Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1805,2,Mod(1,1805)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1805, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1805.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1805 = 5 \cdot 19^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1805.a (trivial) |
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: | yes |
Analytic conductor: | \(14.4129975648\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | 4.4.11344.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 2x^{3} - 4x^{2} + 4x + 3 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 95) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(2.78165\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1805.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.95594 | −1.38306 | −0.691530 | − | 0.722348i | \(-0.743063\pi\) | ||||
−0.691530 | + | 0.722348i | \(0.743063\pi\) | |||||||
\(3\) | −0.296842 | −0.171382 | −0.0856908 | − | 0.996322i | \(-0.527310\pi\) | ||||
−0.0856908 | + | 0.996322i | \(0.527310\pi\) | |||||||
\(4\) | 1.82571 | 0.912855 | ||||||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | 0.580605 | 0.237031 | ||||||||
\(7\) | −3.56331 | −1.34680 | −0.673402 | − | 0.739277i | \(-0.735168\pi\) | ||||
−0.673402 | + | 0.739277i | \(0.735168\pi\) | |||||||
\(8\) | 0.340899 | 0.120526 | ||||||||
\(9\) | −2.91188 | −0.970628 | ||||||||
\(10\) | 1.95594 | 0.618523 | ||||||||
\(11\) | 5.56331 | 1.67740 | 0.838700 | − | 0.544594i | \(-0.183316\pi\) | ||||
0.838700 | + | 0.544594i | \(0.183316\pi\) | |||||||
\(12\) | −0.541947 | −0.156447 | ||||||||
\(13\) | −5.26647 | −1.46065 | −0.730327 | − | 0.683097i | \(-0.760632\pi\) | ||||
−0.730327 | + | 0.683097i | \(0.760632\pi\) | |||||||
\(14\) | 6.96962 | 1.86271 | ||||||||
\(15\) | 0.296842 | 0.0766442 | ||||||||
\(16\) | −4.31820 | −1.07955 | ||||||||
\(17\) | 1.40632 | 0.341082 | 0.170541 | − | 0.985351i | \(-0.445448\pi\) | ||||
0.170541 | + | 0.985351i | \(0.445448\pi\) | |||||||
\(18\) | 5.69548 | 1.34244 | ||||||||
\(19\) | 0 | 0 | ||||||||
\(20\) | −1.82571 | −0.408241 | ||||||||
\(21\) | 1.05774 | 0.230817 | ||||||||
\(22\) | −10.8815 | −2.31995 | ||||||||
\(23\) | −6.96962 | −1.45327 | −0.726633 | − | 0.687025i | \(-0.758916\pi\) | ||||
−0.726633 | + | 0.687025i | \(0.758916\pi\) | |||||||
\(24\) | −0.101193 | −0.0206560 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 10.3009 | 2.02017 | ||||||||
\(27\) | 1.75489 | 0.337730 | ||||||||
\(28\) | −6.50557 | −1.22944 | ||||||||
\(29\) | −1.40632 | −0.261146 | −0.130573 | − | 0.991439i | \(-0.541682\pi\) | ||||
−0.130573 | + | 0.991439i | \(0.541682\pi\) | |||||||
\(30\) | −0.580605 | −0.106004 | ||||||||
\(31\) | −1.75489 | −0.315188 | −0.157594 | − | 0.987504i | \(-0.550374\pi\) | ||||
−0.157594 | + | 0.987504i | \(0.550374\pi\) | |||||||
\(32\) | 7.76435 | 1.37256 | ||||||||
\(33\) | −1.65142 | −0.287476 | ||||||||
\(34\) | −2.75067 | −0.471737 | ||||||||
\(35\) | 3.56331 | 0.602309 | ||||||||
\(36\) | −5.31626 | −0.886043 | ||||||||
\(37\) | −3.61504 | −0.594309 | −0.297155 | − | 0.954829i | \(-0.596038\pi\) | ||||
−0.297155 | + | 0.954829i | \(0.596038\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 1.56331 | 0.250329 | ||||||||
\(40\) | −0.340899 | −0.0539009 | ||||||||
\(41\) | −4.34858 | −0.679134 | −0.339567 | − | 0.940582i | \(-0.610280\pi\) | ||||
−0.339567 | + | 0.940582i | \(0.610280\pi\) | |||||||
\(42\) | −2.06888 | −0.319234 | ||||||||
\(43\) | −3.56331 | −0.543399 | −0.271700 | − | 0.962382i | \(-0.587586\pi\) | ||||
−0.271700 | + | 0.962382i | \(0.587586\pi\) | |||||||
\(44\) | 10.1570 | 1.53122 | ||||||||
\(45\) | 2.91188 | 0.434078 | ||||||||
\(46\) | 13.6322 | 2.00996 | ||||||||
\(47\) | −8.26046 | −1.20491 | −0.602456 | − | 0.798152i | \(-0.705811\pi\) | ||||
−0.602456 | + | 0.798152i | \(0.705811\pi\) | |||||||
\(48\) | 1.28182 | 0.185015 | ||||||||
\(49\) | 5.69716 | 0.813879 | ||||||||
\(50\) | −1.95594 | −0.276612 | ||||||||
\(51\) | −0.417453 | −0.0584552 | ||||||||
\(52\) | −9.61504 | −1.33337 | ||||||||
\(53\) | 7.61504 | 1.04601 | 0.523003 | − | 0.852331i | \(-0.324812\pi\) | ||||
0.523003 | + | 0.852331i | \(0.324812\pi\) | |||||||
\(54\) | −3.43247 | −0.467100 | ||||||||
\(55\) | −5.56331 | −0.750156 | ||||||||
\(56\) | −1.21473 | −0.162325 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 2.75067 | 0.361181 | ||||||||
\(59\) | −9.47519 | −1.23356 | −0.616782 | − | 0.787134i | \(-0.711564\pi\) | ||||
−0.616782 | + | 0.787134i | \(0.711564\pi\) | |||||||
\(60\) | 0.541947 | 0.0699651 | ||||||||
\(61\) | 9.21473 | 1.17983 | 0.589913 | − | 0.807467i | \(-0.299162\pi\) | ||||
0.589913 | + | 0.807467i | \(0.299162\pi\) | |||||||
\(62\) | 3.43247 | 0.435924 | ||||||||
\(63\) | 10.3759 | 1.30725 | ||||||||
\(64\) | −6.55023 | −0.818779 | ||||||||
\(65\) | 5.26647 | 0.653225 | ||||||||
\(66\) | 3.23009 | 0.397596 | ||||||||
\(67\) | 4.76090 | 0.581636 | 0.290818 | − | 0.956778i | \(-0.406073\pi\) | ||||
0.290818 | + | 0.956778i | \(0.406073\pi\) | |||||||
\(68\) | 2.56753 | 0.311358 | ||||||||
\(69\) | 2.06888 | 0.249063 | ||||||||
\(70\) | −6.96962 | −0.833029 | ||||||||
\(71\) | 14.0689 | 1.66967 | 0.834834 | − | 0.550502i | \(-0.185563\pi\) | ||||
0.834834 | + | 0.550502i | \(0.185563\pi\) | |||||||
\(72\) | −0.992660 | −0.116986 | ||||||||
\(73\) | 6.59368 | 0.771732 | 0.385866 | − | 0.922555i | \(-0.373903\pi\) | ||||
0.385866 | + | 0.922555i | \(0.373903\pi\) | |||||||
\(74\) | 7.07082 | 0.821966 | ||||||||
\(75\) | −0.296842 | −0.0342763 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −19.8238 | −2.25913 | ||||||||
\(78\) | −3.05774 | −0.346221 | ||||||||
\(79\) | −5.47519 | −0.616007 | −0.308004 | − | 0.951385i | \(-0.599661\pi\) | ||||
−0.308004 | + | 0.951385i | \(0.599661\pi\) | |||||||
\(80\) | 4.31820 | 0.482790 | ||||||||
\(81\) | 8.21473 | 0.912748 | ||||||||
\(82\) | 8.50557 | 0.939283 | ||||||||
\(83\) | −4.15699 | −0.456289 | −0.228144 | − | 0.973627i | \(-0.573266\pi\) | ||||
−0.228144 | + | 0.973627i | \(0.573266\pi\) | |||||||
\(84\) | 1.93112 | 0.210703 | ||||||||
\(85\) | −1.40632 | −0.152536 | ||||||||
\(86\) | 6.96962 | 0.751554 | ||||||||
\(87\) | 0.417453 | 0.0447557 | ||||||||
\(88\) | 1.89653 | 0.202171 | ||||||||
\(89\) | 9.23009 | 0.978387 | 0.489194 | − | 0.872175i | \(-0.337291\pi\) | ||||
0.489194 | + | 0.872175i | \(0.337291\pi\) | |||||||
\(90\) | −5.69548 | −0.600356 | ||||||||
\(91\) | 18.7660 | 1.96721 | ||||||||
\(92\) | −12.7245 | −1.32662 | ||||||||
\(93\) | 0.520926 | 0.0540175 | ||||||||
\(94\) | 16.1570 | 1.66647 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −2.30478 | −0.235231 | ||||||||
\(97\) | −11.5116 | −1.16882 | −0.584411 | − | 0.811457i | \(-0.698675\pi\) | ||||
−0.584411 | + | 0.811457i | \(0.698675\pi\) | |||||||
\(98\) | −11.1433 | −1.12564 | ||||||||
\(99\) | −16.1997 | −1.62813 | ||||||||
\(100\) | 1.82571 | 0.182571 | ||||||||
\(101\) | −11.8511 | −1.17923 | −0.589616 | − | 0.807684i | \(-0.700721\pi\) | ||||
−0.589616 | + | 0.807684i | \(0.700721\pi\) | |||||||
\(102\) | 0.816515 | 0.0808470 | ||||||||
\(103\) | −1.35458 | −0.133471 | −0.0667354 | − | 0.997771i | \(-0.521258\pi\) | ||||
−0.0667354 | + | 0.997771i | \(0.521258\pi\) | |||||||
\(104\) | −1.79533 | −0.176047 | ||||||||
\(105\) | −1.05774 | −0.103225 | ||||||||
\(106\) | −14.8946 | −1.44669 | ||||||||
\(107\) | 7.06287 | 0.682794 | 0.341397 | − | 0.939919i | \(-0.389100\pi\) | ||||
0.341397 | + | 0.939919i | \(0.389100\pi\) | |||||||
\(108\) | 3.20393 | 0.308298 | ||||||||
\(109\) | −10.1844 | −0.975484 | −0.487742 | − | 0.872988i | \(-0.662179\pi\) | ||||
−0.487742 | + | 0.872988i | \(0.662179\pi\) | |||||||
\(110\) | 10.8815 | 1.03751 | ||||||||
\(111\) | 1.07310 | 0.101854 | ||||||||
\(112\) | 15.3871 | 1.45394 | ||||||||
\(113\) | −1.86015 | −0.174988 | −0.0874940 | − | 0.996165i | \(-0.527886\pi\) | ||||
−0.0874940 | + | 0.996165i | \(0.527886\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 6.96962 | 0.649921 | ||||||||
\(116\) | −2.56753 | −0.238389 | ||||||||
\(117\) | 15.3353 | 1.41775 | ||||||||
\(118\) | 18.5329 | 1.70609 | ||||||||
\(119\) | −5.01114 | −0.459370 | ||||||||
\(120\) | 0.101193 | 0.00923763 | ||||||||
\(121\) | 19.9504 | 1.81367 | ||||||||
\(122\) | −18.0235 | −1.63177 | ||||||||
\(123\) | 1.29084 | 0.116391 | ||||||||
\(124\) | −3.20393 | −0.287721 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | −20.2947 | −1.80800 | ||||||||
\(127\) | 4.89053 | 0.433964 | 0.216982 | − | 0.976176i | \(-0.430379\pi\) | ||||
0.216982 | + | 0.976176i | \(0.430379\pi\) | |||||||
\(128\) | −2.71684 | −0.240137 | ||||||||
\(129\) | 1.05774 | 0.0931287 | ||||||||
\(130\) | −10.3009 | −0.903449 | ||||||||
\(131\) | 2.81263 | 0.245741 | 0.122870 | − | 0.992423i | \(-0.460790\pi\) | ||||
0.122870 | + | 0.992423i | \(0.460790\pi\) | |||||||
\(132\) | −3.01502 | −0.262424 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −9.31204 | −0.804438 | ||||||||
\(135\) | −1.75489 | −0.151037 | ||||||||
\(136\) | 0.479412 | 0.0411093 | ||||||||
\(137\) | 9.23009 | 0.788579 | 0.394290 | − | 0.918986i | \(-0.370991\pi\) | ||||
0.394290 | + | 0.918986i | \(0.370991\pi\) | |||||||
\(138\) | −4.04660 | −0.344470 | ||||||||
\(139\) | −3.67878 | −0.312030 | −0.156015 | − | 0.987755i | \(-0.549865\pi\) | ||||
−0.156015 | + | 0.987755i | \(0.549865\pi\) | |||||||
\(140\) | 6.50557 | 0.549821 | ||||||||
\(141\) | 2.45205 | 0.206500 | ||||||||
\(142\) | −27.5179 | −2.30925 | ||||||||
\(143\) | −29.2990 | −2.45010 | ||||||||
\(144\) | 12.5741 | 1.04784 | ||||||||
\(145\) | 1.40632 | 0.116788 | ||||||||
\(146\) | −12.8969 | −1.06735 | ||||||||
\(147\) | −1.69115 | −0.139484 | ||||||||
\(148\) | −6.60002 | −0.542519 | ||||||||
\(149\) | 7.09925 | 0.581593 | 0.290797 | − | 0.956785i | \(-0.406080\pi\) | ||||
0.290797 | + | 0.956785i | \(0.406080\pi\) | |||||||
\(150\) | 0.580605 | 0.0474062 | ||||||||
\(151\) | 18.3567 | 1.49385 | 0.746924 | − | 0.664910i | \(-0.231530\pi\) | ||||
0.746924 | + | 0.664910i | \(0.231530\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −4.09503 | −0.331064 | ||||||||
\(154\) | 38.7742 | 3.12451 | ||||||||
\(155\) | 1.75489 | 0.140957 | ||||||||
\(156\) | 2.85415 | 0.228515 | ||||||||
\(157\) | 17.2301 | 1.37511 | 0.687555 | − | 0.726132i | \(-0.258684\pi\) | ||||
0.687555 | + | 0.726132i | \(0.258684\pi\) | |||||||
\(158\) | 10.7092 | 0.851975 | ||||||||
\(159\) | −2.26046 | −0.179266 | ||||||||
\(160\) | −7.76435 | −0.613826 | ||||||||
\(161\) | 24.8349 | 1.95726 | ||||||||
\(162\) | −16.0675 | −1.26238 | ||||||||
\(163\) | 10.8662 | 0.851103 | 0.425551 | − | 0.904934i | \(-0.360080\pi\) | ||||
0.425551 | + | 0.904934i | \(0.360080\pi\) | |||||||
\(164\) | −7.93925 | −0.619951 | ||||||||
\(165\) | 1.65142 | 0.128563 | ||||||||
\(166\) | 8.13083 | 0.631075 | ||||||||
\(167\) | −2.82977 | −0.218974 | −0.109487 | − | 0.993988i | \(-0.534921\pi\) | ||||
−0.109487 | + | 0.993988i | \(0.534921\pi\) | |||||||
\(168\) | 0.360582 | 0.0278195 | ||||||||
\(169\) | 14.7357 | 1.13351 | ||||||||
\(170\) | 2.75067 | 0.210967 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −6.50557 | −0.496045 | ||||||||
\(173\) | 9.26647 | 0.704516 | 0.352258 | − | 0.935903i | \(-0.385414\pi\) | ||||
0.352258 | + | 0.935903i | \(0.385414\pi\) | |||||||
\(174\) | −0.816515 | −0.0618998 | ||||||||
\(175\) | −3.56331 | −0.269361 | ||||||||
\(176\) | −24.0235 | −1.81084 | ||||||||
\(177\) | 2.81263 | 0.211410 | ||||||||
\(178\) | −18.0535 | −1.35317 | ||||||||
\(179\) | 3.59067 | 0.268379 | 0.134190 | − | 0.990956i | \(-0.457157\pi\) | ||||
0.134190 | + | 0.990956i | \(0.457157\pi\) | |||||||
\(180\) | 5.31626 | 0.396251 | ||||||||
\(181\) | 19.7630 | 1.46897 | 0.734487 | − | 0.678623i | \(-0.237423\pi\) | ||||
0.734487 | + | 0.678623i | \(0.237423\pi\) | |||||||
\(182\) | −36.7053 | −2.72078 | ||||||||
\(183\) | −2.73532 | −0.202200 | ||||||||
\(184\) | −2.37594 | −0.175157 | ||||||||
\(185\) | 3.61504 | 0.265783 | ||||||||
\(186\) | −1.01890 | −0.0747095 | ||||||||
\(187\) | 7.82377 | 0.572131 | ||||||||
\(188\) | −15.0812 | −1.09991 | ||||||||
\(189\) | −6.25323 | −0.454855 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 8.31398 | 0.601579 | 0.300789 | − | 0.953691i | \(-0.402750\pi\) | ||||
0.300789 | + | 0.953691i | \(0.402750\pi\) | |||||||
\(192\) | 1.94438 | 0.140324 | ||||||||
\(193\) | 22.2514 | 1.60169 | 0.800847 | − | 0.598869i | \(-0.204383\pi\) | ||||
0.800847 | + | 0.598869i | \(0.204383\pi\) | |||||||
\(194\) | 22.5160 | 1.61655 | ||||||||
\(195\) | −1.56331 | −0.111951 | ||||||||
\(196\) | 10.4014 | 0.742954 | ||||||||
\(197\) | −8.81263 | −0.627874 | −0.313937 | − | 0.949444i | \(-0.601648\pi\) | ||||
−0.313937 | + | 0.949444i | \(0.601648\pi\) | |||||||
\(198\) | 31.6857 | 2.25180 | ||||||||
\(199\) | 21.0659 | 1.49332 | 0.746660 | − | 0.665206i | \(-0.231656\pi\) | ||||
0.746660 | + | 0.665206i | \(0.231656\pi\) | |||||||
\(200\) | 0.340899 | 0.0241052 | ||||||||
\(201\) | −1.41323 | −0.0996818 | ||||||||
\(202\) | 23.1801 | 1.63095 | ||||||||
\(203\) | 5.01114 | 0.351713 | ||||||||
\(204\) | −0.762149 | −0.0533611 | ||||||||
\(205\) | 4.34858 | 0.303718 | ||||||||
\(206\) | 2.64948 | 0.184598 | ||||||||
\(207\) | 20.2947 | 1.41058 | ||||||||
\(208\) | 22.7417 | 1.57685 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 2.06888 | 0.142766 | ||||||||
\(211\) | −5.34556 | −0.368004 | −0.184002 | − | 0.982926i | \(-0.558905\pi\) | ||||
−0.184002 | + | 0.982926i | \(0.558905\pi\) | |||||||
\(212\) | 13.9029 | 0.954853 | ||||||||
\(213\) | −4.17623 | −0.286151 | ||||||||
\(214\) | −13.8146 | −0.944345 | ||||||||
\(215\) | 3.56331 | 0.243016 | ||||||||
\(216\) | 0.598242 | 0.0407052 | ||||||||
\(217\) | 6.25323 | 0.424497 | ||||||||
\(218\) | 19.9200 | 1.34915 | ||||||||
\(219\) | −1.95728 | −0.132261 | ||||||||
\(220\) | −10.1570 | −0.684784 | ||||||||
\(221\) | −7.40632 | −0.498203 | ||||||||
\(222\) | −2.09891 | −0.140870 | ||||||||
\(223\) | 3.10947 | 0.208226 | 0.104113 | − | 0.994565i | \(-0.466800\pi\) | ||||
0.104113 | + | 0.994565i | \(0.466800\pi\) | |||||||
\(224\) | −27.6668 | −1.84856 | ||||||||
\(225\) | −2.91188 | −0.194126 | ||||||||
\(226\) | 3.63834 | 0.242019 | ||||||||
\(227\) | −14.4692 | −0.960354 | −0.480177 | − | 0.877172i | \(-0.659428\pi\) | ||||
−0.480177 | + | 0.877172i | \(0.659428\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −5.21473 | −0.344599 | −0.172299 | − | 0.985045i | \(-0.555120\pi\) | ||||
−0.172299 | + | 0.985045i | \(0.555120\pi\) | |||||||
\(230\) | −13.6322 | −0.898879 | ||||||||
\(231\) | 5.88452 | 0.387173 | ||||||||
\(232\) | −0.479412 | −0.0314750 | ||||||||
\(233\) | −3.18737 | −0.208811 | −0.104406 | − | 0.994535i | \(-0.533294\pi\) | ||||
−0.104406 | + | 0.994535i | \(0.533294\pi\) | |||||||
\(234\) | −29.9950 | −1.96084 | ||||||||
\(235\) | 8.26046 | 0.538853 | ||||||||
\(236\) | −17.2990 | −1.12607 | ||||||||
\(237\) | 1.62527 | 0.105572 | ||||||||
\(238\) | 9.80150 | 0.635337 | ||||||||
\(239\) | 16.5209 | 1.06865 | 0.534325 | − | 0.845279i | \(-0.320566\pi\) | ||||
0.534325 | + | 0.845279i | \(0.320566\pi\) | |||||||
\(240\) | −1.28182 | −0.0827413 | ||||||||
\(241\) | 12.2271 | 0.787615 | 0.393807 | − | 0.919193i | \(-0.371158\pi\) | ||||
0.393807 | + | 0.919193i | \(0.371158\pi\) | |||||||
\(242\) | −39.0218 | −2.50842 | ||||||||
\(243\) | −7.70316 | −0.494158 | ||||||||
\(244\) | 16.8234 | 1.07701 | ||||||||
\(245\) | −5.69716 | −0.363978 | ||||||||
\(246\) | −2.52481 | −0.160976 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | −0.598242 | −0.0379884 | ||||||||
\(249\) | 1.23397 | 0.0781996 | ||||||||
\(250\) | 1.95594 | 0.123705 | ||||||||
\(251\) | 4.52093 | 0.285358 | 0.142679 | − | 0.989769i | \(-0.454428\pi\) | ||||
0.142679 | + | 0.989769i | \(0.454428\pi\) | |||||||
\(252\) | 18.9435 | 1.19333 | ||||||||
\(253\) | −38.7742 | −2.43771 | ||||||||
\(254\) | −9.56559 | −0.600198 | ||||||||
\(255\) | 0.417453 | 0.0261420 | ||||||||
\(256\) | 18.4144 | 1.15090 | ||||||||
\(257\) | −15.9290 | −0.993625 | −0.496813 | − | 0.867858i | \(-0.665496\pi\) | ||||
−0.496813 | + | 0.867858i | \(0.665496\pi\) | |||||||
\(258\) | −2.06888 | −0.128803 | ||||||||
\(259\) | 12.8815 | 0.800418 | ||||||||
\(260\) | 9.61504 | 0.596300 | ||||||||
\(261\) | 4.09503 | 0.253476 | ||||||||
\(262\) | −5.50135 | −0.339874 | ||||||||
\(263\) | 0.854147 | 0.0526689 | 0.0263345 | − | 0.999653i | \(-0.491617\pi\) | ||||
0.0263345 | + | 0.999653i | \(0.491617\pi\) | |||||||
\(264\) | −0.562969 | −0.0346483 | ||||||||
\(265\) | −7.61504 | −0.467788 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −2.73988 | −0.167678 | ||||||||
\(268\) | 8.69202 | 0.530950 | ||||||||
\(269\) | −10.3913 | −0.633569 | −0.316784 | − | 0.948498i | \(-0.602603\pi\) | ||||
−0.316784 | + | 0.948498i | \(0.602603\pi\) | |||||||
\(270\) | 3.43247 | 0.208894 | ||||||||
\(271\) | −8.19971 | −0.498097 | −0.249048 | − | 0.968491i | \(-0.580118\pi\) | ||||
−0.249048 | + | 0.968491i | \(0.580118\pi\) | |||||||
\(272\) | −6.07276 | −0.368215 | ||||||||
\(273\) | −5.57054 | −0.337145 | ||||||||
\(274\) | −18.0535 | −1.09065 | ||||||||
\(275\) | 5.56331 | 0.335480 | ||||||||
\(276\) | 3.77717 | 0.227359 | ||||||||
\(277\) | 14.6484 | 0.880137 | 0.440069 | − | 0.897964i | \(-0.354954\pi\) | ||||
0.440069 | + | 0.897964i | \(0.354954\pi\) | |||||||
\(278\) | 7.19549 | 0.431557 | ||||||||
\(279\) | 5.11005 | 0.305931 | ||||||||
\(280\) | 1.21473 | 0.0725939 | ||||||||
\(281\) | 31.6129 | 1.88587 | 0.942935 | − | 0.332977i | \(-0.108053\pi\) | ||||
0.942935 | + | 0.332977i | \(0.108053\pi\) | |||||||
\(282\) | −4.79607 | −0.285602 | ||||||||
\(283\) | 24.7326 | 1.47020 | 0.735101 | − | 0.677957i | \(-0.237135\pi\) | ||||
0.735101 | + | 0.677957i | \(0.237135\pi\) | |||||||
\(284\) | 25.6857 | 1.52417 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 57.3071 | 3.38864 | ||||||||
\(287\) | 15.4953 | 0.914660 | ||||||||
\(288\) | −22.6089 | −1.33224 | ||||||||
\(289\) | −15.0223 | −0.883663 | ||||||||
\(290\) | −2.75067 | −0.161525 | ||||||||
\(291\) | 3.41712 | 0.200315 | ||||||||
\(292\) | 12.0382 | 0.704480 | ||||||||
\(293\) | −30.2857 | −1.76931 | −0.884655 | − | 0.466245i | \(-0.845606\pi\) | ||||
−0.884655 | + | 0.466245i | \(0.845606\pi\) | |||||||
\(294\) | 3.30780 | 0.192915 | ||||||||
\(295\) | 9.47519 | 0.551667 | ||||||||
\(296\) | −1.23237 | −0.0716298 | ||||||||
\(297\) | 9.76302 | 0.566508 | ||||||||
\(298\) | −13.8857 | −0.804379 | ||||||||
\(299\) | 36.7053 | 2.12272 | ||||||||
\(300\) | −0.541947 | −0.0312893 | ||||||||
\(301\) | 12.6972 | 0.731852 | ||||||||
\(302\) | −35.9046 | −2.06608 | ||||||||
\(303\) | 3.51791 | 0.202099 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −9.21473 | −0.527634 | ||||||||
\(306\) | 8.00965 | 0.457881 | ||||||||
\(307\) | 23.0629 | 1.31627 | 0.658134 | − | 0.752901i | \(-0.271346\pi\) | ||||
0.658134 | + | 0.752901i | \(0.271346\pi\) | |||||||
\(308\) | −36.1925 | −2.06226 | ||||||||
\(309\) | 0.402096 | 0.0228744 | ||||||||
\(310\) | −3.43247 | −0.194951 | ||||||||
\(311\) | −10.3152 | −0.584921 | −0.292460 | − | 0.956278i | \(-0.594474\pi\) | ||||
−0.292460 | + | 0.956278i | \(0.594474\pi\) | |||||||
\(312\) | 0.532930 | 0.0301712 | ||||||||
\(313\) | −4.95038 | −0.279812 | −0.139906 | − | 0.990165i | \(-0.544680\pi\) | ||||
−0.139906 | + | 0.990165i | \(0.544680\pi\) | |||||||
\(314\) | −33.7011 | −1.90186 | ||||||||
\(315\) | −10.3759 | −0.584618 | ||||||||
\(316\) | −9.99612 | −0.562326 | ||||||||
\(317\) | 14.2433 | 0.799985 | 0.399992 | − | 0.916518i | \(-0.369013\pi\) | ||||
0.399992 | + | 0.916518i | \(0.369013\pi\) | |||||||
\(318\) | 4.42134 | 0.247936 | ||||||||
\(319\) | −7.82377 | −0.438047 | ||||||||
\(320\) | 6.55023 | 0.366169 | ||||||||
\(321\) | −2.09656 | −0.117018 | ||||||||
\(322\) | −48.5756 | −2.70702 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | 14.9977 | 0.833207 | ||||||||
\(325\) | −5.26647 | −0.292131 | ||||||||
\(326\) | −21.2536 | −1.17713 | ||||||||
\(327\) | 3.02314 | 0.167180 | ||||||||
\(328\) | −1.48243 | −0.0818534 | ||||||||
\(329\) | 29.4346 | 1.62278 | ||||||||
\(330\) | −3.23009 | −0.177810 | ||||||||
\(331\) | −2.04272 | −0.112278 | −0.0561390 | − | 0.998423i | \(-0.517879\pi\) | ||||
−0.0561390 | + | 0.998423i | \(0.517879\pi\) | |||||||
\(332\) | −7.58946 | −0.416526 | ||||||||
\(333\) | 10.5266 | 0.576854 | ||||||||
\(334\) | 5.53487 | 0.302855 | ||||||||
\(335\) | −4.76090 | −0.260116 | ||||||||
\(336\) | −4.56753 | −0.249179 | ||||||||
\(337\) | −34.6951 | −1.88996 | −0.944980 | − | 0.327128i | \(-0.893919\pi\) | ||||
−0.944980 | + | 0.327128i | \(0.893919\pi\) | |||||||
\(338\) | −28.8221 | −1.56772 | ||||||||
\(339\) | 0.552170 | 0.0299898 | ||||||||
\(340\) | −2.56753 | −0.139244 | ||||||||
\(341\) | −9.76302 | −0.528697 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 4.64243 | 0.250668 | ||||||||
\(344\) | −1.21473 | −0.0654938 | ||||||||
\(345\) | −2.06888 | −0.111385 | ||||||||
\(346\) | −18.1247 | −0.974388 | ||||||||
\(347\) | 7.35280 | 0.394719 | 0.197359 | − | 0.980331i | \(-0.436763\pi\) | ||||
0.197359 | + | 0.980331i | \(0.436763\pi\) | |||||||
\(348\) | 0.762149 | 0.0408555 | ||||||||
\(349\) | −31.7630 | −1.70024 | −0.850118 | − | 0.526593i | \(-0.823469\pi\) | ||||
−0.850118 | + | 0.526593i | \(0.823469\pi\) | |||||||
\(350\) | 6.96962 | 0.372542 | ||||||||
\(351\) | −9.24209 | −0.493306 | ||||||||
\(352\) | 43.1955 | 2.30233 | ||||||||
\(353\) | −7.52179 | −0.400345 | −0.200172 | − | 0.979761i | \(-0.564150\pi\) | ||||
−0.200172 | + | 0.979761i | \(0.564150\pi\) | |||||||
\(354\) | −5.50135 | −0.292393 | ||||||||
\(355\) | −14.0689 | −0.746698 | ||||||||
\(356\) | 16.8515 | 0.893126 | ||||||||
\(357\) | 1.48751 | 0.0787276 | ||||||||
\(358\) | −7.02314 | −0.371185 | ||||||||
\(359\) | −30.3982 | −1.60436 | −0.802178 | − | 0.597085i | \(-0.796326\pi\) | ||||
−0.802178 | + | 0.597085i | \(0.796326\pi\) | |||||||
\(360\) | 0.992660 | 0.0523178 | ||||||||
\(361\) | 0 | 0 | ||||||||
\(362\) | −38.6553 | −2.03168 | ||||||||
\(363\) | −5.92211 | −0.310830 | ||||||||
\(364\) | 34.2613 | 1.79578 | ||||||||
\(365\) | −6.59368 | −0.345129 | ||||||||
\(366\) | 5.35012 | 0.279655 | ||||||||
\(367\) | 3.91577 | 0.204401 | 0.102201 | − | 0.994764i | \(-0.467412\pi\) | ||||
0.102201 | + | 0.994764i | \(0.467412\pi\) | |||||||
\(368\) | 30.0962 | 1.56887 | ||||||||
\(369\) | 12.6626 | 0.659186 | ||||||||
\(370\) | −7.07082 | −0.367594 | ||||||||
\(371\) | −27.1347 | −1.40877 | ||||||||
\(372\) | 0.951060 | 0.0493102 | ||||||||
\(373\) | −26.7759 | −1.38641 | −0.693203 | − | 0.720743i | \(-0.743801\pi\) | ||||
−0.693203 | + | 0.720743i | \(0.743801\pi\) | |||||||
\(374\) | −15.3028 | −0.791291 | ||||||||
\(375\) | 0.296842 | 0.0153288 | ||||||||
\(376\) | −2.81599 | −0.145223 | ||||||||
\(377\) | 7.40632 | 0.381445 | ||||||||
\(378\) | 12.2310 | 0.629092 | ||||||||
\(379\) | −14.9504 | −0.767950 | −0.383975 | − | 0.923344i | \(-0.625445\pi\) | ||||
−0.383975 | + | 0.923344i | \(0.625445\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −1.45171 | −0.0743735 | ||||||||
\(382\) | −16.2617 | −0.832019 | ||||||||
\(383\) | 27.9910 | 1.43027 | 0.715136 | − | 0.698985i | \(-0.246365\pi\) | ||||
0.715136 | + | 0.698985i | \(0.246365\pi\) | |||||||
\(384\) | 0.806471 | 0.0411551 | ||||||||
\(385\) | 19.8238 | 1.01031 | ||||||||
\(386\) | −43.5225 | −2.21524 | ||||||||
\(387\) | 10.3759 | 0.527439 | ||||||||
\(388\) | −21.0168 | −1.06697 | ||||||||
\(389\) | −35.2036 | −1.78489 | −0.892447 | − | 0.451152i | \(-0.851013\pi\) | ||||
−0.892447 | + | 0.451152i | \(0.851013\pi\) | |||||||
\(390\) | 3.05774 | 0.154835 | ||||||||
\(391\) | −9.80150 | −0.495683 | ||||||||
\(392\) | 1.94216 | 0.0980937 | ||||||||
\(393\) | −0.834907 | −0.0421155 | ||||||||
\(394\) | 17.2370 | 0.868388 | ||||||||
\(395\) | 5.47519 | 0.275487 | ||||||||
\(396\) | −29.5760 | −1.48625 | ||||||||
\(397\) | −35.9735 | −1.80546 | −0.902730 | − | 0.430208i | \(-0.858440\pi\) | ||||
−0.902730 | + | 0.430208i | \(0.858440\pi\) | |||||||
\(398\) | −41.2036 | −2.06535 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −4.31820 | −0.215910 | ||||||||
\(401\) | −23.2421 | −1.16065 | −0.580327 | − | 0.814383i | \(-0.697075\pi\) | ||||
−0.580327 | + | 0.814383i | \(0.697075\pi\) | |||||||
\(402\) | 2.76420 | 0.137866 | ||||||||
\(403\) | 9.24209 | 0.460381 | ||||||||
\(404\) | −21.6367 | −1.07647 | ||||||||
\(405\) | −8.21473 | −0.408193 | ||||||||
\(406\) | −9.80150 | −0.486440 | ||||||||
\(407\) | −20.1116 | −0.996895 | ||||||||
\(408\) | −0.142310 | −0.00704538 | ||||||||
\(409\) | 31.8926 | 1.57699 | 0.788495 | − | 0.615041i | \(-0.210861\pi\) | ||||
0.788495 | + | 0.615041i | \(0.210861\pi\) | |||||||
\(410\) | −8.50557 | −0.420060 | ||||||||
\(411\) | −2.73988 | −0.135148 | ||||||||
\(412\) | −2.47307 | −0.121840 | ||||||||
\(413\) | 33.7630 | 1.66137 | ||||||||
\(414\) | −39.6953 | −1.95092 | ||||||||
\(415\) | 4.15699 | 0.204059 | ||||||||
\(416\) | −40.8907 | −2.00483 | ||||||||
\(417\) | 1.09202 | 0.0534763 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 31.8238 | 1.55469 | 0.777346 | − | 0.629073i | \(-0.216565\pi\) | ||||
0.777346 | + | 0.629073i | \(0.216565\pi\) | |||||||
\(420\) | −1.93112 | −0.0942292 | ||||||||
\(421\) | −0.348578 | −0.0169887 | −0.00849433 | − | 0.999964i | \(-0.502704\pi\) | ||||
−0.00849433 | + | 0.999964i | \(0.502704\pi\) | |||||||
\(422\) | 10.4556 | 0.508971 | ||||||||
\(423\) | 24.0535 | 1.16952 | ||||||||
\(424\) | 2.59596 | 0.126071 | ||||||||
\(425\) | 1.40632 | 0.0682164 | ||||||||
\(426\) | 8.16847 | 0.395763 | ||||||||
\(427\) | −32.8349 | −1.58899 | ||||||||
\(428\) | 12.8948 | 0.623292 | ||||||||
\(429\) | 8.69716 | 0.419903 | ||||||||
\(430\) | −6.96962 | −0.336105 | ||||||||
\(431\) | −29.2764 | −1.41019 | −0.705097 | − | 0.709111i | \(-0.749096\pi\) | ||||
−0.705097 | + | 0.709111i | \(0.749096\pi\) | |||||||
\(432\) | −7.57799 | −0.364596 | ||||||||
\(433\) | 0.883290 | 0.0424482 | 0.0212241 | − | 0.999775i | \(-0.493244\pi\) | ||||
0.0212241 | + | 0.999775i | \(0.493244\pi\) | |||||||
\(434\) | −12.2310 | −0.587105 | ||||||||
\(435\) | −0.417453 | −0.0200154 | ||||||||
\(436\) | −18.5937 | −0.890476 | ||||||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 3.82833 | 0.182925 | ||||||||
\(439\) | 13.8584 | 0.661424 | 0.330712 | − | 0.943732i | \(-0.392711\pi\) | ||||
0.330712 | + | 0.943732i | \(0.392711\pi\) | |||||||
\(440\) | −1.89653 | −0.0904134 | ||||||||
\(441\) | −16.5895 | −0.789974 | ||||||||
\(442\) | 14.4863 | 0.689044 | ||||||||
\(443\) | −13.5753 | −0.644982 | −0.322491 | − | 0.946572i | \(-0.604520\pi\) | ||||
−0.322491 | + | 0.946572i | \(0.604520\pi\) | |||||||
\(444\) | 1.95916 | 0.0929778 | ||||||||
\(445\) | −9.23009 | −0.437548 | ||||||||
\(446\) | −6.08195 | −0.287989 | ||||||||
\(447\) | −2.10735 | −0.0996745 | ||||||||
\(448\) | 23.3405 | 1.10273 | ||||||||
\(449\) | 15.6334 | 0.737785 | 0.368893 | − | 0.929472i | \(-0.379737\pi\) | ||||
0.368893 | + | 0.929472i | \(0.379737\pi\) | |||||||
\(450\) | 5.69548 | 0.268487 | ||||||||
\(451\) | −24.1925 | −1.13918 | ||||||||
\(452\) | −3.39609 | −0.159739 | ||||||||
\(453\) | −5.44904 | −0.256018 | ||||||||
\(454\) | 28.3009 | 1.32823 | ||||||||
\(455\) | −18.7660 | −0.879765 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 5.30284 | 0.248057 | 0.124028 | − | 0.992279i | \(-0.460419\pi\) | ||||
0.124028 | + | 0.992279i | \(0.460419\pi\) | |||||||
\(458\) | 10.1997 | 0.476601 | ||||||||
\(459\) | 2.46794 | 0.115193 | ||||||||
\(460\) | 12.7245 | 0.593284 | ||||||||
\(461\) | 0.374734 | 0.0174531 | 0.00872656 | − | 0.999962i | \(-0.497222\pi\) | ||||
0.00872656 | + | 0.999962i | \(0.497222\pi\) | |||||||
\(462\) | −11.5098 | −0.535484 | ||||||||
\(463\) | 6.65564 | 0.309314 | 0.154657 | − | 0.987968i | \(-0.450573\pi\) | ||||
0.154657 | + | 0.987968i | \(0.450573\pi\) | |||||||
\(464\) | 6.07276 | 0.281921 | ||||||||
\(465\) | −0.520926 | −0.0241574 | ||||||||
\(466\) | 6.23431 | 0.288799 | ||||||||
\(467\) | −0.854147 | −0.0395252 | −0.0197626 | − | 0.999805i | \(-0.506291\pi\) | ||||
−0.0197626 | + | 0.999805i | \(0.506291\pi\) | |||||||
\(468\) | 27.9979 | 1.29420 | ||||||||
\(469\) | −16.9645 | −0.783349 | ||||||||
\(470\) | −16.1570 | −0.745266 | ||||||||
\(471\) | −5.11461 | −0.235669 | ||||||||
\(472\) | −3.23009 | −0.148677 | ||||||||
\(473\) | −19.8238 | −0.911498 | ||||||||
\(474\) | −3.17893 | −0.146013 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −9.14889 | −0.419339 | ||||||||
\(477\) | −22.1741 | −1.01528 | ||||||||
\(478\) | −32.3140 | −1.47801 | ||||||||
\(479\) | −17.0731 | −0.780090 | −0.390045 | − | 0.920796i | \(-0.627540\pi\) | ||||
−0.390045 | + | 0.920796i | \(0.627540\pi\) | |||||||
\(480\) | 2.30478 | 0.105199 | ||||||||
\(481\) | 19.0385 | 0.868081 | ||||||||
\(482\) | −23.9154 | −1.08932 | ||||||||
\(483\) | −7.37204 | −0.335439 | ||||||||
\(484\) | 36.4236 | 1.65562 | ||||||||
\(485\) | 11.5116 | 0.522713 | ||||||||
\(486\) | 15.0669 | 0.683450 | ||||||||
\(487\) | −12.8259 | −0.581197 | −0.290598 | − | 0.956845i | \(-0.593854\pi\) | ||||
−0.290598 | + | 0.956845i | \(0.593854\pi\) | |||||||
\(488\) | 3.14129 | 0.142200 | ||||||||
\(489\) | −3.22553 | −0.145863 | ||||||||
\(490\) | 11.1433 | 0.503403 | ||||||||
\(491\) | −10.4054 | −0.469591 | −0.234796 | − | 0.972045i | \(-0.575442\pi\) | ||||
−0.234796 | + | 0.972045i | \(0.575442\pi\) | |||||||
\(492\) | 2.35670 | 0.106248 | ||||||||
\(493\) | −1.97773 | −0.0890723 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 16.1997 | 0.728123 | ||||||||
\(496\) | 7.57799 | 0.340262 | ||||||||
\(497\) | −50.1317 | −2.24872 | ||||||||
\(498\) | −2.41357 | −0.108155 | ||||||||
\(499\) | 36.1612 | 1.61880 | 0.809399 | − | 0.587258i | \(-0.199793\pi\) | ||||
0.809399 | + | 0.587258i | \(0.199793\pi\) | |||||||
\(500\) | −1.82571 | −0.0816483 | ||||||||
\(501\) | 0.839995 | 0.0375282 | ||||||||
\(502\) | −8.84267 | −0.394668 | ||||||||
\(503\) | 33.2536 | 1.48270 | 0.741352 | − | 0.671117i | \(-0.234185\pi\) | ||||
0.741352 | + | 0.671117i | \(0.234185\pi\) | |||||||
\(504\) | 3.53715 | 0.157557 | ||||||||
\(505\) | 11.8511 | 0.527368 | ||||||||
\(506\) | 75.8400 | 3.37150 | ||||||||
\(507\) | −4.37416 | −0.194263 | ||||||||
\(508\) | 8.92869 | 0.396146 | ||||||||
\(509\) | −7.29084 | −0.323161 | −0.161580 | − | 0.986860i | \(-0.551659\pi\) | ||||
−0.161580 | + | 0.986860i | \(0.551659\pi\) | |||||||
\(510\) | −0.816515 | −0.0361559 | ||||||||
\(511\) | −23.4953 | −1.03937 | ||||||||
\(512\) | −30.5839 | −1.35163 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 31.1563 | 1.37424 | ||||||||
\(515\) | 1.35458 | 0.0596899 | ||||||||
\(516\) | 1.93112 | 0.0850130 | ||||||||
\(517\) | −45.9555 | −2.02112 | ||||||||
\(518\) | −25.1955 | −1.10703 | ||||||||
\(519\) | −2.75067 | −0.120741 | ||||||||
\(520\) | 1.79533 | 0.0787306 | ||||||||
\(521\) | 9.87849 | 0.432785 | 0.216392 | − | 0.976306i | \(-0.430571\pi\) | ||||
0.216392 | + | 0.976306i | \(0.430571\pi\) | |||||||
\(522\) | −8.00965 | −0.350573 | ||||||||
\(523\) | 11.1925 | 0.489414 | 0.244707 | − | 0.969597i | \(-0.421308\pi\) | ||||
0.244707 | + | 0.969597i | \(0.421308\pi\) | |||||||
\(524\) | 5.13505 | 0.224326 | ||||||||
\(525\) | 1.05774 | 0.0461635 | ||||||||
\(526\) | −1.67066 | −0.0728443 | ||||||||
\(527\) | −2.46794 | −0.107505 | ||||||||
\(528\) | 7.13117 | 0.310344 | ||||||||
\(529\) | 25.5756 | 1.11198 | ||||||||
\(530\) | 14.8946 | 0.646979 | ||||||||
\(531\) | 27.5907 | 1.19733 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 22.9016 | 0.991980 | ||||||||
\(534\) | 5.35904 | 0.231908 | ||||||||
\(535\) | −7.06287 | −0.305355 | ||||||||
\(536\) | 1.62299 | 0.0701023 | ||||||||
\(537\) | −1.06586 | −0.0459953 | ||||||||
\(538\) | 20.3248 | 0.876263 | ||||||||
\(539\) | 31.6950 | 1.36520 | ||||||||
\(540\) | −3.20393 | −0.137875 | ||||||||
\(541\) | 2.22587 | 0.0956974 | 0.0478487 | − | 0.998855i | \(-0.484763\pi\) | ||||
0.0478487 | + | 0.998855i | \(0.484763\pi\) | |||||||
\(542\) | 16.0382 | 0.688898 | ||||||||
\(543\) | −5.86649 | −0.251755 | ||||||||
\(544\) | 10.9191 | 0.468154 | ||||||||
\(545\) | 10.1844 | 0.436250 | ||||||||
\(546\) | 10.8957 | 0.466291 | ||||||||
\(547\) | 34.9675 | 1.49510 | 0.747552 | − | 0.664204i | \(-0.231229\pi\) | ||||
0.747552 | + | 0.664204i | \(0.231229\pi\) | |||||||
\(548\) | 16.8515 | 0.719859 | ||||||||
\(549\) | −26.8322 | −1.14517 | ||||||||
\(550\) | −10.8815 | −0.463989 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 0.705278 | 0.0300186 | ||||||||
\(553\) | 19.5098 | 0.829641 | ||||||||
\(554\) | −28.6514 | −1.21728 | ||||||||
\(555\) | −1.07310 | −0.0455504 | ||||||||
\(556\) | −6.71640 | −0.284839 | ||||||||
\(557\) | −8.88539 | −0.376486 | −0.188243 | − | 0.982122i | \(-0.560279\pi\) | ||||
−0.188243 | + | 0.982122i | \(0.560279\pi\) | |||||||
\(558\) | −9.99497 | −0.423121 | ||||||||
\(559\) | 18.7660 | 0.793719 | ||||||||
\(560\) | −15.3871 | −0.650223 | ||||||||
\(561\) | −2.32242 | −0.0980527 | ||||||||
\(562\) | −61.8331 | −2.60827 | ||||||||
\(563\) | 29.6767 | 1.25072 | 0.625362 | − | 0.780335i | \(-0.284952\pi\) | ||||
0.625362 | + | 0.780335i | \(0.284952\pi\) | |||||||
\(564\) | 4.47674 | 0.188505 | ||||||||
\(565\) | 1.86015 | 0.0782570 | ||||||||
\(566\) | −48.3756 | −2.03338 | ||||||||
\(567\) | −29.2716 | −1.22929 | ||||||||
\(568\) | 4.79607 | 0.201239 | ||||||||
\(569\) | 22.1152 | 0.927116 | 0.463558 | − | 0.886067i | \(-0.346573\pi\) | ||||
0.463558 | + | 0.886067i | \(0.346573\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −33.2656 | −1.39212 | −0.696060 | − | 0.717983i | \(-0.745065\pi\) | ||||
−0.696060 | + | 0.717983i | \(0.745065\pi\) | |||||||
\(572\) | −53.4914 | −2.23659 | ||||||||
\(573\) | −2.46794 | −0.103100 | ||||||||
\(574\) | −30.3080 | −1.26503 | ||||||||
\(575\) | −6.96962 | −0.290653 | ||||||||
\(576\) | 19.0735 | 0.794730 | ||||||||
\(577\) | 0.934140 | 0.0388887 | 0.0194444 | − | 0.999811i | \(-0.493810\pi\) | ||||
0.0194444 | + | 0.999811i | \(0.493810\pi\) | |||||||
\(578\) | 29.3827 | 1.22216 | ||||||||
\(579\) | −6.60516 | −0.274501 | ||||||||
\(580\) | 2.56753 | 0.106611 | ||||||||
\(581\) | 14.8126 | 0.614532 | ||||||||
\(582\) | −6.68368 | −0.277047 | ||||||||
\(583\) | 42.3648 | 1.75457 | ||||||||
\(584\) | 2.24778 | 0.0930139 | ||||||||
\(585\) | −15.3353 | −0.634038 | ||||||||
\(586\) | 59.2371 | 2.44706 | ||||||||
\(587\) | 1.57531 | 0.0650200 | 0.0325100 | − | 0.999471i | \(-0.489650\pi\) | ||||
0.0325100 | + | 0.999471i | \(0.489650\pi\) | |||||||
\(588\) | −3.08756 | −0.127329 | ||||||||
\(589\) | 0 | 0 | ||||||||
\(590\) | −18.5329 | −0.762989 | ||||||||
\(591\) | 2.61596 | 0.107606 | ||||||||
\(592\) | 15.6105 | 0.641587 | ||||||||
\(593\) | 26.0162 | 1.06836 | 0.534180 | − | 0.845371i | \(-0.320621\pi\) | ||||
0.534180 | + | 0.845371i | \(0.320621\pi\) | |||||||
\(594\) | −19.0959 | −0.783514 | ||||||||
\(595\) | 5.01114 | 0.205437 | ||||||||
\(596\) | 12.9612 | 0.530911 | ||||||||
\(597\) | −6.25323 | −0.255928 | ||||||||
\(598\) | −71.7934 | −2.93585 | ||||||||
\(599\) | −19.5359 | −0.798217 | −0.399109 | − | 0.916904i | \(-0.630680\pi\) | ||||
−0.399109 | + | 0.916904i | \(0.630680\pi\) | |||||||
\(600\) | −0.101193 | −0.00413119 | ||||||||
\(601\) | −43.5299 | −1.77562 | −0.887811 | − | 0.460208i | \(-0.847775\pi\) | ||||
−0.887811 | + | 0.460208i | \(0.847775\pi\) | |||||||
\(602\) | −24.8349 | −1.01220 | ||||||||
\(603\) | −13.8632 | −0.564552 | ||||||||
\(604\) | 33.5140 | 1.36367 | ||||||||
\(605\) | −19.9504 | −0.811098 | ||||||||
\(606\) | −6.88083 | −0.279515 | ||||||||
\(607\) | 12.5847 | 0.510796 | 0.255398 | − | 0.966836i | \(-0.417794\pi\) | ||||
0.255398 | + | 0.966836i | \(0.417794\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −1.48751 | −0.0602771 | ||||||||
\(610\) | 18.0235 | 0.729749 | ||||||||
\(611\) | 43.5034 | 1.75996 | ||||||||
\(612\) | −7.47634 | −0.302213 | ||||||||
\(613\) | −18.2412 | −0.736756 | −0.368378 | − | 0.929676i | \(-0.620087\pi\) | ||||
−0.368378 | + | 0.929676i | \(0.620087\pi\) | |||||||
\(614\) | −45.1097 | −1.82048 | ||||||||
\(615\) | −1.29084 | −0.0520517 | ||||||||
\(616\) | −6.75791 | −0.272284 | ||||||||
\(617\) | 26.7314 | 1.07617 | 0.538084 | − | 0.842892i | \(-0.319148\pi\) | ||||
0.538084 | + | 0.842892i | \(0.319148\pi\) | |||||||
\(618\) | −0.786477 | −0.0316367 | ||||||||
\(619\) | 2.92690 | 0.117642 | 0.0588211 | − | 0.998269i | \(-0.481266\pi\) | ||||
0.0588211 | + | 0.998269i | \(0.481266\pi\) | |||||||
\(620\) | 3.20393 | 0.128673 | ||||||||
\(621\) | −12.2310 | −0.490811 | ||||||||
\(622\) | 20.1759 | 0.808980 | ||||||||
\(623\) | −32.8896 | −1.31770 | ||||||||
\(624\) | −6.75067 | −0.270243 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 9.68267 | 0.386997 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 31.4572 | 1.25528 | ||||||||
\(629\) | −5.08389 | −0.202708 | ||||||||
\(630\) | 20.2947 | 0.808562 | ||||||||
\(631\) | −13.2493 | −0.527447 | −0.263724 | − | 0.964598i | \(-0.584951\pi\) | ||||
−0.263724 | + | 0.964598i | \(0.584951\pi\) | |||||||
\(632\) | −1.86649 | −0.0742450 | ||||||||
\(633\) | 1.58679 | 0.0630691 | ||||||||
\(634\) | −27.8591 | −1.10643 | ||||||||
\(635\) | −4.89053 | −0.194075 | ||||||||
\(636\) | −4.12695 | −0.163644 | ||||||||
\(637\) | −30.0039 | −1.18880 | ||||||||
\(638\) | 15.3028 | 0.605845 | ||||||||
\(639\) | −40.9669 | −1.62063 | ||||||||
\(640\) | 2.71684 | 0.107392 | ||||||||
\(641\) | −6.93026 | −0.273729 | −0.136864 | − | 0.990590i | \(-0.543702\pi\) | ||||
−0.136864 | + | 0.990590i | \(0.543702\pi\) | |||||||
\(642\) | 4.10074 | 0.161843 | ||||||||
\(643\) | 14.4794 | 0.571012 | 0.285506 | − | 0.958377i | \(-0.407838\pi\) | ||||
0.285506 | + | 0.958377i | \(0.407838\pi\) | |||||||
\(644\) | 45.3414 | 1.78670 | ||||||||
\(645\) | −1.05774 | −0.0416484 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 6.35549 | 0.249860 | 0.124930 | − | 0.992166i | \(-0.460129\pi\) | ||||
0.124930 | + | 0.992166i | \(0.460129\pi\) | |||||||
\(648\) | 2.80040 | 0.110010 | ||||||||
\(649\) | −52.7134 | −2.06918 | ||||||||
\(650\) | 10.3009 | 0.404035 | ||||||||
\(651\) | −1.85622 | −0.0727510 | ||||||||
\(652\) | 19.8385 | 0.776934 | ||||||||
\(653\) | −34.4030 | −1.34629 | −0.673146 | − | 0.739509i | \(-0.735058\pi\) | ||||
−0.673146 | + | 0.739509i | \(0.735058\pi\) | |||||||
\(654\) | −5.91309 | −0.231220 | ||||||||
\(655\) | −2.81263 | −0.109899 | ||||||||
\(656\) | 18.7780 | 0.733159 | ||||||||
\(657\) | −19.2000 | −0.749065 | ||||||||
\(658\) | −57.5723 | −2.24440 | ||||||||
\(659\) | 19.6214 | 0.764341 | 0.382170 | − | 0.924092i | \(-0.375177\pi\) | ||||
0.382170 | + | 0.924092i | \(0.375177\pi\) | |||||||
\(660\) | 3.01502 | 0.117359 | ||||||||
\(661\) | −39.8054 | −1.54825 | −0.774126 | − | 0.633032i | \(-0.781810\pi\) | ||||
−0.774126 | + | 0.633032i | \(0.781810\pi\) | |||||||
\(662\) | 3.99544 | 0.155287 | ||||||||
\(663\) | 2.19850 | 0.0853828 | ||||||||
\(664\) | −1.41712 | −0.0549947 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −20.5894 | −0.797823 | ||||||||
\(667\) | 9.80150 | 0.379515 | ||||||||
\(668\) | −5.16635 | −0.199892 | ||||||||
\(669\) | −0.923022 | −0.0356861 | ||||||||
\(670\) | 9.31204 | 0.359755 | ||||||||
\(671\) | 51.2644 | 1.97904 | ||||||||
\(672\) | 8.21266 | 0.316810 | ||||||||
\(673\) | 8.90374 | 0.343214 | 0.171607 | − | 0.985166i | \(-0.445104\pi\) | ||||
0.171607 | + | 0.985166i | \(0.445104\pi\) | |||||||
\(674\) | 67.8615 | 2.61393 | ||||||||
\(675\) | 1.75489 | 0.0675459 | ||||||||
\(676\) | 26.9030 | 1.03473 | ||||||||
\(677\) | −22.2695 | −0.855886 | −0.427943 | − | 0.903806i | \(-0.640762\pi\) | ||||
−0.427943 | + | 0.903806i | \(0.640762\pi\) | |||||||
\(678\) | −1.08001 | −0.0414776 | ||||||||
\(679\) | 41.0193 | 1.57417 | ||||||||
\(680\) | −0.479412 | −0.0183846 | ||||||||
\(681\) | 4.29506 | 0.164587 | ||||||||
\(682\) | 19.0959 | 0.731220 | ||||||||
\(683\) | −15.4054 | −0.589472 | −0.294736 | − | 0.955579i | \(-0.595232\pi\) | ||||
−0.294736 | + | 0.955579i | \(0.595232\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −9.23009 | −0.352663 | ||||||||
\(686\) | −9.08033 | −0.346689 | ||||||||
\(687\) | 1.54795 | 0.0590580 | ||||||||
\(688\) | 15.3871 | 0.586627 | ||||||||
\(689\) | −40.1044 | −1.52785 | ||||||||
\(690\) | 4.04660 | 0.154051 | ||||||||
\(691\) | −17.8773 | −0.680084 | −0.340042 | − | 0.940410i | \(-0.610441\pi\) | ||||
−0.340042 | + | 0.940410i | \(0.610441\pi\) | |||||||
\(692\) | 16.9179 | 0.643122 | ||||||||
\(693\) | 57.7245 | 2.19277 | ||||||||
\(694\) | −14.3817 | −0.545920 | ||||||||
\(695\) | 3.67878 | 0.139544 | ||||||||
\(696\) | 0.142310 | 0.00539423 | ||||||||
\(697\) | −6.11548 | −0.231640 | ||||||||
\(698\) | 62.1266 | 2.35153 | ||||||||
\(699\) | 0.946144 | 0.0357864 | ||||||||
\(700\) | −6.50557 | −0.245887 | ||||||||
\(701\) | 35.3609 | 1.33556 | 0.667782 | − | 0.744357i | \(-0.267244\pi\) | ||||
0.667782 | + | 0.744357i | \(0.267244\pi\) | |||||||
\(702\) | 18.0770 | 0.682272 | ||||||||
\(703\) | 0 | 0 | ||||||||
\(704\) | −36.4409 | −1.37342 | ||||||||
\(705\) | −2.45205 | −0.0923496 | ||||||||
\(706\) | 14.7122 | 0.553701 | ||||||||
\(707\) | 42.2292 | 1.58819 | ||||||||
\(708\) | 5.13505 | 0.192987 | ||||||||
\(709\) | 6.90410 | 0.259289 | 0.129644 | − | 0.991561i | \(-0.458616\pi\) | ||||
0.129644 | + | 0.991561i | \(0.458616\pi\) | |||||||
\(710\) | 27.5179 | 1.03273 | ||||||||
\(711\) | 15.9431 | 0.597914 | ||||||||
\(712\) | 3.14653 | 0.117921 | ||||||||
\(713\) | 12.2310 | 0.458053 | ||||||||
\(714\) | −2.90949 | −0.108885 | ||||||||
\(715\) | 29.2990 | 1.09572 | ||||||||
\(716\) | 6.55552 | 0.244991 | ||||||||
\(717\) | −4.90410 | −0.183147 | ||||||||
\(718\) | 59.4572 | 2.21892 | ||||||||
\(719\) | −38.9431 | −1.45233 | −0.726167 | − | 0.687518i | \(-0.758700\pi\) | ||||
−0.726167 | + | 0.687518i | \(0.758700\pi\) | |||||||
\(720\) | −12.5741 | −0.468609 | ||||||||
\(721\) | 4.82678 | 0.179759 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −3.62951 | −0.134983 | ||||||||
\(724\) | 36.0816 | 1.34096 | ||||||||
\(725\) | −1.40632 | −0.0522293 | ||||||||
\(726\) | 11.5833 | 0.429897 | ||||||||
\(727\) | −6.18347 | −0.229332 | −0.114666 | − | 0.993404i | \(-0.536580\pi\) | ||||
−0.114666 | + | 0.993404i | \(0.536580\pi\) | |||||||
\(728\) | 6.39733 | 0.237101 | ||||||||
\(729\) | −22.3576 | −0.828058 | ||||||||
\(730\) | 12.8969 | 0.477334 | ||||||||
\(731\) | −5.01114 | −0.185344 | ||||||||
\(732\) | −4.99390 | −0.184580 | ||||||||
\(733\) | −0.688715 | −0.0254383 | −0.0127191 | − | 0.999919i | \(-0.504049\pi\) | ||||
−0.0127191 | + | 0.999919i | \(0.504049\pi\) | |||||||
\(734\) | −7.65902 | −0.282699 | ||||||||
\(735\) | 1.69115 | 0.0623792 | ||||||||
\(736\) | −54.1146 | −1.99469 | ||||||||
\(737\) | 26.4863 | 0.975636 | ||||||||
\(738\) | −24.7672 | −0.911695 | ||||||||
\(739\) | −26.2532 | −0.965741 | −0.482870 | − | 0.875692i | \(-0.660406\pi\) | ||||
−0.482870 | + | 0.875692i | \(0.660406\pi\) | |||||||
\(740\) | 6.60002 | 0.242622 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 53.0740 | 1.94841 | ||||||||
\(743\) | 32.5688 | 1.19483 | 0.597416 | − | 0.801931i | \(-0.296194\pi\) | ||||
0.597416 | + | 0.801931i | \(0.296194\pi\) | |||||||
\(744\) | 0.177583 | 0.00651052 | ||||||||
\(745\) | −7.09925 | −0.260096 | ||||||||
\(746\) | 52.3722 | 1.91748 | ||||||||
\(747\) | 12.1047 | 0.442887 | ||||||||
\(748\) | 14.2839 | 0.522273 | ||||||||
\(749\) | −25.1672 | −0.919589 | ||||||||
\(750\) | −0.580605 | −0.0212007 | ||||||||
\(751\) | −45.4833 | −1.65971 | −0.829855 | − | 0.557979i | \(-0.811577\pi\) | ||||
−0.829855 | + | 0.557979i | \(0.811577\pi\) | |||||||
\(752\) | 35.6703 | 1.30076 | ||||||||
\(753\) | −1.34200 | −0.0489052 | ||||||||
\(754\) | −14.4863 | −0.527561 | ||||||||
\(755\) | −18.3567 | −0.668069 | ||||||||
\(756\) | −11.4166 | −0.415217 | ||||||||
\(757\) | 2.74947 | 0.0999311 | 0.0499656 | − | 0.998751i | \(-0.484089\pi\) | ||||
0.0499656 | + | 0.998751i | \(0.484089\pi\) | |||||||
\(758\) | 29.2421 | 1.06212 | ||||||||
\(759\) | 11.5098 | 0.417779 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −33.2978 | −1.20704 | −0.603521 | − | 0.797347i | \(-0.706236\pi\) | ||||
−0.603521 | + | 0.797347i | \(0.706236\pi\) | |||||||
\(762\) | 2.83947 | 0.102863 | ||||||||
\(763\) | 36.2900 | 1.31379 | ||||||||
\(764\) | 15.1789 | 0.549154 | ||||||||
\(765\) | 4.09503 | 0.148056 | ||||||||
\(766\) | −54.7488 | −1.97815 | ||||||||
\(767\) | 49.9008 | 1.80181 | ||||||||
\(768\) | −5.46617 | −0.197244 | ||||||||
\(769\) | −19.1540 | −0.690710 | −0.345355 | − | 0.938472i | \(-0.612241\pi\) | ||||
−0.345355 | + | 0.938472i | \(0.612241\pi\) | |||||||
\(770\) | −38.7742 | −1.39732 | ||||||||
\(771\) | 4.72840 | 0.170289 | ||||||||
\(772\) | 40.6247 | 1.46212 | ||||||||
\(773\) | −0.569309 | −0.0204766 | −0.0102383 | − | 0.999948i | \(-0.503259\pi\) | ||||
−0.0102383 | + | 0.999948i | \(0.503259\pi\) | |||||||
\(774\) | −20.2947 | −0.729479 | ||||||||
\(775\) | −1.75489 | −0.0630377 | ||||||||
\(776\) | −3.92429 | −0.140874 | ||||||||
\(777\) | −3.82377 | −0.137177 | ||||||||
\(778\) | 68.8562 | 2.46862 | ||||||||
\(779\) | 0 | 0 | ||||||||
\(780\) | −2.85415 | −0.102195 | ||||||||
\(781\) | 78.2695 | 2.80070 | ||||||||
\(782\) | 19.1712 | 0.685559 | ||||||||
\(783\) | −2.46794 | −0.0881969 | ||||||||
\(784\) | −24.6015 | −0.878624 | ||||||||
\(785\) | −17.2301 | −0.614968 | ||||||||
\(786\) | 1.63303 | 0.0582483 | ||||||||
\(787\) | −15.9991 | −0.570307 | −0.285153 | − | 0.958482i | \(-0.592044\pi\) | ||||
−0.285153 | + | 0.958482i | \(0.592044\pi\) | |||||||
\(788\) | −16.0893 | −0.573158 | ||||||||
\(789\) | −0.253546 | −0.00902649 | ||||||||
\(790\) | −10.7092 | −0.381015 | ||||||||
\(791\) | 6.62828 | 0.235675 | ||||||||
\(792\) | −5.52247 | −0.196232 | ||||||||
\(793\) | −48.5290 | −1.72332 | ||||||||
\(794\) | 70.3621 | 2.49706 | ||||||||
\(795\) | 2.26046 | 0.0801704 | ||||||||
\(796\) | 38.4602 | 1.36318 | ||||||||
\(797\) | 35.7528 | 1.26643 | 0.633214 | − | 0.773976i | \(-0.281735\pi\) | ||||
0.633214 | + | 0.773976i | \(0.281735\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −11.6168 | −0.410974 | ||||||||
\(800\) | 7.76435 | 0.274511 | ||||||||
\(801\) | −26.8769 | −0.949650 | ||||||||
\(802\) | 45.4602 | 1.60526 | ||||||||
\(803\) | 36.6827 | 1.29450 | ||||||||
\(804\) | −2.58016 | −0.0909951 | ||||||||
\(805\) | −24.8349 | −0.875315 | ||||||||
\(806\) | −18.0770 | −0.636735 | ||||||||
\(807\) | 3.08457 | 0.108582 | ||||||||
\(808\) | −4.04004 | −0.142128 | ||||||||
\(809\) | 23.2036 | 0.815796 | 0.407898 | − | 0.913028i | \(-0.366262\pi\) | ||||
0.407898 | + | 0.913028i | \(0.366262\pi\) | |||||||
\(810\) | 16.0675 | 0.564556 | ||||||||
\(811\) | 21.7549 | 0.763918 | 0.381959 | − | 0.924179i | \(-0.375250\pi\) | ||||
0.381959 | + | 0.924179i | \(0.375250\pi\) | |||||||
\(812\) | 9.14889 | 0.321063 | ||||||||
\(813\) | 2.43402 | 0.0853647 | ||||||||
\(814\) | 39.3371 | 1.37877 | ||||||||
\(815\) | −10.8662 | −0.380625 | ||||||||
\(816\) | 1.80265 | 0.0631053 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | −62.3802 | −2.18107 | ||||||||
\(819\) | −54.6445 | −1.90943 | ||||||||
\(820\) | 7.93925 | 0.277251 | ||||||||
\(821\) | 52.2532 | 1.82365 | 0.911825 | − | 0.410579i | \(-0.134673\pi\) | ||||
0.911825 | + | 0.410579i | \(0.134673\pi\) | |||||||
\(822\) | 5.35904 | 0.186918 | ||||||||
\(823\) | −9.44783 | −0.329331 | −0.164665 | − | 0.986349i | \(-0.552654\pi\) | ||||
−0.164665 | + | 0.986349i | \(0.552654\pi\) | |||||||
\(824\) | −0.461775 | −0.0160867 | ||||||||
\(825\) | −1.65142 | −0.0574951 | ||||||||
\(826\) | −66.0385 | −2.29777 | ||||||||
\(827\) | 50.2216 | 1.74638 | 0.873188 | − | 0.487383i | \(-0.162048\pi\) | ||||
0.873188 | + | 0.487383i | \(0.162048\pi\) | |||||||
\(828\) | 37.0523 | 1.28766 | ||||||||
\(829\) | −44.2066 | −1.53536 | −0.767680 | − | 0.640834i | \(-0.778589\pi\) | ||||
−0.767680 | + | 0.640834i | \(0.778589\pi\) | |||||||
\(830\) | −8.13083 | −0.282225 | ||||||||
\(831\) | −4.34826 | −0.150839 | ||||||||
\(832\) | 34.4966 | 1.19595 | ||||||||
\(833\) | 8.01200 | 0.277599 | ||||||||
\(834\) | −2.13592 | −0.0739609 | ||||||||
\(835\) | 2.82977 | 0.0979283 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −3.07965 | −0.106448 | ||||||||
\(838\) | −62.2455 | −2.15023 | ||||||||
\(839\) | 30.4033 | 1.04964 | 0.524819 | − | 0.851214i | \(-0.324133\pi\) | ||||
0.524819 | + | 0.851214i | \(0.324133\pi\) | |||||||
\(840\) | −0.360582 | −0.0124413 | ||||||||
\(841\) | −27.0223 | −0.931803 | ||||||||
\(842\) | 0.681799 | 0.0234963 | ||||||||
\(843\) | −9.38404 | −0.323204 | ||||||||
\(844\) | −9.75945 | −0.335934 | ||||||||
\(845\) | −14.7357 | −0.506922 | ||||||||
\(846\) | −47.0473 | −1.61752 | ||||||||
\(847\) | −71.0893 | −2.44266 | ||||||||
\(848\) | −32.8833 | −1.12922 | ||||||||
\(849\) | −7.34168 | −0.251966 | ||||||||
\(850\) | −2.75067 | −0.0943473 | ||||||||
\(851\) | 25.1955 | 0.863690 | ||||||||
\(852\) | −7.62459 | −0.261214 | ||||||||
\(853\) | 3.93925 | 0.134877 | 0.0674386 | − | 0.997723i | \(-0.478517\pi\) | ||||
0.0674386 | + | 0.997723i | \(0.478517\pi\) | |||||||
\(854\) | 64.2232 | 2.19767 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 2.40773 | 0.0822945 | ||||||||
\(857\) | −27.4388 | −0.937292 | −0.468646 | − | 0.883386i | \(-0.655258\pi\) | ||||
−0.468646 | + | 0.883386i | \(0.655258\pi\) | |||||||
\(858\) | −17.0111 | −0.580751 | ||||||||
\(859\) | 32.4517 | 1.10724 | 0.553619 | − | 0.832770i | \(-0.313246\pi\) | ||||
0.553619 | + | 0.832770i | \(0.313246\pi\) | |||||||
\(860\) | 6.50557 | 0.221838 | ||||||||
\(861\) | −4.59966 | −0.156756 | ||||||||
\(862\) | 57.2629 | 1.95038 | ||||||||
\(863\) | 2.10861 | 0.0717778 | 0.0358889 | − | 0.999356i | \(-0.488574\pi\) | ||||
0.0358889 | + | 0.999356i | \(0.488574\pi\) | |||||||
\(864\) | 13.6256 | 0.463553 | ||||||||
\(865\) | −9.26647 | −0.315069 | ||||||||
\(866\) | −1.72766 | −0.0587084 | ||||||||
\(867\) | 4.45924 | 0.151444 | ||||||||
\(868\) | 11.4166 | 0.387504 | ||||||||
\(869\) | −30.4602 | −1.03329 | ||||||||
\(870\) | 0.816515 | 0.0276825 | ||||||||
\(871\) | −25.0731 | −0.849569 | ||||||||
\(872\) | −3.47184 | −0.117571 | ||||||||
\(873\) | 33.5204 | 1.13449 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 3.56331 | 0.120462 | ||||||||
\(876\) | −3.57343 | −0.120735 | ||||||||
\(877\) | 37.6613 | 1.27173 | 0.635866 | − | 0.771799i | \(-0.280643\pi\) | ||||
0.635866 | + | 0.771799i | \(0.280643\pi\) | |||||||
\(878\) | −27.1062 | −0.914789 | ||||||||
\(879\) | 8.99007 | 0.303227 | ||||||||
\(880\) | 24.0235 | 0.809831 | ||||||||
\(881\) | −39.8818 | −1.34365 | −0.671827 | − | 0.740708i | \(-0.734490\pi\) | ||||
−0.671827 | + | 0.740708i | \(0.734490\pi\) | |||||||
\(882\) | 32.4480 | 1.09258 | ||||||||
\(883\) | 36.0458 | 1.21304 | 0.606518 | − | 0.795070i | \(-0.292566\pi\) | ||||
0.606518 | + | 0.795070i | \(0.292566\pi\) | |||||||
\(884\) | −13.5218 | −0.454787 | ||||||||
\(885\) | −2.81263 | −0.0945456 | ||||||||
\(886\) | 26.5525 | 0.892050 | ||||||||
\(887\) | 26.2057 | 0.879902 | 0.439951 | − | 0.898022i | \(-0.354996\pi\) | ||||
0.439951 | + | 0.898022i | \(0.354996\pi\) | |||||||
\(888\) | 0.365818 | 0.0122760 | ||||||||
\(889\) | −17.4264 | −0.584464 | ||||||||
\(890\) | 18.0535 | 0.605155 | ||||||||
\(891\) | 45.7011 | 1.53104 | ||||||||
\(892\) | 5.67700 | 0.190080 | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 4.12186 | 0.137856 | ||||||||
\(895\) | −3.59067 | −0.120023 | ||||||||
\(896\) | 9.68093 | 0.323417 | ||||||||
\(897\) | −10.8957 | −0.363796 | ||||||||
\(898\) | −30.5780 | −1.02040 | ||||||||
\(899\) | 2.46794 | 0.0823103 | ||||||||
\(900\) | −5.31626 | −0.177209 | ||||||||
\(901\) | 10.7092 | 0.356774 | ||||||||
\(902\) | 47.3191 | 1.57555 | ||||||||
\(903\) | −3.76905 | −0.125426 | ||||||||
\(904\) | −0.634123 | −0.0210906 | ||||||||
\(905\) | −19.7630 | −0.656945 | ||||||||
\(906\) | 10.6580 | 0.354088 | ||||||||
\(907\) | 22.8036 | 0.757182 | 0.378591 | − | 0.925564i | \(-0.376409\pi\) | ||||
0.378591 | + | 0.925564i | \(0.376409\pi\) | |||||||
\(908\) | −26.4166 | −0.876664 | ||||||||
\(909\) | 34.5091 | 1.14460 | ||||||||
\(910\) | 36.7053 | 1.21677 | ||||||||
\(911\) | −4.44146 | −0.147152 | −0.0735761 | − | 0.997290i | \(-0.523441\pi\) | ||||
−0.0735761 | + | 0.997290i | \(0.523441\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −23.1266 | −0.765379 | ||||||||
\(914\) | −10.3721 | −0.343077 | ||||||||
\(915\) | 2.73532 | 0.0904268 | ||||||||
\(916\) | −9.52059 | −0.314569 | ||||||||
\(917\) | −10.0223 | −0.330965 | ||||||||
\(918\) | −4.82714 | −0.159319 | ||||||||
\(919\) | 37.0111 | 1.22088 | 0.610442 | − | 0.792061i | \(-0.290992\pi\) | ||||
0.610442 | + | 0.792061i | \(0.290992\pi\) | |||||||
\(920\) | 2.37594 | 0.0783324 | ||||||||
\(921\) | −6.84602 | −0.225584 | ||||||||
\(922\) | −0.732959 | −0.0241387 | ||||||||
\(923\) | −74.0932 | −2.43881 | ||||||||
\(924\) | 10.7434 | 0.353433 | ||||||||
\(925\) | −3.61504 | −0.118862 | ||||||||
\(926\) | −13.0181 | −0.427800 | ||||||||
\(927\) | 3.94438 | 0.129550 | ||||||||
\(928\) | −10.9191 | −0.358438 | ||||||||
\(929\) | −3.04185 | −0.0997999 | −0.0499000 | − | 0.998754i | \(-0.515890\pi\) | ||||
−0.0499000 | + | 0.998754i | \(0.515890\pi\) | |||||||
\(930\) | 1.01890 | 0.0334111 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −5.81921 | −0.190615 | ||||||||
\(933\) | 3.06198 | 0.100245 | ||||||||
\(934\) | 1.67066 | 0.0546657 | ||||||||
\(935\) | −7.82377 | −0.255865 | ||||||||
\(936\) | 5.22781 | 0.170876 | ||||||||
\(937\) | 38.6099 | 1.26133 | 0.630666 | − | 0.776055i | \(-0.282782\pi\) | ||||
0.630666 | + | 0.776055i | \(0.282782\pi\) | |||||||
\(938\) | 33.1817 | 1.08342 | ||||||||
\(939\) | 1.46948 | 0.0479547 | ||||||||
\(940\) | 15.0812 | 0.491895 | ||||||||
\(941\) | −2.69716 | −0.0879248 | −0.0439624 | − | 0.999033i | \(-0.513998\pi\) | ||||
−0.0439624 | + | 0.999033i | \(0.513998\pi\) | |||||||
\(942\) | 10.0039 | 0.325944 | ||||||||
\(943\) | 30.3080 | 0.986963 | ||||||||
\(944\) | 40.9158 | 1.33170 | ||||||||
\(945\) | 6.25323 | 0.203418 | ||||||||
\(946\) | 38.7742 | 1.26066 | ||||||||
\(947\) | −20.1877 | −0.656012 | −0.328006 | − | 0.944676i | \(-0.606377\pi\) | ||||
−0.328006 | + | 0.944676i | \(0.606377\pi\) | |||||||
\(948\) | 2.96727 | 0.0963723 | ||||||||
\(949\) | −34.7254 | −1.12723 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −4.22801 | −0.137103 | ||||||||
\(952\) | −1.70829 | −0.0553661 | ||||||||
\(953\) | −5.18559 | −0.167978 | −0.0839888 | − | 0.996467i | \(-0.526766\pi\) | ||||
−0.0839888 | + | 0.996467i | \(0.526766\pi\) | |||||||
\(954\) | 43.3713 | 1.40420 | ||||||||
\(955\) | −8.31398 | −0.269034 | ||||||||
\(956\) | 30.1624 | 0.975523 | ||||||||
\(957\) | 2.32242 | 0.0750732 | ||||||||
\(958\) | 33.3940 | 1.07891 | ||||||||
\(959\) | −32.8896 | −1.06206 | ||||||||
\(960\) | −1.94438 | −0.0627546 | ||||||||
\(961\) | −27.9203 | −0.900656 | ||||||||
\(962\) | −37.2382 | −1.20061 | ||||||||
\(963\) | −20.5663 | −0.662739 | ||||||||
\(964\) | 22.3231 | 0.718979 | ||||||||
\(965\) | −22.2514 | −0.716299 | ||||||||
\(966\) | 14.4193 | 0.463933 | ||||||||
\(967\) | 58.0054 | 1.86533 | 0.932665 | − | 0.360744i | \(-0.117477\pi\) | ||||
0.932665 | + | 0.360744i | \(0.117477\pi\) | |||||||
\(968\) | 6.80107 | 0.218595 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −22.5160 | −0.722944 | ||||||||
\(971\) | 24.3221 | 0.780533 | 0.390267 | − | 0.920702i | \(-0.372383\pi\) | ||||
0.390267 | + | 0.920702i | \(0.372383\pi\) | |||||||
\(972\) | −14.0637 | −0.451095 | ||||||||
\(973\) | 13.1086 | 0.420244 | ||||||||
\(974\) | 25.0867 | 0.803830 | ||||||||
\(975\) | 1.56331 | 0.0500659 | ||||||||
\(976\) | −39.7911 | −1.27368 | ||||||||
\(977\) | 36.1134 | 1.15537 | 0.577685 | − | 0.816260i | \(-0.303956\pi\) | ||||
0.577685 | + | 0.816260i | \(0.303956\pi\) | |||||||
\(978\) | 6.30895 | 0.201738 | ||||||||
\(979\) | 51.3498 | 1.64115 | ||||||||
\(980\) | −10.4014 | −0.332259 | ||||||||
\(981\) | 29.6557 | 0.946832 | ||||||||
\(982\) | 20.3525 | 0.649473 | ||||||||
\(983\) | −21.1603 | −0.674909 | −0.337455 | − | 0.941342i | \(-0.609566\pi\) | ||||
−0.337455 | + | 0.941342i | \(0.609566\pi\) | |||||||
\(984\) | 0.440046 | 0.0140282 | ||||||||
\(985\) | 8.81263 | 0.280794 | ||||||||
\(986\) | 3.86832 | 0.123192 | ||||||||
\(987\) | −8.73741 | −0.278115 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 24.8349 | 0.789704 | ||||||||
\(990\) | −31.6857 | −1.00704 | ||||||||
\(991\) | −20.2652 | −0.643746 | −0.321873 | − | 0.946783i | \(-0.604312\pi\) | ||||
−0.321873 | + | 0.946783i | \(0.604312\pi\) | |||||||
\(992\) | −13.6256 | −0.432614 | ||||||||
\(993\) | 0.606364 | 0.0192424 | ||||||||
\(994\) | 98.0548 | 3.11011 | ||||||||
\(995\) | −21.0659 | −0.667833 | ||||||||
\(996\) | 2.25287 | 0.0713849 | ||||||||
\(997\) | 24.2875 | 0.769193 | 0.384597 | − | 0.923085i | \(-0.374341\pi\) | ||||
0.384597 | + | 0.923085i | \(0.374341\pi\) | |||||||
\(998\) | −70.7293 | −2.23890 | ||||||||
\(999\) | −6.34402 | −0.200716 |
(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 | 1805.2.a.p.1.1 | 4 | ||
5.4 | even | 2 | 9025.2.a.bf.1.4 | 4 | |||
19.18 | odd | 2 | 95.2.a.b.1.4 | ✓ | 4 | ||
57.56 | even | 2 | 855.2.a.m.1.1 | 4 | |||
76.75 | even | 2 | 1520.2.a.t.1.3 | 4 | |||
95.18 | even | 4 | 475.2.b.e.324.3 | 8 | |||
95.37 | even | 4 | 475.2.b.e.324.6 | 8 | |||
95.94 | odd | 2 | 475.2.a.i.1.1 | 4 | |||
133.132 | even | 2 | 4655.2.a.y.1.4 | 4 | |||
152.37 | odd | 2 | 6080.2.a.cc.1.3 | 4 | |||
152.75 | even | 2 | 6080.2.a.ch.1.2 | 4 | |||
285.284 | even | 2 | 4275.2.a.bo.1.4 | 4 | |||
380.379 | even | 2 | 7600.2.a.cf.1.2 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
95.2.a.b.1.4 | ✓ | 4 | 19.18 | odd | 2 | ||
475.2.a.i.1.1 | 4 | 95.94 | odd | 2 | |||
475.2.b.e.324.3 | 8 | 95.18 | even | 4 | |||
475.2.b.e.324.6 | 8 | 95.37 | even | 4 | |||
855.2.a.m.1.1 | 4 | 57.56 | even | 2 | |||
1520.2.a.t.1.3 | 4 | 76.75 | even | 2 | |||
1805.2.a.p.1.1 | 4 | 1.1 | even | 1 | trivial | ||
4275.2.a.bo.1.4 | 4 | 285.284 | even | 2 | |||
4655.2.a.y.1.4 | 4 | 133.132 | even | 2 | |||
6080.2.a.cc.1.3 | 4 | 152.37 | odd | 2 | |||
6080.2.a.ch.1.2 | 4 | 152.75 | even | 2 | |||
7600.2.a.cf.1.2 | 4 | 380.379 | even | 2 | |||
9025.2.a.bf.1.4 | 4 | 5.4 | even | 2 |