Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [363,3,Mod(245,363)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(363, base_ring=CyclotomicField(10))
chi = DirichletCharacter(H, H._module([5, 8]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("363.245");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 363 = 3 \cdot 11^{2} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 363.h (of order \(10\), 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: | \(9.89103359628\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{10})\) |
Coefficient field: | 16.0.23612624896000000000000.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: |
\( x^{16} - 2 x^{15} - 5 x^{14} + 20 x^{13} + 19 x^{12} + 88 x^{11} - 497 x^{10} + 10 x^{9} + 3711 x^{8} + \cdots + 16 \)
|
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2^{16} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{10}]$ |
Embedding invariants
Embedding label | 269.1 | ||
Root | \(-0.241376 + 0.447303i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 363.269 |
Dual form | 363.3.h.k.251.1 |
$q$-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 \(\left(\mathbb{Z}/363\mathbb{Z}\right)^\times\).
\(n\) | \(122\) | \(244\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{2}{5}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.51626 | + | 0.817582i | −1.25813 | + | 0.408791i | −0.860828 | − | 0.508897i | \(-0.830053\pi\) |
−0.397302 | + | 0.917688i | \(0.630053\pi\) | |||||||
\(3\) | −0.853491 | + | 2.87603i | −0.284497 | + | 0.958677i | ||||
\(4\) | 2.42705 | − | 1.76336i | 0.606763 | − | 0.440839i | ||||
\(5\) | −2.68999 | − | 0.874032i | −0.537999 | − | 0.174806i | 0.0273993 | − | 0.999625i | \(-0.491277\pi\) |
−0.565398 | + | 0.824818i | \(0.691277\pi\) | |||||||
\(6\) | −0.203788 | − | 7.93464i | −0.0339646 | − | 1.32244i | ||||
\(7\) | 6.05413 | − | 4.39858i | 0.864876 | − | 0.628369i | −0.0643314 | − | 0.997929i | \(-0.520491\pi\) |
0.929207 | + | 0.369560i | \(0.120491\pi\) | |||||||
\(8\) | 1.55513 | − | 2.14046i | 0.194392 | − | 0.267557i | ||||
\(9\) | −7.54311 | − | 4.90933i | −0.838123 | − | 0.545481i | ||||
\(10\) | 7.48331 | 0.748331 | ||||||||
\(11\) | 0 | 0 | ||||||||
\(12\) | 3.00000 | + | 8.48528i | 0.250000 | + | 0.707107i | ||||
\(13\) | 6.93741 | + | 21.3512i | 0.533647 | + | 1.64240i | 0.746554 | + | 0.665325i | \(0.231707\pi\) |
−0.212907 | + | 0.977073i | \(0.568293\pi\) | |||||||
\(14\) | −11.6376 | + | 16.0177i | −0.831254 | + | 1.14412i | ||||
\(15\) | 4.80963 | − | 6.99053i | 0.320642 | − | 0.466035i | ||||
\(16\) | −5.87132 | + | 18.0701i | −0.366958 | + | 1.12938i | ||||
\(17\) | 20.1301 | + | 6.54066i | 1.18412 | + | 0.384745i | 0.833896 | − | 0.551921i | \(-0.186105\pi\) |
0.350225 | + | 0.936665i | \(0.386105\pi\) | |||||||
\(18\) | 22.9942 | + | 6.18604i | 1.27746 | + | 0.343669i | ||||
\(19\) | −12.1083 | − | 8.79716i | −0.637277 | − | 0.463009i | 0.221637 | − | 0.975129i | \(-0.428860\pi\) |
−0.858914 | + | 0.512121i | \(0.828860\pi\) | |||||||
\(20\) | −8.06998 | + | 2.62210i | −0.403499 | + | 0.131105i | ||||
\(21\) | 7.48331 | + | 21.1660i | 0.356348 | + | 1.00791i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 31.1127i | 1.35273i | 0.736568 | + | 0.676363i | \(0.236445\pi\) | ||||
−0.736568 | + | 0.676363i | \(0.763555\pi\) | |||||||
\(24\) | 4.82873 | + | 6.29947i | 0.201197 | + | 0.262478i | ||||
\(25\) | −13.7533 | − | 9.99235i | −0.550132 | − | 0.399694i | ||||
\(26\) | −34.9127 | − | 48.0532i | −1.34279 | − | 1.84820i | ||||
\(27\) | 20.5574 | − | 17.5041i | 0.761384 | − | 0.648301i | ||||
\(28\) | 6.93741 | − | 21.3512i | 0.247765 | − | 0.762542i | ||||
\(29\) | −12.4411 | − | 17.1237i | −0.429002 | − | 0.590471i | 0.538722 | − | 0.842484i | \(-0.318907\pi\) |
−0.967724 | + | 0.252013i | \(0.918907\pi\) | |||||||
\(30\) | −6.38694 | + | 21.5222i | −0.212898 | + | 0.717408i | ||||
\(31\) | 9.27051 | + | 28.5317i | 0.299049 | + | 0.920377i | 0.981831 | + | 0.189756i | \(0.0607696\pi\) |
−0.682783 | + | 0.730622i | \(0.739230\pi\) | |||||||
\(32\) | − | 39.6863i | − | 1.24020i | ||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −56.0000 | −1.64706 | ||||||||
\(35\) | −20.1301 | + | 6.54066i | −0.575145 | + | 0.186876i | ||||
\(36\) | −26.9644 | + | 1.38598i | −0.749011 | + | 0.0384995i | ||||
\(37\) | 8.09017 | − | 5.87785i | 0.218653 | − | 0.158861i | −0.473067 | − | 0.881026i | \(-0.656853\pi\) |
0.691720 | + | 0.722166i | \(0.256853\pi\) | |||||||
\(38\) | 37.6599 | + | 12.2364i | 0.991050 | + | 0.322012i | ||||
\(39\) | −67.3276 | + | 1.72920i | −1.72635 | + | 0.0443383i | ||||
\(40\) | −6.05413 | + | 4.39858i | −0.151353 | + | 0.109965i | ||||
\(41\) | 24.8821 | − | 34.2473i | 0.606881 | − | 0.835301i | −0.389435 | − | 0.921054i | \(-0.627330\pi\) |
0.996316 | + | 0.0857534i | \(0.0273297\pi\) | |||||||
\(42\) | −36.1349 | − | 47.1409i | −0.860355 | − | 1.12240i | ||||
\(43\) | −14.9666 | −0.348061 | −0.174031 | − | 0.984740i | \(-0.555679\pi\) | ||||
−0.174031 | + | 0.984740i | \(0.555679\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 16.0000 | + | 19.7990i | 0.355556 | + | 0.439978i | ||||
\(46\) | −25.4372 | − | 78.2876i | −0.552982 | − | 1.70190i | ||||
\(47\) | −21.6126 | + | 29.7472i | −0.459843 | + | 0.632919i | −0.974476 | − | 0.224491i | \(-0.927928\pi\) |
0.514634 | + | 0.857410i | \(0.327928\pi\) | |||||||
\(48\) | −46.9590 | − | 32.3087i | −0.978312 | − | 0.673099i | ||||
\(49\) | 2.16312 | − | 6.65740i | 0.0441453 | − | 0.135865i | ||||
\(50\) | 42.7764 | + | 13.8989i | 0.855528 | + | 0.277978i | ||||
\(51\) | −35.9920 | + | 52.3123i | −0.705725 | + | 1.02573i | ||||
\(52\) | 54.4872 | + | 39.5872i | 1.04783 | + | 0.761293i | ||||
\(53\) | −40.3499 | + | 13.1105i | −0.761319 | + | 0.247368i | −0.663845 | − | 0.747870i | \(-0.731076\pi\) |
−0.0974744 | + | 0.995238i | \(0.531076\pi\) | |||||||
\(54\) | −37.4166 | + | 60.8523i | −0.692900 | + | 1.12689i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | − | 19.7990i | − | 0.353553i | ||||||
\(57\) | 35.6352 | − | 27.3154i | 0.625179 | − | 0.479218i | ||||
\(58\) | 45.3050 | + | 32.9160i | 0.781120 | + | 0.567517i | ||||
\(59\) | 19.9501 | + | 27.4589i | 0.338137 | + | 0.465406i | 0.943896 | − | 0.330242i | \(-0.107130\pi\) |
−0.605759 | + | 0.795648i | \(0.707130\pi\) | |||||||
\(60\) | −0.653574 | − | 25.4475i | −0.0108929 | − | 0.424124i | ||||
\(61\) | −30.0621 | + | 92.5217i | −0.492822 | + | 1.51675i | 0.327502 | + | 0.944850i | \(0.393793\pi\) |
−0.820324 | + | 0.571899i | \(0.806207\pi\) | |||||||
\(62\) | −46.6540 | − | 64.2137i | −0.752484 | − | 1.03571i | ||||
\(63\) | −67.2610 | + | 3.45725i | −1.06764 | + | 0.0548770i | ||||
\(64\) | 8.96149 | + | 27.5806i | 0.140023 | + | 0.430947i | ||||
\(65\) | − | 63.4980i | − | 0.976893i | ||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −42.0000 | −0.626866 | −0.313433 | − | 0.949610i | \(-0.601479\pi\) | ||||
−0.313433 | + | 0.949610i | \(0.601479\pi\) | |||||||
\(68\) | 60.3902 | − | 19.6220i | 0.888091 | − | 0.288558i | ||||
\(69\) | −89.4811 | − | 26.5544i | −1.29683 | − | 0.384846i | ||||
\(70\) | 45.3050 | − | 32.9160i | 0.647214 | − | 0.470228i | ||||
\(71\) | −61.8699 | − | 20.1027i | −0.871407 | − | 0.283137i | −0.161022 | − | 0.986951i | \(-0.551479\pi\) |
−0.710385 | + | 0.703814i | \(0.751479\pi\) | |||||||
\(72\) | −22.2388 | + | 8.51104i | −0.308872 | + | 0.118209i | ||||
\(73\) | −60.5413 | + | 43.9858i | −0.829333 | + | 0.602545i | −0.919370 | − | 0.393393i | \(-0.871301\pi\) |
0.0900377 | + | 0.995938i | \(0.471301\pi\) | |||||||
\(74\) | −15.5513 | + | 21.4046i | −0.210153 | + | 0.289251i | ||||
\(75\) | 40.4766 | − | 31.0265i | 0.539688 | − | 0.413687i | ||||
\(76\) | −44.8999 | −0.590788 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 168.000 | − | 59.3970i | 2.15385 | − | 0.761500i | ||||
\(79\) | 6.93741 | + | 21.3512i | 0.0878154 | + | 0.270268i | 0.985315 | − | 0.170748i | \(-0.0546183\pi\) |
−0.897499 | + | 0.441016i | \(0.854618\pi\) | |||||||
\(80\) | 31.5876 | − | 43.4767i | 0.394846 | − | 0.543458i | ||||
\(81\) | 32.7969 | + | 74.0632i | 0.404900 | + | 0.914361i | ||||
\(82\) | −34.6099 | + | 106.518i | −0.422072 | + | 1.29900i | ||||
\(83\) | 20.1301 | + | 6.54066i | 0.242531 | + | 0.0788031i | 0.427760 | − | 0.903892i | \(-0.359303\pi\) |
−0.185229 | + | 0.982695i | \(0.559303\pi\) | |||||||
\(84\) | 55.4856 | + | 38.1752i | 0.660543 | + | 0.454467i | ||||
\(85\) | −48.4330 | − | 35.1887i | −0.569800 | − | 0.413984i | ||||
\(86\) | 37.6599 | − | 12.2364i | 0.437906 | − | 0.142284i | ||||
\(87\) | 59.8665 | − | 21.1660i | 0.688121 | − | 0.243287i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 62.2254i | 0.699162i | 0.936906 | + | 0.349581i | \(0.113676\pi\) | ||||
−0.936906 | + | 0.349581i | \(0.886324\pi\) | |||||||
\(90\) | −56.4474 | − | 36.7381i | −0.627194 | − | 0.408201i | ||||
\(91\) | 135.915 | + | 98.7479i | 1.49357 | + | 1.08514i | ||||
\(92\) | 54.8628 | + | 75.5121i | 0.596334 | + | 0.820784i | ||||
\(93\) | −89.9703 | + | 2.31073i | −0.967423 | + | 0.0248466i | ||||
\(94\) | 30.0621 | − | 92.5217i | 0.319810 | − | 0.984274i | ||||
\(95\) | 24.8821 | + | 34.2473i | 0.261917 | + | 0.360498i | ||||
\(96\) | 114.139 | + | 33.8719i | 1.18895 | + | 0.352832i | ||||
\(97\) | 22.8673 | + | 70.3782i | 0.235745 | + | 0.725548i | 0.997022 | + | 0.0771212i | \(0.0245728\pi\) |
−0.761277 | + | 0.648427i | \(0.775427\pi\) | |||||||
\(98\) | 18.5203i | 0.188982i | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −51.0000 | −0.510000 | ||||||||
\(101\) | −140.911 | + | 45.7846i | −1.39515 | + | 0.453313i | −0.907620 | − | 0.419792i | \(-0.862103\pi\) |
−0.487533 | + | 0.873105i | \(0.662103\pi\) | |||||||
\(102\) | 47.7955 | − | 161.058i | 0.468583 | − | 1.57900i | ||||
\(103\) | −27.5066 | + | 19.9847i | −0.267054 | + | 0.194026i | −0.713251 | − | 0.700909i | \(-0.752778\pi\) |
0.446197 | + | 0.894935i | \(0.352778\pi\) | |||||||
\(104\) | 56.4899 | + | 18.3547i | 0.543172 | + | 0.176487i | ||||
\(105\) | −1.63030 | − | 63.4771i | −0.0155267 | − | 0.604544i | ||||
\(106\) | 90.8119 | − | 65.9787i | 0.856716 | − | 0.622441i | ||||
\(107\) | 24.8821 | − | 34.2473i | 0.232543 | − | 0.320068i | −0.676759 | − | 0.736205i | \(-0.736616\pi\) |
0.909302 | + | 0.416136i | \(0.136616\pi\) | |||||||
\(108\) | 19.0277 | − | 78.7334i | 0.176183 | − | 0.729013i | ||||
\(109\) | 67.3498 | 0.617888 | 0.308944 | − | 0.951080i | \(-0.400024\pi\) | ||||
0.308944 | + | 0.951080i | \(0.400024\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 10.0000 | + | 28.2843i | 0.0900901 | + | 0.254813i | ||||
\(112\) | 43.9370 | + | 135.224i | 0.392294 | + | 1.20736i | ||||
\(113\) | 69.8253 | − | 96.1063i | 0.617923 | − | 0.850498i | −0.379276 | − | 0.925283i | \(-0.623827\pi\) |
0.997200 | + | 0.0747850i | \(0.0238271\pi\) | |||||||
\(114\) | −67.3348 | + | 97.8674i | −0.590656 | + | 0.858486i | ||||
\(115\) | 27.1935 | − | 83.6930i | 0.236465 | − | 0.727765i | ||||
\(116\) | −60.3902 | − | 19.6220i | −0.520605 | − | 0.169155i | ||||
\(117\) | 52.4903 | − | 195.112i | 0.448635 | − | 1.66763i | ||||
\(118\) | −72.6495 | − | 52.7830i | −0.615674 | − | 0.447313i | ||||
\(119\) | 150.640 | − | 48.9458i | 1.26588 | − | 0.411309i | ||||
\(120\) | −7.48331 | − | 21.1660i | −0.0623610 | − | 0.176383i | ||||
\(121\) | 0 | 0 | ||||||||
\(122\) | − | 257.387i | − | 2.10973i | ||||||
\(123\) | 77.2597 | + | 100.792i | 0.628128 | + | 0.819444i | ||||
\(124\) | 72.8115 | + | 52.9007i | 0.587190 | + | 0.426618i | ||||
\(125\) | 69.8253 | + | 96.1063i | 0.558603 | + | 0.768851i | ||||
\(126\) | 166.420 | − | 63.6908i | 1.32079 | − | 0.505482i | ||||
\(127\) | 20.8122 | − | 64.0535i | 0.163876 | − | 0.504358i | −0.835076 | − | 0.550135i | \(-0.814576\pi\) |
0.998952 | + | 0.0457767i | \(0.0145763\pi\) | |||||||
\(128\) | 48.2091 | + | 66.3542i | 0.376634 | + | 0.518392i | ||||
\(129\) | 12.7739 | − | 43.0445i | 0.0990223 | − | 0.333678i | ||||
\(130\) | 51.9149 | + | 159.777i | 0.399345 | + | 1.22906i | ||||
\(131\) | 232.826i | 1.77730i | 0.458587 | + | 0.888649i | \(0.348356\pi\) | ||||
−0.458587 | + | 0.888649i | \(0.651644\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −112.000 | −0.842105 | ||||||||
\(134\) | 105.683 | − | 34.3384i | 0.788678 | − | 0.256257i | ||||
\(135\) | −70.5984 | + | 29.1182i | −0.522951 | + | 0.215691i | ||||
\(136\) | 45.3050 | − | 32.9160i | 0.333125 | − | 0.242029i | ||||
\(137\) | −150.640 | − | 48.9458i | −1.09956 | − | 0.357269i | −0.297626 | − | 0.954682i | \(-0.596195\pi\) |
−0.801933 | + | 0.597414i | \(0.796195\pi\) | |||||||
\(138\) | 246.868 | − | 6.34038i | 1.78890 | − | 0.0459448i | ||||
\(139\) | 72.6495 | − | 52.7830i | 0.522659 | − | 0.379734i | −0.294946 | − | 0.955514i | \(-0.595302\pi\) |
0.817604 | + | 0.575780i | \(0.195302\pi\) | |||||||
\(140\) | −37.3232 | + | 51.3710i | −0.266594 | + | 0.366936i | ||||
\(141\) | −67.1077 | − | 87.5475i | −0.475941 | − | 0.620904i | ||||
\(142\) | 172.116 | 1.21209 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 133.000 | − | 107.480i | 0.923611 | − | 0.746390i | ||||
\(145\) | 18.4998 | + | 56.9364i | 0.127585 | + | 0.392665i | ||||
\(146\) | 116.376 | − | 160.177i | 0.797093 | − | 1.09710i | ||||
\(147\) | 17.3007 | + | 11.9032i | 0.117692 | + | 0.0809743i | ||||
\(148\) | 9.27051 | − | 28.5317i | 0.0626386 | − | 0.192782i | ||||
\(149\) | 20.1301 | + | 6.54066i | 0.135101 | + | 0.0438970i | 0.375787 | − | 0.926706i | \(-0.377372\pi\) |
−0.240686 | + | 0.970603i | \(0.577372\pi\) | |||||||
\(150\) | −76.4829 | + | 111.164i | −0.509886 | + | 0.741091i | ||||
\(151\) | 54.4872 | + | 39.5872i | 0.360842 | + | 0.262167i | 0.753403 | − | 0.657559i | \(-0.228411\pi\) |
−0.392561 | + | 0.919726i | \(0.628411\pi\) | |||||||
\(152\) | −37.6599 | + | 12.2364i | −0.247763 | + | 0.0805030i | ||||
\(153\) | −119.733 | − | 148.162i | −0.782569 | − | 0.968380i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | − | 84.8528i | − | 0.547438i | ||||||
\(156\) | −160.358 | + | 122.919i | −1.02794 | + | 0.787945i | ||||
\(157\) | −69.5755 | − | 50.5495i | −0.443156 | − | 0.321972i | 0.343732 | − | 0.939068i | \(-0.388309\pi\) |
−0.786888 | + | 0.617096i | \(0.788309\pi\) | |||||||
\(158\) | −34.9127 | − | 48.0532i | −0.220966 | − | 0.304134i | ||||
\(159\) | −3.26787 | − | 127.237i | −0.0205527 | − | 0.800234i | ||||
\(160\) | −34.6871 | + | 106.756i | −0.216794 | + | 0.667224i | ||||
\(161\) | 136.852 | + | 188.360i | 0.850011 | + | 1.16994i | ||||
\(162\) | −143.078 | − | 159.548i | −0.883200 | − | 0.984865i | ||||
\(163\) | −4.32624 | − | 13.3148i | −0.0265413 | − | 0.0816858i | 0.936908 | − | 0.349575i | \(-0.113674\pi\) |
−0.963450 | + | 0.267889i | \(0.913674\pi\) | |||||||
\(164\) | − | 126.996i | − | 0.774366i | ||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −56.0000 | −0.337349 | ||||||||
\(167\) | 80.5203 | − | 26.1626i | 0.482157 | − | 0.156662i | −0.0578456 | − | 0.998326i | \(-0.518423\pi\) |
0.540003 | + | 0.841663i | \(0.318423\pi\) | |||||||
\(168\) | 56.9425 | + | 16.8983i | 0.338943 | + | 0.100585i | ||||
\(169\) | −271.021 | + | 196.908i | −1.60367 | + | 1.16514i | ||||
\(170\) | 150.640 | + | 48.9458i | 0.886116 | + | 0.287916i | ||||
\(171\) | 48.1457 | + | 125.801i | 0.281554 | + | 0.735681i | ||||
\(172\) | −36.3248 | + | 26.3915i | −0.211191 | + | 0.153439i | ||||
\(173\) | −111.970 | + | 154.113i | −0.647223 | + | 0.890826i | −0.998975 | − | 0.0452670i | \(-0.985586\pi\) |
0.351752 | + | 0.936093i | \(0.385586\pi\) | |||||||
\(174\) | −133.335 | + | 102.205i | −0.766291 | + | 0.587385i | ||||
\(175\) | −127.216 | −0.726951 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −96.0000 | + | 33.9411i | −0.542373 | + | 0.191758i | ||||
\(178\) | −50.8744 | − | 156.575i | −0.285811 | − | 0.879636i | ||||
\(179\) | −186.201 | + | 256.284i | −1.04023 | + | 1.43175i | −0.143245 | + | 0.989687i | \(0.545754\pi\) |
−0.896983 | + | 0.442064i | \(0.854246\pi\) | |||||||
\(180\) | 73.7455 | + | 19.8395i | 0.409697 | + | 0.110219i | ||||
\(181\) | −80.9625 | + | 249.177i | −0.447306 | + | 1.37667i | 0.432628 | + | 0.901572i | \(0.357586\pi\) |
−0.879935 | + | 0.475095i | \(0.842414\pi\) | |||||||
\(182\) | −422.732 | − | 137.354i | −2.32270 | − | 0.754691i | ||||
\(183\) | −240.438 | − | 165.426i | −1.31387 | − | 0.903967i | ||||
\(184\) | 66.5954 | + | 48.3844i | 0.361932 | + | 0.262959i | ||||
\(185\) | −26.8999 | + | 8.74032i | −0.145405 | + | 0.0472450i | ||||
\(186\) | 224.499 | − | 79.3725i | 1.20699 | − | 0.426734i | ||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 110.309i | 0.586748i | ||||||||
\(189\) | 47.4635 | − | 196.396i | 0.251130 | − | 1.03913i | ||||
\(190\) | −90.6099 | − | 65.8319i | −0.476894 | − | 0.346484i | ||||
\(191\) | −34.9127 | − | 48.0532i | −0.182789 | − | 0.251587i | 0.707783 | − | 0.706430i | \(-0.249695\pi\) |
−0.890572 | + | 0.454843i | \(0.849695\pi\) | |||||||
\(192\) | −86.9713 | + | 2.23371i | −0.452976 | + | 0.0116339i | ||||
\(193\) | 46.2494 | − | 142.341i | 0.239634 | − | 0.737519i | −0.756838 | − | 0.653602i | \(-0.773257\pi\) |
0.996473 | − | 0.0839167i | \(-0.0267430\pi\) | |||||||
\(194\) | −115.080 | − | 158.394i | −0.593195 | − | 0.816463i | ||||
\(195\) | 182.622 | + | 54.1950i | 0.936525 | + | 0.277923i | ||||
\(196\) | −6.48936 | − | 19.9722i | −0.0331090 | − | 0.101899i | ||||
\(197\) | 232.826i | 1.18186i | 0.806723 | + | 0.590929i | \(0.201239\pi\) | ||||
−0.806723 | + | 0.590929i | \(0.798761\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 222.000 | 1.11558 | 0.557789 | − | 0.829983i | \(-0.311650\pi\) | ||||
0.557789 | + | 0.829983i | \(0.311650\pi\) | |||||||
\(200\) | −42.7764 | + | 13.8989i | −0.213882 | + | 0.0694945i | ||||
\(201\) | 35.8466 | − | 120.793i | 0.178341 | − | 0.600962i | ||||
\(202\) | 317.135 | − | 230.412i | 1.56997 | − | 1.14065i | ||||
\(203\) | −150.640 | − | 48.9458i | −0.742067 | − | 0.241112i | ||||
\(204\) | 4.89090 | + | 190.431i | 0.0239750 | + | 0.933487i | ||||
\(205\) | −96.8661 | + | 70.3773i | −0.472517 | + | 0.343304i | ||||
\(206\) | 52.8745 | − | 72.7756i | 0.256673 | − | 0.353279i | ||||
\(207\) | 152.743 | − | 234.686i | 0.737887 | − | 1.13375i | ||||
\(208\) | −426.549 | −2.05072 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 56.0000 | + | 158.392i | 0.266667 | + | 0.754247i | ||||
\(211\) | −120.249 | − | 370.087i | −0.569898 | − | 1.75397i | −0.652929 | − | 0.757419i | \(-0.726460\pi\) |
0.0830307 | − | 0.996547i | \(-0.473540\pi\) | |||||||
\(212\) | −74.8128 | + | 102.971i | −0.352891 | + | 0.485713i | ||||
\(213\) | 110.621 | − | 160.782i | 0.519350 | − | 0.754846i | ||||
\(214\) | −34.6099 | + | 106.518i | −0.161729 | + | 0.497749i | ||||
\(215\) | 40.2601 | + | 13.0813i | 0.187256 | + | 0.0608433i | ||||
\(216\) | −5.49743 | − | 71.2234i | −0.0254511 | − | 0.329738i | ||||
\(217\) | 181.624 | + | 131.957i | 0.836976 | + | 0.608099i | ||||
\(218\) | −169.470 | + | 55.0640i | −0.777384 | + | 0.252587i | ||||
\(219\) | −74.8331 | − | 211.660i | −0.341704 | − | 0.966484i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 475.176i | 2.15012i | ||||||||
\(222\) | −48.2873 | − | 62.9947i | −0.217510 | − | 0.283760i | ||||
\(223\) | 37.2148 | + | 27.0381i | 0.166882 | + | 0.121247i | 0.668092 | − | 0.744079i | \(-0.267111\pi\) |
−0.501209 | + | 0.865326i | \(0.667111\pi\) | |||||||
\(224\) | −174.563 | − | 240.266i | −0.779301 | − | 1.07262i | ||||
\(225\) | 54.6868 | + | 142.893i | 0.243052 | + | 0.635079i | ||||
\(226\) | −97.1238 | + | 298.916i | −0.429751 | + | 1.32264i | ||||
\(227\) | 124.411 | + | 171.237i | 0.548065 | + | 0.754346i | 0.989748 | − | 0.142825i | \(-0.0456185\pi\) |
−0.441683 | + | 0.897171i | \(0.645619\pi\) | |||||||
\(228\) | 38.3216 | − | 129.133i | 0.168077 | − | 0.566375i | ||||
\(229\) | 36.4640 | + | 112.225i | 0.159231 | + | 0.490064i | 0.998565 | − | 0.0535527i | \(-0.0170545\pi\) |
−0.839334 | + | 0.543617i | \(0.817055\pi\) | |||||||
\(230\) | 232.826i | 1.01229i | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −56.0000 | −0.241379 | ||||||||
\(233\) | 80.5203 | − | 26.1626i | 0.345581 | − | 0.112286i | −0.131084 | − | 0.991371i | \(-0.541846\pi\) |
0.476664 | + | 0.879085i | \(0.341846\pi\) | |||||||
\(234\) | 27.4411 | + | 533.868i | 0.117270 | + | 2.28149i | ||||
\(235\) | 84.1378 | − | 61.1297i | 0.358033 | − | 0.260126i | ||||
\(236\) | 96.8398 | + | 31.4652i | 0.410338 | + | 0.133327i | ||||
\(237\) | −67.3276 | + | 1.72920i | −0.284083 | + | 0.00729618i | ||||
\(238\) | −339.031 | + | 246.321i | −1.42450 | + | 1.03496i | ||||
\(239\) | 24.8821 | − | 34.2473i | 0.104109 | − | 0.143294i | −0.753784 | − | 0.657123i | \(-0.771773\pi\) |
0.857893 | + | 0.513829i | \(0.171773\pi\) | |||||||
\(240\) | 98.0805 | + | 127.954i | 0.408669 | + | 0.533142i | ||||
\(241\) | 149.666 | 0.621022 | 0.310511 | − | 0.950570i | \(-0.399500\pi\) | ||||
0.310511 | + | 0.950570i | \(0.399500\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −241.000 | + | 31.1127i | −0.991770 | + | 0.128036i | ||||
\(244\) | 90.1864 | + | 277.565i | 0.369616 | + | 1.13756i | ||||
\(245\) | −11.6376 | + | 16.0177i | −0.0475002 | + | 0.0653784i | ||||
\(246\) | −276.811 | − | 190.452i | −1.12525 | − | 0.774193i | ||||
\(247\) | 103.830 | − | 319.555i | 0.420363 | − | 1.29374i | ||||
\(248\) | 75.4878 | + | 24.5275i | 0.304386 | + | 0.0989011i | ||||
\(249\) | −35.9920 | + | 52.3123i | −0.144546 | + | 0.210090i | ||||
\(250\) | −254.273 | − | 184.740i | −1.01709 | − | 0.738962i | ||||
\(251\) | 48.4199 | − | 15.7326i | 0.192908 | − | 0.0626796i | −0.210970 | − | 0.977493i | \(-0.567662\pi\) |
0.403878 | + | 0.914813i | \(0.367662\pi\) | |||||||
\(252\) | −157.150 | + | 126.996i | −0.623610 | + | 0.503953i | ||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 178.191i | 0.701539i | ||||||||
\(255\) | 142.541 | − | 109.262i | 0.558984 | − | 0.428477i | ||||
\(256\) | −269.403 | − | 195.732i | −1.05235 | − | 0.764580i | ||||
\(257\) | 56.5253 | + | 77.8004i | 0.219943 | + | 0.302725i | 0.904703 | − | 0.426044i | \(-0.140093\pi\) |
−0.684760 | + | 0.728769i | \(0.740093\pi\) | |||||||
\(258\) | 3.05001 | + | 118.755i | 0.0118218 | + | 0.460290i | ||||
\(259\) | 23.1247 | − | 71.1706i | 0.0892846 | − | 0.274790i | ||||
\(260\) | −111.970 | − | 154.113i | −0.430652 | − | 0.592742i | ||||
\(261\) | 9.77858 | + | 190.243i | 0.0374658 | + | 0.728900i | ||||
\(262\) | −190.354 | − | 585.851i | −0.726544 | − | 2.23607i | ||||
\(263\) | − | 465.652i | − | 1.77054i | −0.465077 | − | 0.885270i | \(-0.653973\pi\) | ||
0.465077 | − | 0.885270i | \(-0.346027\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 120.000 | 0.452830 | ||||||||
\(266\) | 281.821 | − | 91.5692i | 1.05948 | − | 0.344245i | ||||
\(267\) | −178.962 | − | 53.1088i | −0.670270 | − | 0.198909i | ||||
\(268\) | −101.936 | + | 74.0609i | −0.380359 | + | 0.276347i | ||||
\(269\) | 352.389 | + | 114.498i | 1.31000 | + | 0.425644i | 0.879048 | − | 0.476733i | \(-0.158179\pi\) |
0.430949 | + | 0.902376i | \(0.358179\pi\) | |||||||
\(270\) | 153.837 | − | 130.989i | 0.569767 | − | 0.485144i | ||||
\(271\) | 272.436 | − | 197.936i | 1.00530 | − | 0.730392i | 0.0420805 | − | 0.999114i | \(-0.486601\pi\) |
0.963218 | + | 0.268722i | \(0.0866014\pi\) | |||||||
\(272\) | −236.380 | + | 325.350i | −0.869045 | + | 1.19614i | ||||
\(273\) | −400.004 | + | 306.615i | −1.46522 | + | 1.12313i | ||||
\(274\) | 419.066 | 1.52944 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −264.000 | + | 93.3381i | −0.956522 | + | 0.338182i | ||||
\(277\) | 6.93741 | + | 21.3512i | 0.0250448 | + | 0.0770800i | 0.962798 | − | 0.270223i | \(-0.0870975\pi\) |
−0.937753 | + | 0.347303i | \(0.887097\pi\) | |||||||
\(278\) | −139.651 | + | 192.213i | −0.502340 | + | 0.691412i | ||||
\(279\) | 70.1431 | − | 260.730i | 0.251409 | − | 0.934515i | ||||
\(280\) | −17.3050 | + | 53.2592i | −0.0618034 | + | 0.190211i | ||||
\(281\) | 20.1301 | + | 6.54066i | 0.0716373 | + | 0.0232764i | 0.344616 | − | 0.938744i | \(-0.388009\pi\) |
−0.272979 | + | 0.962020i | \(0.588009\pi\) | |||||||
\(282\) | 240.438 | + | 165.426i | 0.852615 | + | 0.586617i | ||||
\(283\) | −145.299 | − | 105.566i | −0.513424 | − | 0.373025i | 0.300697 | − | 0.953720i | \(-0.402781\pi\) |
−0.814121 | + | 0.580695i | \(0.802781\pi\) | |||||||
\(284\) | −185.610 | + | 60.3082i | −0.653555 | + | 0.212353i | ||||
\(285\) | −119.733 | + | 42.3320i | −0.420116 | + | 0.148533i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | − | 316.784i | − | 1.10378i | ||||||
\(288\) | −194.833 | + | 299.358i | −0.676504 | + | 1.03944i | ||||
\(289\) | 128.634 | + | 93.4579i | 0.445099 | + | 0.323384i | ||||
\(290\) | −93.1004 | − | 128.142i | −0.321036 | − | 0.441868i | ||||
\(291\) | −221.927 | + | 5.69981i | −0.762635 | + | 0.0195870i | ||||
\(292\) | −69.3741 | + | 213.512i | −0.237583 | + | 0.731204i | ||||
\(293\) | −12.4411 | − | 17.1237i | −0.0424610 | − | 0.0584425i | 0.787259 | − | 0.616623i | \(-0.211500\pi\) |
−0.829720 | + | 0.558180i | \(0.811500\pi\) | |||||||
\(294\) | −53.2648 | − | 15.8069i | −0.181173 | − | 0.0537649i | ||||
\(295\) | −29.6656 | − | 91.3014i | −0.100561 | − | 0.309496i | ||||
\(296\) | − | 26.4575i | − | 0.0893835i | ||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −56.0000 | −0.187919 | ||||||||
\(299\) | −664.292 | + | 215.842i | −2.22171 | + | 0.721879i | ||||
\(300\) | 43.5280 | − | 146.678i | 0.145093 | − | 0.488925i | ||||
\(301\) | −90.6099 | + | 65.8319i | −0.301030 | + | 0.218711i | ||||
\(302\) | −169.470 | − | 55.0640i | −0.561158 | − | 0.182331i | ||||
\(303\) | −11.4121 | − | 444.340i | −0.0376637 | − | 1.46647i | ||||
\(304\) | 230.057 | − | 167.146i | 0.756766 | − | 0.549823i | ||||
\(305\) | 161.734 | − | 222.608i | 0.530275 | − | 0.729861i | ||||
\(306\) | 422.414 | + | 274.923i | 1.38044 | + | 0.898440i | ||||
\(307\) | 149.666 | 0.487512 | 0.243756 | − | 0.969837i | \(-0.421620\pi\) | ||||
0.243756 | + | 0.969837i | \(0.421620\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −34.0000 | − | 96.1665i | −0.110032 | − | 0.311219i | ||||
\(310\) | 69.3741 | + | 213.512i | 0.223788 | + | 0.688747i | ||||
\(311\) | 14.9626 | − | 20.5942i | 0.0481112 | − | 0.0662193i | −0.784284 | − | 0.620402i | \(-0.786969\pi\) |
0.832395 | + | 0.554183i | \(0.186969\pi\) | |||||||
\(312\) | −101.002 | + | 146.801i | −0.323725 | + | 0.470516i | ||||
\(313\) | 122.989 | − | 378.520i | 0.392935 | − | 1.20933i | −0.537622 | − | 0.843186i | \(-0.680677\pi\) |
0.930558 | − | 0.366145i | \(-0.119323\pi\) | |||||||
\(314\) | 216.398 | + | 70.3121i | 0.689166 | + | 0.223924i | ||||
\(315\) | 183.954 | + | 49.4883i | 0.583980 | + | 0.157106i | ||||
\(316\) | 54.4872 | + | 39.5872i | 0.172428 | + | 0.125276i | ||||
\(317\) | −395.429 | + | 128.483i | −1.24741 | + | 0.405308i | −0.856992 | − | 0.515329i | \(-0.827670\pi\) |
−0.390418 | + | 0.920638i | \(0.627670\pi\) | |||||||
\(318\) | 112.250 | + | 317.490i | 0.352987 | + | 0.998397i | ||||
\(319\) | 0 | 0 | ||||||||
\(320\) | − | 82.0244i | − | 0.256326i | ||||||
\(321\) | 77.2597 | + | 100.792i | 0.240684 | + | 0.313992i | ||||
\(322\) | −498.354 | − | 362.076i | −1.54768 | − | 1.12446i | ||||
\(323\) | −186.201 | − | 256.284i | −0.576473 | − | 0.793447i | ||||
\(324\) | 210.200 | + | 121.923i | 0.648764 | + | 0.376304i | ||||
\(325\) | 117.936 | − | 362.970i | 0.362880 | − | 1.11683i | ||||
\(326\) | 21.7719 | + | 29.9664i | 0.0667849 | + | 0.0919215i | ||||
\(327\) | −57.4825 | + | 193.700i | −0.175787 | + | 0.592355i | ||||
\(328\) | −34.6099 | − | 106.518i | −0.105518 | − | 0.324751i | ||||
\(329\) | 275.158i | 0.836347i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 178.000 | 0.537764 | 0.268882 | − | 0.963173i | \(-0.413346\pi\) | ||||
0.268882 | + | 0.963173i | \(0.413346\pi\) | |||||||
\(332\) | 60.3902 | − | 19.6220i | 0.181898 | − | 0.0591023i | ||||
\(333\) | −89.8813 | + | 4.61994i | −0.269914 | + | 0.0138737i | ||||
\(334\) | −181.220 | + | 131.664i | −0.542574 | + | 0.394203i | ||||
\(335\) | 112.980 | + | 36.7093i | 0.337253 | + | 0.109580i | ||||
\(336\) | −426.408 | + | 10.9516i | −1.26907 | + | 0.0325940i | ||||
\(337\) | 205.840 | − | 149.552i | 0.610802 | − | 0.443774i | −0.238894 | − | 0.971046i | \(-0.576785\pi\) |
0.849697 | + | 0.527272i | \(0.176785\pi\) | |||||||
\(338\) | 520.970 | − | 717.053i | 1.54133 | − | 2.12146i | ||||
\(339\) | 216.809 | + | 282.846i | 0.639556 | + | 0.834353i | ||||
\(340\) | −179.600 | −0.528234 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | −224.000 | − | 277.186i | −0.654971 | − | 0.810485i | ||||
\(343\) | 97.1238 | + | 298.916i | 0.283160 | + | 0.871476i | ||||
\(344\) | −23.2751 | + | 32.0354i | −0.0676602 | + | 0.0931263i | ||||
\(345\) | 217.494 | + | 149.641i | 0.630418 | + | 0.433741i | ||||
\(346\) | 155.745 | − | 479.332i | 0.450129 | − | 1.38535i | ||||
\(347\) | 462.992 | + | 150.435i | 1.33427 | + | 0.433531i | 0.887372 | − | 0.461054i | \(-0.152529\pi\) |
0.446898 | + | 0.894585i | \(0.352529\pi\) | |||||||
\(348\) | 107.976 | − | 156.937i | 0.310276 | − | 0.450968i | ||||
\(349\) | 54.4872 | + | 39.5872i | 0.156124 | + | 0.113430i | 0.663104 | − | 0.748527i | \(-0.269239\pi\) |
−0.506981 | + | 0.861957i | \(0.669239\pi\) | |||||||
\(350\) | 320.109 | − | 104.010i | 0.914598 | − | 0.297171i | ||||
\(351\) | 516.349 | + | 317.490i | 1.47108 | + | 0.904530i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − | 124.451i | − | 0.352552i | −0.984341 | − | 0.176276i | \(-0.943595\pi\) | ||
0.984341 | − | 0.176276i | \(-0.0564051\pi\) | |||||||
\(354\) | 213.811 | − | 163.893i | 0.603986 | − | 0.462973i | ||||
\(355\) | 148.859 | + | 108.152i | 0.419321 | + | 0.304655i | ||||
\(356\) | 109.726 | + | 151.024i | 0.308218 | + | 0.424225i | ||||
\(357\) | 12.2001 | + | 475.019i | 0.0341738 | + | 1.33059i | ||||
\(358\) | 258.997 | − | 797.110i | 0.723455 | − | 2.22656i | ||||
\(359\) | −149.293 | − | 205.484i | −0.415857 | − | 0.572379i | 0.548777 | − | 0.835969i | \(-0.315093\pi\) |
−0.964635 | + | 0.263590i | \(0.915093\pi\) | |||||||
\(360\) | 67.2610 | − | 3.45725i | 0.186836 | − | 0.00960347i | ||||
\(361\) | −42.3353 | − | 130.295i | −0.117272 | − | 0.360927i | ||||
\(362\) | − | 693.187i | − | 1.91488i | ||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 504.000 | 1.38462 | ||||||||
\(365\) | 201.301 | − | 65.4066i | 0.551509 | − | 0.179196i | ||||
\(366\) | 740.253 | + | 219.677i | 2.02255 | + | 0.600211i | ||||
\(367\) | 114.880 | − | 83.4655i | 0.313026 | − | 0.227426i | −0.420168 | − | 0.907446i | \(-0.638029\pi\) |
0.733194 | + | 0.680020i | \(0.238029\pi\) | |||||||
\(368\) | −562.209 | − | 182.673i | −1.52774 | − | 0.496393i | ||||
\(369\) | −355.820 | + | 136.177i | −0.964282 | + | 0.369042i | ||||
\(370\) | 60.5413 | − | 43.9858i | 0.163625 | − | 0.118881i | ||||
\(371\) | −186.616 | + | 256.855i | −0.503008 | + | 0.692331i | ||||
\(372\) | −214.288 | + | 164.258i | −0.576043 | + | 0.441554i | ||||
\(373\) | −426.549 | −1.14356 | −0.571781 | − | 0.820406i | \(-0.693747\pi\) | ||||
−0.571781 | + | 0.820406i | \(0.693747\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −336.000 | + | 118.794i | −0.896000 | + | 0.316784i | ||||
\(376\) | 30.0621 | + | 92.5217i | 0.0799525 | + | 0.246068i | ||||
\(377\) | 279.301 | − | 384.425i | 0.740852 | − | 1.01970i | ||||
\(378\) | 41.1390 | + | 532.987i | 0.108833 | + | 1.41002i | ||||
\(379\) | −108.156 | + | 332.870i | −0.285372 | + | 0.878284i | 0.700915 | + | 0.713245i | \(0.252775\pi\) |
−0.986287 | + | 0.165040i | \(0.947225\pi\) | |||||||
\(380\) | 120.780 | + | 39.2439i | 0.317843 | + | 0.103274i | ||||
\(381\) | 166.457 | + | 114.526i | 0.436894 | + | 0.300592i | ||||
\(382\) | 127.137 | + | 92.3702i | 0.332819 | + | 0.241807i | ||||
\(383\) | 492.269 | − | 159.948i | 1.28530 | − | 0.417618i | 0.414854 | − | 0.909888i | \(-0.363832\pi\) |
0.870443 | + | 0.492269i | \(0.163832\pi\) | |||||||
\(384\) | −231.983 | + | 82.0183i | −0.604122 | + | 0.213589i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 395.980i | 1.02585i | ||||||||
\(387\) | 112.895 | + | 73.4761i | 0.291718 | + | 0.189861i | ||||
\(388\) | 179.602 | + | 130.488i | 0.462891 | + | 0.336310i | ||||
\(389\) | 257.689 | + | 354.678i | 0.662439 | + | 0.911769i | 0.999559 | − | 0.0296928i | \(-0.00945289\pi\) |
−0.337120 | + | 0.941462i | \(0.609453\pi\) | |||||||
\(390\) | −503.834 | + | 12.9401i | −1.29188 | + | 0.0331798i | ||||
\(391\) | −203.497 | + | 626.301i | −0.520454 | + | 1.60179i | ||||
\(392\) | −10.8859 | − | 14.9832i | −0.0277702 | − | 0.0382225i | ||||
\(393\) | −669.615 | − | 198.715i | −1.70386 | − | 0.505636i | ||||
\(394\) | −190.354 | − | 585.851i | −0.483133 | − | 1.48693i | ||||
\(395\) | − | 63.4980i | − | 0.160755i | ||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 442.000 | 1.11335 | 0.556675 | − | 0.830730i | \(-0.312077\pi\) | ||||
0.556675 | + | 0.830730i | \(0.312077\pi\) | |||||||
\(398\) | −558.610 | + | 181.503i | −1.40354 | + | 0.456038i | ||||
\(399\) | 95.5910 | − | 322.115i | 0.239576 | − | 0.807307i | ||||
\(400\) | 261.312 | − | 189.855i | 0.653281 | − | 0.474637i | ||||
\(401\) | 500.339 | + | 162.570i | 1.24773 | + | 0.405411i | 0.857106 | − | 0.515140i | \(-0.172260\pi\) |
0.390622 | + | 0.920551i | \(0.372260\pi\) | |||||||
\(402\) | 8.55908 | + | 333.255i | 0.0212912 | + | 0.828992i | ||||
\(403\) | −544.872 | + | 395.872i | −1.35204 | + | 0.982314i | ||||
\(404\) | −261.262 | + | 359.597i | −0.646689 | + | 0.890091i | ||||
\(405\) | −23.4899 | − | 227.895i | −0.0579998 | − | 0.562704i | ||||
\(406\) | 419.066 | 1.03218 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 56.0000 | + | 158.392i | 0.137255 | + | 0.388215i | ||||
\(409\) | −69.3741 | − | 213.512i | −0.169619 | − | 0.522033i | 0.829728 | − | 0.558168i | \(-0.188496\pi\) |
−0.999347 | + | 0.0361345i | \(0.988496\pi\) | |||||||
\(410\) | 186.201 | − | 256.284i | 0.454148 | − | 0.625082i | ||||
\(411\) | 269.339 | − | 391.470i | 0.655326 | − | 0.952481i | ||||
\(412\) | −31.5197 | + | 97.0078i | −0.0765042 | + | 0.235456i | ||||
\(413\) | 241.561 | + | 78.4879i | 0.584893 | + | 0.190043i | ||||
\(414\) | −192.464 | + | 715.411i | −0.464890 | + | 1.72805i | ||||
\(415\) | −48.4330 | − | 35.1887i | −0.116706 | − | 0.0847919i | ||||
\(416\) | 847.348 | − | 275.320i | 2.03689 | − | 0.661827i | ||||
\(417\) | 89.7998 | + | 253.992i | 0.215347 | + | 0.609094i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − | 684.479i | − | 1.63360i | −0.576919 | − | 0.816801i | \(-0.695745\pi\) | ||
0.576919 | − | 0.816801i | \(-0.304255\pi\) | |||||||
\(420\) | −115.890 | − | 151.187i | −0.275927 | − | 0.359970i | ||||
\(421\) | 215.199 | + | 156.351i | 0.511160 | + | 0.371380i | 0.813264 | − | 0.581895i | \(-0.197689\pi\) |
−0.302103 | + | 0.953275i | \(0.597689\pi\) | |||||||
\(422\) | 605.153 | + | 832.921i | 1.43401 | + | 1.97375i | ||||
\(423\) | 309.065 | − | 118.283i | 0.730650 | − | 0.279628i | ||||
\(424\) | −34.6871 | + | 106.756i | −0.0818091 | + | 0.251783i | ||||
\(425\) | −211.498 | − | 291.102i | −0.497643 | − | 0.684946i | ||||
\(426\) | −146.900 | + | 495.012i | −0.344835 | + | 1.16200i | ||||
\(427\) | 224.964 | + | 692.369i | 0.526849 | + | 1.62147i | ||||
\(428\) | − | 126.996i | − | 0.296720i | ||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −112.000 | −0.260465 | ||||||||
\(431\) | 523.382 | − | 170.057i | 1.21434 | − | 0.394564i | 0.369324 | − | 0.929301i | \(-0.379589\pi\) |
0.845019 | + | 0.534737i | \(0.179589\pi\) | |||||||
\(432\) | 195.602 | + | 474.245i | 0.452783 | + | 1.09779i | ||||
\(433\) | −597.055 | + | 433.786i | −1.37888 | + | 1.00181i | −0.381895 | + | 0.924206i | \(0.624728\pi\) |
−0.996984 | + | 0.0776084i | \(0.975272\pi\) | |||||||
\(434\) | −564.899 | − | 183.547i | −1.30161 | − | 0.422919i | ||||
\(435\) | −179.540 | + | 4.61119i | −0.412736 | + | 0.0106004i | ||||
\(436\) | 163.461 | − | 118.762i | 0.374912 | − | 0.272389i | ||||
\(437\) | 273.704 | − | 376.721i | 0.626324 | − | 0.862061i | ||||
\(438\) | 361.349 | + | 471.409i | 0.824998 | + | 1.07628i | ||||
\(439\) | −426.549 | −0.971638 | −0.485819 | − | 0.874060i | \(-0.661479\pi\) | ||||
−0.485819 | + | 0.874060i | \(0.661479\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −49.0000 | + | 39.5980i | −0.111111 | + | 0.0897913i | ||||
\(442\) | −388.495 | − | 1195.67i | −0.878948 | − | 2.70513i | ||||
\(443\) | 69.8253 | − | 96.1063i | 0.157619 | − | 0.216944i | −0.722902 | − | 0.690950i | \(-0.757192\pi\) |
0.880522 | + | 0.474006i | \(0.157192\pi\) | |||||||
\(444\) | 74.1457 | + | 51.0138i | 0.166995 | + | 0.114896i | ||||
\(445\) | 54.3870 | − | 167.386i | 0.122218 | − | 0.376148i | ||||
\(446\) | −115.748 | − | 37.6088i | −0.259524 | − | 0.0843246i | ||||
\(447\) | −35.9920 | + | 52.3123i | −0.0805189 | + | 0.117030i | ||||
\(448\) | 175.570 | + | 127.559i | 0.391897 | + | 0.284730i | ||||
\(449\) | −484.199 | + | 157.326i | −1.07839 | + | 0.350391i | −0.793751 | − | 0.608242i | \(-0.791875\pi\) |
−0.284643 | + | 0.958634i | \(0.591875\pi\) | |||||||
\(450\) | −254.433 | − | 314.844i | −0.565406 | − | 0.699654i | ||||
\(451\) | 0 | 0 | ||||||||
\(452\) | − | 356.382i | − | 0.788455i | ||||||
\(453\) | −160.358 | + | 122.919i | −0.353992 | + | 0.271345i | ||||
\(454\) | −453.050 | − | 329.160i | −0.997906 | − | 0.725021i | ||||
\(455\) | −279.301 | − | 384.425i | −0.613849 | − | 0.844891i | ||||
\(456\) | −3.05001 | − | 118.755i | −0.00668863 | − | 0.260427i | ||||
\(457\) | −208.122 | + | 640.535i | −0.455410 | + | 1.40161i | 0.415243 | + | 0.909711i | \(0.363697\pi\) |
−0.870653 | + | 0.491898i | \(0.836303\pi\) | |||||||
\(458\) | −183.506 | − | 252.574i | −0.400668 | − | 0.551472i | ||||
\(459\) | 528.310 | − | 217.901i | 1.15100 | − | 0.474730i | ||||
\(460\) | −81.5805 | − | 251.079i | −0.177349 | − | 0.545824i | ||||
\(461\) | − | 698.478i | − | 1.51514i | −0.652755 | − | 0.757569i | \(-0.726387\pi\) | ||
0.652755 | − | 0.757569i | \(-0.273613\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 882.000 | 1.90497 | 0.952484 | − | 0.304589i | \(-0.0985192\pi\) | ||||
0.952484 | + | 0.304589i | \(0.0985192\pi\) | |||||||
\(464\) | 382.471 | − | 124.272i | 0.824292 | − | 0.267829i | ||||
\(465\) | 244.039 | + | 72.4211i | 0.524816 | + | 0.155744i | ||||
\(466\) | −181.220 | + | 131.664i | −0.388884 | + | 0.282541i | ||||
\(467\) | −505.719 | − | 164.318i | −1.08291 | − | 0.351859i | −0.287407 | − | 0.957809i | \(-0.592793\pi\) |
−0.795503 | + | 0.605950i | \(0.792793\pi\) | |||||||
\(468\) | −216.656 | − | 566.106i | −0.462939 | − | 1.20963i | ||||
\(469\) | −254.273 | + | 184.740i | −0.542161 | + | 0.393903i | ||||
\(470\) | −161.734 | + | 222.608i | −0.344115 | + | 0.473633i | ||||
\(471\) | 204.764 | − | 156.958i | 0.434743 | − | 0.333243i | ||||
\(472\) | 89.7998 | 0.190254 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 168.000 | − | 59.3970i | 0.354430 | − | 0.125310i | ||||
\(475\) | 78.6240 | + | 241.980i | 0.165524 | + | 0.509431i | ||||
\(476\) | 279.301 | − | 384.425i | 0.586767 | − | 0.807616i | ||||
\(477\) | 368.727 | + | 99.1973i | 0.773013 | + | 0.207961i | ||||
\(478\) | −34.6099 | + | 106.518i | −0.0724057 | + | 0.222842i | ||||
\(479\) | −644.162 | − | 209.301i | −1.34481 | − | 0.436954i | −0.453864 | − | 0.891071i | \(-0.649955\pi\) |
−0.890942 | + | 0.454117i | \(0.849955\pi\) | |||||||
\(480\) | −277.428 | − | 190.876i | −0.577975 | − | 0.397659i | ||||
\(481\) | 181.624 | + | 131.957i | 0.377596 | + | 0.274340i | ||||
\(482\) | −376.599 | + | 122.364i | −0.781326 | + | 0.253868i | ||||
\(483\) | −658.532 | + | 232.826i | −1.36342 | + | 0.482042i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | − | 209.304i | − | 0.431554i | ||||||
\(486\) | 580.981 | − | 275.325i | 1.19543 | − | 0.566512i | ||||
\(487\) | −283.156 | − | 205.725i | −0.581429 | − | 0.422433i | 0.257810 | − | 0.966196i | \(-0.416999\pi\) |
−0.839239 | + | 0.543763i | \(0.816999\pi\) | |||||||
\(488\) | 151.288 | + | 208.230i | 0.310017 | + | 0.426702i | ||||
\(489\) | 41.9862 | − | 1.07834i | 0.0858613 | − | 0.00220520i | ||||
\(490\) | 16.1873 | − | 49.8194i | 0.0330353 | − | 0.101672i | ||||
\(491\) | −149.293 | − | 205.484i | −0.304059 | − | 0.418501i | 0.629458 | − | 0.777034i | \(-0.283277\pi\) |
−0.933517 | + | 0.358533i | \(0.883277\pi\) | |||||||
\(492\) | 365.245 | + | 108.390i | 0.742367 | + | 0.220305i | ||||
\(493\) | −138.440 | − | 426.073i | −0.280811 | − | 0.864246i | ||||
\(494\) | 888.972i | 1.79954i | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −570.000 | −1.14919 | ||||||||
\(497\) | −462.992 | + | 150.435i | −0.931573 | + | 0.302686i | ||||
\(498\) | 47.7955 | − | 161.058i | 0.0959749 | − | 0.323409i | ||||
\(499\) | 79.2837 | − | 57.6030i | 0.158885 | − | 0.115437i | −0.505502 | − | 0.862825i | \(-0.668693\pi\) |
0.664387 | + | 0.747389i | \(0.268693\pi\) | |||||||
\(500\) | 338.939 | + | 110.128i | 0.677879 | + | 0.220256i | ||||
\(501\) | 6.52120 | + | 253.908i | 0.0130164 | + | 0.506803i | ||||
\(502\) | −108.974 | + | 79.1745i | −0.217080 | + | 0.157718i | ||||
\(503\) | 298.586 | − | 410.968i | 0.593610 | − | 0.817034i | −0.401495 | − | 0.915861i | \(-0.631509\pi\) |
0.995105 | + | 0.0988277i | \(0.0315093\pi\) | |||||||
\(504\) | −97.1998 | + | 149.346i | −0.192857 | + | 0.296321i | ||||
\(505\) | 419.066 | 0.829833 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −335.000 | − | 947.523i | −0.660750 | − | 1.86888i | ||||
\(508\) | −62.4367 | − | 192.160i | −0.122907 | − | 0.378269i | ||||
\(509\) | −94.7629 | + | 130.430i | −0.186175 | + | 0.256248i | −0.891894 | − | 0.452244i | \(-0.850624\pi\) |
0.705720 | + | 0.708491i | \(0.250624\pi\) | |||||||
\(510\) | −269.339 | + | 391.470i | −0.528116 | + | 0.767587i | ||||
\(511\) | −173.050 | + | 532.592i | −0.338649 | + | 1.04225i | ||||
\(512\) | 525.898 | + | 170.875i | 1.02714 | + | 0.333740i | ||||
\(513\) | −402.901 | + | 31.0982i | −0.785381 | + | 0.0606202i | ||||
\(514\) | −205.840 | − | 149.552i | −0.400468 | − | 0.290957i | ||||
\(515\) | 91.4598 | − | 29.7171i | 0.177592 | − | 0.0577031i | ||||
\(516\) | −44.8999 | − | 126.996i | −0.0870153 | − | 0.246116i | ||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 197.990i | 0.382220i | ||||||||
\(519\) | −347.669 | − | 453.562i | −0.669882 | − | 0.873915i | ||||
\(520\) | −135.915 | − | 98.7479i | −0.261375 | − | 0.189900i | ||||
\(521\) | −89.7754 | − | 123.565i | −0.172314 | − | 0.237169i | 0.714122 | − | 0.700021i | \(-0.246826\pi\) |
−0.886436 | + | 0.462852i | \(0.846826\pi\) | |||||||
\(522\) | −180.145 | − | 470.706i | −0.345105 | − | 0.901735i | ||||
\(523\) | −4.62494 | + | 14.2341i | −0.00884310 | + | 0.0272163i | −0.955381 | − | 0.295377i | \(-0.904555\pi\) |
0.946538 | + | 0.322593i | \(0.104555\pi\) | |||||||
\(524\) | 410.555 | + | 565.081i | 0.783502 | + | 1.07840i | ||||
\(525\) | 108.578 | − | 365.878i | 0.206815 | − | 0.696911i | ||||
\(526\) | 380.709 | + | 1171.70i | 0.723781 | + | 2.22757i | ||||
\(527\) | 634.980i | 1.20490i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −439.000 | −0.829868 | ||||||||
\(530\) | −301.951 | + | 98.1099i | −0.569719 | + | 0.185113i | ||||
\(531\) | −15.6806 | − | 305.067i | −0.0295303 | − | 0.574515i | ||||
\(532\) | −271.830 | + | 197.496i | −0.510958 | + | 0.371233i | ||||
\(533\) | 903.838 | + | 293.675i | 1.69576 | + | 0.550985i | ||||
\(534\) | 493.736 | − | 12.6808i | 0.924599 | − | 0.0237467i | ||||
\(535\) | −96.8661 | + | 70.3773i | −0.181058 | + | 0.131546i | ||||
\(536\) | −65.3156 | + | 89.8992i | −0.121857 | + | 0.167722i | ||||
\(537\) | −578.159 | − | 754.255i | −1.07665 | − | 1.40457i | ||||
\(538\) | −980.314 | −1.82215 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −120.000 | + | 195.161i | −0.222222 | + | 0.361410i | ||||
\(541\) | 159.561 | + | 491.077i | 0.294936 | + | 0.907721i | 0.983243 | + | 0.182301i | \(0.0583544\pi\) |
−0.688307 | + | 0.725420i | \(0.741646\pi\) | |||||||
\(542\) | −523.690 | + | 720.797i | −0.966218 | + | 1.32988i | ||||
\(543\) | −647.539 | − | 445.521i | −1.19252 | − | 0.820480i | ||||
\(544\) | 259.574 | − | 798.887i | 0.477159 | − | 1.46854i | ||||
\(545\) | −181.171 | − | 58.8659i | −0.332423 | − | 0.108011i | ||||
\(546\) | 755.831 | − | 1098.56i | 1.38431 | − | 2.01201i | ||||
\(547\) | −544.872 | − | 395.872i | −0.996109 | − | 0.723716i | −0.0348585 | − | 0.999392i | \(-0.511098\pi\) |
−0.961250 | + | 0.275677i | \(0.911098\pi\) | |||||||
\(548\) | −451.919 | + | 146.837i | −0.824670 | + | 0.267951i | ||||
\(549\) | 680.982 | − | 550.316i | 1.24040 | − | 1.00240i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 316.784i | 0.574925i | ||||||||
\(552\) | −195.994 | + | 150.235i | −0.355061 | + | 0.272165i | ||||
\(553\) | 135.915 | + | 98.7479i | 0.245777 | + | 0.178568i | ||||
\(554\) | −34.9127 | − | 48.0532i | −0.0630192 | − | 0.0867386i | ||||
\(555\) | −2.17858 | − | 84.8248i | −0.00392537 | − | 0.152838i | ||||
\(556\) | 83.2490 | − | 256.214i | 0.149728 | − | 0.460817i | ||||
\(557\) | 261.262 | + | 359.597i | 0.469053 | + | 0.645596i | 0.976355 | − | 0.216172i | \(-0.0693573\pi\) |
−0.507302 | + | 0.861768i | \(0.669357\pi\) | |||||||
\(558\) | 36.6697 | + | 713.411i | 0.0657163 | + | 1.27851i | ||||
\(559\) | −103.830 | − | 319.555i | −0.185742 | − | 0.571655i | ||||
\(560\) | − | 402.154i | − | 0.718132i | ||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −56.0000 | −0.0996441 | ||||||||
\(563\) | 523.382 | − | 170.057i | 0.929630 | − | 0.302055i | 0.195219 | − | 0.980760i | \(-0.437458\pi\) |
0.734411 | + | 0.678704i | \(0.237458\pi\) | |||||||
\(564\) | −317.251 | − | 94.1474i | −0.562502 | − | 0.166928i | ||||
\(565\) | −271.830 | + | 197.496i | −0.481115 | + | 0.349550i | ||||
\(566\) | 451.919 | + | 146.837i | 0.798443 | + | 0.259430i | ||||
\(567\) | 524.330 | + | 304.128i | 0.924744 | + | 0.536382i | ||||
\(568\) | −139.245 | + | 101.167i | −0.245150 | + | 0.178112i | ||||
\(569\) | −659.377 | + | 907.554i | −1.15883 | + | 1.59500i | −0.443389 | + | 0.896329i | \(0.646224\pi\) |
−0.715445 | + | 0.698669i | \(0.753776\pi\) | |||||||
\(570\) | 266.669 | − | 204.410i | 0.467841 | − | 0.358614i | ||||
\(571\) | 808.198 | 1.41541 | 0.707704 | − | 0.706509i | \(-0.249731\pi\) | ||||
0.707704 | + | 0.706509i | \(0.249731\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 168.000 | − | 59.3970i | 0.293194 | − | 0.103660i | ||||
\(574\) | 258.997 | + | 797.110i | 0.451214 | + | 1.38869i | ||||
\(575\) | 310.889 | − | 427.902i | 0.540676 | − | 0.744177i | ||||
\(576\) | 67.8050 | − | 252.039i | 0.117717 | − | 0.437567i | ||||
\(577\) | 95.7953 | − | 294.828i | 0.166023 | − | 0.510966i | −0.833087 | − | 0.553142i | \(-0.813429\pi\) |
0.999110 | + | 0.0421754i | \(0.0134288\pi\) | |||||||
\(578\) | −400.085 | − | 129.996i | −0.692189 | − | 0.224906i | ||||
\(579\) | 369.904 | + | 254.502i | 0.638867 | + | 0.439554i | ||||
\(580\) | 145.299 | + | 105.566i | 0.250516 | + | 0.182010i | ||||
\(581\) | 150.640 | − | 48.9458i | 0.259277 | − | 0.0842441i | ||||
\(582\) | 553.765 | − | 195.786i | 0.951487 | − | 0.336401i | ||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 197.990i | 0.339024i | ||||||||
\(585\) | −311.733 | + | 478.972i | −0.532877 | + | 0.818756i | ||||
\(586\) | 45.3050 | + | 32.9160i | 0.0773122 | + | 0.0561706i | ||||
\(587\) | −565.253 | − | 778.004i | −0.962952 | − | 1.32539i | −0.945528 | − | 0.325541i | \(-0.894454\pi\) |
−0.0174238 | − | 0.999848i | \(-0.505546\pi\) | |||||||
\(588\) | 62.9792 | − | 1.61751i | 0.107108 | − | 0.00275087i | ||||
\(589\) | 138.748 | − | 427.023i | 0.235566 | − | 0.724997i | ||||
\(590\) | 149.293 | + | 205.484i | 0.253039 | + | 0.348278i | ||||
\(591\) | −669.615 | − | 198.715i | −1.13302 | − | 0.336235i | ||||
\(592\) | 58.7132 | + | 180.701i | 0.0991778 | + | 0.305238i | ||||
\(593\) | − | 232.826i | − | 0.392624i | −0.980541 | − | 0.196312i | \(-0.937103\pi\) | ||
0.980541 | − | 0.196312i | \(-0.0628966\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −448.000 | −0.752941 | ||||||||
\(596\) | 60.3902 | − | 19.6220i | 0.101326 | − | 0.0329228i | ||||
\(597\) | −189.475 | + | 638.479i | −0.317378 | + | 1.06948i | ||||
\(598\) | 1495.06 | − | 1086.23i | 2.50011 | − | 1.81643i | ||||
\(599\) | −831.208 | − | 270.076i | −1.38766 | − | 0.450878i | −0.482480 | − | 0.875907i | \(-0.660264\pi\) |
−0.905180 | + | 0.425029i | \(0.860264\pi\) | |||||||
\(600\) | −3.46439 | − | 134.889i | −0.00577398 | − | 0.224815i | ||||
\(601\) | 472.222 | − | 343.089i | 0.785727 | − | 0.570864i | −0.120965 | − | 0.992657i | \(-0.538599\pi\) |
0.906692 | + | 0.421793i | \(0.138599\pi\) | |||||||
\(602\) | 174.175 | − | 239.731i | 0.289327 | − | 0.398225i | ||||
\(603\) | 316.810 | + | 206.192i | 0.525391 | + | 0.341943i | ||||
\(604\) | 202.049 | 0.334519 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 392.000 | + | 1108.74i | 0.646865 | + | 1.82961i | ||||
\(607\) | 261.309 | + | 804.227i | 0.430493 | + | 1.32492i | 0.897635 | + | 0.440739i | \(0.145284\pi\) |
−0.467142 | + | 0.884182i | \(0.654716\pi\) | |||||||
\(608\) | −349.127 | + | 480.532i | −0.574221 | + | 0.790348i | ||||
\(609\) | 269.339 | − | 391.470i | 0.442265 | − | 0.642807i | ||||
\(610\) | −224.964 | + | 692.369i | −0.368794 | + | 1.13503i | ||||
\(611\) | −785.073 | − | 255.086i | −1.28490 | − | 0.417489i | ||||
\(612\) | −551.861 | − | 148.465i | −0.901733 | − | 0.242590i | ||||
\(613\) | −478.276 | − | 347.488i | −0.780222 | − | 0.566865i | 0.124824 | − | 0.992179i | \(-0.460164\pi\) |
−0.905046 | + | 0.425314i | \(0.860164\pi\) | |||||||
\(614\) | −376.599 | + | 122.364i | −0.613354 | + | 0.199291i | ||||
\(615\) | −119.733 | − | 338.656i | −0.194688 | − | 0.550660i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 435.578i | 0.705961i | 0.935631 | + | 0.352980i | \(0.114832\pi\) | ||||
−0.935631 | + | 0.352980i | \(0.885168\pi\) | |||||||
\(618\) | 164.177 | + | 214.182i | 0.265658 | + | 0.346573i | ||||
\(619\) | 677.956 | + | 492.564i | 1.09524 | + | 0.795742i | 0.980277 | − | 0.197628i | \(-0.0633237\pi\) |
0.114967 | + | 0.993369i | \(0.463324\pi\) | |||||||
\(620\) | −149.626 | − | 205.942i | −0.241332 | − | 0.332165i | ||||
\(621\) | 544.601 | + | 639.595i | 0.876974 | + | 1.02994i | ||||
\(622\) | −20.8122 | + | 64.0535i | −0.0334602 | + | 0.102980i | ||||
\(623\) | 273.704 | + | 376.721i | 0.439331 | + | 0.604688i | ||||
\(624\) | 364.056 | − | 1226.77i | 0.583422 | − | 1.96597i | ||||
\(625\) | 27.5025 | + | 84.6440i | 0.0440040 | + | 0.135430i | ||||
\(626\) | 1053.01i | 1.68212i | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −258.000 | −0.410828 | ||||||||
\(629\) | 201.301 | − | 65.4066i | 0.320033 | − | 0.103985i | ||||
\(630\) | −503.336 | + | 25.8717i | −0.798945 | + | 0.0410662i | ||||
\(631\) | −205.490 | + | 149.297i | −0.325658 | + | 0.236605i | −0.738586 | − | 0.674159i | \(-0.764506\pi\) |
0.412928 | + | 0.910764i | \(0.364506\pi\) | |||||||
\(632\) | 56.4899 | + | 18.3547i | 0.0893827 | + | 0.0290422i | ||||
\(633\) | 1167.01 | − | 29.9727i | 1.84362 | − | 0.0473503i | ||||
\(634\) | 889.957 | − | 646.592i | 1.40372 | − | 1.01986i | ||||
\(635\) | −111.970 | + | 154.113i | −0.176330 | + | 0.242698i | ||||
\(636\) | −232.296 | − | 303.049i | −0.365245 | − | 0.476492i | ||||
\(637\) | 157.150 | 0.246703 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 368.000 | + | 455.377i | 0.575900 | + | 0.712640i | ||||
\(640\) | −71.6866 | − | 220.629i | −0.112010 | − | 0.344732i | ||||
\(641\) | 69.8253 | − | 96.1063i | 0.108932 | − | 0.149932i | −0.751070 | − | 0.660222i | \(-0.770462\pi\) |
0.860002 | + | 0.510290i | \(0.170462\pi\) | |||||||
\(642\) | −276.811 | − | 190.452i | −0.431169 | − | 0.296654i | ||||
\(643\) | −135.349 | + | 416.563i | −0.210497 | + | 0.647843i | 0.788946 | + | 0.614463i | \(0.210627\pi\) |
−0.999443 | + | 0.0333799i | \(0.989373\pi\) | |||||||
\(644\) | 664.292 | + | 215.842i | 1.03151 | + | 0.335158i | ||||
\(645\) | −71.9839 | + | 104.625i | −0.111603 | + | 0.162209i | ||||
\(646\) | 678.062 | + | 492.641i | 1.04963 | + | 0.762602i | ||||
\(647\) | 314.729 | − | 102.262i | 0.486444 | − | 0.158055i | −0.0555189 | − | 0.998458i | \(-0.517681\pi\) |
0.541963 | + | 0.840402i | \(0.317681\pi\) | |||||||
\(648\) | 209.533 | + | 44.9778i | 0.323353 | + | 0.0694101i | ||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 1009.75i | 1.55346i | ||||||||
\(651\) | −534.528 | + | 409.731i | −0.821088 | + | 0.629388i | ||||
\(652\) | −33.9787 | − | 24.6870i | −0.0521146 | − | 0.0378635i | ||||
\(653\) | 367.414 | + | 505.702i | 0.562656 | + | 0.774429i | 0.991661 | − | 0.128873i | \(-0.0411359\pi\) |
−0.429005 | + | 0.903302i | \(0.641136\pi\) | |||||||
\(654\) | −13.7251 | − | 534.397i | −0.0209863 | − | 0.817120i | ||||
\(655\) | 203.497 | − | 626.301i | 0.310683 | − | 0.956185i | ||||
\(656\) | 472.761 | + | 650.699i | 0.720672 | + | 0.991919i | ||||
\(657\) | 672.610 | − | 34.5725i | 1.02376 | − | 0.0526218i | ||||
\(658\) | −224.964 | − | 692.369i | −0.341891 | − | 1.05223i | ||||
\(659\) | 465.652i | 0.706604i | 0.935509 | + | 0.353302i | \(0.114941\pi\) | ||||
−0.935509 | + | 0.353302i | \(0.885059\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −394.000 | −0.596067 | −0.298033 | − | 0.954555i | \(-0.596331\pi\) | ||||
−0.298033 | + | 0.954555i | \(0.596331\pi\) | |||||||
\(662\) | −447.894 | + | 145.530i | −0.676577 | + | 0.219833i | ||||
\(663\) | −1366.62 | − | 405.558i | −2.06127 | − | 0.611702i | ||||
\(664\) | 45.3050 | − | 32.9160i | 0.0682303 | − | 0.0495723i | ||||
\(665\) | 301.279 | + | 97.8916i | 0.453052 | + | 0.147205i | ||||
\(666\) | 222.388 | − | 85.1104i | 0.333915 | − | 0.127793i | ||||
\(667\) | 532.763 | − | 387.075i | 0.798746 | − | 0.580323i | ||||
\(668\) | 149.293 | − | 205.484i | 0.223492 | − | 0.307611i | ||||
\(669\) | −109.525 | + | 83.9541i | −0.163714 | + | 0.125492i | ||||
\(670\) | −314.299 | −0.469103 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 840.000 | − | 296.985i | 1.25000 | − | 0.441942i | ||||
\(673\) | −272.872 | − | 839.813i | −0.405456 | − | 1.24786i | −0.920514 | − | 0.390709i | \(-0.872230\pi\) |
0.515059 | − | 0.857155i | \(-0.327770\pi\) | |||||||
\(674\) | −395.677 | + | 544.602i | −0.587058 | + | 0.808016i | ||||
\(675\) | −457.639 | + | 35.3232i | −0.677983 | + | 0.0523306i | ||||
\(676\) | −310.562 | + | 955.812i | −0.459411 | + | 1.41392i | ||||
\(677\) | −865.593 | − | 281.248i | −1.27857 | − | 0.415433i | −0.410495 | − | 0.911863i | \(-0.634644\pi\) |
−0.868077 | + | 0.496430i | \(0.834644\pi\) | |||||||
\(678\) | −776.798 | − | 534.453i | −1.14572 | − | 0.788279i | ||||
\(679\) | 448.006 | + | 325.495i | 0.659802 | + | 0.479374i | ||||
\(680\) | −150.640 | + | 48.9458i | −0.221529 | + | 0.0719791i | ||||
\(681\) | −598.665 | + | 211.660i | −0.879097 | + | 0.310808i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − | 435.578i | − | 0.637742i | −0.947798 | − | 0.318871i | \(-0.896696\pi\) | ||
0.947798 | − | 0.318871i | \(-0.103304\pi\) | |||||||
\(684\) | 338.685 | + | 220.428i | 0.495153 | + | 0.322264i | ||||
\(685\) | 362.440 | + | 263.328i | 0.529109 | + | 0.384420i | ||||
\(686\) | −488.777 | − | 672.744i | −0.712503 | − | 0.980677i | ||||
\(687\) | −353.883 | + | 9.08889i | −0.515114 | + | 0.0132298i | ||||
\(688\) | 87.8739 | − | 270.448i | 0.127724 | − | 0.393093i | ||||
\(689\) | −559.848 | − | 770.565i | −0.812552 | − | 1.11838i | ||||
\(690\) | −669.615 | − | 198.715i | −0.970457 | − | 0.287993i | ||||
\(691\) | 131.641 | + | 405.150i | 0.190508 | + | 0.586324i | 1.00000 | 0.000807501i | \(-0.000257036\pi\) | |
−0.809491 | + | 0.587132i | \(0.800257\pi\) | |||||||
\(692\) | 571.482i | 0.825841i | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −1288.00 | −1.85591 | ||||||||
\(695\) | −241.561 | + | 78.4879i | −0.347570 | + | 0.112932i | ||||
\(696\) | 47.7955 | − | 161.058i | 0.0686717 | − | 0.231405i | ||||
\(697\) | 724.879 | − | 526.656i | 1.04000 | − | 0.755603i | ||||
\(698\) | −169.470 | − | 55.0640i | −0.242793 | − | 0.0788883i | ||||
\(699\) | 6.52120 | + | 253.908i | 0.00932933 | + | 0.363245i | ||||
\(700\) | −308.761 | + | 224.328i | −0.441087 | + | 0.320468i | ||||
\(701\) | 161.734 | − | 222.608i | 0.230719 | − | 0.317557i | −0.677924 | − | 0.735132i | \(-0.737120\pi\) |
0.908642 | + | 0.417575i | \(0.137120\pi\) | |||||||
\(702\) | −1558.84 | − | 376.730i | −2.22057 | − | 0.536652i | ||||
\(703\) | −149.666 | −0.212897 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 104.000 | + | 294.156i | 0.147518 | + | 0.417243i | ||||
\(706\) | 101.749 | + | 313.150i | 0.144120 | + | 0.443556i | ||||
\(707\) | −651.703 | + | 896.992i | −0.921786 | + | 1.26873i | ||||
\(708\) | −173.147 | + | 251.659i | −0.244557 | + | 0.355451i | ||||
\(709\) | −12.9787 | + | 39.9444i | −0.0183057 | + | 0.0563390i | −0.959792 | − | 0.280712i | \(-0.909429\pi\) |
0.941486 | + | 0.337051i | \(0.109429\pi\) | |||||||
\(710\) | −462.992 | − | 150.435i | −0.652101 | − | 0.211880i | ||||
\(711\) | 52.4903 | − | 195.112i | 0.0738260 | − | 0.274419i | ||||
\(712\) | 133.191 | + | 96.7688i | 0.187066 | + | 0.135911i | ||||
\(713\) | −887.698 | + | 288.431i | −1.24502 | + | 0.404531i | ||||
\(714\) | −419.066 | − | 1185.30i | −0.586927 | − | 1.66008i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 950.352i | 1.32731i | ||||||||
\(717\) | 77.2597 | + | 100.792i | 0.107754 | + | 0.140574i | ||||
\(718\) | 543.659 | + | 394.992i | 0.757186 | + | 0.550128i | ||||
\(719\) | −254.364 | − | 350.102i | −0.353774 | − | 0.486928i | 0.594627 | − | 0.804002i | \(-0.297300\pi\) |
−0.948401 | + | 0.317073i | \(0.897300\pi\) | |||||||
\(720\) | −451.710 | + | 172.875i | −0.627376 | + | 0.240104i | ||||
\(721\) | −78.6240 | + | 241.980i | −0.109049 | + | 0.335617i | ||||
\(722\) | 213.053 | + | 293.243i | 0.295088 | + | 0.406153i | ||||
\(723\) | −127.739 | + | 430.445i | −0.176679 | + | 0.595359i | ||||
\(724\) | 242.887 | + | 747.530i | 0.335480 | + | 1.03250i | ||||
\(725\) | 359.822i | 0.496306i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 1102.00 | 1.51582 | 0.757909 | − | 0.652360i | \(-0.226221\pi\) | ||||
0.757909 | + | 0.652360i | \(0.226221\pi\) | |||||||
\(728\) | 422.732 | − | 137.354i | 0.580675 | − | 0.188673i | ||||
\(729\) | 116.210 | − | 719.678i | 0.159410 | − | 0.987212i | ||||
\(730\) | −453.050 | + | 329.160i | −0.620616 | + | 0.450904i | ||||
\(731\) | −301.279 | − | 97.8916i | −0.412147 | − | 0.133915i | ||||
\(732\) | −875.259 | + | 22.4795i | −1.19571 | + | 0.0307097i | ||||
\(733\) | −393.518 | + | 285.908i | −0.536860 | + | 0.390052i | −0.822918 | − | 0.568161i | \(-0.807655\pi\) |
0.286058 | + | 0.958212i | \(0.407655\pi\) | |||||||
\(734\) | −220.829 | + | 303.945i | −0.300857 | + | 0.414094i | ||||
\(735\) | −36.1349 | − | 47.1409i | −0.0491631 | − | 0.0641373i | ||||
\(736\) | 1234.75 | 1.67765 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 784.000 | − | 633.568i | 1.06233 | − | 0.858493i | ||||
\(739\) | −323.746 | − | 996.388i | −0.438087 | − | 1.34829i | −0.889890 | − | 0.456175i | \(-0.849219\pi\) |
0.451804 | − | 0.892117i | \(-0.350781\pi\) | |||||||
\(740\) | −49.8752 | + | 68.6474i | −0.0673990 | + | 0.0927667i | ||||
\(741\) | 830.432 | + | 571.355i | 1.12069 | + | 0.771059i | ||||
\(742\) | 259.574 | − | 798.887i | 0.349831 | − | 1.07667i | ||||
\(743\) | 241.561 | + | 78.4879i | 0.325116 | + | 0.105636i | 0.467027 | − | 0.884243i | \(-0.345325\pi\) |
−0.141912 | + | 0.989879i | \(0.545325\pi\) | |||||||
\(744\) | −134.970 | + | 196.171i | −0.181411 | + | 0.263671i | ||||
\(745\) | −48.4330 | − | 35.1887i | −0.0650108 | − | 0.0472331i | ||||
\(746\) | 1073.31 | − | 348.739i | 1.43875 | − | 0.467478i | ||||
\(747\) | −119.733 | − | 148.162i | −0.160285 | − | 0.198343i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | − | 316.784i | − | 0.422942i | ||||||
\(750\) | 748.339 | − | 573.624i | 0.997786 | − | 0.764832i | ||||
\(751\) | −283.156 | − | 205.725i | −0.377039 | − | 0.273935i | 0.383085 | − | 0.923713i | \(-0.374862\pi\) |
−0.760124 | + | 0.649779i | \(0.774862\pi\) | |||||||
\(752\) | −410.639 | − | 565.197i | −0.546063 | − | 0.751591i | ||||
\(753\) | 3.92145 | + | 152.685i | 0.00520776 | + | 0.202769i | ||||
\(754\) | −388.495 | + | 1195.67i | −0.515246 | + | 1.58576i | ||||
\(755\) | −111.970 | − | 154.113i | −0.148304 | − | 0.204123i | ||||
\(756\) | −231.119 | − | 560.357i | −0.305713 | − | 0.741213i | ||||
\(757\) | 90.8510 | + | 279.611i | 0.120015 | + | 0.369367i | 0.992960 | − | 0.118451i | \(-0.0377930\pi\) |
−0.872945 | + | 0.487818i | \(0.837793\pi\) | |||||||
\(758\) | − | 926.013i | − | 1.22165i | ||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 112.000 | 0.147368 | ||||||||
\(761\) | 744.813 | − | 242.004i | 0.978729 | − | 0.318008i | 0.224394 | − | 0.974498i | \(-0.427960\pi\) |
0.754335 | + | 0.656490i | \(0.227960\pi\) | |||||||
\(762\) | −512.483 | − | 152.084i | −0.672549 | − | 0.199586i | ||||
\(763\) | 407.745 | − | 296.244i | 0.534397 | − | 0.388262i | ||||
\(764\) | −169.470 | − | 55.0640i | −0.221819 | − | 0.0720733i | ||||
\(765\) | 192.583 | + | 503.206i | 0.251742 | + | 0.657785i | ||||
\(766\) | −1107.91 | + | 804.941i | −1.44635 | + | 1.05084i | ||||
\(767\) | −447.878 | + | 616.452i | −0.583935 | + | 0.803718i | ||||
\(768\) | 792.865 | − | 607.754i | 1.03238 | − | 0.791347i | ||||
\(769\) | −838.131 | −1.08990 | −0.544949 | − | 0.838469i | \(-0.683451\pi\) | ||||
−0.544949 | + | 0.838469i | \(0.683451\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −272.000 | + | 96.1665i | −0.352789 | + | 0.124730i | ||||
\(772\) | −138.748 | − | 427.023i | −0.179726 | − | 0.553139i | ||||
\(773\) | −241.064 | + | 331.796i | −0.311855 | + | 0.429231i | −0.935959 | − | 0.352110i | \(-0.885464\pi\) |
0.624104 | + | 0.781341i | \(0.285464\pi\) | |||||||
\(774\) | −344.146 | − | 92.5842i | −0.444633 | − | 0.119618i | ||||
\(775\) | 157.599 | − | 485.039i | 0.203353 | − | 0.625857i | ||||
\(776\) | 186.203 | + | 60.5011i | 0.239953 | + | 0.0779653i | ||||
\(777\) | 184.952 | + | 127.251i | 0.238033 | + | 0.163772i | ||||
\(778\) | −938.390 | − | 681.780i | −1.20616 | − | 0.876324i | ||||
\(779\) | −602.559 | + | 195.783i | −0.773503 | + | 0.251326i | ||||
\(780\) | 538.799 | − | 190.494i | 0.690768 | − | 0.244223i | ||||
\(781\) | 0 | 0 | ||||||||
\(782\) | − | 1742.31i | − | 2.22802i | ||||||
\(783\) | −555.491 | − | 134.247i | −0.709439 | − | 0.171452i | ||||
\(784\) | 107.599 | + | 78.1754i | 0.137244 | + | 0.0997136i | ||||
\(785\) | 142.976 | + | 196.789i | 0.182135 | + | 0.250687i | ||||
\(786\) | 1847.39 | − | 47.4471i | 2.35037 | − | 0.0603652i | ||||
\(787\) | 97.1238 | − | 298.916i | 0.123410 | − | 0.379817i | −0.870198 | − | 0.492702i | \(-0.836009\pi\) |
0.993608 | + | 0.112885i | \(0.0360091\pi\) | |||||||
\(788\) | 410.555 | + | 565.081i | 0.521009 | + | 0.717108i | ||||
\(789\) | 1339.23 | + | 397.430i | 1.69738 | + | 0.503713i | ||||
\(790\) | 51.9149 | + | 159.777i | 0.0657150 | + | 0.202250i | ||||
\(791\) | − | 888.972i | − | 1.12386i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −2184.00 | −2.75410 | ||||||||
\(794\) | −1112.19 | + | 361.371i | −1.40074 | + | 0.455128i | ||||
\(795\) | −102.419 | + | 345.124i | −0.128829 | + | 0.434118i | ||||
\(796\) | 538.805 | − | 391.465i | 0.676891 | − | 0.491790i | ||||
\(797\) | 234.029 | + | 76.0408i | 0.293638 | + | 0.0954088i | 0.452132 | − | 0.891951i | \(-0.350664\pi\) |
−0.158494 | + | 0.987360i | \(0.550664\pi\) | |||||||
\(798\) | 22.8242 | + | 888.679i | 0.0286018 | + | 1.11363i | ||||
\(799\) | −629.629 | + | 457.453i | −0.788022 | + | 0.572531i | ||||
\(800\) | −396.559 | + | 545.817i | −0.495699 | + | 0.682271i | ||||
\(801\) | 305.485 | − | 469.373i | 0.381380 | − | 0.585984i | ||||
\(802\) | −1391.90 | −1.73553 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | −126.000 | − | 356.382i | −0.156716 | − | 0.443261i | ||||
\(805\) | −203.497 | − | 626.301i | −0.252792 | − | 0.778013i | ||||
\(806\) | 1047.38 | − | 1441.59i | 1.29948 | − | 1.78858i | ||||
\(807\) | −630.061 | + | 915.759i | −0.780745 | + | 1.13477i | ||||
\(808\) | −121.135 | + | 372.814i | −0.149919 | + | 0.461404i | ||||
\(809\) | 241.561 | + | 78.4879i | 0.298592 | + | 0.0970184i | 0.454482 | − | 0.890756i | \(-0.349824\pi\) |
−0.155890 | + | 0.987774i | \(0.549824\pi\) | |||||||
\(810\) | 245.430 | + | 554.238i | 0.303000 | + | 0.684245i | ||||
\(811\) | 787.037 | + | 571.816i | 0.970452 | + | 0.705075i | 0.955555 | − | 0.294814i | \(-0.0952578\pi\) |
0.0148976 | + | 0.999889i | \(0.495258\pi\) | |||||||
\(812\) | −451.919 | + | 146.837i | −0.556550 | + | 0.180834i | ||||
\(813\) | 336.749 | + | 952.470i | 0.414206 | + | 1.17155i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 39.5980i | 0.0485865i | ||||||||
\(816\) | −733.967 | − | 957.520i | −0.899469 | − | 1.17343i | ||||
\(817\) | 181.220 | + | 131.664i | 0.221811 | + | 0.161155i | ||||
\(818\) | 349.127 | + | 480.532i | 0.426805 | + | 0.587447i | ||||
\(819\) | −540.434 | − | 1412.12i | −0.659871 | − | 1.72420i | ||||
\(820\) | −110.999 | + | 341.619i | −0.135364 | + | 0.416608i | ||||
\(821\) | −286.145 | − | 393.844i | −0.348532 | − | 0.479713i | 0.598377 | − | 0.801215i | \(-0.295812\pi\) |
−0.946909 | + | 0.321502i | \(0.895812\pi\) | |||||||
\(822\) | −357.669 | + | 1205.25i | −0.435120 | + | 1.46624i | ||||
\(823\) | 321.996 | + | 991.001i | 0.391246 | + | 1.20413i | 0.931847 | + | 0.362853i | \(0.118197\pi\) |
−0.540600 | + | 0.841280i | \(0.681803\pi\) | |||||||
\(824\) | 89.9555i | 0.109169i | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −672.000 | −0.813559 | ||||||||
\(827\) | 1187.67 | − | 385.899i | 1.43612 | − | 0.466625i | 0.515437 | − | 0.856927i | \(-0.327630\pi\) |
0.920687 | + | 0.390303i | \(0.127630\pi\) | |||||||
\(828\) | −43.1217 | − | 838.935i | −0.0520793 | − | 1.01321i | ||||
\(829\) | −953.022 | + | 692.411i | −1.14960 | + | 0.835236i | −0.988428 | − | 0.151689i | \(-0.951529\pi\) |
−0.161176 | + | 0.986926i | \(0.551529\pi\) | |||||||
\(830\) | 150.640 | + | 48.9458i | 0.181494 | + | 0.0589708i | ||||
\(831\) | −67.3276 | + | 1.72920i | −0.0810200 | + | 0.00208086i | ||||
\(832\) | −526.709 | + | 382.677i | −0.633064 | + | 0.459948i | ||||
\(833\) | 87.0875 | − | 119.866i | 0.104547 | − | 0.143896i | ||||
\(834\) | −433.619 | − | 565.691i | −0.519927 | − | 0.678287i | ||||
\(835\) | −239.466 | −0.286786 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 690.000 | + | 424.264i | 0.824373 | + | 0.506887i | ||||
\(838\) | 559.618 | + | 1722.33i | 0.667802 | + | 2.05528i | ||||
\(839\) | 600.165 | − | 826.057i | 0.715334 | − | 0.984573i | −0.284332 | − | 0.958726i | \(-0.591772\pi\) |
0.999666 | − | 0.0258470i | \(-0.00822826\pi\) | |||||||
\(840\) | −138.405 | − | 95.2258i | −0.164768 | − | 0.113364i | ||||
\(841\) | 121.444 | − | 373.765i | 0.144404 | − | 0.444430i | ||||
\(842\) | −669.325 | − | 217.477i | −0.794923 | − | 0.258286i | ||||
\(843\) | −35.9920 | + | 52.3123i | −0.0426951 | + | 0.0620549i | ||||
\(844\) | −944.444 | − | 686.179i | −1.11901 | − | 0.813008i | ||||
\(845\) | 901.148 | − | 292.801i | 1.06645 | − | 0.346510i | ||||
\(846\) | −680.982 | + | 550.316i | −0.804943 | + | 0.650492i | ||||
\(847\) | 0 | 0 | ||||||||
\(848\) | − | 806.102i | − | 0.950592i | ||||||
\(849\) | 427.622 | − | 327.785i | 0.503678 | − | 0.386084i | ||||
\(850\) | 770.184 | + | 559.572i | 0.906099 | + | 0.658319i | ||||
\(851\) | 182.876 | + | 251.707i | 0.214895 | + | 0.295778i | ||||
\(852\) | −15.0322 | − | 585.291i | −0.0176434 | − | 0.686962i | ||||
\(853\) | −182.685 | + | 562.247i | −0.214168 | + | 0.659141i | 0.785044 | + | 0.619440i | \(0.212640\pi\) |
−0.999212 | + | 0.0397007i | \(0.987360\pi\) | |||||||
\(854\) | −1132.14 | − | 1558.25i | −1.32569 | − | 1.82465i | ||||
\(855\) | −19.5572 | − | 380.486i | −0.0228739 | − | 0.445013i | ||||
\(856\) | −34.6099 | − | 106.518i | −0.0404321 | − | 0.124437i | ||||
\(857\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 706.000 | 0.821886 | 0.410943 | − | 0.911661i | \(-0.365200\pi\) | ||||
0.410943 | + | 0.911661i | \(0.365200\pi\) | |||||||
\(860\) | 120.780 | − | 39.2439i | 0.140442 | − | 0.0456325i | ||||
\(861\) | 911.080 | + | 270.372i | 1.05817 | + | 0.314021i | ||||
\(862\) | −1177.93 | + | 855.815i | −1.36651 | + | 0.992825i | ||||
\(863\) | 470.749 | + | 152.956i | 0.545480 | + | 0.177237i | 0.568777 | − | 0.822491i | \(-0.307417\pi\) |
−0.0232978 | + | 0.999729i | \(0.507417\pi\) | |||||||
\(864\) | −694.674 | − | 815.845i | −0.804021 | − | 0.944265i | ||||
\(865\) | 435.897 | − | 316.698i | 0.503927 | − | 0.366125i | ||||
\(866\) | 1147.69 | − | 1579.66i | 1.32528 | − | 1.82409i | ||||
\(867\) | −378.575 | + | 290.189i | −0.436650 | + | 0.334705i | ||||
\(868\) | 673.498 | 0.775920 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 448.000 | − | 158.392i | 0.514943 | − | 0.182060i | ||||
\(871\) | −291.371 | − | 896.749i | −0.334525 | − | 1.02956i | ||||
\(872\) | 104.738 | − | 144.159i | 0.120112 | − | 0.165320i | ||||
\(873\) | 173.020 | − | 643.133i | 0.198190 | − | 0.736693i | ||||
\(874\) | −380.709 | + | 1171.70i | −0.435594 | + | 1.34062i | ||||
\(875\) | 845.463 | + | 274.708i | 0.966243 | + | 0.313952i | ||||
\(876\) | −554.856 | − | 381.752i | −0.633397 | − | 0.435790i | ||||
\(877\) | −78.7037 | − | 57.1816i | −0.0897419 | − | 0.0652013i | 0.542010 | − | 0.840372i | \(-0.317664\pi\) |
−0.631751 | + | 0.775171i | \(0.717664\pi\) | |||||||
\(878\) | 1073.31 | − | 348.739i | 1.22245 | − | 0.397197i | ||||
\(879\) | 59.8665 | − | 21.1660i | 0.0681075 | − | 0.0240796i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 1493.41i | 1.69513i | 0.530692 | + | 0.847565i | \(0.321932\pi\) | ||||
−0.530692 | + | 0.847565i | \(0.678068\pi\) | |||||||
\(882\) | 90.9221 | − | 139.700i | 0.103086 | − | 0.158390i | ||||
\(883\) | −69.5755 | − | 50.5495i | −0.0787944 | − | 0.0572475i | 0.547691 | − | 0.836681i | \(-0.315507\pi\) |
−0.626485 | + | 0.779433i | \(0.715507\pi\) | |||||||
\(884\) | 837.904 | + | 1153.28i | 0.947855 | + | 1.30461i | ||||
\(885\) | 287.905 | − | 7.39435i | 0.325316 | − | 0.00835520i | ||||
\(886\) | −97.1238 | + | 298.916i | −0.109621 | + | 0.337377i | ||||
\(887\) | −149.293 | − | 205.484i | −0.168312 | − | 0.231662i | 0.716526 | − | 0.697560i | \(-0.245731\pi\) |
−0.884838 | + | 0.465899i | \(0.845731\pi\) | |||||||
\(888\) | 76.0926 | + | 22.5812i | 0.0856899 | + | 0.0254293i | ||||
\(889\) | −155.745 | − | 479.332i | −0.175191 | − | 0.539182i | ||||
\(890\) | 465.652i | 0.523205i | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 138.000 | 0.154709 | ||||||||
\(893\) | 523.382 | − | 170.057i | 0.586094 | − | 0.190433i | ||||
\(894\) | 47.7955 | − | 161.058i | 0.0534625 | − | 0.180154i | ||||
\(895\) | 724.879 | − | 526.656i | 0.809921 | − | 0.588442i | ||||
\(896\) | 583.729 | + | 189.665i | 0.651483 | + | 0.211680i | ||||
\(897\) | −53.7999 | − | 2094.74i | −0.0599776 | − | 2.33528i | ||||
\(898\) | 1089.74 | − | 791.745i | 1.21352 | − | 0.881676i | ||||
\(899\) | 373.232 | − | 513.710i | 0.415164 | − | 0.571424i | ||||
\(900\) | 384.698 | + | 250.376i | 0.427443 | + | 0.278195i | ||||
\(901\) | −897.998 | −0.996668 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −112.000 | − | 316.784i | −0.124031 | − | 0.350813i | ||||
\(904\) | −97.1238 | − | 298.916i | −0.107438 | − | 0.330660i | ||||
\(905\) | 435.577 | − | 599.520i | 0.481301 | − | 0.662453i | ||||
\(906\) | 303.007 | − | 440.403i | 0.334444 | − | 0.486096i | ||||
\(907\) | −298.510 | + | 918.721i | −0.329118 | + | 1.01292i | 0.640429 | + | 0.768018i | \(0.278757\pi\) |
−0.969547 | + | 0.244905i | \(0.921243\pi\) | |||||||
\(908\) | 603.902 | + | 196.220i | 0.665090 | + | 0.216101i | ||||
\(909\) | 1287.67 | + | 346.418i | 1.41658 | + | 0.381098i | ||||
\(910\) | 1017.09 | + | 738.962i | 1.11769 | + | 0.812046i | ||||
\(911\) | 1379.97 | − | 448.378i | 1.51478 | − | 0.492183i | 0.570494 | − | 0.821302i | \(-0.306752\pi\) |
0.944288 | + | 0.329119i | \(0.106752\pi\) | |||||||
\(912\) | 284.366 | + | 804.308i | 0.311805 | + | 0.881917i | ||||
\(913\) | 0 | 0 | ||||||||
\(914\) | − | 1781.91i | − | 1.94957i | ||||||
\(915\) | 502.188 | + | 655.145i | 0.548839 | + | 0.716006i | ||||
\(916\) | 286.392 | + | 208.076i | 0.312655 | + | 0.227157i | ||||
\(917\) | 1024.10 | + | 1409.56i | 1.11680 | + | 1.53714i | ||||
\(918\) | −1151.21 | + | 980.232i | −1.25404 | + | 1.06779i | ||||
\(919\) | 122.561 | − | 377.204i | 0.133363 | − | 0.410450i | −0.861968 | − | 0.506962i | \(-0.830768\pi\) |
0.995332 | + | 0.0965115i | \(0.0307685\pi\) | |||||||
\(920\) | −136.852 | − | 188.360i | −0.148752 | − | 0.204739i | ||||
\(921\) | −127.739 | + | 430.445i | −0.138696 | + | 0.467367i | ||||
\(922\) | 571.063 | + | 1757.55i | 0.619375 | + | 1.90624i | ||||
\(923\) | − | 1460.45i | − | 1.58229i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −170.000 | −0.183784 | ||||||||
\(926\) | −2219.34 | + | 721.107i | −2.39670 | + | 0.778734i | ||||
\(927\) | 305.597 | − | 15.7078i | 0.329662 | − | 0.0169448i | ||||
\(928\) | −679.574 | + | 493.740i | −0.732300 | + | 0.532047i | ||||
\(929\) | −1452.60 | − | 471.977i | −1.56361 | − | 0.508049i | −0.605843 | − | 0.795584i | \(-0.707164\pi\) |
−0.957770 | + | 0.287535i | \(0.907164\pi\) | |||||||
\(930\) | −673.276 | + | 17.2920i | −0.723953 | + | 0.0185935i | ||||
\(931\) | −84.7578 | + | 61.5801i | −0.0910395 | + | 0.0661441i | ||||
\(932\) | 149.293 | − | 205.484i | 0.160185 | − | 0.220476i | ||||
\(933\) | 46.4592 | + | 60.6098i | 0.0497955 | + | 0.0649623i | ||||
\(934\) | 1406.86 | 1.50628 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −336.000 | − | 415.779i | −0.358974 | − | 0.444208i | ||||
\(937\) | 388.495 | + | 1195.67i | 0.414616 | + | 1.27606i | 0.912594 | + | 0.408867i | \(0.134076\pi\) |
−0.497978 | + | 0.867190i | \(0.665924\pi\) | |||||||
\(938\) | 488.777 | − | 672.744i | 0.521085 | − | 0.717211i | ||||
\(939\) | 983.667 | + | 676.783i | 1.04757 | + | 0.720749i | ||||
\(940\) | 96.4133 | − | 296.730i | 0.102567 | − | 0.315670i | ||||
\(941\) | 462.992 | + | 150.435i | 0.492021 | + | 0.159867i | 0.544510 | − | 0.838754i | \(-0.316716\pi\) |
−0.0524893 | + | 0.998621i | \(0.516716\pi\) | |||||||
\(942\) | −386.914 | + | 562.357i | −0.410736 | + | 0.596982i | ||||
\(943\) | 1065.53 | + | 774.150i | 1.12993 | + | 0.820944i | ||||
\(944\) | −613.319 | + | 199.279i | −0.649702 | + | 0.211101i | ||||
\(945\) | −299.333 | + | 486.818i | −0.316754 | + | 0.515152i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 435.578i | 0.459955i | 0.973196 | + | 0.229978i | \(0.0738653\pi\) | ||||
−0.973196 | + | 0.229978i | \(0.926135\pi\) | |||||||
\(948\) | −160.358 | + | 122.919i | −0.169154 | + | 0.129662i | ||||
\(949\) | −1359.15 | − | 987.479i | −1.43219 | − | 1.04055i | ||||
\(950\) | −395.677 | − | 544.602i | −0.416502 | − | 0.573266i | ||||
\(951\) | −32.0251 | − | 1246.93i | −0.0336752 | − | 1.31117i | ||||
\(952\) | 129.498 | − | 398.555i | 0.136028 | − | 0.418650i | ||||
\(953\) | 945.521 | + | 1301.40i | 0.992152 | + | 1.36558i | 0.930018 | + | 0.367513i | \(0.119791\pi\) |
0.0621339 | + | 0.998068i | \(0.480209\pi\) | |||||||
\(954\) | −1008.92 | + | 51.8587i | −1.05756 | + | 0.0543593i | ||||
\(955\) | 51.9149 | + | 159.777i | 0.0543611 | + | 0.167306i | ||||
\(956\) | − | 126.996i | − | 0.132841i | ||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 1792.00 | 1.87056 | ||||||||
\(959\) | −1127.28 | + | 366.277i | −1.17548 | + | 0.381936i | ||||
\(960\) | 235.905 | + | 70.0071i | 0.245734 | + | 0.0729240i | ||||
\(961\) | 49.3500 | − | 35.8549i | 0.0513528 | − | 0.0373100i | ||||
\(962\) | −564.899 | − | 183.547i | −0.587213 | − | 0.190797i | ||||
\(963\) | −355.820 | + | 136.177i | −0.369491 | + | 0.141409i | ||||
\(964\) | 363.248 | − | 263.915i | 0.376813 | − | 0.273771i | ||||
\(965\) | −248.821 | + | 342.473i | −0.257846 | + | 0.354895i | ||||
\(966\) | 1466.68 | − | 1124.25i | 1.51830 | − | 1.16382i | ||||
\(967\) | 1055.15 | 1.09116 | 0.545578 | − | 0.838060i | \(-0.316310\pi\) | ||||
0.545578 | + | 0.838060i | \(0.316310\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 896.000 | − | 316.784i | 0.924665 | − | 0.326918i | ||||
\(970\) | 171.123 | + | 526.662i | 0.176415 | + | 0.542951i | ||||
\(971\) | −149.626 | + | 205.942i | −0.154094 | + | 0.212093i | −0.879084 | − | 0.476667i | \(-0.841845\pi\) |
0.724989 | + | 0.688760i | \(0.241845\pi\) | |||||||
\(972\) | −530.057 | + | 500.481i | −0.545326 | + | 0.514898i | ||||
\(973\) | 207.659 | − | 639.110i | 0.213422 | − | 0.656845i | ||||
\(974\) | 880.691 | + | 286.154i | 0.904200 | + | 0.293792i | ||||
\(975\) | 943.255 | + | 648.979i | 0.967441 | + | 0.665620i | ||||
\(976\) | −1495.37 | − | 1086.45i | −1.53214 | − | 1.11317i | ||||
\(977\) | −1371.90 | + | 445.756i | −1.40419 | + | 0.456250i | −0.910544 | − | 0.413411i | \(-0.864337\pi\) |
−0.493649 | + | 0.869661i | \(0.664337\pi\) | |||||||
\(978\) | −104.766 | + | 37.0405i | −0.107123 | + | 0.0378737i | ||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 59.3970i | 0.0606092i | ||||||||
\(981\) | −508.027 | − | 330.643i | −0.517866 | − | 0.337047i | ||||
\(982\) | 543.659 | + | 394.992i | 0.553625 | + | 0.402232i | ||||
\(983\) | 403.989 | + | 556.044i | 0.410976 | + | 0.565660i | 0.963456 | − | 0.267866i | \(-0.0863185\pi\) |
−0.552480 | + | 0.833526i | \(0.686318\pi\) | |||||||
\(984\) | 335.889 | − | 8.62674i | 0.341351 | − | 0.00876701i | ||||
\(985\) | 203.497 | − | 626.301i | 0.206596 | − | 0.635838i | ||||
\(986\) | 696.700 | + | 958.925i | 0.706592 | + | 0.972541i | ||||
\(987\) | −791.363 | − | 234.845i | −0.801787 | − | 0.237938i | ||||
\(988\) | −311.489 | − | 958.665i | −0.315272 | − | 0.970309i | ||||
\(989\) | − | 465.652i | − | 0.470831i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 574.000 | 0.579213 | 0.289606 | − | 0.957146i | \(-0.406476\pi\) | ||||
0.289606 | + | 0.957146i | \(0.406476\pi\) | |||||||
\(992\) | 1132.32 | − | 367.912i | 1.14145 | − | 0.370879i | ||||
\(993\) | −151.921 | + | 511.933i | −0.152992 | + | 0.515542i | ||||
\(994\) | 1042.01 | − | 757.067i | 1.04830 | − | 0.761637i | ||||
\(995\) | −597.179 | − | 194.035i | −0.600180 | − | 0.195010i | ||||
\(996\) | 4.89090 | + | 190.431i | 0.00491054 | + | 0.191196i | ||||
\(997\) | 1071.58 | − | 778.549i | 1.07481 | − | 0.780892i | 0.0980354 | − | 0.995183i | \(-0.468744\pi\) |
0.976770 | + | 0.214291i | \(0.0687442\pi\) | |||||||
\(998\) | −152.403 | + | 209.765i | −0.152709 | + | 0.210185i | ||||
\(999\) | 63.4258 | − | 262.445i | 0.0634893 | − | 0.262707i |
(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 | 363.3.h.k.269.1 | 16 | ||
3.2 | odd | 2 | inner | 363.3.h.k.269.4 | 16 | ||
11.2 | odd | 10 | inner | 363.3.h.k.251.2 | 16 | ||
11.3 | even | 5 | 363.3.b.i.122.3 | yes | 4 | ||
11.4 | even | 5 | inner | 363.3.h.k.245.2 | 16 | ||
11.5 | even | 5 | inner | 363.3.h.k.323.3 | 16 | ||
11.6 | odd | 10 | inner | 363.3.h.k.323.1 | 16 | ||
11.7 | odd | 10 | inner | 363.3.h.k.245.4 | 16 | ||
11.8 | odd | 10 | 363.3.b.i.122.1 | ✓ | 4 | ||
11.9 | even | 5 | inner | 363.3.h.k.251.4 | 16 | ||
11.10 | odd | 2 | inner | 363.3.h.k.269.3 | 16 | ||
33.2 | even | 10 | inner | 363.3.h.k.251.3 | 16 | ||
33.5 | odd | 10 | inner | 363.3.h.k.323.2 | 16 | ||
33.8 | even | 10 | 363.3.b.i.122.4 | yes | 4 | ||
33.14 | odd | 10 | 363.3.b.i.122.2 | yes | 4 | ||
33.17 | even | 10 | inner | 363.3.h.k.323.4 | 16 | ||
33.20 | odd | 10 | inner | 363.3.h.k.251.1 | 16 | ||
33.26 | odd | 10 | inner | 363.3.h.k.245.3 | 16 | ||
33.29 | even | 10 | inner | 363.3.h.k.245.1 | 16 | ||
33.32 | even | 2 | inner | 363.3.h.k.269.2 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
363.3.b.i.122.1 | ✓ | 4 | 11.8 | odd | 10 | ||
363.3.b.i.122.2 | yes | 4 | 33.14 | odd | 10 | ||
363.3.b.i.122.3 | yes | 4 | 11.3 | even | 5 | ||
363.3.b.i.122.4 | yes | 4 | 33.8 | even | 10 | ||
363.3.h.k.245.1 | 16 | 33.29 | even | 10 | inner | ||
363.3.h.k.245.2 | 16 | 11.4 | even | 5 | inner | ||
363.3.h.k.245.3 | 16 | 33.26 | odd | 10 | inner | ||
363.3.h.k.245.4 | 16 | 11.7 | odd | 10 | inner | ||
363.3.h.k.251.1 | 16 | 33.20 | odd | 10 | inner | ||
363.3.h.k.251.2 | 16 | 11.2 | odd | 10 | inner | ||
363.3.h.k.251.3 | 16 | 33.2 | even | 10 | inner | ||
363.3.h.k.251.4 | 16 | 11.9 | even | 5 | inner | ||
363.3.h.k.269.1 | 16 | 1.1 | even | 1 | trivial | ||
363.3.h.k.269.2 | 16 | 33.32 | even | 2 | inner | ||
363.3.h.k.269.3 | 16 | 11.10 | odd | 2 | inner | ||
363.3.h.k.269.4 | 16 | 3.2 | odd | 2 | inner | ||
363.3.h.k.323.1 | 16 | 11.6 | odd | 10 | inner | ||
363.3.h.k.323.2 | 16 | 33.5 | odd | 10 | inner | ||
363.3.h.k.323.3 | 16 | 11.5 | even | 5 | inner | ||
363.3.h.k.323.4 | 16 | 33.17 | even | 10 | inner |