Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [525,2,Mod(299,525)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(525, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 3, 5]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("525.299");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 525 = 3 \cdot 5^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 525.q (of order \(6\), degree \(2\), 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: | \(4.19214610612\) |
Analytic rank: | \(0\) |
Dimension: | \(40\) |
Relative dimension: | \(20\) over \(\Q(\zeta_{6})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 299.9 | ||
Character | \(\chi\) | \(=\) | 525.299 |
Dual form | 525.2.q.g.374.9 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/525\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(176\) | \(451\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(e\left(\frac{5}{6}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.442404 | + | 0.766266i | −0.312827 | + | 0.541832i | −0.978973 | − | 0.203989i | \(-0.934609\pi\) |
0.666146 | + | 0.745821i | \(0.267943\pi\) | |||||||
\(3\) | −1.72165 | + | 0.189492i | −0.993997 | + | 0.109403i | ||||
\(4\) | 0.608557 | + | 1.05405i | 0.304279 | + | 0.527026i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0.616465 | − | 1.40308i | 0.251671 | − | 0.572804i | ||||
\(7\) | 0.206062 | − | 2.63771i | 0.0778841 | − | 0.996962i | ||||
\(8\) | −2.84653 | −1.00640 | ||||||||
\(9\) | 2.92819 | − | 0.652481i | 0.976062 | − | 0.217494i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.25362 | − | 0.723775i | 0.377979 | − | 0.218227i | −0.298959 | − | 0.954266i | \(-0.596640\pi\) |
0.676939 | + | 0.736039i | \(0.263306\pi\) | |||||||
\(12\) | −1.24746 | − | 1.69940i | −0.360111 | − | 0.490573i | ||||
\(13\) | 4.04326 | 1.12140 | 0.560699 | − | 0.828020i | \(-0.310533\pi\) | ||||
0.560699 | + | 0.828020i | \(0.310533\pi\) | |||||||
\(14\) | 1.93003 | + | 1.32483i | 0.515822 | + | 0.354077i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0.0422021 | − | 0.0730962i | 0.0105505 | − | 0.0182741i | ||||
\(17\) | 4.98592 | − | 2.87862i | 1.20926 | − | 0.698168i | 0.246665 | − | 0.969101i | \(-0.420665\pi\) |
0.962598 | + | 0.270933i | \(0.0873321\pi\) | |||||||
\(18\) | −0.795467 | + | 2.53243i | −0.187493 | + | 0.596900i | ||||
\(19\) | 0.356910 | + | 0.206062i | 0.0818807 | + | 0.0472738i | 0.540381 | − | 0.841420i | \(-0.318280\pi\) |
−0.458501 | + | 0.888694i | \(0.651613\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0.145060 | + | 4.58028i | 0.0316546 | + | 0.999499i | ||||
\(22\) | 1.28081i | 0.273069i | ||||||||
\(23\) | −3.65719 | + | 6.33444i | −0.762578 | + | 1.32082i | 0.178940 | + | 0.983860i | \(0.442733\pi\) |
−0.941518 | + | 0.336963i | \(0.890600\pi\) | |||||||
\(24\) | 4.90074 | − | 0.539396i | 1.00036 | − | 0.110104i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −1.78875 | + | 3.09821i | −0.350803 | + | 0.607609i | ||||
\(27\) | −4.91768 | + | 1.67821i | −0.946408 | + | 0.322973i | ||||
\(28\) | 2.90569 | − | 1.38800i | 0.549124 | − | 0.262307i | ||||
\(29\) | − | 1.82121i | − | 0.338191i | −0.985600 | − | 0.169095i | \(-0.945915\pi\) | ||
0.985600 | − | 0.169095i | \(-0.0540846\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 2.30936 | − | 1.33331i | 0.414772 | − | 0.239469i | −0.278066 | − | 0.960562i | \(-0.589693\pi\) |
0.692838 | + | 0.721093i | \(0.256360\pi\) | |||||||
\(32\) | −2.80919 | − | 4.86566i | −0.496599 | − | 0.860135i | ||||
\(33\) | −2.02114 | + | 1.48364i | −0.351836 | + | 0.258269i | ||||
\(34\) | 5.09406i | 0.873623i | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 2.46972 | + | 2.68939i | 0.411619 | + | 0.448231i | ||||
\(37\) | 5.06429 | + | 2.92387i | 0.832565 | + | 0.480682i | 0.854730 | − | 0.519073i | \(-0.173723\pi\) |
−0.0221652 | + | 0.999754i | \(0.507056\pi\) | |||||||
\(38\) | −0.315797 | + | 0.182325i | −0.0512290 | + | 0.0295771i | ||||
\(39\) | −6.96109 | + | 0.766166i | −1.11467 | + | 0.122685i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 6.46287 | 1.00933 | 0.504665 | − | 0.863315i | \(-0.331616\pi\) | ||||
0.504665 | + | 0.863315i | \(0.331616\pi\) | |||||||
\(42\) | −3.57389 | − | 1.91518i | −0.551463 | − | 0.295519i | ||||
\(43\) | 10.3583i | 1.57963i | 0.613345 | + | 0.789815i | \(0.289823\pi\) | ||||
−0.613345 | + | 0.789815i | \(0.710177\pi\) | |||||||
\(44\) | 1.52579 | + | 0.880917i | 0.230022 | + | 0.132803i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −3.23592 | − | 5.60477i | −0.477110 | − | 0.826378i | ||||
\(47\) | 9.41134 | + | 5.43364i | 1.37279 | + | 0.792578i | 0.991278 | − | 0.131788i | \(-0.0420718\pi\) |
0.381507 | + | 0.924366i | \(0.375405\pi\) | |||||||
\(48\) | −0.0588063 | + | 0.133843i | −0.00848796 | + | 0.0193186i | ||||
\(49\) | −6.91508 | − | 1.08706i | −0.987868 | − | 0.155295i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −8.03855 | + | 5.90078i | −1.12562 | + | 0.826275i | ||||
\(52\) | 2.46055 | + | 4.26180i | 0.341217 | + | 0.591005i | ||||
\(53\) | −0.697977 | − | 1.20893i | −0.0958745 | − | 0.166059i | 0.814099 | − | 0.580726i | \(-0.197231\pi\) |
−0.909973 | + | 0.414667i | \(0.863898\pi\) | |||||||
\(54\) | 0.889643 | − | 4.51070i | 0.121065 | − | 0.613829i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −0.586561 | + | 7.50833i | −0.0783825 | + | 1.00334i | ||||
\(57\) | −0.653522 | − | 0.287136i | −0.0865611 | − | 0.0380320i | ||||
\(58\) | 1.39554 | + | 0.805713i | 0.183243 | + | 0.105795i | ||||
\(59\) | 0.583941 | + | 1.01142i | 0.0760227 | + | 0.131675i | 0.901531 | − | 0.432715i | \(-0.142445\pi\) |
−0.825508 | + | 0.564391i | \(0.809111\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 3.58903 | + | 2.07213i | 0.459529 | + | 0.265309i | 0.711846 | − | 0.702335i | \(-0.247859\pi\) |
−0.252317 | + | 0.967645i | \(0.581193\pi\) | |||||||
\(62\) | 2.35944i | 0.299649i | ||||||||
\(63\) | −1.11767 | − | 7.85817i | −0.140813 | − | 0.990036i | ||||
\(64\) | 5.14000 | 0.642499 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −0.242703 | − | 2.20510i | −0.0298747 | − | 0.271429i | ||||
\(67\) | 5.99309 | − | 3.46011i | 0.732173 | − | 0.422720i | −0.0870436 | − | 0.996205i | \(-0.527742\pi\) |
0.819217 | + | 0.573484i | \(0.194409\pi\) | |||||||
\(68\) | 6.06843 | + | 3.50361i | 0.735906 | + | 0.424875i | ||||
\(69\) | 5.09609 | − | 11.5987i | 0.613497 | − | 1.39632i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 13.3217i | − | 1.58100i | −0.612463 | − | 0.790499i | \(-0.709821\pi\) | ||
0.612463 | − | 0.790499i | \(-0.290179\pi\) | |||||||
\(72\) | −8.33517 | + | 1.85731i | −0.982309 | + | 0.218886i | ||||
\(73\) | −1.57238 | − | 2.72344i | −0.184033 | − | 0.318755i | 0.759217 | − | 0.650838i | \(-0.225582\pi\) |
−0.943250 | + | 0.332082i | \(0.892249\pi\) | |||||||
\(74\) | −4.48093 | + | 2.58707i | −0.520898 | + | 0.300740i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0.501602i | 0.0575377i | ||||||||
\(77\) | −1.65079 | − | 3.45582i | −0.188125 | − | 0.393828i | ||||
\(78\) | 2.49253 | − | 5.67300i | 0.282223 | − | 0.642341i | ||||
\(79\) | −6.42216 | + | 11.1235i | −0.722550 | + | 1.25149i | 0.237425 | + | 0.971406i | \(0.423697\pi\) |
−0.959975 | + | 0.280087i | \(0.909637\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 8.14854 | − | 3.82117i | 0.905393 | − | 0.424574i | ||||
\(82\) | −2.85920 | + | 4.95228i | −0.315746 | + | 0.546888i | ||||
\(83\) | − | 11.5010i | − | 1.26240i | −0.775620 | − | 0.631200i | \(-0.782563\pi\) | ||
0.775620 | − | 0.631200i | \(-0.217437\pi\) | |||||||
\(84\) | −4.73957 | + | 2.94026i | −0.517130 | + | 0.320809i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −7.93724 | − | 4.58257i | −0.855894 | − | 0.494151i | ||||
\(87\) | 0.345106 | + | 3.13550i | 0.0369993 | + | 0.336161i | ||||
\(88\) | −3.56845 | + | 2.06025i | −0.380399 | + | 0.219623i | ||||
\(89\) | 3.90111 | − | 6.75692i | 0.413517 | − | 0.716232i | −0.581755 | − | 0.813364i | \(-0.697634\pi\) |
0.995271 | + | 0.0971324i | \(0.0309670\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0.833161 | − | 10.6650i | 0.0873390 | − | 1.11799i | ||||
\(92\) | −8.90244 | −0.928144 | ||||||||
\(93\) | −3.72326 | + | 2.73310i | −0.386084 | + | 0.283409i | ||||
\(94\) | −8.32723 | + | 4.80773i | −0.858889 | + | 0.495880i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 5.75846 | + | 7.84466i | 0.587720 | + | 0.800642i | ||||
\(97\) | −3.86099 | −0.392024 | −0.196012 | − | 0.980601i | \(-0.562799\pi\) | ||||
−0.196012 | + | 0.980601i | \(0.562799\pi\) | |||||||
\(98\) | 3.89224 | − | 4.81787i | 0.393176 | − | 0.486678i | ||||
\(99\) | 3.19857 | − | 2.93731i | 0.321468 | − | 0.295211i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −6.61336 | − | 11.4547i | −0.658054 | − | 1.13978i | −0.981119 | − | 0.193406i | \(-0.938046\pi\) |
0.323065 | − | 0.946377i | \(-0.395287\pi\) | |||||||
\(102\) | −0.965285 | − | 8.77020i | −0.0955774 | − | 0.868379i | ||||
\(103\) | 8.49538 | − | 14.7144i | 0.837075 | − | 1.44986i | −0.0552547 | − | 0.998472i | \(-0.517597\pi\) |
0.892330 | − | 0.451384i | \(-0.149070\pi\) | |||||||
\(104\) | −11.5092 | −1.12857 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 1.23515 | 0.119968 | ||||||||
\(107\) | −6.47403 | + | 11.2134i | −0.625868 | + | 1.08404i | 0.362504 | + | 0.931982i | \(0.381922\pi\) |
−0.988372 | + | 0.152054i | \(0.951411\pi\) | |||||||
\(108\) | −4.76162 | − | 4.16220i | −0.458187 | − | 0.400508i | ||||
\(109\) | 3.63427 | + | 6.29474i | 0.348100 | + | 0.602927i | 0.985912 | − | 0.167265i | \(-0.0534936\pi\) |
−0.637812 | + | 0.770192i | \(0.720160\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −9.27301 | − | 4.07425i | −0.880156 | − | 0.386711i | ||||
\(112\) | −0.184111 | − | 0.126380i | −0.0173968 | − | 0.0119417i | ||||
\(113\) | 4.78517 | 0.450151 | 0.225075 | − | 0.974341i | \(-0.427737\pi\) | ||||
0.225075 | + | 0.974341i | \(0.427737\pi\) | |||||||
\(114\) | 0.509143 | − | 0.373742i | 0.0476856 | − | 0.0350041i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 1.91965 | − | 1.10831i | 0.178235 | − | 0.102904i | ||||
\(117\) | 11.8394 | − | 2.63815i | 1.09455 | − | 0.243897i | ||||
\(118\) | −1.03335 | −0.0951278 | ||||||||
\(119\) | −6.56557 | − | 13.7446i | −0.601865 | − | 1.25997i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −4.45230 | + | 7.71161i | −0.404754 | + | 0.701055i | ||||
\(122\) | −3.17561 | + | 1.83344i | −0.287506 | + | 0.165992i | ||||
\(123\) | −11.1268 | + | 1.22466i | −1.00327 | + | 0.110424i | ||||
\(124\) | 2.81075 | + | 1.62279i | 0.252413 | + | 0.145731i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 6.51591 | + | 2.62005i | 0.580484 | + | 0.233413i | ||||
\(127\) | − | 9.16192i | − | 0.812989i | −0.913653 | − | 0.406495i | \(-0.866751\pi\) | ||
0.913653 | − | 0.406495i | \(-0.133249\pi\) | |||||||
\(128\) | 3.34442 | − | 5.79271i | 0.295608 | − | 0.512008i | ||||
\(129\) | −1.96282 | − | 17.8335i | −0.172817 | − | 1.57015i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −10.4220 | + | 18.0514i | −0.910574 | + | 1.57716i | −0.0973191 | + | 0.995253i | \(0.531027\pi\) |
−0.813255 | + | 0.581907i | \(0.802307\pi\) | |||||||
\(132\) | −2.79382 | − | 1.22751i | −0.243170 | − | 0.106841i | ||||
\(133\) | 0.617078 | − | 0.898964i | 0.0535074 | − | 0.0779501i | ||||
\(134\) | 6.12308i | 0.528953i | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −14.1926 | + | 8.19408i | −1.21700 | + | 0.702637i | ||||
\(137\) | −4.73886 | − | 8.20795i | −0.404868 | − | 0.701253i | 0.589438 | − | 0.807814i | \(-0.299349\pi\) |
−0.994306 | + | 0.106561i | \(0.966016\pi\) | |||||||
\(138\) | 6.63319 | + | 9.03629i | 0.564654 | + | 0.769220i | ||||
\(139\) | 5.75447i | 0.488088i | 0.969764 | + | 0.244044i | \(0.0784741\pi\) | ||||
−0.969764 | + | 0.244044i | \(0.921526\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −17.2327 | − | 7.57147i | −1.45126 | − | 0.637633i | ||||
\(142\) | 10.2080 | + | 5.89359i | 0.856636 | + | 0.494579i | ||||
\(143\) | 5.06869 | − | 2.92641i | 0.423865 | − | 0.244719i | ||||
\(144\) | 0.0758818 | − | 0.241575i | 0.00632348 | − | 0.0201313i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 2.78251 | 0.230282 | ||||||||
\(147\) | 12.1114 | + | 0.561195i | 0.998928 | + | 0.0462866i | ||||
\(148\) | 7.11737i | 0.585044i | ||||||||
\(149\) | 5.57080 | + | 3.21630i | 0.456378 | + | 0.263490i | 0.710520 | − | 0.703677i | \(-0.248460\pi\) |
−0.254142 | + | 0.967167i | \(0.581793\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −2.06002 | − | 3.56807i | −0.167642 | − | 0.290365i | 0.769948 | − | 0.638107i | \(-0.220282\pi\) |
−0.937591 | + | 0.347741i | \(0.886949\pi\) | |||||||
\(152\) | −1.01595 | − | 0.586561i | −0.0824047 | − | 0.0475764i | ||||
\(153\) | 12.7214 | − | 11.6824i | 1.02847 | − | 0.944462i | ||||
\(154\) | 3.37840 | + | 0.263925i | 0.272239 | + | 0.0212677i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −5.04380 | − | 6.87109i | −0.403827 | − | 0.550128i | ||||
\(157\) | 0.619880 | + | 1.07366i | 0.0494718 | + | 0.0856877i | 0.889701 | − | 0.456544i | \(-0.150913\pi\) |
−0.840229 | + | 0.542232i | \(0.817580\pi\) | |||||||
\(158\) | −5.68238 | − | 9.84218i | −0.452066 | − | 0.783001i | ||||
\(159\) | 1.43076 | + | 1.94910i | 0.113466 | + | 0.154574i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 15.9548 | + | 10.9519i | 1.25742 | + | 0.863132i | ||||
\(162\) | −0.676913 | + | 7.93445i | −0.0531833 | + | 0.623389i | ||||
\(163\) | −6.44585 | − | 3.72151i | −0.504878 | − | 0.291491i | 0.225848 | − | 0.974163i | \(-0.427485\pi\) |
−0.730726 | + | 0.682671i | \(0.760818\pi\) | |||||||
\(164\) | 3.93302 | + | 6.81220i | 0.307118 | + | 0.531943i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 8.81284 | + | 5.08809i | 0.684009 | + | 0.394913i | ||||
\(167\) | − | 2.50723i | − | 0.194015i | −0.995284 | − | 0.0970077i | \(-0.969073\pi\) | ||
0.995284 | − | 0.0970077i | \(-0.0309271\pi\) | |||||||
\(168\) | −0.412917 | − | 13.0379i | −0.0318572 | − | 1.00590i | ||||
\(169\) | 3.34791 | 0.257532 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 1.17955 | + | 0.370511i | 0.0902023 | + | 0.0283337i | ||||
\(172\) | −10.9182 | + | 6.30363i | −0.832506 | + | 0.480647i | ||||
\(173\) | 14.7654 | + | 8.52481i | 1.12259 | + | 0.648130i | 0.942062 | − | 0.335440i | \(-0.108885\pi\) |
0.180532 | + | 0.983569i | \(0.442218\pi\) | |||||||
\(174\) | −2.55531 | − | 1.12272i | −0.193717 | − | 0.0851128i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | − | 0.122179i | − | 0.00920962i | ||||||
\(177\) | −1.19700 | − | 1.63066i | −0.0899721 | − | 0.122568i | ||||
\(178\) | 3.45173 | + | 5.97858i | 0.258718 | + | 0.448113i | ||||
\(179\) | 10.1751 | − | 5.87462i | 0.760525 | − | 0.439090i | −0.0689590 | − | 0.997619i | \(-0.521968\pi\) |
0.829484 | + | 0.558530i | \(0.188634\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 2.41221i | − | 0.179298i | −0.995973 | − | 0.0896490i | \(-0.971425\pi\) | ||
0.995973 | − | 0.0896490i | \(-0.0285745\pi\) | |||||||
\(182\) | 7.80360 | + | 5.35664i | 0.578442 | + | 0.397061i | ||||
\(183\) | −6.57173 | − | 2.88740i | −0.485796 | − | 0.213442i | ||||
\(184\) | 10.4103 | − | 18.0312i | 0.767458 | − | 1.32928i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −0.447096 | − | 4.06214i | −0.0327827 | − | 0.297851i | ||||
\(187\) | 4.16695 | − | 7.21737i | 0.304718 | − | 0.527786i | ||||
\(188\) | 13.2267i | 0.964658i | ||||||||
\(189\) | 3.41331 | + | 13.3173i | 0.248281 | + | 0.968688i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −11.9159 | − | 6.87963i | −0.862202 | − | 0.497793i | 0.00254675 | − | 0.999997i | \(-0.499189\pi\) |
−0.864749 | + | 0.502204i | \(0.832523\pi\) | |||||||
\(192\) | −8.84929 | + | 0.973990i | −0.638643 | + | 0.0702917i | ||||
\(193\) | 7.97929 | − | 4.60685i | 0.574362 | − | 0.331608i | −0.184528 | − | 0.982827i | \(-0.559075\pi\) |
0.758890 | + | 0.651219i | \(0.225742\pi\) | |||||||
\(194\) | 1.70812 | − | 2.95855i | 0.122636 | − | 0.212411i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −3.06240 | − | 7.95039i | −0.218743 | − | 0.567885i | ||||
\(197\) | 4.11728 | 0.293344 | 0.146672 | − | 0.989185i | \(-0.453144\pi\) | ||||
0.146672 | + | 0.989185i | \(0.453144\pi\) | |||||||
\(198\) | 0.835701 | + | 3.75043i | 0.0593907 | + | 0.266532i | ||||
\(199\) | −0.0694265 | + | 0.0400834i | −0.00492151 | + | 0.00284144i | −0.502459 | − | 0.864601i | \(-0.667571\pi\) |
0.497537 | + | 0.867443i | \(0.334238\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −9.66237 | + | 7.09277i | −0.681531 | + | 0.500285i | ||||
\(202\) | 11.7031 | 0.823428 | ||||||||
\(203\) | −4.80384 | − | 0.375283i | −0.337164 | − | 0.0263397i | ||||
\(204\) | −11.1116 | − | 4.88208i | −0.777971 | − | 0.341814i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 7.51679 | + | 13.0195i | 0.523719 | + | 0.907108i | ||||
\(207\) | −6.57584 | + | 20.9347i | −0.457052 | + | 1.45506i | ||||
\(208\) | 0.170634 | − | 0.295547i | 0.0118313 | − | 0.0204925i | ||||
\(209\) | 0.596570 | 0.0412656 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 17.5804 | 1.21028 | 0.605141 | − | 0.796118i | \(-0.293117\pi\) | ||||
0.605141 | + | 0.796118i | \(0.293117\pi\) | |||||||
\(212\) | 0.849517 | − | 1.47141i | 0.0583451 | − | 0.101057i | ||||
\(213\) | 2.52437 | + | 22.9354i | 0.172967 | + | 1.57151i | ||||
\(214\) | −5.72828 | − | 9.92167i | −0.391577 | − | 0.678231i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 13.9983 | − | 4.77709i | 0.952465 | − | 0.325040i | ||||
\(217\) | −3.04101 | − | 6.36616i | −0.206437 | − | 0.432163i | ||||
\(218\) | −6.43127 | −0.435580 | ||||||||
\(219\) | 3.22317 | + | 4.39088i | 0.217802 | + | 0.296708i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 20.1593 | − | 11.6390i | 1.35606 | − | 0.782924i | ||||
\(222\) | 7.22438 | − | 5.30313i | 0.484869 | − | 0.355923i | ||||
\(223\) | −27.4965 | −1.84130 | −0.920651 | − | 0.390387i | \(-0.872341\pi\) | ||||
−0.920651 | + | 0.390387i | \(0.872341\pi\) | |||||||
\(224\) | −13.4131 | + | 6.40721i | −0.896199 | + | 0.428100i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −2.11698 | + | 3.66671i | −0.140819 | + | 0.243906i | ||||
\(227\) | −10.7431 | + | 6.20253i | −0.713044 | + | 0.411676i | −0.812187 | − | 0.583397i | \(-0.801723\pi\) |
0.0991431 | + | 0.995073i | \(0.468390\pi\) | |||||||
\(228\) | −0.0950497 | − | 0.863584i | −0.00629482 | − | 0.0571923i | ||||
\(229\) | −23.5513 | − | 13.5973i | −1.55631 | − | 0.898538i | −0.997605 | − | 0.0691740i | \(-0.977964\pi\) |
−0.558709 | − | 0.829364i | \(-0.688703\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 3.49694 | + | 5.63692i | 0.230082 | + | 0.370882i | ||||
\(232\) | 5.18414i | 0.340355i | ||||||||
\(233\) | −14.4675 | + | 25.0585i | −0.947798 | + | 1.64163i | −0.197749 | + | 0.980253i | \(0.563363\pi\) |
−0.750049 | + | 0.661382i | \(0.769970\pi\) | |||||||
\(234\) | −3.21628 | + | 10.2393i | −0.210255 | + | 0.669362i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −0.710723 | + | 1.23101i | −0.0462641 | + | 0.0801318i | ||||
\(237\) | 8.94892 | − | 20.3678i | 0.581295 | − | 1.32303i | ||||
\(238\) | 13.4367 | + | 1.04969i | 0.870970 | + | 0.0680413i | ||||
\(239\) | 19.2419i | 1.24465i | 0.782757 | + | 0.622327i | \(0.213813\pi\) | ||||
−0.782757 | + | 0.622327i | \(0.786187\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 4.90603 | − | 2.83250i | 0.316025 | − | 0.182457i | −0.333594 | − | 0.942717i | \(-0.608262\pi\) |
0.649619 | + | 0.760260i | \(0.274928\pi\) | |||||||
\(242\) | −3.93943 | − | 6.82329i | −0.253236 | − | 0.438618i | ||||
\(243\) | −13.3049 | + | 8.12282i | −0.853508 | + | 0.521079i | ||||
\(244\) | 5.04404i | 0.322911i | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 3.98413 | − | 9.06791i | 0.254019 | − | 0.578149i | ||||
\(247\) | 1.44308 | + | 0.833161i | 0.0918208 | + | 0.0530127i | ||||
\(248\) | −6.57365 | + | 3.79530i | −0.417427 | + | 0.241002i | ||||
\(249\) | 2.17935 | + | 19.8008i | 0.138111 | + | 1.25482i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −6.55844 | −0.413965 | −0.206983 | − | 0.978345i | \(-0.566364\pi\) | ||||
−0.206983 | + | 0.978345i | \(0.566364\pi\) | |||||||
\(252\) | 7.60275 | − | 5.96023i | 0.478928 | − | 0.375459i | ||||
\(253\) | 10.5879i | 0.665659i | ||||||||
\(254\) | 7.02047 | + | 4.05327i | 0.440504 | + | 0.254325i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 8.09917 | + | 14.0282i | 0.506198 | + | 0.876761i | ||||
\(257\) | 7.56295 | + | 4.36647i | 0.471764 | + | 0.272373i | 0.716978 | − | 0.697096i | \(-0.245525\pi\) |
−0.245214 | + | 0.969469i | \(0.578858\pi\) | |||||||
\(258\) | 14.5335 | + | 6.38555i | 0.904818 | + | 0.397547i | ||||
\(259\) | 8.75590 | − | 12.7557i | 0.544065 | − | 0.792598i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −1.18831 | − | 5.33285i | −0.0735544 | − | 0.330095i | ||||
\(262\) | −9.22147 | − | 15.9721i | −0.569704 | − | 0.986757i | ||||
\(263\) | −11.2709 | − | 19.5217i | −0.694992 | − | 1.20376i | −0.970183 | − | 0.242372i | \(-0.922075\pi\) |
0.275192 | − | 0.961389i | \(-0.411259\pi\) | |||||||
\(264\) | 5.75324 | − | 4.22323i | 0.354088 | − | 0.259922i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0.415848 | + | 0.870551i | 0.0254973 | + | 0.0533769i | ||||
\(267\) | −5.43597 | + | 12.3723i | −0.332676 | + | 0.757173i | ||||
\(268\) | 7.29428 | + | 4.21135i | 0.445569 | + | 0.257249i | ||||
\(269\) | 7.09460 | + | 12.2882i | 0.432565 | + | 0.749225i | 0.997093 | − | 0.0761890i | \(-0.0242752\pi\) |
−0.564528 | + | 0.825414i | \(0.690942\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −11.0247 | − | 6.36513i | −0.669705 | − | 0.386654i | 0.126260 | − | 0.991997i | \(-0.459703\pi\) |
−0.795965 | + | 0.605343i | \(0.793036\pi\) | |||||||
\(272\) | − | 0.485936i | − | 0.0294642i | ||||||
\(273\) | 0.586513 | + | 18.5192i | 0.0354974 | + | 1.12084i | ||||
\(274\) | 8.38597 | 0.506615 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 15.3269 | − | 1.68695i | 0.922573 | − | 0.101542i | ||||
\(277\) | −24.9564 | + | 14.4086i | −1.49948 | + | 0.865727i | −1.00000 | 0.000595725i | \(-0.999810\pi\) | |
−0.499484 | + | 0.866323i | \(0.666477\pi\) | |||||||
\(278\) | −4.40946 | − | 2.54580i | −0.264462 | − | 0.152687i | ||||
\(279\) | 5.89226 | − | 5.41098i | 0.352761 | − | 0.323947i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 13.4500i | 0.802357i | 0.916000 | + | 0.401179i | \(0.131399\pi\) | ||||
−0.916000 | + | 0.401179i | \(0.868601\pi\) | |||||||
\(282\) | 13.4256 | − | 9.85520i | 0.799482 | − | 0.586868i | ||||
\(283\) | −7.03838 | − | 12.1908i | −0.418388 | − | 0.724670i | 0.577389 | − | 0.816469i | \(-0.304072\pi\) |
−0.995778 | + | 0.0917992i | \(0.970738\pi\) | |||||||
\(284\) | 14.0418 | − | 8.10703i | 0.833227 | − | 0.481064i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 5.17862i | 0.306218i | ||||||||
\(287\) | 1.33175 | − | 17.0472i | 0.0786107 | − | 1.00626i | ||||
\(288\) | −11.4006 | − | 12.4146i | −0.671785 | − | 0.731538i | ||||
\(289\) | 8.07292 | − | 13.9827i | 0.474878 | − | 0.822512i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 6.64729 | − | 0.731629i | 0.389671 | − | 0.0428888i | ||||
\(292\) | 1.91377 | − | 3.31474i | 0.111995 | − | 0.193981i | ||||
\(293\) | 16.7139i | 0.976436i | 0.872722 | + | 0.488218i | \(0.162353\pi\) | ||||
−0.872722 | + | 0.488218i | \(0.837647\pi\) | |||||||
\(294\) | −5.78814 | + | 9.03225i | −0.337571 | + | 0.526772i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −14.4157 | − | 8.32289i | −0.837893 | − | 0.483758i | ||||
\(297\) | −4.95023 | + | 5.66313i | −0.287242 | + | 0.328608i | ||||
\(298\) | −4.92909 | + | 2.84581i | −0.285534 | + | 0.164853i | ||||
\(299\) | −14.7870 | + | 25.6118i | −0.855152 | + | 1.48117i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 27.3223 | + | 2.13446i | 1.57483 | + | 0.123028i | ||||
\(302\) | 3.64545 | 0.209772 | ||||||||
\(303\) | 13.5565 | + | 18.4678i | 0.778800 | + | 1.06095i | ||||
\(304\) | 0.0301247 | − | 0.0173925i | 0.00172777 | − | 0.000997528i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 3.32377 | + | 14.9163i | 0.190007 | + | 0.852710i | ||||
\(307\) | −9.72258 | −0.554897 | −0.277449 | − | 0.960741i | \(-0.589489\pi\) | ||||
−0.277449 | + | 0.960741i | \(0.589489\pi\) | |||||||
\(308\) | 2.63802 | − | 3.84309i | 0.150315 | − | 0.218980i | ||||
\(309\) | −11.8378 | + | 26.9430i | −0.673431 | + | 1.53273i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 2.50723 | + | 4.34265i | 0.142172 | + | 0.246249i | 0.928314 | − | 0.371796i | \(-0.121258\pi\) |
−0.786142 | + | 0.618046i | \(0.787925\pi\) | |||||||
\(312\) | 19.8149 | − | 2.18091i | 1.12180 | − | 0.123470i | ||||
\(313\) | 8.86441 | − | 15.3536i | 0.501046 | − | 0.867837i | −0.498953 | − | 0.866629i | \(-0.666282\pi\) |
0.999999 | − | 0.00120811i | \(-0.000384553\pi\) | |||||||
\(314\) | −1.09695 | −0.0619045 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −15.6330 | −0.879426 | ||||||||
\(317\) | −2.10107 | + | 3.63917i | −0.118008 | + | 0.204396i | −0.918978 | − | 0.394308i | \(-0.870984\pi\) |
0.800970 | + | 0.598704i | \(0.204318\pi\) | |||||||
\(318\) | −2.12650 | + | 0.234052i | −0.119248 | + | 0.0131250i | ||||
\(319\) | −1.31815 | − | 2.28310i | −0.0738022 | − | 0.127829i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 9.02120 | − | 20.5323i | 0.503514 | − | 1.14600i | ||||
\(322\) | −15.4506 | + | 7.38049i | −0.861027 | + | 0.411299i | ||||
\(323\) | 2.37270 | 0.132020 | ||||||||
\(324\) | 8.98656 | + | 6.26358i | 0.499253 | + | 0.347977i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 5.70334 | − | 3.29282i | 0.315879 | − | 0.182373i | ||||
\(327\) | −7.44977 | − | 10.1487i | −0.411973 | − | 0.561225i | ||||
\(328\) | −18.3967 | −1.01579 | ||||||||
\(329\) | 16.2717 | − | 23.7048i | 0.897089 | − | 1.30689i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 0.680140 | − | 1.17804i | 0.0373839 | − | 0.0647508i | −0.846728 | − | 0.532026i | \(-0.821431\pi\) |
0.884112 | + | 0.467275i | \(0.154764\pi\) | |||||||
\(332\) | 12.1227 | − | 6.99902i | 0.665317 | − | 0.384121i | ||||
\(333\) | 16.7370 | + | 5.25728i | 0.917180 | + | 0.288097i | ||||
\(334\) | 1.92121 | + | 1.10921i | 0.105124 | + | 0.0606933i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0.340923 | + | 0.182694i | 0.0185989 | + | 0.00996679i | ||||
\(337\) | − | 26.2620i | − | 1.43058i | −0.698826 | − | 0.715292i | \(-0.746294\pi\) | ||
0.698826 | − | 0.715292i | \(-0.253706\pi\) | |||||||
\(338\) | −1.48113 | + | 2.56539i | −0.0805629 | + | 0.139539i | ||||
\(339\) | −8.23840 | + | 0.906753i | −0.447449 | + | 0.0492480i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 1.93003 | − | 3.34291i | 0.104517 | − | 0.181029i | ||||
\(342\) | −0.805747 | + | 0.739933i | −0.0435698 | + | 0.0400110i | ||||
\(343\) | −4.29230 | + | 18.0160i | −0.231762 | + | 0.972772i | ||||
\(344\) | − | 29.4853i | − | 1.58974i | ||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −13.0646 | + | 7.54283i | −0.702355 | + | 0.405505i | ||||
\(347\) | 3.13913 | + | 5.43714i | 0.168517 | + | 0.291881i | 0.937899 | − | 0.346909i | \(-0.112769\pi\) |
−0.769381 | + | 0.638790i | \(0.779435\pi\) | |||||||
\(348\) | −3.09496 | + | 2.27189i | −0.165907 | + | 0.121786i | ||||
\(349\) | − | 4.99426i | − | 0.267336i | −0.991026 | − | 0.133668i | \(-0.957324\pi\) | ||
0.991026 | − | 0.133668i | \(-0.0426756\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −19.8834 | + | 6.78545i | −1.06130 | + | 0.362181i | ||||
\(352\) | −7.04329 | − | 4.06644i | −0.375408 | − | 0.216742i | ||||
\(353\) | −0.682186 | + | 0.393860i | −0.0363091 | + | 0.0209631i | −0.518045 | − | 0.855354i | \(-0.673340\pi\) |
0.481736 | + | 0.876317i | \(0.340007\pi\) | |||||||
\(354\) | 1.77907 | − | 0.195812i | 0.0945568 | − | 0.0104073i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 9.49619 | 0.503297 | ||||||||
\(357\) | 13.9081 | + | 22.4193i | 0.736097 | + | 1.18656i | ||||
\(358\) | 10.3958i | 0.549436i | ||||||||
\(359\) | −21.9487 | − | 12.6721i | −1.15841 | − | 0.668808i | −0.207487 | − | 0.978238i | \(-0.566528\pi\) |
−0.950922 | + | 0.309430i | \(0.899862\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −9.41508 | − | 16.3074i | −0.495530 | − | 0.858284i | ||||
\(362\) | 1.84840 | + | 1.06717i | 0.0971495 | + | 0.0560893i | ||||
\(363\) | 6.20403 | − | 14.1204i | 0.325627 | − | 0.741129i | ||||
\(364\) | 11.7484 | − | 5.61204i | 0.615786 | − | 0.294151i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 5.11987 | − | 3.75830i | 0.267620 | − | 0.196449i | ||||
\(367\) | 0.912964 | + | 1.58130i | 0.0476563 | + | 0.0825432i | 0.888870 | − | 0.458160i | \(-0.151491\pi\) |
−0.841213 | + | 0.540703i | \(0.818158\pi\) | |||||||
\(368\) | 0.308683 | + | 0.534654i | 0.0160912 | + | 0.0278708i | ||||
\(369\) | 18.9245 | − | 4.21690i | 0.985169 | − | 0.219523i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −3.33264 | + | 1.59195i | −0.173022 | + | 0.0826499i | ||||
\(372\) | −5.14664 | − | 2.26126i | −0.266841 | − | 0.117241i | ||||
\(373\) | 1.81882 | + | 1.05009i | 0.0941748 | + | 0.0543718i | 0.546348 | − | 0.837558i | \(-0.316018\pi\) |
−0.452173 | + | 0.891930i | \(0.649351\pi\) | |||||||
\(374\) | 3.68695 | + | 6.38599i | 0.190648 | + | 0.330212i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −26.7897 | − | 15.4670i | −1.38157 | − | 0.797651i | ||||
\(377\) | − | 7.36363i | − | 0.379246i | ||||||
\(378\) | −11.7146 | − | 3.27611i | −0.602535 | − | 0.168505i | ||||
\(379\) | 19.2106 | 0.986782 | 0.493391 | − | 0.869808i | \(-0.335757\pi\) | ||||
0.493391 | + | 0.869808i | \(0.335757\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 1.73611 | + | 15.7737i | 0.0889439 | + | 0.808109i | ||||
\(382\) | 10.5433 | − | 6.08716i | 0.539440 | − | 0.311446i | ||||
\(383\) | 2.73720 | + | 1.58032i | 0.139864 | + | 0.0807506i | 0.568299 | − | 0.822822i | \(-0.307602\pi\) |
−0.428435 | + | 0.903573i | \(0.640935\pi\) | |||||||
\(384\) | −4.66026 | + | 10.6068i | −0.237818 | + | 0.541275i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 8.15235i | 0.414944i | ||||||||
\(387\) | 6.75861 | + | 30.3311i | 0.343559 | + | 1.54182i | ||||
\(388\) | −2.34963 | − | 4.06969i | −0.119285 | − | 0.206607i | ||||
\(389\) | −9.77019 | + | 5.64082i | −0.495368 | + | 0.286001i | −0.726799 | − | 0.686850i | \(-0.758993\pi\) |
0.231430 | + | 0.972851i | \(0.425659\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 42.1107i | 2.12963i | ||||||||
\(392\) | 19.6840 | + | 3.09436i | 0.994191 | + | 0.156289i | ||||
\(393\) | 14.5225 | − | 33.0532i | 0.732561 | − | 1.66731i | ||||
\(394\) | −1.82150 | + | 3.15493i | −0.0917659 | + | 0.158943i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 5.04259 | + | 1.58394i | 0.253400 | + | 0.0795959i | ||||
\(397\) | −15.3087 | + | 26.5154i | −0.768319 | + | 1.33077i | 0.170154 | + | 0.985417i | \(0.445573\pi\) |
−0.938474 | + | 0.345351i | \(0.887760\pi\) | |||||||
\(398\) | − | 0.0709323i | − | 0.00355551i | ||||||
\(399\) | −0.892048 | + | 1.66464i | −0.0446582 | + | 0.0833361i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 20.4532 | + | 11.8087i | 1.02139 | + | 0.589697i | 0.914505 | − | 0.404574i | \(-0.132580\pi\) |
0.106881 | + | 0.994272i | \(0.465914\pi\) | |||||||
\(402\) | −1.16028 | − | 10.5418i | −0.0578693 | − | 0.525778i | ||||
\(403\) | 9.33731 | − | 5.39090i | 0.465125 | − | 0.268540i | ||||
\(404\) | 8.04922 | − | 13.9417i | 0.400464 | − | 0.693623i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 2.41281 | − | 3.51500i | 0.119746 | − | 0.174446i | ||||
\(407\) | 8.46491 | 0.419590 | ||||||||
\(408\) | 22.8820 | − | 16.7968i | 1.13283 | − | 0.831563i | ||||
\(409\) | 11.1411 | − | 6.43231i | 0.550891 | − | 0.318057i | −0.198590 | − | 0.980083i | \(-0.563636\pi\) |
0.749481 | + | 0.662025i | \(0.230303\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 9.71403 | + | 13.2333i | 0.479158 | + | 0.652749i | ||||
\(412\) | 20.6797 | 1.01882 | ||||||||
\(413\) | 2.78815 | − | 1.33186i | 0.137196 | − | 0.0655364i | ||||
\(414\) | −13.1324 | − | 14.3004i | −0.645420 | − | 0.702828i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −11.3583 | − | 19.6731i | −0.556885 | − | 0.964553i | ||||
\(417\) | −1.09043 | − | 9.90720i | −0.0533985 | − | 0.485158i | ||||
\(418\) | −0.263925 | + | 0.457132i | −0.0129090 | + | 0.0223590i | ||||
\(419\) | 3.78089 | 0.184708 | 0.0923542 | − | 0.995726i | \(-0.470561\pi\) | ||||
0.0923542 | + | 0.995726i | \(0.470561\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −2.43659 | −0.118752 | −0.0593759 | − | 0.998236i | \(-0.518911\pi\) | ||||
−0.0593759 | + | 0.998236i | \(0.518911\pi\) | |||||||
\(422\) | −7.77763 | + | 13.4712i | −0.378609 | + | 0.655770i | ||||
\(423\) | 31.1035 | + | 9.76999i | 1.51230 | + | 0.475033i | ||||
\(424\) | 1.98681 | + | 3.44126i | 0.0964881 | + | 0.167122i | ||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −18.6914 | − | 8.21238i | −0.905603 | − | 0.397891i | ||||
\(427\) | 6.20525 | − | 9.03986i | 0.300293 | − | 0.437470i | ||||
\(428\) | −15.7593 | −0.761753 | ||||||||
\(429\) | −8.17200 | + | 5.99874i | −0.394548 | + | 0.289622i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −26.4558 | + | 15.2743i | −1.27433 | + | 0.735737i | −0.975800 | − | 0.218663i | \(-0.929830\pi\) |
−0.298533 | + | 0.954399i | \(0.596497\pi\) | |||||||
\(432\) | −0.0848655 | + | 0.430288i | −0.00408309 | + | 0.0207023i | ||||
\(433\) | −37.7749 | −1.81534 | −0.907672 | − | 0.419680i | \(-0.862142\pi\) | ||||
−0.907672 | + | 0.419680i | \(0.862142\pi\) | |||||||
\(434\) | 6.22353 | + | 0.486191i | 0.298739 | + | 0.0233379i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −4.42332 | + | 7.66142i | −0.211839 | + | 0.366916i | ||||
\(437\) | −2.61057 | + | 1.50722i | −0.124881 | + | 0.0720999i | ||||
\(438\) | −4.79052 | + | 0.527265i | −0.228900 | + | 0.0251937i | ||||
\(439\) | 3.55267 | + | 2.05113i | 0.169560 | + | 0.0978953i | 0.582378 | − | 0.812918i | \(-0.302122\pi\) |
−0.412819 | + | 0.910813i | \(0.635456\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −20.9579 | + | 1.32883i | −0.997996 | + | 0.0632775i | ||||
\(442\) | 20.5966i | 0.979679i | ||||||||
\(443\) | 13.1240 | − | 22.7315i | 0.623541 | − | 1.08001i | −0.365280 | − | 0.930898i | \(-0.619027\pi\) |
0.988821 | − | 0.149107i | \(-0.0476400\pi\) | |||||||
\(444\) | −1.34869 | − | 12.2537i | −0.0640059 | − | 0.581533i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 12.1646 | − | 21.0696i | 0.576009 | − | 0.997677i | ||||
\(447\) | −10.2005 | − | 4.48174i | −0.482465 | − | 0.211979i | ||||
\(448\) | 1.05916 | − | 13.5578i | 0.0500405 | − | 0.640548i | ||||
\(449\) | 14.6382i | 0.690821i | 0.938452 | + | 0.345411i | \(0.112260\pi\) | ||||
−0.938452 | + | 0.345411i | \(0.887740\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 8.10195 | − | 4.67766i | 0.381506 | − | 0.220263i | ||||
\(452\) | 2.91205 | + | 5.04381i | 0.136971 | + | 0.237241i | ||||
\(453\) | 4.22277 | + | 5.75262i | 0.198403 | + | 0.270282i | ||||
\(454\) | − | 10.9761i | − | 0.515134i | ||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 1.86027 | + | 0.817340i | 0.0871151 | + | 0.0382754i | ||||
\(457\) | −25.2776 | − | 14.5940i | −1.18244 | − | 0.682679i | −0.225858 | − | 0.974160i | \(-0.572519\pi\) |
−0.956577 | + | 0.291481i | \(0.905852\pi\) | |||||||
\(458\) | 20.8384 | − | 12.0310i | 0.973714 | − | 0.562174i | ||||
\(459\) | −19.6882 | + | 22.5236i | −0.918967 | + | 1.05131i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −15.8295 | −0.737255 | −0.368627 | − | 0.929577i | \(-0.620172\pi\) | ||||
−0.368627 | + | 0.929577i | \(0.620172\pi\) | |||||||
\(462\) | −5.86644 | + | 0.185793i | −0.272932 | + | 0.00864388i | ||||
\(463\) | − | 19.1466i | − | 0.889816i | −0.895576 | − | 0.444908i | \(-0.853236\pi\) | ||
0.895576 | − | 0.444908i | \(-0.146764\pi\) | |||||||
\(464\) | −0.133124 | − | 0.0768591i | −0.00618012 | − | 0.00356809i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −12.8010 | − | 22.1719i | −0.592994 | − | 1.02710i | ||||
\(467\) | −12.9081 | − | 7.45251i | −0.597317 | − | 0.344861i | 0.170669 | − | 0.985328i | \(-0.445407\pi\) |
−0.767985 | + | 0.640468i | \(0.778741\pi\) | |||||||
\(468\) | 9.98570 | + | 10.8739i | 0.461589 | + | 0.502645i | ||||
\(469\) | −7.89185 | − | 16.5211i | −0.364412 | − | 0.762872i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −1.27067 | − | 1.73102i | −0.0585494 | − | 0.0797610i | ||||
\(472\) | −1.66221 | − | 2.87903i | −0.0765092 | − | 0.132518i | ||||
\(473\) | 7.49710 | + | 12.9854i | 0.344717 | + | 0.597067i | ||||
\(474\) | 11.6481 | + | 15.8681i | 0.535016 | + | 0.728844i | ||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 10.4920 | − | 15.2848i | 0.480900 | − | 0.700579i | ||||
\(477\) | −2.83261 | − | 3.08456i | −0.129696 | − | 0.141232i | ||||
\(478\) | −14.7444 | − | 8.51269i | −0.674394 | − | 0.389362i | ||||
\(479\) | −10.9530 | − | 18.9712i | −0.500456 | − | 0.866815i | −1.00000 | 0.000526656i | \(-0.999832\pi\) | |
0.499544 | − | 0.866289i | \(-0.333501\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 20.4762 | + | 11.8220i | 0.933636 | + | 0.539035i | ||||
\(482\) | 5.01243i | 0.228310i | ||||||||
\(483\) | −29.5440 | − | 15.8321i | −1.34430 | − | 0.720385i | ||||
\(484\) | −10.8379 | −0.492632 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −0.338108 | − | 13.7887i | −0.0153369 | − | 0.625466i | ||||
\(487\) | 10.7731 | − | 6.21983i | 0.488174 | − | 0.281848i | −0.235642 | − | 0.971840i | \(-0.575719\pi\) |
0.723817 | + | 0.689992i | \(0.242386\pi\) | |||||||
\(488\) | −10.2163 | − | 5.89838i | −0.462470 | − | 0.267007i | ||||
\(489\) | 11.8027 | + | 5.18572i | 0.533737 | + | 0.234506i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 23.2765i | − | 1.05045i | −0.850962 | − | 0.525227i | \(-0.823980\pi\) | ||
0.850962 | − | 0.525227i | \(-0.176020\pi\) | |||||||
\(492\) | −8.06217 | − | 10.9830i | −0.363470 | − | 0.495150i | ||||
\(493\) | −5.24259 | − | 9.08043i | −0.236114 | − | 0.408962i | ||||
\(494\) | −1.27685 | + | 0.737187i | −0.0574480 | + | 0.0331676i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | − | 0.225074i | − | 0.0101061i | ||||||
\(497\) | −35.1389 | − | 2.74510i | −1.57620 | − | 0.123135i | ||||
\(498\) | −16.1368 | − | 7.08997i | −0.723108 | − | 0.317709i | ||||
\(499\) | −13.2171 | + | 22.8927i | −0.591680 | + | 1.02482i | 0.402327 | + | 0.915496i | \(0.368202\pi\) |
−0.994006 | + | 0.109323i | \(0.965132\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0.475101 | + | 4.31659i | 0.0212260 | + | 0.192851i | ||||
\(502\) | 2.90148 | − | 5.02551i | 0.129499 | − | 0.224300i | ||||
\(503\) | − | 17.4645i | − | 0.778702i | −0.921090 | − | 0.389351i | \(-0.872699\pi\) | ||
0.921090 | − | 0.389351i | \(-0.127301\pi\) | |||||||
\(504\) | 3.18148 | + | 22.3685i | 0.141714 | + | 0.996373i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −8.11319 | − | 4.68415i | −0.360675 | − | 0.208236i | ||||
\(507\) | −5.76395 | + | 0.634404i | −0.255986 | + | 0.0281749i | ||||
\(508\) | 9.65714 | − | 5.57555i | 0.428466 | − | 0.247375i | ||||
\(509\) | 1.20504 | − | 2.08719i | 0.0534124 | − | 0.0925129i | −0.838083 | − | 0.545543i | \(-0.816324\pi\) |
0.891495 | + | 0.453030i | \(0.149657\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −7.50768 | + | 3.58630i | −0.332120 | + | 0.158648i | ||||
\(512\) | −0.954733 | −0.0421937 | ||||||||
\(513\) | −2.10098 | − | 0.414376i | −0.0927607 | − | 0.0182951i | ||||
\(514\) | −6.69176 | + | 3.86349i | −0.295161 | + | 0.170411i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 17.6029 | − | 12.9216i | 0.774924 | − | 0.568841i | ||||
\(517\) | 15.7309 | 0.691846 | ||||||||
\(518\) | 5.90059 | + | 12.3525i | 0.259257 | + | 0.542738i | ||||
\(519\) | −27.0363 | − | 11.8788i | −1.18676 | − | 0.521424i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −15.7340 | − | 27.2520i | −0.689317 | − | 1.19393i | −0.972059 | − | 0.234736i | \(-0.924577\pi\) |
0.282742 | − | 0.959196i | \(-0.408756\pi\) | |||||||
\(522\) | 4.61210 | + | 1.44872i | 0.201866 | + | 0.0634086i | ||||
\(523\) | 8.54828 | − | 14.8061i | 0.373790 | − | 0.647424i | −0.616355 | − | 0.787469i | \(-0.711391\pi\) |
0.990145 | + | 0.140045i | \(0.0447246\pi\) | |||||||
\(524\) | −25.3695 | −1.10827 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 19.9451 | 0.869649 | ||||||||
\(527\) | 7.67617 | − | 13.2955i | 0.334379 | − | 0.579162i | ||||
\(528\) | 0.0231521 | + | 0.210351i | 0.00100756 | + | 0.00915434i | ||||
\(529\) | −15.2501 | − | 26.4140i | −0.663049 | − | 1.14843i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 2.36982 | + | 2.58060i | 0.102841 | + | 0.111989i | ||||
\(532\) | 1.32308 | + | 0.103361i | 0.0573629 | + | 0.00448127i | ||||
\(533\) | 26.1310 | 1.13186 | ||||||||
\(534\) | −7.07558 | − | 9.63896i | −0.306190 | − | 0.417119i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −17.0595 | + | 9.84932i | −0.736859 | + | 0.425426i | ||||
\(537\) | −16.4049 | + | 12.0422i | −0.707922 | + | 0.519658i | ||||
\(538\) | −12.5547 | −0.541272 | ||||||||
\(539\) | −9.45564 | + | 3.64220i | −0.407283 | + | 0.156881i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 10.8422 | − | 18.7792i | 0.466142 | − | 0.807382i | −0.533110 | − | 0.846046i | \(-0.678977\pi\) |
0.999252 | + | 0.0386641i | \(0.0123102\pi\) | |||||||
\(542\) | 9.75478 | − | 5.63192i | 0.419004 | − | 0.241912i | ||||
\(543\) | 0.457095 | + | 4.15299i | 0.0196158 | + | 0.178222i | ||||
\(544\) | −28.0128 | − | 16.1732i | −1.20104 | − | 0.693419i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −14.4501 | − | 7.74356i | −0.618409 | − | 0.331394i | ||||
\(547\) | 9.42694i | 0.403067i | 0.979482 | + | 0.201533i | \(0.0645925\pi\) | ||||
−0.979482 | + | 0.201533i | \(0.935408\pi\) | |||||||
\(548\) | 5.76774 | − | 9.99001i | 0.246386 | − | 0.426752i | ||||
\(549\) | 11.8614 | + | 3.72580i | 0.506231 | + | 0.159013i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0.375283 | − | 0.650009i | 0.0159876 | − | 0.0276913i | ||||
\(552\) | −14.5062 | + | 33.0161i | −0.617424 | + | 1.40526i | ||||
\(553\) | 28.0173 | + | 19.2320i | 1.19142 | + | 0.817826i | ||||
\(554\) | − | 25.4977i | − | 1.08329i | ||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −6.06551 | + | 3.50192i | −0.257235 | + | 0.148515i | ||||
\(557\) | 2.82874 | + | 4.89952i | 0.119858 | + | 0.207599i | 0.919711 | − | 0.392596i | \(-0.128423\pi\) |
−0.799854 | + | 0.600195i | \(0.795090\pi\) | |||||||
\(558\) | 1.53949 | + | 6.90888i | 0.0651718 | + | 0.292476i | ||||
\(559\) | 41.8814i | 1.77139i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −5.80641 | + | 13.2154i | −0.245147 | + | 0.557956i | ||||
\(562\) | −10.3063 | − | 5.95032i | −0.434743 | − | 0.250999i | ||||
\(563\) | 6.32441 | − | 3.65140i | 0.266542 | − | 0.153888i | −0.360773 | − | 0.932654i | \(-0.617487\pi\) |
0.627315 | + | 0.778765i | \(0.284154\pi\) | |||||||
\(564\) | −2.50636 | − | 22.7718i | −0.105537 | − | 0.958868i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 12.4552 | 0.523533 | ||||||||
\(567\) | −8.40005 | − | 22.2809i | −0.352769 | − | 0.935710i | ||||
\(568\) | 37.9207i | 1.59112i | ||||||||
\(569\) | −12.6704 | − | 7.31525i | −0.531170 | − | 0.306671i | 0.210323 | − | 0.977632i | \(-0.432549\pi\) |
−0.741493 | + | 0.670961i | \(0.765882\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 15.0693 | + | 26.1009i | 0.630632 | + | 1.09229i | 0.987423 | + | 0.158103i | \(0.0505377\pi\) |
−0.356790 | + | 0.934184i | \(0.616129\pi\) | |||||||
\(572\) | 6.16917 | + | 3.56177i | 0.257946 | + | 0.148925i | ||||
\(573\) | 21.8187 | + | 9.58638i | 0.911487 | + | 0.400477i | ||||
\(574\) | 12.4735 | + | 8.56223i | 0.520635 | + | 0.357380i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 15.0509 | − | 3.35375i | 0.627119 | − | 0.139739i | ||||
\(577\) | 22.6632 | + | 39.2538i | 0.943482 | + | 1.63416i | 0.758762 | + | 0.651367i | \(0.225804\pi\) |
0.184720 | + | 0.982791i | \(0.440862\pi\) | |||||||
\(578\) | 7.14299 | + | 12.3720i | 0.297109 | + | 0.514608i | ||||
\(579\) | −12.8646 | + | 9.44341i | −0.534635 | + | 0.392455i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −30.3364 | − | 2.36992i | −1.25856 | − | 0.0983208i | ||||
\(582\) | −2.38017 | + | 5.41727i | −0.0986611 | + | 0.224553i | ||||
\(583\) | −1.74999 | − | 1.01036i | −0.0724771 | − | 0.0418447i | ||||
\(584\) | 4.47583 | + | 7.75237i | 0.185211 | + | 0.320795i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −12.8073 | − | 7.39430i | −0.529065 | − | 0.305456i | ||||
\(587\) | 27.9328i | 1.15291i | 0.817129 | + | 0.576455i | \(0.195564\pi\) | ||||
−0.817129 | + | 0.576455i | \(0.804436\pi\) | |||||||
\(588\) | 6.77893 | + | 13.1075i | 0.279558 | + | 0.540545i | ||||
\(589\) | 1.09897 | 0.0452825 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −7.08853 | + | 0.780193i | −0.291583 | + | 0.0320928i | ||||
\(592\) | 0.427448 | − | 0.246787i | 0.0175680 | − | 0.0101429i | ||||
\(593\) | −25.5085 | − | 14.7273i | −1.04751 | − | 0.604779i | −0.125558 | − | 0.992086i | \(-0.540072\pi\) |
−0.921951 | + | 0.387307i | \(0.873405\pi\) | |||||||
\(594\) | −2.14947 | − | 6.29859i | −0.0881937 | − | 0.258434i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 7.82921i | 0.320697i | ||||||||
\(597\) | 0.111933 | − | 0.0821656i | 0.00458111 | − | 0.00336281i | ||||
\(598\) | −13.0836 | − | 22.6615i | −0.535029 | − | 0.926698i | ||||
\(599\) | −13.1940 | + | 7.61757i | −0.539093 | + | 0.311245i | −0.744711 | − | 0.667387i | \(-0.767413\pi\) |
0.205618 | + | 0.978632i | \(0.434079\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 18.6064i | 0.758970i | 0.925198 | + | 0.379485i | \(0.123899\pi\) | ||||
−0.925198 | + | 0.379485i | \(0.876101\pi\) | |||||||
\(602\) | −13.7231 | + | 19.9919i | −0.559310 | + | 0.814808i | ||||
\(603\) | 15.2912 | − | 14.0422i | 0.622707 | − | 0.571844i | ||||
\(604\) | 2.50729 | − | 4.34275i | 0.102020 | − | 0.176704i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −20.1487 | + | 2.21765i | −0.818486 | + | 0.0900859i | ||||
\(607\) | 9.55240 | − | 16.5452i | 0.387720 | − | 0.671550i | −0.604423 | − | 0.796664i | \(-0.706596\pi\) |
0.992142 | + | 0.125113i | \(0.0399295\pi\) | |||||||
\(608\) | − | 2.31547i | − | 0.0939046i | ||||||
\(609\) | 8.34167 | − | 0.264185i | 0.338022 | − | 0.0107053i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 38.0525 | + | 21.9696i | 1.53944 | + | 0.888795i | ||||
\(612\) | 20.0555 | + | 6.29969i | 0.810697 | + | 0.254650i | ||||
\(613\) | −10.7916 | + | 6.23054i | −0.435869 | + | 0.251649i | −0.701844 | − | 0.712331i | \(-0.747640\pi\) |
0.265975 | + | 0.963980i | \(0.414306\pi\) | |||||||
\(614\) | 4.30131 | − | 7.45009i | 0.173587 | − | 0.300661i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 4.69902 | + | 9.83710i | 0.189329 | + | 0.396348i | ||||
\(617\) | −19.4451 | −0.782829 | −0.391414 | − | 0.920214i | \(-0.628014\pi\) | ||||
−0.391414 | + | 0.920214i | \(0.628014\pi\) | |||||||
\(618\) | −15.4084 | − | 20.9906i | −0.619816 | − | 0.844367i | ||||
\(619\) | 9.61812 | − | 5.55302i | 0.386585 | − | 0.223195i | −0.294095 | − | 0.955776i | \(-0.595018\pi\) |
0.680679 | + | 0.732582i | \(0.261685\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 7.35435 | − | 37.2883i | 0.295120 | − | 1.49633i | ||||
\(622\) | −4.43684 | −0.177901 | ||||||||
\(623\) | −17.0189 | − | 11.6824i | −0.681850 | − | 0.468044i | ||||
\(624\) | −0.237769 | + | 0.541163i | −0.00951837 | + | 0.0216639i | ||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 7.84330 | + | 13.5850i | 0.313481 | + | 0.542966i | ||||
\(627\) | −1.02709 | + | 0.113045i | −0.0410179 | + | 0.00451460i | ||||
\(628\) | −0.754465 | + | 1.30677i | −0.0301064 | + | 0.0521459i | ||||
\(629\) | 33.6669 | 1.34239 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 9.89504 | 0.393915 | 0.196958 | − | 0.980412i | \(-0.436894\pi\) | ||||
0.196958 | + | 0.980412i | \(0.436894\pi\) | |||||||
\(632\) | 18.2809 | − | 31.6634i | 0.727174 | − | 1.25950i | ||||
\(633\) | −30.2673 | + | 3.33135i | −1.20302 | + | 0.132409i | ||||
\(634\) | −1.85905 | − | 3.21996i | −0.0738322 | − | 0.127881i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −1.18375 | + | 2.69423i | −0.0469389 | + | 0.106833i | ||||
\(637\) | −27.9594 | − | 4.39528i | −1.10779 | − | 0.174147i | ||||
\(638\) | 2.33262 | 0.0923493 | ||||||||
\(639\) | −8.69217 | − | 39.0085i | −0.343857 | − | 1.54315i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −2.40816 | + | 1.39035i | −0.0951166 | + | 0.0549156i | −0.546804 | − | 0.837261i | \(-0.684156\pi\) |
0.451687 | + | 0.892176i | \(0.350822\pi\) | |||||||
\(642\) | 11.7422 | + | 15.9962i | 0.463427 | + | 0.631320i | ||||
\(643\) | 37.8005 | 1.49071 | 0.745354 | − | 0.666669i | \(-0.232281\pi\) | ||||
0.745354 | + | 0.666669i | \(0.232281\pi\) | |||||||
\(644\) | −1.83445 | + | 23.4821i | −0.0722876 | + | 0.925325i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −1.04969 | + | 1.81812i | −0.0412995 | + | 0.0715329i | ||||
\(647\) | 17.6163 | − | 10.1708i | 0.692569 | − | 0.399855i | −0.112005 | − | 0.993708i | \(-0.535727\pi\) |
0.804574 | + | 0.593853i | \(0.202394\pi\) | |||||||
\(648\) | −23.1951 | + | 10.8771i | −0.911188 | + | 0.427292i | ||||
\(649\) | 1.46408 | + | 0.845285i | 0.0574700 | + | 0.0331803i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 6.44191 | + | 10.3841i | 0.252478 | + | 0.406984i | ||||
\(652\) | − | 9.05901i | − | 0.354778i | ||||||
\(653\) | 12.4472 | − | 21.5592i | 0.487097 | − | 0.843677i | −0.512793 | − | 0.858512i | \(-0.671389\pi\) |
0.999890 | + | 0.0148355i | \(0.00472247\pi\) | |||||||
\(654\) | 11.0724 | − | 1.21868i | 0.432966 | − | 0.0476540i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0.272747 | − | 0.472411i | 0.0106490 | − | 0.0184446i | ||||
\(657\) | −6.38122 | − | 6.94880i | −0.248955 | − | 0.271099i | ||||
\(658\) | 10.9655 | + | 22.9556i | 0.427480 | + | 0.894901i | ||||
\(659\) | 29.3981i | 1.14519i | 0.819840 | + | 0.572593i | \(0.194062\pi\) | ||||
−0.819840 | + | 0.572593i | \(0.805938\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 17.1948 | − | 9.92744i | 0.668801 | − | 0.386133i | −0.126821 | − | 0.991926i | \(-0.540477\pi\) |
0.795622 | + | 0.605793i | \(0.207144\pi\) | |||||||
\(662\) | 0.601794 | + | 1.04234i | 0.0233894 | + | 0.0405116i | ||||
\(663\) | −32.5019 | + | 23.8584i | −1.26227 | + | 0.926583i | ||||
\(664\) | 32.7380i | 1.27048i | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −11.4330 | + | 10.4991i | −0.443019 | + | 0.406833i | ||||
\(667\) | 11.5364 | + | 6.66053i | 0.446690 | + | 0.257897i | ||||
\(668\) | 2.64275 | − | 1.52579i | 0.102251 | − | 0.0590347i | ||||
\(669\) | 47.3395 | − | 5.21038i | 1.83025 | − | 0.201445i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 5.99903 | 0.231590 | ||||||||
\(672\) | 21.8786 | − | 13.5727i | 0.843984 | − | 0.523577i | ||||
\(673\) | 17.4983i | 0.674509i | 0.941414 | + | 0.337255i | \(0.109498\pi\) | ||||
−0.941414 | + | 0.337255i | \(0.890502\pi\) | |||||||
\(674\) | 20.1237 | + | 11.6184i | 0.775136 | + | 0.447525i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 2.03740 | + | 3.52888i | 0.0783614 | + | 0.135726i | ||||
\(677\) | −3.78846 | − | 2.18727i | −0.145602 | − | 0.0840635i | 0.425429 | − | 0.904992i | \(-0.360123\pi\) |
−0.571031 | + | 0.820928i | \(0.693457\pi\) | |||||||
\(678\) | 2.94989 | − | 6.71396i | 0.113290 | − | 0.257848i | ||||
\(679\) | −0.795603 | + | 10.1842i | −0.0305324 | + | 0.390834i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 17.3206 | − | 12.7143i | 0.663725 | − | 0.487215i | ||||
\(682\) | 1.70771 | + | 2.95783i | 0.0653915 | + | 0.113261i | ||||
\(683\) | 14.7046 | + | 25.4692i | 0.562657 | + | 0.974550i | 0.997263 | + | 0.0739300i | \(0.0235541\pi\) |
−0.434606 | + | 0.900620i | \(0.643113\pi\) | |||||||
\(684\) | 0.327285 | + | 1.46878i | 0.0125141 | + | 0.0561603i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −11.9061 | − | 11.2594i | −0.454578 | − | 0.429886i | ||||
\(687\) | 43.1238 | + | 18.9471i | 1.64527 | + | 0.722878i | ||||
\(688\) | 0.757154 | + | 0.437143i | 0.0288662 | + | 0.0166659i | ||||
\(689\) | −2.82210 | − | 4.88802i | −0.107513 | − | 0.186219i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −43.6753 | − | 25.2160i | −1.66149 | − | 0.959260i | −0.972006 | − | 0.234956i | \(-0.924505\pi\) |
−0.689481 | − | 0.724304i | \(-0.742161\pi\) | |||||||
\(692\) | 20.7513i | 0.788848i | ||||||||
\(693\) | −7.08868 | − | 9.04218i | −0.269277 | − | 0.343484i | ||||
\(694\) | −5.55506 | −0.210867 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −0.982355 | − | 8.92530i | −0.0372361 | − | 0.338312i | ||||
\(697\) | 32.2233 | − | 18.6041i | 1.22055 | − | 0.704682i | ||||
\(698\) | 3.82693 | + | 2.20948i | 0.144852 | + | 0.0836301i | ||||
\(699\) | 20.1597 | − | 45.8835i | 0.762509 | − | 1.73547i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 19.8266i | 0.748842i | 0.927259 | + | 0.374421i | \(0.122159\pi\) | ||||
−0.927259 | + | 0.374421i | \(0.877841\pi\) | |||||||
\(702\) | 3.59705 | − | 18.2379i | 0.135762 | − | 0.688346i | ||||
\(703\) | 1.20500 | + | 2.08712i | 0.0454473 | + | 0.0787171i | ||||
\(704\) | 6.44358 | − | 3.72020i | 0.242852 | − | 0.140210i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | − | 0.696982i | − | 0.0262313i | ||||||
\(707\) | −31.5769 | + | 15.0838i | −1.18757 | + | 0.567284i | ||||
\(708\) | 0.990353 | − | 2.25405i | 0.0372197 | − | 0.0847123i | ||||
\(709\) | −13.2605 | + | 22.9678i | −0.498008 | + | 0.862575i | −0.999997 | − | 0.00229888i | \(-0.999268\pi\) |
0.501990 | + | 0.864874i | \(0.332602\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −11.5474 | + | 36.7620i | −0.433062 | + | 1.37868i | ||||
\(712\) | −11.1046 | + | 19.2338i | −0.416163 | + | 0.720816i | ||||
\(713\) | 19.5046i | 0.730455i | ||||||||
\(714\) | −23.3322 | + | 0.738942i | −0.873186 | + | 0.0276542i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 12.3843 | + | 7.15008i | 0.462823 | + | 0.267211i | ||||
\(717\) | −3.64619 | − | 33.1279i | −0.136170 | − | 1.23718i | ||||
\(718\) | 19.4204 | − | 11.2124i | 0.724763 | − | 0.418442i | ||||
\(719\) | −1.12519 | + | 1.94889i | −0.0419627 | + | 0.0726815i | −0.886244 | − | 0.463219i | \(-0.846694\pi\) |
0.844281 | + | 0.535900i | \(0.180028\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −37.0619 | − | 25.4405i | −1.38026 | − | 0.947453i | ||||
\(722\) | 16.6611 | 0.620061 | ||||||||
\(723\) | −7.90974 | + | 5.80623i | −0.294167 | + | 0.215936i | ||||
\(724\) | 2.54259 | − | 1.46797i | 0.0944947 | − | 0.0545566i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 8.07530 | + | 11.0009i | 0.299702 | + | 0.408280i | ||||
\(727\) | −6.85964 | −0.254410 | −0.127205 | − | 0.991876i | \(-0.540601\pi\) | ||||
−0.127205 | + | 0.991876i | \(0.540601\pi\) | |||||||
\(728\) | −2.37162 | + | 30.3581i | −0.0878980 | + | 1.12515i | ||||
\(729\) | 21.3672 | − | 16.5059i | 0.791377 | − | 0.611328i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 29.8177 | + | 51.6458i | 1.10285 | + | 1.91019i | ||||
\(732\) | −0.955807 | − | 8.68409i | −0.0353276 | − | 0.320973i | ||||
\(733\) | 2.75930 | − | 4.77925i | 0.101917 | − | 0.176526i | −0.810557 | − | 0.585659i | \(-0.800836\pi\) |
0.912474 | + | 0.409134i | \(0.134169\pi\) | |||||||
\(734\) | −1.61560 | −0.0596327 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 41.0950 | 1.51478 | ||||||||
\(737\) | 5.00869 | − | 8.67531i | 0.184498 | − | 0.319559i | ||||
\(738\) | −5.14100 | + | 16.3668i | −0.189243 | + | 0.602469i | ||||
\(739\) | 5.01222 | + | 8.68142i | 0.184378 | + | 0.319351i | 0.943367 | − | 0.331752i | \(-0.107640\pi\) |
−0.758989 | + | 0.651103i | \(0.774306\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −2.64236 | − | 1.16096i | −0.0970694 | − | 0.0426490i | ||||
\(742\) | 0.254518 | − | 3.25798i | 0.00934363 | − | 0.119604i | ||||
\(743\) | −26.2588 | −0.963342 | −0.481671 | − | 0.876352i | \(-0.659970\pi\) | ||||
−0.481671 | + | 0.876352i | \(0.659970\pi\) | |||||||
\(744\) | 10.5984 | − | 7.77985i | 0.388555 | − | 0.285223i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −1.60930 | + | 0.929132i | −0.0589208 | + | 0.0340180i | ||||
\(747\) | −7.50419 | − | 33.6771i | −0.274564 | − | 1.23218i | ||||
\(748\) | 10.1433 | 0.370876 | ||||||||
\(749\) | 28.2436 | + | 19.3873i | 1.03200 | + | 0.708396i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −5.68833 | + | 9.85247i | −0.207570 | + | 0.359522i | −0.950949 | − | 0.309349i | \(-0.899889\pi\) |
0.743378 | + | 0.668871i | \(0.233222\pi\) | |||||||
\(752\) | 0.794357 | − | 0.458622i | 0.0289672 | − | 0.0167242i | ||||
\(753\) | 11.2914 | − | 1.24277i | 0.411480 | − | 0.0452892i | ||||
\(754\) | 5.64251 | + | 3.25770i | 0.205488 | + | 0.118639i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −11.9599 | + | 11.7021i | −0.434977 | + | 0.425602i | ||||
\(757\) | − | 20.1866i | − | 0.733693i | −0.930281 | − | 0.366847i | \(-0.880437\pi\) | ||
0.930281 | − | 0.366847i | \(-0.119563\pi\) | |||||||
\(758\) | −8.49884 | + | 14.7204i | −0.308692 | + | 0.534670i | ||||
\(759\) | −2.00634 | − | 18.2288i | −0.0728254 | − | 0.661663i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 2.04697 | − | 3.54546i | 0.0742026 | − | 0.128523i | −0.826537 | − | 0.562883i | \(-0.809692\pi\) |
0.900739 | + | 0.434360i | \(0.143026\pi\) | |||||||
\(762\) | −12.8549 | − | 5.64801i | −0.465684 | − | 0.204606i | ||||
\(763\) | 17.3526 | − | 8.28907i | 0.628207 | − | 0.300084i | ||||
\(764\) | − | 16.7466i | − | 0.605871i | ||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −2.42189 | + | 1.39828i | −0.0875066 | + | 0.0505219i | ||||
\(767\) | 2.36102 | + | 4.08941i | 0.0852516 | + | 0.147660i | ||||
\(768\) | −16.6022 | − | 22.6169i | −0.599080 | − | 0.816118i | ||||
\(769\) | − | 8.66796i | − | 0.312575i | −0.987712 | − | 0.156287i | \(-0.950047\pi\) | ||
0.987712 | − | 0.156287i | \(-0.0499526\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −13.8482 | − | 6.08443i | −0.498730 | − | 0.219125i | ||||
\(772\) | 9.71171 | + | 5.60706i | 0.349532 | + | 0.201803i | ||||
\(773\) | −38.3891 | + | 22.1640i | −1.38076 | + | 0.797183i | −0.992250 | − | 0.124261i | \(-0.960344\pi\) |
−0.388512 | + | 0.921444i | \(0.627011\pi\) | |||||||
\(774\) | −26.2317 | − | 8.23971i | −0.942880 | − | 0.296170i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 10.9904 | 0.394533 | ||||||||
\(777\) | −12.6575 | + | 23.6200i | −0.454086 | + | 0.847363i | ||||
\(778\) | − | 9.98209i | − | 0.357875i | ||||||
\(779\) | 2.30666 | + | 1.33175i | 0.0826446 | + | 0.0477149i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −9.64194 | − | 16.7003i | −0.345016 | − | 0.597585i | ||||
\(782\) | −32.2680 | − | 18.6299i | −1.15390 | − | 0.666206i | ||||
\(783\) | 3.05639 | + | 8.95615i | 0.109226 | + | 0.320067i | ||||
\(784\) | −0.371291 | + | 0.459590i | −0.0132604 | + | 0.0164139i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 18.9028 | + | 25.7510i | 0.674239 | + | 0.918506i | ||||
\(787\) | 12.5896 | + | 21.8059i | 0.448772 | + | 0.777296i | 0.998306 | − | 0.0581753i | \(-0.0185282\pi\) |
−0.549535 | + | 0.835471i | \(0.685195\pi\) | |||||||
\(788\) | 2.50560 | + | 4.33982i | 0.0892583 | + | 0.154600i | ||||
\(789\) | 23.1038 | + | 31.4739i | 0.822516 | + | 1.12050i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0.986040 | − | 12.6219i | 0.0350596 | − | 0.448783i | ||||
\(792\) | −9.10482 | + | 8.36114i | −0.323526 | + | 0.297100i | ||||
\(793\) | 14.5114 | + | 8.37815i | 0.515314 | + | 0.297517i | ||||
\(794\) | −13.5452 | − | 23.4610i | −0.480702 | − | 0.832600i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −0.0845000 | − | 0.0487861i | −0.00299502 | − | 0.00172918i | ||||
\(797\) | − | 48.5237i | − | 1.71880i | −0.511305 | − | 0.859400i | \(-0.670838\pi\) | ||
0.511305 | − | 0.859400i | \(-0.329162\pi\) | |||||||
\(798\) | −0.880910 | − | 1.41999i | −0.0311839 | − | 0.0502670i | ||||
\(799\) | 62.5656 | 2.21341 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 7.01441 | − | 22.3309i | 0.247842 | − | 0.789024i | ||||
\(802\) | −18.0972 | + | 10.4484i | −0.639034 | + | 0.368947i | ||||
\(803\) | −3.94232 | − | 2.27610i | −0.139122 | − | 0.0803219i | ||||
\(804\) | −13.3562 | − | 5.86829i | −0.471039 | − | 0.206958i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 9.53983i | 0.336026i | ||||||||
\(807\) | −14.5430 | − | 19.8117i | −0.511936 | − | 0.697403i | ||||
\(808\) | 18.8251 | + | 32.6061i | 0.662266 | + | 1.14708i | ||||
\(809\) | −0.751275 | + | 0.433749i | −0.0264134 | + | 0.0152498i | −0.513149 | − | 0.858300i | \(-0.671521\pi\) |
0.486735 | + | 0.873550i | \(0.338188\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 19.2304i | − | 0.675271i | −0.941277 | − | 0.337636i | \(-0.890373\pi\) | ||
0.941277 | − | 0.337636i | \(-0.109627\pi\) | |||||||
\(812\) | −2.52785 | − | 5.29188i | −0.0887100 | − | 0.185709i | ||||
\(813\) | 20.1869 | + | 8.86946i | 0.707986 | + | 0.311065i | ||||
\(814\) | −3.74491 | + | 6.48637i | −0.131259 | + | 0.227347i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0.0920811 | + | 0.836613i | 0.00322348 | + | 0.0292873i | ||||
\(817\) | −2.13446 | + | 3.69699i | −0.0746751 | + | 0.129341i | ||||
\(818\) | 11.3827i | 0.397987i | ||||||||
\(819\) | −4.51903 | − | 31.7726i | −0.157908 | − | 1.11022i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 32.0917 | + | 18.5281i | 1.12001 | + | 0.646636i | 0.941403 | − | 0.337285i | \(-0.109509\pi\) |
0.178604 | + | 0.983921i | \(0.442842\pi\) | |||||||
\(822\) | −14.4377 | + | 1.58908i | −0.503574 | + | 0.0554254i | ||||
\(823\) | 21.2677 | − | 12.2789i | 0.741345 | − | 0.428016i | −0.0812133 | − | 0.996697i | \(-0.525879\pi\) |
0.822558 | + | 0.568681i | \(0.192546\pi\) | |||||||
\(824\) | −24.1824 | + | 41.8851i | −0.842432 | + | 1.45914i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −0.212934 | + | 2.72569i | −0.00740894 | + | 0.0948388i | ||||
\(827\) | 28.2836 | 0.983518 | 0.491759 | − | 0.870731i | \(-0.336354\pi\) | ||||
0.491759 | + | 0.870731i | \(0.336354\pi\) | |||||||
\(828\) | −26.0680 | + | 5.80867i | −0.905926 | + | 0.201865i | ||||
\(829\) | −41.6000 | + | 24.0178i | −1.44483 | + | 0.834171i | −0.998166 | − | 0.0605325i | \(-0.980720\pi\) |
−0.446660 | + | 0.894704i | \(0.647387\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 40.2359 | − | 29.5356i | 1.39577 | − | 1.02458i | ||||
\(832\) | 20.7823 | 0.720497 | ||||||||
\(833\) | −37.6073 | + | 14.4859i | −1.30301 | + | 0.501906i | ||||
\(834\) | 8.07397 | + | 3.54743i | 0.279579 | + | 0.122837i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0.363047 | + | 0.628816i | 0.0125562 | + | 0.0217480i | ||||
\(837\) | −9.11910 | + | 10.4324i | −0.315202 | + | 0.360596i | ||||
\(838\) | −1.67268 | + | 2.89717i | −0.0577818 | + | 0.100081i | ||||
\(839\) | 26.6446 | 0.919874 | 0.459937 | − | 0.887952i | \(-0.347872\pi\) | ||||
0.459937 | + | 0.887952i | \(0.347872\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 25.6832 | 0.885627 | ||||||||
\(842\) | 1.07796 | − | 1.86707i | 0.0371488 | − | 0.0643436i | ||||
\(843\) | −2.54867 | − | 23.1562i | −0.0877807 | − | 0.797541i | ||||
\(844\) | 10.6987 | + | 18.5306i | 0.368263 | + | 0.637850i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −21.2467 | + | 19.5113i | −0.730478 | + | 0.670812i | ||||
\(847\) | 19.4236 | + | 13.3330i | 0.667402 | + | 0.458126i | ||||
\(848\) | −0.117824 | −0.00404611 | ||||||||
\(849\) | 14.4277 | + | 19.6547i | 0.495158 | + | 0.674547i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −37.0422 | + | 21.3863i | −1.26979 | + | 0.733114i | ||||
\(852\) | −22.6389 | + | 16.6183i | −0.775596 | + | 0.569334i | ||||
\(853\) | −35.4466 | −1.21367 | −0.606834 | − | 0.794829i | \(-0.707561\pi\) | ||||
−0.606834 | + | 0.794829i | \(0.707561\pi\) | |||||||
\(854\) | 4.18171 | + | 8.75415i | 0.143095 | + | 0.299561i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 18.4285 | − | 31.9191i | 0.629874 | − | 1.09097i | ||||
\(857\) | −9.87394 | + | 5.70072i | −0.337287 | + | 0.194733i | −0.659072 | − | 0.752080i | \(-0.729051\pi\) |
0.321785 | + | 0.946813i | \(0.395717\pi\) | |||||||
\(858\) | −0.981310 | − | 8.91580i | −0.0335014 | − | 0.304380i | ||||
\(859\) | 18.3838 | + | 10.6139i | 0.627248 | + | 0.362142i | 0.779686 | − | 0.626171i | \(-0.215379\pi\) |
−0.152438 | + | 0.988313i | \(0.548712\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0.937501 | + | 29.6017i | 0.0319500 | + | 1.00882i | ||||
\(862\) | − | 27.0296i | − | 0.920633i | ||||||
\(863\) | 0.702733 | − | 1.21717i | 0.0239213 | − | 0.0414329i | −0.853817 | − | 0.520573i | \(-0.825718\pi\) |
0.877738 | + | 0.479140i | \(0.159052\pi\) | |||||||
\(864\) | 21.9803 | + | 19.2133i | 0.747785 | + | 0.653651i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 16.7118 | − | 28.9456i | 0.567889 | − | 0.983612i | ||||
\(867\) | −11.2492 | + | 25.6031i | −0.382042 | + | 0.869528i | ||||
\(868\) | 4.85964 | − | 7.07956i | 0.164947 | − | 0.240296i | ||||
\(869\) | 18.5928i | 0.630718i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 24.2316 | − | 13.9901i | 0.821057 | − | 0.474037i | ||||
\(872\) | −10.3451 | − | 17.9182i | −0.350328 | − | 0.606786i | ||||
\(873\) | −11.3057 | + | 2.51922i | −0.382640 | + | 0.0852628i | ||||
\(874\) | − | 2.66719i | − | 0.0902192i | ||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −2.66673 | + | 6.06949i | −0.0901004 | + | 0.205069i | ||||
\(877\) | 1.82900 | + | 1.05597i | 0.0617610 | + | 0.0356577i | 0.530563 | − | 0.847646i | \(-0.321981\pi\) |
−0.468802 | + | 0.883304i | \(0.655314\pi\) | |||||||
\(878\) | −3.14343 | + | 1.81486i | −0.106086 | + | 0.0612486i | ||||
\(879\) | −3.16716 | − | 28.7755i | −0.106826 | − | 0.970575i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −35.9949 | −1.21270 | −0.606349 | − | 0.795199i | \(-0.707366\pi\) | ||||
−0.606349 | + | 0.795199i | \(0.707366\pi\) | |||||||
\(882\) | 8.25363 | − | 16.6472i | 0.277914 | − | 0.560541i | ||||
\(883\) | 17.2298i | 0.579828i | 0.957053 | + | 0.289914i | \(0.0936267\pi\) | ||||
−0.957053 | + | 0.289914i | \(0.906373\pi\) | |||||||
\(884\) | 24.5362 | + | 14.1660i | 0.825242 | + | 0.476454i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 11.6122 | + | 20.1130i | 0.390121 | + | 0.675709i | ||||
\(887\) | −5.40675 | − | 3.12159i | −0.181541 | − | 0.104813i | 0.406476 | − | 0.913662i | \(-0.366758\pi\) |
−0.588016 | + | 0.808849i | \(0.700091\pi\) | |||||||
\(888\) | 26.3959 | + | 11.5975i | 0.885789 | + | 0.389186i | ||||
\(889\) | −24.1665 | − | 1.88792i | −0.810520 | − | 0.0633189i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 7.44947 | − | 10.6880i | 0.249567 | − | 0.358061i | ||||
\(892\) | −16.7332 | − | 28.9827i | −0.560269 | − | 0.970414i | ||||
\(893\) | 2.23933 | + | 3.87864i | 0.0749364 | + | 0.129794i | ||||
\(894\) | 7.94693 | − | 5.83353i | 0.265785 | − | 0.195102i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −14.5904 | − | 10.0153i | −0.487430 | − | 0.334587i | ||||
\(897\) | 20.6048 | − | 46.8966i | 0.687974 | − | 1.56583i | ||||
\(898\) | −11.2168 | − | 6.47602i | −0.374309 | − | 0.216108i | ||||
\(899\) | −2.42824 | − | 4.20583i | −0.0809863 | − | 0.140272i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −6.96011 | − | 4.01842i | −0.231875 | − | 0.133873i | ||||
\(902\) | 8.27767i | 0.275616i | ||||||||
\(903\) | −47.4440 | + | 1.50257i | −1.57884 | + | 0.0500026i | ||||
\(904\) | −13.6211 | −0.453032 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −6.27621 | + | 0.690786i | −0.208513 | + | 0.0229498i | ||||
\(907\) | 34.2738 | − | 19.7880i | 1.13804 | − | 0.657049i | 0.192097 | − | 0.981376i | \(-0.438471\pi\) |
0.945945 | + | 0.324327i | \(0.105138\pi\) | |||||||
\(908\) | −13.0756 | − | 7.54918i | −0.433928 | − | 0.250528i | ||||
\(909\) | −26.8391 | − | 29.2263i | −0.890197 | − | 0.969376i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 24.4007i | − | 0.808431i | −0.914664 | − | 0.404215i | \(-0.867545\pi\) | ||
0.914664 | − | 0.404215i | \(-0.132455\pi\) | |||||||
\(912\) | −0.0485685 | + | 0.0356523i | −0.00160827 | + | 0.00118056i | ||||
\(913\) | −8.32415 | − | 14.4178i | −0.275489 | − | 0.477161i | ||||
\(914\) | 22.3658 | − | 12.9129i | 0.739795 | − | 0.427121i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | − | 33.0990i | − | 1.09362i | ||||||
\(917\) | 45.4669 | + | 31.2100i | 1.50145 | + | 1.03064i | ||||
\(918\) | −8.54892 | − | 25.0509i | −0.282156 | − | 0.826804i | ||||
\(919\) | −10.5155 | + | 18.2133i | −0.346873 | + | 0.600802i | −0.985692 | − | 0.168555i | \(-0.946090\pi\) |
0.638819 | + | 0.769357i | \(0.279423\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 16.7389 | − | 1.84236i | 0.551566 | − | 0.0607077i | ||||
\(922\) | 7.00305 | − | 12.1296i | 0.230633 | − | 0.399468i | ||||
\(923\) | − | 53.8632i | − | 1.77293i | ||||||
\(924\) | −3.81352 | + | 7.11635i | −0.125455 | + | 0.234111i | ||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 14.6714 | + | 8.47052i | 0.482131 | + | 0.278358i | ||||
\(927\) | 15.2752 | − | 48.6297i | 0.501702 | − | 1.59721i | ||||
\(928\) | −8.86140 | + | 5.11613i | −0.290890 | + | 0.167945i | ||||
\(929\) | 6.50741 | − | 11.2712i | 0.213501 | − | 0.369795i | −0.739307 | − | 0.673369i | \(-0.764847\pi\) |
0.952808 | + | 0.303574i | \(0.0981799\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −2.24405 | − | 1.81292i | −0.0735459 | − | 0.0594160i | ||||
\(932\) | −35.2172 | −1.15358 | ||||||||
\(933\) | −5.13949 | − | 7.00144i | −0.168259 | − | 0.229217i | ||||
\(934\) | 11.4212 | − | 6.59404i | 0.373713 | − | 0.215764i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −33.7012 | + | 7.50956i | −1.10156 | + | 0.245458i | ||||
\(937\) | −29.9338 | −0.977896 | −0.488948 | − | 0.872313i | \(-0.662619\pi\) | ||||
−0.488948 | + | 0.872313i | \(0.662619\pi\) | |||||||
\(938\) | 16.1509 | + | 1.26173i | 0.527346 | + | 0.0411970i | ||||
\(939\) | −12.3521 | + | 28.1133i | −0.403094 | + | 0.917444i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 3.58035 | + | 6.20135i | 0.116716 | + | 0.202158i | 0.918464 | − | 0.395504i | \(-0.129430\pi\) |
−0.801748 | + | 0.597662i | \(0.796097\pi\) | |||||||
\(942\) | 1.88857 | − | 0.207864i | 0.0615329 | − | 0.00677257i | ||||
\(943\) | −23.6360 | + | 40.9387i | −0.769693 | + | 1.33315i | ||||
\(944\) | 0.0985743 | 0.00320832 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −13.2670 | −0.431347 | ||||||||
\(947\) | −11.5521 | + | 20.0088i | −0.375393 | + | 0.650200i | −0.990386 | − | 0.138333i | \(-0.955826\pi\) |
0.614993 | + | 0.788533i | \(0.289159\pi\) | |||||||
\(948\) | 26.9146 | − | 2.96234i | 0.874147 | − | 0.0962122i | ||||
\(949\) | −6.35754 | − | 11.0116i | −0.206374 | − | 0.357451i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 2.92773 | − | 6.66352i | 0.0949380 | − | 0.216079i | ||||
\(952\) | 18.6891 | + | 39.1244i | 0.605717 | + | 1.26803i | ||||
\(953\) | 42.4806 | 1.37608 | 0.688040 | − | 0.725672i | \(-0.258471\pi\) | ||||
0.688040 | + | 0.725672i | \(0.258471\pi\) | |||||||
\(954\) | 3.61675 | − | 0.805912i | 0.117097 | − | 0.0260924i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −20.2820 | + | 11.7098i | −0.655965 | + | 0.378722i | ||||
\(957\) | 2.70203 | + | 3.68093i | 0.0873442 | + | 0.118988i | ||||
\(958\) | 19.3826 | 0.626225 | ||||||||
\(959\) | −22.6267 | + | 10.8084i | −0.730655 | + | 0.349022i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −11.9446 | + | 20.6886i | −0.385309 | + | 0.667375i | ||||
\(962\) | −18.1175 | + | 10.4602i | −0.584133 | + | 0.337249i | ||||
\(963\) | −11.6407 | + | 37.0590i | −0.375115 | + | 1.19421i | ||||
\(964\) | 5.97119 | + | 3.44747i | 0.192319 | + | 0.111036i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 25.2020 | − | 15.6344i | 0.810861 | − | 0.503029i | ||||
\(967\) | 2.04795i | 0.0658575i | 0.999458 | + | 0.0329288i | \(0.0104834\pi\) | ||||
−0.999458 | + | 0.0329288i | \(0.989517\pi\) | |||||||
\(968\) | 12.6736 | − | 21.9513i | 0.407345 | − | 0.705542i | ||||
\(969\) | −4.08496 | + | 0.449608i | −0.131228 | + | 0.0144435i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 29.0027 | − | 50.2341i | 0.930740 | − | 1.61209i | 0.148679 | − | 0.988885i | \(-0.452498\pi\) |
0.782060 | − | 0.623203i | \(-0.214169\pi\) | |||||||
\(972\) | −16.6587 | − | 9.08084i | −0.534326 | − | 0.291268i | ||||
\(973\) | 15.1786 | + | 1.18578i | 0.486605 | + | 0.0380142i | ||||
\(974\) | 11.0067i | 0.352678i | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0.302930 | − | 0.174897i | 0.00969655 | − | 0.00559830i | ||||
\(977\) | 24.8661 | + | 43.0694i | 0.795538 | + | 1.37791i | 0.922497 | + | 0.386004i | \(0.126145\pi\) |
−0.126960 | + | 0.991908i | \(0.540522\pi\) | |||||||
\(978\) | −9.19521 | + | 6.74984i | −0.294030 | + | 0.215836i | ||||
\(979\) | − | 11.2941i | − | 0.360961i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 14.7490 | + | 16.0609i | 0.470900 | + | 0.512785i | ||||
\(982\) | 17.8360 | + | 10.2976i | 0.569170 | + | 0.328610i | ||||
\(983\) | −12.0399 | + | 6.95123i | −0.384013 | + | 0.221710i | −0.679563 | − | 0.733617i | \(-0.737830\pi\) |
0.295550 | + | 0.955327i | \(0.404497\pi\) | |||||||
\(984\) | 31.6728 | − | 3.48604i | 1.00969 | − | 0.111131i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 9.27737 | 0.295452 | ||||||||
\(987\) | −23.5224 | + | 43.8948i | −0.748726 | + | 1.39719i | ||||
\(988\) | 2.02810i | 0.0645226i | ||||||||
\(989\) | −65.6142 | − | 37.8824i | −2.08641 | − | 1.20459i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −4.79414 | − | 8.30370i | −0.152291 | − | 0.263776i | 0.779778 | − | 0.626056i | \(-0.215332\pi\) |
−0.932069 | + | 0.362280i | \(0.881998\pi\) | |||||||
\(992\) | −12.9748 | − | 7.49102i | −0.411951 | − | 0.237840i | ||||
\(993\) | −0.947737 | + | 2.15705i | −0.0300755 | + | 0.0684521i | ||||
\(994\) | 17.6491 | − | 25.7113i | 0.559795 | − | 0.815514i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −19.5448 | + | 14.3470i | −0.619299 | + | 0.454603i | ||||
\(997\) | 11.8733 | + | 20.5651i | 0.376030 | + | 0.651303i | 0.990481 | − | 0.137652i | \(-0.0439556\pi\) |
−0.614451 | + | 0.788955i | \(0.710622\pi\) | |||||||
\(998\) | −11.6946 | − | 20.2557i | −0.370187 | − | 0.641182i | ||||
\(999\) | −29.8115 | − | 5.87970i | −0.943193 | − | 0.186025i |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(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 | 525.2.q.g.299.9 | 40 | ||
3.2 | odd | 2 | inner | 525.2.q.g.299.11 | 40 | ||
5.2 | odd | 4 | 525.2.t.i.26.5 | yes | 20 | ||
5.3 | odd | 4 | 525.2.t.h.26.6 | yes | 20 | ||
5.4 | even | 2 | inner | 525.2.q.g.299.12 | 40 | ||
7.3 | odd | 6 | inner | 525.2.q.g.374.10 | 40 | ||
15.2 | even | 4 | 525.2.t.i.26.6 | yes | 20 | ||
15.8 | even | 4 | 525.2.t.h.26.5 | ✓ | 20 | ||
15.14 | odd | 2 | inner | 525.2.q.g.299.10 | 40 | ||
21.17 | even | 6 | inner | 525.2.q.g.374.12 | 40 | ||
35.3 | even | 12 | 525.2.t.h.101.5 | yes | 20 | ||
35.17 | even | 12 | 525.2.t.i.101.6 | yes | 20 | ||
35.24 | odd | 6 | inner | 525.2.q.g.374.11 | 40 | ||
105.17 | odd | 12 | 525.2.t.i.101.5 | yes | 20 | ||
105.38 | odd | 12 | 525.2.t.h.101.6 | yes | 20 | ||
105.59 | even | 6 | inner | 525.2.q.g.374.9 | 40 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
525.2.q.g.299.9 | 40 | 1.1 | even | 1 | trivial | ||
525.2.q.g.299.10 | 40 | 15.14 | odd | 2 | inner | ||
525.2.q.g.299.11 | 40 | 3.2 | odd | 2 | inner | ||
525.2.q.g.299.12 | 40 | 5.4 | even | 2 | inner | ||
525.2.q.g.374.9 | 40 | 105.59 | even | 6 | inner | ||
525.2.q.g.374.10 | 40 | 7.3 | odd | 6 | inner | ||
525.2.q.g.374.11 | 40 | 35.24 | odd | 6 | inner | ||
525.2.q.g.374.12 | 40 | 21.17 | even | 6 | inner | ||
525.2.t.h.26.5 | ✓ | 20 | 15.8 | even | 4 | ||
525.2.t.h.26.6 | yes | 20 | 5.3 | odd | 4 | ||
525.2.t.h.101.5 | yes | 20 | 35.3 | even | 12 | ||
525.2.t.h.101.6 | yes | 20 | 105.38 | odd | 12 | ||
525.2.t.i.26.5 | yes | 20 | 5.2 | odd | 4 | ||
525.2.t.i.26.6 | yes | 20 | 15.2 | even | 4 | ||
525.2.t.i.101.5 | yes | 20 | 105.17 | odd | 12 | ||
525.2.t.i.101.6 | yes | 20 | 35.17 | even | 12 |