Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3150,2,Mod(1457,3150)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3150, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([2, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("3150.1457");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3150 = 2 \cdot 3^{2} \cdot 5^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3150.m (of order \(4\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(25.1528766367\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(i)\) |
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: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 1457.2 | ||
Root | \(0.707107 - 0.707107i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3150.1457 |
Dual form | 3150.2.m.d.2843.2 |
$q$-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 \(\left(\mathbb{Z}/3150\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(451\) | \(2801\) |
\(\chi(n)\) | \(e\left(\frac{1}{4}\right)\) | \(1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.707107 | − | 0.707107i | 0.500000 | − | 0.500000i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | − | 1.00000i | − | 0.500000i | ||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.707107 | + | 0.707107i | 0.267261 | + | 0.267261i | ||||
\(8\) | −0.707107 | − | 0.707107i | −0.250000 | − | 0.250000i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − | 4.82843i | − | 1.45583i | −0.685670 | − | 0.727913i | \(-0.740491\pi\) | ||
0.685670 | − | 0.727913i | \(-0.259509\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −3.41421 | + | 3.41421i | −0.946932 | + | 0.946932i | −0.998661 | − | 0.0517287i | \(-0.983527\pi\) |
0.0517287 | + | 0.998661i | \(0.483527\pi\) | |||||||
\(14\) | 1.00000 | 0.267261 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −1.00000 | −0.250000 | ||||||||
\(17\) | 1.58579 | − | 1.58579i | 0.384610 | − | 0.384610i | −0.488150 | − | 0.872760i | \(-0.662328\pi\) |
0.872760 | + | 0.488150i | \(0.162328\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − | 7.07107i | − | 1.62221i | −0.584898 | − | 0.811107i | \(-0.698865\pi\) | ||
0.584898 | − | 0.811107i | \(-0.301135\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −3.41421 | − | 3.41421i | −0.727913 | − | 0.727913i | ||||
\(23\) | 4.82843 | + | 4.82843i | 1.00680 | + | 1.00680i | 0.999977 | + | 0.00681991i | \(0.00217086\pi\) |
0.00681991 | + | 0.999977i | \(0.497829\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 4.82843i | 0.946932i | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0.707107 | − | 0.707107i | 0.133631 | − | 0.133631i | ||||
\(29\) | −3.17157 | −0.588946 | −0.294473 | − | 0.955660i | \(-0.595144\pi\) | ||||
−0.294473 | + | 0.955660i | \(0.595144\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −8.82843 | −1.58563 | −0.792816 | − | 0.609461i | \(-0.791386\pi\) | ||||
−0.792816 | + | 0.609461i | \(0.791386\pi\) | |||||||
\(32\) | −0.707107 | + | 0.707107i | −0.125000 | + | 0.125000i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | − | 2.24264i | − | 0.384610i | ||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −6.07107 | − | 6.07107i | −0.998077 | − | 0.998077i | 0.00192076 | − | 0.999998i | \(-0.499389\pi\) |
−0.999998 | + | 0.00192076i | \(0.999389\pi\) | |||||||
\(38\) | −5.00000 | − | 5.00000i | −0.811107 | − | 0.811107i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 4.82843i | 0.754074i | 0.926198 | + | 0.377037i | \(0.123057\pi\) | ||||
−0.926198 | + | 0.377037i | \(0.876943\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 6.41421 | − | 6.41421i | 0.978158 | − | 0.978158i | −0.0216081 | − | 0.999767i | \(-0.506879\pi\) |
0.999767 | + | 0.0216081i | \(0.00687861\pi\) | |||||||
\(44\) | −4.82843 | −0.727913 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 6.82843 | 1.00680 | ||||||||
\(47\) | 6.41421 | − | 6.41421i | 0.935609 | − | 0.935609i | −0.0624395 | − | 0.998049i | \(-0.519888\pi\) |
0.998049 | + | 0.0624395i | \(0.0198881\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000i | 0.142857i | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 3.41421 | + | 3.41421i | 0.473466 | + | 0.473466i | ||||
\(53\) | −4.82843 | − | 4.82843i | −0.663235 | − | 0.663235i | 0.292906 | − | 0.956141i | \(-0.405378\pi\) |
−0.956141 | + | 0.292906i | \(0.905378\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | − | 1.00000i | − | 0.133631i | ||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −2.24264 | + | 2.24264i | −0.294473 | + | 0.294473i | ||||
\(59\) | −8.00000 | −1.04151 | −0.520756 | − | 0.853706i | \(-0.674350\pi\) | ||||
−0.520756 | + | 0.853706i | \(0.674350\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 6.58579 | 0.843224 | 0.421612 | − | 0.906776i | \(-0.361465\pi\) | ||||
0.421612 | + | 0.906776i | \(0.361465\pi\) | |||||||
\(62\) | −6.24264 | + | 6.24264i | −0.792816 | + | 0.792816i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.00000i | 0.125000i | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 0.414214 | + | 0.414214i | 0.0506042 | + | 0.0506042i | 0.731956 | − | 0.681352i | \(-0.238608\pi\) |
−0.681352 | + | 0.731956i | \(0.738608\pi\) | |||||||
\(68\) | −1.58579 | − | 1.58579i | −0.192305 | − | 0.192305i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 12.2426i | 1.45293i | 0.687201 | + | 0.726467i | \(0.258839\pi\) | ||||
−0.687201 | + | 0.726467i | \(0.741161\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −6.00000 | + | 6.00000i | −0.702247 | + | 0.702247i | −0.964892 | − | 0.262646i | \(-0.915405\pi\) |
0.262646 | + | 0.964892i | \(0.415405\pi\) | |||||||
\(74\) | −8.58579 | −0.998077 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −7.07107 | −0.811107 | ||||||||
\(77\) | 3.41421 | − | 3.41421i | 0.389086 | − | 0.389086i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − | 13.3137i | − | 1.49791i | −0.662621 | − | 0.748955i | \(-0.730556\pi\) | ||
0.662621 | − | 0.748955i | \(-0.269444\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 3.41421 | + | 3.41421i | 0.377037 | + | 0.377037i | ||||
\(83\) | −9.65685 | − | 9.65685i | −1.05998 | − | 1.05998i | −0.998083 | − | 0.0618948i | \(-0.980286\pi\) |
−0.0618948 | − | 0.998083i | \(-0.519714\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | − | 9.07107i | − | 0.978158i | ||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −3.41421 | + | 3.41421i | −0.363956 | + | 0.363956i | ||||
\(89\) | −13.3137 | −1.41125 | −0.705625 | − | 0.708585i | \(-0.749334\pi\) | ||||
−0.705625 | + | 0.708585i | \(0.749334\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −4.82843 | −0.506157 | ||||||||
\(92\) | 4.82843 | − | 4.82843i | 0.503398 | − | 0.503398i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | − | 9.07107i | − | 0.935609i | ||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −8.24264 | − | 8.24264i | −0.836913 | − | 0.836913i | 0.151538 | − | 0.988451i | \(-0.451577\pi\) |
−0.988451 | + | 0.151538i | \(0.951577\pi\) | |||||||
\(98\) | 0.707107 | + | 0.707107i | 0.0714286 | + | 0.0714286i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 4.34315i | 0.432159i | 0.976376 | + | 0.216080i | \(0.0693271\pi\) | ||||
−0.976376 | + | 0.216080i | \(0.930673\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 3.41421 | − | 3.41421i | 0.336412 | − | 0.336412i | −0.518603 | − | 0.855015i | \(-0.673548\pi\) |
0.855015 | + | 0.518603i | \(0.173548\pi\) | |||||||
\(104\) | 4.82843 | 0.473466 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −6.82843 | −0.663235 | ||||||||
\(107\) | 9.07107 | − | 9.07107i | 0.876933 | − | 0.876933i | −0.116283 | − | 0.993216i | \(-0.537098\pi\) |
0.993216 | + | 0.116283i | \(0.0370979\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − | 20.1421i | − | 1.92927i | −0.263595 | − | 0.964633i | \(-0.584908\pi\) | ||
0.263595 | − | 0.964633i | \(-0.415092\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −0.707107 | − | 0.707107i | −0.0668153 | − | 0.0668153i | ||||
\(113\) | 5.41421 | + | 5.41421i | 0.509326 | + | 0.509326i | 0.914320 | − | 0.404993i | \(-0.132726\pi\) |
−0.404993 | + | 0.914320i | \(0.632726\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 3.17157i | 0.294473i | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −5.65685 | + | 5.65685i | −0.520756 | + | 0.520756i | ||||
\(119\) | 2.24264 | 0.205583 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −12.3137 | −1.11943 | ||||||||
\(122\) | 4.65685 | − | 4.65685i | 0.421612 | − | 0.421612i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 8.82843i | 0.792816i | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1.17157 | + | 1.17157i | 0.103960 | + | 0.103960i | 0.757174 | − | 0.653213i | \(-0.226580\pi\) |
−0.653213 | + | 0.757174i | \(0.726580\pi\) | |||||||
\(128\) | 0.707107 | + | 0.707107i | 0.0625000 | + | 0.0625000i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − | 6.00000i | − | 0.524222i | −0.965038 | − | 0.262111i | \(-0.915581\pi\) | ||
0.965038 | − | 0.262111i | \(-0.0844187\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 5.00000 | − | 5.00000i | 0.433555 | − | 0.433555i | ||||
\(134\) | 0.585786 | 0.0506042 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −2.24264 | −0.192305 | ||||||||
\(137\) | −1.07107 | + | 1.07107i | −0.0915075 | + | 0.0915075i | −0.751379 | − | 0.659871i | \(-0.770611\pi\) |
0.659871 | + | 0.751379i | \(0.270611\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 0.242641i | − | 0.0205805i | −0.999947 | − | 0.0102903i | \(-0.996724\pi\) | ||
0.999947 | − | 0.0102903i | \(-0.00327555\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 8.65685 | + | 8.65685i | 0.726467 | + | 0.726467i | ||||
\(143\) | 16.4853 | + | 16.4853i | 1.37857 | + | 1.37857i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 8.48528i | 0.702247i | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −6.07107 | + | 6.07107i | −0.499039 | + | 0.499039i | ||||
\(149\) | 5.31371 | 0.435316 | 0.217658 | − | 0.976025i | \(-0.430158\pi\) | ||||
0.217658 | + | 0.976025i | \(0.430158\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −13.3137 | −1.08345 | −0.541727 | − | 0.840554i | \(-0.682229\pi\) | ||||
−0.541727 | + | 0.840554i | \(0.682229\pi\) | |||||||
\(152\) | −5.00000 | + | 5.00000i | −0.405554 | + | 0.405554i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | − | 4.82843i | − | 0.389086i | ||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 2.58579 | + | 2.58579i | 0.206368 | + | 0.206368i | 0.802722 | − | 0.596354i | \(-0.203384\pi\) |
−0.596354 | + | 0.802722i | \(0.703384\pi\) | |||||||
\(158\) | −9.41421 | − | 9.41421i | −0.748955 | − | 0.748955i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 6.82843i | 0.538155i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 4.89949 | − | 4.89949i | 0.383758 | − | 0.383758i | −0.488696 | − | 0.872454i | \(-0.662527\pi\) |
0.872454 | + | 0.488696i | \(0.162527\pi\) | |||||||
\(164\) | 4.82843 | 0.377037 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −13.6569 | −1.05998 | ||||||||
\(167\) | −6.89949 | + | 6.89949i | −0.533899 | + | 0.533899i | −0.921730 | − | 0.387831i | \(-0.873224\pi\) |
0.387831 | + | 0.921730i | \(0.373224\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | − | 10.3137i | − | 0.793362i | ||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −6.41421 | − | 6.41421i | −0.489079 | − | 0.489079i | ||||
\(173\) | 8.00000 | + | 8.00000i | 0.608229 | + | 0.608229i | 0.942483 | − | 0.334254i | \(-0.108484\pi\) |
−0.334254 | + | 0.942483i | \(0.608484\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 4.82843i | 0.363956i | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −9.41421 | + | 9.41421i | −0.705625 | + | 0.705625i | ||||
\(179\) | 13.3137 | 0.995113 | 0.497557 | − | 0.867431i | \(-0.334231\pi\) | ||||
0.497557 | + | 0.867431i | \(0.334231\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −11.0711 | −0.822906 | −0.411453 | − | 0.911431i | \(-0.634979\pi\) | ||||
−0.411453 | + | 0.911431i | \(0.634979\pi\) | |||||||
\(182\) | −3.41421 | + | 3.41421i | −0.253078 | + | 0.253078i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | − | 6.82843i | − | 0.503398i | ||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −7.65685 | − | 7.65685i | −0.559925 | − | 0.559925i | ||||
\(188\) | −6.41421 | − | 6.41421i | −0.467805 | − | 0.467805i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 13.4142i | 0.970618i | 0.874343 | + | 0.485309i | \(0.161293\pi\) | ||||
−0.874343 | + | 0.485309i | \(0.838707\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 6.00000 | − | 6.00000i | 0.431889 | − | 0.431889i | −0.457381 | − | 0.889271i | \(-0.651213\pi\) |
0.889271 | + | 0.457381i | \(0.151213\pi\) | |||||||
\(194\) | −11.6569 | −0.836913 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 1.00000 | 0.0714286 | ||||||||
\(197\) | 3.17157 | − | 3.17157i | 0.225965 | − | 0.225965i | −0.585040 | − | 0.811005i | \(-0.698921\pi\) |
0.811005 | + | 0.585040i | \(0.198921\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 0.343146i | 0.0243250i | 0.999926 | + | 0.0121625i | \(0.00387153\pi\) | ||||
−0.999926 | + | 0.0121625i | \(0.996128\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 3.07107 | + | 3.07107i | 0.216080 | + | 0.216080i | ||||
\(203\) | −2.24264 | − | 2.24264i | −0.157403 | − | 0.157403i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | − | 4.82843i | − | 0.336412i | ||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 3.41421 | − | 3.41421i | 0.236733 | − | 0.236733i | ||||
\(209\) | −34.1421 | −2.36166 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 3.51472 | 0.241963 | 0.120982 | − | 0.992655i | \(-0.461396\pi\) | ||||
0.120982 | + | 0.992655i | \(0.461396\pi\) | |||||||
\(212\) | −4.82843 | + | 4.82843i | −0.331618 | + | 0.331618i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | − | 12.8284i | − | 0.876933i | ||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −6.24264 | − | 6.24264i | −0.423778 | − | 0.423778i | ||||
\(218\) | −14.2426 | − | 14.2426i | −0.964633 | − | 0.964633i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 10.8284i | 0.728399i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 7.89949 | − | 7.89949i | 0.528989 | − | 0.528989i | −0.391282 | − | 0.920271i | \(-0.627968\pi\) |
0.920271 | + | 0.391282i | \(0.127968\pi\) | |||||||
\(224\) | −1.00000 | −0.0668153 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 7.65685 | 0.509326 | ||||||||
\(227\) | −4.34315 | + | 4.34315i | −0.288265 | + | 0.288265i | −0.836394 | − | 0.548129i | \(-0.815340\pi\) |
0.548129 | + | 0.836394i | \(0.315340\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 4.92893i | 0.325713i | 0.986650 | + | 0.162857i | \(0.0520708\pi\) | ||||
−0.986650 | + | 0.162857i | \(0.947929\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 2.24264 | + | 2.24264i | 0.147237 | + | 0.147237i | ||||
\(233\) | −5.41421 | − | 5.41421i | −0.354697 | − | 0.354697i | 0.507157 | − | 0.861854i | \(-0.330696\pi\) |
−0.861854 | + | 0.507157i | \(0.830696\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 8.00000i | 0.520756i | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 1.58579 | − | 1.58579i | 0.102791 | − | 0.102791i | ||||
\(239\) | −25.2132 | −1.63091 | −0.815453 | − | 0.578823i | \(-0.803512\pi\) | ||||
−0.815453 | + | 0.578823i | \(0.803512\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −7.65685 | −0.493221 | −0.246611 | − | 0.969115i | \(-0.579317\pi\) | ||||
−0.246611 | + | 0.969115i | \(0.579317\pi\) | |||||||
\(242\) | −8.70711 | + | 8.70711i | −0.559714 | + | 0.559714i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | − | 6.58579i | − | 0.421612i | ||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 24.1421 | + | 24.1421i | 1.53613 | + | 1.53613i | ||||
\(248\) | 6.24264 | + | 6.24264i | 0.396408 | + | 0.396408i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 6.97056i | − | 0.439978i | −0.975502 | − | 0.219989i | \(-0.929398\pi\) | ||
0.975502 | − | 0.219989i | \(-0.0706022\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 23.3137 | − | 23.3137i | 1.46572 | − | 1.46572i | ||||
\(254\) | 1.65685 | 0.103960 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 6.89949 | − | 6.89949i | 0.430379 | − | 0.430379i | −0.458378 | − | 0.888757i | \(-0.651570\pi\) |
0.888757 | + | 0.458378i | \(0.151570\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − | 8.58579i | − | 0.533495i | ||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −4.24264 | − | 4.24264i | −0.262111 | − | 0.262111i | ||||
\(263\) | 22.0000 | + | 22.0000i | 1.35658 | + | 1.35658i | 0.878099 | + | 0.478479i | \(0.158812\pi\) |
0.478479 | + | 0.878099i | \(0.341188\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | − | 7.07107i | − | 0.433555i | ||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0.414214 | − | 0.414214i | 0.0253021 | − | 0.0253021i | ||||
\(269\) | 21.3137 | 1.29952 | 0.649760 | − | 0.760140i | \(-0.274869\pi\) | ||||
0.649760 | + | 0.760140i | \(0.274869\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 7.17157 | 0.435642 | 0.217821 | − | 0.975989i | \(-0.430105\pi\) | ||||
0.217821 | + | 0.975989i | \(0.430105\pi\) | |||||||
\(272\) | −1.58579 | + | 1.58579i | −0.0961524 | + | 0.0961524i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 1.51472i | 0.0915075i | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −18.0711 | − | 18.0711i | −1.08579 | − | 1.08579i | −0.995957 | − | 0.0898279i | \(-0.971368\pi\) |
−0.0898279 | − | 0.995957i | \(-0.528632\pi\) | |||||||
\(278\) | −0.171573 | − | 0.171573i | −0.0102903 | − | 0.0102903i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 12.9289i | − | 0.771275i | −0.922650 | − | 0.385638i | \(-0.873981\pi\) | ||
0.922650 | − | 0.385638i | \(-0.126019\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −18.0000 | + | 18.0000i | −1.06999 | + | 1.06999i | −0.0726300 | + | 0.997359i | \(0.523139\pi\) |
−0.997359 | + | 0.0726300i | \(0.976861\pi\) | |||||||
\(284\) | 12.2426 | 0.726467 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 23.3137 | 1.37857 | ||||||||
\(287\) | −3.41421 | + | 3.41421i | −0.201535 | + | 0.201535i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 11.9706i | 0.704151i | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 6.00000 | + | 6.00000i | 0.351123 | + | 0.351123i | ||||
\(293\) | 22.4853 | + | 22.4853i | 1.31360 | + | 1.31360i | 0.918739 | + | 0.394865i | \(0.129209\pi\) |
0.394865 | + | 0.918739i | \(0.370791\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 8.58579i | 0.499039i | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 3.75736 | − | 3.75736i | 0.217658 | − | 0.217658i | ||||
\(299\) | −32.9706 | −1.90674 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 9.07107 | 0.522848 | ||||||||
\(302\) | −9.41421 | + | 9.41421i | −0.541727 | + | 0.541727i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 7.07107i | 0.405554i | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −7.51472 | − | 7.51472i | −0.428888 | − | 0.428888i | 0.459362 | − | 0.888249i | \(-0.348078\pi\) |
−0.888249 | + | 0.459362i | \(0.848078\pi\) | |||||||
\(308\) | −3.41421 | − | 3.41421i | −0.194543 | − | 0.194543i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − | 16.0000i | − | 0.907277i | −0.891186 | − | 0.453638i | \(-0.850126\pi\) | ||
0.891186 | − | 0.453638i | \(-0.149874\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −19.6569 | + | 19.6569i | −1.11107 | + | 1.11107i | −0.118065 | + | 0.993006i | \(0.537669\pi\) |
−0.993006 | + | 0.118065i | \(0.962331\pi\) | |||||||
\(314\) | 3.65685 | 0.206368 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −13.3137 | −0.748955 | ||||||||
\(317\) | 12.2426 | − | 12.2426i | 0.687615 | − | 0.687615i | −0.274089 | − | 0.961704i | \(-0.588376\pi\) |
0.961704 | + | 0.274089i | \(0.0883763\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 15.3137i | 0.857403i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 4.82843 | + | 4.82843i | 0.269078 | + | 0.269078i | ||||
\(323\) | −11.2132 | − | 11.2132i | −0.623919 | − | 0.623919i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | − | 6.92893i | − | 0.383758i | ||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 3.41421 | − | 3.41421i | 0.188518 | − | 0.188518i | ||||
\(329\) | 9.07107 | 0.500104 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −1.85786 | −0.102117 | −0.0510587 | − | 0.998696i | \(-0.516260\pi\) | ||||
−0.0510587 | + | 0.998696i | \(0.516260\pi\) | |||||||
\(332\) | −9.65685 | + | 9.65685i | −0.529989 | + | 0.529989i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 9.75736i | 0.533899i | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −1.51472 | − | 1.51472i | −0.0825120 | − | 0.0825120i | 0.664646 | − | 0.747158i | \(-0.268582\pi\) |
−0.747158 | + | 0.664646i | \(0.768582\pi\) | |||||||
\(338\) | −7.29289 | − | 7.29289i | −0.396681 | − | 0.396681i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 42.6274i | 2.30840i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −0.707107 | + | 0.707107i | −0.0381802 | + | 0.0381802i | ||||
\(344\) | −9.07107 | −0.489079 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 11.3137 | 0.608229 | ||||||||
\(347\) | −14.8284 | + | 14.8284i | −0.796032 | + | 0.796032i | −0.982467 | − | 0.186436i | \(-0.940306\pi\) |
0.186436 | + | 0.982467i | \(0.440306\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 8.72792i | − | 0.467195i | −0.972333 | − | 0.233597i | \(-0.924950\pi\) | ||
0.972333 | − | 0.233597i | \(-0.0750498\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 3.41421 | + | 3.41421i | 0.181978 | + | 0.181978i | ||||
\(353\) | 15.3848 | + | 15.3848i | 0.818849 | + | 0.818849i | 0.985941 | − | 0.167092i | \(-0.0534378\pi\) |
−0.167092 | + | 0.985941i | \(0.553438\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 13.3137i | 0.705625i | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 9.41421 | − | 9.41421i | 0.497557 | − | 0.497557i | ||||
\(359\) | 20.7279 | 1.09398 | 0.546989 | − | 0.837140i | \(-0.315774\pi\) | ||||
0.546989 | + | 0.837140i | \(0.315774\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −31.0000 | −1.63158 | ||||||||
\(362\) | −7.82843 | + | 7.82843i | −0.411453 | + | 0.411453i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 4.82843i | 0.253078i | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 20.0000 | + | 20.0000i | 1.04399 | + | 1.04399i | 0.998987 | + | 0.0450047i | \(0.0143303\pi\) |
0.0450047 | + | 0.998987i | \(0.485670\pi\) | |||||||
\(368\) | −4.82843 | − | 4.82843i | −0.251699 | − | 0.251699i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − | 6.82843i | − | 0.354514i | ||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −11.2426 | + | 11.2426i | −0.582122 | + | 0.582122i | −0.935486 | − | 0.353364i | \(-0.885038\pi\) |
0.353364 | + | 0.935486i | \(0.385038\pi\) | |||||||
\(374\) | −10.8284 | −0.559925 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −9.07107 | −0.467805 | ||||||||
\(377\) | 10.8284 | − | 10.8284i | 0.557692 | − | 0.557692i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 5.65685i | − | 0.290573i | −0.989390 | − | 0.145287i | \(-0.953590\pi\) | ||
0.989390 | − | 0.145287i | \(-0.0464104\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 9.48528 | + | 9.48528i | 0.485309 | + | 0.485309i | ||||
\(383\) | 5.24264 | + | 5.24264i | 0.267886 | + | 0.267886i | 0.828248 | − | 0.560362i | \(-0.189338\pi\) |
−0.560362 | + | 0.828248i | \(0.689338\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | − | 8.48528i | − | 0.431889i | ||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −8.24264 | + | 8.24264i | −0.418457 | + | 0.418457i | ||||
\(389\) | 5.31371 | 0.269416 | 0.134708 | − | 0.990885i | \(-0.456990\pi\) | ||||
0.134708 | + | 0.990885i | \(0.456990\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 15.3137 | 0.774448 | ||||||||
\(392\) | 0.707107 | − | 0.707107i | 0.0357143 | − | 0.0357143i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | − | 4.48528i | − | 0.225965i | ||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 25.4142 | + | 25.4142i | 1.27550 | + | 1.27550i | 0.943158 | + | 0.332345i | \(0.107840\pi\) |
0.332345 | + | 0.943158i | \(0.392160\pi\) | |||||||
\(398\) | 0.242641 | + | 0.242641i | 0.0121625 | + | 0.0121625i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − | 31.0711i | − | 1.55162i | −0.630970 | − | 0.775808i | \(-0.717343\pi\) | ||
0.630970 | − | 0.775808i | \(-0.282657\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 30.1421 | − | 30.1421i | 1.50149 | − | 1.50149i | ||||
\(404\) | 4.34315 | 0.216080 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −3.17157 | −0.157403 | ||||||||
\(407\) | −29.3137 | + | 29.3137i | −1.45303 | + | 1.45303i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 37.3137i | − | 1.84504i | −0.385944 | − | 0.922522i | \(-0.626124\pi\) | ||
0.385944 | − | 0.922522i | \(-0.373876\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −3.41421 | − | 3.41421i | −0.168206 | − | 0.168206i | ||||
\(413\) | −5.65685 | − | 5.65685i | −0.278356 | − | 0.278356i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | − | 4.82843i | − | 0.236733i | ||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −24.1421 | + | 24.1421i | −1.18083 | + | 1.18083i | ||||
\(419\) | 20.0000 | 0.977064 | 0.488532 | − | 0.872546i | \(-0.337533\pi\) | ||||
0.488532 | + | 0.872546i | \(0.337533\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 28.1421 | 1.37156 | 0.685782 | − | 0.727807i | \(-0.259460\pi\) | ||||
0.685782 | + | 0.727807i | \(0.259460\pi\) | |||||||
\(422\) | 2.48528 | − | 2.48528i | 0.120982 | − | 0.120982i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 6.82843i | 0.331618i | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 4.65685 | + | 4.65685i | 0.225361 | + | 0.225361i | ||||
\(428\) | −9.07107 | − | 9.07107i | −0.438467 | − | 0.438467i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 13.2132i | − | 0.636458i | −0.948014 | − | 0.318229i | \(-0.896912\pi\) | ||
0.948014 | − | 0.318229i | \(-0.103088\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 24.2426 | − | 24.2426i | 1.16503 | − | 1.16503i | 0.181667 | − | 0.983360i | \(-0.441851\pi\) |
0.983360 | − | 0.181667i | \(-0.0581492\pi\) | |||||||
\(434\) | −8.82843 | −0.423778 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −20.1421 | −0.964633 | ||||||||
\(437\) | 34.1421 | − | 34.1421i | 1.63324 | − | 1.63324i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 25.7990i | 1.23132i | 0.788012 | + | 0.615659i | \(0.211110\pi\) | ||||
−0.788012 | + | 0.615659i | \(0.788890\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 7.65685 | + | 7.65685i | 0.364199 | + | 0.364199i | ||||
\(443\) | 24.4853 | + | 24.4853i | 1.16333 | + | 1.16333i | 0.983742 | + | 0.179589i | \(0.0574768\pi\) |
0.179589 | + | 0.983742i | \(0.442523\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | − | 11.1716i | − | 0.528989i | ||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −0.707107 | + | 0.707107i | −0.0334077 | + | 0.0334077i | ||||
\(449\) | 32.2426 | 1.52162 | 0.760812 | − | 0.648972i | \(-0.224801\pi\) | ||||
0.760812 | + | 0.648972i | \(0.224801\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 23.3137 | 1.09780 | ||||||||
\(452\) | 5.41421 | − | 5.41421i | 0.254663 | − | 0.254663i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 6.14214i | 0.288265i | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 7.51472 | + | 7.51472i | 0.351524 | + | 0.351524i | 0.860676 | − | 0.509153i | \(-0.170041\pi\) |
−0.509153 | + | 0.860676i | \(0.670041\pi\) | |||||||
\(458\) | 3.48528 | + | 3.48528i | 0.162857 | + | 0.162857i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − | 37.3137i | − | 1.73787i | −0.494924 | − | 0.868936i | \(-0.664804\pi\) | ||
0.494924 | − | 0.868936i | \(-0.335196\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 5.51472 | − | 5.51472i | 0.256291 | − | 0.256291i | −0.567253 | − | 0.823544i | \(-0.691994\pi\) |
0.823544 | + | 0.567253i | \(0.191994\pi\) | |||||||
\(464\) | 3.17157 | 0.147237 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −7.65685 | −0.354697 | ||||||||
\(467\) | −9.65685 | + | 9.65685i | −0.446866 | + | 0.446866i | −0.894311 | − | 0.447445i | \(-0.852334\pi\) |
0.447445 | + | 0.894311i | \(0.352334\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0.585786i | 0.0270491i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 5.65685 | + | 5.65685i | 0.260378 | + | 0.260378i | ||||
\(473\) | −30.9706 | − | 30.9706i | −1.42403 | − | 1.42403i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | − | 2.24264i | − | 0.102791i | ||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −17.8284 | + | 17.8284i | −0.815453 | + | 0.815453i | ||||
\(479\) | −9.65685 | −0.441233 | −0.220616 | − | 0.975361i | \(-0.570807\pi\) | ||||
−0.220616 | + | 0.975361i | \(0.570807\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 41.4558 | 1.89022 | ||||||||
\(482\) | −5.41421 | + | 5.41421i | −0.246611 | + | 0.246611i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 12.3137i | 0.559714i | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −20.0000 | − | 20.0000i | −0.906287 | − | 0.906287i | 0.0896838 | − | 0.995970i | \(-0.471414\pi\) |
−0.995970 | + | 0.0896838i | \(0.971414\pi\) | |||||||
\(488\) | −4.65685 | − | 4.65685i | −0.210806 | − | 0.210806i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 22.9706i | 1.03665i | 0.855185 | + | 0.518323i | \(0.173444\pi\) | ||||
−0.855185 | + | 0.518323i | \(0.826556\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −5.02944 | + | 5.02944i | −0.226514 | + | 0.226514i | ||||
\(494\) | 34.1421 | 1.53613 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 8.82843 | 0.396408 | ||||||||
\(497\) | −8.65685 | + | 8.65685i | −0.388313 | + | 0.388313i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − | 24.0000i | − | 1.07439i | −0.843459 | − | 0.537194i | \(-0.819484\pi\) | ||
0.843459 | − | 0.537194i | \(-0.180516\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −4.92893 | − | 4.92893i | −0.219989 | − | 0.219989i | ||||
\(503\) | 20.4142 | + | 20.4142i | 0.910225 | + | 0.910225i | 0.996290 | − | 0.0860648i | \(-0.0274292\pi\) |
−0.0860648 | + | 0.996290i | \(0.527429\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | − | 32.9706i | − | 1.46572i | ||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 1.17157 | − | 1.17157i | 0.0519801 | − | 0.0519801i | ||||
\(509\) | 18.3431 | 0.813046 | 0.406523 | − | 0.913641i | \(-0.366741\pi\) | ||||
0.406523 | + | 0.913641i | \(0.366741\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −8.48528 | −0.375367 | ||||||||
\(512\) | 0.707107 | − | 0.707107i | 0.0312500 | − | 0.0312500i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | − | 9.75736i | − | 0.430379i | ||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −30.9706 | − | 30.9706i | −1.36208 | − | 1.36208i | ||||
\(518\) | −6.07107 | − | 6.07107i | −0.266747 | − | 0.266747i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 6.97056i | − | 0.305386i | −0.988274 | − | 0.152693i | \(-0.951205\pi\) | ||
0.988274 | − | 0.152693i | \(-0.0487946\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 30.2843 | − | 30.2843i | 1.32424 | − | 1.32424i | 0.413930 | − | 0.910309i | \(-0.364156\pi\) |
0.910309 | − | 0.413930i | \(-0.135844\pi\) | |||||||
\(524\) | −6.00000 | −0.262111 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 31.1127 | 1.35658 | ||||||||
\(527\) | −14.0000 | + | 14.0000i | −0.609850 | + | 0.609850i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 23.6274i | 1.02728i | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −5.00000 | − | 5.00000i | −0.216777 | − | 0.216777i | ||||
\(533\) | −16.4853 | − | 16.4853i | −0.714057 | − | 0.714057i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | − | 0.585786i | − | 0.0253021i | ||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 15.0711 | − | 15.0711i | 0.649760 | − | 0.649760i | ||||
\(539\) | 4.82843 | 0.207975 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 9.51472 | 0.409070 | 0.204535 | − | 0.978859i | \(-0.434432\pi\) | ||||
0.204535 | + | 0.978859i | \(0.434432\pi\) | |||||||
\(542\) | 5.07107 | − | 5.07107i | 0.217821 | − | 0.217821i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 2.24264i | 0.0961524i | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −23.7279 | − | 23.7279i | −1.01453 | − | 1.01453i | −0.999893 | − | 0.0146399i | \(-0.995340\pi\) |
−0.0146399 | − | 0.999893i | \(-0.504660\pi\) | |||||||
\(548\) | 1.07107 | + | 1.07107i | 0.0457537 | + | 0.0457537i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 22.4264i | 0.955397i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 9.41421 | − | 9.41421i | 0.400333 | − | 0.400333i | ||||
\(554\) | −25.5563 | −1.08579 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −0.242641 | −0.0102903 | ||||||||
\(557\) | 2.10051 | − | 2.10051i | 0.0890013 | − | 0.0890013i | −0.661204 | − | 0.750206i | \(-0.729954\pi\) |
0.750206 | + | 0.661204i | \(0.229954\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 43.7990i | 1.85250i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −9.14214 | − | 9.14214i | −0.385638 | − | 0.385638i | ||||
\(563\) | 20.1421 | + | 20.1421i | 0.848890 | + | 0.848890i | 0.989995 | − | 0.141105i | \(-0.0450655\pi\) |
−0.141105 | + | 0.989995i | \(0.545065\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 25.4558i | 1.06999i | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 8.65685 | − | 8.65685i | 0.363234 | − | 0.363234i | ||||
\(569\) | 10.3848 | 0.435352 | 0.217676 | − | 0.976021i | \(-0.430152\pi\) | ||||
0.217676 | + | 0.976021i | \(0.430152\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 8.97056 | 0.375406 | 0.187703 | − | 0.982226i | \(-0.439896\pi\) | ||||
0.187703 | + | 0.982226i | \(0.439896\pi\) | |||||||
\(572\) | 16.4853 | − | 16.4853i | 0.689284 | − | 0.689284i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 4.82843i | 0.201535i | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 11.1716 | + | 11.1716i | 0.465079 | + | 0.465079i | 0.900316 | − | 0.435237i | \(-0.143335\pi\) |
−0.435237 | + | 0.900316i | \(0.643335\pi\) | |||||||
\(578\) | 8.46447 | + | 8.46447i | 0.352075 | + | 0.352075i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | − | 13.6569i | − | 0.566582i | ||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −23.3137 | + | 23.3137i | −0.965555 | + | 0.965555i | ||||
\(584\) | 8.48528 | 0.351123 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 31.7990 | 1.31360 | ||||||||
\(587\) | −14.0000 | + | 14.0000i | −0.577842 | + | 0.577842i | −0.934308 | − | 0.356466i | \(-0.883981\pi\) |
0.356466 | + | 0.934308i | \(0.383981\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 62.4264i | 2.57224i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 6.07107 | + | 6.07107i | 0.249519 | + | 0.249519i | ||||
\(593\) | −14.4142 | − | 14.4142i | −0.591921 | − | 0.591921i | 0.346229 | − | 0.938150i | \(-0.387462\pi\) |
−0.938150 | + | 0.346229i | \(0.887462\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | − | 5.31371i | − | 0.217658i | ||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −23.3137 | + | 23.3137i | −0.953368 | + | 0.953368i | ||||
\(599\) | −4.92893 | −0.201391 | −0.100695 | − | 0.994917i | \(-0.532107\pi\) | ||||
−0.100695 | + | 0.994917i | \(0.532107\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −18.0000 | −0.734235 | −0.367118 | − | 0.930175i | \(-0.619655\pi\) | ||||
−0.367118 | + | 0.930175i | \(0.619655\pi\) | |||||||
\(602\) | 6.41421 | − | 6.41421i | 0.261424 | − | 0.261424i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 13.3137i | 0.541727i | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 12.3848 | + | 12.3848i | 0.502683 | + | 0.502683i | 0.912271 | − | 0.409588i | \(-0.134328\pi\) |
−0.409588 | + | 0.912271i | \(0.634328\pi\) | |||||||
\(608\) | 5.00000 | + | 5.00000i | 0.202777 | + | 0.202777i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 43.7990i | 1.77192i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 3.58579 | − | 3.58579i | 0.144829 | − | 0.144829i | −0.630975 | − | 0.775803i | \(-0.717345\pi\) |
0.775803 | + | 0.630975i | \(0.217345\pi\) | |||||||
\(614\) | −10.6274 | −0.428888 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −4.82843 | −0.194543 | ||||||||
\(617\) | 24.5858 | − | 24.5858i | 0.989786 | − | 0.989786i | −0.0101619 | − | 0.999948i | \(-0.503235\pi\) |
0.999948 | + | 0.0101619i | \(0.00323468\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 34.8701i | 1.40155i | 0.713384 | + | 0.700773i | \(0.247161\pi\) | ||||
−0.713384 | + | 0.700773i | \(0.752839\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −11.3137 | − | 11.3137i | −0.453638 | − | 0.453638i | ||||
\(623\) | −9.41421 | − | 9.41421i | −0.377173 | − | 0.377173i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 27.7990i | 1.11107i | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 2.58579 | − | 2.58579i | 0.103184 | − | 0.103184i | ||||
\(629\) | −19.2548 | −0.767741 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 4.97056 | 0.197875 | 0.0989375 | − | 0.995094i | \(-0.468456\pi\) | ||||
0.0989375 | + | 0.995094i | \(0.468456\pi\) | |||||||
\(632\) | −9.41421 | + | 9.41421i | −0.374477 | + | 0.374477i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | − | 17.3137i | − | 0.687615i | ||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −3.41421 | − | 3.41421i | −0.135276 | − | 0.135276i | ||||
\(638\) | 10.8284 | + | 10.8284i | 0.428702 | + | 0.428702i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − | 40.5269i | − | 1.60072i | −0.599522 | − | 0.800358i | \(-0.704643\pi\) | ||
0.599522 | − | 0.800358i | \(-0.295357\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −0.142136 | + | 0.142136i | −0.00560528 | + | 0.00560528i | −0.709904 | − | 0.704299i | \(-0.751262\pi\) |
0.704299 | + | 0.709904i | \(0.251262\pi\) | |||||||
\(644\) | 6.82843 | 0.269078 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −15.8579 | −0.623919 | ||||||||
\(647\) | 18.2132 | − | 18.2132i | 0.716035 | − | 0.716035i | −0.251756 | − | 0.967791i | \(-0.581008\pi\) |
0.967791 | + | 0.251756i | \(0.0810080\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 38.6274i | 1.51626i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −4.89949 | − | 4.89949i | −0.191879 | − | 0.191879i | ||||
\(653\) | 2.58579 | + | 2.58579i | 0.101190 | + | 0.101190i | 0.755889 | − | 0.654700i | \(-0.227205\pi\) |
−0.654700 | + | 0.755889i | \(0.727205\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | − | 4.82843i | − | 0.188518i | ||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 6.41421 | − | 6.41421i | 0.250052 | − | 0.250052i | ||||
\(659\) | 17.7990 | 0.693350 | 0.346675 | − | 0.937985i | \(-0.387311\pi\) | ||||
0.346675 | + | 0.937985i | \(0.387311\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −27.7574 | −1.07964 | −0.539818 | − | 0.841782i | \(-0.681507\pi\) | ||||
−0.539818 | + | 0.841782i | \(0.681507\pi\) | |||||||
\(662\) | −1.31371 | + | 1.31371i | −0.0510587 | + | 0.0510587i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 13.6569i | 0.529989i | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −15.3137 | − | 15.3137i | −0.592949 | − | 0.592949i | ||||
\(668\) | 6.89949 | + | 6.89949i | 0.266949 | + | 0.266949i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − | 31.7990i | − | 1.22759i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −13.7990 | + | 13.7990i | −0.531912 | + | 0.531912i | −0.921141 | − | 0.389229i | \(-0.872741\pi\) |
0.389229 | + | 0.921141i | \(0.372741\pi\) | |||||||
\(674\) | −2.14214 | −0.0825120 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −10.3137 | −0.396681 | ||||||||
\(677\) | 7.51472 | − | 7.51472i | 0.288814 | − | 0.288814i | −0.547797 | − | 0.836611i | \(-0.684533\pi\) |
0.836611 | + | 0.547797i | \(0.184533\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − | 11.6569i | − | 0.447349i | ||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 30.1421 | + | 30.1421i | 1.15420 | + | 1.15420i | ||||
\(683\) | 3.89949 | + | 3.89949i | 0.149210 | + | 0.149210i | 0.777765 | − | 0.628555i | \(-0.216353\pi\) |
−0.628555 | + | 0.777765i | \(0.716353\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 1.00000i | 0.0381802i | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −6.41421 | + | 6.41421i | −0.244540 | + | 0.244540i | ||||
\(689\) | 32.9706 | 1.25608 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −17.2132 | −0.654821 | −0.327411 | − | 0.944882i | \(-0.606176\pi\) | ||||
−0.327411 | + | 0.944882i | \(0.606176\pi\) | |||||||
\(692\) | 8.00000 | − | 8.00000i | 0.304114 | − | 0.304114i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 20.9706i | 0.796032i | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 7.65685 | + | 7.65685i | 0.290024 | + | 0.290024i | ||||
\(698\) | −6.17157 | − | 6.17157i | −0.233597 | − | 0.233597i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 26.4853i | 1.00034i | 0.865929 | + | 0.500168i | \(0.166728\pi\) | ||||
−0.865929 | + | 0.500168i | \(0.833272\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −42.9289 | + | 42.9289i | −1.61910 | + | 1.61910i | ||||
\(704\) | 4.82843 | 0.181978 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 21.7574 | 0.818849 | ||||||||
\(707\) | −3.07107 | + | 3.07107i | −0.115499 | + | 0.115499i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 5.31371i | 0.199561i | 0.995009 | + | 0.0997803i | \(0.0318140\pi\) | ||||
−0.995009 | + | 0.0997803i | \(0.968186\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 9.41421 | + | 9.41421i | 0.352813 | + | 0.352813i | ||||
\(713\) | −42.6274 | − | 42.6274i | −1.59641 | − | 1.59641i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | − | 13.3137i | − | 0.497557i | ||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 14.6569 | − | 14.6569i | 0.546989 | − | 0.546989i | ||||
\(719\) | −5.45584 | −0.203469 | −0.101734 | − | 0.994812i | \(-0.532439\pi\) | ||||
−0.101734 | + | 0.994812i | \(0.532439\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 4.82843 | 0.179820 | ||||||||
\(722\) | −21.9203 | + | 21.9203i | −0.815789 | + | 0.815789i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 11.0711i | 0.411453i | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 10.2426 | + | 10.2426i | 0.379879 | + | 0.379879i | 0.871058 | − | 0.491180i | \(-0.163434\pi\) |
−0.491180 | + | 0.871058i | \(0.663434\pi\) | |||||||
\(728\) | 3.41421 | + | 3.41421i | 0.126539 | + | 0.126539i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − | 20.3431i | − | 0.752418i | ||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −20.7279 | + | 20.7279i | −0.765603 | + | 0.765603i | −0.977329 | − | 0.211726i | \(-0.932092\pi\) |
0.211726 | + | 0.977329i | \(0.432092\pi\) | |||||||
\(734\) | 28.2843 | 1.04399 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −6.82843 | −0.251699 | ||||||||
\(737\) | 2.00000 | − | 2.00000i | 0.0736709 | − | 0.0736709i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 2.62742i | 0.0966511i | 0.998832 | + | 0.0483255i | \(0.0153885\pi\) | ||||
−0.998832 | + | 0.0483255i | \(0.984612\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −4.82843 | − | 4.82843i | −0.177257 | − | 0.177257i | ||||
\(743\) | −18.1421 | − | 18.1421i | −0.665570 | − | 0.665570i | 0.291117 | − | 0.956687i | \(-0.405973\pi\) |
−0.956687 | + | 0.291117i | \(0.905973\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 15.8995i | 0.582122i | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −7.65685 | + | 7.65685i | −0.279962 | + | 0.279962i | ||||
\(749\) | 12.8284 | 0.468741 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 44.9706 | 1.64100 | 0.820500 | − | 0.571647i | \(-0.193695\pi\) | ||||
0.820500 | + | 0.571647i | \(0.193695\pi\) | |||||||
\(752\) | −6.41421 | + | 6.41421i | −0.233902 | + | 0.233902i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | − | 15.3137i | − | 0.557692i | ||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −24.0711 | − | 24.0711i | −0.874878 | − | 0.874878i | 0.118121 | − | 0.992999i | \(-0.462313\pi\) |
−0.992999 | + | 0.118121i | \(0.962313\pi\) | |||||||
\(758\) | −4.00000 | − | 4.00000i | −0.145287 | − | 0.145287i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − | 15.6569i | − | 0.567561i | −0.958889 | − | 0.283780i | \(-0.908411\pi\) | ||
0.958889 | − | 0.283780i | \(-0.0915886\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 14.2426 | − | 14.2426i | 0.515618 | − | 0.515618i | ||||
\(764\) | 13.4142 | 0.485309 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 7.41421 | 0.267886 | ||||||||
\(767\) | 27.3137 | − | 27.3137i | 0.986241 | − | 0.986241i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 12.1421i | 0.437857i | 0.975741 | + | 0.218928i | \(0.0702561\pi\) | ||||
−0.975741 | + | 0.218928i | \(0.929744\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −6.00000 | − | 6.00000i | −0.215945 | − | 0.215945i | ||||
\(773\) | 31.9411 | + | 31.9411i | 1.14884 | + | 1.14884i | 0.986781 | + | 0.162062i | \(0.0518144\pi\) |
0.162062 | + | 0.986781i | \(0.448186\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 11.6569i | 0.418457i | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 3.75736 | − | 3.75736i | 0.134708 | − | 0.134708i | ||||
\(779\) | 34.1421 | 1.22327 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 59.1127 | 2.11522 | ||||||||
\(782\) | 10.8284 | − | 10.8284i | 0.387224 | − | 0.387224i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | − | 1.00000i | − | 0.0357143i | ||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 35.3137 | + | 35.3137i | 1.25880 | + | 1.25880i | 0.951667 | + | 0.307130i | \(0.0993687\pi\) |
0.307130 | + | 0.951667i | \(0.400631\pi\) | |||||||
\(788\) | −3.17157 | − | 3.17157i | −0.112983 | − | 0.112983i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 7.65685i | 0.272246i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −22.4853 | + | 22.4853i | −0.798476 | + | 0.798476i | ||||
\(794\) | 35.9411 | 1.27550 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0.343146 | 0.0121625 | ||||||||
\(797\) | −3.79899 | + | 3.79899i | −0.134567 | + | 0.134567i | −0.771182 | − | 0.636615i | \(-0.780334\pi\) |
0.636615 | + | 0.771182i | \(0.280334\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 20.3431i | − | 0.719689i | ||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −21.9706 | − | 21.9706i | −0.775808 | − | 0.775808i | ||||
\(803\) | 28.9706 | + | 28.9706i | 1.02235 | + | 1.02235i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | − | 42.6274i | − | 1.50149i | ||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 3.07107 | − | 3.07107i | 0.108040 | − | 0.108040i | ||||
\(809\) | −9.69848 | −0.340981 | −0.170490 | − | 0.985359i | \(-0.554535\pi\) | ||||
−0.170490 | + | 0.985359i | \(0.554535\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −23.7574 | −0.834234 | −0.417117 | − | 0.908853i | \(-0.636959\pi\) | ||||
−0.417117 | + | 0.908853i | \(0.636959\pi\) | |||||||
\(812\) | −2.24264 | + | 2.24264i | −0.0787013 | + | 0.0787013i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 41.4558i | 1.45303i | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −45.3553 | − | 45.3553i | −1.58678 | − | 1.58678i | ||||
\(818\) | −26.3848 | − | 26.3848i | −0.922522 | − | 0.922522i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − | 11.8579i | − | 0.413842i | −0.978358 | − | 0.206921i | \(-0.933656\pi\) | ||
0.978358 | − | 0.206921i | \(-0.0663444\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 14.6863 | − | 14.6863i | 0.511932 | − | 0.511932i | −0.403186 | − | 0.915118i | \(-0.632097\pi\) |
0.915118 | + | 0.403186i | \(0.132097\pi\) | |||||||
\(824\) | −4.82843 | −0.168206 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −8.00000 | −0.278356 | ||||||||
\(827\) | −5.17157 | + | 5.17157i | −0.179833 | + | 0.179833i | −0.791283 | − | 0.611450i | \(-0.790587\pi\) |
0.611450 | + | 0.791283i | \(0.290587\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 18.8701i | 0.655384i | 0.944785 | + | 0.327692i | \(0.106271\pi\) | ||||
−0.944785 | + | 0.327692i | \(0.893729\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −3.41421 | − | 3.41421i | −0.118367 | − | 0.118367i | ||||
\(833\) | 1.58579 | + | 1.58579i | 0.0549442 | + | 0.0549442i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 34.1421i | 1.18083i | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 14.1421 | − | 14.1421i | 0.488532 | − | 0.488532i | ||||
\(839\) | 26.8284 | 0.926220 | 0.463110 | − | 0.886301i | \(-0.346733\pi\) | ||||
0.463110 | + | 0.886301i | \(0.346733\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −18.9411 | −0.653142 | ||||||||
\(842\) | 19.8995 | − | 19.8995i | 0.685782 | − | 0.685782i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | − | 3.51472i | − | 0.120982i | ||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −8.70711 | − | 8.70711i | −0.299180 | − | 0.299180i | ||||
\(848\) | 4.82843 | + | 4.82843i | 0.165809 | + | 0.165809i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − | 58.6274i | − | 2.00972i | ||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −3.55635 | + | 3.55635i | −0.121767 | + | 0.121767i | −0.765364 | − | 0.643597i | \(-0.777441\pi\) |
0.643597 | + | 0.765364i | \(0.277441\pi\) | |||||||
\(854\) | 6.58579 | 0.225361 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −12.8284 | −0.438467 | ||||||||
\(857\) | 27.0416 | − | 27.0416i | 0.923725 | − | 0.923725i | −0.0735659 | − | 0.997290i | \(-0.523438\pi\) |
0.997290 | + | 0.0735659i | \(0.0234379\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 15.2721i | 0.521077i | 0.965464 | + | 0.260538i | \(0.0839000\pi\) | ||||
−0.965464 | + | 0.260538i | \(0.916100\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −9.34315 | − | 9.34315i | −0.318229 | − | 0.318229i | ||||
\(863\) | 18.6274 | + | 18.6274i | 0.634085 | + | 0.634085i | 0.949090 | − | 0.315005i | \(-0.102006\pi\) |
−0.315005 | + | 0.949090i | \(0.602006\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | − | 34.2843i | − | 1.16503i | ||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −6.24264 | + | 6.24264i | −0.211889 | + | 0.211889i | ||||
\(869\) | −64.2843 | −2.18069 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −2.82843 | −0.0958376 | ||||||||
\(872\) | −14.2426 | + | 14.2426i | −0.482317 | + | 0.482317i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | − | 48.2843i | − | 1.63324i | ||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 19.7279 | + | 19.7279i | 0.666165 | + | 0.666165i | 0.956826 | − | 0.290661i | \(-0.0938753\pi\) |
−0.290661 | + | 0.956826i | \(0.593875\pi\) | |||||||
\(878\) | 18.2426 | + | 18.2426i | 0.615659 | + | 0.615659i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 42.4853i | 1.43137i | 0.698426 | + | 0.715683i | \(0.253884\pi\) | ||||
−0.698426 | + | 0.715683i | \(0.746116\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 38.8995 | − | 38.8995i | 1.30907 | − | 1.30907i | 0.386987 | − | 0.922085i | \(-0.373516\pi\) |
0.922085 | − | 0.386987i | \(-0.126484\pi\) | |||||||
\(884\) | 10.8284 | 0.364199 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 34.6274 | 1.16333 | ||||||||
\(887\) | −0.615224 | + | 0.615224i | −0.0206572 | + | 0.0206572i | −0.717360 | − | 0.696703i | \(-0.754650\pi\) |
0.696703 | + | 0.717360i | \(0.254650\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 1.65685i | 0.0555691i | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −7.89949 | − | 7.89949i | −0.264495 | − | 0.264495i | ||||
\(893\) | −45.3553 | − | 45.3553i | −1.51776 | − | 1.51776i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 1.00000i | 0.0334077i | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 22.7990 | − | 22.7990i | 0.760812 | − | 0.760812i | ||||
\(899\) | 28.0000 | 0.933852 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −15.3137 | −0.510174 | ||||||||
\(902\) | 16.4853 | − | 16.4853i | 0.548900 | − | 0.548900i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | − | 7.65685i | − | 0.254663i | ||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 2.75736 | + | 2.75736i | 0.0915566 | + | 0.0915566i | 0.751402 | − | 0.659845i | \(-0.229378\pi\) |
−0.659845 | + | 0.751402i | \(0.729378\pi\) | |||||||
\(908\) | 4.34315 | + | 4.34315i | 0.144132 | + | 0.144132i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 10.1005i | − | 0.334645i | −0.985902 | − | 0.167322i | \(-0.946488\pi\) | ||
0.985902 | − | 0.167322i | \(-0.0535121\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −46.6274 | + | 46.6274i | −1.54314 | + | 1.54314i | ||||
\(914\) | 10.6274 | 0.351524 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 4.92893 | 0.162857 | ||||||||
\(917\) | 4.24264 | − | 4.24264i | 0.140104 | − | 0.140104i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 31.3137i | − | 1.03294i | −0.856304 | − | 0.516472i | \(-0.827245\pi\) | ||
0.856304 | − | 0.516472i | \(-0.172755\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −26.3848 | − | 26.3848i | −0.868936 | − | 0.868936i | ||||
\(923\) | −41.7990 | − | 41.7990i | −1.37583 | − | 1.37583i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | − | 7.79899i | − | 0.256291i | ||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 2.24264 | − | 2.24264i | 0.0736183 | − | 0.0736183i | ||||
\(929\) | −12.3431 | −0.404965 | −0.202483 | − | 0.979286i | \(-0.564901\pi\) | ||||
−0.202483 | + | 0.979286i | \(0.564901\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 7.07107 | 0.231745 | ||||||||
\(932\) | −5.41421 | + | 5.41421i | −0.177348 | + | 0.177348i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 13.6569i | 0.446866i | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 31.0711 | + | 31.0711i | 1.01505 | + | 1.01505i | 0.999885 | + | 0.0151625i | \(0.00482656\pi\) |
0.0151625 | + | 0.999885i | \(0.495173\pi\) | |||||||
\(938\) | 0.414214 | + | 0.414214i | 0.0135246 | + | 0.0135246i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − | 9.31371i | − | 0.303618i | −0.988410 | − | 0.151809i | \(-0.951490\pi\) | ||
0.988410 | − | 0.151809i | \(-0.0485099\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −23.3137 | + | 23.3137i | −0.759199 | + | 0.759199i | ||||
\(944\) | 8.00000 | 0.260378 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −43.7990 | −1.42403 | ||||||||
\(947\) | 11.4142 | − | 11.4142i | 0.370912 | − | 0.370912i | −0.496897 | − | 0.867809i | \(-0.665527\pi\) |
0.867809 | + | 0.496897i | \(0.165527\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − | 40.9706i | − | 1.32996i | ||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −1.58579 | − | 1.58579i | −0.0513956 | − | 0.0513956i | ||||
\(953\) | −40.3848 | − | 40.3848i | −1.30819 | − | 1.30819i | −0.922720 | − | 0.385471i | \(-0.874039\pi\) |
−0.385471 | − | 0.922720i | \(-0.625961\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 25.2132i | 0.815453i | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −6.82843 | + | 6.82843i | −0.220616 | + | 0.220616i | ||||
\(959\) | −1.51472 | −0.0489128 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 46.9411 | 1.51423 | ||||||||
\(962\) | 29.3137 | − | 29.3137i | 0.945112 | − | 0.945112i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 7.65685i | 0.246611i | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −7.02944 | − | 7.02944i | −0.226051 | − | 0.226051i | 0.584989 | − | 0.811041i | \(-0.301099\pi\) |
−0.811041 | + | 0.584989i | \(0.801099\pi\) | |||||||
\(968\) | 8.70711 | + | 8.70711i | 0.279857 | + | 0.279857i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 35.6569i | 1.14428i | 0.820155 | + | 0.572141i | \(0.193887\pi\) | ||||
−0.820155 | + | 0.572141i | \(0.806113\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0.171573 | − | 0.171573i | 0.00550037 | − | 0.00550037i | ||||
\(974\) | −28.2843 | −0.906287 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −6.58579 | −0.210806 | ||||||||
\(977\) | −38.3848 | + | 38.3848i | −1.22804 | + | 1.22804i | −0.263333 | + | 0.964705i | \(0.584822\pi\) |
−0.964705 | + | 0.263333i | \(0.915178\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 64.2843i | 2.05453i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 16.2426 | + | 16.2426i | 0.518323 | + | 0.518323i | ||||
\(983\) | −21.5858 | − | 21.5858i | −0.688480 | − | 0.688480i | 0.273416 | − | 0.961896i | \(-0.411846\pi\) |
−0.961896 | + | 0.273416i | \(0.911846\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 7.11270i | 0.226514i | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 24.1421 | − | 24.1421i | 0.768064 | − | 0.768064i | ||||
\(989\) | 61.9411 | 1.96961 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −0.686292 | −0.0218008 | −0.0109004 | − | 0.999941i | \(-0.503470\pi\) | ||||
−0.0109004 | + | 0.999941i | \(0.503470\pi\) | |||||||
\(992\) | 6.24264 | − | 6.24264i | 0.198204 | − | 0.198204i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 12.2426i | 0.388313i | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −28.5269 | − | 28.5269i | −0.903456 | − | 0.903456i | 0.0922770 | − | 0.995733i | \(-0.470585\pi\) |
−0.995733 | + | 0.0922770i | \(0.970585\pi\) | |||||||
\(998\) | −16.9706 | − | 16.9706i | −0.537194 | − | 0.537194i | ||||
\(999\) | 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 | 3150.2.m.d.1457.2 | yes | 4 | |
3.2 | odd | 2 | 3150.2.m.c.1457.1 | ✓ | 4 | ||
5.2 | odd | 4 | 3150.2.m.e.2843.2 | yes | 4 | ||
5.3 | odd | 4 | 3150.2.m.c.2843.1 | yes | 4 | ||
5.4 | even | 2 | 3150.2.m.f.1457.1 | yes | 4 | ||
15.2 | even | 4 | 3150.2.m.f.2843.1 | yes | 4 | ||
15.8 | even | 4 | inner | 3150.2.m.d.2843.2 | yes | 4 | |
15.14 | odd | 2 | 3150.2.m.e.1457.2 | yes | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
3150.2.m.c.1457.1 | ✓ | 4 | 3.2 | odd | 2 | ||
3150.2.m.c.2843.1 | yes | 4 | 5.3 | odd | 4 | ||
3150.2.m.d.1457.2 | yes | 4 | 1.1 | even | 1 | trivial | |
3150.2.m.d.2843.2 | yes | 4 | 15.8 | even | 4 | inner | |
3150.2.m.e.1457.2 | yes | 4 | 15.14 | odd | 2 | ||
3150.2.m.e.2843.2 | yes | 4 | 5.2 | odd | 4 | ||
3150.2.m.f.1457.1 | yes | 4 | 5.4 | even | 2 | ||
3150.2.m.f.2843.1 | yes | 4 | 15.2 | even | 4 |