Properties

Label 72.2.f.a.35.1
Level $72$
Weight $2$
Character 72.35
Analytic conductor $0.575$
Analytic rank $0$
Dimension $4$
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] = [72,2,Mod(35,72)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(72, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([1, 1, 1]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("72.35");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 72 = 2^{3} \cdot 3^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 72.f (of order \(2\), degree \(1\), 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: \(0.574922894553\)
Analytic rank: \(0\)
Dimension: \(4\)
Coefficient field: \(\Q(\sqrt{-2}, \sqrt{-3})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{4} - 2x^{2} + 4 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 2 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 35.1
Root \(-1.22474 - 0.707107i\) of defining polynomial
Character \(\chi\) \(=\) 72.35
Dual form 72.2.f.a.35.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.22474 - 0.707107i) q^{2} +(1.00000 + 1.73205i) q^{4} +2.44949 q^{5} -3.46410i q^{7} -2.82843i q^{8} +O(q^{10})\) \(q+(-1.22474 - 0.707107i) q^{2} +(1.00000 + 1.73205i) q^{4} +2.44949 q^{5} -3.46410i q^{7} -2.82843i q^{8} +(-3.00000 - 1.73205i) q^{10} +2.82843i q^{11} +3.46410i q^{13} +(-2.44949 + 4.24264i) q^{14} +(-2.00000 + 3.46410i) q^{16} -1.41421i q^{17} -4.00000 q^{19} +(2.44949 + 4.24264i) q^{20} +(2.00000 - 3.46410i) q^{22} -4.89898 q^{23} +1.00000 q^{25} +(2.44949 - 4.24264i) q^{26} +(6.00000 - 3.46410i) q^{28} -2.44949 q^{29} +3.46410i q^{31} +(4.89898 - 2.82843i) q^{32} +(-1.00000 + 1.73205i) q^{34} -8.48528i q^{35} +(4.89898 + 2.82843i) q^{38} -6.92820i q^{40} -1.41421i q^{41} +8.00000 q^{43} +(-4.89898 + 2.82843i) q^{44} +(6.00000 + 3.46410i) q^{46} +4.89898 q^{47} -5.00000 q^{49} +(-1.22474 - 0.707107i) q^{50} +(-6.00000 + 3.46410i) q^{52} -7.34847 q^{53} +6.92820i q^{55} -9.79796 q^{56} +(3.00000 + 1.73205i) q^{58} +11.3137i q^{59} -13.8564i q^{61} +(2.44949 - 4.24264i) q^{62} -8.00000 q^{64} +8.48528i q^{65} -4.00000 q^{67} +(2.44949 - 1.41421i) q^{68} +(-6.00000 + 10.3923i) q^{70} +14.6969 q^{71} -4.00000 q^{73} +(-4.00000 - 6.92820i) q^{76} +9.79796 q^{77} -3.46410i q^{79} +(-4.89898 + 8.48528i) q^{80} +(-1.00000 + 1.73205i) q^{82} -14.1421i q^{83} -3.46410i q^{85} +(-9.79796 - 5.65685i) q^{86} +8.00000 q^{88} +7.07107i q^{89} +12.0000 q^{91} +(-4.89898 - 8.48528i) q^{92} +(-6.00000 - 3.46410i) q^{94} -9.79796 q^{95} +8.00000 q^{97} +(6.12372 + 3.53553i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q + 4 q^{4}+O(q^{10}) \) Copy content Toggle raw display \( 4 q + 4 q^{4} - 12 q^{10} - 8 q^{16} - 16 q^{19} + 8 q^{22} + 4 q^{25} + 24 q^{28} - 4 q^{34} + 32 q^{43} + 24 q^{46} - 20 q^{49} - 24 q^{52} + 12 q^{58} - 32 q^{64} - 16 q^{67} - 24 q^{70} - 16 q^{73} - 16 q^{76} - 4 q^{82} + 32 q^{88} + 48 q^{91} - 24 q^{94} + 32 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/72\mathbb{Z}\right)^\times\).

\(n\) \(37\) \(55\) \(65\)
\(\chi(n)\) \(-1\) \(-1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.22474 0.707107i −0.866025 0.500000i
\(3\) 0 0
\(4\) 1.00000 + 1.73205i 0.500000 + 0.866025i
\(5\) 2.44949 1.09545 0.547723 0.836660i \(-0.315495\pi\)
0.547723 + 0.836660i \(0.315495\pi\)
\(6\) 0 0
\(7\) 3.46410i 1.30931i −0.755929 0.654654i \(-0.772814\pi\)
0.755929 0.654654i \(-0.227186\pi\)
\(8\) 2.82843i 1.00000i
\(9\) 0 0
\(10\) −3.00000 1.73205i −0.948683 0.547723i
\(11\) 2.82843i 0.852803i 0.904534 + 0.426401i \(0.140219\pi\)
−0.904534 + 0.426401i \(0.859781\pi\)
\(12\) 0 0
\(13\) 3.46410i 0.960769i 0.877058 + 0.480384i \(0.159503\pi\)
−0.877058 + 0.480384i \(0.840497\pi\)
\(14\) −2.44949 + 4.24264i −0.654654 + 1.13389i
\(15\) 0 0
\(16\) −2.00000 + 3.46410i −0.500000 + 0.866025i
\(17\) 1.41421i 0.342997i −0.985184 0.171499i \(-0.945139\pi\)
0.985184 0.171499i \(-0.0548609\pi\)
\(18\) 0 0
\(19\) −4.00000 −0.917663 −0.458831 0.888523i \(-0.651732\pi\)
−0.458831 + 0.888523i \(0.651732\pi\)
\(20\) 2.44949 + 4.24264i 0.547723 + 0.948683i
\(21\) 0 0
\(22\) 2.00000 3.46410i 0.426401 0.738549i
\(23\) −4.89898 −1.02151 −0.510754 0.859727i \(-0.670634\pi\)
−0.510754 + 0.859727i \(0.670634\pi\)
\(24\) 0 0
\(25\) 1.00000 0.200000
\(26\) 2.44949 4.24264i 0.480384 0.832050i
\(27\) 0 0
\(28\) 6.00000 3.46410i 1.13389 0.654654i
\(29\) −2.44949 −0.454859 −0.227429 0.973795i \(-0.573032\pi\)
−0.227429 + 0.973795i \(0.573032\pi\)
\(30\) 0 0
\(31\) 3.46410i 0.622171i 0.950382 + 0.311086i \(0.100693\pi\)
−0.950382 + 0.311086i \(0.899307\pi\)
\(32\) 4.89898 2.82843i 0.866025 0.500000i
\(33\) 0 0
\(34\) −1.00000 + 1.73205i −0.171499 + 0.297044i
\(35\) 8.48528i 1.43427i
\(36\) 0 0
\(37\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(38\) 4.89898 + 2.82843i 0.794719 + 0.458831i
\(39\) 0 0
\(40\) 6.92820i 1.09545i
\(41\) 1.41421i 0.220863i −0.993884 0.110432i \(-0.964777\pi\)
0.993884 0.110432i \(-0.0352233\pi\)
\(42\) 0 0
\(43\) 8.00000 1.21999 0.609994 0.792406i \(-0.291172\pi\)
0.609994 + 0.792406i \(0.291172\pi\)
\(44\) −4.89898 + 2.82843i −0.738549 + 0.426401i
\(45\) 0 0
\(46\) 6.00000 + 3.46410i 0.884652 + 0.510754i
\(47\) 4.89898 0.714590 0.357295 0.933992i \(-0.383699\pi\)
0.357295 + 0.933992i \(0.383699\pi\)
\(48\) 0 0
\(49\) −5.00000 −0.714286
\(50\) −1.22474 0.707107i −0.173205 0.100000i
\(51\) 0 0
\(52\) −6.00000 + 3.46410i −0.832050 + 0.480384i
\(53\) −7.34847 −1.00939 −0.504695 0.863298i \(-0.668395\pi\)
−0.504695 + 0.863298i \(0.668395\pi\)
\(54\) 0 0
\(55\) 6.92820i 0.934199i
\(56\) −9.79796 −1.30931
\(57\) 0 0
\(58\) 3.00000 + 1.73205i 0.393919 + 0.227429i
\(59\) 11.3137i 1.47292i 0.676481 + 0.736460i \(0.263504\pi\)
−0.676481 + 0.736460i \(0.736496\pi\)
\(60\) 0 0
\(61\) 13.8564i 1.77413i −0.461644 0.887066i \(-0.652740\pi\)
0.461644 0.887066i \(-0.347260\pi\)
\(62\) 2.44949 4.24264i 0.311086 0.538816i
\(63\) 0 0
\(64\) −8.00000 −1.00000
\(65\) 8.48528i 1.05247i
\(66\) 0 0
\(67\) −4.00000 −0.488678 −0.244339 0.969690i \(-0.578571\pi\)
−0.244339 + 0.969690i \(0.578571\pi\)
\(68\) 2.44949 1.41421i 0.297044 0.171499i
\(69\) 0 0
\(70\) −6.00000 + 10.3923i −0.717137 + 1.24212i
\(71\) 14.6969 1.74421 0.872103 0.489323i \(-0.162756\pi\)
0.872103 + 0.489323i \(0.162756\pi\)
\(72\) 0 0
\(73\) −4.00000 −0.468165 −0.234082 0.972217i \(-0.575209\pi\)
−0.234082 + 0.972217i \(0.575209\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) −4.00000 6.92820i −0.458831 0.794719i
\(77\) 9.79796 1.11658
\(78\) 0 0
\(79\) 3.46410i 0.389742i −0.980829 0.194871i \(-0.937571\pi\)
0.980829 0.194871i \(-0.0624288\pi\)
\(80\) −4.89898 + 8.48528i −0.547723 + 0.948683i
\(81\) 0 0
\(82\) −1.00000 + 1.73205i −0.110432 + 0.191273i
\(83\) 14.1421i 1.55230i −0.630548 0.776151i \(-0.717170\pi\)
0.630548 0.776151i \(-0.282830\pi\)
\(84\) 0 0
\(85\) 3.46410i 0.375735i
\(86\) −9.79796 5.65685i −1.05654 0.609994i
\(87\) 0 0
\(88\) 8.00000 0.852803
\(89\) 7.07107i 0.749532i 0.927119 + 0.374766i \(0.122277\pi\)
−0.927119 + 0.374766i \(0.877723\pi\)
\(90\) 0 0
\(91\) 12.0000 1.25794
\(92\) −4.89898 8.48528i −0.510754 0.884652i
\(93\) 0 0
\(94\) −6.00000 3.46410i −0.618853 0.357295i
\(95\) −9.79796 −1.00525
\(96\) 0 0
\(97\) 8.00000 0.812277 0.406138 0.913812i \(-0.366875\pi\)
0.406138 + 0.913812i \(0.366875\pi\)
\(98\) 6.12372 + 3.53553i 0.618590 + 0.357143i
\(99\) 0 0
\(100\) 1.00000 + 1.73205i 0.100000 + 0.173205i
\(101\) −2.44949 −0.243733 −0.121867 0.992546i \(-0.538888\pi\)
−0.121867 + 0.992546i \(0.538888\pi\)
\(102\) 0 0
\(103\) 3.46410i 0.341328i 0.985329 + 0.170664i \(0.0545913\pi\)
−0.985329 + 0.170664i \(0.945409\pi\)
\(104\) 9.79796 0.960769
\(105\) 0 0
\(106\) 9.00000 + 5.19615i 0.874157 + 0.504695i
\(107\) 11.3137i 1.09374i 0.837218 + 0.546869i \(0.184180\pi\)
−0.837218 + 0.546869i \(0.815820\pi\)
\(108\) 0 0
\(109\) 10.3923i 0.995402i 0.867349 + 0.497701i \(0.165822\pi\)
−0.867349 + 0.497701i \(0.834178\pi\)
\(110\) 4.89898 8.48528i 0.467099 0.809040i
\(111\) 0 0
\(112\) 12.0000 + 6.92820i 1.13389 + 0.654654i
\(113\) 18.3848i 1.72949i −0.502208 0.864747i \(-0.667479\pi\)
0.502208 0.864747i \(-0.332521\pi\)
\(114\) 0 0
\(115\) −12.0000 −1.11901
\(116\) −2.44949 4.24264i −0.227429 0.393919i
\(117\) 0 0
\(118\) 8.00000 13.8564i 0.736460 1.27559i
\(119\) −4.89898 −0.449089
\(120\) 0 0
\(121\) 3.00000 0.272727
\(122\) −9.79796 + 16.9706i −0.887066 + 1.53644i
\(123\) 0 0
\(124\) −6.00000 + 3.46410i −0.538816 + 0.311086i
\(125\) −9.79796 −0.876356
\(126\) 0 0
\(127\) 10.3923i 0.922168i −0.887357 0.461084i \(-0.847461\pi\)
0.887357 0.461084i \(-0.152539\pi\)
\(128\) 9.79796 + 5.65685i 0.866025 + 0.500000i
\(129\) 0 0
\(130\) 6.00000 10.3923i 0.526235 0.911465i
\(131\) 5.65685i 0.494242i −0.968985 0.247121i \(-0.920516\pi\)
0.968985 0.247121i \(-0.0794845\pi\)
\(132\) 0 0
\(133\) 13.8564i 1.20150i
\(134\) 4.89898 + 2.82843i 0.423207 + 0.244339i
\(135\) 0 0
\(136\) −4.00000 −0.342997
\(137\) 9.89949i 0.845771i −0.906183 0.422885i \(-0.861017\pi\)
0.906183 0.422885i \(-0.138983\pi\)
\(138\) 0 0
\(139\) −4.00000 −0.339276 −0.169638 0.985506i \(-0.554260\pi\)
−0.169638 + 0.985506i \(0.554260\pi\)
\(140\) 14.6969 8.48528i 1.24212 0.717137i
\(141\) 0 0
\(142\) −18.0000 10.3923i −1.51053 0.872103i
\(143\) −9.79796 −0.819346
\(144\) 0 0
\(145\) −6.00000 −0.498273
\(146\) 4.89898 + 2.82843i 0.405442 + 0.234082i
\(147\) 0 0
\(148\) 0 0
\(149\) 17.1464 1.40469 0.702345 0.711837i \(-0.252136\pi\)
0.702345 + 0.711837i \(0.252136\pi\)
\(150\) 0 0
\(151\) 3.46410i 0.281905i −0.990016 0.140952i \(-0.954984\pi\)
0.990016 0.140952i \(-0.0450164\pi\)
\(152\) 11.3137i 0.917663i
\(153\) 0 0
\(154\) −12.0000 6.92820i −0.966988 0.558291i
\(155\) 8.48528i 0.681554i
\(156\) 0 0
\(157\) 13.8564i 1.10586i 0.833227 + 0.552931i \(0.186491\pi\)
−0.833227 + 0.552931i \(0.813509\pi\)
\(158\) −2.44949 + 4.24264i −0.194871 + 0.337526i
\(159\) 0 0
\(160\) 12.0000 6.92820i 0.948683 0.547723i
\(161\) 16.9706i 1.33747i
\(162\) 0 0
\(163\) −16.0000 −1.25322 −0.626608 0.779334i \(-0.715557\pi\)
−0.626608 + 0.779334i \(0.715557\pi\)
\(164\) 2.44949 1.41421i 0.191273 0.110432i
\(165\) 0 0
\(166\) −10.0000 + 17.3205i −0.776151 + 1.34433i
\(167\) −19.5959 −1.51638 −0.758189 0.652035i \(-0.773915\pi\)
−0.758189 + 0.652035i \(0.773915\pi\)
\(168\) 0 0
\(169\) 1.00000 0.0769231
\(170\) −2.44949 + 4.24264i −0.187867 + 0.325396i
\(171\) 0 0
\(172\) 8.00000 + 13.8564i 0.609994 + 1.05654i
\(173\) −2.44949 −0.186231 −0.0931156 0.995655i \(-0.529683\pi\)
−0.0931156 + 0.995655i \(0.529683\pi\)
\(174\) 0 0
\(175\) 3.46410i 0.261861i
\(176\) −9.79796 5.65685i −0.738549 0.426401i
\(177\) 0 0
\(178\) 5.00000 8.66025i 0.374766 0.649113i
\(179\) 5.65685i 0.422813i −0.977398 0.211407i \(-0.932196\pi\)
0.977398 0.211407i \(-0.0678044\pi\)
\(180\) 0 0
\(181\) 10.3923i 0.772454i −0.922404 0.386227i \(-0.873778\pi\)
0.922404 0.386227i \(-0.126222\pi\)
\(182\) −14.6969 8.48528i −1.08941 0.628971i
\(183\) 0 0
\(184\) 13.8564i 1.02151i
\(185\) 0 0
\(186\) 0 0
\(187\) 4.00000 0.292509
\(188\) 4.89898 + 8.48528i 0.357295 + 0.618853i
\(189\) 0 0
\(190\) 12.0000 + 6.92820i 0.870572 + 0.502625i
\(191\) 19.5959 1.41791 0.708955 0.705253i \(-0.249167\pi\)
0.708955 + 0.705253i \(0.249167\pi\)
\(192\) 0 0
\(193\) 14.0000 1.00774 0.503871 0.863779i \(-0.331909\pi\)
0.503871 + 0.863779i \(0.331909\pi\)
\(194\) −9.79796 5.65685i −0.703452 0.406138i
\(195\) 0 0
\(196\) −5.00000 8.66025i −0.357143 0.618590i
\(197\) 7.34847 0.523557 0.261778 0.965128i \(-0.415691\pi\)
0.261778 + 0.965128i \(0.415691\pi\)
\(198\) 0 0
\(199\) 10.3923i 0.736691i −0.929689 0.368345i \(-0.879924\pi\)
0.929689 0.368345i \(-0.120076\pi\)
\(200\) 2.82843i 0.200000i
\(201\) 0 0
\(202\) 3.00000 + 1.73205i 0.211079 + 0.121867i
\(203\) 8.48528i 0.595550i
\(204\) 0 0
\(205\) 3.46410i 0.241943i
\(206\) 2.44949 4.24264i 0.170664 0.295599i
\(207\) 0 0
\(208\) −12.0000 6.92820i −0.832050 0.480384i
\(209\) 11.3137i 0.782586i
\(210\) 0 0
\(211\) 20.0000 1.37686 0.688428 0.725304i \(-0.258301\pi\)
0.688428 + 0.725304i \(0.258301\pi\)
\(212\) −7.34847 12.7279i −0.504695 0.874157i
\(213\) 0 0
\(214\) 8.00000 13.8564i 0.546869 0.947204i
\(215\) 19.5959 1.33643
\(216\) 0 0
\(217\) 12.0000 0.814613
\(218\) 7.34847 12.7279i 0.497701 0.862044i
\(219\) 0 0
\(220\) −12.0000 + 6.92820i −0.809040 + 0.467099i
\(221\) 4.89898 0.329541
\(222\) 0 0
\(223\) 17.3205i 1.15987i 0.814664 + 0.579934i \(0.196921\pi\)
−0.814664 + 0.579934i \(0.803079\pi\)
\(224\) −9.79796 16.9706i −0.654654 1.13389i
\(225\) 0 0
\(226\) −13.0000 + 22.5167i −0.864747 + 1.49779i
\(227\) 2.82843i 0.187729i 0.995585 + 0.0938647i \(0.0299221\pi\)
−0.995585 + 0.0938647i \(0.970078\pi\)
\(228\) 0 0
\(229\) 17.3205i 1.14457i −0.820054 0.572286i \(-0.806057\pi\)
0.820054 0.572286i \(-0.193943\pi\)
\(230\) 14.6969 + 8.48528i 0.969087 + 0.559503i
\(231\) 0 0
\(232\) 6.92820i 0.454859i
\(233\) 1.41421i 0.0926482i −0.998926 0.0463241i \(-0.985249\pi\)
0.998926 0.0463241i \(-0.0147507\pi\)
\(234\) 0 0
\(235\) 12.0000 0.782794
\(236\) −19.5959 + 11.3137i −1.27559 + 0.736460i
\(237\) 0 0
\(238\) 6.00000 + 3.46410i 0.388922 + 0.224544i
\(239\) 9.79796 0.633777 0.316889 0.948463i \(-0.397362\pi\)
0.316889 + 0.948463i \(0.397362\pi\)
\(240\) 0 0
\(241\) −28.0000 −1.80364 −0.901819 0.432113i \(-0.857768\pi\)
−0.901819 + 0.432113i \(0.857768\pi\)
\(242\) −3.67423 2.12132i −0.236189 0.136364i
\(243\) 0 0
\(244\) 24.0000 13.8564i 1.53644 0.887066i
\(245\) −12.2474 −0.782461
\(246\) 0 0
\(247\) 13.8564i 0.881662i
\(248\) 9.79796 0.622171
\(249\) 0 0
\(250\) 12.0000 + 6.92820i 0.758947 + 0.438178i
\(251\) 14.1421i 0.892644i −0.894873 0.446322i \(-0.852734\pi\)
0.894873 0.446322i \(-0.147266\pi\)
\(252\) 0 0
\(253\) 13.8564i 0.871145i
\(254\) −7.34847 + 12.7279i −0.461084 + 0.798621i
\(255\) 0 0
\(256\) −8.00000 13.8564i −0.500000 0.866025i
\(257\) 24.0416i 1.49968i 0.661622 + 0.749838i \(0.269869\pi\)
−0.661622 + 0.749838i \(0.730131\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) −14.6969 + 8.48528i −0.911465 + 0.526235i
\(261\) 0 0
\(262\) −4.00000 + 6.92820i −0.247121 + 0.428026i
\(263\) −9.79796 −0.604168 −0.302084 0.953281i \(-0.597682\pi\)
−0.302084 + 0.953281i \(0.597682\pi\)
\(264\) 0 0
\(265\) −18.0000 −1.10573
\(266\) 9.79796 16.9706i 0.600751 1.04053i
\(267\) 0 0
\(268\) −4.00000 6.92820i −0.244339 0.423207i
\(269\) −7.34847 −0.448044 −0.224022 0.974584i \(-0.571919\pi\)
−0.224022 + 0.974584i \(0.571919\pi\)
\(270\) 0 0
\(271\) 31.1769i 1.89386i 0.321436 + 0.946931i \(0.395835\pi\)
−0.321436 + 0.946931i \(0.604165\pi\)
\(272\) 4.89898 + 2.82843i 0.297044 + 0.171499i
\(273\) 0 0
\(274\) −7.00000 + 12.1244i −0.422885 + 0.732459i
\(275\) 2.82843i 0.170561i
\(276\) 0 0
\(277\) 17.3205i 1.04069i 0.853957 + 0.520344i \(0.174196\pi\)
−0.853957 + 0.520344i \(0.825804\pi\)
\(278\) 4.89898 + 2.82843i 0.293821 + 0.169638i
\(279\) 0 0
\(280\) −24.0000 −1.43427
\(281\) 24.0416i 1.43420i 0.696969 + 0.717102i \(0.254532\pi\)
−0.696969 + 0.717102i \(0.745468\pi\)
\(282\) 0 0
\(283\) −16.0000 −0.951101 −0.475551 0.879688i \(-0.657751\pi\)
−0.475551 + 0.879688i \(0.657751\pi\)
\(284\) 14.6969 + 25.4558i 0.872103 + 1.51053i
\(285\) 0 0
\(286\) 12.0000 + 6.92820i 0.709575 + 0.409673i
\(287\) −4.89898 −0.289178
\(288\) 0 0
\(289\) 15.0000 0.882353
\(290\) 7.34847 + 4.24264i 0.431517 + 0.249136i
\(291\) 0 0
\(292\) −4.00000 6.92820i −0.234082 0.405442i
\(293\) −26.9444 −1.57411 −0.787054 0.616884i \(-0.788395\pi\)
−0.787054 + 0.616884i \(0.788395\pi\)
\(294\) 0 0
\(295\) 27.7128i 1.61350i
\(296\) 0 0
\(297\) 0 0
\(298\) −21.0000 12.1244i −1.21650 0.702345i
\(299\) 16.9706i 0.981433i
\(300\) 0 0
\(301\) 27.7128i 1.59734i
\(302\) −2.44949 + 4.24264i −0.140952 + 0.244137i
\(303\) 0 0
\(304\) 8.00000 13.8564i 0.458831 0.794719i
\(305\) 33.9411i 1.94346i
\(306\) 0 0
\(307\) −4.00000 −0.228292 −0.114146 0.993464i \(-0.536413\pi\)
−0.114146 + 0.993464i \(0.536413\pi\)
\(308\) 9.79796 + 16.9706i 0.558291 + 0.966988i
\(309\) 0 0
\(310\) 6.00000 10.3923i 0.340777 0.590243i
\(311\) 9.79796 0.555591 0.277796 0.960640i \(-0.410396\pi\)
0.277796 + 0.960640i \(0.410396\pi\)
\(312\) 0 0
\(313\) −10.0000 −0.565233 −0.282617 0.959233i \(-0.591202\pi\)
−0.282617 + 0.959233i \(0.591202\pi\)
\(314\) 9.79796 16.9706i 0.552931 0.957704i
\(315\) 0 0
\(316\) 6.00000 3.46410i 0.337526 0.194871i
\(317\) 12.2474 0.687885 0.343943 0.938991i \(-0.388237\pi\)
0.343943 + 0.938991i \(0.388237\pi\)
\(318\) 0 0
\(319\) 6.92820i 0.387905i
\(320\) −19.5959 −1.09545
\(321\) 0 0
\(322\) 12.0000 20.7846i 0.668734 1.15828i
\(323\) 5.65685i 0.314756i
\(324\) 0 0
\(325\) 3.46410i 0.192154i
\(326\) 19.5959 + 11.3137i 1.08532 + 0.626608i
\(327\) 0 0
\(328\) −4.00000 −0.220863
\(329\) 16.9706i 0.935617i
\(330\) 0 0
\(331\) −4.00000 −0.219860 −0.109930 0.993939i \(-0.535063\pi\)
−0.109930 + 0.993939i \(0.535063\pi\)
\(332\) 24.4949 14.1421i 1.34433 0.776151i
\(333\) 0 0
\(334\) 24.0000 + 13.8564i 1.31322 + 0.758189i
\(335\) −9.79796 −0.535320
\(336\) 0 0
\(337\) −4.00000 −0.217894 −0.108947 0.994048i \(-0.534748\pi\)
−0.108947 + 0.994048i \(0.534748\pi\)
\(338\) −1.22474 0.707107i −0.0666173 0.0384615i
\(339\) 0 0
\(340\) 6.00000 3.46410i 0.325396 0.187867i
\(341\) −9.79796 −0.530589
\(342\) 0 0
\(343\) 6.92820i 0.374088i
\(344\) 22.6274i 1.21999i
\(345\) 0 0
\(346\) 3.00000 + 1.73205i 0.161281 + 0.0931156i
\(347\) 14.1421i 0.759190i −0.925153 0.379595i \(-0.876063\pi\)
0.925153 0.379595i \(-0.123937\pi\)
\(348\) 0 0
\(349\) 27.7128i 1.48343i 0.670714 + 0.741716i \(0.265988\pi\)
−0.670714 + 0.741716i \(0.734012\pi\)
\(350\) −2.44949 + 4.24264i −0.130931 + 0.226779i
\(351\) 0 0
\(352\) 8.00000 + 13.8564i 0.426401 + 0.738549i
\(353\) 15.5563i 0.827981i 0.910281 + 0.413990i \(0.135865\pi\)
−0.910281 + 0.413990i \(0.864135\pi\)
\(354\) 0 0
\(355\) 36.0000 1.91068
\(356\) −12.2474 + 7.07107i −0.649113 + 0.374766i
\(357\) 0 0
\(358\) −4.00000 + 6.92820i −0.211407 + 0.366167i
\(359\) −14.6969 −0.775675 −0.387837 0.921728i \(-0.626778\pi\)
−0.387837 + 0.921728i \(0.626778\pi\)
\(360\) 0 0
\(361\) −3.00000 −0.157895
\(362\) −7.34847 + 12.7279i −0.386227 + 0.668965i
\(363\) 0 0
\(364\) 12.0000 + 20.7846i 0.628971 + 1.08941i
\(365\) −9.79796 −0.512849
\(366\) 0 0
\(367\) 24.2487i 1.26577i −0.774245 0.632886i \(-0.781870\pi\)
0.774245 0.632886i \(-0.218130\pi\)
\(368\) 9.79796 16.9706i 0.510754 0.884652i
\(369\) 0 0
\(370\) 0 0
\(371\) 25.4558i 1.32160i
\(372\) 0 0
\(373\) 13.8564i 0.717458i 0.933442 + 0.358729i \(0.116790\pi\)
−0.933442 + 0.358729i \(0.883210\pi\)
\(374\) −4.89898 2.82843i −0.253320 0.146254i
\(375\) 0 0
\(376\) 13.8564i 0.714590i
\(377\) 8.48528i 0.437014i
\(378\) 0 0
\(379\) −4.00000 −0.205466 −0.102733 0.994709i \(-0.532759\pi\)
−0.102733 + 0.994709i \(0.532759\pi\)
\(380\) −9.79796 16.9706i −0.502625 0.870572i
\(381\) 0 0
\(382\) −24.0000 13.8564i −1.22795 0.708955i
\(383\) 9.79796 0.500652 0.250326 0.968162i \(-0.419462\pi\)
0.250326 + 0.968162i \(0.419462\pi\)
\(384\) 0 0
\(385\) 24.0000 1.22315
\(386\) −17.1464 9.89949i −0.872730 0.503871i
\(387\) 0 0
\(388\) 8.00000 + 13.8564i 0.406138 + 0.703452i
\(389\) 26.9444 1.36613 0.683067 0.730355i \(-0.260646\pi\)
0.683067 + 0.730355i \(0.260646\pi\)
\(390\) 0 0
\(391\) 6.92820i 0.350374i
\(392\) 14.1421i 0.714286i
\(393\) 0 0
\(394\) −9.00000 5.19615i −0.453413 0.261778i
\(395\) 8.48528i 0.426941i
\(396\) 0 0
\(397\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(398\) −7.34847 + 12.7279i −0.368345 + 0.637993i
\(399\) 0 0
\(400\) −2.00000 + 3.46410i −0.100000 + 0.173205i
\(401\) 1.41421i 0.0706225i −0.999376 0.0353112i \(-0.988758\pi\)
0.999376 0.0353112i \(-0.0112422\pi\)
\(402\) 0 0
\(403\) −12.0000 −0.597763
\(404\) −2.44949 4.24264i −0.121867 0.211079i
\(405\) 0 0
\(406\) 6.00000 10.3923i 0.297775 0.515761i
\(407\) 0 0
\(408\) 0 0
\(409\) 32.0000 1.58230 0.791149 0.611623i \(-0.209483\pi\)
0.791149 + 0.611623i \(0.209483\pi\)
\(410\) −2.44949 + 4.24264i −0.120972 + 0.209529i
\(411\) 0 0
\(412\) −6.00000 + 3.46410i −0.295599 + 0.170664i
\(413\) 39.1918 1.92850
\(414\) 0 0
\(415\) 34.6410i 1.70046i
\(416\) 9.79796 + 16.9706i 0.480384 + 0.832050i
\(417\) 0 0
\(418\) −8.00000 + 13.8564i −0.391293 + 0.677739i
\(419\) 19.7990i 0.967244i 0.875277 + 0.483622i \(0.160679\pi\)
−0.875277 + 0.483622i \(0.839321\pi\)
\(420\) 0 0
\(421\) 24.2487i 1.18181i −0.806741 0.590905i \(-0.798771\pi\)
0.806741 0.590905i \(-0.201229\pi\)
\(422\) −24.4949 14.1421i −1.19239 0.688428i
\(423\) 0 0
\(424\) 20.7846i 1.00939i
\(425\) 1.41421i 0.0685994i
\(426\) 0 0
\(427\) −48.0000 −2.32288
\(428\) −19.5959 + 11.3137i −0.947204 + 0.546869i
\(429\) 0 0
\(430\) −24.0000 13.8564i −1.15738 0.668215i
\(431\) −14.6969 −0.707927 −0.353963 0.935259i \(-0.615166\pi\)
−0.353963 + 0.935259i \(0.615166\pi\)
\(432\) 0 0
\(433\) −22.0000 −1.05725 −0.528626 0.848855i \(-0.677293\pi\)
−0.528626 + 0.848855i \(0.677293\pi\)
\(434\) −14.6969 8.48528i −0.705476 0.407307i
\(435\) 0 0
\(436\) −18.0000 + 10.3923i −0.862044 + 0.497701i
\(437\) 19.5959 0.937400
\(438\) 0 0
\(439\) 3.46410i 0.165333i −0.996577 0.0826663i \(-0.973656\pi\)
0.996577 0.0826663i \(-0.0263436\pi\)
\(440\) 19.5959 0.934199
\(441\) 0 0
\(442\) −6.00000 3.46410i −0.285391 0.164771i
\(443\) 2.82843i 0.134383i 0.997740 + 0.0671913i \(0.0214038\pi\)
−0.997740 + 0.0671913i \(0.978596\pi\)
\(444\) 0 0
\(445\) 17.3205i 0.821071i
\(446\) 12.2474 21.2132i 0.579934 1.00447i
\(447\) 0 0
\(448\) 27.7128i 1.30931i
\(449\) 24.0416i 1.13459i 0.823513 + 0.567297i \(0.192011\pi\)
−0.823513 + 0.567297i \(0.807989\pi\)
\(450\) 0 0
\(451\) 4.00000 0.188353
\(452\) 31.8434 18.3848i 1.49779 0.864747i
\(453\) 0 0
\(454\) 2.00000 3.46410i 0.0938647 0.162578i
\(455\) 29.3939 1.37801
\(456\) 0 0
\(457\) 8.00000 0.374224 0.187112 0.982339i \(-0.440087\pi\)
0.187112 + 0.982339i \(0.440087\pi\)
\(458\) −12.2474 + 21.2132i −0.572286 + 0.991228i
\(459\) 0 0
\(460\) −12.0000 20.7846i −0.559503 0.969087i
\(461\) −17.1464 −0.798589 −0.399294 0.916823i \(-0.630745\pi\)
−0.399294 + 0.916823i \(0.630745\pi\)
\(462\) 0 0
\(463\) 17.3205i 0.804952i −0.915430 0.402476i \(-0.868150\pi\)
0.915430 0.402476i \(-0.131850\pi\)
\(464\) 4.89898 8.48528i 0.227429 0.393919i
\(465\) 0 0
\(466\) −1.00000 + 1.73205i −0.0463241 + 0.0802357i
\(467\) 36.7696i 1.70149i 0.525577 + 0.850746i \(0.323849\pi\)
−0.525577 + 0.850746i \(0.676151\pi\)
\(468\) 0 0
\(469\) 13.8564i 0.639829i
\(470\) −14.6969 8.48528i −0.677919 0.391397i
\(471\) 0 0
\(472\) 32.0000 1.47292
\(473\) 22.6274i 1.04041i
\(474\) 0 0
\(475\) −4.00000 −0.183533
\(476\) −4.89898 8.48528i −0.224544 0.388922i
\(477\) 0 0
\(478\) −12.0000 6.92820i −0.548867 0.316889i
\(479\) −24.4949 −1.11920 −0.559600 0.828763i \(-0.689045\pi\)
−0.559600 + 0.828763i \(0.689045\pi\)
\(480\) 0 0
\(481\) 0 0
\(482\) 34.2929 + 19.7990i 1.56200 + 0.901819i
\(483\) 0 0
\(484\) 3.00000 + 5.19615i 0.136364 + 0.236189i
\(485\) 19.5959 0.889805
\(486\) 0 0
\(487\) 10.3923i 0.470920i −0.971884 0.235460i \(-0.924340\pi\)
0.971884 0.235460i \(-0.0756597\pi\)
\(488\) −39.1918 −1.77413
\(489\) 0 0
\(490\) 15.0000 + 8.66025i 0.677631 + 0.391230i
\(491\) 39.5980i 1.78703i −0.449032 0.893516i \(-0.648231\pi\)
0.449032 0.893516i \(-0.351769\pi\)
\(492\) 0 0
\(493\) 3.46410i 0.156015i
\(494\) −9.79796 + 16.9706i −0.440831 + 0.763542i
\(495\) 0 0
\(496\) −12.0000 6.92820i −0.538816 0.311086i
\(497\) 50.9117i 2.28370i
\(498\) 0 0
\(499\) 32.0000 1.43252 0.716258 0.697835i \(-0.245853\pi\)
0.716258 + 0.697835i \(0.245853\pi\)
\(500\) −9.79796 16.9706i −0.438178 0.758947i
\(501\) 0 0
\(502\) −10.0000 + 17.3205i −0.446322 + 0.773052i
\(503\) −14.6969 −0.655304 −0.327652 0.944798i \(-0.606257\pi\)
−0.327652 + 0.944798i \(0.606257\pi\)
\(504\) 0 0
\(505\) −6.00000 −0.266996
\(506\) −9.79796 + 16.9706i −0.435572 + 0.754434i
\(507\) 0 0
\(508\) 18.0000 10.3923i 0.798621 0.461084i
\(509\) −41.6413 −1.84572 −0.922860 0.385136i \(-0.874154\pi\)
−0.922860 + 0.385136i \(0.874154\pi\)
\(510\) 0 0
\(511\) 13.8564i 0.612971i
\(512\) 22.6274i 1.00000i
\(513\) 0 0
\(514\) 17.0000 29.4449i 0.749838 1.29876i
\(515\) 8.48528i 0.373906i
\(516\) 0 0
\(517\) 13.8564i 0.609404i
\(518\) 0 0
\(519\) 0 0
\(520\) 24.0000 1.05247
\(521\) 26.8701i 1.17720i −0.808425 0.588599i \(-0.799680\pi\)
0.808425 0.588599i \(-0.200320\pi\)
\(522\) 0 0
\(523\) 20.0000 0.874539 0.437269 0.899331i \(-0.355946\pi\)
0.437269 + 0.899331i \(0.355946\pi\)
\(524\) 9.79796 5.65685i 0.428026 0.247121i
\(525\) 0 0
\(526\) 12.0000 + 6.92820i 0.523225 + 0.302084i
\(527\) 4.89898 0.213403
\(528\) 0 0
\(529\) 1.00000 0.0434783
\(530\) 22.0454 + 12.7279i 0.957591 + 0.552866i
\(531\) 0 0
\(532\) −24.0000 + 13.8564i −1.04053 + 0.600751i
\(533\) 4.89898 0.212198
\(534\) 0 0
\(535\) 27.7128i 1.19813i
\(536\) 11.3137i 0.488678i
\(537\) 0 0
\(538\) 9.00000 + 5.19615i 0.388018 + 0.224022i
\(539\) 14.1421i 0.609145i
\(540\) 0 0
\(541\) 10.3923i 0.446800i 0.974727 + 0.223400i \(0.0717156\pi\)
−0.974727 + 0.223400i \(0.928284\pi\)
\(542\) 22.0454 38.1838i 0.946931 1.64013i
\(543\) 0 0
\(544\) −4.00000 6.92820i −0.171499 0.297044i
\(545\) 25.4558i 1.09041i
\(546\) 0 0
\(547\) 8.00000 0.342055 0.171028 0.985266i \(-0.445291\pi\)
0.171028 + 0.985266i \(0.445291\pi\)
\(548\) 17.1464 9.89949i 0.732459 0.422885i
\(549\) 0 0
\(550\) 2.00000 3.46410i 0.0852803 0.147710i
\(551\) 9.79796 0.417407
\(552\) 0 0
\(553\) −12.0000 −0.510292
\(554\) 12.2474 21.2132i 0.520344 0.901263i
\(555\) 0 0
\(556\) −4.00000 6.92820i −0.169638 0.293821i
\(557\) −7.34847 −0.311365 −0.155682 0.987807i \(-0.549758\pi\)
−0.155682 + 0.987807i \(0.549758\pi\)
\(558\) 0 0
\(559\) 27.7128i 1.17213i
\(560\) 29.3939 + 16.9706i 1.24212 + 0.717137i
\(561\) 0 0
\(562\) 17.0000 29.4449i 0.717102 1.24206i
\(563\) 14.1421i 0.596020i −0.954563 0.298010i \(-0.903677\pi\)
0.954563 0.298010i \(-0.0963229\pi\)
\(564\) 0 0
\(565\) 45.0333i 1.89457i
\(566\) 19.5959 + 11.3137i 0.823678 + 0.475551i
\(567\) 0 0
\(568\) 41.5692i 1.74421i
\(569\) 9.89949i 0.415008i −0.978234 0.207504i \(-0.933466\pi\)
0.978234 0.207504i \(-0.0665341\pi\)
\(570\) 0 0
\(571\) −40.0000 −1.67395 −0.836974 0.547243i \(-0.815677\pi\)
−0.836974 + 0.547243i \(0.815677\pi\)
\(572\) −9.79796 16.9706i −0.409673 0.709575i
\(573\) 0 0
\(574\) 6.00000 + 3.46410i 0.250435 + 0.144589i
\(575\) −4.89898 −0.204302
\(576\) 0 0
\(577\) 14.0000 0.582828 0.291414 0.956597i \(-0.405874\pi\)
0.291414 + 0.956597i \(0.405874\pi\)
\(578\) −18.3712 10.6066i −0.764140 0.441176i
\(579\) 0 0
\(580\) −6.00000 10.3923i −0.249136 0.431517i
\(581\) −48.9898 −2.03244
\(582\) 0 0
\(583\) 20.7846i 0.860811i
\(584\) 11.3137i 0.468165i
\(585\) 0 0
\(586\) 33.0000 + 19.0526i 1.36322 + 0.787054i
\(587\) 22.6274i 0.933933i −0.884275 0.466967i \(-0.845347\pi\)
0.884275 0.466967i \(-0.154653\pi\)
\(588\) 0 0
\(589\) 13.8564i 0.570943i
\(590\) 19.5959 33.9411i 0.806751 1.39733i
\(591\) 0 0
\(592\) 0 0
\(593\) 7.07107i 0.290374i 0.989404 + 0.145187i \(0.0463784\pi\)
−0.989404 + 0.145187i \(0.953622\pi\)
\(594\) 0 0
\(595\) −12.0000 −0.491952
\(596\) 17.1464 + 29.6985i 0.702345 + 1.21650i
\(597\) 0 0
\(598\) −12.0000 + 20.7846i −0.490716 + 0.849946i
\(599\) −4.89898 −0.200167 −0.100083 0.994979i \(-0.531911\pi\)
−0.100083 + 0.994979i \(0.531911\pi\)
\(600\) 0 0
\(601\) −10.0000 −0.407909 −0.203954 0.978980i \(-0.565379\pi\)
−0.203954 + 0.978980i \(0.565379\pi\)
\(602\) −19.5959 + 33.9411i −0.798670 + 1.38334i
\(603\) 0 0
\(604\) 6.00000 3.46410i 0.244137 0.140952i
\(605\) 7.34847 0.298758
\(606\) 0 0
\(607\) 45.0333i 1.82785i 0.405887 + 0.913923i \(0.366962\pi\)
−0.405887 + 0.913923i \(0.633038\pi\)
\(608\) −19.5959 + 11.3137i −0.794719 + 0.458831i
\(609\) 0 0
\(610\) −24.0000 + 41.5692i −0.971732 + 1.68309i
\(611\) 16.9706i 0.686555i
\(612\) 0 0
\(613\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(614\) 4.89898 + 2.82843i 0.197707 + 0.114146i
\(615\) 0 0
\(616\) 27.7128i 1.11658i
\(617\) 24.0416i 0.967880i 0.875101 + 0.483940i \(0.160795\pi\)
−0.875101 + 0.483940i \(0.839205\pi\)
\(618\) 0 0
\(619\) 8.00000 0.321547 0.160774 0.986991i \(-0.448601\pi\)
0.160774 + 0.986991i \(0.448601\pi\)
\(620\) −14.6969 + 8.48528i −0.590243 + 0.340777i
\(621\) 0 0
\(622\) −12.0000 6.92820i −0.481156 0.277796i
\(623\) 24.4949 0.981367
\(624\) 0 0
\(625\) −29.0000 −1.16000
\(626\) 12.2474 + 7.07107i 0.489506 + 0.282617i
\(627\) 0 0
\(628\) −24.0000 + 13.8564i −0.957704 + 0.552931i
\(629\) 0 0
\(630\) 0 0
\(631\) 31.1769i 1.24113i 0.784154 + 0.620567i \(0.213097\pi\)
−0.784154 + 0.620567i \(0.786903\pi\)
\(632\) −9.79796 −0.389742
\(633\) 0 0
\(634\) −15.0000 8.66025i −0.595726 0.343943i
\(635\) 25.4558i 1.01018i
\(636\) 0 0
\(637\) 17.3205i 0.686264i
\(638\) −4.89898 + 8.48528i −0.193952 + 0.335936i
\(639\) 0 0
\(640\) 24.0000 + 13.8564i 0.948683 + 0.547723i
\(641\) 15.5563i 0.614439i 0.951639 + 0.307219i \(0.0993986\pi\)
−0.951639 + 0.307219i \(0.900601\pi\)
\(642\) 0 0
\(643\) 32.0000 1.26196 0.630978 0.775800i \(-0.282654\pi\)
0.630978 + 0.775800i \(0.282654\pi\)
\(644\) −29.3939 + 16.9706i −1.15828 + 0.668734i
\(645\) 0 0
\(646\) 4.00000 6.92820i 0.157378 0.272587i
\(647\) −14.6969 −0.577796 −0.288898 0.957360i \(-0.593289\pi\)
−0.288898 + 0.957360i \(0.593289\pi\)
\(648\) 0 0
\(649\) −32.0000 −1.25611
\(650\) 2.44949 4.24264i 0.0960769 0.166410i
\(651\) 0 0
\(652\) −16.0000 27.7128i −0.626608 1.08532i
\(653\) 17.1464 0.670992 0.335496 0.942042i \(-0.391096\pi\)
0.335496 + 0.942042i \(0.391096\pi\)
\(654\) 0 0
\(655\) 13.8564i 0.541415i
\(656\) 4.89898 + 2.82843i 0.191273 + 0.110432i
\(657\) 0 0
\(658\) −12.0000 + 20.7846i −0.467809 + 0.810268i
\(659\) 11.3137i 0.440720i 0.975419 + 0.220360i \(0.0707231\pi\)
−0.975419 + 0.220360i \(0.929277\pi\)
\(660\) 0 0
\(661\) 13.8564i 0.538952i 0.963007 + 0.269476i \(0.0868504\pi\)
−0.963007 + 0.269476i \(0.913150\pi\)
\(662\) 4.89898 + 2.82843i 0.190404 + 0.109930i
\(663\) 0 0
\(664\) −40.0000 −1.55230
\(665\) 33.9411i 1.31618i
\(666\) 0 0
\(667\) 12.0000 0.464642
\(668\) −19.5959 33.9411i −0.758189 1.31322i
\(669\) 0 0
\(670\) 12.0000 + 6.92820i 0.463600 + 0.267660i
\(671\) 39.1918 1.51298
\(672\) 0 0
\(673\) 14.0000 0.539660 0.269830 0.962908i \(-0.413032\pi\)
0.269830 + 0.962908i \(0.413032\pi\)
\(674\) 4.89898 + 2.82843i 0.188702 + 0.108947i
\(675\) 0 0
\(676\) 1.00000 + 1.73205i 0.0384615 + 0.0666173i
\(677\) −17.1464 −0.658991 −0.329495 0.944157i \(-0.606879\pi\)
−0.329495 + 0.944157i \(0.606879\pi\)
\(678\) 0 0
\(679\) 27.7128i 1.06352i
\(680\) −9.79796 −0.375735
\(681\) 0 0
\(682\) 12.0000 + 6.92820i 0.459504 + 0.265295i
\(683\) 36.7696i 1.40695i 0.710721 + 0.703474i \(0.248369\pi\)
−0.710721 + 0.703474i \(0.751631\pi\)
\(684\) 0 0
\(685\) 24.2487i 0.926496i
\(686\) −4.89898 + 8.48528i −0.187044 + 0.323970i
\(687\) 0 0
\(688\) −16.0000 + 27.7128i −0.609994 + 1.05654i
\(689\) 25.4558i 0.969790i
\(690\) 0 0
\(691\) 32.0000 1.21734 0.608669 0.793424i \(-0.291704\pi\)
0.608669 + 0.793424i \(0.291704\pi\)
\(692\) −2.44949 4.24264i −0.0931156 0.161281i
\(693\) 0 0
\(694\) −10.0000 + 17.3205i −0.379595 + 0.657477i
\(695\) −9.79796 −0.371658
\(696\) 0 0
\(697\) −2.00000 −0.0757554
\(698\) 19.5959 33.9411i 0.741716 1.28469i
\(699\) 0 0
\(700\) 6.00000 3.46410i 0.226779 0.130931i
\(701\) 7.34847 0.277548 0.138774 0.990324i \(-0.455684\pi\)
0.138774 + 0.990324i \(0.455684\pi\)
\(702\) 0 0
\(703\) 0 0
\(704\) 22.6274i 0.852803i
\(705\) 0 0
\(706\) 11.0000 19.0526i 0.413990 0.717053i
\(707\) 8.48528i 0.319122i
\(708\) 0 0
\(709\) 3.46410i 0.130097i −0.997882 0.0650485i \(-0.979280\pi\)
0.997882 0.0650485i \(-0.0207202\pi\)
\(710\) −44.0908 25.4558i −1.65470 0.955341i
\(711\) 0 0
\(712\) 20.0000 0.749532
\(713\) 16.9706i 0.635553i
\(714\) 0 0
\(715\) −24.0000 −0.897549
\(716\) 9.79796 5.65685i 0.366167 0.211407i
\(717\) 0 0
\(718\) 18.0000 + 10.3923i 0.671754 + 0.387837i
\(719\) 44.0908 1.64431 0.822155 0.569264i \(-0.192772\pi\)
0.822155 + 0.569264i \(0.192772\pi\)
\(720\) 0 0
\(721\) 12.0000 0.446903
\(722\) 3.67423 + 2.12132i 0.136741 + 0.0789474i
\(723\) 0 0
\(724\) 18.0000 10.3923i 0.668965 0.386227i
\(725\) −2.44949 −0.0909718
\(726\) 0 0
\(727\) 24.2487i 0.899335i −0.893196 0.449667i \(-0.851542\pi\)
0.893196 0.449667i \(-0.148458\pi\)
\(728\) 33.9411i 1.25794i
\(729\) 0 0
\(730\) 12.0000 + 6.92820i 0.444140 + 0.256424i
\(731\) 11.3137i 0.418453i
\(732\) 0 0
\(733\) 38.1051i 1.40744i −0.710475 0.703722i \(-0.751520\pi\)
0.710475 0.703722i \(-0.248480\pi\)
\(734\) −17.1464 + 29.6985i −0.632886 + 1.09619i
\(735\) 0 0
\(736\) −24.0000 + 13.8564i −0.884652 + 0.510754i
\(737\) 11.3137i 0.416746i
\(738\) 0 0
\(739\) −40.0000 −1.47142 −0.735712 0.677295i \(-0.763152\pi\)
−0.735712 + 0.677295i \(0.763152\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 18.0000 31.1769i 0.660801 1.14454i
\(743\) 39.1918 1.43781 0.718905 0.695109i \(-0.244644\pi\)
0.718905 + 0.695109i \(0.244644\pi\)
\(744\) 0 0
\(745\) 42.0000 1.53876
\(746\) 9.79796 16.9706i 0.358729 0.621336i
\(747\) 0 0
\(748\) 4.00000 + 6.92820i 0.146254 + 0.253320i
\(749\) 39.1918 1.43204
\(750\) 0 0
\(751\) 3.46410i 0.126407i 0.998001 + 0.0632034i \(0.0201317\pi\)
−0.998001 + 0.0632034i \(0.979868\pi\)
\(752\) −9.79796 + 16.9706i −0.357295 + 0.618853i
\(753\) 0 0
\(754\) −6.00000 + 10.3923i −0.218507 + 0.378465i
\(755\) 8.48528i 0.308811i
\(756\) 0 0
\(757\) 10.3923i 0.377715i 0.982005 + 0.188857i \(0.0604784\pi\)
−0.982005 + 0.188857i \(0.939522\pi\)
\(758\) 4.89898 + 2.82843i 0.177939 + 0.102733i
\(759\) 0 0
\(760\) 27.7128i 1.00525i
\(761\) 18.3848i 0.666448i −0.942848 0.333224i \(-0.891864\pi\)
0.942848 0.333224i \(-0.108136\pi\)
\(762\) 0 0
\(763\) 36.0000 1.30329
\(764\) 19.5959 + 33.9411i 0.708955 + 1.22795i
\(765\) 0 0
\(766\) −12.0000 6.92820i −0.433578 0.250326i
\(767\) −39.1918 −1.41514
\(768\) 0 0
\(769\) 2.00000 0.0721218 0.0360609 0.999350i \(-0.488519\pi\)
0.0360609 + 0.999350i \(0.488519\pi\)
\(770\) −29.3939 16.9706i −1.05928 0.611577i
\(771\) 0 0
\(772\) 14.0000 + 24.2487i 0.503871 + 0.872730i
\(773\) 22.0454 0.792918 0.396459 0.918052i \(-0.370239\pi\)
0.396459 + 0.918052i \(0.370239\pi\)
\(774\) 0 0
\(775\) 3.46410i 0.124434i
\(776\) 22.6274i 0.812277i
\(777\) 0 0
\(778\) −33.0000 19.0526i −1.18311 0.683067i
\(779\) 5.65685i 0.202678i
\(780\) 0 0
\(781\) 41.5692i 1.48746i
\(782\) 4.89898 8.48528i 0.175187 0.303433i
\(783\) 0 0
\(784\) 10.0000 17.3205i 0.357143 0.618590i
\(785\) 33.9411i 1.21141i
\(786\) 0 0
\(787\) 20.0000 0.712923 0.356462 0.934310i \(-0.383983\pi\)
0.356462 + 0.934310i \(0.383983\pi\)
\(788\) 7.34847 + 12.7279i 0.261778 + 0.453413i
\(789\) 0 0
\(790\) −6.00000 + 10.3923i −0.213470 + 0.369742i
\(791\) −63.6867 −2.26444
\(792\) 0 0
\(793\) 48.0000 1.70453
\(794\) 0 0
\(795\) 0 0
\(796\) 18.0000 10.3923i 0.637993 0.368345i
\(797\) −12.2474 −0.433827 −0.216913 0.976191i \(-0.569599\pi\)
−0.216913 + 0.976191i \(0.569599\pi\)
\(798\) 0 0
\(799\) 6.92820i 0.245102i
\(800\) 4.89898 2.82843i 0.173205 0.100000i
\(801\) 0 0
\(802\) −1.00000 + 1.73205i −0.0353112 + 0.0611608i
\(803\) 11.3137i 0.399252i
\(804\) 0 0
\(805\) 41.5692i 1.46512i
\(806\) 14.6969 + 8.48528i 0.517678 + 0.298881i
\(807\) 0 0
\(808\) 6.92820i 0.243733i
\(809\) 1.41421i 0.0497211i −0.999691 0.0248606i \(-0.992086\pi\)
0.999691 0.0248606i \(-0.00791417\pi\)
\(810\) 0 0
\(811\) −4.00000 −0.140459 −0.0702295 0.997531i \(-0.522373\pi\)
−0.0702295 + 0.997531i \(0.522373\pi\)
\(812\) −14.6969 + 8.48528i −0.515761 + 0.297775i
\(813\) 0 0
\(814\) 0 0
\(815\) −39.1918 −1.37283
\(816\) 0 0
\(817\) −32.0000 −1.11954
\(818\) −39.1918 22.6274i −1.37031 0.791149i
\(819\) 0 0
\(820\) 6.00000 3.46410i 0.209529 0.120972i
\(821\) −2.44949 −0.0854878 −0.0427439 0.999086i \(-0.513610\pi\)
−0.0427439 + 0.999086i \(0.513610\pi\)
\(822\) 0 0
\(823\) 17.3205i 0.603755i −0.953347 0.301877i \(-0.902387\pi\)
0.953347 0.301877i \(-0.0976134\pi\)
\(824\) 9.79796 0.341328
\(825\) 0 0
\(826\) −48.0000 27.7128i −1.67013 0.964252i
\(827\) 5.65685i 0.196708i −0.995151 0.0983540i \(-0.968642\pi\)
0.995151 0.0983540i \(-0.0313578\pi\)
\(828\) 0 0
\(829\) 10.3923i 0.360940i 0.983581 + 0.180470i \(0.0577618\pi\)
−0.983581 + 0.180470i \(0.942238\pi\)
\(830\) −24.4949 + 42.4264i −0.850230 + 1.47264i
\(831\) 0 0
\(832\) 27.7128i 0.960769i
\(833\) 7.07107i 0.244998i
\(834\) 0 0
\(835\) −48.0000 −1.66111
\(836\) 19.5959 11.3137i 0.677739 0.391293i
\(837\) 0 0
\(838\) 14.0000 24.2487i 0.483622 0.837658i
\(839\) 4.89898 0.169132 0.0845658 0.996418i \(-0.473050\pi\)
0.0845658 + 0.996418i \(0.473050\pi\)
\(840\) 0 0
\(841\) −23.0000 −0.793103
\(842\) −17.1464 + 29.6985i −0.590905 + 1.02348i
\(843\) 0 0
\(844\) 20.0000 + 34.6410i 0.688428 + 1.19239i
\(845\) 2.44949 0.0842650
\(846\) 0 0
\(847\) 10.3923i 0.357084i
\(848\) 14.6969 25.4558i 0.504695 0.874157i
\(849\) 0 0
\(850\) −1.00000 + 1.73205i −0.0342997 + 0.0594089i
\(851\) 0 0
\(852\) 0 0
\(853\) 13.8564i 0.474434i −0.971457 0.237217i \(-0.923765\pi\)
0.971457 0.237217i \(-0.0762353\pi\)
\(854\) 58.7878 + 33.9411i 2.01168 + 1.16144i
\(855\) 0 0
\(856\) 32.0000 1.09374
\(857\) 1.41421i 0.0483086i −0.999708 0.0241543i \(-0.992311\pi\)
0.999708 0.0241543i \(-0.00768930\pi\)
\(858\) 0 0
\(859\) −40.0000 −1.36478 −0.682391 0.730987i \(-0.739060\pi\)
−0.682391 + 0.730987i \(0.739060\pi\)
\(860\) 19.5959 + 33.9411i 0.668215 + 1.15738i
\(861\) 0 0
\(862\) 18.0000 + 10.3923i 0.613082 + 0.353963i
\(863\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(864\) 0 0
\(865\) −6.00000 −0.204006
\(866\) 26.9444 + 15.5563i 0.915608 + 0.528626i
\(867\) 0 0
\(868\) 12.0000 + 20.7846i 0.407307 + 0.705476i
\(869\) 9.79796 0.332373
\(870\) 0 0
\(871\) 13.8564i 0.469506i
\(872\) 29.3939 0.995402
\(873\) 0 0
\(874\) −24.0000 13.8564i −0.811812 0.468700i
\(875\) 33.9411i 1.14742i
\(876\) 0 0
\(877\) 55.4256i 1.87159i 0.352544 + 0.935795i \(0.385317\pi\)
−0.352544 + 0.935795i \(0.614683\pi\)
\(878\) −2.44949 + 4.24264i −0.0826663 + 0.143182i
\(879\) 0 0
\(880\) −24.0000 13.8564i −0.809040 0.467099i
\(881\) 43.8406i 1.47703i −0.674238 0.738514i \(-0.735528\pi\)
0.674238 0.738514i \(-0.264472\pi\)
\(882\) 0 0
\(883\) −40.0000 −1.34611 −0.673054 0.739594i \(-0.735018\pi\)
−0.673054 + 0.739594i \(0.735018\pi\)
\(884\) 4.89898 + 8.48528i 0.164771 + 0.285391i
\(885\) 0 0
\(886\) 2.00000 3.46410i 0.0671913 0.116379i
\(887\) 9.79796 0.328983 0.164492 0.986378i \(-0.447402\pi\)
0.164492 + 0.986378i \(0.447402\pi\)
\(888\) 0 0
\(889\) −36.0000 −1.20740
\(890\) 12.2474 21.2132i 0.410535 0.711068i
\(891\) 0 0
\(892\) −30.0000 + 17.3205i −1.00447 + 0.579934i
\(893\) −19.5959 −0.655752
\(894\) 0 0
\(895\) 13.8564i 0.463169i
\(896\) 19.5959 33.9411i 0.654654 1.13389i
\(897\) 0 0
\(898\) 17.0000 29.4449i 0.567297 0.982588i
\(899\) 8.48528i 0.283000i
\(900\) 0 0
\(901\) 10.3923i 0.346218i
\(902\) −4.89898 2.82843i −0.163118 0.0941763i
\(903\) 0 0
\(904\) −52.0000 −1.72949
\(905\) 25.4558i 0.846181i
\(906\) 0 0
\(907\) 8.00000 0.265636 0.132818 0.991140i \(-0.457597\pi\)
0.132818 + 0.991140i \(0.457597\pi\)
\(908\) −4.89898 + 2.82843i −0.162578 + 0.0938647i
\(909\) 0 0
\(910\) −36.0000 20.7846i −1.19339 0.689003i
\(911\) −39.1918 −1.29848 −0.649242 0.760582i \(-0.724914\pi\)
−0.649242 + 0.760582i \(0.724914\pi\)
\(912\) 0 0
\(913\) 40.0000 1.32381
\(914\) −9.79796 5.65685i −0.324088 0.187112i
\(915\) 0 0
\(916\) 30.0000 17.3205i 0.991228 0.572286i
\(917\) −19.5959 −0.647114
\(918\) 0 0
\(919\) 10.3923i 0.342811i 0.985201 + 0.171405i \(0.0548307\pi\)
−0.985201 + 0.171405i \(0.945169\pi\)
\(920\) 33.9411i 1.11901i
\(921\) 0 0
\(922\) 21.0000 + 12.1244i 0.691598 + 0.399294i
\(923\) 50.9117i 1.67578i
\(924\) 0 0
\(925\) 0 0
\(926\) −12.2474 + 21.2132i −0.402476 + 0.697109i
\(927\) 0 0
\(928\) −12.0000 + 6.92820i −0.393919 + 0.227429i
\(929\) 1.41421i 0.0463988i −0.999731 0.0231994i \(-0.992615\pi\)
0.999731 0.0231994i \(-0.00738527\pi\)
\(930\) 0 0
\(931\) 20.0000 0.655474
\(932\) 2.44949 1.41421i 0.0802357 0.0463241i
\(933\) 0 0
\(934\) 26.0000 45.0333i 0.850746 1.47354i
\(935\) 9.79796 0.320428
\(936\) 0 0
\(937\) 2.00000 0.0653372 0.0326686 0.999466i \(-0.489599\pi\)
0.0326686 + 0.999466i \(0.489599\pi\)
\(938\) 9.79796 16.9706i 0.319915 0.554109i
\(939\) 0 0
\(940\) 12.0000 + 20.7846i 0.391397 + 0.677919i
\(941\) 2.44949 0.0798511 0.0399255 0.999203i \(-0.487288\pi\)
0.0399255 + 0.999203i \(0.487288\pi\)
\(942\) 0 0
\(943\) 6.92820i 0.225613i
\(944\) −39.1918 22.6274i −1.27559 0.736460i
\(945\) 0 0
\(946\) 16.0000 27.7128i 0.520205 0.901021i
\(947\) 22.6274i 0.735292i −0.929966 0.367646i \(-0.880164\pi\)
0.929966 0.367646i \(-0.119836\pi\)
\(948\) 0 0
\(949\) 13.8564i 0.449798i
\(950\) 4.89898 + 2.82843i 0.158944 + 0.0917663i
\(951\) 0 0
\(952\) 13.8564i 0.449089i
\(953\) 26.8701i 0.870407i −0.900332 0.435203i \(-0.856677\pi\)
0.900332 0.435203i \(-0.143323\pi\)
\(954\) 0 0
\(955\) 48.0000 1.55324
\(956\) 9.79796 + 16.9706i 0.316889 + 0.548867i
\(957\) 0 0
\(958\) 30.0000 + 17.3205i 0.969256 + 0.559600i
\(959\) −34.2929 −1.10737
\(960\) 0 0
\(961\) 19.0000 0.612903
\(962\) 0 0
\(963\) 0 0
\(964\) −28.0000 48.4974i −0.901819 1.56200i
\(965\) 34.2929 1.10393
\(966\) 0 0
\(967\) 45.0333i 1.44817i 0.689709 + 0.724087i \(0.257739\pi\)
−0.689709 + 0.724087i \(0.742261\pi\)
\(968\) 8.48528i 0.272727i
\(969\) 0 0
\(970\) −24.0000 13.8564i −0.770594 0.444902i
\(971\) 31.1127i 0.998454i −0.866471 0.499227i \(-0.833617\pi\)
0.866471 0.499227i \(-0.166383\pi\)
\(972\) 0 0
\(973\) 13.8564i 0.444216i
\(974\) −7.34847 + 12.7279i −0.235460 + 0.407829i
\(975\) 0 0
\(976\) 48.0000 + 27.7128i 1.53644 + 0.887066i
\(977\) 24.0416i 0.769160i 0.923092 + 0.384580i \(0.125654\pi\)
−0.923092 + 0.384580i \(0.874346\pi\)
\(978\) 0 0
\(979\) −20.0000 −0.639203
\(980\) −12.2474 21.2132i −0.391230 0.677631i
\(981\) 0 0
\(982\) −28.0000 + 48.4974i −0.893516 + 1.54761i
\(983\) 48.9898 1.56253 0.781266 0.624198i \(-0.214574\pi\)
0.781266 + 0.624198i \(0.214574\pi\)
\(984\) 0 0
\(985\) 18.0000 0.573528
\(986\) 2.44949 4.24264i 0.0780076 0.135113i
\(987\) 0 0
\(988\) 24.0000 13.8564i 0.763542 0.440831i
\(989\) −39.1918 −1.24623
\(990\) 0 0
\(991\) 51.9615i 1.65061i −0.564686 0.825306i \(-0.691003\pi\)
0.564686 0.825306i \(-0.308997\pi\)
\(992\) 9.79796 + 16.9706i 0.311086 + 0.538816i
\(993\) 0 0
\(994\) −36.0000 + 62.3538i −1.14185 + 1.97774i
\(995\) 25.4558i 0.807005i
\(996\) 0 0
\(997\) 13.8564i 0.438837i −0.975631 0.219418i \(-0.929584\pi\)
0.975631 0.219418i \(-0.0704160\pi\)
\(998\) −39.1918 22.6274i −1.24060 0.716258i
\(999\) 0 0
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 72.2.f.a.35.1 4
3.2 odd 2 inner 72.2.f.a.35.4 yes 4
4.3 odd 2 288.2.f.a.143.4 4
5.2 odd 4 1800.2.m.c.899.6 8
5.3 odd 4 1800.2.m.c.899.3 8
5.4 even 2 1800.2.b.c.251.4 4
8.3 odd 2 inner 72.2.f.a.35.3 yes 4
8.5 even 2 288.2.f.a.143.1 4
9.2 odd 6 648.2.l.a.539.1 4
9.4 even 3 648.2.l.c.107.2 4
9.5 odd 6 648.2.l.c.107.1 4
9.7 even 3 648.2.l.a.539.2 4
12.11 even 2 288.2.f.a.143.2 4
15.2 even 4 1800.2.m.c.899.4 8
15.8 even 4 1800.2.m.c.899.5 8
15.14 odd 2 1800.2.b.c.251.1 4
16.3 odd 4 2304.2.c.i.2303.1 8
16.5 even 4 2304.2.c.i.2303.8 8
16.11 odd 4 2304.2.c.i.2303.6 8
16.13 even 4 2304.2.c.i.2303.3 8
20.3 even 4 7200.2.m.c.3599.5 8
20.7 even 4 7200.2.m.c.3599.2 8
20.19 odd 2 7200.2.b.c.4751.1 4
24.5 odd 2 288.2.f.a.143.3 4
24.11 even 2 inner 72.2.f.a.35.2 yes 4
36.7 odd 6 2592.2.p.c.2159.1 4
36.11 even 6 2592.2.p.c.2159.2 4
36.23 even 6 2592.2.p.a.431.2 4
36.31 odd 6 2592.2.p.a.431.1 4
40.3 even 4 1800.2.m.c.899.2 8
40.13 odd 4 7200.2.m.c.3599.1 8
40.19 odd 2 1800.2.b.c.251.2 4
40.27 even 4 1800.2.m.c.899.7 8
40.29 even 2 7200.2.b.c.4751.3 4
40.37 odd 4 7200.2.m.c.3599.6 8
48.5 odd 4 2304.2.c.i.2303.4 8
48.11 even 4 2304.2.c.i.2303.2 8
48.29 odd 4 2304.2.c.i.2303.7 8
48.35 even 4 2304.2.c.i.2303.5 8
60.23 odd 4 7200.2.m.c.3599.8 8
60.47 odd 4 7200.2.m.c.3599.3 8
60.59 even 2 7200.2.b.c.4751.2 4
72.5 odd 6 2592.2.p.c.431.1 4
72.11 even 6 648.2.l.c.539.2 4
72.13 even 6 2592.2.p.c.431.2 4
72.29 odd 6 2592.2.p.a.2159.1 4
72.43 odd 6 648.2.l.c.539.1 4
72.59 even 6 648.2.l.a.107.1 4
72.61 even 6 2592.2.p.a.2159.2 4
72.67 odd 6 648.2.l.a.107.2 4
120.29 odd 2 7200.2.b.c.4751.4 4
120.53 even 4 7200.2.m.c.3599.4 8
120.59 even 2 1800.2.b.c.251.3 4
120.77 even 4 7200.2.m.c.3599.7 8
120.83 odd 4 1800.2.m.c.899.8 8
120.107 odd 4 1800.2.m.c.899.1 8
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
72.2.f.a.35.1 4 1.1 even 1 trivial
72.2.f.a.35.2 yes 4 24.11 even 2 inner
72.2.f.a.35.3 yes 4 8.3 odd 2 inner
72.2.f.a.35.4 yes 4 3.2 odd 2 inner
288.2.f.a.143.1 4 8.5 even 2
288.2.f.a.143.2 4 12.11 even 2
288.2.f.a.143.3 4 24.5 odd 2
288.2.f.a.143.4 4 4.3 odd 2
648.2.l.a.107.1 4 72.59 even 6
648.2.l.a.107.2 4 72.67 odd 6
648.2.l.a.539.1 4 9.2 odd 6
648.2.l.a.539.2 4 9.7 even 3
648.2.l.c.107.1 4 9.5 odd 6
648.2.l.c.107.2 4 9.4 even 3
648.2.l.c.539.1 4 72.43 odd 6
648.2.l.c.539.2 4 72.11 even 6
1800.2.b.c.251.1 4 15.14 odd 2
1800.2.b.c.251.2 4 40.19 odd 2
1800.2.b.c.251.3 4 120.59 even 2
1800.2.b.c.251.4 4 5.4 even 2
1800.2.m.c.899.1 8 120.107 odd 4
1800.2.m.c.899.2 8 40.3 even 4
1800.2.m.c.899.3 8 5.3 odd 4
1800.2.m.c.899.4 8 15.2 even 4
1800.2.m.c.899.5 8 15.8 even 4
1800.2.m.c.899.6 8 5.2 odd 4
1800.2.m.c.899.7 8 40.27 even 4
1800.2.m.c.899.8 8 120.83 odd 4
2304.2.c.i.2303.1 8 16.3 odd 4
2304.2.c.i.2303.2 8 48.11 even 4
2304.2.c.i.2303.3 8 16.13 even 4
2304.2.c.i.2303.4 8 48.5 odd 4
2304.2.c.i.2303.5 8 48.35 even 4
2304.2.c.i.2303.6 8 16.11 odd 4
2304.2.c.i.2303.7 8 48.29 odd 4
2304.2.c.i.2303.8 8 16.5 even 4
2592.2.p.a.431.1 4 36.31 odd 6
2592.2.p.a.431.2 4 36.23 even 6
2592.2.p.a.2159.1 4 72.29 odd 6
2592.2.p.a.2159.2 4 72.61 even 6
2592.2.p.c.431.1 4 72.5 odd 6
2592.2.p.c.431.2 4 72.13 even 6
2592.2.p.c.2159.1 4 36.7 odd 6
2592.2.p.c.2159.2 4 36.11 even 6
7200.2.b.c.4751.1 4 20.19 odd 2
7200.2.b.c.4751.2 4 60.59 even 2
7200.2.b.c.4751.3 4 40.29 even 2
7200.2.b.c.4751.4 4 120.29 odd 2
7200.2.m.c.3599.1 8 40.13 odd 4
7200.2.m.c.3599.2 8 20.7 even 4
7200.2.m.c.3599.3 8 60.47 odd 4
7200.2.m.c.3599.4 8 120.53 even 4
7200.2.m.c.3599.5 8 20.3 even 4
7200.2.m.c.3599.6 8 40.37 odd 4
7200.2.m.c.3599.7 8 120.77 even 4
7200.2.m.c.3599.8 8 60.23 odd 4