Properties

Label 567.2.ba.a.143.19
Level $567$
Weight $2$
Character 567.143
Analytic conductor $4.528$
Analytic rank $0$
Dimension $132$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [567,2,Mod(143,567)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(567, base_ring=CyclotomicField(18))
 
chi = DirichletCharacter(H, H._module([7, 3]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("567.143");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 567 = 3^{4} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 567.ba (of order \(18\), degree \(6\), 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: \(4.52751779461\)
Analytic rank: \(0\)
Dimension: \(132\)
Relative dimension: \(22\) over \(\Q(\zeta_{18})\)
Twist minimal: no (minimal twist has level 189)
Sato-Tate group: $\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label 143.19
Character \(\chi\) \(=\) 567.143
Dual form 567.2.ba.a.341.19

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(1.22264 - 1.45709i) q^{2} +(-0.280959 - 1.59339i) q^{4} +(0.691544 - 0.580274i) q^{5} +(-0.448602 + 2.60744i) q^{7} +(0.629295 + 0.363324i) q^{8} +O(q^{10})\) \(q+(1.22264 - 1.45709i) q^{2} +(-0.280959 - 1.59339i) q^{4} +(0.691544 - 0.580274i) q^{5} +(-0.448602 + 2.60744i) q^{7} +(0.629295 + 0.363324i) q^{8} -1.71711i q^{10} +(2.24705 - 2.67793i) q^{11} +(1.35464 - 3.72184i) q^{13} +(3.25080 + 3.84163i) q^{14} +(4.33960 - 1.57949i) q^{16} +0.467865 q^{17} -3.62874i q^{19} +(-1.11890 - 0.938869i) q^{20} +(-1.15465 - 6.54832i) q^{22} +(1.19589 - 3.28569i) q^{23} +(-0.726726 + 4.12147i) q^{25} +(-3.76682 - 6.52432i) q^{26} +(4.28072 - 0.0177830i) q^{28} +(1.79273 + 4.92550i) q^{29} +(-6.86071 + 1.20973i) q^{31} +(2.50728 - 6.88869i) q^{32} +(0.572032 - 0.681722i) q^{34} +(1.20280 + 2.06347i) q^{35} +(-4.92689 + 8.53362i) q^{37} +(-5.28741 - 4.43666i) q^{38} +(0.646012 - 0.113909i) q^{40} +(2.71326 + 0.987547i) q^{41} +(-1.54504 + 8.76238i) q^{43} +(-4.89833 - 2.82805i) q^{44} +(-3.32540 - 5.75976i) q^{46} +(0.579339 - 3.28560i) q^{47} +(-6.59751 - 2.33941i) q^{49} +(5.11683 + 6.09800i) q^{50} +(-6.31096 - 1.11279i) q^{52} +(-8.75304 - 5.05357i) q^{53} -3.15581i q^{55} +(-1.22965 + 1.47786i) q^{56} +(9.36878 + 3.40996i) q^{58} +(3.04590 + 1.10862i) q^{59} +(0.0601824 + 0.0106118i) q^{61} +(-6.62553 + 11.4757i) q^{62} +(-2.35384 - 4.07697i) q^{64} +(-1.22290 - 3.35988i) q^{65} +(7.85348 - 6.58985i) q^{67} +(-0.131451 - 0.745493i) q^{68} +(4.47727 + 0.770299i) q^{70} +(2.19935 - 1.26979i) q^{71} +(-7.24870 + 4.18504i) q^{73} +(6.41043 + 17.6125i) q^{74} +(-5.78202 + 1.01953i) q^{76} +(5.97452 + 7.06039i) q^{77} +(7.23876 + 6.07404i) q^{79} +(2.08449 - 3.61044i) q^{80} +(4.75630 - 2.74605i) q^{82} +(-10.6153 + 3.86367i) q^{83} +(0.323549 - 0.271490i) q^{85} +(10.8786 + 12.9646i) q^{86} +(2.38702 - 0.868803i) q^{88} +3.03736 q^{89} +(9.09679 + 5.20177i) q^{91} +(-5.57140 - 0.982388i) q^{92} +(-4.07909 - 4.86127i) q^{94} +(-2.10566 - 2.50943i) q^{95} +(-5.02929 - 0.886800i) q^{97} +(-11.4751 + 6.75291i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 132 q + 3 q^{2} - 3 q^{4} + 9 q^{5} - 6 q^{7} + 18 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 132 q + 3 q^{2} - 3 q^{4} + 9 q^{5} - 6 q^{7} + 18 q^{8} + 9 q^{11} - 3 q^{14} + 3 q^{16} + 18 q^{17} - 18 q^{20} - 12 q^{22} + 6 q^{23} - 3 q^{25} - 12 q^{28} - 6 q^{29} - 9 q^{31} - 3 q^{32} - 18 q^{34} - 18 q^{35} + 3 q^{37} + 99 q^{38} - 54 q^{40} - 12 q^{43} + 9 q^{44} + 3 q^{46} - 45 q^{47} - 24 q^{49} + 9 q^{50} - 9 q^{52} + 45 q^{53} - 3 q^{56} - 3 q^{58} - 36 q^{59} - 9 q^{61} + 99 q^{62} + 18 q^{64} - 69 q^{65} - 3 q^{67} - 36 q^{68} + 66 q^{70} - 18 q^{71} - 9 q^{73} - 75 q^{74} + 36 q^{76} - 15 q^{77} - 21 q^{79} - 72 q^{80} - 18 q^{82} + 90 q^{83} + 9 q^{85} + 105 q^{86} - 63 q^{88} + 18 q^{89} + 6 q^{91} - 150 q^{92} - 9 q^{94} - 45 q^{95} - 27 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/567\mathbb{Z}\right)^\times\).

\(n\) \(325\) \(407\)
\(\chi(n)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{7}{18}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.22264 1.45709i 0.864540 1.03032i −0.134682 0.990889i \(-0.543001\pi\)
0.999222 0.0394303i \(-0.0125543\pi\)
\(3\) 0 0
\(4\) −0.280959 1.59339i −0.140479 0.796697i
\(5\) 0.691544 0.580274i 0.309268 0.259506i −0.474922 0.880028i \(-0.657524\pi\)
0.784189 + 0.620522i \(0.213079\pi\)
\(6\) 0 0
\(7\) −0.448602 + 2.60744i −0.169556 + 0.985521i
\(8\) 0.629295 + 0.363324i 0.222489 + 0.128454i
\(9\) 0 0
\(10\) 1.71711i 0.542998i
\(11\) 2.24705 2.67793i 0.677512 0.807427i −0.312274 0.949992i \(-0.601091\pi\)
0.989785 + 0.142565i \(0.0455350\pi\)
\(12\) 0 0
\(13\) 1.35464 3.72184i 0.375709 1.03225i −0.597407 0.801938i \(-0.703802\pi\)
0.973116 0.230315i \(-0.0739755\pi\)
\(14\) 3.25080 + 3.84163i 0.868813 + 1.02672i
\(15\) 0 0
\(16\) 4.33960 1.57949i 1.08490 0.394871i
\(17\) 0.467865 0.113474 0.0567369 0.998389i \(-0.481930\pi\)
0.0567369 + 0.998389i \(0.481930\pi\)
\(18\) 0 0
\(19\) 3.62874i 0.832490i −0.909252 0.416245i \(-0.863346\pi\)
0.909252 0.416245i \(-0.136654\pi\)
\(20\) −1.11890 0.938869i −0.250194 0.209938i
\(21\) 0 0
\(22\) −1.15465 6.54832i −0.246171 1.39611i
\(23\) 1.19589 3.28569i 0.249361 0.685114i −0.750349 0.661042i \(-0.770115\pi\)
0.999710 0.0240721i \(-0.00766312\pi\)
\(24\) 0 0
\(25\) −0.726726 + 4.12147i −0.145345 + 0.824294i
\(26\) −3.76682 6.52432i −0.738734 1.27953i
\(27\) 0 0
\(28\) 4.28072 0.0177830i 0.808981 0.00336068i
\(29\) 1.79273 + 4.92550i 0.332902 + 0.914642i 0.987353 + 0.158537i \(0.0506777\pi\)
−0.654451 + 0.756105i \(0.727100\pi\)
\(30\) 0 0
\(31\) −6.86071 + 1.20973i −1.23222 + 0.217274i −0.751579 0.659644i \(-0.770707\pi\)
−0.480641 + 0.876917i \(0.659596\pi\)
\(32\) 2.50728 6.88869i 0.443229 1.21776i
\(33\) 0 0
\(34\) 0.572032 0.681722i 0.0981027 0.116914i
\(35\) 1.20280 + 2.06347i 0.203311 + 0.348790i
\(36\) 0 0
\(37\) −4.92689 + 8.53362i −0.809975 + 1.40292i 0.102905 + 0.994691i \(0.467186\pi\)
−0.912881 + 0.408227i \(0.866147\pi\)
\(38\) −5.28741 4.43666i −0.857731 0.719721i
\(39\) 0 0
\(40\) 0.646012 0.113909i 0.102144 0.0180107i
\(41\) 2.71326 + 0.987547i 0.423741 + 0.154229i 0.545084 0.838382i \(-0.316498\pi\)
−0.121343 + 0.992611i \(0.538720\pi\)
\(42\) 0 0
\(43\) −1.54504 + 8.76238i −0.235617 + 1.33625i 0.605693 + 0.795698i \(0.292896\pi\)
−0.841310 + 0.540553i \(0.818215\pi\)
\(44\) −4.89833 2.82805i −0.738452 0.426345i
\(45\) 0 0
\(46\) −3.32540 5.75976i −0.490303 0.849230i
\(47\) 0.579339 3.28560i 0.0845053 0.479253i −0.912957 0.408056i \(-0.866207\pi\)
0.997462 0.0711975i \(-0.0226821\pi\)
\(48\) 0 0
\(49\) −6.59751 2.33941i −0.942502 0.334201i
\(50\) 5.11683 + 6.09800i 0.723629 + 0.862387i
\(51\) 0 0
\(52\) −6.31096 1.11279i −0.875173 0.154317i
\(53\) −8.75304 5.05357i −1.20232 0.694161i −0.241251 0.970463i \(-0.577558\pi\)
−0.961071 + 0.276302i \(0.910891\pi\)
\(54\) 0 0
\(55\) 3.15581i 0.425530i
\(56\) −1.22965 + 1.47786i −0.164319 + 0.197488i
\(57\) 0 0
\(58\) 9.36878 + 3.40996i 1.23018 + 0.447749i
\(59\) 3.04590 + 1.10862i 0.396543 + 0.144330i 0.532592 0.846372i \(-0.321218\pi\)
−0.136049 + 0.990702i \(0.543440\pi\)
\(60\) 0 0
\(61\) 0.0601824 + 0.0106118i 0.00770557 + 0.00135870i 0.177500 0.984121i \(-0.443199\pi\)
−0.169794 + 0.985480i \(0.554310\pi\)
\(62\) −6.62553 + 11.4757i −0.841443 + 1.45742i
\(63\) 0 0
\(64\) −2.35384 4.07697i −0.294230 0.509621i
\(65\) −1.22290 3.35988i −0.151681 0.416741i
\(66\) 0 0
\(67\) 7.85348 6.58985i 0.959455 0.805078i −0.0214094 0.999771i \(-0.506815\pi\)
0.980864 + 0.194693i \(0.0623709\pi\)
\(68\) −0.131451 0.745493i −0.0159407 0.0904043i
\(69\) 0 0
\(70\) 4.47727 + 0.770299i 0.535136 + 0.0920684i
\(71\) 2.19935 1.26979i 0.261014 0.150697i −0.363783 0.931484i \(-0.618515\pi\)
0.624797 + 0.780787i \(0.285182\pi\)
\(72\) 0 0
\(73\) −7.24870 + 4.18504i −0.848396 + 0.489822i −0.860109 0.510110i \(-0.829605\pi\)
0.0117134 + 0.999931i \(0.496271\pi\)
\(74\) 6.41043 + 17.6125i 0.745197 + 2.04741i
\(75\) 0 0
\(76\) −5.78202 + 1.01953i −0.663243 + 0.116948i
\(77\) 5.97452 + 7.06039i 0.680860 + 0.804606i
\(78\) 0 0
\(79\) 7.23876 + 6.07404i 0.814424 + 0.683383i 0.951659 0.307156i \(-0.0993773\pi\)
−0.137236 + 0.990538i \(0.543822\pi\)
\(80\) 2.08449 3.61044i 0.233053 0.403659i
\(81\) 0 0
\(82\) 4.75630 2.74605i 0.525246 0.303251i
\(83\) −10.6153 + 3.86367i −1.16518 + 0.424092i −0.850947 0.525252i \(-0.823971\pi\)
−0.314237 + 0.949344i \(0.601749\pi\)
\(84\) 0 0
\(85\) 0.323549 0.271490i 0.0350938 0.0294472i
\(86\) 10.8786 + 12.9646i 1.17306 + 1.39800i
\(87\) 0 0
\(88\) 2.38702 0.868803i 0.254457 0.0926147i
\(89\) 3.03736 0.321959 0.160980 0.986958i \(-0.448535\pi\)
0.160980 + 0.986958i \(0.448535\pi\)
\(90\) 0 0
\(91\) 9.09679 + 5.20177i 0.953603 + 0.545294i
\(92\) −5.57140 0.982388i −0.580858 0.102421i
\(93\) 0 0
\(94\) −4.07909 4.86127i −0.420726 0.501401i
\(95\) −2.10566 2.50943i −0.216036 0.257462i
\(96\) 0 0
\(97\) −5.02929 0.886800i −0.510647 0.0900409i −0.0876131 0.996155i \(-0.527924\pi\)
−0.423034 + 0.906114i \(0.639035\pi\)
\(98\) −11.4751 + 6.75291i −1.15916 + 0.682147i
\(99\) 0 0
\(100\) 6.77131 0.677131
\(101\) −12.6062 + 4.58829i −1.25436 + 0.456552i −0.881874 0.471484i \(-0.843718\pi\)
−0.372491 + 0.928036i \(0.621496\pi\)
\(102\) 0 0
\(103\) −9.69011 11.5482i −0.954795 1.13788i −0.990361 0.138513i \(-0.955768\pi\)
0.0355656 0.999367i \(-0.488677\pi\)
\(104\) 2.20470 1.84996i 0.216189 0.181404i
\(105\) 0 0
\(106\) −18.0654 + 6.57525i −1.75466 + 0.638645i
\(107\) 12.8332 7.40924i 1.24063 0.716278i 0.271407 0.962465i \(-0.412511\pi\)
0.969222 + 0.246187i \(0.0791777\pi\)
\(108\) 0 0
\(109\) −1.48332 + 2.56918i −0.142076 + 0.246083i −0.928278 0.371886i \(-0.878711\pi\)
0.786202 + 0.617969i \(0.212044\pi\)
\(110\) −4.59831 3.85844i −0.438431 0.367888i
\(111\) 0 0
\(112\) 2.17166 + 12.0238i 0.205203 + 1.13614i
\(113\) −12.0005 + 2.11601i −1.12891 + 0.199058i −0.706751 0.707463i \(-0.749840\pi\)
−0.422162 + 0.906520i \(0.638729\pi\)
\(114\) 0 0
\(115\) −1.07959 2.96614i −0.100672 0.276594i
\(116\) 7.34458 4.24039i 0.681927 0.393711i
\(117\) 0 0
\(118\) 5.33942 3.08271i 0.491533 0.283787i
\(119\) −0.209885 + 1.21993i −0.0192401 + 0.111831i
\(120\) 0 0
\(121\) −0.211950 1.20203i −0.0192682 0.109275i
\(122\) 0.0890440 0.0747168i 0.00806167 0.00676454i
\(123\) 0 0
\(124\) 3.85515 + 10.5919i 0.346203 + 0.951184i
\(125\) 4.14588 + 7.18088i 0.370819 + 0.642277i
\(126\) 0 0
\(127\) −4.12812 + 7.15011i −0.366311 + 0.634469i −0.988986 0.148012i \(-0.952713\pi\)
0.622675 + 0.782481i \(0.286046\pi\)
\(128\) 5.62043 + 0.991033i 0.496780 + 0.0875958i
\(129\) 0 0
\(130\) −6.39081 2.32607i −0.560511 0.204009i
\(131\) −19.4938 7.09515i −1.70318 0.619906i −0.706996 0.707217i \(-0.749950\pi\)
−0.996181 + 0.0873113i \(0.972173\pi\)
\(132\) 0 0
\(133\) 9.46173 + 1.62786i 0.820436 + 0.141153i
\(134\) 19.5003i 1.68457i
\(135\) 0 0
\(136\) 0.294425 + 0.169986i 0.0252467 + 0.0145762i
\(137\) 12.0168 + 2.11888i 1.02666 + 0.181028i 0.661522 0.749925i \(-0.269911\pi\)
0.365138 + 0.930953i \(0.381022\pi\)
\(138\) 0 0
\(139\) 11.5620 + 13.7791i 0.980677 + 1.16873i 0.985661 + 0.168738i \(0.0539691\pi\)
−0.00498385 + 0.999988i \(0.501586\pi\)
\(140\) 2.94999 2.49629i 0.249319 0.210975i
\(141\) 0 0
\(142\) 0.838815 4.75716i 0.0703918 0.399212i
\(143\) −6.92290 11.9908i −0.578922 1.00272i
\(144\) 0 0
\(145\) 4.09789 + 2.36592i 0.340311 + 0.196479i
\(146\) −2.76460 + 15.6788i −0.228800 + 1.29759i
\(147\) 0 0
\(148\) 14.9817 + 5.45288i 1.23149 + 0.448224i
\(149\) −11.0919 + 1.95580i −0.908685 + 0.160226i −0.608406 0.793626i \(-0.708191\pi\)
−0.300279 + 0.953852i \(0.597080\pi\)
\(150\) 0 0
\(151\) −4.66440 3.91390i −0.379583 0.318508i 0.432955 0.901415i \(-0.357471\pi\)
−0.812539 + 0.582907i \(0.801915\pi\)
\(152\) 1.31841 2.28355i 0.106937 0.185220i
\(153\) 0 0
\(154\) 17.5924 0.0730824i 1.41763 0.00588915i
\(155\) −4.04251 + 4.81767i −0.324702 + 0.386965i
\(156\) 0 0
\(157\) −1.63498 + 4.49206i −0.130485 + 0.358505i −0.987680 0.156487i \(-0.949983\pi\)
0.857195 + 0.514992i \(0.172205\pi\)
\(158\) 17.7009 3.12114i 1.40820 0.248304i
\(159\) 0 0
\(160\) −2.26344 6.21874i −0.178940 0.491635i
\(161\) 8.03077 + 4.59219i 0.632913 + 0.361915i
\(162\) 0 0
\(163\) 3.98040 + 6.89426i 0.311769 + 0.540000i 0.978745 0.205079i \(-0.0657451\pi\)
−0.666976 + 0.745079i \(0.732412\pi\)
\(164\) 0.811238 4.60076i 0.0633471 0.359259i
\(165\) 0 0
\(166\) −7.34907 + 20.1914i −0.570398 + 1.56716i
\(167\) −3.90196 22.1291i −0.301943 1.71240i −0.637556 0.770404i \(-0.720055\pi\)
0.335613 0.942000i \(-0.391057\pi\)
\(168\) 0 0
\(169\) −2.05848 1.72727i −0.158344 0.132867i
\(170\) 0.803376i 0.0616161i
\(171\) 0 0
\(172\) 14.3960 1.09769
\(173\) −7.27776 + 2.64889i −0.553317 + 0.201391i −0.603520 0.797348i \(-0.706236\pi\)
0.0502024 + 0.998739i \(0.484013\pi\)
\(174\) 0 0
\(175\) −10.4205 3.74380i −0.787715 0.283004i
\(176\) 5.52155 15.1703i 0.416203 1.14351i
\(177\) 0 0
\(178\) 3.71361 4.42571i 0.278347 0.331721i
\(179\) 1.87108i 0.139851i 0.997552 + 0.0699256i \(0.0222762\pi\)
−0.997552 + 0.0699256i \(0.977724\pi\)
\(180\) 0 0
\(181\) 18.1786 + 10.4954i 1.35121 + 0.780121i 0.988419 0.151751i \(-0.0484910\pi\)
0.362790 + 0.931871i \(0.381824\pi\)
\(182\) 18.7016 6.89494i 1.38625 0.511087i
\(183\) 0 0
\(184\) 1.94634 1.63317i 0.143486 0.120399i
\(185\) 1.54468 + 8.76031i 0.113567 + 0.644071i
\(186\) 0 0
\(187\) 1.05132 1.25291i 0.0768799 0.0916219i
\(188\) −5.39802 −0.393691
\(189\) 0 0
\(190\) −6.23095 −0.452041
\(191\) 6.58893 7.85238i 0.476758 0.568178i −0.473040 0.881041i \(-0.656843\pi\)
0.949798 + 0.312862i \(0.101288\pi\)
\(192\) 0 0
\(193\) −1.75083 9.92947i −0.126028 0.714739i −0.980692 0.195558i \(-0.937348\pi\)
0.854664 0.519181i \(-0.173763\pi\)
\(194\) −7.44119 + 6.24390i −0.534246 + 0.448286i
\(195\) 0 0
\(196\) −1.87397 + 11.1697i −0.133855 + 0.797837i
\(197\) 23.0223 + 13.2919i 1.64027 + 0.947010i 0.980737 + 0.195334i \(0.0625791\pi\)
0.659533 + 0.751676i \(0.270754\pi\)
\(198\) 0 0
\(199\) 19.4827i 1.38109i −0.723288 0.690546i \(-0.757370\pi\)
0.723288 0.690546i \(-0.242630\pi\)
\(200\) −1.95475 + 2.32958i −0.138222 + 0.164726i
\(201\) 0 0
\(202\) −8.72737 + 23.9782i −0.614055 + 1.68710i
\(203\) −13.6472 + 2.46486i −0.957844 + 0.173000i
\(204\) 0 0
\(205\) 2.44939 0.891504i 0.171073 0.0622654i
\(206\) −28.6744 −1.99784
\(207\) 0 0
\(208\) 18.2909i 1.26825i
\(209\) −9.71752 8.15397i −0.672175 0.564022i
\(210\) 0 0
\(211\) −0.926175 5.25260i −0.0637605 0.361604i −0.999949 0.0101053i \(-0.996783\pi\)
0.936188 0.351499i \(-0.114328\pi\)
\(212\) −5.59309 + 15.3669i −0.384135 + 1.05540i
\(213\) 0 0
\(214\) 4.89448 27.7580i 0.334580 1.89750i
\(215\) 4.01612 + 6.95612i 0.273897 + 0.474403i
\(216\) 0 0
\(217\) −0.0765688 18.4316i −0.00519783 1.25122i
\(218\) 1.92996 + 5.30253i 0.130713 + 0.359132i
\(219\) 0 0
\(220\) −5.02846 + 0.886653i −0.339019 + 0.0597781i
\(221\) 0.633788 1.74132i 0.0426332 0.117134i
\(222\) 0 0
\(223\) −5.44697 + 6.49144i −0.364756 + 0.434699i −0.916941 0.399022i \(-0.869350\pi\)
0.552185 + 0.833721i \(0.313794\pi\)
\(224\) 16.8371 + 9.62787i 1.12498 + 0.643289i
\(225\) 0 0
\(226\) −11.5891 + 20.0730i −0.770898 + 1.33523i
\(227\) 17.2296 + 14.4573i 1.14357 + 0.959567i 0.999550 0.0300086i \(-0.00955346\pi\)
0.144017 + 0.989575i \(0.453998\pi\)
\(228\) 0 0
\(229\) 0.780937 0.137700i 0.0516057 0.00909948i −0.147786 0.989019i \(-0.547215\pi\)
0.199391 + 0.979920i \(0.436103\pi\)
\(230\) −5.64189 2.05348i −0.372015 0.135403i
\(231\) 0 0
\(232\) −0.661391 + 3.75093i −0.0434224 + 0.246261i
\(233\) −7.51477 4.33866i −0.492309 0.284235i 0.233223 0.972423i \(-0.425073\pi\)
−0.725532 + 0.688189i \(0.758406\pi\)
\(234\) 0 0
\(235\) −1.50591 2.60831i −0.0982346 0.170147i
\(236\) 0.910694 5.16480i 0.0592812 0.336200i
\(237\) 0 0
\(238\) 1.52093 + 1.79736i 0.0985876 + 0.116506i
\(239\) −14.4054 17.1677i −0.931810 1.11049i −0.993663 0.112403i \(-0.964145\pi\)
0.0618527 0.998085i \(-0.480299\pi\)
\(240\) 0 0
\(241\) 10.3548 + 1.82584i 0.667014 + 0.117613i 0.496895 0.867811i \(-0.334474\pi\)
0.170119 + 0.985423i \(0.445585\pi\)
\(242\) −2.01061 1.16082i −0.129247 0.0746206i
\(243\) 0 0
\(244\) 0.0988758i 0.00632987i
\(245\) −5.91996 + 2.21056i −0.378213 + 0.141228i
\(246\) 0 0
\(247\) −13.5056 4.91563i −0.859340 0.312774i
\(248\) −4.75694 1.73138i −0.302066 0.109943i
\(249\) 0 0
\(250\) 15.5321 + 2.73874i 0.982339 + 0.173213i
\(251\) −4.71175 + 8.16098i −0.297403 + 0.515117i −0.975541 0.219818i \(-0.929454\pi\)
0.678138 + 0.734934i \(0.262787\pi\)
\(252\) 0 0
\(253\) −6.11162 10.5856i −0.384234 0.665514i
\(254\) 5.37114 + 14.7571i 0.337015 + 0.925942i
\(255\) 0 0
\(256\) 15.5284 13.0299i 0.970524 0.814367i
\(257\) 2.04743 + 11.6115i 0.127715 + 0.724308i 0.979658 + 0.200673i \(0.0643130\pi\)
−0.851943 + 0.523634i \(0.824576\pi\)
\(258\) 0 0
\(259\) −20.0407 16.6748i −1.24527 1.03612i
\(260\) −5.01003 + 2.89254i −0.310709 + 0.179388i
\(261\) 0 0
\(262\) −34.1722 + 19.7293i −2.11117 + 1.21888i
\(263\) −1.58821 4.36356i −0.0979331 0.269069i 0.881046 0.473031i \(-0.156840\pi\)
−0.978979 + 0.203962i \(0.934618\pi\)
\(264\) 0 0
\(265\) −8.98556 + 1.58440i −0.551978 + 0.0973287i
\(266\) 13.9403 11.7963i 0.854733 0.723278i
\(267\) 0 0
\(268\) −12.7067 10.6622i −0.776187 0.651299i
\(269\) 13.5452 23.4609i 0.825864 1.43044i −0.0753937 0.997154i \(-0.524021\pi\)
0.901257 0.433284i \(-0.142645\pi\)
\(270\) 0 0
\(271\) −3.93162 + 2.26992i −0.238829 + 0.137888i −0.614638 0.788809i \(-0.710698\pi\)
0.375810 + 0.926697i \(0.377365\pi\)
\(272\) 2.03035 0.738985i 0.123108 0.0448076i
\(273\) 0 0
\(274\) 17.7796 14.9189i 1.07411 0.901282i
\(275\) 9.40403 + 11.2073i 0.567084 + 0.675825i
\(276\) 0 0
\(277\) −7.49116 + 2.72656i −0.450100 + 0.163823i −0.557117 0.830434i \(-0.688092\pi\)
0.107016 + 0.994257i \(0.465870\pi\)
\(278\) 34.2136 2.05200
\(279\) 0 0
\(280\) 0.00720981 + 1.73554i 0.000430868 + 0.103718i
\(281\) −6.05459 1.06759i −0.361187 0.0636870i −0.00988990 0.999951i \(-0.503148\pi\)
−0.351297 + 0.936264i \(0.614259\pi\)
\(282\) 0 0
\(283\) −7.37481 8.78895i −0.438387 0.522449i 0.500936 0.865484i \(-0.332989\pi\)
−0.939322 + 0.343036i \(0.888545\pi\)
\(284\) −2.64121 3.14767i −0.156727 0.186780i
\(285\) 0 0
\(286\) −25.9359 4.57321i −1.53362 0.270419i
\(287\) −3.79215 + 6.63166i −0.223843 + 0.391455i
\(288\) 0 0
\(289\) −16.7811 −0.987124
\(290\) 8.45762 3.07832i 0.496649 0.180765i
\(291\) 0 0
\(292\) 8.70500 + 10.3742i 0.509422 + 0.607105i
\(293\) −0.840836 + 0.705545i −0.0491222 + 0.0412184i −0.667018 0.745041i \(-0.732430\pi\)
0.617896 + 0.786260i \(0.287985\pi\)
\(294\) 0 0
\(295\) 2.74968 1.00080i 0.160092 0.0582689i
\(296\) −6.20093 + 3.58011i −0.360422 + 0.208090i
\(297\) 0 0
\(298\) −10.7117 + 18.5532i −0.620511 + 1.07476i
\(299\) −10.6088 8.90185i −0.613523 0.514807i
\(300\) 0 0
\(301\) −22.1543 7.95944i −1.27695 0.458774i
\(302\) −11.4058 + 2.01115i −0.656331 + 0.115729i
\(303\) 0 0
\(304\) −5.73154 15.7473i −0.328726 0.903169i
\(305\) 0.0477765 0.0275838i 0.00273567 0.00157944i
\(306\) 0 0
\(307\) 5.93612 3.42722i 0.338792 0.195602i −0.320945 0.947098i \(-0.604001\pi\)
0.659738 + 0.751496i \(0.270667\pi\)
\(308\) 9.57139 11.5035i 0.545381 0.655470i
\(309\) 0 0
\(310\) 2.07724 + 11.7806i 0.117979 + 0.669093i
\(311\) 17.1024 14.3506i 0.969788 0.813749i −0.0127297 0.999919i \(-0.504052\pi\)
0.982517 + 0.186170i \(0.0596077\pi\)
\(312\) 0 0
\(313\) −0.345892 0.950332i −0.0195510 0.0537159i 0.929533 0.368738i \(-0.120210\pi\)
−0.949084 + 0.315022i \(0.897988\pi\)
\(314\) 4.54635 + 7.87450i 0.256565 + 0.444384i
\(315\) 0 0
\(316\) 7.64455 13.2408i 0.430040 0.744850i
\(317\) −24.4774 4.31603i −1.37479 0.242412i −0.563044 0.826427i \(-0.690370\pi\)
−0.811743 + 0.584015i \(0.801481\pi\)
\(318\) 0 0
\(319\) 17.2185 + 6.26703i 0.964052 + 0.350886i
\(320\) −3.99354 1.45353i −0.223246 0.0812547i
\(321\) 0 0
\(322\) 16.5100 6.08694i 0.920067 0.339212i
\(323\) 1.69776i 0.0944659i
\(324\) 0 0
\(325\) 14.3550 + 8.28786i 0.796272 + 0.459728i
\(326\) 14.9122 + 2.62942i 0.825910 + 0.145630i
\(327\) 0 0
\(328\) 1.34864 + 1.60725i 0.0744664 + 0.0887457i
\(329\) 8.30711 + 2.98452i 0.457986 + 0.164542i
\(330\) 0 0
\(331\) 4.60947 26.1416i 0.253360 1.43687i −0.546889 0.837205i \(-0.684188\pi\)
0.800248 0.599669i \(-0.204701\pi\)
\(332\) 9.13881 + 15.8289i 0.501558 + 0.868723i
\(333\) 0 0
\(334\) −37.0149 21.3706i −2.02536 1.16934i
\(335\) 1.60710 9.11434i 0.0878054 0.497969i
\(336\) 0 0
\(337\) 23.2967 + 8.47930i 1.26905 + 0.461897i 0.886796 0.462161i \(-0.152926\pi\)
0.382254 + 0.924057i \(0.375148\pi\)
\(338\) −5.03357 + 0.887554i −0.273790 + 0.0482766i
\(339\) 0 0
\(340\) −0.523494 0.439264i −0.0283904 0.0238224i
\(341\) −12.1768 + 21.0908i −0.659411 + 1.14213i
\(342\) 0 0
\(343\) 9.05953 16.1532i 0.489169 0.872189i
\(344\) −4.15587 + 4.95278i −0.224070 + 0.267036i
\(345\) 0 0
\(346\) −5.03844 + 13.8430i −0.270868 + 0.744204i
\(347\) −18.4568 + 3.25443i −0.990813 + 0.174707i −0.645483 0.763774i \(-0.723344\pi\)
−0.345330 + 0.938481i \(0.612233\pi\)
\(348\) 0 0
\(349\) 8.31455 + 22.8440i 0.445067 + 1.22281i 0.936119 + 0.351682i \(0.114390\pi\)
−0.491052 + 0.871130i \(0.663387\pi\)
\(350\) −18.1956 + 10.6063i −0.972596 + 0.566929i
\(351\) 0 0
\(352\) −12.8135 22.1936i −0.682960 1.18292i
\(353\) 3.97293 22.5316i 0.211458 1.19924i −0.675490 0.737369i \(-0.736068\pi\)
0.886948 0.461869i \(-0.152821\pi\)
\(354\) 0 0
\(355\) 0.784116 2.15434i 0.0416166 0.114341i
\(356\) −0.853371 4.83971i −0.0452286 0.256504i
\(357\) 0 0
\(358\) 2.72634 + 2.28767i 0.144091 + 0.120907i
\(359\) 8.35250i 0.440828i −0.975406 0.220414i \(-0.929259\pi\)
0.975406 0.220414i \(-0.0707409\pi\)
\(360\) 0 0
\(361\) 5.83224 0.306960
\(362\) 37.5189 13.6557i 1.97195 0.717730i
\(363\) 0 0
\(364\) 5.73265 15.9563i 0.300473 0.836336i
\(365\) −2.58432 + 7.10037i −0.135270 + 0.371650i
\(366\) 0 0
\(367\) −6.27438 + 7.47752i −0.327520 + 0.390323i −0.904527 0.426416i \(-0.859776\pi\)
0.577007 + 0.816739i \(0.304220\pi\)
\(368\) 16.1475i 0.841745i
\(369\) 0 0
\(370\) 14.6532 + 8.46001i 0.761782 + 0.439815i
\(371\) 17.1035 20.5560i 0.887970 1.06721i
\(372\) 0 0
\(373\) 8.11869 6.81239i 0.420370 0.352732i −0.407934 0.913012i \(-0.633751\pi\)
0.828304 + 0.560279i \(0.189306\pi\)
\(374\) −0.540218 3.06373i −0.0279340 0.158422i
\(375\) 0 0
\(376\) 1.55831 1.85712i 0.0803637 0.0957738i
\(377\) 20.7604 1.06922
\(378\) 0 0
\(379\) −6.26462 −0.321792 −0.160896 0.986971i \(-0.551438\pi\)
−0.160896 + 0.986971i \(0.551438\pi\)
\(380\) −3.40691 + 4.06020i −0.174771 + 0.208284i
\(381\) 0 0
\(382\) −3.38572 19.2013i −0.173228 0.982427i
\(383\) −6.40797 + 5.37692i −0.327432 + 0.274748i −0.791652 0.610972i \(-0.790779\pi\)
0.464221 + 0.885720i \(0.346334\pi\)
\(384\) 0 0
\(385\) 8.22860 + 1.41570i 0.419368 + 0.0721510i
\(386\) −16.6088 9.58909i −0.845365 0.488072i
\(387\) 0 0
\(388\) 8.26281i 0.419480i
\(389\) 12.4908 14.8860i 0.633309 0.754748i −0.349989 0.936754i \(-0.613815\pi\)
0.983297 + 0.182006i \(0.0582590\pi\)
\(390\) 0 0
\(391\) 0.559516 1.53726i 0.0282960 0.0777425i
\(392\) −3.30182 3.86921i −0.166767 0.195425i
\(393\) 0 0
\(394\) 47.5156 17.2943i 2.39380 0.871273i
\(395\) 8.53052 0.429217
\(396\) 0 0
\(397\) 28.3683i 1.42376i 0.702299 + 0.711882i \(0.252157\pi\)
−0.702299 + 0.711882i \(0.747843\pi\)
\(398\) −28.3881 23.8204i −1.42297 1.19401i
\(399\) 0 0
\(400\) 3.35610 + 19.0334i 0.167805 + 0.951669i
\(401\) −6.67751 + 18.3463i −0.333459 + 0.916171i 0.653746 + 0.756714i \(0.273197\pi\)
−0.987205 + 0.159457i \(0.949026\pi\)
\(402\) 0 0
\(403\) −4.79137 + 27.1732i −0.238675 + 1.35359i
\(404\) 10.8528 + 18.7976i 0.539946 + 0.935213i
\(405\) 0 0
\(406\) −13.0941 + 22.8988i −0.649850 + 1.13645i
\(407\) 11.7815 + 32.3694i 0.583986 + 1.60449i
\(408\) 0 0
\(409\) 34.4362 6.07202i 1.70276 0.300242i 0.764102 0.645096i \(-0.223183\pi\)
0.938657 + 0.344854i \(0.112071\pi\)
\(410\) 1.69573 4.65897i 0.0837460 0.230090i
\(411\) 0 0
\(412\) −15.6784 + 18.6847i −0.772418 + 0.920531i
\(413\) −4.25706 + 7.44469i −0.209476 + 0.366329i
\(414\) 0 0
\(415\) −5.09898 + 8.83169i −0.250299 + 0.433531i
\(416\) −22.2422 18.6634i −1.09051 0.915048i
\(417\) 0 0
\(418\) −23.7622 + 4.18991i −1.16225 + 0.204935i
\(419\) 38.1160 + 13.8731i 1.86209 + 0.677745i 0.977340 + 0.211674i \(0.0678916\pi\)
0.884748 + 0.466070i \(0.154331\pi\)
\(420\) 0 0
\(421\) 2.74861 15.5881i 0.133959 0.759718i −0.841620 0.540070i \(-0.818398\pi\)
0.975579 0.219649i \(-0.0704911\pi\)
\(422\) −8.78590 5.07254i −0.427691 0.246927i
\(423\) 0 0
\(424\) −3.67216 6.36037i −0.178336 0.308887i
\(425\) −0.340010 + 1.92829i −0.0164929 + 0.0935358i
\(426\) 0 0
\(427\) −0.0546675 + 0.152162i −0.00264555 + 0.00736362i
\(428\) −15.4114 18.3666i −0.744939 0.887784i
\(429\) 0 0
\(430\) 15.0460 + 2.65301i 0.725582 + 0.127940i
\(431\) −6.88208 3.97337i −0.331498 0.191391i 0.325008 0.945711i \(-0.394633\pi\)
−0.656506 + 0.754321i \(0.727966\pi\)
\(432\) 0 0
\(433\) 16.4757i 0.791770i −0.918300 0.395885i \(-0.870438\pi\)
0.918300 0.395885i \(-0.129562\pi\)
\(434\) −26.9501 22.4237i −1.29365 1.07637i
\(435\) 0 0
\(436\) 4.51047 + 1.64168i 0.216012 + 0.0786221i
\(437\) −11.9229 4.33959i −0.570350 0.207591i
\(438\) 0 0
\(439\) 6.00878 + 1.05951i 0.286783 + 0.0505677i 0.315189 0.949029i \(-0.397932\pi\)
−0.0284059 + 0.999596i \(0.509043\pi\)
\(440\) 1.14658 1.98594i 0.0546612 0.0946759i
\(441\) 0 0
\(442\) −1.76236 3.05250i −0.0838270 0.145193i
\(443\) −6.80864 18.7066i −0.323488 0.888776i −0.989718 0.143030i \(-0.954315\pi\)
0.666230 0.745746i \(-0.267907\pi\)
\(444\) 0 0
\(445\) 2.10046 1.76250i 0.0995716 0.0835505i
\(446\) 2.79892 + 15.8735i 0.132533 + 0.751630i
\(447\) 0 0
\(448\) 11.6864 4.30856i 0.552130 0.203560i
\(449\) 0.412263 0.238020i 0.0194559 0.0112329i −0.490241 0.871587i \(-0.663091\pi\)
0.509696 + 0.860354i \(0.329758\pi\)
\(450\) 0 0
\(451\) 8.74143 5.04687i 0.411618 0.237648i
\(452\) 6.74329 + 18.5270i 0.317178 + 0.871438i
\(453\) 0 0
\(454\) 42.1313 7.42888i 1.97732 0.348655i
\(455\) 9.30928 1.68138i 0.436426 0.0788244i
\(456\) 0 0
\(457\) 8.85251 + 7.42814i 0.414103 + 0.347474i 0.825914 0.563795i \(-0.190659\pi\)
−0.411812 + 0.911269i \(0.635104\pi\)
\(458\) 0.754166 1.30625i 0.0352399 0.0610373i
\(459\) 0 0
\(460\) −4.42292 + 2.55357i −0.206220 + 0.119061i
\(461\) 19.0273 6.92536i 0.886189 0.322546i 0.141484 0.989941i \(-0.454813\pi\)
0.744705 + 0.667394i \(0.232590\pi\)
\(462\) 0 0
\(463\) −4.74389 + 3.98059i −0.220467 + 0.184994i −0.746331 0.665575i \(-0.768186\pi\)
0.525864 + 0.850569i \(0.323742\pi\)
\(464\) 15.5595 + 18.5431i 0.722332 + 0.860841i
\(465\) 0 0
\(466\) −15.5097 + 5.64507i −0.718474 + 0.261503i
\(467\) −3.80696 −0.176165 −0.0880826 0.996113i \(-0.528074\pi\)
−0.0880826 + 0.996113i \(0.528074\pi\)
\(468\) 0 0
\(469\) 13.6596 + 23.4337i 0.630740 + 1.08207i
\(470\) −5.64173 0.994790i −0.260234 0.0458862i
\(471\) 0 0
\(472\) 1.51399 + 1.80430i 0.0696868 + 0.0830495i
\(473\) 19.9933 + 23.8271i 0.919292 + 1.09557i
\(474\) 0 0
\(475\) 14.9557 + 2.63710i 0.686217 + 0.120998i
\(476\) 2.00280 0.00832006i 0.0917982 0.000381349i
\(477\) 0 0
\(478\) −42.6277 −1.94974
\(479\) 28.2447 10.2802i 1.29053 0.469716i 0.396632 0.917978i \(-0.370179\pi\)
0.893902 + 0.448262i \(0.147957\pi\)
\(480\) 0 0
\(481\) 25.0866 + 29.8971i 1.14385 + 1.36319i
\(482\) 15.3207 12.8556i 0.697839 0.585556i
\(483\) 0 0
\(484\) −1.85576 + 0.675440i −0.0843526 + 0.0307018i
\(485\) −3.99256 + 2.30511i −0.181293 + 0.104670i
\(486\) 0 0
\(487\) −18.9944 + 32.8993i −0.860720 + 1.49081i 0.0105150 + 0.999945i \(0.496653\pi\)
−0.871235 + 0.490866i \(0.836680\pi\)
\(488\) 0.0340170 + 0.0285436i 0.00153988 + 0.00129211i
\(489\) 0 0
\(490\) −4.01702 + 11.3287i −0.181471 + 0.511777i
\(491\) 31.0131 5.46844i 1.39960 0.246787i 0.577622 0.816305i \(-0.303981\pi\)
0.821979 + 0.569517i \(0.192870\pi\)
\(492\) 0 0
\(493\) 0.838757 + 2.30447i 0.0377757 + 0.103788i
\(494\) −23.6751 + 13.6688i −1.06519 + 0.614989i
\(495\) 0 0
\(496\) −27.8620 + 16.0861i −1.25104 + 0.722288i
\(497\) 2.32428 + 6.30430i 0.104258 + 0.282787i
\(498\) 0 0
\(499\) −3.26628 18.5240i −0.146219 0.829247i −0.966381 0.257116i \(-0.917228\pi\)
0.820162 0.572131i \(-0.193883\pi\)
\(500\) 10.2772 8.62356i 0.459608 0.385657i
\(501\) 0 0
\(502\) 6.13051 + 16.8434i 0.273618 + 0.751759i
\(503\) 3.04934 + 5.28161i 0.135963 + 0.235495i 0.925965 0.377609i \(-0.123254\pi\)
−0.790002 + 0.613105i \(0.789920\pi\)
\(504\) 0 0
\(505\) −6.05528 + 10.4881i −0.269456 + 0.466712i
\(506\) −22.8966 4.03729i −1.01788 0.179479i
\(507\) 0 0
\(508\) 12.5528 + 4.56884i 0.556939 + 0.202709i
\(509\) −40.6536 14.7967i −1.80194 0.655852i −0.998141 0.0609481i \(-0.980588\pi\)
−0.803797 0.594904i \(-0.797190\pi\)
\(510\) 0 0
\(511\) −7.66046 20.7780i −0.338879 0.919164i
\(512\) 27.1429i 1.19956i
\(513\) 0 0
\(514\) 19.4223 + 11.2135i 0.856683 + 0.494606i
\(515\) −13.4023 2.36318i −0.590574 0.104134i
\(516\) 0 0
\(517\) −7.49680 8.93434i −0.329709 0.392932i
\(518\) −48.7993 + 8.81382i −2.14412 + 0.387257i
\(519\) 0 0
\(520\) 0.451161 2.55866i 0.0197847 0.112205i
\(521\) 10.0216 + 17.3579i 0.439053 + 0.760462i 0.997617 0.0689999i \(-0.0219808\pi\)
−0.558564 + 0.829461i \(0.688647\pi\)
\(522\) 0 0
\(523\) −23.1000 13.3368i −1.01009 0.583177i −0.0988740 0.995100i \(-0.531524\pi\)
−0.911219 + 0.411923i \(0.864857\pi\)
\(524\) −5.82843 + 33.0547i −0.254616 + 1.44400i
\(525\) 0 0
\(526\) −8.29992 3.02093i −0.361894 0.131719i
\(527\) −3.20988 + 0.565989i −0.139825 + 0.0246549i
\(528\) 0 0
\(529\) 8.25343 + 6.92545i 0.358845 + 0.301106i
\(530\) −8.67754 + 15.0299i −0.376928 + 0.652859i
\(531\) 0 0
\(532\) −0.0645301 15.5336i −0.00279773 0.673469i
\(533\) 7.35099 8.76057i 0.318407 0.379462i
\(534\) 0 0
\(535\) 4.57531 12.5706i 0.197808 0.543473i
\(536\) 7.33641 1.29361i 0.316884 0.0558753i
\(537\) 0 0
\(538\) −17.6238 48.4209i −0.759815 2.08757i
\(539\) −21.0897 + 12.4109i −0.908399 + 0.534576i
\(540\) 0 0
\(541\) −5.16825 8.95167i −0.222200 0.384862i 0.733275 0.679932i \(-0.237991\pi\)
−0.955476 + 0.295069i \(0.904657\pi\)
\(542\) −1.49949 + 8.50404i −0.0644086 + 0.365280i
\(543\) 0 0
\(544\) 1.17307 3.22298i 0.0502948 0.138184i
\(545\) 0.465050 + 2.63743i 0.0199206 + 0.112975i
\(546\) 0 0
\(547\) 2.39360 + 2.00847i 0.102343 + 0.0858758i 0.692523 0.721396i \(-0.256499\pi\)
−0.590181 + 0.807271i \(0.700943\pi\)
\(548\) 19.7428i 0.843369i
\(549\) 0 0
\(550\) 27.8278 1.18658
\(551\) 17.8733 6.50537i 0.761430 0.277138i
\(552\) 0 0
\(553\) −19.0850 + 16.1498i −0.811578 + 0.686760i
\(554\) −5.18618 + 14.2489i −0.220340 + 0.605379i
\(555\) 0 0
\(556\) 18.7071 22.2942i 0.793356 0.945485i
\(557\) 14.1576i 0.599878i 0.953958 + 0.299939i \(0.0969663\pi\)
−0.953958 + 0.299939i \(0.903034\pi\)
\(558\) 0 0
\(559\) 30.5192 + 17.6203i 1.29083 + 0.745259i
\(560\) 8.47891 + 7.05483i 0.358299 + 0.298121i
\(561\) 0 0
\(562\) −8.95819 + 7.51681i −0.377878 + 0.317078i
\(563\) 3.90078 + 22.1224i 0.164398 + 0.932348i 0.949683 + 0.313213i \(0.101405\pi\)
−0.785285 + 0.619135i \(0.787483\pi\)
\(564\) 0 0
\(565\) −7.07101 + 8.42690i −0.297479 + 0.354522i
\(566\) −21.8231 −0.917292
\(567\) 0 0
\(568\) 1.84539 0.0774306
\(569\) −12.0098 + 14.3127i −0.503478 + 0.600021i −0.956592 0.291431i \(-0.905869\pi\)
0.453114 + 0.891453i \(0.350313\pi\)
\(570\) 0 0
\(571\) −6.32831 35.8896i −0.264832 1.50193i −0.769514 0.638630i \(-0.779502\pi\)
0.504683 0.863305i \(-0.331610\pi\)
\(572\) −17.1610 + 14.3998i −0.717539 + 0.602087i
\(573\) 0 0
\(574\) 5.02649 + 13.6337i 0.209802 + 0.569059i
\(575\) 12.6728 + 7.31663i 0.528492 + 0.305125i
\(576\) 0 0
\(577\) 28.9410i 1.20483i −0.798183 0.602416i \(-0.794205\pi\)
0.798183 0.602416i \(-0.205795\pi\)
\(578\) −20.5173 + 24.4516i −0.853408 + 1.01705i
\(579\) 0 0
\(580\) 2.61850 7.19428i 0.108728 0.298726i
\(581\) −5.31223 29.4121i −0.220388 1.22022i
\(582\) 0 0
\(583\) −33.2016 + 12.0844i −1.37507 + 0.500485i
\(584\) −6.08210 −0.251679
\(585\) 0 0
\(586\) 2.08781i 0.0862465i
\(587\) 24.4251 + 20.4951i 1.00813 + 0.845924i 0.988090 0.153875i \(-0.0491752\pi\)
0.0200431 + 0.999799i \(0.493620\pi\)
\(588\) 0 0
\(589\) 4.38979 + 24.8957i 0.180878 + 1.02581i
\(590\) 1.90362 5.23016i 0.0783708 0.215322i
\(591\) 0 0
\(592\) −7.90199 + 44.8144i −0.324770 + 1.84186i
\(593\) 2.99491 + 5.18734i 0.122986 + 0.213018i 0.920944 0.389695i \(-0.127420\pi\)
−0.797958 + 0.602713i \(0.794086\pi\)
\(594\) 0 0
\(595\) 0.562749 + 0.965426i 0.0230705 + 0.0395786i
\(596\) 6.23273 + 17.1243i 0.255303 + 0.701438i
\(597\) 0 0
\(598\) −25.9416 + 4.57421i −1.06083 + 0.187053i
\(599\) −2.80083 + 7.69521i −0.114439 + 0.314418i −0.983668 0.179991i \(-0.942393\pi\)
0.869230 + 0.494409i \(0.164615\pi\)
\(600\) 0 0
\(601\) 11.1245 13.2576i 0.453777 0.540791i −0.489847 0.871808i \(-0.662948\pi\)
0.943625 + 0.331018i \(0.107392\pi\)
\(602\) −38.6845 + 22.5493i −1.57666 + 0.919040i
\(603\) 0 0
\(604\) −4.92588 + 8.53187i −0.200431 + 0.347157i
\(605\) −0.844079 0.708266i −0.0343167 0.0287951i
\(606\) 0 0
\(607\) −19.3178 + 3.40626i −0.784087 + 0.138256i −0.551339 0.834281i \(-0.685883\pi\)
−0.232748 + 0.972537i \(0.574772\pi\)
\(608\) −24.9973 9.09826i −1.01377 0.368983i
\(609\) 0 0
\(610\) 0.0182216 0.103340i 0.000737771 0.00418411i
\(611\) −11.4437 6.60701i −0.462961 0.267291i
\(612\) 0 0
\(613\) −13.9117 24.0958i −0.561889 0.973220i −0.997332 0.0730039i \(-0.976741\pi\)
0.435443 0.900216i \(-0.356592\pi\)
\(614\) 2.26399 12.8397i 0.0913674 0.518170i
\(615\) 0 0
\(616\) 1.19453 + 6.61376i 0.0481291 + 0.266476i
\(617\) 18.1901 + 21.6782i 0.732308 + 0.872730i 0.995764 0.0919408i \(-0.0293071\pi\)
−0.263457 + 0.964671i \(0.584863\pi\)
\(618\) 0 0
\(619\) −28.6553 5.05271i −1.15176 0.203086i −0.435014 0.900424i \(-0.643256\pi\)
−0.716742 + 0.697338i \(0.754368\pi\)
\(620\) 8.81223 + 5.08774i 0.353908 + 0.204329i
\(621\) 0 0
\(622\) 42.4655i 1.70271i
\(623\) −1.36256 + 7.91973i −0.0545900 + 0.317297i
\(624\) 0 0
\(625\) −12.6294 4.59671i −0.505175 0.183869i
\(626\) −1.80762 0.657921i −0.0722472 0.0262958i
\(627\) 0 0
\(628\) 7.61699 + 1.34308i 0.303951 + 0.0535947i
\(629\) −2.30512 + 3.99258i −0.0919110 + 0.159194i
\(630\) 0 0
\(631\) 3.11061 + 5.38773i 0.123831 + 0.214482i 0.921275 0.388911i \(-0.127149\pi\)
−0.797444 + 0.603393i \(0.793815\pi\)
\(632\) 2.34847 + 6.45238i 0.0934172 + 0.256662i
\(633\) 0 0
\(634\) −36.2160 + 30.3888i −1.43832 + 1.20689i
\(635\) 1.29425 + 7.34005i 0.0513607 + 0.291281i
\(636\) 0 0
\(637\) −17.6442 + 21.3858i −0.699087 + 0.847338i
\(638\) 30.1838 17.4266i 1.19499 0.689926i
\(639\) 0 0
\(640\) 4.46184 2.57605i 0.176370 0.101827i
\(641\) 2.18684 + 6.00829i 0.0863749 + 0.237313i 0.975359 0.220626i \(-0.0708100\pi\)
−0.888984 + 0.457939i \(0.848588\pi\)
\(642\) 0 0
\(643\) −2.20568 + 0.388920i −0.0869834 + 0.0153375i −0.216970 0.976178i \(-0.569618\pi\)
0.129987 + 0.991516i \(0.458506\pi\)
\(644\) 5.06086 14.0864i 0.199426 0.555082i
\(645\) 0 0
\(646\) −2.47379 2.07576i −0.0973300 0.0816696i
\(647\) −13.4891 + 23.3638i −0.530311 + 0.918525i 0.469064 + 0.883164i \(0.344591\pi\)
−0.999375 + 0.0353609i \(0.988742\pi\)
\(648\) 0 0
\(649\) 9.81311 5.66560i 0.385198 0.222394i
\(650\) 29.6272 10.7834i 1.16208 0.422961i
\(651\) 0 0
\(652\) 9.86695 8.27936i 0.386420 0.324245i
\(653\) 14.6649 + 17.4769i 0.573880 + 0.683924i 0.972423 0.233226i \(-0.0749283\pi\)
−0.398542 + 0.917150i \(0.630484\pi\)
\(654\) 0 0
\(655\) −17.5979 + 6.40512i −0.687607 + 0.250269i
\(656\) 13.3343 0.520617
\(657\) 0 0
\(658\) 14.5054 8.45521i 0.565478 0.329618i
\(659\) −21.2918 3.75431i −0.829409 0.146247i −0.257203 0.966357i \(-0.582801\pi\)
−0.572206 + 0.820110i \(0.693912\pi\)
\(660\) 0 0
\(661\) 18.7716 + 22.3711i 0.730130 + 0.870135i 0.995573 0.0939915i \(-0.0299627\pi\)
−0.265443 + 0.964127i \(0.585518\pi\)
\(662\) −32.4550 38.6784i −1.26140 1.50328i
\(663\) 0 0
\(664\) −8.08394 1.42542i −0.313718 0.0553169i
\(665\) 7.48780 4.36466i 0.290365 0.169254i
\(666\) 0 0
\(667\) 18.3276 0.709646
\(668\) −34.1642 + 12.4347i −1.32185 + 0.481114i
\(669\) 0 0
\(670\) −11.3155 13.4853i −0.437156 0.520982i
\(671\) 0.163651 0.137319i 0.00631766 0.00530115i
\(672\) 0 0
\(673\) 22.4647 8.17648i 0.865950 0.315180i 0.129424 0.991589i \(-0.458687\pi\)
0.736526 + 0.676409i \(0.236465\pi\)
\(674\) 40.8387 23.5782i 1.57305 0.908199i
\(675\) 0 0
\(676\) −2.17387 + 3.76525i −0.0836104 + 0.144817i
\(677\) −23.7257 19.9082i −0.911852 0.765135i 0.0606183 0.998161i \(-0.480693\pi\)
−0.972470 + 0.233026i \(0.925137\pi\)
\(678\) 0 0
\(679\) 4.56843 12.7158i 0.175320 0.487987i
\(680\) 0.302246 0.0532942i 0.0115906 0.00204374i
\(681\) 0 0
\(682\) 15.8434 + 43.5293i 0.606674 + 1.66682i
\(683\) 3.31809 1.91570i 0.126963 0.0733022i −0.435173 0.900347i \(-0.643313\pi\)
0.562136 + 0.827044i \(0.309980\pi\)
\(684\) 0 0
\(685\) 9.53964 5.50771i 0.364491 0.210439i
\(686\) −12.4601 32.9502i −0.475727 1.25804i
\(687\) 0 0
\(688\) 7.13518 + 40.4656i 0.272026 + 1.54274i
\(689\) −30.6658 + 25.7316i −1.16827 + 0.980298i
\(690\) 0 0
\(691\) 2.82846 + 7.77112i 0.107600 + 0.295627i 0.981794 0.189949i \(-0.0608321\pi\)
−0.874194 + 0.485576i \(0.838610\pi\)
\(692\) 6.26547 + 10.8521i 0.238177 + 0.412535i
\(693\) 0 0
\(694\) −17.8241 + 30.8723i −0.676594 + 1.17190i
\(695\) 15.9913 + 2.81969i 0.606583 + 0.106957i
\(696\) 0 0
\(697\) 1.26944 + 0.462038i 0.0480835 + 0.0175010i
\(698\) 43.4516 + 15.8151i 1.64467 + 0.598609i
\(699\) 0 0
\(700\) −3.03762 + 17.6558i −0.114811 + 0.667326i
\(701\) 19.8898i 0.751226i 0.926777 + 0.375613i \(0.122568\pi\)
−0.926777 + 0.375613i \(0.877432\pi\)
\(702\) 0 0
\(703\) 30.9663 + 17.8784i 1.16792 + 0.674296i
\(704\) −16.2070 2.85774i −0.610826 0.107705i
\(705\) 0 0
\(706\) −27.9732 33.3371i −1.05278 1.25466i
\(707\) −6.30852 34.9283i −0.237256 1.31361i
\(708\) 0 0
\(709\) 2.42708 13.7647i 0.0911511 0.516943i −0.904708 0.426032i \(-0.859911\pi\)
0.995859 0.0909111i \(-0.0289779\pi\)
\(710\) −2.18038 3.77652i −0.0818281 0.141730i
\(711\) 0 0
\(712\) 1.91139 + 1.10354i 0.0716325 + 0.0413571i
\(713\) −4.22989 + 23.9889i −0.158410 + 0.898390i
\(714\) 0 0
\(715\) −11.7454 4.27499i −0.439254 0.159876i
\(716\) 2.98137 0.525696i 0.111419 0.0196462i
\(717\) 0 0
\(718\) −12.1704 10.2121i −0.454194 0.381114i
\(719\) 15.7165 27.2219i 0.586128 1.01520i −0.408606 0.912711i \(-0.633985\pi\)
0.994734 0.102493i \(-0.0326818\pi\)
\(720\) 0 0
\(721\) 34.4583 20.0859i 1.28330 0.748036i
\(722\) 7.13076 8.49811i 0.265380 0.316267i
\(723\) 0 0
\(724\) 11.6159 31.9146i 0.431703 1.18610i
\(725\) −21.6031 + 3.80921i −0.802319 + 0.141471i
\(726\) 0 0
\(727\) 9.57818 + 26.3158i 0.355235 + 0.976000i 0.980661 + 0.195716i \(0.0627031\pi\)
−0.625426 + 0.780284i \(0.715075\pi\)
\(728\) 3.83464 + 6.57853i 0.142121 + 0.243817i
\(729\) 0 0
\(730\) 7.18617 + 12.4468i 0.265972 + 0.460677i
\(731\) −0.722872 + 4.09961i −0.0267364 + 0.151630i
\(732\) 0 0
\(733\) −8.51889 + 23.4055i −0.314653 + 0.864501i 0.677049 + 0.735938i \(0.263259\pi\)
−0.991701 + 0.128563i \(0.958964\pi\)
\(734\) 3.22409 + 18.2847i 0.119003 + 0.674900i
\(735\) 0 0
\(736\) −19.6357 16.4763i −0.723780 0.607324i
\(737\) 35.8388i 1.32014i
\(738\) 0 0
\(739\) 46.5319 1.71170 0.855851 0.517222i \(-0.173034\pi\)
0.855851 + 0.517222i \(0.173034\pi\)
\(740\) 13.5246 4.92257i 0.497176 0.180957i
\(741\) 0 0
\(742\) −9.04044 50.0541i −0.331885 1.83754i
\(743\) 11.9890 32.9395i 0.439834 1.20843i −0.499767 0.866160i \(-0.666581\pi\)
0.939600 0.342273i \(-0.111197\pi\)
\(744\) 0 0
\(745\) −6.53564 + 7.78887i −0.239447 + 0.285362i
\(746\) 20.1588i 0.738067i
\(747\) 0 0
\(748\) −2.29176 1.32315i −0.0837949 0.0483790i
\(749\) 13.5622 + 36.7856i 0.495551 + 1.34411i
\(750\) 0 0
\(751\) 3.14628 2.64004i 0.114809 0.0963364i −0.583576 0.812059i \(-0.698347\pi\)
0.698385 + 0.715722i \(0.253902\pi\)
\(752\) −2.67545 15.1732i −0.0975636 0.553311i
\(753\) 0 0
\(754\) 25.3826 30.2498i 0.924381 1.10163i
\(755\) −5.49677 −0.200048
\(756\) 0 0
\(757\) −15.6872 −0.570161 −0.285081 0.958504i \(-0.592020\pi\)
−0.285081 + 0.958504i \(0.592020\pi\)
\(758\) −7.65941 + 9.12813i −0.278202 + 0.331549i
\(759\) 0 0
\(760\) −0.413348 2.34421i −0.0149937 0.0850335i
\(761\) 21.5384 18.0728i 0.780766 0.655140i −0.162676 0.986680i \(-0.552012\pi\)
0.943441 + 0.331539i \(0.107568\pi\)
\(762\) 0 0
\(763\) −6.03357 5.02020i −0.218430 0.181744i
\(764\) −14.3632 8.29258i −0.519641 0.300015i
\(765\) 0 0
\(766\) 15.9111i 0.574890i
\(767\) 8.25220 9.83459i 0.297970 0.355107i
\(768\) 0 0
\(769\) −9.49574 + 26.0893i −0.342425 + 0.940806i 0.642263 + 0.766484i \(0.277996\pi\)
−0.984689 + 0.174322i \(0.944227\pi\)
\(770\) 12.1235 10.2589i 0.436899 0.369706i
\(771\) 0 0
\(772\) −15.3297 + 5.57954i −0.551726 + 0.200812i
\(773\) 13.0962 0.471036 0.235518 0.971870i \(-0.424321\pi\)
0.235518 + 0.971870i \(0.424321\pi\)
\(774\) 0 0
\(775\) 29.1553i 1.04729i
\(776\) −2.84272 2.38532i −0.102048 0.0856280i
\(777\) 0 0
\(778\) −6.41839 36.4005i −0.230110 1.30502i
\(779\) 3.58355 9.84573i 0.128394 0.352760i
\(780\) 0 0
\(781\) 1.54163 8.74300i 0.0551637 0.312849i
\(782\) −1.55584 2.69479i −0.0556366 0.0963654i
\(783\) 0 0
\(784\) −32.3256 + 0.268580i −1.15449 + 0.00959214i
\(785\) 1.47597 + 4.05519i 0.0526796 + 0.144736i
\(786\) 0 0
\(787\) 46.4006 8.18167i 1.65400 0.291645i 0.732717 0.680533i \(-0.238252\pi\)
0.921285 + 0.388888i \(0.127141\pi\)
\(788\) 14.7110 40.4181i 0.524057 1.43983i
\(789\) 0 0
\(790\) 10.4298 12.4297i 0.371076 0.442231i
\(791\) −0.133931 32.2399i −0.00476205 1.14632i
\(792\) 0 0
\(793\) 0.121021 0.209614i 0.00429757 0.00744362i
\(794\) 41.3352 + 34.6844i 1.46693 + 1.23090i
\(795\) 0 0
\(796\) −31.0437 + 5.47383i −1.10031 + 0.194015i
\(797\) −35.7462 13.0105i −1.26619 0.460857i −0.380352 0.924842i \(-0.624197\pi\)
−0.885843 + 0.463985i \(0.846419\pi\)
\(798\) 0 0
\(799\) 0.271052 1.53721i 0.00958914 0.0543827i
\(800\) 26.5694 + 15.3399i 0.939371 + 0.542346i
\(801\) 0 0
\(802\) 18.5680 + 32.1608i 0.655660 + 1.13564i
\(803\) −5.08096 + 28.8155i −0.179303 + 1.01688i
\(804\) 0 0
\(805\) 8.21835 1.48435i 0.289659 0.0523163i
\(806\) 33.7357 + 40.2047i 1.18829 + 1.41615i
\(807\) 0 0
\(808\) −9.60006 1.69275i −0.337729 0.0595507i
\(809\) −7.26934 4.19695i −0.255576 0.147557i 0.366739 0.930324i \(-0.380474\pi\)
−0.622315 + 0.782767i \(0.713808\pi\)
\(810\) 0 0
\(811\) 36.2880i 1.27425i −0.770762 0.637123i \(-0.780124\pi\)
0.770762 0.637123i \(-0.219876\pi\)
\(812\) 7.76179 + 21.0528i 0.272385 + 0.738809i
\(813\) 0 0
\(814\) 61.5697 + 22.4095i 2.15802 + 0.785454i
\(815\) 6.75318 + 2.45796i 0.236554 + 0.0860985i
\(816\) 0 0
\(817\) 31.7964 + 5.60657i 1.11242 + 0.196149i
\(818\) 33.2557 57.6006i 1.16276 2.01396i
\(819\) 0 0
\(820\) −2.10869 3.65237i −0.0736388 0.127546i
\(821\) −17.4948 48.0666i −0.610573 1.67754i −0.728950 0.684567i \(-0.759991\pi\)
0.118377 0.992969i \(-0.462231\pi\)
\(822\) 0 0
\(823\) 3.25771 2.73354i 0.113556 0.0952852i −0.584241 0.811580i \(-0.698608\pi\)
0.697798 + 0.716295i \(0.254163\pi\)
\(824\) −1.90220 10.7879i −0.0662661 0.375814i
\(825\) 0 0
\(826\) 5.64273 + 15.3051i 0.196336 + 0.532534i
\(827\) −15.9647 + 9.21722i −0.555147 + 0.320514i −0.751195 0.660080i \(-0.770522\pi\)
0.196048 + 0.980594i \(0.437189\pi\)
\(828\) 0 0
\(829\) 2.14109 1.23616i 0.0743630 0.0429335i −0.462357 0.886694i \(-0.652996\pi\)
0.536720 + 0.843760i \(0.319663\pi\)
\(830\) 6.63434 + 18.2277i 0.230281 + 0.632693i
\(831\) 0 0
\(832\) −18.3624 + 3.23779i −0.636602 + 0.112250i
\(833\) −3.08674 1.09453i −0.106949 0.0379231i
\(834\) 0 0
\(835\) −15.5393 13.0391i −0.537761 0.451235i
\(836\) −10.2623 + 17.7748i −0.354928 + 0.614754i
\(837\) 0 0
\(838\) 66.8167 38.5766i 2.30814 1.33261i
\(839\) 11.0811 4.03321i 0.382563 0.139242i −0.143578 0.989639i \(-0.545861\pi\)
0.526141 + 0.850397i \(0.323638\pi\)
\(840\) 0 0
\(841\) 1.16867 0.980630i 0.0402989 0.0338148i
\(842\) −19.3527 23.0637i −0.666940 0.794828i
\(843\) 0 0
\(844\) −8.10925 + 2.95152i −0.279132 + 0.101596i
\(845\) −2.42581 −0.0834505
\(846\) 0 0
\(847\) 3.22930 0.0134152i 0.110960 0.000460952i
\(848\) −45.9667 8.10517i −1.57850 0.278333i
\(849\) 0 0
\(850\) 2.39398 + 2.85304i 0.0821130 + 0.0978584i
\(851\) 22.1468 + 26.3935i 0.759182 + 0.904758i
\(852\) 0 0
\(853\) −14.3072 2.52275i −0.489869 0.0863772i −0.0767431 0.997051i \(-0.524452\pi\)
−0.413126 + 0.910674i \(0.635563\pi\)
\(854\) 0.154874 + 0.265695i 0.00529969 + 0.00909191i
\(855\) 0 0
\(856\) 10.7678 0.368036
\(857\) −15.5951 + 5.67614i −0.532717 + 0.193893i −0.594351 0.804206i \(-0.702591\pi\)
0.0616339 + 0.998099i \(0.480369\pi\)
\(858\) 0 0
\(859\) −14.0869 16.7881i −0.480639 0.572803i 0.470172 0.882575i \(-0.344192\pi\)
−0.950811 + 0.309772i \(0.899747\pi\)
\(860\) 9.95548 8.35364i 0.339479 0.284857i
\(861\) 0 0
\(862\) −14.2039 + 5.16980i −0.483787 + 0.176084i
\(863\) 6.94716 4.01095i 0.236484 0.136534i −0.377076 0.926182i \(-0.623070\pi\)
0.613560 + 0.789648i \(0.289737\pi\)
\(864\) 0 0
\(865\) −3.49580 + 6.05491i −0.118861 + 0.205873i
\(866\) −24.0066 20.1439i −0.815776 0.684517i
\(867\) 0 0
\(868\) −29.3473 + 5.30052i −0.996112 + 0.179911i
\(869\) 32.5317 5.73622i 1.10356 0.194588i
\(870\) 0 0
\(871\) −13.8877 38.1563i −0.470568 1.29288i
\(872\) −1.86689 + 1.07785i −0.0632209 + 0.0365006i
\(873\) 0 0
\(874\) −20.9007 + 12.0670i −0.706976 + 0.408173i
\(875\) −20.5836 + 7.58879i −0.695852 + 0.256548i
\(876\) 0 0
\(877\) 6.25755 + 35.4883i 0.211302 + 1.19836i 0.887209 + 0.461368i \(0.152641\pi\)
−0.675906 + 0.736988i \(0.736248\pi\)
\(878\) 8.89041 7.45994i 0.300037 0.251761i
\(879\) 0 0
\(880\) −4.98456 13.6950i −0.168030 0.461657i
\(881\) −21.1819 36.6881i −0.713636 1.23605i −0.963483 0.267769i \(-0.913714\pi\)
0.249847 0.968285i \(-0.419620\pi\)
\(882\) 0 0
\(883\) −3.68137 + 6.37633i −0.123888 + 0.214580i −0.921298 0.388858i \(-0.872870\pi\)
0.797410 + 0.603438i \(0.206203\pi\)
\(884\) −2.95268 0.520636i −0.0993092 0.0175109i
\(885\) 0 0
\(886\) −35.5817 12.9507i −1.19539 0.435087i
\(887\) −0.457707 0.166592i −0.0153683 0.00559360i 0.334325 0.942458i \(-0.391492\pi\)
−0.349693 + 0.936864i \(0.613714\pi\)
\(888\) 0 0
\(889\) −16.7916 13.9714i −0.563173 0.468585i
\(890\) 5.21548i 0.174823i
\(891\) 0 0
\(892\) 11.8738 + 6.85534i 0.397564 + 0.229534i
\(893\) −11.9226 2.10227i −0.398974 0.0703498i
\(894\) 0 0
\(895\) 1.08574 + 1.29393i 0.0362923 + 0.0432515i
\(896\) −5.10540 + 14.2104i −0.170559 + 0.474735i
\(897\) 0 0
\(898\) 0.157234 0.891718i 0.00524696 0.0297570i
\(899\) −18.2579 31.6237i −0.608936 1.05471i
\(900\) 0 0
\(901\) −4.09524 2.36439i −0.136432 0.0787691i
\(902\) 3.33392 18.9076i 0.111007 0.629554i
\(903\) 0 0
\(904\) −8.32066 3.02847i −0.276741 0.100726i
\(905\) 18.6616 3.29054i 0.620331 0.109381i
\(906\) 0 0
\(907\) −1.78620 1.49880i −0.0593098 0.0497668i 0.612651 0.790354i \(-0.290103\pi\)
−0.671961 + 0.740587i \(0.734548\pi\)
\(908\) 18.1954 31.5154i 0.603837 1.04588i
\(909\) 0 0
\(910\) 8.93202 15.6202i 0.296093 0.517805i
\(911\) 17.0700 20.3432i 0.565553 0.674000i −0.405159 0.914246i \(-0.632784\pi\)
0.970712 + 0.240246i \(0.0772281\pi\)
\(912\) 0 0
\(913\) −13.5066 + 37.1090i −0.447002 + 1.22813i
\(914\) 21.6469 3.81694i 0.716017 0.126253i
\(915\) 0 0
\(916\) −0.438822 1.20565i −0.0144991 0.0398359i
\(917\) 27.2451 47.6460i 0.899713 1.57341i
\(918\) 0 0
\(919\) −4.06315 7.03758i −0.134031 0.232148i 0.791196 0.611563i \(-0.209459\pi\)
−0.925227 + 0.379414i \(0.876125\pi\)
\(920\) 0.398291 2.25882i 0.0131313 0.0744711i
\(921\) 0 0
\(922\) 13.1727 36.1917i 0.433820 1.19191i
\(923\) −1.74665 9.90573i −0.0574916 0.326051i
\(924\) 0 0
\(925\) −31.5905 26.5076i −1.03869 0.871565i
\(926\) 11.7791i 0.387086i
\(927\) 0 0
\(928\) 38.4251 1.26137
\(929\) −19.2006 + 6.98845i −0.629952 + 0.229284i −0.637210 0.770690i \(-0.719912\pi\)
0.00725854 + 0.999974i \(0.497690\pi\)
\(930\) 0 0
\(931\) −8.48910 + 23.9407i −0.278219 + 0.784623i
\(932\) −4.80185 + 13.1930i −0.157290 + 0.432150i
\(933\) 0 0
\(934\) −4.65456 + 5.54709i −0.152302 + 0.181506i
\(935\) 1.47649i 0.0482865i
\(936\) 0 0
\(937\) −29.2827 16.9064i −0.956625 0.552308i −0.0614921 0.998108i \(-0.519586\pi\)
−0.895133 + 0.445800i \(0.852919\pi\)
\(938\) 50.8459 + 8.74786i 1.66018 + 0.285628i
\(939\) 0 0
\(940\) −3.73297 + 3.13233i −0.121756 + 0.102165i
\(941\) 7.81855 + 44.3412i 0.254878 + 1.44548i 0.796387 + 0.604788i \(0.206742\pi\)
−0.541509 + 0.840695i \(0.682147\pi\)
\(942\) 0 0
\(943\) 6.48955 7.73394i 0.211329 0.251852i
\(944\) 14.9691 0.487201
\(945\) 0 0
\(946\) 59.1629 1.92355
\(947\) −0.805471 + 0.959923i −0.0261743 + 0.0311933i −0.778973 0.627058i \(-0.784259\pi\)
0.752799 + 0.658251i \(0.228703\pi\)
\(948\) 0 0
\(949\) 5.75667 + 32.6477i 0.186870 + 1.05979i
\(950\) 22.1281 18.5676i 0.717929 0.602414i
\(951\) 0 0
\(952\) −0.575309 + 0.691440i −0.0186459 + 0.0224097i
\(953\) −41.3947 23.8992i −1.34091 0.774172i −0.353965 0.935259i \(-0.615167\pi\)
−0.986940 + 0.161086i \(0.948500\pi\)
\(954\) 0 0
\(955\) 9.25365i 0.299441i
\(956\) −23.3076 + 27.7770i −0.753823 + 0.898371i
\(957\) 0 0
\(958\) 19.5540 53.7242i 0.631762 1.73575i
\(959\) −10.9156 + 30.3825i −0.352483 + 0.981101i
\(960\) 0 0
\(961\) 16.4754 5.99657i 0.531465 0.193438i
\(962\) 74.2348 2.39342
\(963\) 0 0
\(964\) 17.0123i 0.547930i
\(965\) −6.97259 5.85070i −0.224456 0.188341i
\(966\) 0 0
\(967\) −3.01993 17.1269i −0.0971143 0.550763i −0.994079 0.108660i \(-0.965344\pi\)
0.896965 0.442102i \(-0.145767\pi\)
\(968\) 0.303346 0.833438i 0.00974992 0.0267877i
\(969\) 0 0
\(970\) −1.52273 + 8.63586i −0.0488921 + 0.277281i
\(971\) 13.6117 + 23.5762i 0.436821 + 0.756596i 0.997442 0.0714765i \(-0.0227711\pi\)
−0.560622 + 0.828072i \(0.689438\pi\)
\(972\) 0 0
\(973\) −41.1149 + 23.9660i −1.31808 + 0.768314i
\(974\) 24.7139 + 67.9008i 0.791884 + 2.17568i
\(975\) 0 0
\(976\) 0.277929 0.0490063i 0.00889628 0.00156865i
\(977\) 7.73653 21.2560i 0.247514 0.680038i −0.752262 0.658864i \(-0.771037\pi\)
0.999776 0.0211742i \(-0.00674047\pi\)
\(978\) 0 0
\(979\) 6.82510 8.13384i 0.218131 0.259959i
\(980\) 5.18556 + 8.81176i 0.165647 + 0.281482i
\(981\) 0 0
\(982\) 29.9500 51.8749i 0.955742 1.65539i
\(983\) 16.9151 + 14.1935i 0.539509 + 0.452702i 0.871370 0.490626i \(-0.163232\pi\)
−0.331861 + 0.943328i \(0.607676\pi\)
\(984\) 0 0
\(985\) 23.6339 4.16729i 0.753037 0.132781i
\(986\) 4.38332 + 1.59540i 0.139593 + 0.0508078i
\(987\) 0 0
\(988\) −4.03804 + 22.9008i −0.128467 + 0.728573i
\(989\) 26.9428 + 15.5554i 0.856730 + 0.494633i
\(990\) 0 0
\(991\) −5.44079 9.42373i −0.172832 0.299355i 0.766577 0.642153i \(-0.221959\pi\)
−0.939409 + 0.342798i \(0.888625\pi\)
\(992\) −8.86827 + 50.2944i −0.281568 + 1.59685i
\(993\) 0 0
\(994\) 12.0277 + 4.32123i 0.381496 + 0.137061i
\(995\) −11.3053 13.4731i −0.358402 0.427127i
\(996\) 0 0
\(997\) 5.88948 + 1.03847i 0.186522 + 0.0328888i 0.266129 0.963938i \(-0.414255\pi\)
−0.0796069 + 0.996826i \(0.525367\pi\)
\(998\) −30.9846 17.8890i −0.980801 0.566266i
\(999\) 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 567.2.ba.a.143.19 132
3.2 odd 2 189.2.ba.a.101.4 132
7.5 odd 6 567.2.bd.a.467.4 132
21.5 even 6 189.2.bd.a.47.19 yes 132
27.4 even 9 189.2.bd.a.185.19 yes 132
27.23 odd 18 567.2.bd.a.17.4 132
189.131 even 18 inner 567.2.ba.a.341.19 132
189.166 odd 18 189.2.ba.a.131.4 yes 132
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
189.2.ba.a.101.4 132 3.2 odd 2
189.2.ba.a.131.4 yes 132 189.166 odd 18
189.2.bd.a.47.19 yes 132 21.5 even 6
189.2.bd.a.185.19 yes 132 27.4 even 9
567.2.ba.a.143.19 132 1.1 even 1 trivial
567.2.ba.a.341.19 132 189.131 even 18 inner
567.2.bd.a.17.4 132 27.23 odd 18
567.2.bd.a.467.4 132 7.5 odd 6