Properties

Label 819.2.ct.a.316.4
Level $819$
Weight $2$
Character 819.316
Analytic conductor $6.540$
Analytic rank $0$
Dimension $12$
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] = [819,2,Mod(127,819)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(819, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([0, 0, 5]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("819.127");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 819 = 3^{2} \cdot 7 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 819.ct (of order \(6\), degree \(2\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(6.53974792554\)
Analytic rank: \(0\)
Dimension: \(12\)
Relative dimension: \(6\) over \(\Q(\zeta_{6})\)
Coefficient field: 12.0.58891012706304.1
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{12} - 5x^{10} - 2x^{9} + 15x^{8} + 2x^{7} - 30x^{6} + 4x^{5} + 60x^{4} - 16x^{3} - 80x^{2} + 64 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 91)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 316.4
Root \(1.34408 - 0.439820i\) of defining polynomial
Character \(\chi\) \(=\) 819.316
Dual form 819.2.ct.a.127.4

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.104235 + 0.0601799i) q^{2} +(-0.992757 - 1.71951i) q^{4} +1.68817i q^{5} +(0.866025 - 0.500000i) q^{7} -0.479696i q^{8} +O(q^{10})\) \(q+(0.104235 + 0.0601799i) q^{2} +(-0.992757 - 1.71951i) q^{4} +1.68817i q^{5} +(0.866025 - 0.500000i) q^{7} -0.479696i q^{8} +(-0.101594 + 0.175965i) q^{10} +(0.315769 + 0.182309i) q^{11} +(1.80124 + 3.12338i) q^{13} +0.120360 q^{14} +(-1.95665 + 3.38901i) q^{16} +(1.59277 + 2.75877i) q^{17} +(1.25046 - 0.721954i) q^{19} +(2.90281 - 1.67594i) q^{20} +(0.0219427 + 0.0380059i) q^{22} +(2.54161 - 4.40219i) q^{23} +2.15010 q^{25} +(-0.000212944 + 0.433964i) q^{26} +(-1.71951 - 0.992757i) q^{28} +(4.09831 - 7.09848i) q^{29} -4.69775i q^{31} +(-1.23876 + 0.715198i) q^{32} +0.383412i q^{34} +(0.844083 + 1.46199i) q^{35} +(5.46967 + 3.15792i) q^{37} +0.173789 q^{38} +0.809806 q^{40} +(5.04661 + 2.91366i) q^{41} +(-0.386561 - 0.669543i) q^{43} -0.723954i q^{44} +(0.529847 - 0.305907i) q^{46} +12.7905i q^{47} +(0.500000 - 0.866025i) q^{49} +(0.224115 + 0.129393i) q^{50} +(3.58248 - 6.19801i) q^{52} -1.37110 q^{53} +(-0.307768 + 0.533070i) q^{55} +(-0.239848 - 0.415429i) q^{56} +(0.854372 - 0.493272i) q^{58} +(8.10770 - 4.68098i) q^{59} +(4.51242 + 7.81574i) q^{61} +(0.282711 - 0.489669i) q^{62} +7.65442 q^{64} +(-5.27279 + 3.04080i) q^{65} +(-11.6705 - 6.73797i) q^{67} +(3.16247 - 5.47757i) q^{68} +0.203187i q^{70} +(6.13246 - 3.54058i) q^{71} +2.16083i q^{73} +(0.380087 + 0.658329i) q^{74} +(-2.48281 - 1.43345i) q^{76} +0.364618 q^{77} -6.88781 q^{79} +(-5.72121 - 3.30314i) q^{80} +(0.350688 + 0.607409i) q^{82} -0.567380i q^{83} +(-4.65725 + 2.68887i) q^{85} -0.0930528i q^{86} +(0.0874529 - 0.151473i) q^{88} +(0.986346 + 0.569467i) q^{89} +(3.12161 + 1.80431i) q^{91} -10.0928 q^{92} +(-0.769734 + 1.33322i) q^{94} +(1.21878 + 2.11098i) q^{95} +(6.86572 - 3.96393i) q^{97} +(0.104235 - 0.0601799i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12 q + 4 q^{4}+O(q^{10}) \) Copy content Toggle raw display \( 12 q + 4 q^{4} + 12 q^{10} - 6 q^{11} + 4 q^{13} + 8 q^{14} - 8 q^{16} + 4 q^{17} + 12 q^{20} + 6 q^{22} + 12 q^{23} - 20 q^{25} + 42 q^{26} - 8 q^{29} - 36 q^{32} - 6 q^{35} - 42 q^{37} - 4 q^{38} + 92 q^{40} - 30 q^{41} + 2 q^{43} + 12 q^{46} + 6 q^{49} + 18 q^{50} + 2 q^{52} + 44 q^{53} - 6 q^{55} + 12 q^{56} - 12 q^{58} - 18 q^{59} + 14 q^{61} + 4 q^{62} - 52 q^{64} - 60 q^{65} - 24 q^{67} + 8 q^{68} + 24 q^{71} - 6 q^{74} - 18 q^{76} - 8 q^{77} - 56 q^{79} + 72 q^{80} + 14 q^{82} - 48 q^{85} - 14 q^{88} + 12 q^{89} + 14 q^{91} - 24 q^{92} + 4 q^{94} + 22 q^{95} + 6 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/819\mathbb{Z}\right)^\times\).

\(n\) \(92\) \(379\) \(703\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{6}\right)\) \(1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.104235 + 0.0601799i 0.0737051 + 0.0425536i 0.536400 0.843964i \(-0.319784\pi\)
−0.462695 + 0.886518i \(0.653117\pi\)
\(3\) 0 0
\(4\) −0.992757 1.71951i −0.496378 0.859753i
\(5\) 1.68817i 0.754971i 0.926016 + 0.377485i \(0.123211\pi\)
−0.926016 + 0.377485i \(0.876789\pi\)
\(6\) 0 0
\(7\) 0.866025 0.500000i 0.327327 0.188982i
\(8\) 0.479696i 0.169598i
\(9\) 0 0
\(10\) −0.101594 + 0.175965i −0.0321267 + 0.0556452i
\(11\) 0.315769 + 0.182309i 0.0952078 + 0.0549682i 0.546848 0.837232i \(-0.315828\pi\)
−0.451640 + 0.892200i \(0.649161\pi\)
\(12\) 0 0
\(13\) 1.80124 + 3.12338i 0.499575 + 0.866271i
\(14\) 0.120360 0.0321675
\(15\) 0 0
\(16\) −1.95665 + 3.38901i −0.489161 + 0.847252i
\(17\) 1.59277 + 2.75877i 0.386304 + 0.669099i 0.991949 0.126636i \(-0.0404181\pi\)
−0.605645 + 0.795735i \(0.707085\pi\)
\(18\) 0 0
\(19\) 1.25046 0.721954i 0.286875 0.165628i −0.349657 0.936878i \(-0.613702\pi\)
0.636532 + 0.771250i \(0.280368\pi\)
\(20\) 2.90281 1.67594i 0.649088 0.374751i
\(21\) 0 0
\(22\) 0.0219427 + 0.0380059i 0.00467820 + 0.00810288i
\(23\) 2.54161 4.40219i 0.529962 0.917920i −0.469428 0.882971i \(-0.655540\pi\)
0.999389 0.0349493i \(-0.0111270\pi\)
\(24\) 0 0
\(25\) 2.15010 0.430020
\(26\) −0.000212944 0.433964i −4.17617e−5 0.0851073i
\(27\) 0 0
\(28\) −1.71951 0.992757i −0.324956 0.187613i
\(29\) 4.09831 7.09848i 0.761037 1.31815i −0.181280 0.983432i \(-0.558024\pi\)
0.942317 0.334723i \(-0.108643\pi\)
\(30\) 0 0
\(31\) 4.69775i 0.843742i −0.906656 0.421871i \(-0.861374\pi\)
0.906656 0.421871i \(-0.138626\pi\)
\(32\) −1.23876 + 0.715198i −0.218984 + 0.126430i
\(33\) 0 0
\(34\) 0.383412i 0.0657546i
\(35\) 0.844083 + 1.46199i 0.142676 + 0.247122i
\(36\) 0 0
\(37\) 5.46967 + 3.15792i 0.899209 + 0.519159i 0.876943 0.480594i \(-0.159579\pi\)
0.0222655 + 0.999752i \(0.492912\pi\)
\(38\) 0.173789 0.0281922
\(39\) 0 0
\(40\) 0.809806 0.128042
\(41\) 5.04661 + 2.91366i 0.788148 + 0.455037i 0.839310 0.543653i \(-0.182959\pi\)
−0.0511624 + 0.998690i \(0.516293\pi\)
\(42\) 0 0
\(43\) −0.386561 0.669543i −0.0589500 0.102104i 0.835044 0.550183i \(-0.185442\pi\)
−0.893994 + 0.448078i \(0.852109\pi\)
\(44\) 0.723954i 0.109140i
\(45\) 0 0
\(46\) 0.529847 0.305907i 0.0781217 0.0451036i
\(47\) 12.7905i 1.86569i 0.360275 + 0.932846i \(0.382683\pi\)
−0.360275 + 0.932846i \(0.617317\pi\)
\(48\) 0 0
\(49\) 0.500000 0.866025i 0.0714286 0.123718i
\(50\) 0.224115 + 0.129393i 0.0316946 + 0.0182989i
\(51\) 0 0
\(52\) 3.58248 6.19801i 0.496800 0.859509i
\(53\) −1.37110 −0.188334 −0.0941672 0.995556i \(-0.530019\pi\)
−0.0941672 + 0.995556i \(0.530019\pi\)
\(54\) 0 0
\(55\) −0.307768 + 0.533070i −0.0414994 + 0.0718791i
\(56\) −0.239848 0.415429i −0.0320510 0.0555140i
\(57\) 0 0
\(58\) 0.854372 0.493272i 0.112185 0.0647698i
\(59\) 8.10770 4.68098i 1.05553 0.609412i 0.131340 0.991337i \(-0.458072\pi\)
0.924193 + 0.381925i \(0.124739\pi\)
\(60\) 0 0
\(61\) 4.51242 + 7.81574i 0.577756 + 1.00070i 0.995736 + 0.0922469i \(0.0294049\pi\)
−0.417980 + 0.908456i \(0.637262\pi\)
\(62\) 0.282711 0.489669i 0.0359043 0.0621880i
\(63\) 0 0
\(64\) 7.65442 0.956802
\(65\) −5.27279 + 3.04080i −0.654009 + 0.377164i
\(66\) 0 0
\(67\) −11.6705 6.73797i −1.42578 0.823174i −0.428995 0.903307i \(-0.641132\pi\)
−0.996784 + 0.0801330i \(0.974466\pi\)
\(68\) 3.16247 5.47757i 0.383506 0.664252i
\(69\) 0 0
\(70\) 0.203187i 0.0242855i
\(71\) 6.13246 3.54058i 0.727789 0.420189i −0.0898239 0.995958i \(-0.528630\pi\)
0.817613 + 0.575769i \(0.195297\pi\)
\(72\) 0 0
\(73\) 2.16083i 0.252906i 0.991973 + 0.126453i \(0.0403592\pi\)
−0.991973 + 0.126453i \(0.959641\pi\)
\(74\) 0.380087 + 0.658329i 0.0441842 + 0.0765292i
\(75\) 0 0
\(76\) −2.48281 1.43345i −0.284797 0.164428i
\(77\) 0.364618 0.0415521
\(78\) 0 0
\(79\) −6.88781 −0.774940 −0.387470 0.921882i \(-0.626651\pi\)
−0.387470 + 0.921882i \(0.626651\pi\)
\(80\) −5.72121 3.30314i −0.639651 0.369302i
\(81\) 0 0
\(82\) 0.350688 + 0.607409i 0.0387270 + 0.0670771i
\(83\) 0.567380i 0.0622780i −0.999515 0.0311390i \(-0.990087\pi\)
0.999515 0.0311390i \(-0.00991345\pi\)
\(84\) 0 0
\(85\) −4.65725 + 2.68887i −0.505150 + 0.291648i
\(86\) 0.0930528i 0.0100341i
\(87\) 0 0
\(88\) 0.0874529 0.151473i 0.00932251 0.0161471i
\(89\) 0.986346 + 0.569467i 0.104553 + 0.0603634i 0.551364 0.834264i \(-0.314107\pi\)
−0.446812 + 0.894628i \(0.647441\pi\)
\(90\) 0 0
\(91\) 3.12161 + 1.80431i 0.327234 + 0.189143i
\(92\) −10.0928 −1.05225
\(93\) 0 0
\(94\) −0.769734 + 1.33322i −0.0793920 + 0.137511i
\(95\) 1.21878 + 2.11098i 0.125044 + 0.216582i
\(96\) 0 0
\(97\) 6.86572 3.96393i 0.697109 0.402476i −0.109161 0.994024i \(-0.534816\pi\)
0.806270 + 0.591548i \(0.201483\pi\)
\(98\) 0.104235 0.0601799i 0.0105293 0.00607909i
\(99\) 0 0
\(100\) −2.13452 3.69710i −0.213452 0.369710i
\(101\) 7.77322 13.4636i 0.773465 1.33968i −0.162189 0.986760i \(-0.551855\pi\)
0.935653 0.352920i \(-0.114811\pi\)
\(102\) 0 0
\(103\) −10.2982 −1.01471 −0.507354 0.861738i \(-0.669376\pi\)
−0.507354 + 0.861738i \(0.669376\pi\)
\(104\) 1.49827 0.864049i 0.146918 0.0847270i
\(105\) 0 0
\(106\) −0.142916 0.0825124i −0.0138812 0.00801432i
\(107\) −6.56220 + 11.3661i −0.634391 + 1.09880i 0.352252 + 0.935905i \(0.385416\pi\)
−0.986644 + 0.162893i \(0.947917\pi\)
\(108\) 0 0
\(109\) 10.4459i 1.00054i 0.865871 + 0.500268i \(0.166765\pi\)
−0.865871 + 0.500268i \(0.833235\pi\)
\(110\) −0.0641602 + 0.0370429i −0.00611743 + 0.00353190i
\(111\) 0 0
\(112\) 3.91329i 0.369771i
\(113\) 2.47631 + 4.28909i 0.232952 + 0.403484i 0.958675 0.284502i \(-0.0918283\pi\)
−0.725724 + 0.687986i \(0.758495\pi\)
\(114\) 0 0
\(115\) 7.43163 + 4.29065i 0.693003 + 0.400105i
\(116\) −16.2745 −1.51105
\(117\) 0 0
\(118\) 1.12681 0.103731
\(119\) 2.75877 + 1.59277i 0.252896 + 0.146009i
\(120\) 0 0
\(121\) −5.43353 9.41114i −0.493957 0.855559i
\(122\) 1.08623i 0.0983425i
\(123\) 0 0
\(124\) −8.07781 + 4.66373i −0.725409 + 0.418815i
\(125\) 12.0705i 1.07962i
\(126\) 0 0
\(127\) 4.03366 6.98650i 0.357929 0.619951i −0.629686 0.776850i \(-0.716816\pi\)
0.987615 + 0.156899i \(0.0501496\pi\)
\(128\) 3.27537 + 1.89104i 0.289505 + 0.167146i
\(129\) 0 0
\(130\) −0.732603 0.000359484i −0.0642535 3.15288e-5i
\(131\) −18.9039 −1.65164 −0.825820 0.563934i \(-0.809287\pi\)
−0.825820 + 0.563934i \(0.809287\pi\)
\(132\) 0 0
\(133\) 0.721954 1.25046i 0.0626013 0.108429i
\(134\) −0.810981 1.40466i −0.0700581 0.121344i
\(135\) 0 0
\(136\) 1.32337 0.764047i 0.113478 0.0655165i
\(137\) −15.7837 + 9.11274i −1.34850 + 0.778554i −0.988036 0.154221i \(-0.950713\pi\)
−0.360459 + 0.932775i \(0.617380\pi\)
\(138\) 0 0
\(139\) −2.62542 4.54737i −0.222686 0.385703i 0.732937 0.680297i \(-0.238149\pi\)
−0.955623 + 0.294594i \(0.904816\pi\)
\(140\) 1.67594 2.90281i 0.141643 0.245332i
\(141\) 0 0
\(142\) 0.852287 0.0715223
\(143\) −0.000645091 1.31465i −5.39452e−5 0.109936i
\(144\) 0 0
\(145\) 11.9834 + 6.91862i 0.995167 + 0.574560i
\(146\) −0.130038 + 0.225233i −0.0107621 + 0.0186404i
\(147\) 0 0
\(148\) 12.5402i 1.03080i
\(149\) −8.03073 + 4.63654i −0.657903 + 0.379841i −0.791478 0.611198i \(-0.790688\pi\)
0.133574 + 0.991039i \(0.457354\pi\)
\(150\) 0 0
\(151\) 14.0132i 1.14038i 0.821513 + 0.570189i \(0.193130\pi\)
−0.821513 + 0.570189i \(0.806870\pi\)
\(152\) −0.346318 0.599841i −0.0280901 0.0486535i
\(153\) 0 0
\(154\) 0.0380059 + 0.0219427i 0.00306260 + 0.00176819i
\(155\) 7.93059 0.637000
\(156\) 0 0
\(157\) −17.1825 −1.37131 −0.685656 0.727925i \(-0.740485\pi\)
−0.685656 + 0.727925i \(0.740485\pi\)
\(158\) −0.717949 0.414508i −0.0571170 0.0329765i
\(159\) 0 0
\(160\) −1.20737 2.09123i −0.0954511 0.165326i
\(161\) 5.08321i 0.400613i
\(162\) 0 0
\(163\) 10.2128 5.89637i 0.799930 0.461840i −0.0435169 0.999053i \(-0.513856\pi\)
0.843447 + 0.537213i \(0.180523\pi\)
\(164\) 11.5702i 0.903482i
\(165\) 0 0
\(166\) 0.0341449 0.0591407i 0.00265016 0.00459021i
\(167\) −3.73852 2.15843i −0.289295 0.167025i 0.348329 0.937372i \(-0.386749\pi\)
−0.637624 + 0.770348i \(0.720083\pi\)
\(168\) 0 0
\(169\) −6.51105 + 11.2519i −0.500850 + 0.865534i
\(170\) −0.647263 −0.0496428
\(171\) 0 0
\(172\) −0.767522 + 1.32939i −0.0585230 + 0.101365i
\(173\) −6.25985 10.8424i −0.475928 0.824331i 0.523692 0.851908i \(-0.324554\pi\)
−0.999620 + 0.0275769i \(0.991221\pi\)
\(174\) 0 0
\(175\) 1.86204 1.07505i 0.140757 0.0812660i
\(176\) −1.23569 + 0.713428i −0.0931440 + 0.0537767i
\(177\) 0 0
\(178\) 0.0685410 + 0.118717i 0.00513737 + 0.00889818i
\(179\) 3.29767 5.71173i 0.246479 0.426915i −0.716067 0.698031i \(-0.754060\pi\)
0.962547 + 0.271117i \(0.0873929\pi\)
\(180\) 0 0
\(181\) −11.0157 −0.818791 −0.409395 0.912357i \(-0.634260\pi\)
−0.409395 + 0.912357i \(0.634260\pi\)
\(182\) 0.216797 + 0.375930i 0.0160701 + 0.0278658i
\(183\) 0 0
\(184\) −2.11171 1.21920i −0.155678 0.0898805i
\(185\) −5.33109 + 9.23371i −0.391949 + 0.678876i
\(186\) 0 0
\(187\) 1.16151i 0.0849379i
\(188\) 21.9934 12.6979i 1.60403 0.926089i
\(189\) 0 0
\(190\) 0.293384i 0.0212843i
\(191\) 2.96606 + 5.13737i 0.214617 + 0.371727i 0.953154 0.302486i \(-0.0978164\pi\)
−0.738537 + 0.674213i \(0.764483\pi\)
\(192\) 0 0
\(193\) 3.63380 + 2.09798i 0.261567 + 0.151016i 0.625049 0.780586i \(-0.285079\pi\)
−0.363482 + 0.931601i \(0.618412\pi\)
\(194\) 0.954196 0.0685073
\(195\) 0 0
\(196\) −1.98551 −0.141822
\(197\) −5.00990 2.89247i −0.356941 0.206080i 0.310797 0.950476i \(-0.399404\pi\)
−0.667738 + 0.744396i \(0.732737\pi\)
\(198\) 0 0
\(199\) 5.97988 + 10.3575i 0.423903 + 0.734221i 0.996317 0.0857435i \(-0.0273266\pi\)
−0.572415 + 0.819964i \(0.693993\pi\)
\(200\) 1.03139i 0.0729305i
\(201\) 0 0
\(202\) 1.62048 0.935584i 0.114017 0.0658275i
\(203\) 8.19662i 0.575290i
\(204\) 0 0
\(205\) −4.91874 + 8.51951i −0.343540 + 0.595028i
\(206\) −1.07343 0.619743i −0.0747891 0.0431795i
\(207\) 0 0
\(208\) −14.1096 0.00692349i −0.978323 0.000480057i
\(209\) 0.526475 0.0364170
\(210\) 0 0
\(211\) 4.11795 7.13251i 0.283492 0.491022i −0.688751 0.724998i \(-0.741840\pi\)
0.972242 + 0.233976i \(0.0751738\pi\)
\(212\) 1.36116 + 2.35761i 0.0934851 + 0.161921i
\(213\) 0 0
\(214\) −1.36802 + 0.789825i −0.0935157 + 0.0539913i
\(215\) 1.13030 0.652579i 0.0770858 0.0445055i
\(216\) 0 0
\(217\) −2.34888 4.06838i −0.159452 0.276179i
\(218\) −0.628633 + 1.08882i −0.0425764 + 0.0737445i
\(219\) 0 0
\(220\) 1.22215 0.0823976
\(221\) −5.74771 + 9.94405i −0.386633 + 0.668909i
\(222\) 0 0
\(223\) 13.2515 + 7.65073i 0.887383 + 0.512331i 0.873086 0.487567i \(-0.162115\pi\)
0.0142977 + 0.999898i \(0.495449\pi\)
\(224\) −0.715198 + 1.23876i −0.0477861 + 0.0827680i
\(225\) 0 0
\(226\) 0.596097i 0.0396518i
\(227\) 6.02292 3.47733i 0.399755 0.230799i −0.286623 0.958043i \(-0.592533\pi\)
0.686378 + 0.727245i \(0.259199\pi\)
\(228\) 0 0
\(229\) 27.4219i 1.81209i −0.423180 0.906045i \(-0.639086\pi\)
0.423180 0.906045i \(-0.360914\pi\)
\(230\) 0.516422 + 0.894470i 0.0340519 + 0.0589796i
\(231\) 0 0
\(232\) −3.40511 1.96594i −0.223556 0.129070i
\(233\) −6.85333 −0.448976 −0.224488 0.974477i \(-0.572071\pi\)
−0.224488 + 0.974477i \(0.572071\pi\)
\(234\) 0 0
\(235\) −21.5926 −1.40854
\(236\) −16.0980 9.29416i −1.04789 0.604998i
\(237\) 0 0
\(238\) 0.191706 + 0.332045i 0.0124265 + 0.0215233i
\(239\) 22.0754i 1.42794i −0.700177 0.713970i \(-0.746895\pi\)
0.700177 0.713970i \(-0.253105\pi\)
\(240\) 0 0
\(241\) 13.6807 7.89855i 0.881251 0.508790i 0.0101802 0.999948i \(-0.496759\pi\)
0.871071 + 0.491158i \(0.163426\pi\)
\(242\) 1.30796i 0.0840787i
\(243\) 0 0
\(244\) 8.95947 15.5183i 0.573571 0.993455i
\(245\) 1.46199 + 0.844083i 0.0934034 + 0.0539265i
\(246\) 0 0
\(247\) 4.50732 + 2.60525i 0.286794 + 0.165768i
\(248\) −2.25349 −0.143097
\(249\) 0 0
\(250\) −0.726405 + 1.25817i −0.0459419 + 0.0795737i
\(251\) −11.2783 19.5346i −0.711882 1.23302i −0.964150 0.265359i \(-0.914510\pi\)
0.252268 0.967658i \(-0.418824\pi\)
\(252\) 0 0
\(253\) 1.60512 0.926716i 0.100913 0.0582621i
\(254\) 0.840894 0.485490i 0.0527624 0.0304624i
\(255\) 0 0
\(256\) −7.42681 12.8636i −0.464176 0.803976i
\(257\) −10.2064 + 17.6781i −0.636660 + 1.10273i 0.349501 + 0.936936i \(0.386351\pi\)
−0.986161 + 0.165791i \(0.946982\pi\)
\(258\) 0 0
\(259\) 6.31584 0.392447
\(260\) 10.4633 + 6.04781i 0.648904 + 0.375069i
\(261\) 0 0
\(262\) −1.97044 1.13763i −0.121734 0.0702833i
\(263\) −14.7701 + 25.5826i −0.910764 + 1.57749i −0.0977768 + 0.995208i \(0.531173\pi\)
−0.812987 + 0.582281i \(0.802160\pi\)
\(264\) 0 0
\(265\) 2.31464i 0.142187i
\(266\) 0.150505 0.0868943i 0.00922807 0.00532783i
\(267\) 0 0
\(268\) 26.7567i 1.63442i
\(269\) 13.9581 + 24.1762i 0.851043 + 1.47405i 0.880268 + 0.474477i \(0.157363\pi\)
−0.0292252 + 0.999573i \(0.509304\pi\)
\(270\) 0 0
\(271\) −25.5036 14.7245i −1.54924 0.894451i −0.998200 0.0599690i \(-0.980900\pi\)
−0.551035 0.834482i \(-0.685767\pi\)
\(272\) −12.4660 −0.755861
\(273\) 0 0
\(274\) −2.19362 −0.132521
\(275\) 0.678933 + 0.391982i 0.0409412 + 0.0236374i
\(276\) 0 0
\(277\) 3.42927 + 5.93967i 0.206045 + 0.356880i 0.950465 0.310831i \(-0.100607\pi\)
−0.744420 + 0.667711i \(0.767274\pi\)
\(278\) 0.631992i 0.0379043i
\(279\) 0 0
\(280\) 0.701313 0.404903i 0.0419114 0.0241976i
\(281\) 29.0940i 1.73561i 0.496909 + 0.867803i \(0.334468\pi\)
−0.496909 + 0.867803i \(0.665532\pi\)
\(282\) 0 0
\(283\) 5.80511 10.0547i 0.345078 0.597692i −0.640290 0.768133i \(-0.721186\pi\)
0.985368 + 0.170441i \(0.0545192\pi\)
\(284\) −12.1761 7.02986i −0.722517 0.417146i
\(285\) 0 0
\(286\) −0.0791828 + 0.136993i −0.00468217 + 0.00810058i
\(287\) 5.82732 0.343976
\(288\) 0 0
\(289\) 3.42614 5.93425i 0.201538 0.349074i
\(290\) 0.832724 + 1.44232i 0.0488993 + 0.0846960i
\(291\) 0 0
\(292\) 3.71555 2.14517i 0.217436 0.125537i
\(293\) 15.4054 8.89430i 0.899992 0.519610i 0.0227942 0.999740i \(-0.492744\pi\)
0.877197 + 0.480130i \(0.159410\pi\)
\(294\) 0 0
\(295\) 7.90228 + 13.6871i 0.460088 + 0.796896i
\(296\) 1.51484 2.62378i 0.0880483 0.152504i
\(297\) 0 0
\(298\) −1.11611 −0.0646544
\(299\) 18.3278 + 0.00899334i 1.05992 + 0.000520098i
\(300\) 0 0
\(301\) −0.669543 0.386561i −0.0385918 0.0222810i
\(302\) −0.843314 + 1.46066i −0.0485273 + 0.0840517i
\(303\) 0 0
\(304\) 5.65043i 0.324074i
\(305\) −13.1943 + 7.61771i −0.755501 + 0.436189i
\(306\) 0 0
\(307\) 9.07966i 0.518204i 0.965850 + 0.259102i \(0.0834265\pi\)
−0.965850 + 0.259102i \(0.916573\pi\)
\(308\) −0.361977 0.626963i −0.0206256 0.0357245i
\(309\) 0 0
\(310\) 0.826643 + 0.477262i 0.0469501 + 0.0271067i
\(311\) 1.57073 0.0890677 0.0445338 0.999008i \(-0.485820\pi\)
0.0445338 + 0.999008i \(0.485820\pi\)
\(312\) 0 0
\(313\) 20.6232 1.16569 0.582846 0.812582i \(-0.301939\pi\)
0.582846 + 0.812582i \(0.301939\pi\)
\(314\) −1.79101 1.03404i −0.101073 0.0583544i
\(315\) 0 0
\(316\) 6.83792 + 11.8436i 0.384663 + 0.666256i
\(317\) 30.5435i 1.71549i −0.514072 0.857747i \(-0.671863\pi\)
0.514072 0.857747i \(-0.328137\pi\)
\(318\) 0 0
\(319\) 2.58823 1.49432i 0.144913 0.0836657i
\(320\) 12.9219i 0.722358i
\(321\) 0 0
\(322\) 0.305907 0.529847i 0.0170476 0.0295272i
\(323\) 3.98340 + 2.29982i 0.221642 + 0.127965i
\(324\) 0 0
\(325\) 3.87285 + 6.71558i 0.214827 + 0.372513i
\(326\) 1.41937 0.0786118
\(327\) 0 0
\(328\) 1.39767 2.42084i 0.0771735 0.133668i
\(329\) 6.39527 + 11.0769i 0.352583 + 0.610691i
\(330\) 0 0
\(331\) −22.3894 + 12.9265i −1.23063 + 0.710507i −0.967162 0.254161i \(-0.918201\pi\)
−0.263472 + 0.964667i \(0.584868\pi\)
\(332\) −0.975612 + 0.563270i −0.0535437 + 0.0309135i
\(333\) 0 0
\(334\) −0.259789 0.449967i −0.0142150 0.0246211i
\(335\) 11.3748 19.7017i 0.621472 1.07642i
\(336\) 0 0
\(337\) −21.3954 −1.16548 −0.582742 0.812657i \(-0.698020\pi\)
−0.582742 + 0.812657i \(0.698020\pi\)
\(338\) −1.35582 + 0.781009i −0.0737468 + 0.0424813i
\(339\) 0 0
\(340\) 9.24704 + 5.33878i 0.501491 + 0.289536i
\(341\) 0.856443 1.48340i 0.0463790 0.0803308i
\(342\) 0 0
\(343\) 1.00000i 0.0539949i
\(344\) −0.321177 + 0.185432i −0.0173167 + 0.00999781i
\(345\) 0 0
\(346\) 1.50687i 0.0810098i
\(347\) 1.10442 + 1.91291i 0.0592882 + 0.102690i 0.894146 0.447775i \(-0.147784\pi\)
−0.834858 + 0.550466i \(0.814450\pi\)
\(348\) 0 0
\(349\) −9.77843 5.64558i −0.523427 0.302201i 0.214908 0.976634i \(-0.431055\pi\)
−0.738336 + 0.674433i \(0.764388\pi\)
\(350\) 0.258786 0.0138327
\(351\) 0 0
\(352\) −0.521548 −0.0277986
\(353\) 30.8680 + 17.8217i 1.64294 + 0.948552i 0.979781 + 0.200072i \(0.0641177\pi\)
0.663158 + 0.748479i \(0.269216\pi\)
\(354\) 0 0
\(355\) 5.97708 + 10.3526i 0.317230 + 0.549459i
\(356\) 2.26137i 0.119852i
\(357\) 0 0
\(358\) 0.687464 0.396907i 0.0363336 0.0209772i
\(359\) 19.3218i 1.01976i −0.860244 0.509882i \(-0.829689\pi\)
0.860244 0.509882i \(-0.170311\pi\)
\(360\) 0 0
\(361\) −8.45757 + 14.6489i −0.445135 + 0.770997i
\(362\) −1.14822 0.662924i −0.0603490 0.0348425i
\(363\) 0 0
\(364\) 0.00351282 7.15887i 0.000184122 0.375227i
\(365\) −3.64783 −0.190936
\(366\) 0 0
\(367\) 1.86032 3.22218i 0.0971082 0.168196i −0.813378 0.581735i \(-0.802374\pi\)
0.910487 + 0.413539i \(0.135707\pi\)
\(368\) 9.94604 + 17.2271i 0.518473 + 0.898022i
\(369\) 0 0
\(370\) −1.11137 + 0.641649i −0.0577773 + 0.0333578i
\(371\) −1.18740 + 0.685548i −0.0616469 + 0.0355919i
\(372\) 0 0
\(373\) 1.75638 + 3.04214i 0.0909420 + 0.157516i 0.907908 0.419170i \(-0.137679\pi\)
−0.816966 + 0.576686i \(0.804346\pi\)
\(374\) −0.0698995 + 0.121070i −0.00361442 + 0.00626035i
\(375\) 0 0
\(376\) 6.13557 0.316418
\(377\) 29.5533 + 0.0145016i 1.52207 + 0.000746873i
\(378\) 0 0
\(379\) 21.6647 + 12.5081i 1.11284 + 0.642500i 0.939564 0.342373i \(-0.111230\pi\)
0.173279 + 0.984873i \(0.444564\pi\)
\(380\) 2.41990 4.19139i 0.124138 0.215014i
\(381\) 0 0
\(382\) 0.713990i 0.0365309i
\(383\) 19.4556 11.2327i 0.994134 0.573964i 0.0876266 0.996153i \(-0.472072\pi\)
0.906507 + 0.422190i \(0.138738\pi\)
\(384\) 0 0
\(385\) 0.615536i 0.0313706i
\(386\) 0.252512 + 0.437364i 0.0128525 + 0.0222612i
\(387\) 0 0
\(388\) −13.6320 7.87043i −0.692059 0.399561i
\(389\) −13.3364 −0.676184 −0.338092 0.941113i \(-0.609781\pi\)
−0.338092 + 0.941113i \(0.609781\pi\)
\(390\) 0 0
\(391\) 16.1928 0.818906
\(392\) −0.415429 0.239848i −0.0209823 0.0121142i
\(393\) 0 0
\(394\) −0.348137 0.602991i −0.0175389 0.0303783i
\(395\) 11.6278i 0.585057i
\(396\) 0 0
\(397\) −22.3723 + 12.9166i −1.12283 + 0.648268i −0.942123 0.335268i \(-0.891173\pi\)
−0.180710 + 0.983536i \(0.557840\pi\)
\(398\) 1.43948i 0.0721544i
\(399\) 0 0
\(400\) −4.20698 + 7.28670i −0.210349 + 0.364335i
\(401\) −15.2078 8.78025i −0.759443 0.438465i 0.0696524 0.997571i \(-0.477811\pi\)
−0.829096 + 0.559106i \(0.811144\pi\)
\(402\) 0 0
\(403\) 14.6729 8.46180i 0.730909 0.421512i
\(404\) −30.8677 −1.53572
\(405\) 0 0
\(406\) 0.493272 0.854372i 0.0244807 0.0424018i
\(407\) 1.15143 + 1.99434i 0.0570745 + 0.0988559i
\(408\) 0 0
\(409\) 12.5818 7.26410i 0.622129 0.359186i −0.155568 0.987825i \(-0.549721\pi\)
0.777698 + 0.628639i \(0.216388\pi\)
\(410\) −1.02541 + 0.592019i −0.0506412 + 0.0292377i
\(411\) 0 0
\(412\) 10.2236 + 17.7077i 0.503679 + 0.872398i
\(413\) 4.68098 8.10770i 0.230336 0.398954i
\(414\) 0 0
\(415\) 0.957831 0.0470181
\(416\) −4.46514 2.58087i −0.218922 0.126538i
\(417\) 0 0
\(418\) 0.0548769 + 0.0316832i 0.00268412 + 0.00154968i
\(419\) −2.30096 + 3.98538i −0.112409 + 0.194699i −0.916741 0.399482i \(-0.869190\pi\)
0.804332 + 0.594180i \(0.202523\pi\)
\(420\) 0 0
\(421\) 19.2645i 0.938895i −0.882960 0.469447i \(-0.844453\pi\)
0.882960 0.469447i \(-0.155547\pi\)
\(422\) 0.858468 0.495637i 0.0417896 0.0241272i
\(423\) 0 0
\(424\) 0.657709i 0.0319412i
\(425\) 3.42462 + 5.93161i 0.166118 + 0.287726i
\(426\) 0 0
\(427\) 7.81574 + 4.51242i 0.378230 + 0.218371i
\(428\) 26.0587 1.25959
\(429\) 0 0
\(430\) 0.157089 0.00757548
\(431\) 24.5649 + 14.1825i 1.18325 + 0.683149i 0.956764 0.290865i \(-0.0939432\pi\)
0.226485 + 0.974015i \(0.427277\pi\)
\(432\) 0 0
\(433\) −6.26014 10.8429i −0.300843 0.521076i 0.675484 0.737375i \(-0.263935\pi\)
−0.976327 + 0.216299i \(0.930601\pi\)
\(434\) 0.565421i 0.0271411i
\(435\) 0 0
\(436\) 17.9618 10.3702i 0.860213 0.496644i
\(437\) 7.33969i 0.351105i
\(438\) 0 0
\(439\) 15.8637 27.4767i 0.757132 1.31139i −0.187176 0.982326i \(-0.559933\pi\)
0.944307 0.329064i \(-0.106733\pi\)
\(440\) 0.255711 + 0.147635i 0.0121906 + 0.00703822i
\(441\) 0 0
\(442\) −1.19754 + 0.690619i −0.0569613 + 0.0328494i
\(443\) −1.73048 −0.0822177 −0.0411088 0.999155i \(-0.513089\pi\)
−0.0411088 + 0.999155i \(0.513089\pi\)
\(444\) 0 0
\(445\) −0.961355 + 1.66512i −0.0455726 + 0.0789341i
\(446\) 0.920842 + 1.59494i 0.0436031 + 0.0755228i
\(447\) 0 0
\(448\) 6.62892 3.82721i 0.313187 0.180819i
\(449\) 9.14208 5.27818i 0.431442 0.249093i −0.268519 0.963274i \(-0.586534\pi\)
0.699961 + 0.714181i \(0.253201\pi\)
\(450\) 0 0
\(451\) 1.06237 + 1.84008i 0.0500252 + 0.0866462i
\(452\) 4.91675 8.51605i 0.231264 0.400561i
\(453\) 0 0
\(454\) 0.837063 0.0392853
\(455\) −3.04597 + 5.26980i −0.142797 + 0.247052i
\(456\) 0 0
\(457\) −6.88399 3.97447i −0.322019 0.185918i 0.330273 0.943885i \(-0.392859\pi\)
−0.652292 + 0.757968i \(0.726193\pi\)
\(458\) 1.65025 2.85832i 0.0771111 0.133560i
\(459\) 0 0
\(460\) 17.0383i 0.794415i
\(461\) −9.43262 + 5.44592i −0.439321 + 0.253642i −0.703309 0.710884i \(-0.748295\pi\)
0.263989 + 0.964526i \(0.414962\pi\)
\(462\) 0 0
\(463\) 35.8227i 1.66482i −0.554158 0.832411i \(-0.686960\pi\)
0.554158 0.832411i \(-0.313040\pi\)
\(464\) 16.0379 + 27.7784i 0.744539 + 1.28958i
\(465\) 0 0
\(466\) −0.714355 0.412433i −0.0330918 0.0191056i
\(467\) 19.8983 0.920785 0.460393 0.887715i \(-0.347709\pi\)
0.460393 + 0.887715i \(0.347709\pi\)
\(468\) 0 0
\(469\) −13.4759 −0.622261
\(470\) −2.25069 1.29944i −0.103817 0.0599386i
\(471\) 0 0
\(472\) −2.24545 3.88923i −0.103355 0.179016i
\(473\) 0.281894i 0.0129615i
\(474\) 0 0
\(475\) 2.68861 1.55227i 0.123362 0.0712231i
\(476\) 6.32495i 0.289904i
\(477\) 0 0
\(478\) 1.32850 2.30102i 0.0607640 0.105246i
\(479\) −22.7680 13.1451i −1.04030 0.600615i −0.120379 0.992728i \(-0.538411\pi\)
−0.919917 + 0.392113i \(0.871744\pi\)
\(480\) 0 0
\(481\) −0.0111741 + 22.7721i −0.000509496 + 1.03832i
\(482\) 1.90134 0.0866035
\(483\) 0 0
\(484\) −10.7883 + 18.6860i −0.490379 + 0.849362i
\(485\) 6.69177 + 11.5905i 0.303857 + 0.526296i
\(486\) 0 0
\(487\) 5.52491 3.18981i 0.250358 0.144544i −0.369570 0.929203i \(-0.620495\pi\)
0.619928 + 0.784659i \(0.287162\pi\)
\(488\) 3.74918 2.16459i 0.169717 0.0979864i
\(489\) 0 0
\(490\) 0.101594 + 0.175965i 0.00458954 + 0.00794931i
\(491\) 1.48384 2.57008i 0.0669647 0.115986i −0.830599 0.556871i \(-0.812002\pi\)
0.897564 + 0.440885i \(0.145335\pi\)
\(492\) 0 0
\(493\) 26.1107 1.17597
\(494\) 0.313035 + 0.542808i 0.0140841 + 0.0244221i
\(495\) 0 0
\(496\) 15.9207 + 9.19184i 0.714862 + 0.412726i
\(497\) 3.54058 6.13246i 0.158817 0.275078i
\(498\) 0 0
\(499\) 28.1331i 1.25941i −0.776835 0.629704i \(-0.783176\pi\)
0.776835 0.629704i \(-0.216824\pi\)
\(500\) 20.7554 11.9831i 0.928208 0.535901i
\(501\) 0 0
\(502\) 2.71492i 0.121173i
\(503\) −15.7688 27.3124i −0.703097 1.21780i −0.967374 0.253353i \(-0.918467\pi\)
0.264277 0.964447i \(-0.414867\pi\)
\(504\) 0 0
\(505\) 22.7288 + 13.1225i 1.01142 + 0.583943i
\(506\) 0.223079 0.00991706
\(507\) 0 0
\(508\) −16.0178 −0.710673
\(509\) −11.7731 6.79719i −0.521832 0.301280i 0.215852 0.976426i \(-0.430747\pi\)
−0.737684 + 0.675146i \(0.764081\pi\)
\(510\) 0 0
\(511\) 1.08041 + 1.87133i 0.0477947 + 0.0827828i
\(512\) 9.35193i 0.413301i
\(513\) 0 0
\(514\) −2.12773 + 1.22845i −0.0938502 + 0.0541844i
\(515\) 17.3850i 0.766074i
\(516\) 0 0
\(517\) −2.33183 + 4.03885i −0.102554 + 0.177628i
\(518\) 0.658329 + 0.380087i 0.0289253 + 0.0167000i
\(519\) 0 0
\(520\) 1.45866 + 2.52933i 0.0639664 + 0.110919i
\(521\) −8.78344 −0.384810 −0.192405 0.981316i \(-0.561629\pi\)
−0.192405 + 0.981316i \(0.561629\pi\)
\(522\) 0 0
\(523\) −16.2849 + 28.2063i −0.712088 + 1.23337i 0.251983 + 0.967732i \(0.418917\pi\)
−0.964072 + 0.265642i \(0.914416\pi\)
\(524\) 18.7670 + 32.5053i 0.819838 + 1.42000i
\(525\) 0 0
\(526\) −3.07912 + 1.77773i −0.134256 + 0.0775127i
\(527\) 12.9600 7.48246i 0.564547 0.325941i
\(528\) 0 0
\(529\) −1.41953 2.45869i −0.0617185 0.106900i
\(530\) 0.139295 0.241265i 0.00605057 0.0104799i
\(531\) 0 0
\(532\) −2.86690 −0.124296
\(533\) −0.0103098 + 21.0107i −0.000446568 + 0.910074i
\(534\) 0 0
\(535\) −19.1878 11.0781i −0.829560 0.478947i
\(536\) −3.23218 + 5.59829i −0.139609 + 0.241809i
\(537\) 0 0
\(538\) 3.36000i 0.144860i
\(539\) 0.315769 0.182309i 0.0136011 0.00785261i
\(540\) 0 0
\(541\) 6.94870i 0.298748i −0.988781 0.149374i \(-0.952274\pi\)
0.988781 0.149374i \(-0.0477258\pi\)
\(542\) −1.77224 3.06961i −0.0761243 0.131851i
\(543\) 0 0
\(544\) −3.94612 2.27830i −0.169189 0.0976811i
\(545\) −17.6344 −0.755375
\(546\) 0 0
\(547\) 10.9095 0.466457 0.233229 0.972422i \(-0.425071\pi\)
0.233229 + 0.972422i \(0.425071\pi\)
\(548\) 31.3388 + 18.0935i 1.33873 + 0.772915i
\(549\) 0 0
\(550\) 0.0471789 + 0.0817163i 0.00201172 + 0.00348440i
\(551\) 11.8352i 0.504194i
\(552\) 0 0
\(553\) −5.96502 + 3.44391i −0.253659 + 0.146450i
\(554\) 0.825493i 0.0350718i
\(555\) 0 0
\(556\) −5.21282 + 9.02886i −0.221073 + 0.382909i
\(557\) −29.9901 17.3148i −1.27072 0.733650i −0.295596 0.955313i \(-0.595518\pi\)
−0.975123 + 0.221662i \(0.928852\pi\)
\(558\) 0 0
\(559\) 1.39495 2.41339i 0.0590001 0.102075i
\(560\) −6.60628 −0.279166
\(561\) 0 0
\(562\) −1.75088 + 3.03261i −0.0738563 + 0.127923i
\(563\) −4.56839 7.91269i −0.192535 0.333480i 0.753555 0.657385i \(-0.228338\pi\)
−0.946090 + 0.323905i \(0.895004\pi\)
\(564\) 0 0
\(565\) −7.24070 + 4.18042i −0.304618 + 0.175872i
\(566\) 1.21019 0.698702i 0.0508680 0.0293686i
\(567\) 0 0
\(568\) −1.69840 2.94172i −0.0712633 0.123432i
\(569\) −9.15000 + 15.8483i −0.383588 + 0.664394i −0.991572 0.129555i \(-0.958645\pi\)
0.607984 + 0.793949i \(0.291978\pi\)
\(570\) 0 0
\(571\) −10.1791 −0.425981 −0.212990 0.977054i \(-0.568320\pi\)
−0.212990 + 0.977054i \(0.568320\pi\)
\(572\) 2.26119 1.30402i 0.0945450 0.0545237i
\(573\) 0 0
\(574\) 0.607409 + 0.350688i 0.0253528 + 0.0146374i
\(575\) 5.46470 9.46514i 0.227894 0.394724i
\(576\) 0 0
\(577\) 19.5165i 0.812482i 0.913766 + 0.406241i \(0.133161\pi\)
−0.913766 + 0.406241i \(0.866839\pi\)
\(578\) 0.714246 0.412370i 0.0297087 0.0171523i
\(579\) 0 0
\(580\) 27.4740i 1.14080i
\(581\) −0.283690 0.491365i −0.0117694 0.0203853i
\(582\) 0 0
\(583\) −0.432949 0.249963i −0.0179309 0.0103524i
\(584\) 1.03654 0.0428923
\(585\) 0 0
\(586\) 2.14103 0.0884453
\(587\) 30.6486 + 17.6950i 1.26501 + 0.730351i 0.974039 0.226382i \(-0.0726898\pi\)
0.290967 + 0.956733i \(0.406023\pi\)
\(588\) 0 0
\(589\) −3.39156 5.87436i −0.139747 0.242049i
\(590\) 1.90223i 0.0783137i
\(591\) 0 0
\(592\) −21.4044 + 12.3579i −0.879716 + 0.507905i
\(593\) 18.0881i 0.742790i 0.928475 + 0.371395i \(0.121120\pi\)
−0.928475 + 0.371395i \(0.878880\pi\)
\(594\) 0 0
\(595\) −2.68887 + 4.65725i −0.110233 + 0.190929i
\(596\) 15.9451 + 9.20592i 0.653138 + 0.377089i
\(597\) 0 0
\(598\) 1.90985 + 1.10390i 0.0780996 + 0.0451419i
\(599\) −9.05992 −0.370178 −0.185089 0.982722i \(-0.559257\pi\)
−0.185089 + 0.982722i \(0.559257\pi\)
\(600\) 0 0
\(601\) −14.6440 + 25.3642i −0.597343 + 1.03463i 0.395869 + 0.918307i \(0.370444\pi\)
−0.993212 + 0.116321i \(0.962890\pi\)
\(602\) −0.0465264 0.0805861i −0.00189628 0.00328444i
\(603\) 0 0
\(604\) 24.0958 13.9117i 0.980444 0.566059i
\(605\) 15.8876 9.17269i 0.645922 0.372923i
\(606\) 0 0
\(607\) 19.6825 + 34.0911i 0.798887 + 1.38371i 0.920341 + 0.391116i \(0.127911\pi\)
−0.121454 + 0.992597i \(0.538756\pi\)
\(608\) −1.03268 + 1.78865i −0.0418807 + 0.0725394i
\(609\) 0 0
\(610\) −1.83373 −0.0742457
\(611\) −39.9498 + 23.0389i −1.61619 + 0.932053i
\(612\) 0 0
\(613\) 4.79186 + 2.76658i 0.193541 + 0.111741i 0.593639 0.804731i \(-0.297691\pi\)
−0.400098 + 0.916472i \(0.631024\pi\)
\(614\) −0.546413 + 0.946416i −0.0220514 + 0.0381942i
\(615\) 0 0
\(616\) 0.174906i 0.00704716i
\(617\) −10.8959 + 6.29077i −0.438654 + 0.253257i −0.703026 0.711164i \(-0.748168\pi\)
0.264373 + 0.964421i \(0.414835\pi\)
\(618\) 0 0
\(619\) 22.3955i 0.900149i 0.892991 + 0.450075i \(0.148603\pi\)
−0.892991 + 0.450075i \(0.851397\pi\)
\(620\) −7.87314 13.6367i −0.316193 0.547662i
\(621\) 0 0
\(622\) 0.163724 + 0.0945262i 0.00656474 + 0.00379015i
\(623\) 1.13893 0.0456305
\(624\) 0 0
\(625\) −9.62659 −0.385064
\(626\) 2.14965 + 1.24110i 0.0859175 + 0.0496045i
\(627\) 0 0
\(628\) 17.0580 + 29.5454i 0.680690 + 1.17899i
\(629\) 20.1194i 0.802213i
\(630\) 0 0
\(631\) 1.68778 0.974439i 0.0671894 0.0387918i −0.466029 0.884769i \(-0.654316\pi\)
0.533218 + 0.845978i \(0.320982\pi\)
\(632\) 3.30406i 0.131428i
\(633\) 0 0
\(634\) 1.83811 3.18369i 0.0730005 0.126441i
\(635\) 11.7944 + 6.80948i 0.468045 + 0.270226i
\(636\) 0 0
\(637\) 3.60555 + 0.00176922i 0.142857 + 7.00992e-5i
\(638\) 0.359712 0.0142411
\(639\) 0 0
\(640\) −3.19238 + 5.52937i −0.126190 + 0.218568i
\(641\) −5.21051 9.02487i −0.205803 0.356461i 0.744585 0.667527i \(-0.232647\pi\)
−0.950388 + 0.311066i \(0.899314\pi\)
\(642\) 0 0
\(643\) 13.2247 7.63531i 0.521533 0.301107i −0.216029 0.976387i \(-0.569310\pi\)
0.737562 + 0.675280i \(0.235977\pi\)
\(644\) −8.74061 + 5.04639i −0.344428 + 0.198856i
\(645\) 0 0
\(646\) 0.276806 + 0.479442i 0.0108908 + 0.0188634i
\(647\) −8.75328 + 15.1611i −0.344127 + 0.596045i −0.985195 0.171439i \(-0.945158\pi\)
0.641068 + 0.767484i \(0.278492\pi\)
\(648\) 0 0
\(649\) 3.41354 0.133993
\(650\) −0.000457849 0.933064i −1.79583e−5 0.0365978i
\(651\) 0 0
\(652\) −20.2777 11.7073i −0.794136 0.458494i
\(653\) −5.09169 + 8.81906i −0.199253 + 0.345117i −0.948287 0.317416i \(-0.897185\pi\)
0.749033 + 0.662532i \(0.230518\pi\)
\(654\) 0 0
\(655\) 31.9129i 1.24694i
\(656\) −19.7488 + 11.4020i −0.771063 + 0.445173i
\(657\) 0 0
\(658\) 1.53947i 0.0600147i
\(659\) −21.9294 37.9828i −0.854247 1.47960i −0.877342 0.479866i \(-0.840685\pi\)
0.0230945 0.999733i \(-0.492648\pi\)
\(660\) 0 0
\(661\) −28.5156 16.4635i −1.10913 0.640356i −0.170526 0.985353i \(-0.554547\pi\)
−0.938604 + 0.344997i \(0.887880\pi\)
\(662\) −3.11167 −0.120939
\(663\) 0 0
\(664\) −0.272170 −0.0105622
\(665\) 2.11098 + 1.21878i 0.0818604 + 0.0472621i
\(666\) 0 0
\(667\) −20.8326 36.0831i −0.806640 1.39714i
\(668\) 8.57120i 0.331630i
\(669\) 0 0
\(670\) 2.37130 1.36907i 0.0916113 0.0528918i
\(671\) 3.29062i 0.127033i
\(672\) 0 0
\(673\) 13.3423 23.1095i 0.514307 0.890806i −0.485555 0.874206i \(-0.661383\pi\)
0.999862 0.0165997i \(-0.00528409\pi\)
\(674\) −2.23015 1.28758i −0.0859021 0.0495956i
\(675\) 0 0
\(676\) 25.8117 + 0.0253313i 0.992756 + 0.000974280i
\(677\) −29.5328 −1.13504 −0.567519 0.823361i \(-0.692096\pi\)
−0.567519 + 0.823361i \(0.692096\pi\)
\(678\) 0 0
\(679\) 3.96393 6.86572i 0.152122 0.263482i
\(680\) 1.28984 + 2.23406i 0.0494630 + 0.0856725i
\(681\) 0 0
\(682\) 0.178542 0.103081i 0.00683674 0.00394719i
\(683\) 15.8379 9.14400i 0.606019 0.349885i −0.165387 0.986229i \(-0.552887\pi\)
0.771406 + 0.636343i \(0.219554\pi\)
\(684\) 0 0
\(685\) −15.3838 26.6456i −0.587786 1.01807i
\(686\) 0.0601799 0.104235i 0.00229768 0.00397970i
\(687\) 0 0
\(688\) 3.02545 0.115344
\(689\) −2.46968 4.28246i −0.0940872 0.163149i
\(690\) 0 0
\(691\) −8.95525 5.17031i −0.340674 0.196688i 0.319896 0.947453i \(-0.396352\pi\)
−0.660570 + 0.750765i \(0.729685\pi\)
\(692\) −12.4290 + 21.5277i −0.472480 + 0.818360i
\(693\) 0 0
\(694\) 0.265855i 0.0100917i
\(695\) 7.67671 4.43215i 0.291194 0.168121i
\(696\) 0 0
\(697\) 18.5632i 0.703131i
\(698\) −0.679501 1.17693i −0.0257195 0.0445475i
\(699\) 0 0
\(700\) −3.69710 2.13452i −0.139737 0.0806774i
\(701\) −41.6959 −1.57483 −0.787415 0.616423i \(-0.788581\pi\)
−0.787415 + 0.616423i \(0.788581\pi\)
\(702\) 0 0
\(703\) 9.11948 0.343948
\(704\) 2.41702 + 1.39547i 0.0910951 + 0.0525938i
\(705\) 0 0
\(706\) 2.14501 + 3.71527i 0.0807287 + 0.139826i
\(707\) 15.5464i 0.584684i
\(708\) 0 0
\(709\) 0.00947974 0.00547313i 0.000356019 0.000205548i −0.499822 0.866128i \(-0.666601\pi\)
0.500178 + 0.865923i \(0.333268\pi\)
\(710\) 1.43880i 0.0539972i
\(711\) 0 0
\(712\) 0.273171 0.473146i 0.0102375 0.0177319i
\(713\) −20.6804 11.9398i −0.774488 0.447151i
\(714\) 0 0
\(715\) −2.21935 0.00108902i −0.0829988 4.07271e-5i
\(716\) −13.0951 −0.489388
\(717\) 0 0
\(718\) 1.16278 2.01400i 0.0433947 0.0751618i
\(719\) 12.7330 + 22.0542i 0.474861 + 0.822484i 0.999586 0.0287885i \(-0.00916494\pi\)
−0.524724 + 0.851272i \(0.675832\pi\)
\(720\) 0 0
\(721\) −8.91847 + 5.14908i −0.332141 + 0.191762i
\(722\) −1.76314 + 1.01795i −0.0656174 + 0.0378842i
\(723\) 0 0
\(724\) 10.9359 + 18.9416i 0.406430 + 0.703957i
\(725\) 8.81176 15.2624i 0.327261 0.566832i
\(726\) 0 0
\(727\) −23.5565 −0.873663 −0.436831 0.899543i \(-0.643899\pi\)
−0.436831 + 0.899543i \(0.643899\pi\)
\(728\) 0.865519 1.49743i 0.0320783 0.0554983i
\(729\) 0 0
\(730\) −0.380231 0.219526i −0.0140730 0.00812503i
\(731\) 1.23141 2.13286i 0.0455453 0.0788867i
\(732\) 0 0
\(733\) 6.23249i 0.230202i 0.993354 + 0.115101i \(0.0367192\pi\)
−0.993354 + 0.115101i \(0.963281\pi\)
\(734\) 0.387821 0.223909i 0.0143147 0.00826461i
\(735\) 0 0
\(736\) 7.27100i 0.268013i
\(737\) −2.45679 4.25528i −0.0904969 0.156745i
\(738\) 0 0
\(739\) 1.12339 + 0.648588i 0.0413244 + 0.0238587i 0.520520 0.853850i \(-0.325738\pi\)
−0.479195 + 0.877708i \(0.659071\pi\)
\(740\) 21.1699 0.778221
\(741\) 0 0
\(742\) −0.165025 −0.00605825
\(743\) −5.25627 3.03471i −0.192834 0.111333i 0.400475 0.916308i \(-0.368845\pi\)
−0.593309 + 0.804975i \(0.702179\pi\)
\(744\) 0 0
\(745\) −7.82725 13.5572i −0.286768 0.496697i
\(746\) 0.422796i 0.0154797i
\(747\) 0 0
\(748\) 1.99722 1.15310i 0.0730256 0.0421613i
\(749\) 13.1244i 0.479555i
\(750\) 0 0
\(751\) −18.3023 + 31.7005i −0.667860 + 1.15677i 0.310641 + 0.950527i \(0.399456\pi\)
−0.978501 + 0.206241i \(0.933877\pi\)
\(752\) −43.3473 25.0266i −1.58071 0.912625i
\(753\) 0 0
\(754\) 3.07961 + 1.78003i 0.112153 + 0.0648248i
\(755\) −23.6566 −0.860952
\(756\) 0 0
\(757\) −5.83991 + 10.1150i −0.212255 + 0.367636i −0.952420 0.304789i \(-0.901414\pi\)
0.740165 + 0.672425i \(0.234747\pi\)
\(758\) 1.50548 + 2.60757i 0.0546815 + 0.0947111i
\(759\) 0 0
\(760\) 1.01263 0.584642i 0.0367320 0.0212072i
\(761\) 34.4408 19.8844i 1.24848 0.720810i 0.277673 0.960676i \(-0.410437\pi\)
0.970806 + 0.239866i \(0.0771035\pi\)
\(762\) 0 0
\(763\) 5.22295 + 9.04641i 0.189083 + 0.327502i
\(764\) 5.88916 10.2003i 0.213062 0.369035i
\(765\) 0 0
\(766\) 2.70393 0.0976970
\(767\) 29.2245 + 16.8919i 1.05523 + 0.609930i
\(768\) 0 0
\(769\) −8.62507 4.97969i −0.311028 0.179572i 0.336358 0.941734i \(-0.390805\pi\)
−0.647386 + 0.762162i \(0.724138\pi\)
\(770\) −0.0370429 + 0.0641602i −0.00133493 + 0.00231217i
\(771\) 0 0
\(772\) 8.33112i 0.299843i
\(773\) −11.0433 + 6.37588i −0.397201 + 0.229324i −0.685276 0.728284i \(-0.740318\pi\)
0.288074 + 0.957608i \(0.406985\pi\)
\(774\) 0 0
\(775\) 10.1006i 0.362825i
\(776\) −1.90148 3.29346i −0.0682592 0.118228i
\(777\) 0 0
\(778\) −1.39012 0.802586i −0.0498382 0.0287741i
\(779\) 8.41411 0.301467
\(780\) 0 0
\(781\) 2.58192 0.0923882
\(782\) 1.68785 + 0.974483i 0.0603575 + 0.0348474i
\(783\) 0 0
\(784\) 1.95665 + 3.38901i 0.0698802 + 0.121036i
\(785\) 29.0069i 1.03530i
\(786\) 0 0
\(787\) 7.52380 4.34387i 0.268194 0.154842i −0.359872 0.933002i \(-0.617180\pi\)
0.628067 + 0.778159i \(0.283846\pi\)
\(788\) 11.4861i 0.409174i
\(789\) 0 0
\(790\) 0.699759 1.21202i 0.0248963 0.0431216i
\(791\) 4.28909 + 2.47631i 0.152503 + 0.0880474i
\(792\) 0 0
\(793\) −16.2836 + 28.1721i −0.578247 + 1.00042i
\(794\) −3.10929 −0.110345
\(795\) 0 0
\(796\) 11.8731 20.5649i 0.420832 0.728903i
\(797\) −19.3719 33.5531i −0.686187 1.18851i −0.973062 0.230543i \(-0.925950\pi\)
0.286875 0.957968i \(-0.407384\pi\)
\(798\) 0 0
\(799\) −35.2861 + 20.3724i −1.24833 + 0.720725i
\(800\) −2.66345 + 1.53774i −0.0941672 + 0.0543675i
\(801\) 0 0
\(802\) −1.05679 1.83041i −0.0373166 0.0646342i
\(803\) −0.393938 + 0.682321i −0.0139018 + 0.0240786i
\(804\) 0 0
\(805\) 8.58130 0.302451
\(806\) 2.03866 + 0.00100036i 0.0718086 + 3.52361e-5i
\(807\) 0 0
\(808\) −6.45844 3.72878i −0.227207 0.131178i
\(809\) 14.4275 24.9892i 0.507244 0.878573i −0.492721 0.870188i \(-0.663998\pi\)
0.999965 0.00838530i \(-0.00266915\pi\)
\(810\) 0 0
\(811\) 12.3917i 0.435131i −0.976046 0.217566i \(-0.930188\pi\)
0.976046 0.217566i \(-0.0698116\pi\)
\(812\) −14.0941 + 8.13725i −0.494607 + 0.285561i
\(813\) 0 0
\(814\) 0.277173i 0.00971491i
\(815\) 9.95405 + 17.2409i 0.348675 + 0.603923i
\(816\) 0 0
\(817\) −0.966758 0.558158i −0.0338226 0.0195275i
\(818\) 1.74861 0.0611388
\(819\) 0 0
\(820\) 19.5324 0.682103
\(821\) −35.5277 20.5119i −1.23992 0.715870i −0.270845 0.962623i \(-0.587303\pi\)
−0.969079 + 0.246753i \(0.920636\pi\)
\(822\) 0 0
\(823\) −1.06806 1.84994i −0.0372304 0.0644849i 0.846810 0.531896i \(-0.178520\pi\)
−0.884040 + 0.467411i \(0.845187\pi\)
\(824\) 4.93999i 0.172093i
\(825\) 0 0
\(826\) 0.975842 0.563403i 0.0339539 0.0196033i
\(827\) 8.54938i 0.297291i −0.988891 0.148645i \(-0.952509\pi\)
0.988891 0.148645i \(-0.0474913\pi\)
\(828\) 0 0
\(829\) −7.37844 + 12.7798i −0.256264 + 0.443862i −0.965238 0.261373i \(-0.915825\pi\)
0.708974 + 0.705234i \(0.249158\pi\)
\(830\) 0.0998392 + 0.0576422i 0.00346547 + 0.00200079i
\(831\) 0 0
\(832\) 13.7875 + 23.9077i 0.477995 + 0.828850i
\(833\) 3.18555 0.110373
\(834\) 0 0
\(835\) 3.64379 6.31123i 0.126099 0.218409i
\(836\) −0.522661 0.905276i −0.0180766 0.0313096i
\(837\) 0 0
\(838\) −0.479680 + 0.276943i −0.0165703 + 0.00956685i
\(839\) −23.3581 + 13.4858i −0.806411 + 0.465582i −0.845708 0.533646i \(-0.820822\pi\)
0.0392968 + 0.999228i \(0.487488\pi\)
\(840\) 0 0
\(841\) −19.0923 33.0687i −0.658353 1.14030i
\(842\) 1.15934 2.00803i 0.0399534 0.0692013i
\(843\) 0 0
\(844\) −16.3525 −0.562877
\(845\) −18.9951 10.9917i −0.653453 0.378127i
\(846\) 0 0
\(847\) −9.41114 5.43353i −0.323371 0.186698i
\(848\) 2.68275 4.64665i 0.0921259 0.159567i
\(849\) 0 0
\(850\) 0.824374i 0.0282758i
\(851\) 27.8035 16.0524i 0.953092 0.550268i
\(852\) 0 0
\(853\) 25.6332i 0.877665i 0.898569 + 0.438832i \(0.144608\pi\)
−0.898569 + 0.438832i \(0.855392\pi\)
\(854\) 0.543114 + 0.940702i 0.0185850 + 0.0321902i
\(855\) 0 0
\(856\) 5.45225 + 3.14786i 0.186354 + 0.107592i
\(857\) 11.7653 0.401894 0.200947 0.979602i \(-0.435598\pi\)
0.200947 + 0.979602i \(0.435598\pi\)
\(858\) 0 0
\(859\) −21.7761 −0.742992 −0.371496 0.928435i \(-0.621155\pi\)
−0.371496 + 0.928435i \(0.621155\pi\)
\(860\) −2.24422 1.29570i −0.0765274 0.0441831i
\(861\) 0 0
\(862\) 1.70701 + 2.95663i 0.0581410 + 0.100703i
\(863\) 41.0575i 1.39761i −0.715310 0.698807i \(-0.753715\pi\)
0.715310 0.698807i \(-0.246285\pi\)
\(864\) 0 0
\(865\) 18.3037 10.5677i 0.622345 0.359311i
\(866\) 1.50694i 0.0512079i
\(867\) 0 0
\(868\) −4.66373 + 8.07781i −0.158297 + 0.274179i
\(869\) −2.17496 1.25571i −0.0737803 0.0425971i
\(870\) 0 0
\(871\) 0.0238420 48.5882i 0.000807854 1.64635i
\(872\) 5.01085 0.169689
\(873\) 0 0
\(874\) 0.441702 0.765050i 0.0149408 0.0258782i
\(875\) 6.03527 + 10.4534i 0.204029 + 0.353389i
\(876\) 0 0
\(877\) 5.96788 3.44556i 0.201521 0.116348i −0.395844 0.918318i \(-0.629548\pi\)
0.597365 + 0.801970i \(0.296214\pi\)
\(878\) 3.30709 1.90935i 0.111609 0.0644374i
\(879\) 0 0
\(880\) −1.20439 2.08606i −0.0405998 0.0703209i
\(881\) 5.32288 9.21950i 0.179332 0.310613i −0.762320 0.647201i \(-0.775940\pi\)
0.941652 + 0.336588i \(0.109273\pi\)
\(882\) 0 0
\(883\) 21.3844 0.719641 0.359821 0.933022i \(-0.382838\pi\)
0.359821 + 0.933022i \(0.382838\pi\)
\(884\) 22.8049 + 0.0111902i 0.767012 + 0.000376369i
\(885\) 0 0
\(886\) −0.180376 0.104140i −0.00605986 0.00349866i
\(887\) −17.0575 + 29.5445i −0.572735 + 0.992007i 0.423548 + 0.905874i \(0.360784\pi\)
−0.996284 + 0.0861333i \(0.972549\pi\)
\(888\) 0 0
\(889\) 8.06731i 0.270569i
\(890\) −0.200413 + 0.115709i −0.00671786 + 0.00387856i
\(891\) 0 0
\(892\) 30.3813i 1.01724i
\(893\) 9.23418 + 15.9941i 0.309010 + 0.535221i
\(894\) 0 0
\(895\) 9.64235 + 5.56701i 0.322308 + 0.186085i
\(896\) 3.78208 0.126350
\(897\) 0 0
\(898\) 1.27056 0.0423992
\(899\) −33.3469 19.2528i −1.11218 0.642118i
\(900\) 0 0
\(901\) −2.18384 3.78253i −0.0727544 0.126014i
\(902\) 0.255734i 0.00851502i
\(903\) 0 0
\(904\) 2.05746 1.18788i 0.0684301 0.0395081i
\(905\) 18.5963i 0.618163i
\(906\) 0 0
\(907\) 21.0758 36.5043i 0.699810 1.21211i −0.268723 0.963218i \(-0.586601\pi\)
0.968532 0.248888i \(-0.0800652\pi\)
\(908\) −11.9586 6.90429i −0.396860 0.229127i
\(909\) 0 0
\(910\) −0.634632 + 0.365990i −0.0210379 + 0.0121324i
\(911\) −20.9947 −0.695584 −0.347792 0.937572i \(-0.613068\pi\)
−0.347792 + 0.937572i \(0.613068\pi\)
\(912\) 0 0
\(913\) 0.103438 0.179161i 0.00342331 0.00592935i
\(914\) −0.478367 0.828556i −0.0158230 0.0274062i
\(915\) 0 0
\(916\) −47.1521 + 27.2233i −1.55795 + 0.899483i
\(917\) −16.3712 + 9.45194i −0.540626 + 0.312131i
\(918\) 0 0
\(919\) 7.14699 + 12.3789i 0.235757 + 0.408344i 0.959493 0.281734i \(-0.0909096\pi\)
−0.723735 + 0.690078i \(0.757576\pi\)
\(920\) 2.05821 3.56492i 0.0678571 0.117532i
\(921\) 0 0
\(922\) −1.31094 −0.0431736
\(923\) 22.1046 + 12.7766i 0.727583 + 0.420546i
\(924\) 0 0
\(925\) 11.7603 + 6.78983i 0.386677 + 0.223248i
\(926\) 2.15581 3.73397i 0.0708443 0.122706i
\(927\) 0 0
\(928\) 11.7244i 0.384872i
\(929\) −5.89524 + 3.40362i −0.193416 + 0.111669i −0.593581 0.804774i \(-0.702286\pi\)
0.400164 + 0.916443i \(0.368953\pi\)
\(930\) 0 0
\(931\) 1.44391i 0.0473221i
\(932\) 6.80369 + 11.7843i 0.222862 + 0.386009i
\(933\) 0 0
\(934\) 2.07410 + 1.19748i 0.0678666 + 0.0391828i
\(935\) −1.96082 −0.0641256
\(936\) 0 0
\(937\) −5.22890 −0.170821 −0.0854104 0.996346i \(-0.527220\pi\)
−0.0854104 + 0.996346i \(0.527220\pi\)
\(938\) −1.40466 0.810981i −0.0458638 0.0264795i
\(939\) 0 0
\(940\) 21.4362 + 37.1285i 0.699170 + 1.21100i
\(941\) 56.4403i 1.83990i 0.392033 + 0.919951i \(0.371772\pi\)
−0.392033 + 0.919951i \(0.628228\pi\)
\(942\) 0 0
\(943\) 25.6530 14.8108i 0.835376 0.482304i
\(944\) 36.6361i 1.19240i
\(945\) 0 0
\(946\) 0.0169644 0.0293832i 0.000551559 0.000955329i
\(947\) 5.06648 + 2.92513i 0.164639 + 0.0950541i 0.580055 0.814577i \(-0.303031\pi\)
−0.415417 + 0.909631i \(0.636364\pi\)
\(948\) 0 0
\(949\) −6.74909 + 3.89217i −0.219085 + 0.126345i
\(950\) 0.373662 0.0121232
\(951\) 0 0
\(952\) 0.764047 1.32337i 0.0247629 0.0428906i
\(953\) 10.8742 + 18.8346i 0.352249 + 0.610114i 0.986643 0.162896i \(-0.0520836\pi\)
−0.634394 + 0.773010i \(0.718750\pi\)
\(954\) 0 0
\(955\) −8.67273 + 5.00720i −0.280643 + 0.162029i
\(956\) −37.9588 + 21.9155i −1.22767 + 0.708798i
\(957\) 0 0
\(958\) −1.58214 2.74035i −0.0511167 0.0885368i
\(959\) −9.11274 + 15.7837i −0.294266 + 0.509683i
\(960\) 0 0
\(961\) 8.93110 0.288100
\(962\) −1.37159 + 2.37297i −0.0442217 + 0.0765075i
\(963\) 0 0
\(964\) −27.1632 15.6827i −0.874868 0.505105i
\(965\) −3.54173 + 6.13446i −0.114012 + 0.197475i
\(966\) 0 0
\(967\) 13.3251i 0.428507i 0.976778 + 0.214253i \(0.0687318\pi\)
−0.976778 + 0.214253i \(0.931268\pi\)
\(968\) −4.51449 + 2.60644i −0.145101 + 0.0837742i
\(969\) 0 0
\(970\) 1.61084i 0.0517210i
\(971\) 3.73092 + 6.46215i 0.119731 + 0.207380i 0.919661 0.392713i \(-0.128463\pi\)
−0.799930 + 0.600093i \(0.795130\pi\)
\(972\) 0 0
\(973\) −4.54737 2.62542i −0.145782 0.0841673i
\(974\) 0.767850 0.0246035
\(975\) 0 0
\(976\) −35.3168 −1.13046
\(977\) 9.49204 + 5.48023i 0.303677 + 0.175328i 0.644094 0.764947i \(-0.277235\pi\)
−0.340416 + 0.940275i \(0.610568\pi\)
\(978\) 0 0
\(979\) 0.207638 + 0.359640i 0.00663614 + 0.0114941i
\(980\) 3.35188i 0.107072i
\(981\) 0 0
\(982\) 0.309335 0.178595i 0.00987127 0.00569918i
\(983\) 16.1441i 0.514918i −0.966289 0.257459i \(-0.917115\pi\)
0.966289 0.257459i \(-0.0828852\pi\)
\(984\) 0 0
\(985\) 4.88296 8.45754i 0.155584 0.269480i
\(986\) 2.72164 + 1.57134i 0.0866747 + 0.0500417i
\(987\) 0 0
\(988\) 0.00507218 10.3367i 0.000161368 0.328856i
\(989\) −3.92994 −0.124965
\(990\) 0 0
\(991\) −3.35748 + 5.81533i −0.106654 + 0.184730i −0.914413 0.404783i \(-0.867347\pi\)
0.807759 + 0.589513i \(0.200680\pi\)
\(992\) 3.35982 + 5.81938i 0.106674 + 0.184766i
\(993\) 0 0
\(994\) 0.738102 0.426143i 0.0234112 0.0135164i
\(995\) −17.4851 + 10.0950i −0.554315 + 0.320034i
\(996\) 0 0
\(997\) 9.22057 + 15.9705i 0.292018 + 0.505791i 0.974287 0.225311i \(-0.0723399\pi\)
−0.682269 + 0.731102i \(0.739007\pi\)
\(998\) 1.69305 2.93244i 0.0535924 0.0928248i
\(999\) 0 0
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 819.2.ct.a.316.4 12
3.2 odd 2 91.2.q.a.43.3 yes 12
12.11 even 2 1456.2.cc.c.225.3 12
13.10 even 6 inner 819.2.ct.a.127.4 12
21.2 odd 6 637.2.k.h.459.4 12
21.5 even 6 637.2.k.g.459.4 12
21.11 odd 6 637.2.u.h.30.4 12
21.17 even 6 637.2.u.i.30.4 12
21.20 even 2 637.2.q.h.589.3 12
39.17 odd 6 1183.2.c.i.337.6 12
39.20 even 12 1183.2.a.m.1.4 6
39.23 odd 6 91.2.q.a.36.3 12
39.32 even 12 1183.2.a.p.1.3 6
39.35 odd 6 1183.2.c.i.337.7 12
156.23 even 6 1456.2.cc.c.673.3 12
273.20 odd 12 8281.2.a.by.1.4 6
273.23 odd 6 637.2.u.h.361.4 12
273.62 even 6 637.2.q.h.491.3 12
273.101 even 6 637.2.k.g.569.3 12
273.179 odd 6 637.2.k.h.569.3 12
273.188 odd 12 8281.2.a.ch.1.3 6
273.257 even 6 637.2.u.i.361.4 12
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
91.2.q.a.36.3 12 39.23 odd 6
91.2.q.a.43.3 yes 12 3.2 odd 2
637.2.k.g.459.4 12 21.5 even 6
637.2.k.g.569.3 12 273.101 even 6
637.2.k.h.459.4 12 21.2 odd 6
637.2.k.h.569.3 12 273.179 odd 6
637.2.q.h.491.3 12 273.62 even 6
637.2.q.h.589.3 12 21.20 even 2
637.2.u.h.30.4 12 21.11 odd 6
637.2.u.h.361.4 12 273.23 odd 6
637.2.u.i.30.4 12 21.17 even 6
637.2.u.i.361.4 12 273.257 even 6
819.2.ct.a.127.4 12 13.10 even 6 inner
819.2.ct.a.316.4 12 1.1 even 1 trivial
1183.2.a.m.1.4 6 39.20 even 12
1183.2.a.p.1.3 6 39.32 even 12
1183.2.c.i.337.6 12 39.17 odd 6
1183.2.c.i.337.7 12 39.35 odd 6
1456.2.cc.c.225.3 12 12.11 even 2
1456.2.cc.c.673.3 12 156.23 even 6
8281.2.a.by.1.4 6 273.20 odd 12
8281.2.a.ch.1.3 6 273.188 odd 12