Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1045,2,Mod(419,1045)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1045, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("1045.419");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1045 = 5 \cdot 11 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1045.b (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: | \(8.34436701122\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(\zeta_{8})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 2^{3} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 419.4 | ||
Root | \(0.707107 + 0.707107i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1045.419 |
Dual form | 1045.2.b.a.419.1 |
$q$-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 \(\left(\mathbb{Z}/1045\mathbb{Z}\right)^\times\).
\(n\) | \(496\) | \(761\) | \(837\) |
\(\chi(n)\) | \(1\) | \(1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.41421i | 1.70711i | 0.521005 | + | 0.853553i | \(0.325557\pi\) | ||||
−0.521005 | + | 0.853553i | \(0.674443\pi\) | |||||||
\(3\) | − | 2.00000i | − | 1.15470i | −0.816497 | − | 0.577350i | \(-0.804087\pi\) | ||
0.816497 | − | 0.577350i | \(-0.195913\pi\) | |||||||
\(4\) | −3.82843 | −1.91421 | ||||||||
\(5\) | −1.00000 | + | 2.00000i | −0.447214 | + | 0.894427i | ||||
\(6\) | 4.82843 | 1.97120 | ||||||||
\(7\) | 4.82843i | 1.82497i | 0.409106 | + | 0.912487i | \(0.365841\pi\) | ||||
−0.409106 | + | 0.912487i | \(0.634159\pi\) | |||||||
\(8\) | − | 4.41421i | − | 1.56066i | ||||||
\(9\) | −1.00000 | −0.333333 | ||||||||
\(10\) | −4.82843 | − | 2.41421i | −1.52688 | − | 0.763441i | ||||
\(11\) | −1.00000 | −0.301511 | ||||||||
\(12\) | 7.65685i | 2.21034i | ||||||||
\(13\) | − | 1.17157i | − | 0.324936i | −0.986714 | − | 0.162468i | \(-0.948055\pi\) | ||
0.986714 | − | 0.162468i | \(-0.0519454\pi\) | |||||||
\(14\) | −11.6569 | −3.11543 | ||||||||
\(15\) | 4.00000 | + | 2.00000i | 1.03280 | + | 0.516398i | ||||
\(16\) | 3.00000 | 0.750000 | ||||||||
\(17\) | 1.17157i | 0.284148i | 0.989856 | + | 0.142074i | \(0.0453771\pi\) | ||||
−0.989856 | + | 0.142074i | \(0.954623\pi\) | |||||||
\(18\) | − | 2.41421i | − | 0.569036i | ||||||
\(19\) | 1.00000 | 0.229416 | ||||||||
\(20\) | 3.82843 | − | 7.65685i | 0.856062 | − | 1.71212i | ||||
\(21\) | 9.65685 | 2.10730 | ||||||||
\(22\) | − | 2.41421i | − | 0.514712i | ||||||
\(23\) | 3.65685i | 0.762507i | 0.924471 | + | 0.381253i | \(0.124507\pi\) | ||||
−0.924471 | + | 0.381253i | \(0.875493\pi\) | |||||||
\(24\) | −8.82843 | −1.80210 | ||||||||
\(25\) | −3.00000 | − | 4.00000i | −0.600000 | − | 0.800000i | ||||
\(26\) | 2.82843 | 0.554700 | ||||||||
\(27\) | − | 4.00000i | − | 0.769800i | ||||||
\(28\) | − | 18.4853i | − | 3.49339i | ||||||
\(29\) | −0.828427 | −0.153835 | −0.0769175 | − | 0.997037i | \(-0.524508\pi\) | ||||
−0.0769175 | + | 0.997037i | \(0.524508\pi\) | |||||||
\(30\) | −4.82843 | + | 9.65685i | −0.881546 | + | 1.76309i | ||||
\(31\) | −1.17157 | −0.210421 | −0.105210 | − | 0.994450i | \(-0.533552\pi\) | ||||
−0.105210 | + | 0.994450i | \(0.533552\pi\) | |||||||
\(32\) | − | 1.58579i | − | 0.280330i | ||||||
\(33\) | 2.00000i | 0.348155i | ||||||||
\(34\) | −2.82843 | −0.485071 | ||||||||
\(35\) | −9.65685 | − | 4.82843i | −1.63231 | − | 0.816153i | ||||
\(36\) | 3.82843 | 0.638071 | ||||||||
\(37\) | 8.48528i | 1.39497i | 0.716599 | + | 0.697486i | \(0.245698\pi\) | ||||
−0.716599 | + | 0.697486i | \(0.754302\pi\) | |||||||
\(38\) | 2.41421i | 0.391637i | ||||||||
\(39\) | −2.34315 | −0.375204 | ||||||||
\(40\) | 8.82843 | + | 4.41421i | 1.39590 | + | 0.697948i | ||||
\(41\) | −10.4853 | −1.63753 | −0.818763 | − | 0.574132i | \(-0.805340\pi\) | ||||
−0.818763 | + | 0.574132i | \(0.805340\pi\) | |||||||
\(42\) | 23.3137i | 3.59738i | ||||||||
\(43\) | − | 4.82843i | − | 0.736328i | −0.929761 | − | 0.368164i | \(-0.879986\pi\) | ||
0.929761 | − | 0.368164i | \(-0.120014\pi\) | |||||||
\(44\) | 3.82843 | 0.577157 | ||||||||
\(45\) | 1.00000 | − | 2.00000i | 0.149071 | − | 0.298142i | ||||
\(46\) | −8.82843 | −1.30168 | ||||||||
\(47\) | 0.343146i | 0.0500530i | 0.999687 | + | 0.0250265i | \(0.00796701\pi\) | ||||
−0.999687 | + | 0.0250265i | \(0.992033\pi\) | |||||||
\(48\) | − | 6.00000i | − | 0.866025i | ||||||
\(49\) | −16.3137 | −2.33053 | ||||||||
\(50\) | 9.65685 | − | 7.24264i | 1.36569 | − | 1.02426i | ||||
\(51\) | 2.34315 | 0.328106 | ||||||||
\(52\) | 4.48528i | 0.621997i | ||||||||
\(53\) | − | 5.17157i | − | 0.710370i | −0.934796 | − | 0.355185i | \(-0.884418\pi\) | ||
0.934796 | − | 0.355185i | \(-0.115582\pi\) | |||||||
\(54\) | 9.65685 | 1.31413 | ||||||||
\(55\) | 1.00000 | − | 2.00000i | 0.134840 | − | 0.269680i | ||||
\(56\) | 21.3137 | 2.84816 | ||||||||
\(57\) | − | 2.00000i | − | 0.264906i | ||||||
\(58\) | − | 2.00000i | − | 0.262613i | ||||||
\(59\) | −2.82843 | −0.368230 | −0.184115 | − | 0.982905i | \(-0.558942\pi\) | ||||
−0.184115 | + | 0.982905i | \(0.558942\pi\) | |||||||
\(60\) | −15.3137 | − | 7.65685i | −1.97699 | − | 0.988496i | ||||
\(61\) | −2.00000 | −0.256074 | −0.128037 | − | 0.991769i | \(-0.540868\pi\) | ||||
−0.128037 | + | 0.991769i | \(0.540868\pi\) | |||||||
\(62\) | − | 2.82843i | − | 0.359211i | ||||||
\(63\) | − | 4.82843i | − | 0.608325i | ||||||
\(64\) | 9.82843 | 1.22855 | ||||||||
\(65\) | 2.34315 | + | 1.17157i | 0.290631 | + | 0.145316i | ||||
\(66\) | −4.82843 | −0.594338 | ||||||||
\(67\) | 6.00000i | 0.733017i | 0.930415 | + | 0.366508i | \(0.119447\pi\) | ||||
−0.930415 | + | 0.366508i | \(0.880553\pi\) | |||||||
\(68\) | − | 4.48528i | − | 0.543920i | ||||||
\(69\) | 7.31371 | 0.880467 | ||||||||
\(70\) | 11.6569 | − | 23.3137i | 1.39326 | − | 2.78652i | ||||
\(71\) | −9.17157 | −1.08847 | −0.544233 | − | 0.838934i | \(-0.683179\pi\) | ||||
−0.544233 | + | 0.838934i | \(0.683179\pi\) | |||||||
\(72\) | 4.41421i | 0.520220i | ||||||||
\(73\) | − | 6.82843i | − | 0.799207i | −0.916688 | − | 0.399603i | \(-0.869148\pi\) | ||
0.916688 | − | 0.399603i | \(-0.130852\pi\) | |||||||
\(74\) | −20.4853 | −2.38137 | ||||||||
\(75\) | −8.00000 | + | 6.00000i | −0.923760 | + | 0.692820i | ||||
\(76\) | −3.82843 | −0.439151 | ||||||||
\(77\) | − | 4.82843i | − | 0.550250i | ||||||
\(78\) | − | 5.65685i | − | 0.640513i | ||||||
\(79\) | 5.65685 | 0.636446 | 0.318223 | − | 0.948016i | \(-0.396914\pi\) | ||||
0.318223 | + | 0.948016i | \(0.396914\pi\) | |||||||
\(80\) | −3.00000 | + | 6.00000i | −0.335410 | + | 0.670820i | ||||
\(81\) | −11.0000 | −1.22222 | ||||||||
\(82\) | − | 25.3137i | − | 2.79543i | ||||||
\(83\) | − | 10.4853i | − | 1.15091i | −0.817834 | − | 0.575455i | \(-0.804825\pi\) | ||
0.817834 | − | 0.575455i | \(-0.195175\pi\) | |||||||
\(84\) | −36.9706 | −4.03382 | ||||||||
\(85\) | −2.34315 | − | 1.17157i | −0.254150 | − | 0.127075i | ||||
\(86\) | 11.6569 | 1.25699 | ||||||||
\(87\) | 1.65685i | 0.177633i | ||||||||
\(88\) | 4.41421i | 0.470557i | ||||||||
\(89\) | 15.6569 | 1.65962 | 0.829812 | − | 0.558044i | \(-0.188448\pi\) | ||||
0.829812 | + | 0.558044i | \(0.188448\pi\) | |||||||
\(90\) | 4.82843 | + | 2.41421i | 0.508961 | + | 0.254480i | ||||
\(91\) | 5.65685 | 0.592999 | ||||||||
\(92\) | − | 14.0000i | − | 1.45960i | ||||||
\(93\) | 2.34315i | 0.242973i | ||||||||
\(94\) | −0.828427 | −0.0854457 | ||||||||
\(95\) | −1.00000 | + | 2.00000i | −0.102598 | + | 0.205196i | ||||
\(96\) | −3.17157 | −0.323697 | ||||||||
\(97\) | 6.82843i | 0.693322i | 0.937991 | + | 0.346661i | \(0.112685\pi\) | ||||
−0.937991 | + | 0.346661i | \(0.887315\pi\) | |||||||
\(98\) | − | 39.3848i | − | 3.97846i | ||||||
\(99\) | 1.00000 | 0.100504 | ||||||||
\(100\) | 11.4853 | + | 15.3137i | 1.14853 | + | 1.53137i | ||||
\(101\) | −13.3137 | −1.32476 | −0.662382 | − | 0.749166i | \(-0.730454\pi\) | ||||
−0.662382 | + | 0.749166i | \(0.730454\pi\) | |||||||
\(102\) | 5.65685i | 0.560112i | ||||||||
\(103\) | 15.6569i | 1.54272i | 0.636402 | + | 0.771358i | \(0.280422\pi\) | ||||
−0.636402 | + | 0.771358i | \(0.719578\pi\) | |||||||
\(104\) | −5.17157 | −0.507114 | ||||||||
\(105\) | −9.65685 | + | 19.3137i | −0.942412 | + | 1.88482i | ||||
\(106\) | 12.4853 | 1.21268 | ||||||||
\(107\) | − | 14.9706i | − | 1.44726i | −0.690189 | − | 0.723629i | \(-0.742472\pi\) | ||
0.690189 | − | 0.723629i | \(-0.257528\pi\) | |||||||
\(108\) | 15.3137i | 1.47356i | ||||||||
\(109\) | 4.82843 | 0.462479 | 0.231240 | − | 0.972897i | \(-0.425722\pi\) | ||||
0.231240 | + | 0.972897i | \(0.425722\pi\) | |||||||
\(110\) | 4.82843 | + | 2.41421i | 0.460372 | + | 0.230186i | ||||
\(111\) | 16.9706 | 1.61077 | ||||||||
\(112\) | 14.4853i | 1.36873i | ||||||||
\(113\) | 18.1421i | 1.70667i | 0.521364 | + | 0.853334i | \(0.325423\pi\) | ||||
−0.521364 | + | 0.853334i | \(0.674577\pi\) | |||||||
\(114\) | 4.82843 | 0.452224 | ||||||||
\(115\) | −7.31371 | − | 3.65685i | −0.682007 | − | 0.341003i | ||||
\(116\) | 3.17157 | 0.294473 | ||||||||
\(117\) | 1.17157i | 0.108312i | ||||||||
\(118\) | − | 6.82843i | − | 0.628608i | ||||||
\(119\) | −5.65685 | −0.518563 | ||||||||
\(120\) | 8.82843 | − | 17.6569i | 0.805921 | − | 1.61184i | ||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | − | 4.82843i | − | 0.437145i | ||||||
\(123\) | 20.9706i | 1.89085i | ||||||||
\(124\) | 4.48528 | 0.402790 | ||||||||
\(125\) | 11.0000 | − | 2.00000i | 0.983870 | − | 0.178885i | ||||
\(126\) | 11.6569 | 1.03848 | ||||||||
\(127\) | 14.0000i | 1.24230i | 0.783692 | + | 0.621150i | \(0.213334\pi\) | ||||
−0.783692 | + | 0.621150i | \(0.786666\pi\) | |||||||
\(128\) | 20.5563i | 1.81694i | ||||||||
\(129\) | −9.65685 | −0.850239 | ||||||||
\(130\) | −2.82843 | + | 5.65685i | −0.248069 | + | 0.496139i | ||||
\(131\) | −15.3137 | −1.33796 | −0.668982 | − | 0.743278i | \(-0.733270\pi\) | ||||
−0.668982 | + | 0.743278i | \(0.733270\pi\) | |||||||
\(132\) | − | 7.65685i | − | 0.666444i | ||||||
\(133\) | 4.82843i | 0.418678i | ||||||||
\(134\) | −14.4853 | −1.25134 | ||||||||
\(135\) | 8.00000 | + | 4.00000i | 0.688530 | + | 0.344265i | ||||
\(136\) | 5.17157 | 0.443459 | ||||||||
\(137\) | 8.00000i | 0.683486i | 0.939793 | + | 0.341743i | \(0.111017\pi\) | ||||
−0.939793 | + | 0.341743i | \(0.888983\pi\) | |||||||
\(138\) | 17.6569i | 1.50305i | ||||||||
\(139\) | −4.00000 | −0.339276 | −0.169638 | − | 0.985506i | \(-0.554260\pi\) | ||||
−0.169638 | + | 0.985506i | \(0.554260\pi\) | |||||||
\(140\) | 36.9706 | + | 18.4853i | 3.12458 | + | 1.56229i | ||||
\(141\) | 0.686292 | 0.0577962 | ||||||||
\(142\) | − | 22.1421i | − | 1.85813i | ||||||
\(143\) | 1.17157i | 0.0979718i | ||||||||
\(144\) | −3.00000 | −0.250000 | ||||||||
\(145\) | 0.828427 | − | 1.65685i | 0.0687971 | − | 0.137594i | ||||
\(146\) | 16.4853 | 1.36433 | ||||||||
\(147\) | 32.6274i | 2.69106i | ||||||||
\(148\) | − | 32.4853i | − | 2.67027i | ||||||
\(149\) | 19.6569 | 1.61035 | 0.805176 | − | 0.593036i | \(-0.202071\pi\) | ||||
0.805176 | + | 0.593036i | \(0.202071\pi\) | |||||||
\(150\) | −14.4853 | − | 19.3137i | −1.18272 | − | 1.57696i | ||||
\(151\) | 21.6569 | 1.76241 | 0.881205 | − | 0.472735i | \(-0.156733\pi\) | ||||
0.881205 | + | 0.472735i | \(0.156733\pi\) | |||||||
\(152\) | − | 4.41421i | − | 0.358040i | ||||||
\(153\) | − | 1.17157i | − | 0.0947161i | ||||||
\(154\) | 11.6569 | 0.939336 | ||||||||
\(155\) | 1.17157 | − | 2.34315i | 0.0941030 | − | 0.188206i | ||||
\(156\) | 8.97056 | 0.718220 | ||||||||
\(157\) | 12.0000i | 0.957704i | 0.877896 | + | 0.478852i | \(0.158947\pi\) | ||||
−0.877896 | + | 0.478852i | \(0.841053\pi\) | |||||||
\(158\) | 13.6569i | 1.08648i | ||||||||
\(159\) | −10.3431 | −0.820265 | ||||||||
\(160\) | 3.17157 | + | 1.58579i | 0.250735 | + | 0.125367i | ||||
\(161\) | −17.6569 | −1.39156 | ||||||||
\(162\) | − | 26.5563i | − | 2.08646i | ||||||
\(163\) | 2.00000i | 0.156652i | 0.996928 | + | 0.0783260i | \(0.0249575\pi\) | ||||
−0.996928 | + | 0.0783260i | \(0.975042\pi\) | |||||||
\(164\) | 40.1421 | 3.13457 | ||||||||
\(165\) | −4.00000 | − | 2.00000i | −0.311400 | − | 0.155700i | ||||
\(166\) | 25.3137 | 1.96472 | ||||||||
\(167\) | 19.6569i | 1.52109i | 0.649283 | + | 0.760547i | \(0.275069\pi\) | ||||
−0.649283 | + | 0.760547i | \(0.724931\pi\) | |||||||
\(168\) | − | 42.6274i | − | 3.28878i | ||||||
\(169\) | 11.6274 | 0.894417 | ||||||||
\(170\) | 2.82843 | − | 5.65685i | 0.216930 | − | 0.433861i | ||||
\(171\) | −1.00000 | −0.0764719 | ||||||||
\(172\) | 18.4853i | 1.40949i | ||||||||
\(173\) | 4.48528i | 0.341010i | 0.985357 | + | 0.170505i | \(0.0545398\pi\) | ||||
−0.985357 | + | 0.170505i | \(0.945460\pi\) | |||||||
\(174\) | −4.00000 | −0.303239 | ||||||||
\(175\) | 19.3137 | − | 14.4853i | 1.45998 | − | 1.09498i | ||||
\(176\) | −3.00000 | −0.226134 | ||||||||
\(177\) | 5.65685i | 0.425195i | ||||||||
\(178\) | 37.7990i | 2.83315i | ||||||||
\(179\) | 0.485281 | 0.0362716 | 0.0181358 | − | 0.999836i | \(-0.494227\pi\) | ||||
0.0181358 | + | 0.999836i | \(0.494227\pi\) | |||||||
\(180\) | −3.82843 | + | 7.65685i | −0.285354 | + | 0.570708i | ||||
\(181\) | 14.0000 | 1.04061 | 0.520306 | − | 0.853980i | \(-0.325818\pi\) | ||||
0.520306 | + | 0.853980i | \(0.325818\pi\) | |||||||
\(182\) | 13.6569i | 1.01231i | ||||||||
\(183\) | 4.00000i | 0.295689i | ||||||||
\(184\) | 16.1421 | 1.19001 | ||||||||
\(185\) | −16.9706 | − | 8.48528i | −1.24770 | − | 0.623850i | ||||
\(186\) | −5.65685 | −0.414781 | ||||||||
\(187\) | − | 1.17157i | − | 0.0856739i | ||||||
\(188\) | − | 1.31371i | − | 0.0958120i | ||||||
\(189\) | 19.3137 | 1.40487 | ||||||||
\(190\) | −4.82843 | − | 2.41421i | −0.350291 | − | 0.175145i | ||||
\(191\) | −16.9706 | −1.22795 | −0.613973 | − | 0.789327i | \(-0.710430\pi\) | ||||
−0.613973 | + | 0.789327i | \(0.710430\pi\) | |||||||
\(192\) | − | 19.6569i | − | 1.41861i | ||||||
\(193\) | − | 14.1421i | − | 1.01797i | −0.860774 | − | 0.508987i | \(-0.830020\pi\) | ||
0.860774 | − | 0.508987i | \(-0.169980\pi\) | |||||||
\(194\) | −16.4853 | −1.18357 | ||||||||
\(195\) | 2.34315 | − | 4.68629i | 0.167796 | − | 0.335592i | ||||
\(196\) | 62.4558 | 4.46113 | ||||||||
\(197\) | 22.1421i | 1.57756i | 0.614674 | + | 0.788781i | \(0.289287\pi\) | ||||
−0.614674 | + | 0.788781i | \(0.710713\pi\) | |||||||
\(198\) | 2.41421i | 0.171571i | ||||||||
\(199\) | −5.65685 | −0.401004 | −0.200502 | − | 0.979693i | \(-0.564257\pi\) | ||||
−0.200502 | + | 0.979693i | \(0.564257\pi\) | |||||||
\(200\) | −17.6569 | + | 13.2426i | −1.24853 | + | 0.936396i | ||||
\(201\) | 12.0000 | 0.846415 | ||||||||
\(202\) | − | 32.1421i | − | 2.26151i | ||||||
\(203\) | − | 4.00000i | − | 0.280745i | ||||||
\(204\) | −8.97056 | −0.628065 | ||||||||
\(205\) | 10.4853 | − | 20.9706i | 0.732324 | − | 1.46465i | ||||
\(206\) | −37.7990 | −2.63358 | ||||||||
\(207\) | − | 3.65685i | − | 0.254169i | ||||||
\(208\) | − | 3.51472i | − | 0.243702i | ||||||
\(209\) | −1.00000 | −0.0691714 | ||||||||
\(210\) | −46.6274 | − | 23.3137i | −3.21760 | − | 1.60880i | ||||
\(211\) | −7.31371 | −0.503496 | −0.251748 | − | 0.967793i | \(-0.581005\pi\) | ||||
−0.251748 | + | 0.967793i | \(0.581005\pi\) | |||||||
\(212\) | 19.7990i | 1.35980i | ||||||||
\(213\) | 18.3431i | 1.25685i | ||||||||
\(214\) | 36.1421 | 2.47063 | ||||||||
\(215\) | 9.65685 | + | 4.82843i | 0.658592 | + | 0.329296i | ||||
\(216\) | −17.6569 | −1.20140 | ||||||||
\(217\) | − | 5.65685i | − | 0.384012i | ||||||
\(218\) | 11.6569i | 0.789502i | ||||||||
\(219\) | −13.6569 | −0.922845 | ||||||||
\(220\) | −3.82843 | + | 7.65685i | −0.258113 | + | 0.516225i | ||||
\(221\) | 1.37258 | 0.0923299 | ||||||||
\(222\) | 40.9706i | 2.74976i | ||||||||
\(223\) | − | 0.343146i | − | 0.0229787i | −0.999934 | − | 0.0114894i | \(-0.996343\pi\) | ||
0.999934 | − | 0.0114894i | \(-0.00365726\pi\) | |||||||
\(224\) | 7.65685 | 0.511595 | ||||||||
\(225\) | 3.00000 | + | 4.00000i | 0.200000 | + | 0.266667i | ||||
\(226\) | −43.7990 | −2.91347 | ||||||||
\(227\) | 23.6569i | 1.57016i | 0.619394 | + | 0.785080i | \(0.287378\pi\) | ||||
−0.619394 | + | 0.785080i | \(0.712622\pi\) | |||||||
\(228\) | 7.65685i | 0.507088i | ||||||||
\(229\) | 22.0000 | 1.45380 | 0.726900 | − | 0.686743i | \(-0.240960\pi\) | ||||
0.726900 | + | 0.686743i | \(0.240960\pi\) | |||||||
\(230\) | 8.82843 | − | 17.6569i | 0.582129 | − | 1.16426i | ||||
\(231\) | −9.65685 | −0.635374 | ||||||||
\(232\) | 3.65685i | 0.240084i | ||||||||
\(233\) | − | 12.4853i | − | 0.817938i | −0.912548 | − | 0.408969i | \(-0.865888\pi\) | ||
0.912548 | − | 0.408969i | \(-0.134112\pi\) | |||||||
\(234\) | −2.82843 | −0.184900 | ||||||||
\(235\) | −0.686292 | − | 0.343146i | −0.0447687 | − | 0.0223844i | ||||
\(236\) | 10.8284 | 0.704871 | ||||||||
\(237\) | − | 11.3137i | − | 0.734904i | ||||||
\(238\) | − | 13.6569i | − | 0.885242i | ||||||
\(239\) | −27.3137 | −1.76678 | −0.883388 | − | 0.468641i | \(-0.844744\pi\) | ||||
−0.883388 | + | 0.468641i | \(0.844744\pi\) | |||||||
\(240\) | 12.0000 | + | 6.00000i | 0.774597 | + | 0.387298i | ||||
\(241\) | −10.4853 | −0.675416 | −0.337708 | − | 0.941251i | \(-0.609652\pi\) | ||||
−0.337708 | + | 0.941251i | \(0.609652\pi\) | |||||||
\(242\) | 2.41421i | 0.155192i | ||||||||
\(243\) | 10.0000i | 0.641500i | ||||||||
\(244\) | 7.65685 | 0.490180 | ||||||||
\(245\) | 16.3137 | − | 32.6274i | 1.04224 | − | 2.08449i | ||||
\(246\) | −50.6274 | −3.22789 | ||||||||
\(247\) | − | 1.17157i | − | 0.0745454i | ||||||
\(248\) | 5.17157i | 0.328395i | ||||||||
\(249\) | −20.9706 | −1.32896 | ||||||||
\(250\) | 4.82843 | + | 26.5563i | 0.305377 | + | 1.67957i | ||||
\(251\) | −4.00000 | −0.252478 | −0.126239 | − | 0.992000i | \(-0.540291\pi\) | ||||
−0.126239 | + | 0.992000i | \(0.540291\pi\) | |||||||
\(252\) | 18.4853i | 1.16446i | ||||||||
\(253\) | − | 3.65685i | − | 0.229904i | ||||||
\(254\) | −33.7990 | −2.12074 | ||||||||
\(255\) | −2.34315 | + | 4.68629i | −0.146733 | + | 0.293467i | ||||
\(256\) | −29.9706 | −1.87316 | ||||||||
\(257\) | 10.1421i | 0.632649i | 0.948651 | + | 0.316325i | \(0.102449\pi\) | ||||
−0.948651 | + | 0.316325i | \(0.897551\pi\) | |||||||
\(258\) | − | 23.3137i | − | 1.45145i | ||||||
\(259\) | −40.9706 | −2.54579 | ||||||||
\(260\) | −8.97056 | − | 4.48528i | −0.556331 | − | 0.278165i | ||||
\(261\) | 0.828427 | 0.0512784 | ||||||||
\(262\) | − | 36.9706i | − | 2.28405i | ||||||
\(263\) | 1.51472i | 0.0934016i | 0.998909 | + | 0.0467008i | \(0.0148707\pi\) | ||||
−0.998909 | + | 0.0467008i | \(0.985129\pi\) | |||||||
\(264\) | 8.82843 | 0.543352 | ||||||||
\(265\) | 10.3431 | + | 5.17157i | 0.635374 | + | 0.317687i | ||||
\(266\) | −11.6569 | −0.714728 | ||||||||
\(267\) | − | 31.3137i | − | 1.91637i | ||||||
\(268\) | − | 22.9706i | − | 1.40315i | ||||||
\(269\) | −10.9706 | −0.668887 | −0.334444 | − | 0.942416i | \(-0.608548\pi\) | ||||
−0.334444 | + | 0.942416i | \(0.608548\pi\) | |||||||
\(270\) | −9.65685 | + | 19.3137i | −0.587697 | + | 1.17539i | ||||
\(271\) | −11.3137 | −0.687259 | −0.343629 | − | 0.939105i | \(-0.611656\pi\) | ||||
−0.343629 | + | 0.939105i | \(0.611656\pi\) | |||||||
\(272\) | 3.51472i | 0.213111i | ||||||||
\(273\) | − | 11.3137i | − | 0.684737i | ||||||
\(274\) | −19.3137 | −1.16678 | ||||||||
\(275\) | 3.00000 | + | 4.00000i | 0.180907 | + | 0.241209i | ||||
\(276\) | −28.0000 | −1.68540 | ||||||||
\(277\) | − | 13.1716i | − | 0.791403i | −0.918379 | − | 0.395702i | \(-0.870501\pi\) | ||
0.918379 | − | 0.395702i | \(-0.129499\pi\) | |||||||
\(278\) | − | 9.65685i | − | 0.579180i | ||||||
\(279\) | 1.17157 | 0.0701402 | ||||||||
\(280\) | −21.3137 | + | 42.6274i | −1.27374 | + | 2.54748i | ||||
\(281\) | 31.4558 | 1.87650 | 0.938249 | − | 0.345960i | \(-0.112447\pi\) | ||||
0.938249 | + | 0.345960i | \(0.112447\pi\) | |||||||
\(282\) | 1.65685i | 0.0986642i | ||||||||
\(283\) | − | 10.4853i | − | 0.623285i | −0.950199 | − | 0.311643i | \(-0.899121\pi\) | ||
0.950199 | − | 0.311643i | \(-0.100879\pi\) | |||||||
\(284\) | 35.1127 | 2.08356 | ||||||||
\(285\) | 4.00000 | + | 2.00000i | 0.236940 | + | 0.118470i | ||||
\(286\) | −2.82843 | −0.167248 | ||||||||
\(287\) | − | 50.6274i | − | 2.98844i | ||||||
\(288\) | 1.58579i | 0.0934434i | ||||||||
\(289\) | 15.6274 | 0.919260 | ||||||||
\(290\) | 4.00000 | + | 2.00000i | 0.234888 | + | 0.117444i | ||||
\(291\) | 13.6569 | 0.800579 | ||||||||
\(292\) | 26.1421i | 1.52985i | ||||||||
\(293\) | − | 2.14214i | − | 0.125145i | −0.998040 | − | 0.0625724i | \(-0.980070\pi\) | ||
0.998040 | − | 0.0625724i | \(-0.0199304\pi\) | |||||||
\(294\) | −78.7696 | −4.59393 | ||||||||
\(295\) | 2.82843 | − | 5.65685i | 0.164677 | − | 0.329355i | ||||
\(296\) | 37.4558 | 2.17708 | ||||||||
\(297\) | 4.00000i | 0.232104i | ||||||||
\(298\) | 47.4558i | 2.74904i | ||||||||
\(299\) | 4.28427 | 0.247766 | ||||||||
\(300\) | 30.6274 | − | 22.9706i | 1.76827 | − | 1.32621i | ||||
\(301\) | 23.3137 | 1.34378 | ||||||||
\(302\) | 52.2843i | 3.00862i | ||||||||
\(303\) | 26.6274i | 1.52971i | ||||||||
\(304\) | 3.00000 | 0.172062 | ||||||||
\(305\) | 2.00000 | − | 4.00000i | 0.114520 | − | 0.229039i | ||||
\(306\) | 2.82843 | 0.161690 | ||||||||
\(307\) | − | 6.97056i | − | 0.397831i | −0.980017 | − | 0.198916i | \(-0.936258\pi\) | ||
0.980017 | − | 0.198916i | \(-0.0637419\pi\) | |||||||
\(308\) | 18.4853i | 1.05330i | ||||||||
\(309\) | 31.3137 | 1.78137 | ||||||||
\(310\) | 5.65685 | + | 2.82843i | 0.321288 | + | 0.160644i | ||||
\(311\) | −32.9706 | −1.86959 | −0.934795 | − | 0.355189i | \(-0.884417\pi\) | ||||
−0.934795 | + | 0.355189i | \(0.884417\pi\) | |||||||
\(312\) | 10.3431i | 0.585565i | ||||||||
\(313\) | 16.9706i | 0.959233i | 0.877478 | + | 0.479616i | \(0.159224\pi\) | ||||
−0.877478 | + | 0.479616i | \(0.840776\pi\) | |||||||
\(314\) | −28.9706 | −1.63490 | ||||||||
\(315\) | 9.65685 | + | 4.82843i | 0.544102 | + | 0.272051i | ||||
\(316\) | −21.6569 | −1.21829 | ||||||||
\(317\) | 22.1421i | 1.24363i | 0.783166 | + | 0.621813i | \(0.213604\pi\) | ||||
−0.783166 | + | 0.621813i | \(0.786396\pi\) | |||||||
\(318\) | − | 24.9706i | − | 1.40028i | ||||||
\(319\) | 0.828427 | 0.0463830 | ||||||||
\(320\) | −9.82843 | + | 19.6569i | −0.549426 | + | 1.09885i | ||||
\(321\) | −29.9411 | −1.67115 | ||||||||
\(322\) | − | 42.6274i | − | 2.37553i | ||||||
\(323\) | 1.17157i | 0.0651881i | ||||||||
\(324\) | 42.1127 | 2.33959 | ||||||||
\(325\) | −4.68629 | + | 3.51472i | −0.259949 | + | 0.194962i | ||||
\(326\) | −4.82843 | −0.267422 | ||||||||
\(327\) | − | 9.65685i | − | 0.534025i | ||||||
\(328\) | 46.2843i | 2.55562i | ||||||||
\(329\) | −1.65685 | −0.0913453 | ||||||||
\(330\) | 4.82843 | − | 9.65685i | 0.265796 | − | 0.531592i | ||||
\(331\) | 22.1421 | 1.21704 | 0.608521 | − | 0.793538i | \(-0.291763\pi\) | ||||
0.608521 | + | 0.793538i | \(0.291763\pi\) | |||||||
\(332\) | 40.1421i | 2.20309i | ||||||||
\(333\) | − | 8.48528i | − | 0.464991i | ||||||
\(334\) | −47.4558 | −2.59667 | ||||||||
\(335\) | −12.0000 | − | 6.00000i | −0.655630 | − | 0.327815i | ||||
\(336\) | 28.9706 | 1.58047 | ||||||||
\(337\) | − | 2.82843i | − | 0.154074i | −0.997028 | − | 0.0770371i | \(-0.975454\pi\) | ||
0.997028 | − | 0.0770371i | \(-0.0245460\pi\) | |||||||
\(338\) | 28.0711i | 1.52686i | ||||||||
\(339\) | 36.2843 | 1.97069 | ||||||||
\(340\) | 8.97056 | + | 4.48528i | 0.486497 | + | 0.243249i | ||||
\(341\) | 1.17157 | 0.0634442 | ||||||||
\(342\) | − | 2.41421i | − | 0.130546i | ||||||
\(343\) | − | 44.9706i | − | 2.42818i | ||||||
\(344\) | −21.3137 | −1.14916 | ||||||||
\(345\) | −7.31371 | + | 14.6274i | −0.393757 | + | 0.787514i | ||||
\(346\) | −10.8284 | −0.582140 | ||||||||
\(347\) | 19.1716i | 1.02918i | 0.857435 | + | 0.514592i | \(0.172057\pi\) | ||||
−0.857435 | + | 0.514592i | \(0.827943\pi\) | |||||||
\(348\) | − | 6.34315i | − | 0.340028i | ||||||
\(349\) | 16.3431 | 0.874829 | 0.437414 | − | 0.899260i | \(-0.355894\pi\) | ||||
0.437414 | + | 0.899260i | \(0.355894\pi\) | |||||||
\(350\) | 34.9706 | + | 46.6274i | 1.86926 | + | 2.49234i | ||||
\(351\) | −4.68629 | −0.250136 | ||||||||
\(352\) | 1.58579i | 0.0845227i | ||||||||
\(353\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(354\) | −13.6569 | −0.725854 | ||||||||
\(355\) | 9.17157 | − | 18.3431i | 0.486777 | − | 0.973553i | ||||
\(356\) | −59.9411 | −3.17687 | ||||||||
\(357\) | 11.3137i | 0.598785i | ||||||||
\(358\) | 1.17157i | 0.0619196i | ||||||||
\(359\) | 16.9706 | 0.895672 | 0.447836 | − | 0.894116i | \(-0.352195\pi\) | ||||
0.447836 | + | 0.894116i | \(0.352195\pi\) | |||||||
\(360\) | −8.82843 | − | 4.41421i | −0.465299 | − | 0.232649i | ||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | 33.7990i | 1.77644i | ||||||||
\(363\) | − | 2.00000i | − | 0.104973i | ||||||
\(364\) | −21.6569 | −1.13513 | ||||||||
\(365\) | 13.6569 | + | 6.82843i | 0.714832 | + | 0.357416i | ||||
\(366\) | −9.65685 | −0.504772 | ||||||||
\(367\) | − | 31.6569i | − | 1.65247i | −0.563322 | − | 0.826237i | \(-0.690477\pi\) | ||
0.563322 | − | 0.826237i | \(-0.309523\pi\) | |||||||
\(368\) | 10.9706i | 0.571880i | ||||||||
\(369\) | 10.4853 | 0.545842 | ||||||||
\(370\) | 20.4853 | − | 40.9706i | 1.06498 | − | 2.12996i | ||||
\(371\) | 24.9706 | 1.29641 | ||||||||
\(372\) | − | 8.97056i | − | 0.465102i | ||||||
\(373\) | 22.8284i | 1.18201i | 0.806667 | + | 0.591006i | \(0.201269\pi\) | ||||
−0.806667 | + | 0.591006i | \(0.798731\pi\) | |||||||
\(374\) | 2.82843 | 0.146254 | ||||||||
\(375\) | −4.00000 | − | 22.0000i | −0.206559 | − | 1.13608i | ||||
\(376\) | 1.51472 | 0.0781156 | ||||||||
\(377\) | 0.970563i | 0.0499865i | ||||||||
\(378\) | 46.6274i | 2.39826i | ||||||||
\(379\) | −5.17157 | −0.265646 | −0.132823 | − | 0.991140i | \(-0.542404\pi\) | ||||
−0.132823 | + | 0.991140i | \(0.542404\pi\) | |||||||
\(380\) | 3.82843 | − | 7.65685i | 0.196394 | − | 0.392788i | ||||
\(381\) | 28.0000 | 1.43448 | ||||||||
\(382\) | − | 40.9706i | − | 2.09624i | ||||||
\(383\) | − | 6.97056i | − | 0.356179i | −0.984014 | − | 0.178090i | \(-0.943008\pi\) | ||
0.984014 | − | 0.178090i | \(-0.0569917\pi\) | |||||||
\(384\) | 41.1127 | 2.09802 | ||||||||
\(385\) | 9.65685 | + | 4.82843i | 0.492159 | + | 0.246079i | ||||
\(386\) | 34.1421 | 1.73779 | ||||||||
\(387\) | 4.82843i | 0.245443i | ||||||||
\(388\) | − | 26.1421i | − | 1.32717i | ||||||
\(389\) | 9.31371 | 0.472224 | 0.236112 | − | 0.971726i | \(-0.424127\pi\) | ||||
0.236112 | + | 0.971726i | \(0.424127\pi\) | |||||||
\(390\) | 11.3137 | + | 5.65685i | 0.572892 | + | 0.286446i | ||||
\(391\) | −4.28427 | −0.216665 | ||||||||
\(392\) | 72.0122i | 3.63717i | ||||||||
\(393\) | 30.6274i | 1.54495i | ||||||||
\(394\) | −53.4558 | −2.69307 | ||||||||
\(395\) | −5.65685 | + | 11.3137i | −0.284627 | + | 0.569254i | ||||
\(396\) | −3.82843 | −0.192386 | ||||||||
\(397\) | − | 15.3137i | − | 0.768573i | −0.923214 | − | 0.384286i | \(-0.874447\pi\) | ||
0.923214 | − | 0.384286i | \(-0.125553\pi\) | |||||||
\(398\) | − | 13.6569i | − | 0.684556i | ||||||
\(399\) | 9.65685 | 0.483447 | ||||||||
\(400\) | −9.00000 | − | 12.0000i | −0.450000 | − | 0.600000i | ||||
\(401\) | −17.3137 | −0.864605 | −0.432303 | − | 0.901729i | \(-0.642299\pi\) | ||||
−0.432303 | + | 0.901729i | \(0.642299\pi\) | |||||||
\(402\) | 28.9706i | 1.44492i | ||||||||
\(403\) | 1.37258i | 0.0683732i | ||||||||
\(404\) | 50.9706 | 2.53588 | ||||||||
\(405\) | 11.0000 | − | 22.0000i | 0.546594 | − | 1.09319i | ||||
\(406\) | 9.65685 | 0.479262 | ||||||||
\(407\) | − | 8.48528i | − | 0.420600i | ||||||
\(408\) | − | 10.3431i | − | 0.512062i | ||||||
\(409\) | 19.1716 | 0.947973 | 0.473987 | − | 0.880532i | \(-0.342814\pi\) | ||||
0.473987 | + | 0.880532i | \(0.342814\pi\) | |||||||
\(410\) | 50.6274 | + | 25.3137i | 2.50031 | + | 1.25015i | ||||
\(411\) | 16.0000 | 0.789222 | ||||||||
\(412\) | − | 59.9411i | − | 2.95309i | ||||||
\(413\) | − | 13.6569i | − | 0.672010i | ||||||
\(414\) | 8.82843 | 0.433894 | ||||||||
\(415\) | 20.9706 | + | 10.4853i | 1.02940 | + | 0.514702i | ||||
\(416\) | −1.85786 | −0.0910893 | ||||||||
\(417\) | 8.00000i | 0.391762i | ||||||||
\(418\) | − | 2.41421i | − | 0.118083i | ||||||
\(419\) | −12.9706 | −0.633653 | −0.316827 | − | 0.948483i | \(-0.602617\pi\) | ||||
−0.316827 | + | 0.948483i | \(0.602617\pi\) | |||||||
\(420\) | 36.9706 | − | 73.9411i | 1.80398 | − | 3.60796i | ||||
\(421\) | 6.97056 | 0.339724 | 0.169862 | − | 0.985468i | \(-0.445668\pi\) | ||||
0.169862 | + | 0.985468i | \(0.445668\pi\) | |||||||
\(422\) | − | 17.6569i | − | 0.859522i | ||||||
\(423\) | − | 0.343146i | − | 0.0166843i | ||||||
\(424\) | −22.8284 | −1.10865 | ||||||||
\(425\) | 4.68629 | − | 3.51472i | 0.227319 | − | 0.170489i | ||||
\(426\) | −44.2843 | −2.14558 | ||||||||
\(427\) | − | 9.65685i | − | 0.467328i | ||||||
\(428\) | 57.3137i | 2.77036i | ||||||||
\(429\) | 2.34315 | 0.113128 | ||||||||
\(430\) | −11.6569 | + | 23.3137i | −0.562143 | + | 1.12429i | ||||
\(431\) | −38.6274 | −1.86062 | −0.930309 | − | 0.366778i | \(-0.880461\pi\) | ||||
−0.930309 | + | 0.366778i | \(0.880461\pi\) | |||||||
\(432\) | − | 12.0000i | − | 0.577350i | ||||||
\(433\) | − | 6.82843i | − | 0.328153i | −0.986448 | − | 0.164077i | \(-0.947536\pi\) | ||
0.986448 | − | 0.164077i | \(-0.0524644\pi\) | |||||||
\(434\) | 13.6569 | 0.655550 | ||||||||
\(435\) | −3.31371 | − | 1.65685i | −0.158880 | − | 0.0794401i | ||||
\(436\) | −18.4853 | −0.885284 | ||||||||
\(437\) | 3.65685i | 0.174931i | ||||||||
\(438\) | − | 32.9706i | − | 1.57539i | ||||||
\(439\) | −29.6569 | −1.41544 | −0.707722 | − | 0.706491i | \(-0.750277\pi\) | ||||
−0.707722 | + | 0.706491i | \(0.750277\pi\) | |||||||
\(440\) | −8.82843 | − | 4.41421i | −0.420879 | − | 0.210439i | ||||
\(441\) | 16.3137 | 0.776843 | ||||||||
\(442\) | 3.31371i | 0.157617i | ||||||||
\(443\) | 13.3137i | 0.632553i | 0.948667 | + | 0.316277i | \(0.102433\pi\) | ||||
−0.948667 | + | 0.316277i | \(0.897567\pi\) | |||||||
\(444\) | −64.9706 | −3.08337 | ||||||||
\(445\) | −15.6569 | + | 31.3137i | −0.742206 | + | 1.48441i | ||||
\(446\) | 0.828427 | 0.0392272 | ||||||||
\(447\) | − | 39.3137i | − | 1.85947i | ||||||
\(448\) | 47.4558i | 2.24208i | ||||||||
\(449\) | −30.9706 | −1.46159 | −0.730796 | − | 0.682596i | \(-0.760851\pi\) | ||||
−0.730796 | + | 0.682596i | \(0.760851\pi\) | |||||||
\(450\) | −9.65685 | + | 7.24264i | −0.455228 | + | 0.341421i | ||||
\(451\) | 10.4853 | 0.493733 | ||||||||
\(452\) | − | 69.4558i | − | 3.26693i | ||||||
\(453\) | − | 43.3137i | − | 2.03506i | ||||||
\(454\) | −57.1127 | −2.68043 | ||||||||
\(455\) | −5.65685 | + | 11.3137i | −0.265197 | + | 0.530395i | ||||
\(456\) | −8.82843 | −0.413429 | ||||||||
\(457\) | 23.7990i | 1.11327i | 0.830757 | + | 0.556635i | \(0.187908\pi\) | ||||
−0.830757 | + | 0.556635i | \(0.812092\pi\) | |||||||
\(458\) | 53.1127i | 2.48179i | ||||||||
\(459\) | 4.68629 | 0.218737 | ||||||||
\(460\) | 28.0000 | + | 14.0000i | 1.30551 | + | 0.652753i | ||||
\(461\) | 34.2843 | 1.59678 | 0.798389 | − | 0.602142i | \(-0.205686\pi\) | ||||
0.798389 | + | 0.602142i | \(0.205686\pi\) | |||||||
\(462\) | − | 23.3137i | − | 1.08465i | ||||||
\(463\) | 26.2843i | 1.22153i | 0.791811 | + | 0.610767i | \(0.209139\pi\) | ||||
−0.791811 | + | 0.610767i | \(0.790861\pi\) | |||||||
\(464\) | −2.48528 | −0.115376 | ||||||||
\(465\) | −4.68629 | − | 2.34315i | −0.217322 | − | 0.108661i | ||||
\(466\) | 30.1421 | 1.39631 | ||||||||
\(467\) | 15.6569i | 0.724513i | 0.932078 | + | 0.362256i | \(0.117994\pi\) | ||||
−0.932078 | + | 0.362256i | \(0.882006\pi\) | |||||||
\(468\) | − | 4.48528i | − | 0.207332i | ||||||
\(469\) | −28.9706 | −1.33774 | ||||||||
\(470\) | 0.828427 | − | 1.65685i | 0.0382125 | − | 0.0764250i | ||||
\(471\) | 24.0000 | 1.10586 | ||||||||
\(472\) | 12.4853i | 0.574682i | ||||||||
\(473\) | 4.82843i | 0.222011i | ||||||||
\(474\) | 27.3137 | 1.25456 | ||||||||
\(475\) | −3.00000 | − | 4.00000i | −0.137649 | − | 0.183533i | ||||
\(476\) | 21.6569 | 0.992640 | ||||||||
\(477\) | 5.17157i | 0.236790i | ||||||||
\(478\) | − | 65.9411i | − | 3.01608i | ||||||
\(479\) | −19.3137 | −0.882466 | −0.441233 | − | 0.897393i | \(-0.645459\pi\) | ||||
−0.441233 | + | 0.897393i | \(0.645459\pi\) | |||||||
\(480\) | 3.17157 | − | 6.34315i | 0.144762 | − | 0.289524i | ||||
\(481\) | 9.94113 | 0.453276 | ||||||||
\(482\) | − | 25.3137i | − | 1.15301i | ||||||
\(483\) | 35.3137i | 1.60683i | ||||||||
\(484\) | −3.82843 | −0.174019 | ||||||||
\(485\) | −13.6569 | − | 6.82843i | −0.620126 | − | 0.310063i | ||||
\(486\) | −24.1421 | −1.09511 | ||||||||
\(487\) | 4.34315i | 0.196807i | 0.995147 | + | 0.0984034i | \(0.0313735\pi\) | ||||
−0.995147 | + | 0.0984034i | \(0.968626\pi\) | |||||||
\(488\) | 8.82843i | 0.399644i | ||||||||
\(489\) | 4.00000 | 0.180886 | ||||||||
\(490\) | 78.7696 | + | 39.3848i | 3.55845 | + | 1.77922i | ||||
\(491\) | −3.02944 | −0.136717 | −0.0683583 | − | 0.997661i | \(-0.521776\pi\) | ||||
−0.0683583 | + | 0.997661i | \(0.521776\pi\) | |||||||
\(492\) | − | 80.2843i | − | 3.61949i | ||||||
\(493\) | − | 0.970563i | − | 0.0437119i | ||||||
\(494\) | 2.82843 | 0.127257 | ||||||||
\(495\) | −1.00000 | + | 2.00000i | −0.0449467 | + | 0.0898933i | ||||
\(496\) | −3.51472 | −0.157816 | ||||||||
\(497\) | − | 44.2843i | − | 1.98642i | ||||||
\(498\) | − | 50.6274i | − | 2.26867i | ||||||
\(499\) | −23.3137 | −1.04366 | −0.521832 | − | 0.853048i | \(-0.674751\pi\) | ||||
−0.521832 | + | 0.853048i | \(0.674751\pi\) | |||||||
\(500\) | −42.1127 | + | 7.65685i | −1.88334 | + | 0.342425i | ||||
\(501\) | 39.3137 | 1.75641 | ||||||||
\(502\) | − | 9.65685i | − | 0.431006i | ||||||
\(503\) | − | 2.20101i | − | 0.0981382i | −0.998795 | − | 0.0490691i | \(-0.984375\pi\) | ||
0.998795 | − | 0.0490691i | \(-0.0156255\pi\) | |||||||
\(504\) | −21.3137 | −0.949388 | ||||||||
\(505\) | 13.3137 | − | 26.6274i | 0.592452 | − | 1.18490i | ||||
\(506\) | 8.82843 | 0.392471 | ||||||||
\(507\) | − | 23.2548i | − | 1.03278i | ||||||
\(508\) | − | 53.5980i | − | 2.37803i | ||||||
\(509\) | −20.3431 | −0.901694 | −0.450847 | − | 0.892601i | \(-0.648878\pi\) | ||||
−0.450847 | + | 0.892601i | \(0.648878\pi\) | |||||||
\(510\) | −11.3137 | − | 5.65685i | −0.500979 | − | 0.250490i | ||||
\(511\) | 32.9706 | 1.45853 | ||||||||
\(512\) | − | 31.2426i | − | 1.38074i | ||||||
\(513\) | − | 4.00000i | − | 0.176604i | ||||||
\(514\) | −24.4853 | −1.08000 | ||||||||
\(515\) | −31.3137 | − | 15.6569i | −1.37985 | − | 0.689923i | ||||
\(516\) | 36.9706 | 1.62754 | ||||||||
\(517\) | − | 0.343146i | − | 0.0150915i | ||||||
\(518\) | − | 98.9117i | − | 4.34593i | ||||||
\(519\) | 8.97056 | 0.393764 | ||||||||
\(520\) | 5.17157 | − | 10.3431i | 0.226788 | − | 0.453577i | ||||
\(521\) | −14.0000 | −0.613351 | −0.306676 | − | 0.951814i | \(-0.599217\pi\) | ||||
−0.306676 | + | 0.951814i | \(0.599217\pi\) | |||||||
\(522\) | 2.00000i | 0.0875376i | ||||||||
\(523\) | 26.9706i | 1.17934i | 0.807644 | + | 0.589670i | \(0.200742\pi\) | ||||
−0.807644 | + | 0.589670i | \(0.799258\pi\) | |||||||
\(524\) | 58.6274 | 2.56115 | ||||||||
\(525\) | −28.9706 | − | 38.6274i | −1.26438 | − | 1.68584i | ||||
\(526\) | −3.65685 | −0.159446 | ||||||||
\(527\) | − | 1.37258i | − | 0.0597907i | ||||||
\(528\) | 6.00000i | 0.261116i | ||||||||
\(529\) | 9.62742 | 0.418583 | ||||||||
\(530\) | −12.4853 | + | 24.9706i | −0.542326 | + | 1.08465i | ||||
\(531\) | 2.82843 | 0.122743 | ||||||||
\(532\) | − | 18.4853i | − | 0.801439i | ||||||
\(533\) | 12.2843i | 0.532091i | ||||||||
\(534\) | 75.5980 | 3.27144 | ||||||||
\(535\) | 29.9411 | + | 14.9706i | 1.29447 | + | 0.647234i | ||||
\(536\) | 26.4853 | 1.14399 | ||||||||
\(537\) | − | 0.970563i | − | 0.0418829i | ||||||
\(538\) | − | 26.4853i | − | 1.14186i | ||||||
\(539\) | 16.3137 | 0.702681 | ||||||||
\(540\) | −30.6274 | − | 15.3137i | −1.31799 | − | 0.658997i | ||||
\(541\) | −23.6569 | −1.01709 | −0.508544 | − | 0.861036i | \(-0.669816\pi\) | ||||
−0.508544 | + | 0.861036i | \(0.669816\pi\) | |||||||
\(542\) | − | 27.3137i | − | 1.17322i | ||||||
\(543\) | − | 28.0000i | − | 1.20160i | ||||||
\(544\) | 1.85786 | 0.0796553 | ||||||||
\(545\) | −4.82843 | + | 9.65685i | −0.206827 | + | 0.413654i | ||||
\(546\) | 27.3137 | 1.16892 | ||||||||
\(547\) | 22.2843i | 0.952807i | 0.879227 | + | 0.476403i | \(0.158060\pi\) | ||||
−0.879227 | + | 0.476403i | \(0.841940\pi\) | |||||||
\(548\) | − | 30.6274i | − | 1.30834i | ||||||
\(549\) | 2.00000 | 0.0853579 | ||||||||
\(550\) | −9.65685 | + | 7.24264i | −0.411770 | + | 0.308827i | ||||
\(551\) | −0.828427 | −0.0352922 | ||||||||
\(552\) | − | 32.2843i | − | 1.37411i | ||||||
\(553\) | 27.3137i | 1.16150i | ||||||||
\(554\) | 31.7990 | 1.35101 | ||||||||
\(555\) | −16.9706 | + | 33.9411i | −0.720360 | + | 1.44072i | ||||
\(556\) | 15.3137 | 0.649446 | ||||||||
\(557\) | − | 39.1127i | − | 1.65726i | −0.559798 | − | 0.828629i | \(-0.689121\pi\) | ||
0.559798 | − | 0.828629i | \(-0.310879\pi\) | |||||||
\(558\) | 2.82843i | 0.119737i | ||||||||
\(559\) | −5.65685 | −0.239259 | ||||||||
\(560\) | −28.9706 | − | 14.4853i | −1.22423 | − | 0.612115i | ||||
\(561\) | −2.34315 | −0.0989277 | ||||||||
\(562\) | 75.9411i | 3.20338i | ||||||||
\(563\) | − | 14.9706i | − | 0.630934i | −0.948937 | − | 0.315467i | \(-0.897839\pi\) | ||
0.948937 | − | 0.315467i | \(-0.102161\pi\) | |||||||
\(564\) | −2.62742 | −0.110634 | ||||||||
\(565\) | −36.2843 | − | 18.1421i | −1.52649 | − | 0.763245i | ||||
\(566\) | 25.3137 | 1.06401 | ||||||||
\(567\) | − | 53.1127i | − | 2.23052i | ||||||
\(568\) | 40.4853i | 1.69872i | ||||||||
\(569\) | 27.1716 | 1.13909 | 0.569546 | − | 0.821960i | \(-0.307119\pi\) | ||||
0.569546 | + | 0.821960i | \(0.307119\pi\) | |||||||
\(570\) | −4.82843 | + | 9.65685i | −0.202241 | + | 0.404481i | ||||
\(571\) | 32.2843 | 1.35105 | 0.675527 | − | 0.737335i | \(-0.263916\pi\) | ||||
0.675527 | + | 0.737335i | \(0.263916\pi\) | |||||||
\(572\) | − | 4.48528i | − | 0.187539i | ||||||
\(573\) | 33.9411i | 1.41791i | ||||||||
\(574\) | 122.225 | 5.10159 | ||||||||
\(575\) | 14.6274 | − | 10.9706i | 0.610005 | − | 0.457504i | ||||
\(576\) | −9.82843 | −0.409518 | ||||||||
\(577\) | 32.0000i | 1.33218i | 0.745873 | + | 0.666089i | \(0.232033\pi\) | ||||
−0.745873 | + | 0.666089i | \(0.767967\pi\) | |||||||
\(578\) | 37.7279i | 1.56927i | ||||||||
\(579\) | −28.2843 | −1.17545 | ||||||||
\(580\) | −3.17157 | + | 6.34315i | −0.131692 | + | 0.263385i | ||||
\(581\) | 50.6274 | 2.10038 | ||||||||
\(582\) | 32.9706i | 1.36667i | ||||||||
\(583\) | 5.17157i | 0.214185i | ||||||||
\(584\) | −30.1421 | −1.24729 | ||||||||
\(585\) | −2.34315 | − | 1.17157i | −0.0968772 | − | 0.0484386i | ||||
\(586\) | 5.17157 | 0.213636 | ||||||||
\(587\) | − | 34.2843i | − | 1.41506i | −0.706682 | − | 0.707532i | \(-0.749809\pi\) | ||
0.706682 | − | 0.707532i | \(-0.250191\pi\) | |||||||
\(588\) | − | 124.912i | − | 5.15127i | ||||||
\(589\) | −1.17157 | −0.0482738 | ||||||||
\(590\) | 13.6569 | + | 6.82843i | 0.562244 | + | 0.281122i | ||||
\(591\) | 44.2843 | 1.82161 | ||||||||
\(592\) | 25.4558i | 1.04623i | ||||||||
\(593\) | − | 45.4558i | − | 1.86665i | −0.359036 | − | 0.933324i | \(-0.616894\pi\) | ||
0.359036 | − | 0.933324i | \(-0.383106\pi\) | |||||||
\(594\) | −9.65685 | −0.396226 | ||||||||
\(595\) | 5.65685 | − | 11.3137i | 0.231908 | − | 0.463817i | ||||
\(596\) | −75.2548 | −3.08256 | ||||||||
\(597\) | 11.3137i | 0.463039i | ||||||||
\(598\) | 10.3431i | 0.422963i | ||||||||
\(599\) | −25.1716 | −1.02848 | −0.514241 | − | 0.857646i | \(-0.671926\pi\) | ||||
−0.514241 | + | 0.857646i | \(0.671926\pi\) | |||||||
\(600\) | 26.4853 | + | 35.3137i | 1.08126 | + | 1.44168i | ||||
\(601\) | 37.1127 | 1.51386 | 0.756929 | − | 0.653497i | \(-0.226699\pi\) | ||||
0.756929 | + | 0.653497i | \(0.226699\pi\) | |||||||
\(602\) | 56.2843i | 2.29398i | ||||||||
\(603\) | − | 6.00000i | − | 0.244339i | ||||||
\(604\) | −82.9117 | −3.37363 | ||||||||
\(605\) | −1.00000 | + | 2.00000i | −0.0406558 | + | 0.0813116i | ||||
\(606\) | −64.2843 | −2.61137 | ||||||||
\(607\) | − | 39.6569i | − | 1.60962i | −0.593531 | − | 0.804811i | \(-0.702267\pi\) | ||
0.593531 | − | 0.804811i | \(-0.297733\pi\) | |||||||
\(608\) | − | 1.58579i | − | 0.0643121i | ||||||
\(609\) | −8.00000 | −0.324176 | ||||||||
\(610\) | 9.65685 | + | 4.82843i | 0.390995 | + | 0.195497i | ||||
\(611\) | 0.402020 | 0.0162640 | ||||||||
\(612\) | 4.48528i | 0.181307i | ||||||||
\(613\) | 18.8284i | 0.760473i | 0.924889 | + | 0.380237i | \(0.124157\pi\) | ||||
−0.924889 | + | 0.380237i | \(0.875843\pi\) | |||||||
\(614\) | 16.8284 | 0.679140 | ||||||||
\(615\) | −41.9411 | − | 20.9706i | −1.69123 | − | 0.845615i | ||||
\(616\) | −21.3137 | −0.858754 | ||||||||
\(617\) | 10.3431i | 0.416399i | 0.978086 | + | 0.208200i | \(0.0667604\pi\) | ||||
−0.978086 | + | 0.208200i | \(0.933240\pi\) | |||||||
\(618\) | 75.5980i | 3.04100i | ||||||||
\(619\) | −18.6274 | −0.748699 | −0.374350 | − | 0.927288i | \(-0.622134\pi\) | ||||
−0.374350 | + | 0.927288i | \(0.622134\pi\) | |||||||
\(620\) | −4.48528 | + | 8.97056i | −0.180133 | + | 0.360266i | ||||
\(621\) | 14.6274 | 0.586978 | ||||||||
\(622\) | − | 79.5980i | − | 3.19159i | ||||||
\(623\) | 75.5980i | 3.02877i | ||||||||
\(624\) | −7.02944 | −0.281403 | ||||||||
\(625\) | −7.00000 | + | 24.0000i | −0.280000 | + | 0.960000i | ||||
\(626\) | −40.9706 | −1.63751 | ||||||||
\(627\) | 2.00000i | 0.0798723i | ||||||||
\(628\) | − | 45.9411i | − | 1.83325i | ||||||
\(629\) | −9.94113 | −0.396379 | ||||||||
\(630\) | −11.6569 | + | 23.3137i | −0.464420 | + | 0.928840i | ||||
\(631\) | −0.970563 | −0.0386375 | −0.0193187 | − | 0.999813i | \(-0.506150\pi\) | ||||
−0.0193187 | + | 0.999813i | \(0.506150\pi\) | |||||||
\(632\) | − | 24.9706i | − | 0.993276i | ||||||
\(633\) | 14.6274i | 0.581388i | ||||||||
\(634\) | −53.4558 | −2.12300 | ||||||||
\(635\) | −28.0000 | − | 14.0000i | −1.11115 | − | 0.555573i | ||||
\(636\) | 39.5980 | 1.57016 | ||||||||
\(637\) | 19.1127i | 0.757273i | ||||||||
\(638\) | 2.00000i | 0.0791808i | ||||||||
\(639\) | 9.17157 | 0.362822 | ||||||||
\(640\) | −41.1127 | − | 20.5563i | −1.62512 | − | 0.812561i | ||||
\(641\) | −3.65685 | −0.144437 | −0.0722185 | − | 0.997389i | \(-0.523008\pi\) | ||||
−0.0722185 | + | 0.997389i | \(0.523008\pi\) | |||||||
\(642\) | − | 72.2843i | − | 2.85283i | ||||||
\(643\) | 19.9411i | 0.786401i | 0.919453 | + | 0.393201i | \(0.128632\pi\) | ||||
−0.919453 | + | 0.393201i | \(0.871368\pi\) | |||||||
\(644\) | 67.5980 | 2.66373 | ||||||||
\(645\) | 9.65685 | − | 19.3137i | 0.380238 | − | 0.760477i | ||||
\(646\) | −2.82843 | −0.111283 | ||||||||
\(647\) | 25.3137i | 0.995185i | 0.867411 | + | 0.497592i | \(0.165782\pi\) | ||||
−0.867411 | + | 0.497592i | \(0.834218\pi\) | |||||||
\(648\) | 48.5563i | 1.90747i | ||||||||
\(649\) | 2.82843 | 0.111025 | ||||||||
\(650\) | −8.48528 | − | 11.3137i | −0.332820 | − | 0.443760i | ||||
\(651\) | −11.3137 | −0.443419 | ||||||||
\(652\) | − | 7.65685i | − | 0.299866i | ||||||
\(653\) | − | 10.6274i | − | 0.415883i | −0.978141 | − | 0.207941i | \(-0.933324\pi\) | ||
0.978141 | − | 0.207941i | \(-0.0666764\pi\) | |||||||
\(654\) | 23.3137 | 0.911638 | ||||||||
\(655\) | 15.3137 | − | 30.6274i | 0.598356 | − | 1.19671i | ||||
\(656\) | −31.4558 | −1.22814 | ||||||||
\(657\) | 6.82843i | 0.266402i | ||||||||
\(658\) | − | 4.00000i | − | 0.155936i | ||||||
\(659\) | 18.6274 | 0.725621 | 0.362811 | − | 0.931863i | \(-0.381817\pi\) | ||||
0.362811 | + | 0.931863i | \(0.381817\pi\) | |||||||
\(660\) | 15.3137 | + | 7.65685i | 0.596085 | + | 0.298043i | ||||
\(661\) | 17.3137 | 0.673425 | 0.336713 | − | 0.941607i | \(-0.390685\pi\) | ||||
0.336713 | + | 0.941607i | \(0.390685\pi\) | |||||||
\(662\) | 53.4558i | 2.07762i | ||||||||
\(663\) | − | 2.74517i | − | 0.106613i | ||||||
\(664\) | −46.2843 | −1.79618 | ||||||||
\(665\) | −9.65685 | − | 4.82843i | −0.374477 | − | 0.187238i | ||||
\(666\) | 20.4853 | 0.793789 | ||||||||
\(667\) | − | 3.02944i | − | 0.117300i | ||||||
\(668\) | − | 75.2548i | − | 2.91170i | ||||||
\(669\) | −0.686292 | −0.0265336 | ||||||||
\(670\) | 14.4853 | − | 28.9706i | 0.559615 | − | 1.11923i | ||||
\(671\) | 2.00000 | 0.0772091 | ||||||||
\(672\) | − | 15.3137i | − | 0.590739i | ||||||
\(673\) | 6.14214i | 0.236762i | 0.992968 | + | 0.118381i | \(0.0377704\pi\) | ||||
−0.992968 | + | 0.118381i | \(0.962230\pi\) | |||||||
\(674\) | 6.82843 | 0.263021 | ||||||||
\(675\) | −16.0000 | + | 12.0000i | −0.615840 | + | 0.461880i | ||||
\(676\) | −44.5147 | −1.71210 | ||||||||
\(677\) | 36.4853i | 1.40224i | 0.713042 | + | 0.701122i | \(0.247317\pi\) | ||||
−0.713042 | + | 0.701122i | \(0.752683\pi\) | |||||||
\(678\) | 87.5980i | 3.36418i | ||||||||
\(679\) | −32.9706 | −1.26529 | ||||||||
\(680\) | −5.17157 | + | 10.3431i | −0.198321 | + | 0.396642i | ||||
\(681\) | 47.3137 | 1.81307 | ||||||||
\(682\) | 2.82843i | 0.108306i | ||||||||
\(683\) | 28.6274i | 1.09540i | 0.836676 | + | 0.547699i | \(0.184496\pi\) | ||||
−0.836676 | + | 0.547699i | \(0.815504\pi\) | |||||||
\(684\) | 3.82843 | 0.146384 | ||||||||
\(685\) | −16.0000 | − | 8.00000i | −0.611329 | − | 0.305664i | ||||
\(686\) | 108.569 | 4.14517 | ||||||||
\(687\) | − | 44.0000i | − | 1.67870i | ||||||
\(688\) | − | 14.4853i | − | 0.552246i | ||||||
\(689\) | −6.05887 | −0.230825 | ||||||||
\(690\) | −35.3137 | − | 17.6569i | −1.34437 | − | 0.672185i | ||||
\(691\) | −28.0000 | −1.06517 | −0.532585 | − | 0.846376i | \(-0.678779\pi\) | ||||
−0.532585 | + | 0.846376i | \(0.678779\pi\) | |||||||
\(692\) | − | 17.1716i | − | 0.652765i | ||||||
\(693\) | 4.82843i | 0.183417i | ||||||||
\(694\) | −46.2843 | −1.75693 | ||||||||
\(695\) | 4.00000 | − | 8.00000i | 0.151729 | − | 0.303457i | ||||
\(696\) | 7.31371 | 0.277225 | ||||||||
\(697\) | − | 12.2843i | − | 0.465300i | ||||||
\(698\) | 39.4558i | 1.49343i | ||||||||
\(699\) | −24.9706 | −0.944473 | ||||||||
\(700\) | −73.9411 | + | 55.4558i | −2.79471 | + | 2.09603i | ||||
\(701\) | −22.2843 | −0.841665 | −0.420833 | − | 0.907138i | \(-0.638262\pi\) | ||||
−0.420833 | + | 0.907138i | \(0.638262\pi\) | |||||||
\(702\) | − | 11.3137i | − | 0.427008i | ||||||
\(703\) | 8.48528i | 0.320028i | ||||||||
\(704\) | −9.82843 | −0.370423 | ||||||||
\(705\) | −0.686292 | + | 1.37258i | −0.0258472 | + | 0.0516945i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | − | 64.2843i | − | 2.41766i | ||||||
\(708\) | − | 21.6569i | − | 0.813914i | ||||||
\(709\) | −29.3137 | −1.10090 | −0.550450 | − | 0.834868i | \(-0.685544\pi\) | ||||
−0.550450 | + | 0.834868i | \(0.685544\pi\) | |||||||
\(710\) | 44.2843 | + | 22.1421i | 1.66196 | + | 0.830980i | ||||
\(711\) | −5.65685 | −0.212149 | ||||||||
\(712\) | − | 69.1127i | − | 2.59011i | ||||||
\(713\) | − | 4.28427i | − | 0.160447i | ||||||
\(714\) | −27.3137 | −1.02219 | ||||||||
\(715\) | −2.34315 | − | 1.17157i | −0.0876287 | − | 0.0438143i | ||||
\(716\) | −1.85786 | −0.0694317 | ||||||||
\(717\) | 54.6274i | 2.04010i | ||||||||
\(718\) | 40.9706i | 1.52901i | ||||||||
\(719\) | 30.6274 | 1.14221 | 0.571105 | − | 0.820877i | \(-0.306515\pi\) | ||||
0.571105 | + | 0.820877i | \(0.306515\pi\) | |||||||
\(720\) | 3.00000 | − | 6.00000i | 0.111803 | − | 0.223607i | ||||
\(721\) | −75.5980 | −2.81542 | ||||||||
\(722\) | 2.41421i | 0.0898477i | ||||||||
\(723\) | 20.9706i | 0.779904i | ||||||||
\(724\) | −53.5980 | −1.99195 | ||||||||
\(725\) | 2.48528 | + | 3.31371i | 0.0923010 | + | 0.123068i | ||||
\(726\) | 4.82843 | 0.179200 | ||||||||
\(727\) | 9.31371i | 0.345426i | 0.984972 | + | 0.172713i | \(0.0552534\pi\) | ||||
−0.984972 | + | 0.172713i | \(0.944747\pi\) | |||||||
\(728\) | − | 24.9706i | − | 0.925471i | ||||||
\(729\) | −13.0000 | −0.481481 | ||||||||
\(730\) | −16.4853 | + | 32.9706i | −0.610148 | + | 1.22030i | ||||
\(731\) | 5.65685 | 0.209226 | ||||||||
\(732\) | − | 15.3137i | − | 0.566011i | ||||||
\(733\) | − | 8.48528i | − | 0.313411i | −0.987645 | − | 0.156706i | \(-0.949913\pi\) | ||
0.987645 | − | 0.156706i | \(-0.0500874\pi\) | |||||||
\(734\) | 76.4264 | 2.82095 | ||||||||
\(735\) | −65.2548 | − | 32.6274i | −2.40696 | − | 1.20348i | ||||
\(736\) | 5.79899 | 0.213754 | ||||||||
\(737\) | − | 6.00000i | − | 0.221013i | ||||||
\(738\) | 25.3137i | 0.931810i | ||||||||
\(739\) | 44.0000 | 1.61857 | 0.809283 | − | 0.587419i | \(-0.199856\pi\) | ||||
0.809283 | + | 0.587419i | \(0.199856\pi\) | |||||||
\(740\) | 64.9706 | + | 32.4853i | 2.38837 | + | 1.19418i | ||||
\(741\) | −2.34315 | −0.0860776 | ||||||||
\(742\) | 60.2843i | 2.21311i | ||||||||
\(743\) | 22.9706i | 0.842708i | 0.906896 | + | 0.421354i | \(0.138445\pi\) | ||||
−0.906896 | + | 0.421354i | \(0.861555\pi\) | |||||||
\(744\) | 10.3431 | 0.379198 | ||||||||
\(745\) | −19.6569 | + | 39.3137i | −0.720171 | + | 1.44034i | ||||
\(746\) | −55.1127 | −2.01782 | ||||||||
\(747\) | 10.4853i | 0.383636i | ||||||||
\(748\) | 4.48528i | 0.163998i | ||||||||
\(749\) | 72.2843 | 2.64121 | ||||||||
\(750\) | 53.1127 | − | 9.65685i | 1.93940 | − | 0.352618i | ||||
\(751\) | 19.5147 | 0.712102 | 0.356051 | − | 0.934466i | \(-0.384123\pi\) | ||||
0.356051 | + | 0.934466i | \(0.384123\pi\) | |||||||
\(752\) | 1.02944i | 0.0375397i | ||||||||
\(753\) | 8.00000i | 0.291536i | ||||||||
\(754\) | −2.34315 | −0.0853323 | ||||||||
\(755\) | −21.6569 | + | 43.3137i | −0.788174 | + | 1.57635i | ||||
\(756\) | −73.9411 | −2.68921 | ||||||||
\(757\) | 20.0000i | 0.726912i | 0.931611 | + | 0.363456i | \(0.118403\pi\) | ||||
−0.931611 | + | 0.363456i | \(0.881597\pi\) | |||||||
\(758\) | − | 12.4853i | − | 0.453486i | ||||||
\(759\) | −7.31371 | −0.265471 | ||||||||
\(760\) | 8.82843 | + | 4.41421i | 0.320241 | + | 0.160120i | ||||
\(761\) | 19.9411 | 0.722865 | 0.361433 | − | 0.932398i | \(-0.382288\pi\) | ||||
0.361433 | + | 0.932398i | \(0.382288\pi\) | |||||||
\(762\) | 67.5980i | 2.44882i | ||||||||
\(763\) | 23.3137i | 0.844013i | ||||||||
\(764\) | 64.9706 | 2.35055 | ||||||||
\(765\) | 2.34315 | + | 1.17157i | 0.0847166 | + | 0.0423583i | ||||
\(766\) | 16.8284 | 0.608036 | ||||||||
\(767\) | 3.31371i | 0.119651i | ||||||||
\(768\) | 59.9411i | 2.16294i | ||||||||
\(769\) | −19.6569 | −0.708844 | −0.354422 | − | 0.935086i | \(-0.615322\pi\) | ||||
−0.354422 | + | 0.935086i | \(0.615322\pi\) | |||||||
\(770\) | −11.6569 | + | 23.3137i | −0.420084 | + | 0.840168i | ||||
\(771\) | 20.2843 | 0.730520 | ||||||||
\(772\) | 54.1421i | 1.94862i | ||||||||
\(773\) | 10.8284i | 0.389471i | 0.980856 | + | 0.194736i | \(0.0623849\pi\) | ||||
−0.980856 | + | 0.194736i | \(0.937615\pi\) | |||||||
\(774\) | −11.6569 | −0.418997 | ||||||||
\(775\) | 3.51472 | + | 4.68629i | 0.126252 | + | 0.168337i | ||||
\(776\) | 30.1421 | 1.08204 | ||||||||
\(777\) | 81.9411i | 2.93962i | ||||||||
\(778\) | 22.4853i | 0.806136i | ||||||||
\(779\) | −10.4853 | −0.375674 | ||||||||
\(780\) | −8.97056 | + | 17.9411i | −0.321198 | + | 0.642395i | ||||
\(781\) | 9.17157 | 0.328185 | ||||||||
\(782\) | − | 10.3431i | − | 0.369870i | ||||||
\(783\) | 3.31371i | 0.118422i | ||||||||
\(784\) | −48.9411 | −1.74790 | ||||||||
\(785\) | −24.0000 | − | 12.0000i | −0.856597 | − | 0.428298i | ||||
\(786\) | −73.9411 | −2.63739 | ||||||||
\(787\) | − | 30.9706i | − | 1.10398i | −0.833850 | − | 0.551991i | \(-0.813868\pi\) | ||
0.833850 | − | 0.551991i | \(-0.186132\pi\) | |||||||
\(788\) | − | 84.7696i | − | 3.01979i | ||||||
\(789\) | 3.02944 | 0.107851 | ||||||||
\(790\) | −27.3137 | − | 13.6569i | −0.971778 | − | 0.485889i | ||||
\(791\) | −87.5980 | −3.11463 | ||||||||
\(792\) | − | 4.41421i | − | 0.156852i | ||||||
\(793\) | 2.34315i | 0.0832075i | ||||||||
\(794\) | 36.9706 | 1.31204 | ||||||||
\(795\) | 10.3431 | − | 20.6863i | 0.366834 | − | 0.733667i | ||||
\(796\) | 21.6569 | 0.767607 | ||||||||
\(797\) | − | 5.17157i | − | 0.183187i | −0.995797 | − | 0.0915933i | \(-0.970804\pi\) | ||
0.995797 | − | 0.0915933i | \(-0.0291960\pi\) | |||||||
\(798\) | 23.3137i | 0.825296i | ||||||||
\(799\) | −0.402020 | −0.0142225 | ||||||||
\(800\) | −6.34315 | + | 4.75736i | −0.224264 | + | 0.168198i | ||||
\(801\) | −15.6569 | −0.553208 | ||||||||
\(802\) | − | 41.7990i | − | 1.47597i | ||||||
\(803\) | 6.82843i | 0.240970i | ||||||||
\(804\) | −45.9411 | −1.62022 | ||||||||
\(805\) | 17.6569 | − | 35.3137i | 0.622322 | − | 1.24464i | ||||
\(806\) | −3.31371 | −0.116720 | ||||||||
\(807\) | 21.9411i | 0.772364i | ||||||||
\(808\) | 58.7696i | 2.06751i | ||||||||
\(809\) | 30.6863 | 1.07887 | 0.539436 | − | 0.842026i | \(-0.318637\pi\) | ||||
0.539436 | + | 0.842026i | \(0.318637\pi\) | |||||||
\(810\) | 53.1127 | + | 26.5563i | 1.86619 | + | 0.933095i | ||||
\(811\) | 40.2843 | 1.41457 | 0.707286 | − | 0.706927i | \(-0.249919\pi\) | ||||
0.707286 | + | 0.706927i | \(0.249919\pi\) | |||||||
\(812\) | 15.3137i | 0.537406i | ||||||||
\(813\) | 22.6274i | 0.793578i | ||||||||
\(814\) | 20.4853 | 0.718009 | ||||||||
\(815\) | −4.00000 | − | 2.00000i | −0.140114 | − | 0.0700569i | ||||
\(816\) | 7.02944 | 0.246080 | ||||||||
\(817\) | − | 4.82843i | − | 0.168925i | ||||||
\(818\) | 46.2843i | 1.61829i | ||||||||
\(819\) | −5.65685 | −0.197666 | ||||||||
\(820\) | −40.1421 | + | 80.2843i | −1.40182 | + | 2.80365i | ||||
\(821\) | 15.9411 | 0.556349 | 0.278175 | − | 0.960531i | \(-0.410271\pi\) | ||||
0.278175 | + | 0.960531i | \(0.410271\pi\) | |||||||
\(822\) | 38.6274i | 1.34729i | ||||||||
\(823\) | − | 13.3137i | − | 0.464087i | −0.972705 | − | 0.232043i | \(-0.925459\pi\) | ||
0.972705 | − | 0.232043i | \(-0.0745411\pi\) | |||||||
\(824\) | 69.1127 | 2.40765 | ||||||||
\(825\) | 8.00000 | − | 6.00000i | 0.278524 | − | 0.208893i | ||||
\(826\) | 32.9706 | 1.14719 | ||||||||
\(827\) | 37.3137i | 1.29752i | 0.760991 | + | 0.648762i | \(0.224713\pi\) | ||||
−0.760991 | + | 0.648762i | \(0.775287\pi\) | |||||||
\(828\) | 14.0000i | 0.486534i | ||||||||
\(829\) | 48.9117 | 1.69877 | 0.849387 | − | 0.527771i | \(-0.176972\pi\) | ||||
0.849387 | + | 0.527771i | \(0.176972\pi\) | |||||||
\(830\) | −25.3137 | + | 50.6274i | −0.878652 | + | 1.75730i | ||||
\(831\) | −26.3431 | −0.913834 | ||||||||
\(832\) | − | 11.5147i | − | 0.399201i | ||||||
\(833\) | − | 19.1127i | − | 0.662216i | ||||||
\(834\) | −19.3137 | −0.668779 | ||||||||
\(835\) | −39.3137 | − | 19.6569i | −1.36051 | − | 0.680253i | ||||
\(836\) | 3.82843 | 0.132409 | ||||||||
\(837\) | 4.68629i | 0.161982i | ||||||||
\(838\) | − | 31.3137i | − | 1.08171i | ||||||
\(839\) | 31.7990 | 1.09782 | 0.548912 | − | 0.835880i | \(-0.315042\pi\) | ||||
0.548912 | + | 0.835880i | \(0.315042\pi\) | |||||||
\(840\) | 85.2548 | + | 42.6274i | 2.94157 | + | 1.47079i | ||||
\(841\) | −28.3137 | −0.976335 | ||||||||
\(842\) | 16.8284i | 0.579946i | ||||||||
\(843\) | − | 62.9117i | − | 2.16679i | ||||||
\(844\) | 28.0000 | 0.963800 | ||||||||
\(845\) | −11.6274 | + | 23.2548i | −0.399995 | + | 0.799991i | ||||
\(846\) | 0.828427 | 0.0284819 | ||||||||
\(847\) | 4.82843i | 0.165907i | ||||||||
\(848\) | − | 15.5147i | − | 0.532778i | ||||||
\(849\) | −20.9706 | −0.719708 | ||||||||
\(850\) | 8.48528 | + | 11.3137i | 0.291043 | + | 0.388057i | ||||
\(851\) | −31.0294 | −1.06368 | ||||||||
\(852\) | − | 70.2254i | − | 2.40588i | ||||||
\(853\) | − | 39.5147i | − | 1.35296i | −0.736462 | − | 0.676479i | \(-0.763505\pi\) | ||
0.736462 | − | 0.676479i | \(-0.236495\pi\) | |||||||
\(854\) | 23.3137 | 0.797779 | ||||||||
\(855\) | 1.00000 | − | 2.00000i | 0.0341993 | − | 0.0683986i | ||||
\(856\) | −66.0833 | −2.25868 | ||||||||
\(857\) | − | 48.0833i | − | 1.64249i | −0.570574 | − | 0.821246i | \(-0.693279\pi\) | ||
0.570574 | − | 0.821246i | \(-0.306721\pi\) | |||||||
\(858\) | 5.65685i | 0.193122i | ||||||||
\(859\) | 24.6863 | 0.842285 | 0.421143 | − | 0.906994i | \(-0.361629\pi\) | ||||
0.421143 | + | 0.906994i | \(0.361629\pi\) | |||||||
\(860\) | −36.9706 | − | 18.4853i | −1.26069 | − | 0.630343i | ||||
\(861\) | −101.255 | −3.45076 | ||||||||
\(862\) | − | 93.2548i | − | 3.17627i | ||||||
\(863\) | 9.02944i | 0.307366i | 0.988120 | + | 0.153683i | \(0.0491134\pi\) | ||||
−0.988120 | + | 0.153683i | \(0.950887\pi\) | |||||||
\(864\) | −6.34315 | −0.215798 | ||||||||
\(865\) | −8.97056 | − | 4.48528i | −0.305008 | − | 0.152504i | ||||
\(866\) | 16.4853 | 0.560193 | ||||||||
\(867\) | − | 31.2548i | − | 1.06147i | ||||||
\(868\) | 21.6569i | 0.735082i | ||||||||
\(869\) | −5.65685 | −0.191896 | ||||||||
\(870\) | 4.00000 | − | 8.00000i | 0.135613 | − | 0.271225i | ||||
\(871\) | 7.02944 | 0.238183 | ||||||||
\(872\) | − | 21.3137i | − | 0.721773i | ||||||
\(873\) | − | 6.82843i | − | 0.231107i | ||||||
\(874\) | −8.82843 | −0.298626 | ||||||||
\(875\) | 9.65685 | + | 53.1127i | 0.326461 | + | 1.79554i | ||||
\(876\) | 52.2843 | 1.76652 | ||||||||
\(877\) | 26.1421i | 0.882757i | 0.897321 | + | 0.441379i | \(0.145510\pi\) | ||||
−0.897321 | + | 0.441379i | \(0.854490\pi\) | |||||||
\(878\) | − | 71.5980i | − | 2.41631i | ||||||
\(879\) | −4.28427 | −0.144505 | ||||||||
\(880\) | 3.00000 | − | 6.00000i | 0.101130 | − | 0.202260i | ||||
\(881\) | 35.9411 | 1.21089 | 0.605444 | − | 0.795888i | \(-0.292996\pi\) | ||||
0.605444 | + | 0.795888i | \(0.292996\pi\) | |||||||
\(882\) | 39.3848i | 1.32615i | ||||||||
\(883\) | − | 10.6863i | − | 0.359622i | −0.983701 | − | 0.179811i | \(-0.942451\pi\) | ||
0.983701 | − | 0.179811i | \(-0.0575487\pi\) | |||||||
\(884\) | −5.25483 | −0.176739 | ||||||||
\(885\) | −11.3137 | − | 5.65685i | −0.380306 | − | 0.190153i | ||||
\(886\) | −32.1421 | −1.07984 | ||||||||
\(887\) | − | 51.9411i | − | 1.74401i | −0.489495 | − | 0.872006i | \(-0.662819\pi\) | ||
0.489495 | − | 0.872006i | \(-0.337181\pi\) | |||||||
\(888\) | − | 74.9117i | − | 2.51387i | ||||||
\(889\) | −67.5980 | −2.26716 | ||||||||
\(890\) | −75.5980 | − | 37.7990i | −2.53405 | − | 1.26703i | ||||
\(891\) | 11.0000 | 0.368514 | ||||||||
\(892\) | 1.31371i | 0.0439862i | ||||||||
\(893\) | 0.343146i | 0.0114829i | ||||||||
\(894\) | 94.9117 | 3.17432 | ||||||||
\(895\) | −0.485281 | + | 0.970563i | −0.0162212 | + | 0.0324423i | ||||
\(896\) | −99.2548 | −3.31587 | ||||||||
\(897\) | − | 8.56854i | − | 0.286095i | ||||||
\(898\) | − | 74.7696i | − | 2.49509i | ||||||
\(899\) | 0.970563 | 0.0323701 | ||||||||
\(900\) | −11.4853 | − | 15.3137i | −0.382843 | − | 0.510457i | ||||
\(901\) | 6.05887 | 0.201850 | ||||||||
\(902\) | 25.3137i | 0.842854i | ||||||||
\(903\) | − | 46.6274i | − | 1.55166i | ||||||
\(904\) | 80.0833 | 2.66353 | ||||||||
\(905\) | −14.0000 | + | 28.0000i | −0.465376 | + | 0.930751i | ||||
\(906\) | 104.569 | 3.47406 | ||||||||
\(907\) | − | 16.6274i | − | 0.552104i | −0.961143 | − | 0.276052i | \(-0.910974\pi\) | ||
0.961143 | − | 0.276052i | \(-0.0890263\pi\) | |||||||
\(908\) | − | 90.5685i | − | 3.00562i | ||||||
\(909\) | 13.3137 | 0.441588 | ||||||||
\(910\) | −27.3137 | − | 13.6569i | −0.905441 | − | 0.452720i | ||||
\(911\) | 30.8284 | 1.02139 | 0.510696 | − | 0.859762i | \(-0.329388\pi\) | ||||
0.510696 | + | 0.859762i | \(0.329388\pi\) | |||||||
\(912\) | − | 6.00000i | − | 0.198680i | ||||||
\(913\) | 10.4853i | 0.347012i | ||||||||
\(914\) | −57.4558 | −1.90047 | ||||||||
\(915\) | −8.00000 | − | 4.00000i | −0.264472 | − | 0.132236i | ||||
\(916\) | −84.2254 | −2.78289 | ||||||||
\(917\) | − | 73.9411i | − | 2.44175i | ||||||
\(918\) | 11.3137i | 0.373408i | ||||||||
\(919\) | 15.0294 | 0.495775 | 0.247888 | − | 0.968789i | \(-0.420264\pi\) | ||||
0.247888 | + | 0.968789i | \(0.420264\pi\) | |||||||
\(920\) | −16.1421 | + | 32.2843i | −0.532190 | + | 1.06438i | ||||
\(921\) | −13.9411 | −0.459376 | ||||||||
\(922\) | 82.7696i | 2.72587i | ||||||||
\(923\) | 10.7452i | 0.353681i | ||||||||
\(924\) | 36.9706 | 1.21624 | ||||||||
\(925\) | 33.9411 | − | 25.4558i | 1.11598 | − | 0.836983i | ||||
\(926\) | −63.4558 | −2.08529 | ||||||||
\(927\) | − | 15.6569i | − | 0.514239i | ||||||
\(928\) | 1.31371i | 0.0431246i | ||||||||
\(929\) | 11.9411 | 0.391776 | 0.195888 | − | 0.980626i | \(-0.437241\pi\) | ||||
0.195888 | + | 0.980626i | \(0.437241\pi\) | |||||||
\(930\) | 5.65685 | − | 11.3137i | 0.185496 | − | 0.370991i | ||||
\(931\) | −16.3137 | −0.534660 | ||||||||
\(932\) | 47.7990i | 1.56571i | ||||||||
\(933\) | 65.9411i | 2.15882i | ||||||||
\(934\) | −37.7990 | −1.23682 | ||||||||
\(935\) | 2.34315 | + | 1.17157i | 0.0766291 | + | 0.0383145i | ||||
\(936\) | 5.17157 | 0.169038 | ||||||||
\(937\) | 43.1127i | 1.40843i | 0.709987 | + | 0.704215i | \(0.248701\pi\) | ||||
−0.709987 | + | 0.704215i | \(0.751299\pi\) | |||||||
\(938\) | − | 69.9411i | − | 2.28366i | ||||||
\(939\) | 33.9411 | 1.10763 | ||||||||
\(940\) | 2.62742 | + | 1.31371i | 0.0856969 | + | 0.0428484i | ||||
\(941\) | −52.1421 | −1.69979 | −0.849893 | − | 0.526956i | \(-0.823333\pi\) | ||||
−0.849893 | + | 0.526956i | \(0.823333\pi\) | |||||||
\(942\) | 57.9411i | 1.88782i | ||||||||
\(943\) | − | 38.3431i | − | 1.24862i | ||||||
\(944\) | −8.48528 | −0.276172 | ||||||||
\(945\) | −19.3137 | + | 38.6274i | −0.628275 | + | 1.25655i | ||||
\(946\) | −11.6569 | −0.378997 | ||||||||
\(947\) | − | 1.71573i | − | 0.0557537i | −0.999611 | − | 0.0278768i | \(-0.991125\pi\) | ||
0.999611 | − | 0.0278768i | \(-0.00887463\pi\) | |||||||
\(948\) | 43.3137i | 1.40676i | ||||||||
\(949\) | −8.00000 | −0.259691 | ||||||||
\(950\) | 9.65685 | − | 7.24264i | 0.313310 | − | 0.234982i | ||||
\(951\) | 44.2843 | 1.43602 | ||||||||
\(952\) | 24.9706i | 0.809301i | ||||||||
\(953\) | 23.1127i | 0.748694i | 0.927289 | + | 0.374347i | \(0.122133\pi\) | ||||
−0.927289 | + | 0.374347i | \(0.877867\pi\) | |||||||
\(954\) | −12.4853 | −0.404226 | ||||||||
\(955\) | 16.9706 | − | 33.9411i | 0.549155 | − | 1.09831i | ||||
\(956\) | 104.569 | 3.38199 | ||||||||
\(957\) | − | 1.65685i | − | 0.0535585i | ||||||
\(958\) | − | 46.6274i | − | 1.50646i | ||||||
\(959\) | −38.6274 | −1.24734 | ||||||||
\(960\) | 39.3137 | + | 19.6569i | 1.26884 | + | 0.634422i | ||||
\(961\) | −29.6274 | −0.955723 | ||||||||
\(962\) | 24.0000i | 0.773791i | ||||||||
\(963\) | 14.9706i | 0.482420i | ||||||||
\(964\) | 40.1421 | 1.29289 | ||||||||
\(965\) | 28.2843 | + | 14.1421i | 0.910503 | + | 0.455251i | ||||
\(966\) | −85.2548 | −2.74303 | ||||||||
\(967\) | 16.1421i | 0.519096i | 0.965730 | + | 0.259548i | \(0.0835736\pi\) | ||||
−0.965730 | + | 0.259548i | \(0.916426\pi\) | |||||||
\(968\) | − | 4.41421i | − | 0.141878i | ||||||
\(969\) | 2.34315 | 0.0752727 | ||||||||
\(970\) | 16.4853 | − | 32.9706i | 0.529310 | − | 1.05862i | ||||
\(971\) | 47.1127 | 1.51192 | 0.755959 | − | 0.654619i | \(-0.227171\pi\) | ||||
0.755959 | + | 0.654619i | \(0.227171\pi\) | |||||||
\(972\) | − | 38.2843i | − | 1.22797i | ||||||
\(973\) | − | 19.3137i | − | 0.619169i | ||||||
\(974\) | −10.4853 | −0.335970 | ||||||||
\(975\) | 7.02944 | + | 9.37258i | 0.225122 | + | 0.300163i | ||||
\(976\) | −6.00000 | −0.192055 | ||||||||
\(977\) | 31.7990i | 1.01734i | 0.860962 | + | 0.508670i | \(0.169863\pi\) | ||||
−0.860962 | + | 0.508670i | \(0.830137\pi\) | |||||||
\(978\) | 9.65685i | 0.308792i | ||||||||
\(979\) | −15.6569 | −0.500395 | ||||||||
\(980\) | −62.4558 | + | 124.912i | −1.99508 | + | 3.99016i | ||||
\(981\) | −4.82843 | −0.154160 | ||||||||
\(982\) | − | 7.31371i | − | 0.233390i | ||||||
\(983\) | − | 19.6569i | − | 0.626956i | −0.949595 | − | 0.313478i | \(-0.898506\pi\) | ||
0.949595 | − | 0.313478i | \(-0.101494\pi\) | |||||||
\(984\) | 92.5685 | 2.95098 | ||||||||
\(985\) | −44.2843 | − | 22.1421i | −1.41101 | − | 0.705507i | ||||
\(986\) | 2.34315 | 0.0746210 | ||||||||
\(987\) | 3.31371i | 0.105477i | ||||||||
\(988\) | 4.48528i | 0.142696i | ||||||||
\(989\) | 17.6569 | 0.561455 | ||||||||
\(990\) | −4.82843 | − | 2.41421i | −0.153457 | − | 0.0767287i | ||||
\(991\) | 17.1716 | 0.545473 | 0.272736 | − | 0.962089i | \(-0.412071\pi\) | ||||
0.272736 | + | 0.962089i | \(0.412071\pi\) | |||||||
\(992\) | 1.85786i | 0.0589873i | ||||||||
\(993\) | − | 44.2843i | − | 1.40532i | ||||||
\(994\) | 106.912 | 3.39103 | ||||||||
\(995\) | 5.65685 | − | 11.3137i | 0.179334 | − | 0.358669i | ||||
\(996\) | 80.2843 | 2.54390 | ||||||||
\(997\) | 0.485281i | 0.0153690i | 0.999970 | + | 0.00768451i | \(0.00244608\pi\) | ||||
−0.999970 | + | 0.00768451i | \(0.997554\pi\) | |||||||
\(998\) | − | 56.2843i | − | 1.78165i | ||||||
\(999\) | 33.9411 | 1.07385 |
(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 | 1045.2.b.a.419.4 | yes | 4 | |
5.2 | odd | 4 | 5225.2.a.d.1.1 | 2 | |||
5.3 | odd | 4 | 5225.2.a.g.1.2 | 2 | |||
5.4 | even | 2 | inner | 1045.2.b.a.419.1 | ✓ | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1045.2.b.a.419.1 | ✓ | 4 | 5.4 | even | 2 | inner | |
1045.2.b.a.419.4 | yes | 4 | 1.1 | even | 1 | trivial | |
5225.2.a.d.1.1 | 2 | 5.2 | odd | 4 | |||
5225.2.a.g.1.2 | 2 | 5.3 | odd | 4 |