Properties

Label 128.2.g.a.81.1
Level $128$
Weight $2$
Character 128.81
Analytic conductor $1.022$
Analytic rank $0$
Dimension $4$
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: \(4\)
Coefficient field: \(\Q(\zeta_{8})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{4} + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 32)
Sato-Tate group: $\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label 81.1
Root \(-0.707107 + 0.707107i\) of defining polynomial
Character \(\chi\) \(=\) 128.81
Dual form 128.2.g.a.49.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.707107 + 0.292893i) q^{3} +(1.12132 + 2.70711i) q^{5} +(-1.00000 + 1.00000i) q^{7} +(-1.70711 - 1.70711i) q^{9} +O(q^{10})\) \(q+(0.707107 + 0.292893i) q^{3} +(1.12132 + 2.70711i) q^{5} +(-1.00000 + 1.00000i) q^{7} +(-1.70711 - 1.70711i) q^{9} +(4.12132 - 1.70711i) q^{11} +(0.292893 - 0.707107i) q^{13} +2.24264i q^{15} -2.82843i q^{17} +(-1.53553 + 3.70711i) q^{19} +(-1.00000 + 0.414214i) q^{21} +(-5.82843 - 5.82843i) q^{23} +(-2.53553 + 2.53553i) q^{25} +(-1.58579 - 3.82843i) q^{27} +(-3.12132 - 1.29289i) q^{29} +4.00000 q^{31} +3.41421 q^{33} +(-3.82843 - 1.58579i) q^{35} +(0.292893 + 0.707107i) q^{37} +(0.414214 - 0.414214i) q^{39} +(-0.171573 - 0.171573i) q^{41} +(-4.70711 + 1.94975i) q^{43} +(2.70711 - 6.53553i) q^{45} +0.343146i q^{47} +5.00000i q^{49} +(0.828427 - 2.00000i) q^{51} +(-1.12132 + 0.464466i) q^{53} +(9.24264 + 9.24264i) q^{55} +(-2.17157 + 2.17157i) q^{57} +(1.87868 + 4.53553i) q^{59} +(1.70711 + 0.707107i) q^{61} +3.41421 q^{63} +2.24264 q^{65} +(5.53553 + 2.29289i) q^{67} +(-2.41421 - 5.82843i) q^{69} +(5.82843 - 5.82843i) q^{71} +(7.00000 + 7.00000i) q^{73} +(-2.53553 + 1.05025i) q^{75} +(-2.41421 + 5.82843i) q^{77} -6.00000i q^{79} +4.07107i q^{81} +(-1.87868 + 4.53553i) q^{83} +(7.65685 - 3.17157i) q^{85} +(-1.82843 - 1.82843i) q^{87} +(8.65685 - 8.65685i) q^{89} +(0.414214 + 1.00000i) q^{91} +(2.82843 + 1.17157i) q^{93} -11.7574 q^{95} -18.4853 q^{97} +(-9.94975 - 4.12132i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q - 4 q^{5} - 4 q^{7} - 4 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 4 q - 4 q^{5} - 4 q^{7} - 4 q^{9} + 8 q^{11} + 4 q^{13} + 8 q^{19} - 4 q^{21} - 12 q^{23} + 4 q^{25} - 12 q^{27} - 4 q^{29} + 16 q^{31} + 8 q^{33} - 4 q^{35} + 4 q^{37} - 4 q^{39} - 12 q^{41} - 16 q^{43} + 8 q^{45} - 8 q^{51} + 4 q^{53} + 20 q^{55} - 20 q^{57} + 16 q^{59} + 4 q^{61} + 8 q^{63} - 8 q^{65} + 8 q^{67} - 4 q^{69} + 12 q^{71} + 28 q^{73} + 4 q^{75} - 4 q^{77} - 16 q^{83} + 8 q^{85} + 4 q^{87} + 12 q^{89} - 4 q^{91} - 64 q^{95} - 40 q^{97} - 20 q^{99}+O(q^{100}) \) 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
\(3\) 0.707107 + 0.292893i 0.408248 + 0.169102i 0.577350 0.816497i \(-0.304087\pi\)
−0.169102 + 0.985599i \(0.554087\pi\)
\(4\) 0 0
\(5\) 1.12132 + 2.70711i 0.501470 + 1.21065i 0.948683 + 0.316228i \(0.102416\pi\)
−0.447214 + 0.894427i \(0.647584\pi\)
\(6\) 0 0
\(7\) −1.00000 + 1.00000i −0.377964 + 0.377964i −0.870367 0.492403i \(-0.836119\pi\)
0.492403 + 0.870367i \(0.336119\pi\)
\(8\) 0 0
\(9\) −1.70711 1.70711i −0.569036 0.569036i
\(10\) 0 0
\(11\) 4.12132 1.70711i 1.24262 0.514712i 0.338091 0.941113i \(-0.390219\pi\)
0.904534 + 0.426401i \(0.140219\pi\)
\(12\) 0 0
\(13\) 0.292893 0.707107i 0.0812340 0.196116i −0.878044 0.478580i \(-0.841152\pi\)
0.959278 + 0.282464i \(0.0911517\pi\)
\(14\) 0 0
\(15\) 2.24264i 0.579047i
\(16\) 0 0
\(17\) 2.82843i 0.685994i −0.939336 0.342997i \(-0.888558\pi\)
0.939336 0.342997i \(-0.111442\pi\)
\(18\) 0 0
\(19\) −1.53553 + 3.70711i −0.352276 + 0.850469i 0.644063 + 0.764973i \(0.277248\pi\)
−0.996339 + 0.0854961i \(0.972752\pi\)
\(20\) 0 0
\(21\) −1.00000 + 0.414214i −0.218218 + 0.0903888i
\(22\) 0 0
\(23\) −5.82843 5.82843i −1.21531 1.21531i −0.969256 0.246055i \(-0.920866\pi\)
−0.246055 0.969256i \(-0.579134\pi\)
\(24\) 0 0
\(25\) −2.53553 + 2.53553i −0.507107 + 0.507107i
\(26\) 0 0
\(27\) −1.58579 3.82843i −0.305185 0.736781i
\(28\) 0 0
\(29\) −3.12132 1.29289i −0.579615 0.240084i 0.0735609 0.997291i \(-0.476564\pi\)
−0.653176 + 0.757206i \(0.726564\pi\)
\(30\) 0 0
\(31\) 4.00000 0.718421 0.359211 0.933257i \(-0.383046\pi\)
0.359211 + 0.933257i \(0.383046\pi\)
\(32\) 0 0
\(33\) 3.41421 0.594338
\(34\) 0 0
\(35\) −3.82843 1.58579i −0.647122 0.268047i
\(36\) 0 0
\(37\) 0.292893 + 0.707107i 0.0481513 + 0.116248i 0.946125 0.323802i \(-0.104961\pi\)
−0.897974 + 0.440049i \(0.854961\pi\)
\(38\) 0 0
\(39\) 0.414214 0.414214i 0.0663273 0.0663273i
\(40\) 0 0
\(41\) −0.171573 0.171573i −0.0267952 0.0267952i 0.693582 0.720377i \(-0.256031\pi\)
−0.720377 + 0.693582i \(0.756031\pi\)
\(42\) 0 0
\(43\) −4.70711 + 1.94975i −0.717827 + 0.297334i −0.711539 0.702647i \(-0.752002\pi\)
−0.00628798 + 0.999980i \(0.502002\pi\)
\(44\) 0 0
\(45\) 2.70711 6.53553i 0.403552 0.974260i
\(46\) 0 0
\(47\) 0.343146i 0.0500530i 0.999687 + 0.0250265i \(0.00796701\pi\)
−0.999687 + 0.0250265i \(0.992033\pi\)
\(48\) 0 0
\(49\) 5.00000i 0.714286i
\(50\) 0 0
\(51\) 0.828427 2.00000i 0.116003 0.280056i
\(52\) 0 0
\(53\) −1.12132 + 0.464466i −0.154025 + 0.0637993i −0.458364 0.888764i \(-0.651564\pi\)
0.304339 + 0.952564i \(0.401564\pi\)
\(54\) 0 0
\(55\) 9.24264 + 9.24264i 1.24628 + 1.24628i
\(56\) 0 0
\(57\) −2.17157 + 2.17157i −0.287632 + 0.287632i
\(58\) 0 0
\(59\) 1.87868 + 4.53553i 0.244583 + 0.590476i 0.997727 0.0673793i \(-0.0214638\pi\)
−0.753144 + 0.657855i \(0.771464\pi\)
\(60\) 0 0
\(61\) 1.70711 + 0.707107i 0.218573 + 0.0905357i 0.489283 0.872125i \(-0.337259\pi\)
−0.270710 + 0.962661i \(0.587259\pi\)
\(62\) 0 0
\(63\) 3.41421 0.430150
\(64\) 0 0
\(65\) 2.24264 0.278165
\(66\) 0 0
\(67\) 5.53553 + 2.29289i 0.676273 + 0.280121i 0.694268 0.719717i \(-0.255728\pi\)
−0.0179949 + 0.999838i \(0.505728\pi\)
\(68\) 0 0
\(69\) −2.41421 5.82843i −0.290637 0.701660i
\(70\) 0 0
\(71\) 5.82843 5.82843i 0.691707 0.691707i −0.270900 0.962607i \(-0.587321\pi\)
0.962607 + 0.270900i \(0.0873214\pi\)
\(72\) 0 0
\(73\) 7.00000 + 7.00000i 0.819288 + 0.819288i 0.986005 0.166717i \(-0.0533166\pi\)
−0.166717 + 0.986005i \(0.553317\pi\)
\(74\) 0 0
\(75\) −2.53553 + 1.05025i −0.292778 + 0.121273i
\(76\) 0 0
\(77\) −2.41421 + 5.82843i −0.275125 + 0.664211i
\(78\) 0 0
\(79\) 6.00000i 0.675053i −0.941316 0.337526i \(-0.890410\pi\)
0.941316 0.337526i \(-0.109590\pi\)
\(80\) 0 0
\(81\) 4.07107i 0.452341i
\(82\) 0 0
\(83\) −1.87868 + 4.53553i −0.206212 + 0.497840i −0.992821 0.119612i \(-0.961835\pi\)
0.786609 + 0.617452i \(0.211835\pi\)
\(84\) 0 0
\(85\) 7.65685 3.17157i 0.830502 0.344005i
\(86\) 0 0
\(87\) −1.82843 1.82843i −0.196028 0.196028i
\(88\) 0 0
\(89\) 8.65685 8.65685i 0.917625 0.917625i −0.0792315 0.996856i \(-0.525247\pi\)
0.996856 + 0.0792315i \(0.0252466\pi\)
\(90\) 0 0
\(91\) 0.414214 + 1.00000i 0.0434214 + 0.104828i
\(92\) 0 0
\(93\) 2.82843 + 1.17157i 0.293294 + 0.121486i
\(94\) 0 0
\(95\) −11.7574 −1.20628
\(96\) 0 0
\(97\) −18.4853 −1.87690 −0.938448 0.345421i \(-0.887736\pi\)
−0.938448 + 0.345421i \(0.887736\pi\)
\(98\) 0 0
\(99\) −9.94975 4.12132i −0.999987 0.414208i
\(100\) 0 0
\(101\) −1.36396 3.29289i −0.135719 0.327655i 0.841379 0.540446i \(-0.181745\pi\)
−0.977098 + 0.212791i \(0.931745\pi\)
\(102\) 0 0
\(103\) −9.48528 + 9.48528i −0.934613 + 0.934613i −0.997990 0.0633771i \(-0.979813\pi\)
0.0633771 + 0.997990i \(0.479813\pi\)
\(104\) 0 0
\(105\) −2.24264 2.24264i −0.218859 0.218859i
\(106\) 0 0
\(107\) 4.12132 1.70711i 0.398423 0.165032i −0.174470 0.984663i \(-0.555821\pi\)
0.572893 + 0.819630i \(0.305821\pi\)
\(108\) 0 0
\(109\) −5.70711 + 13.7782i −0.546642 + 1.31971i 0.373320 + 0.927702i \(0.378219\pi\)
−0.919962 + 0.392007i \(0.871781\pi\)
\(110\) 0 0
\(111\) 0.585786i 0.0556004i
\(112\) 0 0
\(113\) 6.34315i 0.596713i −0.954455 0.298356i \(-0.903562\pi\)
0.954455 0.298356i \(-0.0964384\pi\)
\(114\) 0 0
\(115\) 9.24264 22.3137i 0.861881 2.08076i
\(116\) 0 0
\(117\) −1.70711 + 0.707107i −0.157822 + 0.0653720i
\(118\) 0 0
\(119\) 2.82843 + 2.82843i 0.259281 + 0.259281i
\(120\) 0 0
\(121\) 6.29289 6.29289i 0.572081 0.572081i
\(122\) 0 0
\(123\) −0.0710678 0.171573i −0.00640797 0.0154702i
\(124\) 0 0
\(125\) 3.82843 + 1.58579i 0.342425 + 0.141837i
\(126\) 0 0
\(127\) −12.9706 −1.15095 −0.575476 0.817819i \(-0.695183\pi\)
−0.575476 + 0.817819i \(0.695183\pi\)
\(128\) 0 0
\(129\) −3.89949 −0.343331
\(130\) 0 0
\(131\) 16.3640 + 6.77817i 1.42973 + 0.592212i 0.957284 0.289150i \(-0.0933726\pi\)
0.472442 + 0.881362i \(0.343373\pi\)
\(132\) 0 0
\(133\) −2.17157 5.24264i −0.188299 0.454595i
\(134\) 0 0
\(135\) 8.58579 8.58579i 0.738947 0.738947i
\(136\) 0 0
\(137\) −8.65685 8.65685i −0.739605 0.739605i 0.232897 0.972502i \(-0.425180\pi\)
−0.972502 + 0.232897i \(0.925180\pi\)
\(138\) 0 0
\(139\) −13.1924 + 5.46447i −1.11896 + 0.463490i −0.864016 0.503465i \(-0.832058\pi\)
−0.254948 + 0.966955i \(0.582058\pi\)
\(140\) 0 0
\(141\) −0.100505 + 0.242641i −0.00846405 + 0.0204340i
\(142\) 0 0
\(143\) 3.41421i 0.285511i
\(144\) 0 0
\(145\) 9.89949i 0.822108i
\(146\) 0 0
\(147\) −1.46447 + 3.53553i −0.120787 + 0.291606i
\(148\) 0 0
\(149\) −15.6066 + 6.46447i −1.27854 + 0.529590i −0.915551 0.402203i \(-0.868245\pi\)
−0.362992 + 0.931792i \(0.618245\pi\)
\(150\) 0 0
\(151\) 1.48528 + 1.48528i 0.120870 + 0.120870i 0.764955 0.644084i \(-0.222761\pi\)
−0.644084 + 0.764955i \(0.722761\pi\)
\(152\) 0 0
\(153\) −4.82843 + 4.82843i −0.390355 + 0.390355i
\(154\) 0 0
\(155\) 4.48528 + 10.8284i 0.360266 + 0.869760i
\(156\) 0 0
\(157\) 1.70711 + 0.707107i 0.136242 + 0.0564333i 0.449763 0.893148i \(-0.351509\pi\)
−0.313521 + 0.949581i \(0.601509\pi\)
\(158\) 0 0
\(159\) −0.928932 −0.0736691
\(160\) 0 0
\(161\) 11.6569 0.918689
\(162\) 0 0
\(163\) −0.464466 0.192388i −0.0363798 0.0150690i 0.364419 0.931235i \(-0.381267\pi\)
−0.400799 + 0.916166i \(0.631267\pi\)
\(164\) 0 0
\(165\) 3.82843 + 9.24264i 0.298043 + 0.719539i
\(166\) 0 0
\(167\) −14.6569 + 14.6569i −1.13418 + 1.13418i −0.144707 + 0.989475i \(0.546224\pi\)
−0.989475 + 0.144707i \(0.953776\pi\)
\(168\) 0 0
\(169\) 8.77817 + 8.77817i 0.675244 + 0.675244i
\(170\) 0 0
\(171\) 8.94975 3.70711i 0.684404 0.283490i
\(172\) 0 0
\(173\) 3.12132 7.53553i 0.237310 0.572916i −0.759693 0.650282i \(-0.774651\pi\)
0.997003 + 0.0773656i \(0.0246509\pi\)
\(174\) 0 0
\(175\) 5.07107i 0.383337i
\(176\) 0 0
\(177\) 3.75736i 0.282420i
\(178\) 0 0
\(179\) 1.63604 3.94975i 0.122283 0.295218i −0.850870 0.525377i \(-0.823924\pi\)
0.973153 + 0.230159i \(0.0739245\pi\)
\(180\) 0 0
\(181\) 16.1924 6.70711i 1.20357 0.498535i 0.311420 0.950272i \(-0.399196\pi\)
0.892151 + 0.451737i \(0.149196\pi\)
\(182\) 0 0
\(183\) 1.00000 + 1.00000i 0.0739221 + 0.0739221i
\(184\) 0 0
\(185\) −1.58579 + 1.58579i −0.116589 + 0.116589i
\(186\) 0 0
\(187\) −4.82843 11.6569i −0.353090 0.852434i
\(188\) 0 0
\(189\) 5.41421 + 2.24264i 0.393826 + 0.163128i
\(190\) 0 0
\(191\) 12.0000 0.868290 0.434145 0.900843i \(-0.357051\pi\)
0.434145 + 0.900843i \(0.357051\pi\)
\(192\) 0 0
\(193\) −1.51472 −0.109032 −0.0545159 0.998513i \(-0.517362\pi\)
−0.0545159 + 0.998513i \(0.517362\pi\)
\(194\) 0 0
\(195\) 1.58579 + 0.656854i 0.113561 + 0.0470383i
\(196\) 0 0
\(197\) 4.63604 + 11.1924i 0.330304 + 0.797425i 0.998568 + 0.0535002i \(0.0170378\pi\)
−0.668264 + 0.743924i \(0.732962\pi\)
\(198\) 0 0
\(199\) 15.9706 15.9706i 1.13212 1.13212i 0.142300 0.989824i \(-0.454550\pi\)
0.989824 0.142300i \(-0.0454496\pi\)
\(200\) 0 0
\(201\) 3.24264 + 3.24264i 0.228718 + 0.228718i
\(202\) 0 0
\(203\) 4.41421 1.82843i 0.309817 0.128330i
\(204\) 0 0
\(205\) 0.272078 0.656854i 0.0190027 0.0458767i
\(206\) 0 0
\(207\) 19.8995i 1.38311i
\(208\) 0 0
\(209\) 17.8995i 1.23813i
\(210\) 0 0
\(211\) −7.53553 + 18.1924i −0.518768 + 1.25242i 0.419893 + 0.907574i \(0.362068\pi\)
−0.938661 + 0.344842i \(0.887932\pi\)
\(212\) 0 0
\(213\) 5.82843 2.41421i 0.399357 0.165419i
\(214\) 0 0
\(215\) −10.5563 10.5563i −0.719937 0.719937i
\(216\) 0 0
\(217\) −4.00000 + 4.00000i −0.271538 + 0.271538i
\(218\) 0 0
\(219\) 2.89949 + 7.00000i 0.195930 + 0.473016i
\(220\) 0 0
\(221\) −2.00000 0.828427i −0.134535 0.0557260i
\(222\) 0 0
\(223\) 20.9706 1.40429 0.702146 0.712033i \(-0.252225\pi\)
0.702146 + 0.712033i \(0.252225\pi\)
\(224\) 0 0
\(225\) 8.65685 0.577124
\(226\) 0 0
\(227\) −18.6066 7.70711i −1.23496 0.511539i −0.332826 0.942988i \(-0.608002\pi\)
−0.902137 + 0.431449i \(0.858002\pi\)
\(228\) 0 0
\(229\) −9.22183 22.2635i −0.609395 1.47121i −0.863659 0.504076i \(-0.831833\pi\)
0.254264 0.967135i \(-0.418167\pi\)
\(230\) 0 0
\(231\) −3.41421 + 3.41421i −0.224639 + 0.224639i
\(232\) 0 0
\(233\) −2.65685 2.65685i −0.174056 0.174056i 0.614703 0.788759i \(-0.289276\pi\)
−0.788759 + 0.614703i \(0.789276\pi\)
\(234\) 0 0
\(235\) −0.928932 + 0.384776i −0.0605969 + 0.0251000i
\(236\) 0 0
\(237\) 1.75736 4.24264i 0.114153 0.275589i
\(238\) 0 0
\(239\) 5.31371i 0.343715i 0.985122 + 0.171858i \(0.0549769\pi\)
−0.985122 + 0.171858i \(0.945023\pi\)
\(240\) 0 0
\(241\) 8.48528i 0.546585i −0.961931 0.273293i \(-0.911887\pi\)
0.961931 0.273293i \(-0.0881127\pi\)
\(242\) 0 0
\(243\) −5.94975 + 14.3640i −0.381676 + 0.921449i
\(244\) 0 0
\(245\) −13.5355 + 5.60660i −0.864754 + 0.358193i
\(246\) 0 0
\(247\) 2.17157 + 2.17157i 0.138174 + 0.138174i
\(248\) 0 0
\(249\) −2.65685 + 2.65685i −0.168371 + 0.168371i
\(250\) 0 0
\(251\) −6.60660 15.9497i −0.417005 1.00674i −0.983210 0.182475i \(-0.941589\pi\)
0.566205 0.824264i \(-0.308411\pi\)
\(252\) 0 0
\(253\) −33.9706 14.0711i −2.13571 0.884640i
\(254\) 0 0
\(255\) 6.34315 0.397223
\(256\) 0 0
\(257\) 6.00000 0.374270 0.187135 0.982334i \(-0.440080\pi\)
0.187135 + 0.982334i \(0.440080\pi\)
\(258\) 0 0
\(259\) −1.00000 0.414214i −0.0621370 0.0257380i
\(260\) 0 0
\(261\) 3.12132 + 7.53553i 0.193205 + 0.466438i
\(262\) 0 0
\(263\) 5.82843 5.82843i 0.359396 0.359396i −0.504194 0.863590i \(-0.668210\pi\)
0.863590 + 0.504194i \(0.168210\pi\)
\(264\) 0 0
\(265\) −2.51472 2.51472i −0.154478 0.154478i
\(266\) 0 0
\(267\) 8.65685 3.58579i 0.529791 0.219447i
\(268\) 0 0
\(269\) 9.12132 22.0208i 0.556137 1.34263i −0.356666 0.934232i \(-0.616087\pi\)
0.912803 0.408401i \(-0.133913\pi\)
\(270\) 0 0
\(271\) 18.0000i 1.09342i −0.837321 0.546711i \(-0.815880\pi\)
0.837321 0.546711i \(-0.184120\pi\)
\(272\) 0 0
\(273\) 0.828427i 0.0501387i
\(274\) 0 0
\(275\) −6.12132 + 14.7782i −0.369130 + 0.891157i
\(276\) 0 0
\(277\) 1.70711 0.707107i 0.102570 0.0424859i −0.330808 0.943698i \(-0.607321\pi\)
0.433378 + 0.901212i \(0.357321\pi\)
\(278\) 0 0
\(279\) −6.82843 6.82843i −0.408807 0.408807i
\(280\) 0 0
\(281\) −11.8284 + 11.8284i −0.705625 + 0.705625i −0.965612 0.259987i \(-0.916282\pi\)
0.259987 + 0.965612i \(0.416282\pi\)
\(282\) 0 0
\(283\) −5.77817 13.9497i −0.343477 0.829226i −0.997359 0.0726300i \(-0.976861\pi\)
0.653882 0.756596i \(-0.273139\pi\)
\(284\) 0 0
\(285\) −8.31371 3.44365i −0.492462 0.203984i
\(286\) 0 0
\(287\) 0.343146 0.0202553
\(288\) 0 0
\(289\) 9.00000 0.529412
\(290\) 0 0
\(291\) −13.0711 5.41421i −0.766240 0.317387i
\(292\) 0 0
\(293\) 9.60660 + 23.1924i 0.561224 + 1.35491i 0.908788 + 0.417258i \(0.137009\pi\)
−0.347565 + 0.937656i \(0.612991\pi\)
\(294\) 0 0
\(295\) −10.1716 + 10.1716i −0.592212 + 0.592212i
\(296\) 0 0
\(297\) −13.0711 13.0711i −0.758460 0.758460i
\(298\) 0 0
\(299\) −5.82843 + 2.41421i −0.337067 + 0.139618i
\(300\) 0 0
\(301\) 2.75736 6.65685i 0.158932 0.383695i
\(302\) 0 0
\(303\) 2.72792i 0.156715i
\(304\) 0 0
\(305\) 5.41421i 0.310017i
\(306\) 0 0
\(307\) 6.94975 16.7782i 0.396643 0.957581i −0.591813 0.806075i \(-0.701588\pi\)
0.988456 0.151506i \(-0.0484123\pi\)
\(308\) 0 0
\(309\) −9.48528 + 3.92893i −0.539599 + 0.223509i
\(310\) 0 0
\(311\) 2.65685 + 2.65685i 0.150656 + 0.150656i 0.778411 0.627755i \(-0.216026\pi\)
−0.627755 + 0.778411i \(0.716026\pi\)
\(312\) 0 0
\(313\) −7.48528 + 7.48528i −0.423093 + 0.423093i −0.886267 0.463174i \(-0.846710\pi\)
0.463174 + 0.886267i \(0.346710\pi\)
\(314\) 0 0
\(315\) 3.82843 + 9.24264i 0.215707 + 0.520764i
\(316\) 0 0
\(317\) 17.3640 + 7.19239i 0.975257 + 0.403965i 0.812667 0.582729i \(-0.198015\pi\)
0.162591 + 0.986694i \(0.448015\pi\)
\(318\) 0 0
\(319\) −15.0711 −0.843818
\(320\) 0 0
\(321\) 3.41421 0.190563
\(322\) 0 0
\(323\) 10.4853 + 4.34315i 0.583417 + 0.241659i
\(324\) 0 0
\(325\) 1.05025 + 2.53553i 0.0582575 + 0.140646i
\(326\) 0 0
\(327\) −8.07107 + 8.07107i −0.446331 + 0.446331i
\(328\) 0 0
\(329\) −0.343146 0.343146i −0.0189182 0.0189182i
\(330\) 0 0
\(331\) 1.29289 0.535534i 0.0710638 0.0294356i −0.346868 0.937914i \(-0.612755\pi\)
0.417932 + 0.908478i \(0.362755\pi\)
\(332\) 0 0
\(333\) 0.707107 1.70711i 0.0387492 0.0935489i
\(334\) 0 0
\(335\) 17.5563i 0.959206i
\(336\) 0 0
\(337\) 16.9706i 0.924445i −0.886764 0.462223i \(-0.847052\pi\)
0.886764 0.462223i \(-0.152948\pi\)
\(338\) 0 0
\(339\) 1.85786 4.48528i 0.100905 0.243607i
\(340\) 0 0
\(341\) 16.4853 6.82843i 0.892728 0.369780i
\(342\) 0 0
\(343\) −12.0000 12.0000i −0.647939 0.647939i
\(344\) 0 0
\(345\) 13.0711 13.0711i 0.703723 0.703723i
\(346\) 0 0
\(347\) −1.63604 3.94975i −0.0878272 0.212034i 0.873863 0.486172i \(-0.161607\pi\)
−0.961690 + 0.274139i \(0.911607\pi\)
\(348\) 0 0
\(349\) 24.6777 + 10.2218i 1.32097 + 0.547162i 0.928065 0.372419i \(-0.121472\pi\)
0.392901 + 0.919581i \(0.371472\pi\)
\(350\) 0 0
\(351\) −3.17157 −0.169286
\(352\) 0 0
\(353\) 6.00000 0.319348 0.159674 0.987170i \(-0.448956\pi\)
0.159674 + 0.987170i \(0.448956\pi\)
\(354\) 0 0
\(355\) 22.3137 + 9.24264i 1.18429 + 0.490548i
\(356\) 0 0
\(357\) 1.17157 + 2.82843i 0.0620062 + 0.149696i
\(358\) 0 0
\(359\) 17.8284 17.8284i 0.940948 0.940948i −0.0574027 0.998351i \(-0.518282\pi\)
0.998351 + 0.0574027i \(0.0182819\pi\)
\(360\) 0 0
\(361\) 2.05025 + 2.05025i 0.107908 + 0.107908i
\(362\) 0 0
\(363\) 6.29289 2.60660i 0.330291 0.136811i
\(364\) 0 0
\(365\) −11.1005 + 26.7990i −0.581027 + 1.40272i
\(366\) 0 0
\(367\) 6.00000i 0.313197i 0.987662 + 0.156599i \(0.0500529\pi\)
−0.987662 + 0.156599i \(0.949947\pi\)
\(368\) 0 0
\(369\) 0.585786i 0.0304948i
\(370\) 0 0
\(371\) 0.656854 1.58579i 0.0341022 0.0823299i
\(372\) 0 0
\(373\) −10.2929 + 4.26346i −0.532946 + 0.220753i −0.632893 0.774239i \(-0.718133\pi\)
0.0999471 + 0.994993i \(0.468133\pi\)
\(374\) 0 0
\(375\) 2.24264 + 2.24264i 0.115809 + 0.115809i
\(376\) 0 0
\(377\) −1.82843 + 1.82843i −0.0941688 + 0.0941688i
\(378\) 0 0
\(379\) 13.6777 + 33.0208i 0.702575 + 1.69617i 0.717769 + 0.696281i \(0.245163\pi\)
−0.0151948 + 0.999885i \(0.504837\pi\)
\(380\) 0 0
\(381\) −9.17157 3.79899i −0.469874 0.194628i
\(382\) 0 0
\(383\) 16.9706 0.867155 0.433578 0.901116i \(-0.357251\pi\)
0.433578 + 0.901116i \(0.357251\pi\)
\(384\) 0 0
\(385\) −18.4853 −0.942097
\(386\) 0 0
\(387\) 11.3640 + 4.70711i 0.577663 + 0.239276i
\(388\) 0 0
\(389\) −8.39340 20.2635i −0.425562 1.02740i −0.980679 0.195625i \(-0.937326\pi\)
0.555117 0.831773i \(-0.312674\pi\)
\(390\) 0 0
\(391\) −16.4853 + 16.4853i −0.833697 + 0.833697i
\(392\) 0 0
\(393\) 9.58579 + 9.58579i 0.483539 + 0.483539i
\(394\) 0 0
\(395\) 16.2426 6.72792i 0.817256 0.338518i
\(396\) 0 0
\(397\) −9.22183 + 22.2635i −0.462830 + 1.11737i 0.504400 + 0.863470i \(0.331714\pi\)
−0.967230 + 0.253901i \(0.918286\pi\)
\(398\) 0 0
\(399\) 4.34315i 0.217429i
\(400\) 0 0
\(401\) 2.82843i 0.141245i −0.997503 0.0706225i \(-0.977501\pi\)
0.997503 0.0706225i \(-0.0224986\pi\)
\(402\) 0 0
\(403\) 1.17157 2.82843i 0.0583602 0.140894i
\(404\) 0 0
\(405\) −11.0208 + 4.56497i −0.547629 + 0.226835i
\(406\) 0 0
\(407\) 2.41421 + 2.41421i 0.119668 + 0.119668i
\(408\) 0 0
\(409\) 21.4853 21.4853i 1.06238 1.06238i 0.0644584 0.997920i \(-0.479468\pi\)
0.997920 0.0644584i \(-0.0205320\pi\)
\(410\) 0 0
\(411\) −3.58579 8.65685i −0.176874 0.427011i
\(412\) 0 0
\(413\) −6.41421 2.65685i −0.315623 0.130735i
\(414\) 0 0
\(415\) −14.3848 −0.706121
\(416\) 0 0
\(417\) −10.9289 −0.535192
\(418\) 0 0
\(419\) −12.6066 5.22183i −0.615873 0.255103i 0.0528644 0.998602i \(-0.483165\pi\)
−0.668737 + 0.743499i \(0.733165\pi\)
\(420\) 0 0
\(421\) 6.29289 + 15.1924i 0.306697 + 0.740432i 0.999808 + 0.0196009i \(0.00623955\pi\)
−0.693111 + 0.720831i \(0.743760\pi\)
\(422\) 0 0
\(423\) 0.585786 0.585786i 0.0284819 0.0284819i
\(424\) 0 0
\(425\) 7.17157 + 7.17157i 0.347872 + 0.347872i
\(426\) 0 0
\(427\) −2.41421 + 1.00000i −0.116832 + 0.0483934i
\(428\) 0 0
\(429\) 1.00000 2.41421i 0.0482805 0.116559i
\(430\) 0 0
\(431\) 12.3431i 0.594548i 0.954792 + 0.297274i \(0.0960775\pi\)
−0.954792 + 0.297274i \(0.903922\pi\)
\(432\) 0 0
\(433\) 15.5147i 0.745590i −0.927914 0.372795i \(-0.878400\pi\)
0.927914 0.372795i \(-0.121600\pi\)
\(434\) 0 0
\(435\) 2.89949 7.00000i 0.139020 0.335624i
\(436\) 0 0
\(437\) 30.5563 12.6569i 1.46171 0.605459i
\(438\) 0 0
\(439\) 17.0000 + 17.0000i 0.811366 + 0.811366i 0.984839 0.173473i \(-0.0554989\pi\)
−0.173473 + 0.984839i \(0.555499\pi\)
\(440\) 0 0
\(441\) 8.53553 8.53553i 0.406454 0.406454i
\(442\) 0 0
\(443\) −0.606602 1.46447i −0.0288205 0.0695789i 0.908814 0.417201i \(-0.136989\pi\)
−0.937635 + 0.347623i \(0.886989\pi\)
\(444\) 0 0
\(445\) 33.1421 + 13.7279i 1.57109 + 0.650766i
\(446\) 0 0
\(447\) −12.9289 −0.611518
\(448\) 0 0
\(449\) −19.4558 −0.918178 −0.459089 0.888390i \(-0.651824\pi\)
−0.459089 + 0.888390i \(0.651824\pi\)
\(450\) 0 0
\(451\) −1.00000 0.414214i −0.0470882 0.0195046i
\(452\) 0 0
\(453\) 0.615224 + 1.48528i 0.0289057 + 0.0697846i
\(454\) 0 0
\(455\) −2.24264 + 2.24264i −0.105137 + 0.105137i
\(456\) 0 0
\(457\) −7.48528 7.48528i −0.350147 0.350147i 0.510017 0.860164i \(-0.329639\pi\)
−0.860164 + 0.510017i \(0.829639\pi\)
\(458\) 0 0
\(459\) −10.8284 + 4.48528i −0.505428 + 0.209355i
\(460\) 0 0
\(461\) 0.636039 1.53553i 0.0296233 0.0715169i −0.908376 0.418155i \(-0.862677\pi\)
0.937999 + 0.346638i \(0.112677\pi\)
\(462\) 0 0
\(463\) 22.9706i 1.06753i −0.845632 0.533766i \(-0.820776\pi\)
0.845632 0.533766i \(-0.179224\pi\)
\(464\) 0 0
\(465\) 8.97056i 0.416000i
\(466\) 0 0
\(467\) 9.09188 21.9497i 0.420722 1.01571i −0.561413 0.827536i \(-0.689742\pi\)
0.982135 0.188177i \(-0.0602580\pi\)
\(468\) 0 0
\(469\) −7.82843 + 3.24264i −0.361483 + 0.149731i
\(470\) 0 0
\(471\) 1.00000 + 1.00000i 0.0460776 + 0.0460776i
\(472\) 0 0
\(473\) −16.0711 + 16.0711i −0.738948 + 0.738948i
\(474\) 0 0
\(475\) −5.50610 13.2929i −0.252637 0.609920i
\(476\) 0 0
\(477\) 2.70711 + 1.12132i 0.123950 + 0.0513417i
\(478\) 0 0
\(479\) −28.9706 −1.32370 −0.661849 0.749637i \(-0.730228\pi\)
−0.661849 + 0.749637i \(0.730228\pi\)
\(480\) 0 0
\(481\) 0.585786 0.0267096
\(482\) 0 0
\(483\) 8.24264 + 3.41421i 0.375053 + 0.155352i
\(484\) 0 0
\(485\) −20.7279 50.0416i −0.941206 2.27227i
\(486\) 0 0
\(487\) 11.0000 11.0000i 0.498458 0.498458i −0.412500 0.910958i \(-0.635344\pi\)
0.910958 + 0.412500i \(0.135344\pi\)
\(488\) 0 0
\(489\) −0.272078 0.272078i −0.0123038 0.0123038i
\(490\) 0 0
\(491\) −39.3345 + 16.2929i −1.77514 + 0.735288i −0.781343 + 0.624102i \(0.785465\pi\)
−0.993800 + 0.111186i \(0.964535\pi\)
\(492\) 0 0
\(493\) −3.65685 + 8.82843i −0.164696 + 0.397612i
\(494\) 0 0
\(495\) 31.5563i 1.41835i
\(496\) 0 0
\(497\) 11.6569i 0.522881i
\(498\) 0 0
\(499\) 0.949747 2.29289i 0.0425165 0.102644i −0.901195 0.433415i \(-0.857309\pi\)
0.943711 + 0.330771i \(0.107309\pi\)
\(500\) 0 0
\(501\) −14.6569 + 6.07107i −0.654820 + 0.271235i
\(502\) 0 0
\(503\) 11.1421 + 11.1421i 0.496803 + 0.496803i 0.910441 0.413638i \(-0.135742\pi\)
−0.413638 + 0.910441i \(0.635742\pi\)
\(504\) 0 0
\(505\) 7.38478 7.38478i 0.328618 0.328618i
\(506\) 0 0
\(507\) 3.63604 + 8.77817i 0.161482 + 0.389852i
\(508\) 0 0
\(509\) −26.0919 10.8076i −1.15650 0.479039i −0.279793 0.960060i \(-0.590266\pi\)
−0.876709 + 0.481021i \(0.840266\pi\)
\(510\) 0 0
\(511\) −14.0000 −0.619324
\(512\) 0 0
\(513\) 16.6274 0.734118
\(514\) 0 0
\(515\) −36.3137 15.0416i −1.60017 0.662813i
\(516\) 0 0
\(517\) 0.585786 + 1.41421i 0.0257629 + 0.0621970i
\(518\) 0 0
\(519\) 4.41421 4.41421i 0.193762 0.193762i
\(520\) 0 0
\(521\) 3.34315 + 3.34315i 0.146466 + 0.146466i 0.776537 0.630071i \(-0.216974\pi\)
−0.630071 + 0.776537i \(0.716974\pi\)
\(522\) 0 0
\(523\) −19.1924 + 7.94975i −0.839225 + 0.347618i −0.760548 0.649282i \(-0.775070\pi\)
−0.0786768 + 0.996900i \(0.525070\pi\)
\(524\) 0 0
\(525\) 1.48528 3.58579i 0.0648230 0.156497i
\(526\) 0 0
\(527\) 11.3137i 0.492833i
\(528\) 0 0
\(529\) 44.9411i 1.95396i
\(530\) 0 0
\(531\) 4.53553 10.9497i 0.196825 0.475179i
\(532\) 0 0
\(533\) −0.171573 + 0.0710678i −0.00743165 + 0.00307829i
\(534\) 0 0
\(535\) 9.24264 + 9.24264i 0.399594 + 0.399594i
\(536\) 0 0
\(537\) 2.31371 2.31371i 0.0998439 0.0998439i
\(538\) 0 0
\(539\) 8.53553 + 20.6066i 0.367651 + 0.887589i
\(540\) 0 0
\(541\) −27.2635 11.2929i −1.17215 0.485519i −0.290246 0.956952i \(-0.593737\pi\)
−0.881902 + 0.471433i \(0.843737\pi\)
\(542\) 0 0
\(543\) 13.4142 0.575659
\(544\) 0 0
\(545\) −43.6985 −1.87184
\(546\) 0 0
\(547\) 17.5355 + 7.26346i 0.749765 + 0.310563i 0.724646 0.689122i \(-0.242003\pi\)
0.0251195 + 0.999684i \(0.492003\pi\)
\(548\) 0 0
\(549\) −1.70711 4.12132i −0.0728575 0.175894i
\(550\) 0 0
\(551\) 9.58579 9.58579i 0.408368 0.408368i
\(552\) 0 0
\(553\) 6.00000 + 6.00000i 0.255146 + 0.255146i
\(554\) 0 0
\(555\) −1.58579 + 0.656854i −0.0673129 + 0.0278819i
\(556\) 0 0
\(557\) 15.1213 36.5061i 0.640711 1.54681i −0.185012 0.982736i \(-0.559232\pi\)
0.825722 0.564077i \(-0.190768\pi\)
\(558\) 0 0
\(559\) 3.89949i 0.164931i
\(560\) 0 0
\(561\) 9.65685i 0.407713i
\(562\) 0 0
\(563\) −7.87868 + 19.0208i −0.332047 + 0.801632i 0.666383 + 0.745610i \(0.267842\pi\)
−0.998430 + 0.0560220i \(0.982158\pi\)
\(564\) 0 0
\(565\) 17.1716 7.11270i 0.722414 0.299233i
\(566\) 0 0
\(567\) −4.07107 4.07107i −0.170969 0.170969i
\(568\) 0 0
\(569\) 14.6569 14.6569i 0.614447 0.614447i −0.329654 0.944102i \(-0.606932\pi\)
0.944102 + 0.329654i \(0.106932\pi\)
\(570\) 0 0
\(571\) 2.70711 + 6.53553i 0.113289 + 0.273504i 0.970347 0.241716i \(-0.0777103\pi\)
−0.857058 + 0.515220i \(0.827710\pi\)
\(572\) 0 0
\(573\) 8.48528 + 3.51472i 0.354478 + 0.146829i
\(574\) 0 0
\(575\) 29.5563 1.23258
\(576\) 0 0
\(577\) 18.9706 0.789755 0.394877 0.918734i \(-0.370787\pi\)
0.394877 + 0.918734i \(0.370787\pi\)
\(578\) 0 0
\(579\) −1.07107 0.443651i −0.0445121 0.0184375i
\(580\) 0 0
\(581\) −2.65685 6.41421i −0.110225 0.266106i
\(582\) 0 0
\(583\) −3.82843 + 3.82843i −0.158557 + 0.158557i
\(584\) 0 0
\(585\) −3.82843 3.82843i −0.158286 0.158286i
\(586\) 0 0
\(587\) 12.6066 5.22183i 0.520330 0.215528i −0.107032 0.994256i \(-0.534135\pi\)
0.627362 + 0.778728i \(0.284135\pi\)
\(588\) 0 0
\(589\) −6.14214 + 14.8284i −0.253082 + 0.610995i
\(590\) 0 0
\(591\) 9.27208i 0.381402i
\(592\) 0 0
\(593\) 28.2843i 1.16150i −0.814083 0.580748i \(-0.802760\pi\)
0.814083 0.580748i \(-0.197240\pi\)
\(594\) 0 0
\(595\) −4.48528 + 10.8284i −0.183879 + 0.443922i
\(596\) 0 0
\(597\) 15.9706 6.61522i 0.653632 0.270743i
\(598\) 0 0
\(599\) 26.6569 + 26.6569i 1.08917 + 1.08917i 0.995614 + 0.0935555i \(0.0298232\pi\)
0.0935555 + 0.995614i \(0.470177\pi\)
\(600\) 0 0
\(601\) −21.9706 + 21.9706i −0.896198 + 0.896198i −0.995097 0.0988995i \(-0.968468\pi\)
0.0988995 + 0.995097i \(0.468468\pi\)
\(602\) 0 0
\(603\) −5.53553 13.3640i −0.225424 0.544223i
\(604\) 0 0
\(605\) 24.0919 + 9.97918i 0.979474 + 0.405712i
\(606\) 0 0
\(607\) 32.9706 1.33823 0.669117 0.743157i \(-0.266673\pi\)
0.669117 + 0.743157i \(0.266673\pi\)
\(608\) 0 0
\(609\) 3.65685 0.148183
\(610\) 0 0
\(611\) 0.242641 + 0.100505i 0.00981619 + 0.00406600i
\(612\) 0 0
\(613\) 1.32233 + 3.19239i 0.0534084 + 0.128939i 0.948332 0.317281i \(-0.102770\pi\)
−0.894923 + 0.446220i \(0.852770\pi\)
\(614\) 0 0
\(615\) 0.384776 0.384776i 0.0155157 0.0155157i
\(616\) 0 0
\(617\) 22.7990 + 22.7990i 0.917853 + 0.917853i 0.996873 0.0790202i \(-0.0251792\pi\)
−0.0790202 + 0.996873i \(0.525179\pi\)
\(618\) 0 0
\(619\) 21.7782 9.02082i 0.875339 0.362577i 0.100651 0.994922i \(-0.467907\pi\)
0.774687 + 0.632345i \(0.217907\pi\)
\(620\) 0 0
\(621\) −13.0711 + 31.5563i −0.524524 + 1.26631i
\(622\) 0 0
\(623\) 17.3137i 0.693659i
\(624\) 0 0
\(625\) 30.0711i 1.20284i
\(626\) 0 0
\(627\) −5.24264 + 12.6569i −0.209371 + 0.505466i
\(628\) 0 0
\(629\) 2.00000 0.828427i 0.0797452 0.0330316i
\(630\) 0 0
\(631\) −32.4558 32.4558i −1.29205 1.29205i −0.933519 0.358528i \(-0.883279\pi\)
−0.358528 0.933519i \(-0.616721\pi\)
\(632\) 0 0
\(633\) −10.6569 + 10.6569i −0.423572 + 0.423572i
\(634\) 0 0
\(635\) −14.5442 35.1127i −0.577167 1.39340i
\(636\) 0 0
\(637\) 3.53553 + 1.46447i 0.140083 + 0.0580243i
\(638\) 0 0
\(639\) −19.8995 −0.787212
\(640\) 0 0
\(641\) 7.45584 0.294488 0.147244 0.989100i \(-0.452960\pi\)
0.147244 + 0.989100i \(0.452960\pi\)
\(642\) 0 0
\(643\) −11.4350 4.73654i −0.450954 0.186791i 0.145635 0.989338i \(-0.453478\pi\)
−0.596588 + 0.802547i \(0.703478\pi\)
\(644\) 0 0
\(645\) −4.37258 10.5563i −0.172170 0.415656i
\(646\) 0 0
\(647\) −6.17157 + 6.17157i −0.242630 + 0.242630i −0.817937 0.575308i \(-0.804882\pi\)
0.575308 + 0.817937i \(0.304882\pi\)
\(648\) 0 0
\(649\) 15.4853 + 15.4853i 0.607850 + 0.607850i
\(650\) 0 0
\(651\) −4.00000 + 1.65685i −0.156772 + 0.0649372i
\(652\) 0 0
\(653\) 2.09188 5.05025i 0.0818617 0.197632i −0.877649 0.479304i \(-0.840889\pi\)
0.959511 + 0.281672i \(0.0908891\pi\)
\(654\) 0 0
\(655\) 51.8995i 2.02788i
\(656\) 0 0
\(657\) 23.8995i 0.932408i
\(658\) 0 0
\(659\) 10.1213 24.4350i 0.394271 0.951854i −0.594728 0.803927i \(-0.702740\pi\)
0.988998 0.147926i \(-0.0472599\pi\)
\(660\) 0 0
\(661\) −41.7487 + 17.2929i −1.62384 + 0.672616i −0.994521 0.104534i \(-0.966665\pi\)
−0.629316 + 0.777149i \(0.716665\pi\)
\(662\) 0 0
\(663\) −1.17157 1.17157i −0.0455001 0.0455001i
\(664\) 0 0
\(665\) 11.7574 11.7574i 0.455931 0.455931i
\(666\) 0 0
\(667\) 10.6569 + 25.7279i 0.412635 + 0.996189i
\(668\) 0 0
\(669\) 14.8284 + 6.14214i 0.573300 + 0.237469i
\(670\) 0 0
\(671\) 8.24264 0.318204
\(672\) 0 0
\(673\) 22.4853 0.866744 0.433372 0.901215i \(-0.357324\pi\)
0.433372 + 0.901215i \(0.357324\pi\)
\(674\) 0 0
\(675\) 13.7279 + 5.68629i 0.528388 + 0.218865i
\(676\) 0 0
\(677\) 15.6066 + 37.6777i 0.599810 + 1.44807i 0.873775 + 0.486331i \(0.161665\pi\)
−0.273964 + 0.961740i \(0.588335\pi\)
\(678\) 0 0
\(679\) 18.4853 18.4853i 0.709400 0.709400i
\(680\) 0 0
\(681\) −10.8995 10.8995i −0.417670 0.417670i
\(682\) 0 0
\(683\) 10.1213 4.19239i 0.387282 0.160417i −0.180543 0.983567i \(-0.557785\pi\)
0.567824 + 0.823150i \(0.307785\pi\)
\(684\) 0 0
\(685\) 13.7279 33.1421i 0.524517 1.26630i
\(686\) 0 0
\(687\) 18.4437i 0.703669i
\(688\) 0 0
\(689\) 0.928932i 0.0353895i
\(690\) 0 0
\(691\) −12.5061 + 30.1924i −0.475754 + 1.14857i 0.485828 + 0.874055i \(0.338518\pi\)
−0.961582 + 0.274518i \(0.911482\pi\)
\(692\) 0 0
\(693\) 14.0711 5.82843i 0.534516 0.221404i
\(694\) 0 0
\(695\) −29.5858 29.5858i −1.12225 1.12225i
\(696\) 0 0
\(697\) −0.485281 + 0.485281i −0.0183813 + 0.0183813i
\(698\) 0 0
\(699\) −1.10051 2.65685i −0.0416249 0.100491i
\(700\) 0 0
\(701\) 2.87868 + 1.19239i 0.108726 + 0.0450359i 0.436383 0.899761i \(-0.356259\pi\)
−0.327657 + 0.944797i \(0.606259\pi\)
\(702\) 0 0
\(703\) −3.07107 −0.115828
\(704\) 0 0
\(705\) −0.769553 −0.0289830
\(706\) 0 0
\(707\) 4.65685 + 1.92893i 0.175139 + 0.0725450i
\(708\) 0 0
\(709\) 8.77817 + 21.1924i 0.329671 + 0.795897i 0.998616 + 0.0525851i \(0.0167461\pi\)
−0.668945 + 0.743312i \(0.733254\pi\)
\(710\) 0 0
\(711\) −10.2426 + 10.2426i −0.384129 + 0.384129i
\(712\) 0 0
\(713\) −23.3137 23.3137i −0.873105 0.873105i
\(714\) 0 0
\(715\) 9.24264 3.82843i 0.345655 0.143175i
\(716\) 0 0
\(717\) −1.55635 + 3.75736i −0.0581229 + 0.140321i
\(718\) 0 0
\(719\) 35.6569i 1.32978i −0.746943 0.664888i \(-0.768479\pi\)
0.746943 0.664888i \(-0.231521\pi\)
\(720\) 0 0
\(721\) 18.9706i 0.706501i
\(722\) 0 0
\(723\) 2.48528 6.00000i 0.0924286 0.223142i
\(724\) 0 0
\(725\) 11.1924 4.63604i 0.415675 0.172178i
\(726\) 0 0
\(727\) 9.97056 + 9.97056i 0.369788 + 0.369788i 0.867400 0.497612i \(-0.165790\pi\)
−0.497612 + 0.867400i \(0.665790\pi\)
\(728\) 0 0
\(729\) 0.221825 0.221825i 0.00821576 0.00821576i
\(730\) 0 0
\(731\) 5.51472 + 13.3137i 0.203969 + 0.492425i
\(732\) 0 0
\(733\) −33.2635 13.7782i −1.22861 0.508908i −0.328475 0.944513i \(-0.606535\pi\)
−0.900138 + 0.435604i \(0.856535\pi\)
\(734\) 0 0
\(735\) −11.2132 −0.413605
\(736\) 0 0
\(737\) 26.7279 0.984536
\(738\) 0 0
\(739\) −0.464466 0.192388i −0.0170857 0.00707711i 0.374124 0.927379i \(-0.377943\pi\)
−0.391210 + 0.920301i \(0.627943\pi\)
\(740\) 0 0
\(741\) 0.899495 + 2.17157i 0.0330438 + 0.0797747i
\(742\) 0 0
\(743\) −31.6274 + 31.6274i −1.16030 + 1.16030i −0.175887 + 0.984410i \(0.556279\pi\)
−0.984410 + 0.175887i \(0.943721\pi\)
\(744\) 0 0
\(745\) −35.0000 35.0000i −1.28230 1.28230i
\(746\) 0 0
\(747\) 10.9497 4.53553i 0.400630 0.165947i
\(748\) 0 0
\(749\) −2.41421 + 5.82843i −0.0882134 + 0.212966i
\(750\) 0 0
\(751\) 10.9706i 0.400322i 0.979763 + 0.200161i \(0.0641464\pi\)
−0.979763 + 0.200161i \(0.935854\pi\)
\(752\) 0 0
\(753\) 13.2132i 0.481516i
\(754\) 0 0
\(755\) −2.35534 + 5.68629i −0.0857196 + 0.206945i
\(756\) 0 0
\(757\) −33.2635 + 13.7782i −1.20898 + 0.500776i −0.893890 0.448285i \(-0.852035\pi\)
−0.315090 + 0.949062i \(0.602035\pi\)
\(758\) 0 0
\(759\) −19.8995 19.8995i −0.722306 0.722306i
\(760\) 0 0
\(761\) −29.8284 + 29.8284i −1.08128 + 1.08128i −0.0848892 + 0.996390i \(0.527054\pi\)
−0.996390 + 0.0848892i \(0.972946\pi\)
\(762\) 0 0
\(763\) −8.07107 19.4853i −0.292192 0.705415i
\(764\) 0 0
\(765\) −18.4853 7.65685i −0.668337 0.276834i
\(766\) 0 0
\(767\) 3.75736 0.135670
\(768\) 0 0
\(769\) 5.51472 0.198866 0.0994329 0.995044i \(-0.468297\pi\)
0.0994329 + 0.995044i \(0.468297\pi\)
\(770\) 0 0
\(771\) 4.24264 + 1.75736i 0.152795 + 0.0632897i
\(772\) 0 0
\(773\) 12.0919 + 29.1924i 0.434915 + 1.04998i 0.977681 + 0.210094i \(0.0673769\pi\)
−0.542766 + 0.839884i \(0.682623\pi\)
\(774\) 0 0
\(775\) −10.1421 + 10.1421i −0.364316 + 0.364316i
\(776\) 0 0
\(777\) −0.585786 0.585786i −0.0210150 0.0210150i
\(778\) 0 0
\(779\) 0.899495 0.372583i 0.0322278 0.0133492i
\(780\) 0 0
\(781\) 14.0711 33.9706i 0.503502 1.21556i
\(782\) 0 0
\(783\) 14.0000i 0.500319i
\(784\) 0 0
\(785\) 5.41421i 0.193242i
\(786\) 0 0
\(787\) 0.949747 2.29289i 0.0338548 0.0817328i −0.906048 0.423175i \(-0.860915\pi\)
0.939903 + 0.341442i \(0.110915\pi\)
\(788\) 0 0
\(789\) 5.82843 2.41421i 0.207498 0.0859483i
\(790\) 0 0
\(791\) 6.34315 + 6.34315i 0.225536 + 0.225536i
\(792\) 0 0
\(793\) 1.00000 1.00000i 0.0355110 0.0355110i
\(794\) 0 0
\(795\) −1.04163 2.51472i −0.0369428 0.0891879i
\(796\) 0 0
\(797\) −26.0919 10.8076i −0.924222 0.382825i −0.130738 0.991417i \(-0.541735\pi\)
−0.793484 + 0.608592i \(0.791735\pi\)
\(798\) 0 0
\(799\) 0.970563 0.0343360
\(800\) 0 0
\(801\) −29.5563 −1.04432
\(802\) 0 0
\(803\) 40.7990 + 16.8995i 1.43977 + 0.596370i
\(804\) 0 0
\(805\) 13.0711 + 31.5563i 0.460695 + 1.11222i
\(806\) 0 0
\(807\) 12.8995 12.8995i 0.454084 0.454084i
\(808\) 0 0
\(809\) −29.1421 29.1421i −1.02458 1.02458i −0.999690 0.0248928i \(-0.992076\pi\)
−0.0248928 0.999690i \(-0.507924\pi\)
\(810\) 0 0
\(811\) 42.2635 17.5061i 1.48407 0.614722i 0.514053 0.857758i \(-0.328143\pi\)
0.970017 + 0.243036i \(0.0781433\pi\)
\(812\) 0 0
\(813\) 5.27208 12.7279i 0.184900 0.446388i
\(814\) 0 0
\(815\) 1.47309i 0.0516000i
\(816\) 0 0
\(817\) 20.4437i 0.715233i
\(818\) 0 0
\(819\) 1.00000 2.41421i 0.0349428 0.0843594i
\(820\) 0 0
\(821\) −21.6066 + 8.94975i −0.754076 + 0.312348i −0.726403 0.687269i \(-0.758809\pi\)
−0.0276723 + 0.999617i \(0.508809\pi\)
\(822\) 0 0
\(823\) −35.9706 35.9706i −1.25385 1.25385i −0.953978 0.299877i \(-0.903054\pi\)
−0.299877 0.953978i \(-0.596946\pi\)
\(824\) 0 0
\(825\) −8.65685 + 8.65685i −0.301393 + 0.301393i
\(826\) 0 0
\(827\) −16.1213 38.9203i −0.560593 1.35339i −0.909293 0.416157i \(-0.863377\pi\)
0.348699 0.937235i \(-0.386623\pi\)
\(828\) 0 0
\(829\) 34.1924 + 14.1630i 1.18755 + 0.491900i 0.886957 0.461853i \(-0.152815\pi\)
0.300594 + 0.953752i \(0.402815\pi\)
\(830\) 0 0
\(831\) 1.41421 0.0490585
\(832\) 0 0
\(833\) 14.1421 0.489996
\(834\) 0 0
\(835\) −56.1127 23.2426i −1.94186 0.804345i
\(836\) 0 0
\(837\) −6.34315 15.3137i −0.219251 0.529319i
\(838\) 0 0
\(839\) −9.68629 + 9.68629i −0.334408 + 0.334408i −0.854258 0.519850i \(-0.825988\pi\)
0.519850 + 0.854258i \(0.325988\pi\)
\(840\) 0 0
\(841\) −12.4350 12.4350i −0.428794 0.428794i
\(842\) 0 0
\(843\) −11.8284 + 4.89949i −0.407393 + 0.168748i
\(844\) 0 0
\(845\) −13.9203 + 33.6066i −0.478873 + 1.15610i
\(846\) 0 0
\(847\) 12.5858i 0.432453i
\(848\) 0 0
\(849\) 11.5563i 0.396613i
\(850\) 0 0
\(851\) 2.41421 5.82843i 0.0827582 0.199796i
\(852\) 0 0
\(853\) 51.1630 21.1924i 1.75179 0.725614i 0.754164 0.656686i \(-0.228042\pi\)
0.997622 0.0689279i \(-0.0219579\pi\)
\(854\) 0 0
\(855\) 20.0711 + 20.0711i 0.686416 + 0.686416i
\(856\) 0 0
\(857\) 9.68629 9.68629i 0.330877 0.330877i −0.522042 0.852920i \(-0.674830\pi\)
0.852920 + 0.522042i \(0.174830\pi\)
\(858\) 0 0
\(859\) 1.67767 + 4.05025i 0.0572413 + 0.138193i 0.949913 0.312515i \(-0.101172\pi\)
−0.892671 + 0.450708i \(0.851172\pi\)
\(860\) 0 0
\(861\) 0.242641 + 0.100505i 0.00826917 + 0.00342520i
\(862\) 0 0
\(863\) −21.9411 −0.746885 −0.373442 0.927653i \(-0.621823\pi\)
−0.373442 + 0.927653i \(0.621823\pi\)
\(864\) 0 0
\(865\) 23.8995 0.812607
\(866\) 0 0
\(867\) 6.36396 + 2.63604i 0.216131 + 0.0895246i
\(868\) 0 0
\(869\) −10.2426 24.7279i −0.347458 0.838837i
\(870\) 0 0
\(871\) 3.24264 3.24264i 0.109873 0.109873i
\(872\) 0 0
\(873\) 31.5563 + 31.5563i 1.06802 + 1.06802i
\(874\) 0 0
\(875\) −5.41421 + 2.24264i −0.183034 + 0.0758151i
\(876\) 0 0
\(877\) −0.736544 + 1.77817i −0.0248713 + 0.0600447i −0.935827 0.352459i \(-0.885346\pi\)
0.910956 + 0.412504i \(0.135346\pi\)
\(878\) 0 0
\(879\) 19.2132i 0.648045i
\(880\) 0 0
\(881\) 22.6274i 0.762337i 0.924506 + 0.381169i \(0.124478\pi\)
−0.924506 + 0.381169i \(0.875522\pi\)
\(882\) 0 0
\(883\) −20.5650 + 49.6482i −0.692066 + 1.67080i 0.0485090 + 0.998823i \(0.484553\pi\)
−0.740575 + 0.671973i \(0.765447\pi\)
\(884\) 0 0
\(885\) −10.1716 + 4.21320i −0.341914 + 0.141625i
\(886\) 0 0
\(887\) −2.31371 2.31371i −0.0776867 0.0776867i 0.667196 0.744882i \(-0.267494\pi\)
−0.744882 + 0.667196i \(0.767494\pi\)
\(888\) 0 0
\(889\) 12.9706 12.9706i 0.435019 0.435019i
\(890\) 0 0
\(891\) 6.94975 + 16.7782i 0.232825 + 0.562090i
\(892\) 0 0
\(893\) −1.27208 0.526912i −0.0425685 0.0176324i
\(894\) 0 0
\(895\) 12.5269 0.418728
\(896\) 0 0
\(897\) −4.82843 −0.161216
\(898\) 0 0
\(899\) −12.4853 5.17157i −0.416407 0.172482i
\(900\) 0 0
\(901\) 1.31371 + 3.17157i 0.0437660 + 0.105660i
\(902\) 0 0
\(903\) 3.89949 3.89949i 0.129767 0.129767i
\(904\) 0 0
\(905\) 36.3137 + 36.3137i 1.20711 + 1.20711i
\(906\) 0 0
\(907\) 15.7782 6.53553i 0.523906 0.217009i −0.105026 0.994469i \(-0.533493\pi\)
0.628932 + 0.777461i \(0.283493\pi\)
\(908\) 0 0
\(909\) −3.29289 + 7.94975i −0.109218 + 0.263676i
\(910\) 0 0
\(911\) 33.5980i 1.11315i −0.830797 0.556575i \(-0.812115\pi\)
0.830797 0.556575i \(-0.187885\pi\)
\(912\) 0 0
\(913\) 21.8995i 0.724767i
\(914\) 0 0
\(915\) −1.58579 + 3.82843i −0.0524245 + 0.126564i
\(916\) 0 0
\(917\) −23.1421 + 9.58579i −0.764221 + 0.316551i
\(918\) 0 0
\(919\) 8.51472 + 8.51472i 0.280875 + 0.280875i 0.833458 0.552583i \(-0.186358\pi\)
−0.552583 + 0.833458i \(0.686358\pi\)
\(920\) 0 0
\(921\) 9.82843 9.82843i 0.323858 0.323858i
\(922\) 0 0
\(923\) −2.41421 5.82843i −0.0794648 0.191845i
\(924\) 0 0
\(925\) −2.53553 1.05025i −0.0833678 0.0345321i
\(926\) 0 0
\(927\) 32.3848 1.06366
\(928\) 0 0
\(929\) −9.51472 −0.312168 −0.156084 0.987744i \(-0.549887\pi\)
−0.156084 + 0.987744i \(0.549887\pi\)
\(930\) 0 0
\(931\) −18.5355 7.67767i −0.607478 0.251625i
\(932\) 0 0
\(933\) 1.10051 + 2.65685i 0.0360289 + 0.0869815i
\(934\) 0 0
\(935\) 26.1421 26.1421i 0.854939 0.854939i
\(936\) 0 0
\(937\) 19.0000 + 19.0000i 0.620703 + 0.620703i 0.945711 0.325008i \(-0.105367\pi\)
−0.325008 + 0.945711i \(0.605367\pi\)
\(938\) 0 0
\(939\) −7.48528 + 3.10051i −0.244273 + 0.101181i
\(940\) 0 0
\(941\) 0.636039 1.53553i 0.0207343 0.0500570i −0.913173 0.407571i \(-0.866376\pi\)
0.933908 + 0.357514i \(0.116376\pi\)
\(942\) 0 0
\(943\) 2.00000i 0.0651290i
\(944\) 0 0
\(945\) 17.1716i 0.558591i
\(946\) 0 0
\(947\) −9.33452 + 22.5355i −0.303331 + 0.732306i 0.696559 + 0.717499i \(0.254713\pi\)
−0.999890 + 0.0148070i \(0.995287\pi\)
\(948\) 0 0
\(949\) 7.00000 2.89949i 0.227230 0.0941216i
\(950\) 0 0
\(951\) 10.1716 + 10.1716i 0.329836 + 0.329836i
\(952\) 0 0
\(953\) 14.6569 14.6569i 0.474782 0.474782i −0.428676 0.903458i \(-0.641020\pi\)
0.903458 + 0.428676i \(0.141020\pi\)
\(954\) 0 0
\(955\) 13.4558 + 32.4853i 0.435421 + 1.05120i
\(956\) 0 0
\(957\) −10.6569 4.41421i −0.344487 0.142691i
\(958\) 0 0
\(959\) 17.3137 0.559089
\(960\) 0 0
\(961\) −15.0000 −0.483871
\(962\) 0 0
\(963\) −9.94975 4.12132i −0.320626 0.132808i
\(964\) 0 0
\(965\) −1.69848 4.10051i −0.0546762 0.132000i
\(966\) 0 0
\(967\) 6.02944 6.02944i 0.193894 0.193894i −0.603483 0.797376i \(-0.706221\pi\)
0.797376 + 0.603483i \(0.206221\pi\)
\(968\) 0 0
\(969\) 6.14214 + 6.14214i 0.197314 + 0.197314i
\(970\) 0 0
\(971\) −22.3640 + 9.26346i −0.717694 + 0.297278i −0.711484 0.702702i \(-0.751977\pi\)
−0.00620964 + 0.999981i \(0.501977\pi\)
\(972\) 0 0
\(973\) 7.72792 18.6569i 0.247746 0.598111i
\(974\) 0 0
\(975\) 2.10051i 0.0672700i
\(976\) 0 0
\(977\) 14.1421i 0.452447i 0.974075 + 0.226224i \(0.0726380\pi\)
−0.974075 + 0.226224i \(0.927362\pi\)
\(978\) 0 0
\(979\) 20.8995 50.4558i 0.667951 1.61258i
\(980\) 0 0
\(981\) 33.2635 13.7782i 1.06202 0.439903i
\(982\) 0 0
\(983\) 19.6274 + 19.6274i 0.626017 + 0.626017i 0.947064 0.321046i \(-0.104034\pi\)
−0.321046 + 0.947064i \(0.604034\pi\)
\(984\) 0 0
\(985\) −25.1005 + 25.1005i −0.799769 + 0.799769i
\(986\) 0 0
\(987\) −0.142136 0.343146i −0.00452423 0.0109224i
\(988\) 0 0
\(989\) 38.7990 + 16.0711i 1.23374 + 0.511030i
\(990\) 0 0
\(991\) 16.0000 0.508257 0.254128 0.967170i \(-0.418211\pi\)
0.254128 + 0.967170i \(0.418211\pi\)
\(992\) 0 0
\(993\) 1.07107 0.0339893
\(994\) 0 0
\(995\) 61.1421 + 25.3259i 1.93834 + 0.802885i
\(996\) 0 0
\(997\) −20.1924 48.7487i −0.639499 1.54389i −0.827348 0.561690i \(-0.810151\pi\)
0.187848 0.982198i \(-0.439849\pi\)
\(998\) 0 0
\(999\) 2.24264 2.24264i 0.0709540 0.0709540i
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.a.81.1 4
3.2 odd 2 1152.2.v.a.721.1 4
4.3 odd 2 32.2.g.a.29.1 yes 4
8.3 odd 2 256.2.g.b.161.1 4
8.5 even 2 256.2.g.a.161.1 4
12.11 even 2 288.2.v.a.253.1 4
16.3 odd 4 512.2.g.d.65.1 4
16.5 even 4 512.2.g.c.65.1 4
16.11 odd 4 512.2.g.a.65.1 4
16.13 even 4 512.2.g.b.65.1 4
20.3 even 4 800.2.ba.b.349.1 4
20.7 even 4 800.2.ba.a.349.1 4
20.19 odd 2 800.2.y.a.701.1 4
32.3 odd 8 512.2.g.a.449.1 4
32.5 even 8 256.2.g.a.97.1 4
32.11 odd 8 32.2.g.a.21.1 4
32.13 even 8 512.2.g.b.449.1 4
32.19 odd 8 512.2.g.d.449.1 4
32.21 even 8 inner 128.2.g.a.49.1 4
32.27 odd 8 256.2.g.b.97.1 4
32.29 even 8 512.2.g.c.449.1 4
64.11 odd 16 4096.2.a.e.1.2 4
64.21 even 16 4096.2.a.f.1.2 4
64.43 odd 16 4096.2.a.e.1.3 4
64.53 even 16 4096.2.a.f.1.3 4
96.11 even 8 288.2.v.a.181.1 4
96.53 odd 8 1152.2.v.a.433.1 4
160.43 even 8 800.2.ba.a.149.1 4
160.107 even 8 800.2.ba.b.149.1 4
160.139 odd 8 800.2.y.a.501.1 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
32.2.g.a.21.1 4 32.11 odd 8
32.2.g.a.29.1 yes 4 4.3 odd 2
128.2.g.a.49.1 4 32.21 even 8 inner
128.2.g.a.81.1 4 1.1 even 1 trivial
256.2.g.a.97.1 4 32.5 even 8
256.2.g.a.161.1 4 8.5 even 2
256.2.g.b.97.1 4 32.27 odd 8
256.2.g.b.161.1 4 8.3 odd 2
288.2.v.a.181.1 4 96.11 even 8
288.2.v.a.253.1 4 12.11 even 2
512.2.g.a.65.1 4 16.11 odd 4
512.2.g.a.449.1 4 32.3 odd 8
512.2.g.b.65.1 4 16.13 even 4
512.2.g.b.449.1 4 32.13 even 8
512.2.g.c.65.1 4 16.5 even 4
512.2.g.c.449.1 4 32.29 even 8
512.2.g.d.65.1 4 16.3 odd 4
512.2.g.d.449.1 4 32.19 odd 8
800.2.y.a.501.1 4 160.139 odd 8
800.2.y.a.701.1 4 20.19 odd 2
800.2.ba.a.149.1 4 160.43 even 8
800.2.ba.a.349.1 4 20.7 even 4
800.2.ba.b.149.1 4 160.107 even 8
800.2.ba.b.349.1 4 20.3 even 4
1152.2.v.a.433.1 4 96.53 odd 8
1152.2.v.a.721.1 4 3.2 odd 2
4096.2.a.e.1.2 4 64.11 odd 16
4096.2.a.e.1.3 4 64.43 odd 16
4096.2.a.f.1.2 4 64.21 even 16
4096.2.a.f.1.3 4 64.53 even 16