Properties

Label 567.2.e.f.163.2
Level $567$
Weight $2$
Character 567.163
Analytic conductor $4.528$
Analytic rank $0$
Dimension $10$
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(163,567)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(567, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([0, 2]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("567.163");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 567 = 3^{4} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 567.e (of order \(3\), 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: \(4.52751779461\)
Analytic rank: \(0\)
Dimension: \(10\)
Relative dimension: \(5\) over \(\Q(\zeta_{3})\)
Coefficient field: 10.0.991381711347.1
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{10} - 2x^{9} + 9x^{8} - 8x^{7} + 40x^{6} - 36x^{5} + 90x^{4} - 3x^{3} + 36x^{2} - 9x + 9 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{4}]\)
Coefficient ring index: \( 3^{2} \)
Twist minimal: no (minimal twist has level 63)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 163.2
Root \(-0.335166 + 0.580525i\) of defining polynomial
Character \(\chi\) \(=\) 567.163
Dual form 567.2.e.f.487.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.335166 + 0.580525i) q^{2} +(0.775327 + 1.34291i) q^{4} +(-0.712469 + 1.23403i) q^{5} +(0.145107 - 2.64177i) q^{7} -2.38012 q^{8} +O(q^{10})\) \(q+(-0.335166 + 0.580525i) q^{2} +(0.775327 + 1.34291i) q^{4} +(-0.712469 + 1.23403i) q^{5} +(0.145107 - 2.64177i) q^{7} -2.38012 q^{8} +(-0.477591 - 0.827212i) q^{10} +(2.46539 + 4.27018i) q^{11} +2.75460 q^{13} +(1.48498 + 0.969670i) q^{14} +(-0.752918 + 1.30409i) q^{16} +(0.559839 + 0.969670i) q^{17} +(-2.00752 + 3.47713i) q^{19} -2.20958 q^{20} -3.30526 q^{22} +(-2.71830 + 4.70824i) q^{23} +(1.48478 + 2.57171i) q^{25} +(-0.923251 + 1.59912i) q^{26} +(3.66015 - 1.85337i) q^{28} -6.81109 q^{29} +(-1.25292 - 2.17012i) q^{31} +(-2.88483 - 4.99666i) q^{32} -0.750557 q^{34} +(3.15664 + 2.06124i) q^{35} +(0.709787 - 1.22939i) q^{37} +(-1.34571 - 2.33083i) q^{38} +(1.69576 - 2.93714i) q^{40} -0.248768 q^{41} +0.996627 q^{43} +(-3.82296 + 6.62156i) q^{44} +(-1.82217 - 3.15609i) q^{46} +(4.73790 - 8.20628i) q^{47} +(-6.95789 - 0.766676i) q^{49} -1.99059 q^{50} +(2.13572 + 3.69917i) q^{52} +(-0.410229 - 0.710537i) q^{53} -7.02604 q^{55} +(-0.345371 + 6.28773i) q^{56} +(2.28285 - 3.95401i) q^{58} +(3.29204 + 5.70197i) q^{59} +(-0.0376322 + 0.0651809i) q^{61} +1.67974 q^{62} +0.855913 q^{64} +(-1.96257 + 3.39927i) q^{65} +(6.29385 + 10.9013i) q^{67} +(-0.868117 + 1.50362i) q^{68} +(-2.25460 + 1.14165i) q^{70} +0.0804951 q^{71} +(5.34551 + 9.25869i) q^{73} +(0.475793 + 0.824098i) q^{74} -6.22595 q^{76} +(11.6386 - 5.89335i) q^{77} +(0.922457 - 1.59774i) q^{79} +(-1.07286 - 1.85825i) q^{80} +(0.0833788 - 0.144416i) q^{82} +14.4717 q^{83} -1.59547 q^{85} +(-0.334036 + 0.578567i) q^{86} +(-5.86792 - 10.1635i) q^{88} +(6.76292 - 11.7137i) q^{89} +(0.399711 - 7.27703i) q^{91} -8.43030 q^{92} +(3.17597 + 5.50094i) q^{94} +(-2.86059 - 4.95469i) q^{95} -5.40319 q^{97} +(2.77712 - 3.78226i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 10 q + 2 q^{2} - 4 q^{4} + 4 q^{5} + 5 q^{7} - 6 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 10 q + 2 q^{2} - 4 q^{4} + 4 q^{5} + 5 q^{7} - 6 q^{8} - 7 q^{10} + 4 q^{11} + 16 q^{13} + 4 q^{14} + 2 q^{16} + 12 q^{17} + q^{19} - 10 q^{20} + 2 q^{22} + 3 q^{23} - q^{25} + 11 q^{26} - 2 q^{28} - 14 q^{29} - 3 q^{31} - 2 q^{32} - 6 q^{34} + 5 q^{35} + 20 q^{38} - 3 q^{40} - 10 q^{41} + 14 q^{43} - 10 q^{44} + 3 q^{46} + 27 q^{47} - 17 q^{49} - 38 q^{50} - 10 q^{52} - 21 q^{53} + 4 q^{55} + 27 q^{56} - 10 q^{58} + 30 q^{59} - 14 q^{61} - 12 q^{62} - 50 q^{64} - 11 q^{65} - 2 q^{67} + 27 q^{68} - 11 q^{70} - 6 q^{71} + 15 q^{73} - 36 q^{74} - 10 q^{76} + 20 q^{77} - 4 q^{79} + 20 q^{80} - 5 q^{82} - 18 q^{83} + 12 q^{85} - 8 q^{86} - 18 q^{88} + 28 q^{89} - 4 q^{91} - 54 q^{92} - 3 q^{94} - 14 q^{95} + 24 q^{97} + 59 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

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

\(n\) \(325\) \(407\)
\(\chi(n)\) \(e\left(\frac{1}{3}\right)\) \(1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.335166 + 0.580525i −0.236998 + 0.410493i −0.959852 0.280508i \(-0.909497\pi\)
0.722853 + 0.691002i \(0.242830\pi\)
\(3\) 0 0
\(4\) 0.775327 + 1.34291i 0.387664 + 0.671453i
\(5\) −0.712469 + 1.23403i −0.318626 + 0.551876i −0.980202 0.198002i \(-0.936555\pi\)
0.661576 + 0.749878i \(0.269888\pi\)
\(6\) 0 0
\(7\) 0.145107 2.64177i 0.0548451 0.998495i
\(8\) −2.38012 −0.841499
\(9\) 0 0
\(10\) −0.477591 0.827212i −0.151028 0.261587i
\(11\) 2.46539 + 4.27018i 0.743342 + 1.28751i 0.950965 + 0.309297i \(0.100094\pi\)
−0.207623 + 0.978209i \(0.566573\pi\)
\(12\) 0 0
\(13\) 2.75460 0.763990 0.381995 0.924164i \(-0.375237\pi\)
0.381995 + 0.924164i \(0.375237\pi\)
\(14\) 1.48498 + 0.969670i 0.396877 + 0.259155i
\(15\) 0 0
\(16\) −0.752918 + 1.30409i −0.188230 + 0.326023i
\(17\) 0.559839 + 0.969670i 0.135781 + 0.235180i 0.925896 0.377780i \(-0.123312\pi\)
−0.790115 + 0.612959i \(0.789979\pi\)
\(18\) 0 0
\(19\) −2.00752 + 3.47713i −0.460557 + 0.797709i −0.998989 0.0449606i \(-0.985684\pi\)
0.538431 + 0.842669i \(0.319017\pi\)
\(20\) −2.20958 −0.494078
\(21\) 0 0
\(22\) −3.30526 −0.704684
\(23\) −2.71830 + 4.70824i −0.566806 + 0.981736i 0.430073 + 0.902794i \(0.358488\pi\)
−0.996879 + 0.0789424i \(0.974846\pi\)
\(24\) 0 0
\(25\) 1.48478 + 2.57171i 0.296955 + 0.514342i
\(26\) −0.923251 + 1.59912i −0.181064 + 0.313613i
\(27\) 0 0
\(28\) 3.66015 1.85337i 0.691704 0.350254i
\(29\) −6.81109 −1.26479 −0.632394 0.774647i \(-0.717928\pi\)
−0.632394 + 0.774647i \(0.717928\pi\)
\(30\) 0 0
\(31\) −1.25292 2.17012i −0.225031 0.389765i 0.731298 0.682058i \(-0.238915\pi\)
−0.956329 + 0.292294i \(0.905582\pi\)
\(32\) −2.88483 4.99666i −0.509970 0.883294i
\(33\) 0 0
\(34\) −0.750557 −0.128719
\(35\) 3.15664 + 2.06124i 0.533570 + 0.348414i
\(36\) 0 0
\(37\) 0.709787 1.22939i 0.116688 0.202110i −0.801765 0.597639i \(-0.796106\pi\)
0.918453 + 0.395529i \(0.129439\pi\)
\(38\) −1.34571 2.33083i −0.218303 0.378111i
\(39\) 0 0
\(40\) 1.69576 2.93714i 0.268123 0.464403i
\(41\) −0.248768 −0.0388511 −0.0194256 0.999811i \(-0.506184\pi\)
−0.0194256 + 0.999811i \(0.506184\pi\)
\(42\) 0 0
\(43\) 0.996627 0.151984 0.0759921 0.997108i \(-0.475788\pi\)
0.0759921 + 0.997108i \(0.475788\pi\)
\(44\) −3.82296 + 6.62156i −0.576333 + 0.998238i
\(45\) 0 0
\(46\) −1.82217 3.15609i −0.268664 0.465340i
\(47\) 4.73790 8.20628i 0.691093 1.19701i −0.280387 0.959887i \(-0.590463\pi\)
0.971480 0.237122i \(-0.0762040\pi\)
\(48\) 0 0
\(49\) −6.95789 0.766676i −0.993984 0.109525i
\(50\) −1.99059 −0.281512
\(51\) 0 0
\(52\) 2.13572 + 3.69917i 0.296171 + 0.512983i
\(53\) −0.410229 0.710537i −0.0563493 0.0975998i 0.836475 0.548005i \(-0.184613\pi\)
−0.892824 + 0.450406i \(0.851279\pi\)
\(54\) 0 0
\(55\) −7.02604 −0.947392
\(56\) −0.345371 + 6.28773i −0.0461521 + 0.840233i
\(57\) 0 0
\(58\) 2.28285 3.95401i 0.299753 0.519187i
\(59\) 3.29204 + 5.70197i 0.428586 + 0.742334i 0.996748 0.0805836i \(-0.0256784\pi\)
−0.568161 + 0.822917i \(0.692345\pi\)
\(60\) 0 0
\(61\) −0.0376322 + 0.0651809i −0.00481831 + 0.00834556i −0.868425 0.495821i \(-0.834867\pi\)
0.863606 + 0.504167i \(0.168200\pi\)
\(62\) 1.67974 0.213328
\(63\) 0 0
\(64\) 0.855913 0.106989
\(65\) −1.96257 + 3.39927i −0.243427 + 0.421628i
\(66\) 0 0
\(67\) 6.29385 + 10.9013i 0.768916 + 1.33180i 0.938151 + 0.346226i \(0.112537\pi\)
−0.169235 + 0.985576i \(0.554130\pi\)
\(68\) −0.868117 + 1.50362i −0.105275 + 0.182341i
\(69\) 0 0
\(70\) −2.25460 + 1.14165i −0.269477 + 0.136453i
\(71\) 0.0804951 0.00955301 0.00477651 0.999989i \(-0.498480\pi\)
0.00477651 + 0.999989i \(0.498480\pi\)
\(72\) 0 0
\(73\) 5.34551 + 9.25869i 0.625644 + 1.08365i 0.988416 + 0.151769i \(0.0484971\pi\)
−0.362772 + 0.931878i \(0.618170\pi\)
\(74\) 0.475793 + 0.824098i 0.0553098 + 0.0957995i
\(75\) 0 0
\(76\) −6.22595 −0.714165
\(77\) 11.6386 5.89335i 1.32634 0.671610i
\(78\) 0 0
\(79\) 0.922457 1.59774i 0.103785 0.179760i −0.809456 0.587180i \(-0.800238\pi\)
0.913241 + 0.407420i \(0.133571\pi\)
\(80\) −1.07286 1.85825i −0.119950 0.207759i
\(81\) 0 0
\(82\) 0.0833788 0.144416i 0.00920765 0.0159481i
\(83\) 14.4717 1.58847 0.794236 0.607610i \(-0.207872\pi\)
0.794236 + 0.607610i \(0.207872\pi\)
\(84\) 0 0
\(85\) −1.59547 −0.173053
\(86\) −0.334036 + 0.578567i −0.0360200 + 0.0623885i
\(87\) 0 0
\(88\) −5.86792 10.1635i −0.625522 1.08344i
\(89\) 6.76292 11.7137i 0.716868 1.24165i −0.245366 0.969430i \(-0.578908\pi\)
0.962235 0.272222i \(-0.0877584\pi\)
\(90\) 0 0
\(91\) 0.399711 7.27703i 0.0419011 0.762840i
\(92\) −8.43030 −0.878920
\(93\) 0 0
\(94\) 3.17597 + 5.50094i 0.327576 + 0.567378i
\(95\) −2.86059 4.95469i −0.293491 0.508341i
\(96\) 0 0
\(97\) −5.40319 −0.548611 −0.274306 0.961643i \(-0.588448\pi\)
−0.274306 + 0.961643i \(0.588448\pi\)
\(98\) 2.77712 3.78226i 0.280532 0.382066i
\(99\) 0 0
\(100\) −2.30238 + 3.98783i −0.230238 + 0.398783i
\(101\) 2.56770 + 4.44739i 0.255496 + 0.442531i 0.965030 0.262139i \(-0.0844280\pi\)
−0.709534 + 0.704671i \(0.751095\pi\)
\(102\) 0 0
\(103\) 7.10561 12.3073i 0.700137 1.21267i −0.268282 0.963341i \(-0.586456\pi\)
0.968418 0.249332i \(-0.0802109\pi\)
\(104\) −6.55629 −0.642897
\(105\) 0 0
\(106\) 0.549980 0.0534188
\(107\) 3.83015 6.63401i 0.370274 0.641334i −0.619333 0.785128i \(-0.712597\pi\)
0.989608 + 0.143794i \(0.0459303\pi\)
\(108\) 0 0
\(109\) −0.849394 1.47119i −0.0813572 0.140915i 0.822476 0.568800i \(-0.192592\pi\)
−0.903833 + 0.427885i \(0.859259\pi\)
\(110\) 2.35489 4.07880i 0.224530 0.388898i
\(111\) 0 0
\(112\) 3.33586 + 2.17827i 0.315209 + 0.205827i
\(113\) 0.600703 0.0565093 0.0282547 0.999601i \(-0.491005\pi\)
0.0282547 + 0.999601i \(0.491005\pi\)
\(114\) 0 0
\(115\) −3.87341 6.70895i −0.361198 0.625613i
\(116\) −5.28083 9.14666i −0.490312 0.849246i
\(117\) 0 0
\(118\) −4.41352 −0.406297
\(119\) 2.64288 1.33826i 0.242273 0.122678i
\(120\) 0 0
\(121\) −6.65626 + 11.5290i −0.605115 + 1.04809i
\(122\) −0.0252261 0.0436929i −0.00228386 0.00395577i
\(123\) 0 0
\(124\) 1.94284 3.36510i 0.174472 0.302195i
\(125\) −11.3561 −1.01572
\(126\) 0 0
\(127\) 7.25977 0.644200 0.322100 0.946706i \(-0.395611\pi\)
0.322100 + 0.946706i \(0.395611\pi\)
\(128\) 5.48278 9.49645i 0.484614 0.839375i
\(129\) 0 0
\(130\) −1.31557 2.27864i −0.115384 0.199850i
\(131\) 10.2265 17.7128i 0.893492 1.54757i 0.0578326 0.998326i \(-0.481581\pi\)
0.835660 0.549248i \(-0.185086\pi\)
\(132\) 0 0
\(133\) 8.89447 + 5.80797i 0.771249 + 0.503615i
\(134\) −8.43794 −0.728927
\(135\) 0 0
\(136\) −1.33248 2.30793i −0.114260 0.197903i
\(137\) −6.10581 10.5756i −0.521655 0.903532i −0.999683 0.0251879i \(-0.991982\pi\)
0.478028 0.878345i \(-0.341352\pi\)
\(138\) 0 0
\(139\) 2.48183 0.210506 0.105253 0.994445i \(-0.466435\pi\)
0.105253 + 0.994445i \(0.466435\pi\)
\(140\) −0.320625 + 5.83721i −0.0270978 + 0.493335i
\(141\) 0 0
\(142\) −0.0269793 + 0.0467294i −0.00226405 + 0.00392145i
\(143\) 6.79117 + 11.7626i 0.567906 + 0.983642i
\(144\) 0 0
\(145\) 4.85269 8.40511i 0.402994 0.698006i
\(146\) −7.16654 −0.593107
\(147\) 0 0
\(148\) 2.20127 0.180943
\(149\) 4.27797 7.40966i 0.350465 0.607023i −0.635866 0.771799i \(-0.719357\pi\)
0.986331 + 0.164777i \(0.0526903\pi\)
\(150\) 0 0
\(151\) 8.82962 + 15.2933i 0.718544 + 1.24455i 0.961577 + 0.274537i \(0.0885244\pi\)
−0.243033 + 0.970018i \(0.578142\pi\)
\(152\) 4.77814 8.27599i 0.387559 0.671271i
\(153\) 0 0
\(154\) −0.479615 + 8.73173i −0.0386485 + 0.703623i
\(155\) 3.57066 0.286802
\(156\) 0 0
\(157\) −3.16074 5.47457i −0.252255 0.436918i 0.711891 0.702289i \(-0.247839\pi\)
−0.964146 + 0.265371i \(0.914505\pi\)
\(158\) 0.618353 + 1.07102i 0.0491936 + 0.0852057i
\(159\) 0 0
\(160\) 8.22139 0.649958
\(161\) 12.0436 + 7.86433i 0.949172 + 0.619796i
\(162\) 0 0
\(163\) −4.01134 + 6.94784i −0.314192 + 0.544197i −0.979265 0.202581i \(-0.935067\pi\)
0.665073 + 0.746778i \(0.268400\pi\)
\(164\) −0.192877 0.334073i −0.0150612 0.0260867i
\(165\) 0 0
\(166\) −4.85041 + 8.40116i −0.376465 + 0.652057i
\(167\) −2.12076 −0.164109 −0.0820545 0.996628i \(-0.526148\pi\)
−0.0820545 + 0.996628i \(0.526148\pi\)
\(168\) 0 0
\(169\) −5.41215 −0.416319
\(170\) 0.534749 0.926212i 0.0410133 0.0710372i
\(171\) 0 0
\(172\) 0.772712 + 1.33838i 0.0589187 + 0.102050i
\(173\) 9.14404 15.8379i 0.695208 1.20414i −0.274902 0.961472i \(-0.588646\pi\)
0.970110 0.242664i \(-0.0780212\pi\)
\(174\) 0 0
\(175\) 7.00931 3.54927i 0.529854 0.268299i
\(176\) −7.42494 −0.559676
\(177\) 0 0
\(178\) 4.53341 + 7.85209i 0.339793 + 0.588539i
\(179\) 3.81276 + 6.60389i 0.284979 + 0.493598i 0.972604 0.232468i \(-0.0746801\pi\)
−0.687625 + 0.726066i \(0.741347\pi\)
\(180\) 0 0
\(181\) 15.5305 1.15438 0.577188 0.816611i \(-0.304150\pi\)
0.577188 + 0.816611i \(0.304150\pi\)
\(182\) 4.09053 + 2.67106i 0.303210 + 0.197992i
\(183\) 0 0
\(184\) 6.46989 11.2062i 0.476967 0.826130i
\(185\) 1.01140 + 1.75180i 0.0743597 + 0.128795i
\(186\) 0 0
\(187\) −2.76044 + 4.78122i −0.201863 + 0.349638i
\(188\) 14.6937 1.07165
\(189\) 0 0
\(190\) 3.83510 0.278227
\(191\) −7.41624 + 12.8453i −0.536620 + 0.929454i 0.462463 + 0.886639i \(0.346966\pi\)
−0.999083 + 0.0428150i \(0.986367\pi\)
\(192\) 0 0
\(193\) −8.28387 14.3481i −0.596286 1.03280i −0.993364 0.115013i \(-0.963309\pi\)
0.397078 0.917785i \(-0.370024\pi\)
\(194\) 1.81097 3.13669i 0.130020 0.225201i
\(195\) 0 0
\(196\) −4.36506 9.93821i −0.311790 0.709872i
\(197\) −4.03740 −0.287653 −0.143826 0.989603i \(-0.545941\pi\)
−0.143826 + 0.989603i \(0.545941\pi\)
\(198\) 0 0
\(199\) −12.6407 21.8943i −0.896076 1.55205i −0.832468 0.554074i \(-0.813073\pi\)
−0.0636081 0.997975i \(-0.520261\pi\)
\(200\) −3.53395 6.12097i −0.249888 0.432818i
\(201\) 0 0
\(202\) −3.44243 −0.242208
\(203\) −0.988335 + 17.9933i −0.0693675 + 1.26288i
\(204\) 0 0
\(205\) 0.177240 0.306988i 0.0123790 0.0214410i
\(206\) 4.76312 + 8.24997i 0.331862 + 0.574803i
\(207\) 0 0
\(208\) −2.07399 + 3.59226i −0.143805 + 0.249078i
\(209\) −19.7973 −1.36941
\(210\) 0 0
\(211\) 7.52493 0.518037 0.259019 0.965872i \(-0.416601\pi\)
0.259019 + 0.965872i \(0.416601\pi\)
\(212\) 0.636123 1.10180i 0.0436891 0.0756718i
\(213\) 0 0
\(214\) 2.56747 + 4.44699i 0.175509 + 0.303990i
\(215\) −0.710065 + 1.22987i −0.0484261 + 0.0838764i
\(216\) 0 0
\(217\) −5.91476 + 2.99502i −0.401520 + 0.203315i
\(218\) 1.13875 0.0771261
\(219\) 0 0
\(220\) −5.44748 9.43531i −0.367269 0.636129i
\(221\) 1.54214 + 2.67106i 0.103735 + 0.179675i
\(222\) 0 0
\(223\) −12.9846 −0.869513 −0.434757 0.900548i \(-0.643166\pi\)
−0.434757 + 0.900548i \(0.643166\pi\)
\(224\) −13.6186 + 6.89599i −0.909934 + 0.460758i
\(225\) 0 0
\(226\) −0.201335 + 0.348723i −0.0133926 + 0.0231967i
\(227\) 14.4832 + 25.0857i 0.961286 + 1.66500i 0.719277 + 0.694723i \(0.244473\pi\)
0.242009 + 0.970274i \(0.422194\pi\)
\(228\) 0 0
\(229\) −7.71790 + 13.3678i −0.510013 + 0.883369i 0.489919 + 0.871768i \(0.337026\pi\)
−0.999933 + 0.0116012i \(0.996307\pi\)
\(230\) 5.19295 0.342413
\(231\) 0 0
\(232\) 16.2112 1.06432
\(233\) −2.47324 + 4.28378i −0.162027 + 0.280640i −0.935596 0.353073i \(-0.885137\pi\)
0.773568 + 0.633713i \(0.218470\pi\)
\(234\) 0 0
\(235\) 6.75121 + 11.6934i 0.440400 + 0.762795i
\(236\) −5.10481 + 8.84179i −0.332295 + 0.575551i
\(237\) 0 0
\(238\) −0.108911 + 1.98280i −0.00705964 + 0.128526i
\(239\) −13.0346 −0.843141 −0.421571 0.906796i \(-0.638521\pi\)
−0.421571 + 0.906796i \(0.638521\pi\)
\(240\) 0 0
\(241\) −7.29123 12.6288i −0.469670 0.813492i 0.529729 0.848167i \(-0.322294\pi\)
−0.999399 + 0.0346754i \(0.988960\pi\)
\(242\) −4.46191 7.72826i −0.286823 0.496791i
\(243\) 0 0
\(244\) −0.116709 −0.00747154
\(245\) 5.90338 8.04002i 0.377153 0.513658i
\(246\) 0 0
\(247\) −5.52993 + 9.57812i −0.351861 + 0.609441i
\(248\) 2.98209 + 5.16514i 0.189363 + 0.327987i
\(249\) 0 0
\(250\) 3.80619 6.59251i 0.240724 0.416947i
\(251\) −14.0715 −0.888187 −0.444094 0.895980i \(-0.646474\pi\)
−0.444094 + 0.895980i \(0.646474\pi\)
\(252\) 0 0
\(253\) −26.8067 −1.68532
\(254\) −2.43323 + 4.21448i −0.152674 + 0.264440i
\(255\) 0 0
\(256\) 4.53120 + 7.84826i 0.283200 + 0.490517i
\(257\) 4.18108 7.24184i 0.260808 0.451733i −0.705649 0.708562i \(-0.749344\pi\)
0.966457 + 0.256829i \(0.0826776\pi\)
\(258\) 0 0
\(259\) −3.14476 2.05349i −0.195406 0.127597i
\(260\) −6.08653 −0.377471
\(261\) 0 0
\(262\) 6.85515 + 11.8735i 0.423512 + 0.733545i
\(263\) −1.63533 2.83247i −0.100839 0.174658i 0.811192 0.584780i \(-0.198819\pi\)
−0.912030 + 0.410122i \(0.865486\pi\)
\(264\) 0 0
\(265\) 1.16910 0.0718173
\(266\) −6.35280 + 3.21683i −0.389515 + 0.197237i
\(267\) 0 0
\(268\) −9.75958 + 16.9041i −0.596161 + 1.03258i
\(269\) −7.69349 13.3255i −0.469081 0.812471i 0.530295 0.847813i \(-0.322081\pi\)
−0.999375 + 0.0353420i \(0.988748\pi\)
\(270\) 0 0
\(271\) 4.06308 7.03747i 0.246815 0.427496i −0.715825 0.698279i \(-0.753949\pi\)
0.962640 + 0.270783i \(0.0872827\pi\)
\(272\) −1.68605 −0.102232
\(273\) 0 0
\(274\) 8.18585 0.494525
\(275\) −7.32110 + 12.6805i −0.441479 + 0.764664i
\(276\) 0 0
\(277\) −6.42287 11.1247i −0.385913 0.668421i 0.605982 0.795478i \(-0.292780\pi\)
−0.991895 + 0.127057i \(0.959447\pi\)
\(278\) −0.831826 + 1.44077i −0.0498896 + 0.0864114i
\(279\) 0 0
\(280\) −7.51319 4.90601i −0.448999 0.293190i
\(281\) 1.44816 0.0863901 0.0431951 0.999067i \(-0.486246\pi\)
0.0431951 + 0.999067i \(0.486246\pi\)
\(282\) 0 0
\(283\) 8.71926 + 15.1022i 0.518306 + 0.897732i 0.999774 + 0.0212686i \(0.00677053\pi\)
−0.481468 + 0.876464i \(0.659896\pi\)
\(284\) 0.0624100 + 0.108097i 0.00370335 + 0.00641440i
\(285\) 0 0
\(286\) −9.10468 −0.538371
\(287\) −0.0360979 + 0.657189i −0.00213079 + 0.0387926i
\(288\) 0 0
\(289\) 7.87316 13.6367i 0.463127 0.802160i
\(290\) 3.25292 + 5.63422i 0.191018 + 0.330853i
\(291\) 0 0
\(292\) −8.28903 + 14.3570i −0.485079 + 0.840181i
\(293\) 1.80010 0.105163 0.0525814 0.998617i \(-0.483255\pi\)
0.0525814 + 0.998617i \(0.483255\pi\)
\(294\) 0 0
\(295\) −9.38189 −0.546235
\(296\) −1.68938 + 2.92609i −0.0981931 + 0.170075i
\(297\) 0 0
\(298\) 2.86766 + 4.96693i 0.166119 + 0.287727i
\(299\) −7.48786 + 12.9693i −0.433034 + 0.750037i
\(300\) 0 0
\(301\) 0.144617 2.63286i 0.00833559 0.151755i
\(302\) −11.8376 −0.681175
\(303\) 0 0
\(304\) −3.02300 5.23599i −0.173381 0.300305i
\(305\) −0.0536236 0.0928787i −0.00307048 0.00531822i
\(306\) 0 0
\(307\) 1.06478 0.0607699 0.0303850 0.999538i \(-0.490327\pi\)
0.0303850 + 0.999538i \(0.490327\pi\)
\(308\) 16.9379 + 11.0602i 0.965127 + 0.630214i
\(309\) 0 0
\(310\) −1.19676 + 2.07286i −0.0679717 + 0.117730i
\(311\) 8.46463 + 14.6612i 0.479985 + 0.831359i 0.999736 0.0229591i \(-0.00730874\pi\)
−0.519751 + 0.854318i \(0.673975\pi\)
\(312\) 0 0
\(313\) 4.13928 7.16944i 0.233966 0.405241i −0.725006 0.688743i \(-0.758163\pi\)
0.958972 + 0.283502i \(0.0914963\pi\)
\(314\) 4.23750 0.239136
\(315\) 0 0
\(316\) 2.86082 0.160934
\(317\) −3.27371 + 5.67023i −0.183870 + 0.318472i −0.943195 0.332239i \(-0.892196\pi\)
0.759325 + 0.650711i \(0.225529\pi\)
\(318\) 0 0
\(319\) −16.7920 29.0846i −0.940171 1.62842i
\(320\) −0.609811 + 1.05622i −0.0340895 + 0.0590447i
\(321\) 0 0
\(322\) −8.60207 + 4.35578i −0.479374 + 0.242738i
\(323\) −4.49556 −0.250140
\(324\) 0 0
\(325\) 4.08997 + 7.08404i 0.226871 + 0.392952i
\(326\) −2.68893 4.65736i −0.148926 0.257947i
\(327\) 0 0
\(328\) 0.592099 0.0326932
\(329\) −20.9916 13.7072i −1.15730 0.755703i
\(330\) 0 0
\(331\) 13.3629 23.1453i 0.734493 1.27218i −0.220453 0.975398i \(-0.570754\pi\)
0.954946 0.296781i \(-0.0959131\pi\)
\(332\) 11.2203 + 19.4341i 0.615792 + 1.06658i
\(333\) 0 0
\(334\) 0.710806 1.23115i 0.0388936 0.0673657i
\(335\) −17.9367 −0.979985
\(336\) 0 0
\(337\) 9.52328 0.518766 0.259383 0.965775i \(-0.416481\pi\)
0.259383 + 0.965775i \(0.416481\pi\)
\(338\) 1.81397 3.14189i 0.0986670 0.170896i
\(339\) 0 0
\(340\) −1.23701 2.14257i −0.0670864 0.116197i
\(341\) 6.17786 10.7004i 0.334550 0.579457i
\(342\) 0 0
\(343\) −3.03502 + 18.2699i −0.163876 + 0.986481i
\(344\) −2.37209 −0.127895
\(345\) 0 0
\(346\) 6.12955 + 10.6167i 0.329526 + 0.570757i
\(347\) 9.35156 + 16.1974i 0.502018 + 0.869521i 0.999997 + 0.00233189i \(0.000742265\pi\)
−0.497979 + 0.867189i \(0.665924\pi\)
\(348\) 0 0
\(349\) 30.1084 1.61167 0.805834 0.592142i \(-0.201718\pi\)
0.805834 + 0.592142i \(0.201718\pi\)
\(350\) −0.288848 + 5.25868i −0.0154396 + 0.281088i
\(351\) 0 0
\(352\) 14.2244 24.6374i 0.758164 1.31318i
\(353\) −3.12966 5.42074i −0.166575 0.288517i 0.770638 0.637273i \(-0.219938\pi\)
−0.937214 + 0.348756i \(0.886604\pi\)
\(354\) 0 0
\(355\) −0.0573502 + 0.0993335i −0.00304383 + 0.00527208i
\(356\) 20.9739 1.11161
\(357\) 0 0
\(358\) −5.11163 −0.270158
\(359\) −5.09755 + 8.82921i −0.269038 + 0.465988i −0.968614 0.248571i \(-0.920039\pi\)
0.699575 + 0.714559i \(0.253372\pi\)
\(360\) 0 0
\(361\) 1.43970 + 2.49364i 0.0757739 + 0.131244i
\(362\) −5.20532 + 9.01587i −0.273585 + 0.473864i
\(363\) 0 0
\(364\) 10.0823 5.10530i 0.528455 0.267591i
\(365\) −15.2340 −0.797385
\(366\) 0 0
\(367\) 14.3278 + 24.8165i 0.747906 + 1.29541i 0.948824 + 0.315804i \(0.102274\pi\)
−0.200918 + 0.979608i \(0.564392\pi\)
\(368\) −4.09332 7.08984i −0.213379 0.369584i
\(369\) 0 0
\(370\) −1.35595 −0.0704926
\(371\) −1.93660 + 0.980627i −0.100543 + 0.0509116i
\(372\) 0 0
\(373\) 8.03670 13.9200i 0.416124 0.720749i −0.579421 0.815028i \(-0.696721\pi\)
0.995546 + 0.0942796i \(0.0300548\pi\)
\(374\) −1.85041 3.20501i −0.0956826 0.165727i
\(375\) 0 0
\(376\) −11.2768 + 19.5319i −0.581555 + 1.00728i
\(377\) −18.7619 −0.966286
\(378\) 0 0
\(379\) −1.01893 −0.0523388 −0.0261694 0.999658i \(-0.508331\pi\)
−0.0261694 + 0.999658i \(0.508331\pi\)
\(380\) 4.43579 7.68302i 0.227551 0.394130i
\(381\) 0 0
\(382\) −4.97135 8.61063i −0.254356 0.440558i
\(383\) 5.79327 10.0342i 0.296022 0.512725i −0.679200 0.733953i \(-0.737673\pi\)
0.975222 + 0.221228i \(0.0710065\pi\)
\(384\) 0 0
\(385\) −1.01953 + 18.5612i −0.0519598 + 0.945966i
\(386\) 11.1059 0.565275
\(387\) 0 0
\(388\) −4.18924 7.25598i −0.212677 0.368367i
\(389\) −8.90675 15.4270i −0.451590 0.782178i 0.546895 0.837201i \(-0.315810\pi\)
−0.998485 + 0.0550239i \(0.982476\pi\)
\(390\) 0 0
\(391\) −6.08726 −0.307846
\(392\) 16.5606 + 1.82478i 0.836437 + 0.0921654i
\(393\) 0 0
\(394\) 1.35320 2.34381i 0.0681732 0.118079i
\(395\) 1.31444 + 2.27668i 0.0661369 + 0.114552i
\(396\) 0 0
\(397\) −6.54229 + 11.3316i −0.328348 + 0.568715i −0.982184 0.187921i \(-0.939825\pi\)
0.653836 + 0.756636i \(0.273159\pi\)
\(398\) 16.9470 0.849474
\(399\) 0 0
\(400\) −4.47166 −0.223583
\(401\) −7.05165 + 12.2138i −0.352143 + 0.609929i −0.986625 0.163009i \(-0.947880\pi\)
0.634482 + 0.772938i \(0.281213\pi\)
\(402\) 0 0
\(403\) −3.45129 5.97782i −0.171921 0.297776i
\(404\) −3.98161 + 6.89636i −0.198093 + 0.343107i
\(405\) 0 0
\(406\) −10.1143 6.60452i −0.501966 0.327777i
\(407\) 6.99960 0.346957
\(408\) 0 0
\(409\) 1.32300 + 2.29150i 0.0654179 + 0.113307i 0.896879 0.442275i \(-0.145829\pi\)
−0.831461 + 0.555583i \(0.812495\pi\)
\(410\) 0.118810 + 0.205784i 0.00586759 + 0.0101630i
\(411\) 0 0
\(412\) 22.0367 1.08567
\(413\) 15.5410 7.86940i 0.764722 0.387228i
\(414\) 0 0
\(415\) −10.3106 + 17.8585i −0.506128 + 0.876639i
\(416\) −7.94655 13.7638i −0.389612 0.674827i
\(417\) 0 0
\(418\) 6.63538 11.4928i 0.324547 0.562132i
\(419\) −33.5134 −1.63724 −0.818619 0.574337i \(-0.805260\pi\)
−0.818619 + 0.574337i \(0.805260\pi\)
\(420\) 0 0
\(421\) 4.83901 0.235839 0.117919 0.993023i \(-0.462378\pi\)
0.117919 + 0.993023i \(0.462378\pi\)
\(422\) −2.52210 + 4.36841i −0.122774 + 0.212651i
\(423\) 0 0
\(424\) 0.976394 + 1.69116i 0.0474179 + 0.0821302i
\(425\) −1.66247 + 2.87949i −0.0806418 + 0.139676i
\(426\) 0 0
\(427\) 0.166732 + 0.108874i 0.00806874 + 0.00526877i
\(428\) 11.8785 0.574167
\(429\) 0 0
\(430\) −0.475980 0.824422i −0.0229538 0.0397571i
\(431\) 17.6643 + 30.5954i 0.850858 + 1.47373i 0.880435 + 0.474166i \(0.157251\pi\)
−0.0295774 + 0.999562i \(0.509416\pi\)
\(432\) 0 0
\(433\) 5.47404 0.263066 0.131533 0.991312i \(-0.458010\pi\)
0.131533 + 0.991312i \(0.458010\pi\)
\(434\) 0.243742 4.43750i 0.0117000 0.213007i
\(435\) 0 0
\(436\) 1.31712 2.28131i 0.0630785 0.109255i
\(437\) −10.9141 18.9038i −0.522093 0.904292i
\(438\) 0 0
\(439\) −3.19906 + 5.54093i −0.152683 + 0.264454i −0.932213 0.361911i \(-0.882125\pi\)
0.779530 + 0.626365i \(0.215458\pi\)
\(440\) 16.7228 0.797229
\(441\) 0 0
\(442\) −2.06749 −0.0983404
\(443\) 3.19341 5.53115i 0.151723 0.262793i −0.780138 0.625608i \(-0.784851\pi\)
0.931861 + 0.362815i \(0.118184\pi\)
\(444\) 0 0
\(445\) 9.63674 + 16.6913i 0.456825 + 0.791245i
\(446\) 4.35200 7.53789i 0.206073 0.356929i
\(447\) 0 0
\(448\) 0.124199 2.26112i 0.00586783 0.106828i
\(449\) −11.7460 −0.554327 −0.277163 0.960823i \(-0.589394\pi\)
−0.277163 + 0.960823i \(0.589394\pi\)
\(450\) 0 0
\(451\) −0.613311 1.06229i −0.0288797 0.0500210i
\(452\) 0.465741 + 0.806687i 0.0219066 + 0.0379434i
\(453\) 0 0
\(454\) −19.4172 −0.911293
\(455\) 8.69531 + 5.67791i 0.407642 + 0.266185i
\(456\) 0 0
\(457\) −5.26120 + 9.11266i −0.246108 + 0.426272i −0.962443 0.271485i \(-0.912485\pi\)
0.716334 + 0.697757i \(0.245819\pi\)
\(458\) −5.17356 8.96087i −0.241745 0.418714i
\(459\) 0 0
\(460\) 6.00633 10.4033i 0.280046 0.485055i
\(461\) 7.08555 0.330007 0.165004 0.986293i \(-0.447236\pi\)
0.165004 + 0.986293i \(0.447236\pi\)
\(462\) 0 0
\(463\) −32.7521 −1.52212 −0.761059 0.648683i \(-0.775320\pi\)
−0.761059 + 0.648683i \(0.775320\pi\)
\(464\) 5.12820 8.88230i 0.238071 0.412350i
\(465\) 0 0
\(466\) −1.65789 2.87156i −0.0768004 0.133022i
\(467\) 1.96216 3.39856i 0.0907978 0.157266i −0.817049 0.576568i \(-0.804392\pi\)
0.907847 + 0.419301i \(0.137725\pi\)
\(468\) 0 0
\(469\) 29.7119 15.0450i 1.37197 0.694716i
\(470\) −9.05111 −0.417497
\(471\) 0 0
\(472\) −7.83544 13.5714i −0.360655 0.624673i
\(473\) 2.45707 + 4.25577i 0.112976 + 0.195681i
\(474\) 0 0
\(475\) −11.9229 −0.547060
\(476\) 3.84626 + 2.51155i 0.176293 + 0.115117i
\(477\) 0 0
\(478\) 4.36878 7.56694i 0.199823 0.346104i
\(479\) −8.04324 13.9313i −0.367505 0.636537i 0.621670 0.783279i \(-0.286455\pi\)
−0.989175 + 0.146742i \(0.953121\pi\)
\(480\) 0 0
\(481\) 1.95518 3.38647i 0.0891486 0.154410i
\(482\) 9.77510 0.445244
\(483\) 0 0
\(484\) −20.6431 −0.938324
\(485\) 3.84961 6.66771i 0.174802 0.302765i
\(486\) 0 0
\(487\) −1.75172 3.03407i −0.0793781 0.137487i 0.823604 0.567166i \(-0.191960\pi\)
−0.902982 + 0.429679i \(0.858627\pi\)
\(488\) 0.0895692 0.155138i 0.00405461 0.00702279i
\(489\) 0 0
\(490\) 2.68882 + 6.12181i 0.121469 + 0.276555i
\(491\) 41.1093 1.85524 0.927618 0.373531i \(-0.121853\pi\)
0.927618 + 0.373531i \(0.121853\pi\)
\(492\) 0 0
\(493\) −3.81312 6.60452i −0.171734 0.297452i
\(494\) −3.70689 6.42053i −0.166781 0.288873i
\(495\) 0 0
\(496\) 3.77338 0.169430
\(497\) 0.0116804 0.212649i 0.000523936 0.00953863i
\(498\) 0 0
\(499\) −5.91486 + 10.2448i −0.264785 + 0.458622i −0.967507 0.252843i \(-0.918634\pi\)
0.702722 + 0.711465i \(0.251968\pi\)
\(500\) −8.80470 15.2502i −0.393758 0.682009i
\(501\) 0 0
\(502\) 4.71631 8.16888i 0.210499 0.364595i
\(503\) 21.8595 0.974665 0.487332 0.873217i \(-0.337970\pi\)
0.487332 + 0.873217i \(0.337970\pi\)
\(504\) 0 0
\(505\) −7.31762 −0.325630
\(506\) 8.98470 15.5620i 0.399419 0.691813i
\(507\) 0 0
\(508\) 5.62869 + 9.74918i 0.249733 + 0.432550i
\(509\) −8.44831 + 14.6329i −0.374465 + 0.648592i −0.990247 0.139324i \(-0.955507\pi\)
0.615782 + 0.787917i \(0.288840\pi\)
\(510\) 0 0
\(511\) 25.2350 12.7781i 1.11633 0.565270i
\(512\) 15.8563 0.700756
\(513\) 0 0
\(514\) 2.80271 + 4.85444i 0.123622 + 0.214120i
\(515\) 10.1250 + 17.5371i 0.446163 + 0.772777i
\(516\) 0 0
\(517\) 46.7230 2.05487
\(518\) 2.24612 1.13735i 0.0986888 0.0499725i
\(519\) 0 0
\(520\) 4.67115 8.09067i 0.204843 0.354799i
\(521\) −17.2466 29.8720i −0.755587 1.30872i −0.945082 0.326834i \(-0.894018\pi\)
0.189495 0.981882i \(-0.439315\pi\)
\(522\) 0 0
\(523\) 0.995615 1.72445i 0.0435352 0.0754051i −0.843437 0.537229i \(-0.819471\pi\)
0.886972 + 0.461823i \(0.152805\pi\)
\(524\) 31.7155 1.38550
\(525\) 0 0
\(526\) 2.19243 0.0955945
\(527\) 1.40287 2.42983i 0.0611098 0.105845i
\(528\) 0 0
\(529\) −3.27836 5.67829i −0.142538 0.246882i
\(530\) −0.391843 + 0.678693i −0.0170206 + 0.0294805i
\(531\) 0 0
\(532\) −0.903426 + 16.4475i −0.0391685 + 0.713090i
\(533\) −0.685259 −0.0296819
\(534\) 0 0
\(535\) 5.45772 + 9.45305i 0.235958 + 0.408691i
\(536\) −14.9801 25.9463i −0.647042 1.12071i
\(537\) 0 0
\(538\) 10.3144 0.444685
\(539\) −13.8800 31.6016i −0.597856 1.36118i
\(540\) 0 0
\(541\) −15.0681 + 26.0988i −0.647830 + 1.12207i 0.335810 + 0.941930i \(0.390990\pi\)
−0.983640 + 0.180145i \(0.942343\pi\)
\(542\) 2.72362 + 4.71745i 0.116989 + 0.202632i
\(543\) 0 0
\(544\) 3.23008 5.59466i 0.138488 0.239869i
\(545\) 2.42067 0.103690
\(546\) 0 0
\(547\) −15.3614 −0.656806 −0.328403 0.944538i \(-0.606510\pi\)
−0.328403 + 0.944538i \(0.606510\pi\)
\(548\) 9.46800 16.3991i 0.404453 0.700533i
\(549\) 0 0
\(550\) −4.90757 8.50016i −0.209260 0.362448i
\(551\) 13.6734 23.6831i 0.582508 1.00893i
\(552\) 0 0
\(553\) −4.08701 2.66876i −0.173797 0.113487i
\(554\) 8.61092 0.365843
\(555\) 0 0
\(556\) 1.92423 + 3.33287i 0.0816056 + 0.141345i
\(557\) −11.6412 20.1631i −0.493252 0.854338i 0.506718 0.862112i \(-0.330859\pi\)
−0.999970 + 0.00777438i \(0.997525\pi\)
\(558\) 0 0
\(559\) 2.74531 0.116114
\(560\) −5.06475 + 2.56461i −0.214025 + 0.108374i
\(561\) 0 0
\(562\) −0.485375 + 0.840695i −0.0204743 + 0.0354626i
\(563\) −2.27942 3.94808i −0.0960663 0.166392i 0.813987 0.580883i \(-0.197293\pi\)
−0.910053 + 0.414492i \(0.863959\pi\)
\(564\) 0 0
\(565\) −0.427982 + 0.741286i −0.0180053 + 0.0311861i
\(566\) −11.6896 −0.491351
\(567\) 0 0
\(568\) −0.191588 −0.00803885
\(569\) −9.09976 + 15.7612i −0.381482 + 0.660746i −0.991274 0.131815i \(-0.957919\pi\)
0.609793 + 0.792561i \(0.291253\pi\)
\(570\) 0 0
\(571\) 8.52275 + 14.7618i 0.356666 + 0.617763i 0.987402 0.158234i \(-0.0505801\pi\)
−0.630736 + 0.775998i \(0.717247\pi\)
\(572\) −10.5307 + 18.2398i −0.440313 + 0.762644i
\(573\) 0 0
\(574\) −0.369416 0.241223i −0.0154191 0.0100685i
\(575\) −16.1443 −0.673264
\(576\) 0 0
\(577\) −5.70473 9.88088i −0.237491 0.411346i 0.722503 0.691368i \(-0.242992\pi\)
−0.959994 + 0.280022i \(0.909658\pi\)
\(578\) 5.27764 + 9.14113i 0.219521 + 0.380221i
\(579\) 0 0
\(580\) 15.0497 0.624904
\(581\) 2.09993 38.2308i 0.0871199 1.58608i
\(582\) 0 0
\(583\) 2.02275 3.50350i 0.0837736 0.145100i
\(584\) −12.7229 22.0368i −0.526479 0.911889i
\(585\) 0 0
\(586\) −0.603332 + 1.04500i −0.0249234 + 0.0431686i
\(587\) −5.05089 −0.208473 −0.104236 0.994553i \(-0.533240\pi\)
−0.104236 + 0.994553i \(0.533240\pi\)
\(588\) 0 0
\(589\) 10.0610 0.414558
\(590\) 3.14449 5.44642i 0.129457 0.224226i
\(591\) 0 0
\(592\) 1.06882 + 1.85126i 0.0439283 + 0.0760861i
\(593\) −9.98892 + 17.3013i −0.410196 + 0.710480i −0.994911 0.100759i \(-0.967873\pi\)
0.584715 + 0.811239i \(0.301206\pi\)
\(594\) 0 0
\(595\) −0.231513 + 4.21487i −0.00949113 + 0.172793i
\(596\) 13.2673 0.543449
\(597\) 0 0
\(598\) −5.01935 8.69378i −0.205257 0.355515i
\(599\) −2.19660 3.80463i −0.0897508 0.155453i 0.817655 0.575709i \(-0.195274\pi\)
−0.907406 + 0.420256i \(0.861940\pi\)
\(600\) 0 0
\(601\) −24.3556 −0.993487 −0.496743 0.867897i \(-0.665471\pi\)
−0.496743 + 0.867897i \(0.665471\pi\)
\(602\) 1.47997 + 0.966399i 0.0603191 + 0.0393875i
\(603\) 0 0
\(604\) −13.6917 + 23.7147i −0.557107 + 0.964937i
\(605\) −9.48476 16.4281i −0.385610 0.667897i
\(606\) 0 0
\(607\) −6.56281 + 11.3671i −0.266376 + 0.461377i −0.967923 0.251246i \(-0.919160\pi\)
0.701547 + 0.712623i \(0.252493\pi\)
\(608\) 23.1654 0.939481
\(609\) 0 0
\(610\) 0.0718913 0.00291079
\(611\) 13.0510 22.6051i 0.527988 0.914502i
\(612\) 0 0
\(613\) −23.2403 40.2534i −0.938667 1.62582i −0.767960 0.640497i \(-0.778728\pi\)
−0.170707 0.985322i \(-0.554605\pi\)
\(614\) −0.356877 + 0.618129i −0.0144024 + 0.0249456i
\(615\) 0 0
\(616\) −27.7012 + 14.0269i −1.11611 + 0.565159i
\(617\) −28.3897 −1.14293 −0.571463 0.820628i \(-0.693624\pi\)
−0.571463 + 0.820628i \(0.693624\pi\)
\(618\) 0 0
\(619\) −15.9606 27.6446i −0.641511 1.11113i −0.985096 0.172008i \(-0.944975\pi\)
0.343585 0.939122i \(-0.388359\pi\)
\(620\) 2.76843 + 4.79506i 0.111183 + 0.192574i
\(621\) 0 0
\(622\) −11.3482 −0.455023
\(623\) −29.9636 19.5658i −1.20047 0.783888i
\(624\) 0 0
\(625\) 0.666993 1.15527i 0.0266797 0.0462106i
\(626\) 2.77469 + 4.80591i 0.110899 + 0.192083i
\(627\) 0 0
\(628\) 4.90122 8.48916i 0.195580 0.338754i
\(629\) 1.58947 0.0633762
\(630\) 0 0
\(631\) 38.7184 1.54135 0.770677 0.637226i \(-0.219918\pi\)
0.770677 + 0.637226i \(0.219918\pi\)
\(632\) −2.19556 + 3.80282i −0.0873346 + 0.151268i
\(633\) 0 0
\(634\) −2.19447 3.80094i −0.0871537 0.150955i
\(635\) −5.17236 + 8.95878i −0.205259 + 0.355519i
\(636\) 0 0
\(637\) −19.1662 2.11189i −0.759394 0.0836761i
\(638\) 22.5124 0.891276
\(639\) 0 0
\(640\) 7.81261 + 13.5318i 0.308821 + 0.534893i
\(641\) 20.2001 + 34.9875i 0.797854 + 1.38192i 0.921011 + 0.389537i \(0.127365\pi\)
−0.123157 + 0.992387i \(0.539302\pi\)
\(642\) 0 0
\(643\) −12.5471 −0.494809 −0.247405 0.968912i \(-0.579578\pi\)
−0.247405 + 0.968912i \(0.579578\pi\)
\(644\) −1.22329 + 22.2709i −0.0482045 + 0.877597i
\(645\) 0 0
\(646\) 1.50676 2.60979i 0.0592827 0.102681i
\(647\) 17.2774 + 29.9253i 0.679245 + 1.17649i 0.975209 + 0.221287i \(0.0710258\pi\)
−0.295964 + 0.955199i \(0.595641\pi\)
\(648\) 0 0
\(649\) −16.2323 + 28.1151i −0.637173 + 1.10362i
\(650\) −5.48329 −0.215072
\(651\) 0 0
\(652\) −12.4404 −0.487203
\(653\) 11.1472 19.3075i 0.436223 0.755560i −0.561172 0.827699i \(-0.689649\pi\)
0.997395 + 0.0721392i \(0.0229826\pi\)
\(654\) 0 0
\(655\) 14.5721 + 25.2396i 0.569379 + 0.986194i
\(656\) 0.187302 0.324417i 0.00731293 0.0126664i
\(657\) 0 0
\(658\) 14.9931 7.59195i 0.584490 0.295965i
\(659\) −7.14986 −0.278519 −0.139259 0.990256i \(-0.544472\pi\)
−0.139259 + 0.990256i \(0.544472\pi\)
\(660\) 0 0
\(661\) −21.4530 37.1577i −0.834425 1.44527i −0.894498 0.447072i \(-0.852467\pi\)
0.0600736 0.998194i \(-0.480866\pi\)
\(662\) 8.95760 + 15.5150i 0.348147 + 0.603008i
\(663\) 0 0
\(664\) −34.4443 −1.33670
\(665\) −13.5043 + 6.83807i −0.523672 + 0.265169i
\(666\) 0 0
\(667\) 18.5146 32.0683i 0.716889 1.24169i
\(668\) −1.64428 2.84798i −0.0636191 0.110192i
\(669\) 0 0
\(670\) 6.01177 10.4127i 0.232255 0.402277i
\(671\) −0.371112 −0.0143266
\(672\) 0 0
\(673\) 37.6541 1.45146 0.725729 0.687980i \(-0.241503\pi\)
0.725729 + 0.687980i \(0.241503\pi\)
\(674\) −3.19188 + 5.52850i −0.122947 + 0.212950i
\(675\) 0 0
\(676\) −4.19619 7.26801i −0.161392 0.279539i
\(677\) 13.1808 22.8298i 0.506580 0.877422i −0.493391 0.869808i \(-0.664243\pi\)
0.999971 0.00761453i \(-0.00242380\pi\)
\(678\) 0 0
\(679\) −0.784039 + 14.2740i −0.0300887 + 0.547785i
\(680\) 3.79741 0.145624
\(681\) 0 0
\(682\) 4.14122 + 7.17280i 0.158575 + 0.274661i
\(683\) 1.96588 + 3.40500i 0.0752222 + 0.130289i 0.901183 0.433439i \(-0.142700\pi\)
−0.825961 + 0.563728i \(0.809367\pi\)
\(684\) 0 0
\(685\) 17.4008 0.664850
\(686\) −9.58889 7.88535i −0.366106 0.301064i
\(687\) 0 0
\(688\) −0.750378 + 1.29969i −0.0286079 + 0.0495503i
\(689\) −1.13002 1.95725i −0.0430503 0.0745653i
\(690\) 0 0
\(691\) −9.95052 + 17.2348i −0.378536 + 0.655643i −0.990849 0.134972i \(-0.956906\pi\)
0.612314 + 0.790615i \(0.290239\pi\)
\(692\) 28.3585 1.07803
\(693\) 0 0
\(694\) −12.5373 −0.475910
\(695\) −1.76823 + 3.06266i −0.0670727 + 0.116173i
\(696\) 0 0
\(697\) −0.139270 0.241223i −0.00527524 0.00913699i
\(698\) −10.0913 + 17.4787i −0.381963 + 0.661579i
\(699\) 0 0
\(700\) 10.2008 + 6.66100i 0.385555 + 0.251762i
\(701\) 43.7908 1.65396 0.826979 0.562234i \(-0.190058\pi\)
0.826979 + 0.562234i \(0.190058\pi\)
\(702\) 0 0
\(703\) 2.84983 + 4.93604i 0.107483 + 0.186166i
\(704\) 2.11016 + 3.65490i 0.0795295 + 0.137749i
\(705\) 0 0
\(706\) 4.19583 0.157912
\(707\) 12.1216 6.13792i 0.455878 0.230840i
\(708\) 0 0
\(709\) −22.3172 + 38.6545i −0.838139 + 1.45170i 0.0533097 + 0.998578i \(0.483023\pi\)
−0.891449 + 0.453121i \(0.850310\pi\)
\(710\) −0.0384437 0.0665865i −0.00144277 0.00249895i
\(711\) 0 0
\(712\) −16.0966 + 27.8801i −0.603244 + 1.04485i
\(713\) 13.6233 0.510195
\(714\) 0 0
\(715\) −19.3540 −0.723798
\(716\) −5.91227 + 10.2403i −0.220952 + 0.382700i
\(717\) 0 0
\(718\) −3.41705 5.91851i −0.127523 0.220877i
\(719\) −19.5096 + 33.7917i −0.727586 + 1.26022i 0.230315 + 0.973116i \(0.426024\pi\)
−0.957901 + 0.287100i \(0.907309\pi\)
\(720\) 0 0
\(721\) −31.4819 20.5572i −1.17245 0.765592i
\(722\) −1.93016 −0.0718332
\(723\) 0 0
\(724\) 12.0413 + 20.8561i 0.447510 + 0.775109i
\(725\) −10.1130 17.5162i −0.375586 0.650534i
\(726\) 0 0
\(727\) 22.5107 0.834877 0.417439 0.908705i \(-0.362928\pi\)
0.417439 + 0.908705i \(0.362928\pi\)
\(728\) −0.951361 + 17.3202i −0.0352598 + 0.641929i
\(729\) 0 0
\(730\) 5.10593 8.84373i 0.188979 0.327321i
\(731\) 0.557951 + 0.966399i 0.0206366 + 0.0357436i
\(732\) 0 0
\(733\) 0.448519 0.776858i 0.0165664 0.0286939i −0.857623 0.514278i \(-0.828060\pi\)
0.874190 + 0.485584i \(0.161393\pi\)
\(734\) −19.2088 −0.709011
\(735\) 0 0
\(736\) 31.3673 1.15622
\(737\) −31.0335 + 53.7517i −1.14314 + 1.97997i
\(738\) 0 0
\(739\) 1.79032 + 3.10092i 0.0658578 + 0.114069i 0.897074 0.441880i \(-0.145688\pi\)
−0.831216 + 0.555949i \(0.812355\pi\)
\(740\) −1.56833 + 2.71643i −0.0576531 + 0.0998581i
\(741\) 0 0
\(742\) 0.0798057 1.45292i 0.00292976 0.0533384i
\(743\) 49.5928 1.81938 0.909691 0.415286i \(-0.136318\pi\)
0.909691 + 0.415286i \(0.136318\pi\)
\(744\) 0 0
\(745\) 6.09583 + 10.5583i 0.223334 + 0.386826i
\(746\) 5.38726 + 9.33101i 0.197242 + 0.341633i
\(747\) 0 0
\(748\) −8.56098 −0.313020
\(749\) −16.9697 11.0810i −0.620061 0.404891i
\(750\) 0 0
\(751\) 21.4515 37.1551i 0.782776 1.35581i −0.147543 0.989056i \(-0.547136\pi\)
0.930319 0.366752i \(-0.119530\pi\)
\(752\) 7.13450 + 12.3573i 0.260168 + 0.450625i
\(753\) 0 0
\(754\) 6.28835 10.8917i 0.229008 0.396654i
\(755\) −25.1633 −0.915786
\(756\) 0 0
\(757\) 13.8029 0.501677 0.250838 0.968029i \(-0.419294\pi\)
0.250838 + 0.968029i \(0.419294\pi\)
\(758\) 0.341510 0.591513i 0.0124042 0.0214847i
\(759\) 0 0
\(760\) 6.80856 + 11.7928i 0.246972 + 0.427769i
\(761\) −20.3599 + 35.2643i −0.738044 + 1.27833i 0.215330 + 0.976541i \(0.430917\pi\)
−0.953375 + 0.301789i \(0.902416\pi\)
\(762\) 0 0
\(763\) −4.00981 + 2.03042i −0.145165 + 0.0735063i
\(764\) −23.0001 −0.832113
\(765\) 0 0
\(766\) 3.88342 + 6.72627i 0.140313 + 0.243030i
\(767\) 9.06826 + 15.7067i 0.327436 + 0.567135i
\(768\) 0 0
\(769\) −11.1476 −0.401994 −0.200997 0.979592i \(-0.564418\pi\)
−0.200997 + 0.979592i \(0.564418\pi\)
\(770\) −10.4335 6.81294i −0.375998 0.245521i
\(771\) 0 0
\(772\) 12.8454 22.2489i 0.462317 0.800756i
\(773\) −0.462831 0.801647i −0.0166469 0.0288332i 0.857582 0.514347i \(-0.171966\pi\)
−0.874229 + 0.485514i \(0.838632\pi\)
\(774\) 0 0
\(775\) 3.72061 6.44428i 0.133648 0.231485i
\(776\) 12.8602 0.461656
\(777\) 0 0
\(778\) 11.9410 0.428105
\(779\) 0.499408 0.865001i 0.0178932 0.0309919i
\(780\) 0 0
\(781\) 0.198452 + 0.343728i 0.00710116 + 0.0122996i
\(782\) 2.04024 3.53381i 0.0729590 0.126369i
\(783\) 0 0
\(784\) 6.23854 8.49648i 0.222805 0.303446i
\(785\) 9.00772 0.321499
\(786\) 0 0
\(787\) −11.5120 19.9393i −0.410358 0.710761i 0.584571 0.811343i \(-0.301263\pi\)
−0.994929 + 0.100582i \(0.967930\pi\)
\(788\) −3.13030 5.42184i −0.111512 0.193145i
\(789\) 0 0
\(790\) −1.76223 −0.0626973
\(791\) 0.0871659 1.58692i 0.00309926 0.0564243i
\(792\) 0 0
\(793\) −0.103662 + 0.179548i −0.00368114 + 0.00637593i
\(794\) −4.38551 7.59592i −0.155636 0.269569i
\(795\) 0 0
\(796\) 19.6014 33.9505i 0.694752 1.20335i
\(797\) −22.7851 −0.807089 −0.403544 0.914960i \(-0.632222\pi\)
−0.403544 + 0.914960i \(0.632222\pi\)
\(798\) 0 0
\(799\) 10.6098 0.375349
\(800\) 8.56664 14.8379i 0.302877 0.524598i
\(801\) 0 0
\(802\) −4.72695 8.18732i −0.166914 0.289104i
\(803\) −26.3575 + 45.6525i −0.930135 + 1.61104i
\(804\) 0 0
\(805\) −18.2856 + 9.25915i −0.644481 + 0.326342i
\(806\) 4.62703 0.162980
\(807\) 0 0
\(808\) −6.11143 10.5853i −0.214999 0.372390i
\(809\) 6.73753 + 11.6697i 0.236879 + 0.410286i 0.959817 0.280627i \(-0.0905422\pi\)
−0.722938 + 0.690913i \(0.757209\pi\)
\(810\) 0 0
\(811\) −30.7348 −1.07924 −0.539622 0.841907i \(-0.681433\pi\)
−0.539622 + 0.841907i \(0.681433\pi\)
\(812\) −24.9296 + 12.6235i −0.874859 + 0.442997i
\(813\) 0 0
\(814\) −2.34603 + 4.06344i −0.0822283 + 0.142424i
\(815\) −5.71590 9.90023i −0.200219 0.346790i
\(816\) 0 0
\(817\) −2.00075 + 3.46540i −0.0699974 + 0.121239i
\(818\) −1.77369 −0.0620158
\(819\) 0 0
\(820\) 0.549675 0.0191955
\(821\) 8.49319 14.7106i 0.296414 0.513405i −0.678899 0.734232i \(-0.737542\pi\)
0.975313 + 0.220827i \(0.0708757\pi\)
\(822\) 0 0
\(823\) 9.29157 + 16.0935i 0.323884 + 0.560983i 0.981286 0.192557i \(-0.0616780\pi\)
−0.657402 + 0.753540i \(0.728345\pi\)
\(824\) −16.9122 + 29.2928i −0.589164 + 1.02046i
\(825\) 0 0
\(826\) −0.640430 + 11.6595i −0.0222834 + 0.405686i
\(827\) 14.5419 0.505670 0.252835 0.967509i \(-0.418637\pi\)
0.252835 + 0.967509i \(0.418637\pi\)
\(828\) 0 0
\(829\) 4.78717 + 8.29161i 0.166265 + 0.287980i 0.937104 0.349051i \(-0.113496\pi\)
−0.770839 + 0.637030i \(0.780163\pi\)
\(830\) −6.91154 11.9711i −0.239903 0.415524i
\(831\) 0 0
\(832\) 2.35770 0.0817386
\(833\) −3.15188 7.17607i −0.109206 0.248636i
\(834\) 0 0
\(835\) 1.51097 2.61708i 0.0522894 0.0905678i
\(836\) −15.3494 26.5859i −0.530869 0.919492i
\(837\) 0 0
\(838\) 11.2326 19.4554i 0.388023 0.672075i
\(839\) −42.4606 −1.46590 −0.732952 0.680281i \(-0.761858\pi\)
−0.732952 + 0.680281i \(0.761858\pi\)
\(840\) 0 0
\(841\) 17.3910 0.599690
\(842\) −1.62187 + 2.80917i −0.0558934 + 0.0968103i
\(843\) 0 0
\(844\) 5.83428 + 10.1053i 0.200824 + 0.347838i
\(845\) 3.85599 6.67877i 0.132650 0.229757i
\(846\) 0 0
\(847\) 29.4911 + 19.2572i 1.01332 + 0.661687i
\(848\) 1.23548 0.0424264
\(849\) 0 0
\(850\) −1.11441 1.93021i −0.0382239 0.0662058i
\(851\) 3.85883 + 6.68370i 0.132279 + 0.229114i
\(852\) 0 0
\(853\) −14.2808 −0.488965 −0.244482 0.969654i \(-0.578618\pi\)
−0.244482 + 0.969654i \(0.578618\pi\)
\(854\) −0.119087 + 0.0603014i −0.00407507 + 0.00206347i
\(855\) 0 0
\(856\) −9.11621 + 15.7897i −0.311586 + 0.539682i
\(857\) −17.3895 30.1195i −0.594013 1.02886i −0.993685 0.112203i \(-0.964209\pi\)
0.399672 0.916658i \(-0.369124\pi\)
\(858\) 0 0
\(859\) 6.32429 10.9540i 0.215782 0.373745i −0.737732 0.675093i \(-0.764103\pi\)
0.953514 + 0.301348i \(0.0974366\pi\)
\(860\) −2.20213 −0.0750921
\(861\) 0 0
\(862\) −23.6819 −0.806608
\(863\) 13.2398 22.9321i 0.450690 0.780617i −0.547739 0.836649i \(-0.684511\pi\)
0.998429 + 0.0560318i \(0.0178448\pi\)
\(864\) 0 0
\(865\) 13.0297 + 22.5681i 0.443022 + 0.767337i
\(866\) −1.83471 + 3.17782i −0.0623461 + 0.107987i
\(867\) 0 0
\(868\) −8.60790 5.62084i −0.292171 0.190784i
\(869\) 9.09686 0.308590
\(870\) 0 0
\(871\) 17.3371 + 30.0287i 0.587444 + 1.01748i
\(872\) 2.02166 + 3.50162i 0.0684621 + 0.118580i
\(873\) 0 0
\(874\) 14.6322 0.494941
\(875\) −1.64785 + 30.0002i −0.0557074 + 1.01419i
\(876\) 0 0
\(877\) −14.2267 + 24.6414i −0.480402 + 0.832081i −0.999747 0.0224835i \(-0.992843\pi\)
0.519345 + 0.854565i \(0.326176\pi\)
\(878\) −2.14443 3.71427i −0.0723711 0.125350i
\(879\) 0 0
\(880\) 5.29004 9.16261i 0.178327 0.308872i
\(881\) −20.3637 −0.686071 −0.343036 0.939322i \(-0.611455\pi\)
−0.343036 + 0.939322i \(0.611455\pi\)
\(882\) 0 0
\(883\) 49.1950 1.65554 0.827772 0.561065i \(-0.189608\pi\)
0.827772 + 0.561065i \(0.189608\pi\)
\(884\) −2.39132 + 4.14189i −0.0804288 + 0.139307i
\(885\) 0 0
\(886\) 2.14065 + 3.70771i 0.0719164 + 0.124563i
\(887\) 2.10846 3.65196i 0.0707952 0.122621i −0.828455 0.560056i \(-0.810780\pi\)
0.899250 + 0.437435i \(0.144113\pi\)
\(888\) 0 0
\(889\) 1.05344 19.1786i 0.0353312 0.643231i
\(890\) −12.9196 −0.433067
\(891\) 0 0
\(892\) −10.0673 17.4371i −0.337078 0.583837i
\(893\) 19.0229 + 32.9486i 0.636576 + 1.10258i
\(894\) 0 0
\(895\) −10.8659 −0.363206
\(896\) −24.2918 15.8622i −0.811533 0.529920i
\(897\) 0 0
\(898\) 3.93685 6.81883i 0.131375 0.227547i
\(899\) 8.53374 + 14.7809i 0.284616 + 0.492970i
\(900\) 0 0
\(901\) 0.459325 0.795574i 0.0153023 0.0265044i
\(902\) 0.822244 0.0273777
\(903\) 0 0
\(904\) −1.42974 −0.0475526
\(905\) −11.0650 + 19.1652i −0.367814 + 0.637072i
\(906\) 0 0
\(907\) −23.9925 41.5563i −0.796659 1.37985i −0.921780 0.387713i \(-0.873265\pi\)
0.125121 0.992142i \(-0.460068\pi\)
\(908\) −22.4585 + 38.8993i −0.745311 + 1.29092i
\(909\) 0 0
\(910\) −6.21054 + 3.14480i −0.205878 + 0.104249i
\(911\) 25.7335 0.852587 0.426294 0.904585i \(-0.359819\pi\)
0.426294 + 0.904585i \(0.359819\pi\)
\(912\) 0 0
\(913\) 35.6782 + 61.7965i 1.18078 + 2.04517i
\(914\) −3.52675 6.10852i −0.116655 0.202052i
\(915\) 0 0
\(916\) −23.9356 −0.790854
\(917\) −45.3092 29.5863i −1.49624 0.977024i
\(918\) 0 0
\(919\) 1.13478 1.96550i 0.0374330 0.0648359i −0.846702 0.532068i \(-0.821415\pi\)
0.884135 + 0.467232i \(0.154749\pi\)
\(920\) 9.21919 + 15.9681i 0.303948 + 0.526453i
\(921\) 0 0
\(922\) −2.37484 + 4.11334i −0.0782111 + 0.135466i
\(923\) 0.221732 0.00729840
\(924\) 0 0
\(925\) 4.21550 0.138605
\(926\) 10.9774 19.0134i 0.360740 0.624819i
\(927\) 0 0
\(928\) 19.6488 + 34.0328i 0.645004 + 1.11718i
\(929\) −22.9248 + 39.7069i −0.752138 + 1.30274i 0.194647 + 0.980873i \(0.437644\pi\)
−0.946785 + 0.321868i \(0.895689\pi\)
\(930\) 0 0
\(931\) 16.6340 22.6544i 0.545156 0.742467i
\(932\) −7.67028 −0.251248
\(933\) 0 0
\(934\) 1.31530 + 2.27816i 0.0430379 + 0.0745438i
\(935\) −3.93346 6.81294i −0.128638 0.222807i
\(936\) 0 0
\(937\) −56.2075 −1.83622 −0.918110 0.396325i \(-0.870285\pi\)
−0.918110 + 0.396325i \(0.870285\pi\)
\(938\) −1.22440 + 22.2911i −0.0399781 + 0.727830i
\(939\) 0 0
\(940\) −10.4688 + 18.1325i −0.341454 + 0.591416i
\(941\) 17.6402 + 30.5536i 0.575053 + 0.996020i 0.996036 + 0.0889519i \(0.0283517\pi\)
−0.420983 + 0.907068i \(0.638315\pi\)
\(942\) 0 0
\(943\) 0.676229 1.17126i 0.0220210 0.0381415i
\(944\) −9.91453 −0.322691
\(945\) 0 0
\(946\) −3.29411 −0.107101
\(947\) 25.3565 43.9188i 0.823976 1.42717i −0.0787236 0.996896i \(-0.525084\pi\)
0.902699 0.430272i \(-0.141582\pi\)
\(948\) 0 0
\(949\) 14.7248 + 25.5040i 0.477986 + 0.827896i
\(950\) 3.99615 6.92154i 0.129652 0.224564i
\(951\) 0 0
\(952\) −6.29037 + 3.18522i −0.203872 + 0.103234i
\(953\) 25.9988 0.842184 0.421092 0.907018i \(-0.361647\pi\)
0.421092 + 0.907018i \(0.361647\pi\)
\(954\) 0 0
\(955\) −10.5677 18.3038i −0.341962 0.592296i
\(956\) −10.1061 17.5043i −0.326855 0.566130i
\(957\) 0 0
\(958\) 10.7833 0.348392
\(959\) −28.8242 + 14.5956i −0.930783 + 0.471315i
\(960\) 0 0
\(961\) 12.3604 21.4088i 0.398722 0.690607i
\(962\) 1.31062 + 2.27006i 0.0422562 + 0.0731898i
\(963\) 0 0
\(964\) 11.3062 19.5829i 0.364148 0.630722i
\(965\) 23.6080 0.759968
\(966\) 0 0
\(967\) 25.9621 0.834885 0.417442 0.908703i \(-0.362927\pi\)
0.417442 + 0.908703i \(0.362927\pi\)
\(968\) 15.8427 27.4404i 0.509204 0.881967i
\(969\) 0 0
\(970\) 2.58052 + 4.46959i 0.0828554 + 0.143510i
\(971\) −3.97206 + 6.87981i −0.127469 + 0.220783i −0.922696 0.385530i \(-0.874019\pi\)
0.795226 + 0.606313i \(0.207352\pi\)
\(972\) 0 0
\(973\) 0.360130 6.55643i 0.0115452 0.210189i
\(974\) 2.34847 0.0752499
\(975\) 0 0
\(976\) −0.0566680 0.0981518i −0.00181390 0.00314176i
\(977\) 26.1274 + 45.2540i 0.835889 + 1.44780i 0.893304 + 0.449452i \(0.148381\pi\)
−0.0574149 + 0.998350i \(0.518286\pi\)
\(978\) 0 0
\(979\) 66.6929 2.13151
\(980\) 15.3740 + 1.69404i 0.491106 + 0.0541140i
\(981\) 0 0
\(982\) −13.7784 + 23.8650i −0.439688 + 0.761562i
\(983\) 19.4190 + 33.6346i 0.619369 + 1.07278i 0.989601 + 0.143839i \(0.0459448\pi\)
−0.370232 + 0.928939i \(0.620722\pi\)
\(984\) 0 0
\(985\) 2.87652 4.98228i 0.0916535 0.158749i
\(986\) 5.11212 0.162803
\(987\) 0 0
\(988\) −17.1500 −0.545615
\(989\) −2.70914 + 4.69236i −0.0861455 + 0.149208i
\(990\) 0 0
\(991\) −15.4689 26.7929i −0.491385 0.851104i 0.508565 0.861023i \(-0.330176\pi\)
−0.999951 + 0.00991892i \(0.996843\pi\)
\(992\) −7.22890 + 12.5208i −0.229518 + 0.397536i
\(993\) 0 0
\(994\) 0.119534 + 0.0780537i 0.00379137 + 0.00247571i
\(995\) 36.0244 1.14205
\(996\) 0 0
\(997\) −23.5335 40.7612i −0.745313 1.29092i −0.950048 0.312103i \(-0.898967\pi\)
0.204735 0.978817i \(-0.434367\pi\)
\(998\) −3.96492 6.86745i −0.125507 0.217385i
\(999\) 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.e.f.163.2 10
3.2 odd 2 567.2.e.e.163.4 10
7.2 even 3 3969.2.a.z.1.4 5
7.4 even 3 inner 567.2.e.f.487.2 10
7.5 odd 6 3969.2.a.ba.1.4 5
9.2 odd 6 189.2.h.b.37.2 10
9.4 even 3 63.2.g.b.16.2 yes 10
9.5 odd 6 189.2.g.b.100.4 10
9.7 even 3 63.2.h.b.58.4 yes 10
21.2 odd 6 3969.2.a.bc.1.2 5
21.5 even 6 3969.2.a.bb.1.2 5
21.11 odd 6 567.2.e.e.487.4 10
36.7 odd 6 1008.2.q.i.625.1 10
36.11 even 6 3024.2.q.i.2305.5 10
36.23 even 6 3024.2.t.i.289.1 10
36.31 odd 6 1008.2.t.i.961.4 10
63.2 odd 6 1323.2.f.e.442.4 10
63.4 even 3 63.2.h.b.25.4 yes 10
63.5 even 6 1323.2.f.f.883.4 10
63.11 odd 6 189.2.g.b.172.4 10
63.13 odd 6 441.2.g.f.79.2 10
63.16 even 3 441.2.f.e.148.2 10
63.20 even 6 1323.2.h.f.226.2 10
63.23 odd 6 1323.2.f.e.883.4 10
63.25 even 3 63.2.g.b.4.2 10
63.31 odd 6 441.2.h.f.214.4 10
63.32 odd 6 189.2.h.b.46.2 10
63.34 odd 6 441.2.h.f.373.4 10
63.38 even 6 1323.2.g.f.361.4 10
63.40 odd 6 441.2.f.f.295.2 10
63.41 even 6 1323.2.g.f.667.4 10
63.47 even 6 1323.2.f.f.442.4 10
63.52 odd 6 441.2.g.f.67.2 10
63.58 even 3 441.2.f.e.295.2 10
63.59 even 6 1323.2.h.f.802.2 10
63.61 odd 6 441.2.f.f.148.2 10
252.11 even 6 3024.2.t.i.1873.1 10
252.67 odd 6 1008.2.q.i.529.1 10
252.95 even 6 3024.2.q.i.2881.5 10
252.151 odd 6 1008.2.t.i.193.4 10
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
63.2.g.b.4.2 10 63.25 even 3
63.2.g.b.16.2 yes 10 9.4 even 3
63.2.h.b.25.4 yes 10 63.4 even 3
63.2.h.b.58.4 yes 10 9.7 even 3
189.2.g.b.100.4 10 9.5 odd 6
189.2.g.b.172.4 10 63.11 odd 6
189.2.h.b.37.2 10 9.2 odd 6
189.2.h.b.46.2 10 63.32 odd 6
441.2.f.e.148.2 10 63.16 even 3
441.2.f.e.295.2 10 63.58 even 3
441.2.f.f.148.2 10 63.61 odd 6
441.2.f.f.295.2 10 63.40 odd 6
441.2.g.f.67.2 10 63.52 odd 6
441.2.g.f.79.2 10 63.13 odd 6
441.2.h.f.214.4 10 63.31 odd 6
441.2.h.f.373.4 10 63.34 odd 6
567.2.e.e.163.4 10 3.2 odd 2
567.2.e.e.487.4 10 21.11 odd 6
567.2.e.f.163.2 10 1.1 even 1 trivial
567.2.e.f.487.2 10 7.4 even 3 inner
1008.2.q.i.529.1 10 252.67 odd 6
1008.2.q.i.625.1 10 36.7 odd 6
1008.2.t.i.193.4 10 252.151 odd 6
1008.2.t.i.961.4 10 36.31 odd 6
1323.2.f.e.442.4 10 63.2 odd 6
1323.2.f.e.883.4 10 63.23 odd 6
1323.2.f.f.442.4 10 63.47 even 6
1323.2.f.f.883.4 10 63.5 even 6
1323.2.g.f.361.4 10 63.38 even 6
1323.2.g.f.667.4 10 63.41 even 6
1323.2.h.f.226.2 10 63.20 even 6
1323.2.h.f.802.2 10 63.59 even 6
3024.2.q.i.2305.5 10 36.11 even 6
3024.2.q.i.2881.5 10 252.95 even 6
3024.2.t.i.289.1 10 36.23 even 6
3024.2.t.i.1873.1 10 252.11 even 6
3969.2.a.z.1.4 5 7.2 even 3
3969.2.a.ba.1.4 5 7.5 odd 6
3969.2.a.bb.1.2 5 21.5 even 6
3969.2.a.bc.1.2 5 21.2 odd 6