Properties

Label 360.2.bs.a.113.16
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 113.16
Character \(\chi\) \(=\) 360.113
Dual form 360.2.bs.a.137.16

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(1.60229 - 0.657781i) q^{3} +(2.22211 - 0.249468i) q^{5} +(2.85561 + 0.765158i) q^{7} +(2.13465 - 2.10791i) q^{9} +O(q^{10})\) \(q+(1.60229 - 0.657781i) q^{3} +(2.22211 - 0.249468i) q^{5} +(2.85561 + 0.765158i) q^{7} +(2.13465 - 2.10791i) q^{9} +(-3.16595 + 1.82786i) q^{11} +(-5.61711 + 1.50510i) q^{13} +(3.39636 - 1.86138i) q^{15} +(-2.79242 - 2.79242i) q^{17} +3.15582i q^{19} +(5.07881 - 0.652362i) q^{21} +(0.00442531 + 0.0165155i) q^{23} +(4.87553 - 1.10869i) q^{25} +(2.03378 - 4.78161i) q^{27} +(-0.867889 - 1.50323i) q^{29} +(0.0235550 - 0.0407985i) q^{31} +(-3.87043 + 5.01126i) q^{33} +(6.53635 + 0.987880i) q^{35} +(5.93650 - 5.93650i) q^{37} +(-8.01019 + 6.10643i) q^{39} +(-10.7692 - 6.21760i) q^{41} +(-2.95353 + 11.0227i) q^{43} +(4.21756 - 5.21653i) q^{45} +(0.133675 - 0.498880i) q^{47} +(1.50685 + 0.869979i) q^{49} +(-6.31105 - 2.63746i) q^{51} +(4.87002 - 4.87002i) q^{53} +(-6.57909 + 4.85151i) q^{55} +(2.07584 + 5.05652i) q^{57} +(-1.07064 + 1.85441i) q^{59} +(1.16162 + 2.01199i) q^{61} +(7.70860 - 4.38602i) q^{63} +(-12.1063 + 4.74578i) q^{65} +(3.05975 + 11.4191i) q^{67} +(0.0179542 + 0.0235517i) q^{69} -7.67122i q^{71} +(7.97978 + 7.97978i) q^{73} +(7.08273 - 4.98347i) q^{75} +(-10.4393 + 2.79720i) q^{77} +(0.452608 - 0.261313i) q^{79} +(0.113447 - 8.99928i) q^{81} +(-9.28798 - 2.48871i) q^{83} +(-6.90167 - 5.50843i) q^{85} +(-2.37940 - 1.83772i) q^{87} -7.16365 q^{89} -17.1919 q^{91} +(0.0109054 - 0.0808649i) q^{93} +(0.787276 + 7.01257i) q^{95} +(-6.80611 - 1.82369i) q^{97} +(-2.90522 + 10.5754i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 72 q+O(q^{10}) \) 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
\(3\) 1.60229 0.657781i 0.925081 0.379770i
\(4\) 0 0
\(5\) 2.22211 0.249468i 0.993757 0.111566i
\(6\) 0 0
\(7\) 2.85561 + 0.765158i 1.07932 + 0.289202i 0.754316 0.656511i \(-0.227968\pi\)
0.325002 + 0.945713i \(0.394635\pi\)
\(8\) 0 0
\(9\) 2.13465 2.10791i 0.711549 0.702636i
\(10\) 0 0
\(11\) −3.16595 + 1.82786i −0.954569 + 0.551121i −0.894497 0.447073i \(-0.852466\pi\)
−0.0600718 + 0.998194i \(0.519133\pi\)
\(12\) 0 0
\(13\) −5.61711 + 1.50510i −1.55790 + 0.417439i −0.931999 0.362460i \(-0.881937\pi\)
−0.625905 + 0.779899i \(0.715270\pi\)
\(14\) 0 0
\(15\) 3.39636 1.86138i 0.876936 0.480606i
\(16\) 0 0
\(17\) −2.79242 2.79242i −0.677261 0.677261i 0.282119 0.959379i \(-0.408963\pi\)
−0.959379 + 0.282119i \(0.908963\pi\)
\(18\) 0 0
\(19\) 3.15582i 0.723994i 0.932179 + 0.361997i \(0.117905\pi\)
−0.932179 + 0.361997i \(0.882095\pi\)
\(20\) 0 0
\(21\) 5.07881 0.652362i 1.10829 0.142357i
\(22\) 0 0
\(23\) 0.00442531 + 0.0165155i 0.000922741 + 0.00344371i 0.966386 0.257097i \(-0.0827659\pi\)
−0.965463 + 0.260540i \(0.916099\pi\)
\(24\) 0 0
\(25\) 4.87553 1.10869i 0.975106 0.221738i
\(26\) 0 0
\(27\) 2.03378 4.78161i 0.391401 0.920220i
\(28\) 0 0
\(29\) −0.867889 1.50323i −0.161163 0.279143i 0.774123 0.633035i \(-0.218191\pi\)
−0.935286 + 0.353893i \(0.884858\pi\)
\(30\) 0 0
\(31\) 0.0235550 0.0407985i 0.00423061 0.00732762i −0.863902 0.503659i \(-0.831987\pi\)
0.868133 + 0.496332i \(0.165320\pi\)
\(32\) 0 0
\(33\) −3.87043 + 5.01126i −0.673755 + 0.872348i
\(34\) 0 0
\(35\) 6.53635 + 0.987880i 1.10485 + 0.166982i
\(36\) 0 0
\(37\) 5.93650 5.93650i 0.975955 0.975955i −0.0237623 0.999718i \(-0.507564\pi\)
0.999718 + 0.0237623i \(0.00756450\pi\)
\(38\) 0 0
\(39\) −8.01019 + 6.10643i −1.28266 + 0.977811i
\(40\) 0 0
\(41\) −10.7692 6.21760i −1.68187 0.971027i −0.960419 0.278558i \(-0.910143\pi\)
−0.721448 0.692468i \(-0.756523\pi\)
\(42\) 0 0
\(43\) −2.95353 + 11.0227i −0.450409 + 1.68095i 0.250837 + 0.968029i \(0.419294\pi\)
−0.701246 + 0.712920i \(0.747372\pi\)
\(44\) 0 0
\(45\) 4.21756 5.21653i 0.628717 0.777634i
\(46\) 0 0
\(47\) 0.133675 0.498880i 0.0194984 0.0727691i −0.955491 0.295020i \(-0.904674\pi\)
0.974990 + 0.222251i \(0.0713404\pi\)
\(48\) 0 0
\(49\) 1.50685 + 0.869979i 0.215264 + 0.124283i
\(50\) 0 0
\(51\) −6.31105 2.63746i −0.883724 0.369318i
\(52\) 0 0
\(53\) 4.87002 4.87002i 0.668949 0.668949i −0.288524 0.957473i \(-0.593164\pi\)
0.957473 + 0.288524i \(0.0931643\pi\)
\(54\) 0 0
\(55\) −6.57909 + 4.85151i −0.887124 + 0.654177i
\(56\) 0 0
\(57\) 2.07584 + 5.05652i 0.274951 + 0.669753i
\(58\) 0 0
\(59\) −1.07064 + 1.85441i −0.139386 + 0.241424i −0.927264 0.374407i \(-0.877846\pi\)
0.787878 + 0.615831i \(0.211180\pi\)
\(60\) 0 0
\(61\) 1.16162 + 2.01199i 0.148731 + 0.257609i 0.930759 0.365634i \(-0.119148\pi\)
−0.782028 + 0.623244i \(0.785815\pi\)
\(62\) 0 0
\(63\) 7.70860 4.38602i 0.971192 0.552586i
\(64\) 0 0
\(65\) −12.1063 + 4.74578i −1.50161 + 0.588642i
\(66\) 0 0
\(67\) 3.05975 + 11.4191i 0.373808 + 1.39507i 0.855078 + 0.518499i \(0.173509\pi\)
−0.481270 + 0.876572i \(0.659824\pi\)
\(68\) 0 0
\(69\) 0.0179542 + 0.0235517i 0.00216143 + 0.00283529i
\(70\) 0 0
\(71\) 7.67122i 0.910406i −0.890388 0.455203i \(-0.849567\pi\)
0.890388 0.455203i \(-0.150433\pi\)
\(72\) 0 0
\(73\) 7.97978 + 7.97978i 0.933962 + 0.933962i 0.997951 0.0639883i \(-0.0203820\pi\)
−0.0639883 + 0.997951i \(0.520382\pi\)
\(74\) 0 0
\(75\) 7.08273 4.98347i 0.817843 0.575442i
\(76\) 0 0
\(77\) −10.4393 + 2.79720i −1.18967 + 0.318771i
\(78\) 0 0
\(79\) 0.452608 0.261313i 0.0509223 0.0294000i −0.474323 0.880351i \(-0.657307\pi\)
0.525245 + 0.850951i \(0.323974\pi\)
\(80\) 0 0
\(81\) 0.113447 8.99928i 0.0126052 0.999921i
\(82\) 0 0
\(83\) −9.28798 2.48871i −1.01949 0.273171i −0.289900 0.957057i \(-0.593622\pi\)
−0.729589 + 0.683886i \(0.760289\pi\)
\(84\) 0 0
\(85\) −6.90167 5.50843i −0.748592 0.597474i
\(86\) 0 0
\(87\) −2.37940 1.83772i −0.255099 0.197025i
\(88\) 0 0
\(89\) −7.16365 −0.759346 −0.379673 0.925121i \(-0.623963\pi\)
−0.379673 + 0.925121i \(0.623963\pi\)
\(90\) 0 0
\(91\) −17.1919 −1.80220
\(92\) 0 0
\(93\) 0.0109054 0.0808649i 0.00113084 0.00838530i
\(94\) 0 0
\(95\) 0.787276 + 7.01257i 0.0807728 + 0.719474i
\(96\) 0 0
\(97\) −6.80611 1.82369i −0.691056 0.185168i −0.103835 0.994595i \(-0.533111\pi\)
−0.587221 + 0.809427i \(0.699778\pi\)
\(98\) 0 0
\(99\) −2.90522 + 10.5754i −0.291986 + 1.06286i
\(100\) 0 0
\(101\) −2.95553 + 1.70638i −0.294086 + 0.169791i −0.639783 0.768555i \(-0.720976\pi\)
0.345697 + 0.938346i \(0.387643\pi\)
\(102\) 0 0
\(103\) 3.63782 0.974751i 0.358445 0.0960451i −0.0751023 0.997176i \(-0.523928\pi\)
0.433547 + 0.901131i \(0.357262\pi\)
\(104\) 0 0
\(105\) 11.1229 2.71662i 1.08549 0.265115i
\(106\) 0 0
\(107\) 6.18949 + 6.18949i 0.598360 + 0.598360i 0.939876 0.341516i \(-0.110940\pi\)
−0.341516 + 0.939876i \(0.610940\pi\)
\(108\) 0 0
\(109\) 7.51076i 0.719400i −0.933068 0.359700i \(-0.882879\pi\)
0.933068 0.359700i \(-0.117121\pi\)
\(110\) 0 0
\(111\) 5.60706 13.4169i 0.532199 1.27348i
\(112\) 0 0
\(113\) 4.25011 + 15.8616i 0.399817 + 1.49214i 0.813419 + 0.581679i \(0.197604\pi\)
−0.413602 + 0.910458i \(0.635729\pi\)
\(114\) 0 0
\(115\) 0.0139536 + 0.0355952i 0.00130118 + 0.00331927i
\(116\) 0 0
\(117\) −8.81793 + 15.0532i −0.815218 + 1.39167i
\(118\) 0 0
\(119\) −5.83741 10.1107i −0.535114 0.926845i
\(120\) 0 0
\(121\) 1.18215 2.04754i 0.107468 0.186140i
\(122\) 0 0
\(123\) −21.3452 2.87861i −1.92463 0.259555i
\(124\) 0 0
\(125\) 10.5574 3.67992i 0.944280 0.329142i
\(126\) 0 0
\(127\) 9.64093 9.64093i 0.855495 0.855495i −0.135309 0.990803i \(-0.543203\pi\)
0.990803 + 0.135309i \(0.0432027\pi\)
\(128\) 0 0
\(129\) 2.51813 + 19.6043i 0.221709 + 1.72607i
\(130\) 0 0
\(131\) 13.8254 + 7.98211i 1.20793 + 0.697400i 0.962307 0.271965i \(-0.0876733\pi\)
0.245625 + 0.969365i \(0.421007\pi\)
\(132\) 0 0
\(133\) −2.41470 + 9.01177i −0.209381 + 0.781420i
\(134\) 0 0
\(135\) 3.32642 11.1326i 0.286292 0.958142i
\(136\) 0 0
\(137\) 1.93154 7.20862i 0.165023 0.615874i −0.833014 0.553251i \(-0.813387\pi\)
0.998037 0.0626224i \(-0.0199464\pi\)
\(138\) 0 0
\(139\) −10.7638 6.21447i −0.912971 0.527104i −0.0315853 0.999501i \(-0.510056\pi\)
−0.881386 + 0.472397i \(0.843389\pi\)
\(140\) 0 0
\(141\) −0.113969 0.887278i −0.00959791 0.0747223i
\(142\) 0 0
\(143\) 15.0324 15.0324i 1.25707 1.25707i
\(144\) 0 0
\(145\) −2.30355 3.12383i −0.191300 0.259420i
\(146\) 0 0
\(147\) 2.98666 + 0.402781i 0.246336 + 0.0332208i
\(148\) 0 0
\(149\) −9.40866 + 16.2963i −0.770787 + 1.33504i 0.166345 + 0.986068i \(0.446803\pi\)
−0.937132 + 0.348975i \(0.886530\pi\)
\(150\) 0 0
\(151\) −10.5767 18.3195i −0.860724 1.49082i −0.871232 0.490872i \(-0.836678\pi\)
0.0105079 0.999945i \(-0.496655\pi\)
\(152\) 0 0
\(153\) −11.8470 0.0746697i −0.957772 0.00603669i
\(154\) 0 0
\(155\) 0.0421639 0.0965349i 0.00338668 0.00775387i
\(156\) 0 0
\(157\) 4.00602 + 14.9507i 0.319716 + 1.19319i 0.919518 + 0.393047i \(0.128579\pi\)
−0.599803 + 0.800148i \(0.704754\pi\)
\(158\) 0 0
\(159\) 4.59977 11.0066i 0.364785 0.872879i
\(160\) 0 0
\(161\) 0.0505478i 0.00398372i
\(162\) 0 0
\(163\) −3.05208 3.05208i −0.239057 0.239057i 0.577402 0.816460i \(-0.304066\pi\)
−0.816460 + 0.577402i \(0.804066\pi\)
\(164\) 0 0
\(165\) −7.35036 + 12.1011i −0.572224 + 0.942070i
\(166\) 0 0
\(167\) 19.5890 5.24886i 1.51584 0.406169i 0.597473 0.801889i \(-0.296172\pi\)
0.918371 + 0.395720i \(0.129505\pi\)
\(168\) 0 0
\(169\) 18.0282 10.4086i 1.38679 0.800661i
\(170\) 0 0
\(171\) 6.65217 + 6.73656i 0.508704 + 0.515158i
\(172\) 0 0
\(173\) 15.0750 + 4.03932i 1.14613 + 0.307104i 0.781412 0.624015i \(-0.214500\pi\)
0.364715 + 0.931119i \(0.381166\pi\)
\(174\) 0 0
\(175\) 14.7709 + 0.564566i 1.11658 + 0.0426771i
\(176\) 0 0
\(177\) −0.495684 + 3.67555i −0.0372579 + 0.276271i
\(178\) 0 0
\(179\) −3.89096 −0.290824 −0.145412 0.989371i \(-0.546451\pi\)
−0.145412 + 0.989371i \(0.546451\pi\)
\(180\) 0 0
\(181\) 14.5521 1.08165 0.540826 0.841134i \(-0.318112\pi\)
0.540826 + 0.841134i \(0.318112\pi\)
\(182\) 0 0
\(183\) 3.18471 + 2.45970i 0.235420 + 0.181826i
\(184\) 0 0
\(185\) 11.7106 14.6725i 0.860980 1.07875i
\(186\) 0 0
\(187\) 13.9448 + 3.73650i 1.01974 + 0.273240i
\(188\) 0 0
\(189\) 9.46635 12.0982i 0.688576 0.880016i
\(190\) 0 0
\(191\) −6.08036 + 3.51050i −0.439960 + 0.254011i −0.703580 0.710616i \(-0.748417\pi\)
0.263621 + 0.964626i \(0.415083\pi\)
\(192\) 0 0
\(193\) 13.7922 3.69562i 0.992787 0.266017i 0.274366 0.961625i \(-0.411532\pi\)
0.718421 + 0.695609i \(0.244865\pi\)
\(194\) 0 0
\(195\) −16.2762 + 15.5674i −1.16556 + 1.11481i
\(196\) 0 0
\(197\) −2.76470 2.76470i −0.196977 0.196977i 0.601726 0.798703i \(-0.294480\pi\)
−0.798703 + 0.601726i \(0.794480\pi\)
\(198\) 0 0
\(199\) 7.66540i 0.543386i 0.962384 + 0.271693i \(0.0875835\pi\)
−0.962384 + 0.271693i \(0.912416\pi\)
\(200\) 0 0
\(201\) 12.4139 + 16.2841i 0.875609 + 1.14859i
\(202\) 0 0
\(203\) −1.32814 4.95670i −0.0932175 0.347892i
\(204\) 0 0
\(205\) −25.4814 11.1296i −1.77970 0.777326i
\(206\) 0 0
\(207\) 0.0442596 + 0.0259266i 0.00307625 + 0.00180202i
\(208\) 0 0
\(209\) −5.76839 9.99115i −0.399008 0.691102i
\(210\) 0 0
\(211\) 9.56336 16.5642i 0.658369 1.14033i −0.322669 0.946512i \(-0.604580\pi\)
0.981038 0.193816i \(-0.0620866\pi\)
\(212\) 0 0
\(213\) −5.04598 12.2915i −0.345745 0.842199i
\(214\) 0 0
\(215\) −3.81324 + 25.2305i −0.260061 + 1.72070i
\(216\) 0 0
\(217\) 0.0984811 0.0984811i 0.00668533 0.00668533i
\(218\) 0 0
\(219\) 18.0348 + 7.53695i 1.21868 + 0.509300i
\(220\) 0 0
\(221\) 19.8882 + 11.4824i 1.33782 + 0.772392i
\(222\) 0 0
\(223\) −6.72248 + 25.0887i −0.450171 + 1.68006i 0.251740 + 0.967795i \(0.418997\pi\)
−0.701910 + 0.712265i \(0.747669\pi\)
\(224\) 0 0
\(225\) 8.07053 12.6438i 0.538035 0.842922i
\(226\) 0 0
\(227\) 4.17675 15.5878i 0.277221 1.03460i −0.677118 0.735874i \(-0.736771\pi\)
0.954339 0.298727i \(-0.0965620\pi\)
\(228\) 0 0
\(229\) −8.20334 4.73620i −0.542092 0.312977i 0.203834 0.979005i \(-0.434660\pi\)
−0.745926 + 0.666028i \(0.767993\pi\)
\(230\) 0 0
\(231\) −14.8868 + 11.3487i −0.979481 + 0.746690i
\(232\) 0 0
\(233\) 8.35560 8.35560i 0.547393 0.547393i −0.378293 0.925686i \(-0.623489\pi\)
0.925686 + 0.378293i \(0.123489\pi\)
\(234\) 0 0
\(235\) 0.172585 1.14191i 0.0112582 0.0744902i
\(236\) 0 0
\(237\) 0.553321 0.716416i 0.0359420 0.0465362i
\(238\) 0 0
\(239\) −0.475159 + 0.823000i −0.0307355 + 0.0532355i −0.880984 0.473146i \(-0.843118\pi\)
0.850249 + 0.526382i \(0.176452\pi\)
\(240\) 0 0
\(241\) −6.38145 11.0530i −0.411065 0.711986i 0.583941 0.811796i \(-0.301510\pi\)
−0.995007 + 0.0998100i \(0.968177\pi\)
\(242\) 0 0
\(243\) −5.73778 14.4941i −0.368079 0.929794i
\(244\) 0 0
\(245\) 3.56541 + 1.55728i 0.227786 + 0.0994908i
\(246\) 0 0
\(247\) −4.74982 17.7266i −0.302224 1.12791i
\(248\) 0 0
\(249\) −16.5190 + 2.12183i −1.04685 + 0.134466i
\(250\) 0 0
\(251\) 18.7575i 1.18396i 0.805951 + 0.591982i \(0.201654\pi\)
−0.805951 + 0.591982i \(0.798346\pi\)
\(252\) 0 0
\(253\) −0.0441983 0.0441983i −0.00277872 0.00277872i
\(254\) 0 0
\(255\) −14.6818 4.28630i −0.919410 0.268419i
\(256\) 0 0
\(257\) 3.78980 1.01547i 0.236401 0.0633435i −0.138673 0.990338i \(-0.544284\pi\)
0.375074 + 0.926995i \(0.377617\pi\)
\(258\) 0 0
\(259\) 21.4947 12.4100i 1.33561 0.771118i
\(260\) 0 0
\(261\) −5.02131 1.37943i −0.310811 0.0853848i
\(262\) 0 0
\(263\) 20.2488 + 5.42565i 1.24860 + 0.334560i 0.821794 0.569785i \(-0.192974\pi\)
0.426802 + 0.904345i \(0.359640\pi\)
\(264\) 0 0
\(265\) 9.60681 12.0366i 0.590141 0.739405i
\(266\) 0 0
\(267\) −11.4782 + 4.71212i −0.702456 + 0.288377i
\(268\) 0 0
\(269\) −2.04943 −0.124956 −0.0624778 0.998046i \(-0.519900\pi\)
−0.0624778 + 0.998046i \(0.519900\pi\)
\(270\) 0 0
\(271\) −7.06017 −0.428875 −0.214437 0.976738i \(-0.568792\pi\)
−0.214437 + 0.976738i \(0.568792\pi\)
\(272\) 0 0
\(273\) −27.5463 + 11.3085i −1.66718 + 0.684421i
\(274\) 0 0
\(275\) −13.4091 + 12.4218i −0.808602 + 0.749066i
\(276\) 0 0
\(277\) −19.2827 5.16678i −1.15858 0.310442i −0.372184 0.928159i \(-0.621391\pi\)
−0.786400 + 0.617717i \(0.788058\pi\)
\(278\) 0 0
\(279\) −0.0357178 0.136742i −0.00213837 0.00818654i
\(280\) 0 0
\(281\) −10.8727 + 6.27735i −0.648610 + 0.374475i −0.787923 0.615773i \(-0.788844\pi\)
0.139313 + 0.990248i \(0.455510\pi\)
\(282\) 0 0
\(283\) −5.70224 + 1.52791i −0.338963 + 0.0908248i −0.424285 0.905529i \(-0.639475\pi\)
0.0853225 + 0.996353i \(0.472808\pi\)
\(284\) 0 0
\(285\) 5.87417 + 10.7183i 0.347956 + 0.634897i
\(286\) 0 0
\(287\) −25.9952 25.9952i −1.53445 1.53445i
\(288\) 0 0
\(289\) 1.40481i 0.0826359i
\(290\) 0 0
\(291\) −12.1049 + 1.55485i −0.709604 + 0.0911470i
\(292\) 0 0
\(293\) 2.11779 + 7.90371i 0.123723 + 0.461740i 0.999791 0.0204476i \(-0.00650912\pi\)
−0.876068 + 0.482187i \(0.839842\pi\)
\(294\) 0 0
\(295\) −1.91647 + 4.38779i −0.111581 + 0.255467i
\(296\) 0 0
\(297\) 2.30128 + 18.8558i 0.133534 + 1.09412i
\(298\) 0 0
\(299\) −0.0497148 0.0861086i −0.00287508 0.00497979i
\(300\) 0 0
\(301\) −16.8682 + 29.2166i −0.972269 + 1.68402i
\(302\) 0 0
\(303\) −3.61319 + 4.67820i −0.207572 + 0.268756i
\(304\) 0 0
\(305\) 3.08318 + 4.18108i 0.176543 + 0.239408i
\(306\) 0 0
\(307\) −11.0523 + 11.0523i −0.630790 + 0.630790i −0.948266 0.317477i \(-0.897165\pi\)
0.317477 + 0.948266i \(0.397165\pi\)
\(308\) 0 0
\(309\) 5.18766 3.95472i 0.295116 0.224976i
\(310\) 0 0
\(311\) 10.0045 + 5.77608i 0.567301 + 0.327532i 0.756071 0.654490i \(-0.227117\pi\)
−0.188769 + 0.982021i \(0.560450\pi\)
\(312\) 0 0
\(313\) 3.94044 14.7059i 0.222727 0.831228i −0.760576 0.649249i \(-0.775083\pi\)
0.983302 0.181979i \(-0.0582502\pi\)
\(314\) 0 0
\(315\) 16.0352 11.6693i 0.903480 0.657488i
\(316\) 0 0
\(317\) 1.65400 6.17280i 0.0928977 0.346699i −0.903795 0.427967i \(-0.859230\pi\)
0.996692 + 0.0812674i \(0.0258968\pi\)
\(318\) 0 0
\(319\) 5.49539 + 3.17276i 0.307683 + 0.177641i
\(320\) 0 0
\(321\) 13.9887 + 5.84601i 0.780771 + 0.326292i
\(322\) 0 0
\(323\) 8.81236 8.81236i 0.490333 0.490333i
\(324\) 0 0
\(325\) −25.7177 + 13.5658i −1.42656 + 0.752495i
\(326\) 0 0
\(327\) −4.94043 12.0344i −0.273207 0.665503i
\(328\) 0 0
\(329\) 0.763444 1.32232i 0.0420900 0.0729020i
\(330\) 0 0
\(331\) −6.76353 11.7148i −0.371757 0.643903i 0.618079 0.786116i \(-0.287911\pi\)
−0.989836 + 0.142214i \(0.954578\pi\)
\(332\) 0 0
\(333\) 0.158743 25.1860i 0.00869907 1.38018i
\(334\) 0 0
\(335\) 9.64781 + 24.6113i 0.527116 + 1.34466i
\(336\) 0 0
\(337\) −1.82116 6.79666i −0.0992048 0.370237i 0.898419 0.439140i \(-0.144717\pi\)
−0.997623 + 0.0689028i \(0.978050\pi\)
\(338\) 0 0
\(339\) 17.2434 + 22.6192i 0.936532 + 1.22851i
\(340\) 0 0
\(341\) 0.172221i 0.00932630i
\(342\) 0 0
\(343\) −10.9959 10.9959i −0.593720 0.593720i
\(344\) 0 0
\(345\) 0.0457715 + 0.0478553i 0.00246426 + 0.00257644i
\(346\) 0 0
\(347\) −29.5309 + 7.91278i −1.58530 + 0.424780i −0.940562 0.339622i \(-0.889701\pi\)
−0.644739 + 0.764403i \(0.723034\pi\)
\(348\) 0 0
\(349\) 26.7285 15.4317i 1.43074 0.826039i 0.433565 0.901122i \(-0.357255\pi\)
0.997177 + 0.0750829i \(0.0239221\pi\)
\(350\) 0 0
\(351\) −4.22715 + 29.9198i −0.225629 + 1.59700i
\(352\) 0 0
\(353\) −15.0664 4.03704i −0.801905 0.214870i −0.165485 0.986212i \(-0.552919\pi\)
−0.636420 + 0.771342i \(0.719586\pi\)
\(354\) 0 0
\(355\) −1.91372 17.0463i −0.101570 0.904723i
\(356\) 0 0
\(357\) −16.0038 12.3605i −0.847012 0.654186i
\(358\) 0 0
\(359\) 5.34799 0.282256 0.141128 0.989991i \(-0.454927\pi\)
0.141128 + 0.989991i \(0.454927\pi\)
\(360\) 0 0
\(361\) 9.04082 0.475833
\(362\) 0 0
\(363\) 0.547308 4.05835i 0.0287262 0.213008i
\(364\) 0 0
\(365\) 19.7226 + 15.7412i 1.03233 + 0.823934i
\(366\) 0 0
\(367\) 3.30973 + 0.886840i 0.172767 + 0.0462927i 0.344165 0.938909i \(-0.388162\pi\)
−0.171399 + 0.985202i \(0.554829\pi\)
\(368\) 0 0
\(369\) −36.0946 + 9.42810i −1.87901 + 0.490807i
\(370\) 0 0
\(371\) 17.6332 10.1805i 0.915471 0.528547i
\(372\) 0 0
\(373\) −8.26293 + 2.21404i −0.427838 + 0.114639i −0.466311 0.884621i \(-0.654417\pi\)
0.0384731 + 0.999260i \(0.487751\pi\)
\(374\) 0 0
\(375\) 14.4954 12.8407i 0.748538 0.663092i
\(376\) 0 0
\(377\) 7.13753 + 7.13753i 0.367602 + 0.367602i
\(378\) 0 0
\(379\) 17.4965i 0.898737i 0.893346 + 0.449369i \(0.148351\pi\)
−0.893346 + 0.449369i \(0.851649\pi\)
\(380\) 0 0
\(381\) 9.10592 21.7892i 0.466510 1.11629i
\(382\) 0 0
\(383\) −3.59627 13.4215i −0.183761 0.685805i −0.994892 0.100941i \(-0.967815\pi\)
0.811132 0.584864i \(-0.198852\pi\)
\(384\) 0 0
\(385\) −22.4995 + 8.81996i −1.14668 + 0.449507i
\(386\) 0 0
\(387\) 16.9301 + 29.7554i 0.860607 + 1.51255i
\(388\) 0 0
\(389\) −0.179116 0.310238i −0.00908155 0.0157297i 0.861449 0.507844i \(-0.169557\pi\)
−0.870530 + 0.492115i \(0.836224\pi\)
\(390\) 0 0
\(391\) 0.0337608 0.0584754i 0.00170736 0.00295723i
\(392\) 0 0
\(393\) 27.4028 + 3.69553i 1.38229 + 0.186415i
\(394\) 0 0
\(395\) 0.940554 0.693577i 0.0473244 0.0348977i
\(396\) 0 0
\(397\) 17.2262 17.2262i 0.864557 0.864557i −0.127306 0.991863i \(-0.540633\pi\)
0.991863 + 0.127306i \(0.0406332\pi\)
\(398\) 0 0
\(399\) 2.05873 + 16.0278i 0.103066 + 0.802393i
\(400\) 0 0
\(401\) −7.61875 4.39869i −0.380462 0.219660i 0.297557 0.954704i \(-0.403828\pi\)
−0.678019 + 0.735044i \(0.737161\pi\)
\(402\) 0 0
\(403\) −0.0709052 + 0.264622i −0.00353204 + 0.0131818i
\(404\) 0 0
\(405\) −1.99294 20.0257i −0.0990302 0.995084i
\(406\) 0 0
\(407\) −7.94356 + 29.6458i −0.393748 + 1.46949i
\(408\) 0 0
\(409\) 6.59212 + 3.80596i 0.325959 + 0.188193i 0.654046 0.756455i \(-0.273070\pi\)
−0.328086 + 0.944648i \(0.606404\pi\)
\(410\) 0 0
\(411\) −1.64680 12.8208i −0.0812309 0.632404i
\(412\) 0 0
\(413\) −4.47625 + 4.47625i −0.220262 + 0.220262i
\(414\) 0 0
\(415\) −21.2598 3.21312i −1.04360 0.157726i
\(416\) 0 0
\(417\) −21.3344 2.87716i −1.04475 0.140895i
\(418\) 0 0
\(419\) 6.80742 11.7908i 0.332564 0.576018i −0.650450 0.759549i \(-0.725420\pi\)
0.983014 + 0.183531i \(0.0587529\pi\)
\(420\) 0 0
\(421\) 8.75046 + 15.1562i 0.426471 + 0.738670i 0.996557 0.0829155i \(-0.0264231\pi\)
−0.570085 + 0.821586i \(0.693090\pi\)
\(422\) 0 0
\(423\) −0.766245 1.34671i −0.0372561 0.0654791i
\(424\) 0 0
\(425\) −16.7104 10.5186i −0.810576 0.510227i
\(426\) 0 0
\(427\) 1.77765 + 6.63429i 0.0860266 + 0.321056i
\(428\) 0 0
\(429\) 14.1981 33.9741i 0.685493 1.64029i
\(430\) 0 0
\(431\) 6.51527i 0.313830i 0.987612 + 0.156915i \(0.0501548\pi\)
−0.987612 + 0.156915i \(0.949845\pi\)
\(432\) 0 0
\(433\) 11.3750 + 11.3750i 0.546646 + 0.546646i 0.925469 0.378823i \(-0.123671\pi\)
−0.378823 + 0.925469i \(0.623671\pi\)
\(434\) 0 0
\(435\) −5.74575 3.49003i −0.275487 0.167334i
\(436\) 0 0
\(437\) −0.0521198 + 0.0139655i −0.00249323 + 0.000668059i
\(438\) 0 0
\(439\) −15.7213 + 9.07671i −0.750338 + 0.433208i −0.825816 0.563940i \(-0.809285\pi\)
0.0754782 + 0.997147i \(0.475952\pi\)
\(440\) 0 0
\(441\) 5.05043 1.31920i 0.240497 0.0628190i
\(442\) 0 0
\(443\) −17.6627 4.73270i −0.839179 0.224857i −0.186465 0.982462i \(-0.559703\pi\)
−0.652714 + 0.757604i \(0.726370\pi\)
\(444\) 0 0
\(445\) −15.9184 + 1.78710i −0.754605 + 0.0847168i
\(446\) 0 0
\(447\) −4.35599 + 32.3001i −0.206031 + 1.52774i
\(448\) 0 0
\(449\) 21.4573 1.01263 0.506317 0.862347i \(-0.331006\pi\)
0.506317 + 0.862347i \(0.331006\pi\)
\(450\) 0 0
\(451\) 45.4597 2.14061
\(452\) 0 0
\(453\) −28.9972 22.3959i −1.36241 1.05225i
\(454\) 0 0
\(455\) −38.2022 + 4.28883i −1.79095 + 0.201063i
\(456\) 0 0
\(457\) 12.1591 + 3.25801i 0.568778 + 0.152404i 0.531736 0.846910i \(-0.321540\pi\)
0.0370417 + 0.999314i \(0.488207\pi\)
\(458\) 0 0
\(459\) −19.0314 + 7.67308i −0.888309 + 0.358149i
\(460\) 0 0
\(461\) −11.8369 + 6.83406i −0.551301 + 0.318294i −0.749647 0.661838i \(-0.769777\pi\)
0.198346 + 0.980132i \(0.436443\pi\)
\(462\) 0 0
\(463\) 22.2066 5.95025i 1.03203 0.276531i 0.297223 0.954808i \(-0.403940\pi\)
0.734807 + 0.678277i \(0.237273\pi\)
\(464\) 0 0
\(465\) 0.00405983 0.182411i 0.000188270 0.00845912i
\(466\) 0 0
\(467\) −20.8793 20.8793i −0.966177 0.966177i 0.0332691 0.999446i \(-0.489408\pi\)
−0.999446 + 0.0332691i \(0.989408\pi\)
\(468\) 0 0
\(469\) 34.9498i 1.61383i
\(470\) 0 0
\(471\) 16.2531 + 21.3202i 0.748902 + 0.982383i
\(472\) 0 0
\(473\) −10.7973 40.2960i −0.496459 1.85281i
\(474\) 0 0
\(475\) 3.49882 + 15.3863i 0.160537 + 0.705971i
\(476\) 0 0
\(477\) 0.130225 20.6614i 0.00596260 0.946018i
\(478\) 0 0
\(479\) −18.0800 31.3155i −0.826096 1.43084i −0.901078 0.433656i \(-0.857223\pi\)
0.0749821 0.997185i \(-0.476110\pi\)
\(480\) 0 0
\(481\) −24.4109 + 42.2810i −1.11304 + 1.92785i
\(482\) 0 0
\(483\) 0.0332494 + 0.0809920i 0.00151290 + 0.00368527i
\(484\) 0 0
\(485\) −15.5789 2.35453i −0.707400 0.106914i
\(486\) 0 0
\(487\) 19.8415 19.8415i 0.899103 0.899103i −0.0962539 0.995357i \(-0.530686\pi\)
0.995357 + 0.0962539i \(0.0306861\pi\)
\(488\) 0 0
\(489\) −6.89791 2.88271i −0.311934 0.130361i
\(490\) 0 0
\(491\) −14.8519 8.57477i −0.670259 0.386974i 0.125916 0.992041i \(-0.459813\pi\)
−0.796175 + 0.605067i \(0.793146\pi\)
\(492\) 0 0
\(493\) −1.77413 + 6.62115i −0.0799029 + 0.298202i
\(494\) 0 0
\(495\) −3.81750 + 24.2244i −0.171584 + 1.08880i
\(496\) 0 0
\(497\) 5.86969 21.9060i 0.263292 0.982618i
\(498\) 0 0
\(499\) −19.8823 11.4791i −0.890056 0.513874i −0.0160952 0.999870i \(-0.505123\pi\)
−0.873961 + 0.485996i \(0.838457\pi\)
\(500\) 0 0
\(501\) 27.9346 21.2955i 1.24803 0.951412i
\(502\) 0 0
\(503\) −0.820890 + 0.820890i −0.0366017 + 0.0366017i −0.725171 0.688569i \(-0.758239\pi\)
0.688569 + 0.725171i \(0.258239\pi\)
\(504\) 0 0
\(505\) −6.14183 + 4.52907i −0.273308 + 0.201541i
\(506\) 0 0
\(507\) 22.0398 28.5362i 0.978822 1.26734i
\(508\) 0 0
\(509\) 13.1122 22.7110i 0.581188 1.00665i −0.414151 0.910208i \(-0.635921\pi\)
0.995339 0.0964388i \(-0.0307452\pi\)
\(510\) 0 0
\(511\) 16.6813 + 28.8929i 0.737938 + 1.27815i
\(512\) 0 0
\(513\) 15.0899 + 6.41823i 0.666234 + 0.283372i
\(514\) 0 0
\(515\) 7.84046 3.07352i 0.345492 0.135436i
\(516\) 0 0
\(517\) 0.488677 + 1.82377i 0.0214920 + 0.0802092i
\(518\) 0 0
\(519\) 26.8114 3.44386i 1.17689 0.151169i
\(520\) 0 0
\(521\) 11.8958i 0.521166i 0.965451 + 0.260583i \(0.0839147\pi\)
−0.965451 + 0.260583i \(0.916085\pi\)
\(522\) 0 0
\(523\) 10.6324 + 10.6324i 0.464923 + 0.464923i 0.900265 0.435342i \(-0.143373\pi\)
−0.435342 + 0.900265i \(0.643373\pi\)
\(524\) 0 0
\(525\) 24.0386 8.81144i 1.04913 0.384563i
\(526\) 0 0
\(527\) −0.179702 + 0.0481510i −0.00782793 + 0.00209749i
\(528\) 0 0
\(529\) 19.9183 11.4999i 0.866014 0.499994i
\(530\) 0 0
\(531\) 1.62348 + 6.21533i 0.0704529 + 0.269722i
\(532\) 0 0
\(533\) 69.8499 + 18.7162i 3.02553 + 0.810689i
\(534\) 0 0
\(535\) 15.2978 + 12.2096i 0.661381 + 0.527869i
\(536\) 0 0
\(537\) −6.23444 + 2.55940i −0.269036 + 0.110446i
\(538\) 0 0
\(539\) −6.36081 −0.273979
\(540\) 0 0
\(541\) 9.59421 0.412487 0.206244 0.978501i \(-0.433876\pi\)
0.206244 + 0.978501i \(0.433876\pi\)
\(542\) 0 0
\(543\) 23.3167 9.57212i 1.00062 0.410779i
\(544\) 0 0
\(545\) −1.87369 16.6897i −0.0802603 0.714909i
\(546\) 0 0
\(547\) 13.9852 + 3.74733i 0.597965 + 0.160224i 0.545091 0.838377i \(-0.316495\pi\)
0.0528744 + 0.998601i \(0.483162\pi\)
\(548\) 0 0
\(549\) 6.72076 + 1.84630i 0.286835 + 0.0787981i
\(550\) 0 0
\(551\) 4.74391 2.73890i 0.202098 0.116681i
\(552\) 0 0
\(553\) 1.49242 0.399892i 0.0634640 0.0170051i
\(554\) 0 0
\(555\) 9.11242 31.2126i 0.386801 1.32490i
\(556\) 0 0
\(557\) 25.1923 + 25.1923i 1.06743 + 1.06743i 0.997556 + 0.0698778i \(0.0222609\pi\)
0.0698778 + 0.997556i \(0.477739\pi\)
\(558\) 0 0
\(559\) 66.3611i 2.80678i
\(560\) 0 0
\(561\) 24.8014 3.18568i 1.04711 0.134500i
\(562\) 0 0
\(563\) 0.362891 + 1.35433i 0.0152940 + 0.0570781i 0.973151 0.230167i \(-0.0739272\pi\)
−0.957857 + 0.287245i \(0.907261\pi\)
\(564\) 0 0
\(565\) 13.4012 + 34.1860i 0.563792 + 1.43822i
\(566\) 0 0
\(567\) 7.20983 25.6116i 0.302784 1.07559i
\(568\) 0 0
\(569\) 12.3719 + 21.4287i 0.518657 + 0.898339i 0.999765 + 0.0216784i \(0.00690098\pi\)
−0.481108 + 0.876661i \(0.659766\pi\)
\(570\) 0 0
\(571\) 8.92196 15.4533i 0.373373 0.646700i −0.616709 0.787191i \(-0.711535\pi\)
0.990082 + 0.140491i \(0.0448680\pi\)
\(572\) 0 0
\(573\) −7.43335 + 9.62437i −0.310532 + 0.402064i
\(574\) 0 0
\(575\) 0.0398863 + 0.0756154i 0.00166337 + 0.00315338i
\(576\) 0 0
\(577\) −16.2195 + 16.2195i −0.675226 + 0.675226i −0.958916 0.283690i \(-0.908441\pi\)
0.283690 + 0.958916i \(0.408441\pi\)
\(578\) 0 0
\(579\) 19.6682 14.9937i 0.817383 0.623118i
\(580\) 0 0
\(581\) −24.6186 14.2135i −1.02135 0.589677i
\(582\) 0 0
\(583\) −6.51652 + 24.3200i −0.269887 + 1.00723i
\(584\) 0 0
\(585\) −15.8391 + 35.6496i −0.654867 + 1.47393i
\(586\) 0 0
\(587\) −9.45896 + 35.3013i −0.390413 + 1.45704i 0.439041 + 0.898467i \(0.355318\pi\)
−0.829454 + 0.558574i \(0.811348\pi\)
\(588\) 0 0
\(589\) 0.128753 + 0.0743353i 0.00530516 + 0.00306293i
\(590\) 0 0
\(591\) −6.24842 2.61128i −0.257026 0.107414i
\(592\) 0 0
\(593\) −21.8715 + 21.8715i −0.898153 + 0.898153i −0.995273 0.0971194i \(-0.969037\pi\)
0.0971194 + 0.995273i \(0.469037\pi\)
\(594\) 0 0
\(595\) −15.4936 21.0108i −0.635178 0.861359i
\(596\) 0 0
\(597\) 5.04216 + 12.2822i 0.206362 + 0.502676i
\(598\) 0 0
\(599\) 3.01176 5.21653i 0.123057 0.213142i −0.797915 0.602771i \(-0.794063\pi\)
0.920972 + 0.389629i \(0.127397\pi\)
\(600\) 0 0
\(601\) −22.1359 38.3405i −0.902942 1.56394i −0.823656 0.567090i \(-0.808069\pi\)
−0.0792867 0.996852i \(-0.525264\pi\)
\(602\) 0 0
\(603\) 30.6020 + 17.9262i 1.24621 + 0.730011i
\(604\) 0 0
\(605\) 2.11607 4.84477i 0.0860304 0.196968i
\(606\) 0 0
\(607\) 9.40334 + 35.0937i 0.381670 + 1.42441i 0.843350 + 0.537365i \(0.180580\pi\)
−0.461680 + 0.887046i \(0.652753\pi\)
\(608\) 0 0
\(609\) −5.38849 7.06843i −0.218353 0.286427i
\(610\) 0 0
\(611\) 3.00346i 0.121507i
\(612\) 0 0
\(613\) −22.6310 22.6310i −0.914056 0.914056i 0.0825324 0.996588i \(-0.473699\pi\)
−0.996588 + 0.0825324i \(0.973699\pi\)
\(614\) 0 0
\(615\) −48.1494 1.07164i −1.94157 0.0432125i
\(616\) 0 0
\(617\) 17.6990 4.74243i 0.712535 0.190923i 0.115697 0.993285i \(-0.463090\pi\)
0.596838 + 0.802361i \(0.296423\pi\)
\(618\) 0 0
\(619\) −0.246643 + 0.142399i −0.00991341 + 0.00572351i −0.504949 0.863149i \(-0.668489\pi\)
0.495035 + 0.868873i \(0.335155\pi\)
\(620\) 0 0
\(621\) 0.0879706 + 0.0124287i 0.00353014 + 0.000498748i
\(622\) 0 0
\(623\) −20.4566 5.48132i −0.819576 0.219605i
\(624\) 0 0
\(625\) 22.5416 10.8109i 0.901664 0.432436i
\(626\) 0 0
\(627\) −15.8146 12.2144i −0.631575 0.487794i
\(628\) 0 0
\(629\) −33.1544 −1.32195
\(630\) 0 0
\(631\) −11.6964 −0.465625 −0.232813 0.972522i \(-0.574793\pi\)
−0.232813 + 0.972522i \(0.574793\pi\)
\(632\) 0 0
\(633\) 4.42762 32.8312i 0.175982 1.30492i
\(634\) 0 0
\(635\) 19.0181 23.8283i 0.754710 0.945597i
\(636\) 0 0
\(637\) −9.77353 2.61881i −0.387241 0.103761i
\(638\) 0 0
\(639\) −16.1702 16.3754i −0.639684 0.647799i
\(640\) 0 0
\(641\) −7.50621 + 4.33372i −0.296478 + 0.171171i −0.640859 0.767658i \(-0.721422\pi\)
0.344382 + 0.938830i \(0.388089\pi\)
\(642\) 0 0
\(643\) −46.4536 + 12.4472i −1.83195 + 0.490870i −0.998128 0.0611592i \(-0.980520\pi\)
−0.833825 + 0.552029i \(0.813854\pi\)
\(644\) 0 0
\(645\) 10.4862 + 42.9348i 0.412895 + 1.69055i
\(646\) 0 0
\(647\) 8.10316 + 8.10316i 0.318568 + 0.318568i 0.848217 0.529649i \(-0.177676\pi\)
−0.529649 + 0.848217i \(0.677676\pi\)
\(648\) 0 0
\(649\) 7.82795i 0.307274i
\(650\) 0 0
\(651\) 0.0930160 0.222574i 0.00364559 0.00872337i
\(652\) 0 0
\(653\) −4.32971 16.1587i −0.169435 0.632338i −0.997433 0.0716077i \(-0.977187\pi\)
0.827998 0.560731i \(-0.189480\pi\)
\(654\) 0 0
\(655\) 32.7129 + 14.2881i 1.27820 + 0.558283i
\(656\) 0 0
\(657\) 33.8547 + 0.213380i 1.32080 + 0.00832477i
\(658\) 0 0
\(659\) 24.1363 + 41.8053i 0.940218 + 1.62850i 0.765055 + 0.643965i \(0.222712\pi\)
0.175163 + 0.984540i \(0.443955\pi\)
\(660\) 0 0
\(661\) 0.548876 0.950681i 0.0213488 0.0369772i −0.855154 0.518375i \(-0.826537\pi\)
0.876502 + 0.481397i \(0.159871\pi\)
\(662\) 0 0
\(663\) 39.4195 + 5.31611i 1.53093 + 0.206460i
\(664\) 0 0
\(665\) −3.11757 + 20.6275i −0.120894 + 0.799901i
\(666\) 0 0
\(667\) 0.0209859 0.0209859i 0.000812576 0.000812576i
\(668\) 0 0
\(669\) 5.73149 + 44.6211i 0.221592 + 1.72515i
\(670\) 0 0
\(671\) −7.35529 4.24658i −0.283948 0.163937i
\(672\) 0 0
\(673\) −0.0180520 + 0.0673708i −0.000695852 + 0.00259695i −0.966273 0.257520i \(-0.917095\pi\)
0.965577 + 0.260117i \(0.0837612\pi\)
\(674\) 0 0
\(675\) 4.61443 25.5677i 0.177609 0.984101i
\(676\) 0 0
\(677\) 0.177161 0.661175i 0.00680886 0.0254110i −0.962438 0.271502i \(-0.912480\pi\)
0.969247 + 0.246091i \(0.0791463\pi\)
\(678\) 0 0
\(679\) −18.0402 10.4155i −0.692318 0.399710i
\(680\) 0 0
\(681\) −3.56103 27.7236i −0.136459 1.06237i
\(682\) 0 0
\(683\) 17.5217 17.5217i 0.670448 0.670448i −0.287371 0.957819i \(-0.592781\pi\)
0.957819 + 0.287371i \(0.0927813\pi\)
\(684\) 0 0
\(685\) 2.49378 16.5002i 0.0952823 0.630440i
\(686\) 0 0
\(687\) −16.2595 2.19275i −0.620338 0.0836587i
\(688\) 0 0
\(689\) −20.0256 + 34.6853i −0.762914 + 1.32141i
\(690\) 0 0
\(691\) −3.48505 6.03629i −0.132578 0.229631i 0.792092 0.610402i \(-0.208992\pi\)
−0.924670 + 0.380771i \(0.875659\pi\)
\(692\) 0 0
\(693\) −16.3880 + 27.9761i −0.622529 + 1.06273i
\(694\) 0 0
\(695\) −25.4686 11.1240i −0.966078 0.421957i
\(696\) 0 0
\(697\) 12.7100 + 47.4343i 0.481425 + 1.79670i
\(698\) 0 0
\(699\) 7.89191 18.8842i 0.298499 0.714267i
\(700\) 0 0
\(701\) 27.7664i 1.04872i −0.851496 0.524362i \(-0.824304\pi\)
0.851496 0.524362i \(-0.175696\pi\)
\(702\) 0 0
\(703\) 18.7345 + 18.7345i 0.706586 + 0.706586i
\(704\) 0 0
\(705\) −0.474599 1.94320i −0.0178744 0.0731850i
\(706\) 0 0
\(707\) −9.74549 + 2.61130i −0.366517 + 0.0982079i
\(708\) 0 0
\(709\) −39.1415 + 22.5984i −1.46999 + 0.848700i −0.999433 0.0336686i \(-0.989281\pi\)
−0.470559 + 0.882369i \(0.655948\pi\)
\(710\) 0 0
\(711\) 0.415334 1.51187i 0.0155762 0.0566995i
\(712\) 0 0
\(713\) 0.000778044 0 0.000208476i 2.91380e−5 0 7.80750e-6i
\(714\) 0 0
\(715\) 29.6534 37.1536i 1.10898 1.38947i
\(716\) 0 0
\(717\) −0.219988 + 1.63123i −0.00821560 + 0.0609195i
\(718\) 0 0
\(719\) −47.7179 −1.77958 −0.889789 0.456372i \(-0.849149\pi\)
−0.889789 + 0.456372i \(0.849149\pi\)
\(720\) 0 0
\(721\) 11.1340 0.414653
\(722\) 0 0
\(723\) −17.4954 13.5125i −0.650660 0.502534i
\(724\) 0 0
\(725\) −5.89804 6.36682i −0.219048 0.236458i
\(726\) 0 0
\(727\) −26.9083 7.21005i −0.997972 0.267406i −0.277377 0.960761i \(-0.589465\pi\)
−0.720596 + 0.693355i \(0.756132\pi\)
\(728\) 0 0
\(729\) −18.7275 19.4494i −0.693611 0.720350i
\(730\) 0 0
\(731\) 39.0275 22.5325i 1.44348 0.833396i
\(732\) 0 0
\(733\) 8.53774 2.28768i 0.315348 0.0844974i −0.0976733 0.995219i \(-0.531140\pi\)
0.413022 + 0.910721i \(0.364473\pi\)
\(734\) 0 0
\(735\) 6.73716 + 0.149945i 0.248504 + 0.00553082i
\(736\) 0 0
\(737\) −30.5596 30.5596i −1.12568 1.12568i
\(738\) 0 0
\(739\) 43.7202i 1.60827i 0.594444 + 0.804137i \(0.297372\pi\)
−0.594444 + 0.804137i \(0.702628\pi\)
\(740\) 0 0
\(741\) −19.2708 25.2787i −0.707929 0.928636i
\(742\) 0 0
\(743\) −1.33009 4.96395i −0.0487962 0.182110i 0.937226 0.348721i \(-0.113384\pi\)
−0.986023 + 0.166612i \(0.946717\pi\)
\(744\) 0 0
\(745\) −16.8417 + 38.5592i −0.617030 + 1.41270i
\(746\) 0 0
\(747\) −25.0725 + 14.2657i −0.917356 + 0.521955i
\(748\) 0 0
\(749\) 12.9388 + 22.4107i 0.472774 + 0.818869i
\(750\) 0 0
\(751\) −14.7247 + 25.5039i −0.537311 + 0.930650i 0.461737 + 0.887017i \(0.347227\pi\)
−0.999048 + 0.0436330i \(0.986107\pi\)
\(752\) 0 0
\(753\) 12.3383 + 30.0549i 0.449634 + 1.09526i
\(754\) 0 0
\(755\) −28.0728 38.0693i −1.02167 1.38548i
\(756\) 0 0
\(757\) −6.41487 + 6.41487i −0.233152 + 0.233152i −0.814007 0.580855i \(-0.802718\pi\)
0.580855 + 0.814007i \(0.302718\pi\)
\(758\) 0 0
\(759\) −0.0998911 0.0417456i −0.00362582 0.00151527i
\(760\) 0 0
\(761\) −12.4480 7.18686i −0.451240 0.260524i 0.257114 0.966381i \(-0.417228\pi\)
−0.708354 + 0.705858i \(0.750562\pi\)
\(762\) 0 0
\(763\) 5.74691 21.4478i 0.208052 0.776462i
\(764\) 0 0
\(765\) −26.3439 + 2.78952i −0.952466 + 0.100855i
\(766\) 0 0
\(767\) 3.22285 12.0278i 0.116370 0.434300i
\(768\) 0 0
\(769\) 7.51296 + 4.33761i 0.270924 + 0.156418i 0.629308 0.777156i \(-0.283339\pi\)
−0.358383 + 0.933575i \(0.616672\pi\)
\(770\) 0 0
\(771\) 5.40438 4.11993i 0.194634 0.148376i
\(772\) 0 0
\(773\) −27.7586 + 27.7586i −0.998407 + 0.998407i −0.999999 0.00159176i \(-0.999493\pi\)
0.00159176 + 0.999999i \(0.499493\pi\)
\(774\) 0 0
\(775\) 0.0696103 0.225029i 0.00250048 0.00808330i
\(776\) 0 0
\(777\) 26.2776 34.0231i 0.942704 1.22057i
\(778\) 0 0
\(779\) 19.6216 33.9856i 0.703018 1.21766i
\(780\) 0 0
\(781\) 14.0219 + 24.2867i 0.501744 + 0.869046i
\(782\) 0 0
\(783\) −8.95294 + 1.09267i −0.319952 + 0.0390489i
\(784\) 0 0
\(785\) 12.6315 + 32.2227i 0.450839 + 1.15008i
\(786\) 0 0
\(787\) −6.08276 22.7012i −0.216827 0.809209i −0.985515 0.169586i \(-0.945757\pi\)
0.768689 0.639623i \(-0.220910\pi\)
\(788\) 0 0
\(789\) 36.0133 4.62583i 1.28211 0.164684i
\(790\) 0 0
\(791\) 48.5466i 1.72612i
\(792\) 0 0
\(793\) −9.55322 9.55322i −0.339245 0.339245i
\(794\) 0 0
\(795\) 7.47539 25.6053i 0.265125 0.908127i
\(796\) 0 0
\(797\) −0.512177 + 0.137238i −0.0181423 + 0.00486120i −0.267879 0.963453i \(-0.586323\pi\)
0.249737 + 0.968314i \(0.419656\pi\)
\(798\) 0 0
\(799\) −1.76636 + 1.01981i −0.0624892 + 0.0360782i
\(800\) 0 0
\(801\) −15.2919 + 15.1003i −0.540312 + 0.533544i
\(802\) 0 0
\(803\) −39.8495 10.6776i −1.40626 0.376806i
\(804\) 0 0
\(805\) 0.0126101 + 0.112323i 0.000444446 + 0.00395885i
\(806\) 0 0
\(807\) −3.28377 + 1.34807i −0.115594 + 0.0474544i
\(808\) 0 0
\(809\) 10.8852 0.382705 0.191352 0.981521i \(-0.438713\pi\)
0.191352 + 0.981521i \(0.438713\pi\)
\(810\) 0 0
\(811\) −22.7758 −0.799767 −0.399884 0.916566i \(-0.630949\pi\)
−0.399884 + 0.916566i \(0.630949\pi\)
\(812\) 0 0
\(813\) −11.3124 + 4.64405i −0.396744 + 0.162874i
\(814\) 0 0
\(815\) −7.54345 6.02066i −0.264236 0.210894i
\(816\) 0 0
\(817\) −34.7857 9.32079i −1.21700 0.326093i
\(818\) 0 0
\(819\) −36.6986 + 36.2389i −1.28235 + 1.26629i
\(820\) 0 0
\(821\) −24.1402 + 13.9374i −0.842499 + 0.486417i −0.858113 0.513461i \(-0.828363\pi\)
0.0156138 + 0.999878i \(0.495030\pi\)
\(822\) 0 0
\(823\) 2.15599 0.577696i 0.0751531 0.0201372i −0.221047 0.975263i \(-0.570947\pi\)
0.296200 + 0.955126i \(0.404281\pi\)
\(824\) 0 0
\(825\) −13.3144 + 28.7237i −0.463550 + 1.00003i
\(826\) 0 0
\(827\) 29.5100 + 29.5100i 1.02616 + 1.02616i 0.999648 + 0.0265159i \(0.00844126\pi\)
0.0265159 + 0.999648i \(0.491559\pi\)
\(828\) 0 0
\(829\) 42.1717i 1.46468i 0.680938 + 0.732341i \(0.261573\pi\)
−0.680938 + 0.732341i \(0.738427\pi\)
\(830\) 0 0
\(831\) −34.2950 + 4.40512i −1.18968 + 0.152812i
\(832\) 0 0
\(833\) −1.77840 6.63710i −0.0616181 0.229962i
\(834\) 0 0
\(835\) 42.2195 16.5504i 1.46107 0.572749i
\(836\) 0 0
\(837\) −0.147177 0.195606i −0.00508717 0.00676113i
\(838\) 0 0
\(839\) 16.7092 + 28.9412i 0.576866 + 0.999162i 0.995836 + 0.0911617i \(0.0290580\pi\)
−0.418970 + 0.908000i \(0.637609\pi\)
\(840\) 0 0
\(841\) 12.9935 22.5055i 0.448053 0.776050i
\(842\) 0 0
\(843\) −13.2920 + 17.2100i −0.457802 + 0.592742i
\(844\) 0 0
\(845\) 37.4640 27.6265i 1.28880 0.950381i
\(846\) 0 0
\(847\) 4.94245 4.94245i 0.169825 0.169825i
\(848\) 0 0
\(849\) −8.13159 + 6.19897i −0.279075 + 0.212748i
\(850\) 0 0
\(851\) 0.124315 + 0.0717733i 0.00426147 + 0.00246036i
\(852\) 0 0
\(853\) 10.4930 39.1602i 0.359272 1.34082i −0.515750 0.856739i \(-0.672487\pi\)
0.875022 0.484082i \(-0.160847\pi\)
\(854\) 0 0
\(855\) 16.4624 + 13.3099i 0.563002 + 0.455188i
\(856\) 0 0
\(857\) 2.08925 7.79718i 0.0713673 0.266346i −0.921018 0.389521i \(-0.872641\pi\)
0.992385 + 0.123174i \(0.0393074\pi\)
\(858\) 0 0
\(859\) 0.136572 + 0.0788501i 0.00465979 + 0.00269033i 0.502328 0.864677i \(-0.332477\pi\)
−0.497668 + 0.867367i \(0.665810\pi\)
\(860\) 0 0
\(861\) −58.7509 24.5526i −2.00222 0.836751i
\(862\) 0 0
\(863\) −14.5279 + 14.5279i −0.494536 + 0.494536i −0.909732 0.415196i \(-0.863713\pi\)
0.415196 + 0.909732i \(0.363713\pi\)
\(864\) 0 0
\(865\) 34.5059 + 5.21509i 1.17323 + 0.177318i
\(866\) 0 0
\(867\) −0.924058 2.25091i −0.0313826 0.0764449i
\(868\) 0 0
\(869\) −0.955288 + 1.65461i −0.0324059 + 0.0561287i
\(870\) 0 0
\(871\) −34.3739 59.5373i −1.16471 2.01735i
\(872\) 0 0
\(873\) −18.3728 + 10.4537i −0.621826 + 0.353805i
\(874\) 0 0
\(875\) 32.9634 2.43035i 1.11437 0.0821608i
\(876\) 0 0
\(877\) −10.3564 38.6505i −0.349710 1.30513i −0.887013 0.461745i \(-0.847223\pi\)
0.537303 0.843389i \(-0.319443\pi\)
\(878\) 0 0
\(879\) 8.59222 + 11.2710i 0.289809 + 0.380160i
\(880\) 0 0
\(881\) 18.9638i 0.638908i −0.947602 0.319454i \(-0.896500\pi\)
0.947602 0.319454i \(-0.103500\pi\)
\(882\) 0 0
\(883\) 1.93666 + 1.93666i 0.0651736 + 0.0651736i 0.738942 0.673769i \(-0.235326\pi\)
−0.673769 + 0.738942i \(0.735326\pi\)
\(884\) 0 0
\(885\) −0.184531 + 8.29112i −0.00620294 + 0.278703i
\(886\) 0 0
\(887\) −0.573135 + 0.153571i −0.0192440 + 0.00515641i −0.268428 0.963300i \(-0.586504\pi\)
0.249184 + 0.968456i \(0.419838\pi\)
\(888\) 0 0
\(889\) 34.9076 20.1539i 1.17076 0.675940i
\(890\) 0 0
\(891\) 16.0903 + 28.6986i 0.539044 + 0.961440i
\(892\) 0 0
\(893\) 1.57437 + 0.421852i 0.0526844 + 0.0141167i
\(894\) 0 0
\(895\) −8.64614 + 0.970671i −0.289009 + 0.0324460i
\(896\) 0 0
\(897\) −0.136298 0.105269i −0.00455086 0.00351484i
\(898\) 0 0
\(899\) −0.0817726 −0.00272727
\(900\) 0 0
\(901\) −27.1983 −0.906106
\(902\) 0 0
\(903\) −7.80961 + 57.9091i −0.259887 + 1.92709i
\(904\) 0 0
\(905\) 32.3364 3.63030i 1.07490 0.120675i
\(906\) 0 0
\(907\) −44.1094 11.8191i −1.46463 0.392446i −0.563543 0.826087i \(-0.690562\pi\)
−0.901086 + 0.433640i \(0.857229\pi\)
\(908\) 0 0
\(909\) −2.71214 + 9.87251i −0.0899559 + 0.327450i
\(910\) 0 0
\(911\) 27.8735 16.0928i 0.923491 0.533177i 0.0387436 0.999249i \(-0.487664\pi\)
0.884747 + 0.466072i \(0.154331\pi\)
\(912\) 0 0
\(913\) 33.9543 9.09802i 1.12372 0.301101i
\(914\) 0 0
\(915\) 7.69038 + 4.67123i 0.254236 + 0.154426i
\(916\) 0 0
\(917\) 33.3724 + 33.3724i 1.10205 + 1.10205i
\(918\) 0 0
\(919\) 51.4113i 1.69590i 0.530074 + 0.847951i \(0.322164\pi\)
−0.530074 + 0.847951i \(0.677836\pi\)
\(920\) 0 0
\(921\) −10.4390 + 24.9790i −0.343976 + 0.823086i
\(922\) 0 0
\(923\) 11.5459 + 43.0901i 0.380039 + 1.41833i
\(924\) 0 0
\(925\) 22.3619 35.5254i 0.735254 1.16807i
\(926\) 0 0
\(927\) 5.71078 9.74894i 0.187567 0.320197i
\(928\) 0 0
\(929\) −13.8456 23.9813i −0.454260 0.786802i 0.544385 0.838835i \(-0.316763\pi\)
−0.998645 + 0.0520338i \(0.983430\pi\)
\(930\) 0 0
\(931\) −2.74550 + 4.75534i −0.0899800 + 0.155850i
\(932\) 0 0
\(933\) 19.8294 + 2.67419i 0.649186 + 0.0875492i
\(934\) 0 0
\(935\) 31.9190 + 4.82412i 1.04386 + 0.157766i
\(936\) 0 0
\(937\) 26.9248 26.9248i 0.879596 0.879596i −0.113896 0.993493i \(-0.536333\pi\)
0.993493 + 0.113896i \(0.0363332\pi\)
\(938\) 0 0
\(939\) −3.35956 26.1551i −0.109635 0.853538i
\(940\) 0 0
\(941\) −1.32622 0.765694i −0.0432336 0.0249609i 0.478227 0.878236i \(-0.341279\pi\)
−0.521461 + 0.853275i \(0.674613\pi\)
\(942\) 0 0
\(943\) 0.0550296 0.205373i 0.00179201 0.00668788i
\(944\) 0 0
\(945\) 18.0171 29.2451i 0.586098 0.951344i
\(946\) 0 0
\(947\) 4.61913 17.2388i 0.150102 0.560187i −0.849373 0.527792i \(-0.823020\pi\)
0.999475 0.0323948i \(-0.0103134\pi\)
\(948\) 0 0
\(949\) −56.8336 32.8129i −1.84490 1.06515i
\(950\) 0 0
\(951\) −1.41017 10.9786i −0.0457280 0.356004i
\(952\) 0 0
\(953\) −28.0955 + 28.0955i −0.910103 + 0.910103i −0.996280 0.0861773i \(-0.972535\pi\)
0.0861773 + 0.996280i \(0.472535\pi\)
\(954\) 0 0
\(955\) −12.6355 + 9.31756i −0.408874 + 0.301509i
\(956\) 0 0
\(957\) 10.8922 + 1.46892i 0.352094 + 0.0474833i
\(958\) 0 0
\(959\) 11.0315 19.1070i 0.356224 0.616999i
\(960\) 0 0
\(961\) 15.4989 + 26.8449i 0.499964 + 0.865963i
\(962\) 0 0
\(963\) 26.2593 + 0.165508i 0.846193 + 0.00533342i
\(964\) 0 0
\(965\) 29.7259 11.6528i 0.956911 0.375117i
\(966\) 0 0
\(967\) 12.6150 + 47.0797i 0.405670 + 1.51398i 0.802817 + 0.596225i \(0.203333\pi\)
−0.397148 + 0.917755i \(0.630000\pi\)
\(968\) 0 0
\(969\) 8.32333 19.9165i 0.267384 0.639811i
\(970\) 0 0
\(971\) 27.3898i 0.878981i −0.898247 0.439490i \(-0.855159\pi\)
0.898247 0.439490i \(-0.144841\pi\)
\(972\) 0 0
\(973\) −25.9821 25.9821i −0.832947 0.832947i
\(974\) 0 0
\(975\) −32.2838 + 38.6529i −1.03391 + 1.23788i
\(976\) 0 0
\(977\) −1.51332 + 0.405493i −0.0484155 + 0.0129729i −0.282945 0.959136i \(-0.591312\pi\)
0.234530 + 0.972109i \(0.424645\pi\)
\(978\) 0 0
\(979\) 22.6798 13.0942i 0.724848 0.418491i
\(980\) 0 0
\(981\) −15.8320 16.0328i −0.505476 0.511889i
\(982\) 0 0
\(983\) 25.9807 + 6.96151i 0.828656 + 0.222038i 0.648127 0.761532i \(-0.275553\pi\)
0.180529 + 0.983570i \(0.442219\pi\)
\(984\) 0 0
\(985\) −6.83317 5.45376i −0.217723 0.173771i
\(986\) 0 0
\(987\) 0.353457 2.62092i 0.0112507 0.0834248i
\(988\) 0 0
\(989\) −0.195116 −0.00620432
\(990\) 0 0
\(991\) 22.3249 0.709175 0.354588 0.935023i \(-0.384621\pi\)
0.354588 + 0.935023i \(0.384621\pi\)
\(992\) 0 0
\(993\) −18.5429 14.3215i −0.588440 0.454480i
\(994\) 0 0
\(995\) 1.91227 + 17.0334i 0.0606232 + 0.539994i
\(996\) 0 0
\(997\) 42.1763 + 11.3011i 1.33574 + 0.357909i 0.854850 0.518874i \(-0.173649\pi\)
0.480885 + 0.876784i \(0.340315\pi\)
\(998\) 0 0
\(999\) −16.3125 40.4595i −0.516104 1.28008i
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.113.16 72
3.2 odd 2 1080.2.bt.a.233.1 72
4.3 odd 2 720.2.cu.e.113.3 72
5.2 odd 4 inner 360.2.bs.a.257.7 yes 72
9.2 odd 6 inner 360.2.bs.a.353.7 yes 72
9.7 even 3 1080.2.bt.a.953.7 72
15.2 even 4 1080.2.bt.a.17.7 72
20.7 even 4 720.2.cu.e.257.12 72
36.11 even 6 720.2.cu.e.353.12 72
45.2 even 12 inner 360.2.bs.a.137.16 yes 72
45.7 odd 12 1080.2.bt.a.737.1 72
180.47 odd 12 720.2.cu.e.497.3 72
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
360.2.bs.a.113.16 72 1.1 even 1 trivial
360.2.bs.a.137.16 yes 72 45.2 even 12 inner
360.2.bs.a.257.7 yes 72 5.2 odd 4 inner
360.2.bs.a.353.7 yes 72 9.2 odd 6 inner
720.2.cu.e.113.3 72 4.3 odd 2
720.2.cu.e.257.12 72 20.7 even 4
720.2.cu.e.353.12 72 36.11 even 6
720.2.cu.e.497.3 72 180.47 odd 12
1080.2.bt.a.17.7 72 15.2 even 4
1080.2.bt.a.233.1 72 3.2 odd 2
1080.2.bt.a.737.1 72 45.7 odd 12
1080.2.bt.a.953.7 72 9.7 even 3