Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [847,2,Mod(148,847)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(847, base_ring=CyclotomicField(10))
chi = DirichletCharacter(H, H._module([0, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("847.148");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 847 = 7 \cdot 11^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 847.f (of order \(5\), degree \(4\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(6.76332905120\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{5})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 3 x^{15} + 14 x^{14} - 32 x^{13} + 86 x^{12} - 145 x^{11} + 245 x^{10} - 245 x^{9} + 640 x^{8} - 1175 x^{7} + 2135 x^{6} - 2300 x^{5} + 1850 x^{4} - 925 x^{3} + 700 x^{2} + \cdots + 25 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 5 \) |
Twist minimal: | no (minimal twist has level 77) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{5}]$ |
Embedding invariants
Embedding label | 323.2 | ||
Root | \(0.435488 + 1.34029i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 847.323 |
Dual form | 847.2.f.v.729.2 |
$q$-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 \(\left(\mathbb{Z}/847\mathbb{Z}\right)^\times\).
\(n\) | \(122\) | \(365\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{5}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.14012 | − | 0.828347i | −0.806188 | − | 0.585730i | 0.106535 | − | 0.994309i | \(-0.466024\pi\) |
−0.912723 | + | 0.408579i | \(0.866024\pi\) | |||||||
\(3\) | −0.668522 | + | 2.05750i | −0.385971 | + | 1.18790i | 0.549802 | + | 0.835295i | \(0.314703\pi\) |
−0.935773 | + | 0.352602i | \(0.885297\pi\) | |||||||
\(4\) | −0.00431527 | − | 0.0132810i | −0.00215764 | − | 0.00664052i | ||||
\(5\) | 1.48162 | − | 1.07646i | 0.662602 | − | 0.481408i | −0.204939 | − | 0.978775i | \(-0.565700\pi\) |
0.867541 | + | 0.497366i | \(0.165700\pi\) | |||||||
\(6\) | 2.46652 | − | 1.79203i | 1.00695 | − | 0.731593i | ||||
\(7\) | −0.309017 | − | 0.951057i | −0.116797 | − | 0.359466i | ||||
\(8\) | −0.877057 | + | 2.69930i | −0.310086 | + | 0.954348i | ||||
\(9\) | −1.35932 | − | 0.987607i | −0.453108 | − | 0.329202i | ||||
\(10\) | −2.58091 | −0.816157 | ||||||||
\(11\) | 0 | 0 | ||||||||
\(12\) | 0.0302106 | 0.00872104 | ||||||||
\(13\) | −3.75955 | − | 2.73147i | −1.04271 | − | 0.757574i | −0.0718980 | − | 0.997412i | \(-0.522906\pi\) |
−0.970813 | + | 0.239838i | \(0.922906\pi\) | |||||||
\(14\) | −0.435488 | + | 1.34029i | −0.116389 | + | 0.358208i | ||||
\(15\) | 1.22432 | + | 3.76807i | 0.316118 | + | 0.972912i | ||||
\(16\) | 3.21332 | − | 2.33461i | 0.803329 | − | 0.583653i | ||||
\(17\) | −4.42550 | + | 3.21531i | −1.07334 | + | 0.779827i | −0.976510 | − | 0.215473i | \(-0.930871\pi\) |
−0.0968307 | + | 0.995301i | \(0.530871\pi\) | |||||||
\(18\) | 0.731714 | + | 2.25198i | 0.172467 | + | 0.530798i | ||||
\(19\) | 1.79266 | − | 5.51725i | 0.411265 | − | 1.26574i | −0.504285 | − | 0.863538i | \(-0.668244\pi\) |
0.915549 | − | 0.402206i | \(-0.131756\pi\) | |||||||
\(20\) | −0.0206901 | − | 0.0150323i | −0.00462646 | − | 0.00336132i | ||||
\(21\) | 2.16338 | 0.472088 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −0.719682 | −0.150064 | −0.0750321 | − | 0.997181i | \(-0.523906\pi\) | ||||
−0.0750321 | + | 0.997181i | \(0.523906\pi\) | |||||||
\(24\) | −4.96748 | − | 3.60908i | −1.01398 | − | 0.736701i | ||||
\(25\) | −0.508649 | + | 1.56546i | −0.101730 | + | 0.313092i | ||||
\(26\) | 2.02374 | + | 6.22842i | 0.396887 | + | 1.22149i | ||||
\(27\) | −2.30990 | + | 1.67824i | −0.444540 | + | 0.322977i | ||||
\(28\) | −0.0112975 | + | 0.00820814i | −0.00213503 | + | 0.00155119i | ||||
\(29\) | 0.362314 | + | 1.11509i | 0.0672801 | + | 0.207067i | 0.979044 | − | 0.203647i | \(-0.0652795\pi\) |
−0.911764 | + | 0.410714i | \(0.865280\pi\) | |||||||
\(30\) | 1.72540 | − | 5.31022i | 0.315013 | − | 0.969510i | ||||
\(31\) | 1.05809 | + | 0.768744i | 0.190038 | + | 0.138070i | 0.678736 | − | 0.734382i | \(-0.262528\pi\) |
−0.488698 | + | 0.872453i | \(0.662528\pi\) | |||||||
\(32\) | 0.0789938 | 0.0139643 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 7.70900 | 1.32208 | ||||||||
\(35\) | −1.48162 | − | 1.07646i | −0.250440 | − | 0.181955i | ||||
\(36\) | −0.00725060 | + | 0.0223150i | −0.00120843 | + | 0.00371917i | ||||
\(37\) | 0.647310 | + | 1.99221i | 0.106417 | + | 0.327518i | 0.990060 | − | 0.140643i | \(-0.0449168\pi\) |
−0.883643 | + | 0.468161i | \(0.844917\pi\) | |||||||
\(38\) | −6.61405 | + | 4.80539i | −1.07294 | + | 0.779536i | ||||
\(39\) | 8.13333 | − | 5.90921i | 1.30238 | − | 0.946231i | ||||
\(40\) | 1.60623 | + | 4.94347i | 0.253967 | + | 0.781631i | ||||
\(41\) | 0.283259 | − | 0.871781i | 0.0442376 | − | 0.136149i | −0.926498 | − | 0.376299i | \(-0.877197\pi\) |
0.970736 | + | 0.240150i | \(0.0771965\pi\) | |||||||
\(42\) | −2.46652 | − | 1.79203i | −0.380592 | − | 0.276516i | ||||
\(43\) | −8.02379 | −1.22362 | −0.611808 | − | 0.791006i | \(-0.709558\pi\) | ||||
−0.611808 | + | 0.791006i | \(0.709558\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −3.07713 | −0.458711 | ||||||||
\(46\) | 0.820525 | + | 0.596147i | 0.120980 | + | 0.0878970i | ||||
\(47\) | 1.84663 | − | 5.68336i | 0.269359 | − | 0.829003i | −0.721298 | − | 0.692625i | \(-0.756454\pi\) |
0.990657 | − | 0.136378i | \(-0.0435460\pi\) | |||||||
\(48\) | 2.65528 | + | 8.17213i | 0.383257 | + | 1.17954i | ||||
\(49\) | −0.809017 | + | 0.587785i | −0.115574 | + | 0.0839693i | ||||
\(50\) | 1.87667 | − | 1.36348i | 0.265401 | − | 0.192825i | ||||
\(51\) | −3.65696 | − | 11.2550i | −0.512076 | − | 1.57601i | ||||
\(52\) | −0.0200533 | + | 0.0617178i | −0.00278089 | + | 0.00855871i | ||||
\(53\) | −8.20742 | − | 5.96304i | −1.12738 | − | 0.819087i | −0.142065 | − | 0.989857i | \(-0.545374\pi\) |
−0.985311 | + | 0.170771i | \(0.945374\pi\) | |||||||
\(54\) | 4.02373 | 0.547560 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 2.83822 | 0.379272 | ||||||||
\(57\) | 10.1533 | + | 7.37680i | 1.34484 | + | 0.977080i | ||||
\(58\) | 0.510598 | − | 1.57146i | 0.0670448 | − | 0.206343i | ||||
\(59\) | −2.37350 | − | 7.30488i | −0.309003 | − | 0.951014i | −0.978153 | − | 0.207887i | \(-0.933341\pi\) |
0.669150 | − | 0.743128i | \(-0.266659\pi\) | |||||||
\(60\) | 0.0447607 | − | 0.0325205i | 0.00577858 | − | 0.00419838i | ||||
\(61\) | −5.07749 | + | 3.68901i | −0.650106 | + | 0.472330i | −0.863307 | − | 0.504679i | \(-0.831611\pi\) |
0.213201 | + | 0.977008i | \(0.431611\pi\) | |||||||
\(62\) | −0.569559 | − | 1.75292i | −0.0723341 | − | 0.222621i | ||||
\(63\) | −0.519216 | + | 1.59798i | −0.0654151 | + | 0.201327i | ||||
\(64\) | −6.51669 | − | 4.73465i | −0.814587 | − | 0.591832i | ||||
\(65\) | −8.51056 | −1.05560 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −15.4673 | −1.88963 | −0.944814 | − | 0.327608i | \(-0.893758\pi\) | ||||
−0.944814 | + | 0.327608i | \(0.893758\pi\) | |||||||
\(68\) | 0.0617999 | + | 0.0449003i | 0.00749434 | + | 0.00544496i | ||||
\(69\) | 0.481123 | − | 1.48075i | 0.0579204 | − | 0.178261i | ||||
\(70\) | 0.797546 | + | 2.45459i | 0.0953250 | + | 0.293380i | ||||
\(71\) | −11.2469 | + | 8.17134i | −1.33476 | + | 0.969759i | −0.335140 | + | 0.942168i | \(0.608784\pi\) |
−0.999619 | + | 0.0275910i | \(0.991216\pi\) | |||||||
\(72\) | 3.85806 | − | 2.80304i | 0.454676 | − | 0.330342i | ||||
\(73\) | −1.85862 | − | 5.72025i | −0.217535 | − | 0.669504i | −0.998964 | − | 0.0455099i | \(-0.985509\pi\) |
0.781429 | − | 0.623994i | \(-0.214491\pi\) | |||||||
\(74\) | 0.912233 | − | 2.80756i | 0.106045 | − | 0.326373i | ||||
\(75\) | −2.88089 | − | 2.09309i | −0.332657 | − | 0.241689i | ||||
\(76\) | −0.0810106 | −0.00929255 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −14.1679 | −1.60420 | ||||||||
\(79\) | −12.6538 | − | 9.19351i | −1.42366 | − | 1.03435i | −0.991153 | − | 0.132722i | \(-0.957628\pi\) |
−0.432509 | − | 0.901630i | \(-0.642372\pi\) | |||||||
\(80\) | 2.24780 | − | 6.91802i | 0.251312 | − | 0.773458i | ||||
\(81\) | −3.46640 | − | 10.6685i | −0.385156 | − | 1.18539i | ||||
\(82\) | −1.04509 | + | 0.759300i | −0.115411 | + | 0.0838507i | ||||
\(83\) | −3.54004 | + | 2.57199i | −0.388570 | + | 0.282313i | −0.764869 | − | 0.644186i | \(-0.777196\pi\) |
0.376299 | + | 0.926498i | \(0.377196\pi\) | |||||||
\(84\) | −0.00933558 | − | 0.0287320i | −0.00101860 | − | 0.00313491i | ||||
\(85\) | −3.09576 | + | 9.52776i | −0.335782 | + | 1.03343i | ||||
\(86\) | 9.14810 | + | 6.64648i | 0.986465 | + | 0.716708i | ||||
\(87\) | −2.53651 | −0.271942 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 15.3437 | 1.62643 | 0.813215 | − | 0.581963i | \(-0.197715\pi\) | ||||
0.813215 | + | 0.581963i | \(0.197715\pi\) | |||||||
\(90\) | 3.50830 | + | 2.54893i | 0.369807 | + | 0.268681i | ||||
\(91\) | −1.43602 | + | 4.41961i | −0.150536 | + | 0.463301i | ||||
\(92\) | 0.00310563 | + | 0.00955813i | 0.000323784 | + | 0.000996504i | ||||
\(93\) | −2.28904 | + | 1.66309i | −0.237363 | + | 0.172454i | ||||
\(94\) | −6.81318 | + | 4.95006i | −0.702726 | + | 0.510560i | ||||
\(95\) | −3.28306 | − | 10.1042i | −0.336835 | − | 1.03667i | ||||
\(96\) | −0.0528090 | + | 0.162530i | −0.00538980 | + | 0.0165881i | ||||
\(97\) | −1.95073 | − | 1.41729i | −0.198067 | − | 0.143904i | 0.484331 | − | 0.874885i | \(-0.339063\pi\) |
−0.682398 | + | 0.730981i | \(0.739063\pi\) | |||||||
\(98\) | 1.40927 | 0.142358 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0.0229859 | 0.00229859 | ||||||||
\(101\) | 9.62396 | + | 6.99222i | 0.957620 | + | 0.695752i | 0.952597 | − | 0.304236i | \(-0.0984011\pi\) |
0.00502316 | + | 0.999987i | \(0.498401\pi\) | |||||||
\(102\) | −5.15363 | + | 15.8612i | −0.510285 | + | 1.57050i | ||||
\(103\) | 0.122468 | + | 0.376917i | 0.0120671 | + | 0.0371387i | 0.956909 | − | 0.290389i | \(-0.0937846\pi\) |
−0.944842 | + | 0.327527i | \(0.893785\pi\) | |||||||
\(104\) | 10.6704 | − | 7.75250i | 1.04632 | − | 0.760195i | ||||
\(105\) | 3.20531 | − | 2.32880i | 0.312807 | − | 0.227267i | ||||
\(106\) | 4.41799 | + | 13.5972i | 0.429113 | + | 1.32068i | ||||
\(107\) | 1.01029 | − | 3.10934i | 0.0976680 | − | 0.300591i | −0.890272 | − | 0.455430i | \(-0.849486\pi\) |
0.987940 | + | 0.154838i | \(0.0494857\pi\) | |||||||
\(108\) | 0.0322566 | + | 0.0234358i | 0.00310389 | + | 0.00225511i | ||||
\(109\) | 2.84638 | 0.272634 | 0.136317 | − | 0.990665i | \(-0.456473\pi\) | ||||
0.136317 | + | 0.990665i | \(0.456473\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −4.53172 | −0.430132 | ||||||||
\(112\) | −3.21332 | − | 2.33461i | −0.303630 | − | 0.220600i | ||||
\(113\) | 4.49451 | − | 13.8327i | 0.422807 | − | 1.30127i | −0.482271 | − | 0.876022i | \(-0.660188\pi\) |
0.905078 | − | 0.425245i | \(-0.139812\pi\) | |||||||
\(114\) | −5.46544 | − | 16.8209i | −0.511885 | − | 1.57542i | ||||
\(115\) | −1.06630 | + | 0.774711i | −0.0994328 | + | 0.0722421i | ||||
\(116\) | 0.0132461 | − | 0.00962382i | 0.00122987 | − | 0.000893550i | ||||
\(117\) | 2.41283 | + | 7.42591i | 0.223066 | + | 0.686526i | ||||
\(118\) | −3.34490 | + | 10.2945i | −0.307923 | + | 0.947688i | ||||
\(119\) | 4.42550 | + | 3.21531i | 0.405685 | + | 0.294747i | ||||
\(120\) | −11.2450 | −1.02652 | ||||||||
\(121\) | 0 | 0 | ||||||||
\(122\) | 8.84474 | 0.800765 | ||||||||
\(123\) | 1.60432 | + | 1.16561i | 0.144657 | + | 0.105099i | ||||
\(124\) | 0.00564379 | − | 0.0173698i | 0.000506828 | − | 0.00155986i | ||||
\(125\) | 3.76118 | + | 11.5757i | 0.336410 | + | 1.03536i | ||||
\(126\) | 1.91565 | − | 1.39180i | 0.170660 | − | 0.123992i | ||||
\(127\) | 4.07168 | − | 2.95825i | 0.361303 | − | 0.262502i | −0.392292 | − | 0.919841i | \(-0.628318\pi\) |
0.753595 | + | 0.657339i | \(0.228318\pi\) | |||||||
\(128\) | 3.45907 | + | 10.6459i | 0.305741 | + | 0.940974i | ||||
\(129\) | 5.36408 | − | 16.5089i | 0.472281 | − | 1.45353i | ||||
\(130\) | 9.70307 | + | 7.04969i | 0.851015 | + | 0.618299i | ||||
\(131\) | 0.180053 | 0.0157313 | 0.00786565 | − | 0.999969i | \(-0.497496\pi\) | ||||
0.00786565 | + | 0.999969i | \(0.497496\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −5.80118 | −0.503026 | ||||||||
\(134\) | 17.6346 | + | 12.8123i | 1.52339 | + | 1.10681i | ||||
\(135\) | −1.61584 | + | 4.97304i | −0.139069 | + | 0.428011i | ||||
\(136\) | −4.79769 | − | 14.7658i | −0.411398 | − | 1.26615i | ||||
\(137\) | −6.73422 | + | 4.89270i | −0.575343 | + | 0.418011i | −0.837042 | − | 0.547138i | \(-0.815717\pi\) |
0.261699 | + | 0.965150i | \(0.415717\pi\) | |||||||
\(138\) | −1.77511 | + | 1.28969i | −0.151107 | + | 0.109786i | ||||
\(139\) | 2.15113 | + | 6.62049i | 0.182456 | + | 0.561543i | 0.999895 | − | 0.0144726i | \(-0.00460693\pi\) |
−0.817439 | + | 0.576015i | \(0.804607\pi\) | |||||||
\(140\) | −0.00790293 | + | 0.0243227i | −0.000667920 | + | 0.00205565i | ||||
\(141\) | 10.4590 | + | 7.59889i | 0.880805 | + | 0.639942i | ||||
\(142\) | 19.5915 | 1.64408 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | −6.67362 | −0.556135 | ||||||||
\(145\) | 1.73716 | + | 1.26212i | 0.144264 | + | 0.104814i | ||||
\(146\) | −2.61929 | + | 8.06136i | −0.216774 | + | 0.667163i | ||||
\(147\) | −0.668522 | − | 2.05750i | −0.0551387 | − | 0.169700i | ||||
\(148\) | 0.0236654 | − | 0.0171939i | 0.00194528 | − | 0.00141333i | ||||
\(149\) | −2.60043 | + | 1.88933i | −0.213036 | + | 0.154780i | −0.689186 | − | 0.724584i | \(-0.742032\pi\) |
0.476150 | + | 0.879364i | \(0.342032\pi\) | |||||||
\(150\) | 1.55076 | + | 4.77275i | 0.126619 | + | 0.389694i | ||||
\(151\) | −6.88088 | + | 21.1772i | −0.559958 | + | 1.72337i | 0.122517 | + | 0.992466i | \(0.460903\pi\) |
−0.682476 | + | 0.730908i | \(0.739097\pi\) | |||||||
\(152\) | 13.3205 | + | 9.67788i | 1.08043 | + | 0.784979i | ||||
\(153\) | 9.19115 | 0.743061 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 2.39521 | 0.192388 | ||||||||
\(156\) | −0.113578 | − | 0.0825193i | −0.00909352 | − | 0.00660683i | ||||
\(157\) | 4.09595 | − | 12.6060i | 0.326892 | − | 1.00607i | −0.643687 | − | 0.765289i | \(-0.722596\pi\) |
0.970579 | − | 0.240782i | \(-0.0774040\pi\) | |||||||
\(158\) | 6.81144 | + | 20.9634i | 0.541889 | + | 1.66776i | ||||
\(159\) | 17.7558 | − | 12.9003i | 1.40813 | − | 1.02306i | ||||
\(160\) | 0.117039 | − | 0.0850338i | 0.00925274 | − | 0.00672251i | ||||
\(161\) | 0.222394 | + | 0.684459i | 0.0175271 | + | 0.0539429i | ||||
\(162\) | −4.88509 | + | 15.0348i | −0.383809 | + | 1.18124i | ||||
\(163\) | −11.0984 | − | 8.06344i | −0.869292 | − | 0.631577i | 0.0611050 | − | 0.998131i | \(-0.480538\pi\) |
−0.930397 | + | 0.366554i | \(0.880538\pi\) | |||||||
\(164\) | −0.0128005 | −0.000999552 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 6.16657 | 0.478619 | ||||||||
\(167\) | 7.53081 | + | 5.47146i | 0.582752 | + | 0.423394i | 0.839715 | − | 0.543027i | \(-0.182722\pi\) |
−0.256963 | + | 0.966421i | \(0.582722\pi\) | |||||||
\(168\) | −1.89741 | + | 5.83962i | −0.146388 | + | 0.450537i | ||||
\(169\) | 2.65604 | + | 8.17446i | 0.204311 | + | 0.628804i | ||||
\(170\) | 11.4218 | − | 8.29844i | 0.876014 | − | 0.636461i | ||||
\(171\) | −7.88568 | + | 5.72928i | −0.603033 | + | 0.438129i | ||||
\(172\) | 0.0346248 | + | 0.106564i | 0.00264012 | + | 0.00812545i | ||||
\(173\) | −3.24643 | + | 9.99149i | −0.246822 | + | 0.759639i | 0.748510 | + | 0.663124i | \(0.230770\pi\) |
−0.995331 | + | 0.0965154i | \(0.969230\pi\) | |||||||
\(174\) | 2.89193 | + | 2.10111i | 0.219236 | + | 0.159285i | ||||
\(175\) | 1.64602 | 0.124428 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 16.6165 | 1.24897 | ||||||||
\(178\) | −17.4937 | − | 12.7099i | −1.31121 | − | 0.952648i | ||||
\(179\) | −2.57204 | + | 7.91594i | −0.192244 | + | 0.591665i | 0.807754 | + | 0.589520i | \(0.200683\pi\) |
−0.999998 | + | 0.00214538i | \(0.999317\pi\) | |||||||
\(180\) | 0.0132786 | + | 0.0408675i | 0.000989732 | + | 0.00304608i | ||||
\(181\) | 11.9758 | − | 8.70096i | 0.890158 | − | 0.646738i | −0.0457613 | − | 0.998952i | \(-0.514571\pi\) |
0.935919 | + | 0.352215i | \(0.114571\pi\) | |||||||
\(182\) | 5.29821 | − | 3.84937i | 0.392729 | − | 0.285335i | ||||
\(183\) | −4.19572 | − | 12.9131i | −0.310157 | − | 0.954565i | ||||
\(184\) | 0.631202 | − | 1.94264i | 0.0465329 | − | 0.143213i | ||||
\(185\) | 3.10361 | + | 2.25491i | 0.228182 | + | 0.165784i | ||||
\(186\) | 3.98740 | 0.292370 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | −0.0834496 | −0.00608619 | ||||||||
\(189\) | 2.30990 | + | 1.67824i | 0.168020 | + | 0.122074i | ||||
\(190\) | −4.62671 | + | 14.2395i | −0.335657 | + | 1.03304i | ||||
\(191\) | −2.96865 | − | 9.13657i | −0.214804 | − | 0.661099i | −0.999167 | − | 0.0407974i | \(-0.987010\pi\) |
0.784363 | − | 0.620302i | \(-0.212990\pi\) | |||||||
\(192\) | 14.0981 | − | 10.2429i | 1.01744 | − | 0.739215i | ||||
\(193\) | −1.20366 | + | 0.874512i | −0.0866415 | + | 0.0629487i | −0.630263 | − | 0.776382i | \(-0.717053\pi\) |
0.543621 | + | 0.839331i | \(0.317053\pi\) | |||||||
\(194\) | 1.05007 | + | 3.23177i | 0.0753903 | + | 0.232027i | ||||
\(195\) | 5.68949 | − | 17.5104i | 0.407433 | − | 1.25395i | ||||
\(196\) | 0.0112975 | + | 0.00820814i | 0.000806966 | + | 0.000586295i | ||||
\(197\) | 14.0434 | 1.00055 | 0.500274 | − | 0.865867i | \(-0.333233\pi\) | ||||
0.500274 | + | 0.865867i | \(0.333233\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −4.28729 | −0.303918 | −0.151959 | − | 0.988387i | \(-0.548558\pi\) | ||||
−0.151959 | + | 0.988387i | \(0.548558\pi\) | |||||||
\(200\) | −3.77954 | − | 2.74600i | −0.267254 | − | 0.194171i | ||||
\(201\) | 10.3402 | − | 31.8239i | 0.729342 | − | 2.24468i | ||||
\(202\) | −5.18050 | − | 15.9440i | −0.364499 | − | 1.12181i | ||||
\(203\) | 0.948551 | − | 0.689163i | 0.0665753 | − | 0.0483698i | ||||
\(204\) | −0.133697 | + | 0.0971364i | −0.00936064 | + | 0.00680091i | ||||
\(205\) | −0.518757 | − | 1.59657i | −0.0362315 | − | 0.111509i | ||||
\(206\) | 0.172590 | − | 0.531177i | 0.0120249 | − | 0.0370088i | ||||
\(207\) | 0.978282 | + | 0.710764i | 0.0679953 | + | 0.0494015i | ||||
\(208\) | −18.4575 | −1.27980 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | −5.58350 | −0.385298 | ||||||||
\(211\) | −1.17734 | − | 0.855387i | −0.0810514 | − | 0.0588873i | 0.546522 | − | 0.837445i | \(-0.315952\pi\) |
−0.627573 | + | 0.778558i | \(0.715952\pi\) | |||||||
\(212\) | −0.0437781 | + | 0.134735i | −0.00300670 | + | 0.00925366i | ||||
\(213\) | −9.29373 | − | 28.6031i | −0.636796 | − | 1.95986i | ||||
\(214\) | −3.72746 | + | 2.70816i | −0.254804 | + | 0.185126i | ||||
\(215\) | −11.8882 | + | 8.63730i | −0.810771 | + | 0.589059i | ||||
\(216\) | −2.50416 | − | 7.70703i | −0.170387 | − | 0.524397i | ||||
\(217\) | 0.404153 | − | 1.24385i | 0.0274357 | − | 0.0844383i | ||||
\(218\) | −3.24522 | − | 2.35779i | −0.219794 | − | 0.159690i | ||||
\(219\) | 13.0119 | 0.879264 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 25.4204 | 1.70996 | ||||||||
\(222\) | 5.16671 | + | 3.75383i | 0.346767 | + | 0.251941i | ||||
\(223\) | −1.50072 | + | 4.61873i | −0.100495 | + | 0.309293i | −0.988647 | − | 0.150258i | \(-0.951990\pi\) |
0.888151 | + | 0.459551i | \(0.151990\pi\) | |||||||
\(224\) | −0.0244104 | − | 0.0751275i | −0.00163099 | − | 0.00501967i | ||||
\(225\) | 2.23748 | − | 1.62563i | 0.149165 | − | 0.108375i | ||||
\(226\) | −16.5825 | + | 12.0479i | −1.10305 | + | 0.801415i | ||||
\(227\) | −0.122724 | − | 0.377706i | −0.00814549 | − | 0.0250692i | 0.946901 | − | 0.321525i | \(-0.104195\pi\) |
−0.955047 | + | 0.296456i | \(0.904195\pi\) | |||||||
\(228\) | 0.0541573 | − | 0.166679i | 0.00358666 | − | 0.0110386i | ||||
\(229\) | −1.77145 | − | 1.28703i | −0.117061 | − | 0.0850496i | 0.527715 | − | 0.849422i | \(-0.323049\pi\) |
−0.644775 | + | 0.764372i | \(0.723049\pi\) | |||||||
\(230\) | 1.85744 | 0.122476 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −3.32773 | −0.218476 | ||||||||
\(233\) | −1.01949 | − | 0.740701i | −0.0667888 | − | 0.0485249i | 0.553890 | − | 0.832590i | \(-0.313143\pi\) |
−0.620679 | + | 0.784065i | \(0.713143\pi\) | |||||||
\(234\) | 3.40032 | − | 10.4651i | 0.222286 | − | 0.684125i | ||||
\(235\) | −3.38190 | − | 10.4084i | −0.220611 | − | 0.678971i | ||||
\(236\) | −0.0867741 | + | 0.0630451i | −0.00564851 | + | 0.00410389i | ||||
\(237\) | 27.3750 | − | 19.8891i | 1.77820 | − | 1.29193i | ||||
\(238\) | −2.38221 | − | 7.33169i | −0.154416 | − | 0.475243i | ||||
\(239\) | 3.44914 | − | 10.6154i | 0.223106 | − | 0.686651i | −0.775372 | − | 0.631505i | \(-0.782438\pi\) |
0.998478 | − | 0.0551459i | \(-0.0175624\pi\) | |||||||
\(240\) | 12.7311 | + | 9.24969i | 0.821790 | + | 0.597065i | ||||
\(241\) | 21.4843 | 1.38392 | 0.691962 | − | 0.721934i | \(-0.256746\pi\) | ||||
0.691962 | + | 0.721934i | \(0.256746\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 15.7022 | 1.00730 | ||||||||
\(244\) | 0.0709047 | + | 0.0515153i | 0.00453921 | + | 0.00329793i | ||||
\(245\) | −0.565930 | + | 1.74175i | −0.0361559 | + | 0.111276i | ||||
\(246\) | −0.863595 | − | 2.65787i | −0.0550608 | − | 0.169460i | ||||
\(247\) | −21.8098 | + | 15.8457i | −1.38772 | + | 1.00824i | ||||
\(248\) | −3.00307 | + | 2.18186i | −0.190695 | + | 0.138548i | ||||
\(249\) | −2.92527 | − | 9.00305i | −0.185381 | − | 0.570545i | ||||
\(250\) | 5.30051 | − | 16.3133i | 0.335234 | − | 1.03174i | ||||
\(251\) | 0.342877 | + | 0.249115i | 0.0216422 | + | 0.0157240i | 0.598554 | − | 0.801083i | \(-0.295742\pi\) |
−0.576912 | + | 0.816807i | \(0.695742\pi\) | |||||||
\(252\) | 0.0234634 | 0.00147806 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | −7.09267 | −0.445033 | ||||||||
\(255\) | −17.5338 | − | 12.7390i | −1.09801 | − | 0.797748i | ||||
\(256\) | −0.103561 | + | 0.318729i | −0.00647259 | + | 0.0199206i | ||||
\(257\) | 5.38928 | + | 16.5865i | 0.336174 | + | 1.03464i | 0.966141 | + | 0.258015i | \(0.0830684\pi\) |
−0.629967 | + | 0.776622i | \(0.716932\pi\) | |||||||
\(258\) | −19.7908 | + | 14.3789i | −1.23212 | + | 0.895189i | ||||
\(259\) | 1.69468 | − | 1.23126i | 0.105302 | − | 0.0765066i | ||||
\(260\) | 0.0367254 | + | 0.113029i | 0.00227761 | + | 0.00700976i | ||||
\(261\) | 0.608767 | − | 1.87359i | 0.0376817 | − | 0.115972i | ||||
\(262\) | −0.205282 | − | 0.149146i | −0.0126824 | − | 0.00921429i | ||||
\(263\) | −1.51519 | −0.0934307 | −0.0467153 | − | 0.998908i | \(-0.514875\pi\) | ||||
−0.0467153 | + | 0.998908i | \(0.514875\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −18.5793 | −1.14132 | ||||||||
\(266\) | 6.61405 | + | 4.80539i | 0.405533 | + | 0.294637i | ||||
\(267\) | −10.2576 | + | 31.5697i | −0.627755 | + | 1.93203i | ||||
\(268\) | 0.0667455 | + | 0.205421i | 0.00407713 | + | 0.0125481i | ||||
\(269\) | 1.64314 | − | 1.19381i | 0.100184 | − | 0.0727878i | −0.536566 | − | 0.843859i | \(-0.680279\pi\) |
0.636749 | + | 0.771071i | \(0.280279\pi\) | |||||||
\(270\) | 5.96165 | − | 4.33139i | 0.362814 | − | 0.263600i | ||||
\(271\) | −2.34990 | − | 7.23225i | −0.142746 | − | 0.439328i | 0.853968 | − | 0.520326i | \(-0.174189\pi\) |
−0.996714 | + | 0.0809976i | \(0.974189\pi\) | |||||||
\(272\) | −6.71402 | + | 20.6636i | −0.407097 | + | 1.25292i | ||||
\(273\) | −8.13333 | − | 5.90921i | −0.492252 | − | 0.357642i | ||||
\(274\) | 11.7307 | 0.708676 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −0.0217420 | −0.00130872 | ||||||||
\(277\) | 11.6715 | + | 8.47987i | 0.701274 | + | 0.509506i | 0.880347 | − | 0.474330i | \(-0.157310\pi\) |
−0.179073 | + | 0.983836i | \(0.557310\pi\) | |||||||
\(278\) | 3.03151 | − | 9.33004i | 0.181818 | − | 0.559579i | ||||
\(279\) | −0.679064 | − | 2.08995i | −0.0406545 | − | 0.125122i | ||||
\(280\) | 4.20516 | − | 3.05523i | 0.251307 | − | 0.182585i | ||||
\(281\) | 14.3598 | − | 10.4330i | 0.856632 | − | 0.622379i | −0.0703347 | − | 0.997523i | \(-0.522407\pi\) |
0.926967 | + | 0.375144i | \(0.122407\pi\) | |||||||
\(282\) | −5.62999 | − | 17.3273i | −0.335261 | − | 1.03183i | ||||
\(283\) | 9.62160 | − | 29.6122i | 0.571945 | − | 1.76026i | −0.0744107 | − | 0.997228i | \(-0.523708\pi\) |
0.646355 | − | 0.763037i | \(-0.276292\pi\) | |||||||
\(284\) | 0.157057 | + | 0.114109i | 0.00931963 | + | 0.00677111i | ||||
\(285\) | 22.9842 | 1.36147 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −0.916645 | −0.0541079 | ||||||||
\(288\) | −0.107378 | − | 0.0780148i | −0.00632732 | − | 0.00459707i | ||||
\(289\) | 3.99350 | − | 12.2907i | 0.234912 | − | 0.722984i | ||||
\(290\) | −0.935102 | − | 2.87795i | −0.0549111 | − | 0.168999i | ||||
\(291\) | 4.22018 | − | 3.06614i | 0.247391 | − | 0.179740i | ||||
\(292\) | −0.0679504 | + | 0.0493689i | −0.00397650 | + | 0.00288909i | ||||
\(293\) | 7.42577 | + | 22.8542i | 0.433818 | + | 1.33515i | 0.894293 | + | 0.447482i | \(0.147679\pi\) |
−0.460475 | + | 0.887673i | \(0.652321\pi\) | |||||||
\(294\) | −0.942126 | + | 2.89957i | −0.0549459 | + | 0.169106i | ||||
\(295\) | −11.3801 | − | 8.26809i | −0.662572 | − | 0.481387i | ||||
\(296\) | −5.94532 | −0.345565 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 4.52983 | 0.262406 | ||||||||
\(299\) | 2.70568 | + | 1.96579i | 0.156474 | + | 0.113685i | ||||
\(300\) | −0.0153666 | + | 0.0472935i | −0.000887190 | + | 0.00273049i | ||||
\(301\) | 2.47949 | + | 7.63108i | 0.142915 | + | 0.439848i | ||||
\(302\) | 25.3871 | − | 18.4448i | 1.46086 | − | 1.06138i | ||||
\(303\) | −20.8203 | + | 15.1268i | −1.19609 | + | 0.869014i | ||||
\(304\) | −7.12023 | − | 21.9138i | −0.408373 | − | 1.25684i | ||||
\(305\) | −3.55184 | + | 10.9315i | −0.203378 | + | 0.625933i | ||||
\(306\) | −10.4790 | − | 7.61346i | −0.599046 | − | 0.435233i | ||||
\(307\) | 5.46298 | 0.311789 | 0.155894 | − | 0.987774i | \(-0.450174\pi\) | ||||
0.155894 | + | 0.987774i | \(0.450174\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −0.857378 | −0.0487745 | ||||||||
\(310\) | −2.73083 | − | 1.98406i | −0.155101 | − | 0.112687i | ||||
\(311\) | 4.29176 | − | 13.2087i | 0.243364 | − | 0.748996i | −0.752538 | − | 0.658549i | \(-0.771170\pi\) |
0.995901 | − | 0.0904468i | \(-0.0288295\pi\) | |||||||
\(312\) | 8.81736 | + | 27.1371i | 0.499185 | + | 1.53633i | ||||
\(313\) | −22.2064 | + | 16.1339i | −1.25518 | + | 0.911940i | −0.998510 | − | 0.0545602i | \(-0.982624\pi\) |
−0.256667 | + | 0.966500i | \(0.582624\pi\) | |||||||
\(314\) | −15.1121 | + | 10.9796i | −0.852823 | + | 0.619612i | ||||
\(315\) | 0.950885 | + | 2.92652i | 0.0535763 | + | 0.164891i | ||||
\(316\) | −0.0674949 | + | 0.207728i | −0.00379689 | + | 0.0116856i | ||||
\(317\) | −6.33113 | − | 4.59983i | −0.355592 | − | 0.258352i | 0.395619 | − | 0.918415i | \(-0.370530\pi\) |
−0.751211 | + | 0.660062i | \(0.770530\pi\) | |||||||
\(318\) | −30.9297 | −1.73445 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | −14.7520 | −0.824659 | ||||||||
\(321\) | 5.72206 | + | 4.15732i | 0.319374 | + | 0.232039i | ||||
\(322\) | 0.313413 | − | 0.964586i | 0.0174658 | − | 0.0537543i | ||||
\(323\) | 9.80624 | + | 30.1805i | 0.545634 | + | 1.67929i | ||||
\(324\) | −0.126730 | + | 0.0920749i | −0.00704057 | + | 0.00511527i | ||||
\(325\) | 6.18831 | − | 4.49607i | 0.343265 | − | 0.249397i | ||||
\(326\) | 5.97417 | + | 18.3866i | 0.330879 | + | 1.01834i | ||||
\(327\) | −1.90287 | + | 5.85643i | −0.105229 | + | 0.323861i | ||||
\(328\) | 2.10477 | + | 1.52920i | 0.116216 | + | 0.0844361i | ||||
\(329\) | −5.97584 | −0.329458 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −28.1462 | −1.54705 | −0.773527 | − | 0.633764i | \(-0.781509\pi\) | ||||
−0.773527 | + | 0.633764i | \(0.781509\pi\) | |||||||
\(332\) | 0.0494349 | + | 0.0359166i | 0.00271309 | + | 0.00197118i | ||||
\(333\) | 1.08762 | − | 3.34736i | 0.0596013 | − | 0.183434i | ||||
\(334\) | −4.05378 | − | 12.4762i | −0.221813 | − | 0.682670i | ||||
\(335\) | −22.9167 | + | 16.6499i | −1.25207 | + | 0.909683i | ||||
\(336\) | 6.95163 | − | 5.05065i | 0.379242 | − | 0.275536i | ||||
\(337\) | 7.71892 | + | 23.7564i | 0.420476 | + | 1.29409i | 0.907260 | + | 0.420570i | \(0.138170\pi\) |
−0.486784 | + | 0.873523i | \(0.661830\pi\) | |||||||
\(338\) | 3.74308 | − | 11.5200i | 0.203596 | − | 0.626605i | ||||
\(339\) | 25.4560 | + | 18.4949i | 1.38258 | + | 1.00450i | ||||
\(340\) | 0.139898 | 0.00758701 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 13.7365 | 0.742783 | ||||||||
\(343\) | 0.809017 | + | 0.587785i | 0.0436828 | + | 0.0317374i | ||||
\(344\) | 7.03732 | − | 21.6586i | 0.379427 | − | 1.16776i | ||||
\(345\) | −0.881123 | − | 2.71182i | −0.0474380 | − | 0.145999i | ||||
\(346\) | 11.9778 | − | 8.70235i | 0.643928 | − | 0.467841i | ||||
\(347\) | 16.7056 | − | 12.1373i | 0.896802 | − | 0.651565i | −0.0408403 | − | 0.999166i | \(-0.513003\pi\) |
0.937643 | + | 0.347601i | \(0.113003\pi\) | |||||||
\(348\) | 0.0109457 | + | 0.0336875i | 0.000586752 | + | 0.00180584i | ||||
\(349\) | 1.85324 | − | 5.70369i | 0.0992017 | − | 0.305311i | −0.889124 | − | 0.457666i | \(-0.848686\pi\) |
0.988326 | + | 0.152355i | \(0.0486856\pi\) | |||||||
\(350\) | −1.87667 | − | 1.36348i | −0.100312 | − | 0.0728810i | ||||
\(351\) | 13.2682 | 0.708206 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 24.0382 | 1.27942 | 0.639712 | − | 0.768615i | \(-0.279054\pi\) | ||||
0.639712 | + | 0.768615i | \(0.279054\pi\) | |||||||
\(354\) | −18.9448 | − | 13.7642i | −1.00691 | − | 0.731561i | ||||
\(355\) | −7.86750 | + | 24.2137i | −0.417564 | + | 1.28513i | ||||
\(356\) | −0.0662123 | − | 0.203780i | −0.00350924 | − | 0.0108003i | ||||
\(357\) | −9.57403 | + | 6.95594i | −0.506712 | + | 0.368148i | ||||
\(358\) | 9.48958 | − | 6.89459i | 0.501540 | − | 0.364390i | ||||
\(359\) | 3.38377 | + | 10.4142i | 0.178589 | + | 0.549640i | 0.999779 | − | 0.0210147i | \(-0.00668966\pi\) |
−0.821190 | + | 0.570654i | \(0.806690\pi\) | |||||||
\(360\) | 2.69882 | − | 8.30610i | 0.142240 | − | 0.437770i | ||||
\(361\) | −11.8550 | − | 8.61319i | −0.623950 | − | 0.453326i | ||||
\(362\) | −20.8613 | −1.09645 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0.0648939 | 0.00340136 | ||||||||
\(365\) | −8.91140 | − | 6.47451i | −0.466444 | − | 0.338892i | ||||
\(366\) | −5.91290 | + | 18.1980i | −0.309072 | + | 0.951226i | ||||
\(367\) | 3.28107 | + | 10.0981i | 0.171270 | + | 0.527116i | 0.999444 | − | 0.0333563i | \(-0.0106196\pi\) |
−0.828173 | + | 0.560472i | \(0.810620\pi\) | |||||||
\(368\) | −2.31257 | + | 1.68018i | −0.120551 | + | 0.0875853i | ||||
\(369\) | −1.24602 | + | 0.905286i | −0.0648651 | + | 0.0471273i | ||||
\(370\) | −1.67065 | − | 5.14173i | −0.0868530 | − | 0.267306i | ||||
\(371\) | −3.13496 | + | 9.64840i | −0.162759 | + | 0.500920i | ||||
\(372\) | 0.0319654 | + | 0.0232242i | 0.00165733 | + | 0.00120412i | ||||
\(373\) | −36.6036 | −1.89526 | −0.947631 | − | 0.319367i | \(-0.896530\pi\) | ||||
−0.947631 | + | 0.319367i | \(0.896530\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −26.3315 | −1.35975 | ||||||||
\(376\) | 13.7215 | + | 9.96925i | 0.707632 | + | 0.514125i | ||||
\(377\) | 1.68370 | − | 5.18188i | 0.0867147 | − | 0.266880i | ||||
\(378\) | −1.24340 | − | 3.82679i | −0.0639536 | − | 0.196829i | ||||
\(379\) | 10.2404 | − | 7.44005i | 0.526012 | − | 0.382170i | −0.292852 | − | 0.956158i | \(-0.594604\pi\) |
0.818864 | + | 0.573988i | \(0.194604\pi\) | |||||||
\(380\) | −0.120027 | + | 0.0872048i | −0.00615726 | + | 0.00447351i | ||||
\(381\) | 3.36458 | + | 10.3551i | 0.172373 | + | 0.530509i | ||||
\(382\) | −4.18363 | + | 12.8759i | −0.214053 | + | 0.658787i | ||||
\(383\) | 12.5138 | + | 9.09179i | 0.639424 | + | 0.464569i | 0.859652 | − | 0.510879i | \(-0.170680\pi\) |
−0.220228 | + | 0.975448i | \(0.570680\pi\) | |||||||
\(384\) | −24.2164 | −1.23579 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 2.09672 | 0.106720 | ||||||||
\(387\) | 10.9069 | + | 7.92435i | 0.554431 | + | 0.402818i | ||||
\(388\) | −0.0104052 | + | 0.0320238i | −0.000528242 | + | 0.00162576i | ||||
\(389\) | −3.92852 | − | 12.0907i | −0.199184 | − | 0.613025i | −0.999902 | − | 0.0139838i | \(-0.995549\pi\) |
0.800718 | − | 0.599041i | \(-0.204451\pi\) | |||||||
\(390\) | −20.9914 | + | 15.2512i | −1.06294 | + | 0.772273i | ||||
\(391\) | 3.18495 | − | 2.31400i | 0.161070 | − | 0.117024i | ||||
\(392\) | −0.877057 | − | 2.69930i | −0.0442981 | − | 0.136335i | ||||
\(393\) | −0.120369 | + | 0.370459i | −0.00607183 | + | 0.0186872i | ||||
\(394\) | −16.0111 | − | 11.6328i | −0.806630 | − | 0.586051i | ||||
\(395\) | −28.6446 | −1.44127 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −18.9574 | −0.951445 | −0.475722 | − | 0.879596i | \(-0.657813\pi\) | ||||
−0.475722 | + | 0.879596i | \(0.657813\pi\) | |||||||
\(398\) | 4.88803 | + | 3.55136i | 0.245015 | + | 0.178014i | ||||
\(399\) | 3.87821 | − | 11.9359i | 0.194153 | − | 0.597543i | ||||
\(400\) | 2.02029 | + | 6.21782i | 0.101015 | + | 0.310891i | ||||
\(401\) | 7.02395 | − | 5.10320i | 0.350759 | − | 0.254842i | −0.398428 | − | 0.917200i | \(-0.630444\pi\) |
0.749188 | + | 0.662358i | \(0.230444\pi\) | |||||||
\(402\) | −38.1503 | + | 27.7178i | −1.90276 | + | 1.38244i | ||||
\(403\) | −1.87812 | − | 5.78026i | −0.0935558 | − | 0.287935i | ||||
\(404\) | 0.0513339 | − | 0.157990i | 0.00255396 | − | 0.00786027i | ||||
\(405\) | −16.6201 | − | 12.0752i | −0.825861 | − | 0.600023i | ||||
\(406\) | −1.65233 | −0.0820037 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 33.5879 | 1.66285 | ||||||||
\(409\) | 4.62277 | + | 3.35864i | 0.228581 | + | 0.166074i | 0.696181 | − | 0.717866i | \(-0.254881\pi\) |
−0.467600 | + | 0.883940i | \(0.654881\pi\) | |||||||
\(410\) | −0.731067 | + | 2.24999i | −0.0361048 | + | 0.111119i | ||||
\(411\) | −5.56474 | − | 17.1265i | −0.274489 | − | 0.844789i | ||||
\(412\) | 0.00447737 | − | 0.00325300i | 0.000220584 | − | 0.000160264i | ||||
\(413\) | −6.21390 | + | 4.51466i | −0.305766 | + | 0.222152i | ||||
\(414\) | −0.526602 | − | 1.62071i | −0.0258811 | − | 0.0796537i | ||||
\(415\) | −2.47635 | + | 7.62144i | −0.121559 | + | 0.374122i | ||||
\(416\) | −0.296981 | − | 0.215769i | −0.0145607 | − | 0.0105790i | ||||
\(417\) | −15.0597 | −0.737477 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −27.1909 | −1.32836 | −0.664181 | − | 0.747571i | \(-0.731220\pi\) | ||||
−0.664181 | + | 0.747571i | \(0.731220\pi\) | |||||||
\(420\) | −0.0447607 | − | 0.0325205i | −0.00218410 | − | 0.00158684i | ||||
\(421\) | −7.40561 | + | 22.7921i | −0.360928 | + | 1.11082i | 0.591565 | + | 0.806258i | \(0.298510\pi\) |
−0.952492 | + | 0.304563i | \(0.901490\pi\) | |||||||
\(422\) | 0.633753 | + | 1.95049i | 0.0308506 | + | 0.0949484i | ||||
\(423\) | −8.12310 | + | 5.90178i | −0.394959 | + | 0.286954i | ||||
\(424\) | 23.2944 | − | 16.9244i | 1.13128 | − | 0.821921i | ||||
\(425\) | −2.78242 | − | 8.56341i | −0.134967 | − | 0.415386i | ||||
\(426\) | −13.0973 | + | 40.3095i | −0.634569 | + | 1.95300i | ||||
\(427\) | 5.07749 | + | 3.68901i | 0.245717 | + | 0.178524i | ||||
\(428\) | −0.0456549 | −0.00220681 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 20.7087 | 0.998663 | ||||||||
\(431\) | 13.3271 | + | 9.68268i | 0.641942 | + | 0.466398i | 0.860517 | − | 0.509422i | \(-0.170141\pi\) |
−0.218575 | + | 0.975820i | \(0.570141\pi\) | |||||||
\(432\) | −3.50440 | + | 10.7854i | −0.168605 | + | 0.518914i | ||||
\(433\) | 6.20844 | + | 19.1076i | 0.298359 | + | 0.918253i | 0.982073 | + | 0.188503i | \(0.0603636\pi\) |
−0.683714 | + | 0.729750i | \(0.739636\pi\) | |||||||
\(434\) | −1.49113 | + | 1.08337i | −0.0715763 | + | 0.0520032i | ||||
\(435\) | −3.75815 | + | 2.73045i | −0.180189 | + | 0.130915i | ||||
\(436\) | −0.0122829 | − | 0.0378030i | −0.000588245 | − | 0.00181043i | ||||
\(437\) | −1.29015 | + | 3.97067i | −0.0617161 | + | 0.189943i | ||||
\(438\) | −14.8352 | − | 10.7784i | −0.708852 | − | 0.515011i | ||||
\(439\) | −26.7682 | −1.27758 | −0.638788 | − | 0.769383i | \(-0.720564\pi\) | ||||
−0.638788 | + | 0.769383i | \(0.720564\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 1.68022 | 0.0800104 | ||||||||
\(442\) | −28.9823 | − | 21.0569i | −1.37855 | − | 1.00157i | ||||
\(443\) | 8.10098 | − | 24.9323i | 0.384889 | − | 1.18457i | −0.551671 | − | 0.834062i | \(-0.686010\pi\) |
0.936561 | − | 0.350506i | \(-0.113990\pi\) | |||||||
\(444\) | 0.0195556 | + | 0.0601859i | 0.000928068 | + | 0.00285630i | ||||
\(445\) | 22.7336 | − | 16.5169i | 1.07768 | − | 0.782977i | ||||
\(446\) | 5.53691 | − | 4.02280i | 0.262180 | − | 0.190485i | ||||
\(447\) | −2.14884 | − | 6.61344i | −0.101637 | − | 0.312805i | ||||
\(448\) | −2.48916 | + | 7.66083i | −0.117602 | + | 0.361940i | ||||
\(449\) | −7.88582 | − | 5.72938i | −0.372155 | − | 0.270386i | 0.385949 | − | 0.922520i | \(-0.373874\pi\) |
−0.758104 | + | 0.652134i | \(0.773874\pi\) | |||||||
\(450\) | −3.89758 | −0.183734 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | −0.203107 | −0.00955336 | ||||||||
\(453\) | −38.9720 | − | 28.3148i | −1.83106 | − | 1.33035i | ||||
\(454\) | −0.172951 | + | 0.532289i | −0.00811700 | + | 0.0249816i | ||||
\(455\) | 2.62991 | + | 8.09402i | 0.123292 | + | 0.379453i | ||||
\(456\) | −28.8172 | + | 20.9369i | −1.34949 | + | 0.980462i | ||||
\(457\) | 9.61541 | − | 6.98601i | 0.449790 | − | 0.326792i | −0.339723 | − | 0.940526i | \(-0.610333\pi\) |
0.789513 | + | 0.613734i | \(0.210333\pi\) | |||||||
\(458\) | 0.953558 | + | 2.93475i | 0.0445568 | + | 0.137132i | ||||
\(459\) | 4.82638 | − | 14.8541i | 0.225276 | − | 0.693329i | ||||
\(460\) | 0.0148903 | + | 0.0108185i | 0.000694265 | + | 0.000504413i | ||||
\(461\) | −9.14737 | −0.426035 | −0.213018 | − | 0.977048i | \(-0.568329\pi\) | ||||
−0.213018 | + | 0.977048i | \(0.568329\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 38.9342 | 1.80943 | 0.904713 | − | 0.426021i | \(-0.140085\pi\) | ||||
0.904713 | + | 0.426021i | \(0.140085\pi\) | |||||||
\(464\) | 3.76753 | + | 2.73727i | 0.174903 | + | 0.127075i | ||||
\(465\) | −1.60125 | + | 4.92813i | −0.0742561 | + | 0.228537i | ||||
\(466\) | 0.548782 | + | 1.68898i | 0.0254218 | + | 0.0782404i | ||||
\(467\) | 16.8141 | − | 12.2162i | 0.778066 | − | 0.565298i | −0.126332 | − | 0.991988i | \(-0.540320\pi\) |
0.904398 | + | 0.426690i | \(0.140320\pi\) | |||||||
\(468\) | 0.0882119 | − | 0.0640897i | 0.00407760 | − | 0.00296255i | ||||
\(469\) | 4.77965 | + | 14.7102i | 0.220704 | + | 0.679256i | ||||
\(470\) | −4.76600 | + | 14.6683i | −0.219839 | + | 0.676596i | ||||
\(471\) | 23.1987 | + | 16.8548i | 1.06894 | + | 0.776629i | ||||
\(472\) | 21.7998 | 1.00342 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | −47.6858 | −2.19028 | ||||||||
\(475\) | 7.72520 | + | 5.61269i | 0.354457 | + | 0.257528i | ||||
\(476\) | 0.0236055 | − | 0.0726501i | 0.00108195 | − | 0.00332991i | ||||
\(477\) | 5.26741 | + | 16.2114i | 0.241178 | + | 0.742270i | ||||
\(478\) | −12.7256 | + | 9.24572i | −0.582057 | + | 0.422889i | ||||
\(479\) | −19.8503 | + | 14.4221i | −0.906983 | + | 0.658962i | −0.940250 | − | 0.340485i | \(-0.889409\pi\) |
0.0332672 | + | 0.999446i | \(0.489409\pi\) | |||||||
\(480\) | 0.0967138 | + | 0.297654i | 0.00441436 | + | 0.0135860i | ||||
\(481\) | 3.00809 | − | 9.25794i | 0.137157 | − | 0.422126i | ||||
\(482\) | −24.4947 | − | 17.7964i | −1.11570 | − | 0.810606i | ||||
\(483\) | −1.55695 | −0.0708436 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −4.41591 | −0.200516 | ||||||||
\(486\) | −17.9024 | − | 13.0069i | −0.812070 | − | 0.590003i | ||||
\(487\) | −3.82295 | + | 11.7658i | −0.173234 | + | 0.533160i | −0.999548 | − | 0.0300493i | \(-0.990434\pi\) |
0.826314 | + | 0.563209i | \(0.190434\pi\) | |||||||
\(488\) | −5.50452 | − | 16.9412i | −0.249178 | − | 0.766890i | ||||
\(489\) | 24.0100 | − | 17.4443i | 1.08577 | − | 0.788858i | ||||
\(490\) | 2.08800 | − | 1.51702i | 0.0943264 | − | 0.0685321i | ||||
\(491\) | −5.10653 | − | 15.7163i | −0.230454 | − | 0.709266i | −0.997692 | − | 0.0679027i | \(-0.978369\pi\) |
0.767238 | − | 0.641363i | \(-0.221631\pi\) | |||||||
\(492\) | 0.00855741 | − | 0.0263370i | 0.000385798 | − | 0.00118736i | ||||
\(493\) | −5.18878 | − | 3.76987i | −0.233691 | − | 0.169786i | ||||
\(494\) | 37.9916 | 1.70932 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 5.19468 | 0.233248 | ||||||||
\(497\) | 11.2469 | + | 8.17134i | 0.504492 | + | 0.366535i | ||||
\(498\) | −4.12249 | + | 12.6877i | −0.184733 | + | 0.568550i | ||||
\(499\) | −4.24619 | − | 13.0684i | −0.190085 | − | 0.585023i | 0.809913 | − | 0.586549i | \(-0.199514\pi\) |
−0.999999 | + | 0.00152665i | \(0.999514\pi\) | |||||||
\(500\) | 0.137507 | − | 0.0999048i | 0.00614951 | − | 0.00446788i | ||||
\(501\) | −16.2920 | + | 11.8368i | −0.727874 | + | 0.528831i | ||||
\(502\) | −0.184568 | − | 0.568043i | −0.00823769 | − | 0.0253530i | ||||
\(503\) | 6.98278 | − | 21.4908i | 0.311347 | − | 0.958227i | −0.665885 | − | 0.746054i | \(-0.731946\pi\) |
0.977232 | − | 0.212173i | \(-0.0680541\pi\) | |||||||
\(504\) | −3.85806 | − | 2.80304i | −0.171851 | − | 0.124857i | ||||
\(505\) | 21.7859 | 0.969461 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −18.5946 | −0.825813 | ||||||||
\(508\) | −0.0568590 | − | 0.0413105i | −0.00252271 | − | 0.00183286i | ||||
\(509\) | −6.63262 | + | 20.4131i | −0.293986 | + | 0.904795i | 0.689575 | + | 0.724215i | \(0.257798\pi\) |
−0.983560 | + | 0.180580i | \(0.942202\pi\) | |||||||
\(510\) | 9.43829 | + | 29.0481i | 0.417934 | + | 1.28627i | ||||
\(511\) | −4.86593 | + | 3.53531i | −0.215256 | + | 0.156393i | ||||
\(512\) | 18.4940 | − | 13.4367i | 0.817327 | − | 0.593823i | ||||
\(513\) | 5.11839 | + | 15.7528i | 0.225983 | + | 0.695503i | ||||
\(514\) | 7.59493 | − | 23.3748i | 0.334998 | − | 1.03102i | ||||
\(515\) | 0.587188 | + | 0.426617i | 0.0258746 | + | 0.0187990i | ||||
\(516\) | −0.242403 | −0.0106712 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | −2.95205 | −0.129706 | ||||||||
\(519\) | −18.3872 | − | 13.3591i | −0.807107 | − | 0.586398i | ||||
\(520\) | 7.46424 | − | 22.9726i | 0.327329 | − | 1.00741i | ||||
\(521\) | 10.7265 | + | 33.0127i | 0.469935 | + | 1.44631i | 0.852669 | + | 0.522452i | \(0.174983\pi\) |
−0.382734 | + | 0.923859i | \(0.625017\pi\) | |||||||
\(522\) | −2.24605 | + | 1.63185i | −0.0983071 | + | 0.0714243i | ||||
\(523\) | 15.9604 | − | 11.5959i | 0.697900 | − | 0.507054i | −0.181348 | − | 0.983419i | \(-0.558046\pi\) |
0.879247 | + | 0.476365i | \(0.158046\pi\) | |||||||
\(524\) | −0.000776978 | − | 0.00239129i | −3.39424e−5 | − | 0.000104464i | ||||
\(525\) | −1.10040 | + | 3.38669i | −0.0480255 | + | 0.147807i | ||||
\(526\) | 1.72750 | + | 1.25510i | 0.0753227 | + | 0.0547251i | ||||
\(527\) | −7.15430 | −0.311646 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −22.4821 | −0.977481 | ||||||||
\(530\) | 21.1826 | + | 15.3901i | 0.920115 | + | 0.668503i | ||||
\(531\) | −3.98800 | + | 12.2738i | −0.173064 | + | 0.532637i | ||||
\(532\) | 0.0250337 | + | 0.0770457i | 0.00108535 | + | 0.00334035i | ||||
\(533\) | −3.44617 | + | 2.50379i | −0.149270 | + | 0.108451i | ||||
\(534\) | 37.8455 | − | 27.4964i | 1.63774 | − | 1.18989i | ||||
\(535\) | −1.85022 | − | 5.69440i | −0.0799921 | − | 0.246190i | ||||
\(536\) | 13.5657 | − | 41.7508i | 0.585948 | − | 1.80336i | ||||
\(537\) | −14.5676 | − | 10.5839i | −0.628636 | − | 0.456731i | ||||
\(538\) | −2.86226 | −0.123401 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0.0730199 | 0.00314227 | ||||||||
\(541\) | −4.48958 | − | 3.26187i | −0.193022 | − | 0.140239i | 0.487077 | − | 0.873359i | \(-0.338063\pi\) |
−0.680099 | + | 0.733120i | \(0.738063\pi\) | |||||||
\(542\) | −3.31164 | + | 10.1922i | −0.142247 | + | 0.437792i | ||||
\(543\) | 9.89610 | + | 30.4571i | 0.424682 | + | 1.30704i | ||||
\(544\) | −0.349587 | + | 0.253990i | −0.0149884 | + | 0.0108897i | ||||
\(545\) | 4.21727 | − | 3.06402i | 0.180648 | − | 0.131248i | ||||
\(546\) | 4.37811 | + | 13.4744i | 0.187366 | + | 0.576653i | ||||
\(547\) | 2.61018 | − | 8.03330i | 0.111603 | − | 0.343479i | −0.879620 | − | 0.475677i | \(-0.842203\pi\) |
0.991223 | + | 0.132197i | \(0.0422033\pi\) | |||||||
\(548\) | 0.0940401 | + | 0.0683241i | 0.00401719 | + | 0.00291866i | ||||
\(549\) | 10.5453 | 0.450061 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 6.80173 | 0.289763 | ||||||||
\(552\) | 3.57501 | + | 2.59739i | 0.152162 | + | 0.110552i | ||||
\(553\) | −4.83332 | + | 14.8754i | −0.205534 | + | 0.632567i | ||||
\(554\) | −6.28270 | − | 19.3362i | −0.266926 | − | 0.821514i | ||||
\(555\) | −6.71430 | + | 4.87822i | −0.285006 | + | 0.207069i | ||||
\(556\) | 0.0786443 | − | 0.0571384i | 0.00333526 | − | 0.00242321i | ||||
\(557\) | 3.76491 | + | 11.5872i | 0.159524 | + | 0.490965i | 0.998591 | − | 0.0530632i | \(-0.0168985\pi\) |
−0.839067 | + | 0.544028i | \(0.816898\pi\) | |||||||
\(558\) | −0.956984 | + | 2.94529i | −0.0405123 | + | 0.124684i | ||||
\(559\) | 30.1658 | + | 21.9168i | 1.27588 | + | 0.926980i | ||||
\(560\) | −7.27404 | −0.307384 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −25.0140 | −1.05515 | ||||||||
\(563\) | −22.1295 | − | 16.0780i | −0.932646 | − | 0.677607i | 0.0139935 | − | 0.999902i | \(-0.495546\pi\) |
−0.946639 | + | 0.322295i | \(0.895546\pi\) | |||||||
\(564\) | 0.0557879 | − | 0.171697i | 0.00234909 | − | 0.00722977i | ||||
\(565\) | −8.23118 | − | 25.3330i | −0.346288 | − | 1.06577i | ||||
\(566\) | −35.4990 | + | 25.7915i | −1.49213 | + | 1.08410i | ||||
\(567\) | −9.07517 | + | 6.59349i | −0.381121 | + | 0.276901i | ||||
\(568\) | −12.1928 | − | 37.5255i | −0.511597 | − | 1.57453i | ||||
\(569\) | −2.20491 | + | 6.78602i | −0.0924346 | + | 0.284485i | −0.986577 | − | 0.163299i | \(-0.947786\pi\) |
0.894142 | + | 0.447784i | \(0.147786\pi\) | |||||||
\(570\) | −26.2048 | − | 19.0389i | −1.09760 | − | 0.797451i | ||||
\(571\) | −32.4839 | −1.35941 | −0.679705 | − | 0.733486i | \(-0.737892\pi\) | ||||
−0.679705 | + | 0.733486i | \(0.737892\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 20.7831 | 0.868226 | ||||||||
\(574\) | 1.04509 | + | 0.759300i | 0.0436211 | + | 0.0316926i | ||||
\(575\) | 0.366066 | − | 1.12664i | 0.0152660 | − | 0.0469839i | ||||
\(576\) | 4.18232 | + | 12.8719i | 0.174263 | + | 0.536328i | ||||
\(577\) | −28.1391 | + | 20.4443i | −1.17145 | + | 0.851107i | −0.991182 | − | 0.132511i | \(-0.957696\pi\) |
−0.180266 | + | 0.983618i | \(0.557696\pi\) | |||||||
\(578\) | −14.7341 | + | 10.7049i | −0.612856 | + | 0.445266i | ||||
\(579\) | −0.994632 | − | 3.06116i | −0.0413355 | − | 0.127218i | ||||
\(580\) | 0.00926598 | − | 0.0285178i | 0.000384749 | − | 0.00118414i | ||||
\(581\) | 3.54004 | + | 2.57199i | 0.146866 | + | 0.106704i | ||||
\(582\) | −7.35135 | −0.304723 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 17.0708 | 0.706395 | ||||||||
\(585\) | 11.5686 | + | 8.40509i | 0.478303 | + | 0.347508i | ||||
\(586\) | 10.4649 | − | 32.2076i | 0.432301 | − | 1.33049i | ||||
\(587\) | −4.47300 | − | 13.7665i | −0.184621 | − | 0.568204i | 0.815321 | − | 0.579009i | \(-0.196560\pi\) |
−0.999942 | + | 0.0108054i | \(0.996560\pi\) | |||||||
\(588\) | −0.0244409 | + | 0.0177573i | −0.00100792 | + | 0.000732300i | ||||
\(589\) | 6.13814 | − | 4.45962i | 0.252918 | − | 0.183755i | ||||
\(590\) | 6.12580 | + | 18.8533i | 0.252195 | + | 0.776177i | ||||
\(591\) | −9.38829 | + | 28.8942i | −0.386183 | + | 1.18855i | ||||
\(592\) | 6.73106 | + | 4.89040i | 0.276645 | + | 0.200994i | ||||
\(593\) | 15.0291 | 0.617169 | 0.308585 | − | 0.951197i | \(-0.400145\pi\) | ||||
0.308585 | + | 0.951197i | \(0.400145\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 10.0181 | 0.410701 | ||||||||
\(596\) | 0.0363138 | + | 0.0263835i | 0.00148747 | + | 0.00108071i | ||||
\(597\) | 2.86614 | − | 8.82108i | 0.117303 | − | 0.361023i | ||||
\(598\) | −1.45645 | − | 4.48248i | −0.0595586 | − | 0.183302i | ||||
\(599\) | −1.42424 | + | 1.03477i | −0.0581927 | + | 0.0422795i | −0.616501 | − | 0.787354i | \(-0.711451\pi\) |
0.558309 | + | 0.829633i | \(0.311451\pi\) | |||||||
\(600\) | 8.17659 | − | 5.94064i | 0.333808 | − | 0.242526i | ||||
\(601\) | −7.24227 | − | 22.2894i | −0.295418 | − | 0.909204i | −0.983081 | − | 0.183173i | \(-0.941363\pi\) |
0.687662 | − | 0.726031i | \(-0.258637\pi\) | |||||||
\(602\) | 3.49426 | − | 10.7542i | 0.142415 | − | 0.438310i | ||||
\(603\) | 21.0250 | + | 15.2756i | 0.856206 | + | 0.622070i | ||||
\(604\) | 0.310948 | 0.0126523 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 36.2679 | 1.47328 | ||||||||
\(607\) | −20.4508 | − | 14.8583i | −0.830070 | − | 0.603081i | 0.0895088 | − | 0.995986i | \(-0.471470\pi\) |
−0.919579 | + | 0.392905i | \(0.871470\pi\) | |||||||
\(608\) | 0.141609 | − | 0.435828i | 0.00574301 | − | 0.0176752i | ||||
\(609\) | 0.783824 | + | 2.41236i | 0.0317622 | + | 0.0977539i | ||||
\(610\) | 13.1046 | − | 9.52102i | 0.530588 | − | 0.385495i | ||||
\(611\) | −22.4664 | + | 16.3228i | −0.908895 | + | 0.660351i | ||||
\(612\) | −0.0396623 | − | 0.122068i | −0.00160325 | − | 0.00493431i | ||||
\(613\) | −0.358751 | + | 1.10412i | −0.0144898 | + | 0.0445951i | −0.958040 | − | 0.286635i | \(-0.907463\pi\) |
0.943550 | + | 0.331230i | \(0.107463\pi\) | |||||||
\(614\) | −6.22846 | − | 4.52524i | −0.251360 | − | 0.182624i | ||||
\(615\) | 3.63174 | 0.146446 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 12.9711 | 0.522197 | 0.261098 | − | 0.965312i | \(-0.415915\pi\) | ||||
0.261098 | + | 0.965312i | \(0.415915\pi\) | |||||||
\(618\) | 0.977515 | + | 0.710206i | 0.0393214 | + | 0.0285687i | ||||
\(619\) | 14.1505 | − | 43.5507i | 0.568756 | − | 1.75045i | −0.0877618 | − | 0.996141i | \(-0.527971\pi\) |
0.656518 | − | 0.754310i | \(-0.272029\pi\) | |||||||
\(620\) | −0.0103360 | − | 0.0318108i | −0.000415102 | − | 0.00127755i | ||||
\(621\) | 1.66239 | − | 1.20780i | 0.0667095 | − | 0.0484673i | ||||
\(622\) | −15.8345 | + | 11.5044i | −0.634906 | + | 0.461286i | ||||
\(623\) | −4.74147 | − | 14.5927i | −0.189963 | − | 0.584646i | ||||
\(624\) | 12.3393 | − | 37.9763i | 0.493966 | − | 1.52027i | ||||
\(625\) | 11.3752 | + | 8.26455i | 0.455007 | + | 0.330582i | ||||
\(626\) | 38.6824 | 1.54606 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −0.185097 | −0.00738615 | ||||||||
\(629\) | −9.27026 | − | 6.73524i | −0.369629 | − | 0.268551i | ||||
\(630\) | 1.34005 | − | 4.12425i | 0.0533889 | − | 0.164314i | ||||
\(631\) | −3.90000 | − | 12.0030i | −0.155257 | − | 0.477831i | 0.842930 | − | 0.538023i | \(-0.180829\pi\) |
−0.998187 | + | 0.0601922i | \(0.980829\pi\) | |||||||
\(632\) | 35.9142 | − | 26.0932i | 1.42859 | − | 1.03793i | ||||
\(633\) | 2.54703 | − | 1.85053i | 0.101236 | − | 0.0735519i | ||||
\(634\) | 3.40800 | + | 10.4887i | 0.135349 | + | 0.416561i | ||||
\(635\) | 2.84825 | − | 8.76602i | 0.113029 | − | 0.347869i | ||||
\(636\) | −0.247951 | − | 0.180147i | −0.00983189 | − | 0.00714329i | ||||
\(637\) | 4.64706 | 0.184123 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 23.3582 | 0.924038 | ||||||||
\(640\) | 16.5849 | + | 12.0497i | 0.655577 | + | 0.476305i | ||||
\(641\) | 8.63910 | − | 26.5884i | 0.341224 | − | 1.05018i | −0.622350 | − | 0.782739i | \(-0.713822\pi\) |
0.963574 | − | 0.267441i | \(-0.0861780\pi\) | |||||||
\(642\) | −3.08014 | − | 9.47970i | −0.121564 | − | 0.374134i | ||||
\(643\) | 40.2066 | − | 29.2118i | 1.58559 | − | 1.15200i | 0.675684 | − | 0.737191i | \(-0.263848\pi\) |
0.909908 | − | 0.414809i | \(-0.136152\pi\) | |||||||
\(644\) | 0.00813063 | − | 0.00590725i | 0.000320392 | − | 0.000232778i | ||||
\(645\) | −9.82370 | − | 30.2342i | −0.386808 | − | 1.19047i | ||||
\(646\) | 13.8196 | − | 42.5324i | 0.543726 | − | 1.67342i | ||||
\(647\) | 8.90460 | + | 6.46957i | 0.350076 | + | 0.254345i | 0.748901 | − | 0.662682i | \(-0.230582\pi\) |
−0.398825 | + | 0.917027i | \(0.630582\pi\) | |||||||
\(648\) | 31.8377 | 1.25070 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | −10.7797 | −0.422816 | ||||||||
\(651\) | 2.28904 | + | 1.66309i | 0.0897146 | + | 0.0651815i | ||||
\(652\) | −0.0591984 | + | 0.182194i | −0.00231839 | + | 0.00713526i | ||||
\(653\) | 8.94184 | + | 27.5202i | 0.349921 | + | 1.07695i | 0.958896 | + | 0.283757i | \(0.0915811\pi\) |
−0.608975 | + | 0.793190i | \(0.708419\pi\) | |||||||
\(654\) | 7.02066 | − | 5.10081i | 0.274529 | − | 0.199457i | ||||
\(655\) | 0.266771 | − | 0.193820i | 0.0104236 | − | 0.00757318i | ||||
\(656\) | −1.12507 | − | 3.46261i | −0.0439266 | − | 0.135192i | ||||
\(657\) | −3.12289 | + | 9.61126i | −0.121835 | + | 0.374971i | ||||
\(658\) | 6.81318 | + | 4.95006i | 0.265605 | + | 0.192974i | ||||
\(659\) | −10.8405 | −0.422288 | −0.211144 | − | 0.977455i | \(-0.567719\pi\) | ||||
−0.211144 | + | 0.977455i | \(0.567719\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 20.3444 | 0.791305 | 0.395652 | − | 0.918400i | \(-0.370519\pi\) | ||||
0.395652 | + | 0.918400i | \(0.370519\pi\) | |||||||
\(662\) | 32.0901 | + | 23.3148i | 1.24722 | + | 0.906155i | ||||
\(663\) | −16.9941 | + | 52.3024i | −0.659995 | + | 2.03126i | ||||
\(664\) | −3.83776 | − | 11.8114i | −0.148934 | − | 0.458372i | ||||
\(665\) | −8.59515 | + | 6.24474i | −0.333306 | + | 0.242161i | ||||
\(666\) | −4.01279 | + | 2.91546i | −0.155493 | + | 0.112972i | ||||
\(667\) | −0.260751 | − | 0.802510i | −0.0100963 | − | 0.0310733i | ||||
\(668\) | 0.0401691 | − | 0.123628i | 0.00155419 | − | 0.00478331i | ||||
\(669\) | −8.49977 | − | 6.17545i | −0.328620 | − | 0.238757i | ||||
\(670\) | 39.9197 | 1.54223 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0.170894 | 0.00659237 | ||||||||
\(673\) | −9.77196 | − | 7.09974i | −0.376681 | − | 0.273675i | 0.383295 | − | 0.923626i | \(-0.374789\pi\) |
−0.759976 | + | 0.649951i | \(0.774789\pi\) | |||||||
\(674\) | 10.8780 | − | 33.4791i | 0.419006 | − | 1.28957i | ||||
\(675\) | −1.45229 | − | 4.46969i | −0.0558987 | − | 0.172039i | ||||
\(676\) | 0.0971038 | − | 0.0705500i | 0.00373476 | − | 0.00271346i | ||||
\(677\) | 2.74766 | − | 1.99629i | 0.105601 | − | 0.0767238i | −0.533731 | − | 0.845654i | \(-0.679211\pi\) |
0.639333 | + | 0.768930i | \(0.279211\pi\) | |||||||
\(678\) | −13.7028 | − | 42.1728i | −0.526252 | − | 1.61964i | ||||
\(679\) | −0.745114 | + | 2.29323i | −0.0285949 | + | 0.0880059i | ||||
\(680\) | −23.0031 | − | 16.7128i | −0.882130 | − | 0.640905i | ||||
\(681\) | 0.859173 | 0.0329236 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −4.75643 | −0.182000 | −0.0909999 | − | 0.995851i | \(-0.529006\pi\) | ||||
−0.0909999 | + | 0.995851i | \(0.529006\pi\) | |||||||
\(684\) | 0.110120 | + | 0.0800067i | 0.00421053 | + | 0.00305913i | ||||
\(685\) | −4.71077 | + | 14.4983i | −0.179989 | + | 0.553950i | ||||
\(686\) | −0.435488 | − | 1.34029i | −0.0166270 | − | 0.0511726i | ||||
\(687\) | 3.83232 | − | 2.78434i | 0.146212 | − | 0.106229i | ||||
\(688\) | −25.7830 | + | 18.7324i | −0.982966 | + | 0.714167i | ||||
\(689\) | 14.5683 | + | 44.8367i | 0.555009 | + | 1.70814i | ||||
\(690\) | −1.24174 | + | 3.82168i | −0.0472721 | + | 0.145489i | ||||
\(691\) | −5.36692 | − | 3.89930i | −0.204167 | − | 0.148336i | 0.481003 | − | 0.876719i | \(-0.340272\pi\) |
−0.685171 | + | 0.728382i | \(0.740272\pi\) | |||||||
\(692\) | 0.146707 | 0.00557695 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −29.1003 | −1.10463 | ||||||||
\(695\) | 10.3139 | + | 7.49346i | 0.391227 | + | 0.284243i | ||||
\(696\) | 2.22466 | − | 6.84680i | 0.0843256 | − | 0.259527i | ||||
\(697\) | 1.54949 | + | 4.76883i | 0.0586910 | + | 0.180632i | ||||
\(698\) | −6.83755 | + | 4.96777i | −0.258805 | + | 0.188033i | ||||
\(699\) | 2.20554 | − | 1.60242i | 0.0834212 | − | 0.0606090i | ||||
\(700\) | −0.00710304 | − | 0.0218609i | −0.000268470 | − | 0.000826265i | ||||
\(701\) | −0.936330 | + | 2.88173i | −0.0353647 | + | 0.108841i | −0.967181 | − | 0.254090i | \(-0.918224\pi\) |
0.931816 | + | 0.362931i | \(0.118224\pi\) | |||||||
\(702\) | −15.1274 | − | 10.9907i | −0.570947 | − | 0.414817i | ||||
\(703\) | 12.1519 | 0.458319 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 23.6762 | 0.891697 | ||||||||
\(706\) | −27.4065 | − | 19.9120i | −1.03146 | − | 0.749396i | ||||
\(707\) | 3.67603 | − | 11.3136i | 0.138251 | − | 0.425493i | ||||
\(708\) | −0.0717048 | − | 0.220685i | −0.00269483 | − | 0.00829383i | ||||
\(709\) | 11.0488 | − | 8.02741i | 0.414946 | − | 0.301476i | −0.360655 | − | 0.932699i | \(-0.617447\pi\) |
0.775601 | + | 0.631223i | \(0.217447\pi\) | |||||||
\(710\) | 29.0272 | − | 21.0895i | 1.08937 | − | 0.791475i | ||||
\(711\) | 8.12103 | + | 24.9939i | 0.304562 | + | 0.937346i | ||||
\(712\) | −13.4573 | + | 41.4173i | −0.504334 | + | 1.55218i | ||||
\(713\) | −0.761485 | − | 0.553251i | −0.0285178 | − | 0.0207194i | ||||
\(714\) | 16.6775 | 0.624140 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0.116231 | 0.00434376 | ||||||||
\(717\) | 19.5353 | + | 14.1932i | 0.729558 | + | 0.530055i | ||||
\(718\) | 4.76864 | − | 14.6764i | 0.177964 | − | 0.547717i | ||||
\(719\) | −0.587222 | − | 1.80728i | −0.0218997 | − | 0.0674003i | 0.939509 | − | 0.342523i | \(-0.111281\pi\) |
−0.961409 | + | 0.275123i | \(0.911281\pi\) | |||||||
\(720\) | −9.88778 | + | 7.18390i | −0.368496 | + | 0.267728i | ||||
\(721\) | 0.320625 | − | 0.232947i | 0.0119407 | − | 0.00867541i | ||||
\(722\) | 6.38148 | + | 19.6402i | 0.237494 | + | 0.730932i | ||||
\(723\) | −14.3627 | + | 44.2039i | −0.534155 | + | 1.64396i | ||||
\(724\) | −0.167237 | − | 0.121505i | −0.00621531 | − | 0.00451569i | ||||
\(725\) | −1.92992 | −0.0716754 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −13.8211 | −0.512595 | −0.256298 | − | 0.966598i | \(-0.582503\pi\) | ||||
−0.256298 | + | 0.966598i | \(0.582503\pi\) | |||||||
\(728\) | −10.6704 | − | 7.75250i | −0.395472 | − | 0.287327i | ||||
\(729\) | −0.0980447 | + | 0.301750i | −0.00363128 | + | 0.0111759i | ||||
\(730\) | 4.79694 | + | 14.7635i | 0.177543 | + | 0.546420i | ||||
\(731\) | 35.5092 | − | 25.7990i | 1.31336 | − | 0.954210i | ||||
\(732\) | −0.153394 | + | 0.111447i | −0.00566960 | + | 0.00411921i | ||||
\(733\) | −14.9485 | − | 46.0068i | −0.552136 | − | 1.69930i | −0.703391 | − | 0.710804i | \(-0.748331\pi\) |
0.151255 | − | 0.988495i | \(-0.451669\pi\) | |||||||
\(734\) | 4.62390 | − | 14.2309i | 0.170671 | − | 0.525273i | ||||
\(735\) | −3.20531 | − | 2.32880i | −0.118230 | − | 0.0858990i | ||||
\(736\) | −0.0568504 | −0.00209553 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 2.17050 | 0.0798973 | ||||||||
\(739\) | 18.7757 | + | 13.6414i | 0.690677 | + | 0.501806i | 0.876883 | − | 0.480705i | \(-0.159619\pi\) |
−0.186206 | + | 0.982511i | \(0.559619\pi\) | |||||||
\(740\) | 0.0165546 | − | 0.0509497i | 0.000608558 | − | 0.00187295i | ||||
\(741\) | −18.0223 | − | 55.4668i | −0.662064 | − | 2.03762i | ||||
\(742\) | 11.5665 | − | 8.40352i | 0.424618 | − | 0.308503i | ||||
\(743\) | −36.2691 | + | 26.3511i | −1.33059 | + | 0.966727i | −0.330851 | + | 0.943683i | \(0.607336\pi\) |
−0.999734 | + | 0.0230437i | \(0.992664\pi\) | |||||||
\(744\) | −2.48155 | − | 7.63744i | −0.0909782 | − | 0.280002i | ||||
\(745\) | −1.81907 | + | 5.59854i | −0.0666457 | + | 0.205114i | ||||
\(746\) | 41.7325 | + | 30.3205i | 1.52794 | + | 1.11011i | ||||
\(747\) | 7.35218 | 0.269002 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −3.26935 | −0.119460 | ||||||||
\(750\) | 30.0211 | + | 21.8116i | 1.09621 | + | 0.796446i | ||||
\(751\) | −12.7271 | + | 39.1698i | −0.464417 | + | 1.42933i | 0.395298 | + | 0.918553i | \(0.370641\pi\) |
−0.859715 | + | 0.510775i | \(0.829359\pi\) | |||||||
\(752\) | −7.33460 | − | 22.5736i | −0.267465 | − | 0.823174i | ||||
\(753\) | −0.741775 | + | 0.538931i | −0.0270318 | + | 0.0196397i | ||||
\(754\) | −6.21201 | + | 4.51329i | −0.226228 | + | 0.164364i | ||||
\(755\) | 12.6016 | + | 38.7836i | 0.458618 | + | 1.41148i | ||||
\(756\) | 0.0123209 | − | 0.0379199i | 0.000448108 | − | 0.00137913i | ||||
\(757\) | 17.7084 | + | 12.8659i | 0.643623 | + | 0.467619i | 0.861093 | − | 0.508448i | \(-0.169781\pi\) |
−0.217470 | + | 0.976067i | \(0.569781\pi\) | |||||||
\(758\) | −17.8382 | −0.647912 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 30.1537 | 1.09379 | ||||||||
\(761\) | −28.8943 | − | 20.9930i | −1.04742 | − | 0.760994i | −0.0756987 | − | 0.997131i | \(-0.524119\pi\) |
−0.971720 | + | 0.236137i | \(0.924119\pi\) | |||||||
\(762\) | 4.74160 | − | 14.5931i | 0.171770 | − | 0.528654i | ||||
\(763\) | −0.879581 | − | 2.70707i | −0.0318430 | − | 0.0980026i | ||||
\(764\) | −0.108533 | + | 0.0788536i | −0.00392657 | + | 0.00285282i | ||||
\(765\) | 13.6178 | − | 9.89392i | 0.492353 | − | 0.357716i | ||||
\(766\) | −6.73607 | − | 20.7315i | −0.243384 | − | 0.749060i | ||||
\(767\) | −11.0298 | + | 33.9462i | −0.398263 | + | 1.22573i | ||||
\(768\) | −0.586552 | − | 0.426155i | −0.0211654 | − | 0.0153775i | ||||
\(769\) | −5.30246 | −0.191212 | −0.0956058 | − | 0.995419i | \(-0.530479\pi\) | ||||
−0.0956058 | + | 0.995419i | \(0.530479\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −37.7295 | −1.35880 | ||||||||
\(772\) | 0.0168086 | + | 0.0122121i | 0.000604953 | + | 0.000439524i | ||||
\(773\) | −15.4172 | + | 47.4494i | −0.554519 | + | 1.70663i | 0.142690 | + | 0.989767i | \(0.454425\pi\) |
−0.697209 | + | 0.716868i | \(0.745575\pi\) | |||||||
\(774\) | −5.87112 | − | 18.0695i | −0.211033 | − | 0.649493i | ||||
\(775\) | −1.74163 | + | 1.26537i | −0.0625613 | + | 0.0454535i | ||||
\(776\) | 5.53660 | − | 4.02258i | 0.198752 | − | 0.144402i | ||||
\(777\) | 1.40038 | + | 4.30992i | 0.0502383 | + | 0.154618i | ||||
\(778\) | −5.53633 | + | 17.0391i | −0.198487 | + | 0.610881i | ||||
\(779\) | −4.30205 | − | 3.12562i | −0.154137 | − | 0.111987i | ||||
\(780\) | −0.257109 | −0.00920597 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | −5.54803 | −0.198397 | ||||||||
\(783\) | −2.70830 | − | 1.96769i | −0.0967866 | − | 0.0703196i | ||||
\(784\) | −1.22738 | + | 3.77748i | −0.0438349 | + | 0.134910i | ||||
\(785\) | −7.50127 | − | 23.0865i | −0.267732 | − | 0.823994i | ||||
\(786\) | 0.444104 | − | 0.322660i | 0.0158407 | − | 0.0115089i | ||||
\(787\) | 29.0089 | − | 21.0762i | 1.03406 | − | 0.751285i | 0.0649388 | − | 0.997889i | \(-0.479315\pi\) |
0.969116 | + | 0.246604i | \(0.0793148\pi\) | |||||||
\(788\) | −0.0606010 | − | 0.186511i | −0.00215882 | − | 0.00664416i | ||||
\(789\) | 1.01294 | − | 3.11750i | 0.0360615 | − | 0.110986i | ||||
\(790\) | 32.6583 | + | 23.7277i | 1.16193 | + | 0.844193i | ||||
\(791\) | −14.5445 | −0.517144 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 29.1655 | 1.03570 | ||||||||
\(794\) | 21.6137 | + | 15.7033i | 0.767043 | + | 0.557289i | ||||
\(795\) | 12.4207 | − | 38.2268i | 0.440515 | − | 1.35577i | ||||
\(796\) | 0.0185008 | + | 0.0569396i | 0.000655744 | + | 0.00201817i | ||||
\(797\) | −11.9259 | + | 8.66470i | −0.422438 | + | 0.306919i | −0.778618 | − | 0.627498i | \(-0.784079\pi\) |
0.356180 | + | 0.934417i | \(0.384079\pi\) | |||||||
\(798\) | −14.3087 | + | 10.3959i | −0.506523 | + | 0.368010i | ||||
\(799\) | 10.1015 | + | 31.0892i | 0.357365 | + | 1.09986i | ||||
\(800\) | −0.0401801 | + | 0.123662i | −0.00142058 | + | 0.00437210i | ||||
\(801\) | −20.8571 | − | 15.1536i | −0.736949 | − | 0.535425i | ||||
\(802\) | −12.2354 | −0.432046 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | −0.467275 | −0.0164795 | ||||||||
\(805\) | 1.06630 | + | 0.774711i | 0.0375821 | + | 0.0273050i | ||||
\(806\) | −2.64677 | + | 8.14593i | −0.0932286 | + | 0.286928i | ||||
\(807\) | 1.35779 | + | 4.17883i | 0.0477963 | + | 0.147102i | ||||
\(808\) | −27.3149 | + | 19.8454i | −0.960934 | + | 0.698159i | ||||
\(809\) | −21.8239 | + | 15.8560i | −0.767288 | + | 0.557467i | −0.901137 | − | 0.433534i | \(-0.857266\pi\) |
0.133849 | + | 0.991002i | \(0.457266\pi\) | |||||||
\(810\) | 8.94649 | + | 27.5345i | 0.314348 | + | 0.967463i | ||||
\(811\) | −0.452523 | + | 1.39272i | −0.0158902 | + | 0.0489051i | −0.958687 | − | 0.284462i | \(-0.908185\pi\) |
0.942797 | + | 0.333367i | \(0.108185\pi\) | |||||||
\(812\) | −0.0132461 | − | 0.00962382i | −0.000464846 | − | 0.000337730i | ||||
\(813\) | 16.4513 | 0.576972 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −25.1236 | −0.880041 | ||||||||
\(816\) | −38.0269 | − | 27.6281i | −1.33121 | − | 0.967178i | ||||
\(817\) | −14.3839 | + | 44.2692i | −0.503230 | + | 1.54878i | ||||
\(818\) | −2.48840 | − | 7.65852i | −0.0870050 | − | 0.267774i | ||||
\(819\) | 6.31686 | − | 4.58947i | 0.220729 | − | 0.160369i | ||||
\(820\) | −0.0189655 | + | 0.0137793i | −0.000662305 | + | 0.000481193i | ||||
\(821\) | −9.46478 | − | 29.1296i | −0.330323 | − | 1.01663i | −0.968980 | − | 0.247139i | \(-0.920510\pi\) |
0.638657 | − | 0.769492i | \(-0.279490\pi\) | |||||||
\(822\) | −7.84221 | + | 24.1358i | −0.273529 | + | 0.841834i | ||||
\(823\) | 19.8483 | + | 14.4206i | 0.691867 | + | 0.502671i | 0.877273 | − | 0.479991i | \(-0.159360\pi\) |
−0.185406 | + | 0.982662i | \(0.559360\pi\) | |||||||
\(824\) | −1.12482 | −0.0391851 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 10.8243 | 0.376626 | ||||||||
\(827\) | −5.31270 | − | 3.85990i | −0.184741 | − | 0.134222i | 0.491571 | − | 0.870837i | \(-0.336423\pi\) |
−0.676312 | + | 0.736615i | \(0.736423\pi\) | |||||||
\(828\) | 0.00521813 | − | 0.0160597i | 0.000181342 | − | 0.000558115i | ||||
\(829\) | −6.13221 | − | 18.8730i | −0.212980 | − | 0.655486i | −0.999291 | − | 0.0376547i | \(-0.988011\pi\) |
0.786310 | − | 0.617832i | \(-0.211989\pi\) | |||||||
\(830\) | 9.13654 | − | 6.63808i | 0.317134 | − | 0.230411i | ||||
\(831\) | −25.2500 | + | 18.3452i | −0.875912 | + | 0.636387i | ||||
\(832\) | 11.5672 | + | 35.6003i | 0.401022 | + | 1.23422i | ||||
\(833\) | 1.69039 | − | 5.20248i | 0.0585685 | − | 0.180255i | ||||
\(834\) | 17.1699 | + | 12.4747i | 0.594545 | + | 0.431962i | ||||
\(835\) | 17.0476 | 0.589958 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −3.73421 | −0.129073 | ||||||||
\(838\) | 31.0009 | + | 22.5235i | 1.07091 | + | 0.778061i | ||||
\(839\) | −2.45993 | + | 7.57090i | −0.0849263 | + | 0.261376i | −0.984498 | − | 0.175397i | \(-0.943879\pi\) |
0.899571 | + | 0.436774i | \(0.143879\pi\) | |||||||
\(840\) | 3.47489 | + | 10.6946i | 0.119895 | + | 0.368999i | ||||
\(841\) | 22.3493 | − | 16.2377i | 0.770667 | − | 0.559922i | ||||
\(842\) | 27.3231 | − | 19.8514i | 0.941616 | − | 0.684124i | ||||
\(843\) | 11.8660 | + | 36.5199i | 0.408687 | + | 1.25781i | ||||
\(844\) | −0.00627989 | + | 0.0193275i | −0.000216163 | + | 0.000665281i | ||||
\(845\) | 12.7347 | + | 9.25233i | 0.438089 | + | 0.318290i | ||||
\(846\) | 14.1500 | 0.486489 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −40.2944 | −1.38372 | ||||||||
\(849\) | 54.4949 | + | 39.5928i | 1.87026 | + | 1.35882i | ||||
\(850\) | −3.92118 | + | 12.0681i | −0.134495 | + | 0.413934i | ||||
\(851\) | −0.465858 | − | 1.43376i | −0.0159694 | − | 0.0491487i | ||||
\(852\) | −0.339775 | + | 0.246861i | −0.0116405 | + | 0.00845731i | ||||
\(853\) | 27.5658 | − | 20.0277i | 0.943834 | − | 0.685736i | −0.00550627 | − | 0.999985i | \(-0.501753\pi\) |
0.949341 | + | 0.314249i | \(0.101753\pi\) | |||||||
\(854\) | −2.73317 | − | 8.41185i | −0.0935273 | − | 0.287847i | ||||
\(855\) | −5.51625 | + | 16.9773i | −0.188652 | + | 0.580611i | ||||
\(856\) | 7.50697 | + | 5.45413i | 0.256583 | + | 0.186418i | ||||
\(857\) | −24.8539 | −0.848992 | −0.424496 | − | 0.905430i | \(-0.639549\pi\) | ||||
−0.424496 | + | 0.905430i | \(0.639549\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 2.05654 | 0.0701683 | 0.0350841 | − | 0.999384i | \(-0.488830\pi\) | ||||
0.0350841 | + | 0.999384i | \(0.488830\pi\) | |||||||
\(860\) | 0.166013 | + | 0.120616i | 0.00566101 | + | 0.00411296i | ||||
\(861\) | 0.612797 | − | 1.88600i | 0.0208841 | − | 0.0642746i | ||||
\(862\) | −7.17386 | − | 22.0789i | −0.244343 | − | 0.752009i | ||||
\(863\) | 0.209920 | − | 0.152516i | 0.00714576 | − | 0.00519170i | −0.584207 | − | 0.811605i | \(-0.698594\pi\) |
0.591352 | + | 0.806413i | \(0.298594\pi\) | |||||||
\(864\) | −0.182468 | + | 0.132570i | −0.00620767 | + | 0.00451014i | ||||
\(865\) | 5.94547 | + | 18.2983i | 0.202152 | + | 0.622160i | ||||
\(866\) | 8.74936 | − | 26.9277i | 0.297315 | − | 0.915042i | ||||
\(867\) | 22.6184 | + | 16.4332i | 0.768161 | + | 0.558102i | ||||
\(868\) | −0.0182637 | −0.000619910 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 6.54651 | 0.221947 | ||||||||
\(871\) | 58.1499 | + | 42.2484i | 1.97034 | + | 1.43153i | ||||
\(872\) | −2.49644 | + | 7.68326i | −0.0845402 | + | 0.260188i | ||||
\(873\) | 1.25195 | + | 3.85312i | 0.0423722 | + | 0.130408i | ||||
\(874\) | 4.76001 | − | 3.45835i | 0.161010 | − | 0.116980i | ||||
\(875\) | 9.84690 | − | 7.15419i | 0.332886 | − | 0.241856i | ||||
\(876\) | −0.0561500 | − | 0.172812i | −0.00189713 | − | 0.00583877i | ||||
\(877\) | −5.74555 | + | 17.6830i | −0.194013 | + | 0.597112i | 0.805973 | + | 0.591952i | \(0.201642\pi\) |
−0.999987 | + | 0.00515985i | \(0.998358\pi\) | |||||||
\(878\) | 30.5190 | + | 22.1733i | 1.02997 | + | 0.748314i | ||||
\(879\) | −51.9867 | −1.75347 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 6.45292 | 0.217404 | 0.108702 | − | 0.994074i | \(-0.465330\pi\) | ||||
0.108702 | + | 0.994074i | \(0.465330\pi\) | |||||||
\(882\) | −1.91565 | − | 1.39180i | −0.0645034 | − | 0.0468645i | ||||
\(883\) | −0.0860573 | + | 0.264857i | −0.00289606 | + | 0.00891316i | −0.952494 | − | 0.304557i | \(-0.901492\pi\) |
0.949598 | + | 0.313470i | \(0.101492\pi\) | |||||||
\(884\) | −0.109696 | − | 0.337609i | −0.00368947 | − | 0.0113550i | ||||
\(885\) | 24.6194 | − | 17.8870i | 0.827572 | − | 0.601266i | ||||
\(886\) | −29.8887 | + | 21.7154i | −1.00413 | + | 0.729543i | ||||
\(887\) | −9.44262 | − | 29.0614i | −0.317052 | − | 0.975787i | −0.974901 | − | 0.222637i | \(-0.928534\pi\) |
0.657849 | − | 0.753150i | \(-0.271466\pi\) | |||||||
\(888\) | 3.97457 | − | 12.2325i | 0.133378 | − | 0.410495i | ||||
\(889\) | −4.07168 | − | 2.95825i | −0.136560 | − | 0.0992165i | ||||
\(890\) | −39.6008 | −1.32742 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0.0678176 | 0.00227070 | ||||||||
\(893\) | −28.0461 | − | 20.3767i | −0.938527 | − | 0.681879i | ||||
\(894\) | −3.02829 | + | 9.32011i | −0.101281 | + | 0.311711i | ||||
\(895\) | 4.71041 | + | 14.4971i | 0.157452 | + | 0.484586i | ||||
\(896\) | 9.05595 | − | 6.57953i | 0.302538 | − | 0.219807i | ||||
\(897\) | −5.85342 | + | 4.25276i | −0.195440 | + | 0.141995i | ||||
\(898\) | 4.24487 | + | 13.0644i | 0.141653 | + | 0.435964i | ||||
\(899\) | −0.473858 | + | 1.45839i | −0.0158041 | + | 0.0486399i | ||||
\(900\) | −0.0312453 | − | 0.0227011i | −0.00104151 | − | 0.000756702i | ||||
\(901\) | 55.4949 | 1.84880 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −17.3585 | −0.577655 | ||||||||
\(904\) | 33.3966 | + | 24.2641i | 1.11076 | + | 0.807011i | ||||
\(905\) | 8.37743 | − | 25.7831i | 0.278475 | − | 0.857059i | ||||
\(906\) | 20.9783 | + | 64.5646i | 0.696958 | + | 2.14502i | ||||
\(907\) | −25.8357 | + | 18.7707i | −0.857860 | + | 0.623272i | −0.927302 | − | 0.374314i | \(-0.877878\pi\) |
0.0694417 | + | 0.997586i | \(0.477878\pi\) | |||||||
\(908\) | −0.00448674 | + | 0.00325981i | −0.000148898 | + | 0.000108181i | ||||
\(909\) | −6.17653 | − | 19.0094i | −0.204862 | − | 0.630502i | ||||
\(910\) | 3.70624 | − | 11.4066i | 0.122861 | − | 0.378126i | ||||
\(911\) | −2.26559 | − | 1.64605i | −0.0750623 | − | 0.0545360i | 0.549621 | − | 0.835414i | \(-0.314772\pi\) |
−0.624684 | + | 0.780878i | \(0.714772\pi\) | |||||||
\(912\) | 49.8477 | 1.65062 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | −16.7496 | −0.554027 | ||||||||
\(915\) | −20.1170 | − | 14.6158i | −0.665046 | − | 0.483184i | ||||
\(916\) | −0.00944886 | + | 0.0290806i | −0.000312199 | + | 0.000960850i | ||||
\(917\) | −0.0556394 | − | 0.171241i | −0.00183738 | − | 0.00565486i | ||||
\(918\) | −17.8070 | + | 12.9375i | −0.587718 | + | 0.427002i | ||||
\(919\) | −12.8099 | + | 9.30691i | −0.422559 | + | 0.307007i | −0.778666 | − | 0.627438i | \(-0.784104\pi\) |
0.356108 | + | 0.934445i | \(0.384104\pi\) | |||||||
\(920\) | −1.15598 | − | 3.55773i | −0.0381114 | − | 0.117295i | ||||
\(921\) | −3.65212 | + | 11.2401i | −0.120341 | + | 0.370373i | ||||
\(922\) | 10.4291 | + | 7.57719i | 0.343464 | + | 0.249541i | ||||
\(923\) | 64.6030 | 2.12643 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −3.44799 | −0.113369 | ||||||||
\(926\) | −44.3897 | − | 32.2510i | −1.45874 | − | 1.05983i | ||||
\(927\) | 0.205772 | − | 0.633302i | 0.00675845 | − | 0.0208004i | ||||
\(928\) | 0.0286206 | + | 0.0880851i | 0.000939517 | + | 0.00289153i | ||||
\(929\) | 22.2345 | − | 16.1543i | 0.729490 | − | 0.530006i | −0.159912 | − | 0.987131i | \(-0.551121\pi\) |
0.889402 | + | 0.457126i | \(0.151121\pi\) | |||||||
\(930\) | 5.90782 | − | 4.29228i | 0.193725 | − | 0.140749i | ||||
\(931\) | 1.79266 | + | 5.51725i | 0.0587521 | + | 0.180820i | ||||
\(932\) | −0.00543791 | + | 0.0167362i | −0.000178125 | + | 0.000548212i | ||||
\(933\) | 24.3077 | + | 17.6606i | 0.795799 | + | 0.578182i | ||||
\(934\) | −29.2894 | −0.958379 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −22.1610 | −0.724354 | ||||||||
\(937\) | −9.95789 | − | 7.23483i | −0.325310 | − | 0.236352i | 0.413128 | − | 0.910673i | \(-0.364436\pi\) |
−0.738438 | + | 0.674321i | \(0.764436\pi\) | |||||||
\(938\) | 6.73581 | − | 20.7307i | 0.219932 | − | 0.676881i | ||||
\(939\) | −18.3500 | − | 56.4754i | −0.598828 | − | 1.84300i | ||||
\(940\) | −0.123641 | + | 0.0898304i | −0.00403272 | + | 0.00292994i | ||||
\(941\) | 1.18128 | − | 0.858248i | 0.0385085 | − | 0.0279781i | −0.568365 | − | 0.822777i | \(-0.692424\pi\) |
0.606873 | + | 0.794799i | \(0.292424\pi\) | |||||||
\(942\) | −12.4877 | − | 38.4331i | −0.406870 | − | 1.25222i | ||||
\(943\) | −0.203857 | + | 0.627406i | −0.00663848 | + | 0.0204311i | ||||
\(944\) | −24.6808 | − | 17.9317i | −0.803293 | − | 0.583627i | ||||
\(945\) | 5.22896 | 0.170098 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 11.0714 | 0.359771 | 0.179885 | − | 0.983688i | \(-0.442427\pi\) | ||||
0.179885 | + | 0.983688i | \(0.442427\pi\) | |||||||
\(948\) | −0.382278 | − | 0.277741i | −0.0124158 | − | 0.00902062i | ||||
\(949\) | −8.63712 | + | 26.5823i | −0.280373 | + | 0.862898i | ||||
\(950\) | −4.15842 | − | 12.7983i | −0.134917 | − | 0.415231i | ||||
\(951\) | 13.6966 | − | 9.95119i | 0.444144 | − | 0.322690i | ||||
\(952\) | −12.5605 | + | 9.12574i | −0.407088 | + | 0.295767i | ||||
\(953\) | 4.58067 | + | 14.0979i | 0.148383 | + | 0.456675i | 0.997430 | − | 0.0716413i | \(-0.0228237\pi\) |
−0.849048 | + | 0.528316i | \(0.822824\pi\) | |||||||
\(954\) | 7.42319 | − | 22.8462i | 0.240335 | − | 0.739674i | ||||
\(955\) | −14.2336 | − | 10.3413i | −0.460588 | − | 0.334637i | ||||
\(956\) | −0.155867 | −0.00504110 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 34.5782 | 1.11717 | ||||||||
\(959\) | 6.73422 | + | 4.89270i | 0.217459 | + | 0.157993i | ||||
\(960\) | 9.86200 | − | 30.3521i | 0.318295 | − | 0.979610i | ||||
\(961\) | −9.05095 | − | 27.8560i | −0.291966 | − | 0.898579i | ||||
\(962\) | −11.0984 | + | 8.06343i | −0.357826 | + | 0.259976i | ||||
\(963\) | −4.44411 | + | 3.22884i | −0.143210 | + | 0.104048i | ||||
\(964\) | −0.0927105 | − | 0.285334i | −0.00298601 | − | 0.00918998i | ||||
\(965\) | −0.841995 | + | 2.59139i | −0.0271048 | + | 0.0834199i | ||||
\(966\) | 1.77511 | + | 1.28969i | 0.0571132 | + | 0.0414952i | ||||
\(967\) | −16.5193 | −0.531224 | −0.265612 | − | 0.964080i | \(-0.585574\pi\) | ||||
−0.265612 | + | 0.964080i | \(0.585574\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −68.6520 | −2.20542 | ||||||||
\(970\) | 5.03468 | + | 3.65791i | 0.161654 | + | 0.117448i | ||||
\(971\) | 12.6077 | − | 38.8025i | 0.404600 | − | 1.24523i | −0.516629 | − | 0.856209i | \(-0.672813\pi\) |
0.921229 | − | 0.389021i | \(-0.127187\pi\) | |||||||
\(972\) | −0.0677593 | − | 0.208542i | −0.00217338 | − | 0.00668897i | ||||
\(973\) | 5.63172 | − | 4.09169i | 0.180545 | − | 0.131173i | ||||
\(974\) | 14.1048 | − | 10.2477i | 0.451947 | − | 0.328359i | ||||
\(975\) | 5.11363 | + | 15.7381i | 0.163767 | + | 0.504024i | ||||
\(976\) | −7.70317 | + | 23.7079i | −0.246573 | + | 0.758872i | ||||
\(977\) | −39.7345 | − | 28.8688i | −1.27122 | − | 0.923594i | −0.271967 | − | 0.962306i | \(-0.587674\pi\) |
−0.999250 | + | 0.0387127i | \(0.987674\pi\) | |||||||
\(978\) | −41.8243 | −1.33739 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 0.0255744 | 0.000816945 | ||||||||
\(981\) | −3.86916 | − | 2.81111i | −0.123533 | − | 0.0897519i | ||||
\(982\) | −7.19647 | + | 22.1484i | −0.229648 | + | 0.706785i | ||||
\(983\) | 0.342017 | + | 1.05262i | 0.0109086 | + | 0.0335733i | 0.956363 | − | 0.292182i | \(-0.0943814\pi\) |
−0.945454 | + | 0.325756i | \(0.894381\pi\) | |||||||
\(984\) | −4.55342 | + | 3.30825i | −0.145158 | + | 0.105463i | ||||
\(985\) | 20.8070 | − | 15.1172i | 0.662965 | − | 0.481672i | ||||
\(986\) | 2.79308 | + | 8.59622i | 0.0889498 | + | 0.273759i | ||||
\(987\) | 3.99497 | − | 12.2953i | 0.127161 | − | 0.391363i | ||||
\(988\) | 0.304563 | + | 0.221278i | 0.00968945 | + | 0.00703980i | ||||
\(989\) | 5.77458 | 0.183621 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 41.7851 | 1.32735 | 0.663674 | − | 0.748022i | \(-0.268996\pi\) | ||||
0.663674 | + | 0.748022i | \(0.268996\pi\) | |||||||
\(992\) | 0.0835821 | + | 0.0607260i | 0.00265374 | + | 0.00192805i | ||||
\(993\) | 18.8163 | − | 57.9107i | 0.597118 | − | 1.83774i | ||||
\(994\) | −6.05411 | − | 18.6326i | −0.192025 | − | 0.590991i | ||||
\(995\) | −6.35214 | + | 4.61510i | −0.201376 | + | 0.146308i | ||||
\(996\) | −0.106947 | + | 0.0777013i | −0.00338873 | + | 0.00246206i | ||||
\(997\) | −13.6568 | − | 42.0314i | −0.432517 | − | 1.33115i | −0.895610 | − | 0.444840i | \(-0.853261\pi\) |
0.463094 | − | 0.886309i | \(-0.346739\pi\) | |||||||
\(998\) | −5.98401 | + | 18.4169i | −0.189421 | + | 0.582977i | ||||
\(999\) | −4.83863 | − | 3.51547i | −0.153088 | − | 0.111225i |
(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 | 847.2.f.v.323.2 | 16 | ||
11.2 | odd | 10 | 77.2.f.b.71.2 | yes | 16 | ||
11.3 | even | 5 | inner | 847.2.f.v.729.2 | 16 | ||
11.4 | even | 5 | 847.2.f.x.372.3 | 16 | |||
11.5 | even | 5 | 847.2.a.o.1.6 | 8 | |||
11.6 | odd | 10 | 847.2.a.p.1.3 | 8 | |||
11.7 | odd | 10 | 77.2.f.b.64.2 | ✓ | 16 | ||
11.8 | odd | 10 | 847.2.f.w.729.3 | 16 | |||
11.9 | even | 5 | 847.2.f.x.148.3 | 16 | |||
11.10 | odd | 2 | 847.2.f.w.323.3 | 16 | |||
33.2 | even | 10 | 693.2.m.i.379.3 | 16 | |||
33.5 | odd | 10 | 7623.2.a.cw.1.3 | 8 | |||
33.17 | even | 10 | 7623.2.a.ct.1.6 | 8 | |||
33.29 | even | 10 | 693.2.m.i.64.3 | 16 | |||
77.2 | odd | 30 | 539.2.q.g.214.2 | 32 | |||
77.6 | even | 10 | 5929.2.a.bt.1.3 | 8 | |||
77.13 | even | 10 | 539.2.f.e.148.2 | 16 | |||
77.18 | odd | 30 | 539.2.q.g.471.2 | 32 | |||
77.24 | even | 30 | 539.2.q.f.324.3 | 32 | |||
77.27 | odd | 10 | 5929.2.a.bs.1.6 | 8 | |||
77.40 | even | 30 | 539.2.q.f.361.3 | 32 | |||
77.46 | odd | 30 | 539.2.q.g.324.3 | 32 | |||
77.51 | odd | 30 | 539.2.q.g.361.3 | 32 | |||
77.62 | even | 10 | 539.2.f.e.295.2 | 16 | |||
77.68 | even | 30 | 539.2.q.f.214.2 | 32 | |||
77.73 | even | 30 | 539.2.q.f.471.2 | 32 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
77.2.f.b.64.2 | ✓ | 16 | 11.7 | odd | 10 | ||
77.2.f.b.71.2 | yes | 16 | 11.2 | odd | 10 | ||
539.2.f.e.148.2 | 16 | 77.13 | even | 10 | |||
539.2.f.e.295.2 | 16 | 77.62 | even | 10 | |||
539.2.q.f.214.2 | 32 | 77.68 | even | 30 | |||
539.2.q.f.324.3 | 32 | 77.24 | even | 30 | |||
539.2.q.f.361.3 | 32 | 77.40 | even | 30 | |||
539.2.q.f.471.2 | 32 | 77.73 | even | 30 | |||
539.2.q.g.214.2 | 32 | 77.2 | odd | 30 | |||
539.2.q.g.324.3 | 32 | 77.46 | odd | 30 | |||
539.2.q.g.361.3 | 32 | 77.51 | odd | 30 | |||
539.2.q.g.471.2 | 32 | 77.18 | odd | 30 | |||
693.2.m.i.64.3 | 16 | 33.29 | even | 10 | |||
693.2.m.i.379.3 | 16 | 33.2 | even | 10 | |||
847.2.a.o.1.6 | 8 | 11.5 | even | 5 | |||
847.2.a.p.1.3 | 8 | 11.6 | odd | 10 | |||
847.2.f.v.323.2 | 16 | 1.1 | even | 1 | trivial | ||
847.2.f.v.729.2 | 16 | 11.3 | even | 5 | inner | ||
847.2.f.w.323.3 | 16 | 11.10 | odd | 2 | |||
847.2.f.w.729.3 | 16 | 11.8 | odd | 10 | |||
847.2.f.x.148.3 | 16 | 11.9 | even | 5 | |||
847.2.f.x.372.3 | 16 | 11.4 | even | 5 | |||
5929.2.a.bs.1.6 | 8 | 77.27 | odd | 10 | |||
5929.2.a.bt.1.3 | 8 | 77.6 | even | 10 | |||
7623.2.a.ct.1.6 | 8 | 33.17 | even | 10 | |||
7623.2.a.cw.1.3 | 8 | 33.5 | odd | 10 |