Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [625,2,Mod(126,625)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(625, base_ring=CyclotomicField(10))
chi = DirichletCharacter(H, H._module([4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("625.126");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 625 = 5^{4} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 625.d (of order \(5\), degree \(4\), 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: | \(4.99065012633\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{5})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} + 25x^{14} + 239x^{12} + 1165x^{10} + 3166x^{8} + 4820x^{6} + 3809x^{4} + 1205x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 5^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{5}]$ |
Embedding invariants
Embedding label | 251.3 | ||
Root | \(-2.04679i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 625.251 |
Dual form | 625.2.d.n.376.3 |
$q$-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 \(\left(\mathbb{Z}/625\mathbb{Z}\right)^\times\).
\(n\) | \(2\) |
\(\chi(n)\) | \(e\left(\frac{4}{5}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.264347 | − | 0.192059i | 0.186922 | − | 0.135807i | −0.490389 | − | 0.871504i | \(-0.663145\pi\) |
0.677311 | + | 0.735697i | \(0.263145\pi\) | |||||||
\(3\) | −0.530081 | + | 1.63142i | −0.306042 | + | 0.941901i | 0.673244 | + | 0.739421i | \(0.264900\pi\) |
−0.979286 | + | 0.202481i | \(0.935100\pi\) | |||||||
\(4\) | −0.585041 | + | 1.80057i | −0.292521 | + | 0.900286i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0.173205 | + | 0.533069i | 0.0707104 | + | 0.217624i | ||||
\(7\) | 3.42409 | 1.29419 | 0.647093 | − | 0.762411i | \(-0.275984\pi\) | ||||
0.647093 | + | 0.762411i | \(0.275984\pi\) | |||||||
\(8\) | 0.393106 | + | 1.20986i | 0.138984 | + | 0.427749i | ||||
\(9\) | 0.0465016 | + | 0.0337854i | 0.0155005 | + | 0.0112618i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 4.32105 | − | 3.13943i | 1.30285 | − | 0.946573i | 0.302867 | − | 0.953033i | \(-0.402056\pi\) |
0.999979 | + | 0.00645946i | \(0.00205613\pi\) | |||||||
\(12\) | −2.62737 | − | 1.90890i | −0.758457 | − | 0.551051i | ||||
\(13\) | 2.84866 | + | 2.06967i | 0.790076 | + | 0.574024i | 0.907986 | − | 0.419000i | \(-0.137619\pi\) |
−0.117910 | + | 0.993024i | \(0.537619\pi\) | |||||||
\(14\) | 0.905150 | − | 0.657630i | 0.241911 | − | 0.175759i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −2.72704 | − | 1.98131i | −0.681759 | − | 0.495327i | ||||
\(17\) | 0.790426 | + | 2.43268i | 0.191706 | + | 0.590012i | 0.999999 | + | 0.00123106i | \(0.000391859\pi\) |
−0.808293 | + | 0.588781i | \(0.799608\pi\) | |||||||
\(18\) | 0.0187814 | 0.00442681 | ||||||||
\(19\) | −0.626004 | − | 1.92664i | −0.143615 | − | 0.442002i | 0.853215 | − | 0.521559i | \(-0.174649\pi\) |
−0.996830 | + | 0.0795572i | \(0.974649\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −1.81505 | + | 5.58614i | −0.396076 | + | 1.21900i | ||||
\(22\) | 0.539301 | − | 1.65980i | 0.114979 | − | 0.353870i | ||||
\(23\) | −6.12492 | + | 4.45002i | −1.27714 | + | 0.927893i | −0.999462 | − | 0.0327828i | \(-0.989563\pi\) |
−0.277673 | + | 0.960676i | \(0.589563\pi\) | |||||||
\(24\) | −2.18216 | −0.445432 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 1.15054 | 0.225639 | ||||||||
\(27\) | −4.24308 | + | 3.08278i | −0.816581 | + | 0.593281i | ||||
\(28\) | −2.00324 | + | 6.16533i | −0.378576 | + | 1.16514i | ||||
\(29\) | 1.46557 | − | 4.51057i | 0.272150 | − | 0.837593i | −0.717809 | − | 0.696240i | \(-0.754855\pi\) |
0.989959 | − | 0.141352i | \(-0.0451451\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0.501908 | + | 1.54471i | 0.0901453 | + | 0.277439i | 0.985958 | − | 0.166993i | \(-0.0534057\pi\) |
−0.895813 | + | 0.444432i | \(0.853406\pi\) | |||||||
\(32\) | −3.64565 | −0.644466 | ||||||||
\(33\) | 2.83122 | + | 8.71361i | 0.492853 | + | 1.51684i | ||||
\(34\) | 0.676166 | + | 0.491264i | 0.115962 | + | 0.0842510i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −0.0880383 | + | 0.0639636i | −0.0146731 | + | 0.0106606i | ||||
\(37\) | 0.0108643 | + | 0.00789335i | 0.00178607 | + | 0.00129766i | 0.588678 | − | 0.808368i | \(-0.299649\pi\) |
−0.586892 | + | 0.809665i | \(0.699649\pi\) | |||||||
\(38\) | −0.535512 | − | 0.389072i | −0.0868715 | − | 0.0631159i | ||||
\(39\) | −4.88653 | + | 3.55027i | −0.782471 | + | 0.568498i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −7.82918 | − | 5.68823i | −1.22271 | − | 0.888353i | −0.226390 | − | 0.974037i | \(-0.572693\pi\) |
−0.996322 | + | 0.0856838i | \(0.972693\pi\) | |||||||
\(42\) | 0.593069 | + | 1.82528i | 0.0915125 | + | 0.281646i | ||||
\(43\) | 2.32645 | 0.354780 | 0.177390 | − | 0.984141i | \(-0.443235\pi\) | ||||
0.177390 | + | 0.984141i | \(0.443235\pi\) | |||||||
\(44\) | 3.12477 | + | 9.61706i | 0.471077 | + | 1.44983i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −0.764438 | + | 2.35270i | −0.112710 | + | 0.346887i | ||||
\(47\) | 2.14658 | − | 6.60649i | 0.313111 | − | 0.963656i | −0.663414 | − | 0.748252i | \(-0.730893\pi\) |
0.976525 | − | 0.215403i | \(-0.0691066\pi\) | |||||||
\(48\) | 4.67790 | − | 3.39869i | 0.675196 | − | 0.490559i | ||||
\(49\) | 4.72443 | 0.674918 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −4.38772 | −0.614403 | ||||||||
\(52\) | −5.39318 | + | 3.91837i | −0.747899 | + | 0.543381i | ||||
\(53\) | 0.532270 | − | 1.63816i | 0.0731129 | − | 0.225018i | −0.907822 | − | 0.419356i | \(-0.862256\pi\) |
0.980935 | + | 0.194338i | \(0.0622558\pi\) | |||||||
\(54\) | −0.529569 | + | 1.62985i | −0.0720652 | + | 0.221794i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 1.34603 | + | 4.14266i | 0.179871 | + | 0.553587i | ||||
\(57\) | 3.47500 | 0.460275 | ||||||||
\(58\) | −0.478878 | − | 1.47384i | −0.0628798 | − | 0.193524i | ||||
\(59\) | 0.0179464 | + | 0.0130388i | 0.00233642 | + | 0.00169751i | 0.588953 | − | 0.808167i | \(-0.299540\pi\) |
−0.586616 | + | 0.809865i | \(0.699540\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −3.16947 | + | 2.30275i | −0.405809 | + | 0.294837i | −0.771903 | − | 0.635740i | \(-0.780695\pi\) |
0.366094 | + | 0.930578i | \(0.380695\pi\) | |||||||
\(62\) | 0.429355 | + | 0.311944i | 0.0545281 | + | 0.0396170i | ||||
\(63\) | 0.159226 | + | 0.115684i | 0.0200606 | + | 0.0145749i | ||||
\(64\) | 4.49035 | − | 3.26243i | 0.561294 | − | 0.407804i | ||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 2.42196 | + | 1.75965i | 0.298122 | + | 0.216599i | ||||
\(67\) | 1.27263 | + | 3.91676i | 0.155477 | + | 0.478508i | 0.998209 | − | 0.0598251i | \(-0.0190543\pi\) |
−0.842732 | + | 0.538333i | \(0.819054\pi\) | |||||||
\(68\) | −4.84265 | −0.587258 | ||||||||
\(69\) | −4.01315 | − | 12.3512i | −0.483126 | − | 1.48691i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0.722772 | − | 2.22446i | 0.0857772 | − | 0.263995i | −0.898963 | − | 0.438024i | \(-0.855679\pi\) |
0.984741 | + | 0.174029i | \(0.0556785\pi\) | |||||||
\(72\) | −0.0225954 | + | 0.0695415i | −0.00266289 | + | 0.00819554i | ||||
\(73\) | −1.22463 | + | 0.889748i | −0.143332 | + | 0.104137i | −0.657141 | − | 0.753768i | \(-0.728234\pi\) |
0.513808 | + | 0.857905i | \(0.328234\pi\) | |||||||
\(74\) | 0.00438793 | 0.000510086 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 3.83530 | 0.439939 | ||||||||
\(77\) | 14.7957 | − | 10.7497i | 1.68613 | − | 1.22504i | ||||
\(78\) | −0.609877 | + | 1.87701i | −0.0690550 | + | 0.212529i | ||||
\(79\) | 0.131898 | − | 0.405940i | 0.0148397 | − | 0.0456719i | −0.943362 | − | 0.331764i | \(-0.892356\pi\) |
0.958202 | + | 0.286092i | \(0.0923563\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −2.72685 | − | 8.39237i | −0.302983 | − | 0.932485i | ||||
\(82\) | −3.16210 | −0.349196 | ||||||||
\(83\) | −1.86704 | − | 5.74616i | −0.204934 | − | 0.630723i | −0.999716 | − | 0.0238275i | \(-0.992415\pi\) |
0.794782 | − | 0.606895i | \(-0.207585\pi\) | |||||||
\(84\) | −8.99637 | − | 6.53625i | −0.981585 | − | 0.713163i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0.614990 | − | 0.446817i | 0.0663161 | − | 0.0481815i | ||||
\(87\) | 6.58177 | + | 4.78194i | 0.705640 | + | 0.512678i | ||||
\(88\) | 5.49689 | + | 3.99372i | 0.585970 | + | 0.425732i | ||||
\(89\) | 4.92984 | − | 3.58174i | 0.522562 | − | 0.379663i | −0.295006 | − | 0.955495i | \(-0.595322\pi\) |
0.817568 | + | 0.575832i | \(0.195322\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 9.75408 | + | 7.08676i | 1.02251 | + | 0.742894i | ||||
\(92\) | −4.42924 | − | 13.6318i | −0.461781 | − | 1.42121i | ||||
\(93\) | −2.78613 | −0.288908 | ||||||||
\(94\) | −0.701397 | − | 2.15868i | −0.0723436 | − | 0.222651i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 1.93249 | − | 5.94759i | 0.197234 | − | 0.607023i | ||||
\(97\) | −4.94484 | + | 15.2186i | −0.502072 | + | 1.54522i | 0.303565 | + | 0.952811i | \(0.401823\pi\) |
−0.805638 | + | 0.592409i | \(0.798177\pi\) | |||||||
\(98\) | 1.24889 | − | 0.907371i | 0.126157 | − | 0.0916583i | ||||
\(99\) | 0.307002 | 0.0308549 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 1.44418 | 0.143701 | 0.0718505 | − | 0.997415i | \(-0.477110\pi\) | ||||
0.0718505 | + | 0.997415i | \(0.477110\pi\) | |||||||
\(102\) | −1.15988 | + | 0.842703i | −0.114845 | + | 0.0834400i | ||||
\(103\) | 4.53196 | − | 13.9479i | 0.446547 | − | 1.37433i | −0.434231 | − | 0.900802i | \(-0.642980\pi\) |
0.880778 | − | 0.473530i | \(-0.157020\pi\) | |||||||
\(104\) | −1.38418 | + | 4.26007i | −0.135730 | + | 0.417734i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −0.173920 | − | 0.535270i | −0.0168926 | − | 0.0519900i | ||||
\(107\) | 12.2169 | 1.18106 | 0.590528 | − | 0.807017i | \(-0.298919\pi\) | ||||
0.590528 | + | 0.807017i | \(0.298919\pi\) | |||||||
\(108\) | −3.06839 | − | 9.44352i | −0.295255 | − | 0.908703i | ||||
\(109\) | 12.4197 | + | 9.02343i | 1.18959 | + | 0.864287i | 0.993221 | − | 0.116243i | \(-0.0370850\pi\) |
0.196369 | + | 0.980530i | \(0.437085\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −0.0186363 | + | 0.0135401i | −0.00176888 | + | 0.00128517i | ||||
\(112\) | −9.33763 | − | 6.78418i | −0.882323 | − | 0.641045i | ||||
\(113\) | −15.0108 | − | 10.9060i | −1.41210 | − | 1.02595i | −0.993013 | − | 0.118007i | \(-0.962350\pi\) |
−0.419089 | − | 0.907945i | \(-0.637650\pi\) | |||||||
\(114\) | 0.918606 | − | 0.667406i | 0.0860353 | − | 0.0625083i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 7.26419 | + | 5.27774i | 0.674463 | + | 0.490026i | ||||
\(117\) | 0.0625425 | + | 0.192486i | 0.00578206 | + | 0.0177953i | ||||
\(118\) | 0.00724831 | 0.000667261 | ||||||||
\(119\) | 2.70649 | + | 8.32973i | 0.248104 | + | 0.763585i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 5.41630 | − | 16.6696i | 0.492391 | − | 1.51542i | ||||
\(122\) | −0.395575 | + | 1.21745i | −0.0358136 | + | 0.110223i | ||||
\(123\) | 13.4300 | − | 9.75747i | 1.21094 | − | 0.879801i | ||||
\(124\) | −3.07500 | −0.276144 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0.0643092 | 0.00572911 | ||||||||
\(127\) | −0.548435 | + | 0.398461i | −0.0486657 | + | 0.0353577i | −0.611852 | − | 0.790972i | \(-0.709575\pi\) |
0.563186 | + | 0.826330i | \(0.309575\pi\) | |||||||
\(128\) | 2.81357 | − | 8.65927i | 0.248687 | − | 0.765378i | ||||
\(129\) | −1.23321 | + | 3.79542i | −0.108578 | + | 0.334168i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 2.17875 | + | 6.70550i | 0.190358 | + | 0.585863i | 0.999999 | − | 0.00106268i | \(-0.000338260\pi\) |
−0.809641 | + | 0.586925i | \(0.800338\pi\) | |||||||
\(132\) | −17.3459 | −1.50976 | ||||||||
\(133\) | −2.14350 | − | 6.59700i | −0.185865 | − | 0.572033i | ||||
\(134\) | 1.08867 | + | 0.790962i | 0.0940465 | + | 0.0683288i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −2.63247 | + | 1.91260i | −0.225733 | + | 0.164004i | ||||
\(137\) | 8.83331 | + | 6.41778i | 0.754681 | + | 0.548308i | 0.897274 | − | 0.441474i | \(-0.145544\pi\) |
−0.142593 | + | 0.989781i | \(0.545544\pi\) | |||||||
\(138\) | −3.43303 | − | 2.49424i | −0.292239 | − | 0.212324i | ||||
\(139\) | −15.7841 | + | 11.4678i | −1.33879 | + | 0.972686i | −0.339300 | + | 0.940678i | \(0.610190\pi\) |
−0.999488 | + | 0.0320076i | \(0.989810\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 9.64011 | + | 7.00395i | 0.811843 | + | 0.589839i | ||||
\(142\) | −0.236166 | − | 0.726846i | −0.0198186 | − | 0.0609955i | ||||
\(143\) | 18.8068 | 1.57270 | ||||||||
\(144\) | −0.0598722 | − | 0.184268i | −0.00498935 | − | 0.0153556i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −0.152844 | + | 0.470405i | −0.0126494 | + | 0.0389310i | ||||
\(147\) | −2.50433 | + | 7.70753i | −0.206553 | + | 0.635706i | ||||
\(148\) | −0.0205686 | + | 0.0149440i | −0.00169073 | + | 0.00122839i | ||||
\(149\) | −12.7945 | −1.04817 | −0.524085 | − | 0.851666i | \(-0.675593\pi\) | ||||
−0.524085 | + | 0.851666i | \(0.675593\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 2.15617 | 0.175466 | 0.0877331 | − | 0.996144i | \(-0.472038\pi\) | ||||
0.0877331 | + | 0.996144i | \(0.472038\pi\) | |||||||
\(152\) | 2.08487 | − | 1.51475i | 0.169106 | − | 0.122862i | ||||
\(153\) | −0.0454330 | + | 0.139828i | −0.00367304 | + | 0.0113044i | ||||
\(154\) | 1.84662 | − | 5.68331i | 0.148805 | − | 0.457974i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −3.53370 | − | 10.8756i | −0.282922 | − | 0.870745i | ||||
\(157\) | −15.7474 | −1.25678 | −0.628389 | − | 0.777899i | \(-0.716285\pi\) | ||||
−0.628389 | + | 0.777899i | \(0.716285\pi\) | |||||||
\(158\) | −0.0430978 | − | 0.132641i | −0.00342868 | − | 0.0105524i | ||||
\(159\) | 2.39038 | + | 1.73671i | 0.189569 | + | 0.137730i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −20.9723 | + | 15.2373i | −1.65285 | + | 1.20087i | ||||
\(162\) | −2.33267 | − | 1.69478i | −0.183272 | − | 0.133155i | ||||
\(163\) | −5.98040 | − | 4.34502i | −0.468421 | − | 0.340328i | 0.328404 | − | 0.944537i | \(-0.393489\pi\) |
−0.796826 | + | 0.604209i | \(0.793489\pi\) | |||||||
\(164\) | 14.8225 | − | 10.7692i | 1.15744 | − | 0.840930i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −1.59715 | − | 1.16040i | −0.123963 | − | 0.0900643i | ||||
\(167\) | −3.34249 | − | 10.2871i | −0.258649 | − | 0.796041i | −0.993089 | − | 0.117367i | \(-0.962555\pi\) |
0.734439 | − | 0.678675i | \(-0.237445\pi\) | |||||||
\(168\) | −7.47194 | −0.576472 | ||||||||
\(169\) | −0.185902 | − | 0.572147i | −0.0143001 | − | 0.0440113i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0.0359821 | − | 0.110742i | 0.00275162 | − | 0.00846862i | ||||
\(172\) | −1.36107 | + | 4.18894i | −0.103781 | + | 0.319404i | ||||
\(173\) | −12.1339 | + | 8.81577i | −0.922521 | + | 0.670251i | −0.944150 | − | 0.329515i | \(-0.893115\pi\) |
0.0216293 | + | 0.999766i | \(0.493115\pi\) | |||||||
\(174\) | 2.65829 | 0.201524 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −18.0038 | −1.35709 | ||||||||
\(177\) | −0.0307849 | + | 0.0223665i | −0.00231393 | + | 0.00168117i | ||||
\(178\) | 0.615282 | − | 1.89364i | 0.0461174 | − | 0.141935i | ||||
\(179\) | 2.28624 | − | 7.03631i | 0.170881 | − | 0.525919i | −0.828540 | − | 0.559930i | \(-0.810828\pi\) |
0.999421 | + | 0.0340111i | \(0.0108282\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −3.37374 | − | 10.3833i | −0.250768 | − | 0.771785i | −0.994634 | − | 0.103456i | \(-0.967010\pi\) |
0.743866 | − | 0.668329i | \(-0.232990\pi\) | |||||||
\(182\) | 3.93954 | 0.292018 | ||||||||
\(183\) | −2.07669 | − | 6.39139i | −0.153513 | − | 0.472465i | ||||
\(184\) | −7.79163 | − | 5.66095i | −0.574407 | − | 0.417331i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −0.736505 | + | 0.535102i | −0.0540032 | + | 0.0392356i | ||||
\(187\) | 11.0527 | + | 8.03026i | 0.808253 | + | 0.587231i | ||||
\(188\) | 10.6396 | + | 7.73014i | 0.775974 | + | 0.563778i | ||||
\(189\) | −14.5287 | + | 10.5557i | −1.05681 | + | 0.767815i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 1.41693 | + | 1.02946i | 0.102525 | + | 0.0744891i | 0.637867 | − | 0.770147i | \(-0.279817\pi\) |
−0.535341 | + | 0.844636i | \(0.679817\pi\) | |||||||
\(192\) | 2.94215 | + | 9.05501i | 0.212332 | + | 0.653489i | ||||
\(193\) | −9.53146 | −0.686089 | −0.343045 | − | 0.939319i | \(-0.611458\pi\) | ||||
−0.343045 | + | 0.939319i | \(0.611458\pi\) | |||||||
\(194\) | 1.61573 | + | 4.97271i | 0.116003 | + | 0.357020i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −2.76398 | + | 8.50667i | −0.197427 | + | 0.607619i | ||||
\(197\) | 7.39073 | − | 22.7463i | 0.526567 | − | 1.62061i | −0.234628 | − | 0.972085i | \(-0.575387\pi\) |
0.761195 | − | 0.648523i | \(-0.224613\pi\) | |||||||
\(198\) | 0.0811552 | − | 0.0589627i | 0.00576745 | − | 0.00419030i | ||||
\(199\) | 23.8281 | 1.68913 | 0.844566 | − | 0.535451i | \(-0.179858\pi\) | ||||
0.844566 | + | 0.535451i | \(0.179858\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −7.06448 | −0.498290 | ||||||||
\(202\) | 0.381764 | − | 0.277368i | 0.0268608 | − | 0.0195155i | ||||
\(203\) | 5.01827 | − | 15.4446i | 0.352213 | − | 1.08400i | ||||
\(204\) | 2.56700 | − | 7.90040i | 0.179726 | − | 0.553139i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −1.48082 | − | 4.55750i | −0.103174 | − | 0.317536i | ||||
\(207\) | −0.435164 | −0.0302460 | ||||||||
\(208\) | −3.66774 | − | 11.2881i | −0.254312 | − | 0.782692i | ||||
\(209\) | −8.75355 | − | 6.35982i | −0.605496 | − | 0.439918i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 12.4527 | − | 9.04738i | 0.857276 | − | 0.622847i | −0.0698666 | − | 0.997556i | \(-0.522257\pi\) |
0.927142 | + | 0.374709i | \(0.122257\pi\) | |||||||
\(212\) | 2.63822 | + | 1.91678i | 0.181194 | + | 0.131645i | ||||
\(213\) | 3.24591 | + | 2.35829i | 0.222406 | + | 0.161587i | ||||
\(214\) | 3.22951 | − | 2.34638i | 0.220765 | − | 0.160395i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −5.39770 | − | 3.92166i | −0.367267 | − | 0.266835i | ||||
\(217\) | 1.71858 | + | 5.28924i | 0.116665 | + | 0.359057i | ||||
\(218\) | 5.01614 | 0.339736 | ||||||||
\(219\) | −0.802399 | − | 2.46953i | −0.0542211 | − | 0.166875i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −2.78320 | + | 8.56580i | −0.187218 | + | 0.576198i | ||||
\(222\) | −0.00232596 | + | 0.00715856i | −0.000156108 | + | 0.000480451i | ||||
\(223\) | 15.8367 | − | 11.5061i | 1.06051 | − | 0.770503i | 0.0863242 | − | 0.996267i | \(-0.472488\pi\) |
0.974182 | + | 0.225764i | \(0.0724879\pi\) | |||||||
\(224\) | −12.4831 | −0.834059 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −6.06268 | −0.403283 | ||||||||
\(227\) | −1.08575 | + | 0.788847i | −0.0720640 | + | 0.0523576i | −0.623234 | − | 0.782035i | \(-0.714182\pi\) |
0.551170 | + | 0.834393i | \(0.314182\pi\) | |||||||
\(228\) | −2.03302 | + | 6.25698i | −0.134640 | + | 0.414379i | ||||
\(229\) | −6.91278 | + | 21.2753i | −0.456809 | + | 1.40591i | 0.412189 | + | 0.911098i | \(0.364764\pi\) |
−0.868998 | + | 0.494815i | \(0.835236\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 9.69438 | + | 29.8362i | 0.637843 | + | 1.96308i | ||||
\(232\) | 6.03327 | 0.396104 | ||||||||
\(233\) | 5.67512 | + | 17.4662i | 0.371789 | + | 1.14425i | 0.945619 | + | 0.325276i | \(0.105457\pi\) |
−0.573830 | + | 0.818975i | \(0.694543\pi\) | |||||||
\(234\) | 0.0535017 | + | 0.0388713i | 0.00349752 | + | 0.00254109i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −0.0339768 | + | 0.0246856i | −0.00221170 | + | 0.00160689i | ||||
\(237\) | 0.592343 | + | 0.430362i | 0.0384768 | + | 0.0279550i | ||||
\(238\) | 2.31526 | + | 1.68213i | 0.150076 | + | 0.109037i | ||||
\(239\) | 9.71123 | − | 7.05562i | 0.628168 | − | 0.456390i | −0.227597 | − | 0.973755i | \(-0.573087\pi\) |
0.855765 | + | 0.517365i | \(0.173087\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −8.18481 | − | 5.94661i | −0.527230 | − | 0.383055i | 0.292091 | − | 0.956391i | \(-0.405649\pi\) |
−0.819321 | + | 0.573336i | \(0.805649\pi\) | |||||||
\(242\) | −1.76978 | − | 5.44683i | −0.113766 | − | 0.350135i | ||||
\(243\) | −0.597258 | −0.0383141 | ||||||||
\(244\) | −2.29200 | − | 7.05406i | −0.146731 | − | 0.451590i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 1.67617 | − | 5.15872i | 0.106869 | − | 0.328908i | ||||
\(247\) | 2.20425 | − | 6.78397i | 0.140253 | − | 0.431654i | ||||
\(248\) | −1.67158 | + | 1.21447i | −0.106145 | + | 0.0771191i | ||||
\(249\) | 10.3641 | 0.656797 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 16.7258 | 1.05573 | 0.527863 | − | 0.849330i | \(-0.322994\pi\) | ||||
0.527863 | + | 0.849330i | \(0.322994\pi\) | |||||||
\(252\) | −0.301452 | + | 0.219017i | −0.0189897 | + | 0.0137968i | ||||
\(253\) | −12.4956 | + | 38.4575i | −0.785592 | + | 2.41780i | ||||
\(254\) | −0.0684489 | + | 0.210664i | −0.00429487 | + | 0.0132182i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 2.51099 | + | 7.72803i | 0.156937 | + | 0.483002i | ||||
\(257\) | 15.0170 | 0.936732 | 0.468366 | − | 0.883535i | \(-0.344843\pi\) | ||||
0.468366 | + | 0.883535i | \(0.344843\pi\) | |||||||
\(258\) | 0.402952 | + | 1.24016i | 0.0250867 | + | 0.0772088i | ||||
\(259\) | 0.0372003 | + | 0.0270276i | 0.00231151 | + | 0.00167941i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0.220543 | − | 0.160234i | 0.0136513 | − | 0.00991822i | ||||
\(262\) | 1.86380 | + | 1.35413i | 0.115146 | + | 0.0836585i | ||||
\(263\) | −4.99311 | − | 3.62771i | −0.307888 | − | 0.223694i | 0.423102 | − | 0.906082i | \(-0.360941\pi\) |
−0.730990 | + | 0.682388i | \(0.760941\pi\) | |||||||
\(264\) | −9.42924 | + | 6.85075i | −0.580330 | + | 0.421634i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −1.83364 | − | 1.33222i | −0.112428 | − | 0.0816837i | ||||
\(267\) | 3.23011 | + | 9.94126i | 0.197679 | + | 0.608395i | ||||
\(268\) | −7.79694 | −0.476274 | ||||||||
\(269\) | 3.43171 | + | 10.5617i | 0.209235 | + | 0.643959i | 0.999513 | + | 0.0312102i | \(0.00993614\pi\) |
−0.790278 | + | 0.612749i | \(0.790064\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −0.358920 | + | 1.10464i | −0.0218028 | + | 0.0671022i | −0.961366 | − | 0.275274i | \(-0.911232\pi\) |
0.939563 | + | 0.342376i | \(0.111232\pi\) | |||||||
\(272\) | 2.66437 | − | 8.20008i | 0.161551 | − | 0.497203i | ||||
\(273\) | −16.7319 | + | 12.1565i | −1.01266 | + | 0.735743i | ||||
\(274\) | 3.56766 | 0.215530 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 24.5871 | 1.47997 | ||||||||
\(277\) | 1.75950 | − | 1.27835i | 0.105718 | − | 0.0768087i | −0.533670 | − | 0.845693i | \(-0.679188\pi\) |
0.639388 | + | 0.768884i | \(0.279188\pi\) | |||||||
\(278\) | −1.96998 | + | 6.06296i | −0.118151 | + | 0.363632i | ||||
\(279\) | −0.0288492 | + | 0.0887887i | −0.00172716 | + | 0.00531564i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −7.45277 | − | 22.9373i | −0.444595 | − | 1.36832i | −0.882927 | − | 0.469510i | \(-0.844431\pi\) |
0.438332 | − | 0.898813i | \(-0.355569\pi\) | |||||||
\(282\) | 3.89351 | 0.231855 | ||||||||
\(283\) | 5.01052 | + | 15.4208i | 0.297845 | + | 0.916672i | 0.982251 | + | 0.187571i | \(0.0600614\pi\) |
−0.684406 | + | 0.729101i | \(0.739939\pi\) | |||||||
\(284\) | 3.58245 | + | 2.60281i | 0.212580 | + | 0.154448i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 4.97152 | − | 3.61202i | 0.293972 | − | 0.213583i | ||||
\(287\) | −26.8079 | − | 19.4771i | −1.58242 | − | 1.14969i | ||||
\(288\) | −0.169528 | − | 0.123170i | −0.00998956 | − | 0.00725784i | ||||
\(289\) | 8.46013 | − | 6.14664i | 0.497654 | − | 0.361567i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −22.2069 | − | 16.1342i | −1.30179 | − | 0.945805i | ||||
\(292\) | −0.885595 | − | 2.72558i | −0.0518255 | − | 0.159503i | ||||
\(293\) | 3.48929 | 0.203846 | 0.101923 | − | 0.994792i | \(-0.467500\pi\) | ||||
0.101923 | + | 0.994792i | \(0.467500\pi\) | |||||||
\(294\) | 0.818292 | + | 2.51844i | 0.0477238 | + | 0.146879i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −0.00527901 | + | 0.0162471i | −0.000306836 | + | 0.000944345i | ||||
\(297\) | −8.65640 | + | 26.6417i | −0.502296 | + | 1.54591i | ||||
\(298\) | −3.38220 | + | 2.45731i | −0.195926 | + | 0.142348i | ||||
\(299\) | −26.6579 | −1.54167 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 7.96599 | 0.459152 | ||||||||
\(302\) | 0.569976 | − | 0.414112i | 0.0327984 | − | 0.0238295i | ||||
\(303\) | −0.765530 | + | 2.35606i | −0.0439786 | + | 0.135352i | ||||
\(304\) | −2.11013 | + | 6.49433i | −0.121025 | + | 0.372475i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0.0148453 | + | 0.0456891i | 0.000848648 | + | 0.00261187i | ||||
\(307\) | 8.92690 | 0.509485 | 0.254742 | − | 0.967009i | \(-0.418009\pi\) | ||||
0.254742 | + | 0.967009i | \(0.418009\pi\) | |||||||
\(308\) | 10.6995 | + | 32.9297i | 0.609662 | + | 1.87635i | ||||
\(309\) | 20.3527 | + | 14.7871i | 1.15782 | + | 0.841207i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 21.9325 | − | 15.9349i | 1.24368 | − | 0.903585i | 0.245840 | − | 0.969310i | \(-0.420936\pi\) |
0.997838 | + | 0.0657255i | \(0.0209362\pi\) | |||||||
\(312\) | −6.21624 | − | 4.51636i | −0.351925 | − | 0.255689i | ||||
\(313\) | 16.2672 | + | 11.8188i | 0.919475 | + | 0.668038i | 0.943393 | − | 0.331676i | \(-0.107614\pi\) |
−0.0239180 | + | 0.999714i | \(0.507614\pi\) | |||||||
\(314\) | −4.16278 | + | 3.02443i | −0.234919 | + | 0.170679i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0.653759 | + | 0.474984i | 0.0367768 | + | 0.0267199i | ||||
\(317\) | 2.99126 | + | 9.20616i | 0.168006 | + | 0.517070i | 0.999245 | − | 0.0388454i | \(-0.0123680\pi\) |
−0.831239 | + | 0.555915i | \(0.812368\pi\) | |||||||
\(318\) | 0.965442 | 0.0541393 | ||||||||
\(319\) | −7.82780 | − | 24.0915i | −0.438273 | − | 1.34886i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −6.47597 | + | 19.9310i | −0.361453 | + | 1.11244i | ||||
\(322\) | −2.61751 | + | 8.05587i | −0.145868 | + | 0.448936i | ||||
\(323\) | 4.19209 | − | 3.04573i | 0.233254 | − | 0.169469i | ||||
\(324\) | 16.7064 | 0.928132 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −2.41540 | −0.133777 | ||||||||
\(327\) | −21.3044 | + | 15.4786i | −1.17814 | + | 0.855968i | ||||
\(328\) | 3.80425 | − | 11.7083i | 0.210054 | − | 0.646481i | ||||
\(329\) | 7.35009 | − | 22.6212i | 0.405224 | − | 1.24715i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 6.08018 | + | 18.7129i | 0.334197 | + | 1.02855i | 0.967116 | + | 0.254334i | \(0.0818564\pi\) |
−0.632919 | + | 0.774218i | \(0.718144\pi\) | |||||||
\(332\) | 11.4387 | 0.627778 | ||||||||
\(333\) | 0.000238526 | 0 | 0.000734106i | 1.30711e−5 | 0 | 4.02288e-5i | ||||
\(334\) | −2.85932 | − | 2.07741i | −0.156455 | − | 0.113671i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 16.0176 | − | 11.6374i | 0.873830 | − | 0.634874i | ||||
\(337\) | −15.2542 | − | 11.0828i | −0.830948 | − | 0.603719i | 0.0888795 | − | 0.996042i | \(-0.471671\pi\) |
−0.919827 | + | 0.392323i | \(0.871671\pi\) | |||||||
\(338\) | −0.159029 | − | 0.115541i | −0.00865003 | − | 0.00628462i | ||||
\(339\) | 25.7493 | − | 18.7079i | 1.39851 | − | 1.01608i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 7.01828 | + | 5.09908i | 0.380061 | + | 0.276131i | ||||
\(342\) | −0.0117572 | − | 0.0361849i | −0.000635757 | − | 0.00195666i | ||||
\(343\) | −7.79178 | −0.420717 | ||||||||
\(344\) | 0.914542 | + | 2.81467i | 0.0493088 | + | 0.151757i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −1.51440 | + | 4.66085i | −0.0814147 | + | 0.250569i | ||||
\(347\) | 8.02679 | − | 24.7039i | 0.430901 | − | 1.32618i | −0.466328 | − | 0.884612i | \(-0.654423\pi\) |
0.897229 | − | 0.441565i | \(-0.145577\pi\) | |||||||
\(348\) | −12.4608 | + | 9.05333i | −0.667971 | + | 0.485309i | ||||
\(349\) | −26.1490 | −1.39972 | −0.699861 | − | 0.714279i | \(-0.746755\pi\) | ||||
−0.699861 | + | 0.714279i | \(0.746755\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −18.4674 | −0.985718 | ||||||||
\(352\) | −15.7530 | + | 11.4453i | −0.839640 | + | 0.610034i | ||||
\(353\) | −1.64673 | + | 5.06811i | −0.0876465 | + | 0.269748i | −0.985268 | − | 0.171020i | \(-0.945294\pi\) |
0.897621 | + | 0.440768i | \(0.145294\pi\) | |||||||
\(354\) | −0.00384219 | + | 0.0118251i | −0.000204210 | + | 0.000628495i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 3.56502 | + | 10.9720i | 0.188946 | + | 0.581515i | ||||
\(357\) | −15.0240 | −0.795152 | ||||||||
\(358\) | −0.747030 | − | 2.29912i | −0.0394818 | − | 0.121512i | ||||
\(359\) | −8.00869 | − | 5.81866i | −0.422683 | − | 0.307097i | 0.356034 | − | 0.934473i | \(-0.384129\pi\) |
−0.778716 | + | 0.627376i | \(0.784129\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 12.0513 | − | 8.75575i | 0.634277 | − | 0.460829i | ||||
\(362\) | −2.88605 | − | 2.09684i | −0.151688 | − | 0.110207i | ||||
\(363\) | 24.3241 | + | 17.6725i | 1.27669 | + | 0.927567i | ||||
\(364\) | −18.4668 | + | 13.4169i | −0.967921 | + | 0.703236i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −1.77649 | − | 1.29070i | −0.0928587 | − | 0.0674658i | ||||
\(367\) | 5.07999 | + | 15.6346i | 0.265173 | + | 0.816119i | 0.991653 | + | 0.128932i | \(0.0411548\pi\) |
−0.726480 | + | 0.687187i | \(0.758845\pi\) | |||||||
\(368\) | 25.5197 | 1.33031 | ||||||||
\(369\) | −0.171890 | − | 0.529024i | −0.00894824 | − | 0.0275399i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 1.82254 | − | 5.60921i | 0.0946217 | − | 0.291216i | ||||
\(372\) | 1.63000 | − | 5.01663i | 0.0845116 | − | 0.260100i | ||||
\(373\) | −18.6019 | + | 13.5151i | −0.963172 | + | 0.699785i | −0.953885 | − | 0.300172i | \(-0.902956\pi\) |
−0.00928655 | + | 0.999957i | \(0.502956\pi\) | |||||||
\(374\) | 4.46404 | 0.230830 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 8.83674 | 0.455720 | ||||||||
\(377\) | 13.5103 | − | 9.81583i | 0.695818 | − | 0.505541i | ||||
\(378\) | −1.81330 | + | 5.58075i | −0.0932658 | + | 0.287043i | ||||
\(379\) | 5.07547 | − | 15.6207i | 0.260710 | − | 0.802382i | −0.731941 | − | 0.681368i | \(-0.761385\pi\) |
0.992651 | − | 0.121014i | \(-0.0386146\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −0.359343 | − | 1.10594i | −0.0184097 | − | 0.0566593i | ||||
\(382\) | 0.572279 | 0.0292803 | ||||||||
\(383\) | 1.45393 | + | 4.47475i | 0.0742926 | + | 0.228649i | 0.981306 | − | 0.192452i | \(-0.0616439\pi\) |
−0.907014 | + | 0.421101i | \(0.861644\pi\) | |||||||
\(384\) | 12.6355 | + | 9.18023i | 0.644802 | + | 0.468476i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −2.51961 | + | 1.83061i | −0.128245 | + | 0.0931754i | ||||
\(387\) | 0.108184 | + | 0.0786000i | 0.00549928 | + | 0.00399546i | ||||
\(388\) | −24.5093 | − | 17.8071i | −1.24427 | − | 0.904017i | ||||
\(389\) | −2.86283 | + | 2.07997i | −0.145151 | + | 0.105458i | −0.657991 | − | 0.753026i | \(-0.728593\pi\) |
0.512840 | + | 0.858484i | \(0.328593\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −15.6668 | − | 11.3826i | −0.792303 | − | 0.575642i | ||||
\(392\) | 1.85720 | + | 5.71588i | 0.0938028 | + | 0.288695i | ||||
\(393\) | −12.0944 | −0.610082 | ||||||||
\(394\) | −2.41493 | − | 7.43238i | −0.121662 | − | 0.374438i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −0.179609 | + | 0.552780i | −0.00902570 | + | 0.0277782i | ||||
\(397\) | −2.70814 | + | 8.33481i | −0.135918 | + | 0.418312i | −0.995732 | − | 0.0922956i | \(-0.970580\pi\) |
0.859814 | + | 0.510608i | \(0.170580\pi\) | |||||||
\(398\) | 6.29890 | − | 4.57642i | 0.315735 | − | 0.229395i | ||||
\(399\) | 11.8987 | 0.595681 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 22.7677 | 1.13697 | 0.568483 | − | 0.822695i | \(-0.307531\pi\) | ||||
0.568483 | + | 0.822695i | \(0.307531\pi\) | |||||||
\(402\) | −1.86747 | + | 1.35680i | −0.0931412 | + | 0.0676710i | ||||
\(403\) | −1.76729 | + | 5.43915i | −0.0880348 | + | 0.270943i | ||||
\(404\) | −0.844903 | + | 2.60034i | −0.0420355 | + | 0.129372i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −1.63972 | − | 5.04655i | −0.0813781 | − | 0.250456i | ||||
\(407\) | 0.0717256 | 0.00355531 | ||||||||
\(408\) | −1.72484 | − | 5.30851i | −0.0853922 | − | 0.262810i | ||||
\(409\) | −22.6870 | − | 16.4830i | −1.12180 | − | 0.815034i | −0.137318 | − | 0.990527i | \(-0.543848\pi\) |
−0.984481 | + | 0.175493i | \(0.943848\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −15.1525 | + | 11.0089i | −0.747416 | + | 0.543030i | ||||
\(412\) | 22.4629 | + | 16.3202i | 1.10667 | + | 0.804041i | ||||
\(413\) | 0.0614502 | + | 0.0446462i | 0.00302377 | + | 0.00219690i | ||||
\(414\) | −0.115034 | + | 0.0835774i | −0.00565363 | + | 0.00410760i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −10.3852 | − | 7.54530i | −0.509177 | − | 0.369939i | ||||
\(417\) | −10.3420 | − | 31.8293i | −0.506449 | − | 1.55869i | ||||
\(418\) | −3.53544 | −0.172924 | ||||||||
\(419\) | 10.5344 | + | 32.4216i | 0.514640 | + | 1.58390i | 0.783936 | + | 0.620842i | \(0.213209\pi\) |
−0.269296 | + | 0.963057i | \(0.586791\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −9.93150 | + | 30.5660i | −0.484032 | + | 1.48970i | 0.349347 | + | 0.936993i | \(0.386403\pi\) |
−0.833379 | + | 0.552703i | \(0.813597\pi\) | |||||||
\(422\) | 1.55419 | − | 4.78330i | 0.0756567 | − | 0.232847i | ||||
\(423\) | 0.323022 | − | 0.234689i | 0.0157059 | − | 0.0114110i | ||||
\(424\) | 2.19117 | 0.106413 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 1.31098 | 0.0635171 | ||||||||
\(427\) | −10.8526 | + | 7.88485i | −0.525192 | + | 0.381575i | ||||
\(428\) | −7.14742 | + | 21.9975i | −0.345483 | + | 1.06329i | ||||
\(429\) | −9.96912 | + | 30.6818i | −0.481314 | + | 1.48133i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −5.48656 | − | 16.8859i | −0.264278 | − | 0.813364i | −0.991859 | − | 0.127342i | \(-0.959355\pi\) |
0.727581 | − | 0.686022i | \(-0.240645\pi\) | |||||||
\(432\) | 17.6789 | 0.850579 | ||||||||
\(433\) | 0.947953 | + | 2.91750i | 0.0455557 | + | 0.140206i | 0.971247 | − | 0.238073i | \(-0.0765159\pi\) |
−0.925691 | + | 0.378279i | \(0.876516\pi\) | |||||||
\(434\) | 1.47015 | + | 1.06813i | 0.0705695 | + | 0.0512717i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −23.5134 | + | 17.0835i | −1.12609 | + | 0.818149i | ||||
\(437\) | 12.4078 | + | 9.01481i | 0.593546 | + | 0.431237i | ||||
\(438\) | −0.686409 | − | 0.498705i | −0.0327979 | − | 0.0238291i | ||||
\(439\) | −11.9310 | + | 8.66838i | −0.569436 | + | 0.413719i | −0.834900 | − | 0.550401i | \(-0.814475\pi\) |
0.265464 | + | 0.964121i | \(0.414475\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0.219693 | + | 0.159616i | 0.0104616 | + | 0.00760078i | ||||
\(442\) | 0.909413 | + | 2.79889i | 0.0432564 | + | 0.133129i | ||||
\(443\) | −10.1857 | −0.483935 | −0.241968 | − | 0.970284i | \(-0.577793\pi\) | ||||
−0.241968 | + | 0.970284i | \(0.577793\pi\) | |||||||
\(444\) | −0.0134769 | − | 0.0414775i | −0.000639584 | − | 0.00196844i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 1.97655 | − | 6.08319i | 0.0935923 | − | 0.288047i | ||||
\(447\) | 6.78214 | − | 20.8733i | 0.320784 | − | 0.987273i | ||||
\(448\) | 15.3754 | − | 11.1709i | 0.726419 | − | 0.527774i | ||||
\(449\) | 18.9484 | 0.894230 | 0.447115 | − | 0.894477i | \(-0.352451\pi\) | ||||
0.447115 | + | 0.894477i | \(0.352451\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −51.6881 | −2.43390 | ||||||||
\(452\) | 28.4190 | − | 20.6476i | 1.33672 | − | 0.971183i | ||||
\(453\) | −1.14294 | + | 3.51761i | −0.0537001 | + | 0.165272i | ||||
\(454\) | −0.135511 | + | 0.417059i | −0.00635983 | + | 0.0195735i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 1.36604 | + | 4.20425i | 0.0639708 | + | 0.196882i | ||||
\(457\) | −30.4392 | −1.42389 | −0.711943 | − | 0.702237i | \(-0.752185\pi\) | ||||
−0.711943 | + | 0.702237i | \(0.752185\pi\) | |||||||
\(458\) | 2.25876 | + | 6.95174i | 0.105545 | + | 0.324833i | ||||
\(459\) | −10.8532 | − | 7.88535i | −0.506586 | − | 0.368056i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −1.91714 | + | 1.39289i | −0.0892903 | + | 0.0648732i | −0.631535 | − | 0.775348i | \(-0.717575\pi\) |
0.542244 | + | 0.840221i | \(0.317575\pi\) | |||||||
\(462\) | 8.29301 | + | 6.02522i | 0.385826 | + | 0.280319i | ||||
\(463\) | −0.259680 | − | 0.188669i | −0.0120684 | − | 0.00876817i | 0.581735 | − | 0.813379i | \(-0.302374\pi\) |
−0.593803 | + | 0.804610i | \(0.702374\pi\) | |||||||
\(464\) | −12.9335 | + | 9.39674i | −0.600423 | + | 0.436233i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 4.85475 | + | 3.52719i | 0.224892 | + | 0.163394i | ||||
\(467\) | 3.95762 | + | 12.1803i | 0.183137 | + | 0.563637i | 0.999911 | − | 0.0133197i | \(-0.00423993\pi\) |
−0.816774 | + | 0.576957i | \(0.804240\pi\) | |||||||
\(468\) | −0.383175 | −0.0177123 | ||||||||
\(469\) | 4.35761 | + | 13.4113i | 0.201216 | + | 0.619278i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 8.34739 | − | 25.6906i | 0.384627 | − | 1.18376i | ||||
\(472\) | −0.00872027 | + | 0.0268382i | −0.000401383 | + | 0.00123533i | ||||
\(473\) | 10.0527 | − | 7.30372i | 0.462224 | − | 0.335826i | ||||
\(474\) | 0.239239 | 0.0109886 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −16.5817 | −0.760021 | ||||||||
\(477\) | 0.0800972 | − | 0.0581940i | 0.00366740 | − | 0.00266452i | ||||
\(478\) | 1.21204 | − | 3.73027i | 0.0554373 | − | 0.170619i | ||||
\(479\) | −6.28683 | + | 19.3489i | −0.287253 | + | 0.884072i | 0.698462 | + | 0.715647i | \(0.253868\pi\) |
−0.985714 | + | 0.168425i | \(0.946132\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0.0146119 | + | 0.0449709i | 0.000666247 | + | 0.00205050i | ||||
\(482\) | −3.30573 | −0.150572 | ||||||||
\(483\) | −13.7414 | − | 42.2917i | −0.625255 | − | 1.92434i | ||||
\(484\) | 26.8461 | + | 19.5049i | 1.22028 | + | 0.886585i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −0.157883 | + | 0.114709i | −0.00716173 | + | 0.00520330i | ||||
\(487\) | −12.5332 | − | 9.10589i | −0.567933 | − | 0.412627i | 0.266421 | − | 0.963857i | \(-0.414159\pi\) |
−0.834354 | + | 0.551230i | \(0.814159\pi\) | |||||||
\(488\) | −4.03194 | − | 2.92938i | −0.182517 | − | 0.132607i | ||||
\(489\) | 10.2587 | − | 7.45335i | 0.463912 | − | 0.337052i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 22.2549 | + | 16.1691i | 1.00435 | + | 0.729702i | 0.963016 | − | 0.269443i | \(-0.0868397\pi\) |
0.0413326 | + | 0.999145i | \(0.486840\pi\) | |||||||
\(492\) | 9.71192 | + | 29.8902i | 0.437847 | + | 1.34756i | ||||
\(493\) | 12.1312 | 0.546362 | ||||||||
\(494\) | −0.720240 | − | 2.21667i | −0.0324051 | − | 0.0997327i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 1.69183 | − | 5.20692i | 0.0759655 | − | 0.233798i | ||||
\(497\) | 2.47484 | − | 7.61677i | 0.111012 | − | 0.341659i | ||||
\(498\) | 2.73972 | − | 1.99052i | 0.122770 | − | 0.0891974i | ||||
\(499\) | 4.91044 | 0.219821 | 0.109911 | − | 0.993941i | \(-0.464943\pi\) | ||||
0.109911 | + | 0.993941i | \(0.464943\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 18.5544 | 0.828950 | ||||||||
\(502\) | 4.42143 | − | 3.21235i | 0.197338 | − | 0.143374i | ||||
\(503\) | 12.6837 | − | 39.0365i | 0.565539 | − | 1.74055i | −0.100805 | − | 0.994906i | \(-0.532142\pi\) |
0.666344 | − | 0.745644i | \(-0.267858\pi\) | |||||||
\(504\) | −0.0773688 | + | 0.238117i | −0.00344628 | + | 0.0106066i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 4.08295 | + | 12.5660i | 0.181509 | + | 0.558629i | ||||
\(507\) | 1.03196 | 0.0458308 | ||||||||
\(508\) | −0.396601 | − | 1.22061i | −0.0175963 | − | 0.0541559i | ||||
\(509\) | −33.5260 | − | 24.3581i | −1.48601 | − | 1.07965i | −0.975556 | − | 0.219750i | \(-0.929476\pi\) |
−0.510458 | − | 0.859903i | \(-0.670524\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −4.19326 | + | 3.04658i | −0.185499 | + | 0.134773i | ||||
\(512\) | 16.8800 | + | 12.2641i | 0.745999 | + | 0.542000i | ||||
\(513\) | 8.59559 | + | 6.24506i | 0.379504 | + | 0.275726i | ||||
\(514\) | 3.96969 | − | 2.88415i | 0.175095 | − | 0.127214i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −6.11245 | − | 4.44096i | −0.269086 | − | 0.195502i | ||||
\(517\) | −11.4651 | − | 35.2860i | −0.504235 | − | 1.55188i | ||||
\(518\) | 0.0150247 | 0.000660147 | ||||||||
\(519\) | −7.95030 | − | 24.4685i | −0.348980 | − | 1.07405i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −0.501988 | + | 1.54496i | −0.0219925 | + | 0.0676859i | −0.961450 | − | 0.274978i | \(-0.911329\pi\) |
0.939458 | + | 0.342664i | \(0.111329\pi\) | |||||||
\(522\) | 0.0275255 | − | 0.0847147i | 0.00120476 | − | 0.00370786i | ||||
\(523\) | 15.3721 | − | 11.1685i | 0.672174 | − | 0.488363i | −0.198578 | − | 0.980085i | \(-0.563632\pi\) |
0.870752 | + | 0.491722i | \(0.163632\pi\) | |||||||
\(524\) | −13.3484 | −0.583128 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −2.01665 | −0.0879301 | ||||||||
\(527\) | −3.36107 | + | 2.44196i | −0.146411 | + | 0.106374i | ||||
\(528\) | 9.54349 | − | 29.3718i | 0.415327 | − | 1.27825i | ||||
\(529\) | 10.6046 | − | 32.6378i | 0.461072 | − | 1.41903i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0.000394015 | 0.00121265i | 1.70988e−5 | 5.26246e-5i | ||||||
\(532\) | 13.1324 | 0.569362 | ||||||||
\(533\) | −10.5299 | − | 32.4077i | −0.456100 | − | 1.40373i | ||||
\(534\) | 2.76318 | + | 2.00757i | 0.119575 | + | 0.0868760i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −4.23843 | + | 3.07940i | −0.183072 | + | 0.133010i | ||||
\(537\) | 10.2673 | + | 7.45963i | 0.443067 | + | 0.321907i | ||||
\(538\) | 2.93564 | + | 2.13287i | 0.126564 | + | 0.0919544i | ||||
\(539\) | 20.4145 | − | 14.8320i | 0.879314 | − | 0.638859i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 27.1179 | + | 19.7023i | 1.16589 | + | 0.847067i | 0.990511 | − | 0.137434i | \(-0.0438856\pi\) |
0.175377 | + | 0.984501i | \(0.443886\pi\) | |||||||
\(542\) | 0.117277 | + | 0.360943i | 0.00503750 | + | 0.0155038i | ||||
\(543\) | 18.7279 | 0.803691 | ||||||||
\(544\) | −2.88162 | − | 8.86870i | −0.123548 | − | 0.380243i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −2.08828 | + | 6.42705i | −0.0893700 | + | 0.275053i | ||||
\(547\) | −5.38486 | + | 16.5729i | −0.230240 | + | 0.708606i | 0.767477 | + | 0.641076i | \(0.221512\pi\) |
−0.997717 | + | 0.0675298i | \(0.978488\pi\) | |||||||
\(548\) | −16.7235 | + | 12.1504i | −0.714394 | + | 0.519037i | ||||
\(549\) | −0.225185 | −0.00961065 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −9.60771 | −0.409302 | ||||||||
\(552\) | 13.3656 | − | 9.71067i | 0.568877 | − | 0.413313i | ||||
\(553\) | 0.451631 | − | 1.38998i | 0.0192053 | − | 0.0591079i | ||||
\(554\) | 0.219599 | − | 0.675857i | 0.00932988 | − | 0.0287144i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −11.4143 | − | 35.1295i | −0.484073 | − | 1.48982i | ||||
\(557\) | −16.2929 | −0.690351 | −0.345175 | − | 0.938538i | \(-0.612181\pi\) | ||||
−0.345175 | + | 0.938538i | \(0.612181\pi\) | |||||||
\(558\) | 0.00942651 | + | 0.0290118i | 0.000399056 | + | 0.00122817i | ||||
\(559\) | 6.62726 | + | 4.81499i | 0.280303 | + | 0.203652i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −18.9596 | + | 13.7749i | −0.800473 | + | 0.581578i | ||||
\(562\) | −6.37544 | − | 4.63203i | −0.268932 | − | 0.195390i | ||||
\(563\) | −18.6882 | − | 13.5778i | −0.787615 | − | 0.572236i | 0.119640 | − | 0.992817i | \(-0.461826\pi\) |
−0.907255 | + | 0.420582i | \(0.861826\pi\) | |||||||
\(564\) | −18.2510 | + | 13.2601i | −0.768505 | + | 0.558351i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 4.28623 | + | 3.11413i | 0.180164 | + | 0.130897i | ||||
\(567\) | −9.33698 | − | 28.7363i | −0.392116 | − | 1.20681i | ||||
\(568\) | 2.97541 | 0.124845 | ||||||||
\(569\) | −2.86871 | − | 8.82898i | −0.120263 | − | 0.370130i | 0.872746 | − | 0.488175i | \(-0.162337\pi\) |
−0.993008 | + | 0.118045i | \(0.962337\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 6.86460 | − | 21.1271i | 0.287275 | − | 0.884140i | −0.698433 | − | 0.715675i | \(-0.746119\pi\) |
0.985708 | − | 0.168465i | \(-0.0538809\pi\) | |||||||
\(572\) | −11.0028 | + | 33.8630i | −0.460048 | + | 1.41588i | ||||
\(573\) | −2.43057 | + | 1.76591i | −0.101539 | + | 0.0737721i | ||||
\(574\) | −10.8273 | −0.451924 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0.319031 | 0.0132930 | ||||||||
\(577\) | −11.8191 | + | 8.58711i | −0.492037 | + | 0.357486i | −0.805967 | − | 0.591960i | \(-0.798354\pi\) |
0.313930 | + | 0.949446i | \(0.398354\pi\) | |||||||
\(578\) | 1.05589 | − | 3.24969i | 0.0439192 | − | 0.135169i | ||||
\(579\) | 5.05244 | − | 15.5498i | 0.209972 | − | 0.646229i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −6.39292 | − | 19.6754i | −0.265223 | − | 0.816273i | ||||
\(582\) | −8.96905 | −0.371779 | ||||||||
\(583\) | −2.84291 | − | 8.74959i | −0.117741 | − | 0.362371i | ||||
\(584\) | −1.55788 | − | 1.13186i | −0.0644655 | − | 0.0468369i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0.922384 | − | 0.670151i | 0.0381033 | − | 0.0276837i | ||||
\(587\) | −18.8853 | − | 13.7210i | −0.779479 | − | 0.566325i | 0.125344 | − | 0.992113i | \(-0.459997\pi\) |
−0.904823 | + | 0.425789i | \(0.859997\pi\) | |||||||
\(588\) | −12.4128 | − | 9.01845i | −0.511896 | − | 0.371914i | ||||
\(589\) | 2.66191 | − | 1.93399i | 0.109682 | − | 0.0796888i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 33.1911 | + | 24.1148i | 1.36530 | + | 0.991949i | ||||
\(592\) | −0.0139881 | − | 0.0430509i | −0.000574907 | − | 0.00176938i | ||||
\(593\) | −41.9815 | −1.72397 | −0.861986 | − | 0.506932i | \(-0.830780\pi\) | ||||
−0.861986 | + | 0.506932i | \(0.830780\pi\) | |||||||
\(594\) | 2.82849 | + | 8.70520i | 0.116054 | + | 0.357179i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 7.48534 | − | 23.0375i | 0.306611 | − | 0.943653i | ||||
\(597\) | −12.6308 | + | 38.8737i | −0.516946 | + | 1.59100i | ||||
\(598\) | −7.04694 | + | 5.11990i | −0.288171 | + | 0.209368i | ||||
\(599\) | −25.4160 | −1.03847 | −0.519236 | − | 0.854631i | \(-0.673783\pi\) | ||||
−0.519236 | + | 0.854631i | \(0.673783\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 37.1379 | 1.51489 | 0.757444 | − | 0.652900i | \(-0.226448\pi\) | ||||
0.757444 | + | 0.652900i | \(0.226448\pi\) | |||||||
\(602\) | 2.10579 | − | 1.52994i | 0.0858254 | − | 0.0623558i | ||||
\(603\) | −0.0731497 | + | 0.225132i | −0.00297889 | + | 0.00916807i | ||||
\(604\) | −1.26145 | + | 3.88233i | −0.0513275 | + | 0.157970i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0.250138 | + | 0.769845i | 0.0101612 | + | 0.0312728i | ||||
\(607\) | −18.9242 | −0.768109 | −0.384054 | − | 0.923310i | \(-0.625473\pi\) | ||||
−0.384054 | + | 0.923310i | \(0.625473\pi\) | |||||||
\(608\) | 2.28219 | + | 7.02386i | 0.0925550 | + | 0.284855i | ||||
\(609\) | 22.5366 | + | 16.3738i | 0.913230 | + | 0.663500i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 19.7881 | − | 14.3769i | 0.800543 | − | 0.581628i | ||||
\(612\) | −0.225191 | − | 0.163611i | −0.00910280 | − | 0.00661357i | ||||
\(613\) | −7.44552 | − | 5.40949i | −0.300722 | − | 0.218487i | 0.427183 | − | 0.904165i | \(-0.359506\pi\) |
−0.727905 | + | 0.685678i | \(0.759506\pi\) | |||||||
\(614\) | 2.35980 | − | 1.71450i | 0.0952338 | − | 0.0691914i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 18.8219 | + | 13.6749i | 0.758355 | + | 0.550977i | ||||
\(617\) | −10.1164 | − | 31.1352i | −0.407273 | − | 1.25346i | −0.918982 | − | 0.394298i | \(-0.870988\pi\) |
0.511710 | − | 0.859158i | \(-0.329012\pi\) | |||||||
\(618\) | 8.22017 | 0.330664 | ||||||||
\(619\) | 11.2467 | + | 34.6139i | 0.452045 | + | 1.39125i | 0.874570 | + | 0.484900i | \(0.161144\pi\) |
−0.422525 | + | 0.906351i | \(0.638856\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 12.2701 | − | 37.7635i | 0.492383 | − | 1.51540i | ||||
\(622\) | 2.73735 | − | 8.42469i | 0.109758 | − | 0.337799i | ||||
\(623\) | 16.8802 | − | 12.2642i | 0.676292 | − | 0.491355i | ||||
\(624\) | 20.3599 | 0.815049 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 6.57010 | 0.262594 | ||||||||
\(627\) | 15.0156 | − | 10.9095i | 0.599667 | − | 0.435684i | ||||
\(628\) | 9.21287 | − | 28.3543i | 0.367634 | − | 1.13146i | ||||
\(629\) | −0.0106146 | + | 0.0326684i | −0.000423232 | + | 0.00130257i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 3.74167 | + | 11.5157i | 0.148953 | + | 0.458432i | 0.997498 | − | 0.0706920i | \(-0.0225207\pi\) |
−0.848545 | + | 0.529124i | \(0.822521\pi\) | |||||||
\(632\) | 0.542980 | 0.0215986 | ||||||||
\(633\) | 8.15918 | + | 25.1114i | 0.324298 | + | 0.998087i | ||||
\(634\) | 2.55886 | + | 1.85912i | 0.101625 | + | 0.0738352i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −4.52555 | + | 3.28800i | −0.179450 | + | 0.130378i | ||||
\(637\) | 13.4583 | + | 9.77801i | 0.533237 | + | 0.387419i | ||||
\(638\) | −6.69626 | − | 4.86512i | −0.265107 | − | 0.192612i | ||||
\(639\) | 0.108764 | − | 0.0790219i | 0.00430265 | − | 0.00312606i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −7.88935 | − | 5.73195i | −0.311610 | − | 0.226398i | 0.420977 | − | 0.907071i | \(-0.361687\pi\) |
−0.732587 | + | 0.680673i | \(0.761687\pi\) | |||||||
\(642\) | 2.11603 | + | 6.51247i | 0.0835130 | + | 0.257027i | ||||
\(643\) | 6.77862 | 0.267323 | 0.133661 | − | 0.991027i | \(-0.457327\pi\) | ||||
0.133661 | + | 0.991027i | \(0.457327\pi\) | |||||||
\(644\) | −15.1662 | − | 46.6766i | −0.597630 | − | 1.83932i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0.523206 | − | 1.61026i | 0.0205853 | − | 0.0633549i | ||||
\(647\) | −12.3974 | + | 38.1552i | −0.487392 | + | 1.50004i | 0.341096 | + | 0.940029i | \(0.389202\pi\) |
−0.828487 | + | 0.560008i | \(0.810798\pi\) | |||||||
\(648\) | 9.08162 | − | 6.59818i | 0.356760 | − | 0.259201i | ||||
\(649\) | 0.118482 | 0.00465082 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −9.53997 | −0.373901 | ||||||||
\(652\) | 11.3223 | − | 8.22613i | 0.443416 | − | 0.322160i | ||||
\(653\) | 1.89801 | − | 5.84148i | 0.0742750 | − | 0.228595i | −0.907026 | − | 0.421075i | \(-0.861653\pi\) |
0.981301 | + | 0.192480i | \(0.0616530\pi\) | |||||||
\(654\) | −2.65896 | + | 8.18344i | −0.103974 | + | 0.319998i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 10.0803 | + | 31.0240i | 0.393570 | + | 1.21128i | ||||
\(657\) | −0.0870078 | −0.00339450 | ||||||||
\(658\) | −2.40165 | − | 7.39152i | −0.0936260 | − | 0.288151i | ||||
\(659\) | 35.7298 | + | 25.9592i | 1.39184 | + | 1.01123i | 0.995661 | + | 0.0930526i | \(0.0296625\pi\) |
0.396175 | + | 0.918175i | \(0.370338\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −22.4460 | + | 16.3079i | −0.873047 | + | 0.634306i | −0.931403 | − | 0.363990i | \(-0.881414\pi\) |
0.0583560 | + | 0.998296i | \(0.481414\pi\) | |||||||
\(662\) | 5.20126 | + | 3.77894i | 0.202153 | + | 0.146873i | ||||
\(663\) | −12.4991 | − | 9.08114i | −0.485425 | − | 0.352682i | ||||
\(664\) | 6.21808 | − | 4.51770i | 0.241308 | − | 0.175321i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0.000204046 | 0 | 0.000148248i | 7.90661e−6 | 0 | 5.74449e-6i | ||||
\(667\) | 11.0956 | + | 34.1488i | 0.429624 | + | 1.32225i | ||||
\(668\) | 20.4782 | 0.792325 | ||||||||
\(669\) | 10.3765 | + | 31.9355i | 0.401178 | + | 1.23470i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −6.46611 | + | 19.9006i | −0.249621 | + | 0.768256i | ||||
\(672\) | 6.61703 | − | 20.3651i | 0.255257 | − | 0.785601i | ||||
\(673\) | 33.8431 | − | 24.5884i | 1.30456 | − | 0.947815i | 0.304566 | − | 0.952491i | \(-0.401489\pi\) |
0.999989 | + | 0.00467644i | \(0.00148856\pi\) | |||||||
\(674\) | −6.16096 | −0.237311 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 1.13895 | 0.0438059 | ||||||||
\(677\) | −18.3060 | + | 13.3001i | −0.703556 | + | 0.511163i | −0.881088 | − | 0.472952i | \(-0.843188\pi\) |
0.177533 | + | 0.984115i | \(0.443188\pi\) | |||||||
\(678\) | 3.21371 | − | 9.89078i | 0.123422 | − | 0.379853i | ||||
\(679\) | −16.9316 | + | 52.1101i | −0.649775 | + | 1.99980i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −0.711404 | − | 2.18947i | −0.0272610 | − | 0.0839009i | ||||
\(682\) | 2.83459 | 0.108542 | ||||||||
\(683\) | −15.1426 | − | 46.6040i | −0.579414 | − | 1.78325i | −0.620630 | − | 0.784104i | \(-0.713123\pi\) |
0.0412155 | − | 0.999150i | \(-0.486877\pi\) | |||||||
\(684\) | 0.178347 | + | 0.129577i | 0.00681928 | + | 0.00495449i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −2.05974 | + | 1.49649i | −0.0786411 | + | 0.0571361i | ||||
\(687\) | −31.0447 | − | 22.5553i | −1.18443 | − | 0.860538i | ||||
\(688\) | −6.34431 | − | 4.60941i | −0.241875 | − | 0.175732i | ||||
\(689\) | 4.90671 | − | 3.56493i | 0.186931 | − | 0.135813i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −29.3336 | − | 21.3121i | −1.11590 | − | 0.810750i | −0.132319 | − | 0.991207i | \(-0.542242\pi\) |
−0.983583 | + | 0.180457i | \(0.942242\pi\) | |||||||
\(692\) | −8.77462 | − | 27.0055i | −0.333561 | − | 1.02659i | ||||
\(693\) | 1.05121 | 0.0399320 | ||||||||
\(694\) | −2.62276 | − | 8.07204i | −0.0995588 | − | 0.306410i | ||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −3.19812 | + | 9.84281i | −0.121225 | + | 0.373091i | ||||
\(697\) | 7.64927 | − | 23.5420i | 0.289737 | − | 0.891718i | ||||
\(698\) | −6.91241 | + | 5.02216i | −0.261639 | + | 0.190091i | ||||
\(699\) | −31.5030 | −1.19155 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −8.32362 | −0.314379 | −0.157189 | − | 0.987568i | \(-0.550243\pi\) | ||||
−0.157189 | + | 0.987568i | \(0.550243\pi\) | |||||||
\(702\) | −4.88181 | + | 3.54684i | −0.184252 | + | 0.133867i | ||||
\(703\) | 0.00840658 | − | 0.0258728i | 0.000317060 | − | 0.000975811i | ||||
\(704\) | 9.16088 | − | 28.1943i | 0.345264 | − | 1.06261i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0.538070 | + | 1.65601i | 0.0202505 | + | 0.0623247i | ||||
\(707\) | 4.94500 | 0.185976 | ||||||||
\(708\) | −0.0222621 | − | 0.0685157i | −0.000836661 | − | 0.00257498i | ||||
\(709\) | −30.1841 | − | 21.9301i | −1.13359 | − | 0.823601i | −0.147376 | − | 0.989081i | \(-0.547083\pi\) |
−0.986213 | + | 0.165480i | \(0.947083\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0.0198483 | − | 0.0144206i | 0.000744370 | − | 0.000540816i | ||||
\(712\) | 6.27134 | + | 4.55639i | 0.235028 | + | 0.170758i | ||||
\(713\) | −9.94815 | − | 7.22775i | −0.372561 | − | 0.270681i | ||||
\(714\) | −3.97154 | + | 2.88549i | −0.148631 | + | 0.107987i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 11.3318 | + | 8.23307i | 0.423491 | + | 0.307684i | ||||
\(717\) | 6.36296 | + | 19.5832i | 0.237629 | + | 0.731347i | ||||
\(718\) | −3.23460 | −0.120714 | ||||||||
\(719\) | −2.36869 | − | 7.29008i | −0.0883373 | − | 0.271874i | 0.897123 | − | 0.441781i | \(-0.145653\pi\) |
−0.985460 | + | 0.169907i | \(0.945653\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 15.5179 | − | 47.7591i | 0.577915 | − | 1.77864i | ||||
\(722\) | 1.50409 | − | 4.62912i | 0.0559765 | − | 0.172278i | ||||
\(723\) | 14.0400 | − | 10.2007i | 0.522155 | − | 0.379368i | ||||
\(724\) | 20.6697 | 0.768183 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 9.82419 | 0.364610 | ||||||||
\(727\) | 37.1411 | − | 26.9846i | 1.37749 | − | 1.00080i | 0.380377 | − | 0.924832i | \(-0.375794\pi\) |
0.997110 | − | 0.0759713i | \(-0.0242057\pi\) | |||||||
\(728\) | −4.73957 | + | 14.5869i | −0.175660 | + | 0.540626i | ||||
\(729\) | 8.49713 | − | 26.1515i | 0.314709 | − | 0.968574i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 1.83889 | + | 5.65951i | 0.0680137 | + | 0.209325i | ||||
\(732\) | 12.7231 | 0.470259 | ||||||||
\(733\) | 7.32776 | + | 22.5525i | 0.270657 | + | 0.832996i | 0.990336 | + | 0.138689i | \(0.0442890\pi\) |
−0.719679 | + | 0.694307i | \(0.755711\pi\) | |||||||
\(734\) | 4.34565 | + | 3.15730i | 0.160401 | + | 0.116538i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 22.3293 | − | 16.2232i | 0.823070 | − | 0.597995i | ||||
\(737\) | 17.7955 | + | 12.9292i | 0.655505 | + | 0.476252i | ||||
\(738\) | −0.147043 | − | 0.106833i | −0.00541272 | − | 0.00393257i | ||||
\(739\) | 2.86135 | − | 2.07890i | 0.105257 | − | 0.0764734i | −0.533912 | − | 0.845540i | \(-0.679279\pi\) |
0.639169 | + | 0.769067i | \(0.279279\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 9.89908 | + | 7.19210i | 0.363652 | + | 0.264209i | ||||
\(742\) | −0.595518 | − | 1.83282i | −0.0218621 | − | 0.0672848i | ||||
\(743\) | −15.7201 | −0.576715 | −0.288358 | − | 0.957523i | \(-0.593109\pi\) | ||||
−0.288358 | + | 0.957523i | \(0.593109\pi\) | |||||||
\(744\) | −1.09524 | − | 3.37082i | −0.0401536 | − | 0.123580i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −2.32167 | + | 7.14536i | −0.0850023 | + | 0.261610i | ||||
\(747\) | 0.107316 | − | 0.330284i | 0.00392648 | − | 0.0120845i | ||||
\(748\) | −20.9253 | + | 15.2032i | −0.765106 | + | 0.555882i | ||||
\(749\) | 41.8320 | 1.52851 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −14.1856 | −0.517642 | −0.258821 | − | 0.965925i | \(-0.583334\pi\) | ||||
−0.258821 | + | 0.965925i | \(0.583334\pi\) | |||||||
\(752\) | −18.9433 | + | 13.7631i | −0.690790 | + | 0.501889i | ||||
\(753\) | −8.86604 | + | 27.2869i | −0.323097 | + | 0.994389i | ||||
\(754\) | 1.68620 | − | 5.18958i | 0.0614076 | − | 0.188993i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −10.5064 | − | 32.3355i | −0.382116 | − | 1.17603i | ||||
\(757\) | 12.7388 | 0.463000 | 0.231500 | − | 0.972835i | \(-0.425637\pi\) | ||||
0.231500 | + | 0.972835i | \(0.425637\pi\) | |||||||
\(758\) | −1.65842 | − | 5.10408i | −0.0602364 | − | 0.185389i | ||||
\(759\) | −56.1167 | − | 40.7712i | −2.03691 | − | 1.47990i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −26.0746 | + | 18.9443i | −0.945203 | + | 0.686730i | −0.949667 | − | 0.313260i | \(-0.898579\pi\) |
0.00446471 | + | 0.999990i | \(0.498579\pi\) | |||||||
\(762\) | −0.307398 | − | 0.223338i | −0.0111359 | − | 0.00809068i | ||||
\(763\) | 42.5262 | + | 30.8971i | 1.53955 | + | 1.11855i | ||||
\(764\) | −2.68258 | + | 1.94901i | −0.0970523 | + | 0.0705127i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 1.24376 | + | 0.903646i | 0.0449389 | + | 0.0326500i | ||||
\(767\) | 0.0241371 | + | 0.0742864i | 0.000871541 | + | 0.00268233i | ||||
\(768\) | −13.9387 | −0.502969 | ||||||||
\(769\) | −3.51312 | − | 10.8123i | −0.126686 | − | 0.389900i | 0.867518 | − | 0.497405i | \(-0.165714\pi\) |
−0.994205 | + | 0.107505i | \(0.965714\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −7.96020 | + | 24.4990i | −0.286680 | + | 0.882309i | ||||
\(772\) | 5.57630 | − | 17.1621i | 0.200695 | − | 0.617677i | ||||
\(773\) | −22.0048 | + | 15.9874i | −0.791457 | + | 0.575027i | −0.908396 | − | 0.418112i | \(-0.862692\pi\) |
0.116938 | + | 0.993139i | \(0.462692\pi\) | |||||||
\(774\) | 0.0436939 | 0.00157054 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −20.3562 | −0.730746 | ||||||||
\(777\) | −0.0638125 | + | 0.0463625i | −0.00228926 | + | 0.00166325i | ||||
\(778\) | −0.357303 | + | 1.09967i | −0.0128099 | + | 0.0394249i | ||||
\(779\) | −6.05809 | + | 18.6449i | −0.217054 | + | 0.668022i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −3.86041 | − | 11.8811i | −0.138136 | − | 0.425140i | ||||
\(782\) | −6.32760 | −0.226275 | ||||||||
\(783\) | 7.68654 | + | 23.6568i | 0.274695 | + | 0.845423i | ||||
\(784\) | −12.8837 | − | 9.36054i | −0.460131 | − | 0.334305i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −3.19712 | + | 2.32285i | −0.114038 | + | 0.0828532i | ||||
\(787\) | 20.8133 | + | 15.1217i | 0.741912 | + | 0.539031i | 0.893309 | − | 0.449442i | \(-0.148377\pi\) |
−0.151397 | + | 0.988473i | \(0.548377\pi\) | |||||||
\(788\) | 36.6325 | + | 26.6151i | 1.30498 | + | 0.948123i | ||||
\(789\) | 8.56507 | − | 6.22289i | 0.304925 | − | 0.221541i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −51.3986 | − | 37.3432i | −1.82752 | − | 1.32777i | ||||
\(792\) | 0.120685 | + | 0.371429i | 0.00428834 | + | 0.0131982i | ||||
\(793\) | −13.7947 | −0.489864 | ||||||||
\(794\) | 0.884889 | + | 2.72341i | 0.0314035 | + | 0.0966501i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −13.9404 | + | 42.9043i | −0.494106 | + | 1.52070i | ||||
\(797\) | 5.46074 | − | 16.8064i | 0.193429 | − | 0.595314i | −0.806562 | − | 0.591150i | \(-0.798674\pi\) |
0.999991 | − | 0.00416480i | \(-0.00132570\pi\) | |||||||
\(798\) | 3.14539 | − | 2.28526i | 0.111346 | − | 0.0808974i | ||||
\(799\) | 17.7682 | 0.628593 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0.350256 | 0.0123757 | ||||||||
\(802\) | 6.01858 | − | 4.37276i | 0.212524 | − | 0.154407i | ||||
\(803\) | −2.49840 | + | 7.68930i | −0.0881668 | + | 0.271349i | ||||
\(804\) | 4.13301 | − | 12.7201i | 0.145760 | − | 0.448603i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0.577463 | + | 1.77725i | 0.0203403 | + | 0.0626009i | ||||
\(807\) | −19.0497 | −0.670580 | ||||||||
\(808\) | 0.567715 | + | 1.74725i | 0.0199721 | + | 0.0614679i | ||||
\(809\) | 33.0545 | + | 24.0155i | 1.16213 | + | 0.844339i | 0.990046 | − | 0.140743i | \(-0.0449491\pi\) |
0.172087 | + | 0.985082i | \(0.444949\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −13.4470 | + | 9.76981i | −0.472188 | + | 0.343064i | −0.798293 | − | 0.602269i | \(-0.794263\pi\) |
0.326106 | + | 0.945333i | \(0.394263\pi\) | |||||||
\(812\) | 24.8733 | + | 18.0715i | 0.872881 | + | 0.634185i | ||||
\(813\) | −1.61188 | − | 1.17110i | −0.0565311 | − | 0.0410722i | ||||
\(814\) | 0.0189605 | − | 0.0137756i | 0.000664564 | − | 0.000482834i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 11.9655 | + | 8.69342i | 0.418875 | + | 0.304330i | ||||
\(817\) | −1.45637 | − | 4.48223i | −0.0509518 | − | 0.156814i | ||||
\(818\) | −9.16296 | −0.320375 | ||||||||
\(819\) | 0.214151 | + | 0.659090i | 0.00748306 | + | 0.0230305i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −13.5653 | + | 41.7498i | −0.473433 | + | 1.45708i | 0.374626 | + | 0.927176i | \(0.377771\pi\) |
−0.848059 | + | 0.529902i | \(0.822229\pi\) | |||||||
\(822\) | −1.89115 | + | 5.82035i | −0.0659613 | + | 0.203008i | ||||
\(823\) | −21.1932 | + | 15.3977i | −0.738748 | + | 0.536732i | −0.892319 | − | 0.451406i | \(-0.850923\pi\) |
0.153571 | + | 0.988138i | \(0.450923\pi\) | |||||||
\(824\) | 18.6565 | 0.649932 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0.0248189 | 0.000863561 | ||||||||
\(827\) | −18.1079 | + | 13.1562i | −0.629675 | + | 0.457486i | −0.856288 | − | 0.516499i | \(-0.827235\pi\) |
0.226613 | + | 0.973985i | \(0.427235\pi\) | |||||||
\(828\) | 0.254589 | − | 0.783544i | 0.00884758 | − | 0.0272300i | ||||
\(829\) | 0.259970 | − | 0.800106i | 0.00902914 | − | 0.0277888i | −0.946440 | − | 0.322878i | \(-0.895349\pi\) |
0.955470 | + | 0.295090i | \(0.0953495\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 1.15285 | + | 3.54812i | 0.0399920 | + | 0.123083i | ||||
\(832\) | 19.5437 | 0.677554 | ||||||||
\(833\) | 3.73431 | + | 11.4930i | 0.129386 | + | 0.398210i | ||||
\(834\) | −8.84700 | − | 6.42772i | −0.306346 | − | 0.222574i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 16.5725 | − | 12.0406i | 0.573172 | − | 0.416434i | ||||
\(837\) | −6.89164 | − | 5.00707i | −0.238210 | − | 0.173070i | ||||
\(838\) | 9.01162 | + | 6.54733i | 0.311301 | + | 0.226174i | ||||
\(839\) | −28.7628 | + | 20.8974i | −0.993003 | + | 0.721459i | −0.960577 | − | 0.278015i | \(-0.910323\pi\) |
−0.0324264 | + | 0.999474i | \(0.510323\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 5.26412 | + | 3.82461i | 0.181521 | + | 0.131883i | ||||
\(842\) | 3.24513 | + | 9.98748i | 0.111834 | + | 0.344191i | ||||
\(843\) | 41.3709 | 1.42489 | ||||||||
\(844\) | 9.00515 | + | 27.7150i | 0.309970 | + | 0.953989i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0.0403157 | − | 0.124079i | 0.00138608 | − | 0.00426592i | ||||
\(847\) | 18.5459 | − | 57.0785i | 0.637245 | − | 1.96124i | ||||
\(848\) | −4.69721 | + | 3.41273i | −0.161303 | + | 0.117193i | ||||
\(849\) | −27.8138 | −0.954567 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −0.101668 | −0.00348515 | ||||||||
\(852\) | −6.14526 | + | 4.46479i | −0.210533 | + | 0.152961i | ||||
\(853\) | −6.03838 | + | 18.5842i | −0.206750 | + | 0.636312i | 0.792887 | + | 0.609369i | \(0.208577\pi\) |
−0.999637 | + | 0.0269427i | \(0.991423\pi\) | |||||||
\(854\) | −1.35448 | + | 4.16868i | −0.0463495 | + | 0.142649i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 4.80256 | + | 14.7807i | 0.164148 | + | 0.505196i | ||||
\(857\) | −0.570622 | −0.0194921 | −0.00974604 | − | 0.999953i | \(-0.503102\pi\) | ||||
−0.00974604 | + | 0.999953i | \(0.503102\pi\) | |||||||
\(858\) | 3.25742 | + | 10.0253i | 0.111207 | + | 0.342259i | ||||
\(859\) | 16.2598 | + | 11.8135i | 0.554778 | + | 0.403070i | 0.829544 | − | 0.558441i | \(-0.188600\pi\) |
−0.274766 | + | 0.961511i | \(0.588600\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 45.9856 | − | 33.4105i | 1.56719 | − | 1.13863i | ||||
\(862\) | −4.69345 | − | 3.40999i | −0.159860 | − | 0.116145i | ||||
\(863\) | −11.2975 | − | 8.20815i | −0.384573 | − | 0.279409i | 0.378655 | − | 0.925538i | \(-0.376387\pi\) |
−0.763228 | + | 0.646129i | \(0.776387\pi\) | |||||||
\(864\) | 15.4688 | − | 11.2387i | 0.526258 | − | 0.382349i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0.810922 | + | 0.589170i | 0.0275563 | + | 0.0200208i | ||||
\(867\) | 5.54321 | + | 17.0602i | 0.188257 | + | 0.579396i | ||||
\(868\) | −10.5291 | −0.357381 | ||||||||
\(869\) | −0.704482 | − | 2.16817i | −0.0238979 | − | 0.0735503i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −4.48111 | + | 13.7914i | −0.151837 | + | 0.467305i | ||||
\(872\) | −6.03480 | + | 18.5732i | −0.204364 | + | 0.628968i | ||||
\(873\) | −0.744110 | + | 0.540628i | −0.0251843 | + | 0.0182975i | ||||
\(874\) | 5.01135 | 0.169511 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 4.91601 | 0.166096 | ||||||||
\(877\) | −18.9724 | + | 13.7843i | −0.640653 | + | 0.465462i | −0.860075 | − | 0.510168i | \(-0.829583\pi\) |
0.219421 | + | 0.975630i | \(0.429583\pi\) | |||||||
\(878\) | −1.48908 | + | 4.58293i | −0.0502541 | + | 0.154666i | ||||
\(879\) | −1.84961 | + | 5.69250i | −0.0623857 | + | 0.192003i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 13.7424 | + | 42.2948i | 0.462994 | + | 1.42495i | 0.861488 | + | 0.507777i | \(0.169533\pi\) |
−0.398495 | + | 0.917171i | \(0.630467\pi\) | |||||||
\(882\) | 0.0887311 | 0.00298773 | ||||||||
\(883\) | −0.234287 | − | 0.721061i | −0.00788439 | − | 0.0242656i | 0.947037 | − | 0.321125i | \(-0.104061\pi\) |
−0.954921 | + | 0.296859i | \(0.904061\pi\) | |||||||
\(884\) | −13.7951 | − | 10.0227i | −0.463978 | − | 0.337100i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −2.69255 | + | 1.95625i | −0.0904580 | + | 0.0657216i | ||||
\(887\) | −44.8758 | − | 32.6041i | −1.50678 | − | 1.09474i | −0.967581 | − | 0.252562i | \(-0.918727\pi\) |
−0.539200 | − | 0.842178i | \(-0.681273\pi\) | |||||||
\(888\) | −0.0237076 | − | 0.0172246i | −0.000795575 | − | 0.000578019i | ||||
\(889\) | −1.87789 | + | 1.36437i | −0.0629825 | + | 0.0457595i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −38.1301 | − | 27.7031i | −1.27741 | − | 0.928090i | ||||
\(892\) | 11.4523 | + | 35.2467i | 0.383453 | + | 1.18015i | ||||
\(893\) | −14.0721 | −0.470905 | ||||||||
\(894\) | −2.21607 | − | 6.82037i | −0.0741166 | − | 0.228107i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 9.63392 | − | 29.6502i | 0.321847 | − | 0.990542i | ||||
\(897\) | 14.1308 | − | 43.4903i | 0.471815 | − | 1.45210i | ||||
\(898\) | 5.00895 | − | 3.63922i | 0.167151 | − | 0.121442i | ||||
\(899\) | 7.70312 | 0.256914 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 4.40584 | 0.146780 | ||||||||
\(902\) | −13.6636 | + | 9.92719i | −0.454948 | + | 0.330539i | ||||
\(903\) | −4.22262 | + | 12.9959i | −0.140520 | + | 0.432476i | ||||
\(904\) | 7.29386 | − | 22.4482i | 0.242590 | − | 0.746616i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0.373458 | + | 1.14938i | 0.0124073 | + | 0.0381857i | ||||
\(907\) | 15.8193 | 0.525271 | 0.262636 | − | 0.964895i | \(-0.415408\pi\) | ||||
0.262636 | + | 0.964895i | \(0.415408\pi\) | |||||||
\(908\) | −0.785164 | − | 2.41649i | −0.0260566 | − | 0.0801939i | ||||
\(909\) | 0.0671565 | + | 0.0487920i | 0.00222744 | + | 0.00161833i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 6.49164 | − | 4.71646i | 0.215078 | − | 0.156263i | −0.475030 | − | 0.879969i | \(-0.657563\pi\) |
0.690108 | + | 0.723706i | \(0.257563\pi\) | |||||||
\(912\) | −9.47644 | − | 6.88504i | −0.313796 | − | 0.227986i | ||||
\(913\) | −26.1072 | − | 18.9680i | −0.864023 | − | 0.627750i | ||||
\(914\) | −8.04652 | + | 5.84614i | −0.266155 | + | 0.193373i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −34.2635 | − | 24.8939i | −1.13210 | − | 0.822518i | ||||
\(917\) | 7.46025 | + | 22.9603i | 0.246359 | + | 0.758215i | ||||
\(918\) | −4.38348 | −0.144676 | ||||||||
\(919\) | 7.05800 | + | 21.7223i | 0.232822 | + | 0.716552i | 0.997403 | + | 0.0720245i | \(0.0229460\pi\) |
−0.764581 | + | 0.644528i | \(0.777054\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −4.73198 | + | 14.5635i | −0.155924 | + | 0.479885i | ||||
\(922\) | −0.239274 | + | 0.736411i | −0.00788008 | + | 0.0242524i | ||||
\(923\) | 6.66284 | − | 4.84084i | 0.219310 | − | 0.159338i | ||||
\(924\) | −59.3939 | −1.95392 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −0.104881 | −0.00344661 | ||||||||
\(927\) | 0.681979 | − | 0.495487i | 0.0223991 | − | 0.0162739i | ||||
\(928\) | −5.34297 | + | 16.4440i | −0.175392 | + | 0.539800i | ||||
\(929\) | −12.2766 | + | 37.7834i | −0.402781 | + | 1.23963i | 0.519953 | + | 0.854195i | \(0.325950\pi\) |
−0.922734 | + | 0.385438i | \(0.874050\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −2.95751 | − | 9.10227i | −0.0969284 | − | 0.298315i | ||||
\(932\) | −34.7694 | −1.13891 | ||||||||
\(933\) | 14.3705 | + | 44.2279i | 0.470470 | + | 1.44796i | ||||
\(934\) | 3.38553 | + | 2.45973i | 0.110778 | + | 0.0804849i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −0.208295 | + | 0.151335i | −0.00680832 | + | 0.00494654i | ||||
\(937\) | −24.6238 | − | 17.8903i | −0.804426 | − | 0.584449i | 0.107784 | − | 0.994174i | \(-0.465625\pi\) |
−0.912209 | + | 0.409725i | \(0.865625\pi\) | |||||||
\(938\) | 3.72770 | + | 2.70833i | 0.121714 | + | 0.0884301i | ||||
\(939\) | −27.9044 | + | 20.2737i | −0.910624 | + | 0.661607i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −20.7203 | − | 15.0542i | −0.675461 | − | 0.490752i | 0.196387 | − | 0.980526i | \(-0.437079\pi\) |
−0.871849 | + | 0.489775i | \(0.837079\pi\) | |||||||
\(942\) | −2.72752 | − | 8.39444i | −0.0888674 | − | 0.273506i | ||||
\(943\) | 73.2659 | 2.38587 | ||||||||
\(944\) | −0.0231066 | − | 0.0711147i | −0.000752055 | − | 0.00231459i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 1.25466 | − | 3.86144i | 0.0407924 | − | 0.125546i | ||||
\(947\) | −17.9459 | + | 55.2318i | −0.583163 | + | 1.79479i | 0.0233616 | + | 0.999727i | \(0.492563\pi\) |
−0.606525 | + | 0.795065i | \(0.707437\pi\) | |||||||
\(948\) | −1.12144 | + | 0.814777i | −0.0364228 | + | 0.0264627i | ||||
\(949\) | −5.33005 | −0.173021 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −16.6047 | −0.538446 | ||||||||
\(952\) | −9.01384 | + | 6.54894i | −0.292140 | + | 0.212252i | ||||
\(953\) | −14.0979 | + | 43.3888i | −0.456675 | + | 1.40550i | 0.412483 | + | 0.910965i | \(0.364661\pi\) |
−0.869158 | + | 0.494535i | \(0.835339\pi\) | |||||||
\(954\) | 0.00999675 | − | 0.0307668i | 0.000323657 | − | 0.000996113i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 7.02269 | + | 21.6136i | 0.227130 | + | 0.699034i | ||||
\(957\) | 43.4527 | 1.40463 | ||||||||
\(958\) | 2.05423 | + | 6.32226i | 0.0663691 | + | 0.204263i | ||||
\(959\) | 30.2461 | + | 21.9751i | 0.976698 | + | 0.709612i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 22.9453 | − | 16.6707i | 0.740171 | − | 0.537766i | ||||
\(962\) | 0.0124997 | + | 0.00908158i | 0.000403007 | + | 0.000292802i | ||||
\(963\) | 0.568107 | + | 0.412754i | 0.0183070 | + | 0.0133008i | ||||
\(964\) | 15.4958 | − | 11.2583i | 0.499085 | − | 0.362606i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −11.7550 | − | 8.54052i | −0.378212 | − | 0.274787i | ||||
\(967\) | −13.1162 | − | 40.3675i | −0.421788 | − | 1.29813i | −0.906036 | − | 0.423200i | \(-0.860907\pi\) |
0.484248 | − | 0.874931i | \(-0.339093\pi\) | |||||||
\(968\) | 22.2971 | 0.716655 | ||||||||
\(969\) | 2.74673 | + | 8.45356i | 0.0882376 | + | 0.271567i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −4.46009 | + | 13.7268i | −0.143131 | + | 0.440512i | −0.996766 | − | 0.0803596i | \(-0.974393\pi\) |
0.853635 | + | 0.520872i | \(0.174393\pi\) | |||||||
\(972\) | 0.349420 | − | 1.07541i | 0.0112077 | − | 0.0344936i | ||||
\(973\) | −54.0462 | + | 39.2668i | −1.73264 | + | 1.25884i | ||||
\(974\) | −5.06198 | −0.162196 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 13.2057 | 0.422705 | ||||||||
\(977\) | −13.4093 | + | 9.74244i | −0.429002 | + | 0.311688i | −0.781250 | − | 0.624219i | \(-0.785417\pi\) |
0.352248 | + | 0.935907i | \(0.385417\pi\) | |||||||
\(978\) | 1.28036 | − | 3.94054i | 0.0409414 | − | 0.126005i | ||||
\(979\) | 10.0575 | − | 30.9538i | 0.321439 | − | 0.989286i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0.272675 | + | 0.839207i | 0.00870584 | + | 0.0267938i | ||||
\(982\) | 8.98845 | 0.286833 | ||||||||
\(983\) | 10.2956 | + | 31.6867i | 0.328380 | + | 1.01065i | 0.969892 | + | 0.243537i | \(0.0783076\pi\) |
−0.641512 | + | 0.767113i | \(0.721692\pi\) | |||||||
\(984\) | 17.0846 | + | 12.4127i | 0.544636 | + | 0.395701i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 3.20685 | − | 2.32992i | 0.102127 | − | 0.0741996i | ||||
\(987\) | 33.0086 | + | 23.9822i | 1.05068 | + | 0.763361i | ||||
\(988\) | 10.9255 | + | 7.93781i | 0.347585 | + | 0.252535i | ||||
\(989\) | −14.2493 | + | 10.3527i | −0.453102 | + | 0.329198i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 19.8178 | + | 14.3985i | 0.629534 | + | 0.457383i | 0.856239 | − | 0.516580i | \(-0.172795\pi\) |
−0.226705 | + | 0.973963i | \(0.572795\pi\) | |||||||
\(992\) | −1.82978 | − | 5.63148i | −0.0580956 | − | 0.178800i | ||||
\(993\) | −33.7516 | −1.07107 | ||||||||
\(994\) | −0.808656 | − | 2.48879i | −0.0256490 | − | 0.0789396i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −6.06342 | + | 18.6613i | −0.192127 | + | 0.591305i | ||||
\(997\) | −18.4970 | + | 56.9279i | −0.585806 | + | 1.80292i | 0.0102041 | + | 0.999948i | \(0.496752\pi\) |
−0.596010 | + | 0.802977i | \(0.703248\pi\) | |||||||
\(998\) | 1.29806 | − | 0.943097i | 0.0410894 | − | 0.0298532i | ||||
\(999\) | −0.0704313 | −0.00222835 |
(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 | 625.2.d.n.251.3 | 16 | ||
5.2 | odd | 4 | 625.2.e.k.374.5 | 32 | |||
5.3 | odd | 4 | 625.2.e.k.374.4 | 32 | |||
5.4 | even | 2 | 625.2.d.p.251.2 | 16 | |||
25.2 | odd | 20 | 625.2.e.j.499.5 | 32 | |||
25.3 | odd | 20 | 625.2.b.d.624.9 | 16 | |||
25.4 | even | 10 | 625.2.a.e.1.6 | ✓ | 8 | ||
25.6 | even | 5 | 625.2.d.m.501.2 | 16 | |||
25.8 | odd | 20 | 625.2.e.j.124.5 | 32 | |||
25.9 | even | 10 | 625.2.d.p.376.2 | 16 | |||
25.11 | even | 5 | 625.2.d.m.126.2 | 16 | |||
25.12 | odd | 20 | 625.2.e.k.249.4 | 32 | |||
25.13 | odd | 20 | 625.2.e.k.249.5 | 32 | |||
25.14 | even | 10 | 625.2.d.q.126.3 | 16 | |||
25.16 | even | 5 | inner | 625.2.d.n.376.3 | 16 | ||
25.17 | odd | 20 | 625.2.e.j.124.4 | 32 | |||
25.19 | even | 10 | 625.2.d.q.501.3 | 16 | |||
25.21 | even | 5 | 625.2.a.g.1.3 | yes | 8 | ||
25.22 | odd | 20 | 625.2.b.d.624.8 | 16 | |||
25.23 | odd | 20 | 625.2.e.j.499.4 | 32 | |||
75.29 | odd | 10 | 5625.2.a.be.1.3 | 8 | |||
75.71 | odd | 10 | 5625.2.a.s.1.6 | 8 | |||
100.71 | odd | 10 | 10000.2.a.be.1.7 | 8 | |||
100.79 | odd | 10 | 10000.2.a.bn.1.2 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
625.2.a.e.1.6 | ✓ | 8 | 25.4 | even | 10 | ||
625.2.a.g.1.3 | yes | 8 | 25.21 | even | 5 | ||
625.2.b.d.624.8 | 16 | 25.22 | odd | 20 | |||
625.2.b.d.624.9 | 16 | 25.3 | odd | 20 | |||
625.2.d.m.126.2 | 16 | 25.11 | even | 5 | |||
625.2.d.m.501.2 | 16 | 25.6 | even | 5 | |||
625.2.d.n.251.3 | 16 | 1.1 | even | 1 | trivial | ||
625.2.d.n.376.3 | 16 | 25.16 | even | 5 | inner | ||
625.2.d.p.251.2 | 16 | 5.4 | even | 2 | |||
625.2.d.p.376.2 | 16 | 25.9 | even | 10 | |||
625.2.d.q.126.3 | 16 | 25.14 | even | 10 | |||
625.2.d.q.501.3 | 16 | 25.19 | even | 10 | |||
625.2.e.j.124.4 | 32 | 25.17 | odd | 20 | |||
625.2.e.j.124.5 | 32 | 25.8 | odd | 20 | |||
625.2.e.j.499.4 | 32 | 25.23 | odd | 20 | |||
625.2.e.j.499.5 | 32 | 25.2 | odd | 20 | |||
625.2.e.k.249.4 | 32 | 25.12 | odd | 20 | |||
625.2.e.k.249.5 | 32 | 25.13 | odd | 20 | |||
625.2.e.k.374.4 | 32 | 5.3 | odd | 4 | |||
625.2.e.k.374.5 | 32 | 5.2 | odd | 4 | |||
5625.2.a.s.1.6 | 8 | 75.71 | odd | 10 | |||
5625.2.a.be.1.3 | 8 | 75.29 | odd | 10 | |||
10000.2.a.be.1.7 | 8 | 100.71 | odd | 10 | |||
10000.2.a.bn.1.2 | 8 | 100.79 | odd | 10 |