Properties

Label 256.2.g.d.97.2
Level $256$
Weight $2$
Character 256.97
Analytic conductor $2.044$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [256,2,Mod(33,256)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(256, base_ring=CyclotomicField(8))
 
chi = DirichletCharacter(H, H._module([0, 7]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("256.33");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 256 = 2^{8} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 256.g (of order \(8\), degree \(4\), not minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(2.04417029174\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(2\) over \(\Q(\zeta_{8})\)
Coefficient field: 8.0.18939904.2
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{8} - 4x^{7} + 14x^{6} - 28x^{5} + 43x^{4} - 44x^{3} + 30x^{2} - 12x + 2 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 2^{3} \)
Twist minimal: no (minimal twist has level 32)
Sato-Tate group: $\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label 97.2
Root \(0.500000 - 1.44392i\) of defining polynomial
Character \(\chi\) \(=\) 256.97
Dual form 256.2.g.d.161.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(2.27882 - 0.943920i) q^{3} +(0.707107 - 1.70711i) q^{5} +(-0.665096 - 0.665096i) q^{7} +(2.18073 - 2.18073i) q^{9} +O(q^{10})\) \(q+(2.27882 - 0.943920i) q^{3} +(0.707107 - 1.70711i) q^{5} +(-0.665096 - 0.665096i) q^{7} +(2.18073 - 2.18073i) q^{9} +(-3.69304 - 1.52971i) q^{11} +(1.76652 + 4.26475i) q^{13} -4.55765i q^{15} +3.61706i q^{17} +(-0.194802 - 0.470294i) q^{19} +(-2.14343 - 0.887839i) q^{21} +(-1.33490 + 1.33490i) q^{23} +(1.12132 + 1.12132i) q^{25} +(0.0793096 - 0.191470i) q^{27} +(5.73838 - 2.37691i) q^{29} +1.17157 q^{31} -9.85970 q^{33} +(-1.60568 + 0.665096i) q^{35} +(-0.510925 + 1.23348i) q^{37} +(8.05117 + 8.05117i) q^{39} +(1.66981 - 1.66981i) q^{41} +(2.54960 + 1.05608i) q^{43} +(-2.18073 - 5.26475i) q^{45} -1.49824i q^{47} -6.11529i q^{49} +(3.41421 + 8.24264i) q^{51} +(-4.59495 - 1.90329i) q^{53} +(-5.22274 + 5.22274i) q^{55} +(-0.887839 - 0.887839i) q^{57} +(-2.04784 + 4.94392i) q^{59} +(-13.7102 + 5.67897i) q^{61} -2.90079 q^{63} +8.52951 q^{65} +(3.40617 - 1.41088i) q^{67} +(-1.78197 + 4.30205i) q^{69} +(-9.66157 - 9.66157i) q^{71} +(-7.55765 + 7.55765i) q^{73} +(3.61373 + 1.49685i) q^{75} +(1.43882 + 3.47363i) q^{77} +17.2176i q^{79} +8.74088i q^{81} +(-4.82981 - 11.6602i) q^{83} +(6.17471 + 2.55765i) q^{85} +(10.8331 - 10.8331i) q^{87} +(-5.43882 - 5.43882i) q^{89} +(1.66157 - 4.01138i) q^{91} +(2.66981 - 1.10587i) q^{93} -0.940588 q^{95} +6.15862 q^{97} +(-11.3894 + 4.71765i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q + 4 q^{3} - 8 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 8 q + 4 q^{3} - 8 q^{7} - 4 q^{11} + 8 q^{13} - 4 q^{19} - 8 q^{23} - 8 q^{25} - 8 q^{27} + 32 q^{31} - 16 q^{33} - 16 q^{35} + 8 q^{37} + 16 q^{39} + 8 q^{41} + 12 q^{43} + 16 q^{51} - 8 q^{53} - 16 q^{55} + 16 q^{57} + 20 q^{59} - 24 q^{61} - 40 q^{63} + 36 q^{67} - 32 q^{69} - 24 q^{71} - 32 q^{73} + 12 q^{75} - 16 q^{77} - 20 q^{83} - 8 q^{85} + 56 q^{87} - 16 q^{89} - 40 q^{91} + 16 q^{93} - 8 q^{95} + 32 q^{97} - 28 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

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

\(n\) \(5\) \(255\)
\(\chi(n)\) \(e\left(\frac{5}{8}\right)\) \(1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) 2.27882 0.943920i 1.31568 0.544972i 0.389143 0.921177i \(-0.372771\pi\)
0.926536 + 0.376205i \(0.122771\pi\)
\(4\) 0 0
\(5\) 0.707107 1.70711i 0.316228 0.763441i −0.683220 0.730213i \(-0.739421\pi\)
0.999448 0.0332288i \(-0.0105790\pi\)
\(6\) 0 0
\(7\) −0.665096 0.665096i −0.251383 0.251383i 0.570155 0.821537i \(-0.306883\pi\)
−0.821537 + 0.570155i \(0.806883\pi\)
\(8\) 0 0
\(9\) 2.18073 2.18073i 0.726911 0.726911i
\(10\) 0 0
\(11\) −3.69304 1.52971i −1.11349 0.461224i −0.251353 0.967895i \(-0.580876\pi\)
−0.862139 + 0.506672i \(0.830876\pi\)
\(12\) 0 0
\(13\) 1.76652 + 4.26475i 0.489944 + 1.18283i 0.954748 + 0.297416i \(0.0961249\pi\)
−0.464804 + 0.885414i \(0.653875\pi\)
\(14\) 0 0
\(15\) 4.55765i 1.17678i
\(16\) 0 0
\(17\) 3.61706i 0.877266i 0.898666 + 0.438633i \(0.144537\pi\)
−0.898666 + 0.438633i \(0.855463\pi\)
\(18\) 0 0
\(19\) −0.194802 0.470294i −0.0446907 0.107893i 0.899958 0.435977i \(-0.143597\pi\)
−0.944649 + 0.328084i \(0.893597\pi\)
\(20\) 0 0
\(21\) −2.14343 0.887839i −0.467736 0.193742i
\(22\) 0 0
\(23\) −1.33490 + 1.33490i −0.278347 + 0.278347i −0.832449 0.554102i \(-0.813062\pi\)
0.554102 + 0.832449i \(0.313062\pi\)
\(24\) 0 0
\(25\) 1.12132 + 1.12132i 0.224264 + 0.224264i
\(26\) 0 0
\(27\) 0.0793096 0.191470i 0.0152631 0.0368485i
\(28\) 0 0
\(29\) 5.73838 2.37691i 1.06559 0.441382i 0.220158 0.975464i \(-0.429343\pi\)
0.845433 + 0.534082i \(0.179343\pi\)
\(30\) 0 0
\(31\) 1.17157 0.210421 0.105210 0.994450i \(-0.466448\pi\)
0.105210 + 0.994450i \(0.466448\pi\)
\(32\) 0 0
\(33\) −9.85970 −1.71635
\(34\) 0 0
\(35\) −1.60568 + 0.665096i −0.271410 + 0.112422i
\(36\) 0 0
\(37\) −0.510925 + 1.23348i −0.0839955 + 0.202783i −0.960297 0.278980i \(-0.910004\pi\)
0.876301 + 0.481763i \(0.160004\pi\)
\(38\) 0 0
\(39\) 8.05117 + 8.05117i 1.28922 + 1.28922i
\(40\) 0 0
\(41\) 1.66981 1.66981i 0.260780 0.260780i −0.564591 0.825371i \(-0.690966\pi\)
0.825371 + 0.564591i \(0.190966\pi\)
\(42\) 0 0
\(43\) 2.54960 + 1.05608i 0.388811 + 0.161051i 0.568521 0.822669i \(-0.307516\pi\)
−0.179710 + 0.983720i \(0.557516\pi\)
\(44\) 0 0
\(45\) −2.18073 5.26475i −0.325084 0.784823i
\(46\) 0 0
\(47\) 1.49824i 0.218540i −0.994012 0.109270i \(-0.965149\pi\)
0.994012 0.109270i \(-0.0348513\pi\)
\(48\) 0 0
\(49\) 6.11529i 0.873614i
\(50\) 0 0
\(51\) 3.41421 + 8.24264i 0.478086 + 1.15420i
\(52\) 0 0
\(53\) −4.59495 1.90329i −0.631164 0.261437i 0.0440833 0.999028i \(-0.485963\pi\)
−0.675248 + 0.737591i \(0.735963\pi\)
\(54\) 0 0
\(55\) −5.22274 + 5.22274i −0.704235 + 0.704235i
\(56\) 0 0
\(57\) −0.887839 0.887839i −0.117597 0.117597i
\(58\) 0 0
\(59\) −2.04784 + 4.94392i −0.266606 + 0.643644i −0.999319 0.0368939i \(-0.988254\pi\)
0.732713 + 0.680537i \(0.238254\pi\)
\(60\) 0 0
\(61\) −13.7102 + 5.67897i −1.75542 + 0.727117i −0.758244 + 0.651971i \(0.773942\pi\)
−0.997173 + 0.0751463i \(0.976058\pi\)
\(62\) 0 0
\(63\) −2.90079 −0.365466
\(64\) 0 0
\(65\) 8.52951 1.05796
\(66\) 0 0
\(67\) 3.40617 1.41088i 0.416130 0.172367i −0.164788 0.986329i \(-0.552694\pi\)
0.580918 + 0.813962i \(0.302694\pi\)
\(68\) 0 0
\(69\) −1.78197 + 4.30205i −0.214524 + 0.517906i
\(70\) 0 0
\(71\) −9.66157 9.66157i −1.14662 1.14662i −0.987214 0.159403i \(-0.949043\pi\)
−0.159403 0.987214i \(-0.550957\pi\)
\(72\) 0 0
\(73\) −7.55765 + 7.55765i −0.884556 + 0.884556i −0.993994 0.109438i \(-0.965095\pi\)
0.109438 + 0.993994i \(0.465095\pi\)
\(74\) 0 0
\(75\) 3.61373 + 1.49685i 0.417277 + 0.172842i
\(76\) 0 0
\(77\) 1.43882 + 3.47363i 0.163969 + 0.395856i
\(78\) 0 0
\(79\) 17.2176i 1.93714i 0.248750 + 0.968568i \(0.419980\pi\)
−0.248750 + 0.968568i \(0.580020\pi\)
\(80\) 0 0
\(81\) 8.74088i 0.971208i
\(82\) 0 0
\(83\) −4.82981 11.6602i −0.530140 1.27987i −0.931430 0.363921i \(-0.881438\pi\)
0.401290 0.915951i \(-0.368562\pi\)
\(84\) 0 0
\(85\) 6.17471 + 2.55765i 0.669741 + 0.277416i
\(86\) 0 0
\(87\) 10.8331 10.8331i 1.16143 1.16143i
\(88\) 0 0
\(89\) −5.43882 5.43882i −0.576514 0.576514i 0.357427 0.933941i \(-0.383654\pi\)
−0.933941 + 0.357427i \(0.883654\pi\)
\(90\) 0 0
\(91\) 1.66157 4.01138i 0.174179 0.420506i
\(92\) 0 0
\(93\) 2.66981 1.10587i 0.276846 0.114673i
\(94\) 0 0
\(95\) −0.940588 −0.0965023
\(96\) 0 0
\(97\) 6.15862 0.625313 0.312657 0.949866i \(-0.398781\pi\)
0.312657 + 0.949866i \(0.398781\pi\)
\(98\) 0 0
\(99\) −11.3894 + 4.71765i −1.14468 + 0.474141i
\(100\) 0 0
\(101\) 3.09671 7.47612i 0.308134 0.743902i −0.691631 0.722251i \(-0.743108\pi\)
0.999766 0.0216512i \(-0.00689233\pi\)
\(102\) 0 0
\(103\) −4.72764 4.72764i −0.465828 0.465828i 0.434732 0.900560i \(-0.356843\pi\)
−0.900560 + 0.434732i \(0.856843\pi\)
\(104\) 0 0
\(105\) −3.03127 + 3.03127i −0.295822 + 0.295822i
\(106\) 0 0
\(107\) −2.57774 1.06774i −0.249200 0.103222i 0.254587 0.967050i \(-0.418060\pi\)
−0.503787 + 0.863828i \(0.668060\pi\)
\(108\) 0 0
\(109\) −3.46094 8.35544i −0.331498 0.800306i −0.998474 0.0552270i \(-0.982412\pi\)
0.666976 0.745079i \(-0.267588\pi\)
\(110\) 0 0
\(111\) 3.29316i 0.312573i
\(112\) 0 0
\(113\) 11.7757i 1.10776i −0.832596 0.553881i \(-0.813146\pi\)
0.832596 0.553881i \(-0.186854\pi\)
\(114\) 0 0
\(115\) 1.33490 + 3.22274i 0.124480 + 0.300522i
\(116\) 0 0
\(117\) 13.1526 + 5.44798i 1.21596 + 0.503666i
\(118\) 0 0
\(119\) 2.40569 2.40569i 0.220529 0.220529i
\(120\) 0 0
\(121\) 3.52035 + 3.52035i 0.320032 + 0.320032i
\(122\) 0 0
\(123\) 2.22903 5.38136i 0.200985 0.485221i
\(124\) 0 0
\(125\) 11.2426 4.65685i 1.00557 0.416522i
\(126\) 0 0
\(127\) 13.0590 1.15880 0.579400 0.815043i \(-0.303287\pi\)
0.579400 + 0.815043i \(0.303287\pi\)
\(128\) 0 0
\(129\) 6.80695 0.599319
\(130\) 0 0
\(131\) 6.52146 2.70128i 0.569783 0.236012i −0.0791431 0.996863i \(-0.525218\pi\)
0.648926 + 0.760851i \(0.275218\pi\)
\(132\) 0 0
\(133\) −0.183228 + 0.442353i −0.0158879 + 0.0383568i
\(134\) 0 0
\(135\) −0.270780 0.270780i −0.0233050 0.0233050i
\(136\) 0 0
\(137\) 4.88118 4.88118i 0.417027 0.417027i −0.467151 0.884178i \(-0.654719\pi\)
0.884178 + 0.467151i \(0.154719\pi\)
\(138\) 0 0
\(139\) 11.7837 + 4.88098i 0.999482 + 0.413999i 0.821607 0.570054i \(-0.193078\pi\)
0.177875 + 0.984053i \(0.443078\pi\)
\(140\) 0 0
\(141\) −1.41421 3.41421i −0.119098 0.287529i
\(142\) 0 0
\(143\) 18.4522i 1.54305i
\(144\) 0 0
\(145\) 11.4768i 0.953093i
\(146\) 0 0
\(147\) −5.77235 13.9357i −0.476095 1.14940i
\(148\) 0 0
\(149\) 5.73838 + 2.37691i 0.470106 + 0.194724i 0.605144 0.796116i \(-0.293116\pi\)
−0.135038 + 0.990840i \(0.543116\pi\)
\(150\) 0 0
\(151\) 11.1504 11.1504i 0.907405 0.907405i −0.0886573 0.996062i \(-0.528258\pi\)
0.996062 + 0.0886573i \(0.0282576\pi\)
\(152\) 0 0
\(153\) 7.88784 + 7.88784i 0.637694 + 0.637694i
\(154\) 0 0
\(155\) 0.828427 2.00000i 0.0665409 0.160644i
\(156\) 0 0
\(157\) −1.22496 + 0.507395i −0.0977624 + 0.0404945i −0.431029 0.902338i \(-0.641849\pi\)
0.333266 + 0.942833i \(0.391849\pi\)
\(158\) 0 0
\(159\) −12.2676 −0.972886
\(160\) 0 0
\(161\) 1.77568 0.139943
\(162\) 0 0
\(163\) −21.3218 + 8.83176i −1.67005 + 0.691757i −0.998776 0.0494542i \(-0.984252\pi\)
−0.671272 + 0.741211i \(0.734252\pi\)
\(164\) 0 0
\(165\) −6.97186 + 16.8316i −0.542759 + 1.31034i
\(166\) 0 0
\(167\) 10.8863 + 10.8863i 0.842404 + 0.842404i 0.989171 0.146767i \(-0.0468867\pi\)
−0.146767 + 0.989171i \(0.546887\pi\)
\(168\) 0 0
\(169\) −5.87515 + 5.87515i −0.451935 + 0.451935i
\(170\) 0 0
\(171\) −1.45040 0.600774i −0.110915 0.0459423i
\(172\) 0 0
\(173\) −0.735246 1.77504i −0.0558997 0.134954i 0.893462 0.449138i \(-0.148269\pi\)
−0.949362 + 0.314184i \(0.898269\pi\)
\(174\) 0 0
\(175\) 1.49157i 0.112752i
\(176\) 0 0
\(177\) 13.1993i 0.992121i
\(178\) 0 0
\(179\) 1.87980 + 4.53823i 0.140503 + 0.339203i 0.978430 0.206578i \(-0.0662329\pi\)
−0.837928 + 0.545782i \(0.816233\pi\)
\(180\) 0 0
\(181\) −1.87868 0.778175i −0.139641 0.0578413i 0.311768 0.950158i \(-0.399079\pi\)
−0.451410 + 0.892317i \(0.649079\pi\)
\(182\) 0 0
\(183\) −25.8827 + 25.8827i −1.91331 + 1.91331i
\(184\) 0 0
\(185\) 1.74441 + 1.74441i 0.128251 + 0.128251i
\(186\) 0 0
\(187\) 5.53304 13.3579i 0.404616 0.976829i
\(188\) 0 0
\(189\) −0.180095 + 0.0745976i −0.0131000 + 0.00542618i
\(190\) 0 0
\(191\) −19.4022 −1.40389 −0.701946 0.712231i \(-0.747685\pi\)
−0.701946 + 0.712231i \(0.747685\pi\)
\(192\) 0 0
\(193\) −18.0461 −1.29898 −0.649492 0.760368i \(-0.725018\pi\)
−0.649492 + 0.760368i \(0.725018\pi\)
\(194\) 0 0
\(195\) 19.4372 8.05117i 1.39193 0.576556i
\(196\) 0 0
\(197\) 0.0865175 0.208872i 0.00616412 0.0148815i −0.920768 0.390112i \(-0.872436\pi\)
0.926932 + 0.375230i \(0.122436\pi\)
\(198\) 0 0
\(199\) −11.8992 11.8992i −0.843513 0.843513i 0.145801 0.989314i \(-0.453424\pi\)
−0.989314 + 0.145801i \(0.953424\pi\)
\(200\) 0 0
\(201\) 6.43030 6.43030i 0.453558 0.453558i
\(202\) 0 0
\(203\) −5.39745 2.23570i −0.378827 0.156915i
\(204\) 0 0
\(205\) −1.66981 4.03127i −0.116624 0.281556i
\(206\) 0 0
\(207\) 5.82214i 0.404667i
\(208\) 0 0
\(209\) 2.03480i 0.140750i
\(210\) 0 0
\(211\) 3.73060 + 9.00647i 0.256825 + 0.620031i 0.998725 0.0504799i \(-0.0160751\pi\)
−0.741900 + 0.670511i \(0.766075\pi\)
\(212\) 0 0
\(213\) −31.1367 12.8973i −2.13345 0.883706i
\(214\) 0 0
\(215\) 3.60568 3.60568i 0.245906 0.245906i
\(216\) 0 0
\(217\) −0.779208 0.779208i −0.0528961 0.0528961i
\(218\) 0 0
\(219\) −10.0887 + 24.3564i −0.681733 + 1.64585i
\(220\) 0 0
\(221\) −15.4259 + 6.38960i −1.03766 + 0.429811i
\(222\) 0 0
\(223\) 22.6174 1.51458 0.757288 0.653081i \(-0.226524\pi\)
0.757288 + 0.653081i \(0.226524\pi\)
\(224\) 0 0
\(225\) 4.89060 0.326040
\(226\) 0 0
\(227\) 9.51294 3.94039i 0.631396 0.261533i −0.0439500 0.999034i \(-0.513994\pi\)
0.675346 + 0.737501i \(0.263994\pi\)
\(228\) 0 0
\(229\) 6.53200 15.7697i 0.431647 1.04209i −0.547109 0.837061i \(-0.684272\pi\)
0.978756 0.205027i \(-0.0657282\pi\)
\(230\) 0 0
\(231\) 6.55765 + 6.55765i 0.431462 + 0.431462i
\(232\) 0 0
\(233\) 10.4486 10.4486i 0.684512 0.684512i −0.276502 0.961013i \(-0.589175\pi\)
0.961013 + 0.276502i \(0.0891751\pi\)
\(234\) 0 0
\(235\) −2.55765 1.05941i −0.166843 0.0691084i
\(236\) 0 0
\(237\) 16.2521 + 39.2360i 1.05569 + 2.54865i
\(238\) 0 0
\(239\) 11.6733i 0.755085i 0.925992 + 0.377543i \(0.123231\pi\)
−0.925992 + 0.377543i \(0.876769\pi\)
\(240\) 0 0
\(241\) 13.8288i 0.890791i 0.895334 + 0.445396i \(0.146937\pi\)
−0.895334 + 0.445396i \(0.853063\pi\)
\(242\) 0 0
\(243\) 8.48861 + 20.4933i 0.544545 + 1.31465i
\(244\) 0 0
\(245\) −10.4395 4.32417i −0.666953 0.276261i
\(246\) 0 0
\(247\) 1.66157 1.66157i 0.105723 0.105723i
\(248\) 0 0
\(249\) −22.0126 22.0126i −1.39499 1.39499i
\(250\) 0 0
\(251\) −5.38745 + 13.0065i −0.340053 + 0.820961i 0.657656 + 0.753318i \(0.271548\pi\)
−0.997710 + 0.0676429i \(0.978452\pi\)
\(252\) 0 0
\(253\) 6.97186 2.88784i 0.438317 0.181557i
\(254\) 0 0
\(255\) 16.4853 1.03235
\(256\) 0 0
\(257\) −18.9043 −1.17922 −0.589609 0.807689i \(-0.700718\pi\)
−0.589609 + 0.807689i \(0.700718\pi\)
\(258\) 0 0
\(259\) 1.16020 0.480569i 0.0720911 0.0298611i
\(260\) 0 0
\(261\) 7.33046 17.6973i 0.453744 1.09543i
\(262\) 0 0
\(263\) 13.9086 + 13.9086i 0.857643 + 0.857643i 0.991060 0.133417i \(-0.0425948\pi\)
−0.133417 + 0.991060i \(0.542595\pi\)
\(264\) 0 0
\(265\) −6.49824 + 6.49824i −0.399183 + 0.399183i
\(266\) 0 0
\(267\) −17.5279 7.26031i −1.07269 0.444324i
\(268\) 0 0
\(269\) −5.05209 12.1968i −0.308031 0.743653i −0.999769 0.0215042i \(-0.993154\pi\)
0.691737 0.722149i \(-0.256846\pi\)
\(270\) 0 0
\(271\) 4.41512i 0.268199i −0.990968 0.134100i \(-0.957186\pi\)
0.990968 0.134100i \(-0.0428142\pi\)
\(272\) 0 0
\(273\) 10.7096i 0.648175i
\(274\) 0 0
\(275\) −2.42579 5.85637i −0.146280 0.353152i
\(276\) 0 0
\(277\) 23.0454 + 9.54573i 1.38467 + 0.573547i 0.945725 0.324969i \(-0.105354\pi\)
0.438941 + 0.898516i \(0.355354\pi\)
\(278\) 0 0
\(279\) 2.55489 2.55489i 0.152957 0.152957i
\(280\) 0 0
\(281\) −5.83509 5.83509i −0.348092 0.348092i 0.511306 0.859399i \(-0.329162\pi\)
−0.859399 + 0.511306i \(0.829162\pi\)
\(282\) 0 0
\(283\) −1.31992 + 3.18656i −0.0784609 + 0.189421i −0.958243 0.285957i \(-0.907689\pi\)
0.879782 + 0.475378i \(0.157689\pi\)
\(284\) 0 0
\(285\) −2.14343 + 0.887839i −0.126966 + 0.0525911i
\(286\) 0 0
\(287\) −2.22117 −0.131111
\(288\) 0 0
\(289\) 3.91688 0.230405
\(290\) 0 0
\(291\) 14.0344 5.81324i 0.822712 0.340778i
\(292\) 0 0
\(293\) −2.89663 + 6.99307i −0.169223 + 0.408540i −0.985626 0.168943i \(-0.945965\pi\)
0.816403 + 0.577482i \(0.195965\pi\)
\(294\) 0 0
\(295\) 6.99176 + 6.99176i 0.407076 + 0.407076i
\(296\) 0 0
\(297\) −0.585786 + 0.585786i −0.0339908 + 0.0339908i
\(298\) 0 0
\(299\) −8.05117 3.33490i −0.465611 0.192862i
\(300\) 0 0
\(301\) −0.993336 2.39813i −0.0572550 0.138226i
\(302\) 0 0
\(303\) 19.9598i 1.14666i
\(304\) 0 0
\(305\) 27.4205i 1.57009i
\(306\) 0 0
\(307\) 3.14481 + 7.59225i 0.179484 + 0.433313i 0.987859 0.155356i \(-0.0496524\pi\)
−0.808375 + 0.588668i \(0.799652\pi\)
\(308\) 0 0
\(309\) −15.2360 6.31095i −0.866744 0.359017i
\(310\) 0 0
\(311\) −15.0543 + 15.0543i −0.853651 + 0.853651i −0.990581 0.136930i \(-0.956277\pi\)
0.136930 + 0.990581i \(0.456277\pi\)
\(312\) 0 0
\(313\) 18.3365 + 18.3365i 1.03644 + 1.03644i 0.999311 + 0.0371274i \(0.0118208\pi\)
0.0371274 + 0.999311i \(0.488179\pi\)
\(314\) 0 0
\(315\) −2.05117 + 4.95196i −0.115570 + 0.279012i
\(316\) 0 0
\(317\) 9.52348 3.94476i 0.534892 0.221560i −0.0988523 0.995102i \(-0.531517\pi\)
0.633744 + 0.773543i \(0.281517\pi\)
\(318\) 0 0
\(319\) −24.8280 −1.39010
\(320\) 0 0
\(321\) −6.88208 −0.384120
\(322\) 0 0
\(323\) 1.70108 0.704611i 0.0946507 0.0392056i
\(324\) 0 0
\(325\) −2.80132 + 6.76299i −0.155389 + 0.375143i
\(326\) 0 0
\(327\) −15.7737 15.7737i −0.872289 0.872289i
\(328\) 0 0
\(329\) −0.996470 + 0.996470i −0.0549372 + 0.0549372i
\(330\) 0 0
\(331\) −7.57421 3.13734i −0.416316 0.172444i 0.164685 0.986346i \(-0.447339\pi\)
−0.581002 + 0.813902i \(0.697339\pi\)
\(332\) 0 0
\(333\) 1.57570 + 3.80408i 0.0863480 + 0.208462i
\(334\) 0 0
\(335\) 6.81234i 0.372198i
\(336\) 0 0
\(337\) 16.8910i 0.920110i −0.887890 0.460055i \(-0.847830\pi\)
0.887890 0.460055i \(-0.152170\pi\)
\(338\) 0 0
\(339\) −11.1153 26.8347i −0.603700 1.45746i
\(340\) 0 0
\(341\) −4.32666 1.79216i −0.234302 0.0970510i
\(342\) 0 0
\(343\) −8.72293 + 8.72293i −0.470994 + 0.470994i
\(344\) 0 0
\(345\) 6.08402 + 6.08402i 0.327553 + 0.327553i
\(346\) 0 0
\(347\) 11.6582 28.1455i 0.625847 1.51093i −0.218892 0.975749i \(-0.570244\pi\)
0.844739 0.535179i \(-0.179756\pi\)
\(348\) 0 0
\(349\) −9.99044 + 4.13818i −0.534776 + 0.221512i −0.633694 0.773584i \(-0.718462\pi\)
0.0989174 + 0.995096i \(0.468462\pi\)
\(350\) 0 0
\(351\) 0.956675 0.0510636
\(352\) 0 0
\(353\) 0.673711 0.0358580 0.0179290 0.999839i \(-0.494293\pi\)
0.0179290 + 0.999839i \(0.494293\pi\)
\(354\) 0 0
\(355\) −23.3251 + 9.66157i −1.23797 + 0.512783i
\(356\) 0 0
\(357\) 3.21137 7.75293i 0.169964 0.410328i
\(358\) 0 0
\(359\) 3.92568 + 3.92568i 0.207190 + 0.207190i 0.803072 0.595882i \(-0.203198\pi\)
−0.595882 + 0.803072i \(0.703198\pi\)
\(360\) 0 0
\(361\) 13.2518 13.2518i 0.697463 0.697463i
\(362\) 0 0
\(363\) 11.3452 + 4.69933i 0.595467 + 0.246651i
\(364\) 0 0
\(365\) 7.55765 + 18.2458i 0.395585 + 0.955027i
\(366\) 0 0
\(367\) 16.4759i 0.860033i −0.902821 0.430016i \(-0.858508\pi\)
0.902821 0.430016i \(-0.141492\pi\)
\(368\) 0 0
\(369\) 7.28281i 0.379128i
\(370\) 0 0
\(371\) 1.79021 + 4.32195i 0.0929431 + 0.224384i
\(372\) 0 0
\(373\) 12.6790 + 5.25180i 0.656492 + 0.271928i 0.685962 0.727638i \(-0.259382\pi\)
−0.0294695 + 0.999566i \(0.509382\pi\)
\(374\) 0 0
\(375\) 21.2243 21.2243i 1.09602 1.09602i
\(376\) 0 0
\(377\) 20.2739 + 20.2739i 1.04416 + 1.04416i
\(378\) 0 0
\(379\) 5.06746 12.2339i 0.260298 0.628414i −0.738659 0.674079i \(-0.764541\pi\)
0.998957 + 0.0456649i \(0.0145406\pi\)
\(380\) 0 0
\(381\) 29.7592 12.3267i 1.52461 0.631514i
\(382\) 0 0
\(383\) 14.5667 0.744322 0.372161 0.928168i \(-0.378617\pi\)
0.372161 + 0.928168i \(0.378617\pi\)
\(384\) 0 0
\(385\) 6.94725 0.354065
\(386\) 0 0
\(387\) 7.86303 3.25697i 0.399700 0.165561i
\(388\) 0 0
\(389\) −14.2795 + 34.4739i −0.724002 + 1.74789i −0.0623850 + 0.998052i \(0.519871\pi\)
−0.661617 + 0.749842i \(0.730129\pi\)
\(390\) 0 0
\(391\) −4.82843 4.82843i −0.244184 0.244184i
\(392\) 0 0
\(393\) 12.3115 12.3115i 0.621032 0.621032i
\(394\) 0 0
\(395\) 29.3923 + 12.1747i 1.47889 + 0.612576i
\(396\) 0 0
\(397\) −8.88405 21.4480i −0.445877 1.07644i −0.973852 0.227183i \(-0.927048\pi\)
0.527975 0.849260i \(-0.322952\pi\)
\(398\) 0 0
\(399\) 1.18100i 0.0591238i
\(400\) 0 0
\(401\) 2.51509i 0.125598i −0.998026 0.0627989i \(-0.979997\pi\)
0.998026 0.0627989i \(-0.0200027\pi\)
\(402\) 0 0
\(403\) 2.06961 + 4.99647i 0.103094 + 0.248892i
\(404\) 0 0
\(405\) 14.9216 + 6.18073i 0.741461 + 0.307123i
\(406\) 0 0
\(407\) 3.77373 3.77373i 0.187057 0.187057i
\(408\) 0 0
\(409\) −5.32666 5.32666i −0.263386 0.263386i 0.563042 0.826428i \(-0.309631\pi\)
−0.826428 + 0.563042i \(0.809631\pi\)
\(410\) 0 0
\(411\) 6.51590 15.7308i 0.321406 0.775942i
\(412\) 0 0
\(413\) 4.65019 1.92617i 0.228821 0.0947807i
\(414\) 0 0
\(415\) −23.3204 −1.14475
\(416\) 0 0
\(417\) 31.4603 1.54062
\(418\) 0 0
\(419\) −10.5509 + 4.37032i −0.515444 + 0.213504i −0.625214 0.780453i \(-0.714988\pi\)
0.109770 + 0.993957i \(0.464988\pi\)
\(420\) 0 0
\(421\) −1.72505 + 4.16464i −0.0840739 + 0.202972i −0.960326 0.278881i \(-0.910036\pi\)
0.876252 + 0.481854i \(0.160036\pi\)
\(422\) 0 0
\(423\) −3.26725 3.26725i −0.158859 0.158859i
\(424\) 0 0
\(425\) −4.05588 + 4.05588i −0.196739 + 0.196739i
\(426\) 0 0
\(427\) 12.8957 + 5.34157i 0.624066 + 0.258497i
\(428\) 0 0
\(429\) −17.4173 42.0492i −0.840917 2.03015i
\(430\) 0 0
\(431\) 16.9800i 0.817897i 0.912557 + 0.408949i \(0.134104\pi\)
−0.912557 + 0.408949i \(0.865896\pi\)
\(432\) 0 0
\(433\) 16.9567i 0.814886i −0.913231 0.407443i \(-0.866421\pi\)
0.913231 0.407443i \(-0.133579\pi\)
\(434\) 0 0
\(435\) −10.8331 26.1535i −0.519409 1.25396i
\(436\) 0 0
\(437\) 0.887839 + 0.367755i 0.0424711 + 0.0175921i
\(438\) 0 0
\(439\) 10.5596 10.5596i 0.503982 0.503982i −0.408691 0.912673i \(-0.634015\pi\)
0.912673 + 0.408691i \(0.134015\pi\)
\(440\) 0 0
\(441\) −13.3358 13.3358i −0.635039 0.635039i
\(442\) 0 0
\(443\) −6.31087 + 15.2358i −0.299838 + 0.723874i 0.700113 + 0.714032i \(0.253133\pi\)
−0.999952 + 0.00984190i \(0.996867\pi\)
\(444\) 0 0
\(445\) −13.1305 + 5.43882i −0.622444 + 0.257825i
\(446\) 0 0
\(447\) 15.3204 0.724629
\(448\) 0 0
\(449\) 8.07197 0.380940 0.190470 0.981693i \(-0.438999\pi\)
0.190470 + 0.981693i \(0.438999\pi\)
\(450\) 0 0
\(451\) −8.72098 + 3.61235i −0.410655 + 0.170099i
\(452\) 0 0
\(453\) 14.8847 35.9348i 0.699343 1.68836i
\(454\) 0 0
\(455\) −5.67294 5.67294i −0.265952 0.265952i
\(456\) 0 0
\(457\) −7.68314 + 7.68314i −0.359402 + 0.359402i −0.863592 0.504191i \(-0.831791\pi\)
0.504191 + 0.863592i \(0.331791\pi\)
\(458\) 0 0
\(459\) 0.692559 + 0.286867i 0.0323259 + 0.0133898i
\(460\) 0 0
\(461\) 5.90199 + 14.2487i 0.274883 + 0.663627i 0.999679 0.0253371i \(-0.00806593\pi\)
−0.724796 + 0.688964i \(0.758066\pi\)
\(462\) 0 0
\(463\) 27.3231i 1.26981i 0.772589 + 0.634907i \(0.218962\pi\)
−0.772589 + 0.634907i \(0.781038\pi\)
\(464\) 0 0
\(465\) 5.33962i 0.247619i
\(466\) 0 0
\(467\) 9.40577 + 22.7075i 0.435247 + 1.05078i 0.977570 + 0.210610i \(0.0675449\pi\)
−0.542323 + 0.840170i \(0.682455\pi\)
\(468\) 0 0
\(469\) −3.20380 1.32706i −0.147938 0.0612779i
\(470\) 0 0
\(471\) −2.31253 + 2.31253i −0.106556 + 0.106556i
\(472\) 0 0
\(473\) −7.80029 7.80029i −0.358658 0.358658i
\(474\) 0 0
\(475\) 0.308915 0.745786i 0.0141740 0.0342190i
\(476\) 0 0
\(477\) −14.1709 + 5.86978i −0.648842 + 0.268759i
\(478\) 0 0
\(479\) 3.91155 0.178723 0.0893616 0.995999i \(-0.471517\pi\)
0.0893616 + 0.995999i \(0.471517\pi\)
\(480\) 0 0
\(481\) −6.16305 −0.281011
\(482\) 0 0
\(483\) 4.04646 1.67610i 0.184120 0.0762651i
\(484\) 0 0
\(485\) 4.35480 10.5134i 0.197741 0.477390i
\(486\) 0 0
\(487\) −8.14685 8.14685i −0.369169 0.369169i 0.498005 0.867174i \(-0.334066\pi\)
−0.867174 + 0.498005i \(0.834066\pi\)
\(488\) 0 0
\(489\) −40.2520 + 40.2520i −1.82026 + 1.82026i
\(490\) 0 0
\(491\) −11.2886 4.67590i −0.509448 0.211020i 0.113127 0.993581i \(-0.463913\pi\)
−0.622575 + 0.782560i \(0.713913\pi\)
\(492\) 0 0
\(493\) 8.59744 + 20.7561i 0.387209 + 0.934806i
\(494\) 0 0
\(495\) 22.7788i 1.02383i
\(496\) 0 0
\(497\) 12.8517i 0.576479i
\(498\) 0 0
\(499\) −12.4071 29.9533i −0.555417 1.34089i −0.913361 0.407152i \(-0.866522\pi\)
0.357944 0.933743i \(-0.383478\pi\)
\(500\) 0 0
\(501\) 35.0836 + 14.5321i 1.56742 + 0.649247i
\(502\) 0 0
\(503\) 8.77059 8.77059i 0.391061 0.391061i −0.484004 0.875066i \(-0.660818\pi\)
0.875066 + 0.484004i \(0.160818\pi\)
\(504\) 0 0
\(505\) −10.5728 10.5728i −0.470485 0.470485i
\(506\) 0 0
\(507\) −7.84276 + 18.9341i −0.348309 + 0.840893i
\(508\) 0 0
\(509\) −20.0994 + 8.32546i −0.890892 + 0.369020i −0.780711 0.624892i \(-0.785143\pi\)
−0.110181 + 0.993912i \(0.535143\pi\)
\(510\) 0 0
\(511\) 10.0531 0.444724
\(512\) 0 0
\(513\) −0.105497 −0.00465780
\(514\) 0 0
\(515\) −11.4135 + 4.72764i −0.502941 + 0.208325i
\(516\) 0 0
\(517\) −2.29186 + 5.53304i −0.100796 + 0.243343i
\(518\) 0 0
\(519\) −3.35099 3.35099i −0.147092 0.147092i
\(520\) 0 0
\(521\) −29.8910 + 29.8910i −1.30955 + 1.30955i −0.387807 + 0.921741i \(0.626767\pi\)
−0.921741 + 0.387807i \(0.873233\pi\)
\(522\) 0 0
\(523\) −32.7654 13.5719i −1.43273 0.593456i −0.474706 0.880144i \(-0.657446\pi\)
−0.958024 + 0.286688i \(0.907446\pi\)
\(524\) 0 0
\(525\) −1.40792 3.39903i −0.0614468 0.148346i
\(526\) 0 0
\(527\) 4.23765i 0.184595i
\(528\) 0 0
\(529\) 19.4361i 0.845046i
\(530\) 0 0
\(531\) 6.31558 + 15.2472i 0.274073 + 0.661670i
\(532\) 0 0
\(533\) 10.0711 + 4.17157i 0.436226 + 0.180691i
\(534\) 0 0
\(535\) −3.64548 + 3.64548i −0.157608 + 0.157608i
\(536\) 0 0
\(537\) 8.56744 + 8.56744i 0.369713 + 0.369713i
\(538\) 0 0
\(539\) −9.35460 + 22.5840i −0.402931 + 0.972762i
\(540\) 0 0
\(541\) 11.2925 4.67751i 0.485502 0.201102i −0.126486 0.991968i \(-0.540370\pi\)
0.611988 + 0.790867i \(0.290370\pi\)
\(542\) 0 0
\(543\) −5.01571 −0.215245
\(544\) 0 0
\(545\) −16.7109 −0.715815
\(546\) 0 0
\(547\) 19.1256 7.92207i 0.817750 0.338723i 0.0657087 0.997839i \(-0.479069\pi\)
0.752042 + 0.659116i \(0.229069\pi\)
\(548\) 0 0
\(549\) −17.5141 + 42.2827i −0.747482 + 1.80458i
\(550\) 0 0
\(551\) −2.23570 2.23570i −0.0952439 0.0952439i
\(552\) 0 0
\(553\) 11.4514 11.4514i 0.486962 0.486962i
\(554\) 0 0
\(555\) 5.62177 + 2.32861i 0.238631 + 0.0988442i
\(556\) 0 0
\(557\) −12.3617 29.8439i −0.523783 1.26452i −0.935537 0.353229i \(-0.885084\pi\)
0.411753 0.911295i \(-0.364916\pi\)
\(558\) 0 0
\(559\) 12.7390i 0.538803i
\(560\) 0 0
\(561\) 35.6631i 1.50570i
\(562\) 0 0
\(563\) 10.5540 + 25.4797i 0.444800 + 1.07384i 0.974244 + 0.225497i \(0.0724004\pi\)
−0.529444 + 0.848345i \(0.677600\pi\)
\(564\) 0 0
\(565\) −20.1023 8.32666i −0.845712 0.350305i
\(566\) 0 0
\(567\) 5.81352 5.81352i 0.244145 0.244145i
\(568\) 0 0
\(569\) −23.7855 23.7855i −0.997139 0.997139i 0.00285688 0.999996i \(-0.499091\pi\)
−0.999996 + 0.00285688i \(0.999091\pi\)
\(570\) 0 0
\(571\) 0.904405 2.18343i 0.0378482 0.0913736i −0.903825 0.427902i \(-0.859253\pi\)
0.941673 + 0.336528i \(0.109253\pi\)
\(572\) 0 0
\(573\) −44.2141 + 18.3141i −1.84707 + 0.765082i
\(574\) 0 0
\(575\) −2.99371 −0.124846
\(576\) 0 0
\(577\) 24.8839 1.03593 0.517965 0.855402i \(-0.326690\pi\)
0.517965 + 0.855402i \(0.326690\pi\)
\(578\) 0 0
\(579\) −41.1238 + 17.0340i −1.70905 + 0.707910i
\(580\) 0 0
\(581\) −4.54286 + 10.9674i −0.188469 + 0.455006i
\(582\) 0 0
\(583\) 14.0578 + 14.0578i 0.582216 + 0.582216i
\(584\) 0 0
\(585\) 18.6006 18.6006i 0.769039 0.769039i
\(586\) 0 0
\(587\) 40.1685 + 16.6383i 1.65793 + 0.686738i 0.997917 0.0645151i \(-0.0205501\pi\)
0.660015 + 0.751253i \(0.270550\pi\)
\(588\) 0 0
\(589\) −0.228225 0.550984i −0.00940384 0.0227029i
\(590\) 0 0
\(591\) 0.557647i 0.0229385i
\(592\) 0 0
\(593\) 9.10197i 0.373773i 0.982382 + 0.186886i \(0.0598397\pi\)
−0.982382 + 0.186886i \(0.940160\pi\)
\(594\) 0 0
\(595\) −2.40569 5.80785i −0.0986238 0.238099i
\(596\) 0 0
\(597\) −38.3481 15.8843i −1.56948 0.650102i
\(598\) 0 0
\(599\) 3.04488 3.04488i 0.124410 0.124410i −0.642160 0.766571i \(-0.721962\pi\)
0.766571 + 0.642160i \(0.221962\pi\)
\(600\) 0 0
\(601\) 9.53880 + 9.53880i 0.389096 + 0.389096i 0.874365 0.485269i \(-0.161278\pi\)
−0.485269 + 0.874365i \(0.661278\pi\)
\(602\) 0 0
\(603\) 4.35119 10.5047i 0.177194 0.427784i
\(604\) 0 0
\(605\) 8.49887 3.52035i 0.345528 0.143123i
\(606\) 0 0
\(607\) −3.66391 −0.148714 −0.0743568 0.997232i \(-0.523690\pi\)
−0.0743568 + 0.997232i \(0.523690\pi\)
\(608\) 0 0
\(609\) −14.4102 −0.583929
\(610\) 0 0
\(611\) 6.38960 2.64666i 0.258496 0.107072i
\(612\) 0 0
\(613\) 11.6012 28.0079i 0.468570 1.13123i −0.496218 0.868198i \(-0.665278\pi\)
0.964788 0.263029i \(-0.0847215\pi\)
\(614\) 0 0
\(615\) −7.61040 7.61040i −0.306881 0.306881i
\(616\) 0 0
\(617\) 5.86100 5.86100i 0.235955 0.235955i −0.579218 0.815173i \(-0.696642\pi\)
0.815173 + 0.579218i \(0.196642\pi\)
\(618\) 0 0
\(619\) 36.9173 + 15.2917i 1.48383 + 0.614624i 0.969965 0.243245i \(-0.0782120\pi\)
0.513868 + 0.857869i \(0.328212\pi\)
\(620\) 0 0
\(621\) 0.149724 + 0.361465i 0.00600821 + 0.0145051i
\(622\) 0 0
\(623\) 7.23468i 0.289851i
\(624\) 0 0
\(625\) 14.5563i 0.582254i
\(626\) 0 0
\(627\) 1.92069 + 4.63696i 0.0767050 + 0.185182i
\(628\) 0 0
\(629\) −4.46157 1.84804i −0.177895 0.0736864i
\(630\) 0 0
\(631\) −21.0543 + 21.0543i −0.838159 + 0.838159i −0.988616 0.150458i \(-0.951925\pi\)
0.150458 + 0.988616i \(0.451925\pi\)
\(632\) 0 0
\(633\) 17.0028 + 17.0028i 0.675799 + 0.675799i
\(634\) 0 0
\(635\) 9.23412 22.2931i 0.366445 0.884676i
\(636\) 0 0
\(637\) 26.0802 10.8028i 1.03334 0.428022i
\(638\) 0 0
\(639\) −42.1386 −1.66698
\(640\) 0 0
\(641\) −6.57429 −0.259669 −0.129835 0.991536i \(-0.541445\pi\)
−0.129835 + 0.991536i \(0.541445\pi\)
\(642\) 0 0
\(643\) 24.1050 9.98462i 0.950608 0.393755i 0.147149 0.989114i \(-0.452990\pi\)
0.803459 + 0.595360i \(0.202990\pi\)
\(644\) 0 0
\(645\) 4.81324 11.6202i 0.189521 0.457545i
\(646\) 0 0
\(647\) 19.1598 + 19.1598i 0.753250 + 0.753250i 0.975084 0.221835i \(-0.0712046\pi\)
−0.221835 + 0.975084i \(0.571205\pi\)
\(648\) 0 0
\(649\) 15.1255 15.1255i 0.593727 0.593727i
\(650\) 0 0
\(651\) −2.51119 1.04017i −0.0984212 0.0407674i
\(652\) 0 0
\(653\) 5.73339 + 13.8416i 0.224365 + 0.541665i 0.995474 0.0950389i \(-0.0302975\pi\)
−0.771109 + 0.636703i \(0.780298\pi\)
\(654\) 0 0
\(655\) 13.0429i 0.509629i
\(656\) 0 0
\(657\) 32.9624i 1.28599i
\(658\) 0 0
\(659\) 0.202554 + 0.489009i 0.00789039 + 0.0190491i 0.927776 0.373139i \(-0.121718\pi\)
−0.919885 + 0.392188i \(0.871718\pi\)
\(660\) 0 0
\(661\) −6.45241 2.67268i −0.250970 0.103955i 0.253652 0.967295i \(-0.418368\pi\)
−0.504622 + 0.863340i \(0.668368\pi\)
\(662\) 0 0
\(663\) −29.1216 + 29.1216i −1.13099 + 1.13099i
\(664\) 0 0
\(665\) 0.625581 + 0.625581i 0.0242590 + 0.0242590i
\(666\) 0 0
\(667\) −4.48723 + 10.8331i −0.173746 + 0.419461i
\(668\) 0 0
\(669\) 51.5411 21.3490i 1.99270 0.825402i
\(670\) 0 0
\(671\) 59.3196 2.29001
\(672\) 0 0
\(673\) −24.3285 −0.937793 −0.468897 0.883253i \(-0.655348\pi\)
−0.468897 + 0.883253i \(0.655348\pi\)
\(674\) 0 0
\(675\) 0.303631 0.125768i 0.0116868 0.00484081i
\(676\) 0 0
\(677\) −1.60737 + 3.88054i −0.0617763 + 0.149141i −0.951753 0.306864i \(-0.900720\pi\)
0.889977 + 0.456005i \(0.150720\pi\)
\(678\) 0 0
\(679\) −4.09607 4.09607i −0.157193 0.157193i
\(680\) 0 0
\(681\) 17.9589 17.9589i 0.688187 0.688187i
\(682\) 0 0
\(683\) −24.8133 10.2780i −0.949455 0.393277i −0.146429 0.989221i \(-0.546778\pi\)
−0.803026 + 0.595944i \(0.796778\pi\)
\(684\) 0 0
\(685\) −4.88118 11.7842i −0.186500 0.450251i
\(686\) 0 0
\(687\) 42.1019i 1.60629i
\(688\) 0 0
\(689\) 22.9585i 0.874650i
\(690\) 0 0
\(691\) −8.56885 20.6870i −0.325974 0.786972i −0.998883 0.0472463i \(-0.984955\pi\)
0.672909 0.739725i \(-0.265045\pi\)
\(692\) 0 0
\(693\) 10.7127 + 4.43736i 0.406943 + 0.168561i
\(694\) 0 0
\(695\) 16.6647 16.6647i 0.632128 0.632128i
\(696\) 0 0
\(697\) 6.03979 + 6.03979i 0.228774 + 0.228774i
\(698\) 0 0
\(699\) 13.9479 33.6732i 0.527558 1.27364i
\(700\) 0 0
\(701\) −28.1557 + 11.6625i −1.06343 + 0.440486i −0.844667 0.535293i \(-0.820201\pi\)
−0.218760 + 0.975779i \(0.570201\pi\)
\(702\) 0 0
\(703\) 0.679628 0.0256326
\(704\) 0 0
\(705\) −6.82843 −0.257173
\(706\) 0 0
\(707\) −7.03195 + 2.91273i −0.264464 + 0.109544i
\(708\) 0 0
\(709\) −12.4408 + 30.0346i −0.467223 + 1.12797i 0.498148 + 0.867092i \(0.334014\pi\)
−0.965370 + 0.260883i \(0.915986\pi\)
\(710\) 0 0
\(711\) 37.5471 + 37.5471i 1.40812 + 1.40812i
\(712\) 0 0
\(713\) −1.56394 + 1.56394i −0.0585699 + 0.0585699i
\(714\) 0 0
\(715\) −31.4998 13.0476i −1.17803 0.487954i
\(716\) 0 0
\(717\) 11.0187 + 26.6015i 0.411501 + 0.993450i
\(718\) 0 0
\(719\) 33.6333i 1.25431i −0.778894 0.627155i \(-0.784219\pi\)
0.778894 0.627155i \(-0.215781\pi\)
\(720\) 0 0
\(721\) 6.28867i 0.234202i
\(722\) 0 0
\(723\) 13.0533 + 31.5134i 0.485457 + 1.17200i
\(724\) 0 0
\(725\) 9.09984 + 3.76928i 0.337960 + 0.139988i
\(726\) 0 0
\(727\) −7.43334 + 7.43334i −0.275687 + 0.275687i −0.831385 0.555697i \(-0.812451\pi\)
0.555697 + 0.831385i \(0.312451\pi\)
\(728\) 0 0
\(729\) 20.1459 + 20.1459i 0.746145 + 0.746145i
\(730\) 0 0
\(731\) −3.81991 + 9.22207i −0.141284 + 0.341090i
\(732\) 0 0
\(733\) 0.328598 0.136110i 0.0121371 0.00502733i −0.376607 0.926373i \(-0.622909\pi\)
0.388744 + 0.921346i \(0.372909\pi\)
\(734\) 0 0
\(735\) −27.8714 −1.02805
\(736\) 0 0
\(737\) −14.7373 −0.542857
\(738\) 0 0
\(739\) 43.8857 18.1780i 1.61436 0.668690i 0.621008 0.783804i \(-0.286723\pi\)
0.993352 + 0.115114i \(0.0367234\pi\)
\(740\) 0 0
\(741\) 2.21803 5.35480i 0.0814814 0.196714i
\(742\) 0 0
\(743\) −30.3220 30.3220i −1.11240 1.11240i −0.992825 0.119580i \(-0.961845\pi\)
−0.119580 0.992825i \(-0.538155\pi\)
\(744\) 0 0
\(745\) 8.11529 8.11529i 0.297321 0.297321i
\(746\) 0 0
\(747\) −35.9603 14.8952i −1.31572 0.544988i
\(748\) 0 0
\(749\) 1.00430 + 2.42459i 0.0366963 + 0.0885927i
\(750\) 0 0
\(751\) 51.3686i 1.87447i −0.348701 0.937234i \(-0.613377\pi\)
0.348701 0.937234i \(-0.386623\pi\)
\(752\) 0 0
\(753\) 34.7248i 1.26544i
\(754\) 0 0
\(755\) −11.1504 26.9194i −0.405804 0.979697i
\(756\) 0 0
\(757\) −15.2644 6.32270i −0.554793 0.229803i 0.0876302 0.996153i \(-0.472071\pi\)
−0.642423 + 0.766350i \(0.722071\pi\)
\(758\) 0 0
\(759\) 13.1618 13.1618i 0.477741 0.477741i
\(760\) 0 0
\(761\) 26.6859 + 26.6859i 0.967362 + 0.967362i 0.999484 0.0321218i \(-0.0102264\pi\)
−0.0321218 + 0.999484i \(0.510226\pi\)
\(762\) 0 0
\(763\) −3.25531 + 7.85902i −0.117850 + 0.284516i
\(764\) 0 0
\(765\) 19.0429 7.88784i 0.688499 0.285185i
\(766\) 0 0
\(767\) −24.7021 −0.891943
\(768\) 0 0
\(769\) 44.0390 1.58809 0.794044 0.607861i \(-0.207972\pi\)
0.794044 + 0.607861i \(0.207972\pi\)
\(770\) 0 0
\(771\) −43.0796 + 17.8441i −1.55147 + 0.642641i
\(772\) 0 0
\(773\) 15.4001 37.1790i 0.553902 1.33724i −0.360625 0.932711i \(-0.617436\pi\)
0.914526 0.404526i \(-0.132564\pi\)
\(774\) 0 0
\(775\) 1.31371 + 1.31371i 0.0471898 + 0.0471898i
\(776\) 0 0
\(777\) 2.19027 2.19027i 0.0785754 0.0785754i
\(778\) 0 0
\(779\) −1.11058 0.460018i −0.0397908 0.0164819i
\(780\) 0 0
\(781\) 20.9012 + 50.4599i 0.747903 + 1.80560i
\(782\) 0 0
\(783\) 1.28724i 0.0460022i
\(784\) 0 0
\(785\) 2.44992i 0.0874413i
\(786\) 0 0
\(787\) −0.948632 2.29020i −0.0338151 0.0816368i 0.906070 0.423128i \(-0.139068\pi\)
−0.939885 + 0.341491i \(0.889068\pi\)
\(788\) 0 0
\(789\) 44.8240 + 18.5667i 1.59578 + 0.660992i
\(790\) 0 0
\(791\) −7.83196 + 7.83196i −0.278472 + 0.278472i
\(792\) 0 0
\(793\) −48.4388 48.4388i −1.72011 1.72011i
\(794\) 0 0
\(795\) −8.67452 + 20.9421i −0.307654 + 0.742741i
\(796\) 0 0
\(797\) 2.76562 1.14556i 0.0979632 0.0405777i −0.333164 0.942869i \(-0.608116\pi\)
0.431127 + 0.902291i \(0.358116\pi\)
\(798\) 0 0
\(799\) 5.41921 0.191718
\(800\) 0 0
\(801\) −23.7212 −0.838149
\(802\) 0 0
\(803\) 39.4717 16.3497i 1.39292 0.576968i
\(804\) 0 0
\(805\) 1.25559 3.03127i 0.0442539 0.106838i
\(806\) 0 0
\(807\) −23.0256 23.0256i −0.810541 0.810541i
\(808\) 0 0
\(809\) −7.12825 + 7.12825i −0.250616 + 0.250616i −0.821223 0.570607i \(-0.806708\pi\)
0.570607 + 0.821223i \(0.306708\pi\)
\(810\) 0 0
\(811\) −27.4750 11.3805i −0.964777 0.399624i −0.156012 0.987755i \(-0.549864\pi\)
−0.808765 + 0.588131i \(0.799864\pi\)
\(812\) 0 0
\(813\) −4.16751 10.0613i −0.146161 0.352864i
\(814\) 0 0
\(815\) 42.6435i 1.49374i
\(816\) 0 0
\(817\) 1.40479i 0.0491474i
\(818\) 0 0
\(819\) −5.12431 12.3712i −0.179058 0.432284i
\(820\) 0 0
\(821\) −34.1861 14.1603i −1.19310 0.494199i −0.304339 0.952564i \(-0.598435\pi\)
−0.888764 + 0.458364i \(0.848435\pi\)
\(822\) 0 0
\(823\) 27.3810 27.3810i 0.954440 0.954440i −0.0445659 0.999006i \(-0.514190\pi\)
0.999006 + 0.0445659i \(0.0141905\pi\)
\(824\) 0 0
\(825\) −11.0559 11.0559i −0.384916 0.384916i
\(826\) 0 0
\(827\) −7.98030 + 19.2661i −0.277502 + 0.669950i −0.999765 0.0216689i \(-0.993102\pi\)
0.722263 + 0.691619i \(0.243102\pi\)
\(828\) 0 0
\(829\) 3.59585 1.48945i 0.124889 0.0517307i −0.319364 0.947632i \(-0.603469\pi\)
0.444253 + 0.895901i \(0.353469\pi\)
\(830\) 0 0
\(831\) 61.5269 2.13434
\(832\) 0 0
\(833\) 22.1194 0.766391
\(834\) 0 0
\(835\) 26.2818 10.8863i 0.909518 0.376735i
\(836\) 0 0
\(837\) 0.0929169 0.224321i 0.00321168 0.00775368i
\(838\) 0 0
\(839\) 13.8461 + 13.8461i 0.478020 + 0.478020i 0.904498 0.426478i \(-0.140246\pi\)
−0.426478 + 0.904498i \(0.640246\pi\)
\(840\) 0 0
\(841\) 6.77318 6.77318i 0.233558 0.233558i
\(842\) 0 0
\(843\) −18.8050 7.78929i −0.647679 0.268277i
\(844\) 0 0
\(845\) 5.87515 + 14.1839i 0.202111 + 0.487940i
\(846\) 0 0
\(847\) 4.68274i 0.160901i
\(848\) 0 0
\(849\) 8.50750i 0.291977i
\(850\) 0 0
\(851\) −0.964543 2.32861i −0.0330641 0.0798239i
\(852\) 0 0
\(853\) −18.0597 7.48055i −0.618351 0.256129i 0.0514436 0.998676i \(-0.483618\pi\)
−0.669794 + 0.742547i \(0.733618\pi\)
\(854\) 0 0
\(855\) −2.05117 + 2.05117i −0.0701485 + 0.0701485i
\(856\) 0 0
\(857\) −6.35294 6.35294i −0.217012 0.217012i 0.590226 0.807238i \(-0.299039\pi\)
−0.807238 + 0.590226i \(0.799039\pi\)
\(858\) 0 0
\(859\) −9.72800 + 23.4855i −0.331915 + 0.801314i 0.666525 + 0.745483i \(0.267781\pi\)
−0.998440 + 0.0558315i \(0.982219\pi\)
\(860\) 0 0
\(861\) −5.06164 + 2.09660i −0.172500 + 0.0714520i
\(862\) 0 0
\(863\) −0.0884535 −0.00301099 −0.00150550 0.999999i \(-0.500479\pi\)
−0.00150550 + 0.999999i \(0.500479\pi\)
\(864\) 0 0
\(865\) −3.55008 −0.120706
\(866\) 0 0
\(867\) 8.92588 3.69722i 0.303139 0.125564i
\(868\) 0 0
\(869\) 26.3379 63.5854i 0.893453 2.15699i
\(870\) 0 0
\(871\) 12.0341 + 12.0341i 0.407761 + 0.407761i
\(872\) 0 0
\(873\) 13.4303 13.4303i 0.454547 0.454547i
\(874\) 0 0
\(875\) −10.5747 4.38018i −0.357490 0.148077i
\(876\) 0 0
\(877\) 4.24514 + 10.2487i 0.143348 + 0.346073i 0.979205 0.202875i \(-0.0650285\pi\)
−0.835857 + 0.548948i \(0.815029\pi\)
\(878\) 0 0
\(879\) 18.6702i 0.629729i
\(880\) 0 0
\(881\) 23.9859i 0.808105i −0.914736 0.404052i \(-0.867601\pi\)
0.914736 0.404052i \(-0.132399\pi\)
\(882\) 0 0
\(883\) 7.74892 + 18.7075i 0.260772 + 0.629559i 0.998987 0.0450067i \(-0.0143309\pi\)
−0.738215 + 0.674566i \(0.764331\pi\)
\(884\) 0 0
\(885\) 22.5326 + 9.33333i 0.757426 + 0.313736i
\(886\) 0 0
\(887\) −36.4494 + 36.4494i −1.22385 + 1.22385i −0.257600 + 0.966252i \(0.582932\pi\)
−0.966252 + 0.257600i \(0.917068\pi\)
\(888\) 0 0
\(889\) −8.68550 8.68550i −0.291302 0.291302i
\(890\) 0 0
\(891\) 13.3710 32.2804i 0.447944 1.08143i
\(892\) 0 0
\(893\) −0.704611 + 0.291859i −0.0235789 + 0.00976670i
\(894\) 0 0
\(895\) 9.07646 0.303392
\(896\) 0 0
\(897\) −21.4951 −0.717700
\(898\) 0 0
\(899\) 6.72293 2.78473i 0.224222 0.0928759i
\(900\) 0 0
\(901\) 6.88431 16.6202i 0.229350 0.553699i
\(902\) 0 0
\(903\) −4.52728 4.52728i −0.150658 0.150658i
\(904\) 0 0
\(905\) −2.65685 + 2.65685i −0.0883168 + 0.0883168i
\(906\) 0 0
\(907\) 38.2753 + 15.8541i 1.27091 + 0.526428i 0.913241 0.407421i \(-0.133572\pi\)
0.357669 + 0.933848i \(0.383572\pi\)
\(908\) 0 0
\(909\) −9.55032 23.0565i −0.316764 0.764737i
\(910\) 0 0
\(911\) 12.5214i 0.414851i 0.978251 + 0.207426i \(0.0665085\pi\)
−0.978251 + 0.207426i \(0.933492\pi\)
\(912\) 0 0
\(913\) 50.4497i 1.66964i
\(914\) 0 0
\(915\) 25.8827 + 62.4864i 0.855657 + 2.06574i
\(916\) 0 0
\(917\) −6.13401 2.54079i −0.202563 0.0839043i
\(918\) 0 0
\(919\) 1.19513 1.19513i 0.0394238 0.0394238i −0.687120 0.726544i \(-0.741125\pi\)
0.726544 + 0.687120i \(0.241125\pi\)
\(920\) 0 0
\(921\) 14.3330 + 14.3330i 0.472287 + 0.472287i
\(922\) 0 0
\(923\) 24.1369 58.2715i 0.794475 1.91803i
\(924\) 0 0
\(925\) −1.95604 + 0.810217i −0.0643141 + 0.0266398i
\(926\) 0 0
\(927\) −20.6194 −0.677231
\(928\) 0 0
\(929\) 45.1410 1.48103 0.740514 0.672041i \(-0.234582\pi\)
0.740514 + 0.672041i \(0.234582\pi\)
\(930\) 0 0
\(931\) −2.87599 + 1.19127i −0.0942566 + 0.0390424i
\(932\) 0 0
\(933\) −20.0961 + 48.5162i −0.657915 + 1.58835i
\(934\) 0 0
\(935\) −18.8910 18.8910i −0.617801 0.617801i
\(936\) 0 0
\(937\) 2.58002 2.58002i 0.0842857 0.0842857i −0.663707 0.747993i \(-0.731018\pi\)
0.747993 + 0.663707i \(0.231018\pi\)
\(938\) 0 0
\(939\) 59.0937 + 24.4774i 1.92845 + 0.798790i
\(940\) 0 0
\(941\) −2.24720 5.42523i −0.0732568 0.176857i 0.883009 0.469355i \(-0.155514\pi\)
−0.956266 + 0.292498i \(0.905514\pi\)
\(942\) 0 0
\(943\) 4.45807i 0.145175i
\(944\) 0 0
\(945\) 0.360189i 0.0117170i
\(946\) 0 0
\(947\) −17.5640 42.4032i −0.570753 1.37792i −0.900915 0.433996i \(-0.857103\pi\)
0.330162 0.943924i \(-0.392897\pi\)
\(948\) 0 0
\(949\) −45.5822 18.8808i −1.47966 0.612896i
\(950\) 0 0
\(951\) 17.9788 17.9788i 0.583003 0.583003i
\(952\) 0 0
\(953\) 14.8079 + 14.8079i 0.479673 + 0.479673i 0.905027 0.425354i \(-0.139850\pi\)
−0.425354 + 0.905027i \(0.639850\pi\)
\(954\) 0 0
\(955\) −13.7194 + 33.1216i −0.443949 + 1.07179i
\(956\) 0 0
\(957\) −56.5787 + 23.4357i −1.82893 + 0.757568i
\(958\) 0 0
\(959\) −6.49290 −0.209667
\(960\) 0 0
\(961\) −29.6274 −0.955723
\(962\) 0 0
\(963\) −7.94981 + 3.29292i −0.256179 + 0.106113i
\(964\) 0 0
\(965\) −12.7605 + 30.8066i −0.410775 + 0.991698i
\(966\) 0 0
\(967\) 24.8604 + 24.8604i 0.799455 + 0.799455i 0.983010 0.183554i \(-0.0587604\pi\)
−0.183554 + 0.983010i \(0.558760\pi\)
\(968\) 0 0
\(969\) 3.21137 3.21137i 0.103164 0.103164i
\(970\) 0 0
\(971\) 23.3388 + 9.66725i 0.748978 + 0.310237i 0.724324 0.689459i \(-0.242152\pi\)
0.0246533 + 0.999696i \(0.492152\pi\)
\(972\) 0 0
\(973\) −4.59099 11.0836i −0.147180 0.355325i
\(974\) 0 0
\(975\) 18.0559i 0.578251i
\(976\) 0 0
\(977\) 54.7057i 1.75019i −0.483952 0.875094i \(-0.660799\pi\)
0.483952 0.875094i \(-0.339201\pi\)
\(978\) 0 0
\(979\) 11.7660 + 28.4056i 0.376042 + 0.907846i
\(980\) 0 0
\(981\) −25.7684 10.6736i −0.822720 0.340782i
\(982\) 0 0
\(983\) −7.85315 + 7.85315i −0.250477 + 0.250477i −0.821166 0.570689i \(-0.806676\pi\)
0.570689 + 0.821166i \(0.306676\pi\)
\(984\) 0 0
\(985\) −0.295389 0.295389i −0.00941188 0.00941188i
\(986\) 0 0
\(987\) −1.33019 + 3.21137i −0.0423405 + 0.102219i
\(988\) 0 0
\(989\) −4.81324 + 1.99371i −0.153052 + 0.0633963i
\(990\) 0 0
\(991\) −52.4878 −1.66733 −0.833665 0.552270i \(-0.813762\pi\)
−0.833665 + 0.552270i \(0.813762\pi\)
\(992\) 0 0
\(993\) −20.2217 −0.641716
\(994\) 0 0
\(995\) −28.7272 + 11.8992i −0.910715 + 0.377230i
\(996\) 0 0
\(997\) −12.8431 + 31.0060i −0.406745 + 0.981970i 0.579243 + 0.815155i \(0.303348\pi\)
−0.985988 + 0.166815i \(0.946652\pi\)
\(998\) 0 0
\(999\) 0.195654 + 0.195654i 0.00619021 + 0.00619021i
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.g.d.97.2 8
4.3 odd 2 256.2.g.c.97.1 8
8.3 odd 2 128.2.g.b.49.2 8
8.5 even 2 32.2.g.b.21.2 8
16.3 odd 4 512.2.g.g.449.1 8
16.5 even 4 512.2.g.h.449.1 8
16.11 odd 4 512.2.g.f.449.2 8
16.13 even 4 512.2.g.e.449.2 8
24.5 odd 2 288.2.v.b.181.1 8
24.11 even 2 1152.2.v.b.433.1 8
32.3 odd 8 256.2.g.c.161.1 8
32.5 even 8 512.2.g.h.65.1 8
32.11 odd 8 512.2.g.g.65.1 8
32.13 even 8 32.2.g.b.29.2 yes 8
32.19 odd 8 128.2.g.b.81.2 8
32.21 even 8 512.2.g.e.65.2 8
32.27 odd 8 512.2.g.f.65.2 8
32.29 even 8 inner 256.2.g.d.161.2 8
40.13 odd 4 800.2.ba.d.149.1 8
40.29 even 2 800.2.y.b.501.1 8
40.37 odd 4 800.2.ba.c.149.2 8
64.3 odd 16 4096.2.a.q.1.7 8
64.29 even 16 4096.2.a.k.1.7 8
64.35 odd 16 4096.2.a.q.1.2 8
64.61 even 16 4096.2.a.k.1.2 8
96.77 odd 8 288.2.v.b.253.1 8
96.83 even 8 1152.2.v.b.721.1 8
160.13 odd 8 800.2.ba.c.349.2 8
160.77 odd 8 800.2.ba.d.349.1 8
160.109 even 8 800.2.y.b.701.1 8
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
32.2.g.b.21.2 8 8.5 even 2
32.2.g.b.29.2 yes 8 32.13 even 8
128.2.g.b.49.2 8 8.3 odd 2
128.2.g.b.81.2 8 32.19 odd 8
256.2.g.c.97.1 8 4.3 odd 2
256.2.g.c.161.1 8 32.3 odd 8
256.2.g.d.97.2 8 1.1 even 1 trivial
256.2.g.d.161.2 8 32.29 even 8 inner
288.2.v.b.181.1 8 24.5 odd 2
288.2.v.b.253.1 8 96.77 odd 8
512.2.g.e.65.2 8 32.21 even 8
512.2.g.e.449.2 8 16.13 even 4
512.2.g.f.65.2 8 32.27 odd 8
512.2.g.f.449.2 8 16.11 odd 4
512.2.g.g.65.1 8 32.11 odd 8
512.2.g.g.449.1 8 16.3 odd 4
512.2.g.h.65.1 8 32.5 even 8
512.2.g.h.449.1 8 16.5 even 4
800.2.y.b.501.1 8 40.29 even 2
800.2.y.b.701.1 8 160.109 even 8
800.2.ba.c.149.2 8 40.37 odd 4
800.2.ba.c.349.2 8 160.13 odd 8
800.2.ba.d.149.1 8 40.13 odd 4
800.2.ba.d.349.1 8 160.77 odd 8
1152.2.v.b.433.1 8 24.11 even 2
1152.2.v.b.721.1 8 96.83 even 8
4096.2.a.k.1.2 8 64.61 even 16
4096.2.a.k.1.7 8 64.29 even 16
4096.2.a.q.1.2 8 64.35 odd 16
4096.2.a.q.1.7 8 64.3 odd 16