Properties

Label 1008.2.ca.d.353.7
Level $1008$
Weight $2$
Character 1008.353
Analytic conductor $8.049$
Analytic rank $0$
Dimension $16$
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [1008,2,Mod(257,1008)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1008, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([0, 0, 5, 5]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("1008.257");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1008 = 2^{4} \cdot 3^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1008.ca (of order \(6\), degree \(2\), not minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(8.04892052375\)
Analytic rank: \(0\)
Dimension: \(16\)
Relative dimension: \(8\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{16} - 2 x^{15} + 5 x^{14} - 17 x^{13} + 22 x^{12} - 31 x^{11} + 62 x^{10} - 52 x^{9} + 52 x^{8} + \cdots + 6561 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 3^{4} \)
Twist minimal: no (minimal twist has level 252)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 353.7
Root \(-1.61108 + 0.635951i\) of defining polynomial
Character \(\chi\) \(=\) 1008.353
Dual form 1008.2.ca.d.257.7

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(1.43204 - 0.974295i) q^{3} +(1.09150 - 1.89054i) q^{5} +(1.25859 + 2.32722i) q^{7} +(1.10150 - 2.79047i) q^{9} +(1.26889 - 0.732592i) q^{11} +(2.92752 - 1.69021i) q^{13} +(-0.278862 - 3.77077i) q^{15} +(1.32136 - 2.28866i) q^{17} +(-6.87816 + 3.97111i) q^{19} +(4.06975 + 2.10644i) q^{21} +(3.47245 + 2.00482i) q^{23} +(0.117249 + 0.203081i) q^{25} +(-1.14134 - 5.06925i) q^{27} +(-6.71261 - 3.87553i) q^{29} -0.706968i q^{31} +(1.10334 - 2.28537i) q^{33} +(5.77345 + 0.160752i) q^{35} +(1.41738 + 2.45498i) q^{37} +(2.54558 - 5.27272i) q^{39} +(3.74173 + 6.48086i) q^{41} +(1.27112 - 2.20164i) q^{43} +(-4.07319 - 5.12822i) q^{45} +12.5508 q^{47} +(-3.83190 + 5.85803i) q^{49} +(-0.337586 - 4.56485i) q^{51} +(-2.41675 - 1.39531i) q^{53} -3.19850i q^{55} +(-5.98079 + 12.3881i) q^{57} -13.4330 q^{59} -7.79493i q^{61} +(7.88036 - 0.948624i) q^{63} -7.37945i q^{65} -5.84058 q^{67} +(6.92598 - 0.512200i) q^{69} -11.6854i q^{71} +(-3.95924 - 2.28587i) q^{73} +(0.365767 + 0.176586i) q^{75} +(3.30191 + 2.03094i) q^{77} -9.38377 q^{79} +(-6.57340 - 6.14739i) q^{81} +(-1.70847 + 2.95917i) q^{83} +(-2.88452 - 4.99614i) q^{85} +(-13.3887 + 0.990137i) q^{87} +(4.61937 + 8.00099i) q^{89} +(7.61803 + 4.68571i) q^{91} +(-0.688796 - 1.01241i) q^{93} +17.3379i q^{95} +(6.38394 + 3.68577i) q^{97} +(-0.646596 - 4.34773i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16 q + q^{7} + 6 q^{9} + 6 q^{11} - 3 q^{13} + 3 q^{15} + 9 q^{17} + 6 q^{21} - 21 q^{23} - 8 q^{25} - 9 q^{27} + 6 q^{29} + 15 q^{35} + q^{37} + 3 q^{39} - 6 q^{41} + 2 q^{43} - 30 q^{45} + 36 q^{47}+ \cdots + 9 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1008\mathbb{Z}\right)^\times\).

\(n\) \(127\) \(577\) \(757\) \(785\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{6}\right)\) \(1\) \(e\left(\frac{1}{6}\right)\)

Coefficient data

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



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
\(3\) 1.43204 0.974295i 0.826791 0.562509i
\(4\) 0 0
\(5\) 1.09150 1.89054i 0.488134 0.845473i −0.511773 0.859121i \(-0.671011\pi\)
0.999907 + 0.0136476i \(0.00434429\pi\)
\(6\) 0 0
\(7\) 1.25859 + 2.32722i 0.475703 + 0.879606i
\(8\) 0 0
\(9\) 1.10150 2.79047i 0.367166 0.930155i
\(10\) 0 0
\(11\) 1.26889 0.732592i 0.382584 0.220885i −0.296358 0.955077i \(-0.595772\pi\)
0.678942 + 0.734192i \(0.262439\pi\)
\(12\) 0 0
\(13\) 2.92752 1.69021i 0.811948 0.468779i −0.0356837 0.999363i \(-0.511361\pi\)
0.847632 + 0.530585i \(0.178028\pi\)
\(14\) 0 0
\(15\) −0.278862 3.77077i −0.0720017 0.973610i
\(16\) 0 0
\(17\) 1.32136 2.28866i 0.320476 0.555081i −0.660110 0.751169i \(-0.729491\pi\)
0.980586 + 0.196088i \(0.0628238\pi\)
\(18\) 0 0
\(19\) −6.87816 + 3.97111i −1.57796 + 0.911034i −0.582813 + 0.812606i \(0.698048\pi\)
−0.995144 + 0.0984279i \(0.968619\pi\)
\(20\) 0 0
\(21\) 4.06975 + 2.10644i 0.888093 + 0.459663i
\(22\) 0 0
\(23\) 3.47245 + 2.00482i 0.724056 + 0.418034i 0.816244 0.577708i \(-0.196053\pi\)
−0.0921879 + 0.995742i \(0.529386\pi\)
\(24\) 0 0
\(25\) 0.117249 + 0.203081i 0.0234498 + 0.0406163i
\(26\) 0 0
\(27\) −1.14134 5.06925i −0.219651 0.975578i
\(28\) 0 0
\(29\) −6.71261 3.87553i −1.24650 0.719667i −0.276091 0.961132i \(-0.589039\pi\)
−0.970410 + 0.241464i \(0.922372\pi\)
\(30\) 0 0
\(31\) 0.706968i 0.126975i −0.997983 0.0634876i \(-0.979778\pi\)
0.997983 0.0634876i \(-0.0202223\pi\)
\(32\) 0 0
\(33\) 1.10334 2.28537i 0.192067 0.397833i
\(34\) 0 0
\(35\) 5.77345 + 0.160752i 0.975890 + 0.0271721i
\(36\) 0 0
\(37\) 1.41738 + 2.45498i 0.233016 + 0.403596i 0.958694 0.284438i \(-0.0918071\pi\)
−0.725678 + 0.688034i \(0.758474\pi\)
\(38\) 0 0
\(39\) 2.54558 5.27272i 0.407619 0.844310i
\(40\) 0 0
\(41\) 3.74173 + 6.48086i 0.584360 + 1.01214i 0.994955 + 0.100323i \(0.0319876\pi\)
−0.410595 + 0.911818i \(0.634679\pi\)
\(42\) 0 0
\(43\) 1.27112 2.20164i 0.193844 0.335748i −0.752677 0.658390i \(-0.771238\pi\)
0.946521 + 0.322642i \(0.104571\pi\)
\(44\) 0 0
\(45\) −4.07319 5.12822i −0.607195 0.764470i
\(46\) 0 0
\(47\) 12.5508 1.83072 0.915358 0.402640i \(-0.131907\pi\)
0.915358 + 0.402640i \(0.131907\pi\)
\(48\) 0 0
\(49\) −3.83190 + 5.85803i −0.547414 + 0.836862i
\(50\) 0 0
\(51\) −0.337586 4.56485i −0.0472715 0.639206i
\(52\) 0 0
\(53\) −2.41675 1.39531i −0.331966 0.191661i 0.324748 0.945801i \(-0.394721\pi\)
−0.656714 + 0.754140i \(0.728054\pi\)
\(54\) 0 0
\(55\) 3.19850i 0.431286i
\(56\) 0 0
\(57\) −5.98079 + 12.3881i −0.792176 + 1.64085i
\(58\) 0 0
\(59\) −13.4330 −1.74883 −0.874414 0.485180i \(-0.838754\pi\)
−0.874414 + 0.485180i \(0.838754\pi\)
\(60\) 0 0
\(61\) 7.79493i 0.998039i −0.866591 0.499020i \(-0.833694\pi\)
0.866591 0.499020i \(-0.166306\pi\)
\(62\) 0 0
\(63\) 7.88036 0.948624i 0.992832 0.119515i
\(64\) 0 0
\(65\) 7.37945i 0.915308i
\(66\) 0 0
\(67\) −5.84058 −0.713541 −0.356770 0.934192i \(-0.616122\pi\)
−0.356770 + 0.934192i \(0.616122\pi\)
\(68\) 0 0
\(69\) 6.92598 0.512200i 0.833791 0.0616616i
\(70\) 0 0
\(71\) 11.6854i 1.38680i −0.720554 0.693398i \(-0.756113\pi\)
0.720554 0.693398i \(-0.243887\pi\)
\(72\) 0 0
\(73\) −3.95924 2.28587i −0.463394 0.267541i 0.250076 0.968226i \(-0.419544\pi\)
−0.713470 + 0.700685i \(0.752878\pi\)
\(74\) 0 0
\(75\) 0.365767 + 0.176586i 0.0422351 + 0.0203904i
\(76\) 0 0
\(77\) 3.30191 + 2.03094i 0.376288 + 0.231448i
\(78\) 0 0
\(79\) −9.38377 −1.05576 −0.527879 0.849320i \(-0.677012\pi\)
−0.527879 + 0.849320i \(0.677012\pi\)
\(80\) 0 0
\(81\) −6.57340 6.14739i −0.730378 0.683043i
\(82\) 0 0
\(83\) −1.70847 + 2.95917i −0.187529 + 0.324811i −0.944426 0.328724i \(-0.893381\pi\)
0.756896 + 0.653535i \(0.226715\pi\)
\(84\) 0 0
\(85\) −2.88452 4.99614i −0.312871 0.541908i
\(86\) 0 0
\(87\) −13.3887 + 0.990137i −1.43541 + 0.106154i
\(88\) 0 0
\(89\) 4.61937 + 8.00099i 0.489653 + 0.848103i 0.999929 0.0119070i \(-0.00379021\pi\)
−0.510276 + 0.860010i \(0.670457\pi\)
\(90\) 0 0
\(91\) 7.61803 + 4.68571i 0.798586 + 0.491196i
\(92\) 0 0
\(93\) −0.688796 1.01241i −0.0714248 0.104982i
\(94\) 0 0
\(95\) 17.3379i 1.77883i
\(96\) 0 0
\(97\) 6.38394 + 3.68577i 0.648191 + 0.374233i 0.787763 0.615979i \(-0.211239\pi\)
−0.139572 + 0.990212i \(0.544573\pi\)
\(98\) 0 0
\(99\) −0.646596 4.34773i −0.0649853 0.436964i
\(100\) 0 0
\(101\) 3.96357 + 6.86510i 0.394390 + 0.683103i 0.993023 0.117920i \(-0.0376226\pi\)
−0.598633 + 0.801023i \(0.704289\pi\)
\(102\) 0 0
\(103\) 3.26825 + 1.88693i 0.322031 + 0.185924i 0.652297 0.757963i \(-0.273805\pi\)
−0.330267 + 0.943888i \(0.607139\pi\)
\(104\) 0 0
\(105\) 8.42445 5.39483i 0.822142 0.526482i
\(106\) 0 0
\(107\) 6.88241 3.97356i 0.665347 0.384138i −0.128964 0.991649i \(-0.541165\pi\)
0.794311 + 0.607511i \(0.207832\pi\)
\(108\) 0 0
\(109\) 0.505142 0.874932i 0.0483838 0.0838033i −0.840819 0.541316i \(-0.817926\pi\)
0.889203 + 0.457513i \(0.151260\pi\)
\(110\) 0 0
\(111\) 4.42163 + 2.13469i 0.419682 + 0.202616i
\(112\) 0 0
\(113\) −10.5557 + 6.09431i −0.992992 + 0.573304i −0.906167 0.422919i \(-0.861005\pi\)
−0.0868250 + 0.996224i \(0.527672\pi\)
\(114\) 0 0
\(115\) 7.58037 4.37653i 0.706873 0.408113i
\(116\) 0 0
\(117\) −1.49180 10.0309i −0.137917 0.927358i
\(118\) 0 0
\(119\) 6.98925 + 0.194605i 0.640703 + 0.0178394i
\(120\) 0 0
\(121\) −4.42662 + 7.66713i −0.402420 + 0.697012i
\(122\) 0 0
\(123\) 11.6726 + 5.63533i 1.05248 + 0.508121i
\(124\) 0 0
\(125\) 11.4269 1.02206
\(126\) 0 0
\(127\) −6.79350 −0.602826 −0.301413 0.953494i \(-0.597458\pi\)
−0.301413 + 0.953494i \(0.597458\pi\)
\(128\) 0 0
\(129\) −0.324751 4.39130i −0.0285927 0.386632i
\(130\) 0 0
\(131\) −6.86790 + 11.8956i −0.600051 + 1.03932i 0.392761 + 0.919640i \(0.371520\pi\)
−0.992813 + 0.119679i \(0.961813\pi\)
\(132\) 0 0
\(133\) −17.8984 11.0090i −1.55199 0.954600i
\(134\) 0 0
\(135\) −10.8294 3.37535i −0.932045 0.290504i
\(136\) 0 0
\(137\) 17.4028 10.0475i 1.48682 0.858416i 0.486933 0.873439i \(-0.338116\pi\)
0.999887 + 0.0150235i \(0.00478229\pi\)
\(138\) 0 0
\(139\) −8.51403 + 4.91558i −0.722151 + 0.416934i −0.815544 0.578695i \(-0.803562\pi\)
0.0933930 + 0.995629i \(0.470229\pi\)
\(140\) 0 0
\(141\) 17.9732 12.2281i 1.51362 1.02980i
\(142\) 0 0
\(143\) 2.47646 4.28936i 0.207092 0.358694i
\(144\) 0 0
\(145\) −14.6536 + 8.46029i −1.21692 + 0.702589i
\(146\) 0 0
\(147\) 0.220003 + 12.1224i 0.0181456 + 0.999835i
\(148\) 0 0
\(149\) 17.3512 + 10.0177i 1.42146 + 0.820682i 0.996424 0.0844939i \(-0.0269274\pi\)
0.425038 + 0.905175i \(0.360261\pi\)
\(150\) 0 0
\(151\) −11.1168 19.2549i −0.904675 1.56694i −0.821353 0.570420i \(-0.806780\pi\)
−0.0833218 0.996523i \(-0.526553\pi\)
\(152\) 0 0
\(153\) −4.93094 6.20815i −0.398643 0.501899i
\(154\) 0 0
\(155\) −1.33655 0.771657i −0.107354 0.0619810i
\(156\) 0 0
\(157\) 8.02869i 0.640759i 0.947289 + 0.320380i \(0.103811\pi\)
−0.947289 + 0.320380i \(0.896189\pi\)
\(158\) 0 0
\(159\) −4.82034 + 0.356480i −0.382278 + 0.0282707i
\(160\) 0 0
\(161\) −0.295263 + 10.6044i −0.0232700 + 0.835744i
\(162\) 0 0
\(163\) 6.22604 + 10.7838i 0.487661 + 0.844654i 0.999899 0.0141893i \(-0.00451676\pi\)
−0.512238 + 0.858844i \(0.671183\pi\)
\(164\) 0 0
\(165\) −3.11628 4.58039i −0.242602 0.356583i
\(166\) 0 0
\(167\) 9.85984 + 17.0777i 0.762978 + 1.32152i 0.941309 + 0.337546i \(0.109597\pi\)
−0.178332 + 0.983970i \(0.557070\pi\)
\(168\) 0 0
\(169\) −0.786412 + 1.36211i −0.0604933 + 0.104777i
\(170\) 0 0
\(171\) 3.50495 + 23.5674i 0.268030 + 1.80225i
\(172\) 0 0
\(173\) 1.82747 0.138940 0.0694699 0.997584i \(-0.477869\pi\)
0.0694699 + 0.997584i \(0.477869\pi\)
\(174\) 0 0
\(175\) −0.325046 + 0.528460i −0.0245712 + 0.0399479i
\(176\) 0 0
\(177\) −19.2367 + 13.0877i −1.44592 + 0.983732i
\(178\) 0 0
\(179\) −12.1182 6.99645i −0.905757 0.522939i −0.0266934 0.999644i \(-0.508498\pi\)
−0.879064 + 0.476705i \(0.841831\pi\)
\(180\) 0 0
\(181\) 16.3594i 1.21599i 0.793942 + 0.607994i \(0.208025\pi\)
−0.793942 + 0.607994i \(0.791975\pi\)
\(182\) 0 0
\(183\) −7.59456 11.1627i −0.561406 0.825170i
\(184\) 0 0
\(185\) 6.18830 0.454973
\(186\) 0 0
\(187\) 3.87206i 0.283153i
\(188\) 0 0
\(189\) 10.3608 9.03627i 0.753636 0.657292i
\(190\) 0 0
\(191\) 13.6631i 0.988624i 0.869285 + 0.494312i \(0.164580\pi\)
−0.869285 + 0.494312i \(0.835420\pi\)
\(192\) 0 0
\(193\) −4.37769 −0.315113 −0.157557 0.987510i \(-0.550362\pi\)
−0.157557 + 0.987510i \(0.550362\pi\)
\(194\) 0 0
\(195\) −7.18976 10.5677i −0.514869 0.756768i
\(196\) 0 0
\(197\) 1.00603i 0.0716767i −0.999358 0.0358384i \(-0.988590\pi\)
0.999358 0.0358384i \(-0.0114101\pi\)
\(198\) 0 0
\(199\) 5.67639 + 3.27726i 0.402388 + 0.232319i 0.687514 0.726171i \(-0.258702\pi\)
−0.285126 + 0.958490i \(0.592035\pi\)
\(200\) 0 0
\(201\) −8.36397 + 5.69045i −0.589949 + 0.401373i
\(202\) 0 0
\(203\) 0.570774 20.4994i 0.0400605 1.43878i
\(204\) 0 0
\(205\) 16.3364 1.14098
\(206\) 0 0
\(207\) 9.41928 7.48144i 0.654685 0.519996i
\(208\) 0 0
\(209\) −5.81840 + 10.0778i −0.402467 + 0.697094i
\(210\) 0 0
\(211\) 9.11202 + 15.7825i 0.627297 + 1.08651i 0.988092 + 0.153866i \(0.0491723\pi\)
−0.360794 + 0.932645i \(0.617494\pi\)
\(212\) 0 0
\(213\) −11.3850 16.7339i −0.780086 1.14659i
\(214\) 0 0
\(215\) −2.77486 4.80620i −0.189244 0.327780i
\(216\) 0 0
\(217\) 1.64527 0.889784i 0.111688 0.0604024i
\(218\) 0 0
\(219\) −7.89692 + 0.584004i −0.533625 + 0.0394633i
\(220\) 0 0
\(221\) 8.93345i 0.600929i
\(222\) 0 0
\(223\) 8.71705 + 5.03279i 0.583737 + 0.337021i 0.762617 0.646850i \(-0.223914\pi\)
−0.178880 + 0.983871i \(0.557247\pi\)
\(224\) 0 0
\(225\) 0.695841 0.103486i 0.0463894 0.00689904i
\(226\) 0 0
\(227\) −9.94372 17.2230i −0.659988 1.14313i −0.980618 0.195928i \(-0.937228\pi\)
0.320630 0.947204i \(-0.396105\pi\)
\(228\) 0 0
\(229\) −15.3854 8.88275i −1.01669 0.586988i −0.103549 0.994624i \(-0.533020\pi\)
−0.913145 + 0.407636i \(0.866353\pi\)
\(230\) 0 0
\(231\) 6.70722 0.308634i 0.441303 0.0203066i
\(232\) 0 0
\(233\) −13.9077 + 8.02962i −0.911124 + 0.526038i −0.880793 0.473502i \(-0.842990\pi\)
−0.0303317 + 0.999540i \(0.509656\pi\)
\(234\) 0 0
\(235\) 13.6992 23.7277i 0.893636 1.54782i
\(236\) 0 0
\(237\) −13.4380 + 9.14256i −0.872890 + 0.593873i
\(238\) 0 0
\(239\) 7.11117 4.10564i 0.459983 0.265572i −0.252054 0.967713i \(-0.581106\pi\)
0.712037 + 0.702142i \(0.247773\pi\)
\(240\) 0 0
\(241\) −24.6614 + 14.2382i −1.58858 + 0.917166i −0.595037 + 0.803698i \(0.702863\pi\)
−0.993542 + 0.113468i \(0.963804\pi\)
\(242\) 0 0
\(243\) −15.4028 2.39890i −0.988088 0.153890i
\(244\) 0 0
\(245\) 6.89230 + 13.6384i 0.440333 + 0.871325i
\(246\) 0 0
\(247\) −13.4240 + 23.2510i −0.854147 + 1.47943i
\(248\) 0 0
\(249\) 0.436489 + 5.90221i 0.0276613 + 0.374038i
\(250\) 0 0
\(251\) −0.656343 −0.0414280 −0.0207140 0.999785i \(-0.506594\pi\)
−0.0207140 + 0.999785i \(0.506594\pi\)
\(252\) 0 0
\(253\) 5.87486 0.369349
\(254\) 0 0
\(255\) −8.99848 4.34432i −0.563507 0.272052i
\(256\) 0 0
\(257\) −3.82042 + 6.61716i −0.238311 + 0.412767i −0.960230 0.279211i \(-0.909927\pi\)
0.721918 + 0.691978i \(0.243261\pi\)
\(258\) 0 0
\(259\) −3.92937 + 6.38837i −0.244159 + 0.396954i
\(260\) 0 0
\(261\) −18.2085 + 14.4624i −1.12708 + 0.895201i
\(262\) 0 0
\(263\) 5.73888 3.31334i 0.353874 0.204310i −0.312516 0.949913i \(-0.601172\pi\)
0.666390 + 0.745603i \(0.267838\pi\)
\(264\) 0 0
\(265\) −5.27577 + 3.04597i −0.324088 + 0.187112i
\(266\) 0 0
\(267\) 14.4105 + 6.95714i 0.881907 + 0.425770i
\(268\) 0 0
\(269\) 4.38347 7.59239i 0.267265 0.462916i −0.700890 0.713270i \(-0.747214\pi\)
0.968154 + 0.250354i \(0.0805469\pi\)
\(270\) 0 0
\(271\) −14.2608 + 8.23346i −0.866280 + 0.500147i −0.866110 0.499853i \(-0.833387\pi\)
−0.000169619 1.00000i \(0.500054\pi\)
\(272\) 0 0
\(273\) 15.4746 0.712068i 0.936566 0.0430963i
\(274\) 0 0
\(275\) 0.297551 + 0.171791i 0.0179430 + 0.0103594i
\(276\) 0 0
\(277\) 8.88732 + 15.3933i 0.533987 + 0.924893i 0.999212 + 0.0397001i \(0.0126402\pi\)
−0.465225 + 0.885193i \(0.654026\pi\)
\(278\) 0 0
\(279\) −1.97277 0.778725i −0.118107 0.0466210i
\(280\) 0 0
\(281\) −14.0252 8.09748i −0.836676 0.483055i 0.0194568 0.999811i \(-0.493806\pi\)
−0.856133 + 0.516755i \(0.827140\pi\)
\(282\) 0 0
\(283\) 28.3729i 1.68660i −0.537447 0.843298i \(-0.680611\pi\)
0.537447 0.843298i \(-0.319389\pi\)
\(284\) 0 0
\(285\) 16.8922 + 24.8286i 1.00061 + 1.47072i
\(286\) 0 0
\(287\) −10.3731 + 16.8646i −0.612304 + 0.995484i
\(288\) 0 0
\(289\) 5.00804 + 8.67417i 0.294590 + 0.510246i
\(290\) 0 0
\(291\) 12.7331 0.941657i 0.746429 0.0552009i
\(292\) 0 0
\(293\) −4.38260 7.59088i −0.256034 0.443464i 0.709142 0.705066i \(-0.249083\pi\)
−0.965176 + 0.261602i \(0.915749\pi\)
\(294\) 0 0
\(295\) −14.6621 + 25.3956i −0.853663 + 1.47859i
\(296\) 0 0
\(297\) −5.16193 5.59617i −0.299525 0.324723i
\(298\) 0 0
\(299\) 13.5542 0.783861
\(300\) 0 0
\(301\) 6.72353 + 0.187206i 0.387538 + 0.0107904i
\(302\) 0 0
\(303\) 12.3646 + 5.96944i 0.710330 + 0.342936i
\(304\) 0 0
\(305\) −14.7366 8.50818i −0.843816 0.487177i
\(306\) 0 0
\(307\) 12.8497i 0.733372i 0.930345 + 0.366686i \(0.119508\pi\)
−0.930345 + 0.366686i \(0.880492\pi\)
\(308\) 0 0
\(309\) 6.51871 0.482080i 0.370836 0.0274246i
\(310\) 0 0
\(311\) 6.59343 0.373879 0.186939 0.982371i \(-0.440143\pi\)
0.186939 + 0.982371i \(0.440143\pi\)
\(312\) 0 0
\(313\) 3.41458i 0.193004i 0.995333 + 0.0965018i \(0.0307654\pi\)
−0.995333 + 0.0965018i \(0.969235\pi\)
\(314\) 0 0
\(315\) 6.80802 15.9335i 0.383588 0.897753i
\(316\) 0 0
\(317\) 32.1010i 1.80297i −0.432810 0.901485i \(-0.642478\pi\)
0.432810 0.901485i \(-0.357522\pi\)
\(318\) 0 0
\(319\) −11.3567 −0.635854
\(320\) 0 0
\(321\) 5.98449 12.3958i 0.334022 0.691866i
\(322\) 0 0
\(323\) 20.9890i 1.16786i
\(324\) 0 0
\(325\) 0.686498 + 0.396350i 0.0380801 + 0.0219855i
\(326\) 0 0
\(327\) −0.129056 1.74510i −0.00713681 0.0965042i
\(328\) 0 0
\(329\) 15.7963 + 29.2084i 0.870877 + 1.61031i
\(330\) 0 0
\(331\) 28.8833 1.58757 0.793784 0.608199i \(-0.208108\pi\)
0.793784 + 0.608199i \(0.208108\pi\)
\(332\) 0 0
\(333\) 8.41178 1.25100i 0.460963 0.0685544i
\(334\) 0 0
\(335\) −6.37501 + 11.0418i −0.348304 + 0.603280i
\(336\) 0 0
\(337\) 4.82568 + 8.35833i 0.262872 + 0.455307i 0.967004 0.254762i \(-0.0819971\pi\)
−0.704132 + 0.710069i \(0.748664\pi\)
\(338\) 0 0
\(339\) −9.17851 + 19.0116i −0.498508 + 1.03257i
\(340\) 0 0
\(341\) −0.517919 0.897063i −0.0280469 0.0485787i
\(342\) 0 0
\(343\) −18.4557 1.54481i −0.996515 0.0834117i
\(344\) 0 0
\(345\) 6.59139 13.6529i 0.354869 0.735047i
\(346\) 0 0
\(347\) 12.3273i 0.661766i 0.943672 + 0.330883i \(0.107347\pi\)
−0.943672 + 0.330883i \(0.892653\pi\)
\(348\) 0 0
\(349\) −10.2211 5.90115i −0.547123 0.315881i 0.200838 0.979624i \(-0.435634\pi\)
−0.747961 + 0.663743i \(0.768967\pi\)
\(350\) 0 0
\(351\) −11.9094 12.9112i −0.635676 0.689151i
\(352\) 0 0
\(353\) 6.59855 + 11.4290i 0.351205 + 0.608305i 0.986461 0.163997i \(-0.0524386\pi\)
−0.635256 + 0.772302i \(0.719105\pi\)
\(354\) 0 0
\(355\) −22.0916 12.7546i −1.17250 0.676943i
\(356\) 0 0
\(357\) 10.1985 6.53091i 0.539763 0.345652i
\(358\) 0 0
\(359\) 5.22483 3.01656i 0.275756 0.159208i −0.355745 0.934583i \(-0.615773\pi\)
0.631501 + 0.775375i \(0.282439\pi\)
\(360\) 0 0
\(361\) 22.0394 38.1733i 1.15997 2.00912i
\(362\) 0 0
\(363\) 1.13093 + 15.2925i 0.0593585 + 0.802648i
\(364\) 0 0
\(365\) −8.64304 + 4.99006i −0.452397 + 0.261192i
\(366\) 0 0
\(367\) −14.8755 + 8.58836i −0.776494 + 0.448309i −0.835186 0.549967i \(-0.814640\pi\)
0.0586924 + 0.998276i \(0.481307\pi\)
\(368\) 0 0
\(369\) 22.2061 3.30250i 1.15601 0.171921i
\(370\) 0 0
\(371\) 0.205496 7.38043i 0.0106688 0.383173i
\(372\) 0 0
\(373\) −2.35902 + 4.08595i −0.122146 + 0.211562i −0.920614 0.390475i \(-0.872311\pi\)
0.798468 + 0.602037i \(0.205644\pi\)
\(374\) 0 0
\(375\) 16.3639 11.1332i 0.845026 0.574916i
\(376\) 0 0
\(377\) −26.2017 −1.34946
\(378\) 0 0
\(379\) −9.34015 −0.479771 −0.239886 0.970801i \(-0.577110\pi\)
−0.239886 + 0.970801i \(0.577110\pi\)
\(380\) 0 0
\(381\) −9.72859 + 6.61887i −0.498411 + 0.339095i
\(382\) 0 0
\(383\) −2.85036 + 4.93696i −0.145646 + 0.252267i −0.929614 0.368535i \(-0.879860\pi\)
0.783968 + 0.620802i \(0.213193\pi\)
\(384\) 0 0
\(385\) 7.44361 4.02560i 0.379362 0.205164i
\(386\) 0 0
\(387\) −4.74347 5.97212i −0.241124 0.303580i
\(388\) 0 0
\(389\) 6.63671 3.83171i 0.336495 0.194275i −0.322226 0.946663i \(-0.604431\pi\)
0.658721 + 0.752387i \(0.271098\pi\)
\(390\) 0 0
\(391\) 9.17668 5.29816i 0.464085 0.267939i
\(392\) 0 0
\(393\) 1.75464 + 23.7263i 0.0885100 + 1.19683i
\(394\) 0 0
\(395\) −10.2424 + 17.7404i −0.515351 + 0.892615i
\(396\) 0 0
\(397\) −1.12810 + 0.651310i −0.0566178 + 0.0326883i −0.528042 0.849218i \(-0.677074\pi\)
0.471424 + 0.881907i \(0.343740\pi\)
\(398\) 0 0
\(399\) −36.3573 + 1.67299i −1.82014 + 0.0837542i
\(400\) 0 0
\(401\) −8.18778 4.72722i −0.408878 0.236066i 0.281429 0.959582i \(-0.409191\pi\)
−0.690308 + 0.723516i \(0.742525\pi\)
\(402\) 0 0
\(403\) −1.19492 2.06966i −0.0595233 0.103097i
\(404\) 0 0
\(405\) −18.7967 + 5.71736i −0.934018 + 0.284098i
\(406\) 0 0
\(407\) 3.59700 + 2.07673i 0.178296 + 0.102940i
\(408\) 0 0
\(409\) 19.0736i 0.943126i −0.881832 0.471563i \(-0.843690\pi\)
0.881832 0.471563i \(-0.156310\pi\)
\(410\) 0 0
\(411\) 15.1323 31.3439i 0.746422 1.54608i
\(412\) 0 0
\(413\) −16.9067 31.2615i −0.831922 1.53828i
\(414\) 0 0
\(415\) 3.72961 + 6.45987i 0.183079 + 0.317102i
\(416\) 0 0
\(417\) −7.40324 + 15.3345i −0.362538 + 0.750934i
\(418\) 0 0
\(419\) 4.20003 + 7.27466i 0.205185 + 0.355390i 0.950192 0.311666i \(-0.100887\pi\)
−0.745007 + 0.667057i \(0.767554\pi\)
\(420\) 0 0
\(421\) 19.7178 34.1522i 0.960985 1.66448i 0.240951 0.970537i \(-0.422541\pi\)
0.720035 0.693938i \(-0.244126\pi\)
\(422\) 0 0
\(423\) 13.8247 35.0225i 0.672178 1.70285i
\(424\) 0 0
\(425\) 0.619711 0.0300604
\(426\) 0 0
\(427\) 18.1405 9.81063i 0.877881 0.474770i
\(428\) 0 0
\(429\) −0.632697 8.55535i −0.0305469 0.413056i
\(430\) 0 0
\(431\) −10.3340 5.96634i −0.497772 0.287389i 0.230021 0.973186i \(-0.426120\pi\)
−0.727793 + 0.685797i \(0.759454\pi\)
\(432\) 0 0
\(433\) 12.2121i 0.586875i −0.955978 0.293437i \(-0.905201\pi\)
0.955978 0.293437i \(-0.0947992\pi\)
\(434\) 0 0
\(435\) −12.7419 + 26.3925i −0.610925 + 1.26542i
\(436\) 0 0
\(437\) −31.8454 −1.52337
\(438\) 0 0
\(439\) 16.7015i 0.797120i 0.917142 + 0.398560i \(0.130490\pi\)
−0.917142 + 0.398560i \(0.869510\pi\)
\(440\) 0 0
\(441\) 12.1258 + 17.1454i 0.577419 + 0.816448i
\(442\) 0 0
\(443\) 30.2997i 1.43958i −0.694190 0.719791i \(-0.744237\pi\)
0.694190 0.719791i \(-0.255763\pi\)
\(444\) 0 0
\(445\) 20.1682 0.956065
\(446\) 0 0
\(447\) 34.6078 2.55936i 1.63689 0.121054i
\(448\) 0 0
\(449\) 30.1253i 1.42170i −0.703343 0.710851i \(-0.748310\pi\)
0.703343 0.710851i \(-0.251690\pi\)
\(450\) 0 0
\(451\) 9.49566 + 5.48232i 0.447133 + 0.258152i
\(452\) 0 0
\(453\) −34.6798 16.7428i −1.62940 0.786646i
\(454\) 0 0
\(455\) 17.1736 9.28770i 0.805110 0.435414i
\(456\) 0 0
\(457\) 25.2318 1.18029 0.590146 0.807297i \(-0.299070\pi\)
0.590146 + 0.807297i \(0.299070\pi\)
\(458\) 0 0
\(459\) −13.1099 4.08615i −0.611918 0.190725i
\(460\) 0 0
\(461\) −12.3174 + 21.3344i −0.573680 + 0.993643i 0.422503 + 0.906361i \(0.361151\pi\)
−0.996184 + 0.0872820i \(0.972182\pi\)
\(462\) 0 0
\(463\) 6.33215 + 10.9676i 0.294280 + 0.509708i 0.974817 0.223006i \(-0.0715869\pi\)
−0.680537 + 0.732713i \(0.738254\pi\)
\(464\) 0 0
\(465\) −2.66582 + 0.197146i −0.123624 + 0.00914244i
\(466\) 0 0
\(467\) −10.4723 18.1385i −0.484599 0.839350i 0.515245 0.857043i \(-0.327701\pi\)
−0.999843 + 0.0176932i \(0.994368\pi\)
\(468\) 0 0
\(469\) −7.35090 13.5923i −0.339433 0.627635i
\(470\) 0 0
\(471\) 7.82231 + 11.4974i 0.360433 + 0.529774i
\(472\) 0 0
\(473\) 3.72485i 0.171269i
\(474\) 0 0
\(475\) −1.61291 0.931217i −0.0740056 0.0427271i
\(476\) 0 0
\(477\) −6.55562 + 5.20692i −0.300161 + 0.238409i
\(478\) 0 0
\(479\) −15.8852 27.5141i −0.725816 1.25715i −0.958637 0.284630i \(-0.908129\pi\)
0.232822 0.972519i \(-0.425204\pi\)
\(480\) 0 0
\(481\) 8.29884 + 4.79134i 0.378394 + 0.218466i
\(482\) 0 0
\(483\) 9.90898 + 15.4736i 0.450874 + 0.704075i
\(484\) 0 0
\(485\) 13.9362 8.04605i 0.632809 0.365352i
\(486\) 0 0
\(487\) 17.7821 30.7995i 0.805784 1.39566i −0.109977 0.993934i \(-0.535078\pi\)
0.915761 0.401724i \(-0.131589\pi\)
\(488\) 0 0
\(489\) 19.4226 + 9.37691i 0.878320 + 0.424038i
\(490\) 0 0
\(491\) −2.75734 + 1.59195i −0.124437 + 0.0718437i −0.560926 0.827866i \(-0.689555\pi\)
0.436490 + 0.899709i \(0.356222\pi\)
\(492\) 0 0
\(493\) −17.7395 + 10.2419i −0.798947 + 0.461272i
\(494\) 0 0
\(495\) −8.92531 3.52315i −0.401163 0.158354i
\(496\) 0 0
\(497\) 27.1944 14.7071i 1.21983 0.659703i
\(498\) 0 0
\(499\) 16.0214 27.7498i 0.717215 1.24225i −0.244884 0.969552i \(-0.578750\pi\)
0.962099 0.272700i \(-0.0879168\pi\)
\(500\) 0 0
\(501\) 30.7585 + 14.8497i 1.37419 + 0.663435i
\(502\) 0 0
\(503\) −11.6608 −0.519930 −0.259965 0.965618i \(-0.583711\pi\)
−0.259965 + 0.965618i \(0.583711\pi\)
\(504\) 0 0
\(505\) 17.3050 0.770061
\(506\) 0 0
\(507\) 0.200916 + 2.71679i 0.00892299 + 0.120657i
\(508\) 0 0
\(509\) −13.4427 + 23.2834i −0.595836 + 1.03202i 0.397592 + 0.917562i \(0.369846\pi\)
−0.993428 + 0.114457i \(0.963487\pi\)
\(510\) 0 0
\(511\) 0.336655 12.0910i 0.0148927 0.534875i
\(512\) 0 0
\(513\) 27.9809 + 30.3347i 1.23539 + 1.33931i
\(514\) 0 0
\(515\) 7.13461 4.11917i 0.314388 0.181512i
\(516\) 0 0
\(517\) 15.9255 9.19459i 0.700402 0.404378i
\(518\) 0 0
\(519\) 2.61701 1.78049i 0.114874 0.0781549i
\(520\) 0 0
\(521\) 17.0385 29.5116i 0.746471 1.29293i −0.203033 0.979172i \(-0.565080\pi\)
0.949504 0.313754i \(-0.101587\pi\)
\(522\) 0 0
\(523\) −4.71003 + 2.71933i −0.205955 + 0.118908i −0.599430 0.800427i \(-0.704606\pi\)
0.393475 + 0.919335i \(0.371273\pi\)
\(524\) 0 0
\(525\) 0.0493959 + 1.07347i 0.00215581 + 0.0468500i
\(526\) 0 0
\(527\) −1.61801 0.934157i −0.0704815 0.0406925i
\(528\) 0 0
\(529\) −3.46140 5.99532i −0.150496 0.260666i
\(530\) 0 0
\(531\) −14.7964 + 37.4843i −0.642111 + 1.62668i
\(532\) 0 0
\(533\) 21.9080 + 12.6486i 0.948940 + 0.547871i
\(534\) 0 0
\(535\) 17.3486i 0.750045i
\(536\) 0 0
\(537\) −24.1704 + 1.78748i −1.04303 + 0.0771356i
\(538\) 0 0
\(539\) −0.570698 + 10.2404i −0.0245817 + 0.441085i
\(540\) 0 0
\(541\) 11.8329 + 20.4952i 0.508737 + 0.881158i 0.999949 + 0.0101183i \(0.00322080\pi\)
−0.491212 + 0.871040i \(0.663446\pi\)
\(542\) 0 0
\(543\) 15.9389 + 23.4274i 0.684004 + 1.00537i
\(544\) 0 0
\(545\) −1.10273 1.90998i −0.0472356 0.0818145i
\(546\) 0 0
\(547\) 12.0824 20.9273i 0.516606 0.894788i −0.483208 0.875505i \(-0.660529\pi\)
0.999814 0.0192822i \(-0.00613809\pi\)
\(548\) 0 0
\(549\) −21.7515 8.58611i −0.928331 0.366446i
\(550\) 0 0
\(551\) 61.5605 2.62257
\(552\) 0 0
\(553\) −11.8103 21.8381i −0.502226 0.928650i
\(554\) 0 0
\(555\) 8.86192 6.02923i 0.376167 0.255927i
\(556\) 0 0
\(557\) −7.36315 4.25111i −0.311987 0.180126i 0.335829 0.941923i \(-0.390984\pi\)
−0.647815 + 0.761798i \(0.724317\pi\)
\(558\) 0 0
\(559\) 8.59381i 0.363480i
\(560\) 0 0
\(561\) −3.77253 5.54496i −0.159276 0.234108i
\(562\) 0 0
\(563\) −0.947553 −0.0399346 −0.0199673 0.999801i \(-0.506356\pi\)
−0.0199673 + 0.999801i \(0.506356\pi\)
\(564\) 0 0
\(565\) 26.6078i 1.11940i
\(566\) 0 0
\(567\) 6.03311 23.0348i 0.253367 0.967370i
\(568\) 0 0
\(569\) 18.2280i 0.764158i −0.924130 0.382079i \(-0.875208\pi\)
0.924130 0.382079i \(-0.124792\pi\)
\(570\) 0 0
\(571\) 12.2424 0.512330 0.256165 0.966633i \(-0.417541\pi\)
0.256165 + 0.966633i \(0.417541\pi\)
\(572\) 0 0
\(573\) 13.3118 + 19.5661i 0.556110 + 0.817385i
\(574\) 0 0
\(575\) 0.940253i 0.0392112i
\(576\) 0 0
\(577\) −10.2500 5.91784i −0.426713 0.246363i 0.271232 0.962514i \(-0.412569\pi\)
−0.697945 + 0.716151i \(0.745902\pi\)
\(578\) 0 0
\(579\) −6.26905 + 4.26516i −0.260533 + 0.177254i
\(580\) 0 0
\(581\) −9.03690 0.251618i −0.374914 0.0104389i
\(582\) 0 0
\(583\) −4.08878 −0.169340
\(584\) 0 0
\(585\) −20.5921 8.12845i −0.851378 0.336070i
\(586\) 0 0
\(587\) −3.57681 + 6.19521i −0.147631 + 0.255704i −0.930351 0.366669i \(-0.880498\pi\)
0.782721 + 0.622373i \(0.213831\pi\)
\(588\) 0 0
\(589\) 2.80745 + 4.86264i 0.115679 + 0.200362i
\(590\) 0 0
\(591\) −0.980171 1.44068i −0.0403188 0.0592617i
\(592\) 0 0
\(593\) 13.4811 + 23.3500i 0.553603 + 0.958869i 0.998011 + 0.0630442i \(0.0200809\pi\)
−0.444408 + 0.895825i \(0.646586\pi\)
\(594\) 0 0
\(595\) 7.99668 13.0010i 0.327832 0.532990i
\(596\) 0 0
\(597\) 11.3219 0.837289i 0.463373 0.0342680i
\(598\) 0 0
\(599\) 35.2441i 1.44004i −0.693955 0.720018i \(-0.744133\pi\)
0.693955 0.720018i \(-0.255867\pi\)
\(600\) 0 0
\(601\) 3.39266 + 1.95875i 0.138389 + 0.0798991i 0.567596 0.823307i \(-0.307874\pi\)
−0.429207 + 0.903206i \(0.641207\pi\)
\(602\) 0 0
\(603\) −6.43340 + 16.2979i −0.261988 + 0.663704i
\(604\) 0 0
\(605\) 9.66332 + 16.7374i 0.392870 + 0.680470i
\(606\) 0 0
\(607\) 12.5377 + 7.23862i 0.508888 + 0.293807i 0.732376 0.680900i \(-0.238411\pi\)
−0.223488 + 0.974707i \(0.571744\pi\)
\(608\) 0 0
\(609\) −19.1551 29.9122i −0.776204 1.21210i
\(610\) 0 0
\(611\) 36.7426 21.2134i 1.48645 0.858201i
\(612\) 0 0
\(613\) −6.51761 + 11.2888i −0.263244 + 0.455952i −0.967102 0.254389i \(-0.918126\pi\)
0.703858 + 0.710341i \(0.251459\pi\)
\(614\) 0 0
\(615\) 23.3944 15.9165i 0.943355 0.641814i
\(616\) 0 0
\(617\) −3.14491 + 1.81571i −0.126609 + 0.0730979i −0.561967 0.827160i \(-0.689955\pi\)
0.435358 + 0.900258i \(0.356622\pi\)
\(618\) 0 0
\(619\) 14.2737 8.24091i 0.573708 0.331230i −0.184921 0.982753i \(-0.559203\pi\)
0.758629 + 0.651523i \(0.225870\pi\)
\(620\) 0 0
\(621\) 6.19969 19.8909i 0.248785 0.798195i
\(622\) 0 0
\(623\) −12.8062 + 20.8203i −0.513068 + 0.834147i
\(624\) 0 0
\(625\) 11.8863 20.5876i 0.475450 0.823504i
\(626\) 0 0
\(627\) 1.48651 + 20.1006i 0.0593655 + 0.802742i
\(628\) 0 0
\(629\) 7.49147 0.298704
\(630\) 0 0
\(631\) 34.8383 1.38689 0.693446 0.720508i \(-0.256091\pi\)
0.693446 + 0.720508i \(0.256091\pi\)
\(632\) 0 0
\(633\) 28.4256 + 13.7234i 1.12982 + 0.545457i
\(634\) 0 0
\(635\) −7.41512 + 12.8434i −0.294260 + 0.509673i
\(636\) 0 0
\(637\) −1.31669 + 23.6262i −0.0521692 + 0.936105i
\(638\) 0 0
\(639\) −32.6076 12.8714i −1.28994 0.509185i
\(640\) 0 0
\(641\) 7.25538 4.18889i 0.286570 0.165451i −0.349824 0.936815i \(-0.613759\pi\)
0.636394 + 0.771364i \(0.280425\pi\)
\(642\) 0 0
\(643\) 18.0021 10.3935i 0.709934 0.409881i −0.101103 0.994876i \(-0.532237\pi\)
0.811037 + 0.584995i \(0.198904\pi\)
\(644\) 0 0
\(645\) −8.65637 4.17915i −0.340844 0.164554i
\(646\) 0 0
\(647\) −4.74770 + 8.22325i −0.186651 + 0.323289i −0.944132 0.329568i \(-0.893097\pi\)
0.757480 + 0.652858i \(0.226430\pi\)
\(648\) 0 0
\(649\) −17.0450 + 9.84091i −0.669073 + 0.386290i
\(650\) 0 0
\(651\) 1.48919 2.87719i 0.0583659 0.112766i
\(652\) 0 0
\(653\) −6.64747 3.83792i −0.260136 0.150189i 0.364261 0.931297i \(-0.381322\pi\)
−0.624396 + 0.781108i \(0.714655\pi\)
\(654\) 0 0
\(655\) 14.9927 + 25.9680i 0.585811 + 1.01465i
\(656\) 0 0
\(657\) −10.7397 + 8.53025i −0.418997 + 0.332797i
\(658\) 0 0
\(659\) −38.0493 21.9678i −1.48219 0.855743i −0.482395 0.875954i \(-0.660233\pi\)
−0.999796 + 0.0202102i \(0.993566\pi\)
\(660\) 0 0
\(661\) 25.5938i 0.995484i −0.867325 0.497742i \(-0.834163\pi\)
0.867325 0.497742i \(-0.165837\pi\)
\(662\) 0 0
\(663\) −8.70382 12.7931i −0.338028 0.496843i
\(664\) 0 0
\(665\) −40.3490 + 21.8213i −1.56467 + 0.846193i
\(666\) 0 0
\(667\) −15.5395 26.9151i −0.601691 1.04216i
\(668\) 0 0
\(669\) 17.3866 1.28580i 0.672206 0.0497119i
\(670\) 0 0
\(671\) −5.71051 9.89089i −0.220452 0.381834i
\(672\) 0 0
\(673\) −7.64671 + 13.2445i −0.294759 + 0.510538i −0.974929 0.222517i \(-0.928573\pi\)
0.680170 + 0.733055i \(0.261906\pi\)
\(674\) 0 0
\(675\) 0.895649 0.826150i 0.0344736 0.0317985i
\(676\) 0 0
\(677\) 45.2918 1.74070 0.870352 0.492430i \(-0.163891\pi\)
0.870352 + 0.492430i \(0.163891\pi\)
\(678\) 0 0
\(679\) −0.542827 + 19.4957i −0.0208318 + 0.748177i
\(680\) 0 0
\(681\) −31.0202 14.9760i −1.18870 0.573882i
\(682\) 0 0
\(683\) −24.0891 13.9079i −0.921744 0.532169i −0.0375529 0.999295i \(-0.511956\pi\)
−0.884191 + 0.467126i \(0.845290\pi\)
\(684\) 0 0
\(685\) 43.8674i 1.67609i
\(686\) 0 0
\(687\) −30.6869 + 2.26940i −1.17078 + 0.0865831i
\(688\) 0 0
\(689\) −9.43345 −0.359386
\(690\) 0 0
\(691\) 16.2946i 0.619875i 0.950757 + 0.309938i \(0.100308\pi\)
−0.950757 + 0.309938i \(0.899692\pi\)
\(692\) 0 0
\(693\) 9.30433 6.97679i 0.353442 0.265026i
\(694\) 0 0
\(695\) 21.4614i 0.814079i
\(696\) 0 0
\(697\) 19.7766 0.749093
\(698\) 0 0
\(699\) −12.0932 + 25.0490i −0.457408 + 0.947439i
\(700\) 0 0
\(701\) 0.393403i 0.0148586i 0.999972 + 0.00742932i \(0.00236485\pi\)
−0.999972 + 0.00742932i \(0.997635\pi\)
\(702\) 0 0
\(703\) −19.4980 11.2572i −0.735379 0.424572i
\(704\) 0 0
\(705\) −3.49992 47.3261i −0.131815 1.78240i
\(706\) 0 0
\(707\) −10.9881 + 17.8644i −0.413250 + 0.671862i
\(708\) 0 0
\(709\) −32.6366 −1.22569 −0.612846 0.790202i \(-0.709975\pi\)
−0.612846 + 0.790202i \(0.709975\pi\)
\(710\) 0 0
\(711\) −10.3362 + 26.1851i −0.387638 + 0.982018i
\(712\) 0 0
\(713\) 1.41734 2.45491i 0.0530799 0.0919372i
\(714\) 0 0
\(715\) −5.40612 9.36368i −0.202178 0.350182i
\(716\) 0 0
\(717\) 6.18341 12.8078i 0.230924 0.478317i
\(718\) 0 0
\(719\) −0.106604 0.184643i −0.00397565 0.00688602i 0.864031 0.503439i \(-0.167932\pi\)
−0.868006 + 0.496553i \(0.834599\pi\)
\(720\) 0 0
\(721\) −0.277900 + 9.98081i −0.0103495 + 0.371705i
\(722\) 0 0
\(723\) −21.4439 + 44.4172i −0.797508 + 1.65190i
\(724\) 0 0
\(725\) 1.81761i 0.0675042i
\(726\) 0 0
\(727\) −31.8208 18.3717i −1.18017 0.681370i −0.224114 0.974563i \(-0.571949\pi\)
−0.956053 + 0.293193i \(0.905282\pi\)
\(728\) 0 0
\(729\) −24.3947 + 11.5715i −0.903507 + 0.428574i
\(730\) 0 0
\(731\) −3.35920 5.81831i −0.124245 0.215198i
\(732\) 0 0
\(733\) 9.41829 + 5.43765i 0.347873 + 0.200844i 0.663748 0.747956i \(-0.268965\pi\)
−0.315875 + 0.948801i \(0.602298\pi\)
\(734\) 0 0
\(735\) 23.1579 + 12.8156i 0.854192 + 0.472712i
\(736\) 0 0
\(737\) −7.41104 + 4.27877i −0.272989 + 0.157610i
\(738\) 0 0
\(739\) −6.91282 + 11.9734i −0.254292 + 0.440447i −0.964703 0.263340i \(-0.915176\pi\)
0.710411 + 0.703787i \(0.248509\pi\)
\(740\) 0 0
\(741\) 3.42961 + 46.3753i 0.125990 + 1.70364i
\(742\) 0 0
\(743\) 15.8751 9.16552i 0.582403 0.336250i −0.179685 0.983724i \(-0.557508\pi\)
0.762088 + 0.647474i \(0.224175\pi\)
\(744\) 0 0
\(745\) 37.8776 21.8687i 1.38773 0.801206i
\(746\) 0 0
\(747\) 6.37557 + 8.02696i 0.233270 + 0.293691i
\(748\) 0 0
\(749\) 17.9095 + 11.0158i 0.654398 + 0.402508i
\(750\) 0 0
\(751\) −9.97084 + 17.2700i −0.363841 + 0.630191i −0.988589 0.150635i \(-0.951868\pi\)
0.624748 + 0.780826i \(0.285202\pi\)
\(752\) 0 0
\(753\) −0.939912 + 0.639471i −0.0342523 + 0.0233036i
\(754\) 0 0
\(755\) −48.5362 −1.76641
\(756\) 0 0
\(757\) −46.9292 −1.70567 −0.852836 0.522178i \(-0.825119\pi\)
−0.852836 + 0.522178i \(0.825119\pi\)
\(758\) 0 0
\(759\) 8.41306 5.72385i 0.305375 0.207762i
\(760\) 0 0
\(761\) 26.7769 46.3789i 0.970661 1.68123i 0.277093 0.960843i \(-0.410629\pi\)
0.693568 0.720391i \(-0.256038\pi\)
\(762\) 0 0
\(763\) 2.67193 + 0.0743955i 0.0967302 + 0.00269330i
\(764\) 0 0
\(765\) −17.1189 + 2.54592i −0.618934 + 0.0920479i
\(766\) 0 0
\(767\) −39.3254 + 22.7045i −1.41996 + 0.819813i
\(768\) 0 0
\(769\) −34.7306 + 20.0517i −1.25242 + 0.723085i −0.971589 0.236673i \(-0.923943\pi\)
−0.280830 + 0.959758i \(0.590610\pi\)
\(770\) 0 0
\(771\) 0.976058 + 13.1983i 0.0351519 + 0.475325i
\(772\) 0 0
\(773\) −7.82375 + 13.5511i −0.281401 + 0.487400i −0.971730 0.236095i \(-0.924132\pi\)
0.690329 + 0.723495i \(0.257466\pi\)
\(774\) 0 0
\(775\) 0.143572 0.0828913i 0.00515726 0.00297755i
\(776\) 0 0
\(777\) 0.597130 + 12.9768i 0.0214219 + 0.465540i
\(778\) 0 0
\(779\) −51.4724 29.7176i −1.84419 1.06474i
\(780\) 0 0
\(781\) −8.56060 14.8274i −0.306322 0.530566i
\(782\) 0 0
\(783\) −11.9847 + 38.4512i −0.428297 + 1.37413i
\(784\) 0 0
\(785\) 15.1785 + 8.76333i 0.541745 + 0.312777i
\(786\) 0 0
\(787\) 46.1788i 1.64610i 0.567972 + 0.823048i \(0.307728\pi\)
−0.567972 + 0.823048i \(0.692272\pi\)
\(788\) 0 0
\(789\) 4.99015 10.3362i 0.177654 0.367979i
\(790\) 0 0
\(791\) −27.4680 16.8951i −0.976651 0.600720i
\(792\) 0 0
\(793\) −13.1750 22.8198i −0.467859 0.810356i
\(794\) 0 0
\(795\) −4.58747 + 9.50212i −0.162701 + 0.337005i
\(796\) 0 0
\(797\) −16.9388 29.3388i −0.600002 1.03923i −0.992820 0.119618i \(-0.961833\pi\)
0.392818 0.919616i \(-0.371500\pi\)
\(798\) 0 0
\(799\) 16.5840 28.7244i 0.586701 1.01620i
\(800\) 0 0
\(801\) 27.4147 4.07712i 0.968652 0.144058i
\(802\) 0 0
\(803\) −6.69844 −0.236383
\(804\) 0 0
\(805\) 19.7257 + 12.1329i 0.695240 + 0.427629i
\(806\) 0 0
\(807\) −1.11991 15.1434i −0.0394226 0.533073i
\(808\) 0 0
\(809\) −33.7873 19.5071i −1.18790 0.685834i −0.230070 0.973174i \(-0.573896\pi\)
−0.957829 + 0.287340i \(0.907229\pi\)
\(810\) 0 0
\(811\) 7.73397i 0.271577i −0.990738 0.135788i \(-0.956643\pi\)
0.990738 0.135788i \(-0.0433567\pi\)
\(812\) 0 0
\(813\) −12.4002 + 25.6849i −0.434895 + 0.900807i
\(814\) 0 0
\(815\) 27.1829 0.952177
\(816\) 0 0
\(817\) 20.1910i 0.706394i
\(818\) 0 0
\(819\) 21.4666 16.0965i 0.750102 0.562459i
\(820\) 0 0
\(821\) 0.512269i 0.0178783i −0.999960 0.00893915i \(-0.997155\pi\)
0.999960 0.00893915i \(-0.00284546\pi\)
\(822\) 0 0
\(823\) 48.3506 1.68540 0.842698 0.538387i \(-0.180966\pi\)
0.842698 + 0.538387i \(0.180966\pi\)
\(824\) 0 0
\(825\) 0.593482 0.0438900i 0.0206624 0.00152805i
\(826\) 0 0
\(827\) 17.3086i 0.601879i −0.953643 0.300940i \(-0.902700\pi\)
0.953643 0.300940i \(-0.0973003\pi\)
\(828\) 0 0
\(829\) 33.0205 + 19.0644i 1.14685 + 0.662134i 0.948118 0.317919i \(-0.102984\pi\)
0.198733 + 0.980054i \(0.436317\pi\)
\(830\) 0 0
\(831\) 27.7246 + 13.3850i 0.961757 + 0.464320i
\(832\) 0 0
\(833\) 8.34372 + 16.5104i 0.289093 + 0.572053i
\(834\) 0 0
\(835\) 43.0481 1.48974
\(836\) 0 0
\(837\) −3.58380 + 0.806892i −0.123874 + 0.0278903i
\(838\) 0 0
\(839\) 15.2026 26.3317i 0.524852 0.909071i −0.474729 0.880132i \(-0.657454\pi\)
0.999581 0.0289389i \(-0.00921281\pi\)
\(840\) 0 0
\(841\) 15.5394 + 26.9151i 0.535842 + 0.928106i
\(842\) 0 0
\(843\) −27.9741 + 2.06878i −0.963479 + 0.0712526i
\(844\) 0 0
\(845\) 1.71674 + 2.97348i 0.0590577 + 0.102291i
\(846\) 0 0
\(847\) −23.4144 0.651937i −0.804528 0.0224008i
\(848\) 0 0
\(849\) −27.6436 40.6313i −0.948726 1.39446i
\(850\) 0 0
\(851\) 11.3664i 0.389635i
\(852\) 0 0
\(853\) 27.7143 + 16.0008i 0.948919 + 0.547858i 0.892745 0.450563i \(-0.148777\pi\)
0.0561738 + 0.998421i \(0.482110\pi\)
\(854\) 0 0
\(855\) 48.3807 + 19.0976i 1.65459 + 0.653126i
\(856\) 0 0
\(857\) −22.5774 39.1053i −0.771230 1.33581i −0.936889 0.349627i \(-0.886308\pi\)
0.165659 0.986183i \(-0.447025\pi\)
\(858\) 0 0
\(859\) 15.7911 + 9.11701i 0.538786 + 0.311068i 0.744587 0.667526i \(-0.232647\pi\)
−0.205801 + 0.978594i \(0.565980\pi\)
\(860\) 0 0
\(861\) 1.57635 + 34.2572i 0.0537220 + 1.16748i
\(862\) 0 0
\(863\) 6.61966 3.82186i 0.225336 0.130098i −0.383083 0.923714i \(-0.625138\pi\)
0.608419 + 0.793616i \(0.291804\pi\)
\(864\) 0 0
\(865\) 1.99468 3.45489i 0.0678213 0.117470i
\(866\) 0 0
\(867\) 15.6229 + 7.54249i 0.530583 + 0.256157i
\(868\) 0 0
\(869\) −11.9069 + 6.87448i −0.403915 + 0.233201i
\(870\) 0 0
\(871\) −17.0984 + 9.87179i −0.579358 + 0.334493i
\(872\) 0 0
\(873\) 17.3169 13.7543i 0.586089 0.465513i
\(874\) 0 0
\(875\) 14.3818 + 26.5930i 0.486194 + 0.899006i
\(876\) 0 0
\(877\) −8.01581 + 13.8838i −0.270675 + 0.468822i −0.969035 0.246924i \(-0.920580\pi\)
0.698360 + 0.715747i \(0.253913\pi\)
\(878\) 0 0
\(879\) −13.6718 6.60053i −0.461139 0.222630i
\(880\) 0 0
\(881\) 24.7532 0.833958 0.416979 0.908916i \(-0.363089\pi\)
0.416979 + 0.908916i \(0.363089\pi\)
\(882\) 0 0
\(883\) 11.6958 0.393595 0.196798 0.980444i \(-0.436946\pi\)
0.196798 + 0.980444i \(0.436946\pi\)
\(884\) 0 0
\(885\) 3.74595 + 50.6528i 0.125919 + 1.70268i
\(886\) 0 0
\(887\) −27.5429 + 47.7058i −0.924801 + 1.60180i −0.132921 + 0.991127i \(0.542436\pi\)
−0.791880 + 0.610676i \(0.790898\pi\)
\(888\) 0 0
\(889\) −8.55024 15.8100i −0.286766 0.530249i
\(890\) 0 0
\(891\) −12.8444 2.98472i −0.430305 0.0999920i
\(892\) 0 0
\(893\) −86.3261 + 49.8404i −2.88879 + 1.66785i
\(894\) 0 0
\(895\) −26.4541 + 15.2733i −0.884262 + 0.510529i
\(896\) 0 0
\(897\) 19.4102 13.2058i 0.648089 0.440929i
\(898\) 0 0
\(899\) −2.73987 + 4.74560i −0.0913799 + 0.158275i
\(900\) 0 0
\(901\) −6.38677 + 3.68741i −0.212774 + 0.122845i
\(902\) 0 0
\(903\) 9.81078 6.28261i 0.326482 0.209072i
\(904\) 0 0
\(905\) 30.9281 + 17.8563i 1.02808 + 0.593565i
\(906\) 0 0
\(907\) −12.9383 22.4098i −0.429610 0.744107i 0.567228 0.823560i \(-0.308016\pi\)
−0.996839 + 0.0794540i \(0.974682\pi\)
\(908\) 0 0
\(909\) 23.5227 3.49830i 0.780199 0.116031i
\(910\) 0 0
\(911\) 3.86306 + 2.23034i 0.127989 + 0.0738944i 0.562627 0.826711i \(-0.309791\pi\)
−0.434639 + 0.900605i \(0.643124\pi\)
\(912\) 0 0
\(913\) 5.00646i 0.165690i
\(914\) 0 0
\(915\) −29.3929 + 2.17371i −0.971701 + 0.0718606i
\(916\) 0 0
\(917\) −36.3274 1.01148i −1.19964 0.0334020i
\(918\) 0 0
\(919\) 21.2352 + 36.7805i 0.700485 + 1.21328i 0.968296 + 0.249804i \(0.0803663\pi\)
−0.267811 + 0.963471i \(0.586300\pi\)
\(920\) 0 0
\(921\) 12.5194 + 18.4014i 0.412529 + 0.606346i
\(922\) 0 0
\(923\) −19.7507 34.2091i −0.650101 1.12601i
\(924\) 0 0
\(925\) −0.332373 + 0.575688i −0.0109284 + 0.0189285i
\(926\) 0 0
\(927\) 8.86538 7.04150i 0.291177 0.231273i
\(928\) 0 0
\(929\) −15.4502 −0.506903 −0.253452 0.967348i \(-0.581566\pi\)
−0.253452 + 0.967348i \(0.581566\pi\)
\(930\) 0 0
\(931\) 3.09354 55.5093i 0.101387 1.81925i
\(932\) 0 0
\(933\) 9.44207 6.42394i 0.309120 0.210310i
\(934\) 0 0
\(935\) −7.32027 4.22636i −0.239398 0.138217i
\(936\) 0 0
\(937\) 46.1410i 1.50736i 0.657241 + 0.753680i \(0.271723\pi\)
−0.657241 + 0.753680i \(0.728277\pi\)
\(938\) 0 0
\(939\) 3.32681 + 4.88983i 0.108566 + 0.159574i
\(940\) 0 0
\(941\) −41.0104 −1.33690 −0.668451 0.743756i \(-0.733042\pi\)
−0.668451 + 0.743756i \(0.733042\pi\)
\(942\) 0 0
\(943\) 30.0060i 0.977128i
\(944\) 0 0
\(945\) −5.77458 29.4505i −0.187847 0.958026i
\(946\) 0 0
\(947\) 9.82254i 0.319190i 0.987183 + 0.159595i \(0.0510188\pi\)
−0.987183 + 0.159595i \(0.948981\pi\)
\(948\) 0 0
\(949\) −15.4544 −0.501670
\(950\) 0 0
\(951\) −31.2758 45.9700i −1.01419 1.49068i
\(952\) 0 0
\(953\) 17.0826i 0.553359i 0.960962 + 0.276679i \(0.0892340\pi\)
−0.960962 + 0.276679i \(0.910766\pi\)
\(954\) 0 0
\(955\) 25.8305 + 14.9132i 0.835855 + 0.482581i
\(956\) 0 0
\(957\) −16.2633 + 11.0648i −0.525719 + 0.357674i
\(958\) 0 0
\(959\) 45.2857 + 27.8544i 1.46235 + 0.899466i
\(960\) 0 0
\(961\) 30.5002 0.983877
\(962\) 0 0
\(963\) −3.50712 23.5820i −0.113015 0.759919i
\(964\) 0 0
\(965\) −4.77826 + 8.27619i −0.153818 + 0.266420i
\(966\) 0 0
\(967\) −21.3240 36.9343i −0.685735 1.18773i −0.973205 0.229938i \(-0.926148\pi\)
0.287471 0.957789i \(-0.407186\pi\)
\(968\) 0 0
\(969\) 20.4495 + 30.0571i 0.656931 + 0.965574i
\(970\) 0 0
\(971\) −11.7562 20.3623i −0.377275 0.653459i 0.613390 0.789780i \(-0.289805\pi\)
−0.990665 + 0.136321i \(0.956472\pi\)
\(972\) 0 0
\(973\) −22.1553 13.6273i −0.710267 0.436872i
\(974\) 0 0
\(975\) 1.36926 0.101261i 0.0438513 0.00324295i
\(976\) 0 0
\(977\) 34.8654i 1.11544i 0.830028 + 0.557722i \(0.188325\pi\)
−0.830028 + 0.557722i \(0.811675\pi\)
\(978\) 0 0
\(979\) 11.7229 + 6.76824i 0.374666 + 0.216314i
\(980\) 0 0
\(981\) −1.88505 2.37332i −0.0601851 0.0757742i
\(982\) 0 0
\(983\) 13.1804 + 22.8292i 0.420390 + 0.728137i 0.995978 0.0896033i \(-0.0285599\pi\)
−0.575587 + 0.817740i \(0.695227\pi\)
\(984\) 0 0
\(985\) −1.90194 1.09808i −0.0606008 0.0349879i
\(986\) 0 0
\(987\) 51.0785 + 26.4374i 1.62585 + 0.841513i
\(988\) 0 0
\(989\) 8.82780 5.09673i 0.280708 0.162067i
\(990\) 0 0
\(991\) −0.0805213 + 0.139467i −0.00255784 + 0.00443031i −0.867301 0.497783i \(-0.834148\pi\)
0.864744 + 0.502214i \(0.167481\pi\)
\(992\) 0 0
\(993\) 41.3621 28.1408i 1.31259 0.893022i
\(994\) 0 0
\(995\) 12.3916 7.15427i 0.392839 0.226806i
\(996\) 0 0
\(997\) 14.5820 8.41890i 0.461816 0.266629i −0.250992 0.967989i \(-0.580757\pi\)
0.712807 + 0.701360i \(0.247423\pi\)
\(998\) 0 0
\(999\) 10.8272 9.98704i 0.342557 0.315976i
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 1008.2.ca.d.353.7 16
3.2 odd 2 3024.2.ca.d.2033.3 16
4.3 odd 2 252.2.w.a.101.2 yes 16
7.5 odd 6 1008.2.df.d.929.5 16
9.4 even 3 3024.2.df.d.17.3 16
9.5 odd 6 1008.2.df.d.689.5 16
12.11 even 2 756.2.w.a.521.3 16
21.5 even 6 3024.2.df.d.1601.3 16
28.3 even 6 1764.2.x.b.1469.2 16
28.11 odd 6 1764.2.x.a.1469.7 16
28.19 even 6 252.2.bm.a.173.4 yes 16
28.23 odd 6 1764.2.bm.a.1685.5 16
28.27 even 2 1764.2.w.b.1109.7 16
36.7 odd 6 2268.2.t.b.1781.6 16
36.11 even 6 2268.2.t.a.1781.3 16
36.23 even 6 252.2.bm.a.185.4 yes 16
36.31 odd 6 756.2.bm.a.17.3 16
63.5 even 6 inner 1008.2.ca.d.257.7 16
63.40 odd 6 3024.2.ca.d.2609.3 16
84.11 even 6 5292.2.x.a.4409.3 16
84.23 even 6 5292.2.bm.a.4625.6 16
84.47 odd 6 756.2.bm.a.89.3 16
84.59 odd 6 5292.2.x.b.4409.6 16
84.83 odd 2 5292.2.w.b.521.6 16
252.23 even 6 1764.2.w.b.509.7 16
252.31 even 6 5292.2.x.a.881.3 16
252.47 odd 6 2268.2.t.b.2105.6 16
252.59 odd 6 1764.2.x.a.293.7 16
252.67 odd 6 5292.2.x.b.881.6 16
252.95 even 6 1764.2.x.b.293.2 16
252.103 even 6 756.2.w.a.341.3 16
252.131 odd 6 252.2.w.a.5.2 16
252.139 even 6 5292.2.bm.a.2285.6 16
252.167 odd 6 1764.2.bm.a.1697.5 16
252.187 even 6 2268.2.t.a.2105.3 16
252.247 odd 6 5292.2.w.b.1097.6 16
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
252.2.w.a.5.2 16 252.131 odd 6
252.2.w.a.101.2 yes 16 4.3 odd 2
252.2.bm.a.173.4 yes 16 28.19 even 6
252.2.bm.a.185.4 yes 16 36.23 even 6
756.2.w.a.341.3 16 252.103 even 6
756.2.w.a.521.3 16 12.11 even 2
756.2.bm.a.17.3 16 36.31 odd 6
756.2.bm.a.89.3 16 84.47 odd 6
1008.2.ca.d.257.7 16 63.5 even 6 inner
1008.2.ca.d.353.7 16 1.1 even 1 trivial
1008.2.df.d.689.5 16 9.5 odd 6
1008.2.df.d.929.5 16 7.5 odd 6
1764.2.w.b.509.7 16 252.23 even 6
1764.2.w.b.1109.7 16 28.27 even 2
1764.2.x.a.293.7 16 252.59 odd 6
1764.2.x.a.1469.7 16 28.11 odd 6
1764.2.x.b.293.2 16 252.95 even 6
1764.2.x.b.1469.2 16 28.3 even 6
1764.2.bm.a.1685.5 16 28.23 odd 6
1764.2.bm.a.1697.5 16 252.167 odd 6
2268.2.t.a.1781.3 16 36.11 even 6
2268.2.t.a.2105.3 16 252.187 even 6
2268.2.t.b.1781.6 16 36.7 odd 6
2268.2.t.b.2105.6 16 252.47 odd 6
3024.2.ca.d.2033.3 16 3.2 odd 2
3024.2.ca.d.2609.3 16 63.40 odd 6
3024.2.df.d.17.3 16 9.4 even 3
3024.2.df.d.1601.3 16 21.5 even 6
5292.2.w.b.521.6 16 84.83 odd 2
5292.2.w.b.1097.6 16 252.247 odd 6
5292.2.x.a.881.3 16 252.31 even 6
5292.2.x.a.4409.3 16 84.11 even 6
5292.2.x.b.881.6 16 252.67 odd 6
5292.2.x.b.4409.6 16 84.59 odd 6
5292.2.bm.a.2285.6 16 252.139 even 6
5292.2.bm.a.4625.6 16 84.23 even 6