Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [605,2,Mod(364,605)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(605, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("605.364");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 605 = 5 \cdot 11^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 605.b (of order \(2\), degree \(1\), minimal) |
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: | no |
Analytic conductor: | \(4.83094932229\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 4 x^{11} + x^{10} + 34 x^{9} - 123 x^{8} - 20 x^{7} + 516 x^{6} - 668 x^{5} - 67 x^{4} + \cdots + 1089 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{3} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 364.5 | ||
Root | \(-2.40330 - 0.316825i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 605.364 |
Dual form | 605.2.b.h.364.8 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/605\mathbb{Z}\right)^\times\).
\(n\) | \(122\) | \(486\) |
\(\chi(n)\) | \(-1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − | 0.328351i | − | 0.232179i | −0.993239 | − | 0.116089i | \(-0.962964\pi\) | ||
0.993239 | − | 0.116089i | \(-0.0370359\pi\) | |||||||
\(3\) | − | 0.962000i | − | 0.555411i | −0.960666 | − | 0.277706i | \(-0.910426\pi\) | ||
0.960666 | − | 0.277706i | \(-0.0895740\pi\) | |||||||
\(4\) | 1.89219 | 0.946093 | ||||||||
\(5\) | −0.591185 | − | 2.15650i | −0.264386 | − | 0.964417i | ||||
\(6\) | −0.315873 | −0.128955 | ||||||||
\(7\) | 3.27259i | 1.23692i | 0.785816 | + | 0.618461i | \(0.212243\pi\) | ||||
−0.785816 | + | 0.618461i | \(0.787757\pi\) | |||||||
\(8\) | − | 1.27800i | − | 0.451842i | ||||||
\(9\) | 2.07456 | 0.691518 | ||||||||
\(10\) | −0.708089 | + | 0.194116i | −0.223917 | + | 0.0613848i | ||||
\(11\) | 0 | 0 | ||||||||
\(12\) | − | 1.82028i | − | 0.525471i | ||||||
\(13\) | − | 5.20729i | − | 1.44424i | −0.691767 | − | 0.722121i | \(-0.743167\pi\) | ||
0.691767 | − | 0.722121i | \(-0.256833\pi\) | |||||||
\(14\) | 1.07456 | 0.287187 | ||||||||
\(15\) | −2.07456 | + | 0.568720i | −0.535648 | + | 0.146843i | ||||
\(16\) | 3.36474 | 0.841185 | ||||||||
\(17\) | 3.60094i | 0.873355i | 0.899618 | + | 0.436678i | \(0.143845\pi\) | ||||
−0.899618 | + | 0.436678i | \(0.856155\pi\) | |||||||
\(18\) | − | 0.681182i | − | 0.160556i | ||||||
\(19\) | 5.00941 | 1.14924 | 0.574619 | − | 0.818421i | \(-0.305150\pi\) | ||||
0.574619 | + | 0.818421i | \(0.305150\pi\) | |||||||
\(20\) | −1.11863 | − | 4.08050i | −0.250134 | − | 0.912428i | ||||
\(21\) | 3.14823 | 0.687000 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − | 5.84372i | − | 1.21850i | −0.792978 | − | 0.609250i | \(-0.791470\pi\) | ||
0.792978 | − | 0.609250i | \(-0.208530\pi\) | |||||||
\(24\) | −1.22944 | −0.250958 | ||||||||
\(25\) | −4.30100 | + | 2.54978i | −0.860200 | + | 0.509956i | ||||
\(26\) | −1.70982 | −0.335323 | ||||||||
\(27\) | − | 4.88172i | − | 0.939488i | ||||||
\(28\) | 6.19234i | 1.17024i | ||||||||
\(29\) | −2.04792 | −0.380290 | −0.190145 | − | 0.981756i | \(-0.560896\pi\) | ||||
−0.190145 | + | 0.981756i | \(0.560896\pi\) | |||||||
\(30\) | 0.186740 | + | 0.681182i | 0.0340938 | + | 0.124366i | ||||
\(31\) | −3.25693 | −0.584961 | −0.292481 | − | 0.956271i | \(-0.594481\pi\) | ||||
−0.292481 | + | 0.956271i | \(0.594481\pi\) | |||||||
\(32\) | − | 3.66082i | − | 0.647147i | ||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 1.18237 | 0.202775 | ||||||||
\(35\) | 7.05734 | − | 1.93470i | 1.19291 | − | 0.327024i | ||||
\(36\) | 3.92544 | 0.654241 | ||||||||
\(37\) | 6.23700i | 1.02536i | 0.858581 | + | 0.512679i | \(0.171347\pi\) | ||||
−0.858581 | + | 0.512679i | \(0.828653\pi\) | |||||||
\(38\) | − | 1.64484i | − | 0.266829i | ||||||
\(39\) | −5.00941 | −0.802148 | ||||||||
\(40\) | −2.75601 | + | 0.755535i | −0.435764 | + | 0.119461i | ||||
\(41\) | −10.2056 | −1.59384 | −0.796921 | − | 0.604084i | \(-0.793539\pi\) | ||||
−0.796921 | + | 0.604084i | \(0.793539\pi\) | |||||||
\(42\) | − | 1.03372i | − | 0.159507i | ||||||
\(43\) | − | 0.596820i | − | 0.0910142i | −0.998964 | − | 0.0455071i | \(-0.985510\pi\) | ||
0.998964 | − | 0.0455071i | \(-0.0144904\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −1.22645 | − | 4.47378i | −0.182828 | − | 0.666912i | ||||
\(46\) | −1.91879 | −0.282910 | ||||||||
\(47\) | − | 0.962000i | − | 0.140322i | −0.997536 | − | 0.0701611i | \(-0.977649\pi\) | ||
0.997536 | − | 0.0701611i | \(-0.0223513\pi\) | |||||||
\(48\) | − | 3.23688i | − | 0.467203i | ||||||
\(49\) | −3.70982 | −0.529974 | ||||||||
\(50\) | 0.837223 | + | 1.41224i | 0.118401 | + | 0.199720i | ||||
\(51\) | 3.46410 | 0.485071 | ||||||||
\(52\) | − | 9.85316i | − | 1.36639i | ||||||
\(53\) | − | 0.393280i | − | 0.0540212i | −0.999635 | − | 0.0270106i | \(-0.991401\pi\) | ||
0.999635 | − | 0.0270106i | \(-0.00859879\pi\) | |||||||
\(54\) | −1.60292 | −0.218129 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 4.18237 | 0.558893 | ||||||||
\(57\) | − | 4.81906i | − | 0.638300i | ||||||
\(58\) | 0.672437i | 0.0882953i | ||||||||
\(59\) | 0.527447 | 0.0686677 | 0.0343339 | − | 0.999410i | \(-0.489069\pi\) | ||||
0.0343339 | + | 0.999410i | \(0.489069\pi\) | |||||||
\(60\) | −3.92544 | + | 1.07612i | −0.506773 | + | 0.138927i | ||||
\(61\) | 5.32529 | 0.681833 | 0.340917 | − | 0.940094i | \(-0.389263\pi\) | ||||
0.340917 | + | 0.940094i | \(0.389263\pi\) | |||||||
\(62\) | 1.06941i | 0.135816i | ||||||||
\(63\) | 6.78916i | 0.855354i | ||||||||
\(64\) | 5.52745 | 0.690931 | ||||||||
\(65\) | −11.2295 | + | 3.07847i | −1.39285 | + | 0.381837i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 8.45057i | 1.03240i | 0.856468 | + | 0.516201i | \(0.172654\pi\) | ||||
−0.856468 | + | 0.516201i | \(0.827346\pi\) | |||||||
\(68\) | 6.81364i | 0.826275i | ||||||||
\(69\) | −5.62166 | −0.676769 | ||||||||
\(70\) | −0.635261 | − | 2.31728i | −0.0759282 | − | 0.276968i | ||||
\(71\) | 12.5274 | 1.48673 | 0.743367 | − | 0.668884i | \(-0.233228\pi\) | ||||
0.743367 | + | 0.668884i | \(0.233228\pi\) | |||||||
\(72\) | − | 2.65129i | − | 0.312457i | ||||||
\(73\) | 8.51527i | 0.996638i | 0.866994 | + | 0.498319i | \(0.166049\pi\) | ||||
−0.866994 | + | 0.498319i | \(0.833951\pi\) | |||||||
\(74\) | 2.04792 | 0.238066 | ||||||||
\(75\) | 2.45289 | + | 4.13756i | 0.283235 | + | 0.477765i | ||||
\(76\) | 9.47874 | 1.08729 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 1.64484i | 0.186242i | ||||||||
\(79\) | 2.83235 | 0.318665 | 0.159332 | − | 0.987225i | \(-0.449066\pi\) | ||||
0.159332 | + | 0.987225i | \(0.449066\pi\) | |||||||
\(80\) | −1.98918 | − | 7.25607i | −0.222397 | − | 0.811253i | ||||
\(81\) | 1.52745 | 0.169716 | ||||||||
\(82\) | 3.35100i | 0.370056i | ||||||||
\(83\) | − | 12.1407i | − | 1.33261i | −0.745678 | − | 0.666307i | \(-0.767874\pi\) | ||
0.745678 | − | 0.666307i | \(-0.232126\pi\) | |||||||
\(84\) | 5.95703 | 0.649966 | ||||||||
\(85\) | 7.76543 | − | 2.12882i | 0.842279 | − | 0.230903i | ||||
\(86\) | −0.195966 | −0.0211316 | ||||||||
\(87\) | 1.97010i | 0.211217i | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −9.00000 | −0.953998 | −0.476999 | − | 0.878904i | \(-0.658275\pi\) | ||||
−0.476999 | + | 0.878904i | \(0.658275\pi\) | |||||||
\(90\) | −1.46897 | + | 0.402704i | −0.154843 | + | 0.0424487i | ||||
\(91\) | 17.0413 | 1.78641 | ||||||||
\(92\) | − | 11.0574i | − | 1.15281i | ||||||
\(93\) | 3.13316i | 0.324894i | ||||||||
\(94\) | −0.315873 | −0.0325799 | ||||||||
\(95\) | −2.96149 | − | 10.8028i | −0.303842 | − | 1.10834i | ||||
\(96\) | −3.52171 | −0.359433 | ||||||||
\(97\) | 11.2942i | 1.14675i | 0.819293 | + | 0.573374i | \(0.194366\pi\) | ||||
−0.819293 | + | 0.573374i | \(0.805634\pi\) | |||||||
\(98\) | 1.21812i | 0.123049i | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −8.13829 | + | 4.82466i | −0.813829 | + | 0.482466i | ||||
\(101\) | −13.1671 | −1.31017 | −0.655085 | − | 0.755555i | \(-0.727367\pi\) | ||||
−0.655085 | + | 0.755555i | \(0.727367\pi\) | |||||||
\(102\) | − | 1.13744i | − | 0.112623i | ||||||
\(103\) | 2.78228i | 0.274147i | 0.990561 | + | 0.137073i | \(0.0437696\pi\) | ||||
−0.990561 | + | 0.137073i | \(0.956230\pi\) | |||||||
\(104\) | −6.65492 | −0.652569 | ||||||||
\(105\) | −1.86118 | − | 6.78916i | −0.181633 | − | 0.662554i | ||||
\(106\) | −0.129134 | −0.0125426 | ||||||||
\(107\) | 15.9502i | 1.54197i | 0.636856 | + | 0.770983i | \(0.280235\pi\) | ||||
−0.636856 | + | 0.770983i | \(0.719765\pi\) | |||||||
\(108\) | − | 9.23713i | − | 0.888843i | ||||||
\(109\) | −3.90911 | −0.374425 | −0.187212 | − | 0.982319i | \(-0.559945\pi\) | ||||
−0.187212 | + | 0.982319i | \(0.559945\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 6.00000 | 0.569495 | ||||||||
\(112\) | 11.0114i | 1.04048i | ||||||||
\(113\) | 9.87757i | 0.929204i | 0.885520 | + | 0.464602i | \(0.153803\pi\) | ||||
−0.885520 | + | 0.464602i | \(0.846197\pi\) | |||||||
\(114\) | −1.58234 | −0.148200 | ||||||||
\(115\) | −12.6020 | + | 3.45472i | −1.17514 | + | 0.322154i | ||||
\(116\) | −3.87505 | −0.359790 | ||||||||
\(117\) | − | 10.8028i | − | 0.998720i | ||||||
\(118\) | − | 0.173187i | − | 0.0159432i | ||||||
\(119\) | −11.7844 | −1.08027 | ||||||||
\(120\) | 0.726825 | + | 2.65129i | 0.0663497 | + | 0.242028i | ||||
\(121\) | 0 | 0 | ||||||||
\(122\) | − | 1.74856i | − | 0.158307i | ||||||
\(123\) | 9.81776i | 0.885237i | ||||||||
\(124\) | −6.16271 | −0.553427 | ||||||||
\(125\) | 8.04130 | + | 7.76772i | 0.719235 | + | 0.694766i | ||||
\(126\) | 2.22922 | 0.198595 | ||||||||
\(127\) | − | 5.41588i | − | 0.480581i | −0.970701 | − | 0.240291i | \(-0.922757\pi\) | ||
0.970701 | − | 0.240291i | \(-0.0772428\pi\) | |||||||
\(128\) | − | 9.13658i | − | 0.807567i | ||||||
\(129\) | −0.574141 | −0.0505503 | ||||||||
\(130\) | 1.01082 | + | 3.68722i | 0.0886545 | + | 0.323391i | ||||
\(131\) | 19.1241 | 1.67088 | 0.835440 | − | 0.549582i | \(-0.185213\pi\) | ||||
0.835440 | + | 0.549582i | \(0.185213\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 16.3937i | 1.42152i | ||||||||
\(134\) | 2.77475 | 0.239702 | ||||||||
\(135\) | −10.5274 | + | 2.88600i | −0.906058 | + | 0.248387i | ||||
\(136\) | 4.60200 | 0.394618 | ||||||||
\(137\) | 16.0429i | 1.37063i | 0.728245 | + | 0.685317i | \(0.240336\pi\) | ||||
−0.728245 | + | 0.685317i | \(0.759664\pi\) | |||||||
\(138\) | 1.84588i | 0.157131i | ||||||||
\(139\) | −12.5694 | −1.06612 | −0.533060 | − | 0.846078i | \(-0.678958\pi\) | ||||
−0.533060 | + | 0.846078i | \(0.678958\pi\) | |||||||
\(140\) | 13.3538 | − | 3.66082i | 1.12860 | − | 0.309396i | ||||
\(141\) | −0.925445 | −0.0779365 | ||||||||
\(142\) | − | 4.11339i | − | 0.345188i | ||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 6.98034 | 0.581695 | ||||||||
\(145\) | 1.21070 | + | 4.41635i | 0.100543 | + | 0.366758i | ||||
\(146\) | 2.79600 | 0.231398 | ||||||||
\(147\) | 3.56884i | 0.294353i | ||||||||
\(148\) | 11.8016i | 0.970083i | ||||||||
\(149\) | 13.9279 | 1.14102 | 0.570510 | − | 0.821290i | \(-0.306745\pi\) | ||||
0.570510 | + | 0.821290i | \(0.306745\pi\) | |||||||
\(150\) | 1.35857 | − | 0.805408i | 0.110927 | − | 0.0657613i | ||||
\(151\) | −16.0335 | −1.30478 | −0.652392 | − | 0.757881i | \(-0.726235\pi\) | ||||
−0.652392 | + | 0.757881i | \(0.726235\pi\) | |||||||
\(152\) | − | 6.40204i | − | 0.519274i | ||||||
\(153\) | 7.47034i | 0.603941i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 1.92544 | + | 7.02357i | 0.154655 | + | 0.564146i | ||||
\(156\) | −9.47874 | −0.758907 | ||||||||
\(157\) | 2.27488i | 0.181555i | 0.995871 | + | 0.0907776i | \(0.0289352\pi\) | ||||
−0.995871 | + | 0.0907776i | \(0.971065\pi\) | |||||||
\(158\) | − | 0.930005i | − | 0.0739873i | ||||||
\(159\) | −0.378336 | −0.0300040 | ||||||||
\(160\) | −7.89456 | + | 2.16422i | −0.624120 | + | 0.171097i | ||||
\(161\) | 19.1241 | 1.50719 | ||||||||
\(162\) | − | 0.501538i | − | 0.0394046i | ||||||
\(163\) | 22.5694i | 1.76777i | 0.467701 | + | 0.883887i | \(0.345082\pi\) | ||||
−0.467701 | + | 0.883887i | \(0.654918\pi\) | |||||||
\(164\) | −19.3108 | −1.50792 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −3.98640 | −0.309405 | ||||||||
\(167\) | 3.80952i | 0.294790i | 0.989078 | + | 0.147395i | \(0.0470888\pi\) | ||||
−0.989078 | + | 0.147395i | \(0.952911\pi\) | |||||||
\(168\) | − | 4.02344i | − | 0.310415i | ||||||
\(169\) | −14.1159 | −1.08583 | ||||||||
\(170\) | −0.698999 | − | 2.54978i | −0.0536108 | − | 0.195559i | ||||
\(171\) | 10.3923 | 0.794719 | ||||||||
\(172\) | − | 1.12929i | − | 0.0861079i | ||||||
\(173\) | 0.949651i | 0.0722006i | 0.999348 | + | 0.0361003i | \(0.0114936\pi\) | ||||
−0.999348 | + | 0.0361003i | \(0.988506\pi\) | |||||||
\(174\) | 0.646885 | 0.0490402 | ||||||||
\(175\) | −8.34438 | − | 14.0754i | −0.630776 | − | 1.06400i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | − | 0.507404i | − | 0.0381388i | ||||||
\(178\) | 2.95516i | 0.221498i | ||||||||
\(179\) | −3.63526 | −0.271712 | −0.135856 | − | 0.990729i | \(-0.543378\pi\) | ||||
−0.135856 | + | 0.990729i | \(0.543378\pi\) | |||||||
\(180\) | −2.32066 | − | 8.46523i | −0.172972 | − | 0.630961i | ||||
\(181\) | 12.5687 | 0.934227 | 0.467114 | − | 0.884197i | \(-0.345294\pi\) | ||||
0.467114 | + | 0.884197i | \(0.345294\pi\) | |||||||
\(182\) | − | 5.59552i | − | 0.414768i | ||||||
\(183\) | − | 5.12293i | − | 0.378698i | ||||||
\(184\) | −7.46829 | −0.550570 | ||||||||
\(185\) | 13.4501 | − | 3.68722i | 0.988872 | − | 0.271090i | ||||
\(186\) | 1.02878 | 0.0754335 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | − | 1.82028i | − | 0.132758i | ||||||
\(189\) | 15.9759 | 1.16207 | ||||||||
\(190\) | −3.54711 | + | 0.972407i | −0.257334 | + | 0.0705458i | ||||
\(191\) | −2.67656 | −0.193669 | −0.0968345 | − | 0.995301i | \(-0.530872\pi\) | ||||
−0.0968345 | + | 0.995301i | \(0.530872\pi\) | |||||||
\(192\) | − | 5.31741i | − | 0.383751i | ||||||
\(193\) | − | 0.388232i | − | 0.0279455i | −0.999902 | − | 0.0139728i | \(-0.995552\pi\) | ||
0.999902 | − | 0.0139728i | \(-0.00444781\pi\) | |||||||
\(194\) | 3.70845 | 0.266251 | ||||||||
\(195\) | 2.96149 | + | 10.8028i | 0.212077 | + | 0.773605i | ||||
\(196\) | −7.01966 | −0.501404 | ||||||||
\(197\) | 18.5416i | 1.32104i | 0.750810 | + | 0.660518i | \(0.229663\pi\) | ||||
−0.750810 | + | 0.660518i | \(0.770337\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −10.1491 | −0.719451 | −0.359726 | − | 0.933058i | \(-0.617130\pi\) | ||||
−0.359726 | + | 0.933058i | \(0.617130\pi\) | |||||||
\(200\) | 3.25863 | + | 5.49669i | 0.230420 | + | 0.388674i | ||||
\(201\) | 8.12945 | 0.573407 | ||||||||
\(202\) | 4.32341i | 0.304194i | ||||||||
\(203\) | − | 6.70201i | − | 0.470389i | ||||||
\(204\) | 6.55472 | 0.458922 | ||||||||
\(205\) | 6.03337 | + | 22.0083i | 0.421389 | + | 1.53713i | ||||
\(206\) | 0.913565 | 0.0636511 | ||||||||
\(207\) | − | 12.1231i | − | 0.842616i | ||||||
\(208\) | − | 17.5212i | − | 1.21487i | ||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | −2.22922 | + | 0.611121i | −0.153831 | + | 0.0421714i | ||||
\(211\) | −8.47351 | −0.583341 | −0.291670 | − | 0.956519i | \(-0.594211\pi\) | ||||
−0.291670 | + | 0.956519i | \(0.594211\pi\) | |||||||
\(212\) | − | 0.744160i | − | 0.0511091i | ||||||
\(213\) | − | 12.0514i | − | 0.825749i | ||||||
\(214\) | 5.23726 | 0.358012 | ||||||||
\(215\) | −1.28704 | + | 0.352831i | −0.0877756 | + | 0.0240629i | ||||
\(216\) | −6.23885 | −0.424500 | ||||||||
\(217\) | − | 10.6586i | − | 0.723551i | ||||||
\(218\) | 1.28356i | 0.0869335i | ||||||||
\(219\) | 8.19170 | 0.553544 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 18.7511 | 1.26134 | ||||||||
\(222\) | − | 1.97010i | − | 0.132225i | ||||||
\(223\) | − | 23.7069i | − | 1.58753i | −0.608225 | − | 0.793764i | \(-0.708118\pi\) | ||
0.608225 | − | 0.793764i | \(-0.291882\pi\) | |||||||
\(224\) | 11.9803 | 0.800470 | ||||||||
\(225\) | −8.92267 | + | 5.28966i | −0.594844 | + | 0.352644i | ||||
\(226\) | 3.24331 | 0.215742 | ||||||||
\(227\) | − | 0.716582i | − | 0.0475612i | −0.999717 | − | 0.0237806i | \(-0.992430\pi\) | ||
0.999717 | − | 0.0237806i | \(-0.00757032\pi\) | |||||||
\(228\) | − | 9.11855i | − | 0.603891i | ||||||
\(229\) | −13.1491 | −0.868918 | −0.434459 | − | 0.900692i | \(-0.643060\pi\) | ||||
−0.434459 | + | 0.900692i | \(0.643060\pi\) | |||||||
\(230\) | 1.13436 | + | 4.13788i | 0.0747975 | + | 0.272843i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 2.61725i | 0.171831i | ||||||||
\(233\) | − | 26.9327i | − | 1.76442i | −0.470858 | − | 0.882209i | \(-0.656056\pi\) | ||
0.470858 | − | 0.882209i | \(-0.343944\pi\) | |||||||
\(234\) | −3.54711 | −0.231882 | ||||||||
\(235\) | −2.07456 | + | 0.568720i | −0.135329 | + | 0.0370992i | ||||
\(236\) | 0.998027 | 0.0649660 | ||||||||
\(237\) | − | 2.72473i | − | 0.176990i | ||||||
\(238\) | 3.86941i | 0.250816i | ||||||||
\(239\) | 5.00941 | 0.324032 | 0.162016 | − | 0.986788i | \(-0.448200\pi\) | ||||
0.162016 | + | 0.986788i | \(0.448200\pi\) | |||||||
\(240\) | −6.98034 | + | 1.91359i | −0.450579 | + | 0.123522i | ||||
\(241\) | 4.69354 | 0.302337 | 0.151169 | − | 0.988508i | \(-0.451696\pi\) | ||||
0.151169 | + | 0.988508i | \(0.451696\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | − | 16.1146i | − | 1.03375i | ||||||
\(244\) | 10.0764 | 0.645077 | ||||||||
\(245\) | 2.19319 | + | 8.00023i | 0.140118 | + | 0.511116i | ||||
\(246\) | 3.22367 | 0.205533 | ||||||||
\(247\) | − | 26.0855i | − | 1.65978i | ||||||
\(248\) | 4.16236i | 0.264310i | ||||||||
\(249\) | −11.6793 | −0.740149 | ||||||||
\(250\) | 2.55054 | − | 2.64036i | 0.161310 | − | 0.166991i | ||||
\(251\) | 4.37834 | 0.276358 | 0.138179 | − | 0.990407i | \(-0.455875\pi\) | ||||
0.138179 | + | 0.990407i | \(0.455875\pi\) | |||||||
\(252\) | 12.8464i | 0.809244i | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | −1.77831 | −0.111581 | ||||||||
\(255\) | −2.04792 | − | 7.47034i | −0.128246 | − | 0.467811i | ||||
\(256\) | 8.05489 | 0.503431 | ||||||||
\(257\) | − | 6.51616i | − | 0.406467i | −0.979130 | − | 0.203233i | \(-0.934855\pi\) | ||
0.979130 | − | 0.203233i | \(-0.0651450\pi\) | |||||||
\(258\) | 0.188520i | 0.0117367i | ||||||||
\(259\) | −20.4111 | −1.26829 | ||||||||
\(260\) | −21.2484 | + | 5.82504i | −1.31777 | + | 0.361253i | ||||
\(261\) | −4.24853 | −0.262978 | ||||||||
\(262\) | − | 6.27941i | − | 0.387943i | ||||||
\(263\) | 4.28212i | 0.264047i | 0.991247 | + | 0.132023i | \(0.0421474\pi\) | ||||
−0.991247 | + | 0.132023i | \(0.957853\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −0.848110 | + | 0.232501i | −0.0520990 | + | 0.0142824i | ||||
\(266\) | 5.38289 | 0.330046 | ||||||||
\(267\) | 8.65800i | 0.529861i | ||||||||
\(268\) | 15.9900i | 0.976747i | ||||||||
\(269\) | −10.6217 | −0.647614 | −0.323807 | − | 0.946123i | \(-0.604963\pi\) | ||||
−0.323807 | + | 0.946123i | \(0.604963\pi\) | |||||||
\(270\) | 0.947620 | + | 3.45669i | 0.0576703 | + | 0.210368i | ||||
\(271\) | −10.6506 | −0.646976 | −0.323488 | − | 0.946232i | \(-0.604856\pi\) | ||||
−0.323488 | + | 0.946232i | \(0.604856\pi\) | |||||||
\(272\) | 12.1162i | 0.734653i | ||||||||
\(273\) | − | 16.3937i | − | 0.992194i | ||||||
\(274\) | 5.26768 | 0.318232 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −10.6372 | −0.640286 | ||||||||
\(277\) | − | 7.35058i | − | 0.441654i | −0.975313 | − | 0.220827i | \(-0.929124\pi\) | ||
0.975313 | − | 0.220827i | \(-0.0708755\pi\) | |||||||
\(278\) | 4.12716i | 0.247530i | ||||||||
\(279\) | −6.75667 | −0.404511 | ||||||||
\(280\) | −2.47255 | − | 9.01929i | −0.147763 | − | 0.539006i | ||||
\(281\) | −28.2293 | −1.68402 | −0.842011 | − | 0.539461i | \(-0.818628\pi\) | ||||
−0.842011 | + | 0.539461i | \(0.818628\pi\) | |||||||
\(282\) | 0.303870i | 0.0180952i | ||||||||
\(283\) | − | 10.0617i | − | 0.598109i | −0.954236 | − | 0.299054i | \(-0.903329\pi\) | ||
0.954236 | − | 0.299054i | \(-0.0966712\pi\) | |||||||
\(284\) | 23.7043 | 1.40659 | ||||||||
\(285\) | −10.3923 | + | 2.84895i | −0.615587 | + | 0.168757i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | − | 33.3986i | − | 1.97146i | ||||||
\(288\) | − | 7.59457i | − | 0.447514i | ||||||
\(289\) | 4.03326 | 0.237251 | ||||||||
\(290\) | 1.45011 | − | 0.397535i | 0.0851535 | − | 0.0233440i | ||||
\(291\) | 10.8650 | 0.636917 | ||||||||
\(292\) | 16.1125i | 0.942912i | ||||||||
\(293\) | 0.0244803i | 0.00143016i | 1.00000 | 0.000715078i | \(0.000227616\pi\) | |||||
−1.00000 | 0.000715078i | \(0.999772\pi\) | ||||||||
\(294\) | 1.17183 | 0.0683426 | ||||||||
\(295\) | −0.311818 | − | 1.13744i | −0.0181548 | − | 0.0662243i | ||||
\(296\) | 7.97090 | 0.463299 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | − | 4.57325i | − | 0.264921i | ||||||
\(299\) | −30.4300 | −1.75981 | ||||||||
\(300\) | 4.64133 | + | 7.82904i | 0.267967 | + | 0.452010i | ||||
\(301\) | 1.95314 | 0.112577 | ||||||||
\(302\) | 5.26460i | 0.302944i | ||||||||
\(303\) | 12.6667i | 0.727683i | ||||||||
\(304\) | 16.8554 | 0.966722 | ||||||||
\(305\) | −3.14823 | − | 11.4840i | −0.180267 | − | 0.657571i | ||||
\(306\) | 2.45289 | 0.140222 | ||||||||
\(307\) | − | 32.9698i | − | 1.88169i | −0.338839 | − | 0.940844i | \(-0.610034\pi\) | ||
0.338839 | − | 0.940844i | \(-0.389966\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 2.67656 | 0.152264 | ||||||||
\(310\) | 2.30619 | − | 0.632221i | 0.130983 | − | 0.0359077i | ||||
\(311\) | −4.82567 | −0.273639 | −0.136819 | − | 0.990596i | \(-0.543688\pi\) | ||||
−0.136819 | + | 0.990596i | \(0.543688\pi\) | |||||||
\(312\) | 6.40204i | 0.362444i | ||||||||
\(313\) | − | 17.0662i | − | 0.964637i | −0.875996 | − | 0.482318i | \(-0.839795\pi\) | ||
0.875996 | − | 0.482318i | \(-0.160205\pi\) | |||||||
\(314\) | 0.746958 | 0.0421533 | ||||||||
\(315\) | 14.6408 | − | 4.01365i | 0.824918 | − | 0.226143i | ||||
\(316\) | 5.35934 | 0.301487 | ||||||||
\(317\) | − | 1.71657i | − | 0.0964120i | −0.998837 | − | 0.0482060i | \(-0.984650\pi\) | ||
0.998837 | − | 0.0482060i | \(-0.0153504\pi\) | |||||||
\(318\) | 0.124227i | 0.00696629i | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | −3.26774 | − | 11.9199i | −0.182672 | − | 0.666345i | ||||
\(321\) | 15.3441 | 0.856425 | ||||||||
\(322\) | − | 6.27941i | − | 0.349938i | ||||||
\(323\) | 18.0386i | 1.00369i | ||||||||
\(324\) | 2.89021 | 0.160567 | ||||||||
\(325\) | 13.2775 | + | 22.3966i | 0.736501 | + | 1.24234i | ||||
\(326\) | 7.41068 | 0.410440 | ||||||||
\(327\) | 3.76056i | 0.207960i | ||||||||
\(328\) | 13.0427i | 0.720164i | ||||||||
\(329\) | 3.14823 | 0.173567 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 0.892186 | 0.0490390 | 0.0245195 | − | 0.999699i | \(-0.492194\pi\) | ||||
0.0245195 | + | 0.999699i | \(0.492194\pi\) | |||||||
\(332\) | − | 22.9724i | − | 1.26078i | ||||||
\(333\) | 12.9390i | 0.709053i | ||||||||
\(334\) | 1.25086 | 0.0684440 | ||||||||
\(335\) | 18.2237 | − | 4.99585i | 0.995665 | − | 0.272952i | ||||
\(336\) | 10.5930 | 0.577894 | ||||||||
\(337\) | 18.7856i | 1.02332i | 0.859189 | + | 0.511659i | \(0.170969\pi\) | ||||
−0.859189 | + | 0.511659i | \(0.829031\pi\) | |||||||
\(338\) | 4.63495i | 0.252108i | ||||||||
\(339\) | 9.50223 | 0.516090 | ||||||||
\(340\) | 14.6936 | − | 4.02812i | 0.796874 | − | 0.218456i | ||||
\(341\) | 0 | 0 | ||||||||
\(342\) | − | 3.41232i | − | 0.184517i | ||||||
\(343\) | 10.7674i | 0.581385i | ||||||||
\(344\) | −0.762737 | −0.0411240 | ||||||||
\(345\) | 3.32344 | + | 12.1231i | 0.178928 | + | 0.652687i | ||||
\(346\) | 0.311818 | 0.0167635 | ||||||||
\(347\) | 20.9598i | 1.12518i | 0.826735 | + | 0.562591i | \(0.190196\pi\) | ||||
−0.826735 | + | 0.562591i | \(0.809804\pi\) | |||||||
\(348\) | 3.72780i | 0.199831i | ||||||||
\(349\) | 27.1866 | 1.45527 | 0.727634 | − | 0.685966i | \(-0.240620\pi\) | ||||
0.727634 | + | 0.685966i | \(0.240620\pi\) | |||||||
\(350\) | −4.62166 | + | 2.73988i | −0.247038 | + | 0.146453i | ||||
\(351\) | −25.4205 | −1.35685 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 8.66841i | 0.461373i | 0.973028 | + | 0.230686i | \(0.0740972\pi\) | ||||
−0.973028 | + | 0.230686i | \(0.925903\pi\) | |||||||
\(354\) | −0.166606 | −0.00885503 | ||||||||
\(355\) | −7.40604 | − | 27.0155i | −0.393072 | − | 1.43383i | ||||
\(356\) | −17.0297 | −0.902571 | ||||||||
\(357\) | 11.3366i | 0.599995i | ||||||||
\(358\) | 1.19364i | 0.0630858i | ||||||||
\(359\) | 6.90465 | 0.364414 | 0.182207 | − | 0.983260i | \(-0.441676\pi\) | ||||
0.182207 | + | 0.983260i | \(0.441676\pi\) | |||||||
\(360\) | −5.71750 | + | 1.56740i | −0.301339 | + | 0.0826092i | ||||
\(361\) | 6.09422 | 0.320748 | ||||||||
\(362\) | − | 4.12695i | − | 0.216908i | ||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 32.2453 | 1.69011 | ||||||||
\(365\) | 18.3632 | − | 5.03410i | 0.961174 | − | 0.263497i | ||||
\(366\) | −1.68212 | −0.0879256 | ||||||||
\(367\) | − | 16.2900i | − | 0.850332i | −0.905115 | − | 0.425166i | \(-0.860216\pi\) | ||
0.905115 | − | 0.425166i | \(-0.139784\pi\) | |||||||
\(368\) | − | 19.6626i | − | 1.02498i | ||||||
\(369\) | −21.1720 | −1.10217 | ||||||||
\(370\) | −1.21070 | − | 4.41635i | −0.0629414 | − | 0.229595i | ||||
\(371\) | 1.28704 | 0.0668200 | ||||||||
\(372\) | 5.92853i | 0.307380i | ||||||||
\(373\) | − | 3.69622i | − | 0.191383i | −0.995411 | − | 0.0956915i | \(-0.969494\pi\) | ||
0.995411 | − | 0.0956915i | \(-0.0305062\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 7.47255 | − | 7.73573i | 0.385881 | − | 0.399471i | ||||
\(376\) | −1.22944 | −0.0634034 | ||||||||
\(377\) | 10.6641i | 0.549231i | ||||||||
\(378\) | − | 5.24568i | − | 0.269809i | ||||||
\(379\) | 3.70178 | 0.190148 | 0.0950738 | − | 0.995470i | \(-0.469691\pi\) | ||||
0.0950738 | + | 0.995470i | \(0.469691\pi\) | |||||||
\(380\) | −5.60369 | − | 20.4409i | −0.287463 | − | 1.04860i | ||||
\(381\) | −5.21007 | −0.266920 | ||||||||
\(382\) | 0.878849i | 0.0449658i | ||||||||
\(383\) | − | 31.3709i | − | 1.60298i | −0.598011 | − | 0.801488i | \(-0.704042\pi\) | ||
0.598011 | − | 0.801488i | \(-0.295958\pi\) | |||||||
\(384\) | −8.78939 | −0.448532 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −0.127476 | −0.00648836 | ||||||||
\(387\) | − | 1.23814i | − | 0.0629380i | ||||||
\(388\) | 21.3707i | 1.08493i | ||||||||
\(389\) | 13.8257 | 0.700989 | 0.350495 | − | 0.936565i | \(-0.386013\pi\) | ||||
0.350495 | + | 0.936565i | \(0.386013\pi\) | |||||||
\(390\) | 3.54711 | − | 0.972407i | 0.179615 | − | 0.0492397i | ||||
\(391\) | 21.0429 | 1.06418 | ||||||||
\(392\) | 4.74115i | 0.239464i | ||||||||
\(393\) | − | 18.3974i | − | 0.928025i | ||||||
\(394\) | 6.08815 | 0.306717 | ||||||||
\(395\) | −1.67445 | − | 6.10798i | −0.0842505 | − | 0.307326i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 9.73413i | 0.488542i | 0.969707 | + | 0.244271i | \(0.0785486\pi\) | ||||
−0.969707 | + | 0.244271i | \(0.921451\pi\) | |||||||
\(398\) | 3.33247i | 0.167041i | ||||||||
\(399\) | 15.7708 | 0.789526 | ||||||||
\(400\) | −14.4717 | + | 8.57935i | −0.723587 | + | 0.428968i | ||||
\(401\) | −26.1768 | −1.30721 | −0.653604 | − | 0.756837i | \(-0.726744\pi\) | ||||
−0.653604 | + | 0.756837i | \(0.726744\pi\) | |||||||
\(402\) | − | 2.66931i | − | 0.133133i | ||||||
\(403\) | 16.9597i | 0.844825i | ||||||||
\(404\) | −24.9145 | −1.23954 | ||||||||
\(405\) | −0.903003 | − | 3.29394i | −0.0448706 | − | 0.163677i | ||||
\(406\) | −2.20061 | −0.109214 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | − | 4.42713i | − | 0.219175i | ||||||
\(409\) | −2.64562 | −0.130817 | −0.0654086 | − | 0.997859i | \(-0.520835\pi\) | ||||
−0.0654086 | + | 0.997859i | \(0.520835\pi\) | |||||||
\(410\) | 7.22645 | − | 1.98106i | 0.356889 | − | 0.0978377i | ||||
\(411\) | 15.4332 | 0.761265 | ||||||||
\(412\) | 5.26460i | 0.259368i | ||||||||
\(413\) | 1.72611i | 0.0849365i | ||||||||
\(414\) | −3.98064 | −0.195638 | ||||||||
\(415\) | −26.1814 | + | 7.17739i | −1.28520 | + | 0.352324i | ||||
\(416\) | −19.0629 | −0.934637 | ||||||||
\(417\) | 12.0917i | 0.592135i | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −24.3118 | −1.18771 | −0.593855 | − | 0.804572i | \(-0.702395\pi\) | ||||
−0.593855 | + | 0.804572i | \(0.702395\pi\) | |||||||
\(420\) | −3.52171 | − | 12.8464i | −0.171842 | − | 0.626838i | ||||
\(421\) | −27.8922 | −1.35938 | −0.679691 | − | 0.733499i | \(-0.737886\pi\) | ||||
−0.679691 | + | 0.733499i | \(0.737886\pi\) | |||||||
\(422\) | 2.78228i | 0.135439i | ||||||||
\(423\) | − | 1.99572i | − | 0.0970354i | ||||||
\(424\) | −0.502613 | −0.0244090 | ||||||||
\(425\) | −9.18160 | − | 15.4876i | −0.445373 | − | 0.751260i | ||||
\(426\) | −3.95709 | −0.191721 | ||||||||
\(427\) | 17.4275i | 0.843374i | ||||||||
\(428\) | 30.1808i | 1.45884i | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0.115852 | + | 0.422602i | 0.00558689 | + | 0.0203797i | ||||
\(431\) | 20.0377 | 0.965180 | 0.482590 | − | 0.875846i | \(-0.339696\pi\) | ||||
0.482590 | + | 0.875846i | \(0.339696\pi\) | |||||||
\(432\) | − | 16.4257i | − | 0.790283i | ||||||
\(433\) | − | 4.38473i | − | 0.210716i | −0.994434 | − | 0.105358i | \(-0.966401\pi\) | ||
0.994434 | − | 0.105358i | \(-0.0335989\pi\) | |||||||
\(434\) | −3.49975 | −0.167993 | ||||||||
\(435\) | 4.24853 | − | 1.16470i | 0.203702 | − | 0.0558429i | ||||
\(436\) | −7.39676 | −0.354241 | ||||||||
\(437\) | − | 29.2736i | − | 1.40035i | ||||||
\(438\) | − | 2.68975i | − | 0.128521i | ||||||
\(439\) | 34.2675 | 1.63550 | 0.817750 | − | 0.575573i | \(-0.195221\pi\) | ||||
0.817750 | + | 0.575573i | \(0.195221\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −7.69622 | −0.366487 | ||||||||
\(442\) | − | 6.15694i | − | 0.292856i | ||||||
\(443\) | − | 18.4932i | − | 0.878637i | −0.898331 | − | 0.439319i | \(-0.855220\pi\) | ||
0.898331 | − | 0.439319i | \(-0.144780\pi\) | |||||||
\(444\) | 11.3531 | 0.538795 | ||||||||
\(445\) | 5.32066 | + | 19.4085i | 0.252224 | + | 0.920052i | ||||
\(446\) | −7.78416 | −0.368591 | ||||||||
\(447\) | − | 13.3987i | − | 0.633736i | ||||||
\(448\) | 18.0890i | 0.854627i | ||||||||
\(449\) | −18.7708 | −0.885848 | −0.442924 | − | 0.896559i | \(-0.646059\pi\) | ||||
−0.442924 | + | 0.896559i | \(0.646059\pi\) | |||||||
\(450\) | 1.73686 | + | 2.92976i | 0.0818766 | + | 0.138110i | ||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 18.6902i | 0.879113i | ||||||||
\(453\) | 15.4242i | 0.724692i | ||||||||
\(454\) | −0.235290 | −0.0110427 | ||||||||
\(455\) | −10.0746 | − | 36.7496i | −0.472302 | − | 1.72285i | ||||
\(456\) | −6.15876 | −0.288410 | ||||||||
\(457\) | − | 14.4990i | − | 0.678236i | −0.940744 | − | 0.339118i | \(-0.889871\pi\) | ||
0.940744 | − | 0.339118i | \(-0.110129\pi\) | |||||||
\(458\) | 4.31752i | 0.201744i | ||||||||
\(459\) | 17.5788 | 0.820507 | ||||||||
\(460\) | −23.8453 | + | 6.53697i | −1.11179 | + | 0.304788i | ||||
\(461\) | −15.2150 | −0.708632 | −0.354316 | − | 0.935126i | \(-0.615286\pi\) | ||||
−0.354316 | + | 0.935126i | \(0.615286\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 9.08060i | 0.422011i | 0.977485 | + | 0.211006i | \(0.0676739\pi\) | ||||
−0.977485 | + | 0.211006i | \(0.932326\pi\) | |||||||
\(464\) | −6.89073 | −0.319894 | ||||||||
\(465\) | 6.75667 | − | 1.85228i | 0.313333 | − | 0.0858973i | ||||
\(466\) | −8.84336 | −0.409661 | ||||||||
\(467\) | − | 17.2840i | − | 0.799809i | −0.916557 | − | 0.399904i | \(-0.869043\pi\) | ||
0.916557 | − | 0.399904i | \(-0.130957\pi\) | |||||||
\(468\) | − | 20.4409i | − | 0.944882i | ||||||
\(469\) | −27.6552 | −1.27700 | ||||||||
\(470\) | 0.186740 | + | 0.681182i | 0.00861365 | + | 0.0314206i | ||||
\(471\) | 2.18843 | 0.100838 | ||||||||
\(472\) | − | 0.674078i | − | 0.0310269i | ||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | −0.894665 | −0.0410933 | ||||||||
\(475\) | −21.5455 | + | 12.7729i | −0.988575 | + | 0.586061i | ||||
\(476\) | −22.2982 | −1.02204 | ||||||||
\(477\) | − | 0.815882i | − | 0.0373567i | ||||||
\(478\) | − | 1.64484i | − | 0.0752334i | ||||||
\(479\) | 32.6306 | 1.49093 | 0.745464 | − | 0.666546i | \(-0.232228\pi\) | ||||
0.745464 | + | 0.666546i | \(0.232228\pi\) | |||||||
\(480\) | 2.08198 | + | 7.59457i | 0.0950289 | + | 0.346643i | ||||
\(481\) | 32.4779 | 1.48086 | ||||||||
\(482\) | − | 1.54113i | − | 0.0701964i | ||||||
\(483\) | − | 18.3974i | − | 0.837110i | ||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 24.3559 | − | 6.67694i | 1.10594 | − | 0.303184i | ||||
\(486\) | −5.29123 | −0.240015 | ||||||||
\(487\) | − | 15.2563i | − | 0.691329i | −0.938358 | − | 0.345664i | \(-0.887654\pi\) | ||
0.938358 | − | 0.345664i | \(-0.112346\pi\) | |||||||
\(488\) | − | 6.80572i | − | 0.308081i | ||||||
\(489\) | 21.7118 | 0.981841 | ||||||||
\(490\) | 2.62688 | − | 0.720134i | 0.118670 | − | 0.0325324i | ||||
\(491\) | −6.66994 | −0.301010 | −0.150505 | − | 0.988609i | \(-0.548090\pi\) | ||||
−0.150505 | + | 0.988609i | \(0.548090\pi\) | |||||||
\(492\) | 18.5770i | 0.837517i | ||||||||
\(493\) | − | 7.37444i | − | 0.332128i | ||||||
\(494\) | −8.56518 | −0.385365 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −10.9587 | −0.492060 | ||||||||
\(497\) | 40.9971i | 1.83897i | ||||||||
\(498\) | 3.83492i | 0.171847i | ||||||||
\(499\) | 6.14911 | 0.275272 | 0.137636 | − | 0.990483i | \(-0.456050\pi\) | ||||
0.137636 | + | 0.990483i | \(0.456050\pi\) | |||||||
\(500\) | 15.2156 | + | 14.6980i | 0.680464 | + | 0.657314i | ||||
\(501\) | 3.66476 | 0.163730 | ||||||||
\(502\) | − | 1.43763i | − | 0.0641645i | ||||||
\(503\) | 25.7081i | 1.14627i | 0.819462 | + | 0.573134i | \(0.194272\pi\) | ||||
−0.819462 | + | 0.573134i | \(0.805728\pi\) | |||||||
\(504\) | 8.67656 | 0.386485 | ||||||||
\(505\) | 7.78416 | + | 28.3948i | 0.346391 | + | 1.26355i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 13.5795i | 0.603085i | ||||||||
\(508\) | − | 10.2478i | − | 0.454675i | ||||||
\(509\) | 16.8453 | 0.746656 | 0.373328 | − | 0.927699i | \(-0.378217\pi\) | ||||
0.373328 | + | 0.927699i | \(0.378217\pi\) | |||||||
\(510\) | −2.45289 | + | 0.672437i | −0.108616 | + | 0.0297760i | ||||
\(511\) | −27.8670 | −1.23276 | ||||||||
\(512\) | − | 20.9180i | − | 0.924453i | ||||||
\(513\) | − | 24.4546i | − | 1.07970i | ||||||
\(514\) | −2.13959 | −0.0943731 | ||||||||
\(515\) | 6.00000 | − | 1.64484i | 0.264392 | − | 0.0724805i | ||||
\(516\) | −1.08638 | −0.0478253 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 6.70201i | 0.294469i | ||||||||
\(519\) | 0.913565 | 0.0401010 | ||||||||
\(520\) | 3.93429 | + | 14.3514i | 0.172530 | + | 0.629349i | ||||
\(521\) | −25.1707 | −1.10275 | −0.551375 | − | 0.834257i | \(-0.685897\pi\) | ||||
−0.551375 | + | 0.834257i | \(0.685897\pi\) | |||||||
\(522\) | 1.39501i | 0.0610578i | ||||||||
\(523\) | − | 17.9094i | − | 0.783123i | −0.920152 | − | 0.391562i | \(-0.871935\pi\) | ||
0.920152 | − | 0.391562i | \(-0.128065\pi\) | |||||||
\(524\) | 36.1863 | 1.58081 | ||||||||
\(525\) | −13.5405 | + | 8.02730i | −0.590957 | + | 0.350340i | ||||
\(526\) | 1.40604 | 0.0613061 | ||||||||
\(527\) | − | 11.7280i | − | 0.510879i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −11.1491 | −0.484744 | ||||||||
\(530\) | 0.0763420 | + | 0.278477i | 0.00331608 | + | 0.0120963i | ||||
\(531\) | 1.09422 | 0.0474850 | ||||||||
\(532\) | 31.0200i | 1.34489i | ||||||||
\(533\) | 53.1433i | 2.30189i | ||||||||
\(534\) | 2.84286 | 0.123023 | ||||||||
\(535\) | 34.3967 | − | 9.42952i | 1.48710 | − | 0.407674i | ||||
\(536\) | 10.7998 | 0.466482 | ||||||||
\(537\) | 3.49712i | 0.150912i | ||||||||
\(538\) | 3.48763i | 0.150362i | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −19.9199 | + | 5.46085i | −0.857215 | + | 0.234998i | ||||
\(541\) | 9.44468 | 0.406059 | 0.203029 | − | 0.979173i | \(-0.434921\pi\) | ||||
0.203029 | + | 0.979173i | \(0.434921\pi\) | |||||||
\(542\) | 3.49712i | 0.150214i | ||||||||
\(543\) | − | 12.0911i | − | 0.518880i | ||||||
\(544\) | 13.1824 | 0.565189 | ||||||||
\(545\) | 2.31101 | + | 8.43000i | 0.0989926 | + | 0.361102i | ||||
\(546\) | −5.38289 | −0.230367 | ||||||||
\(547\) | − | 15.3044i | − | 0.654370i | −0.944960 | − | 0.327185i | \(-0.893900\pi\) | ||
0.944960 | − | 0.327185i | \(-0.106100\pi\) | |||||||
\(548\) | 30.3561i | 1.29675i | ||||||||
\(549\) | 11.0476 | 0.471500 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −10.2589 | −0.437044 | ||||||||
\(552\) | 7.18450i | 0.305792i | ||||||||
\(553\) | 9.26912i | 0.394163i | ||||||||
\(554\) | −2.41357 | −0.102543 | ||||||||
\(555\) | −3.54711 | − | 12.9390i | −0.150566 | − | 0.549230i | ||||
\(556\) | −23.7836 | −1.00865 | ||||||||
\(557\) | − | 9.94844i | − | 0.421529i | −0.977537 | − | 0.210764i | \(-0.932405\pi\) | ||
0.977537 | − | 0.210764i | \(-0.0675953\pi\) | |||||||
\(558\) | 2.21856i | 0.0939190i | ||||||||
\(559\) | −3.10781 | −0.131447 | ||||||||
\(560\) | 23.7461 | − | 6.50977i | 1.00346 | − | 0.275088i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 9.26912i | 0.390994i | ||||||||
\(563\) | 28.0419i | 1.18183i | 0.806735 | + | 0.590914i | \(0.201233\pi\) | ||||
−0.806735 | + | 0.590914i | \(0.798767\pi\) | |||||||
\(564\) | −1.75111 | −0.0737352 | ||||||||
\(565\) | 21.3010 | − | 5.83947i | 0.896140 | − | 0.245668i | ||||
\(566\) | −3.30378 | −0.138868 | ||||||||
\(567\) | 4.99870i | 0.209926i | ||||||||
\(568\) | − | 16.0101i | − | 0.671769i | ||||||
\(569\) | −20.3771 | −0.854251 | −0.427126 | − | 0.904192i | \(-0.640474\pi\) | ||||
−0.427126 | + | 0.904192i | \(0.640474\pi\) | |||||||
\(570\) | 0.935455 | + | 3.41232i | 0.0391819 | + | 0.142926i | ||||
\(571\) | −43.6546 | −1.82689 | −0.913444 | − | 0.406964i | \(-0.866588\pi\) | ||||
−0.913444 | + | 0.406964i | \(0.866588\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 2.57485i | 0.107566i | ||||||||
\(574\) | −10.9664 | −0.457731 | ||||||||
\(575\) | 14.9002 | + | 25.1339i | 0.621382 | + | 1.04815i | ||||
\(576\) | 11.4670 | 0.477791 | ||||||||
\(577\) | 37.4644i | 1.55966i | 0.625989 | + | 0.779832i | \(0.284696\pi\) | ||||
−0.625989 | + | 0.779832i | \(0.715304\pi\) | |||||||
\(578\) | − | 1.32432i | − | 0.0550846i | ||||||
\(579\) | −0.373479 | −0.0155213 | ||||||||
\(580\) | 2.29087 | + | 8.35656i | 0.0951233 | + | 0.346987i | ||||
\(581\) | 39.7315 | 1.64834 | ||||||||
\(582\) | − | 3.56753i | − | 0.147879i | ||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 10.8825 | 0.450322 | ||||||||
\(585\) | −23.2963 | + | 6.38646i | −0.963183 | + | 0.264047i | ||||
\(586\) | 0.00803813 | 0.000332052 | ||||||||
\(587\) | 6.01916i | 0.248437i | 0.992255 | + | 0.124219i | \(0.0396425\pi\) | ||||
−0.992255 | + | 0.124219i | \(0.960358\pi\) | |||||||
\(588\) | 6.75292i | 0.278486i | ||||||||
\(589\) | −16.3153 | −0.672259 | ||||||||
\(590\) | −0.373479 | + | 0.102386i | −0.0153759 | + | 0.00421516i | ||||
\(591\) | 17.8370 | 0.733718 | ||||||||
\(592\) | 20.9859i | 0.862515i | ||||||||
\(593\) | − | 14.3574i | − | 0.589589i | −0.955561 | − | 0.294794i | \(-0.904749\pi\) | ||
0.955561 | − | 0.294794i | \(-0.0952511\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 6.96674 | + | 25.4130i | 0.285609 | + | 1.04183i | ||||
\(596\) | 26.3542 | 1.07951 | ||||||||
\(597\) | 9.76345i | 0.399591i | ||||||||
\(598\) | 9.99169i | 0.408591i | ||||||||
\(599\) | −27.9471 | −1.14189 | −0.570943 | − | 0.820989i | \(-0.693422\pi\) | ||||
−0.570943 | + | 0.820989i | \(0.693422\pi\) | |||||||
\(600\) | 5.28781 | − | 3.13480i | 0.215874 | − | 0.127978i | ||||
\(601\) | 20.5638 | 0.838815 | 0.419408 | − | 0.907798i | \(-0.362238\pi\) | ||||
0.419408 | + | 0.907798i | \(0.362238\pi\) | |||||||
\(602\) | − | 0.641316i | − | 0.0261381i | ||||||
\(603\) | 17.5312i | 0.713925i | ||||||||
\(604\) | −30.3383 | −1.23445 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 4.15912 | 0.168953 | ||||||||
\(607\) | 19.1738i | 0.778242i | 0.921187 | + | 0.389121i | \(0.127221\pi\) | ||||
−0.921187 | + | 0.389121i | \(0.872779\pi\) | |||||||
\(608\) | − | 18.3385i | − | 0.743726i | ||||||
\(609\) | −6.44733 | −0.261259 | ||||||||
\(610\) | −3.77078 | + | 1.03372i | −0.152674 | + | 0.0418542i | ||||
\(611\) | −5.00941 | −0.202659 | ||||||||
\(612\) | 14.1353i | 0.571385i | ||||||||
\(613\) | − | 18.0536i | − | 0.729180i | −0.931168 | − | 0.364590i | \(-0.881209\pi\) | ||
0.931168 | − | 0.364590i | \(-0.118791\pi\) | |||||||
\(614\) | −10.8257 | −0.436888 | ||||||||
\(615\) | 21.1720 | − | 5.80411i | 0.853738 | − | 0.234044i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 32.0433i | 1.29001i | 0.764176 | + | 0.645007i | \(0.223146\pi\) | ||||
−0.764176 | + | 0.645007i | \(0.776854\pi\) | |||||||
\(618\) | − | 0.878849i | − | 0.0353525i | ||||||
\(619\) | 5.30985 | 0.213421 | 0.106710 | − | 0.994290i | \(-0.465968\pi\) | ||||
0.106710 | + | 0.994290i | \(0.465968\pi\) | |||||||
\(620\) | 3.64330 | + | 13.2899i | 0.146318 | + | 0.533735i | ||||
\(621\) | −28.5274 | −1.14477 | ||||||||
\(622\) | 1.58451i | 0.0635331i | ||||||||
\(623\) | − | 29.4533i | − | 1.18002i | ||||||
\(624\) | −16.8554 | −0.674755 | ||||||||
\(625\) | 11.9972 | − | 21.9332i | 0.479889 | − | 0.877329i | ||||
\(626\) | −5.60369 | −0.223968 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 4.30450i | 0.171768i | ||||||||
\(629\) | −22.4591 | −0.895501 | ||||||||
\(630\) | −1.31788 | − | 4.80733i | −0.0525057 | − | 0.191529i | ||||
\(631\) | 39.3924 | 1.56819 | 0.784094 | − | 0.620642i | \(-0.213128\pi\) | ||||
0.784094 | + | 0.620642i | \(0.213128\pi\) | |||||||
\(632\) | − | 3.61975i | − | 0.143986i | ||||||
\(633\) | 8.15152i | 0.323994i | ||||||||
\(634\) | −0.563636 | −0.0223848 | ||||||||
\(635\) | −11.6793 | + | 3.20178i | −0.463481 | + | 0.127059i | ||||
\(636\) | −0.715882 | −0.0283866 | ||||||||
\(637\) | 19.3181i | 0.765410i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 25.9889 | 1.02810 | ||||||||
\(640\) | −19.7030 | + | 5.40140i | −0.778831 | + | 0.213509i | ||||
\(641\) | −47.2650 | −1.86685 | −0.933427 | − | 0.358768i | \(-0.883197\pi\) | ||||
−0.933427 | + | 0.358768i | \(0.883197\pi\) | |||||||
\(642\) | − | 5.03825i | − | 0.198844i | ||||||
\(643\) | 2.37860i | 0.0938027i | 0.998900 | + | 0.0469014i | \(0.0149346\pi\) | ||||
−0.998900 | + | 0.0469014i | \(0.985065\pi\) | |||||||
\(644\) | 36.1863 | 1.42594 | ||||||||
\(645\) | 0.339423 | + | 1.23814i | 0.0133648 | + | 0.0487516i | ||||
\(646\) | 5.92298 | 0.233036 | ||||||||
\(647\) | 0.890278i | 0.0350004i | 0.999847 | + | 0.0175002i | \(0.00557078\pi\) | ||||
−0.999847 | + | 0.0175002i | \(0.994429\pi\) | |||||||
\(648\) | − | 1.95208i | − | 0.0766849i | ||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 7.35392 | − | 4.35966i | 0.288445 | − | 0.171000i | ||||
\(651\) | −10.2535 | −0.401868 | ||||||||
\(652\) | 42.7055i | 1.67248i | ||||||||
\(653\) | − | 13.0531i | − | 0.510809i | −0.966834 | − | 0.255404i | \(-0.917791\pi\) | ||
0.966834 | − | 0.255404i | \(-0.0822086\pi\) | |||||||
\(654\) | 1.23478 | 0.0482839 | ||||||||
\(655\) | −11.3059 | − | 41.2411i | −0.441757 | − | 1.61142i | ||||
\(656\) | −34.3391 | −1.34072 | ||||||||
\(657\) | 17.6654i | 0.689193i | ||||||||
\(658\) | − | 1.03372i | − | 0.0402987i | ||||||
\(659\) | 24.8805 | 0.969205 | 0.484603 | − | 0.874734i | \(-0.338964\pi\) | ||||
0.484603 | + | 0.874734i | \(0.338964\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −33.1788 | −1.29051 | −0.645253 | − | 0.763969i | \(-0.723248\pi\) | ||||
−0.645253 | + | 0.763969i | \(0.723248\pi\) | |||||||
\(662\) | − | 0.292950i | − | 0.0113858i | ||||||
\(663\) | − | 18.0386i | − | 0.700560i | ||||||
\(664\) | −15.5158 | −0.602131 | ||||||||
\(665\) | 35.3531 | − | 9.69173i | 1.37094 | − | 0.375829i | ||||
\(666\) | 4.24853 | 0.164627 | ||||||||
\(667\) | 11.9675i | 0.463384i | ||||||||
\(668\) | 7.20833i | 0.278899i | ||||||||
\(669\) | −22.8060 | −0.881731 | ||||||||
\(670\) | −1.64039 | − | 5.98375i | −0.0633738 | − | 0.231173i | ||||
\(671\) | 0 | 0 | ||||||||
\(672\) | − | 11.5251i | − | 0.444590i | ||||||
\(673\) | − | 23.8197i | − | 0.918182i | −0.888389 | − | 0.459091i | \(-0.848175\pi\) | ||
0.888389 | − | 0.459091i | \(-0.151825\pi\) | |||||||
\(674\) | 6.16827 | 0.237593 | ||||||||
\(675\) | 12.4473 | + | 20.9963i | 0.479098 | + | 0.808148i | ||||
\(676\) | −26.7098 | −1.02730 | ||||||||
\(677\) | − | 1.87036i | − | 0.0718837i | −0.999354 | − | 0.0359418i | \(-0.988557\pi\) | ||
0.999354 | − | 0.0359418i | \(-0.0114431\pi\) | |||||||
\(678\) | − | 3.12006i | − | 0.119825i | ||||||
\(679\) | −36.9611 | −1.41844 | ||||||||
\(680\) | −2.72063 | − | 9.92423i | −0.104332 | − | 0.380577i | ||||
\(681\) | −0.689352 | −0.0264160 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − | 9.51629i | − | 0.364131i | −0.983286 | − | 0.182065i | \(-0.941722\pi\) | ||
0.983286 | − | 0.182065i | \(-0.0582782\pi\) | |||||||
\(684\) | 19.6642 | 0.751878 | ||||||||
\(685\) | 34.5964 | − | 9.48429i | 1.32186 | − | 0.362376i | ||||
\(686\) | 3.53548 | 0.134985 | ||||||||
\(687\) | 12.6494i | 0.482607i | ||||||||
\(688\) | − | 2.00814i | − | 0.0765598i | ||||||
\(689\) | −2.04792 | −0.0780197 | ||||||||
\(690\) | 3.98064 | − | 1.09125i | 0.151540 | − | 0.0415433i | ||||
\(691\) | −4.56677 | −0.173728 | −0.0868641 | − | 0.996220i | \(-0.527685\pi\) | ||||
−0.0868641 | + | 0.996220i | \(0.527685\pi\) | |||||||
\(692\) | 1.79692i | 0.0683085i | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 6.88217 | 0.261244 | ||||||||
\(695\) | 7.43082 | + | 27.1059i | 0.281867 | + | 1.02818i | ||||
\(696\) | 2.51780 | 0.0954368 | ||||||||
\(697\) | − | 36.7496i | − | 1.39199i | ||||||
\(698\) | − | 8.92675i | − | 0.337883i | ||||||
\(699\) | −25.9092 | −0.979977 | ||||||||
\(700\) | −15.7891 | − | 26.6333i | −0.596773 | − | 1.00664i | ||||
\(701\) | 28.7555 | 1.08608 | 0.543040 | − | 0.839707i | \(-0.317273\pi\) | ||||
0.543040 | + | 0.839707i | \(0.317273\pi\) | |||||||
\(702\) | 8.34685i | 0.315032i | ||||||||
\(703\) | 31.2437i | 1.17838i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0.547109 | + | 1.99572i | 0.0206053 | + | 0.0751633i | ||||
\(706\) | 2.84628 | 0.107121 | ||||||||
\(707\) | − | 43.0903i | − | 1.62058i | ||||||
\(708\) | − | 0.960102i | − | 0.0360829i | ||||||
\(709\) | 36.4141 | 1.36756 | 0.683780 | − | 0.729689i | \(-0.260335\pi\) | ||||
0.683780 | + | 0.729689i | \(0.260335\pi\) | |||||||
\(710\) | −8.87054 | + | 2.43178i | −0.332906 | + | 0.0912629i | ||||
\(711\) | 5.87588 | 0.220363 | ||||||||
\(712\) | 11.5020i | 0.431056i | ||||||||
\(713\) | 19.0326i | 0.712775i | ||||||||
\(714\) | 3.72237 | 0.139306 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −6.87859 | −0.257065 | ||||||||
\(717\) | − | 4.81906i | − | 0.179971i | ||||||
\(718\) | − | 2.26715i | − | 0.0846092i | ||||||
\(719\) | −39.1239 | −1.45907 | −0.729537 | − | 0.683941i | \(-0.760265\pi\) | ||||
−0.729537 | + | 0.683941i | \(0.760265\pi\) | |||||||
\(720\) | −4.12667 | − | 15.0531i | −0.153792 | − | 0.560996i | ||||
\(721\) | −9.10526 | −0.339098 | ||||||||
\(722\) | − | 2.00104i | − | 0.0744710i | ||||||
\(723\) | − | 4.51519i | − | 0.167922i | ||||||
\(724\) | 23.7824 | 0.883866 | ||||||||
\(725\) | 8.80812 | − | 5.22176i | 0.327126 | − | 0.193931i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 32.8912i | − | 1.21987i | −0.792453 | − | 0.609933i | \(-0.791196\pi\) | ||
0.792453 | − | 0.609933i | \(-0.208804\pi\) | |||||||
\(728\) | − | 21.7788i | − | 0.807176i | ||||||
\(729\) | −10.9199 | −0.404440 | ||||||||
\(730\) | −1.65295 | − | 6.02957i | −0.0611784 | − | 0.223164i | ||||
\(731\) | 2.14911 | 0.0794877 | ||||||||
\(732\) | − | 9.69353i | − | 0.358283i | ||||||
\(733\) | 11.9256i | 0.440484i | 0.975445 | + | 0.220242i | \(0.0706847\pi\) | ||||
−0.975445 | + | 0.220242i | \(0.929315\pi\) | |||||||
\(734\) | −5.34884 | −0.197429 | ||||||||
\(735\) | 7.69622 | − | 2.10985i | 0.283879 | − | 0.0778229i | ||||
\(736\) | −21.3928 | −0.788549 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 6.95184i | 0.255901i | ||||||||
\(739\) | 37.2429 | 1.37000 | 0.685002 | − | 0.728541i | \(-0.259801\pi\) | ||||
0.685002 | + | 0.728541i | \(0.259801\pi\) | |||||||
\(740\) | 25.4501 | − | 6.97691i | 0.935565 | − | 0.256476i | ||||
\(741\) | −25.0942 | −0.921859 | ||||||||
\(742\) | − | 0.422602i | − | 0.0155142i | ||||||
\(743\) | 13.3453i | 0.489590i | 0.969575 | + | 0.244795i | \(0.0787206\pi\) | ||||
−0.969575 | + | 0.244795i | \(0.921279\pi\) | |||||||
\(744\) | 4.00419 | 0.146801 | ||||||||
\(745\) | −8.23398 | − | 30.0356i | −0.301670 | − | 1.10042i | ||||
\(746\) | −1.21366 | −0.0444351 | ||||||||
\(747\) | − | 25.1865i | − | 0.921527i | ||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −52.1984 | −1.90729 | ||||||||
\(750\) | −2.54003 | − | 2.45362i | −0.0927488 | − | 0.0895934i | ||||
\(751\) | 0.795996 | 0.0290463 | 0.0145231 | − | 0.999895i | \(-0.495377\pi\) | ||||
0.0145231 | + | 0.999895i | \(0.495377\pi\) | |||||||
\(752\) | − | 3.23688i | − | 0.118037i | ||||||
\(753\) | − | 4.21196i | − | 0.153492i | ||||||
\(754\) | 3.50157 | 0.127520 | ||||||||
\(755\) | 9.47874 | + | 34.5762i | 0.344967 | + | 1.25836i | ||||
\(756\) | 30.2293 | 1.09943 | ||||||||
\(757\) | − | 40.6693i | − | 1.47815i | −0.673622 | − | 0.739076i | \(-0.735263\pi\) | ||
0.673622 | − | 0.739076i | \(-0.264737\pi\) | |||||||
\(758\) | − | 1.21548i | − | 0.0441483i | ||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −13.8060 | + | 3.78479i | −0.500796 | + | 0.137289i | ||||
\(761\) | −5.77029 | −0.209173 | −0.104586 | − | 0.994516i | \(-0.533352\pi\) | ||||
−0.104586 | + | 0.994516i | \(0.533352\pi\) | |||||||
\(762\) | 1.71073i | 0.0619733i | ||||||||
\(763\) | − | 12.7929i | − | 0.463134i | ||||||
\(764\) | −5.06454 | −0.183229 | ||||||||
\(765\) | 16.1098 | − | 4.41635i | 0.582451 | − | 0.159674i | ||||
\(766\) | −10.3006 | −0.372177 | ||||||||
\(767\) | − | 2.74657i | − | 0.0991728i | ||||||
\(768\) | − | 7.74881i | − | 0.279611i | ||||||
\(769\) | 16.4209 | 0.592152 | 0.296076 | − | 0.955164i | \(-0.404322\pi\) | ||||
0.296076 | + | 0.955164i | \(0.404322\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −6.26855 | −0.225756 | ||||||||
\(772\) | − | 0.734607i | − | 0.0264391i | ||||||
\(773\) | 24.5841i | 0.884227i | 0.896959 | + | 0.442114i | \(0.145771\pi\) | ||||
−0.896959 | + | 0.442114i | \(0.854229\pi\) | |||||||
\(774\) | −0.406543 | −0.0146129 | ||||||||
\(775\) | 14.0080 | − | 8.30445i | 0.503184 | − | 0.298305i | ||||
\(776\) | 14.4340 | 0.518149 | ||||||||
\(777\) | 19.6355i | 0.704420i | ||||||||
\(778\) | − | 4.53967i | − | 0.162755i | ||||||
\(779\) | −51.1239 | −1.83170 | ||||||||
\(780\) | 5.60369 | + | 20.4409i | 0.200644 | + | 0.731902i | ||||
\(781\) | 0 | 0 | ||||||||
\(782\) | − | 6.90944i | − | 0.247081i | ||||||
\(783\) | 9.99740i | 0.357278i | ||||||||
\(784\) | −12.4826 | −0.445806 | ||||||||
\(785\) | 4.90578 | − | 1.34487i | 0.175095 | − | 0.0480006i | ||||
\(786\) | −6.04079 | −0.215468 | ||||||||
\(787\) | 1.83496i | 0.0654091i | 0.999465 | + | 0.0327046i | \(0.0104120\pi\) | ||||
−0.999465 | + | 0.0327046i | \(0.989588\pi\) | |||||||
\(788\) | 35.0842i | 1.24982i | ||||||||
\(789\) | 4.11940 | 0.146654 | ||||||||
\(790\) | −2.00556 | + | 0.549805i | −0.0713546 | + | 0.0195612i | ||||
\(791\) | −32.3252 | −1.14935 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 27.7303i | − | 0.984732i | ||||||
\(794\) | 3.19621 | 0.113429 | ||||||||
\(795\) | 0.223666 | + | 0.815882i | 0.00793263 | + | 0.0289363i | ||||
\(796\) | −19.2040 | −0.680668 | ||||||||
\(797\) | − | 42.0057i | − | 1.48792i | −0.668226 | − | 0.743959i | \(-0.732946\pi\) | ||
0.668226 | − | 0.743959i | \(-0.267054\pi\) | |||||||
\(798\) | − | 5.17834i | − | 0.183311i | ||||||
\(799\) | 3.46410 | 0.122551 | ||||||||
\(800\) | 9.33429 | + | 15.7452i | 0.330017 | + | 0.556676i | ||||
\(801\) | −18.6710 | −0.659707 | ||||||||
\(802\) | 8.59517i | 0.303506i | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 15.3824 | 0.542496 | ||||||||
\(805\) | −11.3059 | − | 41.2411i | −0.398480 | − | 1.45356i | ||||
\(806\) | 5.56874 | 0.196151 | ||||||||
\(807\) | 10.2180i | 0.359692i | ||||||||
\(808\) | 16.8275i | 0.591990i | ||||||||
\(809\) | 27.0811 | 0.952120 | 0.476060 | − | 0.879413i | \(-0.342065\pi\) | ||||
0.476060 | + | 0.879413i | \(0.342065\pi\) | |||||||
\(810\) | −1.08157 | + | 0.296502i | −0.0380024 | + | 0.0104180i | ||||
\(811\) | 1.02878 | 0.0361252 | 0.0180626 | − | 0.999837i | \(-0.494250\pi\) | ||||
0.0180626 | + | 0.999837i | \(0.494250\pi\) | |||||||
\(812\) | − | 12.6814i | − | 0.445031i | ||||||
\(813\) | 10.2459i | 0.359338i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 48.6710 | − | 13.3427i | 1.70487 | − | 0.467374i | ||||
\(816\) | 11.6558 | 0.408035 | ||||||||
\(817\) | − | 2.98972i | − | 0.104597i | ||||||
\(818\) | 0.868689i | 0.0303730i | ||||||||
\(819\) | 35.3531 | 1.23534 | ||||||||
\(820\) | 11.4163 | + | 41.6438i | 0.398673 | + | 1.45427i | ||||
\(821\) | −11.5065 | −0.401581 | −0.200790 | − | 0.979634i | \(-0.564351\pi\) | ||||
−0.200790 | + | 0.979634i | \(0.564351\pi\) | |||||||
\(822\) | − | 5.06751i | − | 0.176750i | ||||||
\(823\) | − | 28.7640i | − | 1.00265i | −0.865259 | − | 0.501325i | \(-0.832846\pi\) | ||
0.865259 | − | 0.501325i | \(-0.167154\pi\) | |||||||
\(824\) | 3.55576 | 0.123871 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0.566771 | 0.0197205 | ||||||||
\(827\) | − | 54.0494i | − | 1.87948i | −0.341885 | − | 0.939742i | \(-0.611065\pi\) | ||
0.341885 | − | 0.939742i | \(-0.388935\pi\) | |||||||
\(828\) | − | 22.9392i | − | 0.797193i | ||||||
\(829\) | −4.64886 | −0.161461 | −0.0807307 | − | 0.996736i | \(-0.525725\pi\) | ||||
−0.0807307 | + | 0.996736i | \(0.525725\pi\) | |||||||
\(830\) | 2.35670 | + | 8.59669i | 0.0818023 | + | 0.298395i | ||||
\(831\) | −7.07126 | −0.245299 | ||||||||
\(832\) | − | 28.7830i | − | 0.997871i | ||||||
\(833\) | − | 13.3588i | − | 0.462855i | ||||||
\(834\) | 3.97033 | 0.137481 | ||||||||
\(835\) | 8.21525 | − | 2.25213i | 0.284300 | − | 0.0779383i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 15.8994i | 0.549564i | ||||||||
\(838\) | 7.98280i | 0.275761i | ||||||||
\(839\) | −4.94511 | −0.170724 | −0.0853620 | − | 0.996350i | \(-0.527205\pi\) | ||||
−0.0853620 | + | 0.996350i | \(0.527205\pi\) | |||||||
\(840\) | −8.67656 | + | 2.37860i | −0.299370 | + | 0.0820694i | ||||
\(841\) | −24.8060 | −0.855380 | ||||||||
\(842\) | 9.15842i | 0.315620i | ||||||||
\(843\) | 27.1566i | 0.935324i | ||||||||
\(844\) | −16.0335 | −0.551895 | ||||||||
\(845\) | 8.34508 | + | 30.4409i | 0.287079 | + | 1.04720i | ||||
\(846\) | −0.655297 | −0.0225296 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | − | 1.32329i | − | 0.0454418i | ||||||
\(849\) | −9.67940 | −0.332196 | ||||||||
\(850\) | −5.08537 | + | 3.01478i | −0.174427 | + | 0.103406i | ||||
\(851\) | 36.4473 | 1.24940 | ||||||||
\(852\) | − | 22.8035i | − | 0.781235i | ||||||
\(853\) | 29.3155i | 1.00374i | 0.864942 | + | 0.501872i | \(0.167355\pi\) | ||||
−0.864942 | + | 0.501872i | \(0.832645\pi\) | |||||||
\(854\) | 5.72232 | 0.195814 | ||||||||
\(855\) | −6.14377 | − | 22.4110i | −0.210113 | − | 0.766441i | ||||
\(856\) | 20.3844 | 0.696724 | ||||||||
\(857\) | 0.656701i | 0.0224325i | 0.999937 | + | 0.0112162i | \(0.00357032\pi\) | ||||
−0.999937 | + | 0.0112162i | \(0.996430\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 40.0569 | 1.36672 | 0.683361 | − | 0.730080i | \(-0.260517\pi\) | ||||
0.683361 | + | 0.730080i | \(0.260517\pi\) | |||||||
\(860\) | −2.43533 | + | 0.667622i | −0.0830439 | + | 0.0227657i | ||||
\(861\) | −32.1294 | −1.09497 | ||||||||
\(862\) | − | 6.57938i | − | 0.224094i | ||||||
\(863\) | − | 19.9306i | − | 0.678445i | −0.940706 | − | 0.339222i | \(-0.889836\pi\) | ||
0.940706 | − | 0.339222i | \(-0.110164\pi\) | |||||||
\(864\) | −17.8711 | −0.607987 | ||||||||
\(865\) | 2.04792 | − | 0.561419i | 0.0696315 | − | 0.0190888i | ||||
\(866\) | −1.43973 | −0.0489239 | ||||||||
\(867\) | − | 3.88000i | − | 0.131772i | ||||||
\(868\) | − | 20.1680i | − | 0.684546i | ||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | −0.382428 | − | 1.39501i | −0.0129655 | − | 0.0472952i | ||||
\(871\) | 44.0045 | 1.49104 | ||||||||
\(872\) | 4.99585i | 0.169181i | ||||||||
\(873\) | 23.4304i | 0.792998i | ||||||||
\(874\) | −9.61201 | −0.325131 | ||||||||
\(875\) | −25.4205 | + | 26.3158i | −0.859371 | + | 0.889637i | ||||
\(876\) | 15.5002 | 0.523704 | ||||||||
\(877\) | 4.79011i | 0.161751i | 0.996724 | + | 0.0808753i | \(0.0257716\pi\) | ||||
−0.996724 | + | 0.0808753i | \(0.974228\pi\) | |||||||
\(878\) | − | 11.2518i | − | 0.379729i | ||||||
\(879\) | 0.0235501 | 0.000794325 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 33.9748 | 1.14464 | 0.572320 | − | 0.820031i | \(-0.306044\pi\) | ||||
0.572320 | + | 0.820031i | \(0.306044\pi\) | |||||||
\(882\) | 2.52706i | 0.0850905i | ||||||||
\(883\) | 39.2743i | 1.32169i | 0.750524 | + | 0.660843i | \(0.229801\pi\) | ||||
−0.750524 | + | 0.660843i | \(0.770199\pi\) | |||||||
\(884\) | 35.4806 | 1.19334 | ||||||||
\(885\) | −1.09422 | + | 0.299969i | −0.0367817 | + | 0.0100834i | ||||
\(886\) | −6.07224 | −0.204001 | ||||||||
\(887\) | − | 33.2519i | − | 1.11649i | −0.829677 | − | 0.558244i | \(-0.811475\pi\) | ||
0.829677 | − | 0.558244i | \(-0.188525\pi\) | |||||||
\(888\) | − | 7.66801i | − | 0.257322i | ||||||
\(889\) | 17.7239 | 0.594441 | ||||||||
\(890\) | 6.37280 | − | 1.74704i | 0.213617 | − | 0.0585610i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | − | 44.8578i | − | 1.50195i | ||||||
\(893\) | − | 4.81906i | − | 0.161264i | ||||||
\(894\) | −4.39946 | −0.147140 | ||||||||
\(895\) | 2.14911 | + | 7.83945i | 0.0718369 | + | 0.262044i | ||||
\(896\) | 29.9002 | 0.998896 | ||||||||
\(897\) | 29.2736i | 0.977418i | ||||||||
\(898\) | 6.16340i | 0.205675i | ||||||||
\(899\) | 6.66994 | 0.222455 | ||||||||
\(900\) | −16.8833 | + | 10.0090i | −0.562778 | + | 0.333634i | ||||
\(901\) | 1.41618 | 0.0471797 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | − | 1.87893i | − | 0.0625267i | ||||||
\(904\) | 12.6236 | 0.419853 | ||||||||
\(905\) | −7.43045 | − | 27.1045i | −0.246997 | − | 0.900985i | ||||
\(906\) | 5.06454 | 0.168258 | ||||||||
\(907\) | − | 18.3497i | − | 0.609293i | −0.952466 | − | 0.304646i | \(-0.901462\pi\) | ||
0.952466 | − | 0.304646i | \(-0.0985383\pi\) | |||||||
\(908\) | − | 1.35591i | − | 0.0449974i | ||||||
\(909\) | −27.3158 | −0.906007 | ||||||||
\(910\) | −12.0667 | + | 3.30799i | −0.400009 | + | 0.109659i | ||||
\(911\) | 38.8121 | 1.28590 | 0.642951 | − | 0.765908i | \(-0.277710\pi\) | ||||
0.642951 | + | 0.765908i | \(0.277710\pi\) | |||||||
\(912\) | − | 16.2149i | − | 0.536928i | ||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | −4.76076 | −0.157472 | ||||||||
\(915\) | −11.0476 | + | 3.02860i | −0.365222 | + | 0.100122i | ||||
\(916\) | −24.8806 | −0.822077 | ||||||||
\(917\) | 62.5852i | 2.06675i | ||||||||
\(918\) | − | 5.77200i | − | 0.190504i | ||||||
\(919\) | 0.981676 | 0.0323825 | 0.0161912 | − | 0.999869i | \(-0.494846\pi\) | ||||
0.0161912 | + | 0.999869i | \(0.494846\pi\) | |||||||
\(920\) | 4.41514 | + | 16.1054i | 0.145563 | + | 0.530979i | ||||
\(921\) | −31.7170 | −1.04511 | ||||||||
\(922\) | 4.99585i | 0.164529i | ||||||||
\(923\) | − | 65.2340i | − | 2.14720i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −15.9030 | − | 26.8254i | −0.522888 | − | 0.882012i | ||||
\(926\) | 2.98162 | 0.0979822 | ||||||||
\(927\) | 5.77200i | 0.189577i | ||||||||
\(928\) | 7.49708i | 0.246104i | ||||||||
\(929\) | −35.0100 | −1.14864 | −0.574321 | − | 0.818630i | \(-0.694734\pi\) | ||||
−0.574321 | + | 0.818630i | \(0.694734\pi\) | |||||||
\(930\) | −0.608197 | − | 2.21856i | −0.0199436 | − | 0.0727494i | ||||
\(931\) | −18.5840 | −0.609066 | ||||||||
\(932\) | − | 50.9616i | − | 1.66930i | ||||||
\(933\) | 4.64229i | 0.151982i | ||||||||
\(934\) | −5.67522 | −0.185699 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −13.8060 | −0.451263 | ||||||||
\(937\) | − | 30.8555i | − | 1.00801i | −0.863702 | − | 0.504003i | \(-0.831860\pi\) | ||
0.863702 | − | 0.504003i | \(-0.168140\pi\) | |||||||
\(938\) | 9.08060i | 0.296492i | ||||||||
\(939\) | −16.4177 | −0.535770 | ||||||||
\(940\) | −3.92544 | + | 1.07612i | −0.128034 | + | 0.0350993i | ||||
\(941\) | −30.0766 | −0.980469 | −0.490235 | − | 0.871590i | \(-0.663089\pi\) | ||||
−0.490235 | + | 0.871590i | \(0.663089\pi\) | |||||||
\(942\) | − | 0.718574i | − | 0.0234124i | ||||||
\(943\) | 59.6385i | 1.94210i | ||||||||
\(944\) | 1.77472 | 0.0577622 | ||||||||
\(945\) | −9.44468 | − | 34.4520i | −0.307236 | − | 1.12072i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 10.1860i | 0.331002i | 0.986210 | + | 0.165501i | \(0.0529241\pi\) | ||||
−0.986210 | + | 0.165501i | \(0.947076\pi\) | |||||||
\(948\) | − | 5.15569i | − | 0.167449i | ||||||
\(949\) | 44.3415 | 1.43939 | ||||||||
\(950\) | 4.19399 | + | 7.07447i | 0.136071 | + | 0.229526i | ||||
\(951\) | −1.65134 | −0.0535483 | ||||||||
\(952\) | 15.0604i | 0.488112i | ||||||||
\(953\) | 40.1472i | 1.30050i | 0.759722 | + | 0.650248i | \(0.225335\pi\) | ||||
−0.759722 | + | 0.650248i | \(0.774665\pi\) | |||||||
\(954\) | −0.267895 | −0.00867343 | ||||||||
\(955\) | 1.58234 | + | 5.77200i | 0.0512033 | + | 0.186778i | ||||
\(956\) | 9.47874 | 0.306564 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | − | 10.7143i | − | 0.346162i | ||||||
\(959\) | −52.5016 | −1.69537 | ||||||||
\(960\) | −11.4670 | + | 3.14357i | −0.370096 | + | 0.101458i | ||||
\(961\) | −20.3924 | −0.657821 | ||||||||
\(962\) | − | 10.6641i | − | 0.343825i | ||||||
\(963\) | 33.0896i | 1.06630i | ||||||||
\(964\) | 8.88105 | 0.286039 | ||||||||
\(965\) | −0.837223 | + | 0.229517i | −0.0269511 | + | 0.00738840i | ||||
\(966\) | −6.04079 | −0.194359 | ||||||||
\(967\) | 58.0856i | 1.86791i | 0.357395 | + | 0.933953i | \(0.383665\pi\) | ||||
−0.357395 | + | 0.933953i | \(0.616335\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 17.3531 | 0.557462 | ||||||||
\(970\) | −2.19238 | − | 7.99727i | −0.0703930 | − | 0.256777i | ||||
\(971\) | 32.8121 | 1.05299 | 0.526495 | − | 0.850178i | \(-0.323506\pi\) | ||||
0.526495 | + | 0.850178i | \(0.323506\pi\) | |||||||
\(972\) | − | 30.4918i | − | 0.978024i | ||||||
\(973\) | − | 41.1343i | − | 1.31871i | ||||||
\(974\) | −5.00941 | −0.160512 | ||||||||
\(975\) | 21.5455 | − | 12.7729i | 0.690008 | − | 0.409061i | ||||
\(976\) | 17.9182 | 0.573548 | ||||||||
\(977\) | − | 17.9245i | − | 0.573454i | −0.958012 | − | 0.286727i | \(-0.907433\pi\) | ||
0.958012 | − | 0.286727i | \(-0.0925673\pi\) | |||||||
\(978\) | − | 7.12908i | − | 0.227963i | ||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 4.14992 | + | 15.1379i | 0.132564 | + | 0.483563i | ||||
\(981\) | −8.10966 | −0.258922 | ||||||||
\(982\) | 2.19008i | 0.0698882i | ||||||||
\(983\) | 17.0766i | 0.544658i | 0.962204 | + | 0.272329i | \(0.0877939\pi\) | ||||
−0.962204 | + | 0.272329i | \(0.912206\pi\) | |||||||
\(984\) | 12.5471 | 0.399987 | ||||||||
\(985\) | 39.9850 | − | 10.9615i | 1.27403 | − | 0.349263i | ||||
\(986\) | −2.42140 | −0.0771132 | ||||||||
\(987\) | − | 3.02860i | − | 0.0964013i | ||||||
\(988\) | − | 49.3585i | − | 1.57030i | ||||||
\(989\) | −3.48765 | −0.110901 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 17.5551 | 0.557658 | 0.278829 | − | 0.960341i | \(-0.410054\pi\) | ||||
0.278829 | + | 0.960341i | \(0.410054\pi\) | |||||||
\(992\) | 11.9230i | 0.378556i | ||||||||
\(993\) | − | 0.858283i | − | 0.0272368i | ||||||
\(994\) | 13.4614 | 0.426971 | ||||||||
\(995\) | 6.00000 | + | 21.8866i | 0.190213 | + | 0.693851i | ||||
\(996\) | −22.0995 | −0.700249 | ||||||||
\(997\) | − | 15.2047i | − | 0.481537i | −0.970583 | − | 0.240769i | \(-0.922600\pi\) | ||
0.970583 | − | 0.240769i | \(-0.0773995\pi\) | |||||||
\(998\) | − | 2.01906i | − | 0.0639124i | ||||||
\(999\) | 30.4473 | 0.963311 |
(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 | 605.2.b.h.364.5 | ✓ | 12 | |
5.2 | odd | 4 | 3025.2.a.bo.1.7 | 12 | |||
5.3 | odd | 4 | 3025.2.a.bo.1.6 | 12 | |||
5.4 | even | 2 | inner | 605.2.b.h.364.8 | yes | 12 | |
11.2 | odd | 10 | 605.2.j.k.444.7 | 48 | |||
11.3 | even | 5 | 605.2.j.k.9.6 | 48 | |||
11.4 | even | 5 | 605.2.j.k.269.7 | 48 | |||
11.5 | even | 5 | 605.2.j.k.124.8 | 48 | |||
11.6 | odd | 10 | 605.2.j.k.124.6 | 48 | |||
11.7 | odd | 10 | 605.2.j.k.269.5 | 48 | |||
11.8 | odd | 10 | 605.2.j.k.9.8 | 48 | |||
11.9 | even | 5 | 605.2.j.k.444.5 | 48 | |||
11.10 | odd | 2 | inner | 605.2.b.h.364.7 | yes | 12 | |
55.4 | even | 10 | 605.2.j.k.269.6 | 48 | |||
55.9 | even | 10 | 605.2.j.k.444.8 | 48 | |||
55.14 | even | 10 | 605.2.j.k.9.7 | 48 | |||
55.19 | odd | 10 | 605.2.j.k.9.5 | 48 | |||
55.24 | odd | 10 | 605.2.j.k.444.6 | 48 | |||
55.29 | odd | 10 | 605.2.j.k.269.8 | 48 | |||
55.32 | even | 4 | 3025.2.a.bo.1.5 | 12 | |||
55.39 | odd | 10 | 605.2.j.k.124.7 | 48 | |||
55.43 | even | 4 | 3025.2.a.bo.1.8 | 12 | |||
55.49 | even | 10 | 605.2.j.k.124.5 | 48 | |||
55.54 | odd | 2 | inner | 605.2.b.h.364.6 | yes | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
605.2.b.h.364.5 | ✓ | 12 | 1.1 | even | 1 | trivial | |
605.2.b.h.364.6 | yes | 12 | 55.54 | odd | 2 | inner | |
605.2.b.h.364.7 | yes | 12 | 11.10 | odd | 2 | inner | |
605.2.b.h.364.8 | yes | 12 | 5.4 | even | 2 | inner | |
605.2.j.k.9.5 | 48 | 55.19 | odd | 10 | |||
605.2.j.k.9.6 | 48 | 11.3 | even | 5 | |||
605.2.j.k.9.7 | 48 | 55.14 | even | 10 | |||
605.2.j.k.9.8 | 48 | 11.8 | odd | 10 | |||
605.2.j.k.124.5 | 48 | 55.49 | even | 10 | |||
605.2.j.k.124.6 | 48 | 11.6 | odd | 10 | |||
605.2.j.k.124.7 | 48 | 55.39 | odd | 10 | |||
605.2.j.k.124.8 | 48 | 11.5 | even | 5 | |||
605.2.j.k.269.5 | 48 | 11.7 | odd | 10 | |||
605.2.j.k.269.6 | 48 | 55.4 | even | 10 | |||
605.2.j.k.269.7 | 48 | 11.4 | even | 5 | |||
605.2.j.k.269.8 | 48 | 55.29 | odd | 10 | |||
605.2.j.k.444.5 | 48 | 11.9 | even | 5 | |||
605.2.j.k.444.6 | 48 | 55.24 | odd | 10 | |||
605.2.j.k.444.7 | 48 | 11.2 | odd | 10 | |||
605.2.j.k.444.8 | 48 | 55.9 | even | 10 | |||
3025.2.a.bo.1.5 | 12 | 55.32 | even | 4 | |||
3025.2.a.bo.1.6 | 12 | 5.3 | odd | 4 | |||
3025.2.a.bo.1.7 | 12 | 5.2 | odd | 4 | |||
3025.2.a.bo.1.8 | 12 | 55.43 | even | 4 |