Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3234,2,Mod(1,3234)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3234, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("3234.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3234 = 2 \cdot 3 \cdot 7^{2} \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3234.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: | \(25.8236200137\) |
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: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | yes |
Fricke sign: | \(+1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-0.618034\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3234.1 |
$q$-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 | ||||||||
\(5\) | 1.23607 | 0.552786 | 0.276393 | − | 0.961045i | \(-0.410861\pi\) | ||||
0.276393 | + | 0.961045i | \(0.410861\pi\) | |||||||
\(6\) | −1.00000 | −0.408248 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 1.23607 | 0.390879 | ||||||||
\(11\) | −1.00000 | −0.301511 | ||||||||
\(12\) | −1.00000 | −0.288675 | ||||||||
\(13\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −1.23607 | −0.319151 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −5.23607 | −1.26993 | −0.634967 | − | 0.772540i | \(-0.718986\pi\) | ||||
−0.634967 | + | 0.772540i | \(0.718986\pi\) | |||||||
\(18\) | 1.00000 | 0.235702 | ||||||||
\(19\) | −7.70820 | −1.76838 | −0.884192 | − | 0.467124i | \(-0.845290\pi\) | ||||
−0.884192 | + | 0.467124i | \(0.845290\pi\) | |||||||
\(20\) | 1.23607 | 0.276393 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −1.00000 | −0.213201 | ||||||||
\(23\) | −2.47214 | −0.515476 | −0.257738 | − | 0.966215i | \(-0.582977\pi\) | ||||
−0.257738 | + | 0.966215i | \(0.582977\pi\) | |||||||
\(24\) | −1.00000 | −0.204124 | ||||||||
\(25\) | −3.47214 | −0.694427 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 4.47214 | 0.830455 | 0.415227 | − | 0.909718i | \(-0.363702\pi\) | ||||
0.415227 | + | 0.909718i | \(0.363702\pi\) | |||||||
\(30\) | −1.23607 | −0.225674 | ||||||||
\(31\) | −2.76393 | −0.496417 | −0.248208 | − | 0.968707i | \(-0.579842\pi\) | ||||
−0.248208 | + | 0.968707i | \(0.579842\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | 1.00000 | 0.174078 | ||||||||
\(34\) | −5.23607 | −0.897978 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | −10.9443 | −1.79923 | −0.899614 | − | 0.436687i | \(-0.856152\pi\) | ||||
−0.899614 | + | 0.436687i | \(0.856152\pi\) | |||||||
\(38\) | −7.70820 | −1.25044 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 1.23607 | 0.195440 | ||||||||
\(41\) | −5.23607 | −0.817736 | −0.408868 | − | 0.912593i | \(-0.634076\pi\) | ||||
−0.408868 | + | 0.912593i | \(0.634076\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 6.47214 | 0.986991 | 0.493496 | − | 0.869748i | \(-0.335719\pi\) | ||||
0.493496 | + | 0.869748i | \(0.335719\pi\) | |||||||
\(44\) | −1.00000 | −0.150756 | ||||||||
\(45\) | 1.23607 | 0.184262 | ||||||||
\(46\) | −2.47214 | −0.364497 | ||||||||
\(47\) | 3.70820 | 0.540897 | 0.270449 | − | 0.962734i | \(-0.412828\pi\) | ||||
0.270449 | + | 0.962734i | \(0.412828\pi\) | |||||||
\(48\) | −1.00000 | −0.144338 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −3.47214 | −0.491034 | ||||||||
\(51\) | 5.23607 | 0.733196 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −6.00000 | −0.824163 | −0.412082 | − | 0.911147i | \(-0.635198\pi\) | ||||
−0.412082 | + | 0.911147i | \(0.635198\pi\) | |||||||
\(54\) | −1.00000 | −0.136083 | ||||||||
\(55\) | −1.23607 | −0.166671 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 7.70820 | 1.02098 | ||||||||
\(58\) | 4.47214 | 0.587220 | ||||||||
\(59\) | −1.52786 | −0.198911 | −0.0994555 | − | 0.995042i | \(-0.531710\pi\) | ||||
−0.0994555 | + | 0.995042i | \(0.531710\pi\) | |||||||
\(60\) | −1.23607 | −0.159576 | ||||||||
\(61\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(62\) | −2.76393 | −0.351020 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 1.00000 | 0.123091 | ||||||||
\(67\) | 15.4164 | 1.88341 | 0.941707 | − | 0.336434i | \(-0.109221\pi\) | ||||
0.941707 | + | 0.336434i | \(0.109221\pi\) | |||||||
\(68\) | −5.23607 | −0.634967 | ||||||||
\(69\) | 2.47214 | 0.297610 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −2.47214 | −0.293389 | −0.146694 | − | 0.989182i | \(-0.546863\pi\) | ||||
−0.146694 | + | 0.989182i | \(0.546863\pi\) | |||||||
\(72\) | 1.00000 | 0.117851 | ||||||||
\(73\) | −15.7082 | −1.83851 | −0.919253 | − | 0.393667i | \(-0.871206\pi\) | ||||
−0.919253 | + | 0.393667i | \(0.871206\pi\) | |||||||
\(74\) | −10.9443 | −1.27225 | ||||||||
\(75\) | 3.47214 | 0.400928 | ||||||||
\(76\) | −7.70820 | −0.884192 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 11.4164 | 1.28445 | 0.642223 | − | 0.766518i | \(-0.278012\pi\) | ||||
0.642223 | + | 0.766518i | \(0.278012\pi\) | |||||||
\(80\) | 1.23607 | 0.138197 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −5.23607 | −0.578227 | ||||||||
\(83\) | 1.23607 | 0.135676 | 0.0678380 | − | 0.997696i | \(-0.478390\pi\) | ||||
0.0678380 | + | 0.997696i | \(0.478390\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −6.47214 | −0.702002 | ||||||||
\(86\) | 6.47214 | 0.697908 | ||||||||
\(87\) | −4.47214 | −0.479463 | ||||||||
\(88\) | −1.00000 | −0.106600 | ||||||||
\(89\) | −6.47214 | −0.686045 | −0.343023 | − | 0.939327i | \(-0.611451\pi\) | ||||
−0.343023 | + | 0.939327i | \(0.611451\pi\) | |||||||
\(90\) | 1.23607 | 0.130293 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −2.47214 | −0.257738 | ||||||||
\(93\) | 2.76393 | 0.286606 | ||||||||
\(94\) | 3.70820 | 0.382472 | ||||||||
\(95\) | −9.52786 | −0.977538 | ||||||||
\(96\) | −1.00000 | −0.102062 | ||||||||
\(97\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −1.00000 | −0.100504 | ||||||||
\(100\) | −3.47214 | −0.347214 | ||||||||
\(101\) | −12.0000 | −1.19404 | −0.597022 | − | 0.802225i | \(-0.703650\pi\) | ||||
−0.597022 | + | 0.802225i | \(0.703650\pi\) | |||||||
\(102\) | 5.23607 | 0.518448 | ||||||||
\(103\) | 10.7639 | 1.06060 | 0.530301 | − | 0.847810i | \(-0.322079\pi\) | ||||
0.530301 | + | 0.847810i | \(0.322079\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −6.00000 | −0.582772 | ||||||||
\(107\) | 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 | \(-0.407226\pi\) | ||||
0.287348 | + | 0.957826i | \(0.407226\pi\) | |||||||
\(110\) | −1.23607 | −0.117854 | ||||||||
\(111\) | 10.9443 | 1.03878 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 13.4164 | 1.26211 | 0.631055 | − | 0.775738i | \(-0.282622\pi\) | ||||
0.631055 | + | 0.775738i | \(0.282622\pi\) | |||||||
\(114\) | 7.70820 | 0.721939 | ||||||||
\(115\) | −3.05573 | −0.284948 | ||||||||
\(116\) | 4.47214 | 0.415227 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −1.52786 | −0.140651 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −1.23607 | −0.112837 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 5.23607 | 0.472120 | ||||||||
\(124\) | −2.76393 | −0.248208 | ||||||||
\(125\) | −10.4721 | −0.936656 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −6.47214 | −0.574309 | −0.287155 | − | 0.957884i | \(-0.592709\pi\) | ||||
−0.287155 | + | 0.957884i | \(0.592709\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | −6.47214 | −0.569840 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 6.76393 | 0.590967 | 0.295484 | − | 0.955348i | \(-0.404519\pi\) | ||||
0.295484 | + | 0.955348i | \(0.404519\pi\) | |||||||
\(132\) | 1.00000 | 0.0870388 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 15.4164 | 1.33177 | ||||||||
\(135\) | −1.23607 | −0.106384 | ||||||||
\(136\) | −5.23607 | −0.448989 | ||||||||
\(137\) | −16.4721 | −1.40731 | −0.703655 | − | 0.710542i | \(-0.748450\pi\) | ||||
−0.703655 | + | 0.710542i | \(0.748450\pi\) | |||||||
\(138\) | 2.47214 | 0.210442 | ||||||||
\(139\) | −10.1803 | −0.863485 | −0.431743 | − | 0.901997i | \(-0.642101\pi\) | ||||
−0.431743 | + | 0.901997i | \(0.642101\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −3.70820 | −0.312287 | ||||||||
\(142\) | −2.47214 | −0.207457 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | 5.52786 | 0.459064 | ||||||||
\(146\) | −15.7082 | −1.30002 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −10.9443 | −0.899614 | ||||||||
\(149\) | −6.00000 | −0.491539 | −0.245770 | − | 0.969328i | \(-0.579041\pi\) | ||||
−0.245770 | + | 0.969328i | \(0.579041\pi\) | |||||||
\(150\) | 3.47214 | 0.283499 | ||||||||
\(151\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(152\) | −7.70820 | −0.625218 | ||||||||
\(153\) | −5.23607 | −0.423311 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −3.41641 | −0.274412 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −14.7639 | −1.17829 | −0.589145 | − | 0.808027i | \(-0.700535\pi\) | ||||
−0.589145 | + | 0.808027i | \(0.700535\pi\) | |||||||
\(158\) | 11.4164 | 0.908241 | ||||||||
\(159\) | 6.00000 | 0.475831 | ||||||||
\(160\) | 1.23607 | 0.0977198 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 1.00000 | 0.0785674 | ||||||||
\(163\) | −12.0000 | −0.939913 | −0.469956 | − | 0.882690i | \(-0.655730\pi\) | ||||
−0.469956 | + | 0.882690i | \(0.655730\pi\) | |||||||
\(164\) | −5.23607 | −0.408868 | ||||||||
\(165\) | 1.23607 | 0.0962278 | ||||||||
\(166\) | 1.23607 | 0.0959375 | ||||||||
\(167\) | 18.4721 | 1.42942 | 0.714708 | − | 0.699423i | \(-0.246559\pi\) | ||||
0.714708 | + | 0.699423i | \(0.246559\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −13.0000 | −1.00000 | ||||||||
\(170\) | −6.47214 | −0.496390 | ||||||||
\(171\) | −7.70820 | −0.589461 | ||||||||
\(172\) | 6.47214 | 0.493496 | ||||||||
\(173\) | 19.4164 | 1.47620 | 0.738101 | − | 0.674690i | \(-0.235723\pi\) | ||||
0.738101 | + | 0.674690i | \(0.235723\pi\) | |||||||
\(174\) | −4.47214 | −0.339032 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −1.00000 | −0.0753778 | ||||||||
\(177\) | 1.52786 | 0.114841 | ||||||||
\(178\) | −6.47214 | −0.485107 | ||||||||
\(179\) | −5.52786 | −0.413172 | −0.206586 | − | 0.978428i | \(-0.566235\pi\) | ||||
−0.206586 | + | 0.978428i | \(0.566235\pi\) | |||||||
\(180\) | 1.23607 | 0.0921311 | ||||||||
\(181\) | 11.7082 | 0.870264 | 0.435132 | − | 0.900367i | \(-0.356702\pi\) | ||||
0.435132 | + | 0.900367i | \(0.356702\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −2.47214 | −0.182248 | ||||||||
\(185\) | −13.5279 | −0.994588 | ||||||||
\(186\) | 2.76393 | 0.202661 | ||||||||
\(187\) | 5.23607 | 0.382899 | ||||||||
\(188\) | 3.70820 | 0.270449 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −9.52786 | −0.691224 | ||||||||
\(191\) | −10.4721 | −0.757737 | −0.378869 | − | 0.925450i | \(-0.623687\pi\) | ||||
−0.378869 | + | 0.925450i | \(0.623687\pi\) | |||||||
\(192\) | −1.00000 | −0.0721688 | ||||||||
\(193\) | 5.05573 | 0.363919 | 0.181960 | − | 0.983306i | \(-0.441756\pi\) | ||||
0.181960 | + | 0.983306i | \(0.441756\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −22.3607 | −1.59313 | −0.796566 | − | 0.604551i | \(-0.793352\pi\) | ||||
−0.796566 | + | 0.604551i | \(0.793352\pi\) | |||||||
\(198\) | −1.00000 | −0.0710669 | ||||||||
\(199\) | −23.1246 | −1.63926 | −0.819630 | − | 0.572893i | \(-0.805821\pi\) | ||||
−0.819630 | + | 0.572893i | \(0.805821\pi\) | |||||||
\(200\) | −3.47214 | −0.245517 | ||||||||
\(201\) | −15.4164 | −1.08739 | ||||||||
\(202\) | −12.0000 | −0.844317 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 5.23607 | 0.366598 | ||||||||
\(205\) | −6.47214 | −0.452034 | ||||||||
\(206\) | 10.7639 | 0.749959 | ||||||||
\(207\) | −2.47214 | −0.171825 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 7.70820 | 0.533188 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 3.41641 | 0.235195 | 0.117598 | − | 0.993061i | \(-0.462481\pi\) | ||||
0.117598 | + | 0.993061i | \(0.462481\pi\) | |||||||
\(212\) | −6.00000 | −0.412082 | ||||||||
\(213\) | 2.47214 | 0.169388 | ||||||||
\(214\) | 0.944272 | 0.0645491 | ||||||||
\(215\) | 8.00000 | 0.545595 | ||||||||
\(216\) | −1.00000 | −0.0680414 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 6.00000 | 0.406371 | ||||||||
\(219\) | 15.7082 | 1.06146 | ||||||||
\(220\) | −1.23607 | −0.0833357 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 10.9443 | 0.734531 | ||||||||
\(223\) | −15.7082 | −1.05190 | −0.525950 | − | 0.850516i | \(-0.676290\pi\) | ||||
−0.525950 | + | 0.850516i | \(0.676290\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −3.47214 | −0.231476 | ||||||||
\(226\) | 13.4164 | 0.892446 | ||||||||
\(227\) | 8.65248 | 0.574285 | 0.287142 | − | 0.957888i | \(-0.407295\pi\) | ||||
0.287142 | + | 0.957888i | \(0.407295\pi\) | |||||||
\(228\) | 7.70820 | 0.510488 | ||||||||
\(229\) | 19.7082 | 1.30235 | 0.651177 | − | 0.758926i | \(-0.274275\pi\) | ||||
0.651177 | + | 0.758926i | \(0.274275\pi\) | |||||||
\(230\) | −3.05573 | −0.201489 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 4.47214 | 0.293610 | ||||||||
\(233\) | −9.05573 | −0.593260 | −0.296630 | − | 0.954992i | \(-0.595863\pi\) | ||||
−0.296630 | + | 0.954992i | \(0.595863\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 4.58359 | 0.299001 | ||||||||
\(236\) | −1.52786 | −0.0994555 | ||||||||
\(237\) | −11.4164 | −0.741575 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(240\) | −1.23607 | −0.0797878 | ||||||||
\(241\) | 18.1803 | 1.17110 | 0.585549 | − | 0.810637i | \(-0.300879\pi\) | ||||
0.585549 | + | 0.810637i | \(0.300879\pi\) | |||||||
\(242\) | 1.00000 | 0.0642824 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 5.23607 | 0.333840 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | −2.76393 | −0.175510 | ||||||||
\(249\) | −1.23607 | −0.0783326 | ||||||||
\(250\) | −10.4721 | −0.662316 | ||||||||
\(251\) | −6.47214 | −0.408518 | −0.204259 | − | 0.978917i | \(-0.565478\pi\) | ||||
−0.204259 | + | 0.978917i | \(0.565478\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 2.47214 | 0.155422 | ||||||||
\(254\) | −6.47214 | −0.406098 | ||||||||
\(255\) | 6.47214 | 0.405301 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 22.4721 | 1.40177 | 0.700887 | − | 0.713273i | \(-0.252788\pi\) | ||||
0.700887 | + | 0.713273i | \(0.252788\pi\) | |||||||
\(258\) | −6.47214 | −0.402938 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 4.47214 | 0.276818 | ||||||||
\(262\) | 6.76393 | 0.417877 | ||||||||
\(263\) | −9.52786 | −0.587513 | −0.293757 | − | 0.955880i | \(-0.594906\pi\) | ||||
−0.293757 | + | 0.955880i | \(0.594906\pi\) | |||||||
\(264\) | 1.00000 | 0.0615457 | ||||||||
\(265\) | −7.41641 | −0.455586 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 6.47214 | 0.396088 | ||||||||
\(268\) | 15.4164 | 0.941707 | ||||||||
\(269\) | −27.7082 | −1.68940 | −0.844700 | − | 0.535241i | \(-0.820221\pi\) | ||||
−0.844700 | + | 0.535241i | \(0.820221\pi\) | |||||||
\(270\) | −1.23607 | −0.0752247 | ||||||||
\(271\) | −2.47214 | −0.150172 | −0.0750858 | − | 0.997177i | \(-0.523923\pi\) | ||||
−0.0750858 | + | 0.997177i | \(0.523923\pi\) | |||||||
\(272\) | −5.23607 | −0.317483 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −16.4721 | −0.995118 | ||||||||
\(275\) | 3.47214 | 0.209378 | ||||||||
\(276\) | 2.47214 | 0.148805 | ||||||||
\(277\) | 26.0000 | 1.56219 | 0.781094 | − | 0.624413i | \(-0.214662\pi\) | ||||
0.781094 | + | 0.624413i | \(0.214662\pi\) | |||||||
\(278\) | −10.1803 | −0.610576 | ||||||||
\(279\) | −2.76393 | −0.165472 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 19.8885 | 1.18645 | 0.593226 | − | 0.805036i | \(-0.297854\pi\) | ||||
0.593226 | + | 0.805036i | \(0.297854\pi\) | |||||||
\(282\) | −3.70820 | −0.220820 | ||||||||
\(283\) | 23.7082 | 1.40931 | 0.704653 | − | 0.709552i | \(-0.251103\pi\) | ||||
0.704653 | + | 0.709552i | \(0.251103\pi\) | |||||||
\(284\) | −2.47214 | −0.146694 | ||||||||
\(285\) | 9.52786 | 0.564382 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 1.00000 | 0.0589256 | ||||||||
\(289\) | 10.4164 | 0.612730 | ||||||||
\(290\) | 5.52786 | 0.324607 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −15.7082 | −0.919253 | ||||||||
\(293\) | −4.58359 | −0.267776 | −0.133888 | − | 0.990996i | \(-0.542746\pi\) | ||||
−0.133888 | + | 0.990996i | \(0.542746\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −1.88854 | −0.109955 | ||||||||
\(296\) | −10.9443 | −0.636123 | ||||||||
\(297\) | 1.00000 | 0.0580259 | ||||||||
\(298\) | −6.00000 | −0.347571 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 3.47214 | 0.200464 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 12.0000 | 0.689382 | ||||||||
\(304\) | −7.70820 | −0.442096 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −5.23607 | −0.299326 | ||||||||
\(307\) | 25.5967 | 1.46088 | 0.730442 | − | 0.682975i | \(-0.239314\pi\) | ||||
0.730442 | + | 0.682975i | \(0.239314\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −10.7639 | −0.612339 | ||||||||
\(310\) | −3.41641 | −0.194039 | ||||||||
\(311\) | −8.65248 | −0.490637 | −0.245318 | − | 0.969443i | \(-0.578893\pi\) | ||||
−0.245318 | + | 0.969443i | \(0.578893\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 5.52786 | 0.312453 | 0.156227 | − | 0.987721i | \(-0.450067\pi\) | ||||
0.156227 | + | 0.987721i | \(0.450067\pi\) | |||||||
\(314\) | −14.7639 | −0.833177 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 11.4164 | 0.642223 | ||||||||
\(317\) | −31.8885 | −1.79104 | −0.895520 | − | 0.445022i | \(-0.853196\pi\) | ||||
−0.895520 | + | 0.445022i | \(0.853196\pi\) | |||||||
\(318\) | 6.00000 | 0.336463 | ||||||||
\(319\) | −4.47214 | −0.250392 | ||||||||
\(320\) | 1.23607 | 0.0690983 | ||||||||
\(321\) | −0.944272 | −0.0527041 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 40.3607 | 2.24573 | ||||||||
\(324\) | 1.00000 | 0.0555556 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −12.0000 | −0.664619 | ||||||||
\(327\) | −6.00000 | −0.331801 | ||||||||
\(328\) | −5.23607 | −0.289113 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 1.23607 | 0.0680433 | ||||||||
\(331\) | −7.41641 | −0.407643 | −0.203821 | − | 0.979008i | \(-0.565336\pi\) | ||||
−0.203821 | + | 0.979008i | \(0.565336\pi\) | |||||||
\(332\) | 1.23607 | 0.0678380 | ||||||||
\(333\) | −10.9443 | −0.599742 | ||||||||
\(334\) | 18.4721 | 1.01075 | ||||||||
\(335\) | 19.0557 | 1.04113 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −18.0000 | −0.980522 | −0.490261 | − | 0.871576i | \(-0.663099\pi\) | ||||
−0.490261 | + | 0.871576i | \(0.663099\pi\) | |||||||
\(338\) | −13.0000 | −0.707107 | ||||||||
\(339\) | −13.4164 | −0.728679 | ||||||||
\(340\) | −6.47214 | −0.351001 | ||||||||
\(341\) | 2.76393 | 0.149675 | ||||||||
\(342\) | −7.70820 | −0.416812 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 6.47214 | 0.348954 | ||||||||
\(345\) | 3.05573 | 0.164515 | ||||||||
\(346\) | 19.4164 | 1.04383 | ||||||||
\(347\) | −26.8328 | −1.44046 | −0.720231 | − | 0.693735i | \(-0.755964\pi\) | ||||
−0.720231 | + | 0.693735i | \(0.755964\pi\) | |||||||
\(348\) | −4.47214 | −0.239732 | ||||||||
\(349\) | −0.583592 | −0.0312390 | −0.0156195 | − | 0.999878i | \(-0.504972\pi\) | ||||
−0.0156195 | + | 0.999878i | \(0.504972\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −1.00000 | −0.0533002 | ||||||||
\(353\) | 24.3607 | 1.29659 | 0.648294 | − | 0.761390i | \(-0.275483\pi\) | ||||
0.648294 | + | 0.761390i | \(0.275483\pi\) | |||||||
\(354\) | 1.52786 | 0.0812051 | ||||||||
\(355\) | −3.05573 | −0.162181 | ||||||||
\(356\) | −6.47214 | −0.343023 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −5.52786 | −0.292157 | ||||||||
\(359\) | 1.52786 | 0.0806376 | 0.0403188 | − | 0.999187i | \(-0.487163\pi\) | ||||
0.0403188 | + | 0.999187i | \(0.487163\pi\) | |||||||
\(360\) | 1.23607 | 0.0651465 | ||||||||
\(361\) | 40.4164 | 2.12718 | ||||||||
\(362\) | 11.7082 | 0.615370 | ||||||||
\(363\) | −1.00000 | −0.0524864 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −19.4164 | −1.01630 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 8.29180 | 0.432828 | 0.216414 | − | 0.976302i | \(-0.430564\pi\) | ||||
0.216414 | + | 0.976302i | \(0.430564\pi\) | |||||||
\(368\) | −2.47214 | −0.128869 | ||||||||
\(369\) | −5.23607 | −0.272579 | ||||||||
\(370\) | −13.5279 | −0.703280 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 2.76393 | 0.143303 | ||||||||
\(373\) | −1.41641 | −0.0733388 | −0.0366694 | − | 0.999327i | \(-0.511675\pi\) | ||||
−0.0366694 | + | 0.999327i | \(0.511675\pi\) | |||||||
\(374\) | 5.23607 | 0.270751 | ||||||||
\(375\) | 10.4721 | 0.540779 | ||||||||
\(376\) | 3.70820 | 0.191236 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −4.00000 | −0.205466 | −0.102733 | − | 0.994709i | \(-0.532759\pi\) | ||||
−0.102733 | + | 0.994709i | \(0.532759\pi\) | |||||||
\(380\) | −9.52786 | −0.488769 | ||||||||
\(381\) | 6.47214 | 0.331578 | ||||||||
\(382\) | −10.4721 | −0.535801 | ||||||||
\(383\) | −0.652476 | −0.0333400 | −0.0166700 | − | 0.999861i | \(-0.505306\pi\) | ||||
−0.0166700 | + | 0.999861i | \(0.505306\pi\) | |||||||
\(384\) | −1.00000 | −0.0510310 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 5.05573 | 0.257330 | ||||||||
\(387\) | 6.47214 | 0.328997 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −6.94427 | −0.352089 | −0.176044 | − | 0.984382i | \(-0.556330\pi\) | ||||
−0.176044 | + | 0.984382i | \(0.556330\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 12.9443 | 0.654620 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −6.76393 | −0.341195 | ||||||||
\(394\) | −22.3607 | −1.12651 | ||||||||
\(395\) | 14.1115 | 0.710024 | ||||||||
\(396\) | −1.00000 | −0.0502519 | ||||||||
\(397\) | −1.81966 | −0.0913261 | −0.0456631 | − | 0.998957i | \(-0.514540\pi\) | ||||
−0.0456631 | + | 0.998957i | \(0.514540\pi\) | |||||||
\(398\) | −23.1246 | −1.15913 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −3.47214 | −0.173607 | ||||||||
\(401\) | −8.47214 | −0.423078 | −0.211539 | − | 0.977370i | \(-0.567848\pi\) | ||||
−0.211539 | + | 0.977370i | \(0.567848\pi\) | |||||||
\(402\) | −15.4164 | −0.768901 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | −12.0000 | −0.597022 | ||||||||
\(405\) | 1.23607 | 0.0614207 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 10.9443 | 0.542487 | ||||||||
\(408\) | 5.23607 | 0.259224 | ||||||||
\(409\) | 2.76393 | 0.136668 | 0.0683338 | − | 0.997663i | \(-0.478232\pi\) | ||||
0.0683338 | + | 0.997663i | \(0.478232\pi\) | |||||||
\(410\) | −6.47214 | −0.319636 | ||||||||
\(411\) | 16.4721 | 0.812511 | ||||||||
\(412\) | 10.7639 | 0.530301 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | −2.47214 | −0.121499 | ||||||||
\(415\) | 1.52786 | 0.0749999 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 10.1803 | 0.498533 | ||||||||
\(418\) | 7.70820 | 0.377021 | ||||||||
\(419\) | 15.0557 | 0.735520 | 0.367760 | − | 0.929921i | \(-0.380125\pi\) | ||||
0.367760 | + | 0.929921i | \(0.380125\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −5.05573 | −0.246401 | −0.123201 | − | 0.992382i | \(-0.539316\pi\) | ||||
−0.123201 | + | 0.992382i | \(0.539316\pi\) | |||||||
\(422\) | 3.41641 | 0.166308 | ||||||||
\(423\) | 3.70820 | 0.180299 | ||||||||
\(424\) | −6.00000 | −0.291386 | ||||||||
\(425\) | 18.1803 | 0.881876 | ||||||||
\(426\) | 2.47214 | 0.119775 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0.944272 | 0.0456431 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 8.00000 | 0.385794 | ||||||||
\(431\) | −22.4721 | −1.08244 | −0.541222 | − | 0.840880i | \(-0.682038\pi\) | ||||
−0.541222 | + | 0.840880i | \(0.682038\pi\) | |||||||
\(432\) | −1.00000 | −0.0481125 | ||||||||
\(433\) | 9.88854 | 0.475213 | 0.237607 | − | 0.971361i | \(-0.423637\pi\) | ||||
0.237607 | + | 0.971361i | \(0.423637\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −5.52786 | −0.265041 | ||||||||
\(436\) | 6.00000 | 0.287348 | ||||||||
\(437\) | 19.0557 | 0.911559 | ||||||||
\(438\) | 15.7082 | 0.750567 | ||||||||
\(439\) | 31.4164 | 1.49942 | 0.749712 | − | 0.661765i | \(-0.230192\pi\) | ||||
0.749712 | + | 0.661765i | \(0.230192\pi\) | |||||||
\(440\) | −1.23607 | −0.0589272 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 7.41641 | 0.352364 | 0.176182 | − | 0.984358i | \(-0.443625\pi\) | ||||
0.176182 | + | 0.984358i | \(0.443625\pi\) | |||||||
\(444\) | 10.9443 | 0.519392 | ||||||||
\(445\) | −8.00000 | −0.379236 | ||||||||
\(446\) | −15.7082 | −0.743805 | ||||||||
\(447\) | 6.00000 | 0.283790 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 19.5279 | 0.921577 | 0.460788 | − | 0.887510i | \(-0.347567\pi\) | ||||
0.460788 | + | 0.887510i | \(0.347567\pi\) | |||||||
\(450\) | −3.47214 | −0.163678 | ||||||||
\(451\) | 5.23607 | 0.246557 | ||||||||
\(452\) | 13.4164 | 0.631055 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 8.65248 | 0.406081 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 7.70820 | 0.360970 | ||||||||
\(457\) | 18.0000 | 0.842004 | 0.421002 | − | 0.907060i | \(-0.361678\pi\) | ||||
0.421002 | + | 0.907060i | \(0.361678\pi\) | |||||||
\(458\) | 19.7082 | 0.920904 | ||||||||
\(459\) | 5.23607 | 0.244399 | ||||||||
\(460\) | −3.05573 | −0.142474 | ||||||||
\(461\) | −26.8328 | −1.24973 | −0.624864 | − | 0.780733i | \(-0.714846\pi\) | ||||
−0.624864 | + | 0.780733i | \(0.714846\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −1.88854 | −0.0877681 | −0.0438840 | − | 0.999037i | \(-0.513973\pi\) | ||||
−0.0438840 | + | 0.999037i | \(0.513973\pi\) | |||||||
\(464\) | 4.47214 | 0.207614 | ||||||||
\(465\) | 3.41641 | 0.158432 | ||||||||
\(466\) | −9.05573 | −0.419499 | ||||||||
\(467\) | −29.8885 | −1.38308 | −0.691538 | − | 0.722340i | \(-0.743067\pi\) | ||||
−0.691538 | + | 0.722340i | \(0.743067\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 4.58359 | 0.211425 | ||||||||
\(471\) | 14.7639 | 0.680286 | ||||||||
\(472\) | −1.52786 | −0.0703256 | ||||||||
\(473\) | −6.47214 | −0.297589 | ||||||||
\(474\) | −11.4164 | −0.524373 | ||||||||
\(475\) | 26.7639 | 1.22801 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −6.00000 | −0.274721 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 35.7771 | 1.63470 | 0.817348 | − | 0.576144i | \(-0.195443\pi\) | ||||
0.817348 | + | 0.576144i | \(0.195443\pi\) | |||||||
\(480\) | −1.23607 | −0.0564185 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 18.1803 | 0.828092 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 1.00000 | 0.0454545 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −1.00000 | −0.0453609 | ||||||||
\(487\) | 36.9443 | 1.67410 | 0.837052 | − | 0.547123i | \(-0.184277\pi\) | ||||
0.837052 | + | 0.547123i | \(0.184277\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 12.0000 | 0.542659 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −29.8885 | −1.34885 | −0.674426 | − | 0.738343i | \(-0.735609\pi\) | ||||
−0.674426 | + | 0.738343i | \(0.735609\pi\) | |||||||
\(492\) | 5.23607 | 0.236060 | ||||||||
\(493\) | −23.4164 | −1.05462 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −1.23607 | −0.0555571 | ||||||||
\(496\) | −2.76393 | −0.124104 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −1.23607 | −0.0553895 | ||||||||
\(499\) | 7.41641 | 0.332004 | 0.166002 | − | 0.986125i | \(-0.446914\pi\) | ||||
0.166002 | + | 0.986125i | \(0.446914\pi\) | |||||||
\(500\) | −10.4721 | −0.468328 | ||||||||
\(501\) | −18.4721 | −0.825274 | ||||||||
\(502\) | −6.47214 | −0.288866 | ||||||||
\(503\) | −41.3050 | −1.84170 | −0.920848 | − | 0.389921i | \(-0.872502\pi\) | ||||
−0.920848 | + | 0.389921i | \(0.872502\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −14.8328 | −0.660052 | ||||||||
\(506\) | 2.47214 | 0.109900 | ||||||||
\(507\) | 13.0000 | 0.577350 | ||||||||
\(508\) | −6.47214 | −0.287155 | ||||||||
\(509\) | −6.76393 | −0.299806 | −0.149903 | − | 0.988701i | \(-0.547896\pi\) | ||||
−0.149903 | + | 0.988701i | \(0.547896\pi\) | |||||||
\(510\) | 6.47214 | 0.286591 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 7.70820 | 0.340326 | ||||||||
\(514\) | 22.4721 | 0.991203 | ||||||||
\(515\) | 13.3050 | 0.586286 | ||||||||
\(516\) | −6.47214 | −0.284920 | ||||||||
\(517\) | −3.70820 | −0.163087 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −19.4164 | −0.852286 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −21.3050 | −0.933387 | −0.466693 | − | 0.884419i | \(-0.654555\pi\) | ||||
−0.466693 | + | 0.884419i | \(0.654555\pi\) | |||||||
\(522\) | 4.47214 | 0.195740 | ||||||||
\(523\) | −24.2918 | −1.06221 | −0.531103 | − | 0.847307i | \(-0.678222\pi\) | ||||
−0.531103 | + | 0.847307i | \(0.678222\pi\) | |||||||
\(524\) | 6.76393 | 0.295484 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −9.52786 | −0.415435 | ||||||||
\(527\) | 14.4721 | 0.630416 | ||||||||
\(528\) | 1.00000 | 0.0435194 | ||||||||
\(529\) | −16.8885 | −0.734285 | ||||||||
\(530\) | −7.41641 | −0.322148 | ||||||||
\(531\) | −1.52786 | −0.0663037 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 6.47214 | 0.280077 | ||||||||
\(535\) | 1.16718 | 0.0504618 | ||||||||
\(536\) | 15.4164 | 0.665887 | ||||||||
\(537\) | 5.52786 | 0.238545 | ||||||||
\(538\) | −27.7082 | −1.19459 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −1.23607 | −0.0531919 | ||||||||
\(541\) | 21.4164 | 0.920763 | 0.460382 | − | 0.887721i | \(-0.347713\pi\) | ||||
0.460382 | + | 0.887721i | \(0.347713\pi\) | |||||||
\(542\) | −2.47214 | −0.106187 | ||||||||
\(543\) | −11.7082 | −0.502447 | ||||||||
\(544\) | −5.23607 | −0.224495 | ||||||||
\(545\) | 7.41641 | 0.317684 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 38.4721 | 1.64495 | 0.822475 | − | 0.568801i | \(-0.192593\pi\) | ||||
0.822475 | + | 0.568801i | \(0.192593\pi\) | |||||||
\(548\) | −16.4721 | −0.703655 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 3.47214 | 0.148052 | ||||||||
\(551\) | −34.4721 | −1.46856 | ||||||||
\(552\) | 2.47214 | 0.105221 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 26.0000 | 1.10463 | ||||||||
\(555\) | 13.5279 | 0.574226 | ||||||||
\(556\) | −10.1803 | −0.431743 | ||||||||
\(557\) | −10.5836 | −0.448441 | −0.224221 | − | 0.974538i | \(-0.571984\pi\) | ||||
−0.224221 | + | 0.974538i | \(0.571984\pi\) | |||||||
\(558\) | −2.76393 | −0.117007 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −5.23607 | −0.221067 | ||||||||
\(562\) | 19.8885 | 0.838948 | ||||||||
\(563\) | 6.76393 | 0.285066 | 0.142533 | − | 0.989790i | \(-0.454475\pi\) | ||||
0.142533 | + | 0.989790i | \(0.454475\pi\) | |||||||
\(564\) | −3.70820 | −0.156144 | ||||||||
\(565\) | 16.5836 | 0.697677 | ||||||||
\(566\) | 23.7082 | 0.996530 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −2.47214 | −0.103729 | ||||||||
\(569\) | −34.9443 | −1.46494 | −0.732470 | − | 0.680799i | \(-0.761633\pi\) | ||||
−0.732470 | + | 0.680799i | \(0.761633\pi\) | |||||||
\(570\) | 9.52786 | 0.399078 | ||||||||
\(571\) | −17.5279 | −0.733518 | −0.366759 | − | 0.930316i | \(-0.619533\pi\) | ||||
−0.366759 | + | 0.930316i | \(0.619533\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 10.4721 | 0.437480 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 8.58359 | 0.357961 | ||||||||
\(576\) | 1.00000 | 0.0416667 | ||||||||
\(577\) | −39.4164 | −1.64093 | −0.820463 | − | 0.571699i | \(-0.806284\pi\) | ||||
−0.820463 | + | 0.571699i | \(0.806284\pi\) | |||||||
\(578\) | 10.4164 | 0.433265 | ||||||||
\(579\) | −5.05573 | −0.210109 | ||||||||
\(580\) | 5.52786 | 0.229532 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 6.00000 | 0.248495 | ||||||||
\(584\) | −15.7082 | −0.650010 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −4.58359 | −0.189346 | ||||||||
\(587\) | 17.5279 | 0.723452 | 0.361726 | − | 0.932284i | \(-0.382188\pi\) | ||||
0.361726 | + | 0.932284i | \(0.382188\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 21.3050 | 0.877855 | ||||||||
\(590\) | −1.88854 | −0.0777501 | ||||||||
\(591\) | 22.3607 | 0.919795 | ||||||||
\(592\) | −10.9443 | −0.449807 | ||||||||
\(593\) | 18.7639 | 0.770542 | 0.385271 | − | 0.922803i | \(-0.374108\pi\) | ||||
0.385271 | + | 0.922803i | \(0.374108\pi\) | |||||||
\(594\) | 1.00000 | 0.0410305 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −6.00000 | −0.245770 | ||||||||
\(597\) | 23.1246 | 0.946427 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 25.3050 | 1.03393 | 0.516966 | − | 0.856006i | \(-0.327061\pi\) | ||||
0.516966 | + | 0.856006i | \(0.327061\pi\) | |||||||
\(600\) | 3.47214 | 0.141749 | ||||||||
\(601\) | −0.291796 | −0.0119026 | −0.00595130 | − | 0.999982i | \(-0.501894\pi\) | ||||
−0.00595130 | + | 0.999982i | \(0.501894\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 15.4164 | 0.627805 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 1.23607 | 0.0502533 | ||||||||
\(606\) | 12.0000 | 0.487467 | ||||||||
\(607\) | −8.00000 | −0.324710 | −0.162355 | − | 0.986732i | \(-0.551909\pi\) | ||||
−0.162355 | + | 0.986732i | \(0.551909\pi\) | |||||||
\(608\) | −7.70820 | −0.312609 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | −5.23607 | −0.211656 | ||||||||
\(613\) | 12.4721 | 0.503745 | 0.251872 | − | 0.967760i | \(-0.418954\pi\) | ||||
0.251872 | + | 0.967760i | \(0.418954\pi\) | |||||||
\(614\) | 25.5967 | 1.03300 | ||||||||
\(615\) | 6.47214 | 0.260982 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 23.8885 | 0.961717 | 0.480858 | − | 0.876798i | \(-0.340325\pi\) | ||||
0.480858 | + | 0.876798i | \(0.340325\pi\) | |||||||
\(618\) | −10.7639 | −0.432989 | ||||||||
\(619\) | 18.8328 | 0.756955 | 0.378477 | − | 0.925611i | \(-0.376448\pi\) | ||||
0.378477 | + | 0.925611i | \(0.376448\pi\) | |||||||
\(620\) | −3.41641 | −0.137206 | ||||||||
\(621\) | 2.47214 | 0.0992034 | ||||||||
\(622\) | −8.65248 | −0.346933 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 4.41641 | 0.176656 | ||||||||
\(626\) | 5.52786 | 0.220938 | ||||||||
\(627\) | −7.70820 | −0.307836 | ||||||||
\(628\) | −14.7639 | −0.589145 | ||||||||
\(629\) | 57.3050 | 2.28490 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 9.88854 | 0.393657 | 0.196828 | − | 0.980438i | \(-0.436936\pi\) | ||||
0.196828 | + | 0.980438i | \(0.436936\pi\) | |||||||
\(632\) | 11.4164 | 0.454120 | ||||||||
\(633\) | −3.41641 | −0.135790 | ||||||||
\(634\) | −31.8885 | −1.26646 | ||||||||
\(635\) | −8.00000 | −0.317470 | ||||||||
\(636\) | 6.00000 | 0.237915 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −4.47214 | −0.177054 | ||||||||
\(639\) | −2.47214 | −0.0977962 | ||||||||
\(640\) | 1.23607 | 0.0488599 | ||||||||
\(641\) | −35.8885 | −1.41751 | −0.708756 | − | 0.705454i | \(-0.750743\pi\) | ||||
−0.708756 | + | 0.705454i | \(0.750743\pi\) | |||||||
\(642\) | −0.944272 | −0.0372674 | ||||||||
\(643\) | 43.4164 | 1.71218 | 0.856088 | − | 0.516830i | \(-0.172888\pi\) | ||||
0.856088 | + | 0.516830i | \(0.172888\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −8.00000 | −0.315000 | ||||||||
\(646\) | 40.3607 | 1.58797 | ||||||||
\(647\) | 45.0132 | 1.76965 | 0.884825 | − | 0.465924i | \(-0.154278\pi\) | ||||
0.884825 | + | 0.465924i | \(0.154278\pi\) | |||||||
\(648\) | 1.00000 | 0.0392837 | ||||||||
\(649\) | 1.52786 | 0.0599739 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −12.0000 | −0.469956 | ||||||||
\(653\) | −14.9443 | −0.584815 | −0.292407 | − | 0.956294i | \(-0.594456\pi\) | ||||
−0.292407 | + | 0.956294i | \(0.594456\pi\) | |||||||
\(654\) | −6.00000 | −0.234619 | ||||||||
\(655\) | 8.36068 | 0.326679 | ||||||||
\(656\) | −5.23607 | −0.204434 | ||||||||
\(657\) | −15.7082 | −0.612835 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 13.8885 | 0.541021 | 0.270510 | − | 0.962717i | \(-0.412808\pi\) | ||||
0.270510 | + | 0.962717i | \(0.412808\pi\) | |||||||
\(660\) | 1.23607 | 0.0481139 | ||||||||
\(661\) | 5.59675 | 0.217688 | 0.108844 | − | 0.994059i | \(-0.465285\pi\) | ||||
0.108844 | + | 0.994059i | \(0.465285\pi\) | |||||||
\(662\) | −7.41641 | −0.288247 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 1.23607 | 0.0479687 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −10.9443 | −0.424082 | ||||||||
\(667\) | −11.0557 | −0.428080 | ||||||||
\(668\) | 18.4721 | 0.714708 | ||||||||
\(669\) | 15.7082 | 0.607314 | ||||||||
\(670\) | 19.0557 | 0.736187 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 34.9443 | 1.34700 | 0.673501 | − | 0.739186i | \(-0.264790\pi\) | ||||
0.673501 | + | 0.739186i | \(0.264790\pi\) | |||||||
\(674\) | −18.0000 | −0.693334 | ||||||||
\(675\) | 3.47214 | 0.133643 | ||||||||
\(676\) | −13.0000 | −0.500000 | ||||||||
\(677\) | −46.4721 | −1.78607 | −0.893035 | − | 0.449988i | \(-0.851428\pi\) | ||||
−0.893035 | + | 0.449988i | \(0.851428\pi\) | |||||||
\(678\) | −13.4164 | −0.515254 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −6.47214 | −0.248195 | ||||||||
\(681\) | −8.65248 | −0.331564 | ||||||||
\(682\) | 2.76393 | 0.105836 | ||||||||
\(683\) | −4.36068 | −0.166857 | −0.0834284 | − | 0.996514i | \(-0.526587\pi\) | ||||
−0.0834284 | + | 0.996514i | \(0.526587\pi\) | |||||||
\(684\) | −7.70820 | −0.294731 | ||||||||
\(685\) | −20.3607 | −0.777942 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −19.7082 | −0.751915 | ||||||||
\(688\) | 6.47214 | 0.246748 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 3.05573 | 0.116330 | ||||||||
\(691\) | −17.5279 | −0.666791 | −0.333396 | − | 0.942787i | \(-0.608194\pi\) | ||||
−0.333396 | + | 0.942787i | \(0.608194\pi\) | |||||||
\(692\) | 19.4164 | 0.738101 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −26.8328 | −1.01856 | ||||||||
\(695\) | −12.5836 | −0.477323 | ||||||||
\(696\) | −4.47214 | −0.169516 | ||||||||
\(697\) | 27.4164 | 1.03847 | ||||||||
\(698\) | −0.583592 | −0.0220893 | ||||||||
\(699\) | 9.05573 | 0.342519 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −8.11146 | −0.306365 | −0.153183 | − | 0.988198i | \(-0.548952\pi\) | ||||
−0.153183 | + | 0.988198i | \(0.548952\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 84.3607 | 3.18172 | ||||||||
\(704\) | −1.00000 | −0.0376889 | ||||||||
\(705\) | −4.58359 | −0.172628 | ||||||||
\(706\) | 24.3607 | 0.916826 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 1.52786 | 0.0574206 | ||||||||
\(709\) | 5.05573 | 0.189872 | 0.0949359 | − | 0.995483i | \(-0.469735\pi\) | ||||
0.0949359 | + | 0.995483i | \(0.469735\pi\) | |||||||
\(710\) | −3.05573 | −0.114679 | ||||||||
\(711\) | 11.4164 | 0.428149 | ||||||||
\(712\) | −6.47214 | −0.242554 | ||||||||
\(713\) | 6.83282 | 0.255891 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −5.52786 | −0.206586 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 1.52786 | 0.0570194 | ||||||||
\(719\) | 20.2918 | 0.756756 | 0.378378 | − | 0.925651i | \(-0.376482\pi\) | ||||
0.378378 | + | 0.925651i | \(0.376482\pi\) | |||||||
\(720\) | 1.23607 | 0.0460655 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 40.4164 | 1.50414 | ||||||||
\(723\) | −18.1803 | −0.676134 | ||||||||
\(724\) | 11.7082 | 0.435132 | ||||||||
\(725\) | −15.5279 | −0.576690 | ||||||||
\(726\) | −1.00000 | −0.0371135 | ||||||||
\(727\) | 45.2361 | 1.67771 | 0.838856 | − | 0.544353i | \(-0.183225\pi\) | ||||
0.838856 | + | 0.544353i | \(0.183225\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −19.4164 | −0.718633 | ||||||||
\(731\) | −33.8885 | −1.25341 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −22.8328 | −0.843349 | −0.421675 | − | 0.906747i | \(-0.638558\pi\) | ||||
−0.421675 | + | 0.906747i | \(0.638558\pi\) | |||||||
\(734\) | 8.29180 | 0.306056 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −2.47214 | −0.0911241 | ||||||||
\(737\) | −15.4164 | −0.567871 | ||||||||
\(738\) | −5.23607 | −0.192742 | ||||||||
\(739\) | 43.4164 | 1.59710 | 0.798549 | − | 0.601930i | \(-0.205601\pi\) | ||||
0.798549 | + | 0.601930i | \(0.205601\pi\) | |||||||
\(740\) | −13.5279 | −0.497294 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −25.8885 | −0.949759 | −0.474879 | − | 0.880051i | \(-0.657508\pi\) | ||||
−0.474879 | + | 0.880051i | \(0.657508\pi\) | |||||||
\(744\) | 2.76393 | 0.101331 | ||||||||
\(745\) | −7.41641 | −0.271716 | ||||||||
\(746\) | −1.41641 | −0.0518584 | ||||||||
\(747\) | 1.23607 | 0.0452254 | ||||||||
\(748\) | 5.23607 | 0.191450 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 10.4721 | 0.382388 | ||||||||
\(751\) | −14.8328 | −0.541257 | −0.270629 | − | 0.962684i | \(-0.587232\pi\) | ||||
−0.270629 | + | 0.962684i | \(0.587232\pi\) | |||||||
\(752\) | 3.70820 | 0.135224 | ||||||||
\(753\) | 6.47214 | 0.235858 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 22.9443 | 0.833924 | 0.416962 | − | 0.908924i | \(-0.363095\pi\) | ||||
0.416962 | + | 0.908924i | \(0.363095\pi\) | |||||||
\(758\) | −4.00000 | −0.145287 | ||||||||
\(759\) | −2.47214 | −0.0897329 | ||||||||
\(760\) | −9.52786 | −0.345612 | ||||||||
\(761\) | 23.1246 | 0.838267 | 0.419133 | − | 0.907925i | \(-0.362334\pi\) | ||||
0.419133 | + | 0.907925i | \(0.362334\pi\) | |||||||
\(762\) | 6.47214 | 0.234461 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −10.4721 | −0.378869 | ||||||||
\(765\) | −6.47214 | −0.234001 | ||||||||
\(766\) | −0.652476 | −0.0235749 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | −1.00000 | −0.0360844 | ||||||||
\(769\) | −12.0689 | −0.435215 | −0.217608 | − | 0.976036i | \(-0.569825\pi\) | ||||
−0.217608 | + | 0.976036i | \(0.569825\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −22.4721 | −0.809314 | ||||||||
\(772\) | 5.05573 | 0.181960 | ||||||||
\(773\) | −49.9574 | −1.79684 | −0.898422 | − | 0.439133i | \(-0.855286\pi\) | ||||
−0.898422 | + | 0.439133i | \(0.855286\pi\) | |||||||
\(774\) | 6.47214 | 0.232636 | ||||||||
\(775\) | 9.59675 | 0.344725 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −6.94427 | −0.248964 | ||||||||
\(779\) | 40.3607 | 1.44607 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 2.47214 | 0.0884600 | ||||||||
\(782\) | 12.9443 | 0.462886 | ||||||||
\(783\) | −4.47214 | −0.159821 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −18.2492 | −0.651343 | ||||||||
\(786\) | −6.76393 | −0.241261 | ||||||||
\(787\) | −22.5410 | −0.803501 | −0.401750 | − | 0.915749i | \(-0.631598\pi\) | ||||
−0.401750 | + | 0.915749i | \(0.631598\pi\) | |||||||
\(788\) | −22.3607 | −0.796566 | ||||||||
\(789\) | 9.52786 | 0.339201 | ||||||||
\(790\) | 14.1115 | 0.502063 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | −1.00000 | −0.0355335 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | −1.81966 | −0.0645773 | ||||||||
\(795\) | 7.41641 | 0.263033 | ||||||||
\(796\) | −23.1246 | −0.819630 | ||||||||
\(797\) | 12.8754 | 0.456070 | 0.228035 | − | 0.973653i | \(-0.426770\pi\) | ||||
0.228035 | + | 0.973653i | \(0.426770\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −19.4164 | −0.686903 | ||||||||
\(800\) | −3.47214 | −0.122759 | ||||||||
\(801\) | −6.47214 | −0.228682 | ||||||||
\(802\) | −8.47214 | −0.299162 | ||||||||
\(803\) | 15.7082 | 0.554330 | ||||||||
\(804\) | −15.4164 | −0.543695 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 27.7082 | 0.975375 | ||||||||
\(808\) | −12.0000 | −0.422159 | ||||||||
\(809\) | 44.8328 | 1.57624 | 0.788119 | − | 0.615523i | \(-0.211055\pi\) | ||||
0.788119 | + | 0.615523i | \(0.211055\pi\) | |||||||
\(810\) | 1.23607 | 0.0434310 | ||||||||
\(811\) | 17.5967 | 0.617905 | 0.308953 | − | 0.951077i | \(-0.400022\pi\) | ||||
0.308953 | + | 0.951077i | \(0.400022\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 2.47214 | 0.0867016 | ||||||||
\(814\) | 10.9443 | 0.383597 | ||||||||
\(815\) | −14.8328 | −0.519571 | ||||||||
\(816\) | 5.23607 | 0.183299 | ||||||||
\(817\) | −49.8885 | −1.74538 | ||||||||
\(818\) | 2.76393 | 0.0966386 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −6.47214 | −0.226017 | ||||||||
\(821\) | 29.7771 | 1.03923 | 0.519614 | − | 0.854401i | \(-0.326076\pi\) | ||||
0.519614 | + | 0.854401i | \(0.326076\pi\) | |||||||
\(822\) | 16.4721 | 0.574532 | ||||||||
\(823\) | −30.8328 | −1.07476 | −0.537382 | − | 0.843339i | \(-0.680587\pi\) | ||||
−0.537382 | + | 0.843339i | \(0.680587\pi\) | |||||||
\(824\) | 10.7639 | 0.374979 | ||||||||
\(825\) | −3.47214 | −0.120884 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 36.7214 | 1.27693 | 0.638463 | − | 0.769652i | \(-0.279570\pi\) | ||||
0.638463 | + | 0.769652i | \(0.279570\pi\) | |||||||
\(828\) | −2.47214 | −0.0859127 | ||||||||
\(829\) | 47.4853 | 1.64923 | 0.824616 | − | 0.565693i | \(-0.191391\pi\) | ||||
0.824616 | + | 0.565693i | \(0.191391\pi\) | |||||||
\(830\) | 1.52786 | 0.0530329 | ||||||||
\(831\) | −26.0000 | −0.901930 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 10.1803 | 0.352516 | ||||||||
\(835\) | 22.8328 | 0.790162 | ||||||||
\(836\) | 7.70820 | 0.266594 | ||||||||
\(837\) | 2.76393 | 0.0955355 | ||||||||
\(838\) | 15.0557 | 0.520091 | ||||||||
\(839\) | 25.2361 | 0.871246 | 0.435623 | − | 0.900129i | \(-0.356528\pi\) | ||||
0.435623 | + | 0.900129i | \(0.356528\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −9.00000 | −0.310345 | ||||||||
\(842\) | −5.05573 | −0.174232 | ||||||||
\(843\) | −19.8885 | −0.684998 | ||||||||
\(844\) | 3.41641 | 0.117598 | ||||||||
\(845\) | −16.0689 | −0.552786 | ||||||||
\(846\) | 3.70820 | 0.127491 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −6.00000 | −0.206041 | ||||||||
\(849\) | −23.7082 | −0.813663 | ||||||||
\(850\) | 18.1803 | 0.623581 | ||||||||
\(851\) | 27.0557 | 0.927458 | ||||||||
\(852\) | 2.47214 | 0.0846940 | ||||||||
\(853\) | −33.8885 | −1.16032 | −0.580161 | − | 0.814502i | \(-0.697010\pi\) | ||||
−0.580161 | + | 0.814502i | \(0.697010\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −9.52786 | −0.325846 | ||||||||
\(856\) | 0.944272 | 0.0322745 | ||||||||
\(857\) | 47.1246 | 1.60975 | 0.804873 | − | 0.593447i | \(-0.202233\pi\) | ||||
0.804873 | + | 0.593447i | \(0.202233\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −43.4164 | −1.48135 | −0.740674 | − | 0.671864i | \(-0.765494\pi\) | ||||
−0.740674 | + | 0.671864i | \(0.765494\pi\) | |||||||
\(860\) | 8.00000 | 0.272798 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −22.4721 | −0.765404 | ||||||||
\(863\) | −44.3607 | −1.51006 | −0.755028 | − | 0.655693i | \(-0.772377\pi\) | ||||
−0.755028 | + | 0.655693i | \(0.772377\pi\) | |||||||
\(864\) | −1.00000 | −0.0340207 | ||||||||
\(865\) | 24.0000 | 0.816024 | ||||||||
\(866\) | 9.88854 | 0.336026 | ||||||||
\(867\) | −10.4164 | −0.353760 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −11.4164 | −0.387275 | ||||||||
\(870\) | −5.52786 | −0.187412 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 6.00000 | 0.203186 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 19.0557 | 0.644570 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 15.7082 | 0.530731 | ||||||||
\(877\) | 30.0000 | 1.01303 | 0.506514 | − | 0.862232i | \(-0.330934\pi\) | ||||
0.506514 | + | 0.862232i | \(0.330934\pi\) | |||||||
\(878\) | 31.4164 | 1.06025 | ||||||||
\(879\) | 4.58359 | 0.154601 | ||||||||
\(880\) | −1.23607 | −0.0416678 | ||||||||
\(881\) | 26.8328 | 0.904021 | 0.452010 | − | 0.892013i | \(-0.350707\pi\) | ||||
0.452010 | + | 0.892013i | \(0.350707\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 12.0000 | 0.403832 | 0.201916 | − | 0.979403i | \(-0.435283\pi\) | ||||
0.201916 | + | 0.979403i | \(0.435283\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 1.88854 | 0.0634827 | ||||||||
\(886\) | 7.41641 | 0.249159 | ||||||||
\(887\) | −36.9443 | −1.24047 | −0.620234 | − | 0.784417i | \(-0.712962\pi\) | ||||
−0.620234 | + | 0.784417i | \(0.712962\pi\) | |||||||
\(888\) | 10.9443 | 0.367266 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −8.00000 | −0.268161 | ||||||||
\(891\) | −1.00000 | −0.0335013 | ||||||||
\(892\) | −15.7082 | −0.525950 | ||||||||
\(893\) | −28.5836 | −0.956513 | ||||||||
\(894\) | 6.00000 | 0.200670 | ||||||||
\(895\) | −6.83282 | −0.228396 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 19.5279 | 0.651653 | ||||||||
\(899\) | −12.3607 | −0.412252 | ||||||||
\(900\) | −3.47214 | −0.115738 | ||||||||
\(901\) | 31.4164 | 1.04663 | ||||||||
\(902\) | 5.23607 | 0.174342 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 13.4164 | 0.446223 | ||||||||
\(905\) | 14.4721 | 0.481070 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −33.3050 | −1.10587 | −0.552936 | − | 0.833223i | \(-0.686493\pi\) | ||||
−0.552936 | + | 0.833223i | \(0.686493\pi\) | |||||||
\(908\) | 8.65248 | 0.287142 | ||||||||
\(909\) | −12.0000 | −0.398015 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −31.4164 | −1.04087 | −0.520436 | − | 0.853901i | \(-0.674231\pi\) | ||||
−0.520436 | + | 0.853901i | \(0.674231\pi\) | |||||||
\(912\) | 7.70820 | 0.255244 | ||||||||
\(913\) | −1.23607 | −0.0409079 | ||||||||
\(914\) | 18.0000 | 0.595387 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 19.7082 | 0.651177 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 5.23607 | 0.172816 | ||||||||
\(919\) | −53.6656 | −1.77027 | −0.885133 | − | 0.465338i | \(-0.845933\pi\) | ||||
−0.885133 | + | 0.465338i | \(0.845933\pi\) | |||||||
\(920\) | −3.05573 | −0.100744 | ||||||||
\(921\) | −25.5967 | −0.843442 | ||||||||
\(922\) | −26.8328 | −0.883692 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 38.0000 | 1.24943 | ||||||||
\(926\) | −1.88854 | −0.0620614 | ||||||||
\(927\) | 10.7639 | 0.353534 | ||||||||
\(928\) | 4.47214 | 0.146805 | ||||||||
\(929\) | 8.36068 | 0.274305 | 0.137153 | − | 0.990550i | \(-0.456205\pi\) | ||||
0.137153 | + | 0.990550i | \(0.456205\pi\) | |||||||
\(930\) | 3.41641 | 0.112028 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −9.05573 | −0.296630 | ||||||||
\(933\) | 8.65248 | 0.283269 | ||||||||
\(934\) | −29.8885 | −0.977983 | ||||||||
\(935\) | 6.47214 | 0.211661 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −1.59675 | −0.0521635 | −0.0260817 | − | 0.999660i | \(-0.508303\pi\) | ||||
−0.0260817 | + | 0.999660i | \(0.508303\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −5.52786 | −0.180395 | ||||||||
\(940\) | 4.58359 | 0.149500 | ||||||||
\(941\) | −7.63932 | −0.249035 | −0.124517 | − | 0.992217i | \(-0.539738\pi\) | ||||
−0.124517 | + | 0.992217i | \(0.539738\pi\) | |||||||
\(942\) | 14.7639 | 0.481035 | ||||||||
\(943\) | 12.9443 | 0.421523 | ||||||||
\(944\) | −1.52786 | −0.0497277 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −6.47214 | −0.210427 | ||||||||
\(947\) | −37.8885 | −1.23121 | −0.615606 | − | 0.788054i | \(-0.711089\pi\) | ||||
−0.615606 | + | 0.788054i | \(0.711089\pi\) | |||||||
\(948\) | −11.4164 | −0.370788 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 26.7639 | 0.868337 | ||||||||
\(951\) | 31.8885 | 1.03406 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −30.9443 | −1.00238 | −0.501192 | − | 0.865336i | \(-0.667105\pi\) | ||||
−0.501192 | + | 0.865336i | \(0.667105\pi\) | |||||||
\(954\) | −6.00000 | −0.194257 | ||||||||
\(955\) | −12.9443 | −0.418867 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 4.47214 | 0.144564 | ||||||||
\(958\) | 35.7771 | 1.15591 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | −1.23607 | −0.0398939 | ||||||||
\(961\) | −23.3607 | −0.753570 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0.944272 | 0.0304287 | ||||||||
\(964\) | 18.1803 | 0.585549 | ||||||||
\(965\) | 6.24922 | 0.201170 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 54.8328 | 1.76330 | 0.881652 | − | 0.471900i | \(-0.156432\pi\) | ||||
0.881652 | + | 0.471900i | \(0.156432\pi\) | |||||||
\(968\) | 1.00000 | 0.0321412 | ||||||||
\(969\) | −40.3607 | −1.29657 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −39.0557 | −1.25336 | −0.626679 | − | 0.779278i | \(-0.715586\pi\) | ||||
−0.626679 | + | 0.779278i | \(0.715586\pi\) | |||||||
\(972\) | −1.00000 | −0.0320750 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 36.9443 | 1.18377 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −11.8885 | −0.380348 | −0.190174 | − | 0.981750i | \(-0.560905\pi\) | ||||
−0.190174 | + | 0.981750i | \(0.560905\pi\) | |||||||
\(978\) | 12.0000 | 0.383718 | ||||||||
\(979\) | 6.47214 | 0.206850 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 6.00000 | 0.191565 | ||||||||
\(982\) | −29.8885 | −0.953782 | ||||||||
\(983\) | 51.7082 | 1.64924 | 0.824618 | − | 0.565690i | \(-0.191390\pi\) | ||||
0.824618 | + | 0.565690i | \(0.191390\pi\) | |||||||
\(984\) | 5.23607 | 0.166920 | ||||||||
\(985\) | −27.6393 | −0.880662 | ||||||||
\(986\) | −23.4164 | −0.745730 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −16.0000 | −0.508770 | ||||||||
\(990\) | −1.23607 | −0.0392848 | ||||||||
\(991\) | −30.8328 | −0.979437 | −0.489718 | − | 0.871881i | \(-0.662900\pi\) | ||||
−0.489718 | + | 0.871881i | \(0.662900\pi\) | |||||||
\(992\) | −2.76393 | −0.0877549 | ||||||||
\(993\) | 7.41641 | 0.235353 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −28.5836 | −0.906161 | ||||||||
\(996\) | −1.23607 | −0.0391663 | ||||||||
\(997\) | 54.2492 | 1.71809 | 0.859045 | − | 0.511900i | \(-0.171058\pi\) | ||||
0.859045 | + | 0.511900i | \(0.171058\pi\) | |||||||
\(998\) | 7.41641 | 0.234762 | ||||||||
\(999\) | 10.9443 | 0.346261 |
(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 | 3234.2.a.bb.1.2 | ✓ | 2 | |
3.2 | odd | 2 | 9702.2.a.cw.1.1 | 2 | |||
7.6 | odd | 2 | 3234.2.a.be.1.1 | yes | 2 | ||
21.20 | even | 2 | 9702.2.a.ck.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
3234.2.a.bb.1.2 | ✓ | 2 | 1.1 | even | 1 | trivial | |
3234.2.a.be.1.1 | yes | 2 | 7.6 | odd | 2 | ||
9702.2.a.ck.1.2 | 2 | 21.20 | even | 2 | |||
9702.2.a.cw.1.1 | 2 | 3.2 | odd | 2 |