Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [20,3,Mod(13,20)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(20, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 3]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("20.13");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 20 = 2^{2} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 20.f (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: | \(0.544960528721\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(i)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 13.1 | ||
Root | \(-1.00000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 20.13 |
Dual form | 20.3.f.a.17.1 |
$q$-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 \(\left(\mathbb{Z}/20\mathbb{Z}\right)^\times\).
\(n\) | \(11\) | \(17\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{3}{4}\right)\) |
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 | 0 | ||||||||
\(3\) | 1.00000 | + | 1.00000i | 0.333333 | + | 0.333333i | 0.853851 | − | 0.520518i | \(-0.174261\pi\) |
−0.520518 | + | 0.853851i | \(0.674261\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −3.00000 | − | 4.00000i | −0.600000 | − | 0.800000i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −7.00000 | + | 7.00000i | −1.00000 | + | 1.00000i | 1.00000i | \(0.5\pi\) | ||
−1.00000 | \(\pi\) | |||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | − | 7.00000i | − | 0.777778i | ||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 10.0000 | 0.909091 | 0.454545 | − | 0.890724i | \(-0.349802\pi\) | ||||
0.454545 | + | 0.890724i | \(0.349802\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 9.00000 | + | 9.00000i | 0.692308 | + | 0.692308i | 0.962739 | − | 0.270432i | \(-0.0871664\pi\) |
−0.270432 | + | 0.962739i | \(0.587166\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 1.00000 | − | 7.00000i | 0.0666667 | − | 0.466667i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 1.00000 | − | 1.00000i | 0.0588235 | − | 0.0588235i | −0.677083 | − | 0.735907i | \(-0.736756\pi\) |
0.735907 | + | 0.677083i | \(0.236756\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 8.00000i | 0.421053i | 0.977588 | + | 0.210526i | \(0.0675178\pi\) | ||||
−0.977588 | + | 0.210526i | \(0.932482\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −14.0000 | −0.666667 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −23.0000 | − | 23.0000i | −1.00000 | − | 1.00000i | − | 1.00000i | \(-0.5\pi\) | |
−1.00000 | \(\pi\) | |||||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −7.00000 | + | 24.0000i | −0.280000 | + | 0.960000i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 16.0000 | − | 16.0000i | 0.592593 | − | 0.592593i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 8.00000i | 0.275862i | 0.990442 | + | 0.137931i | \(0.0440452\pi\) | ||||
−0.990442 | + | 0.137931i | \(0.955955\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −14.0000 | −0.451613 | −0.225806 | − | 0.974172i | \(-0.572502\pi\) | ||||
−0.225806 | + | 0.974172i | \(0.572502\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 10.0000 | + | 10.0000i | 0.303030 | + | 0.303030i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 49.0000 | + | 7.00000i | 1.40000 | + | 0.200000i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 33.0000 | − | 33.0000i | 0.891892 | − | 0.891892i | −0.102809 | − | 0.994701i | \(-0.532783\pi\) |
0.994701 | + | 0.102809i | \(0.0327831\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 18.0000i | 0.461538i | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −14.0000 | −0.341463 | −0.170732 | − | 0.985318i | \(-0.554613\pi\) | ||||
−0.170732 | + | 0.985318i | \(0.554613\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −15.0000 | − | 15.0000i | −0.348837 | − | 0.348837i | 0.510839 | − | 0.859676i | \(-0.329335\pi\) |
−0.859676 | + | 0.510839i | \(0.829335\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −28.0000 | + | 21.0000i | −0.622222 | + | 0.466667i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −39.0000 | + | 39.0000i | −0.829787 | + | 0.829787i | −0.987487 | − | 0.157700i | \(-0.949592\pi\) |
0.157700 | + | 0.987487i | \(0.449592\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | − | 49.0000i | − | 1.00000i | ||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 2.00000 | 0.0392157 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −7.00000 | − | 7.00000i | −0.132075 | − | 0.132075i | 0.637979 | − | 0.770054i | \(-0.279771\pi\) |
−0.770054 | + | 0.637979i | \(0.779771\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −30.0000 | − | 40.0000i | −0.545455 | − | 0.727273i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −8.00000 | + | 8.00000i | −0.140351 | + | 0.140351i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 56.0000i | 0.949153i | 0.880214 | + | 0.474576i | \(0.157399\pi\) | ||||
−0.880214 | + | 0.474576i | \(0.842601\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 42.0000 | 0.688525 | 0.344262 | − | 0.938874i | \(-0.388129\pi\) | ||||
0.344262 | + | 0.938874i | \(0.388129\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 49.0000 | + | 49.0000i | 0.777778 | + | 0.777778i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 9.00000 | − | 63.0000i | 0.138462 | − | 0.969231i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −7.00000 | + | 7.00000i | −0.104478 | + | 0.104478i | −0.757413 | − | 0.652936i | \(-0.773537\pi\) |
0.652936 | + | 0.757413i | \(0.273537\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | − | 46.0000i | − | 0.666667i | ||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 98.0000 | 1.38028 | 0.690141 | − | 0.723675i | \(-0.257549\pi\) | ||||
0.690141 | + | 0.723675i | \(0.257549\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 49.0000 | + | 49.0000i | 0.671233 | + | 0.671233i | 0.958000 | − | 0.286767i | \(-0.0925807\pi\) |
−0.286767 | + | 0.958000i | \(0.592581\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −31.0000 | + | 17.0000i | −0.413333 | + | 0.226667i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −70.0000 | + | 70.0000i | −0.909091 | + | 0.909091i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − | 96.0000i | − | 1.21519i | −0.794247 | − | 0.607595i | \(-0.792134\pi\) | ||
0.794247 | − | 0.607595i | \(-0.207866\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −31.0000 | −0.382716 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −63.0000 | − | 63.0000i | −0.759036 | − | 0.759036i | 0.217111 | − | 0.976147i | \(-0.430337\pi\) |
−0.976147 | + | 0.217111i | \(0.930337\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −7.00000 | − | 1.00000i | −0.0823529 | − | 0.0117647i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −8.00000 | + | 8.00000i | −0.0919540 | + | 0.0919540i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 112.000i | 1.25843i | 0.777233 | + | 0.629213i | \(0.216623\pi\) | ||||
−0.777233 | + | 0.629213i | \(0.783377\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −126.000 | −1.38462 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −14.0000 | − | 14.0000i | −0.150538 | − | 0.150538i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 32.0000 | − | 24.0000i | 0.336842 | − | 0.252632i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 33.0000 | − | 33.0000i | 0.340206 | − | 0.340206i | −0.516239 | − | 0.856445i | \(-0.672668\pi\) |
0.856445 | + | 0.516239i | \(0.172668\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | − | 70.0000i | − | 0.707071i | ||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 26.0000 | 0.257426 | 0.128713 | − | 0.991682i | \(-0.458915\pi\) | ||||
0.128713 | + | 0.991682i | \(0.458915\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 73.0000 | + | 73.0000i | 0.708738 | + | 0.708738i | 0.966270 | − | 0.257532i | \(-0.0829093\pi\) |
−0.257532 | + | 0.966270i | \(0.582909\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 42.0000 | + | 56.0000i | 0.400000 | + | 0.533333i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 121.000 | − | 121.000i | 1.13084 | − | 1.13084i | 0.140804 | − | 0.990038i | \(-0.455031\pi\) |
0.990038 | − | 0.140804i | \(-0.0449686\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 136.000i | 1.24771i | 0.781542 | + | 0.623853i | \(0.214434\pi\) | ||||
−0.781542 | + | 0.623853i | \(0.785566\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 66.0000 | 0.594595 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −127.000 | − | 127.000i | −1.12389 | − | 1.12389i | −0.991150 | − | 0.132743i | \(-0.957621\pi\) |
−0.132743 | − | 0.991150i | \(-0.542379\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −23.0000 | + | 161.000i | −0.200000 | + | 1.40000i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 63.0000 | − | 63.0000i | 0.538462 | − | 0.538462i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 14.0000i | 0.117647i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −21.0000 | −0.173554 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −14.0000 | − | 14.0000i | −0.113821 | − | 0.113821i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 117.000 | − | 44.0000i | 0.936000 | − | 0.352000i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −7.00000 | + | 7.00000i | −0.0551181 | + | 0.0551181i | −0.734129 | − | 0.679010i | \(-0.762409\pi\) |
0.679010 | + | 0.734129i | \(0.262409\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | − | 30.0000i | − | 0.232558i | ||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −230.000 | −1.75573 | −0.877863 | − | 0.478913i | \(-0.841031\pi\) | ||||
−0.877863 | + | 0.478913i | \(0.841031\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −56.0000 | − | 56.0000i | −0.421053 | − | 0.421053i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −112.000 | − | 16.0000i | −0.829630 | − | 0.118519i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −63.0000 | + | 63.0000i | −0.459854 | + | 0.459854i | −0.898607 | − | 0.438753i | \(-0.855420\pi\) |
0.438753 | + | 0.898607i | \(0.355420\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 88.0000i | 0.633094i | 0.948577 | + | 0.316547i | \(0.102523\pi\) | ||||
−0.948577 | + | 0.316547i | \(0.897477\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −78.0000 | −0.553191 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 90.0000 | + | 90.0000i | 0.629371 | + | 0.629371i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 32.0000 | − | 24.0000i | 0.220690 | − | 0.165517i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 49.0000 | − | 49.0000i | 0.333333 | − | 0.333333i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | − | 168.000i | − | 1.12752i | −0.825940 | − | 0.563758i | \(-0.809355\pi\) | ||
0.825940 | − | 0.563758i | \(-0.190645\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 130.000 | 0.860927 | 0.430464 | − | 0.902608i | \(-0.358350\pi\) | ||||
0.430464 | + | 0.902608i | \(0.358350\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −7.00000 | − | 7.00000i | −0.0457516 | − | 0.0457516i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 42.0000 | + | 56.0000i | 0.270968 | + | 0.361290i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −63.0000 | + | 63.0000i | −0.401274 | + | 0.401274i | −0.878682 | − | 0.477408i | \(-0.841576\pi\) |
0.477408 | + | 0.878682i | \(0.341576\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | − | 14.0000i | − | 0.0880503i | ||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 322.000 | 2.00000 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 65.0000 | + | 65.0000i | 0.398773 | + | 0.398773i | 0.877800 | − | 0.479027i | \(-0.159010\pi\) |
−0.479027 | + | 0.877800i | \(0.659010\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 10.0000 | − | 70.0000i | 0.0606061 | − | 0.424242i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −103.000 | + | 103.000i | −0.616766 | + | 0.616766i | −0.944701 | − | 0.327934i | \(-0.893648\pi\) |
0.327934 | + | 0.944701i | \(0.393648\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | − | 7.00000i | − | 0.0414201i | ||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 56.0000 | 0.327485 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 73.0000 | + | 73.0000i | 0.421965 | + | 0.421965i | 0.885880 | − | 0.463915i | \(-0.153556\pi\) |
−0.463915 | + | 0.885880i | \(0.653556\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −119.000 | − | 217.000i | −0.680000 | − | 1.24000i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −56.0000 | + | 56.0000i | −0.316384 | + | 0.316384i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − | 56.0000i | − | 0.312849i | −0.987690 | − | 0.156425i | \(-0.950003\pi\) | ||
0.987690 | − | 0.156425i | \(-0.0499968\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −70.0000 | −0.386740 | −0.193370 | − | 0.981126i | \(-0.561942\pi\) | ||||
−0.193370 | + | 0.981126i | \(0.561942\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 42.0000 | + | 42.0000i | 0.229508 | + | 0.229508i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −231.000 | − | 33.0000i | −1.24865 | − | 0.178378i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 10.0000 | − | 10.0000i | 0.0534759 | − | 0.0534759i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 224.000i | 1.18519i | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −142.000 | −0.743455 | −0.371728 | − | 0.928342i | \(-0.621235\pi\) | ||||
−0.371728 | + | 0.928342i | \(0.621235\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −63.0000 | − | 63.0000i | −0.326425 | − | 0.326425i | 0.524800 | − | 0.851225i | \(-0.324140\pi\) |
−0.851225 | + | 0.524800i | \(0.824140\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 72.0000 | − | 54.0000i | 0.369231 | − | 0.276923i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −63.0000 | + | 63.0000i | −0.319797 | + | 0.319797i | −0.848689 | − | 0.528892i | \(-0.822608\pi\) |
0.528892 | + | 0.848689i | \(0.322608\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 336.000i | − | 1.68844i | −0.535995 | − | 0.844221i | \(-0.680063\pi\) | ||
0.535995 | − | 0.844221i | \(-0.319937\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −14.0000 | −0.0696517 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −56.0000 | − | 56.0000i | −0.275862 | − | 0.275862i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 42.0000 | + | 56.0000i | 0.204878 | + | 0.273171i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −161.000 | + | 161.000i | −0.777778 | + | 0.777778i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 80.0000i | 0.382775i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 314.000 | 1.48815 | 0.744076 | − | 0.668095i | \(-0.232890\pi\) | ||||
0.744076 | + | 0.668095i | \(0.232890\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 98.0000 | + | 98.0000i | 0.460094 | + | 0.460094i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −15.0000 | + | 105.000i | −0.0697674 | + | 0.488372i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 98.0000 | − | 98.0000i | 0.451613 | − | 0.451613i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 98.0000i | 0.447489i | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 18.0000 | 0.0814480 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −135.000 | − | 135.000i | −0.605381 | − | 0.605381i | 0.336354 | − | 0.941736i | \(-0.390806\pi\) |
−0.941736 | + | 0.336354i | \(0.890806\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 168.000 | + | 49.0000i | 0.746667 | + | 0.217778i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 281.000 | − | 281.000i | 1.23789 | − | 1.23789i | 0.277022 | − | 0.960864i | \(-0.410653\pi\) |
0.960864 | − | 0.277022i | \(-0.0893474\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − | 168.000i | − | 0.733624i | −0.930295 | − | 0.366812i | \(-0.880449\pi\) | ||
0.930295 | − | 0.366812i | \(-0.119551\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −140.000 | −0.606061 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 273.000 | + | 273.000i | 1.17167 | + | 1.17167i | 0.981811 | + | 0.189863i | \(0.0608045\pi\) |
0.189863 | + | 0.981811i | \(0.439196\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 273.000 | + | 39.0000i | 1.16170 | + | 0.165957i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 96.0000 | − | 96.0000i | 0.405063 | − | 0.405063i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 288.000i | 1.20502i | 0.798111 | + | 0.602510i | \(0.205833\pi\) | ||||
−0.798111 | + | 0.602510i | \(0.794167\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −446.000 | −1.85062 | −0.925311 | − | 0.379209i | \(-0.876196\pi\) | ||||
−0.925311 | + | 0.379209i | \(0.876196\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −175.000 | − | 175.000i | −0.720165 | − | 0.720165i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −196.000 | + | 147.000i | −0.800000 | + | 0.600000i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −72.0000 | + | 72.0000i | −0.291498 | + | 0.291498i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | − | 126.000i | − | 0.506024i | ||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −150.000 | −0.597610 | −0.298805 | − | 0.954314i | \(-0.596588\pi\) | ||||
−0.298805 | + | 0.954314i | \(0.596588\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −230.000 | − | 230.000i | −0.909091 | − | 0.909091i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −6.00000 | − | 8.00000i | −0.0235294 | − | 0.0313725i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 161.000 | − | 161.000i | 0.626459 | − | 0.626459i | −0.320716 | − | 0.947175i | \(-0.603924\pi\) |
0.947175 | + | 0.320716i | \(0.103924\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 462.000i | 1.78378i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 56.0000 | 0.214559 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −151.000 | − | 151.000i | −0.574144 | − | 0.574144i | 0.359139 | − | 0.933284i | \(-0.383070\pi\) |
−0.933284 | + | 0.359139i | \(0.883070\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −7.00000 | + | 49.0000i | −0.0264151 | + | 0.184906i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −112.000 | + | 112.000i | −0.419476 | + | 0.419476i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − | 376.000i | − | 1.39777i | −0.715234 | − | 0.698885i | \(-0.753680\pi\) | ||
0.715234 | − | 0.698885i | \(-0.246320\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 210.000 | 0.774908 | 0.387454 | − | 0.921889i | \(-0.373355\pi\) | ||||
0.387454 | + | 0.921889i | \(0.373355\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −126.000 | − | 126.000i | −0.461538 | − | 0.461538i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −70.0000 | + | 240.000i | −0.254545 | + | 0.872727i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 129.000 | − | 129.000i | 0.465704 | − | 0.465704i | −0.434816 | − | 0.900520i | \(-0.643186\pi\) |
0.900520 | + | 0.434816i | \(0.143186\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 98.0000i | 0.351254i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −174.000 | −0.619217 | −0.309609 | − | 0.950864i | \(-0.600198\pi\) | ||||
−0.309609 | + | 0.950864i | \(0.600198\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 113.000 | + | 113.000i | 0.399293 | + | 0.399293i | 0.877984 | − | 0.478690i | \(-0.158888\pi\) |
−0.478690 | + | 0.877984i | \(0.658888\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 56.0000 | + | 8.00000i | 0.196491 | + | 0.0280702i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 98.0000 | − | 98.0000i | 0.341463 | − | 0.341463i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 287.000i | 0.993080i | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 66.0000 | 0.226804 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 345.000 | + | 345.000i | 1.17747 | + | 1.17747i | 0.980386 | + | 0.197089i | \(0.0631487\pi\) |
0.197089 | + | 0.980386i | \(0.436851\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 224.000 | − | 168.000i | 0.759322 | − | 0.569492i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 160.000 | − | 160.000i | 0.538721 | − | 0.538721i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | − | 414.000i | − | 1.38462i | ||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 210.000 | 0.697674 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 26.0000 | + | 26.0000i | 0.0858086 | + | 0.0858086i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −126.000 | − | 168.000i | −0.413115 | − | 0.550820i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −327.000 | + | 327.000i | −1.06515 | + | 1.06515i | −0.0674220 | + | 0.997725i | \(0.521477\pi\) |
−0.997725 | + | 0.0674220i | \(0.978523\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 146.000i | 0.472492i | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 2.00000 | 0.00643087 | 0.00321543 | − | 0.999995i | \(-0.498976\pi\) | ||||
0.00321543 | + | 0.999995i | \(0.498976\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 81.0000 | + | 81.0000i | 0.258786 | + | 0.258786i | 0.824560 | − | 0.565774i | \(-0.191423\pi\) |
−0.565774 | + | 0.824560i | \(0.691423\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 49.0000 | − | 343.000i | 0.155556 | − | 1.08889i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −159.000 | + | 159.000i | −0.501577 | + | 0.501577i | −0.911928 | − | 0.410351i | \(-0.865406\pi\) |
0.410351 | + | 0.911928i | \(0.365406\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 80.0000i | 0.250784i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 242.000 | 0.753894 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 8.00000 | + | 8.00000i | 0.0247678 | + | 0.0247678i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −279.000 | + | 153.000i | −0.858462 | + | 0.470769i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −136.000 | + | 136.000i | −0.415902 | + | 0.415902i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | − | 546.000i | − | 1.65957i | ||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −182.000 | −0.549849 | −0.274924 | − | 0.961466i | \(-0.588653\pi\) | ||||
−0.274924 | + | 0.961466i | \(0.588653\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −231.000 | − | 231.000i | −0.693694 | − | 0.693694i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 49.0000 | + | 7.00000i | 0.146269 | + | 0.0208955i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −447.000 | + | 447.000i | −1.32641 | + | 1.32641i | −0.417930 | + | 0.908479i | \(0.637244\pi\) |
−0.908479 | + | 0.417930i | \(0.862756\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | − | 254.000i | − | 0.749263i | ||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −140.000 | −0.410557 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −184.000 | + | 138.000i | −0.533333 | + | 0.400000i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 25.0000 | − | 25.0000i | 0.0720461 | − | 0.0720461i | −0.670166 | − | 0.742212i | \(-0.733777\pi\) |
0.742212 | + | 0.670166i | \(0.233777\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 200.000i | 0.573066i | 0.958070 | + | 0.286533i | \(0.0925028\pi\) | ||||
−0.958070 | + | 0.286533i | \(0.907497\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 288.000 | 0.820513 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 321.000 | + | 321.000i | 0.909348 | + | 0.909348i | 0.996220 | − | 0.0868711i | \(-0.0276868\pi\) |
−0.0868711 | + | 0.996220i | \(0.527687\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −294.000 | − | 392.000i | −0.828169 | − | 1.10423i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −14.0000 | + | 14.0000i | −0.0392157 | + | 0.0392157i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 112.000i | 0.311978i | 0.987759 | + | 0.155989i | \(0.0498564\pi\) | ||||
−0.987759 | + | 0.155989i | \(0.950144\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 297.000 | 0.822715 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −21.0000 | − | 21.0000i | −0.0578512 | − | 0.0578512i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 49.0000 | − | 343.000i | 0.134247 | − | 0.939726i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 377.000 | − | 377.000i | 1.02725 | − | 1.02725i | 0.0276297 | − | 0.999618i | \(-0.491204\pi\) |
0.999618 | − | 0.0276297i | \(-0.00879594\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 98.0000i | 0.265583i | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 98.0000 | 0.264151 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 217.000 | + | 217.000i | 0.581769 | + | 0.581769i | 0.935389 | − | 0.353620i | \(-0.115049\pi\) |
−0.353620 | + | 0.935389i | \(0.615049\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 161.000 | + | 73.0000i | 0.429333 | + | 0.194667i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −72.0000 | + | 72.0000i | −0.190981 | + | 0.190981i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 56.0000i | 0.147757i | 0.997267 | + | 0.0738786i | \(0.0235377\pi\) | ||||
−0.997267 | + | 0.0738786i | \(0.976462\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −14.0000 | −0.0367454 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 57.0000 | + | 57.0000i | 0.148825 | + | 0.148825i | 0.777593 | − | 0.628768i | \(-0.216440\pi\) |
−0.628768 | + | 0.777593i | \(0.716440\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 490.000 | + | 70.0000i | 1.27273 | + | 0.181818i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −105.000 | + | 105.000i | −0.271318 | + | 0.271318i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 312.000i | 0.802057i | 0.916066 | + | 0.401028i | \(0.131347\pi\) | ||||
−0.916066 | + | 0.401028i | \(0.868653\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −46.0000 | −0.117647 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −230.000 | − | 230.000i | −0.585242 | − | 0.585242i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −384.000 | + | 288.000i | −0.972152 | + | 0.729114i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 193.000 | − | 193.000i | 0.486146 | − | 0.486146i | −0.420942 | − | 0.907088i | \(-0.638300\pi\) |
0.907088 | + | 0.420942i | \(0.138300\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | − | 112.000i | − | 0.280702i | ||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −30.0000 | −0.0748130 | −0.0374065 | − | 0.999300i | \(-0.511910\pi\) | ||||
−0.0374065 | + | 0.999300i | \(0.511910\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −126.000 | − | 126.000i | −0.312655 | − | 0.312655i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 93.0000 | + | 124.000i | 0.229630 | + | 0.306173i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 330.000 | − | 330.000i | 0.810811 | − | 0.810811i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 432.000i | − | 1.05623i | −0.849171 | − | 0.528117i | \(-0.822898\pi\) | ||
0.849171 | − | 0.528117i | \(-0.177102\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −126.000 | −0.306569 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −392.000 | − | 392.000i | −0.949153 | − | 0.949153i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −63.0000 | + | 441.000i | −0.151807 | + | 1.06265i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −88.0000 | + | 88.0000i | −0.211031 | + | 0.211031i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 168.000i | 0.400955i | 0.979698 | + | 0.200477i | \(0.0642493\pi\) | ||||
−0.979698 | + | 0.200477i | \(0.935751\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −454.000 | −1.07838 | −0.539192 | − | 0.842183i | \(-0.681270\pi\) | ||||
−0.539192 | + | 0.842183i | \(0.681270\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 273.000 | + | 273.000i | 0.645390 | + | 0.645390i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 17.0000 | + | 31.0000i | 0.0400000 | + | 0.0729412i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −294.000 | + | 294.000i | −0.688525 | + | 0.688525i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 180.000i | 0.419580i | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −494.000 | −1.14617 | −0.573086 | − | 0.819495i | \(-0.694254\pi\) | ||||
−0.573086 | + | 0.819495i | \(0.694254\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −511.000 | − | 511.000i | −1.18014 | − | 1.18014i | −0.979708 | − | 0.200431i | \(-0.935766\pi\) |
−0.200431 | − | 0.979708i | \(-0.564234\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 56.0000 | + | 8.00000i | 0.128736 | + | 0.0183908i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 184.000 | − | 184.000i | 0.421053 | − | 0.421053i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 176.000i | − | 0.400911i | −0.979703 | − | 0.200456i | \(-0.935758\pi\) | ||
0.979703 | − | 0.200456i | \(-0.0642422\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −343.000 | −0.777778 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 177.000 | + | 177.000i | 0.399549 | + | 0.399549i | 0.878074 | − | 0.478525i | \(-0.158828\pi\) |
−0.478525 | + | 0.878074i | \(0.658828\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 448.000 | − | 336.000i | 1.00674 | − | 0.755056i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 168.000 | − | 168.000i | 0.375839 | − | 0.375839i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 608.000i | 1.35412i | 0.735928 | + | 0.677060i | \(0.236746\pi\) | ||||
−0.735928 | + | 0.677060i | \(0.763254\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −140.000 | −0.310421 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 130.000 | + | 130.000i | 0.286976 | + | 0.286976i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 378.000 | + | 504.000i | 0.830769 | + | 1.10769i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 609.000 | − | 609.000i | 1.33260 | − | 1.33260i | 0.429571 | − | 0.903033i | \(-0.358665\pi\) |
0.903033 | − | 0.429571i | \(-0.141335\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | − | 32.0000i | − | 0.0697168i | ||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 490.000 | 1.06291 | 0.531453 | − | 0.847088i | \(-0.321646\pi\) | ||||
0.531453 | + | 0.847088i | \(0.321646\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −7.00000 | − | 7.00000i | −0.0151188 | − | 0.0151188i | 0.699507 | − | 0.714626i | \(-0.253403\pi\) |
−0.714626 | + | 0.699507i | \(0.753403\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −14.0000 | + | 98.0000i | −0.0301075 | + | 0.210753i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 25.0000 | − | 25.0000i | 0.0535332 | − | 0.0535332i | −0.679833 | − | 0.733367i | \(-0.737948\pi\) |
0.733367 | + | 0.679833i | \(0.237948\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − | 98.0000i | − | 0.208955i | ||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −126.000 | −0.267516 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −150.000 | − | 150.000i | −0.317125 | − | 0.317125i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −192.000 | − | 56.0000i | −0.404211 | − | 0.117895i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −49.0000 | + | 49.0000i | −0.102725 | + | 0.102725i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 128.000i | 0.267223i | 0.991034 | + | 0.133612i | \(0.0426575\pi\) | ||||
−0.991034 | + | 0.133612i | \(0.957343\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 594.000 | 1.23493 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 322.000 | + | 322.000i | 0.666667 | + | 0.666667i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −231.000 | − | 33.0000i | −0.476289 | − | 0.0680412i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 249.000 | − | 249.000i | 0.511294 | − | 0.511294i | −0.403629 | − | 0.914923i | \(-0.632251\pi\) |
0.914923 | + | 0.403629i | \(0.132251\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 130.000i | 0.265849i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 650.000 | 1.32383 | 0.661914 | − | 0.749579i | \(-0.269744\pi\) | ||||
0.661914 | + | 0.749579i | \(0.269744\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 8.00000 | + | 8.00000i | 0.0162272 | + | 0.0162272i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −280.000 | + | 210.000i | −0.565657 | + | 0.424242i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −686.000 | + | 686.000i | −1.38028 | + | 1.38028i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − | 632.000i | − | 1.26653i | −0.773934 | − | 0.633267i | \(-0.781714\pi\) | ||
0.773934 | − | 0.633267i | \(-0.218286\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −206.000 | −0.411178 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −471.000 | − | 471.000i | −0.936382 | − | 0.936382i | 0.0617123 | − | 0.998094i | \(-0.480344\pi\) |
−0.998094 | + | 0.0617123i | \(0.980344\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −78.0000 | − | 104.000i | −0.154455 | − | 0.205941i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 7.00000 | − | 7.00000i | 0.0138067 | − | 0.0138067i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 8.00000i | 0.0157171i | 0.999969 | + | 0.00785855i | \(0.00250148\pi\) | ||||
−0.999969 | + | 0.00785855i | \(0.997499\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −686.000 | −1.34247 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 128.000 | + | 128.000i | 0.249513 | + | 0.249513i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 73.0000 | − | 511.000i | 0.141748 | − | 0.992233i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −390.000 | + | 390.000i | −0.754352 | + | 0.754352i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 146.000i | 0.281310i | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −366.000 | −0.702495 | −0.351248 | − | 0.936283i | \(-0.614242\pi\) | ||||
−0.351248 | + | 0.936283i | \(0.614242\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 273.000 | + | 273.000i | 0.521989 | + | 0.521989i | 0.918172 | − | 0.396183i | \(-0.129665\pi\) |
−0.396183 | + | 0.918172i | \(0.629665\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 98.0000 | − | 336.000i | 0.186667 | − | 0.640000i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −14.0000 | + | 14.0000i | −0.0265655 | + | 0.0265655i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 529.000i | 1.00000i | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 392.000 | 0.738230 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −126.000 | − | 126.000i | −0.236398 | − | 0.236398i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −847.000 | − | 121.000i | −1.58318 | − | 0.226168i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 56.0000 | − | 56.0000i | 0.104283 | − | 0.104283i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | − | 490.000i | − | 0.909091i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 394.000 | 0.728281 | 0.364140 | − | 0.931344i | \(-0.381363\pi\) | ||||
0.364140 | + | 0.931344i | \(0.381363\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −70.0000 | − | 70.0000i | −0.128913 | − | 0.128913i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 544.000 | − | 408.000i | 0.998165 | − | 0.748624i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −231.000 | + | 231.000i | −0.422303 | + | 0.422303i | −0.885996 | − | 0.463693i | \(-0.846524\pi\) |
0.463693 | + | 0.885996i | \(0.346524\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | − | 294.000i | − | 0.535519i | ||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −64.0000 | −0.116152 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 672.000 | + | 672.000i | 1.21519 | + | 1.21519i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −198.000 | − | 264.000i | −0.356757 | − | 0.475676i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −735.000 | + | 735.000i | −1.31957 | + | 1.31957i | −0.405453 | + | 0.914116i | \(0.632886\pi\) |
−0.914116 | + | 0.405453i | \(0.867114\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 270.000i | − | 0.483005i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 20.0000 | 0.0356506 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 609.000 | + | 609.000i | 1.08171 | + | 1.08171i | 0.996351 | + | 0.0853545i | \(0.0272023\pi\) |
0.0853545 | + | 0.996351i | \(0.472798\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −127.000 | + | 889.000i | −0.224779 | + | 1.57345i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 217.000 | − | 217.000i | 0.382716 | − | 0.382716i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − | 560.000i | − | 0.984183i | −0.870544 | − | 0.492091i | \(-0.836233\pi\) | ||
0.870544 | − | 0.492091i | \(-0.163767\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 938.000 | 1.64273 | 0.821366 | − | 0.570401i | \(-0.193212\pi\) | ||||
0.821366 | + | 0.570401i | \(0.193212\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −142.000 | − | 142.000i | −0.247818 | − | 0.247818i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 713.000 | − | 391.000i | 1.24000 | − | 0.680000i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 97.0000 | − | 97.0000i | 0.168111 | − | 0.168111i | −0.618038 | − | 0.786149i | \(-0.712072\pi\) |
0.786149 | + | 0.618038i | \(0.212072\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | − | 126.000i | − | 0.217617i | ||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 882.000 | 1.51807 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −70.0000 | − | 70.0000i | −0.120069 | − | 0.120069i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −441.000 | − | 63.0000i | −0.753846 | − | 0.107692i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −39.0000 | + | 39.0000i | −0.0664395 | + | 0.0664395i | −0.739546 | − | 0.673106i | \(-0.764960\pi\) |
0.673106 | + | 0.739546i | \(0.264960\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − | 112.000i | − | 0.190153i | ||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −126.000 | −0.213198 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −479.000 | − | 479.000i | −0.807757 | − | 0.807757i | 0.176537 | − | 0.984294i | \(-0.443511\pi\) |
−0.984294 | + | 0.176537i | \(0.943511\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 56.0000 | − | 42.0000i | 0.0941176 | − | 0.0705882i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 336.000 | − | 336.000i | 0.562814 | − | 0.562814i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 1040.00i | 1.73623i | 0.496366 | + | 0.868114i | \(0.334668\pi\) | ||||
−0.496366 | + | 0.868114i | \(0.665332\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −430.000 | −0.715474 | −0.357737 | − | 0.933822i | \(-0.616452\pi\) | ||||
−0.357737 | + | 0.933822i | \(0.616452\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 49.0000 | + | 49.0000i | 0.0812604 | + | 0.0812604i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 63.0000 | + | 84.0000i | 0.104132 | + | 0.138843i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −423.000 | + | 423.000i | −0.696870 | + | 0.696870i | −0.963734 | − | 0.266864i | \(-0.914012\pi\) |
0.266864 | + | 0.963734i | \(0.414012\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | − | 112.000i | − | 0.183908i | ||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −702.000 | −1.14894 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 249.000 | + | 249.000i | 0.406199 | + | 0.406199i | 0.880411 | − | 0.474212i | \(-0.157267\pi\) |
−0.474212 | + | 0.880411i | \(0.657267\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −14.0000 | + | 98.0000i | −0.0227642 | + | 0.159350i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 321.000 | − | 321.000i | 0.520259 | − | 0.520259i | −0.397390 | − | 0.917650i | \(-0.630084\pi\) |
0.917650 | + | 0.397390i | \(0.130084\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 600.000i | 0.969305i | 0.874707 | + | 0.484653i | \(0.161054\pi\) | ||||
−0.874707 | + | 0.484653i | \(0.838946\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −736.000 | −1.18519 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −784.000 | − | 784.000i | −1.25843 | − | 1.25843i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −527.000 | − | 336.000i | −0.843200 | − | 0.537600i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −80.0000 | + | 80.0000i | −0.127592 | + | 0.127592i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − | 66.0000i | − | 0.104928i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −638.000 | −1.01109 | −0.505547 | − | 0.862799i | \(-0.668709\pi\) | ||||
−0.505547 | + | 0.862799i | \(0.668709\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 314.000 | + | 314.000i | 0.496051 | + | 0.496051i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 49.0000 | + | 7.00000i | 0.0771654 | + | 0.0110236i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 441.000 | − | 441.000i | 0.692308 | − | 0.692308i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | − | 686.000i | − | 1.07355i | ||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 482.000 | 0.751950 | 0.375975 | − | 0.926630i | \(-0.377308\pi\) | ||||
0.375975 | + | 0.926630i | \(0.377308\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 33.0000 | + | 33.0000i | 0.0513219 | + | 0.0513219i | 0.732302 | − | 0.680980i | \(-0.238446\pi\) |
−0.680980 | + | 0.732302i | \(0.738446\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −120.000 | + | 90.0000i | −0.186047 | + | 0.139535i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −7.00000 | + | 7.00000i | −0.0108192 | + | 0.0108192i | −0.712496 | − | 0.701677i | \(-0.752435\pi\) |
0.701677 | + | 0.712496i | \(0.252435\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 560.000i | 0.862866i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 196.000 | 0.301075 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −471.000 | − | 471.000i | −0.721286 | − | 0.721286i | 0.247581 | − | 0.968867i | \(-0.420364\pi\) |
−0.968867 | + | 0.247581i | \(0.920364\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 690.000 | + | 920.000i | 1.05344 | + | 1.40458i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 343.000 | − | 343.000i | 0.522070 | − | 0.522070i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 328.000i | 0.497724i | 0.968539 | + | 0.248862i | \(0.0800565\pi\) | ||||
−0.968539 | + | 0.248862i | \(0.919943\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −742.000 | −1.12254 | −0.561271 | − | 0.827632i | \(-0.689687\pi\) | ||||
−0.561271 | + | 0.827632i | \(0.689687\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 18.0000 | + | 18.0000i | 0.0271493 | + | 0.0271493i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −56.0000 | + | 392.000i | −0.0842105 | + | 0.589474i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 184.000 | − | 184.000i | 0.275862 | − | 0.275862i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | − | 270.000i | − | 0.403587i | ||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 420.000 | 0.625931 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −287.000 | − | 287.000i | −0.426449 | − | 0.426449i | 0.460968 | − | 0.887417i | \(-0.347502\pi\) |
−0.887417 | + | 0.460968i | \(0.847502\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 272.000 | + | 496.000i | 0.402963 | + | 0.734815i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 577.000 | − | 577.000i | 0.852290 | − | 0.852290i | −0.138125 | − | 0.990415i | \(-0.544108\pi\) |
0.990415 | + | 0.138125i | \(0.0441077\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 462.000i | 0.680412i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 562.000 | 0.825257 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −399.000 | − | 399.000i | −0.584187 | − | 0.584187i | 0.351864 | − | 0.936051i | \(-0.385548\pi\) |
−0.936051 | + | 0.351864i | \(0.885548\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 441.000 | + | 63.0000i | 0.643796 | + | 0.0919708i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 168.000 | − | 168.000i | 0.244541 | − | 0.244541i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | − | 126.000i | − | 0.182874i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 378.000 | 0.547033 | 0.273517 | − | 0.961867i | \(-0.411813\pi\) | ||||
0.273517 | + | 0.961867i | \(0.411813\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 490.000 | + | 490.000i | 0.707071 | + | 0.707071i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 352.000 | − | 264.000i | 0.506475 | − | 0.379856i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −14.0000 | + | 14.0000i | −0.0200861 | + | 0.0200861i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 546.000i | 0.781116i | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −470.000 | −0.670471 | −0.335235 | − | 0.942134i | \(-0.608816\pi\) | ||||
−0.335235 | + | 0.942134i | \(0.608816\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 264.000 | + | 264.000i | 0.375533 | + | 0.375533i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 234.000 | + | 312.000i | 0.331915 | + | 0.442553i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −182.000 | + | 182.000i | −0.257426 | + | 0.257426i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − | 1192.00i | − | 1.68124i | −0.541624 | − | 0.840621i | \(-0.682190\pi\) | ||
0.541624 | − | 0.840621i | \(-0.317810\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −672.000 | −0.945148 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 322.000 | + | 322.000i | 0.451613 | + | 0.451613i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 90.0000 | − | 630.000i | 0.125874 | − | 0.881119i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −288.000 | + | 288.000i | −0.401674 | + | 0.401674i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 608.000i | 0.845619i | 0.906219 | + | 0.422809i | \(0.138956\pi\) | ||||
−0.906219 | + | 0.422809i | \(0.861044\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −1022.00 | −1.41748 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −446.000 | − | 446.000i | −0.616874 | − | 0.616874i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −192.000 | − | 56.0000i | −0.264828 | − | 0.0772414i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 441.000 | − | 441.000i | 0.606602 | − | 0.606602i | −0.335454 | − | 0.942057i | \(-0.608890\pi\) |
0.942057 | + | 0.335454i | \(0.108890\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | − | 71.0000i | − | 0.0973937i | ||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −30.0000 | −0.0410397 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 361.000 | + | 361.000i | 0.492497 | + | 0.492497i | 0.909092 | − | 0.416595i | \(-0.136777\pi\) |
−0.416595 | + | 0.909092i | \(0.636777\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −343.000 | − | 49.0000i | −0.466667 | − | 0.0666667i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −70.0000 | + | 70.0000i | −0.0949796 | + | 0.0949796i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − | 920.000i | − | 1.24493i | −0.782649 | − | 0.622463i | \(-0.786132\pi\) | ||
0.782649 | − | 0.622463i | \(-0.213868\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −144.000 | −0.194332 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −343.000 | − | 343.000i | −0.461642 | − | 0.461642i | 0.437551 | − | 0.899193i | \(-0.355846\pi\) |
−0.899193 | + | 0.437551i | \(0.855846\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −672.000 | + | 504.000i | −0.902013 | + | 0.676510i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −441.000 | + | 441.000i | −0.590361 | + | 0.590361i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 1694.00i | 2.26168i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 786.000 | 1.04660 | 0.523302 | − | 0.852147i | \(-0.324700\pi\) | ||||
0.523302 | + | 0.852147i | \(0.324700\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −150.000 | − | 150.000i | −0.199203 | − | 0.199203i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −390.000 | − | 520.000i | −0.516556 | − | 0.688742i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −63.0000 | + | 63.0000i | −0.0832232 | + | 0.0832232i | −0.747493 | − | 0.664270i | \(-0.768743\pi\) |
0.664270 | + | 0.747493i | \(0.268743\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | − | 460.000i | − | 0.606061i | ||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −398.000 | −0.522996 | −0.261498 | − | 0.965204i | \(-0.584216\pi\) | ||||
−0.261498 | + | 0.965204i | \(0.584216\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −952.000 | − | 952.000i | −1.24771 | − | 1.24771i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −7.00000 | + | 49.0000i | −0.00915033 | + | 0.0640523i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −504.000 | + | 504.000i | −0.657106 | + | 0.657106i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 704.000i | − | 0.915475i | −0.889087 | − | 0.457737i | \(-0.848660\pi\) | ||
0.889087 | − | 0.457737i | \(-0.151340\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 322.000 | 0.417639 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 825.000 | + | 825.000i | 1.06727 | + | 1.06727i | 0.997568 | + | 0.0697026i | \(0.0222050\pi\) |
0.0697026 | + | 0.997568i | \(0.477795\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 98.0000 | − | 336.000i | 0.126452 | − | 0.433548i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −462.000 | + | 462.000i | −0.594595 | + | 0.594595i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | − | 112.000i | − | 0.143774i | ||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 980.000 | 1.25480 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 128.000 | + | 128.000i | 0.163474 | + | 0.163474i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 441.000 | + | 63.0000i | 0.561783 | + | 0.0802548i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −71.0000 | + | 71.0000i | −0.0902160 | + | 0.0902160i | −0.750775 | − | 0.660559i | \(-0.770320\pi\) |
0.660559 | + | 0.750775i | \(0.270320\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | − | 302.000i | − | 0.382763i | ||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 1778.00 | 2.24779 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 378.000 | + | 378.000i | 0.476671 | + | 0.476671i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −56.0000 | + | 42.0000i | −0.0704403 | + | 0.0528302i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 33.0000 | − | 33.0000i | 0.0414053 | − | 0.0414053i | −0.686101 | − | 0.727506i | \(-0.740679\pi\) |
0.727506 | + | 0.686101i | \(0.240679\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 78.0000i | 0.0976220i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 784.000 | 0.978777 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 490.000 | + | 490.000i | 0.610212 | + | 0.610212i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −966.000 | − | 1288.00i | −1.20000 | − | 1.60000i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 376.000 | − | 376.000i | 0.465923 | − | 0.465923i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − | 368.000i | − | 0.454883i | −0.973792 | − | 0.227441i | \(-0.926964\pi\) | ||
0.973792 | − | 0.227441i | \(-0.0730360\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −886.000 | −1.09248 | −0.546239 | − | 0.837629i | \(-0.683941\pi\) | ||||
−0.546239 | + | 0.837629i | \(0.683941\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 210.000 | + | 210.000i | 0.258303 | + | 0.258303i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 65.0000 | − | 455.000i | 0.0797546 | − | 0.558282i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 120.000 | − | 120.000i | 0.146879 | − | 0.146879i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 882.000i | 1.07692i | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −614.000 | −0.747868 | −0.373934 | − | 0.927455i | \(-0.621991\pi\) | ||||
−0.373934 | + | 0.927455i | \(0.621991\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 1001.00 | + | 1001.00i | 1.21628 | + | 1.21628i | 0.968924 | + | 0.247358i | \(0.0795623\pi\) |
0.247358 | + | 0.968924i | \(0.420438\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −310.000 | + | 170.000i | −0.375758 | + | 0.206061i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −615.000 | + | 615.000i | −0.743652 | + | 0.743652i | −0.973279 | − | 0.229627i | \(-0.926249\pi\) |
0.229627 | + | 0.973279i | \(0.426249\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 616.000i | 0.743064i | 0.928420 | + | 0.371532i | \(0.121167\pi\) | ||||
−0.928420 | + | 0.371532i | \(0.878833\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 258.000 | 0.310469 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −49.0000 | − | 49.0000i | −0.0588235 | − | 0.0588235i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 721.000 | + | 103.000i | 0.863473 | + | 0.123353i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −224.000 | + | 224.000i | −0.267622 | + | 0.267622i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | − | 1424.00i | − | 1.69726i | −0.528988 | − | 0.848629i | \(-0.677428\pi\) | ||
0.528988 | − | 0.848629i | \(-0.322572\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 777.000 | 0.923900 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −174.000 | − | 174.000i | −0.206406 | − | 0.206406i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −28.0000 | + | 21.0000i | −0.0331361 | + | 0.0248521i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 147.000 | − | 147.000i | 0.173554 | − | 0.173554i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 226.000i | 0.266196i | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −1518.00 | −1.78378 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −935.000 | − | 935.000i | −1.09613 | − | 1.09613i | −0.994859 | − | 0.101273i | \(-0.967709\pi\) |
−0.101273 | − | 0.994859i | \(-0.532291\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −168.000 | − | 224.000i | −0.196491 | − | 0.261988i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −63.0000 | + | 63.0000i | −0.0735123 | + | 0.0735123i | −0.742907 | − | 0.669395i | \(-0.766554\pi\) |
0.669395 | + | 0.742907i | \(0.266554\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 392.000i | − | 0.456345i | −0.973621 | − | 0.228172i | \(-0.926725\pi\) | ||
0.973621 | − | 0.228172i | \(-0.0732749\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 196.000 | 0.227642 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 217.000 | + | 217.000i | 0.251448 | + | 0.251448i | 0.821564 | − | 0.570116i | \(-0.193102\pi\) |
−0.570116 | + | 0.821564i | \(0.693102\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 73.0000 | − | 511.000i | 0.0843931 | − | 0.590751i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −287.000 | + | 287.000i | −0.331027 | + | 0.331027i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − | 960.000i | − | 1.10472i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −126.000 | −0.144661 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −231.000 | − | 231.000i | −0.264605 | − | 0.264605i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −511.000 | + | 1127.00i | −0.584000 | + | 1.28800i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −831.000 | + | 831.000i | −0.947548 | + | 0.947548i | −0.998691 | − | 0.0511429i | \(-0.983714\pi\) |
0.0511429 | + | 0.998691i | \(0.483714\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 690.000i | 0.784983i | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 322.000 | 0.365494 | 0.182747 | − | 0.983160i | \(-0.441501\pi\) | ||||
0.182747 | + | 0.983160i | \(0.441501\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −287.000 | − | 287.000i | −0.325028 | − | 0.325028i | 0.525664 | − | 0.850692i | \(-0.323817\pi\) |
−0.850692 | + | 0.525664i | \(0.823817\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 392.000 | + | 56.0000i | 0.442938 | + | 0.0632768i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −903.000 | + | 903.000i | −1.01804 | + | 1.01804i | −0.0182040 | + | 0.999834i | \(0.505795\pi\) |
−0.999834 | + | 0.0182040i | \(0.994205\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | − | 98.0000i | − | 0.110236i | ||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −310.000 | −0.347924 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −312.000 | − | 312.000i | −0.349384 | − | 0.349384i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −224.000 | + | 168.000i | −0.250279 | + | 0.187709i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 414.000 | − | 414.000i | 0.461538 | − | 0.461538i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | − | 112.000i | − | 0.124583i | ||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −14.0000 | −0.0155383 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 210.000 | + | 210.000i | 0.232558 | + | 0.232558i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 210.000 | + | 280.000i | 0.232044 | + | 0.309392i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 1081.00 | − | 1081.00i | 1.19184 | − | 1.19184i | 0.215291 | − | 0.976550i | \(-0.430930\pi\) |
0.976550 | − | 0.215291i | \(-0.0690701\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | − | 182.000i | − | 0.200220i | ||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −238.000 | −0.261251 | −0.130626 | − | 0.991432i | \(-0.541699\pi\) | ||||
−0.130626 | + | 0.991432i | \(0.541699\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −630.000 | − | 630.000i | −0.690033 | − | 0.690033i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 42.0000 | − | 294.000i | 0.0459016 | − | 0.321311i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 1610.00 | − | 1610.00i | 1.75573 | − | 1.75573i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 1552.00i | 1.68879i | 0.535719 | + | 0.844396i | \(0.320040\pi\) | ||||
−0.535719 | + | 0.844396i | \(0.679960\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −654.000 | −0.710098 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 882.000 | + | 882.000i | 0.955580 | + | 0.955580i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 561.000 | + | 1023.00i | 0.606486 | + | 1.10595i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 511.000 | − | 511.000i | 0.551241 | − | 0.551241i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 224.000i | 0.241119i | 0.992706 | + | 0.120560i | \(0.0384689\pi\) | ||||
−0.992706 | + | 0.120560i | \(0.961531\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 392.000 | 0.421053 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 2.00000 | + | 2.00000i | 0.00214362 | + | 0.00214362i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −70.0000 | − | 10.0000i | −0.0748663 | − | 0.0106952i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −383.000 | + | 383.000i | −0.408751 | + | 0.408751i | −0.881303 | − | 0.472552i | \(-0.843333\pi\) |
0.472552 | + | 0.881303i | \(0.343333\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 162.000i | 0.172524i | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 42.0000 | 0.0446334 | 0.0223167 | − | 0.999751i | \(-0.492896\pi\) | ||||
0.0223167 | + | 0.999751i | \(0.492896\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 322.000 | + | 322.000i | 0.341463 | + | 0.341463i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 896.000 | − | 672.000i | 0.948148 | − | 0.711111i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 1337.00 | − | 1337.00i | 1.41183 | − | 1.41183i | 0.664849 | − | 0.746977i | \(-0.268496\pi\) |
0.746977 | − | 0.664849i | \(-0.231504\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 882.000i | 0.929399i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −318.000 | −0.334385 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 273.000 | + | 273.000i | 0.286464 | + | 0.286464i | 0.835680 | − | 0.549216i | \(-0.185074\pi\) |
−0.549216 | + | 0.835680i | \(0.685074\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 426.000 | + | 568.000i | 0.446073 | + | 0.594764i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −80.0000 | + | 80.0000i | −0.0835946 | + | 0.0835946i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | − | 882.000i | − | 0.919708i | ||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −765.000 | −0.796046 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −847.000 | − | 847.000i | −0.879543 | − | 0.879543i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −63.0000 | + | 441.000i | −0.0652850 | + | 0.456995i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −743.000 | + | 743.000i | −0.768356 | + | 0.768356i | −0.977817 | − | 0.209461i | \(-0.932829\pi\) |
0.209461 | + | 0.977817i | \(0.432829\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 16.0000i | 0.0165119i | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 266.000 | 0.273944 | 0.136972 | − | 0.990575i | \(-0.456263\pi\) | ||||
0.136972 | + | 0.990575i | \(0.456263\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −616.000 | − | 616.000i | −0.633094 | − | 0.633094i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −432.000 | − | 126.000i | −0.443077 | − | 0.129231i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 417.000 | − | 417.000i | 0.426817 | − | 0.426817i | −0.460726 | − | 0.887543i | \(-0.652411\pi\) |
0.887543 | + | 0.460726i | \(0.152411\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 1120.00i | 1.14402i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 952.000 | 0.970438 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −631.000 | − | 631.000i | −0.641913 | − | 0.641913i | 0.309113 | − | 0.951025i | \(-0.399968\pi\) |
−0.951025 | + | 0.309113i | \(0.899968\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 441.000 | + | 63.0000i | 0.447716 | + | 0.0639594i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 546.000 | − | 546.000i | 0.553191 | − | 0.553191i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 690.000i | 0.697674i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −14.0000 | −0.0141271 | −0.00706357 | − | 0.999975i | \(-0.502248\pi\) | ||||
−0.00706357 | + | 0.999975i | \(0.502248\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −182.000 | − | 182.000i | −0.183283 | − | 0.183283i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −1344.00 | + | 1008.00i | −1.35075 | + | 1.01307i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −671.000 | + | 671.000i | −0.673019 | + | 0.673019i | −0.958411 | − | 0.285392i | \(-0.907876\pi\) |
0.285392 | + | 0.958411i | \(0.407876\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | − | 1056.00i | − | 1.05706i |
(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 | 20.3.f.a.13.1 | ✓ | 2 | |
3.2 | odd | 2 | 180.3.l.a.73.1 | 2 | |||
4.3 | odd | 2 | 80.3.p.a.33.1 | 2 | |||
5.2 | odd | 4 | inner | 20.3.f.a.17.1 | yes | 2 | |
5.3 | odd | 4 | 100.3.f.a.57.1 | 2 | |||
5.4 | even | 2 | 100.3.f.a.93.1 | 2 | |||
7.6 | odd | 2 | 980.3.l.a.393.1 | 2 | |||
8.3 | odd | 2 | 320.3.p.g.193.1 | 2 | |||
8.5 | even | 2 | 320.3.p.c.193.1 | 2 | |||
12.11 | even | 2 | 720.3.bh.e.433.1 | 2 | |||
15.2 | even | 4 | 180.3.l.a.37.1 | 2 | |||
15.8 | even | 4 | 900.3.l.a.757.1 | 2 | |||
15.14 | odd | 2 | 900.3.l.a.793.1 | 2 | |||
20.3 | even | 4 | 400.3.p.d.257.1 | 2 | |||
20.7 | even | 4 | 80.3.p.a.17.1 | 2 | |||
20.19 | odd | 2 | 400.3.p.d.193.1 | 2 | |||
35.27 | even | 4 | 980.3.l.a.197.1 | 2 | |||
40.27 | even | 4 | 320.3.p.g.257.1 | 2 | |||
40.37 | odd | 4 | 320.3.p.c.257.1 | 2 | |||
60.47 | odd | 4 | 720.3.bh.e.577.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
20.3.f.a.13.1 | ✓ | 2 | 1.1 | even | 1 | trivial | |
20.3.f.a.17.1 | yes | 2 | 5.2 | odd | 4 | inner | |
80.3.p.a.17.1 | 2 | 20.7 | even | 4 | |||
80.3.p.a.33.1 | 2 | 4.3 | odd | 2 | |||
100.3.f.a.57.1 | 2 | 5.3 | odd | 4 | |||
100.3.f.a.93.1 | 2 | 5.4 | even | 2 | |||
180.3.l.a.37.1 | 2 | 15.2 | even | 4 | |||
180.3.l.a.73.1 | 2 | 3.2 | odd | 2 | |||
320.3.p.c.193.1 | 2 | 8.5 | even | 2 | |||
320.3.p.c.257.1 | 2 | 40.37 | odd | 4 | |||
320.3.p.g.193.1 | 2 | 8.3 | odd | 2 | |||
320.3.p.g.257.1 | 2 | 40.27 | even | 4 | |||
400.3.p.d.193.1 | 2 | 20.19 | odd | 2 | |||
400.3.p.d.257.1 | 2 | 20.3 | even | 4 | |||
720.3.bh.e.433.1 | 2 | 12.11 | even | 2 | |||
720.3.bh.e.577.1 | 2 | 60.47 | odd | 4 | |||
900.3.l.a.757.1 | 2 | 15.8 | even | 4 | |||
900.3.l.a.793.1 | 2 | 15.14 | odd | 2 | |||
980.3.l.a.197.1 | 2 | 35.27 | even | 4 | |||
980.3.l.a.393.1 | 2 | 7.6 | odd | 2 |