Properties

Label 448.2.i.b.193.1
Level $448$
Weight $2$
Character 448.193
Analytic conductor $3.577$
Analytic rank $0$
Dimension $2$
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] = [448,2,Mod(65,448)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(448, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([0, 0, 2]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("448.65");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 448 = 2^{6} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 448.i (of order \(3\), 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: \(3.57729801055\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\zeta_{6})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{2} - x + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 56)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 193.1
Root \(0.500000 + 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 448.193
Dual form 448.2.i.b.65.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.500000 + 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{5} +(-2.00000 - 1.73205i) q^{7} +(1.00000 + 1.73205i) q^{9} +O(q^{10})\) \(q+(-0.500000 + 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{5} +(-2.00000 - 1.73205i) q^{7} +(1.00000 + 1.73205i) q^{9} +(1.50000 - 2.59808i) q^{11} +6.00000 q^{13} +1.00000 q^{15} +(2.50000 - 4.33013i) q^{17} +(0.500000 + 0.866025i) q^{19} +(2.50000 - 0.866025i) q^{21} +(3.50000 + 6.06218i) q^{23} +(2.00000 - 3.46410i) q^{25} -5.00000 q^{27} -2.00000 q^{29} +(2.50000 - 4.33013i) q^{31} +(1.50000 + 2.59808i) q^{33} +(-0.500000 + 2.59808i) q^{35} +(1.50000 + 2.59808i) q^{37} +(-3.00000 + 5.19615i) q^{39} -2.00000 q^{41} +4.00000 q^{43} +(1.00000 - 1.73205i) q^{45} +(-2.50000 - 4.33013i) q^{47} +(1.00000 + 6.92820i) q^{49} +(2.50000 + 4.33013i) q^{51} +(-0.500000 + 0.866025i) q^{53} -3.00000 q^{55} -1.00000 q^{57} +(7.50000 - 12.9904i) q^{59} +(-2.50000 - 4.33013i) q^{61} +(1.00000 - 5.19615i) q^{63} +(-3.00000 - 5.19615i) q^{65} +(-4.50000 + 7.79423i) q^{67} -7.00000 q^{69} +(-3.50000 + 6.06218i) q^{73} +(2.00000 + 3.46410i) q^{75} +(-7.50000 + 2.59808i) q^{77} +(-0.500000 - 0.866025i) q^{79} +(-0.500000 + 0.866025i) q^{81} -12.0000 q^{83} -5.00000 q^{85} +(1.00000 - 1.73205i) q^{87} +(-3.50000 - 6.06218i) q^{89} +(-12.0000 - 10.3923i) q^{91} +(2.50000 + 4.33013i) q^{93} +(0.500000 - 0.866025i) q^{95} -2.00000 q^{97} +6.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q - q^{3} - q^{5} - 4 q^{7} + 2 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 2 q - q^{3} - q^{5} - 4 q^{7} + 2 q^{9} + 3 q^{11} + 12 q^{13} + 2 q^{15} + 5 q^{17} + q^{19} + 5 q^{21} + 7 q^{23} + 4 q^{25} - 10 q^{27} - 4 q^{29} + 5 q^{31} + 3 q^{33} - q^{35} + 3 q^{37} - 6 q^{39} - 4 q^{41} + 8 q^{43} + 2 q^{45} - 5 q^{47} + 2 q^{49} + 5 q^{51} - q^{53} - 6 q^{55} - 2 q^{57} + 15 q^{59} - 5 q^{61} + 2 q^{63} - 6 q^{65} - 9 q^{67} - 14 q^{69} - 7 q^{73} + 4 q^{75} - 15 q^{77} - q^{79} - q^{81} - 24 q^{83} - 10 q^{85} + 2 q^{87} - 7 q^{89} - 24 q^{91} + 5 q^{93} + q^{95} - 4 q^{97} + 12 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/448\mathbb{Z}\right)^\times\).

\(n\) \(127\) \(129\) \(197\)
\(\chi(n)\) \(1\) \(e\left(\frac{2}{3}\right)\) \(1\)

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
\(3\) −0.500000 + 0.866025i −0.288675 + 0.500000i −0.973494 0.228714i \(-0.926548\pi\)
0.684819 + 0.728714i \(0.259881\pi\)
\(4\) 0 0
\(5\) −0.500000 0.866025i −0.223607 0.387298i 0.732294 0.680989i \(-0.238450\pi\)
−0.955901 + 0.293691i \(0.905116\pi\)
\(6\) 0 0
\(7\) −2.00000 1.73205i −0.755929 0.654654i
\(8\) 0 0
\(9\) 1.00000 + 1.73205i 0.333333 + 0.577350i
\(10\) 0 0
\(11\) 1.50000 2.59808i 0.452267 0.783349i −0.546259 0.837616i \(-0.683949\pi\)
0.998526 + 0.0542666i \(0.0172821\pi\)
\(12\) 0 0
\(13\) 6.00000 1.66410 0.832050 0.554700i \(-0.187167\pi\)
0.832050 + 0.554700i \(0.187167\pi\)
\(14\) 0 0
\(15\) 1.00000 0.258199
\(16\) 0 0
\(17\) 2.50000 4.33013i 0.606339 1.05021i −0.385499 0.922708i \(-0.625971\pi\)
0.991838 0.127502i \(-0.0406959\pi\)
\(18\) 0 0
\(19\) 0.500000 + 0.866025i 0.114708 + 0.198680i 0.917663 0.397360i \(-0.130073\pi\)
−0.802955 + 0.596040i \(0.796740\pi\)
\(20\) 0 0
\(21\) 2.50000 0.866025i 0.545545 0.188982i
\(22\) 0 0
\(23\) 3.50000 + 6.06218i 0.729800 + 1.26405i 0.956967 + 0.290196i \(0.0937204\pi\)
−0.227167 + 0.973856i \(0.572946\pi\)
\(24\) 0 0
\(25\) 2.00000 3.46410i 0.400000 0.692820i
\(26\) 0 0
\(27\) −5.00000 −0.962250
\(28\) 0 0
\(29\) −2.00000 −0.371391 −0.185695 0.982607i \(-0.559454\pi\)
−0.185695 + 0.982607i \(0.559454\pi\)
\(30\) 0 0
\(31\) 2.50000 4.33013i 0.449013 0.777714i −0.549309 0.835619i \(-0.685109\pi\)
0.998322 + 0.0579057i \(0.0184423\pi\)
\(32\) 0 0
\(33\) 1.50000 + 2.59808i 0.261116 + 0.452267i
\(34\) 0 0
\(35\) −0.500000 + 2.59808i −0.0845154 + 0.439155i
\(36\) 0 0
\(37\) 1.50000 + 2.59808i 0.246598 + 0.427121i 0.962580 0.270998i \(-0.0873538\pi\)
−0.715981 + 0.698119i \(0.754020\pi\)
\(38\) 0 0
\(39\) −3.00000 + 5.19615i −0.480384 + 0.832050i
\(40\) 0 0
\(41\) −2.00000 −0.312348 −0.156174 0.987730i \(-0.549916\pi\)
−0.156174 + 0.987730i \(0.549916\pi\)
\(42\) 0 0
\(43\) 4.00000 0.609994 0.304997 0.952353i \(-0.401344\pi\)
0.304997 + 0.952353i \(0.401344\pi\)
\(44\) 0 0
\(45\) 1.00000 1.73205i 0.149071 0.258199i
\(46\) 0 0
\(47\) −2.50000 4.33013i −0.364662 0.631614i 0.624059 0.781377i \(-0.285482\pi\)
−0.988722 + 0.149763i \(0.952149\pi\)
\(48\) 0 0
\(49\) 1.00000 + 6.92820i 0.142857 + 0.989743i
\(50\) 0 0
\(51\) 2.50000 + 4.33013i 0.350070 + 0.606339i
\(52\) 0 0
\(53\) −0.500000 + 0.866025i −0.0686803 + 0.118958i −0.898321 0.439340i \(-0.855212\pi\)
0.829640 + 0.558298i \(0.188546\pi\)
\(54\) 0 0
\(55\) −3.00000 −0.404520
\(56\) 0 0
\(57\) −1.00000 −0.132453
\(58\) 0 0
\(59\) 7.50000 12.9904i 0.976417 1.69120i 0.301239 0.953549i \(-0.402600\pi\)
0.675178 0.737655i \(-0.264067\pi\)
\(60\) 0 0
\(61\) −2.50000 4.33013i −0.320092 0.554416i 0.660415 0.750901i \(-0.270381\pi\)
−0.980507 + 0.196485i \(0.937047\pi\)
\(62\) 0 0
\(63\) 1.00000 5.19615i 0.125988 0.654654i
\(64\) 0 0
\(65\) −3.00000 5.19615i −0.372104 0.644503i
\(66\) 0 0
\(67\) −4.50000 + 7.79423i −0.549762 + 0.952217i 0.448528 + 0.893769i \(0.351948\pi\)
−0.998290 + 0.0584478i \(0.981385\pi\)
\(68\) 0 0
\(69\) −7.00000 −0.842701
\(70\) 0 0
\(71\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(72\) 0 0
\(73\) −3.50000 + 6.06218i −0.409644 + 0.709524i −0.994850 0.101361i \(-0.967680\pi\)
0.585206 + 0.810885i \(0.301014\pi\)
\(74\) 0 0
\(75\) 2.00000 + 3.46410i 0.230940 + 0.400000i
\(76\) 0 0
\(77\) −7.50000 + 2.59808i −0.854704 + 0.296078i
\(78\) 0 0
\(79\) −0.500000 0.866025i −0.0562544 0.0974355i 0.836527 0.547926i \(-0.184582\pi\)
−0.892781 + 0.450490i \(0.851249\pi\)
\(80\) 0 0
\(81\) −0.500000 + 0.866025i −0.0555556 + 0.0962250i
\(82\) 0 0
\(83\) −12.0000 −1.31717 −0.658586 0.752506i \(-0.728845\pi\)
−0.658586 + 0.752506i \(0.728845\pi\)
\(84\) 0 0
\(85\) −5.00000 −0.542326
\(86\) 0 0
\(87\) 1.00000 1.73205i 0.107211 0.185695i
\(88\) 0 0
\(89\) −3.50000 6.06218i −0.370999 0.642590i 0.618720 0.785611i \(-0.287651\pi\)
−0.989720 + 0.143022i \(0.954318\pi\)
\(90\) 0 0
\(91\) −12.0000 10.3923i −1.25794 1.08941i
\(92\) 0 0
\(93\) 2.50000 + 4.33013i 0.259238 + 0.449013i
\(94\) 0 0
\(95\) 0.500000 0.866025i 0.0512989 0.0888523i
\(96\) 0 0
\(97\) −2.00000 −0.203069 −0.101535 0.994832i \(-0.532375\pi\)
−0.101535 + 0.994832i \(0.532375\pi\)
\(98\) 0 0
\(99\) 6.00000 0.603023
\(100\) 0 0
\(101\) 1.50000 2.59808i 0.149256 0.258518i −0.781697 0.623658i \(-0.785646\pi\)
0.930953 + 0.365140i \(0.118979\pi\)
\(102\) 0 0
\(103\) 7.50000 + 12.9904i 0.738997 + 1.27998i 0.952947 + 0.303136i \(0.0980336\pi\)
−0.213950 + 0.976845i \(0.568633\pi\)
\(104\) 0 0
\(105\) −2.00000 1.73205i −0.195180 0.169031i
\(106\) 0 0
\(107\) 4.50000 + 7.79423i 0.435031 + 0.753497i 0.997298 0.0734594i \(-0.0234039\pi\)
−0.562267 + 0.826956i \(0.690071\pi\)
\(108\) 0 0
\(109\) −2.50000 + 4.33013i −0.239457 + 0.414751i −0.960558 0.278078i \(-0.910303\pi\)
0.721102 + 0.692829i \(0.243636\pi\)
\(110\) 0 0
\(111\) −3.00000 −0.284747
\(112\) 0 0
\(113\) −18.0000 −1.69330 −0.846649 0.532152i \(-0.821383\pi\)
−0.846649 + 0.532152i \(0.821383\pi\)
\(114\) 0 0
\(115\) 3.50000 6.06218i 0.326377 0.565301i
\(116\) 0 0
\(117\) 6.00000 + 10.3923i 0.554700 + 0.960769i
\(118\) 0 0
\(119\) −12.5000 + 4.33013i −1.14587 + 0.396942i
\(120\) 0 0
\(121\) 1.00000 + 1.73205i 0.0909091 + 0.157459i
\(122\) 0 0
\(123\) 1.00000 1.73205i 0.0901670 0.156174i
\(124\) 0 0
\(125\) −9.00000 −0.804984
\(126\) 0 0
\(127\) 8.00000 0.709885 0.354943 0.934888i \(-0.384500\pi\)
0.354943 + 0.934888i \(0.384500\pi\)
\(128\) 0 0
\(129\) −2.00000 + 3.46410i −0.176090 + 0.304997i
\(130\) 0 0
\(131\) 2.50000 + 4.33013i 0.218426 + 0.378325i 0.954327 0.298764i \(-0.0965744\pi\)
−0.735901 + 0.677089i \(0.763241\pi\)
\(132\) 0 0
\(133\) 0.500000 2.59808i 0.0433555 0.225282i
\(134\) 0 0
\(135\) 2.50000 + 4.33013i 0.215166 + 0.372678i
\(136\) 0 0
\(137\) −5.50000 + 9.52628i −0.469897 + 0.813885i −0.999408 0.0344182i \(-0.989042\pi\)
0.529511 + 0.848303i \(0.322376\pi\)
\(138\) 0 0
\(139\) 12.0000 1.01783 0.508913 0.860818i \(-0.330047\pi\)
0.508913 + 0.860818i \(0.330047\pi\)
\(140\) 0 0
\(141\) 5.00000 0.421076
\(142\) 0 0
\(143\) 9.00000 15.5885i 0.752618 1.30357i
\(144\) 0 0
\(145\) 1.00000 + 1.73205i 0.0830455 + 0.143839i
\(146\) 0 0
\(147\) −6.50000 2.59808i −0.536111 0.214286i
\(148\) 0 0
\(149\) −8.50000 14.7224i −0.696347 1.20611i −0.969724 0.244202i \(-0.921474\pi\)
0.273377 0.961907i \(-0.411859\pi\)
\(150\) 0 0
\(151\) 2.50000 4.33013i 0.203447 0.352381i −0.746190 0.665733i \(-0.768119\pi\)
0.949637 + 0.313353i \(0.101452\pi\)
\(152\) 0 0
\(153\) 10.0000 0.808452
\(154\) 0 0
\(155\) −5.00000 −0.401610
\(156\) 0 0
\(157\) −4.50000 + 7.79423i −0.359139 + 0.622047i −0.987817 0.155618i \(-0.950263\pi\)
0.628678 + 0.777666i \(0.283596\pi\)
\(158\) 0 0
\(159\) −0.500000 0.866025i −0.0396526 0.0686803i
\(160\) 0 0
\(161\) 3.50000 18.1865i 0.275839 1.43330i
\(162\) 0 0
\(163\) 6.50000 + 11.2583i 0.509119 + 0.881820i 0.999944 + 0.0105623i \(0.00336213\pi\)
−0.490825 + 0.871258i \(0.663305\pi\)
\(164\) 0 0
\(165\) 1.50000 2.59808i 0.116775 0.202260i
\(166\) 0 0
\(167\) −12.0000 −0.928588 −0.464294 0.885681i \(-0.653692\pi\)
−0.464294 + 0.885681i \(0.653692\pi\)
\(168\) 0 0
\(169\) 23.0000 1.76923
\(170\) 0 0
\(171\) −1.00000 + 1.73205i −0.0764719 + 0.132453i
\(172\) 0 0
\(173\) −6.50000 11.2583i −0.494186 0.855955i 0.505792 0.862656i \(-0.331200\pi\)
−0.999978 + 0.00670064i \(0.997867\pi\)
\(174\) 0 0
\(175\) −10.0000 + 3.46410i −0.755929 + 0.261861i
\(176\) 0 0
\(177\) 7.50000 + 12.9904i 0.563735 + 0.976417i
\(178\) 0 0
\(179\) −6.50000 + 11.2583i −0.485833 + 0.841487i −0.999867 0.0162823i \(-0.994817\pi\)
0.514035 + 0.857769i \(0.328150\pi\)
\(180\) 0 0
\(181\) 10.0000 0.743294 0.371647 0.928374i \(-0.378793\pi\)
0.371647 + 0.928374i \(0.378793\pi\)
\(182\) 0 0
\(183\) 5.00000 0.369611
\(184\) 0 0
\(185\) 1.50000 2.59808i 0.110282 0.191014i
\(186\) 0 0
\(187\) −7.50000 12.9904i −0.548454 0.949951i
\(188\) 0 0
\(189\) 10.0000 + 8.66025i 0.727393 + 0.629941i
\(190\) 0 0
\(191\) 5.50000 + 9.52628i 0.397966 + 0.689297i 0.993475 0.114051i \(-0.0363829\pi\)
−0.595509 + 0.803349i \(0.703050\pi\)
\(192\) 0 0
\(193\) −1.50000 + 2.59808i −0.107972 + 0.187014i −0.914949 0.403570i \(-0.867769\pi\)
0.806976 + 0.590584i \(0.201102\pi\)
\(194\) 0 0
\(195\) 6.00000 0.429669
\(196\) 0 0
\(197\) 6.00000 0.427482 0.213741 0.976890i \(-0.431435\pi\)
0.213741 + 0.976890i \(0.431435\pi\)
\(198\) 0 0
\(199\) 6.50000 11.2583i 0.460773 0.798082i −0.538227 0.842800i \(-0.680906\pi\)
0.999000 + 0.0447181i \(0.0142390\pi\)
\(200\) 0 0
\(201\) −4.50000 7.79423i −0.317406 0.549762i
\(202\) 0 0
\(203\) 4.00000 + 3.46410i 0.280745 + 0.243132i
\(204\) 0 0
\(205\) 1.00000 + 1.73205i 0.0698430 + 0.120972i
\(206\) 0 0
\(207\) −7.00000 + 12.1244i −0.486534 + 0.842701i
\(208\) 0 0
\(209\) 3.00000 0.207514
\(210\) 0 0
\(211\) 4.00000 0.275371 0.137686 0.990476i \(-0.456034\pi\)
0.137686 + 0.990476i \(0.456034\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) −2.00000 3.46410i −0.136399 0.236250i
\(216\) 0 0
\(217\) −12.5000 + 4.33013i −0.848555 + 0.293948i
\(218\) 0 0
\(219\) −3.50000 6.06218i −0.236508 0.409644i
\(220\) 0 0
\(221\) 15.0000 25.9808i 1.00901 1.74766i
\(222\) 0 0
\(223\) −24.0000 −1.60716 −0.803579 0.595198i \(-0.797074\pi\)
−0.803579 + 0.595198i \(0.797074\pi\)
\(224\) 0 0
\(225\) 8.00000 0.533333
\(226\) 0 0
\(227\) 5.50000 9.52628i 0.365048 0.632281i −0.623736 0.781635i \(-0.714386\pi\)
0.988784 + 0.149354i \(0.0477193\pi\)
\(228\) 0 0
\(229\) 11.5000 + 19.9186i 0.759941 + 1.31626i 0.942880 + 0.333133i \(0.108106\pi\)
−0.182939 + 0.983124i \(0.558561\pi\)
\(230\) 0 0
\(231\) 1.50000 7.79423i 0.0986928 0.512823i
\(232\) 0 0
\(233\) −5.50000 9.52628i −0.360317 0.624087i 0.627696 0.778459i \(-0.283998\pi\)
−0.988013 + 0.154371i \(0.950665\pi\)
\(234\) 0 0
\(235\) −2.50000 + 4.33013i −0.163082 + 0.282466i
\(236\) 0 0
\(237\) 1.00000 0.0649570
\(238\) 0 0
\(239\) 20.0000 1.29369 0.646846 0.762620i \(-0.276088\pi\)
0.646846 + 0.762620i \(0.276088\pi\)
\(240\) 0 0
\(241\) 8.50000 14.7224i 0.547533 0.948355i −0.450910 0.892570i \(-0.648900\pi\)
0.998443 0.0557856i \(-0.0177663\pi\)
\(242\) 0 0
\(243\) −8.00000 13.8564i −0.513200 0.888889i
\(244\) 0 0
\(245\) 5.50000 4.33013i 0.351382 0.276642i
\(246\) 0 0
\(247\) 3.00000 + 5.19615i 0.190885 + 0.330623i
\(248\) 0 0
\(249\) 6.00000 10.3923i 0.380235 0.658586i
\(250\) 0 0
\(251\) −16.0000 −1.00991 −0.504956 0.863145i \(-0.668491\pi\)
−0.504956 + 0.863145i \(0.668491\pi\)
\(252\) 0 0
\(253\) 21.0000 1.32026
\(254\) 0 0
\(255\) 2.50000 4.33013i 0.156556 0.271163i
\(256\) 0 0
\(257\) 10.5000 + 18.1865i 0.654972 + 1.13444i 0.981901 + 0.189396i \(0.0606529\pi\)
−0.326929 + 0.945049i \(0.606014\pi\)
\(258\) 0 0
\(259\) 1.50000 7.79423i 0.0932055 0.484310i
\(260\) 0 0
\(261\) −2.00000 3.46410i −0.123797 0.214423i
\(262\) 0 0
\(263\) 4.50000 7.79423i 0.277482 0.480613i −0.693276 0.720672i \(-0.743833\pi\)
0.970758 + 0.240059i \(0.0771668\pi\)
\(264\) 0 0
\(265\) 1.00000 0.0614295
\(266\) 0 0
\(267\) 7.00000 0.428393
\(268\) 0 0
\(269\) −4.50000 + 7.79423i −0.274370 + 0.475223i −0.969976 0.243201i \(-0.921803\pi\)
0.695606 + 0.718423i \(0.255136\pi\)
\(270\) 0 0
\(271\) 3.50000 + 6.06218i 0.212610 + 0.368251i 0.952531 0.304443i \(-0.0984703\pi\)
−0.739921 + 0.672694i \(0.765137\pi\)
\(272\) 0 0
\(273\) 15.0000 5.19615i 0.907841 0.314485i
\(274\) 0 0
\(275\) −6.00000 10.3923i −0.361814 0.626680i
\(276\) 0 0
\(277\) −8.50000 + 14.7224i −0.510716 + 0.884585i 0.489207 + 0.872167i \(0.337286\pi\)
−0.999923 + 0.0124177i \(0.996047\pi\)
\(278\) 0 0
\(279\) 10.0000 0.598684
\(280\) 0 0
\(281\) 6.00000 0.357930 0.178965 0.983855i \(-0.442725\pi\)
0.178965 + 0.983855i \(0.442725\pi\)
\(282\) 0 0
\(283\) −6.50000 + 11.2583i −0.386385 + 0.669238i −0.991960 0.126550i \(-0.959610\pi\)
0.605575 + 0.795788i \(0.292943\pi\)
\(284\) 0 0
\(285\) 0.500000 + 0.866025i 0.0296174 + 0.0512989i
\(286\) 0 0
\(287\) 4.00000 + 3.46410i 0.236113 + 0.204479i
\(288\) 0 0
\(289\) −4.00000 6.92820i −0.235294 0.407541i
\(290\) 0 0
\(291\) 1.00000 1.73205i 0.0586210 0.101535i
\(292\) 0 0
\(293\) −6.00000 −0.350524 −0.175262 0.984522i \(-0.556077\pi\)
−0.175262 + 0.984522i \(0.556077\pi\)
\(294\) 0 0
\(295\) −15.0000 −0.873334
\(296\) 0 0
\(297\) −7.50000 + 12.9904i −0.435194 + 0.753778i
\(298\) 0 0
\(299\) 21.0000 + 36.3731i 1.21446 + 2.10351i
\(300\) 0 0
\(301\) −8.00000 6.92820i −0.461112 0.399335i
\(302\) 0 0
\(303\) 1.50000 + 2.59808i 0.0861727 + 0.149256i
\(304\) 0 0
\(305\) −2.50000 + 4.33013i −0.143150 + 0.247942i
\(306\) 0 0
\(307\) −4.00000 −0.228292 −0.114146 0.993464i \(-0.536413\pi\)
−0.114146 + 0.993464i \(0.536413\pi\)
\(308\) 0 0
\(309\) −15.0000 −0.853320
\(310\) 0 0
\(311\) −7.50000 + 12.9904i −0.425286 + 0.736617i −0.996447 0.0842210i \(-0.973160\pi\)
0.571161 + 0.820838i \(0.306493\pi\)
\(312\) 0 0
\(313\) 0.500000 + 0.866025i 0.0282617 + 0.0489506i 0.879810 0.475325i \(-0.157669\pi\)
−0.851549 + 0.524276i \(0.824336\pi\)
\(314\) 0 0
\(315\) −5.00000 + 1.73205i −0.281718 + 0.0975900i
\(316\) 0 0
\(317\) 1.50000 + 2.59808i 0.0842484 + 0.145922i 0.905071 0.425261i \(-0.139818\pi\)
−0.820822 + 0.571184i \(0.806484\pi\)
\(318\) 0 0
\(319\) −3.00000 + 5.19615i −0.167968 + 0.290929i
\(320\) 0 0
\(321\) −9.00000 −0.502331
\(322\) 0 0
\(323\) 5.00000 0.278207
\(324\) 0 0
\(325\) 12.0000 20.7846i 0.665640 1.15292i
\(326\) 0 0
\(327\) −2.50000 4.33013i −0.138250 0.239457i
\(328\) 0 0
\(329\) −2.50000 + 12.9904i −0.137829 + 0.716183i
\(330\) 0 0
\(331\) 14.5000 + 25.1147i 0.796992 + 1.38043i 0.921567 + 0.388221i \(0.126910\pi\)
−0.124574 + 0.992210i \(0.539757\pi\)
\(332\) 0 0
\(333\) −3.00000 + 5.19615i −0.164399 + 0.284747i
\(334\) 0 0
\(335\) 9.00000 0.491723
\(336\) 0 0
\(337\) −10.0000 −0.544735 −0.272367 0.962193i \(-0.587807\pi\)
−0.272367 + 0.962193i \(0.587807\pi\)
\(338\) 0 0
\(339\) 9.00000 15.5885i 0.488813 0.846649i
\(340\) 0 0
\(341\) −7.50000 12.9904i −0.406148 0.703469i
\(342\) 0 0
\(343\) 10.0000 15.5885i 0.539949 0.841698i
\(344\) 0 0
\(345\) 3.50000 + 6.06218i 0.188434 + 0.326377i
\(346\) 0 0
\(347\) 7.50000 12.9904i 0.402621 0.697360i −0.591420 0.806363i \(-0.701433\pi\)
0.994041 + 0.109003i \(0.0347659\pi\)
\(348\) 0 0
\(349\) −2.00000 −0.107058 −0.0535288 0.998566i \(-0.517047\pi\)
−0.0535288 + 0.998566i \(0.517047\pi\)
\(350\) 0 0
\(351\) −30.0000 −1.60128
\(352\) 0 0
\(353\) −1.50000 + 2.59808i −0.0798369 + 0.138282i −0.903179 0.429263i \(-0.858773\pi\)
0.823343 + 0.567545i \(0.192107\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 0 0
\(357\) 2.50000 12.9904i 0.132314 0.687524i
\(358\) 0 0
\(359\) −10.5000 18.1865i −0.554169 0.959849i −0.997968 0.0637221i \(-0.979703\pi\)
0.443799 0.896126i \(-0.353630\pi\)
\(360\) 0 0
\(361\) 9.00000 15.5885i 0.473684 0.820445i
\(362\) 0 0
\(363\) −2.00000 −0.104973
\(364\) 0 0
\(365\) 7.00000 0.366397
\(366\) 0 0
\(367\) −11.5000 + 19.9186i −0.600295 + 1.03974i 0.392481 + 0.919760i \(0.371617\pi\)
−0.992776 + 0.119982i \(0.961716\pi\)
\(368\) 0 0
\(369\) −2.00000 3.46410i −0.104116 0.180334i
\(370\) 0 0
\(371\) 2.50000 0.866025i 0.129794 0.0449618i
\(372\) 0 0
\(373\) 5.50000 + 9.52628i 0.284779 + 0.493252i 0.972556 0.232671i \(-0.0747464\pi\)
−0.687776 + 0.725923i \(0.741413\pi\)
\(374\) 0 0
\(375\) 4.50000 7.79423i 0.232379 0.402492i
\(376\) 0 0
\(377\) −12.0000 −0.618031
\(378\) 0 0
\(379\) −24.0000 −1.23280 −0.616399 0.787434i \(-0.711409\pi\)
−0.616399 + 0.787434i \(0.711409\pi\)
\(380\) 0 0
\(381\) −4.00000 + 6.92820i −0.204926 + 0.354943i
\(382\) 0 0
\(383\) 1.50000 + 2.59808i 0.0766464 + 0.132755i 0.901801 0.432151i \(-0.142245\pi\)
−0.825155 + 0.564907i \(0.808912\pi\)
\(384\) 0 0
\(385\) 6.00000 + 5.19615i 0.305788 + 0.264820i
\(386\) 0 0
\(387\) 4.00000 + 6.92820i 0.203331 + 0.352180i
\(388\) 0 0
\(389\) −14.5000 + 25.1147i −0.735179 + 1.27337i 0.219465 + 0.975620i \(0.429569\pi\)
−0.954645 + 0.297747i \(0.903765\pi\)
\(390\) 0 0
\(391\) 35.0000 1.77003
\(392\) 0 0
\(393\) −5.00000 −0.252217
\(394\) 0 0
\(395\) −0.500000 + 0.866025i −0.0251577 + 0.0435745i
\(396\) 0 0
\(397\) −8.50000 14.7224i −0.426603 0.738898i 0.569966 0.821668i \(-0.306956\pi\)
−0.996569 + 0.0827707i \(0.973623\pi\)
\(398\) 0 0
\(399\) 2.00000 + 1.73205i 0.100125 + 0.0867110i
\(400\) 0 0
\(401\) −13.5000 23.3827i −0.674158 1.16768i −0.976714 0.214544i \(-0.931173\pi\)
0.302556 0.953131i \(-0.402160\pi\)
\(402\) 0 0
\(403\) 15.0000 25.9808i 0.747203 1.29419i
\(404\) 0 0
\(405\) 1.00000 0.0496904
\(406\) 0 0
\(407\) 9.00000 0.446113
\(408\) 0 0
\(409\) −13.5000 + 23.3827i −0.667532 + 1.15620i 0.311060 + 0.950390i \(0.399316\pi\)
−0.978592 + 0.205809i \(0.934017\pi\)
\(410\) 0 0
\(411\) −5.50000 9.52628i −0.271295 0.469897i
\(412\) 0 0
\(413\) −37.5000 + 12.9904i −1.84525 + 0.639215i
\(414\) 0 0
\(415\) 6.00000 + 10.3923i 0.294528 + 0.510138i
\(416\) 0 0
\(417\) −6.00000 + 10.3923i −0.293821 + 0.508913i
\(418\) 0 0
\(419\) −20.0000 −0.977064 −0.488532 0.872546i \(-0.662467\pi\)
−0.488532 + 0.872546i \(0.662467\pi\)
\(420\) 0 0
\(421\) −34.0000 −1.65706 −0.828529 0.559946i \(-0.810822\pi\)
−0.828529 + 0.559946i \(0.810822\pi\)
\(422\) 0 0
\(423\) 5.00000 8.66025i 0.243108 0.421076i
\(424\) 0 0
\(425\) −10.0000 17.3205i −0.485071 0.840168i
\(426\) 0 0
\(427\) −2.50000 + 12.9904i −0.120983 + 0.628649i
\(428\) 0 0
\(429\) 9.00000 + 15.5885i 0.434524 + 0.752618i
\(430\) 0 0
\(431\) −1.50000 + 2.59808i −0.0722525 + 0.125145i −0.899888 0.436121i \(-0.856352\pi\)
0.827636 + 0.561266i \(0.189685\pi\)
\(432\) 0 0
\(433\) −2.00000 −0.0961139 −0.0480569 0.998845i \(-0.515303\pi\)
−0.0480569 + 0.998845i \(0.515303\pi\)
\(434\) 0 0
\(435\) −2.00000 −0.0958927
\(436\) 0 0
\(437\) −3.50000 + 6.06218i −0.167428 + 0.289993i
\(438\) 0 0
\(439\) −10.5000 18.1865i −0.501138 0.867996i −0.999999 0.00131415i \(-0.999582\pi\)
0.498861 0.866682i \(-0.333752\pi\)
\(440\) 0 0
\(441\) −11.0000 + 8.66025i −0.523810 + 0.412393i
\(442\) 0 0
\(443\) −15.5000 26.8468i −0.736427 1.27553i −0.954094 0.299506i \(-0.903178\pi\)
0.217667 0.976023i \(-0.430155\pi\)
\(444\) 0 0
\(445\) −3.50000 + 6.06218i −0.165916 + 0.287375i
\(446\) 0 0
\(447\) 17.0000 0.804072
\(448\) 0 0
\(449\) −26.0000 −1.22702 −0.613508 0.789689i \(-0.710242\pi\)
−0.613508 + 0.789689i \(0.710242\pi\)
\(450\) 0 0
\(451\) −3.00000 + 5.19615i −0.141264 + 0.244677i
\(452\) 0 0
\(453\) 2.50000 + 4.33013i 0.117460 + 0.203447i
\(454\) 0 0
\(455\) −3.00000 + 15.5885i −0.140642 + 0.730798i
\(456\) 0 0
\(457\) 8.50000 + 14.7224i 0.397613 + 0.688686i 0.993431 0.114433i \(-0.0365053\pi\)
−0.595818 + 0.803120i \(0.703172\pi\)
\(458\) 0 0
\(459\) −12.5000 + 21.6506i −0.583450 + 1.01057i
\(460\) 0 0
\(461\) 30.0000 1.39724 0.698620 0.715493i \(-0.253798\pi\)
0.698620 + 0.715493i \(0.253798\pi\)
\(462\) 0 0
\(463\) −16.0000 −0.743583 −0.371792 0.928316i \(-0.621256\pi\)
−0.371792 + 0.928316i \(0.621256\pi\)
\(464\) 0 0
\(465\) 2.50000 4.33013i 0.115935 0.200805i
\(466\) 0 0
\(467\) −1.50000 2.59808i −0.0694117 0.120225i 0.829231 0.558906i \(-0.188779\pi\)
−0.898642 + 0.438682i \(0.855446\pi\)
\(468\) 0 0
\(469\) 22.5000 7.79423i 1.03895 0.359904i
\(470\) 0 0
\(471\) −4.50000 7.79423i −0.207349 0.359139i
\(472\) 0 0
\(473\) 6.00000 10.3923i 0.275880 0.477839i
\(474\) 0 0
\(475\) 4.00000 0.183533
\(476\) 0 0
\(477\) −2.00000 −0.0915737
\(478\) 0 0
\(479\) −15.5000 + 26.8468i −0.708213 + 1.22666i 0.257306 + 0.966330i \(0.417165\pi\)
−0.965519 + 0.260331i \(0.916168\pi\)
\(480\) 0 0
\(481\) 9.00000 + 15.5885i 0.410365 + 0.710772i
\(482\) 0 0
\(483\) 14.0000 + 12.1244i 0.637022 + 0.551677i
\(484\) 0 0
\(485\) 1.00000 + 1.73205i 0.0454077 + 0.0786484i
\(486\) 0 0
\(487\) −3.50000 + 6.06218i −0.158600 + 0.274703i −0.934364 0.356320i \(-0.884031\pi\)
0.775764 + 0.631023i \(0.217365\pi\)
\(488\) 0 0
\(489\) −13.0000 −0.587880
\(490\) 0 0
\(491\) 24.0000 1.08310 0.541552 0.840667i \(-0.317837\pi\)
0.541552 + 0.840667i \(0.317837\pi\)
\(492\) 0 0
\(493\) −5.00000 + 8.66025i −0.225189 + 0.390038i
\(494\) 0 0
\(495\) −3.00000 5.19615i −0.134840 0.233550i
\(496\) 0 0
\(497\) 0 0
\(498\) 0 0
\(499\) −17.5000 30.3109i −0.783408 1.35690i −0.929946 0.367697i \(-0.880146\pi\)
0.146538 0.989205i \(-0.453187\pi\)
\(500\) 0 0
\(501\) 6.00000 10.3923i 0.268060 0.464294i
\(502\) 0 0
\(503\) −32.0000 −1.42681 −0.713405 0.700752i \(-0.752848\pi\)
−0.713405 + 0.700752i \(0.752848\pi\)
\(504\) 0 0
\(505\) −3.00000 −0.133498
\(506\) 0 0
\(507\) −11.5000 + 19.9186i −0.510733 + 0.884615i
\(508\) 0 0
\(509\) −4.50000 7.79423i −0.199459 0.345473i 0.748894 0.662690i \(-0.230585\pi\)
−0.948353 + 0.317217i \(0.897252\pi\)
\(510\) 0 0
\(511\) 17.5000 6.06218i 0.774154 0.268175i
\(512\) 0 0
\(513\) −2.50000 4.33013i −0.110378 0.191180i
\(514\) 0 0
\(515\) 7.50000 12.9904i 0.330489 0.572425i
\(516\) 0 0
\(517\) −15.0000 −0.659699
\(518\) 0 0
\(519\) 13.0000 0.570637
\(520\) 0 0
\(521\) 16.5000 28.5788i 0.722878 1.25206i −0.236963 0.971519i \(-0.576152\pi\)
0.959841 0.280543i \(-0.0905145\pi\)
\(522\) 0 0
\(523\) −3.50000 6.06218i −0.153044 0.265081i 0.779301 0.626650i \(-0.215574\pi\)
−0.932345 + 0.361569i \(0.882241\pi\)
\(524\) 0 0
\(525\) 2.00000 10.3923i 0.0872872 0.453557i
\(526\) 0 0
\(527\) −12.5000 21.6506i −0.544509 0.943116i
\(528\) 0 0
\(529\) −13.0000 + 22.5167i −0.565217 + 0.978985i
\(530\) 0 0
\(531\) 30.0000 1.30189
\(532\) 0 0
\(533\) −12.0000 −0.519778
\(534\) 0 0
\(535\) 4.50000 7.79423i 0.194552 0.336974i
\(536\) 0 0
\(537\) −6.50000 11.2583i −0.280496 0.485833i
\(538\) 0 0
\(539\) 19.5000 + 7.79423i 0.839924 + 0.335721i
\(540\) 0 0
\(541\) −20.5000 35.5070i −0.881364 1.52657i −0.849825 0.527064i \(-0.823293\pi\)
−0.0315385 0.999503i \(-0.510041\pi\)
\(542\) 0 0
\(543\) −5.00000 + 8.66025i −0.214571 + 0.371647i
\(544\) 0 0
\(545\) 5.00000 0.214176
\(546\) 0 0
\(547\) 8.00000 0.342055 0.171028 0.985266i \(-0.445291\pi\)
0.171028 + 0.985266i \(0.445291\pi\)
\(548\) 0 0
\(549\) 5.00000 8.66025i 0.213395 0.369611i
\(550\) 0 0
\(551\) −1.00000 1.73205i −0.0426014 0.0737878i
\(552\) 0 0
\(553\) −0.500000 + 2.59808i −0.0212622 + 0.110481i
\(554\) 0 0
\(555\) 1.50000 + 2.59808i 0.0636715 + 0.110282i
\(556\) 0 0
\(557\) −2.50000 + 4.33013i −0.105928 + 0.183473i −0.914117 0.405450i \(-0.867115\pi\)
0.808189 + 0.588924i \(0.200448\pi\)
\(558\) 0 0
\(559\) 24.0000 1.01509
\(560\) 0 0
\(561\) 15.0000 0.633300
\(562\) 0 0
\(563\) −20.5000 + 35.5070i −0.863972 + 1.49644i 0.00409232 + 0.999992i \(0.498697\pi\)
−0.868064 + 0.496452i \(0.834636\pi\)
\(564\) 0 0
\(565\) 9.00000 + 15.5885i 0.378633 + 0.655811i
\(566\) 0 0
\(567\) 2.50000 0.866025i 0.104990 0.0363696i
\(568\) 0 0
\(569\) 16.5000 + 28.5788i 0.691716 + 1.19809i 0.971275 + 0.237959i \(0.0764783\pi\)
−0.279559 + 0.960128i \(0.590188\pi\)
\(570\) 0 0
\(571\) −6.50000 + 11.2583i −0.272017 + 0.471146i −0.969378 0.245573i \(-0.921024\pi\)
0.697362 + 0.716720i \(0.254357\pi\)
\(572\) 0 0
\(573\) −11.0000 −0.459532
\(574\) 0 0
\(575\) 28.0000 1.16768
\(576\) 0 0
\(577\) 16.5000 28.5788i 0.686904 1.18975i −0.285930 0.958250i \(-0.592303\pi\)
0.972834 0.231502i \(-0.0743641\pi\)
\(578\) 0 0
\(579\) −1.50000 2.59808i −0.0623379 0.107972i
\(580\) 0 0
\(581\) 24.0000 + 20.7846i 0.995688 + 0.862291i
\(582\) 0 0
\(583\) 1.50000 + 2.59808i 0.0621237 + 0.107601i
\(584\) 0 0
\(585\) 6.00000 10.3923i 0.248069 0.429669i
\(586\) 0 0
\(587\) 20.0000 0.825488 0.412744 0.910847i \(-0.364570\pi\)
0.412744 + 0.910847i \(0.364570\pi\)
\(588\) 0 0
\(589\) 5.00000 0.206021
\(590\) 0 0
\(591\) −3.00000 + 5.19615i −0.123404 + 0.213741i
\(592\) 0 0
\(593\) 22.5000 + 38.9711i 0.923964 + 1.60035i 0.793219 + 0.608937i \(0.208404\pi\)
0.130746 + 0.991416i \(0.458263\pi\)
\(594\) 0 0
\(595\) 10.0000 + 8.66025i 0.409960 + 0.355036i
\(596\) 0 0
\(597\) 6.50000 + 11.2583i 0.266027 + 0.460773i
\(598\) 0 0
\(599\) 8.50000 14.7224i 0.347301 0.601542i −0.638468 0.769648i \(-0.720432\pi\)
0.985769 + 0.168106i \(0.0537650\pi\)
\(600\) 0 0
\(601\) 22.0000 0.897399 0.448699 0.893683i \(-0.351887\pi\)
0.448699 + 0.893683i \(0.351887\pi\)
\(602\) 0 0
\(603\) −18.0000 −0.733017
\(604\) 0 0
\(605\) 1.00000 1.73205i 0.0406558 0.0704179i
\(606\) 0 0
\(607\) −6.50000 11.2583i −0.263827 0.456962i 0.703429 0.710766i \(-0.251651\pi\)
−0.967256 + 0.253804i \(0.918318\pi\)
\(608\) 0 0
\(609\) −5.00000 + 1.73205i −0.202610 + 0.0701862i
\(610\) 0 0
\(611\) −15.0000 25.9808i −0.606835 1.05107i
\(612\) 0 0
\(613\) 21.5000 37.2391i 0.868377 1.50407i 0.00472215 0.999989i \(-0.498497\pi\)
0.863655 0.504084i \(-0.168170\pi\)
\(614\) 0 0
\(615\) −2.00000 −0.0806478
\(616\) 0 0
\(617\) 30.0000 1.20775 0.603877 0.797077i \(-0.293622\pi\)
0.603877 + 0.797077i \(0.293622\pi\)
\(618\) 0 0
\(619\) −4.50000 + 7.79423i −0.180870 + 0.313276i −0.942177 0.335115i \(-0.891225\pi\)
0.761307 + 0.648392i \(0.224558\pi\)
\(620\) 0 0
\(621\) −17.5000 30.3109i −0.702251 1.21633i
\(622\) 0 0
\(623\) −3.50000 + 18.1865i −0.140225 + 0.728628i
\(624\) 0 0
\(625\) −5.50000 9.52628i −0.220000 0.381051i
\(626\) 0 0
\(627\) −1.50000 + 2.59808i −0.0599042 + 0.103757i
\(628\) 0 0
\(629\) 15.0000 0.598089
\(630\) 0 0
\(631\) −16.0000 −0.636950 −0.318475 0.947931i \(-0.603171\pi\)
−0.318475 + 0.947931i \(0.603171\pi\)
\(632\) 0 0
\(633\) −2.00000 + 3.46410i −0.0794929 + 0.137686i
\(634\) 0 0
\(635\) −4.00000 6.92820i −0.158735 0.274937i
\(636\) 0 0
\(637\) 6.00000 + 41.5692i 0.237729 + 1.64703i
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) 8.50000 14.7224i 0.335730 0.581501i −0.647895 0.761730i \(-0.724350\pi\)
0.983625 + 0.180229i \(0.0576838\pi\)
\(642\) 0 0
\(643\) 44.0000 1.73519 0.867595 0.497271i \(-0.165665\pi\)
0.867595 + 0.497271i \(0.165665\pi\)
\(644\) 0 0
\(645\) 4.00000 0.157500
\(646\) 0 0
\(647\) −7.50000 + 12.9904i −0.294855 + 0.510705i −0.974951 0.222419i \(-0.928605\pi\)
0.680096 + 0.733123i \(0.261938\pi\)
\(648\) 0 0
\(649\) −22.5000 38.9711i −0.883202 1.52975i
\(650\) 0 0
\(651\) 2.50000 12.9904i 0.0979827 0.509133i
\(652\) 0 0
\(653\) 17.5000 + 30.3109i 0.684828 + 1.18616i 0.973491 + 0.228726i \(0.0734560\pi\)
−0.288663 + 0.957431i \(0.593211\pi\)
\(654\) 0 0
\(655\) 2.50000 4.33013i 0.0976831 0.169192i
\(656\) 0 0
\(657\) −14.0000 −0.546192
\(658\) 0 0
\(659\) −44.0000 −1.71400 −0.856998 0.515319i \(-0.827673\pi\)
−0.856998 + 0.515319i \(0.827673\pi\)
\(660\) 0 0
\(661\) 11.5000 19.9186i 0.447298 0.774743i −0.550911 0.834564i \(-0.685720\pi\)
0.998209 + 0.0598209i \(0.0190530\pi\)
\(662\) 0 0
\(663\) 15.0000 + 25.9808i 0.582552 + 1.00901i
\(664\) 0 0
\(665\) −2.50000 + 0.866025i −0.0969458 + 0.0335830i
\(666\) 0 0
\(667\) −7.00000 12.1244i −0.271041 0.469457i
\(668\) 0 0
\(669\) 12.0000 20.7846i 0.463947 0.803579i
\(670\) 0 0
\(671\) −15.0000 −0.579069
\(672\) 0 0
\(673\) −26.0000 −1.00223 −0.501113 0.865382i \(-0.667076\pi\)
−0.501113 + 0.865382i \(0.667076\pi\)
\(674\) 0 0
\(675\) −10.0000 + 17.3205i −0.384900 + 0.666667i
\(676\) 0 0
\(677\) 19.5000 + 33.7750i 0.749446 + 1.29808i 0.948089 + 0.318006i \(0.103013\pi\)
−0.198643 + 0.980072i \(0.563653\pi\)
\(678\) 0 0
\(679\) 4.00000 + 3.46410i 0.153506 + 0.132940i
\(680\) 0 0
\(681\) 5.50000 + 9.52628i 0.210760 + 0.365048i
\(682\) 0 0
\(683\) 13.5000 23.3827i 0.516563 0.894714i −0.483252 0.875481i \(-0.660544\pi\)
0.999815 0.0192323i \(-0.00612219\pi\)
\(684\) 0 0
\(685\) 11.0000 0.420288
\(686\) 0 0
\(687\) −23.0000 −0.877505
\(688\) 0 0
\(689\) −3.00000 + 5.19615i −0.114291 + 0.197958i
\(690\) 0 0
\(691\) 2.50000 + 4.33013i 0.0951045 + 0.164726i 0.909652 0.415371i \(-0.136348\pi\)
−0.814548 + 0.580097i \(0.803015\pi\)
\(692\) 0 0
\(693\) −12.0000 10.3923i −0.455842 0.394771i
\(694\) 0 0
\(695\) −6.00000 10.3923i −0.227593 0.394203i
\(696\) 0 0
\(697\) −5.00000 + 8.66025i −0.189389 + 0.328031i
\(698\) 0 0
\(699\) 11.0000 0.416058
\(700\) 0 0
\(701\) 50.0000 1.88847 0.944237 0.329267i \(-0.106802\pi\)
0.944237 + 0.329267i \(0.106802\pi\)
\(702\) 0 0
\(703\) −1.50000 + 2.59808i −0.0565736 + 0.0979883i
\(704\) 0 0
\(705\) −2.50000 4.33013i −0.0941554 0.163082i
\(706\) 0 0
\(707\) −7.50000 + 2.59808i −0.282067 + 0.0977107i
\(708\) 0 0
\(709\) −14.5000 25.1147i −0.544559 0.943204i −0.998635 0.0522406i \(-0.983364\pi\)
0.454076 0.890963i \(-0.349970\pi\)
\(710\) 0 0
\(711\) 1.00000 1.73205i 0.0375029 0.0649570i
\(712\) 0 0
\(713\) 35.0000 1.31076
\(714\) 0 0
\(715\) −18.0000 −0.673162
\(716\) 0 0
\(717\) −10.0000 + 17.3205i −0.373457 + 0.646846i
\(718\) 0 0
\(719\) 19.5000 + 33.7750i 0.727227 + 1.25959i 0.958051 + 0.286599i \(0.0925247\pi\)
−0.230823 + 0.972996i \(0.574142\pi\)
\(720\) 0 0
\(721\) 7.50000 38.9711i 0.279315 1.45136i
\(722\) 0 0
\(723\) 8.50000 + 14.7224i 0.316118 + 0.547533i
\(724\) 0 0
\(725\) −4.00000 + 6.92820i −0.148556 + 0.257307i
\(726\) 0 0
\(727\) 32.0000 1.18681 0.593407 0.804902i \(-0.297782\pi\)
0.593407 + 0.804902i \(0.297782\pi\)
\(728\) 0 0
\(729\) 13.0000 0.481481
\(730\) 0 0
\(731\) 10.0000 17.3205i 0.369863 0.640622i
\(732\) 0 0
\(733\) 9.50000 + 16.4545i 0.350891 + 0.607760i 0.986406 0.164328i \(-0.0525456\pi\)
−0.635515 + 0.772088i \(0.719212\pi\)
\(734\) 0 0
\(735\) 1.00000 + 6.92820i 0.0368856 + 0.255551i
\(736\) 0 0
\(737\) 13.5000 + 23.3827i 0.497279 + 0.861312i
\(738\) 0 0
\(739\) −2.50000 + 4.33013i −0.0919640 + 0.159286i −0.908337 0.418238i \(-0.862648\pi\)
0.816373 + 0.577524i \(0.195981\pi\)
\(740\) 0 0
\(741\) −6.00000 −0.220416
\(742\) 0 0
\(743\) −16.0000 −0.586983 −0.293492 0.955962i \(-0.594817\pi\)
−0.293492 + 0.955962i \(0.594817\pi\)
\(744\) 0 0
\(745\) −8.50000 + 14.7224i −0.311416 + 0.539388i
\(746\) 0 0
\(747\) −12.0000 20.7846i −0.439057 0.760469i
\(748\) 0 0
\(749\) 4.50000 23.3827i 0.164426 0.854385i
\(750\) 0 0
\(751\) −26.5000 45.8993i −0.966999 1.67489i −0.704146 0.710055i \(-0.748670\pi\)
−0.262852 0.964836i \(-0.584663\pi\)
\(752\) 0 0
\(753\) 8.00000 13.8564i 0.291536 0.504956i
\(754\) 0 0
\(755\) −5.00000 −0.181969
\(756\) 0 0
\(757\) −10.0000 −0.363456 −0.181728 0.983349i \(-0.558169\pi\)
−0.181728 + 0.983349i \(0.558169\pi\)
\(758\) 0 0
\(759\) −10.5000 + 18.1865i −0.381126 + 0.660129i
\(760\) 0 0
\(761\) −1.50000 2.59808i −0.0543750 0.0941802i 0.837557 0.546350i \(-0.183983\pi\)
−0.891932 + 0.452170i \(0.850650\pi\)
\(762\) 0 0
\(763\) 12.5000 4.33013i 0.452530 0.156761i
\(764\) 0 0
\(765\) −5.00000 8.66025i −0.180775 0.313112i
\(766\) 0 0
\(767\) 45.0000 77.9423i 1.62486 2.81433i
\(768\) 0 0
\(769\) 22.0000 0.793340 0.396670 0.917961i \(-0.370166\pi\)
0.396670 + 0.917961i \(0.370166\pi\)
\(770\) 0 0
\(771\) −21.0000 −0.756297
\(772\) 0 0
\(773\) 9.50000 16.4545i 0.341691 0.591827i −0.643056 0.765819i \(-0.722334\pi\)
0.984747 + 0.173993i \(0.0556670\pi\)
\(774\) 0 0
\(775\) −10.0000 17.3205i −0.359211 0.622171i
\(776\) 0 0
\(777\) 6.00000 + 5.19615i 0.215249 + 0.186411i
\(778\) 0 0
\(779\) −1.00000 1.73205i −0.0358287 0.0620572i
\(780\) 0 0
\(781\) 0 0
\(782\) 0 0
\(783\) 10.0000 0.357371
\(784\) 0 0
\(785\) 9.00000 0.321224
\(786\) 0 0
\(787\) −8.50000 + 14.7224i −0.302992 + 0.524798i −0.976812 0.214097i \(-0.931319\pi\)
0.673820 + 0.738896i \(0.264652\pi\)
\(788\) 0 0
\(789\) 4.50000 + 7.79423i 0.160204 + 0.277482i
\(790\) 0 0
\(791\) 36.0000 + 31.1769i 1.28001 + 1.10852i
\(792\) 0 0
\(793\) −15.0000 25.9808i −0.532666 0.922604i
\(794\) 0 0
\(795\) −0.500000 + 0.866025i −0.0177332 + 0.0307148i
\(796\) 0 0
\(797\) −18.0000 −0.637593 −0.318796 0.947823i \(-0.603279\pi\)
−0.318796 + 0.947823i \(0.603279\pi\)
\(798\) 0 0
\(799\) −25.0000 −0.884436
\(800\) 0 0
\(801\) 7.00000 12.1244i 0.247333 0.428393i
\(802\) 0 0
\(803\) 10.5000 + 18.1865i 0.370537 + 0.641789i
\(804\) 0 0
\(805\) −17.5000 + 6.06218i −0.616794 + 0.213664i
\(806\) 0 0
\(807\) −4.50000 7.79423i −0.158408 0.274370i
\(808\) 0 0
\(809\) −19.5000 + 33.7750i −0.685583 + 1.18747i 0.287670 + 0.957730i \(0.407120\pi\)
−0.973253 + 0.229736i \(0.926214\pi\)
\(810\) 0 0
\(811\) −12.0000 −0.421377 −0.210688 0.977553i \(-0.567571\pi\)
−0.210688 + 0.977553i \(0.567571\pi\)
\(812\) 0 0
\(813\) −7.00000 −0.245501
\(814\) 0 0
\(815\) 6.50000 11.2583i 0.227685 0.394362i
\(816\) 0 0
\(817\) 2.00000 + 3.46410i 0.0699711 + 0.121194i
\(818\) 0 0
\(819\) 6.00000 31.1769i 0.209657 1.08941i
\(820\) 0 0
\(821\) −4.50000 7.79423i −0.157051 0.272020i 0.776753 0.629805i \(-0.216865\pi\)
−0.933804 + 0.357785i \(0.883532\pi\)
\(822\) 0 0
\(823\) −23.5000 + 40.7032i −0.819159 + 1.41882i 0.0871445 + 0.996196i \(0.472226\pi\)
−0.906303 + 0.422628i \(0.861108\pi\)
\(824\) 0 0
\(825\) 12.0000 0.417786
\(826\) 0 0
\(827\) 36.0000 1.25184 0.625921 0.779886i \(-0.284723\pi\)
0.625921 + 0.779886i \(0.284723\pi\)
\(828\) 0 0
\(829\) 5.50000 9.52628i 0.191023 0.330861i −0.754567 0.656223i \(-0.772153\pi\)
0.945589 + 0.325362i \(0.105486\pi\)
\(830\) 0 0
\(831\) −8.50000 14.7224i −0.294862 0.510716i
\(832\) 0 0
\(833\) 32.5000 + 12.9904i 1.12606 + 0.450090i
\(834\) 0 0
\(835\) 6.00000 + 10.3923i 0.207639 + 0.359641i
\(836\) 0 0
\(837\) −12.5000 + 21.6506i −0.432063 + 0.748355i
\(838\) 0 0
\(839\) −24.0000 −0.828572 −0.414286 0.910147i \(-0.635969\pi\)
−0.414286 + 0.910147i \(0.635969\pi\)
\(840\) 0 0
\(841\) −25.0000 −0.862069
\(842\) 0 0
\(843\) −3.00000 + 5.19615i −0.103325 + 0.178965i
\(844\) 0 0
\(845\) −11.5000 19.9186i −0.395612 0.685220i
\(846\) 0 0
\(847\) 1.00000 5.19615i 0.0343604 0.178542i
\(848\) 0 0
\(849\) −6.50000 11.2583i −0.223079 0.386385i
\(850\) 0 0
\(851\) −10.5000 + 18.1865i −0.359935 + 0.623426i
\(852\) 0 0
\(853\) −34.0000 −1.16414 −0.582069 0.813139i \(-0.697757\pi\)
−0.582069 + 0.813139i \(0.697757\pi\)
\(854\) 0 0
\(855\) 2.00000 0.0683986
\(856\) 0 0
\(857\) −19.5000 + 33.7750i −0.666107 + 1.15373i 0.312877 + 0.949794i \(0.398707\pi\)
−0.978984 + 0.203938i \(0.934626\pi\)
\(858\) 0 0
\(859\) 0.500000 + 0.866025i 0.0170598 + 0.0295484i 0.874429 0.485153i \(-0.161236\pi\)
−0.857369 + 0.514701i \(0.827903\pi\)
\(860\) 0 0
\(861\) −5.00000 + 1.73205i −0.170400 + 0.0590281i
\(862\) 0 0
\(863\) −8.50000 14.7224i −0.289343 0.501157i 0.684310 0.729191i \(-0.260104\pi\)
−0.973653 + 0.228034i \(0.926770\pi\)
\(864\) 0 0
\(865\) −6.50000 + 11.2583i −0.221007 + 0.382795i
\(866\) 0 0
\(867\) 8.00000 0.271694
\(868\) 0 0
\(869\) −3.00000 −0.101768
\(870\) 0 0
\(871\) −27.0000 + 46.7654i −0.914860 + 1.58458i
\(872\) 0 0
\(873\) −2.00000 3.46410i −0.0676897 0.117242i
\(874\) 0 0
\(875\) 18.0000 + 15.5885i 0.608511 + 0.526986i
\(876\) 0 0
\(877\) 11.5000 + 19.9186i 0.388327 + 0.672603i 0.992225 0.124459i \(-0.0397196\pi\)
−0.603897 + 0.797062i \(0.706386\pi\)
\(878\) 0 0
\(879\) 3.00000 5.19615i 0.101187 0.175262i
\(880\) 0 0
\(881\) −14.0000 −0.471672 −0.235836 0.971793i \(-0.575783\pi\)
−0.235836 + 0.971793i \(0.575783\pi\)
\(882\) 0 0
\(883\) 20.0000 0.673054 0.336527 0.941674i \(-0.390748\pi\)
0.336527 + 0.941674i \(0.390748\pi\)
\(884\) 0 0
\(885\) 7.50000 12.9904i 0.252110 0.436667i
\(886\) 0 0
\(887\) 1.50000 + 2.59808i 0.0503651 + 0.0872349i 0.890109 0.455748i \(-0.150628\pi\)
−0.839744 + 0.542983i \(0.817295\pi\)
\(888\) 0 0
\(889\) −16.0000 13.8564i −0.536623 0.464729i
\(890\) 0 0
\(891\) 1.50000 + 2.59808i 0.0502519 + 0.0870388i
\(892\) 0 0
\(893\) 2.50000 4.33013i 0.0836593 0.144902i
\(894\) 0 0
\(895\) 13.0000 0.434542
\(896\) 0 0
\(897\) −42.0000 −1.40234
\(898\) 0 0
\(899\) −5.00000 + 8.66025i −0.166759 + 0.288836i
\(900\) 0 0
\(901\) 2.50000 + 4.33013i 0.0832871 + 0.144257i
\(902\) 0 0
\(903\) 10.0000 3.46410i 0.332779 0.115278i
\(904\) 0 0
\(905\) −5.00000 8.66025i −0.166206 0.287877i
\(906\) 0 0
\(907\) −0.500000 + 0.866025i −0.0166022 + 0.0287559i −0.874207 0.485553i \(-0.838618\pi\)
0.857605 + 0.514309i \(0.171952\pi\)
\(908\) 0 0
\(909\) 6.00000 0.199007
\(910\) 0 0
\(911\) 16.0000 0.530104 0.265052 0.964234i \(-0.414611\pi\)
0.265052 + 0.964234i \(0.414611\pi\)
\(912\) 0 0
\(913\) −18.0000 + 31.1769i −0.595713 + 1.03181i
\(914\) 0 0
\(915\) −2.50000 4.33013i −0.0826475 0.143150i
\(916\) 0 0
\(917\) 2.50000 12.9904i 0.0825573 0.428980i
\(918\) 0 0
\(919\) 5.50000 + 9.52628i 0.181428 + 0.314243i 0.942367 0.334581i \(-0.108595\pi\)
−0.760939 + 0.648824i \(0.775261\pi\)
\(920\) 0 0
\(921\) 2.00000 3.46410i 0.0659022 0.114146i
\(922\) 0 0
\(923\) 0 0
\(924\) 0 0
\(925\) 12.0000 0.394558
\(926\) 0 0
\(927\) −15.0000 + 25.9808i −0.492665 + 0.853320i
\(928\) 0 0
\(929\) −3.50000 6.06218i −0.114831 0.198894i 0.802881 0.596139i \(-0.203299\pi\)
−0.917712 + 0.397246i \(0.869966\pi\)
\(930\) 0 0
\(931\) −5.50000 + 4.33013i −0.180255 + 0.141914i
\(932\) 0 0
\(933\) −7.50000 12.9904i −0.245539 0.425286i
\(934\) 0 0
\(935\) −7.50000 + 12.9904i −0.245276 + 0.424831i
\(936\) 0 0
\(937\) −6.00000 −0.196011 −0.0980057 0.995186i \(-0.531246\pi\)
−0.0980057 + 0.995186i \(0.531246\pi\)
\(938\) 0 0
\(939\) −1.00000 −0.0326338
\(940\) 0 0
\(941\) −16.5000 + 28.5788i −0.537885 + 0.931644i 0.461133 + 0.887331i \(0.347443\pi\)
−0.999018 + 0.0443125i \(0.985890\pi\)
\(942\) 0 0
\(943\) −7.00000 12.1244i −0.227951 0.394823i
\(944\) 0 0
\(945\) 2.50000 12.9904i 0.0813250 0.422577i
\(946\) 0 0
\(947\) 18.5000 + 32.0429i 0.601169 + 1.04126i 0.992644 + 0.121067i \(0.0386316\pi\)
−0.391475 + 0.920189i \(0.628035\pi\)
\(948\) 0 0
\(949\) −21.0000 + 36.3731i −0.681689 + 1.18072i
\(950\) 0 0
\(951\) −3.00000 −0.0972817
\(952\) 0 0
\(953\) 22.0000 0.712650 0.356325 0.934362i \(-0.384030\pi\)
0.356325 + 0.934362i \(0.384030\pi\)
\(954\) 0 0
\(955\) 5.50000 9.52628i 0.177976 0.308263i
\(956\) 0 0
\(957\) −3.00000 5.19615i −0.0969762 0.167968i
\(958\) 0 0
\(959\) 27.5000 9.52628i 0.888021 0.307620i
\(960\) 0 0
\(961\) 3.00000 + 5.19615i 0.0967742 + 0.167618i
\(962\) 0 0
\(963\) −9.00000 + 15.5885i −0.290021 + 0.502331i
\(964\) 0 0
\(965\) 3.00000 0.0965734
\(966\) 0 0
\(967\) 48.0000 1.54358 0.771788 0.635880i \(-0.219363\pi\)
0.771788 + 0.635880i \(0.219363\pi\)
\(968\) 0 0
\(969\) −2.50000 + 4.33013i −0.0803116 + 0.139104i
\(970\) 0 0
\(971\) −17.5000 30.3109i −0.561602 0.972723i −0.997357 0.0726575i \(-0.976852\pi\)
0.435755 0.900065i \(-0.356481\pi\)
\(972\) 0 0
\(973\) −24.0000 20.7846i −0.769405 0.666324i
\(974\) 0 0
\(975\) 12.0000 + 20.7846i 0.384308 + 0.665640i
\(976\) 0 0
\(977\) −1.50000 + 2.59808i −0.0479893 + 0.0831198i −0.889022 0.457864i \(-0.848615\pi\)
0.841033 + 0.540984i \(0.181948\pi\)
\(978\) 0 0
\(979\) −21.0000 −0.671163
\(980\) 0 0
\(981\) −10.0000 −0.319275
\(982\) 0 0
\(983\) 10.5000 18.1865i 0.334898 0.580060i −0.648567 0.761157i \(-0.724631\pi\)
0.983465 + 0.181097i \(0.0579648\pi\)
\(984\) 0 0
\(985\) −3.00000 5.19615i −0.0955879 0.165563i
\(986\) 0 0
\(987\) −10.0000 8.66025i −0.318304 0.275659i
\(988\) 0 0
\(989\) 14.0000 + 24.2487i 0.445174 + 0.771064i
\(990\) 0 0
\(991\) −7.50000 + 12.9904i −0.238245 + 0.412653i −0.960211 0.279276i \(-0.909906\pi\)
0.721966 + 0.691929i \(0.243239\pi\)
\(992\) 0 0
\(993\) −29.0000 −0.920287
\(994\) 0 0
\(995\) −13.0000 −0.412128
\(996\) 0 0
\(997\) −20.5000 + 35.5070i −0.649242 + 1.12452i 0.334063 + 0.942551i \(0.391580\pi\)
−0.983304 + 0.181968i \(0.941753\pi\)
\(998\) 0 0
\(999\) −7.50000 12.9904i −0.237289 0.410997i
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 448.2.i.b.193.1 2
4.3 odd 2 448.2.i.d.193.1 2
7.2 even 3 inner 448.2.i.b.65.1 2
7.3 odd 6 3136.2.a.i.1.1 1
7.4 even 3 3136.2.a.u.1.1 1
8.3 odd 2 112.2.i.a.81.1 2
8.5 even 2 56.2.i.b.25.1 yes 2
24.5 odd 2 504.2.s.c.361.1 2
24.11 even 2 1008.2.s.g.865.1 2
28.3 even 6 3136.2.a.t.1.1 1
28.11 odd 6 3136.2.a.j.1.1 1
28.23 odd 6 448.2.i.d.65.1 2
40.13 odd 4 1400.2.bh.a.249.2 4
40.29 even 2 1400.2.q.d.1201.1 2
40.37 odd 4 1400.2.bh.a.249.1 4
56.3 even 6 784.2.a.c.1.1 1
56.5 odd 6 392.2.i.b.177.1 2
56.11 odd 6 784.2.a.h.1.1 1
56.13 odd 2 392.2.i.b.361.1 2
56.19 even 6 784.2.i.h.177.1 2
56.27 even 2 784.2.i.h.753.1 2
56.37 even 6 56.2.i.b.9.1 2
56.45 odd 6 392.2.a.e.1.1 1
56.51 odd 6 112.2.i.a.65.1 2
56.53 even 6 392.2.a.c.1.1 1
168.5 even 6 3528.2.s.q.3313.1 2
168.11 even 6 7056.2.a.bj.1.1 1
168.53 odd 6 3528.2.a.p.1.1 1
168.59 odd 6 7056.2.a.u.1.1 1
168.101 even 6 3528.2.a.j.1.1 1
168.107 even 6 1008.2.s.g.289.1 2
168.125 even 2 3528.2.s.q.361.1 2
168.149 odd 6 504.2.s.c.289.1 2
280.37 odd 12 1400.2.bh.a.849.2 4
280.93 odd 12 1400.2.bh.a.849.1 4
280.109 even 6 9800.2.a.be.1.1 1
280.149 even 6 1400.2.q.d.401.1 2
280.269 odd 6 9800.2.a.s.1.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
56.2.i.b.9.1 2 56.37 even 6
56.2.i.b.25.1 yes 2 8.5 even 2
112.2.i.a.65.1 2 56.51 odd 6
112.2.i.a.81.1 2 8.3 odd 2
392.2.a.c.1.1 1 56.53 even 6
392.2.a.e.1.1 1 56.45 odd 6
392.2.i.b.177.1 2 56.5 odd 6
392.2.i.b.361.1 2 56.13 odd 2
448.2.i.b.65.1 2 7.2 even 3 inner
448.2.i.b.193.1 2 1.1 even 1 trivial
448.2.i.d.65.1 2 28.23 odd 6
448.2.i.d.193.1 2 4.3 odd 2
504.2.s.c.289.1 2 168.149 odd 6
504.2.s.c.361.1 2 24.5 odd 2
784.2.a.c.1.1 1 56.3 even 6
784.2.a.h.1.1 1 56.11 odd 6
784.2.i.h.177.1 2 56.19 even 6
784.2.i.h.753.1 2 56.27 even 2
1008.2.s.g.289.1 2 168.107 even 6
1008.2.s.g.865.1 2 24.11 even 2
1400.2.q.d.401.1 2 280.149 even 6
1400.2.q.d.1201.1 2 40.29 even 2
1400.2.bh.a.249.1 4 40.37 odd 4
1400.2.bh.a.249.2 4 40.13 odd 4
1400.2.bh.a.849.1 4 280.93 odd 12
1400.2.bh.a.849.2 4 280.37 odd 12
3136.2.a.i.1.1 1 7.3 odd 6
3136.2.a.j.1.1 1 28.11 odd 6
3136.2.a.t.1.1 1 28.3 even 6
3136.2.a.u.1.1 1 7.4 even 3
3528.2.a.j.1.1 1 168.101 even 6
3528.2.a.p.1.1 1 168.53 odd 6
3528.2.s.q.361.1 2 168.125 even 2
3528.2.s.q.3313.1 2 168.5 even 6
7056.2.a.u.1.1 1 168.59 odd 6
7056.2.a.bj.1.1 1 168.11 even 6
9800.2.a.s.1.1 1 280.269 odd 6
9800.2.a.be.1.1 1 280.109 even 6