Properties

Label 360.2.bs.a.113.9
Level $360$
Weight $2$
Character 360.113
Analytic conductor $2.875$
Analytic rank $0$
Dimension $72$
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(113,360)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(360, base_ring=CyclotomicField(12))
 
chi = DirichletCharacter(H, H._module([0, 0, 10, 9]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("360.113");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 360 = 2^{3} \cdot 3^{2} \cdot 5 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 360.bs (of order \(12\), degree \(4\), 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: \(72\)
Relative dimension: \(18\) over \(\Q(\zeta_{12})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label 113.9
Character \(\chi\) \(=\) 360.113
Dual form 360.2.bs.a.137.9

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.254049 - 1.71332i) q^{3} +(-0.831407 - 2.07576i) q^{5} +(-1.77070 - 0.474457i) q^{7} +(-2.87092 - 0.870532i) q^{9} +O(q^{10})\) \(q+(0.254049 - 1.71332i) q^{3} +(-0.831407 - 2.07576i) q^{5} +(-1.77070 - 0.474457i) q^{7} +(-2.87092 - 0.870532i) q^{9} +(1.26602 - 0.730936i) q^{11} +(-5.80362 + 1.55507i) q^{13} +(-3.76765 + 0.897122i) q^{15} +(5.23679 + 5.23679i) q^{17} -7.79507i q^{19} +(-1.26274 + 2.91323i) q^{21} +(-0.159588 - 0.595592i) q^{23} +(-3.61752 + 3.45160i) q^{25} +(-2.22085 + 4.69764i) q^{27} +(-2.16701 - 3.75337i) q^{29} +(4.30635 - 7.45881i) q^{31} +(-0.930696 - 2.35479i) q^{33} +(0.487314 + 4.07000i) q^{35} +(2.01827 - 2.01827i) q^{37} +(1.18994 + 10.3385i) q^{39} +(1.08175 + 0.624550i) q^{41} +(1.00528 - 3.75176i) q^{43} +(0.579890 + 6.68309i) q^{45} +(0.559597 - 2.08844i) q^{47} +(-3.15192 - 1.81976i) q^{49} +(10.3027 - 7.64189i) q^{51} +(4.07847 - 4.07847i) q^{53} +(-2.56982 - 2.02024i) q^{55} +(-13.3554 - 1.98033i) q^{57} +(5.12738 - 8.88087i) q^{59} +(0.400201 + 0.693169i) q^{61} +(4.67049 + 2.90357i) q^{63} +(8.05313 + 10.7540i) q^{65} +(1.72680 + 6.44449i) q^{67} +(-1.06098 + 0.122116i) q^{69} +7.50776i q^{71} +(0.173786 + 0.173786i) q^{73} +(4.99466 + 7.07484i) q^{75} +(-2.58853 + 0.693595i) q^{77} +(2.61017 - 1.50698i) q^{79} +(7.48435 + 4.99846i) q^{81} +(7.38340 + 1.97838i) q^{83} +(6.51639 - 15.2242i) q^{85} +(-6.98124 + 2.75924i) q^{87} +12.3650 q^{89} +11.0143 q^{91} +(-11.6853 - 9.27304i) q^{93} +(-16.1807 + 6.48088i) q^{95} +(0.515150 + 0.138034i) q^{97} +(-4.27094 + 0.996348i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 72 q+O(q^{10}) \) Copy content Toggle raw display \( 72 q + 12 q^{15} + 16 q^{21} + 24 q^{23} - 12 q^{27} + 12 q^{33} + 12 q^{41} - 16 q^{45} - 36 q^{47} + 24 q^{51} - 40 q^{57} + 12 q^{61} - 44 q^{63} - 72 q^{65} - 36 q^{75} - 48 q^{77} - 20 q^{81} - 60 q^{83} + 24 q^{85} - 40 q^{87} - 84 q^{93} - 60 q^{95} + 24 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

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

\(n\) \(181\) \(217\) \(271\) \(281\)
\(\chi(n)\) \(1\) \(e\left(\frac{3}{4}\right)\) \(1\) \(e\left(\frac{5}{6}\right)\)

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
\(3\) 0.254049 1.71332i 0.146675 0.989185i
\(4\) 0 0
\(5\) −0.831407 2.07576i −0.371817 0.928306i
\(6\) 0 0
\(7\) −1.77070 0.474457i −0.669260 0.179328i −0.0918386 0.995774i \(-0.529274\pi\)
−0.577422 + 0.816446i \(0.695941\pi\)
\(8\) 0 0
\(9\) −2.87092 0.870532i −0.956973 0.290177i
\(10\) 0 0
\(11\) 1.26602 0.730936i 0.381719 0.220386i −0.296847 0.954925i \(-0.595935\pi\)
0.678566 + 0.734539i \(0.262602\pi\)
\(12\) 0 0
\(13\) −5.80362 + 1.55507i −1.60963 + 0.431300i −0.947934 0.318468i \(-0.896832\pi\)
−0.661700 + 0.749768i \(0.730165\pi\)
\(14\) 0 0
\(15\) −3.76765 + 0.897122i −0.972803 + 0.231636i
\(16\) 0 0
\(17\) 5.23679 + 5.23679i 1.27011 + 1.27011i 0.946030 + 0.324078i \(0.105054\pi\)
0.324078 + 0.946030i \(0.394946\pi\)
\(18\) 0 0
\(19\) 7.79507i 1.78831i −0.447757 0.894155i \(-0.647777\pi\)
0.447757 0.894155i \(-0.352223\pi\)
\(20\) 0 0
\(21\) −1.26274 + 2.91323i −0.275552 + 0.635719i
\(22\) 0 0
\(23\) −0.159588 0.595592i −0.0332765 0.124190i 0.947290 0.320378i \(-0.103810\pi\)
−0.980566 + 0.196189i \(0.937143\pi\)
\(24\) 0 0
\(25\) −3.61752 + 3.45160i −0.723505 + 0.690319i
\(26\) 0 0
\(27\) −2.22085 + 4.69764i −0.427403 + 0.904061i
\(28\) 0 0
\(29\) −2.16701 3.75337i −0.402404 0.696983i 0.591612 0.806223i \(-0.298492\pi\)
−0.994015 + 0.109240i \(0.965158\pi\)
\(30\) 0 0
\(31\) 4.30635 7.45881i 0.773443 1.33964i −0.162223 0.986754i \(-0.551866\pi\)
0.935666 0.352888i \(-0.114800\pi\)
\(32\) 0 0
\(33\) −0.930696 2.35479i −0.162013 0.409916i
\(34\) 0 0
\(35\) 0.487314 + 4.07000i 0.0823710 + 0.687955i
\(36\) 0 0
\(37\) 2.01827 2.01827i 0.331802 0.331802i −0.521469 0.853271i \(-0.674616\pi\)
0.853271 + 0.521469i \(0.174616\pi\)
\(38\) 0 0
\(39\) 1.18994 + 10.3385i 0.190542 + 1.65549i
\(40\) 0 0
\(41\) 1.08175 + 0.624550i 0.168941 + 0.0975383i 0.582087 0.813127i \(-0.302236\pi\)
−0.413145 + 0.910665i \(0.635570\pi\)
\(42\) 0 0
\(43\) 1.00528 3.75176i 0.153304 0.572137i −0.845941 0.533277i \(-0.820960\pi\)
0.999245 0.0388607i \(-0.0123729\pi\)
\(44\) 0 0
\(45\) 0.579890 + 6.68309i 0.0864449 + 0.996257i
\(46\) 0 0
\(47\) 0.559597 2.08844i 0.0816256 0.304631i −0.913028 0.407896i \(-0.866262\pi\)
0.994654 + 0.103265i \(0.0329291\pi\)
\(48\) 0 0
\(49\) −3.15192 1.81976i −0.450275 0.259966i
\(50\) 0 0
\(51\) 10.3027 7.64189i 1.44266 1.07008i
\(52\) 0 0
\(53\) 4.07847 4.07847i 0.560221 0.560221i −0.369149 0.929370i \(-0.620351\pi\)
0.929370 + 0.369149i \(0.120351\pi\)
\(54\) 0 0
\(55\) −2.56982 2.02024i −0.346515 0.272409i
\(56\) 0 0
\(57\) −13.3554 1.98033i −1.76897 0.262301i
\(58\) 0 0
\(59\) 5.12738 8.88087i 0.667527 1.15619i −0.311066 0.950388i \(-0.600686\pi\)
0.978593 0.205803i \(-0.0659806\pi\)
\(60\) 0 0
\(61\) 0.400201 + 0.693169i 0.0512405 + 0.0887512i 0.890508 0.454968i \(-0.150349\pi\)
−0.839267 + 0.543719i \(0.817016\pi\)
\(62\) 0 0
\(63\) 4.67049 + 2.90357i 0.588427 + 0.365816i
\(64\) 0 0
\(65\) 8.05313 + 10.7540i 0.998867 + 1.33387i
\(66\) 0 0
\(67\) 1.72680 + 6.44449i 0.210962 + 0.787319i 0.987549 + 0.157310i \(0.0502822\pi\)
−0.776588 + 0.630009i \(0.783051\pi\)
\(68\) 0 0
\(69\) −1.06098 + 0.122116i −0.127727 + 0.0147011i
\(70\) 0 0
\(71\) 7.50776i 0.891008i 0.895280 + 0.445504i \(0.146975\pi\)
−0.895280 + 0.445504i \(0.853025\pi\)
\(72\) 0 0
\(73\) 0.173786 + 0.173786i 0.0203401 + 0.0203401i 0.717204 0.696864i \(-0.245422\pi\)
−0.696864 + 0.717204i \(0.745422\pi\)
\(74\) 0 0
\(75\) 4.99466 + 7.07484i 0.576733 + 0.816933i
\(76\) 0 0
\(77\) −2.58853 + 0.693595i −0.294991 + 0.0790425i
\(78\) 0 0
\(79\) 2.61017 1.50698i 0.293667 0.169549i −0.345927 0.938261i \(-0.612436\pi\)
0.639594 + 0.768713i \(0.279102\pi\)
\(80\) 0 0
\(81\) 7.48435 + 4.99846i 0.831594 + 0.555384i
\(82\) 0 0
\(83\) 7.38340 + 1.97838i 0.810433 + 0.217155i 0.640160 0.768242i \(-0.278868\pi\)
0.170273 + 0.985397i \(0.445535\pi\)
\(84\) 0 0
\(85\) 6.51639 15.2242i 0.706802 1.65130i
\(86\) 0 0
\(87\) −6.98124 + 2.75924i −0.748468 + 0.295821i
\(88\) 0 0
\(89\) 12.3650 1.31069 0.655343 0.755332i \(-0.272524\pi\)
0.655343 + 0.755332i \(0.272524\pi\)
\(90\) 0 0
\(91\) 11.0143 1.15461
\(92\) 0 0
\(93\) −11.6853 9.27304i −1.21171 0.961570i
\(94\) 0 0
\(95\) −16.1807 + 6.48088i −1.66010 + 0.664924i
\(96\) 0 0
\(97\) 0.515150 + 0.138034i 0.0523055 + 0.0140152i 0.284877 0.958564i \(-0.408047\pi\)
−0.232571 + 0.972579i \(0.574714\pi\)
\(98\) 0 0
\(99\) −4.27094 + 0.996348i −0.429246 + 0.100137i
\(100\) 0 0
\(101\) 4.43379 2.55985i 0.441179 0.254715i −0.262919 0.964818i \(-0.584685\pi\)
0.704098 + 0.710103i \(0.251352\pi\)
\(102\) 0 0
\(103\) −13.8189 + 3.70276i −1.36161 + 0.364843i −0.864409 0.502789i \(-0.832307\pi\)
−0.497205 + 0.867633i \(0.665640\pi\)
\(104\) 0 0
\(105\) 7.09700 + 0.199055i 0.692597 + 0.0194257i
\(106\) 0 0
\(107\) 2.72473 + 2.72473i 0.263409 + 0.263409i 0.826438 0.563028i \(-0.190364\pi\)
−0.563028 + 0.826438i \(0.690364\pi\)
\(108\) 0 0
\(109\) 15.1331i 1.44949i 0.689017 + 0.724745i \(0.258042\pi\)
−0.689017 + 0.724745i \(0.741958\pi\)
\(110\) 0 0
\(111\) −2.94520 3.97068i −0.279546 0.376881i
\(112\) 0 0
\(113\) −0.175699 0.655717i −0.0165284 0.0616847i 0.957169 0.289529i \(-0.0934988\pi\)
−0.973697 + 0.227845i \(0.926832\pi\)
\(114\) 0 0
\(115\) −1.10362 + 0.826446i −0.102913 + 0.0770665i
\(116\) 0 0
\(117\) 18.0155 + 0.587745i 1.66553 + 0.0543370i
\(118\) 0 0
\(119\) −6.78813 11.7574i −0.622267 1.07780i
\(120\) 0 0
\(121\) −4.43146 + 7.67552i −0.402860 + 0.697775i
\(122\) 0 0
\(123\) 1.34487 1.69472i 0.121263 0.152808i
\(124\) 0 0
\(125\) 10.1723 + 4.63941i 0.909839 + 0.414962i
\(126\) 0 0
\(127\) −2.70790 + 2.70790i −0.240287 + 0.240287i −0.816969 0.576682i \(-0.804347\pi\)
0.576682 + 0.816969i \(0.304347\pi\)
\(128\) 0 0
\(129\) −6.17256 2.67549i −0.543464 0.235564i
\(130\) 0 0
\(131\) 1.28977 + 0.744648i 0.112688 + 0.0650602i 0.555284 0.831661i \(-0.312609\pi\)
−0.442597 + 0.896721i \(0.645943\pi\)
\(132\) 0 0
\(133\) −3.69842 + 13.8027i −0.320694 + 1.19685i
\(134\) 0 0
\(135\) 11.5976 + 0.704295i 0.998161 + 0.0606161i
\(136\) 0 0
\(137\) 5.14839 19.2141i 0.439857 1.64157i −0.289312 0.957235i \(-0.593427\pi\)
0.729169 0.684334i \(-0.239907\pi\)
\(138\) 0 0
\(139\) 7.84605 + 4.52992i 0.665493 + 0.384223i 0.794367 0.607438i \(-0.207803\pi\)
−0.128874 + 0.991661i \(0.541136\pi\)
\(140\) 0 0
\(141\) −3.43601 1.48933i −0.289364 0.125425i
\(142\) 0 0
\(143\) −6.21083 + 6.21083i −0.519376 + 0.519376i
\(144\) 0 0
\(145\) −5.98941 + 7.61876i −0.497394 + 0.632704i
\(146\) 0 0
\(147\) −3.91858 + 4.93794i −0.323199 + 0.407274i
\(148\) 0 0
\(149\) −4.39200 + 7.60718i −0.359807 + 0.623204i −0.987928 0.154911i \(-0.950491\pi\)
0.628121 + 0.778115i \(0.283824\pi\)
\(150\) 0 0
\(151\) −6.02080 10.4283i −0.489966 0.848645i 0.509968 0.860194i \(-0.329657\pi\)
−0.999933 + 0.0115482i \(0.996324\pi\)
\(152\) 0 0
\(153\) −10.4756 19.5932i −0.846902 1.58402i
\(154\) 0 0
\(155\) −19.0630 2.73761i −1.53118 0.219890i
\(156\) 0 0
\(157\) −2.14188 7.99361i −0.170941 0.637959i −0.997208 0.0746804i \(-0.976206\pi\)
0.826267 0.563279i \(-0.190460\pi\)
\(158\) 0 0
\(159\) −5.95159 8.02385i −0.471992 0.636332i
\(160\) 0 0
\(161\) 1.13033i 0.0890825i
\(162\) 0 0
\(163\) −15.1653 15.1653i −1.18784 1.18784i −0.977663 0.210178i \(-0.932596\pi\)
−0.210178 0.977663i \(-0.567404\pi\)
\(164\) 0 0
\(165\) −4.11417 + 3.88968i −0.320288 + 0.302812i
\(166\) 0 0
\(167\) −8.34829 + 2.23692i −0.646010 + 0.173098i −0.566924 0.823770i \(-0.691867\pi\)
−0.0790857 + 0.996868i \(0.525200\pi\)
\(168\) 0 0
\(169\) 20.0054 11.5501i 1.53888 0.888471i
\(170\) 0 0
\(171\) −6.78586 + 22.3790i −0.518928 + 1.71137i
\(172\) 0 0
\(173\) 9.52603 + 2.55249i 0.724250 + 0.194062i 0.602067 0.798445i \(-0.294344\pi\)
0.122183 + 0.992508i \(0.461011\pi\)
\(174\) 0 0
\(175\) 8.04317 4.39537i 0.608006 0.332259i
\(176\) 0 0
\(177\) −13.9132 11.0410i −1.04578 0.829892i
\(178\) 0 0
\(179\) −15.0695 −1.12635 −0.563175 0.826338i \(-0.690420\pi\)
−0.563175 + 0.826338i \(0.690420\pi\)
\(180\) 0 0
\(181\) 5.20300 0.386736 0.193368 0.981126i \(-0.438059\pi\)
0.193368 + 0.981126i \(0.438059\pi\)
\(182\) 0 0
\(183\) 1.28929 0.509573i 0.0953070 0.0376687i
\(184\) 0 0
\(185\) −5.86745 2.51143i −0.431383 0.184644i
\(186\) 0 0
\(187\) 10.4576 + 2.80211i 0.764738 + 0.204911i
\(188\) 0 0
\(189\) 6.16128 7.26439i 0.448167 0.528407i
\(190\) 0 0
\(191\) 6.00774 3.46857i 0.434705 0.250977i −0.266644 0.963795i \(-0.585915\pi\)
0.701349 + 0.712818i \(0.252582\pi\)
\(192\) 0 0
\(193\) −3.43559 + 0.920564i −0.247299 + 0.0662636i −0.380339 0.924847i \(-0.624193\pi\)
0.133040 + 0.991111i \(0.457526\pi\)
\(194\) 0 0
\(195\) 20.4709 11.0655i 1.46595 0.792419i
\(196\) 0 0
\(197\) −13.5113 13.5113i −0.962643 0.962643i 0.0366836 0.999327i \(-0.488321\pi\)
−0.999327 + 0.0366836i \(0.988321\pi\)
\(198\) 0 0
\(199\) 3.62623i 0.257057i −0.991706 0.128528i \(-0.958975\pi\)
0.991706 0.128528i \(-0.0410253\pi\)
\(200\) 0 0
\(201\) 11.4801 1.32134i 0.809747 0.0931999i
\(202\) 0 0
\(203\) 2.05630 + 7.67423i 0.144324 + 0.538625i
\(204\) 0 0
\(205\) 0.397036 2.76471i 0.0277302 0.193096i
\(206\) 0 0
\(207\) −0.0603169 + 1.84882i −0.00419231 + 0.128502i
\(208\) 0 0
\(209\) −5.69770 9.86870i −0.394118 0.682632i
\(210\) 0 0
\(211\) −1.18158 + 2.04656i −0.0813433 + 0.140891i −0.903827 0.427898i \(-0.859254\pi\)
0.822484 + 0.568788i \(0.192588\pi\)
\(212\) 0 0
\(213\) 12.8632 + 1.90734i 0.881371 + 0.130689i
\(214\) 0 0
\(215\) −8.62353 + 1.03252i −0.588120 + 0.0704174i
\(216\) 0 0
\(217\) −11.1641 + 11.1641i −0.757869 + 0.757869i
\(218\) 0 0
\(219\) 0.341901 0.253601i 0.0231035 0.0171367i
\(220\) 0 0
\(221\) −38.5359 22.2487i −2.59221 1.49661i
\(222\) 0 0
\(223\) −3.96195 + 14.7862i −0.265312 + 0.990157i 0.696747 + 0.717317i \(0.254630\pi\)
−0.962059 + 0.272841i \(0.912037\pi\)
\(224\) 0 0
\(225\) 13.3903 6.76008i 0.892690 0.450672i
\(226\) 0 0
\(227\) 2.56474 9.57172i 0.170227 0.635297i −0.827088 0.562072i \(-0.810004\pi\)
0.997315 0.0732250i \(-0.0233291\pi\)
\(228\) 0 0
\(229\) 7.54945 + 4.35868i 0.498882 + 0.288030i 0.728252 0.685310i \(-0.240333\pi\)
−0.229370 + 0.973339i \(0.573667\pi\)
\(230\) 0 0
\(231\) 0.530736 + 4.61119i 0.0349199 + 0.303394i
\(232\) 0 0
\(233\) −20.0201 + 20.0201i −1.31156 + 1.31156i −0.391295 + 0.920265i \(0.627973\pi\)
−0.920265 + 0.391295i \(0.872027\pi\)
\(234\) 0 0
\(235\) −4.80035 + 0.574761i −0.313141 + 0.0374933i
\(236\) 0 0
\(237\) −1.91883 4.85490i −0.124641 0.315359i
\(238\) 0 0
\(239\) −0.254031 + 0.439994i −0.0164319 + 0.0284608i −0.874124 0.485702i \(-0.838564\pi\)
0.857693 + 0.514163i \(0.171897\pi\)
\(240\) 0 0
\(241\) −3.88251 6.72471i −0.250095 0.433177i 0.713457 0.700699i \(-0.247128\pi\)
−0.963552 + 0.267522i \(0.913795\pi\)
\(242\) 0 0
\(243\) 10.4653 11.5532i 0.671351 0.741139i
\(244\) 0 0
\(245\) −1.15685 + 8.05559i −0.0739086 + 0.514653i
\(246\) 0 0
\(247\) 12.1219 + 45.2396i 0.771299 + 2.87853i
\(248\) 0 0
\(249\) 5.26533 12.1475i 0.333677 0.769817i
\(250\) 0 0
\(251\) 14.5557i 0.918750i 0.888242 + 0.459375i \(0.151927\pi\)
−0.888242 + 0.459375i \(0.848073\pi\)
\(252\) 0 0
\(253\) −0.637382 0.637382i −0.0400718 0.0400718i
\(254\) 0 0
\(255\) −24.4284 15.0323i −1.52977 0.941362i
\(256\) 0 0
\(257\) 19.7382 5.28884i 1.23124 0.329909i 0.416176 0.909284i \(-0.363370\pi\)
0.815061 + 0.579375i \(0.196703\pi\)
\(258\) 0 0
\(259\) −4.53133 + 2.61616i −0.281563 + 0.162561i
\(260\) 0 0
\(261\) 2.95388 + 12.6621i 0.182840 + 0.783763i
\(262\) 0 0
\(263\) 16.1042 + 4.31511i 0.993028 + 0.266081i 0.718522 0.695504i \(-0.244819\pi\)
0.274506 + 0.961585i \(0.411486\pi\)
\(264\) 0 0
\(265\) −11.8568 5.07504i −0.728356 0.311757i
\(266\) 0 0
\(267\) 3.14131 21.1851i 0.192245 1.29651i
\(268\) 0 0
\(269\) −15.1547 −0.924001 −0.462001 0.886880i \(-0.652868\pi\)
−0.462001 + 0.886880i \(0.652868\pi\)
\(270\) 0 0
\(271\) 18.8037 1.14225 0.571123 0.820864i \(-0.306508\pi\)
0.571123 + 0.820864i \(0.306508\pi\)
\(272\) 0 0
\(273\) 2.79816 18.8709i 0.169352 1.14212i
\(274\) 0 0
\(275\) −2.05696 + 7.01397i −0.124039 + 0.422958i
\(276\) 0 0
\(277\) 19.2663 + 5.16238i 1.15760 + 0.310177i 0.786006 0.618219i \(-0.212145\pi\)
0.371592 + 0.928396i \(0.378812\pi\)
\(278\) 0 0
\(279\) −18.8563 + 17.6648i −1.12890 + 1.05757i
\(280\) 0 0
\(281\) −4.01544 + 2.31831i −0.239541 + 0.138299i −0.614966 0.788554i \(-0.710830\pi\)
0.375425 + 0.926853i \(0.377497\pi\)
\(282\) 0 0
\(283\) 21.4603 5.75027i 1.27568 0.341818i 0.443478 0.896285i \(-0.353745\pi\)
0.832206 + 0.554467i \(0.187078\pi\)
\(284\) 0 0
\(285\) 6.99313 + 29.3691i 0.414237 + 1.73967i
\(286\) 0 0
\(287\) −1.61913 1.61913i −0.0955743 0.0955743i
\(288\) 0 0
\(289\) 37.8479i 2.22635i
\(290\) 0 0
\(291\) 0.367369 0.847548i 0.0215356 0.0496841i
\(292\) 0 0
\(293\) 5.41478 + 20.2082i 0.316335 + 1.18058i 0.922741 + 0.385422i \(0.125944\pi\)
−0.606406 + 0.795155i \(0.707389\pi\)
\(294\) 0 0
\(295\) −22.6975 3.25955i −1.32150 0.189779i
\(296\) 0 0
\(297\) 0.622035 + 7.57060i 0.0360941 + 0.439291i
\(298\) 0 0
\(299\) 1.85238 + 3.20842i 0.107126 + 0.185547i
\(300\) 0 0
\(301\) −3.56009 + 6.16626i −0.205200 + 0.355417i
\(302\) 0 0
\(303\) −3.25944 8.24683i −0.187250 0.473768i
\(304\) 0 0
\(305\) 1.10612 1.40703i 0.0633362 0.0805660i
\(306\) 0 0
\(307\) 2.56011 2.56011i 0.146113 0.146113i −0.630266 0.776379i \(-0.717054\pi\)
0.776379 + 0.630266i \(0.217054\pi\)
\(308\) 0 0
\(309\) 2.83333 + 24.6168i 0.161183 + 1.40040i
\(310\) 0 0
\(311\) −8.91524 5.14722i −0.505537 0.291872i 0.225460 0.974252i \(-0.427611\pi\)
−0.730997 + 0.682381i \(0.760945\pi\)
\(312\) 0 0
\(313\) −0.629684 + 2.35001i −0.0355918 + 0.132830i −0.981436 0.191791i \(-0.938570\pi\)
0.945844 + 0.324622i \(0.105237\pi\)
\(314\) 0 0
\(315\) 2.14403 12.1089i 0.120802 0.682257i
\(316\) 0 0
\(317\) −1.26665 + 4.72720i −0.0711422 + 0.265506i −0.992331 0.123610i \(-0.960553\pi\)
0.921189 + 0.389116i \(0.127220\pi\)
\(318\) 0 0
\(319\) −5.48695 3.16789i −0.307210 0.177368i
\(320\) 0 0
\(321\) 5.36054 3.97611i 0.299196 0.221925i
\(322\) 0 0
\(323\) 40.8211 40.8211i 2.27135 2.27135i
\(324\) 0 0
\(325\) 15.6272 25.6573i 0.866843 1.42321i
\(326\) 0 0
\(327\) 25.9278 + 3.84455i 1.43381 + 0.212604i
\(328\) 0 0
\(329\) −1.98175 + 3.43250i −0.109258 + 0.189240i
\(330\) 0 0
\(331\) −9.76782 16.9184i −0.536888 0.929918i −0.999069 0.0431321i \(-0.986266\pi\)
0.462181 0.886786i \(-0.347067\pi\)
\(332\) 0 0
\(333\) −7.55127 + 4.03732i −0.413807 + 0.221244i
\(334\) 0 0
\(335\) 11.9415 8.94240i 0.652434 0.488575i
\(336\) 0 0
\(337\) 1.15676 + 4.31709i 0.0630127 + 0.235167i 0.990249 0.139311i \(-0.0444887\pi\)
−0.927236 + 0.374478i \(0.877822\pi\)
\(338\) 0 0
\(339\) −1.16809 + 0.134444i −0.0634418 + 0.00730200i
\(340\) 0 0
\(341\) 12.5907i 0.681822i
\(342\) 0 0
\(343\) 13.7914 + 13.7914i 0.744664 + 0.744664i
\(344\) 0 0
\(345\) 1.13559 + 2.10081i 0.0611382 + 0.113104i
\(346\) 0 0
\(347\) −14.4554 + 3.87331i −0.776006 + 0.207930i −0.625023 0.780606i \(-0.714911\pi\)
−0.150983 + 0.988536i \(0.548244\pi\)
\(348\) 0 0
\(349\) 14.3093 8.26145i 0.765957 0.442225i −0.0654736 0.997854i \(-0.520856\pi\)
0.831430 + 0.555629i \(0.187522\pi\)
\(350\) 0 0
\(351\) 5.58380 30.7169i 0.298041 1.63955i
\(352\) 0 0
\(353\) 26.2963 + 7.04608i 1.39961 + 0.375025i 0.878206 0.478283i \(-0.158741\pi\)
0.521407 + 0.853308i \(0.325407\pi\)
\(354\) 0 0
\(355\) 15.5843 6.24201i 0.827128 0.331291i
\(356\) 0 0
\(357\) −21.8687 + 8.64328i −1.15741 + 0.457451i
\(358\) 0 0
\(359\) 24.0540 1.26952 0.634760 0.772709i \(-0.281099\pi\)
0.634760 + 0.772709i \(0.281099\pi\)
\(360\) 0 0
\(361\) −41.7631 −2.19806
\(362\) 0 0
\(363\) 12.0248 + 9.54246i 0.631138 + 0.500849i
\(364\) 0 0
\(365\) 0.216250 0.505224i 0.0113191 0.0264446i
\(366\) 0 0
\(367\) −24.9352 6.68136i −1.30161 0.348764i −0.459549 0.888152i \(-0.651989\pi\)
−0.842057 + 0.539388i \(0.818656\pi\)
\(368\) 0 0
\(369\) −2.56193 2.73473i −0.133369 0.142364i
\(370\) 0 0
\(371\) −9.15679 + 5.28667i −0.475397 + 0.274470i
\(372\) 0 0
\(373\) 13.2848 3.55965i 0.687861 0.184312i 0.102074 0.994777i \(-0.467452\pi\)
0.585787 + 0.810465i \(0.300785\pi\)
\(374\) 0 0
\(375\) 10.5331 16.2498i 0.543924 0.839134i
\(376\) 0 0
\(377\) 18.4133 + 18.4133i 0.948331 + 0.948331i
\(378\) 0 0
\(379\) 20.7180i 1.06421i 0.846677 + 0.532107i \(0.178599\pi\)
−0.846677 + 0.532107i \(0.821401\pi\)
\(380\) 0 0
\(381\) 3.95155 + 5.32743i 0.202444 + 0.272932i
\(382\) 0 0
\(383\) 3.40046 + 12.6907i 0.173755 + 0.648464i 0.996760 + 0.0804295i \(0.0256292\pi\)
−0.823005 + 0.568034i \(0.807704\pi\)
\(384\) 0 0
\(385\) 3.59186 + 4.79650i 0.183058 + 0.244452i
\(386\) 0 0
\(387\) −6.15210 + 9.89586i −0.312729 + 0.503035i
\(388\) 0 0
\(389\) −7.34592 12.7235i −0.372453 0.645108i 0.617489 0.786579i \(-0.288150\pi\)
−0.989942 + 0.141472i \(0.954817\pi\)
\(390\) 0 0
\(391\) 2.28326 3.95472i 0.115469 0.199999i
\(392\) 0 0
\(393\) 1.60348 2.02061i 0.0808850 0.101926i
\(394\) 0 0
\(395\) −5.29824 4.16516i −0.266583 0.209572i
\(396\) 0 0
\(397\) 21.3106 21.3106i 1.06955 1.06955i 0.0721575 0.997393i \(-0.477012\pi\)
0.997393 0.0721575i \(-0.0229884\pi\)
\(398\) 0 0
\(399\) 22.7088 + 9.84313i 1.13686 + 0.492773i
\(400\) 0 0
\(401\) 31.3918 + 18.1240i 1.56763 + 0.905071i 0.996445 + 0.0842496i \(0.0268493\pi\)
0.571185 + 0.820822i \(0.306484\pi\)
\(402\) 0 0
\(403\) −13.3934 + 49.9848i −0.667172 + 2.48992i
\(404\) 0 0
\(405\) 4.15303 19.6914i 0.206366 0.978475i
\(406\) 0 0
\(407\) 1.07994 4.03040i 0.0535308 0.199780i
\(408\) 0 0
\(409\) 16.1733 + 9.33767i 0.799719 + 0.461718i 0.843373 0.537329i \(-0.180567\pi\)
−0.0436539 + 0.999047i \(0.513900\pi\)
\(410\) 0 0
\(411\) −31.6119 13.7021i −1.55930 0.675877i
\(412\) 0 0
\(413\) −13.2926 + 13.2926i −0.654087 + 0.654087i
\(414\) 0 0
\(415\) −2.03199 16.9710i −0.0997463 0.833072i
\(416\) 0 0
\(417\) 9.75447 12.2920i 0.477679 0.601940i
\(418\) 0 0
\(419\) 7.61327 13.1866i 0.371933 0.644206i −0.617930 0.786233i \(-0.712029\pi\)
0.989863 + 0.142027i \(0.0453619\pi\)
\(420\) 0 0
\(421\) −0.527028 0.912840i −0.0256858 0.0444891i 0.852897 0.522080i \(-0.174844\pi\)
−0.878583 + 0.477590i \(0.841510\pi\)
\(422\) 0 0
\(423\) −3.42462 + 5.50861i −0.166511 + 0.267838i
\(424\) 0 0
\(425\) −37.0195 0.868924i −1.79571 0.0421490i
\(426\) 0 0
\(427\) −0.379756 1.41727i −0.0183777 0.0685865i
\(428\) 0 0
\(429\) 9.06327 + 12.2190i 0.437579 + 0.589938i
\(430\) 0 0
\(431\) 8.98631i 0.432855i 0.976299 + 0.216428i \(0.0694406\pi\)
−0.976299 + 0.216428i \(0.930559\pi\)
\(432\) 0 0
\(433\) −6.68320 6.68320i −0.321174 0.321174i 0.528043 0.849217i \(-0.322926\pi\)
−0.849217 + 0.528043i \(0.822926\pi\)
\(434\) 0 0
\(435\) 11.5318 + 12.1973i 0.552906 + 0.584816i
\(436\) 0 0
\(437\) −4.64268 + 1.24400i −0.222089 + 0.0595087i
\(438\) 0 0
\(439\) 30.4340 17.5711i 1.45253 0.838620i 0.453909 0.891048i \(-0.350029\pi\)
0.998625 + 0.0524278i \(0.0166959\pi\)
\(440\) 0 0
\(441\) 7.46475 + 7.96824i 0.355464 + 0.379440i
\(442\) 0 0
\(443\) −11.6926 3.13303i −0.555533 0.148855i −0.0298795 0.999554i \(-0.509512\pi\)
−0.525653 + 0.850699i \(0.676179\pi\)
\(444\) 0 0
\(445\) −10.2803 25.6667i −0.487335 1.21672i
\(446\) 0 0
\(447\) 11.9177 + 9.45749i 0.563689 + 0.447324i
\(448\) 0 0
\(449\) −23.8523 −1.12566 −0.562830 0.826573i \(-0.690287\pi\)
−0.562830 + 0.826573i \(0.690287\pi\)
\(450\) 0 0
\(451\) 1.82602 0.0859841
\(452\) 0 0
\(453\) −19.3966 + 7.66624i −0.911333 + 0.360191i
\(454\) 0 0
\(455\) −9.15733 22.8629i −0.429302 1.07183i
\(456\) 0 0
\(457\) −28.1504 7.54288i −1.31682 0.352841i −0.469035 0.883180i \(-0.655398\pi\)
−0.847786 + 0.530339i \(0.822065\pi\)
\(458\) 0 0
\(459\) −36.2307 + 12.9704i −1.69110 + 0.605407i
\(460\) 0 0
\(461\) −30.5491 + 17.6375i −1.42281 + 0.821462i −0.996539 0.0831308i \(-0.973508\pi\)
−0.426276 + 0.904593i \(0.640175\pi\)
\(462\) 0 0
\(463\) −36.7523 + 9.84776i −1.70803 + 0.457664i −0.974939 0.222471i \(-0.928588\pi\)
−0.733086 + 0.680135i \(0.761921\pi\)
\(464\) 0 0
\(465\) −9.53333 + 31.9655i −0.442098 + 1.48236i
\(466\) 0 0
\(467\) −8.21539 8.21539i −0.380163 0.380163i 0.490998 0.871161i \(-0.336632\pi\)
−0.871161 + 0.490998i \(0.836632\pi\)
\(468\) 0 0
\(469\) 12.2305i 0.564753i
\(470\) 0 0
\(471\) −14.2397 + 1.63896i −0.656132 + 0.0755192i
\(472\) 0 0
\(473\) −1.46959 5.48459i −0.0675719 0.252182i
\(474\) 0 0
\(475\) 26.9054 + 28.1988i 1.23451 + 1.29385i
\(476\) 0 0
\(477\) −15.2594 + 8.15852i −0.698680 + 0.373553i
\(478\) 0 0
\(479\) 16.9516 + 29.3611i 0.774540 + 1.34154i 0.935053 + 0.354508i \(0.115352\pi\)
−0.160513 + 0.987034i \(0.551315\pi\)
\(480\) 0 0
\(481\) −8.57472 + 14.8518i −0.390974 + 0.677186i
\(482\) 0 0
\(483\) 1.93661 + 0.287159i 0.0881190 + 0.0130662i
\(484\) 0 0
\(485\) −0.141774 1.18409i −0.00643765 0.0537666i
\(486\) 0 0
\(487\) 25.1199 25.1199i 1.13829 1.13829i 0.149532 0.988757i \(-0.452223\pi\)
0.988757 0.149532i \(-0.0477768\pi\)
\(488\) 0 0
\(489\) −29.8358 + 22.1303i −1.34922 + 1.00077i
\(490\) 0 0
\(491\) 12.6088 + 7.27970i 0.569027 + 0.328528i 0.756761 0.653692i \(-0.226781\pi\)
−0.187733 + 0.982220i \(0.560114\pi\)
\(492\) 0 0
\(493\) 8.30744 31.0038i 0.374148 1.39634i
\(494\) 0 0
\(495\) 5.61907 + 8.03706i 0.252558 + 0.361239i
\(496\) 0 0
\(497\) 3.56211 13.2940i 0.159782 0.596316i
\(498\) 0 0
\(499\) −34.7190 20.0450i −1.55424 0.897339i −0.997789 0.0664573i \(-0.978830\pi\)
−0.556448 0.830882i \(-0.687836\pi\)
\(500\) 0 0
\(501\) 1.71168 + 14.8716i 0.0764722 + 0.664412i
\(502\) 0 0
\(503\) 14.0724 14.0724i 0.627459 0.627459i −0.319969 0.947428i \(-0.603672\pi\)
0.947428 + 0.319969i \(0.103672\pi\)
\(504\) 0 0
\(505\) −8.99992 7.07519i −0.400491 0.314842i
\(506\) 0 0
\(507\) −14.7067 37.2099i −0.653147 1.65255i
\(508\) 0 0
\(509\) 5.24682 9.08776i 0.232561 0.402808i −0.726000 0.687695i \(-0.758623\pi\)
0.958561 + 0.284887i \(0.0919560\pi\)
\(510\) 0 0
\(511\) −0.225268 0.390176i −0.00996528 0.0172604i
\(512\) 0 0
\(513\) 36.6184 + 17.3117i 1.61674 + 0.764330i
\(514\) 0 0
\(515\) 19.1751 + 25.6061i 0.844957 + 1.12834i
\(516\) 0 0
\(517\) −0.818060 3.05304i −0.0359782 0.134273i
\(518\) 0 0
\(519\) 6.79330 15.6727i 0.298193 0.687953i
\(520\) 0 0
\(521\) 20.4281i 0.894970i −0.894291 0.447485i \(-0.852320\pi\)
0.894291 0.447485i \(-0.147680\pi\)
\(522\) 0 0
\(523\) −24.6965 24.6965i −1.07990 1.07990i −0.996517 0.0833870i \(-0.973426\pi\)
−0.0833870 0.996517i \(-0.526574\pi\)
\(524\) 0 0
\(525\) −5.48731 14.8971i −0.239486 0.650165i
\(526\) 0 0
\(527\) 61.6116 16.5088i 2.68385 0.719134i
\(528\) 0 0
\(529\) 19.5893 11.3099i 0.851710 0.491735i
\(530\) 0 0
\(531\) −22.4514 + 21.0327i −0.974306 + 0.912742i
\(532\) 0 0
\(533\) −7.24930 1.94244i −0.314002 0.0841366i
\(534\) 0 0
\(535\) 3.39051 7.92123i 0.146585 0.342465i
\(536\) 0 0
\(537\) −3.82839 + 25.8189i −0.165207 + 1.11417i
\(538\) 0 0
\(539\) −5.32052 −0.229171
\(540\) 0 0
\(541\) 1.43317 0.0616167 0.0308083 0.999525i \(-0.490192\pi\)
0.0308083 + 0.999525i \(0.490192\pi\)
\(542\) 0 0
\(543\) 1.32182 8.91440i 0.0567246 0.382554i
\(544\) 0 0
\(545\) 31.4127 12.5818i 1.34557 0.538944i
\(546\) 0 0
\(547\) −32.2567 8.64315i −1.37920 0.369554i −0.508366 0.861141i \(-0.669750\pi\)
−0.870829 + 0.491587i \(0.836417\pi\)
\(548\) 0 0
\(549\) −0.545519 2.33842i −0.0232822 0.0998013i
\(550\) 0 0
\(551\) −29.2578 + 16.8920i −1.24642 + 0.719623i
\(552\) 0 0
\(553\) −5.33681 + 1.42999i −0.226944 + 0.0608096i
\(554\) 0 0
\(555\) −5.79350 + 9.41478i −0.245921 + 0.399635i
\(556\) 0 0
\(557\) 7.50833 + 7.50833i 0.318138 + 0.318138i 0.848052 0.529913i \(-0.177776\pi\)
−0.529913 + 0.848052i \(0.677776\pi\)
\(558\) 0 0
\(559\) 23.3370i 0.987052i
\(560\) 0 0
\(561\) 7.45766 17.2054i 0.314863 0.726412i
\(562\) 0 0
\(563\) 2.30163 + 8.58979i 0.0970020 + 0.362017i 0.997315 0.0732258i \(-0.0233294\pi\)
−0.900313 + 0.435242i \(0.856663\pi\)
\(564\) 0 0
\(565\) −1.21503 + 0.909876i −0.0511167 + 0.0382788i
\(566\) 0 0
\(567\) −10.8810 12.4017i −0.456957 0.520824i
\(568\) 0 0
\(569\) −1.40287 2.42983i −0.0588112 0.101864i 0.835121 0.550067i \(-0.185398\pi\)
−0.893932 + 0.448203i \(0.852064\pi\)
\(570\) 0 0
\(571\) 12.8577 22.2702i 0.538078 0.931978i −0.460930 0.887437i \(-0.652484\pi\)
0.999008 0.0445413i \(-0.0141826\pi\)
\(572\) 0 0
\(573\) −4.41651 11.1744i −0.184502 0.466815i
\(574\) 0 0
\(575\) 2.63306 + 1.60373i 0.109806 + 0.0668803i
\(576\) 0 0
\(577\) 13.0019 13.0019i 0.541278 0.541278i −0.382625 0.923904i \(-0.624980\pi\)
0.923904 + 0.382625i \(0.124980\pi\)
\(578\) 0 0
\(579\) 0.704411 + 6.12013i 0.0292743 + 0.254344i
\(580\) 0 0
\(581\) −12.1351 7.00620i −0.503449 0.290666i
\(582\) 0 0
\(583\) 2.18232 8.14452i 0.0903824 0.337312i
\(584\) 0 0
\(585\) −13.7582 37.8843i −0.568830 1.56632i
\(586\) 0 0
\(587\) −0.405924 + 1.51493i −0.0167543 + 0.0625278i −0.973797 0.227420i \(-0.926971\pi\)
0.957043 + 0.289947i \(0.0936378\pi\)
\(588\) 0 0
\(589\) −58.1419 33.5683i −2.39570 1.38316i
\(590\) 0 0
\(591\) −26.5818 + 19.7167i −1.09343 + 0.811036i
\(592\) 0 0
\(593\) −3.47807 + 3.47807i −0.142827 + 0.142827i −0.774905 0.632078i \(-0.782202\pi\)
0.632078 + 0.774905i \(0.282202\pi\)
\(594\) 0 0
\(595\) −18.7618 + 23.8657i −0.769158 + 0.978398i
\(596\) 0 0
\(597\) −6.21289 0.921239i −0.254277 0.0377038i
\(598\) 0 0
\(599\) 15.1505 26.2415i 0.619033 1.07220i −0.370629 0.928781i \(-0.620858\pi\)
0.989662 0.143416i \(-0.0458088\pi\)
\(600\) 0 0
\(601\) 0.302116 + 0.523281i 0.0123236 + 0.0213451i 0.872121 0.489290i \(-0.162744\pi\)
−0.859798 + 0.510635i \(0.829411\pi\)
\(602\) 0 0
\(603\) 0.652647 20.0048i 0.0265778 0.814660i
\(604\) 0 0
\(605\) 19.6169 + 2.81715i 0.797539 + 0.114534i
\(606\) 0 0
\(607\) −1.07322 4.00531i −0.0435606 0.162570i 0.940719 0.339186i \(-0.110152\pi\)
−0.984280 + 0.176616i \(0.943485\pi\)
\(608\) 0 0
\(609\) 13.6708 1.57347i 0.553969 0.0637604i
\(610\) 0 0
\(611\) 12.9908i 0.525550i
\(612\) 0 0
\(613\) 25.1010 + 25.1010i 1.01382 + 1.01382i 0.999903 + 0.0139172i \(0.00443013\pi\)
0.0139172 + 0.999903i \(0.495570\pi\)
\(614\) 0 0
\(615\) −4.63596 1.38262i −0.186940 0.0557526i
\(616\) 0 0
\(617\) −1.88928 + 0.506231i −0.0760595 + 0.0203801i −0.296648 0.954987i \(-0.595869\pi\)
0.220589 + 0.975367i \(0.429202\pi\)
\(618\) 0 0
\(619\) −32.7306 + 18.8970i −1.31555 + 0.759535i −0.983010 0.183553i \(-0.941240\pi\)
−0.332543 + 0.943088i \(0.607907\pi\)
\(620\) 0 0
\(621\) 3.15230 + 0.573033i 0.126497 + 0.0229950i
\(622\) 0 0
\(623\) −21.8946 5.86664i −0.877189 0.235042i
\(624\) 0 0
\(625\) 1.17296 24.9725i 0.0469183 0.998899i
\(626\) 0 0
\(627\) −18.3557 + 7.25484i −0.733057 + 0.289730i
\(628\) 0 0
\(629\) 21.1385 0.842849
\(630\) 0 0
\(631\) 22.9460 0.913467 0.456734 0.889604i \(-0.349019\pi\)
0.456734 + 0.889604i \(0.349019\pi\)
\(632\) 0 0
\(633\) 3.20622 + 2.54435i 0.127436 + 0.101129i
\(634\) 0 0
\(635\) 7.87230 + 3.36957i 0.312403 + 0.133717i
\(636\) 0 0
\(637\) 21.1224 + 5.65974i 0.836901 + 0.224247i
\(638\) 0 0
\(639\) 6.53575 21.5542i 0.258550 0.852670i
\(640\) 0 0
\(641\) 0.807840 0.466407i 0.0319078 0.0184220i −0.483961 0.875089i \(-0.660802\pi\)
0.515869 + 0.856667i \(0.327469\pi\)
\(642\) 0 0
\(643\) −9.64822 + 2.58523i −0.380489 + 0.101952i −0.443994 0.896030i \(-0.646439\pi\)
0.0635050 + 0.997982i \(0.479772\pi\)
\(644\) 0 0
\(645\) −0.421757 + 15.0372i −0.0166067 + 0.592087i
\(646\) 0 0
\(647\) −14.9808 14.9808i −0.588955 0.588955i 0.348393 0.937348i \(-0.386727\pi\)
−0.937348 + 0.348393i \(0.886727\pi\)
\(648\) 0 0
\(649\) 14.9911i 0.588454i
\(650\) 0 0
\(651\) 16.2914 + 21.9639i 0.638512 + 0.860833i
\(652\) 0 0
\(653\) −2.93068 10.9375i −0.114687 0.428016i 0.884577 0.466395i \(-0.154447\pi\)
−0.999263 + 0.0383787i \(0.987781\pi\)
\(654\) 0 0
\(655\) 0.473385 3.29635i 0.0184967 0.128799i
\(656\) 0 0
\(657\) −0.347639 0.650212i −0.0135627 0.0253672i
\(658\) 0 0
\(659\) 16.3472 + 28.3142i 0.636796 + 1.10296i 0.986132 + 0.165965i \(0.0530739\pi\)
−0.349336 + 0.936998i \(0.613593\pi\)
\(660\) 0 0
\(661\) 0.0453877 0.0786137i 0.00176538 0.00305772i −0.865141 0.501528i \(-0.832771\pi\)
0.866907 + 0.498470i \(0.166105\pi\)
\(662\) 0 0
\(663\) −47.9092 + 60.3720i −1.86064 + 2.34466i
\(664\) 0 0
\(665\) 31.7259 3.79864i 1.23028 0.147305i
\(666\) 0 0
\(667\) −1.88965 + 1.88965i −0.0731674 + 0.0731674i
\(668\) 0 0
\(669\) 24.3269 + 10.5445i 0.940534 + 0.407674i
\(670\) 0 0
\(671\) 1.01332 + 0.585043i 0.0391190 + 0.0225853i
\(672\) 0 0
\(673\) −3.20385 + 11.9569i −0.123499 + 0.460906i −0.999782 0.0208918i \(-0.993349\pi\)
0.876282 + 0.481798i \(0.160016\pi\)
\(674\) 0 0
\(675\) −8.18037 24.6593i −0.314863 0.949137i
\(676\) 0 0
\(677\) −5.19243 + 19.3784i −0.199561 + 0.744773i 0.791477 + 0.611198i \(0.209312\pi\)
−0.991039 + 0.133575i \(0.957354\pi\)
\(678\) 0 0
\(679\) −0.846682 0.488832i −0.0324927 0.0187597i
\(680\) 0 0
\(681\) −15.7478 6.82589i −0.603458 0.261569i
\(682\) 0 0
\(683\) −3.05629 + 3.05629i −0.116946 + 0.116946i −0.763158 0.646212i \(-0.776352\pi\)
0.646212 + 0.763158i \(0.276352\pi\)
\(684\) 0 0
\(685\) −44.1641 + 5.28791i −1.68742 + 0.202041i
\(686\) 0 0
\(687\) 9.38573 11.8273i 0.358088 0.451240i
\(688\) 0 0
\(689\) −17.3276 + 30.0122i −0.660127 + 1.14337i
\(690\) 0 0
\(691\) 10.3415 + 17.9120i 0.393410 + 0.681406i 0.992897 0.118978i \(-0.0379619\pi\)
−0.599487 + 0.800385i \(0.704629\pi\)
\(692\) 0 0
\(693\) 8.03526 + 0.262146i 0.305234 + 0.00995811i
\(694\) 0 0
\(695\) 2.87974 20.0527i 0.109235 0.760642i
\(696\) 0 0
\(697\) 2.39427 + 8.93554i 0.0906895 + 0.338458i
\(698\) 0 0
\(699\) 29.2147 + 39.3869i 1.10500 + 1.48975i
\(700\) 0 0
\(701\) 46.6921i 1.76354i −0.471682 0.881769i \(-0.656353\pi\)
0.471682 0.881769i \(-0.343647\pi\)
\(702\) 0 0
\(703\) −15.7326 15.7326i −0.593365 0.593365i
\(704\) 0 0
\(705\) −0.234775 + 8.37055i −0.00884212 + 0.315253i
\(706\) 0 0
\(707\) −9.06544 + 2.42908i −0.340941 + 0.0913548i
\(708\) 0 0
\(709\) −14.1385 + 8.16289i −0.530984 + 0.306564i −0.741417 0.671045i \(-0.765846\pi\)
0.210433 + 0.977608i \(0.432513\pi\)
\(710\) 0 0
\(711\) −8.80546 + 2.05419i −0.330231 + 0.0770380i
\(712\) 0 0
\(713\) −5.12965 1.37449i −0.192107 0.0514749i
\(714\) 0 0
\(715\) 18.0559 + 7.72844i 0.675252 + 0.289027i
\(716\) 0 0
\(717\) 0.689313 + 0.547015i 0.0257429 + 0.0204287i
\(718\) 0 0
\(719\) 44.7865 1.67026 0.835128 0.550056i \(-0.185394\pi\)
0.835128 + 0.550056i \(0.185394\pi\)
\(720\) 0 0
\(721\) 26.2258 0.976701
\(722\) 0 0
\(723\) −12.5079 + 4.94358i −0.465175 + 0.183854i
\(724\) 0 0
\(725\) 20.7943 + 6.09826i 0.772282 + 0.226484i
\(726\) 0 0
\(727\) 16.9830 + 4.55058i 0.629865 + 0.168772i 0.559608 0.828757i \(-0.310952\pi\)
0.0702565 + 0.997529i \(0.477618\pi\)
\(728\) 0 0
\(729\) −17.1356 20.8655i −0.634653 0.772797i
\(730\) 0 0
\(731\) 24.9116 14.3827i 0.921389 0.531964i
\(732\) 0 0
\(733\) 44.6819 11.9725i 1.65036 0.442214i 0.690650 0.723190i \(-0.257325\pi\)
0.959715 + 0.280976i \(0.0906581\pi\)
\(734\) 0 0
\(735\) 13.5079 + 4.02857i 0.498246 + 0.148596i
\(736\) 0 0
\(737\) 6.89666 + 6.89666i 0.254042 + 0.254042i
\(738\) 0 0
\(739\) 26.3743i 0.970194i −0.874460 0.485097i \(-0.838784\pi\)
0.874460 0.485097i \(-0.161216\pi\)
\(740\) 0 0
\(741\) 80.5894 9.27563i 2.96052 0.340749i
\(742\) 0 0
\(743\) 0.327054 + 1.22058i 0.0119985 + 0.0447789i 0.971666 0.236360i \(-0.0759545\pi\)
−0.959667 + 0.281139i \(0.909288\pi\)
\(744\) 0 0
\(745\) 19.4422 + 2.79207i 0.712306 + 0.102293i
\(746\) 0 0
\(747\) −19.4749 12.1072i −0.712549 0.442981i
\(748\) 0 0
\(749\) −3.53190 6.11743i −0.129053 0.223526i
\(750\) 0 0
\(751\) −16.9258 + 29.3164i −0.617633 + 1.06977i 0.372284 + 0.928119i \(0.378575\pi\)
−0.989916 + 0.141652i \(0.954759\pi\)
\(752\) 0 0
\(753\) 24.9386 + 3.69787i 0.908813 + 0.134758i
\(754\) 0 0
\(755\) −16.6409 + 21.1679i −0.605625 + 0.770379i
\(756\) 0 0
\(757\) −7.27687 + 7.27687i −0.264482 + 0.264482i −0.826872 0.562390i \(-0.809882\pi\)
0.562390 + 0.826872i \(0.309882\pi\)
\(758\) 0 0
\(759\) −1.25396 + 0.930112i −0.0455160 + 0.0337609i
\(760\) 0 0
\(761\) 38.3111 + 22.1189i 1.38878 + 0.801810i 0.993177 0.116614i \(-0.0372040\pi\)
0.395598 + 0.918424i \(0.370537\pi\)
\(762\) 0 0
\(763\) 7.18001 26.7962i 0.259934 0.970086i
\(764\) 0 0
\(765\) −31.9612 + 38.0347i −1.15556 + 1.37515i
\(766\) 0 0
\(767\) −15.9469 + 59.5147i −0.575809 + 2.14895i
\(768\) 0 0
\(769\) 26.7495 + 15.4438i 0.964611 + 0.556918i 0.897589 0.440833i \(-0.145317\pi\)
0.0670216 + 0.997752i \(0.478650\pi\)
\(770\) 0 0
\(771\) −4.04700 35.1615i −0.145749 1.26631i
\(772\) 0 0
\(773\) −3.78933 + 3.78933i −0.136293 + 0.136293i −0.771962 0.635669i \(-0.780724\pi\)
0.635669 + 0.771962i \(0.280724\pi\)
\(774\) 0 0
\(775\) 10.1665 + 41.8462i 0.365191 + 1.50316i
\(776\) 0 0
\(777\) 3.33114 + 8.42824i 0.119504 + 0.302362i
\(778\) 0 0
\(779\) 4.86841 8.43233i 0.174429 0.302120i
\(780\) 0 0
\(781\) 5.48770 + 9.50497i 0.196365 + 0.340115i
\(782\) 0 0
\(783\) 22.4446 1.84415i 0.802104 0.0659045i
\(784\) 0 0
\(785\) −14.8120 + 11.0920i −0.528663 + 0.395889i
\(786\) 0 0
\(787\) −2.36210 8.81547i −0.0841997 0.314238i 0.910962 0.412491i \(-0.135341\pi\)
−0.995161 + 0.0982533i \(0.968674\pi\)
\(788\) 0 0
\(789\) 11.4844 26.4954i 0.408856 0.943261i
\(790\) 0 0
\(791\) 1.24444i 0.0442471i
\(792\) 0 0
\(793\) −3.40054 3.40054i −0.120757 0.120757i
\(794\) 0 0
\(795\) −11.7074 + 19.0251i −0.415217 + 0.674752i
\(796\) 0 0
\(797\) −18.0705 + 4.84198i −0.640090 + 0.171512i −0.564244 0.825608i \(-0.690832\pi\)
−0.0758457 + 0.997120i \(0.524166\pi\)
\(798\) 0 0
\(799\) 13.8672 8.00625i 0.490588 0.283241i
\(800\) 0 0
\(801\) −35.4988 10.7641i −1.25429 0.380331i
\(802\) 0 0
\(803\) 0.347043 + 0.0929899i 0.0122469 + 0.00328154i
\(804\) 0 0
\(805\) 2.34629 0.939765i 0.0826958 0.0331223i
\(806\) 0 0
\(807\) −3.85004 + 25.9649i −0.135528 + 0.914008i
\(808\) 0 0
\(809\) −17.3943 −0.611551 −0.305776 0.952104i \(-0.598916\pi\)
−0.305776 + 0.952104i \(0.598916\pi\)
\(810\) 0 0
\(811\) −12.0872 −0.424441 −0.212220 0.977222i \(-0.568069\pi\)
−0.212220 + 0.977222i \(0.568069\pi\)
\(812\) 0 0
\(813\) 4.77707 32.2168i 0.167539 1.12989i
\(814\) 0 0
\(815\) −18.8710 + 44.0881i −0.661021 + 1.54434i
\(816\) 0 0
\(817\) −29.2452 7.83622i −1.02316 0.274155i
\(818\) 0 0
\(819\) −31.6210 9.58827i −1.10493 0.335041i
\(820\) 0 0
\(821\) 26.7757 15.4590i 0.934480 0.539522i 0.0462541 0.998930i \(-0.485272\pi\)
0.888226 + 0.459408i \(0.151938\pi\)
\(822\) 0 0
\(823\) 16.7879 4.49831i 0.585190 0.156801i 0.0459362 0.998944i \(-0.485373\pi\)
0.539254 + 0.842143i \(0.318706\pi\)
\(824\) 0 0
\(825\) 11.4946 + 5.30611i 0.400190 + 0.184735i
\(826\) 0 0
\(827\) −31.3405 31.3405i −1.08982 1.08982i −0.995547 0.0942693i \(-0.969949\pi\)
−0.0942693 0.995547i \(-0.530051\pi\)
\(828\) 0 0
\(829\) 40.7122i 1.41399i 0.707216 + 0.706997i \(0.249951\pi\)
−0.707216 + 0.706997i \(0.750049\pi\)
\(830\) 0 0
\(831\) 13.7394 31.6978i 0.476614 1.09958i
\(832\) 0 0
\(833\) −6.97624 26.0357i −0.241712 0.902083i
\(834\) 0 0
\(835\) 11.5841 + 15.4692i 0.400885 + 0.535334i
\(836\) 0 0
\(837\) 25.4750 + 36.7946i 0.880546 + 1.27181i
\(838\) 0 0
\(839\) −15.5669 26.9626i −0.537427 0.930851i −0.999042 0.0437707i \(-0.986063\pi\)
0.461614 0.887081i \(-0.347270\pi\)
\(840\) 0 0
\(841\) 5.10814 8.84756i 0.176143 0.305088i
\(842\) 0 0
\(843\) 2.95189 + 7.46869i 0.101669 + 0.257235i
\(844\) 0 0
\(845\) −40.6079 31.9235i −1.39695 1.09820i
\(846\) 0 0
\(847\) 11.4885 11.4885i 0.394749 0.394749i
\(848\) 0 0
\(849\) −4.40008 38.2292i −0.151010 1.31202i
\(850\) 0 0
\(851\) −1.52416 0.879974i −0.0522475 0.0301651i
\(852\) 0 0
\(853\) 1.58215 5.90466i 0.0541718 0.202172i −0.933536 0.358484i \(-0.883294\pi\)
0.987708 + 0.156312i \(0.0499605\pi\)
\(854\) 0 0
\(855\) 52.0952 4.52028i 1.78162 0.154590i
\(856\) 0 0
\(857\) −9.19733 + 34.3249i −0.314175 + 1.17252i 0.610581 + 0.791954i \(0.290936\pi\)
−0.924755 + 0.380562i \(0.875731\pi\)
\(858\) 0 0
\(859\) −0.0418217 0.0241458i −0.00142694 0.000823843i 0.499286 0.866437i \(-0.333596\pi\)
−0.500713 + 0.865613i \(0.666929\pi\)
\(860\) 0 0
\(861\) −3.18543 + 2.36275i −0.108559 + 0.0805223i
\(862\) 0 0
\(863\) −17.6902 + 17.6902i −0.602182 + 0.602182i −0.940891 0.338709i \(-0.890010\pi\)
0.338709 + 0.940891i \(0.390010\pi\)
\(864\) 0 0
\(865\) −2.62166 21.8959i −0.0891391 0.744482i
\(866\) 0 0
\(867\) 64.8456 + 9.61522i 2.20227 + 0.326550i
\(868\) 0 0
\(869\) 2.20302 3.81573i 0.0747322 0.129440i
\(870\) 0 0
\(871\) −20.0433 34.7160i −0.679142 1.17631i
\(872\) 0 0
\(873\) −1.35879 0.844739i −0.0459881 0.0285901i
\(874\) 0 0
\(875\) −15.8109 13.0413i −0.534505 0.440877i
\(876\) 0 0
\(877\) 9.46068 + 35.3077i 0.319464 + 1.19226i 0.919761 + 0.392480i \(0.128383\pi\)
−0.600296 + 0.799778i \(0.704951\pi\)
\(878\) 0 0
\(879\) 35.9987 4.14336i 1.21421 0.139752i
\(880\) 0 0
\(881\) 11.1310i 0.375012i −0.982264 0.187506i \(-0.939960\pi\)
0.982264 0.187506i \(-0.0600403\pi\)
\(882\) 0 0
\(883\) 8.73609 + 8.73609i 0.293993 + 0.293993i 0.838655 0.544662i \(-0.183342\pi\)
−0.544662 + 0.838655i \(0.683342\pi\)
\(884\) 0 0
\(885\) −11.3509 + 38.0599i −0.381557 + 1.27937i
\(886\) 0 0
\(887\) 6.73775 1.80538i 0.226232 0.0606186i −0.143922 0.989589i \(-0.545972\pi\)
0.370154 + 0.928970i \(0.379305\pi\)
\(888\) 0 0
\(889\) 6.07964 3.51008i 0.203905 0.117724i
\(890\) 0 0
\(891\) 13.1289 + 0.857558i 0.439834 + 0.0287293i
\(892\) 0 0
\(893\) −16.2796 4.36210i −0.544775 0.145972i
\(894\) 0 0
\(895\) 12.5289 + 31.2807i 0.418795 + 1.04560i
\(896\) 0 0
\(897\) 5.96763 2.35862i 0.199253 0.0787521i
\(898\) 0 0
\(899\) −37.3276 −1.24494
\(900\) 0 0
\(901\) 42.7162 1.42308
\(902\) 0 0
\(903\) 9.66032 + 7.66610i 0.321475 + 0.255112i
\(904\) 0 0
\(905\) −4.32581 10.8002i −0.143795 0.359010i
\(906\) 0 0
\(907\) −9.02482 2.41819i −0.299664 0.0802948i 0.105854 0.994382i \(-0.466242\pi\)
−0.405518 + 0.914087i \(0.632909\pi\)
\(908\) 0 0
\(909\) −14.9575 + 3.48937i −0.496109 + 0.115735i
\(910\) 0 0
\(911\) 32.7455 18.9056i 1.08491 0.626372i 0.152692 0.988274i \(-0.451206\pi\)
0.932216 + 0.361902i \(0.117872\pi\)
\(912\) 0 0
\(913\) 10.7936 2.89213i 0.357216 0.0957156i
\(914\) 0 0
\(915\) −2.12967 2.25259i −0.0704049 0.0744682i
\(916\) 0 0
\(917\) −1.93048 1.93048i −0.0637502 0.0637502i
\(918\) 0 0
\(919\) 4.94192i 0.163019i −0.996673 0.0815094i \(-0.974026\pi\)
0.996673 0.0815094i \(-0.0259741\pi\)
\(920\) 0 0
\(921\) −3.73590 5.03668i −0.123102 0.165964i
\(922\) 0 0
\(923\) −11.6751 43.5722i −0.384292 1.43420i
\(924\) 0 0
\(925\) −0.334886 + 14.2674i −0.0110110 + 0.469110i
\(926\) 0 0
\(927\) 42.8962 + 1.39947i 1.40890 + 0.0459645i
\(928\) 0 0
\(929\) 20.1464 + 34.8946i 0.660983 + 1.14486i 0.980358 + 0.197227i \(0.0631937\pi\)
−0.319375 + 0.947628i \(0.603473\pi\)
\(930\) 0 0
\(931\) −14.1852 + 24.5694i −0.464900 + 0.805231i
\(932\) 0 0
\(933\) −11.0837 + 13.9670i −0.362865 + 0.457259i
\(934\) 0 0
\(935\) −2.87805 24.0372i −0.0941222 0.786100i
\(936\) 0 0
\(937\) −13.5389 + 13.5389i −0.442297 + 0.442297i −0.892783 0.450486i \(-0.851251\pi\)
0.450486 + 0.892783i \(0.351251\pi\)
\(938\) 0 0
\(939\) 3.86635 + 1.67587i 0.126173 + 0.0546898i
\(940\) 0 0
\(941\) 34.6711 + 20.0174i 1.13025 + 0.652547i 0.943997 0.329955i \(-0.107034\pi\)
0.186248 + 0.982503i \(0.440367\pi\)
\(942\) 0 0
\(943\) 0.199342 0.743954i 0.00649146 0.0242265i
\(944\) 0 0
\(945\) −20.2016 6.74964i −0.657159 0.219566i
\(946\) 0 0
\(947\) −1.97013 + 7.35262i −0.0640206 + 0.238928i −0.990520 0.137368i \(-0.956136\pi\)
0.926500 + 0.376296i \(0.122802\pi\)
\(948\) 0 0
\(949\) −1.27884 0.738337i −0.0415128 0.0239674i
\(950\) 0 0
\(951\) 7.77741 + 3.37111i 0.252200 + 0.109316i
\(952\) 0 0
\(953\) 11.0032 11.0032i 0.356429 0.356429i −0.506066 0.862495i \(-0.668901\pi\)
0.862495 + 0.506066i \(0.168901\pi\)
\(954\) 0 0
\(955\) −12.1948 9.58681i −0.394614 0.310222i
\(956\) 0 0
\(957\) −6.82156 + 8.59609i −0.220510 + 0.277872i
\(958\) 0 0
\(959\) −18.2325 + 31.5796i −0.588757 + 1.01976i
\(960\) 0 0
\(961\) −21.5892 37.3936i −0.696427 1.20625i
\(962\) 0 0
\(963\) −5.45051 10.1944i −0.175640 0.328511i
\(964\) 0 0
\(965\) 4.76724 + 6.36608i 0.153463 + 0.204931i
\(966\) 0 0
\(967\) −0.648313 2.41954i −0.0208483 0.0778070i 0.954718 0.297513i \(-0.0961570\pi\)
−0.975566 + 0.219706i \(0.929490\pi\)
\(968\) 0 0
\(969\) −59.5690 80.3101i −1.91363 2.57993i
\(970\) 0 0
\(971\) 16.0074i 0.513701i 0.966451 + 0.256850i \(0.0826848\pi\)
−0.966451 + 0.256850i \(0.917315\pi\)
\(972\) 0 0
\(973\) −11.7437 11.7437i −0.376486 0.376486i
\(974\) 0 0
\(975\) −39.9890 33.2926i −1.28067 1.06622i
\(976\) 0 0
\(977\) 12.1641 3.25935i 0.389163 0.104276i −0.0589319 0.998262i \(-0.518769\pi\)
0.448094 + 0.893986i \(0.352103\pi\)
\(978\) 0 0
\(979\) 15.6543 9.03801i 0.500313 0.288856i
\(980\) 0 0
\(981\) 13.1739 43.4460i 0.420609 1.38712i
\(982\) 0 0
\(983\) −51.1769 13.7128i −1.63229 0.437371i −0.677712 0.735328i \(-0.737028\pi\)
−0.954579 + 0.297957i \(0.903695\pi\)
\(984\) 0 0
\(985\) −16.8128 + 39.2797i −0.535701 + 1.25155i
\(986\) 0 0
\(987\) 5.37750 + 4.26739i 0.171168 + 0.135833i
\(988\) 0 0
\(989\) −2.39495 −0.0761549
\(990\) 0 0
\(991\) 14.4832 0.460073 0.230036 0.973182i \(-0.426115\pi\)
0.230036 + 0.973182i \(0.426115\pi\)
\(992\) 0 0
\(993\) −31.4680 + 12.4373i −0.998608 + 0.394686i
\(994\) 0 0
\(995\) −7.52717 + 3.01488i −0.238627 + 0.0955780i
\(996\) 0 0
\(997\) −55.8004 14.9517i −1.76722 0.473524i −0.779058 0.626952i \(-0.784302\pi\)
−0.988160 + 0.153428i \(0.950969\pi\)
\(998\) 0 0
\(999\) 4.99883 + 13.9634i 0.158156 + 0.441782i
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.bs.a.113.9 72
3.2 odd 2 1080.2.bt.a.233.12 72
4.3 odd 2 720.2.cu.e.113.10 72
5.2 odd 4 inner 360.2.bs.a.257.1 yes 72
9.2 odd 6 inner 360.2.bs.a.353.1 yes 72
9.7 even 3 1080.2.bt.a.953.18 72
15.2 even 4 1080.2.bt.a.17.18 72
20.7 even 4 720.2.cu.e.257.18 72
36.11 even 6 720.2.cu.e.353.18 72
45.2 even 12 inner 360.2.bs.a.137.9 yes 72
45.7 odd 12 1080.2.bt.a.737.12 72
180.47 odd 12 720.2.cu.e.497.10 72
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
360.2.bs.a.113.9 72 1.1 even 1 trivial
360.2.bs.a.137.9 yes 72 45.2 even 12 inner
360.2.bs.a.257.1 yes 72 5.2 odd 4 inner
360.2.bs.a.353.1 yes 72 9.2 odd 6 inner
720.2.cu.e.113.10 72 4.3 odd 2
720.2.cu.e.257.18 72 20.7 even 4
720.2.cu.e.353.18 72 36.11 even 6
720.2.cu.e.497.10 72 180.47 odd 12
1080.2.bt.a.17.18 72 15.2 even 4
1080.2.bt.a.233.12 72 3.2 odd 2
1080.2.bt.a.737.12 72 45.7 odd 12
1080.2.bt.a.953.18 72 9.7 even 3