Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [546,2,Mod(79,546)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(546, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 2, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("546.79");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 546 = 2 \cdot 3 \cdot 7 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 546.i (of order \(3\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(4.35983195036\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\Q(\sqrt{2}, \sqrt{-3})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 2x^{2} + 4 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 235.2 | ||
Root | \(0.707107 + 1.22474i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 546.235 |
Dual form | 546.2.i.h.79.2 |
$q$-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 \(\left(\mathbb{Z}/546\mathbb{Z}\right)^\times\).
\(n\) | \(157\) | \(365\) | \(379\) |
\(\chi(n)\) | \(e\left(\frac{2}{3}\right)\) | \(1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.500000 | − | 0.866025i | −0.353553 | − | 0.612372i | ||||
\(3\) | −0.500000 | + | 0.866025i | −0.288675 | + | 0.500000i | ||||
\(4\) | −0.500000 | + | 0.866025i | −0.250000 | + | 0.433013i | ||||
\(5\) | 0.707107 | + | 1.22474i | 0.316228 | + | 0.547723i | 0.979698 | − | 0.200480i | \(-0.0642503\pi\) |
−0.663470 | + | 0.748203i | \(0.730917\pi\) | |||||||
\(6\) | 1.00000 | 0.408248 | ||||||||
\(7\) | 2.62132 | − | 0.358719i | 0.990766 | − | 0.135583i | ||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | −0.500000 | − | 0.866025i | −0.166667 | − | 0.288675i | ||||
\(10\) | 0.707107 | − | 1.22474i | 0.223607 | − | 0.387298i | ||||
\(11\) | −0.207107 | + | 0.358719i | −0.0624450 | + | 0.108158i | −0.895558 | − | 0.444945i | \(-0.853223\pi\) |
0.833113 | + | 0.553103i | \(0.186556\pi\) | |||||||
\(12\) | −0.500000 | − | 0.866025i | −0.144338 | − | 0.250000i | ||||
\(13\) | 1.00000 | 0.277350 | ||||||||
\(14\) | −1.62132 | − | 2.09077i | −0.433316 | − | 0.558782i | ||||
\(15\) | −1.41421 | −0.365148 | ||||||||
\(16\) | −0.500000 | − | 0.866025i | −0.125000 | − | 0.216506i | ||||
\(17\) | −2.62132 | + | 4.54026i | −0.635764 | + | 1.10117i | 0.350589 | + | 0.936529i | \(0.385981\pi\) |
−0.986353 | + | 0.164645i | \(0.947352\pi\) | |||||||
\(18\) | −0.500000 | + | 0.866025i | −0.117851 | + | 0.204124i | ||||
\(19\) | −1.50000 | − | 2.59808i | −0.344124 | − | 0.596040i | 0.641071 | − | 0.767482i | \(-0.278491\pi\) |
−0.985194 | + | 0.171442i | \(0.945157\pi\) | |||||||
\(20\) | −1.41421 | −0.316228 | ||||||||
\(21\) | −1.00000 | + | 2.44949i | −0.218218 | + | 0.534522i | ||||
\(22\) | 0.414214 | 0.0883106 | ||||||||
\(23\) | 4.53553 | + | 7.85578i | 0.945724 | + | 1.63804i | 0.754295 | + | 0.656536i | \(0.227979\pi\) |
0.191429 | + | 0.981506i | \(0.438688\pi\) | |||||||
\(24\) | −0.500000 | + | 0.866025i | −0.102062 | + | 0.176777i | ||||
\(25\) | 1.50000 | − | 2.59808i | 0.300000 | − | 0.519615i | ||||
\(26\) | −0.500000 | − | 0.866025i | −0.0980581 | − | 0.169842i | ||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | −1.00000 | + | 2.44949i | −0.188982 | + | 0.462910i | ||||
\(29\) | 5.00000 | 0.928477 | 0.464238 | − | 0.885710i | \(-0.346328\pi\) | ||||
0.464238 | + | 0.885710i | \(0.346328\pi\) | |||||||
\(30\) | 0.707107 | + | 1.22474i | 0.129099 | + | 0.223607i | ||||
\(31\) | −3.41421 | + | 5.91359i | −0.613211 | + | 1.06211i | 0.377485 | + | 0.926016i | \(0.376789\pi\) |
−0.990696 | + | 0.136097i | \(0.956544\pi\) | |||||||
\(32\) | −0.500000 | + | 0.866025i | −0.0883883 | + | 0.153093i | ||||
\(33\) | −0.207107 | − | 0.358719i | −0.0360527 | − | 0.0624450i | ||||
\(34\) | 5.24264 | 0.899105 | ||||||||
\(35\) | 2.29289 | + | 2.95680i | 0.387570 | + | 0.499790i | ||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | 2.53553 | + | 4.39167i | 0.416839 | + | 0.721987i | 0.995620 | − | 0.0934968i | \(-0.0298045\pi\) |
−0.578780 | + | 0.815483i | \(0.696471\pi\) | |||||||
\(38\) | −1.50000 | + | 2.59808i | −0.243332 | + | 0.421464i | ||||
\(39\) | −0.500000 | + | 0.866025i | −0.0800641 | + | 0.138675i | ||||
\(40\) | 0.707107 | + | 1.22474i | 0.111803 | + | 0.193649i | ||||
\(41\) | 4.58579 | 0.716180 | 0.358090 | − | 0.933687i | \(-0.383428\pi\) | ||||
0.358090 | + | 0.933687i | \(0.383428\pi\) | |||||||
\(42\) | 2.62132 | − | 0.358719i | 0.404479 | − | 0.0553516i | ||||
\(43\) | 4.82843 | 0.736328 | 0.368164 | − | 0.929761i | \(-0.379986\pi\) | ||||
0.368164 | + | 0.929761i | \(0.379986\pi\) | |||||||
\(44\) | −0.207107 | − | 0.358719i | −0.0312225 | − | 0.0540790i | ||||
\(45\) | 0.707107 | − | 1.22474i | 0.105409 | − | 0.182574i | ||||
\(46\) | 4.53553 | − | 7.85578i | 0.668728 | − | 1.15827i | ||||
\(47\) | −4.50000 | − | 7.79423i | −0.656392 | − | 1.13691i | −0.981543 | − | 0.191243i | \(-0.938748\pi\) |
0.325150 | − | 0.945662i | \(-0.394585\pi\) | |||||||
\(48\) | 1.00000 | 0.144338 | ||||||||
\(49\) | 6.74264 | − | 1.88064i | 0.963234 | − | 0.268662i | ||||
\(50\) | −3.00000 | −0.424264 | ||||||||
\(51\) | −2.62132 | − | 4.54026i | −0.367058 | − | 0.635764i | ||||
\(52\) | −0.500000 | + | 0.866025i | −0.0693375 | + | 0.120096i | ||||
\(53\) | −6.15685 | + | 10.6640i | −0.845709 | + | 1.46481i | 0.0392951 | + | 0.999228i | \(0.487489\pi\) |
−0.885004 | + | 0.465583i | \(0.845845\pi\) | |||||||
\(54\) | −0.500000 | − | 0.866025i | −0.0680414 | − | 0.117851i | ||||
\(55\) | −0.585786 | −0.0789874 | ||||||||
\(56\) | 2.62132 | − | 0.358719i | 0.350289 | − | 0.0479359i | ||||
\(57\) | 3.00000 | 0.397360 | ||||||||
\(58\) | −2.50000 | − | 4.33013i | −0.328266 | − | 0.568574i | ||||
\(59\) | −3.79289 | + | 6.56948i | −0.493793 | + | 0.855274i | −0.999974 | − | 0.00715287i | \(-0.997723\pi\) |
0.506182 | + | 0.862427i | \(0.331056\pi\) | |||||||
\(60\) | 0.707107 | − | 1.22474i | 0.0912871 | − | 0.158114i | ||||
\(61\) | 2.62132 | + | 4.54026i | 0.335626 | + | 0.581321i | 0.983605 | − | 0.180337i | \(-0.0577189\pi\) |
−0.647979 | + | 0.761658i | \(0.724386\pi\) | |||||||
\(62\) | 6.82843 | 0.867211 | ||||||||
\(63\) | −1.62132 | − | 2.09077i | −0.204267 | − | 0.263412i | ||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 0.707107 | + | 1.22474i | 0.0877058 | + | 0.151911i | ||||
\(66\) | −0.207107 | + | 0.358719i | −0.0254931 | + | 0.0441553i | ||||
\(67\) | 7.32843 | − | 12.6932i | 0.895310 | − | 1.55072i | 0.0618892 | − | 0.998083i | \(-0.480287\pi\) |
0.833421 | − | 0.552639i | \(-0.186379\pi\) | |||||||
\(68\) | −2.62132 | − | 4.54026i | −0.317882 | − | 0.550587i | ||||
\(69\) | −9.07107 | −1.09203 | ||||||||
\(70\) | 1.41421 | − | 3.46410i | 0.169031 | − | 0.414039i | ||||
\(71\) | −1.00000 | −0.118678 | −0.0593391 | − | 0.998238i | \(-0.518899\pi\) | ||||
−0.0593391 | + | 0.998238i | \(0.518899\pi\) | |||||||
\(72\) | −0.500000 | − | 0.866025i | −0.0589256 | − | 0.102062i | ||||
\(73\) | 0.535534 | − | 0.927572i | 0.0626795 | − | 0.108564i | −0.832983 | − | 0.553299i | \(-0.813369\pi\) |
0.895662 | + | 0.444735i | \(0.146702\pi\) | |||||||
\(74\) | 2.53553 | − | 4.39167i | 0.294750 | − | 0.510522i | ||||
\(75\) | 1.50000 | + | 2.59808i | 0.173205 | + | 0.300000i | ||||
\(76\) | 3.00000 | 0.344124 | ||||||||
\(77\) | −0.414214 | + | 1.01461i | −0.0472040 | + | 0.115626i | ||||
\(78\) | 1.00000 | 0.113228 | ||||||||
\(79\) | −6.65685 | − | 11.5300i | −0.748955 | − | 1.29723i | −0.948324 | − | 0.317303i | \(-0.897223\pi\) |
0.199370 | − | 0.979924i | \(-0.436111\pi\) | |||||||
\(80\) | 0.707107 | − | 1.22474i | 0.0790569 | − | 0.136931i | ||||
\(81\) | −0.500000 | + | 0.866025i | −0.0555556 | + | 0.0962250i | ||||
\(82\) | −2.29289 | − | 3.97141i | −0.253208 | − | 0.438569i | ||||
\(83\) | −7.65685 | −0.840449 | −0.420224 | − | 0.907420i | \(-0.638049\pi\) | ||||
−0.420224 | + | 0.907420i | \(0.638049\pi\) | |||||||
\(84\) | −1.62132 | − | 2.09077i | −0.176901 | − | 0.228122i | ||||
\(85\) | −7.41421 | −0.804184 | ||||||||
\(86\) | −2.41421 | − | 4.18154i | −0.260331 | − | 0.450907i | ||||
\(87\) | −2.50000 | + | 4.33013i | −0.268028 | + | 0.464238i | ||||
\(88\) | −0.207107 | + | 0.358719i | −0.0220777 | + | 0.0382396i | ||||
\(89\) | 3.12132 | + | 5.40629i | 0.330859 | + | 0.573065i | 0.982681 | − | 0.185307i | \(-0.0593281\pi\) |
−0.651821 | + | 0.758373i | \(0.725995\pi\) | |||||||
\(90\) | −1.41421 | −0.149071 | ||||||||
\(91\) | 2.62132 | − | 0.358719i | 0.274789 | − | 0.0376040i | ||||
\(92\) | −9.07107 | −0.945724 | ||||||||
\(93\) | −3.41421 | − | 5.91359i | −0.354037 | − | 0.613211i | ||||
\(94\) | −4.50000 | + | 7.79423i | −0.464140 | + | 0.803913i | ||||
\(95\) | 2.12132 | − | 3.67423i | 0.217643 | − | 0.376969i | ||||
\(96\) | −0.500000 | − | 0.866025i | −0.0510310 | − | 0.0883883i | ||||
\(97\) | 7.89949 | 0.802072 | 0.401036 | − | 0.916062i | \(-0.368650\pi\) | ||||
0.401036 | + | 0.916062i | \(0.368650\pi\) | |||||||
\(98\) | −5.00000 | − | 4.89898i | −0.505076 | − | 0.494872i | ||||
\(99\) | 0.414214 | 0.0416300 | ||||||||
\(100\) | 1.50000 | + | 2.59808i | 0.150000 | + | 0.259808i | ||||
\(101\) | 0.585786 | − | 1.01461i | 0.0582879 | − | 0.100958i | −0.835409 | − | 0.549629i | \(-0.814769\pi\) |
0.893697 | + | 0.448671i | \(0.148103\pi\) | |||||||
\(102\) | −2.62132 | + | 4.54026i | −0.259549 | + | 0.449553i | ||||
\(103\) | −3.24264 | − | 5.61642i | −0.319507 | − | 0.553402i | 0.660878 | − | 0.750493i | \(-0.270184\pi\) |
−0.980385 | + | 0.197091i | \(0.936851\pi\) | |||||||
\(104\) | 1.00000 | 0.0980581 | ||||||||
\(105\) | −3.70711 | + | 0.507306i | −0.361777 | + | 0.0495080i | ||||
\(106\) | 12.3137 | 1.19601 | ||||||||
\(107\) | −6.82843 | − | 11.8272i | −0.660129 | − | 1.14338i | −0.980581 | − | 0.196112i | \(-0.937168\pi\) |
0.320452 | − | 0.947265i | \(-0.396165\pi\) | |||||||
\(108\) | −0.500000 | + | 0.866025i | −0.0481125 | + | 0.0833333i | ||||
\(109\) | −0.828427 | + | 1.43488i | −0.0793489 | + | 0.137436i | −0.902969 | − | 0.429705i | \(-0.858617\pi\) |
0.823620 | + | 0.567142i | \(0.191951\pi\) | |||||||
\(110\) | 0.292893 | + | 0.507306i | 0.0279263 | + | 0.0483697i | ||||
\(111\) | −5.07107 | −0.481324 | ||||||||
\(112\) | −1.62132 | − | 2.09077i | −0.153200 | − | 0.197559i | ||||
\(113\) | −6.07107 | −0.571118 | −0.285559 | − | 0.958361i | \(-0.592179\pi\) | ||||
−0.285559 | + | 0.958361i | \(0.592179\pi\) | |||||||
\(114\) | −1.50000 | − | 2.59808i | −0.140488 | − | 0.243332i | ||||
\(115\) | −6.41421 | + | 11.1097i | −0.598128 | + | 1.03599i | ||||
\(116\) | −2.50000 | + | 4.33013i | −0.232119 | + | 0.402042i | ||||
\(117\) | −0.500000 | − | 0.866025i | −0.0462250 | − | 0.0800641i | ||||
\(118\) | 7.58579 | 0.698328 | ||||||||
\(119\) | −5.24264 | + | 12.8418i | −0.480592 | + | 1.17721i | ||||
\(120\) | −1.41421 | −0.129099 | ||||||||
\(121\) | 5.41421 | + | 9.37769i | 0.492201 | + | 0.852518i | ||||
\(122\) | 2.62132 | − | 4.54026i | 0.237323 | − | 0.411056i | ||||
\(123\) | −2.29289 | + | 3.97141i | −0.206743 | + | 0.358090i | ||||
\(124\) | −3.41421 | − | 5.91359i | −0.306605 | − | 0.531056i | ||||
\(125\) | 11.3137 | 1.01193 | ||||||||
\(126\) | −1.00000 | + | 2.44949i | −0.0890871 | + | 0.218218i | ||||
\(127\) | 9.89949 | 0.878438 | 0.439219 | − | 0.898380i | \(-0.355255\pi\) | ||||
0.439219 | + | 0.898380i | \(0.355255\pi\) | |||||||
\(128\) | −0.500000 | − | 0.866025i | −0.0441942 | − | 0.0765466i | ||||
\(129\) | −2.41421 | + | 4.18154i | −0.212560 | + | 0.368164i | ||||
\(130\) | 0.707107 | − | 1.22474i | 0.0620174 | − | 0.107417i | ||||
\(131\) | −4.94975 | − | 8.57321i | −0.432461 | − | 0.749045i | 0.564623 | − | 0.825349i | \(-0.309022\pi\) |
−0.997085 | + | 0.0763036i | \(0.975688\pi\) | |||||||
\(132\) | 0.414214 | 0.0360527 | ||||||||
\(133\) | −4.86396 | − | 6.27231i | −0.421759 | − | 0.543878i | ||||
\(134\) | −14.6569 | −1.26616 | ||||||||
\(135\) | 0.707107 | + | 1.22474i | 0.0608581 | + | 0.105409i | ||||
\(136\) | −2.62132 | + | 4.54026i | −0.224776 | + | 0.389324i | ||||
\(137\) | 6.53553 | − | 11.3199i | 0.558368 | − | 0.967122i | −0.439265 | − | 0.898358i | \(-0.644761\pi\) |
0.997633 | − | 0.0687646i | \(-0.0219057\pi\) | |||||||
\(138\) | 4.53553 | + | 7.85578i | 0.386090 | + | 0.668728i | ||||
\(139\) | −21.2132 | −1.79928 | −0.899640 | − | 0.436632i | \(-0.856171\pi\) | ||||
−0.899640 | + | 0.436632i | \(0.856171\pi\) | |||||||
\(140\) | −3.70711 | + | 0.507306i | −0.313308 | + | 0.0428752i | ||||
\(141\) | 9.00000 | 0.757937 | ||||||||
\(142\) | 0.500000 | + | 0.866025i | 0.0419591 | + | 0.0726752i | ||||
\(143\) | −0.207107 | + | 0.358719i | −0.0173191 | + | 0.0299976i | ||||
\(144\) | −0.500000 | + | 0.866025i | −0.0416667 | + | 0.0721688i | ||||
\(145\) | 3.53553 | + | 6.12372i | 0.293610 | + | 0.508548i | ||||
\(146\) | −1.07107 | −0.0886422 | ||||||||
\(147\) | −1.74264 | + | 6.77962i | −0.143731 | + | 0.559173i | ||||
\(148\) | −5.07107 | −0.416839 | ||||||||
\(149\) | −7.94975 | − | 13.7694i | −0.651269 | − | 1.12803i | −0.982815 | − | 0.184592i | \(-0.940904\pi\) |
0.331547 | − | 0.943439i | \(-0.392430\pi\) | |||||||
\(150\) | 1.50000 | − | 2.59808i | 0.122474 | − | 0.212132i | ||||
\(151\) | 3.79289 | − | 6.56948i | 0.308661 | − | 0.534617i | −0.669408 | − | 0.742895i | \(-0.733452\pi\) |
0.978070 | + | 0.208278i | \(0.0667857\pi\) | |||||||
\(152\) | −1.50000 | − | 2.59808i | −0.121666 | − | 0.210732i | ||||
\(153\) | 5.24264 | 0.423842 | ||||||||
\(154\) | 1.08579 | − | 0.148586i | 0.0874952 | − | 0.0119734i | ||||
\(155\) | −9.65685 | −0.775657 | ||||||||
\(156\) | −0.500000 | − | 0.866025i | −0.0400320 | − | 0.0693375i | ||||
\(157\) | −3.96447 | + | 6.86666i | −0.316399 | + | 0.548019i | −0.979734 | − | 0.200304i | \(-0.935807\pi\) |
0.663335 | + | 0.748323i | \(0.269140\pi\) | |||||||
\(158\) | −6.65685 | + | 11.5300i | −0.529591 | + | 0.917278i | ||||
\(159\) | −6.15685 | − | 10.6640i | −0.488270 | − | 0.845709i | ||||
\(160\) | −1.41421 | −0.111803 | ||||||||
\(161\) | 14.7071 | + | 18.9655i | 1.15908 | + | 1.49469i | ||||
\(162\) | 1.00000 | 0.0785674 | ||||||||
\(163\) | −8.57107 | − | 14.8455i | −0.671338 | − | 1.16279i | −0.977525 | − | 0.210820i | \(-0.932387\pi\) |
0.306187 | − | 0.951971i | \(-0.400947\pi\) | |||||||
\(164\) | −2.29289 | + | 3.97141i | −0.179045 | + | 0.310115i | ||||
\(165\) | 0.292893 | − | 0.507306i | 0.0228017 | − | 0.0394937i | ||||
\(166\) | 3.82843 | + | 6.63103i | 0.297144 | + | 0.514668i | ||||
\(167\) | 12.3137 | 0.952863 | 0.476432 | − | 0.879211i | \(-0.341930\pi\) | ||||
0.476432 | + | 0.879211i | \(0.341930\pi\) | |||||||
\(168\) | −1.00000 | + | 2.44949i | −0.0771517 | + | 0.188982i | ||||
\(169\) | 1.00000 | 0.0769231 | ||||||||
\(170\) | 3.70711 | + | 6.42090i | 0.284322 | + | 0.492460i | ||||
\(171\) | −1.50000 | + | 2.59808i | −0.114708 | + | 0.198680i | ||||
\(172\) | −2.41421 | + | 4.18154i | −0.184082 | + | 0.318839i | ||||
\(173\) | −10.1569 | − | 17.5922i | −0.772211 | − | 1.33751i | −0.936349 | − | 0.351072i | \(-0.885817\pi\) |
0.164137 | − | 0.986438i | \(-0.447516\pi\) | |||||||
\(174\) | 5.00000 | 0.379049 | ||||||||
\(175\) | 3.00000 | − | 7.34847i | 0.226779 | − | 0.555492i | ||||
\(176\) | 0.414214 | 0.0312225 | ||||||||
\(177\) | −3.79289 | − | 6.56948i | −0.285091 | − | 0.493793i | ||||
\(178\) | 3.12132 | − | 5.40629i | 0.233953 | − | 0.405218i | ||||
\(179\) | 6.17157 | − | 10.6895i | 0.461285 | − | 0.798969i | −0.537740 | − | 0.843111i | \(-0.680722\pi\) |
0.999025 | + | 0.0441415i | \(0.0140552\pi\) | |||||||
\(180\) | 0.707107 | + | 1.22474i | 0.0527046 | + | 0.0912871i | ||||
\(181\) | −11.5858 | −0.861165 | −0.430582 | − | 0.902551i | \(-0.641692\pi\) | ||||
−0.430582 | + | 0.902551i | \(0.641692\pi\) | |||||||
\(182\) | −1.62132 | − | 2.09077i | −0.120180 | − | 0.154978i | ||||
\(183\) | −5.24264 | −0.387547 | ||||||||
\(184\) | 4.53553 | + | 7.85578i | 0.334364 | + | 0.579135i | ||||
\(185\) | −3.58579 | + | 6.21076i | −0.263632 | + | 0.456624i | ||||
\(186\) | −3.41421 | + | 5.91359i | −0.250342 | + | 0.433606i | ||||
\(187\) | −1.08579 | − | 1.88064i | −0.0794006 | − | 0.137526i | ||||
\(188\) | 9.00000 | 0.656392 | ||||||||
\(189\) | 2.62132 | − | 0.358719i | 0.190673 | − | 0.0260930i | ||||
\(190\) | −4.24264 | −0.307794 | ||||||||
\(191\) | −1.17157 | − | 2.02922i | −0.0847720 | − | 0.146829i | 0.820522 | − | 0.571615i | \(-0.193683\pi\) |
−0.905294 | + | 0.424785i | \(0.860350\pi\) | |||||||
\(192\) | −0.500000 | + | 0.866025i | −0.0360844 | + | 0.0625000i | ||||
\(193\) | 7.87868 | − | 13.6463i | 0.567120 | − | 0.982280i | −0.429729 | − | 0.902958i | \(-0.641391\pi\) |
0.996849 | − | 0.0793225i | \(-0.0252757\pi\) | |||||||
\(194\) | −3.94975 | − | 6.84116i | −0.283575 | − | 0.491167i | ||||
\(195\) | −1.41421 | −0.101274 | ||||||||
\(196\) | −1.74264 | + | 6.77962i | −0.124474 | + | 0.484258i | ||||
\(197\) | 9.55635 | 0.680862 | 0.340431 | − | 0.940270i | \(-0.389427\pi\) | ||||
0.340431 | + | 0.940270i | \(0.389427\pi\) | |||||||
\(198\) | −0.207107 | − | 0.358719i | −0.0147184 | − | 0.0254931i | ||||
\(199\) | −5.29289 | + | 9.16756i | −0.375203 | + | 0.649871i | −0.990357 | − | 0.138536i | \(-0.955760\pi\) |
0.615154 | + | 0.788407i | \(0.289094\pi\) | |||||||
\(200\) | 1.50000 | − | 2.59808i | 0.106066 | − | 0.183712i | ||||
\(201\) | 7.32843 | + | 12.6932i | 0.516907 | + | 0.895310i | ||||
\(202\) | −1.17157 | −0.0824316 | ||||||||
\(203\) | 13.1066 | − | 1.79360i | 0.919903 | − | 0.125886i | ||||
\(204\) | 5.24264 | 0.367058 | ||||||||
\(205\) | 3.24264 | + | 5.61642i | 0.226476 | + | 0.392268i | ||||
\(206\) | −3.24264 | + | 5.61642i | −0.225925 | + | 0.391314i | ||||
\(207\) | 4.53553 | − | 7.85578i | 0.315241 | − | 0.546014i | ||||
\(208\) | −0.500000 | − | 0.866025i | −0.0346688 | − | 0.0600481i | ||||
\(209\) | 1.24264 | 0.0859553 | ||||||||
\(210\) | 2.29289 | + | 2.95680i | 0.158225 | + | 0.204038i | ||||
\(211\) | −28.3848 | −1.95409 | −0.977044 | − | 0.213036i | \(-0.931665\pi\) | ||||
−0.977044 | + | 0.213036i | \(0.931665\pi\) | |||||||
\(212\) | −6.15685 | − | 10.6640i | −0.422854 | − | 0.732405i | ||||
\(213\) | 0.500000 | − | 0.866025i | 0.0342594 | − | 0.0593391i | ||||
\(214\) | −6.82843 | + | 11.8272i | −0.466782 | + | 0.808490i | ||||
\(215\) | 3.41421 | + | 5.91359i | 0.232847 | + | 0.403304i | ||||
\(216\) | 1.00000 | 0.0680414 | ||||||||
\(217\) | −6.82843 | + | 16.7262i | −0.463544 | + | 1.13545i | ||||
\(218\) | 1.65685 | 0.112216 | ||||||||
\(219\) | 0.535534 | + | 0.927572i | 0.0361880 | + | 0.0626795i | ||||
\(220\) | 0.292893 | − | 0.507306i | 0.0197469 | − | 0.0342026i | ||||
\(221\) | −2.62132 | + | 4.54026i | −0.176329 | + | 0.305411i | ||||
\(222\) | 2.53553 | + | 4.39167i | 0.170174 | + | 0.294750i | ||||
\(223\) | 21.3848 | 1.43203 | 0.716015 | − | 0.698085i | \(-0.245964\pi\) | ||||
0.716015 | + | 0.698085i | \(0.245964\pi\) | |||||||
\(224\) | −1.00000 | + | 2.44949i | −0.0668153 | + | 0.163663i | ||||
\(225\) | −3.00000 | −0.200000 | ||||||||
\(226\) | 3.03553 | + | 5.25770i | 0.201921 | + | 0.349737i | ||||
\(227\) | 13.0711 | − | 22.6398i | 0.867557 | − | 1.50265i | 0.00307185 | − | 0.999995i | \(-0.499022\pi\) |
0.864485 | − | 0.502658i | \(-0.167644\pi\) | |||||||
\(228\) | −1.50000 | + | 2.59808i | −0.0993399 | + | 0.172062i | ||||
\(229\) | 3.58579 | + | 6.21076i | 0.236955 | + | 0.410419i | 0.959839 | − | 0.280551i | \(-0.0905171\pi\) |
−0.722884 | + | 0.690970i | \(0.757184\pi\) | |||||||
\(230\) | 12.8284 | 0.845881 | ||||||||
\(231\) | −0.671573 | − | 0.866025i | −0.0441863 | − | 0.0569803i | ||||
\(232\) | 5.00000 | 0.328266 | ||||||||
\(233\) | 1.86396 | + | 3.22848i | 0.122112 | + | 0.211504i | 0.920600 | − | 0.390506i | \(-0.127700\pi\) |
−0.798488 | + | 0.602010i | \(0.794367\pi\) | |||||||
\(234\) | −0.500000 | + | 0.866025i | −0.0326860 | + | 0.0566139i | ||||
\(235\) | 6.36396 | − | 11.0227i | 0.415139 | − | 0.719042i | ||||
\(236\) | −3.79289 | − | 6.56948i | −0.246896 | − | 0.427637i | ||||
\(237\) | 13.3137 | 0.864818 | ||||||||
\(238\) | 13.7426 | − | 1.88064i | 0.890803 | − | 0.121904i | ||||
\(239\) | −2.51472 | −0.162664 | −0.0813318 | − | 0.996687i | \(-0.525917\pi\) | ||||
−0.0813318 | + | 0.996687i | \(0.525917\pi\) | |||||||
\(240\) | 0.707107 | + | 1.22474i | 0.0456435 | + | 0.0790569i | ||||
\(241\) | 8.24264 | − | 14.2767i | 0.530955 | − | 0.919641i | −0.468392 | − | 0.883521i | \(-0.655167\pi\) |
0.999347 | − | 0.0361207i | \(-0.0115001\pi\) | |||||||
\(242\) | 5.41421 | − | 9.37769i | 0.348039 | − | 0.602821i | ||||
\(243\) | −0.500000 | − | 0.866025i | −0.0320750 | − | 0.0555556i | ||||
\(244\) | −5.24264 | −0.335626 | ||||||||
\(245\) | 7.07107 | + | 6.92820i | 0.451754 | + | 0.442627i | ||||
\(246\) | 4.58579 | 0.292379 | ||||||||
\(247\) | −1.50000 | − | 2.59808i | −0.0954427 | − | 0.165312i | ||||
\(248\) | −3.41421 | + | 5.91359i | −0.216803 | + | 0.375513i | ||||
\(249\) | 3.82843 | − | 6.63103i | 0.242617 | − | 0.420224i | ||||
\(250\) | −5.65685 | − | 9.79796i | −0.357771 | − | 0.619677i | ||||
\(251\) | 12.8284 | 0.809723 | 0.404862 | − | 0.914378i | \(-0.367320\pi\) | ||||
0.404862 | + | 0.914378i | \(0.367320\pi\) | |||||||
\(252\) | 2.62132 | − | 0.358719i | 0.165128 | − | 0.0225972i | ||||
\(253\) | −3.75736 | −0.236223 | ||||||||
\(254\) | −4.94975 | − | 8.57321i | −0.310575 | − | 0.537931i | ||||
\(255\) | 3.70711 | − | 6.42090i | 0.232148 | − | 0.402092i | ||||
\(256\) | −0.500000 | + | 0.866025i | −0.0312500 | + | 0.0541266i | ||||
\(257\) | 10.8995 | + | 18.8785i | 0.679892 | + | 1.17761i | 0.975013 | + | 0.222147i | \(0.0713066\pi\) |
−0.295121 | + | 0.955460i | \(0.595360\pi\) | |||||||
\(258\) | 4.82843 | 0.300605 | ||||||||
\(259\) | 8.22183 | + | 10.6024i | 0.510879 | + | 0.658803i | ||||
\(260\) | −1.41421 | −0.0877058 | ||||||||
\(261\) | −2.50000 | − | 4.33013i | −0.154746 | − | 0.268028i | ||||
\(262\) | −4.94975 | + | 8.57321i | −0.305796 | + | 0.529655i | ||||
\(263\) | 3.77817 | − | 6.54399i | 0.232972 | − | 0.403520i | −0.725709 | − | 0.688002i | \(-0.758488\pi\) |
0.958681 | + | 0.284482i | \(0.0918215\pi\) | |||||||
\(264\) | −0.207107 | − | 0.358719i | −0.0127465 | − | 0.0220777i | ||||
\(265\) | −17.4142 | −1.06975 | ||||||||
\(266\) | −3.00000 | + | 7.34847i | −0.183942 | + | 0.450564i | ||||
\(267\) | −6.24264 | −0.382043 | ||||||||
\(268\) | 7.32843 | + | 12.6932i | 0.447655 | + | 0.775361i | ||||
\(269\) | 1.84315 | − | 3.19242i | 0.112379 | − | 0.194645i | −0.804350 | − | 0.594155i | \(-0.797486\pi\) |
0.916729 | + | 0.399510i | \(0.130820\pi\) | |||||||
\(270\) | 0.707107 | − | 1.22474i | 0.0430331 | − | 0.0745356i | ||||
\(271\) | 7.69239 | + | 13.3236i | 0.467279 | + | 0.809351i | 0.999301 | − | 0.0373791i | \(-0.0119009\pi\) |
−0.532022 | + | 0.846731i | \(0.678568\pi\) | |||||||
\(272\) | 5.24264 | 0.317882 | ||||||||
\(273\) | −1.00000 | + | 2.44949i | −0.0605228 | + | 0.148250i | ||||
\(274\) | −13.0711 | −0.789652 | ||||||||
\(275\) | 0.621320 | + | 1.07616i | 0.0374670 | + | 0.0648948i | ||||
\(276\) | 4.53553 | − | 7.85578i | 0.273007 | − | 0.472862i | ||||
\(277\) | 8.20711 | − | 14.2151i | 0.493117 | − | 0.854104i | −0.506851 | − | 0.862033i | \(-0.669191\pi\) |
0.999969 | + | 0.00792936i | \(0.00252402\pi\) | |||||||
\(278\) | 10.6066 | + | 18.3712i | 0.636142 | + | 1.10183i | ||||
\(279\) | 6.82843 | 0.408807 | ||||||||
\(280\) | 2.29289 | + | 2.95680i | 0.137027 | + | 0.176702i | ||||
\(281\) | 7.31371 | 0.436299 | 0.218150 | − | 0.975915i | \(-0.429998\pi\) | ||||
0.218150 | + | 0.975915i | \(0.429998\pi\) | |||||||
\(282\) | −4.50000 | − | 7.79423i | −0.267971 | − | 0.464140i | ||||
\(283\) | −8.53553 | + | 14.7840i | −0.507385 | + | 0.878816i | 0.492579 | + | 0.870268i | \(0.336054\pi\) |
−0.999963 | + | 0.00854836i | \(0.997279\pi\) | |||||||
\(284\) | 0.500000 | − | 0.866025i | 0.0296695 | − | 0.0513892i | ||||
\(285\) | 2.12132 | + | 3.67423i | 0.125656 | + | 0.217643i | ||||
\(286\) | 0.414214 | 0.0244930 | ||||||||
\(287\) | 12.0208 | − | 1.64501i | 0.709566 | − | 0.0971019i | ||||
\(288\) | 1.00000 | 0.0589256 | ||||||||
\(289\) | −5.24264 | − | 9.08052i | −0.308391 | − | 0.534148i | ||||
\(290\) | 3.53553 | − | 6.12372i | 0.207614 | − | 0.359597i | ||||
\(291\) | −3.94975 | + | 6.84116i | −0.231538 | + | 0.401036i | ||||
\(292\) | 0.535534 | + | 0.927572i | 0.0313398 | + | 0.0542820i | ||||
\(293\) | −18.7279 | −1.09410 | −0.547048 | − | 0.837101i | \(-0.684249\pi\) | ||||
−0.547048 | + | 0.837101i | \(0.684249\pi\) | |||||||
\(294\) | 6.74264 | − | 1.88064i | 0.393239 | − | 0.109681i | ||||
\(295\) | −10.7279 | −0.624604 | ||||||||
\(296\) | 2.53553 | + | 4.39167i | 0.147375 | + | 0.255261i | ||||
\(297\) | −0.207107 | + | 0.358719i | −0.0120176 | + | 0.0208150i | ||||
\(298\) | −7.94975 | + | 13.7694i | −0.460517 | + | 0.797638i | ||||
\(299\) | 4.53553 | + | 7.85578i | 0.262297 | + | 0.454311i | ||||
\(300\) | −3.00000 | −0.173205 | ||||||||
\(301\) | 12.6569 | − | 1.73205i | 0.729529 | − | 0.0998337i | ||||
\(302\) | −7.58579 | −0.436513 | ||||||||
\(303\) | 0.585786 | + | 1.01461i | 0.0336526 | + | 0.0582879i | ||||
\(304\) | −1.50000 | + | 2.59808i | −0.0860309 | + | 0.149010i | ||||
\(305\) | −3.70711 | + | 6.42090i | −0.212268 | + | 0.367660i | ||||
\(306\) | −2.62132 | − | 4.54026i | −0.149851 | − | 0.259549i | ||||
\(307\) | −19.6274 | −1.12020 | −0.560098 | − | 0.828426i | \(-0.689237\pi\) | ||||
−0.560098 | + | 0.828426i | \(0.689237\pi\) | |||||||
\(308\) | −0.671573 | − | 0.866025i | −0.0382664 | − | 0.0493464i | ||||
\(309\) | 6.48528 | 0.368935 | ||||||||
\(310\) | 4.82843 | + | 8.36308i | 0.274236 | + | 0.474991i | ||||
\(311\) | 3.29289 | − | 5.70346i | 0.186723 | − | 0.323413i | −0.757433 | − | 0.652913i | \(-0.773547\pi\) |
0.944156 | + | 0.329500i | \(0.106880\pi\) | |||||||
\(312\) | −0.500000 | + | 0.866025i | −0.0283069 | + | 0.0490290i | ||||
\(313\) | −9.07107 | − | 15.7116i | −0.512727 | − | 0.888069i | −0.999891 | − | 0.0147588i | \(-0.995302\pi\) |
0.487164 | − | 0.873310i | \(-0.338031\pi\) | |||||||
\(314\) | 7.92893 | 0.447456 | ||||||||
\(315\) | 1.41421 | − | 3.46410i | 0.0796819 | − | 0.195180i | ||||
\(316\) | 13.3137 | 0.748955 | ||||||||
\(317\) | −0.414214 | − | 0.717439i | −0.0232646 | − | 0.0402954i | 0.854159 | − | 0.520012i | \(-0.174073\pi\) |
−0.877423 | + | 0.479717i | \(0.840739\pi\) | |||||||
\(318\) | −6.15685 | + | 10.6640i | −0.345259 | + | 0.598007i | ||||
\(319\) | −1.03553 | + | 1.79360i | −0.0579788 | + | 0.100422i | ||||
\(320\) | 0.707107 | + | 1.22474i | 0.0395285 | + | 0.0684653i | ||||
\(321\) | 13.6569 | 0.762251 | ||||||||
\(322\) | 9.07107 | − | 22.2195i | 0.505511 | − | 1.23824i | ||||
\(323\) | 15.7279 | 0.875125 | ||||||||
\(324\) | −0.500000 | − | 0.866025i | −0.0277778 | − | 0.0481125i | ||||
\(325\) | 1.50000 | − | 2.59808i | 0.0832050 | − | 0.144115i | ||||
\(326\) | −8.57107 | + | 14.8455i | −0.474708 | + | 0.822218i | ||||
\(327\) | −0.828427 | − | 1.43488i | −0.0458121 | − | 0.0793489i | ||||
\(328\) | 4.58579 | 0.253208 | ||||||||
\(329\) | −14.5919 | − | 18.8169i | −0.804477 | − | 1.03741i | ||||
\(330\) | −0.585786 | −0.0322465 | ||||||||
\(331\) | 11.2426 | + | 19.4728i | 0.617951 | + | 1.07032i | 0.989859 | + | 0.142053i | \(0.0453705\pi\) |
−0.371908 | + | 0.928270i | \(0.621296\pi\) | |||||||
\(332\) | 3.82843 | − | 6.63103i | 0.210112 | − | 0.363925i | ||||
\(333\) | 2.53553 | − | 4.39167i | 0.138946 | − | 0.240662i | ||||
\(334\) | −6.15685 | − | 10.6640i | −0.336888 | − | 0.583507i | ||||
\(335\) | 20.7279 | 1.13249 | ||||||||
\(336\) | 2.62132 | − | 0.358719i | 0.143005 | − | 0.0195698i | ||||
\(337\) | 28.6569 | 1.56104 | 0.780519 | − | 0.625132i | \(-0.214955\pi\) | ||||
0.780519 | + | 0.625132i | \(0.214955\pi\) | |||||||
\(338\) | −0.500000 | − | 0.866025i | −0.0271964 | − | 0.0471056i | ||||
\(339\) | 3.03553 | − | 5.25770i | 0.164868 | − | 0.285559i | ||||
\(340\) | 3.70711 | − | 6.42090i | 0.201046 | − | 0.348222i | ||||
\(341\) | −1.41421 | − | 2.44949i | −0.0765840 | − | 0.132647i | ||||
\(342\) | 3.00000 | 0.162221 | ||||||||
\(343\) | 17.0000 | − | 7.34847i | 0.917914 | − | 0.396780i | ||||
\(344\) | 4.82843 | 0.260331 | ||||||||
\(345\) | −6.41421 | − | 11.1097i | −0.345330 | − | 0.598128i | ||||
\(346\) | −10.1569 | + | 17.5922i | −0.546036 | + | 0.945762i | ||||
\(347\) | −2.87868 | + | 4.98602i | −0.154536 | + | 0.267664i | −0.932890 | − | 0.360162i | \(-0.882721\pi\) |
0.778354 | + | 0.627825i | \(0.216055\pi\) | |||||||
\(348\) | −2.50000 | − | 4.33013i | −0.134014 | − | 0.232119i | ||||
\(349\) | 5.41421 | 0.289816 | 0.144908 | − | 0.989445i | \(-0.453711\pi\) | ||||
0.144908 | + | 0.989445i | \(0.453711\pi\) | |||||||
\(350\) | −7.86396 | + | 1.07616i | −0.420346 | + | 0.0575231i | ||||
\(351\) | 1.00000 | 0.0533761 | ||||||||
\(352\) | −0.207107 | − | 0.358719i | −0.0110388 | − | 0.0191198i | ||||
\(353\) | −6.31371 | + | 10.9357i | −0.336045 | + | 0.582047i | −0.983685 | − | 0.179900i | \(-0.942423\pi\) |
0.647640 | + | 0.761946i | \(0.275756\pi\) | |||||||
\(354\) | −3.79289 | + | 6.56948i | −0.201590 | + | 0.349164i | ||||
\(355\) | −0.707107 | − | 1.22474i | −0.0375293 | − | 0.0650027i | ||||
\(356\) | −6.24264 | −0.330859 | ||||||||
\(357\) | −8.50000 | − | 10.9612i | −0.449868 | − | 0.580126i | ||||
\(358\) | −12.3431 | −0.652356 | ||||||||
\(359\) | 7.72792 | + | 13.3852i | 0.407864 | + | 0.706441i | 0.994650 | − | 0.103301i | \(-0.0329404\pi\) |
−0.586786 | + | 0.809742i | \(0.699607\pi\) | |||||||
\(360\) | 0.707107 | − | 1.22474i | 0.0372678 | − | 0.0645497i | ||||
\(361\) | 5.00000 | − | 8.66025i | 0.263158 | − | 0.455803i | ||||
\(362\) | 5.79289 | + | 10.0336i | 0.304468 | + | 0.527354i | ||||
\(363\) | −10.8284 | −0.568345 | ||||||||
\(364\) | −1.00000 | + | 2.44949i | −0.0524142 | + | 0.128388i | ||||
\(365\) | 1.51472 | 0.0792840 | ||||||||
\(366\) | 2.62132 | + | 4.54026i | 0.137019 | + | 0.237323i | ||||
\(367\) | −7.00000 | + | 12.1244i | −0.365397 | + | 0.632886i | −0.988840 | − | 0.148983i | \(-0.952400\pi\) |
0.623443 | + | 0.781869i | \(0.285733\pi\) | |||||||
\(368\) | 4.53553 | − | 7.85578i | 0.236431 | − | 0.409511i | ||||
\(369\) | −2.29289 | − | 3.97141i | −0.119363 | − | 0.206743i | ||||
\(370\) | 7.17157 | 0.372832 | ||||||||
\(371\) | −12.3137 | + | 30.1623i | −0.639296 | + | 1.56595i | ||||
\(372\) | 6.82843 | 0.354037 | ||||||||
\(373\) | 5.55025 | + | 9.61332i | 0.287381 | + | 0.497759i | 0.973184 | − | 0.230029i | \(-0.0738820\pi\) |
−0.685803 | + | 0.727788i | \(0.740549\pi\) | |||||||
\(374\) | −1.08579 | + | 1.88064i | −0.0561447 | + | 0.0972454i | ||||
\(375\) | −5.65685 | + | 9.79796i | −0.292119 | + | 0.505964i | ||||
\(376\) | −4.50000 | − | 7.79423i | −0.232070 | − | 0.401957i | ||||
\(377\) | 5.00000 | 0.257513 | ||||||||
\(378\) | −1.62132 | − | 2.09077i | −0.0833917 | − | 0.107538i | ||||
\(379\) | −33.6569 | −1.72884 | −0.864418 | − | 0.502773i | \(-0.832313\pi\) | ||||
−0.864418 | + | 0.502773i | \(0.832313\pi\) | |||||||
\(380\) | 2.12132 | + | 3.67423i | 0.108821 | + | 0.188484i | ||||
\(381\) | −4.94975 | + | 8.57321i | −0.253583 | + | 0.439219i | ||||
\(382\) | −1.17157 | + | 2.02922i | −0.0599429 | + | 0.103824i | ||||
\(383\) | −3.24264 | − | 5.61642i | −0.165691 | − | 0.286986i | 0.771209 | − | 0.636582i | \(-0.219652\pi\) |
−0.936901 | + | 0.349596i | \(0.886319\pi\) | |||||||
\(384\) | 1.00000 | 0.0510310 | ||||||||
\(385\) | −1.53553 | + | 0.210133i | −0.0782581 | + | 0.0107094i | ||||
\(386\) | −15.7574 | −0.802028 | ||||||||
\(387\) | −2.41421 | − | 4.18154i | −0.122721 | − | 0.212560i | ||||
\(388\) | −3.94975 | + | 6.84116i | −0.200518 | + | 0.347307i | ||||
\(389\) | −11.5000 | + | 19.9186i | −0.583073 | + | 1.00991i | 0.412039 | + | 0.911166i | \(0.364817\pi\) |
−0.995113 | + | 0.0987463i | \(0.968517\pi\) | |||||||
\(390\) | 0.707107 | + | 1.22474i | 0.0358057 | + | 0.0620174i | ||||
\(391\) | −47.5563 | −2.40503 | ||||||||
\(392\) | 6.74264 | − | 1.88064i | 0.340555 | − | 0.0949865i | ||||
\(393\) | 9.89949 | 0.499363 | ||||||||
\(394\) | −4.77817 | − | 8.27604i | −0.240721 | − | 0.416941i | ||||
\(395\) | 9.41421 | − | 16.3059i | 0.473680 | − | 0.820439i | ||||
\(396\) | −0.207107 | + | 0.358719i | −0.0104075 | + | 0.0180263i | ||||
\(397\) | 9.87868 | + | 17.1104i | 0.495797 | + | 0.858745i | 0.999988 | − | 0.00484675i | \(-0.00154277\pi\) |
−0.504192 | + | 0.863592i | \(0.668209\pi\) | |||||||
\(398\) | 10.5858 | 0.530618 | ||||||||
\(399\) | 7.86396 | − | 1.07616i | 0.393690 | − | 0.0538753i | ||||
\(400\) | −3.00000 | −0.150000 | ||||||||
\(401\) | −9.53553 | − | 16.5160i | −0.476182 | − | 0.824771i | 0.523446 | − | 0.852059i | \(-0.324646\pi\) |
−0.999628 | + | 0.0272878i | \(0.991313\pi\) | |||||||
\(402\) | 7.32843 | − | 12.6932i | 0.365509 | − | 0.633080i | ||||
\(403\) | −3.41421 | + | 5.91359i | −0.170074 | + | 0.294577i | ||||
\(404\) | 0.585786 | + | 1.01461i | 0.0291440 | + | 0.0504788i | ||||
\(405\) | −1.41421 | −0.0702728 | ||||||||
\(406\) | −8.10660 | − | 10.4539i | −0.402324 | − | 0.518816i | ||||
\(407\) | −2.10051 | −0.104118 | ||||||||
\(408\) | −2.62132 | − | 4.54026i | −0.129775 | − | 0.224776i | ||||
\(409\) | 1.29289 | − | 2.23936i | 0.0639295 | − | 0.110729i | −0.832289 | − | 0.554342i | \(-0.812970\pi\) |
0.896219 | + | 0.443613i | \(0.146303\pi\) | |||||||
\(410\) | 3.24264 | − | 5.61642i | 0.160143 | − | 0.277375i | ||||
\(411\) | 6.53553 | + | 11.3199i | 0.322374 | + | 0.558368i | ||||
\(412\) | 6.48528 | 0.319507 | ||||||||
\(413\) | −7.58579 | + | 18.5813i | −0.373272 | + | 0.914326i | ||||
\(414\) | −9.07107 | −0.445819 | ||||||||
\(415\) | −5.41421 | − | 9.37769i | −0.265773 | − | 0.460333i | ||||
\(416\) | −0.500000 | + | 0.866025i | −0.0245145 | + | 0.0424604i | ||||
\(417\) | 10.6066 | − | 18.3712i | 0.519408 | − | 0.899640i | ||||
\(418\) | −0.621320 | − | 1.07616i | −0.0303898 | − | 0.0526366i | ||||
\(419\) | −27.4558 | −1.34131 | −0.670653 | − | 0.741771i | \(-0.733986\pi\) | ||||
−0.670653 | + | 0.741771i | \(0.733986\pi\) | |||||||
\(420\) | 1.41421 | − | 3.46410i | 0.0690066 | − | 0.169031i | ||||
\(421\) | 10.5858 | 0.515920 | 0.257960 | − | 0.966156i | \(-0.416950\pi\) | ||||
0.257960 | + | 0.966156i | \(0.416950\pi\) | |||||||
\(422\) | 14.1924 | + | 24.5819i | 0.690875 | + | 1.19663i | ||||
\(423\) | −4.50000 | + | 7.79423i | −0.218797 | + | 0.378968i | ||||
\(424\) | −6.15685 | + | 10.6640i | −0.299003 | + | 0.517889i | ||||
\(425\) | 7.86396 | + | 13.6208i | 0.381458 | + | 0.660705i | ||||
\(426\) | −1.00000 | −0.0484502 | ||||||||
\(427\) | 8.50000 | + | 10.9612i | 0.411344 | + | 0.530448i | ||||
\(428\) | 13.6569 | 0.660129 | ||||||||
\(429\) | −0.207107 | − | 0.358719i | −0.00999921 | − | 0.0173191i | ||||
\(430\) | 3.41421 | − | 5.91359i | 0.164648 | − | 0.285179i | ||||
\(431\) | −7.24264 | + | 12.5446i | −0.348866 | + | 0.604253i | −0.986048 | − | 0.166460i | \(-0.946766\pi\) |
0.637183 | + | 0.770713i | \(0.280100\pi\) | |||||||
\(432\) | −0.500000 | − | 0.866025i | −0.0240563 | − | 0.0416667i | ||||
\(433\) | −19.0000 | −0.913082 | −0.456541 | − | 0.889702i | \(-0.650912\pi\) | ||||
−0.456541 | + | 0.889702i | \(0.650912\pi\) | |||||||
\(434\) | 17.8995 | − | 2.44949i | 0.859203 | − | 0.117579i | ||||
\(435\) | −7.07107 | −0.339032 | ||||||||
\(436\) | −0.828427 | − | 1.43488i | −0.0396745 | − | 0.0687182i | ||||
\(437\) | 13.6066 | − | 23.5673i | 0.650892 | − | 1.12738i | ||||
\(438\) | 0.535534 | − | 0.927572i | 0.0255888 | − | 0.0443211i | ||||
\(439\) | 5.29289 | + | 9.16756i | 0.252616 | + | 0.437544i | 0.964245 | − | 0.265011i | \(-0.0853757\pi\) |
−0.711629 | + | 0.702555i | \(0.752042\pi\) | |||||||
\(440\) | −0.585786 | −0.0279263 | ||||||||
\(441\) | −5.00000 | − | 4.89898i | −0.238095 | − | 0.233285i | ||||
\(442\) | 5.24264 | 0.249367 | ||||||||
\(443\) | −11.3640 | − | 19.6830i | −0.539918 | − | 0.935166i | −0.998908 | − | 0.0467240i | \(-0.985122\pi\) |
0.458990 | − | 0.888442i | \(-0.348211\pi\) | |||||||
\(444\) | 2.53553 | − | 4.39167i | 0.120331 | − | 0.208420i | ||||
\(445\) | −4.41421 | + | 7.64564i | −0.209254 | + | 0.362438i | ||||
\(446\) | −10.6924 | − | 18.5198i | −0.506299 | − | 0.876936i | ||||
\(447\) | 15.8995 | 0.752020 | ||||||||
\(448\) | 2.62132 | − | 0.358719i | 0.123846 | − | 0.0169479i | ||||
\(449\) | −33.9411 | −1.60178 | −0.800890 | − | 0.598811i | \(-0.795640\pi\) | ||||
−0.800890 | + | 0.598811i | \(0.795640\pi\) | |||||||
\(450\) | 1.50000 | + | 2.59808i | 0.0707107 | + | 0.122474i | ||||
\(451\) | −0.949747 | + | 1.64501i | −0.0447219 | + | 0.0774605i | ||||
\(452\) | 3.03553 | − | 5.25770i | 0.142780 | − | 0.247301i | ||||
\(453\) | 3.79289 | + | 6.56948i | 0.178206 | + | 0.308661i | ||||
\(454\) | −26.1421 | −1.22691 | ||||||||
\(455\) | 2.29289 | + | 2.95680i | 0.107492 | + | 0.138617i | ||||
\(456\) | 3.00000 | 0.140488 | ||||||||
\(457\) | 7.60660 | + | 13.1750i | 0.355822 | + | 0.616301i | 0.987258 | − | 0.159126i | \(-0.0508677\pi\) |
−0.631436 | + | 0.775428i | \(0.717534\pi\) | |||||||
\(458\) | 3.58579 | − | 6.21076i | 0.167553 | − | 0.290210i | ||||
\(459\) | −2.62132 | + | 4.54026i | −0.122353 | + | 0.211921i | ||||
\(460\) | −6.41421 | − | 11.1097i | −0.299064 | − | 0.517994i | ||||
\(461\) | −33.4558 | −1.55819 | −0.779097 | − | 0.626903i | \(-0.784322\pi\) | ||||
−0.779097 | + | 0.626903i | \(0.784322\pi\) | |||||||
\(462\) | −0.414214 | + | 1.01461i | −0.0192710 | + | 0.0472040i | ||||
\(463\) | −37.9411 | −1.76327 | −0.881637 | − | 0.471929i | \(-0.843558\pi\) | ||||
−0.881637 | + | 0.471929i | \(0.843558\pi\) | |||||||
\(464\) | −2.50000 | − | 4.33013i | −0.116060 | − | 0.201021i | ||||
\(465\) | 4.82843 | − | 8.36308i | 0.223913 | − | 0.387829i | ||||
\(466\) | 1.86396 | − | 3.22848i | 0.0863463 | − | 0.149556i | ||||
\(467\) | 0.121320 | + | 0.210133i | 0.00561404 | + | 0.00972380i | 0.868819 | − | 0.495130i | \(-0.164880\pi\) |
−0.863205 | + | 0.504854i | \(0.831546\pi\) | |||||||
\(468\) | 1.00000 | 0.0462250 | ||||||||
\(469\) | 14.6569 | − | 35.9018i | 0.676791 | − | 1.65779i | ||||
\(470\) | −12.7279 | −0.587095 | ||||||||
\(471\) | −3.96447 | − | 6.86666i | −0.182673 | − | 0.316399i | ||||
\(472\) | −3.79289 | + | 6.56948i | −0.174582 | + | 0.302385i | ||||
\(473\) | −1.00000 | + | 1.73205i | −0.0459800 | + | 0.0796398i | ||||
\(474\) | −6.65685 | − | 11.5300i | −0.305759 | − | 0.529591i | ||||
\(475\) | −9.00000 | −0.412948 | ||||||||
\(476\) | −8.50000 | − | 10.9612i | −0.389597 | − | 0.502404i | ||||
\(477\) | 12.3137 | 0.563806 | ||||||||
\(478\) | 1.25736 | + | 2.17781i | 0.0575103 | + | 0.0996107i | ||||
\(479\) | 15.5711 | − | 26.9699i | 0.711460 | − | 1.23229i | −0.252849 | − | 0.967506i | \(-0.581368\pi\) |
0.964309 | − | 0.264779i | \(-0.0852992\pi\) | |||||||
\(480\) | 0.707107 | − | 1.22474i | 0.0322749 | − | 0.0559017i | ||||
\(481\) | 2.53553 | + | 4.39167i | 0.115610 | + | 0.200243i | ||||
\(482\) | −16.4853 | −0.750884 | ||||||||
\(483\) | −23.7782 | + | 3.25397i | −1.08194 | + | 0.148061i | ||||
\(484\) | −10.8284 | −0.492201 | ||||||||
\(485\) | 5.58579 | + | 9.67487i | 0.253637 | + | 0.439313i | ||||
\(486\) | −0.500000 | + | 0.866025i | −0.0226805 | + | 0.0392837i | ||||
\(487\) | 11.8640 | − | 20.5490i | 0.537607 | − | 0.931163i | −0.461425 | − | 0.887179i | \(-0.652662\pi\) |
0.999032 | − | 0.0439840i | \(-0.0140051\pi\) | |||||||
\(488\) | 2.62132 | + | 4.54026i | 0.118662 | + | 0.205528i | ||||
\(489\) | 17.1421 | 0.775194 | ||||||||
\(490\) | 2.46447 | − | 9.58783i | 0.111333 | − | 0.433134i | ||||
\(491\) | −26.2843 | −1.18619 | −0.593096 | − | 0.805132i | \(-0.702095\pi\) | ||||
−0.593096 | + | 0.805132i | \(0.702095\pi\) | |||||||
\(492\) | −2.29289 | − | 3.97141i | −0.103372 | − | 0.179045i | ||||
\(493\) | −13.1066 | + | 22.7013i | −0.590292 | + | 1.02242i | ||||
\(494\) | −1.50000 | + | 2.59808i | −0.0674882 | + | 0.116893i | ||||
\(495\) | 0.292893 | + | 0.507306i | 0.0131646 | + | 0.0228017i | ||||
\(496\) | 6.82843 | 0.306605 | ||||||||
\(497\) | −2.62132 | + | 0.358719i | −0.117582 | + | 0.0160908i | ||||
\(498\) | −7.65685 | −0.343112 | ||||||||
\(499\) | 15.0000 | + | 25.9808i | 0.671492 | + | 1.16306i | 0.977481 | + | 0.211024i | \(0.0676797\pi\) |
−0.305989 | + | 0.952035i | \(0.598987\pi\) | |||||||
\(500\) | −5.65685 | + | 9.79796i | −0.252982 | + | 0.438178i | ||||
\(501\) | −6.15685 | + | 10.6640i | −0.275068 | + | 0.476432i | ||||
\(502\) | −6.41421 | − | 11.1097i | −0.286280 | − | 0.495852i | ||||
\(503\) | 35.7990 | 1.59620 | 0.798099 | − | 0.602526i | \(-0.205839\pi\) | ||||
0.798099 | + | 0.602526i | \(0.205839\pi\) | |||||||
\(504\) | −1.62132 | − | 2.09077i | −0.0722193 | − | 0.0931303i | ||||
\(505\) | 1.65685 | 0.0737290 | ||||||||
\(506\) | 1.87868 | + | 3.25397i | 0.0835175 | + | 0.144657i | ||||
\(507\) | −0.500000 | + | 0.866025i | −0.0222058 | + | 0.0384615i | ||||
\(508\) | −4.94975 | + | 8.57321i | −0.219610 | + | 0.380375i | ||||
\(509\) | −6.48528 | − | 11.2328i | −0.287455 | − | 0.497887i | 0.685747 | − | 0.727840i | \(-0.259476\pi\) |
−0.973202 | + | 0.229954i | \(0.926143\pi\) | |||||||
\(510\) | −7.41421 | −0.328307 | ||||||||
\(511\) | 1.07107 | − | 2.62357i | 0.0473813 | − | 0.116060i | ||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | −1.50000 | − | 2.59808i | −0.0662266 | − | 0.114708i | ||||
\(514\) | 10.8995 | − | 18.8785i | 0.480756 | − | 0.832694i | ||||
\(515\) | 4.58579 | − | 7.94282i | 0.202074 | − | 0.350002i | ||||
\(516\) | −2.41421 | − | 4.18154i | −0.106280 | − | 0.184082i | ||||
\(517\) | 3.72792 | 0.163954 | ||||||||
\(518\) | 5.07107 | − | 12.4215i | 0.222810 | − | 0.545771i | ||||
\(519\) | 20.3137 | 0.891673 | ||||||||
\(520\) | 0.707107 | + | 1.22474i | 0.0310087 | + | 0.0537086i | ||||
\(521\) | 7.00000 | − | 12.1244i | 0.306676 | − | 0.531178i | −0.670957 | − | 0.741496i | \(-0.734117\pi\) |
0.977633 | + | 0.210318i | \(0.0674500\pi\) | |||||||
\(522\) | −2.50000 | + | 4.33013i | −0.109422 | + | 0.189525i | ||||
\(523\) | 1.92893 | + | 3.34101i | 0.0843463 | + | 0.146092i | 0.905112 | − | 0.425172i | \(-0.139786\pi\) |
−0.820766 | + | 0.571264i | \(0.806453\pi\) | |||||||
\(524\) | 9.89949 | 0.432461 | ||||||||
\(525\) | 4.86396 | + | 6.27231i | 0.212281 | + | 0.273746i | ||||
\(526\) | −7.55635 | −0.329472 | ||||||||
\(527\) | −17.8995 | − | 31.0028i | −0.779714 | − | 1.35050i | ||||
\(528\) | −0.207107 | + | 0.358719i | −0.00901317 | + | 0.0156113i | ||||
\(529\) | −29.6421 | + | 51.3417i | −1.28879 | + | 2.23225i | ||||
\(530\) | 8.70711 | + | 15.0812i | 0.378213 | + | 0.655083i | ||||
\(531\) | 7.58579 | 0.329195 | ||||||||
\(532\) | 7.86396 | − | 1.07616i | 0.340946 | − | 0.0466574i | ||||
\(533\) | 4.58579 | 0.198632 | ||||||||
\(534\) | 3.12132 | + | 5.40629i | 0.135073 | + | 0.233953i | ||||
\(535\) | 9.65685 | − | 16.7262i | 0.417502 | − | 0.723135i | ||||
\(536\) | 7.32843 | − | 12.6932i | 0.316540 | − | 0.548263i | ||||
\(537\) | 6.17157 | + | 10.6895i | 0.266323 | + | 0.461285i | ||||
\(538\) | −3.68629 | −0.158927 | ||||||||
\(539\) | −0.721825 | + | 2.80821i | −0.0310912 | + | 0.120958i | ||||
\(540\) | −1.41421 | −0.0608581 | ||||||||
\(541\) | −6.43503 | − | 11.1458i | −0.276663 | − | 0.479195i | 0.693890 | − | 0.720081i | \(-0.255895\pi\) |
−0.970553 | + | 0.240886i | \(0.922562\pi\) | |||||||
\(542\) | 7.69239 | − | 13.3236i | 0.330416 | − | 0.572298i | ||||
\(543\) | 5.79289 | − | 10.0336i | 0.248597 | − | 0.430582i | ||||
\(544\) | −2.62132 | − | 4.54026i | −0.112388 | − | 0.194662i | ||||
\(545\) | −2.34315 | −0.100369 | ||||||||
\(546\) | 2.62132 | − | 0.358719i | 0.112182 | − | 0.0153518i | ||||
\(547\) | −5.75736 | −0.246167 | −0.123083 | − | 0.992396i | \(-0.539278\pi\) | ||||
−0.123083 | + | 0.992396i | \(0.539278\pi\) | |||||||
\(548\) | 6.53553 | + | 11.3199i | 0.279184 | + | 0.483561i | ||||
\(549\) | 2.62132 | − | 4.54026i | 0.111875 | − | 0.193774i | ||||
\(550\) | 0.621320 | − | 1.07616i | 0.0264932 | − | 0.0458875i | ||||
\(551\) | −7.50000 | − | 12.9904i | −0.319511 | − | 0.553409i | ||||
\(552\) | −9.07107 | −0.386090 | ||||||||
\(553\) | −21.5858 | − | 27.8359i | −0.917921 | − | 1.18370i | ||||
\(554\) | −16.4142 | −0.697373 | ||||||||
\(555\) | −3.58579 | − | 6.21076i | −0.152208 | − | 0.263632i | ||||
\(556\) | 10.6066 | − | 18.3712i | 0.449820 | − | 0.779111i | ||||
\(557\) | 5.48528 | − | 9.50079i | 0.232419 | − | 0.402561i | −0.726101 | − | 0.687589i | \(-0.758669\pi\) |
0.958519 | + | 0.285027i | \(0.0920027\pi\) | |||||||
\(558\) | −3.41421 | − | 5.91359i | −0.144535 | − | 0.250342i | ||||
\(559\) | 4.82843 | 0.204221 | ||||||||
\(560\) | 1.41421 | − | 3.46410i | 0.0597614 | − | 0.146385i | ||||
\(561\) | 2.17157 | 0.0916839 | ||||||||
\(562\) | −3.65685 | − | 6.33386i | −0.154255 | − | 0.267178i | ||||
\(563\) | 0.242641 | − | 0.420266i | 0.0102261 | − | 0.0177121i | −0.860867 | − | 0.508830i | \(-0.830078\pi\) |
0.871093 | + | 0.491118i | \(0.163412\pi\) | |||||||
\(564\) | −4.50000 | + | 7.79423i | −0.189484 | + | 0.328196i | ||||
\(565\) | −4.29289 | − | 7.43551i | −0.180603 | − | 0.312814i | ||||
\(566\) | 17.0711 | 0.717551 | ||||||||
\(567\) | −1.00000 | + | 2.44949i | −0.0419961 | + | 0.102869i | ||||
\(568\) | −1.00000 | −0.0419591 | ||||||||
\(569\) | 12.7929 | + | 22.1579i | 0.536306 | + | 0.928909i | 0.999099 | + | 0.0424428i | \(0.0135140\pi\) |
−0.462793 | + | 0.886466i | \(0.653153\pi\) | |||||||
\(570\) | 2.12132 | − | 3.67423i | 0.0888523 | − | 0.153897i | ||||
\(571\) | 0.828427 | − | 1.43488i | 0.0346686 | − | 0.0600478i | −0.848171 | − | 0.529723i | \(-0.822296\pi\) |
0.882839 | + | 0.469676i | \(0.155629\pi\) | |||||||
\(572\) | −0.207107 | − | 0.358719i | −0.00865957 | − | 0.0149988i | ||||
\(573\) | 2.34315 | 0.0978863 | ||||||||
\(574\) | −7.43503 | − | 9.58783i | −0.310332 | − | 0.400188i | ||||
\(575\) | 27.2132 | 1.13487 | ||||||||
\(576\) | −0.500000 | − | 0.866025i | −0.0208333 | − | 0.0360844i | ||||
\(577\) | 9.00000 | − | 15.5885i | 0.374675 | − | 0.648956i | −0.615603 | − | 0.788056i | \(-0.711088\pi\) |
0.990278 | + | 0.139100i | \(0.0444210\pi\) | |||||||
\(578\) | −5.24264 | + | 9.08052i | −0.218065 | + | 0.377700i | ||||
\(579\) | 7.87868 | + | 13.6463i | 0.327427 | + | 0.567120i | ||||
\(580\) | −7.07107 | −0.293610 | ||||||||
\(581\) | −20.0711 | + | 2.74666i | −0.832688 | + | 0.113951i | ||||
\(582\) | 7.89949 | 0.327445 | ||||||||
\(583\) | −2.55025 | − | 4.41717i | −0.105621 | − | 0.182940i | ||||
\(584\) | 0.535534 | − | 0.927572i | 0.0221606 | − | 0.0383832i | ||||
\(585\) | 0.707107 | − | 1.22474i | 0.0292353 | − | 0.0506370i | ||||
\(586\) | 9.36396 | + | 16.2189i | 0.386822 | + | 0.669995i | ||||
\(587\) | 11.2426 | 0.464033 | 0.232017 | − | 0.972712i | \(-0.425468\pi\) | ||||
0.232017 | + | 0.972712i | \(0.425468\pi\) | |||||||
\(588\) | −5.00000 | − | 4.89898i | −0.206197 | − | 0.202031i | ||||
\(589\) | 20.4853 | 0.844081 | ||||||||
\(590\) | 5.36396 | + | 9.29065i | 0.220831 | + | 0.382490i | ||||
\(591\) | −4.77817 | + | 8.27604i | −0.196548 | + | 0.340431i | ||||
\(592\) | 2.53553 | − | 4.39167i | 0.104210 | − | 0.180497i | ||||
\(593\) | 14.2929 | + | 24.7560i | 0.586939 | + | 1.01661i | 0.994631 | + | 0.103488i | \(0.0330004\pi\) |
−0.407692 | + | 0.913120i | \(0.633666\pi\) | |||||||
\(594\) | 0.414214 | 0.0169954 | ||||||||
\(595\) | −19.4350 | + | 2.65962i | −0.796759 | + | 0.109034i | ||||
\(596\) | 15.8995 | 0.651269 | ||||||||
\(597\) | −5.29289 | − | 9.16756i | −0.216624 | − | 0.375203i | ||||
\(598\) | 4.53553 | − | 7.85578i | 0.185472 | − | 0.321247i | ||||
\(599\) | 7.43503 | − | 12.8778i | 0.303787 | − | 0.526175i | −0.673203 | − | 0.739457i | \(-0.735082\pi\) |
0.976991 | + | 0.213283i | \(0.0684155\pi\) | |||||||
\(600\) | 1.50000 | + | 2.59808i | 0.0612372 | + | 0.106066i | ||||
\(601\) | −17.8284 | −0.727237 | −0.363618 | − | 0.931548i | \(-0.618459\pi\) | ||||
−0.363618 | + | 0.931548i | \(0.618459\pi\) | |||||||
\(602\) | −7.82843 | − | 10.0951i | −0.319063 | − | 0.411447i | ||||
\(603\) | −14.6569 | −0.596873 | ||||||||
\(604\) | 3.79289 | + | 6.56948i | 0.154331 | + | 0.267309i | ||||
\(605\) | −7.65685 | + | 13.2621i | −0.311295 | + | 0.539179i | ||||
\(606\) | 0.585786 | − | 1.01461i | 0.0237959 | − | 0.0412158i | ||||
\(607\) | −13.5355 | − | 23.4442i | −0.549390 | − | 0.951572i | −0.998316 | − | 0.0580031i | \(-0.981527\pi\) |
0.448926 | − | 0.893569i | \(-0.351807\pi\) | |||||||
\(608\) | 3.00000 | 0.121666 | ||||||||
\(609\) | −5.00000 | + | 12.2474i | −0.202610 | + | 0.496292i | ||||
\(610\) | 7.41421 | 0.300193 | ||||||||
\(611\) | −4.50000 | − | 7.79423i | −0.182051 | − | 0.315321i | ||||
\(612\) | −2.62132 | + | 4.54026i | −0.105961 | + | 0.183529i | ||||
\(613\) | 17.8995 | − | 31.0028i | 0.722954 | − | 1.25219i | −0.236857 | − | 0.971545i | \(-0.576117\pi\) |
0.959811 | − | 0.280648i | \(-0.0905494\pi\) | |||||||
\(614\) | 9.81371 | + | 16.9978i | 0.396049 | + | 0.685977i | ||||
\(615\) | −6.48528 | −0.261512 | ||||||||
\(616\) | −0.414214 | + | 1.01461i | −0.0166891 | + | 0.0408799i | ||||
\(617\) | −6.48528 | −0.261088 | −0.130544 | − | 0.991443i | \(-0.541672\pi\) | ||||
−0.130544 | + | 0.991443i | \(0.541672\pi\) | |||||||
\(618\) | −3.24264 | − | 5.61642i | −0.130438 | − | 0.225925i | ||||
\(619\) | −21.7279 | + | 37.6339i | −0.873319 | + | 1.51263i | −0.0147761 | + | 0.999891i | \(0.504704\pi\) |
−0.858543 | + | 0.512742i | \(0.828630\pi\) | |||||||
\(620\) | 4.82843 | − | 8.36308i | 0.193914 | − | 0.335869i | ||||
\(621\) | 4.53553 | + | 7.85578i | 0.182005 | + | 0.315241i | ||||
\(622\) | −6.58579 | −0.264066 | ||||||||
\(623\) | 10.1213 | + | 13.0519i | 0.405502 | + | 0.522914i | ||||
\(624\) | 1.00000 | 0.0400320 | ||||||||
\(625\) | 0.500000 | + | 0.866025i | 0.0200000 | + | 0.0346410i | ||||
\(626\) | −9.07107 | + | 15.7116i | −0.362553 | + | 0.627960i | ||||
\(627\) | −0.621320 | + | 1.07616i | −0.0248131 | + | 0.0429776i | ||||
\(628\) | −3.96447 | − | 6.86666i | −0.158199 | − | 0.274009i | ||||
\(629\) | −26.5858 | −1.06004 | ||||||||
\(630\) | −3.70711 | + | 0.507306i | −0.147695 | + | 0.0202116i | ||||
\(631\) | 36.6274 | 1.45811 | 0.729057 | − | 0.684453i | \(-0.239959\pi\) | ||||
0.729057 | + | 0.684453i | \(0.239959\pi\) | |||||||
\(632\) | −6.65685 | − | 11.5300i | −0.264795 | − | 0.458639i | ||||
\(633\) | 14.1924 | − | 24.5819i | 0.564097 | − | 0.977044i | ||||
\(634\) | −0.414214 | + | 0.717439i | −0.0164505 | + | 0.0284931i | ||||
\(635\) | 7.00000 | + | 12.1244i | 0.277787 | + | 0.481140i | ||||
\(636\) | 12.3137 | 0.488270 | ||||||||
\(637\) | 6.74264 | − | 1.88064i | 0.267153 | − | 0.0745136i | ||||
\(638\) | 2.07107 | 0.0819944 | ||||||||
\(639\) | 0.500000 | + | 0.866025i | 0.0197797 | + | 0.0342594i | ||||
\(640\) | 0.707107 | − | 1.22474i | 0.0279508 | − | 0.0484123i | ||||
\(641\) | −16.5858 | + | 28.7274i | −0.655099 | + | 1.13467i | 0.326770 | + | 0.945104i | \(0.394040\pi\) |
−0.981869 | + | 0.189561i | \(0.939293\pi\) | |||||||
\(642\) | −6.82843 | − | 11.8272i | −0.269497 | − | 0.466782i | ||||
\(643\) | 36.3137 | 1.43207 | 0.716036 | − | 0.698063i | \(-0.245954\pi\) | ||||
0.716036 | + | 0.698063i | \(0.245954\pi\) | |||||||
\(644\) | −23.7782 | + | 3.25397i | −0.936991 | + | 0.128224i | ||||
\(645\) | −6.82843 | −0.268869 | ||||||||
\(646\) | −7.86396 | − | 13.6208i | −0.309403 | − | 0.535902i | ||||
\(647\) | −14.3137 | + | 24.7921i | −0.562730 | + | 0.974677i | 0.434527 | + | 0.900659i | \(0.356916\pi\) |
−0.997257 | + | 0.0740180i | \(0.976418\pi\) | |||||||
\(648\) | −0.500000 | + | 0.866025i | −0.0196419 | + | 0.0340207i | ||||
\(649\) | −1.57107 | − | 2.72117i | −0.0616698 | − | 0.106815i | ||||
\(650\) | −3.00000 | −0.117670 | ||||||||
\(651\) | −11.0711 | − | 14.2767i | −0.433909 | − | 0.559547i | ||||
\(652\) | 17.1421 | 0.671338 | ||||||||
\(653\) | −7.55635 | − | 13.0880i | −0.295703 | − | 0.512172i | 0.679445 | − | 0.733726i | \(-0.262220\pi\) |
−0.975148 | + | 0.221554i | \(0.928887\pi\) | |||||||
\(654\) | −0.828427 | + | 1.43488i | −0.0323941 | + | 0.0561082i | ||||
\(655\) | 7.00000 | − | 12.1244i | 0.273513 | − | 0.473738i | ||||
\(656\) | −2.29289 | − | 3.97141i | −0.0895224 | − | 0.155057i | ||||
\(657\) | −1.07107 | −0.0417863 | ||||||||
\(658\) | −9.00000 | + | 22.0454i | −0.350857 | + | 0.859419i | ||||
\(659\) | 30.7279 | 1.19699 | 0.598495 | − | 0.801127i | \(-0.295766\pi\) | ||||
0.598495 | + | 0.801127i | \(0.295766\pi\) | |||||||
\(660\) | 0.292893 | + | 0.507306i | 0.0114009 | + | 0.0197469i | ||||
\(661\) | 6.77817 | − | 11.7401i | 0.263640 | − | 0.456639i | −0.703566 | − | 0.710630i | \(-0.748410\pi\) |
0.967207 | + | 0.253991i | \(0.0817434\pi\) | |||||||
\(662\) | 11.2426 | − | 19.4728i | 0.436958 | − | 0.756833i | ||||
\(663\) | −2.62132 | − | 4.54026i | −0.101804 | − | 0.176329i | ||||
\(664\) | −7.65685 | −0.297144 | ||||||||
\(665\) | 4.24264 | − | 10.3923i | 0.164523 | − | 0.402996i | ||||
\(666\) | −5.07107 | −0.196500 | ||||||||
\(667\) | 22.6777 | + | 39.2789i | 0.878083 | + | 1.52088i | ||||
\(668\) | −6.15685 | + | 10.6640i | −0.238216 | + | 0.412602i | ||||
\(669\) | −10.6924 | + | 18.5198i | −0.413392 | + | 0.716015i | ||||
\(670\) | −10.3640 | − | 17.9509i | −0.400395 | − | 0.693504i | ||||
\(671\) | −2.17157 | −0.0838326 | ||||||||
\(672\) | −1.62132 | − | 2.09077i | −0.0625438 | − | 0.0806532i | ||||
\(673\) | −1.17157 | −0.0451608 | −0.0225804 | − | 0.999745i | \(-0.507188\pi\) | ||||
−0.0225804 | + | 0.999745i | \(0.507188\pi\) | |||||||
\(674\) | −14.3284 | − | 24.8176i | −0.551910 | − | 0.955937i | ||||
\(675\) | 1.50000 | − | 2.59808i | 0.0577350 | − | 0.100000i | ||||
\(676\) | −0.500000 | + | 0.866025i | −0.0192308 | + | 0.0333087i | ||||
\(677\) | −14.0858 | − | 24.3973i | −0.541361 | − | 0.937664i | −0.998826 | − | 0.0484369i | \(-0.984576\pi\) |
0.457465 | − | 0.889227i | \(-0.348757\pi\) | |||||||
\(678\) | −6.07107 | −0.233158 | ||||||||
\(679\) | 20.7071 | − | 2.83370i | 0.794666 | − | 0.108748i | ||||
\(680\) | −7.41421 | −0.284322 | ||||||||
\(681\) | 13.0711 | + | 22.6398i | 0.500884 | + | 0.867557i | ||||
\(682\) | −1.41421 | + | 2.44949i | −0.0541530 | + | 0.0937958i | ||||
\(683\) | −2.72792 | + | 4.72490i | −0.104381 | + | 0.180793i | −0.913485 | − | 0.406872i | \(-0.866619\pi\) |
0.809104 | + | 0.587665i | \(0.199953\pi\) | |||||||
\(684\) | −1.50000 | − | 2.59808i | −0.0573539 | − | 0.0993399i | ||||
\(685\) | 18.4853 | 0.706286 | ||||||||
\(686\) | −14.8640 | − | 11.0482i | −0.567509 | − | 0.421822i | ||||
\(687\) | −7.17157 | −0.273613 | ||||||||
\(688\) | −2.41421 | − | 4.18154i | −0.0920410 | − | 0.159420i | ||||
\(689\) | −6.15685 | + | 10.6640i | −0.234557 | + | 0.406265i | ||||
\(690\) | −6.41421 | + | 11.1097i | −0.244185 | + | 0.422941i | ||||
\(691\) | −5.57107 | − | 9.64937i | −0.211933 | − | 0.367079i | 0.740386 | − | 0.672182i | \(-0.234643\pi\) |
−0.952320 | + | 0.305102i | \(0.901309\pi\) | |||||||
\(692\) | 20.3137 | 0.772211 | ||||||||
\(693\) | 1.08579 | − | 0.148586i | 0.0412456 | − | 0.00564433i | ||||
\(694\) | 5.75736 | 0.218546 | ||||||||
\(695\) | −15.0000 | − | 25.9808i | −0.568982 | − | 0.985506i | ||||
\(696\) | −2.50000 | + | 4.33013i | −0.0947623 | + | 0.164133i | ||||
\(697\) | −12.0208 | + | 20.8207i | −0.455321 | + | 0.788639i | ||||
\(698\) | −2.70711 | − | 4.68885i | −0.102466 | − | 0.177475i | ||||
\(699\) | −3.72792 | −0.141003 | ||||||||
\(700\) | 4.86396 | + | 6.27231i | 0.183840 | + | 0.237071i | ||||
\(701\) | 48.4853 | 1.83126 | 0.915632 | − | 0.402018i | \(-0.131691\pi\) | ||||
0.915632 | + | 0.402018i | \(0.131691\pi\) | |||||||
\(702\) | −0.500000 | − | 0.866025i | −0.0188713 | − | 0.0326860i | ||||
\(703\) | 7.60660 | − | 13.1750i | 0.286888 | − | 0.496905i | ||||
\(704\) | −0.207107 | + | 0.358719i | −0.00780563 | + | 0.0135197i | ||||
\(705\) | 6.36396 | + | 11.0227i | 0.239681 | + | 0.415139i | ||||
\(706\) | 12.6274 | 0.475239 | ||||||||
\(707\) | 1.17157 | − | 2.86976i | 0.0440615 | − | 0.107928i | ||||
\(708\) | 7.58579 | 0.285091 | ||||||||
\(709\) | 16.0208 | + | 27.7489i | 0.601674 | + | 1.04213i | 0.992568 | + | 0.121695i | \(0.0388328\pi\) |
−0.390893 | + | 0.920436i | \(0.627834\pi\) | |||||||
\(710\) | −0.707107 | + | 1.22474i | −0.0265372 | + | 0.0459639i | ||||
\(711\) | −6.65685 | + | 11.5300i | −0.249652 | + | 0.432409i | ||||
\(712\) | 3.12132 | + | 5.40629i | 0.116976 | + | 0.202609i | ||||
\(713\) | −61.9411 | −2.31971 | ||||||||
\(714\) | −5.24264 | + | 12.8418i | −0.196201 | + | 0.480592i | ||||
\(715\) | −0.585786 | −0.0219072 | ||||||||
\(716\) | 6.17157 | + | 10.6895i | 0.230643 | + | 0.399485i | ||||
\(717\) | 1.25736 | − | 2.17781i | 0.0469569 | − | 0.0813318i | ||||
\(718\) | 7.72792 | − | 13.3852i | 0.288403 | − | 0.499529i | ||||
\(719\) | 11.1421 | + | 19.2987i | 0.415532 | + | 0.719722i | 0.995484 | − | 0.0949285i | \(-0.0302623\pi\) |
−0.579953 | + | 0.814650i | \(0.696929\pi\) | |||||||
\(720\) | −1.41421 | −0.0527046 | ||||||||
\(721\) | −10.5147 | − | 13.5592i | −0.391589 | − | 0.504972i | ||||
\(722\) | −10.0000 | −0.372161 | ||||||||
\(723\) | 8.24264 | + | 14.2767i | 0.306547 | + | 0.530955i | ||||
\(724\) | 5.79289 | − | 10.0336i | 0.215291 | − | 0.372895i | ||||
\(725\) | 7.50000 | − | 12.9904i | 0.278543 | − | 0.482451i | ||||
\(726\) | 5.41421 | + | 9.37769i | 0.200940 | + | 0.348039i | ||||
\(727\) | −38.8284 | −1.44007 | −0.720033 | − | 0.693939i | \(-0.755874\pi\) | ||||
−0.720033 | + | 0.693939i | \(0.755874\pi\) | |||||||
\(728\) | 2.62132 | − | 0.358719i | 0.0971526 | − | 0.0132950i | ||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −0.757359 | − | 1.31178i | −0.0280311 | − | 0.0485513i | ||||
\(731\) | −12.6569 | + | 21.9223i | −0.468131 | + | 0.810826i | ||||
\(732\) | 2.62132 | − | 4.54026i | 0.0968868 | − | 0.167813i | ||||
\(733\) | 14.5061 | + | 25.1253i | 0.535795 | + | 0.928024i | 0.999124 | + | 0.0418379i | \(0.0133213\pi\) |
−0.463330 | + | 0.886186i | \(0.653345\pi\) | |||||||
\(734\) | 14.0000 | 0.516749 | ||||||||
\(735\) | −9.53553 | + | 2.65962i | −0.351723 | + | 0.0981017i | ||||
\(736\) | −9.07107 | −0.334364 | ||||||||
\(737\) | 3.03553 | + | 5.25770i | 0.111815 | + | 0.193670i | ||||
\(738\) | −2.29289 | + | 3.97141i | −0.0844026 | + | 0.146190i | ||||
\(739\) | −3.48528 | + | 6.03668i | −0.128208 | + | 0.222063i | −0.922982 | − | 0.384842i | \(-0.874256\pi\) |
0.794774 | + | 0.606905i | \(0.207589\pi\) | |||||||
\(740\) | −3.58579 | − | 6.21076i | −0.131816 | − | 0.228312i | ||||
\(741\) | 3.00000 | 0.110208 | ||||||||
\(742\) | 32.2782 | − | 4.41717i | 1.18497 | − | 0.162159i | ||||
\(743\) | 11.4853 | 0.421354 | 0.210677 | − | 0.977556i | \(-0.432433\pi\) | ||||
0.210677 | + | 0.977556i | \(0.432433\pi\) | |||||||
\(744\) | −3.41421 | − | 5.91359i | −0.125171 | − | 0.216803i | ||||
\(745\) | 11.2426 | − | 19.4728i | 0.411898 | − | 0.713429i | ||||
\(746\) | 5.55025 | − | 9.61332i | 0.203209 | − | 0.351969i | ||||
\(747\) | 3.82843 | + | 6.63103i | 0.140075 | + | 0.242617i | ||||
\(748\) | 2.17157 | 0.0794006 | ||||||||
\(749\) | −22.1421 | − | 28.5533i | −0.809056 | − | 1.04332i | ||||
\(750\) | 11.3137 | 0.413118 | ||||||||
\(751\) | 17.1716 | + | 29.7420i | 0.626600 | + | 1.08530i | 0.988229 | + | 0.152980i | \(0.0488872\pi\) |
−0.361630 | + | 0.932322i | \(0.617780\pi\) | |||||||
\(752\) | −4.50000 | + | 7.79423i | −0.164098 | + | 0.284226i | ||||
\(753\) | −6.41421 | + | 11.1097i | −0.233747 | + | 0.404862i | ||||
\(754\) | −2.50000 | − | 4.33013i | −0.0910446 | − | 0.157694i | ||||
\(755\) | 10.7279 | 0.390429 | ||||||||
\(756\) | −1.00000 | + | 2.44949i | −0.0363696 | + | 0.0890871i | ||||
\(757\) | 23.4437 | 0.852074 | 0.426037 | − | 0.904706i | \(-0.359909\pi\) | ||||
0.426037 | + | 0.904706i | \(0.359909\pi\) | |||||||
\(758\) | 16.8284 | + | 29.1477i | 0.611236 | + | 1.05869i | ||||
\(759\) | 1.87868 | − | 3.25397i | 0.0681918 | − | 0.118112i | ||||
\(760\) | 2.12132 | − | 3.67423i | 0.0769484 | − | 0.133278i | ||||
\(761\) | 8.92893 | + | 15.4654i | 0.323674 | + | 0.560619i | 0.981243 | − | 0.192775i | \(-0.0617487\pi\) |
−0.657569 | + | 0.753394i | \(0.728415\pi\) | |||||||
\(762\) | 9.89949 | 0.358621 | ||||||||
\(763\) | −1.65685 | + | 4.05845i | −0.0599822 | + | 0.146926i | ||||
\(764\) | 2.34315 | 0.0847720 | ||||||||
\(765\) | 3.70711 | + | 6.42090i | 0.134031 | + | 0.232148i | ||||
\(766\) | −3.24264 | + | 5.61642i | −0.117161 | + | 0.202929i | ||||
\(767\) | −3.79289 | + | 6.56948i | −0.136953 | + | 0.237210i | ||||
\(768\) | −0.500000 | − | 0.866025i | −0.0180422 | − | 0.0312500i | ||||
\(769\) | −6.92893 | −0.249864 | −0.124932 | − | 0.992165i | \(-0.539871\pi\) | ||||
−0.124932 | + | 0.992165i | \(0.539871\pi\) | |||||||
\(770\) | 0.949747 | + | 1.22474i | 0.0342265 | + | 0.0441367i | ||||
\(771\) | −21.7990 | −0.785071 | ||||||||
\(772\) | 7.87868 | + | 13.6463i | 0.283560 | + | 0.491140i | ||||
\(773\) | 14.7990 | − | 25.6326i | 0.532283 | − | 0.921941i | −0.467007 | − | 0.884254i | \(-0.654668\pi\) |
0.999290 | − | 0.0376870i | \(-0.0119990\pi\) | |||||||
\(774\) | −2.41421 | + | 4.18154i | −0.0867771 | + | 0.150302i | ||||
\(775\) | 10.2426 | + | 17.7408i | 0.367927 | + | 0.637267i | ||||
\(776\) | 7.89949 | 0.283575 | ||||||||
\(777\) | −13.2929 | + | 1.81909i | −0.476880 | + | 0.0652595i | ||||
\(778\) | 23.0000 | 0.824590 | ||||||||
\(779\) | −6.87868 | − | 11.9142i | −0.246454 | − | 0.426871i | ||||
\(780\) | 0.707107 | − | 1.22474i | 0.0253185 | − | 0.0438529i | ||||
\(781\) | 0.207107 | − | 0.358719i | 0.00741086 | − | 0.0128360i | ||||
\(782\) | 23.7782 | + | 41.1850i | 0.850306 | + | 1.47277i | ||||
\(783\) | 5.00000 | 0.178685 | ||||||||
\(784\) | −5.00000 | − | 4.89898i | −0.178571 | − | 0.174964i | ||||
\(785\) | −11.2132 | −0.400216 | ||||||||
\(786\) | −4.94975 | − | 8.57321i | −0.176552 | − | 0.305796i | ||||
\(787\) | 4.08579 | − | 7.07679i | 0.145643 | − | 0.252260i | −0.783970 | − | 0.620799i | \(-0.786808\pi\) |
0.929612 | + | 0.368538i | \(0.120142\pi\) | |||||||
\(788\) | −4.77817 | + | 8.27604i | −0.170215 | + | 0.294822i | ||||
\(789\) | 3.77817 | + | 6.54399i | 0.134507 | + | 0.232972i | ||||
\(790\) | −18.8284 | −0.669885 | ||||||||
\(791\) | −15.9142 | + | 2.17781i | −0.565844 | + | 0.0774340i | ||||
\(792\) | 0.414214 | 0.0147184 | ||||||||
\(793\) | 2.62132 | + | 4.54026i | 0.0930858 | + | 0.161229i | ||||
\(794\) | 9.87868 | − | 17.1104i | 0.350581 | − | 0.607224i | ||||
\(795\) | 8.70711 | − | 15.0812i | 0.308809 | − | 0.534873i | ||||
\(796\) | −5.29289 | − | 9.16756i | −0.187602 | − | 0.324936i | ||||
\(797\) | −36.9706 | −1.30956 | −0.654782 | − | 0.755818i | \(-0.727240\pi\) | ||||
−0.654782 | + | 0.755818i | \(0.727240\pi\) | |||||||
\(798\) | −4.86396 | − | 6.27231i | −0.172182 | − | 0.222037i | ||||
\(799\) | 47.1838 | 1.66924 | ||||||||
\(800\) | 1.50000 | + | 2.59808i | 0.0530330 | + | 0.0918559i | ||||
\(801\) | 3.12132 | − | 5.40629i | 0.110286 | − | 0.191022i | ||||
\(802\) | −9.53553 | + | 16.5160i | −0.336711 | + | 0.583201i | ||||
\(803\) | 0.221825 | + | 0.384213i | 0.00782805 | + | 0.0135586i | ||||
\(804\) | −14.6569 | −0.516907 | ||||||||
\(805\) | −12.8284 | + | 31.4231i | −0.452143 | + | 1.10752i | ||||
\(806\) | 6.82843 | 0.240521 | ||||||||
\(807\) | 1.84315 | + | 3.19242i | 0.0648818 | + | 0.112379i | ||||
\(808\) | 0.585786 | − | 1.01461i | 0.0206079 | − | 0.0356939i | ||||
\(809\) | −17.5208 | + | 30.3469i | −0.615999 | + | 1.06694i | 0.374209 | + | 0.927344i | \(0.377914\pi\) |
−0.990208 | + | 0.139597i | \(0.955419\pi\) | |||||||
\(810\) | 0.707107 | + | 1.22474i | 0.0248452 | + | 0.0430331i | ||||
\(811\) | 26.7696 | 0.940006 | 0.470003 | − | 0.882665i | \(-0.344253\pi\) | ||||
0.470003 | + | 0.882665i | \(0.344253\pi\) | |||||||
\(812\) | −5.00000 | + | 12.2474i | −0.175466 | + | 0.429801i | ||||
\(813\) | −15.3848 | −0.539568 | ||||||||
\(814\) | 1.05025 | + | 1.81909i | 0.0368113 | + | 0.0637591i | ||||
\(815\) | 12.1213 | − | 20.9947i | 0.424591 | − | 0.735414i | ||||
\(816\) | −2.62132 | + | 4.54026i | −0.0917646 | + | 0.158941i | ||||
\(817\) | −7.24264 | − | 12.5446i | −0.253388 | − | 0.438881i | ||||
\(818\) | −2.58579 | −0.0904099 | ||||||||
\(819\) | −1.62132 | − | 2.09077i | −0.0566535 | − | 0.0730574i | ||||
\(820\) | −6.48528 | −0.226476 | ||||||||
\(821\) | 4.80761 | + | 8.32703i | 0.167787 | + | 0.290615i | 0.937641 | − | 0.347604i | \(-0.113005\pi\) |
−0.769855 | + | 0.638219i | \(0.779671\pi\) | |||||||
\(822\) | 6.53553 | − | 11.3199i | 0.227953 | − | 0.394826i | ||||
\(823\) | 4.05025 | − | 7.01524i | 0.141183 | − | 0.244536i | −0.786759 | − | 0.617260i | \(-0.788243\pi\) |
0.927942 | + | 0.372724i | \(0.121576\pi\) | |||||||
\(824\) | −3.24264 | − | 5.61642i | −0.112963 | − | 0.195657i | ||||
\(825\) | −1.24264 | −0.0432632 | ||||||||
\(826\) | 19.8848 | − | 2.72117i | 0.691880 | − | 0.0946816i | ||||
\(827\) | 13.5269 | 0.470377 | 0.235188 | − | 0.971950i | \(-0.424429\pi\) | ||||
0.235188 | + | 0.971950i | \(0.424429\pi\) | |||||||
\(828\) | 4.53553 | + | 7.85578i | 0.157621 | + | 0.273007i | ||||
\(829\) | −9.34924 | + | 16.1934i | −0.324713 | + | 0.562419i | −0.981454 | − | 0.191697i | \(-0.938601\pi\) |
0.656742 | + | 0.754116i | \(0.271934\pi\) | |||||||
\(830\) | −5.41421 | + | 9.37769i | −0.187930 | + | 0.325504i | ||||
\(831\) | 8.20711 | + | 14.2151i | 0.284701 | + | 0.493117i | ||||
\(832\) | 1.00000 | 0.0346688 | ||||||||
\(833\) | −9.13604 | + | 35.5431i | −0.316545 | + | 1.23150i | ||||
\(834\) | −21.2132 | −0.734553 | ||||||||
\(835\) | 8.70711 | + | 15.0812i | 0.301322 | + | 0.521905i | ||||
\(836\) | −0.621320 | + | 1.07616i | −0.0214888 | + | 0.0372197i | ||||
\(837\) | −3.41421 | + | 5.91359i | −0.118012 | + | 0.204404i | ||||
\(838\) | 13.7279 | + | 23.7775i | 0.474223 | + | 0.821379i | ||||
\(839\) | 2.51472 | 0.0868177 | 0.0434089 | − | 0.999057i | \(-0.486178\pi\) | ||||
0.0434089 | + | 0.999057i | \(0.486178\pi\) | |||||||
\(840\) | −3.70711 | + | 0.507306i | −0.127907 | + | 0.0175037i | ||||
\(841\) | −4.00000 | −0.137931 | ||||||||
\(842\) | −5.29289 | − | 9.16756i | −0.182405 | − | 0.315935i | ||||
\(843\) | −3.65685 | + | 6.33386i | −0.125949 | + | 0.218150i | ||||
\(844\) | 14.1924 | − | 24.5819i | 0.488522 | − | 0.846145i | ||||
\(845\) | 0.707107 | + | 1.22474i | 0.0243252 | + | 0.0421325i | ||||
\(846\) | 9.00000 | 0.309426 | ||||||||
\(847\) | 17.5563 | + | 22.6398i | 0.603243 | + | 0.777911i | ||||
\(848\) | 12.3137 | 0.422854 | ||||||||
\(849\) | −8.53553 | − | 14.7840i | −0.292939 | − | 0.507385i | ||||
\(850\) | 7.86396 | − | 13.6208i | 0.269732 | − | 0.467189i | ||||
\(851\) | −23.0000 | + | 39.8372i | −0.788430 | + | 1.36560i | ||||
\(852\) | 0.500000 | + | 0.866025i | 0.0171297 | + | 0.0296695i | ||||
\(853\) | −17.6985 | −0.605985 | −0.302992 | − | 0.952993i | \(-0.597986\pi\) | ||||
−0.302992 | + | 0.952993i | \(0.597986\pi\) | |||||||
\(854\) | 5.24264 | − | 12.8418i | 0.179399 | − | 0.439437i | ||||
\(855\) | −4.24264 | −0.145095 | ||||||||
\(856\) | −6.82843 | − | 11.8272i | −0.233391 | − | 0.404245i | ||||
\(857\) | 25.6924 | − | 44.5005i | 0.877635 | − | 1.52011i | 0.0237065 | − | 0.999719i | \(-0.492453\pi\) |
0.853929 | − | 0.520390i | \(-0.174213\pi\) | |||||||
\(858\) | −0.207107 | + | 0.358719i | −0.00707051 | + | 0.0122465i | ||||
\(859\) | −0.100505 | − | 0.174080i | −0.00342919 | − | 0.00593953i | 0.864306 | − | 0.502967i | \(-0.167758\pi\) |
−0.867735 | + | 0.497027i | \(0.834425\pi\) | |||||||
\(860\) | −6.82843 | −0.232847 | ||||||||
\(861\) | −4.58579 | + | 11.2328i | −0.156283 | + | 0.382814i | ||||
\(862\) | 14.4853 | 0.493371 | ||||||||
\(863\) | −2.00000 | − | 3.46410i | −0.0680808 | − | 0.117919i | 0.829976 | − | 0.557800i | \(-0.188354\pi\) |
−0.898056 | + | 0.439880i | \(0.855021\pi\) | |||||||
\(864\) | −0.500000 | + | 0.866025i | −0.0170103 | + | 0.0294628i | ||||
\(865\) | 14.3640 | − | 24.8791i | 0.488389 | − | 0.845915i | ||||
\(866\) | 9.50000 | + | 16.4545i | 0.322823 | + | 0.559146i | ||||
\(867\) | 10.4853 | 0.356099 | ||||||||
\(868\) | −11.0711 | − | 14.2767i | −0.375777 | − | 0.484582i | ||||
\(869\) | 5.51472 | 0.187074 | ||||||||
\(870\) | 3.53553 | + | 6.12372i | 0.119866 | + | 0.207614i | ||||
\(871\) | 7.32843 | − | 12.6932i | 0.248314 | − | 0.430093i | ||||
\(872\) | −0.828427 | + | 1.43488i | −0.0280541 | + | 0.0485911i | ||||
\(873\) | −3.94975 | − | 6.84116i | −0.133679 | − | 0.231538i | ||||
\(874\) | −27.2132 | −0.920500 | ||||||||
\(875\) | 29.6569 | − | 4.05845i | 1.00258 | − | 0.137201i | ||||
\(876\) | −1.07107 | −0.0361880 | ||||||||
\(877\) | −11.7071 | − | 20.2773i | −0.395321 | − | 0.684716i | 0.597821 | − | 0.801629i | \(-0.296033\pi\) |
−0.993142 | + | 0.116914i | \(0.962700\pi\) | |||||||
\(878\) | 5.29289 | − | 9.16756i | 0.178626 | − | 0.309390i | ||||
\(879\) | 9.36396 | − | 16.2189i | 0.315839 | − | 0.547048i | ||||
\(880\) | 0.292893 | + | 0.507306i | 0.00987343 | + | 0.0171013i | ||||
\(881\) | −41.1127 | −1.38512 | −0.692561 | − | 0.721359i | \(-0.743518\pi\) | ||||
−0.692561 | + | 0.721359i | \(0.743518\pi\) | |||||||
\(882\) | −1.74264 | + | 6.77962i | −0.0586778 | + | 0.228282i | ||||
\(883\) | −0.928932 | −0.0312611 | −0.0156305 | − | 0.999878i | \(-0.504976\pi\) | ||||
−0.0156305 | + | 0.999878i | \(0.504976\pi\) | |||||||
\(884\) | −2.62132 | − | 4.54026i | −0.0881645 | − | 0.152705i | ||||
\(885\) | 5.36396 | − | 9.29065i | 0.180308 | − | 0.312302i | ||||
\(886\) | −11.3640 | + | 19.6830i | −0.381780 | + | 0.661262i | ||||
\(887\) | −20.6569 | − | 35.7787i | −0.693589 | − | 1.20133i | −0.970654 | − | 0.240481i | \(-0.922695\pi\) |
0.277065 | − | 0.960851i | \(-0.410638\pi\) | |||||||
\(888\) | −5.07107 | −0.170174 | ||||||||
\(889\) | 25.9497 | − | 3.55114i | 0.870327 | − | 0.119101i | ||||
\(890\) | 8.82843 | 0.295930 | ||||||||
\(891\) | −0.207107 | − | 0.358719i | −0.00693834 | − | 0.0120176i | ||||
\(892\) | −10.6924 | + | 18.5198i | −0.358008 | + | 0.620087i | ||||
\(893\) | −13.5000 | + | 23.3827i | −0.451760 | + | 0.782472i | ||||
\(894\) | −7.94975 | − | 13.7694i | −0.265879 | − | 0.460517i | ||||
\(895\) | 17.4558 | 0.583485 | ||||||||
\(896\) | −1.62132 | − | 2.09077i | −0.0541645 | − | 0.0698477i | ||||
\(897\) | −9.07107 | −0.302874 | ||||||||
\(898\) | 16.9706 | + | 29.3939i | 0.566315 | + | 0.980886i | ||||
\(899\) | −17.0711 | + | 29.5680i | −0.569352 | + | 0.986147i | ||||
\(900\) | 1.50000 | − | 2.59808i | 0.0500000 | − | 0.0866025i | ||||
\(901\) | −32.2782 | − | 55.9074i | −1.07534 | − | 1.86255i | ||||
\(902\) | 1.89949 | 0.0632463 | ||||||||
\(903\) | −4.82843 | + | 11.8272i | −0.160680 | + | 0.393584i | ||||
\(904\) | −6.07107 | −0.201921 | ||||||||
\(905\) | −8.19239 | − | 14.1896i | −0.272324 | − | 0.471679i | ||||
\(906\) | 3.79289 | − | 6.56948i | 0.126010 | − | 0.218256i | ||||
\(907\) | 16.0503 | − | 27.7999i | 0.532940 | − | 0.923079i | −0.466320 | − | 0.884616i | \(-0.654421\pi\) |
0.999260 | − | 0.0384629i | \(-0.0122462\pi\) | |||||||
\(908\) | 13.0711 | + | 22.6398i | 0.433779 | + | 0.751327i | ||||
\(909\) | −1.17157 | −0.0388586 | ||||||||
\(910\) | 1.41421 | − | 3.46410i | 0.0468807 | − | 0.114834i | ||||
\(911\) | 54.0000 | 1.78910 | 0.894550 | − | 0.446968i | \(-0.147496\pi\) | ||||
0.894550 | + | 0.446968i | \(0.147496\pi\) | |||||||
\(912\) | −1.50000 | − | 2.59808i | −0.0496700 | − | 0.0860309i | ||||
\(913\) | 1.58579 | − | 2.74666i | 0.0524819 | − | 0.0909013i | ||||
\(914\) | 7.60660 | − | 13.1750i | 0.251604 | − | 0.435791i | ||||
\(915\) | −3.70711 | − | 6.42090i | −0.122553 | − | 0.212268i | ||||
\(916\) | −7.17157 | −0.236955 | ||||||||
\(917\) | −16.0503 | − | 20.6976i | −0.530026 | − | 0.683494i | ||||
\(918\) | 5.24264 | 0.173033 | ||||||||
\(919\) | 12.8995 | + | 22.3426i | 0.425515 | + | 0.737014i | 0.996468 | − | 0.0839688i | \(-0.0267596\pi\) |
−0.570953 | + | 0.820983i | \(0.693426\pi\) | |||||||
\(920\) | −6.41421 | + | 11.1097i | −0.211470 | + | 0.366277i | ||||
\(921\) | 9.81371 | − | 16.9978i | 0.323373 | − | 0.560098i | ||||
\(922\) | 16.7279 | + | 28.9736i | 0.550905 | + | 0.954195i | ||||
\(923\) | −1.00000 | −0.0329154 | ||||||||
\(924\) | 1.08579 | − | 0.148586i | 0.0357198 | − | 0.00488814i | ||||
\(925\) | 15.2132 | 0.500207 | ||||||||
\(926\) | 18.9706 | + | 32.8580i | 0.623411 | + | 1.07978i | ||||
\(927\) | −3.24264 | + | 5.61642i | −0.106502 | + | 0.184467i | ||||
\(928\) | −2.50000 | + | 4.33013i | −0.0820665 | + | 0.142143i | ||||
\(929\) | −9.14214 | − | 15.8346i | −0.299944 | − | 0.519518i | 0.676179 | − | 0.736737i | \(-0.263635\pi\) |
−0.976123 | + | 0.217220i | \(0.930301\pi\) | |||||||
\(930\) | −9.65685 | −0.316661 | ||||||||
\(931\) | −15.0000 | − | 14.6969i | −0.491605 | − | 0.481673i | ||||
\(932\) | −3.72792 | −0.122112 | ||||||||
\(933\) | 3.29289 | + | 5.70346i | 0.107804 | + | 0.186723i | ||||
\(934\) | 0.121320 | − | 0.210133i | 0.00396972 | − | 0.00687576i | ||||
\(935\) | 1.53553 | − | 2.65962i | 0.0502173 | − | 0.0869790i | ||||
\(936\) | −0.500000 | − | 0.866025i | −0.0163430 | − | 0.0283069i | ||||
\(937\) | 40.5980 | 1.32628 | 0.663139 | − | 0.748496i | \(-0.269224\pi\) | ||||
0.663139 | + | 0.748496i | \(0.269224\pi\) | |||||||
\(938\) | −38.4203 | + | 5.25770i | −1.25447 | + | 0.171670i | ||||
\(939\) | 18.1421 | 0.592046 | ||||||||
\(940\) | 6.36396 | + | 11.0227i | 0.207570 | + | 0.359521i | ||||
\(941\) | 10.4853 | − | 18.1610i | 0.341810 | − | 0.592033i | −0.642959 | − | 0.765901i | \(-0.722293\pi\) |
0.984769 | + | 0.173868i | \(0.0556266\pi\) | |||||||
\(942\) | −3.96447 | + | 6.86666i | −0.129169 | + | 0.223728i | ||||
\(943\) | 20.7990 | + | 36.0249i | 0.677308 | + | 1.17313i | ||||
\(944\) | 7.58579 | 0.246896 | ||||||||
\(945\) | 2.29289 | + | 2.95680i | 0.0745878 | + | 0.0961846i | ||||
\(946\) | 2.00000 | 0.0650256 | ||||||||
\(947\) | −8.62132 | − | 14.9326i | −0.280155 | − | 0.485243i | 0.691268 | − | 0.722599i | \(-0.257053\pi\) |
−0.971423 | + | 0.237356i | \(0.923719\pi\) | |||||||
\(948\) | −6.65685 | + | 11.5300i | −0.216205 | + | 0.374477i | ||||
\(949\) | 0.535534 | − | 0.927572i | 0.0173842 | − | 0.0301103i | ||||
\(950\) | 4.50000 | + | 7.79423i | 0.145999 | + | 0.252878i | ||||
\(951\) | 0.828427 | 0.0268636 | ||||||||
\(952\) | −5.24264 | + | 12.8418i | −0.169915 | + | 0.416205i | ||||
\(953\) | −10.2132 | −0.330838 | −0.165419 | − | 0.986223i | \(-0.552898\pi\) | ||||
−0.165419 | + | 0.986223i | \(0.552898\pi\) | |||||||
\(954\) | −6.15685 | − | 10.6640i | −0.199336 | − | 0.345259i | ||||
\(955\) | 1.65685 | − | 2.86976i | 0.0536145 | − | 0.0928631i | ||||
\(956\) | 1.25736 | − | 2.17781i | 0.0406659 | − | 0.0704354i | ||||
\(957\) | −1.03553 | − | 1.79360i | −0.0334741 | − | 0.0579788i | ||||
\(958\) | −31.1421 | −1.00616 | ||||||||
\(959\) | 13.0711 | − | 32.0174i | 0.422087 | − | 1.03390i | ||||
\(960\) | −1.41421 | −0.0456435 | ||||||||
\(961\) | −7.81371 | − | 13.5337i | −0.252055 | − | 0.436572i | ||||
\(962\) | 2.53553 | − | 4.39167i | 0.0817489 | − | 0.141593i | ||||
\(963\) | −6.82843 | + | 11.8272i | −0.220043 | + | 0.381126i | ||||
\(964\) | 8.24264 | + | 14.2767i | 0.265478 | + | 0.459821i | ||||
\(965\) | 22.2843 | 0.717356 | ||||||||
\(966\) | 14.7071 | + | 18.9655i | 0.473193 | + | 0.610206i | ||||
\(967\) | 9.38478 | 0.301794 | 0.150897 | − | 0.988549i | \(-0.451784\pi\) | ||||
0.150897 | + | 0.988549i | \(0.451784\pi\) | |||||||
\(968\) | 5.41421 | + | 9.37769i | 0.174019 | + | 0.301410i | ||||
\(969\) | −7.86396 | + | 13.6208i | −0.252627 | + | 0.437562i | ||||
\(970\) | 5.58579 | − | 9.67487i | 0.179349 | − | 0.310641i | ||||
\(971\) | −28.7782 | − | 49.8453i | −0.923536 | − | 1.59961i | −0.793900 | − | 0.608049i | \(-0.791952\pi\) |
−0.129636 | − | 0.991562i | \(-0.541381\pi\) | |||||||
\(972\) | 1.00000 | 0.0320750 | ||||||||
\(973\) | −55.6066 | + | 7.60959i | −1.78267 | + | 0.243952i | ||||
\(974\) | −23.7279 | −0.760292 | ||||||||
\(975\) | 1.50000 | + | 2.59808i | 0.0480384 | + | 0.0832050i | ||||
\(976\) | 2.62132 | − | 4.54026i | 0.0839064 | − | 0.145330i | ||||
\(977\) | −1.24264 | + | 2.15232i | −0.0397556 | + | 0.0688587i | −0.885219 | − | 0.465175i | \(-0.845991\pi\) |
0.845463 | + | 0.534034i | \(0.179325\pi\) | |||||||
\(978\) | −8.57107 | − | 14.8455i | −0.274073 | − | 0.474708i | ||||
\(979\) | −2.58579 | −0.0826421 | ||||||||
\(980\) | −9.53553 | + | 2.65962i | −0.304601 | + | 0.0849585i | ||||
\(981\) | 1.65685 | 0.0528993 | ||||||||
\(982\) | 13.1421 | + | 22.7628i | 0.419382 | + | 0.726392i | ||||
\(983\) | 11.0858 | − | 19.2011i | 0.353582 | − | 0.612421i | −0.633292 | − | 0.773913i | \(-0.718297\pi\) |
0.986874 | + | 0.161491i | \(0.0516303\pi\) | |||||||
\(984\) | −2.29289 | + | 3.97141i | −0.0730948 | + | 0.126604i | ||||
\(985\) | 6.75736 | + | 11.7041i | 0.215307 | + | 0.372923i | ||||
\(986\) | 26.2132 | 0.834798 | ||||||||
\(987\) | 23.5919 | − | 3.22848i | 0.750938 | − | 0.102763i | ||||
\(988\) | 3.00000 | 0.0954427 | ||||||||
\(989\) | 21.8995 | + | 37.9310i | 0.696363 | + | 1.20614i | ||||
\(990\) | 0.292893 | − | 0.507306i | 0.00930876 | − | 0.0161232i | ||||
\(991\) | 3.65685 | − | 6.33386i | 0.116164 | − | 0.201202i | −0.802081 | − | 0.597216i | \(-0.796274\pi\) |
0.918244 | + | 0.396014i | \(0.129607\pi\) | |||||||
\(992\) | −3.41421 | − | 5.91359i | −0.108401 | − | 0.187757i | ||||
\(993\) | −22.4853 | −0.713549 | ||||||||
\(994\) | 1.62132 | + | 2.09077i | 0.0514252 | + | 0.0663152i | ||||
\(995\) | −14.9706 | −0.474599 | ||||||||
\(996\) | 3.82843 | + | 6.63103i | 0.121308 | + | 0.210112i | ||||
\(997\) | −3.34924 | + | 5.80106i | −0.106072 | + | 0.183721i | −0.914176 | − | 0.405319i | \(-0.867161\pi\) |
0.808104 | + | 0.589040i | \(0.200494\pi\) | |||||||
\(998\) | 15.0000 | − | 25.9808i | 0.474817 | − | 0.822407i | ||||
\(999\) | 2.53553 | + | 4.39167i | 0.0802207 | + | 0.138946i |
(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 | 546.2.i.h.235.2 | yes | 4 | |
3.2 | odd | 2 | 1638.2.j.n.235.1 | 4 | |||
7.2 | even | 3 | inner | 546.2.i.h.79.2 | ✓ | 4 | |
7.3 | odd | 6 | 3822.2.a.bp.1.2 | 2 | |||
7.4 | even | 3 | 3822.2.a.bs.1.1 | 2 | |||
21.2 | odd | 6 | 1638.2.j.n.1171.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
546.2.i.h.79.2 | ✓ | 4 | 7.2 | even | 3 | inner | |
546.2.i.h.235.2 | yes | 4 | 1.1 | even | 1 | trivial | |
1638.2.j.n.235.1 | 4 | 3.2 | odd | 2 | |||
1638.2.j.n.1171.1 | 4 | 21.2 | odd | 6 | |||
3822.2.a.bp.1.2 | 2 | 7.3 | odd | 6 | |||
3822.2.a.bs.1.1 | 2 | 7.4 | even | 3 |