Properties

Label 891.2.n.a.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.a.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 −0.578976 0.815344i \(-0.696548\pi\)
0.871397 + 0.490578i \(0.163214\pi\)
\(3\) 0 0
\(4\) 0.169131 + 1.60917i 0.0845653 + 0.804585i
\(5\) 1.75181 + 1.94558i 0.783432 + 0.870089i 0.994211 0.107445i \(-0.0342668\pi\)
−0.210779 + 0.977534i \(0.567600\pi\)
\(6\) 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 −0.993203 0.116398i \(-0.962865\pi\)
0.871935 + 0.489622i \(0.162865\pi\)
\(18\) 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 −0.626294 0.779587i \(-0.715429\pi\)
0.988289 + 0.152593i \(0.0487623\pi\)
\(24\) 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 −0.00931360 0.999957i \(-0.502965\pi\)
−0.749345 + 0.662180i \(0.769631\pi\)
\(30\) 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 \(-0.250788\pi\)
0.998756 0.0498651i \(-0.0158791\pi\)
\(42\) 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 \(-0.929016\pi\)
0.999908 0.0135627i \(-0.00431728\pi\)
\(48\) 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 \(0.129685\pi\)
−0.509893 + 0.860238i \(0.670315\pi\)
\(54\) 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 \(0.201309\pi\)
−0.666069 + 0.745890i \(0.732024\pi\)
\(60\) 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 \(-0.792930\pi\)
0.999753 0.0222083i \(-0.00706970\pi\)
\(72\) 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 −0.169736 0.985490i \(-0.554292\pi\)
0.245773 + 0.969327i \(0.420958\pi\)
\(84\) 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 \(-0.508906\pi\)
−0.0279767 + 0.999609i \(0.508906\pi\)
\(90\) 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 −0.634949 0.772554i \(-0.718979\pi\)
0.834692 + 0.550717i \(0.185646\pi\)
\(102\) 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 0.409679 0.912230i \(-0.365641\pi\)
−0.740984 + 0.671522i \(0.765641\pi\)
\(108\) 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 −0.436942 0.899490i \(-0.643939\pi\)
0.376080 + 0.926587i \(0.377272\pi\)
\(114\) 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 −0.978832 0.204666i \(-0.934389\pi\)
0.666662 + 0.745360i \(0.267723\pi\)
\(132\) 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 0.115183 0.993344i \(-0.463255\pi\)
0.509254 + 0.860616i \(0.329921\pi\)
\(138\) 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 0.175194 0.984534i \(-0.443945\pi\)
−0.997453 + 0.0713221i \(0.977278\pi\)
\(150\) 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 0.571363 0.820698i \(-0.306415\pi\)
0.188158 + 0.982139i \(0.439748\pi\)
\(168\) 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 \(-0.767865\pi\)
0.867902 0.496735i \(-0.165468\pi\)
\(174\) 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 0.518123 0.855306i \(-0.326631\pi\)
−0.653335 + 0.757069i \(0.726631\pi\)
\(180\) 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 0.638554 0.769577i \(-0.279533\pi\)
−0.144632 + 0.989486i \(0.546200\pi\)
\(192\) 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 \(-0.834961\pi\)
−0.868572 + 0.495564i \(0.834961\pi\)
\(198\) 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 0.983840 0.179052i \(-0.0573030\pi\)
0.525256 + 0.850944i \(0.323970\pi\)
\(228\) 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 \(-0.806507\pi\)
0.328394 0.944541i \(-0.393493\pi\)
\(234\) 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 −0.481044 0.876696i \(-0.659742\pi\)
0.329631 + 0.944110i \(0.393076\pi\)
\(240\) 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 0.997856 0.0654431i \(-0.0208461\pi\)
−0.845749 + 0.533581i \(0.820846\pi\)
\(252\) 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 \(-0.914712\pi\)
0.888202 0.459454i \(-0.151955\pi\)
\(258\) 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 \(-0.998764\pi\)
0.496633 0.867961i \(-0.334570\pi\)
\(264\) 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 \(0.256965\pi\)
−0.984029 + 0.178006i \(0.943035\pi\)
\(270\) 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 −0.230146 0.973156i \(-0.573920\pi\)
0.185569 + 0.982631i \(0.440587\pi\)
\(282\) 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 0.994691 0.102909i \(-0.0328152\pi\)
−0.994350 + 0.106147i \(0.966149\pi\)
\(294\) 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 −0.471165 0.882045i \(-0.656167\pi\)
0.340216 + 0.940347i \(0.389500\pi\)
\(312\) 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 −0.259898 0.965636i \(-0.583689\pi\)
0.987513 + 0.157537i \(0.0503555\pi\)
\(318\) 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 0.990763 0.135607i \(-0.0432986\pi\)
−0.238427 + 0.971160i \(0.576632\pi\)
\(348\) 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 0.692371 0.721542i \(-0.256566\pi\)
−0.971059 + 0.238840i \(0.923233\pi\)
\(354\) 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 −0.825938 0.563761i \(-0.809354\pi\)
0.280940 + 0.959725i \(0.409354\pi\)
\(360\) 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 0.823045 0.567977i \(-0.192274\pi\)
0.520872 + 0.853635i \(0.325607\pi\)
\(384\) 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 −0.241455 0.970412i \(-0.577624\pi\)
−0.882721 + 0.469897i \(0.844291\pi\)
\(390\) 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 0.999723 0.0235546i \(-0.00749836\pi\)
−0.127925 + 0.991784i \(0.540832\pi\)
\(402\) 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 −0.590911 0.806737i \(-0.701231\pi\)
0.994110 + 0.108375i \(0.0345647\pi\)
\(420\) 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 \(0.300440\pi\)
0.00138127 + 0.999999i \(0.499560\pi\)
\(432\) 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 \(0.464849\pi\)
−0.314442 + 0.949277i \(0.601817\pi\)
\(444\) 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 \(0.0959544\pi\)
−0.598020 + 0.801481i \(0.704046\pi\)
\(450\) 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 0.508814 0.860876i \(-0.330084\pi\)
−0.999948 + 0.0102080i \(0.996751\pi\)
\(462\) 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 −0.856660 0.515882i \(-0.827464\pi\)
0.996280 + 0.0861747i \(0.0274643\pi\)
\(468\) 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 −0.787166 0.616742i \(-0.788452\pi\)
−0.468260 + 0.883591i \(0.655119\pi\)
\(480\) 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 \(0.159322\pi\)
−0.758385 + 0.651807i \(0.774011\pi\)
\(492\) 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 0.964734 0.263227i \(-0.0847870\pi\)
0.0477750 + 0.998858i \(0.484787\pi\)
\(504\) 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 −0.824742 0.565510i \(-0.808679\pi\)
−0.131604 + 0.991302i \(0.542013\pi\)
\(510\) 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 −0.818758 0.574139i \(-0.805337\pi\)
0.293028 + 0.956104i \(0.405337\pi\)
\(522\) 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 −0.302143 0.953263i \(-0.597702\pi\)
0.813239 + 0.581929i \(0.197702\pi\)
\(558\) 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 0.0210214 0.999779i \(-0.493308\pi\)
−0.387443 + 0.921894i \(0.626642\pi\)
\(564\) 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 \(0.201660\pi\)
−0.911412 + 0.411496i \(0.865006\pi\)
\(570\) 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 0.971271 0.237975i \(-0.0764837\pi\)
0.473057 + 0.881032i \(0.343150\pi\)
\(588\) 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 \(-0.650763\pi\)
−0.456126 + 0.889915i \(0.650763\pi\)
\(594\) 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 0.845753 0.533574i \(-0.179151\pi\)
−0.619056 + 0.785347i \(0.712485\pi\)
\(600\) 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 −0.598796 0.800901i \(-0.704354\pi\)
0.992999 + 0.118122i \(0.0376874\pi\)
\(618\) 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 \(-0.717221\pi\)
0.778240 0.627967i \(-0.216113\pi\)
\(642\) 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 \(-0.915985\pi\)
0.627655 0.778492i \(-0.284015\pi\)
\(648\) 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 \(0.449618\pi\)
0.0511377 + 0.998692i \(0.483715\pi\)
\(654\) 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 0.743440 0.668803i \(-0.233193\pi\)
−0.950920 + 0.309436i \(0.899860\pi\)
\(660\) 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 0.0535147 0.998567i \(-0.482958\pi\)
0.455042 + 0.890470i \(0.349624\pi\)
\(678\) 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 \(-0.481040\pi\)
0.0595283 + 0.998227i \(0.481040\pi\)
\(684\) 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 0.412415 0.910996i \(-0.364685\pi\)
−0.738966 + 0.673743i \(0.764685\pi\)
\(702\) 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 −0.611418 0.791307i \(-0.709401\pi\)
0.563639 + 0.826021i \(0.309401\pi\)
\(720\) 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 0.135893 0.990723i \(-0.456610\pi\)
−0.999501 + 0.0315899i \(0.989943\pi\)
\(744\) 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 −0.375347 0.926885i \(-0.622476\pi\)
−0.719894 + 0.694084i \(0.755810\pi\)
\(762\) 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 0.0315378 0.999503i \(-0.489960\pi\)
−0.940838 + 0.338858i \(0.889960\pi\)
\(774\) 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 0.601953 0.798531i \(-0.294389\pi\)
−0.857078 + 0.515186i \(0.827723\pi\)
\(798\) 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 −0.989754 0.142783i \(-0.954395\pi\)
0.884654 + 0.466249i \(0.154395\pi\)
\(810\) 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 −0.355946 0.934506i \(-0.615841\pi\)
−0.932648 + 0.360787i \(0.882508\pi\)
\(822\) 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 \(-0.725181\pi\)
0.0790257 0.996873i \(-0.474819\pi\)
\(828\) 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 \(0.251779\pi\)
−0.835614 + 0.549318i \(0.814888\pi\)
\(840\) 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 \(0.136632\pi\)
−0.0942157 + 0.995552i \(0.530034\pi\)
\(858\) 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 −0.993911 0.110183i \(-0.964856\pi\)
0.868855 + 0.495067i \(0.164856\pi\)
\(864\) 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 \(-0.575285\pi\)
−0.234317 + 0.972160i \(0.575285\pi\)
\(882\) 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 0.998524 0.0543066i \(-0.0172948\pi\)
−0.987995 + 0.154485i \(0.950628\pi\)
\(888\) 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 −0.909265 0.416218i \(-0.863355\pi\)
0.508982 + 0.860777i \(0.330022\pi\)
\(912\) 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 −0.702785 0.711402i \(-0.748061\pi\)
−0.352673 + 0.935747i \(0.614727\pi\)
\(930\) 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 \(0.0259695\pi\)
−0.0231321 + 0.999732i \(0.507364\pi\)
\(942\) 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 0.975623 0.219451i \(-0.0704267\pi\)
−0.677862 + 0.735189i \(0.737093\pi\)
\(948\) 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 0.0309585 0.999521i \(-0.490144\pi\)
0.960167 + 0.279426i \(0.0901440\pi\)
\(954\) 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 0.957885 0.287151i \(-0.0927082\pi\)
0.0229058 + 0.999738i \(0.492708\pi\)
\(972\) 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 0.134748 0.990880i \(-0.456978\pi\)
−0.279929 + 0.960021i \(0.590311\pi\)
\(978\) 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 0.763950 0.645275i \(-0.223257\pi\)
0.0316497 + 0.999499i \(0.489924\pi\)
\(984\) 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.a.676.1 8
3.2 odd 2 891.2.n.d.676.1 8
9.2 odd 6 891.2.n.d.379.1 8
9.4 even 3 99.2.f.b.82.1 4
9.5 odd 6 33.2.e.a.16.1 4
9.7 even 3 inner 891.2.n.a.379.1 8
11.9 even 5 inner 891.2.n.a.757.1 8
33.20 odd 10 891.2.n.d.757.1 8
36.23 even 6 528.2.y.f.49.1 4
45.14 odd 6 825.2.n.f.676.1 4
45.23 even 12 825.2.bx.b.49.1 8
45.32 even 12 825.2.bx.b.49.2 8
99.5 odd 30 363.2.e.h.202.1 4
99.14 odd 30 363.2.a.h.1.1 2
99.20 odd 30 891.2.n.d.460.1 8
99.31 even 15 99.2.f.b.64.1 4
99.32 even 6 363.2.e.j.148.1 4
99.41 even 30 363.2.a.e.1.2 2
99.50 even 30 363.2.e.c.202.1 4
99.58 even 15 1089.2.a.m.1.2 2
99.59 odd 30 363.2.e.h.124.1 4
99.68 even 30 363.2.e.j.130.1 4
99.85 odd 30 1089.2.a.s.1.1 2
99.86 odd 30 33.2.e.a.31.1 yes 4
99.95 even 30 363.2.e.c.124.1 4
99.97 even 15 inner 891.2.n.a.460.1 8
396.239 odd 30 5808.2.a.bm.1.1 2
396.311 even 30 5808.2.a.bl.1.1 2
396.383 even 30 528.2.y.f.97.1 4
495.14 odd 30 9075.2.a.x.1.2 2
495.239 even 30 9075.2.a.bv.1.1 2
495.284 odd 30 825.2.n.f.526.1 4
495.383 even 60 825.2.bx.b.724.2 8
495.482 even 60 825.2.bx.b.724.1 8
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
33.2.e.a.16.1 4 9.5 odd 6
33.2.e.a.31.1 yes 4 99.86 odd 30
99.2.f.b.64.1 4 99.31 even 15
99.2.f.b.82.1 4 9.4 even 3
363.2.a.e.1.2 2 99.41 even 30
363.2.a.h.1.1 2 99.14 odd 30
363.2.e.c.124.1 4 99.95 even 30
363.2.e.c.202.1 4 99.50 even 30
363.2.e.h.124.1 4 99.59 odd 30
363.2.e.h.202.1 4 99.5 odd 30
363.2.e.j.130.1 4 99.68 even 30
363.2.e.j.148.1 4 99.32 even 6
528.2.y.f.49.1 4 36.23 even 6
528.2.y.f.97.1 4 396.383 even 30
825.2.n.f.526.1 4 495.284 odd 30
825.2.n.f.676.1 4 45.14 odd 6
825.2.bx.b.49.1 8 45.23 even 12
825.2.bx.b.49.2 8 45.32 even 12
825.2.bx.b.724.1 8 495.482 even 60
825.2.bx.b.724.2 8 495.383 even 60
891.2.n.a.379.1 8 9.7 even 3 inner
891.2.n.a.460.1 8 99.97 even 15 inner
891.2.n.a.676.1 8 1.1 even 1 trivial
891.2.n.a.757.1 8 11.9 even 5 inner
891.2.n.d.379.1 8 9.2 odd 6
891.2.n.d.460.1 8 99.20 odd 30
891.2.n.d.676.1 8 3.2 odd 2
891.2.n.d.757.1 8 33.20 odd 10
1089.2.a.m.1.2 2 99.58 even 15
1089.2.a.s.1.1 2 99.85 odd 30
5808.2.a.bl.1.1 2 396.311 even 30
5808.2.a.bm.1.1 2 396.239 odd 30
9075.2.a.x.1.2 2 495.14 odd 30
9075.2.a.bv.1.1 2 495.239 even 30