Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [735,2,Mod(226,735)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(735, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 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("735.226");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 735 = 3 \cdot 5 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 735.i (of order \(3\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(5.86900454856\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\Q(\sqrt{-3}, \sqrt{5})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{3} + 2x^{2} + x + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | no (minimal twist has level 105) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 361.2 | ||
Root | \(-0.309017 - 0.535233i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 735.361 |
Dual form | 735.2.i.i.226.2 |
$q$-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 \(\left(\mathbb{Z}/735\mathbb{Z}\right)^\times\).
\(n\) | \(346\) | \(442\) | \(491\) |
\(\chi(n)\) | \(e\left(\frac{2}{3}\right)\) | \(1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.11803 | + | 1.93649i | 0.790569 | + | 1.36931i | 0.925615 | + | 0.378467i | \(0.123549\pi\) |
−0.135045 | + | 0.990839i | \(0.543118\pi\) | |||||||
\(3\) | −0.500000 | + | 0.866025i | −0.288675 | + | 0.500000i | ||||
\(4\) | −1.50000 | + | 2.59808i | −0.750000 | + | 1.29904i | ||||
\(5\) | −0.500000 | − | 0.866025i | −0.223607 | − | 0.387298i | ||||
\(6\) | −2.23607 | −0.912871 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −2.23607 | −0.790569 | ||||||||
\(9\) | −0.500000 | − | 0.866025i | −0.166667 | − | 0.288675i | ||||
\(10\) | 1.11803 | − | 1.93649i | 0.353553 | − | 0.612372i | ||||
\(11\) | −3.23607 | + | 5.60503i | −0.975711 | + | 1.68998i | −0.298143 | + | 0.954521i | \(0.596367\pi\) |
−0.677568 | + | 0.735460i | \(0.736966\pi\) | |||||||
\(12\) | −1.50000 | − | 2.59808i | −0.433013 | − | 0.750000i | ||||
\(13\) | −4.47214 | −1.24035 | −0.620174 | − | 0.784465i | \(-0.712938\pi\) | ||||
−0.620174 | + | 0.784465i | \(0.712938\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 1.00000 | 0.258199 | ||||||||
\(16\) | 0.500000 | + | 0.866025i | 0.125000 | + | 0.216506i | ||||
\(17\) | −1.00000 | + | 1.73205i | −0.242536 | + | 0.420084i | −0.961436 | − | 0.275029i | \(-0.911312\pi\) |
0.718900 | + | 0.695113i | \(0.244646\pi\) | |||||||
\(18\) | 1.11803 | − | 1.93649i | 0.263523 | − | 0.456435i | ||||
\(19\) | −1.23607 | − | 2.14093i | −0.283573 | − | 0.491164i | 0.688689 | − | 0.725057i | \(-0.258187\pi\) |
−0.972262 | + | 0.233893i | \(0.924853\pi\) | |||||||
\(20\) | 3.00000 | 0.670820 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −14.4721 | −3.08547 | ||||||||
\(23\) | −2.00000 | − | 3.46410i | −0.417029 | − | 0.722315i | 0.578610 | − | 0.815604i | \(-0.303595\pi\) |
−0.995639 | + | 0.0932891i | \(0.970262\pi\) | |||||||
\(24\) | 1.11803 | − | 1.93649i | 0.228218 | − | 0.395285i | ||||
\(25\) | −0.500000 | + | 0.866025i | −0.100000 | + | 0.173205i | ||||
\(26\) | −5.00000 | − | 8.66025i | −0.980581 | − | 1.69842i | ||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −2.00000 | −0.371391 | −0.185695 | − | 0.982607i | \(-0.559454\pi\) | ||||
−0.185695 | + | 0.982607i | \(0.559454\pi\) | |||||||
\(30\) | 1.11803 | + | 1.93649i | 0.204124 | + | 0.353553i | ||||
\(31\) | 0.763932 | − | 1.32317i | 0.137206 | − | 0.237648i | −0.789232 | − | 0.614095i | \(-0.789521\pi\) |
0.926438 | + | 0.376447i | \(0.122854\pi\) | |||||||
\(32\) | −3.35410 | + | 5.80948i | −0.592927 | + | 1.02698i | ||||
\(33\) | −3.23607 | − | 5.60503i | −0.563327 | − | 0.975711i | ||||
\(34\) | −4.47214 | −0.766965 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 3.00000 | 0.500000 | ||||||||
\(37\) | 3.47214 | + | 6.01392i | 0.570816 | + | 0.988682i | 0.996482 | + | 0.0838017i | \(0.0267062\pi\) |
−0.425667 | + | 0.904880i | \(0.639960\pi\) | |||||||
\(38\) | 2.76393 | − | 4.78727i | 0.448369 | − | 0.776598i | ||||
\(39\) | 2.23607 | − | 3.87298i | 0.358057 | − | 0.620174i | ||||
\(40\) | 1.11803 | + | 1.93649i | 0.176777 | + | 0.306186i | ||||
\(41\) | 2.00000 | 0.312348 | 0.156174 | − | 0.987730i | \(-0.450084\pi\) | ||||
0.156174 | + | 0.987730i | \(0.450084\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 8.94427 | 1.36399 | 0.681994 | − | 0.731357i | \(-0.261113\pi\) | ||||
0.681994 | + | 0.731357i | \(0.261113\pi\) | |||||||
\(44\) | −9.70820 | − | 16.8151i | −1.46357 | − | 2.53497i | ||||
\(45\) | −0.500000 | + | 0.866025i | −0.0745356 | + | 0.129099i | ||||
\(46\) | 4.47214 | − | 7.74597i | 0.659380 | − | 1.14208i | ||||
\(47\) | 6.47214 | + | 11.2101i | 0.944058 | + | 1.63516i | 0.757626 | + | 0.652689i | \(0.226359\pi\) |
0.186432 | + | 0.982468i | \(0.440308\pi\) | |||||||
\(48\) | −1.00000 | −0.144338 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −2.23607 | −0.316228 | ||||||||
\(51\) | −1.00000 | − | 1.73205i | −0.140028 | − | 0.242536i | ||||
\(52\) | 6.70820 | − | 11.6190i | 0.930261 | − | 1.61126i | ||||
\(53\) | 1.76393 | − | 3.05522i | 0.242295 | − | 0.419667i | −0.719073 | − | 0.694935i | \(-0.755433\pi\) |
0.961368 | + | 0.275268i | \(0.0887666\pi\) | |||||||
\(54\) | 1.11803 | + | 1.93649i | 0.152145 | + | 0.263523i | ||||
\(55\) | 6.47214 | 0.872703 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 2.47214 | 0.327442 | ||||||||
\(58\) | −2.23607 | − | 3.87298i | −0.293610 | − | 0.508548i | ||||
\(59\) | −4.47214 | + | 7.74597i | −0.582223 | + | 1.00844i | 0.412993 | + | 0.910734i | \(0.364483\pi\) |
−0.995215 | + | 0.0977047i | \(0.968850\pi\) | |||||||
\(60\) | −1.50000 | + | 2.59808i | −0.193649 | + | 0.335410i | ||||
\(61\) | −1.00000 | − | 1.73205i | −0.128037 | − | 0.221766i | 0.794879 | − | 0.606768i | \(-0.207534\pi\) |
−0.922916 | + | 0.385002i | \(0.874201\pi\) | |||||||
\(62\) | 3.41641 | 0.433884 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −13.0000 | −1.62500 | ||||||||
\(65\) | 2.23607 | + | 3.87298i | 0.277350 | + | 0.480384i | ||||
\(66\) | 7.23607 | − | 12.5332i | 0.890698 | − | 1.54273i | ||||
\(67\) | 2.00000 | − | 3.46410i | 0.244339 | − | 0.423207i | −0.717607 | − | 0.696449i | \(-0.754762\pi\) |
0.961946 | + | 0.273241i | \(0.0880957\pi\) | |||||||
\(68\) | −3.00000 | − | 5.19615i | −0.363803 | − | 0.630126i | ||||
\(69\) | 4.00000 | 0.481543 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 5.52786 | 0.656037 | 0.328018 | − | 0.944671i | \(-0.393619\pi\) | ||||
0.328018 | + | 0.944671i | \(0.393619\pi\) | |||||||
\(72\) | 1.11803 | + | 1.93649i | 0.131762 | + | 0.228218i | ||||
\(73\) | −6.23607 | + | 10.8012i | −0.729877 | + | 1.26418i | 0.227058 | + | 0.973881i | \(0.427089\pi\) |
−0.956935 | + | 0.290302i | \(0.906244\pi\) | |||||||
\(74\) | −7.76393 | + | 13.4475i | −0.902539 | + | 1.56324i | ||||
\(75\) | −0.500000 | − | 0.866025i | −0.0577350 | − | 0.100000i | ||||
\(76\) | 7.41641 | 0.850720 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 10.0000 | 1.13228 | ||||||||
\(79\) | −6.47214 | − | 11.2101i | −0.728172 | − | 1.26123i | −0.957655 | − | 0.287918i | \(-0.907037\pi\) |
0.229483 | − | 0.973313i | \(-0.426297\pi\) | |||||||
\(80\) | 0.500000 | − | 0.866025i | 0.0559017 | − | 0.0968246i | ||||
\(81\) | −0.500000 | + | 0.866025i | −0.0555556 | + | 0.0962250i | ||||
\(82\) | 2.23607 | + | 3.87298i | 0.246932 | + | 0.427699i | ||||
\(83\) | 16.9443 | 1.85988 | 0.929938 | − | 0.367717i | \(-0.119860\pi\) | ||||
0.929938 | + | 0.367717i | \(0.119860\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 2.00000 | 0.216930 | ||||||||
\(86\) | 10.0000 | + | 17.3205i | 1.07833 | + | 1.86772i | ||||
\(87\) | 1.00000 | − | 1.73205i | 0.107211 | − | 0.185695i | ||||
\(88\) | 7.23607 | − | 12.5332i | 0.771367 | − | 1.33605i | ||||
\(89\) | −1.00000 | − | 1.73205i | −0.106000 | − | 0.183597i | 0.808146 | − | 0.588982i | \(-0.200471\pi\) |
−0.914146 | + | 0.405385i | \(0.867138\pi\) | |||||||
\(90\) | −2.23607 | −0.235702 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 12.0000 | 1.25109 | ||||||||
\(93\) | 0.763932 | + | 1.32317i | 0.0792161 | + | 0.137206i | ||||
\(94\) | −14.4721 | + | 25.0665i | −1.49269 | + | 2.58541i | ||||
\(95\) | −1.23607 | + | 2.14093i | −0.126818 | + | 0.219655i | ||||
\(96\) | −3.35410 | − | 5.80948i | −0.342327 | − | 0.592927i | ||||
\(97\) | −8.47214 | −0.860215 | −0.430108 | − | 0.902778i | \(-0.641524\pi\) | ||||
−0.430108 | + | 0.902778i | \(0.641524\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 6.47214 | 0.650474 | ||||||||
\(100\) | −1.50000 | − | 2.59808i | −0.150000 | − | 0.259808i | ||||
\(101\) | −7.00000 | + | 12.1244i | −0.696526 | + | 1.20642i | 0.273138 | + | 0.961975i | \(0.411939\pi\) |
−0.969664 | + | 0.244443i | \(0.921395\pi\) | |||||||
\(102\) | 2.23607 | − | 3.87298i | 0.221404 | − | 0.383482i | ||||
\(103\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(104\) | 10.0000 | 0.980581 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 7.88854 | 0.766203 | ||||||||
\(107\) | 6.47214 | + | 11.2101i | 0.625685 | + | 1.08372i | 0.988408 | + | 0.151821i | \(0.0485138\pi\) |
−0.362723 | + | 0.931897i | \(0.618153\pi\) | |||||||
\(108\) | −1.50000 | + | 2.59808i | −0.144338 | + | 0.250000i | ||||
\(109\) | 1.00000 | − | 1.73205i | 0.0957826 | − | 0.165900i | −0.814152 | − | 0.580651i | \(-0.802798\pi\) |
0.909935 | + | 0.414751i | \(0.136131\pi\) | |||||||
\(110\) | 7.23607 | + | 12.5332i | 0.689932 | + | 1.19500i | ||||
\(111\) | −6.94427 | −0.659121 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 0.472136 | 0.0444148 | 0.0222074 | − | 0.999753i | \(-0.492931\pi\) | ||||
0.0222074 | + | 0.999753i | \(0.492931\pi\) | |||||||
\(114\) | 2.76393 | + | 4.78727i | 0.258866 | + | 0.448369i | ||||
\(115\) | −2.00000 | + | 3.46410i | −0.186501 | + | 0.323029i | ||||
\(116\) | 3.00000 | − | 5.19615i | 0.278543 | − | 0.482451i | ||||
\(117\) | 2.23607 | + | 3.87298i | 0.206725 | + | 0.358057i | ||||
\(118\) | −20.0000 | −1.84115 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −2.23607 | −0.204124 | ||||||||
\(121\) | −15.4443 | − | 26.7503i | −1.40402 | − | 2.43184i | ||||
\(122\) | 2.23607 | − | 3.87298i | 0.202444 | − | 0.350643i | ||||
\(123\) | −1.00000 | + | 1.73205i | −0.0901670 | + | 0.156174i | ||||
\(124\) | 2.29180 | + | 3.96951i | 0.205809 | + | 0.356472i | ||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −4.94427 | −0.438733 | −0.219367 | − | 0.975643i | \(-0.570399\pi\) | ||||
−0.219367 | + | 0.975643i | \(0.570399\pi\) | |||||||
\(128\) | −7.82624 | − | 13.5554i | −0.691748 | − | 1.19814i | ||||
\(129\) | −4.47214 | + | 7.74597i | −0.393750 | + | 0.681994i | ||||
\(130\) | −5.00000 | + | 8.66025i | −0.438529 | + | 0.759555i | ||||
\(131\) | 2.00000 | + | 3.46410i | 0.174741 | + | 0.302660i | 0.940072 | − | 0.340977i | \(-0.110758\pi\) |
−0.765331 | + | 0.643637i | \(0.777425\pi\) | |||||||
\(132\) | 19.4164 | 1.68998 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 8.94427 | 0.772667 | ||||||||
\(135\) | −0.500000 | − | 0.866025i | −0.0430331 | − | 0.0745356i | ||||
\(136\) | 2.23607 | − | 3.87298i | 0.191741 | − | 0.332106i | ||||
\(137\) | −1.76393 | + | 3.05522i | −0.150703 | + | 0.261025i | −0.931486 | − | 0.363777i | \(-0.881487\pi\) |
0.780783 | + | 0.624802i | \(0.214820\pi\) | |||||||
\(138\) | 4.47214 | + | 7.74597i | 0.380693 | + | 0.659380i | ||||
\(139\) | −7.41641 | −0.629052 | −0.314526 | − | 0.949249i | \(-0.601845\pi\) | ||||
−0.314526 | + | 0.949249i | \(0.601845\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −12.9443 | −1.09010 | ||||||||
\(142\) | 6.18034 | + | 10.7047i | 0.518643 | + | 0.898315i | ||||
\(143\) | 14.4721 | − | 25.0665i | 1.21022 | − | 2.09616i | ||||
\(144\) | 0.500000 | − | 0.866025i | 0.0416667 | − | 0.0721688i | ||||
\(145\) | 1.00000 | + | 1.73205i | 0.0830455 | + | 0.143839i | ||||
\(146\) | −27.8885 | −2.30807 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −20.8328 | −1.71245 | ||||||||
\(149\) | 7.47214 | + | 12.9421i | 0.612141 | + | 1.06026i | 0.990879 | + | 0.134756i | \(0.0430249\pi\) |
−0.378738 | + | 0.925504i | \(0.623642\pi\) | |||||||
\(150\) | 1.11803 | − | 1.93649i | 0.0912871 | − | 0.158114i | ||||
\(151\) | 8.00000 | − | 13.8564i | 0.651031 | − | 1.12762i | −0.331842 | − | 0.943335i | \(-0.607670\pi\) |
0.982873 | − | 0.184284i | \(-0.0589965\pi\) | |||||||
\(152\) | 2.76393 | + | 4.78727i | 0.224184 | + | 0.388299i | ||||
\(153\) | 2.00000 | 0.161690 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −1.52786 | −0.122721 | ||||||||
\(156\) | 6.70820 | + | 11.6190i | 0.537086 | + | 0.930261i | ||||
\(157\) | −0.236068 | + | 0.408882i | −0.0188403 | + | 0.0326323i | −0.875292 | − | 0.483595i | \(-0.839331\pi\) |
0.856452 | + | 0.516227i | \(0.172664\pi\) | |||||||
\(158\) | 14.4721 | − | 25.0665i | 1.15134 | − | 1.99418i | ||||
\(159\) | 1.76393 | + | 3.05522i | 0.139889 | + | 0.242295i | ||||
\(160\) | 6.70820 | 0.530330 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −2.23607 | −0.175682 | ||||||||
\(163\) | 8.47214 | + | 14.6742i | 0.663589 | + | 1.14937i | 0.979666 | + | 0.200636i | \(0.0643009\pi\) |
−0.316077 | + | 0.948734i | \(0.602366\pi\) | |||||||
\(164\) | −3.00000 | + | 5.19615i | −0.234261 | + | 0.405751i | ||||
\(165\) | −3.23607 | + | 5.60503i | −0.251928 | + | 0.436351i | ||||
\(166\) | 18.9443 | + | 32.8124i | 1.47036 | + | 2.54674i | ||||
\(167\) | 8.00000 | 0.619059 | 0.309529 | − | 0.950890i | \(-0.399829\pi\) | ||||
0.309529 | + | 0.950890i | \(0.399829\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 7.00000 | 0.538462 | ||||||||
\(170\) | 2.23607 | + | 3.87298i | 0.171499 | + | 0.297044i | ||||
\(171\) | −1.23607 | + | 2.14093i | −0.0945245 | + | 0.163721i | ||||
\(172\) | −13.4164 | + | 23.2379i | −1.02299 | + | 1.77187i | ||||
\(173\) | −1.47214 | − | 2.54981i | −0.111924 | − | 0.193859i | 0.804622 | − | 0.593788i | \(-0.202368\pi\) |
−0.916546 | + | 0.399929i | \(0.869035\pi\) | |||||||
\(174\) | 4.47214 | 0.339032 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −6.47214 | −0.487856 | ||||||||
\(177\) | −4.47214 | − | 7.74597i | −0.336146 | − | 0.582223i | ||||
\(178\) | 2.23607 | − | 3.87298i | 0.167600 | − | 0.290292i | ||||
\(179\) | −3.23607 | + | 5.60503i | −0.241875 | + | 0.418940i | −0.961248 | − | 0.275684i | \(-0.911096\pi\) |
0.719373 | + | 0.694624i | \(0.244429\pi\) | |||||||
\(180\) | −1.50000 | − | 2.59808i | −0.111803 | − | 0.193649i | ||||
\(181\) | −1.05573 | −0.0784717 | −0.0392358 | − | 0.999230i | \(-0.512492\pi\) | ||||
−0.0392358 | + | 0.999230i | \(0.512492\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 2.00000 | 0.147844 | ||||||||
\(184\) | 4.47214 | + | 7.74597i | 0.329690 | + | 0.571040i | ||||
\(185\) | 3.47214 | − | 6.01392i | 0.255277 | − | 0.442152i | ||||
\(186\) | −1.70820 | + | 2.95870i | −0.125252 | + | 0.216942i | ||||
\(187\) | −6.47214 | − | 11.2101i | −0.473289 | − | 0.819761i | ||||
\(188\) | −38.8328 | −2.83217 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −5.52786 | −0.401033 | ||||||||
\(191\) | −0.291796 | − | 0.505406i | −0.0211136 | − | 0.0365699i | 0.855276 | − | 0.518173i | \(-0.173388\pi\) |
−0.876389 | + | 0.481604i | \(0.840055\pi\) | |||||||
\(192\) | 6.50000 | − | 11.2583i | 0.469097 | − | 0.812500i | ||||
\(193\) | 7.00000 | − | 12.1244i | 0.503871 | − | 0.872730i | −0.496119 | − | 0.868255i | \(-0.665242\pi\) |
0.999990 | − | 0.00447566i | \(-0.00142465\pi\) | |||||||
\(194\) | −9.47214 | − | 16.4062i | −0.680060 | − | 1.17790i | ||||
\(195\) | −4.47214 | −0.320256 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 15.5279 | 1.10631 | 0.553157 | − | 0.833077i | \(-0.313423\pi\) | ||||
0.553157 | + | 0.833077i | \(0.313423\pi\) | |||||||
\(198\) | 7.23607 | + | 12.5332i | 0.514245 | + | 0.890698i | ||||
\(199\) | 13.7082 | − | 23.7433i | 0.971749 | − | 1.68312i | 0.281477 | − | 0.959568i | \(-0.409176\pi\) |
0.690272 | − | 0.723550i | \(-0.257491\pi\) | |||||||
\(200\) | 1.11803 | − | 1.93649i | 0.0790569 | − | 0.136931i | ||||
\(201\) | 2.00000 | + | 3.46410i | 0.141069 | + | 0.244339i | ||||
\(202\) | −31.3050 | −2.20261 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 6.00000 | 0.420084 | ||||||||
\(205\) | −1.00000 | − | 1.73205i | −0.0698430 | − | 0.120972i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −2.00000 | + | 3.46410i | −0.139010 | + | 0.240772i | ||||
\(208\) | −2.23607 | − | 3.87298i | −0.155043 | − | 0.268543i | ||||
\(209\) | 16.0000 | 1.10674 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −16.9443 | −1.16649 | −0.583246 | − | 0.812296i | \(-0.698218\pi\) | ||||
−0.583246 | + | 0.812296i | \(0.698218\pi\) | |||||||
\(212\) | 5.29180 | + | 9.16566i | 0.363442 | + | 0.629500i | ||||
\(213\) | −2.76393 | + | 4.78727i | −0.189382 | + | 0.328018i | ||||
\(214\) | −14.4721 | + | 25.0665i | −0.989295 | + | 1.71351i | ||||
\(215\) | −4.47214 | − | 7.74597i | −0.304997 | − | 0.528271i | ||||
\(216\) | −2.23607 | −0.152145 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 4.47214 | 0.302891 | ||||||||
\(219\) | −6.23607 | − | 10.8012i | −0.421394 | − | 0.729877i | ||||
\(220\) | −9.70820 | + | 16.8151i | −0.654527 | + | 1.13367i | ||||
\(221\) | 4.47214 | − | 7.74597i | 0.300828 | − | 0.521050i | ||||
\(222\) | −7.76393 | − | 13.4475i | −0.521081 | − | 0.902539i | ||||
\(223\) | 12.9443 | 0.866813 | 0.433406 | − | 0.901199i | \(-0.357312\pi\) | ||||
0.433406 | + | 0.901199i | \(0.357312\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 1.00000 | 0.0666667 | ||||||||
\(226\) | 0.527864 | + | 0.914287i | 0.0351130 | + | 0.0608175i | ||||
\(227\) | 0.472136 | − | 0.817763i | 0.0313368 | − | 0.0542769i | −0.849932 | − | 0.526893i | \(-0.823357\pi\) |
0.881268 | + | 0.472616i | \(0.156690\pi\) | |||||||
\(228\) | −3.70820 | + | 6.42280i | −0.245582 | + | 0.425360i | ||||
\(229\) | 11.9443 | + | 20.6881i | 0.789300 | + | 1.36711i | 0.926396 | + | 0.376550i | \(0.122890\pi\) |
−0.137097 | + | 0.990558i | \(0.543777\pi\) | |||||||
\(230\) | −8.94427 | −0.589768 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 4.47214 | 0.293610 | ||||||||
\(233\) | 4.70820 | + | 8.15485i | 0.308445 | + | 0.534242i | 0.978022 | − | 0.208500i | \(-0.0668582\pi\) |
−0.669578 | + | 0.742742i | \(0.733525\pi\) | |||||||
\(234\) | −5.00000 | + | 8.66025i | −0.326860 | + | 0.566139i | ||||
\(235\) | 6.47214 | − | 11.2101i | 0.422196 | − | 0.731264i | ||||
\(236\) | −13.4164 | − | 23.2379i | −0.873334 | − | 1.51266i | ||||
\(237\) | 12.9443 | 0.840821 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −10.4721 | −0.677386 | −0.338693 | − | 0.940897i | \(-0.609985\pi\) | ||||
−0.338693 | + | 0.940897i | \(0.609985\pi\) | |||||||
\(240\) | 0.500000 | + | 0.866025i | 0.0322749 | + | 0.0559017i | ||||
\(241\) | −9.47214 | + | 16.4062i | −0.610154 | + | 1.05682i | 0.381060 | + | 0.924550i | \(0.375559\pi\) |
−0.991214 | + | 0.132267i | \(0.957774\pi\) | |||||||
\(242\) | 34.5344 | − | 59.8154i | 2.21996 | − | 3.84508i | ||||
\(243\) | −0.500000 | − | 0.866025i | −0.0320750 | − | 0.0555556i | ||||
\(244\) | 6.00000 | 0.384111 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −4.47214 | −0.285133 | ||||||||
\(247\) | 5.52786 | + | 9.57454i | 0.351730 | + | 0.609213i | ||||
\(248\) | −1.70820 | + | 2.95870i | −0.108471 | + | 0.187877i | ||||
\(249\) | −8.47214 | + | 14.6742i | −0.536900 | + | 0.929938i | ||||
\(250\) | 1.11803 | + | 1.93649i | 0.0707107 | + | 0.122474i | ||||
\(251\) | −16.9443 | −1.06951 | −0.534756 | − | 0.845006i | \(-0.679597\pi\) | ||||
−0.534756 | + | 0.845006i | \(0.679597\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 25.8885 | 1.62760 | ||||||||
\(254\) | −5.52786 | − | 9.57454i | −0.346849 | − | 0.600760i | ||||
\(255\) | −1.00000 | + | 1.73205i | −0.0626224 | + | 0.108465i | ||||
\(256\) | 4.50000 | − | 7.79423i | 0.281250 | − | 0.487139i | ||||
\(257\) | 9.47214 | + | 16.4062i | 0.590856 | + | 1.02339i | 0.994117 | + | 0.108307i | \(0.0345430\pi\) |
−0.403262 | + | 0.915085i | \(0.632124\pi\) | |||||||
\(258\) | −20.0000 | −1.24515 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −13.4164 | −0.832050 | ||||||||
\(261\) | 1.00000 | + | 1.73205i | 0.0618984 | + | 0.107211i | ||||
\(262\) | −4.47214 | + | 7.74597i | −0.276289 | + | 0.478547i | ||||
\(263\) | −3.52786 | + | 6.11044i | −0.217537 | + | 0.376786i | −0.954055 | − | 0.299633i | \(-0.903136\pi\) |
0.736517 | + | 0.676419i | \(0.236469\pi\) | |||||||
\(264\) | 7.23607 | + | 12.5332i | 0.445349 | + | 0.771367i | ||||
\(265\) | −3.52786 | −0.216715 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 2.00000 | 0.122398 | ||||||||
\(268\) | 6.00000 | + | 10.3923i | 0.366508 | + | 0.634811i | ||||
\(269\) | 5.94427 | − | 10.2958i | 0.362429 | − | 0.627745i | −0.625931 | − | 0.779878i | \(-0.715281\pi\) |
0.988360 | + | 0.152133i | \(0.0486143\pi\) | |||||||
\(270\) | 1.11803 | − | 1.93649i | 0.0680414 | − | 0.117851i | ||||
\(271\) | −0.763932 | − | 1.32317i | −0.0464056 | − | 0.0803768i | 0.841890 | − | 0.539650i | \(-0.181443\pi\) |
−0.888295 | + | 0.459273i | \(0.848110\pi\) | |||||||
\(272\) | −2.00000 | −0.121268 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −7.88854 | −0.476564 | ||||||||
\(275\) | −3.23607 | − | 5.60503i | −0.195142 | − | 0.337996i | ||||
\(276\) | −6.00000 | + | 10.3923i | −0.361158 | + | 0.625543i | ||||
\(277\) | −9.47214 | + | 16.4062i | −0.569125 | + | 0.985754i | 0.427527 | + | 0.904002i | \(0.359385\pi\) |
−0.996653 | + | 0.0817518i | \(0.973949\pi\) | |||||||
\(278\) | −8.29180 | − | 14.3618i | −0.497309 | − | 0.861364i | ||||
\(279\) | −1.52786 | −0.0914708 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −10.9443 | −0.652881 | −0.326440 | − | 0.945218i | \(-0.605849\pi\) | ||||
−0.326440 | + | 0.945218i | \(0.605849\pi\) | |||||||
\(282\) | −14.4721 | − | 25.0665i | −0.861803 | − | 1.49269i | ||||
\(283\) | 6.00000 | − | 10.3923i | 0.356663 | − | 0.617758i | −0.630738 | − | 0.775996i | \(-0.717248\pi\) |
0.987401 | + | 0.158237i | \(0.0505811\pi\) | |||||||
\(284\) | −8.29180 | + | 14.3618i | −0.492028 | + | 0.852217i | ||||
\(285\) | −1.23607 | − | 2.14093i | −0.0732183 | − | 0.126818i | ||||
\(286\) | 64.7214 | 3.82705 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 6.70820 | 0.395285 | ||||||||
\(289\) | 6.50000 | + | 11.2583i | 0.382353 | + | 0.662255i | ||||
\(290\) | −2.23607 | + | 3.87298i | −0.131306 | + | 0.227429i | ||||
\(291\) | 4.23607 | − | 7.33708i | 0.248323 | − | 0.430108i | ||||
\(292\) | −18.7082 | − | 32.4036i | −1.09481 | − | 1.89627i | ||||
\(293\) | −5.05573 | −0.295359 | −0.147679 | − | 0.989035i | \(-0.547180\pi\) | ||||
−0.147679 | + | 0.989035i | \(0.547180\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 8.94427 | 0.520756 | ||||||||
\(296\) | −7.76393 | − | 13.4475i | −0.451269 | − | 0.781621i | ||||
\(297\) | −3.23607 | + | 5.60503i | −0.187776 | + | 0.325237i | ||||
\(298\) | −16.7082 | + | 28.9395i | −0.967880 | + | 1.67642i | ||||
\(299\) | 8.94427 | + | 15.4919i | 0.517261 | + | 0.895922i | ||||
\(300\) | 3.00000 | 0.173205 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 35.7771 | 2.05874 | ||||||||
\(303\) | −7.00000 | − | 12.1244i | −0.402139 | − | 0.696526i | ||||
\(304\) | 1.23607 | − | 2.14093i | 0.0708934 | − | 0.122791i | ||||
\(305\) | −1.00000 | + | 1.73205i | −0.0572598 | + | 0.0991769i | ||||
\(306\) | 2.23607 | + | 3.87298i | 0.127827 | + | 0.221404i | ||||
\(307\) | 15.0557 | 0.859276 | 0.429638 | − | 0.903001i | \(-0.358641\pi\) | ||||
0.429638 | + | 0.903001i | \(0.358641\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −1.70820 | − | 2.95870i | −0.0970195 | − | 0.168043i | ||||
\(311\) | 12.9443 | − | 22.4201i | 0.734002 | − | 1.27133i | −0.221157 | − | 0.975238i | \(-0.570983\pi\) |
0.955160 | − | 0.296091i | \(-0.0956832\pi\) | |||||||
\(312\) | −5.00000 | + | 8.66025i | −0.283069 | + | 0.490290i | ||||
\(313\) | −8.70820 | − | 15.0831i | −0.492217 | − | 0.852544i | 0.507743 | − | 0.861509i | \(-0.330480\pi\) |
−0.999960 | + | 0.00896408i | \(0.997147\pi\) | |||||||
\(314\) | −1.05573 | −0.0595782 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 38.8328 | 2.18452 | ||||||||
\(317\) | −7.18034 | − | 12.4367i | −0.403288 | − | 0.698515i | 0.590832 | − | 0.806794i | \(-0.298799\pi\) |
−0.994121 | + | 0.108279i | \(0.965466\pi\) | |||||||
\(318\) | −3.94427 | + | 6.83168i | −0.221184 | + | 0.383102i | ||||
\(319\) | 6.47214 | − | 11.2101i | 0.362370 | − | 0.627643i | ||||
\(320\) | 6.50000 | + | 11.2583i | 0.363361 | + | 0.629360i | ||||
\(321\) | −12.9443 | −0.722479 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 4.94427 | 0.275107 | ||||||||
\(324\) | −1.50000 | − | 2.59808i | −0.0833333 | − | 0.144338i | ||||
\(325\) | 2.23607 | − | 3.87298i | 0.124035 | − | 0.214834i | ||||
\(326\) | −18.9443 | + | 32.8124i | −1.04923 | + | 1.81731i | ||||
\(327\) | 1.00000 | + | 1.73205i | 0.0553001 | + | 0.0957826i | ||||
\(328\) | −4.47214 | −0.246932 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | −14.4721 | −0.796665 | ||||||||
\(331\) | −0.472136 | − | 0.817763i | −0.0259509 | − | 0.0449483i | 0.852758 | − | 0.522306i | \(-0.174928\pi\) |
−0.878709 | + | 0.477357i | \(0.841595\pi\) | |||||||
\(332\) | −25.4164 | + | 44.0225i | −1.39491 | + | 2.41605i | ||||
\(333\) | 3.47214 | − | 6.01392i | 0.190272 | − | 0.329561i | ||||
\(334\) | 8.94427 | + | 15.4919i | 0.489409 | + | 0.847681i | ||||
\(335\) | −4.00000 | −0.218543 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −23.8885 | −1.30129 | −0.650646 | − | 0.759381i | \(-0.725502\pi\) | ||||
−0.650646 | + | 0.759381i | \(0.725502\pi\) | |||||||
\(338\) | 7.82624 | + | 13.5554i | 0.425691 | + | 0.737319i | ||||
\(339\) | −0.236068 | + | 0.408882i | −0.0128215 | + | 0.0222074i | ||||
\(340\) | −3.00000 | + | 5.19615i | −0.162698 | + | 0.281801i | ||||
\(341\) | 4.94427 | + | 8.56373i | 0.267747 | + | 0.463752i | ||||
\(342\) | −5.52786 | −0.298913 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −20.0000 | −1.07833 | ||||||||
\(345\) | −2.00000 | − | 3.46410i | −0.107676 | − | 0.186501i | ||||
\(346\) | 3.29180 | − | 5.70156i | 0.176968 | − | 0.306518i | ||||
\(347\) | 4.00000 | − | 6.92820i | 0.214731 | − | 0.371925i | −0.738458 | − | 0.674299i | \(-0.764446\pi\) |
0.953189 | + | 0.302374i | \(0.0977791\pi\) | |||||||
\(348\) | 3.00000 | + | 5.19615i | 0.160817 | + | 0.278543i | ||||
\(349\) | 11.8885 | 0.636379 | 0.318190 | − | 0.948027i | \(-0.396925\pi\) | ||||
0.318190 | + | 0.948027i | \(0.396925\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −4.47214 | −0.238705 | ||||||||
\(352\) | −21.7082 | − | 37.5997i | −1.15705 | − | 2.00407i | ||||
\(353\) | 3.94427 | − | 6.83168i | 0.209932 | − | 0.363614i | −0.741761 | − | 0.670665i | \(-0.766009\pi\) |
0.951693 | + | 0.307051i | \(0.0993423\pi\) | |||||||
\(354\) | 10.0000 | − | 17.3205i | 0.531494 | − | 0.920575i | ||||
\(355\) | −2.76393 | − | 4.78727i | −0.146694 | − | 0.254082i | ||||
\(356\) | 6.00000 | 0.317999 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −14.4721 | −0.764876 | ||||||||
\(359\) | −9.23607 | − | 15.9973i | −0.487461 | − | 0.844307i | 0.512435 | − | 0.858726i | \(-0.328744\pi\) |
−0.999896 | + | 0.0144187i | \(0.995410\pi\) | |||||||
\(360\) | 1.11803 | − | 1.93649i | 0.0589256 | − | 0.102062i | ||||
\(361\) | 6.44427 | − | 11.1618i | 0.339172 | − | 0.587463i | ||||
\(362\) | −1.18034 | − | 2.04441i | −0.0620373 | − | 0.107452i | ||||
\(363\) | 30.8885 | 1.62123 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 12.4721 | 0.652821 | ||||||||
\(366\) | 2.23607 | + | 3.87298i | 0.116881 | + | 0.202444i | ||||
\(367\) | 1.52786 | − | 2.64634i | 0.0797539 | − | 0.138138i | −0.823390 | − | 0.567476i | \(-0.807920\pi\) |
0.903144 | + | 0.429338i | \(0.141253\pi\) | |||||||
\(368\) | 2.00000 | − | 3.46410i | 0.104257 | − | 0.180579i | ||||
\(369\) | −1.00000 | − | 1.73205i | −0.0520579 | − | 0.0901670i | ||||
\(370\) | 15.5279 | 0.807255 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | −4.58359 | −0.237648 | ||||||||
\(373\) | −3.00000 | − | 5.19615i | −0.155334 | − | 0.269047i | 0.777847 | − | 0.628454i | \(-0.216312\pi\) |
−0.933181 | + | 0.359408i | \(0.882979\pi\) | |||||||
\(374\) | 14.4721 | − | 25.0665i | 0.748336 | − | 1.29616i | ||||
\(375\) | −0.500000 | + | 0.866025i | −0.0258199 | + | 0.0447214i | ||||
\(376\) | −14.4721 | − | 25.0665i | −0.746343 | − | 1.29270i | ||||
\(377\) | 8.94427 | 0.460653 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −37.8885 | −1.94620 | −0.973102 | − | 0.230375i | \(-0.926005\pi\) | ||||
−0.973102 | + | 0.230375i | \(0.926005\pi\) | |||||||
\(380\) | −3.70820 | − | 6.42280i | −0.190227 | − | 0.329483i | ||||
\(381\) | 2.47214 | − | 4.28187i | 0.126651 | − | 0.219367i | ||||
\(382\) | 0.652476 | − | 1.13012i | 0.0333836 | − | 0.0578220i | ||||
\(383\) | −4.00000 | − | 6.92820i | −0.204390 | − | 0.354015i | 0.745548 | − | 0.666452i | \(-0.232188\pi\) |
−0.949938 | + | 0.312437i | \(0.898855\pi\) | |||||||
\(384\) | 15.6525 | 0.798762 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 31.3050 | 1.59338 | ||||||||
\(387\) | −4.47214 | − | 7.74597i | −0.227331 | − | 0.393750i | ||||
\(388\) | 12.7082 | − | 22.0113i | 0.645161 | − | 1.11745i | ||||
\(389\) | 3.47214 | − | 6.01392i | 0.176044 | − | 0.304918i | −0.764478 | − | 0.644650i | \(-0.777003\pi\) |
0.940522 | + | 0.339732i | \(0.110336\pi\) | |||||||
\(390\) | −5.00000 | − | 8.66025i | −0.253185 | − | 0.438529i | ||||
\(391\) | 8.00000 | 0.404577 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −4.00000 | −0.201773 | ||||||||
\(394\) | 17.3607 | + | 30.0696i | 0.874618 | + | 1.51488i | ||||
\(395\) | −6.47214 | + | 11.2101i | −0.325649 | + | 0.564040i | ||||
\(396\) | −9.70820 | + | 16.8151i | −0.487856 | + | 0.844991i | ||||
\(397\) | −6.70820 | − | 11.6190i | −0.336675 | − | 0.583138i | 0.647130 | − | 0.762380i | \(-0.275969\pi\) |
−0.983805 | + | 0.179241i | \(0.942636\pi\) | |||||||
\(398\) | 61.3050 | 3.07294 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −1.00000 | −0.0500000 | ||||||||
\(401\) | −5.00000 | − | 8.66025i | −0.249688 | − | 0.432472i | 0.713751 | − | 0.700399i | \(-0.246995\pi\) |
−0.963439 | + | 0.267927i | \(0.913661\pi\) | |||||||
\(402\) | −4.47214 | + | 7.74597i | −0.223050 | + | 0.386334i | ||||
\(403\) | −3.41641 | + | 5.91739i | −0.170183 | + | 0.294766i | ||||
\(404\) | −21.0000 | − | 36.3731i | −1.04479 | − | 1.80963i | ||||
\(405\) | 1.00000 | 0.0496904 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −44.9443 | −2.22780 | ||||||||
\(408\) | 2.23607 | + | 3.87298i | 0.110702 | + | 0.191741i | ||||
\(409\) | 5.94427 | − | 10.2958i | 0.293925 | − | 0.509094i | −0.680809 | − | 0.732461i | \(-0.738372\pi\) |
0.974734 | + | 0.223367i | \(0.0717050\pi\) | |||||||
\(410\) | 2.23607 | − | 3.87298i | 0.110432 | − | 0.191273i | ||||
\(411\) | −1.76393 | − | 3.05522i | −0.0870084 | − | 0.150703i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | −8.94427 | −0.439587 | ||||||||
\(415\) | −8.47214 | − | 14.6742i | −0.415881 | − | 0.720327i | ||||
\(416\) | 15.0000 | − | 25.9808i | 0.735436 | − | 1.27381i | ||||
\(417\) | 3.70820 | − | 6.42280i | 0.181592 | − | 0.314526i | ||||
\(418\) | 17.8885 | + | 30.9839i | 0.874957 | + | 1.51547i | ||||
\(419\) | 29.8885 | 1.46015 | 0.730075 | − | 0.683367i | \(-0.239485\pi\) | ||||
0.730075 | + | 0.683367i | \(0.239485\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 22.0000 | 1.07221 | 0.536107 | − | 0.844150i | \(-0.319894\pi\) | ||||
0.536107 | + | 0.844150i | \(0.319894\pi\) | |||||||
\(422\) | −18.9443 | − | 32.8124i | −0.922193 | − | 1.59728i | ||||
\(423\) | 6.47214 | − | 11.2101i | 0.314686 | − | 0.545052i | ||||
\(424\) | −3.94427 | + | 6.83168i | −0.191551 | + | 0.331776i | ||||
\(425\) | −1.00000 | − | 1.73205i | −0.0485071 | − | 0.0840168i | ||||
\(426\) | −12.3607 | −0.598877 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −38.8328 | −1.87705 | ||||||||
\(429\) | 14.4721 | + | 25.0665i | 0.698721 | + | 1.21022i | ||||
\(430\) | 10.0000 | − | 17.3205i | 0.482243 | − | 0.835269i | ||||
\(431\) | 9.23607 | − | 15.9973i | 0.444886 | − | 0.770565i | −0.553159 | − | 0.833076i | \(-0.686578\pi\) |
0.998044 | + | 0.0625113i | \(0.0199110\pi\) | |||||||
\(432\) | 0.500000 | + | 0.866025i | 0.0240563 | + | 0.0416667i | ||||
\(433\) | −16.4721 | −0.791600 | −0.395800 | − | 0.918337i | \(-0.629533\pi\) | ||||
−0.395800 | + | 0.918337i | \(0.629533\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −2.00000 | −0.0958927 | ||||||||
\(436\) | 3.00000 | + | 5.19615i | 0.143674 | + | 0.248851i | ||||
\(437\) | −4.94427 | + | 8.56373i | −0.236517 | + | 0.409659i | ||||
\(438\) | 13.9443 | − | 24.1522i | 0.666283 | − | 1.15404i | ||||
\(439\) | 0.763932 | + | 1.32317i | 0.0364605 | + | 0.0631514i | 0.883680 | − | 0.468092i | \(-0.155058\pi\) |
−0.847219 | + | 0.531243i | \(0.821725\pi\) | |||||||
\(440\) | −14.4721 | −0.689932 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 20.0000 | 0.951303 | ||||||||
\(443\) | 4.00000 | + | 6.92820i | 0.190046 | + | 0.329169i | 0.945265 | − | 0.326303i | \(-0.105803\pi\) |
−0.755219 | + | 0.655472i | \(0.772470\pi\) | |||||||
\(444\) | 10.4164 | − | 18.0417i | 0.494341 | − | 0.856223i | ||||
\(445\) | −1.00000 | + | 1.73205i | −0.0474045 | + | 0.0821071i | ||||
\(446\) | 14.4721 | + | 25.0665i | 0.685275 | + | 1.18693i | ||||
\(447\) | −14.9443 | −0.706840 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −14.0000 | −0.660701 | −0.330350 | − | 0.943858i | \(-0.607167\pi\) | ||||
−0.330350 | + | 0.943858i | \(0.607167\pi\) | |||||||
\(450\) | 1.11803 | + | 1.93649i | 0.0527046 | + | 0.0912871i | ||||
\(451\) | −6.47214 | + | 11.2101i | −0.304761 | + | 0.527862i | ||||
\(452\) | −0.708204 | + | 1.22665i | −0.0333111 | + | 0.0576965i | ||||
\(453\) | 8.00000 | + | 13.8564i | 0.375873 | + | 0.651031i | ||||
\(454\) | 2.11146 | 0.0990955 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −5.52786 | −0.258866 | ||||||||
\(457\) | −3.47214 | − | 6.01392i | −0.162420 | − | 0.281319i | 0.773316 | − | 0.634020i | \(-0.218597\pi\) |
−0.935736 | + | 0.352701i | \(0.885263\pi\) | |||||||
\(458\) | −26.7082 | + | 46.2600i | −1.24799 | + | 2.16159i | ||||
\(459\) | −1.00000 | + | 1.73205i | −0.0466760 | + | 0.0808452i | ||||
\(460\) | −6.00000 | − | 10.3923i | −0.279751 | − | 0.484544i | ||||
\(461\) | −3.88854 | −0.181108 | −0.0905538 | − | 0.995892i | \(-0.528864\pi\) | ||||
−0.0905538 | + | 0.995892i | \(0.528864\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 20.9443 | 0.973363 | 0.486681 | − | 0.873580i | \(-0.338207\pi\) | ||||
0.486681 | + | 0.873580i | \(0.338207\pi\) | |||||||
\(464\) | −1.00000 | − | 1.73205i | −0.0464238 | − | 0.0804084i | ||||
\(465\) | 0.763932 | − | 1.32317i | 0.0354265 | − | 0.0613605i | ||||
\(466\) | −10.5279 | + | 18.2348i | −0.487694 | + | 0.844711i | ||||
\(467\) | −4.47214 | − | 7.74597i | −0.206946 | − | 0.358441i | 0.743805 | − | 0.668397i | \(-0.233019\pi\) |
−0.950751 | + | 0.309956i | \(0.899686\pi\) | |||||||
\(468\) | −13.4164 | −0.620174 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 28.9443 | 1.33510 | ||||||||
\(471\) | −0.236068 | − | 0.408882i | −0.0108774 | − | 0.0188403i | ||||
\(472\) | 10.0000 | − | 17.3205i | 0.460287 | − | 0.797241i | ||||
\(473\) | −28.9443 | + | 50.1329i | −1.33086 | + | 2.30512i | ||||
\(474\) | 14.4721 | + | 25.0665i | 0.664727 | + | 1.15134i | ||||
\(475\) | 2.47214 | 0.113429 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −3.52786 | −0.161530 | ||||||||
\(478\) | −11.7082 | − | 20.2792i | −0.535521 | − | 0.927549i | ||||
\(479\) | −8.94427 | + | 15.4919i | −0.408674 | + | 0.707845i | −0.994741 | − | 0.102418i | \(-0.967342\pi\) |
0.586067 | + | 0.810262i | \(0.300675\pi\) | |||||||
\(480\) | −3.35410 | + | 5.80948i | −0.153093 | + | 0.265165i | ||||
\(481\) | −15.5279 | − | 26.8950i | −0.708010 | − | 1.22631i | ||||
\(482\) | −42.3607 | −1.92948 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 92.6656 | 4.21207 | ||||||||
\(485\) | 4.23607 | + | 7.33708i | 0.192350 | + | 0.333160i | ||||
\(486\) | 1.11803 | − | 1.93649i | 0.0507151 | − | 0.0878410i | ||||
\(487\) | 10.4721 | − | 18.1383i | 0.474538 | − | 0.821924i | −0.525037 | − | 0.851079i | \(-0.675949\pi\) |
0.999575 | + | 0.0291558i | \(0.00928189\pi\) | |||||||
\(488\) | 2.23607 | + | 3.87298i | 0.101222 | + | 0.175322i | ||||
\(489\) | −16.9443 | −0.766246 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −21.3050 | −0.961479 | −0.480740 | − | 0.876863i | \(-0.659632\pi\) | ||||
−0.480740 | + | 0.876863i | \(0.659632\pi\) | |||||||
\(492\) | −3.00000 | − | 5.19615i | −0.135250 | − | 0.234261i | ||||
\(493\) | 2.00000 | − | 3.46410i | 0.0900755 | − | 0.156015i | ||||
\(494\) | −12.3607 | + | 21.4093i | −0.556133 | + | 0.963251i | ||||
\(495\) | −3.23607 | − | 5.60503i | −0.145450 | − | 0.251928i | ||||
\(496\) | 1.52786 | 0.0686031 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −37.8885 | −1.69783 | ||||||||
\(499\) | 6.94427 | + | 12.0278i | 0.310868 | + | 0.538440i | 0.978551 | − | 0.206007i | \(-0.0660469\pi\) |
−0.667682 | + | 0.744446i | \(0.732714\pi\) | |||||||
\(500\) | −1.50000 | + | 2.59808i | −0.0670820 | + | 0.116190i | ||||
\(501\) | −4.00000 | + | 6.92820i | −0.178707 | + | 0.309529i | ||||
\(502\) | −18.9443 | − | 32.8124i | −0.845524 | − | 1.46449i | ||||
\(503\) | −32.0000 | −1.42681 | −0.713405 | − | 0.700752i | \(-0.752848\pi\) | ||||
−0.713405 | + | 0.700752i | \(0.752848\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 14.0000 | 0.622992 | ||||||||
\(506\) | 28.9443 | + | 50.1329i | 1.28673 | + | 2.22868i | ||||
\(507\) | −3.50000 | + | 6.06218i | −0.155440 | + | 0.269231i | ||||
\(508\) | 7.41641 | − | 12.8456i | 0.329050 | − | 0.569931i | ||||
\(509\) | −11.9443 | − | 20.6881i | −0.529421 | − | 0.916983i | −0.999411 | − | 0.0343119i | \(-0.989076\pi\) |
0.469991 | − | 0.882671i | \(-0.344257\pi\) | |||||||
\(510\) | −4.47214 | −0.198030 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −11.1803 | −0.494106 | ||||||||
\(513\) | −1.23607 | − | 2.14093i | −0.0545737 | − | 0.0945245i | ||||
\(514\) | −21.1803 | + | 36.6854i | −0.934225 | + | 1.61812i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −13.4164 | − | 23.2379i | −0.590624 | − | 1.02299i | ||||
\(517\) | −83.7771 | −3.68451 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 2.94427 | 0.129239 | ||||||||
\(520\) | −5.00000 | − | 8.66025i | −0.219265 | − | 0.379777i | ||||
\(521\) | −9.94427 | + | 17.2240i | −0.435666 | + | 0.754596i | −0.997350 | − | 0.0727559i | \(-0.976821\pi\) |
0.561683 | + | 0.827352i | \(0.310154\pi\) | |||||||
\(522\) | −2.23607 | + | 3.87298i | −0.0978700 | + | 0.169516i | ||||
\(523\) | −4.47214 | − | 7.74597i | −0.195553 | − | 0.338707i | 0.751529 | − | 0.659700i | \(-0.229317\pi\) |
−0.947082 | + | 0.320993i | \(0.895983\pi\) | |||||||
\(524\) | −12.0000 | −0.524222 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −15.7771 | −0.687914 | ||||||||
\(527\) | 1.52786 | + | 2.64634i | 0.0665548 | + | 0.115276i | ||||
\(528\) | 3.23607 | − | 5.60503i | 0.140832 | − | 0.243928i | ||||
\(529\) | 3.50000 | − | 6.06218i | 0.152174 | − | 0.263573i | ||||
\(530\) | −3.94427 | − | 6.83168i | −0.171328 | − | 0.296749i | ||||
\(531\) | 8.94427 | 0.388148 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −8.94427 | −0.387419 | ||||||||
\(534\) | 2.23607 | + | 3.87298i | 0.0967641 | + | 0.167600i | ||||
\(535\) | 6.47214 | − | 11.2101i | 0.279815 | − | 0.484654i | ||||
\(536\) | −4.47214 | + | 7.74597i | −0.193167 | + | 0.334575i | ||||
\(537\) | −3.23607 | − | 5.60503i | −0.139647 | − | 0.241875i | ||||
\(538\) | 26.5836 | 1.14610 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 3.00000 | 0.129099 | ||||||||
\(541\) | 5.94427 | + | 10.2958i | 0.255564 | + | 0.442650i | 0.965049 | − | 0.262071i | \(-0.0844054\pi\) |
−0.709484 | + | 0.704721i | \(0.751072\pi\) | |||||||
\(542\) | 1.70820 | − | 2.95870i | 0.0733736 | − | 0.127087i | ||||
\(543\) | 0.527864 | − | 0.914287i | 0.0226528 | − | 0.0392358i | ||||
\(544\) | −6.70820 | − | 11.6190i | −0.287612 | − | 0.498158i | ||||
\(545\) | −2.00000 | −0.0856706 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 5.88854 | 0.251776 | 0.125888 | − | 0.992044i | \(-0.459822\pi\) | ||||
0.125888 | + | 0.992044i | \(0.459822\pi\) | |||||||
\(548\) | −5.29180 | − | 9.16566i | −0.226054 | − | 0.391538i | ||||
\(549\) | −1.00000 | + | 1.73205i | −0.0426790 | + | 0.0739221i | ||||
\(550\) | 7.23607 | − | 12.5332i | 0.308547 | − | 0.534419i | ||||
\(551\) | 2.47214 | + | 4.28187i | 0.105317 | + | 0.182414i | ||||
\(552\) | −8.94427 | −0.380693 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −42.3607 | −1.79973 | ||||||||
\(555\) | 3.47214 | + | 6.01392i | 0.147384 | + | 0.255277i | ||||
\(556\) | 11.1246 | − | 19.2684i | 0.471789 | − | 0.817162i | ||||
\(557\) | −10.2361 | + | 17.7294i | −0.433716 | + | 0.751218i | −0.997190 | − | 0.0749156i | \(-0.976131\pi\) |
0.563474 | + | 0.826134i | \(0.309465\pi\) | |||||||
\(558\) | −1.70820 | − | 2.95870i | −0.0723140 | − | 0.125252i | ||||
\(559\) | −40.0000 | −1.69182 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 12.9443 | 0.546508 | ||||||||
\(562\) | −12.2361 | − | 21.1935i | −0.516147 | − | 0.893993i | ||||
\(563\) | 6.94427 | − | 12.0278i | 0.292666 | − | 0.506913i | −0.681773 | − | 0.731564i | \(-0.738791\pi\) |
0.974439 | + | 0.224651i | \(0.0721242\pi\) | |||||||
\(564\) | 19.4164 | − | 33.6302i | 0.817578 | − | 1.41609i | ||||
\(565\) | −0.236068 | − | 0.408882i | −0.00993145 | − | 0.0172018i | ||||
\(566\) | 26.8328 | 1.12787 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −12.3607 | −0.518643 | ||||||||
\(569\) | 19.9443 | + | 34.5445i | 0.836107 | + | 1.44818i | 0.893126 | + | 0.449807i | \(0.148507\pi\) |
−0.0570183 | + | 0.998373i | \(0.518159\pi\) | |||||||
\(570\) | 2.76393 | − | 4.78727i | 0.115768 | − | 0.200517i | ||||
\(571\) | 2.00000 | − | 3.46410i | 0.0836974 | − | 0.144968i | −0.821138 | − | 0.570730i | \(-0.806660\pi\) |
0.904835 | + | 0.425762i | \(0.139994\pi\) | |||||||
\(572\) | 43.4164 | + | 75.1994i | 1.81533 | + | 3.14425i | ||||
\(573\) | 0.583592 | 0.0243799 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 4.00000 | 0.166812 | ||||||||
\(576\) | 6.50000 | + | 11.2583i | 0.270833 | + | 0.469097i | ||||
\(577\) | 5.18034 | − | 8.97261i | 0.215660 | − | 0.373535i | −0.737816 | − | 0.675002i | \(-0.764143\pi\) |
0.953477 | + | 0.301467i | \(0.0974763\pi\) | |||||||
\(578\) | −14.5344 | + | 25.1744i | −0.604553 | + | 1.04712i | ||||
\(579\) | 7.00000 | + | 12.1244i | 0.290910 | + | 0.503871i | ||||
\(580\) | −6.00000 | −0.249136 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 18.9443 | 0.785265 | ||||||||
\(583\) | 11.4164 | + | 19.7738i | 0.472819 | + | 0.818947i | ||||
\(584\) | 13.9443 | − | 24.1522i | 0.577018 | − | 0.999425i | ||||
\(585\) | 2.23607 | − | 3.87298i | 0.0924500 | − | 0.160128i | ||||
\(586\) | −5.65248 | − | 9.79038i | −0.233502 | − | 0.404437i | ||||
\(587\) | 4.00000 | 0.165098 | 0.0825488 | − | 0.996587i | \(-0.473694\pi\) | ||||
0.0825488 | + | 0.996587i | \(0.473694\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −3.77709 | −0.155632 | ||||||||
\(590\) | 10.0000 | + | 17.3205i | 0.411693 | + | 0.713074i | ||||
\(591\) | −7.76393 | + | 13.4475i | −0.319365 | + | 0.553157i | ||||
\(592\) | −3.47214 | + | 6.01392i | −0.142704 | + | 0.247170i | ||||
\(593\) | 11.9443 | + | 20.6881i | 0.490492 | + | 0.849558i | 0.999940 | − | 0.0109438i | \(-0.00348359\pi\) |
−0.509448 | + | 0.860502i | \(0.670150\pi\) | |||||||
\(594\) | −14.4721 | −0.593799 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −44.8328 | −1.83642 | ||||||||
\(597\) | 13.7082 | + | 23.7433i | 0.561039 | + | 0.971749i | ||||
\(598\) | −20.0000 | + | 34.6410i | −0.817861 | + | 1.41658i | ||||
\(599\) | −6.18034 | + | 10.7047i | −0.252522 | + | 0.437381i | −0.964219 | − | 0.265105i | \(-0.914593\pi\) |
0.711698 | + | 0.702486i | \(0.247927\pi\) | |||||||
\(600\) | 1.11803 | + | 1.93649i | 0.0456435 | + | 0.0790569i | ||||
\(601\) | −38.9443 | −1.58857 | −0.794285 | − | 0.607545i | \(-0.792154\pi\) | ||||
−0.794285 | + | 0.607545i | \(0.792154\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −4.00000 | −0.162893 | ||||||||
\(604\) | 24.0000 | + | 41.5692i | 0.976546 | + | 1.69143i | ||||
\(605\) | −15.4443 | + | 26.7503i | −0.627899 | + | 1.08755i | ||||
\(606\) | 15.6525 | − | 27.1109i | 0.635838 | − | 1.10130i | ||||
\(607\) | 19.4164 | + | 33.6302i | 0.788088 | + | 1.36501i | 0.927137 | + | 0.374722i | \(0.122262\pi\) |
−0.139049 | + | 0.990285i | \(0.544405\pi\) | |||||||
\(608\) | 16.5836 | 0.672553 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −4.47214 | −0.181071 | ||||||||
\(611\) | −28.9443 | − | 50.1329i | −1.17096 | − | 2.02816i | ||||
\(612\) | −3.00000 | + | 5.19615i | −0.121268 | + | 0.210042i | ||||
\(613\) | 3.47214 | − | 6.01392i | 0.140238 | − | 0.242900i | −0.787348 | − | 0.616509i | \(-0.788546\pi\) |
0.927586 | + | 0.373609i | \(0.121880\pi\) | |||||||
\(614\) | 16.8328 | + | 29.1553i | 0.679317 | + | 1.17661i | ||||
\(615\) | 2.00000 | 0.0806478 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 16.4721 | 0.663143 | 0.331572 | − | 0.943430i | \(-0.392421\pi\) | ||||
0.331572 | + | 0.943430i | \(0.392421\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 19.7082 | − | 34.1356i | 0.792140 | − | 1.37203i | −0.132500 | − | 0.991183i | \(-0.542300\pi\) |
0.924640 | − | 0.380843i | \(-0.124366\pi\) | |||||||
\(620\) | 2.29180 | − | 3.96951i | 0.0920407 | − | 0.159419i | ||||
\(621\) | −2.00000 | − | 3.46410i | −0.0802572 | − | 0.139010i | ||||
\(622\) | 57.8885 | 2.32112 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 4.47214 | 0.179029 | ||||||||
\(625\) | −0.500000 | − | 0.866025i | −0.0200000 | − | 0.0346410i | ||||
\(626\) | 19.4721 | − | 33.7267i | 0.778263 | − | 1.34799i | ||||
\(627\) | −8.00000 | + | 13.8564i | −0.319489 | + | 0.553372i | ||||
\(628\) | −0.708204 | − | 1.22665i | −0.0282604 | − | 0.0489485i | ||||
\(629\) | −13.8885 | −0.553773 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 30.8328 | 1.22744 | 0.613718 | − | 0.789526i | \(-0.289673\pi\) | ||||
0.613718 | + | 0.789526i | \(0.289673\pi\) | |||||||
\(632\) | 14.4721 | + | 25.0665i | 0.575671 | + | 0.997091i | ||||
\(633\) | 8.47214 | − | 14.6742i | 0.336737 | − | 0.583246i | ||||
\(634\) | 16.0557 | − | 27.8093i | 0.637654 | − | 1.10445i | ||||
\(635\) | 2.47214 | + | 4.28187i | 0.0981037 | + | 0.169921i | ||||
\(636\) | −10.5836 | −0.419667 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 28.9443 | 1.14591 | ||||||||
\(639\) | −2.76393 | − | 4.78727i | −0.109339 | − | 0.189382i | ||||
\(640\) | −7.82624 | + | 13.5554i | −0.309359 | + | 0.535826i | ||||
\(641\) | −8.41641 | + | 14.5776i | −0.332428 | + | 0.575782i | −0.982987 | − | 0.183673i | \(-0.941201\pi\) |
0.650559 | + | 0.759455i | \(0.274535\pi\) | |||||||
\(642\) | −14.4721 | − | 25.0665i | −0.571170 | − | 0.989295i | ||||
\(643\) | 15.0557 | 0.593740 | 0.296870 | − | 0.954918i | \(-0.404057\pi\) | ||||
0.296870 | + | 0.954918i | \(0.404057\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 8.94427 | 0.352180 | ||||||||
\(646\) | 5.52786 | + | 9.57454i | 0.217491 | + | 0.376705i | ||||
\(647\) | −0.944272 | + | 1.63553i | −0.0371232 | + | 0.0642992i | −0.883990 | − | 0.467506i | \(-0.845153\pi\) |
0.846867 | + | 0.531805i | \(0.178486\pi\) | |||||||
\(648\) | 1.11803 | − | 1.93649i | 0.0439205 | − | 0.0760726i | ||||
\(649\) | −28.9443 | − | 50.1329i | −1.13616 | − | 1.96789i | ||||
\(650\) | 10.0000 | 0.392232 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −50.8328 | −1.99077 | ||||||||
\(653\) | 11.2918 | + | 19.5580i | 0.441882 | + | 0.765362i | 0.997829 | − | 0.0658554i | \(-0.0209776\pi\) |
−0.555947 | + | 0.831218i | \(0.687644\pi\) | |||||||
\(654\) | −2.23607 | + | 3.87298i | −0.0874372 | + | 0.151446i | ||||
\(655\) | 2.00000 | − | 3.46410i | 0.0781465 | − | 0.135354i | ||||
\(656\) | 1.00000 | + | 1.73205i | 0.0390434 | + | 0.0676252i | ||||
\(657\) | 12.4721 | 0.486584 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 21.3050 | 0.829923 | 0.414962 | − | 0.909839i | \(-0.363795\pi\) | ||||
0.414962 | + | 0.909839i | \(0.363795\pi\) | |||||||
\(660\) | −9.70820 | − | 16.8151i | −0.377891 | − | 0.654527i | ||||
\(661\) | −17.9443 | + | 31.0804i | −0.697951 | + | 1.20889i | 0.271224 | + | 0.962516i | \(0.412571\pi\) |
−0.969176 | + | 0.246371i | \(0.920762\pi\) | |||||||
\(662\) | 1.05573 | − | 1.82857i | 0.0410320 | − | 0.0710696i | ||||
\(663\) | 4.47214 | + | 7.74597i | 0.173683 | + | 0.300828i | ||||
\(664\) | −37.8885 | −1.47036 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 15.5279 | 0.601693 | ||||||||
\(667\) | 4.00000 | + | 6.92820i | 0.154881 | + | 0.268261i | ||||
\(668\) | −12.0000 | + | 20.7846i | −0.464294 | + | 0.804181i | ||||
\(669\) | −6.47214 | + | 11.2101i | −0.250227 | + | 0.433406i | ||||
\(670\) | −4.47214 | − | 7.74597i | −0.172774 | − | 0.299253i | ||||
\(671\) | 12.9443 | 0.499708 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 8.83282 | 0.340480 | 0.170240 | − | 0.985403i | \(-0.445546\pi\) | ||||
0.170240 | + | 0.985403i | \(0.445546\pi\) | |||||||
\(674\) | −26.7082 | − | 46.2600i | −1.02876 | − | 1.78187i | ||||
\(675\) | −0.500000 | + | 0.866025i | −0.0192450 | + | 0.0333333i | ||||
\(676\) | −10.5000 | + | 18.1865i | −0.403846 | + | 0.699482i | ||||
\(677\) | 10.5279 | + | 18.2348i | 0.404619 | + | 0.700820i | 0.994277 | − | 0.106833i | \(-0.0340709\pi\) |
−0.589658 | + | 0.807653i | \(0.700738\pi\) | |||||||
\(678\) | −1.05573 | −0.0405450 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −4.47214 | −0.171499 | ||||||||
\(681\) | 0.472136 | + | 0.817763i | 0.0180923 | + | 0.0313368i | ||||
\(682\) | −11.0557 | + | 19.1491i | −0.423346 | + | 0.733256i | ||||
\(683\) | 0.944272 | − | 1.63553i | 0.0361316 | − | 0.0625817i | −0.847394 | − | 0.530964i | \(-0.821830\pi\) |
0.883526 | + | 0.468383i | \(0.155163\pi\) | |||||||
\(684\) | −3.70820 | − | 6.42280i | −0.141787 | − | 0.245582i | ||||
\(685\) | 3.52786 | 0.134793 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −23.8885 | −0.911405 | ||||||||
\(688\) | 4.47214 | + | 7.74597i | 0.170499 | + | 0.295312i | ||||
\(689\) | −7.88854 | + | 13.6634i | −0.300530 | + | 0.520533i | ||||
\(690\) | 4.47214 | − | 7.74597i | 0.170251 | − | 0.294884i | ||||
\(691\) | 22.1803 | + | 38.4175i | 0.843780 | + | 1.46147i | 0.886677 | + | 0.462390i | \(0.153008\pi\) |
−0.0428967 | + | 0.999080i | \(0.513659\pi\) | |||||||
\(692\) | 8.83282 | 0.335773 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 17.8885 | 0.679040 | ||||||||
\(695\) | 3.70820 | + | 6.42280i | 0.140660 | + | 0.243631i | ||||
\(696\) | −2.23607 | + | 3.87298i | −0.0847579 | + | 0.146805i | ||||
\(697\) | −2.00000 | + | 3.46410i | −0.0757554 | + | 0.131212i | ||||
\(698\) | 13.2918 | + | 23.0221i | 0.503102 | + | 0.871398i | ||||
\(699\) | −9.41641 | −0.356161 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −34.0000 | −1.28416 | −0.642081 | − | 0.766637i | \(-0.721929\pi\) | ||||
−0.642081 | + | 0.766637i | \(0.721929\pi\) | |||||||
\(702\) | −5.00000 | − | 8.66025i | −0.188713 | − | 0.326860i | ||||
\(703\) | 8.58359 | − | 14.8672i | 0.323736 | − | 0.560728i | ||||
\(704\) | 42.0689 | − | 72.8654i | 1.58553 | − | 2.74622i | ||||
\(705\) | 6.47214 | + | 11.2101i | 0.243755 | + | 0.422196i | ||||
\(706\) | 17.6393 | 0.663865 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 26.8328 | 1.00844 | ||||||||
\(709\) | −12.8885 | − | 22.3236i | −0.484039 | − | 0.838381i | 0.515793 | − | 0.856714i | \(-0.327498\pi\) |
−0.999832 | + | 0.0183327i | \(0.994164\pi\) | |||||||
\(710\) | 6.18034 | − | 10.7047i | 0.231944 | − | 0.401739i | ||||
\(711\) | −6.47214 | + | 11.2101i | −0.242724 | + | 0.420410i | ||||
\(712\) | 2.23607 | + | 3.87298i | 0.0838002 | + | 0.145146i | ||||
\(713\) | −6.11146 | −0.228876 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −28.9443 | −1.08245 | ||||||||
\(716\) | −9.70820 | − | 16.8151i | −0.362813 | − | 0.628410i | ||||
\(717\) | 5.23607 | − | 9.06914i | 0.195545 | − | 0.338693i | ||||
\(718\) | 20.6525 | − | 35.7711i | 0.770744 | − | 1.33497i | ||||
\(719\) | −3.41641 | − | 5.91739i | −0.127411 | − | 0.220681i | 0.795262 | − | 0.606266i | \(-0.207333\pi\) |
−0.922673 | + | 0.385584i | \(0.874000\pi\) | |||||||
\(720\) | −1.00000 | −0.0372678 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 28.8197 | 1.07256 | ||||||||
\(723\) | −9.47214 | − | 16.4062i | −0.352273 | − | 0.610154i | ||||
\(724\) | 1.58359 | − | 2.74286i | 0.0588537 | − | 0.101938i | ||||
\(725\) | 1.00000 | − | 1.73205i | 0.0371391 | − | 0.0643268i | ||||
\(726\) | 34.5344 | + | 59.8154i | 1.28169 | + | 2.21996i | ||||
\(727\) | 38.8328 | 1.44023 | 0.720115 | − | 0.693855i | \(-0.244089\pi\) | ||||
0.720115 | + | 0.693855i | \(0.244089\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 13.9443 | + | 24.1522i | 0.516101 | + | 0.893913i | ||||
\(731\) | −8.94427 | + | 15.4919i | −0.330816 | + | 0.572990i | ||||
\(732\) | −3.00000 | + | 5.19615i | −0.110883 | + | 0.192055i | ||||
\(733\) | 5.29180 | + | 9.16566i | 0.195457 | + | 0.338541i | 0.947050 | − | 0.321085i | \(-0.104048\pi\) |
−0.751593 | + | 0.659627i | \(0.770714\pi\) | |||||||
\(734\) | 6.83282 | 0.252204 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 26.8328 | 0.989071 | ||||||||
\(737\) | 12.9443 | + | 22.4201i | 0.476808 | + | 0.825856i | ||||
\(738\) | 2.23607 | − | 3.87298i | 0.0823108 | − | 0.142566i | ||||
\(739\) | 2.94427 | − | 5.09963i | 0.108307 | − | 0.187593i | −0.806778 | − | 0.590855i | \(-0.798790\pi\) |
0.915084 | + | 0.403262i | \(0.132124\pi\) | |||||||
\(740\) | 10.4164 | + | 18.0417i | 0.382915 | + | 0.663228i | ||||
\(741\) | −11.0557 | −0.406142 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 34.8328 | 1.27789 | 0.638946 | − | 0.769252i | \(-0.279371\pi\) | ||||
0.638946 | + | 0.769252i | \(0.279371\pi\) | |||||||
\(744\) | −1.70820 | − | 2.95870i | −0.0626258 | − | 0.108471i | ||||
\(745\) | 7.47214 | − | 12.9421i | 0.273758 | − | 0.474163i | ||||
\(746\) | 6.70820 | − | 11.6190i | 0.245605 | − | 0.425400i | ||||
\(747\) | −8.47214 | − | 14.6742i | −0.309979 | − | 0.536900i | ||||
\(748\) | 38.8328 | 1.41987 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | −2.23607 | −0.0816497 | ||||||||
\(751\) | 10.4721 | + | 18.1383i | 0.382134 | + | 0.661875i | 0.991367 | − | 0.131116i | \(-0.0418561\pi\) |
−0.609233 | + | 0.792991i | \(0.708523\pi\) | |||||||
\(752\) | −6.47214 | + | 11.2101i | −0.236015 | + | 0.408789i | ||||
\(753\) | 8.47214 | − | 14.6742i | 0.308742 | − | 0.534756i | ||||
\(754\) | 10.0000 | + | 17.3205i | 0.364179 | + | 0.630776i | ||||
\(755\) | −16.0000 | −0.582300 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 31.8885 | 1.15901 | 0.579504 | − | 0.814969i | \(-0.303246\pi\) | ||||
0.579504 | + | 0.814969i | \(0.303246\pi\) | |||||||
\(758\) | −42.3607 | − | 73.3708i | −1.53861 | − | 2.66495i | ||||
\(759\) | −12.9443 | + | 22.4201i | −0.469847 | + | 0.813799i | ||||
\(760\) | 2.76393 | − | 4.78727i | 0.100258 | − | 0.173653i | ||||
\(761\) | −13.9443 | − | 24.1522i | −0.505479 | − | 0.875516i | −0.999980 | − | 0.00633874i | \(-0.997982\pi\) |
0.494500 | − | 0.869177i | \(-0.335351\pi\) | |||||||
\(762\) | 11.0557 | 0.400507 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 1.75078 | 0.0633409 | ||||||||
\(765\) | −1.00000 | − | 1.73205i | −0.0361551 | − | 0.0626224i | ||||
\(766\) | 8.94427 | − | 15.4919i | 0.323170 | − | 0.559746i | ||||
\(767\) | 20.0000 | − | 34.6410i | 0.722158 | − | 1.25081i | ||||
\(768\) | 4.50000 | + | 7.79423i | 0.162380 | + | 0.281250i | ||||
\(769\) | 52.8328 | 1.90520 | 0.952600 | − | 0.304226i | \(-0.0983976\pi\) | ||||
0.952600 | + | 0.304226i | \(0.0983976\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −18.9443 | −0.682261 | ||||||||
\(772\) | 21.0000 | + | 36.3731i | 0.755807 | + | 1.30910i | ||||
\(773\) | −21.4721 | + | 37.1908i | −0.772299 | + | 1.33766i | 0.164001 | + | 0.986460i | \(0.447560\pi\) |
−0.936300 | + | 0.351201i | \(0.885773\pi\) | |||||||
\(774\) | 10.0000 | − | 17.3205i | 0.359443 | − | 0.622573i | ||||
\(775\) | 0.763932 | + | 1.32317i | 0.0274412 | + | 0.0475296i | ||||
\(776\) | 18.9443 | 0.680060 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 15.5279 | 0.556701 | ||||||||
\(779\) | −2.47214 | − | 4.28187i | −0.0885735 | − | 0.153414i | ||||
\(780\) | 6.70820 | − | 11.6190i | 0.240192 | − | 0.416025i | ||||
\(781\) | −17.8885 | + | 30.9839i | −0.640102 | + | 1.10869i | ||||
\(782\) | 8.94427 | + | 15.4919i | 0.319847 | + | 0.553990i | ||||
\(783\) | −2.00000 | −0.0714742 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0.472136 | 0.0168513 | ||||||||
\(786\) | −4.47214 | − | 7.74597i | −0.159516 | − | 0.276289i | ||||
\(787\) | 15.5279 | − | 26.8950i | 0.553509 | − | 0.958705i | −0.444509 | − | 0.895774i | \(-0.646622\pi\) |
0.998018 | − | 0.0629307i | \(-0.0200447\pi\) | |||||||
\(788\) | −23.2918 | + | 40.3426i | −0.829736 | + | 1.43714i | ||||
\(789\) | −3.52786 | − | 6.11044i | −0.125595 | − | 0.217537i | ||||
\(790\) | −28.9443 | −1.02979 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | −14.4721 | −0.514245 | ||||||||
\(793\) | 4.47214 | + | 7.74597i | 0.158810 | + | 0.275067i | ||||
\(794\) | 15.0000 | − | 25.9808i | 0.532330 | − | 0.922023i | ||||
\(795\) | 1.76393 | − | 3.05522i | 0.0625602 | − | 0.108357i | ||||
\(796\) | 41.1246 | + | 71.2299i | 1.45762 | + | 2.52468i | ||||
\(797\) | 18.9443 | 0.671041 | 0.335520 | − | 0.942033i | \(-0.391088\pi\) | ||||
0.335520 | + | 0.942033i | \(0.391088\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −25.8885 | −0.915871 | ||||||||
\(800\) | −3.35410 | − | 5.80948i | −0.118585 | − | 0.205396i | ||||
\(801\) | −1.00000 | + | 1.73205i | −0.0353333 | + | 0.0611990i | ||||
\(802\) | 11.1803 | − | 19.3649i | 0.394792 | − | 0.683799i | ||||
\(803\) | −40.3607 | − | 69.9067i | −1.42430 | − | 2.46696i | ||||
\(804\) | −12.0000 | −0.423207 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −15.2786 | −0.538167 | ||||||||
\(807\) | 5.94427 | + | 10.2958i | 0.209248 | + | 0.362429i | ||||
\(808\) | 15.6525 | − | 27.1109i | 0.550652 | − | 0.953758i | ||||
\(809\) | −19.4721 | + | 33.7267i | −0.684604 | + | 1.18577i | 0.288957 | + | 0.957342i | \(0.406691\pi\) |
−0.973561 | + | 0.228427i | \(0.926642\pi\) | |||||||
\(810\) | 1.11803 | + | 1.93649i | 0.0392837 | + | 0.0680414i | ||||
\(811\) | −55.4164 | −1.94593 | −0.972967 | − | 0.230946i | \(-0.925818\pi\) | ||||
−0.972967 | + | 0.230946i | \(0.925818\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 1.52786 | 0.0535845 | ||||||||
\(814\) | −50.2492 | − | 87.0342i | −1.76123 | − | 3.05055i | ||||
\(815\) | 8.47214 | − | 14.6742i | 0.296766 | − | 0.514014i | ||||
\(816\) | 1.00000 | − | 1.73205i | 0.0350070 | − | 0.0606339i | ||||
\(817\) | −11.0557 | − | 19.1491i | −0.386791 | − | 0.669942i | ||||
\(818\) | 26.5836 | 0.929474 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 6.00000 | 0.209529 | ||||||||
\(821\) | −16.8885 | − | 29.2518i | −0.589414 | − | 1.02090i | −0.994309 | − | 0.106532i | \(-0.966025\pi\) |
0.404895 | − | 0.914363i | \(-0.367308\pi\) | |||||||
\(822\) | 3.94427 | − | 6.83168i | 0.137572 | − | 0.238282i | ||||
\(823\) | −22.4721 | + | 38.9229i | −0.783329 | + | 1.35677i | 0.146663 | + | 0.989187i | \(0.453147\pi\) |
−0.929992 | + | 0.367580i | \(0.880186\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 6.47214 | 0.225331 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 12.9443 | 0.450116 | 0.225058 | − | 0.974345i | \(-0.427743\pi\) | ||||
0.225058 | + | 0.974345i | \(0.427743\pi\) | |||||||
\(828\) | −6.00000 | − | 10.3923i | −0.208514 | − | 0.361158i | ||||
\(829\) | −6.52786 | + | 11.3066i | −0.226722 | + | 0.392694i | −0.956835 | − | 0.290633i | \(-0.906134\pi\) |
0.730113 | + | 0.683327i | \(0.239468\pi\) | |||||||
\(830\) | 18.9443 | − | 32.8124i | 0.657565 | − | 1.13894i | ||||
\(831\) | −9.47214 | − | 16.4062i | −0.328585 | − | 0.569125i | ||||
\(832\) | 58.1378 | 2.01556 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 16.5836 | 0.574243 | ||||||||
\(835\) | −4.00000 | − | 6.92820i | −0.138426 | − | 0.239760i | ||||
\(836\) | −24.0000 | + | 41.5692i | −0.830057 | + | 1.43770i | ||||
\(837\) | 0.763932 | − | 1.32317i | 0.0264054 | − | 0.0457354i | ||||
\(838\) | 33.4164 | + | 57.8789i | 1.15435 | + | 1.99939i | ||||
\(839\) | −54.8328 | −1.89304 | −0.946520 | − | 0.322647i | \(-0.895427\pi\) | ||||
−0.946520 | + | 0.322647i | \(0.895427\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −25.0000 | −0.862069 | ||||||||
\(842\) | 24.5967 | + | 42.6028i | 0.847660 | + | 1.46819i | ||||
\(843\) | 5.47214 | − | 9.47802i | 0.188470 | − | 0.326440i | ||||
\(844\) | 25.4164 | − | 44.0225i | 0.874869 | − | 1.51532i | ||||
\(845\) | −3.50000 | − | 6.06218i | −0.120404 | − | 0.208545i | ||||
\(846\) | 28.9443 | 0.995125 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 3.52786 | 0.121147 | ||||||||
\(849\) | 6.00000 | + | 10.3923i | 0.205919 | + | 0.356663i | ||||
\(850\) | 2.23607 | − | 3.87298i | 0.0766965 | − | 0.132842i | ||||
\(851\) | 13.8885 | − | 24.0557i | 0.476093 | − | 0.824618i | ||||
\(852\) | −8.29180 | − | 14.3618i | −0.284072 | − | 0.492028i | ||||
\(853\) | 31.3050 | 1.07186 | 0.535931 | − | 0.844262i | \(-0.319961\pi\) | ||||
0.535931 | + | 0.844262i | \(0.319961\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 2.47214 | 0.0845453 | ||||||||
\(856\) | −14.4721 | − | 25.0665i | −0.494647 | − | 0.856754i | ||||
\(857\) | 18.4164 | − | 31.8982i | 0.629093 | − | 1.08962i | −0.358642 | − | 0.933475i | \(-0.616760\pi\) |
0.987734 | − | 0.156145i | \(-0.0499067\pi\) | |||||||
\(858\) | −32.3607 | + | 56.0503i | −1.10478 | + | 1.91353i | ||||
\(859\) | 25.2361 | + | 43.7102i | 0.861044 | + | 1.49137i | 0.870923 | + | 0.491420i | \(0.163522\pi\) |
−0.00987923 | + | 0.999951i | \(0.503145\pi\) | |||||||
\(860\) | 26.8328 | 0.914991 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 41.3050 | 1.40685 | ||||||||
\(863\) | −10.9443 | − | 18.9560i | −0.372547 | − | 0.645271i | 0.617409 | − | 0.786642i | \(-0.288182\pi\) |
−0.989957 | + | 0.141371i | \(0.954849\pi\) | |||||||
\(864\) | −3.35410 | + | 5.80948i | −0.114109 | + | 0.197642i | ||||
\(865\) | −1.47214 | + | 2.54981i | −0.0500541 | + | 0.0866963i | ||||
\(866\) | −18.4164 | − | 31.8982i | −0.625815 | − | 1.08394i | ||||
\(867\) | −13.0000 | −0.441503 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 83.7771 | 2.84194 | ||||||||
\(870\) | −2.23607 | − | 3.87298i | −0.0758098 | − | 0.131306i | ||||
\(871\) | −8.94427 | + | 15.4919i | −0.303065 | + | 0.524924i | ||||
\(872\) | −2.23607 | + | 3.87298i | −0.0757228 | + | 0.131156i | ||||
\(873\) | 4.23607 | + | 7.33708i | 0.143369 | + | 0.248323i | ||||
\(874\) | −22.1115 | −0.747931 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 37.4164 | 1.26418 | ||||||||
\(877\) | 28.4164 | + | 49.2187i | 0.959554 | + | 1.66200i | 0.723585 | + | 0.690236i | \(0.242493\pi\) |
0.235969 | + | 0.971761i | \(0.424174\pi\) | |||||||
\(878\) | −1.70820 | + | 2.95870i | −0.0576491 | + | 0.0998512i | ||||
\(879\) | 2.52786 | − | 4.37839i | 0.0852627 | − | 0.147679i | ||||
\(880\) | 3.23607 | + | 5.60503i | 0.109088 | + | 0.188946i | ||||
\(881\) | 27.8885 | 0.939589 | 0.469794 | − | 0.882776i | \(-0.344328\pi\) | ||||
0.469794 | + | 0.882776i | \(0.344328\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −37.8885 | −1.27505 | −0.637526 | − | 0.770429i | \(-0.720042\pi\) | ||||
−0.637526 | + | 0.770429i | \(0.720042\pi\) | |||||||
\(884\) | 13.4164 | + | 23.2379i | 0.451243 | + | 0.781575i | ||||
\(885\) | −4.47214 | + | 7.74597i | −0.150329 | + | 0.260378i | ||||
\(886\) | −8.94427 | + | 15.4919i | −0.300489 | + | 0.520462i | ||||
\(887\) | −15.4164 | − | 26.7020i | −0.517632 | − | 0.896565i | −0.999790 | − | 0.0204812i | \(-0.993480\pi\) |
0.482158 | − | 0.876084i | \(-0.339853\pi\) | |||||||
\(888\) | 15.5279 | 0.521081 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −4.47214 | −0.149906 | ||||||||
\(891\) | −3.23607 | − | 5.60503i | −0.108412 | − | 0.187776i | ||||
\(892\) | −19.4164 | + | 33.6302i | −0.650109 | + | 1.12602i | ||||
\(893\) | 16.0000 | − | 27.7128i | 0.535420 | − | 0.927374i | ||||
\(894\) | −16.7082 | − | 28.9395i | −0.558806 | − | 0.967880i | ||||
\(895\) | 6.47214 | 0.216340 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −17.8885 | −0.597281 | ||||||||
\(898\) | −15.6525 | − | 27.1109i | −0.522330 | − | 0.904702i | ||||
\(899\) | −1.52786 | + | 2.64634i | −0.0509571 | + | 0.0882603i | ||||
\(900\) | −1.50000 | + | 2.59808i | −0.0500000 | + | 0.0866025i | ||||
\(901\) | 3.52786 | + | 6.11044i | 0.117530 | + | 0.203568i | ||||
\(902\) | −28.9443 | −0.963739 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −1.05573 | −0.0351130 | ||||||||
\(905\) | 0.527864 | + | 0.914287i | 0.0175468 | + | 0.0303919i | ||||
\(906\) | −17.8885 | + | 30.9839i | −0.594307 | + | 1.02937i | ||||
\(907\) | −26.9443 | + | 46.6688i | −0.894670 | + | 1.54961i | −0.0604572 | + | 0.998171i | \(0.519256\pi\) |
−0.834213 | + | 0.551443i | \(0.814077\pi\) | |||||||
\(908\) | 1.41641 | + | 2.45329i | 0.0470051 | + | 0.0814153i | ||||
\(909\) | 14.0000 | 0.464351 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 46.2492 | 1.53231 | 0.766153 | − | 0.642659i | \(-0.222169\pi\) | ||||
0.766153 | + | 0.642659i | \(0.222169\pi\) | |||||||
\(912\) | 1.23607 | + | 2.14093i | 0.0409303 | + | 0.0708934i | ||||
\(913\) | −54.8328 | + | 94.9732i | −1.81470 | + | 3.14315i | ||||
\(914\) | 7.76393 | − | 13.4475i | 0.256808 | − | 0.444805i | ||||
\(915\) | −1.00000 | − | 1.73205i | −0.0330590 | − | 0.0572598i | ||||
\(916\) | −71.6656 | −2.36790 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | −4.47214 | −0.147602 | ||||||||
\(919\) | 17.5279 | + | 30.3592i | 0.578191 | + | 1.00146i | 0.995687 | + | 0.0927772i | \(0.0295744\pi\) |
−0.417496 | + | 0.908679i | \(0.637092\pi\) | |||||||
\(920\) | 4.47214 | − | 7.74597i | 0.147442 | − | 0.255377i | ||||
\(921\) | −7.52786 | + | 13.0386i | −0.248052 | + | 0.429638i | ||||
\(922\) | −4.34752 | − | 7.53013i | −0.143178 | − | 0.247992i | ||||
\(923\) | −24.7214 | −0.813713 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −6.94427 | −0.228326 | ||||||||
\(926\) | 23.4164 | + | 40.5584i | 0.769511 | + | 1.33283i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 6.70820 | − | 11.6190i | 0.220208 | − | 0.381411i | ||||
\(929\) | −8.05573 | − | 13.9529i | −0.264300 | − | 0.457781i | 0.703080 | − | 0.711111i | \(-0.251808\pi\) |
−0.967380 | + | 0.253330i | \(0.918474\pi\) | |||||||
\(930\) | 3.41641 | 0.112028 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −28.2492 | −0.925334 | ||||||||
\(933\) | 12.9443 | + | 22.4201i | 0.423776 | + | 0.734002i | ||||
\(934\) | 10.0000 | − | 17.3205i | 0.327210 | − | 0.566744i | ||||
\(935\) | −6.47214 | + | 11.2101i | −0.211661 | + | 0.366608i | ||||
\(936\) | −5.00000 | − | 8.66025i | −0.163430 | − | 0.283069i | ||||
\(937\) | 52.4721 | 1.71419 | 0.857095 | − | 0.515158i | \(-0.172267\pi\) | ||||
0.857095 | + | 0.515158i | \(0.172267\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 17.4164 | 0.568363 | ||||||||
\(940\) | 19.4164 | + | 33.6302i | 0.633293 | + | 1.09690i | ||||
\(941\) | −15.0000 | + | 25.9808i | −0.488986 | + | 0.846949i | −0.999920 | − | 0.0126715i | \(-0.995966\pi\) |
0.510934 | + | 0.859620i | \(0.329300\pi\) | |||||||
\(942\) | 0.527864 | − | 0.914287i | 0.0171987 | − | 0.0297891i | ||||
\(943\) | −4.00000 | − | 6.92820i | −0.130258 | − | 0.225613i | ||||
\(944\) | −8.94427 | −0.291111 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −129.443 | −4.20855 | ||||||||
\(947\) | 8.94427 | + | 15.4919i | 0.290650 | + | 0.503420i | 0.973964 | − | 0.226705i | \(-0.0727952\pi\) |
−0.683314 | + | 0.730125i | \(0.739462\pi\) | |||||||
\(948\) | −19.4164 | + | 33.6302i | −0.630616 | + | 1.09226i | ||||
\(949\) | 27.8885 | − | 48.3044i | 0.905300 | − | 1.56803i | ||||
\(950\) | 2.76393 | + | 4.78727i | 0.0896738 | + | 0.155320i | ||||
\(951\) | 14.3607 | 0.465677 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −33.4164 | −1.08246 | −0.541232 | − | 0.840873i | \(-0.682042\pi\) | ||||
−0.541232 | + | 0.840873i | \(0.682042\pi\) | |||||||
\(954\) | −3.94427 | − | 6.83168i | −0.127701 | − | 0.221184i | ||||
\(955\) | −0.291796 | + | 0.505406i | −0.00944230 | + | 0.0163545i | ||||
\(956\) | 15.7082 | − | 27.2074i | 0.508040 | − | 0.879950i | ||||
\(957\) | 6.47214 | + | 11.2101i | 0.209214 | + | 0.362370i | ||||
\(958\) | −40.0000 | −1.29234 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | −13.0000 | −0.419573 | ||||||||
\(961\) | 14.3328 | + | 24.8252i | 0.462349 | + | 0.800812i | ||||
\(962\) | 34.7214 | − | 60.1392i | 1.11946 | − | 1.93896i | ||||
\(963\) | 6.47214 | − | 11.2101i | 0.208562 | − | 0.361239i | ||||
\(964\) | −28.4164 | − | 49.2187i | −0.915231 | − | 1.58523i | ||||
\(965\) | −14.0000 | −0.450676 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 25.8885 | 0.832519 | 0.416260 | − | 0.909246i | \(-0.363341\pi\) | ||||
0.416260 | + | 0.909246i | \(0.363341\pi\) | |||||||
\(968\) | 34.5344 | + | 59.8154i | 1.10998 | + | 1.92254i | ||||
\(969\) | −2.47214 | + | 4.28187i | −0.0794164 | + | 0.137553i | ||||
\(970\) | −9.47214 | + | 16.4062i | −0.304132 | + | 0.526772i | ||||
\(971\) | 20.4721 | + | 35.4588i | 0.656982 | + | 1.13793i | 0.981393 | + | 0.192010i | \(0.0615006\pi\) |
−0.324411 | + | 0.945916i | \(0.605166\pi\) | |||||||
\(972\) | 3.00000 | 0.0962250 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 46.8328 | 1.50062 | ||||||||
\(975\) | 2.23607 | + | 3.87298i | 0.0716115 | + | 0.124035i | ||||
\(976\) | 1.00000 | − | 1.73205i | 0.0320092 | − | 0.0554416i | ||||
\(977\) | −15.2918 | + | 26.4862i | −0.489228 | + | 0.847368i | −0.999923 | − | 0.0123942i | \(-0.996055\pi\) |
0.510695 | + | 0.859762i | \(0.329388\pi\) | |||||||
\(978\) | −18.9443 | − | 32.8124i | −0.605771 | − | 1.04923i | ||||
\(979\) | 12.9443 | 0.413701 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −2.00000 | −0.0638551 | ||||||||
\(982\) | −23.8197 | − | 41.2569i | −0.760116 | − | 1.31656i | ||||
\(983\) | −11.4164 | + | 19.7738i | −0.364127 | + | 0.630686i | −0.988636 | − | 0.150332i | \(-0.951966\pi\) |
0.624509 | + | 0.781018i | \(0.285299\pi\) | |||||||
\(984\) | 2.23607 | − | 3.87298i | 0.0712832 | − | 0.123466i | ||||
\(985\) | −7.76393 | − | 13.4475i | −0.247379 | − | 0.428474i | ||||
\(986\) | 8.94427 | 0.284844 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −33.1672 | −1.05519 | ||||||||
\(989\) | −17.8885 | − | 30.9839i | −0.568823 | − | 0.985230i | ||||
\(990\) | 7.23607 | − | 12.5332i | 0.229977 | − | 0.398332i | ||||
\(991\) | −2.47214 | + | 4.28187i | −0.0785300 | + | 0.136018i | −0.902616 | − | 0.430447i | \(-0.858356\pi\) |
0.824086 | + | 0.566465i | \(0.191689\pi\) | |||||||
\(992\) | 5.12461 | + | 8.87609i | 0.162707 | + | 0.281816i | ||||
\(993\) | 0.944272 | 0.0299656 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −27.4164 | −0.869159 | ||||||||
\(996\) | −25.4164 | − | 44.0225i | −0.805350 | − | 1.39491i | ||||
\(997\) | −2.70820 | + | 4.69075i | −0.0857697 | + | 0.148557i | −0.905719 | − | 0.423879i | \(-0.860668\pi\) |
0.819949 | + | 0.572436i | \(0.194002\pi\) | |||||||
\(998\) | −15.5279 | + | 26.8950i | −0.491526 | + | 0.851348i | ||||
\(999\) | 3.47214 | + | 6.01392i | 0.109854 | + | 0.190272i |
(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 | 735.2.i.i.361.2 | 4 | ||
7.2 | even | 3 | inner | 735.2.i.i.226.2 | 4 | ||
7.3 | odd | 6 | 105.2.a.b.1.1 | ✓ | 2 | ||
7.4 | even | 3 | 735.2.a.k.1.1 | 2 | |||
7.5 | odd | 6 | 735.2.i.k.226.2 | 4 | |||
7.6 | odd | 2 | 735.2.i.k.361.2 | 4 | |||
21.11 | odd | 6 | 2205.2.a.w.1.2 | 2 | |||
21.17 | even | 6 | 315.2.a.d.1.2 | 2 | |||
28.3 | even | 6 | 1680.2.a.v.1.1 | 2 | |||
35.3 | even | 12 | 525.2.d.c.274.3 | 4 | |||
35.4 | even | 6 | 3675.2.a.y.1.2 | 2 | |||
35.17 | even | 12 | 525.2.d.c.274.2 | 4 | |||
35.24 | odd | 6 | 525.2.a.g.1.2 | 2 | |||
56.3 | even | 6 | 6720.2.a.cs.1.2 | 2 | |||
56.45 | odd | 6 | 6720.2.a.cx.1.1 | 2 | |||
84.59 | odd | 6 | 5040.2.a.bw.1.2 | 2 | |||
105.17 | odd | 12 | 1575.2.d.d.1324.4 | 4 | |||
105.38 | odd | 12 | 1575.2.d.d.1324.1 | 4 | |||
105.59 | even | 6 | 1575.2.a.r.1.1 | 2 | |||
140.59 | even | 6 | 8400.2.a.cx.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
105.2.a.b.1.1 | ✓ | 2 | 7.3 | odd | 6 | ||
315.2.a.d.1.2 | 2 | 21.17 | even | 6 | |||
525.2.a.g.1.2 | 2 | 35.24 | odd | 6 | |||
525.2.d.c.274.2 | 4 | 35.17 | even | 12 | |||
525.2.d.c.274.3 | 4 | 35.3 | even | 12 | |||
735.2.a.k.1.1 | 2 | 7.4 | even | 3 | |||
735.2.i.i.226.2 | 4 | 7.2 | even | 3 | inner | ||
735.2.i.i.361.2 | 4 | 1.1 | even | 1 | trivial | ||
735.2.i.k.226.2 | 4 | 7.5 | odd | 6 | |||
735.2.i.k.361.2 | 4 | 7.6 | odd | 2 | |||
1575.2.a.r.1.1 | 2 | 105.59 | even | 6 | |||
1575.2.d.d.1324.1 | 4 | 105.38 | odd | 12 | |||
1575.2.d.d.1324.4 | 4 | 105.17 | odd | 12 | |||
1680.2.a.v.1.1 | 2 | 28.3 | even | 6 | |||
2205.2.a.w.1.2 | 2 | 21.11 | odd | 6 | |||
3675.2.a.y.1.2 | 2 | 35.4 | even | 6 | |||
5040.2.a.bw.1.2 | 2 | 84.59 | odd | 6 | |||
6720.2.a.cs.1.2 | 2 | 56.3 | even | 6 | |||
6720.2.a.cx.1.1 | 2 | 56.45 | odd | 6 | |||
8400.2.a.cx.1.1 | 2 | 140.59 | even | 6 |