Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6045,2,Mod(1,6045)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6045, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("6045.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6045 = 3 \cdot 5 \cdot 13 \cdot 31 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6045.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: | \(48.2695680219\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{12})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - 3 \) |
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 | \(1.73205\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 6045.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.73205 | 1.22474 | 0.612372 | − | 0.790569i | \(-0.290215\pi\) | ||||
0.612372 | + | 0.790569i | \(0.290215\pi\) | |||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | −1.73205 | −0.707107 | ||||||||
\(7\) | 2.00000 | 0.755929 | 0.377964 | − | 0.925820i | \(-0.376624\pi\) | ||||
0.377964 | + | 0.925820i | \(0.376624\pi\) | |||||||
\(8\) | −1.73205 | −0.612372 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | −1.73205 | −0.547723 | ||||||||
\(11\) | −5.73205 | −1.72828 | −0.864139 | − | 0.503253i | \(-0.832136\pi\) | ||||
−0.864139 | + | 0.503253i | \(0.832136\pi\) | |||||||
\(12\) | −1.00000 | −0.288675 | ||||||||
\(13\) | 1.00000 | 0.277350 | ||||||||
\(14\) | 3.46410 | 0.925820 | ||||||||
\(15\) | 1.00000 | 0.258199 | ||||||||
\(16\) | −5.00000 | −1.25000 | ||||||||
\(17\) | 3.46410 | 0.840168 | 0.420084 | − | 0.907485i | \(-0.362001\pi\) | ||||
0.420084 | + | 0.907485i | \(0.362001\pi\) | |||||||
\(18\) | 1.73205 | 0.408248 | ||||||||
\(19\) | 3.00000 | 0.688247 | 0.344124 | − | 0.938924i | \(-0.388176\pi\) | ||||
0.344124 | + | 0.938924i | \(0.388176\pi\) | |||||||
\(20\) | −1.00000 | −0.223607 | ||||||||
\(21\) | −2.00000 | −0.436436 | ||||||||
\(22\) | −9.92820 | −2.11670 | ||||||||
\(23\) | −3.00000 | −0.625543 | −0.312772 | − | 0.949828i | \(-0.601257\pi\) | ||||
−0.312772 | + | 0.949828i | \(0.601257\pi\) | |||||||
\(24\) | 1.73205 | 0.353553 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 1.73205 | 0.339683 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 2.00000 | 0.377964 | ||||||||
\(29\) | −1.73205 | −0.321634 | −0.160817 | − | 0.986984i | \(-0.551413\pi\) | ||||
−0.160817 | + | 0.986984i | \(0.551413\pi\) | |||||||
\(30\) | 1.73205 | 0.316228 | ||||||||
\(31\) | −1.00000 | −0.179605 | ||||||||
\(32\) | −5.19615 | −0.918559 | ||||||||
\(33\) | 5.73205 | 0.997822 | ||||||||
\(34\) | 6.00000 | 1.02899 | ||||||||
\(35\) | −2.00000 | −0.338062 | ||||||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | 4.92820 | 0.810192 | 0.405096 | − | 0.914274i | \(-0.367238\pi\) | ||||
0.405096 | + | 0.914274i | \(0.367238\pi\) | |||||||
\(38\) | 5.19615 | 0.842927 | ||||||||
\(39\) | −1.00000 | −0.160128 | ||||||||
\(40\) | 1.73205 | 0.273861 | ||||||||
\(41\) | 1.00000 | 0.156174 | 0.0780869 | − | 0.996947i | \(-0.475119\pi\) | ||||
0.0780869 | + | 0.996947i | \(0.475119\pi\) | |||||||
\(42\) | −3.46410 | −0.534522 | ||||||||
\(43\) | 4.53590 | 0.691718 | 0.345859 | − | 0.938286i | \(-0.387588\pi\) | ||||
0.345859 | + | 0.938286i | \(0.387588\pi\) | |||||||
\(44\) | −5.73205 | −0.864139 | ||||||||
\(45\) | −1.00000 | −0.149071 | ||||||||
\(46\) | −5.19615 | −0.766131 | ||||||||
\(47\) | −1.73205 | −0.252646 | −0.126323 | − | 0.991989i | \(-0.540318\pi\) | ||||
−0.126323 | + | 0.991989i | \(0.540318\pi\) | |||||||
\(48\) | 5.00000 | 0.721688 | ||||||||
\(49\) | −3.00000 | −0.428571 | ||||||||
\(50\) | 1.73205 | 0.244949 | ||||||||
\(51\) | −3.46410 | −0.485071 | ||||||||
\(52\) | 1.00000 | 0.138675 | ||||||||
\(53\) | 7.46410 | 1.02527 | 0.512637 | − | 0.858606i | \(-0.328669\pi\) | ||||
0.512637 | + | 0.858606i | \(0.328669\pi\) | |||||||
\(54\) | −1.73205 | −0.235702 | ||||||||
\(55\) | 5.73205 | 0.772910 | ||||||||
\(56\) | −3.46410 | −0.462910 | ||||||||
\(57\) | −3.00000 | −0.397360 | ||||||||
\(58\) | −3.00000 | −0.393919 | ||||||||
\(59\) | −0.535898 | −0.0697680 | −0.0348840 | − | 0.999391i | \(-0.511106\pi\) | ||||
−0.0348840 | + | 0.999391i | \(0.511106\pi\) | |||||||
\(60\) | 1.00000 | 0.129099 | ||||||||
\(61\) | −5.46410 | −0.699607 | −0.349803 | − | 0.936823i | \(-0.613752\pi\) | ||||
−0.349803 | + | 0.936823i | \(0.613752\pi\) | |||||||
\(62\) | −1.73205 | −0.219971 | ||||||||
\(63\) | 2.00000 | 0.251976 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −1.00000 | −0.124035 | ||||||||
\(66\) | 9.92820 | 1.22208 | ||||||||
\(67\) | 10.0000 | 1.22169 | 0.610847 | − | 0.791748i | \(-0.290829\pi\) | ||||
0.610847 | + | 0.791748i | \(0.290829\pi\) | |||||||
\(68\) | 3.46410 | 0.420084 | ||||||||
\(69\) | 3.00000 | 0.361158 | ||||||||
\(70\) | −3.46410 | −0.414039 | ||||||||
\(71\) | −2.00000 | −0.237356 | −0.118678 | − | 0.992933i | \(-0.537866\pi\) | ||||
−0.118678 | + | 0.992933i | \(0.537866\pi\) | |||||||
\(72\) | −1.73205 | −0.204124 | ||||||||
\(73\) | 2.53590 | 0.296804 | 0.148402 | − | 0.988927i | \(-0.452587\pi\) | ||||
0.148402 | + | 0.988927i | \(0.452587\pi\) | |||||||
\(74\) | 8.53590 | 0.992278 | ||||||||
\(75\) | −1.00000 | −0.115470 | ||||||||
\(76\) | 3.00000 | 0.344124 | ||||||||
\(77\) | −11.4641 | −1.30646 | ||||||||
\(78\) | −1.73205 | −0.196116 | ||||||||
\(79\) | 3.46410 | 0.389742 | 0.194871 | − | 0.980829i | \(-0.437571\pi\) | ||||
0.194871 | + | 0.980829i | \(0.437571\pi\) | |||||||
\(80\) | 5.00000 | 0.559017 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 1.73205 | 0.191273 | ||||||||
\(83\) | 11.8564 | 1.30141 | 0.650705 | − | 0.759331i | \(-0.274474\pi\) | ||||
0.650705 | + | 0.759331i | \(0.274474\pi\) | |||||||
\(84\) | −2.00000 | −0.218218 | ||||||||
\(85\) | −3.46410 | −0.375735 | ||||||||
\(86\) | 7.85641 | 0.847178 | ||||||||
\(87\) | 1.73205 | 0.185695 | ||||||||
\(88\) | 9.92820 | 1.05835 | ||||||||
\(89\) | 14.0000 | 1.48400 | 0.741999 | − | 0.670402i | \(-0.233878\pi\) | ||||
0.741999 | + | 0.670402i | \(0.233878\pi\) | |||||||
\(90\) | −1.73205 | −0.182574 | ||||||||
\(91\) | 2.00000 | 0.209657 | ||||||||
\(92\) | −3.00000 | −0.312772 | ||||||||
\(93\) | 1.00000 | 0.103695 | ||||||||
\(94\) | −3.00000 | −0.309426 | ||||||||
\(95\) | −3.00000 | −0.307794 | ||||||||
\(96\) | 5.19615 | 0.530330 | ||||||||
\(97\) | −6.92820 | −0.703452 | −0.351726 | − | 0.936103i | \(-0.614405\pi\) | ||||
−0.351726 | + | 0.936103i | \(0.614405\pi\) | |||||||
\(98\) | −5.19615 | −0.524891 | ||||||||
\(99\) | −5.73205 | −0.576093 | ||||||||
\(100\) | 1.00000 | 0.100000 | ||||||||
\(101\) | −13.8564 | −1.37876 | −0.689382 | − | 0.724398i | \(-0.742118\pi\) | ||||
−0.689382 | + | 0.724398i | \(0.742118\pi\) | |||||||
\(102\) | −6.00000 | −0.594089 | ||||||||
\(103\) | 5.73205 | 0.564796 | 0.282398 | − | 0.959297i | \(-0.408870\pi\) | ||||
0.282398 | + | 0.959297i | \(0.408870\pi\) | |||||||
\(104\) | −1.73205 | −0.169842 | ||||||||
\(105\) | 2.00000 | 0.195180 | ||||||||
\(106\) | 12.9282 | 1.25570 | ||||||||
\(107\) | 17.3205 | 1.67444 | 0.837218 | − | 0.546869i | \(-0.184180\pi\) | ||||
0.837218 | + | 0.546869i | \(0.184180\pi\) | |||||||
\(108\) | −1.00000 | −0.0962250 | ||||||||
\(109\) | 10.9282 | 1.04673 | 0.523366 | − | 0.852108i | \(-0.324676\pi\) | ||||
0.523366 | + | 0.852108i | \(0.324676\pi\) | |||||||
\(110\) | 9.92820 | 0.946617 | ||||||||
\(111\) | −4.92820 | −0.467764 | ||||||||
\(112\) | −10.0000 | −0.944911 | ||||||||
\(113\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(114\) | −5.19615 | −0.486664 | ||||||||
\(115\) | 3.00000 | 0.279751 | ||||||||
\(116\) | −1.73205 | −0.160817 | ||||||||
\(117\) | 1.00000 | 0.0924500 | ||||||||
\(118\) | −0.928203 | −0.0854480 | ||||||||
\(119\) | 6.92820 | 0.635107 | ||||||||
\(120\) | −1.73205 | −0.158114 | ||||||||
\(121\) | 21.8564 | 1.98695 | ||||||||
\(122\) | −9.46410 | −0.856840 | ||||||||
\(123\) | −1.00000 | −0.0901670 | ||||||||
\(124\) | −1.00000 | −0.0898027 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 3.46410 | 0.308607 | ||||||||
\(127\) | 11.4641 | 1.01727 | 0.508637 | − | 0.860981i | \(-0.330149\pi\) | ||||
0.508637 | + | 0.860981i | \(0.330149\pi\) | |||||||
\(128\) | 12.1244 | 1.07165 | ||||||||
\(129\) | −4.53590 | −0.399364 | ||||||||
\(130\) | −1.73205 | −0.151911 | ||||||||
\(131\) | 11.0000 | 0.961074 | 0.480537 | − | 0.876974i | \(-0.340442\pi\) | ||||
0.480537 | + | 0.876974i | \(0.340442\pi\) | |||||||
\(132\) | 5.73205 | 0.498911 | ||||||||
\(133\) | 6.00000 | 0.520266 | ||||||||
\(134\) | 17.3205 | 1.49626 | ||||||||
\(135\) | 1.00000 | 0.0860663 | ||||||||
\(136\) | −6.00000 | −0.514496 | ||||||||
\(137\) | −1.92820 | −0.164738 | −0.0823688 | − | 0.996602i | \(-0.526249\pi\) | ||||
−0.0823688 | + | 0.996602i | \(0.526249\pi\) | |||||||
\(138\) | 5.19615 | 0.442326 | ||||||||
\(139\) | −0.660254 | −0.0560020 | −0.0280010 | − | 0.999608i | \(-0.508914\pi\) | ||||
−0.0280010 | + | 0.999608i | \(0.508914\pi\) | |||||||
\(140\) | −2.00000 | −0.169031 | ||||||||
\(141\) | 1.73205 | 0.145865 | ||||||||
\(142\) | −3.46410 | −0.290701 | ||||||||
\(143\) | −5.73205 | −0.479338 | ||||||||
\(144\) | −5.00000 | −0.416667 | ||||||||
\(145\) | 1.73205 | 0.143839 | ||||||||
\(146\) | 4.39230 | 0.363510 | ||||||||
\(147\) | 3.00000 | 0.247436 | ||||||||
\(148\) | 4.92820 | 0.405096 | ||||||||
\(149\) | −17.9282 | −1.46874 | −0.734368 | − | 0.678752i | \(-0.762521\pi\) | ||||
−0.734368 | + | 0.678752i | \(0.762521\pi\) | |||||||
\(150\) | −1.73205 | −0.141421 | ||||||||
\(151\) | 2.39230 | 0.194683 | 0.0973415 | − | 0.995251i | \(-0.468966\pi\) | ||||
0.0973415 | + | 0.995251i | \(0.468966\pi\) | |||||||
\(152\) | −5.19615 | −0.421464 | ||||||||
\(153\) | 3.46410 | 0.280056 | ||||||||
\(154\) | −19.8564 | −1.60007 | ||||||||
\(155\) | 1.00000 | 0.0803219 | ||||||||
\(156\) | −1.00000 | −0.0800641 | ||||||||
\(157\) | −16.5359 | −1.31971 | −0.659854 | − | 0.751394i | \(-0.729382\pi\) | ||||
−0.659854 | + | 0.751394i | \(0.729382\pi\) | |||||||
\(158\) | 6.00000 | 0.477334 | ||||||||
\(159\) | −7.46410 | −0.591942 | ||||||||
\(160\) | 5.19615 | 0.410792 | ||||||||
\(161\) | −6.00000 | −0.472866 | ||||||||
\(162\) | 1.73205 | 0.136083 | ||||||||
\(163\) | 19.4641 | 1.52455 | 0.762273 | − | 0.647256i | \(-0.224083\pi\) | ||||
0.762273 | + | 0.647256i | \(0.224083\pi\) | |||||||
\(164\) | 1.00000 | 0.0780869 | ||||||||
\(165\) | −5.73205 | −0.446240 | ||||||||
\(166\) | 20.5359 | 1.59389 | ||||||||
\(167\) | −18.0000 | −1.39288 | −0.696441 | − | 0.717614i | \(-0.745234\pi\) | ||||
−0.696441 | + | 0.717614i | \(0.745234\pi\) | |||||||
\(168\) | 3.46410 | 0.267261 | ||||||||
\(169\) | 1.00000 | 0.0769231 | ||||||||
\(170\) | −6.00000 | −0.460179 | ||||||||
\(171\) | 3.00000 | 0.229416 | ||||||||
\(172\) | 4.53590 | 0.345859 | ||||||||
\(173\) | 1.19615 | 0.0909418 | 0.0454709 | − | 0.998966i | \(-0.485521\pi\) | ||||
0.0454709 | + | 0.998966i | \(0.485521\pi\) | |||||||
\(174\) | 3.00000 | 0.227429 | ||||||||
\(175\) | 2.00000 | 0.151186 | ||||||||
\(176\) | 28.6603 | 2.16035 | ||||||||
\(177\) | 0.535898 | 0.0402806 | ||||||||
\(178\) | 24.2487 | 1.81752 | ||||||||
\(179\) | 8.00000 | 0.597948 | 0.298974 | − | 0.954261i | \(-0.403356\pi\) | ||||
0.298974 | + | 0.954261i | \(0.403356\pi\) | |||||||
\(180\) | −1.00000 | −0.0745356 | ||||||||
\(181\) | 12.9282 | 0.960946 | 0.480473 | − | 0.877010i | \(-0.340465\pi\) | ||||
0.480473 | + | 0.877010i | \(0.340465\pi\) | |||||||
\(182\) | 3.46410 | 0.256776 | ||||||||
\(183\) | 5.46410 | 0.403918 | ||||||||
\(184\) | 5.19615 | 0.383065 | ||||||||
\(185\) | −4.92820 | −0.362329 | ||||||||
\(186\) | 1.73205 | 0.127000 | ||||||||
\(187\) | −19.8564 | −1.45204 | ||||||||
\(188\) | −1.73205 | −0.126323 | ||||||||
\(189\) | −2.00000 | −0.145479 | ||||||||
\(190\) | −5.19615 | −0.376969 | ||||||||
\(191\) | −21.0000 | −1.51951 | −0.759753 | − | 0.650211i | \(-0.774680\pi\) | ||||
−0.759753 | + | 0.650211i | \(0.774680\pi\) | |||||||
\(192\) | −1.00000 | −0.0721688 | ||||||||
\(193\) | 0.124356 | 0.00895132 | 0.00447566 | − | 0.999990i | \(-0.498575\pi\) | ||||
0.00447566 | + | 0.999990i | \(0.498575\pi\) | |||||||
\(194\) | −12.0000 | −0.861550 | ||||||||
\(195\) | 1.00000 | 0.0716115 | ||||||||
\(196\) | −3.00000 | −0.214286 | ||||||||
\(197\) | 11.9282 | 0.849849 | 0.424925 | − | 0.905229i | \(-0.360301\pi\) | ||||
0.424925 | + | 0.905229i | \(0.360301\pi\) | |||||||
\(198\) | −9.92820 | −0.705567 | ||||||||
\(199\) | 21.1962 | 1.50256 | 0.751278 | − | 0.659986i | \(-0.229438\pi\) | ||||
0.751278 | + | 0.659986i | \(0.229438\pi\) | |||||||
\(200\) | −1.73205 | −0.122474 | ||||||||
\(201\) | −10.0000 | −0.705346 | ||||||||
\(202\) | −24.0000 | −1.68863 | ||||||||
\(203\) | −3.46410 | −0.243132 | ||||||||
\(204\) | −3.46410 | −0.242536 | ||||||||
\(205\) | −1.00000 | −0.0698430 | ||||||||
\(206\) | 9.92820 | 0.691731 | ||||||||
\(207\) | −3.00000 | −0.208514 | ||||||||
\(208\) | −5.00000 | −0.346688 | ||||||||
\(209\) | −17.1962 | −1.18948 | ||||||||
\(210\) | 3.46410 | 0.239046 | ||||||||
\(211\) | 14.5359 | 1.00069 | 0.500346 | − | 0.865825i | \(-0.333206\pi\) | ||||
0.500346 | + | 0.865825i | \(0.333206\pi\) | |||||||
\(212\) | 7.46410 | 0.512637 | ||||||||
\(213\) | 2.00000 | 0.137038 | ||||||||
\(214\) | 30.0000 | 2.05076 | ||||||||
\(215\) | −4.53590 | −0.309346 | ||||||||
\(216\) | 1.73205 | 0.117851 | ||||||||
\(217\) | −2.00000 | −0.135769 | ||||||||
\(218\) | 18.9282 | 1.28198 | ||||||||
\(219\) | −2.53590 | −0.171360 | ||||||||
\(220\) | 5.73205 | 0.386455 | ||||||||
\(221\) | 3.46410 | 0.233021 | ||||||||
\(222\) | −8.53590 | −0.572892 | ||||||||
\(223\) | 26.7128 | 1.78882 | 0.894411 | − | 0.447246i | \(-0.147595\pi\) | ||||
0.894411 | + | 0.447246i | \(0.147595\pi\) | |||||||
\(224\) | −10.3923 | −0.694365 | ||||||||
\(225\) | 1.00000 | 0.0666667 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 22.5167 | 1.49448 | 0.747242 | − | 0.664552i | \(-0.231378\pi\) | ||||
0.747242 | + | 0.664552i | \(0.231378\pi\) | |||||||
\(228\) | −3.00000 | −0.198680 | ||||||||
\(229\) | 4.66025 | 0.307958 | 0.153979 | − | 0.988074i | \(-0.450791\pi\) | ||||
0.153979 | + | 0.988074i | \(0.450791\pi\) | |||||||
\(230\) | 5.19615 | 0.342624 | ||||||||
\(231\) | 11.4641 | 0.754283 | ||||||||
\(232\) | 3.00000 | 0.196960 | ||||||||
\(233\) | 1.73205 | 0.113470 | 0.0567352 | − | 0.998389i | \(-0.481931\pi\) | ||||
0.0567352 | + | 0.998389i | \(0.481931\pi\) | |||||||
\(234\) | 1.73205 | 0.113228 | ||||||||
\(235\) | 1.73205 | 0.112987 | ||||||||
\(236\) | −0.535898 | −0.0348840 | ||||||||
\(237\) | −3.46410 | −0.225018 | ||||||||
\(238\) | 12.0000 | 0.777844 | ||||||||
\(239\) | −5.32051 | −0.344155 | −0.172078 | − | 0.985083i | \(-0.555048\pi\) | ||||
−0.172078 | + | 0.985083i | \(0.555048\pi\) | |||||||
\(240\) | −5.00000 | −0.322749 | ||||||||
\(241\) | −18.5167 | −1.19276 | −0.596381 | − | 0.802701i | \(-0.703395\pi\) | ||||
−0.596381 | + | 0.802701i | \(0.703395\pi\) | |||||||
\(242\) | 37.8564 | 2.43350 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | −5.46410 | −0.349803 | ||||||||
\(245\) | 3.00000 | 0.191663 | ||||||||
\(246\) | −1.73205 | −0.110432 | ||||||||
\(247\) | 3.00000 | 0.190885 | ||||||||
\(248\) | 1.73205 | 0.109985 | ||||||||
\(249\) | −11.8564 | −0.751369 | ||||||||
\(250\) | −1.73205 | −0.109545 | ||||||||
\(251\) | 16.3923 | 1.03467 | 0.517337 | − | 0.855782i | \(-0.326924\pi\) | ||||
0.517337 | + | 0.855782i | \(0.326924\pi\) | |||||||
\(252\) | 2.00000 | 0.125988 | ||||||||
\(253\) | 17.1962 | 1.08111 | ||||||||
\(254\) | 19.8564 | 1.24590 | ||||||||
\(255\) | 3.46410 | 0.216930 | ||||||||
\(256\) | 19.0000 | 1.18750 | ||||||||
\(257\) | 17.7321 | 1.10609 | 0.553047 | − | 0.833150i | \(-0.313465\pi\) | ||||
0.553047 | + | 0.833150i | \(0.313465\pi\) | |||||||
\(258\) | −7.85641 | −0.489119 | ||||||||
\(259\) | 9.85641 | 0.612447 | ||||||||
\(260\) | −1.00000 | −0.0620174 | ||||||||
\(261\) | −1.73205 | −0.107211 | ||||||||
\(262\) | 19.0526 | 1.17707 | ||||||||
\(263\) | −20.8564 | −1.28606 | −0.643031 | − | 0.765841i | \(-0.722323\pi\) | ||||
−0.643031 | + | 0.765841i | \(0.722323\pi\) | |||||||
\(264\) | −9.92820 | −0.611039 | ||||||||
\(265\) | −7.46410 | −0.458516 | ||||||||
\(266\) | 10.3923 | 0.637193 | ||||||||
\(267\) | −14.0000 | −0.856786 | ||||||||
\(268\) | 10.0000 | 0.610847 | ||||||||
\(269\) | −18.9282 | −1.15407 | −0.577036 | − | 0.816718i | \(-0.695791\pi\) | ||||
−0.577036 | + | 0.816718i | \(0.695791\pi\) | |||||||
\(270\) | 1.73205 | 0.105409 | ||||||||
\(271\) | 11.4641 | 0.696395 | 0.348197 | − | 0.937421i | \(-0.386794\pi\) | ||||
0.348197 | + | 0.937421i | \(0.386794\pi\) | |||||||
\(272\) | −17.3205 | −1.05021 | ||||||||
\(273\) | −2.00000 | −0.121046 | ||||||||
\(274\) | −3.33975 | −0.201761 | ||||||||
\(275\) | −5.73205 | −0.345656 | ||||||||
\(276\) | 3.00000 | 0.180579 | ||||||||
\(277\) | 16.0718 | 0.965661 | 0.482830 | − | 0.875714i | \(-0.339609\pi\) | ||||
0.482830 | + | 0.875714i | \(0.339609\pi\) | |||||||
\(278\) | −1.14359 | −0.0685882 | ||||||||
\(279\) | −1.00000 | −0.0598684 | ||||||||
\(280\) | 3.46410 | 0.207020 | ||||||||
\(281\) | −11.7846 | −0.703011 | −0.351505 | − | 0.936186i | \(-0.614330\pi\) | ||||
−0.351505 | + | 0.936186i | \(0.614330\pi\) | |||||||
\(282\) | 3.00000 | 0.178647 | ||||||||
\(283\) | 19.5885 | 1.16441 | 0.582206 | − | 0.813041i | \(-0.302190\pi\) | ||||
0.582206 | + | 0.813041i | \(0.302190\pi\) | |||||||
\(284\) | −2.00000 | −0.118678 | ||||||||
\(285\) | 3.00000 | 0.177705 | ||||||||
\(286\) | −9.92820 | −0.587067 | ||||||||
\(287\) | 2.00000 | 0.118056 | ||||||||
\(288\) | −5.19615 | −0.306186 | ||||||||
\(289\) | −5.00000 | −0.294118 | ||||||||
\(290\) | 3.00000 | 0.176166 | ||||||||
\(291\) | 6.92820 | 0.406138 | ||||||||
\(292\) | 2.53590 | 0.148402 | ||||||||
\(293\) | −3.46410 | −0.202375 | −0.101187 | − | 0.994867i | \(-0.532264\pi\) | ||||
−0.101187 | + | 0.994867i | \(0.532264\pi\) | |||||||
\(294\) | 5.19615 | 0.303046 | ||||||||
\(295\) | 0.535898 | 0.0312012 | ||||||||
\(296\) | −8.53590 | −0.496139 | ||||||||
\(297\) | 5.73205 | 0.332607 | ||||||||
\(298\) | −31.0526 | −1.79883 | ||||||||
\(299\) | −3.00000 | −0.173494 | ||||||||
\(300\) | −1.00000 | −0.0577350 | ||||||||
\(301\) | 9.07180 | 0.522890 | ||||||||
\(302\) | 4.14359 | 0.238437 | ||||||||
\(303\) | 13.8564 | 0.796030 | ||||||||
\(304\) | −15.0000 | −0.860309 | ||||||||
\(305\) | 5.46410 | 0.312874 | ||||||||
\(306\) | 6.00000 | 0.342997 | ||||||||
\(307\) | −21.8564 | −1.24741 | −0.623706 | − | 0.781659i | \(-0.714374\pi\) | ||||
−0.623706 | + | 0.781659i | \(0.714374\pi\) | |||||||
\(308\) | −11.4641 | −0.653228 | ||||||||
\(309\) | −5.73205 | −0.326085 | ||||||||
\(310\) | 1.73205 | 0.0983739 | ||||||||
\(311\) | −20.0000 | −1.13410 | −0.567048 | − | 0.823685i | \(-0.691915\pi\) | ||||
−0.567048 | + | 0.823685i | \(0.691915\pi\) | |||||||
\(312\) | 1.73205 | 0.0980581 | ||||||||
\(313\) | 10.8564 | 0.613640 | 0.306820 | − | 0.951767i | \(-0.400735\pi\) | ||||
0.306820 | + | 0.951767i | \(0.400735\pi\) | |||||||
\(314\) | −28.6410 | −1.61631 | ||||||||
\(315\) | −2.00000 | −0.112687 | ||||||||
\(316\) | 3.46410 | 0.194871 | ||||||||
\(317\) | −4.53590 | −0.254761 | −0.127381 | − | 0.991854i | \(-0.540657\pi\) | ||||
−0.127381 | + | 0.991854i | \(0.540657\pi\) | |||||||
\(318\) | −12.9282 | −0.724978 | ||||||||
\(319\) | 9.92820 | 0.555873 | ||||||||
\(320\) | −1.00000 | −0.0559017 | ||||||||
\(321\) | −17.3205 | −0.966736 | ||||||||
\(322\) | −10.3923 | −0.579141 | ||||||||
\(323\) | 10.3923 | 0.578243 | ||||||||
\(324\) | 1.00000 | 0.0555556 | ||||||||
\(325\) | 1.00000 | 0.0554700 | ||||||||
\(326\) | 33.7128 | 1.86718 | ||||||||
\(327\) | −10.9282 | −0.604331 | ||||||||
\(328\) | −1.73205 | −0.0956365 | ||||||||
\(329\) | −3.46410 | −0.190982 | ||||||||
\(330\) | −9.92820 | −0.546530 | ||||||||
\(331\) | −3.32051 | −0.182512 | −0.0912558 | − | 0.995827i | \(-0.529088\pi\) | ||||
−0.0912558 | + | 0.995827i | \(0.529088\pi\) | |||||||
\(332\) | 11.8564 | 0.650705 | ||||||||
\(333\) | 4.92820 | 0.270064 | ||||||||
\(334\) | −31.1769 | −1.70592 | ||||||||
\(335\) | −10.0000 | −0.546358 | ||||||||
\(336\) | 10.0000 | 0.545545 | ||||||||
\(337\) | 16.0718 | 0.875487 | 0.437743 | − | 0.899100i | \(-0.355778\pi\) | ||||
0.437743 | + | 0.899100i | \(0.355778\pi\) | |||||||
\(338\) | 1.73205 | 0.0942111 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −3.46410 | −0.187867 | ||||||||
\(341\) | 5.73205 | 0.310408 | ||||||||
\(342\) | 5.19615 | 0.280976 | ||||||||
\(343\) | −20.0000 | −1.07990 | ||||||||
\(344\) | −7.85641 | −0.423589 | ||||||||
\(345\) | −3.00000 | −0.161515 | ||||||||
\(346\) | 2.07180 | 0.111380 | ||||||||
\(347\) | 8.07180 | 0.433317 | 0.216658 | − | 0.976247i | \(-0.430484\pi\) | ||||
0.216658 | + | 0.976247i | \(0.430484\pi\) | |||||||
\(348\) | 1.73205 | 0.0928477 | ||||||||
\(349\) | −20.3923 | −1.09158 | −0.545788 | − | 0.837924i | \(-0.683769\pi\) | ||||
−0.545788 | + | 0.837924i | \(0.683769\pi\) | |||||||
\(350\) | 3.46410 | 0.185164 | ||||||||
\(351\) | −1.00000 | −0.0533761 | ||||||||
\(352\) | 29.7846 | 1.58753 | ||||||||
\(353\) | 14.0000 | 0.745145 | 0.372572 | − | 0.928003i | \(-0.378476\pi\) | ||||
0.372572 | + | 0.928003i | \(0.378476\pi\) | |||||||
\(354\) | 0.928203 | 0.0493334 | ||||||||
\(355\) | 2.00000 | 0.106149 | ||||||||
\(356\) | 14.0000 | 0.741999 | ||||||||
\(357\) | −6.92820 | −0.366679 | ||||||||
\(358\) | 13.8564 | 0.732334 | ||||||||
\(359\) | 0.143594 | 0.00757858 | 0.00378929 | − | 0.999993i | \(-0.498794\pi\) | ||||
0.00378929 | + | 0.999993i | \(0.498794\pi\) | |||||||
\(360\) | 1.73205 | 0.0912871 | ||||||||
\(361\) | −10.0000 | −0.526316 | ||||||||
\(362\) | 22.3923 | 1.17691 | ||||||||
\(363\) | −21.8564 | −1.14716 | ||||||||
\(364\) | 2.00000 | 0.104828 | ||||||||
\(365\) | −2.53590 | −0.132735 | ||||||||
\(366\) | 9.46410 | 0.494697 | ||||||||
\(367\) | 32.0000 | 1.67039 | 0.835193 | − | 0.549957i | \(-0.185356\pi\) | ||||
0.835193 | + | 0.549957i | \(0.185356\pi\) | |||||||
\(368\) | 15.0000 | 0.781929 | ||||||||
\(369\) | 1.00000 | 0.0520579 | ||||||||
\(370\) | −8.53590 | −0.443760 | ||||||||
\(371\) | 14.9282 | 0.775034 | ||||||||
\(372\) | 1.00000 | 0.0518476 | ||||||||
\(373\) | 3.07180 | 0.159052 | 0.0795258 | − | 0.996833i | \(-0.474659\pi\) | ||||
0.0795258 | + | 0.996833i | \(0.474659\pi\) | |||||||
\(374\) | −34.3923 | −1.77838 | ||||||||
\(375\) | 1.00000 | 0.0516398 | ||||||||
\(376\) | 3.00000 | 0.154713 | ||||||||
\(377\) | −1.73205 | −0.0892052 | ||||||||
\(378\) | −3.46410 | −0.178174 | ||||||||
\(379\) | 34.8564 | 1.79045 | 0.895227 | − | 0.445611i | \(-0.147014\pi\) | ||||
0.895227 | + | 0.445611i | \(0.147014\pi\) | |||||||
\(380\) | −3.00000 | −0.153897 | ||||||||
\(381\) | −11.4641 | −0.587324 | ||||||||
\(382\) | −36.3731 | −1.86101 | ||||||||
\(383\) | −20.5359 | −1.04934 | −0.524668 | − | 0.851307i | \(-0.675810\pi\) | ||||
−0.524668 | + | 0.851307i | \(0.675810\pi\) | |||||||
\(384\) | −12.1244 | −0.618718 | ||||||||
\(385\) | 11.4641 | 0.584265 | ||||||||
\(386\) | 0.215390 | 0.0109631 | ||||||||
\(387\) | 4.53590 | 0.230573 | ||||||||
\(388\) | −6.92820 | −0.351726 | ||||||||
\(389\) | −2.92820 | −0.148466 | −0.0742329 | − | 0.997241i | \(-0.523651\pi\) | ||||
−0.0742329 | + | 0.997241i | \(0.523651\pi\) | |||||||
\(390\) | 1.73205 | 0.0877058 | ||||||||
\(391\) | −10.3923 | −0.525561 | ||||||||
\(392\) | 5.19615 | 0.262445 | ||||||||
\(393\) | −11.0000 | −0.554877 | ||||||||
\(394\) | 20.6603 | 1.04085 | ||||||||
\(395\) | −3.46410 | −0.174298 | ||||||||
\(396\) | −5.73205 | −0.288046 | ||||||||
\(397\) | −27.0526 | −1.35773 | −0.678865 | − | 0.734264i | \(-0.737528\pi\) | ||||
−0.678865 | + | 0.734264i | \(0.737528\pi\) | |||||||
\(398\) | 36.7128 | 1.84025 | ||||||||
\(399\) | −6.00000 | −0.300376 | ||||||||
\(400\) | −5.00000 | −0.250000 | ||||||||
\(401\) | 34.6410 | 1.72989 | 0.864945 | − | 0.501867i | \(-0.167353\pi\) | ||||
0.864945 | + | 0.501867i | \(0.167353\pi\) | |||||||
\(402\) | −17.3205 | −0.863868 | ||||||||
\(403\) | −1.00000 | −0.0498135 | ||||||||
\(404\) | −13.8564 | −0.689382 | ||||||||
\(405\) | −1.00000 | −0.0496904 | ||||||||
\(406\) | −6.00000 | −0.297775 | ||||||||
\(407\) | −28.2487 | −1.40024 | ||||||||
\(408\) | 6.00000 | 0.297044 | ||||||||
\(409\) | −26.5167 | −1.31116 | −0.655582 | − | 0.755124i | \(-0.727577\pi\) | ||||
−0.655582 | + | 0.755124i | \(0.727577\pi\) | |||||||
\(410\) | −1.73205 | −0.0855399 | ||||||||
\(411\) | 1.92820 | 0.0951113 | ||||||||
\(412\) | 5.73205 | 0.282398 | ||||||||
\(413\) | −1.07180 | −0.0527397 | ||||||||
\(414\) | −5.19615 | −0.255377 | ||||||||
\(415\) | −11.8564 | −0.582008 | ||||||||
\(416\) | −5.19615 | −0.254762 | ||||||||
\(417\) | 0.660254 | 0.0323328 | ||||||||
\(418\) | −29.7846 | −1.45681 | ||||||||
\(419\) | −0.856406 | −0.0418382 | −0.0209191 | − | 0.999781i | \(-0.506659\pi\) | ||||
−0.0209191 | + | 0.999781i | \(0.506659\pi\) | |||||||
\(420\) | 2.00000 | 0.0975900 | ||||||||
\(421\) | −38.6410 | −1.88325 | −0.941624 | − | 0.336667i | \(-0.890701\pi\) | ||||
−0.941624 | + | 0.336667i | \(0.890701\pi\) | |||||||
\(422\) | 25.1769 | 1.22559 | ||||||||
\(423\) | −1.73205 | −0.0842152 | ||||||||
\(424\) | −12.9282 | −0.627849 | ||||||||
\(425\) | 3.46410 | 0.168034 | ||||||||
\(426\) | 3.46410 | 0.167836 | ||||||||
\(427\) | −10.9282 | −0.528853 | ||||||||
\(428\) | 17.3205 | 0.837218 | ||||||||
\(429\) | 5.73205 | 0.276746 | ||||||||
\(430\) | −7.85641 | −0.378870 | ||||||||
\(431\) | −6.39230 | −0.307906 | −0.153953 | − | 0.988078i | \(-0.549201\pi\) | ||||
−0.153953 | + | 0.988078i | \(0.549201\pi\) | |||||||
\(432\) | 5.00000 | 0.240563 | ||||||||
\(433\) | −21.9282 | −1.05380 | −0.526901 | − | 0.849927i | \(-0.676646\pi\) | ||||
−0.526901 | + | 0.849927i | \(0.676646\pi\) | |||||||
\(434\) | −3.46410 | −0.166282 | ||||||||
\(435\) | −1.73205 | −0.0830455 | ||||||||
\(436\) | 10.9282 | 0.523366 | ||||||||
\(437\) | −9.00000 | −0.430528 | ||||||||
\(438\) | −4.39230 | −0.209872 | ||||||||
\(439\) | 1.07180 | 0.0511541 | 0.0255770 | − | 0.999673i | \(-0.491858\pi\) | ||||
0.0255770 | + | 0.999673i | \(0.491858\pi\) | |||||||
\(440\) | −9.92820 | −0.473309 | ||||||||
\(441\) | −3.00000 | −0.142857 | ||||||||
\(442\) | 6.00000 | 0.285391 | ||||||||
\(443\) | −28.3923 | −1.34896 | −0.674480 | − | 0.738294i | \(-0.735632\pi\) | ||||
−0.674480 | + | 0.738294i | \(0.735632\pi\) | |||||||
\(444\) | −4.92820 | −0.233882 | ||||||||
\(445\) | −14.0000 | −0.663664 | ||||||||
\(446\) | 46.2679 | 2.19085 | ||||||||
\(447\) | 17.9282 | 0.847975 | ||||||||
\(448\) | 2.00000 | 0.0944911 | ||||||||
\(449\) | −10.0000 | −0.471929 | −0.235965 | − | 0.971762i | \(-0.575825\pi\) | ||||
−0.235965 | + | 0.971762i | \(0.575825\pi\) | |||||||
\(450\) | 1.73205 | 0.0816497 | ||||||||
\(451\) | −5.73205 | −0.269912 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −2.39230 | −0.112400 | ||||||||
\(454\) | 39.0000 | 1.83036 | ||||||||
\(455\) | −2.00000 | −0.0937614 | ||||||||
\(456\) | 5.19615 | 0.243332 | ||||||||
\(457\) | −19.4641 | −0.910492 | −0.455246 | − | 0.890366i | \(-0.650449\pi\) | ||||
−0.455246 | + | 0.890366i | \(0.650449\pi\) | |||||||
\(458\) | 8.07180 | 0.377170 | ||||||||
\(459\) | −3.46410 | −0.161690 | ||||||||
\(460\) | 3.00000 | 0.139876 | ||||||||
\(461\) | 23.0718 | 1.07456 | 0.537280 | − | 0.843404i | \(-0.319452\pi\) | ||||
0.537280 | + | 0.843404i | \(0.319452\pi\) | |||||||
\(462\) | 19.8564 | 0.923804 | ||||||||
\(463\) | 2.92820 | 0.136085 | 0.0680426 | − | 0.997682i | \(-0.478325\pi\) | ||||
0.0680426 | + | 0.997682i | \(0.478325\pi\) | |||||||
\(464\) | 8.66025 | 0.402042 | ||||||||
\(465\) | −1.00000 | −0.0463739 | ||||||||
\(466\) | 3.00000 | 0.138972 | ||||||||
\(467\) | 26.6410 | 1.23280 | 0.616400 | − | 0.787434i | \(-0.288591\pi\) | ||||
0.616400 | + | 0.787434i | \(0.288591\pi\) | |||||||
\(468\) | 1.00000 | 0.0462250 | ||||||||
\(469\) | 20.0000 | 0.923514 | ||||||||
\(470\) | 3.00000 | 0.138380 | ||||||||
\(471\) | 16.5359 | 0.761934 | ||||||||
\(472\) | 0.928203 | 0.0427240 | ||||||||
\(473\) | −26.0000 | −1.19548 | ||||||||
\(474\) | −6.00000 | −0.275589 | ||||||||
\(475\) | 3.00000 | 0.137649 | ||||||||
\(476\) | 6.92820 | 0.317554 | ||||||||
\(477\) | 7.46410 | 0.341758 | ||||||||
\(478\) | −9.21539 | −0.421502 | ||||||||
\(479\) | 21.6077 | 0.987281 | 0.493640 | − | 0.869666i | \(-0.335666\pi\) | ||||
0.493640 | + | 0.869666i | \(0.335666\pi\) | |||||||
\(480\) | −5.19615 | −0.237171 | ||||||||
\(481\) | 4.92820 | 0.224707 | ||||||||
\(482\) | −32.0718 | −1.46083 | ||||||||
\(483\) | 6.00000 | 0.273009 | ||||||||
\(484\) | 21.8564 | 0.993473 | ||||||||
\(485\) | 6.92820 | 0.314594 | ||||||||
\(486\) | −1.73205 | −0.0785674 | ||||||||
\(487\) | −1.78461 | −0.0808684 | −0.0404342 | − | 0.999182i | \(-0.512874\pi\) | ||||
−0.0404342 | + | 0.999182i | \(0.512874\pi\) | |||||||
\(488\) | 9.46410 | 0.428420 | ||||||||
\(489\) | −19.4641 | −0.880197 | ||||||||
\(490\) | 5.19615 | 0.234738 | ||||||||
\(491\) | 6.00000 | 0.270776 | 0.135388 | − | 0.990793i | \(-0.456772\pi\) | ||||
0.135388 | + | 0.990793i | \(0.456772\pi\) | |||||||
\(492\) | −1.00000 | −0.0450835 | ||||||||
\(493\) | −6.00000 | −0.270226 | ||||||||
\(494\) | 5.19615 | 0.233786 | ||||||||
\(495\) | 5.73205 | 0.257637 | ||||||||
\(496\) | 5.00000 | 0.224507 | ||||||||
\(497\) | −4.00000 | −0.179425 | ||||||||
\(498\) | −20.5359 | −0.920236 | ||||||||
\(499\) | 15.6077 | 0.698696 | 0.349348 | − | 0.936993i | \(-0.386403\pi\) | ||||
0.349348 | + | 0.936993i | \(0.386403\pi\) | |||||||
\(500\) | −1.00000 | −0.0447214 | ||||||||
\(501\) | 18.0000 | 0.804181 | ||||||||
\(502\) | 28.3923 | 1.26721 | ||||||||
\(503\) | −2.00000 | −0.0891756 | −0.0445878 | − | 0.999005i | \(-0.514197\pi\) | ||||
−0.0445878 | + | 0.999005i | \(0.514197\pi\) | |||||||
\(504\) | −3.46410 | −0.154303 | ||||||||
\(505\) | 13.8564 | 0.616602 | ||||||||
\(506\) | 29.7846 | 1.32409 | ||||||||
\(507\) | −1.00000 | −0.0444116 | ||||||||
\(508\) | 11.4641 | 0.508637 | ||||||||
\(509\) | 6.39230 | 0.283334 | 0.141667 | − | 0.989914i | \(-0.454754\pi\) | ||||
0.141667 | + | 0.989914i | \(0.454754\pi\) | |||||||
\(510\) | 6.00000 | 0.265684 | ||||||||
\(511\) | 5.07180 | 0.224363 | ||||||||
\(512\) | 8.66025 | 0.382733 | ||||||||
\(513\) | −3.00000 | −0.132453 | ||||||||
\(514\) | 30.7128 | 1.35468 | ||||||||
\(515\) | −5.73205 | −0.252584 | ||||||||
\(516\) | −4.53590 | −0.199682 | ||||||||
\(517\) | 9.92820 | 0.436642 | ||||||||
\(518\) | 17.0718 | 0.750092 | ||||||||
\(519\) | −1.19615 | −0.0525053 | ||||||||
\(520\) | 1.73205 | 0.0759555 | ||||||||
\(521\) | 7.85641 | 0.344195 | 0.172098 | − | 0.985080i | \(-0.444946\pi\) | ||||
0.172098 | + | 0.985080i | \(0.444946\pi\) | |||||||
\(522\) | −3.00000 | −0.131306 | ||||||||
\(523\) | −12.9282 | −0.565311 | −0.282655 | − | 0.959222i | \(-0.591215\pi\) | ||||
−0.282655 | + | 0.959222i | \(0.591215\pi\) | |||||||
\(524\) | 11.0000 | 0.480537 | ||||||||
\(525\) | −2.00000 | −0.0872872 | ||||||||
\(526\) | −36.1244 | −1.57510 | ||||||||
\(527\) | −3.46410 | −0.150899 | ||||||||
\(528\) | −28.6603 | −1.24728 | ||||||||
\(529\) | −14.0000 | −0.608696 | ||||||||
\(530\) | −12.9282 | −0.561565 | ||||||||
\(531\) | −0.535898 | −0.0232560 | ||||||||
\(532\) | 6.00000 | 0.260133 | ||||||||
\(533\) | 1.00000 | 0.0433148 | ||||||||
\(534\) | −24.2487 | −1.04934 | ||||||||
\(535\) | −17.3205 | −0.748831 | ||||||||
\(536\) | −17.3205 | −0.748132 | ||||||||
\(537\) | −8.00000 | −0.345225 | ||||||||
\(538\) | −32.7846 | −1.41344 | ||||||||
\(539\) | 17.1962 | 0.740691 | ||||||||
\(540\) | 1.00000 | 0.0430331 | ||||||||
\(541\) | 25.3205 | 1.08861 | 0.544307 | − | 0.838886i | \(-0.316793\pi\) | ||||
0.544307 | + | 0.838886i | \(0.316793\pi\) | |||||||
\(542\) | 19.8564 | 0.852906 | ||||||||
\(543\) | −12.9282 | −0.554802 | ||||||||
\(544\) | −18.0000 | −0.771744 | ||||||||
\(545\) | −10.9282 | −0.468113 | ||||||||
\(546\) | −3.46410 | −0.148250 | ||||||||
\(547\) | 27.0526 | 1.15668 | 0.578342 | − | 0.815794i | \(-0.303700\pi\) | ||||
0.578342 | + | 0.815794i | \(0.303700\pi\) | |||||||
\(548\) | −1.92820 | −0.0823688 | ||||||||
\(549\) | −5.46410 | −0.233202 | ||||||||
\(550\) | −9.92820 | −0.423340 | ||||||||
\(551\) | −5.19615 | −0.221364 | ||||||||
\(552\) | −5.19615 | −0.221163 | ||||||||
\(553\) | 6.92820 | 0.294617 | ||||||||
\(554\) | 27.8372 | 1.18269 | ||||||||
\(555\) | 4.92820 | 0.209191 | ||||||||
\(556\) | −0.660254 | −0.0280010 | ||||||||
\(557\) | 29.7846 | 1.26201 | 0.631007 | − | 0.775777i | \(-0.282642\pi\) | ||||
0.631007 | + | 0.775777i | \(0.282642\pi\) | |||||||
\(558\) | −1.73205 | −0.0733236 | ||||||||
\(559\) | 4.53590 | 0.191848 | ||||||||
\(560\) | 10.0000 | 0.422577 | ||||||||
\(561\) | 19.8564 | 0.838338 | ||||||||
\(562\) | −20.4115 | −0.861009 | ||||||||
\(563\) | −34.2487 | −1.44341 | −0.721706 | − | 0.692200i | \(-0.756642\pi\) | ||||
−0.721706 | + | 0.692200i | \(0.756642\pi\) | |||||||
\(564\) | 1.73205 | 0.0729325 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 33.9282 | 1.42611 | ||||||||
\(567\) | 2.00000 | 0.0839921 | ||||||||
\(568\) | 3.46410 | 0.145350 | ||||||||
\(569\) | 19.7128 | 0.826404 | 0.413202 | − | 0.910639i | \(-0.364410\pi\) | ||||
0.413202 | + | 0.910639i | \(0.364410\pi\) | |||||||
\(570\) | 5.19615 | 0.217643 | ||||||||
\(571\) | −23.0526 | −0.964720 | −0.482360 | − | 0.875973i | \(-0.660220\pi\) | ||||
−0.482360 | + | 0.875973i | \(0.660220\pi\) | |||||||
\(572\) | −5.73205 | −0.239669 | ||||||||
\(573\) | 21.0000 | 0.877288 | ||||||||
\(574\) | 3.46410 | 0.144589 | ||||||||
\(575\) | −3.00000 | −0.125109 | ||||||||
\(576\) | 1.00000 | 0.0416667 | ||||||||
\(577\) | −43.3013 | −1.80266 | −0.901328 | − | 0.433138i | \(-0.857406\pi\) | ||||
−0.901328 | + | 0.433138i | \(0.857406\pi\) | |||||||
\(578\) | −8.66025 | −0.360219 | ||||||||
\(579\) | −0.124356 | −0.00516804 | ||||||||
\(580\) | 1.73205 | 0.0719195 | ||||||||
\(581\) | 23.7128 | 0.983773 | ||||||||
\(582\) | 12.0000 | 0.497416 | ||||||||
\(583\) | −42.7846 | −1.77196 | ||||||||
\(584\) | −4.39230 | −0.181755 | ||||||||
\(585\) | −1.00000 | −0.0413449 | ||||||||
\(586\) | −6.00000 | −0.247858 | ||||||||
\(587\) | 24.3923 | 1.00678 | 0.503389 | − | 0.864060i | \(-0.332086\pi\) | ||||
0.503389 | + | 0.864060i | \(0.332086\pi\) | |||||||
\(588\) | 3.00000 | 0.123718 | ||||||||
\(589\) | −3.00000 | −0.123613 | ||||||||
\(590\) | 0.928203 | 0.0382135 | ||||||||
\(591\) | −11.9282 | −0.490661 | ||||||||
\(592\) | −24.6410 | −1.01274 | ||||||||
\(593\) | 23.3205 | 0.957658 | 0.478829 | − | 0.877908i | \(-0.341061\pi\) | ||||
0.478829 | + | 0.877908i | \(0.341061\pi\) | |||||||
\(594\) | 9.92820 | 0.407359 | ||||||||
\(595\) | −6.92820 | −0.284029 | ||||||||
\(596\) | −17.9282 | −0.734368 | ||||||||
\(597\) | −21.1962 | −0.867501 | ||||||||
\(598\) | −5.19615 | −0.212486 | ||||||||
\(599\) | −10.8564 | −0.443581 | −0.221790 | − | 0.975094i | \(-0.571190\pi\) | ||||
−0.221790 | + | 0.975094i | \(0.571190\pi\) | |||||||
\(600\) | 1.73205 | 0.0707107 | ||||||||
\(601\) | 11.6077 | 0.473488 | 0.236744 | − | 0.971572i | \(-0.423920\pi\) | ||||
0.236744 | + | 0.971572i | \(0.423920\pi\) | |||||||
\(602\) | 15.7128 | 0.640406 | ||||||||
\(603\) | 10.0000 | 0.407231 | ||||||||
\(604\) | 2.39230 | 0.0973415 | ||||||||
\(605\) | −21.8564 | −0.888589 | ||||||||
\(606\) | 24.0000 | 0.974933 | ||||||||
\(607\) | 32.2487 | 1.30893 | 0.654467 | − | 0.756090i | \(-0.272893\pi\) | ||||
0.654467 | + | 0.756090i | \(0.272893\pi\) | |||||||
\(608\) | −15.5885 | −0.632195 | ||||||||
\(609\) | 3.46410 | 0.140372 | ||||||||
\(610\) | 9.46410 | 0.383190 | ||||||||
\(611\) | −1.73205 | −0.0700713 | ||||||||
\(612\) | 3.46410 | 0.140028 | ||||||||
\(613\) | 30.7846 | 1.24338 | 0.621689 | − | 0.783264i | \(-0.286447\pi\) | ||||
0.621689 | + | 0.783264i | \(0.286447\pi\) | |||||||
\(614\) | −37.8564 | −1.52776 | ||||||||
\(615\) | 1.00000 | 0.0403239 | ||||||||
\(616\) | 19.8564 | 0.800037 | ||||||||
\(617\) | 25.3205 | 1.01937 | 0.509683 | − | 0.860362i | \(-0.329763\pi\) | ||||
0.509683 | + | 0.860362i | \(0.329763\pi\) | |||||||
\(618\) | −9.92820 | −0.399371 | ||||||||
\(619\) | 4.67949 | 0.188085 | 0.0940423 | − | 0.995568i | \(-0.470021\pi\) | ||||
0.0940423 | + | 0.995568i | \(0.470021\pi\) | |||||||
\(620\) | 1.00000 | 0.0401610 | ||||||||
\(621\) | 3.00000 | 0.120386 | ||||||||
\(622\) | −34.6410 | −1.38898 | ||||||||
\(623\) | 28.0000 | 1.12180 | ||||||||
\(624\) | 5.00000 | 0.200160 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 18.8038 | 0.751553 | ||||||||
\(627\) | 17.1962 | 0.686748 | ||||||||
\(628\) | −16.5359 | −0.659854 | ||||||||
\(629\) | 17.0718 | 0.680697 | ||||||||
\(630\) | −3.46410 | −0.138013 | ||||||||
\(631\) | 17.7128 | 0.705136 | 0.352568 | − | 0.935786i | \(-0.385309\pi\) | ||||
0.352568 | + | 0.935786i | \(0.385309\pi\) | |||||||
\(632\) | −6.00000 | −0.238667 | ||||||||
\(633\) | −14.5359 | −0.577750 | ||||||||
\(634\) | −7.85641 | −0.312018 | ||||||||
\(635\) | −11.4641 | −0.454939 | ||||||||
\(636\) | −7.46410 | −0.295971 | ||||||||
\(637\) | −3.00000 | −0.118864 | ||||||||
\(638\) | 17.1962 | 0.680802 | ||||||||
\(639\) | −2.00000 | −0.0791188 | ||||||||
\(640\) | −12.1244 | −0.479257 | ||||||||
\(641\) | 6.80385 | 0.268736 | 0.134368 | − | 0.990932i | \(-0.457100\pi\) | ||||
0.134368 | + | 0.990932i | \(0.457100\pi\) | |||||||
\(642\) | −30.0000 | −1.18401 | ||||||||
\(643\) | 3.21539 | 0.126803 | 0.0634013 | − | 0.997988i | \(-0.479805\pi\) | ||||
0.0634013 | + | 0.997988i | \(0.479805\pi\) | |||||||
\(644\) | −6.00000 | −0.236433 | ||||||||
\(645\) | 4.53590 | 0.178601 | ||||||||
\(646\) | 18.0000 | 0.708201 | ||||||||
\(647\) | −10.0718 | −0.395963 | −0.197982 | − | 0.980206i | \(-0.563439\pi\) | ||||
−0.197982 | + | 0.980206i | \(0.563439\pi\) | |||||||
\(648\) | −1.73205 | −0.0680414 | ||||||||
\(649\) | 3.07180 | 0.120579 | ||||||||
\(650\) | 1.73205 | 0.0679366 | ||||||||
\(651\) | 2.00000 | 0.0783862 | ||||||||
\(652\) | 19.4641 | 0.762273 | ||||||||
\(653\) | 18.8038 | 0.735851 | 0.367926 | − | 0.929855i | \(-0.380068\pi\) | ||||
0.367926 | + | 0.929855i | \(0.380068\pi\) | |||||||
\(654\) | −18.9282 | −0.740151 | ||||||||
\(655\) | −11.0000 | −0.429806 | ||||||||
\(656\) | −5.00000 | −0.195217 | ||||||||
\(657\) | 2.53590 | 0.0989348 | ||||||||
\(658\) | −6.00000 | −0.233904 | ||||||||
\(659\) | −48.4974 | −1.88919 | −0.944596 | − | 0.328236i | \(-0.893546\pi\) | ||||
−0.944596 | + | 0.328236i | \(0.893546\pi\) | |||||||
\(660\) | −5.73205 | −0.223120 | ||||||||
\(661\) | 20.3923 | 0.793169 | 0.396584 | − | 0.917998i | \(-0.370195\pi\) | ||||
0.396584 | + | 0.917998i | \(0.370195\pi\) | |||||||
\(662\) | −5.75129 | −0.223530 | ||||||||
\(663\) | −3.46410 | −0.134535 | ||||||||
\(664\) | −20.5359 | −0.796947 | ||||||||
\(665\) | −6.00000 | −0.232670 | ||||||||
\(666\) | 8.53590 | 0.330759 | ||||||||
\(667\) | 5.19615 | 0.201196 | ||||||||
\(668\) | −18.0000 | −0.696441 | ||||||||
\(669\) | −26.7128 | −1.03278 | ||||||||
\(670\) | −17.3205 | −0.669150 | ||||||||
\(671\) | 31.3205 | 1.20911 | ||||||||
\(672\) | 10.3923 | 0.400892 | ||||||||
\(673\) | −40.6410 | −1.56660 | −0.783298 | − | 0.621646i | \(-0.786464\pi\) | ||||
−0.783298 | + | 0.621646i | \(0.786464\pi\) | |||||||
\(674\) | 27.8372 | 1.07225 | ||||||||
\(675\) | −1.00000 | −0.0384900 | ||||||||
\(676\) | 1.00000 | 0.0384615 | ||||||||
\(677\) | 5.07180 | 0.194925 | 0.0974625 | − | 0.995239i | \(-0.468927\pi\) | ||||
0.0974625 | + | 0.995239i | \(0.468927\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −13.8564 | −0.531760 | ||||||||
\(680\) | 6.00000 | 0.230089 | ||||||||
\(681\) | −22.5167 | −0.862840 | ||||||||
\(682\) | 9.92820 | 0.380171 | ||||||||
\(683\) | −34.2679 | −1.31123 | −0.655613 | − | 0.755097i | \(-0.727590\pi\) | ||||
−0.655613 | + | 0.755097i | \(0.727590\pi\) | |||||||
\(684\) | 3.00000 | 0.114708 | ||||||||
\(685\) | 1.92820 | 0.0736729 | ||||||||
\(686\) | −34.6410 | −1.32260 | ||||||||
\(687\) | −4.66025 | −0.177800 | ||||||||
\(688\) | −22.6795 | −0.864648 | ||||||||
\(689\) | 7.46410 | 0.284360 | ||||||||
\(690\) | −5.19615 | −0.197814 | ||||||||
\(691\) | 6.14359 | 0.233713 | 0.116857 | − | 0.993149i | \(-0.462718\pi\) | ||||
0.116857 | + | 0.993149i | \(0.462718\pi\) | |||||||
\(692\) | 1.19615 | 0.0454709 | ||||||||
\(693\) | −11.4641 | −0.435485 | ||||||||
\(694\) | 13.9808 | 0.530702 | ||||||||
\(695\) | 0.660254 | 0.0250449 | ||||||||
\(696\) | −3.00000 | −0.113715 | ||||||||
\(697\) | 3.46410 | 0.131212 | ||||||||
\(698\) | −35.3205 | −1.33690 | ||||||||
\(699\) | −1.73205 | −0.0655122 | ||||||||
\(700\) | 2.00000 | 0.0755929 | ||||||||
\(701\) | −48.3923 | −1.82775 | −0.913876 | − | 0.405993i | \(-0.866926\pi\) | ||||
−0.913876 | + | 0.405993i | \(0.866926\pi\) | |||||||
\(702\) | −1.73205 | −0.0653720 | ||||||||
\(703\) | 14.7846 | 0.557612 | ||||||||
\(704\) | −5.73205 | −0.216035 | ||||||||
\(705\) | −1.73205 | −0.0652328 | ||||||||
\(706\) | 24.2487 | 0.912612 | ||||||||
\(707\) | −27.7128 | −1.04225 | ||||||||
\(708\) | 0.535898 | 0.0201403 | ||||||||
\(709\) | 28.6603 | 1.07636 | 0.538179 | − | 0.842830i | \(-0.319112\pi\) | ||||
0.538179 | + | 0.842830i | \(0.319112\pi\) | |||||||
\(710\) | 3.46410 | 0.130005 | ||||||||
\(711\) | 3.46410 | 0.129914 | ||||||||
\(712\) | −24.2487 | −0.908759 | ||||||||
\(713\) | 3.00000 | 0.112351 | ||||||||
\(714\) | −12.0000 | −0.449089 | ||||||||
\(715\) | 5.73205 | 0.214367 | ||||||||
\(716\) | 8.00000 | 0.298974 | ||||||||
\(717\) | 5.32051 | 0.198698 | ||||||||
\(718\) | 0.248711 | 0.00928182 | ||||||||
\(719\) | −47.5692 | −1.77403 | −0.887016 | − | 0.461738i | \(-0.847226\pi\) | ||||
−0.887016 | + | 0.461738i | \(0.847226\pi\) | |||||||
\(720\) | 5.00000 | 0.186339 | ||||||||
\(721\) | 11.4641 | 0.426945 | ||||||||
\(722\) | −17.3205 | −0.644603 | ||||||||
\(723\) | 18.5167 | 0.688642 | ||||||||
\(724\) | 12.9282 | 0.480473 | ||||||||
\(725\) | −1.73205 | −0.0643268 | ||||||||
\(726\) | −37.8564 | −1.40498 | ||||||||
\(727\) | −49.3205 | −1.82920 | −0.914598 | − | 0.404364i | \(-0.867493\pi\) | ||||
−0.914598 | + | 0.404364i | \(0.867493\pi\) | |||||||
\(728\) | −3.46410 | −0.128388 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −4.39230 | −0.162566 | ||||||||
\(731\) | 15.7128 | 0.581159 | ||||||||
\(732\) | 5.46410 | 0.201959 | ||||||||
\(733\) | −13.7321 | −0.507205 | −0.253602 | − | 0.967309i | \(-0.581615\pi\) | ||||
−0.253602 | + | 0.967309i | \(0.581615\pi\) | |||||||
\(734\) | 55.4256 | 2.04580 | ||||||||
\(735\) | −3.00000 | −0.110657 | ||||||||
\(736\) | 15.5885 | 0.574598 | ||||||||
\(737\) | −57.3205 | −2.11143 | ||||||||
\(738\) | 1.73205 | 0.0637577 | ||||||||
\(739\) | −24.7846 | −0.911717 | −0.455858 | − | 0.890052i | \(-0.650668\pi\) | ||||
−0.455858 | + | 0.890052i | \(0.650668\pi\) | |||||||
\(740\) | −4.92820 | −0.181164 | ||||||||
\(741\) | −3.00000 | −0.110208 | ||||||||
\(742\) | 25.8564 | 0.949219 | ||||||||
\(743\) | 9.07180 | 0.332812 | 0.166406 | − | 0.986057i | \(-0.446784\pi\) | ||||
0.166406 | + | 0.986057i | \(0.446784\pi\) | |||||||
\(744\) | −1.73205 | −0.0635001 | ||||||||
\(745\) | 17.9282 | 0.656839 | ||||||||
\(746\) | 5.32051 | 0.194798 | ||||||||
\(747\) | 11.8564 | 0.433803 | ||||||||
\(748\) | −19.8564 | −0.726022 | ||||||||
\(749\) | 34.6410 | 1.26576 | ||||||||
\(750\) | 1.73205 | 0.0632456 | ||||||||
\(751\) | 7.32051 | 0.267129 | 0.133565 | − | 0.991040i | \(-0.457358\pi\) | ||||
0.133565 | + | 0.991040i | \(0.457358\pi\) | |||||||
\(752\) | 8.66025 | 0.315807 | ||||||||
\(753\) | −16.3923 | −0.597369 | ||||||||
\(754\) | −3.00000 | −0.109254 | ||||||||
\(755\) | −2.39230 | −0.0870649 | ||||||||
\(756\) | −2.00000 | −0.0727393 | ||||||||
\(757\) | −39.0000 | −1.41748 | −0.708740 | − | 0.705470i | \(-0.750736\pi\) | ||||
−0.708740 | + | 0.705470i | \(0.750736\pi\) | |||||||
\(758\) | 60.3731 | 2.19285 | ||||||||
\(759\) | −17.1962 | −0.624181 | ||||||||
\(760\) | 5.19615 | 0.188484 | ||||||||
\(761\) | 16.7846 | 0.608442 | 0.304221 | − | 0.952602i | \(-0.401604\pi\) | ||||
0.304221 | + | 0.952602i | \(0.401604\pi\) | |||||||
\(762\) | −19.8564 | −0.719322 | ||||||||
\(763\) | 21.8564 | 0.791255 | ||||||||
\(764\) | −21.0000 | −0.759753 | ||||||||
\(765\) | −3.46410 | −0.125245 | ||||||||
\(766\) | −35.5692 | −1.28517 | ||||||||
\(767\) | −0.535898 | −0.0193502 | ||||||||
\(768\) | −19.0000 | −0.685603 | ||||||||
\(769\) | 22.3923 | 0.807487 | 0.403744 | − | 0.914872i | \(-0.367709\pi\) | ||||
0.403744 | + | 0.914872i | \(0.367709\pi\) | |||||||
\(770\) | 19.8564 | 0.715575 | ||||||||
\(771\) | −17.7321 | −0.638604 | ||||||||
\(772\) | 0.124356 | 0.00447566 | ||||||||
\(773\) | −4.85641 | −0.174673 | −0.0873364 | − | 0.996179i | \(-0.527836\pi\) | ||||
−0.0873364 | + | 0.996179i | \(0.527836\pi\) | |||||||
\(774\) | 7.85641 | 0.282393 | ||||||||
\(775\) | −1.00000 | −0.0359211 | ||||||||
\(776\) | 12.0000 | 0.430775 | ||||||||
\(777\) | −9.85641 | −0.353597 | ||||||||
\(778\) | −5.07180 | −0.181833 | ||||||||
\(779\) | 3.00000 | 0.107486 | ||||||||
\(780\) | 1.00000 | 0.0358057 | ||||||||
\(781\) | 11.4641 | 0.410218 | ||||||||
\(782\) | −18.0000 | −0.643679 | ||||||||
\(783\) | 1.73205 | 0.0618984 | ||||||||
\(784\) | 15.0000 | 0.535714 | ||||||||
\(785\) | 16.5359 | 0.590192 | ||||||||
\(786\) | −19.0526 | −0.679582 | ||||||||
\(787\) | −31.6410 | −1.12788 | −0.563940 | − | 0.825816i | \(-0.690715\pi\) | ||||
−0.563940 | + | 0.825816i | \(0.690715\pi\) | |||||||
\(788\) | 11.9282 | 0.424925 | ||||||||
\(789\) | 20.8564 | 0.742508 | ||||||||
\(790\) | −6.00000 | −0.213470 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 9.92820 | 0.352783 | ||||||||
\(793\) | −5.46410 | −0.194036 | ||||||||
\(794\) | −46.8564 | −1.66287 | ||||||||
\(795\) | 7.46410 | 0.264724 | ||||||||
\(796\) | 21.1962 | 0.751278 | ||||||||
\(797\) | −16.6410 | −0.589455 | −0.294728 | − | 0.955581i | \(-0.595229\pi\) | ||||
−0.294728 | + | 0.955581i | \(0.595229\pi\) | |||||||
\(798\) | −10.3923 | −0.367884 | ||||||||
\(799\) | −6.00000 | −0.212265 | ||||||||
\(800\) | −5.19615 | −0.183712 | ||||||||
\(801\) | 14.0000 | 0.494666 | ||||||||
\(802\) | 60.0000 | 2.11867 | ||||||||
\(803\) | −14.5359 | −0.512961 | ||||||||
\(804\) | −10.0000 | −0.352673 | ||||||||
\(805\) | 6.00000 | 0.211472 | ||||||||
\(806\) | −1.73205 | −0.0610089 | ||||||||
\(807\) | 18.9282 | 0.666304 | ||||||||
\(808\) | 24.0000 | 0.844317 | ||||||||
\(809\) | −20.7846 | −0.730748 | −0.365374 | − | 0.930861i | \(-0.619059\pi\) | ||||
−0.365374 | + | 0.930861i | \(0.619059\pi\) | |||||||
\(810\) | −1.73205 | −0.0608581 | ||||||||
\(811\) | 46.9282 | 1.64787 | 0.823936 | − | 0.566683i | \(-0.191773\pi\) | ||||
0.823936 | + | 0.566683i | \(0.191773\pi\) | |||||||
\(812\) | −3.46410 | −0.121566 | ||||||||
\(813\) | −11.4641 | −0.402064 | ||||||||
\(814\) | −48.9282 | −1.71493 | ||||||||
\(815\) | −19.4641 | −0.681798 | ||||||||
\(816\) | 17.3205 | 0.606339 | ||||||||
\(817\) | 13.6077 | 0.476073 | ||||||||
\(818\) | −45.9282 | −1.60584 | ||||||||
\(819\) | 2.00000 | 0.0698857 | ||||||||
\(820\) | −1.00000 | −0.0349215 | ||||||||
\(821\) | −0.784610 | −0.0273831 | −0.0136915 | − | 0.999906i | \(-0.504358\pi\) | ||||
−0.0136915 | + | 0.999906i | \(0.504358\pi\) | |||||||
\(822\) | 3.33975 | 0.116487 | ||||||||
\(823\) | −29.6077 | −1.03206 | −0.516030 | − | 0.856571i | \(-0.672591\pi\) | ||||
−0.516030 | + | 0.856571i | \(0.672591\pi\) | |||||||
\(824\) | −9.92820 | −0.345865 | ||||||||
\(825\) | 5.73205 | 0.199564 | ||||||||
\(826\) | −1.85641 | −0.0645926 | ||||||||
\(827\) | −24.2487 | −0.843210 | −0.421605 | − | 0.906780i | \(-0.638533\pi\) | ||||
−0.421605 | + | 0.906780i | \(0.638533\pi\) | |||||||
\(828\) | −3.00000 | −0.104257 | ||||||||
\(829\) | −24.5359 | −0.852167 | −0.426083 | − | 0.904684i | \(-0.640107\pi\) | ||||
−0.426083 | + | 0.904684i | \(0.640107\pi\) | |||||||
\(830\) | −20.5359 | −0.712811 | ||||||||
\(831\) | −16.0718 | −0.557524 | ||||||||
\(832\) | 1.00000 | 0.0346688 | ||||||||
\(833\) | −10.3923 | −0.360072 | ||||||||
\(834\) | 1.14359 | 0.0395994 | ||||||||
\(835\) | 18.0000 | 0.622916 | ||||||||
\(836\) | −17.1962 | −0.594741 | ||||||||
\(837\) | 1.00000 | 0.0345651 | ||||||||
\(838\) | −1.48334 | −0.0512411 | ||||||||
\(839\) | 20.9282 | 0.722522 | 0.361261 | − | 0.932465i | \(-0.382346\pi\) | ||||
0.361261 | + | 0.932465i | \(0.382346\pi\) | |||||||
\(840\) | −3.46410 | −0.119523 | ||||||||
\(841\) | −26.0000 | −0.896552 | ||||||||
\(842\) | −66.9282 | −2.30650 | ||||||||
\(843\) | 11.7846 | 0.405884 | ||||||||
\(844\) | 14.5359 | 0.500346 | ||||||||
\(845\) | −1.00000 | −0.0344010 | ||||||||
\(846\) | −3.00000 | −0.103142 | ||||||||
\(847\) | 43.7128 | 1.50199 | ||||||||
\(848\) | −37.3205 | −1.28159 | ||||||||
\(849\) | −19.5885 | −0.672274 | ||||||||
\(850\) | 6.00000 | 0.205798 | ||||||||
\(851\) | −14.7846 | −0.506810 | ||||||||
\(852\) | 2.00000 | 0.0685189 | ||||||||
\(853\) | −19.3397 | −0.662180 | −0.331090 | − | 0.943599i | \(-0.607416\pi\) | ||||
−0.331090 | + | 0.943599i | \(0.607416\pi\) | |||||||
\(854\) | −18.9282 | −0.647710 | ||||||||
\(855\) | −3.00000 | −0.102598 | ||||||||
\(856\) | −30.0000 | −1.02538 | ||||||||
\(857\) | −14.9282 | −0.509938 | −0.254969 | − | 0.966949i | \(-0.582065\pi\) | ||||
−0.254969 | + | 0.966949i | \(0.582065\pi\) | |||||||
\(858\) | 9.92820 | 0.338943 | ||||||||
\(859\) | −35.1769 | −1.20022 | −0.600110 | − | 0.799917i | \(-0.704877\pi\) | ||||
−0.600110 | + | 0.799917i | \(0.704877\pi\) | |||||||
\(860\) | −4.53590 | −0.154673 | ||||||||
\(861\) | −2.00000 | −0.0681598 | ||||||||
\(862\) | −11.0718 | −0.377107 | ||||||||
\(863\) | −6.78461 | −0.230951 | −0.115475 | − | 0.993310i | \(-0.536839\pi\) | ||||
−0.115475 | + | 0.993310i | \(0.536839\pi\) | |||||||
\(864\) | 5.19615 | 0.176777 | ||||||||
\(865\) | −1.19615 | −0.0406704 | ||||||||
\(866\) | −37.9808 | −1.29064 | ||||||||
\(867\) | 5.00000 | 0.169809 | ||||||||
\(868\) | −2.00000 | −0.0678844 | ||||||||
\(869\) | −19.8564 | −0.673582 | ||||||||
\(870\) | −3.00000 | −0.101710 | ||||||||
\(871\) | 10.0000 | 0.338837 | ||||||||
\(872\) | −18.9282 | −0.640990 | ||||||||
\(873\) | −6.92820 | −0.234484 | ||||||||
\(874\) | −15.5885 | −0.527287 | ||||||||
\(875\) | −2.00000 | −0.0676123 | ||||||||
\(876\) | −2.53590 | −0.0856801 | ||||||||
\(877\) | 20.4115 | 0.689249 | 0.344624 | − | 0.938741i | \(-0.388006\pi\) | ||||
0.344624 | + | 0.938741i | \(0.388006\pi\) | |||||||
\(878\) | 1.85641 | 0.0626507 | ||||||||
\(879\) | 3.46410 | 0.116841 | ||||||||
\(880\) | −28.6603 | −0.966137 | ||||||||
\(881\) | 3.33975 | 0.112519 | 0.0562595 | − | 0.998416i | \(-0.482083\pi\) | ||||
0.0562595 | + | 0.998416i | \(0.482083\pi\) | |||||||
\(882\) | −5.19615 | −0.174964 | ||||||||
\(883\) | 47.0333 | 1.58280 | 0.791399 | − | 0.611300i | \(-0.209353\pi\) | ||||
0.791399 | + | 0.611300i | \(0.209353\pi\) | |||||||
\(884\) | 3.46410 | 0.116510 | ||||||||
\(885\) | −0.535898 | −0.0180140 | ||||||||
\(886\) | −49.1769 | −1.65213 | ||||||||
\(887\) | 0.287187 | 0.00964280 | 0.00482140 | − | 0.999988i | \(-0.498465\pi\) | ||||
0.00482140 | + | 0.999988i | \(0.498465\pi\) | |||||||
\(888\) | 8.53590 | 0.286446 | ||||||||
\(889\) | 22.9282 | 0.768987 | ||||||||
\(890\) | −24.2487 | −0.812819 | ||||||||
\(891\) | −5.73205 | −0.192031 | ||||||||
\(892\) | 26.7128 | 0.894411 | ||||||||
\(893\) | −5.19615 | −0.173883 | ||||||||
\(894\) | 31.0526 | 1.03855 | ||||||||
\(895\) | −8.00000 | −0.267411 | ||||||||
\(896\) | 24.2487 | 0.810093 | ||||||||
\(897\) | 3.00000 | 0.100167 | ||||||||
\(898\) | −17.3205 | −0.577993 | ||||||||
\(899\) | 1.73205 | 0.0577671 | ||||||||
\(900\) | 1.00000 | 0.0333333 | ||||||||
\(901\) | 25.8564 | 0.861402 | ||||||||
\(902\) | −9.92820 | −0.330573 | ||||||||
\(903\) | −9.07180 | −0.301890 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −12.9282 | −0.429748 | ||||||||
\(906\) | −4.14359 | −0.137662 | ||||||||
\(907\) | 47.1769 | 1.56648 | 0.783242 | − | 0.621717i | \(-0.213565\pi\) | ||||
0.783242 | + | 0.621717i | \(0.213565\pi\) | |||||||
\(908\) | 22.5167 | 0.747242 | ||||||||
\(909\) | −13.8564 | −0.459588 | ||||||||
\(910\) | −3.46410 | −0.114834 | ||||||||
\(911\) | 37.1769 | 1.23173 | 0.615863 | − | 0.787853i | \(-0.288807\pi\) | ||||
0.615863 | + | 0.787853i | \(0.288807\pi\) | |||||||
\(912\) | 15.0000 | 0.496700 | ||||||||
\(913\) | −67.9615 | −2.24920 | ||||||||
\(914\) | −33.7128 | −1.11512 | ||||||||
\(915\) | −5.46410 | −0.180638 | ||||||||
\(916\) | 4.66025 | 0.153979 | ||||||||
\(917\) | 22.0000 | 0.726504 | ||||||||
\(918\) | −6.00000 | −0.198030 | ||||||||
\(919\) | −2.00000 | −0.0659739 | −0.0329870 | − | 0.999456i | \(-0.510502\pi\) | ||||
−0.0329870 | + | 0.999456i | \(0.510502\pi\) | |||||||
\(920\) | −5.19615 | −0.171312 | ||||||||
\(921\) | 21.8564 | 0.720193 | ||||||||
\(922\) | 39.9615 | 1.31606 | ||||||||
\(923\) | −2.00000 | −0.0658308 | ||||||||
\(924\) | 11.4641 | 0.377141 | ||||||||
\(925\) | 4.92820 | 0.162038 | ||||||||
\(926\) | 5.07180 | 0.166670 | ||||||||
\(927\) | 5.73205 | 0.188265 | ||||||||
\(928\) | 9.00000 | 0.295439 | ||||||||
\(929\) | −24.1051 | −0.790863 | −0.395432 | − | 0.918495i | \(-0.629405\pi\) | ||||
−0.395432 | + | 0.918495i | \(0.629405\pi\) | |||||||
\(930\) | −1.73205 | −0.0567962 | ||||||||
\(931\) | −9.00000 | −0.294963 | ||||||||
\(932\) | 1.73205 | 0.0567352 | ||||||||
\(933\) | 20.0000 | 0.654771 | ||||||||
\(934\) | 46.1436 | 1.50986 | ||||||||
\(935\) | 19.8564 | 0.649374 | ||||||||
\(936\) | −1.73205 | −0.0566139 | ||||||||
\(937\) | −19.8564 | −0.648681 | −0.324340 | − | 0.945940i | \(-0.605142\pi\) | ||||
−0.324340 | + | 0.945940i | \(0.605142\pi\) | |||||||
\(938\) | 34.6410 | 1.13107 | ||||||||
\(939\) | −10.8564 | −0.354285 | ||||||||
\(940\) | 1.73205 | 0.0564933 | ||||||||
\(941\) | −35.3205 | −1.15142 | −0.575708 | − | 0.817655i | \(-0.695273\pi\) | ||||
−0.575708 | + | 0.817655i | \(0.695273\pi\) | |||||||
\(942\) | 28.6410 | 0.933175 | ||||||||
\(943\) | −3.00000 | −0.0976934 | ||||||||
\(944\) | 2.67949 | 0.0872100 | ||||||||
\(945\) | 2.00000 | 0.0650600 | ||||||||
\(946\) | −45.0333 | −1.46416 | ||||||||
\(947\) | −31.0333 | −1.00845 | −0.504224 | − | 0.863573i | \(-0.668221\pi\) | ||||
−0.504224 | + | 0.863573i | \(0.668221\pi\) | |||||||
\(948\) | −3.46410 | −0.112509 | ||||||||
\(949\) | 2.53590 | 0.0823187 | ||||||||
\(950\) | 5.19615 | 0.168585 | ||||||||
\(951\) | 4.53590 | 0.147087 | ||||||||
\(952\) | −12.0000 | −0.388922 | ||||||||
\(953\) | 9.07180 | 0.293864 | 0.146932 | − | 0.989147i | \(-0.453060\pi\) | ||||
0.146932 | + | 0.989147i | \(0.453060\pi\) | |||||||
\(954\) | 12.9282 | 0.418566 | ||||||||
\(955\) | 21.0000 | 0.679544 | ||||||||
\(956\) | −5.32051 | −0.172078 | ||||||||
\(957\) | −9.92820 | −0.320933 | ||||||||
\(958\) | 37.4256 | 1.20917 | ||||||||
\(959\) | −3.85641 | −0.124530 | ||||||||
\(960\) | 1.00000 | 0.0322749 | ||||||||
\(961\) | 1.00000 | 0.0322581 | ||||||||
\(962\) | 8.53590 | 0.275208 | ||||||||
\(963\) | 17.3205 | 0.558146 | ||||||||
\(964\) | −18.5167 | −0.596381 | ||||||||
\(965\) | −0.124356 | −0.00400315 | ||||||||
\(966\) | 10.3923 | 0.334367 | ||||||||
\(967\) | −25.7846 | −0.829177 | −0.414589 | − | 0.910009i | \(-0.636074\pi\) | ||||
−0.414589 | + | 0.910009i | \(0.636074\pi\) | |||||||
\(968\) | −37.8564 | −1.21675 | ||||||||
\(969\) | −10.3923 | −0.333849 | ||||||||
\(970\) | 12.0000 | 0.385297 | ||||||||
\(971\) | −3.21539 | −0.103187 | −0.0515934 | − | 0.998668i | \(-0.516430\pi\) | ||||
−0.0515934 | + | 0.998668i | \(0.516430\pi\) | |||||||
\(972\) | −1.00000 | −0.0320750 | ||||||||
\(973\) | −1.32051 | −0.0423335 | ||||||||
\(974\) | −3.09103 | −0.0990431 | ||||||||
\(975\) | −1.00000 | −0.0320256 | ||||||||
\(976\) | 27.3205 | 0.874508 | ||||||||
\(977\) | 19.4641 | 0.622712 | 0.311356 | − | 0.950293i | \(-0.399217\pi\) | ||||
0.311356 | + | 0.950293i | \(0.399217\pi\) | |||||||
\(978\) | −33.7128 | −1.07802 | ||||||||
\(979\) | −80.2487 | −2.56476 | ||||||||
\(980\) | 3.00000 | 0.0958315 | ||||||||
\(981\) | 10.9282 | 0.348911 | ||||||||
\(982\) | 10.3923 | 0.331632 | ||||||||
\(983\) | 44.1051 | 1.40673 | 0.703367 | − | 0.710826i | \(-0.251679\pi\) | ||||
0.703367 | + | 0.710826i | \(0.251679\pi\) | |||||||
\(984\) | 1.73205 | 0.0552158 | ||||||||
\(985\) | −11.9282 | −0.380064 | ||||||||
\(986\) | −10.3923 | −0.330958 | ||||||||
\(987\) | 3.46410 | 0.110264 | ||||||||
\(988\) | 3.00000 | 0.0954427 | ||||||||
\(989\) | −13.6077 | −0.432700 | ||||||||
\(990\) | 9.92820 | 0.315539 | ||||||||
\(991\) | −26.5167 | −0.842329 | −0.421165 | − | 0.906984i | \(-0.638379\pi\) | ||||
−0.421165 | + | 0.906984i | \(0.638379\pi\) | |||||||
\(992\) | 5.19615 | 0.164978 | ||||||||
\(993\) | 3.32051 | 0.105373 | ||||||||
\(994\) | −6.92820 | −0.219749 | ||||||||
\(995\) | −21.1962 | −0.671963 | ||||||||
\(996\) | −11.8564 | −0.375685 | ||||||||
\(997\) | −2.67949 | −0.0848604 | −0.0424302 | − | 0.999099i | \(-0.513510\pi\) | ||||
−0.0424302 | + | 0.999099i | \(0.513510\pi\) | |||||||
\(998\) | 27.0333 | 0.855725 | ||||||||
\(999\) | −4.92820 | −0.155921 |
(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 | 6045.2.a.o.1.2 | ✓ | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6045.2.a.o.1.2 | ✓ | 2 | 1.1 | even | 1 | trivial |