Properties

Label 400.2.u.g.161.2
Level $400$
Weight $2$
Character 400.161
Analytic conductor $3.194$
Analytic rank $0$
Dimension $16$
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] = [400,2,Mod(81,400)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(400, base_ring=CyclotomicField(10))
 
chi = DirichletCharacter(H, H._module([0, 0, 4]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("400.81");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 400 = 2^{4} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 400.u (of order \(5\), 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: \(3.19401608085\)
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: \( x^{16} - x^{15} + 12 x^{14} - 18 x^{13} + 100 x^{12} + 23 x^{11} + 567 x^{10} + 556 x^{9} + 3841 x^{8} + 1155 x^{7} + 7575 x^{6} - 875 x^{5} + 7485 x^{4} + 900 x^{3} + 2000 x^{2} + \cdots + 6400 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{9}]\)
Coefficient ring index: \( 5 \)
Twist minimal: no (minimal twist has level 200)
Sato-Tate group: $\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label 161.2
Root \(0.372462 - 1.14632i\) of defining polynomial
Character \(\chi\) \(=\) 400.161
Dual form 400.2.u.g.241.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.372462 + 1.14632i) q^{3} +(0.388572 + 2.20205i) q^{5} -1.59935 q^{7} +(1.25173 + 0.909432i) q^{9} +O(q^{10})\) \(q+(-0.372462 + 1.14632i) q^{3} +(0.388572 + 2.20205i) q^{5} -1.59935 q^{7} +(1.25173 + 0.909432i) q^{9} +(-2.86042 + 2.07822i) q^{11} +(-2.38530 - 1.73302i) q^{13} +(-2.66898 - 0.374751i) q^{15} +(-0.357732 - 1.10099i) q^{17} +(0.866689 + 2.66739i) q^{19} +(0.595698 - 1.83337i) q^{21} +(2.55625 - 1.85723i) q^{23} +(-4.69802 + 1.71131i) q^{25} +(-4.43408 + 3.22155i) q^{27} +(-3.04006 + 9.35636i) q^{29} +(-0.572270 - 1.76126i) q^{31} +(-1.31690 - 4.05302i) q^{33} +(-0.621463 - 3.52185i) q^{35} +(-3.63802 - 2.64318i) q^{37} +(2.87503 - 2.08883i) q^{39} +(6.49601 + 4.71963i) q^{41} +11.5345 q^{43} +(-1.51623 + 3.10974i) q^{45} +(-0.728491 + 2.24207i) q^{47} -4.44208 q^{49} +1.39533 q^{51} +(2.15111 - 6.62042i) q^{53} +(-5.68781 - 5.49124i) q^{55} -3.38050 q^{57} +(11.1170 + 8.07696i) q^{59} +(1.96004 - 1.42405i) q^{61} +(-2.00195 - 1.45450i) q^{63} +(2.88933 - 5.92594i) q^{65} +(4.27388 + 13.1537i) q^{67} +(1.17687 + 3.62203i) q^{69} +(1.07380 - 3.30482i) q^{71} +(2.63248 - 1.91261i) q^{73} +(-0.211872 - 6.02284i) q^{75} +(4.57481 - 3.32380i) q^{77} +(3.06650 - 9.43770i) q^{79} +(-0.607051 - 1.86831i) q^{81} +(-3.97495 - 12.2336i) q^{83} +(2.28542 - 1.21556i) q^{85} +(-9.59308 - 6.96978i) q^{87} +(8.85248 - 6.43171i) q^{89} +(3.81493 + 2.77171i) q^{91} +2.23212 q^{93} +(-5.53696 + 2.94497i) q^{95} +(-2.21345 + 6.81231i) q^{97} -5.47046 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16 q - q^{3} - q^{5} + 6 q^{7} - 11 q^{9}+O(q^{10}) \) 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 \(\left(\mathbb{Z}/400\mathbb{Z}\right)^\times\).

\(n\) \(101\) \(177\) \(351\)
\(\chi(n)\) \(1\) \(e\left(\frac{4}{5}\right)\) \(1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) −0.372462 + 1.14632i −0.215041 + 0.661829i 0.784109 + 0.620623i \(0.213120\pi\)
−0.999151 + 0.0412064i \(0.986880\pi\)
\(4\) 0 0
\(5\) 0.388572 + 2.20205i 0.173775 + 0.984785i
\(6\) 0 0
\(7\) −1.59935 −0.604498 −0.302249 0.953229i \(-0.597737\pi\)
−0.302249 + 0.953229i \(0.597737\pi\)
\(8\) 0 0
\(9\) 1.25173 + 0.909432i 0.417242 + 0.303144i
\(10\) 0 0
\(11\) −2.86042 + 2.07822i −0.862449 + 0.626606i −0.928550 0.371207i \(-0.878944\pi\)
0.0661014 + 0.997813i \(0.478944\pi\)
\(12\) 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 \(0.00425999\pi\)
−0.801078 + 0.598559i \(0.795740\pi\)
\(20\) 0 0
\(21\) 0.595698 1.83337i 0.129992 0.400074i
\(22\) 0 0
\(23\) 2.55625 1.85723i 0.533015 0.387258i −0.288469 0.957489i \(-0.593146\pi\)
0.821484 + 0.570231i \(0.193146\pi\)
\(24\) 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 0.886421 0.462880i \(-0.153184\pi\)
−0.989204 + 0.146547i \(0.953184\pi\)
\(32\) 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 \(-0.157880\pi\)
0.879496 + 0.475906i \(0.157880\pi\)
\(44\) 0 0
\(45\) −1.51623 + 3.10974i −0.226026 + 0.463573i
\(46\) 0 0
\(47\) −0.728491 + 2.24207i −0.106261 + 0.327039i −0.990024 0.140896i \(-0.955002\pi\)
0.883763 + 0.467935i \(0.155002\pi\)
\(48\) 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 \(0.0524574\pi\)
0.460856 + 0.887475i \(0.347543\pi\)
\(60\) 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 \(0.220303\pi\)
−0.247769 + 0.968819i \(0.579697\pi\)
\(68\) 0 0
\(69\) 1.17687 + 3.62203i 0.141678 + 0.436042i
\(70\) 0 0
\(71\) 1.07380 3.30482i 0.127437 0.392210i −0.866900 0.498482i \(-0.833891\pi\)
0.994337 + 0.106271i \(0.0338912\pi\)
\(72\) 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 \(-0.711479\pi\)
0.961580 0.274526i \(-0.0885210\pi\)
\(80\) 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 \(-0.850516\pi\)
0.455434 0.890270i \(-0.349484\pi\)
\(84\) 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 −0.975537 0.219835i \(-0.929448\pi\)
0.918442 + 0.395556i \(0.129448\pi\)
\(104\) 0 0
\(105\) 4.26864 + 0.599359i 0.416577 + 0.0584914i
\(106\) 0 0
\(107\) 6.86223 0.663397 0.331699 0.943385i \(-0.392378\pi\)
0.331699 + 0.943385i \(0.392378\pi\)
\(108\) 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 −0.923123 0.384504i \(-0.874373\pi\)
0.0804241 + 0.996761i \(0.474373\pi\)
\(128\) 0 0
\(129\) −4.29616 + 13.2222i −0.378256 + 1.16415i
\(130\) 0 0
\(131\) −0.664422 2.04488i −0.0580508 0.178662i 0.917826 0.396982i \(-0.129942\pi\)
−0.975877 + 0.218320i \(0.929942\pi\)
\(132\) 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 \(0.617880\pi\)
−0.998423 + 0.0561417i \(0.982120\pi\)
\(140\) 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 \(-0.208112\pi\)
0.793777 + 0.608209i \(0.208112\pi\)
\(152\) 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 0.190456 0.981696i \(-0.439004\pi\)
−0.874794 + 0.484495i \(0.839004\pi\)
\(164\) 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 \(-0.933096\pi\)
0.668576 0.743644i \(-0.266904\pi\)
\(168\) 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 −0.991243 0.132048i \(-0.957845\pi\)
0.879549 + 0.475809i \(0.157845\pi\)
\(180\) 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 0.911699 0.410859i \(-0.134771\pi\)
−0.109020 + 0.994040i \(0.534771\pi\)
\(192\) 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 \(-0.828549\pi\)
−0.858413 + 0.512960i \(0.828549\pi\)
\(200\) 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 −0.528372 0.849013i \(-0.677197\pi\)
0.644184 + 0.764871i \(0.277197\pi\)
\(212\) 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 −0.974217 0.225611i \(-0.927562\pi\)
−0.0864809 + 0.996254i \(0.527562\pi\)
\(224\) 0 0
\(225\) −7.43696 2.13044i −0.495797 0.142030i
\(226\) 0 0
\(227\) 5.30621 3.85518i 0.352185 0.255878i −0.397600 0.917559i \(-0.630157\pi\)
0.749785 + 0.661681i \(0.230157\pi\)
\(228\) 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 −0.355117 0.934822i \(-0.615559\pi\)
0.779331 + 0.626612i \(0.215559\pi\)
\(240\) 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 \(-0.733663\pi\)
−0.669899 + 0.742452i \(0.733663\pi\)
\(252\) 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 0.807395 0.590012i \(-0.200877\pi\)
−0.311636 + 0.950202i \(0.600877\pi\)
\(264\) 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 −0.903414 0.428770i \(-0.858947\pi\)
0.982902 + 0.184131i \(0.0589470\pi\)
\(272\) 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 \(-0.876170\pi\)
0.525628 0.850714i \(-0.323830\pi\)
\(284\) 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 \(-0.501513\pi\)
−0.00475384 + 0.999989i \(0.501513\pi\)
\(308\) 0 0
\(309\) −1.82850 1.32848i −0.104020 0.0755748i
\(310\) 0 0
\(311\) −6.42513 + 4.66813i −0.364335 + 0.264705i −0.754858 0.655888i \(-0.772294\pi\)
0.390523 + 0.920593i \(0.372294\pi\)
\(312\) 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 \(-0.750660\pi\)
0.158481 0.987362i \(-0.449340\pi\)
\(332\) 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 \(-0.546047\pi\)
0.698272 0.715832i \(-0.253953\pi\)
\(348\) 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 \(0.129796\pi\)
0.660830 + 0.750536i \(0.270204\pi\)
\(360\) 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 0.919119 0.393980i \(-0.128902\pi\)
−0.975159 + 0.221508i \(0.928902\pi\)
\(368\) 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 −0.909602 0.415481i \(-0.863613\pi\)
0.980097 + 0.198519i \(0.0636133\pi\)
\(380\) 0 0
\(381\) −4.37219 13.4562i −0.223994 0.689383i
\(382\) 0 0
\(383\) 0.726319 + 2.23538i 0.0371132 + 0.114223i 0.967897 0.251348i \(-0.0808739\pi\)
−0.930784 + 0.365571i \(0.880874\pi\)
\(384\) 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 \(-0.971364\pi\)
0.752937 0.658092i \(-0.228636\pi\)
\(420\) 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 \(0.0617601\pi\)
−0.680506 + 0.732743i \(0.738240\pi\)
\(432\) 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 −0.00924884 0.999957i \(-0.502944\pi\)
0.948158 + 0.317800i \(0.102944\pi\)
\(440\) 0 0
\(441\) −5.56026 4.03977i −0.264775 0.192370i
\(442\) 0 0
\(443\) 18.2746 0.868252 0.434126 0.900852i \(-0.357057\pi\)
0.434126 + 0.900852i \(0.357057\pi\)
\(444\) 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 0.972093 0.234594i \(-0.0753762\pi\)
0.0772808 + 0.997009i \(0.475376\pi\)
\(464\) 0 0
\(465\) 0.867341 + 4.91524i 0.0402220 + 0.227939i
\(466\) 0 0
\(467\) −0.730903 2.24949i −0.0338222 0.104094i 0.932720 0.360601i \(-0.117428\pi\)
−0.966542 + 0.256507i \(0.917428\pi\)
\(468\) 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 −0.852221 0.523182i \(-0.824745\pi\)
0.996980 + 0.0776594i \(0.0247447\pi\)
\(480\) 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 0.235551 0.971862i \(-0.424311\pi\)
−0.851506 + 0.524344i \(0.824311\pi\)
\(488\) 0 0
\(489\) 10.5309 7.65114i 0.476223 0.345996i
\(490\) 0 0
\(491\) −22.7142 16.5028i −1.02508 0.744762i −0.0577599 0.998331i \(-0.518396\pi\)
−0.967318 + 0.253568i \(0.918396\pi\)
\(492\) 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 \(-0.726791\pi\)
−0.653717 + 0.756739i \(0.726791\pi\)
\(500\) 0 0
\(501\) 15.5962 0.696787
\(502\) 0 0
\(503\) −9.53123 + 29.3341i −0.424977 + 1.30794i 0.478040 + 0.878338i \(0.341347\pi\)
−0.903017 + 0.429606i \(0.858653\pi\)
\(504\) 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 −0.793819 0.608155i \(-0.791910\pi\)
0.333086 + 0.942896i \(0.391910\pi\)
\(524\) 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 \(0.273497\pi\)
−0.973462 + 0.228850i \(0.926503\pi\)
\(548\) 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 0.451662 0.892189i \(-0.350831\pi\)
−0.708951 + 0.705257i \(0.750831\pi\)
\(564\) 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 \(0.217087\pi\)
−0.998560 + 0.0536545i \(0.982913\pi\)
\(572\) 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 0.872892 0.487914i \(-0.162242\pi\)
−0.194296 + 0.980943i \(0.562242\pi\)
\(588\) 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 \(-0.426817\pi\)
0.227890 + 0.973687i \(0.426817\pi\)
\(600\) 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 \(-0.529559\pi\)
−0.0927275 + 0.995692i \(0.529559\pi\)
\(608\) 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 0.999099 0.0424406i \(-0.0135133\pi\)
−0.833234 + 0.552921i \(0.813513\pi\)
\(620\) 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 0.948183 0.317724i \(-0.102918\pi\)
−0.953850 + 0.300284i \(0.902918\pi\)
\(632\) 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 \(-0.411844\pi\)
0.273424 + 0.961894i \(0.411844\pi\)
\(644\) 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 \(0.307801\pi\)
−0.943198 + 0.332231i \(0.892199\pi\)
\(648\) 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 0.589970 0.807425i \(-0.299140\pi\)
−0.585596 + 0.810603i \(0.699140\pi\)
\(660\) 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 \(-0.925094\pi\)
0.649673 0.760214i \(-0.274906\pi\)
\(684\) 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 0.990274 0.139134i \(-0.0444317\pi\)
0.173688 + 0.984801i \(0.444432\pi\)
\(692\) 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 \(0.0649767\pi\)
−0.673067 + 0.739582i \(0.735023\pi\)
\(720\) 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 −0.608532 0.793529i \(-0.708241\pi\)
0.566644 + 0.823963i \(0.308241\pi\)
\(728\) 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 −0.0221698 0.999754i \(-0.507057\pi\)
0.943972 + 0.330026i \(0.107057\pi\)
\(740\) 0 0
\(741\) 8.06351 + 5.85848i 0.296220 + 0.215217i
\(742\) 0 0
\(743\) −9.18330 −0.336902 −0.168451 0.985710i \(-0.553877\pi\)
−0.168451 + 0.985710i \(0.553877\pi\)
\(744\) 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 \(-0.189871\pi\)
0.827309 + 0.561747i \(0.189871\pi\)
\(752\) 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 0.917237 0.398342i \(-0.130414\pi\)
−0.0954038 + 0.995439i \(0.530414\pi\)
\(788\) 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 \(-0.352381\pi\)
0.988831 0.149042i \(-0.0476189\pi\)
\(812\) 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 −0.235898 0.971778i \(-0.575803\pi\)
0.851319 + 0.524649i \(0.175803\pi\)
\(824\) 0 0
\(825\) 13.1228 + 16.7875i 0.456878 + 0.584467i
\(826\) 0 0
\(827\) 23.7315 17.2419i 0.825224 0.599560i −0.0929802 0.995668i \(-0.529639\pi\)
0.918204 + 0.396108i \(0.129639\pi\)
\(828\) 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 −0.923405 0.383826i \(-0.874606\pi\)
0.0796927 + 0.996819i \(0.474606\pi\)
\(840\) 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 0.647957 0.761677i \(-0.275624\pi\)
−0.524169 + 0.851615i \(0.675624\pi\)
\(860\) 0 0
\(861\) 12.5225 9.09812i 0.426765 0.310063i
\(862\) 0 0
\(863\) −18.7437 13.6181i −0.638044 0.463566i 0.221133 0.975244i \(-0.429024\pi\)
−0.859178 + 0.511677i \(0.829024\pi\)
\(864\) 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 0.915778 0.401684i \(-0.131575\pi\)
−0.976984 + 0.213312i \(0.931575\pi\)
\(884\) 0 0
\(885\) −26.6442 25.7234i −0.895634 0.864681i
\(886\) 0 0
\(887\) −21.1004 15.3304i −0.708484 0.514744i 0.174200 0.984710i \(-0.444266\pi\)
−0.882684 + 0.469967i \(0.844266\pi\)
\(888\) 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 \(-0.878598\pi\)
−0.928146 + 0.372216i \(0.878598\pi\)
\(908\) 0 0
\(909\) 23.0491 + 16.7462i 0.764491 + 0.555435i
\(910\) 0 0
\(911\) 9.01861 6.55240i 0.298800 0.217091i −0.428276 0.903648i \(-0.640879\pi\)
0.727076 + 0.686557i \(0.240879\pi\)
\(912\) 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 0.952485 0.304585i \(-0.0985179\pi\)
−0.949607 + 0.313442i \(0.898518\pi\)
\(920\) 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 \(-0.755154\pi\)
0.990092 0.140422i \(-0.0448460\pi\)
\(948\) 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 \(-0.752560\pi\)
0.164373 0.986398i \(-0.447440\pi\)
\(968\) 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 \(0.328179\pi\)
−0.920012 + 0.391891i \(0.871821\pi\)
\(972\) 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 \(-0.857507\pi\)
0.474877 0.880052i \(-0.342493\pi\)
\(984\) 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 0.388281 0.921541i \(-0.373069\pi\)
−0.756452 + 0.654049i \(0.773069\pi\)
\(992\) 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 400.2.u.g.161.2 16
4.3 odd 2 200.2.m.c.161.3 yes 16
20.3 even 4 1000.2.q.d.449.5 32
20.7 even 4 1000.2.q.d.449.4 32
20.19 odd 2 1000.2.m.c.801.2 16
25.4 even 10 10000.2.a.bh.1.6 8
25.16 even 5 inner 400.2.u.g.241.2 16
25.21 even 5 10000.2.a.bk.1.3 8
100.59 odd 10 1000.2.m.c.201.2 16
100.63 even 20 1000.2.q.d.49.4 32
100.71 odd 10 5000.2.a.l.1.6 8
100.79 odd 10 5000.2.a.m.1.3 8
100.87 even 20 1000.2.q.d.49.5 32
100.91 odd 10 200.2.m.c.41.3 16
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
200.2.m.c.41.3 16 100.91 odd 10
200.2.m.c.161.3 yes 16 4.3 odd 2
400.2.u.g.161.2 16 1.1 even 1 trivial
400.2.u.g.241.2 16 25.16 even 5 inner
1000.2.m.c.201.2 16 100.59 odd 10
1000.2.m.c.801.2 16 20.19 odd 2
1000.2.q.d.49.4 32 100.63 even 20
1000.2.q.d.49.5 32 100.87 even 20
1000.2.q.d.449.4 32 20.7 even 4
1000.2.q.d.449.5 32 20.3 even 4
5000.2.a.l.1.6 8 100.71 odd 10
5000.2.a.m.1.3 8 100.79 odd 10
10000.2.a.bh.1.6 8 25.4 even 10
10000.2.a.bk.1.3 8 25.21 even 5