Properties

Label 128.2.g.b.17.1
Level $128$
Weight $2$
Character 128.17
Analytic conductor $1.022$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [128,2,Mod(17,128)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(128, base_ring=CyclotomicField(8))
 
chi = DirichletCharacter(H, H._module([0, 7]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("128.17");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 128 = 2^{7} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 128.g (of order \(8\), degree \(4\), not minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(1.02208514587\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(2\) over \(\Q(\zeta_{8})\)
Coefficient field: 8.0.18939904.2
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{8} - 4x^{7} + 14x^{6} - 28x^{5} + 43x^{4} - 44x^{3} + 30x^{2} - 12x + 2 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 2^{3} \)
Twist minimal: no (minimal twist has level 32)
Sato-Tate group: $\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label 17.1
Root \(0.500000 + 0.691860i\) of defining polynomial
Character \(\chi\) \(=\) 128.17
Dual form 128.2.g.b.113.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.0794708 + 0.191860i) q^{3} +(0.707107 - 0.292893i) q^{5} +(2.27133 - 2.27133i) q^{7} +(2.09083 + 2.09083i) q^{9} +O(q^{10})\) \(q+(-0.0794708 + 0.191860i) q^{3} +(0.707107 - 0.292893i) q^{5} +(2.27133 - 2.27133i) q^{7} +(2.09083 + 2.09083i) q^{9} +(1.49368 + 3.60607i) q^{11} +(-4.50504 - 1.86605i) q^{13} +0.158942i q^{15} -3.05320i q^{17} +(-3.87740 - 1.60607i) q^{19} +(0.255272 + 0.616281i) q^{21} +(-0.271330 - 0.271330i) q^{23} +(-3.12132 + 3.12132i) q^{25} +(-1.14288 + 0.473398i) q^{27} +(-0.931884 + 2.24977i) q^{29} -6.82843 q^{31} -0.810564 q^{33} +(0.940816 - 2.27133i) q^{35} +(3.63349 - 1.50504i) q^{37} +(0.716038 - 0.716038i) q^{39} +(-1.54266 - 1.54266i) q^{41} +(-0.748956 - 1.80814i) q^{43} +(2.09083 + 0.866048i) q^{45} +7.37109i q^{47} -3.31788i q^{49} +(0.585786 + 0.242641i) q^{51} +(1.67661 + 4.04770i) q^{53} +(2.11239 + 2.11239i) q^{55} +(0.616281 - 0.616281i) q^{57} +(10.1200 - 4.19186i) q^{59} +(1.35873 - 3.28026i) q^{61} +9.49791 q^{63} -3.73210 q^{65} +(1.99577 - 4.81822i) q^{67} +(0.0736202 - 0.0304945i) q^{69} +(-6.47085 + 6.47085i) q^{71} +(-2.84106 - 2.84106i) q^{73} +(-0.350801 - 0.846909i) q^{75} +(11.5832 + 4.79793i) q^{77} -9.74996i q^{79} +8.61373i q^{81} +(9.04642 + 3.74715i) q^{83} +(-0.894263 - 2.15894i) q^{85} +(-0.357582 - 0.357582i) q^{87} +(7.58323 - 7.58323i) q^{89} +(-14.4708 + 5.99402i) q^{91} +(0.542661 - 1.31010i) q^{93} -3.21215 q^{95} +3.71423 q^{97} +(-4.41664 + 10.6627i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q + 4 q^{3} + 8 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 8 q + 4 q^{3} + 8 q^{7} - 4 q^{11} - 8 q^{13} - 4 q^{19} + 8 q^{23} - 8 q^{25} - 8 q^{27} - 32 q^{31} - 16 q^{33} - 16 q^{35} - 8 q^{37} - 16 q^{39} + 8 q^{41} + 12 q^{43} + 16 q^{51} + 8 q^{53} + 16 q^{55} + 16 q^{57} + 20 q^{59} + 24 q^{61} + 40 q^{63} + 36 q^{67} + 32 q^{69} + 24 q^{71} - 32 q^{73} + 12 q^{75} + 16 q^{77} - 20 q^{83} + 8 q^{85} - 56 q^{87} - 16 q^{89} - 40 q^{91} - 16 q^{93} + 8 q^{95} + 32 q^{97} - 28 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/128\mathbb{Z}\right)^\times\).

\(n\) \(5\) \(127\)
\(\chi(n)\) \(e\left(\frac{7}{8}\right)\) \(1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) −0.0794708 + 0.191860i −0.0458825 + 0.110770i −0.945159 0.326610i \(-0.894094\pi\)
0.899277 + 0.437380i \(0.144094\pi\)
\(4\) 0 0
\(5\) 0.707107 0.292893i 0.316228 0.130986i −0.218924 0.975742i \(-0.570255\pi\)
0.535151 + 0.844756i \(0.320255\pi\)
\(6\) 0 0
\(7\) 2.27133 2.27133i 0.858482 0.858482i −0.132677 0.991159i \(-0.542357\pi\)
0.991159 + 0.132677i \(0.0423573\pi\)
\(8\) 0 0
\(9\) 2.09083 + 2.09083i 0.696942 + 0.696942i
\(10\) 0 0
\(11\) 1.49368 + 3.60607i 0.450363 + 1.08727i 0.972184 + 0.234217i \(0.0752527\pi\)
−0.521821 + 0.853055i \(0.674747\pi\)
\(12\) 0 0
\(13\) −4.50504 1.86605i −1.24947 0.517549i −0.342810 0.939405i \(-0.611379\pi\)
−0.906663 + 0.421856i \(0.861379\pi\)
\(14\) 0 0
\(15\) 0.158942i 0.0410386i
\(16\) 0 0
\(17\) 3.05320i 0.740511i −0.928930 0.370255i \(-0.879270\pi\)
0.928930 0.370255i \(-0.120730\pi\)
\(18\) 0 0
\(19\) −3.87740 1.60607i −0.889537 0.368458i −0.109349 0.994003i \(-0.534877\pi\)
−0.780188 + 0.625545i \(0.784877\pi\)
\(20\) 0 0
\(21\) 0.255272 + 0.616281i 0.0557049 + 0.134484i
\(22\) 0 0
\(23\) −0.271330 0.271330i −0.0565763 0.0565763i 0.678253 0.734829i \(-0.262738\pi\)
−0.734829 + 0.678253i \(0.762738\pi\)
\(24\) 0 0
\(25\) −3.12132 + 3.12132i −0.624264 + 0.624264i
\(26\) 0 0
\(27\) −1.14288 + 0.473398i −0.219948 + 0.0911054i
\(28\) 0 0
\(29\) −0.931884 + 2.24977i −0.173047 + 0.417771i −0.986479 0.163888i \(-0.947596\pi\)
0.813432 + 0.581660i \(0.197596\pi\)
\(30\) 0 0
\(31\) −6.82843 −1.22642 −0.613211 0.789919i \(-0.710122\pi\)
−0.613211 + 0.789919i \(0.710122\pi\)
\(32\) 0 0
\(33\) −0.810564 −0.141101
\(34\) 0 0
\(35\) 0.940816 2.27133i 0.159027 0.383925i
\(36\) 0 0
\(37\) 3.63349 1.50504i 0.597342 0.247427i −0.0634640 0.997984i \(-0.520215\pi\)
0.660806 + 0.750557i \(0.270215\pi\)
\(38\) 0 0
\(39\) 0.716038 0.716038i 0.114658 0.114658i
\(40\) 0 0
\(41\) −1.54266 1.54266i −0.240923 0.240923i 0.576309 0.817232i \(-0.304493\pi\)
−0.817232 + 0.576309i \(0.804493\pi\)
\(42\) 0 0
\(43\) −0.748956 1.80814i −0.114215 0.275739i 0.856427 0.516268i \(-0.172679\pi\)
−0.970642 + 0.240529i \(0.922679\pi\)
\(44\) 0 0
\(45\) 2.09083 + 0.866048i 0.311682 + 0.129103i
\(46\) 0 0
\(47\) 7.37109i 1.07518i 0.843205 + 0.537592i \(0.180666\pi\)
−0.843205 + 0.537592i \(0.819334\pi\)
\(48\) 0 0
\(49\) 3.31788i 0.473983i
\(50\) 0 0
\(51\) 0.585786 + 0.242641i 0.0820265 + 0.0339765i
\(52\) 0 0
\(53\) 1.67661 + 4.04770i 0.230300 + 0.555994i 0.996213 0.0869508i \(-0.0277123\pi\)
−0.765912 + 0.642945i \(0.777712\pi\)
\(54\) 0 0
\(55\) 2.11239 + 2.11239i 0.284834 + 0.284834i
\(56\) 0 0
\(57\) 0.616281 0.616281i 0.0816284 0.0816284i
\(58\) 0 0
\(59\) 10.1200 4.19186i 1.31752 0.545734i 0.390449 0.920625i \(-0.372320\pi\)
0.927069 + 0.374891i \(0.122320\pi\)
\(60\) 0 0
\(61\) 1.35873 3.28026i 0.173967 0.419995i −0.812713 0.582664i \(-0.802010\pi\)
0.986681 + 0.162669i \(0.0520104\pi\)
\(62\) 0 0
\(63\) 9.49791 1.19662
\(64\) 0 0
\(65\) −3.73210 −0.462910
\(66\) 0 0
\(67\) 1.99577 4.81822i 0.243822 0.588639i −0.753834 0.657065i \(-0.771798\pi\)
0.997656 + 0.0684259i \(0.0217977\pi\)
\(68\) 0 0
\(69\) 0.0736202 0.0304945i 0.00886283 0.00367110i
\(70\) 0 0
\(71\) −6.47085 + 6.47085i −0.767948 + 0.767948i −0.977745 0.209797i \(-0.932720\pi\)
0.209797 + 0.977745i \(0.432720\pi\)
\(72\) 0 0
\(73\) −2.84106 2.84106i −0.332521 0.332521i 0.521022 0.853543i \(-0.325551\pi\)
−0.853543 + 0.521022i \(0.825551\pi\)
\(74\) 0 0
\(75\) −0.350801 0.846909i −0.0405070 0.0977926i
\(76\) 0 0
\(77\) 11.5832 + 4.79793i 1.32003 + 0.546775i
\(78\) 0 0
\(79\) 9.74996i 1.09696i −0.836165 0.548478i \(-0.815207\pi\)
0.836165 0.548478i \(-0.184793\pi\)
\(80\) 0 0
\(81\) 8.61373i 0.957081i
\(82\) 0 0
\(83\) 9.04642 + 3.74715i 0.992974 + 0.411303i 0.819216 0.573485i \(-0.194409\pi\)
0.173758 + 0.984788i \(0.444409\pi\)
\(84\) 0 0
\(85\) −0.894263 2.15894i −0.0969964 0.234170i
\(86\) 0 0
\(87\) −0.357582 0.357582i −0.0383368 0.0383368i
\(88\) 0 0
\(89\) 7.58323 7.58323i 0.803821 0.803821i −0.179869 0.983691i \(-0.557567\pi\)
0.983691 + 0.179869i \(0.0575675\pi\)
\(90\) 0 0
\(91\) −14.4708 + 5.99402i −1.51696 + 0.628344i
\(92\) 0 0
\(93\) 0.542661 1.31010i 0.0562713 0.135851i
\(94\) 0 0
\(95\) −3.21215 −0.329559
\(96\) 0 0
\(97\) 3.71423 0.377123 0.188562 0.982061i \(-0.439617\pi\)
0.188562 + 0.982061i \(0.439617\pi\)
\(98\) 0 0
\(99\) −4.41664 + 10.6627i −0.443889 + 1.07164i
\(100\) 0 0
\(101\) −9.04770 + 3.74768i −0.900280 + 0.372908i −0.784328 0.620347i \(-0.786992\pi\)
−0.115952 + 0.993255i \(0.536992\pi\)
\(102\) 0 0
\(103\) −0.450688 + 0.450688i −0.0444076 + 0.0444076i −0.728962 0.684554i \(-0.759997\pi\)
0.684554 + 0.728962i \(0.259997\pi\)
\(104\) 0 0
\(105\) 0.361009 + 0.361009i 0.0352309 + 0.0352309i
\(106\) 0 0
\(107\) −6.82420 16.4751i −0.659720 1.59271i −0.798236 0.602345i \(-0.794233\pi\)
0.138515 0.990360i \(-0.455767\pi\)
\(108\) 0 0
\(109\) −7.20664 2.98509i −0.690271 0.285920i 0.00984205 0.999952i \(-0.496867\pi\)
−0.700113 + 0.714032i \(0.746867\pi\)
\(110\) 0 0
\(111\) 0.816726i 0.0775202i
\(112\) 0 0
\(113\) 8.76744i 0.824771i 0.911009 + 0.412386i \(0.135304\pi\)
−0.911009 + 0.412386i \(0.864696\pi\)
\(114\) 0 0
\(115\) −0.271330 0.112389i −0.0253017 0.0104803i
\(116\) 0 0
\(117\) −5.51767 13.3208i −0.510109 1.23151i
\(118\) 0 0
\(119\) −6.93484 6.93484i −0.635715 0.635715i
\(120\) 0 0
\(121\) −2.99450 + 2.99450i −0.272227 + 0.272227i
\(122\) 0 0
\(123\) 0.418571 0.173378i 0.0377412 0.0156329i
\(124\) 0 0
\(125\) −2.75736 + 6.65685i −0.246626 + 0.595407i
\(126\) 0 0
\(127\) 11.4642 1.01728 0.508641 0.860979i \(-0.330148\pi\)
0.508641 + 0.860979i \(0.330148\pi\)
\(128\) 0 0
\(129\) 0.406429 0.0357841
\(130\) 0 0
\(131\) −4.32211 + 10.4345i −0.377625 + 0.911667i 0.614785 + 0.788694i \(0.289243\pi\)
−0.992410 + 0.122972i \(0.960757\pi\)
\(132\) 0 0
\(133\) −12.4548 + 5.15894i −1.07997 + 0.447337i
\(134\) 0 0
\(135\) −0.669485 + 0.669485i −0.0576201 + 0.0576201i
\(136\) 0 0
\(137\) −3.42429 3.42429i −0.292557 0.292557i 0.545533 0.838090i \(-0.316327\pi\)
−0.838090 + 0.545533i \(0.816327\pi\)
\(138\) 0 0
\(139\) 7.35745 + 17.7625i 0.624051 + 1.50659i 0.846907 + 0.531741i \(0.178462\pi\)
−0.222856 + 0.974851i \(0.571538\pi\)
\(140\) 0 0
\(141\) −1.41421 0.585786i −0.119098 0.0493321i
\(142\) 0 0
\(143\) 19.0328i 1.59160i
\(144\) 0 0
\(145\) 1.86377i 0.154778i
\(146\) 0 0
\(147\) 0.636568 + 0.263675i 0.0525032 + 0.0217475i
\(148\) 0 0
\(149\) −0.931884 2.24977i −0.0763429 0.184308i 0.881101 0.472929i \(-0.156803\pi\)
−0.957443 + 0.288621i \(0.906803\pi\)
\(150\) 0 0
\(151\) 4.21395 + 4.21395i 0.342926 + 0.342926i 0.857466 0.514540i \(-0.172037\pi\)
−0.514540 + 0.857466i \(0.672037\pi\)
\(152\) 0 0
\(153\) 6.38372 6.38372i 0.516093 0.516093i
\(154\) 0 0
\(155\) −4.82843 + 2.00000i −0.387829 + 0.160644i
\(156\) 0 0
\(157\) 5.84401 14.1087i 0.466403 1.12600i −0.499319 0.866418i \(-0.666417\pi\)
0.965722 0.259578i \(-0.0835835\pi\)
\(158\) 0 0
\(159\) −0.909832 −0.0721543
\(160\) 0 0
\(161\) −1.23256 −0.0971395
\(162\) 0 0
\(163\) 2.72369 6.57558i 0.213336 0.515039i −0.780596 0.625036i \(-0.785084\pi\)
0.993932 + 0.109997i \(0.0350842\pi\)
\(164\) 0 0
\(165\) −0.573155 + 0.237409i −0.0446201 + 0.0184822i
\(166\) 0 0
\(167\) −3.26355 + 3.26355i −0.252541 + 0.252541i −0.822012 0.569471i \(-0.807148\pi\)
0.569471 + 0.822012i \(0.307148\pi\)
\(168\) 0 0
\(169\) 7.62086 + 7.62086i 0.586220 + 0.586220i
\(170\) 0 0
\(171\) −4.74896 11.4650i −0.363162 0.876750i
\(172\) 0 0
\(173\) 6.86605 + 2.84401i 0.522016 + 0.216226i 0.628102 0.778131i \(-0.283832\pi\)
−0.106086 + 0.994357i \(0.533832\pi\)
\(174\) 0 0
\(175\) 14.1791i 1.07184i
\(176\) 0 0
\(177\) 2.27476i 0.170981i
\(178\) 0 0
\(179\) 1.79370 + 0.742977i 0.134068 + 0.0555327i 0.448709 0.893678i \(-0.351884\pi\)
−0.314641 + 0.949211i \(0.601884\pi\)
\(180\) 0 0
\(181\) 6.12132 + 14.7782i 0.454994 + 1.09845i 0.970399 + 0.241506i \(0.0776415\pi\)
−0.515405 + 0.856947i \(0.672359\pi\)
\(182\) 0 0
\(183\) 0.521370 + 0.521370i 0.0385408 + 0.0385408i
\(184\) 0 0
\(185\) 2.12845 2.12845i 0.156487 0.156487i
\(186\) 0 0
\(187\) 11.0101 4.56052i 0.805137 0.333499i
\(188\) 0 0
\(189\) −1.52062 + 3.67111i −0.110609 + 0.267034i
\(190\) 0 0
\(191\) 6.19266 0.448085 0.224043 0.974579i \(-0.428075\pi\)
0.224043 + 0.974579i \(0.428075\pi\)
\(192\) 0 0
\(193\) 14.5784 1.04938 0.524688 0.851295i \(-0.324182\pi\)
0.524688 + 0.851295i \(0.324182\pi\)
\(194\) 0 0
\(195\) 0.296593 0.716038i 0.0212395 0.0512766i
\(196\) 0 0
\(197\) 18.5025 7.66398i 1.31825 0.546036i 0.390968 0.920404i \(-0.372140\pi\)
0.927280 + 0.374368i \(0.122140\pi\)
\(198\) 0 0
\(199\) 12.3777 12.3777i 0.877435 0.877435i −0.115834 0.993269i \(-0.536954\pi\)
0.993269 + 0.115834i \(0.0369540\pi\)
\(200\) 0 0
\(201\) 0.765816 + 0.765816i 0.0540165 + 0.0540165i
\(202\) 0 0
\(203\) 2.99335 + 7.22658i 0.210092 + 0.507207i
\(204\) 0 0
\(205\) −1.54266 0.638991i −0.107744 0.0446291i
\(206\) 0 0
\(207\) 1.13461i 0.0788608i
\(208\) 0 0
\(209\) 16.3812i 1.13311i
\(210\) 0 0
\(211\) −3.54851 1.46984i −0.244290 0.101188i 0.257179 0.966364i \(-0.417207\pi\)
−0.501469 + 0.865176i \(0.667207\pi\)
\(212\) 0 0
\(213\) −0.727250 1.75574i −0.0498304 0.120301i
\(214\) 0 0
\(215\) −1.05918 1.05918i −0.0722358 0.0722358i
\(216\) 0 0
\(217\) −15.5096 + 15.5096i −1.05286 + 1.05286i
\(218\) 0 0
\(219\) 0.770865 0.319303i 0.0520903 0.0215765i
\(220\) 0 0
\(221\) −5.69743 + 13.7548i −0.383250 + 0.925248i
\(222\) 0 0
\(223\) −27.5550 −1.84522 −0.922611 0.385732i \(-0.873949\pi\)
−0.922611 + 0.385732i \(0.873949\pi\)
\(224\) 0 0
\(225\) −13.0523 −0.870152
\(226\) 0 0
\(227\) 6.02694 14.5503i 0.400022 0.965738i −0.587638 0.809124i \(-0.699942\pi\)
0.987660 0.156614i \(-0.0500580\pi\)
\(228\) 0 0
\(229\) 18.2777 7.57088i 1.20783 0.500298i 0.314306 0.949322i \(-0.398228\pi\)
0.893520 + 0.449024i \(0.148228\pi\)
\(230\) 0 0
\(231\) −1.84106 + 1.84106i −0.121133 + 0.121133i
\(232\) 0 0
\(233\) −6.70939 6.70939i −0.439547 0.439547i 0.452313 0.891859i \(-0.350599\pi\)
−0.891859 + 0.452313i \(0.850599\pi\)
\(234\) 0 0
\(235\) 2.15894 + 5.21215i 0.140834 + 0.340003i
\(236\) 0 0
\(237\) 1.87062 + 0.774837i 0.121510 + 0.0503311i
\(238\) 0 0
\(239\) 26.1995i 1.69471i 0.531030 + 0.847353i \(0.321805\pi\)
−0.531030 + 0.847353i \(0.678195\pi\)
\(240\) 0 0
\(241\) 13.6734i 0.880781i −0.897806 0.440391i \(-0.854840\pi\)
0.897806 0.440391i \(-0.145160\pi\)
\(242\) 0 0
\(243\) −5.08128 2.10473i −0.325964 0.135019i
\(244\) 0 0
\(245\) −0.971786 2.34610i −0.0620851 0.149887i
\(246\) 0 0
\(247\) 14.4708 + 14.4708i 0.920758 + 0.920758i
\(248\) 0 0
\(249\) −1.43785 + 1.43785i −0.0911203 + 0.0911203i
\(250\) 0 0
\(251\) 13.2054 5.46984i 0.833515 0.345253i 0.0752219 0.997167i \(-0.476033\pi\)
0.758293 + 0.651913i \(0.226033\pi\)
\(252\) 0 0
\(253\) 0.573155 1.38372i 0.0360340 0.0869937i
\(254\) 0 0
\(255\) 0.485281 0.0303895
\(256\) 0 0
\(257\) −20.0656 −1.25166 −0.625828 0.779961i \(-0.715239\pi\)
−0.625828 + 0.779961i \(0.715239\pi\)
\(258\) 0 0
\(259\) 4.83441 11.6713i 0.300395 0.725219i
\(260\) 0 0
\(261\) −6.65228 + 2.75546i −0.411766 + 0.170559i
\(262\) 0 0
\(263\) −4.74976 + 4.74976i −0.292883 + 0.292883i −0.838218 0.545335i \(-0.816402\pi\)
0.545335 + 0.838218i \(0.316402\pi\)
\(264\) 0 0
\(265\) 2.37109 + 2.37109i 0.145655 + 0.145655i
\(266\) 0 0
\(267\) 0.852270 + 2.05756i 0.0521581 + 0.125921i
\(268\) 0 0
\(269\) −22.3818 9.27086i −1.36464 0.565254i −0.424313 0.905516i \(-0.639484\pi\)
−0.940331 + 0.340262i \(0.889484\pi\)
\(270\) 0 0
\(271\) 0.693146i 0.0421056i 0.999778 + 0.0210528i \(0.00670181\pi\)
−0.999778 + 0.0210528i \(0.993298\pi\)
\(272\) 0 0
\(273\) 3.25272i 0.196864i
\(274\) 0 0
\(275\) −15.9180 6.59344i −0.959890 0.397600i
\(276\) 0 0
\(277\) 11.1898 + 27.0147i 0.672332 + 1.62315i 0.777637 + 0.628713i \(0.216418\pi\)
−0.105305 + 0.994440i \(0.533582\pi\)
\(278\) 0 0
\(279\) −14.2771 14.2771i −0.854745 0.854745i
\(280\) 0 0
\(281\) −6.97958 + 6.97958i −0.416367 + 0.416367i −0.883949 0.467582i \(-0.845125\pi\)
0.467582 + 0.883949i \(0.345125\pi\)
\(282\) 0 0
\(283\) −14.6079 + 6.05078i −0.868348 + 0.359682i −0.771967 0.635663i \(-0.780727\pi\)
−0.0963814 + 0.995344i \(0.530727\pi\)
\(284\) 0 0
\(285\) 0.255272 0.616281i 0.0151210 0.0365053i
\(286\) 0 0
\(287\) −7.00778 −0.413656
\(288\) 0 0
\(289\) 7.67794 0.451644
\(290\) 0 0
\(291\) −0.295173 + 0.712611i −0.0173034 + 0.0417740i
\(292\) 0 0
\(293\) −9.85571 + 4.08237i −0.575777 + 0.238495i −0.651518 0.758633i \(-0.725868\pi\)
0.0757415 + 0.997127i \(0.475868\pi\)
\(294\) 0 0
\(295\) 5.92818 5.92818i 0.345152 0.345152i
\(296\) 0 0
\(297\) −3.41421 3.41421i −0.198113 0.198113i
\(298\) 0 0
\(299\) 0.716038 + 1.72867i 0.0414096 + 0.0999715i
\(300\) 0 0
\(301\) −5.80801 2.40576i −0.334768 0.138666i
\(302\) 0 0
\(303\) 2.03372i 0.116834i
\(304\) 0 0
\(305\) 2.71746i 0.155601i
\(306\) 0 0
\(307\) −6.96272 2.88406i −0.397384 0.164602i 0.175037 0.984562i \(-0.443996\pi\)
−0.572421 + 0.819960i \(0.693996\pi\)
\(308\) 0 0
\(309\) −0.0506522 0.122285i −0.00288150 0.00695656i
\(310\) 0 0
\(311\) −4.65020 4.65020i −0.263689 0.263689i 0.562862 0.826551i \(-0.309700\pi\)
−0.826551 + 0.562862i \(0.809700\pi\)
\(312\) 0 0
\(313\) −0.325668 + 0.325668i −0.0184078 + 0.0184078i −0.716251 0.697843i \(-0.754143\pi\)
0.697843 + 0.716251i \(0.254143\pi\)
\(314\) 0 0
\(315\) 6.71604 2.78187i 0.378406 0.156741i
\(316\) 0 0
\(317\) 7.92866 19.1415i 0.445318 1.07509i −0.528738 0.848785i \(-0.677335\pi\)
0.974056 0.226307i \(-0.0726654\pi\)
\(318\) 0 0
\(319\) −9.50477 −0.532165
\(320\) 0 0
\(321\) 3.70322 0.206694
\(322\) 0 0
\(323\) −4.90367 + 11.8385i −0.272847 + 0.658712i
\(324\) 0 0
\(325\) 19.8862 8.23714i 1.10309 0.456914i
\(326\) 0 0
\(327\) 1.14544 1.14544i 0.0633427 0.0633427i
\(328\) 0 0
\(329\) 16.7422 + 16.7422i 0.923026 + 0.923026i
\(330\) 0 0
\(331\) 5.91798 + 14.2873i 0.325281 + 0.785299i 0.998930 + 0.0462470i \(0.0147261\pi\)
−0.673649 + 0.739052i \(0.735274\pi\)
\(332\) 0 0
\(333\) 10.7438 + 4.45021i 0.588755 + 0.243870i
\(334\) 0 0
\(335\) 3.99154i 0.218081i
\(336\) 0 0
\(337\) 4.44955i 0.242383i 0.992629 + 0.121191i \(0.0386715\pi\)
−0.992629 + 0.121191i \(0.961329\pi\)
\(338\) 0 0
\(339\) −1.68212 0.696756i −0.0913600 0.0378426i
\(340\) 0 0
\(341\) −10.1995 24.6238i −0.552335 1.33345i
\(342\) 0 0
\(343\) 8.36330 + 8.36330i 0.451576 + 0.451576i
\(344\) 0 0
\(345\) 0.0431257 0.0431257i 0.00232181 0.00232181i
\(346\) 0 0
\(347\) −7.87485 + 3.26187i −0.422744 + 0.175106i −0.583905 0.811822i \(-0.698476\pi\)
0.161161 + 0.986928i \(0.448476\pi\)
\(348\) 0 0
\(349\) −12.9387 + 31.2369i −0.692595 + 1.67207i 0.0468913 + 0.998900i \(0.485069\pi\)
−0.739486 + 0.673172i \(0.764931\pi\)
\(350\) 0 0
\(351\) 6.03212 0.321971
\(352\) 0 0
\(353\) 20.7013 1.10182 0.550911 0.834564i \(-0.314280\pi\)
0.550911 + 0.834564i \(0.314280\pi\)
\(354\) 0 0
\(355\) −2.68031 + 6.47085i −0.142256 + 0.343437i
\(356\) 0 0
\(357\) 1.88163 0.779397i 0.0995865 0.0412501i
\(358\) 0 0
\(359\) 19.9483 19.9483i 1.05283 1.05283i 0.0543091 0.998524i \(-0.482704\pi\)
0.998524 0.0543091i \(-0.0172956\pi\)
\(360\) 0 0
\(361\) −0.980242 0.980242i −0.0515917 0.0515917i
\(362\) 0 0
\(363\) −0.336548 0.812498i −0.0176642 0.0426451i
\(364\) 0 0
\(365\) −2.84106 1.17680i −0.148708 0.0615968i
\(366\) 0 0
\(367\) 9.14270i 0.477245i −0.971112 0.238623i \(-0.923304\pi\)
0.971112 0.238623i \(-0.0766959\pi\)
\(368\) 0 0
\(369\) 6.45087i 0.335819i
\(370\) 0 0
\(371\) 13.0018 + 5.38552i 0.675020 + 0.279602i
\(372\) 0 0
\(373\) −3.71974 8.98024i −0.192601 0.464979i 0.797848 0.602858i \(-0.205972\pi\)
−0.990449 + 0.137879i \(0.955972\pi\)
\(374\) 0 0
\(375\) −1.05805 1.05805i −0.0546375 0.0546375i
\(376\) 0 0
\(377\) 8.39635 8.39635i 0.432434 0.432434i
\(378\) 0 0
\(379\) 7.80216 3.23176i 0.400770 0.166004i −0.173189 0.984889i \(-0.555407\pi\)
0.573959 + 0.818884i \(0.305407\pi\)
\(380\) 0 0
\(381\) −0.911069 + 2.19951i −0.0466755 + 0.112685i
\(382\) 0 0
\(383\) 28.4633 1.45440 0.727202 0.686423i \(-0.240820\pi\)
0.727202 + 0.686423i \(0.240820\pi\)
\(384\) 0 0
\(385\) 9.59587 0.489051
\(386\) 0 0
\(387\) 2.21457 5.34644i 0.112573 0.271775i
\(388\) 0 0
\(389\) −21.0834 + 8.73304i −1.06897 + 0.442783i −0.846628 0.532185i \(-0.821371\pi\)
−0.222344 + 0.974968i \(0.571371\pi\)
\(390\) 0 0
\(391\) −0.828427 + 0.828427i −0.0418954 + 0.0418954i
\(392\) 0 0
\(393\) −1.65848 1.65848i −0.0836591 0.0836591i
\(394\) 0 0
\(395\) −2.85570 6.89426i −0.143686 0.346888i
\(396\) 0 0
\(397\) −6.46808 2.67916i −0.324623 0.134463i 0.214420 0.976742i \(-0.431214\pi\)
−0.539043 + 0.842278i \(0.681214\pi\)
\(398\) 0 0
\(399\) 2.79956i 0.140153i
\(400\) 0 0
\(401\) 24.9871i 1.24780i 0.781505 + 0.623898i \(0.214452\pi\)
−0.781505 + 0.623898i \(0.785548\pi\)
\(402\) 0 0
\(403\) 30.7623 + 12.7422i 1.53238 + 0.634733i
\(404\) 0 0
\(405\) 2.52290 + 6.09083i 0.125364 + 0.302656i
\(406\) 0 0
\(407\) 10.8546 + 10.8546i 0.538041 + 0.538041i
\(408\) 0 0
\(409\) 9.19951 9.19951i 0.454887 0.454887i −0.442086 0.896973i \(-0.645761\pi\)
0.896973 + 0.442086i \(0.145761\pi\)
\(410\) 0 0
\(411\) 0.929115 0.384852i 0.0458298 0.0189833i
\(412\) 0 0
\(413\) 13.4649 32.5071i 0.662563 1.59957i
\(414\) 0 0
\(415\) 7.49430 0.367881
\(416\) 0 0
\(417\) −3.99260 −0.195519
\(418\) 0 0
\(419\) −10.4739 + 25.2863i −0.511685 + 1.23532i 0.431217 + 0.902248i \(0.358084\pi\)
−0.942902 + 0.333070i \(0.891916\pi\)
\(420\) 0 0
\(421\) −16.6841 + 6.91080i −0.813135 + 0.336812i −0.750204 0.661206i \(-0.770045\pi\)
−0.0629310 + 0.998018i \(0.520045\pi\)
\(422\) 0 0
\(423\) −15.4117 + 15.4117i −0.749341 + 0.749341i
\(424\) 0 0
\(425\) 9.53003 + 9.53003i 0.462274 + 0.462274i
\(426\) 0 0
\(427\) −4.36444 10.5367i −0.211210 0.509906i
\(428\) 0 0
\(429\) 3.65162 + 1.51255i 0.176302 + 0.0730267i
\(430\) 0 0
\(431\) 26.5985i 1.28121i −0.767872 0.640603i \(-0.778684\pi\)
0.767872 0.640603i \(-0.221316\pi\)
\(432\) 0 0
\(433\) 9.96788i 0.479026i 0.970893 + 0.239513i \(0.0769878\pi\)
−0.970893 + 0.239513i \(0.923012\pi\)
\(434\) 0 0
\(435\) −0.357582 0.148115i −0.0171447 0.00710158i
\(436\) 0 0
\(437\) 0.616281 + 1.48783i 0.0294807 + 0.0711727i
\(438\) 0 0
\(439\) −17.4631 17.4631i −0.833466 0.833466i 0.154523 0.987989i \(-0.450616\pi\)
−0.987989 + 0.154523i \(0.950616\pi\)
\(440\) 0 0
\(441\) 6.93712 6.93712i 0.330339 0.330339i
\(442\) 0 0
\(443\) −34.7377 + 14.3888i −1.65044 + 0.683634i −0.997288 0.0735956i \(-0.976553\pi\)
−0.653149 + 0.757229i \(0.726553\pi\)
\(444\) 0 0
\(445\) 3.14108 7.58323i 0.148901 0.359480i
\(446\) 0 0
\(447\) 0.505697 0.0239186
\(448\) 0 0
\(449\) −8.35000 −0.394061 −0.197030 0.980397i \(-0.563130\pi\)
−0.197030 + 0.980397i \(0.563130\pi\)
\(450\) 0 0
\(451\) 3.25870 7.86720i 0.153446 0.370452i
\(452\) 0 0
\(453\) −1.14337 + 0.473601i −0.0537203 + 0.0222517i
\(454\) 0 0
\(455\) −8.47682 + 8.47682i −0.397400 + 0.397400i
\(456\) 0 0
\(457\) −18.0734 18.0734i −0.845436 0.845436i 0.144123 0.989560i \(-0.453964\pi\)
−0.989560 + 0.144123i \(0.953964\pi\)
\(458\) 0 0
\(459\) 1.44538 + 3.48946i 0.0674646 + 0.162874i
\(460\) 0 0
\(461\) 26.4451 + 10.9539i 1.23167 + 0.510175i 0.901102 0.433607i \(-0.142759\pi\)
0.330569 + 0.943782i \(0.392759\pi\)
\(462\) 0 0
\(463\) 4.94169i 0.229660i −0.993385 0.114830i \(-0.963368\pi\)
0.993385 0.114830i \(-0.0366323\pi\)
\(464\) 0 0
\(465\) 1.08532i 0.0503306i
\(466\) 0 0
\(467\) −20.6806 8.56617i −0.956983 0.396395i −0.151132 0.988514i \(-0.548292\pi\)
−0.805851 + 0.592118i \(0.798292\pi\)
\(468\) 0 0
\(469\) −6.41071 15.4768i −0.296019 0.714653i
\(470\) 0 0
\(471\) 2.24246 + 2.24246i 0.103327 + 0.103327i
\(472\) 0 0
\(473\) 5.40158 5.40158i 0.248365 0.248365i
\(474\) 0 0
\(475\) 17.1157 7.08955i 0.785322 0.325291i
\(476\) 0 0
\(477\) −4.95753 + 11.9685i −0.226990 + 0.548002i
\(478\) 0 0
\(479\) 5.50637 0.251592 0.125796 0.992056i \(-0.459851\pi\)
0.125796 + 0.992056i \(0.459851\pi\)
\(480\) 0 0
\(481\) −19.1775 −0.874418
\(482\) 0 0
\(483\) 0.0979527 0.236479i 0.00445700 0.0107602i
\(484\) 0 0
\(485\) 2.62636 1.08787i 0.119257 0.0493978i
\(486\) 0 0
\(487\) −24.9561 + 24.9561i −1.13087 + 1.13087i −0.140837 + 0.990033i \(0.544979\pi\)
−0.990033 + 0.140837i \(0.955021\pi\)
\(488\) 0 0
\(489\) 1.04513 + 1.04513i 0.0472626 + 0.0472626i
\(490\) 0 0
\(491\) −4.79438 11.5746i −0.216367 0.522357i 0.778010 0.628252i \(-0.216229\pi\)
−0.994377 + 0.105895i \(0.966229\pi\)
\(492\) 0 0
\(493\) 6.86900 + 2.84523i 0.309364 + 0.128143i
\(494\) 0 0
\(495\) 8.83327i 0.397026i
\(496\) 0 0
\(497\) 29.3949i 1.31854i
\(498\) 0 0
\(499\) −8.71684 3.61063i −0.390219 0.161634i 0.178943 0.983859i \(-0.442732\pi\)
−0.569162 + 0.822225i \(0.692732\pi\)
\(500\) 0 0
\(501\) −0.366786 0.885499i −0.0163868 0.0395612i
\(502\) 0 0
\(503\) −5.07960 5.07960i −0.226488 0.226488i 0.584736 0.811224i \(-0.301198\pi\)
−0.811224 + 0.584736i \(0.801198\pi\)
\(504\) 0 0
\(505\) −5.30002 + 5.30002i −0.235848 + 0.235848i
\(506\) 0 0
\(507\) −2.06777 + 0.856498i −0.0918329 + 0.0380384i
\(508\) 0 0
\(509\) −13.5628 + 32.7435i −0.601161 + 1.45133i 0.271227 + 0.962515i \(0.412571\pi\)
−0.872388 + 0.488815i \(0.837429\pi\)
\(510\) 0 0
\(511\) −12.9060 −0.570926
\(512\) 0 0
\(513\) 5.19173 0.229221
\(514\) 0 0
\(515\) −0.186681 + 0.450688i −0.00822614 + 0.0198597i
\(516\) 0 0
\(517\) −26.5807 + 11.0101i −1.16902 + 0.484223i
\(518\) 0 0
\(519\) −1.09130 + 1.09130i −0.0479028 + 0.0479028i
\(520\) 0 0
\(521\) −17.4496 17.4496i −0.764479 0.764479i 0.212650 0.977129i \(-0.431791\pi\)
−0.977129 + 0.212650i \(0.931791\pi\)
\(522\) 0 0
\(523\) −16.6581 40.2163i −0.728410 1.75854i −0.647825 0.761789i \(-0.724321\pi\)
−0.0805847 0.996748i \(-0.525679\pi\)
\(524\) 0 0
\(525\) −2.72040 1.12682i −0.118728 0.0491787i
\(526\) 0 0
\(527\) 20.8486i 0.908179i
\(528\) 0 0
\(529\) 22.8528i 0.993598i
\(530\) 0 0
\(531\) 29.9237 + 12.3948i 1.29858 + 0.537889i
\(532\) 0 0
\(533\) 4.07107 + 9.82843i 0.176338 + 0.425716i
\(534\) 0 0
\(535\) −9.65087 9.65087i −0.417244 0.417244i
\(536\) 0 0
\(537\) −0.285094 + 0.285094i −0.0123027 + 0.0123027i
\(538\) 0 0
\(539\) 11.9645 4.95587i 0.515349 0.213464i
\(540\) 0 0
\(541\) 15.9692 38.5531i 0.686571 1.65753i −0.0650071 0.997885i \(-0.520707\pi\)
0.751578 0.659644i \(-0.229293\pi\)
\(542\) 0 0
\(543\) −3.32180 −0.142552
\(544\) 0 0
\(545\) −5.97018 −0.255734
\(546\) 0 0
\(547\) −0.383100 + 0.924886i −0.0163802 + 0.0395453i −0.931858 0.362823i \(-0.881813\pi\)
0.915478 + 0.402368i \(0.131813\pi\)
\(548\) 0 0
\(549\) 9.69932 4.01759i 0.413957 0.171467i
\(550\) 0 0
\(551\) 7.22658 7.22658i 0.307863 0.307863i
\(552\) 0 0
\(553\) −22.1454 22.1454i −0.941717 0.941717i
\(554\) 0 0
\(555\) 0.239213 + 0.577512i 0.0101540 + 0.0245140i
\(556\) 0 0
\(557\) 8.29127 + 3.43436i 0.351312 + 0.145518i 0.551359 0.834268i \(-0.314109\pi\)
−0.200047 + 0.979786i \(0.564109\pi\)
\(558\) 0 0
\(559\) 9.54333i 0.403640i
\(560\) 0 0
\(561\) 2.47482i 0.104487i
\(562\) 0 0
\(563\) 22.7143 + 9.40857i 0.957293 + 0.396524i 0.805967 0.591960i \(-0.201646\pi\)
0.151326 + 0.988484i \(0.451646\pi\)
\(564\) 0 0
\(565\) 2.56792 + 6.19951i 0.108033 + 0.260816i
\(566\) 0 0
\(567\) 19.5646 + 19.5646i 0.821637 + 0.821637i
\(568\) 0 0
\(569\) −16.6413 + 16.6413i −0.697639 + 0.697639i −0.963901 0.266262i \(-0.914211\pi\)
0.266262 + 0.963901i \(0.414211\pi\)
\(570\) 0 0
\(571\) −9.37532 + 3.88338i −0.392345 + 0.162515i −0.570129 0.821555i \(-0.693107\pi\)
0.177785 + 0.984069i \(0.443107\pi\)
\(572\) 0 0
\(573\) −0.492136 + 1.18812i −0.0205593 + 0.0496345i
\(574\) 0 0
\(575\) 1.69382 0.0706371
\(576\) 0 0
\(577\) −23.0348 −0.958951 −0.479476 0.877555i \(-0.659173\pi\)
−0.479476 + 0.877555i \(0.659173\pi\)
\(578\) 0 0
\(579\) −1.15856 + 2.79700i −0.0481480 + 0.116239i
\(580\) 0 0
\(581\) 29.0584 12.0364i 1.20555 0.499354i
\(582\) 0 0
\(583\) −12.0920 + 12.0920i −0.500798 + 0.500798i
\(584\) 0 0
\(585\) −7.80316 7.80316i −0.322621 0.322621i
\(586\) 0 0
\(587\) −1.02732 2.48018i −0.0424022 0.102368i 0.901260 0.433280i \(-0.142644\pi\)
−0.943662 + 0.330912i \(0.892644\pi\)
\(588\) 0 0
\(589\) 26.4766 + 10.9670i 1.09095 + 0.451885i
\(590\) 0 0
\(591\) 4.15894i 0.171076i
\(592\) 0 0
\(593\) 13.9339i 0.572197i 0.958200 + 0.286098i \(0.0923584\pi\)
−0.958200 + 0.286098i \(0.907642\pi\)
\(594\) 0 0
\(595\) −6.93484 2.87250i −0.284301 0.117761i
\(596\) 0 0
\(597\) 1.39112 + 3.35846i 0.0569347 + 0.137452i
\(598\) 0 0
\(599\) 7.02222 + 7.02222i 0.286920 + 0.286920i 0.835861 0.548941i \(-0.184969\pi\)
−0.548941 + 0.835861i \(0.684969\pi\)
\(600\) 0 0
\(601\) 24.0970 24.0970i 0.982938 0.982938i −0.0169188 0.999857i \(-0.505386\pi\)
0.999857 + 0.0169188i \(0.00538568\pi\)
\(602\) 0 0
\(603\) 14.2469 5.90125i 0.580177 0.240317i
\(604\) 0 0
\(605\) −1.24036 + 2.99450i −0.0504278 + 0.121744i
\(606\) 0 0
\(607\) 27.8275 1.12948 0.564742 0.825268i \(-0.308976\pi\)
0.564742 + 0.825268i \(0.308976\pi\)
\(608\) 0 0
\(609\) −1.62437 −0.0658229
\(610\) 0 0
\(611\) 13.7548 33.2070i 0.556460 1.34341i
\(612\) 0 0
\(613\) −9.98279 + 4.13501i −0.403201 + 0.167011i −0.575062 0.818110i \(-0.695022\pi\)
0.171861 + 0.985121i \(0.445022\pi\)
\(614\) 0 0
\(615\) 0.245193 0.245193i 0.00988714 0.00988714i
\(616\) 0 0
\(617\) 23.2080 + 23.2080i 0.934318 + 0.934318i 0.997972 0.0636543i \(-0.0202755\pi\)
−0.0636543 + 0.997972i \(0.520275\pi\)
\(618\) 0 0
\(619\) 11.5644 + 27.9189i 0.464811 + 1.12215i 0.966399 + 0.257047i \(0.0827494\pi\)
−0.501588 + 0.865107i \(0.667251\pi\)
\(620\) 0 0
\(621\) 0.438546 + 0.181652i 0.0175982 + 0.00728943i
\(622\) 0 0
\(623\) 34.4481i 1.38013i
\(624\) 0 0
\(625\) 16.5563i 0.662254i
\(626\) 0 0
\(627\) 3.14288 + 1.30182i 0.125515 + 0.0519899i
\(628\) 0 0
\(629\) −4.59519 11.0938i −0.183222 0.442338i
\(630\) 0 0
\(631\) 1.34980 + 1.34980i 0.0537346 + 0.0537346i 0.733463 0.679729i \(-0.237903\pi\)
−0.679729 + 0.733463i \(0.737903\pi\)
\(632\) 0 0
\(633\) 0.564006 0.564006i 0.0224172 0.0224172i
\(634\) 0 0
\(635\) 8.10641 3.35778i 0.321693 0.133250i
\(636\) 0 0
\(637\) −6.19133 + 14.9472i −0.245309 + 0.592229i
\(638\) 0 0
\(639\) −27.0588 −1.07043
\(640\) 0 0
\(641\) 41.5334 1.64047 0.820235 0.572027i \(-0.193843\pi\)
0.820235 + 0.572027i \(0.193843\pi\)
\(642\) 0 0
\(643\) 1.57282 3.79713i 0.0620261 0.149744i −0.889828 0.456297i \(-0.849176\pi\)
0.951854 + 0.306553i \(0.0991755\pi\)
\(644\) 0 0
\(645\) 0.287389 0.119040i 0.0113159 0.00468721i
\(646\) 0 0
\(647\) 5.84193 5.84193i 0.229670 0.229670i −0.582885 0.812555i \(-0.698076\pi\)
0.812555 + 0.582885i \(0.198076\pi\)
\(648\) 0 0
\(649\) 30.2323 + 30.2323i 1.18672 + 1.18672i
\(650\) 0 0
\(651\) −1.74311 4.20823i −0.0683177 0.164934i
\(652\) 0 0
\(653\) −26.0231 10.7791i −1.01836 0.421820i −0.189864 0.981810i \(-0.560805\pi\)
−0.828499 + 0.559991i \(0.810805\pi\)
\(654\) 0 0
\(655\) 8.64422i 0.337758i
\(656\) 0 0
\(657\) 11.8803i 0.463495i
\(658\) 0 0
\(659\) −37.6498 15.5951i −1.46663 0.607497i −0.500541 0.865713i \(-0.666866\pi\)
−0.966087 + 0.258215i \(0.916866\pi\)
\(660\) 0 0
\(661\) 3.14241 + 7.58644i 0.122226 + 0.295078i 0.973136 0.230233i \(-0.0739488\pi\)
−0.850910 + 0.525311i \(0.823949\pi\)
\(662\) 0 0
\(663\) −2.18621 2.18621i −0.0849054 0.0849054i
\(664\) 0 0
\(665\) −7.29585 + 7.29585i −0.282921 + 0.282921i
\(666\) 0 0
\(667\) 0.863279 0.357582i 0.0334263 0.0138456i
\(668\) 0 0
\(669\) 2.18982 5.28670i 0.0846634 0.204395i
\(670\) 0 0
\(671\) 13.8584 0.534997
\(672\) 0 0
\(673\) −5.24262 −0.202088 −0.101044 0.994882i \(-0.532218\pi\)
−0.101044 + 0.994882i \(0.532218\pi\)
\(674\) 0 0
\(675\) 2.08968 5.04493i 0.0804318 0.194179i
\(676\) 0 0
\(677\) 14.5716 6.03574i 0.560031 0.231972i −0.0846677 0.996409i \(-0.526983\pi\)
0.644699 + 0.764437i \(0.276983\pi\)
\(678\) 0 0
\(679\) 8.43625 8.43625i 0.323754 0.323754i
\(680\) 0 0
\(681\) 2.31265 + 2.31265i 0.0886210 + 0.0886210i
\(682\) 0 0
\(683\) 14.9028 + 35.9785i 0.570240 + 1.37668i 0.901351 + 0.433089i \(0.142576\pi\)
−0.331112 + 0.943592i \(0.607424\pi\)
\(684\) 0 0
\(685\) −3.42429 1.41839i −0.130835 0.0541938i
\(686\) 0 0
\(687\) 4.10842i 0.156746i
\(688\) 0 0
\(689\) 21.3637i 0.813892i
\(690\) 0 0
\(691\) −14.6714 6.07710i −0.558127 0.231184i 0.0857448 0.996317i \(-0.472673\pi\)
−0.643872 + 0.765133i \(0.722673\pi\)
\(692\) 0 0
\(693\) 14.1869 + 34.2502i 0.538915 + 1.30106i
\(694\) 0 0
\(695\) 10.4050 + 10.4050i 0.394685 + 0.394685i
\(696\) 0 0
\(697\) −4.71006 + 4.71006i −0.178406 + 0.178406i
\(698\) 0 0
\(699\) 1.82046 0.754059i 0.0688561 0.0285211i
\(700\) 0 0
\(701\) 9.58351 23.1366i 0.361964 0.873859i −0.633049 0.774112i \(-0.718197\pi\)
0.995013 0.0997466i \(-0.0318032\pi\)
\(702\) 0 0
\(703\) −16.5057 −0.622524
\(704\) 0 0
\(705\) −1.17157 −0.0441240
\(706\) 0 0
\(707\) −12.0381 + 29.0625i −0.452739 + 1.09301i
\(708\) 0 0
\(709\) 27.4256 11.3601i 1.02999 0.426636i 0.197282 0.980347i \(-0.436789\pi\)
0.832709 + 0.553711i \(0.186789\pi\)
\(710\) 0 0
\(711\) 20.3855 20.3855i 0.764515 0.764515i
\(712\) 0 0
\(713\) 1.85276 + 1.85276i 0.0693864 + 0.0693864i
\(714\) 0 0
\(715\) −5.57457 13.4582i −0.208477 0.503309i
\(716\) 0 0
\(717\) −5.02663 2.08210i −0.187723 0.0777573i
\(718\) 0 0
\(719\) 38.9976i 1.45436i 0.686445 + 0.727182i \(0.259170\pi\)
−0.686445 + 0.727182i \(0.740830\pi\)
\(720\) 0 0
\(721\) 2.04732i 0.0762462i
\(722\) 0 0
\(723\) 2.62337 + 1.08664i 0.0975643 + 0.0404124i
\(724\) 0 0
\(725\) −4.11354 9.93095i −0.152773 0.368826i
\(726\) 0 0
\(727\) −34.9474 34.9474i −1.29613 1.29613i −0.930930 0.365198i \(-0.881001\pi\)
−0.365198 0.930930i \(-0.618999\pi\)
\(728\) 0 0
\(729\) −17.4649 + 17.4649i −0.646846 + 0.646846i
\(730\) 0 0
\(731\) −5.52062 + 2.28672i −0.204188 + 0.0845773i
\(732\) 0 0
\(733\) −13.8093 + 33.3387i −0.510060 + 1.23139i 0.433789 + 0.901015i \(0.357176\pi\)
−0.943849 + 0.330378i \(0.892824\pi\)
\(734\) 0 0
\(735\) 0.527350 0.0194516
\(736\) 0 0
\(737\) 20.3559 0.749819
\(738\) 0 0
\(739\) −6.75096 + 16.2983i −0.248338 + 0.599542i −0.998063 0.0622080i \(-0.980186\pi\)
0.749725 + 0.661750i \(0.230186\pi\)
\(740\) 0 0
\(741\) −3.92638 + 1.62636i −0.144239 + 0.0597458i
\(742\) 0 0
\(743\) 20.6145 20.6145i 0.756272 0.756272i −0.219370 0.975642i \(-0.570400\pi\)
0.975642 + 0.219370i \(0.0704002\pi\)
\(744\) 0 0
\(745\) −1.31788 1.31788i −0.0482835 0.0482835i
\(746\) 0 0
\(747\) 11.0799 + 26.7491i 0.405391 + 0.978700i
\(748\) 0 0
\(749\) −52.9203 21.9203i −1.93367 0.800951i
\(750\) 0 0
\(751\) 27.0344i 0.986499i −0.869888 0.493249i \(-0.835809\pi\)
0.869888 0.493249i \(-0.164191\pi\)
\(752\) 0 0
\(753\) 2.96827i 0.108170i
\(754\) 0 0
\(755\) 4.21395 + 1.74548i 0.153361 + 0.0635244i
\(756\) 0 0
\(757\) −19.5424 47.1795i −0.710280 1.71477i −0.699300 0.714828i \(-0.746505\pi\)
−0.0109802 0.999940i \(-0.503495\pi\)
\(758\) 0 0
\(759\) 0.219931 + 0.219931i 0.00798297 + 0.00798297i
\(760\) 0 0
\(761\) −2.53714 + 2.53714i −0.0919713 + 0.0919713i −0.751596 0.659624i \(-0.770715\pi\)
0.659624 + 0.751596i \(0.270715\pi\)
\(762\) 0 0
\(763\) −23.1488 + 9.58854i −0.838042 + 0.347129i
\(764\) 0 0
\(765\) 2.64422 6.38372i 0.0956021 0.230804i
\(766\) 0 0
\(767\) −53.4134 −1.92865
\(768\) 0 0
\(769\) −24.0627 −0.867725 −0.433862 0.900979i \(-0.642850\pi\)
−0.433862 + 0.900979i \(0.642850\pi\)
\(770\) 0 0
\(771\) 1.59463 3.84977i 0.0574291 0.138646i
\(772\) 0 0
\(773\) −43.4146 + 17.9829i −1.56152 + 0.646801i −0.985352 0.170534i \(-0.945451\pi\)
−0.576163 + 0.817335i \(0.695451\pi\)
\(774\) 0 0
\(775\) 21.3137 21.3137i 0.765611 0.765611i
\(776\) 0 0
\(777\) 1.85505 + 1.85505i 0.0665497 + 0.0665497i
\(778\) 0 0
\(779\) 3.50389 + 8.45914i 0.125540 + 0.303080i
\(780\) 0 0
\(781\) −32.9997 13.6689i −1.18082 0.489113i
\(782\) 0 0
\(783\) 3.01237i 0.107653i
\(784\) 0 0
\(785\) 11.6880i 0.417163i
\(786\) 0 0
\(787\) 4.62213 + 1.91455i 0.164761 + 0.0682463i 0.463540 0.886076i \(-0.346579\pi\)
−0.298778 + 0.954323i \(0.596579\pi\)
\(788\) 0 0
\(789\) −0.533819 1.28875i −0.0190045 0.0458808i
\(790\) 0 0
\(791\) 19.9137 + 19.9137i 0.708051 + 0.708051i
\(792\) 0 0
\(793\) −12.2423 + 12.2423i −0.434735 + 0.434735i
\(794\) 0 0
\(795\) −0.643348 + 0.266484i −0.0228172 + 0.00945120i
\(796\) 0 0
\(797\) −7.78397 + 18.7922i −0.275722 + 0.665653i −0.999708 0.0241622i \(-0.992308\pi\)
0.723986 + 0.689815i \(0.242308\pi\)
\(798\) 0 0
\(799\) 22.5054 0.796185
\(800\) 0 0
\(801\) 31.7104 1.12043
\(802\) 0 0
\(803\) 6.00142 14.4887i 0.211785 0.511295i
\(804\) 0 0
\(805\) −0.871553 + 0.361009i −0.0307182 + 0.0127239i
\(806\) 0 0
\(807\) 3.55740 3.55740i 0.125227 0.125227i
\(808\) 0 0
\(809\) −5.79631 5.79631i −0.203787 0.203787i 0.597833 0.801621i \(-0.296029\pi\)
−0.801621 + 0.597833i \(0.796029\pi\)
\(810\) 0 0
\(811\) 2.59457 + 6.26386i 0.0911078 + 0.219954i 0.962864 0.269986i \(-0.0870189\pi\)
−0.871757 + 0.489939i \(0.837019\pi\)
\(812\) 0 0
\(813\) −0.132987 0.0550849i −0.00466405 0.00193191i
\(814\) 0 0
\(815\) 5.44739i 0.190814i
\(816\) 0 0
\(817\) 8.21377i 0.287363i
\(818\) 0 0
\(819\) −42.7885 17.7236i −1.49515 0.619311i
\(820\) 0 0
\(821\) 14.5014 + 35.0095i 0.506103 + 1.22184i 0.946110 + 0.323847i \(0.104976\pi\)
−0.440006 + 0.897995i \(0.645024\pi\)
\(822\) 0 0
\(823\) 6.84972 + 6.84972i 0.238766 + 0.238766i 0.816339 0.577573i \(-0.196000\pi\)
−0.577573 + 0.816339i \(0.696000\pi\)
\(824\) 0 0
\(825\) 2.53003 2.53003i 0.0880843 0.0880843i
\(826\) 0 0
\(827\) −27.6932 + 11.4709i −0.962987 + 0.398882i −0.808097 0.589049i \(-0.799502\pi\)
−0.154890 + 0.987932i \(0.549502\pi\)
\(828\) 0 0
\(829\) 1.60232 3.86834i 0.0556509 0.134353i −0.893609 0.448847i \(-0.851835\pi\)
0.949259 + 0.314494i \(0.101835\pi\)
\(830\) 0 0
\(831\) −6.07228 −0.210645
\(832\) 0 0
\(833\) −10.1302 −0.350990
\(834\) 0 0
\(835\) −1.35181 + 3.26355i −0.0467811 + 0.112940i
\(836\) 0 0
\(837\) 7.80409 3.23256i 0.269749 0.111734i
\(838\) 0 0
\(839\) −11.4718 + 11.4718i −0.396050 + 0.396050i −0.876837 0.480787i \(-0.840351\pi\)
0.480787 + 0.876837i \(0.340351\pi\)
\(840\) 0 0
\(841\) 16.3131 + 16.3131i 0.562519 + 0.562519i
\(842\) 0 0
\(843\) −0.784427 1.89377i −0.0270171 0.0652250i
\(844\) 0 0
\(845\) 7.62086 + 3.15666i 0.262165 + 0.108592i
\(846\) 0 0
\(847\) 13.6030i 0.467404i
\(848\) 0 0
\(849\) 3.28352i 0.112690i
\(850\) 0 0
\(851\) −1.39424 0.577512i −0.0477939 0.0197969i
\(852\) 0 0
\(853\) −4.85275 11.7156i −0.166155 0.401133i 0.818769 0.574124i \(-0.194657\pi\)
−0.984924 + 0.172990i \(0.944657\pi\)
\(854\) 0 0
\(855\) −6.71604 6.71604i −0.229684 0.229684i
\(856\) 0 0
\(857\) −13.5307 + 13.5307i −0.462200 + 0.462200i −0.899376 0.437176i \(-0.855979\pi\)
0.437176 + 0.899376i \(0.355979\pi\)
\(858\) 0 0
\(859\) 50.3433 20.8529i 1.71769 0.711491i 0.717808 0.696241i \(-0.245145\pi\)
0.999884 0.0152507i \(-0.00485464\pi\)
\(860\) 0 0
\(861\) 0.556914 1.34451i 0.0189796 0.0458208i
\(862\) 0 0
\(863\) 9.50637 0.323601 0.161800 0.986824i \(-0.448270\pi\)
0.161800 + 0.986824i \(0.448270\pi\)
\(864\) 0 0
\(865\) 5.68802 0.193399
\(866\) 0 0
\(867\) −0.610172 + 1.47309i −0.0207225 + 0.0500286i
\(868\) 0 0
\(869\) 35.1591 14.5634i 1.19269 0.494028i
\(870\) 0 0
\(871\) −17.9821 + 17.9821i −0.609299 + 0.609299i
\(872\) 0 0
\(873\) 7.76582 + 7.76582i 0.262833 + 0.262833i
\(874\) 0 0
\(875\) 8.85704 + 21.3828i 0.299423 + 0.722870i
\(876\) 0 0
\(877\) 16.7883 + 6.95392i 0.566899 + 0.234817i 0.647677 0.761915i \(-0.275741\pi\)
−0.0807782 + 0.996732i \(0.525741\pi\)
\(878\) 0 0
\(879\) 2.21534i 0.0747216i
\(880\) 0 0
\(881\) 46.9687i 1.58242i −0.611547 0.791208i \(-0.709453\pi\)
0.611547 0.791208i \(-0.290547\pi\)
\(882\) 0 0
\(883\) −11.0237 4.56617i −0.370978 0.153664i 0.189403 0.981900i \(-0.439345\pi\)
−0.560380 + 0.828236i \(0.689345\pi\)
\(884\) 0 0
\(885\) 0.666261 + 1.60850i 0.0223961 + 0.0540690i
\(886\) 0 0
\(887\) −31.9419 31.9419i −1.07250 1.07250i −0.997157 0.0753464i \(-0.975994\pi\)
−0.0753464 0.997157i \(-0.524006\pi\)
\(888\) 0 0
\(889\) 26.0390 26.0390i 0.873319 0.873319i
\(890\) 0 0
\(891\) −31.0617 + 12.8662i −1.04061 + 0.431034i
\(892\) 0 0
\(893\) 11.8385 28.5807i 0.396160 0.956416i
\(894\) 0 0
\(895\) 1.48595 0.0496699
\(896\) 0 0
\(897\) −0.388566 −0.0129738
\(898\) 0 0
\(899\) 6.36330 15.3624i 0.212228 0.512364i
\(900\) 0 0
\(901\) 12.3585 5.11904i 0.411720 0.170540i
\(902\) 0 0
\(903\) 0.923135 0.923135i 0.0307200 0.0307200i
\(904\) 0 0
\(905\) 8.65685 + 8.65685i 0.287764 + 0.287764i
\(906\) 0 0
\(907\) −4.99616 12.0618i −0.165895 0.400505i 0.818969 0.573838i \(-0.194546\pi\)
−0.984863 + 0.173333i \(0.944546\pi\)
\(908\) 0 0
\(909\) −26.7529 11.0814i −0.887338 0.367547i
\(910\) 0 0
\(911\) 13.1188i 0.434645i 0.976100 + 0.217322i \(0.0697323\pi\)
−0.976100 + 0.217322i \(0.930268\pi\)
\(912\) 0 0
\(913\) 38.2191i 1.26487i
\(914\) 0 0
\(915\) 0.521370 + 0.215959i 0.0172360 + 0.00713937i
\(916\) 0 0
\(917\) 13.8833 + 33.5171i 0.458465 + 1.10683i
\(918\) 0 0
\(919\) 17.2415 + 17.2415i 0.568746 + 0.568746i 0.931777 0.363031i \(-0.118258\pi\)
−0.363031 + 0.931777i \(0.618258\pi\)
\(920\) 0 0
\(921\) 1.10667 1.10667i 0.0364659 0.0364659i
\(922\) 0 0
\(923\) 41.2263 17.0765i 1.35698 0.562080i
\(924\) 0 0
\(925\) −6.64357 + 16.0390i −0.218439 + 0.527359i
\(926\) 0 0
\(927\) −1.88462 −0.0618990
\(928\) 0 0
\(929\) −45.9966 −1.50910 −0.754550 0.656242i \(-0.772145\pi\)
−0.754550 + 0.656242i \(0.772145\pi\)
\(930\) 0 0
\(931\) −5.32876 + 12.8648i −0.174643 + 0.421626i
\(932\) 0 0
\(933\) 1.26174 0.522630i 0.0413076 0.0171101i
\(934\) 0 0
\(935\) 6.44955 6.44955i 0.210923 0.210923i
\(936\) 0 0
\(937\) −3.67273 3.67273i −0.119983 0.119983i 0.644566 0.764549i \(-0.277038\pi\)
−0.764549 + 0.644566i \(0.777038\pi\)
\(938\) 0 0
\(939\) −0.0366014 0.0883635i −0.00119444 0.00288363i
\(940\) 0 0
\(941\) 41.7873 + 17.3089i 1.36223 + 0.564253i 0.939670 0.342083i \(-0.111132\pi\)
0.422558 + 0.906336i \(0.361132\pi\)
\(942\) 0 0
\(943\) 0.837141i 0.0272611i
\(944\) 0 0
\(945\) 3.04125i 0.0989317i
\(946\) 0 0
\(947\) 43.6427 + 18.0774i 1.41820 + 0.587436i 0.954407 0.298509i \(-0.0964894\pi\)
0.463790 + 0.885945i \(0.346489\pi\)
\(948\) 0 0
\(949\) 7.49753 + 18.1006i 0.243380 + 0.587571i
\(950\) 0 0
\(951\) 3.04238 + 3.04238i 0.0986559 + 0.0986559i
\(952\) 0 0
\(953\) 6.12750 6.12750i 0.198489 0.198489i −0.600863 0.799352i \(-0.705176\pi\)
0.799352 + 0.600863i \(0.205176\pi\)
\(954\) 0 0
\(955\) 4.37887 1.81379i 0.141697 0.0586928i
\(956\) 0 0
\(957\) 0.755352 1.82358i 0.0244171 0.0589480i
\(958\) 0 0
\(959\) −15.5554 −0.502310
\(960\) 0 0
\(961\) 15.6274 0.504110
\(962\) 0 0
\(963\) 20.1783 48.7147i 0.650237 1.56981i
\(964\) 0 0
\(965\) 10.3085 4.26991i 0.331842 0.137453i
\(966\) 0 0
\(967\) −1.03516 + 1.03516i −0.0332885 + 0.0332885i −0.723555 0.690267i \(-0.757493\pi\)
0.690267 + 0.723555i \(0.257493\pi\)
\(968\) 0 0
\(969\) −1.88163 1.88163i −0.0604467 0.0604467i
\(970\) 0 0
\(971\) −15.4218 37.2315i −0.494909 1.19482i −0.952194 0.305495i \(-0.901178\pi\)
0.457285 0.889320i \(-0.348822\pi\)
\(972\) 0 0
\(973\) 57.0556 + 23.6332i 1.82912 + 0.757646i
\(974\) 0 0
\(975\) 4.46997i 0.143154i
\(976\) 0 0
\(977\) 28.8457i 0.922857i −0.887177 0.461429i \(-0.847337\pi\)
0.887177 0.461429i \(-0.152663\pi\)
\(978\) 0 0
\(979\) 38.6727 + 16.0187i 1.23598 + 0.511961i
\(980\) 0 0
\(981\) −8.82653 21.3091i −0.281809 0.680348i
\(982\) 0 0
\(983\) 40.9561 + 40.9561i 1.30630 + 1.30630i 0.924067 + 0.382231i \(0.124844\pi\)
0.382231 + 0.924067i \(0.375156\pi\)
\(984\) 0 0
\(985\) 10.8385 10.8385i 0.345344 0.345344i
\(986\) 0 0
\(987\) −4.54266 + 1.88163i −0.144594 + 0.0598930i
\(988\) 0 0
\(989\) −0.287389 + 0.693818i −0.00913843 + 0.0220621i
\(990\) 0 0
\(991\) 41.9605 1.33292 0.666460 0.745541i \(-0.267809\pi\)
0.666460 + 0.745541i \(0.267809\pi\)
\(992\) 0 0
\(993\) −3.21145 −0.101912
\(994\) 0 0
\(995\) 5.12703 12.3777i 0.162538 0.392401i
\(996\) 0 0
\(997\) −31.4380 + 13.0221i −0.995652 + 0.412413i −0.820201 0.572076i \(-0.806138\pi\)
−0.175451 + 0.984488i \(0.556138\pi\)
\(998\) 0 0
\(999\) −3.44017 + 3.44017i −0.108842 + 0.108842i
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 128.2.g.b.17.1 8
3.2 odd 2 1152.2.v.b.145.2 8
4.3 odd 2 32.2.g.b.13.2 yes 8
8.3 odd 2 256.2.g.d.33.1 8
8.5 even 2 256.2.g.c.33.2 8
12.11 even 2 288.2.v.b.109.1 8
16.3 odd 4 512.2.g.e.321.2 8
16.5 even 4 512.2.g.f.321.2 8
16.11 odd 4 512.2.g.h.321.1 8
16.13 even 4 512.2.g.g.321.1 8
20.3 even 4 800.2.ba.c.749.1 8
20.7 even 4 800.2.ba.d.749.2 8
20.19 odd 2 800.2.y.b.301.1 8
32.3 odd 8 512.2.g.e.193.2 8
32.5 even 8 inner 128.2.g.b.113.1 8
32.11 odd 8 256.2.g.d.225.1 8
32.13 even 8 512.2.g.f.193.2 8
32.19 odd 8 512.2.g.h.193.1 8
32.21 even 8 256.2.g.c.225.2 8
32.27 odd 8 32.2.g.b.5.2 8
32.29 even 8 512.2.g.g.193.1 8
64.5 even 16 4096.2.a.q.1.4 8
64.27 odd 16 4096.2.a.k.1.4 8
64.37 even 16 4096.2.a.q.1.5 8
64.59 odd 16 4096.2.a.k.1.5 8
96.5 odd 8 1152.2.v.b.1009.2 8
96.59 even 8 288.2.v.b.37.1 8
160.27 even 8 800.2.ba.c.549.1 8
160.59 odd 8 800.2.y.b.101.1 8
160.123 even 8 800.2.ba.d.549.2 8
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
32.2.g.b.5.2 8 32.27 odd 8
32.2.g.b.13.2 yes 8 4.3 odd 2
128.2.g.b.17.1 8 1.1 even 1 trivial
128.2.g.b.113.1 8 32.5 even 8 inner
256.2.g.c.33.2 8 8.5 even 2
256.2.g.c.225.2 8 32.21 even 8
256.2.g.d.33.1 8 8.3 odd 2
256.2.g.d.225.1 8 32.11 odd 8
288.2.v.b.37.1 8 96.59 even 8
288.2.v.b.109.1 8 12.11 even 2
512.2.g.e.193.2 8 32.3 odd 8
512.2.g.e.321.2 8 16.3 odd 4
512.2.g.f.193.2 8 32.13 even 8
512.2.g.f.321.2 8 16.5 even 4
512.2.g.g.193.1 8 32.29 even 8
512.2.g.g.321.1 8 16.13 even 4
512.2.g.h.193.1 8 32.19 odd 8
512.2.g.h.321.1 8 16.11 odd 4
800.2.y.b.101.1 8 160.59 odd 8
800.2.y.b.301.1 8 20.19 odd 2
800.2.ba.c.549.1 8 160.27 even 8
800.2.ba.c.749.1 8 20.3 even 4
800.2.ba.d.549.2 8 160.123 even 8
800.2.ba.d.749.2 8 20.7 even 4
1152.2.v.b.145.2 8 3.2 odd 2
1152.2.v.b.1009.2 8 96.5 odd 8
4096.2.a.k.1.4 8 64.27 odd 16
4096.2.a.k.1.5 8 64.59 odd 16
4096.2.a.q.1.4 8 64.5 even 16
4096.2.a.q.1.5 8 64.37 even 16