Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [300,2,Mod(109,300)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(300, base_ring=CyclotomicField(10))
chi = DirichletCharacter(H, H._module([0, 0, 7]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("300.109");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 300 = 2^{2} \cdot 3 \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 300.o (of order \(10\), degree \(4\), 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: | \(2.39551206064\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Relative dimension: | \(6\) over \(\Q(\zeta_{10})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{10}]$ |
Embedding invariants
Embedding label | 109.3 | ||
Character | \(\chi\) | \(=\) | 300.109 |
Dual form | 300.2.o.a.289.3 |
$q$-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 \(\left(\mathbb{Z}/300\mathbb{Z}\right)^\times\).
\(n\) | \(101\) | \(151\) | \(277\) |
\(\chi(n)\) | \(1\) | \(1\) | \(e\left(\frac{7}{10}\right)\) |
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 | 0 | ||||||||
\(3\) | −0.951057 | + | 0.309017i | −0.549093 | + | 0.178411i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0.971442 | − | 2.01403i | 0.434442 | − | 0.900700i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − | 1.04684i | − | 0.395667i | −0.980236 | − | 0.197833i | \(-0.936610\pi\) | ||
0.980236 | − | 0.197833i | \(-0.0633905\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0.809017 | − | 0.587785i | 0.269672 | − | 0.195928i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −5.08783 | − | 3.69653i | −1.53404 | − | 1.11454i | −0.953940 | − | 0.299999i | \(-0.903014\pi\) |
−0.580099 | − | 0.814546i | \(-0.696986\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0.591485 | + | 0.814109i | 0.164048 | + | 0.225793i | 0.883125 | − | 0.469137i | \(-0.155435\pi\) |
−0.719077 | + | 0.694931i | \(0.755435\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −0.301528 | + | 2.21564i | −0.0778542 | + | 0.572077i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 4.46202 | + | 1.44980i | 1.08220 | + | 0.351628i | 0.795228 | − | 0.606311i | \(-0.207351\pi\) |
0.286972 | + | 0.957939i | \(0.407351\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.84654 | − | 5.68307i | 0.423626 | − | 1.30379i | −0.480678 | − | 0.876897i | \(-0.659609\pi\) |
0.904304 | − | 0.426889i | \(-0.140391\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0.323490 | + | 0.995600i | 0.0705913 | + | 0.217258i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 4.73227 | − | 6.51341i | 0.986746 | − | 1.35814i | 0.0536312 | − | 0.998561i | \(-0.482920\pi\) |
0.933115 | − | 0.359579i | \(-0.117080\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −3.11260 | − | 3.91302i | −0.622520 | − | 0.782604i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −0.587785 | + | 0.809017i | −0.113119 | + | 0.155695i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −2.13691 | − | 6.57673i | −0.396814 | − | 1.22127i | −0.927540 | − | 0.373725i | \(-0.878080\pi\) |
0.530725 | − | 0.847544i | \(-0.321920\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −2.94312 | + | 9.05799i | −0.528600 | + | 1.62686i | 0.228485 | + | 0.973547i | \(0.426623\pi\) |
−0.757085 | + | 0.653316i | \(0.773377\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 5.98110 | + | 1.94338i | 1.04118 | + | 0.338299i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −2.10835 | − | 1.01694i | −0.356377 | − | 0.171894i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 4.52472 | + | 6.22774i | 0.743859 | + | 1.02383i | 0.998387 | + | 0.0567693i | \(0.0180799\pi\) |
−0.254528 | + | 0.967065i | \(0.581920\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −0.814109 | − | 0.591485i | −0.130362 | − | 0.0947133i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −1.26960 | + | 0.922421i | −0.198279 | + | 0.144058i | −0.682495 | − | 0.730891i | \(-0.739105\pi\) |
0.484216 | + | 0.874949i | \(0.339105\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 9.94897i | 1.51720i | 0.651555 | + | 0.758602i | \(0.274117\pi\) | ||||
−0.651555 | + | 0.758602i | \(0.725883\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −0.397901 | − | 2.20038i | −0.0593156 | − | 0.328013i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −4.60938 | + | 1.49768i | −0.672347 | + | 0.218459i | −0.625242 | − | 0.780431i | \(-0.715000\pi\) |
−0.0471053 | + | 0.998890i | \(0.515000\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 5.90413 | 0.843448 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −4.69165 | −0.656962 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −2.68802 | + | 0.873389i | −0.369227 | + | 0.119969i | −0.487753 | − | 0.872982i | \(-0.662183\pi\) |
0.118525 | + | 0.992951i | \(0.462183\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −12.3874 | + | 6.65606i | −1.67032 | + | 0.897503i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 5.97554i | 0.791479i | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 3.30248 | − | 2.39939i | 0.429946 | − | 0.312374i | −0.351681 | − | 0.936120i | \(-0.614390\pi\) |
0.781627 | + | 0.623746i | \(0.214390\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −2.55692 | − | 1.85771i | −0.327381 | − | 0.237856i | 0.411938 | − | 0.911212i | \(-0.364852\pi\) |
−0.739318 | + | 0.673356i | \(0.764852\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −0.615315 | − | 0.846908i | −0.0775224 | − | 0.106700i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 2.21423 | − | 0.400406i | 0.274641 | − | 0.0496642i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −3.01519 | − | 0.979694i | −0.368364 | − | 0.119689i | 0.118985 | − | 0.992896i | \(-0.462036\pi\) |
−0.487349 | + | 0.873207i | \(0.662036\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −2.48790 | + | 7.65697i | −0.299508 | + | 0.921791i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 2.01138 | + | 6.19039i | 0.238707 | + | 0.734664i | 0.996608 | + | 0.0822947i | \(0.0262249\pi\) |
−0.757901 | + | 0.652369i | \(0.773775\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −0.216191 | + | 0.297561i | −0.0253032 | + | 0.0348269i | −0.821481 | − | 0.570236i | \(-0.806852\pi\) |
0.796178 | + | 0.605063i | \(0.206852\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 4.16945 | + | 2.75966i | 0.481446 | + | 0.318658i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −3.86966 | + | 5.32612i | −0.440988 | + | 0.606968i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 1.02596 | + | 3.15759i | 0.115430 | + | 0.355257i | 0.992036 | − | 0.125951i | \(-0.0401982\pi\) |
−0.876607 | + | 0.481208i | \(0.840198\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0.309017 | − | 0.951057i | 0.0343352 | − | 0.105673i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 13.1796 | + | 4.28231i | 1.44665 | + | 0.470045i | 0.923964 | − | 0.382480i | \(-0.124930\pi\) |
0.522686 | + | 0.852525i | \(0.324930\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 7.25453 | − | 7.57824i | 0.786865 | − | 0.821975i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 4.06465 | + | 5.59450i | 0.435776 | + | 0.599794i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −2.02776 | − | 1.47326i | −0.214942 | − | 0.156165i | 0.475105 | − | 0.879929i | \(-0.342410\pi\) |
−0.690047 | + | 0.723765i | \(0.742410\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0.852238 | − | 0.619187i | 0.0893388 | − | 0.0649085i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | − | 9.52414i | − | 0.987607i | ||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −9.65205 | − | 9.23976i | −0.990279 | − | 0.947980i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 0.173748 | − | 0.0564542i | 0.0176414 | − | 0.00573205i | −0.300183 | − | 0.953882i | \(-0.597048\pi\) |
0.317824 | + | 0.948150i | \(0.397048\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −6.28891 | −0.632059 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −5.96970 | −0.594008 | −0.297004 | − | 0.954876i | \(-0.595987\pi\) | ||||
−0.297004 | + | 0.954876i | \(0.595987\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 8.52017 | − | 2.76837i | 0.839517 | − | 0.272776i | 0.142468 | − | 0.989799i | \(-0.454496\pi\) |
0.697049 | + | 0.717024i | \(0.254496\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 2.31942 | + | 0.315651i | 0.226352 | + | 0.0308043i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 2.69495i | 0.260530i | 0.991479 | + | 0.130265i | \(0.0415829\pi\) | ||||
−0.991479 | + | 0.130265i | \(0.958417\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 8.33278 | − | 6.05412i | 0.798135 | − | 0.579879i | −0.112231 | − | 0.993682i | \(-0.535800\pi\) |
0.910366 | + | 0.413803i | \(0.135800\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −6.22774 | − | 4.52472i | −0.591111 | − | 0.429467i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 1.98712 | + | 2.73504i | 0.186933 | + | 0.257291i | 0.892190 | − | 0.451661i | \(-0.149168\pi\) |
−0.705257 | + | 0.708952i | \(0.749168\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −8.52105 | − | 15.8583i | −0.794592 | − | 1.47879i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0.957042 | + | 0.310962i | 0.0884786 | + | 0.0287484i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 1.51770 | − | 4.67101i | 0.139128 | − | 0.428191i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 8.82254 | + | 27.1530i | 0.802049 | + | 2.46845i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0.922421 | − | 1.26960i | 0.0831719 | − | 0.114476i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −10.9046 | + | 2.46759i | −0.975340 | + | 0.220708i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 3.51155 | − | 4.83324i | 0.311600 | − | 0.428881i | −0.624279 | − | 0.781201i | \(-0.714607\pi\) |
0.935879 | + | 0.352321i | \(0.114607\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −3.07440 | − | 9.46203i | −0.270686 | − | 0.833085i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 1.91817 | − | 5.90352i | 0.167591 | − | 0.515793i | −0.831627 | − | 0.555335i | \(-0.812590\pi\) |
0.999218 | + | 0.0395422i | \(0.0125900\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −5.94925 | − | 1.93303i | −0.515865 | − | 0.167615i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 1.05838 | + | 1.96973i | 0.0910910 | + | 0.169527i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 7.62811 | + | 10.4992i | 0.651714 | + | 0.897007i | 0.999172 | − | 0.0406885i | \(-0.0129551\pi\) |
−0.347458 | + | 0.937695i | \(0.612955\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 3.23564 | + | 2.35083i | 0.274444 | + | 0.199395i | 0.716490 | − | 0.697597i | \(-0.245747\pi\) |
−0.442047 | + | 0.896992i | \(0.645747\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 3.92097 | − | 2.84875i | 0.330205 | − | 0.239908i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − | 6.32849i | − | 0.529215i | ||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −15.3216 | − | 2.08512i | −1.27239 | − | 0.173160i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −5.61517 | + | 1.82448i | −0.463131 | + | 0.150480i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −5.68762 | −0.465948 | −0.232974 | − | 0.972483i | \(-0.574846\pi\) | ||||
−0.232974 | + | 0.972483i | \(0.574846\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −5.51150 | −0.448519 | −0.224260 | − | 0.974529i | \(-0.571996\pi\) | ||||
−0.224260 | + | 0.974529i | \(0.571996\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 4.46202 | − | 1.44980i | 0.360733 | − | 0.117209i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 15.3840 | + | 14.7268i | 1.23567 | + | 1.18289i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − | 17.0217i | − | 1.35848i | −0.733915 | − | 0.679242i | \(-0.762309\pi\) | ||
0.733915 | − | 0.679242i | \(-0.237691\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 2.28656 | − | 1.66129i | 0.181336 | − | 0.131748i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −6.81847 | − | 4.95391i | −0.537371 | − | 0.390423i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −7.22726 | − | 9.94747i | −0.566083 | − | 0.779146i | 0.426001 | − | 0.904723i | \(-0.359922\pi\) |
−0.992084 | + | 0.125576i | \(0.959922\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 9.72431 | − | 10.1582i | 0.757037 | − | 0.790816i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 5.16289 | + | 1.67752i | 0.399516 | + | 0.129811i | 0.501882 | − | 0.864936i | \(-0.332641\pi\) |
−0.102366 | + | 0.994747i | \(0.532641\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 3.70430 | − | 11.4007i | 0.284946 | − | 0.876975i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −1.84654 | − | 5.68307i | −0.141209 | − | 0.434596i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 6.31611 | − | 8.69337i | 0.480205 | − | 0.660945i | −0.498340 | − | 0.866982i | \(-0.666057\pi\) |
0.978544 | + | 0.206037i | \(0.0660567\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −4.09629 | + | 3.25838i | −0.309650 | + | 0.246310i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −2.39939 | + | 3.30248i | −0.180349 | + | 0.248230i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 5.96596 | + | 18.3613i | 0.445917 | + | 1.37239i | 0.881476 | + | 0.472230i | \(0.156551\pi\) |
−0.435559 | + | 0.900160i | \(0.643449\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 5.17642 | − | 15.9314i | 0.384760 | − | 1.18417i | −0.551894 | − | 0.833914i | \(-0.686095\pi\) |
0.936654 | − | 0.350255i | \(-0.113905\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 3.00585 | + | 0.976658i | 0.222198 | + | 0.0721967i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 16.9383 | − | 3.06301i | 1.24533 | − | 0.225197i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −17.3428 | − | 23.8703i | −1.26823 | − | 1.74557i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0.846908 | + | 0.615315i | 0.0616035 | + | 0.0447576i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 9.66400 | − | 7.02131i | 0.699263 | − | 0.508044i | −0.180429 | − | 0.983588i | \(-0.557749\pi\) |
0.879692 | + | 0.475544i | \(0.157749\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 26.4298i | 1.90246i | 0.308485 | + | 0.951229i | \(0.400178\pi\) | ||||
−0.308485 | + | 0.951229i | \(0.599822\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −1.98212 | + | 1.06504i | −0.141943 | + | 0.0762693i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −10.5299 | + | 3.42138i | −0.750225 | + | 0.243763i | −0.659078 | − | 0.752074i | \(-0.729053\pi\) |
−0.0911471 | + | 0.995837i | \(0.529053\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 16.5548 | 1.17354 | 0.586768 | − | 0.809755i | \(-0.300400\pi\) | ||||
0.586768 | + | 0.809755i | \(0.300400\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 3.17036 | 0.223620 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −6.88476 | + | 2.23699i | −0.483215 | + | 0.157006i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0.624434 | + | 3.45309i | 0.0436123 | + | 0.241175i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | − | 8.05101i | − | 0.559584i | ||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −30.4025 | + | 22.0887i | −2.10299 | + | 1.52791i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 3.32274 | + | 2.41411i | 0.228747 | + | 0.166194i | 0.696255 | − | 0.717794i | \(-0.254848\pi\) |
−0.467508 | + | 0.883989i | \(0.654848\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −3.82587 | − | 5.26586i | −0.262144 | − | 0.360811i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 20.0375 | + | 9.66485i | 1.36654 | + | 0.659137i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 9.48223 | + | 3.08096i | 0.643696 | + | 0.209149i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0.113658 | − | 0.349804i | 0.00768032 | − | 0.0236376i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 1.45892 | + | 4.49011i | 0.0981379 | + | 0.302037i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −3.68040 | + | 5.06564i | −0.246458 | + | 0.339220i | −0.914267 | − | 0.405113i | \(-0.867232\pi\) |
0.667809 | + | 0.744333i | \(0.267232\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −4.81816 | − | 1.33616i | −0.321211 | − | 0.0890772i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 6.16101 | − | 8.47990i | 0.408921 | − | 0.562831i | −0.554034 | − | 0.832494i | \(-0.686912\pi\) |
0.962955 | + | 0.269663i | \(0.0869123\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −2.33827 | − | 7.19645i | −0.154517 | − | 0.475555i | 0.843595 | − | 0.536981i | \(-0.180435\pi\) |
−0.998112 | + | 0.0614260i | \(0.980435\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 2.03440 | − | 6.26123i | 0.133854 | − | 0.411959i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −15.2009 | − | 4.93908i | −0.995846 | − | 0.323570i | −0.234642 | − | 0.972082i | \(-0.575392\pi\) |
−0.761204 | + | 0.648512i | \(0.775392\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −1.46138 | + | 10.7383i | −0.0953301 | + | 0.700491i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −1.95150 | − | 2.68601i | −0.126763 | − | 0.174475i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −2.36231 | − | 1.71632i | −0.152805 | − | 0.111019i | 0.508756 | − | 0.860911i | \(-0.330106\pi\) |
−0.661561 | + | 0.749892i | \(0.730106\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 18.6460 | − | 13.5471i | 1.20109 | − | 0.872644i | 0.206700 | − | 0.978404i | \(-0.433728\pi\) |
0.994392 | + | 0.105760i | \(0.0337277\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1.00000i | 0.0641500i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 5.73553 | − | 11.8911i | 0.366429 | − | 0.759693i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 5.71884 | − | 1.85816i | 0.363881 | − | 0.118232i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −13.8579 | −0.878206 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −9.79130 | −0.618021 | −0.309011 | − | 0.951059i | \(-0.599998\pi\) | ||||
−0.309011 | + | 0.951059i | \(0.599998\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −48.1540 | + | 15.6462i | −3.02741 | + | 0.983666i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −4.55767 | + | 9.44911i | −0.285412 | + | 0.591726i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 22.3147i | 1.39195i | 0.718066 | + | 0.695975i | \(0.245027\pi\) | ||||
−0.718066 | + | 0.695975i | \(0.754973\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 6.51943 | − | 4.73664i | 0.405097 | − | 0.294320i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −5.59450 | − | 4.06465i | −0.346291 | − | 0.251595i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −0.428586 | − | 0.589898i | −0.0264277 | − | 0.0363747i | 0.795599 | − | 0.605824i | \(-0.207156\pi\) |
−0.822026 | + | 0.569449i | \(0.807156\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −0.852223 | + | 6.26218i | −0.0523517 | + | 0.384683i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 2.38378 | + | 0.774536i | 0.145885 | + | 0.0474008i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 0.574531 | − | 1.76822i | 0.0350298 | − | 0.107811i | −0.932013 | − | 0.362425i | \(-0.881949\pi\) |
0.967043 | + | 0.254615i | \(0.0819487\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 6.04232 | + | 18.5964i | 0.367045 | + | 1.12965i | 0.948691 | + | 0.316206i | \(0.102409\pi\) |
−0.581646 | + | 0.813442i | \(0.697591\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −0.619187 | + | 0.852238i | −0.0374749 | + | 0.0515798i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 1.37181 | + | 31.4146i | 0.0827232 | + | 1.89437i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 9.96956 | − | 13.7219i | 0.599013 | − | 0.824471i | −0.396604 | − | 0.917990i | \(-0.629812\pi\) |
0.995618 | + | 0.0935189i | \(0.0298115\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 2.94312 | + | 9.05799i | 0.176200 | + | 0.542288i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −8.06159 | + | 24.8110i | −0.480914 | + | 1.48010i | 0.356898 | + | 0.934143i | \(0.383834\pi\) |
−0.837812 | + | 0.545958i | \(0.816166\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 24.3559 | + | 7.91372i | 1.44781 | + | 0.470422i | 0.924323 | − | 0.381611i | \(-0.124631\pi\) |
0.523487 | + | 0.852033i | \(0.324631\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 12.0349 | + | 5.80489i | 0.712885 | + | 0.343852i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0.965624 | + | 1.32907i | 0.0569990 | + | 0.0784524i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 4.05446 | + | 2.94573i | 0.238497 | + | 0.173279i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −0.147799 | + | 0.107382i | −0.00866412 | + | 0.00629485i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 27.7845i | 1.62319i | 0.584220 | + | 0.811595i | \(0.301400\pi\) | ||||
−0.584220 | + | 0.811595i | \(0.698600\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −1.62427 | − | 8.98215i | −0.0945686 | − | 0.522961i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 5.98110 | − | 1.94338i | 0.347059 | − | 0.112766i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 8.10169 | 0.468533 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 10.4149 | 0.600307 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 5.67753 | − | 1.84474i | 0.326165 | − | 0.105978i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −6.22539 | + | 3.34505i | −0.356465 | + | 0.191537i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 16.1422i | − | 0.921283i | −0.887586 | − | 0.460642i | \(-0.847619\pi\) | ||
0.887586 | − | 0.460642i | \(-0.152381\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −7.24769 | + | 5.26575i | −0.412307 | + | 0.299558i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −23.2496 | − | 16.8918i | −1.31837 | − | 0.957849i | −0.999951 | − | 0.00989736i | \(-0.996850\pi\) |
−0.318415 | − | 0.947951i | \(-0.603150\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −15.5683 | − | 21.4279i | −0.879973 | − | 1.21118i | −0.976428 | − | 0.215841i | \(-0.930751\pi\) |
0.0964557 | − | 0.995337i | \(-0.469249\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −2.30344 | + | 0.416538i | −0.129784 | + | 0.0234692i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −25.0109 | − | 8.12654i | −1.40475 | − | 0.456432i | −0.494028 | − | 0.869446i | \(-0.664476\pi\) |
−0.910725 | + | 0.413014i | \(0.864476\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −13.4388 | + | 41.3605i | −0.752430 | + | 2.31574i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −0.832784 | − | 2.56305i | −0.0464815 | − | 0.143055i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 16.4786 | − | 22.6809i | 0.916896 | − | 1.26200i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 1.34457 | − | 4.84849i | 0.0745832 | − | 0.268946i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −6.05412 | + | 8.33278i | −0.334793 | + | 0.460804i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 1.56782 | + | 4.82526i | 0.0864369 | + | 0.266025i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −9.66091 | + | 29.7332i | −0.531012 | + | 1.63429i | 0.221101 | + | 0.975251i | \(0.429035\pi\) |
−0.752113 | + | 0.659035i | \(0.770965\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 7.32115 | + | 2.37879i | 0.401197 | + | 0.130357i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −4.90221 | + | 5.12095i | −0.267836 | + | 0.279787i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 5.23438 | + | 7.20451i | 0.285135 | + | 0.392455i | 0.927426 | − | 0.374006i | \(-0.122016\pi\) |
−0.642291 | + | 0.766461i | \(0.722016\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −2.73504 | − | 1.98712i | −0.148547 | − | 0.107926i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 48.4572 | − | 35.2062i | 2.62410 | − | 1.90652i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 13.5085i | − | 0.729391i | ||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 13.0045 | + | 12.4490i | 0.700138 | + | 0.670232i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 20.4981 | − | 6.66023i | 1.10039 | − | 0.357540i | 0.298140 | − | 0.954522i | \(-0.403634\pi\) |
0.802255 | + | 0.596982i | \(0.203634\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −17.3958 | −0.931178 | −0.465589 | − | 0.885001i | \(-0.654158\pi\) | ||||
−0.465589 | + | 0.885001i | \(0.654158\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −1.00629 | −0.0537120 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −16.9871 | + | 5.51945i | −0.904133 | + | 0.293770i | −0.723942 | − | 0.689861i | \(-0.757672\pi\) |
−0.180191 | + | 0.983632i | \(0.557672\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 14.4215 | + | 1.96264i | 0.765416 | + | 0.104166i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 4.91139i | 0.259938i | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 2.95995 | − | 2.15053i | 0.156220 | − | 0.113501i | −0.506929 | − | 0.861988i | \(-0.669219\pi\) |
0.663149 | + | 0.748487i | \(0.269219\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −13.5163 | − | 9.82016i | −0.711384 | − | 0.516851i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −16.7815 | − | 23.0977i | −0.880798 | − | 1.21232i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0.389279 | + | 0.724478i | 0.0203758 | + | 0.0379209i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −24.7677 | − | 8.04751i | −1.29286 | − | 0.420077i | −0.419770 | − | 0.907631i | \(-0.637889\pi\) |
−0.873093 | + | 0.487554i | \(0.837889\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −0.484946 | + | 1.49251i | −0.0252453 | + | 0.0776969i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0.914295 | + | 2.81391i | 0.0474678 | + | 0.146091i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −17.1991 | + | 23.6726i | −0.890538 | + | 1.22572i | 0.0828510 | + | 0.996562i | \(0.473597\pi\) |
−0.973389 | + | 0.229159i | \(0.926403\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 9.60840 | − | 5.71653i | 0.496175 | − | 0.295200i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 4.09023 | − | 5.62971i | 0.210657 | − | 0.289945i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 3.17264 | + | 9.76437i | 0.162967 | + | 0.501562i | 0.998881 | − | 0.0472993i | \(-0.0150614\pi\) |
−0.835913 | + | 0.548861i | \(0.815061\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −1.84613 | + | 5.68181i | −0.0945803 | + | 0.291088i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −24.3926 | − | 7.92564i | −1.24640 | − | 0.404981i | −0.389773 | − | 0.920911i | \(-0.627446\pi\) |
−0.856631 | + | 0.515930i | \(0.827446\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 6.96781 | + | 12.9676i | 0.355112 | + | 0.660891i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 5.84786 | + | 8.04888i | 0.297263 | + | 0.409148i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −7.75696 | − | 5.63576i | −0.393293 | − | 0.285744i | 0.373510 | − | 0.927626i | \(-0.378154\pi\) |
−0.766804 | + | 0.641882i | \(0.778154\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 30.5586 | − | 22.2021i | 1.54542 | − | 1.12281i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 6.20733i | 0.313118i | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 7.35614 | + | 1.00110i | 0.370127 | + | 0.0503708i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −11.7274 | + | 3.81045i | −0.588580 | + | 0.191241i | −0.588140 | − | 0.808759i | \(-0.700140\pi\) |
−0.000439093 | 1.00000i | \(0.500140\pi\) | ||||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 6.25541 | 0.313162 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 18.9779 | 0.947709 | 0.473855 | − | 0.880603i | \(-0.342862\pi\) | ||||
0.473855 | + | 0.880603i | \(0.342862\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −9.11500 | + | 2.96164i | −0.454051 | + | 0.147530i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −1.61526 | − | 1.54626i | −0.0802629 | − | 0.0768345i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 48.4115i | − | 2.39967i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 15.7841 | − | 11.4678i | 0.780474 | − | 0.567048i | −0.124647 | − | 0.992201i | \(-0.539780\pi\) |
0.905121 | + | 0.425154i | \(0.139780\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −10.4992 | − | 7.62811i | −0.517887 | − | 0.376267i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −2.51177 | − | 3.45715i | −0.123596 | − | 0.170115i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 21.4279 | − | 22.3840i | 1.05185 | − | 1.09879i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −3.80373 | − | 1.23591i | −0.186269 | − | 0.0605226i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −0.571420 | + | 1.75865i | −0.0279157 | + | 0.0859156i | −0.964044 | − | 0.265744i | \(-0.914382\pi\) |
0.936128 | + | 0.351659i | \(0.114382\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −2.06347 | − | 6.35070i | −0.100567 | − | 0.309514i | 0.888097 | − | 0.459656i | \(-0.152027\pi\) |
−0.988665 | + | 0.150141i | \(0.952027\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −2.84875 | + | 3.92097i | −0.138511 | + | 0.190644i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −8.21540 | − | 21.9726i | −0.398506 | − | 1.06583i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −1.94472 | + | 2.67668i | −0.0941117 | + | 0.129534i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 1.95561 | + | 6.01875i | 0.0944177 | + | 0.290588i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 9.16108 | − | 28.1949i | 0.441274 | − | 1.35810i | −0.445245 | − | 0.895409i | \(-0.646884\pi\) |
0.886519 | − | 0.462692i | \(-0.153116\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 26.6465 | + | 8.65798i | 1.28055 | + | 0.416076i | 0.868774 | − | 0.495209i | \(-0.164909\pi\) |
0.411776 | + | 0.911285i | \(0.364909\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 15.2160 | − | 2.75156i | 0.729553 | − | 0.131927i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −28.2778 | − | 38.9211i | −1.35271 | − | 1.86185i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 8.27205 | + | 6.01000i | 0.394803 | + | 0.286842i | 0.767421 | − | 0.641143i | \(-0.221540\pi\) |
−0.372618 | + | 0.927985i | \(0.621540\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 4.77655 | − | 3.47036i | 0.227455 | − | 0.165255i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 26.5115i | 1.25960i | 0.776757 | + | 0.629800i | \(0.216863\pi\) | ||||
−0.776757 | + | 0.629800i | \(0.783137\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −4.93703 | + | 2.65278i | −0.234038 | + | 0.125754i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 5.40925 | − | 1.75757i | 0.255849 | − | 0.0831303i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 6.39692 | 0.301889 | 0.150945 | − | 0.988542i | \(-0.451768\pi\) | ||||
0.150945 | + | 0.988542i | \(0.451768\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 9.86929 | 0.464727 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 5.24175 | − | 1.70315i | 0.246279 | − | 0.0800208i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −0.419159 | − | 2.31793i | −0.0196505 | − | 0.108666i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 14.9784i | 0.700661i | 0.936626 | + | 0.350330i | \(0.113931\pi\) | ||||
−0.936626 | + | 0.350330i | \(0.886069\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −3.79562 | + | 2.75768i | −0.177165 | + | 0.128718i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 9.85643 | + | 7.16112i | 0.459060 | + | 0.333526i | 0.793162 | − | 0.609010i | \(-0.208433\pi\) |
−0.334103 | + | 0.942537i | \(0.608433\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −4.89012 | − | 6.73067i | −0.227263 | − | 0.312801i | 0.680124 | − | 0.733097i | \(-0.261926\pi\) |
−0.907387 | + | 0.420297i | \(0.861926\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −19.1819 | − | 9.25215i | −0.889537 | − | 0.429058i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 7.89818 | + | 2.56627i | 0.365484 | + | 0.118753i | 0.486001 | − | 0.873958i | \(-0.338455\pi\) |
−0.120517 | + | 0.992711i | \(0.538455\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −1.02558 | + | 3.15641i | −0.0473568 | + | 0.145749i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 5.26001 | + | 16.1886i | 0.242368 | + | 0.745933i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 36.7766 | − | 50.6187i | 1.69099 | − | 2.32745i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −27.9855 | + | 10.4636i | −1.28406 | + | 0.480102i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −1.66129 | + | 2.28656i | −0.0760650 | + | 0.104695i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 0.944475 | + | 2.90680i | 0.0431542 | + | 0.132815i | 0.970312 | − | 0.241855i | \(-0.0777559\pi\) |
−0.927158 | + | 0.374670i | \(0.877756\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −2.39376 | + | 7.36723i | −0.109146 | + | 0.335917i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 8.01559 | + | 2.60442i | 0.364722 | + | 0.118505i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0.0550860 | − | 0.404775i | 0.00250133 | − | 0.0183799i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −6.88809 | − | 9.48064i | −0.312129 | − | 0.429609i | 0.623915 | − | 0.781492i | \(-0.285541\pi\) |
−0.936044 | + | 0.351884i | \(0.885541\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 9.94747 | + | 7.22726i | 0.449840 | + | 0.326828i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −13.7147 | + | 9.96433i | −0.618937 | + | 0.449684i | −0.852550 | − | 0.522646i | \(-0.824945\pi\) |
0.233613 | + | 0.972330i | \(0.424945\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − | 32.4436i | − | 1.46119i | ||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −6.10931 | + | 12.6660i | −0.274593 | + | 0.569295i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 6.48032 | − | 2.10558i | 0.290682 | − | 0.0944484i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −14.0674 | −0.629742 | −0.314871 | − | 0.949135i | \(-0.601961\pi\) | ||||
−0.314871 | + | 0.949135i | \(0.601961\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −5.42858 | −0.242531 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −5.33310 | + | 1.73283i | −0.237791 | + | 0.0772630i | −0.425488 | − | 0.904964i | \(-0.639898\pi\) |
0.187697 | + | 0.982227i | \(0.439898\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −5.79922 | + | 12.0231i | −0.258062 | + | 0.535023i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 11.9874i | 0.532378i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −9.27535 | + | 6.73894i | −0.411123 | + | 0.298698i | −0.774056 | − | 0.633117i | \(-0.781775\pi\) |
0.362933 | + | 0.931815i | \(0.381775\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0.311498 | + | 0.226317i | 0.0137799 | + | 0.0100117i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 3.51233 | + | 4.83431i | 0.155073 | + | 0.213440i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 2.70128 | − | 19.8492i | 0.119033 | − | 0.874658i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 28.9880 | + | 9.41876i | 1.27489 | + | 0.414236i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −3.32057 | + | 10.2197i | −0.145757 | + | 0.448594i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 5.53178 | + | 17.0251i | 0.242352 | + | 0.745882i | 0.996061 | + | 0.0886737i | \(0.0282628\pi\) |
−0.753709 | + | 0.657208i | \(0.771737\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 0.791609 | − | 1.08956i | 0.0346146 | − | 0.0476430i | −0.791359 | − | 0.611352i | \(-0.790626\pi\) |
0.825974 | + | 0.563709i | \(0.190626\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 2.88891 | − | 4.36473i | 0.126082 | − | 0.190492i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −26.2646 | + | 36.1501i | −1.14410 | + | 1.57472i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −12.9227 | − | 39.7721i | −0.561858 | − | 1.72922i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 1.26144 | − | 3.88230i | 0.0547416 | − | 0.168477i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −1.50190 | − | 0.487998i | −0.0650546 | − | 0.0211375i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 5.42769 | + | 2.61799i | 0.234660 | + | 0.113185i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −11.3479 | − | 15.6191i | −0.489699 | − | 0.674013i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −30.0392 | − | 21.8248i | −1.29388 | − | 0.940060i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −9.14001 | + | 6.64061i | −0.392960 | + | 0.285502i | −0.766667 | − | 0.642045i | \(-0.778086\pi\) |
0.373708 | + | 0.927547i | \(0.378086\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 16.7512i | 0.718864i | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −4.09834 | − | 22.6637i | −0.175553 | − | 0.970804i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 24.5513 | − | 7.97719i | 1.04974 | − | 0.341080i | 0.267171 | − | 0.963649i | \(-0.413911\pi\) |
0.782565 | + | 0.622569i | \(0.213911\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −3.16053 | −0.134888 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −41.3220 | −1.76037 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 3.30548 | − | 1.07402i | 0.140563 | − | 0.0456718i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −15.1628 | + | 8.14733i | −0.643625 | + | 0.345835i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 35.3575i | 1.49814i | 0.662489 | + | 0.749072i | \(0.269500\pi\) | ||||
−0.662489 | + | 0.749072i | \(0.730500\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −8.09954 | + | 5.88466i | −0.342574 | + | 0.248895i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 23.8703 | + | 17.3428i | 1.00781 | + | 0.732214i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 2.67693 | + | 3.68448i | 0.112819 | + | 0.155282i | 0.861692 | − | 0.507431i | \(-0.169405\pi\) |
−0.748873 | + | 0.662713i | \(0.769405\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 7.43882 | − | 1.34518i | 0.312954 | − | 0.0565923i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −0.995600 | − | 0.323490i | −0.0418113 | − | 0.0135853i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 11.4772 | − | 35.3231i | 0.481148 | − | 1.48082i | −0.356335 | − | 0.934358i | \(-0.615974\pi\) |
0.837483 | − | 0.546463i | \(-0.184026\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −1.32882 | − | 4.08969i | −0.0556094 | − | 0.171148i | 0.919394 | − | 0.393338i | \(-0.128680\pi\) |
−0.975003 | + | 0.222190i | \(0.928680\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −7.02131 | + | 9.66400i | −0.293319 | + | 0.403720i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −40.2167 | + | 1.75618i | −1.67715 | + | 0.0732378i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −0.274601 | + | 0.377955i | −0.0114318 | + | 0.0157345i | −0.814695 | − | 0.579890i | \(-0.803095\pi\) |
0.803263 | + | 0.595625i | \(0.203095\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −8.16726 | − | 25.1362i | −0.339420 | − | 1.04463i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 4.48288 | − | 13.7969i | 0.185981 | − | 0.572391i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 16.9047 | + | 5.49266i | 0.700120 | + | 0.227483i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 1.55600 | − | 1.62543i | 0.0643325 | − | 0.0672031i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 19.3704 | + | 26.6610i | 0.799500 | + | 1.10042i | 0.992860 | + | 0.119289i | \(0.0380616\pi\) |
−0.193360 | + | 0.981128i | \(0.561938\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 46.0427 | + | 33.4519i | 1.89715 | + | 1.37836i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 8.95728 | − | 6.50784i | 0.368453 | − | 0.267697i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − | 15.5285i | − | 0.637680i | −0.947809 | − | 0.318840i | \(-0.896707\pi\) | ||
0.947809 | − | 0.318840i | \(-0.103293\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −7.93317 | − | 7.59431i | −0.325228 | − | 0.311336i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −15.7445 | + | 5.11571i | −0.644381 | + | 0.209372i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 36.0116 | 1.47140 | 0.735698 | − | 0.677310i | \(-0.236854\pi\) | ||||
0.735698 | + | 0.677310i | \(0.236854\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −24.1503 | −0.985112 | −0.492556 | − | 0.870281i | \(-0.663937\pi\) | ||||
−0.492556 | + | 0.870281i | \(0.663937\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −3.01519 | + | 0.979694i | −0.122788 | + | 0.0398962i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 63.2574 | + | 8.60873i | 2.57178 | + | 0.349995i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 29.8098i | 1.20994i | 0.796248 | + | 0.604970i | \(0.206815\pi\) | ||||
−0.796248 | + | 0.604970i | \(0.793185\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 5.85653 | − | 4.25502i | 0.237318 | − | 0.172422i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −3.94565 | − | 2.86668i | −0.159624 | − | 0.115974i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 18.8873 | + | 25.9961i | 0.762850 | + | 1.04997i | 0.996972 | + | 0.0777657i | \(0.0247786\pi\) |
−0.234122 | + | 0.972207i | \(0.575221\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −1.66094 | − | 3.09113i | −0.0669754 | − | 0.124646i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 16.4065 | + | 5.33081i | 0.660502 | + | 0.214610i | 0.620039 | − | 0.784571i | \(-0.287117\pi\) |
0.0404631 | + | 0.999181i | \(0.487117\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −2.18171 | + | 6.71462i | −0.0876904 | + | 0.269883i | −0.985280 | − | 0.170949i | \(-0.945317\pi\) |
0.897589 | + | 0.440832i | \(0.145317\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 2.48790 | + | 7.65697i | 0.0998360 | + | 0.307264i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −1.54226 | + | 2.12273i | −0.0617892 | + | 0.0850455i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −5.62344 | + | 24.3593i | −0.224938 | + | 0.974373i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 22.0887 | − | 30.4025i | 0.882139 | − | 1.21416i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 11.1604 | + | 34.3483i | 0.444996 | + | 1.36956i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −3.02377 | + | 9.30621i | −0.120374 | + | 0.370474i | −0.993030 | − | 0.117862i | \(-0.962396\pi\) |
0.872656 | + | 0.488336i | \(0.162396\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −3.90612 | − | 1.26917i | −0.155254 | − | 0.0504452i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −6.32300 | − | 11.7676i | −0.250920 | − | 0.466982i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 3.49220 | + | 4.80661i | 0.138366 | + | 0.190445i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 5.26586 | + | 3.82587i | 0.208314 | + | 0.151349i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −12.6773 | + | 9.21063i | −0.500725 | + | 0.363798i | −0.809294 | − | 0.587404i | \(-0.800150\pi\) |
0.308569 | + | 0.951202i | \(0.400150\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 0.766747i | 0.0302375i | 0.999886 | + | 0.0151188i | \(0.00481264\pi\) | ||||
−0.999886 | + | 0.0151188i | \(0.995187\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −22.0434 | − | 2.99989i | −0.867957 | − | 0.118121i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −12.5281 | + | 4.07063i | −0.492531 | + | 0.160033i | −0.544743 | − | 0.838603i | \(-0.683373\pi\) |
0.0522121 | + | 0.998636i | \(0.483373\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −25.6719 | −1.00771 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −9.97021 | −0.390763 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −12.4514 | + | 4.04569i | −0.487259 | + | 0.158320i | −0.542336 | − | 0.840162i | \(-0.682460\pi\) |
0.0550762 | + | 0.998482i | \(0.482460\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −10.0265 | − | 9.59817i | −0.391766 | − | 0.375032i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0.367806i | 0.0143495i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −7.65921 | + | 5.56474i | −0.298361 | + | 0.216772i | −0.726886 | − | 0.686758i | \(-0.759033\pi\) |
0.428526 | + | 0.903530i | \(0.359033\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −4.49719 | − | 3.26740i | −0.174921 | − | 0.127087i | 0.496880 | − | 0.867819i | \(-0.334479\pi\) |
−0.671801 | + | 0.740732i | \(0.734479\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −2.77504 | − | 3.81951i | −0.107774 | − | 0.148338i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −9.67252 | + | 10.1041i | −0.375084 | + | 0.391821i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −52.9494 | − | 17.2043i | −2.05021 | − | 0.666153i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 1.93490 | − | 5.95502i | 0.0748076 | − | 0.230234i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 6.14211 | + | 18.9035i | 0.237114 | + | 0.729761i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −0.178700 | + | 0.245960i | −0.00688840 | + | 0.00948106i | −0.812447 | − | 0.583035i | \(-0.801865\pi\) |
0.805559 | + | 0.592516i | \(0.201865\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 4.99524 | − | 0.218131i | 0.192267 | − | 0.00839589i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 23.2339 | − | 31.9787i | 0.892950 | − | 1.22904i | −0.0797128 | − | 0.996818i | \(-0.525400\pi\) |
0.972663 | − | 0.232222i | \(-0.0745997\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −0.0590982 | − | 0.181886i | −0.00226798 | − | 0.00698013i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −3.23904 | + | 9.96873i | −0.124120 | + | 0.382002i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −30.0040 | − | 9.74888i | −1.14807 | − | 0.373031i | −0.327654 | − | 0.944798i | \(-0.606258\pi\) |
−0.820416 | + | 0.571767i | \(0.806258\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 28.5559 | − | 5.16385i | 1.09107 | − | 0.197301i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 4.44765 | + | 6.12166i | 0.169688 | + | 0.233556i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −2.30095 | − | 1.67174i | −0.0876594 | − | 0.0636883i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −7.59169 | + | 5.51569i | −0.288802 | + | 0.209827i | −0.722747 | − | 0.691112i | \(-0.757121\pi\) |
0.433946 | + | 0.900939i | \(0.357121\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 6.58345i | 0.250085i | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 7.87788 | − | 4.23297i | 0.298825 | − | 0.160566i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −7.00233 | + | 2.27520i | −0.265232 | + | 0.0861792i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 15.9832 | 0.604540 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −20.4347 | −0.771809 | −0.385904 | − | 0.922539i | \(-0.626111\pi\) | ||||
−0.385904 | + | 0.922539i | \(0.626111\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 43.7478 | − | 14.2145i | 1.64998 | − | 0.536111i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −1.92846 | − | 10.6643i | −0.0726302 | − | 0.401642i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 6.24930i | 0.235029i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −4.78774 | + | 3.47850i | −0.179808 | + | 0.130638i | −0.674048 | − | 0.738687i | \(-0.735446\pi\) |
0.494241 | + | 0.869325i | \(0.335446\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 2.68601 | + | 1.95150i | 0.100733 | + | 0.0731869i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 45.0708 | + | 62.0346i | 1.68791 | + | 2.32321i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −12.7457 | − | 6.14776i | −0.476663 | − | 0.229913i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 2.77706 | + | 0.902322i | 0.103711 | + | 0.0336978i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 2.47253 | − | 7.60966i | 0.0922098 | − | 0.283793i | −0.894307 | − | 0.447455i | \(-0.852331\pi\) |
0.986516 | + | 0.163662i | \(0.0523306\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −2.89803 | − | 8.91922i | −0.107928 | − | 0.332169i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −13.5471 | + | 18.6460i | −0.503821 | + | 0.693450i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −19.0835 | + | 28.8325i | −0.708745 | + | 1.07081i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −23.6752 | + | 32.5861i | −0.878065 | + | 1.20855i | 0.0988886 | + | 0.995099i | \(0.468471\pi\) |
−0.976953 | + | 0.213454i | \(0.931529\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −0.309017 | − | 0.951057i | −0.0114451 | − | 0.0352243i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −14.4240 | + | 44.3925i | −0.533491 | + | 1.64192i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −10.0786 | − | 3.27474i | −0.372262 | − | 0.120955i | 0.116910 | − | 0.993143i | \(-0.462701\pi\) |
−0.489172 | + | 0.872187i | \(0.662701\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −1.78026 | + | 13.0815i | −0.0656660 | + | 0.482517i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 11.7193 | + | 16.1302i | 0.431686 | + | 0.594165i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −36.8178 | − | 26.7497i | −1.35437 | − | 0.984005i | −0.998781 | − | 0.0493609i | \(-0.984282\pi\) |
−0.355585 | − | 0.934644i | \(-0.615718\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −4.86474 | + | 3.53444i | −0.178711 | + | 0.129841i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 8.64344i | 0.317097i | 0.987351 | + | 0.158549i | \(0.0506814\pi\) | ||||
−0.987351 | + | 0.158549i | \(0.949319\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −5.52519 | + | 11.4550i | −0.202427 | + | 0.419679i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 13.1796 | − | 4.28231i | 0.482217 | − | 0.156682i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 2.82117 | 0.103083 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −54.4382 | −1.98648 | −0.993239 | − | 0.116086i | \(-0.962965\pi\) | ||||
−0.993239 | + | 0.116086i | \(0.962965\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 9.31208 | − | 3.02568i | 0.339351 | − | 0.110262i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −5.35410 | + | 11.1003i | −0.194856 | + | 0.403981i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 34.1378i | 1.24076i | 0.784302 | + | 0.620380i | \(0.213022\pi\) | ||||
−0.784302 | + | 0.620380i | \(0.786978\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 40.9622 | − | 29.7608i | 1.48683 | − | 1.08025i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −2.52798 | − | 1.83668i | −0.0916391 | − | 0.0665797i | 0.541022 | − | 0.841008i | \(-0.318037\pi\) |
−0.632661 | + | 0.774429i | \(0.718037\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −6.33767 | − | 8.72305i | −0.229439 | − | 0.315796i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 1.41466 | − | 10.3950i | 0.0511473 | − | 0.375833i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 3.90673 | + | 1.26937i | 0.141064 | + | 0.0458344i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 16.4999 | − | 50.7816i | 0.595003 | − | 1.83123i | 0.0402920 | − | 0.999188i | \(-0.487171\pi\) |
0.554711 | − | 0.832043i | \(-0.312829\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −6.89561 | − | 21.2225i | −0.248339 | − | 0.764309i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −0.468593 | + | 0.644963i | −0.0168541 | + | 0.0231977i | −0.817361 | − | 0.576126i | \(-0.804564\pi\) |
0.800507 | + | 0.599324i | \(0.204564\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 44.6049 | − | 16.6774i | 1.60225 | − | 0.599071i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −4.73664 | + | 6.51943i | −0.169926 | + | 0.233883i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 2.89781 | + | 8.91855i | 0.103825 | + | 0.319540i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 12.6494 | − | 38.9308i | 0.452630 | − | 1.39305i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 6.57673 | + | 2.13691i | 0.235033 | + | 0.0763669i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −34.2822 | − | 16.5356i | −1.22359 | − | 0.590182i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 24.5442 | + | 33.7822i | 0.874906 | + | 1.20420i | 0.977806 | + | 0.209513i | \(0.0671877\pi\) |
−0.102900 | + | 0.994692i | \(0.532812\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0.589898 | + | 0.428586i | 0.0210009 | + | 0.0152581i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 2.86314 | − | 2.08019i | 0.101802 | − | 0.0739631i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 3.18042i | − | 0.112940i | ||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −1.12461 | − | 6.21904i | −0.0398857 | − | 0.220567i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 26.2979 | − | 8.54471i | 0.931520 | − | 0.302669i | 0.196336 | − | 0.980537i | \(-0.437096\pi\) |
0.735184 | + | 0.677868i | \(0.237096\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −22.7385 | −0.804430 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −2.50645 | −0.0885611 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 2.19989 | − | 0.714787i | 0.0776323 | − | 0.0252243i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −16.6010 | + | 8.92014i | −0.585110 | + | 0.314394i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 1.85922i | 0.0654477i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 28.2998 | − | 20.5610i | 0.994968 | − | 0.722887i | 0.0339649 | − | 0.999423i | \(-0.489187\pi\) |
0.961004 | + | 0.276536i | \(0.0891866\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −7.40374 | − | 5.37913i | −0.259980 | − | 0.188887i | 0.450158 | − | 0.892949i | \(-0.351368\pi\) |
−0.710138 | + | 0.704062i | \(0.751368\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −11.4932 | − | 15.8190i | −0.403083 | − | 0.554797i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −27.0553 | + | 4.89250i | −0.947707 | + | 0.171377i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 56.5407 | + | 18.3712i | 1.97811 | + | 0.642727i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0.325526 | − | 1.00187i | 0.0113748 | − | 0.0350080i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −0.998901 | − | 3.07430i | −0.0348619 | − | 0.107294i | 0.932111 | − | 0.362172i | \(-0.117965\pi\) |
−0.966973 | + | 0.254878i | \(0.917965\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 26.5706 | − | 36.5713i | 0.926193 | − | 1.27480i | −0.0351334 | − | 0.999383i | \(-0.511186\pi\) |
0.961326 | − | 0.275412i | \(-0.0888144\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −11.0123 | − | 29.4531i | −0.383399 | − | 1.02543i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −13.9051 | + | 19.1388i | −0.483529 | + | 0.665521i | −0.979178 | − | 0.203002i | \(-0.934930\pi\) |
0.495649 | + | 0.868523i | \(0.334930\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −3.94442 | − | 12.1397i | −0.136995 | − | 0.421628i | 0.858900 | − | 0.512144i | \(-0.171148\pi\) |
−0.995895 | + | 0.0905157i | \(0.971148\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −5.24131 | + | 16.1311i | −0.181819 | + | 0.559581i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 26.3444 | + | 8.55981i | 0.912779 | + | 0.296580i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 8.39403 | − | 8.76858i | 0.290487 | − | 0.303449i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −5.59815 | − | 7.70519i | −0.193500 | − | 0.266330i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −42.0974 | − | 30.5855i | −1.45336 | − | 1.05593i | −0.985031 | − | 0.172378i | \(-0.944855\pi\) |
−0.468333 | − | 0.883552i | \(-0.655145\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −15.2255 | + | 11.0620i | −0.525019 | + | 0.381449i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | − | 26.0879i | − | 0.898513i | ||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −19.3627 | − | 18.5357i | −0.666098 | − | 0.637646i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 28.4247 | − | 9.23575i | 0.976685 | − | 0.317344i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −25.6093 | −0.878911 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 61.9760 | 2.12451 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 33.8823 | − | 11.0090i | 1.16011 | − | 0.376942i | 0.335166 | − | 0.942159i | \(-0.391208\pi\) |
0.824942 | + | 0.565217i | \(0.191208\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −13.2397 | − | 1.80179i | −0.452787 | − | 0.0616200i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − | 24.6745i | − | 0.842866i | −0.906860 | − | 0.421433i | \(-0.861527\pi\) | ||
0.906860 | − | 0.421433i | \(-0.138473\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 17.7355 | − | 12.8856i | 0.605127 | − | 0.439650i | −0.242568 | − | 0.970134i | \(-0.577990\pi\) |
0.847695 | + | 0.530484i | \(0.177990\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −1.32907 | − | 0.965624i | −0.0452945 | − | 0.0329084i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 16.2088 | + | 22.3095i | 0.551755 | + | 0.759426i | 0.990249 | − | 0.139308i | \(-0.0444879\pi\) |
−0.438494 | + | 0.898734i | \(0.644488\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −11.3729 | − | 21.1659i | −0.386692 | − | 0.719663i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −4.76630 | − | 1.54866i | −0.161872 | − | 0.0525954i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 6.45219 | − | 19.8578i | 0.218876 | − | 0.673630i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −0.985860 | − | 3.03417i | −0.0334046 | − | 0.102809i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0.107382 | − | 0.147799i | 0.00363434 | − | 0.00500223i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 2.58316 | + | 11.4154i | 0.0873266 | + | 0.385910i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −12.1600 | + | 16.7368i | −0.410615 | + | 0.565163i | −0.963368 | − | 0.268182i | \(-0.913577\pi\) |
0.552754 | + | 0.833345i | \(0.313577\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −8.58590 | − | 26.4247i | −0.289595 | − | 0.891282i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −11.7074 | + | 36.0318i | −0.394434 | + | 1.21394i | 0.534968 | + | 0.844872i | \(0.320324\pi\) |
−0.929402 | + | 0.369069i | \(0.879676\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 37.4188 | + | 12.1581i | 1.25924 | + | 0.409152i | 0.861224 | − | 0.508226i | \(-0.169698\pi\) |
0.398017 | + | 0.917378i | \(0.369698\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 4.32041 | + | 8.04061i | 0.145229 | + | 0.270282i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −14.2693 | − | 19.6400i | −0.479116 | − | 0.659446i | 0.499219 | − | 0.866476i | \(-0.333620\pi\) |
−0.978335 | + | 0.207030i | \(0.933620\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −5.05961 | − | 3.67602i | −0.169694 | − | 0.123290i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −5.08783 | + | 3.69653i | −0.170449 | + | 0.123838i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 28.9610i | 0.969142i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 42.7758 | + | 5.82138i | 1.42984 | + | 0.194587i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −7.70516 | + | 2.50356i | −0.257268 | + | 0.0835914i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 65.8612 | 2.19659 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −13.2602 | −0.441762 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −9.90519 | + | 3.21839i | −0.329624 | + | 0.107101i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −27.0576 | − | 25.9018i | −0.899425 | − | 0.861006i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − | 13.1961i | − | 0.438169i | −0.975706 | − | 0.219085i | \(-0.929693\pi\) | ||
0.975706 | − | 0.219085i | \(-0.0703071\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −4.82959 | + | 3.50890i | −0.160187 | + | 0.116383i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 22.3318 | + | 16.2250i | 0.739884 | + | 0.537557i | 0.892675 | − | 0.450701i | \(-0.148826\pi\) |
−0.152791 | + | 0.988259i | \(0.548826\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −51.2259 | − | 70.5064i | −1.69533 | − | 2.33342i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 4.88702 | − | 5.10508i | 0.161560 | − | 0.168769i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −6.18002 | − | 2.00801i | −0.204082 | − | 0.0663103i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −3.75430 | + | 11.5546i | −0.123843 | + | 0.381150i | −0.993689 | − | 0.112175i | \(-0.964218\pi\) |
0.869845 | + | 0.493324i | \(0.164218\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 4.98821 | + | 15.3521i | 0.164367 | + | 0.505870i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −3.84995 | + | 5.29900i | −0.126723 | + | 0.174419i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 10.2856 | − | 37.0898i | 0.338190 | − | 1.21950i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 5.26575 | − | 7.24769i | 0.172950 | − | 0.238045i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −10.8881 | − | 33.5101i | −0.357227 | − | 1.09943i | −0.954707 | − | 0.297547i | \(-0.903831\pi\) |
0.597481 | − | 0.801883i | \(-0.296169\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 10.9022 | − | 33.5536i | 0.357306 | − | 1.09968i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 27.3316 | + | 8.88057i | 0.894796 | + | 0.290737i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −64.9230 | + | 11.7402i | −2.12321 | + | 0.383946i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −4.00849 | − | 5.51721i | −0.130952 | − | 0.180240i | 0.738506 | − | 0.674247i | \(-0.235532\pi\) |
−0.869458 | + | 0.494007i | \(0.835532\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 21.4279 | + | 15.5683i | 0.699274 | + | 0.508052i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −25.2441 | + | 18.3409i | −0.822934 | + | 0.597897i | −0.917551 | − | 0.397617i | \(-0.869837\pi\) |
0.0946174 | + | 0.995514i | \(0.469837\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 12.6346i | 0.411439i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 2.06198 | − | 1.10795i | 0.0670763 | − | 0.0360417i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −27.0090 | + | 8.77576i | −0.877675 | + | 0.285174i | −0.712991 | − | 0.701173i | \(-0.752660\pi\) |
−0.164683 | + | 0.986347i | \(0.552660\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −0.370121 | −0.0120146 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 26.2980 | 0.852772 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −11.1288 | + | 3.61597i | −0.360497 | + | 0.117133i | −0.483665 | − | 0.875253i | \(-0.660695\pi\) |
0.123168 | + | 0.992386i | \(0.460695\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −4.75308 | − | 26.2844i | −0.153806 | − | 0.850542i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | − | 43.4890i | − | 1.40580i | ||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 10.9909 | − | 7.98538i | 0.354916 | − | 0.257861i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −48.3058 | − | 35.0962i | −1.55825 | − | 1.13214i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 1.58405 | + | 2.18026i | 0.0510453 | + | 0.0702578i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 53.2303 | + | 25.6750i | 1.71354 | + | 0.826508i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 16.1031 | + | 5.23221i | 0.517840 | + | 0.168257i | 0.556265 | − | 0.831005i | \(-0.312234\pi\) |
−0.0384246 | + | 0.999262i | \(0.512234\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −8.66333 | + | 26.6630i | −0.278306 | + | 0.856539i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −3.80798 | − | 11.7198i | −0.122204 | − | 0.376105i | 0.871177 | − | 0.490968i | \(-0.163357\pi\) |
−0.993381 | + | 0.114864i | \(0.963357\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 2.46094 | − | 3.38719i | 0.0788940 | − | 0.108588i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0.219504 | + | 5.02668i | 0.00702977 | + | 0.160983i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −2.44310 | + | 3.36263i | −0.0781615 | + | 0.107580i | −0.846308 | − | 0.532695i | \(-0.821179\pi\) |
0.768146 | + | 0.640275i | \(0.221179\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 4.87098 | + | 14.9913i | 0.155677 | + | 0.479126i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 3.18284 | − | 9.79577i | 0.101620 | − | 0.312755i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −13.0196 | − | 4.23033i | −0.415261 | − | 0.134927i | 0.0939323 | − | 0.995579i | \(-0.470056\pi\) |
−0.509194 | + | 0.860652i | \(0.670056\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −3.33846 | + | 24.5312i | −0.106372 | + | 0.781629i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −2.98218 | − | 4.10461i | −0.0949237 | − | 0.130651i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 64.8017 | + | 47.0812i | 2.06057 | + | 1.49709i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 6.19447 | − | 4.50055i | 0.196774 | − | 0.142965i | −0.485036 | − | 0.874494i | \(-0.661193\pi\) |
0.681809 | + | 0.731530i | \(0.261193\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | − | 31.2634i | − | 0.992113i | ||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 16.0820 | − | 33.3417i | 0.509834 | − | 1.05700i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −49.0006 | + | 15.9213i | −1.55187 | + | 0.504232i | −0.954620 | − | 0.297827i | \(-0.903738\pi\) |
−0.597245 | + | 0.802059i | \(0.703738\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −7.69791 | −0.243551 |
(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 | 300.2.o.a.109.3 | ✓ | 24 | |
3.2 | odd | 2 | 900.2.w.c.109.2 | 24 | |||
5.2 | odd | 4 | 1500.2.m.c.1201.4 | 24 | |||
5.3 | odd | 4 | 1500.2.m.d.1201.3 | 24 | |||
5.4 | even | 2 | 1500.2.o.c.49.4 | 24 | |||
25.2 | odd | 20 | 1500.2.m.c.301.4 | 24 | |||
25.6 | even | 5 | 7500.2.d.g.1249.18 | 24 | |||
25.8 | odd | 20 | 7500.2.a.m.1.6 | 12 | |||
25.11 | even | 5 | 1500.2.o.c.949.4 | 24 | |||
25.14 | even | 10 | inner | 300.2.o.a.289.3 | yes | 24 | |
25.17 | odd | 20 | 7500.2.a.n.1.7 | 12 | |||
25.19 | even | 10 | 7500.2.d.g.1249.7 | 24 | |||
25.23 | odd | 20 | 1500.2.m.d.301.3 | 24 | |||
75.14 | odd | 10 | 900.2.w.c.289.2 | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
300.2.o.a.109.3 | ✓ | 24 | 1.1 | even | 1 | trivial | |
300.2.o.a.289.3 | yes | 24 | 25.14 | even | 10 | inner | |
900.2.w.c.109.2 | 24 | 3.2 | odd | 2 | |||
900.2.w.c.289.2 | 24 | 75.14 | odd | 10 | |||
1500.2.m.c.301.4 | 24 | 25.2 | odd | 20 | |||
1500.2.m.c.1201.4 | 24 | 5.2 | odd | 4 | |||
1500.2.m.d.301.3 | 24 | 25.23 | odd | 20 | |||
1500.2.m.d.1201.3 | 24 | 5.3 | odd | 4 | |||
1500.2.o.c.49.4 | 24 | 5.4 | even | 2 | |||
1500.2.o.c.949.4 | 24 | 25.11 | even | 5 | |||
7500.2.a.m.1.6 | 12 | 25.8 | odd | 20 | |||
7500.2.a.n.1.7 | 12 | 25.17 | odd | 20 | |||
7500.2.d.g.1249.7 | 24 | 25.19 | even | 10 | |||
7500.2.d.g.1249.18 | 24 | 25.6 | even | 5 |