Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [336,4,Mod(193,336)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(336, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 0, 4]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("336.193");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 336 = 2^{4} \cdot 3 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 336.q (of order \(3\), degree \(2\), 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: | \(19.8246417619\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\Q(\sqrt{-3}, \sqrt{1345})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{3} + 337x^{2} + 336x + 112896 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{19}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 42) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 193.1 | ||
Root | \(9.41856 + 16.3134i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 336.193 |
Dual form | 336.4.q.j.289.1 |
$q$-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 \(\left(\mathbb{Z}/336\mathbb{Z}\right)^\times\).
\(n\) | \(85\) | \(113\) | \(127\) | \(241\) |
\(\chi(n)\) | \(1\) | \(1\) | \(1\) | \(e\left(\frac{2}{3}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 1.50000 | − | 2.59808i | 0.288675 | − | 0.500000i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −10.4186 | − | 18.0455i | −0.931864 | − | 1.61404i | −0.780132 | − | 0.625615i | \(-0.784848\pi\) |
−0.151732 | − | 0.988422i | \(-0.548485\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 18.3371 | + | 2.59808i | 0.990111 | + | 0.140283i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −4.50000 | − | 7.79423i | −0.166667 | − | 0.288675i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 7.58144 | − | 13.1314i | 0.207808 | − | 0.359934i | −0.743216 | − | 0.669052i | \(-0.766700\pi\) |
0.951024 | + | 0.309118i | \(0.100034\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.16288 | 0.0461442 | 0.0230721 | − | 0.999734i | \(-0.492655\pi\) | ||||
0.0230721 | + | 0.999734i | \(0.492655\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −62.5114 | −1.07602 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 59.6742 | − | 103.359i | 0.851361 | − | 1.47460i | −0.0286202 | − | 0.999590i | \(-0.509111\pi\) |
0.879981 | − | 0.475009i | \(-0.157555\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −16.7557 | − | 29.0217i | −0.202317 | − | 0.350423i | 0.746958 | − | 0.664871i | \(-0.231514\pi\) |
−0.949274 | + | 0.314449i | \(0.898180\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 34.2557 | − | 43.7441i | 0.355962 | − | 0.454560i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 0.325758 | + | 0.564230i | 0.00295327 | + | 0.00511522i | 0.867498 | − | 0.497440i | \(-0.165727\pi\) |
−0.864545 | + | 0.502555i | \(0.832393\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −154.593 | + | 267.763i | −1.23674 | + | 2.14210i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −27.0000 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −163.208 | −1.04507 | −0.522535 | − | 0.852618i | \(-0.675014\pi\) | ||||
−0.522535 | + | 0.852618i | \(0.675014\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −111.663 | + | 193.406i | −0.646943 | + | 1.12054i | 0.336906 | + | 0.941538i | \(0.390620\pi\) |
−0.983849 | + | 0.179000i | \(0.942714\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −22.7443 | − | 39.3943i | −0.119978 | − | 0.207808i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −144.163 | − | 357.970i | −0.696228 | − | 1.72880i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −84.2670 | − | 145.955i | −0.374417 | − | 0.648509i | 0.615823 | − | 0.787885i | \(-0.288824\pi\) |
−0.990240 | + | 0.139376i | \(0.955490\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 3.24432 | − | 5.61932i | 0.0133207 | − | 0.0230721i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −323.023 | −1.23043 | −0.615216 | − | 0.788359i | \(-0.710931\pi\) | ||||
−0.615216 | + | 0.788359i | \(0.710931\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −221.557 | −0.785746 | −0.392873 | − | 0.919593i | \(-0.628519\pi\) | ||||
−0.392873 | + | 0.919593i | \(0.628519\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −93.7670 | + | 162.409i | −0.310621 | + | 0.538012i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 254.023 | + | 439.980i | 0.788362 | + | 1.36548i | 0.926970 | + | 0.375136i | \(0.122404\pi\) |
−0.138608 | + | 0.990347i | \(0.544263\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 329.500 | + | 95.2825i | 0.960641 | + | 0.277791i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −179.023 | − | 310.076i | −0.491533 | − | 0.851361i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 88.2557 | − | 152.863i | 0.228733 | − | 0.396177i | −0.728700 | − | 0.684833i | \(-0.759875\pi\) |
0.957433 | + | 0.288656i | \(0.0932084\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −315.951 | −0.774596 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −100.534 | −0.233615 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 227.464 | − | 393.979i | 0.501920 | − | 0.869351i | −0.498077 | − | 0.867133i | \(-0.665960\pi\) |
0.999998 | − | 0.00221868i | \(-0.000706227\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −19.3258 | − | 33.4732i | −0.0405641 | − | 0.0702591i | 0.845031 | − | 0.534718i | \(-0.179582\pi\) |
−0.885595 | + | 0.464459i | \(0.846249\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −62.2670 | − | 154.615i | −0.124522 | − | 0.309201i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −22.5341 | − | 39.0302i | −0.0430001 | − | 0.0744784i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 70.8958 | − | 122.795i | 0.129273 | − | 0.223908i | −0.794122 | − | 0.607758i | \(-0.792069\pi\) |
0.923395 | + | 0.383851i | \(0.125402\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 1.95455 | 0.00341015 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −602.742 | −1.00750 | −0.503749 | − | 0.863850i | \(-0.668046\pi\) | ||||
−0.503749 | + | 0.863850i | \(0.668046\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 551.150 | − | 954.619i | 0.883660 | − | 1.53054i | 0.0364183 | − | 0.999337i | \(-0.488405\pi\) |
0.847242 | − | 0.531207i | \(-0.178262\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 463.778 | + | 803.288i | 0.714034 | + | 1.23674i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 173.138 | − | 221.096i | 0.256246 | − | 0.327223i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −58.1515 | − | 100.721i | −0.0828172 | − | 0.143444i | 0.821642 | − | 0.570004i | \(-0.193058\pi\) |
−0.904459 | + | 0.426561i | \(0.859725\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −40.5000 | + | 70.1481i | −0.0555556 | + | 0.0962250i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 568.928 | 0.752385 | 0.376193 | − | 0.926542i | \(-0.377233\pi\) | ||||
0.376193 | + | 0.926542i | \(0.377233\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −2486.88 | −3.17341 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −244.812 | + | 424.028i | −0.301686 | + | 0.522535i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 191.580 | + | 331.825i | 0.228173 | + | 0.395207i | 0.957267 | − | 0.289207i | \(-0.0933915\pi\) |
−0.729094 | + | 0.684414i | \(0.760058\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 39.6610 | + | 5.61932i | 0.0456879 | + | 0.00647325i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 334.989 | + | 580.217i | 0.373513 | + | 0.646943i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −349.140 | + | 604.728i | −0.377063 | + | 0.653093i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 334.701 | 0.350348 | 0.175174 | − | 0.984538i | \(-0.443951\pi\) | ||||
0.175174 | + | 0.984538i | \(0.443951\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −136.466 | −0.138539 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 7.37121 | − | 12.7673i | 0.00726201 | − | 0.0125782i | −0.862372 | − | 0.506276i | \(-0.831022\pi\) |
0.869634 | + | 0.493698i | \(0.164355\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −420.710 | − | 728.691i | −0.402464 | − | 0.697088i | 0.591559 | − | 0.806262i | \(-0.298513\pi\) |
−0.994023 | + | 0.109174i | \(0.965180\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −1146.28 | − | 162.409i | −1.06538 | − | 0.150948i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −357.835 | − | 619.789i | −0.323301 | − | 0.559974i | 0.657866 | − | 0.753135i | \(-0.271459\pi\) |
−0.981167 | + | 0.193161i | \(0.938126\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −300.009 | + | 519.632i | −0.263630 | + | 0.456621i | −0.967204 | − | 0.254001i | \(-0.918253\pi\) |
0.703574 | + | 0.710622i | \(0.251587\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −505.602 | −0.432339 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 622.644 | 0.518349 | 0.259174 | − | 0.965831i | \(-0.416550\pi\) | ||||
0.259174 | + | 0.965831i | \(0.416550\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 6.78787 | − | 11.7569i | 0.00550410 | − | 0.00953339i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −9.73296 | − | 16.8580i | −0.00769070 | − | 0.0133207i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 1362.79 | − | 1740.26i | 1.04980 | − | 1.34059i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 550.544 | + | 953.569i | 0.413632 | + | 0.716431i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −484.534 | + | 839.238i | −0.355195 | + | 0.615216i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 3837.90 | 2.74618 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 180.076 | 0.125820 | 0.0629100 | − | 0.998019i | \(-0.479962\pi\) | ||||
0.0629100 | + | 0.998019i | \(0.479962\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −332.335 | + | 575.621i | −0.226825 | + | 0.392873i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 108.930 | + | 188.672i | 0.0726508 | + | 0.125835i | 0.900062 | − | 0.435761i | \(-0.143521\pi\) |
−0.827411 | + | 0.561596i | \(0.810187\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −231.850 | − | 575.707i | −0.151158 | − | 0.375339i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 281.301 | + | 487.228i | 0.179337 | + | 0.310621i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 1300.93 | − | 2253.27i | 0.811283 | − | 1.40518i | −0.100683 | − | 0.994919i | \(-0.532103\pi\) |
0.911966 | − | 0.410265i | \(-0.134564\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 2651.55 | 1.61800 | 0.808998 | − | 0.587811i | \(-0.200010\pi\) | ||||
0.808998 | + | 0.587811i | \(0.200010\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 1524.14 | 0.910322 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 16.3977 | − | 28.4017i | 0.00958914 | − | 0.0166089i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 1700.40 | + | 2945.17i | 0.973863 | + | 1.68678i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 741.801 | − | 713.142i | 0.416209 | − | 0.400129i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −290.511 | − | 503.180i | −0.159729 | − | 0.276659i | 0.775042 | − | 0.631910i | \(-0.217729\pi\) |
−0.934771 | + | 0.355251i | \(0.884395\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −307.695 | + | 532.943i | −0.165827 | + | 0.287221i | −0.936949 | − | 0.349467i | \(-0.886363\pi\) |
0.771122 | + | 0.636688i | \(0.219696\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −1074.14 | −0.567574 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 4653.47 | 2.41145 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 153.466 | − | 265.811i | 0.0780122 | − | 0.135121i | −0.824380 | − | 0.566037i | \(-0.808476\pi\) |
0.902392 | + | 0.430916i | \(0.141809\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −264.767 | − | 458.590i | −0.132059 | − | 0.228733i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 4.50756 | + | 11.1927i | 0.00220649 | + | 0.00547893i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 1757.25 | + | 3043.65i | 0.844408 | + | 1.46256i | 0.886135 | + | 0.463428i | \(0.153381\pi\) |
−0.0417271 | + | 0.999129i | \(0.513286\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −473.926 | + | 820.864i | −0.223607 | + | 0.387298i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −1123.30 | −0.520502 | −0.260251 | − | 0.965541i | \(-0.583805\pi\) | ||||
−0.260251 | + | 0.965541i | \(0.583805\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −2192.32 | −0.997871 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −150.801 | + | 261.195i | −0.0674389 | + | 0.116808i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −765.299 | − | 1325.54i | −0.336327 | − | 0.582536i | 0.647412 | − | 0.762141i | \(-0.275852\pi\) |
−0.983739 | + | 0.179605i | \(0.942518\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −3530.45 | + | 4508.35i | −1.52501 | + | 1.94742i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −682.392 | − | 1181.94i | −0.289784 | − | 0.501920i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 1706.72 | − | 2956.12i | 0.712659 | − | 1.23436i | −0.251197 | − | 0.967936i | \(-0.580824\pi\) |
0.963856 | − | 0.266425i | \(-0.0858426\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 1286.71 | 0.528399 | 0.264200 | − | 0.964468i | \(-0.414892\pi\) | ||||
0.264200 | + | 0.964468i | \(0.414892\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −115.955 | −0.0468394 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −1755.88 | + | 3041.28i | −0.697811 | + | 1.20864i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −904.833 | − | 1567.22i | −0.353839 | − | 0.612868i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −495.102 | − | 70.1481i | −0.190547 | − | 0.0269975i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 527.648 | + | 913.913i | 0.199891 | + | 0.346222i | 0.948493 | − | 0.316798i | \(-0.102608\pi\) |
−0.748602 | + | 0.663020i | \(0.769274\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 2385.42 | − | 4131.67i | 0.889670 | − | 1.54095i | 0.0494044 | − | 0.998779i | \(-0.484268\pi\) |
0.840266 | − | 0.542175i | \(-0.182399\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −135.205 | −0.0496523 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 1622.31 | 0.586725 | 0.293363 | − | 0.956001i | \(-0.405226\pi\) | ||||
0.293363 | + | 0.956001i | \(0.405226\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −1775.07 | + | 3074.51i | −0.632318 | + | 1.09521i | 0.354759 | + | 0.934958i | \(0.384563\pi\) |
−0.987077 | + | 0.160249i | \(0.948770\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −212.688 | − | 368.386i | −0.0746359 | − | 0.129273i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −2992.77 | − | 424.028i | −1.03474 | − | 0.146605i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 3365.43 | + | 5829.10i | 1.14659 | + | 1.98596i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 2.93183 | − | 5.07807i | 0.000984425 | − | 0.00170507i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −508.129 | −0.168172 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −4653.39 | −1.51826 | −0.759129 | − | 0.650941i | \(-0.774375\pi\) | ||||
−0.759129 | + | 0.650941i | \(0.774375\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −904.114 | + | 1565.97i | −0.290840 | + | 0.503749i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 2308.30 | + | 3998.10i | 0.732209 | + | 1.26822i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −2550.06 | + | 3256.40i | −0.797739 | + | 1.01870i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −1653.45 | − | 2863.86i | −0.510181 | − | 0.883660i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 129.068 | − | 223.553i | 0.0392854 | − | 0.0680442i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 4649.53 | 1.39621 | 0.698107 | − | 0.715993i | \(-0.254026\pi\) | ||||
0.698107 | + | 0.715993i | \(0.254026\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 2782.67 | 0.824495 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 2075.86 | − | 3595.49i | 0.606958 | − | 1.05128i | −0.384780 | − | 0.923008i | \(-0.625723\pi\) |
0.991739 | − | 0.128274i | \(-0.0409438\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −2131.82 | − | 3692.41i | −0.615172 | − | 1.06551i | −0.990354 | − | 0.138558i | \(-0.955753\pi\) |
0.375182 | − | 0.926951i | \(-0.377580\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −314.716 | − | 781.470i | −0.0896398 | − | 0.222584i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −1524.95 | − | 2641.29i | −0.428768 | − | 0.742647i | 0.567996 | − | 0.823031i | \(-0.307719\pi\) |
−0.996764 | + | 0.0803838i | \(0.974385\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 5293.10 | − | 9167.92i | 1.46929 | − | 2.54489i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −348.909 | −0.0956290 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −3987.20 | −1.07912 | −0.539562 | − | 0.841946i | \(-0.681410\pi\) | ||||
−0.539562 | + | 0.841946i | \(0.681410\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 312.324 | − | 540.961i | 0.0834795 | − | 0.144591i | −0.821263 | − | 0.570550i | \(-0.806730\pi\) |
0.904742 | + | 0.425959i | \(0.140063\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 121.500 | + | 210.444i | 0.0320750 | + | 0.0555556i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −1713.50 | − | 6938.69i | −0.446822 | − | 1.80937i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −36.2405 | − | 62.7704i | −0.00933574 | − | 0.0161700i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 853.392 | − | 1478.12i | 0.217195 | − | 0.376193i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 1328.78 | 0.334152 | 0.167076 | − | 0.985944i | \(-0.446568\pi\) | ||||
0.167076 | + | 0.985944i | \(0.446568\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 9.87887 | 0.00245486 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −3730.32 | + | 6461.10i | −0.916085 | + | 1.58671i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 1613.09 | + | 2793.96i | 0.391525 | + | 0.678141i | 0.992651 | − | 0.121013i | \(-0.0386144\pi\) |
−0.601126 | + | 0.799154i | \(0.705281\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −1166.01 | − | 2895.32i | −0.279740 | − | 0.694620i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 734.437 | + | 1272.08i | 0.174178 | + | 0.301686i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 1625.31 | − | 2815.11i | 0.381067 | − | 0.660028i | −0.610148 | − | 0.792288i | \(-0.708890\pi\) |
0.991215 | + | 0.132260i | \(0.0422233\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −3677.99 | −0.852593 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 1149.48 | 0.263471 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −1413.02 | + | 2447.42i | −0.320273 | + | 0.554729i | −0.980544 | − | 0.196298i | \(-0.937108\pi\) |
0.660271 | + | 0.751027i | \(0.270441\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −1198.38 | − | 2075.66i | −0.268622 | − | 0.465268i | 0.699884 | − | 0.714257i | \(-0.253235\pi\) |
−0.968506 | + | 0.248989i | \(0.919902\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 74.0909 | − | 94.6133i | 0.0164256 | − | 0.0209753i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 2344.07 | + | 4060.05i | 0.514010 | + | 0.890292i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −910.233 | + | 1576.57i | −0.197439 | + | 0.341974i | −0.947697 | − | 0.319170i | \(-0.896596\pi\) |
0.750258 | + | 0.661145i | \(0.229929\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 2009.93 | 0.431296 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 3083.81 | 0.654679 | 0.327339 | − | 0.944907i | \(-0.393848\pi\) | ||||
0.327339 | + | 0.944907i | \(0.393848\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 1277.38 | − | 2212.49i | 0.268313 | − | 0.464732i | −0.700113 | − | 0.714032i | \(-0.746867\pi\) |
0.968426 | + | 0.249300i | \(0.0802005\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 1047.42 | + | 1814.19i | 0.217698 | + | 0.377063i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −5923.31 | − | 839.238i | −1.21826 | − | 0.172608i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −4665.53 | − | 8080.94i | −0.949630 | − | 1.64481i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 502.051 | − | 869.578i | 0.101137 | − | 0.175174i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −1846.47 | −0.368163 | −0.184081 | − | 0.982911i | \(-0.558931\pi\) | ||||
−0.184081 | + | 0.982911i | \(0.558931\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −9479.39 | −1.87089 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −204.699 | + | 354.549i | −0.0399927 | + | 0.0692694i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0.704576 | + | 1.22036i | 0.000136277 | + | 0.000236038i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −4062.71 | − | 575.621i | −0.777977 | − | 0.110227i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −22.1136 | − | 38.3019i | −0.00419272 | − | 0.00726201i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −402.693 | + | 697.485i | −0.0756005 | + | 0.130944i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −7041.50 | −1.30905 | −0.654527 | − | 0.756039i | \(-0.727132\pi\) | ||||
−0.654527 | + | 0.756039i | \(0.727132\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −2524.26 | −0.464726 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −1343.00 | + | 2326.14i | −0.244869 | + | 0.424126i | −0.962095 | − | 0.272715i | \(-0.912078\pi\) |
0.717226 | + | 0.696841i | \(0.245412\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −1109.59 | − | 1921.87i | −0.200377 | − | 0.347063i | 0.748273 | − | 0.663391i | \(-0.230883\pi\) |
−0.948650 | + | 0.316328i | \(0.897550\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −2141.37 | + | 2734.50i | −0.383024 | + | 0.489117i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −1110.63 | − | 1923.67i | −0.196780 | − | 0.340833i | 0.750703 | − | 0.660640i | \(-0.229715\pi\) |
−0.947483 | + | 0.319807i | \(0.896382\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −1237.35 | + | 2143.16i | −0.217174 | + | 0.376157i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −2147.01 | −0.373316 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −3999.53 | −0.688978 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −334.366 | + | 579.138i | −0.0570685 | + | 0.0988455i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 900.028 | + | 1558.89i | 0.152207 | + | 0.263630i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 3514.94 | + | 8727.94i | 0.589012 | + | 1.46257i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 2077.03 | + | 3597.52i | 0.344906 | + | 0.597394i | 0.985337 | − | 0.170622i | \(-0.0545775\pi\) |
−0.640431 | + | 0.768016i | \(0.721244\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −758.403 | + | 1313.59i | −0.124806 | + | 0.216170i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −2954.53 | −0.481860 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −254.167 | −0.0410841 | −0.0205420 | − | 0.999789i | \(-0.506539\pi\) | ||||
−0.0205420 | + | 0.999789i | \(0.506539\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 933.966 | − | 1617.68i | 0.149634 | − | 0.259174i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 1693.13 | + | 2932.59i | 0.268880 | + | 0.465714i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 5794.53 | + | 2603.27i | 0.912173 | + | 0.409806i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −20.3636 | − | 35.2708i | −0.00317780 | − | 0.00550410i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −3112.32 | + | 5390.69i | −0.481493 | + | 0.833970i | −0.999774 | − | 0.0212401i | \(-0.993239\pi\) |
0.518282 | + | 0.855210i | \(0.326572\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 9732.21 | 1.49270 | 0.746352 | − | 0.665552i | \(-0.231804\pi\) | ||||
0.746352 | + | 0.665552i | \(0.231804\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −58.3977 | −0.00888046 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −712.807 | + | 1234.62i | −0.107476 | + | 0.186153i | −0.914747 | − | 0.404027i | \(-0.867610\pi\) |
0.807271 | + | 0.590180i | \(0.200943\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 6279.71 | + | 10876.8i | 0.938852 | + | 1.62614i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −2477.16 | − | 6151.02i | −0.367241 | − | 0.911896i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −2883.25 | − | 4993.93i | −0.423877 | − | 0.734177i | 0.572438 | − | 0.819948i | \(-0.305998\pi\) |
−0.996315 | + | 0.0857714i | \(0.972665\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 2867.99 | − | 4967.51i | 0.418136 | − | 0.724233i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 3303.26 | 0.477621 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −22968.7 | −3.29381 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 5772.67 | − | 9998.56i | 0.821065 | − | 1.42213i | −0.0838244 | − | 0.996481i | \(-0.526713\pi\) |
0.904890 | − | 0.425646i | \(-0.139953\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 1453.60 | + | 2517.71i | 0.205072 | + | 0.355195i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 2015.51 | − | 2573.78i | 0.282048 | − | 0.360172i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 3239.79 | + | 5611.47i | 0.449731 | + | 0.778957i | 0.998368 | − | 0.0571033i | \(-0.0181864\pi\) |
−0.548637 | + | 0.836061i | \(0.684853\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 5756.85 | − | 9971.15i | 0.792753 | − | 1.37309i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −353.000 | −0.0482239 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −611.996 | −0.0829449 | −0.0414725 | − | 0.999140i | \(-0.513205\pi\) | ||||
−0.0414725 | + | 0.999140i | \(0.513205\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 270.114 | − | 467.851i | 0.0363211 | − | 0.0629100i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 2180.41 | + | 3776.57i | 0.290897 | + | 0.503848i | 0.974022 | − | 0.226453i | \(-0.0727130\pi\) |
−0.683125 | + | 0.730301i | \(0.739380\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −5793.63 | − | 820.864i | −0.766937 | − | 0.108663i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 997.006 | + | 1726.86i | 0.130958 | + | 0.226825i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 6573.46 | − | 11385.6i | 0.856781 | − | 1.48399i | −0.0182021 | − | 0.999834i | \(-0.505794\pi\) |
0.874983 | − | 0.484154i | \(-0.160872\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 77.7575 | 0.0100572 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 653.580 | 0.0838899 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −1211.71 | + | 2098.74i | −0.154349 | + | 0.267340i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 4239.02 | + | 7342.20i | 0.535895 | + | 0.928198i | 0.999119 | + | 0.0419565i | \(0.0133591\pi\) |
−0.463224 | + | 0.886241i | \(0.653308\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −1843.51 | − | 261.195i | −0.231305 | − | 0.0327722i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −1401.50 | − | 2427.47i | −0.174533 | − | 0.302299i | 0.765467 | − | 0.643475i | \(-0.222508\pi\) |
−0.939999 | + | 0.341176i | \(0.889175\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −241.513 | + | 418.313i | −0.0298527 | + | 0.0517064i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 1687.81 | 0.207081 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −2555.46 | −0.311227 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 3192.69 | − | 5529.91i | 0.385987 | − | 0.668548i | −0.605919 | − | 0.795526i | \(-0.707194\pi\) |
0.991906 | + | 0.126978i | \(0.0405278\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −3902.78 | − | 6759.82i | −0.468395 | − | 0.811283i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 5194.62 | − | 6633.48i | 0.618912 | − | 0.790344i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −5927.41 | − | 10266.6i | −0.701121 | − | 1.21438i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 3977.32 | − | 6888.93i | 0.467075 | − | 0.808998i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −4831.66 | −0.563346 | −0.281673 | − | 0.959510i | \(-0.590889\pi\) | ||||
−0.281673 | + | 0.959510i | \(0.590889\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 7475.37 | 0.865385 | 0.432693 | − | 0.901542i | \(-0.357564\pi\) | ||||
0.432693 | + | 0.901542i | \(0.357564\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 2286.20 | − | 3959.82i | 0.262787 | − | 0.455161i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 18450.4 | + | 31957.1i | 2.10583 | + | 3.64740i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −267.413 | − | 664.012i | −0.0303068 | − | 0.0752548i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −49.1932 | − | 85.2051i | −0.00553630 | − | 0.00958914i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 3495.97 | − | 6055.19i | 0.390707 | − | 0.676725i | −0.601836 | − | 0.798620i | \(-0.705564\pi\) |
0.992543 | + | 0.121895i | \(0.0388972\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −7699.26 | −0.854510 | −0.427255 | − | 0.904131i | \(-0.640519\pi\) | ||||
−0.427255 | + | 0.904131i | \(0.640519\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 10202.4 | 1.12452 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 10.9166 | − | 18.9081i | 0.00119499 | − | 0.00206979i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 4706.16 | + | 8151.31i | 0.511646 | + | 0.886198i | 0.999909 | + | 0.0135008i | \(0.00429758\pi\) |
−0.488262 | + | 0.872697i | \(0.662369\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −740.097 | − | 2996.97i | −0.0799154 | − | 0.323612i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −3129.09 | − | 5419.74i | −0.335593 | − | 0.581263i | 0.648006 | − | 0.761635i | \(-0.275603\pi\) |
−0.983598 | + | 0.180372i | \(0.942270\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 3991.97 | − | 6914.29i | 0.425252 | − | 0.736559i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −1743.07 | −0.184439 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −11633.8 | −1.22279 | −0.611396 | − | 0.791325i | \(-0.709392\pi\) | ||||
−0.611396 | + | 0.791325i | \(0.709392\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −2448.98 | + | 4241.75i | −0.255694 | + | 0.442874i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 923.085 | + | 1598.83i | 0.0957402 | + | 0.165827i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −311.807 | − | 774.246i | −0.0321269 | − | 0.0797741i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 6552.31 | + | 11348.9i | 0.670688 | + | 1.16167i | 0.977709 | + | 0.209963i | \(0.0673343\pi\) |
−0.307022 | + | 0.951703i | \(0.599332\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −1611.20 | + | 2790.69i | −0.163844 | + | 0.283787i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −2594.63 | −0.262134 | −0.131067 | − | 0.991373i | \(-0.541840\pi\) | ||||
−0.131067 | + | 0.991373i | \(0.541840\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 14136.2 | 1.41893 | 0.709465 | − | 0.704741i | \(-0.248937\pi\) | ||||
0.709465 | + | 0.704741i | \(0.248937\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 6980.20 | − | 12090.1i | 0.696127 | − | 1.20573i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 7795.12 | + | 13501.5i | 0.772409 | + | 1.33785i | 0.936239 | + | 0.351363i | \(0.114282\pi\) |
−0.163830 | + | 0.986489i | \(0.552385\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 1619.06 | − | 2067.52i | 0.159405 | − | 0.203559i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −460.398 | − | 797.432i | −0.0450404 | − | 0.0780122i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −1679.72 | + | 2909.36i | −0.163285 | + | 0.282817i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 10361.2 | 1.00085 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −1588.60 | −0.152489 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −4226.75 | + | 7320.95i | −0.403184 | + | 0.698336i | −0.994108 | − | 0.108391i | \(-0.965430\pi\) |
0.590924 | + | 0.806727i | \(0.298763\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −182.259 | − | 315.683i | −0.0172772 | − | 0.0299249i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 35.8408 | + | 5.07807i | 0.00337643 | + | 0.000478386i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −3487.10 | − | 6039.83i | −0.326476 | − | 0.565474i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −2005.53 | + | 3473.69i | −0.186611 | + | 0.323219i | −0.944118 | − | 0.329607i | \(-0.893084\pi\) |
0.757507 | + | 0.652827i | \(0.226417\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 10543.5 | 0.975038 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −13927.9 | −1.28016 | −0.640079 | − | 0.768309i | \(-0.721098\pi\) | ||||
−0.640079 | + | 0.768309i | \(0.721098\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −9739.33 | + | 16869.0i | −0.889731 | + | 1.54106i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 1421.78 | + | 2462.59i | 0.129099 | + | 0.223607i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −11052.6 | − | 1565.97i | −0.997535 | − | 0.141335i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −1973.77 | − | 3418.68i | −0.177071 | − | 0.306695i | 0.763805 | − | 0.645447i | \(-0.223329\pi\) |
−0.940876 | + | 0.338751i | \(0.889995\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −1684.95 | + | 2918.43i | −0.150256 | + | 0.260251i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 13725.3 | 1.21666 | 0.608331 | − | 0.793684i | \(-0.291839\pi\) | ||||
0.608331 | + | 0.793684i | \(0.291839\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −307.190 | −0.0270688 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −3288.48 | + | 5695.82i | −0.288060 | + | 0.498935i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −3915.05 | − | 6781.07i | −0.340926 | − | 0.590502i | 0.643679 | − | 0.765296i | \(-0.277407\pi\) |
−0.984605 | + | 0.174794i | \(0.944074\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 12586.7 | − | 16073.0i | 1.08963 | − | 1.39145i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 452.403 | + | 783.586i | 0.0389359 | + | 0.0674389i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −8766.39 | + | 15183.8i | −0.750084 | + | 1.29918i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 7703.43 | 0.655312 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −4591.80 | −0.388357 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 2953.69 | − | 5115.95i | 0.248376 | − | 0.430199i | −0.714700 | − | 0.699431i | \(-0.753437\pi\) |
0.963075 | + | 0.269232i | \(0.0867700\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 3954.03 | + | 6848.58i | 0.330588 | + | 0.572595i | 0.982627 | − | 0.185590i | \(-0.0594196\pi\) |
−0.652039 | + | 0.758185i | \(0.726086\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 6417.36 | + | 15934.9i | 0.533479 | + | 1.32468i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 13326.8 | + | 23082.7i | 1.10156 | + | 1.90797i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 6083.29 | − | 10536.6i | 0.499983 | − | 0.865995i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −4094.35 | −0.334613 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −698.659 | −0.0567773 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −7456.26 | + | 12914.6i | −0.602546 | + | 1.04364i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −5120.15 | − | 8868.36i | −0.411454 | − | 0.712659i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 3749.28 | − | 3604.43i | 0.299616 | − | 0.288040i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 1970.52 | + | 3413.04i | 0.156598 | + | 0.271235i | 0.933640 | − | 0.358214i | \(-0.116614\pi\) |
−0.777042 | + | 0.629449i | \(0.783281\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 1930.06 | − | 3342.97i | 0.152536 | − | 0.264200i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 12502.7 | 0.982670 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 1828.71 | 0.142943 | 0.0714717 | − | 0.997443i | \(-0.477230\pi\) | ||||
0.0714717 | + | 0.997443i | \(0.477230\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −173.932 | + | 301.259i | −0.0135214 | + | 0.0234197i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 2734.67 | + | 4736.58i | 0.211435 | + | 0.366216i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −804.650 | − | 1998.02i | −0.0618756 | − | 0.153643i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 5267.65 | + | 9123.83i | 0.402881 | + | 0.697811i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −11266.0 | + | 19513.3i | −0.857011 | + | 1.48439i | 0.0177556 | + | 0.999842i | \(0.494348\pi\) |
−0.874767 | + | 0.484544i | \(0.838985\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −479.201 | −0.0362577 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −5429.00 | −0.408579 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 11677.9 | − | 20226.6i | 0.874179 | − | 1.51412i | 0.0165446 | − | 0.999863i | \(-0.494733\pi\) |
0.857635 | − | 0.514260i | \(-0.171933\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −6487.05 | − | 11235.9i | −0.483031 | − | 0.836634i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −924.903 | + | 1181.09i | −0.0685049 | + | 0.0874800i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 10443.8 | + | 18089.2i | 0.769468 | + | 1.33276i | 0.937852 | + | 0.347036i | \(0.112812\pi\) |
−0.168384 | + | 0.985721i | \(0.553855\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 11872.6 | − | 20564.0i | 0.870147 | − | 1.50714i | 0.00830301 | − | 0.999966i | \(-0.497357\pi\) |
0.861844 | − | 0.507173i | \(-0.169310\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 3165.89 | 0.230815 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −201.440 | −0.0146098 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −1227.20 | + | 2125.57i | −0.0885422 | + | 0.153360i | −0.906895 | − | 0.421356i | \(-0.861554\pi\) |
0.818353 | + | 0.574716i | \(0.194887\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −7156.26 | − | 12395.0i | −0.513651 | − | 0.889670i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 10432.5 | + | 1478.12i | 0.744945 | + | 0.105547i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −1338.21 | − | 2317.85i | −0.0950652 | − | 0.164658i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −202.807 | + | 351.272i | −0.0143334 | + | 0.0248261i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −18567.5 | −1.30556 | −0.652780 | − | 0.757547i | \(-0.726397\pi\) | ||||
−0.652780 | + | 0.757547i | \(0.726397\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 7483.95 | 0.523550 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 2433.47 | − | 4214.89i | 0.169373 | − | 0.293363i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −8556.47 | − | 14820.2i | −0.592533 | − | 1.02630i | −0.993890 | − | 0.110375i | \(-0.964795\pi\) |
0.401357 | − | 0.915922i | \(-0.368539\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −45602.2 | − | 6461.10i | −3.14203 | − | 0.445175i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 5325.20 | + | 9223.52i | 0.365069 | + | 0.632318i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 11632.4 | − | 20147.9i | 0.793469 | − | 1.37433i | −0.130338 | − | 0.991470i | \(-0.541606\pi\) |
0.923807 | − | 0.382859i | \(-0.125060\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 25322.3 | 1.71867 | 0.859334 | − | 0.511416i | \(-0.170879\pi\) | ||||
0.859334 | + | 0.511416i | \(0.170879\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −1276.13 | −0.0861821 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 11471.7 | − | 19869.6i | 0.770897 | − | 1.33523i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −10867.2 | − | 18822.5i | −0.726665 | − | 1.25862i | −0.958285 | − | 0.285814i | \(-0.907736\pi\) |
0.231620 | − | 0.972806i | \(-0.425597\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −5590.81 | + | 7139.41i | −0.372005 | + | 0.475046i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 549.420 | + | 951.624i | 0.0363784 | + | 0.0630092i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 6786.19 | − | 11754.0i | 0.447131 | − | 0.774454i | −0.551067 | − | 0.834461i | \(-0.685779\pi\) |
0.998198 | + | 0.0600072i | \(0.0191124\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 20192.6 | 1.32397 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −8497.12 | −0.554427 | −0.277213 | − | 0.960808i | \(-0.589411\pi\) | ||||
−0.277213 | + | 0.960808i | \(0.589411\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −11491.5 | + | 19903.8i | −0.746173 | + | 1.29241i | 0.203472 | + | 0.979081i | \(0.434777\pi\) |
−0.949645 | + | 0.313329i | \(0.898556\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −8.79548 | − | 15.2342i | −0.000568358 | − | 0.000984425i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 2650.91 | + | 6582.46i | 0.170476 | + | 0.423308i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −20661.3 | − | 35786.4i | −1.32232 | − | 2.29033i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −762.193 | + | 1320.16i | −0.0485471 | + | 0.0840861i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −20114.3 | −1.27505 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 15717.9 | 0.991635 | 0.495817 | − | 0.868427i | \(-0.334869\pi\) | ||||
0.495817 | + | 0.868427i | \(0.334869\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −6980.08 | + | 12089.9i | −0.438283 | + | 0.759129i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −1876.13 | − | 3249.55i | −0.117247 | − | 0.203078i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 712.669 | + | 206.084i | 0.0443280 | + | 0.0128185i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 2712.34 | + | 4697.91i | 0.167916 | + | 0.290840i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −14553.7 | + | 25207.7i | −0.896780 | + | 1.55327i | −0.0651930 | + | 0.997873i | \(0.520766\pi\) |
−0.831587 | + | 0.555395i | \(0.812567\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 3112.26 | 0.190880 | 0.0954398 | − | 0.995435i | \(-0.469574\pi\) | ||||
0.0954398 | + | 0.995435i | \(0.469574\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 13849.8 | 0.845482 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −3928.80 | + | 6804.87i | −0.238728 | + | 0.413489i | −0.960349 | − | 0.278799i | \(-0.910064\pi\) |
0.721622 | + | 0.692288i | \(0.243397\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −3449.01 | − | 5973.86i | −0.208606 | − | 0.361317i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 4635.28 | + | 11509.8i | 0.279064 | + | 0.692944i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 9761.01 | + | 16906.6i | 0.584958 | + | 1.01318i | 0.994881 | + | 0.101057i | \(0.0322224\pi\) |
−0.409923 | + | 0.912120i | \(0.634444\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 2269.79 | − | 3931.38i | 0.135401 | − | 0.234522i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −9920.69 | −0.589107 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −664.061 | −0.0392536 | −0.0196268 | − | 0.999807i | \(-0.506248\pi\) | ||||
−0.0196268 | + | 0.999807i | \(0.506248\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −7960.82 | + | 13788.5i | −0.468442 | + | 0.811365i | −0.999349 | − | 0.0360650i | \(-0.988518\pi\) |
0.530908 | + | 0.847430i | \(0.321851\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −387.205 | − | 670.658i | −0.0226814 | − | 0.0392854i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −7973.36 | + | 10181.9i | −0.464953 | + | 0.593739i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −53.1665 | − | 92.0870i | −0.00308638 | − | 0.00534576i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 6974.30 | − | 12079.8i | 0.403052 | − | 0.698107i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −586.068 | −0.0337182 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 24631.0 | 1.41078 | 0.705391 | − | 0.708819i | \(-0.250771\pi\) | ||||
0.705391 | + | 0.708819i | \(0.250771\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 4174.01 | − | 7229.59i | 0.238011 | − | 0.412247i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −8546.39 | − | 14802.8i | −0.485177 | − | 0.840350i | 0.514678 | − | 0.857383i | \(-0.327911\pi\) |
−0.999855 | + | 0.0170329i | \(0.994578\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 6137.45 | + | 869.578i | 0.346883 | + | 0.0491478i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −6227.57 | − | 10786.5i | −0.350428 | − | 0.606958i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −9581.79 | + | 16596.1i | −0.536804 | + | 0.929771i | 0.462270 | + | 0.886739i | \(0.347035\pi\) |
−0.999074 | + | 0.0430322i | \(0.986298\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −54215.2 | −3.02402 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −12790.9 | −0.710339 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 190.886 | − | 330.625i | 0.0105547 | − | 0.0182813i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 4047.94 | + | 7011.23i | 0.222852 | + | 0.385991i | 0.955673 | − | 0.294431i | \(-0.0951300\pi\) |
−0.732821 | + | 0.680422i | \(0.761797\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −2502.39 | − | 354.549i | −0.137169 | − | 0.0194346i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −27625.3 | − | 47848.5i | −1.50775 | − | 2.61150i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −19276.1 | + | 33387.2i | −1.04754 | + | 1.81439i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −9149.70 | −0.495098 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 12354.7 | 0.665664 | 0.332832 | − | 0.942986i | \(-0.391996\pi\) | ||||
0.332832 | + | 0.942986i | \(0.391996\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −2823.90 | + | 4891.14i | −0.151501 | + | 0.262408i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −15879.3 | − | 27503.8i | −0.848297 | − | 1.46929i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 168.337 | − | 214.965i | 0.00895470 | − | 0.0114350i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −1914.41 | − | 3315.85i | −0.101406 | − | 0.175641i | 0.810858 | − | 0.585243i | \(-0.199001\pi\) |
−0.912264 | + | 0.409602i | \(0.865668\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −523.364 | + | 906.492i | −0.0276057 | + | 0.0478145i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −145.500 | −0.00764241 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −683.363 | −0.0357431 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −5980.81 | + | 10359.1i | −0.311516 | + | 0.539562i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 611.500 | + | 1059.15i | 0.0317178 | + | 0.0549368i | 0.881449 | − | 0.472280i | \(-0.156569\pi\) |
−0.849731 | + | 0.527217i | \(0.823236\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −5821.42 | − | 14455.1i | −0.300695 | − | 0.746654i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −936.972 | − | 1622.88i | −0.0481969 | − | 0.0834795i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 25230.8 | − | 43701.1i | 1.29248 | − | 2.23864i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −6368.21 | −0.324875 | −0.162437 | − | 0.986719i | \(-0.551936\pi\) | ||||
−0.162437 | + | 0.986719i | \(0.551936\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 729.000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −13221.2 | + | 22899.9i | −0.668954 | + | 1.15866i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 12577.0 | + | 21784.0i | 0.633753 | + | 1.09769i | 0.986778 | + | 0.162079i | \(0.0518199\pi\) |
−0.353024 | + | 0.935614i | \(0.614847\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −20597.5 | − | 5956.24i | −1.03367 | − | 0.298910i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −1074.98 | − | 1861.93i | −0.0537281 | − | 0.0930597i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −5369.55 | + | 9300.34i | −0.267283 | + | 0.462948i | −0.968159 | − | 0.250335i | \(-0.919459\pi\) |
0.700876 | + | 0.713283i | \(0.252793\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −217.443 | −0.0107800 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −28166.3 | −1.39074 | −0.695370 | − | 0.718652i | \(-0.744760\pi\) | ||||
−0.695370 | + | 0.718652i | \(0.744760\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −6053.42 | + | 10484.8i | −0.297691 | + | 0.515617i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −2560.18 | − | 4434.36i | −0.125398 | − | 0.217195i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −4951.41 | − | 12294.8i | −0.241549 | − | 0.599791i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 14328.5 | + | 24817.7i | 0.696211 | + | 1.20587i | 0.969771 | + | 0.244018i | \(0.0784657\pi\) |
−0.273559 | + | 0.961855i | \(0.588201\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 1993.18 | − | 3452.28i | 0.0964613 | − | 0.167076i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 12823.0 | 0.618113 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −23604.1 | −1.13330 | −0.566648 | − | 0.823960i | \(-0.691760\pi\) | ||||
−0.566648 | + | 0.823960i | \(0.691760\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 14.8183 | − | 25.6661i | 0.000708657 | − | 0.00122743i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −2315.48 | − | 4010.54i | −0.110297 | − | 0.191041i | 0.805593 | − | 0.592470i | \(-0.201847\pi\) |
−0.915890 | + | 0.401429i | \(0.868514\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −6851.35 | + | 8749.10i | −0.325079 | + | 0.415123i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 11191.0 | + | 19383.3i | 0.528902 | + | 0.916085i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 491.977 | − | 852.129i | 0.0231607 | − | 0.0401155i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 33276.8 | 1.56046 | 0.780228 | − | 0.625495i | \(-0.215103\pi\) | ||||
0.780228 | + | 0.625495i | \(0.215103\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 9678.55 | 0.452094 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 11469.4 | − | 19865.6i | 0.533668 | − | 0.924340i | −0.465558 | − | 0.885017i | \(-0.654147\pi\) |
0.999227 | − | 0.0393231i | \(-0.0125202\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −34524.6 | − | 59798.3i | −1.60020 | − | 2.77164i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −9271.29 | − | 1313.59i | −0.428064 | − | 0.0606498i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 5412.47 | + | 9374.67i | 0.248937 | + | 0.431171i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −4569.66 | + | 7914.88i | −0.209366 | + | 0.362633i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 4406.62 | 0.201124 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −6395.58 | −0.290787 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −6757.23 | + | 11703.9i | −0.306060 | + | 0.530112i | −0.977497 | − | 0.210950i | \(-0.932344\pi\) |
0.671437 | + | 0.741062i | \(0.265678\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −4875.92 | − | 8445.34i | −0.220009 | − | 0.381067i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 11417.5 | + | 1617.68i | 0.513223 | + | 0.0727155i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −41.7993 | − | 72.3985i | −0.00187180 | − | 0.00324205i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −5516.98 | + | 9555.69i | −0.246122 | + | 0.426296i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 10473.4 | 0.465480 | 0.232740 | − | 0.972539i | \(-0.425231\pi\) | ||||
0.232740 | + | 0.972539i | \(0.425231\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 60634.5 | 2.68472 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 1724.22 | − | 2986.43i | 0.0760576 | − | 0.131736i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −8357.02 | − | 14474.8i | −0.367264 | − | 0.636119i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 155.015 | − | 197.953i | 0.00678705 | − | 0.00866698i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 4239.06 | + | 7342.27i | 0.184910 | + | 0.320273i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −11784.0 | + | 20410.5i | −0.512117 | + | 0.887013i | 0.487784 | + | 0.872964i | \(0.337805\pi\) |
−0.999901 | + | 0.0140486i | \(0.995528\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 6704.22 | 0.290280 | 0.145140 | − | 0.989411i | \(-0.453637\pi\) | ||||
0.145140 | + | 0.989411i | \(0.453637\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −7190.31 | −0.310178 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 36616.0 | − | 63420.8i | 1.57375 | − | 2.72581i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 3712.34 | + | 6429.95i | 0.158970 | + | 0.275343i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −134.676 | − | 334.414i | −0.00574599 | − | 0.0142678i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −12269.7 | − | 21251.8i | −0.521579 | − | 0.903401i | −0.999685 | − | 0.0250988i | \(-0.992010\pi\) |
0.478106 | − | 0.878302i | \(-0.341323\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −15558.5 | + | 26948.1i | −0.658973 | + | 1.14137i | 0.321909 | + | 0.946771i | \(0.395675\pi\) |
−0.980882 | + | 0.194604i | \(0.937658\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 14064.4 | 0.593528 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −31244.9 | −1.31377 | −0.656887 | − | 0.753989i | \(-0.728127\pi\) | ||||
−0.656887 | + | 0.753989i | \(0.728127\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −2115.75 | + | 3664.58i | −0.0886405 | + | 0.153530i | −0.906937 | − | 0.421267i | \(-0.861586\pi\) |
0.818296 | + | 0.574797i | \(0.194919\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 2730.70 | + | 4729.71i | 0.113991 | + | 0.197439i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 29510.9 | − | 28370.8i | 1.22748 | − | 1.18006i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 11703.2 | + | 20270.5i | 0.485037 | + | 0.840109i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 3014.90 | − | 5221.96i | 0.124504 | − | 0.215648i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 38670.4 | 1.59124 | 0.795621 | − | 0.605795i | \(-0.207145\pi\) | ||||
0.795621 | + | 0.605795i | \(0.207145\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 2247.96 | 0.0921710 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 4625.72 | − | 8011.97i | 0.188989 | − | 0.327339i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 22840.8 | + | 39561.5i | 0.929880 | + | 1.61060i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 7617.94 | + | 18916.1i | 0.309038 | + | 0.767372i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −3832.15 | − | 6637.48i | −0.154911 | − | 0.268313i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 54.9014 | − | 95.0920i | 0.00221151 | − | 0.00383045i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −19944.4 | −0.800565 | −0.400282 | − | 0.916392i | \(-0.631088\pi\) | ||||
−0.400282 | + | 0.916392i | \(0.631088\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 6284.52 | 0.251376 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −6941.10 | + | 12022.3i | −0.276667 | + | 0.479201i | −0.970554 | − | 0.240882i | \(-0.922563\pi\) |
0.693887 | + | 0.720084i | \(0.255897\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −2078.58 | − | 3600.21i | −0.0825614 | − | 0.143000i | 0.821788 | − | 0.569793i | \(-0.192977\pi\) |
−0.904349 | + | 0.426793i | \(0.859643\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −11065.4 | + | 14130.3i | −0.437987 | + | 0.559304i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −8118.96 | − | 14062.5i | −0.320246 | − | 0.554683i | 0.660292 | − | 0.751009i | \(-0.270432\pi\) |
−0.980539 | + | 0.196326i | \(0.937099\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −15946.6 | + | 27620.4i | −0.626823 | + | 1.08569i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −27993.2 | −1.09654 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −1763.49 | −0.0688403 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 153.339 | − | 265.591i | 0.00596521 | − | 0.0103320i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −1506.15 | − | 2608.73i | −0.0583913 | − | 0.101137i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 70376.0 | + | 9971.15i | 2.71902 | + | 0.385242i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 8244.70 | + | 14280.2i | 0.317450 | + | 0.549840i | 0.979955 | − | 0.199218i | \(-0.0638401\pi\) |
−0.662505 | + | 0.749057i | \(0.730507\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −2769.70 | + | 4797.26i | −0.106279 | + | 0.184081i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 45411.7 | 1.73662 | 0.868309 | − | 0.496023i | \(-0.165207\pi\) | ||||
0.868309 | + | 0.496023i | \(0.165207\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 2206.85 | 0.0841070 | 0.0420535 | − | 0.999115i | \(-0.486610\pi\) | ||||
0.0420535 | + | 0.999115i | \(0.486610\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −14219.1 | + | 24628.2i | −0.540078 | + | 0.935443i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 14073.1 | + | 24375.3i | 0.532727 | + | 0.922710i | 0.999270 | + | 0.0382111i | \(0.0121659\pi\) |
−0.466543 | + | 0.884498i | \(0.654501\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 3302.07 | + | 467.851i | 0.124576 | + | 0.0176504i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 614.097 | + | 1063.65i | 0.0230898 | + | 0.0399927i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 8512.65 | − | 14744.3i | 0.318998 | − | 0.552520i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −71126.1 | −2.65641 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 4.22746 | 0.000157359 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 18224.3 | − | 31565.4i | 0.676101 | − | 1.17104i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −10533.2 | − | 18244.0i | −0.389469 | − | 0.674579i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −7589.58 | + | 9691.81i | −0.279696 | + | 0.357169i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −13405.6 | − | 23219.3i | −0.492396 | − | 0.852856i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −2521.12 | + | 4366.71i | −0.0922960 | + | 0.159861i | −0.908477 | − | 0.417935i | \(-0.862754\pi\) |
0.816181 | + | 0.577797i | \(0.196087\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −132.682 | −0.00484134 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −29647.3 | −1.07822 | −0.539110 | − | 0.842235i | \(-0.681239\pi\) | ||||
−0.539110 | + | 0.842235i | \(0.681239\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 4313.29 | − | 7470.84i | 0.156352 | − | 0.270809i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 1208.08 | + | 2092.46i | 0.0436480 | + | 0.0756005i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 1507.28 | + | 3742.71i | 0.0542799 | + | 0.134782i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −5945.64 | − | 10298.1i | −0.213415 | − | 0.369646i | 0.739366 | − | 0.673304i | \(-0.235125\pi\) |
−0.952781 | + | 0.303658i | \(0.901792\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −10562.2 | + | 18294.3i | −0.377891 | + | 0.654527i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −1303.66 | −0.0464902 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 52108.3 | 1.85223 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −3786.39 | + | 6558.22i | −0.134155 | + | 0.232363i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 19594.3 | + | 33938.3i | 0.691999 | + | 1.19858i | 0.971182 | + | 0.238340i | \(0.0766032\pi\) |
−0.279183 | + | 0.960238i | \(0.590063\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −2755.74 | − | 11159.2i | −0.0970093 | − | 0.392832i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 4028.99 | + | 6978.41i | 0.141375 | + | 0.244869i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −18854.1 | + | 32656.3i | −0.659461 | + | 1.14222i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 9716.23 | 0.338757 | 0.169379 | − | 0.985551i | \(-0.445824\pi\) | ||||
0.169379 | + | 0.985551i | \(0.445824\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −6657.57 | −0.231375 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 3497.93 | − | 6058.60i | 0.121179 | − | 0.209888i | −0.799054 | − | 0.601259i | \(-0.794666\pi\) |
0.920233 | + | 0.391371i | \(0.127999\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −105.227 | − | 182.259i | −0.00363380 | − | 0.00629393i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 3892.40 | + | 9665.20i | 0.133989 | + | 0.332708i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 7489.62 | + | 12972.4i | 0.257001 | + | 0.445139i | 0.965437 | − | 0.260636i | \(-0.0839323\pi\) |
−0.708436 | + | 0.705775i | \(0.750599\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 1192.07 | − | 2064.73i | 0.0407758 | − | 0.0706258i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −6663.78 | −0.227222 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 29393.3 | 0.999100 | 0.499550 | − | 0.866285i | \(-0.333499\pi\) | ||||
0.499550 | + | 0.866285i | \(0.333499\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 10994.7 | − | 19043.3i | 0.372543 | − | 0.645264i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 3712.06 | + | 6429.48i | 0.125386 | + | 0.217174i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 29709.5 | − | 37938.6i | 1.00038 | − | 1.27748i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −10041.7 | − | 17392.7i | −0.337072 | − | 0.583825i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −3220.52 | + | 5578.10i | −0.107767 | + | 0.186658i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −99410.6 | −3.31621 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 7133.95 | 0.237241 | 0.118621 | − | 0.992940i | \(-0.462153\pi\) | ||||
0.118621 | + | 0.992940i | \(0.462153\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −5999.30 | + | 10391.1i | −0.198891 | + | 0.344489i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −4844.06 | − | 8390.16i | −0.160096 | − | 0.277295i | 0.774807 | − | 0.632198i | \(-0.217847\pi\) |
−0.934903 | + | 0.354903i | \(0.884514\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 48621.8 | + | 6888.93i | 1.60200 | + | 0.226977i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 1003.10 | + | 1737.41i | 0.0329485 | + | 0.0570685i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −10652.8 | + | 18451.3i | −0.348838 | + | 0.604205i | −0.986043 | − | 0.166489i | \(-0.946757\pi\) |
0.637205 | + | 0.770694i | \(0.280090\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 5809.79 | 0.189665 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 5400.17 | 0.175753 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −18640.4 | + | 32286.1i | −0.604818 | + | 1.04758i | 0.387262 | + | 0.921970i | \(0.373421\pi\) |
−0.992080 | + | 0.125606i | \(0.959913\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −16902.1 | − | 29275.4i | −0.546748 | − | 0.946996i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 27948.3 | + | 3959.82i | 0.901320 | + | 0.127703i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −72.1740 | − | 125.009i | −0.00232052 | − | 0.00401927i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −25698.5 | + | 44511.2i | −0.823755 | + | 1.42678i | 0.0791128 | + | 0.996866i | \(0.474791\pi\) |
−0.902867 | + | 0.429919i | \(0.858542\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 12462.2 | 0.398263 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 73974.6 | 2.35694 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 17186.9 | − | 29768.6i | 0.545953 | − | 0.945618i | −0.452594 | − | 0.891717i | \(-0.649501\pi\) |
0.998546 | − | 0.0539007i | \(-0.0171655\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 2275.21 | + | 3940.78i | 0.0720565 | + | 0.124806i |
(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 | 336.4.q.j.193.1 | 4 | ||
4.3 | odd | 2 | 42.4.e.c.25.1 | ✓ | 4 | ||
7.2 | even | 3 | inner | 336.4.q.j.289.1 | 4 | ||
7.3 | odd | 6 | 2352.4.a.ca.1.1 | 2 | |||
7.4 | even | 3 | 2352.4.a.bq.1.2 | 2 | |||
12.11 | even | 2 | 126.4.g.g.109.2 | 4 | |||
28.3 | even | 6 | 294.4.a.m.1.1 | 2 | |||
28.11 | odd | 6 | 294.4.a.n.1.2 | 2 | |||
28.19 | even | 6 | 294.4.e.l.79.2 | 4 | |||
28.23 | odd | 6 | 42.4.e.c.37.1 | yes | 4 | ||
28.27 | even | 2 | 294.4.e.l.67.2 | 4 | |||
84.11 | even | 6 | 882.4.a.v.1.1 | 2 | |||
84.23 | even | 6 | 126.4.g.g.37.2 | 4 | |||
84.47 | odd | 6 | 882.4.g.bf.667.1 | 4 | |||
84.59 | odd | 6 | 882.4.a.z.1.2 | 2 | |||
84.83 | odd | 2 | 882.4.g.bf.361.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
42.4.e.c.25.1 | ✓ | 4 | 4.3 | odd | 2 | ||
42.4.e.c.37.1 | yes | 4 | 28.23 | odd | 6 | ||
126.4.g.g.37.2 | 4 | 84.23 | even | 6 | |||
126.4.g.g.109.2 | 4 | 12.11 | even | 2 | |||
294.4.a.m.1.1 | 2 | 28.3 | even | 6 | |||
294.4.a.n.1.2 | 2 | 28.11 | odd | 6 | |||
294.4.e.l.67.2 | 4 | 28.27 | even | 2 | |||
294.4.e.l.79.2 | 4 | 28.19 | even | 6 | |||
336.4.q.j.193.1 | 4 | 1.1 | even | 1 | trivial | ||
336.4.q.j.289.1 | 4 | 7.2 | even | 3 | inner | ||
882.4.a.v.1.1 | 2 | 84.11 | even | 6 | |||
882.4.a.z.1.2 | 2 | 84.59 | odd | 6 | |||
882.4.g.bf.361.1 | 4 | 84.83 | odd | 2 | |||
882.4.g.bf.667.1 | 4 | 84.47 | odd | 6 | |||
2352.4.a.bq.1.2 | 2 | 7.4 | even | 3 | |||
2352.4.a.ca.1.1 | 2 | 7.3 | odd | 6 |