Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [504,2,Mod(253,504)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(504, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("504.253");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 504 = 2^{3} \cdot 3^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 504.c (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(4.02446026187\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | 8.0.386672896.3 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - x^{6} - 2x^{5} + 2x^{4} - 4x^{3} - 4x^{2} + 16 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{5} \) |
Twist minimal: | no (minimal twist has level 168) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 253.5 | ||
Root | \(0.621372 + 1.27039i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 504.253 |
Dual form | 504.2.c.f.253.6 |
$q$-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 \(\left(\mathbb{Z}/504\mathbb{Z}\right)^\times\).
\(n\) | \(73\) | \(127\) | \(253\) | \(281\) |
\(\chi(n)\) | \(1\) | \(1\) | \(-1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.621372 | − | 1.27039i | 0.439377 | − | 0.898303i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −1.22779 | − | 1.57877i | −0.613897 | − | 0.789387i | ||||
\(5\) | − | 3.69833i | − | 1.65394i | −0.562243 | − | 0.826972i | \(-0.690062\pi\) | ||
0.562243 | − | 0.826972i | \(-0.309938\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | −2.76858 | + | 0.578773i | −0.978840 | + | 0.204627i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −4.69833 | − | 2.29804i | −1.48574 | − | 0.726704i | ||||
\(11\) | − | 3.21284i | − | 0.968708i | −0.874872 | − | 0.484354i | \(-0.839055\pi\) | ||
0.874872 | − | 0.484354i | \(-0.160945\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 5.08157i | 1.40937i | 0.709518 | + | 0.704687i | \(0.248912\pi\) | ||||
−0.709518 | + | 0.704687i | \(0.751088\pi\) | |||||||
\(14\) | 0.621372 | − | 1.27039i | 0.166069 | − | 0.339527i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −0.985049 | + | 3.87681i | −0.246262 | + | 0.969203i | ||||
\(17\) | −0.616762 | −0.149587 | −0.0747933 | − | 0.997199i | \(-0.523830\pi\) | ||||
−0.0747933 | + | 0.997199i | \(0.523830\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − | 4.48549i | − | 1.02904i | −0.857478 | − | 0.514521i | \(-0.827970\pi\) | ||
0.857478 | − | 0.514521i | \(-0.172030\pi\) | |||||||
\(20\) | −5.83882 | + | 4.54078i | −1.30560 | + | 1.01535i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −4.08157 | − | 1.99637i | −0.870193 | − | 0.425628i | ||||
\(23\) | −1.38324 | −0.288425 | −0.144213 | − | 0.989547i | \(-0.546065\pi\) | ||||
−0.144213 | + | 0.989547i | \(0.546065\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −8.67765 | −1.73553 | ||||||||
\(26\) | 6.45559 | + | 3.15755i | 1.26604 | + | 0.619246i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −1.22779 | − | 1.57877i | −0.232031 | − | 0.298360i | ||||
\(29\) | 5.67765i | 1.05431i | 0.849768 | + | 0.527156i | \(0.176742\pi\) | ||||
−0.849768 | + | 0.527156i | \(0.823258\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 6.91117 | 1.24128 | 0.620642 | − | 0.784094i | \(-0.286872\pi\) | ||||
0.620642 | + | 0.784094i | \(0.286872\pi\) | |||||||
\(32\) | 4.31299 | + | 3.66034i | 0.762436 | + | 0.647063i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −0.383238 | + | 0.783529i | −0.0657249 | + | 0.134374i | ||||
\(35\) | − | 3.69833i | − | 0.625132i | ||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 6.91117i | − | 1.13619i | −0.822963 | − | 0.568095i | \(-0.807681\pi\) | ||
0.822963 | − | 0.568095i | \(-0.192319\pi\) | |||||||
\(38\) | −5.69833 | − | 2.78716i | −0.924391 | − | 0.452137i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 2.14049 | + | 10.2391i | 0.338442 | + | 1.61895i | ||||
\(41\) | 0.616762 | 0.0963220 | 0.0481610 | − | 0.998840i | \(-0.484664\pi\) | ||||
0.0481610 | + | 0.998840i | \(0.484664\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 7.99274i | − | 1.21888i | −0.792832 | − | 0.609441i | \(-0.791394\pi\) | ||
0.792832 | − | 0.609441i | \(-0.208606\pi\) | |||||||
\(44\) | −5.07235 | + | 3.94470i | −0.764685 | + | 0.594687i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −0.859506 | + | 1.75726i | −0.126727 | + | 0.259093i | ||||
\(47\) | −4.97098 | −0.725092 | −0.362546 | − | 0.931966i | \(-0.618092\pi\) | ||||
−0.362546 | + | 0.931966i | \(0.618092\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | −5.39205 | + | 11.0240i | −0.762551 | + | 1.55903i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 8.02264 | − | 6.23912i | 1.11254 | − | 0.865210i | ||||
\(53\) | − | 4.48549i | − | 0.616129i | −0.951365 | − | 0.308065i | \(-0.900319\pi\) | ||
0.951365 | − | 0.308065i | \(-0.0996813\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −11.8822 | −1.60219 | ||||||||
\(56\) | −2.76858 | + | 0.578773i | −0.369967 | + | 0.0773418i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 7.21284 | + | 3.52793i | 0.947092 | + | 0.463240i | ||||
\(59\) | − | 4.00000i | − | 0.520756i | −0.965507 | − | 0.260378i | \(-0.916153\pi\) | ||
0.965507 | − | 0.260378i | \(-0.0838471\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 12.4782i | 1.59767i | 0.601548 | + | 0.798837i | \(0.294551\pi\) | ||||
−0.601548 | + | 0.798837i | \(0.705449\pi\) | |||||||
\(62\) | 4.29441 | − | 8.77990i | 0.545391 | − | 1.11505i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 7.33004 | − | 3.20476i | 0.916255 | − | 0.400595i | ||||
\(65\) | 18.7933 | 2.33102 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − | 9.56706i | − | 1.16880i | −0.811465 | − | 0.584401i | \(-0.801329\pi\) | ||
0.811465 | − | 0.584401i | \(-0.198671\pi\) | |||||||
\(68\) | 0.757255 | + | 0.973726i | 0.0918307 | + | 0.118082i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −4.69833 | − | 2.29804i | −0.561558 | − | 0.274668i | ||||
\(71\) | 15.2056 | 1.80457 | 0.902285 | − | 0.431139i | \(-0.141888\pi\) | ||||
0.902285 | + | 0.431139i | \(0.141888\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 15.5598 | 1.82114 | 0.910568 | − | 0.413358i | \(-0.135644\pi\) | ||||
0.910568 | + | 0.413358i | \(0.135644\pi\) | |||||||
\(74\) | −8.77990 | − | 4.29441i | −1.02064 | − | 0.499215i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −7.08157 | + | 5.50725i | −0.812312 | + | 0.631725i | ||||
\(77\) | − | 3.21284i | − | 0.366137i | ||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −5.23352 | −0.588817 | −0.294409 | − | 0.955680i | \(-0.595123\pi\) | ||||
−0.294409 | + | 0.955680i | \(0.595123\pi\) | |||||||
\(80\) | 14.3377 | + | 3.64304i | 1.60301 | + | 0.407304i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0.383238 | − | 0.783529i | 0.0423216 | − | 0.0865263i | ||||
\(83\) | 10.4257i | 1.14437i | 0.820125 | + | 0.572184i | \(0.193904\pi\) | ||||
−0.820125 | + | 0.572184i | \(0.806096\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 2.28099i | 0.247408i | ||||||||
\(86\) | −10.1539 | − | 4.96647i | −1.09492 | − | 0.535548i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 1.85951 | + | 8.89500i | 0.198224 | + | 0.948210i | ||||
\(89\) | 14.1766 | 1.50271 | 0.751356 | − | 0.659897i | \(-0.229400\pi\) | ||||
0.751356 | + | 0.659897i | \(0.229400\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 5.08157i | 0.532693i | ||||||||
\(92\) | 1.69833 | + | 2.18382i | 0.177063 | + | 0.227679i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −3.08883 | + | 6.31509i | −0.318588 | + | 0.651352i | ||||
\(95\) | −16.5888 | −1.70198 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 9.73746 | 0.988689 | 0.494344 | − | 0.869266i | \(-0.335408\pi\) | ||||
0.494344 | + | 0.869266i | \(0.335408\pi\) | |||||||
\(98\) | 0.621372 | − | 1.27039i | 0.0627681 | − | 0.128329i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 10.6544 | + | 13.7000i | 1.06544 | + | 1.37000i | ||||
\(101\) | 5.27265i | 0.524648i | 0.964980 | + | 0.262324i | \(0.0844889\pi\) | ||||
−0.964980 | + | 0.262324i | \(0.915511\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1.94019 | 0.191173 | 0.0955865 | − | 0.995421i | \(-0.469527\pi\) | ||||
0.0955865 | + | 0.995421i | \(0.469527\pi\) | |||||||
\(104\) | −2.94108 | − | 14.0687i | −0.288396 | − | 1.37955i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −5.69833 | − | 2.78716i | −0.553471 | − | 0.270713i | ||||
\(107\) | − | 4.78716i | − | 0.462792i | −0.972860 | − | 0.231396i | \(-0.925671\pi\) | ||
0.972860 | − | 0.231396i | \(-0.0743293\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 0.970978i | 0.0930028i | 0.998918 | + | 0.0465014i | \(0.0148072\pi\) | ||||
−0.998918 | + | 0.0465014i | \(0.985193\pi\) | |||||||
\(110\) | −7.38324 | + | 15.0950i | −0.703964 | + | 1.43925i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −0.985049 | + | 3.87681i | −0.0930783 | + | 0.366324i | ||||
\(113\) | −15.5598 | −1.46374 | −0.731871 | − | 0.681443i | \(-0.761353\pi\) | ||||
−0.731871 | + | 0.681443i | \(0.761353\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 5.11567i | 0.477039i | ||||||||
\(116\) | 8.96372 | − | 6.97098i | 0.832260 | − | 0.647239i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −5.08157 | − | 2.48549i | −0.467796 | − | 0.228808i | ||||
\(119\) | −0.616762 | −0.0565384 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 0.677649 | 0.0616045 | ||||||||
\(122\) | 15.8522 | + | 7.75363i | 1.43520 | + | 0.701980i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −8.48549 | − | 10.9112i | −0.762019 | − | 0.979852i | ||||
\(125\) | 13.6012i | 1.21652i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −3.73746 | −0.331646 | −0.165823 | − | 0.986156i | \(-0.553028\pi\) | ||||
−0.165823 | + | 0.986156i | \(0.553028\pi\) | |||||||
\(128\) | 0.483388 | − | 11.3034i | 0.0427259 | − | 0.999087i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 11.6776 | − | 23.8749i | 1.02420 | − | 2.09397i | ||||
\(131\) | − | 3.39666i | − | 0.296768i | −0.988930 | − | 0.148384i | \(-0.952593\pi\) | ||
0.988930 | − | 0.148384i | \(-0.0474071\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | − | 4.48549i | − | 0.388941i | ||||||
\(134\) | −12.1539 | − | 5.94470i | −1.04994 | − | 0.513544i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 1.70755 | − | 0.356965i | 0.146421 | − | 0.0306095i | ||||
\(137\) | −13.0559 | −1.11544 | −0.557719 | − | 0.830030i | \(-0.688323\pi\) | ||||
−0.557719 | + | 0.830030i | \(0.688323\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 2.80784i | 0.238158i | 0.992885 | + | 0.119079i | \(0.0379942\pi\) | ||||
−0.992885 | + | 0.119079i | \(0.962006\pi\) | |||||||
\(140\) | −5.83882 | + | 4.54078i | −0.493471 | + | 0.383766i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 9.44833 | − | 19.3171i | 0.792886 | − | 1.62105i | ||||
\(143\) | 16.3263 | 1.36527 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 20.9978 | 1.74377 | ||||||||
\(146\) | 9.66843 | − | 19.7670i | 0.800165 | − | 1.63593i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −10.9112 | + | 8.48549i | −0.896893 | + | 0.697503i | ||||
\(149\) | − | 12.4855i | − | 1.02285i | −0.859328 | − | 0.511426i | \(-0.829118\pi\) | ||
0.859328 | − | 0.511426i | \(-0.170882\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 8.97098 | 0.730048 | 0.365024 | − | 0.930998i | \(-0.381061\pi\) | ||||
0.365024 | + | 0.930998i | \(0.381061\pi\) | |||||||
\(152\) | 2.59608 | + | 12.4184i | 0.210570 | + | 1.00727i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −4.08157 | − | 1.99637i | −0.328902 | − | 0.160872i | ||||
\(155\) | − | 25.5598i | − | 2.05301i | ||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 15.1665i | 1.21042i | 0.796068 | + | 0.605208i | \(0.206910\pi\) | ||||
−0.796068 | + | 0.605208i | \(0.793090\pi\) | |||||||
\(158\) | −3.25197 | + | 6.64863i | −0.258713 | + | 0.528936i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 13.5372 | − | 15.9509i | 1.07021 | − | 1.26103i | ||||
\(161\) | −1.38324 | −0.109014 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 13.2263i | − | 1.03596i | −0.855392 | − | 0.517980i | \(-0.826684\pi\) | ||
0.855392 | − | 0.517980i | \(-0.173316\pi\) | |||||||
\(164\) | −0.757255 | − | 0.973726i | −0.0591317 | − | 0.0760353i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 13.2447 | + | 6.47823i | 1.02799 | + | 0.502808i | ||||
\(167\) | −3.05587 | −0.236470 | −0.118235 | − | 0.992986i | \(-0.537724\pi\) | ||||
−0.118235 | + | 0.992986i | \(0.537724\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −12.8223 | −0.986334 | ||||||||
\(170\) | 2.89775 | + | 1.41734i | 0.222247 | + | 0.108705i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −12.6187 | + | 9.81343i | −0.962169 | + | 0.748267i | ||||
\(173\) | 13.8615i | 1.05387i | 0.849906 | + | 0.526934i | \(0.176658\pi\) | ||||
−0.849906 | + | 0.526934i | \(0.823342\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −8.67765 | −0.655969 | ||||||||
\(176\) | 12.4556 | + | 3.16480i | 0.938875 | + | 0.238556i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 8.80892 | − | 18.0098i | 0.660257 | − | 1.34989i | ||||
\(179\) | 18.3883i | 1.37441i | 0.726465 | + | 0.687204i | \(0.241162\pi\) | ||||
−0.726465 | + | 0.687204i | \(0.758838\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 6.05255i | − | 0.449882i | −0.974372 | − | 0.224941i | \(-0.927781\pi\) | ||
0.974372 | − | 0.224941i | \(-0.0722190\pi\) | |||||||
\(182\) | 6.45559 | + | 3.15755i | 0.478520 | + | 0.234053i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 3.82960 | − | 0.800581i | 0.282322 | − | 0.0590196i | ||||
\(185\) | −25.5598 | −1.87919 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 1.98156i | 0.144906i | ||||||||
\(188\) | 6.10333 | + | 7.84805i | 0.445131 | + | 0.572378i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −10.3078 | + | 21.0743i | −0.747809 | + | 1.52889i | ||||
\(191\) | 15.2056 | 1.10024 | 0.550119 | − | 0.835086i | \(-0.314582\pi\) | ||||
0.550119 | + | 0.835086i | \(0.314582\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −19.4419 | −1.39946 | −0.699731 | − | 0.714406i | \(-0.746697\pi\) | ||||
−0.699731 | + | 0.714406i | \(0.746697\pi\) | |||||||
\(194\) | 6.05058 | − | 12.3704i | 0.434407 | − | 0.888142i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −1.22779 | − | 1.57877i | −0.0876995 | − | 0.112770i | ||||
\(197\) | 15.2520i | 1.08666i | 0.839520 | + | 0.543329i | \(0.182836\pi\) | ||||
−0.839520 | + | 0.543329i | \(0.817164\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −3.02902 | −0.214722 | −0.107361 | − | 0.994220i | \(-0.534240\pi\) | ||||
−0.107361 | + | 0.994220i | \(0.534240\pi\) | |||||||
\(200\) | 24.0247 | − | 5.02239i | 1.69881 | − | 0.355137i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 6.69833 | + | 3.27628i | 0.471293 | + | 0.230518i | ||||
\(203\) | 5.67765i | 0.398493i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | − | 2.28099i | − | 0.159311i | ||||||
\(206\) | 1.20558 | − | 2.46481i | 0.0839969 | − | 0.171731i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −19.7003 | − | 5.00559i | −1.36597 | − | 0.347075i | ||||
\(209\) | −14.4112 | −0.996841 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 0.963719i | 0.0663452i | 0.999450 | + | 0.0331726i | \(0.0105611\pi\) | ||||
−0.999450 | + | 0.0331726i | \(0.989439\pi\) | |||||||
\(212\) | −7.08157 | + | 5.50725i | −0.486364 | + | 0.378240i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −6.08157 | − | 2.97461i | −0.415728 | − | 0.203340i | ||||
\(215\) | −29.5598 | −2.01596 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 6.91117 | 0.469161 | ||||||||
\(218\) | 1.23352 | + | 0.603339i | 0.0835447 | + | 0.0408633i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 14.5888 | + | 18.7592i | 0.983578 | + | 1.26475i | ||||
\(221\) | − | 3.13412i | − | 0.210823i | ||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −22.1486 | −1.48318 | −0.741591 | − | 0.670853i | \(-0.765928\pi\) | ||||
−0.741591 | + | 0.670853i | \(0.765928\pi\) | |||||||
\(224\) | 4.31299 | + | 3.66034i | 0.288174 | + | 0.244567i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −9.66843 | + | 19.7670i | −0.643134 | + | 1.31488i | ||||
\(227\) | − | 0.929615i | − | 0.0617007i | −0.999524 | − | 0.0308504i | \(-0.990178\pi\) | ||
0.999524 | − | 0.0308504i | \(-0.00982153\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 1.42236i | 0.0939924i | 0.998895 | + | 0.0469962i | \(0.0149649\pi\) | ||||
−0.998895 | + | 0.0469962i | \(0.985035\pi\) | |||||||
\(230\) | 6.49891 | + | 3.17874i | 0.428526 | + | 0.209600i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −3.28607 | − | 15.7190i | −0.215741 | − | 1.03200i | ||||
\(233\) | −10.9710 | −0.718733 | −0.359366 | − | 0.933197i | \(-0.617007\pi\) | ||||
−0.359366 | + | 0.933197i | \(0.617007\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 18.3843i | 1.19926i | ||||||||
\(236\) | −6.31509 | + | 4.91117i | −0.411077 | + | 0.319690i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −0.383238 | + | 0.783529i | −0.0248417 | + | 0.0507886i | ||||
\(239\) | 4.82126 | 0.311862 | 0.155931 | − | 0.987768i | \(-0.450162\pi\) | ||||
0.155931 | + | 0.987768i | \(0.450162\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −0.204501 | −0.0131731 | −0.00658654 | − | 0.999978i | \(-0.502097\pi\) | ||||
−0.00658654 | + | 0.999978i | \(0.502097\pi\) | |||||||
\(242\) | 0.421072 | − | 0.860880i | 0.0270676 | − | 0.0553395i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 19.7003 | − | 15.3207i | 1.26118 | − | 0.980806i | ||||
\(245\) | − | 3.69833i | − | 0.236278i | ||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 22.7933 | 1.45030 | ||||||||
\(248\) | −19.1341 | + | 4.00000i | −1.21502 | + | 0.254000i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 17.2788 | + | 8.45138i | 1.09281 | + | 0.534513i | ||||
\(251\) | − | 3.10727i | − | 0.196129i | −0.995180 | − | 0.0980646i | \(-0.968735\pi\) | ||
0.995180 | − | 0.0980646i | \(-0.0312652\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 4.44413i | 0.279400i | ||||||||
\(254\) | −2.32235 | + | 4.74803i | −0.145717 | + | 0.297918i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −14.0594 | − | 7.63770i | −0.878710 | − | 0.477356i | ||||
\(257\) | 14.1497 | 0.882635 | 0.441318 | − | 0.897351i | \(-0.354511\pi\) | ||||
0.441318 | + | 0.897351i | \(0.354511\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − | 6.91117i | − | 0.429439i | ||||||
\(260\) | −23.0743 | − | 29.6704i | −1.43101 | − | 1.84008i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −4.31509 | − | 2.11059i | −0.266587 | − | 0.130393i | ||||
\(263\) | −2.94304 | −0.181475 | −0.0907377 | − | 0.995875i | \(-0.528923\pi\) | ||||
−0.0907377 | + | 0.995875i | \(0.528923\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −16.5888 | −1.01904 | ||||||||
\(266\) | −5.69833 | − | 2.78716i | −0.349387 | − | 0.170892i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −15.1042 | + | 11.7464i | −0.922637 | + | 0.717524i | ||||
\(269\) | − | 0.642463i | − | 0.0391717i | −0.999808 | − | 0.0195858i | \(-0.993765\pi\) | ||
0.999808 | − | 0.0195858i | \(-0.00623476\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −0.526852 | −0.0320040 | −0.0160020 | − | 0.999872i | \(-0.505094\pi\) | ||||
−0.0160020 | + | 0.999872i | \(0.505094\pi\) | |||||||
\(272\) | 0.607540 | − | 2.39107i | 0.0368375 | − | 0.144980i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −8.11255 | + | 16.5861i | −0.490097 | + | 1.00200i | ||||
\(275\) | 27.8799i | 1.68122i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 21.7190i | 1.30497i | 0.757802 | + | 0.652484i | \(0.226273\pi\) | ||||
−0.757802 | + | 0.652484i | \(0.773727\pi\) | |||||||
\(278\) | 3.56706 | + | 1.74471i | 0.213938 | + | 0.104641i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 2.14049 | + | 10.2391i | 0.127919 | + | 0.611904i | ||||
\(281\) | 4.79332 | 0.285946 | 0.142973 | − | 0.989727i | \(-0.454334\pi\) | ||||
0.142973 | + | 0.989727i | \(0.454334\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 22.6486i | 1.34632i | 0.739496 | + | 0.673161i | \(0.235064\pi\) | ||||
−0.739496 | + | 0.673161i | \(0.764936\pi\) | |||||||
\(284\) | −18.6693 | − | 24.0062i | −1.10782 | − | 1.42450i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 10.1447 | − | 20.7408i | 0.599868 | − | 1.22643i | ||||
\(287\) | 0.616762 | 0.0364063 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −16.6196 | −0.977624 | ||||||||
\(290\) | 13.0475 | − | 26.6755i | 0.766174 | − | 1.56644i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −19.1042 | − | 24.5654i | −1.11799 | − | 1.43758i | ||||
\(293\) | 24.3285i | 1.42129i | 0.703552 | + | 0.710644i | \(0.251596\pi\) | ||||
−0.703552 | + | 0.710644i | \(0.748404\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −14.7933 | −0.861301 | ||||||||
\(296\) | 4.00000 | + | 19.1341i | 0.232495 | + | 1.11215i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −15.8615 | − | 7.75814i | −0.918830 | − | 0.449417i | ||||
\(299\) | − | 7.02902i | − | 0.406499i | ||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | − | 7.99274i | − | 0.460694i | ||||||
\(302\) | 5.57432 | − | 11.3967i | 0.320766 | − | 0.655804i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 17.3894 | + | 4.41842i | 0.997351 | + | 0.253414i | ||||
\(305\) | 46.1486 | 2.64246 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 3.51451i | − | 0.200584i | −0.994958 | − | 0.100292i | \(-0.968022\pi\) | ||
0.994958 | − | 0.100292i | \(-0.0319777\pi\) | |||||||
\(308\) | −5.07235 | + | 3.94470i | −0.289024 | + | 0.224770i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −32.4710 | − | 15.8822i | −1.84423 | − | 0.902046i | ||||
\(311\) | 4.97098 | 0.281878 | 0.140939 | − | 0.990018i | \(-0.454988\pi\) | ||||
0.140939 | + | 0.990018i | \(0.454988\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −25.6447 | −1.44952 | −0.724762 | − | 0.689000i | \(-0.758050\pi\) | ||||
−0.724762 | + | 0.689000i | \(0.758050\pi\) | |||||||
\(314\) | 19.2674 | + | 9.42402i | 1.08732 | + | 0.531828i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 6.42568 | + | 8.26254i | 0.361473 | + | 0.464804i | ||||
\(317\) | 3.51451i | 0.197395i | 0.995118 | + | 0.0986973i | \(0.0314676\pi\) | ||||
−0.995118 | + | 0.0986973i | \(0.968532\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 18.2414 | 1.02132 | ||||||||
\(320\) | −11.8522 | − | 27.1089i | −0.662561 | − | 1.51543i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −0.859506 | + | 1.75726i | −0.0478984 | + | 0.0979280i | ||||
\(323\) | 2.76648i | 0.153931i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − | 44.0961i | − | 2.44601i | ||||||
\(326\) | −16.8025 | − | 8.21843i | −0.930607 | − | 0.455177i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −1.70755 | + | 0.356965i | −0.0942838 | + | 0.0197101i | ||||
\(329\) | −4.97098 | −0.274059 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 25.1849i | 1.38429i | 0.721760 | + | 0.692144i | \(0.243334\pi\) | ||||
−0.721760 | + | 0.692144i | \(0.756666\pi\) | |||||||
\(332\) | 16.4598 | − | 12.8006i | 0.903348 | − | 0.702523i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −1.89883 | + | 3.88215i | −0.103899 | + | 0.212422i | ||||
\(335\) | −35.3821 | −1.93313 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 21.7643 | 1.18558 | 0.592788 | − | 0.805358i | \(-0.298027\pi\) | ||||
0.592788 | + | 0.805358i | \(0.298027\pi\) | |||||||
\(338\) | −7.96745 | + | 16.2894i | −0.433372 | + | 0.886027i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 3.60116 | − | 2.80058i | 0.195300 | − | 0.151883i | ||||
\(341\) | − | 22.2045i | − | 1.20244i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | 4.62598 | + | 22.1285i | 0.249416 | + | 1.19309i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 17.6095 | + | 8.61313i | 0.946693 | + | 0.463045i | ||||
\(347\) | 31.9068i | 1.71284i | 0.516276 | + | 0.856422i | \(0.327318\pi\) | ||||
−0.516276 | + | 0.856422i | \(0.672682\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 1.04021i | − | 0.0556810i | −0.999612 | − | 0.0278405i | \(-0.991137\pi\) | ||
0.999612 | − | 0.0278405i | \(-0.00886305\pi\) | |||||||
\(350\) | −5.39205 | + | 11.0240i | −0.288217 | + | 0.589259i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 11.7601 | − | 13.8570i | 0.626815 | − | 0.738578i | ||||
\(353\) | 13.8503 | 0.737176 | 0.368588 | − | 0.929593i | \(-0.379841\pi\) | ||||
0.368588 | + | 0.929593i | \(0.379841\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | − | 56.2353i | − | 2.98466i | ||||||
\(356\) | −17.4059 | − | 22.3816i | −0.922510 | − | 1.18622i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 23.3604 | + | 11.4260i | 1.23463 | + | 0.603882i | ||||
\(359\) | −0.412260 | −0.0217583 | −0.0108791 | − | 0.999941i | \(-0.503463\pi\) | ||||
−0.0108791 | + | 0.999941i | \(0.503463\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −1.11961 | −0.0589269 | ||||||||
\(362\) | −7.68911 | − | 3.76088i | −0.404131 | − | 0.197668i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 8.02264 | − | 6.23912i | 0.420501 | − | 0.327018i | ||||
\(365\) | − | 57.5453i | − | 3.01206i | ||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 4.97098 | 0.259483 | 0.129741 | − | 0.991548i | \(-0.458585\pi\) | ||||
0.129741 | + | 0.991548i | \(0.458585\pi\) | |||||||
\(368\) | 1.36256 | − | 5.36256i | 0.0710282 | − | 0.279543i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −15.8822 | + | 32.4710i | −0.825674 | + | 1.68809i | ||||
\(371\) | − | 4.48549i | − | 0.232875i | ||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − | 2.16314i | − | 0.112003i | −0.998431 | − | 0.0560015i | \(-0.982165\pi\) | ||
0.998431 | − | 0.0560015i | \(-0.0178352\pi\) | |||||||
\(374\) | 2.51735 | + | 1.23128i | 0.130169 | + | 0.0636682i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 13.7625 | − | 2.87707i | 0.709749 | − | 0.148373i | ||||
\(377\) | −28.8514 | −1.48592 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 23.7570i | − | 1.22032i | −0.792279 | − | 0.610159i | \(-0.791106\pi\) | ||
0.792279 | − | 0.610159i | \(-0.208894\pi\) | |||||||
\(380\) | 20.3676 | + | 26.1900i | 1.04484 | + | 1.34352i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 9.44833 | − | 19.3171i | 0.483418 | − | 0.988347i | ||||
\(383\) | 37.5598 | 1.91922 | 0.959608 | − | 0.281340i | \(-0.0907790\pi\) | ||||
0.959608 | + | 0.281340i | \(0.0907790\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −11.8822 | −0.605570 | ||||||||
\(386\) | −12.0807 | + | 24.6989i | −0.614891 | + | 1.25714i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −11.9556 | − | 15.3732i | −0.606953 | − | 0.780458i | ||||
\(389\) | − | 0.826283i | − | 0.0418942i | −0.999781 | − | 0.0209471i | \(-0.993332\pi\) | ||
0.999781 | − | 0.0209471i | \(-0.00666816\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0.853128 | 0.0431446 | ||||||||
\(392\) | −2.76858 | + | 0.578773i | −0.139834 | + | 0.0292325i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 19.3760 | + | 9.47715i | 0.976148 | + | 0.477452i | ||||
\(395\) | 19.3553i | 0.973871i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 8.81902i | 0.442614i | 0.975204 | + | 0.221307i | \(0.0710323\pi\) | ||||
−0.975204 | + | 0.221307i | \(0.928968\pi\) | |||||||
\(398\) | −1.88215 | + | 3.84805i | −0.0943437 | + | 0.192885i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 8.54791 | − | 33.6416i | 0.427395 | − | 1.68208i | ||||
\(401\) | 8.64687 | 0.431804 | 0.215902 | − | 0.976415i | \(-0.430731\pi\) | ||||
0.215902 | + | 0.976415i | \(0.430731\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 35.1196i | 1.74943i | ||||||||
\(404\) | 8.32431 | − | 6.47372i | 0.414150 | − | 0.322080i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 7.21284 | + | 3.52793i | 0.357967 | + | 0.175088i | ||||
\(407\) | −22.2045 | −1.10064 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −18.7084 | −0.925072 | −0.462536 | − | 0.886600i | \(-0.653060\pi\) | ||||
−0.462536 | + | 0.886600i | \(0.653060\pi\) | |||||||
\(410\) | −2.89775 | − | 1.41734i | −0.143110 | − | 0.0699976i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −2.38216 | − | 3.06313i | −0.117360 | − | 0.150909i | ||||
\(413\) | − | 4.00000i | − | 0.196827i | ||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 38.5576 | 1.89272 | ||||||||
\(416\) | −18.6003 | + | 21.9168i | −0.911954 | + | 1.07456i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −8.95470 | + | 18.3078i | −0.437989 | + | 0.895465i | ||||
\(419\) | 12.9710i | 0.633674i | 0.948480 | + | 0.316837i | \(0.102621\pi\) | ||||
−0.948480 | + | 0.316837i | \(0.897379\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 3.54136i | 0.172595i | 0.996269 | + | 0.0862976i | \(0.0275036\pi\) | ||||
−0.996269 | + | 0.0862976i | \(0.972496\pi\) | |||||||
\(422\) | 1.22430 | + | 0.598828i | 0.0595981 | + | 0.0291505i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 2.59608 | + | 12.4184i | 0.126077 | + | 0.603092i | ||||
\(425\) | 5.35204 | 0.259612 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 12.4782i | 0.603864i | ||||||||
\(428\) | −7.55784 | + | 5.87764i | −0.365322 | + | 0.284106i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −18.3676 | + | 37.5525i | −0.885766 | + | 1.81094i | ||||
\(431\) | −14.6168 | −0.704065 | −0.352032 | − | 0.935988i | \(-0.614509\pi\) | ||||
−0.352032 | + | 0.935988i | \(0.614509\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −2.97098 | −0.142776 | −0.0713880 | − | 0.997449i | \(-0.522743\pi\) | ||||
−0.0713880 | + | 0.997449i | \(0.522743\pi\) | |||||||
\(434\) | 4.29441 | − | 8.77990i | 0.206138 | − | 0.421449i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 1.53295 | − | 1.19216i | 0.0734152 | − | 0.0570941i | ||||
\(437\) | 6.20450i | 0.296802i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(440\) | 32.8967 | − | 6.87707i | 1.56829 | − | 0.327851i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −3.98156 | − | 1.94745i | −0.189383 | − | 0.0926309i | ||||
\(443\) | − | 27.1983i | − | 1.29223i | −0.763239 | − | 0.646116i | \(-0.776392\pi\) | ||
0.763239 | − | 0.646116i | \(-0.223608\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | − | 52.4296i | − | 2.48540i | ||||||
\(446\) | −13.7625 | + | 28.1374i | −0.651675 | + | 1.33235i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 7.33004 | − | 3.20476i | 0.346312 | − | 0.151410i | ||||
\(449\) | 31.5598 | 1.48940 | 0.744700 | − | 0.667400i | \(-0.232593\pi\) | ||||
0.744700 | + | 0.667400i | \(0.232593\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 1.98156i | − | 0.0933079i | ||||||
\(452\) | 19.1042 | + | 24.5654i | 0.898587 | + | 1.15546i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −1.18098 | − | 0.577637i | −0.0554259 | − | 0.0271099i | ||||
\(455\) | 18.7933 | 0.881045 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 28.1117 | 1.31501 | 0.657506 | − | 0.753450i | \(-0.271612\pi\) | ||||
0.657506 | + | 0.753450i | \(0.271612\pi\) | |||||||
\(458\) | 1.80696 | + | 0.883817i | 0.0844336 | + | 0.0412981i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 8.07649 | − | 6.28099i | 0.376568 | − | 0.292853i | ||||
\(461\) | − | 5.19440i | − | 0.241927i | −0.992657 | − | 0.120964i | \(-0.961402\pi\) | ||
0.992657 | − | 0.120964i | \(-0.0385984\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −10.7665 | −0.500361 | −0.250180 | − | 0.968199i | \(-0.580490\pi\) | ||||
−0.250180 | + | 0.968199i | \(0.580490\pi\) | |||||||
\(464\) | −22.0112 | − | 5.59276i | −1.02184 | − | 0.259637i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −6.81706 | + | 13.9374i | −0.315794 | + | 0.645640i | ||||
\(467\) | − | 30.7520i | − | 1.42303i | −0.702670 | − | 0.711515i | \(-0.748009\pi\) | ||
0.702670 | − | 0.711515i | \(-0.251991\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − | 9.56706i | − | 0.441766i | ||||||
\(470\) | 23.3553 | + | 11.4235i | 1.07730 | + | 0.526927i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 2.31509 | + | 11.0743i | 0.106561 | + | 0.509736i | ||||
\(473\) | −25.6794 | −1.18074 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 38.9235i | 1.78593i | ||||||||
\(476\) | 0.757255 | + | 0.973726i | 0.0347087 | + | 0.0446307i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 2.99580 | − | 6.12489i | 0.137025 | − | 0.280146i | ||||
\(479\) | −16.3263 | −0.745967 | −0.372983 | − | 0.927838i | \(-0.621665\pi\) | ||||
−0.372983 | + | 0.927838i | \(0.621665\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 35.1196 | 1.60132 | ||||||||
\(482\) | −0.127071 | + | 0.259797i | −0.00578794 | + | 0.0118334i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −0.832013 | − | 1.06985i | −0.0378188 | − | 0.0486297i | ||||
\(485\) | − | 36.0123i | − | 1.63524i | ||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 14.7933 | 0.670349 | 0.335175 | − | 0.942156i | \(-0.391205\pi\) | ||||
0.335175 | + | 0.942156i | \(0.391205\pi\) | |||||||
\(488\) | −7.22206 | − | 34.5469i | −0.326927 | − | 1.56387i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −4.69833 | − | 2.29804i | −0.212249 | − | 0.103815i | ||||
\(491\) | − | 14.0475i | − | 0.633956i | −0.948433 | − | 0.316978i | \(-0.897332\pi\) | ||
0.948433 | − | 0.316978i | \(-0.102668\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − | 3.50176i | − | 0.157711i | ||||||
\(494\) | 14.1631 | − | 28.9565i | 0.637230 | − | 1.30281i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −6.80784 | + | 26.7933i | −0.305681 | + | 1.20306i | ||||
\(497\) | 15.2056 | 0.682064 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 34.1414i | 1.52838i | 0.644993 | + | 0.764189i | \(0.276860\pi\) | ||||
−0.644993 | + | 0.764189i | \(0.723140\pi\) | |||||||
\(500\) | 21.4731 | − | 16.6994i | 0.960308 | − | 0.746820i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −3.94745 | − | 1.93077i | −0.176183 | − | 0.0861746i | ||||
\(503\) | 27.3821 | 1.22091 | 0.610455 | − | 0.792051i | \(-0.290987\pi\) | ||||
0.610455 | + | 0.792051i | \(0.290987\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 19.5000 | 0.867738 | ||||||||
\(506\) | 5.64578 | + | 2.76146i | 0.250986 | + | 0.122762i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 4.58882 | + | 5.90059i | 0.203596 | + | 0.261796i | ||||
\(509\) | − | 2.49165i | − | 0.110441i | −0.998474 | − | 0.0552203i | \(-0.982414\pi\) | ||
0.998474 | − | 0.0552203i | \(-0.0175861\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 15.5598 | 0.688325 | ||||||||
\(512\) | −18.4390 | + | 13.1150i | −0.814895 | + | 0.579609i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 8.79224 | − | 17.9757i | 0.387809 | − | 0.792874i | ||||
\(515\) | − | 7.17548i | − | 0.316189i | ||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 15.9710i | 0.702402i | ||||||||
\(518\) | −8.77990 | − | 4.29441i | −0.385767 | − | 0.188686i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −52.0308 | + | 10.8771i | −2.28170 | + | 0.476991i | ||||
\(521\) | 3.00108 | 0.131480 | 0.0657399 | − | 0.997837i | \(-0.479059\pi\) | ||||
0.0657399 | + | 0.997837i | \(0.479059\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − | 16.8514i | − | 0.736859i | −0.929656 | − | 0.368429i | \(-0.879896\pi\) | ||
0.929656 | − | 0.368429i | \(-0.120104\pi\) | |||||||
\(524\) | −5.36256 | + | 4.17040i | −0.234264 | + | 0.182185i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −1.82872 | + | 3.73881i | −0.0797361 | + | 0.163020i | ||||
\(527\) | −4.26254 | −0.185679 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −21.0867 | −0.916811 | ||||||||
\(530\) | −10.3078 | + | 21.0743i | −0.447744 | + | 0.915410i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −7.08157 | + | 5.50725i | −0.307025 | + | 0.238770i | ||||
\(533\) | 3.13412i | 0.135754i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −17.7045 | −0.765432 | ||||||||
\(536\) | 5.53716 | + | 26.4871i | 0.239169 | + | 1.14407i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −0.816180 | − | 0.399209i | −0.0351880 | − | 0.0172111i | ||||
\(539\) | − | 3.21284i | − | 0.138387i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | − | 24.6319i | − | 1.05901i | −0.848307 | − | 0.529505i | \(-0.822378\pi\) | ||
0.848307 | − | 0.529505i | \(-0.177622\pi\) | |||||||
\(542\) | −0.327371 | + | 0.669309i | −0.0140618 | + | 0.0287493i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −2.66009 | − | 2.25756i | −0.114050 | − | 0.0967920i | ||||
\(545\) | 3.59100 | 0.153821 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 25.8564i | 1.10554i | 0.833333 | + | 0.552771i | \(0.186430\pi\) | ||||
−0.833333 | + | 0.552771i | \(0.813570\pi\) | |||||||
\(548\) | 16.0299 | + | 20.6123i | 0.684764 | + | 0.880512i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 35.4184 | + | 17.3238i | 1.51025 | + | 0.738689i | ||||
\(551\) | 25.4670 | 1.08493 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −5.23352 | −0.222552 | ||||||||
\(554\) | 27.5917 | + | 13.4956i | 1.17226 | + | 0.573373i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 4.43294 | − | 3.44745i | 0.187999 | − | 0.146204i | ||||
\(557\) | 27.2788i | 1.15584i | 0.816093 | + | 0.577920i | \(0.196136\pi\) | ||||
−0.816093 | + | 0.577920i | \(0.803864\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 40.6157 | 1.71786 | ||||||||
\(560\) | 14.3377 | + | 3.64304i | 0.605880 | + | 0.153946i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 2.97844 | − | 6.08940i | 0.125638 | − | 0.256866i | ||||
\(563\) | 13.1776i | 0.555371i | 0.960672 | + | 0.277686i | \(0.0895674\pi\) | ||||
−0.960672 | + | 0.277686i | \(0.910433\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 57.5453i | 2.42095i | ||||||||
\(566\) | 28.7726 | + | 14.0732i | 1.20940 | + | 0.591542i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −42.0978 | + | 8.80058i | −1.76639 | + | 0.369264i | ||||
\(569\) | −17.4380 | −0.731040 | −0.365520 | − | 0.930803i | \(-0.619109\pi\) | ||||
−0.365520 | + | 0.930803i | \(0.619109\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 4.71569i | 0.197346i | 0.995120 | + | 0.0986728i | \(0.0314597\pi\) | ||||
−0.995120 | + | 0.0986728i | \(0.968540\pi\) | |||||||
\(572\) | −20.0453 | − | 25.7755i | −0.838136 | − | 1.07773i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0.383238 | − | 0.783529i | 0.0159961 | − | 0.0327039i | ||||
\(575\) | 12.0033 | 0.500570 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −11.8223 | −0.492171 | −0.246085 | − | 0.969248i | \(-0.579144\pi\) | ||||
−0.246085 | + | 0.969248i | \(0.579144\pi\) | |||||||
\(578\) | −10.3270 | + | 21.1134i | −0.429545 | + | 0.878202i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −25.7810 | − | 33.1508i | −1.07050 | − | 1.37651i | ||||
\(581\) | 10.4257i | 0.432530i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −14.4112 | −0.596849 | ||||||||
\(584\) | −43.0785 | + | 9.00559i | −1.78260 | + | 0.372654i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 30.9068 | + | 15.1171i | 1.27675 | + | 0.624480i | ||||
\(587\) | − | 13.7810i | − | 0.568802i | −0.958705 | − | 0.284401i | \(-0.908205\pi\) | ||
0.958705 | − | 0.284401i | \(-0.0917947\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − | 31.0000i | − | 1.27733i | ||||||
\(590\) | −9.19216 | + | 18.7933i | −0.378435 | + | 0.773709i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 26.7933 | + | 6.80784i | 1.10120 | + | 0.279800i | ||||
\(593\) | −36.8872 | −1.51477 | −0.757387 | − | 0.652966i | \(-0.773524\pi\) | ||||
−0.757387 | + | 0.652966i | \(0.773524\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 2.28099i | 0.0935114i | ||||||||
\(596\) | −19.7118 | + | 15.3296i | −0.807425 | + | 0.627925i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −8.92962 | − | 4.36764i | −0.365159 | − | 0.178606i | ||||
\(599\) | 35.0895 | 1.43372 | 0.716859 | − | 0.697218i | \(-0.245579\pi\) | ||||
0.716859 | + | 0.697218i | \(0.245579\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 18.3263 | 0.747544 | 0.373772 | − | 0.927521i | \(-0.378064\pi\) | ||||
0.373772 | + | 0.927521i | \(0.378064\pi\) | |||||||
\(602\) | −10.1539 | − | 4.96647i | −0.413843 | − | 0.202418i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −11.0145 | − | 14.1631i | −0.448174 | − | 0.576290i | ||||
\(605\) | − | 2.50617i | − | 0.101890i | ||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −12.4459 | −0.505163 | −0.252582 | − | 0.967576i | \(-0.581280\pi\) | ||||
−0.252582 | + | 0.967576i | \(0.581280\pi\) | |||||||
\(608\) | 16.4184 | − | 19.3459i | 0.665855 | − | 0.784579i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 28.6755 | − | 58.6269i | 1.16104 | − | 2.37373i | ||||
\(611\) | − | 25.2604i | − | 1.02193i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − | 14.2682i | − | 0.576288i | −0.957587 | − | 0.288144i | \(-0.906962\pi\) | ||
0.957587 | − | 0.288144i | \(-0.0930383\pi\) | |||||||
\(614\) | −4.46481 | − | 2.18382i | −0.180185 | − | 0.0881318i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 1.85951 | + | 8.89500i | 0.0749216 | + | 0.358390i | ||||
\(617\) | −2.94413 | −0.118526 | −0.0592632 | − | 0.998242i | \(-0.518875\pi\) | ||||
−0.0592632 | + | 0.998242i | \(0.518875\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 13.2604i | − | 0.532979i | −0.963838 | − | 0.266490i | \(-0.914136\pi\) | ||
0.963838 | − | 0.266490i | \(-0.0858638\pi\) | |||||||
\(620\) | −40.3531 | + | 31.3821i | −1.62062 | + | 1.26034i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 3.08883 | − | 6.31509i | 0.123851 | − | 0.253212i | ||||
\(623\) | 14.1766 | 0.567972 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 6.91335 | 0.276534 | ||||||||
\(626\) | −15.9349 | + | 32.5788i | −0.636887 | + | 1.30211i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 23.9444 | − | 18.6213i | 0.955485 | − | 0.743070i | ||||
\(629\) | 4.26254i | 0.169959i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 36.2335 | 1.44243 | 0.721217 | − | 0.692710i | \(-0.243583\pi\) | ||||
0.721217 | + | 0.692710i | \(0.243583\pi\) | |||||||
\(632\) | 14.4894 | − | 3.02902i | 0.576358 | − | 0.120488i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 4.46481 | + | 2.18382i | 0.177320 | + | 0.0867306i | ||||
\(635\) | 13.8223i | 0.548523i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 5.08157i | 0.201339i | ||||||||
\(638\) | 11.3347 | − | 23.1737i | 0.448745 | − | 0.917456i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −41.8036 | − | 1.78773i | −1.65243 | − | 0.0706662i | ||||
\(641\) | −25.9441 | −1.02473 | −0.512366 | − | 0.858767i | \(-0.671231\pi\) | ||||
−0.512366 | + | 0.858767i | \(0.671231\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 27.2643i | − | 1.07520i | −0.843200 | − | 0.537599i | \(-0.819331\pi\) | ||
0.843200 | − | 0.537599i | \(-0.180669\pi\) | |||||||
\(644\) | 1.69833 | + | 2.18382i | 0.0669236 | + | 0.0860545i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 3.51451 | + | 1.71901i | 0.138277 | + | 0.0676336i | ||||
\(647\) | 7.41118 | 0.291364 | 0.145682 | − | 0.989332i | \(-0.453462\pi\) | ||||
0.145682 | + | 0.989332i | \(0.453462\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −12.8514 | −0.504460 | ||||||||
\(650\) | −56.0193 | − | 27.4001i | −2.19726 | − | 1.07472i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −20.8813 | + | 16.2391i | −0.817774 | + | 0.635973i | ||||
\(653\) | − | 17.7045i | − | 0.692830i | −0.938081 | − | 0.346415i | \(-0.887399\pi\) | ||
0.938081 | − | 0.346415i | \(-0.112601\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −12.5620 | −0.490837 | ||||||||
\(656\) | −0.607540 | + | 2.39107i | −0.0237205 | + | 0.0933556i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −3.08883 | + | 6.31509i | −0.120415 | + | 0.246188i | ||||
\(659\) | 39.2252i | 1.52800i | 0.645219 | + | 0.763998i | \(0.276766\pi\) | ||||
−0.645219 | + | 0.763998i | \(0.723234\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − | 8.35862i | − | 0.325113i | −0.986699 | − | 0.162556i | \(-0.948026\pi\) | ||
0.986699 | − | 0.162556i | \(-0.0519739\pi\) | |||||||
\(662\) | 31.9947 | + | 15.6492i | 1.24351 | + | 0.608223i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −6.03410 | − | 28.8643i | −0.234169 | − | 1.12015i | ||||
\(665\) | −16.5888 | −0.643287 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − | 7.85354i | − | 0.304090i | ||||||
\(668\) | 3.75197 | + | 4.82452i | 0.145168 | + | 0.186666i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −21.9855 | + | 44.9492i | −0.849373 | + | 1.73654i | ||||
\(671\) | 40.0906 | 1.54768 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 37.9090 | 1.46128 | 0.730642 | − | 0.682761i | \(-0.239221\pi\) | ||||
0.730642 | + | 0.682761i | \(0.239221\pi\) | |||||||
\(674\) | 13.5237 | − | 27.6492i | 0.520915 | − | 1.06501i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 15.7432 | + | 20.2436i | 0.605507 | + | 0.778599i | ||||
\(677\) | 41.5844i | 1.59822i | 0.601186 | + | 0.799109i | \(0.294695\pi\) | ||||
−0.601186 | + | 0.799109i | \(0.705305\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 9.73746 | 0.373689 | ||||||||
\(680\) | −1.32017 | − | 6.31509i | −0.0506264 | − | 0.242173i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −28.2084 | − | 13.7973i | −1.08016 | − | 0.528324i | ||||
\(683\) | − | 1.49559i | − | 0.0572272i | −0.999591 | − | 0.0286136i | \(-0.990891\pi\) | ||
0.999591 | − | 0.0286136i | \(-0.00910924\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 48.2849i | 1.84487i | ||||||||
\(686\) | 0.621372 | − | 1.27039i | 0.0237241 | − | 0.0485038i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 30.9864 | + | 7.87324i | 1.18134 | + | 0.300164i | ||||
\(689\) | 22.7933 | 0.868356 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − | 19.9028i | − | 0.757137i | −0.925573 | − | 0.378568i | \(-0.876417\pi\) | ||
0.925573 | − | 0.378568i | \(-0.123583\pi\) | |||||||
\(692\) | 21.8841 | − | 17.0190i | 0.831909 | − | 0.646966i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 40.5341 | + | 19.8260i | 1.53865 | + | 0.752584i | ||||
\(695\) | 10.3843 | 0.393900 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −0.380395 | −0.0144085 | ||||||||
\(698\) | −1.32147 | − | 0.646355i | −0.0500184 | − | 0.0244649i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 10.6544 | + | 13.7000i | 0.402697 | + | 0.517813i | ||||
\(701\) | 44.5347i | 1.68205i | 0.540994 | + | 0.841026i | \(0.318048\pi\) | ||||
−0.540994 | + | 0.841026i | \(0.681952\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −31.0000 | −1.16919 | ||||||||
\(704\) | −10.2964 | − | 23.5503i | −0.388059 | − | 0.887584i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 8.60618 | − | 17.5953i | 0.323898 | − | 0.662208i | ||||
\(707\) | 5.27265i | 0.198298i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − | 35.3553i | − | 1.32780i | −0.747823 | − | 0.663898i | \(-0.768901\pi\) | ||
0.747823 | − | 0.663898i | \(-0.231099\pi\) | |||||||
\(710\) | −71.4409 | − | 34.9430i | −2.68113 | − | 1.31139i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −39.2489 | + | 8.20501i | −1.47092 | + | 0.307496i | ||||
\(713\) | −9.55980 | −0.358017 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | − | 60.3800i | − | 2.25808i | ||||||
\(716\) | 29.0310 | − | 22.5771i | 1.08494 | − | 0.843744i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −0.256167 | + | 0.523732i | −0.00956007 | + | 0.0195455i | ||||
\(719\) | −11.0928 | −0.413690 | −0.206845 | − | 0.978374i | \(-0.566320\pi\) | ||||
−0.206845 | + | 0.978374i | \(0.566320\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 1.94019 | 0.0722566 | ||||||||
\(722\) | −0.695696 | + | 1.42235i | −0.0258911 | + | 0.0529342i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −9.55560 | + | 7.43128i | −0.355131 | + | 0.276181i | ||||
\(725\) | − | 49.2686i | − | 1.82979i | ||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −38.1135 | −1.41355 | −0.706776 | − | 0.707438i | \(-0.749851\pi\) | ||||
−0.706776 | + | 0.707438i | \(0.749851\pi\) | |||||||
\(728\) | −2.94108 | − | 14.0687i | −0.109003 | − | 0.521421i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −73.1051 | − | 35.7570i | −2.70574 | − | 1.32343i | ||||
\(731\) | 4.92962i | 0.182328i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − | 27.9576i | − | 1.03264i | −0.856396 | − | 0.516319i | \(-0.827302\pi\) | ||
0.856396 | − | 0.516319i | \(-0.172698\pi\) | |||||||
\(734\) | 3.08883 | − | 6.31509i | 0.114011 | − | 0.233094i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −5.96590 | − | 5.06313i | −0.219906 | − | 0.186629i | ||||
\(737\) | −30.7374 | −1.13223 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 1.56706i | 0.0576452i | 0.999585 | + | 0.0288226i | \(0.00917578\pi\) | ||||
−0.999585 | + | 0.0288226i | \(0.990824\pi\) | |||||||
\(740\) | 31.3821 | + | 40.3531i | 1.15363 | + | 1.48341i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −5.69833 | − | 2.78716i | −0.209192 | − | 0.102320i | ||||
\(743\) | −44.0569 | −1.61629 | −0.808146 | − | 0.588982i | \(-0.799529\pi\) | ||||
−0.808146 | + | 0.588982i | \(0.799529\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −46.1755 | −1.69174 | ||||||||
\(746\) | −2.74803 | − | 1.34411i | −0.100613 | − | 0.0492115i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 3.12843 | − | 2.43294i | 0.114387 | − | 0.0889572i | ||||
\(749\) | − | 4.78716i | − | 0.174919i | ||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −53.5039 | −1.95239 | −0.976193 | − | 0.216904i | \(-0.930404\pi\) | ||||
−0.976193 | + | 0.216904i | \(0.930404\pi\) | |||||||
\(752\) | 4.89665 | − | 19.2716i | 0.178563 | − | 0.702761i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −17.9274 | + | 36.6526i | −0.652879 | + | 1.33481i | ||||
\(755\) | − | 33.1776i | − | 1.20746i | ||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 34.1486i | 1.24115i | 0.784146 | + | 0.620576i | \(0.213101\pi\) | ||||
−0.784146 | + | 0.620576i | \(0.786899\pi\) | |||||||
\(758\) | −30.1808 | − | 14.7620i | −1.09621 | − | 0.536179i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 45.9274 | − | 9.60116i | 1.66596 | − | 0.348271i | ||||
\(761\) | 8.23460 | 0.298504 | 0.149252 | − | 0.988799i | \(-0.452313\pi\) | ||||
0.149252 | + | 0.988799i | \(0.452313\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0.970978i | 0.0351518i | ||||||||
\(764\) | −18.6693 | − | 24.0062i | −0.675432 | − | 0.868513i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 23.3386 | − | 47.7157i | 0.843259 | − | 1.72404i | ||||
\(767\) | 20.3263 | 0.733939 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 17.4380 | 0.628831 | 0.314416 | − | 0.949285i | \(-0.398191\pi\) | ||||
0.314416 | + | 0.949285i | \(0.398191\pi\) | |||||||
\(770\) | −7.38324 | + | 15.0950i | −0.266073 | + | 0.543986i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 23.8707 | + | 30.6944i | 0.859125 | + | 1.10472i | ||||
\(773\) | − | 13.8470i | − | 0.498040i | −0.968498 | − | 0.249020i | \(-0.919891\pi\) | ||
0.968498 | − | 0.249020i | \(-0.0801085\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −59.9727 | −2.15428 | ||||||||
\(776\) | −26.9589 | + | 5.63578i | −0.967768 | + | 0.202313i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −1.04970 | − | 0.513429i | −0.0376337 | − | 0.0184073i | ||||
\(779\) | − | 2.76648i | − | 0.0991193i | ||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | − | 48.8531i | − | 1.74810i | ||||||
\(782\) | 0.530110 | − | 1.08381i | 0.0189567 | − | 0.0387569i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −0.985049 | + | 3.87681i | −0.0351803 | + | 0.138458i | ||||
\(785\) | 56.0906 | 2.00196 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 48.8368i | 1.74085i | 0.492305 | + | 0.870423i | \(0.336155\pi\) | ||||
−0.492305 | + | 0.870423i | \(0.663845\pi\) | |||||||
\(788\) | 24.0794 | − | 18.7263i | 0.857793 | − | 0.667095i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 24.5888 | + | 12.0268i | 0.874831 | + | 0.427896i | ||||
\(791\) | −15.5598 | −0.553243 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −63.4090 | −2.25172 | ||||||||
\(794\) | 11.2036 | + | 5.47990i | 0.397602 | + | 0.194474i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 3.71901 | + | 4.78214i | 0.131817 | + | 0.169498i | ||||
\(797\) | − | 44.7330i | − | 1.58453i | −0.610180 | − | 0.792263i | \(-0.708903\pi\) | ||
0.610180 | − | 0.792263i | \(-0.291097\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 3.06591 | 0.108464 | ||||||||
\(800\) | −37.4266 | − | 31.7632i | −1.32323 | − | 1.12300i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 5.37292 | − | 10.9849i | 0.189724 | − | 0.387891i | ||||
\(803\) | − | 49.9912i | − | 1.76415i | ||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 5.11567i | 0.180304i | ||||||||
\(806\) | 44.6157 | + | 21.8223i | 1.57152 | + | 0.768659i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −3.05167 | − | 14.5977i | −0.107357 | − | 0.513546i | ||||
\(809\) | −7.79550 | −0.274075 | −0.137038 | − | 0.990566i | \(-0.543758\pi\) | ||||
−0.137038 | + | 0.990566i | \(0.543758\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 9.53295i | − | 0.334747i | −0.985894 | − | 0.167374i | \(-0.946471\pi\) | ||
0.985894 | − | 0.167374i | \(-0.0535286\pi\) | |||||||
\(812\) | 8.96372 | − | 6.97098i | 0.314565 | − | 0.244633i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −13.7973 | + | 28.2084i | −0.483594 | + | 0.988705i | ||||
\(815\) | −48.9151 | −1.71342 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −35.8514 | −1.25428 | ||||||||
\(818\) | −11.6249 | + | 23.7670i | −0.406455 | + | 0.830995i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −3.60116 | + | 2.80058i | −0.125758 | + | 0.0978005i | ||||
\(821\) | 12.2498i | 0.427521i | 0.976886 | + | 0.213760i | \(0.0685711\pi\) | ||||
−0.976886 | + | 0.213760i | \(0.931429\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −49.7665 | −1.73475 | −0.867375 | − | 0.497655i | \(-0.834194\pi\) | ||||
−0.867375 | + | 0.497655i | \(0.834194\pi\) | |||||||
\(824\) | −5.37158 | + | 1.12293i | −0.187128 | + | 0.0391192i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −5.08157 | − | 2.48549i | −0.176810 | − | 0.0864812i | ||||
\(827\) | − | 13.1403i | − | 0.456932i | −0.973552 | − | 0.228466i | \(-0.926629\pi\) | ||
0.973552 | − | 0.228466i | \(-0.0733710\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 0.961957i | − | 0.0334102i | −0.999860 | − | 0.0167051i | \(-0.994682\pi\) | ||
0.999860 | − | 0.0167051i | \(-0.00531764\pi\) | |||||||
\(830\) | 23.9586 | − | 48.9833i | 0.831616 | − | 1.70024i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 16.2852 | + | 37.2481i | 0.564587 | + | 1.29135i | ||||
\(833\) | −0.616762 | −0.0213695 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 11.3016i | 0.391108i | ||||||||
\(836\) | 17.6939 | + | 22.7520i | 0.611957 | + | 0.786893i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 16.4782 | + | 8.05981i | 0.569231 | + | 0.278421i | ||||
\(839\) | −51.4727 | −1.77704 | −0.888518 | − | 0.458842i | \(-0.848264\pi\) | ||||
−0.888518 | + | 0.458842i | \(0.848264\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −3.23570 | −0.111576 | ||||||||
\(842\) | 4.49891 | + | 2.20050i | 0.155043 | + | 0.0758343i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 1.52149 | − | 1.18325i | 0.0523720 | − | 0.0407291i | ||||
\(845\) | 47.4213i | 1.63134i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0.677649 | 0.0232843 | ||||||||
\(848\) | 17.3894 | + | 4.41842i | 0.597155 | + | 0.151729i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 3.32561 | − | 6.79919i | 0.114067 | − | 0.233210i | ||||
\(851\) | 9.55980i | 0.327706i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 3.72843i | − | 0.127659i | −0.997961 | − | 0.0638296i | \(-0.979669\pi\) | ||
0.997961 | − | 0.0638296i | \(-0.0203314\pi\) | |||||||
\(854\) | 15.8522 | + | 7.75363i | 0.542453 | + | 0.265324i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 2.77068 | + | 13.2536i | 0.0946998 | + | 0.452999i | ||||
\(857\) | 0.473828 | 0.0161857 | 0.00809283 | − | 0.999967i | \(-0.497424\pi\) | ||||
0.00809283 | + | 0.999967i | \(0.497424\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 41.3078i | 1.40940i | 0.709503 | + | 0.704702i | \(0.248919\pi\) | ||||
−0.709503 | + | 0.704702i | \(0.751081\pi\) | |||||||
\(860\) | 36.2933 | + | 46.6682i | 1.23759 | + | 1.59137i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −9.08245 | + | 18.5690i | −0.309349 | + | 0.632463i | ||||
\(863\) | −29.9162 | −1.01836 | −0.509179 | − | 0.860660i | \(-0.670051\pi\) | ||||
−0.509179 | + | 0.860660i | \(0.670051\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 51.2643 | 1.74304 | ||||||||
\(866\) | −1.84608 | + | 3.77431i | −0.0627325 | + | 0.128256i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −8.48549 | − | 10.9112i | −0.288016 | − | 0.370349i | ||||
\(869\) | 16.8145i | 0.570392i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 48.6157 | 1.64728 | ||||||||
\(872\) | −0.561976 | − | 2.68823i | −0.0190309 | − | 0.0910349i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 7.88215 | + | 3.85530i | 0.266618 | + | 0.130408i | ||||
\(875\) | 13.6012i | 0.459803i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 18.4670i | 0.623588i | 0.950150 | + | 0.311794i | \(0.100930\pi\) | ||||
−0.950150 | + | 0.311794i | \(0.899070\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 11.7045 | − | 46.0649i | 0.394558 | − | 1.55285i | ||||
\(881\) | 50.5297 | 1.70239 | 0.851194 | − | 0.524851i | \(-0.175879\pi\) | ||||
0.851194 | + | 0.524851i | \(0.175879\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 53.8688i | 1.81283i | 0.422390 | + | 0.906414i | \(0.361191\pi\) | ||||
−0.422390 | + | 0.906414i | \(0.638809\pi\) | |||||||
\(884\) | −4.94806 | + | 3.84805i | −0.166421 | + | 0.129424i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −34.5525 | − | 16.9003i | −1.16082 | − | 0.567776i | ||||
\(887\) | −36.9978 | −1.24227 | −0.621133 | − | 0.783705i | \(-0.713327\pi\) | ||||
−0.621133 | + | 0.783705i | \(0.713327\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −3.73746 | −0.125350 | ||||||||
\(890\) | −66.6062 | − | 32.5783i | −2.23264 | − | 1.09203i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 27.1939 | + | 34.9676i | 0.910520 | + | 1.17080i | ||||
\(893\) | 22.2973i | 0.746150i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 68.0061 | 2.27319 | ||||||||
\(896\) | 0.483388 | − | 11.3034i | 0.0161489 | − | 0.377619i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 19.6104 | − | 40.0933i | 0.654407 | − | 1.33793i | ||||
\(899\) | 39.2392i | 1.30870i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 2.76648i | 0.0921647i | ||||||||
\(902\) | −2.51735 | − | 1.23128i | −0.0838187 | − | 0.0409973i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 43.0785 | − | 9.00559i | 1.43277 | − | 0.299522i | ||||
\(905\) | −22.3843 | −0.744080 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − | 53.5112i | − | 1.77681i | −0.459061 | − | 0.888405i | \(-0.651814\pi\) | ||
0.459061 | − | 0.888405i | \(-0.348186\pi\) | |||||||
\(908\) | −1.46765 | + | 1.14137i | −0.0487057 | + | 0.0378779i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 11.6776 | − | 23.8749i | 0.387110 | − | 0.791445i | ||||
\(911\) | 11.0860 | 0.367295 | 0.183647 | − | 0.982992i | \(-0.441210\pi\) | ||||
0.183647 | + | 0.982992i | \(0.441210\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 33.4961 | 1.10856 | ||||||||
\(914\) | 17.4679 | − | 35.7129i | 0.577785 | − | 1.18128i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 2.24559 | − | 1.74637i | 0.0741963 | − | 0.0577016i | ||||
\(917\) | − | 3.39666i | − | 0.112168i | ||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 47.5286 | 1.56782 | 0.783912 | − | 0.620872i | \(-0.213221\pi\) | ||||
0.783912 | + | 0.620872i | \(0.213221\pi\) | |||||||
\(920\) | −2.96081 | − | 14.1631i | −0.0976151 | − | 0.466945i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −6.59892 | − | 3.22766i | −0.217324 | − | 0.106297i | ||||
\(923\) | 77.2682i | 2.54331i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 59.9727i | 1.97189i | ||||||||
\(926\) | −6.68999 | + | 13.6776i | −0.219847 | + | 0.449475i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −20.7821 | + | 24.4877i | −0.682207 | + | 0.803847i | ||||
\(929\) | 33.2425 | 1.09065 | 0.545325 | − | 0.838225i | \(-0.316406\pi\) | ||||
0.545325 | + | 0.838225i | \(0.316406\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | − | 4.48549i | − | 0.147006i | ||||||
\(932\) | 13.4701 | + | 17.3207i | 0.441227 | + | 0.567358i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −39.0671 | − | 19.1084i | −1.27831 | − | 0.625246i | ||||
\(935\) | 7.32845 | 0.239666 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −14.8514 | −0.485173 | −0.242586 | − | 0.970130i | \(-0.577996\pi\) | ||||
−0.242586 | + | 0.970130i | \(0.577996\pi\) | |||||||
\(938\) | −12.1539 | − | 5.94470i | −0.396839 | − | 0.194101i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 29.0247 | − | 22.5721i | 0.946680 | − | 0.736222i | ||||
\(941\) | − | 53.6258i | − | 1.74815i | −0.485791 | − | 0.874075i | \(-0.661468\pi\) | ||
0.485791 | − | 0.874075i | \(-0.338532\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −0.853128 | −0.0277817 | ||||||||
\(944\) | 15.5073 | + | 3.94019i | 0.504718 | + | 0.128242i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −15.9565 | + | 32.6229i | −0.518790 | + | 1.06066i | ||||
\(947\) | 24.1324i | 0.784198i | 0.919923 | + | 0.392099i | \(0.128251\pi\) | ||||
−0.919923 | + | 0.392099i | \(0.871749\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 79.0682i | 2.56666i | ||||||||
\(950\) | 49.4481 | + | 24.1860i | 1.60431 | + | 0.784697i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 1.70755 | − | 0.356965i | 0.0553421 | − | 0.0115693i | ||||
\(953\) | −0.347434 | −0.0112545 | −0.00562725 | − | 0.999984i | \(-0.501791\pi\) | ||||
−0.00562725 | + | 0.999984i | \(0.501791\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − | 56.2353i | − | 1.81973i | ||||||
\(956\) | −5.91951 | − | 7.61168i | −0.191451 | − | 0.246179i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −10.1447 | + | 20.7408i | −0.327760 | + | 0.670104i | ||||
\(959\) | −13.0559 | −0.421596 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 16.7643 | 0.540784 | ||||||||
\(962\) | 21.8223 | − | 44.6157i | 0.703581 | − | 1.43847i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0.251085 | + | 0.322861i | 0.00808690 | + | 0.0103986i | ||||
\(965\) | 71.9028i | 2.31463i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −8.14646 | −0.261972 | −0.130986 | − | 0.991384i | \(-0.541814\pi\) | ||||
−0.130986 | + | 0.991384i | \(0.541814\pi\) | |||||||
\(968\) | −1.87612 | + | 0.392205i | −0.0603009 | + | 0.0126059i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −45.7498 | − | 22.3771i | −1.46894 | − | 0.718484i | ||||
\(971\) | 3.02902i | 0.0972059i | 0.998818 | + | 0.0486030i | \(0.0154769\pi\) | ||||
−0.998818 | + | 0.0486030i | \(0.984523\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 2.80784i | 0.0900152i | ||||||||
\(974\) | 9.19216 | − | 18.7933i | 0.294536 | − | 0.602177i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −48.3758 | − | 12.2917i | −1.54847 | − | 0.393447i | ||||
\(977\) | −18.7353 | −0.599395 | −0.299697 | − | 0.954034i | \(-0.596886\pi\) | ||||
−0.299697 | + | 0.954034i | \(0.596886\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 45.5470i | − | 1.45569i | ||||||
\(980\) | −5.83882 | + | 4.54078i | −0.186514 | + | 0.145050i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −17.8459 | − | 8.72874i | −0.569485 | − | 0.278545i | ||||
\(983\) | −18.2313 | −0.581490 | −0.290745 | − | 0.956801i | \(-0.593903\pi\) | ||||
−0.290745 | + | 0.956801i | \(0.593903\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 56.4068 | 1.79727 | ||||||||
\(986\) | −4.44860 | − | 2.17589i | −0.141672 | − | 0.0692946i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −27.9855 | − | 35.9855i | −0.890337 | − | 1.14485i | ||||
\(989\) | 11.0559i | 0.351556i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −21.2973 | −0.676530 | −0.338265 | − | 0.941051i | \(-0.609840\pi\) | ||||
−0.338265 | + | 0.941051i | \(0.609840\pi\) | |||||||
\(992\) | 29.8078 | + | 25.2973i | 0.946399 | + | 0.803189i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 9.44833 | − | 19.3171i | 0.299683 | − | 0.612700i | ||||
\(995\) | 11.2023i | 0.355138i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 24.7900i | 0.785107i | 0.919729 | + | 0.392553i | \(0.128408\pi\) | ||||
−0.919729 | + | 0.392553i | \(0.871592\pi\) | |||||||
\(998\) | 43.3729 | + | 21.2145i | 1.37295 | + | 0.671533i | ||||
\(999\) | 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 | 504.2.c.f.253.5 | 8 | ||
3.2 | odd | 2 | 168.2.c.b.85.4 | yes | 8 | ||
4.3 | odd | 2 | 2016.2.c.e.1009.2 | 8 | |||
8.3 | odd | 2 | 2016.2.c.e.1009.7 | 8 | |||
8.5 | even | 2 | inner | 504.2.c.f.253.6 | 8 | ||
12.11 | even | 2 | 672.2.c.b.337.8 | 8 | |||
21.20 | even | 2 | 1176.2.c.c.589.4 | 8 | |||
24.5 | odd | 2 | 168.2.c.b.85.3 | ✓ | 8 | ||
24.11 | even | 2 | 672.2.c.b.337.1 | 8 | |||
48.5 | odd | 4 | 5376.2.a.bm.1.1 | 4 | |||
48.11 | even | 4 | 5376.2.a.bq.1.1 | 4 | |||
48.29 | odd | 4 | 5376.2.a.bp.1.4 | 4 | |||
48.35 | even | 4 | 5376.2.a.bl.1.4 | 4 | |||
84.83 | odd | 2 | 4704.2.c.c.2353.1 | 8 | |||
168.83 | odd | 2 | 4704.2.c.c.2353.8 | 8 | |||
168.125 | even | 2 | 1176.2.c.c.589.3 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
168.2.c.b.85.3 | ✓ | 8 | 24.5 | odd | 2 | ||
168.2.c.b.85.4 | yes | 8 | 3.2 | odd | 2 | ||
504.2.c.f.253.5 | 8 | 1.1 | even | 1 | trivial | ||
504.2.c.f.253.6 | 8 | 8.5 | even | 2 | inner | ||
672.2.c.b.337.1 | 8 | 24.11 | even | 2 | |||
672.2.c.b.337.8 | 8 | 12.11 | even | 2 | |||
1176.2.c.c.589.3 | 8 | 168.125 | even | 2 | |||
1176.2.c.c.589.4 | 8 | 21.20 | even | 2 | |||
2016.2.c.e.1009.2 | 8 | 4.3 | odd | 2 | |||
2016.2.c.e.1009.7 | 8 | 8.3 | odd | 2 | |||
4704.2.c.c.2353.1 | 8 | 84.83 | odd | 2 | |||
4704.2.c.c.2353.8 | 8 | 168.83 | odd | 2 | |||
5376.2.a.bl.1.4 | 4 | 48.35 | even | 4 | |||
5376.2.a.bm.1.1 | 4 | 48.5 | odd | 4 | |||
5376.2.a.bp.1.4 | 4 | 48.29 | odd | 4 | |||
5376.2.a.bq.1.1 | 4 | 48.11 | even | 4 |