Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [300,2,Mod(61,300)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(300, base_ring=CyclotomicField(10))
chi = DirichletCharacter(H, H._module([0, 0, 8]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("300.61");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 300 = 2^{2} \cdot 3 \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 300.m (of order \(5\), degree \(4\), 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: | \(2.39551206064\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{5})\) |
Coefficient field: | 8.0.26265625.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 3x^{7} + 2x^{6} + x^{4} + 8x^{2} - 24x + 16 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 5 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{5}]$ |
Embedding invariants
Embedding label | 121.2 | ||
Root | \(-0.0272949 - 1.41395i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 300.121 |
Dual form | 300.2.m.b.181.2 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/300\mathbb{Z}\right)^\times\).
\(n\) | \(101\) | \(151\) | \(277\) |
\(\chi(n)\) | \(1\) | \(1\) | \(e\left(\frac{3}{5}\right)\) |
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 | ||||||||
\(3\) | 0.809017 | + | 0.587785i | 0.467086 | + | 0.339358i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.99851 | + | 1.00297i | 0.893761 | + | 0.448544i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.0883282 | −0.0333849 | −0.0166925 | − | 0.999861i | \(-0.505314\pi\) | ||||
−0.0166925 | + | 0.999861i | \(0.505314\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0.309017 | + | 0.951057i | 0.103006 | + | 0.317019i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0.701409 | − | 2.15871i | 0.211483 | − | 0.650877i | −0.787902 | − | 0.615801i | \(-0.788833\pi\) |
0.999385 | − | 0.0350761i | \(-0.0111674\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0.819443 | + | 2.52199i | 0.227273 | + | 0.699473i | 0.998053 | + | 0.0623720i | \(0.0198665\pi\) |
−0.770780 | + | 0.637101i | \(0.780133\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 1.02729 | + | 1.98612i | 0.265246 | + | 0.512813i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −1.68949 | + | 1.22749i | −0.409762 | + | 0.297710i | −0.773506 | − | 0.633790i | \(-0.781499\pi\) |
0.363743 | + | 0.931499i | \(0.381499\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.42464 | + | 1.03506i | −0.326835 | + | 0.237459i | −0.739086 | − | 0.673611i | \(-0.764742\pi\) |
0.412252 | + | 0.911070i | \(0.364742\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −0.0714590 | − | 0.0519180i | −0.0155936 | − | 0.0113294i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 1.46477 | − | 4.50810i | 0.305426 | − | 0.940005i | −0.674092 | − | 0.738647i | \(-0.735465\pi\) |
0.979518 | − | 0.201357i | \(-0.0645352\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 2.98808 | + | 4.00891i | 0.597617 | + | 0.801782i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −0.309017 | + | 0.951057i | −0.0594703 | + | 0.183031i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −2.99851 | − | 2.17855i | −0.556809 | − | 0.404546i | 0.273480 | − | 0.961878i | \(-0.411825\pi\) |
−0.830290 | + | 0.557332i | \(0.811825\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 3.32199 | − | 2.41356i | 0.596646 | − | 0.433489i | −0.248041 | − | 0.968750i | \(-0.579787\pi\) |
0.844687 | + | 0.535261i | \(0.179787\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 1.83631 | − | 1.33416i | 0.319661 | − | 0.232247i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −0.176525 | − | 0.0885909i | −0.0298381 | − | 0.0149746i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 2.19992 | + | 6.77065i | 0.361664 | + | 1.11309i | 0.952044 | + | 0.305963i | \(0.0989782\pi\) |
−0.590379 | + | 0.807126i | \(0.701022\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −0.819443 | + | 2.52199i | −0.131216 | + | 0.403841i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −2.03623 | − | 6.26687i | −0.318006 | − | 0.978721i | −0.974499 | − | 0.224390i | \(-0.927961\pi\) |
0.656494 | − | 0.754332i | \(-0.272039\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 1.79469 | 0.273688 | 0.136844 | − | 0.990593i | \(-0.456304\pi\) | ||||
0.136844 | + | 0.990593i | \(0.456304\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −0.336312 | + | 2.21063i | −0.0501344 | + | 0.329542i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −8.17999 | − | 5.94311i | −1.19317 | − | 0.866892i | −0.199578 | − | 0.979882i | \(-0.563957\pi\) |
−0.993596 | + | 0.112990i | \(0.963957\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.99220 | −0.998885 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −2.08833 | −0.292424 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 0.777821 | + | 0.565120i | 0.106842 | + | 0.0776252i | 0.639923 | − | 0.768439i | \(-0.278966\pi\) |
−0.533081 | + | 0.846064i | \(0.678966\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 3.56691 | − | 3.61072i | 0.480962 | − | 0.486869i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −1.76095 | −0.233244 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −2.77436 | − | 8.53860i | −0.361191 | − | 1.11163i | −0.952332 | − | 0.305063i | \(-0.901323\pi\) |
0.591142 | − | 0.806568i | \(-0.298677\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 2.92521 | − | 9.00287i | 0.374535 | − | 1.15270i | −0.569257 | − | 0.822159i | \(-0.692769\pi\) |
0.943792 | − | 0.330540i | \(-0.107231\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −0.0272949 | − | 0.0840051i | −0.00343883 | − | 0.0105836i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −0.891823 | + | 5.86209i | −0.110617 | + | 0.727103i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −11.2485 | + | 8.17249i | −1.37422 | + | 0.998429i | −0.376825 | + | 0.926285i | \(0.622984\pi\) |
−0.997394 | + | 0.0721440i | \(0.977016\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 3.83482 | − | 2.78616i | 0.461658 | − | 0.335414i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −4.97363 | − | 3.61355i | −0.590261 | − | 0.428850i | 0.252148 | − | 0.967689i | \(-0.418863\pi\) |
−0.842409 | + | 0.538839i | \(0.818863\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −0.975766 | + | 3.00310i | −0.114205 | + | 0.351486i | −0.991780 | − | 0.127952i | \(-0.959160\pi\) |
0.877576 | + | 0.479438i | \(0.159160\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0.0610333 | + | 4.99963i | 0.00704751 | + | 0.577307i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −0.0619542 | + | 0.190675i | −0.00706033 | + | 0.0217295i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −10.8021 | − | 7.84821i | −1.21534 | − | 0.882993i | −0.219631 | − | 0.975583i | \(-0.570485\pi\) |
−0.995704 | + | 0.0925903i | \(0.970485\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −0.809017 | + | 0.587785i | −0.0898908 | + | 0.0653095i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 12.7982 | − | 9.29846i | 1.40479 | − | 1.02064i | 0.410734 | − | 0.911755i | \(-0.365272\pi\) |
0.994054 | − | 0.108884i | \(-0.0347276\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −4.60761 | + | 0.758630i | −0.499765 | + | 0.0822849i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −1.14533 | − | 3.52496i | −0.122792 | − | 0.377915i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −3.16767 | + | 9.74909i | −0.335772 | + | 1.03340i | 0.630568 | + | 0.776134i | \(0.282822\pi\) |
−0.966340 | + | 0.257267i | \(0.917178\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −0.0723799 | − | 0.222762i | −0.00758747 | − | 0.0233518i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 4.10620 | 0.425793 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −3.88530 | + | 0.639703i | −0.398623 | + | 0.0656322i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 10.3617 | + | 7.52820i | 1.05207 | + | 0.764373i | 0.972605 | − | 0.232465i | \(-0.0746790\pi\) |
0.0794643 | + | 0.996838i | \(0.474679\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 2.26981 | 0.228124 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −2.72537 | −0.271185 | −0.135592 | − | 0.990765i | \(-0.543294\pi\) | ||||
−0.135592 | + | 0.990765i | \(0.543294\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 0.291227 | + | 0.211589i | 0.0286954 | + | 0.0208485i | 0.602041 | − | 0.798466i | \(-0.294355\pi\) |
−0.573345 | + | 0.819314i | \(0.694355\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −0.0907391 | − | 0.175430i | −0.00885523 | − | 0.0171202i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 0.0286533 | 0.00277002 | 0.00138501 | − | 0.999999i | \(-0.499559\pi\) | ||||
0.00138501 | + | 0.999999i | \(0.499559\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −5.84714 | − | 17.9956i | −0.560054 | − | 1.72367i | −0.682207 | − | 0.731159i | \(-0.738980\pi\) |
0.122153 | − | 0.992511i | \(-0.461020\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −2.19992 | + | 6.77065i | −0.208807 | + | 0.642642i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 1.51227 | + | 4.65428i | 0.142262 | + | 0.437838i | 0.996649 | − | 0.0818000i | \(-0.0260669\pi\) |
−0.854387 | + | 0.519638i | \(0.826067\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 7.44887 | − | 7.54036i | 0.694611 | − | 0.703142i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −2.14533 | + | 1.55867i | −0.198336 | + | 0.144099i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0.149230 | − | 0.108422i | 0.0136799 | − | 0.00993901i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 4.73111 | + | 3.43736i | 0.430101 | + | 0.312487i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 2.03623 | − | 6.26687i | 0.183601 | − | 0.565065i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1.95088 | + | 11.0088i | 0.174492 | + | 0.984659i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1.01048 | + | 3.10993i | −0.0896652 | + | 0.275961i | −0.985827 | − | 0.167767i | \(-0.946344\pi\) |
0.896161 | + | 0.443728i | \(0.146344\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 1.45193 | + | 1.05489i | 0.127836 | + | 0.0928781i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −2.90882 | + | 2.11338i | −0.254145 | + | 0.184647i | −0.707562 | − | 0.706651i | \(-0.750205\pi\) |
0.453417 | + | 0.891299i | \(0.350205\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0.125836 | − | 0.0914251i | 0.0109114 | − | 0.00792756i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −1.57146 | + | 1.59076i | −0.135250 | + | 0.136911i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 5.25938 | + | 16.1867i | 0.449339 | + | 1.38292i | 0.877654 | + | 0.479294i | \(0.159107\pi\) |
−0.428315 | + | 0.903629i | \(0.640893\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −5.86699 | + | 18.0567i | −0.497632 | + | 1.53155i | 0.315184 | + | 0.949031i | \(0.397934\pi\) |
−0.812815 | + | 0.582522i | \(0.802066\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −3.12448 | − | 9.61615i | −0.263128 | − | 0.809826i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 6.01901 | 0.503335 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −3.80753 | − | 7.36127i | −0.316198 | − | 0.611320i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −5.65681 | − | 4.10991i | −0.466566 | − | 0.338980i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 20.3441 | 1.66665 | 0.833327 | − | 0.552780i | \(-0.186433\pi\) | ||||
0.833327 | + | 0.552780i | \(0.186433\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 13.2609 | 1.07915 | 0.539577 | − | 0.841936i | \(-0.318584\pi\) | ||||
0.539577 | + | 0.841936i | \(0.318584\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −1.68949 | − | 1.22749i | −0.136587 | − | 0.0992366i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 9.05976 | − | 1.49166i | 0.727698 | − | 0.119813i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 12.8066 | 1.02208 | 0.511039 | − | 0.859558i | \(-0.329261\pi\) | ||||
0.511039 | + | 0.859558i | \(0.329261\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0.297101 | + | 0.914384i | 0.0235617 | + | 0.0725153i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −0.129381 | + | 0.398193i | −0.0101966 | + | 0.0313820i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 4.65524 | + | 14.3273i | 0.364626 | + | 1.12220i | 0.950215 | + | 0.311596i | \(0.100863\pi\) |
−0.585589 | + | 0.810608i | \(0.699137\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 5.00801 | − | 0.824555i | 0.389873 | − | 0.0641916i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 2.79215 | − | 2.02861i | 0.216063 | − | 0.156979i | −0.474490 | − | 0.880261i | \(-0.657367\pi\) |
0.690553 | + | 0.723282i | \(0.257367\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 4.82830 | − | 3.50796i | 0.371407 | − | 0.269843i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −1.42464 | − | 1.03506i | −0.108945 | − | 0.0791531i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −0.746142 | + | 2.29639i | −0.0567281 | + | 0.174591i | −0.975406 | − | 0.220417i | \(-0.929258\pi\) |
0.918678 | + | 0.395008i | \(0.129258\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −0.263932 | − | 0.354100i | −0.0199514 | − | 0.0267674i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 2.77436 | − | 8.53860i | 0.208533 | − | 0.641800i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 3.29228 | + | 2.39198i | 0.246077 | + | 0.178785i | 0.703986 | − | 0.710214i | \(-0.251402\pi\) |
−0.457910 | + | 0.888999i | \(0.651402\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 10.7893 | − | 7.83888i | 0.801962 | − | 0.582660i | −0.109527 | − | 0.993984i | \(-0.534934\pi\) |
0.911489 | + | 0.411324i | \(0.134934\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 7.65830 | − | 5.56408i | 0.566118 | − | 0.411309i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −2.39423 | + | 15.7377i | −0.176028 | + | 1.15706i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 1.46477 | + | 4.50810i | 0.107115 | + | 0.329665i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0.0272949 | − | 0.0840051i | 0.00198541 | − | 0.00611047i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 7.80358 | + | 24.0169i | 0.564647 | + | 1.73780i | 0.668998 | + | 0.743264i | \(0.266723\pi\) |
−0.104351 | + | 0.994541i | \(0.533277\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −24.6399 | −1.77362 | −0.886808 | − | 0.462139i | \(-0.847082\pi\) | ||||
−0.886808 | + | 0.462139i | \(0.847082\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −4.16715 | + | 4.21833i | −0.298416 | + | 0.302081i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −15.0640 | − | 10.9446i | −1.07327 | − | 0.779774i | −0.0967697 | − | 0.995307i | \(-0.530851\pi\) |
−0.976496 | + | 0.215533i | \(0.930851\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 9.85708 | 0.698750 | 0.349375 | − | 0.936983i | \(-0.386394\pi\) | ||||
0.349375 | + | 0.936983i | \(0.386394\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −13.9039 | −0.980703 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0.264853 | + | 0.192427i | 0.0185890 | + | 0.0135057i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 2.21609 | − | 14.5667i | 0.154778 | − | 1.01738i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 4.74010 | 0.329460 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 1.23515 | + | 3.80139i | 0.0854369 | + | 0.262948i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −2.44086 | + | 7.51219i | −0.168036 | + | 0.517161i | −0.999247 | − | 0.0387958i | \(-0.987648\pi\) |
0.831212 | + | 0.555956i | \(0.187648\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −1.89976 | − | 5.84685i | −0.130169 | − | 0.400619i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 3.58671 | + | 1.80003i | 0.244611 | + | 0.122761i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −0.293425 | + | 0.213186i | −0.0199190 | + | 0.0144720i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −2.55459 | + | 1.85602i | −0.172623 | + | 0.125418i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −4.48015 | − | 3.25502i | −0.301368 | − | 0.218956i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −2.83731 | + | 8.73235i | −0.190001 | + | 0.584762i | −0.999999 | − | 0.00167090i | \(-0.999468\pi\) |
0.809998 | + | 0.586433i | \(0.199468\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −2.88933 | + | 4.08066i | −0.192622 | + | 0.272044i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 3.57392 | − | 10.9994i | 0.237209 | − | 0.730056i | −0.759611 | − | 0.650377i | \(-0.774611\pi\) |
0.996821 | − | 0.0796781i | \(-0.0253892\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −20.1820 | − | 14.6631i | −1.33366 | − | 0.968962i | −0.999652 | − | 0.0263923i | \(-0.991598\pi\) |
−0.334010 | − | 0.942570i | \(-0.608402\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −0.162198 | + | 0.117844i | −0.0106718 | + | 0.00775355i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −10.5334 | + | 7.65295i | −0.690065 | + | 0.501361i | −0.876681 | − | 0.481071i | \(-0.840248\pi\) |
0.186617 | + | 0.982433i | \(0.440248\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −10.3870 | − | 20.0817i | −0.677573 | − | 1.30998i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −4.12605 | − | 12.6987i | −0.268016 | − | 0.824867i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −8.16071 | + | 25.1161i | −0.527872 | + | 1.62462i | 0.230693 | + | 0.973027i | \(0.425901\pi\) |
−0.758565 | + | 0.651597i | \(0.774099\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −1.92700 | − | 5.93070i | −0.124129 | − | 0.382030i | 0.869612 | − | 0.493735i | \(-0.164369\pi\) |
−0.993741 | + | 0.111705i | \(0.964369\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −13.9740 | − | 7.01300i | −0.892765 | − | 0.448044i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −3.77782 | − | 2.74475i | −0.240377 | − | 0.174644i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 15.8195 | 1.00252 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 7.46802 | 0.471377 | 0.235689 | − | 0.971829i | \(-0.424265\pi\) | ||||
0.235689 | + | 0.971829i | \(0.424265\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −8.70430 | − | 6.32405i | −0.547235 | − | 0.397589i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −4.17354 | − | 2.09454i | −0.261358 | − | 0.131165i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 8.39880 | 0.523903 | 0.261951 | − | 0.965081i | \(-0.415634\pi\) | ||||
0.261951 | + | 0.965081i | \(0.415634\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −0.194315 | − | 0.598039i | −0.0120741 | − | 0.0371604i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 1.14533 | − | 3.52496i | 0.0708941 | − | 0.218190i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −3.09783 | − | 9.53415i | −0.191021 | − | 0.587901i | −1.00000 | 6.39037e-5i | \(-0.999980\pi\) | |
0.808979 | − | 0.587837i | \(-0.200020\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0.987682 | + | 1.90953i | 0.0606728 | + | 0.117302i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −8.29307 | + | 6.02527i | −0.507528 | + | 0.368740i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 14.2542 | − | 10.3563i | 0.869094 | − | 0.631434i | −0.0612496 | − | 0.998122i | \(-0.519509\pi\) |
0.930344 | + | 0.366689i | \(0.119509\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 3.92718 | + | 2.85327i | 0.238559 | + | 0.173324i | 0.700641 | − | 0.713514i | \(-0.252897\pi\) |
−0.462082 | + | 0.886837i | \(0.652897\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0.0723799 | − | 0.222762i | 0.00438063 | − | 0.0134822i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 10.7500 | − | 3.63854i | 0.648247 | − | 0.219412i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 6.98748 | − | 21.5053i | 0.419837 | − | 1.29213i | −0.488015 | − | 0.872835i | \(-0.662279\pi\) |
0.907852 | − | 0.419291i | \(-0.137721\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 3.32199 | + | 2.41356i | 0.198882 | + | 0.144496i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −23.6671 | + | 17.1952i | −1.41186 | + | 1.02578i | −0.418815 | + | 0.908071i | \(0.637555\pi\) |
−0.993048 | + | 0.117708i | \(0.962445\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −23.6661 | + | 17.1944i | −1.40680 | + | 1.02210i | −0.413026 | + | 0.910719i | \(0.635528\pi\) |
−0.993778 | + | 0.111383i | \(0.964472\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −3.51928 | − | 1.76619i | −0.208464 | − | 0.104620i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0.179857 | + | 0.553541i | 0.0106166 | + | 0.0326745i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −3.90563 | + | 12.0203i | −0.229743 | + | 0.707076i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 3.95781 | + | 12.1809i | 0.232011 | + | 0.714056i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −13.4104 | −0.783447 | −0.391723 | − | 0.920083i | \(-0.628121\pi\) | ||||
−0.391723 | + | 0.920083i | \(0.628121\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 3.01941 | − | 19.8471i | 0.175797 | − | 1.15554i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 1.83631 | + | 1.33416i | 0.106554 | + | 0.0774157i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 12.5697 | 0.726923 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −0.158522 | −0.00913704 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −2.20487 | − | 1.60193i | −0.126667 | − | 0.0920287i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 14.8757 | − | 15.0584i | 0.851781 | − | 0.862242i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 13.5444 | 0.773022 | 0.386511 | − | 0.922285i | \(-0.373680\pi\) | ||||
0.386511 | + | 0.922285i | \(0.373680\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0.111239 | + | 0.342358i | 0.00632815 | + | 0.0194761i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −0.630031 | + | 1.93904i | −0.0357258 | + | 0.109953i | −0.967329 | − | 0.253524i | \(-0.918410\pi\) |
0.931603 | + | 0.363477i | \(0.118410\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −5.64839 | − | 17.3840i | −0.319266 | − | 0.982599i | −0.973963 | − | 0.226708i | \(-0.927204\pi\) |
0.654697 | − | 0.755892i | \(-0.272796\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0.0297058 | − | 0.195261i | 0.00167373 | − | 0.0110017i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 15.2078 | − | 11.0491i | 0.854153 | − | 0.620579i | −0.0721348 | − | 0.997395i | \(-0.522981\pi\) |
0.926288 | + | 0.376816i | \(0.122981\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −6.80604 | + | 4.94488i | −0.381065 | + | 0.276860i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0.0231810 | + | 0.0168420i | 0.00129384 | + | 0.000940029i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 1.13639 | − | 3.49746i | 0.0632306 | − | 0.194604i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −7.66185 | + | 10.8210i | −0.425003 | + | 0.600240i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 5.84714 | − | 17.9956i | 0.323348 | − | 0.995161i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0.722523 | + | 0.524944i | 0.0398340 | + | 0.0289411i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 6.73111 | − | 4.89044i | 0.369976 | − | 0.268803i | −0.387225 | − | 0.921985i | \(-0.626566\pi\) |
0.757201 | + | 0.653182i | \(0.226566\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −5.75946 | + | 4.18449i | −0.315617 | + | 0.229309i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −30.6770 | + | 5.05088i | −1.67606 | + | 0.275959i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 5.43691 | + | 16.7331i | 0.296167 | + | 0.911509i | 0.982827 | + | 0.184530i | \(0.0590763\pi\) |
−0.686660 | + | 0.726979i | \(0.740924\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −1.51227 | + | 4.65428i | −0.0821351 | + | 0.252786i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −2.88012 | − | 8.86411i | −0.155967 | − | 0.480019i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.23591 | 0.0667326 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 10.4584 | − | 1.72194i | 0.563060 | − | 0.0927063i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −24.9333 | − | 18.1151i | −1.33849 | − | 0.972469i | −0.999498 | − | 0.0316789i | \(-0.989915\pi\) |
−0.338990 | − | 0.940790i | \(-0.610085\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 22.0376 | 1.17964 | 0.589822 | − | 0.807533i | \(-0.299198\pi\) | ||||
0.589822 | + | 0.807533i | \(0.299198\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −2.65177 | −0.141541 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −4.94803 | − | 3.59496i | −0.263357 | − | 0.191340i | 0.448269 | − | 0.893899i | \(-0.352041\pi\) |
−0.711626 | + | 0.702559i | \(0.752041\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −6.31554 | − | 12.2101i | −0.335194 | − | 0.648047i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0.184458 | 0.00976256 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 4.57676 | + | 14.0858i | 0.241552 | + | 0.743422i | 0.996184 | + | 0.0872735i | \(0.0278154\pi\) |
−0.754632 | + | 0.656148i | \(0.772185\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −4.91308 | + | 15.1209i | −0.258583 | + | 0.795836i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 1.80712 | + | 5.56176i | 0.0948495 | + | 0.291917i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −4.96211 | + | 5.02306i | −0.259729 | + | 0.262919i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −10.7692 | + | 7.82431i | −0.562150 | + | 0.408426i | −0.832245 | − | 0.554408i | \(-0.812945\pi\) |
0.270095 | + | 0.962834i | \(0.412945\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 5.33092 | − | 3.87314i | 0.277517 | − | 0.201628i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −0.0687035 | − | 0.0499160i | −0.00356691 | − | 0.00259151i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −5.26035 | + | 16.1897i | −0.272371 | + | 0.838271i | 0.717532 | + | 0.696525i | \(0.245272\pi\) |
−0.989903 | + | 0.141746i | \(0.954728\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −4.89252 | + | 10.0530i | −0.252649 | + | 0.519136i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 3.03715 | − | 9.34739i | 0.156421 | − | 0.481415i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 2.29328 | + | 1.66617i | 0.117798 | + | 0.0855852i | 0.645124 | − | 0.764078i | \(-0.276806\pi\) |
−0.527326 | + | 0.849663i | \(0.676806\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −2.64546 | + | 1.92204i | −0.135531 | + | 0.0984691i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −8.12938 | + | 5.90634i | −0.415392 | + | 0.301800i | −0.775781 | − | 0.631002i | \(-0.782644\pi\) |
0.360389 | + | 0.932802i | \(0.382644\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −0.315058 | + | 0.318928i | −0.0160569 | + | 0.0162541i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0.554590 | + | 1.70685i | 0.0281914 | + | 0.0867642i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 2.58687 | − | 7.96156i | 0.131159 | − | 0.403667i | −0.863813 | − | 0.503812i | \(-0.831930\pi\) |
0.994973 | + | 0.100144i | \(0.0319305\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 3.05892 | + | 9.41440i | 0.154696 | + | 0.476107i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −3.59550 | −0.181369 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −13.7166 | − | 26.5190i | −0.690158 | − | 1.33432i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 6.78277 | + | 4.92797i | 0.340418 | + | 0.247328i | 0.744838 | − | 0.667245i | \(-0.232527\pi\) |
−0.404420 | + | 0.914573i | \(0.632527\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0.155542 | 0.00778682 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 2.14450 | 0.107091 | 0.0535455 | − | 0.998565i | \(-0.482948\pi\) | ||||
0.0535455 | + | 0.998565i | \(0.482948\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 8.80915 | + | 6.40022i | 0.438815 | + | 0.318818i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −2.20636 | + | 0.363271i | −0.109635 | + | 0.0180511i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 16.1589 | 0.800969 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −1.10861 | − | 3.41195i | −0.0548173 | − | 0.168710i | 0.919900 | − | 0.392154i | \(-0.128270\pi\) |
−0.974717 | + | 0.223444i | \(0.928270\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −5.25938 | + | 16.1867i | −0.259426 | + | 0.798431i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0.245054 | + | 0.754199i | 0.0120583 | + | 0.0371117i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 34.9035 | − | 5.74677i | 1.71335 | − | 0.282098i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −15.3600 | + | 11.1597i | −0.752181 | + | 0.546492i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 7.44874 | − | 5.41183i | 0.363895 | − | 0.264385i | −0.390780 | − | 0.920484i | \(-0.627795\pi\) |
0.754675 | + | 0.656099i | \(0.227795\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 33.0957 | + | 24.0454i | 1.61299 | + | 1.17190i | 0.852890 | + | 0.522090i | \(0.174848\pi\) |
0.760095 | + | 0.649812i | \(0.225152\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 3.12448 | − | 9.61615i | 0.151917 | − | 0.467553i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −9.96924 | − | 3.10518i | −0.483579 | − | 0.150624i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −0.258378 | + | 0.795207i | −0.0125038 | + | 0.0384828i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 4.86948 | + | 3.53789i | 0.235101 | + | 0.170811i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −1.83058 | + | 1.32999i | −0.0881758 | + | 0.0640634i | −0.631000 | − | 0.775783i | \(-0.717355\pi\) |
0.542824 | + | 0.839847i | \(0.317355\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 3.70141 | − | 2.68923i | 0.177878 | − | 0.129236i | −0.495283 | − | 0.868731i | \(-0.664936\pi\) |
0.673162 | + | 0.739495i | \(0.264936\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 1.24649 | − | 8.19340i | 0.0597648 | − | 0.392844i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 2.57939 | + | 7.93855i | 0.123389 | + | 0.379753i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −0.541703 | + | 1.66719i | −0.0258541 | + | 0.0795706i | −0.963151 | − | 0.268961i | \(-0.913320\pi\) |
0.937297 | + | 0.348532i | \(0.113320\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −2.16071 | − | 6.64998i | −0.102891 | − | 0.316666i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 20.8364 | 0.989967 | 0.494983 | − | 0.868902i | \(-0.335174\pi\) | ||||
0.494983 | + | 0.868902i | \(0.335174\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −16.1087 | + | 16.3066i | −0.763626 | + | 0.773005i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 16.4587 | + | 11.9580i | 0.778471 | + | 0.565592i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 25.1952 | 1.18904 | 0.594518 | − | 0.804082i | \(-0.297343\pi\) | ||||
0.594518 | + | 0.804082i | \(0.297343\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −14.9566 | −0.704280 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 10.7283 | + | 7.79454i | 0.504058 | + | 0.366220i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0.0787731 | − | 0.517788i | 0.00369294 | − | 0.0242743i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 39.5166 | 1.84851 | 0.924255 | − | 0.381775i | \(-0.124687\pi\) | ||||
0.924255 | + | 0.381775i | \(0.124687\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −0.645329 | − | 1.98612i | −0.0301214 | − | 0.0927041i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 4.50731 | − | 13.8721i | 0.209927 | − | 0.646087i | −0.789548 | − | 0.613688i | \(-0.789685\pi\) |
0.999475 | − | 0.0323993i | \(-0.0103148\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 3.05096 | + | 9.38989i | 0.141790 | + | 0.436385i | 0.996584 | − | 0.0825821i | \(-0.0263167\pi\) |
−0.854794 | + | 0.518967i | \(0.826317\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 8.20628 | + | 4.11841i | 0.380557 | + | 0.190987i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 17.1041 | − | 12.4268i | 0.791481 | − | 0.575045i | −0.116921 | − | 0.993141i | \(-0.537303\pi\) |
0.908403 | + | 0.418096i | \(0.137303\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0.993557 | − | 0.721861i | 0.0458782 | − | 0.0333324i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 10.3608 | + | 7.52753i | 0.477399 | + | 0.346850i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 1.25881 | − | 3.87422i | 0.0578802 | − | 0.178137i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −8.40641 | − | 2.61840i | −0.385713 | − | 0.120140i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −0.297101 | + | 0.914384i | −0.0136033 | + | 0.0418667i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −33.5317 | − | 24.3622i | −1.53210 | − | 1.11314i | −0.955055 | − | 0.296429i | \(-0.904204\pi\) |
−0.577049 | − | 0.816710i | \(-0.695796\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −15.2728 | + | 11.0963i | −0.696379 | + | 0.505949i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −0.338723 | + | 0.246097i | −0.0154124 | + | 0.0111978i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 13.1573 | + | 25.4377i | 0.597443 | + | 1.15507i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −1.24834 | − | 3.84198i | −0.0565675 | − | 0.174097i | 0.918781 | − | 0.394768i | \(-0.129175\pi\) |
−0.975348 | + | 0.220671i | \(0.929175\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −4.65524 | + | 14.3273i | −0.210517 | + | 0.647905i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 8.95383 | + | 27.5570i | 0.404081 | + | 1.24363i | 0.921661 | + | 0.387997i | \(0.126833\pi\) |
−0.517580 | + | 0.855635i | \(0.673167\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 7.74010 | 0.348597 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 4.53623 | + | 2.27656i | 0.203888 | + | 0.102324i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0.439311 | + | 0.319178i | 0.0197058 | + | 0.0143171i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 23.6824 | 1.06017 | 0.530086 | − | 0.847944i | \(-0.322160\pi\) | ||||
0.530086 | + | 0.847944i | \(0.322160\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 3.45128 | 0.154192 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −10.7940 | − | 7.84233i | −0.481282 | − | 0.349672i | 0.320540 | − | 0.947235i | \(-0.396136\pi\) |
−0.801822 | + | 0.597563i | \(0.796136\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −5.44668 | − | 2.73348i | −0.242374 | − | 0.121638i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 5.96810 | 0.265053 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −3.20479 | − | 9.86333i | −0.142050 | − | 0.437184i | 0.854570 | − | 0.519336i | \(-0.173821\pi\) |
−0.996620 | + | 0.0821518i | \(0.973821\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0.0861877 | − | 0.265258i | 0.00381272 | − | 0.0117343i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −0.544164 | − | 1.67476i | −0.0240254 | − | 0.0739427i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0.369802 | + | 0.714955i | 0.0162954 | + | 0.0315047i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −18.5670 | + | 13.4897i | −0.816575 | + | 0.593277i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −1.95343 | + | 1.41925i | −0.0857458 | + | 0.0622980i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −23.9450 | − | 17.3970i | −1.04905 | − | 0.762178i | −0.0770169 | − | 0.997030i | \(-0.524540\pi\) |
−0.972031 | + | 0.234852i | \(0.924540\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 0.661227 | − | 2.03505i | 0.0289134 | − | 0.0889864i | −0.935558 | − | 0.353172i | \(-0.885103\pi\) |
0.964472 | + | 0.264185i | \(0.0851031\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −0.00539096 | − | 0.441608i | −0.000235281 | − | 0.0192734i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −2.64985 | + | 8.15540i | −0.115429 | + | 0.355255i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 0.429950 | + | 0.312377i | 0.0186935 | + | 0.0135816i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 7.26336 | − | 5.27714i | 0.315203 | − | 0.229008i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 14.1364 | − | 10.2707i | 0.612315 | − | 0.444873i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0.0572639 | + | 0.0287385i | 0.00247574 | + | 0.00124248i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 1.25754 | + | 3.87031i | 0.0542668 | + | 0.167016i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −4.90439 | + | 15.0942i | −0.211247 | + | 0.650151i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −2.66128 | − | 8.19057i | −0.114417 | − | 0.352140i | 0.877408 | − | 0.479745i | \(-0.159271\pi\) |
−0.991825 | + | 0.127605i | \(0.959271\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 13.3363 | 0.572316 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 6.36361 | − | 41.8290i | 0.272587 | − | 1.79176i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −18.8570 | − | 13.7004i | −0.806267 | − | 0.585787i | 0.106479 | − | 0.994315i | \(-0.466042\pi\) |
−0.912746 | + | 0.408528i | \(0.866042\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 9.46618 | 0.404007 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 6.52673 | 0.278048 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0.954133 | + | 0.693218i | 0.0405739 | + | 0.0294786i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −11.1874 | + | 11.3248i | −0.474877 | + | 0.480709i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −37.2790 | −1.57956 | −0.789781 | − | 0.613389i | \(-0.789806\pi\) | ||||
−0.789781 | + | 0.613389i | \(0.789806\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 1.47065 | + | 4.52618i | 0.0622017 | + | 0.191437i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −1.46477 | + | 4.50810i | −0.0618427 | + | 0.190332i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −3.32150 | − | 10.2225i | −0.139985 | − | 0.430828i | 0.856347 | − | 0.516400i | \(-0.172728\pi\) |
−0.996332 | + | 0.0855718i | \(0.972728\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −1.64584 | + | 10.8184i | −0.0692411 | + | 0.455133i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0.0714590 | − | 0.0519180i | 0.00300100 | − | 0.00218035i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −6.10555 | + | 4.43594i | −0.255958 | + | 0.185964i | −0.708363 | − | 0.705848i | \(-0.750566\pi\) |
0.452405 | + | 0.891812i | \(0.350566\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −23.9648 | − | 17.4115i | −1.00290 | − | 0.728647i | −0.0401891 | − | 0.999192i | \(-0.512796\pi\) |
−0.962707 | + | 0.270545i | \(0.912796\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −7.80358 | + | 24.0169i | −0.325999 | + | 1.00332i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 22.4494 | − | 7.59846i | 0.936206 | − | 0.316878i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 4.81283 | − | 14.8124i | 0.200361 | − | 0.616647i | −0.799511 | − | 0.600651i | \(-0.794908\pi\) |
0.999872 | − | 0.0159961i | \(-0.00509192\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −19.9341 | − | 14.4829i | −0.828431 | − | 0.601891i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −1.13044 | + | 0.821316i | −0.0468987 | + | 0.0340739i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 1.76550 | − | 1.28271i | 0.0731197 | − | 0.0531246i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −5.85077 | + | 0.963313i | −0.241900 | + | 0.0398281i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 12.0799 | + | 37.1780i | 0.498590 | + | 1.53450i | 0.811287 | + | 0.584649i | \(0.198768\pi\) |
−0.312697 | + | 0.949853i | \(0.601232\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −2.23445 | + | 6.87692i | −0.0920688 | + | 0.283358i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −5.75394 | − | 17.7088i | −0.236685 | − | 0.728443i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −18.6722 | −0.766775 | −0.383387 | − | 0.923588i | \(-0.625243\pi\) | ||||
−0.383387 | + | 0.923588i | \(0.625243\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0.406982 | − | 0.0670084i | 0.0166846 | − | 0.00274708i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 7.97455 | + | 5.79385i | 0.326376 | + | 0.237126i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −14.0186 | −0.572783 | −0.286392 | − | 0.958113i | \(-0.592456\pi\) | ||||
−0.286392 | + | 0.958113i | \(0.592456\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −9.89791 | −0.403744 | −0.201872 | − | 0.979412i | \(-0.564703\pi\) | ||||
−0.201872 | + | 0.979412i | \(0.564703\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −11.2485 | − | 8.17249i | −0.458073 | − | 0.332810i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 6.00760 | + | 11.6148i | 0.244244 | + | 0.472208i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −22.2953 | −0.904939 | −0.452469 | − | 0.891780i | \(-0.649457\pi\) | ||||
−0.452469 | + | 0.891780i | \(0.649457\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0.101165 | + | 0.311353i | 0.00409940 | + | 0.0126167i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 8.28540 | − | 25.4998i | 0.335192 | − | 1.03161i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −5.07676 | − | 15.6247i | −0.205049 | − | 0.631075i | −0.999711 | − | 0.0240235i | \(-0.992352\pi\) |
0.794663 | − | 0.607051i | \(-0.207648\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 10.3549 | − | 10.4821i | 0.417552 | − | 0.422680i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 3.06226 | − | 2.22486i | 0.123282 | − | 0.0895696i | −0.524436 | − | 0.851450i | \(-0.675724\pi\) |
0.647718 | + | 0.761880i | \(0.275724\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 0.341478 | − | 0.248098i | 0.0137252 | − | 0.00997192i | −0.580902 | − | 0.813974i | \(-0.697300\pi\) |
0.594627 | + | 0.804002i | \(0.297300\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 3.83482 | + | 2.78616i | 0.153886 | + | 0.111805i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0.279795 | − | 0.861119i | 0.0112097 | − | 0.0345000i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −7.14271 | + | 23.9579i | −0.285708 | + | 0.958317i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −1.23515 | + | 3.80139i | −0.0493270 | + | 0.151813i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −12.0276 | − | 8.73860i | −0.479574 | − | 0.348431i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 28.2527 | − | 20.5268i | 1.12472 | − | 0.817159i | 0.139805 | − | 0.990179i | \(-0.455353\pi\) |
0.984918 | + | 0.173020i | \(0.0553525\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −6.39025 | + | 4.64279i | −0.253990 | + | 0.184534i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −5.13862 | + | 5.20174i | −0.203920 | + | 0.206425i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −5.72971 | − | 17.6342i | −0.227019 | − | 0.698693i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 1.89976 | − | 5.84685i | 0.0751532 | − | 0.231298i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 1.12876 | + | 3.47396i | 0.0445833 | + | 0.137213i | 0.970870 | − | 0.239605i | \(-0.0770180\pi\) |
−0.926287 | + | 0.376819i | \(0.877018\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 34.3967 | 1.35647 | 0.678236 | − | 0.734844i | \(-0.262745\pi\) | ||||
0.678236 | + | 0.734844i | \(0.262745\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 1.84368 | + | 3.56447i | 0.0725947 | + | 0.140351i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −25.4378 | − | 18.4817i | −1.00006 | − | 0.726589i | −0.0379623 | − | 0.999279i | \(-0.512087\pi\) |
−0.962102 | + | 0.272690i | \(0.912087\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −20.3783 | −0.799920 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −0.362693 | −0.0142151 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 28.2185 | + | 20.5020i | 1.10428 | + | 0.802304i | 0.981753 | − | 0.190161i | \(-0.0609011\pi\) |
0.122524 | + | 0.992466i | \(0.460901\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −7.93298 | + | 1.30614i | −0.309967 | + | 0.0510352i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −3.15765 | −0.123192 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −13.3549 | − | 41.1021i | −0.520232 | − | 1.60111i | −0.773555 | − | 0.633729i | \(-0.781523\pi\) |
0.253323 | − | 0.967382i | \(-0.418477\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −3.10111 | + | 9.54425i | −0.120619 | + | 0.371228i | −0.993078 | − | 0.117461i | \(-0.962525\pi\) |
0.872458 | + | 0.488689i | \(0.162525\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −1.71127 | − | 5.26673i | −0.0664600 | − | 0.204543i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0.343181 | − | 0.0565038i | 0.0133080 | − | 0.00219112i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −14.2132 | + | 10.3265i | −0.550339 | + | 0.399845i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −7.42818 | + | 5.39689i | −0.287190 | + | 0.208656i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −17.3829 | − | 12.6294i | −0.671058 | − | 0.487552i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 9.23541 | − | 28.4237i | 0.355999 | − | 1.09565i | −0.599429 | − | 0.800428i | \(-0.704606\pi\) |
0.955428 | − | 0.295224i | \(-0.0953944\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −4.73607 | + | 1.60302i | −0.182291 | + | 0.0617001i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −6.99242 | + | 21.5205i | −0.268740 | + | 0.827098i | 0.722068 | + | 0.691823i | \(0.243192\pi\) |
−0.990808 | + | 0.135276i | \(0.956808\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −0.915228 | − | 0.664952i | −0.0351232 | − | 0.0255185i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 9.35664 | − | 6.79800i | 0.358547 | − | 0.260500i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −20.7599 | + | 15.0830i | −0.794357 | + | 0.577134i | −0.909253 | − | 0.416243i | \(-0.863346\pi\) |
0.114896 | + | 0.993378i | \(0.463346\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −5.72393 | + | 37.6243i | −0.218700 | + | 1.43755i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −7.70882 | − | 23.7253i | −0.294110 | − | 0.905177i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −0.787845 | + | 2.42474i | −0.0300145 | + | 0.0923751i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −10.5879 | − | 32.5862i | −0.402782 | − | 1.23964i | −0.922733 | − | 0.385440i | \(-0.874050\pi\) |
0.519950 | − | 0.854196i | \(-0.325950\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −0.200488 | −0.00761590 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −29.8357 | + | 30.2021i | −1.13173 | + | 1.14563i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 11.1327 | + | 8.08839i | 0.421682 | + | 0.306370i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −13.0200 | −0.492461 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 42.0813 | 1.58939 | 0.794695 | − | 0.607009i | \(-0.207631\pi\) | ||||
0.794695 | + | 0.607009i | \(0.207631\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −10.1421 | − | 7.36869i | −0.382518 | − | 0.277916i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 3.40046 | − | 22.3517i | 0.128069 | − | 0.841816i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0.240727 | 0.00905347 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −6.41915 | − | 19.7561i | −0.241076 | − | 0.741956i | −0.996257 | − | 0.0864398i | \(-0.972451\pi\) |
0.755181 | − | 0.655516i | \(-0.227549\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 4.12605 | − | 12.6987i | 0.154739 | − | 0.476237i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −6.01464 | − | 18.5112i | −0.225250 | − | 0.693249i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 12.0291 | + | 6.03691i | 0.449861 | + | 0.225768i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −21.3650 | + | 15.5226i | −0.797891 | + | 0.579702i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −20.8627 | + | 15.1577i | −0.778049 | + | 0.565285i | −0.904393 | − | 0.426701i | \(-0.859676\pi\) |
0.126344 | + | 0.991986i | \(0.459676\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −0.0257235 | − | 0.0186892i | −0.000957995 | − | 0.000696024i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 1.92700 | − | 5.93070i | 0.0716659 | − | 0.220565i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −0.226211 | − | 18.5304i | −0.00840128 | − | 0.688203i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −2.86409 | + | 8.81476i | −0.106223 | + | 0.326921i | −0.990016 | − | 0.140958i | \(-0.954982\pi\) |
0.883792 | + | 0.467879i | \(0.154982\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −0.809017 | − | 0.587785i | −0.0299636 | − | 0.0217698i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −3.03212 | + | 2.20296i | −0.112147 | + | 0.0814795i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 17.0208 | − | 12.3663i | 0.628676 | − | 0.456760i | −0.227265 | − | 0.973833i | \(-0.572978\pi\) |
0.855941 | + | 0.517073i | \(0.172978\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −7.18305 | − | 13.8873i | −0.264951 | − | 0.512242i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 9.75230 | + | 30.0145i | 0.359230 | + | 1.10560i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −2.73729 | + | 8.42450i | −0.100693 | + | 0.309900i | −0.988695 | − | 0.149938i | \(-0.952093\pi\) |
0.888003 | + | 0.459838i | \(0.152093\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −1.44300 | − | 4.44110i | −0.0530099 | − | 0.163148i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 13.9773 | 0.512778 | 0.256389 | − | 0.966574i | \(-0.417467\pi\) | ||||
0.256389 | + | 0.966574i | \(0.417467\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 40.6579 | + | 20.4046i | 1.48959 | + | 0.747568i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 12.7982 | + | 9.29846i | 0.468263 | + | 0.340213i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −0.00253090 | −9.24769e−5 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −32.8762 | −1.19967 | −0.599834 | − | 0.800124i | \(-0.704767\pi\) | ||||
−0.599834 | + | 0.800124i | \(0.704767\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 6.04175 | + | 4.38959i | 0.220174 | + | 0.159966i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 26.5020 | + | 13.3003i | 0.964506 | + | 0.484048i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −31.4556 | −1.14327 | −0.571636 | − | 0.820507i | \(-0.693691\pi\) | ||||
−0.571636 | + | 0.820507i | \(0.693691\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −3.32475 | − | 10.2325i | −0.120681 | − | 0.371417i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 11.7053 | − | 36.0252i | 0.424317 | − | 1.30591i | −0.479330 | − | 0.877635i | \(-0.659120\pi\) |
0.903647 | − | 0.428279i | \(-0.140880\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0.516467 | + | 1.58952i | 0.0186974 | + | 0.0575446i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −2.14533 | − | 4.14767i | −0.0775645 | − | 0.149959i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 19.2608 | − | 13.9938i | 0.695467 | − | 0.505286i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −11.4835 | + | 8.34323i | −0.414105 | + | 0.300865i | −0.775261 | − | 0.631640i | \(-0.782382\pi\) |
0.361157 | + | 0.932505i | \(0.382382\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 6.79477 | + | 4.93669i | 0.244708 | + | 0.177791i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −11.2415 | + | 34.5978i | −0.404329 | + | 1.24440i | 0.517126 | + | 0.855910i | \(0.327002\pi\) |
−0.921454 | + | 0.388487i | \(0.872998\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 19.6021 | + | 6.10561i | 0.704129 | + | 0.219320i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0.194315 | − | 0.598039i | 0.00697100 | − | 0.0214545i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 9.38750 | + | 6.82041i | 0.336342 | + | 0.244367i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −11.2892 | + | 8.20206i | −0.403958 | + | 0.293493i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 2.99851 | − | 2.17855i | 0.107158 | − | 0.0778548i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 25.5941 | + | 12.8447i | 0.913493 | + | 0.458447i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −10.6448 | − | 32.7612i | −0.379445 | − | 1.16781i | −0.940431 | − | 0.339985i | \(-0.889578\pi\) |
0.560986 | − | 0.827825i | \(-0.310422\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 3.09783 | − | 9.53415i | 0.110286 | − | 0.339425i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −0.133576 | − | 0.411104i | −0.00474941 | − | 0.0146172i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 25.1021 | 0.891403 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −0.323344 | + | 2.12539i | −0.0114678 | + | 0.0753798i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −29.8541 | − | 21.6903i | −1.05749 | − | 0.768310i | −0.0838661 | − | 0.996477i | \(-0.526727\pi\) |
−0.973622 | + | 0.228167i | \(0.926727\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 21.1151 | 0.747000 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −10.2508 | −0.362194 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 5.79842 | + | 4.21280i | 0.204622 | + | 0.148667i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −0.657945 | + | 0.666026i | −0.0231895 | + | 0.0234743i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 17.6192 | 0.620224 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 11.1567 | + | 34.3367i | 0.392248 | + | 1.20721i | 0.931084 | + | 0.364804i | \(0.118864\pi\) |
−0.538837 | + | 0.842410i | \(0.681136\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 4.03780 | − | 12.4271i | 0.141786 | − | 0.436374i | −0.854797 | − | 0.518962i | \(-0.826319\pi\) |
0.996584 | + | 0.0825883i | \(0.0263186\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 1.50005 | + | 4.61668i | 0.0526091 | + | 0.161914i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −5.06642 | + | 33.3024i | −0.177469 | + | 1.16653i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −2.55679 | + | 1.85762i | −0.0894507 | + | 0.0649897i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0.189493 | − | 0.137675i | 0.00662142 | − | 0.00481074i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 20.9421 | + | 15.2153i | 0.730885 | + | 0.531019i | 0.889843 | − | 0.456266i | \(-0.150813\pi\) |
−0.158958 | + | 0.987285i | \(0.550813\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 12.1060 | − | 37.2583i | 0.421987 | − | 1.29874i | −0.483863 | − | 0.875144i | \(-0.660767\pi\) |
0.905850 | − | 0.423599i | \(-0.139233\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 10.8356 | + | 3.37503i | 0.377246 | + | 0.117503i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −14.0369 | + | 43.2012i | −0.488112 | + | 1.50225i | 0.339311 | + | 0.940674i | \(0.389806\pi\) |
−0.827423 | + | 0.561580i | \(0.810194\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −13.0692 | − | 9.49531i | −0.453911 | − | 0.329786i | 0.337227 | − | 0.941423i | \(-0.390511\pi\) |
−0.791138 | + | 0.611638i | \(0.790511\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 18.2935 | − | 13.2910i | 0.634593 | − | 0.461059i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 11.8133 | − | 8.58284i | 0.409306 | − | 0.297378i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 7.61478 | − | 1.25375i | 0.263520 | − | 0.0433879i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 1.26889 | + | 3.90523i | 0.0438591 | + | 0.134984i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 3.23891 | − | 9.96835i | 0.111820 | − | 0.344146i | −0.879451 | − | 0.475990i | \(-0.842090\pi\) |
0.991270 | + | 0.131844i | \(0.0420899\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −4.71649 | − | 14.5159i | −0.162638 | − | 0.500547i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −29.2542 | −1.00757 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 13.1678 | − | 2.16804i | 0.452986 | − | 0.0745829i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −0.417891 | − | 0.303615i | −0.0143589 | − | 0.0104323i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −29.2529 | −1.00396 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 33.7452 | 1.15677 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 30.9215 | + | 22.4658i | 1.05873 | + | 0.769214i | 0.973854 | − | 0.227177i | \(-0.0729495\pi\) |
0.0848793 | + | 0.996391i | \(0.472950\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −1.80902 | − | 3.49746i | −0.0618671 | − | 0.119611i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 25.3637 | 0.866408 | 0.433204 | − | 0.901296i | \(-0.357383\pi\) | ||||
0.433204 | + | 0.901296i | \(0.357383\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 11.0541 | + | 34.0209i | 0.377159 | + | 1.16078i | 0.942010 | + | 0.335584i | \(0.108934\pi\) |
−0.564851 | + | 0.825193i | \(0.691066\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −0.179857 | + | 0.553541i | −0.00612949 | + | 0.0188646i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 13.6865 | + | 42.1228i | 0.465894 | + | 1.43388i | 0.857854 | + | 0.513893i | \(0.171797\pi\) |
−0.391960 | + | 0.919982i | \(0.628203\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −3.79439 | + | 3.84099i | −0.129013 | + | 0.130598i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −10.2251 | + | 7.42895i | −0.347262 | + | 0.252300i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −24.5188 | + | 17.8139i | −0.831742 | + | 0.604296i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −29.8284 | − | 21.6716i | −1.01070 | − | 0.734314i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −3.95781 | + | 12.1809i | −0.133952 | + | 0.412260i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −0.172318 | − | 0.972389i | −0.00582541 | − | 0.0328727i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 3.03057 | − | 9.32715i | 0.102335 | − | 0.314955i | −0.886761 | − | 0.462229i | \(-0.847050\pi\) |
0.989096 | + | 0.147274i | \(0.0470498\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −10.8493 | − | 7.88246i | −0.365937 | − | 0.265869i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 0.794690 | − | 0.577376i | 0.0267738 | − | 0.0194523i | −0.574318 | − | 0.818632i | \(-0.694733\pi\) |
0.601092 | + | 0.799180i | \(0.294733\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 13.0512 | − | 9.48223i | 0.439207 | − | 0.319103i | −0.346113 | − | 0.938193i | \(-0.612499\pi\) |
0.785320 | + | 0.619090i | \(0.212499\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 14.1086 | − | 14.2819i | 0.474255 | − | 0.480079i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 15.5765 | + | 47.9395i | 0.523008 | + | 1.60965i | 0.768222 | + | 0.640183i | \(0.221141\pi\) |
−0.245215 | + | 0.969469i | \(0.578859\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0.0892535 | − | 0.274694i | 0.00299347 | − | 0.00921294i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0.701409 | + | 2.15871i | 0.0234981 | + | 0.0723196i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 17.8050 | 0.595822 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 4.18056 | + | 8.08247i | 0.139741 | + | 0.270167i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 10.1691 | + | 7.38827i | 0.339536 | + | 0.246687i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −15.2191 | −0.507584 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −2.00780 | −0.0668896 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −0.128247 | − | 0.0931767i | −0.00426779 | − | 0.00310073i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 29.4247 | − | 4.84470i | 0.978111 | − | 0.161043i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −26.1281 | −0.867570 | −0.433785 | − | 0.901016i | \(-0.642822\pi\) | ||||
−0.433785 | + | 0.901016i | \(0.642822\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −0.842186 | − | 2.59198i | −0.0279336 | − | 0.0859706i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −9.71659 | + | 29.9046i | −0.321925 | + | 0.990783i | 0.650885 | + | 0.759177i | \(0.274398\pi\) |
−0.972810 | + | 0.231607i | \(0.925602\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −11.0959 | − | 34.1498i | −0.367222 | − | 1.13019i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 20.8858 | − | 3.43879i | 0.690464 | − | 0.113683i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0.256931 | − | 0.186671i | 0.00848461 | − | 0.00616443i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 39.7376 | − | 28.8711i | 1.31082 | − | 0.952368i | 0.310824 | − | 0.950467i | \(-0.399395\pi\) |
0.999998 | − | 0.00190086i | \(-0.000605062\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 10.9577 | + | 7.96122i | 0.361068 | + | 0.262331i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 5.03772 | − | 15.5045i | 0.165819 | − | 0.510337i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −20.5694 | + | 29.0506i | −0.676317 | + | 0.955176i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −0.111239 | + | 0.342358i | −0.00365356 | + | 0.0112445i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −12.9520 | − | 9.41016i | −0.424941 | − | 0.308737i | 0.354682 | − | 0.934987i | \(-0.384589\pi\) |
−0.779623 | + | 0.626249i | \(0.784589\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 9.96137 | − | 7.23736i | 0.326471 | − | 0.237195i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −1.64944 | + | 1.19839i | −0.0540003 | + | 0.0392335i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −1.59415 | + | 10.4786i | −0.0521344 | + | 0.342687i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −9.35301 | − | 28.7856i | −0.305550 | − | 0.940385i | −0.979472 | − | 0.201583i | \(-0.935392\pi\) |
0.673922 | − | 0.738803i | \(-0.264608\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 5.64839 | − | 17.3840i | 0.184328 | − | 0.567304i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −3.80436 | − | 11.7086i | −0.124019 | − | 0.381690i | 0.869702 | − | 0.493577i | \(-0.164311\pi\) |
−0.993721 | + | 0.111886i | \(0.964311\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −31.2343 | −1.01713 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0.138804 | − | 0.140509i | 0.00451530 | − | 0.00457075i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 32.8335 | + | 23.8549i | 1.06695 | + | 0.775181i | 0.975361 | − | 0.220616i | \(-0.0708067\pi\) |
0.0915849 | + | 0.995797i | \(0.470807\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −8.37336 | −0.271811 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 18.7978 | 0.609562 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 6.49765 | + | 4.72082i | 0.210479 | + | 0.152922i | 0.688031 | − | 0.725682i | \(-0.258475\pi\) |
−0.477551 | + | 0.878604i | \(0.658475\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −8.49285 | + | 55.8249i | −0.274822 | + | 1.80645i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −8.41272 | −0.271945 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −0.464551 | − | 1.42974i | −0.0150011 | − | 0.0461688i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −4.36923 | + | 13.4471i | −0.140943 | + | 0.433778i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0.00885436 | + | 0.0272509i | 0.000285328 | + | 0.000878149i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −49.2430 | − | 24.7131i | −1.58519 | − | 0.795544i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −21.8198 | + | 15.8530i | −0.701677 | + | 0.509798i | −0.880478 | − | 0.474087i | \(-0.842778\pi\) |
0.178801 | + | 0.983885i | \(0.442778\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 2.97512 | − | 2.16155i | 0.0955745 | − | 0.0694389i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −24.0715 | − | 17.4889i | −0.772490 | − | 0.561247i | 0.130226 | − | 0.991484i | \(-0.458430\pi\) |
−0.902716 | + | 0.430238i | \(0.858430\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0.518220 | − | 1.59492i | 0.0166134 | − | 0.0511307i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −12.5590 | + | 4.25083i | −0.402209 | + | 0.136136i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −0.439419 | + | 1.35239i | −0.0140583 | + | 0.0432669i | −0.957840 | − | 0.287304i | \(-0.907241\pi\) |
0.943781 | + | 0.330570i | \(0.107241\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 18.8237 | + | 13.6762i | 0.601607 | + | 0.437093i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 15.3080 | − | 11.1219i | 0.488747 | − | 0.355096i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −1.64200 | + | 1.19298i | −0.0523716 | + | 0.0380502i | −0.613663 | − | 0.789568i | \(-0.710305\pi\) |
0.561291 | + | 0.827618i | \(0.310305\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −19.1284 | − | 36.9818i | −0.609481 | − | 1.17834i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0.275979 | + | 0.849377i | 0.00878452 | + | 0.0270360i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 2.62881 | − | 8.09065i | 0.0835913 | − | 0.257268i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 6.25185 | + | 19.2412i | 0.198597 | + | 0.611217i | 0.999916 | + | 0.0129803i | \(0.00413187\pi\) |
−0.801319 | + | 0.598237i | \(0.795868\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 8.32012 | 0.264031 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 19.6995 | + | 9.88640i | 0.624515 | + | 0.313420i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 14.8051 | + | 10.7566i | 0.468883 | + | 0.340663i | 0.797006 | − | 0.603972i | \(-0.206416\pi\) |
−0.328123 | + | 0.944635i | \(0.606416\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −7.11909 | −0.225238 |
(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 | 300.2.m.b.121.2 | ✓ | 8 | |
3.2 | odd | 2 | 900.2.n.b.721.1 | 8 | |||
5.2 | odd | 4 | 1500.2.o.b.649.3 | 16 | |||
5.3 | odd | 4 | 1500.2.o.b.649.2 | 16 | |||
5.4 | even | 2 | 1500.2.m.a.601.2 | 8 | |||
25.6 | even | 5 | inner | 300.2.m.b.181.2 | yes | 8 | |
25.8 | odd | 20 | 1500.2.o.b.349.4 | 16 | |||
25.9 | even | 10 | 7500.2.a.f.1.3 | 4 | |||
25.12 | odd | 20 | 7500.2.d.c.1249.6 | 8 | |||
25.13 | odd | 20 | 7500.2.d.c.1249.3 | 8 | |||
25.16 | even | 5 | 7500.2.a.e.1.2 | 4 | |||
25.17 | odd | 20 | 1500.2.o.b.349.1 | 16 | |||
25.19 | even | 10 | 1500.2.m.a.901.2 | 8 | |||
75.56 | odd | 10 | 900.2.n.b.181.1 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
300.2.m.b.121.2 | ✓ | 8 | 1.1 | even | 1 | trivial | |
300.2.m.b.181.2 | yes | 8 | 25.6 | even | 5 | inner | |
900.2.n.b.181.1 | 8 | 75.56 | odd | 10 | |||
900.2.n.b.721.1 | 8 | 3.2 | odd | 2 | |||
1500.2.m.a.601.2 | 8 | 5.4 | even | 2 | |||
1500.2.m.a.901.2 | 8 | 25.19 | even | 10 | |||
1500.2.o.b.349.1 | 16 | 25.17 | odd | 20 | |||
1500.2.o.b.349.4 | 16 | 25.8 | odd | 20 | |||
1500.2.o.b.649.2 | 16 | 5.3 | odd | 4 | |||
1500.2.o.b.649.3 | 16 | 5.2 | odd | 4 | |||
7500.2.a.e.1.2 | 4 | 25.16 | even | 5 | |||
7500.2.a.f.1.3 | 4 | 25.9 | even | 10 | |||
7500.2.d.c.1249.3 | 8 | 25.13 | odd | 20 | |||
7500.2.d.c.1249.6 | 8 | 25.12 | odd | 20 |