Properties

Label 684.2.ce.a.359.10
Level $684$
Weight $2$
Character 684.359
Analytic conductor $5.462$
Analytic rank $0$
Dimension $240$
CM no
Inner twists $8$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [684,2,Mod(35,684)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(684, base_ring=CyclotomicField(18))
 
chi = DirichletCharacter(H, H._module([9, 9, 4]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("684.35");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 684 = 2^{2} \cdot 3^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 684.ce (of order \(18\), degree \(6\), 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: \(5.46176749826\)
Analytic rank: \(0\)
Dimension: \(240\)
Relative dimension: \(40\) over \(\Q(\zeta_{18})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label 359.10
Character \(\chi\) \(=\) 684.359
Dual form 684.2.ce.a.503.10

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.15058 + 0.822300i) q^{2} +(0.647646 - 1.89224i) q^{4} +(1.01606 + 2.79162i) q^{5} +(1.81271 - 1.04657i) q^{7} +(0.810819 + 2.70972i) q^{8} +O(q^{10})\) \(q+(-1.15058 + 0.822300i) q^{2} +(0.647646 - 1.89224i) q^{4} +(1.01606 + 2.79162i) q^{5} +(1.81271 - 1.04657i) q^{7} +(0.810819 + 2.70972i) q^{8} +(-3.46460 - 2.37645i) q^{10} +(-0.542664 + 0.939922i) q^{11} +(-3.68239 + 3.08989i) q^{13} +(-1.22507 + 2.69475i) q^{14} +(-3.16111 - 2.45100i) q^{16} +(2.52096 + 0.444514i) q^{17} +(3.19887 + 2.96095i) q^{19} +(5.94044 - 0.114655i) q^{20} +(-0.148522 - 1.52768i) q^{22} +(0.120109 + 0.0437162i) q^{23} +(-2.93051 + 2.45899i) q^{25} +(1.69605 - 6.58317i) q^{26} +(-0.806361 - 4.10789i) q^{28} +(-3.05488 + 0.538657i) q^{29} +(7.84124 - 4.52714i) q^{31} +(5.65255 + 0.220679i) q^{32} +(-3.26608 + 1.56154i) q^{34} +(4.76346 + 3.99702i) q^{35} -5.94440 q^{37} +(-6.11533 - 0.776372i) q^{38} +(-6.74065 + 5.01674i) q^{40} +(-2.87061 + 3.42106i) q^{41} +(0.613400 + 1.68530i) q^{43} +(1.42710 + 1.63559i) q^{44} +(-0.174143 + 0.0484671i) q^{46} +(0.132267 + 0.750121i) q^{47} +(-1.30938 + 2.26791i) q^{49} +(1.34974 - 5.23900i) q^{50} +(3.46191 + 8.96909i) q^{52} +(-2.51441 + 6.90828i) q^{53} +(-3.17528 - 0.559888i) q^{55} +(4.30569 + 4.06336i) q^{56} +(3.07193 - 3.13179i) q^{58} +(-1.87438 + 10.6301i) q^{59} +(12.2132 + 4.44524i) q^{61} +(-5.29927 + 11.6567i) q^{62} +(-6.68515 + 4.39418i) q^{64} +(-12.3673 - 7.14028i) q^{65} +(-12.3138 + 2.17126i) q^{67} +(2.47382 - 4.48237i) q^{68} +(-8.76746 - 0.681877i) q^{70} +(-1.31593 + 0.478960i) q^{71} +(5.50196 + 4.61669i) q^{73} +(6.83948 - 4.88808i) q^{74} +(7.67456 - 4.13536i) q^{76} +2.27175i q^{77} +(9.67294 - 11.5278i) q^{79} +(3.63035 - 11.3150i) q^{80} +(0.489716 - 6.29670i) q^{82} +(-7.10895 - 12.3131i) q^{83} +(1.32055 + 7.48922i) q^{85} +(-2.09159 - 1.43467i) q^{86} +(-2.98693 - 0.708361i) q^{88} +(1.26059 + 1.50231i) q^{89} +(-3.44132 + 9.45496i) q^{91} +(0.160510 - 0.198962i) q^{92} +(-0.769007 - 0.754308i) q^{94} +(-5.01559 + 11.9385i) q^{95} +(0.940339 - 5.33293i) q^{97} +(-0.358364 - 3.68611i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 240 q + 12 q^{4}+O(q^{10}) \) Copy content Toggle raw display \( 240 q + 12 q^{4} + 12 q^{10} + 24 q^{13} - 12 q^{16} - 12 q^{34} + 120 q^{49} - 48 q^{52} - 144 q^{58} + 48 q^{61} - 12 q^{64} - 72 q^{70} + 72 q^{73} - 144 q^{76} - 72 q^{82} + 240 q^{85} - 48 q^{88} - 48 q^{94}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/684\mathbb{Z}\right)^\times\).

\(n\) \(325\) \(343\) \(533\)
\(\chi(n)\) \(e\left(\frac{5}{9}\right)\) \(-1\) \(-1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.15058 + 0.822300i −0.813579 + 0.581454i
\(3\) 0 0
\(4\) 0.647646 1.89224i 0.323823 0.946118i
\(5\) 1.01606 + 2.79162i 0.454398 + 1.24845i 0.929600 + 0.368571i \(0.120153\pi\)
−0.475202 + 0.879877i \(0.657625\pi\)
\(6\) 0 0
\(7\) 1.81271 1.04657i 0.685141 0.395567i −0.116648 0.993173i \(-0.537215\pi\)
0.801789 + 0.597607i \(0.203882\pi\)
\(8\) 0.810819 + 2.70972i 0.286668 + 0.958030i
\(9\) 0 0
\(10\) −3.46460 2.37645i −1.09560 0.751500i
\(11\) −0.542664 + 0.939922i −0.163619 + 0.283397i −0.936164 0.351563i \(-0.885650\pi\)
0.772545 + 0.634960i \(0.218984\pi\)
\(12\) 0 0
\(13\) −3.68239 + 3.08989i −1.02131 + 0.856981i −0.989792 0.142522i \(-0.954479\pi\)
−0.0315184 + 0.999503i \(0.510034\pi\)
\(14\) −1.22507 + 2.69475i −0.327413 + 0.720203i
\(15\) 0 0
\(16\) −3.16111 2.45100i −0.790277 0.612750i
\(17\) 2.52096 + 0.444514i 0.611424 + 0.107810i 0.470781 0.882250i \(-0.343972\pi\)
0.140642 + 0.990060i \(0.455083\pi\)
\(18\) 0 0
\(19\) 3.19887 + 2.96095i 0.733871 + 0.679289i
\(20\) 5.94044 0.114655i 1.32832 0.0256375i
\(21\) 0 0
\(22\) −0.148522 1.52768i −0.0316649 0.325703i
\(23\) 0.120109 + 0.0437162i 0.0250445 + 0.00911546i 0.354512 0.935051i \(-0.384647\pi\)
−0.329468 + 0.944167i \(0.606869\pi\)
\(24\) 0 0
\(25\) −2.93051 + 2.45899i −0.586101 + 0.491797i
\(26\) 1.69605 6.58317i 0.332622 1.29107i
\(27\) 0 0
\(28\) −0.806361 4.10789i −0.152388 0.776318i
\(29\) −3.05488 + 0.538657i −0.567276 + 0.100026i −0.449928 0.893065i \(-0.648550\pi\)
−0.117348 + 0.993091i \(0.537439\pi\)
\(30\) 0 0
\(31\) 7.84124 4.52714i 1.40833 0.813099i 0.413101 0.910685i \(-0.364446\pi\)
0.995227 + 0.0975865i \(0.0311123\pi\)
\(32\) 5.65255 + 0.220679i 0.999239 + 0.0390109i
\(33\) 0 0
\(34\) −3.26608 + 1.56154i −0.560128 + 0.267802i
\(35\) 4.76346 + 3.99702i 0.805171 + 0.675619i
\(36\) 0 0
\(37\) −5.94440 −0.977254 −0.488627 0.872493i \(-0.662502\pi\)
−0.488627 + 0.872493i \(0.662502\pi\)
\(38\) −6.11533 0.776372i −0.992037 0.125944i
\(39\) 0 0
\(40\) −6.74065 + 5.01674i −1.06579 + 0.793217i
\(41\) −2.87061 + 3.42106i −0.448314 + 0.534280i −0.942113 0.335296i \(-0.891164\pi\)
0.493798 + 0.869576i \(0.335608\pi\)
\(42\) 0 0
\(43\) 0.613400 + 1.68530i 0.0935426 + 0.257006i 0.977636 0.210304i \(-0.0674454\pi\)
−0.884093 + 0.467310i \(0.845223\pi\)
\(44\) 1.42710 + 1.63559i 0.215143 + 0.246574i
\(45\) 0 0
\(46\) −0.174143 + 0.0484671i −0.0256759 + 0.00714608i
\(47\) 0.132267 + 0.750121i 0.0192931 + 0.109416i 0.992934 0.118672i \(-0.0378636\pi\)
−0.973640 + 0.228088i \(0.926753\pi\)
\(48\) 0 0
\(49\) −1.30938 + 2.26791i −0.187054 + 0.323987i
\(50\) 1.34974 5.23900i 0.190882 0.740907i
\(51\) 0 0
\(52\) 3.46191 + 8.96909i 0.480081 + 1.24379i
\(53\) −2.51441 + 6.90828i −0.345381 + 0.948926i 0.638424 + 0.769685i \(0.279586\pi\)
−0.983805 + 0.179241i \(0.942636\pi\)
\(54\) 0 0
\(55\) −3.17528 0.559888i −0.428155 0.0754953i
\(56\) 4.30569 + 4.06336i 0.575373 + 0.542990i
\(57\) 0 0
\(58\) 3.07193 3.13179i 0.403364 0.411224i
\(59\) −1.87438 + 10.6301i −0.244024 + 1.38393i 0.578726 + 0.815522i \(0.303550\pi\)
−0.822749 + 0.568404i \(0.807561\pi\)
\(60\) 0 0
\(61\) 12.2132 + 4.44524i 1.56374 + 0.569155i 0.971590 0.236672i \(-0.0760566\pi\)
0.592151 + 0.805827i \(0.298279\pi\)
\(62\) −5.29927 + 11.6567i −0.673008 + 1.48040i
\(63\) 0 0
\(64\) −6.68515 + 4.39418i −0.835643 + 0.549273i
\(65\) −12.3673 7.14028i −1.53398 0.885642i
\(66\) 0 0
\(67\) −12.3138 + 2.17126i −1.50437 + 0.265261i −0.864270 0.503029i \(-0.832219\pi\)
−0.640102 + 0.768290i \(0.721108\pi\)
\(68\) 2.47382 4.48237i 0.299994 0.543567i
\(69\) 0 0
\(70\) −8.76746 0.681877i −1.04791 0.0814999i
\(71\) −1.31593 + 0.478960i −0.156172 + 0.0568421i −0.418923 0.908022i \(-0.637592\pi\)
0.262751 + 0.964864i \(0.415370\pi\)
\(72\) 0 0
\(73\) 5.50196 + 4.61669i 0.643956 + 0.540343i 0.905230 0.424921i \(-0.139698\pi\)
−0.261274 + 0.965265i \(0.584143\pi\)
\(74\) 6.83948 4.88808i 0.795074 0.568228i
\(75\) 0 0
\(76\) 7.67456 4.13536i 0.880332 0.474358i
\(77\) 2.27175i 0.258889i
\(78\) 0 0
\(79\) 9.67294 11.5278i 1.08829 1.29697i 0.136360 0.990659i \(-0.456460\pi\)
0.951930 0.306315i \(-0.0990960\pi\)
\(80\) 3.63035 11.3150i 0.405886 1.26505i
\(81\) 0 0
\(82\) 0.489716 6.29670i 0.0540801 0.695354i
\(83\) −7.10895 12.3131i −0.780309 1.35153i −0.931762 0.363070i \(-0.881729\pi\)
0.151453 0.988464i \(-0.451605\pi\)
\(84\) 0 0
\(85\) 1.32055 + 7.48922i 0.143234 + 0.812319i
\(86\) −2.09159 1.43467i −0.225542 0.154704i
\(87\) 0 0
\(88\) −2.98693 0.708361i −0.318407 0.0755115i
\(89\) 1.26059 + 1.50231i 0.133622 + 0.159245i 0.828706 0.559684i \(-0.189077\pi\)
−0.695084 + 0.718928i \(0.744633\pi\)
\(90\) 0 0
\(91\) −3.44132 + 9.45496i −0.360749 + 0.991149i
\(92\) 0.160510 0.198962i 0.0167343 0.0207433i
\(93\) 0 0
\(94\) −0.769007 0.754308i −0.0793170 0.0778009i
\(95\) −5.01559 + 11.9385i −0.514588 + 1.22487i
\(96\) 0 0
\(97\) 0.940339 5.33293i 0.0954769 0.541477i −0.899123 0.437696i \(-0.855795\pi\)
0.994600 0.103781i \(-0.0330941\pi\)
\(98\) −0.358364 3.68611i −0.0362002 0.372353i
\(99\) 0 0
\(100\) 2.75505 + 7.13776i 0.275505 + 0.713776i
\(101\) −9.35047 11.1435i −0.930406 1.10881i −0.993840 0.110829i \(-0.964649\pi\)
0.0634334 0.997986i \(-0.479795\pi\)
\(102\) 0 0
\(103\) 15.3034 + 8.83540i 1.50788 + 0.870578i 0.999958 + 0.00917727i \(0.00292126\pi\)
0.507927 + 0.861400i \(0.330412\pi\)
\(104\) −11.3585 7.47289i −1.11379 0.732777i
\(105\) 0 0
\(106\) −2.78766 10.0161i −0.270762 0.972849i
\(107\) 0.654545 + 1.13371i 0.0632773 + 0.109599i 0.895929 0.444198i \(-0.146511\pi\)
−0.832651 + 0.553798i \(0.813178\pi\)
\(108\) 0 0
\(109\) −9.79690 + 3.56578i −0.938373 + 0.341540i −0.765523 0.643409i \(-0.777520\pi\)
−0.172850 + 0.984948i \(0.555297\pi\)
\(110\) 4.11380 1.96684i 0.392235 0.187531i
\(111\) 0 0
\(112\) −8.29533 1.13463i −0.783835 0.107213i
\(113\) 4.74832i 0.446684i 0.974740 + 0.223342i \(0.0716967\pi\)
−0.974740 + 0.223342i \(0.928303\pi\)
\(114\) 0 0
\(115\) 0.379717i 0.0354088i
\(116\) −0.959213 + 6.12940i −0.0890607 + 0.569101i
\(117\) 0 0
\(118\) −6.58455 13.7721i −0.606157 1.26782i
\(119\) 5.03500 1.83259i 0.461558 0.167993i
\(120\) 0 0
\(121\) 4.91103 + 8.50616i 0.446457 + 0.773287i
\(122\) −17.7075 + 4.92833i −1.60316 + 0.446190i
\(123\) 0 0
\(124\) −3.48807 17.7695i −0.313238 1.59574i
\(125\) 3.02171 + 1.74458i 0.270270 + 0.156040i
\(126\) 0 0
\(127\) −2.86296 3.41194i −0.254046 0.302761i 0.623915 0.781492i \(-0.285541\pi\)
−0.877961 + 0.478732i \(0.841097\pi\)
\(128\) 4.07843 10.5530i 0.360486 0.932765i
\(129\) 0 0
\(130\) 20.1010 1.95422i 1.76297 0.171396i
\(131\) 1.92973 10.9441i 0.168602 0.956187i −0.776671 0.629906i \(-0.783093\pi\)
0.945273 0.326281i \(-0.105795\pi\)
\(132\) 0 0
\(133\) 8.89748 + 2.01952i 0.771509 + 0.175115i
\(134\) 12.3825 12.6238i 1.06969 1.09053i
\(135\) 0 0
\(136\) 0.839537 + 7.19152i 0.0719897 + 0.616668i
\(137\) 4.10971 11.2913i 0.351116 0.964683i −0.630897 0.775867i \(-0.717313\pi\)
0.982013 0.188816i \(-0.0604649\pi\)
\(138\) 0 0
\(139\) 3.99048 + 4.75567i 0.338468 + 0.403371i 0.908252 0.418424i \(-0.137417\pi\)
−0.569783 + 0.821795i \(0.692973\pi\)
\(140\) 10.6483 6.42493i 0.899948 0.543006i
\(141\) 0 0
\(142\) 1.12023 1.63317i 0.0940076 0.137053i
\(143\) −0.905955 5.13793i −0.0757598 0.429655i
\(144\) 0 0
\(145\) −4.60767 7.98073i −0.382647 0.662763i
\(146\) −10.1267 0.787592i −0.838094 0.0651815i
\(147\) 0 0
\(148\) −3.84987 + 11.2482i −0.316457 + 0.924597i
\(149\) 12.9604 15.4456i 1.06176 1.26535i 0.0989704 0.995090i \(-0.468445\pi\)
0.962787 0.270262i \(-0.0871105\pi\)
\(150\) 0 0
\(151\) 19.9710i 1.62522i −0.582809 0.812609i \(-0.698047\pi\)
0.582809 0.812609i \(-0.301953\pi\)
\(152\) −5.42965 + 11.0688i −0.440403 + 0.897800i
\(153\) 0 0
\(154\) −1.86806 2.61381i −0.150532 0.210627i
\(155\) 20.6052 + 17.2899i 1.65505 + 1.38875i
\(156\) 0 0
\(157\) 1.55341 0.565395i 0.123976 0.0451234i −0.279287 0.960208i \(-0.590098\pi\)
0.403263 + 0.915084i \(0.367876\pi\)
\(158\) −1.65017 + 21.2176i −0.131280 + 1.68798i
\(159\) 0 0
\(160\) 5.12730 + 16.0040i 0.405349 + 1.26522i
\(161\) 0.263476 0.0464579i 0.0207648 0.00366140i
\(162\) 0 0
\(163\) 2.97254 + 1.71620i 0.232827 + 0.134423i 0.611876 0.790954i \(-0.290415\pi\)
−0.379048 + 0.925377i \(0.623749\pi\)
\(164\) 4.61432 + 7.64751i 0.360317 + 0.597171i
\(165\) 0 0
\(166\) 18.3044 + 8.32142i 1.42070 + 0.645867i
\(167\) −11.8754 4.32229i −0.918945 0.334469i −0.161126 0.986934i \(-0.551513\pi\)
−0.757819 + 0.652465i \(0.773735\pi\)
\(168\) 0 0
\(169\) 1.75513 9.95382i 0.135010 0.765678i
\(170\) −7.67777 7.53102i −0.588858 0.577603i
\(171\) 0 0
\(172\) 3.58625 0.0692171i 0.273449 0.00527776i
\(173\) 21.3410 + 3.76300i 1.62253 + 0.286096i 0.909708 0.415249i \(-0.136306\pi\)
0.712822 + 0.701345i \(0.247417\pi\)
\(174\) 0 0
\(175\) −2.73866 + 7.52442i −0.207024 + 0.568793i
\(176\) 4.01917 1.64113i 0.302956 0.123705i
\(177\) 0 0
\(178\) −2.68575 0.691940i −0.201305 0.0518631i
\(179\) 11.9400 20.6806i 0.892434 1.54574i 0.0554859 0.998459i \(-0.482329\pi\)
0.836948 0.547282i \(-0.184337\pi\)
\(180\) 0 0
\(181\) −4.09322 23.2138i −0.304247 1.72547i −0.627030 0.778995i \(-0.715730\pi\)
0.322783 0.946473i \(-0.395382\pi\)
\(182\) −3.81531 13.7084i −0.282810 1.01614i
\(183\) 0 0
\(184\) −0.0210717 + 0.360908i −0.00155343 + 0.0266065i
\(185\) −6.03990 16.5945i −0.444062 1.22005i
\(186\) 0 0
\(187\) −1.78585 + 2.12829i −0.130594 + 0.155636i
\(188\) 1.50507 + 0.235534i 0.109768 + 0.0171781i
\(189\) 0 0
\(190\) −4.04624 17.8605i −0.293545 1.29574i
\(191\) 8.66701 0.627123 0.313562 0.949568i \(-0.398478\pi\)
0.313562 + 0.949568i \(0.398478\pi\)
\(192\) 0 0
\(193\) 9.69899 + 8.13842i 0.698149 + 0.585816i 0.921246 0.388980i \(-0.127172\pi\)
−0.223098 + 0.974796i \(0.571617\pi\)
\(194\) 3.30333 + 6.90917i 0.237166 + 0.496050i
\(195\) 0 0
\(196\) 3.44341 + 3.94646i 0.245958 + 0.281890i
\(197\) −5.75213 + 3.32099i −0.409822 + 0.236611i −0.690713 0.723129i \(-0.742703\pi\)
0.280891 + 0.959740i \(0.409370\pi\)
\(198\) 0 0
\(199\) 7.32409 1.29143i 0.519191 0.0915473i 0.0920887 0.995751i \(-0.470646\pi\)
0.427102 + 0.904203i \(0.359535\pi\)
\(200\) −9.03927 5.94705i −0.639173 0.420520i
\(201\) 0 0
\(202\) 19.9217 + 5.13249i 1.40168 + 0.361121i
\(203\) −4.97387 + 4.17357i −0.349097 + 0.292927i
\(204\) 0 0
\(205\) −12.4670 4.53762i −0.870735 0.316921i
\(206\) −24.8730 + 2.41816i −1.73298 + 0.168481i
\(207\) 0 0
\(208\) 19.2137 0.741952i 1.33223 0.0514451i
\(209\) −4.51898 + 1.39988i −0.312584 + 0.0968319i
\(210\) 0 0
\(211\) 1.08908 + 0.192034i 0.0749751 + 0.0132201i 0.211010 0.977484i \(-0.432325\pi\)
−0.136035 + 0.990704i \(0.543436\pi\)
\(212\) 11.4437 + 9.23198i 0.785953 + 0.634055i
\(213\) 0 0
\(214\) −1.68535 0.766181i −0.115208 0.0523751i
\(215\) −4.08146 + 3.42475i −0.278353 + 0.233566i
\(216\) 0 0
\(217\) 9.47595 16.4128i 0.643269 1.11418i
\(218\) 8.33993 12.1587i 0.564851 0.823490i
\(219\) 0 0
\(220\) −3.11590 + 5.64577i −0.210074 + 0.380638i
\(221\) −10.6567 + 6.15262i −0.716844 + 0.413870i
\(222\) 0 0
\(223\) −0.631099 1.73393i −0.0422615 0.116113i 0.916767 0.399423i \(-0.130790\pi\)
−0.959028 + 0.283310i \(0.908567\pi\)
\(224\) 10.4774 5.51576i 0.700051 0.368537i
\(225\) 0 0
\(226\) −3.90454 5.46330i −0.259726 0.363413i
\(227\) −22.6267 −1.50178 −0.750892 0.660425i \(-0.770376\pi\)
−0.750892 + 0.660425i \(0.770376\pi\)
\(228\) 0 0
\(229\) 14.0074 0.925633 0.462817 0.886454i \(-0.346839\pi\)
0.462817 + 0.886454i \(0.346839\pi\)
\(230\) −0.312242 0.436893i −0.0205886 0.0288079i
\(231\) 0 0
\(232\) −3.93656 7.84110i −0.258448 0.514793i
\(233\) 3.53724 + 9.71849i 0.231732 + 0.636680i 0.999994 0.00345641i \(-0.00110021\pi\)
−0.768262 + 0.640136i \(0.778878\pi\)
\(234\) 0 0
\(235\) −1.95966 + 1.13141i −0.127834 + 0.0738050i
\(236\) 18.9008 + 10.4313i 1.23034 + 0.679022i
\(237\) 0 0
\(238\) −4.28621 + 6.24881i −0.277834 + 0.405050i
\(239\) −6.26518 + 10.8516i −0.405261 + 0.701932i −0.994352 0.106135i \(-0.966153\pi\)
0.589091 + 0.808067i \(0.299486\pi\)
\(240\) 0 0
\(241\) −3.27967 + 2.75197i −0.211262 + 0.177270i −0.742278 0.670092i \(-0.766255\pi\)
0.531016 + 0.847362i \(0.321810\pi\)
\(242\) −12.6451 5.74863i −0.812859 0.369536i
\(243\) 0 0
\(244\) 16.3213 20.2313i 1.04486 1.29518i
\(245\) −7.66155 1.35094i −0.489479 0.0863083i
\(246\) 0 0
\(247\) −20.9285 1.01923i −1.33165 0.0648520i
\(248\) 18.6251 + 17.5769i 1.18270 + 1.11613i
\(249\) 0 0
\(250\) −4.91127 + 0.477475i −0.310616 + 0.0301982i
\(251\) 12.4197 + 4.52041i 0.783925 + 0.285326i 0.702809 0.711379i \(-0.251929\pi\)
0.0811169 + 0.996705i \(0.474151\pi\)
\(252\) 0 0
\(253\) −0.106269 + 0.0891702i −0.00668107 + 0.00560608i
\(254\) 6.09968 + 1.57148i 0.382728 + 0.0986037i
\(255\) 0 0
\(256\) 3.98522 + 15.4957i 0.249076 + 0.968484i
\(257\) 21.2568 3.74814i 1.32596 0.233803i 0.534576 0.845121i \(-0.320471\pi\)
0.791385 + 0.611318i \(0.209360\pi\)
\(258\) 0 0
\(259\) −10.7755 + 6.22124i −0.669557 + 0.386569i
\(260\) −21.5207 + 18.7775i −1.33466 + 1.16453i
\(261\) 0 0
\(262\) 6.77899 + 14.1788i 0.418808 + 0.875968i
\(263\) −5.97966 5.01753i −0.368721 0.309394i 0.439534 0.898226i \(-0.355144\pi\)
−0.808256 + 0.588832i \(0.799588\pi\)
\(264\) 0 0
\(265\) −21.8401 −1.34163
\(266\) −11.8979 + 4.99278i −0.729505 + 0.306127i
\(267\) 0 0
\(268\) −3.86647 + 24.7068i −0.236182 + 1.50921i
\(269\) 3.92322 4.67552i 0.239203 0.285071i −0.633065 0.774098i \(-0.718204\pi\)
0.872269 + 0.489027i \(0.162648\pi\)
\(270\) 0 0
\(271\) −6.25603 17.1883i −0.380027 1.04411i −0.971344 0.237676i \(-0.923614\pi\)
0.591318 0.806439i \(-0.298608\pi\)
\(272\) −6.87954 7.58403i −0.417133 0.459850i
\(273\) 0 0
\(274\) 4.55633 + 16.3709i 0.275258 + 0.989004i
\(275\) −0.720975 4.08885i −0.0434764 0.246567i
\(276\) 0 0
\(277\) 3.75525 6.50428i 0.225631 0.390804i −0.730878 0.682509i \(-0.760889\pi\)
0.956509 + 0.291704i \(0.0942223\pi\)
\(278\) −8.50194 2.19039i −0.509913 0.131371i
\(279\) 0 0
\(280\) −6.96848 + 16.1485i −0.416447 + 0.965056i
\(281\) 0.202085 0.555224i 0.0120554 0.0331219i −0.933519 0.358528i \(-0.883279\pi\)
0.945574 + 0.325406i \(0.105501\pi\)
\(282\) 0 0
\(283\) −29.7576 5.24706i −1.76890 0.311905i −0.808081 0.589071i \(-0.799494\pi\)
−0.960822 + 0.277166i \(0.910605\pi\)
\(284\) 0.0540467 + 2.80025i 0.00320708 + 0.166164i
\(285\) 0 0
\(286\) 5.26729 + 5.16660i 0.311461 + 0.305508i
\(287\) −1.62321 + 9.20571i −0.0958153 + 0.543396i
\(288\) 0 0
\(289\) −9.81711 3.57314i −0.577477 0.210184i
\(290\) 11.8640 + 5.39354i 0.696680 + 0.316719i
\(291\) 0 0
\(292\) 12.2992 7.42102i 0.719756 0.434282i
\(293\) 0.230965 + 0.133348i 0.0134931 + 0.00779026i 0.506731 0.862104i \(-0.330854\pi\)
−0.493238 + 0.869894i \(0.664187\pi\)
\(294\) 0 0
\(295\) −31.5798 + 5.56836i −1.83864 + 0.324203i
\(296\) −4.81983 16.1077i −0.280147 0.936239i
\(297\) 0 0
\(298\) −2.21100 + 28.4287i −0.128080 + 1.64683i
\(299\) −0.577367 + 0.210144i −0.0333900 + 0.0121530i
\(300\) 0 0
\(301\) 2.87571 + 2.41300i 0.165753 + 0.139083i
\(302\) 16.4222 + 22.9782i 0.944989 + 1.32224i
\(303\) 0 0
\(304\) −2.85468 17.2003i −0.163727 0.986506i
\(305\) 38.6112i 2.21087i
\(306\) 0 0
\(307\) −5.90629 + 7.03884i −0.337090 + 0.401728i −0.907786 0.419433i \(-0.862229\pi\)
0.570696 + 0.821161i \(0.306673\pi\)
\(308\) 4.29868 + 1.47129i 0.244940 + 0.0838344i
\(309\) 0 0
\(310\) −37.9253 2.94959i −2.15401 0.167525i
\(311\) −14.1660 24.5362i −0.803279 1.39132i −0.917447 0.397859i \(-0.869753\pi\)
0.114167 0.993462i \(-0.463580\pi\)
\(312\) 0 0
\(313\) −0.0956509 0.542463i −0.00540651 0.0306618i 0.981985 0.188958i \(-0.0605110\pi\)
−0.987392 + 0.158296i \(0.949400\pi\)
\(314\) −1.32239 + 1.92790i −0.0746268 + 0.108798i
\(315\) 0 0
\(316\) −15.5486 25.7694i −0.874676 1.44964i
\(317\) −13.6497 16.2670i −0.766642 0.913648i 0.231607 0.972810i \(-0.425602\pi\)
−0.998248 + 0.0591615i \(0.981157\pi\)
\(318\) 0 0
\(319\) 1.15148 3.16365i 0.0644703 0.177131i
\(320\) −19.0594 14.1976i −1.06545 0.793669i
\(321\) 0 0
\(322\) −0.264946 + 0.270109i −0.0147649 + 0.0150526i
\(323\) 6.74804 + 8.88640i 0.375471 + 0.494452i
\(324\) 0 0
\(325\) 3.19326 18.1099i 0.177130 1.00455i
\(326\) −4.83136 + 0.469706i −0.267584 + 0.0260146i
\(327\) 0 0
\(328\) −11.5977 5.00469i −0.640374 0.276338i
\(329\) 1.02482 + 1.22133i 0.0565000 + 0.0673340i
\(330\) 0 0
\(331\) 19.7788 + 11.4193i 1.08714 + 0.627660i 0.932813 0.360360i \(-0.117346\pi\)
0.154326 + 0.988020i \(0.450679\pi\)
\(332\) −27.9033 + 5.47730i −1.53139 + 0.300606i
\(333\) 0 0
\(334\) 17.2177 4.79201i 0.942113 0.262207i
\(335\) −18.5729 32.1693i −1.01475 1.75760i
\(336\) 0 0
\(337\) −9.66442 + 3.51756i −0.526455 + 0.191614i −0.591555 0.806265i \(-0.701486\pi\)
0.0651000 + 0.997879i \(0.479263\pi\)
\(338\) 6.16562 + 12.8959i 0.335365 + 0.701442i
\(339\) 0 0
\(340\) 15.0266 + 2.35157i 0.814932 + 0.127532i
\(341\) 9.82687i 0.532155i
\(342\) 0 0
\(343\) 20.1334i 1.08710i
\(344\) −4.06934 + 3.02862i −0.219404 + 0.163292i
\(345\) 0 0
\(346\) −27.6488 + 13.2191i −1.48641 + 0.710664i
\(347\) 18.2023 6.62508i 0.977148 0.355653i 0.196417 0.980520i \(-0.437069\pi\)
0.780731 + 0.624867i \(0.214847\pi\)
\(348\) 0 0
\(349\) −15.3892 26.6549i −0.823767 1.42681i −0.902858 0.429938i \(-0.858535\pi\)
0.0790915 0.996867i \(-0.474798\pi\)
\(350\) −3.03629 10.9094i −0.162296 0.583133i
\(351\) 0 0
\(352\) −3.27486 + 5.19320i −0.174550 + 0.276798i
\(353\) 29.1983 + 16.8576i 1.55407 + 0.897241i 0.997804 + 0.0662338i \(0.0210983\pi\)
0.556262 + 0.831007i \(0.312235\pi\)
\(354\) 0 0
\(355\) −2.67415 3.18692i −0.141929 0.169144i
\(356\) 3.65914 1.41236i 0.193934 0.0748551i
\(357\) 0 0
\(358\) 3.26784 + 33.6128i 0.172711 + 1.77649i
\(359\) 6.24882 35.4388i 0.329800 1.87039i −0.143738 0.989616i \(-0.545912\pi\)
0.473538 0.880773i \(-0.342977\pi\)
\(360\) 0 0
\(361\) 1.46551 + 18.9434i 0.0771319 + 0.997021i
\(362\) 23.7983 + 23.3434i 1.25081 + 1.22690i
\(363\) 0 0
\(364\) 15.6622 + 12.6353i 0.820925 + 0.662268i
\(365\) −7.29768 + 20.0502i −0.381978 + 1.04948i
\(366\) 0 0
\(367\) 7.66122 + 9.13028i 0.399912 + 0.476597i 0.927993 0.372597i \(-0.121533\pi\)
−0.528081 + 0.849194i \(0.677088\pi\)
\(368\) −0.272530 0.432579i −0.0142066 0.0225498i
\(369\) 0 0
\(370\) 20.5950 + 14.1266i 1.07068 + 0.734407i
\(371\) 2.67210 + 15.1542i 0.138729 + 0.786769i
\(372\) 0 0
\(373\) 11.8611 + 20.5439i 0.614142 + 1.06373i 0.990534 + 0.137265i \(0.0438312\pi\)
−0.376392 + 0.926460i \(0.622835\pi\)
\(374\) 0.304659 3.91725i 0.0157535 0.202556i
\(375\) 0 0
\(376\) −1.92537 + 0.966618i −0.0992935 + 0.0498495i
\(377\) 9.58484 11.4228i 0.493644 0.588302i
\(378\) 0 0
\(379\) 17.7952i 0.914079i −0.889446 0.457039i \(-0.848910\pi\)
0.889446 0.457039i \(-0.151090\pi\)
\(380\) 19.3422 + 17.2226i 0.992233 + 0.883501i
\(381\) 0 0
\(382\) −9.97205 + 7.12688i −0.510214 + 0.364643i
\(383\) −18.1927 15.2655i −0.929603 0.780030i 0.0461430 0.998935i \(-0.485307\pi\)
−0.975746 + 0.218905i \(0.929751\pi\)
\(384\) 0 0
\(385\) −6.34184 + 2.30824i −0.323210 + 0.117639i
\(386\) −17.8516 1.38839i −0.908624 0.0706670i
\(387\) 0 0
\(388\) −9.48214 5.23319i −0.481383 0.265675i
\(389\) 24.8694 4.38515i 1.26093 0.222336i 0.497066 0.867713i \(-0.334411\pi\)
0.763864 + 0.645377i \(0.223300\pi\)
\(390\) 0 0
\(391\) 0.283359 + 0.163597i 0.0143301 + 0.00827347i
\(392\) −7.20707 1.70918i −0.364012 0.0863268i
\(393\) 0 0
\(394\) 3.88740 8.55102i 0.195845 0.430794i
\(395\) 42.0094 + 15.2902i 2.11372 + 0.769332i
\(396\) 0 0
\(397\) −0.332266 + 1.88438i −0.0166760 + 0.0945742i −0.992010 0.126161i \(-0.959734\pi\)
0.975334 + 0.220735i \(0.0708456\pi\)
\(398\) −7.36496 + 7.50849i −0.369172 + 0.376366i
\(399\) 0 0
\(400\) 15.2906 0.590458i 0.764531 0.0295229i
\(401\) 5.66914 + 0.999623i 0.283103 + 0.0499188i 0.313397 0.949622i \(-0.398533\pi\)
−0.0302933 + 0.999541i \(0.509644\pi\)
\(402\) 0 0
\(403\) −14.8861 + 40.8992i −0.741530 + 2.03734i
\(404\) −27.1418 + 10.4763i −1.35036 + 0.521214i
\(405\) 0 0
\(406\) 2.29088 8.89202i 0.113695 0.441304i
\(407\) 3.22582 5.58728i 0.159898 0.276951i
\(408\) 0 0
\(409\) 2.12062 + 12.0266i 0.104858 + 0.594679i 0.991277 + 0.131795i \(0.0420741\pi\)
−0.886419 + 0.462884i \(0.846815\pi\)
\(410\) 18.0755 5.03075i 0.892687 0.248451i
\(411\) 0 0
\(412\) 26.6298 23.2353i 1.31196 1.14472i
\(413\) 7.72748 + 21.2311i 0.380244 + 1.04471i
\(414\) 0 0
\(415\) 27.1502 32.3563i 1.33275 1.58831i
\(416\) −21.4967 + 16.6531i −1.05396 + 0.816486i
\(417\) 0 0
\(418\) 4.04830 5.32662i 0.198009 0.260534i
\(419\) 36.1039 1.76379 0.881895 0.471446i \(-0.156268\pi\)
0.881895 + 0.471446i \(0.156268\pi\)
\(420\) 0 0
\(421\) −0.764455 0.641454i −0.0372572 0.0312625i 0.623969 0.781449i \(-0.285519\pi\)
−0.661226 + 0.750187i \(0.729964\pi\)
\(422\) −1.41097 + 0.674598i −0.0686851 + 0.0328389i
\(423\) 0 0
\(424\) −20.7582 1.21197i −1.00811 0.0588587i
\(425\) −8.48075 + 4.89636i −0.411377 + 0.237509i
\(426\) 0 0
\(427\) 26.7913 4.72403i 1.29652 0.228612i
\(428\) 2.56915 0.504313i 0.124185 0.0243769i
\(429\) 0 0
\(430\) 1.87985 7.29662i 0.0906546 0.351874i
\(431\) −11.1628 + 9.36669i −0.537693 + 0.451178i −0.870748 0.491730i \(-0.836365\pi\)
0.333055 + 0.942907i \(0.391920\pi\)
\(432\) 0 0
\(433\) −12.7534 4.64187i −0.612891 0.223074i 0.0168766 0.999858i \(-0.494628\pi\)
−0.629768 + 0.776783i \(0.716850\pi\)
\(434\) 2.59347 + 26.6763i 0.124491 + 1.28050i
\(435\) 0 0
\(436\) 0.402369 + 20.8474i 0.0192700 + 0.998409i
\(437\) 0.254772 + 0.495480i 0.0121874 + 0.0237020i
\(438\) 0 0
\(439\) −11.4661 2.02178i −0.547246 0.0964943i −0.106812 0.994279i \(-0.534064\pi\)
−0.440434 + 0.897785i \(0.645175\pi\)
\(440\) −1.05744 9.05809i −0.0504115 0.431827i
\(441\) 0 0
\(442\) 7.20198 15.8420i 0.342563 0.753528i
\(443\) −14.0139 + 11.7591i −0.665822 + 0.558691i −0.911825 0.410578i \(-0.865327\pi\)
0.246004 + 0.969269i \(0.420882\pi\)
\(444\) 0 0
\(445\) −2.91303 + 5.04552i −0.138091 + 0.239181i
\(446\) 2.15194 + 1.47607i 0.101897 + 0.0698937i
\(447\) 0 0
\(448\) −7.51943 + 14.9619i −0.355260 + 0.706882i
\(449\) −6.85425 + 3.95730i −0.323472 + 0.186757i −0.652939 0.757410i \(-0.726464\pi\)
0.329467 + 0.944167i \(0.393131\pi\)
\(450\) 0 0
\(451\) −1.65775 4.55464i −0.0780606 0.214470i
\(452\) 8.98493 + 3.07523i 0.422616 + 0.144647i
\(453\) 0 0
\(454\) 26.0337 18.6059i 1.22182 0.873218i
\(455\) −29.8912 −1.40132
\(456\) 0 0
\(457\) −7.99070 −0.373789 −0.186895 0.982380i \(-0.559842\pi\)
−0.186895 + 0.982380i \(0.559842\pi\)
\(458\) −16.1165 + 11.5183i −0.753076 + 0.538213i
\(459\) 0 0
\(460\) 0.718515 + 0.245923i 0.0335009 + 0.0114662i
\(461\) −6.79474 18.6684i −0.316463 0.869474i −0.991314 0.131520i \(-0.958014\pi\)
0.674851 0.737954i \(-0.264208\pi\)
\(462\) 0 0
\(463\) 21.1194 12.1933i 0.981501 0.566670i 0.0787784 0.996892i \(-0.474898\pi\)
0.902723 + 0.430222i \(0.141565\pi\)
\(464\) 10.9770 + 5.78474i 0.509596 + 0.268550i
\(465\) 0 0
\(466\) −12.0614 8.27318i −0.558732 0.383248i
\(467\) 4.85370 8.40686i 0.224603 0.389023i −0.731598 0.681737i \(-0.761225\pi\)
0.956200 + 0.292714i \(0.0945583\pi\)
\(468\) 0 0
\(469\) −20.0490 + 16.8231i −0.925779 + 0.776821i
\(470\) 1.32438 2.91320i 0.0610889 0.134376i
\(471\) 0 0
\(472\) −30.3245 + 3.54008i −1.39580 + 0.162945i
\(473\) −1.91692 0.338005i −0.0881402 0.0155415i
\(474\) 0 0
\(475\) −16.6552 0.811121i −0.764195 0.0372168i
\(476\) −0.206793 10.7143i −0.00947833 0.491088i
\(477\) 0 0
\(478\) −1.71471 17.6374i −0.0784292 0.806718i
\(479\) −39.8198 14.4932i −1.81941 0.662212i −0.995418 0.0956155i \(-0.969518\pi\)
−0.823995 0.566597i \(-0.808260\pi\)
\(480\) 0 0
\(481\) 21.8896 18.3675i 0.998079 0.837488i
\(482\) 1.51056 5.86322i 0.0688042 0.267062i
\(483\) 0 0
\(484\) 19.2763 3.78385i 0.876194 0.171993i
\(485\) 15.8429 2.79353i 0.719390 0.126848i
\(486\) 0 0
\(487\) −9.80518 + 5.66102i −0.444315 + 0.256525i −0.705426 0.708783i \(-0.749244\pi\)
0.261111 + 0.965309i \(0.415911\pi\)
\(488\) −2.14266 + 36.6986i −0.0969936 + 1.66127i
\(489\) 0 0
\(490\) 9.92607 4.74574i 0.448414 0.214390i
\(491\) 29.3285 + 24.6095i 1.32358 + 1.11061i 0.985534 + 0.169481i \(0.0542090\pi\)
0.338042 + 0.941131i \(0.390235\pi\)
\(492\) 0 0
\(493\) −7.94067 −0.357630
\(494\) 24.9179 16.0368i 1.12111 0.721529i
\(495\) 0 0
\(496\) −35.8830 4.90808i −1.61120 0.220379i
\(497\) −1.88414 + 2.24543i −0.0845154 + 0.100721i
\(498\) 0 0
\(499\) −8.46244 23.2504i −0.378831 1.04083i −0.971842 0.235635i \(-0.924283\pi\)
0.593011 0.805195i \(-0.297939\pi\)
\(500\) 5.25816 4.58791i 0.235152 0.205177i
\(501\) 0 0
\(502\) −18.0069 + 5.01166i −0.803689 + 0.223681i
\(503\) 1.46718 + 8.32079i 0.0654183 + 0.371006i 0.999888 + 0.0149630i \(0.00476306\pi\)
−0.934470 + 0.356042i \(0.884126\pi\)
\(504\) 0 0
\(505\) 21.6075 37.4254i 0.961523 1.66541i
\(506\) 0.0489457 0.189982i 0.00217590 0.00844572i
\(507\) 0 0
\(508\) −8.31037 + 3.20766i −0.368713 + 0.142317i
\(509\) 4.15398 11.4130i 0.184122 0.505871i −0.812950 0.582333i \(-0.802140\pi\)
0.997073 + 0.0764616i \(0.0243623\pi\)
\(510\) 0 0
\(511\) 14.8052 + 2.61055i 0.654942 + 0.115484i
\(512\) −17.3274 14.5520i −0.765772 0.643113i
\(513\) 0 0
\(514\) −21.3754 + 21.7920i −0.942829 + 0.961202i
\(515\) −9.11583 + 51.6984i −0.401691 + 2.27810i
\(516\) 0 0
\(517\) −0.776832 0.282744i −0.0341650 0.0124351i
\(518\) 7.28230 16.0187i 0.319966 0.703821i
\(519\) 0 0
\(520\) 9.32048 39.3014i 0.408730 1.72348i
\(521\) −0.230828 0.133269i −0.0101128 0.00583861i 0.494935 0.868930i \(-0.335192\pi\)
−0.505048 + 0.863091i \(0.668525\pi\)
\(522\) 0 0
\(523\) 11.5485 2.03631i 0.504979 0.0890414i 0.0846455 0.996411i \(-0.473024\pi\)
0.420333 + 0.907370i \(0.361913\pi\)
\(524\) −19.4589 10.7394i −0.850068 0.469152i
\(525\) 0 0
\(526\) 11.0060 + 0.855972i 0.479882 + 0.0373222i
\(527\) 21.7799 7.92722i 0.948745 0.345315i
\(528\) 0 0
\(529\) −17.6065 14.7736i −0.765500 0.642331i
\(530\) 25.1286 17.9591i 1.09152 0.780093i
\(531\) 0 0
\(532\) 9.58383 15.5282i 0.415512 0.673232i
\(533\) 21.4675i 0.929863i
\(534\) 0 0
\(535\) −2.49981 + 2.97916i −0.108076 + 0.128800i
\(536\) −15.8678 31.6065i −0.685383 1.36519i
\(537\) 0 0
\(538\) −0.669288 + 8.60560i −0.0288551 + 0.371014i
\(539\) −1.42111 2.46143i −0.0612114 0.106021i
\(540\) 0 0
\(541\) 1.64218 + 9.31328i 0.0706029 + 0.400409i 0.999544 + 0.0301825i \(0.00960885\pi\)
−0.928941 + 0.370227i \(0.879280\pi\)
\(542\) 21.3320 + 14.6321i 0.916286 + 0.628502i
\(543\) 0 0
\(544\) 14.1518 + 3.06896i 0.606752 + 0.131581i
\(545\) −19.9086 23.7261i −0.852789 1.01631i
\(546\) 0 0
\(547\) 4.65565 12.7913i 0.199061 0.546916i −0.799493 0.600676i \(-0.794898\pi\)
0.998554 + 0.0537596i \(0.0171205\pi\)
\(548\) −18.7042 15.0893i −0.799004 0.644583i
\(549\) 0 0
\(550\) 4.19180 + 4.11167i 0.178739 + 0.175322i
\(551\) −11.3671 7.32225i −0.484254 0.311938i
\(552\) 0 0
\(553\) 5.46965 31.0199i 0.232593 1.31910i
\(554\) 1.02777 + 10.5716i 0.0436659 + 0.449145i
\(555\) 0 0
\(556\) 11.5833 4.47094i 0.491240 0.189610i
\(557\) 7.31163 + 8.71366i 0.309804 + 0.369210i 0.898370 0.439239i \(-0.144752\pi\)
−0.588566 + 0.808449i \(0.700307\pi\)
\(558\) 0 0
\(559\) −7.46617 4.31060i −0.315785 0.182319i
\(560\) −5.26113 24.3102i −0.222323 1.02729i
\(561\) 0 0
\(562\) 0.224046 + 0.805001i 0.00945083 + 0.0339569i
\(563\) −11.8828 20.5817i −0.500801 0.867414i −1.00000 0.000925727i \(-0.999705\pi\)
0.499198 0.866488i \(-0.333628\pi\)
\(564\) 0 0
\(565\) −13.2555 + 4.82460i −0.557662 + 0.202972i
\(566\) 38.5530 18.4325i 1.62050 0.774775i
\(567\) 0 0
\(568\) −2.36483 3.17746i −0.0992261 0.133323i
\(569\) 19.2331i 0.806296i −0.915135 0.403148i \(-0.867916\pi\)
0.915135 0.403148i \(-0.132084\pi\)
\(570\) 0 0
\(571\) 19.2556i 0.805823i 0.915239 + 0.402912i \(0.132002\pi\)
−0.915239 + 0.402912i \(0.867998\pi\)
\(572\) −10.3089 1.61328i −0.431037 0.0674546i
\(573\) 0 0
\(574\) −5.70222 11.9266i −0.238006 0.497808i
\(575\) −0.459478 + 0.167236i −0.0191616 + 0.00697424i
\(576\) 0 0
\(577\) 17.8234 + 30.8710i 0.741998 + 1.28518i 0.951584 + 0.307388i \(0.0994550\pi\)
−0.209586 + 0.977790i \(0.567212\pi\)
\(578\) 14.2335 3.96145i 0.592036 0.164774i
\(579\) 0 0
\(580\) −18.0856 + 3.55012i −0.750962 + 0.147411i
\(581\) −25.7730 14.8800i −1.06924 0.617328i
\(582\) 0 0
\(583\) −5.12877 6.11223i −0.212412 0.253143i
\(584\) −8.04884 + 18.6521i −0.333064 + 0.771828i
\(585\) 0 0
\(586\) −0.375394 + 0.0364959i −0.0155074 + 0.00150763i
\(587\) −5.32464 + 30.1975i −0.219771 + 1.24639i 0.652661 + 0.757650i \(0.273653\pi\)
−0.872432 + 0.488735i \(0.837458\pi\)
\(588\) 0 0
\(589\) 38.4877 + 8.73582i 1.58586 + 0.359953i
\(590\) 31.7560 32.3748i 1.30737 1.33285i
\(591\) 0 0
\(592\) 18.7909 + 14.5697i 0.772301 + 0.598812i
\(593\) 1.77307 4.87147i 0.0728113 0.200047i −0.897948 0.440101i \(-0.854943\pi\)
0.970760 + 0.240053i \(0.0771650\pi\)
\(594\) 0 0
\(595\) 10.2318 + 12.1938i 0.419462 + 0.499895i
\(596\) −20.8330 34.5274i −0.853351 1.41430i
\(597\) 0 0
\(598\) 0.491502 0.716556i 0.0200990 0.0293021i
\(599\) 6.51219 + 36.9325i 0.266081 + 1.50902i 0.765940 + 0.642912i \(0.222274\pi\)
−0.499859 + 0.866107i \(0.666615\pi\)
\(600\) 0 0
\(601\) 14.3096 + 24.7849i 0.583699 + 1.01100i 0.995036 + 0.0995133i \(0.0317286\pi\)
−0.411337 + 0.911483i \(0.634938\pi\)
\(602\) −5.29293 0.411650i −0.215724 0.0167776i
\(603\) 0 0
\(604\) −37.7899 12.9342i −1.53765 0.526283i
\(605\) −18.7560 + 22.3525i −0.762539 + 0.908759i
\(606\) 0 0
\(607\) 6.06680i 0.246244i 0.992392 + 0.123122i \(0.0392906\pi\)
−0.992392 + 0.123122i \(0.960709\pi\)
\(608\) 17.4283 + 17.4429i 0.706812 + 0.707401i
\(609\) 0 0
\(610\) −31.7500 44.4251i −1.28552 1.79872i
\(611\) −2.80485 2.35355i −0.113472 0.0952143i
\(612\) 0 0
\(613\) 5.26745 1.91720i 0.212750 0.0774348i −0.233446 0.972370i \(-0.575000\pi\)
0.446197 + 0.894935i \(0.352778\pi\)
\(614\) 1.00759 12.9555i 0.0406631 0.522840i
\(615\) 0 0
\(616\) −6.15579 + 1.84197i −0.248024 + 0.0742153i
\(617\) −43.6181 + 7.69104i −1.75600 + 0.309630i −0.956650 0.291240i \(-0.905932\pi\)
−0.799347 + 0.600870i \(0.794821\pi\)
\(618\) 0 0
\(619\) 31.3295 + 18.0881i 1.25924 + 0.727021i 0.972926 0.231116i \(-0.0742376\pi\)
0.286311 + 0.958137i \(0.407571\pi\)
\(620\) 46.0614 27.7923i 1.84987 1.11616i
\(621\) 0 0
\(622\) 36.4751 + 16.5821i 1.46252 + 0.664880i
\(623\) 3.85736 + 1.40396i 0.154542 + 0.0562486i
\(624\) 0 0
\(625\) −5.12141 + 29.0450i −0.204857 + 1.16180i
\(626\) 0.556121 + 0.545491i 0.0222271 + 0.0218022i
\(627\) 0 0
\(628\) −0.0638002 3.30559i −0.00254590 0.131908i
\(629\) −14.9856 2.64237i −0.597516 0.105358i
\(630\) 0 0
\(631\) −5.47003 + 15.0288i −0.217759 + 0.598287i −0.999685 0.0250835i \(-0.992015\pi\)
0.781927 + 0.623370i \(0.214237\pi\)
\(632\) 39.0800 + 16.8640i 1.55452 + 0.670814i
\(633\) 0 0
\(634\) 29.0814 + 7.49233i 1.15497 + 0.297559i
\(635\) 6.61587 11.4590i 0.262543 0.454738i
\(636\) 0 0
\(637\) −2.18595 12.3972i −0.0866106 0.491193i
\(638\) 1.27661 + 4.58688i 0.0505416 + 0.181596i
\(639\) 0 0
\(640\) 33.6039 + 0.662840i 1.32831 + 0.0262010i
\(641\) −11.2995 31.0452i −0.446305 1.22621i −0.935278 0.353913i \(-0.884851\pi\)
0.488973 0.872299i \(-0.337371\pi\)
\(642\) 0 0
\(643\) 3.50486 4.17693i 0.138218 0.164722i −0.692495 0.721423i \(-0.743489\pi\)
0.830713 + 0.556701i \(0.187933\pi\)
\(644\) 0.0827299 0.528647i 0.00326001 0.0208316i
\(645\) 0 0
\(646\) −15.0714 4.67555i −0.592977 0.183957i
\(647\) 19.1554 0.753077 0.376539 0.926401i \(-0.377114\pi\)
0.376539 + 0.926401i \(0.377114\pi\)
\(648\) 0 0
\(649\) −8.97434 7.53037i −0.352274 0.295593i
\(650\) 11.2177 + 23.4626i 0.439993 + 0.920278i
\(651\) 0 0
\(652\) 5.17261 4.51326i 0.202575 0.176753i
\(653\) 5.24416 3.02772i 0.205220 0.118484i −0.393868 0.919167i \(-0.628863\pi\)
0.599088 + 0.800683i \(0.295530\pi\)
\(654\) 0 0
\(655\) 32.5123 5.73280i 1.27036 0.223999i
\(656\) 17.4593 3.77849i 0.681673 0.147525i
\(657\) 0 0
\(658\) −2.18343 0.562524i −0.0851188 0.0219295i
\(659\) −1.51903 + 1.27461i −0.0591728 + 0.0496519i −0.671894 0.740647i \(-0.734519\pi\)
0.612722 + 0.790299i \(0.290075\pi\)
\(660\) 0 0
\(661\) 35.8153 + 13.0357i 1.39305 + 0.507030i 0.926109 0.377257i \(-0.123133\pi\)
0.466945 + 0.884287i \(0.345355\pi\)
\(662\) −32.1470 + 3.12534i −1.24943 + 0.121470i
\(663\) 0 0
\(664\) 27.6009 29.2469i 1.07112 1.13500i
\(665\) 3.40269 + 26.8903i 0.131951 + 1.04276i
\(666\) 0 0
\(667\) −0.390467 0.0688499i −0.0151189 0.00266588i
\(668\) −15.8698 + 19.6717i −0.614022 + 0.761122i
\(669\) 0 0
\(670\) 47.8224 + 21.7407i 1.84754 + 0.839915i
\(671\) −10.8059 + 9.06719i −0.417155 + 0.350035i
\(672\) 0 0
\(673\) −13.2501 + 22.9498i −0.510754 + 0.884651i 0.489169 + 0.872189i \(0.337300\pi\)
−0.999922 + 0.0124622i \(0.996033\pi\)
\(674\) 8.22715 11.9943i 0.316898 0.462002i
\(675\) 0 0
\(676\) −17.6983 9.76767i −0.680702 0.375679i
\(677\) −13.4208 + 7.74853i −0.515805 + 0.297800i −0.735217 0.677832i \(-0.762920\pi\)
0.219412 + 0.975632i \(0.429586\pi\)
\(678\) 0 0
\(679\) −3.87672 10.6512i −0.148775 0.408756i
\(680\) −19.2229 + 9.65072i −0.737166 + 0.370088i
\(681\) 0 0
\(682\) −8.08063 11.3066i −0.309423 0.432950i
\(683\) 50.5423 1.93395 0.966973 0.254878i \(-0.0820355\pi\)
0.966973 + 0.254878i \(0.0820355\pi\)
\(684\) 0 0
\(685\) 35.6968 1.36390
\(686\) −16.5557 23.1650i −0.632100 0.884444i
\(687\) 0 0
\(688\) 2.19165 6.83087i 0.0835558 0.260424i
\(689\) −12.0868 33.2082i −0.460470 1.26513i
\(690\) 0 0
\(691\) 0.346548 0.200079i 0.0131833 0.00761138i −0.493394 0.869806i \(-0.664244\pi\)
0.506577 + 0.862195i \(0.330911\pi\)
\(692\) 20.9419 37.9452i 0.796093 1.44246i
\(693\) 0 0
\(694\) −15.4953 + 22.5904i −0.588192 + 0.857518i
\(695\) −9.22142 + 15.9720i −0.349788 + 0.605851i
\(696\) 0 0
\(697\) −8.75742 + 7.34835i −0.331711 + 0.278339i
\(698\) 39.6248 + 18.0139i 1.49982 + 0.681838i
\(699\) 0 0
\(700\) 12.4643 + 10.0554i 0.471106 + 0.380057i
\(701\) −18.5285 3.26708i −0.699813 0.123396i −0.187589 0.982248i \(-0.560067\pi\)
−0.512224 + 0.858852i \(0.671178\pi\)
\(702\) 0 0
\(703\) −19.0154 17.6011i −0.717178 0.663838i
\(704\) −0.502398 8.66808i −0.0189349 0.326691i
\(705\) 0 0
\(706\) −47.4568 + 4.61376i −1.78606 + 0.173641i
\(707\) −28.6121 10.4140i −1.07607 0.391657i
\(708\) 0 0
\(709\) −12.4338 + 10.4332i −0.466962 + 0.391827i −0.845685 0.533683i \(-0.820808\pi\)
0.378723 + 0.925510i \(0.376363\pi\)
\(710\) 5.69741 + 1.46784i 0.213820 + 0.0550872i
\(711\) 0 0
\(712\) −3.04873 + 4.63394i −0.114256 + 0.173664i
\(713\) 1.13972 0.200963i 0.0426827 0.00752611i
\(714\) 0 0
\(715\) 13.4226 7.74955i 0.501977 0.289817i
\(716\) −31.3997 35.9869i −1.17346 1.34489i
\(717\) 0 0
\(718\) 21.9516 + 45.9134i 0.819226 + 1.71347i
\(719\) −24.4195 20.4904i −0.910692 0.764161i 0.0615586 0.998103i \(-0.480393\pi\)
−0.972250 + 0.233942i \(0.924837\pi\)
\(720\) 0 0
\(721\) 36.9875 1.37749
\(722\) −17.2633 20.5907i −0.642474 0.766307i
\(723\) 0 0
\(724\) −46.5769 7.28900i −1.73102 0.270893i
\(725\) 7.62778 9.09043i 0.283289 0.337610i
\(726\) 0 0
\(727\) 3.34850 + 9.19992i 0.124189 + 0.341206i 0.986171 0.165733i \(-0.0529991\pi\)
−0.861982 + 0.506939i \(0.830777\pi\)
\(728\) −28.4106 1.65876i −1.05297 0.0614777i
\(729\) 0 0
\(730\) −8.09076 29.0702i −0.299452 1.07593i
\(731\) 0.797219 + 4.52125i 0.0294862 + 0.167225i
\(732\) 0 0
\(733\) −21.6009 + 37.4139i −0.797848 + 1.38191i 0.123167 + 0.992386i \(0.460695\pi\)
−0.921015 + 0.389527i \(0.872639\pi\)
\(734\) −16.3226 4.20526i −0.602479 0.155219i
\(735\) 0 0
\(736\) 0.669276 + 0.273614i 0.0246699 + 0.0100855i
\(737\) 4.64145 12.7523i 0.170970 0.469737i
\(738\) 0 0
\(739\) 8.80551 + 1.55265i 0.323916 + 0.0571151i 0.333242 0.942841i \(-0.391857\pi\)
−0.00932596 + 0.999957i \(0.502969\pi\)
\(740\) −35.3124 + 0.681553i −1.29811 + 0.0250544i
\(741\) 0 0
\(742\) −15.5358 15.2388i −0.570337 0.559435i
\(743\) −6.18773 + 35.0924i −0.227006 + 1.28741i 0.631808 + 0.775125i \(0.282313\pi\)
−0.858814 + 0.512288i \(0.828798\pi\)
\(744\) 0 0
\(745\) 56.2868 + 20.4867i 2.06219 + 0.750575i
\(746\) −30.5403 13.8840i −1.11816 0.508330i
\(747\) 0 0
\(748\) 2.87062 + 4.75762i 0.104960 + 0.173956i
\(749\) 2.37301 + 1.37006i 0.0867078 + 0.0500608i
\(750\) 0 0
\(751\) 31.2808 5.51564i 1.14145 0.201269i 0.429211 0.903204i \(-0.358792\pi\)
0.712241 + 0.701935i \(0.247681\pi\)
\(752\) 1.42044 2.69540i 0.0517980 0.0982911i
\(753\) 0 0
\(754\) −1.63514 + 21.0244i −0.0595483 + 0.765662i
\(755\) 55.7514 20.2918i 2.02900 0.738496i
\(756\) 0 0
\(757\) −19.8401 16.6479i −0.721102 0.605077i 0.206588 0.978428i \(-0.433764\pi\)
−0.927690 + 0.373351i \(0.878209\pi\)
\(758\) 14.6330 + 20.4747i 0.531495 + 0.743676i
\(759\) 0 0
\(760\) −36.4168 3.91084i −1.32098 0.141861i
\(761\) 12.2247i 0.443144i 0.975144 + 0.221572i \(0.0711188\pi\)
−0.975144 + 0.221572i \(0.928881\pi\)
\(762\) 0 0
\(763\) −14.0271 + 16.7169i −0.507816 + 0.605192i
\(764\) 5.61316 16.4000i 0.203077 0.593332i
\(765\) 0 0
\(766\) 33.4849 + 2.60424i 1.20986 + 0.0940949i
\(767\) −25.9438 44.9359i −0.936775 1.62254i
\(768\) 0 0
\(769\) −7.37098 41.8029i −0.265804 1.50745i −0.766735 0.641964i \(-0.778120\pi\)
0.500930 0.865488i \(-0.332991\pi\)
\(770\) 5.39870 7.87070i 0.194556 0.283640i
\(771\) 0 0
\(772\) 21.6813 13.0820i 0.780328 0.470830i
\(773\) 20.4984 + 24.4290i 0.737275 + 0.878650i 0.996186 0.0872509i \(-0.0278082\pi\)
−0.258911 + 0.965901i \(0.583364\pi\)
\(774\) 0 0
\(775\) −11.8466 + 32.5483i −0.425543 + 1.16917i
\(776\) 15.2132 1.77598i 0.546121 0.0637541i
\(777\) 0 0
\(778\) −25.0082 + 25.4956i −0.896589 + 0.914060i
\(779\) −19.3123 + 2.44378i −0.691936 + 0.0875574i
\(780\) 0 0
\(781\) 0.263924 1.49679i 0.00944395 0.0535593i
\(782\) −0.460551 + 0.0447749i −0.0164693 + 0.00160115i
\(783\) 0 0
\(784\) 9.69774 3.95983i 0.346348 0.141422i
\(785\) 3.15673 + 3.76205i 0.112669 + 0.134273i
\(786\) 0 0
\(787\) 4.28508 + 2.47399i 0.152747 + 0.0881884i 0.574425 0.818557i \(-0.305226\pi\)
−0.421679 + 0.906745i \(0.638559\pi\)
\(788\) 2.55875 + 13.0352i 0.0911519 + 0.464360i
\(789\) 0 0
\(790\) −60.9081 + 16.9518i −2.16701 + 0.603119i
\(791\) 4.96945 + 8.60734i 0.176693 + 0.306042i
\(792\) 0 0
\(793\) −58.7090 + 21.3683i −2.08482 + 0.758812i
\(794\) −1.16723 2.44134i −0.0414233 0.0866399i
\(795\) 0 0
\(796\) 2.29972 14.6953i 0.0815114 0.520861i
\(797\) 45.2115i 1.60147i −0.599016 0.800737i \(-0.704441\pi\)
0.599016 0.800737i \(-0.295559\pi\)
\(798\) 0 0
\(799\) 1.94982i 0.0689798i
\(800\) −17.1075 + 13.2528i −0.604840 + 0.468558i
\(801\) 0 0
\(802\) −7.34476 + 3.51159i −0.259353 + 0.123999i
\(803\) −7.32505 + 2.66610i −0.258495 + 0.0940846i
\(804\) 0 0
\(805\) 0.397401 + 0.688319i 0.0140066 + 0.0242601i
\(806\) −16.5038 59.2985i −0.581323 2.08870i
\(807\) 0 0
\(808\) 22.6141 34.3724i 0.795561 1.20922i
\(809\) 18.9572 + 10.9449i 0.666500 + 0.384804i 0.794749 0.606938i \(-0.207602\pi\)
−0.128249 + 0.991742i \(0.540936\pi\)
\(810\) 0 0
\(811\) −10.9577 13.0589i −0.384776 0.458558i 0.538540 0.842600i \(-0.318976\pi\)
−0.923316 + 0.384042i \(0.874532\pi\)
\(812\) 4.67607 + 12.1147i 0.164098 + 0.425144i
\(813\) 0 0
\(814\) 0.882873 + 9.08117i 0.0309447 + 0.318295i
\(815\) −1.77067 + 10.0420i −0.0620238 + 0.351755i
\(816\) 0 0
\(817\) −3.02792 + 7.20731i −0.105933 + 0.252152i
\(818\) −12.3294 12.0938i −0.431088 0.422848i
\(819\) 0 0
\(820\) −16.6605 + 20.6518i −0.581809 + 0.721191i
\(821\) −12.8634 + 35.3419i −0.448936 + 1.23344i 0.484530 + 0.874775i \(0.338991\pi\)
−0.933466 + 0.358667i \(0.883231\pi\)
\(822\) 0 0
\(823\) −26.1314 31.1422i −0.910882 1.08555i −0.996016 0.0891776i \(-0.971576\pi\)
0.0851335 0.996370i \(-0.472868\pi\)
\(824\) −11.5332 + 48.6317i −0.401778 + 1.69417i
\(825\) 0 0
\(826\) −26.3494 18.0736i −0.916811 0.628862i
\(827\) −4.23173 23.9993i −0.147152 0.834538i −0.965614 0.259979i \(-0.916284\pi\)
0.818463 0.574560i \(-0.194827\pi\)
\(828\) 0 0
\(829\) −2.73771 4.74186i −0.0950848 0.164692i 0.814559 0.580080i \(-0.196979\pi\)
−0.909644 + 0.415389i \(0.863646\pi\)
\(830\) −4.63173 + 59.5540i −0.160770 + 2.06715i
\(831\) 0 0
\(832\) 11.0398 36.8374i 0.382735 1.27711i
\(833\) −4.30902 + 5.13529i −0.149299 + 0.177927i
\(834\) 0 0
\(835\) 37.5432i 1.29924i
\(836\) −0.277792 + 9.45760i −0.00960763 + 0.327098i
\(837\) 0 0
\(838\) −41.5402 + 29.6882i −1.43498 + 1.02556i
\(839\) 30.5753 + 25.6557i 1.05558 + 0.885734i 0.993669 0.112348i \(-0.0358372\pi\)
0.0619073 + 0.998082i \(0.480282\pi\)
\(840\) 0 0
\(841\) −18.2090 + 6.62752i −0.627896 + 0.228535i
\(842\) 1.40703 + 0.109430i 0.0484894 + 0.00377120i
\(843\) 0 0
\(844\) 1.06871 1.93642i 0.0367865 0.0666543i
\(845\) 29.5706 5.21409i 1.01726 0.179370i
\(846\) 0 0
\(847\) 17.8046 + 10.2795i 0.611773 + 0.353207i
\(848\) 24.8805 15.6750i 0.854400 0.538282i
\(849\) 0 0
\(850\) 5.73146 12.6074i 0.196588 0.432429i
\(851\) −0.713978 0.259867i −0.0244749 0.00890812i
\(852\) 0 0
\(853\) −8.00712 + 45.4107i −0.274159 + 1.55483i 0.467463 + 0.884013i \(0.345168\pi\)
−0.741622 + 0.670819i \(0.765943\pi\)
\(854\) −26.9408 + 27.4658i −0.921897 + 0.939862i
\(855\) 0 0
\(856\) −2.54131 + 2.69286i −0.0868600 + 0.0920402i
\(857\) −9.36086 1.65057i −0.319761 0.0563825i 0.0114640 0.999934i \(-0.496351\pi\)
−0.331225 + 0.943552i \(0.607462\pi\)
\(858\) 0 0
\(859\) −11.1315 + 30.5835i −0.379801 + 1.04349i 0.591638 + 0.806204i \(0.298482\pi\)
−0.971439 + 0.237291i \(0.923741\pi\)
\(860\) 3.83709 + 9.94111i 0.130844 + 0.338989i
\(861\) 0 0
\(862\) 5.14140 19.9562i 0.175117 0.679712i
\(863\) 0.226430 0.392188i 0.00770775 0.0133502i −0.862146 0.506660i \(-0.830880\pi\)
0.869854 + 0.493310i \(0.164213\pi\)
\(864\) 0 0
\(865\) 11.1790 + 63.3994i 0.380098 + 2.15565i
\(866\) 18.4908 5.14633i 0.628343 0.174879i
\(867\) 0 0
\(868\) −24.9199 28.5604i −0.845835 0.969404i
\(869\) 5.58604 + 15.3475i 0.189493 + 0.520629i
\(870\) 0 0
\(871\) 38.6353 46.0437i 1.30911 1.56013i
\(872\) −17.6058 23.6556i −0.596206 0.801081i
\(873\) 0 0
\(874\) −0.700568 0.360588i −0.0236971 0.0121971i
\(875\) 7.30332 0.246897
\(876\) 0 0
\(877\) −33.0696 27.7487i −1.11668 0.937006i −0.118248 0.992984i \(-0.537728\pi\)
−0.998432 + 0.0559779i \(0.982172\pi\)
\(878\) 14.8551 7.10235i 0.501335 0.239693i
\(879\) 0 0
\(880\) 8.66513 + 9.55248i 0.292101 + 0.322014i
\(881\) −33.0898 + 19.1044i −1.11482 + 0.643644i −0.940074 0.340969i \(-0.889245\pi\)
−0.174749 + 0.984613i \(0.555911\pi\)
\(882\) 0 0
\(883\) 15.1480 2.67100i 0.509771 0.0898864i 0.0871541 0.996195i \(-0.472223\pi\)
0.422617 + 0.906308i \(0.361112\pi\)
\(884\) 4.74047 + 24.1496i 0.159439 + 0.812240i
\(885\) 0 0
\(886\) 6.45459 25.0534i 0.216846 0.841684i
\(887\) 0.283209 0.237641i 0.00950923 0.00797919i −0.638021 0.770019i \(-0.720247\pi\)
0.647530 + 0.762040i \(0.275802\pi\)
\(888\) 0 0
\(889\) −8.76056 3.18858i −0.293820 0.106942i
\(890\) −0.797267 8.20064i −0.0267245 0.274886i
\(891\) 0 0
\(892\) −3.68974 + 0.0712144i −0.123541 + 0.00238443i
\(893\) −1.79797 + 2.79117i −0.0601668 + 0.0934031i
\(894\) 0 0
\(895\) 69.8641 + 12.3189i 2.33530 + 0.411776i
\(896\) −3.65147 23.3980i −0.121987 0.781672i
\(897\) 0 0
\(898\) 4.63224 10.1894i 0.154580 0.340026i
\(899\) −21.5154 + 18.0536i −0.717580 + 0.602121i
\(900\) 0 0
\(901\) −9.40956 + 16.2978i −0.313478 + 0.542960i
\(902\) 5.65265 + 3.87729i 0.188213 + 0.129100i
\(903\) 0 0
\(904\) −12.8666 + 3.85003i −0.427937 + 0.128050i
\(905\) 60.6450 35.0134i 2.01591 1.16389i
\(906\) 0 0
\(907\) 2.22211 + 6.10518i 0.0737838 + 0.202719i 0.971102 0.238665i \(-0.0767098\pi\)
−0.897318 + 0.441384i \(0.854488\pi\)
\(908\) −14.6541 + 42.8150i −0.486312 + 1.42086i
\(909\) 0 0
\(910\) 34.3921 24.5795i 1.14009 0.814804i
\(911\) 22.7159 0.752613 0.376306 0.926495i \(-0.377194\pi\)
0.376306 + 0.926495i \(0.377194\pi\)
\(912\) 0 0
\(913\) 15.4311 0.510695
\(914\) 9.19390 6.57075i 0.304107 0.217341i
\(915\) 0 0
\(916\) 9.07182 26.5052i 0.299741 0.875758i
\(917\) −7.95568 21.8580i −0.262720 0.721816i
\(918\) 0 0
\(919\) −28.2999 + 16.3390i −0.933528 + 0.538973i −0.887926 0.459987i \(-0.847854\pi\)
−0.0456024 + 0.998960i \(0.514521\pi\)
\(920\) −1.02893 + 0.307882i −0.0339227 + 0.0101506i
\(921\) 0 0
\(922\) 23.1689 + 15.8921i 0.763027 + 0.523378i
\(923\) 3.36584 5.82980i 0.110788 0.191890i
\(924\) 0 0
\(925\) 17.4201 14.6172i 0.572770 0.480611i
\(926\) −14.2729 + 31.3958i −0.469037 + 1.03173i
\(927\) 0 0
\(928\) −17.3867 + 2.37064i −0.570746 + 0.0778200i
\(929\) −10.0475 1.77164i −0.329648 0.0581258i 0.00637503 0.999980i \(-0.497971\pi\)
−0.336023 + 0.941854i \(0.609082\pi\)
\(930\) 0 0
\(931\) −10.9037 + 3.37774i −0.357355 + 0.110701i
\(932\) 20.6806 0.399149i 0.677414 0.0130745i
\(933\) 0 0
\(934\) 1.32841 + 13.6639i 0.0434669 + 0.447097i
\(935\) −7.75589 2.82291i −0.253645 0.0923192i
\(936\) 0 0
\(937\) 16.1197 13.5261i 0.526608 0.441877i −0.340320 0.940310i \(-0.610535\pi\)
0.866928 + 0.498433i \(0.166091\pi\)
\(938\) 9.23426 35.8426i 0.301509 1.17030i
\(939\) 0 0
\(940\) 0.871727 + 4.44089i 0.0284326 + 0.144846i
\(941\) −50.4016 + 8.88716i −1.64305 + 0.289713i −0.917284 0.398233i \(-0.869623\pi\)
−0.725761 + 0.687947i \(0.758512\pi\)
\(942\) 0 0
\(943\) −0.494343 + 0.285409i −0.0160980 + 0.00929420i
\(944\) 31.9796 29.0089i 1.04085 0.944160i
\(945\) 0 0
\(946\) 2.48351 1.18738i 0.0807457 0.0386052i
\(947\) −27.4904 23.0672i −0.893317 0.749582i 0.0755553 0.997142i \(-0.475927\pi\)
−0.968873 + 0.247559i \(0.920372\pi\)
\(948\) 0 0
\(949\) −34.5254 −1.12074
\(950\) 19.8301 12.7623i 0.643373 0.414065i
\(951\) 0 0
\(952\) 9.04828 + 12.1575i 0.293256 + 0.394028i
\(953\) −22.6265 + 26.9652i −0.732945 + 0.873490i −0.995820 0.0913399i \(-0.970885\pi\)
0.262875 + 0.964830i \(0.415329\pi\)
\(954\) 0 0
\(955\) 8.80625 + 24.1950i 0.284963 + 0.782931i
\(956\) 16.4762 + 18.8832i 0.532877 + 0.610726i
\(957\) 0 0
\(958\) 57.7335 16.0683i 1.86528 0.519142i
\(959\) −4.36745 24.7690i −0.141032 0.799834i
\(960\) 0 0
\(961\) 25.4900 44.1500i 0.822259 1.42419i
\(962\) −10.0820 + 39.1330i −0.325056 + 1.26170i
\(963\) 0 0
\(964\) 3.08331 + 7.98821i 0.0993067 + 0.257283i
\(965\) −12.8645 + 35.3450i −0.414124 + 1.13780i
\(966\) 0 0
\(967\) −17.4130 3.07038i −0.559964 0.0987367i −0.113499 0.993538i \(-0.536206\pi\)
−0.446464 + 0.894801i \(0.647317\pi\)
\(968\) −19.0673 + 20.2045i −0.612847 + 0.649396i
\(969\) 0 0
\(970\) −15.9314 + 16.2418i −0.511525 + 0.521493i
\(971\) −8.59953 + 48.7703i −0.275972 + 1.56511i 0.459886 + 0.887978i \(0.347890\pi\)
−0.735858 + 0.677136i \(0.763221\pi\)
\(972\) 0 0
\(973\) 12.2108 + 4.44435i 0.391459 + 0.142479i
\(974\) 6.62654 14.5762i 0.212328 0.467052i
\(975\) 0 0
\(976\) −27.7120 43.9864i −0.887039 1.40797i
\(977\) 45.1973 + 26.0947i 1.44599 + 0.834843i 0.998239 0.0593158i \(-0.0188919\pi\)
0.447751 + 0.894158i \(0.352225\pi\)
\(978\) 0 0
\(979\) −2.09613 + 0.369604i −0.0669926 + 0.0118126i
\(980\) −7.51827 + 13.6225i −0.240162 + 0.435156i
\(981\) 0 0
\(982\) −53.9810 4.19830i −1.72260 0.133973i
\(983\) −7.57565 + 2.75731i −0.241626 + 0.0879446i −0.459995 0.887922i \(-0.652149\pi\)
0.218369 + 0.975866i \(0.429926\pi\)
\(984\) 0 0
\(985\) −15.1155 12.6834i −0.481619 0.404126i
\(986\) 9.13634 6.52961i 0.290960 0.207945i
\(987\) 0 0
\(988\) −15.4829 + 38.9415i −0.492576 + 1.23889i
\(989\) 0.229236i 0.00728928i
\(990\) 0 0
\(991\) 9.22028 10.9883i 0.292892 0.349055i −0.599452 0.800410i \(-0.704615\pi\)
0.892344 + 0.451355i \(0.149059\pi\)
\(992\) 45.3220 23.8595i 1.43898 0.757540i
\(993\) 0 0
\(994\) 0.321428 4.13287i 0.0101951 0.131087i
\(995\) 11.0469 + 19.1338i 0.350211 + 0.606584i
\(996\) 0 0
\(997\) −4.28967 24.3279i −0.135855 0.770473i −0.974260 0.225426i \(-0.927623\pi\)
0.838405 0.545048i \(-0.183488\pi\)
\(998\) 28.8555 + 19.7926i 0.913403 + 0.626525i
\(999\) 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 684.2.ce.a.359.10 240
3.2 odd 2 inner 684.2.ce.a.359.31 yes 240
4.3 odd 2 inner 684.2.ce.a.359.14 yes 240
12.11 even 2 inner 684.2.ce.a.359.27 yes 240
19.9 even 9 inner 684.2.ce.a.503.27 yes 240
57.47 odd 18 inner 684.2.ce.a.503.14 yes 240
76.47 odd 18 inner 684.2.ce.a.503.31 yes 240
228.47 even 18 inner 684.2.ce.a.503.10 yes 240
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
684.2.ce.a.359.10 240 1.1 even 1 trivial
684.2.ce.a.359.14 yes 240 4.3 odd 2 inner
684.2.ce.a.359.27 yes 240 12.11 even 2 inner
684.2.ce.a.359.31 yes 240 3.2 odd 2 inner
684.2.ce.a.503.10 yes 240 228.47 even 18 inner
684.2.ce.a.503.14 yes 240 57.47 odd 18 inner
684.2.ce.a.503.27 yes 240 19.9 even 9 inner
684.2.ce.a.503.31 yes 240 76.47 odd 18 inner