Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [336,3,Mod(47,336)]
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([3, 0, 3, 5]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("336.47");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 336 = 2^{4} \cdot 3 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 336.z (of order \(6\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(9.15533688251\) |
Analytic rank: | \(0\) |
Dimension: | \(20\) |
Relative dimension: | \(10\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{20} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{20} + 83 x^{18} + 2702 x^{16} + 44346 x^{14} + 396449 x^{12} + 1961403 x^{10} + 5268164 x^{8} + \cdots + 2304 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{6}\cdot 3^{9} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 47.10 | ||
Root | \(0.0416279i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 336.47 |
Dual form | 336.3.z.f.143.10 |
$q$-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 \(\left(\mathbb{Z}/336\mathbb{Z}\right)^\times\).
\(n\) | \(85\) | \(113\) | \(127\) | \(241\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(-1\) | \(e\left(\frac{5}{6}\right)\) |
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 | ||||||||
\(3\) | 2.99894 | + | 0.0796850i | 0.999647 | + | 0.0265617i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 4.89508 | − | 8.47853i | 0.979017 | − | 1.69571i | 0.313030 | − | 0.949743i | \(-0.398656\pi\) |
0.665987 | − | 0.745964i | \(-0.268011\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.55722 | + | 6.82459i | 0.222460 | + | 0.974942i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 8.98730 | + | 0.477941i | 0.998589 | + | 0.0531046i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.66502 | + | 4.61595i | 0.242275 | + | 0.419632i | 0.961362 | − | 0.275288i | \(-0.0887731\pi\) |
−0.719087 | + | 0.694920i | \(0.755440\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 15.7574i | 1.21211i | 0.795422 | + | 0.606056i | \(0.207249\pi\) | ||||
−0.795422 | + | 0.606056i | \(0.792751\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 15.3557 | − | 25.0366i | 1.02371 | − | 1.66910i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −7.79558 | − | 13.5023i | −0.458563 | − | 0.794255i | 0.540322 | − | 0.841458i | \(-0.318302\pi\) |
−0.998885 | + | 0.0472034i | \(0.984969\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 10.9740 | − | 19.0076i | 0.577580 | − | 1.00040i | −0.418176 | − | 0.908366i | \(-0.637330\pi\) |
0.995756 | − | 0.0920323i | \(-0.0293363\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 4.12619 | + | 20.5906i | 0.196485 | + | 0.980507i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −11.4600 | + | 19.8494i | −0.498263 | + | 0.863017i | −0.999998 | − | 0.00200458i | \(-0.999362\pi\) |
0.501735 | + | 0.865021i | \(0.332695\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −35.4237 | − | 61.3556i | −1.41695 | − | 2.45423i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 26.9143 | + | 2.14947i | 0.996826 | + | 0.0796100i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − | 24.5758i | − | 0.847442i | −0.905793 | − | 0.423721i | \(-0.860724\pi\) | ||
0.905793 | − | 0.423721i | \(-0.139276\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −10.8812 | − | 18.8467i | −0.351005 | − | 0.607958i | 0.635421 | − | 0.772166i | \(-0.280827\pi\) |
−0.986426 | + | 0.164208i | \(0.947493\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 7.62442 | + | 14.0553i | 0.231043 | + | 0.425919i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 65.4853 | + | 20.2040i | 1.87101 | + | 0.577258i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −15.4747 | + | 26.8030i | −0.418235 | + | 0.724404i | −0.995762 | − | 0.0919674i | \(-0.970684\pi\) |
0.577527 | + | 0.816371i | \(0.304018\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −1.25563 | + | 47.2557i | −0.0321957 | + | 1.21168i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 14.7950 | 0.360854 | 0.180427 | − | 0.983588i | \(-0.442252\pi\) | ||||
0.180427 | + | 0.983588i | \(0.442252\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 51.1900i | 1.19047i | 0.803553 | + | 0.595233i | \(0.202940\pi\) | ||||
−0.803553 | + | 0.595233i | \(0.797060\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 48.0458 | − | 73.8596i | 1.06769 | − | 1.64132i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 10.3662 | + | 5.98495i | 0.220558 | + | 0.127339i | 0.606209 | − | 0.795306i | \(-0.292690\pi\) |
−0.385650 | + | 0.922645i | \(0.626023\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −44.1501 | + | 21.2548i | −0.901023 | + | 0.433771i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −22.3025 | − | 41.1139i | −0.437305 | − | 0.806155i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −47.4641 | + | 27.4034i | −0.895549 | + | 0.517045i | −0.875753 | − | 0.482759i | \(-0.839635\pi\) |
−0.0197954 | + | 0.999804i | \(0.506301\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 52.1820 | 0.948764 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 34.4251 | − | 56.1281i | 0.603949 | − | 0.984704i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 40.2875 | − | 23.2600i | 0.682840 | − | 0.394238i | −0.118084 | − | 0.993004i | \(-0.537675\pi\) |
0.800924 | + | 0.598766i | \(0.204342\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −27.2055 | − | 15.7071i | −0.445993 | − | 0.257494i | 0.260144 | − | 0.965570i | \(-0.416230\pi\) |
−0.706136 | + | 0.708076i | \(0.749563\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 10.7334 | + | 62.0789i | 0.170372 | + | 0.985380i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 133.600 | + | 77.1340i | 2.05539 | + | 1.18668i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −14.4100 | + | 8.31959i | −0.215074 | + | 0.124173i | −0.603667 | − | 0.797236i | \(-0.706294\pi\) |
0.388593 | + | 0.921409i | \(0.372961\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −35.9497 | + | 58.6140i | −0.521010 | + | 0.849478i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −73.0574 | −1.02898 | −0.514489 | − | 0.857497i | \(-0.672018\pi\) | ||||
−0.514489 | + | 0.857497i | \(0.672018\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 34.4201 | − | 19.8724i | 0.471508 | − | 0.272225i | −0.245363 | − | 0.969431i | \(-0.578907\pi\) |
0.716871 | + | 0.697206i | \(0.245574\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −101.344 | − | 186.825i | −1.35126 | − | 2.49100i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −27.3520 | + | 25.3757i | −0.355221 | + | 0.329555i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −4.29574 | − | 2.48015i | −0.0543765 | − | 0.0313943i | 0.472565 | − | 0.881296i | \(-0.343328\pi\) |
−0.526942 | + | 0.849901i | \(0.676661\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 80.5431 | + | 8.59080i | 0.994360 | + | 0.106059i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − | 56.0926i | − | 0.675815i | −0.941179 | − | 0.337907i | \(-0.890281\pi\) | ||
0.941179 | − | 0.337907i | \(-0.109719\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −152.640 | −1.79576 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 1.95832 | − | 73.7014i | 0.0225095 | − | 0.847143i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −4.12044 | + | 7.13681i | −0.0462971 | + | 0.0801889i | −0.888245 | − | 0.459369i | \(-0.848075\pi\) |
0.841948 | + | 0.539558i | \(0.181409\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −107.538 | + | 24.5378i | −1.18174 | + | 0.269646i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −31.1301 | − | 57.3872i | −0.334733 | − | 0.617067i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −107.438 | − | 186.087i | −1.13092 | − | 1.95881i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 63.5054i | 0.654695i | 0.944904 | + | 0.327347i | \(0.106155\pi\) | ||||
−0.944904 | + | 0.327347i | \(0.893845\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 21.7452 | + | 42.7587i | 0.219648 | + | 0.431906i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 16.0741 | + | 27.8412i | 0.159150 | + | 0.275656i | 0.934562 | − | 0.355799i | \(-0.115791\pi\) |
−0.775412 | + | 0.631455i | \(0.782458\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −85.1203 | + | 147.433i | −0.826411 | + | 1.43139i | 0.0744256 | + | 0.997227i | \(0.476288\pi\) |
−0.900836 | + | 0.434159i | \(0.857046\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 194.777 | + | 65.8089i | 1.85501 | + | 0.626751i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −101.021 | + | 174.974i | −0.944124 | + | 1.63527i | −0.186629 | + | 0.982431i | \(0.559756\pi\) |
−0.757495 | + | 0.652840i | \(0.773577\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 17.6522 | + | 30.5745i | 0.161947 | + | 0.280500i | 0.935567 | − | 0.353150i | \(-0.114889\pi\) |
−0.773620 | + | 0.633650i | \(0.781556\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −48.5435 | + | 79.1474i | −0.437329 | + | 0.713039i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 92.2111i | − | 0.816027i | −0.912976 | − | 0.408014i | \(-0.866222\pi\) | ||
0.912976 | − | 0.408014i | \(-0.133778\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 112.196 | + | 194.329i | 0.975616 | + | 1.68982i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −7.53113 | + | 141.617i | −0.0643686 | + | 1.21040i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 80.0085 | − | 74.2277i | 0.672340 | − | 0.623762i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 46.2953 | − | 80.1858i | 0.382606 | − | 0.662693i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 44.3694 | + | 1.17894i | 0.360727 | + | 0.00958489i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −448.854 | −3.59083 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 75.3464i | 0.593279i | 0.954990 | + | 0.296640i | \(0.0958660\pi\) | ||||
−0.954990 | + | 0.296640i | \(0.904134\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −4.07907 | + | 153.516i | −0.0316207 | + | 1.19005i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 36.9356 | + | 21.3248i | 0.281951 | + | 0.162785i | 0.634307 | − | 0.773082i | \(-0.281286\pi\) |
−0.352355 | + | 0.935866i | \(0.614619\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 146.808 | + | 45.2943i | 1.10382 | + | 0.340559i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 149.972 | − | 217.672i | 1.11090 | − | 1.61239i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 88.8407 | − | 51.2922i | 0.648472 | − | 0.374396i | −0.139398 | − | 0.990236i | \(-0.544517\pi\) |
0.787871 | + | 0.615841i | \(0.211184\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −90.8399 | −0.653524 | −0.326762 | − | 0.945107i | \(-0.605958\pi\) | ||||
−0.326762 | + | 0.945107i | \(0.605958\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 30.6108 | + | 18.7746i | 0.217098 | + | 0.133153i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −72.7356 | + | 41.9939i | −0.508641 | + | 0.293664i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −208.367 | − | 120.301i | −1.43701 | − | 0.829660i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −134.097 | + | 60.2237i | −0.912227 | + | 0.409685i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 147.329 | + | 85.0603i | 0.988784 | + | 0.570874i | 0.904910 | − | 0.425602i | \(-0.139938\pi\) |
0.0838731 | + | 0.996476i | \(0.473271\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 65.0630 | − | 37.5641i | 0.430881 | − | 0.248769i | −0.268841 | − | 0.963185i | \(-0.586641\pi\) |
0.699722 | + | 0.714415i | \(0.253307\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −63.6079 | − | 125.075i | −0.415738 | − | 0.817486i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −213.057 | −1.37456 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −180.575 | + | 104.255i | −1.15016 | + | 0.664045i | −0.948926 | − | 0.315498i | \(-0.897828\pi\) |
−0.201234 | + | 0.979543i | \(0.564495\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −144.526 | + | 78.3990i | −0.908966 | + | 0.493076i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −153.310 | − | 47.3003i | −0.952235 | − | 0.293791i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −256.887 | − | 148.314i | −1.57599 | − | 0.909900i | −0.995410 | − | 0.0956983i | \(-0.969492\pi\) |
−0.580582 | − | 0.814202i | \(-0.697175\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 156.491 | + | 4.15812i | 0.948429 | + | 0.0252007i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 184.743i | 1.10625i | 0.833100 | + | 0.553123i | \(0.186564\pi\) | ||||
−0.833100 | + | 0.553123i | \(0.813436\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −79.2971 | −0.469213 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 107.711 | − | 165.582i | 0.629891 | − | 0.968315i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 127.316 | − | 220.518i | 0.735931 | − | 1.27467i | −0.218383 | − | 0.975863i | \(-0.570078\pi\) |
0.954314 | − | 0.298807i | \(-0.0965885\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 363.565 | − | 337.296i | 2.07751 | − | 1.92741i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 122.673 | − | 66.5451i | 0.693070 | − | 0.375961i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −58.7396 | − | 101.740i | −0.328154 | − | 0.568380i | 0.653991 | − | 0.756502i | \(-0.273093\pi\) |
−0.982146 | + | 0.188122i | \(0.939760\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 20.4562i | 0.113017i | 0.998402 | + | 0.0565087i | \(0.0179969\pi\) | ||||
−0.998402 | + | 0.0565087i | \(0.982003\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −80.3362 | − | 49.2726i | −0.438996 | − | 0.269249i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 151.500 | + | 262.405i | 0.818918 | + | 1.41841i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 41.5508 | − | 71.9680i | 0.222197 | − | 0.384856i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 27.2422 | + | 187.026i | 0.144139 | + | 0.989558i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 92.0960 | − | 159.515i | 0.482178 | − | 0.835157i | −0.517613 | − | 0.855615i | \(-0.673179\pi\) |
0.999791 | + | 0.0204581i | \(0.00651248\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 2.02801 | + | 3.51262i | 0.0105078 | + | 0.0182001i | 0.871232 | − | 0.490872i | \(-0.163322\pi\) |
−0.860724 | + | 0.509072i | \(0.829989\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 394.512 | + | 241.966i | 2.02314 | + | 1.24085i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 176.763i | − | 0.897272i | −0.893714 | − | 0.448636i | \(-0.851910\pi\) | ||
0.893714 | − | 0.448636i | \(-0.148090\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 21.5178 | + | 37.2699i | 0.108130 | + | 0.187286i | 0.915013 | − | 0.403425i | \(-0.132181\pi\) |
−0.806883 | + | 0.590711i | \(0.798847\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −43.8776 | + | 23.8017i | −0.218296 | + | 0.118416i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 167.720 | − | 38.2699i | 0.826206 | − | 0.188522i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 72.4229 | − | 125.440i | 0.353283 | − | 0.611903i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −112.482 | + | 172.915i | −0.543390 | + | 0.835339i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 116.984 | 0.559732 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 151.863i | 0.719731i | 0.933004 | + | 0.359866i | \(0.117177\pi\) | ||||
−0.933004 | + | 0.359866i | \(0.882823\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −219.095 | − | 5.82158i | −1.02861 | − | 0.0273313i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 434.016 | + | 250.579i | 2.01868 | + | 1.16549i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 111.677 | − | 103.608i | 0.514639 | − | 0.477456i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 104.807 | − | 56.8535i | 0.478572 | − | 0.259605i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 212.762 | − | 122.838i | 0.962725 | − | 0.555830i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −159.992 | −0.717453 | −0.358726 | − | 0.933443i | \(-0.616789\pi\) | ||||
−0.358726 | + | 0.933443i | \(0.616789\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −289.039 | − | 568.352i | −1.28462 | − | 2.52601i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 179.764 | − | 103.787i | 0.791912 | − | 0.457210i | −0.0487235 | − | 0.998812i | \(-0.515515\pi\) |
0.840635 | + | 0.541602i | \(0.182182\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 318.721 | + | 184.014i | 1.39179 | + | 0.803552i | 0.993514 | − | 0.113711i | \(-0.0362739\pi\) |
0.398280 | + | 0.917264i | \(0.369607\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −84.0491 | + | 73.9208i | −0.363849 | + | 0.320004i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 13.9743 | + | 8.06808i | 0.0599757 | + | 0.0346270i | 0.529688 | − | 0.848193i | \(-0.322309\pi\) |
−0.469712 | + | 0.882820i | \(0.655642\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 101.487 | − | 58.5937i | 0.431861 | − | 0.249335i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −12.6850 | − | 7.78012i | −0.0535234 | − | 0.0328275i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 86.2929 | 0.361058 | 0.180529 | − | 0.983570i | \(-0.442219\pi\) | ||||
0.180529 | + | 0.983570i | \(0.442219\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 259.957 | − | 150.086i | 1.07866 | − | 0.622765i | 0.148126 | − | 0.988968i | \(-0.452676\pi\) |
0.930535 | + | 0.366203i | \(0.119342\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 240.860 | + | 32.1814i | 0.991192 | + | 0.132434i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −35.9094 | + | 478.372i | −0.146569 | + | 1.95254i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 299.511 | + | 172.923i | 1.21259 | + | 0.700092i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 4.46974 | − | 168.218i | 0.0179508 | − | 0.675576i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 298.636i | 1.18979i | 0.803805 | + | 0.594893i | \(0.202805\pi\) | ||||
−0.803805 | + | 0.594893i | \(0.797195\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −122.165 | −0.482866 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −457.758 | − | 12.1631i | −1.79513 | − | 0.0476985i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 72.5522 | − | 125.664i | 0.282304 | − | 0.488965i | −0.689648 | − | 0.724145i | \(-0.742235\pi\) |
0.971952 | + | 0.235180i | \(0.0755679\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −207.017 | − | 63.8704i | −0.799292 | − | 0.246604i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 11.7458 | − | 220.870i | 0.0450030 | − | 0.846246i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 111.748 | + | 193.553i | 0.424898 | + | 0.735945i | 0.996411 | − | 0.0846482i | \(-0.0269767\pi\) |
−0.571513 | + | 0.820593i | \(0.693643\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 536.568i | 2.02478i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −12.9257 | + | 21.0745i | −0.0484107 | + | 0.0789309i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −6.39468 | − | 11.0759i | −0.0237720 | − | 0.0411744i | 0.853895 | − | 0.520446i | \(-0.174234\pi\) |
−0.877667 | + | 0.479272i | \(0.840901\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 54.9222 | − | 95.1281i | 0.202665 | − | 0.351026i | −0.746721 | − | 0.665137i | \(-0.768373\pi\) |
0.949386 | + | 0.314111i | \(0.101706\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −324.456 | + | 65.0182i | −1.18848 | + | 0.238162i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 188.810 | − | 327.028i | 0.686581 | − | 1.18919i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −245.860 | − | 425.843i | −0.887583 | − | 1.53734i | −0.842725 | − | 0.538345i | \(-0.819050\pi\) |
−0.0448582 | − | 0.998993i | \(-0.514284\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −88.7846 | − | 174.582i | −0.318224 | − | 0.625740i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 80.2824i | − | 0.285703i | −0.989744 | − | 0.142851i | \(-0.954373\pi\) | ||
0.989744 | − | 0.142851i | \(-0.0456271\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −141.957 | − | 245.877i | −0.501615 | − | 0.868823i | −0.999998 | − | 0.00186632i | \(-0.999406\pi\) |
0.498383 | − | 0.866957i | \(-0.333927\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −307.371 | − | 566.626i | −1.07849 | − | 1.98816i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 23.0391 | + | 100.970i | 0.0802756 | + | 0.351812i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 22.9580 | − | 39.7644i | 0.0794394 | − | 0.137593i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −5.06042 | + | 190.449i | −0.0173898 | + | 0.654464i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −327.509 | −1.11778 | −0.558890 | − | 0.829242i | \(-0.688773\pi\) | ||||
−0.558890 | + | 0.829242i | \(0.688773\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − | 455.439i | − | 1.54386i | ||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 61.8054 | + | 129.964i | 0.208099 | + | 0.437588i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −312.776 | − | 180.581i | −1.04607 | − | 0.603950i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −349.351 | + | 79.7140i | −1.16063 | + | 0.264831i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 45.9869 | + | 84.7751i | 0.151772 | + | 0.279786i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −266.347 | + | 153.775i | −0.873268 | + | 0.504182i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 204.668 | 0.666671 | 0.333335 | − | 0.942808i | \(-0.391826\pi\) | ||||
0.333335 | + | 0.942808i | \(0.391826\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −267.019 | + | 435.359i | −0.864139 | + | 1.40893i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −391.185 | + | 225.851i | −1.25783 | + | 0.726209i | −0.972652 | − | 0.232266i | \(-0.925386\pi\) |
−0.285178 | + | 0.958475i | \(0.592053\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 278.509 | + | 160.797i | 0.889806 | + | 0.513730i | 0.873879 | − | 0.486143i | \(-0.161597\pi\) |
0.0159272 | + | 0.999873i | \(0.494930\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 578.879 | + | 212.878i | 1.83771 | + | 0.675802i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 203.355 | + | 117.407i | 0.641498 | + | 0.370369i | 0.785191 | − | 0.619253i | \(-0.212565\pi\) |
−0.143693 | + | 0.989622i | \(0.545898\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 113.441 | − | 65.4951i | 0.355614 | − | 0.205314i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −316.900 | + | 516.687i | −0.987227 | + | 1.60962i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −342.195 | −1.05943 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 966.808 | − | 558.187i | 2.97479 | − | 1.71750i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 50.5015 | + | 93.0977i | 0.154439 | + | 0.284702i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −24.7024 | + | 80.0652i | −0.0750831 | + | 0.243359i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −136.729 | − | 78.9403i | −0.413077 | − | 0.238490i | 0.279034 | − | 0.960281i | \(-0.409986\pi\) |
−0.692111 | + | 0.721791i | \(0.743319\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −151.886 | + | 233.490i | −0.456114 | + | 0.701172i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 162.900i | 0.486270i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 308.611 | 0.915759 | 0.457880 | − | 0.889014i | \(-0.348609\pi\) | ||||
0.457880 | + | 0.889014i | \(0.348609\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 7.34784 | − | 276.536i | 0.0216750 | − | 0.815739i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 57.9970 | − | 100.454i | 0.170079 | − | 0.294586i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −213.807 | − | 268.208i | −0.623343 | − | 0.781949i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 320.984 | + | 591.721i | 0.930387 | + | 1.71513i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 97.4526 | + | 168.793i | 0.280843 | + | 0.486435i | 0.971593 | − | 0.236659i | \(-0.0760526\pi\) |
−0.690749 | + | 0.723094i | \(0.742719\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 353.944i | 1.01417i | 0.861897 | + | 0.507084i | \(0.169276\pi\) | ||||
−0.861897 | + | 0.507084i | \(0.830724\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −33.8702 | + | 424.101i | −0.0964962 | + | 1.20826i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −322.725 | − | 558.976i | −0.914234 | − | 1.58350i | −0.808018 | − | 0.589157i | \(-0.799460\pi\) |
−0.106216 | − | 0.994343i | \(-0.533873\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −357.622 | + | 619.420i | −1.00739 | + | 1.74484i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 245.856 | − | 216.229i | 0.688671 | − | 0.605684i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 265.046 | − | 459.074i | 0.738291 | − | 1.27876i | −0.214973 | − | 0.976620i | \(-0.568966\pi\) |
0.953264 | − | 0.302138i | \(-0.0977002\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −60.3585 | − | 104.544i | −0.167198 | − | 0.289596i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 145.227 | − | 236.784i | 0.400073 | − | 0.652296i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | − | 389.109i | − | 1.06605i | ||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 83.5711 | + | 144.749i | 0.227714 | + | 0.394412i | 0.957130 | − | 0.289658i | \(-0.0935415\pi\) |
−0.729416 | + | 0.684070i | \(0.760208\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 132.967 | + | 7.07115i | 0.360345 | + | 0.0191630i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −260.929 | − | 281.250i | −0.703313 | − | 0.758086i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −56.0705 | + | 97.1169i | −0.150323 | + | 0.260367i | −0.931346 | − | 0.364135i | \(-0.881365\pi\) |
0.781023 | + | 0.624502i | \(0.214698\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −1346.09 | − | 35.7669i | −3.58956 | − | 0.0953783i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 387.252 | 1.02719 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 427.746i | 1.12862i | 0.825564 | + | 0.564309i | \(0.190857\pi\) | ||||
−0.825564 | + | 0.564309i | \(0.809143\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −6.00398 | + | 225.960i | −0.0157585 | + | 0.593070i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −537.538 | − | 310.348i | −1.40349 | − | 0.810308i | −0.408745 | − | 0.912649i | \(-0.634033\pi\) |
−0.994749 | + | 0.102341i | \(0.967367\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 81.2588 | + | 356.121i | 0.211062 | + | 0.924990i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −24.4658 | + | 460.060i | −0.0632191 | + | 1.18879i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 259.669 | − | 149.920i | 0.667530 | − | 0.385398i | −0.127610 | − | 0.991824i | \(-0.540731\pi\) |
0.795140 | + | 0.606426i | \(0.207397\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 357.351 | 0.913940 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 109.069 | + | 66.8951i | 0.277528 | + | 0.170216i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −42.0560 | + | 24.2811i | −0.106471 | + | 0.0614710i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 398.346 | + | 229.985i | 1.00339 | + | 0.579307i | 0.909249 | − | 0.416252i | \(-0.136657\pi\) |
0.0941399 | + | 0.995559i | \(0.469990\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 436.659 | + | 147.533i | 1.09438 | + | 0.369758i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −592.401 | − | 342.023i | −1.47731 | − | 0.852925i | −0.477637 | − | 0.878557i | \(-0.658507\pi\) |
−0.999671 | + | 0.0256326i | \(0.991840\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 296.976 | − | 171.459i | 0.736913 | − | 0.425457i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 467.103 | − | 640.835i | 1.15334 | − | 1.58231i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −164.962 | −0.405311 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −325.542 | + | 187.952i | −0.795945 | + | 0.459539i | −0.842051 | − | 0.539397i | \(-0.818652\pi\) |
0.0461061 | + | 0.998937i | \(0.485319\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 270.515 | − | 146.743i | 0.658188 | − | 0.357039i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 221.477 | + | 238.725i | 0.536263 | + | 0.578027i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −475.583 | − | 274.578i | −1.14598 | − | 0.661634i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −272.423 | − | 7.23857i | −0.653294 | − | 0.0173587i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − | 285.762i | − | 0.682010i | −0.940061 | − | 0.341005i | \(-0.889233\pi\) | ||
0.940061 | − | 0.341005i | \(-0.110767\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 350.727 | 0.833081 | 0.416540 | − | 0.909117i | \(-0.363242\pi\) | ||||
0.416540 | + | 0.909117i | \(0.363242\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 90.3041 | + | 58.7430i | 0.213485 | + | 0.138872i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −552.296 | + | 956.605i | −1.29952 | + | 2.25084i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 64.8298 | − | 210.126i | 0.151826 | − | 0.492099i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −221.476 | + | 120.141i | −0.516261 | + | 0.280050i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −233.727 | − | 404.826i | −0.542289 | − | 0.939272i | −0.998772 | − | 0.0495402i | \(-0.984224\pi\) |
0.456483 | − | 0.889732i | \(-0.349109\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 217.745i | − | 0.502874i | −0.967874 | − | 0.251437i | \(-0.919097\pi\) | ||
0.967874 | − | 0.251437i | \(-0.0809032\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −615.294 | − | 377.378i | −1.41447 | − | 0.867536i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 251.526 | + | 435.655i | 0.575574 | + | 0.996923i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 230.686 | − | 399.560i | 0.525481 | − | 0.910160i | −0.474078 | − | 0.880483i | \(-0.657219\pi\) |
0.999560 | − | 0.0296775i | \(-0.00944802\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −406.949 | + | 169.922i | −0.922787 | + | 0.385310i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −78.2121 | + | 135.467i | −0.176551 | + | 0.305795i | −0.940697 | − | 0.339248i | \(-0.889827\pi\) |
0.764146 | + | 0.645043i | \(0.223161\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 40.3398 | + | 69.8706i | 0.0906513 | + | 0.157013i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 435.052 | + | 266.831i | 0.973271 | + | 0.596937i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 49.2939i | 0.109786i | 0.998492 | + | 0.0548930i | \(0.0174818\pi\) | ||||
−0.998492 | + | 0.0548930i | \(0.982518\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 39.4291 | + | 68.2932i | 0.0874259 | + | 0.151426i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 198.113 | − | 107.468i | 0.437336 | − | 0.237236i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −318.364 | + | 1031.88i | −0.699701 | + | 2.26787i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 130.664 | − | 226.317i | 0.285917 | − | 0.495222i | −0.686914 | − | 0.726738i | \(-0.741035\pi\) |
0.972831 | + | 0.231516i | \(0.0743686\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −180.790 | − | 380.162i | −0.393877 | − | 0.828240i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −261.457 | −0.567151 | −0.283576 | − | 0.958950i | \(-0.591521\pi\) | ||||
−0.283576 | + | 0.958950i | \(0.591521\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 410.629i | 0.886887i | 0.896302 | + | 0.443444i | \(0.146243\pi\) | ||||
−0.896302 | + | 0.443444i | \(0.853757\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −638.944 | − | 16.9774i | −1.37407 | − | 0.0365105i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −377.906 | − | 218.184i | −0.809220 | − | 0.467203i | 0.0374651 | − | 0.999298i | \(-0.488072\pi\) |
−0.846685 | + | 0.532095i | \(0.821405\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −79.2173 | − | 85.3866i | −0.168907 | − | 0.182061i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −549.842 | + | 298.266i | −1.16739 | + | 0.633261i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −236.291 | + | 136.422i | −0.499557 | + | 0.288420i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −1554.96 | −3.27360 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −439.671 | + | 223.598i | −0.921743 | + | 0.468758i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 712.054 | − | 411.104i | 1.48654 | − | 0.858256i | 0.486660 | − | 0.873592i | \(-0.338215\pi\) |
0.999882 | + | 0.0153361i | \(0.00488182\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −422.346 | − | 243.842i | −0.878058 | − | 0.506947i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −455.998 | − | 154.067i | −0.944095 | − | 0.318980i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 538.432 | + | 310.864i | 1.11017 | + | 0.640957i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 617.211 | − | 356.347i | 1.26737 | − | 0.731719i | 0.292884 | − | 0.956148i | \(-0.405385\pi\) |
0.974490 | + | 0.224429i | \(0.0720518\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −758.570 | − | 465.254i | −1.55127 | − | 0.951440i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 806.962 | 1.64351 | 0.821754 | − | 0.569842i | \(-0.192996\pi\) | ||||
0.821754 | + | 0.569842i | \(0.192996\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −331.831 | + | 191.583i | −0.673085 | + | 0.388606i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 468.976 | + | 24.9399i | 0.947425 | + | 0.0503837i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −113.766 | − | 498.587i | −0.228906 | − | 1.00319i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 45.1352 | + | 26.0588i | 0.0904513 | + | 0.0522221i | 0.544543 | − | 0.838733i | \(-0.316703\pi\) |
−0.454092 | + | 0.890955i | \(0.650036\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −14.7212 | + | 554.033i | −0.0293837 | + | 1.10586i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − | 716.425i | − | 1.42430i | −0.702025 | − | 0.712152i | \(-0.747721\pi\) | ||
0.702025 | − | 0.712152i | \(-0.252279\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 314.737 | 0.623242 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −237.807 | − | 6.31878i | −0.469048 | − | 0.0124631i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −122.636 | + | 212.412i | −0.240935 | + | 0.417312i | −0.960981 | − | 0.276615i | \(-0.910787\pi\) |
0.720046 | + | 0.693926i | \(0.244121\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 189.221 | + | 203.957i | 0.370295 | + | 0.399134i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 336.214 | − | 487.987i | 0.655389 | − | 0.951242i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 833.342 | + | 1443.39i | 1.61814 | + | 2.80270i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 63.8001i | 0.123404i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 399.385 | − | 651.175i | 0.769529 | − | 1.25467i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 278.097 | + | 481.679i | 0.533776 | + | 0.924527i | 0.999222 | + | 0.0394506i | \(0.0125608\pi\) |
−0.465446 | + | 0.885077i | \(0.654106\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −196.110 | + | 339.673i | −0.374972 | + | 0.649470i | −0.990323 | − | 0.138783i | \(-0.955681\pi\) |
0.615351 | + | 0.788253i | \(0.289014\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 1117.19 | − | 982.562i | 2.12798 | − | 1.87155i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −169.650 | + | 293.842i | −0.321916 | + | 0.557575i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1.83458 | + | 3.17759i | 0.00346802 | + | 0.00600678i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 373.193 | − | 189.790i | 0.702812 | − | 0.357419i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 233.132i | 0.437396i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 989.015 | + | 1713.02i | 1.84863 | + | 3.20192i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −168.050 | − | 309.793i | −0.312941 | − | 0.576896i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −215.772 | − | 147.151i | −0.400319 | − | 0.273007i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 166.601 | − | 288.561i | 0.307950 | − | 0.533384i | −0.669964 | − | 0.742394i | \(-0.733691\pi\) |
0.977914 | + | 0.209009i | \(0.0670239\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −1.63005 | + | 61.3468i | −0.00300193 | + | 0.112978i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 345.636 | 0.634194 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 173.083i | − | 0.316422i | −0.987405 | − | 0.158211i | \(-0.949427\pi\) | ||
0.987405 | − | 0.158211i | \(-0.0505726\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −236.997 | − | 154.167i | −0.431689 | − | 0.280815i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −467.126 | − | 269.696i | −0.847779 | − | 0.489466i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 10.2366 | − | 33.1788i | 0.0185110 | − | 0.0599979i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 433.429 | + | 799.011i | 0.780954 | + | 1.43966i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 918.753 | − | 530.442i | 1.64947 | − | 0.952320i | 0.672182 | − | 0.740386i | \(-0.265357\pi\) |
0.977284 | − | 0.211934i | \(-0.0679763\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −806.624 | −1.44298 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 130.343 | − | 212.517i | 0.232341 | − | 0.378818i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 550.654 | − | 317.920i | 0.978071 | − | 0.564689i | 0.0763835 | − | 0.997079i | \(-0.475663\pi\) |
0.901687 | + | 0.432389i | \(0.142329\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −781.815 | − | 451.381i | −1.38374 | − | 0.798904i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 66.7946 | + | 563.052i | 0.117803 | + | 0.993037i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −704.449 | − | 406.714i | −1.23805 | − | 0.714787i | −0.269352 | − | 0.963042i | \(-0.586810\pi\) |
−0.968695 | + | 0.248255i | \(0.920143\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 637.778 | − | 368.221i | 1.11695 | − | 0.644871i | 0.176329 | − | 0.984331i | \(-0.443578\pi\) |
0.940620 | + | 0.339461i | \(0.110245\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 288.902 | − | 471.037i | 0.504191 | − | 0.822055i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 1623.83 | 2.82405 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 106.581 | − | 61.5346i | 0.184716 | − | 0.106646i | −0.404791 | − | 0.914409i | \(-0.632656\pi\) |
0.589507 | + | 0.807764i | \(0.299322\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 5.80198 | + | 10.6957i | 0.0100207 | + | 0.0184728i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 382.809 | − | 87.3485i | 0.658880 | − | 0.150342i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −252.986 | − | 146.061i | −0.433938 | − | 0.250534i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 1163.84 | + | 757.079i | 1.98947 | + | 1.29415i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 939.308i | 1.60018i | 0.599878 | + | 0.800092i | \(0.295216\pi\) | ||||
−0.599878 | + | 0.800092i | \(0.704784\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −477.640 | −0.810934 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 14.0853 | − | 530.101i | 0.0238330 | − | 0.896956i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 64.5058 | − | 111.727i | 0.108779 | − | 0.188410i | −0.806497 | − | 0.591238i | \(-0.798639\pi\) |
0.915276 | + | 0.402828i | \(0.131973\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −237.694 | − | 1041.71i | −0.399485 | − | 1.75077i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 61.5607 | + | 113.485i | 0.103117 | + | 0.190092i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −444.320 | − | 769.585i | −0.741770 | − | 1.28478i | −0.951689 | − | 0.307064i | \(-0.900653\pi\) |
0.209919 | − | 0.977719i | \(-0.432680\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 634.763i | − | 1.05618i | −0.849189 | − | 0.528089i | \(-0.822909\pi\) | ||
0.849189 | − | 0.528089i | \(-0.177091\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −133.483 | + | 67.8836i | −0.221365 | + | 0.112576i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −453.239 | − | 785.033i | −0.749155 | − | 1.29757i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 472.304 | − | 818.054i | 0.778095 | − | 1.34770i | −0.154943 | − | 0.987923i | \(-0.549520\pi\) |
0.933038 | − | 0.359777i | \(-0.117147\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 506.032 | − | 101.404i | 0.830922 | − | 0.166510i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −94.3075 | + | 163.345i | −0.154349 | + | 0.267341i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 50.2939 | + | 87.1115i | 0.0820455 | + | 0.142107i | 0.904128 | − | 0.427261i | \(-0.140521\pi\) |
−0.822083 | + | 0.569368i | \(0.807188\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 227.188 | − | 370.417i | 0.369411 | − | 0.602304i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 544.570i | 0.882610i | 0.897357 | + | 0.441305i | \(0.145484\pi\) | ||||
−0.897357 | + | 0.441305i | \(0.854516\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 33.3779 | + | 57.8123i | 0.0539224 | + | 0.0933963i | 0.891727 | − | 0.452574i | \(-0.149494\pi\) |
−0.837804 | + | 0.545971i | \(0.816161\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −351.105 | + | 509.599i | −0.565386 | + | 0.820611i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −55.1223 | − | 17.0068i | −0.0884788 | − | 0.0272982i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −1311.58 | + | 2271.73i | −2.09853 | + | 3.63477i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 350.828 | + | 9.32187i | 0.559535 | + | 0.0148674i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 482.537 | 0.767149 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 738.431i | − | 1.17026i | −0.810941 | − | 0.585128i | \(-0.801044\pi\) | ||
0.810941 | − | 0.585128i | \(-0.198956\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −12.1012 | + | 455.429i | −0.0191173 | + | 0.719477i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 638.827 | + | 368.827i | 1.00603 | + | 0.580830i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −334.921 | − | 695.693i | −0.525778 | − | 1.09214i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −656.589 | − | 34.9171i | −1.02753 | − | 0.0546434i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 148.471 | − | 85.7195i | 0.231623 | − | 0.133728i | −0.379697 | − | 0.925111i | \(-0.623972\pi\) |
0.611321 | + | 0.791383i | \(0.290639\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 749.426 | 1.16551 | 0.582757 | − | 0.812646i | \(-0.301974\pi\) | ||||
0.582757 | + | 0.812646i | \(0.301974\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 1281.62 | + | 786.057i | 1.98701 | + | 1.21869i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −589.924 | + | 340.593i | −0.911784 | + | 0.526419i | −0.881005 | − | 0.473108i | \(-0.843132\pi\) |
−0.0307791 | + | 0.999526i | \(0.509799\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 214.734 | + | 123.977i | 0.330870 | + | 0.191028i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 343.168 | − | 301.815i | 0.527140 | − | 0.463617i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −727.697 | − | 420.136i | −1.11439 | − | 0.643394i | −0.174428 | − | 0.984670i | \(-0.555808\pi\) |
−0.939963 | + | 0.341276i | \(0.889141\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 361.606 | − | 208.773i | 0.552070 | − | 0.318738i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 318.842 | − | 162.149i | 0.485299 | − | 0.246802i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −1035.77 | −1.57172 | −0.785862 | − | 0.618401i | \(-0.787781\pi\) | ||||
−0.785862 | + | 0.618401i | \(0.787781\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −624.364 | + | 360.477i | −0.944575 | + | 0.545351i | −0.891392 | − | 0.453234i | \(-0.850270\pi\) |
−0.0531835 | + | 0.998585i | \(0.516937\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 647.850 | − | 351.431i | 0.977149 | − | 0.530062i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 1102.67 | − | 1023.00i | 1.65814 | − | 1.53834i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 487.815 | + | 281.640i | 0.731356 | + | 0.422249i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −479.807 | − | 12.7490i | −0.717200 | − | 0.0190567i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − | 167.439i | − | 0.249537i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −705.661 | −1.04853 | −0.524266 | − | 0.851555i | \(-0.675660\pi\) | ||||
−0.524266 | + | 0.851555i | \(0.675660\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −821.522 | − | 1727.49i | −1.21707 | − | 2.55924i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −5.03682 | + | 8.72402i | −0.00743990 | + | 0.0128863i | −0.869721 | − | 0.493543i | \(-0.835702\pi\) |
0.862281 | + | 0.506429i | \(0.169035\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −433.398 | + | 98.8918i | −0.638289 | + | 0.145643i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 547.372 | − | 296.926i | 0.803776 | − | 0.436015i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −73.9512 | − | 128.087i | −0.108274 | − | 0.187536i | 0.806797 | − | 0.590829i | \(-0.201199\pi\) |
−0.915071 | + | 0.403292i | \(0.867866\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − | 1004.32i | − | 1.46616i | ||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 941.162 | + | 577.243i | 1.36996 | + | 0.840237i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −431.808 | − | 747.913i | −0.626716 | − | 1.08550i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −605.873 | + | 1049.40i | −0.876805 | + | 1.51867i | −0.0219783 | + | 0.999758i | \(0.506996\pi\) |
−0.854827 | + | 0.518913i | \(0.826337\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −257.949 | + | 214.987i | −0.372220 | + | 0.310226i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −444.669 | + | 770.189i | −0.639811 | + | 1.10819i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −115.336 | − | 199.767i | −0.165475 | − | 0.286610i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 41.2653 | + | 25.3093i | 0.0590348 | + | 0.0362078i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 34.2631i | − | 0.0488775i | −0.999701 | − | 0.0244387i | \(-0.992220\pi\) | ||
0.999701 | − | 0.0244387i | \(-0.00777986\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 339.639 | + | 588.273i | 0.483129 | + | 0.836803i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 309.023 | − | 167.632i | 0.438331 | − | 0.237776i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −164.974 | + | 153.054i | −0.233344 | + | 0.216484i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 207.128 | − | 358.756i | 0.292141 | − | 0.506003i | −0.682175 | − | 0.731189i | \(-0.738966\pi\) |
0.974316 | + | 0.225186i | \(0.0722990\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −37.4218 | − | 24.3429i | −0.0526326 | − | 0.0342376i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 498.794 | 0.699571 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 822.255i | 1.15001i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 258.787 | + | 6.87625i | 0.360931 | + | 0.00959031i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −68.9380 | − | 39.8014i | −0.0958804 | − | 0.0553566i | 0.451293 | − | 0.892376i | \(-0.350963\pi\) |
−0.547174 | + | 0.837019i | \(0.684296\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −1138.72 | − | 351.326i | −1.57936 | − | 0.487277i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 791.556 | − | 429.386i | 1.09482 | − | 0.593895i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −1507.86 | + | 870.566i | −2.07981 | + | 1.20078i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −9.43364 | −0.0129761 | −0.00648806 | − | 0.999979i | \(-0.502065\pi\) | ||||
−0.00648806 | + | 0.999979i | \(0.502065\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 719.760 | + | 115.703i | 0.987324 | + | 0.158715i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 691.185 | − | 399.056i | 0.945533 | − | 0.545904i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 193.869 | + | 111.930i | 0.264487 | + | 0.152701i | 0.626379 | − | 0.779518i | \(-0.284536\pi\) |
−0.361893 | + | 0.932220i | \(0.617869\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −145.809 | + | 1431.75i | −0.198380 | + | 1.94796i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −76.8057 | − | 44.3438i | −0.104214 | − | 0.0601680i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −541.551 | + | 312.665i | −0.732816 | + | 0.423092i | −0.819452 | − | 0.573148i | \(-0.805722\pi\) |
0.0866354 | + | 0.996240i | \(0.472388\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 884.436 | + | 542.451i | 1.19357 | + | 0.732053i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 209.834 | 0.282415 | 0.141208 | − | 0.989980i | \(-0.454902\pi\) | ||||
0.141208 | + | 0.989980i | \(0.454902\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 1442.37 | − | 832.755i | 1.93607 | − | 1.11779i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 26.8090 | − | 504.121i | 0.0358888 | − | 0.674861i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −1351.44 | − | 416.956i | −1.80432 | − | 0.556684i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −836.749 | − | 483.097i | −1.11418 | − | 0.643272i | −0.174271 | − | 0.984698i | \(-0.555757\pi\) |
−0.939909 | + | 0.341426i | \(0.889090\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −23.7968 | + | 895.592i | −0.0316027 | + | 1.18937i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | − | 735.518i | − | 0.974196i | ||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 318.215 | 0.420363 | 0.210181 | − | 0.977662i | \(-0.432595\pi\) | ||||
0.210181 | + | 0.977662i | \(0.432595\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −366.366 | − | 9.73472i | −0.482696 | − | 0.0128257i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 333.550 | − | 577.725i | 0.438304 | − | 0.759165i | −0.559255 | − | 0.828996i | \(-0.688913\pi\) |
0.997559 | + | 0.0698308i | \(0.0222459\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −181.170 | + | 168.080i | −0.237444 | + | 0.220288i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −1371.82 | − | 72.9529i | −1.79323 | − | 0.0953633i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 366.518 | + | 634.829i | 0.477860 | + | 0.827678i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 774.930i | 1.00771i | 0.863788 | + | 0.503856i | \(0.168086\pi\) | ||||
−0.863788 | + | 0.503856i | \(0.831914\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 227.593 | − | 371.078i | 0.295192 | − | 0.481295i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 61.0922 | + | 105.815i | 0.0790326 | + | 0.136889i | 0.902833 | − | 0.429992i | \(-0.141484\pi\) |
−0.823800 | + | 0.566880i | \(0.808150\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −770.901 | + | 1335.24i | −0.994711 | + | 1.72289i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −615.742 | − | 208.040i | −0.792460 | − | 0.267747i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 162.361 | − | 281.218i | 0.208422 | − | 0.360998i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −194.700 | − | 337.230i | −0.249295 | − | 0.431792i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 52.8250 | − | 661.441i | 0.0674648 | − | 0.844752i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 2041.35i | 2.60045i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 351.265 | + | 608.408i | 0.446334 | + | 0.773073i | 0.998144 | − | 0.0608970i | \(-0.0193961\pi\) |
−0.551810 | + | 0.833970i | \(0.686063\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 319.703 | + | 589.360i | 0.405200 | + | 0.746971i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 629.303 | − | 143.593i | 0.795579 | − | 0.181533i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 247.504 | − | 428.690i | 0.312111 | − | 0.540593i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −42.7564 | + | 1609.14i | −0.0537816 | + | 2.02407i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 615.706 | 0.772530 | 0.386265 | − | 0.922388i | \(-0.373765\pi\) | ||||
0.386265 | + | 0.922388i | \(0.373765\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 186.625i | − | 0.233573i | ||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −40.4426 | + | 62.1714i | −0.0504902 | + | 0.0776172i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 183.461 | + | 105.921i | 0.228469 | + | 0.131907i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −1151.50 | + | 1068.30i | −1.43044 | + | 1.32708i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −18.2947 | − | 33.7255i | −0.0226700 | − | 0.0417913i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −1077.98 | + | 622.375i | −1.33249 | + | 0.769313i | −0.985681 | − | 0.168622i | \(-0.946068\pi\) |
−0.346809 | + | 0.937936i | \(0.612735\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −1339.58 | −1.65176 | −0.825881 | − | 0.563845i | \(-0.809322\pi\) | ||||
−0.825881 | + | 0.563845i | \(0.809322\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 172.289 | − | 280.907i | 0.211917 | − | 0.345519i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −2514.97 | + | 1452.02i | −3.08585 | + | 1.78161i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 972.998 | + | 561.760i | 1.19094 | + | 0.687589i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −978.205 | + | 169.132i | −1.19439 | + | 0.206510i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 263.793 | + | 152.301i | 0.321307 | + | 0.185507i | 0.651975 | − | 0.758241i | \(-0.273941\pi\) |
−0.330668 | + | 0.943747i | \(0.607274\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −297.149 | + | 171.559i | −0.361056 | + | 0.208456i | −0.669544 | − | 0.742773i | \(-0.733510\pi\) |
0.308488 | + | 0.951228i | \(0.400177\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 592.289 | − | 965.693i | 0.717926 | − | 1.17054i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −652.212 | −0.788648 | −0.394324 | − | 0.918972i | \(-0.629021\pi\) | ||||
−0.394324 | + | 0.918972i | \(0.629021\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −314.990 | + | 181.859i | −0.379963 | + | 0.219372i | −0.677802 | − | 0.735244i | \(-0.737067\pi\) |
0.297839 | + | 0.954616i | \(0.403734\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −703.388 | − | 1296.67i | −0.846435 | − | 1.56037i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 631.165 | + | 430.437i | 0.757701 | + | 0.516731i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 1566.35 | + | 904.332i | 1.87587 | + | 1.08303i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −252.348 | − | 530.635i | −0.301491 | − | 0.633972i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | − | 1070.44i | − | 1.27585i | −0.770099 | − | 0.637925i | \(-0.779793\pi\) | ||
0.770099 | − | 0.637925i | \(-0.220207\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 237.030 | 0.281843 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 6.39730 | − | 240.762i | 0.00758873 | − | 0.285602i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −388.166 | + | 672.323i | −0.459368 | + | 0.795648i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 619.328 | + | 191.080i | 0.731201 | + | 0.225596i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −406.129 | − | 748.683i | −0.478361 | − | 0.881841i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −354.681 | − | 614.326i | −0.416782 | − | 0.721887i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 1557.63i | 1.82606i | 0.407891 | + | 0.913031i | \(0.366264\pi\) | ||||
−0.407891 | + | 0.913031i | \(0.633736\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −876.635 | − | 1723.77i | −1.02530 | − | 2.01611i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 117.943 | + | 204.284i | 0.137624 | + | 0.238371i | 0.926597 | − | 0.376057i | \(-0.122720\pi\) |
−0.788973 | + | 0.614428i | \(0.789387\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 557.231 | − | 965.153i | 0.648698 | − | 1.12358i | −0.334737 | − | 0.942312i | \(-0.608647\pi\) |
0.983434 | − | 0.181265i | \(-0.0580193\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 61.0471 | + | 304.639i | 0.0709026 | + | 0.353820i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 375.824 | − | 650.946i | 0.435486 | − | 0.754283i | −0.561849 | − | 0.827239i | \(-0.689910\pi\) |
0.997335 | + | 0.0729562i | \(0.0232433\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −1246.45 | − | 2158.91i | −1.44098 | − | 2.49585i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 72.0183 | − | 117.422i | 0.0830661 | − | 0.135434i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − | 26.4386i | − | 0.0304242i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −131.095 | − | 227.064i | −0.150511 | − | 0.260694i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −30.3518 | + | 570.742i | −0.0347673 | + | 0.653771i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −698.963 | − | 3063.24i | −0.798815 | − | 3.50085i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −613.699 | + | 1062.96i | −0.699770 | + | 1.21204i | 0.268776 | + | 0.963203i | \(0.413381\pi\) |
−0.968546 | + | 0.248835i | \(0.919952\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −982.182 | − | 26.0976i | −1.11739 | − | 0.0296901i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 1209.71 | 1.37311 | 0.686557 | − | 0.727076i | \(-0.259121\pi\) | ||||
0.686557 | + | 0.727076i | \(0.259121\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 990.879i | − | 1.12217i | −0.827757 | − | 0.561087i | \(-0.810383\pi\) | ||
0.827757 | − | 0.561087i | \(-0.189617\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 36.2916 | − | 1365.83i | 0.0410075 | − | 1.54332i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 1395.29 | + | 805.571i | 1.57304 | + | 0.908198i | 0.995793 | + | 0.0916309i | \(0.0292080\pi\) |
0.577251 | + | 0.816567i | \(0.304125\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −514.209 | + | 117.331i | −0.578413 | + | 0.131981i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 174.995 | + | 394.678i | 0.196402 | + | 0.442961i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 227.519 | − | 131.358i | 0.254780 | − | 0.147097i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −1150.14 | −1.28507 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −923.606 | − | 566.476i | −1.02966 | − | 0.631522i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −463.173 | + | 267.413i | −0.515209 | + | 0.297456i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 740.020 | + | 427.251i | 0.821332 | + | 0.474196i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −1054.04 | + | 211.220i | −1.16726 | + | 0.233909i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 173.438 | + | 100.135i | 0.191644 | + | 0.110646i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 967.470 | − | 558.569i | 1.06667 | − | 0.615842i | 0.139400 | − | 0.990236i | \(-0.455483\pi\) |
0.927270 | + | 0.374394i | \(0.122149\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 131.157 | + | 257.900i | 0.144287 | + | 0.283718i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −223.900 | −0.245774 | −0.122887 | − | 0.992421i | \(-0.539215\pi\) | ||||
−0.122887 | + | 0.992421i | \(0.539215\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 258.921 | − | 149.488i | 0.283594 | − | 0.163733i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −811.012 | + | 439.940i | −0.886352 | + | 0.480808i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −88.0162 | + | 285.278i | −0.0959828 | + | 0.311099i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 412.009 | + | 237.874i | 0.448324 | + | 0.258840i | 0.707122 | − | 0.707092i | \(-0.249993\pi\) |
−0.258798 | + | 0.965931i | \(0.583327\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 613.787 | + | 16.3090i | 0.666436 | + | 0.0177079i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − | 1151.20i | − | 1.24724i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 2192.68 | 2.37047 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −835.466 | + | 1284.34i | −0.901258 | + | 1.38548i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 415.674 | − | 719.968i | 0.447442 | − | 0.774992i | −0.550777 | − | 0.834653i | \(-0.685668\pi\) |
0.998219 | + | 0.0596603i | \(0.0190018\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −80.5033 | + | 1072.44i | −0.0864697 | + | 1.15192i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −1191.14 | + | 646.142i | −1.27668 | + | 0.692542i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −406.789 | − | 704.579i | −0.435068 | − | 0.753561i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 358.471i | − | 0.382573i | −0.981534 | − | 0.191286i | \(-0.938734\pi\) | ||
0.981534 | − | 0.191286i | \(-0.0612660\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 822.420 | + | 504.415i | 0.875847 | + | 0.537183i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 485.287 | + | 840.541i | 0.515714 | + | 0.893243i | 0.999834 | + | 0.0182409i | \(0.00580657\pi\) |
−0.484120 | + | 0.875002i | \(0.660860\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −169.552 | + | 293.672i | −0.179800 | + | 0.311423i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 1719.06 | + | 684.536i | 1.81911 | + | 0.724377i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −884.688 | + | 1532.32i | −0.934200 | + | 1.61808i | −0.158147 | + | 0.987416i | \(0.550552\pi\) |
−0.776054 | + | 0.630667i | \(0.782781\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 313.139 | + | 542.373i | 0.329967 | + | 0.571520i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 600.494 | + | 368.301i | 0.631434 | + | 0.387278i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 1028.42i | 1.07914i | 0.841941 | + | 0.539570i | \(0.181413\pi\) | ||||
−0.841941 | + | 0.539570i | \(0.818587\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −901.635 | − | 1561.68i | −0.944121 | − | 1.63527i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 345.421 | − | 187.376i | 0.360942 | − | 0.195796i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 488.393 | + | 526.429i | 0.509273 | + | 0.548935i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 243.701 | − | 422.103i | 0.253591 | − | 0.439233i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −991.536 | + | 1524.26i | −1.02963 | + | 1.58283i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 39.7091 | 0.0411494 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 1136.76i | 1.17555i | 0.809024 | + | 0.587776i | \(0.199996\pi\) | ||||
−0.809024 | + | 0.587776i | \(0.800004\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −1026.22 | − | 27.2678i | −1.05905 | − | 0.0281402i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 418.792 | + | 241.790i | 0.431300 | + | 0.249011i | 0.699900 | − | 0.714241i | \(-0.253228\pi\) |
−0.268600 | + | 0.963252i | \(0.586561\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −141.458 | − | 619.945i | −0.145383 | − | 0.637148i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 2943.88 | − | 1596.93i | 3.01936 | − | 1.63788i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −105.815 | + | 61.0925i | −0.108306 | + | 0.0625307i | −0.553175 | − | 0.833065i | \(-0.686584\pi\) |
0.444868 | + | 0.895596i | \(0.353250\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −43.9243 | −0.0448665 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 144.033 | + | 283.219i | 0.146822 | + | 0.288704i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 1120.41 | − | 646.870i | 1.13979 | − | 0.658057i | 0.193410 | − | 0.981118i | \(-0.438045\pi\) |
0.946378 | + | 0.323061i | \(0.104712\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −1498.69 | − | 865.268i | −1.52151 | − | 0.878445i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −80.4609 | + | 238.143i | −0.0815207 | + | 0.241279i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −1016.09 | − | 586.640i | −1.02739 | − | 0.593165i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −411.728 | + | 237.711i | −0.415468 | + | 0.239870i | −0.693136 | − | 0.720807i | \(-0.743772\pi\) |
0.277669 | + | 0.960677i | \(0.410438\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −403.751 | − | 247.633i | −0.406597 | − | 0.249378i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 421.325 | 0.423443 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −291.989 | + | 168.580i | −0.292868 | + | 0.169087i | −0.639235 | − | 0.769012i | \(-0.720749\pi\) |
0.346367 | + | 0.938099i | \(0.387415\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −474.103 | + | 688.120i | −0.474577 | + | 0.688809i |
(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 | 336.3.z.f.47.10 | yes | 20 | |
3.2 | odd | 2 | inner | 336.3.z.f.47.4 | ✓ | 20 | |
4.3 | odd | 2 | 336.3.z.g.47.1 | yes | 20 | ||
7.3 | odd | 6 | 336.3.z.g.143.7 | yes | 20 | ||
12.11 | even | 2 | 336.3.z.g.47.7 | yes | 20 | ||
21.17 | even | 6 | 336.3.z.g.143.1 | yes | 20 | ||
28.3 | even | 6 | inner | 336.3.z.f.143.4 | yes | 20 | |
84.59 | odd | 6 | inner | 336.3.z.f.143.10 | yes | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
336.3.z.f.47.4 | ✓ | 20 | 3.2 | odd | 2 | inner | |
336.3.z.f.47.10 | yes | 20 | 1.1 | even | 1 | trivial | |
336.3.z.f.143.4 | yes | 20 | 28.3 | even | 6 | inner | |
336.3.z.f.143.10 | yes | 20 | 84.59 | odd | 6 | inner | |
336.3.z.g.47.1 | yes | 20 | 4.3 | odd | 2 | ||
336.3.z.g.47.7 | yes | 20 | 12.11 | even | 2 | ||
336.3.z.g.143.1 | yes | 20 | 21.17 | even | 6 | ||
336.3.z.g.143.7 | yes | 20 | 7.3 | odd | 6 |