Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [5610,2,Mod(1,5610)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(5610, 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("5610.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 5610 = 2 \cdot 3 \cdot 5 \cdot 11 \cdot 17 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 5610.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: | \(44.7960755339\) |
Analytic rank: | \(1\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{10})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: |
\( x^{2} - x - 1 \)
|
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | yes |
Fricke sign: | \(+1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(1.61803\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 5610.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000 | 0.707107 | ||||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | −1.00000 | −0.408248 | ||||||||
\(7\) | 3.23607 | 1.22312 | 0.611559 | − | 0.791199i | \(-0.290543\pi\) | ||||
0.611559 | + | 0.791199i | \(0.290543\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | −1.00000 | −0.316228 | ||||||||
\(11\) | 1.00000 | 0.301511 | ||||||||
\(12\) | −1.00000 | −0.288675 | ||||||||
\(13\) | 1.23607 | 0.342824 | 0.171412 | − | 0.985199i | \(-0.445167\pi\) | ||||
0.171412 | + | 0.985199i | \(0.445167\pi\) | |||||||
\(14\) | 3.23607 | 0.864876 | ||||||||
\(15\) | 1.00000 | 0.258199 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −1.00000 | −0.242536 | ||||||||
\(18\) | 1.00000 | 0.235702 | ||||||||
\(19\) | −7.70820 | −1.76838 | −0.884192 | − | 0.467124i | \(-0.845290\pi\) | ||||
−0.884192 | + | 0.467124i | \(0.845290\pi\) | |||||||
\(20\) | −1.00000 | −0.223607 | ||||||||
\(21\) | −3.23607 | −0.706168 | ||||||||
\(22\) | 1.00000 | 0.213201 | ||||||||
\(23\) | −5.23607 | −1.09180 | −0.545898 | − | 0.837852i | \(-0.683811\pi\) | ||||
−0.545898 | + | 0.837852i | \(0.683811\pi\) | |||||||
\(24\) | −1.00000 | −0.204124 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 1.23607 | 0.242413 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 3.23607 | 0.611559 | ||||||||
\(29\) | −8.47214 | −1.57324 | −0.786618 | − | 0.617440i | \(-0.788170\pi\) | ||||
−0.786618 | + | 0.617440i | \(0.788170\pi\) | |||||||
\(30\) | 1.00000 | 0.182574 | ||||||||
\(31\) | −4.00000 | −0.718421 | −0.359211 | − | 0.933257i | \(-0.616954\pi\) | ||||
−0.359211 | + | 0.933257i | \(0.616954\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | −1.00000 | −0.174078 | ||||||||
\(34\) | −1.00000 | −0.171499 | ||||||||
\(35\) | −3.23607 | −0.546995 | ||||||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | −6.00000 | −0.986394 | −0.493197 | − | 0.869918i | \(-0.664172\pi\) | ||||
−0.493197 | + | 0.869918i | \(0.664172\pi\) | |||||||
\(38\) | −7.70820 | −1.25044 | ||||||||
\(39\) | −1.23607 | −0.197929 | ||||||||
\(40\) | −1.00000 | −0.158114 | ||||||||
\(41\) | −8.94427 | −1.39686 | −0.698430 | − | 0.715678i | \(-0.746118\pi\) | ||||
−0.698430 | + | 0.715678i | \(0.746118\pi\) | |||||||
\(42\) | −3.23607 | −0.499336 | ||||||||
\(43\) | −3.23607 | −0.493496 | −0.246748 | − | 0.969080i | \(-0.579362\pi\) | ||||
−0.246748 | + | 0.969080i | \(0.579362\pi\) | |||||||
\(44\) | 1.00000 | 0.150756 | ||||||||
\(45\) | −1.00000 | −0.149071 | ||||||||
\(46\) | −5.23607 | −0.772016 | ||||||||
\(47\) | 2.47214 | 0.360598 | 0.180299 | − | 0.983612i | \(-0.442293\pi\) | ||||
0.180299 | + | 0.983612i | \(0.442293\pi\) | |||||||
\(48\) | −1.00000 | −0.144338 | ||||||||
\(49\) | 3.47214 | 0.496019 | ||||||||
\(50\) | 1.00000 | 0.141421 | ||||||||
\(51\) | 1.00000 | 0.140028 | ||||||||
\(52\) | 1.23607 | 0.171412 | ||||||||
\(53\) | 3.23607 | 0.444508 | 0.222254 | − | 0.974989i | \(-0.428659\pi\) | ||||
0.222254 | + | 0.974989i | \(0.428659\pi\) | |||||||
\(54\) | −1.00000 | −0.136083 | ||||||||
\(55\) | −1.00000 | −0.134840 | ||||||||
\(56\) | 3.23607 | 0.432438 | ||||||||
\(57\) | 7.70820 | 1.02098 | ||||||||
\(58\) | −8.47214 | −1.11245 | ||||||||
\(59\) | −3.23607 | −0.421300 | −0.210650 | − | 0.977562i | \(-0.567558\pi\) | ||||
−0.210650 | + | 0.977562i | \(0.567558\pi\) | |||||||
\(60\) | 1.00000 | 0.129099 | ||||||||
\(61\) | 6.00000 | 0.768221 | 0.384111 | − | 0.923287i | \(-0.374508\pi\) | ||||
0.384111 | + | 0.923287i | \(0.374508\pi\) | |||||||
\(62\) | −4.00000 | −0.508001 | ||||||||
\(63\) | 3.23607 | 0.407706 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −1.23607 | −0.153315 | ||||||||
\(66\) | −1.00000 | −0.123091 | ||||||||
\(67\) | 6.00000 | 0.733017 | 0.366508 | − | 0.930415i | \(-0.380553\pi\) | ||||
0.366508 | + | 0.930415i | \(0.380553\pi\) | |||||||
\(68\) | −1.00000 | −0.121268 | ||||||||
\(69\) | 5.23607 | 0.630349 | ||||||||
\(70\) | −3.23607 | −0.386784 | ||||||||
\(71\) | −0.763932 | −0.0906621 | −0.0453310 | − | 0.998972i | \(-0.514434\pi\) | ||||
−0.0453310 | + | 0.998972i | \(0.514434\pi\) | |||||||
\(72\) | 1.00000 | 0.117851 | ||||||||
\(73\) | 1.23607 | 0.144671 | 0.0723354 | − | 0.997380i | \(-0.476955\pi\) | ||||
0.0723354 | + | 0.997380i | \(0.476955\pi\) | |||||||
\(74\) | −6.00000 | −0.697486 | ||||||||
\(75\) | −1.00000 | −0.115470 | ||||||||
\(76\) | −7.70820 | −0.884192 | ||||||||
\(77\) | 3.23607 | 0.368784 | ||||||||
\(78\) | −1.23607 | −0.139957 | ||||||||
\(79\) | 3.70820 | 0.417206 | 0.208603 | − | 0.978000i | \(-0.433108\pi\) | ||||
0.208603 | + | 0.978000i | \(0.433108\pi\) | |||||||
\(80\) | −1.00000 | −0.111803 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −8.94427 | −0.987730 | ||||||||
\(83\) | 4.94427 | 0.542704 | 0.271352 | − | 0.962480i | \(-0.412529\pi\) | ||||
0.271352 | + | 0.962480i | \(0.412529\pi\) | |||||||
\(84\) | −3.23607 | −0.353084 | ||||||||
\(85\) | 1.00000 | 0.108465 | ||||||||
\(86\) | −3.23607 | −0.348954 | ||||||||
\(87\) | 8.47214 | 0.908308 | ||||||||
\(88\) | 1.00000 | 0.106600 | ||||||||
\(89\) | −6.94427 | −0.736091 | −0.368046 | − | 0.929808i | \(-0.619973\pi\) | ||||
−0.368046 | + | 0.929808i | \(0.619973\pi\) | |||||||
\(90\) | −1.00000 | −0.105409 | ||||||||
\(91\) | 4.00000 | 0.419314 | ||||||||
\(92\) | −5.23607 | −0.545898 | ||||||||
\(93\) | 4.00000 | 0.414781 | ||||||||
\(94\) | 2.47214 | 0.254981 | ||||||||
\(95\) | 7.70820 | 0.790845 | ||||||||
\(96\) | −1.00000 | −0.102062 | ||||||||
\(97\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(98\) | 3.47214 | 0.350739 | ||||||||
\(99\) | 1.00000 | 0.100504 | ||||||||
\(100\) | 1.00000 | 0.100000 | ||||||||
\(101\) | 8.94427 | 0.889988 | 0.444994 | − | 0.895533i | \(-0.353206\pi\) | ||||
0.444994 | + | 0.895533i | \(0.353206\pi\) | |||||||
\(102\) | 1.00000 | 0.0990148 | ||||||||
\(103\) | 4.00000 | 0.394132 | 0.197066 | − | 0.980390i | \(-0.436859\pi\) | ||||
0.197066 | + | 0.980390i | \(0.436859\pi\) | |||||||
\(104\) | 1.23607 | 0.121206 | ||||||||
\(105\) | 3.23607 | 0.315808 | ||||||||
\(106\) | 3.23607 | 0.314315 | ||||||||
\(107\) | 0.944272 | 0.0912862 | 0.0456431 | − | 0.998958i | \(-0.485466\pi\) | ||||
0.0456431 | + | 0.998958i | \(0.485466\pi\) | |||||||
\(108\) | −1.00000 | −0.0962250 | ||||||||
\(109\) | −6.00000 | −0.574696 | −0.287348 | − | 0.957826i | \(-0.592774\pi\) | ||||
−0.287348 | + | 0.957826i | \(0.592774\pi\) | |||||||
\(110\) | −1.00000 | −0.0953463 | ||||||||
\(111\) | 6.00000 | 0.569495 | ||||||||
\(112\) | 3.23607 | 0.305780 | ||||||||
\(113\) | −15.2361 | −1.43329 | −0.716644 | − | 0.697439i | \(-0.754323\pi\) | ||||
−0.716644 | + | 0.697439i | \(0.754323\pi\) | |||||||
\(114\) | 7.70820 | 0.721939 | ||||||||
\(115\) | 5.23607 | 0.488266 | ||||||||
\(116\) | −8.47214 | −0.786618 | ||||||||
\(117\) | 1.23607 | 0.114275 | ||||||||
\(118\) | −3.23607 | −0.297904 | ||||||||
\(119\) | −3.23607 | −0.296650 | ||||||||
\(120\) | 1.00000 | 0.0912871 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | 6.00000 | 0.543214 | ||||||||
\(123\) | 8.94427 | 0.806478 | ||||||||
\(124\) | −4.00000 | −0.359211 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 3.23607 | 0.288292 | ||||||||
\(127\) | −12.0000 | −1.06483 | −0.532414 | − | 0.846484i | \(-0.678715\pi\) | ||||
−0.532414 | + | 0.846484i | \(0.678715\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | 3.23607 | 0.284920 | ||||||||
\(130\) | −1.23607 | −0.108410 | ||||||||
\(131\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(132\) | −1.00000 | −0.0870388 | ||||||||
\(133\) | −24.9443 | −2.16294 | ||||||||
\(134\) | 6.00000 | 0.518321 | ||||||||
\(135\) | 1.00000 | 0.0860663 | ||||||||
\(136\) | −1.00000 | −0.0857493 | ||||||||
\(137\) | −15.8885 | −1.35745 | −0.678725 | − | 0.734393i | \(-0.737467\pi\) | ||||
−0.678725 | + | 0.734393i | \(0.737467\pi\) | |||||||
\(138\) | 5.23607 | 0.445724 | ||||||||
\(139\) | 8.00000 | 0.678551 | 0.339276 | − | 0.940687i | \(-0.389818\pi\) | ||||
0.339276 | + | 0.940687i | \(0.389818\pi\) | |||||||
\(140\) | −3.23607 | −0.273498 | ||||||||
\(141\) | −2.47214 | −0.208191 | ||||||||
\(142\) | −0.763932 | −0.0641078 | ||||||||
\(143\) | 1.23607 | 0.103365 | ||||||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | 8.47214 | 0.703573 | ||||||||
\(146\) | 1.23607 | 0.102298 | ||||||||
\(147\) | −3.47214 | −0.286377 | ||||||||
\(148\) | −6.00000 | −0.493197 | ||||||||
\(149\) | −9.52786 | −0.780553 | −0.390277 | − | 0.920698i | \(-0.627621\pi\) | ||||
−0.390277 | + | 0.920698i | \(0.627621\pi\) | |||||||
\(150\) | −1.00000 | −0.0816497 | ||||||||
\(151\) | −14.4721 | −1.17773 | −0.588863 | − | 0.808233i | \(-0.700424\pi\) | ||||
−0.588863 | + | 0.808233i | \(0.700424\pi\) | |||||||
\(152\) | −7.70820 | −0.625218 | ||||||||
\(153\) | −1.00000 | −0.0808452 | ||||||||
\(154\) | 3.23607 | 0.260770 | ||||||||
\(155\) | 4.00000 | 0.321288 | ||||||||
\(156\) | −1.23607 | −0.0989646 | ||||||||
\(157\) | 19.4164 | 1.54960 | 0.774799 | − | 0.632208i | \(-0.217851\pi\) | ||||
0.774799 | + | 0.632208i | \(0.217851\pi\) | |||||||
\(158\) | 3.70820 | 0.295009 | ||||||||
\(159\) | −3.23607 | −0.256637 | ||||||||
\(160\) | −1.00000 | −0.0790569 | ||||||||
\(161\) | −16.9443 | −1.33540 | ||||||||
\(162\) | 1.00000 | 0.0785674 | ||||||||
\(163\) | −6.47214 | −0.506937 | −0.253468 | − | 0.967344i | \(-0.581571\pi\) | ||||
−0.253468 | + | 0.967344i | \(0.581571\pi\) | |||||||
\(164\) | −8.94427 | −0.698430 | ||||||||
\(165\) | 1.00000 | 0.0778499 | ||||||||
\(166\) | 4.94427 | 0.383750 | ||||||||
\(167\) | −12.0000 | −0.928588 | −0.464294 | − | 0.885681i | \(-0.653692\pi\) | ||||
−0.464294 | + | 0.885681i | \(0.653692\pi\) | |||||||
\(168\) | −3.23607 | −0.249668 | ||||||||
\(169\) | −11.4721 | −0.882472 | ||||||||
\(170\) | 1.00000 | 0.0766965 | ||||||||
\(171\) | −7.70820 | −0.589461 | ||||||||
\(172\) | −3.23607 | −0.246748 | ||||||||
\(173\) | 13.4164 | 1.02003 | 0.510015 | − | 0.860165i | \(-0.329640\pi\) | ||||
0.510015 | + | 0.860165i | \(0.329640\pi\) | |||||||
\(174\) | 8.47214 | 0.642271 | ||||||||
\(175\) | 3.23607 | 0.244624 | ||||||||
\(176\) | 1.00000 | 0.0753778 | ||||||||
\(177\) | 3.23607 | 0.243238 | ||||||||
\(178\) | −6.94427 | −0.520495 | ||||||||
\(179\) | −12.7639 | −0.954021 | −0.477011 | − | 0.878898i | \(-0.658280\pi\) | ||||
−0.477011 | + | 0.878898i | \(0.658280\pi\) | |||||||
\(180\) | −1.00000 | −0.0745356 | ||||||||
\(181\) | 8.47214 | 0.629729 | 0.314864 | − | 0.949137i | \(-0.398041\pi\) | ||||
0.314864 | + | 0.949137i | \(0.398041\pi\) | |||||||
\(182\) | 4.00000 | 0.296500 | ||||||||
\(183\) | −6.00000 | −0.443533 | ||||||||
\(184\) | −5.23607 | −0.386008 | ||||||||
\(185\) | 6.00000 | 0.441129 | ||||||||
\(186\) | 4.00000 | 0.293294 | ||||||||
\(187\) | −1.00000 | −0.0731272 | ||||||||
\(188\) | 2.47214 | 0.180299 | ||||||||
\(189\) | −3.23607 | −0.235389 | ||||||||
\(190\) | 7.70820 | 0.559212 | ||||||||
\(191\) | 1.52786 | 0.110552 | 0.0552762 | − | 0.998471i | \(-0.482396\pi\) | ||||
0.0552762 | + | 0.998471i | \(0.482396\pi\) | |||||||
\(192\) | −1.00000 | −0.0721688 | ||||||||
\(193\) | 7.70820 | 0.554849 | 0.277424 | − | 0.960747i | \(-0.410519\pi\) | ||||
0.277424 | + | 0.960747i | \(0.410519\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 1.23607 | 0.0885167 | ||||||||
\(196\) | 3.47214 | 0.248010 | ||||||||
\(197\) | 14.9443 | 1.06474 | 0.532368 | − | 0.846513i | \(-0.321302\pi\) | ||||
0.532368 | + | 0.846513i | \(0.321302\pi\) | |||||||
\(198\) | 1.00000 | 0.0710669 | ||||||||
\(199\) | −12.0000 | −0.850657 | −0.425329 | − | 0.905039i | \(-0.639842\pi\) | ||||
−0.425329 | + | 0.905039i | \(0.639842\pi\) | |||||||
\(200\) | 1.00000 | 0.0707107 | ||||||||
\(201\) | −6.00000 | −0.423207 | ||||||||
\(202\) | 8.94427 | 0.629317 | ||||||||
\(203\) | −27.4164 | −1.92425 | ||||||||
\(204\) | 1.00000 | 0.0700140 | ||||||||
\(205\) | 8.94427 | 0.624695 | ||||||||
\(206\) | 4.00000 | 0.278693 | ||||||||
\(207\) | −5.23607 | −0.363932 | ||||||||
\(208\) | 1.23607 | 0.0857059 | ||||||||
\(209\) | −7.70820 | −0.533188 | ||||||||
\(210\) | 3.23607 | 0.223310 | ||||||||
\(211\) | 20.3607 | 1.40169 | 0.700844 | − | 0.713315i | \(-0.252807\pi\) | ||||
0.700844 | + | 0.713315i | \(0.252807\pi\) | |||||||
\(212\) | 3.23607 | 0.222254 | ||||||||
\(213\) | 0.763932 | 0.0523438 | ||||||||
\(214\) | 0.944272 | 0.0645491 | ||||||||
\(215\) | 3.23607 | 0.220698 | ||||||||
\(216\) | −1.00000 | −0.0680414 | ||||||||
\(217\) | −12.9443 | −0.878714 | ||||||||
\(218\) | −6.00000 | −0.406371 | ||||||||
\(219\) | −1.23607 | −0.0835257 | ||||||||
\(220\) | −1.00000 | −0.0674200 | ||||||||
\(221\) | −1.23607 | −0.0831469 | ||||||||
\(222\) | 6.00000 | 0.402694 | ||||||||
\(223\) | −23.4164 | −1.56808 | −0.784039 | − | 0.620711i | \(-0.786844\pi\) | ||||
−0.784039 | + | 0.620711i | \(0.786844\pi\) | |||||||
\(224\) | 3.23607 | 0.216219 | ||||||||
\(225\) | 1.00000 | 0.0666667 | ||||||||
\(226\) | −15.2361 | −1.01349 | ||||||||
\(227\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(228\) | 7.70820 | 0.510488 | ||||||||
\(229\) | 29.4164 | 1.94389 | 0.971945 | − | 0.235206i | \(-0.0755766\pi\) | ||||
0.971945 | + | 0.235206i | \(0.0755766\pi\) | |||||||
\(230\) | 5.23607 | 0.345256 | ||||||||
\(231\) | −3.23607 | −0.212918 | ||||||||
\(232\) | −8.47214 | −0.556223 | ||||||||
\(233\) | −7.52786 | −0.493167 | −0.246583 | − | 0.969122i | \(-0.579308\pi\) | ||||
−0.246583 | + | 0.969122i | \(0.579308\pi\) | |||||||
\(234\) | 1.23607 | 0.0808043 | ||||||||
\(235\) | −2.47214 | −0.161264 | ||||||||
\(236\) | −3.23607 | −0.210650 | ||||||||
\(237\) | −3.70820 | −0.240874 | ||||||||
\(238\) | −3.23607 | −0.209763 | ||||||||
\(239\) | −16.3607 | −1.05828 | −0.529142 | − | 0.848533i | \(-0.677486\pi\) | ||||
−0.529142 | + | 0.848533i | \(0.677486\pi\) | |||||||
\(240\) | 1.00000 | 0.0645497 | ||||||||
\(241\) | 4.18034 | 0.269279 | 0.134640 | − | 0.990895i | \(-0.457012\pi\) | ||||
0.134640 | + | 0.990895i | \(0.457012\pi\) | |||||||
\(242\) | 1.00000 | 0.0642824 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 6.00000 | 0.384111 | ||||||||
\(245\) | −3.47214 | −0.221827 | ||||||||
\(246\) | 8.94427 | 0.570266 | ||||||||
\(247\) | −9.52786 | −0.606243 | ||||||||
\(248\) | −4.00000 | −0.254000 | ||||||||
\(249\) | −4.94427 | −0.313331 | ||||||||
\(250\) | −1.00000 | −0.0632456 | ||||||||
\(251\) | 23.2361 | 1.46665 | 0.733324 | − | 0.679880i | \(-0.237968\pi\) | ||||
0.733324 | + | 0.679880i | \(0.237968\pi\) | |||||||
\(252\) | 3.23607 | 0.203853 | ||||||||
\(253\) | −5.23607 | −0.329189 | ||||||||
\(254\) | −12.0000 | −0.752947 | ||||||||
\(255\) | −1.00000 | −0.0626224 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −4.47214 | −0.278964 | −0.139482 | − | 0.990225i | \(-0.544544\pi\) | ||||
−0.139482 | + | 0.990225i | \(0.544544\pi\) | |||||||
\(258\) | 3.23607 | 0.201469 | ||||||||
\(259\) | −19.4164 | −1.20648 | ||||||||
\(260\) | −1.23607 | −0.0766577 | ||||||||
\(261\) | −8.47214 | −0.524412 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −12.0000 | −0.739952 | −0.369976 | − | 0.929041i | \(-0.620634\pi\) | ||||
−0.369976 | + | 0.929041i | \(0.620634\pi\) | |||||||
\(264\) | −1.00000 | −0.0615457 | ||||||||
\(265\) | −3.23607 | −0.198790 | ||||||||
\(266\) | −24.9443 | −1.52943 | ||||||||
\(267\) | 6.94427 | 0.424983 | ||||||||
\(268\) | 6.00000 | 0.366508 | ||||||||
\(269\) | −24.4721 | −1.49209 | −0.746046 | − | 0.665894i | \(-0.768050\pi\) | ||||
−0.746046 | + | 0.665894i | \(0.768050\pi\) | |||||||
\(270\) | 1.00000 | 0.0608581 | ||||||||
\(271\) | 20.0000 | 1.21491 | 0.607457 | − | 0.794353i | \(-0.292190\pi\) | ||||
0.607457 | + | 0.794353i | \(0.292190\pi\) | |||||||
\(272\) | −1.00000 | −0.0606339 | ||||||||
\(273\) | −4.00000 | −0.242091 | ||||||||
\(274\) | −15.8885 | −0.959862 | ||||||||
\(275\) | 1.00000 | 0.0603023 | ||||||||
\(276\) | 5.23607 | 0.315174 | ||||||||
\(277\) | 14.0000 | 0.841178 | 0.420589 | − | 0.907251i | \(-0.361823\pi\) | ||||
0.420589 | + | 0.907251i | \(0.361823\pi\) | |||||||
\(278\) | 8.00000 | 0.479808 | ||||||||
\(279\) | −4.00000 | −0.239474 | ||||||||
\(280\) | −3.23607 | −0.193392 | ||||||||
\(281\) | −16.4721 | −0.982645 | −0.491323 | − | 0.870978i | \(-0.663486\pi\) | ||||
−0.491323 | + | 0.870978i | \(0.663486\pi\) | |||||||
\(282\) | −2.47214 | −0.147214 | ||||||||
\(283\) | −3.41641 | −0.203084 | −0.101542 | − | 0.994831i | \(-0.532378\pi\) | ||||
−0.101542 | + | 0.994831i | \(0.532378\pi\) | |||||||
\(284\) | −0.763932 | −0.0453310 | ||||||||
\(285\) | −7.70820 | −0.456595 | ||||||||
\(286\) | 1.23607 | 0.0730902 | ||||||||
\(287\) | −28.9443 | −1.70853 | ||||||||
\(288\) | 1.00000 | 0.0589256 | ||||||||
\(289\) | 1.00000 | 0.0588235 | ||||||||
\(290\) | 8.47214 | 0.497501 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 1.23607 | 0.0723354 | ||||||||
\(293\) | −18.0000 | −1.05157 | −0.525786 | − | 0.850617i | \(-0.676229\pi\) | ||||
−0.525786 | + | 0.850617i | \(0.676229\pi\) | |||||||
\(294\) | −3.47214 | −0.202499 | ||||||||
\(295\) | 3.23607 | 0.188411 | ||||||||
\(296\) | −6.00000 | −0.348743 | ||||||||
\(297\) | −1.00000 | −0.0580259 | ||||||||
\(298\) | −9.52786 | −0.551934 | ||||||||
\(299\) | −6.47214 | −0.374293 | ||||||||
\(300\) | −1.00000 | −0.0577350 | ||||||||
\(301\) | −10.4721 | −0.603604 | ||||||||
\(302\) | −14.4721 | −0.832778 | ||||||||
\(303\) | −8.94427 | −0.513835 | ||||||||
\(304\) | −7.70820 | −0.442096 | ||||||||
\(305\) | −6.00000 | −0.343559 | ||||||||
\(306\) | −1.00000 | −0.0571662 | ||||||||
\(307\) | 10.2918 | 0.587384 | 0.293692 | − | 0.955900i | \(-0.405116\pi\) | ||||
0.293692 | + | 0.955900i | \(0.405116\pi\) | |||||||
\(308\) | 3.23607 | 0.184392 | ||||||||
\(309\) | −4.00000 | −0.227552 | ||||||||
\(310\) | 4.00000 | 0.227185 | ||||||||
\(311\) | 11.2361 | 0.637139 | 0.318569 | − | 0.947900i | \(-0.396798\pi\) | ||||
0.318569 | + | 0.947900i | \(0.396798\pi\) | |||||||
\(312\) | −1.23607 | −0.0699786 | ||||||||
\(313\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(314\) | 19.4164 | 1.09573 | ||||||||
\(315\) | −3.23607 | −0.182332 | ||||||||
\(316\) | 3.70820 | 0.208603 | ||||||||
\(317\) | −13.0557 | −0.733283 | −0.366641 | − | 0.930362i | \(-0.619492\pi\) | ||||
−0.366641 | + | 0.930362i | \(0.619492\pi\) | |||||||
\(318\) | −3.23607 | −0.181470 | ||||||||
\(319\) | −8.47214 | −0.474349 | ||||||||
\(320\) | −1.00000 | −0.0559017 | ||||||||
\(321\) | −0.944272 | −0.0527041 | ||||||||
\(322\) | −16.9443 | −0.944267 | ||||||||
\(323\) | 7.70820 | 0.428896 | ||||||||
\(324\) | 1.00000 | 0.0555556 | ||||||||
\(325\) | 1.23607 | 0.0685647 | ||||||||
\(326\) | −6.47214 | −0.358458 | ||||||||
\(327\) | 6.00000 | 0.331801 | ||||||||
\(328\) | −8.94427 | −0.493865 | ||||||||
\(329\) | 8.00000 | 0.441054 | ||||||||
\(330\) | 1.00000 | 0.0550482 | ||||||||
\(331\) | 33.8885 | 1.86268 | 0.931341 | − | 0.364147i | \(-0.118639\pi\) | ||||
0.931341 | + | 0.364147i | \(0.118639\pi\) | |||||||
\(332\) | 4.94427 | 0.271352 | ||||||||
\(333\) | −6.00000 | −0.328798 | ||||||||
\(334\) | −12.0000 | −0.656611 | ||||||||
\(335\) | −6.00000 | −0.327815 | ||||||||
\(336\) | −3.23607 | −0.176542 | ||||||||
\(337\) | −3.70820 | −0.201999 | −0.100999 | − | 0.994886i | \(-0.532204\pi\) | ||||
−0.100999 | + | 0.994886i | \(0.532204\pi\) | |||||||
\(338\) | −11.4721 | −0.624002 | ||||||||
\(339\) | 15.2361 | 0.827510 | ||||||||
\(340\) | 1.00000 | 0.0542326 | ||||||||
\(341\) | −4.00000 | −0.216612 | ||||||||
\(342\) | −7.70820 | −0.416812 | ||||||||
\(343\) | −11.4164 | −0.616428 | ||||||||
\(344\) | −3.23607 | −0.174477 | ||||||||
\(345\) | −5.23607 | −0.281900 | ||||||||
\(346\) | 13.4164 | 0.721271 | ||||||||
\(347\) | 12.9443 | 0.694885 | 0.347442 | − | 0.937701i | \(-0.387050\pi\) | ||||
0.347442 | + | 0.937701i | \(0.387050\pi\) | |||||||
\(348\) | 8.47214 | 0.454154 | ||||||||
\(349\) | 1.70820 | 0.0914381 | 0.0457190 | − | 0.998954i | \(-0.485442\pi\) | ||||
0.0457190 | + | 0.998954i | \(0.485442\pi\) | |||||||
\(350\) | 3.23607 | 0.172975 | ||||||||
\(351\) | −1.23607 | −0.0659764 | ||||||||
\(352\) | 1.00000 | 0.0533002 | ||||||||
\(353\) | −4.47214 | −0.238028 | −0.119014 | − | 0.992893i | \(-0.537973\pi\) | ||||
−0.119014 | + | 0.992893i | \(0.537973\pi\) | |||||||
\(354\) | 3.23607 | 0.171995 | ||||||||
\(355\) | 0.763932 | 0.0405453 | ||||||||
\(356\) | −6.94427 | −0.368046 | ||||||||
\(357\) | 3.23607 | 0.171271 | ||||||||
\(358\) | −12.7639 | −0.674595 | ||||||||
\(359\) | −7.41641 | −0.391423 | −0.195712 | − | 0.980662i | \(-0.562702\pi\) | ||||
−0.195712 | + | 0.980662i | \(0.562702\pi\) | |||||||
\(360\) | −1.00000 | −0.0527046 | ||||||||
\(361\) | 40.4164 | 2.12718 | ||||||||
\(362\) | 8.47214 | 0.445286 | ||||||||
\(363\) | −1.00000 | −0.0524864 | ||||||||
\(364\) | 4.00000 | 0.209657 | ||||||||
\(365\) | −1.23607 | −0.0646988 | ||||||||
\(366\) | −6.00000 | −0.313625 | ||||||||
\(367\) | 28.8328 | 1.50506 | 0.752530 | − | 0.658558i | \(-0.228833\pi\) | ||||
0.752530 | + | 0.658558i | \(0.228833\pi\) | |||||||
\(368\) | −5.23607 | −0.272949 | ||||||||
\(369\) | −8.94427 | −0.465620 | ||||||||
\(370\) | 6.00000 | 0.311925 | ||||||||
\(371\) | 10.4721 | 0.543686 | ||||||||
\(372\) | 4.00000 | 0.207390 | ||||||||
\(373\) | −15.7082 | −0.813340 | −0.406670 | − | 0.913575i | \(-0.633310\pi\) | ||||
−0.406670 | + | 0.913575i | \(0.633310\pi\) | |||||||
\(374\) | −1.00000 | −0.0517088 | ||||||||
\(375\) | 1.00000 | 0.0516398 | ||||||||
\(376\) | 2.47214 | 0.127491 | ||||||||
\(377\) | −10.4721 | −0.539342 | ||||||||
\(378\) | −3.23607 | −0.166445 | ||||||||
\(379\) | −24.9443 | −1.28130 | −0.640651 | − | 0.767833i | \(-0.721335\pi\) | ||||
−0.640651 | + | 0.767833i | \(0.721335\pi\) | |||||||
\(380\) | 7.70820 | 0.395423 | ||||||||
\(381\) | 12.0000 | 0.614779 | ||||||||
\(382\) | 1.52786 | 0.0781723 | ||||||||
\(383\) | 10.4721 | 0.535101 | 0.267551 | − | 0.963544i | \(-0.413786\pi\) | ||||
0.267551 | + | 0.963544i | \(0.413786\pi\) | |||||||
\(384\) | −1.00000 | −0.0510310 | ||||||||
\(385\) | −3.23607 | −0.164925 | ||||||||
\(386\) | 7.70820 | 0.392337 | ||||||||
\(387\) | −3.23607 | −0.164499 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 25.5967 | 1.29781 | 0.648903 | − | 0.760871i | \(-0.275228\pi\) | ||||
0.648903 | + | 0.760871i | \(0.275228\pi\) | |||||||
\(390\) | 1.23607 | 0.0625907 | ||||||||
\(391\) | 5.23607 | 0.264799 | ||||||||
\(392\) | 3.47214 | 0.175369 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 14.9443 | 0.752882 | ||||||||
\(395\) | −3.70820 | −0.186580 | ||||||||
\(396\) | 1.00000 | 0.0502519 | ||||||||
\(397\) | −19.8885 | −0.998177 | −0.499089 | − | 0.866551i | \(-0.666332\pi\) | ||||
−0.499089 | + | 0.866551i | \(0.666332\pi\) | |||||||
\(398\) | −12.0000 | −0.601506 | ||||||||
\(399\) | 24.9443 | 1.24878 | ||||||||
\(400\) | 1.00000 | 0.0500000 | ||||||||
\(401\) | −20.2918 | −1.01332 | −0.506662 | − | 0.862145i | \(-0.669121\pi\) | ||||
−0.506662 | + | 0.862145i | \(0.669121\pi\) | |||||||
\(402\) | −6.00000 | −0.299253 | ||||||||
\(403\) | −4.94427 | −0.246292 | ||||||||
\(404\) | 8.94427 | 0.444994 | ||||||||
\(405\) | −1.00000 | −0.0496904 | ||||||||
\(406\) | −27.4164 | −1.36065 | ||||||||
\(407\) | −6.00000 | −0.297409 | ||||||||
\(408\) | 1.00000 | 0.0495074 | ||||||||
\(409\) | 10.9443 | 0.541159 | 0.270580 | − | 0.962698i | \(-0.412785\pi\) | ||||
0.270580 | + | 0.962698i | \(0.412785\pi\) | |||||||
\(410\) | 8.94427 | 0.441726 | ||||||||
\(411\) | 15.8885 | 0.783724 | ||||||||
\(412\) | 4.00000 | 0.197066 | ||||||||
\(413\) | −10.4721 | −0.515300 | ||||||||
\(414\) | −5.23607 | −0.257339 | ||||||||
\(415\) | −4.94427 | −0.242705 | ||||||||
\(416\) | 1.23607 | 0.0606032 | ||||||||
\(417\) | −8.00000 | −0.391762 | ||||||||
\(418\) | −7.70820 | −0.377021 | ||||||||
\(419\) | 10.4721 | 0.511597 | 0.255799 | − | 0.966730i | \(-0.417662\pi\) | ||||
0.255799 | + | 0.966730i | \(0.417662\pi\) | |||||||
\(420\) | 3.23607 | 0.157904 | ||||||||
\(421\) | −6.94427 | −0.338443 | −0.169222 | − | 0.985578i | \(-0.554125\pi\) | ||||
−0.169222 | + | 0.985578i | \(0.554125\pi\) | |||||||
\(422\) | 20.3607 | 0.991142 | ||||||||
\(423\) | 2.47214 | 0.120199 | ||||||||
\(424\) | 3.23607 | 0.157157 | ||||||||
\(425\) | −1.00000 | −0.0485071 | ||||||||
\(426\) | 0.763932 | 0.0370126 | ||||||||
\(427\) | 19.4164 | 0.939626 | ||||||||
\(428\) | 0.944272 | 0.0456431 | ||||||||
\(429\) | −1.23607 | −0.0596779 | ||||||||
\(430\) | 3.23607 | 0.156057 | ||||||||
\(431\) | −5.05573 | −0.243526 | −0.121763 | − | 0.992559i | \(-0.538855\pi\) | ||||
−0.121763 | + | 0.992559i | \(0.538855\pi\) | |||||||
\(432\) | −1.00000 | −0.0481125 | ||||||||
\(433\) | −6.00000 | −0.288342 | −0.144171 | − | 0.989553i | \(-0.546051\pi\) | ||||
−0.144171 | + | 0.989553i | \(0.546051\pi\) | |||||||
\(434\) | −12.9443 | −0.621345 | ||||||||
\(435\) | −8.47214 | −0.406208 | ||||||||
\(436\) | −6.00000 | −0.287348 | ||||||||
\(437\) | 40.3607 | 1.93071 | ||||||||
\(438\) | −1.23607 | −0.0590616 | ||||||||
\(439\) | −4.29180 | −0.204836 | −0.102418 | − | 0.994741i | \(-0.532658\pi\) | ||||
−0.102418 | + | 0.994741i | \(0.532658\pi\) | |||||||
\(440\) | −1.00000 | −0.0476731 | ||||||||
\(441\) | 3.47214 | 0.165340 | ||||||||
\(442\) | −1.23607 | −0.0587938 | ||||||||
\(443\) | −3.34752 | −0.159046 | −0.0795228 | − | 0.996833i | \(-0.525340\pi\) | ||||
−0.0795228 | + | 0.996833i | \(0.525340\pi\) | |||||||
\(444\) | 6.00000 | 0.284747 | ||||||||
\(445\) | 6.94427 | 0.329190 | ||||||||
\(446\) | −23.4164 | −1.10880 | ||||||||
\(447\) | 9.52786 | 0.450653 | ||||||||
\(448\) | 3.23607 | 0.152890 | ||||||||
\(449\) | 6.18034 | 0.291668 | 0.145834 | − | 0.989309i | \(-0.453413\pi\) | ||||
0.145834 | + | 0.989309i | \(0.453413\pi\) | |||||||
\(450\) | 1.00000 | 0.0471405 | ||||||||
\(451\) | −8.94427 | −0.421169 | ||||||||
\(452\) | −15.2361 | −0.716644 | ||||||||
\(453\) | 14.4721 | 0.679960 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −4.00000 | −0.187523 | ||||||||
\(456\) | 7.70820 | 0.360970 | ||||||||
\(457\) | 18.0000 | 0.842004 | 0.421002 | − | 0.907060i | \(-0.361678\pi\) | ||||
0.421002 | + | 0.907060i | \(0.361678\pi\) | |||||||
\(458\) | 29.4164 | 1.37454 | ||||||||
\(459\) | 1.00000 | 0.0466760 | ||||||||
\(460\) | 5.23607 | 0.244133 | ||||||||
\(461\) | 7.41641 | 0.345417 | 0.172708 | − | 0.984973i | \(-0.444748\pi\) | ||||
0.172708 | + | 0.984973i | \(0.444748\pi\) | |||||||
\(462\) | −3.23607 | −0.150556 | ||||||||
\(463\) | 20.3607 | 0.946241 | 0.473121 | − | 0.880998i | \(-0.343128\pi\) | ||||
0.473121 | + | 0.880998i | \(0.343128\pi\) | |||||||
\(464\) | −8.47214 | −0.393309 | ||||||||
\(465\) | −4.00000 | −0.185496 | ||||||||
\(466\) | −7.52786 | −0.348722 | ||||||||
\(467\) | 14.7639 | 0.683193 | 0.341597 | − | 0.939847i | \(-0.389032\pi\) | ||||
0.341597 | + | 0.939847i | \(0.389032\pi\) | |||||||
\(468\) | 1.23607 | 0.0571373 | ||||||||
\(469\) | 19.4164 | 0.896566 | ||||||||
\(470\) | −2.47214 | −0.114031 | ||||||||
\(471\) | −19.4164 | −0.894661 | ||||||||
\(472\) | −3.23607 | −0.148952 | ||||||||
\(473\) | −3.23607 | −0.148795 | ||||||||
\(474\) | −3.70820 | −0.170323 | ||||||||
\(475\) | −7.70820 | −0.353677 | ||||||||
\(476\) | −3.23607 | −0.148325 | ||||||||
\(477\) | 3.23607 | 0.148169 | ||||||||
\(478\) | −16.3607 | −0.748320 | ||||||||
\(479\) | −27.5279 | −1.25778 | −0.628890 | − | 0.777494i | \(-0.716490\pi\) | ||||
−0.628890 | + | 0.777494i | \(0.716490\pi\) | |||||||
\(480\) | 1.00000 | 0.0456435 | ||||||||
\(481\) | −7.41641 | −0.338159 | ||||||||
\(482\) | 4.18034 | 0.190409 | ||||||||
\(483\) | 16.9443 | 0.770991 | ||||||||
\(484\) | 1.00000 | 0.0454545 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −1.00000 | −0.0453609 | ||||||||
\(487\) | −20.8328 | −0.944025 | −0.472012 | − | 0.881592i | \(-0.656472\pi\) | ||||
−0.472012 | + | 0.881592i | \(0.656472\pi\) | |||||||
\(488\) | 6.00000 | 0.271607 | ||||||||
\(489\) | 6.47214 | 0.292680 | ||||||||
\(490\) | −3.47214 | −0.156855 | ||||||||
\(491\) | 1.05573 | 0.0476443 | 0.0238222 | − | 0.999716i | \(-0.492416\pi\) | ||||
0.0238222 | + | 0.999716i | \(0.492416\pi\) | |||||||
\(492\) | 8.94427 | 0.403239 | ||||||||
\(493\) | 8.47214 | 0.381566 | ||||||||
\(494\) | −9.52786 | −0.428679 | ||||||||
\(495\) | −1.00000 | −0.0449467 | ||||||||
\(496\) | −4.00000 | −0.179605 | ||||||||
\(497\) | −2.47214 | −0.110890 | ||||||||
\(498\) | −4.94427 | −0.221558 | ||||||||
\(499\) | −22.8328 | −1.02214 | −0.511069 | − | 0.859540i | \(-0.670750\pi\) | ||||
−0.511069 | + | 0.859540i | \(0.670750\pi\) | |||||||
\(500\) | −1.00000 | −0.0447214 | ||||||||
\(501\) | 12.0000 | 0.536120 | ||||||||
\(502\) | 23.2361 | 1.03708 | ||||||||
\(503\) | 18.4721 | 0.823632 | 0.411816 | − | 0.911267i | \(-0.364895\pi\) | ||||
0.411816 | + | 0.911267i | \(0.364895\pi\) | |||||||
\(504\) | 3.23607 | 0.144146 | ||||||||
\(505\) | −8.94427 | −0.398015 | ||||||||
\(506\) | −5.23607 | −0.232772 | ||||||||
\(507\) | 11.4721 | 0.509495 | ||||||||
\(508\) | −12.0000 | −0.532414 | ||||||||
\(509\) | 34.7639 | 1.54088 | 0.770442 | − | 0.637510i | \(-0.220036\pi\) | ||||
0.770442 | + | 0.637510i | \(0.220036\pi\) | |||||||
\(510\) | −1.00000 | −0.0442807 | ||||||||
\(511\) | 4.00000 | 0.176950 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 7.70820 | 0.340326 | ||||||||
\(514\) | −4.47214 | −0.197257 | ||||||||
\(515\) | −4.00000 | −0.176261 | ||||||||
\(516\) | 3.23607 | 0.142460 | ||||||||
\(517\) | 2.47214 | 0.108724 | ||||||||
\(518\) | −19.4164 | −0.853108 | ||||||||
\(519\) | −13.4164 | −0.588915 | ||||||||
\(520\) | −1.23607 | −0.0542052 | ||||||||
\(521\) | −35.1246 | −1.53884 | −0.769419 | − | 0.638745i | \(-0.779454\pi\) | ||||
−0.769419 | + | 0.638745i | \(0.779454\pi\) | |||||||
\(522\) | −8.47214 | −0.370815 | ||||||||
\(523\) | 21.1246 | 0.923715 | 0.461857 | − | 0.886954i | \(-0.347183\pi\) | ||||
0.461857 | + | 0.886954i | \(0.347183\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −3.23607 | −0.141234 | ||||||||
\(526\) | −12.0000 | −0.523225 | ||||||||
\(527\) | 4.00000 | 0.174243 | ||||||||
\(528\) | −1.00000 | −0.0435194 | ||||||||
\(529\) | 4.41641 | 0.192018 | ||||||||
\(530\) | −3.23607 | −0.140566 | ||||||||
\(531\) | −3.23607 | −0.140433 | ||||||||
\(532\) | −24.9443 | −1.08147 | ||||||||
\(533\) | −11.0557 | −0.478877 | ||||||||
\(534\) | 6.94427 | 0.300508 | ||||||||
\(535\) | −0.944272 | −0.0408244 | ||||||||
\(536\) | 6.00000 | 0.259161 | ||||||||
\(537\) | 12.7639 | 0.550804 | ||||||||
\(538\) | −24.4721 | −1.05507 | ||||||||
\(539\) | 3.47214 | 0.149555 | ||||||||
\(540\) | 1.00000 | 0.0430331 | ||||||||
\(541\) | −45.7771 | −1.96811 | −0.984055 | − | 0.177862i | \(-0.943082\pi\) | ||||
−0.984055 | + | 0.177862i | \(0.943082\pi\) | |||||||
\(542\) | 20.0000 | 0.859074 | ||||||||
\(543\) | −8.47214 | −0.363574 | ||||||||
\(544\) | −1.00000 | −0.0428746 | ||||||||
\(545\) | 6.00000 | 0.257012 | ||||||||
\(546\) | −4.00000 | −0.171184 | ||||||||
\(547\) | 4.58359 | 0.195980 | 0.0979901 | − | 0.995187i | \(-0.468759\pi\) | ||||
0.0979901 | + | 0.995187i | \(0.468759\pi\) | |||||||
\(548\) | −15.8885 | −0.678725 | ||||||||
\(549\) | 6.00000 | 0.256074 | ||||||||
\(550\) | 1.00000 | 0.0426401 | ||||||||
\(551\) | 65.3050 | 2.78208 | ||||||||
\(552\) | 5.23607 | 0.222862 | ||||||||
\(553\) | 12.0000 | 0.510292 | ||||||||
\(554\) | 14.0000 | 0.594803 | ||||||||
\(555\) | −6.00000 | −0.254686 | ||||||||
\(556\) | 8.00000 | 0.339276 | ||||||||
\(557\) | −20.8328 | −0.882715 | −0.441357 | − | 0.897331i | \(-0.645503\pi\) | ||||
−0.441357 | + | 0.897331i | \(0.645503\pi\) | |||||||
\(558\) | −4.00000 | −0.169334 | ||||||||
\(559\) | −4.00000 | −0.169182 | ||||||||
\(560\) | −3.23607 | −0.136749 | ||||||||
\(561\) | 1.00000 | 0.0422200 | ||||||||
\(562\) | −16.4721 | −0.694835 | ||||||||
\(563\) | −35.7771 | −1.50782 | −0.753912 | − | 0.656975i | \(-0.771836\pi\) | ||||
−0.753912 | + | 0.656975i | \(0.771836\pi\) | |||||||
\(564\) | −2.47214 | −0.104096 | ||||||||
\(565\) | 15.2361 | 0.640986 | ||||||||
\(566\) | −3.41641 | −0.143602 | ||||||||
\(567\) | 3.23607 | 0.135902 | ||||||||
\(568\) | −0.763932 | −0.0320539 | ||||||||
\(569\) | 19.3050 | 0.809306 | 0.404653 | − | 0.914470i | \(-0.367392\pi\) | ||||
0.404653 | + | 0.914470i | \(0.367392\pi\) | |||||||
\(570\) | −7.70820 | −0.322861 | ||||||||
\(571\) | −25.8885 | −1.08340 | −0.541701 | − | 0.840571i | \(-0.682219\pi\) | ||||
−0.541701 | + | 0.840571i | \(0.682219\pi\) | |||||||
\(572\) | 1.23607 | 0.0516826 | ||||||||
\(573\) | −1.52786 | −0.0638274 | ||||||||
\(574\) | −28.9443 | −1.20811 | ||||||||
\(575\) | −5.23607 | −0.218359 | ||||||||
\(576\) | 1.00000 | 0.0416667 | ||||||||
\(577\) | −15.8885 | −0.661449 | −0.330724 | − | 0.943727i | \(-0.607293\pi\) | ||||
−0.330724 | + | 0.943727i | \(0.607293\pi\) | |||||||
\(578\) | 1.00000 | 0.0415945 | ||||||||
\(579\) | −7.70820 | −0.320342 | ||||||||
\(580\) | 8.47214 | 0.351786 | ||||||||
\(581\) | 16.0000 | 0.663792 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 3.23607 | 0.134024 | ||||||||
\(584\) | 1.23607 | 0.0511489 | ||||||||
\(585\) | −1.23607 | −0.0511051 | ||||||||
\(586\) | −18.0000 | −0.743573 | ||||||||
\(587\) | −2.18034 | −0.0899923 | −0.0449961 | − | 0.998987i | \(-0.514328\pi\) | ||||
−0.0449961 | + | 0.998987i | \(0.514328\pi\) | |||||||
\(588\) | −3.47214 | −0.143188 | ||||||||
\(589\) | 30.8328 | 1.27044 | ||||||||
\(590\) | 3.23607 | 0.133227 | ||||||||
\(591\) | −14.9443 | −0.614725 | ||||||||
\(592\) | −6.00000 | −0.246598 | ||||||||
\(593\) | 13.4164 | 0.550946 | 0.275473 | − | 0.961309i | \(-0.411166\pi\) | ||||
0.275473 | + | 0.961309i | \(0.411166\pi\) | |||||||
\(594\) | −1.00000 | −0.0410305 | ||||||||
\(595\) | 3.23607 | 0.132666 | ||||||||
\(596\) | −9.52786 | −0.390277 | ||||||||
\(597\) | 12.0000 | 0.491127 | ||||||||
\(598\) | −6.47214 | −0.264665 | ||||||||
\(599\) | 4.58359 | 0.187280 | 0.0936402 | − | 0.995606i | \(-0.470150\pi\) | ||||
0.0936402 | + | 0.995606i | \(0.470150\pi\) | |||||||
\(600\) | −1.00000 | −0.0408248 | ||||||||
\(601\) | −1.12461 | −0.0458739 | −0.0229369 | − | 0.999737i | \(-0.507302\pi\) | ||||
−0.0229369 | + | 0.999737i | \(0.507302\pi\) | |||||||
\(602\) | −10.4721 | −0.426812 | ||||||||
\(603\) | 6.00000 | 0.244339 | ||||||||
\(604\) | −14.4721 | −0.588863 | ||||||||
\(605\) | −1.00000 | −0.0406558 | ||||||||
\(606\) | −8.94427 | −0.363336 | ||||||||
\(607\) | 29.1246 | 1.18213 | 0.591066 | − | 0.806623i | \(-0.298707\pi\) | ||||
0.591066 | + | 0.806623i | \(0.298707\pi\) | |||||||
\(608\) | −7.70820 | −0.312609 | ||||||||
\(609\) | 27.4164 | 1.11097 | ||||||||
\(610\) | −6.00000 | −0.242933 | ||||||||
\(611\) | 3.05573 | 0.123622 | ||||||||
\(612\) | −1.00000 | −0.0404226 | ||||||||
\(613\) | 7.12461 | 0.287760 | 0.143880 | − | 0.989595i | \(-0.454042\pi\) | ||||
0.143880 | + | 0.989595i | \(0.454042\pi\) | |||||||
\(614\) | 10.2918 | 0.415343 | ||||||||
\(615\) | −8.94427 | −0.360668 | ||||||||
\(616\) | 3.23607 | 0.130385 | ||||||||
\(617\) | −0.763932 | −0.0307547 | −0.0153774 | − | 0.999882i | \(-0.504895\pi\) | ||||
−0.0153774 | + | 0.999882i | \(0.504895\pi\) | |||||||
\(618\) | −4.00000 | −0.160904 | ||||||||
\(619\) | −9.88854 | −0.397454 | −0.198727 | − | 0.980055i | \(-0.563681\pi\) | ||||
−0.198727 | + | 0.980055i | \(0.563681\pi\) | |||||||
\(620\) | 4.00000 | 0.160644 | ||||||||
\(621\) | 5.23607 | 0.210116 | ||||||||
\(622\) | 11.2361 | 0.450525 | ||||||||
\(623\) | −22.4721 | −0.900327 | ||||||||
\(624\) | −1.23607 | −0.0494823 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 7.70820 | 0.307836 | ||||||||
\(628\) | 19.4164 | 0.774799 | ||||||||
\(629\) | 6.00000 | 0.239236 | ||||||||
\(630\) | −3.23607 | −0.128928 | ||||||||
\(631\) | 20.0000 | 0.796187 | 0.398094 | − | 0.917345i | \(-0.369672\pi\) | ||||
0.398094 | + | 0.917345i | \(0.369672\pi\) | |||||||
\(632\) | 3.70820 | 0.147504 | ||||||||
\(633\) | −20.3607 | −0.809264 | ||||||||
\(634\) | −13.0557 | −0.518509 | ||||||||
\(635\) | 12.0000 | 0.476205 | ||||||||
\(636\) | −3.23607 | −0.128318 | ||||||||
\(637\) | 4.29180 | 0.170047 | ||||||||
\(638\) | −8.47214 | −0.335415 | ||||||||
\(639\) | −0.763932 | −0.0302207 | ||||||||
\(640\) | −1.00000 | −0.0395285 | ||||||||
\(641\) | 8.65248 | 0.341752 | 0.170876 | − | 0.985293i | \(-0.445340\pi\) | ||||
0.170876 | + | 0.985293i | \(0.445340\pi\) | |||||||
\(642\) | −0.944272 | −0.0372674 | ||||||||
\(643\) | −36.9443 | −1.45694 | −0.728470 | − | 0.685078i | \(-0.759768\pi\) | ||||
−0.728470 | + | 0.685078i | \(0.759768\pi\) | |||||||
\(644\) | −16.9443 | −0.667698 | ||||||||
\(645\) | −3.23607 | −0.127420 | ||||||||
\(646\) | 7.70820 | 0.303275 | ||||||||
\(647\) | −14.8328 | −0.583138 | −0.291569 | − | 0.956550i | \(-0.594177\pi\) | ||||
−0.291569 | + | 0.956550i | \(0.594177\pi\) | |||||||
\(648\) | 1.00000 | 0.0392837 | ||||||||
\(649\) | −3.23607 | −0.127027 | ||||||||
\(650\) | 1.23607 | 0.0484826 | ||||||||
\(651\) | 12.9443 | 0.507326 | ||||||||
\(652\) | −6.47214 | −0.253468 | ||||||||
\(653\) | 11.8885 | 0.465235 | 0.232617 | − | 0.972568i | \(-0.425271\pi\) | ||||
0.232617 | + | 0.972568i | \(0.425271\pi\) | |||||||
\(654\) | 6.00000 | 0.234619 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −8.94427 | −0.349215 | ||||||||
\(657\) | 1.23607 | 0.0482236 | ||||||||
\(658\) | 8.00000 | 0.311872 | ||||||||
\(659\) | 44.8328 | 1.74644 | 0.873219 | − | 0.487328i | \(-0.162028\pi\) | ||||
0.873219 | + | 0.487328i | \(0.162028\pi\) | |||||||
\(660\) | 1.00000 | 0.0389249 | ||||||||
\(661\) | 1.41641 | 0.0550919 | 0.0275459 | − | 0.999621i | \(-0.491231\pi\) | ||||
0.0275459 | + | 0.999621i | \(0.491231\pi\) | |||||||
\(662\) | 33.8885 | 1.31712 | ||||||||
\(663\) | 1.23607 | 0.0480049 | ||||||||
\(664\) | 4.94427 | 0.191875 | ||||||||
\(665\) | 24.9443 | 0.967297 | ||||||||
\(666\) | −6.00000 | −0.232495 | ||||||||
\(667\) | 44.3607 | 1.71765 | ||||||||
\(668\) | −12.0000 | −0.464294 | ||||||||
\(669\) | 23.4164 | 0.905331 | ||||||||
\(670\) | −6.00000 | −0.231800 | ||||||||
\(671\) | 6.00000 | 0.231627 | ||||||||
\(672\) | −3.23607 | −0.124834 | ||||||||
\(673\) | −45.2361 | −1.74372 | −0.871861 | − | 0.489753i | \(-0.837087\pi\) | ||||
−0.871861 | + | 0.489753i | \(0.837087\pi\) | |||||||
\(674\) | −3.70820 | −0.142835 | ||||||||
\(675\) | −1.00000 | −0.0384900 | ||||||||
\(676\) | −11.4721 | −0.441236 | ||||||||
\(677\) | −39.8885 | −1.53304 | −0.766521 | − | 0.642220i | \(-0.778014\pi\) | ||||
−0.766521 | + | 0.642220i | \(0.778014\pi\) | |||||||
\(678\) | 15.2361 | 0.585138 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 1.00000 | 0.0383482 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −4.00000 | −0.153168 | ||||||||
\(683\) | −23.7771 | −0.909805 | −0.454902 | − | 0.890541i | \(-0.650326\pi\) | ||||
−0.454902 | + | 0.890541i | \(0.650326\pi\) | |||||||
\(684\) | −7.70820 | −0.294731 | ||||||||
\(685\) | 15.8885 | 0.607070 | ||||||||
\(686\) | −11.4164 | −0.435880 | ||||||||
\(687\) | −29.4164 | −1.12231 | ||||||||
\(688\) | −3.23607 | −0.123374 | ||||||||
\(689\) | 4.00000 | 0.152388 | ||||||||
\(690\) | −5.23607 | −0.199334 | ||||||||
\(691\) | 42.8328 | 1.62944 | 0.814719 | − | 0.579857i | \(-0.196891\pi\) | ||||
0.814719 | + | 0.579857i | \(0.196891\pi\) | |||||||
\(692\) | 13.4164 | 0.510015 | ||||||||
\(693\) | 3.23607 | 0.122928 | ||||||||
\(694\) | 12.9443 | 0.491358 | ||||||||
\(695\) | −8.00000 | −0.303457 | ||||||||
\(696\) | 8.47214 | 0.321135 | ||||||||
\(697\) | 8.94427 | 0.338788 | ||||||||
\(698\) | 1.70820 | 0.0646565 | ||||||||
\(699\) | 7.52786 | 0.284730 | ||||||||
\(700\) | 3.23607 | 0.122312 | ||||||||
\(701\) | 26.4721 | 0.999839 | 0.499919 | − | 0.866072i | \(-0.333363\pi\) | ||||
0.499919 | + | 0.866072i | \(0.333363\pi\) | |||||||
\(702\) | −1.23607 | −0.0466524 | ||||||||
\(703\) | 46.2492 | 1.74432 | ||||||||
\(704\) | 1.00000 | 0.0376889 | ||||||||
\(705\) | 2.47214 | 0.0931060 | ||||||||
\(706\) | −4.47214 | −0.168311 | ||||||||
\(707\) | 28.9443 | 1.08856 | ||||||||
\(708\) | 3.23607 | 0.121619 | ||||||||
\(709\) | −24.8328 | −0.932616 | −0.466308 | − | 0.884622i | \(-0.654416\pi\) | ||||
−0.466308 | + | 0.884622i | \(0.654416\pi\) | |||||||
\(710\) | 0.763932 | 0.0286699 | ||||||||
\(711\) | 3.70820 | 0.139069 | ||||||||
\(712\) | −6.94427 | −0.260248 | ||||||||
\(713\) | 20.9443 | 0.784369 | ||||||||
\(714\) | 3.23607 | 0.121107 | ||||||||
\(715\) | −1.23607 | −0.0462263 | ||||||||
\(716\) | −12.7639 | −0.477011 | ||||||||
\(717\) | 16.3607 | 0.611001 | ||||||||
\(718\) | −7.41641 | −0.276778 | ||||||||
\(719\) | 48.5410 | 1.81027 | 0.905137 | − | 0.425119i | \(-0.139768\pi\) | ||||
0.905137 | + | 0.425119i | \(0.139768\pi\) | |||||||
\(720\) | −1.00000 | −0.0372678 | ||||||||
\(721\) | 12.9443 | 0.482070 | ||||||||
\(722\) | 40.4164 | 1.50414 | ||||||||
\(723\) | −4.18034 | −0.155469 | ||||||||
\(724\) | 8.47214 | 0.314864 | ||||||||
\(725\) | −8.47214 | −0.314647 | ||||||||
\(726\) | −1.00000 | −0.0371135 | ||||||||
\(727\) | −18.8328 | −0.698470 | −0.349235 | − | 0.937035i | \(-0.613559\pi\) | ||||
−0.349235 | + | 0.937035i | \(0.613559\pi\) | |||||||
\(728\) | 4.00000 | 0.148250 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −1.23607 | −0.0457489 | ||||||||
\(731\) | 3.23607 | 0.119690 | ||||||||
\(732\) | −6.00000 | −0.221766 | ||||||||
\(733\) | 3.34752 | 0.123644 | 0.0618218 | − | 0.998087i | \(-0.480309\pi\) | ||||
0.0618218 | + | 0.998087i | \(0.480309\pi\) | |||||||
\(734\) | 28.8328 | 1.06424 | ||||||||
\(735\) | 3.47214 | 0.128072 | ||||||||
\(736\) | −5.23607 | −0.193004 | ||||||||
\(737\) | 6.00000 | 0.221013 | ||||||||
\(738\) | −8.94427 | −0.329243 | ||||||||
\(739\) | 28.2918 | 1.04073 | 0.520365 | − | 0.853944i | \(-0.325796\pi\) | ||||
0.520365 | + | 0.853944i | \(0.325796\pi\) | |||||||
\(740\) | 6.00000 | 0.220564 | ||||||||
\(741\) | 9.52786 | 0.350015 | ||||||||
\(742\) | 10.4721 | 0.384444 | ||||||||
\(743\) | −22.4721 | −0.824423 | −0.412211 | − | 0.911088i | \(-0.635243\pi\) | ||||
−0.412211 | + | 0.911088i | \(0.635243\pi\) | |||||||
\(744\) | 4.00000 | 0.146647 | ||||||||
\(745\) | 9.52786 | 0.349074 | ||||||||
\(746\) | −15.7082 | −0.575118 | ||||||||
\(747\) | 4.94427 | 0.180901 | ||||||||
\(748\) | −1.00000 | −0.0365636 | ||||||||
\(749\) | 3.05573 | 0.111654 | ||||||||
\(750\) | 1.00000 | 0.0365148 | ||||||||
\(751\) | 7.41641 | 0.270629 | 0.135314 | − | 0.990803i | \(-0.456796\pi\) | ||||
0.135314 | + | 0.990803i | \(0.456796\pi\) | |||||||
\(752\) | 2.47214 | 0.0901495 | ||||||||
\(753\) | −23.2361 | −0.846769 | ||||||||
\(754\) | −10.4721 | −0.381373 | ||||||||
\(755\) | 14.4721 | 0.526695 | ||||||||
\(756\) | −3.23607 | −0.117695 | ||||||||
\(757\) | 21.8885 | 0.795553 | 0.397776 | − | 0.917482i | \(-0.369782\pi\) | ||||
0.397776 | + | 0.917482i | \(0.369782\pi\) | |||||||
\(758\) | −24.9443 | −0.906017 | ||||||||
\(759\) | 5.23607 | 0.190057 | ||||||||
\(760\) | 7.70820 | 0.279606 | ||||||||
\(761\) | −36.4721 | −1.32211 | −0.661057 | − | 0.750336i | \(-0.729892\pi\) | ||||
−0.661057 | + | 0.750336i | \(0.729892\pi\) | |||||||
\(762\) | 12.0000 | 0.434714 | ||||||||
\(763\) | −19.4164 | −0.702921 | ||||||||
\(764\) | 1.52786 | 0.0552762 | ||||||||
\(765\) | 1.00000 | 0.0361551 | ||||||||
\(766\) | 10.4721 | 0.378374 | ||||||||
\(767\) | −4.00000 | −0.144432 | ||||||||
\(768\) | −1.00000 | −0.0360844 | ||||||||
\(769\) | 24.4721 | 0.882488 | 0.441244 | − | 0.897387i | \(-0.354537\pi\) | ||||
0.441244 | + | 0.897387i | \(0.354537\pi\) | |||||||
\(770\) | −3.23607 | −0.116620 | ||||||||
\(771\) | 4.47214 | 0.161060 | ||||||||
\(772\) | 7.70820 | 0.277424 | ||||||||
\(773\) | −31.2361 | −1.12348 | −0.561742 | − | 0.827313i | \(-0.689868\pi\) | ||||
−0.561742 | + | 0.827313i | \(0.689868\pi\) | |||||||
\(774\) | −3.23607 | −0.116318 | ||||||||
\(775\) | −4.00000 | −0.143684 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 19.4164 | 0.696560 | ||||||||
\(778\) | 25.5967 | 0.917688 | ||||||||
\(779\) | 68.9443 | 2.47018 | ||||||||
\(780\) | 1.23607 | 0.0442583 | ||||||||
\(781\) | −0.763932 | −0.0273356 | ||||||||
\(782\) | 5.23607 | 0.187241 | ||||||||
\(783\) | 8.47214 | 0.302769 | ||||||||
\(784\) | 3.47214 | 0.124005 | ||||||||
\(785\) | −19.4164 | −0.693001 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 19.0557 | 0.679263 | 0.339632 | − | 0.940559i | \(-0.389698\pi\) | ||||
0.339632 | + | 0.940559i | \(0.389698\pi\) | |||||||
\(788\) | 14.9443 | 0.532368 | ||||||||
\(789\) | 12.0000 | 0.427211 | ||||||||
\(790\) | −3.70820 | −0.131932 | ||||||||
\(791\) | −49.3050 | −1.75308 | ||||||||
\(792\) | 1.00000 | 0.0355335 | ||||||||
\(793\) | 7.41641 | 0.263364 | ||||||||
\(794\) | −19.8885 | −0.705818 | ||||||||
\(795\) | 3.23607 | 0.114772 | ||||||||
\(796\) | −12.0000 | −0.425329 | ||||||||
\(797\) | 35.0132 | 1.24023 | 0.620115 | − | 0.784511i | \(-0.287086\pi\) | ||||
0.620115 | + | 0.784511i | \(0.287086\pi\) | |||||||
\(798\) | 24.9443 | 0.883018 | ||||||||
\(799\) | −2.47214 | −0.0874579 | ||||||||
\(800\) | 1.00000 | 0.0353553 | ||||||||
\(801\) | −6.94427 | −0.245364 | ||||||||
\(802\) | −20.2918 | −0.716528 | ||||||||
\(803\) | 1.23607 | 0.0436199 | ||||||||
\(804\) | −6.00000 | −0.211604 | ||||||||
\(805\) | 16.9443 | 0.597207 | ||||||||
\(806\) | −4.94427 | −0.174155 | ||||||||
\(807\) | 24.4721 | 0.861460 | ||||||||
\(808\) | 8.94427 | 0.314658 | ||||||||
\(809\) | −16.3607 | −0.575211 | −0.287605 | − | 0.957749i | \(-0.592859\pi\) | ||||
−0.287605 | + | 0.957749i | \(0.592859\pi\) | |||||||
\(810\) | −1.00000 | −0.0351364 | ||||||||
\(811\) | −30.2492 | −1.06219 | −0.531097 | − | 0.847311i | \(-0.678220\pi\) | ||||
−0.531097 | + | 0.847311i | \(0.678220\pi\) | |||||||
\(812\) | −27.4164 | −0.962127 | ||||||||
\(813\) | −20.0000 | −0.701431 | ||||||||
\(814\) | −6.00000 | −0.210300 | ||||||||
\(815\) | 6.47214 | 0.226709 | ||||||||
\(816\) | 1.00000 | 0.0350070 | ||||||||
\(817\) | 24.9443 | 0.872690 | ||||||||
\(818\) | 10.9443 | 0.382657 | ||||||||
\(819\) | 4.00000 | 0.139771 | ||||||||
\(820\) | 8.94427 | 0.312348 | ||||||||
\(821\) | −10.3607 | −0.361590 | −0.180795 | − | 0.983521i | \(-0.557867\pi\) | ||||
−0.180795 | + | 0.983521i | \(0.557867\pi\) | |||||||
\(822\) | 15.8885 | 0.554177 | ||||||||
\(823\) | 37.4164 | 1.30425 | 0.652127 | − | 0.758110i | \(-0.273877\pi\) | ||||
0.652127 | + | 0.758110i | \(0.273877\pi\) | |||||||
\(824\) | 4.00000 | 0.139347 | ||||||||
\(825\) | −1.00000 | −0.0348155 | ||||||||
\(826\) | −10.4721 | −0.364372 | ||||||||
\(827\) | −32.9443 | −1.14558 | −0.572792 | − | 0.819701i | \(-0.694140\pi\) | ||||
−0.572792 | + | 0.819701i | \(0.694140\pi\) | |||||||
\(828\) | −5.23607 | −0.181966 | ||||||||
\(829\) | −49.7771 | −1.72883 | −0.864415 | − | 0.502779i | \(-0.832311\pi\) | ||||
−0.864415 | + | 0.502779i | \(0.832311\pi\) | |||||||
\(830\) | −4.94427 | −0.171618 | ||||||||
\(831\) | −14.0000 | −0.485655 | ||||||||
\(832\) | 1.23607 | 0.0428529 | ||||||||
\(833\) | −3.47214 | −0.120302 | ||||||||
\(834\) | −8.00000 | −0.277017 | ||||||||
\(835\) | 12.0000 | 0.415277 | ||||||||
\(836\) | −7.70820 | −0.266594 | ||||||||
\(837\) | 4.00000 | 0.138260 | ||||||||
\(838\) | 10.4721 | 0.361754 | ||||||||
\(839\) | 14.2918 | 0.493408 | 0.246704 | − | 0.969091i | \(-0.420653\pi\) | ||||
0.246704 | + | 0.969091i | \(0.420653\pi\) | |||||||
\(840\) | 3.23607 | 0.111655 | ||||||||
\(841\) | 42.7771 | 1.47507 | ||||||||
\(842\) | −6.94427 | −0.239315 | ||||||||
\(843\) | 16.4721 | 0.567330 | ||||||||
\(844\) | 20.3607 | 0.700844 | ||||||||
\(845\) | 11.4721 | 0.394653 | ||||||||
\(846\) | 2.47214 | 0.0849938 | ||||||||
\(847\) | 3.23607 | 0.111193 | ||||||||
\(848\) | 3.23607 | 0.111127 | ||||||||
\(849\) | 3.41641 | 0.117251 | ||||||||
\(850\) | −1.00000 | −0.0342997 | ||||||||
\(851\) | 31.4164 | 1.07694 | ||||||||
\(852\) | 0.763932 | 0.0261719 | ||||||||
\(853\) | −14.3607 | −0.491700 | −0.245850 | − | 0.969308i | \(-0.579067\pi\) | ||||
−0.245850 | + | 0.969308i | \(0.579067\pi\) | |||||||
\(854\) | 19.4164 | 0.664416 | ||||||||
\(855\) | 7.70820 | 0.263615 | ||||||||
\(856\) | 0.944272 | 0.0322745 | ||||||||
\(857\) | −19.8885 | −0.679380 | −0.339690 | − | 0.940538i | \(-0.610322\pi\) | ||||
−0.339690 | + | 0.940538i | \(0.610322\pi\) | |||||||
\(858\) | −1.23607 | −0.0421987 | ||||||||
\(859\) | 12.9443 | 0.441653 | 0.220826 | − | 0.975313i | \(-0.429125\pi\) | ||||
0.220826 | + | 0.975313i | \(0.429125\pi\) | |||||||
\(860\) | 3.23607 | 0.110349 | ||||||||
\(861\) | 28.9443 | 0.986418 | ||||||||
\(862\) | −5.05573 | −0.172199 | ||||||||
\(863\) | −52.9443 | −1.80224 | −0.901122 | − | 0.433566i | \(-0.857255\pi\) | ||||
−0.901122 | + | 0.433566i | \(0.857255\pi\) | |||||||
\(864\) | −1.00000 | −0.0340207 | ||||||||
\(865\) | −13.4164 | −0.456172 | ||||||||
\(866\) | −6.00000 | −0.203888 | ||||||||
\(867\) | −1.00000 | −0.0339618 | ||||||||
\(868\) | −12.9443 | −0.439357 | ||||||||
\(869\) | 3.70820 | 0.125792 | ||||||||
\(870\) | −8.47214 | −0.287232 | ||||||||
\(871\) | 7.41641 | 0.251295 | ||||||||
\(872\) | −6.00000 | −0.203186 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 40.3607 | 1.36522 | ||||||||
\(875\) | −3.23607 | −0.109399 | ||||||||
\(876\) | −1.23607 | −0.0417629 | ||||||||
\(877\) | 42.3607 | 1.43042 | 0.715209 | − | 0.698910i | \(-0.246331\pi\) | ||||
0.715209 | + | 0.698910i | \(0.246331\pi\) | |||||||
\(878\) | −4.29180 | −0.144841 | ||||||||
\(879\) | 18.0000 | 0.607125 | ||||||||
\(880\) | −1.00000 | −0.0337100 | ||||||||
\(881\) | 14.1803 | 0.477748 | 0.238874 | − | 0.971051i | \(-0.423222\pi\) | ||||
0.238874 | + | 0.971051i | \(0.423222\pi\) | |||||||
\(882\) | 3.47214 | 0.116913 | ||||||||
\(883\) | 33.4164 | 1.12455 | 0.562276 | − | 0.826950i | \(-0.309926\pi\) | ||||
0.562276 | + | 0.826950i | \(0.309926\pi\) | |||||||
\(884\) | −1.23607 | −0.0415735 | ||||||||
\(885\) | −3.23607 | −0.108779 | ||||||||
\(886\) | −3.34752 | −0.112462 | ||||||||
\(887\) | −56.7214 | −1.90452 | −0.952258 | − | 0.305293i | \(-0.901246\pi\) | ||||
−0.952258 | + | 0.305293i | \(0.901246\pi\) | |||||||
\(888\) | 6.00000 | 0.201347 | ||||||||
\(889\) | −38.8328 | −1.30241 | ||||||||
\(890\) | 6.94427 | 0.232773 | ||||||||
\(891\) | 1.00000 | 0.0335013 | ||||||||
\(892\) | −23.4164 | −0.784039 | ||||||||
\(893\) | −19.0557 | −0.637676 | ||||||||
\(894\) | 9.52786 | 0.318659 | ||||||||
\(895\) | 12.7639 | 0.426651 | ||||||||
\(896\) | 3.23607 | 0.108109 | ||||||||
\(897\) | 6.47214 | 0.216098 | ||||||||
\(898\) | 6.18034 | 0.206241 | ||||||||
\(899\) | 33.8885 | 1.13025 | ||||||||
\(900\) | 1.00000 | 0.0333333 | ||||||||
\(901\) | −3.23607 | −0.107809 | ||||||||
\(902\) | −8.94427 | −0.297812 | ||||||||
\(903\) | 10.4721 | 0.348491 | ||||||||
\(904\) | −15.2361 | −0.506744 | ||||||||
\(905\) | −8.47214 | −0.281623 | ||||||||
\(906\) | 14.4721 | 0.480805 | ||||||||
\(907\) | −38.8328 | −1.28942 | −0.644711 | − | 0.764426i | \(-0.723022\pi\) | ||||
−0.644711 | + | 0.764426i | \(0.723022\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 8.94427 | 0.296663 | ||||||||
\(910\) | −4.00000 | −0.132599 | ||||||||
\(911\) | 31.2361 | 1.03490 | 0.517449 | − | 0.855714i | \(-0.326882\pi\) | ||||
0.517449 | + | 0.855714i | \(0.326882\pi\) | |||||||
\(912\) | 7.70820 | 0.255244 | ||||||||
\(913\) | 4.94427 | 0.163632 | ||||||||
\(914\) | 18.0000 | 0.595387 | ||||||||
\(915\) | 6.00000 | 0.198354 | ||||||||
\(916\) | 29.4164 | 0.971945 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 1.00000 | 0.0330049 | ||||||||
\(919\) | −6.47214 | −0.213496 | −0.106748 | − | 0.994286i | \(-0.534044\pi\) | ||||
−0.106748 | + | 0.994286i | \(0.534044\pi\) | |||||||
\(920\) | 5.23607 | 0.172628 | ||||||||
\(921\) | −10.2918 | −0.339126 | ||||||||
\(922\) | 7.41641 | 0.244246 | ||||||||
\(923\) | −0.944272 | −0.0310811 | ||||||||
\(924\) | −3.23607 | −0.106459 | ||||||||
\(925\) | −6.00000 | −0.197279 | ||||||||
\(926\) | 20.3607 | 0.669093 | ||||||||
\(927\) | 4.00000 | 0.131377 | ||||||||
\(928\) | −8.47214 | −0.278111 | ||||||||
\(929\) | 33.0132 | 1.08313 | 0.541563 | − | 0.840660i | \(-0.317833\pi\) | ||||
0.541563 | + | 0.840660i | \(0.317833\pi\) | |||||||
\(930\) | −4.00000 | −0.131165 | ||||||||
\(931\) | −26.7639 | −0.877152 | ||||||||
\(932\) | −7.52786 | −0.246583 | ||||||||
\(933\) | −11.2361 | −0.367852 | ||||||||
\(934\) | 14.7639 | 0.483091 | ||||||||
\(935\) | 1.00000 | 0.0327035 | ||||||||
\(936\) | 1.23607 | 0.0404021 | ||||||||
\(937\) | −60.2492 | −1.96826 | −0.984128 | − | 0.177459i | \(-0.943212\pi\) | ||||
−0.984128 | + | 0.177459i | \(0.943212\pi\) | |||||||
\(938\) | 19.4164 | 0.633968 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −2.47214 | −0.0806322 | ||||||||
\(941\) | 12.4721 | 0.406580 | 0.203290 | − | 0.979119i | \(-0.434837\pi\) | ||||
0.203290 | + | 0.979119i | \(0.434837\pi\) | |||||||
\(942\) | −19.4164 | −0.632621 | ||||||||
\(943\) | 46.8328 | 1.52509 | ||||||||
\(944\) | −3.23607 | −0.105325 | ||||||||
\(945\) | 3.23607 | 0.105269 | ||||||||
\(946\) | −3.23607 | −0.105214 | ||||||||
\(947\) | 44.7214 | 1.45325 | 0.726624 | − | 0.687035i | \(-0.241088\pi\) | ||||
0.726624 | + | 0.687035i | \(0.241088\pi\) | |||||||
\(948\) | −3.70820 | −0.120437 | ||||||||
\(949\) | 1.52786 | 0.0495966 | ||||||||
\(950\) | −7.70820 | −0.250087 | ||||||||
\(951\) | 13.0557 | 0.423361 | ||||||||
\(952\) | −3.23607 | −0.104882 | ||||||||
\(953\) | 43.3050 | 1.40278 | 0.701392 | − | 0.712775i | \(-0.252562\pi\) | ||||
0.701392 | + | 0.712775i | \(0.252562\pi\) | |||||||
\(954\) | 3.23607 | 0.104772 | ||||||||
\(955\) | −1.52786 | −0.0494405 | ||||||||
\(956\) | −16.3607 | −0.529142 | ||||||||
\(957\) | 8.47214 | 0.273865 | ||||||||
\(958\) | −27.5279 | −0.889385 | ||||||||
\(959\) | −51.4164 | −1.66032 | ||||||||
\(960\) | 1.00000 | 0.0322749 | ||||||||
\(961\) | −15.0000 | −0.483871 | ||||||||
\(962\) | −7.41641 | −0.239115 | ||||||||
\(963\) | 0.944272 | 0.0304287 | ||||||||
\(964\) | 4.18034 | 0.134640 | ||||||||
\(965\) | −7.70820 | −0.248136 | ||||||||
\(966\) | 16.9443 | 0.545173 | ||||||||
\(967\) | −7.41641 | −0.238496 | −0.119248 | − | 0.992865i | \(-0.538048\pi\) | ||||
−0.119248 | + | 0.992865i | \(0.538048\pi\) | |||||||
\(968\) | 1.00000 | 0.0321412 | ||||||||
\(969\) | −7.70820 | −0.247623 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 48.7639 | 1.56491 | 0.782455 | − | 0.622708i | \(-0.213967\pi\) | ||||
0.782455 | + | 0.622708i | \(0.213967\pi\) | |||||||
\(972\) | −1.00000 | −0.0320750 | ||||||||
\(973\) | 25.8885 | 0.829949 | ||||||||
\(974\) | −20.8328 | −0.667526 | ||||||||
\(975\) | −1.23607 | −0.0395859 | ||||||||
\(976\) | 6.00000 | 0.192055 | ||||||||
\(977\) | −7.52786 | −0.240838 | −0.120419 | − | 0.992723i | \(-0.538424\pi\) | ||||
−0.120419 | + | 0.992723i | \(0.538424\pi\) | |||||||
\(978\) | 6.47214 | 0.206956 | ||||||||
\(979\) | −6.94427 | −0.221940 | ||||||||
\(980\) | −3.47214 | −0.110913 | ||||||||
\(981\) | −6.00000 | −0.191565 | ||||||||
\(982\) | 1.05573 | 0.0336896 | ||||||||
\(983\) | 0.652476 | 0.0208107 | 0.0104054 | − | 0.999946i | \(-0.496688\pi\) | ||||
0.0104054 | + | 0.999946i | \(0.496688\pi\) | |||||||
\(984\) | 8.94427 | 0.285133 | ||||||||
\(985\) | −14.9443 | −0.476164 | ||||||||
\(986\) | 8.47214 | 0.269808 | ||||||||
\(987\) | −8.00000 | −0.254643 | ||||||||
\(988\) | −9.52786 | −0.303122 | ||||||||
\(989\) | 16.9443 | 0.538797 | ||||||||
\(990\) | −1.00000 | −0.0317821 | ||||||||
\(991\) | 34.2492 | 1.08796 | 0.543981 | − | 0.839097i | \(-0.316916\pi\) | ||||
0.543981 | + | 0.839097i | \(0.316916\pi\) | |||||||
\(992\) | −4.00000 | −0.127000 | ||||||||
\(993\) | −33.8885 | −1.07542 | ||||||||
\(994\) | −2.47214 | −0.0784114 | ||||||||
\(995\) | 12.0000 | 0.380426 | ||||||||
\(996\) | −4.94427 | −0.156665 | ||||||||
\(997\) | 5.63932 | 0.178599 | 0.0892995 | − | 0.996005i | \(-0.471537\pi\) | ||||
0.0892995 | + | 0.996005i | \(0.471537\pi\) | |||||||
\(998\) | −22.8328 | −0.722760 | ||||||||
\(999\) | 6.00000 | 0.189832 |
(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 | 5610.2.a.bu.1.2 | ✓ | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
5610.2.a.bu.1.2 | ✓ | 2 | 1.1 | even | 1 | trivial |