Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [912,2,Mod(289,912)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(912, base_ring=CyclotomicField(18))
chi = DirichletCharacter(H, H._module([0, 0, 0, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("912.289");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 912 = 2^{4} \cdot 3 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 912.bo (of order \(9\), degree \(6\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(7.28235666434\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Coefficient field: | \(\Q(\zeta_{18})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - x^{3} + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 228) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{9}]$ |
Embedding invariants
Embedding label | 529.1 | ||
Root | \(0.939693 - 0.342020i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 912.529 |
Dual form | 912.2.bo.e.481.1 |
$q$-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 \(\left(\mathbb{Z}/912\mathbb{Z}\right)^\times\).
\(n\) | \(97\) | \(229\) | \(305\) | \(799\) |
\(\chi(n)\) | \(e\left(\frac{2}{9}\right)\) | \(1\) | \(1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0.939693 | − | 0.342020i | 0.542532 | − | 0.197465i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0.233956 | − | 1.32683i | 0.104628 | − | 0.593375i | −0.886740 | − | 0.462268i | \(-0.847036\pi\) |
0.991368 | − | 0.131107i | \(-0.0418532\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.20574 | + | 2.08840i | 0.455726 | + | 0.789340i | 0.998730 | − | 0.0503900i | \(-0.0160464\pi\) |
−0.543004 | + | 0.839730i | \(0.682713\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0.766044 | − | 0.642788i | 0.255348 | − | 0.214263i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −2.97178 | + | 5.14728i | −0.896026 | + | 1.55196i | −0.0634960 | + | 0.997982i | \(0.520225\pi\) |
−0.832530 | + | 0.553980i | \(0.813108\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 3.47178 | + | 1.26363i | 0.962899 | + | 0.350467i | 0.775169 | − | 0.631754i | \(-0.217665\pi\) |
0.187730 | + | 0.982221i | \(0.439887\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −0.233956 | − | 1.32683i | −0.0604071 | − | 0.342585i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −0.124485 | − | 0.104455i | −0.0301921 | − | 0.0253342i | 0.627567 | − | 0.778563i | \(-0.284051\pi\) |
−0.657759 | + | 0.753229i | \(0.728495\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 4.11721 | − | 1.43128i | 0.944553 | − | 0.328359i | ||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 1.84730 | + | 1.55007i | 0.403113 | + | 0.338252i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 1.14156 | + | 6.47410i | 0.238032 | + | 1.34994i | 0.836134 | + | 0.548525i | \(0.184810\pi\) |
−0.598103 | + | 0.801419i | \(0.704079\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 2.99273 | + | 1.08926i | 0.598545 | + | 0.217853i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0.500000 | − | 0.866025i | 0.0962250 | − | 0.166667i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 1.83022 | − | 1.53574i | 0.339864 | − | 0.285180i | −0.456841 | − | 0.889548i | \(-0.651019\pi\) |
0.796705 | + | 0.604369i | \(0.206575\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −1.29813 | − | 2.24843i | −0.233152 | − | 0.403830i | 0.725582 | − | 0.688135i | \(-0.241571\pi\) |
−0.958734 | + | 0.284305i | \(0.908237\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −1.03209 | + | 5.85327i | −0.179664 | + | 1.01892i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 3.05303 | − | 1.11121i | 0.516057 | − | 0.187829i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −6.94356 | −1.14151 | −0.570757 | − | 0.821119i | \(-0.693350\pi\) | ||||
−0.570757 | + | 0.821119i | \(0.693350\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 3.69459 | 0.591608 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 0.340022 | − | 0.123758i | 0.0531026 | − | 0.0193278i | −0.315332 | − | 0.948981i | \(-0.602116\pi\) |
0.368435 | + | 0.929654i | \(0.379894\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 1.98886 | − | 11.2794i | 0.303298 | − | 1.72009i | −0.328114 | − | 0.944638i | \(-0.606413\pi\) |
0.631411 | − | 0.775448i | \(-0.282476\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −0.673648 | − | 1.16679i | −0.100422 | − | 0.173935i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 5.26991 | − | 4.42198i | 0.768696 | − | 0.645013i | −0.171679 | − | 0.985153i | \(-0.554919\pi\) |
0.940375 | + | 0.340140i | \(0.110475\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0.592396 | − | 1.02606i | 0.0846280 | − | 0.146580i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −0.152704 | − | 0.0555796i | −0.0213828 | − | 0.00778270i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 0.698463 | + | 3.96118i | 0.0959413 | + | 0.544110i | 0.994455 | + | 0.105164i | \(0.0335369\pi\) |
−0.898514 | + | 0.438946i | \(0.855352\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 6.13429 | + | 5.14728i | 0.827147 | + | 0.694059i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 3.37939 | − | 2.75314i | 0.447611 | − | 0.364662i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −9.23055 | − | 7.74535i | −1.20172 | − | 1.00836i | −0.999579 | − | 0.0290016i | \(-0.990767\pi\) |
−0.202136 | − | 0.979357i | \(-0.564788\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 1.07398 | + | 6.09083i | 0.137509 | + | 0.779851i | 0.973080 | + | 0.230469i | \(0.0740259\pi\) |
−0.835571 | + | 0.549383i | \(0.814863\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 2.26604 | + | 0.824773i | 0.285495 | + | 0.103912i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 2.48886 | − | 4.31082i | 0.308705 | − | 0.534692i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 4.41147 | − | 3.70167i | 0.538947 | − | 0.452231i | −0.332230 | − | 0.943198i | \(-0.607801\pi\) |
0.871178 | + | 0.490968i | \(0.163357\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 3.28699 | + | 5.69323i | 0.395707 | + | 0.685385i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −2.11721 | + | 12.0073i | −0.251267 | + | 1.42500i | 0.554210 | + | 0.832377i | \(0.313020\pi\) |
−0.805477 | + | 0.592628i | \(0.798091\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 8.61721 | − | 3.13641i | 1.00857 | − | 0.367089i | 0.215685 | − | 0.976463i | \(-0.430801\pi\) |
0.792883 | + | 0.609374i | \(0.208579\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 3.18479 | 0.367748 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −14.3327 | −1.63337 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −9.10994 | + | 3.31575i | −1.02495 | + | 0.373051i | −0.799155 | − | 0.601125i | \(-0.794719\pi\) |
−0.225793 | + | 0.974175i | \(0.572497\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0.173648 | − | 0.984808i | 0.0192942 | − | 0.109423i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 1.01367 | + | 1.75573i | 0.111265 | + | 0.192716i | 0.916280 | − | 0.400537i | \(-0.131176\pi\) |
−0.805016 | + | 0.593254i | \(0.797843\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −0.167718 | + | 0.140732i | −0.0181916 | + | 0.0152646i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 1.19459 | − | 2.06910i | 0.128074 | − | 0.221830i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −3.24035 | − | 1.17939i | −0.343477 | − | 0.125015i | 0.164521 | − | 0.986374i | \(-0.447392\pi\) |
−0.507998 | + | 0.861358i | \(0.669614\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1.54710 | + | 8.77406i | 0.162181 | + | 0.919771i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −1.98886 | − | 1.66885i | −0.206235 | − | 0.173051i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −0.935822 | − | 5.79769i | −0.0960133 | − | 0.594830i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 9.26264 | + | 7.77228i | 0.940479 | + | 0.789155i | 0.977669 | − | 0.210153i | \(-0.0673962\pi\) |
−0.0371898 | + | 0.999308i | \(0.511841\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 1.03209 | + | 5.85327i | 0.103729 | + | 0.588275i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 3.69846 | + | 1.34613i | 0.368011 | + | 0.133945i | 0.519404 | − | 0.854529i | \(-0.326154\pi\) |
−0.151394 | + | 0.988474i | \(0.548376\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −6.15657 | + | 10.6635i | −0.606625 | + | 1.05071i | 0.385167 | + | 0.922847i | \(0.374144\pi\) |
−0.991792 | + | 0.127859i | \(0.959190\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 2.48886 | − | 2.08840i | 0.242887 | − | 0.203807i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −6.71688 | − | 11.6340i | −0.649345 | − | 1.12470i | −0.983279 | − | 0.182103i | \(-0.941710\pi\) |
0.333934 | − | 0.942596i | \(-0.391624\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 0.393933 | − | 2.23411i | 0.0377320 | − | 0.213989i | −0.960112 | − | 0.279615i | \(-0.909793\pi\) |
0.997844 | + | 0.0656260i | \(0.0209044\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −6.52481 | + | 2.37484i | −0.619308 | + | 0.225410i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −12.7101 | −1.19566 | −0.597832 | − | 0.801622i | \(-0.703971\pi\) | ||||
−0.597832 | + | 0.801622i | \(0.703971\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 8.85710 | 0.825929 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 3.47178 | − | 1.26363i | 0.320966 | − | 0.116822i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0.0680482 | − | 0.385920i | 0.00623797 | − | 0.0353773i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −12.1630 | − | 21.0669i | −1.10572 | − | 1.91517i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0.277189 | − | 0.232589i | 0.0249933 | − | 0.0209718i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 5.51367 | − | 9.54996i | 0.493158 | − | 0.854174i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 7.26517 | + | 2.64430i | 0.644679 | + | 0.234644i | 0.643608 | − | 0.765355i | \(-0.277437\pi\) |
0.00107137 | + | 0.999999i | \(0.499659\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −1.98886 | − | 11.2794i | −0.175109 | − | 0.993092i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −9.62701 | − | 8.07802i | −0.841116 | − | 0.705780i | 0.116699 | − | 0.993167i | \(-0.462769\pi\) |
−0.957814 | + | 0.287387i | \(0.907213\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 7.95336 | + | 6.87262i | 0.689644 | + | 0.595932i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −1.03209 | − | 0.866025i | −0.0888281 | − | 0.0745356i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 2.72803 | + | 15.4714i | 0.233071 | + | 1.32181i | 0.846638 | + | 0.532169i | \(0.178623\pi\) |
−0.613567 | + | 0.789642i | \(0.710266\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 3.03936 | + | 1.10624i | 0.257795 | + | 0.0938298i | 0.467685 | − | 0.883895i | \(-0.345088\pi\) |
−0.209890 | + | 0.977725i | \(0.567310\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 3.43969 | − | 5.95772i | 0.289674 | − | 0.501731i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −16.8216 | + | 14.1150i | −1.40669 | + | 1.18036i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −1.60947 | − | 2.78768i | −0.133659 | − | 0.231505i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0.205737 | − | 1.16679i | 0.0169689 | − | 0.0962355i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −4.19119 | + | 1.52547i | −0.343356 | + | 0.124971i | −0.507942 | − | 0.861392i | \(-0.669593\pi\) |
0.164586 | + | 0.986363i | \(0.447371\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −8.94862 | −0.728228 | −0.364114 | − | 0.931354i | \(-0.618628\pi\) | ||||
−0.364114 | + | 0.931354i | \(0.618628\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −0.162504 | −0.0131377 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −3.28699 | + | 1.19637i | −0.264017 | + | 0.0960944i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −2.00047 | + | 11.3452i | −0.159655 | + | 0.905446i | 0.794751 | + | 0.606935i | \(0.207601\pi\) |
−0.954406 | + | 0.298511i | \(0.903510\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 2.01114 | + | 3.48340i | 0.159494 | + | 0.276252i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −12.1441 | + | 10.1901i | −0.957088 | + | 0.803092i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −5.26217 | + | 9.11435i | −0.412165 | + | 0.713891i | −0.995126 | − | 0.0986089i | \(-0.968561\pi\) |
0.582961 | + | 0.812500i | \(0.301894\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 7.52481 | + | 2.73881i | 0.585806 | + | 0.213216i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −1.86484 | − | 10.5760i | −0.144305 | − | 0.818397i | −0.967922 | − | 0.251250i | \(-0.919158\pi\) |
0.823617 | − | 0.567147i | \(-0.191953\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 0.497941 | + | 0.417822i | 0.0383031 | + | 0.0321401i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 2.23396 | − | 3.74292i | 0.170835 | − | 0.286228i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −5.77584 | − | 4.84651i | −0.439129 | − | 0.368473i | 0.396254 | − | 0.918141i | \(-0.370310\pi\) |
−0.835383 | + | 0.549668i | \(0.814754\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 1.33363 | + | 7.56337i | 0.100813 | + | 0.571737i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −11.3229 | − | 4.12122i | −0.851085 | − | 0.309770i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 13.1814 | − | 22.8308i | 0.985223 | − | 1.70646i | 0.344283 | − | 0.938866i | \(-0.388122\pi\) |
0.640940 | − | 0.767591i | \(-0.278545\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 16.1570 | − | 13.5574i | 1.20094 | − | 1.00771i | 0.201341 | − | 0.979521i | \(-0.435470\pi\) |
0.999603 | − | 0.0281899i | \(-0.00897431\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 3.09240 | + | 5.35619i | 0.228597 | + | 0.395941i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −1.62449 | + | 9.21291i | −0.119435 | + | 0.677347i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0.907604 | − | 0.330341i | 0.0663706 | − | 0.0241569i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 2.41147 | 0.175409 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 0.255777 | 0.0185074 | 0.00925370 | − | 0.999957i | \(-0.497054\pi\) | ||||
0.00925370 | + | 0.999957i | \(0.497054\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −13.4829 | + | 4.90738i | −0.970522 | + | 0.353241i | −0.778148 | − | 0.628081i | \(-0.783841\pi\) |
−0.192374 | + | 0.981322i | \(0.561619\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0.864370 | − | 4.90209i | 0.0618989 | − | 0.351046i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −11.8405 | − | 20.5083i | −0.843600 | − | 1.46116i | −0.886832 | − | 0.462093i | \(-0.847099\pi\) |
0.0432316 | − | 0.999065i | \(-0.486235\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 9.03596 | − | 7.58207i | 0.640542 | − | 0.537479i | −0.263642 | − | 0.964620i | \(-0.584924\pi\) |
0.904185 | + | 0.427142i | \(0.140479\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 2.87939 | − | 4.98724i | 0.203096 | − | 0.351773i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 5.41400 | + | 1.97053i | 0.379988 | + | 0.138304i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −0.0846555 | − | 0.480105i | −0.00591260 | − | 0.0335320i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 5.03596 | + | 4.22567i | 0.350023 | + | 0.293704i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −4.86824 | + | 25.4459i | −0.336743 | + | 1.76013i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −21.3405 | − | 17.9068i | −1.46914 | − | 1.23275i | −0.916929 | − | 0.399050i | \(-0.869340\pi\) |
−0.552211 | − | 0.833705i | \(-0.686216\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 2.11721 | + | 12.0073i | 0.145069 | + | 0.822727i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −14.5005 | − | 5.27774i | −0.988924 | − | 0.359939i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 3.13041 | − | 5.42204i | 0.212506 | − | 0.368072i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 7.02481 | − | 5.89452i | 0.474693 | − | 0.398315i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −0.300193 | − | 0.519949i | −0.0201931 | − | 0.0349756i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 4.29561 | − | 24.3616i | 0.287655 | − | 1.63137i | −0.407989 | − | 0.912987i | \(-0.633770\pi\) |
0.695644 | − | 0.718386i | \(-0.255119\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 2.99273 | − | 1.08926i | 0.199515 | − | 0.0726175i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 22.0155 | 1.46122 | 0.730609 | − | 0.682796i | \(-0.239236\pi\) | ||||
0.730609 | + | 0.682796i | \(0.239236\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −9.29591 | −0.614291 | −0.307146 | − | 0.951663i | \(-0.599374\pi\) | ||||
−0.307146 | + | 0.951663i | \(0.599374\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −13.4684 | + | 4.90209i | −0.886154 | + | 0.322534i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −1.38713 | + | 7.86678i | −0.0908736 | + | 0.515370i | 0.905060 | + | 0.425283i | \(0.139826\pi\) |
−0.995934 | + | 0.0900867i | \(0.971286\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −4.63429 | − | 8.02682i | −0.302307 | − | 0.523612i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −7.42649 | + | 6.23156i | −0.482402 | + | 0.404784i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −13.2246 | + | 22.9057i | −0.855430 | + | 1.48165i | 0.0208161 | + | 0.999783i | \(0.493374\pi\) |
−0.876246 | + | 0.481864i | \(0.839960\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 2.57398 | + | 0.936851i | 0.165804 | + | 0.0603479i | 0.423589 | − | 0.905855i | \(-0.360770\pi\) |
−0.257784 | + | 0.966202i | \(0.582992\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −0.173648 | − | 0.984808i | −0.0111395 | − | 0.0631754i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −1.22281 | − | 1.02606i | −0.0781225 | − | 0.0655526i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 16.1027 | + | 0.233508i | 1.02459 | + | 0.0148578i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 1.55303 | + | 1.30315i | 0.0984195 | + | 0.0825838i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −2.64455 | − | 14.9980i | −0.166923 | − | 0.946665i | −0.947060 | − | 0.321057i | \(-0.895962\pi\) |
0.780137 | − | 0.625608i | \(-0.215149\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −36.7165 | − | 13.3637i | −2.30834 | − | 0.840169i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −0.109470 | + | 0.189608i | −0.00685530 | + | 0.0118737i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 9.98545 | − | 8.37879i | 0.622875 | − | 0.522655i | −0.275831 | − | 0.961206i | \(-0.588953\pi\) |
0.898706 | + | 0.438552i | \(0.144508\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −8.37211 | − | 14.5009i | −0.520218 | − | 0.901043i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0.414878 | − | 2.35289i | 0.0256803 | − | 0.145640i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −11.2071 | + | 4.07904i | −0.691058 | + | 0.251525i | −0.663588 | − | 0.748098i | \(-0.730967\pi\) |
−0.0274700 | + | 0.999623i | \(0.508745\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 5.41921 | 0.332900 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −3.44831 | −0.211033 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −24.2986 | + | 8.84397i | −1.48151 | + | 0.539226i | −0.951200 | − | 0.308576i | \(-0.900148\pi\) |
−0.530312 | + | 0.847802i | \(0.677925\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −2.06165 | + | 11.6922i | −0.125236 | + | 0.710251i | 0.855931 | + | 0.517090i | \(0.172985\pi\) |
−0.981167 | + | 0.193161i | \(0.938126\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 4.45471 | + | 7.71578i | 0.269611 | + | 0.466980i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −14.5005 | + | 12.1673i | −0.874411 | + | 0.733718i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −7.20574 | + | 12.4807i | −0.432951 | + | 0.749893i | −0.997126 | − | 0.0757624i | \(-0.975861\pi\) |
0.564175 | + | 0.825655i | \(0.309194\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −2.43969 | − | 0.887975i | −0.146061 | − | 0.0531617i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −0.456929 | − | 2.59137i | −0.0272581 | − | 0.154588i | 0.968141 | − | 0.250407i | \(-0.0805643\pi\) |
−0.995399 | + | 0.0958183i | \(0.969453\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −4.66637 | − | 3.91555i | −0.277387 | − | 0.232755i | 0.493471 | − | 0.869762i | \(-0.335728\pi\) |
−0.770858 | + | 0.637007i | \(0.780172\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −2.86231 | − | 5.12797i | −0.169549 | − | 0.303755i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0.668434 | + | 0.560882i | 0.0394564 | + | 0.0331078i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −2.94743 | − | 16.7157i | −0.173378 | − | 0.983278i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 11.3623 | + | 4.13554i | 0.666070 | + | 0.242430i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 16.3653 | − | 28.3455i | 0.956071 | − | 1.65596i | 0.224174 | − | 0.974549i | \(-0.428032\pi\) |
0.731897 | − | 0.681415i | \(-0.238635\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −12.4363 | + | 10.4353i | −0.724069 | + | 0.607566i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 2.97178 | + | 5.14728i | 0.172440 | + | 0.298675i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −4.21760 | + | 23.9192i | −0.243910 | + | 1.38328i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 25.9538 | − | 9.44642i | 1.49595 | − | 0.544483i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 3.93582 | 0.226107 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 8.33275 | 0.477132 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −5.83497 | + | 2.12376i | −0.333019 | + | 0.121209i | −0.503118 | − | 0.864218i | \(-0.667814\pi\) |
0.170098 | + | 0.985427i | \(0.445592\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −2.13816 | + | 12.1261i | −0.121635 | + | 0.689829i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 1.55303 | + | 2.68993i | 0.0880644 | + | 0.152532i | 0.906693 | − | 0.421791i | \(-0.138599\pi\) |
−0.818628 | + | 0.574323i | \(0.805265\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −12.9251 | + | 10.8455i | −0.730572 | + | 0.613023i | −0.930288 | − | 0.366831i | \(-0.880443\pi\) |
0.199715 | + | 0.979854i | \(0.435998\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 1.62449 | − | 2.81369i | 0.0915294 | − | 0.158534i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −13.5560 | − | 4.93399i | −0.761382 | − | 0.277120i | −0.0679951 | − | 0.997686i | \(-0.521660\pi\) |
−0.693387 | + | 0.720565i | \(0.743882\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 2.46585 | + | 13.9845i | 0.138061 | + | 0.782984i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −10.2909 | − | 8.63506i | −0.574380 | − | 0.481962i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −0.662037 | − | 0.251892i | −0.0368367 | − | 0.0140156i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 9.01367 | + | 7.56337i | 0.499988 | + | 0.419540i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −0.393933 | − | 2.23411i | −0.0217846 | − | 0.123546i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 15.5890 | + | 5.67393i | 0.859449 | + | 0.312814i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −4.49866 | + | 7.79190i | −0.247268 | + | 0.428282i | −0.962767 | − | 0.270333i | \(-0.912866\pi\) |
0.715498 | + | 0.698614i | \(0.246200\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −5.31908 | + | 4.46324i | −0.291484 | + | 0.244584i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −3.87939 | − | 6.71929i | −0.211953 | − | 0.367114i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −0.395582 | + | 2.24346i | −0.0215487 | + | 0.122209i | −0.993685 | − | 0.112209i | \(-0.964207\pi\) |
0.972136 | + | 0.234418i | \(0.0753185\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −11.9436 | + | 4.34710i | −0.648685 | + | 0.236102i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 15.4311 | 0.835640 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 19.7374 | 1.06572 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 8.32295 | − | 3.02931i | 0.448092 | − | 0.163092i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −1.30288 | + | 7.38901i | −0.0699423 | + | 0.396663i | 0.929659 | + | 0.368422i | \(0.120102\pi\) |
−0.999601 | + | 0.0282410i | \(0.991009\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 14.5175 | + | 25.1451i | 0.777106 | + | 1.34599i | 0.933603 | + | 0.358309i | \(0.116647\pi\) |
−0.156497 | + | 0.987678i | \(0.550020\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 2.83022 | − | 2.37484i | 0.151066 | − | 0.126759i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 11.7096 | − | 20.2816i | 0.623240 | − | 1.07948i | −0.365639 | − | 0.930757i | \(-0.619150\pi\) |
0.988878 | − | 0.148726i | \(-0.0475172\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 15.4363 | + | 5.61835i | 0.819273 | + | 0.298191i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −0.0680482 | − | 0.385920i | −0.00360149 | − | 0.0204251i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 27.3614 | + | 22.9590i | 1.44408 | + | 1.21173i | 0.936761 | + | 0.349971i | \(0.113808\pi\) |
0.507321 | + | 0.861757i | \(0.330636\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 14.9029 | − | 11.7858i | 0.784361 | − | 0.620305i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −18.6348 | − | 15.6364i | −0.978071 | − | 0.820699i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −2.14543 | − | 12.1673i | −0.112297 | − | 0.636867i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −19.6694 | − | 7.15906i | −1.02673 | − | 0.373700i | −0.226897 | − | 0.973919i | \(-0.572858\pi\) |
−0.799836 | + | 0.600219i | \(0.795080\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0.180922 | − | 0.313366i | 0.00941843 | − | 0.0163132i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −7.43036 | + | 6.23481i | −0.385765 | + | 0.323695i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 1.44562 | + | 2.50389i | 0.0748515 | + | 0.129647i | 0.901022 | − | 0.433774i | \(-0.142818\pi\) |
−0.826170 | + | 0.563421i | \(0.809485\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 1.91488 | − | 10.8598i | 0.0988839 | − | 0.560798i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 8.29473 | − | 3.01903i | 0.427200 | − | 0.155488i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 24.7374 | 1.27068 | 0.635338 | − | 0.772234i | \(-0.280861\pi\) | ||||
0.635338 | + | 0.772234i | \(0.280861\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 7.73143 | 0.396093 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 13.9611 | − | 5.08143i | 0.713379 | − | 0.259649i | 0.0402667 | − | 0.999189i | \(-0.487179\pi\) |
0.673112 | + | 0.739540i | \(0.264957\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −3.35323 | + | 19.0171i | −0.170896 | + | 0.969201i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −5.72668 | − | 9.91890i | −0.291104 | − | 0.504206i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 24.3286 | − | 20.4141i | 1.23351 | − | 1.03504i | 0.235507 | − | 0.971873i | \(-0.424325\pi\) |
0.998003 | − | 0.0631656i | \(-0.0201196\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0.534148 | − | 0.925172i | 0.0270130 | − | 0.0467880i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −11.8093 | − | 4.29823i | −0.595699 | − | 0.216817i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 2.26810 | + | 12.8631i | 0.114121 | + | 0.647211i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −13.6138 | − | 11.4233i | −0.683257 | − | 0.573321i | 0.233699 | − | 0.972309i | \(-0.424917\pi\) |
−0.916956 | + | 0.398988i | \(0.869362\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 9.82429 | + | 3.73794i | 0.491830 | + | 0.187131i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −26.8371 | − | 22.5190i | −1.34018 | − | 1.12454i | −0.981580 | − | 0.191053i | \(-0.938810\pi\) |
−0.358600 | − | 0.933491i | \(-0.616746\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −1.66566 | − | 9.44642i | −0.0829724 | − | 0.470560i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −1.26604 | − | 0.460802i | −0.0629103 | − | 0.0228975i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 20.6348 | − | 35.7404i | 1.02283 | − | 1.77159i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −8.83203 | + | 7.41096i | −0.436716 | + | 0.366448i | −0.834479 | − | 0.551040i | \(-0.814231\pi\) |
0.397763 | + | 0.917488i | \(0.369787\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 7.85504 | + | 13.6053i | 0.387460 | + | 0.671101i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 5.04576 | − | 28.6159i | 0.248286 | − | 1.40810i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 2.56670 | − | 0.934204i | 0.125995 | − | 0.0458583i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 3.23442 | 0.158390 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 34.7692 | 1.69859 | 0.849293 | − | 0.527921i | \(-0.177028\pi\) | ||||
0.849293 | + | 0.527921i | \(0.177028\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 14.7579 | − | 5.37143i | 0.719256 | − | 0.261788i | 0.0436459 | − | 0.999047i | \(-0.486103\pi\) |
0.675610 | + | 0.737259i | \(0.263880\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 1.19459 | − | 6.77487i | 0.0580831 | − | 0.329406i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −0.258770 | − | 0.448204i | −0.0125522 | − | 0.0217411i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −11.4251 | + | 9.58683i | −0.552902 | + | 0.463939i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −10.9795 | + | 19.0171i | −0.530096 | + | 0.918154i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −12.6604 | − | 4.60802i | −0.609832 | − | 0.221961i | 0.0185977 | − | 0.999827i | \(-0.494080\pi\) |
−0.628430 | + | 0.777866i | \(0.716302\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 2.04442 | + | 11.5945i | 0.0982483 | + | 0.557194i | 0.993703 | + | 0.112042i | \(0.0357392\pi\) |
−0.895455 | + | 0.445152i | \(0.853150\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −2.46585 | − | 2.06910i | −0.118229 | − | 0.0992055i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 13.9663 | + | 25.0214i | 0.668100 | + | 1.19693i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −12.0385 | − | 10.1015i | −0.574566 | − | 0.482118i | 0.308592 | − | 0.951195i | \(-0.400142\pi\) |
−0.883157 | + | 0.469077i | \(0.844587\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −0.205737 | − | 1.16679i | −0.00979700 | − | 0.0555616i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −14.6998 | − | 5.35029i | −0.698409 | − | 0.254200i | −0.0316775 | − | 0.999498i | \(-0.510085\pi\) |
−0.666731 | + | 0.745298i | \(0.732307\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −2.32295 | + | 4.02346i | −0.110118 | + | 0.190731i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −3.41669 | + | 2.86694i | −0.161604 | + | 0.135602i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 9.09286 | + | 15.7493i | 0.429119 | + | 0.743255i | 0.996795 | − | 0.0799963i | \(-0.0254909\pi\) |
−0.567676 | + | 0.823252i | \(0.692158\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −0.373455 | + | 2.11797i | −0.0175853 | + | 0.0997314i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −8.40895 | + | 3.06061i | −0.395087 | + | 0.143800i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 12.0036 | 0.562738 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 16.8111 | 0.786390 | 0.393195 | − | 0.919455i | \(-0.371370\pi\) | ||||
0.393195 | + | 0.919455i | \(0.371370\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −0.152704 | + | 0.0555796i | −0.00712760 | + | 0.00259423i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −2.19429 | + | 12.4444i | −0.102198 | + | 0.579595i | 0.890104 | + | 0.455757i | \(0.150631\pi\) |
−0.992302 | + | 0.123838i | \(0.960480\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −2.94743 | − | 5.10510i | −0.136979 | − | 0.237254i | 0.789373 | − | 0.613914i | \(-0.210406\pi\) |
−0.926352 | + | 0.376660i | \(0.877073\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −2.67958 | + | 2.24843i | −0.124262 | + | 0.104269i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −2.68479 | + | 4.65020i | −0.124237 | + | 0.215185i | −0.921435 | − | 0.388534i | \(-0.872982\pi\) |
0.797197 | + | 0.603719i | \(0.206315\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 13.0496 | + | 4.74968i | 0.602576 | + | 0.219320i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 2.00047 | + | 11.3452i | 0.0921766 | + | 0.522760i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 52.1475 | + | 43.7570i | 2.39775 | + | 2.01195i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 13.8807 | + | 0.201288i | 0.636892 | + | 0.00923571i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 3.08125 | + | 2.58548i | 0.141081 | + | 0.118381i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 3.44650 | + | 19.5461i | 0.157475 | + | 0.893083i | 0.956488 | + | 0.291770i | \(0.0942442\pi\) |
−0.799014 | + | 0.601313i | \(0.794645\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −24.1065 | − | 8.77406i | −1.09916 | − | 0.400063i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −7.92649 | + | 13.7291i | −0.360668 | + | 0.624695i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 12.4795 | − | 10.4716i | 0.566666 | − | 0.475489i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 6.50387 | + | 11.2650i | 0.294718 | + | 0.510467i | 0.974919 | − | 0.222558i | \(-0.0714408\pi\) |
−0.680201 | + | 0.733026i | \(0.738107\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −1.82753 | + | 10.3645i | −0.0826439 | + | 0.468697i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 27.9538 | − | 10.1744i | 1.26154 | − | 0.459163i | 0.377254 | − | 0.926110i | \(-0.376869\pi\) |
0.884285 | + | 0.466947i | \(0.154646\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −0.388252 | −0.0174860 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 8.00774 | 0.359921 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −27.6288 | + | 10.0561i | −1.23932 | + | 0.451076i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −2.60220 | + | 14.7578i | −0.116490 | + | 0.660649i | 0.869511 | + | 0.493913i | \(0.164434\pi\) |
−0.986002 | + | 0.166736i | \(0.946677\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −5.36959 | − | 9.30039i | −0.239895 | − | 0.415511i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 13.5646 | − | 11.3821i | 0.604818 | − | 0.507502i | −0.288173 | − | 0.957579i | \(-0.593048\pi\) |
0.892990 | + | 0.450076i | \(0.148603\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 2.65136 | − | 4.59229i | 0.117984 | − | 0.204354i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0.610815 | + | 0.222318i | 0.0271272 | + | 0.00987350i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 4.72715 | + | 26.8090i | 0.209527 | + | 1.18829i | 0.890155 | + | 0.455658i | \(0.150596\pi\) |
−0.680628 | + | 0.732629i | \(0.738293\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 16.9402 | + | 14.2145i | 0.749389 | + | 0.628812i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0.819078 | − | 4.28125i | 0.0361632 | − | 0.189022i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 12.7083 | + | 10.6635i | 0.559993 | + | 0.469890i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 7.10014 | + | 40.2669i | 0.312264 | + | 1.77094i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −7.08512 | − | 2.57877i | −0.311002 | − | 0.113196i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −10.2130 | + | 17.6895i | −0.447440 | + | 0.774989i | −0.998219 | − | 0.0596624i | \(-0.980998\pi\) |
0.550778 | + | 0.834651i | \(0.314331\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 31.4957 | − | 26.4280i | 1.37721 | − | 1.15562i | 0.406981 | − | 0.913437i | \(-0.366582\pi\) |
0.970231 | − | 0.242181i | \(-0.0778628\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 3.84002 | + | 6.65111i | 0.167592 | + | 0.290278i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −0.0732627 | + | 0.415494i | −0.00319137 | + | 0.0180992i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −18.9979 | + | 6.91468i | −0.825997 | + | 0.300638i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −12.0496 | −0.522909 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 1.33687 | 0.0579061 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −17.0077 | + | 6.19031i | −0.735309 | + | 0.267630i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 4.57785 | − | 25.9623i | 0.197549 | − | 1.12035i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 3.52094 | + | 6.09845i | 0.151658 | + | 0.262679i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −4.65064 | + | 3.90235i | −0.199947 | + | 0.167775i | −0.737264 | − | 0.675605i | \(-0.763882\pi\) |
0.537317 | + | 0.843381i | \(0.319438\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 10.5458 | − | 18.2658i | 0.452562 | − | 0.783860i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −2.87211 | − | 1.04536i | −0.123028 | − | 0.0447784i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 4.13547 | + | 23.4534i | 0.176820 | + | 1.00280i | 0.936022 | + | 0.351941i | \(0.114478\pi\) |
−0.759203 | + | 0.650854i | \(0.774411\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 4.73783 | + | 3.97551i | 0.202205 | + | 0.169671i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 5.33733 | − | 8.94253i | 0.227378 | − | 0.380964i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −17.9088 | − | 15.0273i | −0.761559 | − | 0.639024i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 1.62449 | + | 9.21291i | 0.0689556 | + | 0.391066i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 21.9094 | + | 7.97437i | 0.928332 | + | 0.337885i | 0.761548 | − | 0.648108i | \(-0.224440\pi\) |
0.166784 | + | 0.985994i | \(0.446662\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 21.1578 | − | 36.6463i | 0.894878 | − | 1.54997i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0.739885 | − | 0.620838i | 0.0312380 | − | 0.0262118i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 7.35369 | + | 12.7370i | 0.309921 | + | 0.536799i | 0.978345 | − | 0.206981i | \(-0.0663640\pi\) |
−0.668424 | + | 0.743781i | \(0.733031\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −2.97359 | + | 16.8641i | −0.125100 | + | 0.709477i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 2.26604 | − | 0.824773i | 0.0951649 | − | 0.0346372i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 32.6750 | 1.36981 | 0.684903 | − | 0.728634i | \(-0.259844\pi\) | ||||
0.684903 | + | 0.728634i | \(0.259844\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −30.3901 | −1.27179 | −0.635893 | − | 0.771777i | \(-0.719368\pi\) | ||||
−0.635893 | + | 0.771777i | \(0.719368\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0.240352 | − | 0.0874810i | 0.0100409 | − | 0.00365457i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −3.63563 | + | 20.6187i | −0.151616 | + | 0.859858i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −15.4324 | − | 26.7297i | −0.642460 | − | 1.11277i | −0.984882 | − | 0.173227i | \(-0.944581\pi\) |
0.342422 | − | 0.939546i | \(-0.388753\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −10.9914 | + | 9.22286i | −0.456786 | + | 0.383289i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −2.44444 | + | 4.23389i | −0.101412 | + | 0.175652i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −22.4650 | − | 8.17658i | −0.930404 | − | 0.338639i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −0.864370 | − | 4.90209i | −0.0357373 | − | 0.202676i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −21.5804 | − | 18.1081i | −0.890717 | − | 0.747401i | 0.0776365 | − | 0.996982i | \(-0.475263\pi\) |
−0.968354 | + | 0.249581i | \(0.919707\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −8.56283 | − | 7.39928i | −0.352825 | − | 0.304882i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −18.1407 | − | 15.2218i | −0.746208 | − | 0.626143i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −1.18438 | − | 6.71696i | −0.0486367 | − | 0.275833i | 0.950784 | − | 0.309853i | \(-0.100280\pi\) |
−0.999421 | + | 0.0340206i | \(0.989169\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −0.496130 | − | 0.180576i | −0.0203393 | − | 0.00740291i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 5.89780 | − | 10.2153i | 0.241381 | − | 0.418084i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 27.3562 | − | 22.9546i | 1.11774 | − | 0.937899i | 0.119256 | − | 0.992863i | \(-0.461949\pi\) |
0.998488 | + | 0.0549642i | \(0.0175045\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −2.76399 | − | 4.78736i | −0.112745 | − | 0.195281i | 0.804131 | − | 0.594452i | \(-0.202631\pi\) |
−0.916876 | + | 0.399172i | \(0.869298\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 1.00000 | − | 5.67128i | 0.0407231 | − | 0.230952i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −30.7977 | + | 11.2095i | −1.25211 | + | 0.455729i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −19.4953 | −0.791288 | −0.395644 | − | 0.918404i | \(-0.629479\pi\) | ||||
−0.395644 | + | 0.918404i | \(0.629479\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 5.76146 | 0.233466 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 23.8837 | − | 8.69296i | 0.966232 | − | 0.351680i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 6.86262 | − | 38.9198i | 0.277178 | − | 1.57196i | −0.454777 | − | 0.890605i | \(-0.650281\pi\) |
0.731956 | − | 0.681352i | \(-0.238608\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −0.243756 | − | 0.422197i | −0.00982918 | − | 0.0170246i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −0.952648 | + | 0.799367i | −0.0383522 | + | 0.0321813i | −0.661762 | − | 0.749714i | \(-0.730191\pi\) |
0.623410 | + | 0.781895i | \(0.285747\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −4.20187 | + | 7.27785i | −0.168887 | + | 0.292521i | −0.938029 | − | 0.346557i | \(-0.887351\pi\) |
0.769142 | + | 0.639078i | \(0.220684\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 6.17752 | + | 2.24843i | 0.247895 | + | 0.0902265i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −1.44397 | − | 8.18918i | −0.0578516 | − | 0.328093i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0.817267 | + | 0.685768i | 0.0326907 | + | 0.0274307i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 4.12836 | + | 25.5763i | 0.164871 | + | 1.02142i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 0.864370 | + | 0.725293i | 0.0344647 | + | 0.0289193i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 1.61159 | + | 9.13976i | 0.0641562 | + | 0.363848i | 0.999937 | + | 0.0112645i | \(0.00358567\pi\) |
−0.935780 | + | 0.352584i | \(0.885303\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −26.1780 | − | 9.52801i | −1.04048 | − | 0.378704i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 5.20826 | − | 9.02098i | 0.206684 | − | 0.357987i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 3.35323 | − | 2.81369i | 0.132860 | − | 0.111482i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 6.09627 | + | 10.5590i | 0.241165 | + | 0.417709i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −1.51320 | + | 8.58180i | −0.0597680 | + | 0.338961i | −0.999999 | − | 0.00157695i | \(-0.999498\pi\) |
0.940231 | + | 0.340538i | \(0.110609\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −14.2185 | + | 5.17512i | −0.560724 | + | 0.204087i | −0.606805 | − | 0.794851i | \(-0.707549\pi\) |
0.0460808 | + | 0.998938i | \(0.485327\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −15.4311 | −0.607598 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −7.31282 | −0.287497 | −0.143748 | − | 0.989614i | \(-0.545916\pi\) | ||||
−0.143748 | + | 0.989614i | \(0.545916\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 67.2987 | − | 24.4947i | 2.64170 | − | 0.961501i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 1.08718 | − | 6.16571i | 0.0426100 | − | 0.241653i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −8.76904 | − | 15.1884i | −0.343159 | − | 0.594369i | 0.641859 | − | 0.766823i | \(-0.278164\pi\) |
−0.985018 | + | 0.172454i | \(0.944830\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −12.9704 | + | 10.8835i | −0.506797 | + | 0.425253i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 4.58512 | − | 7.94166i | 0.178883 | − | 0.309834i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −7.39693 | − | 2.69226i | −0.288143 | − | 0.104876i | 0.193905 | − | 0.981020i | \(-0.437885\pi\) |
−0.482048 | + | 0.876145i | \(0.660107\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 0.167414 | + | 0.949450i | 0.00651164 | + | 0.0369293i | 0.987890 | − | 0.155153i | \(-0.0495871\pi\) |
−0.981379 | + | 0.192082i | \(0.938476\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −0.459922 | − | 0.385920i | −0.0178619 | − | 0.0149879i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 10.9795 | − | 8.94486i | 0.425768 | − | 0.346867i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 12.0318 | + | 10.0959i | 0.465875 | + | 0.390915i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −4.29561 | − | 24.3616i | −0.166078 | − | 0.941874i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −34.5428 | − | 12.5726i | −1.33351 | − | 0.485358i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 12.9265 | − | 22.3893i | 0.498280 | − | 0.863045i | −0.501719 | − | 0.865031i | \(-0.667299\pi\) |
0.999998 | + | 0.00198549i | \(0.000632002\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 2.43969 | − | 2.04715i | 0.0939038 | − | 0.0787947i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −14.9978 | − | 25.9769i | −0.576411 | − | 0.998374i | −0.995887 | − | 0.0906072i | \(-0.971119\pi\) |
0.419475 | − | 0.907767i | \(-0.362214\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −5.06330 | + | 28.7154i | −0.194312 | + | 1.10200i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 20.6878 | − | 7.52974i | 0.792758 | − | 0.288540i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −33.5084 | −1.28216 | −0.641081 | − | 0.767473i | \(-0.721514\pi\) | ||||
−0.641081 | + | 0.767473i | \(0.721514\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 21.1661 | 0.808716 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −8.73530 | + | 3.17939i | −0.333272 | + | 0.121301i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −2.58054 | + | 14.6350i | −0.0983106 | + | 0.557547i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −6.40673 | − | 11.0968i | −0.243723 | − | 0.422141i | 0.718049 | − | 0.695993i | \(-0.245036\pi\) |
−0.961772 | + | 0.273852i | \(0.911702\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −10.9795 | + | 9.21291i | −0.417078 | + | 0.349970i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 2.17886 | − | 3.77390i | 0.0826490 | − | 0.143152i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −0.0552549 | − | 0.0201112i | −0.00209293 | − | 0.000761764i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 1.38713 | + | 7.86678i | 0.0524659 | + | 0.297549i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 3.04323 | + | 2.55358i | 0.114941 | + | 0.0964472i | 0.698447 | − | 0.715662i | \(-0.253875\pi\) |
−0.583505 | + | 0.812109i | \(0.698319\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −28.5881 | + | 9.93821i | −1.07822 | + | 0.374827i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −7.10014 | − | 5.95772i | −0.267407 | − | 0.224381i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 1.64812 | + | 9.34694i | 0.0619839 | + | 0.351528i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −30.3572 | − | 11.0491i | −1.14009 | − | 0.414958i | −0.298142 | − | 0.954521i | \(-0.596367\pi\) |
−0.841945 | + | 0.539564i | \(0.818589\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −4.84730 | + | 8.39576i | −0.181788 | + | 0.314866i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 13.0747 | − | 10.9710i | 0.489651 | − | 0.410866i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 14.7927 | + | 25.6217i | 0.553215 | + | 0.958196i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −4.59286 | + | 26.0474i | −0.171524 | + | 0.972759i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 42.5385 | − | 15.4828i | 1.58642 | − | 0.577410i | 0.609832 | − | 0.792530i | \(-0.291237\pi\) |
0.976587 | + | 0.215121i | \(0.0690145\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −29.6928 | −1.10582 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 2.73917 | 0.101871 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 7.15018 | − | 2.60245i | 0.265551 | − | 0.0966526i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 3.85188 | − | 21.8451i | 0.142858 | − | 0.810190i | −0.826203 | − | 0.563372i | \(-0.809504\pi\) |
0.969062 | − | 0.246818i | \(-0.0793851\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −0.500000 | − | 0.866025i | −0.0185185 | − | 0.0320750i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −1.42577 | + | 1.19637i | −0.0527341 | + | 0.0442492i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −22.9106 | + | 39.6823i | −0.846222 | + | 1.46570i | 0.0383334 | + | 0.999265i | \(0.487795\pi\) |
−0.884556 | + | 0.466435i | \(0.845538\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −1.50000 | − | 0.545955i | −0.0553283 | − | 0.0201379i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 5.94356 | + | 33.7076i | 0.218934 | + | 1.24164i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 2.89124 | + | 2.42604i | 0.106356 | + | 0.0892434i | 0.694415 | − | 0.719575i | \(-0.255663\pi\) |
−0.588059 | + | 0.808818i | \(0.700108\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 15.2114 | − | 5.28801i | 0.558805 | − | 0.194260i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 17.2251 | + | 14.4536i | 0.631927 | + | 0.530250i | 0.901527 | − | 0.432723i | \(-0.142447\pi\) |
−0.269600 | + | 0.962972i | \(0.586891\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 1.04348 | + | 5.91788i | 0.0382302 | + | 0.216814i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 1.90508 | + | 0.693392i | 0.0697031 | + | 0.0253699i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 16.1976 | − | 28.0550i | 0.591847 | − | 1.02511i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 31.7879 | − | 26.6732i | 1.15996 | − | 0.973320i | 0.160053 | − | 0.987108i | \(-0.448834\pi\) |
0.999905 | + | 0.0137883i | \(0.00438909\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −7.61468 | − | 13.1890i | −0.277495 | − | 0.480635i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −2.09358 | + | 11.8733i | −0.0761931 | + | 0.432113i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 16.8037 | − | 6.11603i | 0.610739 | − | 0.222291i | −0.0180875 | − | 0.999836i | \(-0.505758\pi\) |
0.628827 | + | 0.777546i | \(0.283536\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −39.0729 | −1.41825 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 38.0806 | 1.38042 | 0.690210 | − | 0.723609i | \(-0.257518\pi\) | ||||
0.690210 | + | 0.723609i | \(0.257518\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 5.14068 | − | 1.87106i | 0.186105 | − | 0.0677367i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −0.0380187 | + | 0.215615i | −0.00137457 | + | 0.00779556i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −22.2592 | − | 38.5541i | −0.803734 | − | 1.39211i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −9.67096 | + | 8.11490i | −0.348744 | + | 0.292631i | −0.800285 | − | 0.599619i | \(-0.795319\pi\) |
0.451542 | + | 0.892250i | \(0.350874\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 6.51754 | − | 11.2887i | 0.234724 | − | 0.406553i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −31.7606 | − | 11.5599i | −1.14235 | − | 0.415781i | −0.299588 | − | 0.954069i | \(-0.596849\pi\) |
−0.842761 | + | 0.538288i | \(0.819071\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −1.43582 | − | 8.14295i | −0.0515763 | − | 0.292503i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −12.8268 | − | 10.7630i | −0.460160 | − | 0.386120i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 1.22281 | − | 0.996206i | 0.0438118 | − | 0.0356928i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −55.5130 | − | 46.5809i | −1.98641 | − | 1.66680i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −0.414878 | − | 2.35289i | −0.0148265 | − | 0.0840854i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 14.5851 | + | 5.30855i | 0.520565 | + | 0.189470i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −16.8059 | + | 29.1086i | −0.599065 | + | 1.03761i | 0.393895 | + | 0.919156i | \(0.371127\pi\) |
−0.992959 | + | 0.118455i | \(0.962206\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −9.13610 | + | 7.66610i | −0.325254 | + | 0.272920i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −15.3250 | − | 26.5437i | −0.544895 | − | 0.943785i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −3.96791 | + | 22.5031i | −0.140905 | + | 0.799110i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 5.09240 | − | 1.85348i | 0.180609 | − | 0.0657362i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −46.0547 | −1.63134 | −0.815670 | − | 0.578517i | \(-0.803632\pi\) | ||||
−0.815670 | + | 0.578517i | \(0.803632\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −1.11793 | −0.0395494 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −3.24035 | + | 1.17939i | −0.114492 | + | 0.0416718i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −9.46451 | + | 53.6759i | −0.333995 | + | 1.89418i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 10.6793 | + | 18.4971i | 0.376397 | + | 0.651939i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −19.8084 | + | 16.6212i | −0.697289 | + | 0.585095i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −20.1853 | + | 34.9619i | −0.709676 | + | 1.22919i | 0.255301 | + | 0.966862i | \(0.417825\pi\) |
−0.964977 | + | 0.262333i | \(0.915508\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −48.4744 | − | 17.6432i | −1.70217 | − | 0.619537i | −0.706096 | − | 0.708116i | \(-0.749545\pi\) |
−0.996069 | + | 0.0885787i | \(0.971768\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 2.06165 | + | 11.6922i | 0.0723053 | + | 0.410064i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 10.8621 | + | 9.11435i | 0.380481 | + | 0.319262i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −7.95542 | − | 49.2861i | −0.278325 | − | 1.72430i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 6.82501 | + | 5.72686i | 0.238485 | + | 0.200113i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 6.91622 | + | 39.2238i | 0.241378 | + | 1.36892i | 0.828757 | + | 0.559609i | \(0.189049\pi\) |
−0.587379 | + | 0.809312i | \(0.699840\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −17.8293 | − | 6.48935i | −0.621492 | − | 0.226205i | 0.0120321 | − | 0.999928i | \(-0.496170\pi\) |
−0.633524 | + | 0.773723i | \(0.718392\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −9.46451 | + | 16.3930i | −0.329512 | + | 0.570731i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 3.76810 | − | 3.16181i | 0.131030 | − | 0.109947i | −0.574918 | − | 0.818211i | \(-0.694966\pi\) |
0.705947 | + | 0.708264i | \(0.250521\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 16.6400 | + | 28.8213i | 0.577930 | + | 1.00100i | 0.995717 | + | 0.0924588i | \(0.0294726\pi\) |
−0.417787 | + | 0.908545i | \(0.637194\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −2.50253 | + | 14.1925i | −0.0868117 | + | 0.492333i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −0.180922 | + | 0.0658503i | −0.00626858 | + | 0.00228158i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −14.4688 | −0.500715 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −2.59627 | −0.0897401 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 17.3846 | − | 6.32748i | 0.600183 | − | 0.218449i | −0.0240193 | − | 0.999711i | \(-0.507646\pi\) |
0.624202 | + | 0.781263i | \(0.285424\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −4.04458 | + | 22.9379i | −0.139468 | + | 0.790963i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −1.31567 | − | 2.27881i | −0.0453142 | − | 0.0784865i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0.670874 | − | 0.562930i | 0.0230788 | − | 0.0193654i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 29.3307 | − | 50.8022i | 1.00781 | − | 1.74559i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −5.72416 | − | 2.08342i | −0.196453 | − | 0.0715029i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −7.92649 | − | 44.9534i | −0.271717 | − | 1.54098i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 6.64749 | + | 5.57791i | 0.227606 | + | 0.190984i | 0.749458 | − | 0.662052i | \(-0.230314\pi\) |
−0.521852 | + | 0.853036i | \(0.674759\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −4.44356 | − | 3.83975i | −0.151967 | − | 0.131317i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −20.6958 | − | 17.3658i | −0.706954 | − | 0.593205i | 0.216789 | − | 0.976219i | \(-0.430442\pi\) |
−0.923743 | + | 0.383014i | \(0.874886\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 8.89069 | + | 50.4216i | 0.303346 | + | 1.72036i | 0.631187 | + | 0.775630i | \(0.282568\pi\) |
−0.327841 | + | 0.944733i | \(0.606321\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0.819955 | + | 0.298439i | 0.0279440 | + | 0.0101708i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 9.58037 | − | 16.5937i | 0.326120 | − | 0.564856i | −0.655619 | − | 0.755092i | \(-0.727592\pi\) |
0.981738 | + | 0.190236i | \(0.0609254\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −7.78177 | + | 6.52968i | −0.264588 | + | 0.222016i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −8.48680 | − | 14.6996i | −0.288227 | − | 0.499223i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 10.0057 | − | 56.7450i | 0.339419 | − | 1.92494i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 19.9932 | − | 7.27693i | 0.677443 | − | 0.246569i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 12.0915 | 0.409236 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 26.5921 | 0.898979 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −50.1061 | + | 18.2371i | −1.69196 | + | 0.615824i | −0.994871 | − | 0.101156i | \(-0.967746\pi\) |
−0.697093 | + | 0.716981i | \(0.745524\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 5.68361 | − | 32.2334i | 0.191703 | − | 1.08720i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 0.336619 | + | 0.583041i | 0.0113410 | + | 0.0196431i | 0.871640 | − | 0.490146i | \(-0.163057\pi\) |
−0.860299 | + | 0.509789i | \(0.829723\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −7.50047 | + | 6.29364i | −0.252411 | + | 0.211798i | −0.760210 | − | 0.649678i | \(-0.774904\pi\) |
0.507799 | + | 0.861476i | \(0.330459\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −8.11721 | + | 14.0594i | −0.272857 | + | 0.472602i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −8.26429 | − | 3.00796i | −0.277488 | − | 0.100997i | 0.199528 | − | 0.979892i | \(-0.436059\pi\) |
−0.477015 | + | 0.878895i | \(0.658281\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 3.23752 | + | 18.3609i | 0.108583 | + | 0.615805i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 4.55303 | + | 3.82045i | 0.152532 | + | 0.127990i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 15.3682 | − | 25.7490i | 0.514279 | − | 0.861657i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −27.2087 | − | 22.8308i | −0.909488 | − | 0.763151i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 4.21760 | + | 23.9192i | 0.140821 | + | 0.798638i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −5.82888 | − | 2.12154i | −0.194404 | − | 0.0707573i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 0.326819 | − | 0.566067i | 0.0108879 | − | 0.0188584i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 21.1578 | − | 17.7535i | 0.704086 | − | 0.590798i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −14.2083 | − | 24.6094i | −0.472299 | − | 0.818045i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 1.00681 | − | 5.70989i | 0.0334305 | − | 0.189594i | −0.963519 | − | 0.267639i | \(-0.913757\pi\) |
0.996950 | + | 0.0780450i | \(0.0248678\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 3.69846 | − | 1.34613i | 0.122670 | − | 0.0446483i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 16.9145 | 0.560401 | 0.280201 | − | 0.959941i | \(-0.409599\pi\) | ||||
0.280201 | + | 0.959941i | \(0.409599\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −12.0496 | −0.398785 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 7.83022 | − | 2.84997i | 0.258859 | − | 0.0942170i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 5.26248 | − | 29.8450i | 0.173782 | − | 0.985569i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −18.4379 | − | 31.9354i | −0.608211 | − | 1.05345i | −0.991535 | − | 0.129839i | \(-0.958554\pi\) |
0.383324 | − | 0.923614i | \(-0.374779\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −4.75671 | + | 3.99135i | −0.156739 | + | 0.131520i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −22.5232 | + | 39.0114i | −0.741361 | + | 1.28407i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −20.7802 | − | 7.56337i | −0.683248 | − | 0.248682i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 2.13816 | + | 12.1261i | 0.0702262 | + | 0.398273i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 23.0096 | + | 19.3073i | 0.754919 | + | 0.633452i | 0.936799 | − | 0.349869i | \(-0.113774\pi\) |
−0.181880 | + | 0.983321i | \(0.558218\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0.970437 | − | 5.07239i | 0.0318048 | − | 0.166241i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 2.37939 | + | 1.99654i | 0.0778976 | + | 0.0653638i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −0.225966 | − | 1.28152i | −0.00738989 | − | 0.0419102i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 3.95249 | + | 1.43859i | 0.129122 | + | 0.0469966i | 0.405773 | − | 0.913974i | \(-0.367002\pi\) |
−0.276651 | + | 0.960970i | \(0.589225\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −8.43629 | + | 14.6121i | −0.275308 | + | 0.476847i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −27.4329 | + | 23.0189i | −0.894287 | + | 0.750395i | −0.969065 | − | 0.246805i | \(-0.920619\pi\) |
0.0747787 | + | 0.997200i | \(0.476175\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 1.18938 | + | 2.06006i | 0.0387315 | + | 0.0670849i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0.564178 | − | 3.19961i | 0.0183527 | − | 0.104083i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −9.82073 | + | 3.57445i | −0.319131 | + | 0.116154i | −0.496619 | − | 0.867969i | \(-0.665425\pi\) |
0.177488 | + | 0.984123i | \(0.443203\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 33.8803 | 1.09980 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −14.4260 | −0.467796 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −20.3097 | + | 7.39214i | −0.657897 | + | 0.239455i | −0.649328 | − | 0.760508i | \(-0.724950\pi\) |
−0.00856895 | + | 0.999963i | \(0.502728\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0.0598406 | − | 0.339373i | 0.00193639 | − | 0.0109818i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 7.10014 | + | 12.2978i | 0.229515 | + | 0.397531i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −29.0212 | + | 24.3516i | −0.937142 | + | 0.786356i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 12.1297 | − | 21.0093i | 0.391281 | − | 0.677718i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −12.6236 | − | 4.59462i | −0.406790 | − | 0.148059i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 3.35685 | + | 19.0376i | 0.108061 | + | 0.612843i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −6.98751 | − | 5.86322i | −0.224703 | − | 0.188548i | 0.523485 | − | 0.852035i | \(-0.324632\pi\) |
−0.748188 | + | 0.663486i | \(0.769076\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −0.708263 | − | 0.0102707i | −0.0227527 | − | 0.000329942i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 37.3999 | + | 31.3823i | 1.20022 | + | 1.00710i | 0.999624 | + | 0.0274307i | \(0.00873256\pi\) |
0.200597 | + | 0.979674i | \(0.435712\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 1.35441 | + | 7.68123i | 0.0434203 | + | 0.246249i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 11.0569 | + | 4.02438i | 0.354104 | + | 0.128883i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −1.31268 | + | 2.27363i | −0.0419964 | + | 0.0727399i | −0.886260 | − | 0.463189i | \(-0.846705\pi\) |
0.844263 | + | 0.535929i | \(0.180038\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 15.7003 | − | 13.1741i | 0.501783 | − | 0.421046i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −1.13429 | − | 1.96464i | −0.0362149 | − | 0.0627261i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −1.86262 | + | 10.5634i | −0.0594082 | + | 0.336921i | −0.999997 | − | 0.00262836i | \(-0.999163\pi\) |
0.940588 | + | 0.339549i | \(0.110274\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −29.9812 | + | 10.9123i | −0.955280 | + | 0.347693i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 16.5895 | 0.528048 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 75.2942 | 2.39421 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 53.1656 | − | 19.3507i | 1.68886 | − | 0.614695i | 0.694378 | − | 0.719610i | \(-0.255679\pi\) |
0.994481 | + | 0.104916i | \(0.0334572\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −1.56237 | + | 8.86062i | −0.0495802 | + | 0.281183i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −7.94609 | − | 13.7630i | −0.251908 | − | 0.436317i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 8.46791 | − | 7.10542i | 0.268181 | − | 0.225031i | −0.498773 | − | 0.866733i | \(-0.666216\pi\) |
0.766954 | + | 0.641702i | \(0.221771\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −3.47178 | + | 6.01330i | −0.109842 | + | 0.190252i |
(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 | 912.2.bo.e.529.1 | 6 | ||
4.3 | odd | 2 | 228.2.q.a.73.1 | yes | 6 | ||
12.11 | even | 2 | 684.2.bo.a.73.1 | 6 | |||
19.6 | even | 9 | inner | 912.2.bo.e.481.1 | 6 | ||
76.43 | odd | 18 | 4332.2.a.o.1.2 | 3 | |||
76.63 | odd | 18 | 228.2.q.a.25.1 | ✓ | 6 | ||
76.71 | even | 18 | 4332.2.a.n.1.2 | 3 | |||
228.215 | even | 18 | 684.2.bo.a.253.1 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
228.2.q.a.25.1 | ✓ | 6 | 76.63 | odd | 18 | ||
228.2.q.a.73.1 | yes | 6 | 4.3 | odd | 2 | ||
684.2.bo.a.73.1 | 6 | 12.11 | even | 2 | |||
684.2.bo.a.253.1 | 6 | 228.215 | even | 18 | |||
912.2.bo.e.481.1 | 6 | 19.6 | even | 9 | inner | ||
912.2.bo.e.529.1 | 6 | 1.1 | even | 1 | trivial | ||
4332.2.a.n.1.2 | 3 | 76.71 | even | 18 | |||
4332.2.a.o.1.2 | 3 | 76.43 | odd | 18 |