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 | 451.1 | ||
Root | \(0.403374 - 1.68443i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 675.451 |
Dual form | 675.2.e.b.226.1 |
$q$-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 \(\left(\mathbb{Z}/675\mathbb{Z}\right)^\times\).
\(n\) | \(326\) | \(352\) |
\(\chi(n)\) | \(e\left(\frac{2}{3}\right)\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.25707 | + | 2.17731i | −0.888882 | + | 1.53959i | −0.0476826 | + | 0.998863i | \(0.515184\pi\) |
−0.841199 | + | 0.540726i | \(0.818150\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −2.16044 | − | 3.74200i | −1.08022 | − | 1.87100i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.257068 | + | 0.445256i | −0.0971627 | + | 0.168291i | −0.910509 | − | 0.413489i | \(-0.864310\pi\) |
0.813346 | + | 0.581780i | \(0.197643\pi\) | |||||||
\(8\) | 5.83502 | 2.06299 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.66044 | + | 2.87597i | −0.500642 | + | 0.867138i | 0.499358 | + | 0.866396i | \(0.333569\pi\) |
−1.00000 | 0.000741679i | \(0.999764\pi\) | ||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −0.660442 | − | 1.14392i | −0.183174 | − | 0.317266i | 0.759786 | − | 0.650173i | \(-0.225304\pi\) |
−0.942960 | + | 0.332907i | \(0.891970\pi\) | |||||||
\(14\) | −0.646305 | − | 1.11943i | −0.172732 | − | 0.299181i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −3.01414 | + | 5.22064i | −0.753534 | + | 1.30516i | ||||
\(17\) | −3.32088 | −0.805433 | −0.402716 | − | 0.915325i | \(-0.631934\pi\) | ||||
−0.402716 | + | 0.915325i | \(0.631934\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.32088 | −0.303032 | −0.151516 | − | 0.988455i | \(-0.548415\pi\) | ||||
−0.151516 | + | 0.988455i | \(0.548415\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −4.17458 | − | 7.23058i | −0.890023 | − | 1.54157i | ||||
\(23\) | −2.06382 | − | 3.57463i | −0.430335 | − | 0.745363i | 0.566567 | − | 0.824016i | \(-0.308271\pi\) |
−0.996902 | + | 0.0786532i | \(0.974938\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 3.32088 | 0.651279 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 2.22153 | 0.419829 | ||||||||
\(29\) | −0.693252 | + | 1.20075i | −0.128734 | + | 0.222973i | −0.923186 | − | 0.384353i | \(-0.874425\pi\) |
0.794453 | + | 0.607326i | \(0.207758\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −4.36783 | − | 7.56531i | −0.784486 | − | 1.35877i | −0.929306 | − | 0.369311i | \(-0.879594\pi\) |
0.144820 | − | 0.989458i | \(-0.453740\pi\) | |||||||
\(32\) | −1.74293 | − | 3.01885i | −0.308110 | − | 0.533662i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 4.17458 | − | 7.23058i | 0.715934 | − | 1.24003i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −0.292611 | −0.0481049 | −0.0240524 | − | 0.999711i | \(-0.507657\pi\) | ||||
−0.0240524 | + | 0.999711i | \(0.507657\pi\) | |||||||
\(38\) | 1.66044 | − | 2.87597i | 0.269359 | − | 0.466544i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −5.67458 | − | 9.82866i | −0.886220 | − | 1.53498i | −0.844308 | − | 0.535857i | \(-0.819988\pi\) |
−0.0419119 | − | 0.999121i | \(-0.513345\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 5.17458 | − | 8.96263i | 0.789116 | − | 1.36679i | −0.137393 | − | 0.990517i | \(-0.543872\pi\) |
0.926509 | − | 0.376272i | \(-0.122794\pi\) | |||||||
\(44\) | 14.3492 | 2.16322 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 10.3774 | 1.53007 | ||||||||
\(47\) | 2.43165 | − | 4.21174i | 0.354692 | − | 0.614345i | −0.632373 | − | 0.774664i | \(-0.717919\pi\) |
0.987065 | + | 0.160319i | \(0.0512523\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 3.36783 | + | 5.83326i | 0.481119 | + | 0.833322i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −2.85369 | + | 4.94274i | −0.395736 | + | 0.685435i | ||||
\(53\) | −5.02827 | −0.690687 | −0.345343 | − | 0.938476i | \(-0.612238\pi\) | ||||
−0.345343 | + | 0.938476i | \(0.612238\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −1.50000 | + | 2.59808i | −0.200446 | + | 0.347183i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −1.74293 | − | 3.01885i | −0.228858 | − | 0.396394i | ||||
\(59\) | −2.51414 | − | 4.35461i | −0.327313 | − | 0.566922i | 0.654665 | − | 0.755919i | \(-0.272810\pi\) |
−0.981978 | + | 0.188997i | \(0.939476\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −3.67458 | + | 6.36456i | −0.470482 | + | 0.814898i | −0.999430 | − | 0.0337558i | \(-0.989253\pi\) |
0.528948 | + | 0.848654i | \(0.322586\pi\) | |||||||
\(62\) | 21.9627 | 2.78926 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −3.29261 | −0.411576 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 4.72426 | + | 8.18266i | 0.577160 | + | 0.999670i | 0.995803 | + | 0.0915197i | \(0.0291724\pi\) |
−0.418643 | + | 0.908151i | \(0.637494\pi\) | |||||||
\(68\) | 7.17458 | + | 12.4267i | 0.870046 | + | 1.50696i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −8.99093 | −1.06703 | −0.533513 | − | 0.845792i | \(-0.679129\pi\) | ||||
−0.533513 | + | 0.845792i | \(0.679129\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −6.05655 | −0.708865 | −0.354433 | − | 0.935082i | \(-0.615326\pi\) | ||||
−0.354433 | + | 0.935082i | \(0.615326\pi\) | |||||||
\(74\) | 0.367832 | − | 0.637103i | 0.0427596 | − | 0.0740617i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 2.85369 | + | 4.94274i | 0.327341 | + | 0.566972i | ||||
\(77\) | −0.853695 | − | 1.47864i | −0.0972875 | − | 0.168507i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 4.02827 | − | 6.97717i | 0.453216 | − | 0.784994i | −0.545367 | − | 0.838197i | \(-0.683610\pi\) |
0.998584 | + | 0.0532036i | \(0.0169432\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 28.5333 | 3.15098 | ||||||||
\(83\) | −0.771205 | + | 1.33577i | −0.0846508 | + | 0.146619i | −0.905242 | − | 0.424896i | \(-0.860311\pi\) |
0.820592 | + | 0.571515i | \(0.193644\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 13.0096 | + | 22.5333i | 1.40286 | + | 2.42983i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −9.68872 | + | 16.7813i | −1.03282 | + | 1.78890i | ||||
\(89\) | 3.00000 | 0.317999 | 0.159000 | − | 0.987279i | \(-0.449173\pi\) | ||||
0.159000 | + | 0.987279i | \(0.449173\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0.679116 | 0.0711906 | ||||||||
\(92\) | −8.91751 | + | 15.4456i | −0.929715 | + | 1.61031i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 6.11350 | + | 10.5889i | 0.630559 | + | 1.09216i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −6.12763 | + | 10.6134i | −0.622167 | + | 1.07762i | 0.366915 | + | 0.930255i | \(0.380414\pi\) |
−0.989081 | + | 0.147370i | \(0.952919\pi\) | |||||||
\(98\) | −16.9344 | −1.71063 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 5.83502 | − | 10.1066i | 0.580606 | − | 1.00564i | −0.414801 | − | 0.909912i | \(-0.636149\pi\) |
0.995408 | − | 0.0957276i | \(-0.0305178\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 0.146305 | + | 0.253408i | 0.0144159 | + | 0.0249691i | 0.873143 | − | 0.487464i | \(-0.162078\pi\) |
−0.858727 | + | 0.512433i | \(0.828744\pi\) | |||||||
\(104\) | −3.85369 | − | 6.67479i | −0.377886 | − | 0.654517i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 6.32088 | − | 10.9481i | 0.613939 | − | 1.06337i | ||||
\(107\) | 1.87237 | 0.181009 | 0.0905043 | − | 0.995896i | \(-0.471152\pi\) | ||||
0.0905043 | + | 0.995896i | \(0.471152\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 5.54787 | 0.531390 | 0.265695 | − | 0.964057i | \(-0.414399\pi\) | ||||
0.265695 | + | 0.964057i | \(0.414399\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −1.54968 | − | 2.68412i | −0.146431 | − | 0.253626i | ||||
\(113\) | −3.90064 | − | 6.75611i | −0.366942 | − | 0.635561i | 0.622144 | − | 0.782903i | \(-0.286262\pi\) |
−0.989086 | + | 0.147341i | \(0.952928\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 5.99093 | 0.556244 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 12.6418 | 1.16377 | ||||||||
\(119\) | 0.853695 | − | 1.47864i | 0.0782581 | − | 0.135547i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −0.0141369 | − | 0.0244859i | −0.00128518 | − | 0.00222599i | ||||
\(122\) | −9.23840 | − | 16.0014i | −0.836405 | − | 1.44870i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −18.8729 | + | 32.6888i | −1.69484 | + | 2.93554i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −17.8916 | −1.58762 | −0.793810 | − | 0.608166i | \(-0.791906\pi\) | ||||
−0.793810 | + | 0.608166i | \(0.791906\pi\) | |||||||
\(128\) | 7.62490 | − | 13.2067i | 0.673952 | − | 1.16732i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −3.00000 | − | 5.19615i | −0.262111 | − | 0.453990i | 0.704692 | − | 0.709514i | \(-0.251085\pi\) |
−0.966803 | + | 0.255524i | \(0.917752\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0.339558 | − | 0.588131i | 0.0294434 | − | 0.0509974i | ||||
\(134\) | −23.7549 | −2.05211 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −19.3774 | −1.66160 | ||||||||
\(137\) | −2.83502 | + | 4.91040i | −0.242212 | + | 0.419524i | −0.961344 | − | 0.275350i | \(-0.911206\pi\) |
0.719132 | + | 0.694874i | \(0.244540\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −4.00000 | − | 6.92820i | −0.339276 | − | 0.587643i | 0.645021 | − | 0.764165i | \(-0.276849\pi\) |
−0.984297 | + | 0.176522i | \(0.943515\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 11.3022 | − | 19.5760i | 0.948460 | − | 1.64278i | ||||
\(143\) | 4.38650 | 0.366818 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 7.61350 | − | 13.1870i | 0.630097 | − | 1.09136i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0.632168 | + | 1.09495i | 0.0519639 | + | 0.0900042i | ||||
\(149\) | 8.83049 | + | 15.2948i | 0.723422 | + | 1.25300i | 0.959620 | + | 0.281298i | \(0.0907650\pi\) |
−0.236199 | + | 0.971705i | \(0.575902\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −0.632168 | + | 1.09495i | −0.0514451 | + | 0.0891056i | −0.890601 | − | 0.454785i | \(-0.849716\pi\) |
0.839156 | + | 0.543891i | \(0.183049\pi\) | |||||||
\(152\) | −7.70739 | −0.625152 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 4.29261 | 0.345908 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −7.83502 | − | 13.5707i | −0.625303 | − | 1.08306i | −0.988482 | − | 0.151337i | \(-0.951642\pi\) |
0.363179 | − | 0.931719i | \(-0.381691\pi\) | |||||||
\(158\) | 10.1276 | + | 17.5416i | 0.805711 | + | 1.39553i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 2.12217 | 0.167250 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −15.7074 | −1.23030 | −0.615149 | − | 0.788411i | \(-0.710904\pi\) | ||||
−0.615149 | + | 0.788411i | \(0.710904\pi\) | |||||||
\(164\) | −24.5192 | + | 42.4685i | −1.91463 | + | 3.31623i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −1.93892 | − | 3.35830i | −0.150489 | − | 0.260655i | ||||
\(167\) | −3.08249 | − | 5.33903i | −0.238530 | − | 0.413146i | 0.721763 | − | 0.692141i | \(-0.243332\pi\) |
−0.960293 | + | 0.278994i | \(0.909999\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 5.62763 | − | 9.74734i | 0.432895 | − | 0.749796i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −44.7175 | −3.40968 | ||||||||
\(173\) | −4.29261 | + | 7.43502i | −0.326361 | + | 0.565274i | −0.981787 | − | 0.189986i | \(-0.939156\pi\) |
0.655426 | + | 0.755260i | \(0.272489\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −10.0096 | − | 17.3371i | −0.754502 | − | 1.30684i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −3.77121 | + | 6.53192i | −0.282664 | + | 0.489588i | ||||
\(179\) | 1.06562 | 0.0796482 | 0.0398241 | − | 0.999207i | \(-0.487320\pi\) | ||||
0.0398241 | + | 0.999207i | \(0.487320\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −12.6700 | −0.941757 | −0.470878 | − | 0.882198i | \(-0.656063\pi\) | ||||
−0.470878 | + | 0.882198i | \(0.656063\pi\) | |||||||
\(182\) | −0.853695 | + | 1.47864i | −0.0632801 | + | 0.109604i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −12.0424 | − | 20.8581i | −0.887778 | − | 1.53768i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 5.51414 | − | 9.55077i | 0.403234 | − | 0.698421i | ||||
\(188\) | −21.0137 | −1.53258 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −8.46719 | + | 14.6656i | −0.612664 | + | 1.06117i | 0.378125 | + | 0.925754i | \(0.376569\pi\) |
−0.990789 | + | 0.135411i | \(0.956764\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 13.3588 | + | 23.1380i | 0.961585 | + | 1.66551i | 0.718524 | + | 0.695502i | \(0.244818\pi\) |
0.243060 | + | 0.970011i | \(0.421849\pi\) | |||||||
\(194\) | −15.4057 | − | 26.6835i | −1.10607 | − | 1.91576i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 14.5520 | − | 25.2048i | 1.03943 | − | 1.80034i | ||||
\(197\) | −14.2553 | −1.01565 | −0.507823 | − | 0.861462i | \(-0.669550\pi\) | ||||
−0.507823 | + | 0.861462i | \(0.669550\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −24.6610 | −1.74817 | −0.874085 | − | 0.485773i | \(-0.838538\pi\) | ||||
−0.874085 | + | 0.485773i | \(0.838538\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 14.6700 | + | 25.4093i | 1.03218 | + | 1.78779i | ||||
\(203\) | −0.356427 | − | 0.617349i | −0.0250162 | − | 0.0433294i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −0.735663 | −0.0512561 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 7.96265 | 0.552111 | ||||||||
\(209\) | 2.19325 | − | 3.79882i | 0.151710 | − | 0.262770i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 2.68872 | + | 4.65699i | 0.185099 | + | 0.320601i | 0.943610 | − | 0.331060i | \(-0.107406\pi\) |
−0.758511 | + | 0.651660i | \(0.774073\pi\) | |||||||
\(212\) | 10.8633 | + | 18.8158i | 0.746094 | + | 1.29227i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −2.35369 | + | 4.07672i | −0.160895 | + | 0.278679i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 4.49133 | 0.304891 | ||||||||
\(218\) | −6.97406 | + | 12.0794i | −0.472343 | + | 0.818122i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 2.19325 | + | 3.79882i | 0.147534 | + | 0.255537i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 4.33229 | − | 7.50375i | 0.290112 | − | 0.502488i | −0.683724 | − | 0.729740i | \(-0.739641\pi\) |
0.973836 | + | 0.227252i | \(0.0729743\pi\) | |||||||
\(224\) | 1.79221 | 0.119747 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 19.6135 | 1.30467 | ||||||||
\(227\) | −1.66044 | + | 2.87597i | −0.110207 | + | 0.190885i | −0.915854 | − | 0.401512i | \(-0.868485\pi\) |
0.805646 | + | 0.592397i | \(0.201818\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 12.6559 | + | 21.9207i | 0.836326 | + | 1.44856i | 0.892946 | + | 0.450163i | \(0.148634\pi\) |
−0.0566206 | + | 0.998396i | \(0.518033\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −4.04514 | + | 7.00639i | −0.265577 | + | 0.459992i | ||||
\(233\) | 27.6327 | 1.81028 | 0.905139 | − | 0.425116i | \(-0.139767\pi\) | ||||
0.905139 | + | 0.425116i | \(0.139767\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −10.8633 | + | 18.8158i | −0.707140 | + | 1.22480i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 2.14631 | + | 3.71751i | 0.139124 | + | 0.240970i | ||||
\(239\) | −2.09936 | − | 3.63620i | −0.135796 | − | 0.235206i | 0.790105 | − | 0.612971i | \(-0.210026\pi\) |
−0.925901 | + | 0.377765i | \(0.876693\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −1.80221 | + | 3.12152i | −0.116091 | + | 0.201075i | −0.918215 | − | 0.396082i | \(-0.870370\pi\) |
0.802125 | + | 0.597157i | \(0.203703\pi\) | |||||||
\(242\) | 0.0710844 | 0.00456948 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 31.7549 | 2.03290 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0.872368 | + | 1.51099i | 0.0555074 | + | 0.0961417i | ||||
\(248\) | −25.4864 | − | 44.1437i | −1.61839 | − | 2.80313i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 6.87783 | 0.434125 | 0.217062 | − | 0.976158i | \(-0.430352\pi\) | ||||
0.217062 | + | 0.976158i | \(0.430352\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 13.7074 | 0.861776 | ||||||||
\(254\) | 22.4909 | − | 38.9554i | 1.41121 | − | 2.44428i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 15.8774 | + | 27.5005i | 0.992340 | + | 1.71878i | ||||
\(257\) | 9.00000 | + | 15.5885i | 0.561405 | + | 0.972381i | 0.997374 | + | 0.0724199i | \(0.0230722\pi\) |
−0.435970 | + | 0.899961i | \(0.643595\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0.0752210 | − | 0.130287i | 0.00467400 | − | 0.00809561i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 15.0848 | 0.931943 | ||||||||
\(263\) | −3.11803 | + | 5.40059i | −0.192266 | + | 0.333015i | −0.946001 | − | 0.324164i | \(-0.894917\pi\) |
0.753735 | + | 0.657179i | \(0.228250\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0.853695 | + | 1.47864i | 0.0523434 | + | 0.0906614i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 20.4130 | − | 35.3563i | 1.24692 | − | 2.15973i | ||||
\(269\) | −9.92345 | −0.605044 | −0.302522 | − | 0.953142i | \(-0.597828\pi\) | ||||
−0.302522 | + | 0.953142i | \(0.597828\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 6.60442 | 0.401190 | 0.200595 | − | 0.979674i | \(-0.435712\pi\) | ||||
0.200595 | + | 0.979674i | \(0.435712\pi\) | |||||||
\(272\) | 10.0096 | − | 17.3371i | 0.606921 | − | 1.05122i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −7.12763 | − | 12.3454i | −0.430596 | − | 0.745814i | ||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 11.3305 | − | 19.6250i | 0.680783 | − | 1.17915i | −0.293959 | − | 0.955818i | \(-0.594973\pi\) |
0.974742 | − | 0.223333i | \(-0.0716936\pi\) | |||||||
\(278\) | 20.1131 | 1.20630 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −7.77394 | + | 13.4649i | −0.463754 | + | 0.803246i | −0.999144 | − | 0.0413590i | \(-0.986831\pi\) |
0.535390 | + | 0.844605i | \(0.320165\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 0.322689 | + | 0.558913i | 0.0191819 | + | 0.0332240i | 0.875457 | − | 0.483296i | \(-0.160561\pi\) |
−0.856275 | + | 0.516520i | \(0.827227\pi\) | |||||||
\(284\) | 19.4244 | + | 33.6440i | 1.15262 | + | 1.99640i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −5.51414 | + | 9.55077i | −0.326058 | + | 0.564749i | ||||
\(287\) | 5.83502 | 0.344430 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −5.97173 | −0.351278 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 13.0848 | + | 22.6636i | 0.765731 | + | 1.32629i | ||||
\(293\) | 0.688716 | + | 1.19289i | 0.0402352 | + | 0.0696895i | 0.885442 | − | 0.464750i | \(-0.153856\pi\) |
−0.845207 | + | 0.534440i | \(0.820523\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −1.70739 | −0.0992400 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −44.4021 | −2.57214 | ||||||||
\(299\) | −2.72606 | + | 4.72168i | −0.157652 | + | 0.273062i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 2.66044 | + | 4.60802i | 0.153345 | + | 0.265602i | ||||
\(302\) | −1.58936 | − | 2.75285i | −0.0914573 | − | 0.158409i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 3.98133 | − | 6.89586i | 0.228345 | − | 0.395505i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 7.98546 | 0.455754 | 0.227877 | − | 0.973690i | \(-0.426822\pi\) | ||||
0.227877 | + | 0.973690i | \(0.426822\pi\) | |||||||
\(308\) | −3.68872 | + | 6.38904i | −0.210184 | + | 0.364050i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 4.81635 | + | 8.34216i | 0.273110 | + | 0.473040i | 0.969657 | − | 0.244471i | \(-0.0786143\pi\) |
−0.696547 | + | 0.717512i | \(0.745281\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −12.2685 | + | 21.2496i | −0.693455 | + | 1.20110i | 0.277244 | + | 0.960800i | \(0.410579\pi\) |
−0.970699 | + | 0.240300i | \(0.922754\pi\) | |||||||
\(314\) | 39.3966 | 2.22328 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −34.8114 | −1.95829 | ||||||||
\(317\) | 10.1746 | − | 17.6229i | 0.571461 | − | 0.989800i | −0.424955 | − | 0.905215i | \(-0.639710\pi\) |
0.996416 | − | 0.0845855i | \(-0.0269566\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −2.30221 | − | 3.98755i | −0.128899 | − | 0.223260i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −2.66771 | + | 4.62061i | −0.148666 | + | 0.257497i | ||||
\(323\) | 4.38650 | 0.244072 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 19.7453 | − | 34.1998i | 1.09359 | − | 1.89415i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −33.1113 | − | 57.3504i | −1.82827 | − | 3.16665i | ||||
\(329\) | 1.25020 | + | 2.16541i | 0.0689257 | + | 0.119383i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −8.22153 | + | 14.2401i | −0.451896 | + | 0.782707i | −0.998504 | − | 0.0546819i | \(-0.982586\pi\) |
0.546608 | + | 0.837389i | \(0.315919\pi\) | |||||||
\(332\) | 6.66458 | 0.365766 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 15.4996 | 0.848100 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 2.44852 | + | 4.24096i | 0.133379 | + | 0.231020i | 0.924977 | − | 0.380023i | \(-0.124084\pi\) |
−0.791598 | + | 0.611042i | \(0.790751\pi\) | |||||||
\(338\) | 14.1486 | + | 24.5062i | 0.769584 | + | 1.33296i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 29.0101 | 1.57099 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −7.06201 | −0.381313 | ||||||||
\(344\) | 30.1938 | − | 52.2972i | 1.62794 | − | 2.81967i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −10.7922 | − | 18.6927i | −0.580193 | − | 1.00492i | ||||
\(347\) | −11.1372 | − | 19.2903i | −0.597878 | − | 1.03556i | −0.993134 | − | 0.116984i | \(-0.962677\pi\) |
0.395256 | − | 0.918571i | \(-0.370656\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 1.47173 | − | 2.54910i | 0.0787797 | − | 0.136450i | −0.823944 | − | 0.566671i | \(-0.808231\pi\) |
0.902724 | + | 0.430221i | \(0.141564\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 11.5761 | 0.617011 | ||||||||
\(353\) | −9.41478 | + | 16.3069i | −0.501098 | + | 0.867927i | 0.498901 | + | 0.866659i | \(0.333737\pi\) |
−0.999999 | + | 0.00126845i | \(0.999596\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −6.48133 | − | 11.2260i | −0.343510 | − | 0.594976i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −1.33956 | + | 2.32018i | −0.0707978 | + | 0.122625i | ||||
\(359\) | 31.8770 | 1.68241 | 0.841203 | − | 0.540720i | \(-0.181848\pi\) | ||||
0.841203 | + | 0.540720i | \(0.181848\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −17.2553 | −0.908172 | ||||||||
\(362\) | 15.9271 | − | 27.5866i | 0.837110 | − | 1.44992i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −1.46719 | − | 2.54125i | −0.0769016 | − | 0.133198i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −9.17458 | + | 15.8908i | −0.478909 | + | 0.829495i | −0.999708 | − | 0.0241848i | \(-0.992301\pi\) |
0.520798 | + | 0.853680i | \(0.325634\pi\) | |||||||
\(368\) | 24.8825 | 1.29709 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 1.29261 | − | 2.23887i | 0.0671090 | − | 0.116236i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −1.09936 | − | 1.90414i | −0.0569226 | − | 0.0985929i | 0.836160 | − | 0.548486i | \(-0.184795\pi\) |
−0.893083 | + | 0.449893i | \(0.851462\pi\) | |||||||
\(374\) | 13.8633 | + | 24.0119i | 0.716854 | + | 1.24163i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 14.1887 | − | 24.5756i | 0.731727 | − | 1.26739i | ||||
\(377\) | 1.83141 | 0.0943226 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 15.4713 | 0.794709 | 0.397354 | − | 0.917665i | \(-0.369928\pi\) | ||||
0.397354 | + | 0.917665i | \(0.369928\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −21.2877 | − | 36.8713i | −1.08917 | − | 1.88650i | ||||
\(383\) | −3.85369 | − | 6.67479i | −0.196915 | − | 0.341066i | 0.750612 | − | 0.660743i | \(-0.229759\pi\) |
−0.947526 | + | 0.319677i | \(0.896426\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −67.1715 | −3.41894 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 52.9536 | 2.68831 | ||||||||
\(389\) | −12.3163 | + | 21.3325i | −0.624464 | + | 1.08160i | 0.364181 | + | 0.931328i | \(0.381349\pi\) |
−0.988644 | + | 0.150274i | \(0.951984\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 6.85369 | + | 11.8709i | 0.346606 | + | 0.600340i | ||||
\(392\) | 19.6514 | + | 34.0372i | 0.992544 | + | 1.71914i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 17.9198 | − | 31.0381i | 0.902789 | − | 1.56368i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 6.77301 | 0.339928 | 0.169964 | − | 0.985450i | \(-0.445635\pi\) | ||||
0.169964 | + | 0.985450i | \(0.445635\pi\) | |||||||
\(398\) | 31.0005 | − | 53.6945i | 1.55392 | − | 2.69146i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −9.24980 | − | 16.0211i | −0.461913 | − | 0.800057i | 0.537143 | − | 0.843491i | \(-0.319503\pi\) |
−0.999056 | + | 0.0434343i | \(0.986170\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −5.76940 | + | 9.99290i | −0.287394 | + | 0.497782i | ||||
\(404\) | −50.4249 | −2.50873 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 1.79221 | 0.0889459 | ||||||||
\(407\) | 0.485863 | − | 0.841540i | 0.0240833 | − | 0.0417136i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 6.70739 | + | 11.6175i | 0.331659 | + | 0.574450i | 0.982837 | − | 0.184474i | \(-0.0590583\pi\) |
−0.651178 | + | 0.758925i | \(0.725725\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0.632168 | − | 1.09495i | 0.0311447 | − | 0.0539442i | ||||
\(413\) | 2.58522 | 0.127210 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −2.30221 | + | 3.98755i | −0.112875 | + | 0.195506i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 5.51414 | + | 9.55077i | 0.269705 | + | 0.467143i | ||||
\(419\) | −16.5575 | − | 28.6784i | −0.808886 | − | 1.40103i | −0.913636 | − | 0.406532i | \(-0.866738\pi\) |
0.104751 | − | 0.994499i | \(-0.466596\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 7.34916 | − | 12.7291i | 0.358176 | − | 0.620379i | −0.629480 | − | 0.777017i | \(-0.716732\pi\) |
0.987656 | + | 0.156637i | \(0.0500654\pi\) | |||||||
\(422\) | −13.5196 | −0.658124 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −29.3401 | −1.42488 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −1.88924 | − | 3.27225i | −0.0914266 | − | 0.158355i | ||||
\(428\) | −4.04514 | − | 7.00639i | −0.195529 | − | 0.338667i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 32.7549 | 1.57775 | 0.788873 | − | 0.614556i | \(-0.210665\pi\) | ||||
0.788873 | + | 0.614556i | \(0.210665\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 11.8314 | 0.568581 | 0.284291 | − | 0.958738i | \(-0.408242\pi\) | ||||
0.284291 | + | 0.958738i | \(0.408242\pi\) | |||||||
\(434\) | −5.64591 | + | 9.77900i | −0.271012 | + | 0.469407i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −11.9859 | − | 20.7601i | −0.574019 | − | 0.994230i | ||||
\(437\) | 2.72606 | + | 4.72168i | 0.130405 | + | 0.225869i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −4.15591 | + | 7.19824i | −0.198351 | + | 0.343553i | −0.947994 | − | 0.318289i | \(-0.896892\pi\) |
0.749643 | + | 0.661842i | \(0.230225\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −11.0283 | −0.524561 | ||||||||
\(443\) | 14.5876 | − | 25.2664i | 0.693076 | − | 1.20044i | −0.277750 | − | 0.960654i | \(-0.589589\pi\) |
0.970825 | − | 0.239789i | \(-0.0770781\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 10.8920 | + | 18.8654i | 0.515750 | + | 0.893305i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0.846426 | − | 1.46605i | 0.0399899 | − | 0.0692645i | ||||
\(449\) | −18.9717 | −0.895331 | −0.447666 | − | 0.894201i | \(-0.647744\pi\) | ||||
−0.447666 | + | 0.894201i | \(0.647744\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 37.6892 | 1.77472 | ||||||||
\(452\) | −16.8542 | + | 29.1924i | −0.792756 | + | 1.37309i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −4.17458 | − | 7.23058i | −0.195923 | − | 0.339348i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −11.6176 | + | 20.1223i | −0.543450 | + | 0.941283i | 0.455253 | + | 0.890362i | \(0.349549\pi\) |
−0.998703 | + | 0.0509206i | \(0.983784\pi\) | |||||||
\(458\) | −63.6374 | −2.97358 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 2.21285 | − | 3.83277i | 0.103063 | − | 0.178510i | −0.809882 | − | 0.586592i | \(-0.800469\pi\) |
0.912945 | + | 0.408082i | \(0.133802\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −9.75434 | − | 16.8950i | −0.453322 | − | 0.785178i | 0.545268 | − | 0.838262i | \(-0.316428\pi\) |
−0.998590 | + | 0.0530845i | \(0.983095\pi\) | |||||||
\(464\) | −4.17912 | − | 7.23844i | −0.194011 | − | 0.336036i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −34.7362 | + | 60.1648i | −1.60912 | + | 2.78708i | ||||
\(467\) | −24.5935 | −1.13805 | −0.569026 | − | 0.822320i | \(-0.692679\pi\) | ||||
−0.569026 | + | 0.822320i | \(0.692679\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −4.85783 | −0.224314 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −14.6700 | − | 25.4093i | −0.675243 | − | 1.16956i | ||||
\(473\) | 17.1842 | + | 29.7639i | 0.790129 | + | 1.36854i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −7.37743 | −0.338144 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 10.5561 | 0.482827 | ||||||||
\(479\) | 16.3774 | − | 28.3665i | 0.748304 | − | 1.29610i | −0.200331 | − | 0.979728i | \(-0.564202\pi\) |
0.948635 | − | 0.316372i | \(-0.102465\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0.193252 | + | 0.334723i | 0.00881155 | + | 0.0152621i | ||||
\(482\) | −4.53101 | − | 7.84793i | −0.206382 | − | 0.357464i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −0.0610840 | + | 0.105801i | −0.00277655 | + | 0.00480912i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 6.03735 | 0.273578 | 0.136789 | − | 0.990600i | \(-0.456322\pi\) | ||||
0.136789 | + | 0.990600i | \(0.456322\pi\) | |||||||
\(488\) | −21.4412 | + | 37.1373i | −0.970600 | + | 1.68113i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 7.22153 | + | 12.5081i | 0.325903 | + | 0.564480i | 0.981695 | − | 0.190461i | \(-0.0609984\pi\) |
−0.655792 | + | 0.754942i | \(0.727665\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 2.30221 | − | 3.98755i | 0.103686 | − | 0.179590i | ||||
\(494\) | −4.38650 | −0.197358 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 52.6610 | 2.36455 | ||||||||
\(497\) | 2.31128 | − | 4.00326i | 0.103675 | − | 0.179571i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −10.4859 | − | 18.1620i | −0.469412 | − | 0.813045i | 0.529977 | − | 0.848012i | \(-0.322201\pi\) |
−0.999388 | + | 0.0349673i | \(0.988867\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −8.64591 | + | 14.9751i | −0.385886 | + | 0.668374i | ||||
\(503\) | −5.31728 | −0.237086 | −0.118543 | − | 0.992949i | \(-0.537822\pi\) | ||||
−0.118543 | + | 0.992949i | \(0.537822\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −17.2311 | + | 29.8452i | −0.766017 | + | 1.32678i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 38.6537 | + | 66.9502i | 1.71498 | + | 2.97043i | ||||
\(509\) | 9.11350 | + | 15.7850i | 0.403949 | + | 0.699659i | 0.994198 | − | 0.107561i | \(-0.0343041\pi\) |
−0.590250 | + | 0.807221i | \(0.700971\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 1.55695 | − | 2.69671i | 0.0688753 | − | 0.119296i | ||||
\(512\) | −49.3365 | −2.18038 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −45.2545 | −1.99609 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 8.07522 | + | 13.9867i | 0.355148 | + | 0.615134i | ||||
\(518\) | 0.189116 | + | 0.327558i | 0.00830927 | + | 0.0143921i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −40.1232 | −1.75783 | −0.878915 | − | 0.476978i | \(-0.841732\pi\) | ||||
−0.878915 | + | 0.476978i | \(0.841732\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −18.9873 | −0.830257 | −0.415129 | − | 0.909763i | \(-0.636263\pi\) | ||||
−0.415129 | + | 0.909763i | \(0.636263\pi\) | |||||||
\(524\) | −12.9627 | + | 22.4520i | −0.566276 | + | 0.980819i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −7.83916 | − | 13.5778i | −0.341804 | − | 0.592021i | ||||
\(527\) | 14.5051 | + | 25.1235i | 0.631851 | + | 1.09440i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 2.98133 | − | 5.16381i | 0.129623 | − | 0.224513i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −2.93438 | −0.127221 | ||||||||
\(533\) | −7.49546 | + | 12.9825i | −0.324665 | + | 0.562336i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 27.5661 | + | 47.7460i | 1.19068 | + | 2.06231i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 12.4745 | − | 21.6064i | 0.537812 | − | 0.931518i | ||||
\(539\) | −22.3684 | −0.963473 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 16.5279 | 0.710589 | 0.355294 | − | 0.934754i | \(-0.384381\pi\) | ||||
0.355294 | + | 0.934754i | \(0.384381\pi\) | |||||||
\(542\) | −8.30221 | + | 14.3799i | −0.356611 | + | 0.617668i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 5.78807 | + | 10.0252i | 0.248162 | + | 0.429829i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 8.83683 | − | 15.3058i | 0.377835 | − | 0.654430i | −0.612912 | − | 0.790151i | \(-0.710002\pi\) |
0.990747 | + | 0.135721i | \(0.0433352\pi\) | |||||||
\(548\) | 24.4996 | 1.04657 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0.915706 | − | 1.58605i | 0.0390104 | − | 0.0675680i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 2.07108 | + | 3.58722i | 0.0880715 | + | 0.152544i | ||||
\(554\) | 28.4864 | + | 49.3399i | 1.21027 | + | 2.09625i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −17.2835 | + | 29.9360i | −0.732985 | + | 1.26957i | ||||
\(557\) | 17.3401 | 0.734723 | 0.367362 | − | 0.930078i | \(-0.380261\pi\) | ||||
0.367362 | + | 0.930078i | \(0.380261\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −13.6700 | −0.578181 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −19.5447 | − | 33.8525i | −0.824445 | − | 1.42798i | ||||
\(563\) | −6.49727 | − | 11.2536i | −0.273827 | − | 0.474283i | 0.696011 | − | 0.718031i | \(-0.254956\pi\) |
−0.969839 | + | 0.243748i | \(0.921623\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −1.62257 | −0.0682016 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −52.4623 | −2.20127 | ||||||||
\(569\) | −8.34009 | + | 14.4455i | −0.349635 | + | 0.605585i | −0.986184 | − | 0.165651i | \(-0.947028\pi\) |
0.636550 | + | 0.771236i | \(0.280361\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −10.0000 | − | 17.3205i | −0.418487 | − | 0.724841i | 0.577301 | − | 0.816532i | \(-0.304106\pi\) |
−0.995788 | + | 0.0916910i | \(0.970773\pi\) | |||||||
\(572\) | −9.47679 | − | 16.4143i | −0.396245 | − | 0.686316i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −7.33502 | + | 12.7046i | −0.306158 | + | 0.530281i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 23.5953 | 0.982287 | 0.491144 | − | 0.871079i | \(-0.336579\pi\) | ||||
0.491144 | + | 0.871079i | \(0.336579\pi\) | |||||||
\(578\) | 7.50687 | − | 13.0023i | 0.312245 | − | 0.540823i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −0.396505 | − | 0.686767i | −0.0164498 | − | 0.0284919i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 8.34916 | − | 14.4612i | 0.345787 | − | 0.598920i | ||||
\(584\) | −35.3401 | −1.46238 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −3.46305 | −0.143057 | ||||||||
\(587\) | −14.0638 | + | 24.3592i | −0.580476 | + | 1.00541i | 0.414947 | + | 0.909846i | \(0.363800\pi\) |
−0.995423 | + | 0.0955681i | \(0.969533\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 5.76940 | + | 9.99290i | 0.237724 | + | 0.411750i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0.881969 | − | 1.52761i | 0.0362487 | − | 0.0627846i | ||||
\(593\) | −9.17872 | −0.376925 | −0.188462 | − | 0.982080i | \(-0.560350\pi\) | ||||
−0.188462 | + | 0.982080i | \(0.560350\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 38.1555 | − | 66.0873i | 1.56291 | − | 2.70704i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −6.85369 | − | 11.8709i | −0.280268 | − | 0.485439i | ||||
\(599\) | −15.7357 | − | 27.2550i | −0.642942 | − | 1.11361i | −0.984773 | − | 0.173846i | \(-0.944380\pi\) |
0.341831 | − | 0.939761i | \(-0.388953\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 14.6327 | − | 25.3446i | 0.596880 | − | 1.03383i | −0.396398 | − | 0.918079i | \(-0.629740\pi\) |
0.993279 | − | 0.115748i | \(-0.0369265\pi\) | |||||||
\(602\) | −13.3774 | −0.545223 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 5.46305 | 0.222288 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −22.1017 | − | 38.2813i | −0.897080 | − | 1.55379i | −0.831209 | − | 0.555960i | \(-0.812351\pi\) |
−0.0658708 | − | 0.997828i | \(-0.520983\pi\) | |||||||
\(608\) | 2.30221 | + | 3.98755i | 0.0933670 | + | 0.161716i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −6.42385 | −0.259881 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 35.1715 | 1.42056 | 0.710282 | − | 0.703918i | \(-0.248568\pi\) | ||||
0.710282 | + | 0.703918i | \(0.248568\pi\) | |||||||
\(614\) | −10.0383 | + | 17.3868i | −0.405112 | + | 0.701674i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −4.98133 | − | 8.62791i | −0.200703 | − | 0.347628i | ||||
\(617\) | 3.71285 | + | 6.43085i | 0.149474 | + | 0.258896i | 0.931033 | − | 0.364935i | \(-0.118909\pi\) |
−0.781559 | + | 0.623831i | \(0.785575\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −4.27394 | + | 7.40268i | −0.171784 | + | 0.297539i | −0.939044 | − | 0.343798i | \(-0.888286\pi\) |
0.767260 | + | 0.641337i | \(0.221620\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −24.2179 | −0.971050 | ||||||||
\(623\) | −0.771205 | + | 1.33577i | −0.0308977 | + | 0.0535164i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −30.8446 | − | 53.4245i | −1.23280 | − | 2.13527i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −33.8542 | + | 58.6372i | −1.35093 | + | 2.33988i | ||||
\(629\) | 0.971726 | 0.0387453 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −2.36836 | −0.0942829 | −0.0471415 | − | 0.998888i | \(-0.515011\pi\) | ||||
−0.0471415 | + | 0.998888i | \(0.515011\pi\) | |||||||
\(632\) | 23.5051 | − | 40.7120i | 0.934981 | − | 1.61944i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 25.5803 | + | 44.3064i | 1.01592 | + | 1.75963i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 4.44852 | − | 7.70506i | 0.176257 | − | 0.305285i | ||||
\(638\) | 11.5761 | 0.458304 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −0.0665480 | + | 0.115265i | −0.00262849 | + | 0.00455268i | −0.867337 | − | 0.497722i | \(-0.834170\pi\) |
0.864708 | + | 0.502275i | \(0.167503\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −11.3232 | − | 19.6124i | −0.446544 | − | 0.773437i | 0.551614 | − | 0.834099i | \(-0.314012\pi\) |
−0.998158 | + | 0.0606623i | \(0.980679\pi\) | |||||||
\(644\) | −4.58482 | − | 7.94114i | −0.180667 | − | 0.312925i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −5.51414 | + | 9.55077i | −0.216951 | + | 0.375770i | ||||
\(647\) | 46.3912 | 1.82383 | 0.911913 | − | 0.410385i | \(-0.134606\pi\) | ||||
0.911913 | + | 0.410385i | \(0.134606\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 16.6983 | 0.655466 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 33.9349 | + | 58.7770i | 1.32899 | + | 2.30188i | ||||
\(653\) | −18.2029 | − | 31.5283i | −0.712333 | − | 1.23380i | −0.963979 | − | 0.265977i | \(-0.914305\pi\) |
0.251647 | − | 0.967819i | \(-0.419028\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 68.4158 | 2.67119 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −6.28635 | −0.245067 | ||||||||
\(659\) | 9.57068 | − | 16.5769i | 0.372821 | − | 0.645745i | −0.617177 | − | 0.786824i | \(-0.711724\pi\) |
0.989998 | + | 0.141079i | \(0.0450572\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −19.9536 | − | 34.5606i | −0.776104 | − | 1.34425i | −0.934172 | − | 0.356824i | \(-0.883860\pi\) |
0.158067 | − | 0.987428i | \(-0.449474\pi\) | |||||||
\(662\) | −20.6700 | − | 35.8016i | −0.803364 | − | 1.39147i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −4.50000 | + | 7.79423i | −0.174634 | + | 0.302475i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 5.72298 | 0.221595 | ||||||||
\(668\) | −13.3191 | + | 23.0693i | −0.515331 | + | 0.892579i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −12.2029 | − | 21.1360i | −0.471086 | − | 0.815945i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 11.8254 | − | 20.4822i | 0.455836 | − | 0.789532i | −0.542899 | − | 0.839798i | \(-0.682674\pi\) |
0.998736 | + | 0.0502658i | \(0.0160068\pi\) | |||||||
\(674\) | −12.3118 | −0.474233 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −48.6327 | −1.87049 | ||||||||
\(677\) | 7.40157 | − | 12.8199i | 0.284465 | − | 0.492709i | −0.688014 | − | 0.725697i | \(-0.741517\pi\) |
0.972479 | + | 0.232989i | \(0.0748506\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −3.15044 | − | 5.45673i | −0.120903 | − | 0.209410i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −36.4677 | + | 63.1639i | −1.39642 | + | 2.41867i | ||||
\(683\) | −4.95252 | −0.189503 | −0.0947515 | − | 0.995501i | \(-0.530206\pi\) | ||||
−0.0947515 | + | 0.995501i | \(0.530206\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 8.87743 | − | 15.3762i | 0.338942 | − | 0.587065i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 31.1938 | + | 54.0292i | 1.18925 | + | 2.05984i | ||||
\(689\) | 3.32088 | + | 5.75194i | 0.126516 | + | 0.219131i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 9.60442 | − | 16.6353i | 0.365369 | − | 0.632838i | −0.623466 | − | 0.781851i | \(-0.714276\pi\) |
0.988835 | + | 0.149012i | \(0.0476093\pi\) | |||||||
\(692\) | 37.0957 | 1.41017 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 56.0011 | 2.12577 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 18.8446 | + | 32.6398i | 0.713791 | + | 1.23632i | ||||
\(698\) | 3.70012 | + | 6.40880i | 0.140052 | + | 0.242577i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 29.3492 | 1.10850 | 0.554251 | − | 0.832349i | \(-0.313005\pi\) | ||||
0.554251 | + | 0.832349i | \(0.313005\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0.386505 | 0.0145773 | ||||||||
\(704\) | 5.46719 | − | 9.46945i | 0.206052 | − | 0.356893i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −23.6700 | − | 40.9977i | −0.890834 | − | 1.54297i | ||||
\(707\) | 3.00000 | + | 5.19615i | 0.112827 | + | 0.195421i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −19.3633 | + | 33.5382i | −0.727204 | + | 1.25955i | 0.230857 | + | 0.972988i | \(0.425847\pi\) |
−0.958060 | + | 0.286566i | \(0.907486\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 17.5051 | 0.656030 | ||||||||
\(713\) | −18.0288 | + | 31.2268i | −0.675184 | + | 1.16945i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −2.30221 | − | 3.98755i | −0.0860377 | − | 0.149022i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −40.0716 | + | 69.4061i | −1.49546 | + | 2.59021i | ||||
\(719\) | 15.0848 | 0.562569 | 0.281284 | − | 0.959624i | \(-0.409240\pi\) | ||||
0.281284 | + | 0.959624i | \(0.409240\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −0.150442 | −0.00560275 | ||||||||
\(722\) | 21.6910 | − | 37.5700i | 0.807257 | − | 1.39821i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 27.3729 | + | 47.4112i | 1.01731 | + | 1.76203i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 6.17277 | − | 10.6916i | 0.228936 | − | 0.396528i | −0.728557 | − | 0.684985i | \(-0.759809\pi\) |
0.957493 | + | 0.288457i | \(0.0931422\pi\) | |||||||
\(728\) | 3.96265 | 0.146866 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −17.1842 | + | 29.7639i | −0.635580 | + | 1.10086i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −11.0000 | − | 19.0526i | −0.406294 | − | 0.703722i | 0.588177 | − | 0.808732i | \(-0.299846\pi\) |
−0.994471 | + | 0.105010i | \(0.966513\pi\) | |||||||
\(734\) | −23.0661 | − | 39.9517i | −0.851387 | − | 1.47465i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −7.19418 | + | 12.4607i | −0.265181 | + | 0.459307i | ||||
\(737\) | −31.3774 | −1.15580 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 29.7266 | 1.09351 | 0.546755 | − | 0.837293i | \(-0.315863\pi\) | ||||
0.546755 | + | 0.837293i | \(0.315863\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 3.24980 | + | 5.62882i | 0.119304 | + | 0.206640i | ||||
\(743\) | −24.1824 | − | 41.8851i | −0.887165 | − | 1.53662i | −0.843212 | − | 0.537582i | \(-0.819338\pi\) |
−0.0439537 | − | 0.999034i | \(-0.513995\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 5.52787 | 0.202390 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −47.6519 | −1.74233 | ||||||||
\(749\) | −0.481327 | + | 0.833682i | −0.0175873 | + | 0.0304621i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 15.9102 | + | 27.5573i | 0.580573 | + | 1.00558i | 0.995411 | + | 0.0956869i | \(0.0305047\pi\) |
−0.414838 | + | 0.909895i | \(0.636162\pi\) | |||||||
\(752\) | 14.6586 | + | 25.3895i | 0.534546 | + | 0.925860i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −2.30221 | + | 3.98755i | −0.0838416 | + | 0.145218i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −4.94531 | −0.179740 | −0.0898701 | − | 0.995953i | \(-0.528645\pi\) | ||||
−0.0898701 | + | 0.995953i | \(0.528645\pi\) | |||||||
\(758\) | −19.4485 | + | 33.6858i | −0.706402 | + | 1.22352i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 17.7125 | + | 30.6789i | 0.642076 | + | 1.11211i | 0.984969 | + | 0.172734i | \(0.0552600\pi\) |
−0.342893 | + | 0.939375i | \(0.611407\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −1.42618 | + | 2.47022i | −0.0516313 | + | 0.0894281i | ||||
\(764\) | 73.1715 | 2.64725 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 19.3774 | 0.700135 | ||||||||
\(767\) | −3.32088 | + | 5.75194i | −0.119910 | + | 0.207691i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −24.7125 | − | 42.8032i | −0.891154 | − | 1.54352i | −0.838494 | − | 0.544911i | \(-0.816563\pi\) |
−0.0526602 | − | 0.998612i | \(-0.516770\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 57.7217 | − | 99.9768i | 2.07745 | − | 3.59825i | ||||
\(773\) | 12.6599 | 0.455345 | 0.227673 | − | 0.973738i | \(-0.426888\pi\) | ||||
0.227673 | + | 0.973738i | \(0.426888\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −35.7549 | + | 61.9292i | −1.28352 | + | 2.22313i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −30.9650 | − | 53.6329i | −1.11015 | − | 1.92283i | ||||
\(779\) | 7.49546 | + | 12.9825i | 0.268553 | + | 0.465147i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 14.9289 | − | 25.8576i | 0.534199 | − | 0.925259i | ||||
\(782\) | −34.4623 | −1.23237 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −40.6044 | −1.45016 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 15.4672 | + | 26.7900i | 0.551346 | + | 0.954959i | 0.998178 | + | 0.0603410i | \(0.0192188\pi\) |
−0.446832 | + | 0.894618i | \(0.647448\pi\) | |||||||
\(788\) | 30.7977 | + | 53.3431i | 1.09712 | + | 1.90027i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 4.01093 | 0.142612 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 9.70739 | 0.344720 | ||||||||
\(794\) | −8.51414 | + | 14.7469i | −0.302155 | + | 0.523349i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 53.2786 | + | 92.2812i | 1.88841 | + | 3.27082i | ||||
\(797\) | 15.2967 | + | 26.4947i | 0.541839 | + | 0.938492i | 0.998799 | + | 0.0490047i | \(0.0156049\pi\) |
−0.456960 | + | 0.889487i | \(0.651062\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −8.07522 | + | 13.9867i | −0.285681 | + | 0.494814i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 46.5105 | 1.64234 | ||||||||
\(803\) | 10.0565 | − | 17.4185i | 0.354888 | − | 0.614684i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −14.5051 | − | 25.1235i | −0.510919 | − | 0.884938i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 34.0475 | − | 58.9720i | 1.19779 | − | 2.07463i | ||||
\(809\) | 2.89703 | 0.101854 | 0.0509271 | − | 0.998702i | \(-0.483782\pi\) | ||||
0.0509271 | + | 0.998702i | \(0.483782\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −14.8861 | −0.522722 | −0.261361 | − | 0.965241i | \(-0.584171\pi\) | ||||
−0.261361 | + | 0.965241i | \(0.584171\pi\) | |||||||
\(812\) | −1.54008 | + | 2.66749i | −0.0540462 | + | 0.0936107i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 1.22153 | + | 2.11575i | 0.0428145 | + | 0.0741568i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −6.83502 | + | 11.8386i | −0.239127 | + | 0.414180i | ||||
\(818\) | −33.7266 | −1.17922 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −4.47586 | + | 7.75242i | −0.156209 | + | 0.270561i | −0.933498 | − | 0.358581i | \(-0.883261\pi\) |
0.777290 | + | 0.629143i | \(0.216594\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 1.49727 | + | 2.59334i | 0.0521915 | + | 0.0903983i | 0.890941 | − | 0.454119i | \(-0.150046\pi\) |
−0.838749 | + | 0.544518i | \(0.816713\pi\) | |||||||
\(824\) | 0.853695 | + | 1.47864i | 0.0297399 | + | 0.0515110i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −3.24980 | + | 5.62882i | −0.113075 | + | 0.195852i | ||||
\(827\) | 31.9663 | 1.11158 | 0.555788 | − | 0.831324i | \(-0.312417\pi\) | ||||
0.555788 | + | 0.831324i | \(0.312417\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 22.7458 | 0.789994 | 0.394997 | − | 0.918682i | \(-0.370746\pi\) | ||||
0.394997 | + | 0.918682i | \(0.370746\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 2.17458 | + | 3.76648i | 0.0753900 | + | 0.130579i | ||||
\(833\) | −11.1842 | − | 19.3716i | −0.387509 | − | 0.671185i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −18.9536 | −0.655523 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 83.2555 | 2.87601 | ||||||||
\(839\) | −11.6322 | + | 20.1475i | −0.401587 | + | 0.695569i | −0.993918 | − | 0.110126i | \(-0.964875\pi\) |
0.592331 | + | 0.805695i | \(0.298208\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 13.5388 | + | 23.4499i | 0.466855 | + | 0.808617i | ||||
\(842\) | 18.4768 | + | 32.0027i | 0.636752 | + | 1.10289i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 11.6176 | − | 20.1223i | 0.399895 | − | 0.692639i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0.0145366 | 0.000499485 | ||||||||
\(848\) | 15.1559 | − | 26.2508i | 0.520456 | − | 0.901456i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 0.603895 | + | 1.04598i | 0.0207012 | + | 0.0358556i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 5.49546 | − | 9.51842i | 0.188161 | − | 0.325905i | −0.756476 | − | 0.654021i | \(-0.773081\pi\) |
0.944637 | + | 0.328117i | \(0.106414\pi\) | |||||||
\(854\) | 9.49960 | 0.325070 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 10.9253 | 0.373419 | ||||||||
\(857\) | 8.07522 | − | 13.9867i | 0.275844 | − | 0.477776i | −0.694503 | − | 0.719489i | \(-0.744376\pi\) |
0.970348 | + | 0.241713i | \(0.0777093\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −14.2594 | − | 24.6980i | −0.486524 | − | 0.842685i | 0.513356 | − | 0.858176i | \(-0.328402\pi\) |
−0.999880 | + | 0.0154909i | \(0.995069\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −41.1751 | + | 71.3174i | −1.40243 | + | 2.42908i | ||||
\(863\) | 12.2890 | 0.418322 | 0.209161 | − | 0.977881i | \(-0.432927\pi\) | ||||
0.209161 | + | 0.977881i | \(0.432927\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −14.8729 | + | 25.7606i | −0.505402 | + | 0.875381i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −9.70325 | − | 16.8065i | −0.329350 | − | 0.570451i | ||||
\(869\) | 13.3774 | + | 23.1704i | 0.453798 | + | 0.786002i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 6.24020 | − | 10.8083i | 0.211441 | − | 0.366227i | ||||
\(872\) | 32.3720 | 1.09625 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −13.7074 | −0.463659 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −19.8501 | − | 34.3814i | −0.670290 | − | 1.16098i | −0.977822 | − | 0.209438i | \(-0.932836\pi\) |
0.307532 | − | 0.951538i | \(-0.400497\pi\) | |||||||
\(878\) | −10.4485 | − | 18.0974i | −0.352620 | − | 0.610756i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −32.1040 | −1.08161 | −0.540806 | − | 0.841147i | \(-0.681881\pi\) | ||||
−0.540806 | + | 0.841147i | \(0.681881\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −13.5051 | −0.454482 | −0.227241 | − | 0.973839i | \(-0.572970\pi\) | ||||
−0.227241 | + | 0.973839i | \(0.572970\pi\) | |||||||
\(884\) | 9.47679 | − | 16.4143i | 0.318739 | − | 0.552072i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 36.6751 | + | 63.5231i | 1.23212 | + | 2.13410i | ||||
\(887\) | −17.5611 | − | 30.4167i | −0.589643 | − | 1.02129i | −0.994279 | − | 0.106814i | \(-0.965935\pi\) |
0.404635 | − | 0.914478i | \(-0.367398\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 4.59936 | − | 7.96632i | 0.154258 | − | 0.267182i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −37.4386 | −1.25354 | ||||||||
\(893\) | −3.21193 | + | 5.56322i | −0.107483 | + | 0.186166i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 3.92024 | + | 6.79006i | 0.130966 | + | 0.226840i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 23.8488 | − | 41.3073i | 0.795843 | − | 1.37844i | ||||
\(899\) | 12.1120 | 0.403959 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 16.6983 | 0.556302 | ||||||||
\(902\) | −47.3780 | + | 82.0610i | −1.57751 | + | 2.73233i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −22.7603 | − | 39.4220i | −0.756997 | − | 1.31116i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 7.55928 | − | 13.0931i | 0.251002 | − | 0.434748i | −0.712800 | − | 0.701367i | \(-0.752573\pi\) |
0.963802 | + | 0.266619i | \(0.0859067\pi\) | |||||||
\(908\) | 14.3492 | 0.476194 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 26.2781 | − | 45.5150i | 0.870631 | − | 1.50798i | 0.00928675 | − | 0.999957i | \(-0.497044\pi\) |
0.861345 | − | 0.508021i | \(-0.169623\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −2.56108 | − | 4.43593i | −0.0847595 | − | 0.146808i | ||||
\(914\) | −29.2083 | − | 50.5903i | −0.966125 | − | 1.67338i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 54.6847 | − | 94.7167i | 1.80683 | − | 3.12953i | ||||
\(917\) | 3.08482 | 0.101870 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −54.5489 | −1.79940 | −0.899702 | − | 0.436505i | \(-0.856216\pi\) | ||||
−0.899702 | + | 0.436505i | \(0.856216\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 5.56342 | + | 9.63612i | 0.183221 | + | 0.317349i | ||||
\(923\) | 5.93799 | + | 10.2849i | 0.195451 | + | 0.338532i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 49.0475 | 1.61180 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 4.83317 | 0.158656 | ||||||||
\(929\) | 10.1896 | − | 17.6490i | 0.334311 | − | 0.579044i | −0.649041 | − | 0.760753i | \(-0.724830\pi\) |
0.983352 | + | 0.181709i | \(0.0581630\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −4.44852 | − | 7.70506i | −0.145794 | − | 0.252523i | ||||
\(932\) | −59.6988 | − | 103.401i | −1.95550 | − | 3.38703i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 30.9157 | − | 53.5476i | 1.01159 | − | 1.75213i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −49.1979 | −1.60723 | −0.803613 | − | 0.595152i | \(-0.797092\pi\) | ||||
−0.803613 | + | 0.595152i | \(0.797092\pi\) | |||||||
\(938\) | 6.10663 | − | 10.5770i | 0.199388 | − | 0.345351i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −11.6186 | − | 20.1239i | −0.378754 | − | 0.656022i | 0.612127 | − | 0.790759i | \(-0.290314\pi\) |
−0.990881 | + | 0.134738i | \(0.956981\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −23.4226 | + | 40.5691i | −0.762744 | + | 1.32111i | ||||
\(944\) | 30.3118 | 0.986565 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −86.4068 | −2.80933 | ||||||||
\(947\) | −18.5821 | + | 32.1851i | −0.603837 | + | 1.04588i | 0.388397 | + | 0.921492i | \(0.373029\pi\) |
−0.992234 | + | 0.124384i | \(0.960305\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 4.00000 | + | 6.92820i | 0.129845 | + | 0.224899i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 4.98133 | − | 8.62791i | 0.161446 | − | 0.279632i | ||||
\(953\) | −23.5761 | −0.763706 | −0.381853 | − | 0.924223i | \(-0.624714\pi\) | ||||
−0.381853 | + | 0.924223i | \(0.624714\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −9.07108 | + | 15.7116i | −0.293380 | + | 0.508149i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 41.1751 | + | 71.3174i | 1.33031 | + | 2.30416i | ||||
\(959\) | −1.45759 | − | 2.52462i | −0.0470680 | − | 0.0815242i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −22.6559 | + | 39.2412i | −0.730836 | + | 1.26584i | ||||
\(962\) | −0.971726 | −0.0313297 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 15.5743 | 0.501614 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 4.19145 | + | 7.25980i | 0.134788 | + | 0.233459i | 0.925516 | − | 0.378708i | \(-0.123631\pi\) |
−0.790729 | + | 0.612167i | \(0.790298\pi\) | |||||||
\(968\) | −0.0824893 | − | 0.142876i | −0.00265131 | − | 0.00459220i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −13.2078 | −0.423858 | −0.211929 | − | 0.977285i | \(-0.567975\pi\) | ||||
−0.211929 | + | 0.977285i | \(0.567975\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 4.11310 | 0.131860 | ||||||||
\(974\) | −7.58936 | + | 13.1452i | −0.243179 | + | 0.421198i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −22.1514 | − | 38.3673i | −0.709048 | − | 1.22811i | ||||
\(977\) | 7.16551 | + | 12.4110i | 0.229245 | + | 0.397064i | 0.957585 | − | 0.288153i | \(-0.0930410\pi\) |
−0.728340 | + | 0.685216i | \(0.759708\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −4.98133 | + | 8.62791i | −0.159204 | + | 0.275749i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −36.3118 | −1.15876 | ||||||||
\(983\) | 16.1541 | − | 27.9797i | 0.515236 | − | 0.892415i | −0.484608 | − | 0.874732i | \(-0.661038\pi\) |
0.999844 | − | 0.0176831i | \(-0.00562899\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 5.78807 | + | 10.0252i | 0.184330 | + | 0.319269i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 3.76940 | − | 6.52879i | 0.119921 | − | 0.207709i | ||||
\(989\) | −42.7175 | −1.35834 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −39.6700 | −1.26016 | −0.630080 | − | 0.776530i | \(-0.716978\pi\) | ||||
−0.630080 | + | 0.776530i | \(0.716978\pi\) | |||||||
\(992\) | −15.2257 | + | 26.3716i | −0.483415 | + | 0.837300i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 5.81088 | + | 10.0647i | 0.184310 | + | 0.319234i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 19.3437 | − | 33.5043i | 0.612621 | − | 1.06109i | −0.378176 | − | 0.925734i | \(-0.623449\pi\) |
0.990797 | − | 0.135357i | \(-0.0432181\pi\) | |||||||
\(998\) | 52.7258 | 1.66901 | ||||||||
\(999\) | 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.451.1 | 6 | ||
3.2 | odd | 2 | 225.2.e.b.151.3 | 6 | |||
5.2 | odd | 4 | 675.2.k.b.424.1 | 12 | |||
5.3 | odd | 4 | 675.2.k.b.424.6 | 12 | |||
5.4 | even | 2 | 135.2.e.b.46.3 | 6 | |||
9.2 | odd | 6 | 2025.2.a.n.1.1 | 3 | |||
9.4 | even | 3 | inner | 675.2.e.b.226.1 | 6 | ||
9.5 | odd | 6 | 225.2.e.b.76.3 | 6 | |||
9.7 | even | 3 | 2025.2.a.o.1.3 | 3 | |||
15.2 | even | 4 | 225.2.k.b.124.6 | 12 | |||
15.8 | even | 4 | 225.2.k.b.124.1 | 12 | |||
15.14 | odd | 2 | 45.2.e.b.16.1 | ✓ | 6 | ||
20.19 | odd | 2 | 2160.2.q.k.721.1 | 6 | |||
45.2 | even | 12 | 2025.2.b.l.649.1 | 6 | |||
45.4 | even | 6 | 135.2.e.b.91.3 | 6 | |||
45.7 | odd | 12 | 2025.2.b.m.649.6 | 6 | |||
45.13 | odd | 12 | 675.2.k.b.199.1 | 12 | |||
45.14 | odd | 6 | 45.2.e.b.31.1 | yes | 6 | ||
45.22 | odd | 12 | 675.2.k.b.199.6 | 12 | |||
45.23 | even | 12 | 225.2.k.b.49.6 | 12 | |||
45.29 | odd | 6 | 405.2.a.j.1.3 | 3 | |||
45.32 | even | 12 | 225.2.k.b.49.1 | 12 | |||
45.34 | even | 6 | 405.2.a.i.1.1 | 3 | |||
45.38 | even | 12 | 2025.2.b.l.649.6 | 6 | |||
45.43 | odd | 12 | 2025.2.b.m.649.1 | 6 | |||
60.59 | even | 2 | 720.2.q.i.241.1 | 6 | |||
180.59 | even | 6 | 720.2.q.i.481.1 | 6 | |||
180.79 | odd | 6 | 6480.2.a.bs.1.3 | 3 | |||
180.119 | even | 6 | 6480.2.a.bv.1.3 | 3 | |||
180.139 | odd | 6 | 2160.2.q.k.1441.1 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
45.2.e.b.16.1 | ✓ | 6 | 15.14 | odd | 2 | ||
45.2.e.b.31.1 | yes | 6 | 45.14 | odd | 6 | ||
135.2.e.b.46.3 | 6 | 5.4 | even | 2 | |||
135.2.e.b.91.3 | 6 | 45.4 | even | 6 | |||
225.2.e.b.76.3 | 6 | 9.5 | odd | 6 | |||
225.2.e.b.151.3 | 6 | 3.2 | odd | 2 | |||
225.2.k.b.49.1 | 12 | 45.32 | even | 12 | |||
225.2.k.b.49.6 | 12 | 45.23 | even | 12 | |||
225.2.k.b.124.1 | 12 | 15.8 | even | 4 | |||
225.2.k.b.124.6 | 12 | 15.2 | even | 4 | |||
405.2.a.i.1.1 | 3 | 45.34 | even | 6 | |||
405.2.a.j.1.3 | 3 | 45.29 | odd | 6 | |||
675.2.e.b.226.1 | 6 | 9.4 | even | 3 | inner | ||
675.2.e.b.451.1 | 6 | 1.1 | even | 1 | trivial | ||
675.2.k.b.199.1 | 12 | 45.13 | odd | 12 | |||
675.2.k.b.199.6 | 12 | 45.22 | odd | 12 | |||
675.2.k.b.424.1 | 12 | 5.2 | odd | 4 | |||
675.2.k.b.424.6 | 12 | 5.3 | odd | 4 | |||
720.2.q.i.241.1 | 6 | 60.59 | even | 2 | |||
720.2.q.i.481.1 | 6 | 180.59 | even | 6 | |||
2025.2.a.n.1.1 | 3 | 9.2 | odd | 6 | |||
2025.2.a.o.1.3 | 3 | 9.7 | even | 3 | |||
2025.2.b.l.649.1 | 6 | 45.2 | even | 12 | |||
2025.2.b.l.649.6 | 6 | 45.38 | even | 12 | |||
2025.2.b.m.649.1 | 6 | 45.43 | odd | 12 | |||
2025.2.b.m.649.6 | 6 | 45.7 | odd | 12 | |||
2160.2.q.k.721.1 | 6 | 20.19 | odd | 2 | |||
2160.2.q.k.1441.1 | 6 | 180.139 | odd | 6 | |||
6480.2.a.bs.1.3 | 3 | 180.79 | odd | 6 | |||
6480.2.a.bv.1.3 | 3 | 180.119 | even | 6 |