Properties

Label 360.2.bi.b.49.1
Level $360$
Weight $2$
Character 360.49
Analytic conductor $2.875$
Analytic rank $0$
Dimension $32$
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] = [360,2,Mod(49,360)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(360, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([0, 0, 2, 3]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("360.49");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 360 = 2^{3} \cdot 3^{2} \cdot 5 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 360.bi (of order \(6\), degree \(2\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(2.87461447277\)
Analytic rank: \(0\)
Dimension: \(32\)
Relative dimension: \(16\) over \(\Q(\zeta_{6})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 49.1
Character \(\chi\) \(=\) 360.49
Dual form 360.2.bi.b.169.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.72704 + 0.131617i) q^{3} +(2.23514 - 0.0643013i) q^{5} +(-1.19102 + 0.687633i) q^{7} +(2.96535 - 0.454616i) q^{9} +O(q^{10})\) \(q+(-1.72704 + 0.131617i) q^{3} +(2.23514 - 0.0643013i) q^{5} +(-1.19102 + 0.687633i) q^{7} +(2.96535 - 0.454616i) q^{9} +(-0.00579778 - 0.0100420i) q^{11} +(0.919334 + 0.530778i) q^{13} +(-3.85173 + 0.405234i) q^{15} +1.57910i q^{17} +6.38234 q^{19} +(1.96643 - 1.34433i) q^{21} +(6.37844 + 3.68260i) q^{23} +(4.99173 - 0.287445i) q^{25} +(-5.06146 + 1.17543i) q^{27} +(2.66231 + 4.61126i) q^{29} +(1.15651 - 2.00314i) q^{31} +(0.0113347 + 0.0165800i) q^{33} +(-2.61787 + 1.61354i) q^{35} -10.8828i q^{37} +(-1.65759 - 0.795676i) q^{39} +(-4.09133 + 7.08638i) q^{41} +(2.93252 - 1.69309i) q^{43} +(6.59876 - 1.20681i) q^{45} +(-4.60966 + 2.66139i) q^{47} +(-2.55432 + 4.42422i) q^{49} +(-0.207836 - 2.72717i) q^{51} +1.27370i q^{53} +(-0.0136046 - 0.0220726i) q^{55} +(-11.0226 + 0.840025i) q^{57} +(3.39712 - 5.88399i) q^{59} +(-4.29148 - 7.43306i) q^{61} +(-3.21917 + 2.58053i) q^{63} +(2.08897 + 1.12725i) q^{65} +(-8.16967 - 4.71676i) q^{67} +(-11.5005 - 5.52049i) q^{69} -16.4442 q^{71} -8.32462i q^{73} +(-8.58310 + 1.15343i) q^{75} +(0.0138105 + 0.00797348i) q^{77} +(3.86663 + 6.69719i) q^{79} +(8.58665 - 2.69620i) q^{81} +(4.67610 - 2.69975i) q^{83} +(0.101538 + 3.52951i) q^{85} +(-5.20484 - 7.61343i) q^{87} -12.6835 q^{89} -1.45992 q^{91} +(-1.73370 + 3.61172i) q^{93} +(14.2655 - 0.410393i) q^{95} +(-0.0741723 + 0.0428234i) q^{97} +(-0.0217577 - 0.0271425i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 32 q - 2 q^{5} + 4 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 32 q - 2 q^{5} + 4 q^{9} + 16 q^{11} - 10 q^{15} + 8 q^{19} - 4 q^{21} - 6 q^{25} + 20 q^{29} - 12 q^{31} + 4 q^{35} - 28 q^{39} - 8 q^{41} + 38 q^{45} + 36 q^{49} - 84 q^{51} + 20 q^{55} - 20 q^{61} + 10 q^{65} - 4 q^{69} + 16 q^{71} - 10 q^{75} + 4 q^{79} - 52 q^{81} + 36 q^{85} - 96 q^{89} - 8 q^{91} - 32 q^{95} - 28 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/360\mathbb{Z}\right)^\times\).

\(n\) \(181\) \(217\) \(271\) \(281\)
\(\chi(n)\) \(1\) \(-1\) \(1\) \(e\left(\frac{1}{3}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) −1.72704 + 0.131617i −0.997109 + 0.0759891i
\(4\) 0 0
\(5\) 2.23514 0.0643013i 0.999586 0.0287564i
\(6\) 0 0
\(7\) −1.19102 + 0.687633i −0.450161 + 0.259901i −0.707898 0.706314i \(-0.750357\pi\)
0.257737 + 0.966215i \(0.417023\pi\)
\(8\) 0 0
\(9\) 2.96535 0.454616i 0.988451 0.151539i
\(10\) 0 0
\(11\) −0.00579778 0.0100420i −0.00174810 0.00302779i 0.865150 0.501513i \(-0.167223\pi\)
−0.866898 + 0.498485i \(0.833890\pi\)
\(12\) 0 0
\(13\) 0.919334 + 0.530778i 0.254977 + 0.147211i 0.622041 0.782984i \(-0.286304\pi\)
−0.367064 + 0.930196i \(0.619637\pi\)
\(14\) 0 0
\(15\) −3.85173 + 0.405234i −0.994511 + 0.104631i
\(16\) 0 0
\(17\) 1.57910i 0.382987i 0.981494 + 0.191494i \(0.0613331\pi\)
−0.981494 + 0.191494i \(0.938667\pi\)
\(18\) 0 0
\(19\) 6.38234 1.46421 0.732105 0.681192i \(-0.238538\pi\)
0.732105 + 0.681192i \(0.238538\pi\)
\(20\) 0 0
\(21\) 1.96643 1.34433i 0.429110 0.293357i
\(22\) 0 0
\(23\) 6.37844 + 3.68260i 1.33000 + 0.767874i 0.985299 0.170839i \(-0.0546479\pi\)
0.344698 + 0.938714i \(0.387981\pi\)
\(24\) 0 0
\(25\) 4.99173 0.287445i 0.998346 0.0574891i
\(26\) 0 0
\(27\) −5.06146 + 1.17543i −0.974078 + 0.226212i
\(28\) 0 0
\(29\) 2.66231 + 4.61126i 0.494379 + 0.856289i 0.999979 0.00647886i \(-0.00206230\pi\)
−0.505600 + 0.862768i \(0.668729\pi\)
\(30\) 0 0
\(31\) 1.15651 2.00314i 0.207716 0.359774i −0.743279 0.668982i \(-0.766730\pi\)
0.950995 + 0.309207i \(0.100064\pi\)
\(32\) 0 0
\(33\) 0.0113347 + 0.0165800i 0.00197312 + 0.00288620i
\(34\) 0 0
\(35\) −2.61787 + 1.61354i −0.442501 + 0.272738i
\(36\) 0 0
\(37\) 10.8828i 1.78912i −0.446948 0.894560i \(-0.647489\pi\)
0.446948 0.894560i \(-0.352511\pi\)
\(38\) 0 0
\(39\) −1.65759 0.795676i −0.265427 0.127410i
\(40\) 0 0
\(41\) −4.09133 + 7.08638i −0.638958 + 1.10671i 0.346704 + 0.937975i \(0.387301\pi\)
−0.985662 + 0.168733i \(0.946033\pi\)
\(42\) 0 0
\(43\) 2.93252 1.69309i 0.447204 0.258194i −0.259444 0.965758i \(-0.583539\pi\)
0.706649 + 0.707564i \(0.250206\pi\)
\(44\) 0 0
\(45\) 6.59876 1.20681i 0.983685 0.179900i
\(46\) 0 0
\(47\) −4.60966 + 2.66139i −0.672388 + 0.388203i −0.796981 0.604005i \(-0.793571\pi\)
0.124593 + 0.992208i \(0.460237\pi\)
\(48\) 0 0
\(49\) −2.55432 + 4.42422i −0.364903 + 0.632031i
\(50\) 0 0
\(51\) −0.207836 2.72717i −0.0291028 0.381880i
\(52\) 0 0
\(53\) 1.27370i 0.174956i 0.996166 + 0.0874782i \(0.0278808\pi\)
−0.996166 + 0.0874782i \(0.972119\pi\)
\(54\) 0 0
\(55\) −0.0136046 0.0220726i −0.00183444 0.00297627i
\(56\) 0 0
\(57\) −11.0226 + 0.840025i −1.45998 + 0.111264i
\(58\) 0 0
\(59\) 3.39712 5.88399i 0.442268 0.766031i −0.555589 0.831457i \(-0.687507\pi\)
0.997857 + 0.0654262i \(0.0208407\pi\)
\(60\) 0 0
\(61\) −4.29148 7.43306i −0.549468 0.951706i −0.998311 0.0580954i \(-0.981497\pi\)
0.448843 0.893610i \(-0.351836\pi\)
\(62\) 0 0
\(63\) −3.21917 + 2.58053i −0.405578 + 0.325116i
\(64\) 0 0
\(65\) 2.08897 + 1.12725i 0.259105 + 0.139818i
\(66\) 0 0
\(67\) −8.16967 4.71676i −0.998084 0.576244i −0.0904031 0.995905i \(-0.528816\pi\)
−0.907681 + 0.419661i \(0.862149\pi\)
\(68\) 0 0
\(69\) −11.5005 5.52049i −1.38450 0.664589i
\(70\) 0 0
\(71\) −16.4442 −1.95157 −0.975786 0.218727i \(-0.929809\pi\)
−0.975786 + 0.218727i \(0.929809\pi\)
\(72\) 0 0
\(73\) 8.32462i 0.974323i −0.873312 0.487162i \(-0.838032\pi\)
0.873312 0.487162i \(-0.161968\pi\)
\(74\) 0 0
\(75\) −8.58310 + 1.15343i −0.991091 + 0.133186i
\(76\) 0 0
\(77\) 0.0138105 + 0.00797348i 0.00157385 + 0.000908663i
\(78\) 0 0
\(79\) 3.86663 + 6.69719i 0.435030 + 0.753493i 0.997298 0.0734615i \(-0.0234046\pi\)
−0.562269 + 0.826955i \(0.690071\pi\)
\(80\) 0 0
\(81\) 8.58665 2.69620i 0.954072 0.299577i
\(82\) 0 0
\(83\) 4.67610 2.69975i 0.513269 0.296336i −0.220907 0.975295i \(-0.570902\pi\)
0.734176 + 0.678959i \(0.237569\pi\)
\(84\) 0 0
\(85\) 0.101538 + 3.52951i 0.0110133 + 0.382829i
\(86\) 0 0
\(87\) −5.20484 7.61343i −0.558018 0.816246i
\(88\) 0 0
\(89\) −12.6835 −1.34445 −0.672223 0.740349i \(-0.734660\pi\)
−0.672223 + 0.740349i \(0.734660\pi\)
\(90\) 0 0
\(91\) −1.45992 −0.153041
\(92\) 0 0
\(93\) −1.73370 + 3.61172i −0.179776 + 0.374518i
\(94\) 0 0
\(95\) 14.2655 0.410393i 1.46360 0.0421055i
\(96\) 0 0
\(97\) −0.0741723 + 0.0428234i −0.00753106 + 0.00434806i −0.503761 0.863843i \(-0.668051\pi\)
0.496230 + 0.868191i \(0.334717\pi\)
\(98\) 0 0
\(99\) −0.0217577 0.0271425i −0.00218673 0.00272792i
\(100\) 0 0
\(101\) 7.22526 + 12.5145i 0.718940 + 1.24524i 0.961420 + 0.275085i \(0.0887058\pi\)
−0.242480 + 0.970156i \(0.577961\pi\)
\(102\) 0 0
\(103\) 4.27682 + 2.46922i 0.421407 + 0.243300i 0.695679 0.718353i \(-0.255103\pi\)
−0.274272 + 0.961652i \(0.588437\pi\)
\(104\) 0 0
\(105\) 4.30881 3.13121i 0.420497 0.305575i
\(106\) 0 0
\(107\) 13.5968i 1.31445i −0.753693 0.657227i \(-0.771729\pi\)
0.753693 0.657227i \(-0.228271\pi\)
\(108\) 0 0
\(109\) −9.92265 −0.950417 −0.475209 0.879873i \(-0.657627\pi\)
−0.475209 + 0.879873i \(0.657627\pi\)
\(110\) 0 0
\(111\) 1.43236 + 18.7951i 0.135954 + 1.78395i
\(112\) 0 0
\(113\) 2.19397 + 1.26669i 0.206391 + 0.119160i 0.599633 0.800275i \(-0.295313\pi\)
−0.393242 + 0.919435i \(0.628646\pi\)
\(114\) 0 0
\(115\) 14.4935 + 7.82099i 1.35153 + 0.729311i
\(116\) 0 0
\(117\) 2.96745 + 1.15600i 0.274341 + 0.106872i
\(118\) 0 0
\(119\) −1.08584 1.88073i −0.0995387 0.172406i
\(120\) 0 0
\(121\) 5.49993 9.52616i 0.499994 0.866015i
\(122\) 0 0
\(123\) 6.13321 12.7770i 0.553013 1.15206i
\(124\) 0 0
\(125\) 11.1388 0.963456i 0.996280 0.0861742i
\(126\) 0 0
\(127\) 18.2790i 1.62200i 0.585046 + 0.811000i \(0.301076\pi\)
−0.585046 + 0.811000i \(0.698924\pi\)
\(128\) 0 0
\(129\) −4.84174 + 3.31000i −0.426291 + 0.291430i
\(130\) 0 0
\(131\) 1.64613 2.85119i 0.143823 0.249109i −0.785110 0.619356i \(-0.787394\pi\)
0.928933 + 0.370247i \(0.120727\pi\)
\(132\) 0 0
\(133\) −7.60147 + 4.38871i −0.659131 + 0.380549i
\(134\) 0 0
\(135\) −11.2375 + 2.95272i −0.967170 + 0.254129i
\(136\) 0 0
\(137\) −7.56464 + 4.36744i −0.646290 + 0.373136i −0.787034 0.616910i \(-0.788384\pi\)
0.140743 + 0.990046i \(0.455051\pi\)
\(138\) 0 0
\(139\) 3.30750 5.72876i 0.280539 0.485908i −0.690979 0.722875i \(-0.742820\pi\)
0.971518 + 0.236968i \(0.0761535\pi\)
\(140\) 0 0
\(141\) 7.61079 5.20304i 0.640944 0.438175i
\(142\) 0 0
\(143\) 0.0123093i 0.00102936i
\(144\) 0 0
\(145\) 6.24716 + 10.1356i 0.518798 + 0.841718i
\(146\) 0 0
\(147\) 3.82912 7.97700i 0.315821 0.657932i
\(148\) 0 0
\(149\) 3.11139 5.38909i 0.254895 0.441491i −0.709972 0.704230i \(-0.751292\pi\)
0.964867 + 0.262739i \(0.0846257\pi\)
\(150\) 0 0
\(151\) −2.46299 4.26602i −0.200435 0.347164i 0.748233 0.663436i \(-0.230902\pi\)
−0.948669 + 0.316271i \(0.897569\pi\)
\(152\) 0 0
\(153\) 0.717883 + 4.68258i 0.0580374 + 0.378564i
\(154\) 0 0
\(155\) 2.45617 4.55167i 0.197284 0.365599i
\(156\) 0 0
\(157\) −8.14939 4.70505i −0.650392 0.375504i 0.138214 0.990402i \(-0.455864\pi\)
−0.788606 + 0.614898i \(0.789197\pi\)
\(158\) 0 0
\(159\) −0.167641 2.19974i −0.0132948 0.174450i
\(160\) 0 0
\(161\) −10.1291 −0.798285
\(162\) 0 0
\(163\) 0.333348i 0.0261098i −0.999915 0.0130549i \(-0.995844\pi\)
0.999915 0.0130549i \(-0.00415562\pi\)
\(164\) 0 0
\(165\) 0.0264008 + 0.0363297i 0.00205530 + 0.00282827i
\(166\) 0 0
\(167\) −5.75260 3.32126i −0.445150 0.257007i 0.260630 0.965439i \(-0.416070\pi\)
−0.705780 + 0.708432i \(0.749403\pi\)
\(168\) 0 0
\(169\) −5.93655 10.2824i −0.456658 0.790954i
\(170\) 0 0
\(171\) 18.9259 2.90152i 1.44730 0.221885i
\(172\) 0 0
\(173\) −17.7457 + 10.2455i −1.34918 + 0.778952i −0.988134 0.153595i \(-0.950915\pi\)
−0.361050 + 0.932546i \(0.617582\pi\)
\(174\) 0 0
\(175\) −5.74757 + 3.77483i −0.434475 + 0.285350i
\(176\) 0 0
\(177\) −5.09255 + 10.6090i −0.382779 + 0.797423i
\(178\) 0 0
\(179\) 16.0795 1.20184 0.600919 0.799310i \(-0.294802\pi\)
0.600919 + 0.799310i \(0.294802\pi\)
\(180\) 0 0
\(181\) −10.6942 −0.794891 −0.397445 0.917626i \(-0.630103\pi\)
−0.397445 + 0.917626i \(0.630103\pi\)
\(182\) 0 0
\(183\) 8.38989 + 12.2724i 0.620198 + 0.907201i
\(184\) 0 0
\(185\) −0.699778 24.3246i −0.0514487 1.78838i
\(186\) 0 0
\(187\) 0.0158574 0.00915525i 0.00115960 0.000669498i
\(188\) 0 0
\(189\) 5.22001 4.88038i 0.379700 0.354996i
\(190\) 0 0
\(191\) 8.16174 + 14.1366i 0.590563 + 1.02289i 0.994157 + 0.107947i \(0.0344277\pi\)
−0.403594 + 0.914938i \(0.632239\pi\)
\(192\) 0 0
\(193\) 18.0526 + 10.4227i 1.29945 + 0.750240i 0.980310 0.197466i \(-0.0632714\pi\)
0.319144 + 0.947706i \(0.396605\pi\)
\(194\) 0 0
\(195\) −3.75611 1.67187i −0.268981 0.119725i
\(196\) 0 0
\(197\) 4.80666i 0.342460i 0.985231 + 0.171230i \(0.0547742\pi\)
−0.985231 + 0.171230i \(0.945226\pi\)
\(198\) 0 0
\(199\) 7.79500 0.552573 0.276286 0.961075i \(-0.410896\pi\)
0.276286 + 0.961075i \(0.410896\pi\)
\(200\) 0 0
\(201\) 14.7302 + 7.07078i 1.03899 + 0.498734i
\(202\) 0 0
\(203\) −6.34170 3.66138i −0.445100 0.256979i
\(204\) 0 0
\(205\) −8.68903 + 16.1022i −0.606868 + 1.12462i
\(206\) 0 0
\(207\) 20.5885 + 8.02046i 1.43100 + 0.557460i
\(208\) 0 0
\(209\) −0.0370034 0.0640918i −0.00255958 0.00443332i
\(210\) 0 0
\(211\) 10.8034 18.7121i 0.743740 1.28820i −0.207041 0.978332i \(-0.566383\pi\)
0.950781 0.309863i \(-0.100283\pi\)
\(212\) 0 0
\(213\) 28.3999 2.16434i 1.94593 0.148298i
\(214\) 0 0
\(215\) 6.44572 3.97286i 0.439595 0.270947i
\(216\) 0 0
\(217\) 3.18102i 0.215942i
\(218\) 0 0
\(219\) 1.09566 + 14.3770i 0.0740379 + 0.971506i
\(220\) 0 0
\(221\) −0.838149 + 1.45172i −0.0563800 + 0.0976531i
\(222\) 0 0
\(223\) −8.59672 + 4.96332i −0.575679 + 0.332368i −0.759414 0.650607i \(-0.774514\pi\)
0.183735 + 0.982976i \(0.441181\pi\)
\(224\) 0 0
\(225\) 14.6716 3.12170i 0.978105 0.208113i
\(226\) 0 0
\(227\) −1.23057 + 0.710467i −0.0816755 + 0.0471554i −0.540282 0.841484i \(-0.681682\pi\)
0.458606 + 0.888640i \(0.348349\pi\)
\(228\) 0 0
\(229\) −13.7536 + 23.8220i −0.908866 + 1.57420i −0.0932237 + 0.995645i \(0.529717\pi\)
−0.815642 + 0.578557i \(0.803616\pi\)
\(230\) 0 0
\(231\) −0.0249007 0.0119529i −0.00163835 0.000786440i
\(232\) 0 0
\(233\) 27.1509i 1.77871i −0.457213 0.889357i \(-0.651152\pi\)
0.457213 0.889357i \(-0.348848\pi\)
\(234\) 0 0
\(235\) −10.1321 + 6.24499i −0.660946 + 0.407378i
\(236\) 0 0
\(237\) −7.55929 11.0574i −0.491029 0.718257i
\(238\) 0 0
\(239\) 11.9142 20.6361i 0.770668 1.33484i −0.166530 0.986036i \(-0.553256\pi\)
0.937197 0.348799i \(-0.113411\pi\)
\(240\) 0 0
\(241\) −12.1551 21.0533i −0.782979 1.35616i −0.930199 0.367056i \(-0.880366\pi\)
0.147220 0.989104i \(-0.452968\pi\)
\(242\) 0 0
\(243\) −14.4746 + 5.78659i −0.928549 + 0.371210i
\(244\) 0 0
\(245\) −5.42479 + 10.0530i −0.346577 + 0.642263i
\(246\) 0 0
\(247\) 5.86751 + 3.38761i 0.373341 + 0.215548i
\(248\) 0 0
\(249\) −7.72050 + 5.27804i −0.489267 + 0.334482i
\(250\) 0 0
\(251\) −16.1181 −1.01737 −0.508683 0.860954i \(-0.669868\pi\)
−0.508683 + 0.860954i \(0.669868\pi\)
\(252\) 0 0
\(253\) 0.0854035i 0.00536927i
\(254\) 0 0
\(255\) −0.639903 6.08224i −0.0400723 0.380885i
\(256\) 0 0
\(257\) 12.3751 + 7.14475i 0.771936 + 0.445678i 0.833565 0.552422i \(-0.186296\pi\)
−0.0616287 + 0.998099i \(0.519629\pi\)
\(258\) 0 0
\(259\) 7.48337 + 12.9616i 0.464994 + 0.805393i
\(260\) 0 0
\(261\) 9.99104 + 12.4637i 0.618430 + 0.771482i
\(262\) 0 0
\(263\) −5.56810 + 3.21475i −0.343344 + 0.198230i −0.661750 0.749725i \(-0.730186\pi\)
0.318406 + 0.947955i \(0.396853\pi\)
\(264\) 0 0
\(265\) 0.0819007 + 2.84690i 0.00503112 + 0.174884i
\(266\) 0 0
\(267\) 21.9049 1.66936i 1.34056 0.102163i
\(268\) 0 0
\(269\) 8.18395 0.498984 0.249492 0.968377i \(-0.419736\pi\)
0.249492 + 0.968377i \(0.419736\pi\)
\(270\) 0 0
\(271\) −21.8758 −1.32886 −0.664430 0.747350i \(-0.731326\pi\)
−0.664430 + 0.747350i \(0.731326\pi\)
\(272\) 0 0
\(273\) 2.52135 0.192150i 0.152599 0.0116295i
\(274\) 0 0
\(275\) −0.0318275 0.0484606i −0.00191927 0.00292229i
\(276\) 0 0
\(277\) 10.6432 6.14485i 0.639487 0.369208i −0.144930 0.989442i \(-0.546296\pi\)
0.784417 + 0.620234i \(0.212962\pi\)
\(278\) 0 0
\(279\) 2.51881 6.46578i 0.150797 0.387096i
\(280\) 0 0
\(281\) −7.29349 12.6327i −0.435093 0.753603i 0.562210 0.826994i \(-0.309951\pi\)
−0.997303 + 0.0733910i \(0.976618\pi\)
\(282\) 0 0
\(283\) −10.0885 5.82460i −0.599699 0.346236i 0.169224 0.985578i \(-0.445874\pi\)
−0.768923 + 0.639341i \(0.779207\pi\)
\(284\) 0 0
\(285\) −24.5830 + 2.58634i −1.45617 + 0.153202i
\(286\) 0 0
\(287\) 11.2533i 0.664262i
\(288\) 0 0
\(289\) 14.5065 0.853321
\(290\) 0 0
\(291\) 0.122462 0.0837202i 0.00717888 0.00490776i
\(292\) 0 0
\(293\) −4.50023 2.59821i −0.262906 0.151789i 0.362753 0.931885i \(-0.381837\pi\)
−0.625659 + 0.780096i \(0.715170\pi\)
\(294\) 0 0
\(295\) 7.21471 13.3700i 0.420057 0.778432i
\(296\) 0 0
\(297\) 0.0411489 + 0.0440125i 0.00238770 + 0.00255386i
\(298\) 0 0
\(299\) 3.90928 + 6.77107i 0.226080 + 0.391581i
\(300\) 0 0
\(301\) −2.32845 + 4.03299i −0.134209 + 0.232458i
\(302\) 0 0
\(303\) −14.1255 20.6621i −0.811486 1.18701i
\(304\) 0 0
\(305\) −10.0700 16.3380i −0.576608 0.935512i
\(306\) 0 0
\(307\) 31.2676i 1.78453i 0.451509 + 0.892267i \(0.350886\pi\)
−0.451509 + 0.892267i \(0.649114\pi\)
\(308\) 0 0
\(309\) −7.71124 3.70155i −0.438677 0.210574i
\(310\) 0 0
\(311\) −13.5500 + 23.4692i −0.768348 + 1.33082i 0.170110 + 0.985425i \(0.445588\pi\)
−0.938458 + 0.345393i \(0.887746\pi\)
\(312\) 0 0
\(313\) −30.3115 + 17.5004i −1.71331 + 0.989179i −0.783297 + 0.621647i \(0.786464\pi\)
−0.930011 + 0.367532i \(0.880203\pi\)
\(314\) 0 0
\(315\) −7.02938 + 5.97485i −0.396061 + 0.336645i
\(316\) 0 0
\(317\) 15.1212 8.73025i 0.849293 0.490339i −0.0111193 0.999938i \(-0.503539\pi\)
0.860412 + 0.509599i \(0.170206\pi\)
\(318\) 0 0
\(319\) 0.0308710 0.0534701i 0.00172844 0.00299375i
\(320\) 0 0
\(321\) 1.78957 + 23.4823i 0.0998841 + 1.31065i
\(322\) 0 0
\(323\) 10.0783i 0.560774i
\(324\) 0 0
\(325\) 4.74164 + 2.38524i 0.263019 + 0.132309i
\(326\) 0 0
\(327\) 17.1368 1.30599i 0.947669 0.0722213i
\(328\) 0 0
\(329\) 3.66011 6.33950i 0.201789 0.349508i
\(330\) 0 0
\(331\) −14.5945 25.2785i −0.802189 1.38943i −0.918173 0.396181i \(-0.870335\pi\)
0.115984 0.993251i \(-0.462998\pi\)
\(332\) 0 0
\(333\) −4.94749 32.2713i −0.271121 1.76846i
\(334\) 0 0
\(335\) −18.5637 10.0173i −1.01424 0.547304i
\(336\) 0 0
\(337\) 14.5048 + 8.37436i 0.790128 + 0.456181i 0.840008 0.542575i \(-0.182550\pi\)
−0.0498797 + 0.998755i \(0.515884\pi\)
\(338\) 0 0
\(339\) −3.95580 1.89886i −0.214850 0.103132i
\(340\) 0 0
\(341\) −0.0268208 −0.00145243
\(342\) 0 0
\(343\) 16.6526i 0.899156i
\(344\) 0 0
\(345\) −26.0603 11.5996i −1.40304 0.624501i
\(346\) 0 0
\(347\) −18.1261 10.4651i −0.973062 0.561798i −0.0728940 0.997340i \(-0.523223\pi\)
−0.900169 + 0.435542i \(0.856557\pi\)
\(348\) 0 0
\(349\) 6.05625 + 10.4897i 0.324184 + 0.561503i 0.981347 0.192246i \(-0.0615771\pi\)
−0.657163 + 0.753748i \(0.728244\pi\)
\(350\) 0 0
\(351\) −5.27707 1.60589i −0.281669 0.0857163i
\(352\) 0 0
\(353\) 22.1118 12.7663i 1.17689 0.679480i 0.221600 0.975138i \(-0.428872\pi\)
0.955294 + 0.295658i \(0.0955388\pi\)
\(354\) 0 0
\(355\) −36.7552 + 1.05739i −1.95076 + 0.0561202i
\(356\) 0 0
\(357\) 2.12283 + 3.10518i 0.112352 + 0.164344i
\(358\) 0 0
\(359\) −6.41790 −0.338724 −0.169362 0.985554i \(-0.554171\pi\)
−0.169362 + 0.985554i \(0.554171\pi\)
\(360\) 0 0
\(361\) 21.7343 1.14391
\(362\) 0 0
\(363\) −8.24482 + 17.1760i −0.432741 + 0.901505i
\(364\) 0 0
\(365\) −0.535284 18.6067i −0.0280181 0.973920i
\(366\) 0 0
\(367\) −4.01929 + 2.32054i −0.209805 + 0.121131i −0.601221 0.799083i \(-0.705319\pi\)
0.391416 + 0.920214i \(0.371986\pi\)
\(368\) 0 0
\(369\) −8.91064 + 22.8736i −0.463870 + 1.19075i
\(370\) 0 0
\(371\) −0.875839 1.51700i −0.0454713 0.0787586i
\(372\) 0 0
\(373\) 18.9009 + 10.9124i 0.978652 + 0.565025i 0.901863 0.432023i \(-0.142200\pi\)
0.0767888 + 0.997047i \(0.475533\pi\)
\(374\) 0 0
\(375\) −19.1103 + 3.12998i −0.986851 + 0.161631i
\(376\) 0 0
\(377\) 5.65238i 0.291112i
\(378\) 0 0
\(379\) −29.1095 −1.49526 −0.747628 0.664117i \(-0.768808\pi\)
−0.747628 + 0.664117i \(0.768808\pi\)
\(380\) 0 0
\(381\) −2.40583 31.5686i −0.123254 1.61731i
\(382\) 0 0
\(383\) −7.20924 4.16226i −0.368375 0.212681i 0.304373 0.952553i \(-0.401553\pi\)
−0.672748 + 0.739871i \(0.734886\pi\)
\(384\) 0 0
\(385\) 0.0313811 + 0.0169338i 0.00159933 + 0.000863029i
\(386\) 0 0
\(387\) 7.92624 6.35377i 0.402913 0.322981i
\(388\) 0 0
\(389\) −1.42579 2.46953i −0.0722902 0.125210i 0.827614 0.561297i \(-0.189697\pi\)
−0.899905 + 0.436087i \(0.856364\pi\)
\(390\) 0 0
\(391\) −5.81517 + 10.0722i −0.294086 + 0.509372i
\(392\) 0 0
\(393\) −2.46768 + 5.14078i −0.124478 + 0.259318i
\(394\) 0 0
\(395\) 9.07310 + 14.7206i 0.456517 + 0.740672i
\(396\) 0 0
\(397\) 29.4781i 1.47946i −0.672903 0.739731i \(-0.734953\pi\)
0.672903 0.739731i \(-0.265047\pi\)
\(398\) 0 0
\(399\) 12.5504 8.57997i 0.628308 0.429536i
\(400\) 0 0
\(401\) −12.9053 + 22.3526i −0.644460 + 1.11624i 0.339966 + 0.940438i \(0.389584\pi\)
−0.984426 + 0.175799i \(0.943749\pi\)
\(402\) 0 0
\(403\) 2.12644 1.22770i 0.105926 0.0611562i
\(404\) 0 0
\(405\) 19.0190 6.57852i 0.945063 0.326889i
\(406\) 0 0
\(407\) −0.109285 + 0.0630960i −0.00541708 + 0.00312755i
\(408\) 0 0
\(409\) 13.5371 23.4470i 0.669367 1.15938i −0.308714 0.951155i \(-0.599899\pi\)
0.978081 0.208223i \(-0.0667679\pi\)
\(410\) 0 0
\(411\) 12.4896 8.53840i 0.616068 0.421168i
\(412\) 0 0
\(413\) 9.34390i 0.459783i
\(414\) 0 0
\(415\) 10.2782 6.33501i 0.504535 0.310973i
\(416\) 0 0
\(417\) −4.95820 + 10.3291i −0.242804 + 0.505820i
\(418\) 0 0
\(419\) −12.0092 + 20.8005i −0.586688 + 1.01617i 0.407975 + 0.912993i \(0.366235\pi\)
−0.994663 + 0.103180i \(0.967098\pi\)
\(420\) 0 0
\(421\) 4.09439 + 7.09168i 0.199548 + 0.345628i 0.948382 0.317130i \(-0.102719\pi\)
−0.748834 + 0.662758i \(0.769386\pi\)
\(422\) 0 0
\(423\) −12.4594 + 9.98758i −0.605795 + 0.485613i
\(424\) 0 0
\(425\) 0.453904 + 7.88242i 0.0220176 + 0.382354i
\(426\) 0 0
\(427\) 10.2224 + 5.90193i 0.494698 + 0.285614i
\(428\) 0 0
\(429\) 0.00162012 + 0.0212587i 7.82199e−5 + 0.00102638i
\(430\) 0 0
\(431\) 5.20494 0.250713 0.125357 0.992112i \(-0.459992\pi\)
0.125357 + 0.992112i \(0.459992\pi\)
\(432\) 0 0
\(433\) 22.2500i 1.06927i −0.845084 0.534633i \(-0.820450\pi\)
0.845084 0.534633i \(-0.179550\pi\)
\(434\) 0 0
\(435\) −12.1231 16.6824i −0.581259 0.799862i
\(436\) 0 0
\(437\) 40.7094 + 23.5036i 1.94740 + 1.12433i
\(438\) 0 0
\(439\) −6.98693 12.1017i −0.333468 0.577583i 0.649721 0.760172i \(-0.274886\pi\)
−0.983189 + 0.182589i \(0.941552\pi\)
\(440\) 0 0
\(441\) −5.56315 + 14.2806i −0.264912 + 0.680029i
\(442\) 0 0
\(443\) −4.57467 + 2.64119i −0.217349 + 0.125487i −0.604722 0.796436i \(-0.706716\pi\)
0.387373 + 0.921923i \(0.373383\pi\)
\(444\) 0 0
\(445\) −28.3494 + 0.815565i −1.34389 + 0.0386615i
\(446\) 0 0
\(447\) −4.66421 + 9.71670i −0.220610 + 0.459584i
\(448\) 0 0
\(449\) −1.87417 −0.0884474 −0.0442237 0.999022i \(-0.514081\pi\)
−0.0442237 + 0.999022i \(0.514081\pi\)
\(450\) 0 0
\(451\) 0.0948824 0.00446784
\(452\) 0 0
\(453\) 4.81517 + 7.04343i 0.226236 + 0.330929i
\(454\) 0 0
\(455\) −3.26313 + 0.0938749i −0.152978 + 0.00440092i
\(456\) 0 0
\(457\) 19.3262 11.1580i 0.904040 0.521948i 0.0255315 0.999674i \(-0.491872\pi\)
0.878509 + 0.477726i \(0.158539\pi\)
\(458\) 0 0
\(459\) −1.85612 7.99253i −0.0866363 0.373059i
\(460\) 0 0
\(461\) −5.87818 10.1813i −0.273774 0.474191i 0.696051 0.717992i \(-0.254939\pi\)
−0.969825 + 0.243802i \(0.921605\pi\)
\(462\) 0 0
\(463\) 10.2152 + 5.89776i 0.474741 + 0.274092i 0.718222 0.695814i \(-0.244956\pi\)
−0.243481 + 0.969906i \(0.578289\pi\)
\(464\) 0 0
\(465\) −3.64283 + 8.18420i −0.168932 + 0.379533i
\(466\) 0 0
\(467\) 21.4898i 0.994431i 0.867627 + 0.497215i \(0.165644\pi\)
−0.867627 + 0.497215i \(0.834356\pi\)
\(468\) 0 0
\(469\) 12.9736 0.599065
\(470\) 0 0
\(471\) 14.6936 + 7.05323i 0.677046 + 0.324996i
\(472\) 0 0
\(473\) −0.0340041 0.0196323i −0.00156351 0.000902694i
\(474\) 0 0
\(475\) 31.8589 1.83458i 1.46179 0.0841761i
\(476\) 0 0
\(477\) 0.579045 + 3.77697i 0.0265127 + 0.172936i
\(478\) 0 0
\(479\) 1.98546 + 3.43891i 0.0907178 + 0.157128i 0.907813 0.419374i \(-0.137751\pi\)
−0.817096 + 0.576502i \(0.804417\pi\)
\(480\) 0 0
\(481\) 5.77635 10.0049i 0.263379 0.456185i
\(482\) 0 0
\(483\) 17.4934 1.33316i 0.795976 0.0606609i
\(484\) 0 0
\(485\) −0.163032 + 0.100486i −0.00740291 + 0.00456283i
\(486\) 0 0
\(487\) 12.7847i 0.579329i −0.957128 0.289664i \(-0.906456\pi\)
0.957128 0.289664i \(-0.0935437\pi\)
\(488\) 0 0
\(489\) 0.0438742 + 0.575705i 0.00198406 + 0.0260343i
\(490\) 0 0
\(491\) 3.50061 6.06323i 0.157980 0.273630i −0.776160 0.630536i \(-0.782835\pi\)
0.934140 + 0.356906i \(0.116168\pi\)
\(492\) 0 0
\(493\) −7.28162 + 4.20404i −0.327948 + 0.189341i
\(494\) 0 0
\(495\) −0.0503770 0.0592682i −0.00226428 0.00266391i
\(496\) 0 0
\(497\) 19.5853 11.3076i 0.878522 0.507215i
\(498\) 0 0
\(499\) −5.76235 + 9.98068i −0.257958 + 0.446796i −0.965695 0.259680i \(-0.916383\pi\)
0.707737 + 0.706476i \(0.249716\pi\)
\(500\) 0 0
\(501\) 10.3721 + 4.97883i 0.463392 + 0.222438i
\(502\) 0 0
\(503\) 7.38880i 0.329450i 0.986340 + 0.164725i \(0.0526737\pi\)
−0.986340 + 0.164725i \(0.947326\pi\)
\(504\) 0 0
\(505\) 16.9542 + 27.5071i 0.754452 + 1.22405i
\(506\) 0 0
\(507\) 11.6060 + 16.9768i 0.515441 + 0.753966i
\(508\) 0 0
\(509\) 1.11067 1.92373i 0.0492294 0.0852678i −0.840361 0.542028i \(-0.817657\pi\)
0.889590 + 0.456760i \(0.150990\pi\)
\(510\) 0 0
\(511\) 5.72428 + 9.91475i 0.253227 + 0.438603i
\(512\) 0 0
\(513\) −32.3040 + 7.50201i −1.42626 + 0.331222i
\(514\) 0 0
\(515\) 9.71808 + 5.24406i 0.428230 + 0.231081i
\(516\) 0 0
\(517\) 0.0534515 + 0.0308603i 0.00235080 + 0.00135723i
\(518\) 0 0
\(519\) 29.2992 20.0301i 1.28609 0.879223i
\(520\) 0 0
\(521\) 8.09160 0.354499 0.177250 0.984166i \(-0.443280\pi\)
0.177250 + 0.984166i \(0.443280\pi\)
\(522\) 0 0
\(523\) 14.4193i 0.630512i −0.949007 0.315256i \(-0.897910\pi\)
0.949007 0.315256i \(-0.102090\pi\)
\(524\) 0 0
\(525\) 9.42947 7.27577i 0.411536 0.317541i
\(526\) 0 0
\(527\) 3.16315 + 1.82625i 0.137789 + 0.0795525i
\(528\) 0 0
\(529\) 15.6230 + 27.0599i 0.679262 + 1.17652i
\(530\) 0 0
\(531\) 7.39872 18.9925i 0.321077 0.824205i
\(532\) 0 0
\(533\) −7.52259 + 4.34317i −0.325840 + 0.188124i
\(534\) 0 0
\(535\) −0.874293 30.3908i −0.0377990 1.31391i
\(536\) 0 0
\(537\) −27.7700 + 2.11633i −1.19836 + 0.0913265i
\(538\) 0 0
\(539\) 0.0592376 0.00255154
\(540\) 0 0
\(541\) 5.37804 0.231220 0.115610 0.993295i \(-0.463118\pi\)
0.115610 + 0.993295i \(0.463118\pi\)
\(542\) 0 0
\(543\) 18.4693 1.40753i 0.792593 0.0604030i
\(544\) 0 0
\(545\) −22.1785 + 0.638039i −0.950024 + 0.0273306i
\(546\) 0 0
\(547\) 22.1488 12.7876i 0.947016 0.546760i 0.0548630 0.998494i \(-0.482528\pi\)
0.892153 + 0.451734i \(0.149194\pi\)
\(548\) 0 0
\(549\) −16.1049 20.0907i −0.687342 0.857449i
\(550\) 0 0
\(551\) 16.9918 + 29.4306i 0.723874 + 1.25379i
\(552\) 0 0
\(553\) −9.21042 5.31764i −0.391667 0.226129i
\(554\) 0 0
\(555\) 4.41008 + 41.9175i 0.187197 + 1.77930i
\(556\) 0 0
\(557\) 36.1519i 1.53181i 0.642956 + 0.765903i \(0.277708\pi\)
−0.642956 + 0.765903i \(0.722292\pi\)
\(558\) 0 0
\(559\) 3.59462 0.152036
\(560\) 0 0
\(561\) −0.0261813 + 0.0178986i −0.00110538 + 0.000755680i
\(562\) 0 0
\(563\) 29.3594 + 16.9507i 1.23735 + 0.714385i 0.968552 0.248811i \(-0.0800397\pi\)
0.268800 + 0.963196i \(0.413373\pi\)
\(564\) 0 0
\(565\) 4.98529 + 2.69016i 0.209733 + 0.113176i
\(566\) 0 0
\(567\) −8.37284 + 9.11567i −0.351626 + 0.382822i
\(568\) 0 0
\(569\) −14.0057 24.2586i −0.587149 1.01697i −0.994604 0.103747i \(-0.966917\pi\)
0.407454 0.913226i \(-0.366417\pi\)
\(570\) 0 0
\(571\) 17.3040 29.9714i 0.724150 1.25427i −0.235173 0.971954i \(-0.575566\pi\)
0.959323 0.282311i \(-0.0911011\pi\)
\(572\) 0 0
\(573\) −15.9563 23.3402i −0.666584 0.975051i
\(574\) 0 0
\(575\) 32.8980 + 16.5491i 1.37194 + 0.690144i
\(576\) 0 0
\(577\) 1.88098i 0.0783062i 0.999233 + 0.0391531i \(0.0124660\pi\)
−0.999233 + 0.0391531i \(0.987534\pi\)
\(578\) 0 0
\(579\) −32.5494 15.6244i −1.35271 0.649326i
\(580\) 0 0
\(581\) −3.71287 + 6.43089i −0.154036 + 0.266798i
\(582\) 0 0
\(583\) 0.0127906 0.00738463i 0.000529731 0.000305840i
\(584\) 0 0
\(585\) 6.70701 + 2.39301i 0.277301 + 0.0989390i
\(586\) 0 0
\(587\) −4.92665 + 2.84440i −0.203345 + 0.117401i −0.598215 0.801336i \(-0.704123\pi\)
0.394870 + 0.918737i \(0.370790\pi\)
\(588\) 0 0
\(589\) 7.38126 12.7847i 0.304140 0.526785i
\(590\) 0 0
\(591\) −0.632638 8.30131i −0.0260232 0.341470i
\(592\) 0 0
\(593\) 23.6302i 0.970378i 0.874409 + 0.485189i \(0.161249\pi\)
−0.874409 + 0.485189i \(0.838751\pi\)
\(594\) 0 0
\(595\) −2.54794 4.13388i −0.104455 0.169472i
\(596\) 0 0
\(597\) −13.4623 + 1.02595i −0.550975 + 0.0419895i
\(598\) 0 0
\(599\) −11.8923 + 20.5981i −0.485908 + 0.841617i −0.999869 0.0161965i \(-0.994844\pi\)
0.513961 + 0.857814i \(0.328178\pi\)
\(600\) 0 0
\(601\) 4.30901 + 7.46343i 0.175768 + 0.304440i 0.940427 0.339996i \(-0.110426\pi\)
−0.764659 + 0.644436i \(0.777092\pi\)
\(602\) 0 0
\(603\) −26.3703 10.2728i −1.07388 0.418341i
\(604\) 0 0
\(605\) 11.6806 21.6460i 0.474884 0.880035i
\(606\) 0 0
\(607\) −23.7172 13.6931i −0.962652 0.555787i −0.0656637 0.997842i \(-0.520916\pi\)
−0.896988 + 0.442054i \(0.854250\pi\)
\(608\) 0 0
\(609\) 11.4343 + 5.48869i 0.463341 + 0.222413i
\(610\) 0 0
\(611\) −5.65042 −0.228592
\(612\) 0 0
\(613\) 1.61637i 0.0652845i 0.999467 + 0.0326422i \(0.0103922\pi\)
−0.999467 + 0.0326422i \(0.989608\pi\)
\(614\) 0 0
\(615\) 12.8870 28.9527i 0.519655 1.16749i
\(616\) 0 0
\(617\) 8.14521 + 4.70264i 0.327914 + 0.189321i 0.654915 0.755703i \(-0.272705\pi\)
−0.327001 + 0.945024i \(0.606038\pi\)
\(618\) 0 0
\(619\) 1.62429 + 2.81336i 0.0652858 + 0.113078i 0.896821 0.442394i \(-0.145871\pi\)
−0.831535 + 0.555472i \(0.812537\pi\)
\(620\) 0 0
\(621\) −36.6129 11.1419i −1.46922 0.447108i
\(622\) 0 0
\(623\) 15.1062 8.72158i 0.605218 0.349423i
\(624\) 0 0
\(625\) 24.8348 2.86970i 0.993390 0.114788i
\(626\) 0 0
\(627\) 0.0723420 + 0.105819i 0.00288906 + 0.00422600i
\(628\) 0 0
\(629\) 17.1850 0.685210
\(630\) 0 0
\(631\) 22.0746 0.878777 0.439389 0.898297i \(-0.355195\pi\)
0.439389 + 0.898297i \(0.355195\pi\)
\(632\) 0 0
\(633\) −16.1952 + 33.7386i −0.643701 + 1.34099i
\(634\) 0 0
\(635\) 1.17536 + 40.8562i 0.0466429 + 1.62133i
\(636\) 0 0
\(637\) −4.69655 + 2.71155i −0.186084 + 0.107436i
\(638\) 0 0
\(639\) −48.7630 + 7.47582i −1.92903 + 0.295739i
\(640\) 0 0
\(641\) −21.6150 37.4382i −0.853739 1.47872i −0.877809 0.479010i \(-0.840996\pi\)
0.0240700 0.999710i \(-0.492338\pi\)
\(642\) 0 0
\(643\) 13.6233 + 7.86544i 0.537252 + 0.310183i 0.743965 0.668219i \(-0.232943\pi\)
−0.206712 + 0.978402i \(0.566276\pi\)
\(644\) 0 0
\(645\) −10.6091 + 7.70966i −0.417735 + 0.303568i
\(646\) 0 0
\(647\) 25.8513i 1.01632i −0.861263 0.508159i \(-0.830326\pi\)
0.861263 0.508159i \(-0.169674\pi\)
\(648\) 0 0
\(649\) −0.0787831 −0.00309251
\(650\) 0 0
\(651\) −0.418677 5.49377i −0.0164092 0.215318i
\(652\) 0 0
\(653\) −21.9197 12.6553i −0.857784 0.495242i 0.00548578 0.999985i \(-0.498254\pi\)
−0.863269 + 0.504743i \(0.831587\pi\)
\(654\) 0 0
\(655\) 3.49601 6.47866i 0.136600 0.253142i
\(656\) 0 0
\(657\) −3.78451 24.6854i −0.147648 0.963071i
\(658\) 0 0
\(659\) −13.6426 23.6297i −0.531442 0.920484i −0.999327 0.0366946i \(-0.988317\pi\)
0.467885 0.883789i \(-0.345016\pi\)
\(660\) 0 0
\(661\) −11.1277 + 19.2737i −0.432817 + 0.749661i −0.997115 0.0759103i \(-0.975814\pi\)
0.564298 + 0.825571i \(0.309147\pi\)
\(662\) 0 0
\(663\) 1.25645 2.61749i 0.0487964 0.101655i
\(664\) 0 0
\(665\) −16.7082 + 10.2982i −0.647915 + 0.399346i
\(666\) 0 0
\(667\) 39.2169i 1.51848i
\(668\) 0 0
\(669\) 14.1936 9.70333i 0.548758 0.375153i
\(670\) 0 0
\(671\) −0.0497621 + 0.0861905i −0.00192104 + 0.00332735i
\(672\) 0 0
\(673\) −14.9334 + 8.62183i −0.575642 + 0.332347i −0.759400 0.650625i \(-0.774507\pi\)
0.183758 + 0.982972i \(0.441174\pi\)
\(674\) 0 0
\(675\) −24.9276 + 7.32233i −0.959462 + 0.281837i
\(676\) 0 0
\(677\) 0.940266 0.542863i 0.0361373 0.0208639i −0.481822 0.876269i \(-0.660025\pi\)
0.517960 + 0.855405i \(0.326692\pi\)
\(678\) 0 0
\(679\) 0.0588936 0.102007i 0.00226013 0.00391466i
\(680\) 0 0
\(681\) 2.03173 1.38897i 0.0778560 0.0532255i
\(682\) 0 0
\(683\) 3.62926i 0.138870i −0.997586 0.0694349i \(-0.977880\pi\)
0.997586 0.0694349i \(-0.0221196\pi\)
\(684\) 0 0
\(685\) −16.6272 + 10.2483i −0.635293 + 0.391567i
\(686\) 0 0
\(687\) 20.6177 42.9518i 0.786616 1.63871i
\(688\) 0 0
\(689\) −0.676052 + 1.17096i −0.0257555 + 0.0446099i
\(690\) 0 0
\(691\) 14.4867 + 25.0916i 0.551099 + 0.954531i 0.998196 + 0.0600453i \(0.0191245\pi\)
−0.447097 + 0.894485i \(0.647542\pi\)
\(692\) 0 0
\(693\) 0.0445778 + 0.0173657i 0.00169337 + 0.000659670i
\(694\) 0 0
\(695\) 7.02438 13.0173i 0.266450 0.493774i
\(696\) 0 0
\(697\) −11.1901 6.46060i −0.423855 0.244713i
\(698\) 0 0
\(699\) 3.57352 + 46.8908i 0.135163 + 1.77357i
\(700\) 0 0
\(701\) 28.4520 1.07462 0.537309 0.843385i \(-0.319441\pi\)
0.537309 + 0.843385i \(0.319441\pi\)
\(702\) 0 0
\(703\) 69.4577i 2.61965i
\(704\) 0 0
\(705\) 16.6766 12.1189i 0.628079 0.456425i
\(706\) 0 0
\(707\) −17.2108 9.93665i −0.647278 0.373706i
\(708\) 0 0
\(709\) −9.40582 16.2914i −0.353243 0.611835i 0.633573 0.773683i \(-0.281588\pi\)
−0.986816 + 0.161848i \(0.948254\pi\)
\(710\) 0 0
\(711\) 14.5106 + 18.1017i 0.544189 + 0.678868i
\(712\) 0 0
\(713\) 14.7535 8.51794i 0.552523 0.318999i
\(714\) 0 0
\(715\) −0.000791506 0.0275131i −2.96006e−5 0.00102893i
\(716\) 0 0
\(717\) −17.8603 + 37.2075i −0.667007 + 1.38954i
\(718\) 0 0
\(719\) 4.22562 0.157589 0.0787946 0.996891i \(-0.474893\pi\)
0.0787946 + 0.996891i \(0.474893\pi\)
\(720\) 0 0
\(721\) −6.79167 −0.252935
\(722\) 0 0
\(723\) 23.7634 + 34.7601i 0.883769 + 1.29274i
\(724\) 0 0
\(725\) 14.6150 + 22.2529i 0.542788 + 0.826451i
\(726\) 0 0
\(727\) −4.03048 + 2.32700i −0.149482 + 0.0863036i −0.572876 0.819642i \(-0.694172\pi\)
0.423393 + 0.905946i \(0.360839\pi\)
\(728\) 0 0
\(729\) 24.2367 11.8988i 0.897656 0.440696i
\(730\) 0 0
\(731\) 2.67355 + 4.63072i 0.0988848 + 0.171274i
\(732\) 0 0
\(733\) 21.6506 + 12.5000i 0.799683 + 0.461697i 0.843360 0.537348i \(-0.180574\pi\)
−0.0436770 + 0.999046i \(0.513907\pi\)
\(734\) 0 0
\(735\) 8.04570 18.0760i 0.296770 0.666742i
\(736\) 0 0
\(737\) 0.109387i 0.00402932i
\(738\) 0 0
\(739\) −18.4824 −0.679887 −0.339944 0.940446i \(-0.610408\pi\)
−0.339944 + 0.940446i \(0.610408\pi\)
\(740\) 0 0
\(741\) −10.5793 5.07828i −0.388640 0.186555i
\(742\) 0 0
\(743\) 2.86448 + 1.65381i 0.105088 + 0.0606723i 0.551623 0.834094i \(-0.314009\pi\)
−0.446535 + 0.894766i \(0.647342\pi\)
\(744\) 0 0
\(745\) 6.60788 12.2454i 0.242094 0.448639i
\(746\) 0 0
\(747\) 12.6390 10.1315i 0.462435 0.370694i
\(748\) 0 0
\(749\) 9.34962 + 16.1940i 0.341628 + 0.591716i
\(750\) 0 0
\(751\) −22.9233 + 39.7043i −0.836483 + 1.44883i 0.0563335 + 0.998412i \(0.482059\pi\)
−0.892817 + 0.450420i \(0.851274\pi\)
\(752\) 0 0
\(753\) 27.8367 2.12142i 1.01443 0.0773088i
\(754\) 0 0
\(755\) −5.77945 9.37680i −0.210336 0.341257i
\(756\) 0 0
\(757\) 12.2649i 0.445775i −0.974844 0.222888i \(-0.928452\pi\)
0.974844 0.222888i \(-0.0715483\pi\)
\(758\) 0 0
\(759\) 0.0112405 + 0.147495i 0.000408006 + 0.00535375i
\(760\) 0 0
\(761\) −9.54420 + 16.5310i −0.345977 + 0.599250i −0.985531 0.169497i \(-0.945786\pi\)
0.639554 + 0.768746i \(0.279119\pi\)
\(762\) 0 0
\(763\) 11.8180 6.82314i 0.427841 0.247014i
\(764\) 0 0
\(765\) 1.90567 + 10.4201i 0.0688995 + 0.376739i
\(766\) 0 0
\(767\) 6.24619 3.60624i 0.225537 0.130214i
\(768\) 0 0
\(769\) −3.60033 + 6.23595i −0.129831 + 0.224874i −0.923611 0.383331i \(-0.874777\pi\)
0.793780 + 0.608205i \(0.208110\pi\)
\(770\) 0 0
\(771\) −22.3127 10.7105i −0.803571 0.385730i
\(772\) 0 0
\(773\) 1.69028i 0.0607950i 0.999538 + 0.0303975i \(0.00967732\pi\)
−0.999538 + 0.0303975i \(0.990323\pi\)
\(774\) 0 0
\(775\) 5.19721 10.3316i 0.186689 0.371121i
\(776\) 0 0
\(777\) −14.6301 21.4003i −0.524850 0.767730i
\(778\) 0 0
\(779\) −26.1122 + 45.2277i −0.935568 + 1.62045i
\(780\) 0 0
\(781\) 0.0953400 + 0.165134i 0.00341153 + 0.00590895i
\(782\) 0 0
\(783\) −18.8954 20.2103i −0.675266 0.722258i
\(784\) 0 0
\(785\) −18.5176 9.99245i −0.660921 0.356646i
\(786\) 0 0
\(787\) −28.7876 16.6205i −1.02617 0.592457i −0.110282 0.993900i \(-0.535175\pi\)
−0.915884 + 0.401443i \(0.868509\pi\)
\(788\) 0 0
\(789\) 9.19324 6.28486i 0.327288 0.223747i
\(790\) 0 0
\(791\) −3.48407 −0.123879
\(792\) 0 0
\(793\) 9.11129i 0.323551i
\(794\) 0 0
\(795\) −0.516147 4.90595i −0.0183058 0.173996i
\(796\) 0 0
\(797\) −37.4748 21.6361i −1.32743 0.766390i −0.342525 0.939509i \(-0.611282\pi\)
−0.984901 + 0.173119i \(0.944615\pi\)
\(798\) 0 0
\(799\) −4.20259 7.27909i −0.148677 0.257516i
\(800\) 0 0
\(801\) −37.6110 + 5.76611i −1.32892 + 0.203736i
\(802\) 0 0
\(803\) −0.0835962 + 0.0482643i −0.00295005 + 0.00170321i
\(804\) 0 0
\(805\) −22.6400 + 0.651314i −0.797954 + 0.0229558i
\(806\) 0 0
\(807\) −14.1340 + 1.07715i −0.497541 + 0.0379173i
\(808\) 0 0
\(809\) −10.4664 −0.367981 −0.183990 0.982928i \(-0.558902\pi\)
−0.183990 + 0.982928i \(0.558902\pi\)
\(810\) 0 0
\(811\) −21.4200 −0.752158 −0.376079 0.926588i \(-0.622728\pi\)
−0.376079 + 0.926588i \(0.622728\pi\)
\(812\) 0 0
\(813\) 37.7805 2.87923i 1.32502 0.100979i
\(814\) 0 0
\(815\) −0.0214347 0.745079i −0.000750824 0.0260990i
\(816\) 0 0
\(817\) 18.7163 10.8059i 0.654801 0.378050i
\(818\) 0 0
\(819\) −4.32918 + 0.663704i −0.151274 + 0.0231917i
\(820\) 0 0
\(821\) −4.02464 6.97089i −0.140461 0.243286i 0.787209 0.616686i \(-0.211525\pi\)
−0.927670 + 0.373400i \(0.878192\pi\)
\(822\) 0 0
\(823\) 31.6630 + 18.2806i 1.10370 + 0.637223i 0.937191 0.348816i \(-0.113416\pi\)
0.166512 + 0.986039i \(0.446750\pi\)
\(824\) 0 0
\(825\) 0.0613457 + 0.0795046i 0.00213578 + 0.00276799i
\(826\) 0 0
\(827\) 7.52915i 0.261814i −0.991395 0.130907i \(-0.958211\pi\)
0.991395 0.130907i \(-0.0417890\pi\)
\(828\) 0 0
\(829\) −0.188646 −0.00655195 −0.00327597 0.999995i \(-0.501043\pi\)
−0.00327597 + 0.999995i \(0.501043\pi\)
\(830\) 0 0
\(831\) −17.5725 + 12.0132i −0.609582 + 0.416735i
\(832\) 0 0
\(833\) −6.98626 4.03352i −0.242060 0.139753i
\(834\) 0 0
\(835\) −13.0714 7.05360i −0.452356 0.244100i
\(836\) 0 0
\(837\) −3.49909 + 11.4982i −0.120946 + 0.397436i
\(838\) 0 0
\(839\) −8.22498 14.2461i −0.283958 0.491830i 0.688398 0.725333i \(-0.258314\pi\)
−0.972356 + 0.233504i \(0.924981\pi\)
\(840\) 0 0
\(841\) 0.324206 0.561541i 0.0111795 0.0193635i
\(842\) 0 0
\(843\) 14.2588 + 20.8573i 0.491101 + 0.718362i
\(844\) 0 0
\(845\) −13.9302 22.6009i −0.479214 0.777495i
\(846\) 0 0
\(847\) 15.1277i 0.519795i
\(848\) 0 0
\(849\) 18.1899 + 8.73151i 0.624275 + 0.299665i
\(850\) 0 0
\(851\) 40.0769 69.4153i 1.37382 2.37953i
\(852\) 0 0
\(853\) −20.3132 + 11.7278i −0.695509 + 0.401552i −0.805673 0.592361i \(-0.798196\pi\)
0.110163 + 0.993913i \(0.464863\pi\)
\(854\) 0 0
\(855\) 42.1156 7.70227i 1.44032 0.263412i
\(856\) 0 0
\(857\) −16.4722 + 9.51024i −0.562680 + 0.324864i −0.754221 0.656621i \(-0.771985\pi\)
0.191540 + 0.981485i \(0.438652\pi\)
\(858\) 0 0
\(859\) 7.90912 13.6990i 0.269856 0.467404i −0.698969 0.715152i \(-0.746357\pi\)
0.968824 + 0.247749i \(0.0796907\pi\)
\(860\) 0 0
\(861\) 1.48113 + 19.4350i 0.0504767 + 0.662342i
\(862\) 0 0
\(863\) 7.81226i 0.265933i 0.991121 + 0.132966i \(0.0424502\pi\)
−0.991121 + 0.132966i \(0.957550\pi\)
\(864\) 0 0
\(865\) −39.0055 + 24.0413i −1.32623 + 0.817427i
\(866\) 0 0
\(867\) −25.0533 + 1.90929i −0.850854 + 0.0648431i
\(868\) 0 0
\(869\) 0.0448357 0.0776577i 0.00152095 0.00263436i
\(870\) 0 0
\(871\) −5.00710 8.67256i −0.169659 0.293858i
\(872\) 0 0
\(873\) −0.200479 + 0.160706i −0.00678518 + 0.00543909i
\(874\) 0 0
\(875\) −12.6039 + 8.80686i −0.426090 + 0.297726i
\(876\) 0 0
\(877\) −47.5193 27.4353i −1.60461 0.926424i −0.990548 0.137168i \(-0.956200\pi\)
−0.614065 0.789255i \(-0.710467\pi\)
\(878\) 0 0
\(879\) 8.11405 + 3.89491i 0.273680 + 0.131372i
\(880\) 0 0
\(881\) 31.1017 1.04784 0.523922 0.851766i \(-0.324468\pi\)
0.523922 + 0.851766i \(0.324468\pi\)
\(882\) 0 0
\(883\) 20.5411i 0.691264i 0.938370 + 0.345632i \(0.112335\pi\)
−0.938370 + 0.345632i \(0.887665\pi\)
\(884\) 0 0
\(885\) −10.7004 + 24.0401i −0.359690 + 0.808101i
\(886\) 0 0
\(887\) −45.1925 26.0919i −1.51742 0.876081i −0.999790 0.0204736i \(-0.993483\pi\)
−0.517626 0.855607i \(-0.673184\pi\)
\(888\) 0 0
\(889\) −12.5693 21.7706i −0.421559 0.730162i
\(890\) 0 0
\(891\) −0.0768588 0.0705956i −0.00257487 0.00236504i
\(892\) 0 0
\(893\) −29.4204 + 16.9859i −0.984517 + 0.568411i
\(894\) 0 0
\(895\) 35.9400 1.03393i 1.20134 0.0345605i
\(896\) 0 0
\(897\) −7.64268 11.1794i −0.255182 0.373269i
\(898\) 0 0
\(899\) 12.3160 0.410761
\(900\) 0 0
\(901\) −2.01130 −0.0670060
\(902\) 0 0
\(903\) 3.49052 7.27161i 0.116157 0.241984i
\(904\) 0 0
\(905\) −23.9030 + 0.687649i −0.794562 + 0.0228582i
\(906\) 0 0
\(907\) −22.1672 + 12.7983i −0.736051 + 0.424959i −0.820632 0.571457i \(-0.806378\pi\)
0.0845808 + 0.996417i \(0.473045\pi\)
\(908\) 0 0
\(909\) 27.1148 + 33.8253i 0.899340 + 1.12191i
\(910\) 0 0
\(911\) −20.5975 35.6760i −0.682426 1.18200i −0.974238 0.225521i \(-0.927591\pi\)
0.291812 0.956476i \(-0.405742\pi\)
\(912\) 0 0
\(913\) −0.0542220 0.0313051i −0.00179449 0.00103605i
\(914\) 0 0
\(915\) 19.5417 + 26.8911i 0.646030 + 0.888991i
\(916\) 0 0
\(917\) 4.52774i 0.149519i
\(918\) 0 0
\(919\) −4.84011 −0.159661 −0.0798303 0.996808i \(-0.525438\pi\)
−0.0798303 + 0.996808i \(0.525438\pi\)
\(920\) 0 0
\(921\) −4.11534 54.0004i −0.135605 1.77937i
\(922\) 0 0
\(923\) −15.1178 8.72824i −0.497607 0.287293i
\(924\) 0 0
\(925\) −3.12821 54.3240i −0.102855 1.78616i
\(926\) 0 0
\(927\) 13.8048 + 5.37781i 0.453410 + 0.176630i
\(928\) 0 0
\(929\) 19.9319 + 34.5231i 0.653945 + 1.13267i 0.982157 + 0.188063i \(0.0602208\pi\)
−0.328212 + 0.944604i \(0.606446\pi\)
\(930\) 0 0
\(931\) −16.3026 + 28.2369i −0.534295 + 0.925426i
\(932\) 0 0
\(933\) 20.3124 42.3158i 0.664999 1.38536i
\(934\) 0 0
\(935\) 0.0348548 0.0214829i 0.00113987 0.000702567i
\(936\) 0 0
\(937\) 5.03028i 0.164332i −0.996619 0.0821661i \(-0.973816\pi\)
0.996619 0.0821661i \(-0.0261838\pi\)
\(938\) 0 0
\(939\) 50.0459 34.2134i 1.63319 1.11651i
\(940\) 0 0
\(941\) −10.4374 + 18.0781i −0.340250 + 0.589330i −0.984479 0.175503i \(-0.943845\pi\)
0.644229 + 0.764832i \(0.277178\pi\)
\(942\) 0 0
\(943\) −52.1926 + 30.1334i −1.69962 + 0.981278i
\(944\) 0 0
\(945\) 11.3536 11.2440i 0.369334 0.365768i
\(946\) 0 0
\(947\) −0.0653614 + 0.0377364i −0.00212396 + 0.00122627i −0.501062 0.865412i \(-0.667057\pi\)
0.498938 + 0.866638i \(0.333724\pi\)
\(948\) 0 0
\(949\) 4.41852 7.65311i 0.143431 0.248430i
\(950\) 0 0
\(951\) −24.9660 + 17.0677i −0.809577 + 0.553459i
\(952\) 0 0
\(953\) 23.6892i 0.767370i −0.923464 0.383685i \(-0.874655\pi\)
0.923464 0.383685i \(-0.125345\pi\)
\(954\) 0 0
\(955\) 19.1517 + 31.0724i 0.619733 + 1.00548i
\(956\) 0 0
\(957\) −0.0462779 + 0.0964083i −0.00149595 + 0.00311644i
\(958\) 0 0
\(959\) 6.00640 10.4034i 0.193957 0.335943i
\(960\) 0 0
\(961\) 12.8250 + 22.2135i 0.413708 + 0.716564i
\(962\) 0 0
\(963\) −6.18133 40.3194i −0.199191 1.29927i
\(964\) 0 0
\(965\) 41.0203 + 22.1353i 1.32049 + 0.712562i
\(966\) 0 0
\(967\) 39.2206 + 22.6440i 1.26125 + 0.728183i 0.973316 0.229467i \(-0.0736983\pi\)
0.287934 + 0.957650i \(0.407032\pi\)
\(968\) 0 0
\(969\) −1.32648 17.4057i −0.0426127 0.559152i
\(970\) 0 0
\(971\) 25.4586 0.817004 0.408502 0.912757i \(-0.366051\pi\)
0.408502 + 0.912757i \(0.366051\pi\)
\(972\) 0 0
\(973\) 9.09739i 0.291649i
\(974\) 0 0
\(975\) −8.50295 3.49533i −0.272312 0.111940i
\(976\) 0 0
\(977\) −7.09127 4.09415i −0.226870 0.130983i 0.382257 0.924056i \(-0.375147\pi\)
−0.609127 + 0.793073i \(0.708480\pi\)
\(978\) 0 0
\(979\) 0.0735360 + 0.127368i 0.00235022 + 0.00407070i
\(980\) 0 0
\(981\) −29.4242 + 4.51100i −0.939441 + 0.144025i
\(982\) 0 0
\(983\) 10.6001 6.11998i 0.338091 0.195197i −0.321336 0.946965i \(-0.604132\pi\)
0.659428 + 0.751768i \(0.270799\pi\)
\(984\) 0 0
\(985\) 0.309075 + 10.7436i 0.00984794 + 0.342319i
\(986\) 0 0
\(987\) −5.48679 + 11.4303i −0.174646 + 0.363831i
\(988\) 0 0
\(989\) 24.9398 0.793041
\(990\) 0 0
\(991\) 48.0040 1.52490 0.762448 0.647049i \(-0.223997\pi\)
0.762448 + 0.647049i \(0.223997\pi\)
\(992\) 0 0
\(993\) 28.5325 + 41.7362i 0.905451 + 1.32446i
\(994\) 0 0
\(995\) 17.4229 0.501229i 0.552344 0.0158900i
\(996\) 0 0
\(997\) −5.36574 + 3.09791i −0.169935 + 0.0981118i −0.582555 0.812791i \(-0.697947\pi\)
0.412620 + 0.910903i \(0.364614\pi\)
\(998\) 0 0
\(999\) 12.7920 + 55.0828i 0.404721 + 1.74274i
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 360.2.bi.b.49.1 32
3.2 odd 2 1080.2.bi.b.1009.1 32
4.3 odd 2 720.2.by.f.49.16 32
5.4 even 2 inner 360.2.bi.b.49.16 yes 32
9.2 odd 6 1080.2.bi.b.289.11 32
9.4 even 3 3240.2.f.k.649.5 16
9.5 odd 6 3240.2.f.i.649.12 16
9.7 even 3 inner 360.2.bi.b.169.16 yes 32
12.11 even 2 2160.2.by.f.1009.1 32
15.14 odd 2 1080.2.bi.b.1009.11 32
20.19 odd 2 720.2.by.f.49.1 32
36.7 odd 6 720.2.by.f.529.1 32
36.11 even 6 2160.2.by.f.289.11 32
45.4 even 6 3240.2.f.k.649.6 16
45.14 odd 6 3240.2.f.i.649.11 16
45.29 odd 6 1080.2.bi.b.289.1 32
45.34 even 6 inner 360.2.bi.b.169.1 yes 32
60.59 even 2 2160.2.by.f.1009.11 32
180.79 odd 6 720.2.by.f.529.16 32
180.119 even 6 2160.2.by.f.289.1 32
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
360.2.bi.b.49.1 32 1.1 even 1 trivial
360.2.bi.b.49.16 yes 32 5.4 even 2 inner
360.2.bi.b.169.1 yes 32 45.34 even 6 inner
360.2.bi.b.169.16 yes 32 9.7 even 3 inner
720.2.by.f.49.1 32 20.19 odd 2
720.2.by.f.49.16 32 4.3 odd 2
720.2.by.f.529.1 32 36.7 odd 6
720.2.by.f.529.16 32 180.79 odd 6
1080.2.bi.b.289.1 32 45.29 odd 6
1080.2.bi.b.289.11 32 9.2 odd 6
1080.2.bi.b.1009.1 32 3.2 odd 2
1080.2.bi.b.1009.11 32 15.14 odd 2
2160.2.by.f.289.1 32 180.119 even 6
2160.2.by.f.289.11 32 36.11 even 6
2160.2.by.f.1009.1 32 12.11 even 2
2160.2.by.f.1009.11 32 60.59 even 2
3240.2.f.i.649.11 16 45.14 odd 6
3240.2.f.i.649.12 16 9.5 odd 6
3240.2.f.k.649.5 16 9.4 even 3
3240.2.f.k.649.6 16 45.4 even 6