Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1575,2,Mod(26,1575)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1575, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 0, 5]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1575.26");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1575 = 3^{2} \cdot 5^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1575.bk (of order \(6\), degree \(2\), 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: | \(12.5764383184\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Relative dimension: | \(6\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} + 20x^{10} + 144x^{8} + 452x^{6} + 604x^{4} + 312x^{2} + 36 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 3^{2} \) |
Twist minimal: | no (minimal twist has level 315) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 1151.4 | ||
Root | \(-0.398211i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1575.1151 |
Dual form | 1575.2.bk.e.26.4 |
$q$-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 \(\left(\mathbb{Z}/1575\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(451\) | \(1226\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{6}\right)\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.344861 | − | 0.199105i | 0.243853 | − | 0.140789i | −0.373093 | − | 0.927794i | \(-0.621703\pi\) |
0.616946 | + | 0.787005i | \(0.288370\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −0.920714 | + | 1.59472i | −0.460357 | + | 0.797362i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.30243 | − | 1.30338i | 0.870237 | − | 0.492632i | ||||
\(8\) | 1.52970i | 0.540830i | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −4.44725 | − | 2.56762i | −1.34090 | − | 0.774166i | −0.353956 | − | 0.935262i | \(-0.615164\pi\) |
−0.986939 | + | 0.161096i | \(0.948497\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 5.09545i | − | 1.41322i | −0.707601 | − | 0.706612i | \(-0.750222\pi\) | ||
0.707601 | − | 0.706612i | \(-0.249778\pi\) | |||||||
\(14\) | 0.534507 | − | 0.907912i | 0.142853 | − | 0.242650i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −1.53686 | − | 2.66191i | −0.384214 | − | 0.665479i | ||||
\(17\) | −2.24312 | + | 3.88520i | −0.544037 | + | 0.942299i | 0.454630 | + | 0.890680i | \(0.349772\pi\) |
−0.998667 | + | 0.0516191i | \(0.983562\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −3.29211 | + | 1.90070i | −0.755261 | + | 0.436050i | −0.827592 | − | 0.561330i | \(-0.810290\pi\) |
0.0723306 | + | 0.997381i | \(0.476956\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −2.04491 | −0.435976 | ||||||||
\(23\) | 2.29043 | − | 1.32238i | 0.477588 | − | 0.275736i | −0.241823 | − | 0.970320i | \(-0.577745\pi\) |
0.719411 | + | 0.694585i | \(0.244412\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −1.01453 | − | 1.75722i | −0.198966 | − | 0.344619i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −0.0413461 | + | 4.87179i | −0.00781368 | + | 0.920681i | ||||
\(29\) | 9.13574i | 1.69646i | 0.529624 | + | 0.848232i | \(0.322333\pi\) | ||||
−0.529624 | + | 0.848232i | \(0.677667\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −4.11981 | − | 2.37857i | −0.739939 | − | 0.427204i | 0.0821082 | − | 0.996623i | \(-0.473835\pi\) |
−0.822047 | + | 0.569419i | \(0.807168\pi\) | |||||||
\(32\) | −3.70952 | − | 2.14169i | −0.655756 | − | 0.378601i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 1.78647i | 0.306377i | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −4.70077 | − | 8.14197i | −0.772801 | − | 1.33853i | −0.936022 | − | 0.351942i | \(-0.885522\pi\) |
0.163221 | − | 0.986590i | \(-0.447812\pi\) | |||||||
\(38\) | −0.756879 | + | 1.31095i | −0.122782 | + | 0.212665i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −7.51505 | −1.17365 | −0.586827 | − | 0.809712i | \(-0.699623\pi\) | ||||
−0.586827 | + | 0.809712i | \(0.699623\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −6.73246 | −1.02669 | −0.513345 | − | 0.858182i | \(-0.671594\pi\) | ||||
−0.513345 | + | 0.858182i | \(0.671594\pi\) | |||||||
\(44\) | 8.18929 | − | 4.72809i | 1.23458 | − | 0.712786i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0.526586 | − | 0.912074i | 0.0776409 | − | 0.134478i | ||||
\(47\) | −3.91274 | − | 6.77706i | −0.570732 | − | 0.988536i | −0.996491 | − | 0.0836998i | \(-0.973326\pi\) |
0.425759 | − | 0.904836i | \(-0.360007\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 3.60239 | − | 6.00190i | 0.514627 | − | 0.857414i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 8.12584 | + | 4.69146i | 1.12685 | + | 0.650588i | ||||
\(53\) | 2.50449 | + | 1.44597i | 0.344018 | + | 0.198619i | 0.662047 | − | 0.749462i | \(-0.269688\pi\) |
−0.318029 | + | 0.948081i | \(0.603021\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 1.99378 | + | 3.52202i | 0.266430 | + | 0.470650i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 1.81897 | + | 3.15056i | 0.238843 | + | 0.413688i | ||||
\(59\) | 2.46549 | − | 4.27036i | 0.320980 | − | 0.555953i | −0.659711 | − | 0.751520i | \(-0.729321\pi\) |
0.980690 | + | 0.195566i | \(0.0626545\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 10.2772 | − | 5.93354i | 1.31586 | − | 0.759712i | 0.332800 | − | 0.942997i | \(-0.392007\pi\) |
0.983060 | + | 0.183285i | \(0.0586733\pi\) | |||||||
\(62\) | −1.89434 | −0.240582 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 4.44174 | 0.555218 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 3.49905 | − | 6.06052i | 0.427476 | − | 0.740411i | −0.569172 | − | 0.822219i | \(-0.692736\pi\) |
0.996648 | + | 0.0818078i | \(0.0260694\pi\) | |||||||
\(68\) | −4.13055 | − | 7.15432i | −0.500902 | − | 0.867588i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 1.23868i | 0.147004i | 0.997295 | + | 0.0735022i | \(0.0234176\pi\) | ||||
−0.997295 | + | 0.0735022i | \(0.976582\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −0.500701 | − | 0.289080i | −0.0586026 | − | 0.0338342i | 0.470412 | − | 0.882447i | \(-0.344105\pi\) |
−0.529015 | + | 0.848612i | \(0.677438\pi\) | |||||||
\(74\) | −3.24222 | − | 1.87190i | −0.376900 | − | 0.217603i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | − | 7.00000i | − | 0.802955i | ||||||
\(77\) | −13.5861 | − | 0.115303i | −1.54828 | − | 0.0131400i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 2.46562 | + | 4.27058i | 0.277404 | + | 0.480478i | 0.970739 | − | 0.240138i | \(-0.0771926\pi\) |
−0.693335 | + | 0.720616i | \(0.743859\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −2.59164 | + | 1.49629i | −0.286199 | + | 0.165237i | ||||
\(83\) | −9.75683 | −1.07095 | −0.535475 | − | 0.844551i | \(-0.679868\pi\) | ||||
−0.535475 | + | 0.844551i | \(0.679868\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −2.32176 | + | 1.34047i | −0.250362 | + | 0.144547i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 3.92768 | − | 6.80294i | 0.418692 | − | 0.725196i | ||||
\(89\) | −3.63524 | − | 6.29642i | −0.385334 | − | 0.667419i | 0.606481 | − | 0.795098i | \(-0.292581\pi\) |
−0.991816 | + | 0.127679i | \(0.959247\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −6.64133 | − | 11.7319i | −0.696200 | − | 1.22984i | ||||
\(92\) | 4.87014i | 0.507747i | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −2.69870 | − | 1.55809i | −0.278350 | − | 0.160705i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 0.313935i | − | 0.0318752i | −0.999873 | − | 0.0159376i | \(-0.994927\pi\) | ||
0.999873 | − | 0.0159376i | \(-0.00507332\pi\) | |||||||
\(98\) | 0.0473103 | − | 2.78707i | 0.00477906 | − | 0.281537i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −4.92727 | + | 8.53428i | −0.490282 | + | 0.849193i | −0.999937 | − | 0.0111855i | \(-0.996439\pi\) |
0.509656 | + | 0.860378i | \(0.329773\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 5.69390 | − | 3.28738i | 0.561037 | − | 0.323915i | −0.192525 | − | 0.981292i | \(-0.561668\pi\) |
0.753562 | + | 0.657377i | \(0.228334\pi\) | |||||||
\(104\) | 7.79451 | 0.764314 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 1.15160 | 0.111853 | ||||||||
\(107\) | −4.17019 | + | 2.40766i | −0.403148 | + | 0.232757i | −0.687841 | − | 0.725861i | \(-0.741441\pi\) |
0.284694 | + | 0.958619i | \(0.408108\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −2.69220 | + | 4.66303i | −0.257866 | + | 0.446637i | −0.965670 | − | 0.259772i | \(-0.916353\pi\) |
0.707804 | + | 0.706409i | \(0.249686\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −7.00800 | − | 4.12576i | −0.662194 | − | 0.389848i | ||||
\(113\) | − | 9.47858i | − | 0.891669i | −0.895115 | − | 0.445835i | \(-0.852907\pi\) | ||
0.895115 | − | 0.445835i | \(-0.147093\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −14.5690 | − | 8.41141i | −1.35270 | − | 0.780980i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | − | 1.96357i | − | 0.180761i | ||||||
\(119\) | −0.100731 | + | 11.8691i | −0.00923398 | + | 1.08803i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 7.68533 | + | 13.3114i | 0.698667 | + | 1.21013i | ||||
\(122\) | 2.36280 | − | 4.09249i | 0.213918 | − | 0.370516i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 7.58633 | − | 4.37997i | 0.681272 | − | 0.393333i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −8.62994 | −0.765783 | −0.382892 | − | 0.923793i | \(-0.625072\pi\) | ||||
−0.382892 | + | 0.923793i | \(0.625072\pi\) | |||||||
\(128\) | 8.95082 | − | 5.16776i | 0.791148 | − | 0.456769i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −7.75657 | − | 13.4348i | −0.677695 | − | 1.17380i | −0.975673 | − | 0.219229i | \(-0.929646\pi\) |
0.297979 | − | 0.954573i | \(-0.403688\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −5.10251 | + | 8.66711i | −0.442444 | + | 0.751533i | ||||
\(134\) | − | 2.78671i | − | 0.240735i | ||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −5.94318 | − | 3.43130i | −0.509624 | − | 0.294231i | ||||
\(137\) | 0.956258 | + | 0.552096i | 0.0816986 | + | 0.0471687i | 0.540293 | − | 0.841477i | \(-0.318313\pi\) |
−0.458594 | + | 0.888646i | \(0.651647\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 6.48061i | 0.549678i | 0.961490 | + | 0.274839i | \(0.0886246\pi\) | ||||
−0.961490 | + | 0.274839i | \(0.911375\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0.246628 | + | 0.427172i | 0.0206966 | + | 0.0358475i | ||||
\(143\) | −13.0832 | + | 22.6607i | −1.09407 | + | 1.89499i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −0.230229 | −0.0190539 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 17.3123 | 1.42306 | ||||||||
\(149\) | −14.2091 | + | 8.20362i | −1.16405 | + | 0.672066i | −0.952272 | − | 0.305251i | \(-0.901260\pi\) |
−0.211781 | + | 0.977317i | \(0.567926\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −4.67919 | + | 8.10460i | −0.380787 | + | 0.659543i | −0.991175 | − | 0.132560i | \(-0.957680\pi\) |
0.610388 | + | 0.792103i | \(0.291014\pi\) | |||||||
\(152\) | −2.90749 | − | 5.03593i | −0.235829 | − | 0.408468i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −4.70826 | + | 2.66530i | −0.379402 | + | 0.214776i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 7.68946 | + | 4.43951i | 0.613686 | + | 0.354312i | 0.774407 | − | 0.632688i | \(-0.218048\pi\) |
−0.160721 | + | 0.987000i | \(0.551382\pi\) | |||||||
\(158\) | 1.70059 | + | 0.981836i | 0.135292 | + | 0.0781107i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 3.54999 | − | 6.03000i | 0.279779 | − | 0.475231i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −3.53445 | − | 6.12185i | −0.276840 | − | 0.479501i | 0.693758 | − | 0.720208i | \(-0.255954\pi\) |
−0.970598 | + | 0.240708i | \(0.922620\pi\) | |||||||
\(164\) | 6.91921 | − | 11.9844i | 0.540300 | − | 0.935827i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −3.36474 | + | 1.94264i | −0.261155 | + | 0.150778i | ||||
\(167\) | 25.0272 | 1.93666 | 0.968331 | − | 0.249669i | \(-0.0803217\pi\) | ||||
0.968331 | + | 0.249669i | \(0.0803217\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −12.9637 | −0.997204 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 6.19867 | − | 10.7364i | 0.472644 | − | 0.818644i | ||||
\(173\) | 0.364708 | + | 0.631692i | 0.0277282 | + | 0.0480267i | 0.879557 | − | 0.475794i | \(-0.157839\pi\) |
−0.851828 | + | 0.523821i | \(0.824506\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 15.7843i | 1.18978i | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −2.50730 | − | 1.44759i | −0.187930 | − | 0.108502i | ||||
\(179\) | −2.25510 | − | 1.30198i | −0.168554 | − | 0.0973147i | 0.413350 | − | 0.910572i | \(-0.364359\pi\) |
−0.581904 | + | 0.813258i | \(0.697692\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 3.89250i | − | 0.289327i | −0.989481 | − | 0.144663i | \(-0.953790\pi\) | ||
0.989481 | − | 0.144663i | \(-0.0462100\pi\) | |||||||
\(182\) | −4.62622 | − | 2.72356i | −0.342918 | − | 0.201884i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 2.02284 | + | 3.50367i | 0.149126 | + | 0.258294i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 19.9514 | − | 11.5190i | 1.45899 | − | 0.842350i | ||||
\(188\) | 14.4101 | 1.05096 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 6.64485 | − | 3.83640i | 0.480804 | − | 0.277592i | −0.239947 | − | 0.970786i | \(-0.577130\pi\) |
0.720752 | + | 0.693193i | \(0.243797\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −0.0303002 | + | 0.0524815i | −0.00218106 | + | 0.00377770i | −0.867114 | − | 0.498110i | \(-0.834028\pi\) |
0.864933 | + | 0.501888i | \(0.167361\pi\) | |||||||
\(194\) | −0.0625061 | − | 0.108264i | −0.00448768 | − | 0.00777288i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 6.25461 | + | 11.2708i | 0.446758 | + | 0.805060i | ||||
\(197\) | 12.3018i | 0.876464i | 0.898862 | + | 0.438232i | \(0.144395\pi\) | ||||
−0.898862 | + | 0.438232i | \(0.855605\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −9.68559 | − | 5.59198i | −0.686593 | − | 0.396405i | 0.115741 | − | 0.993279i | \(-0.463076\pi\) |
−0.802335 | + | 0.596875i | \(0.796409\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 3.92418i | 0.276105i | ||||||||
\(203\) | 11.9074 | + | 21.0344i | 0.835734 | + | 1.47633i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 1.30907 | − | 2.26737i | 0.0912071 | − | 0.157975i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −13.5637 | + | 7.83099i | −0.940471 | + | 0.542981i | ||||
\(209\) | 19.5211 | 1.35030 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 5.62551 | 0.387276 | 0.193638 | − | 0.981073i | \(-0.437971\pi\) | ||||
0.193638 | + | 0.981073i | \(0.437971\pi\) | |||||||
\(212\) | −4.61184 | + | 2.66265i | −0.316742 | + | 0.182871i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −0.958756 | + | 1.66061i | −0.0655392 | + | 0.113517i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −12.5858 | − | 0.106813i | −0.854377 | − | 0.00725097i | ||||
\(218\) | 2.14412i | 0.145218i | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 19.7969 | + | 11.4297i | 1.33168 | + | 0.768846i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 3.16328i | 0.211829i | 0.994375 | + | 0.105914i | \(0.0337770\pi\) | ||||
−0.994375 | + | 0.105914i | \(0.966223\pi\) | |||||||
\(224\) | −11.3324 | − | 0.0961759i | −0.757175 | − | 0.00642603i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −1.88724 | − | 3.26879i | −0.125537 | − | 0.217436i | ||||
\(227\) | 5.62242 | − | 9.73831i | 0.373173 | − | 0.646354i | −0.616879 | − | 0.787058i | \(-0.711603\pi\) |
0.990052 | + | 0.140704i | \(0.0449365\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 19.7354 | − | 11.3942i | 1.30415 | − | 0.752952i | 0.323038 | − | 0.946386i | \(-0.395296\pi\) |
0.981113 | + | 0.193434i | \(0.0619626\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −13.9749 | −0.917499 | ||||||||
\(233\) | −2.79461 | + | 1.61347i | −0.183081 | + | 0.105702i | −0.588740 | − | 0.808323i | \(-0.700376\pi\) |
0.405658 | + | 0.914025i | \(0.367042\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 4.54003 | + | 7.86356i | 0.295531 | + | 0.511874i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 2.32845 | + | 4.11323i | 0.150931 | + | 0.266621i | ||||
\(239\) | 23.1272i | 1.49598i | 0.663712 | + | 0.747988i | \(0.268980\pi\) | ||||
−0.663712 | + | 0.747988i | \(0.731020\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 12.8600 | + | 7.42473i | 0.828386 | + | 0.478269i | 0.853300 | − | 0.521421i | \(-0.174598\pi\) |
−0.0249139 | + | 0.999690i | \(0.507931\pi\) | |||||||
\(242\) | 5.30074 | + | 3.06038i | 0.340744 | + | 0.196729i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 21.8524i | 1.39896i | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 9.68492 | + | 16.7748i | 0.616237 | + | 1.06735i | ||||
\(248\) | 3.63849 | − | 6.30206i | 0.231045 | − | 0.400181i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 12.6710 | 0.799789 | 0.399895 | − | 0.916561i | \(-0.369047\pi\) | ||||
0.399895 | + | 0.916561i | \(0.369047\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −13.5815 | −0.853861 | ||||||||
\(254\) | −2.97613 | + | 1.71827i | −0.186739 | + | 0.107814i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −2.38389 | + | 4.12901i | −0.148993 | + | 0.258063i | ||||
\(257\) | 3.98336 | + | 6.89937i | 0.248475 | + | 0.430371i | 0.963103 | − | 0.269134i | \(-0.0867373\pi\) |
−0.714628 | + | 0.699505i | \(0.753404\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −21.4353 | − | 12.6194i | −1.33192 | − | 0.784133i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −5.34987 | − | 3.08875i | −0.330516 | − | 0.190824i | ||||
\(263\) | −6.06499 | − | 3.50162i | −0.373983 | − | 0.215919i | 0.301214 | − | 0.953557i | \(-0.402608\pi\) |
−0.675197 | + | 0.737637i | \(0.735942\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −0.0339888 | + | 4.00488i | −0.00208399 | + | 0.245555i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 6.44324 | + | 11.1600i | 0.393584 | + | 0.681707i | ||||
\(269\) | −5.08855 | + | 8.81364i | −0.310255 | + | 0.537377i | −0.978417 | − | 0.206638i | \(-0.933748\pi\) |
0.668163 | + | 0.744015i | \(0.267081\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 2.60706 | − | 1.50519i | 0.158367 | − | 0.0914335i | −0.418722 | − | 0.908115i | \(-0.637522\pi\) |
0.577089 | + | 0.816681i | \(0.304188\pi\) | |||||||
\(272\) | 13.7894 | 0.836107 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0.439701 | 0.0265633 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −16.5884 | + | 28.7319i | −0.996700 | + | 1.72634i | −0.428053 | + | 0.903754i | \(0.640800\pi\) |
−0.568647 | + | 0.822581i | \(0.692533\pi\) | |||||||
\(278\) | 1.29032 | + | 2.23491i | 0.0773885 | + | 0.134041i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 6.12689i | − | 0.365500i | −0.983159 | − | 0.182750i | \(-0.941500\pi\) | ||
0.983159 | − | 0.182750i | \(-0.0584998\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 7.12461 | + | 4.11340i | 0.423514 | + | 0.244516i | 0.696580 | − | 0.717479i | \(-0.254704\pi\) |
−0.273066 | + | 0.961995i | \(0.588038\pi\) | |||||||
\(284\) | −1.97535 | − | 1.14047i | −0.117216 | − | 0.0676745i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 10.4197i | 0.616131i | ||||||||
\(287\) | −17.3029 | + | 9.79499i | −1.02136 | + | 0.578180i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −1.56319 | − | 2.70752i | −0.0919522 | − | 0.159266i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0.922005 | − | 0.532320i | 0.0539562 | − | 0.0311516i | ||||
\(293\) | −31.5059 | −1.84059 | −0.920297 | − | 0.391220i | \(-0.872053\pi\) | ||||
−0.920297 | + | 0.391220i | \(0.872053\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 12.4547 | − | 7.19075i | 0.723918 | − | 0.417954i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −3.26677 | + | 5.65821i | −0.189239 | + | 0.327771i | ||||
\(299\) | −6.73813 | − | 11.6708i | −0.389676 | − | 0.674939i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −15.5010 | + | 8.77498i | −0.893465 | + | 0.505781i | ||||
\(302\) | 3.72661i | 0.214442i | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 10.1190 | + | 5.84221i | 0.580364 | + | 0.335073i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 23.7716i | 1.35672i | 0.734730 | + | 0.678360i | \(0.237309\pi\) | ||||
−0.734730 | + | 0.678360i | \(0.762691\pi\) | |||||||
\(308\) | 12.6928 | − | 21.5599i | 0.723237 | − | 1.22849i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 9.29730 | − | 16.1034i | 0.527201 | − | 0.913139i | −0.472296 | − | 0.881440i | \(-0.656575\pi\) |
0.999497 | − | 0.0316995i | \(-0.0100920\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 7.05481 | − | 4.07310i | 0.398762 | − | 0.230225i | −0.287188 | − | 0.957874i | \(-0.592720\pi\) |
0.685950 | + | 0.727649i | \(0.259387\pi\) | |||||||
\(314\) | 3.53572 | 0.199532 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −9.08053 | −0.510820 | ||||||||
\(317\) | 27.2045 | − | 15.7065i | 1.52795 | − | 0.882165i | 0.528507 | − | 0.848929i | \(-0.322752\pi\) |
0.999448 | − | 0.0332365i | \(-0.0105815\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 23.4571 | − | 40.6289i | 1.31335 | − | 2.27478i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0.0236472 | − | 2.78633i | 0.00131781 | − | 0.155276i | ||||
\(323\) | − | 17.0540i | − | 0.948910i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −2.43779 | − | 1.40746i | −0.135017 | − | 0.0779518i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | − | 11.4958i | − | 0.634747i | ||||||
\(329\) | −17.8419 | − | 10.5039i | −0.983657 | − | 0.579100i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −2.76563 | − | 4.79021i | −0.152013 | − | 0.263294i | 0.779955 | − | 0.625836i | \(-0.215242\pi\) |
−0.931967 | + | 0.362542i | \(0.881909\pi\) | |||||||
\(332\) | 8.98325 | − | 15.5594i | 0.493020 | − | 0.853935i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 8.63089 | − | 4.98305i | 0.472261 | − | 0.272660i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −13.3563 | −0.727566 | −0.363783 | − | 0.931484i | \(-0.618515\pi\) | ||||
−0.363783 | + | 0.931484i | \(0.618515\pi\) | |||||||
\(338\) | −4.47065 | + | 2.58113i | −0.243172 | + | 0.140395i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 12.2145 | + | 21.1562i | 0.661454 | + | 1.14567i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0.471474 | − | 18.5143i | 0.0254572 | − | 0.999676i | ||||
\(344\) | − | 10.2986i | − | 0.555265i | ||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0.251547 | + | 0.145230i | 0.0135232 | + | 0.00780764i | ||||
\(347\) | −28.0670 | − | 16.2045i | −1.50671 | − | 0.869901i | −0.999970 | − | 0.00780492i | \(-0.997516\pi\) |
−0.506744 | − | 0.862097i | \(-0.669151\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 6.33160i | − | 0.338923i | −0.985537 | − | 0.169461i | \(-0.945797\pi\) | ||
0.985537 | − | 0.169461i | \(-0.0542028\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 10.9981 | + | 19.0493i | 0.586200 | + | 1.01533i | ||||
\(353\) | 7.79492 | − | 13.5012i | 0.414882 | − | 0.718596i | −0.580534 | − | 0.814236i | \(-0.697156\pi\) |
0.995416 | + | 0.0956395i | \(0.0304896\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 13.3881 | 0.709566 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −1.03693 | −0.0548032 | ||||||||
\(359\) | 9.43467 | − | 5.44711i | 0.497943 | − | 0.287487i | −0.229921 | − | 0.973209i | \(-0.573847\pi\) |
0.727864 | + | 0.685722i | \(0.240513\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −2.27469 | + | 3.93987i | −0.119720 | + | 0.207362i | ||||
\(362\) | −0.775017 | − | 1.34237i | −0.0407340 | − | 0.0705533i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 24.8240 | + | 0.210677i | 1.30113 | + | 0.0110425i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 4.30786 | + | 2.48714i | 0.224868 | + | 0.129828i | 0.608202 | − | 0.793782i | \(-0.291891\pi\) |
−0.383334 | + | 0.923610i | \(0.625224\pi\) | |||||||
\(368\) | −7.04013 | − | 4.06462i | −0.366992 | − | 0.211883i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 7.65106 | + | 0.0649334i | 0.397223 | + | 0.00337117i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −6.43003 | − | 11.1371i | −0.332934 | − | 0.576659i | 0.650151 | − | 0.759805i | \(-0.274705\pi\) |
−0.983086 | + | 0.183145i | \(0.941372\pi\) | |||||||
\(374\) | 4.58697 | − | 7.94487i | 0.237187 | − | 0.410820i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 10.3669 | − | 5.98531i | 0.534630 | − | 0.308669i | ||||
\(377\) | 46.5508 | 2.39749 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −37.8472 | −1.94408 | −0.972039 | − | 0.234818i | \(-0.924550\pi\) | ||||
−0.972039 | + | 0.234818i | \(0.924550\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 1.52770 | − | 2.64605i | 0.0781638 | − | 0.135384i | ||||
\(383\) | 14.2211 | + | 24.6317i | 0.726665 | + | 1.25862i | 0.958285 | + | 0.285814i | \(0.0922640\pi\) |
−0.231620 | + | 0.972806i | \(0.574403\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0.0241317i | 0.00122827i | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0.500639 | + | 0.289044i | 0.0254161 | + | 0.0146740i | ||||
\(389\) | −8.24116 | − | 4.75803i | −0.417843 | − | 0.241242i | 0.276311 | − | 0.961068i | \(-0.410888\pi\) |
−0.694154 | + | 0.719826i | \(0.744221\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 11.8650i | 0.600041i | ||||||||
\(392\) | 9.18109 | + | 5.51056i | 0.463715 | + | 0.278325i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 2.44935 | + | 4.24239i | 0.123396 | + | 0.213729i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 8.36250 | − | 4.82809i | 0.419702 | − | 0.242315i | −0.275248 | − | 0.961373i | \(-0.588760\pi\) |
0.694950 | + | 0.719058i | \(0.255427\pi\) | |||||||
\(398\) | −4.45357 | −0.223237 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 7.76875 | − | 4.48529i | 0.387953 | − | 0.223985i | −0.293320 | − | 0.956014i | \(-0.594760\pi\) |
0.681273 | + | 0.732030i | \(0.261427\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −12.1199 | + | 20.9923i | −0.603735 | + | 1.04570i | ||||
\(404\) | −9.07322 | − | 15.7153i | −0.451409 | − | 0.781864i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 8.29445 | + | 4.88312i | 0.411647 | + | 0.242345i | ||||
\(407\) | 48.2791i | 2.39311i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 26.3659 | + | 15.2223i | 1.30371 | + | 0.752696i | 0.981038 | − | 0.193815i | \(-0.0620863\pi\) |
0.322670 | + | 0.946512i | \(0.395420\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 12.1069i | 0.596466i | ||||||||
\(413\) | 0.110717 | − | 13.0457i | 0.00544802 | − | 0.641936i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −10.9129 | + | 18.9017i | −0.535048 | + | 0.926731i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 6.73205 | − | 3.88675i | 0.329275 | − | 0.190107i | ||||
\(419\) | −24.0920 | −1.17697 | −0.588485 | − | 0.808508i | \(-0.700276\pi\) | ||||
−0.588485 | + | 0.808508i | \(0.700276\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −22.3663 | −1.09007 | −0.545033 | − | 0.838415i | \(-0.683483\pi\) | ||||
−0.545033 | + | 0.838415i | \(0.683483\pi\) | |||||||
\(422\) | 1.94002 | − | 1.12007i | 0.0944386 | − | 0.0545241i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −2.21189 | + | 3.83111i | −0.107419 | + | 0.186055i | ||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 15.9289 | − | 27.0567i | 0.770852 | − | 1.30937i | ||||
\(428\) | − | 8.86707i | − | 0.428606i | ||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 8.90954 | + | 5.14392i | 0.429157 | + | 0.247774i | 0.698988 | − | 0.715134i | \(-0.253634\pi\) |
−0.269830 | + | 0.962908i | \(0.586968\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 4.91252i | 0.236080i | 0.993009 | + | 0.118040i | \(0.0376612\pi\) | ||||
−0.993009 | + | 0.118040i | \(0.962339\pi\) | |||||||
\(434\) | −4.36160 | + | 2.46906i | −0.209363 | + | 0.118519i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −4.95749 | − | 8.58663i | −0.237421 | − | 0.411225i | ||||
\(437\) | −5.02690 | + | 8.70684i | −0.240469 | + | 0.416505i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −27.0138 | + | 15.5964i | −1.28930 | + | 0.744378i | −0.978529 | − | 0.206107i | \(-0.933920\pi\) |
−0.310771 | + | 0.950485i | \(0.600587\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 9.10288 | 0.432980 | ||||||||
\(443\) | −9.14111 | + | 5.27762i | −0.434307 | + | 0.250747i | −0.701180 | − | 0.712984i | \(-0.747343\pi\) |
0.266873 | + | 0.963732i | \(0.414010\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0.629826 | + | 1.09089i | 0.0298231 | + | 0.0516552i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 10.2268 | − | 5.78929i | 0.483171 | − | 0.273518i | ||||
\(449\) | 32.9402i | 1.55454i | 0.629166 | + | 0.777271i | \(0.283397\pi\) | ||||
−0.629166 | + | 0.777271i | \(0.716603\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 33.4213 | + | 19.2958i | 1.57375 | + | 0.908603i | ||||
\(452\) | 15.1157 | + | 8.72706i | 0.710983 | + | 0.410486i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | − | 4.47781i | − | 0.210154i | ||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −16.0797 | − | 27.8509i | −0.752177 | − | 1.30281i | −0.946766 | − | 0.321923i | \(-0.895671\pi\) |
0.194589 | − | 0.980885i | \(-0.437663\pi\) | |||||||
\(458\) | 4.53730 | − | 7.85884i | 0.212014 | − | 0.367220i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 39.6617 | 1.84723 | 0.923615 | − | 0.383322i | \(-0.125220\pi\) | ||||
0.923615 | + | 0.383322i | \(0.125220\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 34.2241 | 1.59053 | 0.795265 | − | 0.606262i | \(-0.207332\pi\) | ||||
0.795265 | + | 0.606262i | \(0.207332\pi\) | |||||||
\(464\) | 24.3186 | − | 14.0403i | 1.12896 | − | 0.651806i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −0.642501 | + | 1.11284i | −0.0297633 | + | 0.0515515i | ||||
\(467\) | −14.8493 | − | 25.7197i | −0.687144 | − | 1.19017i | −0.972758 | − | 0.231823i | \(-0.925531\pi\) |
0.285614 | − | 0.958345i | \(-0.407802\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0.157130 | − | 18.5145i | 0.00725559 | − | 0.854922i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 6.53236 | + | 3.77146i | 0.300676 | + | 0.173595i | ||||
\(473\) | 29.9409 | + | 17.2864i | 1.37669 | + | 0.794829i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −18.8351 | − | 11.0886i | −0.863306 | − | 0.508247i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 4.60476 | + | 7.97567i | 0.210617 | + | 0.364799i | ||||
\(479\) | −4.69594 | + | 8.13361i | −0.214563 | + | 0.371634i | −0.953137 | − | 0.302538i | \(-0.902166\pi\) |
0.738574 | + | 0.674172i | \(0.235499\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −41.4870 | + | 23.9525i | −1.89165 | + | 1.09214i | ||||
\(482\) | 5.91321 | 0.269339 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −28.3040 | −1.28654 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 3.97135 | − | 6.87859i | 0.179959 | − | 0.311699i | −0.761907 | − | 0.647686i | \(-0.775737\pi\) |
0.941866 | + | 0.335988i | \(0.109070\pi\) | |||||||
\(488\) | 9.07652 | + | 15.7210i | 0.410875 | + | 0.711656i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 10.6921i | − | 0.482526i | −0.970460 | − | 0.241263i | \(-0.922438\pi\) | ||
0.970460 | − | 0.241263i | \(-0.0775616\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −35.4942 | − | 20.4926i | −1.59858 | − | 0.922939i | ||||
\(494\) | 6.67990 | + | 3.85664i | 0.300543 | + | 0.173518i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 14.6221i | 0.656552i | ||||||||
\(497\) | 1.61447 | + | 2.85198i | 0.0724191 | + | 0.127929i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −3.61851 | − | 6.26745i | −0.161987 | − | 0.280570i | 0.773594 | − | 0.633681i | \(-0.218457\pi\) |
−0.935581 | + | 0.353112i | \(0.885124\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 4.36974 | − | 2.52287i | 0.195031 | − | 0.112601i | ||||
\(503\) | 2.22842 | 0.0993603 | 0.0496802 | − | 0.998765i | \(-0.484180\pi\) | ||||
0.0496802 | + | 0.998765i | \(0.484180\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −4.68372 | + | 2.70415i | −0.208217 | + | 0.120214i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 7.94571 | − | 13.7624i | 0.352534 | − | 0.610606i | ||||
\(509\) | −14.2749 | − | 24.7248i | −0.632724 | − | 1.09591i | −0.986993 | − | 0.160766i | \(-0.948604\pi\) |
0.354269 | − | 0.935144i | \(-0.384730\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −1.52961 | − | 0.0129816i | −0.0676660 | − | 0.000574271i | ||||
\(512\) | 22.5696i | 0.997445i | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 2.74740 | + | 1.58621i | 0.121183 | + | 0.0699649i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 40.1857i | 1.76736i | ||||||||
\(518\) | −9.90478 | − | 0.0840604i | −0.435191 | − | 0.00369340i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 0.909280 | − | 1.57492i | 0.0398363 | − | 0.0689985i | −0.845420 | − | 0.534102i | \(-0.820650\pi\) |
0.885256 | + | 0.465104i | \(0.153983\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −25.4727 | + | 14.7067i | −1.11384 | + | 0.643077i | −0.939822 | − | 0.341665i | \(-0.889009\pi\) |
−0.174021 | + | 0.984742i | \(0.555676\pi\) | |||||||
\(524\) | 28.5663 | 1.24793 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −2.78877 | −0.121596 | ||||||||
\(527\) | 18.4824 | − | 10.6708i | 0.805108 | − | 0.464829i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −8.00261 | + | 13.8609i | −0.347940 | + | 0.602649i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −9.12368 | − | 16.1170i | −0.395562 | − | 0.698762i | ||||
\(533\) | 38.2926i | 1.65864i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 9.27077 | + | 5.35248i | 0.400436 | + | 0.231192i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 4.05263i | 0.174721i | ||||||||
\(539\) | −31.4313 | + | 17.4424i | −1.35384 | + | 0.751296i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 0.530113 | + | 0.918183i | 0.0227913 | + | 0.0394758i | 0.877196 | − | 0.480132i | \(-0.159411\pi\) |
−0.854405 | + | 0.519608i | \(0.826078\pi\) | |||||||
\(542\) | 0.599381 | − | 1.03816i | 0.0257456 | − | 0.0445927i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 16.6418 | − | 9.60814i | 0.713511 | − | 0.411946i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −12.4665 | −0.533030 | −0.266515 | − | 0.963831i | \(-0.585872\pi\) | ||||
−0.266515 | + | 0.963831i | \(0.585872\pi\) | |||||||
\(548\) | −1.76088 | + | 1.01664i | −0.0752211 | + | 0.0434289i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −17.3643 | − | 30.0758i | −0.739744 | − | 1.28127i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 11.2431 | + | 6.61907i | 0.478106 | + | 0.281472i | ||||
\(554\) | 13.2114i | 0.561297i | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −10.3348 | − | 5.96679i | −0.438292 | − | 0.253048i | ||||
\(557\) | −17.5701 | − | 10.1441i | −0.744470 | − | 0.429820i | 0.0792222 | − | 0.996857i | \(-0.474756\pi\) |
−0.823692 | + | 0.567037i | \(0.808090\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 34.3050i | 1.45095i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −1.21990 | − | 2.11292i | −0.0514582 | − | 0.0891283i | ||||
\(563\) | 17.8781 | − | 30.9658i | 0.753472 | − | 1.30505i | −0.192658 | − | 0.981266i | \(-0.561711\pi\) |
0.946130 | − | 0.323786i | \(-0.104956\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 3.27600 | 0.137700 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −1.89481 | −0.0795043 | ||||||||
\(569\) | −4.01368 | + | 2.31730i | −0.168262 | + | 0.0971463i | −0.581766 | − | 0.813356i | \(-0.697638\pi\) |
0.413504 | + | 0.910502i | \(0.364305\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 9.64058 | − | 16.6980i | 0.403446 | − | 0.698788i | −0.590694 | − | 0.806896i | \(-0.701146\pi\) |
0.994139 | + | 0.108108i | \(0.0344791\pi\) | |||||||
\(572\) | −24.0917 | − | 41.7281i | −1.00733 | − | 1.74474i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −4.01685 | + | 6.82300i | −0.167660 | + | 0.284787i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 6.14525 | + | 3.54796i | 0.255830 | + | 0.147703i | 0.622431 | − | 0.782675i | \(-0.286145\pi\) |
−0.366601 | + | 0.930378i | \(0.619479\pi\) | |||||||
\(578\) | −1.07816 | − | 0.622478i | −0.0448457 | − | 0.0258917i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −22.4644 | + | 12.7169i | −0.931982 | + | 0.527585i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −7.42539 | − | 12.8611i | −0.307528 | − | 0.532654i | ||||
\(584\) | 0.442205 | − | 0.765921i | 0.0182986 | − | 0.0316940i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −10.8651 | + | 6.27299i | −0.448835 | + | 0.259135i | ||||
\(587\) | −28.1728 | −1.16281 | −0.581407 | − | 0.813613i | \(-0.697498\pi\) | ||||
−0.581407 | + | 0.813613i | \(0.697498\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 18.0838 | 0.745130 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −14.4488 | + | 25.0261i | −0.593843 | + | 1.02857i | ||||
\(593\) | 4.66958 | + | 8.08794i | 0.191757 | + | 0.332132i | 0.945832 | − | 0.324655i | \(-0.105248\pi\) |
−0.754076 | + | 0.656787i | \(0.771915\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | − | 30.2127i | − | 1.23756i | ||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −4.64743 | − | 2.68320i | −0.190048 | − | 0.109724i | ||||
\(599\) | 18.4745 | + | 10.6662i | 0.754846 | + | 0.435811i | 0.827442 | − | 0.561551i | \(-0.189795\pi\) |
−0.0725959 | + | 0.997361i | \(0.523128\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 35.7597i | − | 1.45867i | −0.684157 | − | 0.729335i | \(-0.739830\pi\) | ||
0.684157 | − | 0.729335i | \(-0.260170\pi\) | |||||||
\(602\) | −3.59855 | + | 6.11248i | −0.146666 | + | 0.249126i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −8.61640 | − | 14.9240i | −0.350596 | − | 0.607251i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 2.89774 | − | 1.67301i | 0.117616 | − | 0.0679055i | −0.440038 | − | 0.897979i | \(-0.645035\pi\) |
0.557654 | + | 0.830074i | \(0.311702\pi\) | |||||||
\(608\) | 16.2828 | 0.660356 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −34.5322 | + | 19.9372i | −1.39702 | + | 0.806572i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −19.8654 | + | 34.4079i | −0.802357 | + | 1.38972i | 0.115704 | + | 0.993284i | \(0.463088\pi\) |
−0.918061 | + | 0.396440i | \(0.870246\pi\) | |||||||
\(614\) | 4.73306 | + | 8.19790i | 0.191011 | + | 0.330840i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0.176379 | − | 20.7826i | 0.00710650 | − | 0.837354i | ||||
\(617\) | 33.2529i | 1.33871i | 0.742942 | + | 0.669355i | \(0.233430\pi\) | ||||
−0.742942 | + | 0.669355i | \(0.766570\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 15.8564 | + | 9.15472i | 0.637324 | + | 0.367959i | 0.783583 | − | 0.621287i | \(-0.213390\pi\) |
−0.146259 | + | 0.989246i | \(0.546723\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | − | 7.40457i | − | 0.296896i | ||||||
\(623\) | −16.5765 | − | 9.75897i | −0.664125 | − | 0.390985i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 1.62195 | − | 2.80930i | 0.0648262 | − | 0.112282i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −14.1596 | + | 8.17505i | −0.565029 | + | 0.326220i | ||||
\(629\) | 42.1776 | 1.68173 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 44.2729 | 1.76248 | 0.881238 | − | 0.472673i | \(-0.156711\pi\) | ||||
0.881238 | + | 0.472673i | \(0.156711\pi\) | |||||||
\(632\) | −6.53270 | + | 3.77165i | −0.259857 | + | 0.150028i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 6.25450 | − | 10.8331i | 0.248398 | − | 0.430238i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −30.5824 | − | 18.3558i | −1.21172 | − | 0.727283i | ||||
\(638\) | − | 18.6817i | − | 0.739617i | ||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −2.80892 | − | 1.62173i | −0.110946 | − | 0.0640546i | 0.443500 | − | 0.896274i | \(-0.353737\pi\) |
−0.554446 | + | 0.832220i | \(0.687070\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 38.7849i | − | 1.52953i | −0.644311 | − | 0.764763i | \(-0.722856\pi\) | ||
0.644311 | − | 0.764763i | \(-0.277144\pi\) | |||||||
\(644\) | 6.34766 | + | 11.2132i | 0.250133 | + | 0.441861i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −3.39554 | − | 5.88125i | −0.133596 | − | 0.231395i | ||||
\(647\) | 20.2133 | − | 35.0104i | 0.794665 | − | 1.37640i | −0.128386 | − | 0.991724i | \(-0.540980\pi\) |
0.923051 | − | 0.384677i | \(-0.125687\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −21.9293 | + | 12.6609i | −0.860801 | + | 0.496983i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 13.0169 | 0.509781 | ||||||||
\(653\) | −33.0989 | + | 19.1097i | −1.29526 | + | 0.747819i | −0.979582 | − | 0.201047i | \(-0.935566\pi\) |
−0.315679 | + | 0.948866i | \(0.602232\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 11.5496 | + | 20.0044i | 0.450935 | + | 0.781042i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −8.24436 | − | 0.0699686i | −0.321399 | − | 0.00272766i | ||||
\(659\) | 3.10400i | 0.120915i | 0.998171 | + | 0.0604574i | \(0.0192559\pi\) | ||||
−0.998171 | + | 0.0604574i | \(0.980744\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 12.5985 | + | 7.27377i | 0.490026 | + | 0.282917i | 0.724585 | − | 0.689185i | \(-0.242031\pi\) |
−0.234559 | + | 0.972102i | \(0.575365\pi\) | |||||||
\(662\) | −1.90751 | − | 1.10130i | −0.0741376 | − | 0.0428034i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | − | 14.9250i | − | 0.579202i | ||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 12.0809 | + | 20.9248i | 0.467776 | + | 0.810211i | ||||
\(668\) | −23.0429 | + | 39.9115i | −0.891556 | + | 1.54422i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −60.9403 | −2.35257 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 32.6424 | 1.25827 | 0.629137 | − | 0.777295i | \(-0.283409\pi\) | ||||
0.629137 | + | 0.777295i | \(0.283409\pi\) | |||||||
\(674\) | −4.60607 | + | 2.65932i | −0.177419 | + | 0.102433i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 11.9358 | − | 20.6734i | 0.459070 | − | 0.795133i | ||||
\(677\) | −8.30114 | − | 14.3780i | −0.319039 | − | 0.552591i | 0.661249 | − | 0.750167i | \(-0.270027\pi\) |
−0.980288 | + | 0.197575i | \(0.936693\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −0.409177 | − | 0.722813i | −0.0157028 | − | 0.0277390i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 8.42462 | + | 4.86396i | 0.322595 | + | 0.186250i | ||||
\(683\) | −21.1988 | − | 12.2391i | −0.811149 | − | 0.468317i | 0.0362057 | − | 0.999344i | \(-0.488473\pi\) |
−0.847355 | + | 0.531027i | \(0.821806\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −3.52369 | − | 6.47871i | −0.134535 | − | 0.247358i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 10.3468 | + | 17.9212i | 0.394469 | + | 0.683241i | ||||
\(689\) | 7.36786 | − | 12.7615i | 0.280693 | − | 0.486175i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 26.8707 | − | 15.5138i | 1.02221 | − | 0.590174i | 0.107467 | − | 0.994209i | \(-0.465726\pi\) |
0.914744 | + | 0.404035i | \(0.132393\pi\) | |||||||
\(692\) | −1.34317 | −0.0510595 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −12.9056 | −0.489889 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 16.8572 | − | 29.1975i | 0.638511 | − | 1.10593i | ||||
\(698\) | −1.26066 | − | 2.18352i | −0.0477165 | − | 0.0826474i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 30.5243i | 1.15289i | 0.817137 | + | 0.576443i | \(0.195560\pi\) | ||||
−0.817137 | + | 0.576443i | \(0.804440\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 30.9509 | + | 17.8695i | 1.16733 | + | 0.673960i | ||||
\(704\) | −19.7535 | − | 11.4047i | −0.744489 | − | 0.429831i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | − | 6.20804i | − | 0.233643i | ||||||
\(707\) | −0.221267 | + | 26.0717i | −0.00832159 | + | 0.980528i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −5.70901 | − | 9.88830i | −0.214406 | − | 0.371363i | 0.738682 | − | 0.674054i | \(-0.235448\pi\) |
−0.953089 | + | 0.302691i | \(0.902115\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 9.63162 | − | 5.56082i | 0.360960 | − | 0.208400i | ||||
\(713\) | −12.5815 | −0.471181 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 4.15260 | − | 2.39751i | 0.155190 | − | 0.0895990i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 2.16910 | − | 3.75699i | 0.0809500 | − | 0.140209i | ||||
\(719\) | 0.0976746 | + | 0.169177i | 0.00364265 | + | 0.00630925i | 0.867841 | − | 0.496842i | \(-0.165507\pi\) |
−0.864198 | + | 0.503151i | \(0.832174\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 8.82511 | − | 14.9903i | 0.328664 | − | 0.558268i | ||||
\(722\) | 1.81161i | 0.0674211i | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 6.20745 | + | 3.58388i | 0.230698 | + | 0.133194i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 22.6268i | − | 0.839181i | −0.907714 | − | 0.419590i | \(-0.862174\pi\) | ||
0.907714 | − | 0.419590i | \(-0.137826\pi\) | |||||||
\(728\) | 17.9463 | − | 10.1592i | 0.665135 | − | 0.376526i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 15.1017 | − | 26.1570i | 0.558558 | − | 0.967450i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 14.3883 | − | 8.30708i | 0.531443 | − | 0.306829i | −0.210161 | − | 0.977667i | \(-0.567399\pi\) |
0.741604 | + | 0.670838i | \(0.234065\pi\) | |||||||
\(734\) | 1.98081 | 0.0731131 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −11.3285 | −0.417575 | ||||||||
\(737\) | −31.1222 | + | 17.9684i | −1.14640 | + | 0.661876i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 0.165328 | − | 0.286356i | 0.00608168 | − | 0.0105338i | −0.862969 | − | 0.505258i | \(-0.831397\pi\) |
0.869050 | + | 0.494724i | \(0.164731\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 2.65148 | − | 1.50097i | 0.0973389 | − | 0.0551025i | ||||
\(743\) | − | 42.3387i | − | 1.55325i | −0.629960 | − | 0.776627i | \(-0.716929\pi\) | ||
0.629960 | − | 0.776627i | \(-0.283071\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −4.43493 | − | 2.56051i | −0.162374 | − | 0.0937468i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 42.4227i | 1.55113i | ||||||||
\(749\) | −6.46348 | + | 10.9788i | −0.236170 | + | 0.401158i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −4.52350 | − | 7.83494i | −0.165065 | − | 0.285901i | 0.771613 | − | 0.636092i | \(-0.219450\pi\) |
−0.936678 | + | 0.350191i | \(0.886117\pi\) | |||||||
\(752\) | −12.0266 | + | 20.8308i | −0.438567 | + | 0.759620i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 16.0535 | − | 9.26850i | 0.584635 | − | 0.337539i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −37.8499 | −1.37568 | −0.687839 | − | 0.725863i | \(-0.741441\pi\) | ||||
−0.687839 | + | 0.725863i | \(0.741441\pi\) | |||||||
\(758\) | −13.0520 | + | 7.53557i | −0.474070 | + | 0.273704i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 5.87367 | + | 10.1735i | 0.212920 | + | 0.368789i | 0.952627 | − | 0.304140i | \(-0.0983692\pi\) |
−0.739707 | + | 0.672929i | \(0.765036\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −0.120897 | + | 14.2453i | −0.00437678 | + | 0.515713i | ||||
\(764\) | 14.1289i | 0.511167i | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 9.80860 | + | 5.66300i | 0.354399 | + | 0.204612i | ||||
\(767\) | −21.7594 | − | 12.5628i | −0.785687 | − | 0.453617i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 13.1169i | 0.473007i | 0.971631 | + | 0.236504i | \(0.0760015\pi\) | ||||
−0.971631 | + | 0.236504i | \(0.923998\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −0.0557956 | − | 0.0966409i | −0.00200813 | − | 0.00347818i | ||||
\(773\) | 6.28630 | − | 10.8882i | 0.226102 | − | 0.391621i | −0.730547 | − | 0.682862i | \(-0.760735\pi\) |
0.956650 | + | 0.291241i | \(0.0940682\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0.480225 | 0.0172391 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −3.78940 | −0.135857 | ||||||||
\(779\) | 24.7404 | − | 14.2838i | 0.886415 | − | 0.511772i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 3.18046 | − | 5.50872i | 0.113806 | − | 0.197117i | ||||
\(782\) | 2.36239 | + | 4.09179i | 0.0844790 | + | 0.146322i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −21.5129 | − | 0.365180i | −0.768318 | − | 0.0130421i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −45.4761 | − | 26.2556i | −1.62105 | − | 0.935912i | −0.986641 | − | 0.162912i | \(-0.947911\pi\) |
−0.634406 | − | 0.773000i | \(-0.718755\pi\) | |||||||
\(788\) | −19.6179 | − | 11.3264i | −0.698859 | − | 0.403486i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −12.3542 | − | 21.8238i | −0.439265 | − | 0.775964i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −30.2341 | − | 52.3670i | −1.07364 | − | 1.85961i | ||||
\(794\) | 1.92260 | − | 3.33004i | 0.0682304 | − | 0.118179i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 17.8353 | − | 10.2972i | 0.632156 | − | 0.364976i | ||||
\(797\) | 24.2213 | 0.857964 | 0.428982 | − | 0.903313i | \(-0.358872\pi\) | ||||
0.428982 | + | 0.903313i | \(0.358872\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 35.1070 | 1.24200 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 1.78609 | − | 3.09360i | 0.0630690 | − | 0.109239i | ||||
\(803\) | 1.48449 | + | 2.57122i | 0.0523866 | + | 0.0907363i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 9.65255i | 0.339996i | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −13.0549 | − | 7.53724i | −0.459269 | − | 0.265159i | ||||
\(809\) | −9.52648 | − | 5.50012i | −0.334933 | − | 0.193374i | 0.323096 | − | 0.946366i | \(-0.395276\pi\) |
−0.658029 | + | 0.752992i | \(0.728610\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 7.18512i | 0.252304i | 0.992011 | + | 0.126152i | \(0.0402626\pi\) | ||||
−0.992011 | + | 0.126152i | \(0.959737\pi\) | |||||||
\(812\) | −44.5074 | − | 0.377727i | −1.56190 | − | 0.0132556i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 9.61263 | + | 16.6496i | 0.336922 | + | 0.583567i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 22.1640 | − | 12.7964i | 0.775420 | − | 0.447689i | ||||
\(818\) | 12.1234 | 0.423885 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −39.4307 | + | 22.7653i | −1.37614 | + | 0.794515i | −0.991693 | − | 0.128631i | \(-0.958942\pi\) |
−0.384448 | + | 0.923146i | \(0.625608\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 6.30134 | − | 10.9142i | 0.219651 | − | 0.380447i | −0.735050 | − | 0.678013i | \(-0.762841\pi\) |
0.954701 | + | 0.297566i | \(0.0961748\pi\) | |||||||
\(824\) | 5.02869 | + | 8.70995i | 0.175183 | + | 0.303425i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −2.55928 | − | 4.52099i | −0.0890489 | − | 0.157305i | ||||
\(827\) | − | 50.5644i | − | 1.75830i | −0.476549 | − | 0.879148i | \(-0.658113\pi\) | ||
0.476549 | − | 0.879148i | \(-0.341887\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −13.3885 | − | 7.72987i | −0.465003 | − | 0.268470i | 0.249143 | − | 0.968467i | \(-0.419851\pi\) |
−0.714146 | + | 0.699997i | \(0.753185\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | − | 22.6327i | − | 0.784647i | ||||||
\(833\) | 15.2380 | + | 27.4590i | 0.527965 | + | 0.951397i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −17.9733 | + | 31.1307i | −0.621621 | + | 1.07668i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −8.30838 | + | 4.79684i | −0.287008 | + | 0.165704i | ||||
\(839\) | 48.2725 | 1.66655 | 0.833276 | − | 0.552858i | \(-0.186463\pi\) | ||||
0.833276 | + | 0.552858i | \(0.186463\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −54.4618 | −1.87799 | ||||||||
\(842\) | −7.71325 | + | 4.45325i | −0.265816 | + | 0.153469i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −5.17949 | + | 8.97114i | −0.178285 | + | 0.308799i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 35.0448 | + | 20.6316i | 1.20415 | + | 0.708911i | ||||
\(848\) | − | 8.88898i | − | 0.305249i | ||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −21.5336 | − | 12.4324i | −0.738161 | − | 0.426178i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 7.57394i | − | 0.259327i | −0.991558 | − | 0.129663i | \(-0.958610\pi\) | ||
0.991558 | − | 0.129663i | \(-0.0413897\pi\) | |||||||
\(854\) | 0.106105 | − | 12.5023i | 0.00363084 | − | 0.427820i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −3.68299 | − | 6.37913i | −0.125882 | − | 0.218034i | ||||
\(857\) | −0.260910 | + | 0.451909i | −0.00891251 | + | 0.0154369i | −0.870447 | − | 0.492262i | \(-0.836170\pi\) |
0.861535 | + | 0.507699i | \(0.169504\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 39.1327 | − | 22.5933i | 1.33519 | − | 0.770872i | 0.349100 | − | 0.937085i | \(-0.386487\pi\) |
0.986090 | + | 0.166213i | \(0.0531539\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 4.09673 | 0.139535 | ||||||||
\(863\) | 7.46024 | − | 4.30717i | 0.253950 | − | 0.146618i | −0.367622 | − | 0.929975i | \(-0.619828\pi\) |
0.621571 | + | 0.783358i | \(0.286495\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0.978108 | + | 1.69413i | 0.0332375 | + | 0.0575690i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 11.7582 | − | 19.9725i | 0.399100 | − | 0.677910i | ||||
\(869\) | − | 25.3231i | − | 0.859027i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −30.8811 | − | 17.8292i | −1.04637 | − | 0.604120i | ||||
\(872\) | −7.13302 | − | 4.11825i | −0.241555 | − | 0.139462i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 4.00353i | 0.135421i | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 0.739482 | + | 1.28082i | 0.0249705 | + | 0.0432502i | 0.878241 | − | 0.478219i | \(-0.158717\pi\) |
−0.853270 | + | 0.521469i | \(0.825384\pi\) | |||||||
\(878\) | −6.21067 | + | 10.7572i | −0.209600 | + | 0.363038i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −28.6082 | −0.963835 | −0.481918 | − | 0.876217i | \(-0.660060\pi\) | ||||
−0.481918 | + | 0.876217i | \(0.660060\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 2.70408 | 0.0909996 | 0.0454998 | − | 0.998964i | \(-0.485512\pi\) | ||||
0.0454998 | + | 0.998964i | \(0.485512\pi\) | |||||||
\(884\) | −36.4545 | + | 21.0470i | −1.22610 | + | 0.707888i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −2.10161 | + | 3.64009i | −0.0706048 | + | 0.122291i | ||||
\(887\) | −8.89098 | − | 15.3996i | −0.298530 | − | 0.517069i | 0.677270 | − | 0.735735i | \(-0.263163\pi\) |
−0.975800 | + | 0.218666i | \(0.929830\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −19.8698 | + | 11.2481i | −0.666413 | + | 0.377250i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −5.04456 | − | 2.91248i | −0.168904 | − | 0.0975170i | ||||
\(893\) | 25.7623 | + | 14.8739i | 0.862103 | + | 0.497735i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 13.8731 | − | 23.5647i | 0.463467 | − | 0.787243i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 6.55856 | + | 11.3598i | 0.218862 | + | 0.379080i | ||||
\(899\) | 21.7300 | − | 37.6375i | 0.724736 | − | 1.25528i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −11.2357 | + | 6.48696i | −0.374317 | + | 0.216112i | ||||
\(902\) | 15.3676 | 0.511684 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 14.4994 | 0.482241 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 22.0597 | − | 38.2086i | 0.732481 | − | 1.26869i | −0.223338 | − | 0.974741i | \(-0.571695\pi\) |
0.955820 | − | 0.293954i | \(-0.0949712\pi\) | |||||||
\(908\) | 10.3533 | + | 17.9324i | 0.343585 | + | 0.595108i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 2.01773i | 0.0668505i | 0.999441 | + | 0.0334253i | \(0.0106416\pi\) | ||||
−0.999441 | + | 0.0334253i | \(0.989358\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 43.3910 | + | 25.0518i | 1.43603 | + | 0.829094i | ||||
\(914\) | −11.0905 | − | 6.40311i | −0.366841 | − | 0.211796i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 41.9633i | 1.38651i | ||||||||
\(917\) | −35.3696 | − | 20.8229i | −1.16801 | − | 0.687632i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 18.8068 | + | 32.5743i | 0.620379 | + | 1.07453i | 0.989415 | + | 0.145113i | \(0.0463546\pi\) |
−0.369036 | + | 0.929415i | \(0.620312\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 13.6778 | − | 7.89686i | 0.450453 | − | 0.260069i | ||||
\(923\) | 6.31164 | 0.207750 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 11.8026 | − | 6.81421i | 0.387856 | − | 0.223929i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 19.5659 | − | 33.8892i | 0.642283 | − | 1.11247i | ||||
\(929\) | −19.6901 | − | 34.1042i | −0.646010 | − | 1.11892i | −0.984067 | − | 0.177797i | \(-0.943103\pi\) |
0.338057 | − | 0.941126i | \(-0.390230\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −0.451634 | + | 26.6060i | −0.0148017 | + | 0.871975i | ||||
\(932\) | − | 5.94218i | − | 0.194643i | ||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −10.2419 | − | 5.91315i | −0.335124 | − | 0.193484i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 10.4952i | 0.342864i | 0.985196 | + | 0.171432i | \(0.0548394\pi\) | ||||
−0.985196 | + | 0.171432i | \(0.945161\pi\) | |||||||
\(938\) | −3.63216 | − | 6.41622i | −0.118594 | − | 0.209497i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 11.1934 | − | 19.3875i | 0.364895 | − | 0.632016i | −0.623865 | − | 0.781532i | \(-0.714438\pi\) |
0.988759 | + | 0.149516i | \(0.0477717\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −17.2127 | + | 9.93776i | −0.560523 | + | 0.323618i | ||||
\(944\) | −15.1564 | −0.493300 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 13.7673 | 0.447612 | ||||||||
\(947\) | 13.3007 | − | 7.67919i | 0.432216 | − | 0.249540i | −0.268074 | − | 0.963398i | \(-0.586387\pi\) |
0.700290 | + | 0.713858i | \(0.253054\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −1.47299 | + | 2.55130i | −0.0478154 | + | 0.0828186i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −18.1561 | − | 0.154088i | −0.588442 | − | 0.00499401i | ||||
\(953\) | 7.83975i | 0.253955i | 0.991906 | + | 0.126977i | \(0.0405275\pi\) | ||||
−0.991906 | + | 0.126977i | \(0.959472\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −36.8815 | − | 21.2936i | −1.19283 | − | 0.688683i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 3.73995i | 0.120832i | ||||||||
\(959\) | 2.92131 | + | 0.0247927i | 0.0943341 | + | 0.000800599i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −4.18480 | − | 7.24829i | −0.134994 | − | 0.233816i | ||||
\(962\) | −9.53816 | + | 16.5206i | −0.307523 | + | 0.532645i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −23.6808 | + | 13.6721i | −0.762707 | + | 0.440349i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −31.3647 | −1.00862 | −0.504310 | − | 0.863523i | \(-0.668253\pi\) | ||||
−0.504310 | + | 0.863523i | \(0.668253\pi\) | |||||||
\(968\) | −20.3624 | + | 11.7562i | −0.654472 | + | 0.377860i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −11.3560 | − | 19.6691i | −0.364431 | − | 0.631213i | 0.624254 | − | 0.781222i | \(-0.285403\pi\) |
−0.988685 | + | 0.150009i | \(0.952070\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 8.44671 | + | 14.9212i | 0.270789 | + | 0.478350i | ||||
\(974\) | − | 3.16287i | − | 0.101345i | ||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −31.5892 | − | 18.2380i | −1.01114 | − | 0.583784i | ||||
\(977\) | 9.38128 | + | 5.41629i | 0.300134 | + | 0.173282i | 0.642503 | − | 0.766283i | \(-0.277896\pi\) |
−0.342369 | + | 0.939566i | \(0.611229\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 37.3356i | 1.19325i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −2.12885 | − | 3.68727i | −0.0679342 | − | 0.117665i | ||||
\(983\) | 14.0614 | − | 24.3551i | 0.448490 | − | 0.776808i | −0.549798 | − | 0.835298i | \(-0.685295\pi\) |
0.998288 | + | 0.0584896i | \(0.0186285\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −16.3207 | −0.519758 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −35.6682 | −1.13476 | ||||||||
\(989\) | −15.4202 | + | 8.90288i | −0.490335 | + | 0.283095i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 1.02979 | − | 1.78365i | 0.0327123 | − | 0.0566594i | −0.849206 | − | 0.528062i | \(-0.822919\pi\) |
0.881918 | + | 0.471403i | \(0.156252\pi\) | |||||||
\(992\) | 10.1883 | + | 17.6467i | 0.323480 | + | 0.560283i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 1.12461 | + | 0.662084i | 0.0356705 | + | 0.0210000i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 36.8214 | + | 21.2589i | 1.16615 | + | 0.673275i | 0.952769 | − | 0.303695i | \(-0.0982202\pi\) |
0.213378 | + | 0.976970i | \(0.431554\pi\) | |||||||
\(998\) | −2.49576 | − | 1.44093i | −0.0790021 | − | 0.0456119i | ||||
\(999\) | 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 | 1575.2.bk.e.1151.4 | 12 | ||
3.2 | odd | 2 | 1575.2.bk.f.1151.3 | 12 | |||
5.2 | odd | 4 | 1575.2.bc.c.899.7 | 24 | |||
5.3 | odd | 4 | 1575.2.bc.c.899.6 | 24 | |||
5.4 | even | 2 | 315.2.bj.b.206.3 | yes | 12 | ||
7.5 | odd | 6 | 1575.2.bk.f.26.3 | 12 | |||
15.2 | even | 4 | 1575.2.bc.d.899.6 | 24 | |||
15.8 | even | 4 | 1575.2.bc.d.899.7 | 24 | |||
15.14 | odd | 2 | 315.2.bj.a.206.4 | yes | 12 | ||
21.5 | even | 6 | inner | 1575.2.bk.e.26.4 | 12 | ||
35.4 | even | 6 | 2205.2.b.a.881.6 | 12 | |||
35.12 | even | 12 | 1575.2.bc.d.1349.7 | 24 | |||
35.19 | odd | 6 | 315.2.bj.a.26.4 | ✓ | 12 | ||
35.24 | odd | 6 | 2205.2.b.b.881.6 | 12 | |||
35.33 | even | 12 | 1575.2.bc.d.1349.6 | 24 | |||
105.47 | odd | 12 | 1575.2.bc.c.1349.6 | 24 | |||
105.59 | even | 6 | 2205.2.b.a.881.7 | 12 | |||
105.68 | odd | 12 | 1575.2.bc.c.1349.7 | 24 | |||
105.74 | odd | 6 | 2205.2.b.b.881.7 | 12 | |||
105.89 | even | 6 | 315.2.bj.b.26.3 | yes | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
315.2.bj.a.26.4 | ✓ | 12 | 35.19 | odd | 6 | ||
315.2.bj.a.206.4 | yes | 12 | 15.14 | odd | 2 | ||
315.2.bj.b.26.3 | yes | 12 | 105.89 | even | 6 | ||
315.2.bj.b.206.3 | yes | 12 | 5.4 | even | 2 | ||
1575.2.bc.c.899.6 | 24 | 5.3 | odd | 4 | |||
1575.2.bc.c.899.7 | 24 | 5.2 | odd | 4 | |||
1575.2.bc.c.1349.6 | 24 | 105.47 | odd | 12 | |||
1575.2.bc.c.1349.7 | 24 | 105.68 | odd | 12 | |||
1575.2.bc.d.899.6 | 24 | 15.2 | even | 4 | |||
1575.2.bc.d.899.7 | 24 | 15.8 | even | 4 | |||
1575.2.bc.d.1349.6 | 24 | 35.33 | even | 12 | |||
1575.2.bc.d.1349.7 | 24 | 35.12 | even | 12 | |||
1575.2.bk.e.26.4 | 12 | 21.5 | even | 6 | inner | ||
1575.2.bk.e.1151.4 | 12 | 1.1 | even | 1 | trivial | ||
1575.2.bk.f.26.3 | 12 | 7.5 | odd | 6 | |||
1575.2.bk.f.1151.3 | 12 | 3.2 | odd | 2 | |||
2205.2.b.a.881.6 | 12 | 35.4 | even | 6 | |||
2205.2.b.a.881.7 | 12 | 105.59 | even | 6 | |||
2205.2.b.b.881.6 | 12 | 35.24 | odd | 6 | |||
2205.2.b.b.881.7 | 12 | 105.74 | odd | 6 |