Properties

Label 360.2.bs.a.137.2
Level $360$
Weight $2$
Character 360.137
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 137.2
Character \(\chi\) \(=\) 360.137
Dual form 360.2.bs.a.113.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.71407 - 0.248907i) q^{3} +(0.528278 + 2.17277i) q^{5} +(-0.980572 + 0.262743i) q^{7} +(2.87609 + 0.853289i) q^{9} +O(q^{10})\) \(q+(-1.71407 - 0.248907i) q^{3} +(0.528278 + 2.17277i) q^{5} +(-0.980572 + 0.262743i) q^{7} +(2.87609 + 0.853289i) q^{9} +(-3.66231 - 2.11444i) q^{11} +(-3.89065 - 1.04250i) q^{13} +(-0.364690 - 3.85578i) q^{15} +(-2.61068 + 2.61068i) q^{17} +0.281469i q^{19} +(1.74617 - 0.206290i) q^{21} +(-2.36908 + 8.84152i) q^{23} +(-4.44185 + 2.29565i) q^{25} +(-4.71744 - 2.17848i) q^{27} +(-2.93812 + 5.08896i) q^{29} +(-0.835561 - 1.44723i) q^{31} +(5.75117 + 4.53587i) q^{33} +(-1.08889 - 1.99175i) q^{35} +(-3.09788 - 3.09788i) q^{37} +(6.40937 + 2.75532i) q^{39} +(10.9685 - 6.33265i) q^{41} +(-2.26685 - 8.45998i) q^{43} +(-0.334624 + 6.69985i) q^{45} +(0.481889 + 1.79843i) q^{47} +(-5.16969 + 2.98472i) q^{49} +(5.12470 - 3.82507i) q^{51} +(1.91696 + 1.91696i) q^{53} +(2.65946 - 9.07436i) q^{55} +(0.0700596 - 0.482459i) q^{57} +(4.31085 + 7.46661i) q^{59} +(2.82244 - 4.88861i) q^{61} +(-3.04441 - 0.0810368i) q^{63} +(0.209760 - 9.00420i) q^{65} +(-1.50752 + 5.62615i) q^{67} +(6.26149 - 14.5653i) q^{69} +1.92890i q^{71} +(4.05914 - 4.05914i) q^{73} +(8.18505 - 2.82931i) q^{75} +(4.14671 + 1.11111i) q^{77} +(3.19722 + 1.84591i) q^{79} +(7.54380 + 4.90827i) q^{81} +(-0.950284 + 0.254628i) q^{83} +(-7.05156 - 4.29323i) q^{85} +(6.30282 - 7.99154i) q^{87} -6.94741 q^{89} +4.08897 q^{91} +(1.07199 + 2.68864i) q^{93} +(-0.611567 + 0.148694i) q^{95} +(3.20533 - 0.858865i) q^{97} +(-8.72891 - 9.20632i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 72 q+O(q^{10}) \) 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 \(\left(\mathbb{Z}/360\mathbb{Z}\right)^\times\).

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

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
\(3\) −1.71407 0.248907i −0.989620 0.143706i
\(4\) 0 0
\(5\) 0.528278 + 2.17277i 0.236253 + 0.971692i
\(6\) 0 0
\(7\) −0.980572 + 0.262743i −0.370621 + 0.0993077i −0.439322 0.898330i \(-0.644781\pi\)
0.0687007 + 0.997637i \(0.478115\pi\)
\(8\) 0 0
\(9\) 2.87609 + 0.853289i 0.958697 + 0.284430i
\(10\) 0 0
\(11\) −3.66231 2.11444i −1.10423 0.637526i −0.166900 0.985974i \(-0.553376\pi\)
−0.937328 + 0.348448i \(0.886709\pi\)
\(12\) 0 0
\(13\) −3.89065 1.04250i −1.07907 0.289136i −0.324856 0.945764i \(-0.605316\pi\)
−0.754215 + 0.656627i \(0.771982\pi\)
\(14\) 0 0
\(15\) −0.364690 3.85578i −0.0941624 0.995557i
\(16\) 0 0
\(17\) −2.61068 + 2.61068i −0.633182 + 0.633182i −0.948865 0.315683i \(-0.897766\pi\)
0.315683 + 0.948865i \(0.397766\pi\)
\(18\) 0 0
\(19\) 0.281469i 0.0645734i 0.999479 + 0.0322867i \(0.0102790\pi\)
−0.999479 + 0.0322867i \(0.989721\pi\)
\(20\) 0 0
\(21\) 1.74617 0.206290i 0.381046 0.0450163i
\(22\) 0 0
\(23\) −2.36908 + 8.84152i −0.493987 + 1.84358i 0.0416437 + 0.999133i \(0.486741\pi\)
−0.535631 + 0.844452i \(0.679926\pi\)
\(24\) 0 0
\(25\) −4.44185 + 2.29565i −0.888369 + 0.459130i
\(26\) 0 0
\(27\) −4.71744 2.17848i −0.907872 0.419248i
\(28\) 0 0
\(29\) −2.93812 + 5.08896i −0.545594 + 0.944997i 0.452975 + 0.891523i \(0.350363\pi\)
−0.998569 + 0.0534738i \(0.982971\pi\)
\(30\) 0 0
\(31\) −0.835561 1.44723i −0.150071 0.259931i 0.781182 0.624303i \(-0.214617\pi\)
−0.931253 + 0.364372i \(0.881284\pi\)
\(32\) 0 0
\(33\) 5.75117 + 4.53587i 1.00115 + 0.789594i
\(34\) 0 0
\(35\) −1.08889 1.99175i −0.184057 0.336668i
\(36\) 0 0
\(37\) −3.09788 3.09788i −0.509289 0.509289i 0.405019 0.914308i \(-0.367265\pi\)
−0.914308 + 0.405019i \(0.867265\pi\)
\(38\) 0 0
\(39\) 6.40937 + 2.75532i 1.02632 + 0.441204i
\(40\) 0 0
\(41\) 10.9685 6.33265i 1.71299 0.988993i 0.782514 0.622633i \(-0.213937\pi\)
0.930473 0.366360i \(-0.119396\pi\)
\(42\) 0 0
\(43\) −2.26685 8.45998i −0.345691 1.29014i −0.891803 0.452423i \(-0.850560\pi\)
0.546113 0.837712i \(-0.316107\pi\)
\(44\) 0 0
\(45\) −0.334624 + 6.69985i −0.0498828 + 0.998755i
\(46\) 0 0
\(47\) 0.481889 + 1.79843i 0.0702907 + 0.262329i 0.992124 0.125257i \(-0.0399757\pi\)
−0.921834 + 0.387586i \(0.873309\pi\)
\(48\) 0 0
\(49\) −5.16969 + 2.98472i −0.738527 + 0.426389i
\(50\) 0 0
\(51\) 5.12470 3.82507i 0.717602 0.535618i
\(52\) 0 0
\(53\) 1.91696 + 1.91696i 0.263315 + 0.263315i 0.826399 0.563084i \(-0.190385\pi\)
−0.563084 + 0.826399i \(0.690385\pi\)
\(54\) 0 0
\(55\) 2.65946 9.07436i 0.358602 1.22359i
\(56\) 0 0
\(57\) 0.0700596 0.482459i 0.00927962 0.0639032i
\(58\) 0 0
\(59\) 4.31085 + 7.46661i 0.561225 + 0.972070i 0.997390 + 0.0722032i \(0.0230030\pi\)
−0.436165 + 0.899867i \(0.643664\pi\)
\(60\) 0 0
\(61\) 2.82244 4.88861i 0.361377 0.625923i −0.626811 0.779171i \(-0.715640\pi\)
0.988188 + 0.153249i \(0.0489735\pi\)
\(62\) 0 0
\(63\) −3.04441 0.0810368i −0.383560 0.0102097i
\(64\) 0 0
\(65\) 0.209760 9.00420i 0.0260175 1.11683i
\(66\) 0 0
\(67\) −1.50752 + 5.62615i −0.184173 + 0.687344i 0.810633 + 0.585555i \(0.199123\pi\)
−0.994806 + 0.101789i \(0.967543\pi\)
\(68\) 0 0
\(69\) 6.26149 14.5653i 0.753795 1.75346i
\(70\) 0 0
\(71\) 1.92890i 0.228919i 0.993428 + 0.114459i \(0.0365136\pi\)
−0.993428 + 0.114459i \(0.963486\pi\)
\(72\) 0 0
\(73\) 4.05914 4.05914i 0.475087 0.475087i −0.428470 0.903556i \(-0.640947\pi\)
0.903556 + 0.428470i \(0.140947\pi\)
\(74\) 0 0
\(75\) 8.18505 2.82931i 0.945128 0.326700i
\(76\) 0 0
\(77\) 4.14671 + 1.11111i 0.472562 + 0.126623i
\(78\) 0 0
\(79\) 3.19722 + 1.84591i 0.359715 + 0.207682i 0.668956 0.743302i \(-0.266742\pi\)
−0.309241 + 0.950984i \(0.600075\pi\)
\(80\) 0 0
\(81\) 7.54380 + 4.90827i 0.838200 + 0.545363i
\(82\) 0 0
\(83\) −0.950284 + 0.254628i −0.104307 + 0.0279490i −0.310595 0.950542i \(-0.600528\pi\)
0.206288 + 0.978491i \(0.433862\pi\)
\(84\) 0 0
\(85\) −7.05156 4.29323i −0.764849 0.465667i
\(86\) 0 0
\(87\) 6.30282 7.99154i 0.675733 0.856783i
\(88\) 0 0
\(89\) −6.94741 −0.736423 −0.368212 0.929742i \(-0.620030\pi\)
−0.368212 + 0.929742i \(0.620030\pi\)
\(90\) 0 0
\(91\) 4.08897 0.428640
\(92\) 0 0
\(93\) 1.07199 + 2.68864i 0.111160 + 0.278799i
\(94\) 0 0
\(95\) −0.611567 + 0.148694i −0.0627455 + 0.0152557i
\(96\) 0 0
\(97\) 3.20533 0.858865i 0.325452 0.0872045i −0.0923940 0.995723i \(-0.529452\pi\)
0.417846 + 0.908518i \(0.362785\pi\)
\(98\) 0 0
\(99\) −8.72891 9.20632i −0.877289 0.925270i
\(100\) 0 0
\(101\) 5.37496 + 3.10323i 0.534828 + 0.308783i 0.742980 0.669313i \(-0.233412\pi\)
−0.208152 + 0.978096i \(0.566745\pi\)
\(102\) 0 0
\(103\) 15.5754 + 4.17342i 1.53469 + 0.411219i 0.924546 0.381070i \(-0.124444\pi\)
0.610146 + 0.792289i \(0.291111\pi\)
\(104\) 0 0
\(105\) 1.37068 + 3.68505i 0.133765 + 0.359624i
\(106\) 0 0
\(107\) −9.51835 + 9.51835i −0.920173 + 0.920173i −0.997041 0.0768681i \(-0.975508\pi\)
0.0768681 + 0.997041i \(0.475508\pi\)
\(108\) 0 0
\(109\) 11.0583i 1.05919i 0.848249 + 0.529597i \(0.177657\pi\)
−0.848249 + 0.529597i \(0.822343\pi\)
\(110\) 0 0
\(111\) 4.53891 + 6.08108i 0.430814 + 0.577191i
\(112\) 0 0
\(113\) −1.42849 + 5.33120i −0.134381 + 0.501517i 0.865619 + 0.500704i \(0.166925\pi\)
−1.00000 0.000812894i \(0.999741\pi\)
\(114\) 0 0
\(115\) −20.4621 0.476681i −1.90810 0.0444507i
\(116\) 0 0
\(117\) −10.3003 6.31815i −0.952263 0.584114i
\(118\) 0 0
\(119\) 1.87402 3.24589i 0.171791 0.297551i
\(120\) 0 0
\(121\) 3.44167 + 5.96116i 0.312880 + 0.541923i
\(122\) 0 0
\(123\) −20.3770 + 8.12449i −1.83733 + 0.732561i
\(124\) 0 0
\(125\) −7.33444 8.43836i −0.656013 0.754750i
\(126\) 0 0
\(127\) 7.93844 + 7.93844i 0.704422 + 0.704422i 0.965357 0.260934i \(-0.0840306\pi\)
−0.260934 + 0.965357i \(0.584031\pi\)
\(128\) 0 0
\(129\) 1.77979 + 15.0653i 0.156702 + 1.32642i
\(130\) 0 0
\(131\) −5.94678 + 3.43338i −0.519573 + 0.299975i −0.736760 0.676155i \(-0.763645\pi\)
0.217187 + 0.976130i \(0.430312\pi\)
\(132\) 0 0
\(133\) −0.0739542 0.276001i −0.00641264 0.0239323i
\(134\) 0 0
\(135\) 2.24121 11.4007i 0.192893 0.981220i
\(136\) 0 0
\(137\) −5.49250 20.4983i −0.469256 1.75129i −0.642381 0.766386i \(-0.722053\pi\)
0.173125 0.984900i \(-0.444614\pi\)
\(138\) 0 0
\(139\) 11.7241 6.76891i 0.994425 0.574132i 0.0878311 0.996135i \(-0.472006\pi\)
0.906594 + 0.422004i \(0.138673\pi\)
\(140\) 0 0
\(141\) −0.378350 3.20259i −0.0318628 0.269707i
\(142\) 0 0
\(143\) 12.0445 + 12.0445i 1.00721 + 1.00721i
\(144\) 0 0
\(145\) −12.6093 3.69546i −1.04714 0.306891i
\(146\) 0 0
\(147\) 9.60414 3.82926i 0.792136 0.315832i
\(148\) 0 0
\(149\) 1.79849 + 3.11508i 0.147338 + 0.255198i 0.930243 0.366944i \(-0.119596\pi\)
−0.782905 + 0.622142i \(0.786263\pi\)
\(150\) 0 0
\(151\) 2.41050 4.17511i 0.196164 0.339766i −0.751117 0.660169i \(-0.770485\pi\)
0.947281 + 0.320403i \(0.103818\pi\)
\(152\) 0 0
\(153\) −9.73620 + 5.28088i −0.787125 + 0.426934i
\(154\) 0 0
\(155\) 2.70310 2.58002i 0.217118 0.207232i
\(156\) 0 0
\(157\) 2.13261 7.95901i 0.170201 0.635198i −0.827119 0.562027i \(-0.810022\pi\)
0.997319 0.0731706i \(-0.0233118\pi\)
\(158\) 0 0
\(159\) −2.80867 3.76296i −0.222742 0.298422i
\(160\) 0 0
\(161\) 9.29221i 0.732329i
\(162\) 0 0
\(163\) −4.95634 + 4.95634i −0.388210 + 0.388210i −0.874049 0.485838i \(-0.838514\pi\)
0.485838 + 0.874049i \(0.338514\pi\)
\(164\) 0 0
\(165\) −6.81718 + 14.8922i −0.530717 + 1.15935i
\(166\) 0 0
\(167\) 13.8848 + 3.72041i 1.07443 + 0.287894i 0.752314 0.658805i \(-0.228938\pi\)
0.322121 + 0.946699i \(0.395604\pi\)
\(168\) 0 0
\(169\) 2.79200 + 1.61196i 0.214769 + 0.123997i
\(170\) 0 0
\(171\) −0.240174 + 0.809531i −0.0183666 + 0.0619064i
\(172\) 0 0
\(173\) 14.0437 3.76299i 1.06772 0.286095i 0.318164 0.948036i \(-0.396934\pi\)
0.749556 + 0.661941i \(0.230267\pi\)
\(174\) 0 0
\(175\) 3.75238 3.41812i 0.283653 0.258385i
\(176\) 0 0
\(177\) −5.53062 13.8713i −0.415707 1.04263i
\(178\) 0 0
\(179\) −21.8707 −1.63469 −0.817347 0.576146i \(-0.804556\pi\)
−0.817347 + 0.576146i \(0.804556\pi\)
\(180\) 0 0
\(181\) −23.8617 −1.77363 −0.886814 0.462127i \(-0.847086\pi\)
−0.886814 + 0.462127i \(0.847086\pi\)
\(182\) 0 0
\(183\) −6.05468 + 7.67691i −0.447575 + 0.567494i
\(184\) 0 0
\(185\) 5.09444 8.36752i 0.374551 0.615193i
\(186\) 0 0
\(187\) 15.0812 4.04100i 1.10285 0.295507i
\(188\) 0 0
\(189\) 5.19817 + 0.896677i 0.378111 + 0.0652237i
\(190\) 0 0
\(191\) −14.5962 8.42713i −1.05615 0.609766i −0.131782 0.991279i \(-0.542070\pi\)
−0.924363 + 0.381513i \(0.875403\pi\)
\(192\) 0 0
\(193\) −23.6162 6.32793i −1.69993 0.455494i −0.727007 0.686631i \(-0.759089\pi\)
−0.972921 + 0.231136i \(0.925756\pi\)
\(194\) 0 0
\(195\) −2.60075 + 15.3816i −0.186244 + 1.10150i
\(196\) 0 0
\(197\) −13.2754 + 13.2754i −0.945832 + 0.945832i −0.998606 0.0527741i \(-0.983194\pi\)
0.0527741 + 0.998606i \(0.483194\pi\)
\(198\) 0 0
\(199\) 25.3515i 1.79712i 0.438852 + 0.898559i \(0.355385\pi\)
−0.438852 + 0.898559i \(0.644615\pi\)
\(200\) 0 0
\(201\) 3.98439 9.26840i 0.281037 0.653743i
\(202\) 0 0
\(203\) 1.54394 5.76207i 0.108363 0.404418i
\(204\) 0 0
\(205\) 19.5538 + 20.4865i 1.36569 + 1.43084i
\(206\) 0 0
\(207\) −14.3581 + 23.4075i −0.997954 + 1.62693i
\(208\) 0 0
\(209\) 0.595148 1.03083i 0.0411673 0.0713038i
\(210\) 0 0
\(211\) 6.35077 + 10.9999i 0.437205 + 0.757261i 0.997473 0.0710502i \(-0.0226350\pi\)
−0.560268 + 0.828312i \(0.689302\pi\)
\(212\) 0 0
\(213\) 0.480117 3.30628i 0.0328971 0.226543i
\(214\) 0 0
\(215\) 17.1841 9.39455i 1.17194 0.640703i
\(216\) 0 0
\(217\) 1.19958 + 1.19958i 0.0814327 + 0.0814327i
\(218\) 0 0
\(219\) −7.96801 + 5.94732i −0.538428 + 0.401882i
\(220\) 0 0
\(221\) 12.8788 7.43560i 0.866324 0.500172i
\(222\) 0 0
\(223\) 1.71629 + 6.40529i 0.114931 + 0.428930i 0.999282 0.0378938i \(-0.0120648\pi\)
−0.884350 + 0.466824i \(0.845398\pi\)
\(224\) 0 0
\(225\) −14.7340 + 2.81232i −0.982267 + 0.187488i
\(226\) 0 0
\(227\) −0.0441550 0.164789i −0.00293067 0.0109374i 0.964445 0.264284i \(-0.0851355\pi\)
−0.967376 + 0.253346i \(0.918469\pi\)
\(228\) 0 0
\(229\) 11.7967 6.81084i 0.779550 0.450073i −0.0567210 0.998390i \(-0.518065\pi\)
0.836271 + 0.548317i \(0.184731\pi\)
\(230\) 0 0
\(231\) −6.83120 2.93667i −0.449460 0.193218i
\(232\) 0 0
\(233\) 5.81013 + 5.81013i 0.380634 + 0.380634i 0.871331 0.490697i \(-0.163258\pi\)
−0.490697 + 0.871331i \(0.663258\pi\)
\(234\) 0 0
\(235\) −3.65301 + 1.99711i −0.238296 + 0.130277i
\(236\) 0 0
\(237\) −5.02080 3.95984i −0.326136 0.257219i
\(238\) 0 0
\(239\) −10.5650 18.2991i −0.683394 1.18367i −0.973939 0.226812i \(-0.927170\pi\)
0.290544 0.956861i \(-0.406164\pi\)
\(240\) 0 0
\(241\) −14.2304 + 24.6478i −0.916662 + 1.58771i −0.112212 + 0.993684i \(0.535794\pi\)
−0.804450 + 0.594021i \(0.797540\pi\)
\(242\) 0 0
\(243\) −11.7089 10.2908i −0.751127 0.660157i
\(244\) 0 0
\(245\) −9.21614 9.65578i −0.588798 0.616885i
\(246\) 0 0
\(247\) 0.293430 1.09510i 0.0186705 0.0696793i
\(248\) 0 0
\(249\) 1.69224 0.199919i 0.107241 0.0126693i
\(250\) 0 0
\(251\) 3.25994i 0.205766i −0.994693 0.102883i \(-0.967193\pi\)
0.994693 0.102883i \(-0.0328067\pi\)
\(252\) 0 0
\(253\) 27.3711 27.3711i 1.72081 1.72081i
\(254\) 0 0
\(255\) 11.0183 + 9.11409i 0.689991 + 0.570747i
\(256\) 0 0
\(257\) −27.9940 7.50097i −1.74622 0.467898i −0.762405 0.647100i \(-0.775982\pi\)
−0.983812 + 0.179203i \(0.942648\pi\)
\(258\) 0 0
\(259\) 3.85165 + 2.22375i 0.239330 + 0.138177i
\(260\) 0 0
\(261\) −12.7926 + 12.1293i −0.791845 + 0.750783i
\(262\) 0 0
\(263\) 18.4961 4.95600i 1.14052 0.305600i 0.361357 0.932427i \(-0.382314\pi\)
0.779158 + 0.626827i \(0.215647\pi\)
\(264\) 0 0
\(265\) −3.15243 + 5.17780i −0.193652 + 0.318070i
\(266\) 0 0
\(267\) 11.9084 + 1.72926i 0.728780 + 0.105829i
\(268\) 0 0
\(269\) −4.67111 −0.284803 −0.142401 0.989809i \(-0.545482\pi\)
−0.142401 + 0.989809i \(0.545482\pi\)
\(270\) 0 0
\(271\) −13.0525 −0.792886 −0.396443 0.918059i \(-0.629756\pi\)
−0.396443 + 0.918059i \(0.629756\pi\)
\(272\) 0 0
\(273\) −7.00879 1.01777i −0.424191 0.0615983i
\(274\) 0 0
\(275\) 21.1214 + 0.984614i 1.27367 + 0.0593745i
\(276\) 0 0
\(277\) 24.5784 6.58576i 1.47677 0.395700i 0.571525 0.820585i \(-0.306352\pi\)
0.905248 + 0.424885i \(0.139685\pi\)
\(278\) 0 0
\(279\) −1.16824 4.87535i −0.0699408 0.291880i
\(280\) 0 0
\(281\) 2.62412 + 1.51504i 0.156542 + 0.0903796i 0.576225 0.817291i \(-0.304525\pi\)
−0.419683 + 0.907671i \(0.637859\pi\)
\(282\) 0 0
\(283\) −7.77609 2.08360i −0.462241 0.123857i 0.0201806 0.999796i \(-0.493576\pi\)
−0.482421 + 0.875939i \(0.660243\pi\)
\(284\) 0 0
\(285\) 1.08528 0.102649i 0.0642865 0.00608039i
\(286\) 0 0
\(287\) −9.09151 + 9.09151i −0.536655 + 0.536655i
\(288\) 0 0
\(289\) 3.36874i 0.198161i
\(290\) 0 0
\(291\) −5.70794 + 0.674329i −0.334605 + 0.0395299i
\(292\) 0 0
\(293\) −2.13277 + 7.95962i −0.124598 + 0.465006i −0.999825 0.0187062i \(-0.994045\pi\)
0.875227 + 0.483712i \(0.160712\pi\)
\(294\) 0 0
\(295\) −13.9459 + 13.3109i −0.811961 + 0.774992i
\(296\) 0 0
\(297\) 12.6705 + 17.9530i 0.735216 + 1.04174i
\(298\) 0 0
\(299\) 18.4345 31.9295i 1.06609 1.84653i
\(300\) 0 0
\(301\) 4.44561 + 7.70002i 0.256241 + 0.443822i
\(302\) 0 0
\(303\) −8.44065 6.65703i −0.484903 0.382436i
\(304\) 0 0
\(305\) 12.1129 + 3.54997i 0.693580 + 0.203271i
\(306\) 0 0
\(307\) −1.15439 1.15439i −0.0658844 0.0658844i 0.673397 0.739281i \(-0.264835\pi\)
−0.739281 + 0.673397i \(0.764835\pi\)
\(308\) 0 0
\(309\) −25.6586 11.0304i −1.45967 0.627496i
\(310\) 0 0
\(311\) −4.86996 + 2.81167i −0.276150 + 0.159435i −0.631679 0.775230i \(-0.717634\pi\)
0.355529 + 0.934665i \(0.384301\pi\)
\(312\) 0 0
\(313\) −3.94609 14.7270i −0.223046 0.832420i −0.983178 0.182651i \(-0.941532\pi\)
0.760131 0.649769i \(-0.225134\pi\)
\(314\) 0 0
\(315\) −1.43222 6.65761i −0.0806964 0.375114i
\(316\) 0 0
\(317\) 7.13440 + 26.6259i 0.400708 + 1.49546i 0.811837 + 0.583884i \(0.198468\pi\)
−0.411129 + 0.911577i \(0.634865\pi\)
\(318\) 0 0
\(319\) 21.5206 12.4249i 1.20492 0.695661i
\(320\) 0 0
\(321\) 18.6843 13.9460i 1.04286 0.778387i
\(322\) 0 0
\(323\) −0.734825 0.734825i −0.0408867 0.0408867i
\(324\) 0 0
\(325\) 19.6749 4.30096i 1.09136 0.238574i
\(326\) 0 0
\(327\) 2.75249 18.9548i 0.152213 1.04820i
\(328\) 0 0
\(329\) −0.945053 1.63688i −0.0521025 0.0902441i
\(330\) 0 0
\(331\) 12.9037 22.3499i 0.709253 1.22846i −0.255881 0.966708i \(-0.582366\pi\)
0.965135 0.261754i \(-0.0843010\pi\)
\(332\) 0 0
\(333\) −6.26640 11.5532i −0.343397 0.633110i
\(334\) 0 0
\(335\) −13.0207 0.303328i −0.711398 0.0165726i
\(336\) 0 0
\(337\) −6.30633 + 23.5355i −0.343528 + 1.28206i 0.550795 + 0.834640i \(0.314324\pi\)
−0.894323 + 0.447422i \(0.852342\pi\)
\(338\) 0 0
\(339\) 3.77551 8.78250i 0.205057 0.477000i
\(340\) 0 0
\(341\) 7.06696i 0.382697i
\(342\) 0 0
\(343\) 9.30984 9.30984i 0.502684 0.502684i
\(344\) 0 0
\(345\) 34.9549 + 5.91022i 1.88191 + 0.318196i
\(346\) 0 0
\(347\) 1.43538 + 0.384609i 0.0770552 + 0.0206469i 0.297141 0.954834i \(-0.403967\pi\)
−0.220085 + 0.975481i \(0.570634\pi\)
\(348\) 0 0
\(349\) 11.0207 + 6.36282i 0.589926 + 0.340594i 0.765068 0.643949i \(-0.222705\pi\)
−0.175142 + 0.984543i \(0.556039\pi\)
\(350\) 0 0
\(351\) 16.0828 + 13.3936i 0.858438 + 0.714897i
\(352\) 0 0
\(353\) 13.6377 3.65422i 0.725862 0.194494i 0.123077 0.992397i \(-0.460724\pi\)
0.602786 + 0.797903i \(0.294057\pi\)
\(354\) 0 0
\(355\) −4.19106 + 1.01900i −0.222438 + 0.0540827i
\(356\) 0 0
\(357\) −4.02013 + 5.09724i −0.212768 + 0.269775i
\(358\) 0 0
\(359\) −23.2014 −1.22452 −0.612262 0.790655i \(-0.709740\pi\)
−0.612262 + 0.790655i \(0.709740\pi\)
\(360\) 0 0
\(361\) 18.9208 0.995830
\(362\) 0 0
\(363\) −4.41551 11.0745i −0.231754 0.581261i
\(364\) 0 0
\(365\) 10.9639 + 6.67522i 0.573878 + 0.349397i
\(366\) 0 0
\(367\) −10.2481 + 2.74598i −0.534948 + 0.143339i −0.516172 0.856485i \(-0.672644\pi\)
−0.0187758 + 0.999824i \(0.505977\pi\)
\(368\) 0 0
\(369\) 36.9499 8.85400i 1.92353 0.460921i
\(370\) 0 0
\(371\) −2.38339 1.37605i −0.123739 0.0714409i
\(372\) 0 0
\(373\) 19.0303 + 5.09915i 0.985351 + 0.264024i 0.715296 0.698821i \(-0.246292\pi\)
0.270054 + 0.962845i \(0.412958\pi\)
\(374\) 0 0
\(375\) 10.4714 + 16.2896i 0.540741 + 0.841189i
\(376\) 0 0
\(377\) 16.7364 16.7364i 0.861968 0.861968i
\(378\) 0 0
\(379\) 10.5293i 0.540852i 0.962741 + 0.270426i \(0.0871646\pi\)
−0.962741 + 0.270426i \(0.912835\pi\)
\(380\) 0 0
\(381\) −11.6311 15.5830i −0.595881 0.798341i
\(382\) 0 0
\(383\) 7.55008 28.1773i 0.385791 1.43979i −0.451125 0.892461i \(-0.648977\pi\)
0.836916 0.547331i \(-0.184356\pi\)
\(384\) 0 0
\(385\) −0.223565 + 9.59682i −0.0113940 + 0.489099i
\(386\) 0 0
\(387\) 0.699153 26.2659i 0.0355399 1.33517i
\(388\) 0 0
\(389\) −9.74483 + 16.8785i −0.494082 + 0.855776i −0.999977 0.00681963i \(-0.997829\pi\)
0.505894 + 0.862595i \(0.331163\pi\)
\(390\) 0 0
\(391\) −16.8975 29.2673i −0.854541 1.48011i
\(392\) 0 0
\(393\) 11.0478 4.40486i 0.557288 0.222196i
\(394\) 0 0
\(395\) −2.32173 + 7.92197i −0.116819 + 0.398597i
\(396\) 0 0
\(397\) 0.214255 + 0.214255i 0.0107532 + 0.0107532i 0.712463 0.701710i \(-0.247580\pi\)
−0.701710 + 0.712463i \(0.747580\pi\)
\(398\) 0 0
\(399\) 0.0580644 + 0.491493i 0.00290686 + 0.0246054i
\(400\) 0 0
\(401\) −10.5015 + 6.06307i −0.524422 + 0.302775i −0.738742 0.673988i \(-0.764580\pi\)
0.214320 + 0.976764i \(0.431247\pi\)
\(402\) 0 0
\(403\) 1.74214 + 6.50174i 0.0867820 + 0.323875i
\(404\) 0 0
\(405\) −6.67932 + 18.9839i −0.331898 + 0.943315i
\(406\) 0 0
\(407\) 4.79513 + 17.8957i 0.237686 + 0.887056i
\(408\) 0 0
\(409\) −16.8210 + 9.71162i −0.831745 + 0.480208i −0.854450 0.519534i \(-0.826106\pi\)
0.0227044 + 0.999742i \(0.492772\pi\)
\(410\) 0 0
\(411\) 4.31238 + 36.5027i 0.212714 + 1.80054i
\(412\) 0 0
\(413\) −6.18890 6.18890i −0.304536 0.304536i
\(414\) 0 0
\(415\) −1.05526 1.93023i −0.0518008 0.0947514i
\(416\) 0 0
\(417\) −21.7808 + 8.68420i −1.06661 + 0.425267i
\(418\) 0 0
\(419\) −0.242058 0.419257i −0.0118253 0.0204820i 0.860052 0.510206i \(-0.170431\pi\)
−0.871878 + 0.489724i \(0.837098\pi\)
\(420\) 0 0
\(421\) −8.06103 + 13.9621i −0.392871 + 0.680472i −0.992827 0.119561i \(-0.961851\pi\)
0.599956 + 0.800033i \(0.295185\pi\)
\(422\) 0 0
\(423\) −0.148627 + 5.58365i −0.00722648 + 0.271486i
\(424\) 0 0
\(425\) 5.60302 17.5894i 0.271786 0.853212i
\(426\) 0 0
\(427\) −1.48316 + 5.53521i −0.0717750 + 0.267868i
\(428\) 0 0
\(429\) −17.6471 23.6430i −0.852012 1.14150i
\(430\) 0 0
\(431\) 20.5311i 0.988949i −0.869192 0.494474i \(-0.835361\pi\)
0.869192 0.494474i \(-0.164639\pi\)
\(432\) 0 0
\(433\) 18.0908 18.0908i 0.869389 0.869389i −0.123016 0.992405i \(-0.539257\pi\)
0.992405 + 0.123016i \(0.0392566\pi\)
\(434\) 0 0
\(435\) 20.6934 + 9.47282i 0.992173 + 0.454187i
\(436\) 0 0
\(437\) −2.48862 0.666822i −0.119047 0.0318984i
\(438\) 0 0
\(439\) −31.7433 18.3270i −1.51502 0.874699i −0.999845 0.0176165i \(-0.994392\pi\)
−0.515179 0.857083i \(-0.672274\pi\)
\(440\) 0 0
\(441\) −17.4153 + 4.17309i −0.829301 + 0.198719i
\(442\) 0 0
\(443\) −9.05102 + 2.42521i −0.430027 + 0.115225i −0.467339 0.884078i \(-0.654787\pi\)
0.0373118 + 0.999304i \(0.488121\pi\)
\(444\) 0 0
\(445\) −3.67016 15.0951i −0.173982 0.715577i
\(446\) 0 0
\(447\) −2.30738 5.78714i −0.109136 0.273722i
\(448\) 0 0
\(449\) 6.35277 0.299806 0.149903 0.988701i \(-0.452104\pi\)
0.149903 + 0.988701i \(0.452104\pi\)
\(450\) 0 0
\(451\) −53.5599 −2.52204
\(452\) 0 0
\(453\) −5.17099 + 6.55646i −0.242954 + 0.308049i
\(454\) 0 0
\(455\) 2.16011 + 8.88438i 0.101268 + 0.416506i
\(456\) 0 0
\(457\) 14.9472 4.00508i 0.699199 0.187350i 0.108327 0.994115i \(-0.465451\pi\)
0.590872 + 0.806766i \(0.298784\pi\)
\(458\) 0 0
\(459\) 18.0030 6.62841i 0.840308 0.309388i
\(460\) 0 0
\(461\) 5.28581 + 3.05176i 0.246185 + 0.142135i 0.618016 0.786166i \(-0.287937\pi\)
−0.371831 + 0.928300i \(0.621270\pi\)
\(462\) 0 0
\(463\) −24.8625 6.66190i −1.15546 0.309605i −0.370309 0.928909i \(-0.620748\pi\)
−0.785151 + 0.619304i \(0.787415\pi\)
\(464\) 0 0
\(465\) −5.27549 + 3.74953i −0.244645 + 0.173880i
\(466\) 0 0
\(467\) 24.0615 24.0615i 1.11343 1.11343i 0.120749 0.992683i \(-0.461470\pi\)
0.992683 0.120749i \(-0.0385296\pi\)
\(468\) 0 0
\(469\) 5.91294i 0.273034i
\(470\) 0 0
\(471\) −5.63650 + 13.1115i −0.259716 + 0.604146i
\(472\) 0 0
\(473\) −9.58620 + 35.7762i −0.440774 + 1.64499i
\(474\) 0 0
\(475\) −0.646155 1.25024i −0.0296476 0.0573651i
\(476\) 0 0
\(477\) 3.87763 + 7.14908i 0.177545 + 0.327334i
\(478\) 0 0
\(479\) −15.9283 + 27.5886i −0.727781 + 1.26055i 0.230037 + 0.973182i \(0.426115\pi\)
−0.957819 + 0.287373i \(0.907218\pi\)
\(480\) 0 0
\(481\) 8.82324 + 15.2823i 0.402305 + 0.696813i
\(482\) 0 0
\(483\) −2.31289 + 15.9275i −0.105240 + 0.724727i
\(484\) 0 0
\(485\) 3.55942 + 6.51072i 0.161625 + 0.295636i
\(486\) 0 0
\(487\) −0.615541 0.615541i −0.0278928 0.0278928i 0.693023 0.720916i \(-0.256278\pi\)
−0.720916 + 0.693023i \(0.756278\pi\)
\(488\) 0 0
\(489\) 9.72919 7.26186i 0.439969 0.328393i
\(490\) 0 0
\(491\) −21.5023 + 12.4143i −0.970384 + 0.560252i −0.899353 0.437222i \(-0.855962\pi\)
−0.0710310 + 0.997474i \(0.522629\pi\)
\(492\) 0 0
\(493\) −5.61517 20.9561i −0.252895 0.943816i
\(494\) 0 0
\(495\) 15.3919 23.8294i 0.691815 1.07105i
\(496\) 0 0
\(497\) −0.506806 1.89143i −0.0227334 0.0848421i
\(498\) 0 0
\(499\) 7.45894 4.30642i 0.333908 0.192782i −0.323667 0.946171i \(-0.604916\pi\)
0.657575 + 0.753389i \(0.271582\pi\)
\(500\) 0 0
\(501\) −22.8734 9.83306i −1.02191 0.439309i
\(502\) 0 0
\(503\) 17.0273 + 17.0273i 0.759208 + 0.759208i 0.976178 0.216970i \(-0.0696173\pi\)
−0.216970 + 0.976178i \(0.569617\pi\)
\(504\) 0 0
\(505\) −3.90314 + 13.3179i −0.173687 + 0.592639i
\(506\) 0 0
\(507\) −4.38446 3.45796i −0.194721 0.153574i
\(508\) 0 0
\(509\) 2.76039 + 4.78114i 0.122352 + 0.211920i 0.920695 0.390283i \(-0.127623\pi\)
−0.798343 + 0.602204i \(0.794290\pi\)
\(510\) 0 0
\(511\) −2.91377 + 5.04679i −0.128897 + 0.223257i
\(512\) 0 0
\(513\) 0.613174 1.32781i 0.0270723 0.0586244i
\(514\) 0 0
\(515\) −0.839732 + 36.0465i −0.0370030 + 1.58840i
\(516\) 0 0
\(517\) 2.03785 7.60534i 0.0896244 0.334483i
\(518\) 0 0
\(519\) −25.0085 + 2.95447i −1.09775 + 0.129687i
\(520\) 0 0
\(521\) 20.1806i 0.884126i 0.896984 + 0.442063i \(0.145753\pi\)
−0.896984 + 0.442063i \(0.854247\pi\)
\(522\) 0 0
\(523\) 0.0855088 0.0855088i 0.00373904 0.00373904i −0.705235 0.708974i \(-0.749158\pi\)
0.708974 + 0.705235i \(0.249158\pi\)
\(524\) 0 0
\(525\) −7.28265 + 4.92491i −0.317841 + 0.214941i
\(526\) 0 0
\(527\) 5.95964 + 1.59688i 0.259606 + 0.0695612i
\(528\) 0 0
\(529\) −52.6414 30.3925i −2.28876 1.32141i
\(530\) 0 0
\(531\) 6.02722 + 25.1530i 0.261559 + 1.09155i
\(532\) 0 0
\(533\) −49.2762 + 13.2035i −2.13439 + 0.571908i
\(534\) 0 0
\(535\) −25.7095 15.6528i −1.11152 0.676731i
\(536\) 0 0
\(537\) 37.4880 + 5.44377i 1.61773 + 0.234916i
\(538\) 0 0
\(539\) 25.2440 1.08734
\(540\) 0 0
\(541\) −16.7856 −0.721671 −0.360835 0.932630i \(-0.617508\pi\)
−0.360835 + 0.932630i \(0.617508\pi\)
\(542\) 0 0
\(543\) 40.9007 + 5.93934i 1.75522 + 0.254882i
\(544\) 0 0
\(545\) −24.0272 + 5.84186i −1.02921 + 0.250238i
\(546\) 0 0
\(547\) 8.58350 2.29994i 0.367004 0.0983384i −0.0706037 0.997504i \(-0.522493\pi\)
0.437608 + 0.899166i \(0.355826\pi\)
\(548\) 0 0
\(549\) 12.2890 11.6517i 0.524482 0.497284i
\(550\) 0 0
\(551\) −1.43239 0.826989i −0.0610217 0.0352309i
\(552\) 0 0
\(553\) −3.62010 0.970004i −0.153942 0.0412488i
\(554\) 0 0
\(555\) −10.8150 + 13.0745i −0.459070 + 0.554982i
\(556\) 0 0
\(557\) 0.716676 0.716676i 0.0303665 0.0303665i −0.691760 0.722127i \(-0.743165\pi\)
0.722127 + 0.691760i \(0.243165\pi\)
\(558\) 0 0
\(559\) 35.2780i 1.49210i
\(560\) 0 0
\(561\) −26.8561 + 3.17275i −1.13387 + 0.133954i
\(562\) 0 0
\(563\) 7.55543 28.1972i 0.318423 1.18837i −0.602337 0.798242i \(-0.705764\pi\)
0.920760 0.390130i \(-0.127570\pi\)
\(564\) 0 0
\(565\) −12.3381 0.287426i −0.519067 0.0120921i
\(566\) 0 0
\(567\) −8.68685 2.83083i −0.364814 0.118884i
\(568\) 0 0
\(569\) −15.1381 + 26.2200i −0.634623 + 1.09920i 0.351971 + 0.936011i \(0.385511\pi\)
−0.986595 + 0.163189i \(0.947822\pi\)
\(570\) 0 0
\(571\) 15.2794 + 26.4647i 0.639423 + 1.10751i 0.985560 + 0.169329i \(0.0541602\pi\)
−0.346136 + 0.938184i \(0.612506\pi\)
\(572\) 0 0
\(573\) 22.9214 + 18.0778i 0.957555 + 0.755211i
\(574\) 0 0
\(575\) −9.77396 44.7113i −0.407602 1.86459i
\(576\) 0 0
\(577\) −7.11358 7.11358i −0.296142 0.296142i 0.543359 0.839501i \(-0.317152\pi\)
−0.839501 + 0.543359i \(0.817152\pi\)
\(578\) 0 0
\(579\) 38.9047 + 16.7248i 1.61683 + 0.695057i
\(580\) 0 0
\(581\) 0.864920 0.499362i 0.0358829 0.0207170i
\(582\) 0 0
\(583\) −2.96722 11.0738i −0.122890 0.458630i
\(584\) 0 0
\(585\) 8.28647 25.7179i 0.342603 1.06330i
\(586\) 0 0
\(587\) 2.48476 + 9.27324i 0.102557 + 0.382748i 0.998057 0.0623146i \(-0.0198482\pi\)
−0.895500 + 0.445062i \(0.853182\pi\)
\(588\) 0 0
\(589\) 0.407352 0.235185i 0.0167846 0.00969061i
\(590\) 0 0
\(591\) 26.0593 19.4507i 1.07194 0.800093i
\(592\) 0 0
\(593\) −0.723344 0.723344i −0.0297042 0.0297042i 0.692099 0.721803i \(-0.256686\pi\)
−0.721803 + 0.692099i \(0.756686\pi\)
\(594\) 0 0
\(595\) 8.04258 + 2.35707i 0.329714 + 0.0966306i
\(596\) 0 0
\(597\) 6.31015 43.4543i 0.258257 1.77847i
\(598\) 0 0
\(599\) −3.49913 6.06066i −0.142970 0.247632i 0.785643 0.618680i \(-0.212332\pi\)
−0.928614 + 0.371047i \(0.878999\pi\)
\(600\) 0 0
\(601\) 4.49249 7.78122i 0.183252 0.317402i −0.759734 0.650234i \(-0.774671\pi\)
0.942986 + 0.332832i \(0.108004\pi\)
\(602\) 0 0
\(603\) −9.13651 + 14.8950i −0.372067 + 0.606570i
\(604\) 0 0
\(605\) −11.1341 + 10.6271i −0.452664 + 0.432053i
\(606\) 0 0
\(607\) −5.12710 + 19.1346i −0.208103 + 0.776649i 0.780379 + 0.625307i \(0.215026\pi\)
−0.988481 + 0.151342i \(0.951640\pi\)
\(608\) 0 0
\(609\) −4.08064 + 9.49230i −0.165356 + 0.384648i
\(610\) 0 0
\(611\) 7.49944i 0.303395i
\(612\) 0 0
\(613\) −16.6163 + 16.6163i −0.671124 + 0.671124i −0.957975 0.286851i \(-0.907392\pi\)
0.286851 + 0.957975i \(0.407392\pi\)
\(614\) 0 0
\(615\) −28.4174 39.9825i −1.14590 1.61225i
\(616\) 0 0
\(617\) 11.3965 + 3.05370i 0.458808 + 0.122937i 0.480818 0.876821i \(-0.340340\pi\)
−0.0220100 + 0.999758i \(0.507007\pi\)
\(618\) 0 0
\(619\) 5.05521 + 2.91863i 0.203186 + 0.117309i 0.598141 0.801391i \(-0.295906\pi\)
−0.394955 + 0.918701i \(0.629240\pi\)
\(620\) 0 0
\(621\) 30.4370 36.5484i 1.22140 1.46664i
\(622\) 0 0
\(623\) 6.81243 1.82539i 0.272934 0.0731325i
\(624\) 0 0
\(625\) 14.4600 20.3938i 0.578399 0.815754i
\(626\) 0 0
\(627\) −1.27671 + 1.61878i −0.0509868 + 0.0646477i
\(628\) 0 0
\(629\) 16.1751 0.644945
\(630\) 0 0
\(631\) 46.1124 1.83571 0.917853 0.396920i \(-0.129921\pi\)
0.917853 + 0.396920i \(0.129921\pi\)
\(632\) 0 0
\(633\) −8.14774 20.4353i −0.323844 0.812231i
\(634\) 0 0
\(635\) −13.0547 + 21.4421i −0.518059 + 0.850903i
\(636\) 0 0
\(637\) 23.2250 6.22312i 0.920208 0.246569i
\(638\) 0 0
\(639\) −1.64591 + 5.54770i −0.0651112 + 0.219464i
\(640\) 0 0
\(641\) −33.2725 19.2099i −1.31418 0.758744i −0.331398 0.943491i \(-0.607520\pi\)
−0.982786 + 0.184747i \(0.940854\pi\)
\(642\) 0 0
\(643\) 16.9724 + 4.54774i 0.669326 + 0.179345i 0.577451 0.816425i \(-0.304047\pi\)
0.0918748 + 0.995771i \(0.470714\pi\)
\(644\) 0 0
\(645\) −31.7931 + 11.8257i −1.25185 + 0.465637i
\(646\) 0 0
\(647\) −22.1467 + 22.1467i −0.870677 + 0.870677i −0.992546 0.121870i \(-0.961111\pi\)
0.121870 + 0.992546i \(0.461111\pi\)
\(648\) 0 0
\(649\) 36.4601i 1.43118i
\(650\) 0 0
\(651\) −1.75758 2.35475i −0.0688851 0.0922899i
\(652\) 0 0
\(653\) −8.56014 + 31.9469i −0.334984 + 1.25018i 0.568902 + 0.822405i \(0.307368\pi\)
−0.903886 + 0.427773i \(0.859298\pi\)
\(654\) 0 0
\(655\) −10.6015 11.1072i −0.414234 0.433994i
\(656\) 0 0
\(657\) 15.1381 8.21084i 0.590593 0.320335i
\(658\) 0 0
\(659\) −0.0315958 + 0.0547256i −0.00123080 + 0.00213181i −0.866640 0.498934i \(-0.833725\pi\)
0.865409 + 0.501066i \(0.167058\pi\)
\(660\) 0 0
\(661\) −0.681072 1.17965i −0.0264906 0.0458832i 0.852476 0.522766i \(-0.175100\pi\)
−0.878967 + 0.476883i \(0.841767\pi\)
\(662\) 0 0
\(663\) −23.9260 + 9.53953i −0.929210 + 0.370485i
\(664\) 0 0
\(665\) 0.560617 0.306490i 0.0217398 0.0118852i
\(666\) 0 0
\(667\) −38.0336 38.0336i −1.47267 1.47267i
\(668\) 0 0
\(669\) −1.34753 11.4063i −0.0520985 0.440994i
\(670\) 0 0
\(671\) −20.6733 + 11.9357i −0.798084 + 0.460774i
\(672\) 0 0
\(673\) 6.37147 + 23.7787i 0.245602 + 0.916600i 0.973080 + 0.230469i \(0.0740259\pi\)
−0.727478 + 0.686131i \(0.759307\pi\)
\(674\) 0 0
\(675\) 25.9552 1.15313i 0.999015 0.0443841i
\(676\) 0 0
\(677\) 4.45281 + 16.6181i 0.171135 + 0.638686i 0.997178 + 0.0750779i \(0.0239205\pi\)
−0.826042 + 0.563608i \(0.809413\pi\)
\(678\) 0 0
\(679\) −2.91739 + 1.68436i −0.111959 + 0.0646397i
\(680\) 0 0
\(681\) 0.0346678 + 0.293450i 0.00132847 + 0.0112450i
\(682\) 0 0
\(683\) 7.80388 + 7.80388i 0.298607 + 0.298607i 0.840468 0.541861i \(-0.182280\pi\)
−0.541861 + 0.840468i \(0.682280\pi\)
\(684\) 0 0
\(685\) 41.6364 22.7627i 1.59085 0.869718i
\(686\) 0 0
\(687\) −21.9157 + 8.73800i −0.836137 + 0.333375i
\(688\) 0 0
\(689\) −5.45979 9.45664i −0.208002 0.360269i
\(690\) 0 0
\(691\) 15.3258 26.5451i 0.583023 1.00982i −0.412096 0.911140i \(-0.635203\pi\)
0.995119 0.0986844i \(-0.0314634\pi\)
\(692\) 0 0
\(693\) 10.9782 + 6.73399i 0.417028 + 0.255803i
\(694\) 0 0
\(695\) 20.9009 + 21.8979i 0.792815 + 0.830634i
\(696\) 0 0
\(697\) −12.1026 + 45.1676i −0.458420 + 1.71085i
\(698\) 0 0
\(699\) −8.51280 11.4052i −0.321984 0.431383i
\(700\) 0 0
\(701\) 9.37006i 0.353902i 0.984220 + 0.176951i \(0.0566234\pi\)
−0.984220 + 0.176951i \(0.943377\pi\)
\(702\) 0 0
\(703\) 0.871958 0.871958i 0.0328865 0.0328865i
\(704\) 0 0
\(705\) 6.75862 2.51393i 0.254544 0.0946799i
\(706\) 0 0
\(707\) −6.08589 1.63071i −0.228883 0.0613291i
\(708\) 0 0
\(709\) 1.62031 + 0.935488i 0.0608522 + 0.0351330i 0.530117 0.847924i \(-0.322148\pi\)
−0.469265 + 0.883057i \(0.655481\pi\)
\(710\) 0 0
\(711\) 7.62039 + 8.03716i 0.285787 + 0.301417i
\(712\) 0 0
\(713\) 14.7753 3.95902i 0.553338 0.148266i
\(714\) 0 0
\(715\) −19.8070 + 32.5326i −0.740740 + 1.21665i
\(716\) 0 0
\(717\) 13.5544 + 33.9958i 0.506199 + 1.26960i
\(718\) 0 0
\(719\) 21.7584 0.811452 0.405726 0.913995i \(-0.367019\pi\)
0.405726 + 0.913995i \(0.367019\pi\)
\(720\) 0 0
\(721\) −16.3694 −0.609627
\(722\) 0 0
\(723\) 30.5270 38.7061i 1.13531 1.43950i
\(724\) 0 0
\(725\) 1.36817 29.3493i 0.0508126 1.09000i
\(726\) 0 0
\(727\) −15.6944 + 4.20530i −0.582073 + 0.155966i −0.537828 0.843055i \(-0.680755\pi\)
−0.0442451 + 0.999021i \(0.514088\pi\)
\(728\) 0 0
\(729\) 17.5085 + 20.5537i 0.648462 + 0.761247i
\(730\) 0 0
\(731\) 28.0043 + 16.1683i 1.03578 + 0.598005i
\(732\) 0 0
\(733\) −43.2446 11.5873i −1.59727 0.427988i −0.653057 0.757309i \(-0.726514\pi\)
−0.944218 + 0.329321i \(0.893180\pi\)
\(734\) 0 0
\(735\) 13.3937 + 18.8447i 0.494036 + 0.695096i
\(736\) 0 0
\(737\) 17.4172 17.4172i 0.641569 0.641569i
\(738\) 0 0
\(739\) 15.2703i 0.561726i 0.959748 + 0.280863i \(0.0906206\pi\)
−0.959748 + 0.280863i \(0.909379\pi\)
\(740\) 0 0
\(741\) −0.775538 + 1.80404i −0.0284901 + 0.0662730i
\(742\) 0 0
\(743\) 3.17205 11.8382i 0.116371 0.434303i −0.883015 0.469345i \(-0.844490\pi\)
0.999386 + 0.0350425i \(0.0111567\pi\)
\(744\) 0 0
\(745\) −5.81825 + 5.55334i −0.213164 + 0.203459i
\(746\) 0 0
\(747\) −2.95038 0.0785337i −0.107949 0.00287340i
\(748\) 0 0
\(749\) 6.83254 11.8343i 0.249656 0.432416i
\(750\) 0 0
\(751\) 1.95028 + 3.37798i 0.0711667 + 0.123264i 0.899413 0.437100i \(-0.143994\pi\)
−0.828246 + 0.560364i \(0.810661\pi\)
\(752\) 0 0
\(753\) −0.811421 + 5.58777i −0.0295698 + 0.203630i
\(754\) 0 0
\(755\) 10.3450 + 3.03185i 0.376492 + 0.110340i
\(756\) 0 0
\(757\) −8.02600 8.02600i −0.291710 0.291710i 0.546045 0.837756i \(-0.316133\pi\)
−0.837756 + 0.546045i \(0.816133\pi\)
\(758\) 0 0
\(759\) −53.7290 + 40.1032i −1.95024 + 1.45566i
\(760\) 0 0
\(761\) 23.0744 13.3220i 0.836447 0.482923i −0.0196080 0.999808i \(-0.506242\pi\)
0.856055 + 0.516885i \(0.172908\pi\)
\(762\) 0 0
\(763\) −2.90550 10.8435i −0.105186 0.392560i
\(764\) 0 0
\(765\) −16.6176 18.3647i −0.600809 0.663979i
\(766\) 0 0
\(767\) −8.98808 33.5440i −0.324541 1.21120i
\(768\) 0 0
\(769\) 37.3021 21.5364i 1.34515 0.776621i 0.357590 0.933879i \(-0.383599\pi\)
0.987558 + 0.157258i \(0.0502653\pi\)
\(770\) 0 0
\(771\) 46.1167 + 19.8251i 1.66085 + 0.713983i
\(772\) 0 0
\(773\) −1.43913 1.43913i −0.0517620 0.0517620i 0.680752 0.732514i \(-0.261653\pi\)
−0.732514 + 0.680752i \(0.761653\pi\)
\(774\) 0 0
\(775\) 7.03378 + 4.51023i 0.252661 + 0.162012i
\(776\) 0 0
\(777\) −6.04849 4.77037i −0.216989 0.171136i
\(778\) 0 0
\(779\) 1.78244 + 3.08729i 0.0638627 + 0.110613i
\(780\) 0 0
\(781\) 4.07854 7.06424i 0.145942 0.252778i
\(782\) 0 0
\(783\) 24.9466 17.6063i 0.891518 0.629197i
\(784\) 0 0
\(785\) 18.4197 + 0.429101i 0.657427 + 0.0153153i
\(786\) 0 0
\(787\) 4.88152 18.2181i 0.174007 0.649405i −0.822711 0.568460i \(-0.807540\pi\)
0.996719 0.0809450i \(-0.0257938\pi\)
\(788\) 0 0
\(789\) −32.9372 + 3.89116i −1.17259 + 0.138529i
\(790\) 0 0
\(791\) 5.60295i 0.199218i
\(792\) 0 0
\(793\) −16.0775 + 16.0775i −0.570928 + 0.570928i
\(794\) 0 0
\(795\) 6.69228 8.09047i 0.237351 0.286939i
\(796\) 0 0
\(797\) −22.8838 6.13169i −0.810585 0.217196i −0.170359 0.985382i \(-0.554493\pi\)
−0.640226 + 0.768186i \(0.721159\pi\)
\(798\) 0 0
\(799\) −5.95318 3.43707i −0.210609 0.121595i
\(800\) 0 0
\(801\) −19.9814 5.92814i −0.706007 0.209461i
\(802\) 0 0
\(803\) −23.4486 + 6.28304i −0.827484 + 0.221724i
\(804\) 0 0
\(805\) 20.1898 4.90887i 0.711598 0.173015i
\(806\) 0 0
\(807\) 8.00662 + 1.16267i 0.281846 + 0.0409280i
\(808\) 0 0
\(809\) 4.46997 0.157156 0.0785778 0.996908i \(-0.474962\pi\)
0.0785778 + 0.996908i \(0.474962\pi\)
\(810\) 0 0
\(811\) 43.2622 1.51914 0.759571 0.650424i \(-0.225409\pi\)
0.759571 + 0.650424i \(0.225409\pi\)
\(812\) 0 0
\(813\) 22.3730 + 3.24887i 0.784656 + 0.113943i
\(814\) 0 0
\(815\) −13.3873 8.15065i −0.468937 0.285505i
\(816\) 0 0
\(817\) 2.38122 0.638047i 0.0833085 0.0223224i
\(818\) 0 0
\(819\) 11.7602 + 3.48907i 0.410936 + 0.121918i
\(820\) 0 0
\(821\) 40.3735 + 23.3097i 1.40905 + 0.813513i 0.995296 0.0968772i \(-0.0308854\pi\)
0.413750 + 0.910391i \(0.364219\pi\)
\(822\) 0 0
\(823\) 31.4955 + 8.43920i 1.09787 + 0.294172i 0.761895 0.647700i \(-0.224269\pi\)
0.335970 + 0.941873i \(0.390936\pi\)
\(824\) 0 0
\(825\) −35.9586 6.94496i −1.25192 0.241793i
\(826\) 0 0
\(827\) 6.08734 6.08734i 0.211678 0.211678i −0.593302 0.804980i \(-0.702176\pi\)
0.804980 + 0.593302i \(0.202176\pi\)
\(828\) 0 0
\(829\) 25.7231i 0.893400i 0.894684 + 0.446700i \(0.147401\pi\)
−0.894684 + 0.446700i \(0.852599\pi\)
\(830\) 0 0
\(831\) −43.7684 + 5.17075i −1.51831 + 0.179371i
\(832\) 0 0
\(833\) 5.70425 21.2885i 0.197640 0.737604i
\(834\) 0 0
\(835\) −0.748581 + 32.1338i −0.0259057 + 1.11203i
\(836\) 0 0
\(837\) 0.788942 + 8.64749i 0.0272698 + 0.298901i
\(838\) 0 0
\(839\) −0.00802753 + 0.0139041i −0.000277141 + 0.000480022i −0.866164 0.499760i \(-0.833422\pi\)
0.865887 + 0.500240i \(0.166755\pi\)
\(840\) 0 0
\(841\) −2.76504 4.78919i −0.0953462 0.165145i
\(842\) 0 0
\(843\) −4.12084 3.25005i −0.141929 0.111938i
\(844\) 0 0
\(845\) −2.02747 + 6.91792i −0.0697469 + 0.237984i
\(846\) 0 0
\(847\) −4.94106 4.94106i −0.169777 0.169777i
\(848\) 0 0
\(849\) 12.8102 + 5.50696i 0.439644 + 0.188998i
\(850\) 0 0
\(851\) 34.7291 20.0509i 1.19050 0.687335i
\(852\) 0 0
\(853\) 2.68364 + 10.0155i 0.0918859 + 0.342923i 0.996529 0.0832473i \(-0.0265291\pi\)
−0.904643 + 0.426170i \(0.859862\pi\)
\(854\) 0 0
\(855\) −1.88580 0.0941863i −0.0644931 0.00322110i
\(856\) 0 0
\(857\) 1.23292 + 4.60132i 0.0421157 + 0.157178i 0.983781 0.179372i \(-0.0574066\pi\)
−0.941666 + 0.336550i \(0.890740\pi\)
\(858\) 0 0
\(859\) 31.0689 17.9377i 1.06006 0.612025i 0.134610 0.990899i \(-0.457022\pi\)
0.925448 + 0.378874i \(0.123688\pi\)
\(860\) 0 0
\(861\) 17.8464 13.3206i 0.608205 0.453964i
\(862\) 0 0
\(863\) −35.1155 35.1155i −1.19535 1.19535i −0.975544 0.219803i \(-0.929459\pi\)
−0.219803 0.975544i \(-0.570541\pi\)
\(864\) 0 0
\(865\) 15.5950 + 28.5257i 0.530248 + 0.969903i
\(866\) 0 0
\(867\) 0.838501 5.77426i 0.0284770 0.196104i
\(868\) 0 0
\(869\) −7.80613 13.5206i −0.264805 0.458656i
\(870\) 0 0
\(871\) 11.7305 20.3178i 0.397472 0.688442i
\(872\) 0 0
\(873\) 9.95167 + 0.264896i 0.336813 + 0.00896536i
\(874\) 0 0
\(875\) 9.40907 + 6.34734i 0.318085 + 0.214579i
\(876\) 0 0
\(877\) 5.52326 20.6131i 0.186507 0.696055i −0.807795 0.589463i \(-0.799339\pi\)
0.994303 0.106592i \(-0.0339939\pi\)
\(878\) 0 0
\(879\) 5.63694 13.1125i 0.190129 0.442274i
\(880\) 0 0
\(881\) 46.9670i 1.58236i −0.611584 0.791180i \(-0.709467\pi\)
0.611584 0.791180i \(-0.290533\pi\)
\(882\) 0 0
\(883\) −19.3061 + 19.3061i −0.649703 + 0.649703i −0.952921 0.303218i \(-0.901939\pi\)
0.303218 + 0.952921i \(0.401939\pi\)
\(884\) 0 0
\(885\) 27.2174 19.3447i 0.914904 0.650264i
\(886\) 0 0
\(887\) −11.6307 3.11644i −0.390522 0.104640i 0.0582149 0.998304i \(-0.481459\pi\)
−0.448736 + 0.893664i \(0.648126\pi\)
\(888\) 0 0
\(889\) −9.86998 5.69844i −0.331029 0.191119i
\(890\) 0 0
\(891\) −17.2495 33.9265i −0.577880 1.13658i
\(892\) 0 0
\(893\) −0.506204 + 0.135637i −0.0169395 + 0.00453891i
\(894\) 0 0
\(895\) −11.5538 47.5200i −0.386201 1.58842i
\(896\) 0 0
\(897\) −39.5455 + 50.1410i −1.32039 + 1.67416i
\(898\) 0 0
\(899\) 9.81990 0.327512
\(900\) 0 0
\(901\) −10.0091 −0.333453
\(902\) 0 0
\(903\) −5.70351 14.3049i −0.189801 0.476039i
\(904\) 0 0
\(905\) −12.6056 51.8460i −0.419025 1.72342i
\(906\) 0 0
\(907\) −4.14289 + 1.11008i −0.137562 + 0.0368598i −0.326943 0.945044i \(-0.606019\pi\)
0.189381 + 0.981904i \(0.439352\pi\)
\(908\) 0 0
\(909\) 12.8109 + 13.5116i 0.424911 + 0.448151i
\(910\) 0 0
\(911\) 31.7547 + 18.3336i 1.05208 + 0.607419i 0.923231 0.384245i \(-0.125538\pi\)
0.128849 + 0.991664i \(0.458872\pi\)
\(912\) 0 0
\(913\) 4.01863 + 1.07679i 0.132997 + 0.0356365i
\(914\) 0 0
\(915\) −19.8787 9.09987i −0.657170 0.300833i
\(916\) 0 0
\(917\) 4.92915 4.92915i 0.162775 0.162775i
\(918\) 0 0
\(919\) 21.3075i 0.702870i −0.936212 0.351435i \(-0.885694\pi\)
0.936212 0.351435i \(-0.114306\pi\)
\(920\) 0 0
\(921\) 1.69137 + 2.26604i 0.0557325 + 0.0746685i
\(922\) 0 0
\(923\) 2.01087 7.50468i 0.0661886 0.247019i
\(924\) 0 0
\(925\) 20.8720 + 6.64866i 0.686266 + 0.218607i
\(926\) 0 0
\(927\) 41.2352 + 25.2935i 1.35434 + 0.830747i
\(928\) 0 0
\(929\) −14.5804 + 25.2540i −0.478367 + 0.828556i −0.999692 0.0248023i \(-0.992104\pi\)
0.521326 + 0.853358i \(0.325438\pi\)
\(930\) 0 0
\(931\) −0.840107 1.45511i −0.0275334 0.0476892i
\(932\) 0 0
\(933\) 9.04731 3.60724i 0.296196 0.118096i
\(934\) 0 0
\(935\) 16.7472 + 30.6332i 0.547693 + 1.00181i
\(936\) 0 0
\(937\) 13.6450 + 13.6450i 0.445761 + 0.445761i 0.893943 0.448181i \(-0.147928\pi\)
−0.448181 + 0.893943i \(0.647928\pi\)
\(938\) 0 0
\(939\) 3.09824 + 26.2254i 0.101107 + 0.855833i
\(940\) 0 0
\(941\) 19.1984 11.0842i 0.625849 0.361334i −0.153294 0.988181i \(-0.548988\pi\)
0.779143 + 0.626847i \(0.215655\pi\)
\(942\) 0 0
\(943\) 30.0051 + 111.980i 0.977100 + 3.64659i
\(944\) 0 0
\(945\) 0.797805 + 11.7681i 0.0259526 + 0.382817i
\(946\) 0 0
\(947\) −5.22747 19.5092i −0.169870 0.633964i −0.997369 0.0724959i \(-0.976904\pi\)
0.827499 0.561468i \(-0.189763\pi\)
\(948\) 0 0
\(949\) −20.0243 + 11.5610i −0.650017 + 0.375287i
\(950\) 0 0
\(951\) −5.60150 47.4146i −0.181641 1.53752i
\(952\) 0 0
\(953\) −20.3870 20.3870i −0.660399 0.660399i 0.295075 0.955474i \(-0.404655\pi\)
−0.955474 + 0.295075i \(0.904655\pi\)
\(954\) 0 0
\(955\) 10.5993 36.1661i 0.342987 1.17031i
\(956\) 0 0
\(957\) −39.9805 + 15.9406i −1.29239 + 0.515286i
\(958\) 0 0
\(959\) 10.7716 + 18.6569i 0.347832 + 0.602463i
\(960\) 0 0
\(961\) 14.1037 24.4283i 0.454957 0.788009i
\(962\) 0 0
\(963\) −35.4975 + 19.2537i −1.14389 + 0.620443i
\(964\) 0 0
\(965\) 1.27324 54.6553i 0.0409870 1.75942i
\(966\) 0 0
\(967\) −6.12383 + 22.8544i −0.196929 + 0.734949i 0.794830 + 0.606832i \(0.207560\pi\)
−0.991759 + 0.128117i \(0.959107\pi\)
\(968\) 0 0
\(969\) 1.07664 + 1.44245i 0.0345867 + 0.0463380i
\(970\) 0 0
\(971\) 32.0761i 1.02937i 0.857379 + 0.514686i \(0.172092\pi\)
−0.857379 + 0.514686i \(0.827908\pi\)
\(972\) 0 0
\(973\) −9.71784 + 9.71784i −0.311540 + 0.311540i
\(974\) 0 0
\(975\) −34.7947 + 2.47495i −1.11432 + 0.0792619i
\(976\) 0 0
\(977\) −23.3058 6.24476i −0.745618 0.199788i −0.134044 0.990975i \(-0.542796\pi\)
−0.611573 + 0.791188i \(0.709463\pi\)
\(978\) 0 0
\(979\) 25.4435 + 14.6898i 0.813179 + 0.469489i
\(980\) 0 0
\(981\) −9.43594 + 31.8047i −0.301266 + 1.01545i
\(982\) 0 0
\(983\) −5.39530 + 1.44566i −0.172083 + 0.0461096i −0.343832 0.939031i \(-0.611725\pi\)
0.171749 + 0.985141i \(0.445058\pi\)
\(984\) 0 0
\(985\) −35.8574 21.8313i −1.14251 0.695602i
\(986\) 0 0
\(987\) 1.21246 + 3.04096i 0.0385930 + 0.0967949i
\(988\) 0 0
\(989\) 80.1694 2.54924
\(990\) 0 0
\(991\) 12.1955 0.387401 0.193701 0.981061i \(-0.437951\pi\)
0.193701 + 0.981061i \(0.437951\pi\)
\(992\) 0 0
\(993\) −27.6810 + 35.0976i −0.878429 + 1.11379i
\(994\) 0 0
\(995\) −55.0829 + 13.3926i −1.74625 + 0.424575i
\(996\) 0 0
\(997\) −50.3044 + 13.4790i −1.59316 + 0.426885i −0.942967 0.332886i \(-0.891978\pi\)
−0.650191 + 0.759771i \(0.725311\pi\)
\(998\) 0 0
\(999\) 7.86541 + 21.3627i 0.248851 + 0.675887i
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.137.2 yes 72
3.2 odd 2 1080.2.bt.a.737.8 72
4.3 odd 2 720.2.cu.e.497.17 72
5.3 odd 4 inner 360.2.bs.a.353.11 yes 72
9.4 even 3 1080.2.bt.a.17.15 72
9.5 odd 6 inner 360.2.bs.a.257.11 yes 72
15.8 even 4 1080.2.bt.a.953.15 72
20.3 even 4 720.2.cu.e.353.8 72
36.23 even 6 720.2.cu.e.257.8 72
45.13 odd 12 1080.2.bt.a.233.8 72
45.23 even 12 inner 360.2.bs.a.113.2 72
180.23 odd 12 720.2.cu.e.113.17 72
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
360.2.bs.a.113.2 72 45.23 even 12 inner
360.2.bs.a.137.2 yes 72 1.1 even 1 trivial
360.2.bs.a.257.11 yes 72 9.5 odd 6 inner
360.2.bs.a.353.11 yes 72 5.3 odd 4 inner
720.2.cu.e.113.17 72 180.23 odd 12
720.2.cu.e.257.8 72 36.23 even 6
720.2.cu.e.353.8 72 20.3 even 4
720.2.cu.e.497.17 72 4.3 odd 2
1080.2.bt.a.17.15 72 9.4 even 3
1080.2.bt.a.233.8 72 45.13 odd 12
1080.2.bt.a.737.8 72 3.2 odd 2
1080.2.bt.a.953.15 72 15.8 even 4