Properties

Label 256.2.i.a.81.6
Level $256$
Weight $2$
Character 256.81
Analytic conductor $2.044$
Analytic rank $0$
Dimension $56$
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] = [256,2,Mod(17,256)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(256, base_ring=CyclotomicField(16))
 
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("256.17");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 256 = 2^{8} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 256.i (of order \(16\), degree \(8\), 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: \(2.04417029174\)
Analytic rank: \(0\)
Dimension: \(56\)
Relative dimension: \(7\) over \(\Q(\zeta_{16})\)
Twist minimal: no (minimal twist has level 64)
Sato-Tate group: $\mathrm{SU}(2)[C_{16}]$

Embedding invariants

Embedding label 81.6
Character \(\chi\) \(=\) 256.81
Dual form 256.2.i.a.177.6

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.435353 - 2.18867i) q^{3} +(0.649649 + 0.434082i) q^{5} +(3.64486 - 1.50975i) q^{7} +(-1.82909 - 0.757635i) q^{9} +O(q^{10})\) \(q+(0.435353 - 2.18867i) q^{3} +(0.649649 + 0.434082i) q^{5} +(3.64486 - 1.50975i) q^{7} +(-1.82909 - 0.757635i) q^{9} +(-5.80194 + 1.15408i) q^{11} +(2.03484 - 1.35963i) q^{13} +(1.23289 - 1.23289i) q^{15} +(0.960477 + 0.960477i) q^{17} +(-0.435978 - 0.652487i) q^{19} +(-1.71754 - 8.63465i) q^{21} +(-0.421603 + 1.01784i) q^{23} +(-1.67980 - 4.05540i) q^{25} +(1.26483 - 1.89295i) q^{27} +(-1.43977 - 0.286388i) q^{29} +6.88004i q^{31} +13.2009i q^{33} +(3.02323 + 0.601358i) q^{35} +(-1.07856 + 1.61417i) q^{37} +(-2.08991 - 5.04550i) q^{39} +(-2.79324 + 6.74347i) q^{41} +(1.20307 + 6.04824i) q^{43} +(-0.859393 - 1.28617i) q^{45} +(6.30014 + 6.30014i) q^{47} +(6.05588 - 6.05588i) q^{49} +(2.52031 - 1.68402i) q^{51} +(10.2655 - 2.04194i) q^{53} +(-4.27019 - 1.76877i) q^{55} +(-1.61788 + 0.670148i) q^{57} +(-4.21278 - 2.81489i) q^{59} +(-2.08276 + 10.4707i) q^{61} -7.81061 q^{63} +1.91212 q^{65} +(-1.42195 + 7.14864i) q^{67} +(2.04417 + 1.36587i) q^{69} +(-2.49385 + 1.03299i) q^{71} +(-1.90488 - 0.789026i) q^{73} +(-9.60722 + 1.91099i) q^{75} +(-19.4049 + 12.9659i) q^{77} +(6.20432 - 6.20432i) q^{79} +(-7.79217 - 7.79217i) q^{81} +(-1.13685 - 1.70141i) q^{83} +(0.207047 + 1.04090i) q^{85} +(-1.25361 + 3.02649i) q^{87} +(1.15743 + 2.79429i) q^{89} +(5.36398 - 8.02776i) q^{91} +(15.0581 + 2.99524i) q^{93} -0.613137i q^{95} -13.1193i q^{97} +(11.4867 + 2.28484i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 56 q + 8 q^{3} - 8 q^{5} + 8 q^{7} - 8 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 56 q + 8 q^{3} - 8 q^{5} + 8 q^{7} - 8 q^{9} + 8 q^{11} - 8 q^{13} + 8 q^{15} - 8 q^{17} + 8 q^{19} - 8 q^{21} + 8 q^{23} - 8 q^{25} + 8 q^{27} - 8 q^{29} + 8 q^{35} - 8 q^{37} + 8 q^{39} - 8 q^{41} + 8 q^{43} - 8 q^{45} + 8 q^{47} - 8 q^{49} - 24 q^{51} - 8 q^{53} - 56 q^{55} - 8 q^{57} - 56 q^{59} - 8 q^{61} - 64 q^{63} - 16 q^{65} - 72 q^{67} - 8 q^{69} - 56 q^{71} - 8 q^{73} - 56 q^{75} - 8 q^{77} - 24 q^{79} - 8 q^{81} + 8 q^{83} - 8 q^{85} + 8 q^{87} - 8 q^{89} + 8 q^{91} + 16 q^{93} - 16 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/256\mathbb{Z}\right)^\times\).

\(n\) \(5\) \(255\)
\(\chi(n)\) \(e\left(\frac{3}{16}\right)\) \(1\)

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
\(3\) 0.435353 2.18867i 0.251351 1.26363i −0.624492 0.781031i \(-0.714694\pi\)
0.875843 0.482596i \(-0.160306\pi\)
\(4\) 0 0
\(5\) 0.649649 + 0.434082i 0.290532 + 0.194127i 0.692292 0.721618i \(-0.256601\pi\)
−0.401760 + 0.915745i \(0.631601\pi\)
\(6\) 0 0
\(7\) 3.64486 1.50975i 1.37763 0.570631i 0.433780 0.901019i \(-0.357179\pi\)
0.943845 + 0.330387i \(0.107179\pi\)
\(8\) 0 0
\(9\) −1.82909 0.757635i −0.609697 0.252545i
\(10\) 0 0
\(11\) −5.80194 + 1.15408i −1.74935 + 0.347968i −0.962936 0.269730i \(-0.913065\pi\)
−0.786415 + 0.617698i \(0.788065\pi\)
\(12\) 0 0
\(13\) 2.03484 1.35963i 0.564362 0.377095i −0.240417 0.970670i \(-0.577284\pi\)
0.804779 + 0.593575i \(0.202284\pi\)
\(14\) 0 0
\(15\) 1.23289 1.23289i 0.318330 0.318330i
\(16\) 0 0
\(17\) 0.960477 + 0.960477i 0.232950 + 0.232950i 0.813923 0.580973i \(-0.197328\pi\)
−0.580973 + 0.813923i \(0.697328\pi\)
\(18\) 0 0
\(19\) −0.435978 0.652487i −0.100020 0.149691i 0.778084 0.628160i \(-0.216192\pi\)
−0.878104 + 0.478469i \(0.841192\pi\)
\(20\) 0 0
\(21\) −1.71754 8.63465i −0.374798 1.88423i
\(22\) 0 0
\(23\) −0.421603 + 1.01784i −0.0879104 + 0.212234i −0.961720 0.274033i \(-0.911642\pi\)
0.873810 + 0.486268i \(0.161642\pi\)
\(24\) 0 0
\(25\) −1.67980 4.05540i −0.335960 0.811079i
\(26\) 0 0
\(27\) 1.26483 1.89295i 0.243417 0.364299i
\(28\) 0 0
\(29\) −1.43977 0.286388i −0.267358 0.0531809i 0.0595906 0.998223i \(-0.481020\pi\)
−0.326949 + 0.945042i \(0.606020\pi\)
\(30\) 0 0
\(31\) 6.88004i 1.23569i 0.786300 + 0.617845i \(0.211994\pi\)
−0.786300 + 0.617845i \(0.788006\pi\)
\(32\) 0 0
\(33\) 13.2009i 2.29799i
\(34\) 0 0
\(35\) 3.02323 + 0.601358i 0.511019 + 0.101648i
\(36\) 0 0
\(37\) −1.07856 + 1.61417i −0.177313 + 0.265368i −0.909471 0.415767i \(-0.863513\pi\)
0.732158 + 0.681135i \(0.238513\pi\)
\(38\) 0 0
\(39\) −2.08991 5.04550i −0.334654 0.807926i
\(40\) 0 0
\(41\) −2.79324 + 6.74347i −0.436230 + 1.05315i 0.541010 + 0.841016i \(0.318042\pi\)
−0.977240 + 0.212136i \(0.931958\pi\)
\(42\) 0 0
\(43\) 1.20307 + 6.04824i 0.183467 + 0.922349i 0.957330 + 0.288996i \(0.0933215\pi\)
−0.773864 + 0.633352i \(0.781678\pi\)
\(44\) 0 0
\(45\) −0.859393 1.28617i −0.128111 0.191731i
\(46\) 0 0
\(47\) 6.30014 + 6.30014i 0.918970 + 0.918970i 0.996955 0.0779845i \(-0.0248485\pi\)
−0.0779845 + 0.996955i \(0.524848\pi\)
\(48\) 0 0
\(49\) 6.05588 6.05588i 0.865126 0.865126i
\(50\) 0 0
\(51\) 2.52031 1.68402i 0.352914 0.235810i
\(52\) 0 0
\(53\) 10.2655 2.04194i 1.41008 0.280482i 0.569421 0.822046i \(-0.307168\pi\)
0.840660 + 0.541564i \(0.182168\pi\)
\(54\) 0 0
\(55\) −4.27019 1.76877i −0.575792 0.238501i
\(56\) 0 0
\(57\) −1.61788 + 0.670148i −0.214293 + 0.0887632i
\(58\) 0 0
\(59\) −4.21278 2.81489i −0.548458 0.366468i 0.250255 0.968180i \(-0.419485\pi\)
−0.798713 + 0.601712i \(0.794485\pi\)
\(60\) 0 0
\(61\) −2.08276 + 10.4707i −0.266670 + 1.34064i 0.582633 + 0.812736i \(0.302023\pi\)
−0.849303 + 0.527906i \(0.822977\pi\)
\(62\) 0 0
\(63\) −7.81061 −0.984045
\(64\) 0 0
\(65\) 1.91212 0.237169
\(66\) 0 0
\(67\) −1.42195 + 7.14864i −0.173719 + 0.873345i 0.791353 + 0.611360i \(0.209377\pi\)
−0.965072 + 0.261985i \(0.915623\pi\)
\(68\) 0 0
\(69\) 2.04417 + 1.36587i 0.246089 + 0.164431i
\(70\) 0 0
\(71\) −2.49385 + 1.03299i −0.295965 + 0.122593i −0.525725 0.850655i \(-0.676206\pi\)
0.229760 + 0.973247i \(0.426206\pi\)
\(72\) 0 0
\(73\) −1.90488 0.789026i −0.222949 0.0923485i 0.268413 0.963304i \(-0.413501\pi\)
−0.491362 + 0.870955i \(0.663501\pi\)
\(74\) 0 0
\(75\) −9.60722 + 1.91099i −1.10935 + 0.220663i
\(76\) 0 0
\(77\) −19.4049 + 12.9659i −2.21139 + 1.47760i
\(78\) 0 0
\(79\) 6.20432 6.20432i 0.698040 0.698040i −0.265947 0.963988i \(-0.585685\pi\)
0.963988 + 0.265947i \(0.0856847\pi\)
\(80\) 0 0
\(81\) −7.79217 7.79217i −0.865797 0.865797i
\(82\) 0 0
\(83\) −1.13685 1.70141i −0.124785 0.186755i 0.763817 0.645433i \(-0.223323\pi\)
−0.888602 + 0.458678i \(0.848323\pi\)
\(84\) 0 0
\(85\) 0.207047 + 1.04090i 0.0224575 + 0.112901i
\(86\) 0 0
\(87\) −1.25361 + 3.02649i −0.134402 + 0.324474i
\(88\) 0 0
\(89\) 1.15743 + 2.79429i 0.122688 + 0.296194i 0.973276 0.229638i \(-0.0737541\pi\)
−0.850589 + 0.525832i \(0.823754\pi\)
\(90\) 0 0
\(91\) 5.36398 8.02776i 0.562298 0.841538i
\(92\) 0 0
\(93\) 15.0581 + 2.99524i 1.56145 + 0.310592i
\(94\) 0 0
\(95\) 0.613137i 0.0629066i
\(96\) 0 0
\(97\) 13.1193i 1.33207i −0.745922 0.666034i \(-0.767991\pi\)
0.745922 0.666034i \(-0.232009\pi\)
\(98\) 0 0
\(99\) 11.4867 + 2.28484i 1.15445 + 0.229635i
\(100\) 0 0
\(101\) −2.49376 + 3.73217i −0.248138 + 0.371365i −0.934540 0.355857i \(-0.884189\pi\)
0.686402 + 0.727222i \(0.259189\pi\)
\(102\) 0 0
\(103\) −4.09230 9.87970i −0.403227 0.973476i −0.986878 0.161471i \(-0.948376\pi\)
0.583651 0.812005i \(-0.301624\pi\)
\(104\) 0 0
\(105\) 2.63235 6.35504i 0.256891 0.620189i
\(106\) 0 0
\(107\) −0.745466 3.74771i −0.0720669 0.362305i 0.927877 0.372886i \(-0.121632\pi\)
−0.999944 + 0.0105812i \(0.996632\pi\)
\(108\) 0 0
\(109\) −5.47688 8.19674i −0.524590 0.785105i 0.470674 0.882307i \(-0.344011\pi\)
−0.995265 + 0.0972021i \(0.969011\pi\)
\(110\) 0 0
\(111\) 3.06333 + 3.06333i 0.290759 + 0.290759i
\(112\) 0 0
\(113\) −3.26239 + 3.26239i −0.306900 + 0.306900i −0.843706 0.536806i \(-0.819631\pi\)
0.536806 + 0.843706i \(0.319631\pi\)
\(114\) 0 0
\(115\) −0.715720 + 0.478229i −0.0667412 + 0.0445951i
\(116\) 0 0
\(117\) −4.75201 + 0.945233i −0.439323 + 0.0873868i
\(118\) 0 0
\(119\) 4.95088 + 2.05072i 0.453846 + 0.187989i
\(120\) 0 0
\(121\) 22.1680 9.18227i 2.01527 0.834752i
\(122\) 0 0
\(123\) 13.5432 + 9.04925i 1.22115 + 0.815943i
\(124\) 0 0
\(125\) 1.43124 7.19532i 0.128014 0.643569i
\(126\) 0 0
\(127\) −6.57619 −0.583543 −0.291771 0.956488i \(-0.594245\pi\)
−0.291771 + 0.956488i \(0.594245\pi\)
\(128\) 0 0
\(129\) 13.7614 1.21162
\(130\) 0 0
\(131\) −0.948444 + 4.76815i −0.0828659 + 0.416595i 0.916978 + 0.398937i \(0.130621\pi\)
−0.999844 + 0.0176578i \(0.994379\pi\)
\(132\) 0 0
\(133\) −2.57417 1.72000i −0.223209 0.149143i
\(134\) 0 0
\(135\) 1.64339 0.680715i 0.141441 0.0585866i
\(136\) 0 0
\(137\) −19.4588 8.06010i −1.66248 0.688621i −0.664214 0.747542i \(-0.731234\pi\)
−0.998263 + 0.0589215i \(0.981234\pi\)
\(138\) 0 0
\(139\) 18.8196 3.74344i 1.59625 0.317515i 0.684741 0.728786i \(-0.259915\pi\)
0.911513 + 0.411272i \(0.134915\pi\)
\(140\) 0 0
\(141\) 16.5317 11.0461i 1.39222 0.930252i
\(142\) 0 0
\(143\) −10.2369 + 10.2369i −0.856050 + 0.856050i
\(144\) 0 0
\(145\) −0.811028 0.811028i −0.0673522 0.0673522i
\(146\) 0 0
\(147\) −10.6179 15.8908i −0.875747 1.31065i
\(148\) 0 0
\(149\) 0.183778 + 0.923914i 0.0150557 + 0.0756900i 0.987583 0.157100i \(-0.0502145\pi\)
−0.972527 + 0.232790i \(0.925215\pi\)
\(150\) 0 0
\(151\) −4.16374 + 10.0522i −0.338841 + 0.818034i 0.658987 + 0.752154i \(0.270985\pi\)
−0.997828 + 0.0658792i \(0.979015\pi\)
\(152\) 0 0
\(153\) −1.02911 2.48449i −0.0831986 0.200859i
\(154\) 0 0
\(155\) −2.98650 + 4.46961i −0.239881 + 0.359008i
\(156\) 0 0
\(157\) 2.16776 + 0.431195i 0.173006 + 0.0344131i 0.280833 0.959757i \(-0.409389\pi\)
−0.107827 + 0.994170i \(0.534389\pi\)
\(158\) 0 0
\(159\) 23.3568i 1.85232i
\(160\) 0 0
\(161\) 4.34640i 0.342544i
\(162\) 0 0
\(163\) 10.1978 + 2.02847i 0.798753 + 0.158882i 0.577560 0.816348i \(-0.304005\pi\)
0.221193 + 0.975230i \(0.429005\pi\)
\(164\) 0 0
\(165\) −5.73029 + 8.57598i −0.446102 + 0.667640i
\(166\) 0 0
\(167\) −5.67541 13.7016i −0.439176 1.06027i −0.976234 0.216720i \(-0.930464\pi\)
0.537058 0.843546i \(-0.319536\pi\)
\(168\) 0 0
\(169\) −2.68293 + 6.47717i −0.206379 + 0.498244i
\(170\) 0 0
\(171\) 0.303097 + 1.52377i 0.0231784 + 0.116526i
\(172\) 0 0
\(173\) 2.81628 + 4.21486i 0.214118 + 0.320450i 0.922945 0.384933i \(-0.125775\pi\)
−0.708827 + 0.705382i \(0.750775\pi\)
\(174\) 0 0
\(175\) −12.2453 12.2453i −0.925654 0.925654i
\(176\) 0 0
\(177\) −7.99491 + 7.99491i −0.600934 + 0.600934i
\(178\) 0 0
\(179\) −2.53753 + 1.69552i −0.189664 + 0.126729i −0.646777 0.762679i \(-0.723883\pi\)
0.457113 + 0.889409i \(0.348883\pi\)
\(180\) 0 0
\(181\) −6.51424 + 1.29576i −0.484200 + 0.0963133i −0.431153 0.902279i \(-0.641893\pi\)
−0.0530464 + 0.998592i \(0.516893\pi\)
\(182\) 0 0
\(183\) 22.0102 + 9.11694i 1.62704 + 0.673943i
\(184\) 0 0
\(185\) −1.40136 + 0.580464i −0.103030 + 0.0426766i
\(186\) 0 0
\(187\) −6.68109 4.46416i −0.488570 0.326452i
\(188\) 0 0
\(189\) 1.75224 8.80912i 0.127457 0.640769i
\(190\) 0 0
\(191\) 1.58154 0.114436 0.0572181 0.998362i \(-0.481777\pi\)
0.0572181 + 0.998362i \(0.481777\pi\)
\(192\) 0 0
\(193\) −16.3932 −1.18001 −0.590004 0.807401i \(-0.700874\pi\)
−0.590004 + 0.807401i \(0.700874\pi\)
\(194\) 0 0
\(195\) 0.832448 4.18500i 0.0596128 0.299694i
\(196\) 0 0
\(197\) −2.24425 1.49956i −0.159896 0.106839i 0.473048 0.881037i \(-0.343154\pi\)
−0.632944 + 0.774197i \(0.718154\pi\)
\(198\) 0 0
\(199\) −12.1675 + 5.03992i −0.862528 + 0.357271i −0.769696 0.638411i \(-0.779592\pi\)
−0.0928322 + 0.995682i \(0.529592\pi\)
\(200\) 0 0
\(201\) 15.0269 + 6.22436i 1.05992 + 0.439032i
\(202\) 0 0
\(203\) −5.68012 + 1.12985i −0.398666 + 0.0792996i
\(204\) 0 0
\(205\) −4.74184 + 3.16839i −0.331184 + 0.221290i
\(206\) 0 0
\(207\) 1.54230 1.54230i 0.107197 0.107197i
\(208\) 0 0
\(209\) 3.28254 + 3.28254i 0.227058 + 0.227058i
\(210\) 0 0
\(211\) −3.81684 5.71230i −0.262762 0.393251i 0.676505 0.736438i \(-0.263494\pi\)
−0.939267 + 0.343187i \(0.888494\pi\)
\(212\) 0 0
\(213\) 1.17516 + 5.90791i 0.0805205 + 0.404804i
\(214\) 0 0
\(215\) −1.84386 + 4.45147i −0.125750 + 0.303588i
\(216\) 0 0
\(217\) 10.3871 + 25.0767i 0.705124 + 1.70232i
\(218\) 0 0
\(219\) −2.55621 + 3.82564i −0.172733 + 0.258512i
\(220\) 0 0
\(221\) 3.26031 + 0.648516i 0.219312 + 0.0436239i
\(222\) 0 0
\(223\) 3.88311i 0.260032i −0.991512 0.130016i \(-0.958497\pi\)
0.991512 0.130016i \(-0.0415029\pi\)
\(224\) 0 0
\(225\) 8.69037i 0.579358i
\(226\) 0 0
\(227\) −22.5337 4.48224i −1.49562 0.297497i −0.621577 0.783353i \(-0.713508\pi\)
−0.874039 + 0.485856i \(0.838508\pi\)
\(228\) 0 0
\(229\) −3.41606 + 5.11250i −0.225740 + 0.337844i −0.927000 0.375062i \(-0.877621\pi\)
0.701260 + 0.712906i \(0.252621\pi\)
\(230\) 0 0
\(231\) 19.9301 + 48.1156i 1.31131 + 3.16577i
\(232\) 0 0
\(233\) 0.733834 1.77163i 0.0480751 0.116064i −0.898018 0.439960i \(-0.854993\pi\)
0.946093 + 0.323896i \(0.104993\pi\)
\(234\) 0 0
\(235\) 1.35811 + 6.82766i 0.0885930 + 0.445387i
\(236\) 0 0
\(237\) −10.8781 16.2803i −0.706610 1.05752i
\(238\) 0 0
\(239\) 6.09870 + 6.09870i 0.394492 + 0.394492i 0.876285 0.481793i \(-0.160014\pi\)
−0.481793 + 0.876285i \(0.660014\pi\)
\(240\) 0 0
\(241\) 5.21549 5.21549i 0.335959 0.335959i −0.518885 0.854844i \(-0.673653\pi\)
0.854844 + 0.518885i \(0.173653\pi\)
\(242\) 0 0
\(243\) −14.7680 + 9.86763i −0.947365 + 0.633009i
\(244\) 0 0
\(245\) 6.56295 1.30545i 0.419291 0.0834022i
\(246\) 0 0
\(247\) −1.77429 0.734933i −0.112895 0.0467627i
\(248\) 0 0
\(249\) −4.21876 + 1.74747i −0.267353 + 0.110741i
\(250\) 0 0
\(251\) −3.73150 2.49331i −0.235530 0.157376i 0.432204 0.901776i \(-0.357736\pi\)
−0.667735 + 0.744399i \(0.732736\pi\)
\(252\) 0 0
\(253\) 1.27145 6.39201i 0.0799354 0.401862i
\(254\) 0 0
\(255\) 2.36832 0.148310
\(256\) 0 0
\(257\) −5.86891 −0.366092 −0.183046 0.983104i \(-0.558596\pi\)
−0.183046 + 0.983104i \(0.558596\pi\)
\(258\) 0 0
\(259\) −1.49418 + 7.51177i −0.0928441 + 0.466759i
\(260\) 0 0
\(261\) 2.41649 + 1.61465i 0.149577 + 0.0999442i
\(262\) 0 0
\(263\) 27.1667 11.2528i 1.67517 0.693877i 0.676090 0.736819i \(-0.263673\pi\)
0.999078 + 0.0429417i \(0.0136730\pi\)
\(264\) 0 0
\(265\) 7.55537 + 3.12954i 0.464123 + 0.192246i
\(266\) 0 0
\(267\) 6.61966 1.31673i 0.405117 0.0805827i
\(268\) 0 0
\(269\) 9.18707 6.13860i 0.560145 0.374277i −0.243031 0.970019i \(-0.578142\pi\)
0.803176 + 0.595741i \(0.203142\pi\)
\(270\) 0 0
\(271\) 17.2217 17.2217i 1.04614 1.04614i 0.0472600 0.998883i \(-0.484951\pi\)
0.998883 0.0472600i \(-0.0150489\pi\)
\(272\) 0 0
\(273\) −15.2349 15.2349i −0.922056 0.922056i
\(274\) 0 0
\(275\) 14.4263 + 21.5906i 0.869941 + 1.30196i
\(276\) 0 0
\(277\) 5.36979 + 26.9957i 0.322639 + 1.62202i 0.712868 + 0.701299i \(0.247396\pi\)
−0.390228 + 0.920718i \(0.627604\pi\)
\(278\) 0 0
\(279\) 5.21255 12.5842i 0.312067 0.753397i
\(280\) 0 0
\(281\) −6.20216 14.9733i −0.369990 0.893234i −0.993751 0.111619i \(-0.964396\pi\)
0.623762 0.781615i \(-0.285604\pi\)
\(282\) 0 0
\(283\) 4.95606 7.41727i 0.294607 0.440911i −0.654408 0.756142i \(-0.727082\pi\)
0.949015 + 0.315231i \(0.102082\pi\)
\(284\) 0 0
\(285\) −1.34195 0.266931i −0.0794904 0.0158116i
\(286\) 0 0
\(287\) 28.7960i 1.69978i
\(288\) 0 0
\(289\) 15.1550i 0.891469i
\(290\) 0 0
\(291\) −28.7139 5.71155i −1.68324 0.334817i
\(292\) 0 0
\(293\) 13.5525 20.2828i 0.791747 1.18493i −0.187500 0.982265i \(-0.560039\pi\)
0.979247 0.202669i \(-0.0649615\pi\)
\(294\) 0 0
\(295\) −1.51494 3.65738i −0.0882031 0.212941i
\(296\) 0 0
\(297\) −5.15386 + 12.4425i −0.299057 + 0.721988i
\(298\) 0 0
\(299\) 0.525997 + 2.64436i 0.0304192 + 0.152928i
\(300\) 0 0
\(301\) 13.5163 + 20.2286i 0.779069 + 1.16596i
\(302\) 0 0
\(303\) 7.08281 + 7.08281i 0.406897 + 0.406897i
\(304\) 0 0
\(305\) −5.89822 + 5.89822i −0.337731 + 0.337731i
\(306\) 0 0
\(307\) −8.15880 + 5.45154i −0.465647 + 0.311136i −0.766169 0.642639i \(-0.777839\pi\)
0.300521 + 0.953775i \(0.402839\pi\)
\(308\) 0 0
\(309\) −23.4050 + 4.65554i −1.33146 + 0.264844i
\(310\) 0 0
\(311\) −28.3647 11.7490i −1.60842 0.666227i −0.615841 0.787870i \(-0.711184\pi\)
−0.992574 + 0.121643i \(0.961184\pi\)
\(312\) 0 0
\(313\) −22.4586 + 9.30264i −1.26943 + 0.525816i −0.912792 0.408425i \(-0.866078\pi\)
−0.356641 + 0.934242i \(0.616078\pi\)
\(314\) 0 0
\(315\) −5.07416 3.39044i −0.285896 0.191030i
\(316\) 0 0
\(317\) 1.29802 6.52557i 0.0729039 0.366513i −0.927061 0.374911i \(-0.877673\pi\)
0.999965 + 0.00839833i \(0.00267330\pi\)
\(318\) 0 0
\(319\) 8.68396 0.486209
\(320\) 0 0
\(321\) −8.52703 −0.475933
\(322\) 0 0
\(323\) 0.207952 1.04544i 0.0115707 0.0581701i
\(324\) 0 0
\(325\) −8.93197 5.96815i −0.495457 0.331054i
\(326\) 0 0
\(327\) −20.3243 + 8.41860i −1.12394 + 0.465550i
\(328\) 0 0
\(329\) 32.4747 + 13.4515i 1.79039 + 0.741604i
\(330\) 0 0
\(331\) −3.84304 + 0.764428i −0.211233 + 0.0420168i −0.299572 0.954074i \(-0.596844\pi\)
0.0883396 + 0.996090i \(0.471844\pi\)
\(332\) 0 0
\(333\) 3.19573 2.13532i 0.175125 0.117015i
\(334\) 0 0
\(335\) −4.02686 + 4.02686i −0.220011 + 0.220011i
\(336\) 0 0
\(337\) 13.8621 + 13.8621i 0.755119 + 0.755119i 0.975430 0.220311i \(-0.0707072\pi\)
−0.220311 + 0.975430i \(0.570707\pi\)
\(338\) 0 0
\(339\) 5.72000 + 8.56058i 0.310668 + 0.464947i
\(340\) 0 0
\(341\) −7.94010 39.9176i −0.429980 2.16166i
\(342\) 0 0
\(343\) 2.36172 5.70170i 0.127521 0.307863i
\(344\) 0 0
\(345\) 0.735093 + 1.77467i 0.0395761 + 0.0955451i
\(346\) 0 0
\(347\) 13.7444 20.5699i 0.737836 1.10425i −0.252773 0.967526i \(-0.581343\pi\)
0.990609 0.136724i \(-0.0436574\pi\)
\(348\) 0 0
\(349\) −34.6278 6.88789i −1.85358 0.368700i −0.862953 0.505284i \(-0.831388\pi\)
−0.990628 + 0.136584i \(0.956388\pi\)
\(350\) 0 0
\(351\) 5.57155i 0.297388i
\(352\) 0 0
\(353\) 16.3511i 0.870283i 0.900362 + 0.435141i \(0.143302\pi\)
−0.900362 + 0.435141i \(0.856698\pi\)
\(354\) 0 0
\(355\) −2.06853 0.411455i −0.109786 0.0218378i
\(356\) 0 0
\(357\) 6.64372 9.94303i 0.351623 0.526241i
\(358\) 0 0
\(359\) 0.837827 + 2.02269i 0.0442188 + 0.106754i 0.944446 0.328667i \(-0.106599\pi\)
−0.900227 + 0.435421i \(0.856599\pi\)
\(360\) 0 0
\(361\) 7.03532 16.9848i 0.370280 0.893935i
\(362\) 0 0
\(363\) −10.4460 52.5158i −0.548275 2.75636i
\(364\) 0 0
\(365\) −0.895000 1.33946i −0.0468464 0.0701106i
\(366\) 0 0
\(367\) −20.9060 20.9060i −1.09129 1.09129i −0.995392 0.0958935i \(-0.969429\pi\)
−0.0958935 0.995392i \(-0.530571\pi\)
\(368\) 0 0
\(369\) 10.2182 10.2182i 0.531936 0.531936i
\(370\) 0 0
\(371\) 34.3336 22.9410i 1.78251 1.19104i
\(372\) 0 0
\(373\) 23.8329 4.74066i 1.23402 0.245462i 0.465362 0.885121i \(-0.345924\pi\)
0.768659 + 0.639659i \(0.220924\pi\)
\(374\) 0 0
\(375\) −15.1251 6.26501i −0.781055 0.323524i
\(376\) 0 0
\(377\) −3.31907 + 1.37481i −0.170941 + 0.0708061i
\(378\) 0 0
\(379\) 20.7596 + 13.8712i 1.06635 + 0.712513i 0.959485 0.281760i \(-0.0909182\pi\)
0.106867 + 0.994273i \(0.465918\pi\)
\(380\) 0 0
\(381\) −2.86296 + 14.3931i −0.146674 + 0.737381i
\(382\) 0 0
\(383\) 24.5463 1.25426 0.627128 0.778916i \(-0.284230\pi\)
0.627128 + 0.778916i \(0.284230\pi\)
\(384\) 0 0
\(385\) −18.2346 −0.929323
\(386\) 0 0
\(387\) 2.38183 11.9743i 0.121075 0.608687i
\(388\) 0 0
\(389\) 19.0280 + 12.7141i 0.964758 + 0.644630i 0.934895 0.354924i \(-0.115493\pi\)
0.0298624 + 0.999554i \(0.490493\pi\)
\(390\) 0 0
\(391\) −1.38255 + 0.572672i −0.0699187 + 0.0289613i
\(392\) 0 0
\(393\) 10.0230 + 4.15166i 0.505593 + 0.209423i
\(394\) 0 0
\(395\) 6.72381 1.33745i 0.338312 0.0672944i
\(396\) 0 0
\(397\) 20.2490 13.5300i 1.01627 0.679050i 0.0683838 0.997659i \(-0.478216\pi\)
0.947886 + 0.318609i \(0.103216\pi\)
\(398\) 0 0
\(399\) −4.88518 + 4.88518i −0.244565 + 0.244565i
\(400\) 0 0
\(401\) 13.4688 + 13.4688i 0.672599 + 0.672599i 0.958314 0.285716i \(-0.0922312\pi\)
−0.285716 + 0.958314i \(0.592231\pi\)
\(402\) 0 0
\(403\) 9.35433 + 13.9997i 0.465972 + 0.697377i
\(404\) 0 0
\(405\) −1.67974 8.44462i −0.0834669 0.419616i
\(406\) 0 0
\(407\) 4.39483 10.6101i 0.217844 0.525922i
\(408\) 0 0
\(409\) −3.05166 7.36736i −0.150895 0.364293i 0.830299 0.557319i \(-0.188170\pi\)
−0.981194 + 0.193026i \(0.938170\pi\)
\(410\) 0 0
\(411\) −26.1123 + 39.0798i −1.28803 + 1.92767i
\(412\) 0 0
\(413\) −19.6048 3.89963i −0.964688 0.191888i
\(414\) 0 0
\(415\) 1.59881i 0.0784824i
\(416\) 0 0
\(417\) 42.8195i 2.09688i
\(418\) 0 0
\(419\) 12.5395 + 2.49426i 0.612593 + 0.121852i 0.491629 0.870805i \(-0.336402\pi\)
0.120964 + 0.992657i \(0.461402\pi\)
\(420\) 0 0
\(421\) −10.8903 + 16.2984i −0.530759 + 0.794337i −0.995858 0.0909215i \(-0.971019\pi\)
0.465099 + 0.885259i \(0.346019\pi\)
\(422\) 0 0
\(423\) −6.75033 16.2967i −0.328212 0.792375i
\(424\) 0 0
\(425\) 2.28170 5.50852i 0.110679 0.267203i
\(426\) 0 0
\(427\) 8.21683 + 41.3088i 0.397640 + 1.99907i
\(428\) 0 0
\(429\) 17.9485 + 26.8618i 0.866560 + 1.29690i
\(430\) 0 0
\(431\) −18.4810 18.4810i −0.890199 0.890199i 0.104343 0.994541i \(-0.466726\pi\)
−0.994541 + 0.104343i \(0.966726\pi\)
\(432\) 0 0
\(433\) 6.00332 6.00332i 0.288501 0.288501i −0.547986 0.836487i \(-0.684605\pi\)
0.836487 + 0.547986i \(0.184605\pi\)
\(434\) 0 0
\(435\) −2.12815 + 1.42199i −0.102037 + 0.0681791i
\(436\) 0 0
\(437\) 0.847937 0.168665i 0.0405623 0.00806835i
\(438\) 0 0
\(439\) 19.8680 + 8.22958i 0.948246 + 0.392777i 0.802571 0.596556i \(-0.203465\pi\)
0.145675 + 0.989333i \(0.453465\pi\)
\(440\) 0 0
\(441\) −15.6649 + 6.48862i −0.745948 + 0.308982i
\(442\) 0 0
\(443\) −15.5336 10.3792i −0.738023 0.493131i 0.128848 0.991664i \(-0.458872\pi\)
−0.866871 + 0.498533i \(0.833872\pi\)
\(444\) 0 0
\(445\) −0.461025 + 2.31773i −0.0218547 + 0.109871i
\(446\) 0 0
\(447\) 2.10215 0.0994282
\(448\) 0 0
\(449\) 32.6778 1.54216 0.771081 0.636737i \(-0.219716\pi\)
0.771081 + 0.636737i \(0.219716\pi\)
\(450\) 0 0
\(451\) 8.42370 42.3488i 0.396657 1.99413i
\(452\) 0 0
\(453\) 20.1881 + 13.4893i 0.948522 + 0.633782i
\(454\) 0 0
\(455\) 6.96941 2.88682i 0.326731 0.135336i
\(456\) 0 0
\(457\) −23.3834 9.68573i −1.09383 0.453079i −0.238489 0.971145i \(-0.576652\pi\)
−0.855341 + 0.518066i \(0.826652\pi\)
\(458\) 0 0
\(459\) 3.03298 0.603297i 0.141567 0.0281595i
\(460\) 0 0
\(461\) 2.39596 1.60093i 0.111591 0.0745627i −0.498522 0.866877i \(-0.666124\pi\)
0.610113 + 0.792314i \(0.291124\pi\)
\(462\) 0 0
\(463\) −24.5897 + 24.5897i −1.14278 + 1.14278i −0.154840 + 0.987940i \(0.549486\pi\)
−0.987940 + 0.154840i \(0.950514\pi\)
\(464\) 0 0
\(465\) 8.48230 + 8.48230i 0.393357 + 0.393357i
\(466\) 0 0
\(467\) 7.08500 + 10.6035i 0.327855 + 0.490670i 0.958379 0.285500i \(-0.0921598\pi\)
−0.630524 + 0.776170i \(0.717160\pi\)
\(468\) 0 0
\(469\) 5.60983 + 28.2025i 0.259038 + 1.30227i
\(470\) 0 0
\(471\) 1.88748 4.55679i 0.0869707 0.209966i
\(472\) 0 0
\(473\) −13.9603 33.7031i −0.641895 1.54967i
\(474\) 0 0
\(475\) −1.91374 + 2.86411i −0.0878082 + 0.131414i
\(476\) 0 0
\(477\) −20.3237 4.04263i −0.930556 0.185099i
\(478\) 0 0
\(479\) 8.39981i 0.383797i 0.981415 + 0.191899i \(0.0614644\pi\)
−0.981415 + 0.191899i \(0.938536\pi\)
\(480\) 0 0
\(481\) 4.75101i 0.216628i
\(482\) 0 0
\(483\) 9.51281 + 1.89222i 0.432848 + 0.0860988i
\(484\) 0 0
\(485\) 5.69487 8.52297i 0.258591 0.387008i
\(486\) 0 0
\(487\) 6.40268 + 15.4574i 0.290133 + 0.700443i 0.999992 0.00390038i \(-0.00124153\pi\)
−0.709859 + 0.704343i \(0.751242\pi\)
\(488\) 0 0
\(489\) 8.87928 21.4365i 0.401535 0.969391i
\(490\) 0 0
\(491\) −1.85105 9.30587i −0.0835368 0.419968i −0.999811 0.0194174i \(-0.993819\pi\)
0.916275 0.400551i \(-0.131181\pi\)
\(492\) 0 0
\(493\) −1.10779 1.65793i −0.0498926 0.0746695i
\(494\) 0 0
\(495\) 6.47049 + 6.47049i 0.290827 + 0.290827i
\(496\) 0 0
\(497\) −7.53017 + 7.53017i −0.337774 + 0.337774i
\(498\) 0 0
\(499\) −12.4453 + 8.31569i −0.557129 + 0.372261i −0.802027 0.597287i \(-0.796245\pi\)
0.244899 + 0.969549i \(0.421245\pi\)
\(500\) 0 0
\(501\) −32.4591 + 6.45653i −1.45017 + 0.288456i
\(502\) 0 0
\(503\) −7.01440 2.90546i −0.312757 0.129548i 0.220783 0.975323i \(-0.429139\pi\)
−0.533540 + 0.845775i \(0.679139\pi\)
\(504\) 0 0
\(505\) −3.24013 + 1.34211i −0.144184 + 0.0597230i
\(506\) 0 0
\(507\) 13.0083 + 8.69190i 0.577721 + 0.386021i
\(508\) 0 0
\(509\) −6.73996 + 33.8841i −0.298743 + 1.50188i 0.481521 + 0.876435i \(0.340085\pi\)
−0.780264 + 0.625450i \(0.784915\pi\)
\(510\) 0 0
\(511\) −8.13423 −0.359837
\(512\) 0 0
\(513\) −1.78656 −0.0788787
\(514\) 0 0
\(515\) 1.63003 8.19473i 0.0718279 0.361103i
\(516\) 0 0
\(517\) −43.8239 29.2822i −1.92737 1.28783i
\(518\) 0 0
\(519\) 10.4510 4.32894i 0.458748 0.190020i
\(520\) 0 0
\(521\) −35.4201 14.6715i −1.55178 0.642770i −0.568146 0.822928i \(-0.692339\pi\)
−0.983638 + 0.180158i \(0.942339\pi\)
\(522\) 0 0
\(523\) 3.91974 0.779685i 0.171398 0.0340933i −0.108645 0.994081i \(-0.534651\pi\)
0.280043 + 0.959987i \(0.409651\pi\)
\(524\) 0 0
\(525\) −32.1318 + 21.4698i −1.40235 + 0.937018i
\(526\) 0 0
\(527\) −6.60811 + 6.60811i −0.287854 + 0.287854i
\(528\) 0 0
\(529\) 15.4052 + 15.4052i 0.669792 + 0.669792i
\(530\) 0 0
\(531\) 5.57291 + 8.34045i 0.241844 + 0.361945i
\(532\) 0 0
\(533\) 3.48487 + 17.5196i 0.150946 + 0.758859i
\(534\) 0 0
\(535\) 1.14252 2.75829i 0.0493955 0.119251i
\(536\) 0 0
\(537\) 2.60621 + 6.29195i 0.112466 + 0.271518i
\(538\) 0 0
\(539\) −28.1469 + 42.1248i −1.21237 + 1.81445i
\(540\) 0 0
\(541\) 37.1103 + 7.38169i 1.59550 + 0.317364i 0.911239 0.411878i \(-0.135127\pi\)
0.684256 + 0.729242i \(0.260127\pi\)
\(542\) 0 0
\(543\) 14.8216i 0.636056i
\(544\) 0 0
\(545\) 7.70242i 0.329935i
\(546\) 0 0
\(547\) −6.05489 1.20439i −0.258888 0.0514961i 0.0639395 0.997954i \(-0.479634\pi\)
−0.322828 + 0.946458i \(0.604634\pi\)
\(548\) 0 0
\(549\) 11.7426 17.5740i 0.501160 0.750039i
\(550\) 0 0
\(551\) 0.440842 + 1.06429i 0.0187805 + 0.0453402i
\(552\) 0 0
\(553\) 13.2469 31.9808i 0.563315 1.35996i
\(554\) 0 0
\(555\) 0.660355 + 3.31983i 0.0280305 + 0.140919i
\(556\) 0 0
\(557\) 10.4706 + 15.6704i 0.443653 + 0.663974i 0.984143 0.177377i \(-0.0567610\pi\)
−0.540490 + 0.841351i \(0.681761\pi\)
\(558\) 0 0
\(559\) 10.6714 + 10.6714i 0.451354 + 0.451354i
\(560\) 0 0
\(561\) −12.6792 + 12.6792i −0.535316 + 0.535316i
\(562\) 0 0
\(563\) 31.7318 21.2025i 1.33733 0.893578i 0.338458 0.940981i \(-0.390095\pi\)
0.998876 + 0.0474033i \(0.0150946\pi\)
\(564\) 0 0
\(565\) −3.53555 + 0.703266i −0.148742 + 0.0295866i
\(566\) 0 0
\(567\) −40.1656 16.6371i −1.68680 0.698694i
\(568\) 0 0
\(569\) 5.70005 2.36104i 0.238958 0.0989798i −0.259991 0.965611i \(-0.583719\pi\)
0.498949 + 0.866631i \(0.333719\pi\)
\(570\) 0 0
\(571\) −25.4415 16.9994i −1.06469 0.711405i −0.105574 0.994411i \(-0.533668\pi\)
−0.959118 + 0.283007i \(0.908668\pi\)
\(572\) 0 0
\(573\) 0.688527 3.46146i 0.0287636 0.144605i
\(574\) 0 0
\(575\) 4.83596 0.201673
\(576\) 0 0
\(577\) 13.1957 0.549345 0.274673 0.961538i \(-0.411431\pi\)
0.274673 + 0.961538i \(0.411431\pi\)
\(578\) 0 0
\(579\) −7.13682 + 35.8792i −0.296596 + 1.49109i
\(580\) 0 0
\(581\) −6.71236 4.48506i −0.278476 0.186071i
\(582\) 0 0
\(583\) −57.2035 + 23.6945i −2.36913 + 0.981324i
\(584\) 0 0
\(585\) −3.49745 1.44869i −0.144602 0.0598959i
\(586\) 0 0
\(587\) −28.1626 + 5.60188i −1.16239 + 0.231215i −0.738344 0.674424i \(-0.764392\pi\)
−0.424050 + 0.905639i \(0.639392\pi\)
\(588\) 0 0
\(589\) 4.48913 2.99954i 0.184971 0.123594i
\(590\) 0 0
\(591\) −4.25908 + 4.25908i −0.175195 + 0.175195i
\(592\) 0 0
\(593\) 8.50593 + 8.50593i 0.349297 + 0.349297i 0.859848 0.510551i \(-0.170559\pi\)
−0.510551 + 0.859848i \(0.670559\pi\)
\(594\) 0 0
\(595\) 2.32615 + 3.48133i 0.0953630 + 0.142721i
\(596\) 0 0
\(597\) 5.73358 + 28.8246i 0.234660 + 1.17971i
\(598\) 0 0
\(599\) 17.7398 42.8278i 0.724831 1.74990i 0.0657345 0.997837i \(-0.479061\pi\)
0.659096 0.752059i \(-0.270939\pi\)
\(600\) 0 0
\(601\) 9.36011 + 22.5973i 0.381807 + 0.921763i 0.991617 + 0.129215i \(0.0412459\pi\)
−0.609810 + 0.792548i \(0.708754\pi\)
\(602\) 0 0
\(603\) 8.01693 11.9982i 0.326475 0.488604i
\(604\) 0 0
\(605\) 18.3872 + 3.65745i 0.747548 + 0.148697i
\(606\) 0 0
\(607\) 19.9552i 0.809956i 0.914326 + 0.404978i \(0.132721\pi\)
−0.914326 + 0.404978i \(0.867279\pi\)
\(608\) 0 0
\(609\) 12.9238i 0.523698i
\(610\) 0 0
\(611\) 21.3856 + 4.25387i 0.865170 + 0.172093i
\(612\) 0 0
\(613\) 15.7066 23.5066i 0.634384 0.949423i −0.365443 0.930834i \(-0.619083\pi\)
0.999827 0.0185890i \(-0.00591740\pi\)
\(614\) 0 0
\(615\) 4.87019 + 11.7577i 0.196385 + 0.474115i
\(616\) 0 0
\(617\) −7.93425 + 19.1550i −0.319421 + 0.771150i 0.679864 + 0.733338i \(0.262039\pi\)
−0.999285 + 0.0378118i \(0.987961\pi\)
\(618\) 0 0
\(619\) 1.06040 + 5.33101i 0.0426212 + 0.214271i 0.996227 0.0867872i \(-0.0276600\pi\)
−0.953606 + 0.301059i \(0.902660\pi\)
\(620\) 0 0
\(621\) 1.39347 + 2.08547i 0.0559179 + 0.0836871i
\(622\) 0 0
\(623\) 8.43735 + 8.43735i 0.338035 + 0.338035i
\(624\) 0 0
\(625\) −11.4662 + 11.4662i −0.458647 + 0.458647i
\(626\) 0 0
\(627\) 8.61344 5.75532i 0.343988 0.229845i
\(628\) 0 0
\(629\) −2.58630 + 0.514447i −0.103123 + 0.0205124i
\(630\) 0 0
\(631\) 35.9213 + 14.8791i 1.43000 + 0.592327i 0.957353 0.288922i \(-0.0932967\pi\)
0.472652 + 0.881249i \(0.343297\pi\)
\(632\) 0 0
\(633\) −14.1640 + 5.86692i −0.562968 + 0.233189i
\(634\) 0 0
\(635\) −4.27222 2.85460i −0.169538 0.113282i
\(636\) 0 0
\(637\) 4.08894 20.5565i 0.162010 0.814479i
\(638\) 0 0
\(639\) 5.34410 0.211409
\(640\) 0 0
\(641\) 2.72233 0.107526 0.0537629 0.998554i \(-0.482878\pi\)
0.0537629 + 0.998554i \(0.482878\pi\)
\(642\) 0 0
\(643\) −0.135549 + 0.681448i −0.00534551 + 0.0268737i −0.983366 0.181635i \(-0.941861\pi\)
0.978020 + 0.208509i \(0.0668610\pi\)
\(644\) 0 0
\(645\) 8.94005 + 5.97355i 0.352014 + 0.235208i
\(646\) 0 0
\(647\) 29.4862 12.2136i 1.15922 0.480165i 0.281606 0.959530i \(-0.409133\pi\)
0.877616 + 0.479365i \(0.159133\pi\)
\(648\) 0 0
\(649\) 27.6909 + 11.4700i 1.08696 + 0.450235i
\(650\) 0 0
\(651\) 59.4067 11.8167i 2.32833 0.463134i
\(652\) 0 0
\(653\) −35.6443 + 23.8167i −1.39487 + 0.932021i −0.394956 + 0.918700i \(0.629240\pi\)
−0.999911 + 0.0133207i \(0.995760\pi\)
\(654\) 0 0
\(655\) −2.68592 + 2.68592i −0.104948 + 0.104948i
\(656\) 0 0
\(657\) 2.88640 + 2.88640i 0.112609 + 0.112609i
\(658\) 0 0
\(659\) −19.0570 28.5207i −0.742354 1.11101i −0.989849 0.142122i \(-0.954608\pi\)
0.247496 0.968889i \(-0.420392\pi\)
\(660\) 0 0
\(661\) −2.62496 13.1966i −0.102099 0.513287i −0.997661 0.0683508i \(-0.978226\pi\)
0.895562 0.444936i \(-0.146774\pi\)
\(662\) 0 0
\(663\) 2.83877 6.85340i 0.110249 0.266164i
\(664\) 0 0
\(665\) −0.925683 2.23480i −0.0358965 0.0866617i
\(666\) 0 0
\(667\) 0.898508 1.34471i 0.0347904 0.0520675i
\(668\) 0 0
\(669\) −8.49882 1.69052i −0.328584 0.0653593i
\(670\) 0 0
\(671\) 63.1543i 2.43805i
\(672\) 0 0
\(673\) 23.6665i 0.912275i 0.889909 + 0.456137i \(0.150767\pi\)
−0.889909 + 0.456137i \(0.849233\pi\)
\(674\) 0 0
\(675\) −9.80133 1.94961i −0.377254 0.0750404i
\(676\) 0 0
\(677\) 14.9427 22.3633i 0.574294 0.859491i −0.424654 0.905356i \(-0.639604\pi\)
0.998948 + 0.0458647i \(0.0146043\pi\)
\(678\) 0 0
\(679\) −19.8069 47.8181i −0.760120 1.83509i
\(680\) 0 0
\(681\) −19.6203 + 47.3675i −0.751850 + 1.81513i
\(682\) 0 0
\(683\) −4.84474 24.3562i −0.185379 0.931963i −0.955708 0.294316i \(-0.904908\pi\)
0.770329 0.637647i \(-0.220092\pi\)
\(684\) 0 0
\(685\) −9.14265 13.6829i −0.349323 0.522798i
\(686\) 0 0
\(687\) 9.70237 + 9.70237i 0.370168 + 0.370168i
\(688\) 0 0
\(689\) 18.1124 18.1124i 0.690027 0.690027i
\(690\) 0 0
\(691\) −11.5361 + 7.70819i −0.438855 + 0.293233i −0.755302 0.655377i \(-0.772510\pi\)
0.316448 + 0.948610i \(0.397510\pi\)
\(692\) 0 0
\(693\) 45.3167 9.01406i 1.72144 0.342416i
\(694\) 0 0
\(695\) 13.8511 + 5.73730i 0.525401 + 0.217628i
\(696\) 0 0
\(697\) −9.15978 + 3.79410i −0.346951 + 0.143712i
\(698\) 0 0
\(699\) −3.55804 2.37740i −0.134577 0.0899217i
\(700\) 0 0
\(701\) 7.20549 36.2244i 0.272148 1.36818i −0.566750 0.823890i \(-0.691800\pi\)
0.838898 0.544289i \(-0.183200\pi\)
\(702\) 0 0
\(703\) 1.52345 0.0574581
\(704\) 0 0
\(705\) 15.5347 0.585072
\(706\) 0 0
\(707\) −3.45474 + 17.3682i −0.129929 + 0.653197i
\(708\) 0 0
\(709\) −20.0441 13.3930i −0.752770 0.502985i 0.119003 0.992894i \(-0.462030\pi\)
−0.871774 + 0.489909i \(0.837030\pi\)
\(710\) 0 0
\(711\) −16.0489 + 6.64766i −0.601880 + 0.249307i
\(712\) 0 0
\(713\) −7.00278 2.90065i −0.262256 0.108630i
\(714\) 0 0
\(715\) −11.0940 + 2.20674i −0.414893 + 0.0825273i
\(716\) 0 0
\(717\) 16.0031 10.6929i 0.597647 0.399335i
\(718\) 0 0
\(719\) −5.08606 + 5.08606i −0.189678 + 0.189678i −0.795557 0.605879i \(-0.792822\pi\)
0.605879 + 0.795557i \(0.292822\pi\)
\(720\) 0 0
\(721\) −29.8317 29.8317i −1.11099 1.11099i
\(722\) 0 0
\(723\) −9.14439 13.6855i −0.340084 0.508971i
\(724\) 0 0
\(725\) 1.25711 + 6.31990i 0.0466878 + 0.234715i
\(726\) 0 0
\(727\) −16.1339 + 38.9506i −0.598372 + 1.44460i 0.276867 + 0.960908i \(0.410704\pi\)
−0.875240 + 0.483690i \(0.839296\pi\)
\(728\) 0 0
\(729\) 2.51641 + 6.07515i 0.0932003 + 0.225006i
\(730\) 0 0
\(731\) −4.65368 + 6.96472i −0.172122 + 0.257599i
\(732\) 0 0
\(733\) −32.2035 6.40567i −1.18946 0.236599i −0.439601 0.898193i \(-0.644880\pi\)
−0.749862 + 0.661595i \(0.769880\pi\)
\(734\) 0 0
\(735\) 14.9324i 0.550791i
\(736\) 0 0
\(737\) 43.1170i 1.58824i
\(738\) 0 0
\(739\) 1.11174 + 0.221139i 0.0408961 + 0.00813474i 0.215496 0.976505i \(-0.430863\pi\)
−0.174600 + 0.984639i \(0.555863\pi\)
\(740\) 0 0
\(741\) −2.38096 + 3.56336i −0.0874669 + 0.130903i
\(742\) 0 0
\(743\) 11.1248 + 26.8577i 0.408130 + 0.985313i 0.985629 + 0.168922i \(0.0540285\pi\)
−0.577500 + 0.816391i \(0.695972\pi\)
\(744\) 0 0
\(745\) −0.281663 + 0.679995i −0.0103193 + 0.0249131i
\(746\) 0 0
\(747\) 0.790350 + 3.97336i 0.0289174 + 0.145378i
\(748\) 0 0
\(749\) −8.37522 12.5344i −0.306024 0.457997i
\(750\) 0 0
\(751\) 19.2670 + 19.2670i 0.703061 + 0.703061i 0.965066 0.262005i \(-0.0843838\pi\)
−0.262005 + 0.965066i \(0.584384\pi\)
\(752\) 0 0
\(753\) −7.08155 + 7.08155i −0.258066 + 0.258066i
\(754\) 0 0
\(755\) −7.06843 + 4.72298i −0.257247 + 0.171887i
\(756\) 0 0
\(757\) 3.81457 0.758766i 0.138643 0.0275778i −0.125281 0.992121i \(-0.539983\pi\)
0.263924 + 0.964544i \(0.414983\pi\)
\(758\) 0 0
\(759\) −13.4365 5.56556i −0.487713 0.202017i
\(760\) 0 0
\(761\) 14.1327 5.85394i 0.512309 0.212205i −0.111526 0.993762i \(-0.535574\pi\)
0.623835 + 0.781556i \(0.285574\pi\)
\(762\) 0 0
\(763\) −32.3375 21.6072i −1.17069 0.782233i
\(764\) 0 0
\(765\) 0.409911 2.06076i 0.0148204 0.0745071i
\(766\) 0 0
\(767\) −12.3995 −0.447722
\(768\) 0 0
\(769\) −47.4209 −1.71004 −0.855020 0.518595i \(-0.826455\pi\)
−0.855020 + 0.518595i \(0.826455\pi\)
\(770\) 0 0
\(771\) −2.55505 + 12.8451i −0.0920178 + 0.462604i
\(772\) 0 0
\(773\) 18.9615 + 12.6697i 0.681998 + 0.455697i 0.847698 0.530480i \(-0.177988\pi\)
−0.165699 + 0.986176i \(0.552988\pi\)
\(774\) 0 0
\(775\) 27.9013 11.5571i 1.00224 0.415143i
\(776\) 0 0
\(777\) 15.7903 + 6.54054i 0.566473 + 0.234641i
\(778\) 0 0
\(779\) 5.61781 1.11745i 0.201279 0.0400369i
\(780\) 0 0
\(781\) 13.2770 8.87142i 0.475089 0.317444i
\(782\) 0 0
\(783\) −2.36318 + 2.36318i −0.0844532 + 0.0844532i
\(784\) 0 0
\(785\) 1.22111 + 1.22111i 0.0435833 + 0.0435833i
\(786\) 0 0
\(787\) −8.45960 12.6607i −0.301552 0.451305i 0.649488 0.760372i \(-0.274983\pi\)
−0.951040 + 0.309067i \(0.899983\pi\)
\(788\) 0 0
\(789\) −12.8015 64.3577i −0.455747 2.29119i
\(790\) 0 0
\(791\) −6.96556 + 16.8163i −0.247667 + 0.597920i
\(792\) 0 0
\(793\) 9.99830 + 24.1380i 0.355050 + 0.857167i
\(794\) 0 0
\(795\) 10.1388 15.1737i 0.359585 0.538157i
\(796\) 0 0
\(797\) 1.21865 + 0.242404i 0.0431668 + 0.00858640i 0.216626 0.976255i \(-0.430495\pi\)
−0.173460 + 0.984841i \(0.555495\pi\)
\(798\) 0 0
\(799\) 12.1023i 0.428148i
\(800\) 0 0
\(801\) 5.98792i 0.211573i
\(802\) 0 0
\(803\) 11.9626 + 2.37950i 0.422150 + 0.0839709i
\(804\) 0 0
\(805\) −1.88669 + 2.82363i −0.0664971 + 0.0995200i
\(806\) 0 0
\(807\) −9.43574 22.7799i −0.332154 0.801890i
\(808\) 0 0
\(809\) 11.5600 27.9083i 0.406428 0.981203i −0.579642 0.814871i \(-0.696808\pi\)
0.986070 0.166332i \(-0.0531923\pi\)
\(810\) 0 0
\(811\) −1.27743 6.42210i −0.0448568 0.225510i 0.951854 0.306552i \(-0.0991753\pi\)
−0.996711 + 0.0810417i \(0.974175\pi\)
\(812\) 0 0
\(813\) −30.1950 45.1900i −1.05899 1.58488i
\(814\) 0 0
\(815\) 5.74447 + 5.74447i 0.201220 + 0.201220i
\(816\) 0 0
\(817\) 3.42189 3.42189i 0.119717 0.119717i
\(818\) 0 0
\(819\) −15.8933 + 10.6196i −0.555357 + 0.371078i
\(820\) 0 0
\(821\) 0.732994 0.145802i 0.0255817 0.00508851i −0.182283 0.983246i \(-0.558349\pi\)
0.207865 + 0.978158i \(0.433349\pi\)
\(822\) 0 0
\(823\) 40.6921 + 16.8552i 1.41844 + 0.587535i 0.954467 0.298316i \(-0.0964250\pi\)
0.463969 + 0.885852i \(0.346425\pi\)
\(824\) 0 0
\(825\) 53.5351 22.1750i 1.86385 0.772033i
\(826\) 0 0
\(827\) 17.5797 + 11.7464i 0.611308 + 0.408463i 0.822324 0.569020i \(-0.192677\pi\)
−0.211016 + 0.977483i \(0.567677\pi\)
\(828\) 0 0
\(829\) −8.12158 + 40.8299i −0.282074 + 1.41808i 0.536607 + 0.843833i \(0.319706\pi\)
−0.818681 + 0.574249i \(0.805294\pi\)
\(830\) 0 0
\(831\) 61.4224 2.13072
\(832\) 0 0
\(833\) 11.6331 0.403062
\(834\) 0 0
\(835\) 2.26061 11.3649i 0.0782316 0.393297i
\(836\) 0 0
\(837\) 13.0236 + 8.70208i 0.450161 + 0.300788i
\(838\) 0 0
\(839\) −33.4505 + 13.8556i −1.15484 + 0.478350i −0.876154 0.482032i \(-0.839899\pi\)
−0.278686 + 0.960382i \(0.589899\pi\)
\(840\) 0 0
\(841\) −24.8016 10.2732i −0.855227 0.354247i
\(842\) 0 0
\(843\) −35.4718 + 7.05577i −1.22171 + 0.243014i
\(844\) 0 0
\(845\) −4.55459 + 3.04328i −0.156683 + 0.104692i
\(846\) 0 0
\(847\) 66.9361 66.9361i 2.29995 2.29995i
\(848\) 0 0
\(849\) −14.0763 14.0763i −0.483097 0.483097i
\(850\) 0 0
\(851\) −1.18825 1.77834i −0.0407326 0.0609606i
\(852\) 0 0
\(853\) −2.29019 11.5136i −0.0784145 0.394217i −0.999982 0.00599829i \(-0.998091\pi\)
0.921567 0.388218i \(-0.126909\pi\)
\(854\) 0 0
\(855\) −0.464534 + 1.12148i −0.0158867 + 0.0383540i
\(856\) 0 0
\(857\) −3.96261 9.56660i −0.135360 0.326789i 0.841636 0.540045i \(-0.181593\pi\)
−0.976996 + 0.213257i \(0.931593\pi\)
\(858\) 0 0
\(859\) 22.7757 34.0863i 0.777098 1.16301i −0.205753 0.978604i \(-0.565964\pi\)
0.982850 0.184405i \(-0.0590357\pi\)
\(860\) 0 0
\(861\) 63.0249 + 12.5364i 2.14788 + 0.427241i
\(862\) 0 0
\(863\) 22.4117i 0.762902i 0.924389 + 0.381451i \(0.124576\pi\)
−0.924389 + 0.381451i \(0.875424\pi\)
\(864\) 0 0
\(865\) 3.96067i 0.134667i
\(866\) 0 0
\(867\) −33.1692 6.59776i −1.12648 0.224072i
\(868\) 0 0
\(869\) −28.8368 + 43.1574i −0.978223 + 1.46401i
\(870\) 0 0
\(871\) 6.82609 + 16.4796i 0.231293 + 0.558391i
\(872\) 0 0
\(873\) −9.93967 + 23.9965i −0.336407 + 0.812158i
\(874\) 0 0
\(875\) −5.64647 28.3867i −0.190886 0.959646i
\(876\) 0 0
\(877\) 22.8368 + 34.1777i 0.771145 + 1.15410i 0.984200 + 0.177060i \(0.0566587\pi\)
−0.213055 + 0.977040i \(0.568341\pi\)
\(878\) 0 0
\(879\) −38.4921 38.4921i −1.29831 1.29831i
\(880\) 0 0
\(881\) −19.2835 + 19.2835i −0.649677 + 0.649677i −0.952915 0.303238i \(-0.901932\pi\)
0.303238 + 0.952915i \(0.401932\pi\)
\(882\) 0 0
\(883\) −43.0348 + 28.7549i −1.44824 + 0.967681i −0.451068 + 0.892490i \(0.648957\pi\)
−0.997169 + 0.0751915i \(0.976043\pi\)
\(884\) 0 0
\(885\) −8.66433 + 1.72344i −0.291248 + 0.0579329i
\(886\) 0 0
\(887\) 2.36214 + 0.978431i 0.0793129 + 0.0328525i 0.421987 0.906602i \(-0.361333\pi\)
−0.342674 + 0.939454i \(0.611333\pi\)
\(888\) 0 0
\(889\) −23.9693 + 9.92840i −0.803904 + 0.332988i
\(890\) 0 0
\(891\) 54.2025 + 36.2170i 1.81585 + 1.21331i
\(892\) 0 0
\(893\) 1.36404 6.85748i 0.0456458 0.229477i
\(894\) 0 0
\(895\) −2.38450 −0.0797049
\(896\) 0 0
\(897\) 6.01663 0.200889
\(898\) 0 0
\(899\) 1.97036 9.90565i 0.0657151 0.330372i
\(900\) 0 0
\(901\) 11.8210 + 7.89857i 0.393816 + 0.263140i
\(902\) 0 0
\(903\) 50.1581 20.7762i 1.66916 0.691388i
\(904\) 0 0
\(905\) −4.79444 1.98592i −0.159372 0.0660142i
\(906\) 0 0
\(907\) −21.3347 + 4.24373i −0.708405 + 0.140911i −0.536127 0.844138i \(-0.680113\pi\)
−0.172279 + 0.985048i \(0.555113\pi\)
\(908\) 0 0
\(909\) 7.38893 4.93712i 0.245075 0.163754i
\(910\) 0 0
\(911\) −1.38797 + 1.38797i −0.0459856 + 0.0459856i −0.729726 0.683740i \(-0.760352\pi\)
0.683740 + 0.729726i \(0.260352\pi\)
\(912\) 0 0
\(913\) 8.55950 + 8.55950i 0.283278 + 0.283278i
\(914\) 0 0
\(915\) 10.3414 + 15.4771i 0.341877 + 0.511655i
\(916\) 0 0
\(917\) 3.74177 + 18.8111i 0.123564 + 0.621198i
\(918\) 0 0
\(919\) −1.63873 + 3.95625i −0.0540568 + 0.130505i −0.948601 0.316475i \(-0.897501\pi\)
0.894544 + 0.446980i \(0.147501\pi\)
\(920\) 0 0
\(921\) 8.37964 + 20.2302i 0.276119 + 0.666609i
\(922\) 0 0
\(923\) −3.67009 + 5.49268i −0.120802 + 0.180794i
\(924\) 0 0
\(925\) 8.35786 + 1.66248i 0.274805 + 0.0546621i
\(926\) 0 0
\(927\) 21.1713i 0.695358i
\(928\) 0 0
\(929\) 53.4969i 1.75518i 0.479415 + 0.877589i \(0.340849\pi\)
−0.479415 + 0.877589i \(0.659151\pi\)
\(930\) 0 0
\(931\) −6.59161 1.31115i −0.216031 0.0429713i
\(932\) 0 0
\(933\) −38.0634 + 56.9659i −1.24614 + 1.86498i
\(934\) 0 0
\(935\) −2.40255 5.80028i −0.0785719 0.189689i
\(936\) 0 0
\(937\) 9.69070 23.3954i 0.316582 0.764295i −0.682849 0.730559i \(-0.739259\pi\)
0.999431 0.0337361i \(-0.0107406\pi\)
\(938\) 0 0
\(939\) 10.5830 + 53.2042i 0.345362 + 1.73625i
\(940\) 0 0
\(941\) −14.9326 22.3482i −0.486788 0.728529i 0.504037 0.863682i \(-0.331847\pi\)
−0.990825 + 0.135153i \(0.956847\pi\)
\(942\) 0 0
\(943\) −5.68614 5.68614i −0.185166 0.185166i
\(944\) 0 0
\(945\) 4.96222 4.96222i 0.161421 0.161421i
\(946\) 0 0
\(947\) −15.6970 + 10.4884i −0.510083 + 0.340827i −0.783830 0.620975i \(-0.786737\pi\)
0.273747 + 0.961802i \(0.411737\pi\)
\(948\) 0 0
\(949\) −4.94890 + 0.984397i −0.160648 + 0.0319549i
\(950\) 0 0
\(951\) −13.7172 5.68185i −0.444811 0.184247i
\(952\) 0 0
\(953\) 31.0836 12.8753i 1.00690 0.417070i 0.182575 0.983192i \(-0.441557\pi\)
0.824322 + 0.566122i \(0.191557\pi\)
\(954\) 0 0
\(955\) 1.02745 + 0.686517i 0.0332473 + 0.0222152i
\(956\) 0 0
\(957\) 3.78059 19.0063i 0.122209 0.614387i
\(958\) 0 0
\(959\) −83.0932 −2.68322
\(960\) 0 0
\(961\) −16.3349 −0.526932
\(962\) 0 0
\(963\) −1.47587 + 7.41970i −0.0475592 + 0.239096i
\(964\) 0 0
\(965\) −10.6498 7.11598i −0.342830 0.229072i
\(966\) 0 0
\(967\) 39.0826 16.1886i 1.25681 0.520589i 0.347883 0.937538i \(-0.386901\pi\)
0.908930 + 0.416949i \(0.136901\pi\)
\(968\) 0 0
\(969\) −2.19760 0.910274i −0.0705970 0.0292422i
\(970\) 0 0
\(971\) −15.9123 + 3.16514i −0.510649 + 0.101574i −0.443688 0.896181i \(-0.646330\pi\)
−0.0669606 + 0.997756i \(0.521330\pi\)
\(972\) 0 0
\(973\) 62.9429 42.0571i 2.01786 1.34829i
\(974\) 0 0
\(975\) −16.9509 + 16.9509i −0.542862 + 0.542862i
\(976\) 0 0
\(977\) −14.4085 14.4085i −0.460970 0.460970i 0.438004 0.898973i \(-0.355686\pi\)
−0.898973 + 0.438004i \(0.855686\pi\)
\(978\) 0 0
\(979\) −9.94018 14.8765i −0.317690 0.475456i
\(980\) 0 0
\(981\) 3.80759 + 19.1421i 0.121567 + 0.611159i
\(982\) 0 0
\(983\) −14.2810 + 34.4773i −0.455492 + 1.09966i 0.514711 + 0.857364i \(0.327899\pi\)
−0.970203 + 0.242292i \(0.922101\pi\)
\(984\) 0 0
\(985\) −0.807045 1.94838i −0.0257146 0.0620805i
\(986\) 0 0
\(987\) 43.5788 65.2202i 1.38713 2.07598i
\(988\) 0 0
\(989\) −6.66337 1.32543i −0.211883 0.0421461i
\(990\) 0 0
\(991\) 5.17247i 0.164309i −0.996620 0.0821544i \(-0.973820\pi\)
0.996620 0.0821544i \(-0.0261801\pi\)
\(992\) 0 0
\(993\) 8.74393i 0.277480i
\(994\) 0 0
\(995\) −10.0923 2.00749i −0.319948 0.0636416i
\(996\) 0 0
\(997\) −11.3818 + 17.0341i −0.360466 + 0.539476i −0.966734 0.255785i \(-0.917666\pi\)
0.606267 + 0.795261i \(0.292666\pi\)
\(998\) 0 0
\(999\) 1.69136 + 4.08331i 0.0535123 + 0.129190i
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 256.2.i.a.81.6 56
4.3 odd 2 64.2.i.a.61.3 yes 56
8.3 odd 2 512.2.i.b.417.6 56
8.5 even 2 512.2.i.a.417.2 56
12.11 even 2 576.2.bd.a.253.5 56
64.11 odd 16 512.2.i.b.97.6 56
64.21 even 16 inner 256.2.i.a.177.6 56
64.43 odd 16 64.2.i.a.21.3 56
64.53 even 16 512.2.i.a.97.2 56
192.107 even 16 576.2.bd.a.469.5 56
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
64.2.i.a.21.3 56 64.43 odd 16
64.2.i.a.61.3 yes 56 4.3 odd 2
256.2.i.a.81.6 56 1.1 even 1 trivial
256.2.i.a.177.6 56 64.21 even 16 inner
512.2.i.a.97.2 56 64.53 even 16
512.2.i.a.417.2 56 8.5 even 2
512.2.i.b.97.6 56 64.11 odd 16
512.2.i.b.417.6 56 8.3 odd 2
576.2.bd.a.253.5 56 12.11 even 2
576.2.bd.a.469.5 56 192.107 even 16