Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [62,2,Mod(33,62)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(62, base_ring=CyclotomicField(10))
chi = DirichletCharacter(H, H._module([8]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("62.33");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 62 = 2 \cdot 31 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 62.d (of order \(5\), degree \(4\), 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: | \(0.495072492532\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{5})\) |
Coefficient field: | 8.0.1903140625.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 3x^{7} + 6x^{6} + x^{5} + 29x^{4} + 43x^{3} + 194x^{2} + 209x + 361 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{5}]$ |
Embedding invariants
Embedding label | 35.1 | ||
Root | \(2.68070 - 1.94764i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 62.35 |
Dual form | 62.2.d.b.39.1 |
$q$-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 \(\left(\mathbb{Z}/62\mathbb{Z}\right)^\times\).
\(n\) | \(3\) |
\(\chi(n)\) | \(e\left(\frac{3}{5}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.309017 | − | 0.951057i | −0.218508 | − | 0.672499i | ||||
\(3\) | −1.02393 | + | 3.15135i | −0.591169 | + | 1.81943i | −0.0182279 | + | 0.999834i | \(0.505802\pi\) |
−0.572941 | + | 0.819597i | \(0.694198\pi\) | |||||||
\(4\) | −0.809017 | + | 0.587785i | −0.404508 | + | 0.293893i | ||||
\(5\) | 2.66590 | 1.19223 | 0.596114 | − | 0.802900i | \(-0.296711\pi\) | ||||
0.596114 | + | 0.802900i | \(0.296711\pi\) | |||||||
\(6\) | 3.31352 | 1.35274 | ||||||||
\(7\) | −0.500000 | + | 0.363271i | −0.188982 | + | 0.137304i | −0.678253 | − | 0.734828i | \(-0.737263\pi\) |
0.489271 | + | 0.872132i | \(0.337263\pi\) | |||||||
\(8\) | 0.809017 | + | 0.587785i | 0.286031 | + | 0.207813i | ||||
\(9\) | −6.45549 | − | 4.69019i | −2.15183 | − | 1.56340i | ||||
\(10\) | −0.823809 | − | 2.53542i | −0.260511 | − | 0.801772i | ||||
\(11\) | 1.09410 | − | 0.794910i | 0.329883 | − | 0.239674i | −0.410498 | − | 0.911862i | \(-0.634645\pi\) |
0.740381 | + | 0.672187i | \(0.234645\pi\) | |||||||
\(12\) | −1.02393 | − | 3.15135i | −0.295584 | − | 0.909715i | ||||
\(13\) | 0.729710 | − | 2.24582i | 0.202385 | − | 0.622877i | −0.797426 | − | 0.603417i | \(-0.793805\pi\) |
0.999811 | − | 0.0194599i | \(-0.00619466\pi\) | |||||||
\(14\) | 0.500000 | + | 0.363271i | 0.133631 | + | 0.0970883i | ||||
\(15\) | −2.72971 | + | 8.40118i | −0.704808 | + | 2.16918i | ||||
\(16\) | 0.309017 | − | 0.951057i | 0.0772542 | − | 0.237764i | ||||
\(17\) | 2.15676 | + | 1.56698i | 0.523091 | + | 0.380048i | 0.817767 | − | 0.575549i | \(-0.195212\pi\) |
−0.294676 | + | 0.955597i | \(0.595212\pi\) | |||||||
\(18\) | −2.46578 | + | 7.58888i | −0.581189 | + | 1.78872i | ||||
\(19\) | −1.98057 | − | 6.09557i | −0.454374 | − | 1.39842i | −0.871869 | − | 0.489740i | \(-0.837092\pi\) |
0.417495 | − | 0.908679i | \(-0.362908\pi\) | |||||||
\(20\) | −2.15676 | + | 1.56698i | −0.482266 | + | 0.350387i | ||||
\(21\) | −0.632826 | − | 1.94764i | −0.138094 | − | 0.425010i | ||||
\(22\) | −1.09410 | − | 0.794910i | −0.233263 | − | 0.169475i | ||||
\(23\) | 2.37618 | + | 1.72640i | 0.495468 | + | 0.359979i | 0.807283 | − | 0.590164i | \(-0.200937\pi\) |
−0.311815 | + | 0.950143i | \(0.600937\pi\) | |||||||
\(24\) | −2.68070 | + | 1.94764i | −0.547195 | + | 0.397560i | ||||
\(25\) | 2.10704 | 0.421408 | ||||||||
\(26\) | −2.36139 | −0.463107 | ||||||||
\(27\) | 13.3483 | − | 9.69812i | 2.56889 | − | 1.86640i | ||||
\(28\) | 0.190983 | − | 0.587785i | 0.0360924 | − | 0.111081i | ||||
\(29\) | 1.17791 | + | 3.62524i | 0.218733 | + | 0.673190i | 0.998868 | + | 0.0475784i | \(0.0151504\pi\) |
−0.780135 | + | 0.625611i | \(0.784850\pi\) | |||||||
\(30\) | 8.83353 | 1.61277 | ||||||||
\(31\) | −5.42127 | − | 1.26880i | −0.973688 | − | 0.227884i | ||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | 1.38475 | + | 4.26182i | 0.241054 | + | 0.741888i | ||||
\(34\) | 0.823809 | − | 2.53542i | 0.141282 | − | 0.434822i | ||||
\(35\) | −1.33295 | + | 0.968446i | −0.225310 | + | 0.163697i | ||||
\(36\) | 7.97942 | 1.32990 | ||||||||
\(37\) | −4.57017 | −0.751331 | −0.375665 | − | 0.926755i | \(-0.622586\pi\) | ||||
−0.375665 | + | 0.926755i | \(0.622586\pi\) | |||||||
\(38\) | −5.18520 | + | 3.76727i | −0.841150 | + | 0.611132i | ||||
\(39\) | 6.33017 | + | 4.59914i | 1.01364 | + | 0.736451i | ||||
\(40\) | 2.15676 | + | 1.56698i | 0.341014 | + | 0.247761i | ||||
\(41\) | −0.676191 | − | 2.08110i | −0.105603 | − | 0.325013i | 0.884268 | − | 0.466979i | \(-0.154658\pi\) |
−0.989872 | + | 0.141966i | \(0.954658\pi\) | |||||||
\(42\) | −1.65676 | + | 1.20371i | −0.255644 | + | 0.185736i | ||||
\(43\) | 1.92983 | + | 5.93942i | 0.294297 | + | 0.905753i | 0.983457 | + | 0.181144i | \(0.0579799\pi\) |
−0.689160 | + | 0.724610i | \(0.742020\pi\) | |||||||
\(44\) | −0.417909 | + | 1.28619i | −0.0630021 | + | 0.193901i | ||||
\(45\) | −17.2097 | − | 12.5036i | −2.56547 | − | 1.86392i | ||||
\(46\) | 0.907621 | − | 2.79337i | 0.133821 | − | 0.411860i | ||||
\(47\) | −1.50000 | + | 4.61653i | −0.218797 | + | 0.673389i | 0.780065 | + | 0.625699i | \(0.215186\pi\) |
−0.998862 | + | 0.0476905i | \(0.984814\pi\) | |||||||
\(48\) | 2.68070 | + | 1.94764i | 0.386925 | + | 0.281117i | ||||
\(49\) | −2.04508 | + | 6.29412i | −0.292155 | + | 0.899161i | ||||
\(50\) | −0.651111 | − | 2.00391i | −0.0920809 | − | 0.283396i | ||||
\(51\) | −7.14647 | + | 5.19222i | −1.00071 | + | 0.727056i | ||||
\(52\) | 0.729710 | + | 2.24582i | 0.101193 | + | 0.311439i | ||||
\(53\) | −2.78208 | − | 2.02130i | −0.382148 | − | 0.277647i | 0.380082 | − | 0.924953i | \(-0.375896\pi\) |
−0.762231 | + | 0.647306i | \(0.775896\pi\) | |||||||
\(54\) | −13.3483 | − | 9.69812i | −1.81648 | − | 1.31975i | ||||
\(55\) | 2.91676 | − | 2.11915i | 0.393296 | − | 0.285746i | ||||
\(56\) | −0.618034 | −0.0825883 | ||||||||
\(57\) | 21.2372 | 2.81294 | ||||||||
\(58\) | 3.08381 | − | 2.24052i | 0.404924 | − | 0.294195i | ||||
\(59\) | 3.42591 | − | 10.5439i | 0.446015 | − | 1.37269i | −0.435352 | − | 0.900260i | \(-0.643376\pi\) |
0.881367 | − | 0.472432i | \(-0.156624\pi\) | |||||||
\(60\) | −2.72971 | − | 8.40118i | −0.352404 | − | 1.08459i | ||||
\(61\) | −2.39097 | −0.306133 | −0.153066 | − | 0.988216i | \(-0.548915\pi\) | ||||
−0.153066 | + | 0.988216i | \(0.548915\pi\) | |||||||
\(62\) | 0.468562 | + | 5.54801i | 0.0595074 | + | 0.704598i | ||||
\(63\) | 4.93156 | 0.621318 | ||||||||
\(64\) | 0.309017 | + | 0.951057i | 0.0386271 | + | 0.118882i | ||||
\(65\) | 1.94534 | − | 5.98713i | 0.241289 | − | 0.742612i | ||||
\(66\) | 3.62532 | − | 2.63395i | 0.446246 | − | 0.324217i | ||||
\(67\) | −9.40926 | −1.14952 | −0.574762 | − | 0.818321i | \(-0.694905\pi\) | ||||
−0.574762 | + | 0.818321i | \(0.694905\pi\) | |||||||
\(68\) | −2.66590 | −0.323288 | ||||||||
\(69\) | −7.87353 | + | 5.72046i | −0.947862 | + | 0.688662i | ||||
\(70\) | 1.33295 | + | 0.968446i | 0.159318 | + | 0.115751i | ||||
\(71\) | −6.62439 | − | 4.81290i | −0.786171 | − | 0.571186i | 0.120654 | − | 0.992695i | \(-0.461501\pi\) |
−0.906825 | + | 0.421508i | \(0.861501\pi\) | |||||||
\(72\) | −2.46578 | − | 7.58888i | −0.290595 | − | 0.894358i | ||||
\(73\) | 3.47792 | − | 2.52686i | 0.407060 | − | 0.295746i | −0.365351 | − | 0.930870i | \(-0.619051\pi\) |
0.772410 | + | 0.635124i | \(0.219051\pi\) | |||||||
\(74\) | 1.41226 | + | 4.34649i | 0.164172 | + | 0.505269i | ||||
\(75\) | −2.15747 | + | 6.64001i | −0.249123 | + | 0.766722i | ||||
\(76\) | 5.18520 | + | 3.76727i | 0.594783 | + | 0.432135i | ||||
\(77\) | −0.258282 | + | 0.794910i | −0.0294340 | + | 0.0905884i | ||||
\(78\) | 2.41791 | − | 7.44156i | 0.273774 | − | 0.842591i | ||||
\(79\) | 2.64197 | + | 1.91950i | 0.297245 | + | 0.215961i | 0.726404 | − | 0.687268i | \(-0.241190\pi\) |
−0.429159 | + | 0.903229i | \(0.641190\pi\) | |||||||
\(80\) | 0.823809 | − | 2.53542i | 0.0921047 | − | 0.283469i | ||||
\(81\) | 9.49700 | + | 29.2288i | 1.05522 | + | 3.24764i | ||||
\(82\) | −1.77029 | + | 1.28619i | −0.195496 | + | 0.142036i | ||||
\(83\) | −0.354102 | − | 1.08981i | −0.0388677 | − | 0.119623i | 0.929740 | − | 0.368217i | \(-0.120032\pi\) |
−0.968608 | + | 0.248594i | \(0.920032\pi\) | |||||||
\(84\) | 1.65676 | + | 1.20371i | 0.180767 | + | 0.131335i | ||||
\(85\) | 5.74971 | + | 4.17741i | 0.623644 | + | 0.453104i | ||||
\(86\) | 5.05237 | − | 3.67076i | 0.544811 | − | 0.395829i | ||||
\(87\) | −12.6305 | −1.35413 | ||||||||
\(88\) | 1.35238 | 0.144164 | ||||||||
\(89\) | −6.85675 | + | 4.98172i | −0.726814 | + | 0.528062i | −0.888554 | − | 0.458772i | \(-0.848289\pi\) |
0.161740 | + | 0.986833i | \(0.448289\pi\) | |||||||
\(90\) | −6.57352 | + | 20.2312i | −0.692910 | + | 2.13256i | ||||
\(91\) | 0.450985 | + | 1.38799i | 0.0472761 | + | 0.145501i | ||||
\(92\) | −2.93712 | −0.306216 | ||||||||
\(93\) | 9.54946 | − | 15.7851i | 0.990232 | − | 1.63684i | ||||
\(94\) | 4.85410 | 0.500662 | ||||||||
\(95\) | −5.28001 | − | 16.2502i | −0.541717 | − | 1.66723i | ||||
\(96\) | 1.02393 | − | 3.15135i | 0.104505 | − | 0.321633i | ||||
\(97\) | 2.42255 | − | 1.76008i | 0.245972 | − | 0.178709i | −0.457968 | − | 0.888969i | \(-0.651422\pi\) |
0.703940 | + | 0.710260i | \(0.251422\pi\) | |||||||
\(98\) | 6.61803 | 0.668522 | ||||||||
\(99\) | −10.7912 | −1.08456 | ||||||||
\(100\) | −1.70463 | + | 1.23849i | −0.170463 | + | 0.123849i | ||||
\(101\) | 14.3438 | + | 10.4214i | 1.42726 | + | 1.03697i | 0.990518 | + | 0.137382i | \(0.0438687\pi\) |
0.436745 | + | 0.899586i | \(0.356131\pi\) | |||||||
\(102\) | 7.14647 | + | 5.19222i | 0.707606 | + | 0.514106i | ||||
\(103\) | −0.170541 | − | 0.524870i | −0.0168039 | − | 0.0517170i | 0.942303 | − | 0.334761i | \(-0.108656\pi\) |
−0.959107 | + | 0.283044i | \(0.908656\pi\) | |||||||
\(104\) | 1.91040 | − | 1.38799i | 0.187331 | − | 0.136104i | ||||
\(105\) | −1.68705 | − | 5.19222i | −0.164640 | − | 0.506708i | ||||
\(106\) | −1.06266 | + | 3.27053i | −0.103215 | + | 0.317662i | ||||
\(107\) | 7.50150 | + | 5.45016i | 0.725198 | + | 0.526887i | 0.888041 | − | 0.459765i | \(-0.152066\pi\) |
−0.162843 | + | 0.986652i | \(0.552066\pi\) | |||||||
\(108\) | −5.09860 | + | 15.6919i | −0.490613 | + | 1.50995i | ||||
\(109\) | 5.94070 | − | 18.2836i | 0.569016 | − | 1.75125i | −0.0866920 | − | 0.996235i | \(-0.527630\pi\) |
0.655708 | − | 0.755015i | \(-0.272370\pi\) | |||||||
\(110\) | −2.91676 | − | 2.11915i | −0.278102 | − | 0.202053i | ||||
\(111\) | 4.67955 | − | 14.4022i | 0.444163 | − | 1.36699i | ||||
\(112\) | 0.190983 | + | 0.587785i | 0.0180462 | + | 0.0555405i | ||||
\(113\) | 10.9718 | − | 7.97147i | 1.03214 | − | 0.749893i | 0.0634032 | − | 0.997988i | \(-0.479805\pi\) |
0.968736 | + | 0.248095i | \(0.0798046\pi\) | |||||||
\(114\) | −6.56266 | − | 20.1978i | −0.614650 | − | 1.89170i | ||||
\(115\) | 6.33467 | + | 4.60241i | 0.590711 | + | 0.429177i | ||||
\(116\) | −3.08381 | − | 2.24052i | −0.286325 | − | 0.208027i | ||||
\(117\) | −15.2439 | + | 11.0754i | −1.40930 | + | 1.02392i | ||||
\(118\) | −11.0865 | −1.02059 | ||||||||
\(119\) | −1.64762 | −0.151037 | ||||||||
\(120\) | −7.14647 | + | 5.19222i | −0.652381 | + | 0.473982i | ||||
\(121\) | −2.83401 | + | 8.72220i | −0.257638 | + | 0.792927i | ||||
\(122\) | 0.738852 | + | 2.27395i | 0.0668925 | + | 0.205874i | ||||
\(123\) | 7.25064 | 0.653769 | ||||||||
\(124\) | 5.13168 | − | 2.16006i | 0.460839 | − | 0.193979i | ||||
\(125\) | −7.71236 | −0.689814 | ||||||||
\(126\) | −1.52393 | − | 4.69019i | −0.135763 | − | 0.417835i | ||||
\(127\) | −4.36324 | + | 13.4287i | −0.387175 | + | 1.19160i | 0.547715 | + | 0.836665i | \(0.315498\pi\) |
−0.934890 | + | 0.354938i | \(0.884502\pi\) | |||||||
\(128\) | 0.809017 | − | 0.587785i | 0.0715077 | − | 0.0519534i | ||||
\(129\) | −20.6932 | −1.82193 | ||||||||
\(130\) | −6.29524 | −0.552129 | ||||||||
\(131\) | 1.92684 | − | 1.39993i | 0.168348 | − | 0.122312i | −0.500421 | − | 0.865782i | \(-0.666821\pi\) |
0.668769 | + | 0.743470i | \(0.266821\pi\) | |||||||
\(132\) | −3.62532 | − | 2.63395i | −0.315544 | − | 0.229256i | ||||
\(133\) | 3.20463 | + | 2.32830i | 0.277877 | + | 0.201889i | ||||
\(134\) | 2.90762 | + | 8.94874i | 0.251180 | + | 0.773053i | ||||
\(135\) | 35.5853 | − | 25.8542i | 3.06270 | − | 2.22518i | ||||
\(136\) | 0.823809 | + | 2.53542i | 0.0706411 | + | 0.217411i | ||||
\(137\) | −3.97200 | + | 12.2246i | −0.339351 | + | 1.04442i | 0.625188 | + | 0.780474i | \(0.285022\pi\) |
−0.964539 | + | 0.263941i | \(0.914978\pi\) | |||||||
\(138\) | 7.87353 | + | 5.72046i | 0.670240 | + | 0.486958i | ||||
\(139\) | 1.71841 | − | 5.28872i | 0.145754 | − | 0.448583i | −0.851354 | − | 0.524592i | \(-0.824218\pi\) |
0.997107 | + | 0.0760089i | \(0.0242178\pi\) | |||||||
\(140\) | 0.509142 | − | 1.56698i | 0.0430304 | − | 0.132434i | ||||
\(141\) | −13.0124 | − | 9.45404i | −1.09584 | − | 0.796174i | ||||
\(142\) | −2.53029 | + | 7.78744i | −0.212337 | + | 0.653507i | ||||
\(143\) | −0.986846 | − | 3.03720i | −0.0825242 | − | 0.253983i | ||||
\(144\) | −6.45549 | + | 4.69019i | −0.537957 | + | 0.390849i | ||||
\(145\) | 3.14020 | + | 9.66453i | 0.260779 | + | 0.802596i | ||||
\(146\) | −3.47792 | − | 2.52686i | −0.287835 | − | 0.209124i | ||||
\(147\) | −17.7409 | − | 12.8895i | −1.46325 | − | 1.06311i | ||||
\(148\) | 3.69734 | − | 2.68628i | 0.303920 | − | 0.220810i | ||||
\(149\) | 6.23236 | 0.510575 | 0.255287 | − | 0.966865i | \(-0.417830\pi\) | ||||
0.255287 | + | 0.966865i | \(0.417830\pi\) | |||||||
\(150\) | 6.98172 | 0.570055 | ||||||||
\(151\) | −12.8765 | + | 9.35536i | −1.04788 | + | 0.761328i | −0.971808 | − | 0.235774i | \(-0.924237\pi\) |
−0.0760703 | + | 0.997102i | \(0.524237\pi\) | |||||||
\(152\) | 1.98057 | − | 6.09557i | 0.160645 | − | 0.494416i | ||||
\(153\) | −6.57352 | − | 20.2312i | −0.531438 | − | 1.63560i | ||||
\(154\) | 0.835818 | 0.0673521 | ||||||||
\(155\) | −14.4526 | − | 3.38250i | −1.16086 | − | 0.271689i | ||||
\(156\) | −7.82452 | −0.626463 | ||||||||
\(157\) | −1.96856 | − | 6.05861i | −0.157108 | − | 0.483530i | 0.841260 | − | 0.540631i | \(-0.181814\pi\) |
−0.998368 | + | 0.0571009i | \(0.981814\pi\) | |||||||
\(158\) | 1.00914 | − | 3.10582i | 0.0802830 | − | 0.247086i | ||||
\(159\) | 9.21849 | − | 6.69763i | 0.731074 | − | 0.531156i | ||||
\(160\) | −2.66590 | −0.210758 | ||||||||
\(161\) | −1.81524 | −0.143061 | ||||||||
\(162\) | 24.8635 | − | 18.0644i | 1.95346 | − | 1.41927i | ||||
\(163\) | 2.30151 | + | 1.67215i | 0.180268 | + | 0.130973i | 0.674260 | − | 0.738494i | \(-0.264463\pi\) |
−0.493992 | + | 0.869467i | \(0.664463\pi\) | |||||||
\(164\) | 1.77029 | + | 1.28619i | 0.138236 | + | 0.100435i | ||||
\(165\) | 3.69161 | + | 11.3616i | 0.287391 | + | 0.884500i | ||||
\(166\) | −0.927051 | + | 0.673542i | −0.0719531 | + | 0.0522770i | ||||
\(167\) | −0.779432 | − | 2.39885i | −0.0603143 | − | 0.185628i | 0.916360 | − | 0.400356i | \(-0.131114\pi\) |
−0.976674 | + | 0.214728i | \(0.931114\pi\) | |||||||
\(168\) | 0.632826 | − | 1.94764i | 0.0488236 | − | 0.150264i | ||||
\(169\) | 6.00601 | + | 4.36362i | 0.462001 | + | 0.335663i | ||||
\(170\) | 2.19620 | − | 6.75919i | 0.168441 | − | 0.518407i | ||||
\(171\) | −15.8038 | + | 48.6391i | −1.20855 | + | 3.71953i | ||||
\(172\) | −5.05237 | − | 3.67076i | −0.385240 | − | 0.279893i | ||||
\(173\) | −3.56152 | + | 10.9612i | −0.270777 | + | 0.833366i | 0.719529 | + | 0.694462i | \(0.244358\pi\) |
−0.990306 | + | 0.138903i | \(0.955642\pi\) | |||||||
\(174\) | 3.90303 | + | 12.0123i | 0.295888 | + | 0.910650i | ||||
\(175\) | −1.05352 | + | 0.765426i | −0.0796386 | + | 0.0578608i | ||||
\(176\) | −0.417909 | − | 1.28619i | −0.0315011 | − | 0.0969503i | ||||
\(177\) | 29.7194 | + | 21.5924i | 2.23385 | + | 1.62299i | ||||
\(178\) | 6.85675 | + | 4.98172i | 0.513935 | + | 0.373396i | ||||
\(179\) | 14.9497 | − | 10.8616i | 1.11739 | − | 0.811834i | 0.133582 | − | 0.991038i | \(-0.457352\pi\) |
0.983812 | + | 0.179204i | \(0.0573522\pi\) | |||||||
\(180\) | 21.2724 | 1.58555 | ||||||||
\(181\) | −2.75492 | −0.204772 | −0.102386 | − | 0.994745i | \(-0.532648\pi\) | ||||
−0.102386 | + | 0.994745i | \(0.532648\pi\) | |||||||
\(182\) | 1.18070 | − | 0.857825i | 0.0875189 | − | 0.0635862i | ||||
\(183\) | 2.44820 | − | 7.53479i | 0.180976 | − | 0.556988i | ||||
\(184\) | 0.907621 | + | 2.79337i | 0.0669107 | + | 0.205930i | ||||
\(185\) | −12.1836 | −0.895757 | ||||||||
\(186\) | −17.9635 | − | 4.20420i | −1.31715 | − | 0.308267i | ||||
\(187\) | 3.60532 | 0.263647 | ||||||||
\(188\) | −1.50000 | − | 4.61653i | −0.109399 | − | 0.336695i | ||||
\(189\) | −3.15111 | + | 9.69812i | −0.229210 | + | 0.705435i | ||||
\(190\) | −13.8232 | + | 10.0432i | −1.00284 | + | 0.728608i | ||||
\(191\) | 15.8370 | 1.14592 | 0.572961 | − | 0.819582i | \(-0.305794\pi\) | ||||
0.572961 | + | 0.819582i | \(0.305794\pi\) | |||||||
\(192\) | −3.31352 | −0.239133 | ||||||||
\(193\) | −2.49536 | + | 1.81299i | −0.179620 | + | 0.130502i | −0.673962 | − | 0.738766i | \(-0.735409\pi\) |
0.494342 | + | 0.869267i | \(0.335409\pi\) | |||||||
\(194\) | −2.42255 | − | 1.76008i | −0.173929 | − | 0.126367i | ||||
\(195\) | 16.8756 | + | 12.2608i | 1.20849 | + | 0.878018i | ||||
\(196\) | −2.04508 | − | 6.29412i | −0.146077 | − | 0.449580i | ||||
\(197\) | −18.2409 | + | 13.2528i | −1.29961 | + | 0.944224i | −0.999952 | − | 0.00982201i | \(-0.996874\pi\) |
−0.299661 | + | 0.954046i | \(0.596874\pi\) | |||||||
\(198\) | 3.33467 | + | 10.2631i | 0.236985 | + | 0.729364i | ||||
\(199\) | −2.80160 | + | 8.62242i | −0.198600 | + | 0.611227i | 0.801316 | + | 0.598242i | \(0.204134\pi\) |
−0.999916 | + | 0.0129859i | \(0.995866\pi\) | |||||||
\(200\) | 1.70463 | + | 1.23849i | 0.120536 | + | 0.0875742i | ||||
\(201\) | 9.63446 | − | 29.6518i | 0.679563 | − | 2.09148i | ||||
\(202\) | 5.47885 | − | 16.8622i | 0.385491 | − | 1.18642i | ||||
\(203\) | −1.90590 | − | 1.38472i | −0.133768 | − | 0.0971881i | ||||
\(204\) | 2.72971 | − | 8.40118i | 0.191118 | − | 0.588200i | ||||
\(205\) | −1.80266 | − | 5.54801i | −0.125903 | − | 0.387490i | ||||
\(206\) | −0.446481 | + | 0.324387i | −0.0311078 | + | 0.0226011i | ||||
\(207\) | −7.24229 | − | 22.2895i | −0.503374 | − | 1.54923i | ||||
\(208\) | −1.91040 | − | 1.38799i | −0.132463 | − | 0.0962398i | ||||
\(209\) | −7.01237 | − | 5.09478i | −0.485056 | − | 0.352414i | ||||
\(210\) | −4.41676 | + | 3.20897i | −0.304786 | + | 0.221440i | ||||
\(211\) | 10.9297 | 0.752431 | 0.376216 | − | 0.926532i | \(-0.377225\pi\) | ||||
0.376216 | + | 0.926532i | \(0.377225\pi\) | |||||||
\(212\) | 3.43884 | 0.236181 | ||||||||
\(213\) | 21.9501 | − | 15.9477i | 1.50399 | − | 1.09272i | ||||
\(214\) | 2.86532 | − | 8.81855i | 0.195869 | − | 0.602824i | ||||
\(215\) | 5.14475 | + | 15.8339i | 0.350869 | + | 1.07986i | ||||
\(216\) | 16.4994 | 1.12264 | ||||||||
\(217\) | 3.17155 | − | 1.33499i | 0.215299 | − | 0.0906250i | ||||
\(218\) | −19.2245 | −1.30205 | ||||||||
\(219\) | 4.40184 | + | 13.5475i | 0.297449 | + | 0.915453i | ||||
\(220\) | −1.11410 | + | 3.42886i | −0.0751129 | + | 0.231174i | ||||
\(221\) | 5.09295 | − | 3.70025i | 0.342589 | − | 0.248906i | ||||
\(222\) | −15.1433 | −1.01635 | ||||||||
\(223\) | −12.2416 | −0.819761 | −0.409880 | − | 0.912139i | \(-0.634430\pi\) | ||||
−0.409880 | + | 0.912139i | \(0.634430\pi\) | |||||||
\(224\) | 0.500000 | − | 0.363271i | 0.0334077 | − | 0.0242721i | ||||
\(225\) | −13.6020 | − | 9.88240i | −0.906798 | − | 0.658827i | ||||
\(226\) | −10.9718 | − | 7.97147i | −0.729832 | − | 0.530254i | ||||
\(227\) | 2.45849 | + | 7.56645i | 0.163176 | + | 0.502203i | 0.998897 | − | 0.0469503i | \(-0.0149503\pi\) |
−0.835722 | + | 0.549153i | \(0.814950\pi\) | |||||||
\(228\) | −17.1813 | + | 12.4829i | −1.13786 | + | 0.826702i | ||||
\(229\) | −6.66820 | − | 20.5226i | −0.440647 | − | 1.35617i | −0.887188 | − | 0.461409i | \(-0.847344\pi\) |
0.446541 | − | 0.894763i | \(-0.352656\pi\) | |||||||
\(230\) | 2.41963 | − | 7.44685i | 0.159546 | − | 0.491031i | ||||
\(231\) | −2.24057 | − | 1.62787i | −0.147419 | − | 0.107106i | ||||
\(232\) | −1.17791 | + | 3.62524i | −0.0773337 | + | 0.238009i | ||||
\(233\) | −1.59525 | + | 4.90966i | −0.104508 | + | 0.321643i | −0.989615 | − | 0.143746i | \(-0.954085\pi\) |
0.885107 | + | 0.465388i | \(0.154085\pi\) | |||||||
\(234\) | 15.2439 | + | 11.0754i | 0.996527 | + | 0.724019i | ||||
\(235\) | −3.99885 | + | 12.3072i | −0.260856 | + | 0.802834i | ||||
\(236\) | 3.42591 | + | 10.5439i | 0.223007 | + | 0.686346i | ||||
\(237\) | −8.75422 | + | 6.36031i | −0.568648 | + | 0.413147i | ||||
\(238\) | 0.509142 | + | 1.56698i | 0.0330028 | + | 0.101572i | ||||
\(239\) | −5.15676 | − | 3.74661i | −0.333563 | − | 0.242348i | 0.408378 | − | 0.912813i | \(-0.366095\pi\) |
−0.741941 | + | 0.670465i | \(0.766095\pi\) | |||||||
\(240\) | 7.14647 | + | 5.19222i | 0.461303 | + | 0.335156i | ||||
\(241\) | 22.5517 | − | 16.3847i | 1.45268 | − | 1.05543i | 0.467485 | − | 0.884001i | \(-0.345160\pi\) |
0.985196 | − | 0.171433i | \(-0.0548398\pi\) | |||||||
\(242\) | 9.17106 | 0.589538 | ||||||||
\(243\) | −52.3360 | −3.35735 | ||||||||
\(244\) | 1.93434 | − | 1.40538i | 0.123833 | − | 0.0899702i | ||||
\(245\) | −5.45200 | + | 16.7795i | −0.348315 | + | 1.07200i | ||||
\(246\) | −2.24057 | − | 6.89577i | −0.142854 | − | 0.439658i | ||||
\(247\) | −15.1348 | −0.963002 | ||||||||
\(248\) | −3.64011 | − | 4.21302i | −0.231148 | − | 0.267527i | ||||
\(249\) | 3.79696 | 0.240622 | ||||||||
\(250\) | 2.38325 | + | 7.33489i | 0.150730 | + | 0.463899i | ||||
\(251\) | 8.46401 | − | 26.0495i | 0.534243 | − | 1.64423i | −0.211035 | − | 0.977478i | \(-0.567683\pi\) |
0.745278 | − | 0.666753i | \(-0.232317\pi\) | |||||||
\(252\) | −3.98971 | + | 2.89870i | −0.251328 | + | 0.182601i | ||||
\(253\) | 3.97211 | 0.249724 | ||||||||
\(254\) | 14.1198 | 0.885952 | ||||||||
\(255\) | −19.0518 | + | 13.8419i | −1.19307 | + | 0.866816i | ||||
\(256\) | −0.809017 | − | 0.587785i | −0.0505636 | − | 0.0367366i | ||||
\(257\) | −8.96914 | − | 6.51646i | −0.559479 | − | 0.406486i | 0.271789 | − | 0.962357i | \(-0.412385\pi\) |
−0.831268 | + | 0.555871i | \(0.812385\pi\) | |||||||
\(258\) | 6.39455 | + | 19.6804i | 0.398107 | + | 1.22525i | ||||
\(259\) | 2.28508 | − | 1.66021i | 0.141988 | − | 0.103160i | ||||
\(260\) | 1.94534 | + | 5.98713i | 0.120645 | + | 0.371306i | ||||
\(261\) | 9.39905 | − | 28.9273i | 0.581787 | − | 1.79056i | ||||
\(262\) | −1.92684 | − | 1.39993i | −0.119040 | − | 0.0864878i | ||||
\(263\) | −7.74685 | + | 23.8423i | −0.477691 | + | 1.47018i | 0.364603 | + | 0.931163i | \(0.381205\pi\) |
−0.842294 | + | 0.539019i | \(0.818795\pi\) | |||||||
\(264\) | −1.38475 | + | 4.26182i | −0.0852255 | + | 0.262297i | ||||
\(265\) | −7.41676 | − | 5.38859i | −0.455608 | − | 0.331019i | ||||
\(266\) | 1.22406 | − | 3.76727i | 0.0750519 | − | 0.230986i | ||||
\(267\) | −8.67827 | − | 26.7090i | −0.531101 | − | 1.63456i | ||||
\(268\) | 7.61225 | − | 5.53062i | 0.464992 | − | 0.337837i | ||||
\(269\) | 8.14533 | + | 25.0687i | 0.496629 | + | 1.52847i | 0.814402 | + | 0.580301i | \(0.197065\pi\) |
−0.317773 | + | 0.948167i | \(0.602935\pi\) | |||||||
\(270\) | −35.5853 | − | 25.8542i | −2.16565 | − | 1.57344i | ||||
\(271\) | 21.4162 | + | 15.5598i | 1.30094 | + | 0.945189i | 0.999964 | − | 0.00844252i | \(-0.00268737\pi\) |
0.300977 | + | 0.953632i | \(0.402687\pi\) | |||||||
\(272\) | 2.15676 | − | 1.56698i | 0.130773 | − | 0.0950120i | ||||
\(273\) | −4.83582 | −0.292677 | ||||||||
\(274\) | 12.8537 | 0.776519 | ||||||||
\(275\) | 2.30531 | − | 1.67491i | 0.139015 | − | 0.101001i | ||||
\(276\) | 3.00742 | − | 9.25589i | 0.181026 | − | 0.557139i | ||||
\(277\) | −7.80959 | − | 24.0355i | −0.469233 | − | 1.44415i | −0.853580 | − | 0.520962i | \(-0.825573\pi\) |
0.384347 | − | 0.923189i | \(-0.374427\pi\) | |||||||
\(278\) | −5.56089 | −0.333520 | ||||||||
\(279\) | 29.0460 | + | 33.6175i | 1.73894 | + | 2.01263i | ||||
\(280\) | −1.64762 | −0.0984640 | ||||||||
\(281\) | −2.94171 | − | 9.05365i | −0.175488 | − | 0.540096i | 0.824168 | − | 0.566346i | \(-0.191643\pi\) |
−0.999655 | + | 0.0262502i | \(0.991643\pi\) | |||||||
\(282\) | −4.97028 | + | 15.2970i | −0.295976 | + | 0.910920i | ||||
\(283\) | 26.0144 | − | 18.9006i | 1.54640 | − | 1.12352i | 0.600240 | − | 0.799820i | \(-0.295072\pi\) |
0.946158 | − | 0.323704i | \(-0.104928\pi\) | |||||||
\(284\) | 8.18820 | 0.485880 | ||||||||
\(285\) | 56.6164 | 3.35366 | ||||||||
\(286\) | −2.58360 | + | 1.87709i | −0.152771 | + | 0.110995i | ||||
\(287\) | 1.09410 | + | 0.794910i | 0.0645827 | + | 0.0469220i | ||||
\(288\) | 6.45549 | + | 4.69019i | 0.380393 | + | 0.276372i | ||||
\(289\) | −3.05709 | − | 9.40877i | −0.179829 | − | 0.553457i | ||||
\(290\) | 8.22114 | − | 5.97301i | 0.482762 | − | 0.350747i | ||||
\(291\) | 3.06610 | + | 9.43649i | 0.179738 | + | 0.553177i | ||||
\(292\) | −1.32845 | + | 4.08854i | −0.0777415 | + | 0.239264i | ||||
\(293\) | 3.03051 | + | 2.20179i | 0.177044 | + | 0.128630i | 0.672778 | − | 0.739844i | \(-0.265101\pi\) |
−0.495734 | + | 0.868474i | \(0.665101\pi\) | |||||||
\(294\) | −6.77643 | + | 20.8557i | −0.395210 | + | 1.21633i | ||||
\(295\) | 9.13313 | − | 28.1089i | 0.531751 | − | 1.63656i | ||||
\(296\) | −3.69734 | − | 2.68628i | −0.214904 | − | 0.156137i | ||||
\(297\) | 6.89526 | − | 21.2214i | 0.400103 | − | 1.23139i | ||||
\(298\) | −1.92591 | − | 5.92733i | −0.111565 | − | 0.343361i | ||||
\(299\) | 5.61109 | − | 4.07670i | 0.324498 | − | 0.235762i | ||||
\(300\) | −2.15747 | − | 6.64001i | −0.124562 | − | 0.383361i | ||||
\(301\) | −3.12254 | − | 2.26866i | −0.179980 | − | 0.130763i | ||||
\(302\) | 12.8765 | + | 9.35536i | 0.740962 | + | 0.538340i | ||||
\(303\) | −47.5285 | + | 34.5315i | −2.73044 | + | 1.98378i | ||||
\(304\) | −6.40926 | −0.367596 | ||||||||
\(305\) | −6.37411 | −0.364980 | ||||||||
\(306\) | −17.2097 | + | 12.5036i | −0.983814 | + | 0.714782i | ||||
\(307\) | 5.85446 | − | 18.0182i | 0.334132 | − | 1.02835i | −0.633017 | − | 0.774138i | \(-0.718184\pi\) |
0.967148 | − | 0.254213i | \(-0.0818164\pi\) | |||||||
\(308\) | −0.258282 | − | 0.794910i | −0.0147170 | − | 0.0452942i | ||||
\(309\) | 1.82867 | 0.104029 | ||||||||
\(310\) | 1.24914 | + | 14.7905i | 0.0709464 | + | 0.840042i | ||||
\(311\) | 3.89253 | 0.220725 | 0.110363 | − | 0.993891i | \(-0.464799\pi\) | ||||
0.110363 | + | 0.993891i | \(0.464799\pi\) | |||||||
\(312\) | 2.41791 | + | 7.44156i | 0.136887 | + | 0.421295i | ||||
\(313\) | −4.96979 | + | 15.2954i | −0.280909 | + | 0.864549i | 0.706686 | + | 0.707527i | \(0.250189\pi\) |
−0.987595 | + | 0.157022i | \(0.949811\pi\) | |||||||
\(314\) | −5.15376 | + | 3.74443i | −0.290844 | + | 0.211310i | ||||
\(315\) | 13.1470 | 0.740752 | ||||||||
\(316\) | −3.26565 | −0.183707 | ||||||||
\(317\) | −27.8354 | + | 20.2236i | −1.56339 | + | 1.13587i | −0.630232 | + | 0.776407i | \(0.717040\pi\) |
−0.933159 | + | 0.359463i | \(0.882960\pi\) | |||||||
\(318\) | −9.21849 | − | 6.69763i | −0.516947 | − | 0.375584i | ||||
\(319\) | 4.17049 | + | 3.03004i | 0.233503 | + | 0.169650i | ||||
\(320\) | 0.823809 | + | 2.53542i | 0.0460523 | + | 0.141735i | ||||
\(321\) | −24.8564 | + | 18.0592i | −1.38735 | + | 1.00797i | ||||
\(322\) | 0.560941 | + | 1.72640i | 0.0312600 | + | 0.0962084i | ||||
\(323\) | 5.28001 | − | 16.2502i | 0.293787 | − | 0.904185i | ||||
\(324\) | −24.8635 | − | 18.0644i | −1.38130 | − | 1.00358i | ||||
\(325\) | 1.53753 | − | 4.73202i | 0.0852866 | − | 0.262485i | ||||
\(326\) | 0.879100 | − | 2.70559i | 0.0486888 | − | 0.149849i | ||||
\(327\) | 51.5350 | + | 37.4424i | 2.84989 | + | 2.07057i | ||||
\(328\) | 0.676191 | − | 2.08110i | 0.0373364 | − | 0.114910i | ||||
\(329\) | −0.927051 | − | 2.85317i | −0.0511100 | − | 0.157300i | ||||
\(330\) | 9.66476 | − | 7.02186i | 0.532027 | − | 0.386541i | ||||
\(331\) | 6.66489 | + | 20.5124i | 0.366336 | + | 1.12746i | 0.949141 | + | 0.314853i | \(0.101955\pi\) |
−0.582805 | + | 0.812612i | \(0.698045\pi\) | |||||||
\(332\) | 0.927051 | + | 0.673542i | 0.0508785 | + | 0.0369654i | ||||
\(333\) | 29.5027 | + | 21.4349i | 1.61674 | + | 1.17463i | ||||
\(334\) | −2.04058 | + | 1.48257i | −0.111656 | + | 0.0811225i | ||||
\(335\) | −25.0842 | −1.37049 | ||||||||
\(336\) | −2.04787 | −0.111720 | ||||||||
\(337\) | −6.29422 | + | 4.57302i | −0.342868 | + | 0.249108i | −0.745871 | − | 0.666090i | \(-0.767966\pi\) |
0.403003 | + | 0.915199i | \(0.367966\pi\) | |||||||
\(338\) | 2.29409 | − | 7.06049i | 0.124782 | − | 0.384040i | ||||
\(339\) | 13.8865 | + | 42.7382i | 0.754210 | + | 2.32122i | ||||
\(340\) | −7.10704 | −0.385433 | ||||||||
\(341\) | −6.93999 | + | 2.92122i | −0.375822 | + | 0.158193i | ||||
\(342\) | 51.1422 | 2.76545 | ||||||||
\(343\) | −2.60081 | − | 8.00448i | −0.140431 | − | 0.432201i | ||||
\(344\) | −1.92983 | + | 5.93942i | −0.104050 | + | 0.320232i | ||||
\(345\) | −20.9901 | + | 15.2502i | −1.13007 | + | 0.821042i | ||||
\(346\) | 11.5253 | 0.619604 | ||||||||
\(347\) | 8.97598 | 0.481856 | 0.240928 | − | 0.970543i | \(-0.422548\pi\) | ||||
0.240928 | + | 0.970543i | \(0.422548\pi\) | |||||||
\(348\) | 10.2183 | − | 7.42401i | 0.547757 | − | 0.397969i | ||||
\(349\) | −14.6444 | − | 10.6398i | −0.783897 | − | 0.569534i | 0.122249 | − | 0.992499i | \(-0.460989\pi\) |
−0.906146 | + | 0.422965i | \(0.860989\pi\) | |||||||
\(350\) | 1.05352 | + | 0.765426i | 0.0563130 | + | 0.0409138i | ||||
\(351\) | −12.0398 | − | 37.0547i | −0.642637 | − | 1.97783i | ||||
\(352\) | −1.09410 | + | 0.794910i | −0.0583157 | + | 0.0423688i | ||||
\(353\) | −8.65884 | − | 26.6492i | −0.460863 | − | 1.41839i | −0.864111 | − | 0.503301i | \(-0.832119\pi\) |
0.403248 | − | 0.915091i | \(-0.367881\pi\) | |||||||
\(354\) | 11.3518 | − | 34.9373i | 0.603342 | − | 1.85690i | ||||
\(355\) | −17.6600 | − | 12.8307i | −0.937295 | − | 0.680984i | ||||
\(356\) | 2.61905 | − | 8.06060i | 0.138809 | − | 0.427211i | ||||
\(357\) | 1.68705 | − | 5.19222i | 0.0892883 | − | 0.274801i | ||||
\(358\) | −14.9497 | − | 10.8616i | −0.790117 | − | 0.574053i | ||||
\(359\) | 2.85238 | − | 8.77873i | 0.150543 | − | 0.463324i | −0.847139 | − | 0.531371i | \(-0.821677\pi\) |
0.997682 | + | 0.0680476i | \(0.0216770\pi\) | |||||||
\(360\) | −6.57352 | − | 20.2312i | −0.346455 | − | 1.06628i | ||||
\(361\) | −17.8620 | + | 12.9775i | −0.940103 | + | 0.683025i | ||||
\(362\) | 0.851318 | + | 2.62009i | 0.0447443 | + | 0.137709i | ||||
\(363\) | −24.5848 | − | 17.8619i | −1.29037 | − | 0.937508i | ||||
\(364\) | −1.18070 | − | 0.857825i | −0.0618852 | − | 0.0449623i | ||||
\(365\) | 9.27180 | − | 6.73635i | 0.485308 | − | 0.352597i | ||||
\(366\) | −7.92255 | −0.414118 | ||||||||
\(367\) | −11.1699 | −0.583065 | −0.291532 | − | 0.956561i | \(-0.594165\pi\) | ||||
−0.291532 | + | 0.956561i | \(0.594165\pi\) | |||||||
\(368\) | 2.37618 | − | 1.72640i | 0.123867 | − | 0.0899947i | ||||
\(369\) | −5.39561 | + | 16.6060i | −0.280884 | + | 0.864473i | ||||
\(370\) | 3.76494 | + | 11.5873i | 0.195730 | + | 0.602395i | ||||
\(371\) | 2.12532 | 0.110341 | ||||||||
\(372\) | 1.55259 | + | 18.3835i | 0.0804980 | + | 0.953138i | ||||
\(373\) | −1.84237 | −0.0953943 | −0.0476972 | − | 0.998862i | \(-0.515188\pi\) | ||||
−0.0476972 | + | 0.998862i | \(0.515188\pi\) | |||||||
\(374\) | −1.11410 | − | 3.42886i | −0.0576090 | − | 0.177302i | ||||
\(375\) | 7.89695 | − | 24.3043i | 0.407797 | − | 1.25507i | ||||
\(376\) | −3.92705 | + | 2.85317i | −0.202522 | + | 0.147141i | ||||
\(377\) | 9.00115 | 0.463583 | ||||||||
\(378\) | 10.1972 | 0.524488 | ||||||||
\(379\) | 14.5892 | − | 10.5997i | 0.749399 | − | 0.544470i | −0.146242 | − | 0.989249i | \(-0.546718\pi\) |
0.895640 | + | 0.444779i | \(0.146718\pi\) | |||||||
\(380\) | 13.8232 | + | 10.0432i | 0.709117 | + | 0.515204i | ||||
\(381\) | −37.8508 | − | 27.5002i | −1.93915 | − | 1.40888i | ||||
\(382\) | −4.89389 | − | 15.0619i | −0.250393 | − | 0.770631i | ||||
\(383\) | −8.15676 | + | 5.92623i | −0.416791 | + | 0.302816i | −0.776345 | − | 0.630308i | \(-0.782929\pi\) |
0.359554 | + | 0.933124i | \(0.382929\pi\) | |||||||
\(384\) | 1.02393 | + | 3.15135i | 0.0522524 | + | 0.160816i | ||||
\(385\) | −0.688554 | + | 2.11915i | −0.0350920 | + | 0.108002i | ||||
\(386\) | 2.49536 | + | 1.81299i | 0.127011 | + | 0.0922786i | ||||
\(387\) | 15.3990 | − | 47.3932i | 0.782774 | − | 2.40913i | ||||
\(388\) | −0.925330 | + | 2.84787i | −0.0469765 | + | 0.144579i | ||||
\(389\) | 9.44035 | + | 6.85881i | 0.478645 | + | 0.347756i | 0.800801 | − | 0.598931i | \(-0.204408\pi\) |
−0.322156 | + | 0.946687i | \(0.604408\pi\) | |||||||
\(390\) | 6.44591 | − | 19.8385i | 0.326401 | − | 1.00456i | ||||
\(391\) | 2.41963 | + | 7.44685i | 0.122366 | + | 0.376604i | ||||
\(392\) | −5.35410 | + | 3.88998i | −0.270423 | + | 0.196474i | ||||
\(393\) | 2.43870 | + | 7.50556i | 0.123016 | + | 0.378605i | ||||
\(394\) | 18.2409 | + | 13.2528i | 0.918965 | + | 0.667667i | ||||
\(395\) | 7.04323 | + | 5.11721i | 0.354383 | + | 0.257475i | ||||
\(396\) | 8.73028 | − | 6.34292i | 0.438713 | − | 0.318744i | ||||
\(397\) | 21.0966 | 1.05881 | 0.529405 | − | 0.848370i | \(-0.322415\pi\) | ||||
0.529405 | + | 0.848370i | \(0.322415\pi\) | |||||||
\(398\) | 9.06615 | 0.454445 | ||||||||
\(399\) | −10.6186 | + | 7.71487i | −0.531595 | + | 0.386227i | ||||
\(400\) | 0.651111 | − | 2.00391i | 0.0325555 | − | 0.100196i | ||||
\(401\) | 3.40590 | + | 10.4823i | 0.170083 | + | 0.523460i | 0.999375 | − | 0.0353548i | \(-0.0112561\pi\) |
−0.829292 | + | 0.558815i | \(0.811256\pi\) | |||||||
\(402\) | −31.1778 | −1.55501 | ||||||||
\(403\) | −6.80545 | + | 11.2493i | −0.339003 | + | 0.560368i | ||||
\(404\) | −17.7299 | −0.882097 | ||||||||
\(405\) | 25.3181 | + | 77.9210i | 1.25807 | + | 3.87193i | ||||
\(406\) | −0.727989 | + | 2.24052i | −0.0361295 | + | 0.111195i | ||||
\(407\) | −5.00022 | + | 3.63287i | −0.247851 | + | 0.180075i | ||||
\(408\) | −8.83353 | −0.437325 | ||||||||
\(409\) | −27.6133 | −1.36539 | −0.682696 | − | 0.730702i | \(-0.739193\pi\) | ||||
−0.682696 | + | 0.730702i | \(0.739193\pi\) | |||||||
\(410\) | −4.71942 | + | 3.42886i | −0.233076 | + | 0.169339i | ||||
\(411\) | −34.4568 | − | 25.0343i | −1.69963 | − | 1.23485i | ||||
\(412\) | 0.446481 | + | 0.324387i | 0.0219965 | + | 0.0159814i | ||||
\(413\) | 2.11733 | + | 6.51646i | 0.104187 | + | 0.320654i | ||||
\(414\) | −18.9606 | + | 13.7757i | −0.931861 | + | 0.677037i | ||||
\(415\) | −0.944001 | − | 2.90534i | −0.0463392 | − | 0.142617i | ||||
\(416\) | −0.729710 | + | 2.24582i | −0.0357770 | + | 0.110110i | ||||
\(417\) | 14.9071 | + | 10.8306i | 0.730001 | + | 0.530377i | ||||
\(418\) | −2.67849 | + | 8.24353i | −0.131009 | + | 0.403204i | ||||
\(419\) | −1.32037 | + | 4.06368i | −0.0645042 | + | 0.198524i | −0.978114 | − | 0.208068i | \(-0.933283\pi\) |
0.913610 | + | 0.406591i | \(0.133283\pi\) | |||||||
\(420\) | 4.41676 | + | 3.20897i | 0.215516 | + | 0.156582i | ||||
\(421\) | −11.5717 | + | 35.6139i | −0.563969 | + | 1.73572i | 0.107027 | + | 0.994256i | \(0.465867\pi\) |
−0.670996 | + | 0.741461i | \(0.734133\pi\) | |||||||
\(422\) | −3.37746 | − | 10.3948i | −0.164412 | − | 0.506009i | ||||
\(423\) | 31.3356 | − | 22.7667i | 1.52359 | − | 1.10695i | ||||
\(424\) | −1.06266 | − | 3.27053i | −0.0516074 | − | 0.158831i | ||||
\(425\) | 4.54438 | + | 3.30168i | 0.220435 | + | 0.160155i | ||||
\(426\) | −21.9501 | − | 15.9477i | −1.06348 | − | 0.772666i | ||||
\(427\) | 1.19549 | − | 0.868572i | 0.0578537 | − | 0.0420332i | ||||
\(428\) | −9.27237 | −0.448197 | ||||||||
\(429\) | 10.5817 | 0.510891 | ||||||||
\(430\) | 13.4691 | − | 9.78590i | 0.649539 | − | 0.471918i | ||||
\(431\) | −0.799437 | + | 2.46041i | −0.0385075 | + | 0.118514i | −0.968462 | − | 0.249160i | \(-0.919846\pi\) |
0.929955 | + | 0.367674i | \(0.119846\pi\) | |||||||
\(432\) | −5.09860 | − | 15.6919i | −0.245307 | − | 0.754976i | ||||
\(433\) | 25.5179 | 1.22631 | 0.613155 | − | 0.789962i | \(-0.289900\pi\) | ||||
0.613155 | + | 0.789962i | \(0.289900\pi\) | |||||||
\(434\) | −2.24971 | − | 2.60379i | −0.107990 | − | 0.124986i | ||||
\(435\) | −33.6716 | −1.61443 | ||||||||
\(436\) | 5.94070 | + | 18.2836i | 0.284508 | + | 0.875625i | ||||
\(437\) | 5.81718 | − | 17.9034i | 0.278273 | − | 0.856437i | ||||
\(438\) | 11.5242 | − | 8.37279i | 0.550646 | − | 0.400068i | ||||
\(439\) | −24.1961 | −1.15482 | −0.577408 | − | 0.816456i | \(-0.695936\pi\) | ||||
−0.577408 | + | 0.816456i | \(0.695936\pi\) | |||||||
\(440\) | 3.60532 | 0.171877 | ||||||||
\(441\) | 42.7227 | − | 31.0398i | 2.03441 | − | 1.47809i | ||||
\(442\) | −5.09295 | − | 3.70025i | −0.242247 | − | 0.176003i | ||||
\(443\) | 14.2301 | + | 10.3388i | 0.676091 | + | 0.491209i | 0.872059 | − | 0.489402i | \(-0.162785\pi\) |
−0.195968 | + | 0.980610i | \(0.562785\pi\) | |||||||
\(444\) | 4.67955 | + | 14.4022i | 0.222082 | + | 0.683497i | ||||
\(445\) | −18.2794 | + | 13.2808i | −0.866528 | + | 0.629570i | ||||
\(446\) | 3.78287 | + | 11.6425i | 0.179124 | + | 0.551288i | ||||
\(447\) | −6.38153 | + | 19.6403i | −0.301836 | + | 0.928955i | ||||
\(448\) | −0.500000 | − | 0.363271i | −0.0236228 | − | 0.0171630i | ||||
\(449\) | 2.57008 | − | 7.90990i | 0.121290 | − | 0.373291i | −0.871917 | − | 0.489653i | \(-0.837123\pi\) |
0.993207 | + | 0.116362i | \(0.0371233\pi\) | |||||||
\(450\) | −5.19549 | + | 15.9901i | −0.244918 | + | 0.753779i | ||||
\(451\) | −2.39411 | − | 1.73942i | −0.112734 | − | 0.0819061i | ||||
\(452\) | −4.19085 | + | 12.8981i | −0.197121 | + | 0.606676i | ||||
\(453\) | −16.2972 | − | 50.1577i | −0.765711 | − | 2.35661i | ||||
\(454\) | 6.43641 | − | 4.67632i | 0.302076 | − | 0.219471i | ||||
\(455\) | 1.20228 | + | 3.70025i | 0.0563639 | + | 0.173470i | ||||
\(456\) | 17.1813 | + | 12.4829i | 0.804587 | + | 0.584566i | ||||
\(457\) | −1.56810 | − | 1.13929i | −0.0733524 | − | 0.0532937i | 0.550505 | − | 0.834832i | \(-0.314435\pi\) |
−0.623857 | + | 0.781538i | \(0.714435\pi\) | |||||||
\(458\) | −17.4576 | + | 12.6837i | −0.815739 | + | 0.592669i | ||||
\(459\) | 43.9859 | 2.05308 | ||||||||
\(460\) | −7.83009 | −0.365080 | ||||||||
\(461\) | −6.23792 | + | 4.53212i | −0.290529 | + | 0.211082i | −0.723497 | − | 0.690328i | \(-0.757466\pi\) |
0.432968 | + | 0.901409i | \(0.357466\pi\) | |||||||
\(462\) | −0.855823 | + | 2.63395i | −0.0398165 | + | 0.122542i | ||||
\(463\) | 6.38077 | + | 19.6380i | 0.296540 | + | 0.912655i | 0.982700 | + | 0.185205i | \(0.0592948\pi\) |
−0.686160 | + | 0.727450i | \(0.740705\pi\) | |||||||
\(464\) | 3.81180 | 0.176958 | ||||||||
\(465\) | 25.4579 | − | 42.0816i | 1.18058 | − | 1.95149i | ||||
\(466\) | 5.16232 | 0.239140 | ||||||||
\(467\) | 1.02230 | + | 3.14630i | 0.0473062 | + | 0.145594i | 0.971919 | − | 0.235314i | \(-0.0756117\pi\) |
−0.924613 | + | 0.380907i | \(0.875612\pi\) | |||||||
\(468\) | 5.82266 | − | 17.9203i | 0.269153 | − | 0.828367i | ||||
\(469\) | 4.70463 | − | 3.41811i | 0.217240 | − | 0.157834i | ||||
\(470\) | 12.9406 | 0.596904 | ||||||||
\(471\) | 21.1085 | 0.972626 | ||||||||
\(472\) | 8.96914 | − | 6.51646i | 0.412838 | − | 0.299944i | ||||
\(473\) | 6.83274 | + | 4.96427i | 0.314170 | + | 0.228258i | ||||
\(474\) | 8.75422 | + | 6.36031i | 0.402095 | + | 0.292139i | ||||
\(475\) | −4.17314 | − | 12.8436i | −0.191477 | − | 0.589304i | ||||
\(476\) | 1.33295 | − | 0.968446i | 0.0610957 | − | 0.0443886i | ||||
\(477\) | 8.47942 | + | 26.0970i | 0.388246 | + | 1.19490i | ||||
\(478\) | −1.96971 | + | 6.06214i | −0.0900923 | + | 0.277276i | ||||
\(479\) | −7.58381 | − | 5.50996i | −0.346513 | − | 0.251757i | 0.400892 | − | 0.916125i | \(-0.368700\pi\) |
−0.747405 | + | 0.664369i | \(0.768700\pi\) | |||||||
\(480\) | 2.72971 | − | 8.40118i | 0.124594 | − | 0.383460i | ||||
\(481\) | −3.33489 | + | 10.2637i | −0.152058 | + | 0.467987i | ||||
\(482\) | −22.5517 | − | 16.3847i | −1.02720 | − | 0.746305i | ||||
\(483\) | 1.85869 | − | 5.72046i | 0.0845733 | − | 0.260290i | ||||
\(484\) | −2.83401 | − | 8.72220i | −0.128819 | − | 0.396464i | ||||
\(485\) | 6.45827 | − | 4.69221i | 0.293255 | − | 0.213062i | ||||
\(486\) | 16.1727 | + | 49.7745i | 0.733609 | + | 2.25782i | ||||
\(487\) | −6.20383 | − | 4.50735i | −0.281122 | − | 0.204247i | 0.438284 | − | 0.898836i | \(-0.355586\pi\) |
−0.719407 | + | 0.694589i | \(0.755586\pi\) | |||||||
\(488\) | −1.93434 | − | 1.40538i | −0.0875634 | − | 0.0636186i | ||||
\(489\) | −7.62611 | + | 5.54070i | −0.344865 | + | 0.250559i | ||||
\(490\) | 17.6430 | 0.797031 | ||||||||
\(491\) | 15.8167 | 0.713796 | 0.356898 | − | 0.934143i | \(-0.383834\pi\) | ||||
0.356898 | + | 0.934143i | \(0.383834\pi\) | |||||||
\(492\) | −5.86589 | + | 4.26182i | −0.264455 | + | 0.192138i | ||||
\(493\) | −3.14020 | + | 9.66453i | −0.141427 | + | 0.435269i | ||||
\(494\) | 4.67690 | + | 14.3940i | 0.210424 | + | 0.647617i | ||||
\(495\) | −28.7684 | −1.29304 | ||||||||
\(496\) | −2.88197 | + | 4.76385i | −0.129404 | + | 0.213903i | ||||
\(497\) | 5.06059 | 0.226998 | ||||||||
\(498\) | −1.17332 | − | 3.61112i | −0.0525779 | − | 0.161818i | ||||
\(499\) | −4.47448 | + | 13.7710i | −0.200305 | + | 0.616476i | 0.799568 | + | 0.600575i | \(0.205062\pi\) |
−0.999874 | + | 0.0159012i | \(0.994938\pi\) | |||||||
\(500\) | 6.23943 | − | 4.53321i | 0.279036 | − | 0.202731i | ||||
\(501\) | 8.35768 | 0.373394 | ||||||||
\(502\) | −27.3901 | −1.22248 | ||||||||
\(503\) | 20.8674 | − | 15.1611i | 0.930431 | − | 0.675998i | −0.0156670 | − | 0.999877i | \(-0.504987\pi\) |
0.946098 | + | 0.323879i | \(0.104987\pi\) | |||||||
\(504\) | 3.98971 | + | 2.89870i | 0.177716 | + | 0.129118i | ||||
\(505\) | 38.2392 | + | 27.7824i | 1.70162 | + | 1.23630i | ||||
\(506\) | −1.22745 | − | 3.77770i | −0.0545668 | − | 0.167939i | ||||
\(507\) | −19.9010 | + | 14.4590i | −0.883836 | + | 0.642145i | ||||
\(508\) | −4.36324 | − | 13.4287i | −0.193588 | − | 0.595802i | ||||
\(509\) | 9.81202 | − | 30.1983i | 0.434910 | − | 1.33852i | −0.458268 | − | 0.888814i | \(-0.651530\pi\) |
0.893179 | − | 0.449702i | \(-0.148470\pi\) | |||||||
\(510\) | 19.0518 | + | 13.8419i | 0.843628 | + | 0.612932i | ||||
\(511\) | −0.821025 | + | 2.52686i | −0.0363200 | + | 0.111782i | ||||
\(512\) | −0.309017 | + | 0.951057i | −0.0136568 | + | 0.0420312i | ||||
\(513\) | −85.5528 | − | 62.1578i | −3.77725 | − | 2.74433i | ||||
\(514\) | −3.42591 | + | 10.5439i | −0.151110 | + | 0.465069i | ||||
\(515\) | −0.454645 | − | 1.39925i | −0.0200340 | − | 0.0616584i | ||||
\(516\) | 16.7411 | − | 12.1632i | 0.736988 | − | 0.535453i | ||||
\(517\) | 2.02857 | + | 6.24330i | 0.0892165 | + | 0.274580i | ||||
\(518\) | −2.28508 | − | 1.66021i | −0.100401 | − | 0.0729454i | ||||
\(519\) | −30.8958 | − | 22.4471i | −1.35618 | − | 0.985320i | ||||
\(520\) | 5.09295 | − | 3.70025i | 0.223341 | − | 0.162267i | ||||
\(521\) | −37.6339 | −1.64877 | −0.824386 | − | 0.566028i | \(-0.808479\pi\) | ||||
−0.824386 | + | 0.566028i | \(0.808479\pi\) | |||||||
\(522\) | −30.4160 | −1.33127 | ||||||||
\(523\) | 13.2783 | − | 9.64724i | 0.580619 | − | 0.421844i | −0.258328 | − | 0.966057i | \(-0.583172\pi\) |
0.838947 | + | 0.544213i | \(0.183172\pi\) | |||||||
\(524\) | −0.735986 | + | 2.26513i | −0.0321517 | + | 0.0989527i | ||||
\(525\) | −1.33339 | − | 4.10375i | −0.0581939 | − | 0.179102i | ||||
\(526\) | 25.0693 | 1.09307 | ||||||||
\(527\) | −9.70419 | − | 11.2315i | −0.422721 | − | 0.489252i | ||||
\(528\) | 4.48114 | 0.195017 | ||||||||
\(529\) | −4.44160 | − | 13.6698i | −0.193113 | − | 0.594340i | ||||
\(530\) | −2.83295 | + | 8.71893i | −0.123056 | + | 0.378726i | ||||
\(531\) | −71.5685 | + | 51.9976i | −3.10581 | + | 2.25650i | ||||
\(532\) | −3.96114 | −0.171737 | ||||||||
\(533\) | −5.16719 | −0.223816 | ||||||||
\(534\) | −22.7200 | + | 16.5070i | −0.983190 | + | 0.714330i | ||||
\(535\) | 19.9983 | + | 14.5296i | 0.864601 | + | 0.628170i | ||||
\(536\) | −7.61225 | − | 5.53062i | −0.328799 | − | 0.238887i | ||||
\(537\) | 18.9211 | + | 58.2333i | 0.816507 | + | 2.51295i | ||||
\(538\) | 21.3247 | − | 15.4933i | 0.919375 | − | 0.667965i | ||||
\(539\) | 2.76573 | + | 8.51206i | 0.119129 | + | 0.366640i | ||||
\(540\) | −13.5924 | + | 41.8331i | −0.584923 | + | 1.80021i | ||||
\(541\) | 8.57074 | + | 6.22701i | 0.368485 | + | 0.267720i | 0.756582 | − | 0.653898i | \(-0.226868\pi\) |
−0.388097 | + | 0.921618i | \(0.626868\pi\) | |||||||
\(542\) | 8.18026 | − | 25.1762i | 0.351372 | − | 1.08141i | ||||
\(543\) | 2.82086 | − | 8.68172i | 0.121055 | − | 0.372568i | ||||
\(544\) | −2.15676 | − | 1.56698i | −0.0924704 | − | 0.0671836i | ||||
\(545\) | 15.8373 | − | 48.7423i | 0.678396 | − | 2.08789i | ||||
\(546\) | 1.49435 | + | 4.59914i | 0.0639523 | + | 0.196825i | ||||
\(547\) | 6.15663 | − | 4.47305i | 0.263238 | − | 0.191254i | −0.448335 | − | 0.893866i | \(-0.647983\pi\) |
0.711573 | + | 0.702612i | \(0.247983\pi\) | |||||||
\(548\) | −3.97200 | − | 12.2246i | −0.169676 | − | 0.522208i | ||||
\(549\) | 15.4349 | + | 11.2141i | 0.658746 | + | 0.478607i | ||||
\(550\) | −2.30531 | − | 1.67491i | −0.0982987 | − | 0.0714182i | ||||
\(551\) | 19.7649 | − | 14.3601i | 0.842015 | − | 0.611760i | ||||
\(552\) | −9.73222 | −0.414231 | ||||||||
\(553\) | −2.01828 | −0.0858262 | ||||||||
\(554\) | −20.4458 | + | 14.8547i | −0.868658 | + | 0.631117i | ||||
\(555\) | 12.4752 | − | 38.3948i | 0.529544 | − | 1.62977i | ||||
\(556\) | 1.71841 | + | 5.28872i | 0.0728768 | + | 0.224292i | ||||
\(557\) | 21.5577 | 0.913430 | 0.456715 | − | 0.889613i | \(-0.349026\pi\) | ||||
0.456715 | + | 0.889613i | \(0.349026\pi\) | |||||||
\(558\) | 22.9964 | − | 38.0128i | 0.973516 | − | 1.60921i | ||||
\(559\) | 14.7471 | 0.623734 | ||||||||
\(560\) | 0.509142 | + | 1.56698i | 0.0215152 | + | 0.0662169i | ||||
\(561\) | −3.69161 | + | 11.3616i | −0.155860 | + | 0.479687i | ||||
\(562\) | −7.70150 | + | 5.59546i | −0.324868 | + | 0.236030i | ||||
\(563\) | −28.2647 | −1.19121 | −0.595607 | − | 0.803276i | \(-0.703089\pi\) | ||||
−0.595607 | + | 0.803276i | \(0.703089\pi\) | |||||||
\(564\) | 16.0842 | 0.677266 | ||||||||
\(565\) | 29.2497 | − | 21.2512i | 1.23054 | − | 0.894043i | ||||
\(566\) | −26.0144 | − | 18.9006i | −1.09347 | − | 0.794452i | ||||
\(567\) | −15.3665 | − | 11.1644i | −0.645331 | − | 0.468860i | ||||
\(568\) | −2.53029 | − | 7.78744i | −0.106169 | − | 0.326754i | ||||
\(569\) | 21.0763 | − | 15.3128i | 0.883565 | − | 0.641948i | −0.0506271 | − | 0.998718i | \(-0.516122\pi\) |
0.934192 | + | 0.356770i | \(0.116122\pi\) | |||||||
\(570\) | −17.4954 | − | 53.8454i | −0.732802 | − | 2.25533i | ||||
\(571\) | −12.2779 | + | 37.7876i | −0.513816 | + | 1.58136i | 0.271611 | + | 0.962407i | \(0.412444\pi\) |
−0.785427 | + | 0.618955i | \(0.787556\pi\) | |||||||
\(572\) | 2.58360 | + | 1.87709i | 0.108026 | + | 0.0784852i | ||||
\(573\) | −16.2160 | + | 49.9078i | −0.677434 | + | 2.08493i | ||||
\(574\) | 0.417909 | − | 1.28619i | 0.0174432 | − | 0.0536846i | ||||
\(575\) | 5.00671 | + | 3.63759i | 0.208794 | + | 0.151698i | ||||
\(576\) | 2.46578 | − | 7.58888i | 0.102741 | − | 0.316203i | ||||
\(577\) | −0.186561 | − | 0.574175i | −0.00776663 | − | 0.0239032i | 0.947098 | − | 0.320944i | \(-0.104000\pi\) |
−0.954865 | + | 0.297041i | \(0.904000\pi\) | |||||||
\(578\) | −8.00357 | + | 5.81494i | −0.332905 | + | 0.241869i | ||||
\(579\) | −3.15826 | − | 9.72013i | −0.131253 | − | 0.403955i | ||||
\(580\) | −8.22114 | − | 5.97301i | −0.341364 | − | 0.248016i | ||||
\(581\) | 0.572949 | + | 0.416272i | 0.0237699 | + | 0.0172699i | ||||
\(582\) | 8.02716 | − | 5.83207i | 0.332736 | − | 0.241747i | ||||
\(583\) | −4.65063 | −0.192609 | ||||||||
\(584\) | 4.29894 | 0.177892 | ||||||||
\(585\) | −40.6388 | + | 29.5258i | −1.68021 | + | 1.22074i | ||||
\(586\) | 1.15755 | − | 3.56258i | 0.0478180 | − | 0.147169i | ||||
\(587\) | −5.56288 | − | 17.1208i | −0.229605 | − | 0.706650i | −0.997791 | − | 0.0664247i | \(-0.978841\pi\) |
0.768187 | − | 0.640226i | \(-0.221159\pi\) | |||||||
\(588\) | 21.9290 | 0.904337 | ||||||||
\(589\) | 3.00313 | + | 35.5587i | 0.123742 | + | 1.46517i | ||||
\(590\) | −29.5554 | −1.21678 | ||||||||
\(591\) | −23.0867 | − | 71.0535i | −0.949659 | − | 2.92275i | ||||
\(592\) | −1.41226 | + | 4.34649i | −0.0580435 | + | 0.178639i | ||||
\(593\) | 5.54474 | − | 4.02849i | 0.227695 | − | 0.165430i | −0.468089 | − | 0.883682i | \(-0.655057\pi\) |
0.695784 | + | 0.718251i | \(0.255057\pi\) | |||||||
\(594\) | −22.3135 | −0.915535 | ||||||||
\(595\) | −4.39239 | −0.180070 | ||||||||
\(596\) | −5.04209 | + | 3.66329i | −0.206532 | + | 0.150054i | ||||
\(597\) | −24.3036 | − | 17.6576i | −0.994680 | − | 0.722677i | ||||
\(598\) | −5.61109 | − | 4.07670i | −0.229455 | − | 0.166709i | ||||
\(599\) | 1.44935 | + | 4.46064i | 0.0592189 | + | 0.182257i | 0.976290 | − | 0.216467i | \(-0.0694533\pi\) |
−0.917071 | + | 0.398724i | \(0.869453\pi\) | |||||||
\(600\) | −5.64833 | + | 4.10375i | −0.230592 | + | 0.167535i | ||||
\(601\) | 4.84412 | + | 14.9087i | 0.197596 | + | 0.608137i | 0.999936 | + | 0.0112708i | \(0.00358770\pi\) |
−0.802341 | + | 0.596866i | \(0.796412\pi\) | |||||||
\(602\) | −1.19270 | + | 3.67076i | −0.0486110 | + | 0.149609i | ||||
\(603\) | 60.7414 | + | 44.1312i | 2.47358 | + | 1.79716i | ||||
\(604\) | 4.91840 | − | 15.1373i | 0.200127 | − | 0.615927i | ||||
\(605\) | −7.55521 | + | 23.2525i | −0.307163 | + | 0.945350i | ||||
\(606\) | 47.5285 | + | 34.5315i | 1.93071 | + | 1.40275i | ||||
\(607\) | 8.63712 | − | 26.5823i | 0.350570 | − | 1.07894i | −0.607964 | − | 0.793964i | \(-0.708014\pi\) |
0.958534 | − | 0.284978i | \(-0.0919864\pi\) | |||||||
\(608\) | 1.98057 | + | 6.09557i | 0.0803227 | + | 0.247208i | ||||
\(609\) | 6.31524 | − | 4.58829i | 0.255907 | − | 0.185927i | ||||
\(610\) | 1.96971 | + | 6.06214i | 0.0797511 | + | 0.245449i | ||||
\(611\) | 9.27330 | + | 6.73745i | 0.375158 | + | 0.272568i | ||||
\(612\) | 17.2097 | + | 12.5036i | 0.695661 | + | 0.505427i | ||||
\(613\) | 6.67133 | − | 4.84701i | 0.269453 | − | 0.195769i | −0.444851 | − | 0.895604i | \(-0.646743\pi\) |
0.714304 | + | 0.699836i | \(0.246743\pi\) | |||||||
\(614\) | −18.9454 | −0.764575 | ||||||||
\(615\) | 19.3295 | 0.779441 | ||||||||
\(616\) | −0.676191 | + | 0.491281i | −0.0272445 | + | 0.0197943i | ||||
\(617\) | −5.73678 | + | 17.6560i | −0.230954 | + | 0.710803i | 0.766679 | + | 0.642031i | \(0.221908\pi\) |
−0.997632 | + | 0.0687718i | \(0.978092\pi\) | |||||||
\(618\) | −0.565090 | − | 1.73917i | −0.0227312 | − | 0.0699596i | ||||
\(619\) | −21.2657 | −0.854739 | −0.427369 | − | 0.904077i | \(-0.640560\pi\) | ||||
−0.427369 | + | 0.904077i | \(0.640560\pi\) | |||||||
\(620\) | 13.6806 | − | 5.75851i | 0.549425 | − | 0.231267i | ||||
\(621\) | 48.4609 | 1.94467 | ||||||||
\(622\) | −1.20286 | − | 3.70202i | −0.0482302 | − | 0.148437i | ||||
\(623\) | 1.61866 | − | 4.98172i | 0.0648502 | − | 0.199588i | ||||
\(624\) | 6.33017 | − | 4.59914i | 0.253410 | − | 0.184113i | ||||
\(625\) | −31.0956 | −1.24382 | ||||||||
\(626\) | 16.0826 | 0.642789 | ||||||||
\(627\) | 23.2356 | − | 16.8817i | 0.927942 | − | 0.674189i | ||||
\(628\) | 5.15376 | + | 3.74443i | 0.205657 | + | 0.149419i | ||||
\(629\) | −9.85675 | − | 7.16135i | −0.393014 | − | 0.285542i | ||||
\(630\) | −4.06266 | − | 12.5036i | −0.161860 | − | 0.498155i | ||||
\(631\) | 23.9119 | − | 17.3730i | 0.951918 | − | 0.691609i | 0.000658154 | − | 1.00000i | \(-0.499791\pi\) |
0.951260 | + | 0.308391i | \(0.0997905\pi\) | |||||||
\(632\) | 1.00914 | + | 3.10582i | 0.0401415 | + | 0.123543i | ||||
\(633\) | −11.1913 | + | 34.4433i | −0.444814 | + | 1.36900i | ||||
\(634\) | 27.8354 | + | 20.2236i | 1.10548 | + | 0.803182i | ||||
\(635\) | −11.6320 | + | 35.7996i | −0.461601 | + | 1.42066i | ||||
\(636\) | −3.52115 | + | 10.8370i | −0.139623 | + | 0.429714i | ||||
\(637\) | 12.6431 | + | 9.18577i | 0.500939 | + | 0.363953i | ||||
\(638\) | 1.59299 | − | 4.90270i | 0.0630669 | − | 0.194100i | ||||
\(639\) | 20.1903 | + | 62.1393i | 0.798715 | + | 2.45819i | ||||
\(640\) | 2.15676 | − | 1.56698i | 0.0852535 | − | 0.0619403i | ||||
\(641\) | −5.80858 | − | 17.8770i | −0.229425 | − | 0.706098i | −0.997812 | − | 0.0661124i | \(-0.978940\pi\) |
0.768387 | − | 0.639985i | \(-0.221060\pi\) | |||||||
\(642\) | 24.8564 | + | 18.0592i | 0.981004 | + | 0.712741i | ||||
\(643\) | 10.4063 | + | 7.56065i | 0.410386 | + | 0.298163i | 0.773758 | − | 0.633481i | \(-0.218375\pi\) |
−0.363372 | + | 0.931644i | \(0.618375\pi\) | |||||||
\(644\) | 1.46856 | − | 1.06697i | 0.0578694 | − | 0.0420446i | ||||
\(645\) | −55.1661 | −2.17216 | ||||||||
\(646\) | −17.0865 | −0.672258 | ||||||||
\(647\) | −12.3701 | + | 8.98737i | −0.486317 | + | 0.353330i | −0.803766 | − | 0.594945i | \(-0.797174\pi\) |
0.317449 | + | 0.948275i | \(0.397174\pi\) | |||||||
\(648\) | −9.49700 | + | 29.2288i | −0.373077 | + | 1.14821i | ||||
\(649\) | −4.63313 | − | 14.2593i | −0.181866 | − | 0.559727i | ||||
\(650\) | −4.97554 | −0.195157 | ||||||||
\(651\) | 0.959553 | + | 11.3616i | 0.0376078 | + | 0.445296i | ||||
\(652\) | −2.84483 | −0.111412 | ||||||||
\(653\) | 6.90855 | + | 21.2623i | 0.270352 | + | 0.832059i | 0.990412 | + | 0.138147i | \(0.0441146\pi\) |
−0.720059 | + | 0.693913i | \(0.755885\pi\) | |||||||
\(654\) | 19.6846 | − | 60.5831i | 0.769730 | − | 2.36899i | ||||
\(655\) | 5.13676 | − | 3.73207i | 0.200710 | − | 0.145824i | ||||
\(656\) | −2.18820 | −0.0854348 | ||||||||
\(657\) | −34.3031 | −1.33829 | ||||||||
\(658\) | −2.42705 | + | 1.76336i | −0.0946163 | + | 0.0687428i | ||||
\(659\) | −6.85525 | − | 4.98063i | −0.267043 | − | 0.194018i | 0.446203 | − | 0.894932i | \(-0.352776\pi\) |
−0.713246 | + | 0.700914i | \(0.752776\pi\) | |||||||
\(660\) | −9.66476 | − | 7.02186i | −0.376200 | − | 0.273325i | ||||
\(661\) | −8.00862 | − | 24.6480i | −0.311499 | − | 0.958696i | −0.977172 | − | 0.212452i | \(-0.931855\pi\) |
0.665672 | − | 0.746244i | \(-0.268145\pi\) | |||||||
\(662\) | 17.4489 | − | 12.6774i | 0.678171 | − | 0.492720i | ||||
\(663\) | 6.44591 | + | 19.8385i | 0.250338 | + | 0.770462i | ||||
\(664\) | 0.354102 | − | 1.08981i | 0.0137418 | − | 0.0422930i | ||||
\(665\) | 8.54323 | + | 6.20702i | 0.331292 | + | 0.240698i | ||||
\(666\) | 11.2690 | − | 34.6825i | 0.436665 | − | 1.34392i | ||||
\(667\) | −3.45967 | + | 10.6478i | −0.133959 | + | 0.412283i | ||||
\(668\) | 2.04058 | + | 1.48257i | 0.0789524 | + | 0.0573623i | ||||
\(669\) | 12.5346 | − | 38.5776i | 0.484617 | − | 1.49150i | ||||
\(670\) | 7.75144 | + | 23.8565i | 0.299464 | + | 0.921656i | ||||
\(671\) | −2.61596 | + | 1.90061i | −0.100988 | + | 0.0733722i | ||||
\(672\) | 0.632826 | + | 1.94764i | 0.0244118 | + | 0.0751318i | ||||
\(673\) | −37.7404 | − | 27.4200i | −1.45478 | − | 1.05696i | −0.984684 | − | 0.174349i | \(-0.944218\pi\) |
−0.470100 | − | 0.882613i | \(-0.655782\pi\) | |||||||
\(674\) | 6.29422 | + | 4.57302i | 0.242444 | + | 0.176146i | ||||
\(675\) | 28.1254 | − | 20.4343i | 1.08255 | − | 0.786517i | ||||
\(676\) | −7.42384 | −0.285532 | ||||||||
\(677\) | 40.1322 | 1.54241 | 0.771203 | − | 0.636589i | \(-0.219655\pi\) | ||||
0.771203 | + | 0.636589i | \(0.219655\pi\) | |||||||
\(678\) | 36.3553 | − | 26.4136i | 1.39622 | − | 1.01441i | ||||
\(679\) | −0.571886 | + | 1.76008i | −0.0219470 | + | 0.0675458i | ||||
\(680\) | 2.19620 | + | 6.75919i | 0.0842203 | + | 0.259203i | ||||
\(681\) | −26.3618 | −1.01019 | ||||||||
\(682\) | 4.92282 | + | 5.69761i | 0.188505 | + | 0.218173i | ||||
\(683\) | −5.73560 | −0.219467 | −0.109733 | − | 0.993961i | \(-0.535000\pi\) | ||||
−0.109733 | + | 0.993961i | \(0.535000\pi\) | |||||||
\(684\) | −15.8038 | − | 48.6391i | −0.604274 | − | 1.85976i | ||||
\(685\) | −10.5890 | + | 32.5895i | −0.404584 | + | 1.24518i | ||||
\(686\) | −6.80902 | + | 4.94704i | −0.259969 | + | 0.188879i | ||||
\(687\) | 71.5016 | 2.72796 | ||||||||
\(688\) | 6.24508 | 0.238091 | ||||||||
\(689\) | −6.56958 | + | 4.77308i | −0.250281 | + | 0.181840i | ||||
\(690\) | 20.9901 | + | 15.2502i | 0.799078 | + | 0.580564i | ||||
\(691\) | −4.33839 | − | 3.15202i | −0.165040 | − | 0.119909i | 0.502200 | − | 0.864752i | \(-0.332524\pi\) |
−0.667240 | + | 0.744843i | \(0.732524\pi\) | |||||||
\(692\) | −3.56152 | − | 10.9612i | −0.135389 | − | 0.416683i | ||||
\(693\) | 5.39561 | − | 3.92014i | 0.204962 | − | 0.148914i | ||||
\(694\) | −2.77373 | − | 8.53667i | −0.105289 | − | 0.324047i | ||||
\(695\) | 4.58111 | − | 14.0992i | 0.173772 | − | 0.534814i | ||||
\(696\) | −10.2183 | − | 7.42401i | −0.387323 | − | 0.281406i | ||||
\(697\) | 1.80266 | − | 5.54801i | 0.0682806 | − | 0.210146i | ||||
\(698\) | −5.59366 | + | 17.2155i | −0.211723 | + | 0.651617i | ||||
\(699\) | −13.8386 | − | 10.0543i | −0.523424 | − | 0.380290i | ||||
\(700\) | 0.402408 | − | 1.23849i | 0.0152096 | − | 0.0468104i | ||||
\(701\) | −0.295457 | − | 0.909322i | −0.0111592 | − | 0.0343446i | 0.945322 | − | 0.326139i | \(-0.105748\pi\) |
−0.956481 | + | 0.291794i | \(0.905748\pi\) | |||||||
\(702\) | −31.5206 | + | 22.9010i | −1.18967 | + | 0.864344i | ||||
\(703\) | 9.05153 | + | 27.8578i | 0.341385 | + | 1.05067i | ||||
\(704\) | 1.09410 | + | 0.794910i | 0.0412354 | + | 0.0299593i | ||||
\(705\) | −34.6897 | − | 25.2035i | −1.30649 | − | 0.949221i | ||||
\(706\) | −22.6691 | + | 16.4701i | −0.853164 | + | 0.619860i | ||||
\(707\) | −10.9577 | −0.412107 | ||||||||
\(708\) | −36.7352 | −1.38059 | ||||||||
\(709\) | −2.09273 | + | 1.52046i | −0.0785940 | + | 0.0571019i | −0.626388 | − | 0.779511i | \(-0.715468\pi\) |
0.547794 | + | 0.836613i | \(0.315468\pi\) | |||||||
\(710\) | −6.74551 | + | 20.7606i | −0.253155 | + | 0.779130i | ||||
\(711\) | −8.05237 | − | 24.7827i | −0.301988 | − | 0.929422i | ||||
\(712\) | −8.47541 | −0.317630 | ||||||||
\(713\) | −10.6915 | − | 12.3742i | −0.400399 | − | 0.463416i | ||||
\(714\) | −5.45942 | −0.204314 | ||||||||
\(715\) | −2.63084 | − | 8.09688i | −0.0983877 | − | 0.302806i | ||||
\(716\) | −5.71028 | + | 17.5744i | −0.213403 | + | 0.656787i | ||||
\(717\) | 17.0870 | − | 12.4145i | 0.638127 | − | 0.463626i | ||||
\(718\) | −9.23050 | −0.344479 | ||||||||
\(719\) | −13.9417 | −0.519938 | −0.259969 | − | 0.965617i | \(-0.583712\pi\) | ||||
−0.259969 | + | 0.965617i | \(0.583712\pi\) | |||||||
\(720\) | −17.2097 | + | 12.5036i | −0.641368 | + | 0.465981i | ||||
\(721\) | 0.275940 | + | 0.200482i | 0.0102766 | + | 0.00746636i | ||||
\(722\) | 17.8620 | + | 12.9775i | 0.664754 | + | 0.482972i | ||||
\(723\) | 28.5426 | + | 87.8450i | 1.06151 | + | 3.26699i | ||||
\(724\) | 2.22878 | − | 1.61930i | 0.0828319 | − | 0.0601809i | ||||
\(725\) | 2.48190 | + | 7.63851i | 0.0921756 | + | 0.283687i | ||||
\(726\) | −9.39057 | + | 28.9012i | −0.348517 | + | 1.07262i | ||||
\(727\) | −21.5984 | − | 15.6922i | −0.801040 | − | 0.581990i | 0.110179 | − | 0.993912i | \(-0.464858\pi\) |
−0.911219 | + | 0.411922i | \(0.864858\pi\) | |||||||
\(728\) | −0.450985 | + | 1.38799i | −0.0167146 | + | 0.0514423i | ||||
\(729\) | 25.0976 | − | 77.2425i | 0.929541 | − | 2.86083i | ||||
\(730\) | −9.27180 | − | 6.73635i | −0.343165 | − | 0.249324i | ||||
\(731\) | −5.14475 | + | 15.8339i | −0.190286 | + | 0.585639i | ||||
\(732\) | 2.44820 | + | 7.53479i | 0.0904881 | + | 0.278494i | ||||
\(733\) | −3.33903 | + | 2.42595i | −0.123330 | + | 0.0896045i | −0.647740 | − | 0.761861i | \(-0.724286\pi\) |
0.524410 | + | 0.851466i | \(0.324286\pi\) | |||||||
\(734\) | 3.45169 | + | 10.6232i | 0.127404 | + | 0.392110i | ||||
\(735\) | −47.2956 | − | 34.3623i | −1.74452 | − | 1.26747i | ||||
\(736\) | −2.37618 | − | 1.72640i | −0.0875873 | − | 0.0636359i | ||||
\(737\) | −10.2947 | + | 7.47951i | −0.379209 | + | 0.275511i | ||||
\(738\) | 17.4606 | 0.642732 | ||||||||
\(739\) | −28.0676 | −1.03248 | −0.516241 | − | 0.856443i | \(-0.672669\pi\) | ||||
−0.516241 | + | 0.856443i | \(0.672669\pi\) | |||||||
\(740\) | 9.85675 | − | 7.16135i | 0.362341 | − | 0.263256i | ||||
\(741\) | 15.4970 | − | 47.6949i | 0.569297 | − | 1.75212i | ||||
\(742\) | −0.656761 | − | 2.02130i | −0.0241104 | − | 0.0742043i | ||||
\(743\) | 30.8271 | 1.13094 | 0.565468 | − | 0.824770i | \(-0.308696\pi\) | ||||
0.565468 | + | 0.824770i | \(0.308696\pi\) | |||||||
\(744\) | 17.0039 | − | 7.15740i | 0.623394 | − | 0.262403i | ||||
\(745\) | 16.6149 | 0.608722 | ||||||||
\(746\) | 0.569324 | + | 1.75220i | 0.0208444 | + | 0.0641525i | ||||
\(747\) | −2.82553 | + | 8.69609i | −0.103381 | + | 0.318173i | ||||
\(748\) | −2.91676 | + | 2.11915i | −0.106647 | + | 0.0774839i | ||||
\(749\) | −5.73064 | −0.209393 | ||||||||
\(750\) | −25.5551 | −0.933139 | ||||||||
\(751\) | 2.65512 | − | 1.92906i | 0.0968868 | − | 0.0703924i | −0.538287 | − | 0.842762i | \(-0.680928\pi\) |
0.635174 | + | 0.772369i | \(0.280928\pi\) | |||||||
\(752\) | 3.92705 | + | 2.85317i | 0.143205 | + | 0.104044i | ||||
\(753\) | 73.4245 | + | 53.3460i | 2.67574 | + | 1.94404i | ||||
\(754\) | −2.78151 | − | 8.56060i | −0.101297 | − | 0.311759i | ||||
\(755\) | −34.3276 | + | 24.9405i | −1.24931 | + | 0.907677i | ||||
\(756\) | −3.15111 | − | 9.69812i | −0.114605 | − | 0.352717i | ||||
\(757\) | 5.95885 | − | 18.3395i | 0.216578 | − | 0.666559i | −0.782460 | − | 0.622701i | \(-0.786035\pi\) |
0.999038 | − | 0.0438575i | \(-0.0139648\pi\) | |||||||
\(758\) | −14.5892 | − | 10.5997i | −0.529905 | − | 0.384999i | ||||
\(759\) | −4.06718 | + | 12.5175i | −0.147629 | + | 0.454356i | ||||
\(760\) | 5.28001 | − | 16.2502i | 0.191526 | − | 0.589456i | ||||
\(761\) | 26.8430 | + | 19.5026i | 0.973059 | + | 0.706969i | 0.956147 | − | 0.292888i | \(-0.0946164\pi\) |
0.0169123 | + | 0.999857i | \(0.494616\pi\) | |||||||
\(762\) | −14.4577 | + | 44.4962i | −0.523747 | + | 1.61193i | ||||
\(763\) | 3.67155 | + | 11.2999i | 0.132919 | + | 0.409083i | ||||
\(764\) | −12.8124 | + | 9.30874i | −0.463535 | + | 0.336778i | ||||
\(765\) | −17.5244 | − | 53.9345i | −0.633595 | − | 1.95001i | ||||
\(766\) | 8.15676 | + | 5.92623i | 0.294716 | + | 0.214124i | ||||
\(767\) | −21.1796 | − | 15.3879i | −0.764752 | − | 0.555625i | ||||
\(768\) | 2.68070 | − | 1.94764i | 0.0967313 | − | 0.0702794i | ||||
\(769\) | 32.5658 | 1.17435 | 0.587177 | − | 0.809458i | \(-0.300239\pi\) | ||||
0.587177 | + | 0.809458i | \(0.300239\pi\) | |||||||
\(770\) | 2.22821 | 0.0802991 | ||||||||
\(771\) | 29.7194 | − | 21.5924i | 1.07032 | − | 0.777632i | ||||
\(772\) | 0.953144 | − | 2.93347i | 0.0343044 | − | 0.105578i | ||||
\(773\) | −4.27905 | − | 13.1695i | −0.153907 | − | 0.473676i | 0.844142 | − | 0.536120i | \(-0.180110\pi\) |
−0.998048 | + | 0.0624441i | \(0.980110\pi\) | |||||||
\(774\) | −49.8321 | −1.79118 | ||||||||
\(775\) | −11.4228 | − | 2.67341i | −0.410320 | − | 0.0960319i | ||||
\(776\) | 2.99443 | 0.107494 | ||||||||
\(777\) | 2.89212 | + | 8.90103i | 0.103754 | + | 0.319323i | ||||
\(778\) | 3.60589 | − | 11.0978i | 0.129278 | − | 0.397875i | ||||
\(779\) | −11.3462 | + | 8.24353i | −0.406522 | + | 0.295355i | ||||
\(780\) | −20.8594 | −0.746886 | ||||||||
\(781\) | −11.0736 | −0.396243 | ||||||||
\(782\) | 6.33467 | − | 4.60241i | 0.226527 | − | 0.164582i | ||||
\(783\) | 50.8811 | + | 36.9673i | 1.81834 | + | 1.32110i | ||||
\(784\) | 5.35410 | + | 3.88998i | 0.191218 | + | 0.138928i | ||||
\(785\) | −5.24799 | − | 16.1517i | −0.187309 | − | 0.576478i | ||||
\(786\) | 6.38461 | − | 4.63869i | 0.227732 | − | 0.165457i | ||||
\(787\) | −14.3147 | − | 44.0562i | −0.510265 | − | 1.57043i | −0.791736 | − | 0.610864i | \(-0.790822\pi\) |
0.281471 | − | 0.959570i | \(-0.409178\pi\) | |||||||
\(788\) | 6.96742 | − | 21.4435i | 0.248204 | − | 0.763893i | ||||
\(789\) | −67.2032 | − | 48.8260i | −2.39250 | − | 1.73825i | ||||
\(790\) | 2.69027 | − | 8.27981i | 0.0957157 | − | 0.294583i | ||||
\(791\) | −2.59009 | + | 7.97147i | −0.0920929 | + | 0.283433i | ||||
\(792\) | −8.73028 | − | 6.34292i | −0.310217 | − | 0.225386i | ||||
\(793\) | −1.74472 | + | 5.36969i | −0.0619567 | + | 0.190683i | ||||
\(794\) | −6.51921 | − | 20.0641i | −0.231358 | − | 0.712048i | ||||
\(795\) | 24.5756 | − | 17.8552i | 0.871607 | − | 0.633259i | ||||
\(796\) | −2.80160 | − | 8.62242i | −0.0992999 | − | 0.305614i | ||||
\(797\) | 15.9326 | + | 11.5757i | 0.564362 | + | 0.410033i | 0.833053 | − | 0.553193i | \(-0.186591\pi\) |
−0.268691 | + | 0.963226i | \(0.586591\pi\) | |||||||
\(798\) | 10.6186 | + | 7.71487i | 0.375895 | + | 0.273103i | ||||
\(799\) | −10.4691 | + | 7.60627i | −0.370371 | + | 0.269091i | ||||
\(800\) | −2.10704 | −0.0744950 | ||||||||
\(801\) | 67.6289 | 2.38955 | ||||||||
\(802\) | 8.91676 | − | 6.47841i | 0.314862 | − | 0.228761i | ||||
\(803\) | 1.79657 | − | 5.52926i | 0.0633995 | − | 0.195124i | ||||
\(804\) | 9.63446 | + | 29.6518i | 0.339781 | + | 1.04574i | ||||
\(805\) | −4.83926 | −0.170561 | ||||||||
\(806\) | 12.8017 | + | 2.99614i | 0.450922 | + | 0.105534i | ||||
\(807\) | −87.3406 | −3.07453 | ||||||||
\(808\) | 5.47885 | + | 16.8622i | 0.192745 | + | 0.593209i | ||||
\(809\) | 13.3847 | − | 41.1940i | 0.470583 | − | 1.44830i | −0.381241 | − | 0.924476i | \(-0.624503\pi\) |
0.851823 | − | 0.523829i | \(-0.175497\pi\) | |||||||
\(810\) | 66.2836 | − | 48.1579i | 2.32897 | − | 1.69209i | ||||
\(811\) | −4.91283 | −0.172513 | −0.0862563 | − | 0.996273i | \(-0.527490\pi\) | ||||
−0.0862563 | + | 0.996273i | \(0.527490\pi\) | |||||||
\(812\) | 2.35582 | 0.0826732 | ||||||||
\(813\) | −70.9630 | + | 51.5576i | −2.48878 | + | 1.80821i | ||||
\(814\) | 5.00022 | + | 3.63287i | 0.175257 | + | 0.127332i | ||||
\(815\) | 6.13561 | + | 4.45778i | 0.214921 | + | 0.156149i | ||||
\(816\) | 2.72971 | + | 8.40118i | 0.0955590 | + | 0.294100i | ||||
\(817\) | 32.3820 | − | 23.5269i | 1.13290 | − | 0.823101i | ||||
\(818\) | 8.53299 | + | 26.2619i | 0.298349 | + | 0.918224i | ||||
\(819\) | 3.59860 | − | 11.0754i | 0.125745 | − | 0.387005i | ||||
\(820\) | 4.71942 | + | 3.42886i | 0.164809 | + | 0.119741i | ||||
\(821\) | 12.2400 | − | 37.6709i | 0.427179 | − | 1.31472i | −0.473713 | − | 0.880679i | \(-0.657087\pi\) |
0.900892 | − | 0.434043i | \(-0.142913\pi\) | |||||||
\(822\) | −13.1613 | + | 40.5064i | −0.459054 | + | 1.41282i | ||||
\(823\) | −40.8661 | − | 29.6910i | −1.42450 | − | 1.03496i | −0.991007 | − | 0.133807i | \(-0.957280\pi\) |
−0.433496 | − | 0.901156i | \(-0.642720\pi\) | |||||||
\(824\) | 0.170541 | − | 0.524870i | 0.00594106 | − | 0.0182847i | ||||
\(825\) | 2.91772 | + | 8.97982i | 0.101582 | + | 0.312637i | ||||
\(826\) | 5.54323 | − | 4.02739i | 0.192874 | − | 0.140131i | ||||
\(827\) | −0.456414 | − | 1.40470i | −0.0158711 | − | 0.0488461i | 0.942807 | − | 0.333338i | \(-0.108175\pi\) |
−0.958678 | + | 0.284492i | \(0.908175\pi\) | |||||||
\(828\) | 18.9606 | + | 13.7757i | 0.658925 | + | 0.478737i | ||||
\(829\) | −1.59481 | − | 1.15870i | −0.0553900 | − | 0.0402432i | 0.559746 | − | 0.828664i | \(-0.310899\pi\) |
−0.615136 | + | 0.788421i | \(0.710899\pi\) | |||||||
\(830\) | −2.47143 | + | 1.79560i | −0.0857845 | + | 0.0623261i | ||||
\(831\) | 83.7405 | 2.90493 | ||||||||
\(832\) | 2.36139 | 0.0818665 | ||||||||
\(833\) | −14.2735 | + | 10.3703i | −0.494548 | + | 0.359310i | ||||
\(834\) | 5.69399 | − | 17.5243i | 0.197167 | − | 0.606816i | ||||
\(835\) | −2.07789 | − | 6.39509i | −0.0719084 | − | 0.221311i | ||||
\(836\) | 8.66776 | 0.299781 | ||||||||
\(837\) | −84.6698 | + | 35.6397i | −2.92662 | + | 1.23189i | ||||
\(838\) | 4.27280 | 0.147601 | ||||||||
\(839\) | 13.1434 | + | 40.4512i | 0.453760 | + | 1.39653i | 0.872585 | + | 0.488463i | \(0.162442\pi\) |
−0.418824 | + | 0.908067i | \(0.637558\pi\) | |||||||
\(840\) | 1.68705 | − | 5.19222i | 0.0582089 | − | 0.179148i | ||||
\(841\) | 11.7066 | − | 8.50535i | 0.403676 | − | 0.293288i | ||||
\(842\) | 37.4467 | 1.29050 | ||||||||
\(843\) | 31.5433 | 1.08641 | ||||||||
\(844\) | −8.84231 | + | 6.42431i | −0.304365 | + | 0.221134i | ||||
\(845\) | 16.0114 | + | 11.6330i | 0.550810 | + | 0.400187i | ||||
\(846\) | −31.3356 | − | 22.7667i | −1.07734 | − | 0.782734i | ||||
\(847\) | −1.75152 | − | 5.39062i | −0.0601829 | − | 0.185224i | ||||
\(848\) | −2.78208 | + | 2.02130i | −0.0955371 | + | 0.0694118i | ||||
\(849\) | 32.9253 | + | 101.334i | 1.12999 | + | 3.47776i | ||||
\(850\) | 1.73580 | − | 5.34224i | 0.0595374 | − | 0.183237i | ||||
\(851\) | −10.8595 | − | 7.88992i | −0.372260 | − | 0.270463i | ||||
\(852\) | −8.38418 | + | 25.8038i | −0.287237 | + | 0.884025i | ||||
\(853\) | 7.88412 | − | 24.2648i | 0.269947 | − | 0.830812i | −0.720565 | − | 0.693387i | \(-0.756117\pi\) |
0.990512 | − | 0.137425i | \(-0.0438825\pi\) | |||||||
\(854\) | −1.19549 | − | 0.868572i | −0.0409087 | − | 0.0297219i | ||||
\(855\) | −42.1314 | + | 129.667i | −1.44086 | + | 4.43452i | ||||
\(856\) | 2.86532 | + | 8.81855i | 0.0979346 | + | 0.301412i | ||||
\(857\) | 5.73864 | − | 4.16936i | 0.196028 | − | 0.142423i | −0.485442 | − | 0.874269i | \(-0.661341\pi\) |
0.681470 | + | 0.731846i | \(0.261341\pi\) | |||||||
\(858\) | −3.26994 | − | 10.0638i | −0.111634 | − | 0.343573i | ||||
\(859\) | −31.9802 | − | 23.2350i | −1.09115 | − | 0.792767i | −0.111558 | − | 0.993758i | \(-0.535584\pi\) |
−0.979593 | + | 0.200990i | \(0.935584\pi\) | |||||||
\(860\) | −13.4691 | − | 9.78590i | −0.459294 | − | 0.333696i | ||||
\(861\) | −3.62532 | + | 2.63395i | −0.123551 | + | 0.0897648i | ||||
\(862\) | 2.58703 | 0.0881147 | ||||||||
\(863\) | −14.3669 | −0.489053 | −0.244527 | − | 0.969643i | \(-0.578633\pi\) | ||||
−0.244527 | + | 0.969643i | \(0.578633\pi\) | |||||||
\(864\) | −13.3483 | + | 9.69812i | −0.454119 | + | 0.329937i | ||||
\(865\) | −9.49465 | + | 29.2215i | −0.322828 | + | 0.993562i | ||||
\(866\) | −7.88546 | − | 24.2689i | −0.267959 | − | 0.824692i | ||||
\(867\) | 32.7805 | 1.11329 | ||||||||
\(868\) | −1.78115 | + | 2.94422i | −0.0604563 | + | 0.0999334i | ||||
\(869\) | 4.41641 | 0.149816 | ||||||||
\(870\) | 10.4051 | + | 32.0236i | 0.352766 | + | 1.08570i | ||||
\(871\) | −6.86603 | + | 21.1315i | −0.232646 | + | 0.716012i | ||||
\(872\) | 15.5529 | − | 11.2999i | 0.526689 | − | 0.382662i | ||||
\(873\) | −23.8938 | −0.808684 | ||||||||
\(874\) | −18.8248 | −0.636758 | ||||||||
\(875\) | 3.85618 | − | 2.80168i | 0.130363 | − | 0.0947140i | ||||
\(876\) | −11.5242 | − | 8.37279i | −0.389365 | − | 0.282890i | ||||
\(877\) | −34.0462 | − | 24.7360i | −1.14966 | − | 0.835275i | −0.161222 | − | 0.986918i | \(-0.551543\pi\) |
−0.988435 | + | 0.151643i | \(0.951543\pi\) | |||||||
\(878\) | 7.47700 | + | 23.0118i | 0.252336 | + | 0.776612i | ||||
\(879\) | −10.0417 | + | 7.29569i | −0.338697 | + | 0.246077i | ||||
\(880\) | −1.11410 | − | 3.42886i | −0.0375565 | − | 0.115587i | ||||
\(881\) | 8.66342 | − | 26.6633i | 0.291878 | − | 0.898309i | −0.692374 | − | 0.721539i | \(-0.743435\pi\) |
0.984252 | − | 0.176770i | \(-0.0565648\pi\) | |||||||
\(882\) | −42.7227 | − | 31.0398i | −1.43855 | − | 1.04517i | ||||
\(883\) | −7.15796 | + | 22.0299i | −0.240885 | + | 0.741366i | 0.755402 | + | 0.655262i | \(0.227442\pi\) |
−0.996286 | + | 0.0861043i | \(0.972558\pi\) | |||||||
\(884\) | −1.94534 | + | 5.98713i | −0.0654287 | + | 0.201369i | ||||
\(885\) | 79.2291 | + | 57.5633i | 2.66326 | + | 1.93497i | ||||
\(886\) | 5.43540 | − | 16.7284i | 0.182606 | − | 0.562003i | ||||
\(887\) | 14.7695 | + | 45.4558i | 0.495911 | + | 1.52626i | 0.815532 | + | 0.578712i | \(0.196445\pi\) |
−0.319620 | + | 0.947546i | \(0.603555\pi\) | |||||||
\(888\) | 12.2512 | − | 8.90103i | 0.411124 | − | 0.298699i | ||||
\(889\) | −2.69663 | − | 8.29938i | −0.0904422 | − | 0.278352i | ||||
\(890\) | 18.2794 | + | 13.2808i | 0.612728 | + | 0.445173i | ||||
\(891\) | 33.6249 | + | 24.4299i | 1.12648 | + | 0.818433i | ||||
\(892\) | 9.90369 | − | 7.19545i | 0.331600 | − | 0.240922i | ||||
\(893\) | 31.1112 | 1.04110 | ||||||||
\(894\) | 20.6511 | 0.690675 | ||||||||
\(895\) | 39.8545 | − | 28.9560i | 1.33219 | − | 0.967891i | ||||
\(896\) | −0.190983 | + | 0.587785i | −0.00638029 | + | 0.0196365i | ||||
\(897\) | 7.10170 | + | 21.8568i | 0.237119 | + | 0.729776i | ||||
\(898\) | −8.31696 | −0.277541 | ||||||||
\(899\) | −1.78606 | − | 21.1479i | −0.0595686 | − | 0.705323i | ||||
\(900\) | 16.8130 | 0.560432 | ||||||||
\(901\) | −2.83295 | − | 8.71893i | −0.0943793 | − | 0.290470i | ||||
\(902\) | −0.914468 | + | 2.81444i | −0.0304484 | + | 0.0937107i | ||||
\(903\) | 10.3466 | − | 7.51724i | 0.344313 | − | 0.250158i | ||||
\(904\) | 13.5619 | 0.451061 | ||||||||
\(905\) | −7.34436 | −0.244135 | ||||||||
\(906\) | −42.6667 | + | 30.9992i | −1.41751 | + | 1.02988i | ||||
\(907\) | −22.9987 | − | 16.7096i | −0.763660 | − | 0.554832i | 0.136371 | − | 0.990658i | \(-0.456456\pi\) |
−0.900031 | + | 0.435826i | \(0.856456\pi\) | |||||||
\(908\) | −6.43641 | − | 4.67632i | −0.213600 | − | 0.155189i | ||||
\(909\) | −43.7181 | − | 134.550i | −1.45004 | − | 4.46275i | ||||
\(910\) | 3.14762 | − | 2.28688i | 0.104343 | − | 0.0758093i | ||||
\(911\) | −11.4331 | − | 35.1876i | −0.378797 | − | 1.16582i | −0.940881 | − | 0.338737i | \(-0.890000\pi\) |
0.562084 | − | 0.827080i | \(-0.310000\pi\) | |||||||
\(912\) | 6.56266 | − | 20.1978i | 0.217311 | − | 0.668816i | ||||
\(913\) | −1.25373 | − | 0.910886i | −0.0414923 | − | 0.0301459i | ||||
\(914\) | −0.598959 | + | 1.84341i | −0.0198118 | + | 0.0609745i | ||||
\(915\) | 6.52667 | − | 20.0870i | 0.215765 | − | 0.664056i | ||||
\(916\) | 17.4576 | + | 12.6837i | 0.576814 | + | 0.419080i | ||||
\(917\) | −0.454864 | + | 1.39993i | −0.0150209 | + | 0.0462297i | ||||
\(918\) | −13.5924 | − | 41.8331i | −0.448615 | − | 1.38070i | ||||
\(919\) | −22.9803 | + | 16.6962i | −0.758052 | + | 0.550757i | −0.898312 | − | 0.439358i | \(-0.855206\pi\) |
0.140260 | + | 0.990115i | \(0.455206\pi\) | |||||||
\(920\) | 2.41963 | + | 7.44685i | 0.0797728 | + | 0.245515i | ||||
\(921\) | 50.7869 | + | 36.8988i | 1.67349 | + | 1.21586i | ||||
\(922\) | 6.23792 | + | 4.53212i | 0.205435 | + | 0.149257i | ||||
\(923\) | −15.6428 | + | 11.3651i | −0.514888 | + | 0.374088i | ||||
\(924\) | 2.76950 | 0.0911099 | ||||||||
\(925\) | −9.62951 | −0.316616 | ||||||||
\(926\) | 16.7051 | − | 12.1369i | 0.548963 | − | 0.398845i | ||||
\(927\) | −1.36082 | + | 4.18816i | −0.0446950 | + | 0.137557i | ||||
\(928\) | −1.17791 | − | 3.62524i | −0.0386668 | − | 0.119004i | ||||
\(929\) | 31.9767 | 1.04912 | 0.524561 | − | 0.851373i | \(-0.324230\pi\) | ||||
0.524561 | + | 0.851373i | \(0.324230\pi\) | |||||||
\(930\) | −47.8889 | − | 11.2080i | −1.57034 | − | 0.367525i | ||||
\(931\) | 42.4167 | 1.39015 | ||||||||
\(932\) | −1.59525 | − | 4.90966i | −0.0522540 | − | 0.160821i | ||||
\(933\) | −3.98570 | + | 12.2667i | −0.130486 | + | 0.401594i | ||||
\(934\) | 2.67641 | − | 1.94452i | 0.0875747 | − | 0.0636267i | ||||
\(935\) | 9.61143 | 0.314327 | ||||||||
\(936\) | −18.8425 | −0.615888 | ||||||||
\(937\) | 31.8893 | − | 23.1690i | 1.04178 | − | 0.756897i | 0.0711473 | − | 0.997466i | \(-0.477334\pi\) |
0.970632 | + | 0.240569i | \(0.0773340\pi\) | |||||||
\(938\) | −4.70463 | − | 3.41811i | −0.153612 | − | 0.111605i | ||||
\(939\) | −43.1125 | − | 31.3231i | −1.40692 | − | 1.02219i | ||||
\(940\) | −3.99885 | − | 12.3072i | −0.130428 | − | 0.401417i | ||||
\(941\) | −44.9074 | + | 32.6271i | −1.46394 | + | 1.06361i | −0.481625 | + | 0.876377i | \(0.659953\pi\) |
−0.982315 | + | 0.187237i | \(0.940047\pi\) | |||||||
\(942\) | −6.52287 | − | 20.0753i | −0.212527 | − | 0.654090i | ||||
\(943\) | 1.98606 | − | 6.11245i | 0.0646749 | − | 0.199049i | ||||
\(944\) | −8.96914 | − | 6.51646i | −0.291921 | − | 0.212093i | ||||
\(945\) | −8.40055 | + | 25.8542i | −0.273270 | + | 0.841039i | ||||
\(946\) | 2.60987 | − | 8.03236i | 0.0848543 | − | 0.261155i | ||||
\(947\) | 8.43755 | + | 6.13024i | 0.274184 | + | 0.199206i | 0.716377 | − | 0.697714i | \(-0.245799\pi\) |
−0.442193 | + | 0.896920i | \(0.645799\pi\) | |||||||
\(948\) | 3.34381 | − | 10.2912i | 0.108602 | − | 0.334243i | ||||
\(949\) | −3.13698 | − | 9.65464i | −0.101831 | − | 0.313403i | ||||
\(950\) | −10.9254 | + | 7.93778i | −0.354467 | + | 0.257535i | ||||
\(951\) | −35.2299 | − | 108.427i | −1.14241 | − | 3.51597i | ||||
\(952\) | −1.33295 | − | 0.968446i | −0.0432012 | − | 0.0313875i | ||||
\(953\) | 9.39998 | + | 6.82949i | 0.304495 | + | 0.221229i | 0.729531 | − | 0.683948i | \(-0.239738\pi\) |
−0.425036 | + | 0.905177i | \(0.639738\pi\) | |||||||
\(954\) | 22.1994 | − | 16.1288i | 0.718733 | − | 0.522190i | ||||
\(955\) | 42.2198 | 1.36620 | ||||||||
\(956\) | 6.37411 | 0.206153 | ||||||||
\(957\) | −13.8190 | + | 10.0401i | −0.446705 | + | 0.324550i | ||||
\(958\) | −2.89676 | + | 8.91531i | −0.0935900 | + | 0.288040i | ||||
\(959\) | −2.45483 | − | 7.55520i | −0.0792707 | − | 0.243970i | ||||
\(960\) | −8.83353 | −0.285101 | ||||||||
\(961\) | 27.7803 | + | 13.7570i | 0.896138 | + | 0.443775i | ||||
\(962\) | 10.7919 | 0.347946 | ||||||||
\(963\) | −22.8636 | − | 70.3669i | −0.736769 | − | 2.26754i | ||||
\(964\) | −8.61397 | + | 26.5111i | −0.277437 | + | 0.853864i | ||||
\(965\) | −6.65239 | + | 4.83325i | −0.214148 | + | 0.155588i | ||||
\(966\) | −6.01484 | −0.193524 | ||||||||
\(967\) | 20.5330 | 0.660297 | 0.330149 | − | 0.943929i | \(-0.392901\pi\) | ||||
0.330149 | + | 0.943929i | \(0.392901\pi\) | |||||||
\(968\) | −7.41955 | + | 5.39062i | −0.238473 | + | 0.173261i | ||||
\(969\) | 45.8036 | + | 33.2783i | 1.47142 | + | 1.06905i | ||||
\(970\) | −6.45827 | − | 4.69221i | −0.207363 | − | 0.150658i | ||||
\(971\) | 2.40953 | + | 7.41576i | 0.0773254 | + | 0.237983i | 0.982246 | − | 0.187597i | \(-0.0600700\pi\) |
−0.904921 | + | 0.425580i | \(0.860070\pi\) | |||||||
\(972\) | 42.3407 | − | 30.7623i | 1.35808 | − | 0.986702i | ||||
\(973\) | 1.06204 | + | 3.26861i | 0.0340473 | + | 0.104787i | ||||
\(974\) | −2.36965 | + | 7.29304i | −0.0759286 | + | 0.233684i | ||||
\(975\) | 13.3379 | + | 9.69055i | 0.427155 | + | 0.310346i | ||||
\(976\) | −0.738852 | + | 2.27395i | −0.0236501 | + | 0.0727874i | ||||
\(977\) | −6.49806 | + | 19.9990i | −0.207891 | + | 0.639824i | 0.791691 | + | 0.610922i | \(0.209201\pi\) |
−0.999582 | + | 0.0289022i | \(0.990799\pi\) | |||||||
\(978\) | 7.62611 | + | 5.54070i | 0.243856 | + | 0.177172i | ||||
\(979\) | −3.54195 | + | 10.9010i | −0.113201 | + | 0.348397i | ||||
\(980\) | −5.45200 | − | 16.7795i | −0.174158 | − | 0.536002i | ||||
\(981\) | −124.104 | + | 90.1665i | −3.96232 | + | 2.87880i | ||||
\(982\) | −4.88762 | − | 15.0425i | −0.155970 | − | 0.480027i | ||||
\(983\) | 23.0597 | + | 16.7538i | 0.735489 | + | 0.534364i | 0.891295 | − | 0.453424i | \(-0.149798\pi\) |
−0.155806 | + | 0.987788i | \(0.549798\pi\) | |||||||
\(984\) | 5.86589 | + | 4.26182i | 0.186998 | + | 0.135862i | ||||
\(985\) | −48.6286 | + | 35.3307i | −1.54943 | + | 1.12573i | ||||
\(986\) | 10.1619 | 0.323621 | ||||||||
\(987\) | 9.94056 | 0.316412 | ||||||||
\(988\) | 12.2443 | − | 8.89599i | 0.389542 | − | 0.283019i | ||||
\(989\) | −5.66816 | + | 17.4448i | −0.180237 | + | 0.554713i | ||||
\(990\) | 8.88991 | + | 27.3603i | 0.282540 | + | 0.869569i | ||||
\(991\) | −0.0388727 | −0.00123483 | −0.000617417 | − | 1.00000i | \(-0.500197\pi\) | ||||
−0.000617417 | 1.00000i | \(0.500197\pi\) | ||||||||
\(992\) | 5.42127 | + | 1.26880i | 0.172125 | + | 0.0402845i | ||||
\(993\) | −71.4662 | −2.26791 | ||||||||
\(994\) | −1.56381 | − | 4.81290i | −0.0496009 | − | 0.152656i | ||||
\(995\) | −7.46878 | + | 22.9865i | −0.236776 | + | 0.728722i | ||||
\(996\) | −3.07180 | + | 2.23180i | −0.0973338 | + | 0.0707172i | ||||
\(997\) | 61.6176 | 1.95145 | 0.975725 | − | 0.219001i | \(-0.0702798\pi\) | ||||
0.975725 | + | 0.219001i | \(0.0702798\pi\) | |||||||
\(998\) | 14.4797 | 0.458348 | ||||||||
\(999\) | −61.0040 | + | 44.3220i | −1.93008 | + | 1.40229i |
(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 | 62.2.d.b.35.1 | ✓ | 8 | |
3.2 | odd | 2 | 558.2.i.g.469.1 | 8 | |||
4.3 | odd | 2 | 496.2.n.d.97.2 | 8 | |||
31.8 | even | 5 | inner | 62.2.d.b.39.1 | yes | 8 | |
31.15 | odd | 10 | 1922.2.a.l.1.4 | 4 | |||
31.16 | even | 5 | 1922.2.a.i.1.1 | 4 | |||
93.8 | odd | 10 | 558.2.i.g.163.1 | 8 | |||
124.39 | odd | 10 | 496.2.n.d.225.2 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
62.2.d.b.35.1 | ✓ | 8 | 1.1 | even | 1 | trivial | |
62.2.d.b.39.1 | yes | 8 | 31.8 | even | 5 | inner | |
496.2.n.d.97.2 | 8 | 4.3 | odd | 2 | |||
496.2.n.d.225.2 | 8 | 124.39 | odd | 10 | |||
558.2.i.g.163.1 | 8 | 93.8 | odd | 10 | |||
558.2.i.g.469.1 | 8 | 3.2 | odd | 2 | |||
1922.2.a.i.1.1 | 4 | 31.16 | even | 5 | |||
1922.2.a.l.1.4 | 4 | 31.15 | odd | 10 |