Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1368,2,Mod(379,1368)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1368, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1, 0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1368.379");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1368 = 2^{3} \cdot 3^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1368.e (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: | \(10.9235349965\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 379.21 | ||
Character | \(\chi\) | \(=\) | 1368.379 |
Dual form | 1368.2.e.f.379.23 |
$q$-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 \(\left(\mathbb{Z}/1368\mathbb{Z}\right)^\times\).
\(n\) | \(343\) | \(685\) | \(1009\) | \(1217\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(-1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.39298 | − | 0.244153i | 0.984985 | − | 0.172642i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 1.88078 | − | 0.680200i | 0.940389 | − | 0.340100i | ||||
\(5\) | 3.10261i | 1.38753i | 0.720201 | + | 0.693765i | \(0.244049\pi\) | ||||
−0.720201 | + | 0.693765i | \(0.755951\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 4.34495i | 1.64224i | 0.570758 | + | 0.821118i | \(0.306650\pi\) | ||||
−0.570758 | + | 0.821118i | \(0.693350\pi\) | |||||||
\(8\) | 2.45381 | − | 1.40670i | 0.867553 | − | 0.497344i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0.757512 | + | 4.32187i | 0.239546 | + | 1.36670i | ||||
\(11\) | −2.65647 | −0.800957 | −0.400479 | − | 0.916306i | \(-0.631156\pi\) | ||||
−0.400479 | + | 0.916306i | \(0.631156\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −5.10176 | −1.41497 | −0.707486 | − | 0.706727i | \(-0.750171\pi\) | ||||
−0.707486 | + | 0.706727i | \(0.750171\pi\) | |||||||
\(14\) | 1.06083 | + | 6.05242i | 0.283520 | + | 1.61758i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 3.07466 | − | 2.55861i | 0.768664 | − | 0.639653i | ||||
\(17\) | 3.48821 | 0.846016 | 0.423008 | − | 0.906126i | \(-0.360974\pi\) | ||||
0.423008 | + | 0.906126i | \(0.360974\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.86464 | − | 3.93994i | 0.427778 | − | 0.903884i | ||||
\(20\) | 2.11040 | + | 5.83533i | 0.471899 | + | 1.30482i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −3.70041 | + | 0.648586i | −0.788930 | + | 0.138279i | ||||
\(23\) | 5.31965i | 1.10922i | 0.832110 | + | 0.554611i | \(0.187133\pi\) | ||||
−0.832110 | + | 0.554611i | \(0.812867\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.62620 | −0.925240 | ||||||||
\(26\) | −7.10664 | + | 1.24561i | −1.39373 | + | 0.244284i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 2.95543 | + | 8.17189i | 0.558525 | + | 1.54434i | ||||
\(29\) | −7.98077 | −1.48199 | −0.740996 | − | 0.671510i | \(-0.765646\pi\) | ||||
−0.740996 | + | 0.671510i | \(0.765646\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −3.19471 | −0.573787 | −0.286893 | − | 0.957963i | \(-0.592623\pi\) | ||||
−0.286893 | + | 0.957963i | \(0.592623\pi\) | |||||||
\(32\) | 3.65824 | − | 4.31478i | 0.646691 | − | 0.762752i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 4.85901 | − | 0.851658i | 0.833313 | − | 0.146058i | ||||
\(35\) | −13.4807 | −2.27865 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 4.57585 | 0.752265 | 0.376132 | − | 0.926566i | \(-0.377254\pi\) | ||||
0.376132 | + | 0.926566i | \(0.377254\pi\) | |||||||
\(38\) | 1.63546 | − | 5.94351i | 0.265306 | − | 0.964164i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 4.36445 | + | 7.61322i | 0.690080 | + | 1.20376i | ||||
\(41\) | 4.51800i | 0.705593i | 0.935700 | + | 0.352797i | \(0.114769\pi\) | ||||
−0.935700 | + | 0.352797i | \(0.885231\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 6.28467 | 0.958403 | 0.479202 | − | 0.877705i | \(-0.340926\pi\) | ||||
0.479202 | + | 0.877705i | \(0.340926\pi\) | |||||||
\(44\) | −4.99624 | + | 1.80693i | −0.753211 | + | 0.272405i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 1.29881 | + | 7.41015i | 0.191499 | + | 1.09257i | ||||
\(47\) | 7.68246i | 1.12060i | 0.828289 | + | 0.560301i | \(0.189315\pi\) | ||||
−0.828289 | + | 0.560301i | \(0.810685\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −11.8786 | −1.69694 | ||||||||
\(50\) | −6.44419 | + | 1.12950i | −0.911347 | + | 0.159735i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −9.59527 | + | 3.47021i | −1.33062 | + | 0.481232i | ||||
\(53\) | 9.81525 | 1.34823 | 0.674114 | − | 0.738627i | \(-0.264526\pi\) | ||||
0.674114 | + | 0.738627i | \(0.264526\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 8.24201i | − | 1.11135i | ||||||
\(56\) | 6.11205 | + | 10.6617i | 0.816757 | + | 1.42473i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −11.1170 | + | 1.94853i | −1.45974 | + | 0.255854i | ||||
\(59\) | 4.94021i | 0.643161i | 0.946882 | + | 0.321580i | \(0.104214\pi\) | ||||
−0.946882 | + | 0.321580i | \(0.895786\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − | 11.9988i | − | 1.53629i | −0.640274 | − | 0.768146i | \(-0.721179\pi\) | ||
0.640274 | − | 0.768146i | \(-0.278821\pi\) | |||||||
\(62\) | −4.45016 | + | 0.779998i | −0.565171 | + | 0.0990598i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 4.04238 | − | 6.90356i | 0.505298 | − | 0.862945i | ||||
\(65\) | − | 15.8288i | − | 1.96332i | ||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 0.406143i | 0.0496183i | 0.999692 | + | 0.0248092i | \(0.00789781\pi\) | ||||
−0.999692 | + | 0.0248092i | \(0.992102\pi\) | |||||||
\(68\) | 6.56056 | − | 2.37268i | 0.795584 | − | 0.287730i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −18.7783 | + | 3.29135i | −2.24444 | + | 0.393392i | ||||
\(71\) | 2.40885 | 0.285878 | 0.142939 | − | 0.989731i | \(-0.454345\pi\) | ||||
0.142939 | + | 0.989731i | \(0.454345\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 0.373802 | 0.0437502 | 0.0218751 | − | 0.999761i | \(-0.493036\pi\) | ||||
0.0218751 | + | 0.999761i | \(0.493036\pi\) | |||||||
\(74\) | 6.37406 | − | 1.11721i | 0.740969 | − | 0.129873i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0.827031 | − | 8.67848i | 0.0948670 | − | 0.995490i | ||||
\(77\) | − | 11.5422i | − | 1.31536i | ||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 17.2835 | 1.94455 | 0.972273 | − | 0.233850i | \(-0.0751324\pi\) | ||||
0.972273 | + | 0.233850i | \(0.0751324\pi\) | |||||||
\(80\) | 7.93838 | + | 9.53946i | 0.887537 | + | 1.06654i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 1.10308 | + | 6.29348i | 0.121815 | + | 0.694998i | ||||
\(83\) | 12.2894 | 1.34893 | 0.674467 | − | 0.738305i | \(-0.264373\pi\) | ||||
0.674467 | + | 0.738305i | \(0.264373\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 10.8226i | 1.17387i | ||||||||
\(86\) | 8.75441 | − | 1.53442i | 0.944013 | − | 0.165461i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −6.51849 | + | 3.73687i | −0.694873 | + | 0.398351i | ||||
\(89\) | − | 1.95322i | − | 0.207041i | −0.994627 | − | 0.103521i | \(-0.966989\pi\) | ||
0.994627 | − | 0.103521i | \(-0.0330108\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − | 22.1669i | − | 2.32372i | ||||||
\(92\) | 3.61842 | + | 10.0051i | 0.377247 | + | 1.04310i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 1.87570 | + | 10.7015i | 0.193463 | + | 1.10378i | ||||
\(95\) | 12.2241 | + | 5.78526i | 1.25417 | + | 0.593555i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 4.87939i | − | 0.495427i | −0.968833 | − | 0.247713i | \(-0.920321\pi\) | ||
0.968833 | − | 0.247713i | \(-0.0796791\pi\) | |||||||
\(98\) | −16.5466 | + | 2.90019i | −1.67146 | + | 0.292964i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −8.70085 | + | 3.14674i | −0.870085 | + | 0.314674i | ||||
\(101\) | − | 2.87407i | − | 0.285981i | −0.989724 | − | 0.142990i | \(-0.954328\pi\) | ||
0.989724 | − | 0.142990i | \(-0.0456718\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −10.6359 | −1.04799 | −0.523995 | − | 0.851721i | \(-0.675559\pi\) | ||||
−0.523995 | + | 0.851721i | \(0.675559\pi\) | |||||||
\(104\) | −12.5187 | + | 7.17665i | −1.22756 | + | 0.703728i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 13.6724 | − | 2.39642i | 1.32798 | − | 0.232761i | ||||
\(107\) | 10.7564i | 1.03986i | 0.854210 | + | 0.519928i | \(0.174041\pi\) | ||||
−0.854210 | + | 0.519928i | \(0.825959\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 13.0593 | 1.25085 | 0.625425 | − | 0.780284i | \(-0.284926\pi\) | ||||
0.625425 | + | 0.780284i | \(0.284926\pi\) | |||||||
\(110\) | −2.01231 | − | 11.4809i | −0.191866 | − | 1.09466i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 11.1170 | + | 13.3592i | 1.05046 | + | 1.26233i | ||||
\(113\) | 14.9843i | 1.40961i | 0.709402 | + | 0.704804i | \(0.248965\pi\) | ||||
−0.709402 | + | 0.704804i | \(0.751035\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −16.5048 | −1.53908 | ||||||||
\(116\) | −15.0101 | + | 5.42852i | −1.39365 | + | 0.504025i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 1.20617 | + | 6.88161i | 0.111037 | + | 0.633503i | ||||
\(119\) | 15.1561i | 1.38936i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −3.94315 | −0.358468 | ||||||||
\(122\) | −2.92955 | − | 16.7141i | −0.265229 | − | 1.51322i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −6.00854 | + | 2.17304i | −0.539583 | + | 0.195145i | ||||
\(125\) | 1.15976i | 0.103732i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 17.4704 | 1.55025 | 0.775126 | − | 0.631807i | \(-0.217686\pi\) | ||||
0.775126 | + | 0.631807i | \(0.217686\pi\) | |||||||
\(128\) | 3.94542 | − | 10.6035i | 0.348730 | − | 0.937223i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −3.86464 | − | 22.0491i | −0.338951 | − | 1.93384i | ||||
\(131\) | 5.78511 | 0.505447 | 0.252724 | − | 0.967538i | \(-0.418674\pi\) | ||||
0.252724 | + | 0.967538i | \(0.418674\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 17.1188 | + | 8.10177i | 1.48439 | + | 0.702513i | ||||
\(134\) | 0.0991612 | + | 0.565749i | 0.00856622 | + | 0.0488733i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 8.55942 | − | 4.90688i | 0.733964 | − | 0.420761i | ||||
\(137\) | 0.359578 | 0.0307208 | 0.0153604 | − | 0.999882i | \(-0.495110\pi\) | ||||
0.0153604 | + | 0.999882i | \(0.495110\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 2.96772 | 0.251719 | 0.125860 | − | 0.992048i | \(-0.459831\pi\) | ||||
0.125860 | + | 0.992048i | \(0.459831\pi\) | |||||||
\(140\) | −25.3542 | + | 9.16957i | −2.14282 | + | 0.774970i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 3.35548 | − | 0.588129i | 0.281586 | − | 0.0493547i | ||||
\(143\) | 13.5527 | 1.13333 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | − | 24.7612i | − | 2.05631i | ||||||
\(146\) | 0.520698 | − | 0.0912649i | 0.0430933 | − | 0.00755313i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 8.60616 | − | 3.11249i | 0.707422 | − | 0.255845i | ||||
\(149\) | − | 9.69069i | − | 0.793892i | −0.917842 | − | 0.396946i | \(-0.870070\pi\) | ||
0.917842 | − | 0.396946i | \(-0.129930\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −9.32599 | −0.758938 | −0.379469 | − | 0.925204i | \(-0.623893\pi\) | ||||
−0.379469 | + | 0.925204i | \(0.623893\pi\) | |||||||
\(152\) | −0.966841 | − | 12.2909i | −0.0784211 | − | 0.996920i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −2.81808 | − | 16.0781i | −0.227087 | − | 1.29561i | ||||
\(155\) | − | 9.91194i | − | 0.796146i | ||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − | 9.86616i | − | 0.787405i | −0.919238 | − | 0.393703i | \(-0.871194\pi\) | ||
0.919238 | − | 0.393703i | \(-0.128806\pi\) | |||||||
\(158\) | 24.0755 | − | 4.21982i | 1.91535 | − | 0.335711i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 13.3871 | + | 11.3501i | 1.05834 | + | 0.897303i | ||||
\(161\) | −23.1136 | −1.82161 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −1.52311 | −0.119300 | −0.0596498 | − | 0.998219i | \(-0.518998\pi\) | ||||
−0.0596498 | + | 0.998219i | \(0.518998\pi\) | |||||||
\(164\) | 3.07314 | + | 8.49736i | 0.239972 | + | 0.663532i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 17.1188 | − | 3.00049i | 1.32868 | − | 0.232883i | ||||
\(167\) | 2.40885 | 0.186403 | 0.0932013 | − | 0.995647i | \(-0.470290\pi\) | ||||
0.0932013 | + | 0.995647i | \(0.470290\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 13.0279 | 1.00215 | ||||||||
\(170\) | 2.64236 | + | 15.0756i | 0.202660 | + | 1.15625i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 11.8201 | − | 4.27483i | 0.901272 | − | 0.325953i | ||||
\(173\) | −14.6330 | −1.11252 | −0.556261 | − | 0.831007i | \(-0.687765\pi\) | ||||
−0.556261 | + | 0.831007i | \(0.687765\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | − | 20.1006i | − | 1.51946i | ||||||
\(176\) | −8.16774 | + | 6.79688i | −0.615667 | + | 0.512334i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −0.476886 | − | 2.72080i | −0.0357441 | − | 0.203933i | ||||
\(179\) | 4.70734i | 0.351843i | 0.984404 | + | 0.175922i | \(0.0562906\pi\) | ||||
−0.984404 | + | 0.175922i | \(0.943709\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −18.2196 | −1.35425 | −0.677124 | − | 0.735869i | \(-0.736774\pi\) | ||||
−0.677124 | + | 0.735869i | \(0.736774\pi\) | |||||||
\(182\) | −5.41211 | − | 30.8780i | −0.401172 | − | 2.28883i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 7.48315 | + | 13.0534i | 0.551665 | + | 0.962310i | ||||
\(185\) | 14.1971i | 1.04379i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −9.26635 | −0.677623 | ||||||||
\(188\) | 5.22561 | + | 14.4490i | 0.381117 | + | 1.05380i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 18.4404 | + | 5.07419i | 1.33781 | + | 0.368120i | ||||
\(191\) | − | 9.07076i | − | 0.656337i | −0.944619 | − | 0.328169i | \(-0.893569\pi\) | ||
0.944619 | − | 0.328169i | \(-0.106431\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | − | 25.5735i | − | 1.84082i | −0.390953 | − | 0.920411i | \(-0.627855\pi\) | ||
0.390953 | − | 0.920411i | \(-0.372145\pi\) | |||||||
\(194\) | −1.19132 | − | 6.79688i | −0.0855316 | − | 0.487988i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −22.3410 | + | 8.07982i | −1.59579 | + | 0.577130i | ||||
\(197\) | − | 24.0614i | − | 1.71430i | −0.515066 | − | 0.857151i | \(-0.672233\pi\) | ||
0.515066 | − | 0.857151i | \(-0.327767\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 17.3002i | 1.22638i | 0.789936 | + | 0.613189i | \(0.210114\pi\) | ||||
−0.789936 | + | 0.613189i | \(0.789886\pi\) | |||||||
\(200\) | −11.3518 | + | 6.50768i | −0.802695 | + | 0.460163i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −0.701713 | − | 4.00352i | −0.0493724 | − | 0.281687i | ||||
\(203\) | − | 34.6760i | − | 2.43378i | ||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −14.0176 | −0.979032 | ||||||||
\(206\) | −14.8156 | + | 2.59680i | −1.03225 | + | 0.180927i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −15.6861 | + | 13.0534i | −1.08764 | + | 0.905091i | ||||
\(209\) | −4.95337 | + | 10.4663i | −0.342632 | + | 0.723972i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − | 20.2880i | − | 1.39668i | −0.715765 | − | 0.698341i | \(-0.753922\pi\) | ||
0.715765 | − | 0.698341i | \(-0.246078\pi\) | |||||||
\(212\) | 18.4603 | − | 6.67633i | 1.26786 | − | 0.458532i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 2.62620 | + | 14.9834i | 0.179523 | + | 1.02424i | ||||
\(215\) | 19.4989i | 1.32981i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − | 13.8809i | − | 0.942294i | ||||||
\(218\) | 18.1913 | − | 3.18846i | 1.23207 | − | 0.215950i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −5.60621 | − | 15.5014i | −0.377971 | − | 1.04510i | ||||
\(221\) | −17.7960 | −1.19709 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 1.62662 | 0.108927 | 0.0544633 | − | 0.998516i | \(-0.482655\pi\) | ||||
0.0544633 | + | 0.998516i | \(0.482655\pi\) | |||||||
\(224\) | 18.7475 | + | 15.8949i | 1.25262 | + | 1.06202i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 3.65847 | + | 20.8729i | 0.243358 | + | 1.38844i | ||||
\(227\) | 19.8674i | 1.31865i | 0.751860 | + | 0.659323i | \(0.229157\pi\) | ||||
−0.751860 | + | 0.659323i | \(0.770843\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − | 10.8226i | − | 0.715176i | −0.933880 | − | 0.357588i | \(-0.883599\pi\) | ||
0.933880 | − | 0.357588i | \(-0.116401\pi\) | |||||||
\(230\) | −22.9908 | + | 4.02970i | −1.51597 | + | 0.265710i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −19.5833 | + | 11.2266i | −1.28571 | + | 0.737060i | ||||
\(233\) | 23.4732 | 1.53778 | 0.768889 | − | 0.639382i | \(-0.220810\pi\) | ||||
0.768889 | + | 0.639382i | \(0.220810\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −23.8357 | −1.55487 | ||||||||
\(236\) | 3.36033 | + | 9.29144i | 0.218739 | + | 0.604821i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 3.70041 | + | 21.1121i | 0.239862 | + | 1.36850i | ||||
\(239\) | 26.0413i | 1.68447i | 0.539108 | + | 0.842237i | \(0.318761\pi\) | ||||
−0.539108 | + | 0.842237i | \(0.681239\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 14.6931i | 0.946468i | 0.880937 | + | 0.473234i | \(0.156914\pi\) | ||||
−0.880937 | + | 0.473234i | \(0.843086\pi\) | |||||||
\(242\) | −5.49272 | + | 0.962731i | −0.353085 | + | 0.0618867i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −8.16160 | − | 22.5671i | −0.522493 | − | 1.44471i | ||||
\(245\) | − | 36.8547i | − | 2.35456i | ||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −9.51294 | + | 20.1006i | −0.605294 | + | 1.27897i | ||||
\(248\) | −7.83921 | + | 4.49400i | −0.497791 | + | 0.285369i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0.283159 | + | 1.61552i | 0.0179086 | + | 0.102175i | ||||
\(251\) | −9.63290 | −0.608023 | −0.304012 | − | 0.952668i | \(-0.598326\pi\) | ||||
−0.304012 | + | 0.952668i | \(0.598326\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − | 14.1315i | − | 0.888440i | ||||||
\(254\) | 24.3360 | − | 4.26546i | 1.52697 | − | 0.267639i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 2.90702 | − | 15.7337i | 0.181689 | − | 0.983356i | ||||
\(257\) | − | 21.5127i | − | 1.34193i | −0.741491 | − | 0.670963i | \(-0.765881\pi\) | ||
0.741491 | − | 0.670963i | \(-0.234119\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 19.8818i | 1.23540i | ||||||||
\(260\) | −10.7667 | − | 29.7704i | −0.667724 | − | 1.84628i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 8.05853 | − | 1.41245i | 0.497858 | − | 0.0872616i | ||||
\(263\) | − | 3.50520i | − | 0.216140i | −0.994143 | − | 0.108070i | \(-0.965533\pi\) | ||
0.994143 | − | 0.108070i | \(-0.0344670\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 30.4529i | 1.87071i | ||||||||
\(266\) | 25.8242 | + | 7.10598i | 1.58339 | + | 0.435696i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0.276259 | + | 0.763866i | 0.0168752 | + | 0.0466605i | ||||
\(269\) | −3.48912 | −0.212736 | −0.106368 | − | 0.994327i | \(-0.533922\pi\) | ||||
−0.106368 | + | 0.994327i | \(0.533922\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 7.14536i | − | 0.434050i | −0.976166 | − | 0.217025i | \(-0.930365\pi\) | ||
0.976166 | − | 0.217025i | \(-0.0696353\pi\) | |||||||
\(272\) | 10.7251 | − | 8.92498i | 0.650302 | − | 0.541156i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0.500884 | − | 0.0877921i | 0.0302595 | − | 0.00530371i | ||||
\(275\) | 12.2894 | 0.741077 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 5.38097i | 0.323311i | 0.986847 | + | 0.161656i | \(0.0516834\pi\) | ||||
−0.986847 | + | 0.161656i | \(0.948317\pi\) | |||||||
\(278\) | 4.13398 | − | 0.724579i | 0.247939 | − | 0.0434574i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −33.0791 | + | 18.9633i | −1.97685 | + | 1.13327i | ||||
\(281\) | − | 22.9687i | − | 1.37020i | −0.728450 | − | 0.685099i | \(-0.759759\pi\) | ||
0.728450 | − | 0.685099i | \(-0.240241\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −6.19221 | −0.368089 | −0.184044 | − | 0.982918i | \(-0.558919\pi\) | ||||
−0.184044 | + | 0.982918i | \(0.558919\pi\) | |||||||
\(284\) | 4.53052 | − | 1.63850i | 0.268837 | − | 0.0972272i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 18.8786 | − | 3.30893i | 1.11631 | − | 0.195661i | ||||
\(287\) | −19.6305 | −1.15875 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −4.83237 | −0.284257 | ||||||||
\(290\) | −6.04553 | − | 34.4918i | −0.355006 | − | 2.02543i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0.703039 | − | 0.254260i | 0.0411422 | − | 0.0148794i | ||||
\(293\) | −1.32858 | −0.0776166 | −0.0388083 | − | 0.999247i | \(-0.512356\pi\) | ||||
−0.0388083 | + | 0.999247i | \(0.512356\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −15.3276 | −0.892405 | ||||||||
\(296\) | 11.2283 | − | 6.43685i | 0.652630 | − | 0.374134i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −2.36601 | − | 13.4989i | −0.137059 | − | 0.781971i | ||||
\(299\) | − | 27.1395i | − | 1.56952i | ||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 27.3066i | 1.57393i | ||||||||
\(302\) | −12.9909 | + | 2.27697i | −0.747543 | + | 0.131025i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −4.34764 | − | 16.8848i | −0.249354 | − | 0.968412i | ||||
\(305\) | 37.2277 | 2.13165 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 12.4081i | 0.708167i | 0.935214 | + | 0.354084i | \(0.115207\pi\) | ||||
−0.935214 | + | 0.354084i | \(0.884793\pi\) | |||||||
\(308\) | −7.85104 | − | 21.7084i | −0.447354 | − | 1.23695i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −2.42003 | − | 13.8071i | −0.137449 | − | 0.784192i | ||||
\(311\) | 2.11690i | 0.120038i | 0.998197 | + | 0.0600191i | \(0.0191162\pi\) | ||||
−0.998197 | + | 0.0600191i | \(0.980884\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 31.0741 | 1.75641 | 0.878207 | − | 0.478281i | \(-0.158740\pi\) | ||||
0.878207 | + | 0.478281i | \(0.158740\pi\) | |||||||
\(314\) | −2.40885 | − | 13.7433i | −0.135939 | − | 0.775582i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 32.5064 | − | 11.7562i | 1.82863 | − | 0.661340i | ||||
\(317\) | −32.4290 | −1.82139 | −0.910696 | − | 0.413077i | \(-0.864454\pi\) | ||||
−0.910696 | + | 0.413077i | \(0.864454\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 21.2007 | 1.18701 | ||||||||
\(320\) | 21.4191 | + | 12.5419i | 1.19736 | + | 0.701116i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −32.1967 | + | 5.64325i | −1.79425 | + | 0.314486i | ||||
\(323\) | 6.50427 | − | 13.7433i | 0.361907 | − | 0.764700i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 23.6017 | 1.30919 | ||||||||
\(326\) | −2.12167 | + | 0.371873i | −0.117508 | + | 0.0205961i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 6.35548 | + | 11.0863i | 0.350923 | + | 0.612140i | ||||
\(329\) | −33.3799 | −1.84029 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 22.1669i | 1.21840i | 0.793016 | + | 0.609201i | \(0.208510\pi\) | ||||
−0.793016 | + | 0.609201i | \(0.791490\pi\) | |||||||
\(332\) | 23.1136 | − | 8.35923i | 1.26852 | − | 0.458772i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 3.35548 | − | 0.588129i | 0.183604 | − | 0.0321810i | ||||
\(335\) | −1.26011 | −0.0688469 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 9.00147i | 0.490341i | 0.969480 | + | 0.245171i | \(0.0788440\pi\) | ||||
−0.969480 | + | 0.245171i | \(0.921156\pi\) | |||||||
\(338\) | 18.1476 | − | 3.18080i | 0.987099 | − | 0.173013i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 7.36151 | + | 20.3549i | 0.399234 | + | 1.10390i | ||||
\(341\) | 8.48666 | 0.459579 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 21.1972i | − | 1.14454i | ||||||
\(344\) | 15.4214 | − | 8.84066i | 0.831466 | − | 0.476656i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −20.3834 | + | 3.57268i | −1.09582 | + | 0.192068i | ||||
\(347\) | −9.63290 | −0.517121 | −0.258561 | − | 0.965995i | \(-0.583248\pi\) | ||||
−0.258561 | + | 0.965995i | \(0.583248\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 23.0412i | 1.23337i | 0.787210 | + | 0.616685i | \(0.211525\pi\) | ||||
−0.787210 | + | 0.616685i | \(0.788475\pi\) | |||||||
\(350\) | −4.90762 | − | 27.9997i | −0.262323 | − | 1.49665i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −9.71801 | + | 11.4621i | −0.517972 | + | 0.610932i | ||||
\(353\) | 23.8328 | 1.26849 | 0.634245 | − | 0.773132i | \(-0.281311\pi\) | ||||
0.634245 | + | 0.773132i | \(0.281311\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 7.47373i | 0.396665i | ||||||||
\(356\) | −1.32858 | − | 3.67358i | −0.0704148 | − | 0.194699i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 1.14931 | + | 6.55723i | 0.0607430 | + | 0.346560i | ||||
\(359\) | − | 21.8641i | − | 1.15394i | −0.816765 | − | 0.576971i | \(-0.804235\pi\) | ||
0.816765 | − | 0.576971i | \(-0.195765\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −12.0462 | − | 14.6931i | −0.634012 | − | 0.773323i | ||||
\(362\) | −25.3794 | + | 4.44836i | −1.33391 | + | 0.233801i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −15.0779 | − | 41.6910i | −0.790297 | − | 2.18520i | ||||
\(365\) | 1.15976i | 0.0607047i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − | 33.0558i | − | 1.72550i | −0.505630 | − | 0.862751i | \(-0.668740\pi\) | ||
0.505630 | − | 0.862751i | \(-0.331260\pi\) | |||||||
\(368\) | 13.6109 | + | 16.3561i | 0.709517 | + | 0.852620i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 3.46626 | + | 19.7762i | 0.180202 | + | 1.02812i | ||||
\(371\) | 42.6468i | 2.21411i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −9.95803 | −0.515607 | −0.257804 | − | 0.966197i | \(-0.582999\pi\) | ||||
−0.257804 | + | 0.966197i | \(0.582999\pi\) | |||||||
\(374\) | −12.9078 | + | 2.26241i | −0.667448 | + | 0.116986i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 10.8069 | + | 18.8513i | 0.557325 | + | 0.972182i | ||||
\(377\) | 40.7159 | 2.09698 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(380\) | 26.9260 | + | 2.56596i | 1.38127 | + | 0.131631i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −2.21465 | − | 12.6354i | −0.113312 | − | 0.646482i | ||||
\(383\) | −27.1054 | −1.38502 | −0.692510 | − | 0.721409i | \(-0.743495\pi\) | ||||
−0.692510 | + | 0.721409i | \(0.743495\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 35.8111 | 1.82510 | ||||||||
\(386\) | −6.24385 | − | 35.6233i | −0.317804 | − | 1.81318i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −3.31896 | − | 9.17705i | −0.168495 | − | 0.465894i | ||||
\(389\) | − | 30.0380i | − | 1.52299i | −0.648171 | − | 0.761495i | \(-0.724466\pi\) | ||
0.648171 | − | 0.761495i | \(-0.275534\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 18.5561i | 0.938420i | ||||||||
\(392\) | −29.1478 | + | 16.7096i | −1.47219 | + | 0.843964i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −5.87465 | − | 33.5170i | −0.295961 | − | 1.68856i | ||||
\(395\) | 53.6240i | 2.69812i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − | 28.4828i | − | 1.42951i | −0.699373 | − | 0.714756i | \(-0.746538\pi\) | ||
0.699373 | − | 0.714756i | \(-0.253462\pi\) | |||||||
\(398\) | 4.22389 | + | 24.0988i | 0.211725 | + | 1.20796i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −14.2240 | + | 11.8366i | −0.711198 | + | 0.591832i | ||||
\(401\) | − | 5.94834i | − | 0.297046i | −0.988909 | − | 0.148523i | \(-0.952548\pi\) | ||
0.988909 | − | 0.148523i | \(-0.0474519\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 16.2986 | 0.811892 | ||||||||
\(404\) | −1.95494 | − | 5.40549i | −0.0972621 | − | 0.268933i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −8.46626 | − | 48.3030i | −0.420173 | − | 2.39724i | ||||
\(407\) | −12.1556 | −0.602532 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 14.9475i | 0.739105i | 0.929210 | + | 0.369552i | \(0.120489\pi\) | ||||
−0.929210 | + | 0.369552i | \(0.879511\pi\) | |||||||
\(410\) | −19.5262 | + | 3.42244i | −0.964331 | + | 0.169022i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −20.0039 | + | 7.23457i | −0.985519 | + | 0.356422i | ||||
\(413\) | −21.4650 | −1.05622 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 38.1292i | 1.87169i | ||||||||
\(416\) | −18.6634 | + | 22.0129i | −0.915050 | + | 1.07927i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −4.34455 | + | 15.7888i | −0.212499 | + | 0.772254i | ||||
\(419\) | −7.69558 | −0.375954 | −0.187977 | − | 0.982173i | \(-0.560193\pi\) | ||||
−0.187977 | + | 0.982173i | \(0.560193\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 1.48425 | 0.0723379 | 0.0361689 | − | 0.999346i | \(-0.488485\pi\) | ||||
0.0361689 | + | 0.999346i | \(0.488485\pi\) | |||||||
\(422\) | −4.95337 | − | 28.2607i | −0.241126 | − | 1.37571i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 24.0848 | − | 13.8071i | 1.16966 | − | 0.670533i | ||||
\(425\) | −16.1372 | −0.782768 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 52.1343 | 2.52296 | ||||||||
\(428\) | 7.31648 | + | 20.2303i | 0.353655 | + | 0.977870i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 4.76071 | + | 27.1615i | 0.229582 | + | 1.30985i | ||||
\(431\) | 33.1832 | 1.59838 | 0.799189 | − | 0.601080i | \(-0.205263\pi\) | ||||
0.799189 | + | 0.601080i | \(0.205263\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 23.6946i | 1.13869i | 0.822099 | + | 0.569345i | \(0.192803\pi\) | ||||
−0.822099 | + | 0.569345i | \(0.807197\pi\) | |||||||
\(434\) | −3.38905 | − | 19.3357i | −0.162680 | − | 0.928145i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 24.5616 | − | 8.88291i | 1.17629 | − | 0.425414i | ||||
\(437\) | 20.9591 | + | 9.91923i | 1.00261 | + | 0.474501i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −18.8516 | −0.899737 | −0.449869 | − | 0.893095i | \(-0.648529\pi\) | ||||
−0.449869 | + | 0.893095i | \(0.648529\pi\) | |||||||
\(440\) | −11.5940 | − | 20.2243i | −0.552724 | − | 0.964157i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −24.7895 | + | 4.34495i | −1.17911 | + | 0.206668i | ||||
\(443\) | −9.63290 | −0.457673 | −0.228836 | − | 0.973465i | \(-0.573492\pi\) | ||||
−0.228836 | + | 0.973465i | \(0.573492\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 6.06010 | 0.287276 | ||||||||
\(446\) | 2.26585 | − | 0.397145i | 0.107291 | − | 0.0188053i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 29.9956 | + | 17.5639i | 1.41716 | + | 0.829818i | ||||
\(449\) | − | 19.1808i | − | 0.905198i | −0.891714 | − | 0.452599i | \(-0.850497\pi\) | ||
0.891714 | − | 0.452599i | \(-0.149503\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 12.0020i | − | 0.565150i | ||||||
\(452\) | 10.1924 | + | 28.1822i | 0.479408 | + | 1.32558i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 4.85069 | + | 27.6749i | 0.227654 | + | 1.29885i | ||||
\(455\) | 68.7752 | 3.22423 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −21.9894 | −1.02862 | −0.514310 | − | 0.857604i | \(-0.671952\pi\) | ||||
−0.514310 | + | 0.857604i | \(0.671952\pi\) | |||||||
\(458\) | −2.64236 | − | 15.0756i | −0.123470 | − | 0.704437i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −31.0419 | + | 11.2266i | −1.44733 | + | 0.523441i | ||||
\(461\) | − | 13.4851i | − | 0.628064i | −0.949412 | − | 0.314032i | \(-0.898320\pi\) | ||
0.949412 | − | 0.314032i | \(-0.101680\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 0.816179i | − | 0.0379310i | −0.999820 | − | 0.0189655i | \(-0.993963\pi\) | ||
0.999820 | − | 0.0189655i | \(-0.00603727\pi\) | |||||||
\(464\) | −24.5381 | + | 20.4197i | −1.13915 | + | 0.947960i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 32.6976 | − | 5.73105i | 1.51469 | − | 0.265486i | ||||
\(467\) | −41.1881 | −1.90596 | −0.952979 | − | 0.303038i | \(-0.901999\pi\) | ||||
−0.952979 | + | 0.303038i | \(0.901999\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −1.76467 | −0.0814850 | ||||||||
\(470\) | −33.2026 | + | 5.81956i | −1.53152 | + | 0.268436i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 6.94940 | + | 12.1223i | 0.319872 | + | 0.557976i | ||||
\(473\) | −16.6951 | −0.767640 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −8.62620 | + | 18.2269i | −0.395797 | + | 0.836309i | ||||
\(476\) | 10.3092 | + | 28.5053i | 0.472521 | + | 1.30654i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 6.35807 | + | 36.2750i | 0.290811 | + | 1.65918i | ||||
\(479\) | 29.3354i | 1.34037i | 0.742195 | + | 0.670184i | \(0.233785\pi\) | ||||
−0.742195 | + | 0.670184i | \(0.766215\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −23.3449 | −1.06443 | ||||||||
\(482\) | 3.58737 | + | 20.4672i | 0.163400 | + | 0.932257i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −7.41618 | + | 2.68213i | −0.337099 | + | 0.121915i | ||||
\(485\) | 15.1388 | 0.687420 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 31.8174 | 1.44178 | 0.720891 | − | 0.693048i | \(-0.243733\pi\) | ||||
0.720891 | + | 0.693048i | \(0.243733\pi\) | |||||||
\(488\) | −16.8788 | − | 29.4429i | −0.764066 | − | 1.33282i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −8.99818 | − | 51.3378i | −0.406496 | − | 2.31920i | ||||
\(491\) | −2.18431 | −0.0985767 | −0.0492883 | − | 0.998785i | \(-0.515695\pi\) | ||||
−0.0492883 | + | 0.998785i | \(0.515695\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −27.8386 | −1.25379 | ||||||||
\(494\) | −8.34370 | + | 30.3223i | −0.375401 | + | 1.36427i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −9.82263 | + | 8.17402i | −0.441049 | + | 0.367024i | ||||
\(497\) | 10.4663i | 0.469480i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 35.0881 | 1.57076 | 0.785379 | − | 0.619015i | \(-0.212468\pi\) | ||||
0.785379 | + | 0.619015i | \(0.212468\pi\) | |||||||
\(500\) | 0.788870 | + | 2.18126i | 0.0352793 | + | 0.0975487i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −13.4184 | + | 2.35190i | −0.598894 | + | 0.104971i | ||||
\(503\) | − | 11.2681i | − | 0.502418i | −0.967933 | − | 0.251209i | \(-0.919172\pi\) | ||
0.967933 | − | 0.251209i | \(-0.0808282\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 8.91713 | 0.396807 | ||||||||
\(506\) | −3.45025 | − | 19.6849i | −0.153382 | − | 0.875100i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 32.8580 | − | 11.8834i | 1.45784 | − | 0.527240i | ||||
\(509\) | 22.7936 | 1.01031 | 0.505153 | − | 0.863030i | \(-0.331436\pi\) | ||||
0.505153 | + | 0.863030i | \(0.331436\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 1.62415i | 0.0718482i | ||||||||
\(512\) | 0.207989 | − | 22.6265i | 0.00919190 | − | 0.999958i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −5.25240 | − | 29.9668i | −0.231673 | − | 1.32178i | ||||
\(515\) | − | 32.9992i | − | 1.45412i | ||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − | 20.4083i | − | 0.897554i | ||||||
\(518\) | 4.85421 | + | 27.6950i | 0.213282 | + | 1.21685i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −22.2663 | − | 38.8408i | −0.976444 | − | 1.70328i | ||||
\(521\) | − | 41.2795i | − | 1.80849i | −0.427019 | − | 0.904243i | \(-0.640436\pi\) | ||
0.427019 | − | 0.904243i | \(-0.359564\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 22.5730i | 0.987049i | 0.869732 | + | 0.493525i | \(0.164292\pi\) | ||||
−0.869732 | + | 0.493525i | \(0.835708\pi\) | |||||||
\(524\) | 10.8805 | − | 3.93503i | 0.475317 | − | 0.171903i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −0.855805 | − | 4.88267i | −0.0373149 | − | 0.212894i | ||||
\(527\) | −11.1438 | −0.485433 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −5.29862 | −0.230375 | ||||||||
\(530\) | 7.43517 | + | 42.4202i | 0.322963 | + | 1.84262i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 37.7076 | + | 3.59341i | 1.63483 | + | 0.155794i | ||||
\(533\) | − | 23.0497i | − | 0.998395i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −33.3728 | −1.44283 | ||||||||
\(536\) | 0.571323 | + | 0.996599i | 0.0246774 | + | 0.0430465i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −4.86027 | + | 0.851880i | −0.209541 | + | 0.0367271i | ||||
\(539\) | 31.5552 | 1.35918 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 13.0159i | 0.559596i | 0.960059 | + | 0.279798i | \(0.0902675\pi\) | ||||
−0.960059 | + | 0.279798i | \(0.909733\pi\) | |||||||
\(542\) | −1.74456 | − | 9.95333i | −0.0749353 | − | 0.427532i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 12.7607 | − | 15.0509i | 0.547111 | − | 0.645300i | ||||
\(545\) | 40.5178i | 1.73559i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 27.1012i | − | 1.15877i | −0.815056 | − | 0.579383i | \(-0.803294\pi\) | ||
0.815056 | − | 0.579383i | \(-0.196706\pi\) | |||||||
\(548\) | 0.676287 | − | 0.244585i | 0.0288895 | − | 0.0104481i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 17.1188 | − | 3.00049i | 0.729950 | − | 0.127941i | ||||
\(551\) | −14.8813 | + | 31.4437i | −0.633963 | + | 1.33955i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 75.0959i | 3.19340i | ||||||||
\(554\) | 1.31378 | + | 7.49558i | 0.0558172 | + | 0.318457i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 5.58163 | − | 2.01865i | 0.236714 | − | 0.0856097i | ||||
\(557\) | 27.1183i | 1.14904i | 0.818490 | + | 0.574520i | \(0.194811\pi\) | ||||
−0.818490 | + | 0.574520i | \(0.805189\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −32.0629 | −1.35611 | ||||||||
\(560\) | −41.4485 | + | 34.4918i | −1.75152 | + | 1.45755i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −5.60788 | − | 31.9949i | −0.236554 | − | 1.34962i | ||||
\(563\) | − | 4.40370i | − | 0.185594i | −0.995685 | − | 0.0927969i | \(-0.970419\pi\) | ||
0.995685 | − | 0.0927969i | \(-0.0295807\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −46.4906 | −1.95587 | ||||||||
\(566\) | −8.62562 | + | 1.51185i | −0.362562 | + | 0.0635477i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 5.91087 | − | 3.38854i | 0.248015 | − | 0.142180i | ||||
\(569\) | 17.8135i | 0.746781i | 0.927674 | + | 0.373391i | \(0.121805\pi\) | ||||
−0.927674 | + | 0.373391i | \(0.878195\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 27.4219 | 1.14757 | 0.573786 | − | 0.819005i | \(-0.305474\pi\) | ||||
0.573786 | + | 0.819005i | \(0.305474\pi\) | |||||||
\(572\) | 25.4896 | − | 9.21853i | 1.06577 | − | 0.385446i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −27.3449 | + | 4.79284i | −1.14135 | + | 0.200049i | ||||
\(575\) | − | 24.6097i | − | 1.02630i | ||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −28.3651 | −1.18085 | −0.590427 | − | 0.807091i | \(-0.701040\pi\) | ||||
−0.590427 | + | 0.807091i | \(0.701040\pi\) | |||||||
\(578\) | −6.73138 | + | 1.17984i | −0.279989 | + | 0.0490747i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −16.8426 | − | 46.5704i | −0.699350 | − | 1.93373i | ||||
\(581\) | 53.3967i | 2.21527i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −26.0739 | −1.07987 | ||||||||
\(584\) | 0.917239 | − | 0.525828i | 0.0379556 | − | 0.0217589i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −1.85069 | + | 0.324378i | −0.0764512 | + | 0.0133999i | ||||
\(587\) | −2.85480 | −0.117830 | −0.0589150 | − | 0.998263i | \(-0.518764\pi\) | ||||
−0.0589150 | + | 0.998263i | \(0.518764\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −5.95699 | + | 12.5870i | −0.245453 | + | 0.518637i | ||||
\(590\) | −21.3510 | + | 3.74227i | −0.879005 | + | 0.154067i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 14.0692 | − | 11.7078i | 0.578239 | − | 0.481188i | ||||
\(593\) | −14.4737 | −0.594363 | −0.297182 | − | 0.954821i | \(-0.596047\pi\) | ||||
−0.297182 | + | 0.954821i | \(0.596047\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −47.0235 | −1.92778 | ||||||||
\(596\) | −6.59160 | − | 18.2260i | −0.270003 | − | 0.746568i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −6.62620 | − | 37.8048i | −0.270965 | − | 1.54595i | ||||
\(599\) | 3.91727 | 0.160055 | 0.0800277 | − | 0.996793i | \(-0.474499\pi\) | ||||
0.0800277 | + | 0.996793i | \(0.474499\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 0.0549752i | − | 0.00224249i | −0.999999 | − | 0.00112124i | \(-0.999643\pi\) | ||
0.999999 | − | 0.00112124i | \(-0.000356903\pi\) | |||||||
\(602\) | 6.66699 | + | 38.0375i | 0.271726 | + | 1.55029i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −17.5401 | + | 6.34354i | −0.713698 | + | 0.258115i | ||||
\(605\) | − | 12.2340i | − | 0.497385i | ||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 29.9200 | 1.21441 | 0.607207 | − | 0.794544i | \(-0.292290\pi\) | ||||
0.607207 | + | 0.794544i | \(0.292290\pi\) | |||||||
\(608\) | −10.1787 | − | 22.4587i | −0.412799 | − | 0.910822i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 51.8574 | − | 9.08926i | 2.09964 | − | 0.368013i | ||||
\(611\) | − | 39.1940i | − | 1.58562i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 31.5719i | 1.27518i | 0.770377 | + | 0.637589i | \(0.220068\pi\) | ||||
−0.770377 | + | 0.637589i | \(0.779932\pi\) | |||||||
\(614\) | 3.02947 | + | 17.2842i | 0.122260 | + | 0.697534i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −16.2365 | − | 28.3225i | −0.654187 | − | 1.14115i | ||||
\(617\) | 42.9373 | 1.72859 | 0.864295 | − | 0.502985i | \(-0.167765\pi\) | ||||
0.864295 | + | 0.502985i | \(0.167765\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −27.3169 | −1.09796 | −0.548980 | − | 0.835835i | \(-0.684984\pi\) | ||||
−0.548980 | + | 0.835835i | \(0.684984\pi\) | |||||||
\(620\) | −6.74210 | − | 18.6422i | −0.270769 | − | 0.748687i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0.516846 | + | 2.94879i | 0.0207237 | + | 0.118236i | ||||
\(623\) | 8.48666 | 0.340011 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −26.7293 | −1.06917 | ||||||||
\(626\) | 43.2856 | − | 7.58684i | 1.73004 | − | 0.303231i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −6.71096 | − | 18.5561i | −0.267796 | − | 0.740467i | ||||
\(629\) | 15.9615 | 0.636428 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 11.8586i | − | 0.472083i | −0.971743 | − | 0.236042i | \(-0.924150\pi\) | ||
0.971743 | − | 0.236042i | \(-0.0758502\pi\) | |||||||
\(632\) | 42.4104 | − | 24.3127i | 1.68700 | − | 0.967108i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −45.1729 | + | 7.91763i | −1.79404 | + | 0.314449i | ||||
\(635\) | 54.2040i | 2.15102i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 60.6017 | 2.40113 | ||||||||
\(638\) | 29.5321 | − | 5.17622i | 1.16919 | − | 0.204928i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 32.8985 | + | 12.2411i | 1.30043 | + | 0.483873i | ||||
\(641\) | 26.6994i | 1.05456i | 0.849690 | + | 0.527282i | \(0.176789\pi\) | ||||
−0.849690 | + | 0.527282i | \(0.823211\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 35.7711 | 1.41068 | 0.705338 | − | 0.708871i | \(-0.250795\pi\) | ||||
0.705338 | + | 0.708871i | \(0.250795\pi\) | |||||||
\(644\) | −43.4716 | + | 15.7219i | −1.71302 | + | 0.619528i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 5.70482 | − | 20.7322i | 0.224453 | − | 0.815698i | ||||
\(647\) | − | 6.84253i | − | 0.269008i | −0.990913 | − | 0.134504i | \(-0.957056\pi\) | ||
0.990913 | − | 0.134504i | \(-0.0429440\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 13.1235i | − | 0.515144i | ||||||
\(650\) | 32.8767 | − | 5.76243i | 1.28953 | − | 0.226021i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −2.86464 | + | 1.03602i | −0.112188 | + | 0.0405738i | ||||
\(653\) | 10.1996i | 0.399141i | 0.979883 | + | 0.199570i | \(0.0639547\pi\) | ||||
−0.979883 | + | 0.199570i | \(0.936045\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 17.9489i | 0.701323i | ||||||||
\(656\) | 11.5598 | + | 13.8913i | 0.451335 | + | 0.542364i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −46.4975 | + | 8.14981i | −1.81266 | + | 0.317713i | ||||
\(659\) | − | 14.8086i | − | 0.576862i | −0.957501 | − | 0.288431i | \(-0.906866\pi\) | ||
0.957501 | − | 0.288431i | \(-0.0931336\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −8.06062 | −0.313522 | −0.156761 | − | 0.987637i | \(-0.550105\pi\) | ||||
−0.156761 | + | 0.987637i | \(0.550105\pi\) | |||||||
\(662\) | 5.41211 | + | 30.8780i | 0.210348 | + | 1.20011i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 30.1558 | − | 17.2875i | 1.17027 | − | 0.670885i | ||||
\(665\) | −25.1367 | + | 53.1131i | −0.974758 | + | 2.05964i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − | 42.4548i | − | 1.64386i | ||||||
\(668\) | 4.53052 | − | 1.63850i | 0.175291 | − | 0.0633955i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −1.75530 | + | 0.307659i | −0.0678131 | + | 0.0118859i | ||||
\(671\) | 31.8746i | 1.23050i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − | 11.6927i | − | 0.450719i | −0.974276 | − | 0.225359i | \(-0.927644\pi\) | ||
0.974276 | − | 0.225359i | \(-0.0723556\pi\) | |||||||
\(674\) | 2.19774 | + | 12.5388i | 0.0846536 | + | 0.482978i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 24.5026 | − | 8.86158i | 0.942408 | − | 0.340830i | ||||
\(677\) | 7.98077 | 0.306726 | 0.153363 | − | 0.988170i | \(-0.450990\pi\) | ||||
0.153363 | + | 0.988170i | \(0.450990\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 21.2007 | 0.813608 | ||||||||
\(680\) | 15.2241 | + | 26.5566i | 0.583819 | + | 1.01840i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 11.8217 | − | 2.07204i | 0.452678 | − | 0.0793427i | ||||
\(683\) | − | 23.1580i | − | 0.886118i | −0.896493 | − | 0.443059i | \(-0.853893\pi\) | ||
0.896493 | − | 0.443059i | \(-0.146107\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 1.11563i | 0.0426261i | ||||||||
\(686\) | −5.17537 | − | 29.5273i | −0.197597 | − | 1.12736i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 19.3232 | − | 16.0800i | 0.736690 | − | 0.613045i | ||||
\(689\) | −50.0750 | −1.90770 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 11.4446 | 0.435373 | 0.217687 | − | 0.976019i | \(-0.430149\pi\) | ||||
0.217687 | + | 0.976019i | \(0.430149\pi\) | |||||||
\(692\) | −27.5213 | + | 9.95333i | −1.04620 | + | 0.378369i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −13.4184 | + | 2.35190i | −0.509356 | + | 0.0892770i | ||||
\(695\) | 9.20770i | 0.349268i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 15.7598i | 0.596943i | ||||||||
\(698\) | 5.62559 | + | 32.0960i | 0.212932 | + | 1.21485i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −13.6724 | − | 37.8048i | −0.516769 | − | 1.42889i | ||||
\(701\) | 11.4506i | 0.432485i | 0.976340 | + | 0.216242i | \(0.0693801\pi\) | ||||
−0.976340 | + | 0.216242i | \(0.930620\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 8.53231 | − | 18.0286i | 0.321802 | − | 0.679960i | ||||
\(704\) | −10.7385 | + | 18.3391i | −0.404722 | + | 0.691182i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 33.1985 | − | 5.81884i | 1.24944 | − | 0.218995i | ||||
\(707\) | 12.4877 | 0.469648 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − | 45.3623i | − | 1.70362i | −0.523852 | − | 0.851809i | \(-0.675506\pi\) | ||
0.523852 | − | 0.851809i | \(-0.324494\pi\) | |||||||
\(710\) | 1.82473 | + | 10.4108i | 0.0684811 | + | 0.390708i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −2.74760 | − | 4.79284i | −0.102971 | − | 0.179619i | ||||
\(713\) | − | 16.9947i | − | 0.636457i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 42.0487i | 1.57253i | ||||||||
\(716\) | 3.20194 | + | 8.85347i | 0.119662 | + | 0.330870i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −5.33818 | − | 30.4562i | −0.199219 | − | 1.13661i | ||||
\(719\) | − | 12.4081i | − | 0.462744i | −0.972865 | − | 0.231372i | \(-0.925679\pi\) | ||
0.972865 | − | 0.231372i | \(-0.0743214\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | − | 46.2126i | − | 1.72105i | ||||||
\(722\) | −20.3675 | − | 17.5261i | −0.758000 | − | 0.652254i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −34.2669 | + | 12.3929i | −1.27352 | + | 0.460580i | ||||
\(725\) | 36.9206 | 1.37120 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 14.0519i | 0.521156i | 0.965453 | + | 0.260578i | \(0.0839131\pi\) | ||||
−0.965453 | + | 0.260578i | \(0.916087\pi\) | |||||||
\(728\) | −31.1822 | − | 54.3933i | −1.15569 | − | 2.01595i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0.283159 | + | 1.61552i | 0.0104802 | + | 0.0597932i | ||||
\(731\) | 21.9223 | 0.810825 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 19.7323i | 0.728830i | 0.931237 | + | 0.364415i | \(0.118731\pi\) | ||||
−0.931237 | + | 0.364415i | \(0.881269\pi\) | |||||||
\(734\) | −8.07068 | − | 46.0461i | −0.297894 | − | 1.69959i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 22.9531 | + | 19.4605i | 0.846062 | + | 0.717325i | ||||
\(737\) | − | 1.07891i | − | 0.0397421i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 31.2297 | 1.14880 | 0.574402 | − | 0.818574i | \(-0.305235\pi\) | ||||
0.574402 | + | 0.818574i | \(0.305235\pi\) | |||||||
\(740\) | 9.65685 | + | 26.7016i | 0.354993 | + | 0.981569i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 10.4123 | + | 59.4060i | 0.382249 | + | 2.18086i | ||||
\(743\) | −5.06602 | −0.185854 | −0.0929271 | − | 0.995673i | \(-0.529622\pi\) | ||||
−0.0929271 | + | 0.995673i | \(0.529622\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 30.0664 | 1.10155 | ||||||||
\(746\) | −13.8713 | + | 2.43128i | −0.507865 | + | 0.0890156i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −17.4280 | + | 6.30297i | −0.637229 | + | 0.230459i | ||||
\(749\) | −46.7359 | −1.70769 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 4.05958 | 0.148136 | 0.0740680 | − | 0.997253i | \(-0.476402\pi\) | ||||
0.0740680 | + | 0.997253i | \(0.476402\pi\) | |||||||
\(752\) | 19.6564 | + | 23.6209i | 0.716796 | + | 0.861367i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 56.7164 | − | 9.94092i | 2.06549 | − | 0.362027i | ||||
\(755\) | − | 28.9349i | − | 1.05305i | ||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 0.219844i | − | 0.00799035i | −0.999992 | − | 0.00399518i | \(-0.998728\pi\) | ||
0.999992 | − | 0.00399518i | \(-0.00127171\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 38.1338 | − | 2.99973i | 1.38326 | − | 0.108812i | ||||
\(761\) | −30.9704 | −1.12268 | −0.561339 | − | 0.827586i | \(-0.689713\pi\) | ||||
−0.561339 | + | 0.827586i | \(0.689713\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 56.7418i | 2.05419i | ||||||||
\(764\) | −6.16993 | − | 17.0601i | −0.223220 | − | 0.617213i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −37.7572 | + | 6.61786i | −1.36422 | + | 0.239113i | ||||
\(767\) | − | 25.2037i | − | 0.910054i | ||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 27.5770 | 0.994453 | 0.497227 | − | 0.867621i | \(-0.334352\pi\) | ||||
0.497227 | + | 0.867621i | \(0.334352\pi\) | |||||||
\(770\) | 49.8841 | − | 8.74339i | 1.79770 | − | 0.315090i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −17.3951 | − | 48.0981i | −0.626063 | − | 1.73109i | ||||
\(773\) | −17.9758 | −0.646546 | −0.323273 | − | 0.946306i | \(-0.604783\pi\) | ||||
−0.323273 | + | 0.946306i | \(0.604783\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 14.7794 | 0.530890 | ||||||||
\(776\) | −6.86384 | − | 11.9731i | −0.246398 | − | 0.429809i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −7.33388 | − | 41.8424i | −0.262932 | − | 1.50012i | ||||
\(779\) | 17.8006 | + | 8.42445i | 0.637774 | + | 0.301837i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −6.39905 | −0.228976 | ||||||||
\(782\) | 4.53052 | + | 25.8482i | 0.162011 | + | 0.924329i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −36.5226 | + | 30.3927i | −1.30438 | + | 1.08545i | ||||
\(785\) | 30.6109 | 1.09255 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 26.6951i | 0.951577i | 0.879560 | + | 0.475789i | \(0.157837\pi\) | ||||
−0.879560 | + | 0.475789i | \(0.842163\pi\) | |||||||
\(788\) | −16.3665 | − | 45.2541i | −0.583034 | − | 1.61211i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 13.0925 | + | 74.6971i | 0.465809 | + | 2.65760i | ||||
\(791\) | −65.1062 | −2.31491 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 61.2151i | 2.17381i | ||||||||
\(794\) | −6.95417 | − | 39.6760i | −0.246794 | − | 1.40805i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 11.7676 | + | 32.5378i | 0.417091 | + | 1.15327i | ||||
\(797\) | −5.82023 | −0.206163 | −0.103082 | − | 0.994673i | \(-0.532870\pi\) | ||||
−0.103082 | + | 0.994673i | \(0.532870\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 26.7981i | 0.948047i | ||||||||
\(800\) | −16.9237 | + | 19.9610i | −0.598344 | + | 0.705728i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −1.45231 | − | 8.28591i | −0.0512827 | − | 0.292586i | ||||
\(803\) | −0.992995 | −0.0350420 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | − | 71.7125i | − | 2.52753i | ||||||
\(806\) | 22.7036 | − | 3.97936i | 0.799701 | − | 0.140167i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −4.04296 | − | 7.05243i | −0.142231 | − | 0.248104i | ||||
\(809\) | −48.0519 | −1.68942 | −0.844708 | − | 0.535228i | \(-0.820226\pi\) | ||||
−0.844708 | + | 0.535228i | \(0.820226\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 36.8600i | − | 1.29433i | −0.762350 | − | 0.647165i | \(-0.775954\pi\) | ||
0.762350 | − | 0.647165i | \(-0.224046\pi\) | |||||||
\(812\) | −23.5866 | − | 65.2179i | −0.827729 | − | 2.28870i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −16.9325 | + | 2.96783i | −0.593484 | + | 0.104022i | ||||
\(815\) | − | 4.72563i | − | 0.165532i | ||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 11.7187 | − | 24.7612i | 0.409984 | − | 0.866285i | ||||
\(818\) | 3.64947 | + | 20.8215i | 0.127601 | + | 0.728007i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −26.3640 | + | 9.53477i | −0.920671 | + | 0.332969i | ||||
\(821\) | 36.1520i | 1.26171i | 0.775900 | + | 0.630856i | \(0.217296\pi\) | ||||
−0.775900 | + | 0.630856i | \(0.782704\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 15.3874i | 0.536370i | 0.963367 | + | 0.268185i | \(0.0864238\pi\) | ||||
−0.963367 | + | 0.268185i | \(0.913576\pi\) | |||||||
\(824\) | −26.0986 | + | 14.9616i | −0.909188 | + | 0.521212i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −29.9002 | + | 5.24074i | −1.04036 | + | 0.182349i | ||||
\(827\) | − | 1.84666i | − | 0.0642147i | −0.999484 | − | 0.0321073i | \(-0.989778\pi\) | ||
0.999484 | − | 0.0321073i | \(-0.0102218\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −20.3039 | −0.705184 | −0.352592 | − | 0.935777i | \(-0.614700\pi\) | ||||
−0.352592 | + | 0.935777i | \(0.614700\pi\) | |||||||
\(830\) | 9.30935 | + | 53.1131i | 0.323132 | + | 1.84358i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −20.6232 | + | 35.2203i | −0.714982 | + | 1.22104i | ||||
\(833\) | −41.4351 | −1.43564 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 7.47373i | 0.258639i | ||||||||
\(836\) | −2.19699 | + | 23.0542i | −0.0759844 | + | 0.797345i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −10.7198 | + | 1.87890i | −0.370309 | + | 0.0649055i | ||||
\(839\) | 53.7141 | 1.85442 | 0.927208 | − | 0.374546i | \(-0.122201\pi\) | ||||
0.927208 | + | 0.374546i | \(0.122201\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 34.6926 | 1.19630 | ||||||||
\(842\) | 2.06753 | − | 0.362384i | 0.0712517 | − | 0.0124886i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −13.7999 | − | 38.1572i | −0.475011 | − | 1.31342i | ||||
\(845\) | 40.4205i | 1.39051i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 17.1328i | − | 0.588689i | ||||||
\(848\) | 30.1785 | − | 25.1134i | 1.03633 | − | 0.862397i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −22.4787 | + | 3.93994i | −0.771014 | + | 0.135139i | ||||
\(851\) | 24.3419i | 0.834429i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 39.1842i | 1.34164i | 0.741620 | + | 0.670820i | \(0.234058\pi\) | ||||
−0.741620 | + | 0.670820i | \(0.765942\pi\) | |||||||
\(854\) | 72.6220 | − | 12.7288i | 2.48507 | − | 0.435569i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 15.1310 | + | 26.3941i | 0.517167 | + | 0.902131i | ||||
\(857\) | − | 37.5744i | − | 1.28352i | −0.766907 | − | 0.641758i | \(-0.778205\pi\) | ||
0.766907 | − | 0.641758i | \(-0.221795\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −33.0235 | −1.12675 | −0.563374 | − | 0.826202i | \(-0.690497\pi\) | ||||
−0.563374 | + | 0.826202i | \(0.690497\pi\) | |||||||
\(860\) | 13.2631 | + | 36.6731i | 0.452270 | + | 1.25054i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 46.2234 | − | 8.10177i | 1.57438 | − | 0.275947i | ||||
\(863\) | −34.0836 | −1.16022 | −0.580110 | − | 0.814538i | \(-0.696990\pi\) | ||||
−0.580110 | + | 0.814538i | \(0.696990\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | − | 45.4004i | − | 1.54366i | ||||||
\(866\) | 5.78511 | + | 33.0061i | 0.196586 | + | 1.12159i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −9.44176 | − | 26.1068i | −0.320474 | − | 0.886123i | ||||
\(869\) | −45.9132 | −1.55750 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − | 2.07204i | − | 0.0702085i | ||||||
\(872\) | 32.0450 | − | 18.3705i | 1.08518 | − | 0.622103i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 31.6174 | + | 8.70005i | 1.06947 | + | 0.294284i | ||||
\(875\) | −5.03911 | −0.170353 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 20.8395 | 0.703698 | 0.351849 | − | 0.936057i | \(-0.385553\pi\) | ||||
0.351849 | + | 0.936057i | \(0.385553\pi\) | |||||||
\(878\) | −26.2599 | + | 4.60267i | −0.886227 | + | 0.155333i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −21.0881 | − | 25.3413i | −0.710879 | − | 0.854256i | ||||
\(881\) | −4.20737 | −0.141750 | −0.0708749 | − | 0.997485i | \(-0.522579\pi\) | ||||
−0.0708749 | + | 0.997485i | \(0.522579\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 4.68449 | 0.157646 | 0.0788228 | − | 0.996889i | \(-0.474884\pi\) | ||||
0.0788228 | + | 0.996889i | \(0.474884\pi\) | |||||||
\(884\) | −33.4704 | + | 12.1048i | −1.12573 | + | 0.407130i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −13.4184 | + | 2.35190i | −0.450801 | + | 0.0790137i | ||||
\(887\) | −42.8186 | −1.43771 | −0.718854 | − | 0.695161i | \(-0.755333\pi\) | ||||
−0.718854 | + | 0.695161i | \(0.755333\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 75.9082i | 2.54588i | ||||||||
\(890\) | 8.44158 | − | 1.47959i | 0.282963 | − | 0.0495960i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 3.05931 | − | 1.10643i | 0.102433 | − | 0.0370459i | ||||
\(893\) | 30.2684 | + | 14.3250i | 1.01289 | + | 0.479369i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −14.6051 | −0.488193 | ||||||||
\(896\) | 46.0716 | + | 17.1427i | 1.53914 | + | 0.572697i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −4.68305 | − | 26.7185i | −0.156276 | − | 0.891606i | ||||
\(899\) | 25.4962 | 0.850347 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 34.2377 | 1.14062 | ||||||||
\(902\) | −2.93031 | − | 16.7185i | −0.0975688 | − | 0.556664i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 21.0785 | + | 36.7688i | 0.701061 | + | 1.22291i | ||||
\(905\) | − | 56.5282i | − | 1.87906i | ||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − | 56.3357i | − | 1.87060i | −0.353861 | − | 0.935298i | \(-0.615131\pi\) | ||
0.353861 | − | 0.935298i | \(-0.384869\pi\) | |||||||
\(908\) | 13.5138 | + | 37.3662i | 0.448471 | + | 1.24004i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 95.8024 | − | 16.7917i | 3.17582 | − | 0.556639i | ||||
\(911\) | 21.1389 | 0.700363 | 0.350182 | − | 0.936682i | \(-0.386120\pi\) | ||||
0.350182 | + | 0.936682i | \(0.386120\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −32.6464 | −1.08044 | ||||||||
\(914\) | −30.6307 | + | 5.36877i | −1.01317 | + | 0.177583i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −7.36151 | − | 20.3549i | −0.243231 | − | 0.672544i | ||||
\(917\) | 25.1360i | 0.830064i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 27.6142i | − | 0.910910i | −0.890259 | − | 0.455455i | \(-0.849477\pi\) | ||
0.890259 | − | 0.455455i | \(-0.150523\pi\) | |||||||
\(920\) | −40.4996 | + | 23.2173i | −1.33523 | + | 0.765452i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −3.29243 | − | 18.7845i | −0.108430 | − | 0.618633i | ||||
\(923\) | −12.2894 | −0.404510 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −21.1688 | −0.696025 | ||||||||
\(926\) | −0.199272 | − | 1.13692i | −0.00654850 | − | 0.0373615i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −29.1955 | + | 34.4352i | −0.958391 | + | 1.13039i | ||||
\(929\) | 43.2969 | 1.42052 | 0.710262 | − | 0.703937i | \(-0.248576\pi\) | ||||
0.710262 | + | 0.703937i | \(0.248576\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −22.1493 | + | 46.8009i | −0.725914 | + | 1.53384i | ||||
\(932\) | 44.1478 | − | 15.9664i | 1.44611 | − | 0.522998i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −57.3741 | + | 10.0562i | −1.87734 | + | 0.329049i | ||||
\(935\) | − | 28.7499i | − | 0.940222i | ||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 27.8603 | 0.910155 | 0.455078 | − | 0.890452i | \(-0.349611\pi\) | ||||
0.455078 | + | 0.890452i | \(0.349611\pi\) | |||||||
\(938\) | −2.45815 | + | 0.430850i | −0.0802615 | + | 0.0140678i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −44.8297 | + | 16.2130i | −1.46218 | + | 0.528811i | ||||
\(941\) | −3.98575 | −0.129932 | −0.0649658 | − | 0.997887i | \(-0.520694\pi\) | ||||
−0.0649658 | + | 0.997887i | \(0.520694\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −24.0342 | −0.782660 | ||||||||
\(944\) | 12.6401 | + | 15.1894i | 0.411399 | + | 0.494374i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −23.2559 | + | 4.07615i | −0.756114 | + | 0.132527i | ||||
\(947\) | 9.87990 | 0.321053 | 0.160527 | − | 0.987031i | \(-0.448681\pi\) | ||||
0.160527 | + | 0.987031i | \(0.448681\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −1.90705 | −0.0619053 | ||||||||
\(950\) | −7.56595 | + | 27.4958i | −0.245472 | + | 0.892083i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 21.3201 | + | 37.1902i | 0.690989 | + | 1.20534i | ||||
\(953\) | 52.2372i | 1.69213i | 0.533082 | + | 0.846064i | \(0.321034\pi\) | ||||
−0.533082 | + | 0.846064i | \(0.678966\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 28.1431 | 0.910688 | ||||||||
\(956\) | 17.7133 | + | 48.9780i | 0.572889 | + | 1.58406i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 7.16232 | + | 40.8635i | 0.231404 | + | 1.32024i | ||||
\(959\) | 1.56235i | 0.0504509i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −20.7938 | −0.670769 | ||||||||
\(962\) | −32.5189 | + | 5.69972i | −1.04845 | + | 0.183766i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 9.99427 | + | 27.6345i | 0.321894 | + | 0.890049i | ||||
\(965\) | 79.3447 | 2.55419 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 23.4702i | − | 0.754749i | −0.926061 | − | 0.377375i | \(-0.876827\pi\) | ||
0.926061 | − | 0.377375i | \(-0.123173\pi\) | |||||||
\(968\) | −9.67573 | + | 5.54683i | −0.310990 | + | 0.178282i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 21.0881 | − | 3.69620i | 0.677098 | − | 0.118678i | ||||
\(971\) | 23.8446i | 0.765211i | 0.923912 | + | 0.382605i | \(0.124973\pi\) | ||||
−0.923912 | + | 0.382605i | \(0.875027\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 12.8946i | 0.413382i | ||||||||
\(974\) | 44.3209 | − | 7.76831i | 1.42013 | − | 0.248913i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −30.7003 | − | 36.8923i | −0.982694 | − | 1.18089i | ||||
\(977\) | − | 43.5227i | − | 1.39241i | −0.717841 | − | 0.696207i | \(-0.754869\pi\) | ||
0.717841 | − | 0.696207i | \(-0.245131\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 5.18869i | 0.165831i | ||||||||
\(980\) | −25.0685 | − | 69.3155i | −0.800785 | − | 2.21420i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −3.04270 | + | 0.533307i | −0.0970965 | + | 0.0170185i | ||||
\(983\) | −28.1172 | −0.896798 | −0.448399 | − | 0.893834i | \(-0.648006\pi\) | ||||
−0.448399 | + | 0.893834i | \(0.648006\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 74.6531 | 2.37864 | ||||||||
\(986\) | −38.7786 | + | 6.79688i | −1.23496 | + | 0.216457i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −4.21931 | + | 44.2755i | −0.134234 | + | 1.40859i | ||||
\(989\) | 33.4322i | 1.06308i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −37.7810 | −1.20015 | −0.600076 | − | 0.799943i | \(-0.704863\pi\) | ||||
−0.600076 | + | 0.799943i | \(0.704863\pi\) | |||||||
\(992\) | −11.6870 | + | 13.7845i | −0.371063 | + | 0.437657i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 2.55539 | + | 14.5794i | 0.0810520 | + | 0.462430i | ||||
\(995\) | −53.6758 | −1.70164 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 46.5992i | 1.47581i | 0.674904 | + | 0.737906i | \(0.264185\pi\) | ||||
−0.674904 | + | 0.737906i | \(0.735815\pi\) | |||||||
\(998\) | 48.8770 | − | 8.56686i | 1.54717 | − | 0.271179i | ||||
\(999\) | 0 | 0 |
(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 | 1368.2.e.f.379.21 | yes | 24 | |
3.2 | odd | 2 | inner | 1368.2.e.f.379.3 | yes | 24 | |
4.3 | odd | 2 | 5472.2.e.f.5167.4 | 24 | |||
8.3 | odd | 2 | inner | 1368.2.e.f.379.2 | yes | 24 | |
8.5 | even | 2 | 5472.2.e.f.5167.23 | 24 | |||
12.11 | even | 2 | 5472.2.e.f.5167.5 | 24 | |||
19.18 | odd | 2 | inner | 1368.2.e.f.379.4 | yes | 24 | |
24.5 | odd | 2 | 5472.2.e.f.5167.16 | 24 | |||
24.11 | even | 2 | inner | 1368.2.e.f.379.24 | yes | 24 | |
57.56 | even | 2 | inner | 1368.2.e.f.379.22 | yes | 24 | |
76.75 | even | 2 | 5472.2.e.f.5167.24 | 24 | |||
152.37 | odd | 2 | 5472.2.e.f.5167.3 | 24 | |||
152.75 | even | 2 | inner | 1368.2.e.f.379.23 | yes | 24 | |
228.227 | odd | 2 | 5472.2.e.f.5167.15 | 24 | |||
456.227 | odd | 2 | inner | 1368.2.e.f.379.1 | ✓ | 24 | |
456.341 | even | 2 | 5472.2.e.f.5167.6 | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1368.2.e.f.379.1 | ✓ | 24 | 456.227 | odd | 2 | inner | |
1368.2.e.f.379.2 | yes | 24 | 8.3 | odd | 2 | inner | |
1368.2.e.f.379.3 | yes | 24 | 3.2 | odd | 2 | inner | |
1368.2.e.f.379.4 | yes | 24 | 19.18 | odd | 2 | inner | |
1368.2.e.f.379.21 | yes | 24 | 1.1 | even | 1 | trivial | |
1368.2.e.f.379.22 | yes | 24 | 57.56 | even | 2 | inner | |
1368.2.e.f.379.23 | yes | 24 | 152.75 | even | 2 | inner | |
1368.2.e.f.379.24 | yes | 24 | 24.11 | even | 2 | inner | |
5472.2.e.f.5167.3 | 24 | 152.37 | odd | 2 | |||
5472.2.e.f.5167.4 | 24 | 4.3 | odd | 2 | |||
5472.2.e.f.5167.5 | 24 | 12.11 | even | 2 | |||
5472.2.e.f.5167.6 | 24 | 456.341 | even | 2 | |||
5472.2.e.f.5167.15 | 24 | 228.227 | odd | 2 | |||
5472.2.e.f.5167.16 | 24 | 24.5 | odd | 2 | |||
5472.2.e.f.5167.23 | 24 | 8.5 | even | 2 | |||
5472.2.e.f.5167.24 | 24 | 76.75 | even | 2 |