Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [418,2,Mod(45,418)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(418, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("418.45");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 418 = 2 \cdot 11 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 418.e (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: | \(3.33774680449\) |
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: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 3 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 45.2 | ||
Root | \(-1.22474 - 0.707107i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 418.45 |
Dual form | 418.2.e.g.353.2 |
$q$-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 \(\left(\mathbb{Z}/418\mathbb{Z}\right)^\times\).
\(n\) | \(287\) | \(343\) |
\(\chi(n)\) | \(e\left(\frac{1}{3}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.500000 | + | 0.866025i | 0.353553 | + | 0.612372i | ||||
\(3\) | 1.22474 | + | 2.12132i | 0.707107 | + | 1.22474i | 0.965926 | + | 0.258819i | \(0.0833333\pi\) |
−0.258819 | + | 0.965926i | \(0.583333\pi\) | |||||||
\(4\) | −0.500000 | + | 0.866025i | −0.250000 | + | 0.433013i | ||||
\(5\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(6\) | −1.22474 | + | 2.12132i | −0.500000 | + | 0.866025i | ||||
\(7\) | −2.44949 | −0.925820 | −0.462910 | − | 0.886405i | \(-0.653195\pi\) | ||||
−0.462910 | + | 0.886405i | \(0.653195\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | −1.50000 | + | 2.59808i | −0.500000 | + | 0.866025i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.00000 | −0.301511 | ||||||||
\(12\) | −2.44949 | −0.707107 | ||||||||
\(13\) | −1.94949 | + | 3.37662i | −0.540691 | + | 0.936505i | 0.458173 | + | 0.888863i | \(0.348504\pi\) |
−0.998864 | + | 0.0476417i | \(0.984829\pi\) | |||||||
\(14\) | −1.22474 | − | 2.12132i | −0.327327 | − | 0.566947i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −0.500000 | − | 0.866025i | −0.125000 | − | 0.216506i | ||||
\(17\) | 2.22474 | + | 3.85337i | 0.539580 | + | 0.934580i | 0.998927 | + | 0.0463227i | \(0.0147502\pi\) |
−0.459347 | + | 0.888257i | \(0.651916\pi\) | |||||||
\(18\) | −3.00000 | −0.707107 | ||||||||
\(19\) | 4.17423 | + | 1.25529i | 0.957635 | + | 0.287984i | ||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −3.00000 | − | 5.19615i | −0.654654 | − | 1.13389i | ||||
\(22\) | −0.500000 | − | 0.866025i | −0.106600 | − | 0.184637i | ||||
\(23\) | −0.449490 | + | 0.778539i | −0.0937251 | + | 0.162337i | −0.909076 | − | 0.416631i | \(-0.863211\pi\) |
0.815351 | + | 0.578967i | \(0.196544\pi\) | |||||||
\(24\) | −1.22474 | − | 2.12132i | −0.250000 | − | 0.433013i | ||||
\(25\) | 2.50000 | − | 4.33013i | 0.500000 | − | 0.866025i | ||||
\(26\) | −3.89898 | −0.764653 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 1.22474 | − | 2.12132i | 0.231455 | − | 0.400892i | ||||
\(29\) | 0.949490 | − | 1.64456i | 0.176316 | − | 0.305388i | −0.764300 | − | 0.644861i | \(-0.776915\pi\) |
0.940616 | + | 0.339473i | \(0.110249\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 2.00000 | 0.359211 | 0.179605 | − | 0.983739i | \(-0.442518\pi\) | ||||
0.179605 | + | 0.983739i | \(0.442518\pi\) | |||||||
\(32\) | 0.500000 | − | 0.866025i | 0.0883883 | − | 0.153093i | ||||
\(33\) | −1.22474 | − | 2.12132i | −0.213201 | − | 0.369274i | ||||
\(34\) | −2.22474 | + | 3.85337i | −0.381541 | + | 0.660848i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −1.50000 | − | 2.59808i | −0.250000 | − | 0.433013i | ||||
\(37\) | 8.44949 | 1.38909 | 0.694544 | − | 0.719450i | \(-0.255606\pi\) | ||||
0.694544 | + | 0.719450i | \(0.255606\pi\) | |||||||
\(38\) | 1.00000 | + | 4.24264i | 0.162221 | + | 0.688247i | ||||
\(39\) | −9.55051 | −1.52931 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 3.77526 | + | 6.53893i | 0.589596 | + | 1.02121i | 0.994285 | + | 0.106756i | \(0.0340463\pi\) |
−0.404689 | + | 0.914454i | \(0.632620\pi\) | |||||||
\(42\) | 3.00000 | − | 5.19615i | 0.462910 | − | 0.801784i | ||||
\(43\) | −4.72474 | − | 8.18350i | −0.720517 | − | 1.24797i | −0.960793 | − | 0.277267i | \(-0.910571\pi\) |
0.240276 | − | 0.970705i | \(-0.422762\pi\) | |||||||
\(44\) | 0.500000 | − | 0.866025i | 0.0753778 | − | 0.130558i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −0.898979 | −0.132547 | ||||||||
\(47\) | 3.27526 | − | 5.67291i | 0.477745 | − | 0.827479i | −0.521930 | − | 0.852989i | \(-0.674788\pi\) |
0.999675 | + | 0.0255099i | \(0.00812093\pi\) | |||||||
\(48\) | 1.22474 | − | 2.12132i | 0.176777 | − | 0.306186i | ||||
\(49\) | −1.00000 | −0.142857 | ||||||||
\(50\) | 5.00000 | 0.707107 | ||||||||
\(51\) | −5.44949 | + | 9.43879i | −0.763081 | + | 1.32170i | ||||
\(52\) | −1.94949 | − | 3.37662i | −0.270346 | − | 0.468252i | ||||
\(53\) | 3.89898 | − | 6.75323i | 0.535566 | − | 0.927628i | −0.463570 | − | 0.886060i | \(-0.653432\pi\) |
0.999136 | − | 0.0415671i | \(-0.0132350\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 2.44949 | 0.327327 | ||||||||
\(57\) | 2.44949 | + | 10.3923i | 0.324443 | + | 1.37649i | ||||
\(58\) | 1.89898 | 0.249348 | ||||||||
\(59\) | −1.44949 | − | 2.51059i | −0.188707 | − | 0.326851i | 0.756112 | − | 0.654442i | \(-0.227096\pi\) |
−0.944820 | + | 0.327591i | \(0.893763\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −3.94949 | + | 6.84072i | −0.505680 | + | 0.875864i | 0.494298 | + | 0.869292i | \(0.335425\pi\) |
−0.999978 | + | 0.00657156i | \(0.997908\pi\) | |||||||
\(62\) | 1.00000 | + | 1.73205i | 0.127000 | + | 0.219971i | ||||
\(63\) | 3.67423 | − | 6.36396i | 0.462910 | − | 0.801784i | ||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 1.22474 | − | 2.12132i | 0.150756 | − | 0.261116i | ||||
\(67\) | −4.77526 | + | 8.27098i | −0.583390 | + | 1.01046i | 0.411684 | + | 0.911327i | \(0.364941\pi\) |
−0.995074 | + | 0.0991348i | \(0.968392\pi\) | |||||||
\(68\) | −4.44949 | −0.539580 | ||||||||
\(69\) | −2.20204 | −0.265095 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −3.72474 | − | 6.45145i | −0.442046 | − | 0.765646i | 0.555795 | − | 0.831319i | \(-0.312414\pi\) |
−0.997841 | + | 0.0656732i | \(0.979080\pi\) | |||||||
\(72\) | 1.50000 | − | 2.59808i | 0.176777 | − | 0.306186i | ||||
\(73\) | 7.22474 | + | 12.5136i | 0.845592 | + | 1.46461i | 0.885106 | + | 0.465390i | \(0.154086\pi\) |
−0.0395133 | + | 0.999219i | \(0.512581\pi\) | |||||||
\(74\) | 4.22474 | + | 7.31747i | 0.491117 | + | 0.850639i | ||||
\(75\) | 12.2474 | 1.41421 | ||||||||
\(76\) | −3.17423 | + | 2.98735i | −0.364110 | + | 0.342672i | ||||
\(77\) | 2.44949 | 0.279145 | ||||||||
\(78\) | −4.77526 | − | 8.27098i | −0.540691 | − | 0.936505i | ||||
\(79\) | −2.22474 | − | 3.85337i | −0.250303 | − | 0.433538i | 0.713306 | − | 0.700853i | \(-0.247197\pi\) |
−0.963609 | + | 0.267315i | \(0.913864\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 4.50000 | + | 7.79423i | 0.500000 | + | 0.866025i | ||||
\(82\) | −3.77526 | + | 6.53893i | −0.416907 | + | 0.722104i | ||||
\(83\) | −5.44949 | −0.598159 | −0.299080 | − | 0.954228i | \(-0.596680\pi\) | ||||
−0.299080 | + | 0.954228i | \(0.596680\pi\) | |||||||
\(84\) | 6.00000 | 0.654654 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 4.72474 | − | 8.18350i | 0.509482 | − | 0.882449i | ||||
\(87\) | 4.65153 | 0.498696 | ||||||||
\(88\) | 1.00000 | 0.106600 | ||||||||
\(89\) | 4.50000 | − | 7.79423i | 0.476999 | − | 0.826187i | −0.522654 | − | 0.852545i | \(-0.675058\pi\) |
0.999653 | + | 0.0263586i | \(0.00839118\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 4.77526 | − | 8.27098i | 0.500583 | − | 0.867035i | ||||
\(92\) | −0.449490 | − | 0.778539i | −0.0468625 | − | 0.0811683i | ||||
\(93\) | 2.44949 | + | 4.24264i | 0.254000 | + | 0.439941i | ||||
\(94\) | 6.55051 | 0.675634 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 2.44949 | 0.250000 | ||||||||
\(97\) | −1.94949 | − | 3.37662i | −0.197941 | − | 0.342843i | 0.749920 | − | 0.661529i | \(-0.230092\pi\) |
−0.947861 | + | 0.318685i | \(0.896759\pi\) | |||||||
\(98\) | −0.500000 | − | 0.866025i | −0.0505076 | − | 0.0874818i | ||||
\(99\) | 1.50000 | − | 2.59808i | 0.150756 | − | 0.261116i | ||||
\(100\) | 2.50000 | + | 4.33013i | 0.250000 | + | 0.433013i | ||||
\(101\) | −2.50000 | + | 4.33013i | −0.248759 | + | 0.430864i | −0.963182 | − | 0.268851i | \(-0.913356\pi\) |
0.714423 | + | 0.699715i | \(0.246689\pi\) | |||||||
\(102\) | −10.8990 | −1.07916 | ||||||||
\(103\) | −8.34847 | −0.822599 | −0.411300 | − | 0.911500i | \(-0.634925\pi\) | ||||
−0.411300 | + | 0.911500i | \(0.634925\pi\) | |||||||
\(104\) | 1.94949 | − | 3.37662i | 0.191163 | − | 0.331104i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 7.79796 | 0.757405 | ||||||||
\(107\) | 10.3485 | 1.00042 | 0.500212 | − | 0.865903i | \(-0.333255\pi\) | ||||
0.500212 | + | 0.865903i | \(0.333255\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −7.94949 | − | 13.7689i | −0.761423 | − | 1.31882i | −0.942117 | − | 0.335284i | \(-0.891168\pi\) |
0.180694 | − | 0.983539i | \(-0.442166\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 10.3485 | + | 17.9241i | 0.982233 | + | 1.70128i | ||||
\(112\) | 1.22474 | + | 2.12132i | 0.115728 | + | 0.200446i | ||||
\(113\) | 15.6969 | 1.47664 | 0.738322 | − | 0.674449i | \(-0.235619\pi\) | ||||
0.738322 | + | 0.674449i | \(0.235619\pi\) | |||||||
\(114\) | −7.77526 | + | 7.31747i | −0.728219 | + | 0.685344i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0.949490 | + | 1.64456i | 0.0881579 | + | 0.152694i | ||||
\(117\) | −5.84847 | − | 10.1298i | −0.540691 | − | 0.936505i | ||||
\(118\) | 1.44949 | − | 2.51059i | 0.133436 | − | 0.231119i | ||||
\(119\) | −5.44949 | − | 9.43879i | −0.499554 | − | 0.865253i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | −7.89898 | −0.715140 | ||||||||
\(123\) | −9.24745 | + | 16.0171i | −0.833814 | + | 1.44421i | ||||
\(124\) | −1.00000 | + | 1.73205i | −0.0898027 | + | 0.155543i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 7.34847 | 0.654654 | ||||||||
\(127\) | −6.34847 | + | 10.9959i | −0.563336 | + | 0.975726i | 0.433867 | + | 0.900977i | \(0.357149\pi\) |
−0.997202 | + | 0.0747488i | \(0.976185\pi\) | |||||||
\(128\) | 0.500000 | + | 0.866025i | 0.0441942 | + | 0.0765466i | ||||
\(129\) | 11.5732 | − | 20.0454i | 1.01896 | − | 1.76490i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −2.17423 | − | 3.76588i | −0.189964 | − | 0.329027i | 0.755274 | − | 0.655409i | \(-0.227504\pi\) |
−0.945238 | + | 0.326382i | \(0.894170\pi\) | |||||||
\(132\) | 2.44949 | 0.213201 | ||||||||
\(133\) | −10.2247 | − | 3.07483i | −0.886598 | − | 0.266622i | ||||
\(134\) | −9.55051 | −0.825038 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −2.22474 | − | 3.85337i | −0.190770 | − | 0.330424i | ||||
\(137\) | 3.94949 | − | 6.84072i | 0.337428 | − | 0.584442i | −0.646520 | − | 0.762897i | \(-0.723776\pi\) |
0.983948 | + | 0.178455i | \(0.0571098\pi\) | |||||||
\(138\) | −1.10102 | − | 1.90702i | −0.0937251 | − | 0.162337i | ||||
\(139\) | 2.00000 | − | 3.46410i | 0.169638 | − | 0.293821i | −0.768655 | − | 0.639664i | \(-0.779074\pi\) |
0.938293 | + | 0.345843i | \(0.112407\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 16.0454 | 1.35127 | ||||||||
\(142\) | 3.72474 | − | 6.45145i | 0.312574 | − | 0.541393i | ||||
\(143\) | 1.94949 | − | 3.37662i | 0.163025 | − | 0.282367i | ||||
\(144\) | 3.00000 | 0.250000 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −7.22474 | + | 12.5136i | −0.597924 | + | 1.03563i | ||||
\(147\) | −1.22474 | − | 2.12132i | −0.101015 | − | 0.174964i | ||||
\(148\) | −4.22474 | + | 7.31747i | −0.347272 | + | 0.601493i | ||||
\(149\) | −9.34847 | − | 16.1920i | −0.765856 | − | 1.32650i | −0.939793 | − | 0.341745i | \(-0.888982\pi\) |
0.173936 | − | 0.984757i | \(-0.444351\pi\) | |||||||
\(150\) | 6.12372 | + | 10.6066i | 0.500000 | + | 0.866025i | ||||
\(151\) | −8.44949 | −0.687610 | −0.343805 | − | 0.939041i | \(-0.611716\pi\) | ||||
−0.343805 | + | 0.939041i | \(0.611716\pi\) | |||||||
\(152\) | −4.17423 | − | 1.25529i | −0.338575 | − | 0.101818i | ||||
\(153\) | −13.3485 | −1.07916 | ||||||||
\(154\) | 1.22474 | + | 2.12132i | 0.0986928 | + | 0.170941i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 4.77526 | − | 8.27098i | 0.382326 | − | 0.662209i | ||||
\(157\) | 3.00000 | + | 5.19615i | 0.239426 | + | 0.414698i | 0.960550 | − | 0.278108i | \(-0.0897074\pi\) |
−0.721124 | + | 0.692806i | \(0.756374\pi\) | |||||||
\(158\) | 2.22474 | − | 3.85337i | 0.176991 | − | 0.306558i | ||||
\(159\) | 19.1010 | 1.51481 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 1.10102 | − | 1.90702i | 0.0867726 | − | 0.150295i | ||||
\(162\) | −4.50000 | + | 7.79423i | −0.353553 | + | 0.612372i | ||||
\(163\) | 2.89898 | 0.227066 | 0.113533 | − | 0.993534i | \(-0.463783\pi\) | ||||
0.113533 | + | 0.993534i | \(0.463783\pi\) | |||||||
\(164\) | −7.55051 | −0.589596 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −2.72474 | − | 4.71940i | −0.211481 | − | 0.366296i | ||||
\(167\) | 6.57321 | − | 11.3851i | 0.508651 | − | 0.881009i | −0.491299 | − | 0.870991i | \(-0.663478\pi\) |
0.999950 | − | 0.0100178i | \(-0.00318882\pi\) | |||||||
\(168\) | 3.00000 | + | 5.19615i | 0.231455 | + | 0.400892i | ||||
\(169\) | −1.10102 | − | 1.90702i | −0.0846939 | − | 0.146694i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −9.52270 | + | 8.96204i | −0.728219 | + | 0.685344i | ||||
\(172\) | 9.44949 | 0.720517 | ||||||||
\(173\) | −4.89898 | − | 8.48528i | −0.372463 | − | 0.645124i | 0.617481 | − | 0.786586i | \(-0.288153\pi\) |
−0.989944 | + | 0.141462i | \(0.954820\pi\) | |||||||
\(174\) | 2.32577 | + | 4.02834i | 0.176316 | + | 0.305388i | ||||
\(175\) | −6.12372 | + | 10.6066i | −0.462910 | + | 0.801784i | ||||
\(176\) | 0.500000 | + | 0.866025i | 0.0376889 | + | 0.0652791i | ||||
\(177\) | 3.55051 | − | 6.14966i | 0.266873 | − | 0.462237i | ||||
\(178\) | 9.00000 | 0.674579 | ||||||||
\(179\) | −9.79796 | −0.732334 | −0.366167 | − | 0.930549i | \(-0.619330\pi\) | ||||
−0.366167 | + | 0.930549i | \(0.619330\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −2.12372 | + | 3.67840i | −0.157855 | + | 0.273413i | −0.934095 | − | 0.357025i | \(-0.883791\pi\) |
0.776240 | + | 0.630438i | \(0.217125\pi\) | |||||||
\(182\) | 9.55051 | 0.707931 | ||||||||
\(183\) | −19.3485 | −1.43028 | ||||||||
\(184\) | 0.449490 | − | 0.778539i | 0.0331368 | − | 0.0573947i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −2.44949 | + | 4.24264i | −0.179605 | + | 0.311086i | ||||
\(187\) | −2.22474 | − | 3.85337i | −0.162689 | − | 0.281786i | ||||
\(188\) | 3.27526 | + | 5.67291i | 0.238873 | + | 0.413739i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −7.65153 | −0.553645 | −0.276823 | − | 0.960921i | \(-0.589281\pi\) | ||||
−0.276823 | + | 0.960921i | \(0.589281\pi\) | |||||||
\(192\) | 1.22474 | + | 2.12132i | 0.0883883 | + | 0.153093i | ||||
\(193\) | 11.6742 | + | 20.2204i | 0.840330 | + | 1.45549i | 0.889616 | + | 0.456709i | \(0.150972\pi\) |
−0.0492862 | + | 0.998785i | \(0.515695\pi\) | |||||||
\(194\) | 1.94949 | − | 3.37662i | 0.139965 | − | 0.242427i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0.500000 | − | 0.866025i | 0.0357143 | − | 0.0618590i | ||||
\(197\) | 6.10102 | 0.434680 | 0.217340 | − | 0.976096i | \(-0.430262\pi\) | ||||
0.217340 | + | 0.976096i | \(0.430262\pi\) | |||||||
\(198\) | 3.00000 | 0.213201 | ||||||||
\(199\) | −10.1742 | + | 17.6223i | −0.721232 | + | 1.24921i | 0.239274 | + | 0.970952i | \(0.423091\pi\) |
−0.960506 | + | 0.278259i | \(0.910243\pi\) | |||||||
\(200\) | −2.50000 | + | 4.33013i | −0.176777 | + | 0.306186i | ||||
\(201\) | −23.3939 | −1.65008 | ||||||||
\(202\) | −5.00000 | −0.351799 | ||||||||
\(203\) | −2.32577 | + | 4.02834i | −0.163237 | + | 0.282734i | ||||
\(204\) | −5.44949 | − | 9.43879i | −0.381541 | − | 0.660848i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −4.17423 | − | 7.22999i | −0.290833 | − | 0.503737i | ||||
\(207\) | −1.34847 | − | 2.33562i | −0.0937251 | − | 0.162337i | ||||
\(208\) | 3.89898 | 0.270346 | ||||||||
\(209\) | −4.17423 | − | 1.25529i | −0.288738 | − | 0.0868306i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −10.0000 | − | 17.3205i | −0.688428 | − | 1.19239i | −0.972346 | − | 0.233544i | \(-0.924968\pi\) |
0.283918 | − | 0.958849i | \(-0.408366\pi\) | |||||||
\(212\) | 3.89898 | + | 6.75323i | 0.267783 | + | 0.463814i | ||||
\(213\) | 9.12372 | − | 15.8028i | 0.625147 | − | 1.08279i | ||||
\(214\) | 5.17423 | + | 8.96204i | 0.353703 | + | 0.612632i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −4.89898 | −0.332564 | ||||||||
\(218\) | 7.94949 | − | 13.7689i | 0.538407 | − | 0.932549i | ||||
\(219\) | −17.6969 | + | 30.6520i | −1.19585 | + | 2.07127i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −17.3485 | −1.16698 | ||||||||
\(222\) | −10.3485 | + | 17.9241i | −0.694544 | + | 1.20299i | ||||
\(223\) | −0.623724 | − | 1.08032i | −0.0417677 | − | 0.0723437i | 0.844386 | − | 0.535736i | \(-0.179966\pi\) |
−0.886154 | + | 0.463392i | \(0.846632\pi\) | |||||||
\(224\) | −1.22474 | + | 2.12132i | −0.0818317 | + | 0.141737i | ||||
\(225\) | 7.50000 | + | 12.9904i | 0.500000 | + | 0.866025i | ||||
\(226\) | 7.84847 | + | 13.5939i | 0.522072 | + | 0.904256i | ||||
\(227\) | 4.20204 | 0.278899 | 0.139450 | − | 0.990229i | \(-0.455467\pi\) | ||||
0.139450 | + | 0.990229i | \(0.455467\pi\) | |||||||
\(228\) | −10.2247 | − | 3.07483i | −0.677150 | − | 0.203636i | ||||
\(229\) | −0.651531 | −0.0430544 | −0.0215272 | − | 0.999768i | \(-0.506853\pi\) | ||||
−0.0215272 | + | 0.999768i | \(0.506853\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 3.00000 | + | 5.19615i | 0.197386 | + | 0.341882i | ||||
\(232\) | −0.949490 | + | 1.64456i | −0.0623371 | + | 0.107971i | ||||
\(233\) | 5.22474 | + | 9.04952i | 0.342284 | + | 0.592854i | 0.984857 | − | 0.173371i | \(-0.0554660\pi\) |
−0.642572 | + | 0.766225i | \(0.722133\pi\) | |||||||
\(234\) | 5.84847 | − | 10.1298i | 0.382326 | − | 0.662209i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 2.89898 | 0.188707 | ||||||||
\(237\) | 5.44949 | − | 9.43879i | 0.353982 | − | 0.613115i | ||||
\(238\) | 5.44949 | − | 9.43879i | 0.353238 | − | 0.611826i | ||||
\(239\) | 21.7980 | 1.40999 | 0.704996 | − | 0.709211i | \(-0.250949\pi\) | ||||
0.704996 | + | 0.709211i | \(0.250949\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −5.00000 | + | 8.66025i | −0.322078 | + | 0.557856i | −0.980917 | − | 0.194429i | \(-0.937715\pi\) |
0.658838 | + | 0.752285i | \(0.271048\pi\) | |||||||
\(242\) | 0.500000 | + | 0.866025i | 0.0321412 | + | 0.0556702i | ||||
\(243\) | −11.0227 | + | 19.0919i | −0.707107 | + | 1.22474i | ||||
\(244\) | −3.94949 | − | 6.84072i | −0.252840 | − | 0.437932i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −18.4949 | −1.17919 | ||||||||
\(247\) | −12.3763 | + | 11.6476i | −0.787484 | + | 0.741119i | ||||
\(248\) | −2.00000 | −0.127000 | ||||||||
\(249\) | −6.67423 | − | 11.5601i | −0.422962 | − | 0.732592i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −12.1237 | + | 20.9989i | −0.765243 | + | 1.32544i | 0.174875 | + | 0.984591i | \(0.444048\pi\) |
−0.940118 | + | 0.340849i | \(0.889286\pi\) | |||||||
\(252\) | 3.67423 | + | 6.36396i | 0.231455 | + | 0.400892i | ||||
\(253\) | 0.449490 | − | 0.778539i | 0.0282592 | − | 0.0489463i | ||||
\(254\) | −12.6969 | −0.796677 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −0.500000 | + | 0.866025i | −0.0312500 | + | 0.0541266i | ||||
\(257\) | 11.0000 | − | 19.0526i | 0.686161 | − | 1.18847i | −0.286909 | − | 0.957958i | \(-0.592628\pi\) |
0.973070 | − | 0.230508i | \(-0.0740389\pi\) | |||||||
\(258\) | 23.1464 | 1.44103 | ||||||||
\(259\) | −20.6969 | −1.28605 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 2.84847 | + | 4.93369i | 0.176316 | + | 0.305388i | ||||
\(262\) | 2.17423 | − | 3.76588i | 0.134325 | − | 0.232657i | ||||
\(263\) | −0.898979 | − | 1.55708i | −0.0554334 | − | 0.0960136i | 0.836977 | − | 0.547238i | \(-0.184321\pi\) |
−0.892411 | + | 0.451224i | \(0.850987\pi\) | |||||||
\(264\) | 1.22474 | + | 2.12132i | 0.0753778 | + | 0.130558i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −2.44949 | − | 10.3923i | −0.150188 | − | 0.637193i | ||||
\(267\) | 22.0454 | 1.34916 | ||||||||
\(268\) | −4.77526 | − | 8.27098i | −0.291695 | − | 0.505231i | ||||
\(269\) | −10.2247 | − | 17.7098i | −0.623414 | − | 1.07978i | −0.988845 | − | 0.148946i | \(-0.952412\pi\) |
0.365432 | − | 0.930838i | \(-0.380921\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −12.3485 | − | 21.3882i | −0.750116 | − | 1.29924i | −0.947766 | − | 0.318966i | \(-0.896664\pi\) |
0.197650 | − | 0.980273i | \(-0.436669\pi\) | |||||||
\(272\) | 2.22474 | − | 3.85337i | 0.134895 | − | 0.233645i | ||||
\(273\) | 23.3939 | 1.41586 | ||||||||
\(274\) | 7.89898 | 0.477195 | ||||||||
\(275\) | −2.50000 | + | 4.33013i | −0.150756 | + | 0.261116i | ||||
\(276\) | 1.10102 | − | 1.90702i | 0.0662736 | − | 0.114789i | ||||
\(277\) | −31.4949 | −1.89234 | −0.946172 | − | 0.323663i | \(-0.895086\pi\) | ||||
−0.946172 | + | 0.323663i | \(0.895086\pi\) | |||||||
\(278\) | 4.00000 | 0.239904 | ||||||||
\(279\) | −3.00000 | + | 5.19615i | −0.179605 | + | 0.311086i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 8.57321 | − | 14.8492i | 0.511435 | − | 0.885832i | −0.488477 | − | 0.872577i | \(-0.662447\pi\) |
0.999912 | − | 0.0132548i | \(-0.00421926\pi\) | |||||||
\(282\) | 8.02270 | + | 13.8957i | 0.477745 | + | 0.827479i | ||||
\(283\) | −1.55051 | − | 2.68556i | −0.0921683 | − | 0.159640i | 0.816255 | − | 0.577692i | \(-0.196046\pi\) |
−0.908423 | + | 0.418052i | \(0.862713\pi\) | |||||||
\(284\) | 7.44949 | 0.442046 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 3.89898 | 0.230551 | ||||||||
\(287\) | −9.24745 | − | 16.0171i | −0.545860 | − | 0.945457i | ||||
\(288\) | 1.50000 | + | 2.59808i | 0.0883883 | + | 0.153093i | ||||
\(289\) | −1.39898 | + | 2.42310i | −0.0822929 | + | 0.142536i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 4.77526 | − | 8.27098i | 0.279930 | − | 0.484854i | ||||
\(292\) | −14.4495 | −0.845592 | ||||||||
\(293\) | −7.89898 | −0.461463 | −0.230732 | − | 0.973017i | \(-0.574112\pi\) | ||||
−0.230732 | + | 0.973017i | \(0.574112\pi\) | |||||||
\(294\) | 1.22474 | − | 2.12132i | 0.0714286 | − | 0.123718i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −8.44949 | −0.491117 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 9.34847 | − | 16.1920i | 0.541542 | − | 0.937979i | ||||
\(299\) | −1.75255 | − | 3.03551i | −0.101353 | − | 0.175548i | ||||
\(300\) | −6.12372 | + | 10.6066i | −0.353553 | + | 0.612372i | ||||
\(301\) | 11.5732 | + | 20.0454i | 0.667069 | + | 1.15540i | ||||
\(302\) | −4.22474 | − | 7.31747i | −0.243107 | − | 0.421073i | ||||
\(303\) | −12.2474 | −0.703598 | ||||||||
\(304\) | −1.00000 | − | 4.24264i | −0.0573539 | − | 0.243332i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −6.67423 | − | 11.5601i | −0.381541 | − | 0.660848i | ||||
\(307\) | 9.62372 | + | 16.6688i | 0.549255 | + | 0.951337i | 0.998326 | + | 0.0578413i | \(0.0184218\pi\) |
−0.449071 | + | 0.893496i | \(0.648245\pi\) | |||||||
\(308\) | −1.22474 | + | 2.12132i | −0.0697863 | + | 0.120873i | ||||
\(309\) | −10.2247 | − | 17.7098i | −0.581665 | − | 1.00747i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 7.24745 | 0.410965 | 0.205483 | − | 0.978661i | \(-0.434124\pi\) | ||||
0.205483 | + | 0.978661i | \(0.434124\pi\) | |||||||
\(312\) | 9.55051 | 0.540691 | ||||||||
\(313\) | 9.84847 | − | 17.0580i | 0.556668 | − | 0.964178i | −0.441103 | − | 0.897456i | \(-0.645413\pi\) |
0.997772 | − | 0.0667216i | \(-0.0212539\pi\) | |||||||
\(314\) | −3.00000 | + | 5.19615i | −0.169300 | + | 0.293236i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 4.44949 | 0.250303 | ||||||||
\(317\) | 12.0227 | − | 20.8239i | 0.675262 | − | 1.16959i | −0.301130 | − | 0.953583i | \(-0.597364\pi\) |
0.976392 | − | 0.216005i | \(-0.0693029\pi\) | |||||||
\(318\) | 9.55051 | + | 16.5420i | 0.535566 | + | 0.927628i | ||||
\(319\) | −0.949490 | + | 1.64456i | −0.0531612 | + | 0.0920779i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 12.6742 | + | 21.9524i | 0.707407 | + | 1.22526i | ||||
\(322\) | 2.20204 | 0.122715 | ||||||||
\(323\) | 4.44949 | + | 18.8776i | 0.247576 | + | 1.05038i | ||||
\(324\) | −9.00000 | −0.500000 | ||||||||
\(325\) | 9.74745 | + | 16.8831i | 0.540691 | + | 0.936505i | ||||
\(326\) | 1.44949 | + | 2.51059i | 0.0802798 | + | 0.139049i | ||||
\(327\) | 19.4722 | − | 33.7268i | 1.07681 | − | 1.86510i | ||||
\(328\) | −3.77526 | − | 6.53893i | −0.208454 | − | 0.361052i | ||||
\(329\) | −8.02270 | + | 13.8957i | −0.442306 | + | 0.766096i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 5.34847 | 0.293978 | 0.146989 | − | 0.989138i | \(-0.453042\pi\) | ||||
0.146989 | + | 0.989138i | \(0.453042\pi\) | |||||||
\(332\) | 2.72474 | − | 4.71940i | 0.149540 | − | 0.259011i | ||||
\(333\) | −12.6742 | + | 21.9524i | −0.694544 | + | 1.20299i | ||||
\(334\) | 13.1464 | 0.719341 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −3.00000 | + | 5.19615i | −0.163663 | + | 0.283473i | ||||
\(337\) | −6.10102 | − | 10.5673i | −0.332344 | − | 0.575636i | 0.650627 | − | 0.759397i | \(-0.274506\pi\) |
−0.982971 | + | 0.183761i | \(0.941173\pi\) | |||||||
\(338\) | 1.10102 | − | 1.90702i | 0.0598876 | − | 0.103728i | ||||
\(339\) | 19.2247 | + | 33.2982i | 1.04414 | + | 1.80851i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −2.00000 | −0.108306 | ||||||||
\(342\) | −12.5227 | − | 3.76588i | −0.677150 | − | 0.203636i | ||||
\(343\) | 19.5959 | 1.05808 | ||||||||
\(344\) | 4.72474 | + | 8.18350i | 0.254741 | + | 0.441225i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 4.89898 | − | 8.48528i | 0.263371 | − | 0.456172i | ||||
\(347\) | 3.72474 | + | 6.45145i | 0.199955 | + | 0.346332i | 0.948514 | − | 0.316737i | \(-0.102587\pi\) |
−0.748559 | + | 0.663068i | \(0.769254\pi\) | |||||||
\(348\) | −2.32577 | + | 4.02834i | −0.124674 | + | 0.215942i | ||||
\(349\) | 31.0000 | 1.65939 | 0.829696 | − | 0.558216i | \(-0.188514\pi\) | ||||
0.829696 | + | 0.558216i | \(0.188514\pi\) | |||||||
\(350\) | −12.2474 | −0.654654 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −0.500000 | + | 0.866025i | −0.0266501 | + | 0.0461593i | ||||
\(353\) | 27.4949 | 1.46341 | 0.731703 | − | 0.681624i | \(-0.238726\pi\) | ||||
0.731703 | + | 0.681624i | \(0.238726\pi\) | |||||||
\(354\) | 7.10102 | 0.377415 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 4.50000 | + | 7.79423i | 0.238500 | + | 0.413093i | ||||
\(357\) | 13.3485 | − | 23.1202i | 0.706476 | − | 1.22365i | ||||
\(358\) | −4.89898 | − | 8.48528i | −0.258919 | − | 0.448461i | ||||
\(359\) | −12.3485 | − | 21.3882i | −0.651727 | − | 1.12882i | −0.982704 | − | 0.185186i | \(-0.940711\pi\) |
0.330976 | − | 0.943639i | \(-0.392622\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 15.8485 | + | 10.4798i | 0.834130 | + | 0.551568i | ||||
\(362\) | −4.24745 | −0.223241 | ||||||||
\(363\) | 1.22474 | + | 2.12132i | 0.0642824 | + | 0.111340i | ||||
\(364\) | 4.77526 | + | 8.27098i | 0.250291 | + | 0.433517i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −9.67423 | − | 16.7563i | −0.505680 | − | 0.875864i | ||||
\(367\) | 12.7247 | − | 22.0399i | 0.664226 | − | 1.15047i | −0.315268 | − | 0.949003i | \(-0.602094\pi\) |
0.979494 | − | 0.201471i | \(-0.0645722\pi\) | |||||||
\(368\) | 0.898979 | 0.0468625 | ||||||||
\(369\) | −22.6515 | −1.17919 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −9.55051 | + | 16.5420i | −0.495838 | + | 0.858816i | ||||
\(372\) | −4.89898 | −0.254000 | ||||||||
\(373\) | −17.7980 | −0.921543 | −0.460772 | − | 0.887519i | \(-0.652427\pi\) | ||||
−0.460772 | + | 0.887519i | \(0.652427\pi\) | |||||||
\(374\) | 2.22474 | − | 3.85337i | 0.115039 | − | 0.199253i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −3.27526 | + | 5.67291i | −0.168908 | + | 0.292558i | ||||
\(377\) | 3.70204 | + | 6.41212i | 0.190665 | + | 0.330241i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −3.34847 | −0.171999 | −0.0859997 | − | 0.996295i | \(-0.527408\pi\) | ||||
−0.0859997 | + | 0.996295i | \(0.527408\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −31.1010 | −1.59335 | ||||||||
\(382\) | −3.82577 | − | 6.62642i | −0.195743 | − | 0.339037i | ||||
\(383\) | 13.3485 | + | 23.1202i | 0.682075 | + | 1.18139i | 0.974347 | + | 0.225053i | \(0.0722555\pi\) |
−0.292272 | + | 0.956335i | \(0.594411\pi\) | |||||||
\(384\) | −1.22474 | + | 2.12132i | −0.0625000 | + | 0.108253i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −11.6742 | + | 20.2204i | −0.594203 | + | 1.02919i | ||||
\(387\) | 28.3485 | 1.44103 | ||||||||
\(388\) | 3.89898 | 0.197941 | ||||||||
\(389\) | 4.12372 | − | 7.14250i | 0.209081 | − | 0.362139i | −0.742344 | − | 0.670019i | \(-0.766286\pi\) |
0.951425 | + | 0.307880i | \(0.0996194\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −4.00000 | −0.202289 | ||||||||
\(392\) | 1.00000 | 0.0505076 | ||||||||
\(393\) | 5.32577 | − | 9.22450i | 0.268649 | − | 0.465314i | ||||
\(394\) | 3.05051 | + | 5.28364i | 0.153682 | + | 0.266186i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 1.50000 | + | 2.59808i | 0.0753778 | + | 0.130558i | ||||
\(397\) | 12.6742 | + | 21.9524i | 0.636102 | + | 1.10176i | 0.986281 | + | 0.165077i | \(0.0527874\pi\) |
−0.350179 | + | 0.936683i | \(0.613879\pi\) | |||||||
\(398\) | −20.3485 | −1.01998 | ||||||||
\(399\) | −6.00000 | − | 25.4558i | −0.300376 | − | 1.27439i | ||||
\(400\) | −5.00000 | −0.250000 | ||||||||
\(401\) | −19.3485 | − | 33.5125i | −0.966216 | − | 1.67354i | −0.706311 | − | 0.707902i | \(-0.749642\pi\) |
−0.259906 | − | 0.965634i | \(-0.583692\pi\) | |||||||
\(402\) | −11.6969 | − | 20.2597i | −0.583390 | − | 1.01046i | ||||
\(403\) | −3.89898 | + | 6.75323i | −0.194222 | + | 0.336402i | ||||
\(404\) | −2.50000 | − | 4.33013i | −0.124380 | − | 0.215432i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −4.65153 | −0.230852 | ||||||||
\(407\) | −8.44949 | −0.418826 | ||||||||
\(408\) | 5.44949 | − | 9.43879i | 0.269790 | − | 0.467290i | ||||
\(409\) | 11.4722 | − | 19.8704i | 0.567263 | − | 0.982529i | −0.429572 | − | 0.903033i | \(-0.641335\pi\) |
0.996835 | − | 0.0794964i | \(-0.0253312\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 19.3485 | 0.954390 | ||||||||
\(412\) | 4.17423 | − | 7.22999i | 0.205650 | − | 0.356196i | ||||
\(413\) | 3.55051 | + | 6.14966i | 0.174709 | + | 0.302605i | ||||
\(414\) | 1.34847 | − | 2.33562i | 0.0662736 | − | 0.114789i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 1.94949 | + | 3.37662i | 0.0955816 | + | 0.165552i | ||||
\(417\) | 9.79796 | 0.479808 | ||||||||
\(418\) | −1.00000 | − | 4.24264i | −0.0489116 | − | 0.207514i | ||||
\(419\) | −17.3485 | −0.847528 | −0.423764 | − | 0.905773i | \(-0.639291\pi\) | ||||
−0.423764 | + | 0.905773i | \(0.639291\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 17.6742 | + | 30.6127i | 0.861389 | + | 1.49197i | 0.870588 | + | 0.492013i | \(0.163739\pi\) |
−0.00919855 | + | 0.999958i | \(0.502928\pi\) | |||||||
\(422\) | 10.0000 | − | 17.3205i | 0.486792 | − | 0.843149i | ||||
\(423\) | 9.82577 | + | 17.0187i | 0.477745 | + | 0.827479i | ||||
\(424\) | −3.89898 | + | 6.75323i | −0.189351 | + | 0.327966i | ||||
\(425\) | 22.2474 | 1.07916 | ||||||||
\(426\) | 18.2474 | 0.884092 | ||||||||
\(427\) | 9.67423 | − | 16.7563i | 0.468169 | − | 0.810893i | ||||
\(428\) | −5.17423 | + | 8.96204i | −0.250106 | + | 0.433196i | ||||
\(429\) | 9.55051 | 0.461103 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −8.02270 | + | 13.8957i | −0.386440 | + | 0.669334i | −0.991968 | − | 0.126490i | \(-0.959629\pi\) |
0.605528 | + | 0.795824i | \(0.292962\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −15.8485 | + | 27.4504i | −0.761629 | + | 1.31918i | 0.180382 | + | 0.983597i | \(0.442267\pi\) |
−0.942011 | + | 0.335583i | \(0.891067\pi\) | |||||||
\(434\) | −2.44949 | − | 4.24264i | −0.117579 | − | 0.203653i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 15.8990 | 0.761423 | ||||||||
\(437\) | −2.85357 | + | 2.68556i | −0.136505 | + | 0.128468i | ||||
\(438\) | −35.3939 | −1.69118 | ||||||||
\(439\) | −5.79796 | − | 10.0424i | −0.276721 | − | 0.479296i | 0.693847 | − | 0.720123i | \(-0.255915\pi\) |
−0.970568 | + | 0.240827i | \(0.922581\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 1.50000 | − | 2.59808i | 0.0714286 | − | 0.123718i | ||||
\(442\) | −8.67423 | − | 15.0242i | −0.412591 | − | 0.714629i | ||||
\(443\) | 10.6742 | − | 18.4883i | 0.507148 | − | 0.878406i | −0.492818 | − | 0.870133i | \(-0.664033\pi\) |
0.999966 | − | 0.00827378i | \(-0.00263366\pi\) | |||||||
\(444\) | −20.6969 | −0.982233 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0.623724 | − | 1.08032i | 0.0295342 | − | 0.0511547i | ||||
\(447\) | 22.8990 | − | 39.6622i | 1.08308 | − | 1.87596i | ||||
\(448\) | −2.44949 | −0.115728 | ||||||||
\(449\) | 10.2020 | 0.481464 | 0.240732 | − | 0.970592i | \(-0.422612\pi\) | ||||
0.240732 | + | 0.970592i | \(0.422612\pi\) | |||||||
\(450\) | −7.50000 | + | 12.9904i | −0.353553 | + | 0.612372i | ||||
\(451\) | −3.77526 | − | 6.53893i | −0.177770 | − | 0.307906i | ||||
\(452\) | −7.84847 | + | 13.5939i | −0.369161 | + | 0.639406i | ||||
\(453\) | −10.3485 | − | 17.9241i | −0.486213 | − | 0.842146i | ||||
\(454\) | 2.10102 | + | 3.63907i | 0.0986058 | + | 0.170790i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −2.44949 | − | 10.3923i | −0.114708 | − | 0.486664i | ||||
\(457\) | −22.9444 | −1.07329 | −0.536647 | − | 0.843807i | \(-0.680309\pi\) | ||||
−0.536647 | + | 0.843807i | \(0.680309\pi\) | |||||||
\(458\) | −0.325765 | − | 0.564242i | −0.0152220 | − | 0.0263653i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 6.39898 | + | 11.0834i | 0.298030 | + | 0.516203i | 0.975685 | − | 0.219177i | \(-0.0703371\pi\) |
−0.677655 | + | 0.735380i | \(0.737004\pi\) | |||||||
\(462\) | −3.00000 | + | 5.19615i | −0.139573 | + | 0.241747i | ||||
\(463\) | 40.1464 | 1.86576 | 0.932881 | − | 0.360184i | \(-0.117286\pi\) | ||||
0.932881 | + | 0.360184i | \(0.117286\pi\) | |||||||
\(464\) | −1.89898 | −0.0881579 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −5.22474 | + | 9.04952i | −0.242032 | + | 0.419211i | ||||
\(467\) | −6.65153 | −0.307796 | −0.153898 | − | 0.988087i | \(-0.549183\pi\) | ||||
−0.153898 | + | 0.988087i | \(0.549183\pi\) | |||||||
\(468\) | 11.6969 | 0.540691 | ||||||||
\(469\) | 11.6969 | − | 20.2597i | 0.540114 | − | 0.935506i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −7.34847 | + | 12.7279i | −0.338600 | + | 0.586472i | ||||
\(472\) | 1.44949 | + | 2.51059i | 0.0667182 | + | 0.115559i | ||||
\(473\) | 4.72474 | + | 8.18350i | 0.217244 | + | 0.376278i | ||||
\(474\) | 10.8990 | 0.500607 | ||||||||
\(475\) | 15.8712 | − | 14.9367i | 0.728219 | − | 0.685344i | ||||
\(476\) | 10.8990 | 0.499554 | ||||||||
\(477\) | 11.6969 | + | 20.2597i | 0.535566 | + | 0.927628i | ||||
\(478\) | 10.8990 | + | 18.8776i | 0.498508 | + | 0.863441i | ||||
\(479\) | 21.5732 | − | 37.3659i | 0.985705 | − | 1.70729i | 0.346946 | − | 0.937885i | \(-0.387219\pi\) |
0.638759 | − | 0.769407i | \(-0.279448\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −16.4722 | + | 28.5307i | −0.751067 | + | 1.30089i | ||||
\(482\) | −10.0000 | −0.455488 | ||||||||
\(483\) | 5.39388 | 0.245430 | ||||||||
\(484\) | −0.500000 | + | 0.866025i | −0.0227273 | + | 0.0393648i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −22.0454 | −1.00000 | ||||||||
\(487\) | −7.65153 | −0.346724 | −0.173362 | − | 0.984858i | \(-0.555463\pi\) | ||||
−0.173362 | + | 0.984858i | \(0.555463\pi\) | |||||||
\(488\) | 3.94949 | − | 6.84072i | 0.178785 | − | 0.309665i | ||||
\(489\) | 3.55051 | + | 6.14966i | 0.160560 | + | 0.278097i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 6.89898 | + | 11.9494i | 0.311347 | + | 0.539268i | 0.978654 | − | 0.205514i | \(-0.0658867\pi\) |
−0.667308 | + | 0.744782i | \(0.732553\pi\) | |||||||
\(492\) | −9.24745 | − | 16.0171i | −0.416907 | − | 0.722104i | ||||
\(493\) | 8.44949 | 0.380546 | ||||||||
\(494\) | −16.2753 | − | 4.89437i | −0.732258 | − | 0.220208i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −1.00000 | − | 1.73205i | −0.0449013 | − | 0.0777714i | ||||
\(497\) | 9.12372 | + | 15.8028i | 0.409255 | + | 0.708850i | ||||
\(498\) | 6.67423 | − | 11.5601i | 0.299080 | − | 0.518021i | ||||
\(499\) | 0.348469 | + | 0.603566i | 0.0155996 | + | 0.0270193i | 0.873720 | − | 0.486429i | \(-0.161701\pi\) |
−0.858120 | + | 0.513449i | \(0.828368\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 32.2020 | 1.43868 | ||||||||
\(502\) | −24.2474 | −1.08222 | ||||||||
\(503\) | 5.44949 | − | 9.43879i | 0.242981 | − | 0.420855i | −0.718581 | − | 0.695443i | \(-0.755208\pi\) |
0.961562 | + | 0.274588i | \(0.0885415\pi\) | |||||||
\(504\) | −3.67423 | + | 6.36396i | −0.163663 | + | 0.283473i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0.898979 | 0.0399645 | ||||||||
\(507\) | 2.69694 | − | 4.67123i | 0.119775 | − | 0.207457i | ||||
\(508\) | −6.34847 | − | 10.9959i | −0.281668 | − | 0.487863i | ||||
\(509\) | −11.7980 | + | 20.4347i | −0.522935 | + | 0.905751i | 0.476708 | + | 0.879061i | \(0.341830\pi\) |
−0.999644 | + | 0.0266891i | \(0.991504\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −17.6969 | − | 30.6520i | −0.782866 | − | 1.35596i | ||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 22.0000 | 0.970378 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 11.5732 | + | 20.0454i | 0.509482 | + | 0.882449i | ||||
\(517\) | −3.27526 | + | 5.67291i | −0.144046 | + | 0.249494i | ||||
\(518\) | −10.3485 | − | 17.9241i | −0.454686 | − | 0.787539i | ||||
\(519\) | 12.0000 | − | 20.7846i | 0.526742 | − | 0.912343i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −41.6969 | −1.82678 | −0.913388 | − | 0.407090i | \(-0.866544\pi\) | ||||
−0.913388 | + | 0.407090i | \(0.866544\pi\) | |||||||
\(522\) | −2.84847 | + | 4.93369i | −0.124674 | + | 0.215942i | ||||
\(523\) | 14.1742 | − | 24.5505i | 0.619796 | − | 1.07352i | −0.369727 | − | 0.929141i | \(-0.620549\pi\) |
0.989523 | − | 0.144378i | \(-0.0461180\pi\) | |||||||
\(524\) | 4.34847 | 0.189964 | ||||||||
\(525\) | −30.0000 | −1.30931 | ||||||||
\(526\) | 0.898979 | − | 1.55708i | 0.0391974 | − | 0.0678918i | ||||
\(527\) | 4.44949 | + | 7.70674i | 0.193823 | + | 0.335711i | ||||
\(528\) | −1.22474 | + | 2.12132i | −0.0533002 | + | 0.0923186i | ||||
\(529\) | 11.0959 | + | 19.2187i | 0.482431 | + | 0.835595i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 8.69694 | 0.377415 | ||||||||
\(532\) | 7.77526 | − | 7.31747i | 0.337100 | − | 0.317253i | ||||
\(533\) | −29.4393 | −1.27516 | ||||||||
\(534\) | 11.0227 | + | 19.0919i | 0.476999 | + | 0.826187i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 4.77526 | − | 8.27098i | 0.206260 | − | 0.357252i | ||||
\(537\) | −12.0000 | − | 20.7846i | −0.517838 | − | 0.896922i | ||||
\(538\) | 10.2247 | − | 17.7098i | 0.440820 | − | 0.763523i | ||||
\(539\) | 1.00000 | 0.0430730 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −18.8990 | + | 32.7340i | −0.812531 | + | 1.40734i | 0.0985570 | + | 0.995131i | \(0.468577\pi\) |
−0.911088 | + | 0.412213i | \(0.864756\pi\) | |||||||
\(542\) | 12.3485 | − | 21.3882i | 0.530412 | − | 0.918701i | ||||
\(543\) | −10.4041 | −0.446482 | ||||||||
\(544\) | 4.44949 | 0.190770 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 11.6969 | + | 20.2597i | 0.500583 | + | 0.867035i | ||||
\(547\) | −7.82577 | + | 13.5546i | −0.334606 | + | 0.579554i | −0.983409 | − | 0.181402i | \(-0.941936\pi\) |
0.648803 | + | 0.760956i | \(0.275270\pi\) | |||||||
\(548\) | 3.94949 | + | 6.84072i | 0.168714 | + | 0.292221i | ||||
\(549\) | −11.8485 | − | 20.5222i | −0.505680 | − | 0.875864i | ||||
\(550\) | −5.00000 | −0.213201 | ||||||||
\(551\) | 6.02781 | − | 5.67291i | 0.256793 | − | 0.241674i | ||||
\(552\) | 2.20204 | 0.0937251 | ||||||||
\(553\) | 5.44949 | + | 9.43879i | 0.231736 | + | 0.401378i | ||||
\(554\) | −15.7474 | − | 27.2754i | −0.669045 | − | 1.15882i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 2.00000 | + | 3.46410i | 0.0848189 | + | 0.146911i | ||||
\(557\) | −8.29796 | + | 14.3725i | −0.351596 | + | 0.608982i | −0.986529 | − | 0.163585i | \(-0.947694\pi\) |
0.634933 | + | 0.772567i | \(0.281028\pi\) | |||||||
\(558\) | −6.00000 | −0.254000 | ||||||||
\(559\) | 36.8434 | 1.55831 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 5.44949 | − | 9.43879i | 0.230078 | − | 0.398506i | ||||
\(562\) | 17.1464 | 0.723278 | ||||||||
\(563\) | 0.898979 | 0.0378875 | 0.0189437 | − | 0.999821i | \(-0.493970\pi\) | ||||
0.0189437 | + | 0.999821i | \(0.493970\pi\) | |||||||
\(564\) | −8.02270 | + | 13.8957i | −0.337817 | + | 0.585116i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 1.55051 | − | 2.68556i | 0.0651728 | − | 0.112883i | ||||
\(567\) | −11.0227 | − | 19.0919i | −0.462910 | − | 0.801784i | ||||
\(568\) | 3.72474 | + | 6.45145i | 0.156287 | + | 0.270697i | ||||
\(569\) | −33.5959 | −1.40841 | −0.704207 | − | 0.709995i | \(-0.748697\pi\) | ||||
−0.704207 | + | 0.709995i | \(0.748697\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −19.9444 | −0.834647 | −0.417323 | − | 0.908758i | \(-0.637032\pi\) | ||||
−0.417323 | + | 0.908758i | \(0.637032\pi\) | |||||||
\(572\) | 1.94949 | + | 3.37662i | 0.0815123 | + | 0.141183i | ||||
\(573\) | −9.37117 | − | 16.2313i | −0.391486 | − | 0.678074i | ||||
\(574\) | 9.24745 | − | 16.0171i | 0.385981 | − | 0.668539i | ||||
\(575\) | 2.24745 | + | 3.89270i | 0.0937251 | + | 0.162337i | ||||
\(576\) | −1.50000 | + | 2.59808i | −0.0625000 | + | 0.108253i | ||||
\(577\) | −37.7980 | −1.57355 | −0.786775 | − | 0.617240i | \(-0.788251\pi\) | ||||
−0.786775 | + | 0.617240i | \(0.788251\pi\) | |||||||
\(578\) | −2.79796 | −0.116380 | ||||||||
\(579\) | −28.5959 | + | 49.5296i | −1.18841 | + | 2.05838i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 13.3485 | 0.553788 | ||||||||
\(582\) | 9.55051 | 0.395881 | ||||||||
\(583\) | −3.89898 | + | 6.75323i | −0.161479 | + | 0.279690i | ||||
\(584\) | −7.22474 | − | 12.5136i | −0.298962 | − | 0.517817i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −3.94949 | − | 6.84072i | −0.163152 | − | 0.282587i | ||||
\(587\) | 13.6742 | + | 23.6845i | 0.564396 | + | 0.977563i | 0.997106 | + | 0.0760293i | \(0.0242242\pi\) |
−0.432710 | + | 0.901533i | \(0.642442\pi\) | |||||||
\(588\) | 2.44949 | 0.101015 | ||||||||
\(589\) | 8.34847 | + | 2.51059i | 0.343993 | + | 0.103447i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 7.47219 | + | 12.9422i | 0.307365 | + | 0.532372i | ||||
\(592\) | −4.22474 | − | 7.31747i | −0.173636 | − | 0.300746i | ||||
\(593\) | −12.6969 | + | 21.9917i | −0.521401 | + | 0.903093i | 0.478289 | + | 0.878202i | \(0.341257\pi\) |
−0.999690 | + | 0.0248904i | \(0.992076\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 18.6969 | 0.765856 | ||||||||
\(597\) | −49.8434 | −2.03995 | ||||||||
\(598\) | 1.75255 | − | 3.03551i | 0.0716672 | − | 0.124131i | ||||
\(599\) | −17.1742 | + | 29.7466i | −0.701720 | + | 1.21542i | 0.266142 | + | 0.963934i | \(0.414251\pi\) |
−0.967862 | + | 0.251481i | \(0.919082\pi\) | |||||||
\(600\) | −12.2474 | −0.500000 | ||||||||
\(601\) | 4.40408 | 0.179646 | 0.0898231 | − | 0.995958i | \(-0.471370\pi\) | ||||
0.0898231 | + | 0.995958i | \(0.471370\pi\) | |||||||
\(602\) | −11.5732 | + | 20.0454i | −0.471689 | + | 0.816989i | ||||
\(603\) | −14.3258 | − | 24.8130i | −0.583390 | − | 1.01046i | ||||
\(604\) | 4.22474 | − | 7.31747i | 0.171902 | − | 0.297744i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −6.12372 | − | 10.6066i | −0.248759 | − | 0.430864i | ||||
\(607\) | −19.1464 | −0.777130 | −0.388565 | − | 0.921421i | \(-0.627029\pi\) | ||||
−0.388565 | + | 0.921421i | \(0.627029\pi\) | |||||||
\(608\) | 3.17423 | − | 2.98735i | 0.128732 | − | 0.121153i | ||||
\(609\) | −11.3939 | −0.461703 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 12.7702 | + | 22.1186i | 0.516625 | + | 0.894821i | ||||
\(612\) | 6.67423 | − | 11.5601i | 0.269790 | − | 0.467290i | ||||
\(613\) | 13.3990 | + | 23.2077i | 0.541180 | + | 0.937351i | 0.998837 | + | 0.0482219i | \(0.0153555\pi\) |
−0.457657 | + | 0.889129i | \(0.651311\pi\) | |||||||
\(614\) | −9.62372 | + | 16.6688i | −0.388382 | + | 0.672697i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −2.44949 | −0.0986928 | ||||||||
\(617\) | 19.1969 | − | 33.2501i | 0.772840 | − | 1.33860i | −0.163161 | − | 0.986599i | \(-0.552169\pi\) |
0.936001 | − | 0.351998i | \(-0.114498\pi\) | |||||||
\(618\) | 10.2247 | − | 17.7098i | 0.411300 | − | 0.712392i | ||||
\(619\) | −24.6969 | −0.992654 | −0.496327 | − | 0.868136i | \(-0.665318\pi\) | ||||
−0.496327 | + | 0.868136i | \(0.665318\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 3.62372 | + | 6.27647i | 0.145298 | + | 0.251664i | ||||
\(623\) | −11.0227 | + | 19.0919i | −0.441615 | + | 0.764900i | ||||
\(624\) | 4.77526 | + | 8.27098i | 0.191163 | + | 0.331104i | ||||
\(625\) | −12.5000 | − | 21.6506i | −0.500000 | − | 0.866025i | ||||
\(626\) | 19.6969 | 0.787248 | ||||||||
\(627\) | −2.44949 | − | 10.3923i | −0.0978232 | − | 0.415029i | ||||
\(628\) | −6.00000 | −0.239426 | ||||||||
\(629\) | 18.7980 | + | 32.5590i | 0.749524 | + | 1.29821i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −0.477296 | + | 0.826701i | −0.0190009 | + | 0.0329105i | −0.875369 | − | 0.483455i | \(-0.839382\pi\) |
0.856369 | + | 0.516365i | \(0.172715\pi\) | |||||||
\(632\) | 2.22474 | + | 3.85337i | 0.0884956 | + | 0.153279i | ||||
\(633\) | 24.4949 | − | 42.4264i | 0.973585 | − | 1.68630i | ||||
\(634\) | 24.0454 | 0.954965 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −9.55051 | + | 16.5420i | −0.378702 | + | 0.655932i | ||||
\(637\) | 1.94949 | − | 3.37662i | 0.0772416 | − | 0.133786i | ||||
\(638\) | −1.89898 | −0.0751813 | ||||||||
\(639\) | 22.3485 | 0.884092 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 21.7474 | + | 37.6677i | 0.858973 | + | 1.48778i | 0.872910 | + | 0.487881i | \(0.162230\pi\) |
−0.0139374 | + | 0.999903i | \(0.504437\pi\) | |||||||
\(642\) | −12.6742 | + | 21.9524i | −0.500212 | + | 0.866393i | ||||
\(643\) | 1.67423 | + | 2.89986i | 0.0660254 | + | 0.114359i | 0.897148 | − | 0.441729i | \(-0.145635\pi\) |
−0.831123 | + | 0.556089i | \(0.812302\pi\) | |||||||
\(644\) | 1.10102 | + | 1.90702i | 0.0433863 | + | 0.0751473i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −14.1237 | + | 13.2922i | −0.555691 | + | 0.522973i | ||||
\(647\) | −39.2474 | −1.54298 | −0.771488 | − | 0.636244i | \(-0.780487\pi\) | ||||
−0.771488 | + | 0.636244i | \(0.780487\pi\) | |||||||
\(648\) | −4.50000 | − | 7.79423i | −0.176777 | − | 0.306186i | ||||
\(649\) | 1.44949 | + | 2.51059i | 0.0568974 | + | 0.0985493i | ||||
\(650\) | −9.74745 | + | 16.8831i | −0.382326 | + | 0.662209i | ||||
\(651\) | −6.00000 | − | 10.3923i | −0.235159 | − | 0.407307i | ||||
\(652\) | −1.44949 | + | 2.51059i | −0.0567664 | + | 0.0983223i | ||||
\(653\) | 3.34847 | 0.131036 | 0.0655179 | − | 0.997851i | \(-0.479130\pi\) | ||||
0.0655179 | + | 0.997851i | \(0.479130\pi\) | |||||||
\(654\) | 38.9444 | 1.52285 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 3.77526 | − | 6.53893i | 0.147399 | − | 0.255302i | ||||
\(657\) | −43.3485 | −1.69118 | ||||||||
\(658\) | −16.0454 | −0.625515 | ||||||||
\(659\) | 10.9722 | − | 19.0044i | 0.427416 | − | 0.740306i | −0.569227 | − | 0.822181i | \(-0.692757\pi\) |
0.996643 | + | 0.0818744i | \(0.0260906\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −4.57321 | + | 7.92104i | −0.177877 | + | 0.308093i | −0.941153 | − | 0.337980i | \(-0.890256\pi\) |
0.763276 | + | 0.646073i | \(0.223590\pi\) | |||||||
\(662\) | 2.67423 | + | 4.63191i | 0.103937 | + | 0.180024i | ||||
\(663\) | −21.2474 | − | 36.8017i | −0.825183 | − | 1.42926i | ||||
\(664\) | 5.44949 | 0.211481 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −25.3485 | −0.982233 | ||||||||
\(667\) | 0.853572 | + | 1.47843i | 0.0330504 | + | 0.0572450i | ||||
\(668\) | 6.57321 | + | 11.3851i | 0.254325 | + | 0.440504i | ||||
\(669\) | 1.52781 | − | 2.64624i | 0.0590684 | − | 0.102309i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 3.94949 | − | 6.84072i | 0.152468 | − | 0.264083i | ||||
\(672\) | −6.00000 | −0.231455 | ||||||||
\(673\) | −42.7423 | −1.64760 | −0.823798 | − | 0.566883i | \(-0.808149\pi\) | ||||
−0.823798 | + | 0.566883i | \(0.808149\pi\) | |||||||
\(674\) | 6.10102 | − | 10.5673i | 0.235003 | − | 0.407036i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 2.20204 | 0.0846939 | ||||||||
\(677\) | 13.6969 | 0.526416 | 0.263208 | − | 0.964739i | \(-0.415219\pi\) | ||||
0.263208 | + | 0.964739i | \(0.415219\pi\) | |||||||
\(678\) | −19.2247 | + | 33.2982i | −0.738322 | + | 1.27881i | ||||
\(679\) | 4.77526 | + | 8.27098i | 0.183257 | + | 0.317411i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 5.14643 | + | 8.91388i | 0.197212 | + | 0.341580i | ||||
\(682\) | −1.00000 | − | 1.73205i | −0.0382920 | − | 0.0663237i | ||||
\(683\) | −35.1464 | −1.34484 | −0.672420 | − | 0.740169i | \(-0.734745\pi\) | ||||
−0.672420 | + | 0.740169i | \(0.734745\pi\) | |||||||
\(684\) | −3.00000 | − | 12.7279i | −0.114708 | − | 0.486664i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 9.79796 | + | 16.9706i | 0.374088 | + | 0.647939i | ||||
\(687\) | −0.797959 | − | 1.38211i | −0.0304440 | − | 0.0527306i | ||||
\(688\) | −4.72474 | + | 8.18350i | −0.180129 | + | 0.311993i | ||||
\(689\) | 15.2020 | + | 26.3307i | 0.579152 | + | 1.00312i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −39.6413 | −1.50803 | −0.754014 | − | 0.656859i | \(-0.771885\pi\) | ||||
−0.754014 | + | 0.656859i | \(0.771885\pi\) | |||||||
\(692\) | 9.79796 | 0.372463 | ||||||||
\(693\) | −3.67423 | + | 6.36396i | −0.139573 | + | 0.241747i | ||||
\(694\) | −3.72474 | + | 6.45145i | −0.141389 | + | 0.244894i | ||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −4.65153 | −0.176316 | ||||||||
\(697\) | −16.7980 | + | 29.0949i | −0.636268 | + | 1.10205i | ||||
\(698\) | 15.5000 | + | 26.8468i | 0.586684 | + | 1.01617i | ||||
\(699\) | −12.7980 | + | 22.1667i | −0.484063 | + | 0.838422i | ||||
\(700\) | −6.12372 | − | 10.6066i | −0.231455 | − | 0.400892i | ||||
\(701\) | 23.2980 | + | 40.3532i | 0.879952 | + | 1.52412i | 0.851393 | + | 0.524529i | \(0.175759\pi\) |
0.0285592 | + | 0.999592i | \(0.490908\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 35.2702 | + | 10.6066i | 1.33024 | + | 0.400036i | ||||
\(704\) | −1.00000 | −0.0376889 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 13.7474 | + | 23.8113i | 0.517392 | + | 0.896149i | ||||
\(707\) | 6.12372 | − | 10.6066i | 0.230306 | − | 0.398902i | ||||
\(708\) | 3.55051 | + | 6.14966i | 0.133436 | + | 0.231119i | ||||
\(709\) | −7.69694 | + | 13.3315i | −0.289065 | + | 0.500675i | −0.973587 | − | 0.228318i | \(-0.926678\pi\) |
0.684522 | + | 0.728992i | \(0.260011\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 13.3485 | 0.500607 | ||||||||
\(712\) | −4.50000 | + | 7.79423i | −0.168645 | + | 0.292101i | ||||
\(713\) | −0.898979 | + | 1.55708i | −0.0336670 | + | 0.0583130i | ||||
\(714\) | 26.6969 | 0.999108 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 4.89898 | − | 8.48528i | 0.183083 | − | 0.317110i | ||||
\(717\) | 26.6969 | + | 46.2405i | 0.997015 | + | 1.72688i | ||||
\(718\) | 12.3485 | − | 21.3882i | 0.460841 | − | 0.798200i | ||||
\(719\) | 2.92679 | + | 5.06934i | 0.109151 | + | 0.189055i | 0.915426 | − | 0.402485i | \(-0.131854\pi\) |
−0.806276 | + | 0.591540i | \(0.798520\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 20.4495 | 0.761579 | ||||||||
\(722\) | −1.15153 | + | 18.9651i | −0.0428555 | + | 0.705807i | ||||
\(723\) | −24.4949 | −0.910975 | ||||||||
\(724\) | −2.12372 | − | 3.67840i | −0.0789276 | − | 0.136707i | ||||
\(725\) | −4.74745 | − | 8.22282i | −0.176316 | − | 0.305388i | ||||
\(726\) | −1.22474 | + | 2.12132i | −0.0454545 | + | 0.0787296i | ||||
\(727\) | −4.97219 | − | 8.61209i | −0.184408 | − | 0.319405i | 0.758969 | − | 0.651127i | \(-0.225704\pi\) |
−0.943377 | + | 0.331722i | \(0.892370\pi\) | |||||||
\(728\) | −4.77526 | + | 8.27098i | −0.176983 | + | 0.306543i | ||||
\(729\) | −27.0000 | −1.00000 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 21.0227 | − | 36.4124i | 0.777553 | − | 1.34676i | ||||
\(732\) | 9.67423 | − | 16.7563i | 0.357570 | − | 0.619329i | ||||
\(733\) | 31.1010 | 1.14874 | 0.574371 | − | 0.818595i | \(-0.305247\pi\) | ||||
0.574371 | + | 0.818595i | \(0.305247\pi\) | |||||||
\(734\) | 25.4495 | 0.939358 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0.449490 | + | 0.778539i | 0.0165684 | + | 0.0286973i | ||||
\(737\) | 4.77526 | − | 8.27098i | 0.175899 | − | 0.304666i | ||||
\(738\) | −11.3258 | − | 19.6168i | −0.416907 | − | 0.722104i | ||||
\(739\) | −15.8712 | − | 27.4897i | −0.583831 | − | 1.01122i | −0.995020 | − | 0.0996743i | \(-0.968220\pi\) |
0.411190 | − | 0.911550i | \(-0.365113\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −39.8661 | − | 11.9887i | −1.46452 | − | 0.440416i | ||||
\(742\) | −19.1010 | −0.701221 | ||||||||
\(743\) | 18.5732 | + | 32.1698i | 0.681385 | + | 1.18019i | 0.974558 | + | 0.224134i | \(0.0719554\pi\) |
−0.293173 | + | 0.956059i | \(0.594711\pi\) | |||||||
\(744\) | −2.44949 | − | 4.24264i | −0.0898027 | − | 0.155543i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −8.89898 | − | 15.4135i | −0.325815 | − | 0.564328i | ||||
\(747\) | 8.17423 | − | 14.1582i | 0.299080 | − | 0.518021i | ||||
\(748\) | 4.44949 | 0.162689 | ||||||||
\(749\) | −25.3485 | −0.926213 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 23.7702 | − | 41.1711i | 0.867385 | − | 1.50236i | 0.00272600 | − | 0.999996i | \(-0.499132\pi\) |
0.864659 | − | 0.502359i | \(-0.167534\pi\) | |||||||
\(752\) | −6.55051 | −0.238873 | ||||||||
\(753\) | −59.3939 | −2.16443 | ||||||||
\(754\) | −3.70204 | + | 6.41212i | −0.134820 | + | 0.233516i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −8.10102 | − | 14.0314i | −0.294437 | − | 0.509979i | 0.680417 | − | 0.732825i | \(-0.261799\pi\) |
−0.974854 | + | 0.222846i | \(0.928465\pi\) | |||||||
\(758\) | −1.67423 | − | 2.89986i | −0.0608109 | − | 0.105328i | ||||
\(759\) | 2.20204 | 0.0799290 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 31.1918 | 1.13070 | 0.565352 | − | 0.824850i | \(-0.308741\pi\) | ||||
0.565352 | + | 0.824850i | \(0.308741\pi\) | |||||||
\(762\) | −15.5505 | − | 26.9343i | −0.563336 | − | 0.975726i | ||||
\(763\) | 19.4722 | + | 33.7268i | 0.704941 | + | 1.22099i | ||||
\(764\) | 3.82577 | − | 6.62642i | 0.138411 | − | 0.239735i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −13.3485 | + | 23.1202i | −0.482300 | + | 0.835368i | ||||
\(767\) | 11.3031 | 0.408130 | ||||||||
\(768\) | −2.44949 | −0.0883883 | ||||||||
\(769\) | 19.6969 | − | 34.1161i | 0.710290 | − | 1.23026i | −0.254459 | − | 0.967084i | \(-0.581897\pi\) |
0.964748 | − | 0.263174i | \(-0.0847694\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 53.8888 | 1.94076 | ||||||||
\(772\) | −23.3485 | −0.840330 | ||||||||
\(773\) | −5.57321 | + | 9.65309i | −0.200455 | + | 0.347198i | −0.948675 | − | 0.316253i | \(-0.897575\pi\) |
0.748220 | + | 0.663450i | \(0.230909\pi\) | |||||||
\(774\) | 14.1742 | + | 24.5505i | 0.509482 | + | 0.882449i | ||||
\(775\) | 5.00000 | − | 8.66025i | 0.179605 | − | 0.311086i | ||||
\(776\) | 1.94949 | + | 3.37662i | 0.0699826 | + | 0.121213i | ||||
\(777\) | −25.3485 | − | 43.9048i | −0.909371 | − | 1.57508i | ||||
\(778\) | 8.24745 | 0.295685 | ||||||||
\(779\) | 7.55051 | + | 32.0341i | 0.270525 | + | 1.14774i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 3.72474 | + | 6.45145i | 0.133282 | + | 0.230851i | ||||
\(782\) | −2.00000 | − | 3.46410i | −0.0715199 | − | 0.123876i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0.500000 | + | 0.866025i | 0.0178571 | + | 0.0309295i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 10.6515 | 0.379928 | ||||||||
\(787\) | 25.2474 | 0.899974 | 0.449987 | − | 0.893035i | \(-0.351429\pi\) | ||||
0.449987 | + | 0.893035i | \(0.351429\pi\) | |||||||
\(788\) | −3.05051 | + | 5.28364i | −0.108670 | + | 0.188222i | ||||
\(789\) | 2.20204 | − | 3.81405i | 0.0783947 | − | 0.135784i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −38.4495 | −1.36711 | ||||||||
\(792\) | −1.50000 | + | 2.59808i | −0.0533002 | + | 0.0923186i | ||||
\(793\) | −15.3990 | − | 26.6718i | −0.546834 | − | 0.947144i | ||||
\(794\) | −12.6742 | + | 21.9524i | −0.449792 | + | 0.779062i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −10.1742 | − | 17.6223i | −0.360616 | − | 0.624606i | ||||
\(797\) | 2.04541 | 0.0724521 | 0.0362260 | − | 0.999344i | \(-0.488466\pi\) | ||||
0.0362260 | + | 0.999344i | \(0.488466\pi\) | |||||||
\(798\) | 19.0454 | − | 17.9241i | 0.674200 | − | 0.634505i | ||||
\(799\) | 29.1464 | 1.03113 | ||||||||
\(800\) | −2.50000 | − | 4.33013i | −0.0883883 | − | 0.153093i | ||||
\(801\) | 13.5000 | + | 23.3827i | 0.476999 | + | 0.826187i | ||||
\(802\) | 19.3485 | − | 33.5125i | 0.683218 | − | 1.18337i | ||||
\(803\) | −7.22474 | − | 12.5136i | −0.254956 | − | 0.441596i | ||||
\(804\) | 11.6969 | − | 20.2597i | 0.412519 | − | 0.714504i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −7.79796 | −0.274671 | ||||||||
\(807\) | 25.0454 | − | 43.3799i | 0.881640 | − | 1.52705i | ||||
\(808\) | 2.50000 | − | 4.33013i | 0.0879497 | − | 0.152333i | ||||
\(809\) | 0.853572 | 0.0300100 | 0.0150050 | − | 0.999887i | \(-0.495224\pi\) | ||||
0.0150050 | + | 0.999887i | \(0.495224\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 1.27526 | − | 2.20881i | 0.0447803 | − | 0.0775617i | −0.842767 | − | 0.538279i | \(-0.819075\pi\) |
0.887547 | + | 0.460718i | \(0.152408\pi\) | |||||||
\(812\) | −2.32577 | − | 4.02834i | −0.0816184 | − | 0.141367i | ||||
\(813\) | 30.2474 | − | 52.3901i | 1.06082 | − | 1.83740i | ||||
\(814\) | −4.22474 | − | 7.31747i | −0.148077 | − | 0.256477i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 10.8990 | 0.381541 | ||||||||
\(817\) | −9.44949 | − | 40.0908i | −0.330596 | − | 1.40260i | ||||
\(818\) | 22.9444 | 0.802232 | ||||||||
\(819\) | 14.3258 | + | 24.8130i | 0.500583 | + | 0.867035i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −23.1464 | + | 40.0908i | −0.807816 | + | 1.39918i | 0.106558 | + | 0.994307i | \(0.466017\pi\) |
−0.914374 | + | 0.404872i | \(0.867316\pi\) | |||||||
\(822\) | 9.67423 | + | 16.7563i | 0.337428 | + | 0.584442i | ||||
\(823\) | 4.72474 | − | 8.18350i | 0.164694 | − | 0.285259i | −0.771852 | − | 0.635802i | \(-0.780670\pi\) |
0.936547 | + | 0.350543i | \(0.114003\pi\) | |||||||
\(824\) | 8.34847 | 0.290833 | ||||||||
\(825\) | −12.2474 | −0.426401 | ||||||||
\(826\) | −3.55051 | + | 6.14966i | −0.123538 | + | 0.213974i | ||||
\(827\) | 14.4217 | − | 24.9791i | 0.501491 | − | 0.868608i | −0.498507 | − | 0.866885i | \(-0.666118\pi\) |
0.999999 | − | 0.00172259i | \(-0.000548318\pi\) | |||||||
\(828\) | 2.69694 | 0.0937251 | ||||||||
\(829\) | 3.14643 | 0.109280 | 0.0546400 | − | 0.998506i | \(-0.482599\pi\) | ||||
0.0546400 | + | 0.998506i | \(0.482599\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −38.5732 | − | 66.8108i | −1.33809 | − | 2.31764i | ||||
\(832\) | −1.94949 | + | 3.37662i | −0.0675864 | + | 0.117063i | ||||
\(833\) | −2.22474 | − | 3.85337i | −0.0770828 | − | 0.133511i | ||||
\(834\) | 4.89898 | + | 8.48528i | 0.169638 | + | 0.293821i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 3.17423 | − | 2.98735i | 0.109783 | − | 0.103320i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −8.67423 | − | 15.0242i | −0.299646 | − | 0.519003i | ||||
\(839\) | −10.3763 | − | 17.9722i | −0.358229 | − | 0.620471i | 0.629436 | − | 0.777052i | \(-0.283286\pi\) |
−0.987665 | + | 0.156582i | \(0.949953\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 12.6969 | + | 21.9917i | 0.437825 | + | 0.758336i | ||||
\(842\) | −17.6742 | + | 30.6127i | −0.609094 | + | 1.05498i | ||||
\(843\) | 42.0000 | 1.44656 | ||||||||
\(844\) | 20.0000 | 0.688428 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −9.82577 | + | 17.0187i | −0.337817 | + | 0.585116i | ||||
\(847\) | −2.44949 | −0.0841655 | ||||||||
\(848\) | −7.79796 | −0.267783 | ||||||||
\(849\) | 3.79796 | − | 6.57826i | 0.130346 | − | 0.225765i | ||||
\(850\) | 11.1237 | + | 19.2669i | 0.381541 | + | 0.660848i | ||||
\(851\) | −3.79796 | + | 6.57826i | −0.130192 | + | 0.225500i | ||||
\(852\) | 9.12372 | + | 15.8028i | 0.312574 | + | 0.541393i | ||||
\(853\) | 1.34847 | + | 2.33562i | 0.0461707 | + | 0.0799700i | 0.888187 | − | 0.459482i | \(-0.151965\pi\) |
−0.842016 | + | 0.539452i | \(0.818632\pi\) | |||||||
\(854\) | 19.3485 | 0.662091 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −10.3485 | −0.353703 | ||||||||
\(857\) | −5.57321 | − | 9.65309i | −0.190377 | − | 0.329743i | 0.754998 | − | 0.655727i | \(-0.227638\pi\) |
−0.945375 | + | 0.325984i | \(0.894304\pi\) | |||||||
\(858\) | 4.77526 | + | 8.27098i | 0.163025 | + | 0.282367i | ||||
\(859\) | 0.550510 | − | 0.953512i | 0.0187832 | − | 0.0325334i | −0.856481 | − | 0.516178i | \(-0.827354\pi\) |
0.875264 | + | 0.483645i | \(0.160687\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 22.6515 | − | 39.2336i | 0.771962 | − | 1.33708i | ||||
\(862\) | −16.0454 | −0.546509 | ||||||||
\(863\) | −11.6515 | −0.396623 | −0.198311 | − | 0.980139i | \(-0.563546\pi\) | ||||
−0.198311 | + | 0.980139i | \(0.563546\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −31.6969 | −1.07711 | ||||||||
\(867\) | −6.85357 | −0.232760 | ||||||||
\(868\) | 2.44949 | − | 4.24264i | 0.0831411 | − | 0.144005i | ||||
\(869\) | 2.22474 | + | 3.85337i | 0.0754693 | + | 0.130717i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −18.6186 | − | 32.2484i | −0.630868 | − | 1.09270i | ||||
\(872\) | 7.94949 | + | 13.7689i | 0.269204 | + | 0.466274i | ||||
\(873\) | 11.6969 | 0.395881 | ||||||||
\(874\) | −3.75255 | − | 1.12848i | −0.126932 | − | 0.0381716i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −17.6969 | − | 30.6520i | −0.597924 | − | 1.03563i | ||||
\(877\) | −18.7980 | − | 32.5590i | −0.634762 | − | 1.09944i | −0.986566 | − | 0.163366i | \(-0.947765\pi\) |
0.351804 | − | 0.936074i | \(-0.385569\pi\) | |||||||
\(878\) | 5.79796 | − | 10.0424i | 0.195672 | − | 0.338913i | ||||
\(879\) | −9.67423 | − | 16.7563i | −0.326304 | − | 0.565175i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 12.8990 | 0.434578 | 0.217289 | − | 0.976107i | \(-0.430279\pi\) | ||||
0.217289 | + | 0.976107i | \(0.430279\pi\) | |||||||
\(882\) | 3.00000 | 0.101015 | ||||||||
\(883\) | 6.22474 | − | 10.7816i | 0.209479 | − | 0.362829i | −0.742071 | − | 0.670321i | \(-0.766156\pi\) |
0.951551 | + | 0.307492i | \(0.0994898\pi\) | |||||||
\(884\) | 8.67423 | − | 15.0242i | 0.291746 | − | 0.505319i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 21.3485 | 0.717216 | ||||||||
\(887\) | −6.67423 | + | 11.5601i | −0.224099 | + | 0.388151i | −0.956049 | − | 0.293208i | \(-0.905277\pi\) |
0.731950 | + | 0.681359i | \(0.238611\pi\) | |||||||
\(888\) | −10.3485 | − | 17.9241i | −0.347272 | − | 0.601493i | ||||
\(889\) | 15.5505 | − | 26.9343i | 0.521547 | − | 0.903347i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −4.50000 | − | 7.79423i | −0.150756 | − | 0.261116i | ||||
\(892\) | 1.24745 | 0.0417677 | ||||||||
\(893\) | 20.7929 | − | 19.5686i | 0.695806 | − | 0.654840i | ||||
\(894\) | 45.7980 | 1.53171 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −1.22474 | − | 2.12132i | −0.0409159 | − | 0.0708683i | ||||
\(897\) | 4.29286 | − | 7.43545i | 0.143334 | − | 0.248262i | ||||
\(898\) | 5.10102 | + | 8.83523i | 0.170223 | + | 0.294835i | ||||
\(899\) | 1.89898 | − | 3.28913i | 0.0633345 | − | 0.109699i | ||||
\(900\) | −15.0000 | −0.500000 | ||||||||
\(901\) | 34.6969 | 1.15592 | ||||||||
\(902\) | 3.77526 | − | 6.53893i | 0.125702 | − | 0.217723i | ||||
\(903\) | −28.3485 | + | 49.1010i | −0.943378 | + | 1.63398i | ||||
\(904\) | −15.6969 | −0.522072 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 10.3485 | − | 17.9241i | 0.343805 | − | 0.595487i | ||||
\(907\) | −19.4495 | − | 33.6875i | −0.645810 | − | 1.11858i | −0.984114 | − | 0.177538i | \(-0.943187\pi\) |
0.338304 | − | 0.941037i | \(-0.390147\pi\) | |||||||
\(908\) | −2.10102 | + | 3.63907i | −0.0697248 | + | 0.120767i | ||||
\(909\) | −7.50000 | − | 12.9904i | −0.248759 | − | 0.430864i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −24.4949 | −0.811552 | −0.405776 | − | 0.913973i | \(-0.632999\pi\) | ||||
−0.405776 | + | 0.913973i | \(0.632999\pi\) | |||||||
\(912\) | 7.77526 | − | 7.31747i | 0.257464 | − | 0.242306i | ||||
\(913\) | 5.44949 | 0.180352 | ||||||||
\(914\) | −11.4722 | − | 19.8704i | −0.379466 | − | 0.657255i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0.325765 | − | 0.564242i | 0.0107636 | − | 0.0186431i | ||||
\(917\) | 5.32577 | + | 9.22450i | 0.175872 | + | 0.304620i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −25.3485 | −0.836169 | −0.418084 | − | 0.908408i | \(-0.637298\pi\) | ||||
−0.418084 | + | 0.908408i | \(0.637298\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −23.5732 | + | 40.8300i | −0.776764 | + | 1.34539i | ||||
\(922\) | −6.39898 | + | 11.0834i | −0.210739 | + | 0.365011i | ||||
\(923\) | 29.0454 | 0.956041 | ||||||||
\(924\) | −6.00000 | −0.197386 | ||||||||
\(925\) | 21.1237 | − | 36.5874i | 0.694544 | − | 1.20299i | ||||
\(926\) | 20.0732 | + | 34.7678i | 0.659647 | + | 1.14254i | ||||
\(927\) | 12.5227 | − | 21.6900i | 0.411300 | − | 0.712392i | ||||
\(928\) | −0.949490 | − | 1.64456i | −0.0311685 | − | 0.0539855i | ||||
\(929\) | 18.7474 | + | 32.4715i | 0.615084 | + | 1.06536i | 0.990370 | + | 0.138447i | \(0.0442112\pi\) |
−0.375286 | + | 0.926909i | \(0.622455\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −4.17423 | − | 1.25529i | −0.136805 | − | 0.0411406i | ||||
\(932\) | −10.4495 | −0.342284 | ||||||||
\(933\) | 8.87628 | + | 15.3742i | 0.290596 | + | 0.503327i | ||||
\(934\) | −3.32577 | − | 5.76039i | −0.108822 | − | 0.188486i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 5.84847 | + | 10.1298i | 0.191163 | + | 0.331104i | ||||
\(937\) | 6.89898 | − | 11.9494i | 0.225380 | − | 0.390369i | −0.731053 | − | 0.682320i | \(-0.760971\pi\) |
0.956433 | + | 0.291951i | \(0.0943044\pi\) | |||||||
\(938\) | 23.3939 | 0.763837 | ||||||||
\(939\) | 48.2474 | 1.57450 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 22.8990 | − | 39.6622i | 0.746485 | − | 1.29295i | −0.203012 | − | 0.979176i | \(-0.565073\pi\) |
0.949498 | − | 0.313774i | \(-0.101594\pi\) | |||||||
\(942\) | −14.6969 | −0.478852 | ||||||||
\(943\) | −6.78775 | −0.221040 | ||||||||
\(944\) | −1.44949 | + | 2.51059i | −0.0471769 | + | 0.0817127i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −4.72474 | + | 8.18350i | −0.153615 | + | 0.266068i | ||||
\(947\) | 24.1464 | + | 41.8228i | 0.784653 | + | 1.35906i | 0.929206 | + | 0.369563i | \(0.120492\pi\) |
−0.144552 | + | 0.989497i | \(0.546174\pi\) | |||||||
\(948\) | 5.44949 | + | 9.43879i | 0.176991 | + | 0.306558i | ||||
\(949\) | −56.3383 | −1.82882 | ||||||||
\(950\) | 20.8712 | + | 6.27647i | 0.677150 | + | 0.203636i | ||||
\(951\) | 58.8990 | 1.90993 | ||||||||
\(952\) | 5.44949 | + | 9.43879i | 0.176619 | + | 0.305913i | ||||
\(953\) | −20.0000 | − | 34.6410i | −0.647864 | − | 1.12213i | −0.983632 | − | 0.180188i | \(-0.942329\pi\) |
0.335769 | − | 0.941944i | \(-0.391004\pi\) | |||||||
\(954\) | −11.6969 | + | 20.2597i | −0.378702 | + | 0.655932i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −10.8990 | + | 18.8776i | −0.352498 | + | 0.610545i | ||||
\(957\) | −4.65153 | −0.150363 | ||||||||
\(958\) | 43.1464 | 1.39400 | ||||||||
\(959\) | −9.67423 | + | 16.7563i | −0.312397 | + | 0.541088i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −27.0000 | −0.870968 | ||||||||
\(962\) | −32.9444 | −1.06217 | ||||||||
\(963\) | −15.5227 | + | 26.8861i | −0.500212 | + | 0.866393i | ||||
\(964\) | −5.00000 | − | 8.66025i | −0.161039 | − | 0.278928i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 2.69694 | + | 4.67123i | 0.0867726 | + | 0.150295i | ||||
\(967\) | 18.8990 | + | 32.7340i | 0.607750 | + | 1.05265i | 0.991610 | + | 0.129263i | \(0.0412611\pi\) |
−0.383860 | + | 0.923391i | \(0.625406\pi\) | |||||||
\(968\) | −1.00000 | −0.0321412 | ||||||||
\(969\) | −34.5959 | + | 32.5590i | −1.11138 | + | 1.04595i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 21.9217 | + | 37.9695i | 0.703500 | + | 1.21850i | 0.967230 | + | 0.253902i | \(0.0817140\pi\) |
−0.263730 | + | 0.964597i | \(0.584953\pi\) | |||||||
\(972\) | −11.0227 | − | 19.0919i | −0.353553 | − | 0.612372i | ||||
\(973\) | −4.89898 | + | 8.48528i | −0.157054 | + | 0.272026i | ||||
\(974\) | −3.82577 | − | 6.62642i | −0.122585 | − | 0.212324i | ||||
\(975\) | −23.8763 | + | 41.3549i | −0.764653 | + | 1.32442i | ||||
\(976\) | 7.89898 | 0.252840 | ||||||||
\(977\) | −57.0000 | −1.82359 | −0.911796 | − | 0.410644i | \(-0.865304\pi\) | ||||
−0.911796 | + | 0.410644i | \(0.865304\pi\) | |||||||
\(978\) | −3.55051 | + | 6.14966i | −0.113533 | + | 0.196645i | ||||
\(979\) | −4.50000 | + | 7.79423i | −0.143821 | + | 0.249105i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 47.6969 | 1.52285 | ||||||||
\(982\) | −6.89898 | + | 11.9494i | −0.220155 | + | 0.381320i | ||||
\(983\) | −22.8712 | − | 39.6140i | −0.729477 | − | 1.26349i | −0.957104 | − | 0.289743i | \(-0.906430\pi\) |
0.227627 | − | 0.973748i | \(-0.426903\pi\) | |||||||
\(984\) | 9.24745 | − | 16.0171i | 0.294798 | − | 0.510605i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 4.22474 | + | 7.31747i | 0.134543 | + | 0.233036i | ||||
\(987\) | −39.3031 | −1.25103 | ||||||||
\(988\) | −3.89898 | − | 16.5420i | −0.124043 | − | 0.526270i | ||||
\(989\) | 8.49490 | 0.270122 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −0.724745 | − | 1.25529i | −0.0230223 | − | 0.0398758i | 0.854285 | − | 0.519805i | \(-0.173996\pi\) |
−0.877307 | + | 0.479930i | \(0.840662\pi\) | |||||||
\(992\) | 1.00000 | − | 1.73205i | 0.0317500 | − | 0.0549927i | ||||
\(993\) | 6.55051 | + | 11.3458i | 0.207874 | + | 0.360049i | ||||
\(994\) | −9.12372 | + | 15.8028i | −0.289387 | + | 0.501233i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 13.3485 | 0.422962 | ||||||||
\(997\) | 14.5959 | − | 25.2809i | 0.462257 | − | 0.800653i | −0.536816 | − | 0.843700i | \(-0.680373\pi\) |
0.999073 | + | 0.0430463i | \(0.0137063\pi\) | |||||||
\(998\) | −0.348469 | + | 0.603566i | −0.0110306 | + | 0.0191056i | ||||
\(999\) | 0 | 0 |
(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 | 418.2.e.g.45.2 | ✓ | 4 | |
19.7 | even | 3 | 7942.2.a.v.1.1 | 2 | |||
19.11 | even | 3 | inner | 418.2.e.g.353.2 | yes | 4 | |
19.12 | odd | 6 | 7942.2.a.y.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
418.2.e.g.45.2 | ✓ | 4 | 1.1 | even | 1 | trivial | |
418.2.e.g.353.2 | yes | 4 | 19.11 | even | 3 | inner | |
7942.2.a.v.1.1 | 2 | 19.7 | even | 3 | |||
7942.2.a.y.1.2 | 2 | 19.12 | odd | 6 |