Properties

Label 567.2.u.a.100.18
Level $567$
Weight $2$
Character 567.100
Analytic conductor $4.528$
Analytic rank $0$
Dimension $132$
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(100,567)]
 
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([16, 6]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("567.100");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 567 = 3^{4} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 567.u (of order \(9\), 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 \(\Q(\zeta_{9})\)
Twist minimal: no (minimal twist has level 189)
Sato-Tate group: $\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label 100.18
Character \(\chi\) \(=\) 567.100
Dual form 567.2.u.a.550.18

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.310937 - 1.76341i) q^{2} +(-1.13356 - 0.412582i) q^{4} +(0.00172074 + 0.000626297i) q^{5} +(2.59651 - 0.508047i) q^{7} +(0.710598 - 1.23079i) q^{8} +O(q^{10})\) \(q+(0.310937 - 1.76341i) q^{2} +(-1.13356 - 0.412582i) q^{4} +(0.00172074 + 0.000626297i) q^{5} +(2.59651 - 0.508047i) q^{7} +(0.710598 - 1.23079i) q^{8} +(0.00163946 - 0.00283963i) q^{10} +(-2.74403 + 0.998747i) q^{11} +(4.96182 + 1.80596i) q^{13} +(-0.0885434 - 4.73670i) q^{14} +(-3.79762 - 3.18658i) q^{16} +(2.87705 - 4.98319i) q^{17} +(-0.0567992 - 0.0983790i) q^{19} +(-0.00169216 - 0.00141989i) q^{20} +(0.907981 + 5.14941i) q^{22} +(0.681306 + 3.86388i) q^{23} +(-3.83022 - 3.21394i) q^{25} +(4.72746 - 8.18821i) q^{26} +(-3.15292 - 0.495374i) q^{28} +(5.71816 - 2.08124i) q^{29} +(-3.79806 - 1.38238i) q^{31} +(-4.62268 + 3.87889i) q^{32} +(-7.89285 - 6.62288i) q^{34} +(0.00478610 + 0.000751974i) q^{35} -3.24950 q^{37} +(-0.191144 + 0.0695707i) q^{38} +(0.00199359 - 0.00167282i) q^{40} +(-7.51748 - 2.73614i) q^{41} +(0.0535565 - 0.303734i) q^{43} +3.52259 q^{44} +7.02546 q^{46} +(-3.61594 + 1.31609i) q^{47} +(6.48378 - 2.63830i) q^{49} +(-6.85846 + 5.75493i) q^{50} +(-4.87942 - 4.09432i) q^{52} +(7.14507 + 12.3756i) q^{53} -0.00534727 q^{55} +(1.21978 - 3.55679i) q^{56} +(-1.89210 - 10.7306i) q^{58} +(6.17081 - 5.17793i) q^{59} +(-7.38012 + 2.68614i) q^{61} +(-3.61867 + 6.26772i) q^{62} +(0.445282 + 0.771251i) q^{64} +(0.00740692 + 0.00621515i) q^{65} +(1.62756 + 9.23035i) q^{67} +(-5.31728 + 4.46173i) q^{68} +(0.00281422 - 0.00820606i) q^{70} +(1.75785 + 3.04468i) q^{71} -3.09334 q^{73} +(-1.01039 + 5.73022i) q^{74} +(0.0237958 + 0.134953i) q^{76} +(-6.61751 + 3.98736i) q^{77} +(-2.20314 + 12.4946i) q^{79} +(-0.00453895 - 0.00786170i) q^{80} +(-7.16241 + 12.4057i) q^{82} +(-3.21166 + 1.16895i) q^{83} +(0.00807160 - 0.00677287i) q^{85} +(-0.518956 - 0.188884i) q^{86} +(-0.720656 + 4.08704i) q^{88} +(3.32414 + 5.75758i) q^{89} +(13.8010 + 2.16835i) q^{91} +(0.821865 - 4.66103i) q^{92} +(1.19649 + 6.78562i) q^{94} +(-3.61219e-5 - 0.000204857i) q^{95} +(1.79903 - 10.2028i) q^{97} +(-2.63637 - 12.2539i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 132 q + 3 q^{2} - 3 q^{4} + 3 q^{5} - 6 q^{7} + 6 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 132 q + 3 q^{2} - 3 q^{4} + 3 q^{5} - 6 q^{7} + 6 q^{8} + 3 q^{10} + 15 q^{11} - 12 q^{13} + 30 q^{14} + 9 q^{16} - 27 q^{17} + 3 q^{19} + 18 q^{20} - 12 q^{22} + 36 q^{23} - 3 q^{25} - 30 q^{26} - 12 q^{28} + 30 q^{29} - 3 q^{31} + 75 q^{32} - 18 q^{34} - 15 q^{35} - 6 q^{37} - 69 q^{38} + 51 q^{40} - 12 q^{43} + 6 q^{44} - 6 q^{46} + 21 q^{47} - 42 q^{49} + 39 q^{50} + 9 q^{52} - 9 q^{53} - 24 q^{55} - 111 q^{56} - 3 q^{58} - 27 q^{59} - 21 q^{61} - 75 q^{62} - 30 q^{64} + 90 q^{65} - 3 q^{67} + 30 q^{68} + 39 q^{70} + 18 q^{71} - 42 q^{73} - 51 q^{74} - 24 q^{76} - 15 q^{77} + 15 q^{79} - 102 q^{80} - 6 q^{82} + 42 q^{83} - 63 q^{85} + 93 q^{86} - 51 q^{88} - 75 q^{89} - 21 q^{91} + 66 q^{92} + 33 q^{94} - 15 q^{95} - 12 q^{97} + 36 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

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

\(n\) \(325\) \(407\)
\(\chi(n)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{8}{9}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.310937 1.76341i 0.219866 1.24692i −0.652394 0.757880i \(-0.726235\pi\)
0.872260 0.489042i \(-0.162654\pi\)
\(3\) 0 0
\(4\) −1.13356 0.412582i −0.566780 0.206291i
\(5\) 0.00172074 0.000626297i 0.000769537 0.000280088i 0.342405 0.939552i \(-0.388759\pi\)
−0.341635 + 0.939833i \(0.610981\pi\)
\(6\) 0 0
\(7\) 2.59651 0.508047i 0.981390 0.192024i
\(8\) 0.710598 1.23079i 0.251234 0.435151i
\(9\) 0 0
\(10\) 0.00163946 0.00283963i 0.000518443 0.000897970i
\(11\) −2.74403 + 0.998747i −0.827357 + 0.301133i −0.720774 0.693170i \(-0.756213\pi\)
−0.106584 + 0.994304i \(0.533991\pi\)
\(12\) 0 0
\(13\) 4.96182 + 1.80596i 1.37616 + 0.500882i 0.921013 0.389533i \(-0.127364\pi\)
0.455150 + 0.890415i \(0.349586\pi\)
\(14\) −0.0885434 4.73670i −0.0236642 1.26594i
\(15\) 0 0
\(16\) −3.79762 3.18658i −0.949404 0.796645i
\(17\) 2.87705 4.98319i 0.697786 1.20860i −0.271446 0.962454i \(-0.587502\pi\)
0.969232 0.246148i \(-0.0791649\pi\)
\(18\) 0 0
\(19\) −0.0567992 0.0983790i −0.0130306 0.0225697i 0.859437 0.511242i \(-0.170815\pi\)
−0.872467 + 0.488673i \(0.837481\pi\)
\(20\) −0.00169216 0.00141989i −0.000378378 0.000317497i
\(21\) 0 0
\(22\) 0.907981 + 5.14941i 0.193582 + 1.09786i
\(23\) 0.681306 + 3.86388i 0.142062 + 0.805674i 0.969679 + 0.244381i \(0.0785848\pi\)
−0.827617 + 0.561293i \(0.810304\pi\)
\(24\) 0 0
\(25\) −3.83022 3.21394i −0.766044 0.642787i
\(26\) 4.72746 8.18821i 0.927132 1.60584i
\(27\) 0 0
\(28\) −3.15292 0.495374i −0.595845 0.0936168i
\(29\) 5.71816 2.08124i 1.06184 0.386477i 0.248718 0.968576i \(-0.419991\pi\)
0.813118 + 0.582099i \(0.197768\pi\)
\(30\) 0 0
\(31\) −3.79806 1.38238i −0.682152 0.248283i −0.0223808 0.999750i \(-0.507125\pi\)
−0.659771 + 0.751466i \(0.729347\pi\)
\(32\) −4.62268 + 3.87889i −0.817182 + 0.685697i
\(33\) 0 0
\(34\) −7.89285 6.62288i −1.35361 1.13582i
\(35\) 0.00478610 0.000751974i 0.000808999 0.000127107i
\(36\) 0 0
\(37\) −3.24950 −0.534215 −0.267108 0.963667i \(-0.586068\pi\)
−0.267108 + 0.963667i \(0.586068\pi\)
\(38\) −0.191144 + 0.0695707i −0.0310076 + 0.0112859i
\(39\) 0 0
\(40\) 0.00199359 0.00167282i 0.000315215 0.000264497i
\(41\) −7.51748 2.73614i −1.17403 0.427313i −0.319943 0.947437i \(-0.603664\pi\)
−0.854091 + 0.520124i \(0.825886\pi\)
\(42\) 0 0
\(43\) 0.0535565 0.303734i 0.00816729 0.0463190i −0.980452 0.196760i \(-0.936958\pi\)
0.988619 + 0.150441i \(0.0480692\pi\)
\(44\) 3.52259 0.531051
\(45\) 0 0
\(46\) 7.02546 1.03585
\(47\) −3.61594 + 1.31609i −0.527439 + 0.191972i −0.591994 0.805942i \(-0.701659\pi\)
0.0645555 + 0.997914i \(0.479437\pi\)
\(48\) 0 0
\(49\) 6.48378 2.63830i 0.926254 0.376900i
\(50\) −6.85846 + 5.75493i −0.969932 + 0.813870i
\(51\) 0 0
\(52\) −4.87942 4.09432i −0.676654 0.567780i
\(53\) 7.14507 + 12.3756i 0.981451 + 1.69992i 0.656752 + 0.754106i \(0.271930\pi\)
0.324699 + 0.945817i \(0.394737\pi\)
\(54\) 0 0
\(55\) −0.00534727 −0.000721026
\(56\) 1.21978 3.55679i 0.163000 0.475296i
\(57\) 0 0
\(58\) −1.89210 10.7306i −0.248445 1.40900i
\(59\) 6.17081 5.17793i 0.803371 0.674109i −0.145645 0.989337i \(-0.546526\pi\)
0.949016 + 0.315228i \(0.102081\pi\)
\(60\) 0 0
\(61\) −7.38012 + 2.68614i −0.944928 + 0.343926i −0.768110 0.640318i \(-0.778803\pi\)
−0.176818 + 0.984244i \(0.556580\pi\)
\(62\) −3.61867 + 6.26772i −0.459572 + 0.796001i
\(63\) 0 0
\(64\) 0.445282 + 0.771251i 0.0556603 + 0.0964064i
\(65\) 0.00740692 + 0.00621515i 0.000918716 + 0.000770894i
\(66\) 0 0
\(67\) 1.62756 + 9.23035i 0.198838 + 1.12767i 0.906846 + 0.421462i \(0.138483\pi\)
−0.708008 + 0.706204i \(0.750406\pi\)
\(68\) −5.31728 + 4.46173i −0.644815 + 0.541064i
\(69\) 0 0
\(70\) 0.00281422 0.00820606i 0.000336364 0.000980812i
\(71\) 1.75785 + 3.04468i 0.208618 + 0.361337i 0.951279 0.308330i \(-0.0997702\pi\)
−0.742662 + 0.669667i \(0.766437\pi\)
\(72\) 0 0
\(73\) −3.09334 −0.362049 −0.181024 0.983479i \(-0.557941\pi\)
−0.181024 + 0.983479i \(0.557941\pi\)
\(74\) −1.01039 + 5.73022i −0.117456 + 0.666124i
\(75\) 0 0
\(76\) 0.0237958 + 0.134953i 0.00272957 + 0.0154801i
\(77\) −6.61751 + 3.98736i −0.754136 + 0.454402i
\(78\) 0 0
\(79\) −2.20314 + 12.4946i −0.247872 + 1.40575i 0.565855 + 0.824505i \(0.308546\pi\)
−0.813727 + 0.581248i \(0.802565\pi\)
\(80\) −0.00453895 0.00786170i −0.000507470 0.000878964i
\(81\) 0 0
\(82\) −7.16241 + 12.4057i −0.790956 + 1.36998i
\(83\) −3.21166 + 1.16895i −0.352526 + 0.128309i −0.512212 0.858859i \(-0.671174\pi\)
0.159686 + 0.987168i \(0.448952\pi\)
\(84\) 0 0
\(85\) 0.00807160 0.00677287i 0.000875487 0.000734621i
\(86\) −0.518956 0.188884i −0.0559604 0.0203679i
\(87\) 0 0
\(88\) −0.720656 + 4.08704i −0.0768222 + 0.435680i
\(89\) 3.32414 + 5.75758i 0.352358 + 0.610302i 0.986662 0.162781i \(-0.0520466\pi\)
−0.634304 + 0.773084i \(0.718713\pi\)
\(90\) 0 0
\(91\) 13.8010 + 2.16835i 1.44673 + 0.227305i
\(92\) 0.821865 4.66103i 0.0856854 0.485946i
\(93\) 0 0
\(94\) 1.19649 + 6.78562i 0.123408 + 0.699883i
\(95\) −3.61219e−5 0 0.000204857i −3.70603e−6 0 2.10179e-5i
\(96\) 0 0
\(97\) 1.79903 10.2028i 0.182664 1.03594i −0.746256 0.665659i \(-0.768151\pi\)
0.928920 0.370280i \(-0.120738\pi\)
\(98\) −2.63637 12.2539i −0.266314 1.23783i
\(99\) 0 0
\(100\) 3.01577 + 5.22347i 0.301577 + 0.522347i
\(101\) 0.438889 2.48906i 0.0436711 0.247671i −0.955155 0.296105i \(-0.904312\pi\)
0.998826 + 0.0484343i \(0.0154232\pi\)
\(102\) 0 0
\(103\) 17.1586 + 6.24521i 1.69069 + 0.615359i 0.994712 0.102708i \(-0.0327509\pi\)
0.695974 + 0.718067i \(0.254973\pi\)
\(104\) 5.74862 4.82366i 0.563699 0.472999i
\(105\) 0 0
\(106\) 24.0450 8.75167i 2.33546 0.850038i
\(107\) 0.926313 1.60442i 0.0895501 0.155105i −0.817771 0.575544i \(-0.804790\pi\)
0.907321 + 0.420438i \(0.138124\pi\)
\(108\) 0 0
\(109\) 3.47014 + 6.01046i 0.332379 + 0.575698i 0.982978 0.183724i \(-0.0588153\pi\)
−0.650599 + 0.759422i \(0.725482\pi\)
\(110\) −0.00166267 + 0.00942945i −0.000158529 + 0.000899063i
\(111\) 0 0
\(112\) −11.4795 6.34463i −1.08471 0.599511i
\(113\) 0.915044 + 5.18947i 0.0860801 + 0.488184i 0.997118 + 0.0758624i \(0.0241710\pi\)
−0.911038 + 0.412322i \(0.864718\pi\)
\(114\) 0 0
\(115\) −0.00124759 + 0.00707541i −0.000116338 + 0.000659785i
\(116\) −7.34056 −0.681554
\(117\) 0 0
\(118\) −7.21209 12.4917i −0.663927 1.14995i
\(119\) 4.93860 14.4006i 0.452721 1.32010i
\(120\) 0 0
\(121\) −1.89426 + 1.58947i −0.172206 + 0.144498i
\(122\) 2.44203 + 13.8494i 0.221091 + 1.25387i
\(123\) 0 0
\(124\) 3.73498 + 3.13402i 0.335412 + 0.281444i
\(125\) −0.00915584 0.0158584i −0.000818923 0.00141842i
\(126\) 0 0
\(127\) −6.51690 + 11.2876i −0.578281 + 1.00161i 0.417396 + 0.908725i \(0.362943\pi\)
−0.995677 + 0.0928873i \(0.970390\pi\)
\(128\) −9.84262 + 3.58242i −0.869973 + 0.316644i
\(129\) 0 0
\(130\) 0.0132630 0.0111289i 0.00116324 0.000976073i
\(131\) −0.927769 5.26164i −0.0810595 0.459711i −0.998138 0.0610036i \(-0.980570\pi\)
0.917078 0.398708i \(-0.130541\pi\)
\(132\) 0 0
\(133\) −0.197461 0.226586i −0.0171220 0.0196475i
\(134\) 16.7830 1.44983
\(135\) 0 0
\(136\) −4.08885 7.08209i −0.350616 0.607285i
\(137\) −5.66784 4.75589i −0.484237 0.406323i 0.367719 0.929937i \(-0.380139\pi\)
−0.851955 + 0.523614i \(0.824583\pi\)
\(138\) 0 0
\(139\) 8.27992 6.94767i 0.702293 0.589294i −0.220132 0.975470i \(-0.570649\pi\)
0.922425 + 0.386176i \(0.126204\pi\)
\(140\) −0.00511508 0.00282707i −0.000432304 0.000238931i
\(141\) 0 0
\(142\) 5.91560 2.15310i 0.496426 0.180684i
\(143\) −15.4191 −1.28941
\(144\) 0 0
\(145\) 0.0111429 0.000925369
\(146\) −0.961836 + 5.45485i −0.0796021 + 0.451446i
\(147\) 0 0
\(148\) 3.68351 + 1.34069i 0.302782 + 0.110204i
\(149\) −5.37813 + 4.51279i −0.440594 + 0.369702i −0.835932 0.548834i \(-0.815072\pi\)
0.395338 + 0.918536i \(0.370628\pi\)
\(150\) 0 0
\(151\) −11.0412 + 4.01867i −0.898521 + 0.327035i −0.749660 0.661823i \(-0.769783\pi\)
−0.148861 + 0.988858i \(0.547561\pi\)
\(152\) −0.161446 −0.0130950
\(153\) 0 0
\(154\) 4.97373 + 12.9092i 0.400795 + 1.04026i
\(155\) −0.00566968 0.00475743i −0.000455400 0.000382126i
\(156\) 0 0
\(157\) 16.7010 14.0138i 1.33289 1.11843i 0.349494 0.936939i \(-0.386354\pi\)
0.983393 0.181486i \(-0.0580908\pi\)
\(158\) 21.3481 + 7.77008i 1.69836 + 0.618154i
\(159\) 0 0
\(160\) −0.0103837 + 0.00377937i −0.000820907 + 0.000298786i
\(161\) 3.73205 + 9.68648i 0.294127 + 0.763401i
\(162\) 0 0
\(163\) 7.78249 13.4797i 0.609571 1.05581i −0.381740 0.924270i \(-0.624675\pi\)
0.991311 0.131539i \(-0.0419918\pi\)
\(164\) 7.39264 + 6.20316i 0.577268 + 0.484385i
\(165\) 0 0
\(166\) 1.06272 + 6.02696i 0.0824828 + 0.467783i
\(167\) 0.487765 + 2.76625i 0.0377444 + 0.214059i 0.997847 0.0655902i \(-0.0208930\pi\)
−0.960102 + 0.279649i \(0.909782\pi\)
\(168\) 0 0
\(169\) 11.3996 + 9.56543i 0.876895 + 0.735803i
\(170\) −0.00943361 0.0163395i −0.000723525 0.00125318i
\(171\) 0 0
\(172\) −0.186025 + 0.322204i −0.0141842 + 0.0245678i
\(173\) −3.96049 3.32325i −0.301111 0.252662i 0.479696 0.877435i \(-0.340747\pi\)
−0.780806 + 0.624773i \(0.785192\pi\)
\(174\) 0 0
\(175\) −11.5781 6.39910i −0.875218 0.483727i
\(176\) 13.6034 + 4.95122i 1.02539 + 0.373213i
\(177\) 0 0
\(178\) 11.1866 4.07159i 0.838471 0.305178i
\(179\) −8.64845 + 14.9796i −0.646416 + 1.11962i 0.337557 + 0.941305i \(0.390399\pi\)
−0.983973 + 0.178320i \(0.942934\pi\)
\(180\) 0 0
\(181\) −3.02128 + 5.23301i −0.224570 + 0.388966i −0.956190 0.292746i \(-0.905431\pi\)
0.731620 + 0.681712i \(0.238764\pi\)
\(182\) 8.11493 23.6626i 0.601519 1.75399i
\(183\) 0 0
\(184\) 5.23976 + 1.90712i 0.386280 + 0.140595i
\(185\) −0.00559154 0.00203515i −0.000411098 0.000149627i
\(186\) 0 0
\(187\) −2.91777 + 16.5475i −0.213368 + 1.21007i
\(188\) 4.64188 0.338544
\(189\) 0 0
\(190\) −0.000372480 0 −2.70225e−5 0
\(191\) −0.638035 + 3.61848i −0.0461666 + 0.261824i −0.999151 0.0411952i \(-0.986883\pi\)
0.952985 + 0.303019i \(0.0979945\pi\)
\(192\) 0 0
\(193\) −0.130197 0.0473877i −0.00937176 0.00341104i 0.337330 0.941386i \(-0.390476\pi\)
−0.346702 + 0.937975i \(0.612698\pi\)
\(194\) −17.4324 6.34487i −1.25157 0.455535i
\(195\) 0 0
\(196\) −8.43826 + 0.315584i −0.602733 + 0.0225417i
\(197\) −11.3397 + 19.6410i −0.807923 + 1.39936i 0.106377 + 0.994326i \(0.466075\pi\)
−0.914300 + 0.405038i \(0.867258\pi\)
\(198\) 0 0
\(199\) −13.8174 + 23.9324i −0.979489 + 1.69652i −0.315240 + 0.949012i \(0.602085\pi\)
−0.664248 + 0.747512i \(0.731248\pi\)
\(200\) −6.67743 + 2.43039i −0.472166 + 0.171854i
\(201\) 0 0
\(202\) −4.25278 1.54789i −0.299225 0.108909i
\(203\) 13.7899 8.30907i 0.967863 0.583182i
\(204\) 0 0
\(205\) −0.0112220 0.00941635i −0.000783776 0.000657666i
\(206\) 16.3481 28.3158i 1.13903 1.97286i
\(207\) 0 0
\(208\) −13.0883 22.6696i −0.907509 1.57185i
\(209\) 0.254115 + 0.213227i 0.0175775 + 0.0147492i
\(210\) 0 0
\(211\) −2.79342 15.8423i −0.192307 1.09063i −0.916202 0.400717i \(-0.868761\pi\)
0.723895 0.689910i \(-0.242350\pi\)
\(212\) −2.99341 16.9764i −0.205588 1.16595i
\(213\) 0 0
\(214\) −2.54123 2.13235i −0.173715 0.145764i
\(215\) 0.000282384 0 0.000489104i 1.92584e−5 0 3.33566e-5i
\(216\) 0 0
\(217\) −10.5640 1.65978i −0.717134 0.112673i
\(218\) 11.6779 4.25042i 0.790929 0.287875i
\(219\) 0 0
\(220\) 0.00606145 + 0.00220619i 0.000408663 + 0.000148741i
\(221\) 23.2748 19.5299i 1.56563 1.31372i
\(222\) 0 0
\(223\) 11.3720 + 9.54222i 0.761524 + 0.638994i 0.938523 0.345217i \(-0.112195\pi\)
−0.176999 + 0.984211i \(0.556639\pi\)
\(224\) −10.0322 + 12.4201i −0.670304 + 0.829854i
\(225\) 0 0
\(226\) 9.43570 0.627654
\(227\) −12.3380 + 4.49065i −0.818899 + 0.298055i −0.717295 0.696770i \(-0.754620\pi\)
−0.101605 + 0.994825i \(0.532398\pi\)
\(228\) 0 0
\(229\) −0.747003 + 0.626810i −0.0493633 + 0.0414207i −0.667136 0.744936i \(-0.732480\pi\)
0.617772 + 0.786357i \(0.288035\pi\)
\(230\) 0.0120890 + 0.00440002i 0.000797122 + 0.000290129i
\(231\) 0 0
\(232\) 1.50174 8.51679i 0.0985941 0.559155i
\(233\) 0.741911 0.0486042 0.0243021 0.999705i \(-0.492264\pi\)
0.0243021 + 0.999705i \(0.492264\pi\)
\(234\) 0 0
\(235\) −0.00704634 −0.000459653
\(236\) −9.13130 + 3.32352i −0.594397 + 0.216343i
\(237\) 0 0
\(238\) −23.8586 13.1865i −1.54653 0.854753i
\(239\) −16.7661 + 14.0684i −1.08451 + 0.910011i −0.996287 0.0860894i \(-0.972563\pi\)
−0.0882220 + 0.996101i \(0.528118\pi\)
\(240\) 0 0
\(241\) −8.17887 6.86288i −0.526847 0.442077i 0.340164 0.940366i \(-0.389517\pi\)
−0.867011 + 0.498289i \(0.833962\pi\)
\(242\) 2.21390 + 3.83459i 0.142315 + 0.246497i
\(243\) 0 0
\(244\) 9.47406 0.606515
\(245\) 0.0128092 0.000479055i 0.000818352 3.06057e-5i
\(246\) 0 0
\(247\) −0.104159 0.590716i −0.00662749 0.0375864i
\(248\) −4.40032 + 3.69231i −0.279421 + 0.234462i
\(249\) 0 0
\(250\) −0.0308118 + 0.0112146i −0.00194871 + 0.000709272i
\(251\) −2.40742 + 4.16977i −0.151955 + 0.263194i −0.931946 0.362597i \(-0.881890\pi\)
0.779991 + 0.625790i \(0.215224\pi\)
\(252\) 0 0
\(253\) −5.72856 9.92216i −0.360151 0.623801i
\(254\) 17.8784 + 15.0017i 1.12179 + 0.941292i
\(255\) 0 0
\(256\) 3.56614 + 20.2246i 0.222884 + 1.26404i
\(257\) −13.8604 + 11.6302i −0.864587 + 0.725475i −0.962951 0.269676i \(-0.913083\pi\)
0.0983640 + 0.995151i \(0.468639\pi\)
\(258\) 0 0
\(259\) −8.43738 + 1.65090i −0.524273 + 0.102582i
\(260\) −0.00583193 0.0101012i −0.000361681 0.000626450i
\(261\) 0 0
\(262\) −9.56692 −0.591046
\(263\) 1.29613 7.35070i 0.0799226 0.453264i −0.918415 0.395619i \(-0.870530\pi\)
0.998337 0.0576444i \(-0.0183590\pi\)
\(264\) 0 0
\(265\) 0.00454397 + 0.0257701i 0.000279134 + 0.00158305i
\(266\) −0.460963 + 0.277751i −0.0282634 + 0.0170300i
\(267\) 0 0
\(268\) 1.96334 11.1347i 0.119930 0.680157i
\(269\) −6.31420 10.9365i −0.384983 0.666811i 0.606784 0.794867i \(-0.292459\pi\)
−0.991767 + 0.128056i \(0.959126\pi\)
\(270\) 0 0
\(271\) −8.60359 + 14.9018i −0.522631 + 0.905223i 0.477023 + 0.878891i \(0.341716\pi\)
−0.999653 + 0.0263318i \(0.991617\pi\)
\(272\) −26.8053 + 9.75632i −1.62531 + 0.591564i
\(273\) 0 0
\(274\) −10.1489 + 8.51597i −0.613120 + 0.514469i
\(275\) 13.7202 + 4.99373i 0.827357 + 0.301133i
\(276\) 0 0
\(277\) 4.75015 26.9394i 0.285409 1.61863i −0.418414 0.908257i \(-0.637414\pi\)
0.703822 0.710376i \(-0.251475\pi\)
\(278\) −9.67709 16.7612i −0.580393 1.00527i
\(279\) 0 0
\(280\) 0.00432652 0.00535635i 0.000258559 0.000320103i
\(281\) 2.21334 12.5525i 0.132037 0.748817i −0.844841 0.535017i \(-0.820305\pi\)
0.976878 0.213799i \(-0.0685839\pi\)
\(282\) 0 0
\(283\) −2.70525 15.3422i −0.160811 0.912002i −0.953280 0.302090i \(-0.902316\pi\)
0.792469 0.609912i \(-0.208795\pi\)
\(284\) −0.736443 4.17658i −0.0436999 0.247834i
\(285\) 0 0
\(286\) −4.79438 + 27.1903i −0.283497 + 1.60779i
\(287\) −20.9093 3.28519i −1.23424 0.193919i
\(288\) 0 0
\(289\) −8.05480 13.9513i −0.473812 0.820666i
\(290\) 0.00346475 0.0196496i 0.000203457 0.00115386i
\(291\) 0 0
\(292\) 3.50649 + 1.27626i 0.205202 + 0.0746874i
\(293\) 23.0618 19.3511i 1.34728 1.13051i 0.367595 0.929986i \(-0.380181\pi\)
0.979690 0.200520i \(-0.0642633\pi\)
\(294\) 0 0
\(295\) 0.0138613 0.00504508i 0.000807034 0.000293736i
\(296\) −2.30909 + 3.99946i −0.134213 + 0.232464i
\(297\) 0 0
\(298\) 6.28565 + 10.8871i 0.364118 + 0.630671i
\(299\) −3.59747 + 20.4023i −0.208047 + 1.17989i
\(300\) 0 0
\(301\) −0.0152509 0.815859i −0.000879047 0.0470253i
\(302\) 3.65346 + 20.7198i 0.210233 + 1.19229i
\(303\) 0 0
\(304\) −0.0977911 + 0.554601i −0.00560870 + 0.0318085i
\(305\) −0.0143816 −0.000823486
\(306\) 0 0
\(307\) 5.25664 + 9.10477i 0.300012 + 0.519637i 0.976138 0.217149i \(-0.0696758\pi\)
−0.676126 + 0.736786i \(0.736342\pi\)
\(308\) 9.14646 1.78964i 0.521168 0.101974i
\(309\) 0 0
\(310\) −0.0101522 + 0.00851873i −0.000576608 + 0.000483831i
\(311\) −3.40804 19.3279i −0.193252 1.09599i −0.914886 0.403712i \(-0.867720\pi\)
0.721634 0.692275i \(-0.243391\pi\)
\(312\) 0 0
\(313\) 1.78384 + 1.49682i 0.100829 + 0.0846054i 0.691808 0.722081i \(-0.256814\pi\)
−0.590980 + 0.806686i \(0.701259\pi\)
\(314\) −19.5192 33.8082i −1.10153 1.90791i
\(315\) 0 0
\(316\) 7.65243 13.2544i 0.430483 0.745619i
\(317\) 24.4267 8.89060i 1.37194 0.499346i 0.452217 0.891908i \(-0.350633\pi\)
0.919726 + 0.392562i \(0.128411\pi\)
\(318\) 0 0
\(319\) −13.6122 + 11.4220i −0.762137 + 0.639509i
\(320\) 0.000283181 0.00160600i 1.58303e−5 8.97780e-5i
\(321\) 0 0
\(322\) 18.2417 3.56926i 1.01657 0.198907i
\(323\) −0.653655 −0.0363704
\(324\) 0 0
\(325\) −13.2006 22.8642i −0.732240 1.26828i
\(326\) −21.3504 17.9151i −1.18249 0.992224i
\(327\) 0 0
\(328\) −8.70953 + 7.30816i −0.480903 + 0.403526i
\(329\) −8.72020 + 5.25432i −0.480760 + 0.289680i
\(330\) 0 0
\(331\) −24.5229 + 8.92560i −1.34790 + 0.490595i −0.912292 0.409541i \(-0.865689\pi\)
−0.435608 + 0.900137i \(0.643466\pi\)
\(332\) 4.12290 0.226274
\(333\) 0 0
\(334\) 5.02971 0.275213
\(335\) −0.00298034 + 0.0169023i −0.000162833 + 0.000923473i
\(336\) 0 0
\(337\) −20.5364 7.47462i −1.11869 0.407169i −0.284514 0.958672i \(-0.591832\pi\)
−0.834173 + 0.551503i \(0.814054\pi\)
\(338\) 20.4124 17.1280i 1.11029 0.931642i
\(339\) 0 0
\(340\) −0.0119440 + 0.00434726i −0.000647754 + 0.000235763i
\(341\) 11.8027 0.639150
\(342\) 0 0
\(343\) 15.4948 10.1445i 0.836643 0.547749i
\(344\) −0.335776 0.281750i −0.0181038 0.0151909i
\(345\) 0 0
\(346\) −7.09173 + 5.95067i −0.381254 + 0.319910i
\(347\) −32.0887 11.6793i −1.72261 0.626980i −0.724551 0.689221i \(-0.757953\pi\)
−0.998061 + 0.0622414i \(0.980175\pi\)
\(348\) 0 0
\(349\) −14.6096 + 5.31745i −0.782032 + 0.284636i −0.702020 0.712157i \(-0.747718\pi\)
−0.0800123 + 0.996794i \(0.525496\pi\)
\(350\) −14.8843 + 18.4272i −0.795600 + 0.984974i
\(351\) 0 0
\(352\) 8.81076 15.2607i 0.469615 0.813397i
\(353\) 1.15956 + 0.972982i 0.0617169 + 0.0517866i 0.673124 0.739529i \(-0.264952\pi\)
−0.611407 + 0.791316i \(0.709396\pi\)
\(354\) 0 0
\(355\) 0.00111792 + 0.00634002i 5.93328e−5 + 0.000336493i
\(356\) −1.39264 7.89804i −0.0738097 0.418595i
\(357\) 0 0
\(358\) 23.7260 + 19.9085i 1.25396 + 1.05220i
\(359\) 1.62355 + 2.81207i 0.0856876 + 0.148415i 0.905684 0.423953i \(-0.139358\pi\)
−0.819996 + 0.572369i \(0.806025\pi\)
\(360\) 0 0
\(361\) 9.49355 16.4433i 0.499660 0.865437i
\(362\) 8.28853 + 6.95490i 0.435635 + 0.365541i
\(363\) 0 0
\(364\) −14.7496 8.15198i −0.773088 0.427280i
\(365\) −0.00532283 0.00193735i −0.000278610 0.000101406i
\(366\) 0 0
\(367\) −5.97923 + 2.17626i −0.312113 + 0.113600i −0.493327 0.869844i \(-0.664220\pi\)
0.181214 + 0.983444i \(0.441997\pi\)
\(368\) 9.72521 16.8446i 0.506962 0.878083i
\(369\) 0 0
\(370\) −0.00532743 + 0.00922739i −0.000276960 + 0.000479709i
\(371\) 24.8397 + 28.5035i 1.28961 + 1.47983i
\(372\) 0 0
\(373\) −17.8704 6.50428i −0.925293 0.336779i −0.164951 0.986302i \(-0.552746\pi\)
−0.760342 + 0.649523i \(0.774969\pi\)
\(374\) 28.2728 + 10.2905i 1.46195 + 0.532107i
\(375\) 0 0
\(376\) −0.949641 + 5.38568i −0.0489740 + 0.277745i
\(377\) 32.1311 1.65484
\(378\) 0 0
\(379\) 21.5974 1.10938 0.554691 0.832057i \(-0.312837\pi\)
0.554691 + 0.832057i \(0.312837\pi\)
\(380\) −4.35742e−5 0 0.000247121i −2.23531e−6 0 1.26771e-5i
\(381\) 0 0
\(382\) 6.18248 + 2.25024i 0.316323 + 0.115132i
\(383\) −21.1775 7.70799i −1.08212 0.393860i −0.261425 0.965224i \(-0.584192\pi\)
−0.820697 + 0.571364i \(0.806414\pi\)
\(384\) 0 0
\(385\) −0.0138843 + 0.00271666i −0.000707608 + 0.000138454i
\(386\) −0.124047 + 0.214856i −0.00631384 + 0.0109359i
\(387\) 0 0
\(388\) −6.24881 + 10.8233i −0.317235 + 0.549467i
\(389\) 3.17737 1.15647i 0.161099 0.0586353i −0.260212 0.965552i \(-0.583792\pi\)
0.421311 + 0.906916i \(0.361570\pi\)
\(390\) 0 0
\(391\) 21.2146 + 7.72148i 1.07287 + 0.390492i
\(392\) 1.36016 9.85495i 0.0686983 0.497750i
\(393\) 0 0
\(394\) 31.1093 + 26.1038i 1.56726 + 1.31509i
\(395\) −0.0116163 + 0.0201201i −0.000584482 + 0.00101235i
\(396\) 0 0
\(397\) −12.5390 21.7183i −0.629316 1.09001i −0.987689 0.156429i \(-0.950002\pi\)
0.358373 0.933579i \(-0.383332\pi\)
\(398\) 37.9064 + 31.8072i 1.90008 + 1.59435i
\(399\) 0 0
\(400\) 4.30425 + 24.4106i 0.215212 + 1.22053i
\(401\) −4.72763 26.8117i −0.236087 1.33891i −0.840313 0.542101i \(-0.817629\pi\)
0.604227 0.796812i \(-0.293482\pi\)
\(402\) 0 0
\(403\) −16.3488 13.7183i −0.814391 0.683356i
\(404\) −1.52445 + 2.64042i −0.0758442 + 0.131366i
\(405\) 0 0
\(406\) −10.3645 26.9009i −0.514382 1.33507i
\(407\) 8.91675 3.24543i 0.441987 0.160870i
\(408\) 0 0
\(409\) 28.1524 + 10.2466i 1.39205 + 0.506664i 0.925808 0.377994i \(-0.123386\pi\)
0.466240 + 0.884658i \(0.345608\pi\)
\(410\) −0.0200943 + 0.0168611i −0.000992384 + 0.000832709i
\(411\) 0 0
\(412\) −16.8736 14.1586i −0.831303 0.697546i
\(413\) 13.3920 16.5796i 0.658976 0.815830i
\(414\) 0 0
\(415\) −0.00625854 −0.000307219
\(416\) −29.9420 + 10.8980i −1.46803 + 0.534318i
\(417\) 0 0
\(418\) 0.455022 0.381809i 0.0222558 0.0186749i
\(419\) 10.6765 + 3.88594i 0.521583 + 0.189841i 0.589376 0.807859i \(-0.299374\pi\)
−0.0677934 + 0.997699i \(0.521596\pi\)
\(420\) 0 0
\(421\) 1.69681 9.62307i 0.0826973 0.469000i −0.915133 0.403153i \(-0.867914\pi\)
0.997830 0.0658463i \(-0.0209747\pi\)
\(422\) −28.8051 −1.40221
\(423\) 0 0
\(424\) 20.3091 0.986297
\(425\) −27.0354 + 9.84007i −1.31141 + 0.477314i
\(426\) 0 0
\(427\) −17.7979 + 10.7241i −0.861301 + 0.518974i
\(428\) −1.71199 + 1.43653i −0.0827520 + 0.0694372i
\(429\) 0 0
\(430\) −0.000774688 0 0.000650041i −3.73588e−5 0 3.13477e-5i
\(431\) 7.18150 + 12.4387i 0.345921 + 0.599152i 0.985521 0.169556i \(-0.0542333\pi\)
−0.639600 + 0.768708i \(0.720900\pi\)
\(432\) 0 0
\(433\) 34.1628 1.64176 0.820880 0.571100i \(-0.193483\pi\)
0.820880 + 0.571100i \(0.193483\pi\)
\(434\) −6.21163 + 18.1127i −0.298168 + 0.869436i
\(435\) 0 0
\(436\) −1.45380 8.24493i −0.0696246 0.394861i
\(437\) 0.341427 0.286491i 0.0163327 0.0137047i
\(438\) 0 0
\(439\) 25.5052 9.28313i 1.21730 0.443060i 0.348067 0.937470i \(-0.386838\pi\)
0.869229 + 0.494410i \(0.164616\pi\)
\(440\) −0.00379976 + 0.00658138i −0.000181146 + 0.000313755i
\(441\) 0 0
\(442\) −27.2023 47.1157i −1.29388 2.24107i
\(443\) 21.3846 + 17.9438i 1.01601 + 0.852534i 0.989121 0.147104i \(-0.0469952\pi\)
0.0268898 + 0.999638i \(0.491440\pi\)
\(444\) 0 0
\(445\) 0.00211401 + 0.0119892i 0.000100214 + 0.000568341i
\(446\) 20.3629 17.0865i 0.964209 0.809067i
\(447\) 0 0
\(448\) 1.54801 + 1.77634i 0.0731367 + 0.0839242i
\(449\) −15.0828 26.1241i −0.711801 1.23287i −0.964181 0.265247i \(-0.914547\pi\)
0.252380 0.967628i \(-0.418787\pi\)
\(450\) 0 0
\(451\) 23.3609 1.10002
\(452\) 1.10383 6.26011i 0.0519196 0.294451i
\(453\) 0 0
\(454\) 4.08254 + 23.1532i 0.191603 + 1.08664i
\(455\) 0.0223898 + 0.0123747i 0.00104965 + 0.000580133i
\(456\) 0 0
\(457\) −4.26288 + 24.1760i −0.199409 + 1.13091i 0.706589 + 0.707624i \(0.250233\pi\)
−0.905998 + 0.423282i \(0.860878\pi\)
\(458\) 0.873053 + 1.51217i 0.0407951 + 0.0706592i
\(459\) 0 0
\(460\) 0.00433340 0.00750567i 0.000202046 0.000349954i
\(461\) 29.7613 10.8322i 1.38612 0.504507i 0.462094 0.886831i \(-0.347098\pi\)
0.924028 + 0.382324i \(0.124876\pi\)
\(462\) 0 0
\(463\) −14.4821 + 12.1519i −0.673038 + 0.564746i −0.913963 0.405798i \(-0.866994\pi\)
0.240925 + 0.970544i \(0.422549\pi\)
\(464\) −28.3474 10.3176i −1.31600 0.478983i
\(465\) 0 0
\(466\) 0.230688 1.30830i 0.0106864 0.0606056i
\(467\) −5.79658 10.0400i −0.268234 0.464595i 0.700172 0.713974i \(-0.253107\pi\)
−0.968406 + 0.249380i \(0.919773\pi\)
\(468\) 0 0
\(469\) 8.91543 + 23.1399i 0.411676 + 1.06850i
\(470\) −0.00219097 + 0.0124256i −0.000101062 + 0.000573151i
\(471\) 0 0
\(472\) −1.98798 11.2744i −0.0915043 0.518947i
\(473\) 0.156392 + 0.886946i 0.00719093 + 0.0407818i
\(474\) 0 0
\(475\) −0.0986306 + 0.559362i −0.00452548 + 0.0256653i
\(476\) −11.5396 + 14.2864i −0.528918 + 0.654815i
\(477\) 0 0
\(478\) 19.5953 + 33.9400i 0.896266 + 1.55238i
\(479\) 1.15008 6.52246i 0.0525487 0.298019i −0.947195 0.320658i \(-0.896096\pi\)
0.999744 + 0.0226396i \(0.00720703\pi\)
\(480\) 0 0
\(481\) −16.1235 5.86846i −0.735167 0.267579i
\(482\) −14.6452 + 12.2888i −0.667071 + 0.559739i
\(483\) 0 0
\(484\) 2.80305 1.02023i 0.127411 0.0463739i
\(485\) 0.00948565 0.0164296i 0.000430721 0.000746031i
\(486\) 0 0
\(487\) 8.02176 + 13.8941i 0.363501 + 0.629602i 0.988534 0.150996i \(-0.0482481\pi\)
−0.625034 + 0.780598i \(0.714915\pi\)
\(488\) −1.93822 + 10.9922i −0.0877389 + 0.497592i
\(489\) 0 0
\(490\) 0.00313810 0.0227369i 0.000141765 0.00102715i
\(491\) 1.53326 + 8.69553i 0.0691949 + 0.392424i 0.999661 + 0.0260451i \(0.00829134\pi\)
−0.930466 + 0.366378i \(0.880598\pi\)
\(492\) 0 0
\(493\) 6.08020 34.4825i 0.273838 1.55301i
\(494\) −1.07406 −0.0483244
\(495\) 0 0
\(496\) 10.0185 + 17.3526i 0.449845 + 0.779154i
\(497\) 6.11111 + 7.01248i 0.274121 + 0.314553i
\(498\) 0 0
\(499\) 22.8396 19.1647i 1.02244 0.857931i 0.0325101 0.999471i \(-0.489650\pi\)
0.989933 + 0.141540i \(0.0452054\pi\)
\(500\) 0.00383581 + 0.0217540i 0.000171543 + 0.000972867i
\(501\) 0 0
\(502\) 6.60447 + 5.54181i 0.294772 + 0.247343i
\(503\) 18.3458 + 31.7758i 0.817998 + 1.41681i 0.907155 + 0.420797i \(0.138250\pi\)
−0.0891565 + 0.996018i \(0.528417\pi\)
\(504\) 0 0
\(505\) 0.00231410 0.00400815i 0.000102976 0.000178360i
\(506\) −19.2781 + 7.01665i −0.857016 + 0.311928i
\(507\) 0 0
\(508\) 12.0444 10.1064i 0.534382 0.448399i
\(509\) 4.76156 + 27.0042i 0.211053 + 1.19694i 0.887627 + 0.460564i \(0.152353\pi\)
−0.676574 + 0.736375i \(0.736536\pi\)
\(510\) 0 0
\(511\) −8.03191 + 1.57156i −0.355311 + 0.0695219i
\(512\) 15.8246 0.699353
\(513\) 0 0
\(514\) 16.1992 + 28.0579i 0.714517 + 1.23758i
\(515\) 0.0256140 + 0.0214927i 0.00112869 + 0.000947083i
\(516\) 0 0
\(517\) 8.60782 7.22281i 0.378571 0.317659i
\(518\) 0.287722 + 15.3919i 0.0126418 + 0.676282i
\(519\) 0 0
\(520\) 0.0129129 0.00469991i 0.000566268 0.000206105i
\(521\) 14.3142 0.627117 0.313559 0.949569i \(-0.398479\pi\)
0.313559 + 0.949569i \(0.398479\pi\)
\(522\) 0 0
\(523\) −10.3437 −0.452297 −0.226149 0.974093i \(-0.572614\pi\)
−0.226149 + 0.974093i \(0.572614\pi\)
\(524\) −1.11918 + 6.34716i −0.0488914 + 0.277277i
\(525\) 0 0
\(526\) −12.5593 4.57122i −0.547612 0.199315i
\(527\) −17.8159 + 14.9493i −0.776072 + 0.651202i
\(528\) 0 0
\(529\) 7.14757 2.60150i 0.310764 0.113109i
\(530\) 0.0468563 0.00203531
\(531\) 0 0
\(532\) 0.130349 + 0.338318i 0.00565133 + 0.0146679i
\(533\) −32.3591 27.1525i −1.40163 1.17611i
\(534\) 0 0
\(535\) 0.00259879 0.00218064i 0.000112355 9.42773e-5i
\(536\) 12.5172 + 4.55588i 0.540660 + 0.196784i
\(537\) 0 0
\(538\) −21.2489 + 7.73397i −0.916105 + 0.333435i
\(539\) −15.1567 + 13.7152i −0.652846 + 0.590757i
\(540\) 0 0
\(541\) −7.72944 + 13.3878i −0.332315 + 0.575586i −0.982965 0.183791i \(-0.941163\pi\)
0.650651 + 0.759377i \(0.274496\pi\)
\(542\) 23.6029 + 19.8052i 1.01383 + 0.850707i
\(543\) 0 0
\(544\) 6.02958 + 34.1954i 0.258516 + 1.46612i
\(545\) 0.00220686 + 0.0125158i 9.45317e−5 + 0.000536116i
\(546\) 0 0
\(547\) 6.37136 + 5.34621i 0.272420 + 0.228587i 0.768755 0.639544i \(-0.220877\pi\)
−0.496335 + 0.868131i \(0.665321\pi\)
\(548\) 4.46265 + 7.72953i 0.190635 + 0.330189i
\(549\) 0 0
\(550\) 13.0721 22.6416i 0.557397 0.965440i
\(551\) −0.529537 0.444334i −0.0225590 0.0189293i
\(552\) 0 0
\(553\) 0.627371 + 33.5617i 0.0266785 + 1.42719i
\(554\) −46.0283 16.7529i −1.95556 0.711764i
\(555\) 0 0
\(556\) −12.2523 + 4.45946i −0.519612 + 0.189123i
\(557\) 15.4350 26.7341i 0.654000 1.13276i −0.328143 0.944628i \(-0.606423\pi\)
0.982143 0.188134i \(-0.0602438\pi\)
\(558\) 0 0
\(559\) 0.814268 1.41035i 0.0344399 0.0596516i
\(560\) −0.0157796 0.0181070i −0.000666808 0.000765161i
\(561\) 0 0
\(562\) −21.4470 7.80606i −0.904685 0.329279i
\(563\) −18.7640 6.82952i −0.790807 0.287830i −0.0851352 0.996369i \(-0.527132\pi\)
−0.705671 + 0.708539i \(0.749354\pi\)
\(564\) 0 0
\(565\) −0.00167560 + 0.00950280i −7.04930e−5 + 0.000399786i
\(566\) −27.8959 −1.17255
\(567\) 0 0
\(568\) 4.99649 0.209648
\(569\) 4.66103 26.4340i 0.195400 1.10817i −0.716447 0.697641i \(-0.754233\pi\)
0.911848 0.410529i \(-0.134656\pi\)
\(570\) 0 0
\(571\) 28.5000 + 10.3731i 1.19269 + 0.434102i 0.860666 0.509170i \(-0.170048\pi\)
0.332020 + 0.943272i \(0.392270\pi\)
\(572\) 17.4785 + 6.36165i 0.730812 + 0.265994i
\(573\) 0 0
\(574\) −12.2947 + 35.8503i −0.513169 + 1.49636i
\(575\) 9.80870 16.9892i 0.409051 0.708497i
\(576\) 0 0
\(577\) −6.84381 + 11.8538i −0.284912 + 0.493482i −0.972588 0.232536i \(-0.925298\pi\)
0.687676 + 0.726018i \(0.258631\pi\)
\(578\) −27.1065 + 9.86596i −1.12748 + 0.410370i
\(579\) 0 0
\(580\) −0.0126312 0.00459737i −0.000524481 0.000190895i
\(581\) −7.74525 + 4.66687i −0.321327 + 0.193615i
\(582\) 0 0
\(583\) −31.9665 26.8230i −1.32392 1.11090i
\(584\) −2.19812 + 3.80726i −0.0909591 + 0.157546i
\(585\) 0 0
\(586\) −26.9533 46.6845i −1.11343 1.92852i
\(587\) −11.7029 9.81992i −0.483031 0.405312i 0.368490 0.929632i \(-0.379875\pi\)
−0.851521 + 0.524320i \(0.824319\pi\)
\(588\) 0 0
\(589\) 0.0797294 + 0.452168i 0.00328519 + 0.0186312i
\(590\) −0.00458659 0.0260118i −0.000188827 0.00107089i
\(591\) 0 0
\(592\) 12.3404 + 10.3548i 0.507186 + 0.425580i
\(593\) 4.67660 8.10010i 0.192045 0.332631i −0.753883 0.657009i \(-0.771821\pi\)
0.945928 + 0.324377i \(0.105155\pi\)
\(594\) 0 0
\(595\) 0.0175171 0.0216866i 0.000718130 0.000889064i
\(596\) 7.95833 2.89660i 0.325986 0.118649i
\(597\) 0 0
\(598\) 34.8591 + 12.6877i 1.42549 + 0.518837i
\(599\) 24.3174 20.4047i 0.993582 0.833714i 0.00749930 0.999972i \(-0.497613\pi\)
0.986082 + 0.166258i \(0.0531684\pi\)
\(600\) 0 0
\(601\) 1.79900 + 1.50954i 0.0733827 + 0.0615754i 0.678741 0.734378i \(-0.262526\pi\)
−0.605359 + 0.795953i \(0.706970\pi\)
\(602\) −1.44344 0.226787i −0.0588302 0.00924316i
\(603\) 0 0
\(604\) 14.1739 0.576728
\(605\) −0.00425500 + 0.00154870i −0.000172991 + 6.29634e-5i
\(606\) 0 0
\(607\) 4.04355 3.39294i 0.164123 0.137715i −0.557027 0.830494i \(-0.688058\pi\)
0.721150 + 0.692779i \(0.243614\pi\)
\(608\) 0.644165 + 0.234457i 0.0261244 + 0.00950849i
\(609\) 0 0
\(610\) −0.00447177 + 0.0253606i −0.000181056 + 0.00102682i
\(611\) −20.3185 −0.821997
\(612\) 0 0
\(613\) −36.7281 −1.48343 −0.741716 0.670714i \(-0.765988\pi\)
−0.741716 + 0.670714i \(0.765988\pi\)
\(614\) 17.6900 6.43862i 0.713909 0.259842i
\(615\) 0 0
\(616\) 0.205216 + 10.9782i 0.00826839 + 0.442324i
\(617\) 1.43466 1.20382i 0.0577572 0.0484641i −0.613452 0.789732i \(-0.710220\pi\)
0.671209 + 0.741268i \(0.265775\pi\)
\(618\) 0 0
\(619\) 2.32614 + 1.95187i 0.0934956 + 0.0784521i 0.688337 0.725391i \(-0.258341\pi\)
−0.594842 + 0.803843i \(0.702785\pi\)
\(620\) 0.00446409 + 0.00773204i 0.000179282 + 0.000310526i
\(621\) 0 0
\(622\) −35.1428 −1.40910
\(623\) 11.5563 + 13.2608i 0.462993 + 0.531284i
\(624\) 0 0
\(625\) 4.34120 + 24.6201i 0.173648 + 0.984806i
\(626\) 3.19418 2.68024i 0.127665 0.107124i
\(627\) 0 0
\(628\) −24.7135 + 8.99497i −0.986175 + 0.358938i
\(629\) −9.34897 + 16.1929i −0.372768 + 0.645653i
\(630\) 0 0
\(631\) −10.2641 17.7780i −0.408609 0.707732i 0.586125 0.810221i \(-0.300653\pi\)
−0.994734 + 0.102489i \(0.967319\pi\)
\(632\) 13.8127 + 11.5902i 0.549440 + 0.461035i
\(633\) 0 0
\(634\) −8.08263 45.8389i −0.321002 1.82049i
\(635\) −0.0182832 + 0.0153415i −0.000725548 + 0.000608807i
\(636\) 0 0
\(637\) 36.9360 1.38138i 1.46346 0.0547322i
\(638\) 15.9091 + 27.5555i 0.629849 + 1.09093i
\(639\) 0 0
\(640\) −0.0191802 −0.000758164
\(641\) −7.01580 + 39.7886i −0.277107 + 1.57155i 0.455080 + 0.890450i \(0.349611\pi\)
−0.732188 + 0.681103i \(0.761501\pi\)
\(642\) 0 0
\(643\) −7.46629 42.3434i −0.294442 1.66986i −0.669463 0.742845i \(-0.733476\pi\)
0.375021 0.927016i \(-0.377635\pi\)
\(644\) −0.234037 12.5200i −0.00922234 0.493356i
\(645\) 0 0
\(646\) −0.203246 + 1.15266i −0.00799660 + 0.0453510i
\(647\) −19.9166 34.4965i −0.783002 1.35620i −0.930186 0.367089i \(-0.880354\pi\)
0.147184 0.989109i \(-0.452979\pi\)
\(648\) 0 0
\(649\) −11.7615 + 20.3715i −0.461679 + 0.799651i
\(650\) −44.4236 + 16.1689i −1.74244 + 0.634195i
\(651\) 0 0
\(652\) −14.3834 + 12.0691i −0.563297 + 0.472662i
\(653\) 3.55373 + 1.29345i 0.139068 + 0.0506167i 0.410617 0.911808i \(-0.365313\pi\)
−0.271548 + 0.962425i \(0.587536\pi\)
\(654\) 0 0
\(655\) 0.00169890 0.00963495i 6.63816e−5 0.000376469i
\(656\) 19.8296 + 34.3459i 0.774216 + 1.34098i
\(657\) 0 0
\(658\) 6.55411 + 17.0111i 0.255506 + 0.663161i
\(659\) −0.766060 + 4.34454i −0.0298415 + 0.169239i −0.996086 0.0883863i \(-0.971829\pi\)
0.966245 + 0.257626i \(0.0829401\pi\)
\(660\) 0 0
\(661\) −0.578375 3.28013i −0.0224962 0.127582i 0.971491 0.237075i \(-0.0761886\pi\)
−0.993988 + 0.109492i \(0.965077\pi\)
\(662\) 8.11444 + 46.0193i 0.315377 + 1.78859i
\(663\) 0 0
\(664\) −0.843468 + 4.78355i −0.0327329 + 0.185638i
\(665\) −0.000197868 0 0.000513564i −7.67300e−6 0 1.99151e-5i
\(666\) 0 0
\(667\) 11.9375 + 20.6763i 0.462221 + 0.800590i
\(668\) 0.588395 3.33695i 0.0227657 0.129111i
\(669\) 0 0
\(670\) 0.0288791 + 0.0105111i 0.00111570 + 0.000406080i
\(671\) 17.5685 14.7417i 0.678225 0.569099i
\(672\) 0 0
\(673\) 12.1305 4.41516i 0.467598 0.170192i −0.0974659 0.995239i \(-0.531074\pi\)
0.565064 + 0.825047i \(0.308851\pi\)
\(674\) −19.5664 + 33.8899i −0.753668 + 1.30539i
\(675\) 0 0
\(676\) −8.97565 15.5463i −0.345217 0.597934i
\(677\) 5.32513 30.2003i 0.204661 1.16069i −0.693310 0.720639i \(-0.743848\pi\)
0.897972 0.440053i \(-0.145040\pi\)
\(678\) 0 0
\(679\) −0.512298 27.4058i −0.0196602 1.05174i
\(680\) −0.00260034 0.0147472i −9.97184e−5 0.000565531i
\(681\) 0 0
\(682\) 3.66989 20.8130i 0.140527 0.796970i
\(683\) −23.1544 −0.885978 −0.442989 0.896527i \(-0.646082\pi\)
−0.442989 + 0.896527i \(0.646082\pi\)
\(684\) 0 0
\(685\) −0.00677427 0.0117334i −0.000258831 0.000448309i
\(686\) −13.0709 30.4781i −0.499051 1.16366i
\(687\) 0 0
\(688\) −1.17126 + 0.982803i −0.0446538 + 0.0374690i
\(689\) 13.1028 + 74.3094i 0.499175 + 2.83096i
\(690\) 0 0
\(691\) −23.4151 19.6476i −0.890751 0.747429i 0.0776099 0.996984i \(-0.475271\pi\)
−0.968361 + 0.249555i \(0.919716\pi\)
\(692\) 3.11834 + 5.40113i 0.118542 + 0.205320i
\(693\) 0 0
\(694\) −30.5731 + 52.9541i −1.16054 + 2.01011i
\(695\) 0.0185989 0.00676943i 0.000705495 0.000256779i
\(696\) 0 0
\(697\) −35.2629 + 29.5891i −1.33568 + 1.12077i
\(698\) 4.83420 + 27.4161i 0.182977 + 1.03771i
\(699\) 0 0
\(700\) 10.4843 + 12.0307i 0.396268 + 0.454716i
\(701\) 15.5148 0.585987 0.292994 0.956114i \(-0.405349\pi\)
0.292994 + 0.956114i \(0.405349\pi\)
\(702\) 0 0
\(703\) 0.184569 + 0.319683i 0.00696115 + 0.0120571i
\(704\) −1.99215 1.67162i −0.0750821 0.0630014i
\(705\) 0 0
\(706\) 2.07632 1.74224i 0.0781433 0.0655700i
\(707\) −0.124979 6.68587i −0.00470033 0.251448i
\(708\) 0 0
\(709\) 16.5023 6.00633i 0.619756 0.225573i −0.0130108 0.999915i \(-0.504142\pi\)
0.632766 + 0.774343i \(0.281919\pi\)
\(710\) 0.0115277 0.000432626
\(711\) 0 0
\(712\) 9.44851 0.354098
\(713\) 2.75371 15.6171i 0.103127 0.584864i
\(714\) 0 0
\(715\) −0.0265322 0.00965694i −0.000992248 0.000361149i
\(716\) 15.9838 13.4120i 0.597344 0.501231i
\(717\) 0 0
\(718\) 5.46366 1.98861i 0.203902 0.0742142i
\(719\) 35.8972 1.33874 0.669370 0.742929i \(-0.266564\pi\)
0.669370 + 0.742929i \(0.266564\pi\)
\(720\) 0 0
\(721\) 47.7254 + 7.49842i 1.77739 + 0.279256i
\(722\) −26.0445 21.8539i −0.969274 0.813318i
\(723\) 0 0
\(724\) 5.58384 4.68540i 0.207522 0.174132i
\(725\) −28.5908 10.4062i −1.06184 0.386476i
\(726\) 0 0
\(727\) 29.3404 10.6790i 1.08818 0.396064i 0.265231 0.964185i \(-0.414552\pi\)
0.822945 + 0.568121i \(0.192330\pi\)
\(728\) 12.4757 15.4453i 0.462381 0.572440i
\(729\) 0 0
\(730\) −0.00507142 + 0.00878395i −0.000187702 + 0.000325109i
\(731\) −1.35948 1.14074i −0.0502822 0.0421918i
\(732\) 0 0
\(733\) −0.0680805 0.386104i −0.00251461 0.0142611i 0.983525 0.180774i \(-0.0578603\pi\)
−0.986039 + 0.166513i \(0.946749\pi\)
\(734\) 1.97848 + 11.2205i 0.0730272 + 0.414158i
\(735\) 0 0
\(736\) −18.1370 15.2187i −0.668539 0.560970i
\(737\) −13.6849 23.7029i −0.504088 0.873106i
\(738\) 0 0
\(739\) 9.34861 16.1923i 0.343894 0.595643i −0.641258 0.767325i \(-0.721587\pi\)
0.985152 + 0.171683i \(0.0549205\pi\)
\(740\) 0.00549867 + 0.00461394i 0.000202135 + 0.000169612i
\(741\) 0 0
\(742\) 57.9870 34.9399i 2.12877 1.28268i
\(743\) −10.5297 3.83249i −0.386296 0.140600i 0.141569 0.989928i \(-0.454785\pi\)
−0.527865 + 0.849328i \(0.677007\pi\)
\(744\) 0 0
\(745\) −0.0120807 + 0.00439701i −0.000442602 + 0.000161094i
\(746\) −17.0263 + 29.4904i −0.623377 + 1.07972i
\(747\) 0 0
\(748\) 10.1347 17.5537i 0.370560 0.641829i
\(749\) 1.59006 4.63652i 0.0580997 0.169415i
\(750\) 0 0
\(751\) 18.5416 + 6.74860i 0.676594 + 0.246260i 0.657384 0.753556i \(-0.271663\pi\)
0.0192094 + 0.999815i \(0.493885\pi\)
\(752\) 17.9258 + 6.52445i 0.653686 + 0.237922i
\(753\) 0 0
\(754\) 9.99077 56.6605i 0.363842 2.06345i
\(755\) −0.0215159 −0.000783043
\(756\) 0 0
\(757\) −5.30078 −0.192660 −0.0963300 0.995349i \(-0.530710\pi\)
−0.0963300 + 0.995349i \(0.530710\pi\)
\(758\) 6.71543 38.0851i 0.243915 1.38331i
\(759\) 0 0
\(760\) −0.000277805 0 0.000101113i −1.00771e−5 0 3.66775e-6i
\(761\) 18.0471 + 6.56861i 0.654207 + 0.238112i 0.647733 0.761867i \(-0.275717\pi\)
0.00647355 + 0.999979i \(0.497939\pi\)
\(762\) 0 0
\(763\) 12.0639 + 13.8433i 0.436741 + 0.501159i
\(764\) 2.21617 3.83852i 0.0801782 0.138873i
\(765\) 0 0
\(766\) −20.1773 + 34.9480i −0.729034 + 1.26272i
\(767\) 39.9696 14.5477i 1.44322 0.525288i
\(768\) 0 0
\(769\) −33.6033 12.2306i −1.21177 0.441047i −0.344451 0.938804i \(-0.611935\pi\)
−0.867316 + 0.497757i \(0.834157\pi\)
\(770\) 0.000473466 0.0253284i 1.70625e−5 0.000912773i
\(771\) 0 0
\(772\) 0.128034 + 0.107434i 0.00460806 + 0.00386662i
\(773\) −4.22302 + 7.31448i −0.151891 + 0.263084i −0.931923 0.362657i \(-0.881870\pi\)
0.780031 + 0.625740i \(0.215203\pi\)
\(774\) 0 0
\(775\) 10.1045 + 17.5016i 0.362965 + 0.628674i
\(776\) −11.2792 9.46434i −0.404898 0.339750i
\(777\) 0 0
\(778\) −1.05137 5.96261i −0.0376934 0.213770i
\(779\) 0.157808 + 0.894973i 0.00565406 + 0.0320657i
\(780\) 0 0
\(781\) −7.86445 6.59906i −0.281412 0.236133i
\(782\) 20.2126 35.0092i 0.722800