Properties

Label 432.3.bc.a.353.3
Level $432$
Weight $3$
Character 432.353
Analytic conductor $11.771$
Analytic rank $0$
Dimension $30$
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [432,3,Mod(65,432)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(432, base_ring=CyclotomicField(18))
 
chi = DirichletCharacter(H, H._module([0, 0, 13]))
 
N = Newforms(chi, 3, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("432.65");
 
S:= CuspForms(chi, 3);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 432 = 2^{4} \cdot 3^{3} \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 432.bc (of order \(18\), degree \(6\), not minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(11.7711474204\)
Analytic rank: \(0\)
Dimension: \(30\)
Relative dimension: \(5\) over \(\Q(\zeta_{18})\)
Twist minimal: no (minimal twist has level 27)
Sato-Tate group: $\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label 353.3
Character \(\chi\) \(=\) 432.353
Dual form 432.3.bc.a.257.3

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.10490 - 2.78912i) q^{3} +(-3.46013 - 4.12362i) q^{5} +(-9.89907 + 3.60297i) q^{7} +(-6.55839 + 6.16340i) q^{9} +O(q^{10})\) \(q+(-1.10490 - 2.78912i) q^{3} +(-3.46013 - 4.12362i) q^{5} +(-9.89907 + 3.60297i) q^{7} +(-6.55839 + 6.16340i) q^{9} +(7.54888 - 8.99640i) q^{11} +(1.95057 + 11.0622i) q^{13} +(-7.67818 + 14.2069i) q^{15} +(2.73630 - 1.57980i) q^{17} +(-2.26051 + 3.91532i) q^{19} +(20.9866 + 23.6288i) q^{21} +(-6.80880 + 18.7070i) q^{23} +(-0.690550 + 3.91630i) q^{25} +(24.4368 + 11.4822i) q^{27} +(24.9744 + 4.40366i) q^{29} +(20.7874 + 7.56598i) q^{31} +(-33.4328 - 11.1146i) q^{33} +(49.1093 + 28.3533i) q^{35} +(-8.82807 - 15.2907i) q^{37} +(28.6987 - 17.6630i) q^{39} +(-12.2557 + 2.16101i) q^{41} +(-27.9211 - 23.4286i) q^{43} +(48.1084 + 5.71818i) q^{45} +(4.24091 + 11.6518i) q^{47} +(47.4740 - 39.8354i) q^{49} +(-7.42960 - 5.88634i) q^{51} +84.6210i q^{53} -63.2178 q^{55} +(13.4179 + 1.97880i) q^{57} +(43.8854 + 52.3006i) q^{59} +(-73.3637 + 26.7022i) q^{61} +(42.7155 - 84.6415i) q^{63} +(38.8672 - 46.3201i) q^{65} +(16.8654 + 95.6483i) q^{67} +(59.6992 - 1.67882i) q^{69} +(-105.364 + 60.8322i) q^{71} +(-45.5705 + 78.9304i) q^{73} +(11.6860 - 2.40109i) q^{75} +(-42.3131 + 116.254i) q^{77} +(3.54032 - 20.0781i) q^{79} +(5.02506 - 80.8440i) q^{81} +(-31.1219 - 5.48763i) q^{83} +(-15.9824 - 5.81713i) q^{85} +(-15.3119 - 74.5223i) q^{87} +(59.7756 + 34.5114i) q^{89} +(-59.1656 - 102.478i) q^{91} +(-1.86551 - 66.3381i) q^{93} +(23.9669 - 4.22602i) q^{95} +(-61.1335 - 51.2971i) q^{97} +(5.93989 + 105.529i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 30 q + 6 q^{3} - 15 q^{5} + 6 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 30 q + 6 q^{3} - 15 q^{5} + 6 q^{7} + 6 q^{11} - 6 q^{13} + 9 q^{15} - 9 q^{17} + 3 q^{19} + 132 q^{21} - 120 q^{23} - 15 q^{25} + 90 q^{27} - 168 q^{29} - 39 q^{31} - 207 q^{33} + 252 q^{35} - 3 q^{37} - 15 q^{39} + 228 q^{41} + 96 q^{43} + 477 q^{45} - 399 q^{47} - 78 q^{49} - 36 q^{51} + 12 q^{55} - 192 q^{57} + 474 q^{59} + 138 q^{61} + 585 q^{63} - 411 q^{65} - 354 q^{67} + 99 q^{69} - 315 q^{71} - 66 q^{73} - 255 q^{75} + 201 q^{77} - 30 q^{79} + 36 q^{81} + 33 q^{83} - 261 q^{85} + 279 q^{87} + 72 q^{89} - 96 q^{91} + 591 q^{93} - 681 q^{95} - 582 q^{97} - 513 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/432\mathbb{Z}\right)^\times\).

\(n\) \(271\) \(325\) \(353\)
\(\chi(n)\) \(1\) \(1\) \(e\left(\frac{1}{18}\right)\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) −1.10490 2.78912i −0.368300 0.929707i
\(4\) 0 0
\(5\) −3.46013 4.12362i −0.692026 0.824724i 0.299574 0.954073i \(-0.403156\pi\)
−0.991599 + 0.129349i \(0.958711\pi\)
\(6\) 0 0
\(7\) −9.89907 + 3.60297i −1.41415 + 0.514709i −0.932346 0.361568i \(-0.882241\pi\)
−0.481807 + 0.876278i \(0.660019\pi\)
\(8\) 0 0
\(9\) −6.55839 + 6.16340i −0.728710 + 0.684822i
\(10\) 0 0
\(11\) 7.54888 8.99640i 0.686262 0.817855i −0.304636 0.952469i \(-0.598535\pi\)
0.990898 + 0.134614i \(0.0429794\pi\)
\(12\) 0 0
\(13\) 1.95057 + 11.0622i 0.150044 + 0.850940i 0.963178 + 0.268864i \(0.0866482\pi\)
−0.813134 + 0.582076i \(0.802241\pi\)
\(14\) 0 0
\(15\) −7.67818 + 14.2069i −0.511879 + 0.947127i
\(16\) 0 0
\(17\) 2.73630 1.57980i 0.160959 0.0929296i −0.417357 0.908743i \(-0.637044\pi\)
0.578316 + 0.815813i \(0.303710\pi\)
\(18\) 0 0
\(19\) −2.26051 + 3.91532i −0.118974 + 0.206069i −0.919361 0.393414i \(-0.871294\pi\)
0.800387 + 0.599483i \(0.204627\pi\)
\(20\) 0 0
\(21\) 20.9866 + 23.6288i 0.999361 + 1.12518i
\(22\) 0 0
\(23\) −6.80880 + 18.7070i −0.296035 + 0.813349i 0.699118 + 0.715007i \(0.253576\pi\)
−0.995153 + 0.0983427i \(0.968646\pi\)
\(24\) 0 0
\(25\) −0.690550 + 3.91630i −0.0276220 + 0.156652i
\(26\) 0 0
\(27\) 24.4368 + 11.4822i 0.905068 + 0.425267i
\(28\) 0 0
\(29\) 24.9744 + 4.40366i 0.861187 + 0.151851i 0.586763 0.809758i \(-0.300402\pi\)
0.274424 + 0.961609i \(0.411513\pi\)
\(30\) 0 0
\(31\) 20.7874 + 7.56598i 0.670560 + 0.244064i 0.654789 0.755812i \(-0.272757\pi\)
0.0157712 + 0.999876i \(0.494980\pi\)
\(32\) 0 0
\(33\) −33.4328 11.1146i −1.01312 0.336807i
\(34\) 0 0
\(35\) 49.1093 + 28.3533i 1.40312 + 0.810093i
\(36\) 0 0
\(37\) −8.82807 15.2907i −0.238596 0.413261i 0.721715 0.692190i \(-0.243354\pi\)
−0.960312 + 0.278929i \(0.910021\pi\)
\(38\) 0 0
\(39\) 28.6987 17.6630i 0.735864 0.452898i
\(40\) 0 0
\(41\) −12.2557 + 2.16101i −0.298920 + 0.0527076i −0.321096 0.947046i \(-0.604051\pi\)
0.0221770 + 0.999754i \(0.492940\pi\)
\(42\) 0 0
\(43\) −27.9211 23.4286i −0.649329 0.544851i 0.257539 0.966268i \(-0.417089\pi\)
−0.906867 + 0.421417i \(0.861533\pi\)
\(44\) 0 0
\(45\) 48.1084 + 5.71818i 1.06908 + 0.127071i
\(46\) 0 0
\(47\) 4.24091 + 11.6518i 0.0902320 + 0.247910i 0.976597 0.215076i \(-0.0690000\pi\)
−0.886365 + 0.462987i \(0.846778\pi\)
\(48\) 0 0
\(49\) 47.4740 39.8354i 0.968857 0.812967i
\(50\) 0 0
\(51\) −7.42960 5.88634i −0.145678 0.115419i
\(52\) 0 0
\(53\) 84.6210i 1.59662i 0.602245 + 0.798311i \(0.294273\pi\)
−0.602245 + 0.798311i \(0.705727\pi\)
\(54\) 0 0
\(55\) −63.2178 −1.14942
\(56\) 0 0
\(57\) 13.4179 + 1.97880i 0.235402 + 0.0347158i
\(58\) 0 0
\(59\) 43.8854 + 52.3006i 0.743820 + 0.886451i 0.996711 0.0810443i \(-0.0258255\pi\)
−0.252890 + 0.967495i \(0.581381\pi\)
\(60\) 0 0
\(61\) −73.3637 + 26.7022i −1.20268 + 0.437741i −0.864160 0.503217i \(-0.832150\pi\)
−0.338523 + 0.940958i \(0.609927\pi\)
\(62\) 0 0
\(63\) 42.7155 84.6415i 0.678023 1.34352i
\(64\) 0 0
\(65\) 38.8672 46.3201i 0.597956 0.712617i
\(66\) 0 0
\(67\) 16.8654 + 95.6483i 0.251722 + 1.42759i 0.804349 + 0.594157i \(0.202514\pi\)
−0.552627 + 0.833429i \(0.686375\pi\)
\(68\) 0 0
\(69\) 59.6992 1.67882i 0.865206 0.0243307i
\(70\) 0 0
\(71\) −105.364 + 60.8322i −1.48401 + 0.856791i −0.999835 0.0181820i \(-0.994212\pi\)
−0.484171 + 0.874973i \(0.660879\pi\)
\(72\) 0 0
\(73\) −45.5705 + 78.9304i −0.624254 + 1.08124i 0.364431 + 0.931230i \(0.381263\pi\)
−0.988685 + 0.150009i \(0.952070\pi\)
\(74\) 0 0
\(75\) 11.6860 2.40109i 0.155814 0.0320146i
\(76\) 0 0
\(77\) −42.3131 + 116.254i −0.549521 + 1.50980i
\(78\) 0 0
\(79\) 3.54032 20.0781i 0.0448142 0.254154i −0.954167 0.299273i \(-0.903256\pi\)
0.998982 + 0.0451196i \(0.0143669\pi\)
\(80\) 0 0
\(81\) 5.02506 80.8440i 0.0620378 0.998074i
\(82\) 0 0
\(83\) −31.1219 5.48763i −0.374963 0.0661161i −0.0170090 0.999855i \(-0.505414\pi\)
−0.357954 + 0.933739i \(0.616526\pi\)
\(84\) 0 0
\(85\) −15.9824 5.81713i −0.188029 0.0684369i
\(86\) 0 0
\(87\) −15.3119 74.5223i −0.175999 0.856578i
\(88\) 0 0
\(89\) 59.7756 + 34.5114i 0.671636 + 0.387769i 0.796696 0.604380i \(-0.206579\pi\)
−0.125060 + 0.992149i \(0.539912\pi\)
\(90\) 0 0
\(91\) −59.1656 102.478i −0.650171 1.12613i
\(92\) 0 0
\(93\) −1.86551 66.3381i −0.0200592 0.713313i
\(94\) 0 0
\(95\) 23.9669 4.22602i 0.252283 0.0444844i
\(96\) 0 0
\(97\) −61.1335 51.2971i −0.630243 0.528836i 0.270762 0.962646i \(-0.412724\pi\)
−0.901004 + 0.433810i \(0.857169\pi\)
\(98\) 0 0
\(99\) 5.93989 + 105.529i 0.0599989 + 1.06595i
\(100\) 0 0
\(101\) −1.63372 4.48862i −0.0161755 0.0444417i 0.931342 0.364145i \(-0.118639\pi\)
−0.947518 + 0.319704i \(0.896417\pi\)
\(102\) 0 0
\(103\) 55.3795 46.4689i 0.537665 0.451154i −0.333074 0.942901i \(-0.608086\pi\)
0.870738 + 0.491746i \(0.163641\pi\)
\(104\) 0 0
\(105\) 24.8199 168.299i 0.236380 1.60285i
\(106\) 0 0
\(107\) 158.133i 1.47788i −0.673773 0.738938i \(-0.735328\pi\)
0.673773 0.738938i \(-0.264672\pi\)
\(108\) 0 0
\(109\) −18.5788 −0.170448 −0.0852240 0.996362i \(-0.527161\pi\)
−0.0852240 + 0.996362i \(0.527161\pi\)
\(110\) 0 0
\(111\) −32.8934 + 41.5172i −0.296337 + 0.374029i
\(112\) 0 0
\(113\) −11.5806 13.8012i −0.102483 0.122134i 0.712365 0.701809i \(-0.247624\pi\)
−0.814848 + 0.579675i \(0.803180\pi\)
\(114\) 0 0
\(115\) 100.700 36.6518i 0.875652 0.318711i
\(116\) 0 0
\(117\) −80.9734 60.5283i −0.692081 0.517336i
\(118\) 0 0
\(119\) −21.3948 + 25.4974i −0.179788 + 0.214264i
\(120\) 0 0
\(121\) −2.93828 16.6638i −0.0242833 0.137717i
\(122\) 0 0
\(123\) 19.5686 + 31.7949i 0.159095 + 0.258495i
\(124\) 0 0
\(125\) −98.0067 + 56.5842i −0.784054 + 0.452674i
\(126\) 0 0
\(127\) −78.1067 + 135.285i −0.615013 + 1.06523i 0.375369 + 0.926876i \(0.377516\pi\)
−0.990382 + 0.138359i \(0.955817\pi\)
\(128\) 0 0
\(129\) −34.4952 + 103.762i −0.267405 + 0.804354i
\(130\) 0 0
\(131\) −33.6955 + 92.5776i −0.257217 + 0.706699i 0.742119 + 0.670268i \(0.233821\pi\)
−0.999336 + 0.0364307i \(0.988401\pi\)
\(132\) 0 0
\(133\) 8.27018 46.9025i 0.0621818 0.352651i
\(134\) 0 0
\(135\) −37.2062 140.498i −0.275602 1.04073i
\(136\) 0 0
\(137\) −64.6590 11.4011i −0.471963 0.0832199i −0.0673925 0.997727i \(-0.521468\pi\)
−0.404571 + 0.914507i \(0.632579\pi\)
\(138\) 0 0
\(139\) −117.744 42.8553i −0.847080 0.308312i −0.118231 0.992986i \(-0.537722\pi\)
−0.728849 + 0.684674i \(0.759944\pi\)
\(140\) 0 0
\(141\) 27.8125 24.7025i 0.197252 0.175195i
\(142\) 0 0
\(143\) 114.245 + 65.9593i 0.798915 + 0.461254i
\(144\) 0 0
\(145\) −68.2557 118.222i −0.470729 0.815326i
\(146\) 0 0
\(147\) −163.560 88.3966i −1.11265 0.601337i
\(148\) 0 0
\(149\) 198.691 35.0346i 1.33350 0.235132i 0.538953 0.842336i \(-0.318820\pi\)
0.794546 + 0.607204i \(0.207709\pi\)
\(150\) 0 0
\(151\) −98.1613 82.3671i −0.650075 0.545478i 0.257019 0.966406i \(-0.417260\pi\)
−0.907094 + 0.420929i \(0.861704\pi\)
\(152\) 0 0
\(153\) −8.20877 + 27.2259i −0.0536521 + 0.177947i
\(154\) 0 0
\(155\) −40.7277 111.898i −0.262759 0.721926i
\(156\) 0 0
\(157\) −106.439 + 89.3129i −0.677955 + 0.568872i −0.915408 0.402527i \(-0.868132\pi\)
0.237453 + 0.971399i \(0.423687\pi\)
\(158\) 0 0
\(159\) 236.018 93.4977i 1.48439 0.588036i
\(160\) 0 0
\(161\) 209.714i 1.30257i
\(162\) 0 0
\(163\) −39.8569 −0.244521 −0.122261 0.992498i \(-0.539014\pi\)
−0.122261 + 0.992498i \(0.539014\pi\)
\(164\) 0 0
\(165\) 69.8494 + 176.322i 0.423329 + 1.06862i
\(166\) 0 0
\(167\) 106.672 + 127.127i 0.638757 + 0.761241i 0.984173 0.177208i \(-0.0567067\pi\)
−0.345416 + 0.938450i \(0.612262\pi\)
\(168\) 0 0
\(169\) 40.2401 14.6462i 0.238107 0.0866639i
\(170\) 0 0
\(171\) −9.30634 39.6106i −0.0544231 0.231641i
\(172\) 0 0
\(173\) −7.00006 + 8.34234i −0.0404628 + 0.0482216i −0.785896 0.618358i \(-0.787798\pi\)
0.745434 + 0.666580i \(0.232243\pi\)
\(174\) 0 0
\(175\) −7.27451 41.2558i −0.0415686 0.235747i
\(176\) 0 0
\(177\) 97.3837 180.189i 0.550191 1.01801i
\(178\) 0 0
\(179\) 244.720 141.289i 1.36715 0.789326i 0.376590 0.926380i \(-0.377097\pi\)
0.990564 + 0.137054i \(0.0437633\pi\)
\(180\) 0 0
\(181\) 54.3996 94.2228i 0.300550 0.520568i −0.675711 0.737167i \(-0.736163\pi\)
0.976261 + 0.216599i \(0.0694964\pi\)
\(182\) 0 0
\(183\) 155.535 + 175.117i 0.849919 + 0.956923i
\(184\) 0 0
\(185\) −32.5066 + 89.3112i −0.175711 + 0.482763i
\(186\) 0 0
\(187\) 6.44344 36.5426i 0.0344569 0.195415i
\(188\) 0 0
\(189\) −283.272 25.6182i −1.49879 0.135546i
\(190\) 0 0
\(191\) −106.979 18.8633i −0.560100 0.0987607i −0.113571 0.993530i \(-0.536229\pi\)
−0.446529 + 0.894769i \(0.647340\pi\)
\(192\) 0 0
\(193\) −188.040 68.4410i −0.974301 0.354617i −0.194679 0.980867i \(-0.562367\pi\)
−0.779622 + 0.626250i \(0.784589\pi\)
\(194\) 0 0
\(195\) −172.137 57.2262i −0.882752 0.293468i
\(196\) 0 0
\(197\) 253.494 + 146.355i 1.28677 + 0.742918i 0.978077 0.208243i \(-0.0667746\pi\)
0.308694 + 0.951161i \(0.400108\pi\)
\(198\) 0 0
\(199\) −41.1548 71.2822i −0.206808 0.358202i 0.743899 0.668292i \(-0.232974\pi\)
−0.950707 + 0.310090i \(0.899641\pi\)
\(200\) 0 0
\(201\) 248.140 152.721i 1.23453 0.759807i
\(202\) 0 0
\(203\) −263.090 + 46.3898i −1.29601 + 0.228521i
\(204\) 0 0
\(205\) 51.3175 + 43.0605i 0.250329 + 0.210051i
\(206\) 0 0
\(207\) −70.6441 164.653i −0.341276 0.795427i
\(208\) 0 0
\(209\) 18.1595 + 49.8927i 0.0868874 + 0.238721i
\(210\) 0 0
\(211\) −88.7425 + 74.4638i −0.420581 + 0.352909i −0.828384 0.560161i \(-0.810739\pi\)
0.407803 + 0.913070i \(0.366295\pi\)
\(212\) 0 0
\(213\) 286.085 + 226.661i 1.34312 + 1.06413i
\(214\) 0 0
\(215\) 196.202i 0.912568i
\(216\) 0 0
\(217\) −233.036 −1.07390
\(218\) 0 0
\(219\) 270.497 + 39.8915i 1.23515 + 0.182153i
\(220\) 0 0
\(221\) 22.8135 + 27.1880i 0.103228 + 0.123023i
\(222\) 0 0
\(223\) −186.281 + 67.8007i −0.835341 + 0.304039i −0.724049 0.689749i \(-0.757721\pi\)
−0.111292 + 0.993788i \(0.535499\pi\)
\(224\) 0 0
\(225\) −19.6088 29.9408i −0.0871504 0.133070i
\(226\) 0 0
\(227\) 3.31155 3.94655i 0.0145883 0.0173857i −0.758701 0.651439i \(-0.774166\pi\)
0.773289 + 0.634053i \(0.218610\pi\)
\(228\) 0 0
\(229\) 61.3581 + 347.979i 0.267939 + 1.51956i 0.760533 + 0.649299i \(0.224938\pi\)
−0.492594 + 0.870259i \(0.663951\pi\)
\(230\) 0 0
\(231\) 370.999 10.4330i 1.60606 0.0451643i
\(232\) 0 0
\(233\) 121.729 70.2803i 0.522442 0.301632i −0.215491 0.976506i \(-0.569135\pi\)
0.737933 + 0.674874i \(0.235802\pi\)
\(234\) 0 0
\(235\) 33.3735 57.8046i 0.142015 0.245977i
\(236\) 0 0
\(237\) −59.9121 + 12.3100i −0.252794 + 0.0519407i
\(238\) 0 0
\(239\) 50.5074 138.768i 0.211328 0.580619i −0.788060 0.615598i \(-0.788914\pi\)
0.999388 + 0.0349794i \(0.0111366\pi\)
\(240\) 0 0
\(241\) 52.8609 299.789i 0.219340 1.24394i −0.653875 0.756602i \(-0.726858\pi\)
0.873215 0.487335i \(-0.162031\pi\)
\(242\) 0 0
\(243\) −231.036 + 75.3090i −0.950765 + 0.309913i
\(244\) 0 0
\(245\) −328.532 57.9291i −1.34095 0.236445i
\(246\) 0 0
\(247\) −47.7214 17.3692i −0.193204 0.0703205i
\(248\) 0 0
\(249\) 19.0809 + 92.8661i 0.0766302 + 0.372956i
\(250\) 0 0
\(251\) 108.072 + 62.3955i 0.430567 + 0.248588i 0.699588 0.714546i \(-0.253367\pi\)
−0.269021 + 0.963134i \(0.586700\pi\)
\(252\) 0 0
\(253\) 116.897 + 202.472i 0.462044 + 0.800284i
\(254\) 0 0
\(255\) 1.43430 + 51.0043i 0.00562472 + 0.200017i
\(256\) 0 0
\(257\) −450.088 + 79.3627i −1.75132 + 0.308804i −0.955116 0.296231i \(-0.904270\pi\)
−0.796199 + 0.605035i \(0.793159\pi\)
\(258\) 0 0
\(259\) 142.481 + 119.556i 0.550121 + 0.461606i
\(260\) 0 0
\(261\) −190.934 + 125.046i −0.731547 + 0.479105i
\(262\) 0 0
\(263\) 160.047 + 439.726i 0.608545 + 1.67196i 0.733408 + 0.679789i \(0.237929\pi\)
−0.124863 + 0.992174i \(0.539849\pi\)
\(264\) 0 0
\(265\) 348.945 292.799i 1.31677 1.10490i
\(266\) 0 0
\(267\) 30.2106 204.853i 0.113148 0.767240i
\(268\) 0 0
\(269\) 317.049i 1.17862i −0.807907 0.589310i \(-0.799399\pi\)
0.807907 0.589310i \(-0.200601\pi\)
\(270\) 0 0
\(271\) −115.698 −0.426931 −0.213465 0.976951i \(-0.568475\pi\)
−0.213465 + 0.976951i \(0.568475\pi\)
\(272\) 0 0
\(273\) −220.451 + 278.248i −0.807513 + 1.01922i
\(274\) 0 0
\(275\) 30.0198 + 35.7762i 0.109163 + 0.130095i
\(276\) 0 0
\(277\) 108.352 39.4370i 0.391163 0.142372i −0.138949 0.990300i \(-0.544372\pi\)
0.530112 + 0.847928i \(0.322150\pi\)
\(278\) 0 0
\(279\) −182.964 + 78.5001i −0.655785 + 0.281362i
\(280\) 0 0
\(281\) −52.4463 + 62.5031i −0.186642 + 0.222431i −0.851249 0.524762i \(-0.824154\pi\)
0.664607 + 0.747193i \(0.268599\pi\)
\(282\) 0 0
\(283\) 72.4355 + 410.802i 0.255956 + 1.45160i 0.793608 + 0.608430i \(0.208200\pi\)
−0.537652 + 0.843167i \(0.680689\pi\)
\(284\) 0 0
\(285\) −38.2679 62.1773i −0.134273 0.218166i
\(286\) 0 0
\(287\) 113.534 65.5489i 0.395589 0.228393i
\(288\) 0 0
\(289\) −139.508 + 241.636i −0.482728 + 0.836110i
\(290\) 0 0
\(291\) −75.5275 + 227.187i −0.259545 + 0.780712i
\(292\) 0 0
\(293\) −118.282 + 324.977i −0.403693 + 1.10914i 0.556755 + 0.830676i \(0.312046\pi\)
−0.960448 + 0.278460i \(0.910176\pi\)
\(294\) 0 0
\(295\) 63.8186 361.933i 0.216334 1.22689i
\(296\) 0 0
\(297\) 287.769 133.166i 0.968920 0.448369i
\(298\) 0 0
\(299\) −220.222 38.8311i −0.736529 0.129870i
\(300\) 0 0
\(301\) 360.806 + 131.323i 1.19869 + 0.436287i
\(302\) 0 0
\(303\) −10.7142 + 9.51612i −0.0353604 + 0.0314063i
\(304\) 0 0
\(305\) 363.957 + 210.131i 1.19330 + 0.688954i
\(306\) 0 0
\(307\) 288.668 + 499.988i 0.940286 + 1.62862i 0.764925 + 0.644120i \(0.222776\pi\)
0.175362 + 0.984504i \(0.443890\pi\)
\(308\) 0 0
\(309\) −190.796 103.117i −0.617463 0.333711i
\(310\) 0 0
\(311\) −442.280 + 77.9859i −1.42212 + 0.250759i −0.831202 0.555971i \(-0.812347\pi\)
−0.590921 + 0.806730i \(0.701235\pi\)
\(312\) 0 0
\(313\) 8.30206 + 6.96625i 0.0265241 + 0.0222564i 0.655953 0.754801i \(-0.272267\pi\)
−0.629429 + 0.777058i \(0.716711\pi\)
\(314\) 0 0
\(315\) −496.830 + 116.728i −1.57724 + 0.370566i
\(316\) 0 0
\(317\) −74.6402 205.072i −0.235458 0.646916i −0.999997 0.00233841i \(-0.999256\pi\)
0.764539 0.644577i \(-0.222967\pi\)
\(318\) 0 0
\(319\) 228.146 191.437i 0.715191 0.600117i
\(320\) 0 0
\(321\) −441.051 + 174.721i −1.37399 + 0.544302i
\(322\) 0 0
\(323\) 14.2846i 0.0442249i
\(324\) 0 0
\(325\) −44.6700 −0.137446
\(326\) 0 0
\(327\) 20.5277 + 51.8186i 0.0627760 + 0.158467i
\(328\) 0 0
\(329\) −83.9620 100.062i −0.255204 0.304140i
\(330\) 0 0
\(331\) 564.453 205.444i 1.70530 0.620677i 0.708885 0.705324i \(-0.249198\pi\)
0.996411 + 0.0846470i \(0.0269763\pi\)
\(332\) 0 0
\(333\) 152.140 + 45.8713i 0.456878 + 0.137752i
\(334\) 0 0
\(335\) 336.061 400.502i 1.00317 1.19553i
\(336\) 0 0
\(337\) 78.0147 + 442.443i 0.231498 + 1.31289i 0.849865 + 0.527000i \(0.176683\pi\)
−0.618368 + 0.785889i \(0.712206\pi\)
\(338\) 0 0
\(339\) −25.6978 + 47.5485i −0.0758047 + 0.140261i
\(340\) 0 0
\(341\) 224.988 129.897i 0.659789 0.380929i
\(342\) 0 0
\(343\) −68.3305 + 118.352i −0.199214 + 0.345049i
\(344\) 0 0
\(345\) −213.490 240.368i −0.618811 0.696719i
\(346\) 0 0
\(347\) 80.7717 221.918i 0.232771 0.639534i −0.767227 0.641376i \(-0.778364\pi\)
0.999998 + 0.00184170i \(0.000586231\pi\)
\(348\) 0 0
\(349\) 41.6381 236.141i 0.119307 0.676622i −0.865221 0.501391i \(-0.832822\pi\)
0.984527 0.175231i \(-0.0560672\pi\)
\(350\) 0 0
\(351\) −79.3531 + 292.722i −0.226077 + 0.833967i
\(352\) 0 0
\(353\) 25.2020 + 4.44379i 0.0713937 + 0.0125886i 0.209231 0.977866i \(-0.432904\pi\)
−0.137837 + 0.990455i \(0.544015\pi\)
\(354\) 0 0
\(355\) 615.423 + 223.996i 1.73359 + 0.630974i
\(356\) 0 0
\(357\) 94.7544 + 31.5007i 0.265418 + 0.0882374i
\(358\) 0 0
\(359\) −16.7796 9.68773i −0.0467399 0.0269853i 0.476448 0.879203i \(-0.341924\pi\)
−0.523188 + 0.852217i \(0.675257\pi\)
\(360\) 0 0
\(361\) 170.280 + 294.934i 0.471690 + 0.816992i
\(362\) 0 0
\(363\) −43.2308 + 26.6070i −0.119093 + 0.0732976i
\(364\) 0 0
\(365\) 483.159 85.1939i 1.32372 0.233408i
\(366\) 0 0
\(367\) −299.305 251.147i −0.815545 0.684324i 0.136379 0.990657i \(-0.456453\pi\)
−0.951924 + 0.306333i \(0.900898\pi\)
\(368\) 0 0
\(369\) 67.0585 89.7095i 0.181730 0.243115i
\(370\) 0 0
\(371\) −304.886 837.669i −0.821796 2.25787i
\(372\) 0 0
\(373\) −136.986 + 114.945i −0.367255 + 0.308164i −0.807675 0.589628i \(-0.799274\pi\)
0.440419 + 0.897792i \(0.354830\pi\)
\(374\) 0 0
\(375\) 266.108 + 210.833i 0.709621 + 0.562221i
\(376\) 0 0
\(377\) 284.862i 0.755603i
\(378\) 0 0
\(379\) −3.48118 −0.00918518 −0.00459259 0.999989i \(-0.501462\pi\)
−0.00459259 + 0.999989i \(0.501462\pi\)
\(380\) 0 0
\(381\) 463.626 + 68.3730i 1.21687 + 0.179457i
\(382\) 0 0
\(383\) −11.0730 13.1963i −0.0289112 0.0344550i 0.751395 0.659853i \(-0.229381\pi\)
−0.780306 + 0.625398i \(0.784937\pi\)
\(384\) 0 0
\(385\) 625.797 227.772i 1.62545 0.591615i
\(386\) 0 0
\(387\) 327.518 18.4350i 0.846299 0.0476356i
\(388\) 0 0
\(389\) 203.618 242.662i 0.523439 0.623810i −0.437952 0.898999i \(-0.644296\pi\)
0.961390 + 0.275189i \(0.0887403\pi\)
\(390\) 0 0
\(391\) 10.9225 + 61.9446i 0.0279348 + 0.158426i
\(392\) 0 0
\(393\) 295.440 8.30814i 0.751756 0.0211403i
\(394\) 0 0
\(395\) −95.0446 + 54.8740i −0.240619 + 0.138922i
\(396\) 0 0
\(397\) −134.041 + 232.165i −0.337634 + 0.584800i −0.983987 0.178239i \(-0.942960\pi\)
0.646353 + 0.763039i \(0.276293\pi\)
\(398\) 0 0
\(399\) −139.955 + 28.7560i −0.350763 + 0.0720703i
\(400\) 0 0
\(401\) 33.3356 91.5887i 0.0831311 0.228401i −0.891162 0.453685i \(-0.850109\pi\)
0.974293 + 0.225285i \(0.0723312\pi\)
\(402\) 0 0
\(403\) −43.1494 + 244.712i −0.107070 + 0.607227i
\(404\) 0 0
\(405\) −350.757 + 259.009i −0.866067 + 0.639528i
\(406\) 0 0
\(407\) −204.203 36.0065i −0.501727 0.0884680i
\(408\) 0 0
\(409\) 380.898 + 138.636i 0.931292 + 0.338962i 0.762721 0.646727i \(-0.223863\pi\)
0.168570 + 0.985690i \(0.446085\pi\)
\(410\) 0 0
\(411\) 39.6426 + 192.939i 0.0964539 + 0.469437i
\(412\) 0 0
\(413\) −622.862 359.609i −1.50814 0.870725i
\(414\) 0 0
\(415\) 85.0569 + 147.323i 0.204956 + 0.354995i
\(416\) 0 0
\(417\) 10.5666 + 375.753i 0.0253397 + 0.901087i
\(418\) 0 0
\(419\) −115.552 + 20.3750i −0.275781 + 0.0486277i −0.309828 0.950793i \(-0.600272\pi\)
0.0340470 + 0.999420i \(0.489160\pi\)
\(420\) 0 0
\(421\) −399.365 335.107i −0.948610 0.795979i 0.0304527 0.999536i \(-0.490305\pi\)
−0.979063 + 0.203558i \(0.934750\pi\)
\(422\) 0 0
\(423\) −99.6282 50.2787i −0.235528 0.118862i
\(424\) 0 0
\(425\) 4.29744 + 11.8071i 0.0101116 + 0.0277814i
\(426\) 0 0
\(427\) 630.025 528.654i 1.47547 1.23806i
\(428\) 0 0
\(429\) 57.7393 391.521i 0.134591 0.912636i
\(430\) 0 0
\(431\) 263.580i 0.611555i 0.952103 + 0.305777i \(0.0989163\pi\)
−0.952103 + 0.305777i \(0.901084\pi\)
\(432\) 0 0
\(433\) −702.013 −1.62128 −0.810639 0.585547i \(-0.800880\pi\)
−0.810639 + 0.585547i \(0.800880\pi\)
\(434\) 0 0
\(435\) −254.321 + 320.997i −0.584645 + 0.737924i
\(436\) 0 0
\(437\) −57.8526 68.9461i −0.132386 0.157771i
\(438\) 0 0
\(439\) −416.204 + 151.486i −0.948073 + 0.345070i −0.769349 0.638829i \(-0.779419\pi\)
−0.178724 + 0.983899i \(0.557197\pi\)
\(440\) 0 0
\(441\) −65.8317 + 553.857i −0.149278 + 1.25591i
\(442\) 0 0
\(443\) 390.071 464.868i 0.880520 1.04936i −0.117891 0.993026i \(-0.537613\pi\)
0.998412 0.0563369i \(-0.0179421\pi\)
\(444\) 0 0
\(445\) −64.5191 365.906i −0.144987 0.822260i
\(446\) 0 0
\(447\) −317.250 515.464i −0.709731 1.15316i
\(448\) 0 0
\(449\) 347.745 200.771i 0.774488 0.447151i −0.0599853 0.998199i \(-0.519105\pi\)
0.834473 + 0.551048i \(0.185772\pi\)
\(450\) 0 0
\(451\) −73.0755 + 126.570i −0.162030 + 0.280644i
\(452\) 0 0
\(453\) −121.274 + 364.791i −0.267712 + 0.805279i
\(454\) 0 0
\(455\) −217.859 + 598.563i −0.478811 + 1.31552i
\(456\) 0 0
\(457\) −25.5458 + 144.878i −0.0558990 + 0.317019i −0.999917 0.0128747i \(-0.995902\pi\)
0.944018 + 0.329894i \(0.107013\pi\)
\(458\) 0 0
\(459\) 85.0061 7.18658i 0.185198 0.0156570i
\(460\) 0 0
\(461\) −773.480 136.385i −1.67783 0.295847i −0.747963 0.663740i \(-0.768968\pi\)
−0.929868 + 0.367893i \(0.880079\pi\)
\(462\) 0 0
\(463\) −336.835 122.598i −0.727506 0.264791i −0.0483975 0.998828i \(-0.515411\pi\)
−0.679109 + 0.734037i \(0.737634\pi\)
\(464\) 0 0
\(465\) −267.098 + 237.231i −0.574405 + 0.510174i
\(466\) 0 0
\(467\) 88.2727 + 50.9643i 0.189021 + 0.109131i 0.591524 0.806287i \(-0.298526\pi\)
−0.402503 + 0.915419i \(0.631860\pi\)
\(468\) 0 0
\(469\) −511.569 886.063i −1.09077 1.88926i
\(470\) 0 0
\(471\) 366.709 + 198.189i 0.778575 + 0.420784i
\(472\) 0 0
\(473\) −421.547 + 74.3300i −0.891219 + 0.157146i
\(474\) 0 0
\(475\) −13.7726 11.5566i −0.0289949 0.0243296i
\(476\) 0 0
\(477\) −521.553 554.978i −1.09340 1.16348i
\(478\) 0 0
\(479\) −43.2210 118.749i −0.0902318 0.247910i 0.886365 0.462986i \(-0.153222\pi\)
−0.976597 + 0.215077i \(0.931000\pi\)
\(480\) 0 0
\(481\) 151.929 127.483i 0.315860 0.265038i
\(482\) 0 0
\(483\) −584.918 + 231.713i −1.21101 + 0.479737i
\(484\) 0 0
\(485\) 429.586i 0.885745i
\(486\) 0 0
\(487\) −454.010 −0.932258 −0.466129 0.884717i \(-0.654352\pi\)
−0.466129 + 0.884717i \(0.654352\pi\)
\(488\) 0 0
\(489\) 44.0379 + 111.166i 0.0900571 + 0.227333i
\(490\) 0 0
\(491\) −203.177 242.137i −0.413803 0.493151i 0.518374 0.855154i \(-0.326537\pi\)
−0.932177 + 0.362003i \(0.882093\pi\)
\(492\) 0 0
\(493\) 75.2944 27.4049i 0.152727 0.0555881i
\(494\) 0 0
\(495\) 414.607 389.637i 0.837591 0.787145i
\(496\) 0 0
\(497\) 823.833 981.806i 1.65761 1.97547i
\(498\) 0 0
\(499\) −21.2323 120.414i −0.0425497 0.241312i 0.956114 0.292996i \(-0.0946522\pi\)
−0.998663 + 0.0516842i \(0.983541\pi\)
\(500\) 0 0
\(501\) 236.711 437.985i 0.472477 0.874222i
\(502\) 0 0
\(503\) 391.041 225.768i 0.777418 0.448843i −0.0580963 0.998311i \(-0.518503\pi\)
0.835515 + 0.549468i \(0.185170\pi\)
\(504\) 0 0
\(505\) −12.8565 + 22.2680i −0.0254583 + 0.0440951i
\(506\) 0 0
\(507\) −85.3113 96.0519i −0.168267 0.189452i
\(508\) 0 0
\(509\) −170.911 + 469.573i −0.335778 + 0.922541i 0.650800 + 0.759249i \(0.274434\pi\)
−0.986578 + 0.163292i \(0.947789\pi\)
\(510\) 0 0
\(511\) 166.722 945.527i 0.326266 1.85035i
\(512\) 0 0
\(513\) −100.196 + 69.7223i −0.195314 + 0.135911i
\(514\) 0 0
\(515\) −383.240 67.5756i −0.744156 0.131215i
\(516\) 0 0
\(517\) 136.838 + 49.8051i 0.264678 + 0.0963348i
\(518\) 0 0
\(519\) 31.0022 + 10.3066i 0.0597344 + 0.0198585i
\(520\) 0 0
\(521\) −595.632 343.888i −1.14325 0.660054i −0.196015 0.980601i \(-0.562800\pi\)
−0.947233 + 0.320546i \(0.896133\pi\)
\(522\) 0 0
\(523\) −260.218 450.711i −0.497549 0.861780i 0.502447 0.864608i \(-0.332433\pi\)
−0.999996 + 0.00282784i \(0.999100\pi\)
\(524\) 0 0
\(525\) −107.030 + 65.8730i −0.203866 + 0.125472i
\(526\) 0 0
\(527\) 68.8332 12.1372i 0.130613 0.0230306i
\(528\) 0 0
\(529\) 101.644 + 85.2896i 0.192144 + 0.161228i
\(530\) 0 0
\(531\) −610.167 72.5247i −1.14909 0.136581i
\(532\) 0 0
\(533\) −47.8111 131.360i −0.0897020 0.246454i
\(534\) 0 0
\(535\) −652.079 + 547.160i −1.21884 + 1.02273i
\(536\) 0 0
\(537\) −664.465 526.444i −1.23736 0.980343i
\(538\) 0 0
\(539\) 727.808i 1.35029i
\(540\) 0 0
\(541\) 803.120 1.48451 0.742255 0.670117i \(-0.233756\pi\)
0.742255 + 0.670117i \(0.233756\pi\)
\(542\) 0 0
\(543\) −322.905 47.6203i −0.594668 0.0876984i
\(544\) 0 0
\(545\) 64.2851 + 76.6120i 0.117954 + 0.140572i
\(546\) 0 0
\(547\) −64.5461 + 23.4929i −0.118000 + 0.0429486i −0.400345 0.916364i \(-0.631110\pi\)
0.282345 + 0.959313i \(0.408888\pi\)
\(548\) 0 0
\(549\) 316.572 627.293i 0.576633 1.14261i
\(550\) 0 0
\(551\) −73.6967 + 87.8283i −0.133751 + 0.159398i
\(552\) 0 0
\(553\) 37.2950 + 211.511i 0.0674412 + 0.382478i
\(554\) 0 0
\(555\) 285.016 8.01501i 0.513543 0.0144415i
\(556\) 0 0
\(557\) 575.120 332.045i 1.03253 0.596132i 0.114822 0.993386i \(-0.463370\pi\)
0.917709 + 0.397254i \(0.130037\pi\)
\(558\) 0 0
\(559\) 204.710 354.569i 0.366208 0.634291i
\(560\) 0 0
\(561\) −109.041 + 22.4043i −0.194369 + 0.0399364i
\(562\) 0 0
\(563\) 118.905 326.689i 0.211199 0.580264i −0.788182 0.615442i \(-0.788978\pi\)
0.999381 + 0.0351778i \(0.0111997\pi\)
\(564\) 0 0
\(565\) −16.8406 + 95.5076i −0.0298063 + 0.169040i
\(566\) 0 0
\(567\) 241.535 + 818.385i 0.425987 + 1.44336i
\(568\) 0 0
\(569\) −385.078 67.8997i −0.676763 0.119332i −0.175306 0.984514i \(-0.556091\pi\)
−0.501457 + 0.865182i \(0.667203\pi\)
\(570\) 0 0
\(571\) 804.118 + 292.675i 1.40826 + 0.512566i 0.930620 0.365988i \(-0.119269\pi\)
0.477644 + 0.878554i \(0.341491\pi\)
\(572\) 0 0
\(573\) 65.5891 + 319.219i 0.114466 + 0.557102i
\(574\) 0 0
\(575\) −68.5606 39.5835i −0.119236 0.0688408i
\(576\) 0 0
\(577\) 313.746 + 543.423i 0.543753 + 0.941808i 0.998684 + 0.0512815i \(0.0163306\pi\)
−0.454931 + 0.890527i \(0.650336\pi\)
\(578\) 0 0
\(579\) 16.8752 + 600.087i 0.0291454 + 1.03642i
\(580\) 0 0
\(581\) 327.850 57.8088i 0.564285 0.0994987i
\(582\) 0 0
\(583\) 761.285 + 638.794i 1.30581 + 1.09570i
\(584\) 0 0
\(585\) 30.5829 + 543.339i 0.0522785 + 0.928785i
\(586\) 0 0
\(587\) 254.654 + 699.655i 0.433822 + 1.19192i 0.943448 + 0.331520i \(0.107561\pi\)
−0.509626 + 0.860396i \(0.670216\pi\)
\(588\) 0 0
\(589\) −76.6133 + 64.2862i −0.130073 + 0.109145i
\(590\) 0 0
\(591\) 128.116 868.733i 0.216778 1.46994i
\(592\) 0 0
\(593\) 625.722i 1.05518i 0.849499 + 0.527591i \(0.176904\pi\)
−0.849499 + 0.527591i \(0.823096\pi\)
\(594\) 0 0
\(595\) 179.170 0.301126
\(596\) 0 0
\(597\) −153.343 + 193.546i −0.256856 + 0.324197i
\(598\) 0 0
\(599\) 368.344 + 438.975i 0.614932 + 0.732847i 0.980190 0.198059i \(-0.0634638\pi\)
−0.365258 + 0.930906i \(0.619019\pi\)
\(600\) 0 0
\(601\) −1063.24 + 386.989i −1.76912 + 0.643908i −0.769134 + 0.639088i \(0.779312\pi\)
−0.999988 + 0.00482034i \(0.998466\pi\)
\(602\) 0 0
\(603\) −700.128 523.351i −1.16107 0.867912i
\(604\) 0 0
\(605\) −58.5483 + 69.7752i −0.0967741 + 0.115331i
\(606\) 0 0
\(607\) 40.3687 + 228.942i 0.0665052 + 0.377170i 0.999835 + 0.0181503i \(0.00577772\pi\)
−0.933330 + 0.359019i \(0.883111\pi\)
\(608\) 0 0
\(609\) 420.075 + 682.533i 0.689778 + 1.12074i
\(610\) 0 0
\(611\) −120.623 + 69.6414i −0.197418 + 0.113979i
\(612\) 0 0
\(613\) 533.889 924.724i 0.870945 1.50852i 0.00992514 0.999951i \(-0.496841\pi\)
0.861020 0.508571i \(-0.169826\pi\)
\(614\) 0 0
\(615\) 63.4002 190.708i 0.103090 0.310095i
\(616\) 0 0
\(617\) 144.247 396.317i 0.233788 0.642328i −0.766212 0.642588i \(-0.777861\pi\)
1.00000 0.000260046i \(8.27751e-5\pi\)
\(618\) 0 0
\(619\) −104.335 + 591.711i −0.168554 + 0.955915i 0.776771 + 0.629783i \(0.216856\pi\)
−0.945324 + 0.326131i \(0.894255\pi\)
\(620\) 0 0
\(621\) −381.184 + 378.960i −0.613823 + 0.610242i
\(622\) 0 0
\(623\) −716.066 126.262i −1.14938 0.202667i
\(624\) 0 0
\(625\) 665.870 + 242.357i 1.06539 + 0.387771i
\(626\) 0 0
\(627\) 119.092 105.775i 0.189940 0.168701i
\(628\) 0 0
\(629\) −48.3124 27.8932i −0.0768083 0.0443453i
\(630\) 0 0
\(631\) −554.621 960.632i −0.878956 1.52240i −0.852488 0.522747i \(-0.824907\pi\)
−0.0264679 0.999650i \(-0.508426\pi\)
\(632\) 0 0
\(633\) 305.740 + 165.239i 0.483002 + 0.261040i
\(634\) 0 0
\(635\) 828.122 146.020i 1.30413 0.229953i
\(636\) 0 0
\(637\) 533.269 + 447.466i 0.837157 + 0.702458i
\(638\) 0 0
\(639\) 316.089 1048.36i 0.494661 1.64063i
\(640\) 0 0
\(641\) −56.5257 155.303i −0.0881837 0.242283i 0.887760 0.460308i \(-0.152261\pi\)
−0.975943 + 0.218025i \(0.930039\pi\)
\(642\) 0 0
\(643\) −608.717 + 510.774i −0.946683 + 0.794361i −0.978736 0.205125i \(-0.934240\pi\)
0.0320527 + 0.999486i \(0.489796\pi\)
\(644\) 0 0
\(645\) 547.231 216.784i 0.848421 0.336099i
\(646\) 0 0
\(647\) 222.504i 0.343900i −0.985106 0.171950i \(-0.944993\pi\)
0.985106 0.171950i \(-0.0550068\pi\)
\(648\) 0 0
\(649\) 801.803 1.23544
\(650\) 0 0
\(651\) 257.481 + 649.964i 0.395516 + 0.998409i
\(652\) 0 0
\(653\) −299.851 357.348i −0.459190 0.547241i 0.485916 0.874006i \(-0.338486\pi\)
−0.945106 + 0.326764i \(0.894042\pi\)
\(654\) 0 0
\(655\) 498.345 181.383i 0.760833 0.276920i
\(656\) 0 0
\(657\) −187.610 798.526i −0.285556 1.21541i
\(658\) 0 0
\(659\) 133.876 159.547i 0.203150 0.242104i −0.654845 0.755764i \(-0.727266\pi\)
0.857994 + 0.513659i \(0.171710\pi\)
\(660\) 0 0
\(661\) −110.055 624.153i −0.166498 0.944256i −0.947507 0.319736i \(-0.896406\pi\)
0.781009 0.624520i \(-0.214705\pi\)
\(662\) 0 0
\(663\) 50.6241 93.6695i 0.0763561 0.141281i
\(664\) 0 0
\(665\) −222.024 + 128.186i −0.333871 + 0.192760i
\(666\) 0 0
\(667\) −252.425 + 437.214i −0.378449 + 0.655493i
\(668\) 0 0
\(669\) 394.926 + 444.647i 0.590323 + 0.664645i
\(670\) 0 0
\(671\) −313.590 + 861.581i −0.467347 + 1.28403i
\(672\) 0 0
\(673\) 19.1049 108.349i 0.0283877 0.160994i −0.967319 0.253564i \(-0.918397\pi\)
0.995706 + 0.0925699i \(0.0295082\pi\)
\(674\) 0 0
\(675\) −61.8427 + 87.7730i −0.0916188 + 0.130034i
\(676\) 0 0
\(677\) −140.866 24.8384i −0.208073 0.0366890i 0.0686398 0.997642i \(-0.478134\pi\)
−0.276713 + 0.960953i \(0.589245\pi\)
\(678\) 0 0
\(679\) 789.987 + 287.532i 1.16346 + 0.423463i
\(680\) 0 0
\(681\) −14.6663 4.87577i −0.0215365 0.00715972i
\(682\) 0 0
\(683\) −784.050 452.671i −1.14795 0.662769i −0.199563 0.979885i \(-0.563952\pi\)
−0.948387 + 0.317116i \(0.897286\pi\)
\(684\) 0 0
\(685\) 176.714 + 306.078i 0.257977 + 0.446830i
\(686\) 0 0
\(687\) 902.761 555.617i 1.31406 0.808758i
\(688\) 0 0
\(689\) −936.096 + 165.059i −1.35863 + 0.239563i
\(690\) 0 0
\(691\) −407.543 341.969i −0.589788 0.494891i 0.298357 0.954454i \(-0.403561\pi\)
−0.888145 + 0.459564i \(0.848006\pi\)
\(692\) 0 0
\(693\) −439.016 1023.23i −0.633500 1.47653i
\(694\) 0 0
\(695\) 230.690 + 633.817i 0.331929 + 0.911967i
\(696\) 0 0
\(697\) −30.1213 + 25.2748i −0.0432156 + 0.0362622i
\(698\) 0 0
\(699\) −330.519 261.864i −0.472845 0.374627i
\(700\) 0 0
\(701\) 905.026i 1.29105i −0.763739 0.645525i \(-0.776639\pi\)
0.763739 0.645525i \(-0.223361\pi\)
\(702\) 0 0
\(703\) 79.8237 0.113547
\(704\) 0 0
\(705\) −198.098 29.2144i −0.280991 0.0414389i
\(706\) 0 0
\(707\) 32.3447 + 38.5469i 0.0457492 + 0.0545217i
\(708\) 0 0
\(709\) 341.922 124.450i 0.482260 0.175528i −0.0894380 0.995992i \(-0.528507\pi\)
0.571698 + 0.820464i \(0.306285\pi\)
\(710\) 0 0
\(711\) 100.531 + 153.501i 0.141393 + 0.215894i
\(712\) 0 0
\(713\) −283.074 + 337.355i −0.397019 + 0.473148i
\(714\) 0 0
\(715\) −123.311 699.329i −0.172462 0.978083i
\(716\) 0 0
\(717\) −442.846 + 12.4534i −0.617638 + 0.0173687i
\(718\) 0 0
\(719\) 389.328 224.778i 0.541485 0.312626i −0.204196 0.978930i \(-0.565458\pi\)
0.745680 + 0.666304i \(0.232125\pi\)
\(720\) 0 0
\(721\) −380.779 + 659.529i −0.528127 + 0.914742i
\(722\) 0 0
\(723\) −894.553 + 183.801i −1.23728 + 0.254220i
\(724\) 0 0
\(725\) −34.4922 + 94.7665i −0.0475754 + 0.130712i
\(726\) 0 0
\(727\) −100.606 + 570.564i −0.138385 + 0.784820i 0.834058 + 0.551677i \(0.186012\pi\)
−0.972443 + 0.233142i \(0.925099\pi\)
\(728\) 0 0
\(729\) 465.317 + 561.178i 0.638295 + 0.769792i
\(730\) 0 0
\(731\) −113.413 19.9978i −0.155148 0.0273568i
\(732\) 0 0
\(733\) −879.854 320.241i −1.20035 0.436891i −0.337002 0.941504i \(-0.609413\pi\)
−0.863345 + 0.504613i \(0.831635\pi\)
\(734\) 0 0
\(735\) 201.424 + 980.321i 0.274046 + 1.33377i
\(736\) 0 0
\(737\) 987.805 + 570.310i 1.34031 + 0.773826i
\(738\) 0 0
\(739\) 263.918 + 457.119i 0.357128 + 0.618564i 0.987480 0.157746i \(-0.0504227\pi\)
−0.630352 + 0.776310i \(0.717089\pi\)
\(740\) 0 0
\(741\) 4.28263 + 152.292i 0.00577953 + 0.205522i
\(742\) 0 0
\(743\) 36.2725 6.39582i 0.0488190 0.00860811i −0.149185 0.988809i \(-0.547665\pi\)
0.198004 + 0.980201i \(0.436554\pi\)
\(744\) 0 0
\(745\) −831.967 698.103i −1.11673 0.937051i
\(746\) 0 0
\(747\) 237.932 155.827i 0.318517 0.208603i
\(748\) 0 0
\(749\) 569.747 + 1565.37i 0.760677 + 2.08994i
\(750\) 0 0
\(751\) −75.4565 + 63.3155i −0.100475 + 0.0843082i −0.691641 0.722241i \(-0.743112\pi\)
0.591167 + 0.806550i \(0.298668\pi\)
\(752\) 0 0
\(753\) 54.6197 370.367i 0.0725362 0.491856i
\(754\) 0 0
\(755\) 689.781i 0.913617i
\(756\) 0 0
\(757\) −1385.09 −1.82971 −0.914857 0.403779i \(-0.867697\pi\)
−0.914857 + 0.403779i \(0.867697\pi\)
\(758\) 0 0
\(759\) 435.559 549.752i 0.573859 0.724310i
\(760\) 0 0
\(761\) 935.204 + 1114.53i 1.22891 + 1.46456i 0.839374 + 0.543555i \(0.182922\pi\)
0.389541 + 0.921009i \(0.372634\pi\)
\(762\) 0 0
\(763\) 183.913 66.9389i 0.241039 0.0877312i
\(764\) 0 0
\(765\) 140.672 60.3551i 0.183886 0.0788956i
\(766\) 0 0
\(767\) −492.959 + 587.486i −0.642711 + 0.765953i
\(768\) 0 0
\(769\) −17.3763 98.5458i −0.0225959 0.128148i 0.971423 0.237354i \(-0.0762802\pi\)
−0.994019 + 0.109206i \(0.965169\pi\)
\(770\) 0 0
\(771\) 718.654 + 1167.66i 0.932106 + 1.51448i
\(772\) 0 0
\(773\) −547.928 + 316.347i −0.708834 + 0.409245i −0.810629 0.585560i \(-0.800875\pi\)
0.101795 + 0.994805i \(0.467541\pi\)
\(774\) 0 0
\(775\) −43.9854 + 76.1850i −0.0567554 + 0.0983032i
\(776\) 0 0
\(777\) 176.029 529.495i 0.226549 0.681461i
\(778\) 0 0
\(779\) 19.2431 52.8699i 0.0247023 0.0678690i
\(780\) 0 0
\(781\) −248.112 + 1407.12i −0.317686 + 1.80168i
\(782\) 0 0
\(783\) 559.732 + 394.373i 0.714856 + 0.503670i
\(784\) 0 0
\(785\) 736.585 + 129.880i 0.938325 + 0.165452i
\(786\) 0 0
\(787\) −766.476 278.974i −0.973921 0.354478i −0.194447 0.980913i \(-0.562291\pi\)
−0.779474 + 0.626435i \(0.784513\pi\)
\(788\) 0 0
\(789\) 1049.61 932.244i 1.33031 1.18155i
\(790\) 0 0
\(791\) 164.362 + 94.8944i 0.207790 + 0.119968i
\(792\) 0 0
\(793\) −438.486 759.481i −0.552946 0.957731i
\(794\) 0 0
\(795\) −1202.20 649.735i −1.51220 0.817277i
\(796\) 0 0
\(797\) 1233.67 217.529i 1.54789 0.272934i 0.666564 0.745448i \(-0.267764\pi\)
0.881323 + 0.472514i \(0.156653\pi\)
\(798\) 0 0
\(799\) 30.0119 + 25.1830i 0.0375618 + 0.0315181i
\(800\) 0 0
\(801\) −604.740 + 142.081i −0.754981 + 0.177380i
\(802\) 0 0
\(803\) 366.084 + 1005.81i 0.455895 + 1.25256i
\(804\) 0 0
\(805\) −864.781 + 725.637i −1.07426 + 0.901413i
\(806\) 0 0
\(807\) −884.288 + 350.307i −1.09577 + 0.434086i
\(808\) 0 0
\(809\) 1021.88i 1.26313i 0.775321 + 0.631567i \(0.217588\pi\)
−0.775321 + 0.631567i \(0.782412\pi\)
\(810\) 0 0
\(811\) 365.788 0.451034 0.225517 0.974239i \(-0.427593\pi\)
0.225517 + 0.974239i \(0.427593\pi\)
\(812\) 0 0
\(813\) 127.835 + 322.696i 0.157239 + 0.396921i
\(814\) 0 0
\(815\) 137.910 + 164.355i 0.169215 + 0.201662i
\(816\) 0 0
\(817\) 154.846 56.3595i 0.189531 0.0689835i
\(818\) 0 0
\(819\) 1019.64 + 307.429i 1.24498 + 0.375371i
\(820\) 0 0
\(821\) −6.23245 + 7.42755i −0.00759129 + 0.00904695i −0.769827 0.638253i \(-0.779657\pi\)
0.762235 + 0.647300i \(0.224102\pi\)
\(822\) 0 0
\(823\) −0.155222 0.880308i −0.000188605 0.00106963i 0.984713 0.174183i \(-0.0557284\pi\)
−0.984902 + 0.173113i \(0.944617\pi\)
\(824\) 0 0
\(825\) 66.6153 123.258i 0.0807458 0.149403i
\(826\) 0 0
\(827\) 583.611 336.948i 0.705696 0.407434i −0.103769 0.994601i \(-0.533090\pi\)
0.809465 + 0.587168i \(0.199757\pi\)
\(828\) 0 0
\(829\) −14.4804 + 25.0808i −0.0174673 + 0.0302542i −0.874627 0.484797i \(-0.838894\pi\)
0.857160 + 0.515051i \(0.172227\pi\)
\(830\) 0 0
\(831\) −229.713 258.633i −0.276429 0.311231i
\(832\) 0 0
\(833\) 66.9709 184.001i 0.0803972 0.220890i
\(834\) 0 0
\(835\) 155.124 879.753i 0.185778 1.05360i
\(836\) 0 0
\(837\) 421.103 + 423.574i 0.503110 + 0.506062i
\(838\) 0 0
\(839\) −629.012 110.912i −0.749716 0.132195i −0.214282 0.976772i \(-0.568741\pi\)
−0.535434 + 0.844577i \(0.679852\pi\)
\(840\) 0 0
\(841\) −185.952 67.6809i −0.221108 0.0804767i
\(842\) 0 0
\(843\) 232.277 + 77.2195i 0.275536 + 0.0916008i
\(844\) 0 0
\(845\) −199.631 115.257i −0.236250 0.136399i
\(846\) 0 0
\(847\) 89.1253 + 154.370i 0.105225 + 0.182254i
\(848\) 0 0
\(849\) 1065.74 655.926i 1.25529 0.772587i
\(850\) 0 0
\(851\) 346.151 61.0358i 0.406758 0.0717225i
\(852\) 0 0
\(853\) 595.279 + 499.498i 0.697865 + 0.585578i 0.921165 0.389171i \(-0.127239\pi\)
−0.223300 + 0.974750i \(0.571683\pi\)
\(854\) 0 0
\(855\) −131.138 + 175.434i −0.153378 + 0.205185i
\(856\) 0 0
\(857\) 368.296 + 1011.88i 0.429750 + 1.18073i 0.945965 + 0.324269i \(0.105118\pi\)
−0.516215 + 0.856459i \(0.672659\pi\)
\(858\) 0 0
\(859\) 62.0374 52.0556i 0.0722205 0.0606002i −0.605963 0.795493i \(-0.707212\pi\)
0.678183 + 0.734893i \(0.262768\pi\)
\(860\) 0 0
\(861\) −308.267 244.235i −0.358034 0.283664i
\(862\) 0 0
\(863\) 1599.17i 1.85304i 0.376244 + 0.926520i \(0.377215\pi\)
−0.376244 + 0.926520i \(0.622785\pi\)
\(864\) 0 0
\(865\) 58.6217 0.0677708
\(866\) 0 0
\(867\) 828.094 + 122.123i 0.955126 + 0.140857i
\(868\) 0 0
\(869\) −153.906 183.418i −0.177107 0.211067i
\(870\) 0 0
\(871\) −1025.19 + 373.137i −1.17702 + 0.428400i
\(872\) 0 0
\(873\) 717.103 40.3635i 0.821423 0.0462354i
\(874\) 0 0
\(875\) 766.304 913.245i 0.875776 1.04371i
\(876\) 0 0
\(877\) −65.7402 372.831i −0.0749603 0.425121i −0.999075 0.0430055i \(-0.986307\pi\)
0.924115 0.382116i \(-0.124804\pi\)
\(878\) 0 0
\(879\) 1037.09 29.1642i 1.17985 0.0331789i
\(880\) 0 0
\(881\) −1046.81 + 604.374i −1.18820 + 0.686009i −0.957898 0.287109i \(-0.907306\pi\)
−0.230305 + 0.973119i \(0.573972\pi\)
\(882\) 0 0
\(883\) −298.144 + 516.401i −0.337649 + 0.584826i −0.983990 0.178223i \(-0.942965\pi\)
0.646341 + 0.763049i \(0.276298\pi\)
\(884\) 0 0
\(885\) −1079.99 + 221.902i −1.22033 + 0.250737i
\(886\) 0 0
\(887\) −34.7360 + 95.4364i −0.0391612 + 0.107595i −0.957732 0.287662i \(-0.907122\pi\)
0.918571 + 0.395256i \(0.129344\pi\)
\(888\) 0 0
\(889\) 285.757 1620.61i 0.321436 1.82296i
\(890\) 0 0
\(891\) −689.371 655.489i −0.773705 0.735678i
\(892\) 0 0
\(893\) −55.2071 9.73450i −0.0618220 0.0109009i
\(894\) 0 0
\(895\) −1429.39 520.255i −1.59708 0.581290i
\(896\) 0 0
\(897\) 135.019 + 657.131i 0.150523 + 0.732588i
\(898\) 0 0
\(899\) 485.835 + 280.497i 0.540417 + 0.312010i
\(900\) 0 0
\(901\) 133.684 + 231.548i 0.148373 + 0.256990i
\(902\) 0 0
\(903\) −32.3796 1151.43i −0.0358578 1.27511i
\(904\) 0 0
\(905\) −576.769 + 101.700i −0.637313 + 0.112376i
\(906\) 0 0
\(907\) −1321.91 1109.21i −1.45745 1.22295i −0.926906 0.375293i \(-0.877542\pi\)
−0.530547 0.847656i \(-0.678013\pi\)
\(908\) 0 0
\(909\) 38.3797 + 19.3688i 0.0422219 + 0.0213078i
\(910\) 0 0
\(911\) −106.953 293.850i −0.117401 0.322558i 0.867048 0.498224i \(-0.166014\pi\)
−0.984450 + 0.175666i \(0.943792\pi\)
\(912\) 0 0
\(913\) −284.305 + 238.560i −0.311396 + 0.261292i
\(914\) 0 0
\(915\) 183.944 1247.30i 0.201032 1.36316i
\(916\) 0 0
\(917\) 1037.84i 1.13177i
\(918\) 0 0
\(919\) −198.504 −0.216000 −0.108000 0.994151i \(-0.534445\pi\)
−0.108000 + 0.994151i \(0.534445\pi\)
\(920\) 0 0
\(921\) 1075.58 1357.57i 1.16784 1.47401i
\(922\) 0 0
\(923\) −878.459 1046.91i −0.951743 1.13424i
\(924\) 0 0
\(925\) 65.9791 24.0144i 0.0713287 0.0259615i
\(926\) 0 0
\(927\) −76.7941 + 646.087i −0.0828416 + 0.696966i
\(928\) 0 0
\(929\) 854.746 1018.65i 0.920071 1.09650i −0.0749849 0.997185i \(-0.523891\pi\)
0.995056 0.0993136i \(-0.0316647\pi\)
\(930\) 0 0
\(931\) 48.6528 + 275.924i 0.0522587 + 0.296374i
\(932\) 0 0
\(933\) 706.187 + 1147.41i 0.756899 + 1.22980i
\(934\) 0 0
\(935\) −172.983 + 99.8717i −0.185008 + 0.106815i
\(936\) 0 0
\(937\) −675.671 + 1170.30i −0.721100 + 1.24898i 0.239459 + 0.970906i \(0.423030\pi\)
−0.960559 + 0.278076i \(0.910303\pi\)
\(938\) 0 0
\(939\) 10.2568 30.8524i 0.0109231 0.0328567i
\(940\) 0 0
\(941\) 265.840 730.391i 0.282508 0.776186i −0.714553 0.699581i \(-0.753370\pi\)
0.997062 0.0766044i \(-0.0244078\pi\)
\(942\) 0 0
\(943\) 43.0206 243.982i 0.0456210 0.258729i
\(944\) 0 0
\(945\) 874.517 + 1256.75i 0.925415 + 1.32989i
\(946\) 0 0
\(947\) 270.124 + 47.6301i 0.285242 + 0.0502958i 0.314438 0.949278i \(-0.398184\pi\)
−0.0291967 + 0.999574i \(0.509295\pi\)
\(948\) 0 0
\(949\) −962.034 350.152i −1.01373 0.368969i
\(950\) 0 0
\(951\) −489.501 + 434.765i −0.514723 + 0.457166i
\(952\) 0 0
\(953\) 858.313 + 495.548i 0.900644 + 0.519987i 0.877409 0.479743i \(-0.159270\pi\)
0.0232347 + 0.999730i \(0.492603\pi\)
\(954\) 0 0
\(955\) 292.376 + 506.410i 0.306153 + 0.530272i
\(956\) 0 0
\(957\) −786.020 424.808i −0.821338 0.443896i
\(958\) 0 0
\(959\) 681.141 120.104i 0.710262 0.125238i
\(960\) 0 0
\(961\) −361.298 303.165i −0.375961 0.315468i
\(962\) 0 0
\(963\) 974.635 + 1037.10i 1.01208 + 1.07694i
\(964\) 0 0
\(965\) 368.418 + 1012.22i 0.381780 + 1.04893i
\(966\) 0 0
\(967\) −239.352 + 200.840i −0.247520 + 0.207694i −0.758104 0.652134i \(-0.773874\pi\)
0.510583 + 0.859828i \(0.329429\pi\)
\(968\) 0 0
\(969\) 39.8416 15.7831i 0.0411162 0.0162880i
\(970\) 0 0
\(971\) 487.838i 0.502407i −0.967934 0.251204i \(-0.919174\pi\)
0.967934 0.251204i \(-0.0808264\pi\)
\(972\) 0 0
\(973\) 1319.96 1.35659
\(974\) 0 0
\(975\) 49.3558 + 124.590i 0.0506214 + 0.127785i
\(976\) 0 0
\(977\) −413.839 493.194i −0.423582 0.504805i 0.511478 0.859297i \(-0.329098\pi\)
−0.935059 + 0.354492i \(0.884654\pi\)
\(978\) 0 0
\(979\) 761.718 277.243i 0.778057 0.283190i
\(980\) 0 0
\(981\) 121.847 114.509i 0.124207 0.116726i
\(982\) 0 0
\(983\) 989.779 1179.57i 1.00690 1.19997i 0.0271699 0.999631i \(-0.491350\pi\)
0.979726 0.200341i \(-0.0642051\pi\)
\(984\) 0 0
\(985\) −273.610 1551.72i −0.277777 1.57535i
\(986\) 0 0
\(987\) −186.316 + 344.739i −0.188770 + 0.349279i
\(988\) 0 0
\(989\) 628.389 362.801i 0.635378 0.366836i
\(990\) 0 0
\(991\) 155.571 269.456i 0.156984 0.271903i −0.776796 0.629752i \(-0.783156\pi\)
0.933780 + 0.357849i \(0.116490\pi\)
\(992\) 0 0
\(993\) −1196.67 1347.33i −1.20511 1.35683i
\(994\) 0 0
\(995\) −151.540 + 416.352i −0.152301 + 0.418445i
\(996\) 0 0
\(997\) −8.37502 + 47.4971i −0.00840022 + 0.0476400i −0.988720 0.149777i \(-0.952144\pi\)
0.980320 + 0.197417i \(0.0632554\pi\)
\(998\) 0 0
\(999\) −40.1592 475.021i −0.0401994 0.475496i
Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (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 432.3.bc.a.353.3 30
4.3 odd 2 27.3.f.a.2.4 30
12.11 even 2 81.3.f.a.8.2 30
27.14 odd 18 inner 432.3.bc.a.257.3 30
36.7 odd 6 243.3.f.c.188.2 30
36.11 even 6 243.3.f.b.188.4 30
36.23 even 6 243.3.f.a.107.4 30
36.31 odd 6 243.3.f.d.107.2 30
108.11 even 18 729.3.b.a.728.12 30
108.23 even 18 243.3.f.d.134.2 30
108.31 odd 18 243.3.f.a.134.4 30
108.43 odd 18 729.3.b.a.728.19 30
108.59 even 18 243.3.f.c.53.2 30
108.67 odd 18 81.3.f.a.71.2 30
108.95 even 18 27.3.f.a.14.4 yes 30
108.103 odd 18 243.3.f.b.53.4 30
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
27.3.f.a.2.4 30 4.3 odd 2
27.3.f.a.14.4 yes 30 108.95 even 18
81.3.f.a.8.2 30 12.11 even 2
81.3.f.a.71.2 30 108.67 odd 18
243.3.f.a.107.4 30 36.23 even 6
243.3.f.a.134.4 30 108.31 odd 18
243.3.f.b.53.4 30 108.103 odd 18
243.3.f.b.188.4 30 36.11 even 6
243.3.f.c.53.2 30 108.59 even 18
243.3.f.c.188.2 30 36.7 odd 6
243.3.f.d.107.2 30 36.31 odd 6
243.3.f.d.134.2 30 108.23 even 18
432.3.bc.a.257.3 30 27.14 odd 18 inner
432.3.bc.a.353.3 30 1.1 even 1 trivial
729.3.b.a.728.12 30 108.11 even 18
729.3.b.a.728.19 30 108.43 odd 18