Properties

Label 200.2.m.c.161.3
Level $200$
Weight $2$
Character 200.161
Analytic conductor $1.597$
Analytic rank $0$
Dimension $16$
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [200,2,Mod(41,200)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(200, base_ring=CyclotomicField(10))
 
chi = DirichletCharacter(H, H._module([0, 0, 2]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("200.41");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 200 = 2^{3} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 200.m (of order \(5\), degree \(4\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(1.59700804043\)
Analytic rank: \(0\)
Dimension: \(16\)
Relative dimension: \(4\) over \(\Q(\zeta_{5})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{16} - x^{15} + 12 x^{14} - 18 x^{13} + 100 x^{12} + 23 x^{11} + 567 x^{10} + 556 x^{9} + 3841 x^{8} + \cdots + 6400 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{9}]\)
Coefficient ring index: \( 5 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label 161.3
Root \(0.372462 - 1.14632i\) of defining polynomial
Character \(\chi\) \(=\) 200.161
Dual form 200.2.m.c.41.3

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.372462 - 1.14632i) q^{3} +(0.388572 + 2.20205i) q^{5} +1.59935 q^{7} +(1.25173 + 0.909432i) q^{9} +O(q^{10})\) \(q+(0.372462 - 1.14632i) q^{3} +(0.388572 + 2.20205i) q^{5} +1.59935 q^{7} +(1.25173 + 0.909432i) q^{9} +(2.86042 - 2.07822i) q^{11} +(-2.38530 - 1.73302i) q^{13} +(2.66898 + 0.374751i) q^{15} +(-0.357732 - 1.10099i) q^{17} +(-0.866689 - 2.66739i) q^{19} +(0.595698 - 1.83337i) q^{21} +(-2.55625 + 1.85723i) q^{23} +(-4.69802 + 1.71131i) q^{25} +(4.43408 - 3.22155i) q^{27} +(-3.04006 + 9.35636i) q^{29} +(0.572270 + 1.76126i) q^{31} +(-1.31690 - 4.05302i) q^{33} +(0.621463 + 3.52185i) q^{35} +(-3.63802 - 2.64318i) q^{37} +(-2.87503 + 2.08883i) q^{39} +(6.49601 + 4.71963i) q^{41} -11.5345 q^{43} +(-1.51623 + 3.10974i) q^{45} +(0.728491 - 2.24207i) q^{47} -4.44208 q^{49} -1.39533 q^{51} +(2.15111 - 6.62042i) q^{53} +(5.68781 + 5.49124i) q^{55} -3.38050 q^{57} +(-11.1170 - 8.07696i) q^{59} +(1.96004 - 1.42405i) q^{61} +(2.00195 + 1.45450i) q^{63} +(2.88933 - 5.92594i) q^{65} +(-4.27388 - 13.1537i) q^{67} +(1.17687 + 3.62203i) q^{69} +(-1.07380 + 3.30482i) q^{71} +(2.63248 - 1.91261i) q^{73} +(0.211872 + 6.02284i) q^{75} +(4.57481 - 3.32380i) q^{77} +(-3.06650 + 9.43770i) q^{79} +(-0.607051 - 1.86831i) q^{81} +(3.97495 + 12.2336i) q^{83} +(2.28542 - 1.21556i) q^{85} +(9.59308 + 6.96978i) q^{87} +(8.85248 - 6.43171i) q^{89} +(-3.81493 - 2.77171i) q^{91} +2.23212 q^{93} +(5.53696 - 2.94497i) q^{95} +(-2.21345 + 6.81231i) q^{97} +5.47046 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16 q + q^{3} - q^{5} - 6 q^{7} - 11 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 16 q + q^{3} - q^{5} - 6 q^{7} - 11 q^{9} - 10 q^{11} + q^{13} - 10 q^{15} - 4 q^{17} - 3 q^{21} + 11 q^{23} + 9 q^{25} + 13 q^{27} + 5 q^{29} - 9 q^{31} + 16 q^{33} + 24 q^{35} + 30 q^{37} + 14 q^{39} - 2 q^{41} - 42 q^{43} - 77 q^{45} - 16 q^{47} + 18 q^{49} + 100 q^{51} + 11 q^{53} - 24 q^{55} - 64 q^{57} - 53 q^{59} + 4 q^{61} - 38 q^{63} + 37 q^{65} - 14 q^{67} - 7 q^{69} - 6 q^{71} - 24 q^{73} - 15 q^{75} + 23 q^{77} - 22 q^{79} - 6 q^{81} + 33 q^{83} + 8 q^{85} + 37 q^{87} + 20 q^{89} - 27 q^{91} + 40 q^{93} - 24 q^{95} + 11 q^{97} + 122 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/200\mathbb{Z}\right)^\times\).

\(n\) \(101\) \(151\) \(177\)
\(\chi(n)\) \(1\) \(1\) \(e\left(\frac{4}{5}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) 0.372462 1.14632i 0.215041 0.661829i −0.784109 0.620623i \(-0.786880\pi\)
0.999151 0.0412064i \(-0.0131201\pi\)
\(4\) 0 0
\(5\) 0.388572 + 2.20205i 0.173775 + 0.984785i
\(6\) 0 0
\(7\) 1.59935 0.604498 0.302249 0.953229i \(-0.402263\pi\)
0.302249 + 0.953229i \(0.402263\pi\)
\(8\) 0 0
\(9\) 1.25173 + 0.909432i 0.417242 + 0.303144i
\(10\) 0 0
\(11\) 2.86042 2.07822i 0.862449 0.626606i −0.0661014 0.997813i \(-0.521056\pi\)
0.928550 + 0.371207i \(0.121056\pi\)
\(12\) 0 0
\(13\) −2.38530 1.73302i −0.661563 0.480654i 0.205627 0.978630i \(-0.434076\pi\)
−0.867190 + 0.497977i \(0.834076\pi\)
\(14\) 0 0
\(15\) 2.66898 + 0.374751i 0.689128 + 0.0967604i
\(16\) 0 0
\(17\) −0.357732 1.10099i −0.0867628 0.267028i 0.898257 0.439471i \(-0.144834\pi\)
−0.985020 + 0.172443i \(0.944834\pi\)
\(18\) 0 0
\(19\) −0.866689 2.66739i −0.198832 0.611942i −0.999910 0.0133828i \(-0.995740\pi\)
0.801078 0.598559i \(-0.204260\pi\)
\(20\) 0 0
\(21\) 0.595698 1.83337i 0.129992 0.400074i
\(22\) 0 0
\(23\) −2.55625 + 1.85723i −0.533015 + 0.387258i −0.821484 0.570231i \(-0.806854\pi\)
0.288469 + 0.957489i \(0.406854\pi\)
\(24\) 0 0
\(25\) −4.69802 + 1.71131i −0.939605 + 0.342262i
\(26\) 0 0
\(27\) 4.43408 3.22155i 0.853339 0.619987i
\(28\) 0 0
\(29\) −3.04006 + 9.35636i −0.564526 + 1.73743i 0.104830 + 0.994490i \(0.466570\pi\)
−0.669356 + 0.742942i \(0.733430\pi\)
\(30\) 0 0
\(31\) 0.572270 + 1.76126i 0.102783 + 0.316332i 0.989204 0.146547i \(-0.0468161\pi\)
−0.886421 + 0.462880i \(0.846816\pi\)
\(32\) 0 0
\(33\) −1.31690 4.05302i −0.229244 0.705540i
\(34\) 0 0
\(35\) 0.621463 + 3.52185i 0.105046 + 0.595301i
\(36\) 0 0
\(37\) −3.63802 2.64318i −0.598087 0.434535i 0.247112 0.968987i \(-0.420518\pi\)
−0.845199 + 0.534451i \(0.820518\pi\)
\(38\) 0 0
\(39\) −2.87503 + 2.08883i −0.460374 + 0.334481i
\(40\) 0 0
\(41\) 6.49601 + 4.71963i 1.01451 + 0.737082i 0.965149 0.261699i \(-0.0842829\pi\)
0.0493568 + 0.998781i \(0.484283\pi\)
\(42\) 0 0
\(43\) −11.5345 −1.75899 −0.879496 0.475906i \(-0.842120\pi\)
−0.879496 + 0.475906i \(0.842120\pi\)
\(44\) 0 0
\(45\) −1.51623 + 3.10974i −0.226026 + 0.463573i
\(46\) 0 0
\(47\) 0.728491 2.24207i 0.106261 0.327039i −0.883763 0.467935i \(-0.844998\pi\)
0.990024 + 0.140896i \(0.0449982\pi\)
\(48\) 0 0
\(49\) −4.44208 −0.634583
\(50\) 0 0
\(51\) −1.39533 −0.195385
\(52\) 0 0
\(53\) 2.15111 6.62042i 0.295477 0.909385i −0.687584 0.726105i \(-0.741329\pi\)
0.983061 0.183280i \(-0.0586714\pi\)
\(54\) 0 0
\(55\) 5.68781 + 5.49124i 0.766944 + 0.740439i
\(56\) 0 0
\(57\) −3.38050 −0.447758
\(58\) 0 0
\(59\) −11.1170 8.07696i −1.44731 1.05153i −0.986451 0.164055i \(-0.947543\pi\)
−0.460856 0.887475i \(-0.652457\pi\)
\(60\) 0 0
\(61\) 1.96004 1.42405i 0.250958 0.182331i −0.455194 0.890393i \(-0.650430\pi\)
0.706151 + 0.708061i \(0.250430\pi\)
\(62\) 0 0
\(63\) 2.00195 + 1.45450i 0.252222 + 0.183250i
\(64\) 0 0
\(65\) 2.88933 5.92594i 0.358378 0.735023i
\(66\) 0 0
\(67\) −4.27388 13.1537i −0.522138 1.60698i −0.769907 0.638156i \(-0.779697\pi\)
0.247769 0.968819i \(-0.420303\pi\)
\(68\) 0 0
\(69\) 1.17687 + 3.62203i 0.141678 + 0.436042i
\(70\) 0 0
\(71\) −1.07380 + 3.30482i −0.127437 + 0.392210i −0.994337 0.106271i \(-0.966109\pi\)
0.866900 + 0.498482i \(0.166109\pi\)
\(72\) 0 0
\(73\) 2.63248 1.91261i 0.308108 0.223854i −0.422976 0.906141i \(-0.639015\pi\)
0.731084 + 0.682287i \(0.239015\pi\)
\(74\) 0 0
\(75\) 0.211872 + 6.02284i 0.0244649 + 0.695458i
\(76\) 0 0
\(77\) 4.57481 3.32380i 0.521348 0.378782i
\(78\) 0 0
\(79\) −3.06650 + 9.43770i −0.345008 + 1.06182i 0.616572 + 0.787299i \(0.288521\pi\)
−0.961580 + 0.274526i \(0.911479\pi\)
\(80\) 0 0
\(81\) −0.607051 1.86831i −0.0674501 0.207590i
\(82\) 0 0
\(83\) 3.97495 + 12.2336i 0.436307 + 1.34282i 0.891741 + 0.452546i \(0.149484\pi\)
−0.455434 + 0.890270i \(0.650516\pi\)
\(84\) 0 0
\(85\) 2.28542 1.21556i 0.247888 0.131845i
\(86\) 0 0
\(87\) 9.59308 + 6.96978i 1.02849 + 0.747239i
\(88\) 0 0
\(89\) 8.85248 6.43171i 0.938361 0.681759i −0.00966436 0.999953i \(-0.503076\pi\)
0.948026 + 0.318194i \(0.103076\pi\)
\(90\) 0 0
\(91\) −3.81493 2.77171i −0.399913 0.290554i
\(92\) 0 0
\(93\) 2.23212 0.231461
\(94\) 0 0
\(95\) 5.53696 2.94497i 0.568080 0.302147i
\(96\) 0 0
\(97\) −2.21345 + 6.81231i −0.224742 + 0.691685i 0.773576 + 0.633704i \(0.218466\pi\)
−0.998318 + 0.0579809i \(0.981534\pi\)
\(98\) 0 0
\(99\) 5.47046 0.549802
\(100\) 0 0
\(101\) 18.4139 1.83225 0.916124 0.400896i \(-0.131301\pi\)
0.916124 + 0.400896i \(0.131301\pi\)
\(102\) 0 0
\(103\) 0.579455 1.78338i 0.0570954 0.175722i −0.918442 0.395556i \(-0.870552\pi\)
0.975537 + 0.219835i \(0.0705518\pi\)
\(104\) 0 0
\(105\) 4.26864 + 0.599359i 0.416577 + 0.0584914i
\(106\) 0 0
\(107\) −6.86223 −0.663397 −0.331699 0.943385i \(-0.607622\pi\)
−0.331699 + 0.943385i \(0.607622\pi\)
\(108\) 0 0
\(109\) −2.56393 1.86280i −0.245580 0.178424i 0.458186 0.888857i \(-0.348499\pi\)
−0.703766 + 0.710432i \(0.748499\pi\)
\(110\) 0 0
\(111\) −4.38496 + 3.18586i −0.416202 + 0.302388i
\(112\) 0 0
\(113\) 0.108692 + 0.0789696i 0.0102249 + 0.00742883i 0.592886 0.805286i \(-0.297988\pi\)
−0.582661 + 0.812715i \(0.697988\pi\)
\(114\) 0 0
\(115\) −5.08299 4.90732i −0.473991 0.457610i
\(116\) 0 0
\(117\) −1.40968 4.33854i −0.130325 0.401098i
\(118\) 0 0
\(119\) −0.572139 1.76086i −0.0524479 0.161418i
\(120\) 0 0
\(121\) 0.463826 1.42751i 0.0421660 0.129774i
\(122\) 0 0
\(123\) 7.82973 5.68863i 0.705983 0.512927i
\(124\) 0 0
\(125\) −5.59390 9.68030i −0.500334 0.865833i
\(126\) 0 0
\(127\) 9.49674 6.89978i 0.842699 0.612257i −0.0804241 0.996761i \(-0.525627\pi\)
0.923123 + 0.384504i \(0.125627\pi\)
\(128\) 0 0
\(129\) −4.29616 + 13.2222i −0.378256 + 1.16415i
\(130\) 0 0
\(131\) 0.664422 + 2.04488i 0.0580508 + 0.178662i 0.975877 0.218320i \(-0.0700576\pi\)
−0.917826 + 0.396982i \(0.870058\pi\)
\(132\) 0 0
\(133\) −1.38614 4.26610i −0.120194 0.369918i
\(134\) 0 0
\(135\) 8.81696 + 8.51225i 0.758843 + 0.732618i
\(136\) 0 0
\(137\) 12.7949 + 9.29605i 1.09314 + 0.794215i 0.979927 0.199355i \(-0.0638847\pi\)
0.113216 + 0.993570i \(0.463885\pi\)
\(138\) 0 0
\(139\) 16.0382 11.6525i 1.36035 0.988349i 0.361924 0.932208i \(-0.382120\pi\)
0.998423 0.0561417i \(-0.0178799\pi\)
\(140\) 0 0
\(141\) −2.29879 1.67017i −0.193593 0.140654i
\(142\) 0 0
\(143\) −10.4245 −0.871744
\(144\) 0 0
\(145\) −21.7844 3.05875i −1.80910 0.254015i
\(146\) 0 0
\(147\) −1.65451 + 5.09205i −0.136461 + 0.419985i
\(148\) 0 0
\(149\) 9.45736 0.774777 0.387388 0.921917i \(-0.373377\pi\)
0.387388 + 0.921917i \(0.373377\pi\)
\(150\) 0 0
\(151\) −19.5082 −1.58755 −0.793777 0.608209i \(-0.791888\pi\)
−0.793777 + 0.608209i \(0.791888\pi\)
\(152\) 0 0
\(153\) 0.553490 1.70347i 0.0447470 0.137717i
\(154\) 0 0
\(155\) −3.65602 + 1.94454i −0.293659 + 0.156189i
\(156\) 0 0
\(157\) −14.9261 −1.19123 −0.595616 0.803270i \(-0.703092\pi\)
−0.595616 + 0.803270i \(0.703092\pi\)
\(158\) 0 0
\(159\) −6.78793 4.93172i −0.538317 0.391111i
\(160\) 0 0
\(161\) −4.08834 + 2.97035i −0.322207 + 0.234097i
\(162\) 0 0
\(163\) 8.73705 + 6.34784i 0.684339 + 0.497201i 0.874794 0.484495i \(-0.160996\pi\)
−0.190456 + 0.981696i \(0.560996\pi\)
\(164\) 0 0
\(165\) 8.41322 4.47478i 0.654968 0.348361i
\(166\) 0 0
\(167\) 3.99854 + 12.3062i 0.309416 + 0.952285i 0.977992 + 0.208642i \(0.0669042\pi\)
−0.668576 + 0.743644i \(0.733096\pi\)
\(168\) 0 0
\(169\) −1.33093 4.09619i −0.102379 0.315091i
\(170\) 0 0
\(171\) 1.34096 4.12704i 0.102546 0.315603i
\(172\) 0 0
\(173\) −17.5346 + 12.7396i −1.33313 + 0.968575i −0.333463 + 0.942763i \(0.608217\pi\)
−0.999667 + 0.0258121i \(0.991783\pi\)
\(174\) 0 0
\(175\) −7.51379 + 2.73698i −0.567989 + 0.206896i
\(176\) 0 0
\(177\) −13.3994 + 9.73527i −1.00716 + 0.731747i
\(178\) 0 0
\(179\) 1.49437 4.59920i 0.111694 0.343760i −0.879549 0.475809i \(-0.842155\pi\)
0.991243 + 0.132048i \(0.0421554\pi\)
\(180\) 0 0
\(181\) −0.992136 3.05348i −0.0737449 0.226963i 0.907389 0.420291i \(-0.138072\pi\)
−0.981134 + 0.193328i \(0.938072\pi\)
\(182\) 0 0
\(183\) −0.902381 2.77724i −0.0667059 0.205300i
\(184\) 0 0
\(185\) 4.40677 9.03816i 0.323992 0.664498i
\(186\) 0 0
\(187\) −3.31135 2.40584i −0.242150 0.175932i
\(188\) 0 0
\(189\) 7.09165 5.15239i 0.515842 0.374781i
\(190\) 0 0
\(191\) −11.0932 8.05971i −0.802679 0.583180i 0.109020 0.994040i \(-0.465229\pi\)
−0.911699 + 0.410859i \(0.865229\pi\)
\(192\) 0 0
\(193\) 19.7184 1.41936 0.709682 0.704522i \(-0.248838\pi\)
0.709682 + 0.704522i \(0.248838\pi\)
\(194\) 0 0
\(195\) −5.71687 5.51930i −0.409394 0.395245i
\(196\) 0 0
\(197\) −6.67522 + 20.5442i −0.475589 + 1.46371i 0.369572 + 0.929202i \(0.379504\pi\)
−0.845161 + 0.534512i \(0.820496\pi\)
\(198\) 0 0
\(199\) 24.2188 1.71683 0.858413 0.512960i \(-0.171451\pi\)
0.858413 + 0.512960i \(0.171451\pi\)
\(200\) 0 0
\(201\) −16.6702 −1.17582
\(202\) 0 0
\(203\) −4.86213 + 14.9641i −0.341255 + 1.05027i
\(204\) 0 0
\(205\) −7.86867 + 16.1384i −0.549572 + 1.12716i
\(206\) 0 0
\(207\) −4.88875 −0.339791
\(208\) 0 0
\(209\) −8.02251 5.82870i −0.554929 0.403179i
\(210\) 0 0
\(211\) −1.68226 + 1.22223i −0.115812 + 0.0841421i −0.644184 0.764871i \(-0.722803\pi\)
0.528372 + 0.849013i \(0.322803\pi\)
\(212\) 0 0
\(213\) 3.38844 + 2.46185i 0.232172 + 0.168683i
\(214\) 0 0
\(215\) −4.48198 25.3995i −0.305668 1.73223i
\(216\) 0 0
\(217\) 0.915260 + 2.81688i 0.0621319 + 0.191222i
\(218\) 0 0
\(219\) −1.21196 3.73004i −0.0818970 0.252053i
\(220\) 0 0
\(221\) −1.05473 + 3.24614i −0.0709491 + 0.218359i
\(222\) 0 0
\(223\) 15.8396 11.5081i 1.06070 0.770642i 0.0864809 0.996254i \(-0.472438\pi\)
0.974217 + 0.225611i \(0.0724378\pi\)
\(224\) 0 0
\(225\) −7.43696 2.13044i −0.495797 0.142030i
\(226\) 0 0
\(227\) −5.30621 + 3.85518i −0.352185 + 0.255878i −0.749785 0.661681i \(-0.769843\pi\)
0.397600 + 0.917559i \(0.369843\pi\)
\(228\) 0 0
\(229\) −4.68231 + 14.4107i −0.309416 + 0.952285i 0.668576 + 0.743644i \(0.266904\pi\)
−0.977992 + 0.208641i \(0.933096\pi\)
\(230\) 0 0
\(231\) −2.10619 6.48219i −0.138577 0.426497i
\(232\) 0 0
\(233\) −0.532402 1.63857i −0.0348788 0.107346i 0.932101 0.362198i \(-0.117973\pi\)
−0.966980 + 0.254851i \(0.917973\pi\)
\(234\) 0 0
\(235\) 5.22021 + 0.732968i 0.340529 + 0.0478136i
\(236\) 0 0
\(237\) 9.67649 + 7.03038i 0.628556 + 0.456672i
\(238\) 0 0
\(239\) −6.55820 + 4.76481i −0.424215 + 0.308210i −0.779331 0.626612i \(-0.784441\pi\)
0.355117 + 0.934822i \(0.384441\pi\)
\(240\) 0 0
\(241\) −3.19595 2.32199i −0.205869 0.149573i 0.480074 0.877228i \(-0.340610\pi\)
−0.685943 + 0.727656i \(0.740610\pi\)
\(242\) 0 0
\(243\) 14.0747 0.902892
\(244\) 0 0
\(245\) −1.72607 9.78166i −0.110274 0.624928i
\(246\) 0 0
\(247\) −2.55534 + 7.86452i −0.162592 + 0.500408i
\(248\) 0 0
\(249\) 15.5042 0.982539
\(250\) 0 0
\(251\) 21.2264 1.33980 0.669899 0.742452i \(-0.266337\pi\)
0.669899 + 0.742452i \(0.266337\pi\)
\(252\) 0 0
\(253\) −3.45223 + 10.6249i −0.217040 + 0.667981i
\(254\) 0 0
\(255\) −0.542185 3.07257i −0.0339529 0.192412i
\(256\) 0 0
\(257\) 0.186373 0.0116256 0.00581282 0.999983i \(-0.498150\pi\)
0.00581282 + 0.999983i \(0.498150\pi\)
\(258\) 0 0
\(259\) −5.81847 4.22737i −0.361542 0.262676i
\(260\) 0 0
\(261\) −12.3143 + 8.94686i −0.762236 + 0.553797i
\(262\) 0 0
\(263\) −8.03986 5.84130i −0.495759 0.360190i 0.311636 0.950202i \(-0.399123\pi\)
−0.807395 + 0.590012i \(0.799123\pi\)
\(264\) 0 0
\(265\) 15.4143 + 2.16432i 0.946895 + 0.132953i
\(266\) 0 0
\(267\) −4.07558 12.5434i −0.249422 0.767641i
\(268\) 0 0
\(269\) −8.72173 26.8427i −0.531773 1.63663i −0.750520 0.660848i \(-0.770197\pi\)
0.218747 0.975782i \(-0.429803\pi\)
\(270\) 0 0
\(271\) −1.30854 + 4.02727i −0.0794881 + 0.244639i −0.982902 0.184131i \(-0.941053\pi\)
0.903414 + 0.428770i \(0.141053\pi\)
\(272\) 0 0
\(273\) −4.59819 + 3.34078i −0.278295 + 0.202193i
\(274\) 0 0
\(275\) −9.88185 + 14.6586i −0.595898 + 0.883945i
\(276\) 0 0
\(277\) 15.0058 10.9024i 0.901614 0.655061i −0.0372663 0.999305i \(-0.511865\pi\)
0.938880 + 0.344245i \(0.111865\pi\)
\(278\) 0 0
\(279\) −0.885426 + 2.72506i −0.0530091 + 0.163145i
\(280\) 0 0
\(281\) −1.02897 3.16685i −0.0613834 0.188919i 0.915662 0.401948i \(-0.131667\pi\)
−0.977046 + 0.213030i \(0.931667\pi\)
\(282\) 0 0
\(283\) 6.72318 + 20.6918i 0.399651 + 1.23000i 0.925279 + 0.379286i \(0.123830\pi\)
−0.525628 + 0.850714i \(0.676170\pi\)
\(284\) 0 0
\(285\) −1.31357 7.44402i −0.0778091 0.440946i
\(286\) 0 0
\(287\) 10.3894 + 7.54834i 0.613267 + 0.445564i
\(288\) 0 0
\(289\) 12.6691 9.20463i 0.745241 0.541449i
\(290\) 0 0
\(291\) 6.98466 + 5.07466i 0.409448 + 0.297482i
\(292\) 0 0
\(293\) 22.9801 1.34251 0.671257 0.741225i \(-0.265755\pi\)
0.671257 + 0.741225i \(0.265755\pi\)
\(294\) 0 0
\(295\) 13.4661 27.6186i 0.784026 1.60802i
\(296\) 0 0
\(297\) 5.98825 18.4300i 0.347474 1.06941i
\(298\) 0 0
\(299\) 9.31604 0.538760
\(300\) 0 0
\(301\) −18.4477 −1.06331
\(302\) 0 0
\(303\) 6.85847 21.1082i 0.394009 1.21263i
\(304\) 0 0
\(305\) 3.89745 + 3.76276i 0.223167 + 0.215455i
\(306\) 0 0
\(307\) 0.166588 0.00950768 0.00475384 0.999989i \(-0.498487\pi\)
0.00475384 + 0.999989i \(0.498487\pi\)
\(308\) 0 0
\(309\) −1.82850 1.32848i −0.104020 0.0755748i
\(310\) 0 0
\(311\) 6.42513 4.66813i 0.364335 0.264705i −0.390523 0.920593i \(-0.627706\pi\)
0.754858 + 0.655888i \(0.227706\pi\)
\(312\) 0 0
\(313\) 9.65596 + 7.01546i 0.545787 + 0.396537i 0.826230 0.563333i \(-0.190481\pi\)
−0.280443 + 0.959871i \(0.590481\pi\)
\(314\) 0 0
\(315\) −2.42498 + 4.97356i −0.136632 + 0.280229i
\(316\) 0 0
\(317\) −3.09875 9.53696i −0.174043 0.535649i 0.825546 0.564335i \(-0.190868\pi\)
−0.999588 + 0.0286866i \(0.990868\pi\)
\(318\) 0 0
\(319\) 10.7487 + 33.0810i 0.601810 + 1.85218i
\(320\) 0 0
\(321\) −2.55592 + 7.86633i −0.142658 + 0.439056i
\(322\) 0 0
\(323\) −2.62672 + 1.90842i −0.146155 + 0.106188i
\(324\) 0 0
\(325\) 14.1719 + 4.05979i 0.786117 + 0.225197i
\(326\) 0 0
\(327\) −3.09034 + 2.24526i −0.170896 + 0.124163i
\(328\) 0 0
\(329\) 1.16511 3.58585i 0.0642348 0.197694i
\(330\) 0 0
\(331\) 10.0080 + 30.8015i 0.550090 + 1.69300i 0.708570 + 0.705640i \(0.249340\pi\)
−0.158481 + 0.987362i \(0.550660\pi\)
\(332\) 0 0
\(333\) −2.15001 6.61707i −0.117820 0.362613i
\(334\) 0 0
\(335\) 27.3043 14.5224i 1.49179 0.793446i
\(336\) 0 0
\(337\) −8.21206 5.96641i −0.447339 0.325011i 0.341205 0.939989i \(-0.389165\pi\)
−0.788544 + 0.614978i \(0.789165\pi\)
\(338\) 0 0
\(339\) 0.131008 0.0951831i 0.00711540 0.00516964i
\(340\) 0 0
\(341\) 5.29722 + 3.84865i 0.286860 + 0.208416i
\(342\) 0 0
\(343\) −18.2999 −0.988101
\(344\) 0 0
\(345\) −7.51859 + 3.99894i −0.404787 + 0.215296i
\(346\) 0 0
\(347\) −10.3220 + 31.7678i −0.554114 + 1.70539i 0.144158 + 0.989555i \(0.453953\pi\)
−0.698272 + 0.715832i \(0.746047\pi\)
\(348\) 0 0
\(349\) 5.59021 0.299237 0.149619 0.988744i \(-0.452195\pi\)
0.149619 + 0.988744i \(0.452195\pi\)
\(350\) 0 0
\(351\) −16.1596 −0.862537
\(352\) 0 0
\(353\) −7.71318 + 23.7387i −0.410531 + 1.26348i 0.505656 + 0.862735i \(0.331250\pi\)
−0.916188 + 0.400750i \(0.868750\pi\)
\(354\) 0 0
\(355\) −7.69463 1.08040i −0.408388 0.0573417i
\(356\) 0 0
\(357\) −2.23161 −0.118110
\(358\) 0 0
\(359\) −29.9147 21.7343i −1.57884 1.14709i −0.918009 0.396558i \(-0.870204\pi\)
−0.660830 0.750536i \(-0.729796\pi\)
\(360\) 0 0
\(361\) 9.00748 6.54432i 0.474078 0.344438i
\(362\) 0 0
\(363\) −1.46363 1.06339i −0.0768206 0.0558134i
\(364\) 0 0
\(365\) 5.23456 + 5.05366i 0.273990 + 0.264521i
\(366\) 0 0
\(367\) 1.07356 + 3.30408i 0.0560394 + 0.172472i 0.975159 0.221508i \(-0.0710980\pi\)
−0.919119 + 0.393980i \(0.871098\pi\)
\(368\) 0 0
\(369\) 3.83904 + 11.8154i 0.199853 + 0.615083i
\(370\) 0 0
\(371\) 3.44037 10.5884i 0.178615 0.549721i
\(372\) 0 0
\(373\) 11.6934 8.49575i 0.605461 0.439893i −0.242352 0.970188i \(-0.577919\pi\)
0.847813 + 0.530295i \(0.177919\pi\)
\(374\) 0 0
\(375\) −13.1803 + 2.80686i −0.680626 + 0.144946i
\(376\) 0 0
\(377\) 23.4662 17.0492i 1.20857 0.878079i
\(378\) 0 0
\(379\) −1.37239 + 4.22379i −0.0704950 + 0.216961i −0.980097 0.198519i \(-0.936387\pi\)
0.909602 + 0.415481i \(0.136387\pi\)
\(380\) 0 0
\(381\) −4.37219 13.4562i −0.223994 0.689383i
\(382\) 0 0
\(383\) −0.726319 2.23538i −0.0371132 0.114223i 0.930784 0.365571i \(-0.119126\pi\)
−0.967897 + 0.251348i \(0.919126\pi\)
\(384\) 0 0
\(385\) 9.09680 + 8.78242i 0.463616 + 0.447593i
\(386\) 0 0
\(387\) −14.4380 10.4898i −0.733926 0.533228i
\(388\) 0 0
\(389\) −3.70812 + 2.69411i −0.188009 + 0.136597i −0.677808 0.735239i \(-0.737070\pi\)
0.489799 + 0.871835i \(0.337070\pi\)
\(390\) 0 0
\(391\) 2.95923 + 2.15001i 0.149655 + 0.108731i
\(392\) 0 0
\(393\) 2.59156 0.130727
\(394\) 0 0
\(395\) −21.9738 3.08534i −1.10562 0.155240i
\(396\) 0 0
\(397\) −1.21194 + 3.72998i −0.0608258 + 0.187202i −0.976852 0.213916i \(-0.931378\pi\)
0.916026 + 0.401118i \(0.131378\pi\)
\(398\) 0 0
\(399\) −5.40661 −0.270669
\(400\) 0 0
\(401\) 4.06725 0.203109 0.101554 0.994830i \(-0.467618\pi\)
0.101554 + 0.994830i \(0.467618\pi\)
\(402\) 0 0
\(403\) 1.68727 5.19290i 0.0840491 0.258677i
\(404\) 0 0
\(405\) 3.87823 2.06273i 0.192711 0.102498i
\(406\) 0 0
\(407\) −15.8993 −0.788101
\(408\) 0 0
\(409\) −9.51161 6.91059i −0.470319 0.341707i 0.327247 0.944939i \(-0.393879\pi\)
−0.797566 + 0.603232i \(0.793879\pi\)
\(410\) 0 0
\(411\) 15.4219 11.2047i 0.760706 0.552685i
\(412\) 0 0
\(413\) −17.7799 12.9179i −0.874894 0.635648i
\(414\) 0 0
\(415\) −25.3945 + 13.5067i −1.24657 + 0.663017i
\(416\) 0 0
\(417\) −7.38383 22.7251i −0.361588 1.11285i
\(418\) 0 0
\(419\) 4.97447 + 15.3098i 0.243019 + 0.747934i 0.995956 + 0.0898423i \(0.0286363\pi\)
−0.752937 + 0.658092i \(0.771364\pi\)
\(420\) 0 0
\(421\) −0.159992 + 0.492406i −0.00779756 + 0.0239984i −0.954880 0.296993i \(-0.904016\pi\)
0.947082 + 0.320992i \(0.104016\pi\)
\(422\) 0 0
\(423\) 2.95088 2.14394i 0.143477 0.104242i
\(424\) 0 0
\(425\) 3.56476 + 4.56027i 0.172916 + 0.221205i
\(426\) 0 0
\(427\) 3.13479 2.27756i 0.151703 0.110219i
\(428\) 0 0
\(429\) −3.88275 + 11.9499i −0.187461 + 0.576946i
\(430\) 0 0
\(431\) −6.24332 19.2150i −0.300730 0.925553i −0.981236 0.192810i \(-0.938240\pi\)
0.680506 0.732743i \(-0.261760\pi\)
\(432\) 0 0
\(433\) −10.3203 31.7627i −0.495963 1.52642i −0.815451 0.578827i \(-0.803511\pi\)
0.319488 0.947590i \(-0.396489\pi\)
\(434\) 0 0
\(435\) −11.6202 + 23.8327i −0.557145 + 1.14269i
\(436\) 0 0
\(437\) 7.16943 + 5.20889i 0.342960 + 0.249175i
\(438\) 0 0
\(439\) −19.6723 + 14.2928i −0.938909 + 0.682157i −0.948158 0.317800i \(-0.897056\pi\)
0.00924884 + 0.999957i \(0.497056\pi\)
\(440\) 0 0
\(441\) −5.56026 4.03977i −0.264775 0.192370i
\(442\) 0 0
\(443\) −18.2746 −0.868252 −0.434126 0.900852i \(-0.642943\pi\)
−0.434126 + 0.900852i \(0.642943\pi\)
\(444\) 0 0
\(445\) 17.6027 + 16.9944i 0.834450 + 0.805612i
\(446\) 0 0
\(447\) 3.52251 10.8412i 0.166609 0.512770i
\(448\) 0 0
\(449\) −36.1354 −1.70534 −0.852668 0.522454i \(-0.825017\pi\)
−0.852668 + 0.522454i \(0.825017\pi\)
\(450\) 0 0
\(451\) 28.3897 1.33682
\(452\) 0 0
\(453\) −7.26607 + 22.3627i −0.341390 + 1.05069i
\(454\) 0 0
\(455\) 4.62106 9.47766i 0.216639 0.444320i
\(456\) 0 0
\(457\) 9.25903 0.433119 0.216560 0.976269i \(-0.430516\pi\)
0.216560 + 0.976269i \(0.430516\pi\)
\(458\) 0 0
\(459\) −5.13309 3.72941i −0.239592 0.174074i
\(460\) 0 0
\(461\) −4.65453 + 3.38171i −0.216783 + 0.157502i −0.690877 0.722972i \(-0.742776\pi\)
0.474094 + 0.880474i \(0.342776\pi\)
\(462\) 0 0
\(463\) −22.5798 16.4052i −1.04937 0.762415i −0.0772808 0.997009i \(-0.524624\pi\)
−0.972093 + 0.234594i \(0.924624\pi\)
\(464\) 0 0
\(465\) 0.867341 + 4.91524i 0.0402220 + 0.227939i
\(466\) 0 0
\(467\) 0.730903 + 2.24949i 0.0338222 + 0.104094i 0.966542 0.256507i \(-0.0825716\pi\)
−0.932720 + 0.360601i \(0.882572\pi\)
\(468\) 0 0
\(469\) −6.83544 21.0373i −0.315631 0.971413i
\(470\) 0 0
\(471\) −5.55941 + 17.1101i −0.256164 + 0.788391i
\(472\) 0 0
\(473\) −32.9935 + 23.9711i −1.51704 + 1.10219i
\(474\) 0 0
\(475\) 8.63646 + 11.0483i 0.396268 + 0.506931i
\(476\) 0 0
\(477\) 8.71342 6.33067i 0.398960 0.289861i
\(478\) 0 0
\(479\) −3.16821 + 9.75074i −0.144759 + 0.445523i −0.996980 0.0776594i \(-0.975255\pi\)
0.852221 + 0.523182i \(0.175255\pi\)
\(480\) 0 0
\(481\) 4.09708 + 12.6095i 0.186811 + 0.574945i
\(482\) 0 0
\(483\) 1.88223 + 5.79290i 0.0856443 + 0.263586i
\(484\) 0 0
\(485\) −15.8611 2.22705i −0.720216 0.101125i
\(486\) 0 0
\(487\) 13.5930 + 9.87586i 0.615955 + 0.447518i 0.851506 0.524344i \(-0.175689\pi\)
−0.235551 + 0.971862i \(0.575689\pi\)
\(488\) 0 0
\(489\) 10.5309 7.65114i 0.476223 0.345996i
\(490\) 0 0
\(491\) 22.7142 + 16.5028i 1.02508 + 0.744762i 0.967318 0.253568i \(-0.0816042\pi\)
0.0577599 + 0.998331i \(0.481604\pi\)
\(492\) 0 0
\(493\) 11.3887 0.512923
\(494\) 0 0
\(495\) 2.12567 + 12.0462i 0.0955416 + 0.541437i
\(496\) 0 0
\(497\) −1.71739 + 5.28557i −0.0770353 + 0.237090i
\(498\) 0 0
\(499\) 29.2059 1.30743 0.653717 0.756739i \(-0.273209\pi\)
0.653717 + 0.756739i \(0.273209\pi\)
\(500\) 0 0
\(501\) 15.5962 0.696787
\(502\) 0 0
\(503\) 9.53123 29.3341i 0.424977 1.30794i −0.478040 0.878338i \(-0.658653\pi\)
0.903017 0.429606i \(-0.141347\pi\)
\(504\) 0 0
\(505\) 7.15511 + 40.5482i 0.318398 + 1.80437i
\(506\) 0 0
\(507\) −5.19127 −0.230552
\(508\) 0 0
\(509\) −2.55341 1.85516i −0.113178 0.0822287i 0.529757 0.848150i \(-0.322283\pi\)
−0.642935 + 0.765921i \(0.722283\pi\)
\(510\) 0 0
\(511\) 4.21026 3.05893i 0.186251 0.135319i
\(512\) 0 0
\(513\) −12.4361 9.03536i −0.549068 0.398921i
\(514\) 0 0
\(515\) 4.15225 + 0.583016i 0.182970 + 0.0256908i
\(516\) 0 0
\(517\) −2.57571 7.92721i −0.113279 0.348638i
\(518\) 0 0
\(519\) 8.07273 + 24.8453i 0.354353 + 1.09059i
\(520\) 0 0
\(521\) 7.57661 23.3184i 0.331937 1.02160i −0.636274 0.771464i \(-0.719525\pi\)
0.968211 0.250135i \(-0.0804750\pi\)
\(522\) 0 0
\(523\) 10.5366 7.65528i 0.460733 0.334742i −0.333086 0.942896i \(-0.608090\pi\)
0.793819 + 0.608155i \(0.208090\pi\)
\(524\) 0 0
\(525\) 0.338858 + 9.63264i 0.0147890 + 0.420403i
\(526\) 0 0
\(527\) 1.73441 1.26012i 0.0755520 0.0548918i
\(528\) 0 0
\(529\) −4.02226 + 12.3792i −0.174881 + 0.538227i
\(530\) 0 0
\(531\) −6.56996 20.2203i −0.285112 0.877485i
\(532\) 0 0
\(533\) −7.31571 22.5154i −0.316879 0.975252i
\(534\) 0 0
\(535\) −2.66647 15.1110i −0.115282 0.653304i
\(536\) 0 0
\(537\) −4.71556 3.42606i −0.203492 0.147845i
\(538\) 0 0
\(539\) −12.7062 + 9.23160i −0.547295 + 0.397633i
\(540\) 0 0
\(541\) −21.0579 15.2995i −0.905351 0.657776i 0.0344839 0.999405i \(-0.489021\pi\)
−0.939835 + 0.341629i \(0.889021\pi\)
\(542\) 0 0
\(543\) −3.86980 −0.166069
\(544\) 0 0
\(545\) 3.10571 6.36973i 0.133034 0.272849i
\(546\) 0 0
\(547\) 7.49421 23.0648i 0.320429 0.986180i −0.653032 0.757330i \(-0.726503\pi\)
0.973462 0.228850i \(-0.0734966\pi\)
\(548\) 0 0
\(549\) 3.74851 0.159983
\(550\) 0 0
\(551\) 27.5919 1.17545
\(552\) 0 0
\(553\) −4.90440 + 15.0942i −0.208556 + 0.641871i
\(554\) 0 0
\(555\) −8.71928 8.41794i −0.370113 0.357322i
\(556\) 0 0
\(557\) 24.7393 1.04824 0.524118 0.851646i \(-0.324395\pi\)
0.524118 + 0.851646i \(0.324395\pi\)
\(558\) 0 0
\(559\) 27.5132 + 19.9895i 1.16368 + 0.845466i
\(560\) 0 0
\(561\) −3.99122 + 2.89979i −0.168509 + 0.122429i
\(562\) 0 0
\(563\) 6.10487 + 4.43545i 0.257290 + 0.186932i 0.708951 0.705257i \(-0.249169\pi\)
−0.451662 + 0.892189i \(0.649169\pi\)
\(564\) 0 0
\(565\) −0.131660 + 0.270031i −0.00553898 + 0.0113603i
\(566\) 0 0
\(567\) −0.970888 2.98808i −0.0407734 0.125488i
\(568\) 0 0
\(569\) 0.0729216 + 0.224430i 0.00305703 + 0.00940858i 0.952573 0.304309i \(-0.0984255\pi\)
−0.949516 + 0.313718i \(0.898426\pi\)
\(570\) 0 0
\(571\) 5.31068 16.3446i 0.222245 0.684001i −0.776314 0.630346i \(-0.782913\pi\)
0.998560 0.0536545i \(-0.0170870\pi\)
\(572\) 0 0
\(573\) −13.3708 + 9.71448i −0.558575 + 0.405828i
\(574\) 0 0
\(575\) 8.83104 13.0998i 0.368280 0.546300i
\(576\) 0 0
\(577\) −6.15985 + 4.47539i −0.256438 + 0.186313i −0.708575 0.705635i \(-0.750662\pi\)
0.452137 + 0.891948i \(0.350662\pi\)
\(578\) 0 0
\(579\) 7.34438 22.6037i 0.305222 0.939377i
\(580\) 0 0
\(581\) 6.35734 + 19.5659i 0.263747 + 0.811729i
\(582\) 0 0
\(583\) −7.60560 23.4076i −0.314992 0.969445i
\(584\) 0 0
\(585\) 9.00590 4.79001i 0.372348 0.198042i
\(586\) 0 0
\(587\) −16.4411 11.9451i −0.678596 0.493029i 0.194296 0.980943i \(-0.437758\pi\)
−0.872892 + 0.487914i \(0.837758\pi\)
\(588\) 0 0
\(589\) 4.20201 3.05294i 0.173141 0.125794i
\(590\) 0 0
\(591\) 21.0640 + 15.3039i 0.866457 + 0.629518i
\(592\) 0 0
\(593\) −17.3712 −0.713348 −0.356674 0.934229i \(-0.616089\pi\)
−0.356674 + 0.934229i \(0.616089\pi\)
\(594\) 0 0
\(595\) 3.65518 1.94410i 0.149848 0.0797003i
\(596\) 0 0
\(597\) 9.02059 27.7625i 0.369188 1.13624i
\(598\) 0 0
\(599\) −11.1550 −0.455779 −0.227890 0.973687i \(-0.573183\pi\)
−0.227890 + 0.973687i \(0.573183\pi\)
\(600\) 0 0
\(601\) 8.30269 0.338674 0.169337 0.985558i \(-0.445837\pi\)
0.169337 + 0.985558i \(0.445837\pi\)
\(602\) 0 0
\(603\) 6.61263 20.3516i 0.269287 0.828781i
\(604\) 0 0
\(605\) 3.32368 + 0.466677i 0.135127 + 0.0189731i
\(606\) 0 0
\(607\) 4.56913 0.185455 0.0927275 0.995692i \(-0.470441\pi\)
0.0927275 + 0.995692i \(0.470441\pi\)
\(608\) 0 0
\(609\) 15.3427 + 11.1471i 0.621718 + 0.451704i
\(610\) 0 0
\(611\) −5.62322 + 4.08551i −0.227491 + 0.165282i
\(612\) 0 0
\(613\) 23.6078 + 17.1521i 0.953510 + 0.692765i 0.951634 0.307233i \(-0.0994031\pi\)
0.00187525 + 0.999998i \(0.499403\pi\)
\(614\) 0 0
\(615\) 15.5691 + 15.0310i 0.627805 + 0.606108i
\(616\) 0 0
\(617\) 9.42696 + 29.0132i 0.379515 + 1.16803i 0.940382 + 0.340121i \(0.110468\pi\)
−0.560866 + 0.827906i \(0.689532\pi\)
\(618\) 0 0
\(619\) −4.12667 12.7006i −0.165865 0.510480i 0.833234 0.552921i \(-0.186487\pi\)
−0.999099 + 0.0424406i \(0.986487\pi\)
\(620\) 0 0
\(621\) −5.35148 + 16.4702i −0.214748 + 0.660925i
\(622\) 0 0
\(623\) 14.1582 10.2866i 0.567237 0.412122i
\(624\) 0 0
\(625\) 19.1428 16.0795i 0.765714 0.643181i
\(626\) 0 0
\(627\) −9.66965 + 7.02541i −0.386168 + 0.280568i
\(628\) 0 0
\(629\) −1.60866 + 4.95096i −0.0641416 + 0.197408i
\(630\) 0 0
\(631\) 0.142339 + 0.438075i 0.00566643 + 0.0174395i 0.953850 0.300284i \(-0.0970815\pi\)
−0.948183 + 0.317724i \(0.897082\pi\)
\(632\) 0 0
\(633\) 0.774495 + 2.38365i 0.0307834 + 0.0947416i
\(634\) 0 0
\(635\) 18.8838 + 18.2312i 0.749382 + 0.723483i
\(636\) 0 0
\(637\) 10.5957 + 7.69821i 0.419816 + 0.305014i
\(638\) 0 0
\(639\) −4.34962 + 3.16018i −0.172068 + 0.125015i
\(640\) 0 0
\(641\) 22.0956 + 16.0534i 0.872724 + 0.634071i 0.931316 0.364211i \(-0.118661\pi\)
−0.0585926 + 0.998282i \(0.518661\pi\)
\(642\) 0 0
\(643\) −13.8667 −0.546848 −0.273424 0.961894i \(-0.588156\pi\)
−0.273424 + 0.961894i \(0.588156\pi\)
\(644\) 0 0
\(645\) −30.7853 4.32256i −1.21217 0.170201i
\(646\) 0 0
\(647\) 9.54913 29.3892i 0.375415 1.15541i −0.567783 0.823178i \(-0.692199\pi\)
0.943198 0.332231i \(-0.107801\pi\)
\(648\) 0 0
\(649\) −48.5849 −1.90712
\(650\) 0 0
\(651\) 3.56995 0.139917
\(652\) 0 0
\(653\) −4.64737 + 14.3031i −0.181866 + 0.559725i −0.999880 0.0154722i \(-0.995075\pi\)
0.818015 + 0.575198i \(0.195075\pi\)
\(654\) 0 0
\(655\) −4.24475 + 2.25767i −0.165856 + 0.0882146i
\(656\) 0 0
\(657\) 5.03453 0.196416
\(658\) 0 0
\(659\) −0.112275 0.0815727i −0.00437362 0.00317762i 0.585596 0.810603i \(-0.300860\pi\)
−0.589970 + 0.807425i \(0.700860\pi\)
\(660\) 0 0
\(661\) 23.8045 17.2950i 0.925888 0.672697i −0.0190943 0.999818i \(-0.506078\pi\)
0.944983 + 0.327120i \(0.106078\pi\)
\(662\) 0 0
\(663\) 3.32827 + 2.41813i 0.129259 + 0.0939123i
\(664\) 0 0
\(665\) 8.85554 4.71003i 0.343403 0.182647i
\(666\) 0 0
\(667\) −9.60569 29.5633i −0.371934 1.14470i
\(668\) 0 0
\(669\) −7.29238 22.4436i −0.281940 0.867721i
\(670\) 0 0
\(671\) 2.64705 8.14678i 0.102188 0.314503i
\(672\) 0 0
\(673\) 22.1214 16.0722i 0.852719 0.619537i −0.0731753 0.997319i \(-0.523313\pi\)
0.925894 + 0.377782i \(0.123313\pi\)
\(674\) 0 0
\(675\) −15.3184 + 22.7230i −0.589604 + 0.874608i
\(676\) 0 0
\(677\) −14.5307 + 10.5571i −0.558458 + 0.405744i −0.830894 0.556430i \(-0.812171\pi\)
0.272436 + 0.962174i \(0.412171\pi\)
\(678\) 0 0
\(679\) −3.54009 + 10.8953i −0.135856 + 0.418122i
\(680\) 0 0
\(681\) 2.44292 + 7.51853i 0.0936128 + 0.288111i
\(682\) 0 0
\(683\) 8.43526 + 25.9611i 0.322766 + 0.993372i 0.972439 + 0.233158i \(0.0749060\pi\)
−0.649673 + 0.760214i \(0.725094\pi\)
\(684\) 0 0
\(685\) −15.4986 + 31.7872i −0.592171 + 1.21453i
\(686\) 0 0
\(687\) 14.7753 + 10.7349i 0.563712 + 0.409561i
\(688\) 0 0
\(689\) −16.6044 + 12.0638i −0.632576 + 0.459593i
\(690\) 0 0
\(691\) −30.5969 22.2300i −1.16396 0.845667i −0.173688 0.984801i \(-0.555568\pi\)
−0.990274 + 0.139134i \(0.955568\pi\)
\(692\) 0 0
\(693\) 8.74918 0.332354
\(694\) 0 0
\(695\) 31.8913 + 30.7892i 1.20971 + 1.16790i
\(696\) 0 0
\(697\) 2.87241 8.84038i 0.108800 0.334853i
\(698\) 0 0
\(699\) −2.07662 −0.0785451
\(700\) 0 0
\(701\) −34.1068 −1.28820 −0.644098 0.764943i \(-0.722767\pi\)
−0.644098 + 0.764943i \(0.722767\pi\)
\(702\) 0 0
\(703\) −3.89736 + 11.9948i −0.146992 + 0.452394i
\(704\) 0 0
\(705\) 2.78455 5.71103i 0.104872 0.215090i
\(706\) 0 0
\(707\) 29.4502 1.10759
\(708\) 0 0
\(709\) 17.2989 + 12.5684i 0.649673 + 0.472015i 0.863160 0.504931i \(-0.168482\pi\)
−0.213487 + 0.976946i \(0.568482\pi\)
\(710\) 0 0
\(711\) −12.4214 + 9.02465i −0.465838 + 0.338451i
\(712\) 0 0
\(713\) −4.73393 3.43940i −0.177287 0.128807i
\(714\) 0 0
\(715\) −4.05069 22.9553i −0.151487 0.858481i
\(716\) 0 0
\(717\) 3.01932 + 9.29252i 0.112759 + 0.347036i
\(718\) 0 0
\(719\) −8.20972 25.2669i −0.306171 0.942298i −0.979238 0.202716i \(-0.935023\pi\)
0.673067 0.739582i \(-0.264977\pi\)
\(720\) 0 0
\(721\) 0.926752 2.85225i 0.0345140 0.106223i
\(722\) 0 0
\(723\) −3.85212 + 2.79873i −0.143262 + 0.104086i
\(724\) 0 0
\(725\) −1.72932 49.1589i −0.0642252 1.82571i
\(726\) 0 0
\(727\) 1.12942 0.820574i 0.0418880 0.0304334i −0.566644 0.823963i \(-0.691759\pi\)
0.608532 + 0.793529i \(0.291759\pi\)
\(728\) 0 0
\(729\) 7.06345 21.7391i 0.261609 0.805150i
\(730\) 0 0
\(731\) 4.12625 + 12.6993i 0.152615 + 0.469701i
\(732\) 0 0
\(733\) 4.72195 + 14.5327i 0.174409 + 0.536776i 0.999606 0.0280692i \(-0.00893587\pi\)
−0.825197 + 0.564845i \(0.808936\pi\)
\(734\) 0 0
\(735\) −11.8558 1.66467i −0.437309 0.0614024i
\(736\) 0 0
\(737\) −39.5612 28.7429i −1.45726 1.05876i
\(738\) 0 0
\(739\) −25.0588 + 18.2063i −0.921802 + 0.669728i −0.943972 0.330026i \(-0.892943\pi\)
0.0221698 + 0.999754i \(0.492943\pi\)
\(740\) 0 0
\(741\) 8.06351 + 5.85848i 0.296220 + 0.215217i
\(742\) 0 0
\(743\) 9.18330 0.336902 0.168451 0.985710i \(-0.446123\pi\)
0.168451 + 0.985710i \(0.446123\pi\)
\(744\) 0 0
\(745\) 3.67486 + 20.8255i 0.134637 + 0.762989i
\(746\) 0 0
\(747\) −6.15012 + 18.9281i −0.225021 + 0.692543i
\(748\) 0 0
\(749\) −10.9751 −0.401022
\(750\) 0 0
\(751\) −45.3438 −1.65462 −0.827309 0.561747i \(-0.810129\pi\)
−0.827309 + 0.561747i \(0.810129\pi\)
\(752\) 0 0
\(753\) 7.90604 24.3323i 0.288112 0.886718i
\(754\) 0 0
\(755\) −7.58034 42.9579i −0.275877 1.56340i
\(756\) 0 0
\(757\) −45.4782 −1.65293 −0.826467 0.562985i \(-0.809653\pi\)
−0.826467 + 0.562985i \(0.809653\pi\)
\(758\) 0 0
\(759\) 10.8937 + 7.91474i 0.395416 + 0.287287i
\(760\) 0 0
\(761\) 0.515120 0.374257i 0.0186731 0.0135668i −0.578410 0.815747i \(-0.696326\pi\)
0.597083 + 0.802180i \(0.296326\pi\)
\(762\) 0 0
\(763\) −4.10062 2.97928i −0.148453 0.107857i
\(764\) 0 0
\(765\) 3.96618 + 0.556891i 0.143398 + 0.0201344i
\(766\) 0 0
\(767\) 12.5198 + 38.5319i 0.452063 + 1.39131i
\(768\) 0 0
\(769\) 2.87386 + 8.84482i 0.103634 + 0.318952i 0.989407 0.145165i \(-0.0463714\pi\)
−0.885774 + 0.464118i \(0.846371\pi\)
\(770\) 0 0
\(771\) 0.0694170 0.213644i 0.00249999 0.00769419i
\(772\) 0 0
\(773\) −5.91821 + 4.29983i −0.212863 + 0.154654i −0.689108 0.724658i \(-0.741998\pi\)
0.476245 + 0.879313i \(0.341998\pi\)
\(774\) 0 0
\(775\) −5.70260 7.29513i −0.204844 0.262049i
\(776\) 0 0
\(777\) −7.01308 + 5.09530i −0.251593 + 0.182793i
\(778\) 0 0
\(779\) 6.95909 21.4179i 0.249335 0.767375i
\(780\) 0 0
\(781\) 3.79661 + 11.6848i 0.135853 + 0.418114i
\(782\) 0 0
\(783\) 16.6621 + 51.2806i 0.595454 + 1.83262i
\(784\) 0 0
\(785\) −5.79986 32.8679i −0.207006 1.17311i
\(786\) 0 0
\(787\) −23.0553 16.7507i −0.821833 0.597097i 0.0954038 0.995439i \(-0.469586\pi\)
−0.917237 + 0.398342i \(0.869586\pi\)
\(788\) 0 0
\(789\) −9.69055 + 7.04060i −0.344993 + 0.250652i
\(790\) 0 0
\(791\) 0.173837 + 0.126300i 0.00618094 + 0.00449071i
\(792\) 0 0
\(793\) −7.14320 −0.253662
\(794\) 0 0
\(795\) 8.22227 16.8637i 0.291614 0.598092i
\(796\) 0 0
\(797\) −1.53076 + 4.71121i −0.0542225 + 0.166880i −0.974500 0.224386i \(-0.927962\pi\)
0.920278 + 0.391265i \(0.127962\pi\)
\(798\) 0 0
\(799\) −2.72909 −0.0965482
\(800\) 0 0
\(801\) 16.9301 0.598195
\(802\) 0 0
\(803\) 3.55518 10.9417i 0.125460 0.386125i
\(804\) 0 0
\(805\) −8.12948 7.84853i −0.286526 0.276624i
\(806\) 0 0
\(807\) −34.0189 −1.19752
\(808\) 0 0
\(809\) 22.0656 + 16.0316i 0.775787 + 0.563642i 0.903712 0.428142i \(-0.140832\pi\)
−0.127925 + 0.991784i \(0.540832\pi\)
\(810\) 0 0
\(811\) −40.8986 + 29.7146i −1.43614 + 1.04342i −0.447313 + 0.894378i \(0.647619\pi\)
−0.988831 + 0.149042i \(0.952381\pi\)
\(812\) 0 0
\(813\) 4.12917 + 3.00002i 0.144816 + 0.105215i
\(814\) 0 0
\(815\) −10.5833 + 21.7060i −0.370716 + 0.760328i
\(816\) 0 0
\(817\) 9.99681 + 30.7670i 0.349744 + 1.07640i
\(818\) 0 0
\(819\) −2.25457 6.93884i −0.0787809 0.242463i
\(820\) 0 0
\(821\) −4.73239 + 14.5648i −0.165162 + 0.508315i −0.999048 0.0436206i \(-0.986111\pi\)
0.833886 + 0.551936i \(0.186111\pi\)
\(822\) 0 0
\(823\) −17.6552 + 12.8272i −0.615421 + 0.447129i −0.851319 0.524649i \(-0.824197\pi\)
0.235898 + 0.971778i \(0.424197\pi\)
\(824\) 0 0
\(825\) 13.1228 + 16.7875i 0.456878 + 0.584467i
\(826\) 0 0
\(827\) −23.7315 + 17.2419i −0.825224 + 0.599560i −0.918204 0.396108i \(-0.870361\pi\)
0.0929802 + 0.995668i \(0.470361\pi\)
\(828\) 0 0
\(829\) 13.2985 40.9287i 0.461877 1.42151i −0.400990 0.916082i \(-0.631334\pi\)
0.862868 0.505430i \(-0.168666\pi\)
\(830\) 0 0
\(831\) −6.90852 21.2622i −0.239654 0.737579i
\(832\) 0 0
\(833\) 1.58907 + 4.89066i 0.0550581 + 0.169451i
\(834\) 0 0
\(835\) −25.5452 + 13.5868i −0.884028 + 0.470192i
\(836\) 0 0
\(837\) 8.21149 + 5.96600i 0.283831 + 0.206215i
\(838\) 0 0
\(839\) 24.4386 17.7556i 0.843713 0.612993i −0.0796927 0.996819i \(-0.525394\pi\)
0.923405 + 0.383826i \(0.125394\pi\)
\(840\) 0 0
\(841\) −54.8379 39.8421i −1.89096 1.37387i
\(842\) 0 0
\(843\) −4.01348 −0.138232
\(844\) 0 0
\(845\) 8.50283 4.52244i 0.292506 0.155577i
\(846\) 0 0
\(847\) 0.741821 2.28309i 0.0254893 0.0784479i
\(848\) 0 0
\(849\) 26.2236 0.899992
\(850\) 0 0
\(851\) 14.2087 0.487067
\(852\) 0 0
\(853\) 16.8447 51.8426i 0.576751 1.77506i −0.0533875 0.998574i \(-0.517002\pi\)
0.630138 0.776483i \(-0.282998\pi\)
\(854\) 0 0
\(855\) 9.60900 + 1.34920i 0.328621 + 0.0461416i
\(856\) 0 0
\(857\) 28.3459 0.968276 0.484138 0.874992i \(-0.339133\pi\)
0.484138 + 0.874992i \(0.339133\pi\)
\(858\) 0 0
\(859\) −3.62806 2.63594i −0.123788 0.0899372i 0.524169 0.851615i \(-0.324376\pi\)
−0.647957 + 0.761677i \(0.724376\pi\)
\(860\) 0 0
\(861\) 12.5225 9.09812i 0.426765 0.310063i
\(862\) 0 0
\(863\) 18.7437 + 13.6181i 0.638044 + 0.463566i 0.859178 0.511677i \(-0.170976\pi\)
−0.221133 + 0.975244i \(0.570976\pi\)
\(864\) 0 0
\(865\) −34.8667 33.6617i −1.18550 1.14453i
\(866\) 0 0
\(867\) −5.83271 17.9512i −0.198089 0.609656i
\(868\) 0 0
\(869\) 10.8421 + 33.3686i 0.367794 + 1.13195i
\(870\) 0 0
\(871\) −12.6011 + 38.7821i −0.426971 + 1.31408i
\(872\) 0 0
\(873\) −8.96597 + 6.51416i −0.303452 + 0.220471i
\(874\) 0 0
\(875\) −8.94661 15.4822i −0.302451 0.523394i
\(876\) 0 0
\(877\) −27.1415 + 19.7195i −0.916505 + 0.665880i −0.942652 0.333778i \(-0.891676\pi\)
0.0261468 + 0.999658i \(0.491676\pi\)
\(878\) 0 0
\(879\) 8.55924 26.3426i 0.288696 0.888515i
\(880\) 0 0
\(881\) −2.53650 7.80655i −0.0854569 0.263009i 0.899192 0.437553i \(-0.144155\pi\)
−0.984649 + 0.174544i \(0.944155\pi\)
\(882\) 0 0
\(883\) 1.81874 + 5.59752i 0.0612056 + 0.188371i 0.976984 0.213312i \(-0.0684251\pi\)
−0.915778 + 0.401684i \(0.868425\pi\)
\(884\) 0 0
\(885\) −26.6442 25.7234i −0.895634 0.864681i
\(886\) 0 0
\(887\) 21.1004 + 15.3304i 0.708484 + 0.514744i 0.882684 0.469967i \(-0.155734\pi\)
−0.174200 + 0.984710i \(0.555734\pi\)
\(888\) 0 0
\(889\) 15.1886 11.0352i 0.509410 0.370108i
\(890\) 0 0
\(891\) −5.61917 4.08257i −0.188249 0.136771i
\(892\) 0 0
\(893\) −6.61185 −0.221257
\(894\) 0 0
\(895\) 10.7083 + 1.50355i 0.357940 + 0.0502583i
\(896\) 0 0
\(897\) 3.46987 10.6792i 0.115856 0.356567i
\(898\) 0 0
\(899\) −18.2188 −0.607630
\(900\) 0 0
\(901\) −8.05851 −0.268468
\(902\) 0 0
\(903\) −6.87107 + 21.1470i −0.228655 + 0.703727i
\(904\) 0 0
\(905\) 6.33839 3.37123i 0.210695 0.112063i
\(906\) 0 0
\(907\) 55.9049 1.85629 0.928146 0.372216i \(-0.121402\pi\)
0.928146 + 0.372216i \(0.121402\pi\)
\(908\) 0 0
\(909\) 23.0491 + 16.7462i 0.764491 + 0.555435i
\(910\) 0 0
\(911\) −9.01861 + 6.55240i −0.298800 + 0.217091i −0.727076 0.686557i \(-0.759121\pi\)
0.428276 + 0.903648i \(0.359121\pi\)
\(912\) 0 0
\(913\) 36.7941 + 26.7325i 1.21771 + 0.884717i
\(914\) 0 0
\(915\) 5.76498 3.06625i 0.190584 0.101367i
\(916\) 0 0
\(917\) 1.06264 + 3.27048i 0.0350916 + 0.108001i
\(918\) 0 0
\(919\) −0.0872351 0.268482i −0.00287762 0.00885640i 0.949607 0.313442i \(-0.101482\pi\)
−0.952485 + 0.304585i \(0.901482\pi\)
\(920\) 0 0
\(921\) 0.0620478 0.190964i 0.00204454 0.00629246i
\(922\) 0 0
\(923\) 8.28867 6.02207i 0.272825 0.198219i
\(924\) 0 0
\(925\) 21.6148 + 6.19193i 0.710690 + 0.203589i
\(926\) 0 0
\(927\) 2.34718 1.70533i 0.0770916 0.0560103i
\(928\) 0 0
\(929\) 1.82070 5.60354i 0.0597353 0.183846i −0.916736 0.399493i \(-0.869186\pi\)
0.976471 + 0.215647i \(0.0691861\pi\)
\(930\) 0 0
\(931\) 3.84990 + 11.8488i 0.126175 + 0.388328i
\(932\) 0 0
\(933\) −2.95806 9.10396i −0.0968424 0.298050i
\(934\) 0 0
\(935\) 4.01107 8.22659i 0.131176 0.269038i
\(936\) 0 0
\(937\) −3.83443 2.78588i −0.125265 0.0910107i 0.523388 0.852094i \(-0.324668\pi\)
−0.648654 + 0.761084i \(0.724668\pi\)
\(938\) 0 0
\(939\) 11.6385 8.45583i 0.379807 0.275946i
\(940\) 0 0
\(941\) 9.49301 + 6.89708i 0.309463 + 0.224838i 0.731666 0.681663i \(-0.238743\pi\)
−0.422203 + 0.906501i \(0.638743\pi\)
\(942\) 0 0
\(943\) −25.3708 −0.826188
\(944\) 0 0
\(945\) 14.1014 + 13.6141i 0.458719 + 0.442866i
\(946\) 0 0
\(947\) −8.35893 + 25.7261i −0.271629 + 0.835987i 0.718463 + 0.695565i \(0.244846\pi\)
−0.990092 + 0.140422i \(0.955154\pi\)
\(948\) 0 0
\(949\) −9.59384 −0.311429
\(950\) 0 0
\(951\) −12.0866 −0.391934
\(952\) 0 0
\(953\) 3.12461 9.61655i 0.101216 0.311511i −0.887608 0.460600i \(-0.847634\pi\)
0.988824 + 0.149089i \(0.0476342\pi\)
\(954\) 0 0
\(955\) 13.4373 27.5596i 0.434822 0.891808i
\(956\) 0 0
\(957\) 41.9249 1.35524
\(958\) 0 0
\(959\) 20.4636 + 14.8676i 0.660803 + 0.480101i
\(960\) 0 0
\(961\) 22.3050 16.2055i 0.719515 0.522758i
\(962\) 0 0
\(963\) −8.58964 6.24074i −0.276797 0.201105i
\(964\) 0 0
\(965\) 7.66204 + 43.4210i 0.246650 + 1.39777i
\(966\) 0 0
\(967\) 17.0533 + 52.4847i 0.548398 + 1.68780i 0.712771 + 0.701397i \(0.247440\pi\)
−0.164373 + 0.986398i \(0.552560\pi\)
\(968\) 0 0
\(969\) 1.20931 + 3.72188i 0.0388487 + 0.119564i
\(970\) 0 0
\(971\) 12.6530 38.9419i 0.406054 1.24971i −0.513957 0.857816i \(-0.671821\pi\)
0.920012 0.391891i \(-0.128179\pi\)
\(972\) 0 0
\(973\) 25.6508 18.6364i 0.822326 0.597455i
\(974\) 0 0
\(975\) 9.93234 14.7335i 0.318089 0.471848i
\(976\) 0 0
\(977\) −12.9047 + 9.37583i −0.412859 + 0.299959i −0.774758 0.632258i \(-0.782128\pi\)
0.361900 + 0.932217i \(0.382128\pi\)
\(978\) 0 0
\(979\) 11.9553 36.7947i 0.382094 1.17596i
\(980\) 0 0
\(981\) −1.51524 4.66344i −0.0483780 0.148892i
\(982\) 0 0
\(983\) 13.3748 + 41.1633i 0.426588 + 1.31290i 0.901465 + 0.432852i \(0.142493\pi\)
−0.474877 + 0.880052i \(0.657507\pi\)
\(984\) 0 0
\(985\) −47.8331 6.71624i −1.52409 0.213997i
\(986\) 0 0
\(987\) −3.67658 2.67119i −0.117027 0.0850249i
\(988\) 0 0
\(989\) 29.4850 21.4221i 0.937570 0.681184i
\(990\) 0 0
\(991\) 11.5901 + 8.42071i 0.368172 + 0.267493i 0.756452 0.654049i \(-0.226931\pi\)
−0.388281 + 0.921541i \(0.626931\pi\)
\(992\) 0 0
\(993\) 39.0360 1.23877
\(994\) 0 0
\(995\) 9.41075 + 53.3309i 0.298341 + 1.69070i
\(996\) 0 0
\(997\) −7.34905 + 22.6180i −0.232747 + 0.716321i 0.764666 + 0.644427i \(0.222904\pi\)
−0.997412 + 0.0718934i \(0.977096\pi\)
\(998\) 0 0
\(999\) −24.6464 −0.779777
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 200.2.m.c.161.3 yes 16
4.3 odd 2 400.2.u.g.161.2 16
5.2 odd 4 1000.2.q.d.449.4 32
5.3 odd 4 1000.2.q.d.449.5 32
5.4 even 2 1000.2.m.c.801.2 16
25.4 even 10 5000.2.a.m.1.3 8
25.9 even 10 1000.2.m.c.201.2 16
25.12 odd 20 1000.2.q.d.49.5 32
25.13 odd 20 1000.2.q.d.49.4 32
25.16 even 5 inner 200.2.m.c.41.3 16
25.21 even 5 5000.2.a.l.1.6 8
100.71 odd 10 10000.2.a.bk.1.3 8
100.79 odd 10 10000.2.a.bh.1.6 8
100.91 odd 10 400.2.u.g.241.2 16
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
200.2.m.c.41.3 16 25.16 even 5 inner
200.2.m.c.161.3 yes 16 1.1 even 1 trivial
400.2.u.g.161.2 16 4.3 odd 2
400.2.u.g.241.2 16 100.91 odd 10
1000.2.m.c.201.2 16 25.9 even 10
1000.2.m.c.801.2 16 5.4 even 2
1000.2.q.d.49.4 32 25.13 odd 20
1000.2.q.d.49.5 32 25.12 odd 20
1000.2.q.d.449.4 32 5.2 odd 4
1000.2.q.d.449.5 32 5.3 odd 4
5000.2.a.l.1.6 8 25.21 even 5
5000.2.a.m.1.3 8 25.4 even 10
10000.2.a.bh.1.6 8 100.79 odd 10
10000.2.a.bk.1.3 8 100.71 odd 10