Properties

Label 512.2.i.b.33.5
Level $512$
Weight $2$
Character 512.33
Analytic conductor $4.088$
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] = [512,2,Mod(33,512)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(512, base_ring=CyclotomicField(16))
 
chi = DirichletCharacter(H, H._module([0, 15]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("512.33");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 512 = 2^{9} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 512.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: \(4.08834058349\)
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 33.5
Character \(\chi\) \(=\) 512.33
Dual form 512.2.i.b.481.5

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(1.31138 - 0.876237i) q^{3} +(-3.52249 + 0.700667i) q^{5} +(1.02503 + 2.47464i) q^{7} +(-0.196120 + 0.473476i) q^{9} +O(q^{10})\) \(q+(1.31138 - 0.876237i) q^{3} +(-3.52249 + 0.700667i) q^{5} +(1.02503 + 2.47464i) q^{7} +(-0.196120 + 0.473476i) q^{9} +(-1.67900 + 2.51280i) q^{11} +(4.41643 + 0.878483i) q^{13} +(-4.00538 + 4.00538i) q^{15} +(1.12567 + 1.12567i) q^{17} +(-0.432994 + 2.17681i) q^{19} +(3.51257 + 2.34703i) q^{21} +(-4.52287 - 1.87343i) q^{23} +(7.29760 - 3.02276i) q^{25} +(1.08077 + 5.43340i) q^{27} +(3.43450 + 5.14009i) q^{29} +2.88548i q^{31} +4.76643i q^{33} +(-5.34455 - 7.99868i) q^{35} +(-1.20408 - 6.05333i) q^{37} +(6.56139 - 2.71782i) q^{39} +(-3.20440 - 1.32731i) q^{41} +(2.16349 + 1.44560i) q^{43} +(0.359082 - 1.80523i) q^{45} +(-2.37708 - 2.37708i) q^{47} +(-0.123405 + 0.123405i) q^{49} +(2.46253 + 0.489827i) q^{51} +(3.20051 - 4.78991i) q^{53} +(4.15361 - 10.0277i) q^{55} +(1.33958 + 3.23403i) q^{57} +(-1.01300 + 0.201498i) q^{59} +(2.23513 - 1.49347i) q^{61} -1.37271 q^{63} -16.1724 q^{65} +(-12.1226 + 8.10007i) q^{67} +(-7.57278 + 1.50632i) q^{69} +(4.63617 + 11.1927i) q^{71} +(3.99984 - 9.65646i) q^{73} +(6.92128 - 10.3584i) q^{75} +(-7.93928 - 1.57922i) q^{77} +(1.05698 - 1.05698i) q^{79} +(5.09110 + 5.09110i) q^{81} +(1.67409 - 8.41620i) q^{83} +(-4.75386 - 3.17643i) q^{85} +(9.00788 + 3.73119i) q^{87} +(-5.40505 + 2.23885i) q^{89} +(2.35304 + 11.8295i) q^{91} +(2.52837 + 3.78397i) q^{93} -7.97117i q^{95} +11.0691i q^{97} +(-0.860463 - 1.28777i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 56 q + 8 q^{3} + 8 q^{5} - 8 q^{7} - 8 q^{9}+O(q^{10}) \) 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 \(\left(\mathbb{Z}/512\mathbb{Z}\right)^\times\).

\(n\) \(5\) \(511\)
\(\chi(n)\) \(e\left(\frac{15}{16}\right)\) \(1\)

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
\(3\) 1.31138 0.876237i 0.757127 0.505896i −0.116084 0.993239i \(-0.537034\pi\)
0.873210 + 0.487344i \(0.162034\pi\)
\(4\) 0 0
\(5\) −3.52249 + 0.700667i −1.57531 + 0.313348i −0.903900 0.427743i \(-0.859309\pi\)
−0.671405 + 0.741091i \(0.734309\pi\)
\(6\) 0 0
\(7\) 1.02503 + 2.47464i 0.387425 + 0.935326i 0.990484 + 0.137629i \(0.0439482\pi\)
−0.603059 + 0.797696i \(0.706052\pi\)
\(8\) 0 0
\(9\) −0.196120 + 0.473476i −0.0653734 + 0.157825i
\(10\) 0 0
\(11\) −1.67900 + 2.51280i −0.506237 + 0.757636i −0.993279 0.115742i \(-0.963076\pi\)
0.487043 + 0.873378i \(0.338076\pi\)
\(12\) 0 0
\(13\) 4.41643 + 0.878483i 1.22490 + 0.243647i 0.764827 0.644235i \(-0.222824\pi\)
0.460070 + 0.887882i \(0.347824\pi\)
\(14\) 0 0
\(15\) −4.00538 + 4.00538i −1.03418 + 1.03418i
\(16\) 0 0
\(17\) 1.12567 + 1.12567i 0.273014 + 0.273014i 0.830312 0.557298i \(-0.188162\pi\)
−0.557298 + 0.830312i \(0.688162\pi\)
\(18\) 0 0
\(19\) −0.432994 + 2.17681i −0.0993357 + 0.499394i 0.898800 + 0.438359i \(0.144440\pi\)
−0.998136 + 0.0610352i \(0.980560\pi\)
\(20\) 0 0
\(21\) 3.51257 + 2.34703i 0.766507 + 0.512163i
\(22\) 0 0
\(23\) −4.52287 1.87343i −0.943084 0.390638i −0.142457 0.989801i \(-0.545500\pi\)
−0.800627 + 0.599163i \(0.795500\pi\)
\(24\) 0 0
\(25\) 7.29760 3.02276i 1.45952 0.604553i
\(26\) 0 0
\(27\) 1.08077 + 5.43340i 0.207994 + 1.04566i
\(28\) 0 0
\(29\) 3.43450 + 5.14009i 0.637771 + 0.954492i 0.999751 + 0.0223059i \(0.00710078\pi\)
−0.361980 + 0.932186i \(0.617899\pi\)
\(30\) 0 0
\(31\) 2.88548i 0.518248i 0.965844 + 0.259124i \(0.0834339\pi\)
−0.965844 + 0.259124i \(0.916566\pi\)
\(32\) 0 0
\(33\) 4.76643i 0.829730i
\(34\) 0 0
\(35\) −5.34455 7.99868i −0.903394 1.35202i
\(36\) 0 0
\(37\) −1.20408 6.05333i −0.197950 0.995162i −0.944169 0.329461i \(-0.893133\pi\)
0.746219 0.665700i \(-0.231867\pi\)
\(38\) 0 0
\(39\) 6.56139 2.71782i 1.05066 0.435199i
\(40\) 0 0
\(41\) −3.20440 1.32731i −0.500443 0.207290i 0.118159 0.992995i \(-0.462301\pi\)
−0.618602 + 0.785704i \(0.712301\pi\)
\(42\) 0 0
\(43\) 2.16349 + 1.44560i 0.329929 + 0.220452i 0.709491 0.704715i \(-0.248925\pi\)
−0.379561 + 0.925167i \(0.623925\pi\)
\(44\) 0 0
\(45\) 0.359082 1.80523i 0.0535288 0.269108i
\(46\) 0 0
\(47\) −2.37708 2.37708i −0.346733 0.346733i 0.512158 0.858891i \(-0.328846\pi\)
−0.858891 + 0.512158i \(0.828846\pi\)
\(48\) 0 0
\(49\) −0.123405 + 0.123405i −0.0176293 + 0.0176293i
\(50\) 0 0
\(51\) 2.46253 + 0.489827i 0.344823 + 0.0685895i
\(52\) 0 0
\(53\) 3.20051 4.78991i 0.439624 0.657944i −0.543810 0.839208i \(-0.683019\pi\)
0.983434 + 0.181264i \(0.0580189\pi\)
\(54\) 0 0
\(55\) 4.15361 10.0277i 0.560073 1.35214i
\(56\) 0 0
\(57\) 1.33958 + 3.23403i 0.177432 + 0.428358i
\(58\) 0 0
\(59\) −1.01300 + 0.201498i −0.131881 + 0.0262329i −0.260590 0.965450i \(-0.583917\pi\)
0.128708 + 0.991683i \(0.458917\pi\)
\(60\) 0 0
\(61\) 2.23513 1.49347i 0.286179 0.191219i −0.404192 0.914674i \(-0.632447\pi\)
0.690371 + 0.723455i \(0.257447\pi\)
\(62\) 0 0
\(63\) −1.37271 −0.172945
\(64\) 0 0
\(65\) −16.1724 −2.00593
\(66\) 0 0
\(67\) −12.1226 + 8.10007i −1.48101 + 0.989581i −0.487840 + 0.872933i \(0.662215\pi\)
−0.993173 + 0.116648i \(0.962785\pi\)
\(68\) 0 0
\(69\) −7.57278 + 1.50632i −0.911656 + 0.181340i
\(70\) 0 0
\(71\) 4.63617 + 11.1927i 0.550212 + 1.32833i 0.917320 + 0.398151i \(0.130348\pi\)
−0.367108 + 0.930178i \(0.619652\pi\)
\(72\) 0 0
\(73\) 3.99984 9.65646i 0.468146 1.13020i −0.496826 0.867850i \(-0.665501\pi\)
0.964972 0.262353i \(-0.0844986\pi\)
\(74\) 0 0
\(75\) 6.92128 10.3584i 0.799200 1.19609i
\(76\) 0 0
\(77\) −7.93928 1.57922i −0.904765 0.179969i
\(78\) 0 0
\(79\) 1.05698 1.05698i 0.118919 0.118919i −0.645143 0.764062i \(-0.723202\pi\)
0.764062 + 0.645143i \(0.223202\pi\)
\(80\) 0 0
\(81\) 5.09110 + 5.09110i 0.565677 + 0.565677i
\(82\) 0 0
\(83\) 1.67409 8.41620i 0.183755 0.923798i −0.773333 0.634000i \(-0.781412\pi\)
0.957088 0.289798i \(-0.0935881\pi\)
\(84\) 0 0
\(85\) −4.75386 3.17643i −0.515629 0.344532i
\(86\) 0 0
\(87\) 9.00788 + 3.73119i 0.965747 + 0.400025i
\(88\) 0 0
\(89\) −5.40505 + 2.23885i −0.572935 + 0.237317i −0.650290 0.759686i \(-0.725352\pi\)
0.0773551 + 0.997004i \(0.475352\pi\)
\(90\) 0 0
\(91\) 2.35304 + 11.8295i 0.246666 + 1.24007i
\(92\) 0 0
\(93\) 2.52837 + 3.78397i 0.262180 + 0.392380i
\(94\) 0 0
\(95\) 7.97117i 0.817825i
\(96\) 0 0
\(97\) 11.0691i 1.12389i 0.827173 + 0.561947i \(0.189948\pi\)
−0.827173 + 0.561947i \(0.810052\pi\)
\(98\) 0 0
\(99\) −0.860463 1.28777i −0.0864798 0.129426i
\(100\) 0 0
\(101\) 2.42413 + 12.1869i 0.241210 + 1.21264i 0.891522 + 0.452977i \(0.149638\pi\)
−0.650313 + 0.759667i \(0.725362\pi\)
\(102\) 0 0
\(103\) −7.43691 + 3.08047i −0.732781 + 0.303528i −0.717694 0.696358i \(-0.754802\pi\)
−0.0150867 + 0.999886i \(0.504802\pi\)
\(104\) 0 0
\(105\) −14.0175 5.80623i −1.36797 0.566630i
\(106\) 0 0
\(107\) −5.45543 3.64520i −0.527396 0.352395i 0.263192 0.964744i \(-0.415225\pi\)
−0.790588 + 0.612349i \(0.790225\pi\)
\(108\) 0 0
\(109\) 2.09534 10.5340i 0.200697 1.00897i −0.740743 0.671789i \(-0.765526\pi\)
0.941439 0.337182i \(-0.109474\pi\)
\(110\) 0 0
\(111\) −6.88317 6.88317i −0.653321 0.653321i
\(112\) 0 0
\(113\) 10.9546 10.9546i 1.03052 1.03052i 0.0310050 0.999519i \(-0.490129\pi\)
0.999519 0.0310050i \(-0.00987077\pi\)
\(114\) 0 0
\(115\) 17.2444 + 3.43013i 1.60805 + 0.319861i
\(116\) 0 0
\(117\) −1.28209 + 1.91879i −0.118529 + 0.177392i
\(118\) 0 0
\(119\) −1.63178 + 3.93945i −0.149585 + 0.361129i
\(120\) 0 0
\(121\) 0.714404 + 1.72472i 0.0649458 + 0.156793i
\(122\) 0 0
\(123\) −5.36523 + 1.06721i −0.483766 + 0.0962271i
\(124\) 0 0
\(125\) −8.65665 + 5.78419i −0.774274 + 0.517353i
\(126\) 0 0
\(127\) 13.2036 1.17163 0.585815 0.810445i \(-0.300775\pi\)
0.585815 + 0.810445i \(0.300775\pi\)
\(128\) 0 0
\(129\) 4.10385 0.361324
\(130\) 0 0
\(131\) 17.0393 11.3853i 1.48873 0.994739i 0.496814 0.867857i \(-0.334503\pi\)
0.991918 0.126881i \(-0.0404967\pi\)
\(132\) 0 0
\(133\) −5.83065 + 1.15979i −0.505581 + 0.100566i
\(134\) 0 0
\(135\) −7.61400 18.3818i −0.655309 1.58205i
\(136\) 0 0
\(137\) 2.61344 6.30941i 0.223281 0.539049i −0.772050 0.635561i \(-0.780769\pi\)
0.995332 + 0.0965122i \(0.0307687\pi\)
\(138\) 0 0
\(139\) 9.07641 13.5838i 0.769851 1.15216i −0.214634 0.976695i \(-0.568856\pi\)
0.984485 0.175469i \(-0.0561443\pi\)
\(140\) 0 0
\(141\) −5.20015 1.03437i −0.437932 0.0871100i
\(142\) 0 0
\(143\) −9.62262 + 9.62262i −0.804684 + 0.804684i
\(144\) 0 0
\(145\) −15.6995 15.6995i −1.30377 1.30377i
\(146\) 0 0
\(147\) −0.0536992 + 0.269964i −0.00442903 + 0.0222663i
\(148\) 0 0
\(149\) 1.58289 + 1.05765i 0.129675 + 0.0866461i 0.618716 0.785615i \(-0.287653\pi\)
−0.489041 + 0.872261i \(0.662653\pi\)
\(150\) 0 0
\(151\) −12.8207 5.31052i −1.04334 0.432164i −0.205828 0.978588i \(-0.565989\pi\)
−0.837509 + 0.546424i \(0.815989\pi\)
\(152\) 0 0
\(153\) −0.753741 + 0.312210i −0.0609364 + 0.0252407i
\(154\) 0 0
\(155\) −2.02176 10.1641i −0.162392 0.816399i
\(156\) 0 0
\(157\) −1.92287 2.87778i −0.153462 0.229672i 0.746770 0.665082i \(-0.231603\pi\)
−0.900232 + 0.435410i \(0.856603\pi\)
\(158\) 0 0
\(159\) 9.08580i 0.720551i
\(160\) 0 0
\(161\) 13.1128i 1.03343i
\(162\) 0 0
\(163\) −1.50597 2.25384i −0.117956 0.176534i 0.767793 0.640698i \(-0.221355\pi\)
−0.885749 + 0.464164i \(0.846355\pi\)
\(164\) 0 0
\(165\) −3.33968 16.7897i −0.259994 1.30708i
\(166\) 0 0
\(167\) 1.45504 0.602695i 0.112594 0.0466380i −0.325675 0.945482i \(-0.605592\pi\)
0.438269 + 0.898844i \(0.355592\pi\)
\(168\) 0 0
\(169\) 6.72270 + 2.78464i 0.517131 + 0.214203i
\(170\) 0 0
\(171\) −0.945748 0.631929i −0.0723232 0.0483248i
\(172\) 0 0
\(173\) 1.03690 5.21283i 0.0788338 0.396324i −0.921141 0.389229i \(-0.872742\pi\)
0.999975 0.00709516i \(-0.00225848\pi\)
\(174\) 0 0
\(175\) 14.9605 + 14.9605i 1.13091 + 1.13091i
\(176\) 0 0
\(177\) −1.15187 + 1.15187i −0.0865799 + 0.0865799i
\(178\) 0 0
\(179\) −11.4548 2.27850i −0.856171 0.170303i −0.252559 0.967581i \(-0.581272\pi\)
−0.603612 + 0.797279i \(0.706272\pi\)
\(180\) 0 0
\(181\) 2.32452 3.47889i 0.172780 0.258584i −0.734966 0.678104i \(-0.762802\pi\)
0.907746 + 0.419520i \(0.137802\pi\)
\(182\) 0 0
\(183\) 1.62248 3.91701i 0.119937 0.289554i
\(184\) 0 0
\(185\) 8.48274 + 20.4791i 0.623663 + 1.50566i
\(186\) 0 0
\(187\) −4.71856 + 0.938579i −0.345055 + 0.0686357i
\(188\) 0 0
\(189\) −12.3379 + 8.24390i −0.897448 + 0.599656i
\(190\) 0 0
\(191\) 17.8728 1.29323 0.646617 0.762815i \(-0.276183\pi\)
0.646617 + 0.762815i \(0.276183\pi\)
\(192\) 0 0
\(193\) 20.0233 1.44131 0.720654 0.693295i \(-0.243842\pi\)
0.720654 + 0.693295i \(0.243842\pi\)
\(194\) 0 0
\(195\) −21.2081 + 14.1708i −1.51875 + 1.01479i
\(196\) 0 0
\(197\) 16.3511 3.25244i 1.16497 0.231727i 0.425527 0.904946i \(-0.360089\pi\)
0.739444 + 0.673219i \(0.235089\pi\)
\(198\) 0 0
\(199\) 5.64872 + 13.6372i 0.400427 + 0.966716i 0.987562 + 0.157227i \(0.0502555\pi\)
−0.587136 + 0.809489i \(0.699744\pi\)
\(200\) 0 0
\(201\) −8.79979 + 21.2446i −0.620689 + 1.49848i
\(202\) 0 0
\(203\) −9.19941 + 13.7679i −0.645672 + 0.966317i
\(204\) 0 0
\(205\) 12.2175 + 2.43021i 0.853305 + 0.169733i
\(206\) 0 0
\(207\) 1.77405 1.77405i 0.123305 0.123305i
\(208\) 0 0
\(209\) −4.74288 4.74288i −0.328072 0.328072i
\(210\) 0 0
\(211\) −2.18718 + 10.9957i −0.150572 + 0.756975i 0.829527 + 0.558466i \(0.188610\pi\)
−0.980099 + 0.198509i \(0.936390\pi\)
\(212\) 0 0
\(213\) 15.8872 + 10.6155i 1.08858 + 0.727363i
\(214\) 0 0
\(215\) −8.63376 3.57622i −0.588817 0.243896i
\(216\) 0 0
\(217\) −7.14053 + 2.95771i −0.484731 + 0.200782i
\(218\) 0 0
\(219\) −3.21604 16.1681i −0.217320 1.09254i
\(220\) 0 0
\(221\) 3.98255 + 5.96030i 0.267895 + 0.400933i
\(222\) 0 0
\(223\) 7.50358i 0.502477i 0.967925 + 0.251239i \(0.0808379\pi\)
−0.967925 + 0.251239i \(0.919162\pi\)
\(224\) 0 0
\(225\) 4.04806i 0.269871i
\(226\) 0 0
\(227\) 14.7739 + 22.1107i 0.980580 + 1.46754i 0.881343 + 0.472478i \(0.156640\pi\)
0.0992374 + 0.995064i \(0.468360\pi\)
\(228\) 0 0
\(229\) 2.93523 + 14.7564i 0.193966 + 0.975131i 0.947994 + 0.318289i \(0.103108\pi\)
−0.754028 + 0.656842i \(0.771892\pi\)
\(230\) 0 0
\(231\) −11.7952 + 4.88573i −0.776067 + 0.321458i
\(232\) 0 0
\(233\) 17.7995 + 7.37280i 1.16609 + 0.483008i 0.879897 0.475165i \(-0.157612\pi\)
0.286189 + 0.958173i \(0.407612\pi\)
\(234\) 0 0
\(235\) 10.0388 + 6.70771i 0.654859 + 0.437563i
\(236\) 0 0
\(237\) 0.459937 2.31226i 0.0298761 0.150198i
\(238\) 0 0
\(239\) −6.71028 6.71028i −0.434052 0.434052i 0.455952 0.890004i \(-0.349299\pi\)
−0.890004 + 0.455952i \(0.849299\pi\)
\(240\) 0 0
\(241\) 2.62074 2.62074i 0.168816 0.168816i −0.617643 0.786459i \(-0.711912\pi\)
0.786459 + 0.617643i \(0.211912\pi\)
\(242\) 0 0
\(243\) −5.16281 1.02695i −0.331194 0.0658787i
\(244\) 0 0
\(245\) 0.348228 0.521160i 0.0222475 0.0332957i
\(246\) 0 0
\(247\) −3.82458 + 9.23335i −0.243352 + 0.587504i
\(248\) 0 0
\(249\) −5.17922 12.5037i −0.328220 0.792393i
\(250\) 0 0
\(251\) −3.80701 + 0.757262i −0.240296 + 0.0477979i −0.313769 0.949499i \(-0.601592\pi\)
0.0734728 + 0.997297i \(0.476592\pi\)
\(252\) 0 0
\(253\) 12.3014 8.21956i 0.773385 0.516759i
\(254\) 0 0
\(255\) −9.01743 −0.564693
\(256\) 0 0
\(257\) −4.79248 −0.298947 −0.149473 0.988766i \(-0.547758\pi\)
−0.149473 + 0.988766i \(0.547758\pi\)
\(258\) 0 0
\(259\) 13.7456 9.18451i 0.854110 0.570698i
\(260\) 0 0
\(261\) −3.10729 + 0.618078i −0.192336 + 0.0382581i
\(262\) 0 0
\(263\) 5.53072 + 13.3523i 0.341039 + 0.823340i 0.997611 + 0.0690772i \(0.0220055\pi\)
−0.656573 + 0.754263i \(0.727995\pi\)
\(264\) 0 0
\(265\) −7.91764 + 19.1149i −0.486377 + 1.17422i
\(266\) 0 0
\(267\) −5.12633 + 7.67209i −0.313726 + 0.469524i
\(268\) 0 0
\(269\) −12.3558 2.45771i −0.753344 0.149849i −0.196543 0.980495i \(-0.562971\pi\)
−0.556801 + 0.830646i \(0.687971\pi\)
\(270\) 0 0
\(271\) 1.16587 1.16587i 0.0708213 0.0708213i −0.670809 0.741630i \(-0.734053\pi\)
0.741630 + 0.670809i \(0.234053\pi\)
\(272\) 0 0
\(273\) 13.4512 + 13.4512i 0.814105 + 0.814105i
\(274\) 0 0
\(275\) −4.65705 + 23.4126i −0.280831 + 1.41183i
\(276\) 0 0
\(277\) 8.28458 + 5.53558i 0.497772 + 0.332601i 0.778983 0.627045i \(-0.215736\pi\)
−0.281211 + 0.959646i \(0.590736\pi\)
\(278\) 0 0
\(279\) −1.36621 0.565902i −0.0817927 0.0338797i
\(280\) 0 0
\(281\) −1.78965 + 0.741299i −0.106762 + 0.0442222i −0.435425 0.900225i \(-0.643402\pi\)
0.328663 + 0.944447i \(0.393402\pi\)
\(282\) 0 0
\(283\) 2.18457 + 10.9826i 0.129859 + 0.652845i 0.989801 + 0.142454i \(0.0454993\pi\)
−0.859943 + 0.510391i \(0.829501\pi\)
\(284\) 0 0
\(285\) −6.98464 10.4532i −0.413734 0.619197i
\(286\) 0 0
\(287\) 9.29026i 0.548387i
\(288\) 0 0
\(289\) 14.4658i 0.850927i
\(290\) 0 0
\(291\) 9.69913 + 14.5158i 0.568573 + 0.850930i
\(292\) 0 0
\(293\) 0.0277262 + 0.139389i 0.00161978 + 0.00814318i 0.981587 0.191017i \(-0.0611786\pi\)
−0.979967 + 0.199160i \(0.936179\pi\)
\(294\) 0 0
\(295\) 3.42710 1.41955i 0.199534 0.0826495i
\(296\) 0 0
\(297\) −15.4676 6.40690i −0.897523 0.371766i
\(298\) 0 0
\(299\) −18.3292 12.2472i −1.06000 0.708271i
\(300\) 0 0
\(301\) −1.35969 + 6.83564i −0.0783714 + 0.394000i
\(302\) 0 0
\(303\) 13.8576 + 13.8576i 0.796097 + 0.796097i
\(304\) 0 0
\(305\) −6.82680 + 6.82680i −0.390901 + 0.390901i
\(306\) 0 0
\(307\) −1.97782 0.393412i −0.112880 0.0224532i 0.138327 0.990387i \(-0.455828\pi\)
−0.251207 + 0.967933i \(0.580828\pi\)
\(308\) 0 0
\(309\) −7.05341 + 10.5562i −0.401254 + 0.600520i
\(310\) 0 0
\(311\) −5.97814 + 14.4325i −0.338989 + 0.818392i 0.658824 + 0.752297i \(0.271054\pi\)
−0.997813 + 0.0660951i \(0.978946\pi\)
\(312\) 0 0
\(313\) −12.3839 29.8974i −0.699981 1.68990i −0.723635 0.690183i \(-0.757530\pi\)
0.0236544 0.999720i \(-0.492470\pi\)
\(314\) 0 0
\(315\) 4.83536 0.961813i 0.272442 0.0541920i
\(316\) 0 0
\(317\) 2.23554 1.49374i 0.125560 0.0838968i −0.491204 0.871045i \(-0.663443\pi\)
0.616765 + 0.787148i \(0.288443\pi\)
\(318\) 0 0
\(319\) −18.6825 −1.04602
\(320\) 0 0
\(321\) −10.3482 −0.577581
\(322\) 0 0
\(323\) −2.93777 + 1.96295i −0.163462 + 0.109222i
\(324\) 0 0
\(325\) 34.8848 6.93902i 1.93506 0.384907i
\(326\) 0 0
\(327\) −6.48247 15.6501i −0.358481 0.865450i
\(328\) 0 0
\(329\) 3.44584 8.31900i 0.189975 0.458641i
\(330\) 0 0
\(331\) −0.656286 + 0.982201i −0.0360727 + 0.0539866i −0.849068 0.528284i \(-0.822836\pi\)
0.812995 + 0.582271i \(0.197836\pi\)
\(332\) 0 0
\(333\) 3.10225 + 0.617076i 0.170002 + 0.0338156i
\(334\) 0 0
\(335\) 37.0263 37.0263i 2.02296 2.02296i
\(336\) 0 0
\(337\) 23.1614 + 23.1614i 1.26168 + 1.26168i 0.950278 + 0.311402i \(0.100798\pi\)
0.311402 + 0.950278i \(0.399202\pi\)
\(338\) 0 0
\(339\) 4.76684 23.9645i 0.258899 1.30158i
\(340\) 0 0
\(341\) −7.25063 4.84472i −0.392644 0.262356i
\(342\) 0 0
\(343\) 16.8906 + 6.99631i 0.912006 + 0.377765i
\(344\) 0 0
\(345\) 25.6196 10.6120i 1.37931 0.571330i
\(346\) 0 0
\(347\) −2.47211 12.4281i −0.132710 0.667176i −0.988666 0.150129i \(-0.952031\pi\)
0.855957 0.517047i \(-0.172969\pi\)
\(348\) 0 0
\(349\) −14.6597 21.9398i −0.784716 1.17441i −0.981027 0.193869i \(-0.937896\pi\)
0.196312 0.980542i \(-0.437104\pi\)
\(350\) 0 0
\(351\) 24.9457i 1.33150i
\(352\) 0 0
\(353\) 7.76818i 0.413458i 0.978398 + 0.206729i \(0.0662819\pi\)
−0.978398 + 0.206729i \(0.933718\pi\)
\(354\) 0 0
\(355\) −24.1732 36.1778i −1.28298 1.92012i
\(356\) 0 0
\(357\) 1.31202 + 6.59595i 0.0694393 + 0.349095i
\(358\) 0 0
\(359\) −5.48329 + 2.27125i −0.289397 + 0.119872i −0.522659 0.852542i \(-0.675060\pi\)
0.233262 + 0.972414i \(0.425060\pi\)
\(360\) 0 0
\(361\) 13.0027 + 5.38589i 0.684352 + 0.283468i
\(362\) 0 0
\(363\) 2.44812 + 1.63578i 0.128493 + 0.0858564i
\(364\) 0 0
\(365\) −7.32342 + 36.8173i −0.383326 + 1.92711i
\(366\) 0 0
\(367\) −24.0480 24.0480i −1.25530 1.25530i −0.953313 0.301985i \(-0.902351\pi\)
−0.301985 0.953313i \(-0.597649\pi\)
\(368\) 0 0
\(369\) 1.25690 1.25690i 0.0654314 0.0654314i
\(370\) 0 0
\(371\) 15.1339 + 3.01032i 0.785713 + 0.156288i
\(372\) 0 0
\(373\) −0.521412 + 0.780348i −0.0269977 + 0.0404049i −0.844723 0.535204i \(-0.820235\pi\)
0.817725 + 0.575609i \(0.195235\pi\)
\(374\) 0 0
\(375\) −6.28385 + 15.1706i −0.324497 + 0.783404i
\(376\) 0 0
\(377\) 10.6528 + 25.7180i 0.548645 + 1.32455i
\(378\) 0 0
\(379\) 25.2135 5.01528i 1.29513 0.257618i 0.501044 0.865422i \(-0.332950\pi\)
0.794087 + 0.607804i \(0.207950\pi\)
\(380\) 0 0
\(381\) 17.3149 11.5695i 0.887072 0.592722i
\(382\) 0 0
\(383\) −36.1379 −1.84656 −0.923279 0.384130i \(-0.874501\pi\)
−0.923279 + 0.384130i \(0.874501\pi\)
\(384\) 0 0
\(385\) 29.0725 1.48167
\(386\) 0 0
\(387\) −1.10876 + 0.740850i −0.0563615 + 0.0376595i
\(388\) 0 0
\(389\) −17.2404 + 3.42934i −0.874125 + 0.173874i −0.611711 0.791081i \(-0.709518\pi\)
−0.262414 + 0.964955i \(0.584518\pi\)
\(390\) 0 0
\(391\) −2.98238 7.20010i −0.150825 0.364125i
\(392\) 0 0
\(393\) 12.3688 29.8610i 0.623924 1.50629i
\(394\) 0 0
\(395\) −2.98260 + 4.46378i −0.150071 + 0.224597i
\(396\) 0 0
\(397\) −6.70636 1.33398i −0.336583 0.0669505i 0.0239055 0.999714i \(-0.492390\pi\)
−0.360488 + 0.932764i \(0.617390\pi\)
\(398\) 0 0
\(399\) −6.62996 + 6.62996i −0.331913 + 0.331913i
\(400\) 0 0
\(401\) −14.0108 14.0108i −0.699666 0.699666i 0.264672 0.964338i \(-0.414736\pi\)
−0.964338 + 0.264672i \(0.914736\pi\)
\(402\) 0 0
\(403\) −2.53485 + 12.7435i −0.126270 + 0.634801i
\(404\) 0 0
\(405\) −21.5005 14.3662i −1.06837 0.713861i
\(406\) 0 0
\(407\) 17.2324 + 7.13791i 0.854180 + 0.353813i
\(408\) 0 0
\(409\) −20.5325 + 8.50486i −1.01527 + 0.420538i −0.827374 0.561651i \(-0.810166\pi\)
−0.187895 + 0.982189i \(0.560166\pi\)
\(410\) 0 0
\(411\) −2.10132 10.5640i −0.103650 0.521086i
\(412\) 0 0
\(413\) −1.53699 2.30027i −0.0756304 0.113189i
\(414\) 0 0
\(415\) 30.8189i 1.51284i
\(416\) 0 0
\(417\) 25.7667i 1.26180i
\(418\) 0 0
\(419\) 12.2124 + 18.2772i 0.596615 + 0.892898i 0.999753 0.0222415i \(-0.00708026\pi\)
−0.403137 + 0.915140i \(0.632080\pi\)
\(420\) 0 0
\(421\) 2.62271 + 13.1853i 0.127823 + 0.642610i 0.990574 + 0.136980i \(0.0437397\pi\)
−0.862751 + 0.505630i \(0.831260\pi\)
\(422\) 0 0
\(423\) 1.59169 0.659298i 0.0773904 0.0320562i
\(424\) 0 0
\(425\) 11.6173 + 4.81203i 0.563521 + 0.233418i
\(426\) 0 0
\(427\) 5.98686 + 4.00029i 0.289725 + 0.193588i
\(428\) 0 0
\(429\) −4.18723 + 21.0506i −0.202161 + 1.01633i
\(430\) 0 0
\(431\) 11.2500 + 11.2500i 0.541893 + 0.541893i 0.924084 0.382190i \(-0.124830\pi\)
−0.382190 + 0.924084i \(0.624830\pi\)
\(432\) 0 0
\(433\) −17.8833 + 17.8833i −0.859418 + 0.859418i −0.991269 0.131851i \(-0.957908\pi\)
0.131851 + 0.991269i \(0.457908\pi\)
\(434\) 0 0
\(435\) −34.3445 6.83154i −1.64669 0.327547i
\(436\) 0 0
\(437\) 6.03648 9.03424i 0.288764 0.432166i
\(438\) 0 0
\(439\) 7.70310 18.5969i 0.367649 0.887583i −0.626485 0.779433i \(-0.715507\pi\)
0.994135 0.108150i \(-0.0344928\pi\)
\(440\) 0 0
\(441\) −0.0342272 0.0826318i −0.00162987 0.00393485i
\(442\) 0 0
\(443\) 23.1776 4.61031i 1.10120 0.219043i 0.389153 0.921173i \(-0.372768\pi\)
0.712048 + 0.702130i \(0.247768\pi\)
\(444\) 0 0
\(445\) 17.4706 11.6735i 0.828184 0.553375i
\(446\) 0 0
\(447\) 3.00252 0.142014
\(448\) 0 0
\(449\) −25.3135 −1.19462 −0.597310 0.802010i \(-0.703764\pi\)
−0.597310 + 0.802010i \(0.703764\pi\)
\(450\) 0 0
\(451\) 8.71543 5.82346i 0.410394 0.274216i
\(452\) 0 0
\(453\) −21.4661 + 4.26988i −1.00857 + 0.200617i
\(454\) 0 0
\(455\) −16.5771 40.0207i −0.777148 1.87620i
\(456\) 0 0
\(457\) −1.63458 + 3.94622i −0.0764624 + 0.184596i −0.957489 0.288471i \(-0.906853\pi\)
0.881026 + 0.473067i \(0.156853\pi\)
\(458\) 0 0
\(459\) −4.89960 + 7.33277i −0.228694 + 0.342264i
\(460\) 0 0
\(461\) 5.97319 + 1.18814i 0.278199 + 0.0553372i 0.332218 0.943203i \(-0.392203\pi\)
−0.0540188 + 0.998540i \(0.517203\pi\)
\(462\) 0 0
\(463\) −4.21551 + 4.21551i −0.195912 + 0.195912i −0.798245 0.602333i \(-0.794238\pi\)
0.602333 + 0.798245i \(0.294238\pi\)
\(464\) 0 0
\(465\) −11.5575 11.5575i −0.535964 0.535964i
\(466\) 0 0
\(467\) 6.66305 33.4974i 0.308329 1.55007i −0.446882 0.894593i \(-0.647466\pi\)
0.755211 0.655482i \(-0.227534\pi\)
\(468\) 0 0
\(469\) −32.4708 21.6963i −1.49936 1.00184i
\(470\) 0 0
\(471\) −5.04324 2.08898i −0.232380 0.0962551i
\(472\) 0 0
\(473\) −7.26499 + 3.00926i −0.334045 + 0.138366i
\(474\) 0 0
\(475\) 3.42016 + 17.1943i 0.156928 + 0.788929i
\(476\) 0 0
\(477\) 1.64022 + 2.45476i 0.0751005 + 0.112396i
\(478\) 0 0
\(479\) 19.6175i 0.896347i −0.893947 0.448174i \(-0.852075\pi\)
0.893947 0.448174i \(-0.147925\pi\)
\(480\) 0 0
\(481\) 27.7919i 1.26720i
\(482\) 0 0
\(483\) −11.4899 17.1959i −0.522809 0.782439i
\(484\) 0 0
\(485\) −7.75573 38.9907i −0.352170 1.77048i
\(486\) 0 0
\(487\) 39.3985 16.3194i 1.78532 0.739502i 0.794013 0.607901i \(-0.207988\pi\)
0.991303 0.131601i \(-0.0420119\pi\)
\(488\) 0 0
\(489\) −3.94980 1.63606i −0.178616 0.0739852i
\(490\) 0 0
\(491\) −3.04811 2.03668i −0.137559 0.0919141i 0.484887 0.874577i \(-0.338861\pi\)
−0.622446 + 0.782663i \(0.713861\pi\)
\(492\) 0 0
\(493\) −1.91993 + 9.65213i −0.0864692 + 0.434710i
\(494\) 0 0
\(495\) 3.93327 + 3.93327i 0.176788 + 0.176788i
\(496\) 0 0
\(497\) −22.9457 + 22.9457i −1.02925 + 1.02925i
\(498\) 0 0
\(499\) −0.0620242 0.0123374i −0.00277658 0.000552297i 0.193702 0.981060i \(-0.437951\pi\)
−0.196478 + 0.980508i \(0.562951\pi\)
\(500\) 0 0
\(501\) 1.38000 2.06532i 0.0616540 0.0922717i
\(502\) 0 0
\(503\) 9.58180 23.1325i 0.427231 1.03143i −0.552930 0.833228i \(-0.686490\pi\)
0.980162 0.198200i \(-0.0635096\pi\)
\(504\) 0 0
\(505\) −17.0779 41.2298i −0.759958 1.83470i
\(506\) 0 0
\(507\) 11.2560 2.23896i 0.499898 0.0994359i
\(508\) 0 0
\(509\) −28.5244 + 19.0594i −1.26432 + 0.844792i −0.993048 0.117710i \(-0.962445\pi\)
−0.271273 + 0.962503i \(0.587445\pi\)
\(510\) 0 0
\(511\) 27.9962 1.23848
\(512\) 0 0
\(513\) −12.2954 −0.542857
\(514\) 0 0
\(515\) 24.0381 16.0617i 1.05924 0.707764i
\(516\) 0 0
\(517\) 9.96424 1.98201i 0.438227 0.0871687i
\(518\) 0 0
\(519\) −3.20791 7.74457i −0.140812 0.339949i
\(520\) 0 0
\(521\) −10.5629 + 25.5011i −0.462769 + 1.11722i 0.504487 + 0.863420i \(0.331682\pi\)
−0.967256 + 0.253804i \(0.918318\pi\)
\(522\) 0 0
\(523\) −8.36875 + 12.5247i −0.365940 + 0.547668i −0.968054 0.250742i \(-0.919325\pi\)
0.602114 + 0.798410i \(0.294325\pi\)
\(524\) 0 0
\(525\) 32.7279 + 6.50998i 1.42836 + 0.284119i
\(526\) 0 0
\(527\) −3.24809 + 3.24809i −0.141489 + 0.141489i
\(528\) 0 0
\(529\) 0.683141 + 0.683141i 0.0297018 + 0.0297018i
\(530\) 0 0
\(531\) 0.103265 0.519150i 0.00448133 0.0225292i
\(532\) 0 0
\(533\) −12.9860 8.67697i −0.562486 0.375841i
\(534\) 0 0
\(535\) 21.7708 + 9.01774i 0.941232 + 0.389871i
\(536\) 0 0
\(537\) −17.0181 + 7.04913i −0.734385 + 0.304192i
\(538\) 0 0
\(539\) −0.102895 0.517290i −0.00443202 0.0222813i
\(540\) 0 0
\(541\) 4.97281 + 7.44233i 0.213798 + 0.319971i 0.922832 0.385203i \(-0.125869\pi\)
−0.709034 + 0.705174i \(0.750869\pi\)
\(542\) 0 0
\(543\) 6.59898i 0.283189i
\(544\) 0 0
\(545\) 38.5739i 1.65232i
\(546\) 0 0
\(547\) 17.1415 + 25.6541i 0.732920 + 1.09689i 0.991399 + 0.130875i \(0.0417786\pi\)
−0.258479 + 0.966017i \(0.583221\pi\)
\(548\) 0 0
\(549\) 0.268766 + 1.35118i 0.0114707 + 0.0576669i
\(550\) 0 0
\(551\) −12.6761 + 5.25062i −0.540021 + 0.223684i
\(552\) 0 0
\(553\) 3.69907 + 1.53220i 0.157300 + 0.0651559i
\(554\) 0 0
\(555\) 29.0687 + 19.4231i 1.23390 + 0.824464i
\(556\) 0 0
\(557\) 6.97599 35.0707i 0.295582 1.48599i −0.492440 0.870346i \(-0.663895\pi\)
0.788022 0.615647i \(-0.211105\pi\)
\(558\) 0 0
\(559\) 8.28498 + 8.28498i 0.350417 + 0.350417i
\(560\) 0 0
\(561\) −5.36541 + 5.36541i −0.226528 + 0.226528i
\(562\) 0 0
\(563\) −21.7512 4.32658i −0.916704 0.182344i −0.285876 0.958267i \(-0.592285\pi\)
−0.630828 + 0.775923i \(0.717285\pi\)
\(564\) 0 0
\(565\) −30.9120 + 46.2631i −1.30048 + 1.94630i
\(566\) 0 0
\(567\) −7.38010 + 17.8171i −0.309935 + 0.748250i
\(568\) 0 0
\(569\) −13.8493 33.4353i −0.580594 1.40168i −0.892275 0.451492i \(-0.850892\pi\)
0.311681 0.950187i \(-0.399108\pi\)
\(570\) 0 0
\(571\) −40.7190 + 8.09951i −1.70404 + 0.338954i −0.948650 0.316326i \(-0.897551\pi\)
−0.755386 + 0.655280i \(0.772551\pi\)
\(572\) 0 0
\(573\) 23.4381 15.6608i 0.979141 0.654241i
\(574\) 0 0
\(575\) −38.6690 −1.61261
\(576\) 0 0
\(577\) 11.4102 0.475014 0.237507 0.971386i \(-0.423670\pi\)
0.237507 + 0.971386i \(0.423670\pi\)
\(578\) 0 0
\(579\) 26.2582 17.5451i 1.09125 0.729151i
\(580\) 0 0
\(581\) 22.5430 4.48409i 0.935243 0.186031i
\(582\) 0 0
\(583\) 6.66241 + 16.0845i 0.275929 + 0.666151i
\(584\) 0 0
\(585\) 3.17173 7.65722i 0.131135 0.316587i
\(586\) 0 0
\(587\) −12.5001 + 18.7077i −0.515934 + 0.772150i −0.994369 0.105973i \(-0.966204\pi\)
0.478435 + 0.878123i \(0.341204\pi\)
\(588\) 0 0
\(589\) −6.28115 1.24940i −0.258810 0.0514806i
\(590\) 0 0
\(591\) 18.5927 18.5927i 0.764800 0.764800i
\(592\) 0 0
\(593\) −1.24913 1.24913i −0.0512956 0.0512956i 0.680994 0.732289i \(-0.261548\pi\)
−0.732289 + 0.680994i \(0.761548\pi\)
\(594\) 0 0
\(595\) 2.98767 15.0200i 0.122482 0.615761i
\(596\) 0 0
\(597\) 19.3570 + 12.9340i 0.792231 + 0.529352i
\(598\) 0 0
\(599\) 2.75750 + 1.14220i 0.112669 + 0.0466689i 0.438306 0.898826i \(-0.355579\pi\)
−0.325637 + 0.945495i \(0.605579\pi\)
\(600\) 0 0
\(601\) 21.5982 8.94628i 0.881010 0.364926i 0.104121 0.994565i \(-0.466797\pi\)
0.776888 + 0.629638i \(0.216797\pi\)
\(602\) 0 0
\(603\) −1.45770 7.32835i −0.0593621 0.298434i
\(604\) 0 0
\(605\) −3.72494 5.57476i −0.151440 0.226646i
\(606\) 0 0
\(607\) 24.7172i 1.00324i −0.865088 0.501620i \(-0.832738\pi\)
0.865088 0.501620i \(-0.167262\pi\)
\(608\) 0 0
\(609\) 26.1158i 1.05827i
\(610\) 0 0
\(611\) −8.41000 12.5865i −0.340232 0.509193i
\(612\) 0 0
\(613\) 1.44115 + 7.24514i 0.0582074 + 0.292629i 0.998914 0.0465930i \(-0.0148364\pi\)
−0.940707 + 0.339222i \(0.889836\pi\)
\(614\) 0 0
\(615\) 18.1512 7.51847i 0.731927 0.303174i
\(616\) 0 0
\(617\) −3.89273 1.61242i −0.156715 0.0649136i 0.302947 0.953007i \(-0.402030\pi\)
−0.459662 + 0.888094i \(0.652030\pi\)
\(618\) 0 0
\(619\) −6.36631 4.25383i −0.255884 0.170976i 0.421012 0.907055i \(-0.361675\pi\)
−0.676895 + 0.736079i \(0.736675\pi\)
\(620\) 0 0
\(621\) 5.29093 26.5993i 0.212318 1.06739i
\(622\) 0 0
\(623\) −11.0807 11.0807i −0.443938 0.443938i
\(624\) 0 0
\(625\) −1.48653 + 1.48653i −0.0594614 + 0.0594614i
\(626\) 0 0
\(627\) −10.3756 2.06384i −0.414362 0.0824218i
\(628\) 0 0
\(629\) 5.45863 8.16942i 0.217650 0.325736i
\(630\) 0 0
\(631\) 10.3902 25.0842i 0.413628 0.998587i −0.570527 0.821279i \(-0.693261\pi\)
0.984155 0.177308i \(-0.0567390\pi\)
\(632\) 0 0
\(633\) 6.76661 + 16.3360i 0.268949 + 0.649300i
\(634\) 0 0
\(635\) −46.5095 + 9.25132i −1.84567 + 0.367127i
\(636\) 0 0
\(637\) −0.653421 + 0.436602i −0.0258895 + 0.0172988i
\(638\) 0 0
\(639\) −6.20872 −0.245613
\(640\) 0 0
\(641\) 48.6538 1.92171 0.960855 0.277053i \(-0.0893579\pi\)
0.960855 + 0.277053i \(0.0893579\pi\)
\(642\) 0 0
\(643\) −24.2613 + 16.2109i −0.956772 + 0.639295i −0.932791 0.360418i \(-0.882634\pi\)
−0.0239813 + 0.999712i \(0.507634\pi\)
\(644\) 0 0
\(645\) −14.4558 + 2.87543i −0.569195 + 0.113220i
\(646\) 0 0
\(647\) 5.55831 + 13.4190i 0.218520 + 0.527553i 0.994684 0.102978i \(-0.0328371\pi\)
−0.776164 + 0.630531i \(0.782837\pi\)
\(648\) 0 0
\(649\) 1.19450 2.88378i 0.0468883 0.113198i
\(650\) 0 0
\(651\) −6.77231 + 10.1355i −0.265428 + 0.397241i
\(652\) 0 0
\(653\) 32.4067 + 6.44610i 1.26817 + 0.252255i 0.782922 0.622120i \(-0.213728\pi\)
0.485251 + 0.874375i \(0.338728\pi\)
\(654\) 0 0
\(655\) −52.0435 + 52.0435i −2.03351 + 2.03351i
\(656\) 0 0
\(657\) 3.78765 + 3.78765i 0.147770 + 0.147770i
\(658\) 0 0
\(659\) 0.862145 4.33430i 0.0335844 0.168840i −0.960353 0.278786i \(-0.910068\pi\)
0.993938 + 0.109946i \(0.0350679\pi\)
\(660\) 0 0
\(661\) −25.3472 16.9364i −0.985891 0.658751i −0.0455418 0.998962i \(-0.514501\pi\)
−0.940349 + 0.340211i \(0.889501\pi\)
\(662\) 0 0
\(663\) 10.4453 + 4.32658i 0.405661 + 0.168030i
\(664\) 0 0
\(665\) 19.7258 8.17068i 0.764933 0.316845i
\(666\) 0 0
\(667\) −5.90418 29.6823i −0.228611 1.14930i
\(668\) 0 0
\(669\) 6.57492 + 9.84006i 0.254201 + 0.380439i
\(670\) 0 0
\(671\) 8.12395i 0.313622i
\(672\) 0 0
\(673\) 26.5263i 1.02251i 0.859428 + 0.511257i \(0.170820\pi\)
−0.859428 + 0.511257i \(0.829180\pi\)
\(674\) 0 0
\(675\) 24.3109 + 36.3838i 0.935727 + 1.40041i
\(676\) 0 0
\(677\) −5.43408 27.3189i −0.208849 1.04995i −0.932881 0.360186i \(-0.882713\pi\)
0.724032 0.689766i \(-0.242287\pi\)
\(678\) 0 0
\(679\) −27.3920 + 11.3461i −1.05121 + 0.435424i
\(680\) 0 0
\(681\) 38.7485 + 16.0502i 1.48485 + 0.615043i
\(682\) 0 0
\(683\) 31.4771 + 21.0323i 1.20444 + 0.804779i 0.985286 0.170912i \(-0.0546713\pi\)
0.219151 + 0.975691i \(0.429671\pi\)
\(684\) 0 0
\(685\) −4.78503 + 24.0560i −0.182827 + 0.919132i
\(686\) 0 0
\(687\) 16.7793 + 16.7793i 0.640171 + 0.640171i
\(688\) 0 0
\(689\) 18.3427 18.3427i 0.698801 0.698801i
\(690\) 0 0
\(691\) −25.4829 5.06887i −0.969416 0.192829i −0.315107 0.949056i \(-0.602040\pi\)
−0.654309 + 0.756227i \(0.727040\pi\)
\(692\) 0 0
\(693\) 2.30478 3.44934i 0.0875512 0.131030i
\(694\) 0 0
\(695\) −22.4538 + 54.2084i −0.851723 + 2.05624i
\(696\) 0 0
\(697\) −2.11298 5.10119i −0.0800348 0.193221i
\(698\) 0 0
\(699\) 29.8023 5.92804i 1.12723 0.224219i
\(700\) 0 0
\(701\) −30.2742 + 20.2286i −1.14344 + 0.764023i −0.975113 0.221708i \(-0.928837\pi\)
−0.168328 + 0.985731i \(0.553837\pi\)
\(702\) 0 0
\(703\) 13.6983 0.516642
\(704\) 0 0
\(705\) 19.0422 0.717172
\(706\) 0 0
\(707\) −27.6734 + 18.4908i −1.04077 + 0.695417i
\(708\) 0 0
\(709\) 7.11157 1.41458i 0.267081 0.0531256i −0.0597332 0.998214i \(-0.519025\pi\)
0.326814 + 0.945089i \(0.394025\pi\)
\(710\) 0 0
\(711\) 0.293159 + 0.707747i 0.0109943 + 0.0265426i
\(712\) 0 0
\(713\) 5.40577 13.0507i 0.202448 0.488752i
\(714\) 0 0
\(715\) 27.1533 40.6378i 1.01548 1.51977i
\(716\) 0 0
\(717\) −14.6795 2.91994i −0.548217 0.109047i
\(718\) 0 0
\(719\) 24.9786 24.9786i 0.931543 0.931543i −0.0662593 0.997802i \(-0.521106\pi\)
0.997802 + 0.0662593i \(0.0211064\pi\)
\(720\) 0 0
\(721\) −15.2461 15.2461i −0.567795 0.567795i
\(722\) 0 0
\(723\) 1.14040 5.73317i 0.0424119 0.213219i
\(724\) 0 0
\(725\) 40.6009 + 27.1287i 1.50788 + 1.00753i
\(726\) 0 0
\(727\) −49.4936 20.5009i −1.83562 0.760337i −0.961608 0.274425i \(-0.911512\pi\)
−0.874008 0.485912i \(-0.838488\pi\)
\(728\) 0 0
\(729\) −27.6258 + 11.4430i −1.02318 + 0.423814i
\(730\) 0 0
\(731\) 0.808107 + 4.06263i 0.0298889 + 0.150262i
\(732\) 0 0
\(733\) 16.9138 + 25.3133i 0.624725 + 0.934967i 0.999968 + 0.00804070i \(0.00255946\pi\)
−0.375242 + 0.926927i \(0.622441\pi\)
\(734\) 0 0
\(735\) 0.988571i 0.0364640i
\(736\) 0 0
\(737\) 44.0616i 1.62303i
\(738\) 0 0
\(739\) −23.5325 35.2188i −0.865656 1.29555i −0.954107 0.299465i \(-0.903192\pi\)
0.0884513 0.996081i \(-0.471808\pi\)
\(740\) 0 0
\(741\) 3.07512 + 15.4597i 0.112967 + 0.567926i
\(742\) 0 0
\(743\) 14.7692 6.11761i 0.541830 0.224433i −0.0949455 0.995482i \(-0.530268\pi\)
0.636776 + 0.771049i \(0.280268\pi\)
\(744\) 0 0
\(745\) −6.31676 2.61649i −0.231428 0.0958607i
\(746\) 0 0
\(747\) 3.65655 + 2.44323i 0.133786 + 0.0893930i
\(748\) 0 0
\(749\) 3.42858 17.2367i 0.125278 0.629814i
\(750\) 0 0
\(751\) −27.8491 27.8491i −1.01623 1.01623i −0.999866 0.0163606i \(-0.994792\pi\)
−0.0163606 0.999866i \(-0.505208\pi\)
\(752\) 0 0
\(753\) −4.32890 + 4.32890i −0.157754 + 0.157754i
\(754\) 0 0
\(755\) 48.8818 + 9.72319i 1.77899 + 0.353863i
\(756\) 0 0
\(757\) −1.58238 + 2.36820i −0.0575127 + 0.0860738i −0.859111 0.511789i \(-0.828983\pi\)
0.801599 + 0.597862i \(0.203983\pi\)
\(758\) 0 0
\(759\) 8.92960 21.5580i 0.324124 0.782504i
\(760\) 0 0
\(761\) 10.1275 + 24.4500i 0.367123 + 0.886312i 0.994219 + 0.107371i \(0.0342432\pi\)
−0.627096 + 0.778942i \(0.715757\pi\)
\(762\) 0 0
\(763\) 28.2155 5.61242i 1.02147 0.203183i
\(764\) 0 0
\(765\) 2.43629 1.62788i 0.0880843 0.0588560i
\(766\) 0 0
\(767\) −4.65086 −0.167933
\(768\) 0 0
\(769\) −48.9485 −1.76513 −0.882564 0.470193i \(-0.844184\pi\)
−0.882564 + 0.470193i \(0.844184\pi\)
\(770\) 0 0
\(771\) −6.28477 + 4.19935i −0.226341 + 0.151236i
\(772\) 0 0
\(773\) 30.5401 6.07480i 1.09845 0.218495i 0.387593 0.921831i \(-0.373307\pi\)
0.710858 + 0.703335i \(0.248307\pi\)
\(774\) 0 0
\(775\) 8.72214 + 21.0571i 0.313309 + 0.756394i
\(776\) 0 0
\(777\) 9.97791 24.0888i 0.357955 0.864181i
\(778\) 0 0
\(779\) 4.27678 6.40065i 0.153232 0.229327i
\(780\) 0 0
\(781\) −35.9091 7.14276i −1.28493 0.255588i
\(782\) 0 0
\(783\) −24.2163 + 24.2163i −0.865419 + 0.865419i
\(784\) 0 0
\(785\) 8.78967 + 8.78967i 0.313717 + 0.313717i
\(786\) 0 0
\(787\) −7.20769 + 36.2355i −0.256926 + 1.29166i 0.609674 + 0.792652i \(0.291300\pi\)
−0.866600 + 0.499003i \(0.833700\pi\)
\(788\) 0 0
\(789\) 18.9527 + 12.6638i 0.674733 + 0.450842i
\(790\) 0 0
\(791\) 38.3375 + 15.8799i 1.36313 + 0.564625i
\(792\) 0 0
\(793\) 11.1833 4.63227i 0.397130 0.164497i
\(794\) 0 0
\(795\) 6.36612 + 32.0046i 0.225783 + 1.13509i
\(796\) 0 0
\(797\) 7.09159 + 10.6133i 0.251197 + 0.375943i 0.935542 0.353215i \(-0.114912\pi\)
−0.684345 + 0.729158i \(0.739912\pi\)
\(798\) 0 0
\(799\) 5.35160i 0.189326i
\(800\) 0 0
\(801\) 2.99825i 0.105938i
\(802\) 0 0
\(803\) 17.5490 + 26.2639i 0.619291 + 0.926834i
\(804\) 0 0
\(805\) 9.18770 + 46.1897i 0.323824 + 1.62797i
\(806\) 0 0
\(807\) −18.3566 + 7.60357i −0.646185 + 0.267658i
\(808\) 0 0
\(809\) −18.8371 7.80259i −0.662277 0.274324i 0.0261191 0.999659i \(-0.491685\pi\)
−0.688397 + 0.725335i \(0.741685\pi\)
\(810\) 0 0
\(811\) −30.9904 20.7071i −1.08822 0.727126i −0.124015 0.992280i \(-0.539577\pi\)
−0.964206 + 0.265154i \(0.914577\pi\)
\(812\) 0 0
\(813\) 0.507320 2.55047i 0.0177925 0.0894488i
\(814\) 0 0
\(815\) 6.88394 + 6.88394i 0.241134 + 0.241134i
\(816\) 0 0
\(817\) −4.08357 + 4.08357i −0.142866 + 0.142866i
\(818\) 0 0
\(819\) −6.06248 1.20590i −0.211840 0.0421377i
\(820\) 0 0
\(821\) 20.3593 30.4698i 0.710544 1.06340i −0.283974 0.958832i \(-0.591653\pi\)
0.994517 0.104571i \(-0.0333471\pi\)
\(822\) 0 0
\(823\) 4.39690 10.6151i 0.153266 0.370018i −0.828533 0.559941i \(-0.810824\pi\)
0.981799 + 0.189923i \(0.0608239\pi\)
\(824\) 0 0
\(825\) 14.4078 + 34.7835i 0.501615 + 1.21101i
\(826\) 0 0
\(827\) 20.2588 4.02973i 0.704467 0.140127i 0.170159 0.985417i \(-0.445572\pi\)
0.534309 + 0.845289i \(0.320572\pi\)
\(828\) 0 0
\(829\) 0.0650754 0.0434820i 0.00226016 0.00151019i −0.554440 0.832224i \(-0.687067\pi\)
0.556700 + 0.830714i \(0.312067\pi\)
\(830\) 0 0
\(831\) 15.7147 0.545138
\(832\) 0 0
\(833\) −0.277826 −0.00962612
\(834\) 0 0
\(835\) −4.70306 + 3.14248i −0.162756 + 0.108750i
\(836\) 0 0
\(837\) −15.6780 + 3.11854i −0.541910 + 0.107793i
\(838\) 0 0
\(839\) −8.26659 19.9573i −0.285394 0.689003i 0.714550 0.699585i \(-0.246632\pi\)
−0.999944 + 0.0105819i \(0.996632\pi\)
\(840\) 0 0
\(841\) −3.52696 + 8.51482i −0.121619 + 0.293615i
\(842\) 0 0
\(843\) −1.69736 + 2.54029i −0.0584604 + 0.0874921i
\(844\) 0 0
\(845\) −25.6318 5.09847i −0.881759 0.175393i
\(846\) 0 0
\(847\) −3.53578 + 3.53578i −0.121491 + 0.121491i
\(848\) 0 0
\(849\) 12.4881 + 12.4881i 0.428591 + 0.428591i
\(850\) 0 0
\(851\) −5.89461 + 29.6342i −0.202065 + 1.01585i
\(852\) 0 0
\(853\) −29.9713 20.0262i −1.02620 0.685683i −0.0759277 0.997113i \(-0.524192\pi\)
−0.950269 + 0.311431i \(0.899192\pi\)
\(854\) 0 0
\(855\) 3.77416 + 1.56331i 0.129073 + 0.0534640i
\(856\) 0 0
\(857\) 17.6508 7.31122i 0.602941 0.249747i −0.0602657 0.998182i \(-0.519195\pi\)
0.663207 + 0.748436i \(0.269195\pi\)
\(858\) 0 0
\(859\) 2.96755 + 14.9189i 0.101252 + 0.509026i 0.997813 + 0.0661060i \(0.0210575\pi\)
−0.896561 + 0.442920i \(0.853942\pi\)
\(860\) 0 0
\(861\) −8.14047 12.1831i −0.277427 0.415198i
\(862\) 0 0
\(863\) 55.1695i 1.87799i 0.343930 + 0.938995i \(0.388242\pi\)
−0.343930 + 0.938995i \(0.611758\pi\)
\(864\) 0 0
\(865\) 19.0887i 0.649034i
\(866\) 0 0
\(867\) −12.6754 18.9701i −0.430480 0.644259i
\(868\) 0 0
\(869\) 0.881306 + 4.43063i 0.0298963 + 0.150299i
\(870\) 0 0
\(871\) −60.6545 + 25.1239i −2.05520 + 0.851291i
\(872\) 0 0
\(873\) −5.24094 2.17087i −0.177379 0.0734728i
\(874\) 0 0
\(875\) −23.1871 15.4931i −0.783867 0.523763i
\(876\) 0 0
\(877\) −7.99284 + 40.1827i −0.269899 + 1.35687i 0.573332 + 0.819323i \(0.305650\pi\)
−0.843231 + 0.537551i \(0.819350\pi\)
\(878\) 0 0
\(879\) 0.158497 + 0.158497i 0.00534598 + 0.00534598i
\(880\) 0 0
\(881\) 41.4201 41.4201i 1.39548 1.39548i 0.583018 0.812459i \(-0.301872\pi\)
0.812459 0.583018i \(-0.198128\pi\)
\(882\) 0 0
\(883\) 20.2589 + 4.02975i 0.681766 + 0.135612i 0.523811 0.851834i \(-0.324510\pi\)
0.157955 + 0.987446i \(0.449510\pi\)
\(884\) 0 0
\(885\) 3.25037 4.86453i 0.109260 0.163519i
\(886\) 0 0
\(887\) −18.0495 + 43.5752i −0.606042 + 1.46311i 0.261229 + 0.965277i \(0.415872\pi\)
−0.867271 + 0.497837i \(0.834128\pi\)
\(888\) 0 0
\(889\) 13.5341 + 32.6741i 0.453918 + 1.09585i
\(890\) 0 0
\(891\) −21.3408 + 4.24495i −0.714944 + 0.142211i
\(892\) 0 0
\(893\) 6.20372 4.14519i 0.207600 0.138714i
\(894\) 0 0
\(895\) 41.9458 1.40209
\(896\) 0 0
\(897\) −34.7679 −1.16087
\(898\) 0 0
\(899\) −14.8317 + 9.91020i −0.494664 + 0.330524i
\(900\) 0 0
\(901\) 8.99454 1.78912i 0.299651 0.0596044i
\(902\) 0 0
\(903\) 4.20657 + 10.1555i 0.139986 + 0.337955i
\(904\) 0 0
\(905\) −5.75055 + 13.8831i −0.191155 + 0.461489i
\(906\) 0 0
\(907\) 14.0167 20.9775i 0.465418 0.696548i −0.522305 0.852758i \(-0.674928\pi\)
0.987724 + 0.156211i \(0.0499279\pi\)
\(908\) 0 0
\(909\) −6.24563 1.24233i −0.207155 0.0412056i
\(910\) 0 0
\(911\) 3.97097 3.97097i 0.131564 0.131564i −0.638258 0.769822i \(-0.720345\pi\)
0.769822 + 0.638258i \(0.220345\pi\)
\(912\) 0 0
\(913\) 18.3374 + 18.3374i 0.606880 + 0.606880i
\(914\) 0 0
\(915\) −2.97064 + 14.9344i −0.0982064 + 0.493717i
\(916\) 0 0
\(917\) 45.6403 + 30.4959i 1.50718 + 1.00706i
\(918\) 0 0
\(919\) −40.2073 16.6544i −1.32632 0.549378i −0.396714 0.917942i \(-0.629850\pi\)
−0.929602 + 0.368564i \(0.879850\pi\)
\(920\) 0 0
\(921\) −2.93840 + 1.21712i −0.0968235 + 0.0401056i
\(922\) 0 0
\(923\) 10.6427 + 53.5046i 0.350310 + 1.76113i
\(924\) 0 0
\(925\) −27.0847 40.5351i −0.890540 1.33279i
\(926\) 0 0
\(927\) 4.12534i 0.135494i
\(928\) 0 0
\(929\) 5.16429i 0.169435i −0.996405 0.0847174i \(-0.973001\pi\)
0.996405 0.0847174i \(-0.0269987\pi\)
\(930\) 0 0
\(931\) −0.215196 0.322064i −0.00705277 0.0105552i
\(932\) 0 0
\(933\) 4.80667 + 24.1648i 0.157363 + 0.791119i
\(934\) 0 0
\(935\) 15.9634 6.61227i 0.522060 0.216244i
\(936\) 0 0
\(937\) −12.9512 5.36457i −0.423097 0.175253i 0.160967 0.986960i \(-0.448539\pi\)
−0.584065 + 0.811707i \(0.698539\pi\)
\(938\) 0 0
\(939\) −42.4373 28.3557i −1.38489 0.925353i
\(940\) 0 0
\(941\) −3.17307 + 15.9521i −0.103439 + 0.520023i 0.893973 + 0.448121i \(0.147907\pi\)
−0.997412 + 0.0719017i \(0.977093\pi\)
\(942\) 0 0
\(943\) 12.0065 + 12.0065i 0.390984 + 0.390984i
\(944\) 0 0
\(945\) 37.6838 37.6838i 1.22585 1.22585i
\(946\) 0 0
\(947\) 43.7095 + 8.69436i 1.42037 + 0.282529i 0.844737 0.535181i \(-0.179757\pi\)
0.575630 + 0.817710i \(0.304757\pi\)
\(948\) 0 0
\(949\) 26.1480 39.1333i 0.848802 1.27032i
\(950\) 0 0
\(951\) 1.62278 3.91773i 0.0526221 0.127041i
\(952\) 0 0
\(953\) 4.09229 + 9.87966i 0.132562 + 0.320033i 0.976198 0.216883i \(-0.0695890\pi\)
−0.843635 + 0.536916i \(0.819589\pi\)
\(954\) 0 0
\(955\) −62.9569 + 12.5229i −2.03724 + 0.405232i
\(956\) 0 0
\(957\) −24.4999 + 16.3703i −0.791970 + 0.529177i
\(958\) 0 0
\(959\) 18.2924 0.590691
\(960\) 0 0
\(961\) 22.6740 0.731419
\(962\) 0 0
\(963\) 2.79583 1.86812i 0.0900945 0.0601992i
\(964\) 0 0
\(965\) −70.5318 + 14.0296i −2.27050 + 0.451630i
\(966\) 0 0
\(967\) −8.17090 19.7263i −0.262758 0.634355i 0.736349 0.676602i \(-0.236548\pi\)
−0.999107 + 0.0422473i \(0.986548\pi\)
\(968\) 0 0
\(969\) −2.13252 + 5.14836i −0.0685064 + 0.165389i
\(970\) 0 0
\(971\) 12.6361 18.9113i 0.405513 0.606893i −0.571364 0.820697i \(-0.693585\pi\)
0.976877 + 0.213804i \(0.0685854\pi\)
\(972\) 0 0
\(973\) 42.9186 + 8.53704i 1.37591 + 0.273685i
\(974\) 0 0
\(975\) 39.6670 39.6670i 1.27036 1.27036i
\(976\) 0 0
\(977\) −6.39950 6.39950i −0.204738 0.204738i 0.597288 0.802027i \(-0.296245\pi\)
−0.802027 + 0.597288i \(0.796245\pi\)
\(978\) 0 0
\(979\) 3.44930 17.3408i 0.110240 0.554215i
\(980\) 0 0
\(981\) 4.57664 + 3.05801i 0.146121 + 0.0976349i
\(982\) 0 0
\(983\) 0.428626 + 0.177543i 0.0136710 + 0.00566273i 0.389508 0.921023i \(-0.372645\pi\)
−0.375837 + 0.926686i \(0.622645\pi\)
\(984\) 0 0
\(985\) −55.3178 + 22.9134i −1.76257 + 0.730082i
\(986\) 0 0
\(987\) −2.77060 13.9288i −0.0881893 0.443357i
\(988\) 0 0
\(989\) −7.07696 10.5914i −0.225034 0.336787i
\(990\) 0 0
\(991\) 44.6212i 1.41744i −0.705490 0.708720i \(-0.749273\pi\)
0.705490 0.708720i \(-0.250727\pi\)
\(992\) 0 0
\(993\) 1.86310i 0.0591238i
\(994\) 0 0
\(995\) −29.4527 44.0790i −0.933713 1.39740i
\(996\) 0 0
\(997\) −11.3063 56.8407i −0.358075 1.80016i −0.568643 0.822584i \(-0.692531\pi\)
0.210568 0.977579i \(-0.432469\pi\)
\(998\) 0 0
\(999\) 31.5888 13.0845i 0.999426 0.413976i
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 512.2.i.b.33.5 56
4.3 odd 2 512.2.i.a.33.3 56
8.3 odd 2 256.2.i.a.145.5 56
8.5 even 2 64.2.i.a.13.1 yes 56
24.5 odd 2 576.2.bd.a.397.7 56
64.5 even 16 inner 512.2.i.b.481.5 56
64.27 odd 16 256.2.i.a.113.5 56
64.37 even 16 64.2.i.a.5.1 56
64.59 odd 16 512.2.i.a.481.3 56
192.101 odd 16 576.2.bd.a.325.7 56
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
64.2.i.a.5.1 56 64.37 even 16
64.2.i.a.13.1 yes 56 8.5 even 2
256.2.i.a.113.5 56 64.27 odd 16
256.2.i.a.145.5 56 8.3 odd 2
512.2.i.a.33.3 56 4.3 odd 2
512.2.i.a.481.3 56 64.59 odd 16
512.2.i.b.33.5 56 1.1 even 1 trivial
512.2.i.b.481.5 56 64.5 even 16 inner
576.2.bd.a.325.7 56 192.101 odd 16
576.2.bd.a.397.7 56 24.5 odd 2