Properties

Label 128.2.g.b.81.1
Level $128$
Weight $2$
Character 128.81
Analytic conductor $1.022$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [128,2,Mod(17,128)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(128, base_ring=CyclotomicField(8))
 
chi = DirichletCharacter(H, H._module([0, 7]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("128.17");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 128 = 2^{7} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 128.g (of order \(8\), degree \(4\), 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: \(1.02208514587\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(2\) over \(\Q(\zeta_{8})\)
Coefficient field: 8.0.18939904.2
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{8} - 4x^{7} + 14x^{6} - 28x^{5} + 43x^{4} - 44x^{3} + 30x^{2} - 12x + 2 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 2^{3} \)
Twist minimal: no (minimal twist has level 32)
Sato-Tate group: $\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label 81.1
Root \(0.500000 - 0.0297061i\) of defining polynomial
Character \(\chi\) \(=\) 128.81
Dual form 128.2.g.b.49.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.27882 - 0.529706i) q^{3} +(-0.707107 - 1.70711i) q^{5} +(2.74912 - 2.74912i) q^{7} +(-0.766519 - 0.766519i) q^{9} +O(q^{10})\) \(q+(-1.27882 - 0.529706i) q^{3} +(-0.707107 - 1.70711i) q^{5} +(2.74912 - 2.74912i) q^{7} +(-0.766519 - 0.766519i) q^{9} +(-0.135390 + 0.0560803i) q^{11} +(1.18073 - 2.85054i) q^{13} +2.55765i q^{15} +6.44549i q^{17} +(-0.805198 + 1.94392i) q^{19} +(-4.97186 + 2.05941i) q^{21} +(-0.749118 - 0.749118i) q^{23} +(1.12132 - 1.12132i) q^{25} +(2.16333 + 5.22274i) q^{27} +(4.32417 + 1.79113i) q^{29} -1.17157 q^{31} +0.202846 q^{33} +(-6.63696 - 2.74912i) q^{35} +(1.73172 + 4.18073i) q^{37} +(-3.01990 + 3.01990i) q^{39} +(-2.49824 - 2.49824i) q^{41} +(6.10725 - 2.52971i) q^{43} +(-0.766519 + 1.85054i) q^{45} +2.66981i q^{47} -8.11529i q^{49} +(3.41421 - 8.24264i) q^{51} +(1.64769 - 0.682497i) q^{53} +(0.191470 + 0.191470i) q^{55} +(2.05941 - 2.05941i) q^{57} +(-1.43744 - 3.47029i) q^{59} +(-3.46760 - 1.43633i) q^{61} -4.21450 q^{63} -5.70108 q^{65} +(14.0791 + 5.83176i) q^{67} +(0.561177 + 1.35480i) q^{69} +(3.40950 - 3.40950i) q^{71} +(-0.442353 - 0.442353i) q^{73} +(-2.02794 + 0.840001i) q^{75} +(-0.218031 + 0.526374i) q^{77} -7.07550i q^{79} -4.57283i q^{81} +(-2.99862 + 7.23931i) q^{83} +(11.0031 - 4.55765i) q^{85} +(-4.58107 - 4.58107i) q^{87} +(-4.21803 + 4.21803i) q^{89} +(-4.59050 - 11.0824i) q^{91} +(1.49824 + 0.620589i) q^{93} +3.88784 q^{95} +10.3267 q^{97} +(0.146766 + 0.0607923i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q + 4 q^{3} + 8 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 8 q + 4 q^{3} + 8 q^{7} - 4 q^{11} - 8 q^{13} - 4 q^{19} + 8 q^{23} - 8 q^{25} - 8 q^{27} - 32 q^{31} - 16 q^{33} - 16 q^{35} - 8 q^{37} - 16 q^{39} + 8 q^{41} + 12 q^{43} + 16 q^{51} + 8 q^{53} + 16 q^{55} + 16 q^{57} + 20 q^{59} + 24 q^{61} + 40 q^{63} + 36 q^{67} + 32 q^{69} + 24 q^{71} - 32 q^{73} + 12 q^{75} + 16 q^{77} - 20 q^{83} + 8 q^{85} - 56 q^{87} - 16 q^{89} - 40 q^{91} - 16 q^{93} + 8 q^{95} + 32 q^{97} - 28 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/128\mathbb{Z}\right)^\times\).

\(n\) \(5\) \(127\)
\(\chi(n)\) \(e\left(\frac{3}{8}\right)\) \(1\)

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
\(3\) −1.27882 0.529706i −0.738329 0.305826i −0.0183595 0.999831i \(-0.505844\pi\)
−0.719970 + 0.694005i \(0.755844\pi\)
\(4\) 0 0
\(5\) −0.707107 1.70711i −0.316228 0.763441i −0.999448 0.0332288i \(-0.989421\pi\)
0.683220 0.730213i \(-0.260579\pi\)
\(6\) 0 0
\(7\) 2.74912 2.74912i 1.03907 1.03907i 0.0398636 0.999205i \(-0.487308\pi\)
0.999205 0.0398636i \(-0.0126924\pi\)
\(8\) 0 0
\(9\) −0.766519 0.766519i −0.255506 0.255506i
\(10\) 0 0
\(11\) −0.135390 + 0.0560803i −0.0408216 + 0.0169089i −0.403001 0.915200i \(-0.632033\pi\)
0.362179 + 0.932108i \(0.382033\pi\)
\(12\) 0 0
\(13\) 1.18073 2.85054i 0.327476 0.790598i −0.671302 0.741184i \(-0.734265\pi\)
0.998778 0.0494138i \(-0.0157353\pi\)
\(14\) 0 0
\(15\) 2.55765i 0.660382i
\(16\) 0 0
\(17\) 6.44549i 1.56326i 0.623742 + 0.781630i \(0.285611\pi\)
−0.623742 + 0.781630i \(0.714389\pi\)
\(18\) 0 0
\(19\) −0.805198 + 1.94392i −0.184725 + 0.445966i −0.988929 0.148387i \(-0.952592\pi\)
0.804204 + 0.594353i \(0.202592\pi\)
\(20\) 0 0
\(21\) −4.97186 + 2.05941i −1.08495 + 0.449401i
\(22\) 0 0
\(23\) −0.749118 0.749118i −0.156202 0.156202i 0.624679 0.780881i \(-0.285230\pi\)
−0.780881 + 0.624679i \(0.785230\pi\)
\(24\) 0 0
\(25\) 1.12132 1.12132i 0.224264 0.224264i
\(26\) 0 0
\(27\) 2.16333 + 5.22274i 0.416333 + 1.00512i
\(28\) 0 0
\(29\) 4.32417 + 1.79113i 0.802978 + 0.332604i 0.746148 0.665780i \(-0.231901\pi\)
0.0568292 + 0.998384i \(0.481901\pi\)
\(30\) 0 0
\(31\) −1.17157 −0.210421 −0.105210 0.994450i \(-0.533552\pi\)
−0.105210 + 0.994450i \(0.533552\pi\)
\(32\) 0 0
\(33\) 0.202846 0.0353109
\(34\) 0 0
\(35\) −6.63696 2.74912i −1.12185 0.464686i
\(36\) 0 0
\(37\) 1.73172 + 4.18073i 0.284692 + 0.687308i 0.999933 0.0115700i \(-0.00368293\pi\)
−0.715241 + 0.698878i \(0.753683\pi\)
\(38\) 0 0
\(39\) −3.01990 + 3.01990i −0.483571 + 0.483571i
\(40\) 0 0
\(41\) −2.49824 2.49824i −0.390159 0.390159i 0.484585 0.874744i \(-0.338971\pi\)
−0.874744 + 0.484585i \(0.838971\pi\)
\(42\) 0 0
\(43\) 6.10725 2.52971i 0.931347 0.385777i 0.135158 0.990824i \(-0.456846\pi\)
0.796189 + 0.605048i \(0.206846\pi\)
\(44\) 0 0
\(45\) −0.766519 + 1.85054i −0.114266 + 0.275862i
\(46\) 0 0
\(47\) 2.66981i 0.389432i 0.980860 + 0.194716i \(0.0623784\pi\)
−0.980860 + 0.194716i \(0.937622\pi\)
\(48\) 0 0
\(49\) 8.11529i 1.15933i
\(50\) 0 0
\(51\) 3.41421 8.24264i 0.478086 1.15420i
\(52\) 0 0
\(53\) 1.64769 0.682497i 0.226328 0.0937482i −0.266638 0.963797i \(-0.585913\pi\)
0.492966 + 0.870049i \(0.335913\pi\)
\(54\) 0 0
\(55\) 0.191470 + 0.191470i 0.0258178 + 0.0258178i
\(56\) 0 0
\(57\) 2.05941 2.05941i 0.272776 0.272776i
\(58\) 0 0
\(59\) −1.43744 3.47029i −0.187139 0.451794i 0.802267 0.596965i \(-0.203627\pi\)
−0.989407 + 0.145171i \(0.953627\pi\)
\(60\) 0 0
\(61\) −3.46760 1.43633i −0.443981 0.183903i 0.149482 0.988764i \(-0.452239\pi\)
−0.593462 + 0.804862i \(0.702239\pi\)
\(62\) 0 0
\(63\) −4.21450 −0.530977
\(64\) 0 0
\(65\) −5.70108 −0.707132
\(66\) 0 0
\(67\) 14.0791 + 5.83176i 1.72004 + 0.712463i 0.999825 + 0.0187090i \(0.00595560\pi\)
0.720212 + 0.693754i \(0.244044\pi\)
\(68\) 0 0
\(69\) 0.561177 + 1.35480i 0.0675578 + 0.163099i
\(70\) 0 0
\(71\) 3.40950 3.40950i 0.404633 0.404633i −0.475229 0.879862i \(-0.657635\pi\)
0.879862 + 0.475229i \(0.157635\pi\)
\(72\) 0 0
\(73\) −0.442353 0.442353i −0.0517735 0.0517735i 0.680746 0.732520i \(-0.261656\pi\)
−0.732520 + 0.680746i \(0.761656\pi\)
\(74\) 0 0
\(75\) −2.02794 + 0.840001i −0.234166 + 0.0969949i
\(76\) 0 0
\(77\) −0.218031 + 0.526374i −0.0248470 + 0.0599859i
\(78\) 0 0
\(79\) 7.07550i 0.796056i −0.917373 0.398028i \(-0.869695\pi\)
0.917373 0.398028i \(-0.130305\pi\)
\(80\) 0 0
\(81\) 4.57283i 0.508093i
\(82\) 0 0
\(83\) −2.99862 + 7.23931i −0.329141 + 0.794617i 0.669515 + 0.742798i \(0.266502\pi\)
−0.998656 + 0.0518190i \(0.983498\pi\)
\(84\) 0 0
\(85\) 11.0031 4.55765i 1.19346 0.494346i
\(86\) 0 0
\(87\) −4.58107 4.58107i −0.491143 0.491143i
\(88\) 0 0
\(89\) −4.21803 + 4.21803i −0.447110 + 0.447110i −0.894393 0.447282i \(-0.852392\pi\)
0.447282 + 0.894393i \(0.352392\pi\)
\(90\) 0 0
\(91\) −4.59050 11.0824i −0.481215 1.16176i
\(92\) 0 0
\(93\) 1.49824 + 0.620589i 0.155360 + 0.0643521i
\(94\) 0 0
\(95\) 3.88784 0.398884
\(96\) 0 0
\(97\) 10.3267 1.04851 0.524257 0.851560i \(-0.324343\pi\)
0.524257 + 0.851560i \(0.324343\pi\)
\(98\) 0 0
\(99\) 0.146766 + 0.0607923i 0.0147505 + 0.00610986i
\(100\) 0 0
\(101\) −4.31750 10.4234i −0.429608 1.03716i −0.979412 0.201871i \(-0.935298\pi\)
0.549805 0.835293i \(-0.314702\pi\)
\(102\) 0 0
\(103\) −13.3134 + 13.3134i −1.31181 + 1.31181i −0.391732 + 0.920080i \(0.628124\pi\)
−0.920080 + 0.391732i \(0.871876\pi\)
\(104\) 0 0
\(105\) 7.03127 + 7.03127i 0.686182 + 0.686182i
\(106\) 0 0
\(107\) −13.2507 + 5.48861i −1.28099 + 0.530604i −0.916288 0.400519i \(-0.868830\pi\)
−0.364704 + 0.931124i \(0.618830\pi\)
\(108\) 0 0
\(109\) −4.87515 + 11.7697i −0.466955 + 1.12733i 0.498531 + 0.866872i \(0.333873\pi\)
−0.965486 + 0.260456i \(0.916127\pi\)
\(110\) 0 0
\(111\) 6.26372i 0.594526i
\(112\) 0 0
\(113\) 5.88118i 0.553254i 0.960977 + 0.276627i \(0.0892167\pi\)
−0.960977 + 0.276627i \(0.910783\pi\)
\(114\) 0 0
\(115\) −0.749118 + 1.80853i −0.0698556 + 0.168646i
\(116\) 0 0
\(117\) −3.09005 + 1.27994i −0.285675 + 0.118330i
\(118\) 0 0
\(119\) 17.7194 + 17.7194i 1.62433 + 1.62433i
\(120\) 0 0
\(121\) −7.76299 + 7.76299i −0.705726 + 0.705726i
\(122\) 0 0
\(123\) 1.87147 + 4.51813i 0.168745 + 0.407386i
\(124\) 0 0
\(125\) −11.2426 4.65685i −1.00557 0.416522i
\(126\) 0 0
\(127\) 15.4022 1.36672 0.683360 0.730081i \(-0.260518\pi\)
0.683360 + 0.730081i \(0.260518\pi\)
\(128\) 0 0
\(129\) −9.15010 −0.805621
\(130\) 0 0
\(131\) 2.96382 + 1.22765i 0.258950 + 0.107261i 0.508382 0.861132i \(-0.330244\pi\)
−0.249432 + 0.968392i \(0.580244\pi\)
\(132\) 0 0
\(133\) 3.13048 + 7.55765i 0.271447 + 0.655331i
\(134\) 0 0
\(135\) 7.38607 7.38607i 0.635692 0.635692i
\(136\) 0 0
\(137\) 10.7757 + 10.7757i 0.920628 + 0.920628i 0.997074 0.0764454i \(-0.0243571\pi\)
−0.0764454 + 0.997074i \(0.524357\pi\)
\(138\) 0 0
\(139\) −4.78372 + 1.98148i −0.405750 + 0.168067i −0.576218 0.817296i \(-0.695472\pi\)
0.170468 + 0.985363i \(0.445472\pi\)
\(140\) 0 0
\(141\) 1.41421 3.41421i 0.119098 0.287529i
\(142\) 0 0
\(143\) 0.452150i 0.0378107i
\(144\) 0 0
\(145\) 8.64833i 0.718205i
\(146\) 0 0
\(147\) −4.29872 + 10.3780i −0.354553 + 0.855966i
\(148\) 0 0
\(149\) 4.32417 1.79113i 0.354250 0.146735i −0.198460 0.980109i \(-0.563594\pi\)
0.552709 + 0.833374i \(0.313594\pi\)
\(150\) 0 0
\(151\) −13.2344 13.2344i −1.07700 1.07700i −0.996777 0.0802232i \(-0.974437\pi\)
−0.0802232 0.996777i \(-0.525563\pi\)
\(152\) 0 0
\(153\) 4.94059 4.94059i 0.399423 0.399423i
\(154\) 0 0
\(155\) 0.828427 + 2.00000i 0.0665409 + 0.160644i
\(156\) 0 0
\(157\) −15.9529 6.60790i −1.27318 0.527368i −0.359249 0.933242i \(-0.616967\pi\)
−0.913929 + 0.405874i \(0.866967\pi\)
\(158\) 0 0
\(159\) −2.46863 −0.195775
\(160\) 0 0
\(161\) −4.11882 −0.324609
\(162\) 0 0
\(163\) −10.6488 4.41088i −0.834079 0.345487i −0.0755629 0.997141i \(-0.524075\pi\)
−0.758516 + 0.651654i \(0.774075\pi\)
\(164\) 0 0
\(165\) −0.143434 0.346280i −0.0111663 0.0269578i
\(166\) 0 0
\(167\) 2.98677 2.98677i 0.231123 0.231123i −0.582038 0.813161i \(-0.697745\pi\)
0.813161 + 0.582038i \(0.197745\pi\)
\(168\) 0 0
\(169\) 2.46094 + 2.46094i 0.189303 + 0.189303i
\(170\) 0 0
\(171\) 2.10725 0.872852i 0.161145 0.0667486i
\(172\) 0 0
\(173\) 7.85054 18.9529i 0.596866 1.44096i −0.279894 0.960031i \(-0.590299\pi\)
0.876759 0.480930i \(-0.159701\pi\)
\(174\) 0 0
\(175\) 6.16528i 0.466052i
\(176\) 0 0
\(177\) 5.19932i 0.390805i
\(178\) 0 0
\(179\) 9.60549 23.1897i 0.717948 1.73328i 0.0388344 0.999246i \(-0.487636\pi\)
0.679113 0.734033i \(-0.262364\pi\)
\(180\) 0 0
\(181\) 1.87868 0.778175i 0.139641 0.0578413i −0.311768 0.950158i \(-0.600921\pi\)
0.451410 + 0.892317i \(0.350921\pi\)
\(182\) 0 0
\(183\) 3.67362 + 3.67362i 0.271562 + 0.271562i
\(184\) 0 0
\(185\) 5.91245 5.91245i 0.434692 0.434692i
\(186\) 0 0
\(187\) −0.361465 0.872654i −0.0264329 0.0638148i
\(188\) 0 0
\(189\) 20.3052 + 8.41068i 1.47699 + 0.611787i
\(190\) 0 0
\(191\) −9.05902 −0.655487 −0.327744 0.944767i \(-0.606288\pi\)
−0.327744 + 0.944767i \(0.606288\pi\)
\(192\) 0 0
\(193\) 6.24707 0.449674 0.224837 0.974396i \(-0.427815\pi\)
0.224837 + 0.974396i \(0.427815\pi\)
\(194\) 0 0
\(195\) 7.29068 + 3.01990i 0.522096 + 0.216259i
\(196\) 0 0
\(197\) −1.81298 4.37691i −0.129169 0.311842i 0.846043 0.533115i \(-0.178979\pi\)
−0.975212 + 0.221273i \(0.928979\pi\)
\(198\) 0 0
\(199\) −6.14186 + 6.14186i −0.435385 + 0.435385i −0.890455 0.455071i \(-0.849614\pi\)
0.455071 + 0.890455i \(0.349614\pi\)
\(200\) 0 0
\(201\) −14.9156 14.9156i −1.05206 1.05206i
\(202\) 0 0
\(203\) 16.8117 6.96362i 1.17995 0.488750i
\(204\) 0 0
\(205\) −2.49824 + 6.03127i −0.174484 + 0.421242i
\(206\) 0 0
\(207\) 1.14843i 0.0798211i
\(208\) 0 0
\(209\) 0.308343i 0.0213285i
\(210\) 0 0
\(211\) −5.21588 + 12.5923i −0.359076 + 0.866886i 0.636354 + 0.771397i \(0.280442\pi\)
−0.995430 + 0.0954895i \(0.969558\pi\)
\(212\) 0 0
\(213\) −6.16619 + 2.55412i −0.422500 + 0.175005i
\(214\) 0 0
\(215\) −8.63696 8.63696i −0.589036 0.589036i
\(216\) 0 0
\(217\) −3.22079 + 3.22079i −0.218642 + 0.218642i
\(218\) 0 0
\(219\) 0.331374 + 0.800008i 0.0223922 + 0.0540595i
\(220\) 0 0
\(221\) 18.3731 + 7.61040i 1.23591 + 0.511931i
\(222\) 0 0
\(223\) 0.960579 0.0643251 0.0321626 0.999483i \(-0.489761\pi\)
0.0321626 + 0.999483i \(0.489761\pi\)
\(224\) 0 0
\(225\) −1.71903 −0.114602
\(226\) 0 0
\(227\) −14.1698 5.86932i −0.940482 0.389561i −0.140837 0.990033i \(-0.544979\pi\)
−0.799646 + 0.600472i \(0.794979\pi\)
\(228\) 0 0
\(229\) 1.80408 + 4.35544i 0.119217 + 0.287816i 0.972211 0.234105i \(-0.0752159\pi\)
−0.852994 + 0.521920i \(0.825216\pi\)
\(230\) 0 0
\(231\) 0.557647 0.557647i 0.0366905 0.0366905i
\(232\) 0 0
\(233\) −16.7918 16.7918i −1.10007 1.10007i −0.994402 0.105663i \(-0.966303\pi\)
−0.105663 0.994402i \(-0.533697\pi\)
\(234\) 0 0
\(235\) 4.55765 1.88784i 0.297308 0.123149i
\(236\) 0 0
\(237\) −3.74794 + 9.04832i −0.243455 + 0.587751i
\(238\) 0 0
\(239\) 15.8414i 1.02469i 0.858779 + 0.512347i \(0.171224\pi\)
−0.858779 + 0.512347i \(0.828776\pi\)
\(240\) 0 0
\(241\) 0.313335i 0.0201837i −0.999949 0.0100918i \(-0.996788\pi\)
0.999949 0.0100918i \(-0.00321239\pi\)
\(242\) 0 0
\(243\) 4.06774 9.82038i 0.260945 0.629978i
\(244\) 0 0
\(245\) −13.8537 + 5.73838i −0.885079 + 0.366612i
\(246\) 0 0
\(247\) 4.59050 + 4.59050i 0.292086 + 0.292086i
\(248\) 0 0
\(249\) 7.66941 7.66941i 0.486029 0.486029i
\(250\) 0 0
\(251\) 3.55903 + 8.59225i 0.224644 + 0.542338i 0.995510 0.0946593i \(-0.0301762\pi\)
−0.770866 + 0.636997i \(0.780176\pi\)
\(252\) 0 0
\(253\) 0.143434 + 0.0594122i 0.00901760 + 0.00373521i
\(254\) 0 0
\(255\) −16.4853 −1.03235
\(256\) 0 0
\(257\) 18.9043 1.17922 0.589609 0.807689i \(-0.299282\pi\)
0.589609 + 0.807689i \(0.299282\pi\)
\(258\) 0 0
\(259\) 16.2540 + 6.73263i 1.00998 + 0.418346i
\(260\) 0 0
\(261\) −1.94162 4.68749i −0.120183 0.290148i
\(262\) 0 0
\(263\) 16.6366 16.6366i 1.02585 1.02585i 0.0261975 0.999657i \(-0.491660\pi\)
0.999657 0.0261975i \(-0.00833988\pi\)
\(264\) 0 0
\(265\) −2.33019 2.33019i −0.143143 0.143143i
\(266\) 0 0
\(267\) 7.62844 3.15980i 0.466853 0.193377i
\(268\) 0 0
\(269\) −5.01046 + 12.0963i −0.305493 + 0.737525i 0.694347 + 0.719640i \(0.255693\pi\)
−0.999840 + 0.0178850i \(0.994307\pi\)
\(270\) 0 0
\(271\) 28.2141i 1.71388i 0.515412 + 0.856942i \(0.327639\pi\)
−0.515412 + 0.856942i \(0.672361\pi\)
\(272\) 0 0
\(273\) 16.6041i 1.00493i
\(274\) 0 0
\(275\) −0.0889314 + 0.214699i −0.00536277 + 0.0129469i
\(276\) 0 0
\(277\) −21.8246 + 9.04006i −1.31132 + 0.543165i −0.925268 0.379314i \(-0.876160\pi\)
−0.386047 + 0.922479i \(0.626160\pi\)
\(278\) 0 0
\(279\) 0.898033 + 0.898033i 0.0537638 + 0.0537638i
\(280\) 0 0
\(281\) 3.00666 3.00666i 0.179363 0.179363i −0.611715 0.791078i \(-0.709520\pi\)
0.791078 + 0.611715i \(0.209520\pi\)
\(282\) 0 0
\(283\) −0.709521 1.71293i −0.0421766 0.101823i 0.901387 0.433014i \(-0.142550\pi\)
−0.943564 + 0.331190i \(0.892550\pi\)
\(284\) 0 0
\(285\) −4.97186 2.05941i −0.294508 0.121989i
\(286\) 0 0
\(287\) −13.7359 −0.810804
\(288\) 0 0
\(289\) −24.5443 −1.44378
\(290\) 0 0
\(291\) −13.2060 5.47010i −0.774148 0.320663i
\(292\) 0 0
\(293\) 10.5176 + 25.3917i 0.614444 + 1.48340i 0.858071 + 0.513530i \(0.171663\pi\)
−0.243627 + 0.969869i \(0.578337\pi\)
\(294\) 0 0
\(295\) −4.90774 + 4.90774i −0.285739 + 0.285739i
\(296\) 0 0
\(297\) −0.585786 0.585786i −0.0339908 0.0339908i
\(298\) 0 0
\(299\) −3.01990 + 1.25088i −0.174645 + 0.0723404i
\(300\) 0 0
\(301\) 9.83509 23.7440i 0.566885 1.36858i
\(302\) 0 0
\(303\) 15.6167i 0.897154i
\(304\) 0 0
\(305\) 6.93520i 0.397108i
\(306\) 0 0
\(307\) −5.80167 + 14.0065i −0.331119 + 0.799391i 0.667385 + 0.744713i \(0.267413\pi\)
−0.998504 + 0.0546786i \(0.982587\pi\)
\(308\) 0 0
\(309\) 24.0777 9.97332i 1.36973 0.567363i
\(310\) 0 0
\(311\) −7.15481 7.15481i −0.405712 0.405712i 0.474528 0.880240i \(-0.342619\pi\)
−0.880240 + 0.474528i \(0.842619\pi\)
\(312\) 0 0
\(313\) −11.8512 + 11.8512i −0.669868 + 0.669868i −0.957685 0.287817i \(-0.907070\pi\)
0.287817 + 0.957685i \(0.407070\pi\)
\(314\) 0 0
\(315\) 2.98010 + 7.19460i 0.167910 + 0.405370i
\(316\) 0 0
\(317\) 18.9377 + 7.84425i 1.06365 + 0.440577i 0.844745 0.535170i \(-0.179752\pi\)
0.218902 + 0.975747i \(0.429752\pi\)
\(318\) 0 0
\(319\) −0.685896 −0.0384028
\(320\) 0 0
\(321\) 19.8526 1.10807
\(322\) 0 0
\(323\) −12.5295 5.18989i −0.697160 0.288773i
\(324\) 0 0
\(325\) −1.87239 4.52035i −0.103861 0.250744i
\(326\) 0 0
\(327\) 12.4689 12.4689i 0.689533 0.689533i
\(328\) 0 0
\(329\) 7.33962 + 7.33962i 0.404646 + 0.404646i
\(330\) 0 0
\(331\) −9.91107 + 4.10530i −0.544762 + 0.225648i −0.638055 0.769991i \(-0.720261\pi\)
0.0932931 + 0.995639i \(0.470261\pi\)
\(332\) 0 0
\(333\) 1.87722 4.53200i 0.102871 0.248352i
\(334\) 0 0
\(335\) 28.1582i 1.53845i
\(336\) 0 0
\(337\) 3.23412i 0.176174i −0.996113 0.0880868i \(-0.971925\pi\)
0.996113 0.0880868i \(-0.0280753\pi\)
\(338\) 0 0
\(339\) 3.11529 7.52099i 0.169200 0.408484i
\(340\) 0 0
\(341\) 0.158619 0.0657022i 0.00858971 0.00355797i
\(342\) 0 0
\(343\) −3.06608 3.06608i −0.165553 0.165553i
\(344\) 0 0
\(345\) 1.91598 1.91598i 0.103153 0.103153i
\(346\) 0 0
\(347\) 9.82705 + 23.7246i 0.527544 + 1.27360i 0.933128 + 0.359545i \(0.117068\pi\)
−0.405584 + 0.914058i \(0.632932\pi\)
\(348\) 0 0
\(349\) −12.5762 5.20925i −0.673190 0.278845i 0.0197868 0.999804i \(-0.493701\pi\)
−0.692977 + 0.720960i \(0.743701\pi\)
\(350\) 0 0
\(351\) 17.4420 0.930983
\(352\) 0 0
\(353\) −8.67371 −0.461655 −0.230828 0.972995i \(-0.574143\pi\)
−0.230828 + 0.972995i \(0.574143\pi\)
\(354\) 0 0
\(355\) −8.23127 3.40950i −0.436870 0.180958i
\(356\) 0 0
\(357\) −13.2739 32.0461i −0.702530 1.69606i
\(358\) 0 0
\(359\) −13.6307 + 13.6307i −0.719399 + 0.719399i −0.968482 0.249083i \(-0.919871\pi\)
0.249083 + 0.968482i \(0.419871\pi\)
\(360\) 0 0
\(361\) 10.3045 + 10.3045i 0.542345 + 0.542345i
\(362\) 0 0
\(363\) 14.0396 5.81539i 0.736888 0.305229i
\(364\) 0 0
\(365\) −0.442353 + 1.06793i −0.0231538 + 0.0558982i
\(366\) 0 0
\(367\) 28.9800i 1.51274i −0.654142 0.756371i \(-0.726970\pi\)
0.654142 0.756371i \(-0.273030\pi\)
\(368\) 0 0
\(369\) 3.82989i 0.199376i
\(370\) 0 0
\(371\) 2.65344 6.40597i 0.137760 0.332581i
\(372\) 0 0
\(373\) −5.56367 + 2.30455i −0.288076 + 0.119325i −0.522042 0.852920i \(-0.674830\pi\)
0.233966 + 0.972245i \(0.424830\pi\)
\(374\) 0 0
\(375\) 11.9106 + 11.9106i 0.615060 + 0.615060i
\(376\) 0 0
\(377\) 10.2114 10.2114i 0.525912 0.525912i
\(378\) 0 0
\(379\) −8.55274 20.6481i −0.439325 1.06062i −0.976183 0.216951i \(-0.930389\pi\)
0.536858 0.843673i \(-0.319611\pi\)
\(380\) 0 0
\(381\) −19.6966 8.15862i −1.00909 0.417979i
\(382\) 0 0
\(383\) 30.5667 1.56188 0.780942 0.624603i \(-0.214739\pi\)
0.780942 + 0.624603i \(0.214739\pi\)
\(384\) 0 0
\(385\) 1.05275 0.0536530
\(386\) 0 0
\(387\) −6.62039 2.74226i −0.336533 0.139397i
\(388\) 0 0
\(389\) −7.06634 17.0597i −0.358278 0.864959i −0.995543 0.0943139i \(-0.969934\pi\)
0.637265 0.770645i \(-0.280066\pi\)
\(390\) 0 0
\(391\) 4.82843 4.82843i 0.244184 0.244184i
\(392\) 0 0
\(393\) −3.13990 3.13990i −0.158387 0.158387i
\(394\) 0 0
\(395\) −12.0786 + 5.00313i −0.607742 + 0.251735i
\(396\) 0 0
\(397\) 7.15759 17.2799i 0.359229 0.867255i −0.636180 0.771541i \(-0.719486\pi\)
0.995409 0.0957146i \(-0.0305136\pi\)
\(398\) 0 0
\(399\) 11.3231i 0.566866i
\(400\) 0 0
\(401\) 11.0004i 0.549332i −0.961540 0.274666i \(-0.911433\pi\)
0.961540 0.274666i \(-0.0885674\pi\)
\(402\) 0 0
\(403\) −1.38331 + 3.33962i −0.0689078 + 0.166358i
\(404\) 0 0
\(405\) −7.80631 + 3.23348i −0.387899 + 0.160673i
\(406\) 0 0
\(407\) −0.468914 0.468914i −0.0232432 0.0232432i
\(408\) 0 0
\(409\) −1.15862 + 1.15862i −0.0572900 + 0.0572900i −0.735171 0.677881i \(-0.762898\pi\)
0.677881 + 0.735171i \(0.262898\pi\)
\(410\) 0 0
\(411\) −8.07225 19.4881i −0.398175 0.961279i
\(412\) 0 0
\(413\) −13.4919 5.58855i −0.663895 0.274994i
\(414\) 0 0
\(415\) 14.4786 0.710727
\(416\) 0 0
\(417\) 7.16714 0.350976
\(418\) 0 0
\(419\) 32.0362 + 13.2698i 1.56507 + 0.648273i 0.985961 0.166978i \(-0.0534009\pi\)
0.579108 + 0.815251i \(0.303401\pi\)
\(420\) 0 0
\(421\) 9.34602 + 22.5633i 0.455497 + 1.09967i 0.970202 + 0.242299i \(0.0779016\pi\)
−0.514705 + 0.857368i \(0.672098\pi\)
\(422\) 0 0
\(423\) 2.04646 2.04646i 0.0995022 0.0995022i
\(424\) 0 0
\(425\) 7.22746 + 7.22746i 0.350583 + 0.350583i
\(426\) 0 0
\(427\) −13.4815 + 5.58421i −0.652414 + 0.270239i
\(428\) 0 0
\(429\) 0.239507 0.578221i 0.0115635 0.0279168i
\(430\) 0 0
\(431\) 4.47586i 0.215594i 0.994173 + 0.107797i \(0.0343797\pi\)
−0.994173 + 0.107797i \(0.965620\pi\)
\(432\) 0 0
\(433\) 1.44196i 0.0692960i −0.999400 0.0346480i \(-0.988969\pi\)
0.999400 0.0346480i \(-0.0110310\pi\)
\(434\) 0 0
\(435\) −4.58107 + 11.0597i −0.219646 + 0.530272i
\(436\) 0 0
\(437\) 2.05941 0.853036i 0.0985150 0.0408063i
\(438\) 0 0
\(439\) −0.854615 0.854615i −0.0407885 0.0407885i 0.686418 0.727207i \(-0.259182\pi\)
−0.727207 + 0.686418i \(0.759182\pi\)
\(440\) 0 0
\(441\) −6.22053 + 6.22053i −0.296216 + 0.296216i
\(442\) 0 0
\(443\) −4.68913 11.3206i −0.222787 0.537857i 0.772479 0.635040i \(-0.219017\pi\)
−0.995266 + 0.0971838i \(0.969017\pi\)
\(444\) 0 0
\(445\) 10.1832 + 4.21803i 0.482731 + 0.199954i
\(446\) 0 0
\(447\) −6.47862 −0.306428
\(448\) 0 0
\(449\) −24.5573 −1.15893 −0.579464 0.814998i \(-0.696738\pi\)
−0.579464 + 0.814998i \(0.696738\pi\)
\(450\) 0 0
\(451\) 0.478338 + 0.198134i 0.0225240 + 0.00932976i
\(452\) 0 0
\(453\) 9.91412 + 23.9348i 0.465806 + 1.12456i
\(454\) 0 0
\(455\) −15.6729 + 15.6729i −0.734759 + 0.734759i
\(456\) 0 0
\(457\) 14.1684 + 14.1684i 0.662771 + 0.662771i 0.956032 0.293262i \(-0.0947407\pi\)
−0.293262 + 0.956032i \(0.594741\pi\)
\(458\) 0 0
\(459\) −33.6631 + 13.9437i −1.57126 + 0.650837i
\(460\) 0 0
\(461\) −11.7965 + 28.4793i −0.549417 + 1.32641i 0.368496 + 0.929630i \(0.379873\pi\)
−0.917913 + 0.396782i \(0.870127\pi\)
\(462\) 0 0
\(463\) 14.8190i 0.688697i 0.938842 + 0.344349i \(0.111900\pi\)
−0.938842 + 0.344349i \(0.888100\pi\)
\(464\) 0 0
\(465\) 2.99647i 0.138958i
\(466\) 0 0
\(467\) −5.43521 + 13.1218i −0.251512 + 0.607203i −0.998326 0.0578293i \(-0.981582\pi\)
0.746815 + 0.665032i \(0.231582\pi\)
\(468\) 0 0
\(469\) 54.7373 22.6729i 2.52753 1.04694i
\(470\) 0 0
\(471\) 16.9007 + 16.9007i 0.778742 + 0.778742i
\(472\) 0 0
\(473\) −0.684993 + 0.684993i −0.0314960 + 0.0314960i
\(474\) 0 0
\(475\) 1.27687 + 3.08264i 0.0585869 + 0.141441i
\(476\) 0 0
\(477\) −1.78614 0.739842i −0.0817816 0.0338750i
\(478\) 0 0
\(479\) −32.3727 −1.47915 −0.739574 0.673076i \(-0.764973\pi\)
−0.739574 + 0.673076i \(0.764973\pi\)
\(480\) 0 0
\(481\) 13.9620 0.636614
\(482\) 0 0
\(483\) 5.26725 + 2.18177i 0.239668 + 0.0992738i
\(484\) 0 0
\(485\) −7.30205 17.6287i −0.331569 0.800479i
\(486\) 0 0
\(487\) 1.89478 1.89478i 0.0858608 0.0858608i −0.662872 0.748733i \(-0.730663\pi\)
0.748733 + 0.662872i \(0.230663\pi\)
\(488\) 0 0
\(489\) 11.2815 + 11.2815i 0.510166 + 0.510166i
\(490\) 0 0
\(491\) 18.2886 7.57539i 0.825354 0.341873i 0.0702922 0.997526i \(-0.477607\pi\)
0.755062 + 0.655654i \(0.227607\pi\)
\(492\) 0 0
\(493\) −11.5447 + 27.8714i −0.519947 + 1.25526i
\(494\) 0 0
\(495\) 0.293531i 0.0131932i
\(496\) 0 0
\(497\) 18.7462i 0.840884i
\(498\) 0 0
\(499\) 9.54921 23.0538i 0.427481 1.03203i −0.552602 0.833445i \(-0.686365\pi\)
0.980083 0.198586i \(-0.0636349\pi\)
\(500\) 0 0
\(501\) −5.40166 + 2.23744i −0.241328 + 0.0999614i
\(502\) 0 0
\(503\) −22.6436 22.6436i −1.00963 1.00963i −0.999953 0.00967595i \(-0.996920\pi\)
−0.00967595 0.999953i \(-0.503080\pi\)
\(504\) 0 0
\(505\) −14.7409 + 14.7409i −0.655960 + 0.655960i
\(506\) 0 0
\(507\) −1.84353 4.45068i −0.0818741 0.197661i
\(508\) 0 0
\(509\) −21.3715 8.85238i −0.947276 0.392375i −0.145070 0.989421i \(-0.546341\pi\)
−0.802206 + 0.597047i \(0.796341\pi\)
\(510\) 0 0
\(511\) −2.43216 −0.107592
\(512\) 0 0
\(513\) −11.8945 −0.525155
\(514\) 0 0
\(515\) 32.1415 + 13.3134i 1.41632 + 0.586660i
\(516\) 0 0
\(517\) −0.149724 0.361465i −0.00658484 0.0158972i
\(518\) 0 0
\(519\) −20.0789 + 20.0789i −0.881366 + 0.881366i
\(520\) 0 0
\(521\) −9.76588 9.76588i −0.427851 0.427851i 0.460045 0.887896i \(-0.347833\pi\)
−0.887896 + 0.460045i \(0.847833\pi\)
\(522\) 0 0
\(523\) 16.9370 7.01552i 0.740601 0.306767i 0.0197010 0.999806i \(-0.493729\pi\)
0.720900 + 0.693039i \(0.243729\pi\)
\(524\) 0 0
\(525\) −3.26579 + 7.88431i −0.142531 + 0.344099i
\(526\) 0 0
\(527\) 7.55136i 0.328942i
\(528\) 0 0
\(529\) 21.8776i 0.951202i
\(530\) 0 0
\(531\) −1.55822 + 3.76187i −0.0676209 + 0.163251i
\(532\) 0 0
\(533\) −10.0711 + 4.17157i −0.436226 + 0.180691i
\(534\) 0 0
\(535\) 18.7393 + 18.7393i 0.810170 + 0.810170i
\(536\) 0 0
\(537\) −24.5674 + 24.5674i −1.06016 + 1.06016i
\(538\) 0 0
\(539\) 0.455108 + 1.09873i 0.0196029 + 0.0473256i
\(540\) 0 0
\(541\) 14.2214 + 5.89071i 0.611427 + 0.253261i 0.666839 0.745202i \(-0.267647\pi\)
−0.0554115 + 0.998464i \(0.517647\pi\)
\(542\) 0 0
\(543\) −2.81470 −0.120791
\(544\) 0 0
\(545\) 23.5393 1.00831
\(546\) 0 0
\(547\) 9.67342 + 4.00686i 0.413606 + 0.171321i 0.579776 0.814776i \(-0.303140\pi\)
−0.166170 + 0.986097i \(0.553140\pi\)
\(548\) 0 0
\(549\) 1.55701 + 3.75895i 0.0664515 + 0.160428i
\(550\) 0 0
\(551\) −6.96362 + 6.96362i −0.296660 + 0.296660i
\(552\) 0 0
\(553\) −19.4514 19.4514i −0.827157 0.827157i
\(554\) 0 0
\(555\) −10.6928 + 4.42912i −0.453886 + 0.188006i
\(556\) 0 0
\(557\) −3.08965 + 7.45908i −0.130913 + 0.316051i −0.975721 0.219018i \(-0.929715\pi\)
0.844808 + 0.535070i \(0.179715\pi\)
\(558\) 0 0
\(559\) 20.3959i 0.862653i
\(560\) 0 0
\(561\) 1.30744i 0.0552002i
\(562\) 0 0
\(563\) −10.1815 + 24.5802i −0.429097 + 1.03593i 0.550477 + 0.834850i \(0.314446\pi\)
−0.979574 + 0.201082i \(0.935554\pi\)
\(564\) 0 0
\(565\) 10.0398 4.15862i 0.422377 0.174954i
\(566\) 0 0
\(567\) −12.5713 12.5713i −0.527943 0.527943i
\(568\) 0 0
\(569\) 8.12862 8.12862i 0.340770 0.340770i −0.515887 0.856657i \(-0.672538\pi\)
0.856657 + 0.515887i \(0.172538\pi\)
\(570\) 0 0
\(571\) 7.40930 + 17.8876i 0.310070 + 0.748574i 0.999702 + 0.0244147i \(0.00777221\pi\)
−0.689632 + 0.724160i \(0.742228\pi\)
\(572\) 0 0
\(573\) 11.5849 + 4.79862i 0.483965 + 0.200465i
\(574\) 0 0
\(575\) −1.68000 −0.0700609
\(576\) 0 0
\(577\) −11.9134 −0.495959 −0.247980 0.968765i \(-0.579767\pi\)
−0.247980 + 0.968765i \(0.579767\pi\)
\(578\) 0 0
\(579\) −7.98890 3.30911i −0.332008 0.137522i
\(580\) 0 0
\(581\) 11.6582 + 28.1453i 0.483662 + 1.16766i
\(582\) 0 0
\(583\) −0.184807 + 0.184807i −0.00765391 + 0.00765391i
\(584\) 0 0
\(585\) 4.36999 + 4.36999i 0.180677 + 0.180677i
\(586\) 0 0
\(587\) 23.6011 9.77588i 0.974120 0.403494i 0.161876 0.986811i \(-0.448246\pi\)
0.812244 + 0.583318i \(0.198246\pi\)
\(588\) 0 0
\(589\) 0.943348 2.27744i 0.0388700 0.0938404i
\(590\) 0 0
\(591\) 6.55765i 0.269746i
\(592\) 0 0
\(593\) 12.5549i 0.515567i −0.966203 0.257784i \(-0.917008\pi\)
0.966203 0.257784i \(-0.0829922\pi\)
\(594\) 0 0
\(595\) 17.7194 42.7784i 0.726425 1.75374i
\(596\) 0 0
\(597\) 11.1077 4.60097i 0.454609 0.188305i
\(598\) 0 0
\(599\) 6.66010 + 6.66010i 0.272124 + 0.272124i 0.829955 0.557830i \(-0.188366\pi\)
−0.557830 + 0.829955i \(0.688366\pi\)
\(600\) 0 0
\(601\) 27.4318 27.4318i 1.11896 1.11896i 0.127071 0.991894i \(-0.459442\pi\)
0.991894 0.127071i \(-0.0405577\pi\)
\(602\) 0 0
\(603\) −6.32175 15.2621i −0.257442 0.621519i
\(604\) 0 0
\(605\) 18.7415 + 7.76299i 0.761951 + 0.315610i
\(606\) 0 0
\(607\) 20.3361 0.825416 0.412708 0.910863i \(-0.364583\pi\)
0.412708 + 0.910863i \(0.364583\pi\)
\(608\) 0 0
\(609\) −25.1878 −1.02066
\(610\) 0 0
\(611\) 7.61040 + 3.15233i 0.307884 + 0.127530i
\(612\) 0 0
\(613\) −13.3277 32.1759i −0.538301 1.29957i −0.925908 0.377748i \(-0.876699\pi\)
0.387608 0.921824i \(-0.373301\pi\)
\(614\) 0 0
\(615\) 6.38960 6.38960i 0.257654 0.257654i
\(616\) 0 0
\(617\) −11.3168 11.3168i −0.455599 0.455599i 0.441609 0.897208i \(-0.354408\pi\)
−0.897208 + 0.441609i \(0.854408\pi\)
\(618\) 0 0
\(619\) 0.224799 0.0931149i 0.00903545 0.00374260i −0.378161 0.925740i \(-0.623443\pi\)
0.387197 + 0.921997i \(0.373443\pi\)
\(620\) 0 0
\(621\) 2.29186 5.53304i 0.0919691 0.222033i
\(622\) 0 0
\(623\) 23.1917i 0.929157i
\(624\) 0 0
\(625\) 14.5563i 0.582254i
\(626\) 0 0
\(627\) −0.163331 + 0.394316i −0.00652282 + 0.0157475i
\(628\) 0 0
\(629\) −26.9469 + 11.1618i −1.07444 + 0.445048i
\(630\) 0 0
\(631\) −1.15481 1.15481i −0.0459722 0.0459722i 0.683747 0.729719i \(-0.260349\pi\)
−0.729719 + 0.683747i \(0.760349\pi\)
\(632\) 0 0
\(633\) 13.3404 13.3404i 0.530233 0.530233i
\(634\) 0 0
\(635\) −10.8910 26.2931i −0.432195 1.04341i
\(636\) 0 0
\(637\) −23.1330 9.58199i −0.916562 0.379652i
\(638\) 0 0
\(639\) −5.22690 −0.206773
\(640\) 0 0
\(641\) −14.1953 −0.560679 −0.280339 0.959901i \(-0.590447\pi\)
−0.280339 + 0.959901i \(0.590447\pi\)
\(642\) 0 0
\(643\) −33.9334 14.0557i −1.33820 0.554302i −0.405219 0.914219i \(-0.632805\pi\)
−0.932984 + 0.359917i \(0.882805\pi\)
\(644\) 0 0
\(645\) 6.47010 + 15.6202i 0.254760 + 0.615045i
\(646\) 0 0
\(647\) −8.73969 + 8.73969i −0.343593 + 0.343593i −0.857716 0.514123i \(-0.828117\pi\)
0.514123 + 0.857716i \(0.328117\pi\)
\(648\) 0 0
\(649\) 0.389231 + 0.389231i 0.0152786 + 0.0152786i
\(650\) 0 0
\(651\) 5.82490 2.41275i 0.228296 0.0945632i
\(652\) 0 0
\(653\) 16.1182 38.9127i 0.630753 1.52277i −0.207926 0.978145i \(-0.566671\pi\)
0.838679 0.544627i \(-0.183329\pi\)
\(654\) 0 0
\(655\) 5.92763i 0.231612i
\(656\) 0 0
\(657\) 0.678143i 0.0264569i
\(658\) 0 0
\(659\) 8.93958 21.5821i 0.348237 0.840718i −0.648592 0.761136i \(-0.724642\pi\)
0.996828 0.0795812i \(-0.0253583\pi\)
\(660\) 0 0
\(661\) −22.0088 + 9.11633i −0.856042 + 0.354584i −0.767158 0.641458i \(-0.778330\pi\)
−0.0888835 + 0.996042i \(0.528330\pi\)
\(662\) 0 0
\(663\) −19.4647 19.4647i −0.755947 0.755947i
\(664\) 0 0
\(665\) 10.6881 10.6881i 0.414468 0.414468i
\(666\) 0 0
\(667\) −1.89754 4.58107i −0.0734732 0.177380i
\(668\) 0 0
\(669\) −1.22841 0.508825i −0.0474931 0.0196723i
\(670\) 0 0
\(671\) 0.550028 0.0212336
\(672\) 0 0
\(673\) 45.0980 1.73840 0.869200 0.494460i \(-0.164634\pi\)
0.869200 + 0.494460i \(0.164634\pi\)
\(674\) 0 0
\(675\) 8.28216 + 3.43058i 0.318780 + 0.132043i
\(676\) 0 0
\(677\) 13.6058 + 32.8474i 0.522915 + 1.26243i 0.936085 + 0.351774i \(0.114421\pi\)
−0.413170 + 0.910654i \(0.635579\pi\)
\(678\) 0 0
\(679\) 28.3892 28.3892i 1.08948 1.08948i
\(680\) 0 0
\(681\) 15.0117 + 15.0117i 0.575248 + 0.575248i
\(682\) 0 0
\(683\) −18.8141 + 7.79305i −0.719901 + 0.298193i −0.712395 0.701779i \(-0.752389\pi\)
−0.00750651 + 0.999972i \(0.502389\pi\)
\(684\) 0 0
\(685\) 10.7757 26.0148i 0.411718 0.993974i
\(686\) 0 0
\(687\) 6.52547i 0.248962i
\(688\) 0 0
\(689\) 5.50267i 0.209635i
\(690\) 0 0
\(691\) −12.6322 + 30.4967i −0.480550 + 1.16015i 0.478798 + 0.877925i \(0.341073\pi\)
−0.959348 + 0.282226i \(0.908927\pi\)
\(692\) 0 0
\(693\) 0.570601 0.236351i 0.0216753 0.00897822i
\(694\) 0 0
\(695\) 6.76521 + 6.76521i 0.256619 + 0.256619i
\(696\) 0 0
\(697\) 16.1023 16.1023i 0.609920 0.609920i
\(698\) 0 0
\(699\) 12.5790 + 30.3684i 0.475782 + 1.14864i
\(700\) 0 0
\(701\) 0.915341 + 0.379146i 0.0345719 + 0.0143202i 0.399902 0.916558i \(-0.369044\pi\)
−0.365330 + 0.930878i \(0.619044\pi\)
\(702\) 0 0
\(703\) −9.52138 −0.359106
\(704\) 0 0
\(705\) −6.82843 −0.257173
\(706\) 0 0
\(707\) −40.5244 16.7858i −1.52408 0.631293i
\(708\) 0 0
\(709\) −18.9677 45.7920i −0.712346 1.71975i −0.694055 0.719922i \(-0.744177\pi\)
−0.0182911 0.999833i \(-0.505823\pi\)
\(710\) 0 0
\(711\) −5.42350 + 5.42350i −0.203397 + 0.203397i
\(712\) 0 0
\(713\) 0.877646 + 0.877646i 0.0328681 + 0.0328681i
\(714\) 0 0
\(715\) 0.771869 0.319719i 0.0288663 0.0119568i
\(716\) 0 0
\(717\) 8.39128 20.2583i 0.313378 0.756561i
\(718\) 0 0
\(719\) 12.7931i 0.477102i −0.971130 0.238551i \(-0.923328\pi\)
0.971130 0.238551i \(-0.0766724\pi\)
\(720\) 0 0
\(721\) 73.2004i 2.72612i
\(722\) 0 0
\(723\) −0.165975 + 0.400700i −0.00617269 + 0.0149022i
\(724\) 0 0
\(725\) 6.85720 2.84035i 0.254670 0.105488i
\(726\) 0 0
\(727\) 0.466154 + 0.466154i 0.0172887 + 0.0172887i 0.715698 0.698410i \(-0.246109\pi\)
−0.698410 + 0.715698i \(0.746109\pi\)
\(728\) 0 0
\(729\) −20.1043 + 20.1043i −0.744603 + 0.744603i
\(730\) 0 0
\(731\) 16.3052 + 39.3642i 0.603069 + 1.45594i
\(732\) 0 0
\(733\) 34.0271 + 14.0945i 1.25682 + 0.520591i 0.908932 0.416945i \(-0.136899\pi\)
0.347887 + 0.937536i \(0.386899\pi\)
\(734\) 0 0
\(735\) 20.7561 0.765599
\(736\) 0 0
\(737\) −2.23322 −0.0822616
\(738\) 0 0
\(739\) −8.25825 3.42068i −0.303785 0.125832i 0.225584 0.974224i \(-0.427571\pi\)
−0.529368 + 0.848392i \(0.677571\pi\)
\(740\) 0 0
\(741\) −3.43882 8.30205i −0.126328 0.304984i
\(742\) 0 0
\(743\) 32.4060 32.4060i 1.18886 1.18886i 0.211477 0.977383i \(-0.432173\pi\)
0.977383 0.211477i \(-0.0678273\pi\)
\(744\) 0 0
\(745\) −6.11529 6.11529i −0.224047 0.224047i
\(746\) 0 0
\(747\) 7.84757 3.25057i 0.287127 0.118932i
\(748\) 0 0
\(749\) −21.3388 + 51.5165i −0.779704 + 1.88237i
\(750\) 0 0
\(751\) 21.5108i 0.784939i 0.919765 + 0.392470i \(0.128379\pi\)
−0.919765 + 0.392470i \(0.871621\pi\)
\(752\) 0 0
\(753\) 12.8732i 0.469126i
\(754\) 0 0
\(755\) −13.2344 + 31.9507i −0.481649 + 1.16280i
\(756\) 0 0
\(757\) −17.3649 + 7.19276i −0.631137 + 0.261425i −0.675236 0.737602i \(-0.735958\pi\)
0.0440993 + 0.999027i \(0.485958\pi\)
\(758\) 0 0
\(759\) −0.151955 0.151955i −0.00551563 0.00551563i
\(760\) 0 0
\(761\) −37.8574 + 37.8574i −1.37233 + 1.37233i −0.515354 + 0.856977i \(0.672340\pi\)
−0.856977 + 0.515354i \(0.827660\pi\)
\(762\) 0 0
\(763\) 18.9538 + 45.7585i 0.686174 + 1.65657i
\(764\) 0 0
\(765\) −11.9276 4.94059i −0.431245 0.178627i
\(766\) 0 0
\(767\) −11.5894 −0.418471
\(768\) 0 0
\(769\) 3.07370 0.110840 0.0554201 0.998463i \(-0.482350\pi\)
0.0554201 + 0.998463i \(0.482350\pi\)
\(770\) 0 0
\(771\) −24.1753 10.0137i −0.870651 0.360635i
\(772\) 0 0
\(773\) −6.55831 15.8332i −0.235886 0.569479i 0.760964 0.648795i \(-0.224727\pi\)
−0.996850 + 0.0793155i \(0.974727\pi\)
\(774\) 0 0
\(775\) −1.31371 + 1.31371i −0.0471898 + 0.0471898i
\(776\) 0 0
\(777\) −17.2197 17.2197i −0.617753 0.617753i
\(778\) 0 0
\(779\) 6.86794 2.84479i 0.246070 0.101925i
\(780\) 0 0
\(781\) −0.270406 + 0.652818i −0.00967589 + 0.0233597i
\(782\) 0 0
\(783\) 26.4588i 0.945561i
\(784\) 0 0
\(785\) 31.9058i 1.13877i
\(786\) 0 0
\(787\) 6.77706 16.3613i 0.241576 0.583216i −0.755864 0.654729i \(-0.772783\pi\)
0.997440 + 0.0715129i \(0.0227827\pi\)
\(788\) 0 0
\(789\) −30.0877 + 12.4627i −1.07115 + 0.443685i
\(790\) 0 0
\(791\) 16.1680 + 16.1680i 0.574869 + 0.574869i
\(792\) 0 0
\(793\) −8.18862 + 8.18862i −0.290786 + 0.290786i
\(794\) 0 0
\(795\) 1.74559 + 4.21422i 0.0619096 + 0.149463i
\(796\) 0 0
\(797\) −32.4476 13.4402i −1.14935 0.476077i −0.275036 0.961434i \(-0.588690\pi\)
−0.874316 + 0.485356i \(0.838690\pi\)
\(798\) 0 0
\(799\) −17.2082 −0.608783
\(800\) 0 0
\(801\) 6.46640 0.228479
\(802\) 0 0
\(803\) 0.0846974 + 0.0350828i 0.00298891 + 0.00123805i
\(804\) 0 0
\(805\) 2.91245 + 7.03127i 0.102650 + 0.247820i
\(806\) 0 0
\(807\) 12.8150 12.8150i 0.451109 0.451109i
\(808\) 0 0
\(809\) 11.2704 + 11.2704i 0.396246 + 0.396246i 0.876907 0.480661i \(-0.159603\pi\)
−0.480661 + 0.876907i \(0.659603\pi\)
\(810\) 0 0
\(811\) 16.3328 6.76529i 0.573524 0.237561i −0.0770206 0.997029i \(-0.524541\pi\)
0.650545 + 0.759468i \(0.274541\pi\)
\(812\) 0 0
\(813\) 14.9452 36.0809i 0.524150 1.26541i
\(814\) 0 0
\(815\) 21.2976i 0.746023i
\(816\) 0 0
\(817\) 13.9089i 0.486611i
\(818\) 0 0
\(819\) −4.97620 + 12.0136i −0.173882 + 0.419789i
\(820\) 0 0
\(821\) 29.5124 12.2244i 1.02999 0.426636i 0.197281 0.980347i \(-0.436789\pi\)
0.832709 + 0.553711i \(0.186789\pi\)
\(822\) 0 0
\(823\) −1.00381 1.00381i −0.0349906 0.0349906i 0.689395 0.724386i \(-0.257876\pi\)
−0.724386 + 0.689395i \(0.757876\pi\)
\(824\) 0 0
\(825\) 0.227455 0.227455i 0.00791898 0.00791898i
\(826\) 0 0
\(827\) −15.7060 37.9176i −0.546151 1.31852i −0.920321 0.391165i \(-0.872072\pi\)
0.374170 0.927360i \(-0.377928\pi\)
\(828\) 0 0
\(829\) 31.9806 + 13.2468i 1.11073 + 0.460081i 0.861190 0.508283i \(-0.169720\pi\)
0.249543 + 0.968364i \(0.419720\pi\)
\(830\) 0 0
\(831\) 32.6984 1.13430
\(832\) 0 0
\(833\) 52.3070 1.81233
\(834\) 0 0
\(835\) −7.21069 2.98677i −0.249536 0.103361i
\(836\) 0 0
\(837\) −2.53450 6.11882i −0.0876051 0.211498i
\(838\) 0 0
\(839\) −3.42599 + 3.42599i −0.118278 + 0.118278i −0.763768 0.645490i \(-0.776653\pi\)
0.645490 + 0.763768i \(0.276653\pi\)
\(840\) 0 0
\(841\) −5.01582 5.01582i −0.172959 0.172959i
\(842\) 0 0
\(843\) −5.43764 + 2.25234i −0.187282 + 0.0775749i
\(844\) 0 0
\(845\) 2.46094 5.94123i 0.0846588 0.204384i
\(846\) 0 0
\(847\) 42.6827i 1.46660i
\(848\) 0 0
\(849\) 2.56638i 0.0880779i
\(850\) 0 0
\(851\) 1.83460 4.42912i 0.0628893 0.151828i
\(852\) 0 0
\(853\) −33.4739 + 13.8653i −1.14612 + 0.474740i −0.873232 0.487305i \(-0.837980\pi\)
−0.272892 + 0.962045i \(0.587980\pi\)
\(854\) 0 0
\(855\) −2.98010 2.98010i −0.101917 0.101917i
\(856\) 0 0
\(857\) 19.6667 19.6667i 0.671800 0.671800i −0.286331 0.958131i \(-0.592436\pi\)
0.958131 + 0.286331i \(0.0924356\pi\)
\(858\) 0 0
\(859\) −15.0121 36.2424i −0.512207 1.23658i −0.942597 0.333933i \(-0.891624\pi\)
0.430390 0.902643i \(-0.358376\pi\)
\(860\) 0 0
\(861\) 17.5658 + 7.27598i 0.598640 + 0.247965i
\(862\) 0 0
\(863\) −28.3727 −0.965819 −0.482909 0.875670i \(-0.660420\pi\)
−0.482909 + 0.875670i \(0.660420\pi\)
\(864\) 0 0
\(865\) −37.9058 −1.28883
\(866\) 0 0
\(867\) 31.3878 + 13.0013i 1.06599 + 0.441546i
\(868\) 0 0
\(869\) 0.396796 + 0.957951i 0.0134604 + 0.0324963i
\(870\) 0 0
\(871\) 33.2473 33.2473i 1.12654 1.12654i
\(872\) 0 0
\(873\) −7.91558 7.91558i −0.267902 0.267902i
\(874\) 0 0
\(875\) −43.7096 + 18.1051i −1.47765 + 0.612064i
\(876\) 0 0
\(877\) −10.1396 + 24.4793i −0.342391 + 0.826606i 0.655082 + 0.755558i \(0.272634\pi\)
−0.997473 + 0.0710476i \(0.977366\pi\)
\(878\) 0 0
\(879\) 38.0427i 1.28315i
\(880\) 0 0
\(881\) 9.35846i 0.315295i −0.987495 0.157647i \(-0.949609\pi\)
0.987495 0.157647i \(-0.0503909\pi\)
\(882\) 0 0
\(883\) −7.09207 + 17.1218i −0.238667 + 0.576193i −0.997145 0.0755050i \(-0.975943\pi\)
0.758478 + 0.651698i \(0.225943\pi\)
\(884\) 0 0
\(885\) 8.87579 3.67647i 0.298356 0.123583i
\(886\) 0 0
\(887\) −30.8931 30.8931i −1.03729 1.03729i −0.999277 0.0380100i \(-0.987898\pi\)
−0.0380100 0.999277i \(-0.512102\pi\)
\(888\) 0 0
\(889\) 42.3424 42.3424i 1.42012 1.42012i
\(890\) 0 0
\(891\) 0.256446 + 0.619115i 0.00859126 + 0.0207411i
\(892\) 0 0
\(893\) −5.18989 2.14972i −0.173673 0.0719378i
\(894\) 0 0
\(895\) −46.3794 −1.55029
\(896\) 0 0
\(897\) 4.52452 0.151069
\(898\) 0 0
\(899\) −5.06608 2.09844i −0.168963 0.0699868i
\(900\) 0 0
\(901\) 4.39903 + 10.6202i 0.146553 + 0.353810i
\(902\) 0 0
\(903\) −25.1547 + 25.1547i −0.837096 + 0.837096i
\(904\) 0 0
\(905\) −2.65685 2.65685i −0.0883168 0.0883168i
\(906\) 0 0
\(907\) −12.6479 + 5.23891i −0.419965 + 0.173955i −0.582651 0.812723i \(-0.697984\pi\)
0.162686 + 0.986678i \(0.447984\pi\)
\(908\) 0 0
\(909\) −4.68027 + 11.2992i −0.155235 + 0.374770i
\(910\) 0 0
\(911\) 35.3498i 1.17119i −0.810604 0.585595i \(-0.800861\pi\)
0.810604 0.585595i \(-0.199139\pi\)
\(912\) 0 0
\(913\) 1.14829i 0.0380030i
\(914\) 0 0
\(915\) 3.67362 8.86890i 0.121446 0.293197i
\(916\) 0 0
\(917\) 11.5228 4.77292i 0.380518 0.157616i
\(918\) 0 0
\(919\) 30.0652 + 30.0652i 0.991759 + 0.991759i 0.999966 0.00820720i \(-0.00261246\pi\)
−0.00820720 + 0.999966i \(0.502612\pi\)
\(920\) 0 0
\(921\) 14.8386 14.8386i 0.488949 0.488949i
\(922\) 0 0
\(923\) −5.69321 13.7446i −0.187394 0.452410i
\(924\) 0 0
\(925\) 6.62975 + 2.74613i 0.217985 + 0.0902923i
\(926\) 0 0
\(927\) 20.4100 0.670352
\(928\) 0 0
\(929\) 7.62858 0.250286 0.125143 0.992139i \(-0.460061\pi\)
0.125143 + 0.992139i \(0.460061\pi\)
\(930\) 0 0
\(931\) 15.7755 + 6.53442i 0.517020 + 0.214157i
\(932\) 0 0
\(933\) 5.35979 + 12.9397i 0.175472 + 0.423626i
\(934\) 0 0
\(935\) −1.23412 + 1.23412i −0.0403600 + 0.0403600i
\(936\) 0 0
\(937\) −21.2074 21.2074i −0.692817 0.692817i 0.270034 0.962851i \(-0.412965\pi\)
−0.962851 + 0.270034i \(0.912965\pi\)
\(938\) 0 0
\(939\) 21.4332 8.87793i 0.699446 0.289720i
\(940\) 0 0
\(941\) 13.0249 31.4448i 0.424599 1.02507i −0.556375 0.830931i \(-0.687808\pi\)
0.980974 0.194141i \(-0.0621918\pi\)
\(942\) 0 0
\(943\) 3.74294i 0.121887i
\(944\) 0 0
\(945\) 40.6104i 1.32106i
\(946\) 0 0
\(947\) 18.6229 44.9596i 0.605162 1.46099i −0.263043 0.964784i \(-0.584726\pi\)
0.868205 0.496206i \(-0.165274\pi\)
\(948\) 0 0
\(949\) −1.78324 + 0.738644i −0.0578866 + 0.0239774i
\(950\) 0 0
\(951\) −20.0628 20.0628i −0.650582 0.650582i
\(952\) 0 0
\(953\) −33.7784 + 33.7784i −1.09419 + 1.09419i −0.0991142 + 0.995076i \(0.531601\pi\)
−0.995076 + 0.0991142i \(0.968399\pi\)
\(954\) 0 0
\(955\) 6.40569 + 15.4647i 0.207283 + 0.500426i
\(956\) 0 0
\(957\) 0.877140 + 0.363323i 0.0283539 + 0.0117446i
\(958\) 0 0
\(959\) 59.2472 1.91319
\(960\) 0 0
\(961\) −29.6274 −0.955723
\(962\) 0 0
\(963\) 14.3640 + 5.94977i 0.462874 + 0.191729i
\(964\) 0 0
\(965\) −4.41735 10.6644i −0.142199 0.343300i
\(966\) 0 0
\(967\) −19.3234 + 19.3234i −0.621399 + 0.621399i −0.945889 0.324490i \(-0.894807\pi\)
0.324490 + 0.945889i \(0.394807\pi\)
\(968\) 0 0
\(969\) 13.2739 + 13.2739i 0.426420 + 0.426420i
\(970\) 0 0
\(971\) 52.9160 21.9185i 1.69816 0.703399i 0.698234 0.715869i \(-0.253969\pi\)
0.999922 + 0.0124699i \(0.00396940\pi\)
\(972\) 0 0
\(973\) −7.70369 + 18.5983i −0.246969 + 0.596236i
\(974\) 0 0
\(975\) 6.77254i 0.216895i
\(976\) 0 0
\(977\) 12.2792i 0.392848i −0.980519 0.196424i \(-0.937067\pi\)
0.980519 0.196424i \(-0.0629329\pi\)
\(978\) 0 0
\(979\) 0.334530 0.807628i 0.0106916 0.0258119i
\(980\) 0 0
\(981\) 12.7586 5.28477i 0.407349 0.168730i
\(982\) 0 0
\(983\) 14.1052 + 14.1052i 0.449887 + 0.449887i 0.895317 0.445430i \(-0.146949\pi\)
−0.445430 + 0.895317i \(0.646949\pi\)
\(984\) 0 0
\(985\) −6.18989 + 6.18989i −0.197226 + 0.197226i
\(986\) 0 0
\(987\) −5.49824 13.2739i −0.175011 0.422513i
\(988\) 0 0
\(989\) −6.47010 2.68000i −0.205737 0.0852191i
\(990\) 0 0
\(991\) −39.8015 −1.26434 −0.632169 0.774831i \(-0.717835\pi\)
−0.632169 + 0.774831i \(0.717835\pi\)
\(992\) 0 0
\(993\) 14.8491 0.471222
\(994\) 0 0
\(995\) 14.8278 + 6.14186i 0.470071 + 0.194710i
\(996\) 0 0
\(997\) 2.57111 + 6.20720i 0.0814278 + 0.196584i 0.959350 0.282219i \(-0.0910706\pi\)
−0.877922 + 0.478803i \(0.841071\pi\)
\(998\) 0 0
\(999\) −18.0886 + 18.0886i −0.572299 + 0.572299i
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 128.2.g.b.81.1 8
3.2 odd 2 1152.2.v.b.721.2 8
4.3 odd 2 32.2.g.b.29.1 yes 8
8.3 odd 2 256.2.g.d.161.1 8
8.5 even 2 256.2.g.c.161.2 8
12.11 even 2 288.2.v.b.253.2 8
16.3 odd 4 512.2.g.e.65.1 8
16.5 even 4 512.2.g.f.65.1 8
16.11 odd 4 512.2.g.h.65.2 8
16.13 even 4 512.2.g.g.65.2 8
20.3 even 4 800.2.ba.c.349.1 8
20.7 even 4 800.2.ba.d.349.2 8
20.19 odd 2 800.2.y.b.701.2 8
32.3 odd 8 512.2.g.h.449.2 8
32.5 even 8 256.2.g.c.97.2 8
32.11 odd 8 32.2.g.b.21.1 8
32.13 even 8 512.2.g.g.449.2 8
32.19 odd 8 512.2.g.e.449.1 8
32.21 even 8 inner 128.2.g.b.49.1 8
32.27 odd 8 256.2.g.d.97.1 8
32.29 even 8 512.2.g.f.449.1 8
64.11 odd 16 4096.2.a.k.1.6 8
64.21 even 16 4096.2.a.q.1.6 8
64.43 odd 16 4096.2.a.k.1.3 8
64.53 even 16 4096.2.a.q.1.3 8
96.11 even 8 288.2.v.b.181.2 8
96.53 odd 8 1152.2.v.b.433.2 8
160.43 even 8 800.2.ba.d.149.2 8
160.107 even 8 800.2.ba.c.149.1 8
160.139 odd 8 800.2.y.b.501.2 8
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
32.2.g.b.21.1 8 32.11 odd 8
32.2.g.b.29.1 yes 8 4.3 odd 2
128.2.g.b.49.1 8 32.21 even 8 inner
128.2.g.b.81.1 8 1.1 even 1 trivial
256.2.g.c.97.2 8 32.5 even 8
256.2.g.c.161.2 8 8.5 even 2
256.2.g.d.97.1 8 32.27 odd 8
256.2.g.d.161.1 8 8.3 odd 2
288.2.v.b.181.2 8 96.11 even 8
288.2.v.b.253.2 8 12.11 even 2
512.2.g.e.65.1 8 16.3 odd 4
512.2.g.e.449.1 8 32.19 odd 8
512.2.g.f.65.1 8 16.5 even 4
512.2.g.f.449.1 8 32.29 even 8
512.2.g.g.65.2 8 16.13 even 4
512.2.g.g.449.2 8 32.13 even 8
512.2.g.h.65.2 8 16.11 odd 4
512.2.g.h.449.2 8 32.3 odd 8
800.2.y.b.501.2 8 160.139 odd 8
800.2.y.b.701.2 8 20.19 odd 2
800.2.ba.c.149.1 8 160.107 even 8
800.2.ba.c.349.1 8 20.3 even 4
800.2.ba.d.149.2 8 160.43 even 8
800.2.ba.d.349.2 8 20.7 even 4
1152.2.v.b.433.2 8 96.53 odd 8
1152.2.v.b.721.2 8 3.2 odd 2
4096.2.a.k.1.3 8 64.43 odd 16
4096.2.a.k.1.6 8 64.11 odd 16
4096.2.a.q.1.3 8 64.53 even 16
4096.2.a.q.1.6 8 64.21 even 16