Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4025,2,Mod(1,4025)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4025, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("4025.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4025 = 5^{2} \cdot 7 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4025.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: | \(32.1397868136\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{8} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - x^{7} - 10x^{6} + 9x^{5} + 28x^{4} - 22x^{3} - 16x^{2} + 7x + 3 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-2.07739\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4025.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.07739 | −1.46894 | −0.734469 | − | 0.678642i | \(-0.762569\pi\) | ||||
−0.734469 | + | 0.678642i | \(0.762569\pi\) | |||||||
\(3\) | −0.298210 | −0.172172 | −0.0860859 | − | 0.996288i | \(-0.527436\pi\) | ||||
−0.0860859 | + | 0.996288i | \(0.527436\pi\) | |||||||
\(4\) | 2.31556 | 1.15778 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0.619500 | 0.252910 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | −0.655538 | −0.231768 | ||||||||
\(9\) | −2.91107 | −0.970357 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −0.993361 | −0.299509 | −0.149755 | − | 0.988723i | \(-0.547848\pi\) | ||||
−0.149755 | + | 0.988723i | \(0.547848\pi\) | |||||||
\(12\) | −0.690523 | −0.199337 | ||||||||
\(13\) | −1.85378 | −0.514146 | −0.257073 | − | 0.966392i | \(-0.582758\pi\) | ||||
−0.257073 | + | 0.966392i | \(0.582758\pi\) | |||||||
\(14\) | 2.07739 | 0.555206 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −3.26931 | −0.817327 | ||||||||
\(17\) | 7.16751 | 1.73838 | 0.869188 | − | 0.494482i | \(-0.164642\pi\) | ||||
0.869188 | + | 0.494482i | \(0.164642\pi\) | |||||||
\(18\) | 6.04744 | 1.42539 | ||||||||
\(19\) | −2.81417 | −0.645614 | −0.322807 | − | 0.946465i | \(-0.604627\pi\) | ||||
−0.322807 | + | 0.946465i | \(0.604627\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0.298210 | 0.0650748 | ||||||||
\(22\) | 2.06360 | 0.439961 | ||||||||
\(23\) | 1.00000 | 0.208514 | ||||||||
\(24\) | 0.195488 | 0.0399039 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 3.85103 | 0.755248 | ||||||||
\(27\) | 1.76274 | 0.339240 | ||||||||
\(28\) | −2.31556 | −0.437599 | ||||||||
\(29\) | −4.82054 | −0.895151 | −0.447575 | − | 0.894246i | \(-0.647712\pi\) | ||||
−0.447575 | + | 0.894246i | \(0.647712\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −1.53913 | −0.276436 | −0.138218 | − | 0.990402i | \(-0.544137\pi\) | ||||
−0.138218 | + | 0.990402i | \(0.544137\pi\) | |||||||
\(32\) | 8.10271 | 1.43237 | ||||||||
\(33\) | 0.296230 | 0.0515671 | ||||||||
\(34\) | −14.8897 | −2.55357 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −6.74075 | −1.12346 | ||||||||
\(37\) | 10.5690 | 1.73753 | 0.868765 | − | 0.495225i | \(-0.164914\pi\) | ||||
0.868765 | + | 0.495225i | \(0.164914\pi\) | |||||||
\(38\) | 5.84613 | 0.948367 | ||||||||
\(39\) | 0.552816 | 0.0885214 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −9.37957 | −1.46484 | −0.732421 | − | 0.680852i | \(-0.761610\pi\) | ||||
−0.732421 | + | 0.680852i | \(0.761610\pi\) | |||||||
\(42\) | −0.619500 | −0.0955909 | ||||||||
\(43\) | −12.5692 | −1.91679 | −0.958393 | − | 0.285453i | \(-0.907856\pi\) | ||||
−0.958393 | + | 0.285453i | \(0.907856\pi\) | |||||||
\(44\) | −2.30018 | −0.346766 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −2.07739 | −0.306295 | ||||||||
\(47\) | −3.48711 | −0.508648 | −0.254324 | − | 0.967119i | \(-0.581853\pi\) | ||||
−0.254324 | + | 0.967119i | \(0.581853\pi\) | |||||||
\(48\) | 0.974941 | 0.140721 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −2.13742 | −0.299299 | ||||||||
\(52\) | −4.29253 | −0.595267 | ||||||||
\(53\) | −6.38141 | −0.876555 | −0.438277 | − | 0.898840i | \(-0.644411\pi\) | ||||
−0.438277 | + | 0.898840i | \(0.644411\pi\) | |||||||
\(54\) | −3.66191 | −0.498322 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0.655538 | 0.0876000 | ||||||||
\(57\) | 0.839214 | 0.111157 | ||||||||
\(58\) | 10.0141 | 1.31492 | ||||||||
\(59\) | 7.66700 | 0.998159 | 0.499079 | − | 0.866556i | \(-0.333672\pi\) | ||||
0.499079 | + | 0.866556i | \(0.333672\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −0.599994 | −0.0768214 | −0.0384107 | − | 0.999262i | \(-0.512230\pi\) | ||||
−0.0384107 | + | 0.999262i | \(0.512230\pi\) | |||||||
\(62\) | 3.19737 | 0.406067 | ||||||||
\(63\) | 2.91107 | 0.366760 | ||||||||
\(64\) | −10.2939 | −1.28674 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −0.615387 | −0.0757489 | ||||||||
\(67\) | −0.642727 | −0.0785216 | −0.0392608 | − | 0.999229i | \(-0.512500\pi\) | ||||
−0.0392608 | + | 0.999229i | \(0.512500\pi\) | |||||||
\(68\) | 16.5968 | 2.01265 | ||||||||
\(69\) | −0.298210 | −0.0359003 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 10.5715 | 1.25461 | 0.627304 | − | 0.778775i | \(-0.284158\pi\) | ||||
0.627304 | + | 0.778775i | \(0.284158\pi\) | |||||||
\(72\) | 1.90832 | 0.224897 | ||||||||
\(73\) | 1.17644 | 0.137692 | 0.0688460 | − | 0.997627i | \(-0.478068\pi\) | ||||
0.0688460 | + | 0.997627i | \(0.478068\pi\) | |||||||
\(74\) | −21.9559 | −2.55232 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −6.51637 | −0.747479 | ||||||||
\(77\) | 0.993361 | 0.113204 | ||||||||
\(78\) | −1.14842 | −0.130032 | ||||||||
\(79\) | 2.91935 | 0.328453 | 0.164226 | − | 0.986423i | \(-0.447487\pi\) | ||||
0.164226 | + | 0.986423i | \(0.447487\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 8.20754 | 0.911949 | ||||||||
\(82\) | 19.4850 | 2.15176 | ||||||||
\(83\) | −5.83299 | −0.640253 | −0.320127 | − | 0.947375i | \(-0.603725\pi\) | ||||
−0.320127 | + | 0.947375i | \(0.603725\pi\) | |||||||
\(84\) | 0.690523 | 0.0753423 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 26.1112 | 2.81564 | ||||||||
\(87\) | 1.43753 | 0.154120 | ||||||||
\(88\) | 0.651186 | 0.0694166 | ||||||||
\(89\) | 4.38245 | 0.464539 | 0.232269 | − | 0.972651i | \(-0.425385\pi\) | ||||
0.232269 | + | 0.972651i | \(0.425385\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1.85378 | 0.194329 | ||||||||
\(92\) | 2.31556 | 0.241414 | ||||||||
\(93\) | 0.458984 | 0.0475944 | ||||||||
\(94\) | 7.24410 | 0.747172 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −2.41631 | −0.246614 | ||||||||
\(97\) | −1.70164 | −0.172775 | −0.0863876 | − | 0.996262i | \(-0.527532\pi\) | ||||
−0.0863876 | + | 0.996262i | \(0.527532\pi\) | |||||||
\(98\) | −2.07739 | −0.209848 | ||||||||
\(99\) | 2.89174 | 0.290631 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −17.7515 | −1.76634 | −0.883169 | − | 0.469055i | \(-0.844594\pi\) | ||||
−0.883169 | + | 0.469055i | \(0.844594\pi\) | |||||||
\(102\) | 4.44027 | 0.439652 | ||||||||
\(103\) | 10.2506 | 1.01002 | 0.505010 | − | 0.863114i | \(-0.331489\pi\) | ||||
0.505010 | + | 0.863114i | \(0.331489\pi\) | |||||||
\(104\) | 1.21522 | 0.119162 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 13.2567 | 1.28760 | ||||||||
\(107\) | 8.58885 | 0.830316 | 0.415158 | − | 0.909749i | \(-0.363726\pi\) | ||||
0.415158 | + | 0.909749i | \(0.363726\pi\) | |||||||
\(108\) | 4.08173 | 0.392765 | ||||||||
\(109\) | −19.4159 | −1.85970 | −0.929852 | − | 0.367935i | \(-0.880065\pi\) | ||||
−0.929852 | + | 0.367935i | \(0.880065\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −3.15178 | −0.299154 | ||||||||
\(112\) | 3.26931 | 0.308920 | ||||||||
\(113\) | −4.64453 | −0.436921 | −0.218460 | − | 0.975846i | \(-0.570103\pi\) | ||||
−0.218460 | + | 0.975846i | \(0.570103\pi\) | |||||||
\(114\) | −1.74338 | −0.163282 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −11.1622 | −1.03639 | ||||||||
\(117\) | 5.39648 | 0.498905 | ||||||||
\(118\) | −15.9274 | −1.46623 | ||||||||
\(119\) | −7.16751 | −0.657044 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −10.0132 | −0.910294 | ||||||||
\(122\) | 1.24642 | 0.112846 | ||||||||
\(123\) | 2.79708 | 0.252205 | ||||||||
\(124\) | −3.56394 | −0.320052 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −6.04744 | −0.538748 | ||||||||
\(127\) | 17.5660 | 1.55873 | 0.779366 | − | 0.626569i | \(-0.215541\pi\) | ||||
0.779366 | + | 0.626569i | \(0.215541\pi\) | |||||||
\(128\) | 5.17903 | 0.457766 | ||||||||
\(129\) | 3.74827 | 0.330016 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 13.3723 | 1.16834 | 0.584172 | − | 0.811630i | \(-0.301419\pi\) | ||||
0.584172 | + | 0.811630i | \(0.301419\pi\) | |||||||
\(132\) | 0.685939 | 0.0597033 | ||||||||
\(133\) | 2.81417 | 0.244019 | ||||||||
\(134\) | 1.33520 | 0.115343 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −4.69857 | −0.402899 | ||||||||
\(137\) | 5.20003 | 0.444268 | 0.222134 | − | 0.975016i | \(-0.428698\pi\) | ||||
0.222134 | + | 0.975016i | \(0.428698\pi\) | |||||||
\(138\) | 0.619500 | 0.0527353 | ||||||||
\(139\) | 8.63108 | 0.732079 | 0.366039 | − | 0.930599i | \(-0.380714\pi\) | ||||
0.366039 | + | 0.930599i | \(0.380714\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 1.03989 | 0.0875748 | ||||||||
\(142\) | −21.9612 | −1.84294 | ||||||||
\(143\) | 1.84147 | 0.153992 | ||||||||
\(144\) | 9.51718 | 0.793099 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −2.44393 | −0.202261 | ||||||||
\(147\) | −0.298210 | −0.0245960 | ||||||||
\(148\) | 24.4731 | 2.01168 | ||||||||
\(149\) | 3.58784 | 0.293928 | 0.146964 | − | 0.989142i | \(-0.453050\pi\) | ||||
0.146964 | + | 0.989142i | \(0.453050\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −4.23764 | −0.344854 | −0.172427 | − | 0.985022i | \(-0.555161\pi\) | ||||
−0.172427 | + | 0.985022i | \(0.555161\pi\) | |||||||
\(152\) | 1.84479 | 0.149633 | ||||||||
\(153\) | −20.8651 | −1.68684 | ||||||||
\(154\) | −2.06360 | −0.166290 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 1.28008 | 0.102488 | ||||||||
\(157\) | 7.05240 | 0.562843 | 0.281421 | − | 0.959584i | \(-0.409194\pi\) | ||||
0.281421 | + | 0.959584i | \(0.409194\pi\) | |||||||
\(158\) | −6.06464 | −0.482477 | ||||||||
\(159\) | 1.90300 | 0.150918 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −1.00000 | −0.0788110 | ||||||||
\(162\) | −17.0503 | −1.33960 | ||||||||
\(163\) | 19.7321 | 1.54554 | 0.772769 | − | 0.634688i | \(-0.218871\pi\) | ||||
0.772769 | + | 0.634688i | \(0.218871\pi\) | |||||||
\(164\) | −21.7189 | −1.69596 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 12.1174 | 0.940493 | ||||||||
\(167\) | −19.0253 | −1.47222 | −0.736109 | − | 0.676863i | \(-0.763339\pi\) | ||||
−0.736109 | + | 0.676863i | \(0.763339\pi\) | |||||||
\(168\) | −0.195488 | −0.0150822 | ||||||||
\(169\) | −9.56350 | −0.735654 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 8.19224 | 0.626476 | ||||||||
\(172\) | −29.1047 | −2.21921 | ||||||||
\(173\) | −20.6370 | −1.56900 | −0.784500 | − | 0.620129i | \(-0.787080\pi\) | ||||
−0.784500 | + | 0.620129i | \(0.787080\pi\) | |||||||
\(174\) | −2.98632 | −0.226392 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 3.24760 | 0.244797 | ||||||||
\(177\) | −2.28638 | −0.171855 | ||||||||
\(178\) | −9.10407 | −0.682379 | ||||||||
\(179\) | −14.0344 | −1.04898 | −0.524490 | − | 0.851417i | \(-0.675744\pi\) | ||||
−0.524490 | + | 0.851417i | \(0.675744\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 23.3513 | 1.73569 | 0.867846 | − | 0.496833i | \(-0.165504\pi\) | ||||
0.867846 | + | 0.496833i | \(0.165504\pi\) | |||||||
\(182\) | −3.85103 | −0.285457 | ||||||||
\(183\) | 0.178924 | 0.0132265 | ||||||||
\(184\) | −0.655538 | −0.0483269 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −0.953490 | −0.0699133 | ||||||||
\(187\) | −7.11992 | −0.520660 | ||||||||
\(188\) | −8.07461 | −0.588902 | ||||||||
\(189\) | −1.76274 | −0.128221 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 13.8019 | 0.998674 | 0.499337 | − | 0.866408i | \(-0.333577\pi\) | ||||
0.499337 | + | 0.866408i | \(0.333577\pi\) | |||||||
\(192\) | 3.06974 | 0.221540 | ||||||||
\(193\) | 0.492508 | 0.0354515 | 0.0177257 | − | 0.999843i | \(-0.494357\pi\) | ||||
0.0177257 | + | 0.999843i | \(0.494357\pi\) | |||||||
\(194\) | 3.53497 | 0.253796 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 2.31556 | 0.165397 | ||||||||
\(197\) | 19.1684 | 1.36569 | 0.682846 | − | 0.730562i | \(-0.260742\pi\) | ||||
0.682846 | + | 0.730562i | \(0.260742\pi\) | |||||||
\(198\) | −6.00728 | −0.426919 | ||||||||
\(199\) | 3.57382 | 0.253342 | 0.126671 | − | 0.991945i | \(-0.459571\pi\) | ||||
0.126671 | + | 0.991945i | \(0.459571\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0.191668 | 0.0135192 | ||||||||
\(202\) | 36.8768 | 2.59464 | ||||||||
\(203\) | 4.82054 | 0.338335 | ||||||||
\(204\) | −4.94933 | −0.346522 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −21.2945 | −1.48366 | ||||||||
\(207\) | −2.91107 | −0.202333 | ||||||||
\(208\) | 6.06057 | 0.420225 | ||||||||
\(209\) | 2.79548 | 0.193368 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 2.46333 | 0.169583 | 0.0847914 | − | 0.996399i | \(-0.472978\pi\) | ||||
0.0847914 | + | 0.996399i | \(0.472978\pi\) | |||||||
\(212\) | −14.7765 | −1.01486 | ||||||||
\(213\) | −3.15253 | −0.216008 | ||||||||
\(214\) | −17.8424 | −1.21968 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −1.15554 | −0.0786249 | ||||||||
\(217\) | 1.53913 | 0.104483 | ||||||||
\(218\) | 40.3344 | 2.73179 | ||||||||
\(219\) | −0.350827 | −0.0237067 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −13.2870 | −0.893778 | ||||||||
\(222\) | 6.54748 | 0.439438 | ||||||||
\(223\) | 4.73704 | 0.317215 | 0.158608 | − | 0.987342i | \(-0.449300\pi\) | ||||
0.158608 | + | 0.987342i | \(0.449300\pi\) | |||||||
\(224\) | −8.10271 | −0.541385 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 9.64851 | 0.641809 | ||||||||
\(227\) | −27.2245 | −1.80696 | −0.903478 | − | 0.428635i | \(-0.858995\pi\) | ||||
−0.903478 | + | 0.428635i | \(0.858995\pi\) | |||||||
\(228\) | 1.94325 | 0.128695 | ||||||||
\(229\) | −24.7985 | −1.63873 | −0.819366 | − | 0.573270i | \(-0.805675\pi\) | ||||
−0.819366 | + | 0.573270i | \(0.805675\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −0.296230 | −0.0194905 | ||||||||
\(232\) | 3.16004 | 0.207467 | ||||||||
\(233\) | 23.9620 | 1.56980 | 0.784901 | − | 0.619622i | \(-0.212714\pi\) | ||||
0.784901 | + | 0.619622i | \(0.212714\pi\) | |||||||
\(234\) | −11.2106 | −0.732860 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 17.7534 | 1.15565 | ||||||||
\(237\) | −0.870581 | −0.0565503 | ||||||||
\(238\) | 14.8897 | 0.965157 | ||||||||
\(239\) | −8.04766 | −0.520560 | −0.260280 | − | 0.965533i | \(-0.583815\pi\) | ||||
−0.260280 | + | 0.965533i | \(0.583815\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 9.63222 | 0.620466 | 0.310233 | − | 0.950661i | \(-0.399593\pi\) | ||||
0.310233 | + | 0.950661i | \(0.399593\pi\) | |||||||
\(242\) | 20.8014 | 1.33717 | ||||||||
\(243\) | −7.73580 | −0.496252 | ||||||||
\(244\) | −1.38932 | −0.0889422 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −5.81064 | −0.370473 | ||||||||
\(247\) | 5.21684 | 0.331940 | ||||||||
\(248\) | 1.00896 | 0.0640689 | ||||||||
\(249\) | 1.73946 | 0.110234 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −25.1553 | −1.58779 | −0.793894 | − | 0.608056i | \(-0.791949\pi\) | ||||
−0.793894 | + | 0.608056i | \(0.791949\pi\) | |||||||
\(252\) | 6.74075 | 0.424628 | ||||||||
\(253\) | −0.993361 | −0.0624520 | ||||||||
\(254\) | −36.4915 | −2.28968 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 9.82891 | 0.614307 | ||||||||
\(257\) | −15.3143 | −0.955278 | −0.477639 | − | 0.878556i | \(-0.658507\pi\) | ||||
−0.477639 | + | 0.878556i | \(0.658507\pi\) | |||||||
\(258\) | −7.78662 | −0.484774 | ||||||||
\(259\) | −10.5690 | −0.656725 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 14.0329 | 0.868616 | ||||||||
\(262\) | −27.7795 | −1.71622 | ||||||||
\(263\) | −8.09808 | −0.499349 | −0.249675 | − | 0.968330i | \(-0.580324\pi\) | ||||
−0.249675 | + | 0.968330i | \(0.580324\pi\) | |||||||
\(264\) | −0.194190 | −0.0119516 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −5.84613 | −0.358449 | ||||||||
\(267\) | −1.30689 | −0.0799805 | ||||||||
\(268\) | −1.48827 | −0.0909106 | ||||||||
\(269\) | 19.2842 | 1.17578 | 0.587888 | − | 0.808942i | \(-0.299959\pi\) | ||||
0.587888 | + | 0.808942i | \(0.299959\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 3.10068 | 0.188353 | 0.0941763 | − | 0.995556i | \(-0.469978\pi\) | ||||
0.0941763 | + | 0.995556i | \(0.469978\pi\) | |||||||
\(272\) | −23.4328 | −1.42082 | ||||||||
\(273\) | −0.552816 | −0.0334579 | ||||||||
\(274\) | −10.8025 | −0.652603 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −0.690523 | −0.0415646 | ||||||||
\(277\) | 4.48060 | 0.269213 | 0.134607 | − | 0.990899i | \(-0.457023\pi\) | ||||
0.134607 | + | 0.990899i | \(0.457023\pi\) | |||||||
\(278\) | −17.9301 | −1.07538 | ||||||||
\(279\) | 4.48051 | 0.268241 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 24.4264 | 1.45716 | 0.728579 | − | 0.684962i | \(-0.240181\pi\) | ||||
0.728579 | + | 0.684962i | \(0.240181\pi\) | |||||||
\(282\) | −2.16027 | −0.128642 | ||||||||
\(283\) | 33.3345 | 1.98153 | 0.990765 | − | 0.135592i | \(-0.0432936\pi\) | ||||
0.990765 | + | 0.135592i | \(0.0432936\pi\) | |||||||
\(284\) | 24.4789 | 1.45256 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −3.82546 | −0.226204 | ||||||||
\(287\) | 9.37957 | 0.553658 | ||||||||
\(288\) | −23.5876 | −1.38991 | ||||||||
\(289\) | 34.3731 | 2.02195 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0.507446 | 0.0297470 | ||||||||
\(292\) | 2.72412 | 0.159417 | ||||||||
\(293\) | −3.55759 | −0.207837 | −0.103918 | − | 0.994586i | \(-0.533138\pi\) | ||||
−0.103918 | + | 0.994586i | \(0.533138\pi\) | |||||||
\(294\) | 0.619500 | 0.0361300 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −6.92837 | −0.402703 | ||||||||
\(297\) | −1.75104 | −0.101606 | ||||||||
\(298\) | −7.45336 | −0.431761 | ||||||||
\(299\) | −1.85378 | −0.107207 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 12.5692 | 0.724477 | ||||||||
\(302\) | 8.80323 | 0.506569 | ||||||||
\(303\) | 5.29367 | 0.304114 | ||||||||
\(304\) | 9.20037 | 0.527678 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 43.3450 | 2.47787 | ||||||||
\(307\) | 27.6550 | 1.57836 | 0.789178 | − | 0.614165i | \(-0.210507\pi\) | ||||
0.789178 | + | 0.614165i | \(0.210507\pi\) | |||||||
\(308\) | 2.30018 | 0.131065 | ||||||||
\(309\) | −3.05683 | −0.173897 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 27.8032 | 1.57657 | 0.788287 | − | 0.615308i | \(-0.210968\pi\) | ||||
0.788287 | + | 0.615308i | \(0.210968\pi\) | |||||||
\(312\) | −0.362392 | −0.0205164 | ||||||||
\(313\) | 27.8407 | 1.57365 | 0.786824 | − | 0.617178i | \(-0.211724\pi\) | ||||
0.786824 | + | 0.617178i | \(0.211724\pi\) | |||||||
\(314\) | −14.6506 | −0.826781 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 6.75993 | 0.380276 | ||||||||
\(317\) | −14.6354 | −0.822007 | −0.411003 | − | 0.911634i | \(-0.634822\pi\) | ||||
−0.411003 | + | 0.911634i | \(0.634822\pi\) | |||||||
\(318\) | −3.95328 | −0.221689 | ||||||||
\(319\) | 4.78853 | 0.268106 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −2.56128 | −0.142957 | ||||||||
\(322\) | 2.07739 | 0.115769 | ||||||||
\(323\) | −20.1706 | −1.12232 | ||||||||
\(324\) | 19.0050 | 1.05584 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −40.9913 | −2.27030 | ||||||||
\(327\) | 5.79001 | 0.320188 | ||||||||
\(328\) | 6.14866 | 0.339503 | ||||||||
\(329\) | 3.48711 | 0.192251 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 11.4857 | 0.631309 | 0.315655 | − | 0.948874i | \(-0.397776\pi\) | ||||
0.315655 | + | 0.948874i | \(0.397776\pi\) | |||||||
\(332\) | −13.5066 | −0.741272 | ||||||||
\(333\) | −30.7671 | −1.68602 | ||||||||
\(334\) | 39.5229 | 2.16260 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −0.974941 | −0.0531874 | ||||||||
\(337\) | 1.68540 | 0.0918098 | 0.0459049 | − | 0.998946i | \(-0.485383\pi\) | ||||
0.0459049 | + | 0.998946i | \(0.485383\pi\) | |||||||
\(338\) | 19.8671 | 1.08063 | ||||||||
\(339\) | 1.38505 | 0.0752254 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 1.52891 | 0.0827951 | ||||||||
\(342\) | −17.0185 | −0.920255 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | 8.23959 | 0.444249 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 42.8711 | 2.30476 | ||||||||
\(347\) | 10.1978 | 0.547446 | 0.273723 | − | 0.961809i | \(-0.411745\pi\) | ||||
0.273723 | + | 0.961809i | \(0.411745\pi\) | |||||||
\(348\) | 3.32869 | 0.178437 | ||||||||
\(349\) | 8.14441 | 0.435960 | 0.217980 | − | 0.975953i | \(-0.430053\pi\) | ||||
0.217980 | + | 0.975953i | \(0.430053\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −3.26773 | −0.174419 | ||||||||
\(352\) | −8.04891 | −0.429008 | ||||||||
\(353\) | 26.2377 | 1.39649 | 0.698245 | − | 0.715859i | \(-0.253965\pi\) | ||||
0.698245 | + | 0.715859i | \(0.253965\pi\) | |||||||
\(354\) | 4.74971 | 0.252444 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 10.1478 | 0.537833 | ||||||||
\(357\) | 2.13742 | 0.113124 | ||||||||
\(358\) | 29.1549 | 1.54089 | ||||||||
\(359\) | 0.301901 | 0.0159337 | 0.00796687 | − | 0.999968i | \(-0.497464\pi\) | ||||
0.00796687 | + | 0.999968i | \(0.497464\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −11.0805 | −0.583182 | ||||||||
\(362\) | −48.5099 | −2.54962 | ||||||||
\(363\) | 2.98605 | 0.156727 | ||||||||
\(364\) | 4.29253 | 0.224990 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −0.371696 | −0.0194289 | ||||||||
\(367\) | −13.2434 | −0.691299 | −0.345649 | − | 0.938364i | \(-0.612341\pi\) | ||||
−0.345649 | + | 0.938364i | \(0.612341\pi\) | |||||||
\(368\) | −3.26931 | −0.170424 | ||||||||
\(369\) | 27.3046 | 1.42142 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 6.38141 | 0.331306 | ||||||||
\(372\) | 1.06280 | 0.0551038 | ||||||||
\(373\) | 18.1485 | 0.939694 | 0.469847 | − | 0.882748i | \(-0.344309\pi\) | ||||
0.469847 | + | 0.882748i | \(0.344309\pi\) | |||||||
\(374\) | 14.7909 | 0.764817 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 2.28594 | 0.117888 | ||||||||
\(377\) | 8.93621 | 0.460238 | ||||||||
\(378\) | 3.66191 | 0.188348 | ||||||||
\(379\) | 10.4836 | 0.538508 | 0.269254 | − | 0.963069i | \(-0.413223\pi\) | ||||
0.269254 | + | 0.963069i | \(0.413223\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −5.23836 | −0.268370 | ||||||||
\(382\) | −28.6720 | −1.46699 | ||||||||
\(383\) | 12.0027 | 0.613309 | 0.306655 | − | 0.951821i | \(-0.400790\pi\) | ||||
0.306655 | + | 0.951821i | \(0.400790\pi\) | |||||||
\(384\) | −1.54444 | −0.0788144 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −1.02313 | −0.0520760 | ||||||||
\(387\) | 36.5898 | 1.85997 | ||||||||
\(388\) | −3.94024 | −0.200036 | ||||||||
\(389\) | 33.3345 | 1.69013 | 0.845063 | − | 0.534667i | \(-0.179563\pi\) | ||||
0.845063 | + | 0.534667i | \(0.179563\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 7.16751 | 0.362476 | ||||||||
\(392\) | −0.655538 | −0.0331097 | ||||||||
\(393\) | −3.98776 | −0.201156 | ||||||||
\(394\) | −39.8203 | −2.00612 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 6.69600 | 0.336487 | ||||||||
\(397\) | 26.5014 | 1.33007 | 0.665035 | − | 0.746813i | \(-0.268417\pi\) | ||||
0.665035 | + | 0.746813i | \(0.268417\pi\) | |||||||
\(398\) | −7.42424 | −0.372143 | ||||||||
\(399\) | −0.839214 | −0.0420132 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −24.0298 | −1.19999 | −0.599994 | − | 0.800004i | \(-0.704830\pi\) | ||||
−0.599994 | + | 0.800004i | \(0.704830\pi\) | |||||||
\(402\) | −0.398169 | −0.0198589 | ||||||||
\(403\) | 2.85321 | 0.142128 | ||||||||
\(404\) | −41.1046 | −2.04503 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −10.0141 | −0.496994 | ||||||||
\(407\) | −10.4988 | −0.520407 | ||||||||
\(408\) | 1.40116 | 0.0693679 | ||||||||
\(409\) | 14.4436 | 0.714192 | 0.357096 | − | 0.934068i | \(-0.383767\pi\) | ||||
0.357096 | + | 0.934068i | \(0.383767\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −1.55070 | −0.0764905 | ||||||||
\(412\) | 23.7358 | 1.16938 | ||||||||
\(413\) | −7.66700 | −0.377269 | ||||||||
\(414\) | 6.04744 | 0.297215 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −15.0206 | −0.736447 | ||||||||
\(417\) | −2.57388 | −0.126043 | ||||||||
\(418\) | −5.80731 | −0.284045 | ||||||||
\(419\) | −8.42230 | −0.411456 | −0.205728 | − | 0.978609i | \(-0.565956\pi\) | ||||
−0.205728 | + | 0.978609i | \(0.565956\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −0.0309373 | −0.00150779 | −0.000753895 | − | 1.00000i | \(-0.500240\pi\) | ||||
−0.000753895 | 1.00000i | \(0.500240\pi\) | ||||||||
\(422\) | −5.11731 | −0.249107 | ||||||||
\(423\) | 10.1512 | 0.493570 | ||||||||
\(424\) | 4.18326 | 0.203157 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 6.54905 | 0.317302 | ||||||||
\(427\) | 0.599994 | 0.0290358 | ||||||||
\(428\) | 19.8880 | 0.961322 | ||||||||
\(429\) | −0.549146 | −0.0265130 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 12.2045 | 0.587869 | 0.293935 | − | 0.955826i | \(-0.405035\pi\) | ||||
0.293935 | + | 0.955826i | \(0.405035\pi\) | |||||||
\(432\) | −5.76294 | −0.277270 | ||||||||
\(433\) | −31.3645 | −1.50728 | −0.753641 | − | 0.657287i | \(-0.771704\pi\) | ||||
−0.753641 | + | 0.657287i | \(0.771704\pi\) | |||||||
\(434\) | −3.19737 | −0.153479 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −44.9586 | −2.15313 | ||||||||
\(437\) | −2.81417 | −0.134620 | ||||||||
\(438\) | 0.728805 | 0.0348236 | ||||||||
\(439\) | 23.2752 | 1.11086 | 0.555432 | − | 0.831562i | \(-0.312553\pi\) | ||||
0.555432 | + | 0.831562i | \(0.312553\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −2.91107 | −0.138622 | ||||||||
\(442\) | 27.6023 | 1.31291 | ||||||||
\(443\) | −2.43539 | −0.115709 | −0.0578544 | − | 0.998325i | \(-0.518426\pi\) | ||||
−0.0578544 | + | 0.998325i | \(0.518426\pi\) | |||||||
\(444\) | −7.29813 | −0.346354 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −9.84068 | −0.465970 | ||||||||
\(447\) | −1.06993 | −0.0506060 | ||||||||
\(448\) | 10.2939 | 0.486341 | ||||||||
\(449\) | −4.60139 | −0.217153 | −0.108576 | − | 0.994088i | \(-0.534629\pi\) | ||||
−0.108576 | + | 0.994088i | \(0.534629\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 9.31729 | 0.438734 | ||||||||
\(452\) | −10.7547 | −0.505857 | ||||||||
\(453\) | 1.26371 | 0.0593741 | ||||||||
\(454\) | 56.5560 | 2.65431 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −0.550137 | −0.0257625 | ||||||||
\(457\) | 38.0985 | 1.78217 | 0.891086 | − | 0.453834i | \(-0.149944\pi\) | ||||
0.891086 | + | 0.453834i | \(0.149944\pi\) | |||||||
\(458\) | 51.5163 | 2.40720 | ||||||||
\(459\) | 12.6345 | 0.589726 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 0.378240 | 0.0176164 | 0.00880820 | − | 0.999961i | \(-0.497196\pi\) | ||||
0.00880820 | + | 0.999961i | \(0.497196\pi\) | |||||||
\(462\) | 0.615387 | 0.0286304 | ||||||||
\(463\) | 13.6530 | 0.634508 | 0.317254 | − | 0.948341i | \(-0.397239\pi\) | ||||
0.317254 | + | 0.948341i | \(0.397239\pi\) | |||||||
\(464\) | 15.7598 | 0.731631 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −49.7784 | −2.30594 | ||||||||
\(467\) | −9.71913 | −0.449748 | −0.224874 | − | 0.974388i | \(-0.572197\pi\) | ||||
−0.224874 | + | 0.974388i | \(0.572197\pi\) | |||||||
\(468\) | 12.4959 | 0.577622 | ||||||||
\(469\) | 0.642727 | 0.0296784 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −2.10310 | −0.0969057 | ||||||||
\(472\) | −5.02601 | −0.231341 | ||||||||
\(473\) | 12.4858 | 0.574095 | ||||||||
\(474\) | 1.80854 | 0.0830689 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −16.5968 | −0.760712 | ||||||||
\(477\) | 18.5767 | 0.850571 | ||||||||
\(478\) | 16.7182 | 0.764671 | ||||||||
\(479\) | 34.4600 | 1.57452 | 0.787259 | − | 0.616622i | \(-0.211499\pi\) | ||||
0.787259 | + | 0.616622i | \(0.211499\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −19.5926 | −0.893344 | ||||||||
\(482\) | −20.0099 | −0.911426 | ||||||||
\(483\) | 0.298210 | 0.0135690 | ||||||||
\(484\) | −23.1862 | −1.05392 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 16.0703 | 0.728963 | ||||||||
\(487\) | 35.2140 | 1.59570 | 0.797848 | − | 0.602858i | \(-0.205972\pi\) | ||||
0.797848 | + | 0.602858i | \(0.205972\pi\) | |||||||
\(488\) | 0.393319 | 0.0178047 | ||||||||
\(489\) | −5.88431 | −0.266098 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −27.4004 | −1.23656 | −0.618281 | − | 0.785957i | \(-0.712170\pi\) | ||||
−0.618281 | + | 0.785957i | \(0.712170\pi\) | |||||||
\(492\) | 6.47681 | 0.291997 | ||||||||
\(493\) | −34.5512 | −1.55611 | ||||||||
\(494\) | −10.8374 | −0.487599 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 5.03189 | 0.225938 | ||||||||
\(497\) | −10.5715 | −0.474197 | ||||||||
\(498\) | −3.61353 | −0.161926 | ||||||||
\(499\) | −25.9319 | −1.16087 | −0.580436 | − | 0.814306i | \(-0.697118\pi\) | ||||
−0.580436 | + | 0.814306i | \(0.697118\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 5.67353 | 0.253475 | ||||||||
\(502\) | 52.2574 | 2.33236 | ||||||||
\(503\) | −22.6403 | −1.00948 | −0.504740 | − | 0.863271i | \(-0.668412\pi\) | ||||
−0.504740 | + | 0.863271i | \(0.668412\pi\) | |||||||
\(504\) | −1.90832 | −0.0850032 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 2.06360 | 0.0917382 | ||||||||
\(507\) | 2.85194 | 0.126659 | ||||||||
\(508\) | 40.6751 | 1.80467 | ||||||||
\(509\) | −12.2856 | −0.544551 | −0.272275 | − | 0.962219i | \(-0.587776\pi\) | ||||
−0.272275 | + | 0.962219i | \(0.587776\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −1.17644 | −0.0520427 | ||||||||
\(512\) | −30.7765 | −1.36014 | ||||||||
\(513\) | −4.96065 | −0.219018 | ||||||||
\(514\) | 31.8137 | 1.40324 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 8.67933 | 0.382086 | ||||||||
\(517\) | 3.46396 | 0.152345 | ||||||||
\(518\) | 21.9559 | 0.964688 | ||||||||
\(519\) | 6.15416 | 0.270137 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 13.9977 | 0.613252 | 0.306626 | − | 0.951830i | \(-0.400800\pi\) | ||||
0.306626 | + | 0.951830i | \(0.400800\pi\) | |||||||
\(522\) | −29.1519 | −1.27594 | ||||||||
\(523\) | −9.48038 | −0.414548 | −0.207274 | − | 0.978283i | \(-0.566459\pi\) | ||||
−0.207274 | + | 0.978283i | \(0.566459\pi\) | |||||||
\(524\) | 30.9643 | 1.35268 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 16.8229 | 0.733513 | ||||||||
\(527\) | −11.0317 | −0.480549 | ||||||||
\(528\) | −0.968468 | −0.0421472 | ||||||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −22.3192 | −0.968570 | ||||||||
\(532\) | 6.51637 | 0.282520 | ||||||||
\(533\) | 17.3876 | 0.753143 | ||||||||
\(534\) | 2.71493 | 0.117486 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0.421332 | 0.0181988 | ||||||||
\(537\) | 4.18520 | 0.180605 | ||||||||
\(538\) | −40.0608 | −1.72714 | ||||||||
\(539\) | −0.993361 | −0.0427871 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −13.8876 | −0.597073 | −0.298537 | − | 0.954398i | \(-0.596498\pi\) | ||||
−0.298537 | + | 0.954398i | \(0.596498\pi\) | |||||||
\(542\) | −6.44132 | −0.276678 | ||||||||
\(543\) | −6.96361 | −0.298837 | ||||||||
\(544\) | 58.0762 | 2.49000 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 1.14842 | 0.0491477 | ||||||||
\(547\) | 23.4473 | 1.00253 | 0.501267 | − | 0.865293i | \(-0.332868\pi\) | ||||
0.501267 | + | 0.865293i | \(0.332868\pi\) | |||||||
\(548\) | 12.0410 | 0.514365 | ||||||||
\(549\) | 1.74663 | 0.0745442 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 13.5658 | 0.577922 | ||||||||
\(552\) | 0.195488 | 0.00832053 | ||||||||
\(553\) | −2.91935 | −0.124143 | ||||||||
\(554\) | −9.30797 | −0.395458 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 19.9858 | 0.847585 | ||||||||
\(557\) | −30.0479 | −1.27317 | −0.636586 | − | 0.771206i | \(-0.719654\pi\) | ||||
−0.636586 | + | 0.771206i | \(0.719654\pi\) | |||||||
\(558\) | −9.30778 | −0.394030 | ||||||||
\(559\) | 23.3005 | 0.985507 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 2.12323 | 0.0896430 | ||||||||
\(562\) | −50.7433 | −2.14048 | ||||||||
\(563\) | 10.0913 | 0.425299 | 0.212649 | − | 0.977129i | \(-0.431791\pi\) | ||||
0.212649 | + | 0.977129i | \(0.431791\pi\) | |||||||
\(564\) | 2.40793 | 0.101392 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −69.2488 | −2.91074 | ||||||||
\(567\) | −8.20754 | −0.344684 | ||||||||
\(568\) | −6.93003 | −0.290778 | ||||||||
\(569\) | 5.94085 | 0.249053 | 0.124527 | − | 0.992216i | \(-0.460259\pi\) | ||||
0.124527 | + | 0.992216i | \(0.460259\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 38.5350 | 1.61264 | 0.806320 | − | 0.591480i | \(-0.201456\pi\) | ||||
0.806320 | + | 0.591480i | \(0.201456\pi\) | |||||||
\(572\) | 4.26403 | 0.178288 | ||||||||
\(573\) | −4.11588 | −0.171943 | ||||||||
\(574\) | −19.4850 | −0.813290 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 29.9662 | 1.24859 | ||||||||
\(577\) | 42.5350 | 1.77076 | 0.885378 | − | 0.464871i | \(-0.153899\pi\) | ||||
0.885378 | + | 0.464871i | \(0.153899\pi\) | |||||||
\(578\) | −71.4065 | −2.97012 | ||||||||
\(579\) | −0.146871 | −0.00610375 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 5.83299 | 0.241993 | ||||||||
\(582\) | −1.05416 | −0.0436965 | ||||||||
\(583\) | 6.33904 | 0.262536 | ||||||||
\(584\) | −0.771202 | −0.0319126 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 7.39051 | 0.305299 | ||||||||
\(587\) | 6.45934 | 0.266606 | 0.133303 | − | 0.991075i | \(-0.457442\pi\) | ||||
0.133303 | + | 0.991075i | \(0.457442\pi\) | |||||||
\(588\) | −0.690523 | −0.0284767 | ||||||||
\(589\) | 4.33137 | 0.178471 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −5.71622 | −0.235134 | ||||||||
\(592\) | −34.5532 | −1.42013 | ||||||||
\(593\) | −10.8641 | −0.446134 | −0.223067 | − | 0.974803i | \(-0.571607\pi\) | ||||
−0.223067 | + | 0.974803i | \(0.571607\pi\) | |||||||
\(594\) | 3.63759 | 0.149252 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 8.30786 | 0.340303 | ||||||||
\(597\) | −1.06575 | −0.0436183 | ||||||||
\(598\) | 3.85103 | 0.157480 | ||||||||
\(599\) | −2.31346 | −0.0945254 | −0.0472627 | − | 0.998882i | \(-0.515050\pi\) | ||||
−0.0472627 | + | 0.998882i | \(0.515050\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 29.3276 | 1.19630 | 0.598150 | − | 0.801384i | \(-0.295903\pi\) | ||||
0.598150 | + | 0.801384i | \(0.295903\pi\) | |||||||
\(602\) | −26.1112 | −1.06421 | ||||||||
\(603\) | 1.87102 | 0.0761939 | ||||||||
\(604\) | −9.81249 | −0.399265 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −10.9970 | −0.446724 | ||||||||
\(607\) | 27.0080 | 1.09622 | 0.548111 | − | 0.836406i | \(-0.315347\pi\) | ||||
0.548111 | + | 0.836406i | \(0.315347\pi\) | |||||||
\(608\) | −22.8024 | −0.924758 | ||||||||
\(609\) | −1.43753 | −0.0582518 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 6.46434 | 0.261519 | ||||||||
\(612\) | −48.3144 | −1.95299 | ||||||||
\(613\) | −13.1561 | −0.531372 | −0.265686 | − | 0.964060i | \(-0.585598\pi\) | ||||
−0.265686 | + | 0.964060i | \(0.585598\pi\) | |||||||
\(614\) | −57.4503 | −2.31851 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −0.651186 | −0.0262370 | ||||||||
\(617\) | 39.9124 | 1.60681 | 0.803406 | − | 0.595431i | \(-0.203019\pi\) | ||||
0.803406 | + | 0.595431i | \(0.203019\pi\) | |||||||
\(618\) | 6.35023 | 0.255444 | ||||||||
\(619\) | −9.49735 | −0.381731 | −0.190865 | − | 0.981616i | \(-0.561129\pi\) | ||||
−0.190865 | + | 0.981616i | \(0.561129\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 1.76274 | 0.0707364 | ||||||||
\(622\) | −57.7581 | −2.31589 | ||||||||
\(623\) | −4.38245 | −0.175579 | ||||||||
\(624\) | −1.80733 | −0.0723509 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −57.8360 | −2.31159 | ||||||||
\(627\) | −0.833642 | −0.0332924 | ||||||||
\(628\) | 16.3302 | 0.651648 | ||||||||
\(629\) | 75.7532 | 3.02048 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 0.734808 | 0.0292523 | 0.0146261 | − | 0.999893i | \(-0.495344\pi\) | ||||
0.0146261 | + | 0.999893i | \(0.495344\pi\) | |||||||
\(632\) | −1.91375 | −0.0761247 | ||||||||
\(633\) | −0.734591 | −0.0291974 | ||||||||
\(634\) | 30.4035 | 1.20748 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 4.40651 | 0.174730 | ||||||||
\(637\) | −1.85378 | −0.0734494 | ||||||||
\(638\) | −9.94765 | −0.393831 | ||||||||
\(639\) | −30.7744 | −1.21742 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −29.0820 | −1.14867 | −0.574334 | − | 0.818621i | \(-0.694739\pi\) | ||||
−0.574334 | + | 0.818621i | \(0.694739\pi\) | |||||||
\(642\) | 5.32079 | 0.209995 | ||||||||
\(643\) | 7.73214 | 0.304926 | 0.152463 | − | 0.988309i | \(-0.451280\pi\) | ||||
0.152463 | + | 0.988309i | \(0.451280\pi\) | |||||||
\(644\) | −2.31556 | −0.0912458 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 41.9022 | 1.64862 | ||||||||
\(647\) | −9.05936 | −0.356160 | −0.178080 | − | 0.984016i | \(-0.556989\pi\) | ||||
−0.178080 | + | 0.984016i | \(0.556989\pi\) | |||||||
\(648\) | −5.38036 | −0.211360 | ||||||||
\(649\) | −7.61610 | −0.298958 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −0.458984 | −0.0179890 | ||||||||
\(652\) | 45.6908 | 1.78939 | ||||||||
\(653\) | 15.9458 | 0.624007 | 0.312003 | − | 0.950081i | \(-0.399000\pi\) | ||||
0.312003 | + | 0.950081i | \(0.399000\pi\) | |||||||
\(654\) | −12.0281 | −0.470337 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 30.6647 | 1.19725 | ||||||||
\(657\) | −3.42470 | −0.133610 | ||||||||
\(658\) | −7.24410 | −0.282405 | ||||||||
\(659\) | 6.88170 | 0.268073 | 0.134037 | − | 0.990976i | \(-0.457206\pi\) | ||||
0.134037 | + | 0.990976i | \(0.457206\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −30.2502 | −1.17660 | −0.588298 | − | 0.808644i | \(-0.700202\pi\) | ||||
−0.588298 | + | 0.808644i | \(0.700202\pi\) | |||||||
\(662\) | −23.8602 | −0.927354 | ||||||||
\(663\) | 3.96231 | 0.153883 | ||||||||
\(664\) | 3.82374 | 0.148390 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 63.9152 | 2.47666 | ||||||||
\(667\) | −4.82054 | −0.186652 | ||||||||
\(668\) | −44.0541 | −1.70450 | ||||||||
\(669\) | −1.41263 | −0.0546155 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0.596011 | 0.0230087 | ||||||||
\(672\) | 2.41631 | 0.0932112 | ||||||||
\(673\) | 6.95862 | 0.268235 | 0.134117 | − | 0.990965i | \(-0.457180\pi\) | ||||
0.134117 | + | 0.990965i | \(0.457180\pi\) | |||||||
\(674\) | −3.50124 | −0.134863 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −22.1448 | −0.851725 | ||||||||
\(677\) | 18.0549 | 0.693908 | 0.346954 | − | 0.937882i | \(-0.387216\pi\) | ||||
0.346954 | + | 0.937882i | \(0.387216\pi\) | |||||||
\(678\) | −2.87728 | −0.110501 | ||||||||
\(679\) | 1.70164 | 0.0653029 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 8.11863 | 0.311107 | ||||||||
\(682\) | −3.17615 | −0.121621 | ||||||||
\(683\) | 36.4491 | 1.39469 | 0.697343 | − | 0.716738i | \(-0.254366\pi\) | ||||
0.697343 | + | 0.716738i | \(0.254366\pi\) | |||||||
\(684\) | 18.9696 | 0.725321 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 2.07739 | 0.0793152 | ||||||||
\(687\) | 7.39518 | 0.282144 | ||||||||
\(688\) | 41.0926 | 1.56664 | ||||||||
\(689\) | 11.8297 | 0.450677 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 46.7539 | 1.77860 | 0.889302 | − | 0.457321i | \(-0.151191\pi\) | ||||
0.889302 | + | 0.457321i | \(0.151191\pi\) | |||||||
\(692\) | −47.7861 | −1.81655 | ||||||||
\(693\) | −2.89174 | −0.109848 | ||||||||
\(694\) | −21.1848 | −0.804164 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −0.942358 | −0.0357200 | ||||||||
\(697\) | −67.2281 | −2.54645 | ||||||||
\(698\) | −16.9191 | −0.640399 | ||||||||
\(699\) | −7.14571 | −0.270276 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 5.95624 | 0.224964 | 0.112482 | − | 0.993654i | \(-0.464120\pi\) | ||||
0.112482 | + | 0.993654i | \(0.464120\pi\) | |||||||
\(702\) | 6.78837 | 0.256210 | ||||||||
\(703\) | −29.7429 | −1.12177 | ||||||||
\(704\) | 10.2255 | 0.385390 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −54.5059 | −2.05136 | ||||||||
\(707\) | 17.7515 | 0.667613 | ||||||||
\(708\) | −5.29424 | −0.198970 | ||||||||
\(709\) | 27.2995 | 1.02525 | 0.512627 | − | 0.858611i | \(-0.328672\pi\) | ||||
0.512627 | + | 0.858611i | \(0.328672\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −8.49844 | −0.318716 | ||||||||
\(712\) | −2.87286 | −0.107665 | ||||||||
\(713\) | −1.53913 | −0.0576408 | ||||||||
\(714\) | −4.44027 | −0.166173 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −32.4975 | −1.21449 | ||||||||
\(717\) | 2.39990 | 0.0896258 | ||||||||
\(718\) | −0.627167 | −0.0234057 | ||||||||
\(719\) | 18.4674 | 0.688719 | 0.344359 | − | 0.938838i | \(-0.388096\pi\) | ||||
0.344359 | + | 0.938838i | \(0.388096\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −10.2506 | −0.381751 | ||||||||
\(722\) | 23.0185 | 0.856659 | ||||||||
\(723\) | −2.87243 | −0.106827 | ||||||||
\(724\) | 54.0714 | 2.00955 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −6.20320 | −0.230222 | ||||||||
\(727\) | 3.46127 | 0.128371 | 0.0641856 | − | 0.997938i | \(-0.479555\pi\) | ||||
0.0641856 | + | 0.997938i | \(0.479555\pi\) | |||||||
\(728\) | −1.21522 | −0.0450392 | ||||||||
\(729\) | −22.3157 | −0.826509 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −90.0898 | −3.33209 | ||||||||
\(732\) | 0.414310 | 0.0153133 | ||||||||
\(733\) | −25.2147 | −0.931324 | −0.465662 | − | 0.884963i | \(-0.654184\pi\) | ||||
−0.465662 | + | 0.884963i | \(0.654184\pi\) | |||||||
\(734\) | 27.5117 | 1.01548 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 8.10271 | 0.298670 | ||||||||
\(737\) | 0.638459 | 0.0235180 | ||||||||
\(738\) | −56.7223 | −2.08798 | ||||||||
\(739\) | −0.243657 | −0.00896308 | −0.00448154 | − | 0.999990i | \(-0.501427\pi\) | ||||
−0.00448154 | + | 0.999990i | \(0.501427\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −1.55572 | −0.0571507 | ||||||||
\(742\) | −13.2567 | −0.486669 | ||||||||
\(743\) | −18.9236 | −0.694240 | −0.347120 | − | 0.937821i | \(-0.612840\pi\) | ||||
−0.347120 | + | 0.937821i | \(0.612840\pi\) | |||||||
\(744\) | −0.300882 | −0.0110309 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −37.7016 | −1.38035 | ||||||||
\(747\) | 16.9802 | 0.621274 | ||||||||
\(748\) | −16.4866 | −0.602809 | ||||||||
\(749\) | −8.58885 | −0.313830 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 21.4786 | 0.783764 | 0.391882 | − | 0.920015i | \(-0.371824\pi\) | ||||
0.391882 | + | 0.920015i | \(0.371824\pi\) | |||||||
\(752\) | 11.4004 | 0.415731 | ||||||||
\(753\) | 7.50157 | 0.273372 | ||||||||
\(754\) | −18.5640 | −0.676061 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −4.08173 | −0.148451 | ||||||||
\(757\) | −29.6310 | −1.07696 | −0.538479 | − | 0.842639i | \(-0.681001\pi\) | ||||
−0.538479 | + | 0.842639i | \(0.681001\pi\) | |||||||
\(758\) | −21.7786 | −0.791035 | ||||||||
\(759\) | 0.296230 | 0.0107525 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 33.3358 | 1.20842 | 0.604210 | − | 0.796825i | \(-0.293489\pi\) | ||||
0.604210 | + | 0.796825i | \(0.293489\pi\) | |||||||
\(762\) | 10.8821 | 0.394218 | ||||||||
\(763\) | 19.4159 | 0.702902 | ||||||||
\(764\) | 31.9592 | 1.15624 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −24.9343 | −0.900914 | ||||||||
\(767\) | −14.2129 | −0.513199 | ||||||||
\(768\) | −2.93108 | −0.105766 | ||||||||
\(769\) | −10.8543 | −0.391415 | −0.195708 | − | 0.980662i | \(-0.562700\pi\) | ||||
−0.195708 | + | 0.980662i | \(0.562700\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 4.56687 | 0.164472 | ||||||||
\(772\) | 1.14043 | 0.0410450 | ||||||||
\(773\) | 34.3678 | 1.23612 | 0.618062 | − | 0.786129i | \(-0.287918\pi\) | ||||
0.618062 | + | 0.786129i | \(0.287918\pi\) | |||||||
\(774\) | −76.0114 | −2.73217 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 1.11549 | 0.0400437 | ||||||||
\(777\) | 3.15178 | 0.113069 | ||||||||
\(778\) | −69.2488 | −2.48269 | ||||||||
\(779\) | 26.3957 | 0.945723 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −10.5013 | −0.375767 | ||||||||
\(782\) | −14.8897 | −0.532455 | ||||||||
\(783\) | −8.49736 | −0.303671 | ||||||||
\(784\) | −3.26931 | −0.116761 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 8.28414 | 0.295485 | ||||||||
\(787\) | 4.59388 | 0.163754 | 0.0818771 | − | 0.996642i | \(-0.473909\pi\) | ||||
0.0818771 | + | 0.996642i | \(0.473909\pi\) | |||||||
\(788\) | 44.3856 | 1.58117 | ||||||||
\(789\) | 2.41493 | 0.0859738 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 4.64453 | 0.165140 | ||||||||
\(792\) | −1.89565 | −0.0673589 | ||||||||
\(793\) | 1.11226 | 0.0394974 | ||||||||
\(794\) | −55.0539 | −1.95379 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 8.27540 | 0.293314 | ||||||||
\(797\) | 10.3975 | 0.368300 | 0.184150 | − | 0.982898i | \(-0.441047\pi\) | ||||
0.184150 | + | 0.982898i | \(0.441047\pi\) | |||||||
\(798\) | 1.74338 | 0.0617148 | ||||||||
\(799\) | −24.9939 | −0.884221 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −12.7576 | −0.450768 | ||||||||
\(802\) | 49.9192 | 1.76271 | ||||||||
\(803\) | −1.16863 | −0.0412401 | ||||||||
\(804\) | 0.443818 | 0.0156522 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −5.92723 | −0.208778 | ||||||||
\(807\) | −5.75074 | −0.202436 | ||||||||
\(808\) | 11.6368 | 0.409380 | ||||||||
\(809\) | −5.46014 | −0.191968 | −0.0959842 | − | 0.995383i | \(-0.530600\pi\) | ||||
−0.0959842 | + | 0.995383i | \(0.530600\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 32.7801 | 1.15107 | 0.575533 | − | 0.817779i | \(-0.304795\pi\) | ||||
0.575533 | + | 0.817779i | \(0.304795\pi\) | |||||||
\(812\) | 11.1622 | 0.391718 | ||||||||
\(813\) | −0.924654 | −0.0324290 | ||||||||
\(814\) | 21.8101 | 0.764445 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 6.98789 | 0.244625 | ||||||||
\(817\) | 35.3718 | 1.23750 | ||||||||
\(818\) | −30.0051 | −1.04910 | ||||||||
\(819\) | −5.39648 | −0.188568 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −36.4259 | −1.27127 | −0.635637 | − | 0.771988i | \(-0.719262\pi\) | ||||
−0.635637 | + | 0.771988i | \(0.719262\pi\) | |||||||
\(822\) | 3.22142 | 0.112360 | ||||||||
\(823\) | −44.7894 | −1.56126 | −0.780630 | − | 0.624993i | \(-0.785102\pi\) | ||||
−0.780630 | + | 0.624993i | \(0.785102\pi\) | |||||||
\(824\) | −6.71964 | −0.234090 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 15.9274 | 0.554184 | ||||||||
\(827\) | −48.8330 | −1.69809 | −0.849045 | − | 0.528320i | \(-0.822822\pi\) | ||||
−0.849045 | + | 0.528320i | \(0.822822\pi\) | |||||||
\(828\) | −6.74075 | −0.234257 | ||||||||
\(829\) | −32.9943 | −1.14594 | −0.572970 | − | 0.819577i | \(-0.694209\pi\) | ||||
−0.572970 | + | 0.819577i | \(0.694209\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −1.33616 | −0.0463509 | ||||||||
\(832\) | 19.0826 | 0.661570 | ||||||||
\(833\) | 7.16751 | 0.248339 | ||||||||
\(834\) | 5.34695 | 0.185150 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 6.47310 | 0.223877 | ||||||||
\(837\) | −2.71309 | −0.0937780 | ||||||||
\(838\) | 17.4964 | 0.604404 | ||||||||
\(839\) | 34.9466 | 1.20649 | 0.603246 | − | 0.797555i | \(-0.293874\pi\) | ||||
0.603246 | + | 0.797555i | \(0.293874\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −5.76244 | −0.198705 | ||||||||
\(842\) | 0.0642689 | 0.00221485 | ||||||||
\(843\) | −7.28421 | −0.250882 | ||||||||
\(844\) | 5.70399 | 0.196339 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −21.0881 | −0.725024 | ||||||||
\(847\) | 10.0132 | 0.344059 | ||||||||
\(848\) | 20.8628 | 0.716431 | ||||||||
\(849\) | −9.94069 | −0.341164 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 10.5690 | 0.362300 | ||||||||
\(852\) | −7.29987 | −0.250090 | ||||||||
\(853\) | 2.13264 | 0.0730203 | 0.0365102 | − | 0.999333i | \(-0.488376\pi\) | ||||
0.0365102 | + | 0.999333i | \(0.488376\pi\) | |||||||
\(854\) | −1.24642 | −0.0426517 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −5.63032 | −0.192440 | ||||||||
\(857\) | −28.0616 | −0.958566 | −0.479283 | − | 0.877661i | \(-0.659103\pi\) | ||||
−0.479283 | + | 0.877661i | \(0.659103\pi\) | |||||||
\(858\) | 1.14079 | 0.0389460 | ||||||||
\(859\) | −13.2339 | −0.451534 | −0.225767 | − | 0.974181i | \(-0.572489\pi\) | ||||
−0.225767 | + | 0.974181i | \(0.572489\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −2.79708 | −0.0953244 | ||||||||
\(862\) | −25.3535 | −0.863543 | ||||||||
\(863\) | 13.3156 | 0.453268 | 0.226634 | − | 0.973980i | \(-0.427228\pi\) | ||||
0.226634 | + | 0.973980i | \(0.427228\pi\) | |||||||
\(864\) | 14.2830 | 0.485917 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 65.1563 | 2.21410 | ||||||||
\(867\) | −10.2504 | −0.348123 | ||||||||
\(868\) | 3.56394 | 0.120968 | ||||||||
\(869\) | −2.89997 | −0.0983747 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 1.19147 | 0.0403715 | ||||||||
\(872\) | 12.7278 | 0.431019 | ||||||||
\(873\) | 4.95359 | 0.167654 | ||||||||
\(874\) | 5.84613 | 0.197748 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −0.812360 | −0.0274471 | ||||||||
\(877\) | −19.9266 | −0.672872 | −0.336436 | − | 0.941706i | \(-0.609222\pi\) | ||||
−0.336436 | + | 0.941706i | \(0.609222\pi\) | |||||||
\(878\) | −48.3517 | −1.63179 | ||||||||
\(879\) | 1.06091 | 0.0357836 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −44.8358 | −1.51055 | −0.755277 | − | 0.655405i | \(-0.772498\pi\) | ||||
−0.755277 | + | 0.655405i | \(0.772498\pi\) | |||||||
\(882\) | 6.04744 | 0.203628 | ||||||||
\(883\) | 0.0116754 | 0.000392909 0 | 0.000196455 | − | 1.00000i | \(-0.499937\pi\) | ||||
0.000196455 | 1.00000i | \(0.499937\pi\) | ||||||||
\(884\) | −30.7668 | −1.03480 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 5.05926 | 0.169969 | ||||||||
\(887\) | 43.5198 | 1.46125 | 0.730625 | − | 0.682779i | \(-0.239229\pi\) | ||||
0.730625 | + | 0.682779i | \(0.239229\pi\) | |||||||
\(888\) | 2.06611 | 0.0693342 | ||||||||
\(889\) | −17.5660 | −0.589145 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −8.15305 | −0.273137 | ||||||||
\(892\) | 10.9689 | 0.367265 | ||||||||
\(893\) | 9.81332 | 0.328390 | ||||||||
\(894\) | 2.22267 | 0.0743371 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −5.17903 | −0.173019 | ||||||||
\(897\) | 0.552816 | 0.0184580 | ||||||||
\(898\) | 9.55889 | 0.318984 | ||||||||
\(899\) | 7.41943 | 0.247452 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −45.7388 | −1.52378 | ||||||||
\(902\) | −19.3557 | −0.644473 | ||||||||
\(903\) | −3.74827 | −0.124734 | ||||||||
\(904\) | 3.04467 | 0.101264 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −2.62521 | −0.0872169 | ||||||||
\(907\) | 25.9229 | 0.860757 | 0.430379 | − | 0.902649i | \(-0.358380\pi\) | ||||
0.430379 | + | 0.902649i | \(0.358380\pi\) | |||||||
\(908\) | −63.0400 | −2.09206 | ||||||||
\(909\) | 51.6758 | 1.71398 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 4.06454 | 0.134664 | 0.0673321 | − | 0.997731i | \(-0.478551\pi\) | ||||
0.0673321 | + | 0.997731i | \(0.478551\pi\) | |||||||
\(912\) | −2.74365 | −0.0908512 | ||||||||
\(913\) | 5.79426 | 0.191762 | ||||||||
\(914\) | −79.1455 | −2.61790 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −57.4224 | −1.89729 | ||||||||
\(917\) | −13.3723 | −0.441592 | ||||||||
\(918\) | −26.2467 | −0.866271 | ||||||||
\(919\) | −58.6773 | −1.93558 | −0.967792 | − | 0.251750i | \(-0.918994\pi\) | ||||
−0.967792 | + | 0.251750i | \(0.918994\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −8.24701 | −0.271748 | ||||||||
\(922\) | −0.785753 | −0.0258774 | ||||||||
\(923\) | −19.5972 | −0.645051 | ||||||||
\(924\) | −0.685939 | −0.0225657 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −28.3626 | −0.932053 | ||||||||
\(927\) | −29.8401 | −0.980079 | ||||||||
\(928\) | −39.0594 | −1.28219 | ||||||||
\(929\) | 8.04634 | 0.263992 | 0.131996 | − | 0.991250i | \(-0.457861\pi\) | ||||
0.131996 | + | 0.991250i | \(0.457861\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −2.81417 | −0.0922306 | ||||||||
\(932\) | 55.4854 | 1.81748 | ||||||||
\(933\) | −8.29119 | −0.271442 | ||||||||
\(934\) | 20.1904 | 0.660651 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −3.53760 | −0.115630 | ||||||||
\(937\) | −49.6078 | −1.62061 | −0.810307 | − | 0.586005i | \(-0.800700\pi\) | ||||
−0.810307 | + | 0.586005i | \(0.800700\pi\) | |||||||
\(938\) | −1.33520 | −0.0435957 | ||||||||
\(939\) | −8.30237 | −0.270938 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −37.1651 | −1.21155 | −0.605774 | − | 0.795637i | \(-0.707137\pi\) | ||||
−0.605774 | + | 0.795637i | \(0.707137\pi\) | |||||||
\(942\) | 4.36896 | 0.142348 | ||||||||
\(943\) | −9.37957 | −0.305441 | ||||||||
\(944\) | −25.0658 | −0.815822 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −25.9378 | −0.843311 | ||||||||
\(947\) | −23.8951 | −0.776487 | −0.388243 | − | 0.921557i | \(-0.626918\pi\) | ||||
−0.388243 | + | 0.921557i | \(0.626918\pi\) | |||||||
\(948\) | −2.01588 | −0.0654727 | ||||||||
\(949\) | −2.18086 | −0.0707938 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 4.36443 | 0.141526 | ||||||||
\(952\) | 4.69857 | 0.152282 | ||||||||
\(953\) | 29.3745 | 0.951533 | 0.475766 | − | 0.879572i | \(-0.342171\pi\) | ||||
0.475766 | + | 0.879572i | \(0.342171\pi\) | |||||||
\(954\) | −38.5912 | −1.24944 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −18.6348 | −0.602694 | ||||||||
\(957\) | −1.42799 | −0.0461603 | ||||||||
\(958\) | −71.5870 | −2.31287 | ||||||||
\(959\) | −5.20003 | −0.167918 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −28.6311 | −0.923583 | ||||||||
\(962\) | 40.7014 | 1.31227 | ||||||||
\(963\) | −25.0028 | −0.805702 | ||||||||
\(964\) | 22.3040 | 0.718363 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −0.619500 | −0.0199321 | ||||||||
\(967\) | −13.9363 | −0.448161 | −0.224080 | − | 0.974571i | \(-0.571938\pi\) | ||||
−0.224080 | + | 0.974571i | \(0.571938\pi\) | |||||||
\(968\) | 6.56406 | 0.210977 | ||||||||
\(969\) | 6.01507 | 0.193232 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −17.1508 | −0.550395 | −0.275198 | − | 0.961388i | \(-0.588743\pi\) | ||||
−0.275198 | + | 0.961388i | \(0.588743\pi\) | |||||||
\(972\) | −17.9127 | −0.574550 | ||||||||
\(973\) | −8.63108 | −0.276700 | ||||||||
\(974\) | −73.1532 | −2.34398 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 1.96157 | 0.0627882 | ||||||||
\(977\) | −42.0538 | −1.34542 | −0.672709 | − | 0.739907i | \(-0.734870\pi\) | ||||
−0.672709 | + | 0.739907i | \(0.734870\pi\) | |||||||
\(978\) | 12.2240 | 0.390881 | ||||||||
\(979\) | −4.35335 | −0.139134 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 56.5210 | 1.80458 | ||||||||
\(982\) | 56.9213 | 1.81643 | ||||||||
\(983\) | −48.0416 | −1.53229 | −0.766144 | − | 0.642669i | \(-0.777827\pi\) | ||||
−0.766144 | + | 0.642669i | \(0.777827\pi\) | |||||||
\(984\) | −1.83360 | −0.0584529 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 71.7764 | 2.28583 | ||||||||
\(987\) | −1.03989 | −0.0331002 | ||||||||
\(988\) | 12.0799 | 0.384313 | ||||||||
\(989\) | −12.5692 | −0.399677 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −32.0960 | −1.01956 | −0.509781 | − | 0.860304i | \(-0.670274\pi\) | ||||
−0.509781 | + | 0.860304i | \(0.670274\pi\) | |||||||
\(992\) | −12.4711 | −0.395958 | ||||||||
\(993\) | −3.42514 | −0.108694 | ||||||||
\(994\) | 21.9612 | 0.696566 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 4.02781 | 0.127626 | ||||||||
\(997\) | 51.4259 | 1.62867 | 0.814337 | − | 0.580392i | \(-0.197101\pi\) | ||||
0.814337 | + | 0.580392i | \(0.197101\pi\) | |||||||
\(998\) | 53.8708 | 1.70525 | ||||||||
\(999\) | 18.6304 | 0.589439 |
(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 | 4025.2.a.v.1.2 | yes | 8 | |
5.4 | even | 2 | 4025.2.a.u.1.7 | ✓ | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4025.2.a.u.1.7 | ✓ | 8 | 5.4 | even | 2 | ||
4025.2.a.v.1.2 | yes | 8 | 1.1 | even | 1 | trivial |