Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [375,2,Mod(49,375)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(375, base_ring=CyclotomicField(10))
chi = DirichletCharacter(H, H._module([0, 7]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("375.49");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 375 = 3 \cdot 5^{3} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 375.i (of order \(10\), degree \(4\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(2.99439007580\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{10})\) |
Coefficient field: | \(\Q(\zeta_{20})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - x^{6} + x^{4} - x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 75) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{10}]$ |
Embedding invariants
Embedding label | 274.2 | ||
Root | \(0.951057 + 0.309017i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 375.274 |
Dual form | 375.2.i.a.349.2 |
$q$-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 \(\left(\mathbb{Z}/375\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(251\) |
\(\chi(n)\) | \(e\left(\frac{1}{10}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.951057 | + | 0.309017i | 0.672499 | + | 0.218508i | 0.625308 | − | 0.780378i | \(-0.284973\pi\) |
0.0471903 | + | 0.998886i | \(0.484973\pi\) | |||||||
\(3\) | −0.587785 | + | 0.809017i | −0.339358 | + | 0.467086i | ||||
\(4\) | −0.809017 | − | 0.587785i | −0.404508 | − | 0.293893i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −0.809017 | + | 0.587785i | −0.330280 | + | 0.239962i | ||||
\(7\) | − | 4.47214i | − | 1.69031i | −0.534522 | − | 0.845154i | \(-0.679509\pi\) | ||
0.534522 | − | 0.845154i | \(-0.320491\pi\) | |||||||
\(8\) | −1.76336 | − | 2.42705i | −0.623440 | − | 0.858092i | ||||
\(9\) | −0.309017 | − | 0.951057i | −0.103006 | − | 0.317019i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −0.381966 | + | 1.17557i | −0.115167 | + | 0.354448i | −0.991982 | − | 0.126380i | \(-0.959664\pi\) |
0.876815 | + | 0.480828i | \(0.159664\pi\) | |||||||
\(12\) | 0.951057 | − | 0.309017i | 0.274546 | − | 0.0892055i | ||||
\(13\) | 5.34307 | − | 1.73607i | 1.48190 | − | 0.481499i | 0.547220 | − | 0.836989i | \(-0.315686\pi\) |
0.934680 | + | 0.355490i | \(0.115686\pi\) | |||||||
\(14\) | 1.38197 | − | 4.25325i | 0.369346 | − | 1.13673i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −0.309017 | − | 0.951057i | −0.0772542 | − | 0.237764i | ||||
\(17\) | −2.26538 | − | 3.11803i | −0.549436 | − | 0.756234i | 0.440499 | − | 0.897753i | \(-0.354801\pi\) |
−0.989936 | + | 0.141519i | \(0.954801\pi\) | |||||||
\(18\) | − | 1.00000i | − | 0.235702i | ||||||
\(19\) | 1.00000 | − | 0.726543i | 0.229416 | − | 0.166680i | −0.467139 | − | 0.884184i | \(-0.654715\pi\) |
0.696555 | + | 0.717504i | \(0.254715\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 3.61803 | + | 2.62866i | 0.789520 | + | 0.573620i | ||||
\(22\) | −0.726543 | + | 1.00000i | −0.154899 | + | 0.213201i | ||||
\(23\) | −4.25325 | − | 1.38197i | −0.886865 | − | 0.288160i | −0.170060 | − | 0.985434i | \(-0.554396\pi\) |
−0.716805 | + | 0.697274i | \(0.754396\pi\) | |||||||
\(24\) | 3.00000 | 0.612372 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 5.61803 | 1.10179 | ||||||||
\(27\) | 0.951057 | + | 0.309017i | 0.183031 | + | 0.0594703i | ||||
\(28\) | −2.62866 | + | 3.61803i | −0.496769 | + | 0.683744i | ||||
\(29\) | 5.35410 | + | 3.88998i | 0.994232 | + | 0.722352i | 0.960844 | − | 0.277091i | \(-0.0893703\pi\) |
0.0333880 | + | 0.999442i | \(0.489370\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −2.23607 | + | 1.62460i | −0.401610 | + | 0.291787i | −0.770196 | − | 0.637807i | \(-0.779842\pi\) |
0.368587 | + | 0.929593i | \(0.379842\pi\) | |||||||
\(32\) | 5.00000i | 0.883883i | ||||||||
\(33\) | −0.726543 | − | 1.00000i | −0.126475 | − | 0.174078i | ||||
\(34\) | −1.19098 | − | 3.66547i | −0.204252 | − | 0.628623i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −0.309017 | + | 0.951057i | −0.0515028 | + | 0.158509i | ||||
\(37\) | 2.93893 | − | 0.954915i | 0.483157 | − | 0.156987i | −0.0573034 | − | 0.998357i | \(-0.518250\pi\) |
0.540460 | + | 0.841370i | \(0.318250\pi\) | |||||||
\(38\) | 1.17557 | − | 0.381966i | 0.190703 | − | 0.0619631i | ||||
\(39\) | −1.73607 | + | 5.34307i | −0.277993 | + | 0.855576i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −1.11803 | − | 3.44095i | −0.174608 | − | 0.537387i | 0.825008 | − | 0.565121i | \(-0.191171\pi\) |
−0.999615 | + | 0.0277346i | \(0.991171\pi\) | |||||||
\(42\) | 2.62866 | + | 3.61803i | 0.405610 | + | 0.558275i | ||||
\(43\) | − | 7.70820i | − | 1.17549i | −0.809046 | − | 0.587745i | \(-0.800016\pi\) | ||
0.809046 | − | 0.587745i | \(-0.199984\pi\) | |||||||
\(44\) | 1.00000 | − | 0.726543i | 0.150756 | − | 0.109530i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −3.61803 | − | 2.62866i | −0.533450 | − | 0.387574i | ||||
\(47\) | −0.449028 | + | 0.618034i | −0.0654975 | + | 0.0901495i | −0.840509 | − | 0.541797i | \(-0.817744\pi\) |
0.775012 | + | 0.631947i | \(0.217744\pi\) | |||||||
\(48\) | 0.951057 | + | 0.309017i | 0.137273 | + | 0.0446028i | ||||
\(49\) | −13.0000 | −1.85714 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 3.85410 | 0.539682 | ||||||||
\(52\) | −5.34307 | − | 1.73607i | −0.740950 | − | 0.240749i | ||||
\(53\) | −2.12663 | + | 2.92705i | −0.292115 | + | 0.402061i | −0.929700 | − | 0.368319i | \(-0.879934\pi\) |
0.637585 | + | 0.770380i | \(0.279934\pi\) | |||||||
\(54\) | 0.809017 | + | 0.587785i | 0.110093 | + | 0.0799874i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −10.8541 | + | 7.88597i | −1.45044 | + | 1.05381i | ||||
\(57\) | 1.23607i | 0.163721i | ||||||||
\(58\) | 3.88998 | + | 5.35410i | 0.510780 | + | 0.703028i | ||||
\(59\) | 1.23607 | + | 3.80423i | 0.160922 | + | 0.495268i | 0.998713 | − | 0.0507240i | \(-0.0161529\pi\) |
−0.837790 | + | 0.545992i | \(0.816153\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0.500000 | − | 1.53884i | 0.0640184 | − | 0.197028i | −0.913931 | − | 0.405869i | \(-0.866969\pi\) |
0.977950 | + | 0.208840i | \(0.0669689\pi\) | |||||||
\(62\) | −2.62866 | + | 0.854102i | −0.333840 | + | 0.108471i | ||||
\(63\) | −4.25325 | + | 1.38197i | −0.535860 | + | 0.174111i | ||||
\(64\) | −2.16312 | + | 6.65740i | −0.270390 | + | 0.832174i | ||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −0.381966 | − | 1.17557i | −0.0470168 | − | 0.144703i | ||||
\(67\) | −0.449028 | − | 0.618034i | −0.0548575 | − | 0.0755049i | 0.780707 | − | 0.624897i | \(-0.214859\pi\) |
−0.835564 | + | 0.549392i | \(0.814859\pi\) | |||||||
\(68\) | 3.85410i | 0.467379i | ||||||||
\(69\) | 3.61803 | − | 2.62866i | 0.435560 | − | 0.316453i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 4.23607 | + | 3.07768i | 0.502729 | + | 0.365254i | 0.810058 | − | 0.586349i | \(-0.199435\pi\) |
−0.307330 | + | 0.951603i | \(0.599435\pi\) | |||||||
\(72\) | −1.76336 | + | 2.42705i | −0.207813 | + | 0.286031i | ||||
\(73\) | 7.69421 | + | 2.50000i | 0.900539 | + | 0.292603i | 0.722460 | − | 0.691413i | \(-0.243012\pi\) |
0.178080 | + | 0.984016i | \(0.443012\pi\) | |||||||
\(74\) | 3.09017 | 0.359225 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −1.23607 | −0.141787 | ||||||||
\(77\) | 5.25731 | + | 1.70820i | 0.599126 | + | 0.194668i | ||||
\(78\) | −3.30220 | + | 4.54508i | −0.373900 | + | 0.514630i | ||||
\(79\) | 0 | 0 | 0.587785 | − | 0.809017i | \(-0.300000\pi\) | ||||
−0.587785 | + | 0.809017i | \(0.700000\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −0.809017 | + | 0.587785i | −0.0898908 | + | 0.0653095i | ||||
\(82\) | − | 3.61803i | − | 0.399545i | ||||||
\(83\) | 7.33094 | + | 10.0902i | 0.804675 | + | 1.10754i | 0.992123 | + | 0.125266i | \(0.0399783\pi\) |
−0.187448 | + | 0.982274i | \(0.560022\pi\) | |||||||
\(84\) | −1.38197 | − | 4.25325i | −0.150785 | − | 0.464068i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 2.38197 | − | 7.33094i | 0.256854 | − | 0.790515i | ||||
\(87\) | −6.29412 | + | 2.04508i | −0.674801 | + | 0.219256i | ||||
\(88\) | 3.52671 | − | 1.14590i | 0.375949 | − | 0.122153i | ||||
\(89\) | −1.66312 | + | 5.11855i | −0.176290 | + | 0.542566i | −0.999690 | − | 0.0248961i | \(-0.992075\pi\) |
0.823400 | + | 0.567462i | \(0.192075\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −7.76393 | − | 23.8949i | −0.813881 | − | 2.50487i | ||||
\(92\) | 2.62866 | + | 3.61803i | 0.274056 | + | 0.377206i | ||||
\(93\) | − | 2.76393i | − | 0.286606i | ||||||
\(94\) | −0.618034 | + | 0.449028i | −0.0637453 | + | 0.0463137i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −4.04508 | − | 2.93893i | −0.412850 | − | 0.299953i | ||||
\(97\) | 1.26133 | − | 1.73607i | 0.128068 | − | 0.176271i | −0.740168 | − | 0.672422i | \(-0.765254\pi\) |
0.868236 | + | 0.496151i | \(0.165254\pi\) | |||||||
\(98\) | −12.3637 | − | 4.01722i | −1.24893 | − | 0.405801i | ||||
\(99\) | 1.23607 | 0.124230 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 3.56231 | 0.354463 | 0.177231 | − | 0.984169i | \(-0.443286\pi\) | ||||
0.177231 | + | 0.984169i | \(0.443286\pi\) | |||||||
\(102\) | 3.66547 | + | 1.19098i | 0.362935 | + | 0.117925i | ||||
\(103\) | −1.90211 | + | 2.61803i | −0.187421 | + | 0.257963i | −0.892379 | − | 0.451286i | \(-0.850966\pi\) |
0.704959 | + | 0.709248i | \(0.250966\pi\) | |||||||
\(104\) | −13.6353 | − | 9.90659i | −1.33705 | − | 0.971421i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −2.92705 | + | 2.12663i | −0.284300 | + | 0.206556i | ||||
\(107\) | 7.52786i | 0.727746i | 0.931449 | + | 0.363873i | \(0.118546\pi\) | ||||
−0.931449 | + | 0.363873i | \(0.881454\pi\) | |||||||
\(108\) | −0.587785 | − | 0.809017i | −0.0565597 | − | 0.0778477i | ||||
\(109\) | 2.44427 | + | 7.52270i | 0.234119 | + | 0.720544i | 0.997237 | + | 0.0742847i | \(0.0236674\pi\) |
−0.763118 | + | 0.646259i | \(0.776333\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −0.954915 | + | 2.93893i | −0.0906365 | + | 0.278951i | ||||
\(112\) | −4.25325 | + | 1.38197i | −0.401895 | + | 0.130584i | ||||
\(113\) | 17.4293 | − | 5.66312i | 1.63961 | − | 0.532741i | 0.663158 | − | 0.748479i | \(-0.269216\pi\) |
0.976451 | + | 0.215738i | \(0.0692157\pi\) | |||||||
\(114\) | −0.381966 | + | 1.17557i | −0.0357744 | + | 0.110102i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −2.04508 | − | 6.29412i | −0.189881 | − | 0.584395i | ||||
\(117\) | −3.30220 | − | 4.54508i | −0.305288 | − | 0.420193i | ||||
\(118\) | 4.00000i | 0.368230i | ||||||||
\(119\) | −13.9443 | + | 10.1311i | −1.27827 | + | 0.928717i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 7.66312 | + | 5.56758i | 0.696647 | + | 0.506144i | ||||
\(122\) | 0.951057 | − | 1.30902i | 0.0861046 | − | 0.118513i | ||||
\(123\) | 3.44095 | + | 1.11803i | 0.310260 | + | 0.100810i | ||||
\(124\) | 2.76393 | 0.248208 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −4.47214 | −0.398410 | ||||||||
\(127\) | −3.52671 | − | 1.14590i | −0.312945 | − | 0.101682i | 0.148333 | − | 0.988937i | \(-0.452609\pi\) |
−0.461279 | + | 0.887255i | \(0.652609\pi\) | |||||||
\(128\) | 1.76336 | − | 2.42705i | 0.155860 | − | 0.214523i | ||||
\(129\) | 6.23607 | + | 4.53077i | 0.549055 | + | 0.398912i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 6.61803 | − | 4.80828i | 0.578220 | − | 0.420102i | −0.259862 | − | 0.965646i | \(-0.583677\pi\) |
0.838082 | + | 0.545544i | \(0.183677\pi\) | |||||||
\(132\) | 1.23607i | 0.107586i | ||||||||
\(133\) | −3.24920 | − | 4.47214i | −0.281741 | − | 0.387783i | ||||
\(134\) | −0.236068 | − | 0.726543i | −0.0203932 | − | 0.0627637i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −3.57295 | + | 10.9964i | −0.306378 | + | 0.942934i | ||||
\(137\) | 7.24518 | − | 2.35410i | 0.618998 | − | 0.201125i | 0.0173024 | − | 0.999850i | \(-0.494492\pi\) |
0.601695 | + | 0.798726i | \(0.294492\pi\) | |||||||
\(138\) | 4.25325 | − | 1.38197i | 0.362061 | − | 0.117641i | ||||
\(139\) | 7.09017 | − | 21.8213i | 0.601380 | − | 1.85086i | 0.0813976 | − | 0.996682i | \(-0.474062\pi\) |
0.519983 | − | 0.854177i | \(-0.325938\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −0.236068 | − | 0.726543i | −0.0198805 | − | 0.0611859i | ||||
\(142\) | 3.07768 | + | 4.23607i | 0.258273 | + | 0.355483i | ||||
\(143\) | 6.94427i | 0.580709i | ||||||||
\(144\) | −0.809017 | + | 0.587785i | −0.0674181 | + | 0.0489821i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 6.54508 | + | 4.75528i | 0.541675 | + | 0.393550i | ||||
\(147\) | 7.64121 | − | 10.5172i | 0.630236 | − | 0.867446i | ||||
\(148\) | −2.93893 | − | 0.954915i | −0.241578 | − | 0.0784935i | ||||
\(149\) | 18.8541 | 1.54459 | 0.772294 | − | 0.635265i | \(-0.219109\pi\) | ||||
0.772294 | + | 0.635265i | \(0.219109\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 7.52786 | 0.612609 | 0.306304 | − | 0.951934i | \(-0.400907\pi\) | ||||
0.306304 | + | 0.951934i | \(0.400907\pi\) | |||||||
\(152\) | −3.52671 | − | 1.14590i | −0.286054 | − | 0.0929446i | ||||
\(153\) | −2.26538 | + | 3.11803i | −0.183145 | + | 0.252078i | ||||
\(154\) | 4.47214 | + | 3.24920i | 0.360375 | + | 0.261828i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 4.54508 | − | 3.30220i | 0.363898 | − | 0.264387i | ||||
\(157\) | 10.7984i | 0.861804i | 0.902399 | + | 0.430902i | \(0.141805\pi\) | ||||
−0.902399 | + | 0.430902i | \(0.858195\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −1.11803 | − | 3.44095i | −0.0886659 | − | 0.272885i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −6.18034 | + | 19.0211i | −0.487079 | + | 1.49908i | ||||
\(162\) | −0.951057 | + | 0.309017i | −0.0747221 | + | 0.0242787i | ||||
\(163\) | −14.2128 | + | 4.61803i | −1.11324 | + | 0.361712i | −0.807183 | − | 0.590302i | \(-0.799009\pi\) |
−0.306054 | + | 0.952014i | \(0.599009\pi\) | |||||||
\(164\) | −1.11803 | + | 3.44095i | −0.0873038 | + | 0.268693i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 3.85410 | + | 11.8617i | 0.299136 | + | 0.920647i | ||||
\(167\) | −2.00811 | − | 2.76393i | −0.155393 | − | 0.213879i | 0.724222 | − | 0.689567i | \(-0.242199\pi\) |
−0.879614 | + | 0.475688i | \(0.842199\pi\) | |||||||
\(168\) | − | 13.4164i | − | 1.03510i | ||||||
\(169\) | 15.0172 | − | 10.9106i | 1.15517 | − | 0.839281i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −1.00000 | − | 0.726543i | −0.0764719 | − | 0.0555601i | ||||
\(172\) | −4.53077 | + | 6.23607i | −0.345468 | + | 0.475496i | ||||
\(173\) | −20.0579 | − | 6.51722i | −1.52498 | − | 0.495495i | −0.577793 | − | 0.816184i | \(-0.696086\pi\) |
−0.947185 | + | 0.320689i | \(0.896086\pi\) | |||||||
\(174\) | −6.61803 | −0.501712 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 1.23607 | 0.0931721 | ||||||||
\(177\) | −3.80423 | − | 1.23607i | −0.285943 | − | 0.0929086i | ||||
\(178\) | −3.16344 | + | 4.35410i | −0.237110 | + | 0.326354i | ||||
\(179\) | −13.0902 | − | 9.51057i | −0.978405 | − | 0.710853i | −0.0210536 | − | 0.999778i | \(-0.506702\pi\) |
−0.957352 | + | 0.288925i | \(0.906702\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −11.9721 | + | 8.69827i | −0.889882 | + | 0.646537i | −0.935847 | − | 0.352406i | \(-0.885364\pi\) |
0.0459654 | + | 0.998943i | \(0.485364\pi\) | |||||||
\(182\) | − | 25.1246i | − | 1.86236i | ||||||
\(183\) | 0.951057 | + | 1.30902i | 0.0703041 | + | 0.0967653i | ||||
\(184\) | 4.14590 | + | 12.7598i | 0.305640 | + | 0.940662i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0.854102 | − | 2.62866i | 0.0626258 | − | 0.192742i | ||||
\(187\) | 4.53077 | − | 1.47214i | 0.331323 | − | 0.107653i | ||||
\(188\) | 0.726543 | − | 0.236068i | 0.0529886 | − | 0.0172170i | ||||
\(189\) | 1.38197 | − | 4.25325i | 0.100523 | − | 0.309379i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 2.05573 | + | 6.32688i | 0.148747 | + | 0.457797i | 0.997474 | − | 0.0710349i | \(-0.0226302\pi\) |
−0.848727 | + | 0.528832i | \(0.822630\pi\) | |||||||
\(192\) | −4.11450 | − | 5.66312i | −0.296938 | − | 0.408700i | ||||
\(193\) | − | 23.3262i | − | 1.67906i | −0.543314 | − | 0.839530i | \(-0.682831\pi\) | ||
0.543314 | − | 0.839530i | \(-0.317169\pi\) | |||||||
\(194\) | 1.73607 | − | 1.26133i | 0.124642 | − | 0.0905580i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 10.5172 | + | 7.64121i | 0.751230 | + | 0.545801i | ||||
\(197\) | 4.47777 | − | 6.16312i | 0.319028 | − | 0.439104i | −0.619142 | − | 0.785279i | \(-0.712520\pi\) |
0.938170 | + | 0.346175i | \(0.112520\pi\) | |||||||
\(198\) | 1.17557 | + | 0.381966i | 0.0835442 | + | 0.0271451i | ||||
\(199\) | −12.6525 | −0.896910 | −0.448455 | − | 0.893805i | \(-0.648026\pi\) | ||||
−0.448455 | + | 0.893805i | \(0.648026\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0.763932 | 0.0538836 | ||||||||
\(202\) | 3.38795 | + | 1.10081i | 0.238376 | + | 0.0774529i | ||||
\(203\) | 17.3965 | − | 23.9443i | 1.22100 | − | 1.68056i | ||||
\(204\) | −3.11803 | − | 2.26538i | −0.218306 | − | 0.158609i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −2.61803 | + | 1.90211i | −0.182407 | + | 0.132526i | ||||
\(207\) | 4.47214i | 0.310835i | ||||||||
\(208\) | −3.30220 | − | 4.54508i | −0.228966 | − | 0.315145i | ||||
\(209\) | 0.472136 | + | 1.45309i | 0.0326583 | + | 0.100512i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 5.52786 | − | 17.0130i | 0.380554 | − | 1.17122i | −0.559101 | − | 0.829100i | \(-0.688854\pi\) |
0.939655 | − | 0.342125i | \(-0.111146\pi\) | |||||||
\(212\) | 3.44095 | − | 1.11803i | 0.236326 | − | 0.0767869i | ||||
\(213\) | −4.97980 | + | 1.61803i | −0.341210 | + | 0.110866i | ||||
\(214\) | −2.32624 | + | 7.15942i | −0.159018 | + | 0.489408i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −0.927051 | − | 2.85317i | −0.0630778 | − | 0.194134i | ||||
\(217\) | 7.26543 | + | 10.0000i | 0.493209 | + | 0.678844i | ||||
\(218\) | 7.90983i | 0.535721i | ||||||||
\(219\) | −6.54508 | + | 4.75528i | −0.442276 | + | 0.321332i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −17.5172 | − | 12.7270i | −1.17834 | − | 0.856111i | ||||
\(222\) | −1.81636 | + | 2.50000i | −0.121906 | + | 0.167789i | ||||
\(223\) | −7.77997 | − | 2.52786i | −0.520985 | − | 0.169278i | 0.0367073 | − | 0.999326i | \(-0.488313\pi\) |
−0.557692 | + | 0.830048i | \(0.688313\pi\) | |||||||
\(224\) | 22.3607 | 1.49404 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 18.3262 | 1.21904 | ||||||||
\(227\) | −19.0211 | − | 6.18034i | −1.26248 | − | 0.410204i | −0.400100 | − | 0.916471i | \(-0.631025\pi\) |
−0.862376 | + | 0.506268i | \(0.831025\pi\) | |||||||
\(228\) | 0.726543 | − | 1.00000i | 0.0481165 | − | 0.0662266i | ||||
\(229\) | 17.7812 | + | 12.9188i | 1.17501 | + | 0.853696i | 0.991600 | − | 0.129340i | \(-0.0412860\pi\) |
0.183411 | + | 0.983036i | \(0.441286\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −4.47214 | + | 3.24920i | −0.294245 | + | 0.213781i | ||||
\(232\) | − | 19.8541i | − | 1.30349i | ||||||
\(233\) | 7.27794 | + | 10.0172i | 0.476794 | + | 0.656250i | 0.977885 | − | 0.209144i | \(-0.0670679\pi\) |
−0.501091 | + | 0.865394i | \(0.667068\pi\) | |||||||
\(234\) | −1.73607 | − | 5.34307i | −0.113490 | − | 0.349287i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 1.23607 | − | 3.80423i | 0.0804612 | − | 0.247634i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −16.3925 | + | 5.32624i | −1.06257 | + | 0.345249i | ||||
\(239\) | 7.70820 | − | 23.7234i | 0.498602 | − | 1.53454i | −0.312664 | − | 0.949864i | \(-0.601222\pi\) |
0.811267 | − | 0.584676i | \(-0.198778\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 8.66312 | + | 26.6623i | 0.558041 | + | 1.71747i | 0.687775 | + | 0.725923i | \(0.258587\pi\) |
−0.129735 | + | 0.991549i | \(0.541413\pi\) | |||||||
\(242\) | 5.56758 | + | 7.66312i | 0.357898 | + | 0.492604i | ||||
\(243\) | − | 1.00000i | − | 0.0641500i | ||||||
\(244\) | −1.30902 | + | 0.951057i | −0.0838012 | + | 0.0608852i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 2.92705 | + | 2.12663i | 0.186622 | + | 0.135589i | ||||
\(247\) | 4.08174 | − | 5.61803i | 0.259715 | − | 0.357467i | ||||
\(248\) | 7.88597 | + | 2.56231i | 0.500759 | + | 0.162707i | ||||
\(249\) | −12.4721 | −0.790390 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −9.05573 | −0.571592 | −0.285796 | − | 0.958290i | \(-0.592258\pi\) | ||||
−0.285796 | + | 0.958290i | \(0.592258\pi\) | |||||||
\(252\) | 4.25325 | + | 1.38197i | 0.267930 | + | 0.0870557i | ||||
\(253\) | 3.24920 | − | 4.47214i | 0.204275 | − | 0.281161i | ||||
\(254\) | −3.00000 | − | 2.17963i | −0.188237 | − | 0.136762i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 13.7533 | − | 9.99235i | 0.859581 | − | 0.624522i | ||||
\(257\) | 11.7984i | 0.735962i | 0.929833 | + | 0.367981i | \(0.119951\pi\) | ||||
−0.929833 | + | 0.367981i | \(0.880049\pi\) | |||||||
\(258\) | 4.53077 | + | 6.23607i | 0.282073 | + | 0.388241i | ||||
\(259\) | −4.27051 | − | 13.1433i | −0.265357 | − | 0.816684i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 2.04508 | − | 6.29412i | 0.126588 | − | 0.389597i | ||||
\(262\) | 7.77997 | − | 2.52786i | 0.480648 | − | 0.156172i | ||||
\(263\) | −22.7194 | + | 7.38197i | −1.40094 | + | 0.455192i | −0.909493 | − | 0.415719i | \(-0.863530\pi\) |
−0.491442 | + | 0.870910i | \(0.663530\pi\) | |||||||
\(264\) | −1.14590 | + | 3.52671i | −0.0705251 | + | 0.217054i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −1.70820 | − | 5.25731i | −0.104737 | − | 0.322346i | ||||
\(267\) | −3.16344 | − | 4.35410i | −0.193599 | − | 0.266467i | ||||
\(268\) | 0.763932i | 0.0466646i | ||||||||
\(269\) | −5.54508 | + | 4.02874i | −0.338090 | + | 0.245637i | −0.743855 | − | 0.668341i | \(-0.767005\pi\) |
0.405766 | + | 0.913977i | \(0.367005\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 0.145898 | + | 0.106001i | 0.00886267 | + | 0.00643911i | 0.592208 | − | 0.805785i | \(-0.298256\pi\) |
−0.583345 | + | 0.812224i | \(0.698256\pi\) | |||||||
\(272\) | −2.26538 | + | 3.11803i | −0.137359 | + | 0.189059i | ||||
\(273\) | 23.8949 | + | 7.76393i | 1.44619 | + | 0.469895i | ||||
\(274\) | 7.61803 | 0.460222 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −4.47214 | −0.269191 | ||||||||
\(277\) | 17.8783 | + | 5.80902i | 1.07420 | + | 0.349030i | 0.792124 | − | 0.610361i | \(-0.208976\pi\) |
0.282080 | + | 0.959391i | \(0.408976\pi\) | |||||||
\(278\) | 13.4863 | − | 18.5623i | 0.808855 | − | 1.11329i | ||||
\(279\) | 2.23607 | + | 1.62460i | 0.133870 | + | 0.0972622i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 15.8713 | − | 11.5312i | 0.946804 | − | 0.687893i | −0.00324500 | − | 0.999995i | \(-0.501033\pi\) |
0.950049 | + | 0.312102i | \(0.101033\pi\) | |||||||
\(282\) | − | 0.763932i | − | 0.0454915i | ||||||
\(283\) | 8.05748 | + | 11.0902i | 0.478967 | + | 0.659242i | 0.978306 | − | 0.207165i | \(-0.0664236\pi\) |
−0.499339 | + | 0.866407i | \(0.666424\pi\) | |||||||
\(284\) | −1.61803 | − | 4.97980i | −0.0960127 | − | 0.295497i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −2.14590 | + | 6.60440i | −0.126890 | + | 0.390526i | ||||
\(287\) | −15.3884 | + | 5.00000i | −0.908350 | + | 0.295141i | ||||
\(288\) | 4.75528 | − | 1.54508i | 0.280208 | − | 0.0910450i | ||||
\(289\) | 0.663119 | − | 2.04087i | 0.0390070 | − | 0.120051i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0.663119 | + | 2.04087i | 0.0388727 | + | 0.119638i | ||||
\(292\) | −4.75528 | − | 6.54508i | −0.278282 | − | 0.383022i | ||||
\(293\) | 20.7984i | 1.21505i | 0.794299 | + | 0.607527i | \(0.207838\pi\) | ||||
−0.794299 | + | 0.607527i | \(0.792162\pi\) | |||||||
\(294\) | 10.5172 | − | 7.64121i | 0.613377 | − | 0.445644i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −7.50000 | − | 5.44907i | −0.435929 | − | 0.316721i | ||||
\(297\) | −0.726543 | + | 1.00000i | −0.0421583 | + | 0.0580259i | ||||
\(298\) | 17.9313 | + | 5.82624i | 1.03873 | + | 0.337505i | ||||
\(299\) | −25.1246 | −1.45299 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −34.4721 | −1.98694 | ||||||||
\(302\) | 7.15942 | + | 2.32624i | 0.411979 | + | 0.133860i | ||||
\(303\) | −2.09387 | + | 2.88197i | −0.120290 | + | 0.165565i | ||||
\(304\) | −1.00000 | − | 0.726543i | −0.0573539 | − | 0.0416701i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −3.11803 | + | 2.26538i | −0.178246 | + | 0.129503i | ||||
\(307\) | 32.6525i | 1.86358i | 0.363004 | + | 0.931788i | \(0.381751\pi\) | ||||
−0.363004 | + | 0.931788i | \(0.618249\pi\) | |||||||
\(308\) | −3.24920 | − | 4.47214i | −0.185140 | − | 0.254824i | ||||
\(309\) | −1.00000 | − | 3.07768i | −0.0568880 | − | 0.175083i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 5.47214 | − | 16.8415i | 0.310296 | − | 0.954994i | −0.667351 | − | 0.744743i | \(-0.732572\pi\) |
0.977647 | − | 0.210251i | \(-0.0674280\pi\) | |||||||
\(312\) | 16.0292 | − | 5.20820i | 0.907475 | − | 0.294856i | ||||
\(313\) | −0.449028 | + | 0.145898i | −0.0253806 | + | 0.00824664i | −0.321680 | − | 0.946849i | \(-0.604247\pi\) |
0.296299 | + | 0.955095i | \(0.404247\pi\) | |||||||
\(314\) | −3.33688 | + | 10.2699i | −0.188311 | + | 0.579562i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −16.9475 | − | 23.3262i | −0.951867 | − | 1.31013i | −0.950693 | − | 0.310133i | \(-0.899627\pi\) |
−0.00117338 | − | 0.999999i | \(-0.500373\pi\) | |||||||
\(318\) | − | 3.61803i | − | 0.202889i | ||||||
\(319\) | −6.61803 | + | 4.80828i | −0.370539 | + | 0.269212i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −6.09017 | − | 4.42477i | −0.339920 | − | 0.246966i | ||||
\(322\) | −11.7557 | + | 16.1803i | −0.655120 | + | 0.901695i | ||||
\(323\) | −4.53077 | − | 1.47214i | −0.252099 | − | 0.0819118i | ||||
\(324\) | 1.00000 | 0.0555556 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −14.9443 | −0.827687 | ||||||||
\(327\) | −7.52270 | − | 2.44427i | −0.416006 | − | 0.135169i | ||||
\(328\) | −6.37988 | + | 8.78115i | −0.352270 | + | 0.484858i | ||||
\(329\) | 2.76393 | + | 2.00811i | 0.152381 | + | 0.110711i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 5.61803 | − | 4.08174i | 0.308795 | − | 0.224353i | −0.422584 | − | 0.906324i | \(-0.638877\pi\) |
0.731379 | + | 0.681971i | \(0.238877\pi\) | |||||||
\(332\) | − | 12.4721i | − | 0.684497i | ||||||
\(333\) | −1.81636 | − | 2.50000i | −0.0995357 | − | 0.136999i | ||||
\(334\) | −1.05573 | − | 3.24920i | −0.0577669 | − | 0.177788i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 1.38197 | − | 4.25325i | 0.0753924 | − | 0.232034i | ||||
\(337\) | −2.80017 | + | 0.909830i | −0.152535 | + | 0.0495616i | −0.384289 | − | 0.923213i | \(-0.625553\pi\) |
0.231754 | + | 0.972774i | \(0.425553\pi\) | |||||||
\(338\) | 17.6538 | − | 5.73607i | 0.960240 | − | 0.312001i | ||||
\(339\) | −5.66312 | + | 17.4293i | −0.307578 | + | 0.946629i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −1.05573 | − | 3.24920i | −0.0571709 | − | 0.175954i | ||||
\(342\) | −0.726543 | − | 1.00000i | −0.0392869 | − | 0.0540738i | ||||
\(343\) | 26.8328i | 1.44884i | ||||||||
\(344\) | −18.7082 | + | 13.5923i | −1.00868 | + | 0.732848i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −17.0623 | − | 12.3965i | −0.917275 | − | 0.666439i | ||||
\(347\) | −11.9272 | + | 16.4164i | −0.640287 | + | 0.881279i | −0.998631 | − | 0.0523106i | \(-0.983341\pi\) |
0.358344 | + | 0.933590i | \(0.383341\pi\) | |||||||
\(348\) | 6.29412 | + | 2.04508i | 0.337400 | + | 0.109628i | ||||
\(349\) | 4.03444 | 0.215959 | 0.107979 | − | 0.994153i | \(-0.465562\pi\) | ||||
0.107979 | + | 0.994153i | \(0.465562\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 5.61803 | 0.299868 | ||||||||
\(352\) | −5.87785 | − | 1.90983i | −0.313291 | − | 0.101794i | ||||
\(353\) | −8.44100 | + | 11.6180i | −0.449269 | + | 0.618366i | −0.972240 | − | 0.233985i | \(-0.924823\pi\) |
0.522971 | + | 0.852350i | \(0.324823\pi\) | |||||||
\(354\) | −3.23607 | − | 2.35114i | −0.171995 | − | 0.124962i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 4.35410 | − | 3.16344i | 0.230767 | − | 0.167662i | ||||
\(357\) | − | 17.2361i | − | 0.912229i | ||||||
\(358\) | −9.51057 | − | 13.0902i | −0.502649 | − | 0.691837i | ||||
\(359\) | 11.5623 | + | 35.5851i | 0.610235 | + | 1.87811i | 0.455728 | + | 0.890119i | \(0.349379\pi\) |
0.154507 | + | 0.987992i | \(0.450621\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −5.39919 | + | 16.6170i | −0.284168 | + | 0.874578i | ||||
\(362\) | −14.0741 | + | 4.57295i | −0.739718 | + | 0.240349i | ||||
\(363\) | −9.00854 | + | 2.92705i | −0.472826 | + | 0.153630i | ||||
\(364\) | −7.76393 | + | 23.8949i | −0.406941 | + | 1.25243i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0.500000 | + | 1.53884i | 0.0261354 | + | 0.0804365i | ||||
\(367\) | 3.52671 | + | 4.85410i | 0.184093 | + | 0.253382i | 0.891082 | − | 0.453842i | \(-0.149947\pi\) |
−0.706989 | + | 0.707224i | \(0.749947\pi\) | |||||||
\(368\) | 4.47214i | 0.233126i | ||||||||
\(369\) | −2.92705 | + | 2.12663i | −0.152376 | + | 0.110708i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 13.0902 | + | 9.51057i | 0.679608 | + | 0.493764i | ||||
\(372\) | −1.62460 | + | 2.23607i | −0.0842315 | + | 0.115935i | ||||
\(373\) | −2.45714 | − | 0.798374i | −0.127226 | − | 0.0413382i | 0.244712 | − | 0.969596i | \(-0.421307\pi\) |
−0.371938 | + | 0.928258i | \(0.621307\pi\) | |||||||
\(374\) | 4.76393 | 0.246337 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 2.29180 | 0.118190 | ||||||||
\(377\) | 35.3606 | + | 11.4894i | 1.82116 | + | 0.591732i | ||||
\(378\) | 2.62866 | − | 3.61803i | 0.135203 | − | 0.186092i | ||||
\(379\) | −2.76393 | − | 2.00811i | −0.141974 | − | 0.103150i | 0.514531 | − | 0.857472i | \(-0.327966\pi\) |
−0.656505 | + | 0.754322i | \(0.727966\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 3.00000 | − | 2.17963i | 0.153695 | − | 0.111666i | ||||
\(382\) | 6.65248i | 0.340370i | ||||||||
\(383\) | −19.2986 | − | 26.5623i | −0.986115 | − | 1.35727i | −0.933469 | − | 0.358657i | \(-0.883235\pi\) |
−0.0526453 | − | 0.998613i | \(-0.516765\pi\) | |||||||
\(384\) | 0.927051 | + | 2.85317i | 0.0473084 | + | 0.145600i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 7.20820 | − | 22.1846i | 0.366888 | − | 1.12916i | ||||
\(387\) | −7.33094 | + | 2.38197i | −0.372652 | + | 0.121082i | ||||
\(388\) | −2.04087 | + | 0.663119i | −0.103609 | + | 0.0336648i | ||||
\(389\) | 8.00658 | − | 24.6417i | 0.405950 | − | 1.24938i | −0.514150 | − | 0.857700i | \(-0.671893\pi\) |
0.920100 | − | 0.391684i | \(-0.128107\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 5.32624 | + | 16.3925i | 0.269359 | + | 0.829003i | ||||
\(392\) | 22.9236 | + | 31.5517i | 1.15782 | + | 1.59360i | ||||
\(393\) | 8.18034i | 0.412644i | ||||||||
\(394\) | 6.16312 | − | 4.47777i | 0.310493 | − | 0.225587i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −1.00000 | − | 0.726543i | −0.0502519 | − | 0.0365101i | ||||
\(397\) | −4.08174 | + | 5.61803i | −0.204857 | + | 0.281961i | −0.899067 | − | 0.437811i | \(-0.855754\pi\) |
0.694210 | + | 0.719772i | \(0.255754\pi\) | |||||||
\(398\) | −12.0332 | − | 3.90983i | −0.603171 | − | 0.195982i | ||||
\(399\) | 5.52786 | 0.276739 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −22.4508 | −1.12114 | −0.560571 | − | 0.828106i | \(-0.689418\pi\) | ||||
−0.560571 | + | 0.828106i | \(0.689418\pi\) | |||||||
\(402\) | 0.726543 | + | 0.236068i | 0.0362366 | + | 0.0117740i | ||||
\(403\) | −9.12705 | + | 12.5623i | −0.454651 | + | 0.625773i | ||||
\(404\) | −2.88197 | − | 2.09387i | −0.143383 | − | 0.104174i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 23.9443 | − | 17.3965i | 1.18833 | − | 0.863375i | ||||
\(407\) | 3.81966i | 0.189334i | ||||||||
\(408\) | −6.79615 | − | 9.35410i | −0.336460 | − | 0.463097i | ||||
\(409\) | −0.371323 | − | 1.14281i | −0.0183607 | − | 0.0565085i | 0.941456 | − | 0.337135i | \(-0.109458\pi\) |
−0.959817 | + | 0.280626i | \(0.909458\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −2.35410 | + | 7.24518i | −0.116119 | + | 0.357378i | ||||
\(412\) | 3.07768 | − | 1.00000i | 0.151627 | − | 0.0492665i | ||||
\(413\) | 17.0130 | − | 5.52786i | 0.837156 | − | 0.272008i | ||||
\(414\) | −1.38197 | + | 4.25325i | −0.0679199 | + | 0.209036i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 8.68034 | + | 26.7153i | 0.425589 | + | 1.30983i | ||||
\(417\) | 13.4863 | + | 18.5623i | 0.660427 | + | 0.909000i | ||||
\(418\) | 1.52786i | 0.0747303i | ||||||||
\(419\) | 12.1803 | − | 8.84953i | 0.595049 | − | 0.432328i | −0.249069 | − | 0.968486i | \(-0.580125\pi\) |
0.844118 | + | 0.536158i | \(0.180125\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −24.1525 | − | 17.5478i | −1.17712 | − | 0.855227i | −0.185276 | − | 0.982687i | \(-0.559318\pi\) |
−0.991844 | + | 0.127459i | \(0.959318\pi\) | |||||||
\(422\) | 10.5146 | − | 14.4721i | 0.511844 | − | 0.704493i | ||||
\(423\) | 0.726543 | + | 0.236068i | 0.0353257 | + | 0.0114780i | ||||
\(424\) | 10.8541 | 0.527122 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −5.23607 | −0.253688 | ||||||||
\(427\) | −6.88191 | − | 2.23607i | −0.333039 | − | 0.108211i | ||||
\(428\) | 4.42477 | − | 6.09017i | 0.213879 | − | 0.294379i | ||||
\(429\) | −5.61803 | − | 4.08174i | −0.271241 | − | 0.197068i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −16.7082 | + | 12.1392i | −0.804806 | + | 0.584726i | −0.912320 | − | 0.409478i | \(-0.865711\pi\) |
0.107514 | + | 0.994204i | \(0.465711\pi\) | |||||||
\(432\) | − | 1.00000i | − | 0.0481125i | ||||||
\(433\) | −12.9188 | − | 17.7812i | −0.620836 | − | 0.854508i | 0.376577 | − | 0.926385i | \(-0.377101\pi\) |
−0.997413 | + | 0.0718775i | \(0.977101\pi\) | |||||||
\(434\) | 3.81966 | + | 11.7557i | 0.183350 | + | 0.564292i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 2.44427 | − | 7.52270i | 0.117059 | − | 0.360272i | ||||
\(437\) | −5.25731 | + | 1.70820i | −0.251491 | + | 0.0817145i | ||||
\(438\) | −7.69421 | + | 2.50000i | −0.367644 | + | 0.119455i | ||||
\(439\) | −5.00000 | + | 15.3884i | −0.238637 | + | 0.734449i | 0.757981 | + | 0.652276i | \(0.226186\pi\) |
−0.996618 | + | 0.0821726i | \(0.973814\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 4.01722 | + | 12.3637i | 0.191296 | + | 0.588749i | ||||
\(442\) | −12.7270 | − | 17.5172i | −0.605362 | − | 0.833209i | ||||
\(443\) | 35.2361i | 1.67412i | 0.547114 | + | 0.837058i | \(0.315726\pi\) | ||||
−0.547114 | + | 0.837058i | \(0.684274\pi\) | |||||||
\(444\) | 2.50000 | − | 1.81636i | 0.118645 | − | 0.0862005i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −6.61803 | − | 4.80828i | −0.313373 | − | 0.227679i | ||||
\(447\) | −11.0822 | + | 15.2533i | −0.524168 | + | 0.721456i | ||||
\(448\) | 29.7728 | + | 9.67376i | 1.40663 | + | 0.457042i | ||||
\(449\) | −16.7984 | −0.792764 | −0.396382 | − | 0.918086i | \(-0.629734\pi\) | ||||
−0.396382 | + | 0.918086i | \(0.629734\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 4.47214 | 0.210585 | ||||||||
\(452\) | −17.4293 | − | 5.66312i | −0.819805 | − | 0.266371i | ||||
\(453\) | −4.42477 | + | 6.09017i | −0.207894 | + | 0.286141i | ||||
\(454\) | −16.1803 | − | 11.7557i | −0.759381 | − | 0.551723i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 3.00000 | − | 2.17963i | 0.140488 | − | 0.102070i | ||||
\(457\) | − | 22.3607i | − | 1.04599i | −0.852336 | − | 0.522994i | \(-0.824815\pi\) | ||
0.852336 | − | 0.522994i | \(-0.175185\pi\) | |||||||
\(458\) | 12.9188 | + | 17.7812i | 0.603654 | + | 0.830859i | ||||
\(459\) | −1.19098 | − | 3.66547i | −0.0555903 | − | 0.171089i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −10.1353 | + | 31.1931i | −0.472046 | + | 1.45281i | 0.377855 | + | 0.925865i | \(0.376662\pi\) |
−0.849901 | + | 0.526943i | \(0.823338\pi\) | |||||||
\(462\) | −5.25731 | + | 1.70820i | −0.244592 | + | 0.0794728i | ||||
\(463\) | 17.8456 | − | 5.79837i | 0.829353 | − | 0.269473i | 0.136580 | − | 0.990629i | \(-0.456389\pi\) |
0.692773 | + | 0.721156i | \(0.256389\pi\) | |||||||
\(464\) | 2.04508 | − | 6.29412i | 0.0949407 | − | 0.292197i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 3.82624 | + | 11.7759i | 0.177247 | + | 0.545510i | ||||
\(467\) | −16.5640 | − | 22.7984i | −0.766490 | − | 1.05498i | −0.996646 | − | 0.0818293i | \(-0.973924\pi\) |
0.230156 | − | 0.973154i | \(-0.426076\pi\) | |||||||
\(468\) | 5.61803i | 0.259694i | ||||||||
\(469\) | −2.76393 | + | 2.00811i | −0.127627 | + | 0.0927261i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −8.73607 | − | 6.34712i | −0.402537 | − | 0.292460i | ||||
\(472\) | 7.05342 | − | 9.70820i | 0.324660 | − | 0.446856i | ||||
\(473\) | 9.06154 | + | 2.94427i | 0.416650 | + | 0.135378i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 17.2361 | 0.790014 | ||||||||
\(477\) | 3.44095 | + | 1.11803i | 0.157550 | + | 0.0511913i | ||||
\(478\) | 14.6619 | − | 20.1803i | 0.670619 | − | 0.923027i | ||||
\(479\) | 15.3262 | + | 11.1352i | 0.700274 | + | 0.508779i | 0.880021 | − | 0.474934i | \(-0.157528\pi\) |
−0.179748 | + | 0.983713i | \(0.557528\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 14.0451 | − | 10.2044i | 0.640401 | − | 0.465278i | ||||
\(482\) | 28.0344i | 1.27693i | ||||||||
\(483\) | −11.7557 | − | 16.1803i | −0.534903 | − | 0.736231i | ||||
\(484\) | −2.92705 | − | 9.00854i | −0.133048 | − | 0.409479i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0.309017 | − | 0.951057i | 0.0140173 | − | 0.0431408i | ||||
\(487\) | −9.23305 | + | 3.00000i | −0.418389 | + | 0.135943i | −0.510644 | − | 0.859793i | \(-0.670593\pi\) |
0.0922541 | + | 0.995736i | \(0.470593\pi\) | |||||||
\(488\) | −4.61653 | + | 1.50000i | −0.208980 | + | 0.0679018i | ||||
\(489\) | 4.61803 | − | 14.2128i | 0.208835 | − | 0.642727i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 1.81966 | + | 5.60034i | 0.0821201 | + | 0.252740i | 0.983684 | − | 0.179907i | \(-0.0575797\pi\) |
−0.901563 | + | 0.432647i | \(0.857580\pi\) | |||||||
\(492\) | −2.12663 | − | 2.92705i | −0.0958758 | − | 0.131962i | ||||
\(493\) | − | 25.5066i | − | 1.14876i | ||||||
\(494\) | 5.61803 | − | 4.08174i | 0.252767 | − | 0.183646i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 2.23607 | + | 1.62460i | 0.100402 | + | 0.0729466i | ||||
\(497\) | 13.7638 | − | 18.9443i | 0.617392 | − | 0.849767i | ||||
\(498\) | −11.8617 | − | 3.85410i | −0.531536 | − | 0.172706i | ||||
\(499\) | 6.00000 | 0.268597 | 0.134298 | − | 0.990941i | \(-0.457122\pi\) | ||||
0.134298 | + | 0.990941i | \(0.457122\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 3.41641 | 0.152634 | ||||||||
\(502\) | −8.61251 | − | 2.79837i | −0.384395 | − | 0.124898i | ||||
\(503\) | −5.04531 | + | 6.94427i | −0.224959 | + | 0.309630i | −0.906546 | − | 0.422108i | \(-0.861290\pi\) |
0.681586 | + | 0.731738i | \(0.261290\pi\) | |||||||
\(504\) | 10.8541 | + | 7.88597i | 0.483480 | + | 0.351269i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 4.47214 | − | 3.24920i | 0.198811 | − | 0.144444i | ||||
\(507\) | 18.5623i | 0.824381i | ||||||||
\(508\) | 2.17963 | + | 3.00000i | 0.0967053 | + | 0.133103i | ||||
\(509\) | −6.22542 | − | 19.1599i | −0.275937 | − | 0.849247i | −0.988970 | − | 0.148116i | \(-0.952679\pi\) |
0.713033 | − | 0.701131i | \(-0.247321\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 11.1803 | − | 34.4095i | 0.494589 | − | 1.52219i | ||||
\(512\) | 10.4616 | − | 3.39919i | 0.462343 | − | 0.150224i | ||||
\(513\) | 1.17557 | − | 0.381966i | 0.0519027 | − | 0.0168642i | ||||
\(514\) | −3.64590 | + | 11.2209i | −0.160814 | + | 0.494934i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −2.38197 | − | 7.33094i | −0.104860 | − | 0.322727i | ||||
\(517\) | −0.555029 | − | 0.763932i | −0.0244102 | − | 0.0335977i | ||||
\(518\) | − | 13.8197i | − | 0.607201i | ||||||
\(519\) | 17.0623 | − | 12.3965i | 0.748952 | − | 0.544146i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 21.8713 | + | 15.8904i | 0.958200 | + | 0.696173i | 0.952732 | − | 0.303812i | \(-0.0982595\pi\) |
0.00546804 | + | 0.999985i | \(0.498259\pi\) | |||||||
\(522\) | 3.88998 | − | 5.35410i | 0.170260 | − | 0.234343i | ||||
\(523\) | 24.4500 | + | 7.94427i | 1.06912 | + | 0.347379i | 0.790146 | − | 0.612919i | \(-0.210005\pi\) |
0.278976 | + | 0.960298i | \(0.410005\pi\) | |||||||
\(524\) | −8.18034 | −0.357360 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −23.8885 | −1.04159 | ||||||||
\(527\) | 10.1311 | + | 3.29180i | 0.441318 | + | 0.143393i | ||||
\(528\) | −0.726543 | + | 1.00000i | −0.0316187 | + | 0.0435194i | ||||
\(529\) | −2.42705 | − | 1.76336i | −0.105524 | − | 0.0766676i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 3.23607 | − | 2.35114i | 0.140433 | − | 0.102031i | ||||
\(532\) | 5.52786i | 0.239663i | ||||||||
\(533\) | −11.9475 | − | 16.4443i | −0.517502 | − | 0.712280i | ||||
\(534\) | −1.66312 | − | 5.11855i | −0.0719702 | − | 0.221501i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −0.708204 | + | 2.17963i | −0.0305898 | + | 0.0941456i | ||||
\(537\) | 15.3884 | − | 5.00000i | 0.664059 | − | 0.215766i | ||||
\(538\) | −6.51864 | + | 2.11803i | −0.281038 | + | 0.0913149i | ||||
\(539\) | 4.96556 | − | 15.2824i | 0.213882 | − | 0.658260i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −6.07953 | − | 18.7109i | −0.261379 | − | 0.804443i | −0.992505 | − | 0.122200i | \(-0.961005\pi\) |
0.731126 | − | 0.682242i | \(-0.238995\pi\) | |||||||
\(542\) | 0.106001 | + | 0.145898i | 0.00455314 | + | 0.00626686i | ||||
\(543\) | − | 14.7984i | − | 0.635059i | ||||||
\(544\) | 15.5902 | − | 11.3269i | 0.668423 | − | 0.485638i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 20.3262 | + | 14.7679i | 0.869883 | + | 0.632007i | ||||
\(547\) | 24.8990 | − | 34.2705i | 1.06460 | − | 1.46530i | 0.189181 | − | 0.981942i | \(-0.439417\pi\) |
0.875422 | − | 0.483359i | \(-0.160583\pi\) | |||||||
\(548\) | −7.24518 | − | 2.35410i | −0.309499 | − | 0.100562i | ||||
\(549\) | −1.61803 | −0.0690560 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 8.18034 | 0.348494 | ||||||||
\(552\) | −12.7598 | − | 4.14590i | −0.543092 | − | 0.176461i | ||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 15.2082 | + | 11.0494i | 0.646135 | + | 0.469444i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −18.5623 | + | 13.4863i | −0.787217 | + | 0.571947i | ||||
\(557\) | − | 11.2705i | − | 0.477547i | −0.971075 | − | 0.238773i | \(-0.923255\pi\) | ||
0.971075 | − | 0.238773i | \(-0.0767453\pi\) | |||||||
\(558\) | 1.62460 | + | 2.23607i | 0.0687747 | + | 0.0946603i | ||||
\(559\) | −13.3820 | − | 41.1855i | −0.565997 | − | 1.74196i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −1.47214 | + | 4.53077i | −0.0621536 | + | 0.191289i | ||||
\(562\) | 18.6579 | − | 6.06231i | 0.787034 | − | 0.255723i | ||||
\(563\) | −25.1765 | + | 8.18034i | −1.06106 | + | 0.344760i | −0.787001 | − | 0.616952i | \(-0.788367\pi\) |
−0.274062 | + | 0.961712i | \(0.588367\pi\) | |||||||
\(564\) | −0.236068 | + | 0.726543i | −0.00994026 | + | 0.0305930i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 4.23607 | + | 13.0373i | 0.178055 | + | 0.547998i | ||||
\(567\) | 2.62866 | + | 3.61803i | 0.110393 | + | 0.151943i | ||||
\(568\) | − | 15.7082i | − | 0.659102i | ||||||
\(569\) | 2.64590 | − | 1.92236i | 0.110922 | − | 0.0805894i | −0.530942 | − | 0.847408i | \(-0.678162\pi\) |
0.641863 | + | 0.766819i | \(0.278162\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 13.5623 | + | 9.85359i | 0.567565 | + | 0.412360i | 0.834220 | − | 0.551432i | \(-0.185918\pi\) |
−0.266655 | + | 0.963792i | \(0.585918\pi\) | |||||||
\(572\) | 4.08174 | − | 5.61803i | 0.170666 | − | 0.234902i | ||||
\(573\) | −6.32688 | − | 2.05573i | −0.264309 | − | 0.0858793i | ||||
\(574\) | −16.1803 | −0.675354 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 7.00000 | 0.291667 | ||||||||
\(577\) | −12.4167 | − | 4.03444i | −0.516915 | − | 0.167956i | 0.0389296 | − | 0.999242i | \(-0.487605\pi\) |
−0.555845 | + | 0.831286i | \(0.687605\pi\) | |||||||
\(578\) | 1.26133 | − | 1.73607i | 0.0524643 | − | 0.0722109i | ||||
\(579\) | 18.8713 | + | 13.7108i | 0.784265 | + | 0.569802i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 45.1246 | − | 32.7849i | 1.87208 | − | 1.36015i | ||||
\(582\) | 2.14590i | 0.0889503i | ||||||||
\(583\) | −2.62866 | − | 3.61803i | −0.108868 | − | 0.149844i | ||||
\(584\) | −7.50000 | − | 23.0826i | −0.310352 | − | 0.955166i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −6.42705 | + | 19.7804i | −0.265499 | + | 0.817122i | ||||
\(587\) | 39.3893 | − | 12.7984i | 1.62577 | − | 0.528245i | 0.652478 | − | 0.757807i | \(-0.273729\pi\) |
0.973294 | + | 0.229562i | \(0.0737294\pi\) | |||||||
\(588\) | −12.3637 | + | 4.01722i | −0.509872 | + | 0.165667i | ||||
\(589\) | −1.05573 | + | 3.24920i | −0.0435005 | + | 0.133881i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 2.35410 | + | 7.24518i | 0.0968348 | + | 0.298027i | ||||
\(592\) | −1.81636 | − | 2.50000i | −0.0746518 | − | 0.102749i | ||||
\(593\) | − | 9.74265i | − | 0.400083i | −0.979787 | − | 0.200041i | \(-0.935892\pi\) | ||
0.979787 | − | 0.200041i | \(-0.0641076\pi\) | |||||||
\(594\) | −1.00000 | + | 0.726543i | −0.0410305 | + | 0.0298104i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −15.2533 | − | 11.0822i | −0.624799 | − | 0.453943i | ||||
\(597\) | 7.43694 | − | 10.2361i | 0.304374 | − | 0.418934i | ||||
\(598\) | −23.8949 | − | 7.76393i | −0.977136 | − | 0.317491i | ||||
\(599\) | 3.52786 | 0.144145 | 0.0720723 | − | 0.997399i | \(-0.477039\pi\) | ||||
0.0720723 | + | 0.997399i | \(0.477039\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −8.67376 | −0.353810 | −0.176905 | − | 0.984228i | \(-0.556609\pi\) | ||||
−0.176905 | + | 0.984228i | \(0.556609\pi\) | |||||||
\(602\) | −32.7849 | − | 10.6525i | −1.33621 | − | 0.434163i | ||||
\(603\) | −0.449028 | + | 0.618034i | −0.0182858 | + | 0.0251683i | ||||
\(604\) | −6.09017 | − | 4.42477i | −0.247806 | − | 0.180041i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −2.88197 | + | 2.09387i | −0.117072 | + | 0.0850577i | ||||
\(607\) | − | 34.7639i | − | 1.41102i | −0.708698 | − | 0.705512i | \(-0.750717\pi\) | ||
0.708698 | − | 0.705512i | \(-0.249283\pi\) | |||||||
\(608\) | 3.63271 | + | 5.00000i | 0.147326 | + | 0.202777i | ||||
\(609\) | 9.14590 | + | 28.1482i | 0.370610 | + | 1.14062i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −1.32624 | + | 4.08174i | −0.0536538 | + | 0.165130i | ||||
\(612\) | 3.66547 | − | 1.19098i | 0.148168 | − | 0.0481426i | ||||
\(613\) | 1.42033 | − | 0.461493i | 0.0573665 | − | 0.0186395i | −0.280193 | − | 0.959944i | \(-0.590399\pi\) |
0.337560 | + | 0.941304i | \(0.390399\pi\) | |||||||
\(614\) | −10.0902 | + | 31.0543i | −0.407206 | + | 1.25325i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −5.12461 | − | 15.7719i | −0.206476 | − | 0.635469i | ||||
\(617\) | 11.7432 | + | 16.1631i | 0.472763 | + | 0.650703i | 0.977094 | − | 0.212808i | \(-0.0682608\pi\) |
−0.504331 | + | 0.863510i | \(0.668261\pi\) | |||||||
\(618\) | − | 3.23607i | − | 0.130174i | ||||||
\(619\) | −13.2361 | + | 9.61657i | −0.532002 | + | 0.386522i | −0.821106 | − | 0.570775i | \(-0.806643\pi\) |
0.289104 | + | 0.957298i | \(0.406643\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −3.61803 | − | 2.62866i | −0.145187 | − | 0.105484i | ||||
\(622\) | 10.4086 | − | 14.3262i | 0.417348 | − | 0.574430i | ||||
\(623\) | 22.8909 | + | 7.43769i | 0.917103 | + | 0.297985i | ||||
\(624\) | 5.61803 | 0.224901 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −0.472136 | −0.0188703 | ||||||||
\(627\) | −1.45309 | − | 0.472136i | −0.0580306 | − | 0.0188553i | ||||
\(628\) | 6.34712 | − | 8.73607i | 0.253278 | − | 0.348607i | ||||
\(629\) | −9.63525 | − | 7.00042i | −0.384183 | − | 0.279125i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −19.1803 | + | 13.9353i | −0.763557 | + | 0.554757i | −0.899999 | − | 0.435891i | \(-0.856433\pi\) |
0.136442 | + | 0.990648i | \(0.456433\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 10.5146 | + | 14.4721i | 0.417919 | + | 0.575216i | ||||
\(634\) | −8.90983 | − | 27.4216i | −0.353855 | − | 1.08905i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −1.11803 | + | 3.44095i | −0.0443329 | + | 0.136443i | ||||
\(637\) | −69.4599 | + | 22.5689i | −2.75210 | + | 0.894212i | ||||
\(638\) | −7.77997 | + | 2.52786i | −0.308012 | + | 0.100079i | ||||
\(639\) | 1.61803 | − | 4.97980i | 0.0640084 | − | 0.196998i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 6.50658 | + | 20.0252i | 0.256994 | + | 0.790947i | 0.993430 | + | 0.114440i | \(0.0365073\pi\) |
−0.736436 | + | 0.676507i | \(0.763493\pi\) | |||||||
\(642\) | −4.42477 | − | 6.09017i | −0.174632 | − | 0.240360i | ||||
\(643\) | 21.8885i | 0.863200i | 0.902065 | + | 0.431600i | \(0.142051\pi\) | ||||
−0.902065 | + | 0.431600i | \(0.857949\pi\) | |||||||
\(644\) | 16.1803 | − | 11.7557i | 0.637595 | − | 0.463240i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −3.85410 | − | 2.80017i | −0.151638 | − | 0.110171i | ||||
\(647\) | −20.1967 | + | 27.7984i | −0.794014 | + | 1.09287i | 0.199582 | + | 0.979881i | \(0.436041\pi\) |
−0.993597 | + | 0.112986i | \(0.963959\pi\) | |||||||
\(648\) | 2.85317 | + | 0.927051i | 0.112083 | + | 0.0364180i | ||||
\(649\) | −4.94427 | −0.194080 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −12.3607 | −0.484453 | ||||||||
\(652\) | 14.2128 | + | 4.61803i | 0.556618 | + | 0.180856i | ||||
\(653\) | 24.7477 | − | 34.0623i | 0.968453 | − | 1.33296i | 0.0256283 | − | 0.999672i | \(-0.491841\pi\) |
0.942825 | − | 0.333289i | \(-0.108159\pi\) | |||||||
\(654\) | −6.39919 | − | 4.64928i | −0.250228 | − | 0.181801i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −2.92705 | + | 2.12663i | −0.114282 | + | 0.0830308i | ||||
\(657\) | − | 8.09017i | − | 0.315628i | ||||||
\(658\) | 2.00811 | + | 2.76393i | 0.0782844 | + | 0.107749i | ||||
\(659\) | 10.3262 | + | 31.7809i | 0.402253 | + | 1.23801i | 0.923167 | + | 0.384399i | \(0.125591\pi\) |
−0.520914 | + | 0.853609i | \(0.674409\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −0.437694 | + | 1.34708i | −0.0170243 | + | 0.0523955i | −0.959208 | − | 0.282702i | \(-0.908769\pi\) |
0.942183 | + | 0.335097i | \(0.108769\pi\) | |||||||
\(662\) | 6.60440 | − | 2.14590i | 0.256687 | − | 0.0834027i | ||||
\(663\) | 20.5927 | − | 6.69098i | 0.799755 | − | 0.259856i | ||||
\(664\) | 11.5623 | − | 35.5851i | 0.448704 | − | 1.38097i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −0.954915 | − | 2.93893i | −0.0370022 | − | 0.113881i | ||||
\(667\) | −17.3965 | − | 23.9443i | −0.673596 | − | 0.927126i | ||||
\(668\) | 3.41641i | 0.132185i | ||||||||
\(669\) | 6.61803 | − | 4.80828i | 0.255868 | − | 0.185899i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 1.61803 | + | 1.17557i | 0.0624635 | + | 0.0453824i | ||||
\(672\) | −13.1433 | + | 18.0902i | −0.507013 | + | 0.697843i | ||||
\(673\) | −4.94704 | − | 1.60739i | −0.190694 | − | 0.0619604i | 0.212113 | − | 0.977245i | \(-0.431966\pi\) |
−0.402807 | + | 0.915285i | \(0.631966\pi\) | |||||||
\(674\) | −2.94427 | −0.113409 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −18.5623 | −0.713935 | ||||||||
\(677\) | 10.0656 | + | 3.27051i | 0.386852 | + | 0.125696i | 0.495985 | − | 0.868331i | \(-0.334807\pi\) |
−0.109132 | + | 0.994027i | \(0.534807\pi\) | |||||||
\(678\) | −10.7719 | + | 14.8262i | −0.413692 | + | 0.569398i | ||||
\(679\) | −7.76393 | − | 5.64083i | −0.297952 | − | 0.216475i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 16.1803 | − | 11.7557i | 0.620032 | − | 0.450480i | ||||
\(682\) | − | 3.41641i | − | 0.130821i | ||||||
\(683\) | −11.4127 | − | 15.7082i | −0.436694 | − | 0.601058i | 0.532779 | − | 0.846254i | \(-0.321148\pi\) |
−0.969473 | + | 0.245196i | \(0.921148\pi\) | |||||||
\(684\) | 0.381966 | + | 1.17557i | 0.0146048 | + | 0.0449491i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −8.29180 | + | 25.5195i | −0.316582 | + | 0.974340i | ||||
\(687\) | −20.9030 | + | 6.79180i | −0.797499 | + | 0.259123i | ||||
\(688\) | −7.33094 | + | 2.38197i | −0.279489 | + | 0.0908116i | ||||
\(689\) | −6.28115 | + | 19.3314i | −0.239293 | + | 0.736468i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −5.18034 | − | 15.9434i | −0.197069 | − | 0.606517i | −0.999946 | − | 0.0103723i | \(-0.996698\pi\) |
0.802877 | − | 0.596145i | \(-0.203302\pi\) | |||||||
\(692\) | 12.3965 | + | 17.0623i | 0.471244 | + | 0.648612i | ||||
\(693\) | − | 5.52786i | − | 0.209986i | ||||||
\(694\) | −16.4164 | + | 11.9272i | −0.623158 | + | 0.452751i | ||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 16.0623 | + | 11.6699i | 0.608840 | + | 0.442348i | ||||
\(697\) | −8.19624 | + | 11.2812i | −0.310455 | + | 0.427304i | ||||
\(698\) | 3.83698 | + | 1.24671i | 0.145232 | + | 0.0471887i | ||||
\(699\) | −12.3820 | −0.468329 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 20.5623 | 0.776628 | 0.388314 | − | 0.921527i | \(-0.373058\pi\) | ||||
0.388314 | + | 0.921527i | \(0.373058\pi\) | |||||||
\(702\) | 5.34307 | + | 1.73607i | 0.201661 | + | 0.0655237i | ||||
\(703\) | 2.24514 | − | 3.09017i | 0.0846771 | − | 0.116548i | ||||
\(704\) | −7.00000 | − | 5.08580i | −0.263822 | − | 0.191678i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −11.6180 | + | 8.44100i | −0.437250 | + | 0.317681i | ||||
\(707\) | − | 15.9311i | − | 0.599151i | ||||||
\(708\) | 2.35114 | + | 3.23607i | 0.0883613 | + | 0.121619i | ||||
\(709\) | 12.4443 | + | 38.2995i | 0.467354 | + | 1.43837i | 0.855997 | + | 0.516981i | \(0.172944\pi\) |
−0.388643 | + | 0.921389i | \(0.627056\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 15.3557 | − | 4.98936i | 0.575478 | − | 0.186984i | ||||
\(713\) | 11.7557 | − | 3.81966i | 0.440255 | − | 0.143047i | ||||
\(714\) | 5.32624 | − | 16.3925i | 0.199329 | − | 0.613473i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 5.00000 | + | 15.3884i | 0.186859 | + | 0.575092i | ||||
\(717\) | 14.6619 | + | 20.1803i | 0.547558 | + | 0.753649i | ||||
\(718\) | 37.4164i | 1.39637i | ||||||||
\(719\) | −0.0901699 | + | 0.0655123i | −0.00336277 | + | 0.00244320i | −0.589465 | − | 0.807794i | \(-0.700662\pi\) |
0.586103 | + | 0.810237i | \(0.300662\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 11.7082 | + | 8.50651i | 0.436036 | + | 0.316799i | ||||
\(722\) | −10.2699 | + | 14.1353i | −0.382205 | + | 0.526060i | ||||
\(723\) | −26.6623 | − | 8.66312i | −0.991583 | − | 0.322185i | ||||
\(724\) | 14.7984 | 0.549977 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −9.47214 | −0.351544 | ||||||||
\(727\) | 44.3691 | + | 14.4164i | 1.64556 | + | 0.534675i | 0.977771 | − | 0.209675i | \(-0.0672407\pi\) |
0.667789 | + | 0.744350i | \(0.267241\pi\) | |||||||
\(728\) | −44.3036 | + | 60.9787i | −1.64200 | + | 2.26002i | ||||
\(729\) | 0.809017 | + | 0.587785i | 0.0299636 | + | 0.0217698i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −24.0344 | + | 17.4620i | −0.888946 | + | 0.645857i | ||||
\(732\) | − | 1.61803i | − | 0.0598043i | ||||||
\(733\) | 17.2905 | + | 23.7984i | 0.638640 | + | 0.879013i | 0.998542 | − | 0.0539772i | \(-0.0171898\pi\) |
−0.359902 | + | 0.932990i | \(0.617190\pi\) | |||||||
\(734\) | 1.85410 | + | 5.70634i | 0.0684362 | + | 0.210625i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 6.90983 | − | 21.2663i | 0.254700 | − | 0.783885i | ||||
\(737\) | 0.898056 | − | 0.291796i | 0.0330803 | − | 0.0107484i | ||||
\(738\) | −3.44095 | + | 1.11803i | −0.126663 | + | 0.0411554i | ||||
\(739\) | −1.32624 | + | 4.08174i | −0.0487865 | + | 0.150149i | −0.972482 | − | 0.232978i | \(-0.925153\pi\) |
0.923696 | + | 0.383127i | \(0.125153\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 2.14590 | + | 6.60440i | 0.0788315 | + | 0.242619i | ||||
\(742\) | 9.51057 | + | 13.0902i | 0.349144 | + | 0.480555i | ||||
\(743\) | − | 41.1246i | − | 1.50872i | −0.656463 | − | 0.754358i | \(-0.727948\pi\) | ||
0.656463 | − | 0.754358i | \(-0.272052\pi\) | |||||||
\(744\) | −6.70820 | + | 4.87380i | −0.245935 | + | 0.178682i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −2.09017 | − | 1.51860i | −0.0765266 | − | 0.0555998i | ||||
\(747\) | 7.33094 | − | 10.0902i | 0.268225 | − | 0.369180i | ||||
\(748\) | −4.53077 | − | 1.47214i | −0.165661 | − | 0.0538266i | ||||
\(749\) | 33.6656 | 1.23012 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 36.6525 | 1.33747 | 0.668734 | − | 0.743502i | \(-0.266837\pi\) | ||||
0.668734 | + | 0.743502i | \(0.266837\pi\) | |||||||
\(752\) | 0.726543 | + | 0.236068i | 0.0264943 | + | 0.00860851i | ||||
\(753\) | 5.32282 | − | 7.32624i | 0.193974 | − | 0.266983i | ||||
\(754\) | 30.0795 | + | 21.8541i | 1.09543 | + | 0.795878i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −3.61803 | + | 2.62866i | −0.131587 | + | 0.0956033i | ||||
\(757\) | 29.6180i | 1.07649i | 0.842790 | + | 0.538243i | \(0.180912\pi\) | ||||
−0.842790 | + | 0.538243i | \(0.819088\pi\) | |||||||
\(758\) | −2.00811 | − | 2.76393i | −0.0729380 | − | 0.100391i | ||||
\(759\) | 1.70820 | + | 5.25731i | 0.0620039 | + | 0.190828i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 10.1180 | − | 31.1401i | 0.366778 | − | 1.12883i | −0.582081 | − | 0.813130i | \(-0.697762\pi\) |
0.948860 | − | 0.315697i | \(-0.102238\pi\) | |||||||
\(762\) | 3.52671 | − | 1.14590i | 0.127759 | − | 0.0415115i | ||||
\(763\) | 33.6425 | − | 10.9311i | 1.21794 | − | 0.395733i | ||||
\(764\) | 2.05573 | − | 6.32688i | 0.0743736 | − | 0.228899i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −10.1459 | − | 31.2259i | −0.366586 | − | 1.12824i | ||||
\(767\) | 13.2088 | + | 18.1803i | 0.476942 | + | 0.656454i | ||||
\(768\) | 17.0000i | 0.613435i | ||||||||
\(769\) | −40.7426 | + | 29.6013i | −1.46922 | + | 1.06745i | −0.488378 | + | 0.872632i | \(0.662411\pi\) |
−0.980840 | + | 0.194817i | \(0.937589\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −9.54508 | − | 6.93491i | −0.343758 | − | 0.249755i | ||||
\(772\) | −13.7108 | + | 18.8713i | −0.493463 | + | 0.679194i | ||||
\(773\) | −27.5074 | − | 8.93769i | −0.989372 | − | 0.321467i | −0.230761 | − | 0.973010i | \(-0.574122\pi\) |
−0.758611 | + | 0.651544i | \(0.774122\pi\) | |||||||
\(774\) | −7.70820 | −0.277066 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −6.43769 | −0.231100 | ||||||||
\(777\) | 13.1433 | + | 4.27051i | 0.471512 | + | 0.153204i | ||||
\(778\) | 15.2294 | − | 20.9615i | 0.546001 | − | 0.751506i | ||||
\(779\) | −3.61803 | − | 2.62866i | −0.129630 | − | 0.0941814i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −5.23607 | + | 3.80423i | −0.187361 | + | 0.136126i | ||||
\(782\) | 17.2361i | 0.616361i | ||||||||
\(783\) | 3.88998 | + | 5.35410i | 0.139017 | + | 0.191340i | ||||
\(784\) | 4.01722 | + | 12.3637i | 0.143472 | + | 0.441562i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −2.52786 | + | 7.77997i | −0.0901659 | + | 0.277502i | ||||
\(787\) | 13.4863 | − | 4.38197i | 0.480735 | − | 0.156200i | −0.0586173 | − | 0.998281i | \(-0.518669\pi\) |
0.539352 | + | 0.842080i | \(0.318669\pi\) | |||||||
\(788\) | −7.24518 | + | 2.35410i | −0.258099 | + | 0.0838614i | ||||
\(789\) | 7.38197 | − | 22.7194i | 0.262805 | − | 0.808830i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −25.3262 | − | 77.9461i | −0.900497 | − | 2.77145i | ||||
\(792\) | −2.17963 | − | 3.00000i | −0.0774497 | − | 0.106600i | ||||
\(793\) | − | 9.09017i | − | 0.322801i | ||||||
\(794\) | −5.61803 | + | 4.08174i | −0.199377 | + | 0.144856i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 10.2361 | + | 7.43694i | 0.362808 | + | 0.263595i | ||||
\(797\) | −28.8622 | + | 39.7254i | −1.02235 | + | 1.40715i | −0.111810 | + | 0.993730i | \(0.535665\pi\) |
−0.910542 | + | 0.413417i | \(0.864335\pi\) | |||||||
\(798\) | 5.25731 | + | 1.70820i | 0.186107 | + | 0.0604698i | ||||
\(799\) | 2.94427 | 0.104161 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 5.38197 | 0.190162 | ||||||||
\(802\) | −21.3520 | − | 6.93769i | −0.753966 | − | 0.244978i | ||||
\(803\) | −5.87785 | + | 8.09017i | −0.207425 | + | 0.285496i | ||||
\(804\) | −0.618034 | − | 0.449028i | −0.0217964 | − | 0.0158360i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −12.5623 | + | 9.12705i | −0.442488 | + | 0.321487i | ||||
\(807\) | − | 6.85410i | − | 0.241276i | ||||||
\(808\) | −6.28161 | − | 8.64590i | −0.220986 | − | 0.304162i | ||||
\(809\) | −8.71885 | − | 26.8339i | −0.306538 | − | 0.943428i | −0.979099 | − | 0.203386i | \(-0.934805\pi\) |
0.672560 | − | 0.740042i | \(-0.265195\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 1.47214 | − | 4.53077i | 0.0516937 | − | 0.159097i | −0.921877 | − | 0.387483i | \(-0.873345\pi\) |
0.973571 | + | 0.228386i | \(0.0733447\pi\) | |||||||
\(812\) | −28.1482 | + | 9.14590i | −0.987807 | + | 0.320958i | ||||
\(813\) | −0.171513 | + | 0.0557281i | −0.00601524 | + | 0.00195447i | ||||
\(814\) | −1.18034 | + | 3.63271i | −0.0413709 | + | 0.127327i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −1.19098 | − | 3.66547i | −0.0416927 | − | 0.128317i | ||||
\(817\) | −5.60034 | − | 7.70820i | −0.195931 | − | 0.269676i | ||||
\(818\) | − | 1.20163i | − | 0.0420139i | ||||||
\(819\) | −20.3262 | + | 14.7679i | −0.710256 | + | 0.516031i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −18.5623 | − | 13.4863i | −0.647829 | − | 0.470675i | 0.214702 | − | 0.976680i | \(-0.431122\pi\) |
−0.862531 | + | 0.506004i | \(0.831122\pi\) | |||||||
\(822\) | −4.47777 | + | 6.16312i | −0.156180 | + | 0.214963i | ||||
\(823\) | 18.2946 | + | 5.94427i | 0.637709 | + | 0.207204i | 0.609987 | − | 0.792411i | \(-0.291175\pi\) |
0.0277222 | + | 0.999616i | \(0.491175\pi\) | |||||||
\(824\) | 9.70820 | 0.338201 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 17.8885 | 0.622422 | ||||||||
\(827\) | −34.3035 | − | 11.1459i | −1.19285 | − | 0.387581i | −0.355725 | − | 0.934591i | \(-0.615766\pi\) |
−0.837126 | + | 0.547010i | \(0.815766\pi\) | |||||||
\(828\) | 2.62866 | − | 3.61803i | 0.0913521 | − | 0.125735i | ||||
\(829\) | 9.30902 | + | 6.76340i | 0.323316 | + | 0.234902i | 0.737589 | − | 0.675250i | \(-0.235964\pi\) |
−0.414273 | + | 0.910152i | \(0.635964\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −15.2082 | + | 11.0494i | −0.527567 | + | 0.383300i | ||||
\(832\) | 39.3262i | 1.36339i | ||||||||
\(833\) | 29.4500 | + | 40.5344i | 1.02038 | + | 1.40444i | ||||
\(834\) | 7.09017 | + | 21.8213i | 0.245513 | + | 0.755610i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0.472136 | − | 1.45309i | 0.0163292 | − | 0.0502560i | ||||
\(837\) | −2.62866 | + | 0.854102i | −0.0908596 | + | 0.0295221i | ||||
\(838\) | 14.3188 | − | 4.65248i | 0.494636 | − | 0.160717i | ||||
\(839\) | −4.34752 | + | 13.3803i | −0.150093 | + | 0.461939i | −0.997631 | − | 0.0687961i | \(-0.978084\pi\) |
0.847538 | + | 0.530735i | \(0.178084\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 4.57295 | + | 14.0741i | 0.157688 | + | 0.485313i | ||||
\(842\) | −17.5478 | − | 24.1525i | −0.604737 | − | 0.832349i | ||||
\(843\) | 19.6180i | 0.675681i | ||||||||
\(844\) | −14.4721 | + | 10.5146i | −0.498151 | + | 0.361928i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0.618034 | + | 0.449028i | 0.0212484 | + | 0.0154379i | ||||
\(847\) | 24.8990 | − | 34.2705i | 0.855539 | − | 1.17755i | ||||
\(848\) | 3.44095 | + | 1.11803i | 0.118163 | + | 0.0383934i | ||||
\(849\) | −13.7082 | −0.470464 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −13.8197 | −0.473732 | ||||||||
\(852\) | 4.97980 | + | 1.61803i | 0.170605 | + | 0.0554329i | ||||
\(853\) | −13.6048 | + | 18.7254i | −0.465820 | + | 0.641146i | −0.975703 | − | 0.219097i | \(-0.929689\pi\) |
0.509883 | + | 0.860244i | \(0.329689\pi\) | |||||||
\(854\) | −5.85410 | − | 4.25325i | −0.200323 | − | 0.145543i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 18.2705 | − | 13.2743i | 0.624473 | − | 0.453706i | ||||
\(857\) | − | 12.4721i | − | 0.426040i | −0.977048 | − | 0.213020i | \(-0.931670\pi\) | ||
0.977048 | − | 0.213020i | \(-0.0683300\pi\) | |||||||
\(858\) | −4.08174 | − | 5.61803i | −0.139348 | − | 0.191797i | ||||
\(859\) | 7.23607 | + | 22.2703i | 0.246891 | + | 0.759854i | 0.995320 | + | 0.0966379i | \(0.0308089\pi\) |
−0.748428 | + | 0.663216i | \(0.769191\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 5.00000 | − | 15.3884i | 0.170400 | − | 0.524436i | ||||
\(862\) | −19.6417 | + | 6.38197i | −0.668998 | + | 0.217371i | ||||
\(863\) | 10.3431 | − | 3.36068i | 0.352084 | − | 0.114399i | −0.127635 | − | 0.991821i | \(-0.540739\pi\) |
0.479719 | + | 0.877422i | \(0.340739\pi\) | |||||||
\(864\) | −1.54508 | + | 4.75528i | −0.0525649 | + | 0.161778i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −6.79180 | − | 20.9030i | −0.230795 | − | 0.710313i | ||||
\(867\) | 1.26133 | + | 1.73607i | 0.0428369 | + | 0.0589600i | ||||
\(868\) | − | 12.3607i | − | 0.419549i | ||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −3.47214 | − | 2.52265i | −0.117649 | − | 0.0854769i | ||||
\(872\) | 13.9478 | − | 19.1976i | 0.472334 | − | 0.650111i | ||||
\(873\) | −2.04087 | − | 0.663119i | −0.0690730 | − | 0.0224432i | ||||
\(874\) | −5.52786 | −0.186983 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 8.09017 | 0.273342 | ||||||||
\(877\) | −31.5891 | − | 10.2639i | −1.06669 | − | 0.346588i | −0.277492 | − | 0.960728i | \(-0.589503\pi\) |
−0.789197 | + | 0.614140i | \(0.789503\pi\) | |||||||
\(878\) | −9.51057 | + | 13.0902i | −0.320966 | + | 0.441772i | ||||
\(879\) | −16.8262 | − | 12.2250i | −0.567535 | − | 0.412338i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −34.7426 | + | 25.2420i | −1.17051 | + | 0.850425i | −0.991070 | − | 0.133344i | \(-0.957428\pi\) |
−0.179440 | + | 0.983769i | \(0.557428\pi\) | |||||||
\(882\) | 13.0000i | 0.437733i | ||||||||
\(883\) | 13.0373 | + | 17.9443i | 0.438739 | + | 0.603873i | 0.969931 | − | 0.243379i | \(-0.0782557\pi\) |
−0.531192 | + | 0.847251i | \(0.678256\pi\) | |||||||
\(884\) | 6.69098 | + | 20.5927i | 0.225042 | + | 0.692608i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −10.8885 | + | 33.5115i | −0.365808 | + | 1.12584i | ||||
\(887\) | 21.9928 | − | 7.14590i | 0.738446 | − | 0.239936i | 0.0844440 | − | 0.996428i | \(-0.473089\pi\) |
0.654002 | + | 0.756492i | \(0.273089\pi\) | |||||||
\(888\) | 8.81678 | − | 2.86475i | 0.295872 | − | 0.0961346i | ||||
\(889\) | −5.12461 | + | 15.7719i | −0.171874 | + | 0.528974i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −0.381966 | − | 1.17557i | −0.0127963 | − | 0.0393831i | ||||
\(892\) | 4.80828 | + | 6.61803i | 0.160993 | + | 0.221588i | ||||
\(893\) | 0.944272i | 0.0315989i | ||||||||
\(894\) | −15.2533 | + | 11.0822i | −0.510146 | + | 0.370643i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −10.8541 | − | 7.88597i | −0.362610 | − | 0.263452i | ||||
\(897\) | 14.7679 | − | 20.3262i | 0.493085 | − | 0.678673i | ||||
\(898\) | −15.9762 | − | 5.19098i | −0.533133 | − | 0.173225i | ||||
\(899\) | −18.2918 | −0.610066 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 13.9443 | 0.464551 | ||||||||
\(902\) | 4.25325 | + | 1.38197i | 0.141618 | + | 0.0460144i | ||||
\(903\) | 20.2622 | − | 27.8885i | 0.674284 | − | 0.928073i | ||||
\(904\) | −44.4787 | − | 32.3157i | −1.47934 | − | 1.07480i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −6.09017 | + | 4.42477i | −0.202332 | + | 0.147003i | ||||
\(907\) | 7.12461i | 0.236569i | 0.992980 | + | 0.118284i | \(0.0377395\pi\) | ||||
−0.992980 | + | 0.118284i | \(0.962261\pi\) | |||||||
\(908\) | 11.7557 | + | 16.1803i | 0.390127 | + | 0.536963i | ||||
\(909\) | −1.10081 | − | 3.38795i | −0.0365117 | − | 0.112371i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 5.61803 | − | 17.2905i | 0.186134 | − | 0.572861i | −0.813832 | − | 0.581100i | \(-0.802623\pi\) |
0.999966 | + | 0.00823898i | \(0.00262258\pi\) | |||||||
\(912\) | 1.17557 | − | 0.381966i | 0.0389270 | − | 0.0126482i | ||||
\(913\) | −14.6619 | + | 4.76393i | −0.485237 | + | 0.157663i | ||||
\(914\) | 6.90983 | − | 21.2663i | 0.228557 | − | 0.703426i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −6.79180 | − | 20.9030i | −0.224407 | − | 0.690655i | ||||
\(917\) | −21.5033 | − | 29.5967i | −0.710101 | − | 0.977371i | ||||
\(918\) | − | 3.85410i | − | 0.127204i | ||||||
\(919\) | 39.7984 | − | 28.9152i | 1.31283 | − | 0.953825i | 0.312835 | − | 0.949807i | \(-0.398721\pi\) |
0.999992 | − | 0.00401741i | \(-0.00127879\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −26.4164 | − | 19.1926i | −0.870450 | − | 0.632419i | ||||
\(922\) | −19.2784 | + | 26.5344i | −0.634900 | + | 0.873865i | ||||
\(923\) | 27.9767 | + | 9.09017i | 0.920863 | + | 0.299207i | ||||
\(924\) | 5.52786 | 0.181853 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 18.7639 | 0.616621 | ||||||||
\(927\) | 3.07768 | + | 1.00000i | 0.101084 | + | 0.0328443i | ||||
\(928\) | −19.4499 | + | 26.7705i | −0.638475 | + | 0.878785i | ||||
\(929\) | −7.35410 | − | 5.34307i | −0.241280 | − | 0.175300i | 0.460573 | − | 0.887622i | \(-0.347644\pi\) |
−0.701853 | + | 0.712321i | \(0.747644\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −13.0000 | + | 9.44505i | −0.426058 | + | 0.309549i | ||||
\(932\) | − | 12.3820i | − | 0.405585i | ||||||
\(933\) | 10.4086 | + | 14.3262i | 0.340763 | + | 0.469020i | ||||
\(934\) | −8.70820 | − | 26.8011i | −0.284941 | − | 0.876959i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −5.20820 | + | 16.0292i | −0.170235 | + | 0.523931i | ||||
\(937\) | 46.3040 | − | 15.0451i | 1.51269 | − | 0.491502i | 0.568998 | − | 0.822339i | \(-0.307331\pi\) |
0.943688 | + | 0.330837i | \(0.107331\pi\) | |||||||
\(938\) | −3.24920 | + | 1.05573i | −0.106090 | + | 0.0344707i | ||||
\(939\) | 0.145898 | − | 0.449028i | 0.00476120 | − | 0.0146535i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −3.19098 | − | 9.82084i | −0.104023 | − | 0.320150i | 0.885477 | − | 0.464683i | \(-0.153832\pi\) |
−0.989500 | + | 0.144533i | \(0.953832\pi\) | |||||||
\(942\) | −6.34712 | − | 8.73607i | −0.206801 | − | 0.284636i | ||||
\(943\) | 16.1803i | 0.526904i | ||||||||
\(944\) | 3.23607 | − | 2.35114i | 0.105325 | − | 0.0765231i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 7.70820 | + | 5.60034i | 0.250615 | + | 0.182083i | ||||
\(947\) | 1.51860 | − | 2.09017i | 0.0493478 | − | 0.0679214i | −0.783630 | − | 0.621228i | \(-0.786634\pi\) |
0.832978 | + | 0.553306i | \(0.186634\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 45.4508 | 1.47540 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 28.8328 | 0.934968 | ||||||||
\(952\) | 49.1774 | + | 15.9787i | 1.59385 | + | 0.517873i | ||||
\(953\) | 0.640786 | − | 0.881966i | 0.0207571 | − | 0.0285697i | −0.798512 | − | 0.601978i | \(-0.794379\pi\) |
0.819269 | + | 0.573409i | \(0.194379\pi\) | |||||||
\(954\) | 2.92705 | + | 2.12663i | 0.0947668 | + | 0.0688521i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −20.1803 | + | 14.6619i | −0.652679 | + | 0.474199i | ||||
\(957\) | − | 8.18034i | − | 0.264433i | ||||||
\(958\) | 11.1352 | + | 15.3262i | 0.359761 | + | 0.495168i | ||||
\(959\) | −10.5279 | − | 32.4014i | −0.339962 | − | 1.04630i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −7.21885 | + | 22.2173i | −0.232866 | + | 0.716688i | ||||
\(962\) | 16.5110 | − | 5.36475i | 0.532336 | − | 0.172966i | ||||
\(963\) | 7.15942 | − | 2.32624i | 0.230709 | − | 0.0749620i | ||||
\(964\) | 8.66312 | − | 26.6623i | 0.279020 | − | 0.858736i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −6.18034 | − | 19.0211i | −0.198849 | − | 0.611995i | ||||
\(967\) | 11.0697 | + | 15.2361i | 0.355976 | + | 0.489959i | 0.949022 | − | 0.315210i | \(-0.102075\pi\) |
−0.593046 | + | 0.805169i | \(0.702075\pi\) | |||||||
\(968\) | − | 28.4164i | − | 0.913338i | ||||||
\(969\) | 3.85410 | − | 2.80017i | 0.123812 | − | 0.0899544i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 27.0344 | + | 19.6417i | 0.867577 | + | 0.630331i | 0.929936 | − | 0.367723i | \(-0.119862\pi\) |
−0.0623590 | + | 0.998054i | \(0.519862\pi\) | |||||||
\(972\) | −0.587785 | + | 0.809017i | −0.0188532 | + | 0.0259492i | ||||
\(973\) | −97.5878 | − | 31.7082i | −3.12852 | − | 1.01652i | ||||
\(974\) | −9.70820 | −0.311071 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −1.61803 | −0.0517920 | ||||||||
\(977\) | −3.09793 | − | 1.00658i | −0.0991115 | − | 0.0322033i | 0.259041 | − | 0.965866i | \(-0.416593\pi\) |
−0.358153 | + | 0.933663i | \(0.616593\pi\) | |||||||
\(978\) | 8.78402 | − | 12.0902i | 0.280882 | − | 0.386601i | ||||
\(979\) | −5.38197 | − | 3.91023i | −0.172008 | − | 0.124971i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 6.39919 | − | 4.64928i | 0.204310 | − | 0.148440i | ||||
\(982\) | 5.88854i | 0.187911i | ||||||||
\(983\) | 4.87380 | + | 6.70820i | 0.155450 | + | 0.213958i | 0.879638 | − | 0.475644i | \(-0.157785\pi\) |
−0.724188 | + | 0.689603i | \(0.757785\pi\) | |||||||
\(984\) | −3.35410 | − | 10.3229i | −0.106925 | − | 0.329081i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 7.88197 | − | 24.2582i | 0.251013 | − | 0.772538i | ||||
\(987\) | −3.24920 | + | 1.05573i | −0.103423 | + | 0.0336042i | ||||
\(988\) | −6.60440 | + | 2.14590i | −0.210114 | + | 0.0682701i | ||||
\(989\) | −10.6525 | + | 32.7849i | −0.338729 | + | 1.04250i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 11.4721 | + | 35.3076i | 0.364424 | + | 1.12158i | 0.950341 | + | 0.311211i | \(0.100735\pi\) |
−0.585916 | + | 0.810372i | \(0.699265\pi\) | |||||||
\(992\) | −8.12299 | − | 11.1803i | −0.257905 | − | 0.354976i | ||||
\(993\) | 6.94427i | 0.220370i | ||||||||
\(994\) | 18.9443 | − | 13.7638i | 0.600876 | − | 0.436562i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 10.0902 | + | 7.33094i | 0.319719 | + | 0.232290i | ||||
\(997\) | −10.2371 | + | 14.0902i | −0.324212 | + | 0.446240i | −0.939747 | − | 0.341869i | \(-0.888940\pi\) |
0.615535 | + | 0.788110i | \(0.288940\pi\) | |||||||
\(998\) | 5.70634 | + | 1.85410i | 0.180631 | + | 0.0586906i | ||||
\(999\) | 3.09017 | 0.0977687 |
(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 | 375.2.i.a.274.2 | 8 | ||
5.2 | odd | 4 | 375.2.g.a.226.1 | 4 | |||
5.3 | odd | 4 | 75.2.g.a.46.1 | yes | 4 | ||
5.4 | even | 2 | inner | 375.2.i.a.274.1 | 8 | ||
15.8 | even | 4 | 225.2.h.a.46.1 | 4 | |||
25.6 | even | 5 | inner | 375.2.i.a.349.1 | 8 | ||
25.8 | odd | 20 | 75.2.g.a.31.1 | ✓ | 4 | ||
25.9 | even | 10 | 1875.2.b.b.1249.2 | 4 | |||
25.12 | odd | 20 | 1875.2.a.a.1.2 | 2 | |||
25.13 | odd | 20 | 1875.2.a.d.1.1 | 2 | |||
25.16 | even | 5 | 1875.2.b.b.1249.3 | 4 | |||
25.17 | odd | 20 | 375.2.g.a.151.1 | 4 | |||
25.19 | even | 10 | inner | 375.2.i.a.349.2 | 8 | ||
75.8 | even | 20 | 225.2.h.a.181.1 | 4 | |||
75.38 | even | 20 | 5625.2.a.a.1.1 | 2 | |||
75.62 | even | 20 | 5625.2.a.h.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
75.2.g.a.31.1 | ✓ | 4 | 25.8 | odd | 20 | ||
75.2.g.a.46.1 | yes | 4 | 5.3 | odd | 4 | ||
225.2.h.a.46.1 | 4 | 15.8 | even | 4 | |||
225.2.h.a.181.1 | 4 | 75.8 | even | 20 | |||
375.2.g.a.151.1 | 4 | 25.17 | odd | 20 | |||
375.2.g.a.226.1 | 4 | 5.2 | odd | 4 | |||
375.2.i.a.274.1 | 8 | 5.4 | even | 2 | inner | ||
375.2.i.a.274.2 | 8 | 1.1 | even | 1 | trivial | ||
375.2.i.a.349.1 | 8 | 25.6 | even | 5 | inner | ||
375.2.i.a.349.2 | 8 | 25.19 | even | 10 | inner | ||
1875.2.a.a.1.2 | 2 | 25.12 | odd | 20 | |||
1875.2.a.d.1.1 | 2 | 25.13 | odd | 20 | |||
1875.2.b.b.1249.2 | 4 | 25.9 | even | 10 | |||
1875.2.b.b.1249.3 | 4 | 25.16 | even | 5 | |||
5625.2.a.a.1.1 | 2 | 75.38 | even | 20 | |||
5625.2.a.h.1.2 | 2 | 75.62 | even | 20 |