Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [575,2,Mod(26,575)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(575, base_ring=CyclotomicField(22))
chi = DirichletCharacter(H, H._module([0, 16]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("575.26");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 575 = 5^{2} \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 575.k (of order \(11\), degree \(10\), 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: | \(4.59139811622\) |
Analytic rank: | \(0\) |
Dimension: | \(10\) |
Coefficient field: | \(\Q(\zeta_{22})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: |
\( x^{10} - x^{9} + x^{8} - x^{7} + x^{6} - x^{5} + x^{4} - x^{3} + x^{2} - x + 1 \)
|
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 115) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{11}]$ |
Embedding invariants
Embedding label | 351.1 | ||
Root | \(0.959493 - 0.281733i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 575.351 |
Dual form | 575.2.k.a.326.1 |
$q$-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 \(\left(\mathbb{Z}/575\mathbb{Z}\right)^\times\).
\(n\) | \(51\) | \(277\) |
\(\chi(n)\) | \(e\left(\frac{9}{11}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.925839 | + | 2.02730i | −0.654667 | + | 1.43352i | 0.232743 | + | 0.972538i | \(0.425230\pi\) |
−0.887410 | + | 0.460982i | \(0.847497\pi\) | |||||||
\(3\) | −0.959493 | − | 0.281733i | −0.553964 | − | 0.162658i | −0.00724338 | − | 0.999974i | \(-0.502306\pi\) |
−0.546720 | + | 0.837315i | \(0.684124\pi\) | |||||||
\(4\) | −1.94306 | − | 2.24241i | −0.971531 | − | 1.12121i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 1.45949 | − | 1.68434i | 0.595836 | − | 0.687631i | ||||
\(7\) | 0.0125459 | − | 0.0872586i | 0.00474190 | − | 0.0329807i | −0.987313 | − | 0.158785i | \(-0.949242\pi\) |
0.992055 | + | 0.125805i | \(0.0401513\pi\) | |||||||
\(8\) | 2.06815 | − | 0.607265i | 0.731203 | − | 0.214700i | ||||
\(9\) | −1.68251 | − | 1.08128i | −0.560836 | − | 0.360427i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.01365 | + | 2.21959i | 0.305628 | + | 0.669231i | 0.998664 | − | 0.0516714i | \(-0.0164549\pi\) |
−0.693037 | + | 0.720902i | \(0.743728\pi\) | |||||||
\(12\) | 1.23259 | + | 2.69900i | 0.355819 | + | 0.779135i | ||||
\(13\) | −0.512546 | − | 3.56484i | −0.142155 | − | 0.988707i | −0.928609 | − | 0.371059i | \(-0.878995\pi\) |
0.786455 | − | 0.617648i | \(-0.211914\pi\) | |||||||
\(14\) | 0.165284 | + | 0.106222i | 0.0441741 | + | 0.0283890i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0.160869 | − | 1.11887i | 0.0402172 | − | 0.279717i | ||||
\(17\) | 2.21537 | − | 2.55667i | 0.537306 | − | 0.620084i | −0.420572 | − | 0.907259i | \(-0.638171\pi\) |
0.957878 | + | 0.287175i | \(0.0927160\pi\) | |||||||
\(18\) | 3.74982 | − | 2.40986i | 0.883840 | − | 0.568010i | ||||
\(19\) | 1.87358 | + | 2.16222i | 0.429828 | + | 0.496048i | 0.928806 | − | 0.370567i | \(-0.120837\pi\) |
−0.498978 | + | 0.866615i | \(0.666291\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −0.0366213 | + | 0.0801894i | −0.00799142 | + | 0.0174988i | ||||
\(22\) | −5.43826 | −1.15944 | ||||||||
\(23\) | 4.28287 | + | 2.15802i | 0.893039 | + | 0.449979i | ||||
\(24\) | −2.15546 | −0.439982 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 7.70154 | + | 2.26138i | 1.51040 | + | 0.443492i | ||||
\(27\) | 3.27430 | + | 3.77875i | 0.630140 | + | 0.727220i | ||||
\(28\) | −0.220047 | + | 0.141416i | −0.0415850 | + | 0.0267251i | ||||
\(29\) | 4.87604 | − | 5.62725i | 0.905458 | − | 1.04495i | −0.0933249 | − | 0.995636i | \(-0.529750\pi\) |
0.998783 | − | 0.0493188i | \(-0.0157050\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1.65370 | − | 0.485571i | 0.297014 | − | 0.0872110i | −0.129831 | − | 0.991536i | \(-0.541443\pi\) |
0.426844 | + | 0.904325i | \(0.359625\pi\) | |||||||
\(32\) | 5.74593 | + | 3.69269i | 1.01575 | + | 0.652781i | ||||
\(33\) | −0.347262 | − | 2.41526i | −0.0604505 | − | 0.420442i | ||||
\(34\) | 3.13208 | + | 6.85830i | 0.537147 | + | 1.17619i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0.844535 | + | 5.87387i | 0.140756 | + | 0.978979i | ||||
\(37\) | −0.595421 | − | 0.382654i | −0.0978866 | − | 0.0629079i | 0.490782 | − | 0.871283i | \(-0.336711\pi\) |
−0.588668 | + | 0.808375i | \(0.700348\pi\) | |||||||
\(38\) | −6.11811 | + | 1.79644i | −0.992489 | + | 0.291421i | ||||
\(39\) | −0.512546 | + | 3.56484i | −0.0820730 | + | 0.570830i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −4.66991 | + | 3.00117i | −0.729317 | + | 0.468704i | −0.851867 | − | 0.523759i | \(-0.824529\pi\) |
0.122550 | + | 0.992462i | \(0.460893\pi\) | |||||||
\(42\) | −0.128663 | − | 0.148485i | −0.0198531 | − | 0.0229117i | ||||
\(43\) | −2.30014 | − | 0.675383i | −0.350768 | − | 0.102995i | 0.101602 | − | 0.994825i | \(-0.467603\pi\) |
−0.452370 | + | 0.891830i | \(0.649421\pi\) | |||||||
\(44\) | 3.00764 | − | 6.58582i | 0.453419 | − | 0.992850i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −8.34021 | + | 6.68469i | −1.22970 | + | 0.985604i | ||||
\(47\) | 11.6146 | 1.69416 | 0.847079 | − | 0.531466i | \(-0.178359\pi\) | ||||
0.847079 | + | 0.531466i | \(0.178359\pi\) | |||||||
\(48\) | −0.469574 | + | 1.02822i | −0.0677772 | + | 0.148411i | ||||
\(49\) | 6.70899 | + | 1.96994i | 0.958428 | + | 0.281420i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −2.84593 | + | 1.82897i | −0.398510 | + | 0.256107i | ||||
\(52\) | −6.99792 | + | 8.07603i | −0.970437 | + | 1.11994i | ||||
\(53\) | −1.47653 | + | 10.2695i | −0.202817 | + | 1.41062i | 0.593058 | + | 0.805160i | \(0.297921\pi\) |
−0.795874 | + | 0.605462i | \(0.792988\pi\) | |||||||
\(54\) | −10.6921 | + | 3.13950i | −1.45502 | + | 0.427231i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −0.0270422 | − | 0.188083i | −0.00361367 | − | 0.0251336i | ||||
\(57\) | −1.18852 | − | 2.60249i | −0.157423 | − | 0.344708i | ||||
\(58\) | 6.89372 | + | 15.0951i | 0.905190 | + | 1.98209i | ||||
\(59\) | −1.64421 | − | 11.4357i | −0.214058 | − | 1.48881i | −0.759417 | − | 0.650604i | \(-0.774516\pi\) |
0.545359 | − | 0.838203i | \(-0.316393\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −3.89722 | + | 1.14433i | −0.498988 | + | 0.146516i | −0.521535 | − | 0.853230i | \(-0.674641\pi\) |
0.0225474 | + | 0.999746i | \(0.492822\pi\) | |||||||
\(62\) | −0.546662 | + | 3.80211i | −0.0694261 | + | 0.482869i | ||||
\(63\) | −0.115460 | + | 0.133248i | −0.0145466 | + | 0.0167876i | ||||
\(64\) | −10.9041 | + | 7.00766i | −1.36302 | + | 0.875958i | ||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 5.21797 | + | 1.53213i | 0.642288 | + | 0.188593i | ||||
\(67\) | 5.07177 | − | 11.1056i | 0.619615 | − | 1.35677i | −0.296184 | − | 0.955131i | \(-0.595714\pi\) |
0.915799 | − | 0.401637i | \(-0.131559\pi\) | |||||||
\(68\) | −10.0377 | −1.21725 | ||||||||
\(69\) | −3.50140 | − | 3.27723i | −0.421518 | − | 0.394532i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0.787956 | − | 1.72538i | 0.0935131 | − | 0.204765i | −0.857095 | − | 0.515158i | \(-0.827733\pi\) |
0.950608 | + | 0.310393i | \(0.100461\pi\) | |||||||
\(72\) | −4.13631 | − | 1.21453i | −0.487468 | − | 0.143134i | ||||
\(73\) | −3.61246 | − | 4.16900i | −0.422806 | − | 0.487944i | 0.503884 | − | 0.863772i | \(-0.331904\pi\) |
−0.926690 | + | 0.375827i | \(0.877359\pi\) | |||||||
\(74\) | 1.32702 | − | 0.852823i | 0.154263 | − | 0.0991387i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 1.20812 | − | 8.40266i | 0.138581 | − | 0.963852i | ||||
\(77\) | 0.206395 | − | 0.0606031i | 0.0235209 | − | 0.00690637i | ||||
\(78\) | −6.75247 | − | 4.33955i | −0.764566 | − | 0.491357i | ||||
\(79\) | −0.997420 | − | 6.93721i | −0.112219 | − | 0.780497i | −0.965753 | − | 0.259461i | \(-0.916455\pi\) |
0.853535 | − | 0.521036i | \(-0.174454\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0.415415 | + | 0.909632i | 0.0461572 | + | 0.101070i | ||||
\(82\) | −1.76070 | − | 12.2459i | −0.194436 | − | 1.35234i | ||||
\(83\) | −3.51021 | − | 2.25587i | −0.385295 | − | 0.247614i | 0.333626 | − | 0.942705i | \(-0.391728\pi\) |
−0.718922 | + | 0.695091i | \(0.755364\pi\) | |||||||
\(84\) | 0.250975 | − | 0.0736930i | 0.0273836 | − | 0.00804056i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 3.49877 | − | 4.03779i | 0.377282 | − | 0.435406i | ||||
\(87\) | −6.26391 | + | 4.02557i | −0.671561 | + | 0.431586i | ||||
\(88\) | 3.44426 | + | 3.97489i | 0.367160 | + | 0.423725i | ||||
\(89\) | 15.3009 | + | 4.49275i | 1.62189 | + | 0.476231i | 0.961526 | − | 0.274713i | \(-0.0885827\pi\) |
0.660367 | + | 0.750943i | \(0.270401\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −0.317493 | −0.0332823 | ||||||||
\(92\) | −3.48270 | − | 13.7971i | −0.363096 | − | 1.43845i | ||||
\(93\) | −1.72352 | −0.178720 | ||||||||
\(94\) | −10.7532 | + | 23.5463i | −1.10911 | + | 2.42861i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −4.47283 | − | 5.16192i | −0.456506 | − | 0.526836i | ||||
\(97\) | −12.0969 | + | 7.77424i | −1.22826 | + | 0.789354i | −0.983619 | − | 0.180260i | \(-0.942306\pi\) |
−0.244640 | + | 0.969614i | \(0.578670\pi\) | |||||||
\(98\) | −10.2051 | + | 11.7773i | −1.03087 | + | 1.18969i | ||||
\(99\) | 0.694523 | − | 4.83052i | 0.0698022 | − | 0.485485i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 14.6237 | + | 9.39808i | 1.45511 | + | 0.935144i | 0.998976 | + | 0.0452346i | \(0.0144035\pi\) |
0.456137 | + | 0.889910i | \(0.349233\pi\) | |||||||
\(102\) | −1.07300 | − | 7.46289i | −0.106243 | − | 0.738937i | ||||
\(103\) | −0.483270 | − | 1.05821i | −0.0476180 | − | 0.104269i | 0.884328 | − | 0.466867i | \(-0.154617\pi\) |
−0.931946 | + | 0.362598i | \(0.881890\pi\) | |||||||
\(104\) | −3.22482 | − | 7.06137i | −0.316220 | − | 0.692425i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −19.4523 | − | 12.5013i | −1.88938 | − | 1.21423i | ||||
\(107\) | 16.4556 | − | 4.83181i | 1.59083 | − | 0.467108i | 0.637851 | − | 0.770160i | \(-0.279824\pi\) |
0.952974 | + | 0.303051i | \(0.0980053\pi\) | |||||||
\(108\) | 2.11134 | − | 14.6847i | 0.203164 | − | 1.41303i | ||||
\(109\) | −1.71227 | + | 1.97606i | −0.164006 | + | 0.189273i | −0.831804 | − | 0.555070i | \(-0.812692\pi\) |
0.667798 | + | 0.744343i | \(0.267237\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0.463496 | + | 0.534903i | 0.0439931 | + | 0.0507707i | ||||
\(112\) | −0.0956126 | − | 0.0280744i | −0.00903454 | − | 0.00265278i | ||||
\(113\) | 7.44256 | − | 16.2969i | 0.700137 | − | 1.53309i | −0.139668 | − | 0.990198i | \(-0.544604\pi\) |
0.839805 | − | 0.542888i | \(-0.182669\pi\) | |||||||
\(114\) | 6.37640 | 0.597205 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −22.0931 | −2.05129 | ||||||||
\(117\) | −2.99223 | + | 6.55207i | −0.276632 | + | 0.605739i | ||||
\(118\) | 24.7060 | + | 7.25434i | 2.27437 | + | 0.667816i | ||||
\(119\) | −0.195298 | − | 0.225386i | −0.0179029 | − | 0.0206611i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 3.30439 | − | 3.81347i | 0.300399 | − | 0.346679i | ||||
\(122\) | 1.28830 | − | 8.96031i | 0.116637 | − | 0.811228i | ||||
\(123\) | 5.32627 | − | 1.56393i | 0.480254 | − | 0.141015i | ||||
\(124\) | −4.30209 | − | 2.76479i | −0.386339 | − | 0.248285i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −0.163236 | − | 0.357438i | −0.0145422 | − | 0.0318431i | ||||
\(127\) | −1.24283 | − | 2.72142i | −0.110283 | − | 0.241487i | 0.846441 | − | 0.532482i | \(-0.178741\pi\) |
−0.956724 | + | 0.290996i | \(0.906013\pi\) | |||||||
\(128\) | −2.16711 | − | 15.0726i | −0.191548 | − | 1.33224i | ||||
\(129\) | 2.01669 | + | 1.29605i | 0.177560 | + | 0.114111i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 1.91036 | − | 13.2869i | 0.166909 | − | 1.16088i | −0.718316 | − | 0.695716i | \(-0.755087\pi\) |
0.885226 | − | 0.465162i | \(-0.154004\pi\) | |||||||
\(132\) | −4.74125 | + | 5.47170i | −0.412673 | + | 0.476250i | ||||
\(133\) | 0.212178 | − | 0.136359i | 0.0183982 | − | 0.0118238i | ||||
\(134\) | 17.8188 | + | 20.5640i | 1.53931 | + | 1.77646i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 3.02915 | − | 6.63291i | 0.259747 | − | 0.568767i | ||||
\(137\) | −19.2932 | −1.64833 | −0.824165 | − | 0.566350i | \(-0.808355\pi\) | ||||
−0.824165 | + | 0.566350i | \(0.808355\pi\) | |||||||
\(138\) | 9.88567 | − | 4.06421i | 0.841524 | − | 0.345968i | ||||
\(139\) | 15.4962 | 1.31437 | 0.657185 | − | 0.753729i | \(-0.271747\pi\) | ||||
0.657185 | + | 0.753729i | \(0.271747\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −11.1441 | − | 3.27220i | −0.938502 | − | 0.275569i | ||||
\(142\) | 2.76835 | + | 3.19485i | 0.232315 | + | 0.268106i | ||||
\(143\) | 7.39292 | − | 4.75114i | 0.618227 | − | 0.397310i | ||||
\(144\) | −1.48047 | + | 1.70856i | −0.123373 | + | 0.142380i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 11.7964 | − | 3.46373i | 0.976275 | − | 0.286660i | ||||
\(147\) | −5.88224 | − | 3.78028i | −0.485159 | − | 0.311793i | ||||
\(148\) | 0.298872 | + | 2.07870i | 0.0245671 | + | 0.170868i | ||||
\(149\) | −6.62691 | − | 14.5109i | −0.542898 | − | 1.18878i | −0.960020 | − | 0.279930i | \(-0.909689\pi\) |
0.417122 | − | 0.908850i | \(-0.363039\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −0.0629411 | − | 0.437765i | −0.00512208 | − | 0.0356248i | 0.987100 | − | 0.160104i | \(-0.0511830\pi\) |
−0.992222 | + | 0.124479i | \(0.960274\pi\) | |||||||
\(152\) | 5.18789 | + | 3.33405i | 0.420793 | + | 0.270427i | ||||
\(153\) | −6.49186 | + | 1.90618i | −0.524836 | + | 0.154106i | ||||
\(154\) | −0.0682278 | + | 0.474535i | −0.00549795 | + | 0.0382391i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 8.98974 | − | 5.77735i | 0.719755 | − | 0.462559i | ||||
\(157\) | 4.66176 | + | 5.37996i | 0.372049 | + | 0.429367i | 0.910640 | − | 0.413200i | \(-0.135589\pi\) |
−0.538592 | + | 0.842567i | \(0.681043\pi\) | |||||||
\(158\) | 14.9873 | + | 4.40066i | 1.19232 | + | 0.350098i | ||||
\(159\) | 4.30997 | − | 9.43751i | 0.341803 | − | 0.748443i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0.242038 | − | 0.346643i | 0.0190753 | − | 0.0273193i | ||||
\(162\) | −2.22871 | −0.175104 | ||||||||
\(163\) | 2.96870 | − | 6.50054i | 0.232526 | − | 0.509162i | −0.757017 | − | 0.653395i | \(-0.773344\pi\) |
0.989544 | + | 0.144233i | \(0.0460714\pi\) | |||||||
\(164\) | 15.8038 | + | 4.64041i | 1.23407 | + | 0.362355i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 7.82322 | − | 5.02768i | 0.607200 | − | 0.390224i | ||||
\(167\) | 0.872694 | − | 1.00714i | 0.0675311 | − | 0.0779351i | −0.720979 | − | 0.692957i | \(-0.756307\pi\) |
0.788510 | + | 0.615022i | \(0.210853\pi\) | |||||||
\(168\) | −0.0270422 | + | 0.188083i | −0.00208635 | + | 0.0145109i | ||||
\(169\) | 0.0280633 | − | 0.00824014i | 0.00215872 | − | 0.000633857i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −0.814334 | − | 5.66382i | −0.0622737 | − | 0.433123i | ||||
\(172\) | 2.95483 | + | 6.47018i | 0.225304 | + | 0.493346i | ||||
\(173\) | −1.12194 | − | 2.45670i | −0.0852992 | − | 0.186779i | 0.862176 | − | 0.506609i | \(-0.169101\pi\) |
−0.947475 | + | 0.319830i | \(0.896374\pi\) | |||||||
\(174\) | −2.36168 | − | 16.4259i | −0.179039 | − | 1.24524i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 2.64649 | − | 0.777080i | 0.199487 | − | 0.0585746i | ||||
\(177\) | −1.64421 | + | 11.4357i | −0.123587 | + | 0.859563i | ||||
\(178\) | −23.2743 | + | 26.8600i | −1.74449 | + | 2.01324i | ||||
\(179\) | −16.6467 | + | 10.6982i | −1.24423 | + | 0.799620i | −0.986046 | − | 0.166474i | \(-0.946762\pi\) |
−0.258188 | + | 0.966095i | \(0.583125\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −3.82402 | − | 1.12283i | −0.284237 | − | 0.0834596i | 0.136506 | − | 0.990639i | \(-0.456413\pi\) |
−0.420744 | + | 0.907180i | \(0.638231\pi\) | |||||||
\(182\) | 0.293947 | − | 0.643655i | 0.0217888 | − | 0.0477109i | ||||
\(183\) | 4.06175 | 0.300253 | ||||||||
\(184\) | 10.1681 | + | 1.86229i | 0.749603 | + | 0.137290i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 1.59570 | − | 3.49409i | 0.117002 | − | 0.256199i | ||||
\(187\) | 7.92038 | + | 2.32563i | 0.579195 | + | 0.170067i | ||||
\(188\) | −22.5678 | − | 26.0447i | −1.64593 | − | 1.89950i | ||||
\(189\) | 0.370807 | − | 0.238303i | 0.0269723 | − | 0.0173340i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 0.850935 | − | 5.91838i | 0.0615715 | − | 0.428239i | −0.935599 | − | 0.353065i | \(-0.885140\pi\) |
0.997170 | − | 0.0751744i | \(-0.0239513\pi\) | |||||||
\(192\) | 12.4367 | − | 3.65175i | 0.897544 | − | 0.263543i | ||||
\(193\) | −8.48523 | − | 5.45312i | −0.610780 | − | 0.392524i | 0.198370 | − | 0.980127i | \(-0.436435\pi\) |
−0.809149 | + | 0.587603i | \(0.800072\pi\) | |||||||
\(194\) | −4.56092 | − | 31.7219i | −0.327455 | − | 2.27750i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −8.61857 | − | 18.8720i | −0.615612 | − | 1.34800i | ||||
\(197\) | −0.728029 | − | 5.06355i | −0.0518699 | − | 0.360763i | −0.999182 | − | 0.0404498i | \(-0.987121\pi\) |
0.947312 | − | 0.320313i | \(-0.103788\pi\) | |||||||
\(198\) | 9.14991 | + | 5.88029i | 0.650255 | + | 0.417894i | ||||
\(199\) | −25.5033 | + | 7.48844i | −1.80788 | + | 0.530842i | −0.998413 | − | 0.0563229i | \(-0.982062\pi\) |
−0.809468 | + | 0.587164i | \(0.800244\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −7.99514 | + | 9.22689i | −0.563934 | + | 0.650814i | ||||
\(202\) | −32.5920 | + | 20.9456i | −2.29316 | + | 1.47373i | ||||
\(203\) | −0.429852 | − | 0.496076i | −0.0301697 | − | 0.0348177i | ||||
\(204\) | 9.63112 | + | 2.82795i | 0.674313 | + | 0.197996i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 2.59275 | 0.180646 | ||||||||
\(207\) | −4.87252 | − | 8.26187i | −0.338664 | − | 0.574240i | ||||
\(208\) | −4.07103 | −0.282275 | ||||||||
\(209\) | −2.90009 | + | 6.35031i | −0.200603 | + | 0.439260i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 9.65433 | + | 11.1417i | 0.664631 | + | 0.767026i | 0.983526 | − | 0.180765i | \(-0.0578572\pi\) |
−0.318895 | + | 0.947790i | \(0.603312\pi\) | |||||||
\(212\) | 25.8974 | − | 16.6432i | 1.77864 | − | 1.14306i | ||||
\(213\) | −1.24213 | + | 1.43350i | −0.0851096 | + | 0.0982217i | ||||
\(214\) | −5.43971 | + | 37.8340i | −0.371851 | + | 2.58628i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 9.06646 | + | 5.82666i | 0.616895 | + | 0.396454i | ||||
\(217\) | −0.0216231 | − | 0.150392i | −0.00146787 | − | 0.0102092i | ||||
\(218\) | −2.42080 | − | 5.30081i | −0.163957 | − | 0.359016i | ||||
\(219\) | 2.29158 | + | 5.01787i | 0.154851 | + | 0.339076i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −10.2496 | − | 6.58702i | −0.689463 | − | 0.443091i | ||||
\(222\) | −1.51353 | + | 0.444413i | −0.101582 | + | 0.0298271i | ||||
\(223\) | −0.144012 | + | 1.00163i | −0.00964378 | + | 0.0670740i | −0.994075 | − | 0.108696i | \(-0.965332\pi\) |
0.984431 | + | 0.175770i | \(0.0562415\pi\) | |||||||
\(224\) | 0.394306 | − | 0.455054i | 0.0263457 | − | 0.0304046i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 26.1482 | + | 30.1767i | 1.73935 | + | 2.00732i | ||||
\(227\) | 4.83803 | + | 1.42057i | 0.321111 | + | 0.0942867i | 0.438316 | − | 0.898821i | \(-0.355575\pi\) |
−0.117205 | + | 0.993108i | \(0.537393\pi\) | |||||||
\(228\) | −3.52649 | + | 7.72193i | −0.233547 | + | 0.511397i | ||||
\(229\) | −22.9504 | −1.51661 | −0.758304 | − | 0.651901i | \(-0.773972\pi\) | ||||
−0.758304 | + | 0.651901i | \(0.773972\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −0.215109 | −0.0141531 | ||||||||
\(232\) | 6.66717 | − | 14.5991i | 0.437721 | − | 0.958476i | ||||
\(233\) | 20.6511 | + | 6.06370i | 1.35290 | + | 0.397246i | 0.876254 | − | 0.481850i | \(-0.160035\pi\) |
0.476644 | + | 0.879097i | \(0.341853\pi\) | |||||||
\(234\) | −10.5127 | − | 12.1323i | −0.687237 | − | 0.793114i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −22.4489 | + | 25.9074i | −1.46130 | + | 1.68643i | ||||
\(237\) | −0.997420 | + | 6.93721i | −0.0647894 | + | 0.450620i | ||||
\(238\) | 0.637740 | − | 0.187257i | 0.0413386 | − | 0.0121381i | ||||
\(239\) | −7.37760 | − | 4.74129i | −0.477217 | − | 0.306689i | 0.279830 | − | 0.960050i | \(-0.409722\pi\) |
−0.757047 | + | 0.653361i | \(0.773358\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 3.66317 | + | 8.02123i | 0.235966 | + | 0.516693i | 0.990157 | − | 0.139962i | \(-0.0446980\pi\) |
−0.754191 | + | 0.656655i | \(0.771971\pi\) | |||||||
\(242\) | 4.67172 | + | 10.2296i | 0.300310 | + | 0.657587i | ||||
\(243\) | −2.27704 | − | 15.8371i | −0.146072 | − | 1.01595i | ||||
\(244\) | 10.1386 | + | 6.51568i | 0.649057 | + | 0.417123i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −1.76070 | + | 12.2459i | −0.112258 | + | 0.780771i | ||||
\(247\) | 6.74767 | − | 7.78723i | 0.429344 | − | 0.495490i | ||||
\(248\) | 3.12524 | − | 2.00847i | 0.198453 | − | 0.127538i | ||||
\(249\) | 2.73247 | + | 3.15343i | 0.173163 | + | 0.199841i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −2.44763 | + | 5.35957i | −0.154493 | + | 0.338293i | −0.971014 | − | 0.239023i | \(-0.923173\pi\) |
0.816521 | + | 0.577316i | \(0.195900\pi\) | |||||||
\(252\) | 0.523141 | 0.0329548 | ||||||||
\(253\) | −0.448583 | + | 11.6937i | −0.0282022 | + | 0.735175i | ||||
\(254\) | 6.66780 | 0.418375 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 7.68968 | + | 2.25789i | 0.480605 | + | 0.141118i | ||||
\(257\) | −5.05121 | − | 5.82941i | −0.315086 | − | 0.363628i | 0.576011 | − | 0.817442i | \(-0.304609\pi\) |
−0.891097 | + | 0.453814i | \(0.850063\pi\) | |||||||
\(258\) | −4.49462 | + | 2.88852i | −0.279823 | + | 0.179831i | ||||
\(259\) | −0.0408599 | + | 0.0471549i | −0.00253891 | + | 0.00293006i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −14.2886 | + | 4.19552i | −0.884443 | + | 0.259696i | ||||
\(262\) | 25.1678 | + | 16.1744i | 1.55487 | + | 0.999256i | ||||
\(263\) | 3.18652 | + | 22.1627i | 0.196489 | + | 1.36661i | 0.814372 | + | 0.580343i | \(0.197081\pi\) |
−0.617883 | + | 0.786270i | \(0.712009\pi\) | |||||||
\(264\) | −2.18489 | − | 4.78424i | −0.134471 | − | 0.294450i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0.0799977 | + | 0.556396i | 0.00490497 | + | 0.0341148i | ||||
\(267\) | −13.4154 | − | 8.62153i | −0.821007 | − | 0.527629i | ||||
\(268\) | −34.7581 | + | 10.2059i | −2.12319 | + | 0.623425i | ||||
\(269\) | −1.31816 | + | 9.16802i | −0.0803698 | + | 0.558984i | 0.909357 | + | 0.416016i | \(0.136574\pi\) |
−0.989727 | + | 0.142968i | \(0.954335\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 18.4727 | − | 11.8717i | 1.12214 | − | 0.721154i | 0.158233 | − | 0.987402i | \(-0.449420\pi\) |
0.963905 | + | 0.266247i | \(0.0857838\pi\) | |||||||
\(272\) | −2.50419 | − | 2.88999i | −0.151839 | − | 0.175232i | ||||
\(273\) | 0.304632 | + | 0.0894481i | 0.0184372 | + | 0.00541365i | ||||
\(274\) | 17.8624 | − | 39.1132i | 1.07911 | − | 2.36291i | ||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −0.545473 | + | 14.2194i | −0.0328336 | + | 0.855909i | ||||
\(277\) | −12.5089 | −0.751589 | −0.375795 | − | 0.926703i | \(-0.622630\pi\) | ||||
−0.375795 | + | 0.926703i | \(0.622630\pi\) | |||||||
\(278\) | −14.3470 | + | 31.4155i | −0.860474 | + | 1.88418i | ||||
\(279\) | −3.30740 | − | 0.971141i | −0.198009 | − | 0.0581407i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −20.6303 | + | 13.2583i | −1.23070 | + | 0.790922i | −0.984000 | − | 0.178171i | \(-0.942982\pi\) |
−0.246699 | + | 0.969092i | \(0.579346\pi\) | |||||||
\(282\) | 16.9514 | − | 19.5629i | 1.00944 | − | 1.16496i | ||||
\(283\) | −2.51410 | + | 17.4860i | −0.149448 | + | 1.03943i | 0.767678 | + | 0.640836i | \(0.221412\pi\) |
−0.917126 | + | 0.398597i | \(0.869497\pi\) | |||||||
\(284\) | −5.40006 | + | 1.58560i | −0.320435 | + | 0.0940882i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 2.78736 | + | 19.3865i | 0.164820 | + | 1.14635i | ||||
\(287\) | 0.203290 | + | 0.445142i | 0.0119998 | + | 0.0262759i | ||||
\(288\) | −5.67474 | − | 12.4259i | −0.334387 | − | 0.732205i | ||||
\(289\) | 0.790638 | + | 5.49901i | 0.0465081 | + | 0.323471i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 13.7972 | − | 4.05122i | 0.808806 | − | 0.237487i | ||||
\(292\) | −2.32939 | + | 16.2012i | −0.136317 | + | 0.948106i | ||||
\(293\) | 5.55996 | − | 6.41653i | 0.324816 | − | 0.374858i | −0.569731 | − | 0.821831i | \(-0.692953\pi\) |
0.894547 | + | 0.446973i | \(0.147498\pi\) | |||||||
\(294\) | 13.1098 | − | 8.42515i | 0.764578 | − | 0.491365i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −1.46379 | − | 0.429809i | −0.0850813 | − | 0.0249821i | ||||
\(297\) | −5.06826 | + | 11.0979i | −0.294090 | + | 0.643968i | ||||
\(298\) | 35.5535 | 2.05956 | ||||||||
\(299\) | 5.49782 | − | 16.3738i | 0.317947 | − | 0.946921i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −0.0877903 | + | 0.192234i | −0.00506015 | + | 0.0110802i | ||||
\(302\) | 0.945756 | + | 0.277699i | 0.0544222 | + | 0.0159798i | ||||
\(303\) | −11.3836 | − | 13.1374i | −0.653970 | − | 0.754722i | ||||
\(304\) | 2.72064 | − | 1.74845i | 0.156039 | − | 0.100280i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 2.14600 | − | 14.9258i | 0.122679 | − | 0.853251i | ||||
\(307\) | −14.0850 | + | 4.13574i | −0.803875 | + | 0.236039i | −0.657759 | − | 0.753228i | \(-0.728496\pi\) |
−0.146116 | + | 0.989267i | \(0.546677\pi\) | |||||||
\(308\) | −0.536936 | − | 0.345068i | −0.0305948 | − | 0.0196621i | ||||
\(309\) | 0.165561 | + | 1.15150i | 0.00941843 | + | 0.0655066i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 12.5355 | + | 27.4490i | 0.710826 | + | 1.55649i | 0.826332 | + | 0.563184i | \(0.190424\pi\) |
−0.115506 | + | 0.993307i | \(0.536849\pi\) | |||||||
\(312\) | 1.10477 | + | 7.68388i | 0.0625455 | + | 0.435014i | ||||
\(313\) | 4.68243 | + | 3.00922i | 0.264667 | + | 0.170091i | 0.666243 | − | 0.745734i | \(-0.267901\pi\) |
−0.401576 | + | 0.915826i | \(0.631538\pi\) | |||||||
\(314\) | −15.2228 | + | 4.46983i | −0.859074 | + | 0.252247i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −13.6180 | + | 15.7160i | −0.766074 | + | 0.884097i | ||||
\(317\) | −2.36484 | + | 1.51979i | −0.132823 | + | 0.0853600i | −0.605365 | − | 0.795948i | \(-0.706973\pi\) |
0.472542 | + | 0.881308i | \(0.343336\pi\) | |||||||
\(318\) | 15.1424 | + | 17.4752i | 0.849142 | + | 0.979962i | ||||
\(319\) | 17.4328 | + | 5.11873i | 0.976049 | + | 0.286594i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −17.1503 | −0.957238 | ||||||||
\(322\) | 0.478662 | + | 0.811620i | 0.0266748 | + | 0.0452298i | ||||
\(323\) | 9.67876 | 0.538541 | ||||||||
\(324\) | 1.23259 | − | 2.69900i | 0.0684774 | − | 0.149945i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 10.4300 | + | 12.0369i | 0.577667 | + | 0.666663i | ||||
\(327\) | 2.19963 | − | 1.41362i | 0.121640 | − | 0.0781732i | ||||
\(328\) | −7.83558 | + | 9.04274i | −0.432648 | + | 0.499302i | ||||
\(329\) | 0.145715 | − | 1.01347i | 0.00803354 | − | 0.0558745i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −11.6540 | − | 7.48954i | −0.640560 | − | 0.411663i | 0.179646 | − | 0.983731i | \(-0.442505\pi\) |
−0.820206 | + | 0.572069i | \(0.806141\pi\) | |||||||
\(332\) | 1.76195 | + | 12.2546i | 0.0966995 | + | 0.672560i | ||||
\(333\) | 0.588043 | + | 1.28764i | 0.0322246 | + | 0.0705620i | ||||
\(334\) | 1.23381 | + | 2.70167i | 0.0675111 | + | 0.147829i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0.0838301 | + | 0.0538744i | 0.00457331 | + | 0.00293909i | ||||
\(337\) | 20.7059 | − | 6.07980i | 1.12792 | − | 0.331188i | 0.336031 | − | 0.941851i | \(-0.390915\pi\) |
0.791890 | + | 0.610663i | \(0.209097\pi\) | |||||||
\(338\) | −0.00927685 | + | 0.0645219i | −0.000504594 | + | 0.00350953i | ||||
\(339\) | −11.7325 | + | 13.5400i | −0.637220 | + | 0.735391i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 2.75404 | + | 3.17834i | 0.149140 | + | 0.172117i | ||||
\(342\) | 12.2362 | + | 3.59288i | 0.661659 | + | 0.194281i | ||||
\(343\) | 0.512414 | − | 1.12203i | 0.0276677 | − | 0.0605839i | ||||
\(344\) | −5.16718 | −0.278596 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 6.01920 | 0.323594 | ||||||||
\(347\) | −7.85449 | + | 17.1989i | −0.421651 | + | 0.923288i | 0.572957 | + | 0.819585i | \(0.305796\pi\) |
−0.994608 | + | 0.103702i | \(0.966931\pi\) | |||||||
\(348\) | 21.1981 | + | 6.22434i | 1.13634 | + | 0.333659i | ||||
\(349\) | −13.7056 | − | 15.8171i | −0.733643 | − | 0.846669i | 0.259234 | − | 0.965815i | \(-0.416530\pi\) |
−0.992877 | + | 0.119146i | \(0.961984\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 11.7924 | − | 13.6091i | 0.629431 | − | 0.726402i | ||||
\(352\) | −2.37187 | + | 16.4967i | −0.126421 | + | 0.879277i | ||||
\(353\) | 1.54672 | − | 0.454159i | 0.0823238 | − | 0.0241724i | −0.240311 | − | 0.970696i | \(-0.577250\pi\) |
0.322635 | + | 0.946523i | \(0.395431\pi\) | |||||||
\(354\) | −21.6615 | − | 13.9210i | −1.15129 | − | 0.739891i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −19.6560 | − | 43.0406i | −1.04177 | − | 2.28115i | ||||
\(357\) | 0.123889 | + | 0.271278i | 0.00655688 | + | 0.0143576i | ||||
\(358\) | −6.27632 | − | 43.6527i | −0.331714 | − | 2.30712i | ||||
\(359\) | 29.2892 | + | 18.8230i | 1.54583 | + | 0.993442i | 0.986362 | + | 0.164588i | \(0.0526294\pi\) |
0.559464 | + | 0.828854i | \(0.311007\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.53906 | − | 10.7044i | 0.0810034 | − | 0.563391i | ||||
\(362\) | 5.81675 | − | 6.71289i | 0.305722 | − | 0.352822i | ||||
\(363\) | −4.24491 | + | 2.72804i | −0.222800 | + | 0.143185i | ||||
\(364\) | 0.616908 | + | 0.711950i | 0.0323348 | + | 0.0373163i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −3.76052 | + | 8.23440i | −0.196566 | + | 0.430419i | ||||
\(367\) | 22.6244 | 1.18098 | 0.590491 | − | 0.807044i | \(-0.298934\pi\) | ||||
0.590491 | + | 0.807044i | \(0.298934\pi\) | |||||||
\(368\) | 3.10352 | − | 4.44480i | 0.161782 | − | 0.231701i | ||||
\(369\) | 11.1023 | 0.577961 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0.877577 | + | 0.257680i | 0.0455615 | + | 0.0133781i | ||||
\(372\) | 3.34890 | + | 3.86483i | 0.173632 | + | 0.200382i | ||||
\(373\) | −9.08151 | + | 5.83633i | −0.470223 | + | 0.302194i | −0.754209 | − | 0.656635i | \(-0.771979\pi\) |
0.283986 | + | 0.958828i | \(0.408343\pi\) | |||||||
\(374\) | −12.0478 | + | 13.9038i | −0.622974 | + | 0.718951i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 24.0207 | − | 7.05312i | 1.23877 | − | 0.363737i | ||||
\(377\) | −22.5594 | − | 14.4981i | −1.16187 | − | 0.746688i | ||||
\(378\) | 0.139806 | + | 0.972370i | 0.00719083 | + | 0.0500133i | ||||
\(379\) | −1.53173 | − | 3.35401i | −0.0786795 | − | 0.172284i | 0.866204 | − | 0.499690i | \(-0.166553\pi\) |
−0.944884 | + | 0.327406i | \(0.893826\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0.425774 | + | 2.96133i | 0.0218131 | + | 0.151713i | ||||
\(382\) | 11.2105 | + | 7.20457i | 0.573580 | + | 0.368618i | ||||
\(383\) | −5.70202 | + | 1.67426i | −0.291360 | + | 0.0855509i | −0.424146 | − | 0.905594i | \(-0.639426\pi\) |
0.132787 | + | 0.991145i | \(0.457608\pi\) | |||||||
\(384\) | −2.16711 | + | 15.0726i | −0.110590 | + | 0.769171i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 18.9111 | − | 12.1534i | 0.962549 | − | 0.618593i | ||||
\(387\) | 3.13973 | + | 3.62344i | 0.159601 | + | 0.184190i | ||||
\(388\) | 40.9382 | + | 12.0205i | 2.07832 | + | 0.610250i | ||||
\(389\) | 2.75929 | − | 6.04199i | 0.139901 | − | 0.306341i | −0.826693 | − | 0.562654i | \(-0.809780\pi\) |
0.966594 | + | 0.256313i | \(0.0825077\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 15.0055 | − | 6.16908i | 0.758860 | − | 0.311984i | ||||
\(392\) | 15.0715 | 0.761226 | ||||||||
\(393\) | −5.57632 | + | 12.2104i | −0.281288 | + | 0.615935i | ||||
\(394\) | 10.9394 | + | 3.21210i | 0.551119 | + | 0.161823i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −12.1815 | + | 7.82858i | −0.612144 | + | 0.393401i | ||||
\(397\) | −2.98449 | + | 3.44429i | −0.149787 | + | 0.172864i | −0.825685 | − | 0.564132i | \(-0.809211\pi\) |
0.675897 | + | 0.736996i | \(0.263756\pi\) | |||||||
\(398\) | 8.43058 | − | 58.6360i | 0.422587 | − | 2.93916i | ||||
\(399\) | −0.242000 | + | 0.0710577i | −0.0121152 | + | 0.00355733i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 3.97219 | + | 27.6272i | 0.198362 | + | 1.37964i | 0.809038 | + | 0.587756i | \(0.199989\pi\) |
−0.610676 | + | 0.791880i | \(0.709102\pi\) | |||||||
\(402\) | −11.3035 | − | 24.7512i | −0.563767 | − | 1.23448i | ||||
\(403\) | −2.57858 | − | 5.64630i | −0.128448 | − | 0.281262i | ||||
\(404\) | −7.34038 | − | 51.0534i | −0.365197 | − | 2.54000i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 1.40367 | − | 0.412155i | 0.0696629 | − | 0.0204549i | ||||
\(407\) | 0.245784 | − | 1.70947i | 0.0121831 | − | 0.0847351i | ||||
\(408\) | −4.77515 | + | 5.51082i | −0.236405 | + | 0.272826i | ||||
\(409\) | 6.83017 | − | 4.38949i | 0.337730 | − | 0.217046i | −0.360772 | − | 0.932654i | \(-0.617487\pi\) |
0.698502 | + | 0.715608i | \(0.253850\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 18.5117 | + | 5.43552i | 0.913115 | + | 0.268115i | ||||
\(412\) | −1.43393 | + | 3.13987i | −0.0706446 | + | 0.154690i | ||||
\(413\) | −1.01850 | −0.0501169 | ||||||||
\(414\) | 21.2605 | − | 2.22893i | 1.04490 | − | 0.109546i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 10.2188 | − | 22.3760i | 0.501016 | − | 1.09707i | ||||
\(417\) | −14.8685 | − | 4.36578i | −0.728113 | − | 0.213793i | ||||
\(418\) | −10.1890 | − | 11.7587i | −0.498360 | − | 0.575138i | ||||
\(419\) | −23.3315 | + | 14.9942i | −1.13982 | + | 0.732517i | −0.967587 | − | 0.252539i | \(-0.918734\pi\) |
−0.172232 | + | 0.985056i | \(0.555098\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 4.97445 | − | 34.5981i | 0.242440 | − | 1.68621i | −0.397359 | − | 0.917663i | \(-0.630073\pi\) |
0.639799 | − | 0.768543i | \(-0.279018\pi\) | |||||||
\(422\) | −31.5259 | + | 9.25685i | −1.53466 | + | 0.450616i | ||||
\(423\) | −19.5416 | − | 12.5586i | −0.950145 | − | 0.610621i | ||||
\(424\) | 3.18261 | + | 22.1355i | 0.154561 | + | 1.07500i | ||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −1.75612 | − | 3.84537i | −0.0850844 | − | 0.186309i | ||||
\(427\) | 0.0509583 | + | 0.354423i | 0.00246604 | + | 0.0171517i | ||||
\(428\) | −42.8092 | − | 27.5118i | −2.06926 | − | 1.32983i | ||||
\(429\) | −8.43201 | + | 2.47586i | −0.407101 | + | 0.119536i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 6.06858 | − | 7.00351i | 0.292313 | − | 0.337347i | −0.590530 | − | 0.807016i | \(-0.701081\pi\) |
0.882843 | + | 0.469669i | \(0.155627\pi\) | |||||||
\(432\) | 4.75465 | − | 3.05563i | 0.228758 | − | 0.147014i | ||||
\(433\) | 14.8185 | + | 17.1014i | 0.712129 | + | 0.821841i | 0.990337 | − | 0.138680i | \(-0.0442859\pi\) |
−0.278208 | + | 0.960521i | \(0.589740\pi\) | |||||||
\(434\) | 0.324909 | + | 0.0954019i | 0.0155961 | + | 0.00457944i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 7.75820 | 0.371550 | ||||||||
\(437\) | 3.35816 | + | 13.3037i | 0.160642 | + | 0.636404i | ||||
\(438\) | −12.2944 | −0.587448 | ||||||||
\(439\) | −7.68428 | + | 16.8262i | −0.366751 | + | 0.803072i | 0.632835 | + | 0.774287i | \(0.281891\pi\) |
−0.999586 | + | 0.0287853i | \(0.990836\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −9.15787 | − | 10.5687i | −0.436089 | − | 0.503274i | ||||
\(442\) | 22.8434 | − | 14.6805i | 1.08655 | − | 0.698282i | ||||
\(443\) | −14.6551 | + | 16.9129i | −0.696284 | + | 0.803554i | −0.988245 | − | 0.152876i | \(-0.951147\pi\) |
0.291962 | + | 0.956430i | \(0.405692\pi\) | |||||||
\(444\) | 0.298872 | − | 2.07870i | 0.0141838 | − | 0.0986507i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −1.89727 | − | 1.21930i | −0.0898384 | − | 0.0577356i | ||||
\(447\) | 2.27028 | + | 15.7901i | 0.107381 | + | 0.746848i | ||||
\(448\) | 0.474677 | + | 1.03940i | 0.0224264 | + | 0.0491069i | ||||
\(449\) | 2.04143 | + | 4.47012i | 0.0963412 | + | 0.210958i | 0.951666 | − | 0.307134i | \(-0.0993699\pi\) |
−0.855325 | + | 0.518092i | \(0.826643\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −11.3950 | − | 7.32313i | −0.536570 | − | 0.344833i | ||||
\(452\) | −51.0058 | + | 14.9767i | −2.39911 | + | 0.704442i | ||||
\(453\) | −0.0629411 | + | 0.437765i | −0.00295723 | + | 0.0205680i | ||||
\(454\) | −7.35916 | + | 8.49293i | −0.345383 | + | 0.398593i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −4.03843 | − | 4.66060i | −0.189117 | − | 0.218252i | ||||
\(457\) | 11.1134 | + | 3.26318i | 0.519861 | + | 0.152645i | 0.531128 | − | 0.847291i | \(-0.321768\pi\) |
−0.0112669 | + | 0.999937i | \(0.503586\pi\) | |||||||
\(458\) | 21.2484 | − | 46.5275i | 0.992873 | − | 2.17409i | ||||
\(459\) | 16.9148 | 0.789516 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −15.5495 | −0.724210 | −0.362105 | − | 0.932137i | \(-0.617942\pi\) | ||||
−0.362105 | + | 0.932137i | \(0.617942\pi\) | |||||||
\(462\) | 0.199156 | − | 0.436091i | 0.00926558 | − | 0.0202888i | ||||
\(463\) | 9.71687 | + | 2.85313i | 0.451581 | + | 0.132596i | 0.499611 | − | 0.866250i | \(-0.333476\pi\) |
−0.0480300 | + | 0.998846i | \(0.515294\pi\) | |||||||
\(464\) | −5.51175 | − | 6.36089i | −0.255876 | − | 0.295297i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −31.4125 | + | 36.2520i | −1.45516 | + | 1.67934i | ||||
\(467\) | 0.0227489 | − | 0.158222i | 0.00105269 | − | 0.00732164i | −0.989288 | − | 0.145975i | \(-0.953368\pi\) |
0.990341 | + | 0.138653i | \(0.0442773\pi\) | |||||||
\(468\) | 20.5065 | − | 6.02126i | 0.947914 | − | 0.278333i | ||||
\(469\) | −0.905432 | − | 0.581886i | −0.0418089 | − | 0.0268690i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −2.95722 | − | 6.47540i | −0.136261 | − | 0.298371i | ||||
\(472\) | −10.3450 | − | 22.6524i | −0.476168 | − | 1.04266i | ||||
\(473\) | −0.832472 | − | 5.78997i | −0.0382771 | − | 0.266223i | ||||
\(474\) | −13.1404 | − | 8.44481i | −0.603558 | − | 0.387883i | ||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −0.125932 | + | 0.875877i | −0.00577209 | + | 0.0401458i | ||||
\(477\) | 13.5885 | − | 15.6819i | 0.622173 | − | 0.718026i | ||||
\(478\) | 16.4425 | − | 10.5670i | 0.752063 | − | 0.483321i | ||||
\(479\) | −3.84712 | − | 4.43982i | −0.175779 | − | 0.202860i | 0.661022 | − | 0.750366i | \(-0.270123\pi\) |
−0.836802 | + | 0.547506i | \(0.815577\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −1.05892 | + | 2.31870i | −0.0482825 | + | 0.105724i | ||||
\(482\) | −19.6530 | −0.895169 | ||||||||
\(483\) | −0.329895 | + | 0.264411i | −0.0150107 | + | 0.0120311i | ||||
\(484\) | −14.9720 | −0.680545 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 34.2149 | + | 10.0464i | 1.55202 | + | 0.455714i | ||||
\(487\) | −4.54083 | − | 5.24040i | −0.205765 | − | 0.237465i | 0.643482 | − | 0.765461i | \(-0.277489\pi\) |
−0.849247 | + | 0.527996i | \(0.822944\pi\) | |||||||
\(488\) | −7.36514 | + | 4.73329i | −0.333404 | + | 0.214266i | ||||
\(489\) | −4.67986 | + | 5.40085i | −0.211631 | + | 0.244235i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 21.0671 | − | 6.18586i | 0.950745 | − | 0.279164i | 0.230648 | − | 0.973037i | \(-0.425915\pi\) |
0.720097 | + | 0.693873i | \(0.244097\pi\) | |||||||
\(492\) | −13.8563 | − | 8.90487i | −0.624688 | − | 0.401463i | ||||
\(493\) | −3.58481 | − | 24.9329i | −0.161452 | − | 1.12292i | ||||
\(494\) | 9.53982 | + | 20.8893i | 0.429217 | + | 0.939854i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −0.277260 | − | 1.92839i | −0.0124493 | − | 0.0865871i | ||||
\(497\) | −0.140669 | − | 0.0904024i | −0.00630986 | − | 0.00405510i | ||||
\(498\) | −8.92279 | + | 2.61997i | −0.399840 | + | 0.117404i | ||||
\(499\) | 4.04910 | − | 28.1621i | 0.181263 | − | 1.26071i | −0.672520 | − | 0.740079i | \(-0.734788\pi\) |
0.853783 | − | 0.520630i | \(-0.174303\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −1.12109 | + | 0.720480i | −0.0500866 | + | 0.0321887i | ||||
\(502\) | −8.59936 | − | 9.92419i | −0.383808 | − | 0.442938i | ||||
\(503\) | 32.9609 | + | 9.67821i | 1.46966 | + | 0.431530i | 0.915987 | − | 0.401207i | \(-0.131409\pi\) |
0.553668 | + | 0.832737i | \(0.313227\pi\) | |||||||
\(504\) | −0.157872 | + | 0.345691i | −0.00703217 | + | 0.0153983i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −23.2913 | − | 11.7359i | −1.03543 | − | 0.521723i | ||||
\(507\) | −0.0292481 | −0.00129895 | ||||||||
\(508\) | −3.68765 | + | 8.07482i | −0.163613 | + | 0.358262i | ||||
\(509\) | 6.60273 | + | 1.93874i | 0.292661 | + | 0.0859329i | 0.424767 | − | 0.905303i | \(-0.360356\pi\) |
−0.132107 | + | 0.991236i | \(0.542174\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −0.409102 | + | 0.262914i | −0.0180976 | + | 0.0116306i | ||||
\(512\) | 8.24708 | − | 9.51763i | 0.364473 | − | 0.420624i | ||||
\(513\) | −2.03584 | + | 14.1595i | −0.0898843 | + | 0.625159i | ||||
\(514\) | 16.4946 | − | 4.84325i | 0.727545 | − | 0.213626i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −1.01228 | − | 7.04056i | −0.0445631 | − | 0.309943i | ||||
\(517\) | 11.7731 | + | 25.7796i | 0.517782 | + | 1.13378i | ||||
\(518\) | −0.0577675 | − | 0.126493i | −0.00253816 | − | 0.00555779i | ||||
\(519\) | 0.384358 | + | 2.67327i | 0.0168714 | + | 0.117343i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 5.29187 | − | 1.55383i | 0.231841 | − | 0.0680747i | −0.163748 | − | 0.986502i | \(-0.552358\pi\) |
0.395589 | + | 0.918427i | \(0.370540\pi\) | |||||||
\(522\) | 4.72337 | − | 32.8517i | 0.206736 | − | 1.43788i | ||||
\(523\) | −3.11663 | + | 3.59678i | −0.136281 | + | 0.157276i | −0.819787 | − | 0.572668i | \(-0.805908\pi\) |
0.683507 | + | 0.729944i | \(0.260454\pi\) | |||||||
\(524\) | −33.5066 | + | 21.5334i | −1.46374 | + | 0.940689i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −47.8808 | − | 14.0591i | −2.08770 | − | 0.613005i | ||||
\(527\) | 2.42212 | − | 5.30369i | 0.105509 | − | 0.231033i | ||||
\(528\) | −2.75822 | −0.120036 | ||||||||
\(529\) | 13.6859 | + | 18.4850i | 0.595039 | + | 0.803697i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −9.59886 | + | 21.0186i | −0.416555 | + | 0.912129i | ||||
\(532\) | −0.718048 | − | 0.210838i | −0.0311313 | − | 0.00914098i | ||||
\(533\) | 13.0922 | + | 15.1092i | 0.567087 | + | 0.654453i | ||||
\(534\) | 29.8989 | − | 19.2149i | 1.29385 | − | 0.831508i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 3.74514 | − | 26.0480i | 0.161766 | − | 1.12510i | ||||
\(537\) | 18.9864 | − | 5.57492i | 0.819325 | − | 0.240576i | ||||
\(538\) | −17.3660 | − | 11.1604i | −0.748700 | − | 0.481160i | ||||
\(539\) | 2.42813 | + | 16.8880i | 0.104587 | + | 0.727419i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −7.02447 | − | 15.3814i | −0.302006 | − | 0.661300i | 0.696406 | − | 0.717648i | \(-0.254782\pi\) |
−0.998411 | + | 0.0563484i | \(0.982054\pi\) | |||||||
\(542\) | 6.96478 | + | 48.4411i | 0.299163 | + | 2.08072i | ||||
\(543\) | 3.35278 | + | 2.15470i | 0.143882 | + | 0.0924671i | ||||
\(544\) | 22.1704 | − | 6.50980i | 0.950546 | − | 0.279106i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −0.463379 | + | 0.534768i | −0.0198308 | + | 0.0228859i | ||||
\(547\) | 32.4460 | − | 20.8518i | 1.38729 | − | 0.891557i | 0.387746 | − | 0.921766i | \(-0.373254\pi\) |
0.999544 | + | 0.0302093i | \(0.00961739\pi\) | |||||||
\(548\) | 37.4879 | + | 43.2633i | 1.60140 | + | 1.84812i | ||||
\(549\) | 7.79444 | + | 2.28865i | 0.332659 | + | 0.0976774i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 21.3030 | 0.907539 | ||||||||
\(552\) | −9.23157 | − | 4.65154i | −0.392922 | − | 0.197983i | ||||
\(553\) | −0.617845 | −0.0262734 | ||||||||
\(554\) | 11.5813 | − | 25.3594i | 0.492040 | − | 1.07742i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −30.1100 | − | 34.7488i | −1.27695 | − | 1.47368i | ||||
\(557\) | −35.4471 | + | 22.7805i | −1.50194 | + | 0.965239i | −0.507309 | + | 0.861764i | \(0.669360\pi\) |
−0.994632 | + | 0.103475i | \(0.967004\pi\) | |||||||
\(558\) | 5.03092 | − | 5.80599i | 0.212976 | − | 0.245787i | ||||
\(559\) | −1.22870 | + | 8.54579i | −0.0519685 | + | 0.361449i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −6.94434 | − | 4.46286i | −0.293190 | − | 0.188422i | ||||
\(562\) | −7.77824 | − | 54.0988i | −0.328105 | − | 2.28202i | ||||
\(563\) | 2.50064 | + | 5.47564i | 0.105389 | + | 0.230771i | 0.954979 | − | 0.296674i | \(-0.0958775\pi\) |
−0.849589 | + | 0.527445i | \(0.823150\pi\) | |||||||
\(564\) | 14.3160 | + | 31.3477i | 0.602814 | + | 1.31998i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −33.1217 | − | 21.2860i | −1.39221 | − | 0.894719i | ||||
\(567\) | 0.0845850 | − | 0.0248364i | 0.00355224 | − | 0.00104303i | ||||
\(568\) | 0.581849 | − | 4.04685i | 0.0244139 | − | 0.169802i | ||||
\(569\) | 11.4512 | − | 13.2154i | 0.480061 | − | 0.554020i | −0.463121 | − | 0.886295i | \(-0.653271\pi\) |
0.943183 | + | 0.332275i | \(0.107816\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −8.64327 | − | 9.97487i | −0.361710 | − | 0.417435i | 0.545502 | − | 0.838109i | \(-0.316339\pi\) |
−0.907212 | + | 0.420674i | \(0.861794\pi\) | |||||||
\(572\) | −25.0189 | − | 7.34622i | −1.04609 | − | 0.307161i | ||||
\(573\) | −2.48387 | + | 5.43891i | −0.103765 | + | 0.227214i | ||||
\(574\) | −1.09065 | −0.0455229 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 25.9235 | 1.08015 | ||||||||
\(577\) | 13.4953 | − | 29.5506i | 0.561818 | − | 1.23021i | −0.389223 | − | 0.921143i | \(-0.627257\pi\) |
0.951041 | − | 0.309065i | \(-0.100016\pi\) | |||||||
\(578\) | −11.8802 | − | 3.48833i | −0.494149 | − | 0.145095i | ||||
\(579\) | 6.60519 | + | 7.62280i | 0.274502 | + | 0.316793i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −0.240883 | + | 0.277994i | −0.00999351 | + | 0.0115331i | ||||
\(582\) | −4.56092 | + | 31.7219i | −0.189056 | + | 1.31491i | ||||
\(583\) | −24.2907 | + | 7.13240i | −1.00602 | + | 0.295394i | ||||
\(584\) | −10.0028 | − | 6.42841i | −0.413919 | − | 0.266009i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 7.86064 | + | 17.2124i | 0.324720 | + | 0.711037i | ||||
\(587\) | 5.47162 | + | 11.9812i | 0.225838 | + | 0.494516i | 0.988301 | − | 0.152515i | \(-0.0487374\pi\) |
−0.762463 | + | 0.647032i | \(0.776010\pi\) | |||||||
\(588\) | 2.95259 | + | 20.5357i | 0.121763 | + | 0.846879i | ||||
\(589\) | 4.14825 | + | 2.66592i | 0.170926 | + | 0.109847i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −0.728029 | + | 5.06355i | −0.0299471 | + | 0.208287i | ||||
\(592\) | −0.523923 | + | 0.604640i | −0.0215331 | + | 0.0248505i | ||||
\(593\) | −26.5698 | + | 17.0754i | −1.09109 | + | 0.701202i | −0.957094 | − | 0.289779i | \(-0.906418\pi\) |
−0.133999 | + | 0.990982i | \(0.542782\pi\) | |||||||
\(594\) | −17.8065 | − | 20.5498i | −0.730610 | − | 0.843169i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −19.6630 | + | 43.0559i | −0.805426 | + | 1.76364i | ||||
\(597\) | 26.5800 | 1.08785 | ||||||||
\(598\) | 28.1046 | + | 26.3053i | 1.14928 | + | 1.07570i | ||||
\(599\) | −5.38162 | −0.219887 | −0.109943 | − | 0.993938i | \(-0.535067\pi\) | ||||
−0.109943 | + | 0.993938i | \(0.535067\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −32.4793 | − | 9.53678i | −1.32486 | − | 0.389013i | −0.458614 | − | 0.888636i | \(-0.651654\pi\) |
−0.866243 | + | 0.499622i | \(0.833472\pi\) | |||||||
\(602\) | −0.308437 | − | 0.355955i | −0.0125710 | − | 0.0145077i | ||||
\(603\) | −20.5416 | + | 13.2013i | −0.836518 | + | 0.537598i | ||||
\(604\) | −0.859352 | + | 0.991745i | −0.0349665 | + | 0.0403535i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 37.1728 | − | 10.9149i | 1.51004 | − | 0.443388i | ||||
\(607\) | −18.3320 | − | 11.7812i | −0.744072 | − | 0.478186i | 0.112863 | − | 0.993611i | \(-0.463998\pi\) |
−0.856935 | + | 0.515424i | \(0.827634\pi\) | |||||||
\(608\) | 2.78103 | + | 19.3425i | 0.112786 | + | 0.784442i | ||||
\(609\) | 0.272679 | + | 0.597084i | 0.0110495 | + | 0.0241951i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −5.95300 | − | 41.4040i | −0.240833 | − | 1.67503i | ||||
\(612\) | 16.8885 | + | 10.8536i | 0.682678 | + | 0.438731i | ||||
\(613\) | −6.50705 | + | 1.91064i | −0.262817 | + | 0.0771701i | −0.410486 | − | 0.911867i | \(-0.634641\pi\) |
0.147669 | + | 0.989037i | \(0.452823\pi\) | |||||||
\(614\) | 4.65607 | − | 32.3837i | 0.187904 | − | 1.30690i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0.390055 | − | 0.250673i | 0.0157158 | − | 0.0100999i | ||||
\(617\) | −21.1308 | − | 24.3863i | −0.850695 | − | 0.981755i | 0.149280 | − | 0.988795i | \(-0.452304\pi\) |
−0.999975 | + | 0.00704038i | \(0.997759\pi\) | |||||||
\(618\) | −2.48773 | − | 0.730462i | −0.100071 | − | 0.0293835i | ||||
\(619\) | −14.5801 | + | 31.9260i | −0.586024 | + | 1.28321i | 0.351792 | + | 0.936078i | \(0.385573\pi\) |
−0.937815 | + | 0.347134i | \(0.887155\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 5.86879 | + | 23.2499i | 0.235506 | + | 0.932986i | ||||
\(622\) | −67.2534 | −2.69661 | ||||||||
\(623\) | 0.583995 | − | 1.27877i | 0.0233973 | − | 0.0512329i | ||||
\(624\) | 3.90613 | + | 1.14694i | 0.156370 | + | 0.0459144i | ||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −10.4358 | + | 6.70667i | −0.417098 | + | 0.268052i | ||||
\(627\) | 4.57170 | − | 5.27603i | 0.182576 | − | 0.210704i | ||||
\(628\) | 3.00600 | − | 20.9072i | 0.119952 | − | 0.834287i | ||||
\(629\) | −2.29740 | + | 0.674577i | −0.0916033 | + | 0.0268971i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 1.85675 | + | 12.9139i | 0.0739159 | + | 0.514096i | 0.992820 | + | 0.119616i | \(0.0381663\pi\) |
−0.918904 | + | 0.394480i | \(0.870925\pi\) | |||||||
\(632\) | −6.27554 | − | 13.7415i | −0.249628 | − | 0.546608i | ||||
\(633\) | −6.12428 | − | 13.4103i | −0.243418 | − | 0.533012i | ||||
\(634\) | −0.891617 | − | 6.20133i | −0.0354106 | − | 0.246286i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −29.5373 | + | 8.67294i | −1.17123 | + | 0.343904i | ||||
\(637\) | 3.58384 | − | 24.9261i | 0.141997 | − | 0.987610i | ||||
\(638\) | −26.5172 | + | 30.6024i | −1.04982 | + | 1.21156i | ||||
\(639\) | −3.19136 | + | 2.05097i | −0.126248 | + | 0.0811349i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 34.6688 | + | 10.1797i | 1.36934 | + | 0.402073i | 0.882044 | − | 0.471166i | \(-0.156167\pi\) |
0.487291 | + | 0.873239i | \(0.337985\pi\) | |||||||
\(642\) | 15.8784 | − | 34.7689i | 0.626672 | − | 1.37222i | ||||
\(643\) | −31.5510 | −1.24425 | −0.622126 | − | 0.782917i | \(-0.713731\pi\) | ||||
−0.622126 | + | 0.782917i | \(0.713731\pi\) | |||||||
\(644\) | −1.24761 | + | 0.130798i | −0.0491628 | + | 0.00515417i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −8.96097 | + | 19.6218i | −0.352565 | + | 0.772009i | ||||
\(647\) | −13.3013 | − | 3.90562i | −0.522929 | − | 0.153546i | 0.00960580 | − | 0.999954i | \(-0.496942\pi\) |
−0.532535 | + | 0.846408i | \(0.678761\pi\) | |||||||
\(648\) | 1.41153 | + | 1.62899i | 0.0554501 | + | 0.0639928i | ||||
\(649\) | 23.7160 | − | 15.2413i | 0.930934 | − | 0.598275i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −0.0216231 | + | 0.150392i | −0.000847474 | + | 0.00589431i | ||||
\(652\) | −20.3453 | + | 5.97391i | −0.796782 | + | 0.233956i | ||||
\(653\) | 4.75724 | + | 3.05729i | 0.186165 | + | 0.119641i | 0.630404 | − | 0.776267i | \(-0.282889\pi\) |
−0.444239 | + | 0.895909i | \(0.646526\pi\) | |||||||
\(654\) | 0.829328 | + | 5.76810i | 0.0324293 | + | 0.225551i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 2.60667 | + | 5.70780i | 0.101773 | + | 0.222852i | ||||
\(657\) | 1.57012 | + | 10.9204i | 0.0612564 | + | 0.426047i | ||||
\(658\) | 1.91971 | + | 1.23372i | 0.0748379 | + | 0.0480954i | ||||
\(659\) | −28.0838 | + | 8.24614i | −1.09399 | + | 0.321224i | −0.778461 | − | 0.627692i | \(-0.784000\pi\) |
−0.315527 | + | 0.948917i | \(0.602181\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −10.5207 | + | 12.1415i | −0.409207 | + | 0.472250i | −0.922519 | − | 0.385952i | \(-0.873873\pi\) |
0.513312 | + | 0.858202i | \(0.328418\pi\) | |||||||
\(662\) | 25.9733 | − | 16.6920i | 1.00948 | − | 0.648753i | ||||
\(663\) | 7.97864 | + | 9.20784i | 0.309865 | + | 0.357603i | ||||
\(664\) | −8.62956 | − | 2.53387i | −0.334892 | − | 0.0983331i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −3.15486 | −0.122248 | ||||||||
\(667\) | 33.0272 | − | 13.5782i | 1.27882 | − | 0.525749i | ||||
\(668\) | −3.95413 | −0.152990 | ||||||||
\(669\) | 0.420370 | − | 0.920482i | 0.0162524 | − | 0.0355879i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −6.49036 | − | 7.49027i | −0.250558 | − | 0.289159i | ||||
\(672\) | −0.506538 | + | 0.325532i | −0.0195401 | + | 0.0125577i | ||||
\(673\) | 2.50376 | − | 2.88949i | 0.0965128 | − | 0.111382i | −0.705438 | − | 0.708771i | \(-0.749250\pi\) |
0.801951 | + | 0.597389i | \(0.203795\pi\) | |||||||
\(674\) | −6.84471 | + | 47.6060i | −0.263649 | + | 1.83372i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −0.0730065 | − | 0.0469185i | −0.00280794 | − | 0.00180456i | ||||
\(677\) | 2.33764 | + | 16.2586i | 0.0898428 | + | 0.624870i | 0.984140 | + | 0.177396i | \(0.0567673\pi\) |
−0.894297 | + | 0.447474i | \(0.852324\pi\) | |||||||
\(678\) | −16.5873 | − | 36.3211i | −0.637031 | − | 1.39490i | ||||
\(679\) | 0.526602 | + | 1.15310i | 0.0202091 | + | 0.0442518i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −4.24183 | − | 2.72606i | −0.162547 | − | 0.104463i | ||||
\(682\) | −8.99325 | + | 2.64066i | −0.344369 | + | 0.101116i | ||||
\(683\) | 1.04764 | − | 7.28651i | 0.0400869 | − | 0.278811i | −0.959912 | − | 0.280302i | \(-0.909566\pi\) |
0.999999 | + | 0.00149105i | \(0.000474615\pi\) | |||||||
\(684\) | −11.1183 | + | 12.8312i | −0.425119 | + | 0.490614i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 1.80028 | + | 2.07764i | 0.0687351 | + | 0.0793245i | ||||
\(687\) | 22.0208 | + | 6.46589i | 0.840145 | + | 0.246689i | ||||
\(688\) | −1.12569 | + | 2.46491i | −0.0429163 | + | 0.0939737i | ||||
\(689\) | 37.3658 | 1.42352 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −9.67502 | −0.368055 | −0.184028 | − | 0.982921i | \(-0.558914\pi\) | ||||
−0.184028 | + | 0.982921i | \(0.558914\pi\) | |||||||
\(692\) | −3.32894 | + | 7.28935i | −0.126547 | + | 0.277100i | ||||
\(693\) | −0.412791 | − | 0.121206i | −0.0156806 | − | 0.00460425i | ||||
\(694\) | −27.5955 | − | 31.8469i | −1.04751 | − | 1.20889i | ||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −10.5101 | + | 12.1293i | −0.398386 | + | 0.459762i | ||||
\(697\) | −2.67257 | + | 18.5881i | −0.101231 | + | 0.704076i | ||||
\(698\) | 44.7552 | − | 13.1413i | 1.69401 | − | 0.497406i | ||||
\(699\) | −18.1062 | − | 11.6362i | −0.684840 | − | 0.440120i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 17.6838 | + | 38.7221i | 0.667908 | + | 1.46252i | 0.874965 | + | 0.484186i | \(0.160884\pi\) |
−0.207057 | + | 0.978329i | \(0.566388\pi\) | |||||||
\(702\) | 16.6720 | + | 36.5066i | 0.629244 | + | 1.37785i | ||||
\(703\) | −0.288184 | − | 2.00436i | −0.0108691 | − | 0.0755960i | ||||
\(704\) | −26.6071 | − | 17.0994i | −1.00279 | − | 0.644456i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −0.511298 | + | 3.55616i | −0.0192430 | + | 0.133838i | ||||
\(707\) | 1.00353 | − | 1.15814i | 0.0377417 | − | 0.0435562i | ||||
\(708\) | 28.8385 | − | 18.5334i | 1.08382 | − | 0.696526i | ||||
\(709\) | −22.9666 | − | 26.5049i | −0.862529 | − | 0.995411i | −0.999988 | − | 0.00490358i | \(-0.998439\pi\) |
0.137459 | − | 0.990507i | \(-0.456106\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −5.82291 | + | 12.7504i | −0.218376 | + | 0.478177i | ||||
\(712\) | 34.3729 | 1.28818 | ||||||||
\(713\) | 8.13045 | + | 1.48909i | 0.304488 | + | 0.0557668i | ||||
\(714\) | −0.664664 | −0.0248744 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 56.3353 | + | 16.5415i | 2.10535 | + | 0.618187i | ||||
\(717\) | 5.74298 | + | 6.62775i | 0.214475 | + | 0.247518i | ||||
\(718\) | −65.2771 | + | 41.9511i | −2.43612 | + | 1.56560i | ||||
\(719\) | −14.5394 | + | 16.7793i | −0.542226 | + | 0.625763i | −0.959054 | − | 0.283223i | \(-0.908596\pi\) |
0.416828 | + | 0.908986i | \(0.363142\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −0.0984013 | + | 0.0288932i | −0.00366466 | + | 0.00107604i | ||||
\(722\) | 20.2762 | + | 13.0307i | 0.754602 | + | 0.484953i | ||||
\(723\) | −1.25495 | − | 8.72835i | −0.0466720 | − | 0.324611i | ||||
\(724\) | 4.91245 | + | 10.7568i | 0.182570 | + | 0.399772i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −1.60046 | − | 11.1315i | −0.0593987 | − | 0.413127i | ||||
\(727\) | −0.587772 | − | 0.377738i | −0.0217993 | − | 0.0140095i | 0.529696 | − | 0.848188i | \(-0.322306\pi\) |
−0.551495 | + | 0.834178i | \(0.685942\pi\) | |||||||
\(728\) | −0.656624 | + | 0.192802i | −0.0243361 | + | 0.00714573i | ||||
\(729\) | −1.85009 | + | 12.8677i | −0.0685220 | + | 0.476581i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −6.82240 | + | 4.38449i | −0.252336 | + | 0.162166i | ||||
\(732\) | −7.89223 | − | 9.10812i | −0.291705 | − | 0.336646i | ||||
\(733\) | −35.7918 | − | 10.5094i | −1.32200 | − | 0.388174i | −0.456785 | − | 0.889577i | \(-0.650999\pi\) |
−0.865214 | + | 0.501403i | \(0.832817\pi\) | |||||||
\(734\) | −20.9465 | + | 45.8664i | −0.773149 | + | 1.69296i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 16.6402 | + | 28.2151i | 0.613364 | + | 1.04002i | ||||
\(737\) | 29.7909 | 1.09736 | ||||||||
\(738\) | −10.2789 | + | 22.5077i | −0.378372 | + | 0.828518i | ||||
\(739\) | 23.5752 | + | 6.92231i | 0.867229 | + | 0.254641i | 0.684936 | − | 0.728603i | \(-0.259830\pi\) |
0.182293 | + | 0.983244i | \(0.441648\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −8.66826 | + | 5.57075i | −0.318437 | + | 0.204647i | ||||
\(742\) | −1.33489 | + | 1.54054i | −0.0490053 | + | 0.0565552i | ||||
\(743\) | 5.88612 | − | 40.9388i | 0.215941 | − | 1.50190i | −0.536871 | − | 0.843665i | \(-0.680394\pi\) |
0.752811 | − | 0.658236i | \(-0.228697\pi\) | |||||||
\(744\) | −3.56450 | + | 1.04663i | −0.130681 | + | 0.0383713i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −3.42400 | − | 23.8145i | −0.125362 | − | 0.871910i | ||||
\(747\) | 3.46671 | + | 7.59104i | 0.126840 | + | 0.277742i | ||||
\(748\) | −10.1748 | − | 22.2796i | −0.372026 | − | 0.814623i | ||||
\(749\) | −0.215166 | − | 1.49651i | −0.00786201 | − | 0.0546815i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 39.3106 | − | 11.5426i | 1.43446 | − | 0.421197i | 0.530091 | − | 0.847941i | \(-0.322158\pi\) |
0.904372 | + | 0.426744i | \(0.140339\pi\) | |||||||
\(752\) | 1.86842 | − | 12.9952i | 0.0681344 | − | 0.473885i | ||||
\(753\) | 3.85845 | − | 4.45289i | 0.140610 | − | 0.162272i | ||||
\(754\) | 50.2783 | − | 32.3119i | 1.83103 | − | 1.17673i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −1.25488 | − | 0.368465i | −0.0456394 | − | 0.0134009i | ||||
\(757\) | −4.14940 | + | 9.08592i | −0.150812 | + | 0.330233i | −0.969927 | − | 0.243397i | \(-0.921738\pi\) |
0.819114 | + | 0.573630i | \(0.194465\pi\) | |||||||
\(758\) | 8.21774 | 0.298482 | ||||||||
\(759\) | 3.72490 | − | 11.0936i | 0.135205 | − | 0.402673i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −7.00401 | + | 15.3366i | −0.253895 | + | 0.555953i | −0.993065 | − | 0.117566i | \(-0.962491\pi\) |
0.739170 | + | 0.673519i | \(0.235218\pi\) | |||||||
\(762\) | −6.39771 | − | 1.87854i | −0.231764 | − | 0.0680522i | ||||
\(763\) | 0.150947 | + | 0.174202i | 0.00546464 | + | 0.00630653i | ||||
\(764\) | −14.9249 | + | 9.59163i | −0.539963 | + | 0.347013i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 1.88491 | − | 13.1098i | 0.0681045 | − | 0.473677i | ||||
\(767\) | −39.9238 | + | 11.7227i | −1.44157 | + | 0.423282i | ||||
\(768\) | −6.74207 | − | 4.33287i | −0.243283 | − | 0.156349i | ||||
\(769\) | 6.22901 | + | 43.3237i | 0.224624 | + | 1.56229i | 0.720223 | + | 0.693743i | \(0.244039\pi\) |
−0.495599 | + | 0.868551i | \(0.665051\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 3.20427 | + | 7.01636i | 0.115399 | + | 0.252688i | ||||
\(772\) | 4.25916 | + | 29.6231i | 0.153291 | + | 1.06616i | ||||
\(773\) | −28.2907 | − | 18.1814i | −1.01755 | − | 0.653938i | −0.0782114 | − | 0.996937i | \(-0.524921\pi\) |
−0.939336 | + | 0.342999i | \(0.888557\pi\) | |||||||
\(774\) | −10.2527 | + | 3.01046i | −0.368525 | + | 0.108209i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −20.2973 | + | 23.4244i | −0.728632 | + | 0.840886i | ||||
\(777\) | 0.0524899 | − | 0.0337332i | 0.00188306 | − | 0.00121017i | ||||
\(778\) | 9.69430 | + | 11.1878i | 0.347558 | + | 0.401103i | ||||
\(779\) | −15.2386 | − | 4.47446i | −0.545980 | − | 0.160314i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 4.62835 | 0.165615 | ||||||||
\(782\) | −1.38607 | + | 36.1323i | −0.0495659 | + | 1.29209i | ||||
\(783\) | 37.2296 | 1.33048 | ||||||||
\(784\) | 3.28337 | − | 7.18957i | 0.117263 | − | 0.256770i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −19.5915 | − | 22.6098i | −0.698805 | − | 0.806464i | ||||
\(787\) | −1.05221 | + | 0.676215i | −0.0375073 | + | 0.0241045i | −0.559260 | − | 0.828992i | \(-0.688915\pi\) |
0.521753 | + | 0.853097i | \(0.325278\pi\) | |||||||
\(788\) | −9.93997 | + | 11.4713i | −0.354097 | + | 0.408649i | ||||
\(789\) | 3.18652 | − | 22.1627i | 0.113443 | − | 0.789014i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −1.32867 | − | 0.853887i | −0.0472422 | − | 0.0303607i | ||||
\(792\) | −1.49702 | − | 10.4120i | −0.0531943 | − | 0.369975i | ||||
\(793\) | 6.07684 | + | 13.3064i | 0.215795 | + | 0.472525i | ||||
\(794\) | −4.21946 | − | 9.23933i | −0.149743 | − | 0.327892i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 66.3466 | + | 42.6384i | 2.35159 | + | 1.51128i | ||||
\(797\) | −11.7261 | + | 3.44308i | −0.415358 | + | 0.121960i | −0.482733 | − | 0.875768i | \(-0.660356\pi\) |
0.0673749 | + | 0.997728i | \(0.478538\pi\) | |||||||
\(798\) | 0.0799977 | − | 0.556396i | 0.00283189 | − | 0.0196962i | ||||
\(799\) | 25.7306 | − | 29.6947i | 0.910282 | − | 1.05052i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −20.8860 | − | 24.1037i | −0.737969 | − | 0.851662i | ||||
\(802\) | −59.6863 | − | 17.5255i | −2.10760 | − | 0.618846i | ||||
\(803\) | 5.59168 | − | 12.2441i | 0.197326 | − | 0.432084i | ||||
\(804\) | 36.2255 | 1.27758 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 13.8341 | 0.487285 | ||||||||
\(807\) | 3.84770 | − | 8.42528i | 0.135445 | − | 0.296584i | ||||
\(808\) | 35.9512 | + | 10.5562i | 1.26476 | + | 0.371367i | ||||
\(809\) | 17.5520 | + | 20.2561i | 0.617097 | + | 0.712167i | 0.975153 | − | 0.221533i | \(-0.0711059\pi\) |
−0.358056 | + | 0.933700i | \(0.616560\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 25.9259 | − | 29.9201i | 0.910381 | − | 1.05064i | −0.0881316 | − | 0.996109i | \(-0.528090\pi\) |
0.998512 | − | 0.0545266i | \(-0.0173650\pi\) | |||||||
\(812\) | −0.277177 | + | 1.92781i | −0.00972702 | + | 0.0676529i | ||||
\(813\) | −21.0691 | + | 6.18644i | −0.738925 | + | 0.216968i | ||||
\(814\) | 3.23805 | + | 2.08097i | 0.113494 | + | 0.0729379i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 1.58855 | + | 3.47844i | 0.0556104 | + | 0.121770i | ||||
\(817\) | −2.84917 | − | 6.23880i | −0.0996797 | − | 0.218268i | ||||
\(818\) | 2.57518 | + | 17.9108i | 0.0900392 | + | 0.626236i | ||||
\(819\) | 0.534184 | + | 0.343299i | 0.0186659 | + | 0.0119958i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 4.50608 | − | 31.3404i | 0.157263 | − | 1.09379i | −0.746385 | − | 0.665514i | \(-0.768212\pi\) |
0.903648 | − | 0.428275i | \(-0.140879\pi\) | |||||||
\(822\) | −28.1583 | + | 32.4964i | −0.982134 | + | 1.13344i | ||||
\(823\) | 39.4672 | − | 25.3640i | 1.37574 | − | 0.884134i | 0.376632 | − | 0.926363i | \(-0.377082\pi\) |
0.999108 | + | 0.0422285i | \(0.0134457\pi\) | |||||||
\(824\) | −1.64209 | − | 1.89508i | −0.0572050 | − | 0.0660181i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0.942962 | − | 2.06480i | 0.0328099 | − | 0.0718436i | ||||
\(827\) | 24.2676 | 0.843869 | 0.421934 | − | 0.906626i | \(-0.361351\pi\) | ||||
0.421934 | + | 0.906626i | \(0.361351\pi\) | |||||||
\(828\) | −9.05891 | + | 26.9795i | −0.314819 | + | 0.937603i | ||||
\(829\) | −21.8597 | −0.759220 | −0.379610 | − | 0.925147i | \(-0.623942\pi\) | ||||
−0.379610 | + | 0.925147i | \(0.623942\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 12.0022 | + | 3.52417i | 0.416353 | + | 0.122252i | ||||
\(832\) | 30.5700 | + | 35.2797i | 1.05983 | + | 1.22310i | ||||
\(833\) | 19.8994 | − | 12.7886i | 0.689473 | − | 0.443098i | ||||
\(834\) | 22.6166 | − | 26.1009i | 0.783148 | − | 0.903801i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 19.8751 | − | 5.83585i | 0.687393 | − | 0.201837i | ||||
\(837\) | 7.24957 | + | 4.65902i | 0.250582 | + | 0.161039i | ||||
\(838\) | −8.79669 | − | 61.1823i | −0.303876 | − | 2.11351i | ||||
\(839\) | −11.3411 | − | 24.8335i | −0.391538 | − | 0.857348i | −0.998059 | − | 0.0622806i | \(-0.980163\pi\) |
0.606521 | − | 0.795068i | \(-0.292565\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −3.76305 | − | 26.1726i | −0.129760 | − | 0.902504i | ||||
\(842\) | 65.5352 | + | 42.1169i | 2.25849 | + | 1.45145i | ||||
\(843\) | 23.5299 | − | 6.90899i | 0.810412 | − | 0.237958i | ||||
\(844\) | 6.22531 | − | 43.2980i | 0.214284 | − | 1.49038i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 43.5525 | − | 27.9895i | 1.49737 | − | 0.962298i | ||||
\(847\) | −0.291301 | − | 0.336180i | −0.0100092 | − | 0.0115513i | ||||
\(848\) | 11.2527 | + | 3.30408i | 0.386418 | + | 0.113463i | ||||
\(849\) | 7.33863 | − | 16.0694i | 0.251861 | − | 0.551499i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −1.72433 | − | 2.92379i | −0.0591094 | − | 0.100226i | ||||
\(852\) | 5.62804 | 0.192813 | ||||||||
\(853\) | 11.7016 | − | 25.6230i | 0.400657 | − | 0.877316i | −0.596547 | − | 0.802578i | \(-0.703461\pi\) |
0.997203 | − | 0.0747372i | \(-0.0238118\pi\) | |||||||
\(854\) | −0.765701 | − | 0.224830i | −0.0262018 | − | 0.00769353i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 31.0986 | − | 19.9858i | 1.06293 | − | 0.683102i | ||||
\(857\) | −7.35982 | + | 8.49369i | −0.251407 | + | 0.290139i | −0.867399 | − | 0.497613i | \(-0.834210\pi\) |
0.615992 | + | 0.787752i | \(0.288755\pi\) | |||||||
\(858\) | 2.78736 | − | 19.3865i | 0.0951588 | − | 0.661844i | ||||
\(859\) | 8.44772 | − | 2.48047i | 0.288233 | − | 0.0846327i | −0.134420 | − | 0.990924i | \(-0.542917\pi\) |
0.422653 | + | 0.906292i | \(0.361099\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −0.0696439 | − | 0.484384i | −0.00237346 | − | 0.0165078i | ||||
\(862\) | 8.57972 | + | 18.7870i | 0.292226 | + | 0.639887i | ||||
\(863\) | 19.8827 | + | 43.5371i | 0.676816 | + | 1.48202i | 0.865982 | + | 0.500075i | \(0.166694\pi\) |
−0.189166 | + | 0.981945i | \(0.560579\pi\) | |||||||
\(864\) | 4.86019 | + | 33.8034i | 0.165347 | + | 1.15001i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −48.3892 | + | 14.2084i | −1.64433 | + | 0.482820i | ||||
\(867\) | 0.790638 | − | 5.49901i | 0.0268515 | − | 0.186756i | ||||
\(868\) | −0.295225 | + | 0.340708i | −0.0100206 | + | 0.0115644i | ||||
\(869\) | 14.3867 | − | 9.24578i | 0.488036 | − | 0.313641i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −42.1892 | − | 12.3879i | −1.42953 | − | 0.419747i | ||||
\(872\) | −2.34124 | + | 5.12661i | −0.0792845 | + | 0.173609i | ||||
\(873\) | 28.7593 | 0.973356 | ||||||||
\(874\) | −30.0798 | − | 5.50910i | −1.01746 | − | 0.186348i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 6.79944 | − | 14.8887i | 0.229732 | − | 0.503043i | ||||
\(877\) | −45.2435 | − | 13.2847i | −1.52776 | − | 0.448592i | −0.593398 | − | 0.804909i | \(-0.702214\pi\) |
−0.934365 | + | 0.356317i | \(0.884032\pi\) | |||||||
\(878\) | −26.9975 | − | 31.1567i | −0.911121 | − | 1.05149i | ||||
\(879\) | −7.14248 | + | 4.59020i | −0.240910 | + | 0.154823i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −5.26169 | + | 36.5959i | −0.177271 | + | 1.23295i | 0.685773 | + | 0.727816i | \(0.259464\pi\) |
−0.863043 | + | 0.505130i | \(0.831445\pi\) | |||||||
\(882\) | 29.9048 | − | 8.78083i | 1.00695 | − | 0.295666i | ||||
\(883\) | 45.8990 | + | 29.4975i | 1.54462 | + | 0.992670i | 0.986658 | + | 0.162807i | \(0.0520548\pi\) |
0.557967 | + | 0.829863i | \(0.311582\pi\) | |||||||
\(884\) | 5.14479 | + | 35.7828i | 0.173038 | + | 1.20351i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −20.7193 | − | 45.3689i | −0.696077 | − | 1.52420i | ||||
\(887\) | −2.01788 | − | 14.0346i | −0.0677537 | − | 0.471237i | −0.995246 | − | 0.0973946i | \(-0.968949\pi\) |
0.927492 | − | 0.373843i | \(-0.121960\pi\) | |||||||
\(888\) | 1.28341 | + | 0.824797i | 0.0430684 | + | 0.0276784i | ||||
\(889\) | −0.253060 | + | 0.0743050i | −0.00848734 | + | 0.00249211i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −1.59792 | + | 1.84410i | −0.0535324 | + | 0.0617797i | ||||
\(892\) | 2.52589 | − | 1.62329i | 0.0845730 | − | 0.0543517i | ||||
\(893\) | 21.7608 | + | 25.1133i | 0.728197 | + | 0.840384i | ||||
\(894\) | −34.1133 | − | 10.0166i | −1.14092 | − | 0.335004i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −1.34240 | −0.0448465 | ||||||||
\(897\) | −9.88816 | + | 14.1616i | −0.330156 | + | 0.472843i | ||||
\(898\) | −10.9523 | −0.365484 | ||||||||
\(899\) | 5.33109 | − | 11.6735i | 0.177802 | − | 0.389332i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 22.9847 | + | 26.5257i | 0.765730 | + | 0.883699i | ||||
\(902\) | 25.3962 | − | 16.3211i | 0.845600 | − | 0.543434i | ||||
\(903\) | 0.138393 | − | 0.159714i | 0.00460542 | − | 0.00531494i | ||||
\(904\) | 5.49580 | − | 38.2242i | 0.182788 | − | 1.27132i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −0.829210 | − | 0.532901i | −0.0275486 | − | 0.0177044i | ||||
\(907\) | 7.08860 | + | 49.3023i | 0.235373 | + | 1.63706i | 0.674246 | + | 0.738506i | \(0.264469\pi\) |
−0.438873 | + | 0.898549i | \(0.644622\pi\) | |||||||
\(908\) | −6.21507 | − | 13.6091i | −0.206254 | − | 0.451634i | ||||
\(909\) | −14.4425 | − | 31.6247i | −0.479028 | − | 1.04892i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −17.7763 | − | 11.4241i | −0.588955 | − | 0.378498i | 0.211959 | − | 0.977279i | \(-0.432016\pi\) |
−0.800913 | + | 0.598781i | \(0.795652\pi\) | |||||||
\(912\) | −3.10303 | + | 0.911132i | −0.102752 | + | 0.0301706i | ||||
\(913\) | 1.44898 | − | 10.0779i | 0.0479543 | − | 0.333529i | ||||
\(914\) | −16.9046 | + | 19.5090i | −0.559156 | + | 0.645300i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 44.5941 | + | 51.4644i | 1.47343 | + | 1.70043i | ||||
\(917\) | −1.13543 | − | 0.333391i | −0.0374951 | − | 0.0110095i | ||||
\(918\) | −15.6604 | + | 34.2915i | −0.516870 | + | 1.13179i | ||||
\(919\) | −1.66022 | −0.0547657 | −0.0273829 | − | 0.999625i | \(-0.508717\pi\) | ||||
−0.0273829 | + | 0.999625i | \(0.508717\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 14.6797 | 0.483711 | ||||||||
\(922\) | 14.3963 | − | 31.5235i | 0.474116 | − | 1.03817i | ||||
\(923\) | −6.55457 | − | 1.92459i | −0.215746 | − | 0.0633488i | ||||
\(924\) | 0.417970 | + | 0.482363i | 0.0137502 | + | 0.0158686i | ||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −14.7804 | + | 17.0575i | −0.485715 | + | 0.560545i | ||||
\(927\) | −0.331122 | + | 2.30300i | −0.0108755 | + | 0.0756406i | ||||
\(928\) | 48.7971 | − | 14.3281i | 1.60184 | − | 0.470343i | ||||
\(929\) | 24.5455 | + | 15.7744i | 0.805311 | + | 0.517542i | 0.877345 | − | 0.479860i | \(-0.159313\pi\) |
−0.0720340 | + | 0.997402i | \(0.522949\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 8.31037 | + | 18.1972i | 0.272361 | + | 0.596388i | ||||
\(932\) | −26.5290 | − | 58.0904i | −0.868986 | − | 1.90281i | ||||
\(933\) | −4.29449 | − | 29.8688i | −0.140595 | − | 0.977861i | ||||
\(934\) | 0.299702 | + | 0.192607i | 0.00980656 | + | 0.00630229i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −2.20955 | + | 15.3678i | −0.0722214 | + | 0.502311i | ||||
\(937\) | 12.0573 | − | 13.9149i | 0.393895 | − | 0.454580i | −0.523813 | − | 0.851833i | \(-0.675491\pi\) |
0.917709 | + | 0.397253i | \(0.130037\pi\) | |||||||
\(938\) | 2.01794 | − | 1.29685i | 0.0658881 | − | 0.0423437i | ||||
\(939\) | −3.64497 | − | 4.20652i | −0.118949 | − | 0.137275i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 17.9910 | − | 39.3947i | 0.586489 | − | 1.28423i | −0.351052 | − | 0.936356i | \(-0.614176\pi\) |
0.937541 | − | 0.347876i | \(-0.113097\pi\) | |||||||
\(942\) | 15.8655 | 0.516926 | ||||||||
\(943\) | −26.4772 | + | 2.77584i | −0.862215 | + | 0.0903937i | ||||
\(944\) | −13.0596 | −0.425053 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 12.5088 | + | 3.67290i | 0.406695 | + | 0.119416i | ||||
\(947\) | −13.8033 | − | 15.9299i | −0.448548 | − | 0.517652i | 0.485773 | − | 0.874085i | \(-0.338538\pi\) |
−0.934321 | + | 0.356433i | \(0.883993\pi\) | |||||||
\(948\) | 17.4941 | − | 11.2428i | 0.568183 | − | 0.365149i | ||||
\(949\) | −13.0102 | + | 15.0146i | −0.422330 | + | 0.487395i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 2.69722 | − | 0.791977i | 0.0874635 | − | 0.0256816i | ||||
\(952\) | −0.540775 | − | 0.347535i | −0.0175266 | − | 0.0112637i | ||||
\(953\) | 2.09831 | + | 14.5941i | 0.0679710 | + | 0.472749i | 0.995169 | + | 0.0981772i | \(0.0313012\pi\) |
−0.927198 | + | 0.374572i | \(0.877790\pi\) | |||||||
\(954\) | 19.2113 | + | 42.0669i | 0.621989 | + | 1.36197i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 3.70319 | + | 25.7562i | 0.119770 | + | 0.833016i | ||||
\(957\) | −15.2845 | − | 9.82277i | −0.494079 | − | 0.317525i | ||||
\(958\) | 12.5627 | − | 3.68873i | 0.405881 | − | 0.119178i | ||||
\(959\) | −0.242051 | + | 1.68350i | −0.00781622 | + | 0.0543630i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −23.5799 | + | 15.1539i | −0.760642 | + | 0.488835i | ||||
\(962\) | −3.72033 | − | 4.29349i | −0.119948 | − | 0.138428i | ||||
\(963\) | −32.9113 | − | 9.66362i | −1.06055 | − | 0.311406i | ||||
\(964\) | 10.8691 | − | 23.8001i | 0.350071 | − | 0.766549i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −0.230613 | − | 0.913599i | −0.00741984 | − | 0.0293946i | ||||
\(967\) | 25.3720 | 0.815909 | 0.407955 | − | 0.913002i | \(-0.366242\pi\) | ||||
0.407955 | + | 0.913002i | \(0.366242\pi\) | |||||||
\(968\) | 4.51820 | − | 9.89347i | 0.145220 | − | 0.317988i | ||||
\(969\) | −9.28671 | − | 2.72682i | −0.298332 | − | 0.0875982i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −32.9014 | + | 21.1444i | −1.05586 | + | 0.678557i | −0.948858 | − | 0.315702i | \(-0.897760\pi\) |
−0.106997 | + | 0.994259i | \(0.534124\pi\) | |||||||
\(972\) | −31.0890 | + | 35.8786i | −0.997180 | + | 1.15081i | ||||
\(973\) | 0.194414 | − | 1.35218i | 0.00623261 | − | 0.0433488i | ||||
\(974\) | 14.8280 | − | 4.35388i | 0.475118 | − | 0.139507i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0.653409 | + | 4.54456i | 0.0209151 | + | 0.145468i | ||||
\(977\) | 9.66014 | + | 21.1528i | 0.309055 | + | 0.676736i | 0.998884 | − | 0.0472363i | \(-0.0150414\pi\) |
−0.689829 | + | 0.723973i | \(0.742314\pi\) | |||||||
\(978\) | −6.61636 | − | 14.4878i | −0.211568 | − | 0.463269i | ||||
\(979\) | 5.53774 | + | 38.5158i | 0.176987 | + | 1.23097i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 5.01759 | − | 1.47330i | 0.160199 | − | 0.0470387i | ||||
\(982\) | −6.96412 | + | 48.4365i | −0.222234 | + | 1.54567i | ||||
\(983\) | 0.430697 | − | 0.497051i | 0.0137371 | − | 0.0158535i | −0.748839 | − | 0.662751i | \(-0.769389\pi\) |
0.762577 | + | 0.646898i | \(0.223934\pi\) | |||||||
\(984\) | 10.0658 | − | 6.46891i | 0.320887 | − | 0.206221i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 53.8655 | + | 15.8163i | 1.71543 | + | 0.503695i | ||||
\(987\) | −0.425341 | + | 0.931366i | −0.0135387 | + | 0.0296457i | ||||
\(988\) | −30.5733 | −0.972667 | ||||||||
\(989\) | −8.39371 | − | 7.85633i | −0.266905 | − | 0.249817i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 1.31140 | − | 2.87157i | 0.0416581 | − | 0.0912185i | −0.887659 | − | 0.460502i | \(-0.847670\pi\) |
0.929317 | + | 0.369283i | \(0.120397\pi\) | |||||||
\(992\) | 11.2951 | + | 3.31654i | 0.358620 | + | 0.105300i | ||||
\(993\) | 9.07184 | + | 10.4695i | 0.287886 | + | 0.332238i | ||||
\(994\) | 0.313510 | − | 0.201480i | 0.00994392 | − | 0.00639057i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 1.76195 | − | 12.2546i | 0.0558295 | − | 0.388303i | ||||
\(997\) | −8.45136 | + | 2.48154i | −0.267657 | + | 0.0785913i | −0.412807 | − | 0.910818i | \(-0.635452\pi\) |
0.145150 | + | 0.989410i | \(0.453634\pi\) | |||||||
\(998\) | 53.3443 | + | 34.2823i | 1.68858 | + | 1.08519i | ||||
\(999\) | −0.503637 | − | 3.50287i | −0.0159344 | − | 0.110826i |
(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 | 575.2.k.a.351.1 | 10 | ||
5.2 | odd | 4 | 575.2.p.a.374.1 | 20 | |||
5.3 | odd | 4 | 575.2.p.a.374.2 | 20 | |||
5.4 | even | 2 | 115.2.g.a.6.1 | ✓ | 10 | ||
23.4 | even | 11 | inner | 575.2.k.a.326.1 | 10 | ||
115.4 | even | 22 | 115.2.g.a.96.1 | yes | 10 | ||
115.27 | odd | 44 | 575.2.p.a.349.2 | 20 | |||
115.44 | odd | 22 | 2645.2.a.o.1.5 | 5 | |||
115.73 | odd | 44 | 575.2.p.a.349.1 | 20 | |||
115.94 | even | 22 | 2645.2.a.n.1.5 | 5 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
115.2.g.a.6.1 | ✓ | 10 | 5.4 | even | 2 | ||
115.2.g.a.96.1 | yes | 10 | 115.4 | even | 22 | ||
575.2.k.a.326.1 | 10 | 23.4 | even | 11 | inner | ||
575.2.k.a.351.1 | 10 | 1.1 | even | 1 | trivial | ||
575.2.p.a.349.1 | 20 | 115.73 | odd | 44 | |||
575.2.p.a.349.2 | 20 | 115.27 | odd | 44 | |||
575.2.p.a.374.1 | 20 | 5.2 | odd | 4 | |||
575.2.p.a.374.2 | 20 | 5.3 | odd | 4 | |||
2645.2.a.n.1.5 | 5 | 115.94 | even | 22 | |||
2645.2.a.o.1.5 | 5 | 115.44 | odd | 22 |