.7293i −0.586100 + 0.491796i
\(898\) 4.53487 + 3.80521i 0.151331 + 0.126981i
\(899\) 5.84901 + 33.1714i 0.195075 + 1.10633i
\(900\) 0 0
\(901\) −15.0903 + 26.1371i −0.502730 + 0.870754i
\(902\) −11.3766 4.14073i −0.378798 0.137871i
\(903\) 0.686020 + 0.249691i 0.0228293 + 0.00830919i
\(904\) −2.84670 + 4.93062i −0.0946797 + 0.163990i
\(905\) 0 0
\(906\) −7.86485 44.6038i −0.261292 1.48186i
\(907\) −14.6698 12.3094i −0.487103 0.408728i 0.365883 0.930661i \(-0.380767\pi\)
−0.852987 + 0.521932i \(0.825211\pi\)
\(908\) −7.23624 + 6.07192i −0.240143 + 0.201504i
\(909\) −23.7728 + 134.822i −0.788493 + 4.47177i
\(910\) 0 0
\(911\) 24.5134 0.812164 0.406082 0.913837i \(-0.366895\pi\)
0.406082 + 0.913837i \(0.366895\pi\)
\(912\) 1.43203 13.9442i 0.0474191 0.461738i
\(913\) 5.67938 0.187960
\(914\) 27.7569 10.1027i 0.918115 0.334167i
\(915\) 0 0
\(916\) 17.5175 14.6989i 0.578794 0.485666i
\(917\) 0.371797 + 0.311974i 0.0122778 + 0.0103023i
\(918\) 19.3465 + 109.719i 0.638528 + 3.62127i
\(919\) −14.3060 24.7787i −0.471911 0.817374i 0.527573 0.849510i \(-0.323102\pi\)
−0.999483 + 0.0321362i \(0.989769\pi\)
\(920\) 0 0
\(921\) 31.5555 + 11.4853i 1.03979 + 0.378452i
\(922\) −28.6168 10.4157i −0.942445 0.343022i
\(923\) 10.2327 17.7235i 0.336812 0.583375i
\(924\) −0.0812844 0.140789i −0.00267406 0.00463161i
\(925\) 0 0
\(926\) −29.7699 24.9799i −0.978301 0.820892i
\(927\) −19.8859 + 16.6862i −0.653139 + 0.548048i
\(928\) 1.31148 7.43775i 0.0430513 0.244156i
\(929\) −3.68171 + 1.34003i −0.120793 + 0.0439650i −0.401709 0.915767i \(-0.631584\pi\)
0.280917 + 0.959732i \(0.409362\pi\)
\(930\) 0 0
\(931\) 29.3479 + 8.33980i 0.961840 + 0.273326i
\(932\) 10.5766 0.346448
\(933\) 44.3196 16.1310i 1.45096 0.528106i
\(934\) −4.97123 + 28.1933i −0.162664 + 0.922512i
\(935\) 0 0
\(936\) 8.94382 + 7.50475i 0.292338 + 0.245300i
\(937\) 7.63564 + 43.3039i 0.249446 + 1.41468i 0.809937 + 0.586516i \(0.199501\pi\)
−0.560492 + 0.828160i \(0.689388\pi\)
\(938\) 0.0451162 + 0.0781435i 0.00147310 + 0.00255148i
\(939\) −34.5347 + 59.8159i −1.12700 + 1.95202i
\(940\) 0 0
\(941\) 5.71790 + 2.08115i 0.186398 + 0.0678434i 0.433533 0.901138i \(-0.357267\pi\)
−0.247135 + 0.968981i \(0.579489\pi\)
\(942\) 4.35469 7.54254i 0.141883 0.245749i
\(943\) 12.5522 + 21.7410i 0.408755 + 0.707985i
\(944\) −0.630930 3.57818i −0.0205350 0.116460i
\(945\) 0 0
\(946\) −16.0622 + 13.4778i −0.522226 + 0.438199i
\(947\) 1.60281 9.09001i 0.0520845 0.295386i −0.947628 0.319377i \(-0.896526\pi\)
0.999712 + 0.0239914i \(0.00763743\pi\)
\(948\) 28.7427 10.4615i 0.933520 0.339774i
\(949\) 3.02408 0.0981657
\(950\) 0 0
\(951\) −38.0000 −1.23223
\(952\) −0.175427 + 0.0638504i −0.00568564 + 0.00206940i
\(953\) 5.36804 30.4437i 0.173888 0.986167i −0.765532 0.643398i \(-0.777524\pi\)
0.939420 0.342769i \(-0.111365\pi\)
\(954\) 21.2709 17.8484i 0.688671 0.577863i
\(955\) 0 0
\(956\) 3.01327 + 17.0891i 0.0974560 + 0.552701i
\(957\) −26.2405 45.4499i −0.848235 1.46919i
\(958\) 8.34737 14.4581i 0.269691 0.467119i
\(959\) 0.131209 + 0.0477561i 0.00423695 + 0.00154212i
\(960\) 0 0
\(961\) 5.55479 9.62118i 0.179187 0.310360i
\(962\) −0.309417 0.535926i −0.00997601 0.0172790i
\(963\) −7.12981 40.4352i −0.229755 1.30300i
\(964\) −0.367629 0.308477i −0.0118405 0.00993538i
\(965\) 0 0
\(966\) −0.0585372 + 0.331981i −0.00188340 + 0.0106813i
\(967\) −23.8796 + 8.69145i −0.767915 + 0.279498i −0.696124 0.717922i \(-0.745094\pi\)
−0.0717907 + 0.997420i \(0.522871\pi\)
\(968\) −6.33087 −0.203482
\(969\) −102.076 + 45.7390i −3.27917 + 1.46935i
\(970\) 0 0
\(971\) 50.9775 18.5543i 1.63595 0.595436i 0.649623 0.760256i \(-0.274927\pi\)
0.986324 + 0.164820i \(0.0527044\pi\)
\(972\) 5.50023 31.1934i 0.176420 1.00053i
\(973\) −0.252358 + 0.211754i −0.00809024 + 0.00678852i
\(974\) −14.8485 12.4593i −0.475776 0.399223i
\(975\) 0 0
\(976\) 5.77089 + 9.99547i 0.184722 + 0.319947i
\(977\) 19.6132 33.9710i 0.627481 1.08683i −0.360574 0.932731i \(-0.617419\pi\)
0.988055 0.154099i \(-0.0492475\pi\)
\(978\) 41.6907 + 15.1742i 1.33312 + 0.485217i
\(979\) −18.0210 6.55912i −0.575955 0.209630i
\(980\) 0 0
\(981\) −34.5944 59.9193i −1.10452 1.91308i
\(982\) 6.30923 + 35.7814i 0.201336 + 1.14183i
\(983\) 3.62947 + 3.04549i 0.115762 + 0.0971359i 0.698831 0.715287i \(-0.253704\pi\)
−0.583069 + 0.812423i \(0.698148\pi\)
\(984\) 13.8024 11.5816i 0.440005 0.369208i
\(985\) 0 0
\(986\) −56.6321 + 20.6124i −1.80353 + 0.656432i
\(987\) −0.321623 −0.0102374
\(988\) −3.02391 + 6.23760i −0.0962035 + 0.198444i
\(989\) 43.4785 1.38253
\(990\) 0 0
\(991\) −4.17962 + 23.7038i −0.132770 + 0.752976i 0.843617 + 0.536946i \(0.180422\pi\)
−0.976387 + 0.216030i \(0.930689\pi\)
\(992\) 3.41646 2.86675i 0.108473 0.0910193i
\(993\) 43.7549 + 36.7147i 1.38852 + 1.16511i
\(994\) −0.0522800 0.296495i −0.00165822 0.00940425i
\(995\) 0 0
\(996\) −4.22617 + 7.31994i −0.133911 + 0.231941i
\(997\) 13.3716 + 4.86686i 0.423483 + 0.154135i 0.544966 0.838458i \(-0.316543\pi\)
−0.121483 + 0.992594i \(0.538765\pi\)
\(998\) 7.29367 + 2.65468i 0.230877 + 0.0840323i
\(999\) −2.71651 + 4.70514i −0.0859466 + 0.148864i
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 950.2.l.i.651.3 18
5.2 odd 4 950.2.u.g.499.1 36
5.3 odd 4 950.2.u.g.499.6 36
5.4 even 2 190.2.k.d.81.1 yes 18
19.4 even 9 inner 950.2.l.i.251.3 18
95.4 even 18 190.2.k.d.61.1 18
95.23 odd 36 950.2.u.g.99.1 36
95.42 odd 36 950.2.u.g.99.6 36
95.59 odd 18 3610.2.a.bj.1.9 9
95.74 even 18 3610.2.a.bi.1.1 9
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
190.2.k.d.61.1 18 95.4 even 18
190.2.k.d.81.1 yes 18 5.4 even 2
950.2.l.i.251.3 18 19.4 even 9 inner
950.2.l.i.651.3 18 1.1 even 1 trivial
950.2.u.g.99.1 36 95.23 odd 36
950.2.u.g.99.6 36 95.42 odd 36
950.2.u.g.499.1 36 5.2 odd 4
950.2.u.g.499.6 36 5.3 odd 4
3610.2.a.bi.1.1 9 95.74 even 18
3610.2.a.bj.1.9 9 95.59 odd 18