Properties

Label 288.2.r.b.241.1
Level $288$
Weight $2$
Character 288.241
Analytic conductor $2.300$
Analytic rank $0$
Dimension $16$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [288,2,Mod(49,288)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(288, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([0, 3, 2]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("288.49");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 288 = 2^{5} \cdot 3^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 288.r (of order \(6\), degree \(2\), not minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(2.29969157821\)
Analytic rank: \(0\)
Dimension: \(16\)
Relative dimension: \(8\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{16} - x^{15} + x^{14} + 2 x^{12} - 4 x^{11} - 8 x^{9} + 4 x^{8} - 16 x^{7} - 32 x^{5} + 32 x^{4} + 64 x^{2} - 128 x + 256 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{8}\cdot 3^{2} \)
Twist minimal: no (minimal twist has level 72)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 241.1
Root \(0.820200 + 1.15207i\) of defining polynomial
Character \(\chi\) \(=\) 288.241
Dual form 288.2.r.b.49.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.69028 - 0.378078i) q^{3} +(-1.97542 + 1.14051i) q^{5} +(0.907824 - 1.57240i) q^{7} +(2.71411 + 1.27812i) q^{9} +O(q^{10})\) \(q+(-1.69028 - 0.378078i) q^{3} +(-1.97542 + 1.14051i) q^{5} +(0.907824 - 1.57240i) q^{7} +(2.71411 + 1.27812i) q^{9} +(4.24153 + 2.44885i) q^{11} +(4.00895 - 2.31457i) q^{13} +(3.77023 - 1.18092i) q^{15} +1.92788 q^{17} -2.12907i q^{19} +(-2.12897 + 2.31457i) q^{21} +(1.15765 + 2.00511i) q^{23} +(0.101535 - 0.175863i) q^{25} +(-4.10439 - 3.18653i) q^{27} +(3.16440 + 1.82697i) q^{29} +(2.65800 + 4.60379i) q^{31} +(-6.24353 - 5.74287i) q^{33} +4.14154i q^{35} -7.98438i q^{37} +(-7.65135 + 2.39658i) q^{39} +(-2.36240 - 4.09180i) q^{41} +(2.20800 + 1.27479i) q^{43} +(-6.81924 + 0.570655i) q^{45} +(2.02005 - 3.49884i) q^{47} +(1.85171 + 3.20726i) q^{49} +(-3.25866 - 0.728888i) q^{51} +8.95958i q^{53} -11.1718 q^{55} +(-0.804954 + 3.59873i) q^{57} +(-3.05255 + 1.76239i) q^{59} +(1.71675 + 0.991165i) q^{61} +(4.47365 - 3.10736i) q^{63} +(-5.27959 + 9.14451i) q^{65} +(7.72723 - 4.46132i) q^{67} +(-1.19867 - 3.82688i) q^{69} -13.3561 q^{71} -11.5592 q^{73} +(-0.238112 + 0.258870i) q^{75} +(7.70112 - 4.44625i) q^{77} +(4.97330 - 8.61401i) q^{79} +(5.73283 + 6.93791i) q^{81} +(-3.12153 - 1.80221i) q^{83} +(-3.80838 + 2.19877i) q^{85} +(-4.65800 - 4.28448i) q^{87} +2.49965 q^{89} -8.40489i q^{91} +(-2.75218 - 8.78664i) q^{93} +(2.42823 + 4.20582i) q^{95} +(6.99370 - 12.1134i) q^{97} +(8.38208 + 12.0676i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16 q - 6 q^{7} + 2 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 16 q - 6 q^{7} + 2 q^{9} + 10 q^{15} - 28 q^{17} + 10 q^{23} + 2 q^{25} + 10 q^{31} - 2 q^{39} - 8 q^{41} - 6 q^{47} + 18 q^{49} + 4 q^{55} + 10 q^{57} - 2 q^{63} - 14 q^{65} - 72 q^{71} - 44 q^{73} + 30 q^{79} + 10 q^{81} - 42 q^{87} + 64 q^{89} - 44 q^{95}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/288\mathbb{Z}\right)^\times\).

\(n\) \(37\) \(65\) \(127\)
\(\chi(n)\) \(-1\) \(e\left(\frac{2}{3}\right)\) \(1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) −1.69028 0.378078i −0.975885 0.218283i
\(4\) 0 0
\(5\) −1.97542 + 1.14051i −0.883437 + 0.510052i −0.871790 0.489880i \(-0.837041\pi\)
−0.0116467 + 0.999932i \(0.503707\pi\)
\(6\) 0 0
\(7\) 0.907824 1.57240i 0.343125 0.594311i −0.641886 0.766800i \(-0.721848\pi\)
0.985011 + 0.172490i \(0.0551811\pi\)
\(8\) 0 0
\(9\) 2.71411 + 1.27812i 0.904705 + 0.426039i
\(10\) 0 0
\(11\) 4.24153 + 2.44885i 1.27887 + 0.738355i 0.976640 0.214880i \(-0.0689362\pi\)
0.302228 + 0.953236i \(0.402270\pi\)
\(12\) 0 0
\(13\) 4.00895 2.31457i 1.11188 0.641946i 0.172567 0.984998i \(-0.444794\pi\)
0.939317 + 0.343052i \(0.111461\pi\)
\(14\) 0 0
\(15\) 3.77023 1.18092i 0.973469 0.304913i
\(16\) 0 0
\(17\) 1.92788 0.467579 0.233790 0.972287i \(-0.424887\pi\)
0.233790 + 0.972287i \(0.424887\pi\)
\(18\) 0 0
\(19\) 2.12907i 0.488442i −0.969720 0.244221i \(-0.921468\pi\)
0.969720 0.244221i \(-0.0785322\pi\)
\(20\) 0 0
\(21\) −2.12897 + 2.31457i −0.464579 + 0.505080i
\(22\) 0 0
\(23\) 1.15765 + 2.00511i 0.241387 + 0.418094i 0.961109 0.276168i \(-0.0890645\pi\)
−0.719723 + 0.694261i \(0.755731\pi\)
\(24\) 0 0
\(25\) 0.101535 0.175863i 0.0203069 0.0351726i
\(26\) 0 0
\(27\) −4.10439 3.18653i −0.789891 0.613247i
\(28\) 0 0
\(29\) 3.16440 + 1.82697i 0.587615 + 0.339260i 0.764154 0.645034i \(-0.223157\pi\)
−0.176539 + 0.984294i \(0.556490\pi\)
\(30\) 0 0
\(31\) 2.65800 + 4.60379i 0.477391 + 0.826865i 0.999664 0.0259130i \(-0.00824928\pi\)
−0.522273 + 0.852778i \(0.674916\pi\)
\(32\) 0 0
\(33\) −6.24353 5.74287i −1.08686 0.999706i
\(34\) 0 0
\(35\) 4.14154i 0.700048i
\(36\) 0 0
\(37\) 7.98438i 1.31262i −0.754489 0.656312i \(-0.772115\pi\)
0.754489 0.656312i \(-0.227885\pi\)
\(38\) 0 0
\(39\) −7.65135 + 2.39658i −1.22520 + 0.383760i
\(40\) 0 0
\(41\) −2.36240 4.09180i −0.368946 0.639033i 0.620455 0.784242i \(-0.286948\pi\)
−0.989401 + 0.145209i \(0.953614\pi\)
\(42\) 0 0
\(43\) 2.20800 + 1.27479i 0.336717 + 0.194404i 0.658819 0.752301i \(-0.271056\pi\)
−0.322102 + 0.946705i \(0.604390\pi\)
\(44\) 0 0
\(45\) −6.81924 + 0.570655i −1.01655 + 0.0850683i
\(46\) 0 0
\(47\) 2.02005 3.49884i 0.294655 0.510358i −0.680249 0.732981i \(-0.738129\pi\)
0.974905 + 0.222623i \(0.0714619\pi\)
\(48\) 0 0
\(49\) 1.85171 + 3.20726i 0.264530 + 0.458179i
\(50\) 0 0
\(51\) −3.25866 0.728888i −0.456304 0.102065i
\(52\) 0 0
\(53\) 8.95958i 1.23069i 0.788257 + 0.615347i \(0.210984\pi\)
−0.788257 + 0.615347i \(0.789016\pi\)
\(54\) 0 0
\(55\) −11.1718 −1.50640
\(56\) 0 0
\(57\) −0.804954 + 3.59873i −0.106619 + 0.476663i
\(58\) 0 0
\(59\) −3.05255 + 1.76239i −0.397408 + 0.229444i −0.685365 0.728200i \(-0.740357\pi\)
0.287957 + 0.957643i \(0.407024\pi\)
\(60\) 0 0
\(61\) 1.71675 + 0.991165i 0.219807 + 0.126906i 0.605861 0.795571i \(-0.292829\pi\)
−0.386054 + 0.922476i \(0.626162\pi\)
\(62\) 0 0
\(63\) 4.47365 3.10736i 0.563627 0.391491i
\(64\) 0 0
\(65\) −5.27959 + 9.14451i −0.654852 + 1.13424i
\(66\) 0 0
\(67\) 7.72723 4.46132i 0.944031 0.545036i 0.0528093 0.998605i \(-0.483182\pi\)
0.891222 + 0.453568i \(0.149849\pi\)
\(68\) 0 0
\(69\) −1.19867 3.82688i −0.144303 0.460702i
\(70\) 0 0
\(71\) −13.3561 −1.58508 −0.792539 0.609821i \(-0.791241\pi\)
−0.792539 + 0.609821i \(0.791241\pi\)
\(72\) 0 0
\(73\) −11.5592 −1.35290 −0.676450 0.736489i \(-0.736482\pi\)
−0.676450 + 0.736489i \(0.736482\pi\)
\(74\) 0 0
\(75\) −0.238112 + 0.258870i −0.0274948 + 0.0298918i
\(76\) 0 0
\(77\) 7.70112 4.44625i 0.877625 0.506697i
\(78\) 0 0
\(79\) 4.97330 8.61401i 0.559540 0.969151i −0.437995 0.898977i \(-0.644311\pi\)
0.997535 0.0701739i \(-0.0223554\pi\)
\(80\) 0 0
\(81\) 5.73283 + 6.93791i 0.636981 + 0.770879i
\(82\) 0 0
\(83\) −3.12153 1.80221i −0.342632 0.197819i 0.318803 0.947821i \(-0.396719\pi\)
−0.661435 + 0.750002i \(0.730052\pi\)
\(84\) 0 0
\(85\) −3.80838 + 2.19877i −0.413077 + 0.238490i
\(86\) 0 0
\(87\) −4.65800 4.28448i −0.499390 0.459345i
\(88\) 0 0
\(89\) 2.49965 0.264962 0.132481 0.991186i \(-0.457706\pi\)
0.132481 + 0.991186i \(0.457706\pi\)
\(90\) 0 0
\(91\) 8.40489i 0.881072i
\(92\) 0 0
\(93\) −2.75218 8.78664i −0.285388 0.911132i
\(94\) 0 0
\(95\) 2.42823 + 4.20582i 0.249131 + 0.431508i
\(96\) 0 0
\(97\) 6.99370 12.1134i 0.710103 1.22993i −0.254715 0.967016i \(-0.581982\pi\)
0.964818 0.262918i \(-0.0846849\pi\)
\(98\) 0 0
\(99\) 8.38208 + 12.0676i 0.842430 + 1.21284i
\(100\) 0 0
\(101\) −1.13087 0.652911i −0.112526 0.0649671i 0.442681 0.896679i \(-0.354028\pi\)
−0.555207 + 0.831712i \(0.687361\pi\)
\(102\) 0 0
\(103\) 3.22312 + 5.58261i 0.317584 + 0.550071i 0.979983 0.199080i \(-0.0637952\pi\)
−0.662400 + 0.749151i \(0.730462\pi\)
\(104\) 0 0
\(105\) 1.56582 7.00037i 0.152809 0.683166i
\(106\) 0 0
\(107\) 3.10427i 0.300101i −0.988678 0.150051i \(-0.952056\pi\)
0.988678 0.150051i \(-0.0479437\pi\)
\(108\) 0 0
\(109\) 18.0837i 1.73210i 0.499955 + 0.866051i \(0.333350\pi\)
−0.499955 + 0.866051i \(0.666650\pi\)
\(110\) 0 0
\(111\) −3.01872 + 13.4959i −0.286524 + 1.28097i
\(112\) 0 0
\(113\) −1.41718 2.45463i −0.133317 0.230913i 0.791636 0.610993i \(-0.209230\pi\)
−0.924953 + 0.380080i \(0.875896\pi\)
\(114\) 0 0
\(115\) −4.57370 2.64063i −0.426500 0.246240i
\(116\) 0 0
\(117\) 13.8390 1.15810i 1.27942 0.107066i
\(118\) 0 0
\(119\) 1.75018 3.03139i 0.160438 0.277887i
\(120\) 0 0
\(121\) 6.49370 + 11.2474i 0.590337 + 1.02249i
\(122\) 0 0
\(123\) 2.44611 + 7.80948i 0.220558 + 0.704157i
\(124\) 0 0
\(125\) 10.9419i 0.978674i
\(126\) 0 0
\(127\) 7.44962 0.661047 0.330523 0.943798i \(-0.392775\pi\)
0.330523 + 0.943798i \(0.392775\pi\)
\(128\) 0 0
\(129\) −3.25018 2.98955i −0.286162 0.263215i
\(130\) 0 0
\(131\) 3.12153 1.80221i 0.272729 0.157460i −0.357398 0.933952i \(-0.616336\pi\)
0.630127 + 0.776492i \(0.283003\pi\)
\(132\) 0 0
\(133\) −3.34774 1.93282i −0.290286 0.167597i
\(134\) 0 0
\(135\) 11.7422 + 1.61363i 1.01061 + 0.138879i
\(136\) 0 0
\(137\) 5.88147 10.1870i 0.502488 0.870335i −0.497508 0.867460i \(-0.665751\pi\)
0.999996 0.00287543i \(-0.000915278\pi\)
\(138\) 0 0
\(139\) −11.0400 + 6.37395i −0.936400 + 0.540631i −0.888830 0.458237i \(-0.848481\pi\)
−0.0475703 + 0.998868i \(0.515148\pi\)
\(140\) 0 0
\(141\) −4.73730 + 5.15029i −0.398952 + 0.433732i
\(142\) 0 0
\(143\) 22.6721 1.89594
\(144\) 0 0
\(145\) −8.33472 −0.692161
\(146\) 0 0
\(147\) −1.91732 6.12126i −0.158138 0.504873i
\(148\) 0 0
\(149\) −6.59790 + 3.80930i −0.540521 + 0.312070i −0.745290 0.666740i \(-0.767689\pi\)
0.204769 + 0.978810i \(0.434356\pi\)
\(150\) 0 0
\(151\) −2.26988 + 3.93155i −0.184720 + 0.319945i −0.943482 0.331423i \(-0.892471\pi\)
0.758762 + 0.651368i \(0.225805\pi\)
\(152\) 0 0
\(153\) 5.23248 + 2.46405i 0.423021 + 0.199207i
\(154\) 0 0
\(155\) −10.5014 6.06296i −0.843489 0.486989i
\(156\) 0 0
\(157\) −11.4105 + 6.58787i −0.910659 + 0.525769i −0.880643 0.473780i \(-0.842889\pi\)
−0.0300161 + 0.999549i \(0.509556\pi\)
\(158\) 0 0
\(159\) 3.38742 15.1442i 0.268640 1.20102i
\(160\) 0 0
\(161\) 4.20377 0.331303
\(162\) 0 0
\(163\) 20.5911i 1.61282i 0.591358 + 0.806409i \(0.298592\pi\)
−0.591358 + 0.806409i \(0.701408\pi\)
\(164\) 0 0
\(165\) 18.8834 + 4.22379i 1.47007 + 0.328822i
\(166\) 0 0
\(167\) −2.53912 4.39789i −0.196483 0.340319i 0.750903 0.660413i \(-0.229619\pi\)
−0.947386 + 0.320094i \(0.896285\pi\)
\(168\) 0 0
\(169\) 4.21446 7.29967i 0.324190 0.561513i
\(170\) 0 0
\(171\) 2.72120 5.77854i 0.208095 0.441896i
\(172\) 0 0
\(173\) −11.0398 6.37385i −0.839343 0.484595i 0.0176977 0.999843i \(-0.494366\pi\)
−0.857041 + 0.515248i \(0.827700\pi\)
\(174\) 0 0
\(175\) −0.184351 0.319306i −0.0139356 0.0241372i
\(176\) 0 0
\(177\) 5.82599 1.82484i 0.437908 0.137163i
\(178\) 0 0
\(179\) 8.82019i 0.659252i −0.944112 0.329626i \(-0.893077\pi\)
0.944112 0.329626i \(-0.106923\pi\)
\(180\) 0 0
\(181\) 15.4369i 1.14741i −0.819061 0.573707i \(-0.805505\pi\)
0.819061 0.573707i \(-0.194495\pi\)
\(182\) 0 0
\(183\) −2.52705 2.32441i −0.186805 0.171826i
\(184\) 0 0
\(185\) 9.10628 + 15.7725i 0.669507 + 1.15962i
\(186\) 0 0
\(187\) 8.17715 + 4.72108i 0.597972 + 0.345239i
\(188\) 0 0
\(189\) −8.73656 + 3.56093i −0.635491 + 0.259020i
\(190\) 0 0
\(191\) −4.81698 + 8.34326i −0.348545 + 0.603697i −0.985991 0.166797i \(-0.946657\pi\)
0.637446 + 0.770495i \(0.279991\pi\)
\(192\) 0 0
\(193\) 3.49335 + 6.05066i 0.251457 + 0.435536i 0.963927 0.266166i \(-0.0857570\pi\)
−0.712470 + 0.701702i \(0.752424\pi\)
\(194\) 0 0
\(195\) 12.3813 13.4607i 0.886646 0.963942i
\(196\) 0 0
\(197\) 4.31842i 0.307675i −0.988096 0.153837i \(-0.950837\pi\)
0.988096 0.153837i \(-0.0491632\pi\)
\(198\) 0 0
\(199\) −5.90649 −0.418700 −0.209350 0.977841i \(-0.567135\pi\)
−0.209350 + 0.977841i \(0.567135\pi\)
\(200\) 0 0
\(201\) −14.7479 + 4.61939i −1.04024 + 0.325827i
\(202\) 0 0
\(203\) 5.74544 3.31713i 0.403251 0.232817i
\(204\) 0 0
\(205\) 9.33350 + 5.38870i 0.651880 + 0.376363i
\(206\) 0 0
\(207\) 0.579230 + 6.92170i 0.0402593 + 0.481092i
\(208\) 0 0
\(209\) 5.21376 9.03050i 0.360644 0.624653i
\(210\) 0 0
\(211\) −15.8781 + 9.16723i −1.09309 + 0.631098i −0.934399 0.356229i \(-0.884062\pi\)
−0.158696 + 0.987328i \(0.550729\pi\)
\(212\) 0 0
\(213\) 22.5756 + 5.04965i 1.54685 + 0.345996i
\(214\) 0 0
\(215\) −5.81565 −0.396624
\(216\) 0 0
\(217\) 9.65199 0.655220
\(218\) 0 0
\(219\) 19.5383 + 4.37027i 1.32027 + 0.295315i
\(220\) 0 0
\(221\) 7.72877 4.46221i 0.519893 0.300161i
\(222\) 0 0
\(223\) 2.63263 4.55986i 0.176294 0.305350i −0.764314 0.644844i \(-0.776922\pi\)
0.940608 + 0.339494i \(0.110256\pi\)
\(224\) 0 0
\(225\) 0.500350 0.347539i 0.0333567 0.0231693i
\(226\) 0 0
\(227\) 1.53638 + 0.887027i 0.101973 + 0.0588741i 0.550119 0.835086i \(-0.314582\pi\)
−0.448146 + 0.893960i \(0.647916\pi\)
\(228\) 0 0
\(229\) 3.30687 1.90922i 0.218524 0.126165i −0.386742 0.922188i \(-0.626400\pi\)
0.605267 + 0.796023i \(0.293066\pi\)
\(230\) 0 0
\(231\) −14.6981 + 4.60379i −0.967064 + 0.302907i
\(232\) 0 0
\(233\) −20.3207 −1.33125 −0.665627 0.746284i \(-0.731836\pi\)
−0.665627 + 0.746284i \(0.731836\pi\)
\(234\) 0 0
\(235\) 9.21558i 0.601158i
\(236\) 0 0
\(237\) −11.6630 + 12.6798i −0.757596 + 0.823642i
\(238\) 0 0
\(239\) −8.69811 15.0656i −0.562634 0.974510i −0.997266 0.0739020i \(-0.976455\pi\)
0.434632 0.900608i \(-0.356879\pi\)
\(240\) 0 0
\(241\) −6.85611 + 11.8751i −0.441641 + 0.764944i −0.997811 0.0661240i \(-0.978937\pi\)
0.556171 + 0.831068i \(0.312270\pi\)
\(242\) 0 0
\(243\) −7.06704 13.8945i −0.453351 0.891332i
\(244\) 0 0
\(245\) −7.31583 4.22379i −0.467391 0.269848i
\(246\) 0 0
\(247\) −4.92788 8.53534i −0.313553 0.543090i
\(248\) 0 0
\(249\) 4.59489 + 4.22643i 0.291189 + 0.267839i
\(250\) 0 0
\(251\) 4.50751i 0.284512i −0.989830 0.142256i \(-0.954564\pi\)
0.989830 0.142256i \(-0.0454356\pi\)
\(252\) 0 0
\(253\) 11.3396i 0.712916i
\(254\) 0 0
\(255\) 7.26854 2.27668i 0.455174 0.142571i
\(256\) 0 0
\(257\) −4.11258 7.12320i −0.256536 0.444333i 0.708776 0.705434i \(-0.249248\pi\)
−0.965311 + 0.261101i \(0.915914\pi\)
\(258\) 0 0
\(259\) −12.5546 7.24842i −0.780106 0.450395i
\(260\) 0 0
\(261\) 6.25347 + 9.00308i 0.387080 + 0.557277i
\(262\) 0 0
\(263\) −2.51376 + 4.35395i −0.155005 + 0.268476i −0.933061 0.359719i \(-0.882873\pi\)
0.778056 + 0.628195i \(0.216206\pi\)
\(264\) 0 0
\(265\) −10.2185 17.6990i −0.627718 1.08724i
\(266\) 0 0
\(267\) −4.22512 0.945062i −0.258573 0.0578369i
\(268\) 0 0
\(269\) 23.1577i 1.41195i −0.708236 0.705976i \(-0.750509\pi\)
0.708236 0.705976i \(-0.249491\pi\)
\(270\) 0 0
\(271\) −20.9367 −1.27181 −0.635906 0.771766i \(-0.719373\pi\)
−0.635906 + 0.771766i \(0.719373\pi\)
\(272\) 0 0
\(273\) −3.17770 + 14.2066i −0.192323 + 0.859825i
\(274\) 0 0
\(275\) 0.861323 0.497285i 0.0519398 0.0299874i
\(276\) 0 0
\(277\) −19.2687 11.1248i −1.15775 0.668425i −0.206983 0.978345i \(-0.566364\pi\)
−0.950763 + 0.309920i \(0.899698\pi\)
\(278\) 0 0
\(279\) 1.32993 + 15.8924i 0.0796208 + 0.951456i
\(280\) 0 0
\(281\) −9.28029 + 16.0739i −0.553616 + 0.958890i 0.444394 + 0.895831i \(0.353419\pi\)
−0.998010 + 0.0630590i \(0.979914\pi\)
\(282\) 0 0
\(283\) 1.75962 1.01592i 0.104599 0.0603901i −0.446788 0.894640i \(-0.647432\pi\)
0.551387 + 0.834250i \(0.314099\pi\)
\(284\) 0 0
\(285\) −2.51427 8.02708i −0.148932 0.475483i
\(286\) 0 0
\(287\) −8.57859 −0.506378
\(288\) 0 0
\(289\) −13.2833 −0.781370
\(290\) 0 0
\(291\) −16.4012 + 17.8310i −0.961453 + 1.04527i
\(292\) 0 0
\(293\) −29.5484 + 17.0598i −1.72623 + 0.996642i −0.822178 + 0.569231i \(0.807241\pi\)
−0.904057 + 0.427411i \(0.859426\pi\)
\(294\) 0 0
\(295\) 4.02005 6.96294i 0.234057 0.405398i
\(296\) 0 0
\(297\) −9.60558 23.5668i −0.557372 1.36748i
\(298\) 0 0
\(299\) 9.28192 + 5.35892i 0.536787 + 0.309914i
\(300\) 0 0
\(301\) 4.00895 2.31457i 0.231072 0.133410i
\(302\) 0 0
\(303\) 1.66465 + 1.53116i 0.0956315 + 0.0879630i
\(304\) 0 0
\(305\) −4.52174 −0.258914
\(306\) 0 0
\(307\) 4.77588i 0.272574i −0.990669 0.136287i \(-0.956483\pi\)
0.990669 0.136287i \(-0.0435169\pi\)
\(308\) 0 0
\(309\) −3.33733 10.6548i −0.189854 0.606130i
\(310\) 0 0
\(311\) 11.1771 + 19.3592i 0.633793 + 1.09776i 0.986769 + 0.162130i \(0.0518364\pi\)
−0.352976 + 0.935632i \(0.614830\pi\)
\(312\) 0 0
\(313\) 1.22411 2.12022i 0.0691907 0.119842i −0.829355 0.558723i \(-0.811292\pi\)
0.898545 + 0.438881i \(0.144625\pi\)
\(314\) 0 0
\(315\) −5.29337 + 11.2406i −0.298248 + 0.633336i
\(316\) 0 0
\(317\) 14.2886 + 8.24953i 0.802528 + 0.463340i 0.844354 0.535785i \(-0.179984\pi\)
−0.0418263 + 0.999125i \(0.513318\pi\)
\(318\) 0 0
\(319\) 8.94793 + 15.4983i 0.500988 + 0.867737i
\(320\) 0 0
\(321\) −1.17366 + 5.24710i −0.0655071 + 0.292864i
\(322\) 0 0
\(323\) 4.10459i 0.228385i
\(324\) 0 0
\(325\) 0.940035i 0.0521438i
\(326\) 0 0
\(327\) 6.83704 30.5665i 0.378089 1.69033i
\(328\) 0 0
\(329\) −3.66771 6.35266i −0.202207 0.350233i
\(330\) 0 0
\(331\) −0.329200 0.190064i −0.0180945 0.0104469i 0.490925 0.871202i \(-0.336659\pi\)
−0.509020 + 0.860755i \(0.669992\pi\)
\(332\) 0 0
\(333\) 10.2050 21.6705i 0.559229 1.18754i
\(334\) 0 0
\(335\) −10.1764 + 17.6260i −0.555994 + 0.963010i
\(336\) 0 0
\(337\) −2.51872 4.36255i −0.137203 0.237643i 0.789234 0.614093i \(-0.210478\pi\)
−0.926437 + 0.376450i \(0.877145\pi\)
\(338\) 0 0
\(339\) 1.46740 + 4.68483i 0.0796982 + 0.254445i
\(340\) 0 0
\(341\) 26.0361i 1.40994i
\(342\) 0 0
\(343\) 19.4337 1.04932
\(344\) 0 0
\(345\) 6.73248 + 6.19262i 0.362465 + 0.333399i
\(346\) 0 0
\(347\) −8.40337 + 4.85169i −0.451116 + 0.260452i −0.708302 0.705910i \(-0.750538\pi\)
0.257185 + 0.966362i \(0.417205\pi\)
\(348\) 0 0
\(349\) 26.1239 + 15.0827i 1.39838 + 0.807356i 0.994223 0.107333i \(-0.0342312\pi\)
0.404158 + 0.914689i \(0.367564\pi\)
\(350\) 0 0
\(351\) −23.8298 3.27473i −1.27194 0.174792i
\(352\) 0 0
\(353\) 13.2376 22.9282i 0.704565 1.22034i −0.262283 0.964991i \(-0.584475\pi\)
0.966848 0.255352i \(-0.0821913\pi\)
\(354\) 0 0
\(355\) 26.3840 15.2328i 1.40032 0.808473i
\(356\) 0 0
\(357\) −4.10439 + 4.46221i −0.217228 + 0.236165i
\(358\) 0 0
\(359\) 23.4619 1.23827 0.619135 0.785285i \(-0.287483\pi\)
0.619135 + 0.785285i \(0.287483\pi\)
\(360\) 0 0
\(361\) 14.4671 0.761424
\(362\) 0 0
\(363\) −6.72379 21.4665i −0.352908 1.12670i
\(364\) 0 0
\(365\) 22.8343 13.1834i 1.19520 0.690050i
\(366\) 0 0
\(367\) −9.62599 + 16.6727i −0.502472 + 0.870308i 0.497524 + 0.867450i \(0.334243\pi\)
−0.999996 + 0.00285720i \(0.999091\pi\)
\(368\) 0 0
\(369\) −1.18203 14.1251i −0.0615340 0.735321i
\(370\) 0 0
\(371\) 14.0880 + 8.13373i 0.731414 + 0.422282i
\(372\) 0 0
\(373\) 9.09206 5.24930i 0.470769 0.271799i −0.245793 0.969322i \(-0.579048\pi\)
0.716562 + 0.697524i \(0.245715\pi\)
\(374\) 0 0
\(375\) −4.13690 + 18.4949i −0.213628 + 0.955074i
\(376\) 0 0
\(377\) 16.9146 0.871145
\(378\) 0 0
\(379\) 35.5203i 1.82455i −0.409574 0.912277i \(-0.634323\pi\)
0.409574 0.912277i \(-0.365677\pi\)
\(380\) 0 0
\(381\) −12.5920 2.81654i −0.645106 0.144296i
\(382\) 0 0
\(383\) −18.0395 31.2453i −0.921774 1.59656i −0.796669 0.604416i \(-0.793407\pi\)
−0.125105 0.992144i \(-0.539927\pi\)
\(384\) 0 0
\(385\) −10.1420 + 17.5664i −0.516884 + 0.895269i
\(386\) 0 0
\(387\) 4.36343 + 6.28201i 0.221806 + 0.319332i
\(388\) 0 0
\(389\) 17.5243 + 10.1177i 0.888519 + 0.512987i 0.873458 0.486900i \(-0.161872\pi\)
0.0150612 + 0.999887i \(0.495206\pi\)
\(390\) 0 0
\(391\) 2.23181 + 3.86560i 0.112867 + 0.195492i
\(392\) 0 0
\(393\) −5.95764 + 1.86607i −0.300523 + 0.0941309i
\(394\) 0 0
\(395\) 22.6884i 1.14158i
\(396\) 0 0
\(397\) 3.99499i 0.200503i 0.994962 + 0.100251i \(0.0319647\pi\)
−0.994962 + 0.100251i \(0.968035\pi\)
\(398\) 0 0
\(399\) 4.92788 + 4.53272i 0.246702 + 0.226920i
\(400\) 0 0
\(401\) 14.0124 + 24.2702i 0.699747 + 1.21200i 0.968554 + 0.248803i \(0.0800372\pi\)
−0.268807 + 0.963194i \(0.586629\pi\)
\(402\) 0 0
\(403\) 21.3116 + 12.3042i 1.06161 + 0.612918i
\(404\) 0 0
\(405\) −19.2375 7.16696i −0.955921 0.356129i
\(406\) 0 0
\(407\) 19.5525 33.8660i 0.969183 1.67867i
\(408\) 0 0
\(409\) 8.22481 + 14.2458i 0.406691 + 0.704409i 0.994517 0.104579i \(-0.0333494\pi\)
−0.587826 + 0.808987i \(0.700016\pi\)
\(410\) 0 0
\(411\) −13.7928 + 14.9953i −0.680350 + 0.739662i
\(412\) 0 0
\(413\) 6.39976i 0.314912i
\(414\) 0 0
\(415\) 8.22179 0.403592
\(416\) 0 0
\(417\) 21.0706 6.59979i 1.03183 0.323193i
\(418\) 0 0
\(419\) −20.5573 + 11.8688i −1.00429 + 0.579827i −0.909515 0.415672i \(-0.863547\pi\)
−0.0947752 + 0.995499i \(0.530213\pi\)
\(420\) 0 0
\(421\) −25.9420 14.9776i −1.26433 0.729963i −0.290424 0.956898i \(-0.593796\pi\)
−0.973910 + 0.226935i \(0.927130\pi\)
\(422\) 0 0
\(423\) 9.95458 6.91437i 0.484008 0.336188i
\(424\) 0 0
\(425\) 0.195746 0.339043i 0.00949509 0.0164460i
\(426\) 0 0
\(427\) 3.11701 1.79961i 0.150843 0.0870891i
\(428\) 0 0
\(429\) −38.3223 8.57182i −1.85022 0.413851i
\(430\) 0 0
\(431\) 11.0367 0.531621 0.265810 0.964025i \(-0.414360\pi\)
0.265810 + 0.964025i \(0.414360\pi\)
\(432\) 0 0
\(433\) 34.9394 1.67908 0.839541 0.543297i \(-0.182824\pi\)
0.839541 + 0.543297i \(0.182824\pi\)
\(434\) 0 0
\(435\) 14.0880 + 3.15117i 0.675469 + 0.151087i
\(436\) 0 0
\(437\) 4.26901 2.46472i 0.204215 0.117903i
\(438\) 0 0
\(439\) 6.58518 11.4059i 0.314293 0.544372i −0.664994 0.746849i \(-0.731566\pi\)
0.979287 + 0.202477i \(0.0648991\pi\)
\(440\) 0 0
\(441\) 0.926503 + 11.0716i 0.0441192 + 0.527217i
\(442\) 0 0
\(443\) −23.6849 13.6745i −1.12530 0.649694i −0.182554 0.983196i \(-0.558436\pi\)
−0.942749 + 0.333502i \(0.891770\pi\)
\(444\) 0 0
\(445\) −4.93787 + 2.85088i −0.234077 + 0.135145i
\(446\) 0 0
\(447\) 12.5925 3.94427i 0.595606 0.186558i
\(448\) 0 0
\(449\) −13.8225 −0.652323 −0.326161 0.945314i \(-0.605755\pi\)
−0.326161 + 0.945314i \(0.605755\pi\)
\(450\) 0 0
\(451\) 23.1407i 1.08965i
\(452\) 0 0
\(453\) 5.32317 5.78723i 0.250104 0.271908i
\(454\) 0 0
\(455\) 9.58588 + 16.6032i 0.449393 + 0.778371i
\(456\) 0 0
\(457\) −2.86205 + 4.95722i −0.133881 + 0.231889i −0.925170 0.379554i \(-0.876077\pi\)
0.791288 + 0.611443i \(0.209411\pi\)
\(458\) 0 0
\(459\) −7.91277 6.14324i −0.369337 0.286742i
\(460\) 0 0
\(461\) 19.3717 + 11.1843i 0.902231 + 0.520903i 0.877923 0.478801i \(-0.158929\pi\)
0.0243074 + 0.999705i \(0.492262\pi\)
\(462\) 0 0
\(463\) −18.5733 32.1699i −0.863174 1.49506i −0.868849 0.495077i \(-0.835140\pi\)
0.00567564 0.999984i \(-0.498193\pi\)
\(464\) 0 0
\(465\) 15.4580 + 14.2184i 0.716847 + 0.659365i
\(466\) 0 0
\(467\) 22.6850i 1.04974i 0.851184 + 0.524868i \(0.175885\pi\)
−0.851184 + 0.524868i \(0.824115\pi\)
\(468\) 0 0
\(469\) 16.2004i 0.748063i
\(470\) 0 0
\(471\) 21.7778 6.82130i 1.00347 0.314309i
\(472\) 0 0
\(473\) 6.24353 + 10.8141i 0.287078 + 0.497233i
\(474\) 0 0
\(475\) −0.374425 0.216174i −0.0171798 0.00991875i
\(476\) 0 0
\(477\) −11.4514 + 24.3173i −0.524324 + 1.11341i
\(478\) 0 0
\(479\) −13.1576 + 22.7897i −0.601188 + 1.04129i 0.391453 + 0.920198i \(0.371973\pi\)
−0.992641 + 0.121091i \(0.961361\pi\)
\(480\) 0 0
\(481\) −18.4804 32.0090i −0.842634 1.45948i
\(482\) 0 0
\(483\) −7.10556 1.58935i −0.323314 0.0723180i
\(484\) 0 0
\(485\) 31.9056i 1.44876i
\(486\) 0 0
\(487\) 24.0388 1.08930 0.544652 0.838662i \(-0.316662\pi\)
0.544652 + 0.838662i \(0.316662\pi\)
\(488\) 0 0
\(489\) 7.78504 34.8048i 0.352051 1.57393i
\(490\) 0 0
\(491\) 27.2256 15.7187i 1.22867 0.709374i 0.261920 0.965090i \(-0.415644\pi\)
0.966752 + 0.255715i \(0.0823109\pi\)
\(492\) 0 0
\(493\) 6.10058 + 3.52217i 0.274756 + 0.158631i
\(494\) 0 0
\(495\) −30.3214 14.2788i −1.36285 0.641785i
\(496\) 0 0
\(497\) −12.1250 + 21.0011i −0.543881 + 0.942029i
\(498\) 0 0
\(499\) 5.08156 2.93384i 0.227482 0.131337i −0.381928 0.924192i \(-0.624740\pi\)
0.609410 + 0.792855i \(0.291406\pi\)
\(500\) 0 0
\(501\) 2.62909 + 8.39366i 0.117459 + 0.375001i
\(502\) 0 0
\(503\) −32.4317 −1.44606 −0.723029 0.690818i \(-0.757251\pi\)
−0.723029 + 0.690818i \(0.757251\pi\)
\(504\) 0 0
\(505\) 2.97861 0.132546
\(506\) 0 0
\(507\) −9.88348 + 10.7451i −0.438941 + 0.477207i
\(508\) 0 0
\(509\) 13.6855 7.90133i 0.606599 0.350220i −0.165034 0.986288i \(-0.552773\pi\)
0.771633 + 0.636068i \(0.219440\pi\)
\(510\) 0 0
\(511\) −10.4937 + 18.1756i −0.464214 + 0.804042i
\(512\) 0 0
\(513\) −6.78434 + 8.73854i −0.299536 + 0.385816i
\(514\) 0 0
\(515\) −12.7341 7.35202i −0.561130 0.323969i
\(516\) 0 0
\(517\) 17.1362 9.89361i 0.753650 0.435120i
\(518\) 0 0
\(519\) 16.2506 + 14.9475i 0.713324 + 0.656124i
\(520\) 0 0
\(521\) 5.50310 0.241095 0.120548 0.992708i \(-0.461535\pi\)
0.120548 + 0.992708i \(0.461535\pi\)
\(522\) 0 0
\(523\) 38.5894i 1.68740i 0.536818 + 0.843698i \(0.319626\pi\)
−0.536818 + 0.843698i \(0.680374\pi\)
\(524\) 0 0
\(525\) 0.190883 + 0.609416i 0.00833083 + 0.0265971i
\(526\) 0 0
\(527\) 5.12430 + 8.87555i 0.223218 + 0.386625i
\(528\) 0 0
\(529\) 8.81970 15.2762i 0.383465 0.664181i
\(530\) 0 0
\(531\) −10.5375 + 0.881812i −0.457289 + 0.0382674i
\(532\) 0 0
\(533\) −18.9415 10.9359i −0.820449 0.473686i
\(534\) 0 0
\(535\) 3.54046 + 6.13225i 0.153067 + 0.265120i
\(536\) 0 0
\(537\) −3.33472 + 14.9086i −0.143904 + 0.643354i
\(538\) 0 0
\(539\) 18.1382i 0.781268i
\(540\) 0 0
\(541\) 22.5666i 0.970214i −0.874455 0.485107i \(-0.838781\pi\)
0.874455 0.485107i \(-0.161219\pi\)
\(542\) 0 0
\(543\) −5.83634 + 26.0927i −0.250461 + 1.11974i
\(544\) 0 0
\(545\) −20.6246 35.7229i −0.883463 1.53020i
\(546\) 0 0
\(547\) −11.2679 6.50552i −0.481780 0.278156i 0.239378 0.970927i \(-0.423057\pi\)
−0.721158 + 0.692770i \(0.756390\pi\)
\(548\) 0 0
\(549\) 3.39262 + 4.88434i 0.144794 + 0.208458i
\(550\) 0 0
\(551\) 3.88974 6.73723i 0.165709 0.287016i
\(552\) 0 0
\(553\) −9.02976 15.6400i −0.383985 0.665081i
\(554\) 0 0
\(555\) −9.42895 30.1029i −0.400236 1.27780i
\(556\) 0 0
\(557\) 5.73693i 0.243081i 0.992586 + 0.121541i \(0.0387835\pi\)
−0.992586 + 0.121541i \(0.961217\pi\)
\(558\) 0 0
\(559\) 11.8024 0.499186
\(560\) 0 0
\(561\) −12.0368 11.0716i −0.508192 0.467442i
\(562\) 0 0
\(563\) 13.2510 7.65045i 0.558462 0.322428i −0.194066 0.980988i \(-0.562168\pi\)
0.752528 + 0.658560i \(0.228834\pi\)
\(564\) 0 0
\(565\) 5.59908 + 3.23263i 0.235555 + 0.135998i
\(566\) 0 0
\(567\) 16.1136 2.71589i 0.676706 0.114057i
\(568\) 0 0
\(569\) 6.63095 11.4851i 0.277984 0.481482i −0.692900 0.721034i \(-0.743667\pi\)
0.970884 + 0.239552i \(0.0770005\pi\)
\(570\) 0 0
\(571\) 23.4262 13.5251i 0.980357 0.566009i 0.0779788 0.996955i \(-0.475153\pi\)
0.902378 + 0.430946i \(0.141820\pi\)
\(572\) 0 0
\(573\) 11.2965 12.2813i 0.471917 0.513058i
\(574\) 0 0
\(575\) 0.470166 0.0196073
\(576\) 0 0
\(577\) −4.78434 −0.199174 −0.0995872 0.995029i \(-0.531752\pi\)
−0.0995872 + 0.995029i \(0.531752\pi\)
\(578\) 0 0
\(579\) −3.61713 11.5481i −0.150323 0.479922i
\(580\) 0 0
\(581\) −5.66760 + 3.27219i −0.235132 + 0.135753i
\(582\) 0 0
\(583\) −21.9406 + 38.0023i −0.908689 + 1.57390i
\(584\) 0 0
\(585\) −26.0172 + 18.0713i −1.07568 + 0.747157i
\(586\) 0 0
\(587\) 37.0796 + 21.4079i 1.53044 + 0.883598i 0.999341 + 0.0362861i \(0.0115528\pi\)
0.531095 + 0.847312i \(0.321781\pi\)
\(588\) 0 0
\(589\) 9.80179 5.65906i 0.403876 0.233178i
\(590\) 0 0
\(591\) −1.63270 + 7.29935i −0.0671602 + 0.300255i
\(592\) 0 0
\(593\) −0.825572 −0.0339022 −0.0169511 0.999856i \(-0.505396\pi\)
−0.0169511 + 0.999856i \(0.505396\pi\)
\(594\) 0 0
\(595\) 7.98438i 0.327328i
\(596\) 0 0
\(597\) 9.98364 + 2.23311i 0.408603 + 0.0913952i
\(598\) 0 0
\(599\) 0.961228 + 1.66490i 0.0392747 + 0.0680258i 0.884995 0.465601i \(-0.154162\pi\)
−0.845720 + 0.533627i \(0.820829\pi\)
\(600\) 0 0
\(601\) −21.5937 + 37.4014i −0.880825 + 1.52563i −0.0303994 + 0.999538i \(0.509678\pi\)
−0.850425 + 0.526096i \(0.823655\pi\)
\(602\) 0 0
\(603\) 26.6747 2.23222i 1.08628 0.0909030i
\(604\) 0 0
\(605\) −25.6556 14.8123i −1.04305 0.602205i
\(606\) 0 0
\(607\) −20.5078 35.5206i −0.832386 1.44174i −0.896141 0.443770i \(-0.853641\pi\)
0.0637546 0.997966i \(-0.479693\pi\)
\(608\) 0 0
\(609\) −10.9656 + 3.43467i −0.444347 + 0.139180i
\(610\) 0 0
\(611\) 18.7022i 0.756611i
\(612\) 0 0
\(613\) 5.05878i 0.204322i 0.994768 + 0.102161i \(0.0325757\pi\)
−0.994768 + 0.102161i \(0.967424\pi\)
\(614\) 0 0
\(615\) −13.7389 12.6372i −0.554007 0.509582i
\(616\) 0 0
\(617\) −16.0739 27.8408i −0.647112 1.12083i −0.983809 0.179217i \(-0.942643\pi\)
0.336698 0.941613i \(-0.390690\pi\)
\(618\) 0 0
\(619\) −27.3562 15.7941i −1.09954 0.634820i −0.163440 0.986553i \(-0.552259\pi\)
−0.936100 + 0.351734i \(0.885592\pi\)
\(620\) 0 0
\(621\) 1.63788 11.9186i 0.0657259 0.478278i
\(622\) 0 0
\(623\) 2.26924 3.93044i 0.0909153 0.157470i
\(624\) 0 0
\(625\) 12.9871 + 22.4942i 0.519482 + 0.899770i
\(626\) 0 0
\(627\) −12.2270 + 13.2929i −0.488298 + 0.530867i
\(628\) 0 0
\(629\) 15.3929i 0.613756i
\(630\) 0 0
\(631\) 15.4885 0.616586 0.308293 0.951292i \(-0.400242\pi\)
0.308293 + 0.951292i \(0.400242\pi\)
\(632\) 0 0
\(633\) 30.3044 9.49205i 1.20449 0.377275i
\(634\) 0 0
\(635\) −14.7162 + 8.49638i −0.583993 + 0.337168i
\(636\) 0 0
\(637\) 14.8468 + 8.57182i 0.588253 + 0.339628i
\(638\) 0 0
\(639\) −36.2500 17.0707i −1.43403 0.675305i
\(640\) 0 0
\(641\) −15.2248 + 26.3701i −0.601344 + 1.04156i 0.391274 + 0.920274i \(0.372034\pi\)
−0.992618 + 0.121284i \(0.961299\pi\)
\(642\) 0 0
\(643\) −14.5911 + 8.42419i −0.575418 + 0.332218i −0.759310 0.650729i \(-0.774463\pi\)
0.183893 + 0.982946i \(0.441130\pi\)
\(644\) 0 0
\(645\) 9.83009 + 2.19877i 0.387060 + 0.0865764i
\(646\) 0 0
\(647\) −18.6734 −0.734126 −0.367063 0.930196i \(-0.619637\pi\)
−0.367063 + 0.930196i \(0.619637\pi\)
\(648\) 0 0
\(649\) −17.2633 −0.677644
\(650\) 0 0
\(651\) −16.3146 3.64920i −0.639419 0.143024i
\(652\) 0 0
\(653\) −31.4276 + 18.1448i −1.22986 + 0.710059i −0.967000 0.254775i \(-0.917999\pi\)
−0.262858 + 0.964834i \(0.584665\pi\)
\(654\) 0 0
\(655\) −4.11089 + 7.12028i −0.160626 + 0.278212i
\(656\) 0 0
\(657\) −31.3729 14.7740i −1.22397 0.576388i
\(658\) 0 0
\(659\) 19.3088 + 11.1480i 0.752166 + 0.434263i 0.826476 0.562972i \(-0.190342\pi\)
−0.0743103 + 0.997235i \(0.523676\pi\)
\(660\) 0 0
\(661\) −5.19793 + 3.00103i −0.202176 + 0.116726i −0.597670 0.801742i \(-0.703907\pi\)
0.395494 + 0.918469i \(0.370573\pi\)
\(662\) 0 0
\(663\) −14.7509 + 4.62032i −0.572877 + 0.179438i
\(664\) 0 0
\(665\) 8.81762 0.341933
\(666\) 0 0
\(667\) 8.45996i 0.327571i
\(668\) 0 0
\(669\) −6.17388 + 6.71211i −0.238696 + 0.259505i
\(670\) 0 0
\(671\) 4.85442 + 8.40810i 0.187403 + 0.324591i
\(672\) 0 0
\(673\) −3.70444 + 6.41629i −0.142796 + 0.247330i −0.928548 0.371211i \(-0.878943\pi\)
0.785753 + 0.618541i \(0.212276\pi\)
\(674\) 0 0
\(675\) −0.977130 + 0.398269i −0.0376098 + 0.0153294i
\(676\) 0 0
\(677\) −8.57613 4.95143i −0.329607 0.190299i 0.326059 0.945349i \(-0.394279\pi\)
−0.655667 + 0.755050i \(0.727612\pi\)
\(678\) 0 0
\(679\) −12.6981 21.9938i −0.487309 0.844043i
\(680\) 0 0
\(681\) −2.26154 2.08020i −0.0866626 0.0797133i
\(682\) 0 0
\(683\) 39.0736i 1.49511i −0.664200 0.747555i \(-0.731228\pi\)
0.664200 0.747555i \(-0.268772\pi\)
\(684\) 0 0
\(685\) 26.8316i 1.02518i
\(686\) 0 0
\(687\) −6.31139 + 1.97687i −0.240794 + 0.0754224i
\(688\) 0 0
\(689\) 20.7376 + 35.9185i 0.790039 + 1.36839i
\(690\) 0 0
\(691\) 2.07502 + 1.19801i 0.0789375 + 0.0455746i 0.538949 0.842338i \(-0.318821\pi\)
−0.460012 + 0.887913i \(0.652155\pi\)
\(692\) 0 0
\(693\) 26.5846 2.22468i 1.00986 0.0845086i
\(694\) 0 0
\(695\) 14.5391 25.1825i 0.551500 0.955227i
\(696\) 0 0
\(697\) −4.55443 7.88850i −0.172511 0.298798i
\(698\) 0 0
\(699\) 34.3478 + 7.68281i 1.29915 + 0.290591i
\(700\) 0 0
\(701\) 30.9184i 1.16777i −0.811836 0.583885i \(-0.801532\pi\)
0.811836 0.583885i \(-0.198468\pi\)
\(702\) 0 0
\(703\) −16.9993 −0.641141
\(704\) 0 0
\(705\) 3.48421 15.5769i 0.131223 0.586662i
\(706\) 0 0
\(707\) −2.05327 + 1.18546i −0.0772212 + 0.0445837i
\(708\) 0 0
\(709\) 4.46959 + 2.58052i 0.167859 + 0.0969133i 0.581576 0.813492i \(-0.302436\pi\)
−0.413717 + 0.910406i \(0.635770\pi\)
\(710\) 0 0
\(711\) 24.5078 17.0229i 0.919115 0.638410i
\(712\) 0 0
\(713\) −6.15406 + 10.6591i −0.230471 + 0.399188i
\(714\) 0 0
\(715\) −44.7870 + 25.8578i −1.67494 + 0.967027i
\(716\) 0 0
\(717\) 9.00631 + 28.7536i 0.336347 + 1.07382i
\(718\) 0 0
\(719\) −14.7871 −0.551465 −0.275733 0.961234i \(-0.588920\pi\)
−0.275733 + 0.961234i \(0.588920\pi\)
\(720\) 0 0
\(721\) 11.7041 0.435884
\(722\) 0 0
\(723\) 16.0785 17.4802i 0.597965 0.650095i
\(724\) 0 0
\(725\) 0.642593 0.371001i 0.0238653 0.0137786i
\(726\) 0 0
\(727\) 1.06681 1.84777i 0.0395658 0.0685299i −0.845564 0.533873i \(-0.820736\pi\)
0.885130 + 0.465344i \(0.154069\pi\)
\(728\) 0 0
\(729\) 6.69210 + 26.1575i 0.247855 + 0.968797i
\(730\) 0 0
\(731\) 4.25675 + 2.45764i 0.157442 + 0.0908990i
\(732\) 0 0
\(733\) −22.2298 + 12.8344i −0.821076 + 0.474048i −0.850787 0.525510i \(-0.823875\pi\)
0.0297113 + 0.999559i \(0.490541\pi\)
\(734\) 0 0
\(735\) 10.7689 + 9.90536i 0.397217 + 0.365365i
\(736\) 0 0
\(737\) 43.7003 1.60972
\(738\) 0 0
\(739\) 5.46282i 0.200953i −0.994939 0.100476i \(-0.967963\pi\)
0.994939 0.100476i \(-0.0320367\pi\)
\(740\) 0 0
\(741\) 5.10249 + 16.2903i 0.187445 + 0.598438i
\(742\) 0 0
\(743\) 16.8170 + 29.1279i 0.616955 + 1.06860i 0.990038 + 0.140800i \(0.0449674\pi\)
−0.373083 + 0.927798i \(0.621699\pi\)
\(744\) 0 0
\(745\) 8.68910 15.0500i 0.318344 0.551388i
\(746\) 0 0
\(747\) −6.16874 8.88109i −0.225702 0.324942i
\(748\) 0 0
\(749\) −4.88115 2.81813i −0.178353 0.102972i
\(750\) 0 0
\(751\) 12.6727 + 21.9498i 0.462435 + 0.800961i 0.999082 0.0428462i \(-0.0136426\pi\)
−0.536647 + 0.843807i \(0.680309\pi\)
\(752\) 0 0
\(753\) −1.70419 + 7.61897i −0.0621042 + 0.277651i
\(754\) 0 0
\(755\) 10.3553i 0.376868i
\(756\) 0 0
\(757\) 3.95103i 0.143603i −0.997419 0.0718014i \(-0.977125\pi\)
0.997419 0.0718014i \(-0.0228748\pi\)
\(758\) 0 0
\(759\) 4.28726 19.1672i 0.155618 0.695724i
\(760\) 0 0
\(761\) −23.3979 40.5264i −0.848175 1.46908i −0.882835 0.469682i \(-0.844368\pi\)
0.0346607 0.999399i \(-0.488965\pi\)
\(762\) 0 0
\(763\) 28.4347 + 16.4168i 1.02941 + 0.594328i
\(764\) 0 0
\(765\) −13.1467 + 1.10015i −0.475318 + 0.0397761i
\(766\) 0 0
\(767\) −8.15835 + 14.1307i −0.294581 + 0.510229i
\(768\) 0 0
\(769\) 2.60083 + 4.50478i 0.0937885 + 0.162446i 0.909102 0.416573i \(-0.136769\pi\)
−0.815314 + 0.579019i \(0.803436\pi\)
\(770\) 0 0
\(771\) 4.25830 + 13.5951i 0.153359 + 0.489615i
\(772\) 0 0
\(773\) 38.8477i 1.39725i −0.715486 0.698627i \(-0.753795\pi\)
0.715486 0.698627i \(-0.246205\pi\)
\(774\) 0 0
\(775\) 1.07952 0.0387773
\(776\) 0 0
\(777\) 18.4804 + 16.9985i 0.662981 + 0.609818i
\(778\) 0 0
\(779\) −8.71173 + 5.02972i −0.312130 + 0.180209i
\(780\) 0 0
\(781\) −56.6503 32.7071i −2.02711 1.17035i
\(782\) 0 0
\(783\) −7.16627 17.5821i −0.256102 0.628331i
\(784\) 0 0
\(785\) 15.0271 26.0277i 0.536340 0.928968i
\(786\) 0 0
\(787\) −40.8579 + 23.5893i −1.45643 + 0.840869i −0.998833 0.0482918i \(-0.984622\pi\)
−0.457595 + 0.889161i \(0.651289\pi\)
\(788\) 0 0
\(789\) 5.89509 6.40902i 0.209871 0.228167i
\(790\) 0 0
\(791\) −5.14621 −0.182978
\(792\) 0 0
\(793\) 9.17648 0.325866
\(794\) 0 0
\(795\) 10.5806 + 33.7797i 0.375255 + 1.19804i
\(796\) 0 0
\(797\) −6.35645 + 3.66990i −0.225157 + 0.129995i −0.608336 0.793680i \(-0.708163\pi\)
0.383179 + 0.923674i \(0.374829\pi\)
\(798\) 0 0
\(799\) 3.89442 6.74533i 0.137775 0.238633i
\(800\) 0 0
\(801\) 6.78434 + 3.19485i 0.239713 + 0.112884i
\(802\) 0 0
\(803\) −49.0286 28.3067i −1.73018 0.998920i
\(804\) 0 0
\(805\) −8.30423 + 4.79445i −0.292686 + 0.168982i
\(806\) 0 0
\(807\) −8.75542 + 39.1431i −0.308205 + 1.37790i
\(808\) 0 0
\(809\) 2.25520 0.0792887 0.0396443 0.999214i \(-0.487378\pi\)
0.0396443 + 0.999214i \(0.487378\pi\)
\(810\) 0 0
\(811\) 15.9986i 0.561785i 0.959739 + 0.280893i \(0.0906305\pi\)
−0.959739 + 0.280893i \(0.909369\pi\)
\(812\) 0 0
\(813\) 35.3889 + 7.91569i 1.24114 + 0.277615i
\(814\) 0 0
\(815\) −23.4844 40.6761i −0.822622 1.42482i
\(816\) 0 0
\(817\) 2.71411 4.70098i 0.0949548 0.164467i
\(818\) 0 0
\(819\) 10.7424 22.8118i 0.375371 0.797110i
\(820\) 0 0
\(821\) 25.2413 + 14.5731i 0.880928 + 0.508604i 0.870964 0.491347i \(-0.163495\pi\)
0.00996351 + 0.999950i \(0.496828\pi\)
\(822\) 0 0
\(823\) 4.15695 + 7.20005i 0.144902 + 0.250978i 0.929336 0.369234i \(-0.120380\pi\)
−0.784434 + 0.620212i \(0.787047\pi\)
\(824\) 0 0
\(825\) −1.64389 + 0.514906i −0.0572330 + 0.0179267i
\(826\) 0 0
\(827\) 43.5035i 1.51277i −0.654129 0.756383i \(-0.726965\pi\)
0.654129 0.756383i \(-0.273035\pi\)
\(828\) 0 0
\(829\) 15.9248i 0.553092i 0.961001 + 0.276546i \(0.0891897\pi\)
−0.961001 + 0.276546i \(0.910810\pi\)
\(830\) 0 0
\(831\) 28.3636 + 26.0892i 0.983921 + 0.905023i
\(832\) 0 0
\(833\) 3.56987 + 6.18320i 0.123689 + 0.214235i
\(834\) 0 0
\(835\) 10.0317 + 5.79180i 0.347161 + 0.200433i
\(836\) 0 0
\(837\) 3.76062 27.3656i 0.129986 0.945892i
\(838\) 0 0
\(839\) 21.0582 36.4739i 0.727009 1.25922i −0.231132 0.972922i \(-0.574243\pi\)
0.958142 0.286295i \(-0.0924237\pi\)
\(840\) 0 0
\(841\) −7.82437 13.5522i −0.269806 0.467318i
\(842\) 0 0
\(843\) 21.7635 23.6608i 0.749575 0.814922i
\(844\) 0 0
\(845\) 19.2266i 0.661415i
\(846\) 0 0
\(847\) 23.5806 0.810238
\(848\) 0 0
\(849\) −3.35836 + 1.05192i −0.115259 + 0.0361017i
\(850\) 0 0
\(851\) 16.0095 9.24311i 0.548800 0.316850i
\(852\) 0 0
\(853\) 34.2013 + 19.7461i 1.17103 + 0.676095i 0.953923 0.300053i \(-0.0970043\pi\)
0.217108 + 0.976148i \(0.430338\pi\)
\(854\) 0 0
\(855\) 1.21496 + 14.5186i 0.0415509 + 0.496526i
\(856\) 0 0
\(857\) −12.6170 + 21.8532i −0.430988 + 0.746493i −0.996959 0.0779326i \(-0.975168\pi\)
0.565971 + 0.824425i \(0.308501\pi\)
\(858\) 0 0
\(859\) 47.5539 27.4552i 1.62252 0.936761i 0.636274 0.771463i \(-0.280475\pi\)
0.986244 0.165297i \(-0.0528584\pi\)
\(860\) 0 0
\(861\) 14.5003 + 3.24338i 0.494167 + 0.110534i
\(862\) 0 0
\(863\) 54.3877 1.85138 0.925689 0.378285i \(-0.123486\pi\)
0.925689 + 0.378285i \(0.123486\pi\)
\(864\) 0 0
\(865\) 29.0778 0.988675
\(866\) 0 0
\(867\) 22.4525 + 5.02212i 0.762527 + 0.170560i
\(868\) 0 0
\(869\) 42.1888 24.3577i 1.43116 0.826278i
\(870\) 0 0
\(871\) 20.6521 35.7704i 0.699768 1.21203i
\(872\) 0 0
\(873\) 34.4641 23.9385i 1.16643 0.810196i
\(874\) 0 0
\(875\) −17.2050 9.93334i −0.581637 0.335808i
\(876\) 0 0
\(877\) −5.90001 + 3.40637i −0.199229 + 0.115025i −0.596296 0.802765i \(-0.703361\pi\)
0.397067 + 0.917790i \(0.370028\pi\)
\(878\) 0 0
\(879\) 56.3951 17.6642i 1.90216 0.595800i
\(880\) 0 0
\(881\) −43.2881 −1.45841 −0.729207 0.684293i \(-0.760111\pi\)
−0.729207 + 0.684293i \(0.760111\pi\)
\(882\) 0 0
\(883\) 31.1510i 1.04832i 0.851621 + 0.524158i \(0.175620\pi\)
−0.851621 + 0.524158i \(0.824380\pi\)
\(884\) 0 0
\(885\) −9.42756 + 10.2494i −0.316904 + 0.344531i
\(886\) 0 0
\(887\) 24.8886 + 43.1083i 0.835677 + 1.44743i 0.893478 + 0.449107i \(0.148258\pi\)
−0.0578015 + 0.998328i \(0.518409\pi\)
\(888\) 0 0
\(889\) 6.76295 11.7138i 0.226822 0.392867i
\(890\) 0 0
\(891\) 7.32608 + 43.4662i 0.245433 + 1.45617i
\(892\) 0 0
\(893\) −7.44926 4.30083i −0.249280 0.143922i
\(894\) 0 0
\(895\) 10.0595 + 17.4236i 0.336253 + 0.582407i
\(896\) 0 0
\(897\) −13.6630 12.5674i −0.456194 0.419613i
\(898\) 0 0
\(899\) 19.4243i 0.647838i
\(900\) 0 0
\(901\) 17.2730i 0.575447i
\(902\) 0 0
\(903\) −7.65135 + 2.39658i −0.254621 + 0.0797532i
\(904\) 0 0
\(905\) 17.6059 + 30.4944i 0.585241 + 1.01367i
\(906\) 0 0
\(907\) −16.6712 9.62515i −0.553559 0.319598i 0.196997 0.980404i \(-0.436881\pi\)
−0.750556 + 0.660806i \(0.770214\pi\)
\(908\) 0 0
\(909\) −2.23483 3.21747i −0.0741245 0.106717i
\(910\) 0 0
\(911\) −11.1396 + 19.2944i −0.369072 + 0.639252i −0.989421 0.145074i \(-0.953658\pi\)
0.620348 + 0.784326i \(0.286991\pi\)
\(912\) 0 0
\(913\) −8.82669 15.2883i −0.292121 0.505968i
\(914\) 0 0
\(915\) 7.64302 + 1.70957i 0.252670 + 0.0565166i
\(916\) 0 0
\(917\) 6.54438i 0.216114i
\(918\) 0 0
\(919\) −28.0122 −0.924039 −0.462019 0.886870i \(-0.652875\pi\)
−0.462019 + 0.886870i \(0.652875\pi\)
\(920\) 0 0
\(921\) −1.80565 + 8.07259i −0.0594983 + 0.266001i
\(922\) 0 0
\(923\) −53.5440 + 30.9136i −1.76242 + 1.01753i
\(924\) 0 0
\(925\) −1.40416 0.810691i −0.0461684 0.0266554i
\(926\) 0 0
\(927\) 1.61269 + 19.2714i 0.0529677 + 0.632955i
\(928\) 0 0
\(929\) −3.94220 + 6.82809i −0.129339 + 0.224022i −0.923421 0.383789i \(-0.874619\pi\)
0.794081 + 0.607811i \(0.207952\pi\)
\(930\) 0 0
\(931\) 6.82847 3.94242i 0.223794 0.129208i
\(932\) 0 0
\(933\) −11.5731 36.9484i −0.378886 1.20964i
\(934\) 0 0
\(935\) −21.5378 −0.704361
\(936\) 0 0
\(937\) −8.98600 −0.293560 −0.146780 0.989169i \(-0.546891\pi\)
−0.146780 + 0.989169i \(0.546891\pi\)
\(938\) 0 0
\(939\) −2.87070 + 3.12096i −0.0936817 + 0.101849i
\(940\) 0 0
\(941\) 21.0227 12.1375i 0.685322 0.395671i −0.116535 0.993187i \(-0.537179\pi\)
0.801857 + 0.597516i \(0.203845\pi\)
\(942\) 0 0
\(943\) 5.46967 9.47375i 0.178117 0.308508i
\(944\) 0 0
\(945\) 13.1971 16.9985i 0.429302 0.552961i
\(946\) 0 0
\(947\) −1.71382 0.989473i −0.0556916 0.0321536i 0.471896 0.881654i \(-0.343570\pi\)
−0.527587 + 0.849501i \(0.676903\pi\)
\(948\) 0 0
\(949\) −46.3402 + 26.7545i −1.50427 + 0.868488i
\(950\) 0 0
\(951\) −21.0328 19.3462i −0.682036 0.627345i
\(952\) 0 0
\(953\) 28.9674 0.938347 0.469173 0.883106i \(-0.344552\pi\)
0.469173 + 0.883106i \(0.344552\pi\)
\(954\) 0 0
\(955\) 21.9753i 0.711104i
\(956\) 0 0
\(957\) −9.26498 29.5795i −0.299494 0.956169i
\(958\) 0 0
\(959\) −10.6787 18.4960i −0.344833 0.597268i
\(960\) 0 0
\(961\) 1.37008 2.37304i 0.0441961 0.0765498i
\(962\) 0 0
\(963\) 3.96762 8.42535i 0.127855 0.271503i
\(964\) 0 0
\(965\) −13.8017 7.96842i −0.444293 0.256512i
\(966\) 0 0
\(967\) −0.00531192 0.00920052i −0.000170820 0.000295869i 0.865940 0.500148i \(-0.166721\pi\)
−0.866111 + 0.499852i \(0.833388\pi\)
\(968\) 0 0
\(969\) −1.55185 + 6.93791i −0.0498527 + 0.222878i
\(970\) 0 0
\(971\) 17.0984i 0.548715i 0.961628 + 0.274357i \(0.0884651\pi\)
−0.961628 + 0.274357i \(0.911535\pi\)
\(972\) 0 0
\(973\) 23.1457i 0.742017i
\(974\) 0 0
\(975\) −0.355407 + 1.58893i −0.0113821 + 0.0508864i
\(976\) 0 0
\(977\) −5.50612 9.53688i −0.176156 0.305112i 0.764404 0.644737i \(-0.223033\pi\)
−0.940561 + 0.339625i \(0.889700\pi\)
\(978\) 0 0
\(979\) 10.6023 + 6.12126i 0.338852 + 0.195636i
\(980\) 0 0
\(981\) −23.1131 + 49.0812i −0.737943 + 1.56704i
\(982\) 0 0
\(983\) −22.7443 + 39.3943i −0.725432 + 1.25648i 0.233364 + 0.972389i \(0.425027\pi\)
−0.958796 + 0.284095i \(0.908307\pi\)
\(984\) 0 0
\(985\) 4.92521 + 8.53071i 0.156930 + 0.271811i
\(986\) 0 0
\(987\) 3.79767 + 12.1245i 0.120881 + 0.385926i
\(988\) 0 0
\(989\) 5.90304i 0.187706i
\(990\) 0 0
\(991\) −3.93737 −0.125075 −0.0625374 0.998043i \(-0.519919\pi\)
−0.0625374 + 0.998043i \(0.519919\pi\)
\(992\) 0 0
\(993\) 0.484583 + 0.445725i 0.0153778 + 0.0141447i
\(994\) 0 0
\(995\) 11.6678 6.73642i 0.369895 0.213559i
\(996\) 0 0
\(997\) −2.16558 1.25030i −0.0685847 0.0395974i 0.465316 0.885145i \(-0.345941\pi\)
−0.533900 + 0.845547i \(0.679274\pi\)
\(998\) 0 0
\(999\) −25.4424 + 32.7710i −0.804963 + 1.03683i
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 288.2.r.b.241.1 16
3.2 odd 2 864.2.r.b.721.7 16
4.3 odd 2 72.2.n.b.61.5 yes 16
8.3 odd 2 72.2.n.b.61.6 yes 16
8.5 even 2 inner 288.2.r.b.241.8 16
9.2 odd 6 2592.2.d.k.1297.7 8
9.4 even 3 inner 288.2.r.b.49.8 16
9.5 odd 6 864.2.r.b.145.2 16
9.7 even 3 2592.2.d.j.1297.2 8
12.11 even 2 216.2.n.b.181.4 16
24.5 odd 2 864.2.r.b.721.2 16
24.11 even 2 216.2.n.b.181.3 16
36.7 odd 6 648.2.d.j.325.2 8
36.11 even 6 648.2.d.k.325.7 8
36.23 even 6 216.2.n.b.37.3 16
36.31 odd 6 72.2.n.b.13.6 yes 16
72.5 odd 6 864.2.r.b.145.7 16
72.11 even 6 648.2.d.k.325.8 8
72.13 even 6 inner 288.2.r.b.49.1 16
72.29 odd 6 2592.2.d.k.1297.2 8
72.43 odd 6 648.2.d.j.325.1 8
72.59 even 6 216.2.n.b.37.4 16
72.61 even 6 2592.2.d.j.1297.7 8
72.67 odd 6 72.2.n.b.13.5 16
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
72.2.n.b.13.5 16 72.67 odd 6
72.2.n.b.13.6 yes 16 36.31 odd 6
72.2.n.b.61.5 yes 16 4.3 odd 2
72.2.n.b.61.6 yes 16 8.3 odd 2
216.2.n.b.37.3 16 36.23 even 6
216.2.n.b.37.4 16 72.59 even 6
216.2.n.b.181.3 16 24.11 even 2
216.2.n.b.181.4 16 12.11 even 2
288.2.r.b.49.1 16 72.13 even 6 inner
288.2.r.b.49.8 16 9.4 even 3 inner
288.2.r.b.241.1 16 1.1 even 1 trivial
288.2.r.b.241.8 16 8.5 even 2 inner
648.2.d.j.325.1 8 72.43 odd 6
648.2.d.j.325.2 8 36.7 odd 6
648.2.d.k.325.7 8 36.11 even 6
648.2.d.k.325.8 8 72.11 even 6
864.2.r.b.145.2 16 9.5 odd 6
864.2.r.b.145.7 16 72.5 odd 6
864.2.r.b.721.2 16 24.5 odd 2
864.2.r.b.721.7 16 3.2 odd 2
2592.2.d.j.1297.2 8 9.7 even 3
2592.2.d.j.1297.7 8 72.61 even 6
2592.2.d.k.1297.2 8 72.29 odd 6
2592.2.d.k.1297.7 8 9.2 odd 6