Properties

Label 891.2.n.d.676.1
Level $891$
Weight $2$
Character 891.676
Analytic conductor $7.115$
Analytic rank $0$
Dimension $8$
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [891,2,Mod(136,891)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(891, base_ring=CyclotomicField(30))
 
chi = DirichletCharacter(H, H._module([20, 6]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("891.136");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 891 = 3^{4} \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 891.n (of order \(15\), degree \(8\), not 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: \(7.11467082010\)
Analytic rank: \(0\)
Dimension: \(8\)
Coefficient field: \(\Q(\zeta_{15})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{8} - x^{7} + x^{5} - x^{4} + x^{3} - x + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{4}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 33)
Sato-Tate group: $\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label 676.1
Root \(-0.978148 - 0.207912i\) of defining polynomial
Character \(\chi\) \(=\) 891.676
Dual form 891.2.n.d.460.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.413545 + 0.459289i) q^{2} +(0.169131 + 1.60917i) q^{4} +(-1.75181 - 1.94558i) q^{5} +(2.74064 + 1.22021i) q^{7} +(-1.80902 - 1.31433i) q^{8} +1.61803 q^{10} +(-3.31641 - 0.0378495i) q^{11} +(-1.72539 - 0.366742i) q^{13} +(-1.69381 + 0.754131i) q^{14} +(-1.81359 + 0.385489i) q^{16} +(0.500000 - 1.53884i) q^{17} +(-4.73607 - 3.44095i) q^{19} +(2.83448 - 3.14801i) q^{20} +(1.38887 - 1.50754i) q^{22} +(-1.73607 + 3.00696i) q^{23} +(-0.193806 + 1.84395i) q^{25} +(0.881966 - 0.640786i) q^{26} +(-1.50000 + 4.61653i) q^{28} +(4.08550 + 1.81898i) q^{29} +(-2.79173 - 0.593401i) q^{31} +(2.80902 - 4.86536i) q^{32} +(0.500000 + 0.866025i) q^{34} +(-2.42705 - 7.46969i) q^{35} +(-0.190983 + 0.138757i) q^{37} +(3.53897 - 0.752232i) q^{38} +(0.611920 + 5.82203i) q^{40} +(-10.9116 + 4.85817i) q^{41} +(-3.11803 - 5.40059i) q^{43} +(-0.500000 - 5.34307i) q^{44} +(-0.663119 - 2.04087i) q^{46} +(-0.169131 + 1.60917i) q^{47} +(1.33826 + 1.48629i) q^{49} +(-0.766755 - 0.851568i) q^{50} +(0.298335 - 2.83847i) q^{52} +(-2.97214 - 9.14729i) q^{53} +(5.73607 + 6.51864i) q^{55} +(-3.35410 - 5.80948i) q^{56} +(-2.52498 + 1.12419i) q^{58} +(-1.07939 - 10.2697i) q^{59} +(-7.68247 + 1.63296i) q^{61} +(1.42705 - 1.03681i) q^{62} +(-0.0729490 - 0.224514i) q^{64} +(2.30902 + 3.99933i) q^{65} +(4.78115 - 8.28120i) q^{67} +(2.56082 + 0.544320i) q^{68} +(4.43444 + 1.97434i) q^{70} +(-1.71885 + 5.29007i) q^{71} +(2.61803 - 1.90211i) q^{73} +(0.0152505 - 0.145099i) q^{74} +(4.73607 - 8.20311i) q^{76} +(-9.04289 - 4.15045i) q^{77} +(6.33810 - 7.03917i) q^{79} +(3.92705 + 2.85317i) q^{80} +(2.28115 - 7.02067i) q^{82} +(-0.692728 + 0.147244i) q^{83} +(-3.86984 + 1.72296i) q^{85} +(3.76988 + 0.801313i) q^{86} +(5.94969 + 4.42732i) q^{88} +0.527864 q^{89} +(-4.28115 - 3.11044i) q^{91} +(-5.13233 - 2.28506i) q^{92} +(-0.669131 - 0.743145i) q^{94} +(1.60203 + 15.2423i) q^{95} +(-9.39087 + 10.4296i) q^{97} -1.23607 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q + 3 q^{2} - 3 q^{4} + q^{5} + 3 q^{7} - 10 q^{8} + 4 q^{10} - 9 q^{11} + 9 q^{13} - 6 q^{14} - 9 q^{16} + 4 q^{17} - 20 q^{19} - 3 q^{20} + 8 q^{22} + 4 q^{23} + 6 q^{25} + 16 q^{26} - 12 q^{28} + 10 q^{29}+ \cdots + 8 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/891\mathbb{Z}\right)^\times\).

\(n\) \(244\) \(650\)
\(\chi(n)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{1}{3}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.413545 + 0.459289i −0.292421 + 0.324766i −0.871397 0.490578i \(-0.836786\pi\)
0.578976 + 0.815344i \(0.303452\pi\)
\(3\) 0 0
\(4\) 0.169131 + 1.60917i 0.0845653 + 0.804585i
\(5\) −1.75181 1.94558i −0.783432 0.870089i 0.210779 0.977534i \(-0.432400\pi\)
−0.994211 + 0.107445i \(0.965733\pi\)
\(6\) 0 0
\(7\) 2.74064 + 1.22021i 1.03586 + 0.461196i 0.852983 0.521939i \(-0.174791\pi\)
0.182880 + 0.983135i \(0.441458\pi\)
\(8\) −1.80902 1.31433i −0.639584 0.464685i
\(9\) 0 0
\(10\) 1.61803 0.511667
\(11\) −3.31641 0.0378495i −0.999935 0.0114120i
\(12\) 0 0
\(13\) −1.72539 0.366742i −0.478536 0.101716i −0.0376725 0.999290i \(-0.511994\pi\)
−0.440863 + 0.897574i \(0.645328\pi\)
\(14\) −1.69381 + 0.754131i −0.452689 + 0.201550i
\(15\) 0 0
\(16\) −1.81359 + 0.385489i −0.453396 + 0.0963724i
\(17\) 0.500000 1.53884i 0.121268 0.373224i −0.871935 0.489622i \(-0.837135\pi\)
0.993203 + 0.116398i \(0.0371348\pi\)
\(18\) 0 0
\(19\) −4.73607 3.44095i −1.08653 0.789409i −0.107719 0.994181i \(-0.534355\pi\)
−0.978810 + 0.204772i \(0.934355\pi\)
\(20\) 2.83448 3.14801i 0.633810 0.703917i
\(21\) 0 0
\(22\) 1.38887 1.50754i 0.296108 0.321408i
\(23\) −1.73607 + 3.00696i −0.361995 + 0.626994i −0.988289 0.152593i \(-0.951238\pi\)
0.626294 + 0.779587i \(0.284571\pi\)
\(24\) 0 0
\(25\) −0.193806 + 1.84395i −0.0387613 + 0.368789i
\(26\) 0.881966 0.640786i 0.172968 0.125668i
\(27\) 0 0
\(28\) −1.50000 + 4.61653i −0.283473 + 0.872441i
\(29\) 4.08550 + 1.81898i 0.758658 + 0.337776i 0.749345 0.662180i \(-0.230369\pi\)
0.00931360 + 0.999957i \(0.497035\pi\)
\(30\) 0 0
\(31\) −2.79173 0.593401i −0.501410 0.106578i −0.0497385 0.998762i \(-0.515839\pi\)
−0.451672 + 0.892184i \(0.649172\pi\)
\(32\) 2.80902 4.86536i 0.496569 0.860082i
\(33\) 0 0
\(34\) 0.500000 + 0.866025i 0.0857493 + 0.148522i
\(35\) −2.42705 7.46969i −0.410246 1.26261i
\(36\) 0 0
\(37\) −0.190983 + 0.138757i −0.0313974 + 0.0228116i −0.603373 0.797459i \(-0.706177\pi\)
0.571976 + 0.820270i \(0.306177\pi\)
\(38\) 3.53897 0.752232i 0.574097 0.122028i
\(39\) 0 0
\(40\) 0.611920 + 5.82203i 0.0967531 + 0.920544i
\(41\) −10.9116 + 4.85817i −1.70411 + 0.758719i −0.705355 + 0.708854i \(0.749212\pi\)
−0.998756 + 0.0498651i \(0.984121\pi\)
\(42\) 0 0
\(43\) −3.11803 5.40059i −0.475496 0.823583i 0.524110 0.851650i \(-0.324398\pi\)
−0.999606 + 0.0280676i \(0.991065\pi\)
\(44\) −0.500000 5.34307i −0.0753778 0.805498i
\(45\) 0 0
\(46\) −0.663119 2.04087i −0.0977716 0.300910i
\(47\) −0.169131 + 1.60917i −0.0246702 + 0.234722i 0.975238 + 0.221159i \(0.0709839\pi\)
−0.999908 + 0.0135627i \(0.995683\pi\)
\(48\) 0 0
\(49\) 1.33826 + 1.48629i 0.191180 + 0.212327i
\(50\) −0.766755 0.851568i −0.108436 0.120430i
\(51\) 0 0
\(52\) 0.298335 2.83847i 0.0413716 0.393625i
\(53\) −2.97214 9.14729i −0.408254 1.25648i −0.918147 0.396240i \(-0.870315\pi\)
0.509893 0.860238i \(-0.329685\pi\)
\(54\) 0 0
\(55\) 5.73607 + 6.51864i 0.773451 + 0.878973i
\(56\) −3.35410 5.80948i −0.448211 0.776324i
\(57\) 0 0
\(58\) −2.52498 + 1.12419i −0.331546 + 0.147614i
\(59\) −1.07939 10.2697i −0.140524 1.33700i −0.806593 0.591107i \(-0.798691\pi\)
0.666069 0.745890i \(-0.267976\pi\)
\(60\) 0 0
\(61\) −7.68247 + 1.63296i −0.983640 + 0.209079i −0.671538 0.740970i \(-0.734366\pi\)
−0.312101 + 0.950049i \(0.601033\pi\)
\(62\) 1.42705 1.03681i 0.181236 0.131675i
\(63\) 0 0
\(64\) −0.0729490 0.224514i −0.00911863 0.0280642i
\(65\) 2.30902 + 3.99933i 0.286398 + 0.496056i
\(66\) 0 0
\(67\) 4.78115 8.28120i 0.584111 1.01171i −0.410875 0.911692i \(-0.634777\pi\)
0.994986 0.100018i \(-0.0318900\pi\)
\(68\) 2.56082 + 0.544320i 0.310545 + 0.0660085i
\(69\) 0 0
\(70\) 4.43444 + 1.97434i 0.530017 + 0.235979i
\(71\) −1.71885 + 5.29007i −0.203990 + 0.627815i 0.795764 + 0.605607i \(0.207070\pi\)
−0.999753 + 0.0222083i \(0.992930\pi\)
\(72\) 0 0
\(73\) 2.61803 1.90211i 0.306418 0.222625i −0.423940 0.905690i \(-0.639353\pi\)
0.730358 + 0.683065i \(0.239353\pi\)
\(74\) 0.0152505 0.145099i 0.00177283 0.0168674i
\(75\) 0 0
\(76\) 4.73607 8.20311i 0.543264 0.940961i
\(77\) −9.04289 4.15045i −1.03053 0.472987i
\(78\) 0 0
\(79\) 6.33810 7.03917i 0.713092 0.791968i −0.272311 0.962209i \(-0.587788\pi\)
0.985402 + 0.170241i \(0.0544546\pi\)
\(80\) 3.92705 + 2.85317i 0.439058 + 0.318994i
\(81\) 0 0
\(82\) 2.28115 7.02067i 0.251911 0.775303i
\(83\) −0.692728 + 0.147244i −0.0760368 + 0.0161621i −0.245773 0.969327i \(-0.579042\pi\)
0.169736 + 0.985490i \(0.445708\pi\)
\(84\) 0 0
\(85\) −3.86984 + 1.72296i −0.419743 + 0.186882i
\(86\) 3.76988 + 0.801313i 0.406517 + 0.0864078i
\(87\) 0 0
\(88\) 5.94969 + 4.42732i 0.634239 + 0.471954i
\(89\) 0.527864 0.0559535 0.0279767 0.999609i \(-0.491094\pi\)
0.0279767 + 0.999609i \(0.491094\pi\)
\(90\) 0 0
\(91\) −4.28115 3.11044i −0.448787 0.326063i
\(92\) −5.13233 2.28506i −0.535082 0.238234i
\(93\) 0 0
\(94\) −0.669131 0.743145i −0.0690156 0.0766495i
\(95\) 1.60203 + 15.2423i 0.164365 + 1.56382i
\(96\) 0 0
\(97\) −9.39087 + 10.4296i −0.953499 + 1.05897i 0.0447015 + 0.999000i \(0.485766\pi\)
−0.998200 + 0.0599674i \(0.980900\pi\)
\(98\) −1.23607 −0.124862
\(99\) 0 0
\(100\) −3.00000 −0.300000
\(101\) −2.00739 + 2.22943i −0.199743 + 0.221837i −0.834692 0.550717i \(-0.814354\pi\)
0.634949 + 0.772554i \(0.281021\pi\)
\(102\) 0 0
\(103\) 0.627171 + 5.96713i 0.0617970 + 0.587959i 0.980977 + 0.194122i \(0.0621858\pi\)
−0.919180 + 0.393837i \(0.871148\pi\)
\(104\) 2.63923 + 2.93117i 0.258798 + 0.287424i
\(105\) 0 0
\(106\) 5.43036 + 2.41775i 0.527443 + 0.234833i
\(107\) 3.42705 + 2.48990i 0.331306 + 0.240708i 0.740984 0.671522i \(-0.234359\pi\)
−0.409679 + 0.912230i \(0.634359\pi\)
\(108\) 0 0
\(109\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(110\) −5.36606 0.0612417i −0.511634 0.00583917i
\(111\) 0 0
\(112\) −5.44076 1.15647i −0.514103 0.109276i
\(113\) 0.646976 0.288052i 0.0608624 0.0270977i −0.376080 0.926587i \(-0.622728\pi\)
0.436942 + 0.899490i \(0.356061\pi\)
\(114\) 0 0
\(115\) 8.89153 1.88995i 0.829139 0.176239i
\(116\) −2.23607 + 6.88191i −0.207614 + 0.638969i
\(117\) 0 0
\(118\) 5.16312 + 3.75123i 0.475304 + 0.345328i
\(119\) 3.24803 3.60730i 0.297746 0.330681i
\(120\) 0 0
\(121\) 10.9971 + 0.251049i 0.999740 + 0.0228226i
\(122\) 2.42705 4.20378i 0.219735 0.380592i
\(123\) 0 0
\(124\) 0.482716 4.59274i 0.0433492 0.412440i
\(125\) −6.66312 + 4.84104i −0.595967 + 0.432996i
\(126\) 0 0
\(127\) −1.14590 + 3.52671i −0.101682 + 0.312945i −0.988937 0.148333i \(-0.952609\pi\)
0.887255 + 0.461279i \(0.152609\pi\)
\(128\) 10.3979 + 4.62946i 0.919057 + 0.409191i
\(129\) 0 0
\(130\) −2.79173 0.593401i −0.244851 0.0520447i
\(131\) 3.57295 6.18853i 0.312170 0.540694i −0.666662 0.745360i \(-0.732277\pi\)
0.978832 + 0.204666i \(0.0656108\pi\)
\(132\) 0 0
\(133\) −8.78115 15.2094i −0.761423 1.31882i
\(134\) 1.82624 + 5.62058i 0.157763 + 0.485544i
\(135\) 0 0
\(136\) −2.92705 + 2.12663i −0.250993 + 0.182357i
\(137\) −7.30885 + 1.55354i −0.624437 + 0.132728i −0.509254 0.860616i \(-0.670079\pi\)
−0.115183 + 0.993344i \(0.536745\pi\)
\(138\) 0 0
\(139\) 0.0892780 + 0.849423i 0.00757246 + 0.0720471i 0.997655 0.0684363i \(-0.0218010\pi\)
−0.990083 + 0.140483i \(0.955134\pi\)
\(140\) 11.6095 5.16889i 0.981184 0.436851i
\(141\) 0 0
\(142\) −1.71885 2.97713i −0.144242 0.249835i
\(143\) 5.70820 + 1.28157i 0.477344 + 0.107170i
\(144\) 0 0
\(145\) −3.61803 11.1352i −0.300461 0.924725i
\(146\) −0.209057 + 1.98904i −0.0173017 + 0.164614i
\(147\) 0 0
\(148\) −0.255585 0.283856i −0.0210090 0.0233328i
\(149\) 10.0370 + 11.1472i 0.822260 + 0.913212i 0.997453 0.0713221i \(-0.0227218\pi\)
−0.175194 + 0.984534i \(0.556055\pi\)
\(150\) 0 0
\(151\) −0.209057 + 1.98904i −0.0170128 + 0.161866i −0.999730 0.0232487i \(-0.992599\pi\)
0.982717 + 0.185115i \(0.0592657\pi\)
\(152\) 4.04508 + 12.4495i 0.328100 + 1.00979i
\(153\) 0 0
\(154\) 5.64590 2.43690i 0.454959 0.196371i
\(155\) 3.73607 + 6.47106i 0.300088 + 0.519768i
\(156\) 0 0
\(157\) −3.38761 + 1.50826i −0.270361 + 0.120372i −0.537439 0.843302i \(-0.680608\pi\)
0.267079 + 0.963675i \(0.413942\pi\)
\(158\) 0.611920 + 5.82203i 0.0486818 + 0.463176i
\(159\) 0 0
\(160\) −14.3868 + 3.05801i −1.13738 + 0.241757i
\(161\) −8.42705 + 6.12261i −0.664145 + 0.482529i
\(162\) 0 0
\(163\) 5.64590 + 17.3763i 0.442221 + 1.36102i 0.885503 + 0.464634i \(0.153814\pi\)
−0.443282 + 0.896382i \(0.646186\pi\)
\(164\) −9.66312 16.7370i −0.754563 1.30694i
\(165\) 0 0
\(166\) 0.218847 0.379054i 0.0169858 0.0294203i
\(167\) −9.81517 2.08628i −0.759520 0.161441i −0.188158 0.982139i \(-0.560252\pi\)
−0.571363 + 0.820698i \(0.693585\pi\)
\(168\) 0 0
\(169\) −9.03363 4.02203i −0.694895 0.309387i
\(170\) 0.809017 2.48990i 0.0620488 0.190966i
\(171\) 0 0
\(172\) 8.16312 5.93085i 0.622432 0.452223i
\(173\) −1.60785 + 15.2977i −0.122243 + 1.16306i 0.745659 + 0.666327i \(0.232135\pi\)
−0.867902 + 0.496735i \(0.834532\pi\)
\(174\) 0 0
\(175\) −2.78115 + 4.81710i −0.210235 + 0.364138i
\(176\) 6.02918 1.20980i 0.454467 0.0911919i
\(177\) 0 0
\(178\) −0.218296 + 0.242442i −0.0163620 + 0.0181718i
\(179\) 1.80902 + 1.31433i 0.135212 + 0.0982375i 0.653335 0.757069i \(-0.273369\pi\)
−0.518123 + 0.855306i \(0.673369\pi\)
\(180\) 0 0
\(181\) −5.39919 + 16.6170i −0.401318 + 1.23513i 0.522612 + 0.852571i \(0.324958\pi\)
−0.923930 + 0.382560i \(0.875042\pi\)
\(182\) 3.19904 0.679977i 0.237129 0.0504033i
\(183\) 0 0
\(184\) 7.09270 3.15788i 0.522881 0.232802i
\(185\) 0.604528 + 0.128496i 0.0444458 + 0.00944725i
\(186\) 0 0
\(187\) −1.71645 + 5.08450i −0.125519 + 0.371816i
\(188\) −2.61803 −0.190940
\(189\) 0 0
\(190\) −7.66312 5.56758i −0.555941 0.403915i
\(191\) −6.82614 3.03919i −0.493922 0.219908i 0.144632 0.989486i \(-0.453800\pi\)
−0.638554 + 0.769577i \(0.720467\pi\)
\(192\) 0 0
\(193\) −12.4206 13.7945i −0.894055 0.992949i 0.105944 0.994372i \(-0.466214\pi\)
−0.999999 + 0.00142357i \(0.999547\pi\)
\(194\) −0.906655 8.62625i −0.0650940 0.619328i
\(195\) 0 0
\(196\) −2.16535 + 2.40487i −0.154668 + 0.171776i
\(197\) 24.3820 1.73714 0.868572 0.495564i \(-0.165039\pi\)
0.868572 + 0.495564i \(0.165039\pi\)
\(198\) 0 0
\(199\) −16.7082 −1.18441 −0.592207 0.805786i \(-0.701743\pi\)
−0.592207 + 0.805786i \(0.701743\pi\)
\(200\) 2.77415 3.08100i 0.196162 0.217860i
\(201\) 0 0
\(202\) −0.193806 1.84395i −0.0136362 0.129740i
\(203\) 8.97733 + 9.97033i 0.630085 + 0.699780i
\(204\) 0 0
\(205\) 28.5670 + 12.7189i 1.99521 + 0.888324i
\(206\) −3.00000 2.17963i −0.209020 0.151862i
\(207\) 0 0
\(208\) 3.27051 0.226769
\(209\) 15.5765 + 11.5909i 1.07745 + 0.801757i
\(210\) 0 0
\(211\) 21.7838 + 4.63030i 1.49966 + 0.318763i 0.883341 0.468732i \(-0.155289\pi\)
0.616321 + 0.787495i \(0.288622\pi\)
\(212\) 14.2169 6.32976i 0.976419 0.434730i
\(213\) 0 0
\(214\) −2.56082 + 0.544320i −0.175054 + 0.0372089i
\(215\) −5.04508 + 15.5272i −0.344072 + 1.05894i
\(216\) 0 0
\(217\) −6.92705 5.03280i −0.470239 0.341649i
\(218\) 0 0
\(219\) 0 0
\(220\) −9.51945 + 10.3328i −0.641801 + 0.696638i
\(221\) −1.42705 + 2.47172i −0.0959938 + 0.166266i
\(222\) 0 0
\(223\) −0.0740275 + 0.704324i −0.00495725 + 0.0471650i −0.996721 0.0809165i \(-0.974215\pi\)
0.991764 + 0.128082i \(0.0408819\pi\)
\(224\) 13.6353 9.90659i 0.911044 0.661912i
\(225\) 0 0
\(226\) −0.135255 + 0.416272i −0.00899702 + 0.0276900i
\(227\) −22.7368 10.1231i −1.50910 0.671893i −0.525256 0.850944i \(-0.676030\pi\)
−0.983840 + 0.179052i \(0.942697\pi\)
\(228\) 0 0
\(229\) −9.78148 2.07912i −0.646378 0.137392i −0.126954 0.991909i \(-0.540520\pi\)
−0.519424 + 0.854517i \(0.673853\pi\)
\(230\) −2.80902 + 4.86536i −0.185221 + 0.320812i
\(231\) 0 0
\(232\) −5.00000 8.66025i −0.328266 0.568574i
\(233\) 7.51722 + 23.1356i 0.492470 + 1.51567i 0.820863 + 0.571124i \(0.193493\pi\)
−0.328394 + 0.944541i \(0.606507\pi\)
\(234\) 0 0
\(235\) 3.42705 2.48990i 0.223556 0.162423i
\(236\) 16.3431 3.47383i 1.06384 0.226127i
\(237\) 0 0
\(238\) 0.313585 + 2.98357i 0.0203267 + 0.193396i
\(239\) 2.34078 1.04218i 0.151413 0.0674133i −0.329631 0.944110i \(-0.606924\pi\)
0.481044 + 0.876696i \(0.340258\pi\)
\(240\) 0 0
\(241\) 11.5623 + 20.0265i 0.744794 + 1.29002i 0.950291 + 0.311363i \(0.100785\pi\)
−0.205498 + 0.978658i \(0.565881\pi\)
\(242\) −4.66312 + 4.94704i −0.299757 + 0.318008i
\(243\) 0 0
\(244\) −3.92705 12.0862i −0.251404 0.773741i
\(245\) 0.547318 5.20738i 0.0349669 0.332688i
\(246\) 0 0
\(247\) 6.90960 + 7.67389i 0.439647 + 0.488278i
\(248\) 4.27037 + 4.74273i 0.271169 + 0.301163i
\(249\) 0 0
\(250\) 0.532068 5.06229i 0.0336509 0.320167i
\(251\) −2.40983 7.41669i −0.152107 0.468138i 0.845749 0.533581i \(-0.179154\pi\)
−0.997856 + 0.0654431i \(0.979154\pi\)
\(252\) 0 0
\(253\) 5.87132 9.90659i 0.369127 0.622822i
\(254\) −1.14590 1.98475i −0.0719000 0.124535i
\(255\) 0 0
\(256\) −5.99496 + 2.66913i −0.374685 + 0.166821i
\(257\) 1.22024 + 11.6098i 0.0761165 + 0.724200i 0.964318 + 0.264746i \(0.0852882\pi\)
−0.888202 + 0.459454i \(0.848045\pi\)
\(258\) 0 0
\(259\) −0.692728 + 0.147244i −0.0430440 + 0.00914929i
\(260\) −6.04508 + 4.39201i −0.374900 + 0.272381i
\(261\) 0 0
\(262\) 1.36475 + 4.20025i 0.0843142 + 0.259493i
\(263\) 8.16312 + 14.1389i 0.503359 + 0.871844i 0.999992 + 0.00388355i \(0.00123617\pi\)
−0.496633 + 0.867961i \(0.665430\pi\)
\(264\) 0 0
\(265\) −12.5902 + 21.8068i −0.773408 + 1.33958i
\(266\) 10.6169 + 2.25669i 0.650965 + 0.138367i
\(267\) 0 0
\(268\) 14.1345 + 6.29308i 0.863402 + 0.384411i
\(269\) 4.79837 14.7679i 0.292562 0.900413i −0.691467 0.722408i \(-0.743035\pi\)
0.984029 0.178006i \(-0.0569645\pi\)
\(270\) 0 0
\(271\) 22.0623 16.0292i 1.34019 0.973705i 0.340753 0.940153i \(-0.389318\pi\)
0.999437 0.0335518i \(-0.0106819\pi\)
\(272\) −0.313585 + 2.98357i −0.0190139 + 0.180905i
\(273\) 0 0
\(274\) 2.30902 3.99933i 0.139493 0.241609i
\(275\) 0.712534 6.10794i 0.0429674 0.368323i
\(276\) 0 0
\(277\) 20.4502 22.7122i 1.22873 1.36465i 0.319917 0.947446i \(-0.396345\pi\)
0.908815 0.417199i \(-0.136988\pi\)
\(278\) −0.427051 0.310271i −0.0256128 0.0186088i
\(279\) 0 0
\(280\) −5.42705 + 16.7027i −0.324328 + 0.998180i
\(281\) 0.747238 0.158830i 0.0445765 0.00947503i −0.185569 0.982631i \(-0.559413\pi\)
0.230146 + 0.973156i \(0.426080\pi\)
\(282\) 0 0
\(283\) 0.164749 0.0733508i 0.00979329 0.00436025i −0.401834 0.915712i \(-0.631627\pi\)
0.411627 + 0.911352i \(0.364961\pi\)
\(284\) −8.80333 1.87121i −0.522381 0.111036i
\(285\) 0 0
\(286\) −2.94921 + 2.09173i −0.174391 + 0.123686i
\(287\) −35.8328 −2.11514
\(288\) 0 0
\(289\) 11.6353 + 8.45351i 0.684427 + 0.497265i
\(290\) 6.61048 + 2.94317i 0.388181 + 0.172829i
\(291\) 0 0
\(292\) 3.50361 + 3.89116i 0.205033 + 0.227713i
\(293\) −0.00582517 0.0554228i −0.000340310 0.00323783i 0.994350 0.106147i \(-0.0338515\pi\)
−0.994691 + 0.102909i \(0.967185\pi\)
\(294\) 0 0
\(295\) −18.0896 + 20.0905i −1.05322 + 1.16971i
\(296\) 0.527864 0.0306815
\(297\) 0 0
\(298\) −9.27051 −0.537026
\(299\) 4.09817 4.55147i 0.237003 0.263219i
\(300\) 0 0
\(301\) −1.95554 18.6057i −0.112715 1.07242i
\(302\) −0.827091 0.918578i −0.0475937 0.0528582i
\(303\) 0 0
\(304\) 9.91572 + 4.41476i 0.568705 + 0.253204i
\(305\) 16.6353 + 12.0862i 0.952532 + 0.692055i
\(306\) 0 0
\(307\) 0.562306 0.0320925 0.0160462 0.999871i \(-0.494892\pi\)
0.0160462 + 0.999871i \(0.494892\pi\)
\(308\) 5.14935 15.2535i 0.293411 0.869149i
\(309\) 0 0
\(310\) −4.51712 0.960143i −0.256555 0.0545325i
\(311\) 2.30932 1.02817i 0.130949 0.0583025i −0.340216 0.940347i \(-0.610500\pi\)
0.471165 + 0.882045i \(0.343833\pi\)
\(312\) 0 0
\(313\) −25.2683 + 5.37094i −1.42825 + 0.303584i −0.856204 0.516638i \(-0.827183\pi\)
−0.572045 + 0.820222i \(0.693850\pi\)
\(314\) 0.708204 2.17963i 0.0399663 0.123004i
\(315\) 0 0
\(316\) 12.3992 + 9.00854i 0.697509 + 0.506770i
\(317\) −12.9548 + 14.3878i −0.727615 + 0.808099i −0.987513 0.157537i \(-0.949645\pi\)
0.259898 + 0.965636i \(0.416311\pi\)
\(318\) 0 0
\(319\) −13.4803 6.18712i −0.754754 0.346412i
\(320\) −0.309017 + 0.535233i −0.0172746 + 0.0299204i
\(321\) 0 0
\(322\) 0.672922 6.40243i 0.0375005 0.356793i
\(323\) −7.66312 + 5.56758i −0.426387 + 0.309789i
\(324\) 0 0
\(325\) 1.01064 3.11044i 0.0560604 0.172536i
\(326\) −10.3156 4.59279i −0.571327 0.254371i
\(327\) 0 0
\(328\) 26.1246 + 5.55295i 1.44249 + 0.306610i
\(329\) −2.42705 + 4.20378i −0.133808 + 0.231762i
\(330\) 0 0
\(331\) −13.2984 23.0335i −0.730945 1.26603i −0.956480 0.291798i \(-0.905746\pi\)
0.225535 0.974235i \(-0.427587\pi\)
\(332\) −0.354102 1.08981i −0.0194339 0.0598113i
\(333\) 0 0
\(334\) 5.01722 3.64522i 0.274530 0.199458i
\(335\) −24.4874 + 5.20495i −1.33789 + 0.284377i
\(336\) 0 0
\(337\) 0.0305010 + 0.290198i 0.00166150 + 0.0158081i 0.995321 0.0966211i \(-0.0308035\pi\)
−0.993660 + 0.112429i \(0.964137\pi\)
\(338\) 5.58309 2.48575i 0.303680 0.135207i
\(339\) 0 0
\(340\) −3.42705 5.93583i −0.185858 0.321915i
\(341\) 9.23607 + 2.07363i 0.500161 + 0.112293i
\(342\) 0 0
\(343\) −4.63525 14.2658i −0.250280 0.770283i
\(344\) −1.45757 + 13.8679i −0.0785871 + 0.747706i
\(345\) 0 0
\(346\) −6.36114 7.06476i −0.341977 0.379804i
\(347\) −14.0145 15.5646i −0.752335 0.835553i 0.238427 0.971160i \(-0.423368\pi\)
−0.990763 + 0.135607i \(0.956701\pi\)
\(348\) 0 0
\(349\) 1.05831 10.0691i 0.0566500 0.538989i −0.928987 0.370112i \(-0.879319\pi\)
0.985637 0.168877i \(-0.0540141\pi\)
\(350\) −1.06231 3.26944i −0.0567826 0.174759i
\(351\) 0 0
\(352\) −9.50000 + 16.0292i −0.506352 + 0.854359i
\(353\) 5.23607 + 9.06914i 0.278688 + 0.482701i 0.971059 0.238840i \(-0.0767672\pi\)
−0.692371 + 0.721542i \(0.743434\pi\)
\(354\) 0 0
\(355\) 13.3033 5.92302i 0.706067 0.314361i
\(356\) 0.0892780 + 0.849423i 0.00473172 + 0.0450193i
\(357\) 0 0
\(358\) −1.35177 + 0.287327i −0.0714431 + 0.0151857i
\(359\) 10.3262 7.50245i 0.544998 0.395964i −0.280940 0.959725i \(-0.590646\pi\)
0.825938 + 0.563761i \(0.190646\pi\)
\(360\) 0 0
\(361\) 4.71885 + 14.5231i 0.248360 + 0.764375i
\(362\) −5.39919 9.35167i −0.283775 0.491513i
\(363\) 0 0
\(364\) 4.28115 7.41517i 0.224393 0.388661i
\(365\) −8.28700 1.76146i −0.433761 0.0921988i
\(366\) 0 0
\(367\) 5.08142 + 2.26239i 0.265248 + 0.118096i 0.535052 0.844819i \(-0.320292\pi\)
−0.269804 + 0.962915i \(0.586959\pi\)
\(368\) 1.98936 6.12261i 0.103702 0.319163i
\(369\) 0 0
\(370\) −0.309017 + 0.224514i −0.0160650 + 0.0116719i
\(371\) 3.01607 28.6960i 0.156587 1.48982i
\(372\) 0 0
\(373\) 2.20820 3.82472i 0.114336 0.198037i −0.803178 0.595739i \(-0.796859\pi\)
0.917514 + 0.397703i \(0.130192\pi\)
\(374\) −1.62543 2.89102i −0.0840488 0.149491i
\(375\) 0 0
\(376\) 2.42094 2.68872i 0.124850 0.138660i
\(377\) −6.38197 4.63677i −0.328688 0.238806i
\(378\) 0 0
\(379\) 0.489357 1.50609i 0.0251366 0.0773624i −0.937701 0.347443i \(-0.887050\pi\)
0.962838 + 0.270080i \(0.0870502\pi\)
\(380\) −24.2565 + 5.15587i −1.24433 + 0.264491i
\(381\) 0 0
\(382\) 4.21878 1.87832i 0.215852 0.0961034i
\(383\) −26.3010 5.59044i −1.34392 0.285658i −0.520872 0.853635i \(-0.674393\pi\)
−0.823045 + 0.567977i \(0.807726\pi\)
\(384\) 0 0
\(385\) 7.76637 + 24.8644i 0.395811 + 1.26721i
\(386\) 11.4721 0.583916
\(387\) 0 0
\(388\) −18.3713 13.3475i −0.932663 0.677619i
\(389\) 22.1722 + 9.87171i 1.12418 + 0.500515i 0.882721 0.469897i \(-0.155709\pi\)
0.241455 + 0.970412i \(0.422376\pi\)
\(390\) 0 0
\(391\) 3.75920 + 4.17501i 0.190111 + 0.211139i
\(392\) −0.467465 4.44764i −0.0236106 0.224640i
\(393\) 0 0
\(394\) −10.0831 + 11.1984i −0.507977 + 0.564165i
\(395\) −24.7984 −1.24774
\(396\) 0 0
\(397\) −38.7082 −1.94271 −0.971355 0.237635i \(-0.923628\pi\)
−0.971355 + 0.237635i \(0.923628\pi\)
\(398\) 6.90960 7.67389i 0.346347 0.384657i
\(399\) 0 0
\(400\) −0.359337 3.41886i −0.0179668 0.170943i
\(401\) −17.4577 19.3888i −0.871797 0.968229i 0.127925 0.991784i \(-0.459168\pi\)
−0.999723 + 0.0235546i \(0.992502\pi\)
\(402\) 0 0
\(403\) 4.59919 + 2.04769i 0.229102 + 0.102003i
\(404\) −3.92705 2.85317i −0.195378 0.141950i
\(405\) 0 0
\(406\) −8.29180 −0.411515
\(407\) 0.638630 0.452947i 0.0316557 0.0224518i
\(408\) 0 0
\(409\) 10.8141 + 2.29862i 0.534725 + 0.113659i 0.467356 0.884069i \(-0.345206\pi\)
0.0673681 + 0.997728i \(0.478540\pi\)
\(410\) −17.6554 + 7.86069i −0.871938 + 0.388212i
\(411\) 0 0
\(412\) −9.49606 + 2.01845i −0.467837 + 0.0994418i
\(413\) 9.57295 29.4625i 0.471054 1.44976i
\(414\) 0 0
\(415\) 1.50000 + 1.08981i 0.0736321 + 0.0534969i
\(416\) −6.63097 + 7.36444i −0.325110 + 0.361071i
\(417\) 0 0
\(418\) −11.7651 + 2.36076i −0.575452 + 0.115469i
\(419\) −8.25329 + 14.2951i −0.403200 + 0.698362i −0.994110 0.108375i \(-0.965435\pi\)
0.590911 + 0.806737i \(0.298769\pi\)
\(420\) 0 0
\(421\) 3.89583 37.0663i 0.189871 1.80650i −0.321250 0.946994i \(-0.604103\pi\)
0.511121 0.859508i \(-0.329230\pi\)
\(422\) −11.1353 + 8.09024i −0.542056 + 0.393827i
\(423\) 0 0
\(424\) −6.64590 + 20.4540i −0.322753 + 0.993333i
\(425\) 2.74064 + 1.22021i 0.132940 + 0.0591889i
\(426\) 0 0
\(427\) −23.0474 4.89888i −1.11534 0.237073i
\(428\) −3.42705 + 5.93583i −0.165653 + 0.286919i
\(429\) 0 0
\(430\) −5.04508 8.73834i −0.243296 0.421400i
\(431\) −12.2082 37.5730i −0.588048 1.80983i −0.586667 0.809828i \(-0.699560\pi\)
−0.00138127 0.999999i \(-0.500440\pi\)
\(432\) 0 0
\(433\) 4.85410 3.52671i 0.233273 0.169483i −0.465008 0.885307i \(-0.653949\pi\)
0.698281 + 0.715824i \(0.253949\pi\)
\(434\) 5.17616 1.10023i 0.248464 0.0528126i
\(435\) 0 0
\(436\) 0 0
\(437\) 18.5689 8.26743i 0.888273 0.395485i
\(438\) 0 0
\(439\) −1.64590 2.85078i −0.0785544 0.136060i 0.824072 0.566485i \(-0.191697\pi\)
−0.902626 + 0.430425i \(0.858364\pi\)
\(440\) −1.80902 19.3314i −0.0862415 0.921588i
\(441\) 0 0
\(442\) −0.545085 1.67760i −0.0259270 0.0797952i
\(443\) 4.29869 40.8993i 0.204237 1.94319i −0.110205 0.993909i \(-0.535151\pi\)
0.314442 0.949277i \(-0.398183\pi\)
\(444\) 0 0
\(445\) −0.924716 1.02700i −0.0438357 0.0486845i
\(446\) −0.292875 0.325270i −0.0138680 0.0154020i
\(447\) 0 0
\(448\) 0.0740275 0.704324i 0.00349747 0.0332762i
\(449\) −7.56231 23.2744i −0.356887 1.09839i −0.954907 0.296905i \(-0.904046\pi\)
0.598020 0.801481i \(-0.295954\pi\)
\(450\) 0 0
\(451\) 36.3713 15.6987i 1.71266 0.739222i
\(452\) 0.572949 + 0.992377i 0.0269493 + 0.0466775i
\(453\) 0 0
\(454\) 14.0521 6.25641i 0.659499 0.293628i
\(455\) 1.44815 + 13.7782i 0.0678902 + 0.645932i
\(456\) 0 0
\(457\) −8.02240 + 1.70521i −0.375272 + 0.0797665i −0.391687 0.920099i \(-0.628108\pi\)
0.0164144 + 0.999865i \(0.494775\pi\)
\(458\) 5.00000 3.63271i 0.233635 0.169746i
\(459\) 0 0
\(460\) 4.54508 + 13.9883i 0.211916 + 0.652209i
\(461\) 10.5451 + 18.2646i 0.491134 + 0.850668i 0.999948 0.0102080i \(-0.00324936\pi\)
−0.508814 + 0.860876i \(0.669916\pi\)
\(462\) 0 0
\(463\) 7.89919 13.6818i 0.367106 0.635847i −0.622005 0.783013i \(-0.713682\pi\)
0.989112 + 0.147166i \(0.0470152\pi\)
\(464\) −8.11060 1.72396i −0.376525 0.0800329i
\(465\) 0 0
\(466\) −13.7346 6.11506i −0.636245 0.283275i
\(467\) −3.01722 + 9.28605i −0.139620 + 0.429707i −0.996280 0.0861747i \(-0.972536\pi\)
0.856660 + 0.515882i \(0.172536\pi\)
\(468\) 0 0
\(469\) 23.2082 16.8617i 1.07166 0.778603i
\(470\) −0.273659 + 2.60369i −0.0126230 + 0.120099i
\(471\) 0 0
\(472\) −11.5451 + 19.9967i −0.531406 + 0.920422i
\(473\) 10.1363 + 18.0286i 0.466066 + 0.828956i
\(474\) 0 0
\(475\) 7.26281 8.06617i 0.333241 0.370101i
\(476\) 6.35410 + 4.61653i 0.291240 + 0.211598i
\(477\) 0 0
\(478\) −0.489357 + 1.50609i −0.0223827 + 0.0688868i
\(479\) 27.4763 5.84027i 1.25543 0.266849i 0.468260 0.883591i \(-0.344881\pi\)
0.787166 + 0.616742i \(0.211548\pi\)
\(480\) 0 0
\(481\) 0.380408 0.169368i 0.0173451 0.00772253i
\(482\) −13.9795 2.97143i −0.636748 0.135345i
\(483\) 0 0
\(484\) 1.45597 + 17.7387i 0.0661806 + 0.806306i
\(485\) 36.7426 1.66840
\(486\) 0 0
\(487\) −13.6074 9.88635i −0.616610 0.447993i 0.235126 0.971965i \(-0.424450\pi\)
−0.851736 + 0.523972i \(0.824450\pi\)
\(488\) 16.0440 + 7.14323i 0.726276 + 0.323359i
\(489\) 0 0
\(490\) 2.16535 + 2.40487i 0.0978206 + 0.108641i
\(491\) −2.63566 25.0767i −0.118946 1.13169i −0.877331 0.479886i \(-0.840678\pi\)
0.758385 0.651807i \(-0.225989\pi\)
\(492\) 0 0
\(493\) 4.84187 5.37745i 0.218067 0.242188i
\(494\) −6.38197 −0.287138
\(495\) 0 0
\(496\) 5.29180 0.237609
\(497\) −11.1657 + 12.4008i −0.500851 + 0.556252i
\(498\) 0 0
\(499\) 1.83576 + 17.4661i 0.0821799 + 0.781890i 0.955549 + 0.294831i \(0.0952635\pi\)
−0.873369 + 0.487059i \(0.838070\pi\)
\(500\) −8.91699 9.90332i −0.398780 0.442890i
\(501\) 0 0
\(502\) 4.40298 + 1.96033i 0.196515 + 0.0874939i
\(503\) −22.7082 16.4985i −1.01251 0.735631i −0.0477750 0.998858i \(-0.515213\pi\)
−0.964734 + 0.263227i \(0.915213\pi\)
\(504\) 0 0
\(505\) 7.85410 0.349503
\(506\) 2.12193 + 6.79346i 0.0943312 + 0.302006i
\(507\) 0 0
\(508\) −5.86889 1.24747i −0.260390 0.0553475i
\(509\) 21.5761 9.60632i 0.956346 0.425793i 0.131604 0.991302i \(-0.457987\pi\)
0.824742 + 0.565510i \(0.191321\pi\)
\(510\) 0 0
\(511\) 9.49606 2.01845i 0.420081 0.0892909i
\(512\) −5.78115 + 17.7926i −0.255493 + 0.786327i
\(513\) 0 0
\(514\) −5.83688 4.24074i −0.257454 0.187051i
\(515\) 10.5108 11.6735i 0.463163 0.514395i
\(516\) 0 0
\(517\) 0.621812 5.33026i 0.0273473 0.234425i
\(518\) 0.218847 0.379054i 0.00961559 0.0166547i
\(519\) 0 0
\(520\) 1.07939 10.2697i 0.0473342 0.450355i
\(521\) 12.0000 8.71851i 0.525730 0.381965i −0.293028 0.956104i \(-0.594663\pi\)
0.818758 + 0.574139i \(0.194663\pi\)
\(522\) 0 0
\(523\) −3.70163 + 11.3924i −0.161861 + 0.498156i −0.998791 0.0491529i \(-0.984348\pi\)
0.836930 + 0.547309i \(0.184348\pi\)
\(524\) 10.5627 + 4.70281i 0.461433 + 0.205443i
\(525\) 0 0
\(526\) −9.86968 2.09786i −0.430338 0.0914712i
\(527\) −2.30902 + 3.99933i −0.100582 + 0.174214i
\(528\) 0 0
\(529\) 5.47214 + 9.47802i 0.237919 + 0.412088i
\(530\) −4.80902 14.8006i −0.208890 0.642898i
\(531\) 0 0
\(532\) 22.9894 16.7027i 0.996715 0.724156i
\(533\) 20.6085 4.38047i 0.892652 0.189739i
\(534\) 0 0
\(535\) −1.15924 11.0294i −0.0501182 0.476843i
\(536\) −19.5334 + 8.69683i −0.843714 + 0.375646i
\(537\) 0 0
\(538\) 4.79837 + 8.31103i 0.206873 + 0.358314i
\(539\) −4.38197 4.97980i −0.188745 0.214495i
\(540\) 0 0
\(541\) 6.04508 + 18.6049i 0.259899 + 0.799885i 0.992825 + 0.119577i \(0.0381540\pi\)
−0.732926 + 0.680308i \(0.761846\pi\)
\(542\) −1.76173 + 16.7618i −0.0756729 + 0.719980i
\(543\) 0 0
\(544\) −6.08251 6.75531i −0.260786 0.289632i
\(545\) 0 0
\(546\) 0 0
\(547\) −2.25970 + 21.4996i −0.0966178 + 0.919257i 0.833630 + 0.552324i \(0.186259\pi\)
−0.930247 + 0.366933i \(0.880408\pi\)
\(548\) −3.73607 11.4984i −0.159597 0.491189i
\(549\) 0 0
\(550\) 2.51064 + 2.85317i 0.107054 + 0.121660i
\(551\) −13.0902 22.6728i −0.557660 0.965895i
\(552\) 0 0
\(553\) 25.9597 11.5580i 1.10392 0.491496i
\(554\) 1.97439 + 18.7851i 0.0838838 + 0.798101i
\(555\) 0 0
\(556\) −1.35177 + 0.287327i −0.0573277 + 0.0121854i
\(557\) −12.0623 + 8.76378i −0.511096 + 0.371333i −0.813239 0.581929i \(-0.802298\pi\)
0.302143 + 0.953263i \(0.402298\pi\)
\(558\) 0 0
\(559\) 3.39919 + 10.4616i 0.143770 + 0.442479i
\(560\) 7.28115 + 12.6113i 0.307685 + 0.532926i
\(561\) 0 0
\(562\) −0.236068 + 0.408882i −0.00995793 + 0.0172476i
\(563\) 8.69431 + 1.84803i 0.366421 + 0.0778853i 0.387443 0.921894i \(-0.373358\pi\)
−0.0210214 + 0.999779i \(0.506692\pi\)
\(564\) 0 0
\(565\) −1.69381 0.754131i −0.0712590 0.0317265i
\(566\) −0.0344419 + 0.106001i −0.00144770 + 0.00445556i
\(567\) 0 0
\(568\) 10.0623 7.31069i 0.422205 0.306750i
\(569\) 2.51588 23.9370i 0.105471 1.00349i −0.805940 0.591997i \(-0.798340\pi\)
0.911412 0.411496i \(-0.134994\pi\)
\(570\) 0 0
\(571\) −17.3435 + 30.0398i −0.725801 + 1.25712i 0.232842 + 0.972515i \(0.425197\pi\)
−0.958643 + 0.284610i \(0.908136\pi\)
\(572\) −1.09683 + 9.40222i −0.0458610 + 0.393127i
\(573\) 0 0
\(574\) 14.8185 16.4576i 0.618512 0.686927i
\(575\) −5.20820 3.78398i −0.217197 0.157803i
\(576\) 0 0
\(577\) 3.32624 10.2371i 0.138473 0.426176i −0.857641 0.514249i \(-0.828071\pi\)
0.996114 + 0.0880726i \(0.0280707\pi\)
\(578\) −8.69431 + 1.84803i −0.361636 + 0.0768680i
\(579\) 0 0
\(580\) 17.3065 7.70533i 0.718611 0.319946i
\(581\) −2.07818 0.441732i −0.0862176 0.0183261i
\(582\) 0 0
\(583\) 9.51060 + 30.4487i 0.393889 + 1.26105i
\(584\) −7.23607 −0.299431
\(585\) 0 0
\(586\) 0.0278640 + 0.0202444i 0.00115105 + 0.000836289i
\(587\) −34.9933 15.5800i −1.44433 0.643057i −0.473057 0.881032i \(-0.656850\pi\)
−0.971271 + 0.237975i \(0.923516\pi\)
\(588\) 0 0
\(589\) 11.1800 + 12.4166i 0.460663 + 0.511618i
\(590\) −1.74648 16.6167i −0.0719016 0.684098i
\(591\) 0 0
\(592\) 0.292875 0.325270i 0.0120371 0.0133685i
\(593\) 22.2148 0.912252 0.456126 0.889915i \(-0.349237\pi\)
0.456126 + 0.889915i \(0.349237\pi\)
\(594\) 0 0
\(595\) −12.7082 −0.520986
\(596\) −16.2401 + 18.0365i −0.665222 + 0.738804i
\(597\) 0 0
\(598\) 0.395663 + 3.76448i 0.0161799 + 0.153941i
\(599\) −5.54829 6.16201i −0.226697 0.251773i 0.619056 0.785347i \(-0.287515\pi\)
−0.845753 + 0.533574i \(0.820849\pi\)
\(600\) 0 0
\(601\) 30.9078 + 13.7610i 1.26076 + 0.561325i 0.924764 0.380540i \(-0.124262\pi\)
0.335992 + 0.941865i \(0.390929\pi\)
\(602\) 9.35410 + 6.79615i 0.381245 + 0.276991i
\(603\) 0 0
\(604\) −3.23607 −0.131674
\(605\) −18.7764 21.8356i −0.763370 0.887742i
\(606\) 0 0
\(607\) −13.0350 2.77068i −0.529075 0.112458i −0.0643739 0.997926i \(-0.520505\pi\)
−0.464702 + 0.885467i \(0.653838\pi\)
\(608\) −30.0452 + 13.3770i −1.21849 + 0.542508i
\(609\) 0 0
\(610\) −12.4305 + 2.64218i −0.503296 + 0.106979i
\(611\) 0.881966 2.71441i 0.0356805 0.109813i
\(612\) 0 0
\(613\) −28.0344 20.3682i −1.13230 0.822664i −0.146272 0.989244i \(-0.546728\pi\)
−0.986028 + 0.166580i \(0.946728\pi\)
\(614\) −0.232539 + 0.258261i −0.00938451 + 0.0104226i
\(615\) 0 0
\(616\) 10.9037 + 19.3935i 0.439322 + 0.781388i
\(617\) −9.79180 + 16.9599i −0.394203 + 0.682779i −0.992999 0.118122i \(-0.962313\pi\)
0.598796 + 0.800901i \(0.295646\pi\)
\(618\) 0 0
\(619\) 0.921906 8.77135i 0.0370545 0.352550i −0.960248 0.279148i \(-0.909948\pi\)
0.997302 0.0734016i \(-0.0233855\pi\)
\(620\) −9.78115 + 7.10642i −0.392821 + 0.285401i
\(621\) 0 0
\(622\) −0.482779 + 1.48584i −0.0193577 + 0.0595768i
\(623\) 1.44668 + 0.644105i 0.0579601 + 0.0258055i
\(624\) 0 0
\(625\) 30.1590 + 6.41050i 1.20636 + 0.256420i
\(626\) 7.98278 13.8266i 0.319056 0.552621i
\(627\) 0 0
\(628\) −3.00000 5.19615i −0.119713 0.207349i
\(629\) 0.118034 + 0.363271i 0.00470632 + 0.0144846i
\(630\) 0 0
\(631\) −37.4336 + 27.1971i −1.49021 + 1.08270i −0.516125 + 0.856513i \(0.672626\pi\)
−0.974084 + 0.226187i \(0.927374\pi\)
\(632\) −20.7175 + 4.40364i −0.824098 + 0.175167i
\(633\) 0 0
\(634\) −1.25074 11.9000i −0.0496733 0.472610i
\(635\) 8.86889 3.94868i 0.351951 0.156699i
\(636\) 0 0
\(637\) −1.76393 3.05522i −0.0698895 0.121052i
\(638\) 8.41641 3.63271i 0.333209 0.143820i
\(639\) 0 0
\(640\) −9.20820 28.3399i −0.363986 1.12023i
\(641\) −3.73612 + 35.5468i −0.147568 + 1.40402i 0.630672 + 0.776049i \(0.282779\pi\)
−0.778240 + 0.627967i \(0.783887\pi\)
\(642\) 0 0
\(643\) −25.8032 28.6574i −1.01758 1.13014i −0.991451 0.130478i \(-0.958349\pi\)
−0.0261284 0.999659i \(-0.508318\pi\)
\(644\) −11.2776 12.5250i −0.444400 0.493556i
\(645\) 0 0
\(646\) 0.611920 5.82203i 0.0240757 0.229065i
\(647\) 8.59017 + 26.4378i 0.337714 + 1.03938i 0.965369 + 0.260887i \(0.0840149\pi\)
−0.627655 + 0.778492i \(0.715985\pi\)
\(648\) 0 0
\(649\) 3.19098 + 34.0993i 0.125257 + 1.33851i
\(650\) 1.01064 + 1.75049i 0.0396407 + 0.0686597i
\(651\) 0 0
\(652\) −27.0065 + 12.0241i −1.05766 + 0.470899i
\(653\) −5.33455 50.7549i −0.208757 1.98619i −0.157619 0.987500i \(-0.550382\pi\)
−0.0511377 0.998692i \(-0.516285\pi\)
\(654\) 0 0
\(655\) −18.2994 + 3.88965i −0.715016 + 0.151981i
\(656\) 17.9164 13.0170i 0.699518 0.508230i
\(657\) 0 0
\(658\) −0.927051 2.85317i −0.0361402 0.111228i
\(659\) 5.32624 + 9.22531i 0.207481 + 0.359367i 0.950920 0.309436i \(-0.100140\pi\)
−0.743440 + 0.668803i \(0.766807\pi\)
\(660\) 0 0
\(661\) 4.95492 8.58216i 0.192724 0.333808i −0.753428 0.657530i \(-0.771601\pi\)
0.946152 + 0.323723i \(0.104935\pi\)
\(662\) 16.0785 + 3.41759i 0.624908 + 0.132828i
\(663\) 0 0
\(664\) 1.44668 + 0.644105i 0.0561422 + 0.0249961i
\(665\) −14.2082 + 43.7284i −0.550971 + 1.69571i
\(666\) 0 0
\(667\) −12.5623 + 9.12705i −0.486414 + 0.353401i
\(668\) 1.69713 16.1471i 0.0656640 0.624751i
\(669\) 0 0
\(670\) 7.73607 13.3993i 0.298870 0.517659i
\(671\) 25.5400 5.12478i 0.985962 0.197840i
\(672\) 0 0
\(673\) 8.30820 9.22719i 0.320258 0.355682i −0.561423 0.827529i \(-0.689746\pi\)
0.881680 + 0.471847i \(0.156413\pi\)
\(674\) −0.145898 0.106001i −0.00561978 0.00408301i
\(675\) 0 0
\(676\) 4.94427 15.2169i 0.190164 0.585266i
\(677\) −13.2322 + 2.81260i −0.508557 + 0.108097i −0.455042 0.890470i \(-0.650376\pi\)
−0.0535147 + 0.998567i \(0.517042\pi\)
\(678\) 0 0
\(679\) −38.4633 + 17.1250i −1.47609 + 0.657196i
\(680\) 9.26515 + 1.96937i 0.355302 + 0.0755218i
\(681\) 0 0
\(682\) −4.77193 + 3.38448i −0.182727 + 0.129599i
\(683\) −3.11146 −0.119057 −0.0595283 0.998227i \(-0.518960\pi\)
−0.0595283 + 0.998227i \(0.518960\pi\)
\(684\) 0 0
\(685\) 15.8262 + 11.4984i 0.604689 + 0.439333i
\(686\) 8.46903 + 3.77066i 0.323349 + 0.143964i
\(687\) 0 0
\(688\) 7.73669 + 8.59247i 0.294959 + 0.327585i
\(689\) 1.77338 + 16.8726i 0.0675605 + 0.642796i
\(690\) 0 0
\(691\) −17.5926 + 19.5386i −0.669256 + 0.743284i −0.978170 0.207806i \(-0.933368\pi\)
0.308914 + 0.951090i \(0.400034\pi\)
\(692\) −24.8885 −0.946120
\(693\) 0 0
\(694\) 12.9443 0.491358
\(695\) 1.49622 1.66172i 0.0567549 0.0630327i
\(696\) 0 0
\(697\) 2.02014 + 19.2204i 0.0765183 + 0.728023i
\(698\) 4.18699 + 4.65012i 0.158480 + 0.176010i
\(699\) 0 0
\(700\) −8.22191 3.66063i −0.310759 0.138359i
\(701\) 8.64590 + 6.28161i 0.326551 + 0.237253i 0.738966 0.673743i \(-0.235315\pi\)
−0.412415 + 0.910996i \(0.635315\pi\)
\(702\) 0 0
\(703\) 1.38197 0.0521218
\(704\) 0.233431 + 0.747341i 0.00879776 + 0.0281665i
\(705\) 0 0
\(706\) −6.33070 1.34563i −0.238259 0.0506436i
\(707\) −8.22191 + 3.66063i −0.309217 + 0.137672i
\(708\) 0 0
\(709\) −47.6775 + 10.1342i −1.79057 + 0.380597i −0.979032 0.203708i \(-0.934701\pi\)
−0.811534 + 0.584305i \(0.801367\pi\)
\(710\) −2.78115 + 8.55951i −0.104375 + 0.321233i
\(711\) 0 0
\(712\) −0.954915 0.693786i −0.0357870 0.0260007i
\(713\) 6.63097 7.36444i 0.248332 0.275800i
\(714\) 0 0
\(715\) −7.50627 13.3508i −0.280719 0.499293i
\(716\) −1.80902 + 3.13331i −0.0676061 + 0.117097i
\(717\) 0 0
\(718\) −0.824577 + 7.84533i −0.0307730 + 0.292785i
\(719\) 1.28115 0.930812i 0.0477789 0.0347134i −0.563639 0.826021i \(-0.690599\pi\)
0.611418 + 0.791307i \(0.290599\pi\)
\(720\) 0 0
\(721\) −5.56231 + 17.1190i −0.207151 + 0.637546i
\(722\) −8.62176 3.83866i −0.320869 0.142860i
\(723\) 0 0
\(724\) −27.6527 5.87777i −1.02771 0.218446i
\(725\) −4.14590 + 7.18091i −0.153975 + 0.266692i
\(726\) 0 0
\(727\) −19.4271 33.6486i −0.720509 1.24796i −0.960796 0.277257i \(-0.910575\pi\)
0.240286 0.970702i \(-0.422759\pi\)
\(728\) 3.65654 + 11.2537i 0.135520 + 0.417089i
\(729\) 0 0
\(730\) 4.23607 3.07768i 0.156784 0.113910i
\(731\) −9.86968 + 2.09786i −0.365043 + 0.0775923i
\(732\) 0 0
\(733\) 3.94158 + 37.5016i 0.145586 + 1.38515i 0.786523 + 0.617561i \(0.211879\pi\)
−0.640937 + 0.767593i \(0.721454\pi\)
\(734\) −3.14049 + 1.39824i −0.115918 + 0.0516098i
\(735\) 0 0
\(736\) 9.75329 + 16.8932i 0.359511 + 0.622691i
\(737\) −16.1697 + 27.2829i −0.595618 + 1.00498i
\(738\) 0 0
\(739\) −7.72542 23.7764i −0.284184 0.874629i −0.986642 0.162904i \(-0.947914\pi\)
0.702458 0.711726i \(-0.252086\pi\)
\(740\) −0.104528 + 0.994522i −0.00384254 + 0.0365594i
\(741\) 0 0
\(742\) 11.9325 + 13.2524i 0.438055 + 0.486510i
\(743\) 23.5402 + 26.1441i 0.863608 + 0.959134i 0.999501 0.0315899i \(-0.0100571\pi\)
−0.135893 + 0.990723i \(0.543390\pi\)
\(744\) 0 0
\(745\) 4.10489 39.0554i 0.150391 1.43088i
\(746\) 0.843459 + 2.59590i 0.0308812 + 0.0950426i
\(747\) 0 0
\(748\) −8.47214 1.90211i −0.309772 0.0695481i
\(749\) 6.35410 + 11.0056i 0.232174 + 0.402137i
\(750\) 0 0
\(751\) 10.8922 4.84952i 0.397462 0.176961i −0.198265 0.980148i \(-0.563531\pi\)
0.595727 + 0.803187i \(0.296864\pi\)
\(752\) −0.313585 2.98357i −0.0114353 0.108799i
\(753\) 0 0
\(754\) 4.76885 1.01365i 0.173671 0.0369150i
\(755\) 4.23607 3.07768i 0.154166 0.112008i
\(756\) 0 0
\(757\) 0.600813 + 1.84911i 0.0218369 + 0.0672071i 0.961381 0.275220i \(-0.0887509\pi\)
−0.939544 + 0.342428i \(0.888751\pi\)
\(758\) 0.489357 + 0.847591i 0.0177742 + 0.0307859i
\(759\) 0 0
\(760\) 17.1353 29.6791i 0.621561 1.07658i
\(761\) 30.2136 + 6.42209i 1.09524 + 0.232801i 0.719894 0.694084i \(-0.244190\pi\)
0.375347 + 0.926885i \(0.377524\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 3.73607 11.4984i 0.135166 0.415999i
\(765\) 0 0
\(766\) 13.4443 9.76784i 0.485761 0.352926i
\(767\) −1.90396 + 18.1150i −0.0687481 + 0.654095i
\(768\) 0 0
\(769\) −6.34346 + 10.9872i −0.228751 + 0.396208i −0.957438 0.288638i \(-0.906797\pi\)
0.728687 + 0.684847i \(0.240131\pi\)
\(770\) −14.6317 6.71556i −0.527290 0.242012i
\(771\) 0 0
\(772\) 20.0970 22.3199i 0.723306 0.803312i
\(773\) 25.2812 + 18.3678i 0.909300 + 0.660645i 0.940838 0.338858i \(-0.110040\pi\)
−0.0315378 + 0.999503i \(0.510040\pi\)
\(774\) 0 0
\(775\) 1.63525 5.03280i 0.0587401 0.180783i
\(776\) 30.6962 6.52468i 1.10193 0.234222i
\(777\) 0 0
\(778\) −13.7032 + 6.10105i −0.491283 + 0.218733i
\(779\) 68.3950 + 14.5378i 2.45051 + 0.520871i
\(780\) 0 0
\(781\) 5.90063 17.4790i 0.211141 0.625447i
\(782\) −3.47214 −0.124163
\(783\) 0 0
\(784\) −3.00000 2.17963i −0.107143 0.0778438i
\(785\) 8.86889 + 3.94868i 0.316544 + 0.140935i
\(786\) 0 0
\(787\) −6.88656 7.64829i −0.245479 0.272632i 0.607796 0.794093i \(-0.292054\pi\)
−0.853275 + 0.521461i \(0.825387\pi\)
\(788\) 4.12374 + 39.2347i 0.146902 + 1.39768i
\(789\) 0 0
\(790\) 10.2553 11.3896i 0.364866 0.405224i
\(791\) 2.12461 0.0755425
\(792\) 0 0
\(793\) 13.8541 0.491974
\(794\) 16.0076 17.7782i 0.568089 0.630926i
\(795\) 0 0
\(796\) −2.82587 26.8863i −0.100160 0.952961i
\(797\) 7.20248 + 7.99916i 0.255125 + 0.283345i 0.857078 0.515186i \(-0.172277\pi\)
−0.601953 + 0.798531i \(0.705611\pi\)
\(798\) 0 0
\(799\) 2.39169 + 1.06485i 0.0846120 + 0.0376717i
\(800\) 8.42705 + 6.12261i 0.297941 + 0.216467i
\(801\) 0 0
\(802\) 16.1246 0.569380
\(803\) −8.75446 + 6.20909i −0.308938 + 0.219114i
\(804\) 0 0
\(805\) 26.6746 + 5.66986i 0.940156 + 0.199836i
\(806\) −2.84246 + 1.26554i −0.100121 + 0.0445769i
\(807\) 0 0
\(808\) 6.56161 1.39471i 0.230837 0.0490659i
\(809\) 2.98936 9.20029i 0.105100 0.323465i −0.884654 0.466249i \(-0.845605\pi\)
0.989754 + 0.142783i \(0.0456052\pi\)
\(810\) 0 0
\(811\) −2.63525 1.91462i −0.0925363 0.0672316i 0.540555 0.841309i \(-0.318214\pi\)
−0.633091 + 0.774077i \(0.718214\pi\)
\(812\) −14.5256 + 16.1323i −0.509749 + 0.566134i
\(813\) 0 0
\(814\) −0.0560688 + 0.480630i −0.00196521 + 0.0168461i
\(815\) 23.9164 41.4244i 0.837755 1.45103i
\(816\) 0 0
\(817\) −3.81598 + 36.3066i −0.133504 + 1.27021i
\(818\) −5.52786 + 4.01623i −0.193277 + 0.140424i
\(819\) 0 0
\(820\) −15.6353 + 48.1204i −0.546007 + 1.68044i
\(821\) 36.9222 + 16.4388i 1.28859 + 0.573719i 0.932648 0.360787i \(-0.117492\pi\)
0.355946 + 0.934506i \(0.384159\pi\)
\(822\) 0 0
\(823\) 34.6970 + 7.37507i 1.20946 + 0.257079i 0.768147 0.640274i \(-0.221179\pi\)
0.441314 + 0.897353i \(0.354512\pi\)
\(824\) 6.70820 11.6190i 0.233691 0.404765i
\(825\) 0 0
\(826\) 9.57295 + 16.5808i 0.333085 + 0.576921i
\(827\) 16.4164 + 50.5245i 0.570854 + 1.75691i 0.649880 + 0.760037i \(0.274819\pi\)
−0.0790257 + 0.996873i \(0.525181\pi\)
\(828\) 0 0
\(829\) −14.3090 + 10.3961i −0.496973 + 0.361072i −0.807859 0.589375i \(-0.799374\pi\)
0.310887 + 0.950447i \(0.399374\pi\)
\(830\) −1.12086 + 0.238246i −0.0389055 + 0.00826963i
\(831\) 0 0
\(832\) 0.0435265 + 0.414127i 0.00150901 + 0.0143573i
\(833\) 2.95630 1.31623i 0.102430 0.0456046i
\(834\) 0 0
\(835\) 13.1353 + 22.7509i 0.454564 + 0.787328i
\(836\) −16.0172 + 27.0256i −0.553967 + 0.934700i
\(837\) 0 0
\(838\) −3.15248 9.70232i −0.108900 0.335161i
\(839\) 3.83705 36.5071i 0.132470 1.26037i −0.703144 0.711048i \(-0.748221\pi\)
0.835614 0.549318i \(-0.185112\pi\)
\(840\) 0 0
\(841\) −6.02218 6.68830i −0.207661 0.230631i
\(842\) 15.4131 + 17.1179i 0.531169 + 0.589923i
\(843\) 0 0
\(844\) −3.76662 + 35.8370i −0.129653 + 1.23356i
\(845\) 8.00000 + 24.6215i 0.275208 + 0.847004i
\(846\) 0 0
\(847\) 29.8328 + 14.1068i 1.02507 + 0.484717i
\(848\) 8.91641 + 15.4437i 0.306191 + 0.530338i
\(849\) 0 0
\(850\) −1.69381 + 0.754131i −0.0580971 + 0.0258665i
\(851\) −0.0856778 0.815170i −0.00293700 0.0279437i
\(852\) 0 0
\(853\) 9.72697 2.06753i 0.333045 0.0707909i −0.0383541 0.999264i \(-0.512211\pi\)
0.371399 + 0.928473i \(0.378878\pi\)
\(854\) 11.7812 8.55951i 0.403143 0.292900i
\(855\) 0 0
\(856\) −2.92705 9.00854i −0.100045 0.307905i
\(857\) −23.8607 41.3279i −0.815065 1.41173i −0.909281 0.416183i \(-0.863368\pi\)
0.0942157 0.995552i \(-0.469966\pi\)
\(858\) 0 0
\(859\) −3.55573 + 6.15870i −0.121320 + 0.210132i −0.920288 0.391241i \(-0.872046\pi\)
0.798969 + 0.601373i \(0.205379\pi\)
\(860\) −25.8391 5.49228i −0.881108 0.187285i
\(861\) 0 0
\(862\) 22.3055 + 9.93105i 0.759728 + 0.338253i
\(863\) 3.67376 11.3067i 0.125056 0.384884i −0.868855 0.495067i \(-0.835144\pi\)
0.993911 + 0.110183i \(0.0351436\pi\)
\(864\) 0 0
\(865\) 32.5795 23.6704i 1.10774 0.804818i
\(866\) −0.387613 + 3.68789i −0.0131716 + 0.125320i
\(867\) 0 0
\(868\) 6.92705 11.9980i 0.235119 0.407239i
\(869\) −21.2861 + 23.1049i −0.722083 + 0.783779i
\(870\) 0 0
\(871\) −11.2864 + 12.5348i −0.382425 + 0.424726i
\(872\) 0 0
\(873\) 0 0
\(874\) −3.88197 + 11.9475i −0.131309 + 0.404129i
\(875\) −24.1683 + 5.13712i −0.817037 + 0.173667i
\(876\) 0 0
\(877\) 5.86168 2.60979i 0.197935 0.0881263i −0.305375 0.952232i \(-0.598782\pi\)
0.503310 + 0.864106i \(0.332115\pi\)
\(878\) 1.98998 + 0.422984i 0.0671587 + 0.0142750i
\(879\) 0 0
\(880\) −12.9157 9.61091i −0.435389 0.323984i
\(881\) 13.9098 0.468634 0.234317 0.972160i \(-0.424715\pi\)
0.234317 + 0.972160i \(0.424715\pi\)
\(882\) 0 0
\(883\) −8.56231 6.22088i −0.288145 0.209349i 0.434318 0.900760i \(-0.356990\pi\)
−0.722462 + 0.691411i \(0.756990\pi\)
\(884\) −4.21878 1.87832i −0.141893 0.0631749i
\(885\) 0 0
\(886\) 17.0069 + 18.8881i 0.571358 + 0.634557i
\(887\) −0.313585 2.98357i −0.0105292 0.100178i 0.987995 0.154485i \(-0.0493718\pi\)
−0.998524 + 0.0543066i \(0.982705\pi\)
\(888\) 0 0
\(889\) −7.44382 + 8.26720i −0.249658 + 0.277273i
\(890\) 0.854102 0.0286296
\(891\) 0 0
\(892\) −1.14590 −0.0383675
\(893\) 6.33810 7.03917i 0.212096 0.235557i
\(894\) 0 0
\(895\) −0.611920 5.82203i −0.0204542 0.194609i
\(896\) 22.8481 + 25.3753i 0.763300 + 0.847731i
\(897\) 0 0
\(898\) 13.8170 + 6.15173i 0.461080 + 0.205286i
\(899\) −10.3262 7.50245i −0.344399 0.250221i
\(900\) 0 0
\(901\) −15.5623 −0.518456
\(902\) −7.83096 + 23.1971i −0.260743 + 0.772378i
\(903\) 0 0
\(904\) −1.54899 0.329247i −0.0515185 0.0109506i
\(905\) 41.7880 18.6052i 1.38908 0.618458i
\(906\) 0 0
\(907\) 42.0395 8.93578i 1.39590 0.296708i 0.552284 0.833656i \(-0.313756\pi\)
0.843615 + 0.536948i \(0.180423\pi\)
\(908\) 12.4443 38.2995i 0.412978 1.27101i
\(909\) 0 0
\(910\) −6.92705 5.03280i −0.229630 0.166836i
\(911\) 12.0816 13.4180i 0.400283 0.444559i −0.508982 0.860777i \(-0.669978\pi\)
0.909265 + 0.416218i \(0.136645\pi\)
\(912\) 0 0
\(913\) 2.30294 0.462102i 0.0762163 0.0152933i
\(914\) 2.53444 4.38978i 0.0838319 0.145201i
\(915\) 0 0
\(916\) 1.69131 16.0917i 0.0558823 0.531685i
\(917\) 17.3435 12.6008i 0.572731 0.416114i
\(918\) 0 0
\(919\) 14.5106 44.6592i 0.478662 1.47317i −0.362293 0.932064i \(-0.618006\pi\)
0.840955 0.541106i \(-0.181994\pi\)
\(920\) −18.5689 8.26743i −0.612200 0.272569i
\(921\) 0 0
\(922\) −12.7496 2.71001i −0.419886 0.0892495i
\(923\) 4.90576 8.49703i 0.161475 0.279683i
\(924\) 0 0
\(925\) −0.218847 0.379054i −0.00719565 0.0124632i
\(926\) 3.01722 + 9.28605i 0.0991520 + 0.305159i
\(927\) 0 0
\(928\) 20.3262 14.7679i 0.667241 0.484779i
\(929\) 32.1699 6.83791i 1.05546 0.224345i 0.352673 0.935747i \(-0.385273\pi\)
0.702785 + 0.711402i \(0.251939\pi\)
\(930\) 0 0
\(931\) −1.22384 11.6441i −0.0401098 0.381619i
\(932\) −35.9578 + 16.0094i −1.17784 + 0.524406i
\(933\) 0 0
\(934\) −3.01722 5.22598i −0.0987265 0.170999i
\(935\) 12.8992 5.56758i 0.421849 0.182079i
\(936\) 0 0
\(937\) −5.12868 15.7844i −0.167547 0.515655i 0.831668 0.555273i \(-0.187386\pi\)
−0.999215 + 0.0396173i \(0.987386\pi\)
\(938\) −1.85324 + 17.6324i −0.0605103 + 0.575717i
\(939\) 0 0
\(940\) 4.58629 + 5.09359i 0.149588 + 0.166135i
\(941\) −29.8641 33.1674i −0.973542 1.08123i −0.996674 0.0814951i \(-0.974030\pi\)
0.0231321 0.999732i \(-0.492636\pi\)
\(942\) 0 0
\(943\) 4.33502 41.2449i 0.141168 1.34312i
\(944\) 5.91641 + 18.2088i 0.192563 + 0.592647i
\(945\) 0 0
\(946\) −12.4721 2.80017i −0.405504 0.0910413i
\(947\) −9.16312 15.8710i −0.297761 0.515738i 0.677862 0.735189i \(-0.262907\pi\)
−0.975623 + 0.219451i \(0.929573\pi\)
\(948\) 0 0
\(949\) −5.21470 + 2.32174i −0.169276 + 0.0753667i
\(950\) 0.701198 + 6.67146i 0.0227499 + 0.216451i
\(951\) 0 0
\(952\) −10.6169 + 2.25669i −0.344096 + 0.0731399i
\(953\) −30.5967 + 22.2298i −0.991126 + 0.720095i −0.960167 0.279426i \(-0.909856\pi\)
−0.0309585 + 0.999521i \(0.509856\pi\)
\(954\) 0 0
\(955\) 6.04508 + 18.6049i 0.195614 + 0.602039i
\(956\) 2.07295 + 3.59045i 0.0670440 + 0.116124i
\(957\) 0 0
\(958\) −8.68034 + 15.0348i −0.280449 + 0.485752i
\(959\) −21.9266 4.66063i −0.708045 0.150500i
\(960\) 0 0
\(961\) −20.8783 9.29560i −0.673492 0.299858i
\(962\) −0.0795268 + 0.244758i −0.00256405 + 0.00789133i
\(963\) 0 0
\(964\) −30.2705 + 21.9928i −0.974947 + 0.708341i
\(965\) −5.07974 + 48.3305i −0.163523 + 1.55581i
\(966\) 0 0
\(967\) 17.3435 30.0398i 0.557728 0.966013i −0.439958 0.898019i \(-0.645007\pi\)
0.997686 0.0679948i \(-0.0216601\pi\)
\(968\) −19.5640 14.9080i −0.628812 0.479161i
\(969\) 0 0
\(970\) −15.1948 + 16.8755i −0.487874 + 0.541839i
\(971\) −30.5623 22.2048i −0.980791 0.712586i −0.0229058 0.999738i \(-0.507292\pi\)
−0.957885 + 0.287151i \(0.907292\pi\)
\(972\) 0 0
\(973\) −0.791796 + 2.43690i −0.0253838 + 0.0781234i
\(974\) 10.1680 2.16127i 0.325803 0.0692515i
\(975\) 0 0
\(976\) 13.3033 5.92302i 0.425829 0.189591i
\(977\) 4.53794 + 0.964569i 0.145182 + 0.0308593i 0.279929 0.960021i \(-0.409689\pi\)
−0.134748 + 0.990880i \(0.543022\pi\)
\(978\) 0 0
\(979\) −1.75061 0.0199794i −0.0559498 0.000638544i
\(980\) 8.47214 0.270632
\(981\) 0 0
\(982\) 12.6074 + 9.15981i 0.402318 + 0.292301i
\(983\) −24.9443 11.1059i −0.795600 0.354224i −0.0316497 0.999499i \(-0.510076\pi\)
−0.763950 + 0.645275i \(0.776743\pi\)
\(984\) 0 0
\(985\) −42.7125 47.4370i −1.36093 1.51147i
\(986\) 0.467465 + 4.44764i 0.0148871 + 0.141642i
\(987\) 0 0
\(988\) −11.1800 + 12.4166i −0.355682 + 0.395025i
\(989\) 21.6525 0.688509
\(990\) 0 0
\(991\) 21.2705 0.675680 0.337840 0.941204i \(-0.390304\pi\)
0.337840 + 0.941204i \(0.390304\pi\)
\(992\) −10.7291 + 11.9159i −0.340650 + 0.378331i
\(993\) 0 0
\(994\) −1.07801 10.2566i −0.0341924 0.325319i
\(995\) 29.2695 + 32.5071i 0.927907 + 1.03055i
\(996\) 0 0
\(997\) −11.8566 5.27892i −0.375504 0.167185i 0.210302 0.977636i \(-0.432555\pi\)
−0.585806 + 0.810451i \(0.699222\pi\)
\(998\) −8.78115 6.37988i −0.277963 0.201952i
\(999\) 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 891.2.n.d.676.1 8
3.2 odd 2 891.2.n.a.676.1 8
9.2 odd 6 891.2.n.a.379.1 8
9.4 even 3 33.2.e.a.16.1 4
9.5 odd 6 99.2.f.b.82.1 4
9.7 even 3 inner 891.2.n.d.379.1 8
11.9 even 5 inner 891.2.n.d.757.1 8
33.20 odd 10 891.2.n.a.757.1 8
36.31 odd 6 528.2.y.f.49.1 4
45.4 even 6 825.2.n.f.676.1 4
45.13 odd 12 825.2.bx.b.49.1 8
45.22 odd 12 825.2.bx.b.49.2 8
99.4 even 15 363.2.e.h.124.1 4
99.13 odd 30 363.2.e.j.130.1 4
99.14 odd 30 1089.2.a.m.1.2 2
99.20 odd 30 891.2.n.a.460.1 8
99.31 even 15 33.2.e.a.31.1 yes 4
99.40 odd 30 363.2.e.c.124.1 4
99.41 even 30 1089.2.a.s.1.1 2
99.49 even 15 363.2.e.h.202.1 4
99.58 even 15 363.2.a.h.1.1 2
99.76 odd 6 363.2.e.j.148.1 4
99.85 odd 30 363.2.a.e.1.2 2
99.86 odd 30 99.2.f.b.64.1 4
99.94 odd 30 363.2.e.c.202.1 4
99.97 even 15 inner 891.2.n.d.460.1 8
396.31 odd 30 528.2.y.f.97.1 4
396.283 even 30 5808.2.a.bm.1.1 2
396.355 odd 30 5808.2.a.bl.1.1 2
495.184 odd 30 9075.2.a.bv.1.1 2
495.229 even 30 825.2.n.f.526.1 4
495.328 odd 60 825.2.bx.b.724.2 8
495.427 odd 60 825.2.bx.b.724.1 8
495.454 even 30 9075.2.a.x.1.2 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
33.2.e.a.16.1 4 9.4 even 3
33.2.e.a.31.1 yes 4 99.31 even 15
99.2.f.b.64.1 4 99.86 odd 30
99.2.f.b.82.1 4 9.5 odd 6
363.2.a.e.1.2 2 99.85 odd 30
363.2.a.h.1.1 2 99.58 even 15
363.2.e.c.124.1 4 99.40 odd 30
363.2.e.c.202.1 4 99.94 odd 30
363.2.e.h.124.1 4 99.4 even 15
363.2.e.h.202.1 4 99.49 even 15
363.2.e.j.130.1 4 99.13 odd 30
363.2.e.j.148.1 4 99.76 odd 6
528.2.y.f.49.1 4 36.31 odd 6
528.2.y.f.97.1 4 396.31 odd 30
825.2.n.f.526.1 4 495.229 even 30
825.2.n.f.676.1 4 45.4 even 6
825.2.bx.b.49.1 8 45.13 odd 12
825.2.bx.b.49.2 8 45.22 odd 12
825.2.bx.b.724.1 8 495.427 odd 60
825.2.bx.b.724.2 8 495.328 odd 60
891.2.n.a.379.1 8 9.2 odd 6
891.2.n.a.460.1 8 99.20 odd 30
891.2.n.a.676.1 8 3.2 odd 2
891.2.n.a.757.1 8 33.20 odd 10
891.2.n.d.379.1 8 9.7 even 3 inner
891.2.n.d.460.1 8 99.97 even 15 inner
891.2.n.d.676.1 8 1.1 even 1 trivial
891.2.n.d.757.1 8 11.9 even 5 inner
1089.2.a.m.1.2 2 99.14 odd 30
1089.2.a.s.1.1 2 99.41 even 30
5808.2.a.bl.1.1 2 396.355 odd 30
5808.2.a.bm.1.1 2 396.283 even 30
9075.2.a.x.1.2 2 495.454 even 30
9075.2.a.bv.1.1 2 495.184 odd 30