Properties

Label 504.2.bm.c.107.16
Level $504$
Weight $2$
Character 504.107
Analytic conductor $4.024$
Analytic rank $0$
Dimension $48$
CM no
Inner twists $8$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [504,2,Mod(107,504)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(504, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([3, 3, 3, 2]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("504.107");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 504 = 2^{3} \cdot 3^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 504.bm (of order \(6\), degree \(2\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(4.02446026187\)
Analytic rank: \(0\)
Dimension: \(48\)
Relative dimension: \(24\) over \(\Q(\zeta_{6})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 107.16
Character \(\chi\) \(=\) 504.107
Dual form 504.2.bm.c.179.16

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.648862 + 1.25657i) q^{2} +(-1.15796 + 1.63069i) q^{4} +(1.02787 - 1.78033i) q^{5} +(1.24680 - 2.33356i) q^{7} +(-2.80043 - 0.396971i) q^{8} +O(q^{10})\) \(q+(0.648862 + 1.25657i) q^{2} +(-1.15796 + 1.63069i) q^{4} +(1.02787 - 1.78033i) q^{5} +(1.24680 - 2.33356i) q^{7} +(-2.80043 - 0.396971i) q^{8} +(2.90407 + 0.136412i) q^{10} +(5.24912 - 3.03058i) q^{11} -1.77772i q^{13} +(3.74129 + 0.0525476i) q^{14} +(-1.31827 - 3.77653i) q^{16} +(0.786233 - 0.453932i) q^{17} +(-3.37450 + 5.84481i) q^{19} +(1.71292 + 3.73769i) q^{20} +(7.21410 + 4.62948i) q^{22} +(0.351459 - 0.608746i) q^{23} +(0.386948 + 0.670213i) q^{25} +(2.23383 - 1.15349i) q^{26} +(2.36155 + 4.73530i) q^{28} +4.52576 q^{29} +(-7.31501 + 4.22332i) q^{31} +(3.89011 - 4.10695i) q^{32} +(1.08056 + 0.693421i) q^{34} +(-2.87294 - 4.61833i) q^{35} +(6.07548 + 3.50768i) q^{37} +(-9.53402 - 0.447840i) q^{38} +(-3.58523 + 4.57766i) q^{40} -11.6289i q^{41} -4.69997 q^{43} +(-1.13633 + 12.0689i) q^{44} +(0.992982 + 0.0466433i) q^{46} +(-4.42306 + 7.66096i) q^{47} +(-3.89096 - 5.81897i) q^{49} +(-0.591097 + 0.921104i) q^{50} +(2.89889 + 2.05852i) q^{52} +(3.31595 + 5.74340i) q^{53} -12.4602i q^{55} +(-4.41794 + 6.04002i) q^{56} +(2.93659 + 5.68695i) q^{58} +(-1.11754 + 0.645211i) q^{59} +(7.95517 + 4.59292i) q^{61} +(-10.0533 - 6.45150i) q^{62} +(7.68483 + 2.22338i) q^{64} +(-3.16492 - 1.82727i) q^{65} +(-0.562480 - 0.974244i) q^{67} +(-0.170204 + 1.80773i) q^{68} +(3.93913 - 6.60672i) q^{70} +1.43897 q^{71} +(2.08692 + 3.61465i) q^{73} +(-0.465515 + 9.91029i) q^{74} +(-5.62351 - 12.2708i) q^{76} +(-0.527404 - 16.0277i) q^{77} +(-11.6339 - 6.71681i) q^{79} +(-8.07849 - 1.53484i) q^{80} +(14.6126 - 7.54554i) q^{82} +4.71682i q^{83} -1.86634i q^{85} +(-3.04963 - 5.90586i) q^{86} +(-15.9028 + 6.40319i) q^{88} +(-4.08201 - 2.35675i) q^{89} +(-4.14840 - 2.21646i) q^{91} +(0.585697 + 1.27802i) q^{92} +(-12.4965 - 0.586998i) q^{94} +(6.93713 + 12.0155i) q^{95} -12.2014 q^{97} +(4.78728 - 8.66499i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 48 q+O(q^{10}) \) Copy content Toggle raw display \( 48 q - 8 q^{10} - 28 q^{16} - 32 q^{19} + 32 q^{22} + 4 q^{28} + 112 q^{34} - 36 q^{40} - 160 q^{43} + 40 q^{46} + 56 q^{49} - 36 q^{52} + 12 q^{58} - 24 q^{64} + 92 q^{70} + 16 q^{73} - 120 q^{76} + 20 q^{82} - 100 q^{88} - 32 q^{91} - 20 q^{94} + 240 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/504\mathbb{Z}\right)^\times\).

\(n\) \(73\) \(127\) \(253\) \(281\)
\(\chi(n)\) \(e\left(\frac{1}{3}\right)\) \(-1\) \(-1\) \(-1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.648862 + 1.25657i 0.458814 + 0.888532i
\(3\) 0 0
\(4\) −1.15796 + 1.63069i −0.578979 + 0.815343i
\(5\) 1.02787 1.78033i 0.459679 0.796188i −0.539264 0.842137i \(-0.681298\pi\)
0.998944 + 0.0459483i \(0.0146310\pi\)
\(6\) 0 0
\(7\) 1.24680 2.33356i 0.471248 0.882001i
\(8\) −2.80043 0.396971i −0.990102 0.140350i
\(9\) 0 0
\(10\) 2.90407 + 0.136412i 0.918346 + 0.0431374i
\(11\) 5.24912 3.03058i 1.58267 0.913754i 0.588201 0.808715i \(-0.299836\pi\)
0.994468 0.105040i \(-0.0334970\pi\)
\(12\) 0 0
\(13\) 1.77772i 0.493050i −0.969136 0.246525i \(-0.920711\pi\)
0.969136 0.246525i \(-0.0792887\pi\)
\(14\) 3.74129 + 0.0525476i 0.999901 + 0.0140439i
\(15\) 0 0
\(16\) −1.31827 3.77653i −0.329567 0.944132i
\(17\) 0.786233 0.453932i 0.190690 0.110095i −0.401616 0.915808i \(-0.631551\pi\)
0.592305 + 0.805714i \(0.298218\pi\)
\(18\) 0 0
\(19\) −3.37450 + 5.84481i −0.774164 + 1.34089i 0.161100 + 0.986938i \(0.448496\pi\)
−0.935263 + 0.353953i \(0.884837\pi\)
\(20\) 1.71292 + 3.73769i 0.383022 + 0.835772i
\(21\) 0 0
\(22\) 7.21410 + 4.62948i 1.53805 + 0.987009i
\(23\) 0.351459 0.608746i 0.0732843 0.126932i −0.827055 0.562122i \(-0.809985\pi\)
0.900339 + 0.435189i \(0.143319\pi\)
\(24\) 0 0
\(25\) 0.386948 + 0.670213i 0.0773896 + 0.134043i
\(26\) 2.23383 1.15349i 0.438090 0.226218i
\(27\) 0 0
\(28\) 2.36155 + 4.73530i 0.446291 + 0.894888i
\(29\) 4.52576 0.840412 0.420206 0.907429i \(-0.361958\pi\)
0.420206 + 0.907429i \(0.361958\pi\)
\(30\) 0 0
\(31\) −7.31501 + 4.22332i −1.31381 + 0.758531i −0.982726 0.185069i \(-0.940749\pi\)
−0.331088 + 0.943600i \(0.607416\pi\)
\(32\) 3.89011 4.10695i 0.687682 0.726012i
\(33\) 0 0
\(34\) 1.08056 + 0.693421i 0.185314 + 0.118921i
\(35\) −2.87294 4.61833i −0.485616 0.780640i
\(36\) 0 0
\(37\) 6.07548 + 3.50768i 0.998803 + 0.576659i 0.907894 0.419200i \(-0.137689\pi\)
0.0909092 + 0.995859i \(0.471023\pi\)
\(38\) −9.53402 0.447840i −1.54662 0.0726493i
\(39\) 0 0
\(40\) −3.58523 + 4.57766i −0.566875 + 0.723791i
\(41\) 11.6289i 1.81613i −0.418831 0.908064i \(-0.637560\pi\)
0.418831 0.908064i \(-0.362440\pi\)
\(42\) 0 0
\(43\) −4.69997 −0.716739 −0.358369 0.933580i \(-0.616667\pi\)
−0.358369 + 0.933580i \(0.616667\pi\)
\(44\) −1.13633 + 12.0689i −0.171309 + 1.81946i
\(45\) 0 0
\(46\) 0.992982 + 0.0466433i 0.146407 + 0.00687717i
\(47\) −4.42306 + 7.66096i −0.645169 + 1.11747i 0.339093 + 0.940753i \(0.389880\pi\)
−0.984262 + 0.176713i \(0.943453\pi\)
\(48\) 0 0
\(49\) −3.89096 5.81897i −0.555851 0.831282i
\(50\) −0.591097 + 0.921104i −0.0835937 + 0.130264i
\(51\) 0 0
\(52\) 2.89889 + 2.05852i 0.402004 + 0.285465i
\(53\) 3.31595 + 5.74340i 0.455481 + 0.788917i 0.998716 0.0506644i \(-0.0161339\pi\)
−0.543235 + 0.839581i \(0.682801\pi\)
\(54\) 0 0
\(55\) 12.4602i 1.68014i
\(56\) −4.41794 + 6.04002i −0.590372 + 0.807131i
\(57\) 0 0
\(58\) 2.93659 + 5.68695i 0.385593 + 0.746733i
\(59\) −1.11754 + 0.645211i −0.145491 + 0.0839993i −0.570978 0.820965i \(-0.693436\pi\)
0.425487 + 0.904964i \(0.360103\pi\)
\(60\) 0 0
\(61\) 7.95517 + 4.59292i 1.01856 + 0.588063i 0.913685 0.406422i \(-0.133224\pi\)
0.104870 + 0.994486i \(0.466557\pi\)
\(62\) −10.0533 6.45150i −1.27678 0.819341i
\(63\) 0 0
\(64\) 7.68483 + 2.22338i 0.960604 + 0.277922i
\(65\) −3.16492 1.82727i −0.392560 0.226645i
\(66\) 0 0
\(67\) −0.562480 0.974244i −0.0687179 0.119023i 0.829619 0.558330i \(-0.188558\pi\)
−0.898337 + 0.439307i \(0.855224\pi\)
\(68\) −0.170204 + 1.80773i −0.0206403 + 0.219220i
\(69\) 0 0
\(70\) 3.93913 6.60672i 0.470816 0.789654i
\(71\) 1.43897 0.170774 0.0853869 0.996348i \(-0.472787\pi\)
0.0853869 + 0.996348i \(0.472787\pi\)
\(72\) 0 0
\(73\) 2.08692 + 3.61465i 0.244255 + 0.423063i 0.961922 0.273324i \(-0.0881231\pi\)
−0.717667 + 0.696387i \(0.754790\pi\)
\(74\) −0.465515 + 9.91029i −0.0541150 + 1.15205i
\(75\) 0 0
\(76\) −5.62351 12.2708i −0.645061 1.40756i
\(77\) −0.527404 16.0277i −0.0601032 1.82652i
\(78\) 0 0
\(79\) −11.6339 6.71681i −1.30891 0.755701i −0.326997 0.945025i \(-0.606037\pi\)
−0.981915 + 0.189325i \(0.939370\pi\)
\(80\) −8.07849 1.53484i −0.903202 0.171601i
\(81\) 0 0
\(82\) 14.6126 7.54554i 1.61369 0.833266i
\(83\) 4.71682i 0.517738i 0.965912 + 0.258869i \(0.0833499\pi\)
−0.965912 + 0.258869i \(0.916650\pi\)
\(84\) 0 0
\(85\) 1.86634i 0.202433i
\(86\) −3.04963 5.90586i −0.328850 0.636846i
\(87\) 0 0
\(88\) −15.9028 + 6.40319i −1.69525 + 0.682582i
\(89\) −4.08201 2.35675i −0.432692 0.249815i 0.267801 0.963474i \(-0.413703\pi\)
−0.700493 + 0.713660i \(0.747036\pi\)
\(90\) 0 0
\(91\) −4.14840 2.21646i −0.434870 0.232348i
\(92\) 0.585697 + 1.27802i 0.0610632 + 0.133243i
\(93\) 0 0
\(94\) −12.4965 0.586998i −1.28892 0.0605442i
\(95\) 6.93713 + 12.0155i 0.711734 + 1.23276i
\(96\) 0 0
\(97\) −12.2014 −1.23886 −0.619430 0.785052i \(-0.712636\pi\)
−0.619430 + 0.785052i \(0.712636\pi\)
\(98\) 4.78728 8.66499i 0.483588 0.875296i
\(99\) 0 0
\(100\) −1.54098 0.145088i −0.154098 0.0145088i
\(101\) −5.20672 9.01831i −0.518088 0.897355i −0.999779 0.0210140i \(-0.993311\pi\)
0.481691 0.876341i \(-0.340023\pi\)
\(102\) 0 0
\(103\) 5.65349 + 3.26404i 0.557055 + 0.321616i 0.751963 0.659206i \(-0.229107\pi\)
−0.194908 + 0.980822i \(0.562441\pi\)
\(104\) −0.705701 + 4.97837i −0.0691996 + 0.488169i
\(105\) 0 0
\(106\) −5.06541 + 7.89341i −0.491996 + 0.766676i
\(107\) 8.00556 + 4.62201i 0.773926 + 0.446827i 0.834273 0.551351i \(-0.185887\pi\)
−0.0603472 + 0.998177i \(0.519221\pi\)
\(108\) 0 0
\(109\) −4.22453 + 2.43904i −0.404637 + 0.233617i −0.688483 0.725253i \(-0.741723\pi\)
0.283846 + 0.958870i \(0.408390\pi\)
\(110\) 15.6572 8.08496i 1.49286 0.770871i
\(111\) 0 0
\(112\) −10.4564 1.63234i −0.988033 0.154241i
\(113\) 2.39142i 0.224966i 0.993654 + 0.112483i \(0.0358803\pi\)
−0.993654 + 0.112483i \(0.964120\pi\)
\(114\) 0 0
\(115\) −0.722512 1.25143i −0.0673746 0.116696i
\(116\) −5.24064 + 7.38009i −0.486581 + 0.685224i
\(117\) 0 0
\(118\) −1.53588 0.985617i −0.141389 0.0907334i
\(119\) −0.0789966 2.40068i −0.00724160 0.220070i
\(120\) 0 0
\(121\) 12.8688 22.2895i 1.16989 2.02632i
\(122\) −0.609541 + 12.9764i −0.0551852 + 1.17483i
\(123\) 0 0
\(124\) 1.58356 16.8189i 0.142208 1.51038i
\(125\) 11.8697 1.06166
\(126\) 0 0
\(127\) 4.06366i 0.360591i −0.983612 0.180296i \(-0.942295\pi\)
0.983612 0.180296i \(-0.0577055\pi\)
\(128\) 2.19255 + 11.0992i 0.193796 + 0.981042i
\(129\) 0 0
\(130\) 0.242502 5.16260i 0.0212689 0.452790i
\(131\) −0.208033 0.120108i −0.0181760 0.0104939i 0.490884 0.871225i \(-0.336674\pi\)
−0.509060 + 0.860731i \(0.670007\pi\)
\(132\) 0 0
\(133\) 9.43184 + 15.1619i 0.817844 + 1.31470i
\(134\) 0.859239 1.33895i 0.0742269 0.115667i
\(135\) 0 0
\(136\) −2.38199 + 0.959094i −0.204254 + 0.0822416i
\(137\) −13.2051 + 7.62397i −1.12819 + 0.651360i −0.943479 0.331434i \(-0.892468\pi\)
−0.184709 + 0.982793i \(0.559134\pi\)
\(138\) 0 0
\(139\) 7.64300 0.648271 0.324135 0.946011i \(-0.394927\pi\)
0.324135 + 0.946011i \(0.394927\pi\)
\(140\) 10.8578 + 0.662960i 0.917650 + 0.0560303i
\(141\) 0 0
\(142\) 0.933690 + 1.80817i 0.0783535 + 0.151738i
\(143\) −5.38751 9.33144i −0.450526 0.780334i
\(144\) 0 0
\(145\) 4.65191 8.05735i 0.386320 0.669126i
\(146\) −3.18795 + 4.96778i −0.263837 + 0.411136i
\(147\) 0 0
\(148\) −12.7551 + 5.84545i −1.04846 + 0.480493i
\(149\) −8.37831 + 14.5117i −0.686378 + 1.18884i 0.286623 + 0.958043i \(0.407467\pi\)
−0.973002 + 0.230798i \(0.925866\pi\)
\(150\) 0 0
\(151\) −7.10302 + 4.10093i −0.578036 + 0.333729i −0.760352 0.649511i \(-0.774974\pi\)
0.182317 + 0.983240i \(0.441640\pi\)
\(152\) 11.7703 15.0284i 0.954695 1.21896i
\(153\) 0 0
\(154\) 19.7977 11.0624i 1.59535 0.891437i
\(155\) 17.3642i 1.39472i
\(156\) 0 0
\(157\) 1.87900 1.08484i 0.149961 0.0865798i −0.423142 0.906063i \(-0.639073\pi\)
0.573103 + 0.819483i \(0.305740\pi\)
\(158\) 0.891409 18.9771i 0.0709167 1.50974i
\(159\) 0 0
\(160\) −3.31318 11.1471i −0.261930 0.881257i
\(161\) −0.982340 1.57914i −0.0774193 0.124453i
\(162\) 0 0
\(163\) −9.29429 + 16.0982i −0.727985 + 1.26091i 0.229749 + 0.973250i \(0.426210\pi\)
−0.957734 + 0.287657i \(0.907124\pi\)
\(164\) 18.9631 + 13.4658i 1.48077 + 1.05150i
\(165\) 0 0
\(166\) −5.92704 + 3.06056i −0.460027 + 0.237546i
\(167\) −22.6164 −1.75011 −0.875056 0.484022i \(-0.839176\pi\)
−0.875056 + 0.484022i \(0.839176\pi\)
\(168\) 0 0
\(169\) 9.83973 0.756902
\(170\) 2.34520 1.21100i 0.179868 0.0928792i
\(171\) 0 0
\(172\) 5.44237 7.66417i 0.414977 0.584388i
\(173\) −0.544356 + 0.942851i −0.0413866 + 0.0716837i −0.885977 0.463730i \(-0.846511\pi\)
0.844590 + 0.535413i \(0.179844\pi\)
\(174\) 0 0
\(175\) 2.04643 0.0673395i 0.154695 0.00509039i
\(176\) −18.3648 15.8283i −1.38430 1.19311i
\(177\) 0 0
\(178\) 0.312771 6.65855i 0.0234432 0.499079i
\(179\) −5.20593 + 3.00564i −0.389109 + 0.224652i −0.681774 0.731563i \(-0.738791\pi\)
0.292665 + 0.956215i \(0.405458\pi\)
\(180\) 0 0
\(181\) 7.28891i 0.541780i −0.962610 0.270890i \(-0.912682\pi\)
0.962610 0.270890i \(-0.0873180\pi\)
\(182\) 0.0934146 6.65095i 0.00692435 0.493001i
\(183\) 0 0
\(184\) −1.22589 + 1.56523i −0.0903739 + 0.115390i
\(185\) 12.4897 7.21091i 0.918259 0.530157i
\(186\) 0 0
\(187\) 2.75135 4.76549i 0.201199 0.348487i
\(188\) −7.37091 16.0837i −0.537579 1.17302i
\(189\) 0 0
\(190\) −10.5971 + 16.5134i −0.768793 + 1.19801i
\(191\) 2.21264 3.83240i 0.160101 0.277303i −0.774804 0.632202i \(-0.782151\pi\)
0.934905 + 0.354899i \(0.115485\pi\)
\(192\) 0 0
\(193\) 1.26476 + 2.19063i 0.0910393 + 0.157685i 0.907949 0.419081i \(-0.137648\pi\)
−0.816909 + 0.576766i \(0.804314\pi\)
\(194\) −7.91699 15.3319i −0.568407 1.10077i
\(195\) 0 0
\(196\) 13.9945 + 0.393191i 0.999606 + 0.0280851i
\(197\) 11.6259 0.828314 0.414157 0.910205i \(-0.364076\pi\)
0.414157 + 0.910205i \(0.364076\pi\)
\(198\) 0 0
\(199\) −16.8071 + 9.70356i −1.19142 + 0.687867i −0.958629 0.284659i \(-0.908120\pi\)
−0.232792 + 0.972527i \(0.574786\pi\)
\(200\) −0.817566 2.03049i −0.0578106 0.143578i
\(201\) 0 0
\(202\) 7.95373 12.3943i 0.559623 0.872058i
\(203\) 5.64273 10.5611i 0.396042 0.741244i
\(204\) 0 0
\(205\) −20.7033 11.9530i −1.44598 0.834837i
\(206\) −0.433181 + 9.22194i −0.0301812 + 0.642523i
\(207\) 0 0
\(208\) −6.71359 + 2.34351i −0.465504 + 0.162493i
\(209\) 40.9068i 2.82958i
\(210\) 0 0
\(211\) 5.73966 0.395135 0.197567 0.980289i \(-0.436696\pi\)
0.197567 + 0.980289i \(0.436696\pi\)
\(212\) −13.2054 1.24334i −0.906951 0.0853927i
\(213\) 0 0
\(214\) −0.613401 + 13.0586i −0.0419312 + 0.892669i
\(215\) −4.83098 + 8.36750i −0.329470 + 0.570659i
\(216\) 0 0
\(217\) 0.734973 + 22.3356i 0.0498932 + 1.51624i
\(218\) −5.80597 3.72584i −0.393230 0.252346i
\(219\) 0 0
\(220\) 20.3187 + 14.4284i 1.36989 + 0.972763i
\(221\) −0.806962 1.39770i −0.0542821 0.0940194i
\(222\) 0 0
\(223\) 5.21414i 0.349164i −0.984643 0.174582i \(-0.944143\pi\)
0.984643 0.174582i \(-0.0558575\pi\)
\(224\) −4.73358 14.1984i −0.316275 0.948667i
\(225\) 0 0
\(226\) −3.00499 + 1.55170i −0.199889 + 0.103217i
\(227\) −6.08667 + 3.51414i −0.403986 + 0.233242i −0.688203 0.725519i \(-0.741600\pi\)
0.284216 + 0.958760i \(0.408267\pi\)
\(228\) 0 0
\(229\) 22.0239 + 12.7155i 1.45538 + 0.840264i 0.998779 0.0494076i \(-0.0157333\pi\)
0.456601 + 0.889672i \(0.349067\pi\)
\(230\) 1.10370 1.71989i 0.0727759 0.113406i
\(231\) 0 0
\(232\) −12.6741 1.79659i −0.832094 0.117952i
\(233\) 10.0196 + 5.78482i 0.656406 + 0.378976i 0.790906 0.611937i \(-0.209610\pi\)
−0.134500 + 0.990914i \(0.542943\pi\)
\(234\) 0 0
\(235\) 9.09270 + 15.7490i 0.593142 + 1.02735i
\(236\) 0.241926 2.56948i 0.0157480 0.167259i
\(237\) 0 0
\(238\) 2.96538 1.65698i 0.192217 0.107406i
\(239\) 17.2023 1.11272 0.556362 0.830940i \(-0.312197\pi\)
0.556362 + 0.830940i \(0.312197\pi\)
\(240\) 0 0
\(241\) 6.84594 + 11.8575i 0.440986 + 0.763810i 0.997763 0.0668522i \(-0.0212956\pi\)
−0.556777 + 0.830662i \(0.687962\pi\)
\(242\) 36.3585 + 1.70786i 2.33721 + 0.109786i
\(243\) 0 0
\(244\) −16.7014 + 7.65398i −1.06920 + 0.489996i
\(245\) −14.3591 + 0.946023i −0.917370 + 0.0604392i
\(246\) 0 0
\(247\) 10.3904 + 5.99890i 0.661126 + 0.381701i
\(248\) 22.1617 8.92328i 1.40727 0.566629i
\(249\) 0 0
\(250\) 7.70178 + 14.9151i 0.487103 + 0.943316i
\(251\) 9.77570i 0.617037i −0.951218 0.308518i \(-0.900167\pi\)
0.951218 0.308518i \(-0.0998332\pi\)
\(252\) 0 0
\(253\) 4.26050i 0.267856i
\(254\) 5.10629 2.63675i 0.320397 0.165445i
\(255\) 0 0
\(256\) −12.5243 + 9.95696i −0.782771 + 0.622310i
\(257\) −17.9664 10.3729i −1.12071 0.647043i −0.179129 0.983826i \(-0.557328\pi\)
−0.941582 + 0.336783i \(0.890661\pi\)
\(258\) 0 0
\(259\) 15.7603 9.80408i 0.979298 0.609196i
\(260\) 6.64454 3.04509i 0.412077 0.188849i
\(261\) 0 0
\(262\) 0.0159399 0.339343i 0.000984772 0.0209647i
\(263\) 6.61692 + 11.4608i 0.408016 + 0.706705i 0.994667 0.103135i \(-0.0328873\pi\)
−0.586651 + 0.809840i \(0.699554\pi\)
\(264\) 0 0
\(265\) 13.6335 0.837501
\(266\) −12.9321 + 21.6898i −0.792919 + 1.32989i
\(267\) 0 0
\(268\) 2.24001 + 0.210905i 0.136831 + 0.0128831i
\(269\) −6.00719 10.4048i −0.366265 0.634390i 0.622713 0.782450i \(-0.286030\pi\)
−0.988978 + 0.148060i \(0.952697\pi\)
\(270\) 0 0
\(271\) 25.7592 + 14.8721i 1.56476 + 0.903414i 0.996764 + 0.0803814i \(0.0256138\pi\)
0.567994 + 0.823032i \(0.307720\pi\)
\(272\) −2.75075 2.37083i −0.166789 0.143753i
\(273\) 0 0
\(274\) −18.1484 11.6463i −1.09638 0.703578i
\(275\) 4.06227 + 2.34535i 0.244964 + 0.141430i
\(276\) 0 0
\(277\) −7.23966 + 4.17982i −0.434989 + 0.251141i −0.701470 0.712699i \(-0.747472\pi\)
0.266481 + 0.963840i \(0.414139\pi\)
\(278\) 4.95925 + 9.60400i 0.297436 + 0.576010i
\(279\) 0 0
\(280\) 6.21214 + 14.0738i 0.371246 + 0.841069i
\(281\) 3.58062i 0.213602i −0.994280 0.106801i \(-0.965939\pi\)
0.994280 0.106801i \(-0.0340608\pi\)
\(282\) 0 0
\(283\) −10.8564 18.8038i −0.645346 1.11777i −0.984222 0.176940i \(-0.943380\pi\)
0.338876 0.940831i \(-0.389953\pi\)
\(284\) −1.66626 + 2.34650i −0.0988744 + 0.139239i
\(285\) 0 0
\(286\) 8.22990 12.8246i 0.486644 0.758336i
\(287\) −27.1367 14.4990i −1.60183 0.855846i
\(288\) 0 0
\(289\) −8.08789 + 14.0086i −0.475758 + 0.824038i
\(290\) 13.1431 + 0.617370i 0.771790 + 0.0362532i
\(291\) 0 0
\(292\) −8.31092 0.782503i −0.486360 0.0457925i
\(293\) −14.2584 −0.832986 −0.416493 0.909139i \(-0.636741\pi\)
−0.416493 + 0.909139i \(0.636741\pi\)
\(294\) 0 0
\(295\) 2.65278i 0.154451i
\(296\) −15.6215 12.2348i −0.907983 0.711134i
\(297\) 0 0
\(298\) −23.6713 1.11191i −1.37124 0.0644113i
\(299\) −1.08218 0.624795i −0.0625839 0.0361328i
\(300\) 0 0
\(301\) −5.85994 + 10.9676i −0.337762 + 0.632164i
\(302\) −9.76200 6.26454i −0.561740 0.360484i
\(303\) 0 0
\(304\) 26.5216 + 5.03887i 1.52112 + 0.288999i
\(305\) 16.3538 9.44190i 0.936418 0.540641i
\(306\) 0 0
\(307\) 12.0680 0.688757 0.344378 0.938831i \(-0.388090\pi\)
0.344378 + 0.938831i \(0.388090\pi\)
\(308\) 26.7468 + 17.6993i 1.52404 + 1.00851i
\(309\) 0 0
\(310\) −21.8194 + 11.2669i −1.23926 + 0.639920i
\(311\) 4.88095 + 8.45405i 0.276773 + 0.479385i 0.970581 0.240775i \(-0.0774016\pi\)
−0.693808 + 0.720160i \(0.744068\pi\)
\(312\) 0 0
\(313\) −14.1208 + 24.4580i −0.798155 + 1.38245i 0.122661 + 0.992449i \(0.460857\pi\)
−0.920816 + 0.389997i \(0.872476\pi\)
\(314\) 2.58240 + 1.65719i 0.145733 + 0.0935208i
\(315\) 0 0
\(316\) 24.4245 11.1934i 1.37399 0.629677i
\(317\) 12.7790 22.1338i 0.717738 1.24316i −0.244157 0.969736i \(-0.578511\pi\)
0.961894 0.273422i \(-0.0881556\pi\)
\(318\) 0 0
\(319\) 23.7563 13.7157i 1.33009 0.767931i
\(320\) 11.8574 11.3962i 0.662848 0.637066i
\(321\) 0 0
\(322\) 1.34690 2.25902i 0.0750597 0.125890i
\(323\) 6.12718i 0.340925i
\(324\) 0 0
\(325\) 1.19145 0.687883i 0.0660897 0.0381569i
\(326\) −26.2593 1.23347i −1.45437 0.0683158i
\(327\) 0 0
\(328\) −4.61633 + 32.5659i −0.254894 + 1.79815i
\(329\) 12.3626 + 19.8732i 0.681572 + 1.09564i
\(330\) 0 0
\(331\) −5.83423 + 10.1052i −0.320678 + 0.555431i −0.980628 0.195879i \(-0.937244\pi\)
0.659950 + 0.751310i \(0.270577\pi\)
\(332\) −7.69165 5.46188i −0.422134 0.299760i
\(333\) 0 0
\(334\) −14.6749 28.4192i −0.802977 1.55503i
\(335\) −2.31264 −0.126353
\(336\) 0 0
\(337\) 22.5456 1.22814 0.614068 0.789253i \(-0.289532\pi\)
0.614068 + 0.789253i \(0.289532\pi\)
\(338\) 6.38462 + 12.3643i 0.347278 + 0.672532i
\(339\) 0 0
\(340\) 3.04341 + 2.16114i 0.165052 + 0.117204i
\(341\) −25.5982 + 44.3374i −1.38622 + 2.40101i
\(342\) 0 0
\(343\) −18.4302 + 1.82465i −0.995135 + 0.0985219i
\(344\) 13.1619 + 1.86575i 0.709645 + 0.100595i
\(345\) 0 0
\(346\) −1.53797 0.0722431i −0.0826820 0.00388381i
\(347\) −6.94457 + 4.00945i −0.372804 + 0.215238i −0.674683 0.738108i \(-0.735720\pi\)
0.301879 + 0.953346i \(0.402386\pi\)
\(348\) 0 0
\(349\) 18.5648i 0.993750i −0.867822 0.496875i \(-0.834481\pi\)
0.867822 0.496875i \(-0.165519\pi\)
\(350\) 1.41247 + 2.52779i 0.0754994 + 0.135116i
\(351\) 0 0
\(352\) 7.97324 33.3472i 0.424975 1.77741i
\(353\) 16.1137 9.30324i 0.857645 0.495161i −0.00557823 0.999984i \(-0.501776\pi\)
0.863223 + 0.504823i \(0.168442\pi\)
\(354\) 0 0
\(355\) 1.47908 2.56184i 0.0785012 0.135968i
\(356\) 8.56990 3.92746i 0.454204 0.208155i
\(357\) 0 0
\(358\) −7.15474 4.59139i −0.378140 0.242662i
\(359\) 16.9950 29.4361i 0.896959 1.55358i 0.0655985 0.997846i \(-0.479104\pi\)
0.831361 0.555733i \(-0.187562\pi\)
\(360\) 0 0
\(361\) −13.2745 22.9921i −0.698659 1.21011i
\(362\) 9.15905 4.72949i 0.481389 0.248577i
\(363\) 0 0
\(364\) 8.41802 4.19816i 0.441224 0.220043i
\(365\) 8.58037 0.449117
\(366\) 0 0
\(367\) −4.41003 + 2.54613i −0.230202 + 0.132907i −0.610665 0.791889i \(-0.709098\pi\)
0.380463 + 0.924796i \(0.375765\pi\)
\(368\) −2.76226 0.524806i −0.143993 0.0273574i
\(369\) 0 0
\(370\) 17.1651 + 11.0153i 0.892372 + 0.572659i
\(371\) 17.5369 0.577066i 0.910470 0.0299598i
\(372\) 0 0
\(373\) −14.7870 8.53728i −0.765642 0.442044i 0.0656756 0.997841i \(-0.479080\pi\)
−0.831318 + 0.555797i \(0.812413\pi\)
\(374\) 7.77344 + 0.365141i 0.401955 + 0.0188810i
\(375\) 0 0
\(376\) 15.4276 19.6982i 0.795620 1.01586i
\(377\) 8.04551i 0.414365i
\(378\) 0 0
\(379\) 11.2872 0.579783 0.289892 0.957059i \(-0.406381\pi\)
0.289892 + 0.957059i \(0.406381\pi\)
\(380\) −27.6263 2.60112i −1.41720 0.133434i
\(381\) 0 0
\(382\) 6.25139 + 0.293646i 0.319849 + 0.0150242i
\(383\) 10.2813 17.8078i 0.525352 0.909936i −0.474212 0.880410i \(-0.657267\pi\)
0.999564 0.0295252i \(-0.00939952\pi\)
\(384\) 0 0
\(385\) −29.0766 15.5355i −1.48188 0.791760i
\(386\) −1.93203 + 3.01068i −0.0983378 + 0.153239i
\(387\) 0 0
\(388\) 14.1287 19.8966i 0.717274 1.01010i
\(389\) 6.92881 + 12.0011i 0.351305 + 0.608478i 0.986478 0.163892i \(-0.0524048\pi\)
−0.635174 + 0.772369i \(0.719071\pi\)
\(390\) 0 0
\(391\) 0.638155i 0.0322729i
\(392\) 8.58640 + 17.8402i 0.433679 + 0.901067i
\(393\) 0 0
\(394\) 7.54363 + 14.6089i 0.380042 + 0.735984i
\(395\) −23.9163 + 13.8081i −1.20336 + 0.694760i
\(396\) 0 0
\(397\) −29.9634 17.2993i −1.50382 0.868229i −0.999990 0.00442498i \(-0.998591\pi\)
−0.503827 0.863804i \(-0.668075\pi\)
\(398\) −23.0987 14.8231i −1.15783 0.743012i
\(399\) 0 0
\(400\) 2.02098 2.34484i 0.101049 0.117242i
\(401\) −12.1249 7.00029i −0.605486 0.349578i 0.165711 0.986174i \(-0.447008\pi\)
−0.771197 + 0.636597i \(0.780342\pi\)
\(402\) 0 0
\(403\) 7.50786 + 13.0040i 0.373993 + 0.647775i
\(404\) 20.7352 + 1.95229i 1.03161 + 0.0971301i
\(405\) 0 0
\(406\) 16.9322 + 0.237818i 0.840329 + 0.0118027i
\(407\) 42.5212 2.10770
\(408\) 0 0
\(409\) −2.76388 4.78718i −0.136665 0.236711i 0.789567 0.613664i \(-0.210305\pi\)
−0.926232 + 0.376953i \(0.876972\pi\)
\(410\) 1.58633 33.7711i 0.0783430 1.66783i
\(411\) 0 0
\(412\) −11.8691 + 5.43944i −0.584750 + 0.267982i
\(413\) 0.112284 + 3.41229i 0.00552515 + 0.167908i
\(414\) 0 0
\(415\) 8.39750 + 4.84830i 0.412217 + 0.237994i
\(416\) −7.30098 6.91552i −0.357960 0.339061i
\(417\) 0 0
\(418\) −51.4024 + 26.5428i −2.51417 + 1.29825i
\(419\) 13.1122i 0.640574i −0.947320 0.320287i \(-0.896221\pi\)
0.947320 0.320287i \(-0.103779\pi\)
\(420\) 0 0
\(421\) 22.0752i 1.07588i −0.842983 0.537941i \(-0.819202\pi\)
0.842983 0.537941i \(-0.180798\pi\)
\(422\) 3.72424 + 7.21231i 0.181293 + 0.351090i
\(423\) 0 0
\(424\) −7.00614 17.4003i −0.340248 0.845035i
\(425\) 0.608462 + 0.351296i 0.0295148 + 0.0170404i
\(426\) 0 0
\(427\) 20.6364 12.8374i 0.998664 0.621244i
\(428\) −16.8071 + 7.70245i −0.812404 + 0.372312i
\(429\) 0 0
\(430\) −13.6490 0.641134i −0.658215 0.0309182i
\(431\) −12.9464 22.4237i −0.623604 1.08011i −0.988809 0.149187i \(-0.952334\pi\)
0.365205 0.930927i \(-0.380999\pi\)
\(432\) 0 0
\(433\) −32.4535 −1.55961 −0.779807 0.626020i \(-0.784683\pi\)
−0.779807 + 0.626020i \(0.784683\pi\)
\(434\) −27.5895 + 15.4163i −1.32434 + 0.740005i
\(435\) 0 0
\(436\) 0.914531 9.71318i 0.0437981 0.465177i
\(437\) 2.37200 + 4.10843i 0.113468 + 0.196533i
\(438\) 0 0
\(439\) 11.7422 + 6.77937i 0.560425 + 0.323561i 0.753316 0.657659i \(-0.228453\pi\)
−0.192891 + 0.981220i \(0.561786\pi\)
\(440\) −4.94634 + 34.8940i −0.235808 + 1.66351i
\(441\) 0 0
\(442\) 1.23271 1.92092i 0.0586338 0.0913689i
\(443\) −3.78628 2.18601i −0.179892 0.103860i 0.407350 0.913272i \(-0.366453\pi\)
−0.587242 + 0.809412i \(0.699786\pi\)
\(444\) 0 0
\(445\) −8.39158 + 4.84488i −0.397799 + 0.229669i
\(446\) 6.55195 3.38325i 0.310244 0.160202i
\(447\) 0 0
\(448\) 14.7698 15.1609i 0.697810 0.716283i
\(449\) 13.7570i 0.649235i −0.945845 0.324618i \(-0.894764\pi\)
0.945845 0.324618i \(-0.105236\pi\)
\(450\) 0 0
\(451\) −35.2423 61.0415i −1.65950 2.87433i
\(452\) −3.89965 2.76916i −0.183424 0.130250i
\(453\) 0 0
\(454\) −8.36518 5.36816i −0.392598 0.251940i
\(455\) −8.21007 + 5.10727i −0.384894 + 0.239433i
\(456\) 0 0
\(457\) 5.88182 10.1876i 0.275140 0.476557i −0.695030 0.718980i \(-0.744609\pi\)
0.970170 + 0.242424i \(0.0779424\pi\)
\(458\) −1.68751 + 35.9253i −0.0788523 + 1.67868i
\(459\) 0 0
\(460\) 2.87732 + 0.270910i 0.134156 + 0.0126313i
\(461\) 11.1624 0.519887 0.259943 0.965624i \(-0.416296\pi\)
0.259943 + 0.965624i \(0.416296\pi\)
\(462\) 0 0
\(463\) 16.0864i 0.747599i 0.927510 + 0.373799i \(0.121945\pi\)
−0.927510 + 0.373799i \(0.878055\pi\)
\(464\) −5.96617 17.0917i −0.276972 0.793460i
\(465\) 0 0
\(466\) −0.767721 + 16.3439i −0.0355640 + 0.757117i
\(467\) −18.8715 10.8955i −0.873268 0.504181i −0.00483503 0.999988i \(-0.501539\pi\)
−0.868433 + 0.495807i \(0.834872\pi\)
\(468\) 0 0
\(469\) −2.97476 + 0.0978869i −0.137361 + 0.00452000i
\(470\) −13.8899 + 21.6446i −0.640694 + 0.998390i
\(471\) 0 0
\(472\) 3.38572 1.36324i 0.155840 0.0627482i
\(473\) −24.6707 + 14.2436i −1.13436 + 0.654923i
\(474\) 0 0
\(475\) −5.22302 −0.239649
\(476\) 4.00623 + 2.65107i 0.183625 + 0.121512i
\(477\) 0 0
\(478\) 11.1619 + 21.6160i 0.510534 + 0.988691i
\(479\) 10.9014 + 18.8818i 0.498099 + 0.862734i 0.999998 0.00219321i \(-0.000698121\pi\)
−0.501898 + 0.864927i \(0.667365\pi\)
\(480\) 0 0
\(481\) 6.23566 10.8005i 0.284322 0.492459i
\(482\) −10.4578 + 16.2963i −0.476339 + 0.742277i
\(483\) 0 0
\(484\) 21.4456 + 46.7953i 0.974798 + 2.12706i
\(485\) −12.5415 + 21.7225i −0.569479 + 0.986366i
\(486\) 0 0
\(487\) 5.03965 2.90964i 0.228368 0.131849i −0.381451 0.924389i \(-0.624575\pi\)
0.609819 + 0.792541i \(0.291242\pi\)
\(488\) −20.4547 16.0201i −0.925939 0.725197i
\(489\) 0 0
\(490\) −10.5058 17.4295i −0.474605 0.787383i
\(491\) 17.6807i 0.797919i −0.916969 0.398959i \(-0.869371\pi\)
0.916969 0.398959i \(-0.130629\pi\)
\(492\) 0 0
\(493\) 3.55830 2.05439i 0.160258 0.0925249i
\(494\) −0.796133 + 16.9488i −0.0358197 + 0.762561i
\(495\) 0 0
\(496\) 25.5926 + 22.0579i 1.14914 + 0.990427i
\(497\) 1.79411 3.35791i 0.0804768 0.150623i
\(498\) 0 0
\(499\) 4.79931 8.31264i 0.214846 0.372125i −0.738379 0.674386i \(-0.764408\pi\)
0.953225 + 0.302261i \(0.0977416\pi\)
\(500\) −13.7446 + 19.3557i −0.614677 + 0.865614i
\(501\) 0 0
\(502\) 12.2839 6.34308i 0.548257 0.283105i
\(503\) 21.6062 0.963375 0.481687 0.876343i \(-0.340024\pi\)
0.481687 + 0.876343i \(0.340024\pi\)
\(504\) 0 0
\(505\) −21.4074 −0.952618
\(506\) 5.35364 2.76448i 0.237998 0.122896i
\(507\) 0 0
\(508\) 6.62655 + 4.70554i 0.294006 + 0.208775i
\(509\) 8.22302 14.2427i 0.364479 0.631296i −0.624213 0.781254i \(-0.714580\pi\)
0.988692 + 0.149958i \(0.0479138\pi\)
\(510\) 0 0
\(511\) 11.0370 0.363181i 0.488247 0.0160662i
\(512\) −20.6382 9.27706i −0.912089 0.409992i
\(513\) 0 0
\(514\) 1.37662 29.3066i 0.0607200 1.29266i
\(515\) 11.6222 6.71006i 0.512133 0.295680i
\(516\) 0 0
\(517\) 53.6178i 2.35811i
\(518\) 22.5458 + 13.4425i 0.990606 + 0.590630i
\(519\) 0 0
\(520\) 8.13777 + 6.37352i 0.356865 + 0.279497i
\(521\) 22.2819 12.8645i 0.976189 0.563603i 0.0750717 0.997178i \(-0.476081\pi\)
0.901117 + 0.433575i \(0.142748\pi\)
\(522\) 0 0
\(523\) −19.2515 + 33.3445i −0.841808 + 1.45805i 0.0465564 + 0.998916i \(0.485175\pi\)
−0.888365 + 0.459139i \(0.848158\pi\)
\(524\) 0.436752 0.200157i 0.0190796 0.00874389i
\(525\) 0 0
\(526\) −10.1079 + 15.7511i −0.440727 + 0.686782i
\(527\) −3.83420 + 6.64103i −0.167020 + 0.289288i
\(528\) 0 0
\(529\) 11.2530 + 19.4907i 0.489259 + 0.847421i
\(530\) 8.84628 + 17.1315i 0.384258 + 0.744147i
\(531\) 0 0
\(532\) −35.6460 2.17649i −1.54545 0.0943628i
\(533\) −20.6729 −0.895441
\(534\) 0 0
\(535\) 16.4574 9.50169i 0.711516 0.410794i
\(536\) 1.18844 + 2.95159i 0.0513328 + 0.127489i
\(537\) 0 0
\(538\) 9.17652 14.2997i 0.395628 0.616505i
\(539\) −38.0590 18.7526i −1.63932 0.807732i
\(540\) 0 0
\(541\) −32.4037 18.7083i −1.39314 0.804331i −0.399481 0.916741i \(-0.630810\pi\)
−0.993662 + 0.112410i \(0.964143\pi\)
\(542\) −1.97372 + 42.0182i −0.0847784 + 1.80484i
\(543\) 0 0
\(544\) 1.19426 4.99486i 0.0512036 0.214153i
\(545\) 10.0281i 0.429556i
\(546\) 0 0
\(547\) −31.1153 −1.33039 −0.665197 0.746668i \(-0.731652\pi\)
−0.665197 + 0.746668i \(0.731652\pi\)
\(548\) 2.85865 30.3616i 0.122116 1.29698i
\(549\) 0 0
\(550\) −0.311259 + 6.62635i −0.0132721 + 0.282549i
\(551\) −15.2722 + 26.4522i −0.650617 + 1.12690i
\(552\) 0 0
\(553\) −30.1792 + 18.7737i −1.28335 + 0.798339i
\(554\) −9.94978 6.38504i −0.422726 0.271274i
\(555\) 0 0
\(556\) −8.85027 + 12.4633i −0.375335 + 0.528563i
\(557\) 15.0725 + 26.1063i 0.638641 + 1.10616i 0.985731 + 0.168327i \(0.0538364\pi\)
−0.347090 + 0.937832i \(0.612830\pi\)
\(558\) 0 0
\(559\) 8.35521i 0.353388i
\(560\) −13.6539 + 16.9379i −0.576984 + 0.715759i
\(561\) 0 0
\(562\) 4.49932 2.32333i 0.189792 0.0980037i
\(563\) 26.6333 15.3767i 1.12246 0.648051i 0.180431 0.983588i \(-0.442251\pi\)
0.942027 + 0.335536i \(0.108918\pi\)
\(564\) 0 0
\(565\) 4.25752 + 2.45808i 0.179115 + 0.103412i
\(566\) 16.5841 25.8429i 0.697082 1.08626i
\(567\) 0 0
\(568\) −4.02973 0.571227i −0.169084 0.0239682i
\(569\) −38.4227 22.1833i −1.61076 0.929974i −0.989194 0.146613i \(-0.953163\pi\)
−0.621568 0.783361i \(-0.713504\pi\)
\(570\) 0 0
\(571\) −16.2431 28.1338i −0.679751 1.17736i −0.975056 0.221961i \(-0.928754\pi\)
0.295304 0.955403i \(-0.404579\pi\)
\(572\) 21.4552 + 2.02008i 0.897085 + 0.0844637i
\(573\) 0 0
\(574\) 0.611070 43.5070i 0.0255056 1.81595i
\(575\) 0.543986 0.0226858
\(576\) 0 0
\(577\) 19.6946 + 34.1120i 0.819896 + 1.42010i 0.905758 + 0.423795i \(0.139302\pi\)
−0.0858615 + 0.996307i \(0.527364\pi\)
\(578\) −22.8508 1.07337i −0.950469 0.0446463i
\(579\) 0 0
\(580\) 7.75228 + 16.9159i 0.321896 + 0.702393i
\(581\) 11.0070 + 5.88095i 0.456646 + 0.243983i
\(582\) 0 0
\(583\) 34.8117 + 20.0985i 1.44175 + 0.832396i
\(584\) −4.40936 10.9510i −0.182461 0.453157i
\(585\) 0 0
\(586\) −9.25174 17.9168i −0.382186 0.740134i
\(587\) 24.9178i 1.02847i −0.857650 0.514233i \(-0.828077\pi\)
0.857650 0.514233i \(-0.171923\pi\)
\(588\) 0 0
\(589\) 57.0064i 2.34891i
\(590\) −3.33342 + 1.72129i −0.137235 + 0.0708644i
\(591\) 0 0
\(592\) 5.23774 27.5683i 0.215270 1.13305i
\(593\) 12.1405 + 7.00931i 0.498550 + 0.287838i 0.728114 0.685456i \(-0.240397\pi\)
−0.229565 + 0.973293i \(0.573730\pi\)
\(594\) 0 0
\(595\) −4.35521 2.32696i −0.178546 0.0953961i
\(596\) −13.9622 30.4663i −0.571915 1.24795i
\(597\) 0 0
\(598\) 0.0829184 1.76524i 0.00339079 0.0721860i
\(599\) −12.2437 21.2067i −0.500264 0.866483i −1.00000 0.000304857i \(-0.999903\pi\)
0.499736 0.866178i \(-0.333430\pi\)
\(600\) 0 0
\(601\) −17.0204 −0.694275 −0.347138 0.937814i \(-0.612846\pi\)
−0.347138 + 0.937814i \(0.612846\pi\)
\(602\) −17.5839 0.246972i −0.716668 0.0100658i
\(603\) 0 0
\(604\) 1.53767 16.3315i 0.0625668 0.664519i
\(605\) −26.4551 45.8216i −1.07555 1.86291i
\(606\) 0 0
\(607\) −21.1481 12.2099i −0.858375 0.495583i 0.00509301 0.999987i \(-0.498379\pi\)
−0.863468 + 0.504404i \(0.831712\pi\)
\(608\) 10.8771 + 36.5959i 0.441125 + 1.48416i
\(609\) 0 0
\(610\) 22.4758 + 14.4233i 0.910019 + 0.583984i
\(611\) 13.6190 + 7.86294i 0.550966 + 0.318101i
\(612\) 0 0
\(613\) 34.0566 19.6626i 1.37553 0.794164i 0.383915 0.923369i \(-0.374576\pi\)
0.991618 + 0.129205i \(0.0412424\pi\)
\(614\) 7.83045 + 15.1643i 0.316011 + 0.611982i
\(615\) 0 0
\(616\) −4.88555 + 45.0937i −0.196844 + 1.81688i
\(617\) 14.5542i 0.585932i 0.956123 + 0.292966i \(0.0946422\pi\)
−0.956123 + 0.292966i \(0.905358\pi\)
\(618\) 0 0
\(619\) 8.16451 + 14.1413i 0.328159 + 0.568389i 0.982147 0.188117i \(-0.0602383\pi\)
−0.653987 + 0.756506i \(0.726905\pi\)
\(620\) −28.3155 20.1070i −1.13718 0.807516i
\(621\) 0 0
\(622\) −7.45608 + 11.6188i −0.298962 + 0.465871i
\(623\) −10.5891 + 6.58719i −0.424242 + 0.263910i
\(624\) 0 0
\(625\) 10.2658 17.7809i 0.410632 0.711236i
\(626\) −39.8957 1.87402i −1.59455 0.0749007i
\(627\) 0 0
\(628\) −0.406768 + 4.32026i −0.0162318 + 0.172397i
\(629\) 6.36899 0.253948
\(630\) 0 0
\(631\) 32.9828i 1.31302i −0.754315 0.656512i \(-0.772031\pi\)
0.754315 0.656512i \(-0.227969\pi\)
\(632\) 29.9135 + 23.4283i 1.18989 + 0.931927i
\(633\) 0 0
\(634\) 36.1045 + 1.69593i 1.43389 + 0.0673542i
\(635\) −7.23466 4.17693i −0.287099 0.165756i
\(636\) 0 0
\(637\) −10.3445 + 6.91702i −0.409863 + 0.274062i
\(638\) 32.6493 + 20.9519i 1.29260 + 0.829494i
\(639\) 0 0
\(640\) 22.0140 + 7.50514i 0.870178 + 0.296667i
\(641\) 11.8256 6.82749i 0.467081 0.269669i −0.247936 0.968776i \(-0.579752\pi\)
0.715017 + 0.699107i \(0.246419\pi\)
\(642\) 0 0
\(643\) 46.5621 1.83623 0.918115 0.396315i \(-0.129711\pi\)
0.918115 + 0.396315i \(0.129711\pi\)
\(644\) 3.71258 + 0.226685i 0.146296 + 0.00893263i
\(645\) 0 0
\(646\) −7.69925 + 3.97569i −0.302923 + 0.156421i
\(647\) −17.7299 30.7090i −0.697033 1.20730i −0.969491 0.245128i \(-0.921170\pi\)
0.272458 0.962168i \(-0.412163\pi\)
\(648\) 0 0
\(649\) −3.91073 + 6.77358i −0.153509 + 0.265886i
\(650\) 1.63746 + 1.05080i 0.0642265 + 0.0412159i
\(651\) 0 0
\(652\) −15.4887 33.7971i −0.606583 1.32360i
\(653\) 10.6086 18.3747i 0.415148 0.719057i −0.580296 0.814405i \(-0.697063\pi\)
0.995444 + 0.0953486i \(0.0303966\pi\)
\(654\) 0 0
\(655\) −0.427664 + 0.246912i −0.0167102 + 0.00964766i
\(656\) −43.9168 + 15.3300i −1.71466 + 0.598536i
\(657\) 0 0
\(658\) −16.9505 + 28.4295i −0.660799 + 1.10830i
\(659\) 7.62196i 0.296909i −0.988919 0.148455i \(-0.952570\pi\)
0.988919 0.148455i \(-0.0474299\pi\)
\(660\) 0 0
\(661\) 35.1044 20.2675i 1.36540 0.788315i 0.375065 0.926998i \(-0.377620\pi\)
0.990337 + 0.138683i \(0.0442869\pi\)
\(662\) −16.4835 0.774278i −0.640650 0.0300932i
\(663\) 0 0
\(664\) 1.87244 13.2091i 0.0726647 0.512614i
\(665\) 36.6880 1.20725i 1.42270 0.0468151i
\(666\) 0 0
\(667\) 1.59062 2.75504i 0.0615891 0.106675i
\(668\) 26.1889 36.8803i 1.01328 1.42694i
\(669\) 0 0
\(670\) −1.50058 2.90600i −0.0579725 0.112269i
\(671\) 55.6769 2.14938
\(672\) 0 0
\(673\) 25.1754 0.970440 0.485220 0.874392i \(-0.338739\pi\)
0.485220 + 0.874392i \(0.338739\pi\)
\(674\) 14.6289 + 28.3302i 0.563486 + 1.09124i
\(675\) 0 0
\(676\) −11.3940 + 16.0455i −0.438230 + 0.617135i
\(677\) −18.0389 + 31.2442i −0.693290 + 1.20081i 0.277464 + 0.960736i \(0.410506\pi\)
−0.970754 + 0.240077i \(0.922827\pi\)
\(678\) 0 0
\(679\) −15.2127 + 28.4726i −0.583810 + 1.09268i
\(680\) −0.740882 + 5.22656i −0.0284115 + 0.200429i
\(681\) 0 0
\(682\) −72.3230 3.39722i −2.76939 0.130086i
\(683\) 2.69000 1.55307i 0.102930 0.0594268i −0.447651 0.894208i \(-0.647739\pi\)
0.550581 + 0.834781i \(0.314406\pi\)
\(684\) 0 0
\(685\) 31.3459i 1.19767i
\(686\) −14.2514 21.9749i −0.544122 0.839006i
\(687\) 0 0
\(688\) 6.19583 + 17.7496i 0.236214 + 0.676696i
\(689\) 10.2101 5.89482i 0.388975 0.224575i
\(690\) 0 0
\(691\) 3.31148 5.73566i 0.125975 0.218195i −0.796139 0.605114i \(-0.793128\pi\)
0.922114 + 0.386919i \(0.126461\pi\)
\(692\) −0.907153 1.97945i −0.0344848 0.0752476i
\(693\) 0 0
\(694\) −9.54423 6.12479i −0.362294 0.232494i
\(695\) 7.85605 13.6071i 0.297997 0.516146i
\(696\) 0 0
\(697\) −5.27873 9.14302i −0.199946 0.346317i
\(698\) 23.3280 12.0460i 0.882978 0.455947i
\(699\) 0 0
\(700\) −2.25987 + 3.41506i −0.0854149 + 0.129077i
\(701\) 30.4248 1.14913 0.574565 0.818459i \(-0.305171\pi\)
0.574565 + 0.818459i \(0.305171\pi\)
\(702\) 0 0
\(703\) −41.0034 + 23.6734i −1.54647 + 0.892857i
\(704\) 47.0767 11.6187i 1.77427 0.437897i
\(705\) 0 0
\(706\) 22.1458 + 14.2115i 0.833466 + 0.534858i
\(707\) −27.5365 + 0.906112i −1.03562 + 0.0340778i
\(708\) 0 0
\(709\) −4.73691 2.73486i −0.177899 0.102710i 0.408406 0.912800i \(-0.366085\pi\)
−0.586305 + 0.810090i \(0.699418\pi\)
\(710\) 4.17885 + 0.196293i 0.156830 + 0.00736674i
\(711\) 0 0
\(712\) 10.4958 + 8.22035i 0.393347 + 0.308070i
\(713\) 5.93730i 0.222354i
\(714\) 0 0
\(715\) −22.1507 −0.828391
\(716\) 1.12698 11.9696i 0.0421173 0.447326i
\(717\) 0 0
\(718\) 48.0160 + 2.25545i 1.79194 + 0.0841727i
\(719\) −4.25219 + 7.36501i −0.158580 + 0.274669i −0.934357 0.356339i \(-0.884025\pi\)
0.775777 + 0.631007i \(0.217358\pi\)
\(720\) 0 0
\(721\) 14.6656 9.12311i 0.546176 0.339762i
\(722\) 20.2780 31.5991i 0.754669 1.17600i
\(723\) 0 0
\(724\) 11.8859 + 8.44025i 0.441737 + 0.313679i
\(725\) 1.75123 + 3.03322i 0.0650391 + 0.112651i
\(726\) 0 0
\(727\) 31.9931i 1.18656i −0.804997 0.593280i \(-0.797833\pi\)
0.804997 0.593280i \(-0.202167\pi\)
\(728\) 10.7374 + 7.85384i 0.397956 + 0.291083i
\(729\) 0 0
\(730\) 5.56747 + 10.7819i 0.206061 + 0.399055i
\(731\) −3.69527 + 2.13347i −0.136675 + 0.0789091i
\(732\) 0 0
\(733\) −12.6276 7.29054i −0.466411 0.269282i 0.248325 0.968677i \(-0.420120\pi\)
−0.714736 + 0.699394i \(0.753453\pi\)
\(734\) −6.06091 3.88945i −0.223712 0.143562i
\(735\) 0 0
\(736\) −1.13287 3.81151i −0.0417581 0.140494i
\(737\) −5.90505 3.40928i −0.217515 0.125583i
\(738\) 0 0
\(739\) 12.3199 + 21.3387i 0.453194 + 0.784955i 0.998582 0.0532282i \(-0.0169511\pi\)
−0.545388 + 0.838184i \(0.683618\pi\)
\(740\) −2.70377 + 28.7166i −0.0993927 + 1.05565i
\(741\) 0 0
\(742\) 12.1041 + 21.6620i 0.444357 + 0.795235i
\(743\) −44.0203 −1.61495 −0.807474 0.589903i \(-0.799166\pi\)
−0.807474 + 0.589903i \(0.799166\pi\)
\(744\) 0 0
\(745\) 17.2237 + 29.8323i 0.631028 + 1.09297i
\(746\) 1.13301 24.1205i 0.0414824 0.883114i
\(747\) 0 0
\(748\) 4.58506 + 10.0048i 0.167646 + 0.365813i
\(749\) 20.7671 12.9187i 0.758812 0.472038i
\(750\) 0 0
\(751\) 7.28019 + 4.20322i 0.265658 + 0.153378i 0.626913 0.779089i \(-0.284318\pi\)
−0.361255 + 0.932467i \(0.617652\pi\)
\(752\) 34.7626 + 6.60460i 1.26766 + 0.240845i
\(753\) 0 0
\(754\) 10.1098 5.22042i 0.368177 0.190117i
\(755\) 16.8610i 0.613634i
\(756\) 0 0
\(757\) 44.5161i 1.61797i 0.587831 + 0.808983i \(0.299982\pi\)
−0.587831 + 0.808983i \(0.700018\pi\)
\(758\) 7.32381 + 14.1832i 0.266013 + 0.515156i
\(759\) 0 0
\(760\) −14.6572 36.4023i −0.531671 1.32045i
\(761\) 21.8857 + 12.6357i 0.793357 + 0.458045i 0.841143 0.540813i \(-0.181883\pi\)
−0.0477862 + 0.998858i \(0.515217\pi\)
\(762\) 0 0
\(763\) 0.424459 + 12.8992i 0.0153664 + 0.466982i
\(764\) 3.68730 + 8.04588i 0.133402 + 0.291090i
\(765\) 0 0
\(766\) 29.0480 + 1.36447i 1.04955 + 0.0493002i
\(767\) 1.14700 + 1.98666i 0.0414158 + 0.0717343i
\(768\) 0 0
\(769\) −12.1185 −0.437005 −0.218502 0.975836i \(-0.570117\pi\)
−0.218502 + 0.975836i \(0.570117\pi\)
\(770\) 0.654755 46.6173i 0.0235957 1.67997i
\(771\) 0 0
\(772\) −5.03676 0.474229i −0.181277 0.0170679i
\(773\) 9.15261 + 15.8528i 0.329196 + 0.570185i 0.982353 0.187038i \(-0.0598888\pi\)
−0.653156 + 0.757223i \(0.726555\pi\)
\(774\) 0 0
\(775\) −5.66105 3.26841i −0.203351 0.117405i
\(776\) 34.1691 + 4.84358i 1.22660 + 0.173874i
\(777\) 0 0
\(778\) −10.5844 + 16.4936i −0.379468 + 0.591324i
\(779\) 67.9687 + 39.2417i 2.43523 + 1.40598i
\(780\) 0 0
\(781\) 7.55330 4.36090i 0.270278 0.156045i
\(782\) 0.801889 0.414074i 0.0286755 0.0148073i
\(783\) 0 0
\(784\) −16.8462 + 22.3653i −0.601649 + 0.798760i
\(785\) 4.46033i 0.159196i
\(786\) 0 0
\(787\) 11.0540 + 19.1461i 0.394033 + 0.682485i 0.992977 0.118306i \(-0.0377462\pi\)
−0.598944 + 0.800791i \(0.704413\pi\)
\(788\) −13.4623 + 18.9583i −0.479576 + 0.675360i
\(789\) 0 0
\(790\) −32.8692 21.0931i −1.16944 0.750458i
\(791\) 5.58051 + 2.98163i 0.198420 + 0.106015i
\(792\) 0 0
\(793\) 8.16491 14.1420i 0.289944 0.502198i
\(794\) 2.29585 48.8761i 0.0814767 1.73455i
\(795\) 0 0
\(796\) 3.63841 38.6433i 0.128960 1.36968i
\(797\) 11.9294 0.422563 0.211281 0.977425i \(-0.432236\pi\)
0.211281 + 0.977425i \(0.432236\pi\)
\(798\) 0 0
\(799\) 8.03107i 0.284119i
\(800\) 4.25780 + 1.01803i 0.150536 + 0.0359929i
\(801\) 0 0
\(802\) 0.929030 19.7780i 0.0328052 0.698385i
\(803\) 21.9090 + 12.6492i 0.773151 + 0.446379i
\(804\) 0 0
\(805\) −3.82111 + 0.125737i −0.134676 + 0.00443164i
\(806\) −11.4689 + 17.8720i −0.403976 + 0.629514i
\(807\) 0 0
\(808\) 11.0011 + 27.3221i 0.387016 + 0.961187i
\(809\) −13.1494 + 7.59184i −0.462310 + 0.266915i −0.713015 0.701149i \(-0.752671\pi\)
0.250705 + 0.968064i \(0.419338\pi\)
\(810\) 0 0
\(811\) 31.1176 1.09269 0.546344 0.837561i \(-0.316019\pi\)
0.546344 + 0.837561i \(0.316019\pi\)
\(812\) 10.6878 + 21.4308i 0.375068 + 0.752075i
\(813\) 0 0
\(814\) 27.5904 + 53.4311i 0.967043 + 1.87276i
\(815\) 19.1067 + 33.0938i 0.669279 + 1.15923i
\(816\) 0 0
\(817\) 15.8601 27.4704i 0.554873 0.961069i
\(818\) 4.22207 6.57923i 0.147621 0.230037i
\(819\) 0 0
\(820\) 43.4652 19.9194i 1.51787 0.695616i
\(821\) −2.78548 + 4.82459i −0.0972139 + 0.168379i −0.910530 0.413442i \(-0.864326\pi\)
0.813317 + 0.581821i \(0.197660\pi\)
\(822\) 0 0
\(823\) 8.34067 4.81549i 0.290737 0.167857i −0.347537 0.937666i \(-0.612982\pi\)
0.638274 + 0.769809i \(0.279649\pi\)
\(824\) −14.5365 11.3850i −0.506402 0.396615i
\(825\) 0 0
\(826\) −4.21494 + 2.35520i −0.146656 + 0.0819478i
\(827\) 52.4810i 1.82494i 0.409139 + 0.912472i \(0.365829\pi\)
−0.409139 + 0.912472i \(0.634171\pi\)
\(828\) 0 0
\(829\) −24.0623 + 13.8924i −0.835717 + 0.482501i −0.855806 0.517297i \(-0.826938\pi\)
0.0200891 + 0.999798i \(0.493605\pi\)
\(830\) −0.643433 + 13.6980i −0.0223339 + 0.475463i
\(831\) 0 0
\(832\) 3.95253 13.6614i 0.137029 0.473625i
\(833\) −5.70062 2.80884i −0.197515 0.0973205i
\(834\) 0 0
\(835\) −23.2469 + 40.2647i −0.804491 + 1.39342i
\(836\) −66.7061 47.3683i −2.30708 1.63827i
\(837\) 0 0
\(838\) 16.4765 8.50802i 0.569171 0.293905i
\(839\) −22.6418 −0.781681 −0.390841 0.920458i \(-0.627816\pi\)
−0.390841 + 0.920458i \(0.627816\pi\)
\(840\) 0 0
\(841\) −8.51751 −0.293707
\(842\) 27.7392 14.3238i 0.955956 0.493630i
\(843\) 0 0
\(844\) −6.64628 + 9.35958i −0.228774 + 0.322170i
\(845\) 10.1140 17.5180i 0.347932 0.602637i
\(846\) 0 0
\(847\) −35.9688 57.8208i −1.23590 1.98674i
\(848\) 17.3188 20.0941i 0.594730 0.690035i
\(849\) 0 0
\(850\) −0.0466216 + 0.992520i −0.00159911 + 0.0340432i
\(851\) 4.27057 2.46562i 0.146393 0.0845202i
\(852\) 0 0
\(853\) 26.2579i 0.899053i 0.893267 + 0.449526i \(0.148407\pi\)
−0.893267 + 0.449526i \(0.851593\pi\)
\(854\) 29.5213 + 17.6015i 1.01020 + 0.602310i
\(855\) 0 0
\(856\) −20.5842 16.1216i −0.703554 0.551025i
\(857\) −23.8430 + 13.7658i −0.814461 + 0.470229i −0.848503 0.529191i \(-0.822495\pi\)
0.0340416 + 0.999420i \(0.489162\pi\)
\(858\) 0 0
\(859\) 4.71373 8.16443i 0.160831 0.278567i −0.774336 0.632774i \(-0.781916\pi\)
0.935167 + 0.354208i \(0.115249\pi\)
\(860\) −8.05070 17.5670i −0.274526 0.599031i
\(861\) 0 0
\(862\) 19.7767 30.8180i 0.673597 1.04966i
\(863\) −2.57590 + 4.46158i −0.0876846 + 0.151874i −0.906532 0.422137i \(-0.861280\pi\)
0.818847 + 0.574011i \(0.194613\pi\)
\(864\) 0 0
\(865\) 1.11906 + 1.93827i 0.0380491 + 0.0659030i
\(866\) −21.0578 40.7802i −0.715573 1.38577i
\(867\) 0 0
\(868\) −37.2734 24.6652i −1.26514 0.837191i
\(869\) −81.4234 −2.76210
\(870\) 0 0
\(871\) −1.73193 + 0.999930i −0.0586842 + 0.0338813i
\(872\) 12.7987 5.15334i 0.433420 0.174514i
\(873\) 0 0
\(874\) −3.62344 + 5.64639i −0.122565 + 0.190992i
\(875\) 14.7992 27.6986i 0.500303 0.936382i
\(876\) 0 0
\(877\) 33.4832 + 19.3315i 1.13065 + 0.652779i 0.944098 0.329666i \(-0.106936\pi\)
0.186550 + 0.982446i \(0.440270\pi\)
\(878\) −0.899710 + 19.1538i −0.0303638 + 0.646410i
\(879\) 0 0
\(880\) −47.0564 + 16.4259i −1.58627 + 0.553718i
\(881\) 19.8610i 0.669134i −0.942372 0.334567i \(-0.891410\pi\)
0.942372 0.334567i \(-0.108590\pi\)
\(882\) 0 0
\(883\) −16.9587 −0.570707 −0.285353 0.958422i \(-0.592111\pi\)
−0.285353 + 0.958422i \(0.592111\pi\)
\(884\) 3.21363 + 0.302575i 0.108086 + 0.0101767i
\(885\) 0 0
\(886\) 0.290112 6.17616i 0.00974650 0.207492i
\(887\) 1.65637 2.86892i 0.0556154 0.0963287i −0.836877 0.547391i \(-0.815621\pi\)
0.892493 + 0.451062i \(0.148955\pi\)
\(888\) 0 0
\(889\) −9.48277 5.06659i −0.318042 0.169928i
\(890\) −11.5329 7.40099i −0.386585 0.248082i
\(891\) 0 0
\(892\) 8.50262 + 6.03775i 0.284689 + 0.202159i
\(893\) −29.8512 51.7039i −0.998934 1.73020i
\(894\) 0 0
\(895\) 12.3577i 0.413072i
\(896\) 28.6343 + 8.72211i 0.956606 + 0.291385i
\(897\) 0 0
\(898\) 17.2867 8.92642i 0.576866 0.297878i
\(899\) −33.1060 + 19.1137i −1.10415 + 0.637479i
\(900\) 0 0
\(901\) 5.21422 + 3.01043i 0.173711 + 0.100292i
\(902\) 53.8357 83.8920i 1.79253 2.79330i
\(903\) 0 0
\(904\) 0.949322 6.69700i 0.0315740 0.222739i
\(905\) −12.9767 7.49208i −0.431359 0.249045i
\(906\) 0 0
\(907\) 8.58088 + 14.8625i 0.284923 + 0.493502i 0.972591 0.232524i \(-0.0746985\pi\)
−0.687667 + 0.726026i \(0.741365\pi\)
\(908\) 1.31765 13.9947i 0.0437277 0.464429i
\(909\) 0 0
\(910\) −11.7449 7.00265i −0.389339 0.232135i
\(911\) −12.8972 −0.427303 −0.213652 0.976910i \(-0.568536\pi\)
−0.213652 + 0.976910i \(0.568536\pi\)
\(912\) 0 0
\(913\) 14.2947 + 24.7592i 0.473086 + 0.819409i
\(914\) 16.6180 + 0.780595i 0.549674 + 0.0258198i
\(915\) 0 0
\(916\) −46.2377 + 21.1900i −1.52774 + 0.700138i
\(917\) −0.539656 + 0.335706i −0.0178210 + 0.0110860i
\(918\) 0 0
\(919\) 31.2492 + 18.0418i 1.03082 + 0.595142i 0.917219 0.398384i \(-0.130429\pi\)
0.113598 + 0.993527i \(0.463762\pi\)
\(920\) 1.52657 + 3.79135i 0.0503294 + 0.124997i
\(921\) 0 0
\(922\) 7.24288 + 14.0264i 0.238532 + 0.461936i
\(923\) 2.55807i 0.0842000i
\(924\) 0 0
\(925\) 5.42916i 0.178510i
\(926\) −20.2138 + 10.4379i −0.664266 + 0.343009i
\(927\) 0 0
\(928\) 17.6057 18.5871i 0.577936 0.610150i
\(929\) −32.7215 18.8918i −1.07356 0.619818i −0.144406 0.989519i \(-0.546127\pi\)
−0.929151 + 0.369700i \(0.879460\pi\)
\(930\) 0 0
\(931\) 47.1408 3.10578i 1.54498 0.101788i
\(932\) −21.0355 + 9.64024i −0.689040 + 0.315777i
\(933\) 0 0
\(934\) 1.44597 30.7831i 0.0473136 1.00725i
\(935\) −5.65610 9.79664i −0.184974 0.320385i
\(936\) 0 0
\(937\) 26.6280 0.869899 0.434949 0.900455i \(-0.356766\pi\)
0.434949 + 0.900455i \(0.356766\pi\)
\(938\) −2.05321 3.67449i −0.0670396 0.119976i
\(939\) 0 0
\(940\) −36.2107 3.40936i −1.18106 0.111201i
\(941\) −5.35475 9.27469i −0.174560 0.302346i 0.765449 0.643496i \(-0.222517\pi\)
−0.940009 + 0.341150i \(0.889184\pi\)
\(942\) 0 0
\(943\) −7.07904 4.08708i −0.230525 0.133094i
\(944\) 3.90987 + 3.36985i 0.127256 + 0.109679i
\(945\) 0 0
\(946\) −33.9061 21.7584i −1.10238 0.707428i
\(947\) −24.4571 14.1203i −0.794749 0.458849i 0.0468825 0.998900i \(-0.485071\pi\)
−0.841632 + 0.540052i \(0.818405\pi\)
\(948\) 0 0
\(949\) 6.42582 3.70995i 0.208591 0.120430i
\(950\) −3.38902 6.56312i −0.109954 0.212936i
\(951\) 0 0
\(952\) −0.731776 + 6.75431i −0.0237170 + 0.218908i
\(953\) 21.4320i 0.694250i 0.937819 + 0.347125i \(0.112842\pi\)
−0.937819 + 0.347125i \(0.887158\pi\)
\(954\) 0 0
\(955\) −4.54863 7.87846i −0.147190 0.254941i
\(956\) −19.9195 + 28.0515i −0.644244 + 0.907252i
\(957\) 0 0
\(958\) −16.6529 + 25.9502i −0.538031 + 0.838412i
\(959\) 1.32678 + 40.3204i 0.0428439 + 1.30201i
\(960\) 0 0
\(961\) 20.1729 34.9405i 0.650738 1.12711i
\(962\) 17.6177 + 0.827554i 0.568017 + 0.0266814i
\(963\) 0 0
\(964\) −27.2632 2.56693i −0.878088 0.0826751i
\(965\) 5.20005 0.167396
\(966\) 0 0
\(967\) 16.5003i 0.530613i 0.964164 + 0.265307i \(0.0854732\pi\)
−0.964164 + 0.265307i \(0.914527\pi\)
\(968\) −44.8866 + 57.3116i −1.44271 + 1.84206i
\(969\) 0 0
\(970\) −35.4336 1.66442i −1.13770 0.0534412i
\(971\) 20.4371 + 11.7994i 0.655858 + 0.378660i 0.790697 0.612208i \(-0.209718\pi\)
−0.134839 + 0.990868i \(0.543052\pi\)
\(972\) 0 0
\(973\) 9.52933 17.8354i 0.305496 0.571776i
\(974\) 6.92622 + 4.44474i 0.221930 + 0.142419i
\(975\) 0 0
\(976\) 6.85824 36.0976i 0.219527 1.15546i
\(977\) −26.7355 + 15.4358i −0.855346 + 0.493834i −0.862451 0.506141i \(-0.831072\pi\)
0.00710519 + 0.999975i \(0.497738\pi\)
\(978\) 0 0
\(979\) −28.5693 −0.913077
\(980\) 15.0846 24.5107i 0.481859 0.782964i
\(981\) 0 0
\(982\) 22.2171 11.4723i 0.708976 0.366097i
\(983\) 9.83164 + 17.0289i 0.313581 + 0.543138i 0.979135 0.203212i \(-0.0651381\pi\)
−0.665554 + 0.746350i \(0.731805\pi\)
\(984\) 0 0
\(985\) 11.9500 20.6980i 0.380759 0.659494i
\(986\) 4.89033 + 3.13826i 0.155740 + 0.0999425i
\(987\) 0 0
\(988\) −21.8140 + 9.99701i −0.693995 + 0.318047i
\(989\) −1.65185 + 2.86109i −0.0525257 + 0.0909773i
\(990\) 0 0
\(991\) 28.9635 16.7221i 0.920057 0.531195i 0.0364036 0.999337i \(-0.488410\pi\)
0.883653 + 0.468142i \(0.155076\pi\)
\(992\) −11.1113 + 46.4715i −0.352783 + 1.47547i
\(993\) 0 0
\(994\) 5.38359 + 0.0756142i 0.170757 + 0.00239834i
\(995\) 39.8962i 1.26479i
\(996\) 0 0
\(997\) 7.84528 4.52948i 0.248463 0.143450i −0.370597 0.928794i \(-0.620847\pi\)
0.619060 + 0.785344i \(0.287514\pi\)
\(998\) 13.5595 + 0.636931i 0.429220 + 0.0201617i
\(999\) 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 504.2.bm.c.107.16 yes 48
3.2 odd 2 inner 504.2.bm.c.107.9 yes 48
4.3 odd 2 2016.2.bu.c.1871.19 48
7.4 even 3 inner 504.2.bm.c.179.1 yes 48
8.3 odd 2 inner 504.2.bm.c.107.24 yes 48
8.5 even 2 2016.2.bu.c.1871.5 48
12.11 even 2 2016.2.bu.c.1871.6 48
21.11 odd 6 inner 504.2.bm.c.179.24 yes 48
24.5 odd 2 2016.2.bu.c.1871.20 48
24.11 even 2 inner 504.2.bm.c.107.1 48
28.11 odd 6 2016.2.bu.c.431.20 48
56.11 odd 6 inner 504.2.bm.c.179.9 yes 48
56.53 even 6 2016.2.bu.c.431.6 48
84.11 even 6 2016.2.bu.c.431.5 48
168.11 even 6 inner 504.2.bm.c.179.16 yes 48
168.53 odd 6 2016.2.bu.c.431.19 48
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
504.2.bm.c.107.1 48 24.11 even 2 inner
504.2.bm.c.107.9 yes 48 3.2 odd 2 inner
504.2.bm.c.107.16 yes 48 1.1 even 1 trivial
504.2.bm.c.107.24 yes 48 8.3 odd 2 inner
504.2.bm.c.179.1 yes 48 7.4 even 3 inner
504.2.bm.c.179.9 yes 48 56.11 odd 6 inner
504.2.bm.c.179.16 yes 48 168.11 even 6 inner
504.2.bm.c.179.24 yes 48 21.11 odd 6 inner
2016.2.bu.c.431.5 48 84.11 even 6
2016.2.bu.c.431.6 48 56.53 even 6
2016.2.bu.c.431.19 48 168.53 odd 6
2016.2.bu.c.431.20 48 28.11 odd 6
2016.2.bu.c.1871.5 48 8.5 even 2
2016.2.bu.c.1871.6 48 12.11 even 2
2016.2.bu.c.1871.19 48 4.3 odd 2
2016.2.bu.c.1871.20 48 24.5 odd 2