Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [675,2,Mod(226,675)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(675, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([2, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("675.226");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 675 = 3^{3} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 675.e (of order \(3\), degree \(2\), not 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: | \(5.38990213644\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Relative dimension: | \(3\) over \(\Q(\zeta_{3})\) |
Coefficient field: | 6.0.954288.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - x^{5} - 2x^{4} + 3x^{3} - 6x^{2} - 9x + 27 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{4}]\) |
Coefficient ring index: | \( 3 \) |
Twist minimal: | no (minimal twist has level 45) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 226.3 | ||
Root | \(1.71903 - 0.211943i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 675.226 |
Dual form | 675.2.e.b.451.3 |
$q$-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 \(\left(\mathbb{Z}/675\mathbb{Z}\right)^\times\).
\(n\) | \(326\) | \(352\) |
\(\chi(n)\) | \(e\left(\frac{1}{3}\right)\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.04307 | + | 1.80664i | 0.737558 | + | 1.27749i | 0.953592 | + | 0.301103i | \(0.0973547\pi\) |
−0.216033 | + | 0.976386i | \(0.569312\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −1.17597 | + | 2.03684i | −0.587985 | + | 1.01842i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.04307 | + | 3.53869i | 0.772206 | + | 1.33750i | 0.936351 | + | 0.351064i | \(0.114180\pi\) |
−0.164145 | + | 0.986436i | \(0.552487\pi\) | |||||||
\(8\) | −0.734191 | −0.259576 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −0.675970 | − | 1.17081i | −0.203813 | − | 0.353014i | 0.745941 | − | 0.666012i | \(-0.232000\pi\) |
−0.949754 | + | 0.312998i | \(0.898667\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0.324030 | − | 0.561237i | 0.0898699 | − | 0.155659i | −0.817586 | − | 0.575806i | \(-0.804688\pi\) |
0.907456 | + | 0.420147i | \(0.138022\pi\) | |||||||
\(14\) | −4.26210 | + | 7.38217i | −1.13909 | + | 1.97297i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.58613 | + | 2.74726i | 0.396533 | + | 0.686815i | ||||
\(17\) | −1.35194 | −0.327893 | −0.163947 | − | 0.986469i | \(-0.552423\pi\) | ||||
−0.163947 | + | 0.986469i | \(0.552423\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0.648061 | 0.148675 | 0.0743377 | − | 0.997233i | \(-0.476316\pi\) | ||||
0.0743377 | + | 0.997233i | \(0.476316\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 1.41016 | − | 2.44247i | 0.300647 | − | 0.520736i | ||||
\(23\) | −2.39500 | + | 4.14827i | −0.499393 | + | 0.864974i | −1.00000 | 0.000700856i | \(-0.999777\pi\) | |
0.500607 | + | 0.865675i | \(0.333110\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 1.35194 | 0.265137 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −9.61033 | −1.81618 | ||||||||
\(29\) | 1.93807 | + | 3.35683i | 0.359890 | + | 0.623349i | 0.987942 | − | 0.154823i | \(-0.0494807\pi\) |
−0.628052 | + | 0.778172i | \(0.716147\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 3.84823 | − | 6.66533i | 0.691163 | − | 1.19713i | −0.280295 | − | 0.959914i | \(-0.590432\pi\) |
0.971457 | − | 0.237215i | \(-0.0762345\pi\) | |||||||
\(32\) | −4.04307 | + | 7.00279i | −0.714720 | + | 1.23793i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −1.41016 | − | 2.44247i | −0.241841 | − | 0.418880i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −7.52420 | −1.23697 | −0.618485 | − | 0.785796i | \(-0.712253\pi\) | ||||
−0.618485 | + | 0.785796i | \(0.712253\pi\) | |||||||
\(38\) | 0.675970 | + | 1.17081i | 0.109657 | + | 0.189931i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −0.0898394 | + | 0.155606i | −0.0140306 | + | 0.0243016i | −0.872955 | − | 0.487800i | \(-0.837800\pi\) |
0.858925 | + | 0.512102i | \(0.171133\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −0.410161 | − | 0.710419i | −0.0625489 | − | 0.108338i | 0.833055 | − | 0.553190i | \(-0.186590\pi\) |
−0.895604 | + | 0.444852i | \(0.853256\pi\) | |||||||
\(44\) | 3.17968 | 0.479355 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −9.99258 | −1.47333 | ||||||||
\(47\) | −5.45323 | − | 9.44526i | −0.795435 | − | 1.37773i | −0.922563 | − | 0.385847i | \(-0.873909\pi\) |
0.127128 | − | 0.991886i | \(-0.459424\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −4.84823 | + | 8.39738i | −0.692604 | + | 1.19963i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0.762100 | + | 1.32000i | 0.105684 | + | 0.183050i | ||||
\(53\) | 4.17226 | 0.573104 | 0.286552 | − | 0.958065i | \(-0.407491\pi\) | ||||
0.286552 | + | 0.958065i | \(0.407491\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −1.50000 | − | 2.59808i | −0.200446 | − | 0.347183i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −4.04307 | + | 7.00279i | −0.530880 | + | 0.919512i | ||||
\(59\) | 2.08613 | − | 3.61328i | 0.271591 | − | 0.470409i | −0.697678 | − | 0.716411i | \(-0.745784\pi\) |
0.969269 | + | 0.246002i | \(0.0791169\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 1.91016 | + | 3.30850i | 0.244571 | + | 0.423609i | 0.962011 | − | 0.273011i | \(-0.0880195\pi\) |
−0.717440 | + | 0.696620i | \(0.754686\pi\) | |||||||
\(62\) | 16.0558 | 2.03909 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −10.5242 | −1.31552 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 4.07097 | − | 7.05113i | 0.497349 | − | 0.861433i | −0.502647 | − | 0.864492i | \(-0.667640\pi\) |
0.999995 | + | 0.00305885i | \(0.000973664\pi\) | |||||||
\(68\) | 1.58984 | − | 2.75368i | 0.192796 | − | 0.333933i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 6.11644 | 0.725888 | 0.362944 | − | 0.931811i | \(-0.381772\pi\) | ||||
0.362944 | + | 0.931811i | \(0.381772\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 12.3445 | 1.44482 | 0.722408 | − | 0.691467i | \(-0.243035\pi\) | ||||
0.722408 | + | 0.691467i | \(0.243035\pi\) | |||||||
\(74\) | −7.84823 | − | 13.5935i | −0.912338 | − | 1.58022i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −0.762100 | + | 1.32000i | −0.0874188 | + | 0.151414i | ||||
\(77\) | 2.76210 | − | 4.78410i | 0.314770 | − | 0.545198i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −5.17226 | − | 8.95862i | −0.581925 | − | 1.00792i | −0.995251 | − | 0.0973403i | \(-0.968966\pi\) |
0.413326 | − | 0.910583i | \(-0.364367\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −0.374833 | −0.0413934 | ||||||||
\(83\) | 6.12920 | + | 10.6161i | 0.672767 | + | 1.16527i | 0.977116 | + | 0.212706i | \(0.0682275\pi\) |
−0.304350 | + | 0.952560i | \(0.598439\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0.855648 | − | 1.48203i | 0.0922669 | − | 0.159811i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0.496291 | + | 0.859601i | 0.0529048 | + | 0.0916338i | ||||
\(89\) | 3.00000 | 0.317999 | 0.159000 | − | 0.987279i | \(-0.449173\pi\) | ||||
0.159000 | + | 0.987279i | \(0.449173\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 2.64806 | 0.277592 | ||||||||
\(92\) | −5.63290 | − | 9.75648i | −0.587271 | − | 1.01718i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 11.3761 | − | 19.7041i | 1.17336 | − | 2.03232i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −6.79001 | − | 11.7606i | −0.689421 | − | 1.19411i | −0.972025 | − | 0.234876i | \(-0.924532\pi\) |
0.282605 | − | 0.959237i | \(-0.408802\pi\) | |||||||
\(98\) | −20.2281 | −2.04334 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −0.734191 | − | 1.27166i | −0.0730547 | − | 0.126535i | 0.827184 | − | 0.561931i | \(-0.189941\pi\) |
−0.900239 | + | 0.435397i | \(0.856608\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 3.76210 | − | 6.51615i | 0.370691 | − | 0.642055i | −0.618981 | − | 0.785406i | \(-0.712454\pi\) |
0.989672 | + | 0.143351i | \(0.0457877\pi\) | |||||||
\(104\) | −0.237900 | + | 0.412055i | −0.0233280 | + | 0.0404053i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 4.35194 | + | 7.53778i | 0.422698 | + | 0.732134i | ||||
\(107\) | 1.20999 | 0.116974 | 0.0584871 | − | 0.998288i | \(-0.481372\pi\) | ||||
0.0584871 | + | 0.998288i | \(0.481372\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 14.1042 | 1.35094 | 0.675469 | − | 0.737388i | \(-0.263941\pi\) | ||||
0.675469 | + | 0.737388i | \(0.263941\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −6.48113 | + | 11.2257i | −0.612410 | + | 1.06072i | ||||
\(113\) | 5.96227 | − | 10.3270i | 0.560883 | − | 0.971478i | −0.436537 | − | 0.899687i | \(-0.643795\pi\) |
0.997420 | − | 0.0717915i | \(-0.0228716\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −9.11644 | −0.846440 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 8.70388 | 0.801257 | ||||||||
\(119\) | −2.76210 | − | 4.78410i | −0.253201 | − | 0.438557i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 4.58613 | − | 7.94341i | 0.416921 | − | 0.722128i | ||||
\(122\) | −3.98484 | + | 6.90195i | −0.360771 | + | 0.624873i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 9.05080 | + | 15.6765i | 0.812786 | + | 1.40779i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 7.07871 | 0.628134 | 0.314067 | − | 0.949401i | \(-0.398308\pi\) | ||||
0.314067 | + | 0.949401i | \(0.398308\pi\) | |||||||
\(128\) | −2.89130 | − | 5.00787i | −0.255557 | − | 0.442637i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −3.00000 | + | 5.19615i | −0.262111 | + | 0.453990i | −0.966803 | − | 0.255524i | \(-0.917752\pi\) |
0.704692 | + | 0.709514i | \(0.251085\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 1.32403 | + | 2.29329i | 0.114808 | + | 0.198853i | ||||
\(134\) | 16.9852 | 1.46729 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0.992582 | 0.0851132 | ||||||||
\(137\) | 3.73419 | + | 6.46781i | 0.319033 | + | 0.552582i | 0.980287 | − | 0.197581i | \(-0.0633084\pi\) |
−0.661253 | + | 0.750163i | \(0.729975\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −4.00000 | + | 6.92820i | −0.339276 | + | 0.587643i | −0.984297 | − | 0.176522i | \(-0.943515\pi\) |
0.645021 | + | 0.764165i | \(0.276849\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 6.37985 | + | 11.0502i | 0.535385 | + | 0.927314i | ||||
\(143\) | −0.876139 | −0.0732664 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 12.8761 | + | 22.3021i | 1.06564 | + | 1.84574i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 8.84823 | − | 15.3256i | 0.727320 | − | 1.25976i | ||||
\(149\) | −5.29241 | + | 9.16673i | −0.433571 | + | 0.750968i | −0.997178 | − | 0.0750759i | \(-0.976080\pi\) |
0.563607 | + | 0.826043i | \(0.309413\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −8.84823 | − | 15.3256i | −0.720059 | − | 1.24718i | −0.960976 | − | 0.276633i | \(-0.910781\pi\) |
0.240917 | − | 0.970546i | \(-0.422552\pi\) | |||||||
\(152\) | −0.475800 | −0.0385925 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 11.5242 | 0.928646 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −1.26581 | + | 2.19245i | −0.101023 | + | 0.174976i | −0.912106 | − | 0.409954i | \(-0.865545\pi\) |
0.811084 | + | 0.584930i | \(0.198878\pi\) | |||||||
\(158\) | 10.7900 | − | 18.6888i | 0.858407 | − | 1.48680i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −19.5726 | −1.54254 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −8.47580 | −0.663876 | −0.331938 | − | 0.943301i | \(-0.607702\pi\) | ||||
−0.331938 | + | 0.943301i | \(0.607702\pi\) | |||||||
\(164\) | −0.211297 | − | 0.365977i | −0.0164995 | − | 0.0285780i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −12.7863 | + | 22.1465i | −0.992409 | + | 1.71890i | ||||
\(167\) | −6.36710 | + | 11.0281i | −0.492701 | + | 0.853383i | −0.999965 | − | 0.00840816i | \(-0.997324\pi\) |
0.507264 | + | 0.861791i | \(0.330657\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 6.29001 | + | 10.8946i | 0.483847 | + | 0.838047i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 1.92935 | 0.147111 | ||||||||
\(173\) | −11.5242 | − | 19.9605i | −0.876169 | − | 1.51757i | −0.855513 | − | 0.517782i | \(-0.826758\pi\) |
−0.0206561 | − | 0.999787i | \(-0.506576\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 2.14435 | − | 3.71413i | 0.161637 | − | 0.279963i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 3.12920 | + | 5.41993i | 0.234543 | + | 0.406241i | ||||
\(179\) | −2.22808 | −0.166534 | −0.0832672 | − | 0.996527i | \(-0.526535\pi\) | ||||
−0.0832672 | + | 0.996527i | \(0.526535\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 0.468382 | 0.0348146 | 0.0174073 | − | 0.999848i | \(-0.494459\pi\) | ||||
0.0174073 | + | 0.999848i | \(0.494459\pi\) | |||||||
\(182\) | 2.76210 | + | 4.78410i | 0.204740 | + | 0.354621i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 1.75839 | − | 3.04562i | 0.129630 | − | 0.224526i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0.913870 | + | 1.58287i | 0.0668288 | + | 0.115751i | ||||
\(188\) | 25.6513 | 1.87081 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −10.1140 | − | 17.5180i | −0.731826 | − | 1.26756i | −0.956102 | − | 0.293034i | \(-0.905335\pi\) |
0.224276 | − | 0.974526i | \(-0.427998\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −9.96467 | + | 17.2593i | −0.717273 | + | 1.24235i | 0.244804 | + | 0.969573i | \(0.421277\pi\) |
−0.962076 | + | 0.272780i | \(0.912057\pi\) | |||||||
\(194\) | 14.1648 | − | 24.5342i | 1.01698 | − | 1.76145i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −11.4027 | − | 19.7501i | −0.814482 | − | 1.41072i | ||||
\(197\) | −15.5800 | −1.11003 | −0.555015 | − | 0.831840i | \(-0.687288\pi\) | ||||
−0.555015 | + | 0.831840i | \(0.687288\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 3.58482 | 0.254121 | 0.127061 | − | 0.991895i | \(-0.459446\pi\) | ||||
0.127061 | + | 0.991895i | \(0.459446\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 1.53162 | − | 2.65284i | 0.107764 | − | 0.186653i | ||||
\(203\) | −7.91920 | + | 13.7165i | −0.555819 | + | 0.962707i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 15.6965 | 1.09362 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 2.05582 | 0.142545 | ||||||||
\(209\) | −0.438069 | − | 0.758758i | −0.0303019 | − | 0.0524844i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −7.49629 | + | 12.9840i | −0.516066 | + | 0.893852i | 0.483760 | + | 0.875201i | \(0.339271\pi\) |
−0.999826 | + | 0.0186518i | \(0.994063\pi\) | |||||||
\(212\) | −4.90645 | + | 8.49822i | −0.336976 | + | 0.583660i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 1.26210 | + | 2.18602i | 0.0862754 | + | 0.149433i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 31.4487 | 2.13488 | ||||||||
\(218\) | 14.7116 | + | 25.4813i | 0.996396 | + | 1.72581i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −0.438069 | + | 0.758758i | −0.0294677 | + | 0.0510396i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −13.4155 | − | 23.2363i | −0.898368 | − | 1.55602i | −0.829580 | − | 0.558388i | \(-0.811420\pi\) |
−0.0687878 | − | 0.997631i | \(-0.521913\pi\) | |||||||
\(224\) | −33.0410 | −2.20764 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 24.8761 | 1.65474 | ||||||||
\(227\) | −0.675970 | − | 1.17081i | −0.0448657 | − | 0.0777096i | 0.842721 | − | 0.538351i | \(-0.180953\pi\) |
−0.887586 | + | 0.460642i | \(0.847619\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 4.11775 | − | 7.13215i | 0.272108 | − | 0.471306i | −0.697293 | − | 0.716786i | \(-0.745612\pi\) |
0.969402 | + | 0.245480i | \(0.0789457\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −1.42291 | − | 2.46456i | −0.0934188 | − | 0.161806i | ||||
\(233\) | 8.58744 | 0.562582 | 0.281291 | − | 0.959623i | \(-0.409237\pi\) | ||||
0.281291 | + | 0.959623i | \(0.409237\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 4.90645 | + | 8.49822i | 0.319383 | + | 0.553187i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 5.76210 | − | 9.98025i | 0.373501 | − | 0.646923i | ||||
\(239\) | −11.9623 | + | 20.7193i | −0.773775 | + | 1.34022i | 0.161706 | + | 0.986839i | \(0.448300\pi\) |
−0.935480 | + | 0.353378i | \(0.885033\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 3.12015 | + | 5.40426i | 0.200987 | + | 0.348119i | 0.948847 | − | 0.315737i | \(-0.102252\pi\) |
−0.747860 | + | 0.663857i | \(0.768919\pi\) | |||||||
\(242\) | 19.1345 | 1.23001 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −8.98516 | −0.575216 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0.209991 | − | 0.363716i | 0.0133614 | − | 0.0231427i | ||||
\(248\) | −2.82534 | + | 4.89363i | −0.179409 | + | 0.310746i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 28.5726 | 1.80349 | 0.901743 | − | 0.432272i | \(-0.142288\pi\) | ||||
0.901743 | + | 0.432272i | \(0.142288\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 6.47580 | 0.407130 | ||||||||
\(254\) | 7.38356 | + | 12.7887i | 0.463286 | + | 0.802434i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −4.49258 | + | 7.78138i | −0.280786 | + | 0.486336i | ||||
\(257\) | 9.00000 | − | 15.5885i | 0.561405 | − | 0.972381i | −0.435970 | − | 0.899961i | \(-0.643595\pi\) |
0.997374 | − | 0.0724199i | \(-0.0230722\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −15.3724 | − | 26.6258i | −0.955196 | − | 1.65445i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −12.5168 | −0.773289 | ||||||||
\(263\) | −15.9344 | − | 27.5991i | −0.982555 | − | 1.70183i | −0.652335 | − | 0.757931i | \(-0.726211\pi\) |
−0.330220 | − | 0.943904i | \(-0.607123\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −2.76210 | + | 4.78410i | −0.169355 | + | 0.293332i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 9.57468 | + | 16.5838i | 0.584867 | + | 1.01302i | ||||
\(269\) | 31.4971 | 1.92041 | 0.960207 | − | 0.279289i | \(-0.0900987\pi\) | ||||
0.960207 | + | 0.279289i | \(0.0900987\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −3.24030 | −0.196834 | −0.0984172 | − | 0.995145i | \(-0.531378\pi\) | ||||
−0.0984172 | + | 0.995145i | \(0.531378\pi\) | |||||||
\(272\) | −2.14435 | − | 3.71413i | −0.130020 | − | 0.225202i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −7.79001 | + | 13.4927i | −0.470612 | + | 0.815123i | ||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −2.79241 | − | 4.83660i | −0.167780 | − | 0.290603i | 0.769859 | − | 0.638214i | \(-0.220326\pi\) |
−0.937639 | + | 0.347611i | \(0.886993\pi\) | |||||||
\(278\) | −16.6890 | −1.00094 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −12.0521 | − | 20.8749i | −0.718969 | − | 1.24529i | −0.961409 | − | 0.275124i | \(-0.911281\pi\) |
0.242440 | − | 0.970166i | \(-0.422052\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −5.27114 | + | 9.12989i | −0.313337 | + | 0.542715i | −0.979083 | − | 0.203463i | \(-0.934780\pi\) |
0.665746 | + | 0.746179i | \(0.268114\pi\) | |||||||
\(284\) | −7.19275 | + | 12.4582i | −0.426811 | + | 0.739259i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −0.913870 | − | 1.58287i | −0.0540383 | − | 0.0935970i | ||||
\(287\) | −0.734191 | −0.0433379 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −15.1723 | −0.892486 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −14.5168 | + | 25.1438i | −0.849530 | + | 1.47143i | ||||
\(293\) | −9.49629 | + | 16.4481i | −0.554779 | + | 0.960906i | 0.443141 | + | 0.896452i | \(0.353864\pi\) |
−0.997921 | + | 0.0644541i | \(0.979469\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 5.52420 | 0.321088 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −22.0813 | −1.27914 | ||||||||
\(299\) | 1.55211 | + | 2.68833i | 0.0897607 | + | 0.155470i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 1.67597 | − | 2.90286i | 0.0966013 | − | 0.167318i | ||||
\(302\) | 18.4586 | − | 31.9712i | 1.06217 | − | 1.83973i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 1.02791 | + | 1.78039i | 0.0589546 | + | 0.102112i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −29.4791 | −1.68246 | −0.841229 | − | 0.540679i | \(-0.818167\pi\) | ||||
−0.841229 | + | 0.540679i | \(0.818167\pi\) | |||||||
\(308\) | 6.49629 | + | 11.2519i | 0.370161 | + | 0.641137i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −4.70628 | + | 8.15152i | −0.266869 | + | 0.462230i | −0.968052 | − | 0.250751i | \(-0.919322\pi\) |
0.701183 | + | 0.712982i | \(0.252656\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 5.81050 | + | 10.0641i | 0.328429 | + | 0.568855i | 0.982200 | − | 0.187837i | \(-0.0601476\pi\) |
−0.653771 | + | 0.756692i | \(0.726814\pi\) | |||||||
\(314\) | −5.28128 | −0.298040 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 24.3297 | 1.36865 | ||||||||
\(317\) | 4.58984 | + | 7.94984i | 0.257791 | + | 0.446507i | 0.965650 | − | 0.259847i | \(-0.0836720\pi\) |
−0.707859 | + | 0.706354i | \(0.750339\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 2.62015 | − | 4.53824i | 0.146700 | − | 0.254092i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −20.4155 | − | 35.3607i | −1.13771 | − | 1.97057i | ||||
\(323\) | −0.876139 | −0.0487497 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −8.84081 | − | 15.3127i | −0.489647 | − | 0.848094i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0.0659593 | − | 0.114245i | 0.00364199 | − | 0.00630812i | ||||
\(329\) | 22.2826 | − | 38.5946i | 1.22848 | − | 2.12779i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 3.61033 | + | 6.25327i | 0.198442 | + | 0.343711i | 0.948023 | − | 0.318201i | \(-0.103079\pi\) |
−0.749582 | + | 0.661912i | \(0.769745\pi\) | |||||||
\(332\) | −28.8310 | −1.58231 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −26.5652 | −1.45358 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 1.14195 | − | 1.97791i | 0.0622059 | − | 0.107744i | −0.833245 | − | 0.552904i | \(-0.813520\pi\) |
0.895451 | + | 0.445160i | \(0.146853\pi\) | |||||||
\(338\) | −13.1218 | + | 22.7276i | −0.713731 | + | 1.23622i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −10.4051 | −0.563470 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −11.0181 | −0.594921 | ||||||||
\(344\) | 0.301136 | + | 0.521583i | 0.0162362 | + | 0.0281219i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 24.0410 | − | 41.6402i | 1.29245 | − | 2.23859i | ||||
\(347\) | 0.354343 | − | 0.613740i | 0.0190221 | − | 0.0329473i | −0.856358 | − | 0.516383i | \(-0.827278\pi\) |
0.875380 | + | 0.483436i | \(0.160611\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 10.6723 | + | 18.4849i | 0.571273 | + | 0.989474i | 0.996436 | + | 0.0843569i | \(0.0268836\pi\) |
−0.425163 | + | 0.905117i | \(0.639783\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 10.9320 | 0.582675 | ||||||||
\(353\) | 5.04840 | + | 8.74408i | 0.268699 | + | 0.465401i | 0.968526 | − | 0.248912i | \(-0.0800729\pi\) |
−0.699827 | + | 0.714312i | \(0.746740\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −3.52791 | + | 6.11052i | −0.186979 | + | 0.323857i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −2.32403 | − | 4.02534i | −0.122829 | − | 0.212746i | ||||
\(359\) | −30.5578 | −1.61278 | −0.806388 | − | 0.591386i | \(-0.798581\pi\) | ||||
−0.806388 | + | 0.591386i | \(0.798581\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −18.5800 | −0.977896 | ||||||||
\(362\) | 0.488553 | + | 0.846198i | 0.0256778 | + | 0.0444752i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −3.11404 | + | 5.39367i | −0.163220 | + | 0.282705i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −3.58984 | − | 6.21778i | −0.187388 | − | 0.324566i | 0.756991 | − | 0.653426i | \(-0.226669\pi\) |
−0.944379 | + | 0.328860i | \(0.893336\pi\) | |||||||
\(368\) | −15.1952 | −0.792102 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 8.52420 | + | 14.7643i | 0.442554 | + | 0.766527i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −10.9623 | + | 18.9872i | −0.567605 | + | 0.983120i | 0.429197 | + | 0.903211i | \(0.358796\pi\) |
−0.996802 | + | 0.0799096i | \(0.974537\pi\) | |||||||
\(374\) | −1.90645 | + | 3.30207i | −0.0985803 | + | 0.170746i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 4.00371 | + | 6.93463i | 0.206476 | + | 0.357626i | ||||
\(377\) | 2.51197 | 0.129373 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −17.3929 | −0.893414 | −0.446707 | − | 0.894680i | \(-0.647403\pi\) | ||||
−0.446707 | + | 0.894680i | \(0.647403\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 21.0992 | − | 36.5449i | 1.07953 | − | 1.86980i | ||||
\(383\) | −0.237900 | + | 0.412055i | −0.0121561 | + | 0.0210550i | −0.872039 | − | 0.489436i | \(-0.837203\pi\) |
0.859883 | + | 0.510491i | \(0.170536\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −41.5752 | −2.11612 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 31.9394 | 1.62148 | ||||||||
\(389\) | −2.79372 | − | 4.83886i | −0.141647 | − | 0.245340i | 0.786470 | − | 0.617629i | \(-0.211906\pi\) |
−0.928117 | + | 0.372289i | \(0.878573\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 3.23790 | − | 5.60821i | 0.163748 | − | 0.283619i | ||||
\(392\) | 3.55953 | − | 6.16528i | 0.179783 | − | 0.311394i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −16.2510 | − | 28.1475i | −0.818712 | − | 1.41805i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −3.75228 | −0.188321 | −0.0941607 | − | 0.995557i | \(-0.530017\pi\) | ||||
−0.0941607 | + | 0.995557i | \(0.530017\pi\) | |||||||
\(398\) | 3.73921 | + | 6.47649i | 0.187429 | + | 0.324637i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 11.7826 | − | 20.4080i | 0.588394 | − | 1.01913i | −0.406048 | − | 0.913852i | \(-0.633094\pi\) |
0.994443 | − | 0.105278i | \(-0.0335731\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −2.49389 | − | 4.31954i | −0.124229 | − | 0.215172i | ||||
\(404\) | 3.45355 | 0.171820 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −33.0410 | −1.63980 | ||||||||
\(407\) | 5.08613 | + | 8.80944i | 0.252110 | + | 0.436668i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −0.524200 | + | 0.907940i | −0.0259200 | + | 0.0448948i | −0.878694 | − | 0.477385i | \(-0.841585\pi\) |
0.852774 | + | 0.522279i | \(0.174918\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 8.84823 | + | 15.3256i | 0.435921 | + | 0.755037i | ||||
\(413\) | 17.0484 | 0.838897 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 2.62015 | + | 4.53824i | 0.128464 | + | 0.222505i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0.913870 | − | 1.58287i | 0.0446988 | − | 0.0774207i | ||||
\(419\) | −12.9599 | + | 22.4471i | −0.633131 | + | 1.09661i | 0.353777 | + | 0.935330i | \(0.384897\pi\) |
−0.986908 | + | 0.161285i | \(0.948436\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −3.82032 | − | 6.61699i | −0.186191 | − | 0.322492i | 0.757786 | − | 0.652503i | \(-0.226281\pi\) |
−0.943977 | + | 0.330011i | \(0.892948\pi\) | |||||||
\(422\) | −31.2765 | −1.52252 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −3.06324 | −0.148764 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −7.80516 | + | 13.5189i | −0.377718 | + | 0.654227i | ||||
\(428\) | −1.42291 | + | 2.46456i | −0.0687791 | + | 0.119129i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −7.98516 | −0.384632 | −0.192316 | − | 0.981333i | \(-0.561600\pi\) | ||||
−0.192316 | + | 0.981333i | \(0.561600\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 12.5120 | 0.601287 | 0.300644 | − | 0.953737i | \(-0.402799\pi\) | ||||
0.300644 | + | 0.953737i | \(0.402799\pi\) | |||||||
\(434\) | 32.8031 | + | 56.8166i | 1.57460 | + | 2.72728i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −16.5861 | + | 28.7280i | −0.794332 | + | 1.37582i | ||||
\(437\) | −1.55211 | + | 2.68833i | −0.0742474 | + | 0.128600i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 4.38225 | + | 7.59028i | 0.209153 | + | 0.362264i | 0.951448 | − | 0.307809i | \(-0.0995958\pi\) |
−0.742295 | + | 0.670074i | \(0.766263\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −1.82774 | −0.0869367 | ||||||||
\(443\) | −1.83548 | − | 3.17914i | −0.0872062 | − | 0.151046i | 0.819123 | − | 0.573618i | \(-0.194461\pi\) |
−0.906329 | + | 0.422572i | \(0.861127\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 27.9865 | − | 48.4740i | 1.32520 | − | 2.29531i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −21.5016 | − | 37.2419i | −1.01586 | − | 1.75951i | ||||
\(449\) | −28.1723 | −1.32953 | −0.664766 | − | 0.747052i | \(-0.731469\pi\) | ||||
−0.664766 | + | 0.747052i | \(0.731469\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0.242915 | 0.0114384 | ||||||||
\(452\) | 14.0229 | + | 24.2884i | 0.659581 | + | 1.14243i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 1.41016 | − | 2.44247i | 0.0661821 | − | 0.114631i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 17.6308 | + | 30.5375i | 0.824735 | + | 1.42848i | 0.902122 | + | 0.431482i | \(0.142009\pi\) |
−0.0773867 | + | 0.997001i | \(0.524658\pi\) | |||||||
\(458\) | 17.1803 | 0.802784 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 17.3384 | + | 30.0310i | 0.807530 | + | 1.39868i | 0.914570 | + | 0.404428i | \(0.132530\pi\) |
−0.107039 | + | 0.994255i | \(0.534137\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 3.72437 | − | 6.45080i | 0.173086 | − | 0.299794i | −0.766411 | − | 0.642350i | \(-0.777959\pi\) |
0.939497 | + | 0.342556i | \(0.111293\pi\) | |||||||
\(464\) | −6.14806 | + | 10.6488i | −0.285417 | + | 0.494356i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 8.95725 | + | 15.5144i | 0.414937 | + | 0.718692i | ||||
\(467\) | 29.9655 | 1.38664 | 0.693319 | − | 0.720630i | \(-0.256148\pi\) | ||||
0.693319 | + | 0.720630i | \(0.256148\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 33.2691 | 1.53622 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −1.53162 | + | 2.65284i | −0.0704984 | + | 0.122107i | ||||
\(473\) | −0.554512 | + | 0.960443i | −0.0254965 | + | 0.0441612i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 12.9926 | 0.595514 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −49.9097 | −2.28282 | ||||||||
\(479\) | −3.99258 | − | 6.91535i | −0.182426 | − | 0.315971i | 0.760280 | − | 0.649595i | \(-0.225062\pi\) |
−0.942706 | + | 0.333625i | \(0.891728\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −2.43807 | + | 4.22286i | −0.111166 | + | 0.192546i | ||||
\(482\) | −6.50904 | + | 11.2740i | −0.296479 | + | 0.513516i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 10.7863 | + | 18.6824i | 0.490286 | + | 0.849201i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 11.9442 | 0.541243 | 0.270621 | − | 0.962686i | \(-0.412771\pi\) | ||||
0.270621 | + | 0.962686i | \(0.412771\pi\) | |||||||
\(488\) | −1.40242 | − | 2.42907i | −0.0634847 | − | 0.109959i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −4.61033 | + | 7.98533i | −0.208061 | + | 0.360373i | −0.951104 | − | 0.308872i | \(-0.900049\pi\) |
0.743042 | + | 0.669244i | \(0.233382\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −2.62015 | − | 4.53824i | −0.118006 | − | 0.204392i | ||||
\(494\) | 0.876139 | 0.0394193 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 24.4152 | 1.09627 | ||||||||
\(497\) | 12.4963 | + | 21.6442i | 0.560535 | + | 0.970876i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −15.0861 | + | 26.1299i | −0.675348 | + | 1.16974i | 0.301019 | + | 0.953618i | \(0.402673\pi\) |
−0.976367 | + | 0.216119i | \(0.930660\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 29.8031 | + | 51.6204i | 1.33018 | + | 2.30393i | ||||
\(503\) | −10.5981 | −0.472546 | −0.236273 | − | 0.971687i | \(-0.575926\pi\) | ||||
−0.236273 | + | 0.971687i | \(0.575926\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 6.75468 | + | 11.6995i | 0.300282 | + | 0.520104i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −8.32435 | + | 14.4182i | −0.369333 | + | 0.639704i | ||||
\(509\) | 14.3761 | − | 24.9002i | 0.637211 | − | 1.10368i | −0.348831 | − | 0.937186i | \(-0.613421\pi\) |
0.986042 | − | 0.166496i | \(-0.0532454\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 25.2207 | + | 43.6835i | 1.11570 | + | 1.93244i | ||||
\(512\) | −30.3094 | −1.33950 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 37.5503 | 1.65627 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −7.37243 | + | 12.7694i | −0.324239 | + | 0.561599i | ||||
\(518\) | 32.0689 | − | 55.5449i | 1.40903 | − | 2.44050i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 36.0942 | 1.58132 | 0.790658 | − | 0.612259i | \(-0.209739\pi\) | ||||
0.790658 | + | 0.612259i | \(0.209739\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −11.1297 | −0.486669 | −0.243334 | − | 0.969942i | \(-0.578241\pi\) | ||||
−0.243334 | + | 0.969942i | \(0.578241\pi\) | |||||||
\(524\) | −7.05582 | − | 12.2210i | −0.308235 | − | 0.533878i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 33.2411 | − | 57.5754i | 1.44938 | − | 2.51041i | ||||
\(527\) | −5.20257 | + | 9.01112i | −0.226628 | + | 0.392531i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 0.0279088 | + | 0.0483395i | 0.00121343 | + | 0.00210172i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −6.22808 | −0.270021 | ||||||||
\(533\) | 0.0582214 | + | 0.100842i | 0.00252185 | + | 0.00436797i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −2.98887 | + | 5.17688i | −0.129100 | + | 0.223607i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 32.8536 | + | 56.9040i | 1.41642 | + | 2.45331i | ||||
\(539\) | 13.1090 | 0.564646 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −34.7374 | −1.49348 | −0.746740 | − | 0.665116i | \(-0.768382\pi\) | ||||
−0.746740 | + | 0.665116i | \(0.768382\pi\) | |||||||
\(542\) | −3.37985 | − | 5.85407i | −0.145177 | − | 0.251454i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 5.46598 | − | 9.46735i | 0.234352 | − | 0.405909i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −1.35727 | − | 2.35087i | −0.0580328 | − | 0.100516i | 0.835549 | − | 0.549415i | \(-0.185149\pi\) |
−0.893582 | + | 0.448899i | \(0.851816\pi\) | |||||||
\(548\) | −17.5652 | −0.750347 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 1.25599 | + | 2.17543i | 0.0535068 | + | 0.0926766i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 21.1345 | − | 36.6061i | 0.898732 | − | 1.55665i | ||||
\(554\) | 5.82534 | − | 10.0898i | 0.247495 | − | 0.428674i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −9.40776 | − | 16.2947i | −0.398978 | − | 0.691050i | ||||
\(557\) | −8.93676 | −0.378663 | −0.189331 | − | 0.981913i | \(-0.560632\pi\) | ||||
−0.189331 | + | 0.981913i | \(0.560632\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −0.531618 | −0.0224850 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 25.1423 | − | 43.5477i | 1.06056 | − | 1.83695i | ||||
\(563\) | 4.68130 | − | 8.10826i | 0.197293 | − | 0.341722i | −0.750357 | − | 0.661033i | \(-0.770118\pi\) |
0.947650 | + | 0.319311i | \(0.103451\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −21.9926 | −0.924417 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −4.49064 | −0.188423 | ||||||||
\(569\) | 17.9368 | + | 31.0674i | 0.751948 | + | 1.30241i | 0.946877 | + | 0.321595i | \(0.104219\pi\) |
−0.194929 | + | 0.980817i | \(0.562448\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −10.0000 | + | 17.3205i | −0.418487 | + | 0.724841i | −0.995788 | − | 0.0916910i | \(-0.970773\pi\) |
0.577301 | + | 0.816532i | \(0.304106\pi\) | |||||||
\(572\) | 1.03031 | − | 1.78455i | 0.0430795 | − | 0.0746159i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −0.765809 | − | 1.32642i | −0.0319643 | − | 0.0553637i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −1.35675 | −0.0564821 | −0.0282411 | − | 0.999601i | \(-0.508991\pi\) | ||||
−0.0282411 | + | 0.999601i | \(0.508991\pi\) | |||||||
\(578\) | −15.8257 | − | 27.4108i | −0.658260 | − | 1.14014i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −25.0447 | + | 43.3787i | −1.03903 | + | 1.79965i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −2.82032 | − | 4.88494i | −0.116806 | − | 0.202314i | ||||
\(584\) | −9.06324 | −0.375039 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −39.6210 | −1.63673 | ||||||||
\(587\) | −14.3950 | − | 24.9329i | −0.594145 | − | 1.02909i | −0.993667 | − | 0.112366i | \(-0.964157\pi\) |
0.399521 | − | 0.916724i | \(-0.369176\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 2.49389 | − | 4.31954i | 0.102759 | − | 0.177984i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −11.9344 | − | 20.6709i | −0.490499 | − | 0.849570i | ||||
\(593\) | 30.9171 | 1.26961 | 0.634807 | − | 0.772671i | \(-0.281080\pi\) | ||||
0.634807 | + | 0.772671i | \(0.281080\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −12.4474 | − | 21.5596i | −0.509867 | − | 0.883115i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −3.23790 | + | 5.60821i | −0.132408 | + | 0.229337i | ||||
\(599\) | 0.696460 | − | 1.20630i | 0.0284566 | − | 0.0492882i | −0.851446 | − | 0.524442i | \(-0.824274\pi\) |
0.879903 | + | 0.475153i | \(0.157607\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −4.41256 | − | 7.64279i | −0.179992 | − | 0.311756i | 0.761885 | − | 0.647712i | \(-0.224274\pi\) |
−0.941878 | + | 0.335956i | \(0.890941\pi\) | |||||||
\(602\) | 6.99258 | 0.284996 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 41.6210 | 1.69353 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −1.07839 | + | 1.86783i | −0.0437706 | + | 0.0758129i | −0.887081 | − | 0.461614i | \(-0.847270\pi\) |
0.843310 | + | 0.537427i | \(0.180604\pi\) | |||||||
\(608\) | −2.62015 | + | 4.53824i | −0.106261 | + | 0.184050i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −7.06804 | −0.285942 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 9.57521 | 0.386739 | 0.193370 | − | 0.981126i | \(-0.438058\pi\) | ||||
0.193370 | + | 0.981126i | \(0.438058\pi\) | |||||||
\(614\) | −30.7486 | − | 53.2581i | −1.24091 | − | 2.14932i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −2.02791 | + | 3.51244i | −0.0817068 | + | 0.141520i | ||||
\(617\) | 18.8384 | − | 32.6291i | 0.758406 | − | 1.31360i | −0.185258 | − | 0.982690i | \(-0.559312\pi\) |
0.943663 | − | 0.330907i | \(-0.107355\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −8.55211 | − | 14.8127i | −0.343738 | − | 0.595372i | 0.641385 | − | 0.767219i | \(-0.278360\pi\) |
−0.985124 | + | 0.171847i | \(0.945027\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −19.6358 | −0.787325 | ||||||||
\(623\) | 6.12920 | + | 10.6161i | 0.245561 | + | 0.425324i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −12.1215 | + | 20.9950i | −0.484471 | + | 0.839128i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −2.97711 | − | 5.15650i | −0.118799 | − | 0.205767i | ||||
\(629\) | 10.1723 | 0.405595 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 33.1090 | 1.31805 | 0.659025 | − | 0.752121i | \(-0.270969\pi\) | ||||
0.659025 | + | 0.752121i | \(0.270969\pi\) | |||||||
\(632\) | 3.79743 | + | 6.57734i | 0.151054 | + | 0.261632i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −9.57500 | + | 16.5844i | −0.380272 | + | 0.658650i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 3.14195 | + | 5.44201i | 0.124489 | + | 0.215620i | ||||
\(638\) | 10.9320 | 0.432800 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −11.5763 | − | 20.0508i | −0.457237 | − | 0.791957i | 0.541577 | − | 0.840651i | \(-0.317827\pi\) |
−0.998814 | + | 0.0486939i | \(0.984494\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 21.5319 | − | 37.2944i | 0.849137 | − | 1.47075i | −0.0328430 | − | 0.999461i | \(-0.510456\pi\) |
0.881980 | − | 0.471287i | \(-0.156211\pi\) | |||||||
\(644\) | 23.0168 | − | 39.8662i | 0.906988 | − | 1.57095i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −0.913870 | − | 1.58287i | −0.0359557 | − | 0.0622771i | ||||
\(647\) | −20.6439 | −0.811595 | −0.405798 | − | 0.913963i | \(-0.633006\pi\) | ||||
−0.405798 | + | 0.913963i | \(0.633006\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −5.64064 | −0.221415 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 9.96728 | − | 17.2638i | 0.390349 | − | 0.676104i | ||||
\(653\) | −3.41758 | + | 5.91942i | −0.133740 | + | 0.231645i | −0.925116 | − | 0.379686i | \(-0.876032\pi\) |
0.791375 | + | 0.611331i | \(0.209365\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −0.569988 | −0.0222543 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 92.9688 | 3.62430 | ||||||||
\(659\) | −13.4307 | − | 23.2626i | −0.523184 | − | 0.906181i | −0.999636 | − | 0.0269806i | \(-0.991411\pi\) |
0.476452 | − | 0.879200i | \(-0.341923\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 1.06063 | − | 1.83706i | 0.0412535 | − | 0.0714532i | −0.844661 | − | 0.535301i | \(-0.820198\pi\) |
0.885915 | + | 0.463848i | \(0.153532\pi\) | |||||||
\(662\) | −7.53162 | + | 13.0451i | −0.292725 | + | 0.507014i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −4.50000 | − | 7.79423i | −0.174634 | − | 0.302475i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −18.5667 | −0.718907 | ||||||||
\(668\) | −14.9750 | − | 25.9375i | −0.579401 | − | 1.00355i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 2.58242 | − | 4.47288i | 0.0996933 | − | 0.172674i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 17.4102 | + | 30.1553i | 0.671112 | + | 1.16240i | 0.977589 | + | 0.210523i | \(0.0675165\pi\) |
−0.306477 | + | 0.951878i | \(0.599150\pi\) | |||||||
\(674\) | 4.76450 | 0.183522 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −29.5874 | −1.13798 | ||||||||
\(677\) | 12.3421 | + | 21.3772i | 0.474346 | + | 0.821592i | 0.999569 | − | 0.0293735i | \(-0.00935121\pi\) |
−0.525222 | + | 0.850965i | \(0.676018\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 27.7449 | − | 48.0555i | 1.06475 | − | 1.84420i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −10.8532 | − | 18.7984i | −0.415592 | − | 0.719827i | ||||
\(683\) | −38.4610 | −1.47167 | −0.735834 | − | 0.677162i | \(-0.763210\pi\) | ||||
−0.735834 | + | 0.677162i | \(0.763210\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −11.4926 | − | 19.9057i | −0.438789 | − | 0.760005i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 1.30114 | − | 2.25363i | 0.0496054 | − | 0.0859190i | ||||
\(689\) | 1.35194 | − | 2.34163i | 0.0515048 | − | 0.0892089i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −0.240304 | − | 0.416219i | −0.00914159 | − | 0.0158337i | 0.861418 | − | 0.507896i | \(-0.169577\pi\) |
−0.870560 | + | 0.492062i | \(0.836243\pi\) | |||||||
\(692\) | 54.2084 | 2.06070 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 1.47841 | 0.0561197 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0.121457 | − | 0.210370i | 0.00460053 | − | 0.00796835i | ||||
\(698\) | −22.2637 | + | 38.5619i | −0.842694 | + | 1.45959i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 18.1797 | 0.686637 | 0.343318 | − | 0.939219i | \(-0.388449\pi\) | ||||
0.343318 | + | 0.939219i | \(0.388449\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −4.87614 | −0.183907 | ||||||||
\(704\) | 7.11404 | + | 12.3219i | 0.268120 | + | 0.464398i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −10.5316 | + | 18.2413i | −0.396363 | + | 0.686520i | ||||
\(707\) | 3.00000 | − | 5.19615i | 0.112827 | − | 0.195421i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −3.59355 | − | 6.22421i | −0.134959 | − | 0.233755i | 0.790623 | − | 0.612303i | \(-0.209757\pi\) |
−0.925582 | + | 0.378548i | \(0.876423\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −2.20257 | −0.0825449 | ||||||||
\(713\) | 18.4331 | + | 31.9270i | 0.690323 | + | 1.19568i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 2.62015 | − | 4.53824i | 0.0979197 | − | 0.169602i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −31.8737 | − | 55.2069i | −1.18952 | − | 2.06030i | ||||
\(719\) | −12.5168 | −0.466797 | −0.233399 | − | 0.972381i | \(-0.574985\pi\) | ||||
−0.233399 | + | 0.972381i | \(0.574985\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 30.7449 | 1.14500 | ||||||||
\(722\) | −19.3802 | − | 33.5674i | −0.721255 | − | 1.24925i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −0.550803 | + | 0.954019i | −0.0204704 | + | 0.0354558i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 4.21292 | + | 7.29699i | 0.156249 | + | 0.270631i | 0.933513 | − | 0.358544i | \(-0.116727\pi\) |
−0.777264 | + | 0.629174i | \(0.783393\pi\) | |||||||
\(728\) | −1.94418 | −0.0720562 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0.554512 | + | 0.960443i | 0.0205094 | + | 0.0355233i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −11.0000 | + | 19.0526i | −0.406294 | + | 0.703722i | −0.994471 | − | 0.105010i | \(-0.966513\pi\) |
0.588177 | + | 0.808732i | \(0.299846\pi\) | |||||||
\(734\) | 7.48887 | − | 12.9711i | 0.276419 | − | 0.478772i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −19.3663 | − | 33.5434i | −0.713852 | − | 1.23643i | ||||
\(737\) | −11.0074 | −0.405463 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −1.81290 | −0.0666887 | −0.0333444 | − | 0.999444i | \(-0.510616\pi\) | ||||
−0.0333444 | + | 0.999444i | \(0.510616\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −17.7826 | + | 30.8003i | −0.652819 | + | 1.13072i | ||||
\(743\) | −10.0686 | + | 17.4393i | −0.369380 | + | 0.639785i | −0.989469 | − | 0.144747i | \(-0.953763\pi\) |
0.620089 | + | 0.784532i | \(0.287097\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −45.7374 | −1.67457 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −4.29873 | −0.157177 | ||||||||
\(749\) | 2.47209 | + | 4.28179i | 0.0903282 | + | 0.156453i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −6.10662 | + | 10.5770i | −0.222834 | + | 0.385959i | −0.955667 | − | 0.294449i | \(-0.904864\pi\) |
0.732834 | + | 0.680408i | \(0.238197\pi\) | |||||||
\(752\) | 17.2991 | − | 29.9628i | 0.630832 | − | 1.09263i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 2.62015 | + | 4.53824i | 0.0954203 | + | 0.165273i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −52.9533 | −1.92462 | −0.962310 | − | 0.271955i | \(-0.912330\pi\) | ||||
−0.962310 | + | 0.271955i | \(0.912330\pi\) | |||||||
\(758\) | −18.1419 | − | 31.4228i | −0.658945 | − | 1.14133i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −9.22677 | + | 15.9812i | −0.334470 | + | 0.579319i | −0.983383 | − | 0.181543i | \(-0.941891\pi\) |
0.648913 | + | 0.760863i | \(0.275224\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 28.8158 | + | 49.9105i | 1.04320 | + | 1.80688i | ||||
\(764\) | 47.5752 | 1.72121 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −0.992582 | −0.0358634 | ||||||||
\(767\) | −1.35194 | − | 2.34163i | −0.0488157 | − | 0.0845513i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 2.22677 | − | 3.85688i | 0.0802995 | − | 0.139083i | −0.823079 | − | 0.567927i | \(-0.807746\pi\) |
0.903379 | + | 0.428844i | \(0.141079\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −23.4363 | − | 40.5929i | −0.843491 | − | 1.46097i | ||||
\(773\) | 38.9368 | 1.40046 | 0.700229 | − | 0.713918i | \(-0.253081\pi\) | ||||
0.700229 | + | 0.713918i | \(0.253081\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 4.98516 | + | 8.63456i | 0.178957 | + | 0.309962i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 5.82806 | − | 10.0945i | 0.208946 | − | 0.361905i | ||||
\(779\) | −0.0582214 | + | 0.100842i | −0.00208600 | + | 0.00361305i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −4.13453 | − | 7.16121i | −0.147945 | − | 0.256248i | ||||
\(782\) | 13.5094 | 0.483094 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −30.7597 | −1.09856 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 17.1140 | − | 29.6424i | 0.610050 | − | 1.05664i | −0.381182 | − | 0.924500i | \(-0.624483\pi\) |
0.991231 | − | 0.132137i | \(-0.0421838\pi\) | |||||||
\(788\) | 18.3216 | − | 31.7340i | 0.652681 | − | 1.13048i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 48.7252 | 1.73247 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 2.47580 | 0.0879183 | ||||||||
\(794\) | −3.91387 | − | 6.77902i | −0.138898 | − | 0.240578i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −4.21564 | + | 7.30171i | −0.149420 | + | 0.258802i | ||||
\(797\) | −11.9828 | + | 20.7547i | −0.424451 | + | 0.735171i | −0.996369 | − | 0.0851400i | \(-0.972866\pi\) |
0.571918 | + | 0.820311i | \(0.306200\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 7.37243 | + | 12.7694i | 0.260818 | + | 0.451750i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 49.1600 | 1.73590 | ||||||||
\(803\) | −8.34452 | − | 14.4531i | −0.294472 | − | 0.510040i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 5.20257 | − | 9.01112i | 0.183253 | − | 0.317403i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0.539036 | + | 0.933638i | 0.0189632 | + | 0.0328453i | ||||
\(809\) | 0.283896 | 0.00998124 | 0.00499062 | − | 0.999988i | \(-0.498411\pi\) | ||||
0.00499062 | + | 0.999988i | \(0.498411\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 32.4413 | 1.13917 | 0.569584 | − | 0.821933i | \(-0.307104\pi\) | ||||
0.569584 | + | 0.821933i | \(0.307104\pi\) | |||||||
\(812\) | −18.6255 | − | 32.2603i | −0.653626 | − | 1.13211i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −10.6103 | + | 18.3776i | −0.371892 | + | 0.644136i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −0.265809 | − | 0.460395i | −0.00929948 | − | 0.0161072i | ||||
\(818\) | −2.18710 | −0.0764701 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 20.8347 | + | 36.0868i | 0.727136 | + | 1.25944i | 0.958089 | + | 0.286472i | \(0.0924824\pi\) |
−0.230953 | + | 0.972965i | \(0.574184\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −9.68130 | + | 16.7685i | −0.337469 | + | 0.584514i | −0.983956 | − | 0.178412i | \(-0.942904\pi\) |
0.646487 | + | 0.762925i | \(0.276237\pi\) | |||||||
\(824\) | −2.76210 | + | 4.78410i | −0.0962223 | + | 0.166662i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 17.7826 | + | 30.8003i | 0.618735 | + | 1.07168i | ||||
\(827\) | 18.8097 | 0.654076 | 0.327038 | − | 0.945011i | \(-0.393950\pi\) | ||||
0.327038 | + | 0.945011i | \(0.393950\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −33.1016 | −1.14967 | −0.574833 | − | 0.818271i | \(-0.694933\pi\) | ||||
−0.574833 | + | 0.818271i | \(0.694933\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −3.41016 | + | 5.90657i | −0.118226 | + | 0.204774i | ||||
\(833\) | 6.55451 | − | 11.3527i | 0.227100 | − | 0.393349i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 2.06063 | 0.0712682 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −54.0719 | −1.86788 | ||||||||
\(839\) | −19.8482 | − | 34.3781i | −0.685237 | − | 1.18687i | −0.973362 | − | 0.229273i | \(-0.926365\pi\) |
0.288125 | − | 0.957593i | \(-0.406968\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 6.98777 | − | 12.1032i | 0.240958 | − | 0.417351i | ||||
\(842\) | 7.96969 | − | 13.8039i | 0.274654 | − | 0.475714i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −17.6308 | − | 30.5375i | −0.606878 | − | 1.05114i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 37.4791 | 1.28780 | ||||||||
\(848\) | 6.61775 | + | 11.4623i | 0.227254 | + | 0.393616i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 18.0205 | − | 31.2124i | 0.617734 | − | 1.06995i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −2.05822 | − | 3.56494i | −0.0704722 | − | 0.122061i | 0.828636 | − | 0.559788i | \(-0.189117\pi\) |
−0.899108 | + | 0.437726i | \(0.855784\pi\) | |||||||
\(854\) | −32.5652 | −1.11436 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −0.888365 | −0.0303637 | ||||||||
\(857\) | −7.37243 | − | 12.7694i | −0.251837 | − | 0.436195i | 0.712194 | − | 0.701982i | \(-0.247701\pi\) |
−0.964032 | + | 0.265787i | \(0.914368\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 18.9269 | − | 32.7824i | 0.645779 | − | 1.11852i | −0.338342 | − | 0.941023i | \(-0.609866\pi\) |
0.984121 | − | 0.177499i | \(-0.0568006\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −8.32905 | − | 14.4263i | −0.283688 | − | 0.491363i | ||||
\(863\) | 26.7704 | 0.911274 | 0.455637 | − | 0.890166i | \(-0.349412\pi\) | ||||
0.455637 | + | 0.890166i | \(0.349412\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 13.0508 | + | 22.6047i | 0.443484 | + | 0.768137i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −36.9828 | + | 64.0560i | −1.25528 | + | 2.17420i | ||||
\(869\) | −6.99258 | + | 12.1115i | −0.237207 | + | 0.410855i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −2.63824 | − | 4.56956i | −0.0893933 | − | 0.154834i | ||||
\(872\) | −10.3552 | −0.350671 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −6.47580 | −0.219047 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −23.4841 | + | 40.6756i | −0.793001 | + | 1.37352i | 0.131101 | + | 0.991369i | \(0.458149\pi\) |
−0.924101 | + | 0.382148i | \(0.875184\pi\) | |||||||
\(878\) | −9.14195 | + | 15.8343i | −0.308526 | + | 0.534382i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 19.8055 | 0.667264 | 0.333632 | − | 0.942703i | \(-0.391726\pi\) | ||||
0.333632 | + | 0.942703i | \(0.391726\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 6.20257 | 0.208733 | 0.104367 | − | 0.994539i | \(-0.466718\pi\) | ||||
0.104367 | + | 0.994539i | \(0.466718\pi\) | |||||||
\(884\) | −1.03031 | − | 1.78455i | −0.0346532 | − | 0.0600210i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 3.82905 | − | 6.63210i | 0.128639 | − | 0.222810i | ||||
\(887\) | −6.71370 | + | 11.6285i | −0.225424 | + | 0.390446i | −0.956447 | − | 0.291907i | \(-0.905710\pi\) |
0.731023 | + | 0.682353i | \(0.239043\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 14.4623 | + | 25.0494i | 0.485049 | + | 0.840129i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 63.1049 | 2.11291 | ||||||||
\(893\) | −3.53402 | − | 6.12111i | −0.118262 | − | 0.204835i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 11.8142 | − | 20.4628i | 0.394685 | − | 0.683614i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −29.3855 | − | 50.8972i | −0.980607 | − | 1.69846i | ||||
\(899\) | 29.8325 | 0.994971 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −5.64064 | −0.187917 | ||||||||
\(902\) | 0.253376 | + | 0.438860i | 0.00843650 | + | 0.0146124i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −4.37744 | + | 7.58196i | −0.145592 | + | 0.252172i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 0.336783 | + | 0.583325i | 0.0111827 | + | 0.0193690i | 0.871563 | − | 0.490284i | \(-0.163107\pi\) |
−0.860380 | + | 0.509653i | \(0.829774\pi\) | |||||||
\(908\) | 3.17968 | 0.105521 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −3.95485 | − | 6.85000i | −0.131030 | − | 0.226951i | 0.793044 | − | 0.609165i | \(-0.208495\pi\) |
−0.924074 | + | 0.382214i | \(0.875162\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 8.28630 | − | 14.3523i | 0.274236 | − | 0.474992i | ||||
\(914\) | −36.7802 | + | 63.7052i | −1.21658 | + | 2.10718i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 9.68469 | + | 16.7744i | 0.319991 | + | 0.554241i | ||||
\(917\) | −24.5168 | −0.809615 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −8.58263 | −0.283115 | −0.141557 | − | 0.989930i | \(-0.545211\pi\) | ||||
−0.141557 | + | 0.989930i | \(0.545211\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −36.1702 | + | 62.6486i | −1.19120 | + | 2.06322i | ||||
\(923\) | 1.98191 | − | 3.43277i | 0.0652355 | − | 0.112991i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 15.5390 | 0.510644 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −31.3430 | −1.02888 | ||||||||
\(929\) | 14.8081 | + | 25.6484i | 0.485838 | + | 0.841496i | 0.999868 | − | 0.0162766i | \(-0.00518122\pi\) |
−0.514030 | + | 0.857772i | \(0.671848\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −3.14195 | + | 5.44201i | −0.102973 | + | 0.178355i | ||||
\(932\) | −10.0986 | + | 17.4912i | −0.330789 | + | 0.572944i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 31.2560 | + | 54.1370i | 1.02273 | + | 1.77142i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 15.2058 | 0.496753 | 0.248376 | − | 0.968664i | \(-0.420103\pi\) | ||||
0.248376 | + | 0.968664i | \(0.420103\pi\) | |||||||
\(938\) | 34.7018 | + | 60.1053i | 1.13305 | + | 1.96251i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 2.82643 | − | 4.89553i | 0.0921391 | − | 0.159590i | −0.816272 | − | 0.577668i | \(-0.803963\pi\) |
0.908411 | + | 0.418078i | \(0.137296\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −0.430332 | − | 0.745356i | −0.0140135 | − | 0.0242721i | ||||
\(944\) | 13.2355 | 0.430779 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −2.31357 | −0.0752206 | ||||||||
\(947\) | 20.1981 | + | 34.9841i | 0.656350 | + | 1.13683i | 0.981554 | + | 0.191187i | \(0.0612337\pi\) |
−0.325204 | + | 0.945644i | \(0.605433\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 4.00000 | − | 6.92820i | 0.129845 | − | 0.224899i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 2.02791 | + | 3.51244i | 0.0657249 | + | 0.113839i | ||||
\(953\) | −22.9320 | −0.742839 | −0.371419 | − | 0.928465i | \(-0.621129\pi\) | ||||
−0.371419 | + | 0.928465i | \(0.621129\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −28.1345 | − | 48.7304i | −0.909936 | − | 1.57605i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 8.32905 | − | 14.4263i | 0.269099 | − | 0.466094i | ||||
\(959\) | −15.2584 | + | 26.4283i | −0.492719 | + | 0.853415i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −14.1177 | − | 24.4527i | −0.455411 | − | 0.788795i | ||||
\(962\) | −10.1723 | −0.327967 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −14.6768 | −0.472708 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 5.18501 | − | 8.98071i | 0.166739 | − | 0.288800i | −0.770533 | − | 0.637401i | \(-0.780010\pi\) |
0.937271 | + | 0.348601i | \(0.113343\pi\) | |||||||
\(968\) | −3.36710 | + | 5.83198i | −0.108223 | + | 0.187447i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −48.0410 | −1.54171 | −0.770854 | − | 0.637012i | \(-0.780170\pi\) | ||||
−0.770854 | + | 0.637012i | \(0.780170\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −32.6890 | −1.04796 | ||||||||
\(974\) | 12.4586 | + | 21.5789i | 0.399198 | + | 0.691431i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −6.05953 | + | 10.4954i | −0.193961 | + | 0.335950i | ||||
\(977\) | −13.5266 | + | 23.4288i | −0.432754 | + | 0.749553i | −0.997109 | − | 0.0759796i | \(-0.975792\pi\) |
0.564355 | + | 0.825532i | \(0.309125\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −2.02791 | − | 3.51244i | −0.0648122 | − | 0.112258i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −19.2355 | −0.613829 | ||||||||
\(983\) | 11.2408 | + | 19.4697i | 0.358527 | + | 0.620987i | 0.987715 | − | 0.156266i | \(-0.0499458\pi\) |
−0.629188 | + | 0.777253i | \(0.716612\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 5.46598 | − | 9.46735i | 0.174072 | − | 0.301502i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0.493887 | + | 0.855437i | 0.0157126 | + | 0.0272151i | ||||
\(989\) | 3.92935 | 0.124946 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −26.5316 | −0.842805 | −0.421402 | − | 0.906874i | \(-0.638462\pi\) | ||||
−0.421402 | + | 0.906874i | \(0.638462\pi\) | |||||||
\(992\) | 31.1173 | + | 53.8967i | 0.987975 | + | 1.71122i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −26.0689 | + | 45.1526i | −0.826855 | + | 1.43215i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −14.1829 | − | 24.5656i | −0.449178 | − | 0.777999i | 0.549155 | − | 0.835721i | \(-0.314950\pi\) |
−0.998333 | + | 0.0577217i | \(0.981616\pi\) | |||||||
\(998\) | −62.9433 | −1.99243 | ||||||||
\(999\) | 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 | 675.2.e.b.226.3 | 6 | ||
3.2 | odd | 2 | 225.2.e.b.76.1 | 6 | |||
5.2 | odd | 4 | 675.2.k.b.199.2 | 12 | |||
5.3 | odd | 4 | 675.2.k.b.199.5 | 12 | |||
5.4 | even | 2 | 135.2.e.b.91.1 | 6 | |||
9.2 | odd | 6 | 225.2.e.b.151.1 | 6 | |||
9.4 | even | 3 | 2025.2.a.o.1.1 | 3 | |||
9.5 | odd | 6 | 2025.2.a.n.1.3 | 3 | |||
9.7 | even | 3 | inner | 675.2.e.b.451.3 | 6 | ||
15.2 | even | 4 | 225.2.k.b.49.5 | 12 | |||
15.8 | even | 4 | 225.2.k.b.49.2 | 12 | |||
15.14 | odd | 2 | 45.2.e.b.31.3 | yes | 6 | ||
20.19 | odd | 2 | 2160.2.q.k.1441.3 | 6 | |||
45.2 | even | 12 | 225.2.k.b.124.2 | 12 | |||
45.4 | even | 6 | 405.2.a.i.1.3 | 3 | |||
45.7 | odd | 12 | 675.2.k.b.424.5 | 12 | |||
45.13 | odd | 12 | 2025.2.b.m.649.5 | 6 | |||
45.14 | odd | 6 | 405.2.a.j.1.1 | 3 | |||
45.22 | odd | 12 | 2025.2.b.m.649.2 | 6 | |||
45.23 | even | 12 | 2025.2.b.l.649.2 | 6 | |||
45.29 | odd | 6 | 45.2.e.b.16.3 | ✓ | 6 | ||
45.32 | even | 12 | 2025.2.b.l.649.5 | 6 | |||
45.34 | even | 6 | 135.2.e.b.46.1 | 6 | |||
45.38 | even | 12 | 225.2.k.b.124.5 | 12 | |||
45.43 | odd | 12 | 675.2.k.b.424.2 | 12 | |||
60.59 | even | 2 | 720.2.q.i.481.3 | 6 | |||
180.59 | even | 6 | 6480.2.a.bv.1.1 | 3 | |||
180.79 | odd | 6 | 2160.2.q.k.721.3 | 6 | |||
180.119 | even | 6 | 720.2.q.i.241.3 | 6 | |||
180.139 | odd | 6 | 6480.2.a.bs.1.1 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
45.2.e.b.16.3 | ✓ | 6 | 45.29 | odd | 6 | ||
45.2.e.b.31.3 | yes | 6 | 15.14 | odd | 2 | ||
135.2.e.b.46.1 | 6 | 45.34 | even | 6 | |||
135.2.e.b.91.1 | 6 | 5.4 | even | 2 | |||
225.2.e.b.76.1 | 6 | 3.2 | odd | 2 | |||
225.2.e.b.151.1 | 6 | 9.2 | odd | 6 | |||
225.2.k.b.49.2 | 12 | 15.8 | even | 4 | |||
225.2.k.b.49.5 | 12 | 15.2 | even | 4 | |||
225.2.k.b.124.2 | 12 | 45.2 | even | 12 | |||
225.2.k.b.124.5 | 12 | 45.38 | even | 12 | |||
405.2.a.i.1.3 | 3 | 45.4 | even | 6 | |||
405.2.a.j.1.1 | 3 | 45.14 | odd | 6 | |||
675.2.e.b.226.3 | 6 | 1.1 | even | 1 | trivial | ||
675.2.e.b.451.3 | 6 | 9.7 | even | 3 | inner | ||
675.2.k.b.199.2 | 12 | 5.2 | odd | 4 | |||
675.2.k.b.199.5 | 12 | 5.3 | odd | 4 | |||
675.2.k.b.424.2 | 12 | 45.43 | odd | 12 | |||
675.2.k.b.424.5 | 12 | 45.7 | odd | 12 | |||
720.2.q.i.241.3 | 6 | 180.119 | even | 6 | |||
720.2.q.i.481.3 | 6 | 60.59 | even | 2 | |||
2025.2.a.n.1.3 | 3 | 9.5 | odd | 6 | |||
2025.2.a.o.1.1 | 3 | 9.4 | even | 3 | |||
2025.2.b.l.649.2 | 6 | 45.23 | even | 12 | |||
2025.2.b.l.649.5 | 6 | 45.32 | even | 12 | |||
2025.2.b.m.649.2 | 6 | 45.22 | odd | 12 | |||
2025.2.b.m.649.5 | 6 | 45.13 | odd | 12 | |||
2160.2.q.k.721.3 | 6 | 180.79 | odd | 6 | |||
2160.2.q.k.1441.3 | 6 | 20.19 | odd | 2 | |||
6480.2.a.bs.1.1 | 3 | 180.139 | odd | 6 | |||
6480.2.a.bv.1.1 | 3 | 180.59 | even | 6 |