Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [210,2,Mod(13,210)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(210, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 3, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("210.13");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 210 = 2 \cdot 3 \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 210.m (of order \(4\), 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: | \(1.67685844245\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(i)\) |
Coefficient field: | 8.0.1698758656.6 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} + 18x^{6} + 97x^{4} + 176x^{2} + 64 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 97.2 | ||
Root | \(-3.16053i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 210.97 |
Dual form | 210.2.m.b.13.2 |
$q$-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 \(\left(\mathbb{Z}/210\mathbb{Z}\right)^\times\).
\(n\) | \(31\) | \(71\) | \(127\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(e\left(\frac{1}{4}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.707107 | − | 0.707107i | −0.500000 | − | 0.500000i | ||||
\(3\) | 0.707107 | + | 0.707107i | 0.408248 | + | 0.408248i | ||||
\(4\) | 1.00000i | 0.500000i | ||||||||
\(5\) | 1.52773 | + | 1.63280i | 0.683220 | + | 0.730213i | ||||
\(6\) | − | 1.00000i | − | 0.408248i | ||||||
\(7\) | −1.23483 | + | 2.33991i | −0.466723 | + | 0.884404i | ||||
\(8\) | 0.707107 | − | 0.707107i | 0.250000 | − | 0.250000i | ||||
\(9\) | 1.00000i | 0.333333i | ||||||||
\(10\) | 0.0743018 | − | 2.23483i | 0.0234963 | − | 0.706716i | ||||
\(11\) | −5.73528 | −1.72925 | −0.864625 | − | 0.502417i | \(-0.832444\pi\) | ||||
−0.864625 | + | 0.502417i | \(0.832444\pi\) | |||||||
\(12\) | −0.707107 | + | 0.707107i | −0.204124 | + | 0.204124i | ||||
\(13\) | 3.41421 | + | 3.41421i | 0.946932 | + | 0.946932i | 0.998661 | − | 0.0517287i | \(-0.0164731\pi\) |
−0.0517287 | + | 0.998661i | \(0.516473\pi\) | |||||||
\(14\) | 2.52773 | − | 0.781409i | 0.675563 | − | 0.208840i | ||||
\(15\) | −0.0743018 | + | 2.23483i | −0.0191846 | + | 0.577031i | ||||
\(16\) | −1.00000 | −0.250000 | ||||||||
\(17\) | 2.57474 | − | 2.57474i | 0.624467 | − | 0.624467i | −0.322203 | − | 0.946671i | \(-0.604423\pi\) |
0.946671 | + | 0.322203i | \(0.104423\pi\) | |||||||
\(18\) | 0.707107 | − | 0.707107i | 0.166667 | − | 0.166667i | ||||
\(19\) | 1.85140 | 0.424739 | 0.212370 | − | 0.977189i | \(-0.431882\pi\) | ||||
0.212370 | + | 0.977189i | \(0.431882\pi\) | |||||||
\(20\) | −1.63280 | + | 1.52773i | −0.365106 | + | 0.341610i | ||||
\(21\) | −2.52773 | + | 0.781409i | −0.551595 | + | 0.170517i | ||||
\(22\) | 4.05545 | + | 4.05545i | 0.864625 | + | 0.864625i | ||||
\(23\) | 6.46967 | − | 6.46967i | 1.34902 | − | 1.34902i | 0.462290 | − | 0.886729i | \(-0.347028\pi\) |
0.886729 | − | 0.462290i | \(-0.152972\pi\) | |||||||
\(24\) | 1.00000 | 0.204124 | ||||||||
\(25\) | −0.332104 | + | 4.98896i | −0.0664208 | + | 0.997792i | ||||
\(26\) | − | 4.82843i | − | 0.946932i | ||||||
\(27\) | −0.707107 | + | 0.707107i | −0.136083 | + | 0.136083i | ||||
\(28\) | −2.33991 | − | 1.23483i | −0.442202 | − | 0.233362i | ||||
\(29\) | − | 3.47577i | − | 0.645434i | −0.946496 | − | 0.322717i | \(-0.895404\pi\) | ||
0.946496 | − | 0.322717i | \(-0.104596\pi\) | |||||||
\(30\) | 1.63280 | − | 1.52773i | 0.298108 | − | 0.278923i | ||||
\(31\) | 0.469666i | 0.0843546i | 0.999110 | + | 0.0421773i | \(0.0134294\pi\) | ||||
−0.999110 | + | 0.0421773i | \(0.986571\pi\) | |||||||
\(32\) | 0.707107 | + | 0.707107i | 0.125000 | + | 0.125000i | ||||
\(33\) | −4.05545 | − | 4.05545i | −0.705964 | − | 0.705964i | ||||
\(34\) | −3.64124 | −0.624467 | ||||||||
\(35\) | −5.70711 | + | 1.55850i | −0.964677 | + | 0.263435i | ||||
\(36\) | −1.00000 | −0.166667 | ||||||||
\(37\) | 0.574745 | + | 0.574745i | 0.0944875 | + | 0.0944875i | 0.752771 | − | 0.658283i | \(-0.228717\pi\) |
−0.658283 | + | 0.752771i | \(0.728717\pi\) | |||||||
\(38\) | −1.30913 | − | 1.30913i | −0.212370 | − | 0.212370i | ||||
\(39\) | 4.82843i | 0.773167i | ||||||||
\(40\) | 2.23483 | + | 0.0743018i | 0.353358 | + | 0.0117481i | ||||
\(41\) | − | 1.03858i | − | 0.162200i | −0.996706 | − | 0.0810998i | \(-0.974157\pi\) | ||
0.996706 | − | 0.0810998i | \(-0.0258433\pi\) | |||||||
\(42\) | 2.33991 | + | 1.23483i | 0.361056 | + | 0.190539i | ||||
\(43\) | 6.17246 | − | 6.17246i | 0.941291 | − | 0.941291i | −0.0570785 | − | 0.998370i | \(-0.518179\pi\) |
0.998370 | + | 0.0570785i | \(0.0181785\pi\) | |||||||
\(44\) | − | 5.73528i | − | 0.864625i | ||||||
\(45\) | −1.63280 | + | 1.52773i | −0.243404 | + | 0.227740i | ||||
\(46\) | −9.14949 | −1.34902 | ||||||||
\(47\) | −3.85140 | + | 3.85140i | −0.561784 | + | 0.561784i | −0.929814 | − | 0.368030i | \(-0.880032\pi\) |
0.368030 | + | 0.929814i | \(0.380032\pi\) | |||||||
\(48\) | −0.707107 | − | 0.707107i | −0.102062 | − | 0.102062i | ||||
\(49\) | −3.95037 | − | 5.77880i | −0.564339 | − | 0.825543i | ||||
\(50\) | 3.76256 | − | 3.29289i | 0.532106 | − | 0.465685i | ||||
\(51\) | 3.64124 | 0.509875 | ||||||||
\(52\) | −3.41421 | + | 3.41421i | −0.473466 | + | 0.473466i | ||||
\(53\) | −1.85140 | + | 1.85140i | −0.254309 | + | 0.254309i | −0.822735 | − | 0.568426i | \(-0.807553\pi\) |
0.568426 | + | 0.822735i | \(0.307553\pi\) | |||||||
\(54\) | 1.00000 | 0.136083 | ||||||||
\(55\) | −8.76193 | − | 9.36459i | −1.18146 | − | 1.26272i | ||||
\(56\) | 0.781409 | + | 2.52773i | 0.104420 | + | 0.337782i | ||||
\(57\) | 1.30913 | + | 1.30913i | 0.173399 | + | 0.173399i | ||||
\(58\) | −2.45774 | + | 2.45774i | −0.322717 | + | 0.322717i | ||||
\(59\) | −13.3306 | −1.73549 | −0.867747 | − | 0.497007i | \(-0.834432\pi\) | ||||
−0.867747 | + | 0.497007i | \(0.834432\pi\) | |||||||
\(60\) | −2.23483 | − | 0.0743018i | −0.288516 | − | 0.00959232i | ||||
\(61\) | − | 8.53122i | − | 1.09231i | −0.837684 | − | 0.546155i | \(-0.816091\pi\) | ||
0.837684 | − | 0.546155i | \(-0.183909\pi\) | |||||||
\(62\) | 0.332104 | − | 0.332104i | 0.0421773 | − | 0.0421773i | ||||
\(63\) | −2.33991 | − | 1.23483i | −0.294801 | − | 0.155574i | ||||
\(64\) | − | 1.00000i | − | 0.125000i | ||||||
\(65\) | −0.358761 | + | 10.7907i | −0.0444988 | + | 1.33843i | ||||
\(66\) | 5.73528i | 0.705964i | ||||||||
\(67\) | −4.46967 | − | 4.46967i | −0.546057 | − | 0.546057i | 0.379241 | − | 0.925298i | \(-0.376185\pi\) |
−0.925298 | + | 0.379241i | \(0.876185\pi\) | |||||||
\(68\) | 2.57474 | + | 2.57474i | 0.312234 | + | 0.312234i | ||||
\(69\) | 9.14949 | 1.10147 | ||||||||
\(70\) | 5.13756 | + | 2.93351i | 0.614056 | + | 0.350621i | ||||
\(71\) | 5.13387 | 0.609279 | 0.304639 | − | 0.952468i | \(-0.401464\pi\) | ||||
0.304639 | + | 0.952468i | \(0.401464\pi\) | |||||||
\(72\) | 0.707107 | + | 0.707107i | 0.0833333 | + | 0.0833333i | ||||
\(73\) | 7.80177 | + | 7.80177i | 0.913128 | + | 0.913128i | 0.996517 | − | 0.0833889i | \(-0.0265744\pi\) |
−0.0833889 | + | 0.996517i | \(0.526574\pi\) | |||||||
\(74\) | − | 0.812812i | − | 0.0944875i | ||||||
\(75\) | −3.76256 | + | 3.29289i | −0.434463 | + | 0.380231i | ||||
\(76\) | 1.85140i | 0.212370i | ||||||||
\(77\) | 7.08211 | − | 13.4200i | 0.807081 | − | 1.52936i | ||||
\(78\) | 3.41421 | − | 3.41421i | 0.386584 | − | 0.386584i | ||||
\(79\) | − | 4.16422i | − | 0.468511i | −0.972175 | − | 0.234256i | \(-0.924735\pi\) | ||
0.972175 | − | 0.234256i | \(-0.0752653\pi\) | |||||||
\(80\) | −1.52773 | − | 1.63280i | −0.170805 | − | 0.182553i | ||||
\(81\) | −1.00000 | −0.111111 | ||||||||
\(82\) | −0.734390 | + | 0.734390i | −0.0810998 | + | 0.0810998i | ||||
\(83\) | 1.77297 | + | 1.77297i | 0.194609 | + | 0.194609i | 0.797684 | − | 0.603075i | \(-0.206058\pi\) |
−0.603075 | + | 0.797684i | \(0.706058\pi\) | |||||||
\(84\) | −0.781409 | − | 2.52773i | −0.0852587 | − | 0.275798i | ||||
\(85\) | 8.13756 | + | 0.270551i | 0.882643 | + | 0.0293453i | ||||
\(86\) | −8.72918 | −0.941291 | ||||||||
\(87\) | 2.45774 | − | 2.45774i | 0.263497 | − | 0.263497i | ||||
\(88\) | −4.05545 | + | 4.05545i | −0.432313 | + | 0.432313i | ||||
\(89\) | 9.12563 | 0.967315 | 0.483658 | − | 0.875257i | \(-0.339308\pi\) | ||||
0.483658 | + | 0.875257i | \(0.339308\pi\) | |||||||
\(90\) | 2.23483 | + | 0.0743018i | 0.235572 | + | 0.00783210i | ||||
\(91\) | −12.2049 | + | 3.77297i | −1.27943 | + | 0.395515i | ||||
\(92\) | 6.46967 | + | 6.46967i | 0.674509 | + | 0.674509i | ||||
\(93\) | −0.332104 | + | 0.332104i | −0.0344376 | + | 0.0344376i | ||||
\(94\) | 5.44670 | 0.561784 | ||||||||
\(95\) | 2.82843 | + | 3.02297i | 0.290191 | + | 0.310150i | ||||
\(96\) | 1.00000i | 0.102062i | ||||||||
\(97\) | −0.0119278 | + | 0.0119278i | −0.00121108 | + | 0.00121108i | −0.707712 | − | 0.706501i | \(-0.750273\pi\) |
0.706501 | + | 0.707712i | \(0.250273\pi\) | |||||||
\(98\) | −1.29289 | + | 6.87957i | −0.130602 | + | 0.694941i | ||||
\(99\) | − | 5.73528i | − | 0.576417i | ||||||
\(100\) | −4.98896 | − | 0.332104i | −0.498896 | − | 0.0332104i | ||||
\(101\) | − | 6.25088i | − | 0.621986i | −0.950412 | − | 0.310993i | \(-0.899338\pi\) | ||
0.950412 | − | 0.310993i | \(-0.100662\pi\) | |||||||
\(102\) | −2.57474 | − | 2.57474i | −0.254938 | − | 0.254938i | ||||
\(103\) | 1.36459 | + | 1.36459i | 0.134457 | + | 0.134457i | 0.771132 | − | 0.636675i | \(-0.219691\pi\) |
−0.636675 | + | 0.771132i | \(0.719691\pi\) | |||||||
\(104\) | 4.82843 | 0.473466 | ||||||||
\(105\) | −5.13756 | − | 2.93351i | −0.501375 | − | 0.286281i | ||||
\(106\) | 2.61827 | 0.254309 | ||||||||
\(107\) | 11.2981 | + | 11.2981i | 1.09223 | + | 1.09223i | 0.995290 | + | 0.0969374i | \(0.0309047\pi\) |
0.0969374 | + | 0.995290i | \(0.469095\pi\) | |||||||
\(108\) | −0.707107 | − | 0.707107i | −0.0680414 | − | 0.0680414i | ||||
\(109\) | 1.91295i | 0.183227i | 0.995795 | + | 0.0916137i | \(0.0292025\pi\) | ||||
−0.995795 | + | 0.0916137i | \(0.970798\pi\) | |||||||
\(110\) | −0.426141 | + | 12.8174i | −0.0406310 | + | 1.22209i | ||||
\(111\) | 0.812812i | 0.0771487i | ||||||||
\(112\) | 1.23483 | − | 2.33991i | 0.116681 | − | 0.221101i | ||||
\(113\) | −2.37563 | + | 2.37563i | −0.223480 | + | 0.223480i | −0.809962 | − | 0.586482i | \(-0.800512\pi\) |
0.586482 | + | 0.809962i | \(0.300512\pi\) | |||||||
\(114\) | − | 1.85140i | − | 0.173399i | ||||||
\(115\) | 20.4476 | + | 0.679824i | 1.90675 | + | 0.0633939i | ||||
\(116\) | 3.47577 | 0.322717 | ||||||||
\(117\) | −3.41421 | + | 3.41421i | −0.315644 | + | 0.315644i | ||||
\(118\) | 9.42614 | + | 9.42614i | 0.867747 | + | 0.867747i | ||||
\(119\) | 2.84530 | + | 9.20406i | 0.260828 | + | 0.843734i | ||||
\(120\) | 1.52773 | + | 1.63280i | 0.139462 | + | 0.149054i | ||||
\(121\) | 21.8934 | 1.99031 | ||||||||
\(122\) | −6.03248 | + | 6.03248i | −0.546155 | + | 0.546155i | ||||
\(123\) | 0.734390 | − | 0.734390i | 0.0662177 | − | 0.0662177i | ||||
\(124\) | −0.469666 | −0.0421773 | ||||||||
\(125\) | −8.65336 | + | 7.07950i | −0.773980 | + | 0.633210i | ||||
\(126\) | 0.781409 | + | 2.52773i | 0.0696134 | + | 0.225188i | ||||
\(127\) | −13.3802 | − | 13.3802i | −1.18730 | − | 1.18730i | −0.977811 | − | 0.209490i | \(-0.932820\pi\) |
−0.209490 | − | 0.977811i | \(-0.567180\pi\) | |||||||
\(128\) | −0.707107 | + | 0.707107i | −0.0625000 | + | 0.0625000i | ||||
\(129\) | 8.72918 | 0.768561 | ||||||||
\(130\) | 7.88388 | − | 7.37652i | 0.691462 | − | 0.646963i | ||||
\(131\) | 11.5646i | 1.01040i | 0.863001 | + | 0.505201i | \(0.168582\pi\) | ||||
−0.863001 | + | 0.505201i | \(0.831418\pi\) | |||||||
\(132\) | 4.05545 | − | 4.05545i | 0.352982 | − | 0.352982i | ||||
\(133\) | −2.28617 | + | 4.33210i | −0.198236 | + | 0.375641i | ||||
\(134\) | 6.32106i | 0.546057i | ||||||||
\(135\) | −2.23483 | − | 0.0743018i | −0.192344 | − | 0.00639488i | ||||
\(136\) | − | 3.64124i | − | 0.312234i | ||||||
\(137\) | −8.03248 | − | 8.03248i | −0.686261 | − | 0.686261i | 0.275142 | − | 0.961404i | \(-0.411275\pi\) |
−0.961404 | + | 0.275142i | \(0.911275\pi\) | |||||||
\(138\) | −6.46967 | − | 6.46967i | −0.550735 | − | 0.550735i | ||||
\(139\) | −7.02297 | −0.595680 | −0.297840 | − | 0.954616i | \(-0.596266\pi\) | ||||
−0.297840 | + | 0.954616i | \(0.596266\pi\) | |||||||
\(140\) | −1.55850 | − | 5.70711i | −0.131718 | − | 0.482339i | ||||
\(141\) | −5.44670 | −0.458695 | ||||||||
\(142\) | −3.63020 | − | 3.63020i | −0.304639 | − | 0.304639i | ||||
\(143\) | −19.5815 | − | 19.5815i | −1.63748 | − | 1.63748i | ||||
\(144\) | − | 1.00000i | − | 0.0833333i | ||||||
\(145\) | 5.67525 | − | 5.31002i | 0.471304 | − | 0.440973i | ||||
\(146\) | − | 11.0334i | − | 0.913128i | ||||||
\(147\) | 1.29289 | − | 6.87957i | 0.106636 | − | 0.567417i | ||||
\(148\) | −0.574745 | + | 0.574745i | −0.0472437 | + | 0.0472437i | ||||
\(149\) | 1.88388i | 0.154333i | 0.997018 | + | 0.0771667i | \(0.0245874\pi\) | ||||
−0.997018 | + | 0.0771667i | \(0.975413\pi\) | |||||||
\(150\) | 4.98896 | + | 0.332104i | 0.407347 | + | 0.0271162i | ||||
\(151\) | 3.28248 | 0.267124 | 0.133562 | − | 0.991040i | \(-0.457358\pi\) | ||||
0.133562 | + | 0.991040i | \(0.457358\pi\) | |||||||
\(152\) | 1.30913 | − | 1.30913i | 0.106185 | − | 0.106185i | ||||
\(153\) | 2.57474 | + | 2.57474i | 0.208156 | + | 0.208156i | ||||
\(154\) | −14.4972 | + | 4.48159i | −1.16822 | + | 0.361137i | ||||
\(155\) | −0.766874 | + | 0.717522i | −0.0615968 | + | 0.0576327i | ||||
\(156\) | −4.82843 | −0.386584 | ||||||||
\(157\) | −7.57106 | + | 7.57106i | −0.604236 | + | 0.604236i | −0.941434 | − | 0.337198i | \(-0.890521\pi\) |
0.337198 | + | 0.941434i | \(0.390521\pi\) | |||||||
\(158\) | −2.94455 | + | 2.94455i | −0.234256 | + | 0.234256i | ||||
\(159\) | −2.61827 | −0.207642 | ||||||||
\(160\) | −0.0743018 | + | 2.23483i | −0.00587407 | + | 0.176679i | ||||
\(161\) | 7.14949 | + | 23.1274i | 0.563459 | + | 1.82269i | ||||
\(162\) | 0.707107 | + | 0.707107i | 0.0555556 | + | 0.0555556i | ||||
\(163\) | −10.3367 | + | 10.3367i | −0.809631 | + | 0.809631i | −0.984578 | − | 0.174947i | \(-0.944025\pi\) |
0.174947 | + | 0.984578i | \(0.444025\pi\) | |||||||
\(164\) | 1.03858 | 0.0810998 | ||||||||
\(165\) | 0.426141 | − | 12.8174i | 0.0331751 | − | 0.997832i | ||||
\(166\) | − | 2.50736i | − | 0.194609i | ||||||
\(167\) | 9.85140 | − | 9.85140i | 0.762324 | − | 0.762324i | −0.214418 | − | 0.976742i | \(-0.568785\pi\) |
0.976742 | + | 0.214418i | \(0.0687855\pi\) | |||||||
\(168\) | −1.23483 | + | 2.33991i | −0.0952694 | + | 0.180528i | ||||
\(169\) | 10.3137i | 0.793362i | ||||||||
\(170\) | −5.56282 | − | 5.94543i | −0.426649 | − | 0.455994i | ||||
\(171\) | 1.85140i | 0.141580i | ||||||||
\(172\) | 6.17246 | + | 6.17246i | 0.470646 | + | 0.470646i | ||||
\(173\) | −8.83947 | − | 8.83947i | −0.672052 | − | 0.672052i | 0.286137 | − | 0.958189i | \(-0.407629\pi\) |
−0.958189 | + | 0.286137i | \(0.907629\pi\) | |||||||
\(174\) | −3.47577 | −0.263497 | ||||||||
\(175\) | −11.2636 | − | 6.93763i | −0.851450 | − | 0.524435i | ||||
\(176\) | 5.73528 | 0.432313 | ||||||||
\(177\) | −9.42614 | − | 9.42614i | −0.708512 | − | 0.708512i | ||||
\(178\) | −6.45280 | − | 6.45280i | −0.483658 | − | 0.483658i | ||||
\(179\) | 7.68934i | 0.574728i | 0.957821 | + | 0.287364i | \(0.0927789\pi\) | ||||
−0.957821 | + | 0.287364i | \(0.907221\pi\) | |||||||
\(180\) | −1.52773 | − | 1.63280i | −0.113870 | − | 0.121702i | ||||
\(181\) | − | 10.7071i | − | 0.795852i | −0.917418 | − | 0.397926i | \(-0.869730\pi\) | ||
0.917418 | − | 0.397926i | \(-0.130270\pi\) | |||||||
\(182\) | 11.2981 | + | 5.96230i | 0.837470 | + | 0.441955i | ||||
\(183\) | 6.03248 | − | 6.03248i | 0.445934 | − | 0.445934i | ||||
\(184\) | − | 9.14949i | − | 0.674509i | ||||||
\(185\) | −0.0603934 | + | 1.81650i | −0.00444021 | + | 0.133552i | ||||
\(186\) | 0.469666 | 0.0344376 | ||||||||
\(187\) | −14.7669 | + | 14.7669i | −1.07986 | + | 1.07986i | ||||
\(188\) | −3.85140 | − | 3.85140i | −0.280892 | − | 0.280892i | ||||
\(189\) | −0.781409 | − | 2.52773i | −0.0568391 | − | 0.183865i | ||||
\(190\) | 0.137562 | − | 4.13756i | 0.00997980 | − | 0.300170i | ||||
\(191\) | −4.91206 | −0.355424 | −0.177712 | − | 0.984082i | \(-0.556870\pi\) | ||||
−0.177712 | + | 0.984082i | \(0.556870\pi\) | |||||||
\(192\) | 0.707107 | − | 0.707107i | 0.0510310 | − | 0.0510310i | ||||
\(193\) | 16.4706 | − | 16.4706i | 1.18558 | − | 1.18558i | 0.207299 | − | 0.978278i | \(-0.433533\pi\) |
0.978278 | − | 0.207299i | \(-0.0664672\pi\) | |||||||
\(194\) | 0.0168684 | 0.00121108 | ||||||||
\(195\) | −7.88388 | + | 7.37652i | −0.564576 | + | 0.528243i | ||||
\(196\) | 5.77880 | − | 3.95037i | 0.412772 | − | 0.282170i | ||||
\(197\) | −5.13387 | − | 5.13387i | −0.365773 | − | 0.365773i | 0.500160 | − | 0.865933i | \(-0.333275\pi\) |
−0.865933 | + | 0.500160i | \(0.833275\pi\) | |||||||
\(198\) | −4.05545 | + | 4.05545i | −0.288208 | + | 0.288208i | ||||
\(199\) | −8.63388 | −0.612040 | −0.306020 | − | 0.952025i | \(-0.598997\pi\) | ||||
−0.306020 | + | 0.952025i | \(0.598997\pi\) | |||||||
\(200\) | 3.29289 | + | 3.76256i | 0.232843 | + | 0.266053i | ||||
\(201\) | − | 6.32106i | − | 0.445853i | ||||||
\(202\) | −4.42004 | + | 4.42004i | −0.310993 | + | 0.310993i | ||||
\(203\) | 8.13299 | + | 4.29199i | 0.570824 | + | 0.301239i | ||||
\(204\) | 3.64124i | 0.254938i | ||||||||
\(205\) | 1.69581 | − | 1.58667i | 0.118440 | − | 0.110818i | ||||
\(206\) | − | 1.92982i | − | 0.134457i | ||||||
\(207\) | 6.46967 | + | 6.46967i | 0.449673 | + | 0.449673i | ||||
\(208\) | −3.41421 | − | 3.41421i | −0.236733 | − | 0.236733i | ||||
\(209\) | −10.6183 | −0.734481 | ||||||||
\(210\) | 1.55850 | + | 5.70711i | 0.107547 | + | 0.393828i | ||||
\(211\) | 7.73402 | 0.532432 | 0.266216 | − | 0.963913i | \(-0.414227\pi\) | ||||
0.266216 | + | 0.963913i | \(0.414227\pi\) | |||||||
\(212\) | −1.85140 | − | 1.85140i | −0.127154 | − | 0.127154i | ||||
\(213\) | 3.63020 | + | 3.63020i | 0.248737 | + | 0.248737i | ||||
\(214\) | − | 15.9779i | − | 1.09223i | ||||||
\(215\) | 19.5083 | + | 0.648593i | 1.33045 | + | 0.0442337i | ||||
\(216\) | 1.00000i | 0.0680414i | ||||||||
\(217\) | −1.09898 | − | 0.579960i | −0.0746035 | − | 0.0393702i | ||||
\(218\) | 1.35266 | − | 1.35266i | 0.0916137 | − | 0.0916137i | ||||
\(219\) | 11.0334i | 0.745566i | ||||||||
\(220\) | 9.36459 | − | 8.76193i | 0.631360 | − | 0.590729i | ||||
\(221\) | 17.5815 | 1.18266 | ||||||||
\(222\) | 0.574745 | − | 0.574745i | 0.0385744 | − | 0.0385744i | ||||
\(223\) | 8.63883 | + | 8.63883i | 0.578499 | + | 0.578499i | 0.934489 | − | 0.355991i | \(-0.115857\pi\) |
−0.355991 | + | 0.934489i | \(0.615857\pi\) | |||||||
\(224\) | −2.52773 | + | 0.781409i | −0.168891 | + | 0.0522101i | ||||
\(225\) | −4.98896 | − | 0.332104i | −0.332597 | − | 0.0221403i | ||||
\(226\) | 3.35965 | 0.223480 | ||||||||
\(227\) | −4.08705 | + | 4.08705i | −0.271267 | + | 0.271267i | −0.829610 | − | 0.558343i | \(-0.811437\pi\) |
0.558343 | + | 0.829610i | \(0.311437\pi\) | |||||||
\(228\) | −1.30913 | + | 1.30913i | −0.0866996 | + | 0.0866996i | ||||
\(229\) | 9.31371 | 0.615467 | 0.307734 | − | 0.951473i | \(-0.400429\pi\) | ||||
0.307734 | + | 0.951473i | \(0.400429\pi\) | |||||||
\(230\) | −13.9779 | − | 14.9393i | −0.921677 | − | 0.985070i | ||||
\(231\) | 14.4972 | − | 4.48159i | 0.953846 | − | 0.294867i | ||||
\(232\) | −2.45774 | − | 2.45774i | −0.161358 | − | 0.161358i | ||||
\(233\) | −5.22791 | + | 5.22791i | −0.342492 | + | 0.342492i | −0.857303 | − | 0.514812i | \(-0.827862\pi\) |
0.514812 | + | 0.857303i | \(0.327862\pi\) | |||||||
\(234\) | 4.82843 | 0.315644 | ||||||||
\(235\) | −12.1725 | − | 0.404699i | −0.794044 | − | 0.0263997i | ||||
\(236\) | − | 13.3306i | − | 0.867747i | ||||||
\(237\) | 2.94455 | − | 2.94455i | 0.191269 | − | 0.191269i | ||||
\(238\) | 4.49632 | − | 8.52018i | 0.291453 | − | 0.552281i | ||||
\(239\) | − | 7.38514i | − | 0.477705i | −0.971056 | − | 0.238853i | \(-0.923229\pi\) | ||
0.971056 | − | 0.238853i | \(-0.0767713\pi\) | |||||||
\(240\) | 0.0743018 | − | 2.23483i | 0.00479616 | − | 0.144258i | ||||
\(241\) | 4.44417i | 0.286274i | 0.989703 | + | 0.143137i | \(0.0457190\pi\) | ||||
−0.989703 | + | 0.143137i | \(0.954281\pi\) | |||||||
\(242\) | −15.4810 | − | 15.4810i | −0.995154 | − | 0.995154i | ||||
\(243\) | −0.707107 | − | 0.707107i | −0.0453609 | − | 0.0453609i | ||||
\(244\) | 8.53122 | 0.546155 | ||||||||
\(245\) | 3.40056 | − | 15.2786i | 0.217254 | − | 0.976115i | ||||
\(246\) | −1.03858 | −0.0662177 | ||||||||
\(247\) | 6.32106 | + | 6.32106i | 0.402200 | + | 0.402200i | ||||
\(248\) | 0.332104 | + | 0.332104i | 0.0210886 | + | 0.0210886i | ||||
\(249\) | 2.50736i | 0.158898i | ||||||||
\(250\) | 11.1248 | + | 1.11289i | 0.703595 | + | 0.0703851i | ||||
\(251\) | 14.1400i | 0.892507i | 0.894907 | + | 0.446254i | \(0.147242\pi\) | ||||
−0.894907 | + | 0.446254i | \(0.852758\pi\) | |||||||
\(252\) | 1.23483 | − | 2.33991i | 0.0777872 | − | 0.147401i | ||||
\(253\) | −37.1053 | + | 37.1053i | −2.33279 | + | 2.33279i | ||||
\(254\) | 18.9225i | 1.18730i | ||||||||
\(255\) | 5.56282 | + | 5.94543i | 0.348357 | + | 0.372317i | ||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −6.67400 | + | 6.67400i | −0.416312 | + | 0.416312i | −0.883931 | − | 0.467618i | \(-0.845112\pi\) |
0.467618 | + | 0.883931i | \(0.345112\pi\) | |||||||
\(258\) | −6.17246 | − | 6.17246i | −0.384281 | − | 0.384281i | ||||
\(259\) | −2.05457 | + | 0.635138i | −0.127665 | + | 0.0394656i | ||||
\(260\) | −10.7907 | − | 0.358761i | −0.669213 | − | 0.0222494i | ||||
\(261\) | 3.47577 | 0.215145 | ||||||||
\(262\) | 8.17740 | − | 8.17740i | 0.505201 | − | 0.505201i | ||||
\(263\) | 2.21016 | − | 2.21016i | 0.136284 | − | 0.136284i | −0.635674 | − | 0.771958i | \(-0.719278\pi\) |
0.771958 | + | 0.635674i | \(0.219278\pi\) | |||||||
\(264\) | −5.73528 | −0.352982 | ||||||||
\(265\) | −5.85140 | − | 0.194542i | −0.359448 | − | 0.0119506i | ||||
\(266\) | 4.67982 | − | 1.44670i | 0.286938 | − | 0.0887027i | ||||
\(267\) | 6.45280 | + | 6.45280i | 0.394905 | + | 0.394905i | ||||
\(268\) | 4.46967 | − | 4.46967i | 0.273028 | − | 0.273028i | ||||
\(269\) | −16.2362 | −0.989937 | −0.494968 | − | 0.868911i | \(-0.664820\pi\) | ||||
−0.494968 | + | 0.868911i | \(0.664820\pi\) | |||||||
\(270\) | 1.52773 | + | 1.63280i | 0.0929745 | + | 0.0993693i | ||||
\(271\) | − | 30.1841i | − | 1.83355i | −0.399399 | − | 0.916777i | \(-0.630781\pi\) | ||
0.399399 | − | 0.916777i | \(-0.369219\pi\) | |||||||
\(272\) | −2.57474 | + | 2.57474i | −0.156117 | + | 0.156117i | ||||
\(273\) | −11.2981 | − | 5.96230i | −0.683792 | − | 0.360855i | ||||
\(274\) | 11.3596i | 0.686261i | ||||||||
\(275\) | 1.90471 | − | 28.6131i | 0.114858 | − | 1.72543i | ||||
\(276\) | 9.14949i | 0.550735i | ||||||||
\(277\) | 12.3646 | + | 12.3646i | 0.742916 | + | 0.742916i | 0.973138 | − | 0.230222i | \(-0.0739453\pi\) |
−0.230222 | + | 0.973138i | \(0.573945\pi\) | |||||||
\(278\) | 4.96599 | + | 4.96599i | 0.297840 | + | 0.297840i | ||||
\(279\) | −0.469666 | −0.0281182 | ||||||||
\(280\) | −2.93351 | + | 5.13756i | −0.175310 | + | 0.307028i | ||||
\(281\) | −22.1127 | −1.31913 | −0.659566 | − | 0.751647i | \(-0.729260\pi\) | ||||
−0.659566 | + | 0.751647i | \(0.729260\pi\) | |||||||
\(282\) | 3.85140 | + | 3.85140i | 0.229347 | + | 0.229347i | ||||
\(283\) | 14.9172 | + | 14.9172i | 0.886738 | + | 0.886738i | 0.994208 | − | 0.107470i | \(-0.0342749\pi\) |
−0.107470 | + | 0.994208i | \(0.534275\pi\) | |||||||
\(284\) | 5.13387i | 0.304639i | ||||||||
\(285\) | −0.137562 | + | 4.13756i | −0.00814847 | + | 0.245088i | ||||
\(286\) | 27.6924i | 1.63748i | ||||||||
\(287\) | 2.43020 | + | 1.28248i | 0.143450 | + | 0.0757023i | ||||
\(288\) | −0.707107 | + | 0.707107i | −0.0416667 | + | 0.0416667i | ||||
\(289\) | 3.74138i | 0.220081i | ||||||||
\(290\) | −7.76776 | − | 0.258256i | −0.456139 | − | 0.0151653i | ||||
\(291\) | −0.0168684 | −0.000988844 | ||||||||
\(292\) | −7.80177 | + | 7.80177i | −0.456564 | + | 0.456564i | ||||
\(293\) | 11.5977 | + | 11.5977i | 0.677546 | + | 0.677546i | 0.959444 | − | 0.281899i | \(-0.0909642\pi\) |
−0.281899 | + | 0.959444i | \(0.590964\pi\) | |||||||
\(294\) | −5.77880 | + | 3.95037i | −0.337027 | + | 0.230390i | ||||
\(295\) | −20.3655 | − | 21.7662i | −1.18572 | − | 1.26728i | ||||
\(296\) | 0.812812 | 0.0472437 | ||||||||
\(297\) | 4.05545 | − | 4.05545i | 0.235321 | − | 0.235321i | ||||
\(298\) | 1.33210 | − | 1.33210i | 0.0771667 | − | 0.0771667i | ||||
\(299\) | 44.1776 | 2.55486 | ||||||||
\(300\) | −3.29289 | − | 3.76256i | −0.190115 | − | 0.217231i | ||||
\(301\) | 6.82105 | + | 22.0650i | 0.393159 | + | 1.27180i | ||||
\(302\) | −2.32106 | − | 2.32106i | −0.133562 | − | 0.133562i | ||||
\(303\) | 4.42004 | − | 4.42004i | 0.253925 | − | 0.253925i | ||||
\(304\) | −1.85140 | −0.106185 | ||||||||
\(305\) | 13.9298 | − | 13.0334i | 0.797619 | − | 0.746289i | ||||
\(306\) | − | 3.64124i | − | 0.208156i | ||||||
\(307\) | 12.4164 | − | 12.4164i | 0.708639 | − | 0.708639i | −0.257610 | − | 0.966249i | \(-0.582935\pi\) |
0.966249 | + | 0.257610i | \(0.0829350\pi\) | |||||||
\(308\) | 13.4200 | + | 7.08211i | 0.764678 | + | 0.403541i | ||||
\(309\) | 1.92982i | 0.109784i | ||||||||
\(310\) | 1.04963 | + | 0.0348971i | 0.0596147 | + | 0.00198202i | ||||
\(311\) | 9.81370i | 0.556484i | 0.960511 | + | 0.278242i | \(0.0897517\pi\) | ||||
−0.960511 | + | 0.278242i | \(0.910248\pi\) | |||||||
\(312\) | 3.41421 | + | 3.41421i | 0.193292 | + | 0.193292i | ||||
\(313\) | −13.4586 | − | 13.4586i | −0.760726 | − | 0.760726i | 0.215727 | − | 0.976454i | \(-0.430788\pi\) |
−0.976454 | + | 0.215727i | \(0.930788\pi\) | |||||||
\(314\) | 10.7071 | 0.604236 | ||||||||
\(315\) | −1.55850 | − | 5.70711i | −0.0878117 | − | 0.321559i | ||||
\(316\) | 4.16422 | 0.234256 | ||||||||
\(317\) | −8.01040 | − | 8.01040i | −0.449909 | − | 0.449909i | 0.445415 | − | 0.895324i | \(-0.353056\pi\) |
−0.895324 | + | 0.445415i | \(0.853056\pi\) | |||||||
\(318\) | 1.85140 | + | 1.85140i | 0.103821 | + | 0.103821i | ||||
\(319\) | 19.9345i | 1.11612i | ||||||||
\(320\) | 1.63280 | − | 1.52773i | 0.0912766 | − | 0.0854025i | ||||
\(321\) | 15.9779i | 0.891800i | ||||||||
\(322\) | 11.2981 | − | 21.4090i | 0.629618 | − | 1.19308i | ||||
\(323\) | 4.76687 | − | 4.76687i | 0.265236 | − | 0.265236i | ||||
\(324\) | − | 1.00000i | − | 0.0555556i | ||||||
\(325\) | −18.1672 | + | 15.8995i | −1.00774 | + | 0.881945i | ||||
\(326\) | 14.6183 | 0.809631 | ||||||||
\(327\) | −1.35266 | + | 1.35266i | −0.0748023 | + | 0.0748023i | ||||
\(328\) | −0.734390 | − | 0.734390i | −0.0405499 | − | 0.0405499i | ||||
\(329\) | −4.25610 | − | 13.7678i | −0.234646 | − | 0.759041i | ||||
\(330\) | −9.36459 | + | 8.76193i | −0.515504 | + | 0.482329i | ||||
\(331\) | −13.6906 | −0.752503 | −0.376251 | − | 0.926518i | \(-0.622787\pi\) | ||||
−0.376251 | + | 0.926518i | \(0.622787\pi\) | |||||||
\(332\) | −1.77297 | + | 1.77297i | −0.0973046 | + | 0.0973046i | ||||
\(333\) | −0.574745 | + | 0.574745i | −0.0314958 | + | 0.0314958i | ||||
\(334\) | −13.9320 | −0.762324 | ||||||||
\(335\) | 0.469666 | − | 14.1265i | 0.0256606 | − | 0.771814i | ||||
\(336\) | 2.52773 | − | 0.781409i | 0.137899 | − | 0.0426293i | ||||
\(337\) | −4.47055 | − | 4.47055i | −0.243527 | − | 0.243527i | 0.574781 | − | 0.818307i | \(-0.305087\pi\) |
−0.818307 | + | 0.574781i | \(0.805087\pi\) | |||||||
\(338\) | 7.29289 | − | 7.29289i | 0.396681 | − | 0.396681i | ||||
\(339\) | −3.35965 | −0.182471 | ||||||||
\(340\) | −0.270551 | + | 8.13756i | −0.0146727 | + | 0.441321i | ||||
\(341\) | − | 2.69367i | − | 0.145870i | ||||||
\(342\) | 1.30913 | − | 1.30913i | 0.0707899 | − | 0.0707899i | ||||
\(343\) | 18.3999 | − | 2.10767i | 0.993503 | − | 0.113804i | ||||
\(344\) | − | 8.72918i | − | 0.470646i | ||||||
\(345\) | 13.9779 | + | 14.9393i | 0.752546 | + | 0.804307i | ||||
\(346\) | 12.5009i | 0.672052i | ||||||||
\(347\) | 12.9103 | + | 12.9103i | 0.693059 | + | 0.693059i | 0.962904 | − | 0.269845i | \(-0.0869724\pi\) |
−0.269845 | + | 0.962904i | \(0.586972\pi\) | |||||||
\(348\) | 2.45774 | + | 2.45774i | 0.131749 | + | 0.131749i | ||||
\(349\) | −13.5937 | −0.727652 | −0.363826 | − | 0.931467i | \(-0.618530\pi\) | ||||
−0.363826 | + | 0.931467i | \(0.618530\pi\) | |||||||
\(350\) | 3.05895 | + | 12.8702i | 0.163508 | + | 0.687943i | ||||
\(351\) | −4.82843 | −0.257722 | ||||||||
\(352\) | −4.05545 | − | 4.05545i | −0.216156 | − | 0.216156i | ||||
\(353\) | −17.4032 | − | 17.4032i | −0.926277 | − | 0.926277i | 0.0711857 | − | 0.997463i | \(-0.477322\pi\) |
−0.997463 | + | 0.0711857i | \(0.977322\pi\) | |||||||
\(354\) | 13.3306i | 0.708512i | ||||||||
\(355\) | 7.84316 | + | 8.38262i | 0.416271 | + | 0.444903i | ||||
\(356\) | 9.12563i | 0.483658i | ||||||||
\(357\) | −4.49632 | + | 8.52018i | −0.237971 | + | 0.450936i | ||||
\(358\) | 5.43718 | − | 5.43718i | 0.287364 | − | 0.287364i | ||||
\(359\) | 7.02297i | 0.370658i | 0.982677 | + | 0.185329i | \(0.0593351\pi\) | ||||
−0.982677 | + | 0.185329i | \(0.940665\pi\) | |||||||
\(360\) | −0.0743018 | + | 2.23483i | −0.00391605 | + | 0.117786i | ||||
\(361\) | −15.5723 | −0.819596 | ||||||||
\(362\) | −7.57106 | + | 7.57106i | −0.397926 | + | 0.397926i | ||||
\(363\) | 15.4810 | + | 15.4810i | 0.812540 | + | 0.812540i | ||||
\(364\) | −3.77297 | − | 12.2049i | −0.197758 | − | 0.639713i | ||||
\(365\) | −0.819799 | + | 24.6577i | −0.0429103 | + | 1.29065i | ||||
\(366\) | −8.53122 | −0.445934 | ||||||||
\(367\) | 23.0609 | − | 23.0609i | 1.20377 | − | 1.20377i | 0.230759 | − | 0.973011i | \(-0.425879\pi\) |
0.973011 | − | 0.230759i | \(-0.0741209\pi\) | |||||||
\(368\) | −6.46967 | + | 6.46967i | −0.337255 | + | 0.337255i | ||||
\(369\) | 1.03858 | 0.0540665 | ||||||||
\(370\) | 1.32716 | − | 1.24175i | 0.0689959 | − | 0.0645557i | ||||
\(371\) | −2.04594 | − | 6.61827i | −0.106220 | − | 0.343603i | ||||
\(372\) | −0.332104 | − | 0.332104i | −0.0172188 | − | 0.0172188i | ||||
\(373\) | −8.04352 | + | 8.04352i | −0.416478 | + | 0.416478i | −0.883988 | − | 0.467510i | \(-0.845151\pi\) |
0.467510 | + | 0.883988i | \(0.345151\pi\) | |||||||
\(374\) | 20.8835 | 1.07986 | ||||||||
\(375\) | −11.1248 | − | 1.11289i | −0.574483 | − | 0.0574692i | ||||
\(376\) | 5.44670i | 0.280892i | ||||||||
\(377\) | 11.8670 | − | 11.8670i | 0.611182 | − | 0.611182i | ||||
\(378\) | −1.23483 | + | 2.33991i | −0.0635130 | + | 0.120352i | ||||
\(379\) | 11.4368i | 0.587470i | 0.955887 | + | 0.293735i | \(0.0948983\pi\) | ||||
−0.955887 | + | 0.293735i | \(0.905102\pi\) | |||||||
\(380\) | −3.02297 | + | 2.82843i | −0.155075 | + | 0.145095i | ||||
\(381\) | − | 18.9225i | − | 0.969427i | ||||||
\(382\) | 3.47335 | + | 3.47335i | 0.177712 | + | 0.177712i | ||||
\(383\) | −5.71841 | − | 5.71841i | −0.292197 | − | 0.292197i | 0.545751 | − | 0.837948i | \(-0.316245\pi\) |
−0.837948 | + | 0.545751i | \(0.816245\pi\) | |||||||
\(384\) | −1.00000 | −0.0510310 | ||||||||
\(385\) | 32.7318 | − | 8.93845i | 1.66817 | − | 0.455545i | ||||
\(386\) | −23.2929 | −1.18558 | ||||||||
\(387\) | 6.17246 | + | 6.17246i | 0.313764 | + | 0.313764i | ||||
\(388\) | −0.0119278 | − | 0.0119278i | −0.000605541 | − | 0.000605541i | ||||
\(389\) | − | 32.4151i | − | 1.64351i | −0.569840 | − | 0.821755i | \(-0.692995\pi\) | ||
0.569840 | − | 0.821755i | \(-0.307005\pi\) | |||||||
\(390\) | 10.7907 | + | 0.358761i | 0.546410 | + | 0.0181666i | ||||
\(391\) | − | 33.3155i | − | 1.68484i | ||||||
\(392\) | −6.87957 | − | 1.29289i | −0.347471 | − | 0.0653010i | ||||
\(393\) | −8.17740 | + | 8.17740i | −0.412495 | + | 0.412495i | ||||
\(394\) | 7.26040i | 0.365773i | ||||||||
\(395\) | 6.79936 | − | 6.36179i | 0.342113 | − | 0.320096i | ||||
\(396\) | 5.73528 | 0.288208 | ||||||||
\(397\) | −25.6023 | + | 25.6023i | −1.28494 | + | 1.28494i | −0.347122 | + | 0.937820i | \(0.612841\pi\) |
−0.937820 | + | 0.347122i | \(0.887159\pi\) | |||||||
\(398\) | 6.10508 | + | 6.10508i | 0.306020 | + | 0.306020i | ||||
\(399\) | −4.67982 | + | 1.44670i | −0.234284 | + | 0.0724254i | ||||
\(400\) | 0.332104 | − | 4.98896i | 0.0166052 | − | 0.249448i | ||||
\(401\) | −12.8597 | −0.642181 | −0.321090 | − | 0.947049i | \(-0.604049\pi\) | ||||
−0.321090 | + | 0.947049i | \(0.604049\pi\) | |||||||
\(402\) | −4.46967 | + | 4.46967i | −0.222927 | + | 0.222927i | ||||
\(403\) | −1.60354 | + | 1.60354i | −0.0798781 | + | 0.0798781i | ||||
\(404\) | 6.25088 | 0.310993 | ||||||||
\(405\) | −1.52773 | − | 1.63280i | −0.0759133 | − | 0.0811347i | ||||
\(406\) | −2.71599 | − | 8.78579i | −0.134793 | − | 0.436031i | ||||
\(407\) | −3.29632 | − | 3.29632i | −0.163393 | − | 0.163393i | ||||
\(408\) | 2.57474 | − | 2.57474i | 0.127469 | − | 0.127469i | ||||
\(409\) | 7.67894 | 0.379699 | 0.189850 | − | 0.981813i | \(-0.439200\pi\) | ||||
0.189850 | + | 0.981813i | \(0.439200\pi\) | |||||||
\(410\) | −2.32106 | − | 0.0771687i | −0.114629 | − | 0.00381109i | ||||
\(411\) | − | 11.3596i | − | 0.560330i | ||||||
\(412\) | −1.36459 | + | 1.36459i | −0.0672284 | + | 0.0672284i | ||||
\(413\) | 16.4610 | − | 31.1924i | 0.809995 | − | 1.53488i | ||||
\(414\) | − | 9.14949i | − | 0.449673i | ||||||
\(415\) | −0.186302 | + | 5.60354i | −0.00914519 | + | 0.275067i | ||||
\(416\) | 4.82843i | 0.236733i | ||||||||
\(417\) | −4.96599 | − | 4.96599i | −0.243186 | − | 0.243186i | ||||
\(418\) | 7.50825 | + | 7.50825i | 0.367241 | + | 0.367241i | ||||
\(419\) | −15.2534 | −0.745178 | −0.372589 | − | 0.927997i | \(-0.621530\pi\) | ||||
−0.372589 | + | 0.927997i | \(0.621530\pi\) | |||||||
\(420\) | 2.93351 | − | 5.13756i | 0.143140 | − | 0.250687i | ||||
\(421\) | 16.5264 | 0.805447 | 0.402724 | − | 0.915322i | \(-0.368064\pi\) | ||||
0.402724 | + | 0.915322i | \(0.368064\pi\) | |||||||
\(422\) | −5.46878 | − | 5.46878i | −0.266216 | − | 0.266216i | ||||
\(423\) | −3.85140 | − | 3.85140i | −0.187261 | − | 0.187261i | ||||
\(424\) | 2.61827i | 0.127154i | ||||||||
\(425\) | 11.9902 | + | 13.7004i | 0.581611 | + | 0.664566i | ||||
\(426\) | − | 5.13387i | − | 0.248737i | ||||||
\(427\) | 19.9623 | + | 10.5346i | 0.966043 | + | 0.509807i | ||||
\(428\) | −11.2981 | + | 11.2981i | −0.546114 | + | 0.546114i | ||||
\(429\) | − | 27.6924i | − | 1.33700i | ||||||
\(430\) | −13.3358 | − | 14.2530i | −0.643109 | − | 0.687343i | ||||
\(431\) | 7.22830 | 0.348175 | 0.174087 | − | 0.984730i | \(-0.444302\pi\) | ||||
0.174087 | + | 0.984730i | \(0.444302\pi\) | |||||||
\(432\) | 0.707107 | − | 0.707107i | 0.0340207 | − | 0.0340207i | ||||
\(433\) | −13.0916 | − | 13.0916i | −0.629143 | − | 0.629143i | 0.318709 | − | 0.947853i | \(-0.396751\pi\) |
−0.947853 | + | 0.318709i | \(0.896751\pi\) | |||||||
\(434\) | 0.367001 | + | 1.18719i | 0.0176166 | + | 0.0569868i | ||||
\(435\) | 7.76776 | + | 0.258256i | 0.372436 | + | 0.0123824i | ||||
\(436\) | −1.91295 | −0.0916137 | ||||||||
\(437\) | 11.9779 | − | 11.9779i | 0.572981 | − | 0.572981i | ||||
\(438\) | 7.80177 | − | 7.80177i | 0.372783 | − | 0.372783i | ||||
\(439\) | −24.9034 | −1.18857 | −0.594287 | − | 0.804253i | \(-0.702566\pi\) | ||||
−0.594287 | + | 0.804253i | \(0.702566\pi\) | |||||||
\(440\) | −12.8174 | − | 0.426141i | −0.611045 | − | 0.0203155i | ||||
\(441\) | 5.77880 | − | 3.95037i | 0.275181 | − | 0.188113i | ||||
\(442\) | −12.4320 | − | 12.4320i | −0.591328 | − | 0.591328i | ||||
\(443\) | 12.2821 | − | 12.2821i | 0.583541 | − | 0.583541i | −0.352334 | − | 0.935874i | \(-0.614612\pi\) |
0.935874 | + | 0.352334i | \(0.114612\pi\) | |||||||
\(444\) | −0.812812 | −0.0385744 | ||||||||
\(445\) | 13.9415 | + | 14.9004i | 0.660889 | + | 0.706346i | ||||
\(446\) | − | 12.2171i | − | 0.578499i | ||||||
\(447\) | −1.33210 | + | 1.33210i | −0.0630064 | + | 0.0630064i | ||||
\(448\) | 2.33991 | + | 1.23483i | 0.110550 | + | 0.0583404i | ||||
\(449\) | − | 4.53122i | − | 0.213841i | −0.994268 | − | 0.106921i | \(-0.965901\pi\) | ||
0.994268 | − | 0.106921i | \(-0.0340991\pi\) | |||||||
\(450\) | 3.29289 | + | 3.76256i | 0.155228 | + | 0.177369i | ||||
\(451\) | 5.95657i | 0.280484i | ||||||||
\(452\) | −2.37563 | − | 2.37563i | −0.111740 | − | 0.111740i | ||||
\(453\) | 2.32106 | + | 2.32106i | 0.109053 | + | 0.109053i | ||||
\(454\) | 5.77996 | 0.271267 | ||||||||
\(455\) | −24.8063 | − | 14.1642i | −1.16294 | − | 0.664029i | ||||
\(456\) | 1.85140 | 0.0866996 | ||||||||
\(457\) | −5.34315 | − | 5.34315i | −0.249942 | − | 0.249942i | 0.571005 | − | 0.820947i | \(-0.306554\pi\) |
−0.820947 | + | 0.571005i | \(0.806554\pi\) | |||||||
\(458\) | −6.58579 | − | 6.58579i | −0.307734 | − | 0.307734i | ||||
\(459\) | 3.64124i | 0.169958i | ||||||||
\(460\) | −0.679824 | + | 20.4476i | −0.0316969 | + | 0.953373i | ||||
\(461\) | 12.9004i | 0.600831i | 0.953808 | + | 0.300415i | \(0.0971253\pi\) | ||||
−0.953808 | + | 0.300415i | \(0.902875\pi\) | |||||||
\(462\) | −13.4200 | − | 7.08211i | −0.624357 | − | 0.329490i | ||||
\(463\) | 11.9452 | − | 11.9452i | 0.555139 | − | 0.555139i | −0.372781 | − | 0.927919i | \(-0.621596\pi\) |
0.927919 | + | 0.372781i | \(0.121596\pi\) | |||||||
\(464\) | 3.47577i | 0.161358i | ||||||||
\(465\) | −1.04963 | − | 0.0348971i | −0.0486752 | − | 0.00161831i | ||||
\(466\) | 7.39338 | 0.342492 | ||||||||
\(467\) | −25.1204 | + | 25.1204i | −1.16243 | + | 1.16243i | −0.178493 | + | 0.983941i | \(0.557122\pi\) |
−0.983941 | + | 0.178493i | \(0.942878\pi\) | |||||||
\(468\) | −3.41421 | − | 3.41421i | −0.157822 | − | 0.157822i | ||||
\(469\) | 15.9779 | − | 4.93933i | 0.737792 | − | 0.228077i | ||||
\(470\) | 8.32106 | + | 8.89339i | 0.383822 | + | 0.410222i | ||||
\(471\) | −10.7071 | −0.493357 | ||||||||
\(472\) | −9.42614 | + | 9.42614i | −0.433873 | + | 0.433873i | ||||
\(473\) | −35.4008 | + | 35.4008i | −1.62773 | + | 1.62773i | ||||
\(474\) | −4.16422 | −0.191269 | ||||||||
\(475\) | −0.614857 | + | 9.23654i | −0.0282116 | + | 0.423802i | ||||
\(476\) | −9.20406 | + | 2.84530i | −0.421867 | + | 0.130414i | ||||
\(477\) | −1.85140 | − | 1.85140i | −0.0847696 | − | 0.0847696i | ||||
\(478\) | −5.22208 | + | 5.22208i | −0.238853 | + | 0.238853i | ||||
\(479\) | 1.17157 | 0.0535305 | 0.0267653 | − | 0.999642i | \(-0.491479\pi\) | ||||
0.0267653 | + | 0.999642i | \(0.491479\pi\) | |||||||
\(480\) | −1.63280 | + | 1.52773i | −0.0745270 | + | 0.0697308i | ||||
\(481\) | 3.92460i | 0.178947i | ||||||||
\(482\) | 3.14250 | − | 3.14250i | 0.143137 | − | 0.143137i | ||||
\(483\) | −11.2981 | + | 21.4090i | −0.514081 | + | 0.974143i | ||||
\(484\) | 21.8934i | 0.995154i | ||||||||
\(485\) | −0.0376981 | − | 0.00125335i | −0.00171178 | − | 5.69118e-5i | ||||
\(486\) | 1.00000i | 0.0453609i | ||||||||
\(487\) | 5.67741 | + | 5.67741i | 0.257268 | + | 0.257268i | 0.823942 | − | 0.566674i | \(-0.191770\pi\) |
−0.566674 | + | 0.823942i | \(0.691770\pi\) | |||||||
\(488\) | −6.03248 | − | 6.03248i | −0.273078 | − | 0.273078i | ||||
\(489\) | −14.6183 | −0.661061 | ||||||||
\(490\) | −13.2082 | + | 8.39905i | −0.596685 | + | 0.379430i | ||||
\(491\) | −21.3462 | −0.963340 | −0.481670 | − | 0.876353i | \(-0.659970\pi\) | ||||
−0.481670 | + | 0.876353i | \(0.659970\pi\) | |||||||
\(492\) | 0.734390 | + | 0.734390i | 0.0331089 | + | 0.0331089i | ||||
\(493\) | −8.94921 | − | 8.94921i | −0.403052 | − | 0.403052i | ||||
\(494\) | − | 8.93933i | − | 0.402200i | ||||||
\(495\) | 9.36459 | − | 8.76193i | 0.420907 | − | 0.393820i | ||||
\(496\) | − | 0.469666i | − | 0.0210886i | ||||||
\(497\) | −6.33948 | + | 12.0128i | −0.284364 | + | 0.538848i | ||||
\(498\) | 1.77297 | − | 1.77297i | 0.0794489 | − | 0.0794489i | ||||
\(499\) | − | 33.4411i | − | 1.49703i | −0.663118 | − | 0.748515i | \(-0.730767\pi\) | ||
0.663118 | − | 0.748515i | \(-0.269233\pi\) | |||||||
\(500\) | −7.07950 | − | 8.65336i | −0.316605 | − | 0.386990i | ||||
\(501\) | 13.9320 | 0.622435 | ||||||||
\(502\) | 9.99847 | − | 9.99847i | 0.446254 | − | 0.446254i | ||||
\(503\) | −9.00089 | − | 9.00089i | −0.401330 | − | 0.401330i | 0.477372 | − | 0.878701i | \(-0.341590\pi\) |
−0.878701 | + | 0.477372i | \(0.841590\pi\) | |||||||
\(504\) | −2.52773 | + | 0.781409i | −0.112594 | + | 0.0348067i | ||||
\(505\) | 10.2065 | − | 9.54964i | 0.454182 | − | 0.424953i | ||||
\(506\) | 52.4749 | 2.33279 | ||||||||
\(507\) | −7.29289 | + | 7.29289i | −0.323889 | + | 0.323889i | ||||
\(508\) | 13.3802 | − | 13.3802i | 0.593651 | − | 0.593651i | ||||
\(509\) | −24.7938 | −1.09896 | −0.549482 | − | 0.835506i | \(-0.685175\pi\) | ||||
−0.549482 | + | 0.835506i | \(0.685175\pi\) | |||||||
\(510\) | 0.270551 | − | 8.13756i | 0.0119802 | − | 0.360337i | ||||
\(511\) | −27.8893 | + | 8.62157i | −1.23375 | + | 0.381396i | ||||
\(512\) | −0.707107 | − | 0.707107i | −0.0312500 | − | 0.0312500i | ||||
\(513\) | −1.30913 | + | 1.30913i | −0.0577997 | + | 0.0577997i | ||||
\(514\) | 9.43846 | 0.416312 | ||||||||
\(515\) | −0.143389 | + | 4.31282i | −0.00631847 | + | 0.190046i | ||||
\(516\) | 8.72918i | 0.384281i | ||||||||
\(517\) | 22.0888 | − | 22.0888i | 0.971465 | − | 0.971465i | ||||
\(518\) | 1.90191 | + | 1.00369i | 0.0835651 | + | 0.0440995i | ||||
\(519\) | − | 12.5009i | − | 0.548728i | ||||||
\(520\) | 7.37652 | + | 7.88388i | 0.323482 | + | 0.345731i | ||||
\(521\) | − | 36.4871i | − | 1.59853i | −0.600981 | − | 0.799263i | \(-0.705223\pi\) | ||
0.600981 | − | 0.799263i | \(-0.294777\pi\) | |||||||
\(522\) | −2.45774 | − | 2.45774i | −0.107572 | − | 0.107572i | ||||
\(523\) | −22.9887 | − | 22.9887i | −1.00522 | − | 1.00522i | −0.999986 | − | 0.00523871i | \(-0.998332\pi\) |
−0.00523871 | − | 0.999986i | \(-0.501668\pi\) | |||||||
\(524\) | −11.5646 | −0.505201 | ||||||||
\(525\) | −3.05895 | − | 12.8702i | −0.133503 | − | 0.561703i | ||||
\(526\) | −3.12563 | −0.136284 | ||||||||
\(527\) | 1.20927 | + | 1.20927i | 0.0526767 | + | 0.0526767i | ||||
\(528\) | 4.05545 | + | 4.05545i | 0.176491 | + | 0.176491i | ||||
\(529\) | − | 60.7132i | − | 2.63970i | ||||||
\(530\) | 4.00000 | + | 4.27512i | 0.173749 | + | 0.185700i | ||||
\(531\) | − | 13.3306i | − | 0.578498i | ||||||
\(532\) | −4.33210 | − | 2.28617i | −0.187821 | − | 0.0991179i | ||||
\(533\) | 3.54595 | − | 3.54595i | 0.153592 | − | 0.153592i | ||||
\(534\) | − | 9.12563i | − | 0.394905i | ||||||
\(535\) | −1.18719 | + | 35.7080i | −0.0513266 | + | 1.54379i | ||||
\(536\) | −6.32106 | −0.273028 | ||||||||
\(537\) | −5.43718 | + | 5.43718i | −0.234632 | + | 0.234632i | ||||
\(538\) | 11.4807 | + | 11.4807i | 0.494968 | + | 0.494968i | ||||
\(539\) | 22.6565 | + | 33.1430i | 0.975884 | + | 1.42757i | ||||
\(540\) | 0.0743018 | − | 2.23483i | 0.00319744 | − | 0.0961719i | ||||
\(541\) | −17.9896 | −0.773432 | −0.386716 | − | 0.922199i | \(-0.626391\pi\) | ||||
−0.386716 | + | 0.922199i | \(0.626391\pi\) | |||||||
\(542\) | −21.3434 | + | 21.3434i | −0.916777 | + | 0.916777i | ||||
\(543\) | 7.57106 | − | 7.57106i | 0.324905 | − | 0.324905i | ||||
\(544\) | 3.64124 | 0.156117 | ||||||||
\(545\) | −3.12347 | + | 2.92246i | −0.133795 | + | 0.125185i | ||||
\(546\) | 3.77297 | + | 12.2049i | 0.161468 | + | 0.522323i | ||||
\(547\) | 22.6044 | + | 22.6044i | 0.966496 | + | 0.966496i | 0.999457 | − | 0.0329611i | \(-0.0104937\pi\) |
−0.0329611 | + | 0.999457i | \(0.510494\pi\) | |||||||
\(548\) | 8.03248 | − | 8.03248i | 0.343131 | − | 0.343131i | ||||
\(549\) | 8.53122 | 0.364104 | ||||||||
\(550\) | −21.5793 | + | 18.8857i | −0.920145 | + | 0.805287i | ||||
\(551\) | − | 6.43502i | − | 0.274141i | ||||||
\(552\) | 6.46967 | − | 6.46967i | 0.275367 | − | 0.275367i | ||||
\(553\) | 9.74390 | + | 5.14212i | 0.414353 | + | 0.218665i | ||||
\(554\) | − | 17.4862i | − | 0.742916i | ||||||
\(555\) | −1.32716 | + | 1.24175i | −0.0563350 | + | 0.0527095i | ||||
\(556\) | − | 7.02297i | − | 0.297840i | ||||||
\(557\) | 11.1240 | + | 11.1240i | 0.471339 | + | 0.471339i | 0.902348 | − | 0.431009i | \(-0.141842\pi\) |
−0.431009 | + | 0.902348i | \(0.641842\pi\) | |||||||
\(558\) | 0.332104 | + | 0.332104i | 0.0140591 | + | 0.0140591i | ||||
\(559\) | 42.1482 | 1.78268 | ||||||||
\(560\) | 5.70711 | − | 1.55850i | 0.241169 | − | 0.0658588i | ||||
\(561\) | −20.8835 | −0.881703 | ||||||||
\(562\) | 15.6360 | + | 15.6360i | 0.659566 | + | 0.659566i | ||||
\(563\) | 29.1274 | + | 29.1274i | 1.22757 | + | 1.22757i | 0.964879 | + | 0.262695i | \(0.0846113\pi\) |
0.262695 | + | 0.964879i | \(0.415389\pi\) | |||||||
\(564\) | − | 5.44670i | − | 0.229347i | ||||||
\(565\) | −7.50825 | − | 0.249628i | −0.315874 | − | 0.0105019i | ||||
\(566\) | − | 21.0962i | − | 0.886738i | ||||||
\(567\) | 1.23483 | − | 2.33991i | 0.0518581 | − | 0.0982671i | ||||
\(568\) | 3.63020 | − | 3.63020i | 0.152320 | − | 0.152320i | ||||
\(569\) | 8.70532i | 0.364946i | 0.983211 | + | 0.182473i | \(0.0584102\pi\) | ||||
−0.983211 | + | 0.182473i | \(0.941590\pi\) | |||||||
\(570\) | 3.02297 | − | 2.82843i | 0.126618 | − | 0.118470i | ||||
\(571\) | −35.9454 | −1.50427 | −0.752134 | − | 0.659010i | \(-0.770975\pi\) | ||||
−0.752134 | + | 0.659010i | \(0.770975\pi\) | |||||||
\(572\) | 19.5815 | − | 19.5815i | 0.818742 | − | 0.818742i | ||||
\(573\) | −3.47335 | − | 3.47335i | −0.145101 | − | 0.145101i | ||||
\(574\) | −0.811559 | − | 2.62526i | −0.0338738 | − | 0.109576i | ||||
\(575\) | 30.1283 | + | 34.4255i | 1.25644 | + | 1.43564i | ||||
\(576\) | 1.00000 | 0.0416667 | ||||||||
\(577\) | −22.5860 | + | 22.5860i | −0.940269 | + | 0.940269i | −0.998314 | − | 0.0580452i | \(-0.981513\pi\) |
0.0580452 | + | 0.998314i | \(0.481513\pi\) | |||||||
\(578\) | 2.64555 | − | 2.64555i | 0.110041 | − | 0.110041i | ||||
\(579\) | 23.2929 | 0.968019 | ||||||||
\(580\) | 5.31002 | + | 5.67525i | 0.220487 | + | 0.235652i | ||||
\(581\) | −6.33793 | + | 1.95928i | −0.262942 | + | 0.0812845i | ||||
\(582\) | 0.0119278 | + | 0.0119278i | 0.000494422 | + | 0.000494422i | ||||
\(583\) | 10.6183 | − | 10.6183i | 0.439764 | − | 0.439764i | ||||
\(584\) | 11.0334 | 0.456564 | ||||||||
\(585\) | −10.7907 | − | 0.358761i | −0.446142 | − | 0.0148329i | ||||
\(586\) | − | 16.4016i | − | 0.677546i | ||||||
\(587\) | −25.9727 | + | 25.9727i | −1.07201 | + | 1.07201i | −0.0748104 | + | 0.997198i | \(0.523835\pi\) |
−0.997198 | + | 0.0748104i | \(0.976165\pi\) | |||||||
\(588\) | 6.87957 | + | 1.29289i | 0.283709 | + | 0.0533180i | ||||
\(589\) | 0.869539i | 0.0358287i | ||||||||
\(590\) | −0.990486 | + | 29.7916i | −0.0407777 | + | 1.22650i | ||||
\(591\) | − | 7.26040i | − | 0.298653i | ||||||
\(592\) | −0.574745 | − | 0.574745i | −0.0236219 | − | 0.0236219i | ||||
\(593\) | 24.4656 | + | 24.4656i | 1.00468 | + | 1.00468i | 0.999989 | + | 0.00469328i | \(0.00149392\pi\) |
0.00469328 | + | 0.999989i | \(0.498506\pi\) | |||||||
\(594\) | −5.73528 | −0.235321 | ||||||||
\(595\) | −10.6816 | + | 18.7071i | −0.437903 | + | 0.766916i | ||||
\(596\) | −1.88388 | −0.0771667 | ||||||||
\(597\) | −6.10508 | − | 6.10508i | −0.249864 | − | 0.249864i | ||||
\(598\) | −31.2383 | − | 31.2383i | −1.27743 | − | 1.27743i | ||||
\(599\) | 6.72576i | 0.274807i | 0.990515 | + | 0.137404i | \(0.0438757\pi\) | ||||
−0.990515 | + | 0.137404i | \(0.956124\pi\) | |||||||
\(600\) | −0.332104 | + | 4.98896i | −0.0135581 | + | 0.203673i | ||||
\(601\) | 44.3830i | 1.81042i | 0.424965 | + | 0.905210i | \(0.360286\pi\) | ||||
−0.424965 | + | 0.905210i | \(0.639714\pi\) | |||||||
\(602\) | 10.7791 | − | 20.4255i | 0.439322 | − | 0.832481i | ||||
\(603\) | 4.46967 | − | 4.46967i | 0.182019 | − | 0.182019i | ||||
\(604\) | 3.28248i | 0.133562i | ||||||||
\(605\) | 33.4471 | + | 35.7476i | 1.35982 | + | 1.45335i | ||||
\(606\) | −6.25088 | −0.253925 | ||||||||
\(607\) | 7.20378 | − | 7.20378i | 0.292393 | − | 0.292393i | −0.545632 | − | 0.838025i | \(-0.683710\pi\) |
0.838025 | + | 0.545632i | \(0.183710\pi\) | |||||||
\(608\) | 1.30913 | + | 1.30913i | 0.0530924 | + | 0.0530924i | ||||
\(609\) | 2.71599 | + | 8.78579i | 0.110058 | + | 0.356018i | ||||
\(610\) | −19.0659 | − | 0.633885i | −0.771954 | − | 0.0256653i | ||||
\(611\) | −26.2990 | −1.06394 | ||||||||
\(612\) | −2.57474 | + | 2.57474i | −0.104078 | + | 0.104078i | ||||
\(613\) | 21.6324 | − | 21.6324i | 0.873723 | − | 0.873723i | −0.119153 | − | 0.992876i | \(-0.538018\pi\) |
0.992876 | + | 0.119153i | \(0.0380180\pi\) | |||||||
\(614\) | −17.5594 | −0.708639 | ||||||||
\(615\) | 2.32106 | + | 0.0771687i | 0.0935943 | + | 0.00311174i | ||||
\(616\) | −4.48159 | − | 14.4972i | −0.180569 | − | 0.584109i | ||||
\(617\) | 29.8652 | + | 29.8652i | 1.20233 | + | 1.20233i | 0.973457 | + | 0.228871i | \(0.0735035\pi\) |
0.228871 | + | 0.973457i | \(0.426496\pi\) | |||||||
\(618\) | 1.36459 | − | 1.36459i | 0.0548918 | − | 0.0548918i | ||||
\(619\) | 12.6963 | 0.510308 | 0.255154 | − | 0.966900i | \(-0.417874\pi\) | ||||
0.255154 | + | 0.966900i | \(0.417874\pi\) | |||||||
\(620\) | −0.717522 | − | 0.766874i | −0.0288164 | − | 0.0307984i | ||||
\(621\) | 9.14949i | 0.367156i | ||||||||
\(622\) | 6.93933 | − | 6.93933i | 0.278242 | − | 0.278242i | ||||
\(623\) | −11.2686 | + | 21.3532i | −0.451468 | + | 0.855497i | ||||
\(624\) | − | 4.82843i | − | 0.193292i | ||||||
\(625\) | −24.7794 | − | 3.31371i | −0.991177 | − | 0.132548i | ||||
\(626\) | 19.0334i | 0.760726i | ||||||||
\(627\) | −7.50825 | − | 7.50825i | −0.299851 | − | 0.299851i | ||||
\(628\) | −7.57106 | − | 7.57106i | −0.302118 | − | 0.302118i | ||||
\(629\) | 2.95964 | 0.118009 | ||||||||
\(630\) | −2.93351 | + | 5.13756i | −0.116874 | + | 0.204685i | ||||
\(631\) | 36.4650 | 1.45165 | 0.725824 | − | 0.687881i | \(-0.241459\pi\) | ||||
0.725824 | + | 0.687881i | \(0.241459\pi\) | |||||||
\(632\) | −2.94455 | − | 2.94455i | −0.117128 | − | 0.117128i | ||||
\(633\) | 5.46878 | + | 5.46878i | 0.217364 | + | 0.217364i | ||||
\(634\) | 11.3284i | 0.449909i | ||||||||
\(635\) | 1.40597 | − | 42.2886i | 0.0557943 | − | 1.67817i | ||||
\(636\) | − | 2.61827i | − | 0.103821i | ||||||
\(637\) | 6.24264 | − | 33.2175i | 0.247342 | − | 1.31612i | ||||
\(638\) | 14.0958 | − | 14.0958i | 0.558058 | − | 0.558058i | ||||
\(639\) | 5.13387i | 0.203093i | ||||||||
\(640\) | −2.23483 | − | 0.0743018i | −0.0883395 | − | 0.00293704i | ||||
\(641\) | −0.862164 | −0.0340534 | −0.0170267 | − | 0.999855i | \(-0.505420\pi\) | ||||
−0.0170267 | + | 0.999855i | \(0.505420\pi\) | |||||||
\(642\) | 11.2981 | − | 11.2981i | 0.445900 | − | 0.445900i | ||||
\(643\) | −8.58057 | − | 8.58057i | −0.338385 | − | 0.338385i | 0.517374 | − | 0.855759i | \(-0.326909\pi\) |
−0.855759 | + | 0.517374i | \(0.826909\pi\) | |||||||
\(644\) | −23.1274 | + | 7.14949i | −0.911347 | + | 0.281729i | ||||
\(645\) | 13.3358 | + | 14.2530i | 0.525096 | + | 0.561213i | ||||
\(646\) | −6.74138 | −0.265236 | ||||||||
\(647\) | −1.35623 | + | 1.35623i | −0.0533191 | + | 0.0533191i | −0.733264 | − | 0.679945i | \(-0.762004\pi\) |
0.679945 | + | 0.733264i | \(0.262004\pi\) | |||||||
\(648\) | −0.707107 | + | 0.707107i | −0.0277778 | + | 0.0277778i | ||||
\(649\) | 76.4545 | 3.00110 | ||||||||
\(650\) | 24.0888 | + | 1.60354i | 0.944841 | + | 0.0628961i | ||||
\(651\) | −0.367001 | − | 1.18719i | −0.0143839 | − | 0.0465296i | ||||
\(652\) | −10.3367 | − | 10.3367i | −0.404816 | − | 0.404816i | ||||
\(653\) | −15.8873 | + | 15.8873i | −0.621718 | + | 0.621718i | −0.945971 | − | 0.324253i | \(-0.894887\pi\) |
0.324253 | + | 0.945971i | \(0.394887\pi\) | |||||||
\(654\) | 1.91295 | 0.0748023 | ||||||||
\(655\) | −18.8827 | + | 17.6675i | −0.737809 | + | 0.690327i | ||||
\(656\) | 1.03858i | 0.0405499i | ||||||||
\(657\) | −7.80177 | + | 7.80177i | −0.304376 | + | 0.304376i | ||||
\(658\) | −6.72576 | + | 12.7448i | −0.262198 | + | 0.496844i | ||||
\(659\) | − | 25.8315i | − | 1.00625i | −0.864213 | − | 0.503126i | \(-0.832183\pi\) | ||
0.864213 | − | 0.503126i | \(-0.167817\pi\) | |||||||
\(660\) | 12.8174 | + | 0.426141i | 0.498916 | + | 0.0165875i | ||||
\(661\) | − | 30.7383i | − | 1.19558i | −0.801652 | − | 0.597791i | \(-0.796045\pi\) | ||
0.801652 | − | 0.597791i | \(-0.203955\pi\) | |||||||
\(662\) | 9.68071 | + | 9.68071i | 0.376251 | + | 0.376251i | ||||
\(663\) | 12.4320 | + | 12.4320i | 0.482818 | + | 0.482818i | ||||
\(664\) | 2.50736 | 0.0973046 | ||||||||
\(665\) | −10.5661 | + | 2.88541i | −0.409736 | + | 0.111891i | ||||
\(666\) | 0.812812 | 0.0314958 | ||||||||
\(667\) | −22.4871 | − | 22.4871i | −0.870702 | − | 0.870702i | ||||
\(668\) | 9.85140 | + | 9.85140i | 0.381162 | + | 0.381162i | ||||
\(669\) | 12.2171i | 0.472342i | ||||||||
\(670\) | −10.3211 | + | 9.65685i | −0.398737 | + | 0.373077i | ||||
\(671\) | 48.9289i | 1.88888i | ||||||||
\(672\) | −2.33991 | − | 1.23483i | −0.0902641 | − | 0.0476347i | ||||
\(673\) | −4.05024 | + | 4.05024i | −0.156125 | + | 0.156125i | −0.780847 | − | 0.624722i | \(-0.785212\pi\) |
0.624722 | + | 0.780847i | \(0.285212\pi\) | |||||||
\(674\) | 6.32232i | 0.243527i | ||||||||
\(675\) | −3.29289 | − | 3.76256i | −0.126744 | − | 0.144821i | ||||
\(676\) | −10.3137 | −0.396681 | ||||||||
\(677\) | 2.32222 | − | 2.32222i | 0.0892503 | − | 0.0892503i | −0.661072 | − | 0.750322i | \(-0.729898\pi\) |
0.750322 | + | 0.661072i | \(0.229898\pi\) | |||||||
\(678\) | 2.37563 | + | 2.37563i | 0.0912355 | + | 0.0912355i | ||||
\(679\) | −0.0131811 | − | 0.0426387i | −0.000505845 | − | 0.00163632i | ||||
\(680\) | 5.94543 | − | 5.56282i | 0.227997 | − | 0.213324i | ||||
\(681\) | −5.77996 | −0.221489 | ||||||||
\(682\) | −1.90471 | + | 1.90471i | −0.0729351 | + | 0.0729351i | ||||
\(683\) | −13.2028 | + | 13.2028i | −0.505191 | + | 0.505191i | −0.913047 | − | 0.407855i | \(-0.866277\pi\) |
0.407855 | + | 0.913047i | \(0.366277\pi\) | |||||||
\(684\) | −1.85140 | −0.0707899 | ||||||||
\(685\) | 0.844042 | − | 25.3869i | 0.0322492 | − | 0.969984i | ||||
\(686\) | −14.5011 | − | 11.5204i | −0.553653 | − | 0.439850i | ||||
\(687\) | 6.58579 | + | 6.58579i | 0.251263 | + | 0.251263i | ||||
\(688\) | −6.17246 | + | 6.17246i | −0.235323 | + | 0.235323i | ||||
\(689\) | −12.6421 | −0.481627 | ||||||||
\(690\) | 0.679824 | − | 20.4476i | 0.0258804 | − | 0.778426i | ||||
\(691\) | 49.4659i | 1.88177i | 0.338726 | + | 0.940885i | \(0.390004\pi\) | ||||
−0.338726 | + | 0.940885i | \(0.609996\pi\) | |||||||
\(692\) | 8.83947 | − | 8.83947i | 0.336026 | − | 0.336026i | ||||
\(693\) | 13.4200 | + | 7.08211i | 0.509785 | + | 0.269027i | ||||
\(694\) | − | 18.2579i | − | 0.693059i | ||||||
\(695\) | −10.7292 | − | 11.4671i | −0.406981 | − | 0.434973i | ||||
\(696\) | − | 3.47577i | − | 0.131749i | ||||||
\(697\) | −2.67409 | − | 2.67409i | −0.101288 | − | 0.101288i | ||||
\(698\) | 9.61217 | + | 9.61217i | 0.363826 | + | 0.363826i | ||||
\(699\) | −7.39338 | −0.279643 | ||||||||
\(700\) | 6.93763 | − | 11.2636i | 0.262218 | − | 0.425725i | ||||
\(701\) | 31.2773 | 1.18133 | 0.590663 | − | 0.806918i | \(-0.298866\pi\) | ||||
0.590663 | + | 0.806918i | \(0.298866\pi\) | |||||||
\(702\) | 3.41421 | + | 3.41421i | 0.128861 | + | 0.128861i | ||||
\(703\) | 1.06408 | + | 1.06408i | 0.0401326 | + | 0.0401326i | ||||
\(704\) | 5.73528i | 0.216156i | ||||||||
\(705\) | −8.32106 | − | 8.89339i | −0.313389 | − | 0.334945i | ||||
\(706\) | 24.6118i | 0.926277i | ||||||||
\(707\) | 14.6265 | + | 7.71880i | 0.550087 | + | 0.290295i | ||||
\(708\) | 9.42614 | − | 9.42614i | 0.354256 | − | 0.354256i | ||||
\(709\) | 42.4051i | 1.59256i | 0.604931 | + | 0.796278i | \(0.293201\pi\) | ||||
−0.604931 | + | 0.796278i | \(0.706799\pi\) | |||||||
\(710\) | 0.381456 | − | 11.4734i | 0.0143158 | − | 0.430587i | ||||
\(711\) | 4.16422 | 0.156170 | ||||||||
\(712\) | 6.45280 | − | 6.45280i | 0.241829 | − | 0.241829i | ||||
\(713\) | 3.03858 | + | 3.03858i | 0.113796 | + | 0.113796i | ||||
\(714\) | 9.20406 | − | 2.84530i | 0.344453 | − | 0.106483i | ||||
\(715\) | 2.05759 | − | 61.8878i | 0.0769496 | − | 2.31447i | ||||
\(716\) | −7.68934 | −0.287364 | ||||||||
\(717\) | 5.22208 | − | 5.22208i | 0.195022 | − | 0.195022i | ||||
\(718\) | 4.96599 | − | 4.96599i | 0.185329 | − | 0.185329i | ||||
\(719\) | −31.0675 | −1.15862 | −0.579311 | − | 0.815107i | \(-0.696678\pi\) | ||||
−0.579311 | + | 0.815107i | \(0.696678\pi\) | |||||||
\(720\) | 1.63280 | − | 1.52773i | 0.0608510 | − | 0.0569350i | ||||
\(721\) | −4.87805 | + | 1.50798i | −0.181668 | + | 0.0561600i | ||||
\(722\) | 11.0113 | + | 11.0113i | 0.409798 | + | 0.409798i | ||||
\(723\) | −3.14250 | + | 3.14250i | −0.116871 | + | 0.116871i | ||||
\(724\) | 10.7071 | 0.397926 | ||||||||
\(725\) | 17.3405 | + | 1.15432i | 0.644008 | + | 0.0428703i | ||||
\(726\) | − | 21.8934i | − | 0.812540i | ||||||
\(727\) | −6.60937 | + | 6.60937i | −0.245128 | + | 0.245128i | −0.818968 | − | 0.573840i | \(-0.805453\pi\) |
0.573840 | + | 0.818968i | \(0.305453\pi\) | |||||||
\(728\) | −5.96230 | + | 11.2981i | −0.220978 | + | 0.418735i | ||||
\(729\) | − | 1.00000i | − | 0.0370370i | ||||||
\(730\) | 18.0153 | − | 16.8560i | 0.666778 | − | 0.623867i | ||||
\(731\) | − | 31.7850i | − | 1.17561i | ||||||
\(732\) | 6.03248 | + | 6.03248i | 0.222967 | + | 0.222967i | ||||
\(733\) | −3.30331 | − | 3.30331i | −0.122010 | − | 0.122010i | 0.643465 | − | 0.765476i | \(-0.277496\pi\) |
−0.765476 | + | 0.643465i | \(0.777496\pi\) | |||||||
\(734\) | −32.6131 | −1.20377 | ||||||||
\(735\) | 13.2082 | − | 8.39905i | 0.487191 | − | 0.309804i | ||||
\(736\) | 9.14949 | 0.337255 | ||||||||
\(737\) | 25.6348 | + | 25.6348i | 0.944269 | + | 0.944269i | ||||
\(738\) | −0.734390 | − | 0.734390i | −0.0270333 | − | 0.0270333i | ||||
\(739\) | − | 8.70709i | − | 0.320296i | −0.987093 | − | 0.160148i | \(-0.948803\pi\) | ||
0.987093 | − | 0.160148i | \(-0.0511971\pi\) | |||||||
\(740\) | −1.81650 | − | 0.0603934i | −0.0667758 | − | 0.00222011i | ||||
\(741\) | 8.93933i | 0.328395i | ||||||||
\(742\) | −3.23313 | + | 6.12652i | −0.118692 | + | 0.224912i | ||||
\(743\) | 33.9264 | − | 33.9264i | 1.24464 | − | 1.24464i | 0.286582 | − | 0.958056i | \(-0.407481\pi\) |
0.958056 | − | 0.286582i | \(-0.0925192\pi\) | |||||||
\(744\) | 0.469666i | 0.0172188i | ||||||||
\(745\) | −3.07601 | + | 2.87805i | −0.112696 | + | 0.105444i | ||||
\(746\) | 11.3753 | 0.416478 | ||||||||
\(747\) | −1.77297 | + | 1.77297i | −0.0648697 | + | 0.0648697i | ||||
\(748\) | −14.7669 | − | 14.7669i | −0.539930 | − | 0.539930i | ||||
\(749\) | −40.3878 | + | 12.4853i | −1.47574 | + | 0.456202i | ||||
\(750\) | 7.07950 | + | 8.65336i | 0.258507 | + | 0.315976i | ||||
\(751\) | 40.1365 | 1.46460 | 0.732301 | − | 0.680981i | \(-0.238446\pi\) | ||||
0.732301 | + | 0.680981i | \(0.238446\pi\) | |||||||
\(752\) | 3.85140 | − | 3.85140i | 0.140446 | − | 0.140446i | ||||
\(753\) | −9.99847 | + | 9.99847i | −0.364365 | + | 0.364365i | ||||
\(754\) | −16.7825 | −0.611182 | ||||||||
\(755\) | 5.01473 | + | 5.35965i | 0.182505 | + | 0.195058i | ||||
\(756\) | 2.52773 | − | 0.781409i | 0.0919325 | − | 0.0284196i | ||||
\(757\) | 7.01659 | + | 7.01659i | 0.255022 | + | 0.255022i | 0.823026 | − | 0.568004i | \(-0.192284\pi\) |
−0.568004 | + | 0.823026i | \(0.692284\pi\) | |||||||
\(758\) | 8.08705 | − | 8.08705i | 0.293735 | − | 0.293735i | ||||
\(759\) | −52.4749 | −1.90472 | ||||||||
\(760\) | 4.13756 | + | 0.137562i | 0.150085 | + | 0.00498990i | ||||
\(761\) | − | 35.9693i | − | 1.30388i | −0.758269 | − | 0.651942i | \(-0.773954\pi\) | ||
0.758269 | − | 0.651942i | \(-0.226046\pi\) | |||||||
\(762\) | −13.3802 | + | 13.3802i | −0.484714 | + | 0.484714i | ||||
\(763\) | −4.47613 | − | 2.36217i | −0.162047 | − | 0.0855164i | ||||
\(764\) | − | 4.91206i | − | 0.177712i | ||||||
\(765\) | −0.270551 | + | 8.13756i | −0.00978178 | + | 0.294214i | ||||
\(766\) | 8.08705i | 0.292197i | ||||||||
\(767\) | −45.5134 | − | 45.5134i | −1.64339 | − | 1.64339i | ||||
\(768\) | 0.707107 | + | 0.707107i | 0.0255155 | + | 0.0255155i | ||||
\(769\) | −29.0018 | −1.04583 | −0.522916 | − | 0.852384i | \(-0.675156\pi\) | ||||
−0.522916 | + | 0.852384i | \(0.675156\pi\) | |||||||
\(770\) | −29.4653 | − | 16.8245i | −1.06186 | − | 0.606312i | ||||
\(771\) | −9.43846 | −0.339918 | ||||||||
\(772\) | 16.4706 | + | 16.4706i | 0.592788 | + | 0.592788i | ||||
\(773\) | 33.1042 | + | 33.1042i | 1.19067 | + | 1.19067i | 0.976878 | + | 0.213796i | \(0.0685826\pi\) |
0.213796 | + | 0.976878i | \(0.431417\pi\) | |||||||
\(774\) | − | 8.72918i | − | 0.313764i | ||||||
\(775\) | −2.34315 | − | 0.155978i | −0.0841683 | − | 0.00560290i | ||||
\(776\) | 0.0168684i | 0.000605541i | ||||||||
\(777\) | −1.90191 | − | 1.00369i | −0.0682306 | − | 0.0360071i | ||||
\(778\) | −22.9209 | + | 22.9209i | −0.821755 | + | 0.821755i | ||||
\(779\) | − | 1.92283i | − | 0.0688926i | ||||||
\(780\) | −7.37652 | − | 7.88388i | −0.264122 | − | 0.282288i | ||||
\(781\) | −29.4442 | −1.05360 | ||||||||
\(782\) | −23.5576 | + | 23.5576i | −0.842418 | + | 0.842418i | ||||
\(783\) | 2.45774 | + | 2.45774i | 0.0878324 | + | 0.0878324i | ||||
\(784\) | 3.95037 | + | 5.77880i | 0.141085 | + | 0.206386i | ||||
\(785\) | −23.9286 | − | 0.795556i | −0.854047 | − | 0.0283946i | ||||
\(786\) | 11.5646 | 0.412495 | ||||||||
\(787\) | −0.532861 | + | 0.532861i | −0.0189944 | + | 0.0189944i | −0.716540 | − | 0.697546i | \(-0.754275\pi\) |
0.697546 | + | 0.716540i | \(0.254275\pi\) | |||||||
\(788\) | 5.13387 | − | 5.13387i | 0.182887 | − | 0.182887i | ||||
\(789\) | 3.12563 | 0.111276 | ||||||||
\(790\) | −9.30633 | − | 0.309409i | −0.331105 | − | 0.0110083i | ||||
\(791\) | −2.62526 | − | 8.49227i | −0.0933434 | − | 0.301950i | ||||
\(792\) | −4.05545 | − | 4.05545i | −0.144104 | − | 0.144104i | ||||
\(793\) | 29.1274 | − | 29.1274i | 1.03434 | − | 1.03434i | ||||
\(794\) | 36.2071 | 1.28494 | ||||||||
\(795\) | −4.00000 | − | 4.27512i | −0.141865 | − | 0.151623i | ||||
\(796\) | − | 8.63388i | − | 0.306020i | ||||||
\(797\) | 22.6961 | − | 22.6961i | 0.803935 | − | 0.803935i | −0.179773 | − | 0.983708i | \(-0.557536\pi\) |
0.983708 | + | 0.179773i | \(0.0575363\pi\) | |||||||
\(798\) | 4.33210 | + | 2.28617i | 0.153355 | + | 0.0809294i | ||||
\(799\) | 19.8327i | 0.701631i | ||||||||
\(800\) | −3.76256 | + | 3.29289i | −0.133027 | + | 0.116421i | ||||
\(801\) | 9.12563i | 0.322438i | ||||||||
\(802\) | 9.09315 | + | 9.09315i | 0.321090 | + | 0.321090i | ||||
\(803\) | −44.7453 | − | 44.7453i | −1.57903 | − | 1.57903i | ||||
\(804\) | 6.32106 | 0.222927 | ||||||||
\(805\) | −26.8401 | + | 47.0061i | −0.945989 | + | 1.65675i | ||||
\(806\) | 2.26775 | 0.0798781 | ||||||||
\(807\) | −11.4807 | − | 11.4807i | −0.404140 | − | 0.404140i | ||||
\(808\) | −4.42004 | − | 4.42004i | −0.155496 | − | 0.155496i | ||||
\(809\) | − | 16.6404i | − | 0.585044i | −0.956259 | − | 0.292522i | \(-0.905506\pi\) | ||
0.956259 | − | 0.292522i | \(-0.0944944\pi\) | |||||||
\(810\) | −0.0743018 | + | 2.23483i | −0.00261070 | + | 0.0785240i | ||||
\(811\) | − | 13.7933i | − | 0.484347i | −0.970233 | − | 0.242173i | \(-0.922140\pi\) | ||
0.970233 | − | 0.242173i | \(-0.0778603\pi\) | |||||||
\(812\) | −4.29199 | + | 8.13299i | −0.150619 | + | 0.285412i | ||||
\(813\) | 21.3434 | − | 21.3434i | 0.748545 | − | 0.748545i | ||||
\(814\) | 4.66170i | 0.163393i | ||||||||
\(815\) | −32.6694 | − | 1.08616i | −1.14436 | − | 0.0380467i | ||||
\(816\) | −3.64124 | −0.127469 | ||||||||
\(817\) | 11.4277 | − | 11.4277i | 0.399804 | − | 0.399804i | ||||
\(818\) | −5.42983 | − | 5.42983i | −0.189850 | − | 0.189850i | ||||
\(819\) | −3.77297 | − | 12.2049i | −0.131838 | − | 0.426475i | ||||
\(820\) | 1.58667 | + | 1.69581i | 0.0554090 | + | 0.0592201i | ||||
\(821\) | −25.2001 | −0.879489 | −0.439745 | − | 0.898123i | \(-0.644931\pi\) | ||||
−0.439745 | + | 0.898123i | \(0.644931\pi\) | |||||||
\(822\) | −8.03248 | + | 8.03248i | −0.280165 | + | 0.280165i | ||||
\(823\) | 4.45075 | − | 4.45075i | 0.155143 | − | 0.155143i | −0.625267 | − | 0.780411i | \(-0.715010\pi\) |
0.780411 | + | 0.625267i | \(0.215010\pi\) | |||||||
\(824\) | 1.92982 | 0.0672284 | ||||||||
\(825\) | 21.5793 | − | 18.8857i | 0.751295 | − | 0.657514i | ||||
\(826\) | −33.6961 | + | 10.4166i | −1.17244 | + | 0.362441i | ||||
\(827\) | −21.7665 | − | 21.7665i | −0.756896 | − | 0.756896i | 0.218861 | − | 0.975756i | \(-0.429766\pi\) |
−0.975756 | + | 0.218861i | \(0.929766\pi\) | |||||||
\(828\) | −6.46967 | + | 6.46967i | −0.224836 | + | 0.224836i | ||||
\(829\) | −30.3787 | −1.05509 | −0.527547 | − | 0.849526i | \(-0.676888\pi\) | ||||
−0.527547 | + | 0.849526i | \(0.676888\pi\) | |||||||
\(830\) | 4.09404 | − | 3.83057i | 0.142106 | − | 0.132961i | ||||
\(831\) | 17.4862i | 0.606588i | ||||||||
\(832\) | 3.41421 | − | 3.41421i | 0.118367 | − | 0.118367i | ||||
\(833\) | −25.0501 | − | 4.70773i | −0.867936 | − | 0.163113i | ||||
\(834\) | 7.02297i | 0.243186i | ||||||||
\(835\) | 31.1356 | + | 1.03517i | 1.07749 | + | 0.0358236i | ||||
\(836\) | − | 10.6183i | − | 0.367241i | ||||||
\(837\) | −0.332104 | − | 0.332104i | −0.0114792 | − | 0.0114792i | ||||
\(838\) | 10.7858 | + | 10.7858i | 0.372589 | + | 0.372589i | ||||
\(839\) | 16.1464 | 0.557436 | 0.278718 | − | 0.960373i | \(-0.410090\pi\) | ||||
0.278718 | + | 0.960373i | \(0.410090\pi\) | |||||||
\(840\) | −5.70711 | + | 1.55850i | −0.196914 | + | 0.0537735i | ||||
\(841\) | 16.9190 | 0.583415 | ||||||||
\(842\) | −11.6859 | − | 11.6859i | −0.402724 | − | 0.402724i | ||||
\(843\) | −15.6360 | − | 15.6360i | −0.538533 | − | 0.538533i | ||||
\(844\) | 7.73402i | 0.266216i | ||||||||
\(845\) | −16.8403 | + | 15.7565i | −0.579323 | + | 0.542041i | ||||
\(846\) | 5.44670i | 0.187261i | ||||||||
\(847\) | −27.0347 | + | 51.2286i | −0.928923 | + | 1.76024i | ||||
\(848\) | 1.85140 | − | 1.85140i | 0.0635772 | − | 0.0635772i | ||||
\(849\) | 21.0962i | 0.724019i | ||||||||
\(850\) | 1.20927 | − | 18.1660i | 0.0414777 | − | 0.623088i | ||||
\(851\) | 7.43682 | 0.254931 | ||||||||
\(852\) | −3.63020 | + | 3.63020i | −0.124369 | + | 0.124369i | ||||
\(853\) | −26.8216 | − | 26.8216i | −0.918353 | − | 0.918353i | 0.0785565 | − | 0.996910i | \(-0.474969\pi\) |
−0.996910 | + | 0.0785565i | \(0.974969\pi\) | |||||||
\(854\) | −6.66637 | − | 21.5646i | −0.228118 | − | 0.737925i | ||||
\(855\) | −3.02297 | + | 2.82843i | −0.103383 | + | 0.0967302i | ||||
\(856\) | 15.9779 | 0.546114 | ||||||||
\(857\) | 18.6709 | − | 18.6709i | 0.637787 | − | 0.637787i | −0.312222 | − | 0.950009i | \(-0.601073\pi\) |
0.950009 | + | 0.312222i | \(0.101073\pi\) | |||||||
\(858\) | −19.5815 | + | 19.5815i | −0.668500 | + | 0.668500i | ||||
\(859\) | −8.11664 | −0.276936 | −0.138468 | − | 0.990367i | \(-0.544218\pi\) | ||||
−0.138468 | + | 0.990367i | \(0.544218\pi\) | |||||||
\(860\) | −0.648593 | + | 19.5083i | −0.0221169 | + | 0.665226i | ||||
\(861\) | 0.811559 | + | 2.62526i | 0.0276578 | + | 0.0894685i | ||||
\(862\) | −5.11118 | − | 5.11118i | −0.174087 | − | 0.174087i | ||||
\(863\) | 6.62651 | − | 6.62651i | 0.225569 | − | 0.225569i | −0.585270 | − | 0.810839i | \(-0.699011\pi\) |
0.810839 | + | 0.585270i | \(0.199011\pi\) | |||||||
\(864\) | −1.00000 | −0.0340207 | ||||||||
\(865\) | 0.928839 | − | 27.9374i | 0.0315815 | − | 0.949901i | ||||
\(866\) | 18.5144i | 0.629143i | ||||||||
\(867\) | −2.64555 | + | 2.64555i | −0.0898477 | + | 0.0898477i | ||||
\(868\) | 0.579960 | − | 1.09898i | 0.0196851 | − | 0.0373017i | ||||
\(869\) | 23.8829i | 0.810173i | ||||||||
\(870\) | −5.31002 | − | 5.67525i | −0.180027 | − | 0.192409i | ||||
\(871\) | − | 30.5208i | − | 1.03416i | ||||||
\(872\) | 1.35266 | + | 1.35266i | 0.0458068 | + | 0.0458068i | ||||
\(873\) | −0.0119278 | − | 0.0119278i | −0.000403694 | − | 0.000403694i | ||||
\(874\) | −16.9393 | −0.572981 | ||||||||
\(875\) | −5.87995 | − | 28.9901i | −0.198779 | − | 0.980044i | ||||
\(876\) | −11.0334 | −0.372783 | ||||||||
\(877\) | −27.9123 | − | 27.9123i | −0.942532 | − | 0.942532i | 0.0559044 | − | 0.998436i | \(-0.482196\pi\) |
−0.998436 | + | 0.0559044i | \(0.982196\pi\) | |||||||
\(878\) | 17.6094 | + | 17.6094i | 0.594287 | + | 0.594287i | ||||
\(879\) | 16.4016i | 0.553214i | ||||||||
\(880\) | 8.76193 | + | 9.36459i | 0.295365 | + | 0.315680i | ||||
\(881\) | − | 34.6317i | − | 1.16677i | −0.812195 | − | 0.583386i | \(-0.801728\pi\) | ||
0.812195 | − | 0.583386i | \(-0.198272\pi\) | |||||||
\(882\) | −6.87957 | − | 1.29289i | −0.231647 | − | 0.0435340i | ||||
\(883\) | 5.61001 | − | 5.61001i | 0.188792 | − | 0.188792i | −0.606382 | − | 0.795174i | \(-0.707380\pi\) |
0.795174 | + | 0.606382i | \(0.207380\pi\) | |||||||
\(884\) | 17.5815i | 0.591328i | ||||||||
\(885\) | 0.990486 | − | 29.7916i | 0.0332948 | − | 1.00143i | ||||
\(886\) | −17.3695 | −0.583541 | ||||||||
\(887\) | 24.0494 | − | 24.0494i | 0.807498 | − | 0.807498i | −0.176756 | − | 0.984255i | \(-0.556560\pi\) |
0.984255 | + | 0.176756i | \(0.0565605\pi\) | |||||||
\(888\) | 0.574745 | + | 0.574745i | 0.0192872 | + | 0.0192872i | ||||
\(889\) | 47.8308 | − | 14.7862i | 1.60419 | − | 0.495912i | ||||
\(890\) | 0.678051 | − | 20.3943i | 0.0227283 | − | 0.683617i | ||||
\(891\) | 5.73528 | 0.192139 | ||||||||
\(892\) | −8.63883 | + | 8.63883i | −0.289249 | + | 0.289249i | ||||
\(893\) | −7.13046 | + | 7.13046i | −0.238612 | + | 0.238612i | ||||
\(894\) | 1.88388 | 0.0630064 | ||||||||
\(895\) | −12.5552 | + | 11.7472i | −0.419674 | + | 0.392666i | ||||
\(896\) | −0.781409 | − | 2.52773i | −0.0261050 | − | 0.0844454i | ||||
\(897\) | 31.2383 | + | 31.2383i | 1.04302 | + | 1.04302i | ||||
\(898\) | −3.20406 | + | 3.20406i | −0.106921 | + | 0.106921i | ||||
\(899\) | 1.63245 | 0.0544453 | ||||||||
\(900\) | 0.332104 | − | 4.98896i | 0.0110701 | − | 0.166299i | ||||
\(901\) | 9.53375i | 0.317615i | ||||||||
\(902\) | 4.21193 | − | 4.21193i | 0.140242 | − | 0.140242i | ||||
\(903\) | −10.7791 | + | 20.4255i | −0.358705 | + | 0.679718i | ||||
\(904\) | 3.35965i | 0.111740i | ||||||||
\(905\) | 17.4826 | − | 16.3575i | 0.581141 | − | 0.543742i | ||||
\(906\) | − | 3.28248i | − | 0.109053i | ||||||
\(907\) | 34.2153 | + | 34.2153i | 1.13610 | + | 1.13610i | 0.989143 | + | 0.146959i | \(0.0469486\pi\) |
0.146959 | + | 0.989143i | \(0.453051\pi\) | |||||||
\(908\) | −4.08705 | − | 4.08705i | −0.135634 | − | 0.135634i | ||||
\(909\) | 6.25088 | 0.207329 | ||||||||
\(910\) | 7.52512 | + | 27.5563i | 0.249455 | + | 0.913484i | ||||
\(911\) | 56.4059 | 1.86881 | 0.934406 | − | 0.356210i | \(-0.115931\pi\) | ||||
0.934406 | + | 0.356210i | \(0.115931\pi\) | |||||||
\(912\) | −1.30913 | − | 1.30913i | −0.0433498 | − | 0.0433498i | ||||
\(913\) | −10.1685 | − | 10.1685i | −0.336528 | − | 0.336528i | ||||
\(914\) | 7.55635i | 0.249942i | ||||||||
\(915\) | 19.0659 | + | 0.633885i | 0.630298 | + | 0.0209556i | ||||
\(916\) | 9.31371i | 0.307734i | ||||||||
\(917\) | −27.0601 | − | 14.2803i | −0.893604 | − | 0.471578i | ||||
\(918\) | 2.57474 | − | 2.57474i | 0.0849792 | − | 0.0849792i | ||||
\(919\) | 37.1036i | 1.22393i | 0.790884 | + | 0.611967i | \(0.209621\pi\) | ||||
−0.790884 | + | 0.611967i | \(0.790379\pi\) | |||||||
\(920\) | 14.9393 | − | 13.9779i | 0.492535 | − | 0.460838i | ||||
\(921\) | 17.5594 | 0.578601 | ||||||||
\(922\) | 9.12195 | − | 9.12195i | 0.300415 | − | 0.300415i | ||||
\(923\) | 17.5281 | + | 17.5281i | 0.576946 | + | 0.576946i | ||||
\(924\) | 4.48159 | + | 14.4972i | 0.147434 | + | 0.476923i | ||||
\(925\) | −3.05825 | + | 2.67650i | −0.100555 | + | 0.0880029i | ||||
\(926\) | −16.8930 | −0.555139 | ||||||||
\(927\) | −1.36459 | + | 1.36459i | −0.0448189 | + | 0.0448189i | ||||
\(928\) | 2.45774 | − | 2.45774i | 0.0806792 | − | 0.0806792i | ||||
\(929\) | 0.164219 | 0.00538784 | 0.00269392 | − | 0.999996i | \(-0.499142\pi\) | ||||
0.00269392 | + | 0.999996i | \(0.499142\pi\) | |||||||
\(930\) | 0.717522 | + | 0.766874i | 0.0235285 | + | 0.0251468i | ||||
\(931\) | −7.31371 | − | 10.6989i | −0.239697 | − | 0.350641i | ||||
\(932\) | −5.22791 | − | 5.22791i | −0.171246 | − | 0.171246i | ||||
\(933\) | −6.93933 | + | 6.93933i | −0.227184 | + | 0.227184i | ||||
\(934\) | 35.5256 | 1.16243 | ||||||||
\(935\) | −46.6712 | − | 1.55168i | −1.52631 | − | 0.0507454i | ||||
\(936\) | 4.82843i | 0.157822i | ||||||||
\(937\) | 25.1804 | − | 25.1804i | 0.822609 | − | 0.822609i | −0.163872 | − | 0.986482i | \(-0.552398\pi\) |
0.986482 | + | 0.163872i | \(0.0523985\pi\) | |||||||
\(938\) | −14.7907 | − | 7.80546i | −0.482934 | − | 0.254857i | ||||
\(939\) | − | 19.0334i | − | 0.621131i | ||||||
\(940\) | 0.404699 | − | 12.1725i | 0.0131998 | − | 0.397022i | ||||
\(941\) | 46.5762i | 1.51834i | 0.650892 | + | 0.759171i | \(0.274395\pi\) | ||||
−0.650892 | + | 0.759171i | \(0.725605\pi\) | |||||||
\(942\) | 7.57106 | + | 7.57106i | 0.246678 | + | 0.246678i | ||||
\(943\) | −6.71929 | − | 6.71929i | −0.218810 | − | 0.218810i | ||||
\(944\) | 13.3306 | 0.433873 | ||||||||
\(945\) | 2.93351 | − | 5.13756i | 0.0954269 | − | 0.167125i | ||||
\(946\) | 50.0642 | 1.62773 | ||||||||
\(947\) | 15.2362 | + | 15.2362i | 0.495108 | + | 0.495108i | 0.909911 | − | 0.414803i | \(-0.136149\pi\) |
−0.414803 | + | 0.909911i | \(0.636149\pi\) | |||||||
\(948\) | 2.94455 | + | 2.94455i | 0.0956344 | + | 0.0956344i | ||||
\(949\) | 53.2738i | 1.72934i | ||||||||
\(950\) | 6.96599 | − | 6.09645i | 0.226007 | − | 0.197795i | ||||
\(951\) | − | 11.3284i | − | 0.367349i | ||||||
\(952\) | 8.52018 | + | 4.49632i | 0.276141 | + | 0.145727i | ||||
\(953\) | −2.21318 | + | 2.21318i | −0.0716920 | + | 0.0716920i | −0.742044 | − | 0.670352i | \(-0.766143\pi\) |
0.670352 | + | 0.742044i | \(0.266143\pi\) | |||||||
\(954\) | 2.61827i | 0.0847696i | ||||||||
\(955\) | −7.50429 | − | 8.02044i | −0.242833 | − | 0.259535i | ||||
\(956\) | 7.38514 | 0.238853 | ||||||||
\(957\) | −14.0958 | + | 14.0958i | −0.455653 | + | 0.455653i | ||||
\(958\) | −0.828427 | − | 0.828427i | −0.0267653 | − | 0.0267653i | ||||
\(959\) | 28.7141 | − | 8.87653i | 0.927226 | − | 0.286638i | ||||
\(960\) | 2.23483 | + | 0.0743018i | 0.0721289 | + | 0.00239808i | ||||
\(961\) | 30.7794 | 0.992884 | ||||||||
\(962\) | 2.77511 | − | 2.77511i | 0.0894733 | − | 0.0894733i | ||||
\(963\) | −11.2981 | + | 11.2981i | −0.364076 | + | 0.364076i | ||||
\(964\) | −4.44417 | −0.143137 | ||||||||
\(965\) | 52.0557 | + | 1.73070i | 1.67573 | + | 0.0557133i | ||||
\(966\) | 23.1274 | − | 7.14949i | 0.744112 | − | 0.230031i | ||||
\(967\) | 4.58606 | + | 4.58606i | 0.147478 | + | 0.147478i | 0.776990 | − | 0.629513i | \(-0.216745\pi\) |
−0.629513 | + | 0.776990i | \(0.716745\pi\) | |||||||
\(968\) | 15.4810 | − | 15.4810i | 0.497577 | − | 0.497577i | ||||
\(969\) | 6.74138 | 0.216564 | ||||||||
\(970\) | 0.0257703 | + | 0.0275428i | 0.000827435 | + | 0.000884347i | ||||
\(971\) | 37.1737i | 1.19296i | 0.802627 | + | 0.596481i | \(0.203435\pi\) | ||||
−0.802627 | + | 0.596481i | \(0.796565\pi\) | |||||||
\(972\) | 0.707107 | − | 0.707107i | 0.0226805 | − | 0.0226805i | ||||
\(973\) | 8.67220 | − | 16.4331i | 0.278018 | − | 0.526822i | ||||
\(974\) | − | 8.02907i | − | 0.257268i | ||||||
\(975\) | −24.0888 | − | 1.60354i | −0.771460 | − | 0.0513544i | ||||
\(976\) | 8.53122i | 0.273078i | ||||||||
\(977\) | −42.4680 | − | 42.4680i | −1.35867 | − | 1.35867i | −0.875557 | − | 0.483114i | \(-0.839506\pi\) |
−0.483114 | − | 0.875557i | \(-0.660494\pi\) | |||||||
\(978\) | 10.3367 | + | 10.3367i | 0.330531 | + | 0.330531i | ||||
\(979\) | −52.3380 | −1.67273 | ||||||||
\(980\) | 15.2786 | + | 3.40056i | 0.488058 | + | 0.108627i | ||||
\(981\) | −1.91295 | −0.0610758 | ||||||||
\(982\) | 15.0940 | + | 15.0940i | 0.481670 | + | 0.481670i | ||||
\(983\) | 31.8722 | + | 31.8722i | 1.01657 | + | 1.01657i | 0.999860 | + | 0.0167048i | \(0.00531754\pi\) |
0.0167048 | + | 0.999860i | \(0.494682\pi\) | |||||||
\(984\) | − | 1.03858i | − | 0.0331089i | ||||||
\(985\) | 0.539460 | − | 16.2258i | 0.0171886 | − | 0.516996i | ||||
\(986\) | 12.6561i | 0.403052i | ||||||||
\(987\) | 6.72576 | − | 12.7448i | 0.214083 | − | 0.405671i | ||||
\(988\) | −6.32106 | + | 6.32106i | −0.201100 | + | 0.201100i | ||||
\(989\) | − | 79.8675i | − | 2.53964i | ||||||
\(990\) | −12.8174 | − | 0.426141i | −0.407363 | − | 0.0135437i | ||||
\(991\) | 12.2660 | 0.389642 | 0.194821 | − | 0.980839i | \(-0.437587\pi\) | ||||
0.194821 | + | 0.980839i | \(0.437587\pi\) | |||||||
\(992\) | −0.332104 | + | 0.332104i | −0.0105443 | + | 0.0105443i | ||||
\(993\) | −9.68071 | − | 9.68071i | −0.307208 | − | 0.307208i | ||||
\(994\) | 12.9770 | − | 4.01165i | 0.411606 | − | 0.127242i | ||||
\(995\) | −13.1902 | − | 14.0975i | −0.418158 | − | 0.446919i | ||||
\(996\) | −2.50736 | −0.0794489 | ||||||||
\(997\) | 18.0221 | − | 18.0221i | 0.570764 | − | 0.570764i | −0.361578 | − | 0.932342i | \(-0.617762\pi\) |
0.932342 | + | 0.361578i | \(0.117762\pi\) | |||||||
\(998\) | −23.6464 | + | 23.6464i | −0.748515 | + | 0.748515i | ||||
\(999\) | −0.812812 | −0.0257162 |
(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 | 210.2.m.b.97.2 | yes | 8 | |
3.2 | odd | 2 | 630.2.p.c.307.3 | 8 | |||
4.3 | odd | 2 | 1680.2.cz.a.97.2 | 8 | |||
5.2 | odd | 4 | 1050.2.m.b.643.3 | 8 | |||
5.3 | odd | 4 | 210.2.m.a.13.1 | ✓ | 8 | ||
5.4 | even | 2 | 1050.2.m.a.307.4 | 8 | |||
7.6 | odd | 2 | 210.2.m.a.97.1 | yes | 8 | ||
15.8 | even | 4 | 630.2.p.b.433.4 | 8 | |||
20.3 | even | 4 | 1680.2.cz.b.433.3 | 8 | |||
21.20 | even | 2 | 630.2.p.b.307.4 | 8 | |||
28.27 | even | 2 | 1680.2.cz.b.97.3 | 8 | |||
35.13 | even | 4 | inner | 210.2.m.b.13.2 | yes | 8 | |
35.27 | even | 4 | 1050.2.m.a.643.4 | 8 | |||
35.34 | odd | 2 | 1050.2.m.b.307.3 | 8 | |||
105.83 | odd | 4 | 630.2.p.c.433.3 | 8 | |||
140.83 | odd | 4 | 1680.2.cz.a.433.2 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
210.2.m.a.13.1 | ✓ | 8 | 5.3 | odd | 4 | ||
210.2.m.a.97.1 | yes | 8 | 7.6 | odd | 2 | ||
210.2.m.b.13.2 | yes | 8 | 35.13 | even | 4 | inner | |
210.2.m.b.97.2 | yes | 8 | 1.1 | even | 1 | trivial | |
630.2.p.b.307.4 | 8 | 21.20 | even | 2 | |||
630.2.p.b.433.4 | 8 | 15.8 | even | 4 | |||
630.2.p.c.307.3 | 8 | 3.2 | odd | 2 | |||
630.2.p.c.433.3 | 8 | 105.83 | odd | 4 | |||
1050.2.m.a.307.4 | 8 | 5.4 | even | 2 | |||
1050.2.m.a.643.4 | 8 | 35.27 | even | 4 | |||
1050.2.m.b.307.3 | 8 | 35.34 | odd | 2 | |||
1050.2.m.b.643.3 | 8 | 5.2 | odd | 4 | |||
1680.2.cz.a.97.2 | 8 | 4.3 | odd | 2 | |||
1680.2.cz.a.433.2 | 8 | 140.83 | odd | 4 | |||
1680.2.cz.b.97.3 | 8 | 28.27 | even | 2 | |||
1680.2.cz.b.433.3 | 8 | 20.3 | even | 4 |