Properties

Label 912.2.bo.a.625.1
Level $912$
Weight $2$
Character 912.625
Analytic conductor $7.282$
Analytic rank $0$
Dimension $6$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [912,2,Mod(289,912)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(912, base_ring=CyclotomicField(18))
 
chi = DirichletCharacter(H, H._module([0, 0, 0, 2]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("912.289");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 912 = 2^{4} \cdot 3 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 912.bo (of order \(9\), degree \(6\), not 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: \(7.28235666434\)
Analytic rank: \(0\)
Dimension: \(6\)
Coefficient field: \(\Q(\zeta_{18})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{6} - x^{3} + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 114)
Sato-Tate group: $\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label 625.1
Root \(-0.766044 - 0.642788i\) of defining polynomial
Character \(\chi\) \(=\) 912.625
Dual form 912.2.bo.a.769.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.766044 - 0.642788i) q^{3} +(-3.20574 + 1.16679i) q^{5} +(-2.43969 - 4.22567i) q^{7} +(0.173648 + 0.984808i) q^{9} +O(q^{10})\) \(q+(-0.766044 - 0.642788i) q^{3} +(-3.20574 + 1.16679i) q^{5} +(-2.43969 - 4.22567i) q^{7} +(0.173648 + 0.984808i) q^{9} +(-1.70574 + 2.95442i) q^{11} +(2.08125 - 1.74638i) q^{13} +(3.20574 + 1.16679i) q^{15} +(0.205737 - 1.16679i) q^{17} +(2.52094 + 3.55596i) q^{19} +(-0.847296 + 4.80526i) q^{21} +(-3.20574 - 1.16679i) q^{23} +(5.08512 - 4.26692i) q^{25} +(0.500000 - 0.866025i) q^{27} +(0.655230 + 3.71599i) q^{29} +(3.30793 + 5.72951i) q^{31} +(3.20574 - 1.16679i) q^{33} +(12.7515 + 10.6998i) q^{35} +6.75877 q^{37} -2.71688 q^{39} +(5.02094 + 4.21307i) q^{41} +(3.91875 - 1.42631i) q^{43} +(-1.70574 - 2.95442i) q^{45} +(-0.496130 - 2.81369i) q^{47} +(-8.40420 + 14.5565i) q^{49} +(-0.907604 + 0.761570i) q^{51} +(-0.592396 - 0.215615i) q^{53} +(2.02094 - 11.4613i) q^{55} +(0.354570 - 4.34445i) q^{57} +(-2.02094 + 11.4613i) q^{59} +(-6.48545 - 2.36051i) q^{61} +(3.73783 - 3.13641i) q^{63} +(-4.63429 + 8.02682i) q^{65} +(-0.123141 - 0.698367i) q^{67} +(1.70574 + 2.95442i) q^{69} +(7.47818 - 2.72183i) q^{71} +(-9.76264 - 8.19183i) q^{73} -6.63816 q^{75} +16.6459 q^{77} +(-0.228026 - 0.191336i) q^{79} +(-0.939693 + 0.342020i) q^{81} +(7.80200 + 13.5135i) q^{83} +(0.701867 + 3.98048i) q^{85} +(1.88666 - 3.26779i) q^{87} +(5.18866 - 4.35381i) q^{89} +(-12.4572 - 4.53406i) q^{91} +(1.14883 - 6.51536i) q^{93} +(-12.2306 - 8.45805i) q^{95} +(-1.23736 + 7.01741i) q^{97} +(-3.20574 - 1.16679i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6 q - 9 q^{5} - 9 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 6 q - 9 q^{5} - 9 q^{7} + 15 q^{13} + 9 q^{15} - 9 q^{17} + 12 q^{19} - 3 q^{21} - 9 q^{23} + 9 q^{25} + 3 q^{27} - 9 q^{29} + 9 q^{31} + 9 q^{33} + 36 q^{35} + 18 q^{37} + 27 q^{41} + 21 q^{43} - 27 q^{47} - 12 q^{49} - 9 q^{51} + 9 q^{55} + 18 q^{57} - 9 q^{59} - 3 q^{61} + 3 q^{63} - 18 q^{65} + 3 q^{67} - 9 q^{71} - 12 q^{73} - 6 q^{75} + 18 q^{77} + 21 q^{79} + 9 q^{83} + 18 q^{85} + 18 q^{87} - 24 q^{91} + 33 q^{93} - 36 q^{95} - 54 q^{97} - 9 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/912\mathbb{Z}\right)^\times\).

\(n\) \(97\) \(229\) \(305\) \(799\)
\(\chi(n)\) \(e\left(\frac{5}{9}\right)\) \(1\) \(1\) \(1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) −0.766044 0.642788i −0.442276 0.371114i
\(4\) 0 0
\(5\) −3.20574 + 1.16679i −1.43365 + 0.521806i −0.937975 0.346703i \(-0.887301\pi\)
−0.495674 + 0.868509i \(0.665079\pi\)
\(6\) 0 0
\(7\) −2.43969 4.22567i −0.922117 1.59715i −0.796133 0.605121i \(-0.793125\pi\)
−0.125984 0.992032i \(-0.540209\pi\)
\(8\) 0 0
\(9\) 0.173648 + 0.984808i 0.0578827 + 0.328269i
\(10\) 0 0
\(11\) −1.70574 + 2.95442i −0.514299 + 0.890792i 0.485563 + 0.874202i \(0.338615\pi\)
−0.999862 + 0.0165906i \(0.994719\pi\)
\(12\) 0 0
\(13\) 2.08125 1.74638i 0.577235 0.484358i −0.306803 0.951773i \(-0.599259\pi\)
0.884038 + 0.467415i \(0.154815\pi\)
\(14\) 0 0
\(15\) 3.20574 + 1.16679i 0.827718 + 0.301265i
\(16\) 0 0
\(17\) 0.205737 1.16679i 0.0498986 0.282989i −0.949641 0.313341i \(-0.898552\pi\)
0.999539 + 0.0303521i \(0.00966285\pi\)
\(18\) 0 0
\(19\) 2.52094 + 3.55596i 0.578344 + 0.815793i
\(20\) 0 0
\(21\) −0.847296 + 4.80526i −0.184895 + 1.04859i
\(22\) 0 0
\(23\) −3.20574 1.16679i −0.668442 0.243293i −0.0145653 0.999894i \(-0.504636\pi\)
−0.653877 + 0.756601i \(0.726859\pi\)
\(24\) 0 0
\(25\) 5.08512 4.26692i 1.01702 0.853385i
\(26\) 0 0
\(27\) 0.500000 0.866025i 0.0962250 0.166667i
\(28\) 0 0
\(29\) 0.655230 + 3.71599i 0.121673 + 0.690043i 0.983228 + 0.182379i \(0.0583797\pi\)
−0.861555 + 0.507664i \(0.830509\pi\)
\(30\) 0 0
\(31\) 3.30793 + 5.72951i 0.594122 + 1.02905i 0.993670 + 0.112338i \(0.0358339\pi\)
−0.399548 + 0.916712i \(0.630833\pi\)
\(32\) 0 0
\(33\) 3.20574 1.16679i 0.558047 0.203113i
\(34\) 0 0
\(35\) 12.7515 + 10.6998i 2.15540 + 1.80859i
\(36\) 0 0
\(37\) 6.75877 1.11114 0.555568 0.831471i \(-0.312501\pi\)
0.555568 + 0.831471i \(0.312501\pi\)
\(38\) 0 0
\(39\) −2.71688 −0.435049
\(40\) 0 0
\(41\) 5.02094 + 4.21307i 0.784140 + 0.657971i 0.944288 0.329122i \(-0.106753\pi\)
−0.160148 + 0.987093i \(0.551197\pi\)
\(42\) 0 0
\(43\) 3.91875 1.42631i 0.597603 0.217510i −0.0254669 0.999676i \(-0.508107\pi\)
0.623070 + 0.782166i \(0.285885\pi\)
\(44\) 0 0
\(45\) −1.70574 2.95442i −0.254276 0.440419i
\(46\) 0 0
\(47\) −0.496130 2.81369i −0.0723679 0.410419i −0.999374 0.0353731i \(-0.988738\pi\)
0.927006 0.375046i \(-0.122373\pi\)
\(48\) 0 0
\(49\) −8.40420 + 14.5565i −1.20060 + 2.07950i
\(50\) 0 0
\(51\) −0.907604 + 0.761570i −0.127090 + 0.106641i
\(52\) 0 0
\(53\) −0.592396 0.215615i −0.0813719 0.0296169i 0.301013 0.953620i \(-0.402675\pi\)
−0.382385 + 0.924003i \(0.624897\pi\)
\(54\) 0 0
\(55\) 2.02094 11.4613i 0.272504 1.54545i
\(56\) 0 0
\(57\) 0.354570 4.34445i 0.0469640 0.575437i
\(58\) 0 0
\(59\) −2.02094 + 11.4613i −0.263105 + 1.49214i 0.511274 + 0.859418i \(0.329174\pi\)
−0.774379 + 0.632722i \(0.781937\pi\)
\(60\) 0 0
\(61\) −6.48545 2.36051i −0.830377 0.302233i −0.108363 0.994111i \(-0.534561\pi\)
−0.722014 + 0.691879i \(0.756783\pi\)
\(62\) 0 0
\(63\) 3.73783 3.13641i 0.470922 0.395150i
\(64\) 0 0
\(65\) −4.63429 + 8.02682i −0.574812 + 0.995604i
\(66\) 0 0
\(67\) −0.123141 0.698367i −0.0150441 0.0853191i 0.976361 0.216145i \(-0.0693483\pi\)
−0.991405 + 0.130826i \(0.958237\pi\)
\(68\) 0 0
\(69\) 1.70574 + 2.95442i 0.205347 + 0.355671i
\(70\) 0 0
\(71\) 7.47818 2.72183i 0.887496 0.323022i 0.142265 0.989829i \(-0.454561\pi\)
0.745231 + 0.666806i \(0.232339\pi\)
\(72\) 0 0
\(73\) −9.76264 8.19183i −1.14263 0.958781i −0.143109 0.989707i \(-0.545710\pi\)
−0.999522 + 0.0309259i \(0.990154\pi\)
\(74\) 0 0
\(75\) −6.63816 −0.766508
\(76\) 0 0
\(77\) 16.6459 1.89698
\(78\) 0 0
\(79\) −0.228026 0.191336i −0.0256549 0.0215270i 0.629870 0.776701i \(-0.283108\pi\)
−0.655525 + 0.755174i \(0.727553\pi\)
\(80\) 0 0
\(81\) −0.939693 + 0.342020i −0.104410 + 0.0380022i
\(82\) 0 0
\(83\) 7.80200 + 13.5135i 0.856381 + 1.48330i 0.875358 + 0.483476i \(0.160626\pi\)
−0.0189766 + 0.999820i \(0.506041\pi\)
\(84\) 0 0
\(85\) 0.701867 + 3.98048i 0.0761281 + 0.431744i
\(86\) 0 0
\(87\) 1.88666 3.26779i 0.202271 0.350344i
\(88\) 0 0
\(89\) 5.18866 4.35381i 0.549997 0.461502i −0.324943 0.945734i \(-0.605345\pi\)
0.874940 + 0.484231i \(0.160901\pi\)
\(90\) 0 0
\(91\) −12.4572 4.53406i −1.30587 0.475299i
\(92\) 0 0
\(93\) 1.14883 6.51536i 0.119128 0.675611i
\(94\) 0 0
\(95\) −12.2306 8.45805i −1.25483 0.867777i
\(96\) 0 0
\(97\) −1.23736 + 7.01741i −0.125635 + 0.712510i 0.855294 + 0.518143i \(0.173376\pi\)
−0.980929 + 0.194367i \(0.937735\pi\)
\(98\) 0 0
\(99\) −3.20574 1.16679i −0.322189 0.117267i
\(100\) 0 0
\(101\) −3.55896 + 2.98632i −0.354130 + 0.297150i −0.802446 0.596725i \(-0.796468\pi\)
0.448316 + 0.893875i \(0.352024\pi\)
\(102\) 0 0
\(103\) −6.19119 + 10.7235i −0.610036 + 1.05661i 0.381198 + 0.924494i \(0.375512\pi\)
−0.991234 + 0.132120i \(0.957822\pi\)
\(104\) 0 0
\(105\) −2.89053 16.3930i −0.282087 1.59979i
\(106\) 0 0
\(107\) 1.94949 + 3.37662i 0.188465 + 0.326430i 0.944739 0.327825i \(-0.106316\pi\)
−0.756274 + 0.654255i \(0.772982\pi\)
\(108\) 0 0
\(109\) 10.8969 3.96616i 1.04374 0.379889i 0.237441 0.971402i \(-0.423691\pi\)
0.806295 + 0.591513i \(0.201469\pi\)
\(110\) 0 0
\(111\) −5.17752 4.34445i −0.491428 0.412357i
\(112\) 0 0
\(113\) 1.94087 0.182582 0.0912911 0.995824i \(-0.470901\pi\)
0.0912911 + 0.995824i \(0.470901\pi\)
\(114\) 0 0
\(115\) 11.6382 1.08526
\(116\) 0 0
\(117\) 2.08125 + 1.74638i 0.192412 + 0.161453i
\(118\) 0 0
\(119\) −5.43242 + 1.97724i −0.497989 + 0.181253i
\(120\) 0 0
\(121\) −0.319078 0.552659i −0.0290071 0.0502417i
\(122\) 0 0
\(123\) −1.13816 6.45480i −0.102624 0.582010i
\(124\) 0 0
\(125\) −2.79426 + 4.83981i −0.249926 + 0.432885i
\(126\) 0 0
\(127\) 4.66044 3.91058i 0.413548 0.347008i −0.412155 0.911114i \(-0.635224\pi\)
0.825702 + 0.564106i \(0.190779\pi\)
\(128\) 0 0
\(129\) −3.91875 1.42631i −0.345027 0.125579i
\(130\) 0 0
\(131\) 3.23055 18.3214i 0.282255 1.60075i −0.432676 0.901550i \(-0.642430\pi\)
0.714930 0.699196i \(-0.246458\pi\)
\(132\) 0 0
\(133\) 8.87598 19.3281i 0.769645 1.67596i
\(134\) 0 0
\(135\) −0.592396 + 3.35965i −0.0509854 + 0.289152i
\(136\) 0 0
\(137\) −4.27244 1.55504i −0.365019 0.132856i 0.152998 0.988227i \(-0.451107\pi\)
−0.518017 + 0.855370i \(0.673330\pi\)
\(138\) 0 0
\(139\) 2.30928 1.93771i 0.195870 0.164355i −0.539578 0.841936i \(-0.681416\pi\)
0.735448 + 0.677581i \(0.236972\pi\)
\(140\) 0 0
\(141\) −1.42855 + 2.47432i −0.120305 + 0.208375i
\(142\) 0 0
\(143\) 1.60947 + 9.12776i 0.134591 + 0.763302i
\(144\) 0 0
\(145\) −6.43629 11.1480i −0.534505 0.925789i
\(146\) 0 0
\(147\) 15.7947 5.74881i 1.30273 0.474154i
\(148\) 0 0
\(149\) 0.907604 + 0.761570i 0.0743538 + 0.0623902i 0.679207 0.733947i \(-0.262324\pi\)
−0.604853 + 0.796337i \(0.706768\pi\)
\(150\) 0 0
\(151\) 3.63816 0.296069 0.148034 0.988982i \(-0.452705\pi\)
0.148034 + 0.988982i \(0.452705\pi\)
\(152\) 0 0
\(153\) 1.18479 0.0957848
\(154\) 0 0
\(155\) −17.2895 14.5076i −1.38873 1.16528i
\(156\) 0 0
\(157\) −5.89306 + 2.14490i −0.470317 + 0.171181i −0.566296 0.824202i \(-0.691624\pi\)
0.0959789 + 0.995383i \(0.469402\pi\)
\(158\) 0 0
\(159\) 0.315207 + 0.545955i 0.0249976 + 0.0432971i
\(160\) 0 0
\(161\) 2.89053 + 16.3930i 0.227806 + 1.29195i
\(162\) 0 0
\(163\) −9.64930 + 16.7131i −0.755792 + 1.30907i 0.189188 + 0.981941i \(0.439414\pi\)
−0.944980 + 0.327128i \(0.893919\pi\)
\(164\) 0 0
\(165\) −8.91534 + 7.48086i −0.694059 + 0.582384i
\(166\) 0 0
\(167\) −7.25624 2.64106i −0.561505 0.204371i 0.0456458 0.998958i \(-0.485465\pi\)
−0.607151 + 0.794587i \(0.707688\pi\)
\(168\) 0 0
\(169\) −0.975652 + 5.53320i −0.0750501 + 0.425631i
\(170\) 0 0
\(171\) −3.06418 + 3.10013i −0.234324 + 0.237073i
\(172\) 0 0
\(173\) −2.51707 + 14.2750i −0.191370 + 1.08531i 0.726125 + 0.687563i \(0.241319\pi\)
−0.917495 + 0.397748i \(0.869792\pi\)
\(174\) 0 0
\(175\) −30.4368 11.0781i −2.30080 0.837424i
\(176\) 0 0
\(177\) 8.91534 7.48086i 0.670118 0.562296i
\(178\) 0 0
\(179\) −4.91147 + 8.50692i −0.367101 + 0.635837i −0.989111 0.147172i \(-0.952983\pi\)
0.622010 + 0.783009i \(0.286316\pi\)
\(180\) 0 0
\(181\) 3.28446 + 18.6271i 0.244132 + 1.38454i 0.822499 + 0.568766i \(0.192579\pi\)
−0.578367 + 0.815777i \(0.696310\pi\)
\(182\) 0 0
\(183\) 3.45084 + 5.97702i 0.255093 + 0.441834i
\(184\) 0 0
\(185\) −21.6668 + 7.88609i −1.59298 + 0.579797i
\(186\) 0 0
\(187\) 3.09627 + 2.59808i 0.226421 + 0.189990i
\(188\) 0 0
\(189\) −4.87939 −0.354923
\(190\) 0 0
\(191\) 10.0915 0.730197 0.365098 0.930969i \(-0.381035\pi\)
0.365098 + 0.930969i \(0.381035\pi\)
\(192\) 0 0
\(193\) 1.93376 + 1.62262i 0.139195 + 0.116799i 0.709727 0.704477i \(-0.248818\pi\)
−0.570532 + 0.821276i \(0.693263\pi\)
\(194\) 0 0
\(195\) 8.70961 3.17004i 0.623708 0.227011i
\(196\) 0 0
\(197\) −7.42855 12.8666i −0.529262 0.916709i −0.999418 0.0341253i \(-0.989135\pi\)
0.470155 0.882584i \(-0.344198\pi\)
\(198\) 0 0
\(199\) −1.40121 7.94664i −0.0993289 0.563322i −0.993335 0.115267i \(-0.963228\pi\)
0.894006 0.448056i \(-0.147883\pi\)
\(200\) 0 0
\(201\) −0.354570 + 0.614134i −0.0250095 + 0.0433177i
\(202\) 0 0
\(203\) 14.1040 11.8347i 0.989907 0.830631i
\(204\) 0 0
\(205\) −21.0116 7.64760i −1.46751 0.534132i
\(206\) 0 0
\(207\) 0.592396 3.35965i 0.0411744 0.233512i
\(208\) 0 0
\(209\) −14.8059 + 1.38241i −1.02414 + 0.0956231i
\(210\) 0 0
\(211\) −1.37939 + 7.82288i −0.0949608 + 0.538549i 0.899799 + 0.436306i \(0.143713\pi\)
−0.994759 + 0.102244i \(0.967398\pi\)
\(212\) 0 0
\(213\) −7.47818 2.72183i −0.512396 0.186497i
\(214\) 0 0
\(215\) −10.8983 + 9.14473i −0.743256 + 0.623666i
\(216\) 0 0
\(217\) 16.1407 27.9565i 1.09570 1.89781i
\(218\) 0 0
\(219\) 2.21301 + 12.5506i 0.149541 + 0.848092i
\(220\) 0 0
\(221\) −1.60947 2.78768i −0.108265 0.187520i
\(222\) 0 0
\(223\) 11.2464 4.09337i 0.753118 0.274112i 0.0632006 0.998001i \(-0.479869\pi\)
0.689917 + 0.723888i \(0.257647\pi\)
\(224\) 0 0
\(225\) 5.08512 + 4.26692i 0.339008 + 0.284462i
\(226\) 0 0
\(227\) −26.5945 −1.76514 −0.882570 0.470181i \(-0.844189\pi\)
−0.882570 + 0.470181i \(0.844189\pi\)
\(228\) 0 0
\(229\) −19.9026 −1.31520 −0.657601 0.753367i \(-0.728429\pi\)
−0.657601 + 0.753367i \(0.728429\pi\)
\(230\) 0 0
\(231\) −12.7515 10.6998i −0.838987 0.703994i
\(232\) 0 0
\(233\) 4.05051 1.47426i 0.265358 0.0965822i −0.205915 0.978570i \(-0.566017\pi\)
0.471273 + 0.881988i \(0.343795\pi\)
\(234\) 0 0
\(235\) 4.87346 + 8.44107i 0.317909 + 0.550635i
\(236\) 0 0
\(237\) 0.0516892 + 0.293144i 0.00335758 + 0.0190418i
\(238\) 0 0
\(239\) 0.142903 0.247516i 0.00924366 0.0160105i −0.861367 0.507984i \(-0.830391\pi\)
0.870610 + 0.491973i \(0.163724\pi\)
\(240\) 0 0
\(241\) 7.32816 6.14906i 0.472048 0.396096i −0.375493 0.926825i \(-0.622526\pi\)
0.847541 + 0.530730i \(0.178082\pi\)
\(242\) 0 0
\(243\) 0.939693 + 0.342020i 0.0602813 + 0.0219406i
\(244\) 0 0
\(245\) 9.95723 56.4703i 0.636144 3.60775i
\(246\) 0 0
\(247\) 11.4568 + 2.99832i 0.728977 + 0.190779i
\(248\) 0 0
\(249\) 2.70961 15.3669i 0.171714 0.973841i
\(250\) 0 0
\(251\) 27.8974 + 10.1538i 1.76087 + 0.640903i 0.999968 0.00796619i \(-0.00253575\pi\)
0.760900 + 0.648870i \(0.224758\pi\)
\(252\) 0 0
\(253\) 8.91534 7.48086i 0.560503 0.470318i
\(254\) 0 0
\(255\) 2.02094 3.50038i 0.126556 0.219202i
\(256\) 0 0
\(257\) 2.74304 + 15.5566i 0.171106 + 0.970391i 0.942543 + 0.334085i \(0.108427\pi\)
−0.771437 + 0.636306i \(0.780462\pi\)
\(258\) 0 0
\(259\) −16.4893 28.5603i −1.02460 1.77465i
\(260\) 0 0
\(261\) −3.54576 + 1.29055i −0.219477 + 0.0798831i
\(262\) 0 0
\(263\) −8.32295 6.98378i −0.513215 0.430638i 0.349044 0.937106i \(-0.386506\pi\)
−0.862259 + 0.506468i \(0.830951\pi\)
\(264\) 0 0
\(265\) 2.15064 0.132113
\(266\) 0 0
\(267\) −6.77332 −0.414520
\(268\) 0 0
\(269\) −13.2476 11.1161i −0.807722 0.677759i 0.142341 0.989818i \(-0.454537\pi\)
−0.950063 + 0.312058i \(0.898982\pi\)
\(270\) 0 0
\(271\) 1.35844 0.494432i 0.0825194 0.0300346i −0.300431 0.953804i \(-0.597130\pi\)
0.382950 + 0.923769i \(0.374908\pi\)
\(272\) 0 0
\(273\) 6.62836 + 11.4806i 0.401166 + 0.694840i
\(274\) 0 0
\(275\) 3.93242 + 22.3019i 0.237134 + 1.34485i
\(276\) 0 0
\(277\) −10.5954 + 18.3518i −0.636615 + 1.10265i 0.349555 + 0.936916i \(0.386333\pi\)
−0.986170 + 0.165734i \(0.947001\pi\)
\(278\) 0 0
\(279\) −5.06805 + 4.25260i −0.303416 + 0.254596i
\(280\) 0 0
\(281\) 22.8983 + 8.33429i 1.36600 + 0.497182i 0.917903 0.396805i \(-0.129881\pi\)
0.448093 + 0.893987i \(0.352103\pi\)
\(282\) 0 0
\(283\) 0.716415 4.06299i 0.0425864 0.241520i −0.956083 0.293098i \(-0.905314\pi\)
0.998669 + 0.0515779i \(0.0164250\pi\)
\(284\) 0 0
\(285\) 3.93242 + 14.3409i 0.232936 + 0.849481i
\(286\) 0 0
\(287\) 5.55350 31.4955i 0.327813 1.85912i
\(288\) 0 0
\(289\) 14.6557 + 5.33424i 0.862100 + 0.313779i
\(290\) 0 0
\(291\) 5.45858 4.58029i 0.319987 0.268501i
\(292\) 0 0
\(293\) −1.39053 + 2.40847i −0.0812356 + 0.140704i −0.903781 0.427995i \(-0.859220\pi\)
0.822545 + 0.568700i \(0.192553\pi\)
\(294\) 0 0
\(295\) −6.89440 39.1001i −0.401407 2.27649i
\(296\) 0 0
\(297\) 1.70574 + 2.95442i 0.0989769 + 0.171433i
\(298\) 0 0
\(299\) −8.70961 + 3.17004i −0.503690 + 0.183328i
\(300\) 0 0
\(301\) −15.5876 13.0796i −0.898457 0.753895i
\(302\) 0 0
\(303\) 4.64590 0.266900
\(304\) 0 0
\(305\) 23.5449 1.34818
\(306\) 0 0
\(307\) 19.1689 + 16.0846i 1.09403 + 0.917998i 0.997009 0.0772850i \(-0.0246251\pi\)
0.0970179 + 0.995283i \(0.469070\pi\)
\(308\) 0 0
\(309\) 11.6356 4.23502i 0.661928 0.240922i
\(310\) 0 0
\(311\) 11.9868 + 20.7617i 0.679709 + 1.17729i 0.975068 + 0.221904i \(0.0712272\pi\)
−0.295360 + 0.955386i \(0.595439\pi\)
\(312\) 0 0
\(313\) −2.19459 12.4462i −0.124046 0.703498i −0.981870 0.189555i \(-0.939295\pi\)
0.857824 0.513943i \(-0.171816\pi\)
\(314\) 0 0
\(315\) −8.32295 + 14.4158i −0.468945 + 0.812237i
\(316\) 0 0
\(317\) −10.8268 + 9.08478i −0.608095 + 0.510252i −0.894036 0.447995i \(-0.852138\pi\)
0.285941 + 0.958247i \(0.407694\pi\)
\(318\) 0 0
\(319\) −12.0963 4.40268i −0.677261 0.246503i
\(320\) 0 0
\(321\) 0.677052 3.83975i 0.0377893 0.214314i
\(322\) 0 0
\(323\) 4.66772 2.20983i 0.259719 0.122958i
\(324\) 0 0
\(325\) 3.13176 17.7611i 0.173719 0.985208i
\(326\) 0 0
\(327\) −10.8969 3.96616i −0.602601 0.219329i
\(328\) 0 0
\(329\) −10.6793 + 8.96102i −0.588770 + 0.494037i
\(330\) 0 0
\(331\) 14.7490 25.5460i 0.810677 1.40413i −0.101714 0.994814i \(-0.532433\pi\)
0.912391 0.409320i \(-0.134234\pi\)
\(332\) 0 0
\(333\) 1.17365 + 6.65609i 0.0643155 + 0.364751i
\(334\) 0 0
\(335\) 1.20961 + 2.09510i 0.0660879 + 0.114468i
\(336\) 0 0
\(337\) 20.9072 7.60960i 1.13889 0.414521i 0.297376 0.954760i \(-0.403889\pi\)
0.841511 + 0.540239i \(0.181666\pi\)
\(338\) 0 0
\(339\) −1.48680 1.24757i −0.0807517 0.0677587i
\(340\) 0 0
\(341\) −22.5699 −1.22223
\(342\) 0 0
\(343\) 47.8590 2.58414
\(344\) 0 0
\(345\) −8.91534 7.48086i −0.479986 0.402756i
\(346\) 0 0
\(347\) −13.1792 + 4.79682i −0.707495 + 0.257507i −0.670607 0.741812i \(-0.733966\pi\)
−0.0368873 + 0.999319i \(0.511744\pi\)
\(348\) 0 0
\(349\) 17.0560 + 29.5419i 0.912988 + 1.58134i 0.809820 + 0.586678i \(0.199565\pi\)
0.103168 + 0.994664i \(0.467102\pi\)
\(350\) 0 0
\(351\) −0.471782 2.67561i −0.0251818 0.142813i
\(352\) 0 0
\(353\) −15.2219 + 26.3652i −0.810182 + 1.40328i 0.102555 + 0.994727i \(0.467298\pi\)
−0.912737 + 0.408549i \(0.866035\pi\)
\(354\) 0 0
\(355\) −20.7973 + 17.4510i −1.10380 + 0.926201i
\(356\) 0 0
\(357\) 5.43242 + 1.97724i 0.287514 + 0.104647i
\(358\) 0 0
\(359\) −2.36959 + 13.4386i −0.125062 + 0.709261i 0.856209 + 0.516629i \(0.172813\pi\)
−0.981271 + 0.192632i \(0.938298\pi\)
\(360\) 0 0
\(361\) −6.28968 + 17.9287i −0.331036 + 0.943618i
\(362\) 0 0
\(363\) −0.110815 + 0.628461i −0.00581626 + 0.0329856i
\(364\) 0 0
\(365\) 40.8546 + 14.8699i 2.13843 + 0.778324i
\(366\) 0 0
\(367\) −18.2062 + 15.2768i −0.950356 + 0.797443i −0.979357 0.202136i \(-0.935212\pi\)
0.0290014 + 0.999579i \(0.490767\pi\)
\(368\) 0 0
\(369\) −3.27719 + 5.67626i −0.170604 + 0.295494i
\(370\) 0 0
\(371\) 0.534148 + 3.02931i 0.0277316 + 0.157274i
\(372\) 0 0
\(373\) 11.6172 + 20.1216i 0.601516 + 1.04186i 0.992592 + 0.121498i \(0.0387699\pi\)
−0.391075 + 0.920359i \(0.627897\pi\)
\(374\) 0 0
\(375\) 5.25150 1.91139i 0.271186 0.0987037i
\(376\) 0 0
\(377\) 7.85323 + 6.58964i 0.404462 + 0.339384i
\(378\) 0 0
\(379\) 4.50030 0.231165 0.115583 0.993298i \(-0.463127\pi\)
0.115583 + 0.993298i \(0.463127\pi\)
\(380\) 0 0
\(381\) −6.08378 −0.311681
\(382\) 0 0
\(383\) −3.34002 2.80261i −0.170667 0.143207i 0.553453 0.832880i \(-0.313310\pi\)
−0.724121 + 0.689673i \(0.757754\pi\)
\(384\) 0 0
\(385\) −53.3624 + 19.4223i −2.71960 + 0.989853i
\(386\) 0 0
\(387\) 2.08512 + 3.61154i 0.105993 + 0.183585i
\(388\) 0 0
\(389\) −0.227559 1.29055i −0.0115377 0.0654335i 0.978495 0.206269i \(-0.0661322\pi\)
−0.990033 + 0.140836i \(0.955021\pi\)
\(390\) 0 0
\(391\) −2.02094 + 3.50038i −0.102204 + 0.177022i
\(392\) 0 0
\(393\) −14.2515 + 11.9584i −0.718893 + 0.603223i
\(394\) 0 0
\(395\) 0.954241 + 0.347315i 0.0480131 + 0.0174753i
\(396\) 0 0
\(397\) −3.30154 + 18.7239i −0.165699 + 0.939728i 0.782641 + 0.622473i \(0.213872\pi\)
−0.948340 + 0.317255i \(0.897239\pi\)
\(398\) 0 0
\(399\) −19.2233 + 9.10083i −0.962368 + 0.455612i
\(400\) 0 0
\(401\) 6.22756 35.3182i 0.310989 1.76371i −0.282888 0.959153i \(-0.591292\pi\)
0.593877 0.804556i \(-0.297597\pi\)
\(402\) 0 0
\(403\) 16.8905 + 6.14765i 0.841377 + 0.306236i
\(404\) 0 0
\(405\) 2.61334 2.19285i 0.129858 0.108964i
\(406\) 0 0
\(407\) −11.5287 + 19.9683i −0.571456 + 0.989790i
\(408\) 0 0
\(409\) −5.05468 28.6665i −0.249938 1.41747i −0.808739 0.588167i \(-0.799850\pi\)
0.558801 0.829301i \(-0.311261\pi\)
\(410\) 0 0
\(411\) 2.27332 + 3.93750i 0.112135 + 0.194223i
\(412\) 0 0
\(413\) 53.3624 19.4223i 2.62579 0.955710i
\(414\) 0 0
\(415\) −40.7786 34.2173i −2.00174 1.67966i
\(416\) 0 0
\(417\) −3.01455 −0.147623
\(418\) 0 0
\(419\) −13.1584 −0.642829 −0.321415 0.946939i \(-0.604158\pi\)
−0.321415 + 0.946939i \(0.604158\pi\)
\(420\) 0 0
\(421\) −0.115400 0.0968323i −0.00562426 0.00471932i 0.639971 0.768399i \(-0.278946\pi\)
−0.645595 + 0.763680i \(0.723391\pi\)
\(422\) 0 0
\(423\) 2.68479 0.977185i 0.130539 0.0475123i
\(424\) 0 0
\(425\) −3.93242 6.81115i −0.190750 0.330389i
\(426\) 0 0
\(427\) 5.84776 + 33.1643i 0.282993 + 1.60493i
\(428\) 0 0
\(429\) 4.63429 8.02682i 0.223745 0.387538i
\(430\) 0 0
\(431\) 23.5915 19.7956i 1.13636 0.953522i 0.137050 0.990564i \(-0.456238\pi\)
0.999314 + 0.0370420i \(0.0117935\pi\)
\(432\) 0 0
\(433\) 27.6587 + 10.0669i 1.32919 + 0.483786i 0.906392 0.422437i \(-0.138825\pi\)
0.422800 + 0.906223i \(0.361047\pi\)
\(434\) 0 0
\(435\) −2.23530 + 12.6770i −0.107174 + 0.607816i
\(436\) 0 0
\(437\) −3.93242 14.3409i −0.188113 0.686018i
\(438\) 0 0
\(439\) −3.43835 + 19.4998i −0.164103 + 0.930677i 0.785881 + 0.618378i \(0.212210\pi\)
−0.949984 + 0.312298i \(0.898901\pi\)
\(440\) 0 0
\(441\) −15.7947 5.74881i −0.752130 0.273753i
\(442\) 0 0
\(443\) 14.2383 11.9473i 0.676482 0.567636i −0.238494 0.971144i \(-0.576654\pi\)
0.914976 + 0.403508i \(0.132209\pi\)
\(444\) 0 0
\(445\) −11.5535 + 20.0112i −0.547688 + 0.948624i
\(446\) 0 0
\(447\) −0.205737 1.16679i −0.00973103 0.0551874i
\(448\) 0 0
\(449\) −1.68954 2.92637i −0.0797343 0.138104i 0.823401 0.567460i \(-0.192074\pi\)
−0.903135 + 0.429356i \(0.858741\pi\)
\(450\) 0 0
\(451\) −21.0116 + 7.64760i −0.989398 + 0.360111i
\(452\) 0 0
\(453\) −2.78699 2.33856i −0.130944 0.109875i
\(454\) 0 0
\(455\) 45.2249 2.12018
\(456\) 0 0
\(457\) 21.7912 1.01935 0.509674 0.860368i \(-0.329766\pi\)
0.509674 + 0.860368i \(0.329766\pi\)
\(458\) 0 0
\(459\) −0.907604 0.761570i −0.0423633 0.0355470i
\(460\) 0 0
\(461\) −11.0544 + 4.02346i −0.514854 + 0.187391i −0.586363 0.810049i \(-0.699441\pi\)
0.0715092 + 0.997440i \(0.477218\pi\)
\(462\) 0 0
\(463\) 8.49660 + 14.7165i 0.394870 + 0.683935i 0.993085 0.117401i \(-0.0374562\pi\)
−0.598214 + 0.801336i \(0.704123\pi\)
\(464\) 0 0
\(465\) 3.91921 + 22.2270i 0.181749 + 1.03075i
\(466\) 0 0
\(467\) −5.85251 + 10.1368i −0.270822 + 0.469077i −0.969073 0.246776i \(-0.920629\pi\)
0.698251 + 0.715853i \(0.253962\pi\)
\(468\) 0 0
\(469\) −2.65064 + 2.22415i −0.122395 + 0.102702i
\(470\) 0 0
\(471\) 5.89306 + 2.14490i 0.271538 + 0.0988316i
\(472\) 0 0
\(473\) −2.47044 + 14.0105i −0.113591 + 0.644206i
\(474\) 0 0
\(475\) 27.9923 + 7.32580i 1.28438 + 0.336131i
\(476\) 0 0
\(477\) 0.109470 0.620838i 0.00501231 0.0284262i
\(478\) 0 0
\(479\) 28.1716 + 10.2536i 1.28719 + 0.468500i 0.892805 0.450444i \(-0.148734\pi\)
0.394388 + 0.918944i \(0.370957\pi\)
\(480\) 0 0
\(481\) 14.0667 11.8034i 0.641386 0.538187i
\(482\) 0 0
\(483\) 8.32295 14.4158i 0.378707 0.655940i
\(484\) 0 0
\(485\) −4.22122 23.9397i −0.191676 1.08705i
\(486\) 0 0
\(487\) 7.25537 + 12.5667i 0.328772 + 0.569450i 0.982268 0.187480i \(-0.0600319\pi\)
−0.653496 + 0.756930i \(0.726699\pi\)
\(488\) 0 0
\(489\) 18.1348 6.60051i 0.820082 0.298485i
\(490\) 0 0
\(491\) 8.92855 + 7.49194i 0.402940 + 0.338107i 0.821629 0.570023i \(-0.193066\pi\)
−0.418689 + 0.908130i \(0.637510\pi\)
\(492\) 0 0
\(493\) 4.47060 0.201346
\(494\) 0 0
\(495\) 11.6382 0.523096
\(496\) 0 0
\(497\) −29.7460 24.9599i −1.33429 1.11960i
\(498\) 0 0
\(499\) −1.58512 + 0.576937i −0.0709598 + 0.0258273i −0.377256 0.926109i \(-0.623132\pi\)
0.306296 + 0.951936i \(0.400910\pi\)
\(500\) 0 0
\(501\) 3.86097 + 6.68739i 0.172495 + 0.298771i
\(502\) 0 0
\(503\) −3.00299 17.0308i −0.133897 0.759367i −0.975622 0.219460i \(-0.929571\pi\)
0.841725 0.539907i \(-0.181541\pi\)
\(504\) 0 0
\(505\) 7.92468 13.7259i 0.352644 0.610797i
\(506\) 0 0
\(507\) 4.30406 3.61154i 0.191150 0.160394i
\(508\) 0 0
\(509\) −30.4859 11.0960i −1.35126 0.491820i −0.437922 0.899013i \(-0.644286\pi\)
−0.913342 + 0.407193i \(0.866508\pi\)
\(510\) 0 0
\(511\) −10.7981 + 61.2393i −0.477681 + 2.70907i
\(512\) 0 0
\(513\) 4.34002 0.405223i 0.191617 0.0178910i
\(514\) 0 0
\(515\) 7.33527 41.6004i 0.323231 1.83313i
\(516\) 0 0
\(517\) 9.15910 + 3.33364i 0.402817 + 0.146613i
\(518\) 0 0
\(519\) 11.1040 9.31737i 0.487412 0.408987i
\(520\) 0 0
\(521\) −15.5822 + 26.9891i −0.682668 + 1.18242i 0.291496 + 0.956572i \(0.405847\pi\)
−0.974164 + 0.225843i \(0.927486\pi\)
\(522\) 0 0
\(523\) 2.89306 + 16.4073i 0.126504 + 0.717443i 0.980403 + 0.197003i \(0.0631208\pi\)
−0.853898 + 0.520440i \(0.825768\pi\)
\(524\) 0 0
\(525\) 16.1951 + 28.0507i 0.706810 + 1.22423i
\(526\) 0 0
\(527\) 7.36571 2.68090i 0.320856 0.116782i
\(528\) 0 0
\(529\) −8.70368 7.30325i −0.378421 0.317533i
\(530\) 0 0
\(531\) −11.6382 −0.505053
\(532\) 0 0
\(533\) 17.8075 0.771327
\(534\) 0 0
\(535\) −10.1894 8.54990i −0.440525 0.369645i
\(536\) 0 0
\(537\) 9.23055 3.35965i 0.398328 0.144979i
\(538\) 0 0
\(539\) −28.6707 49.6591i −1.23493 2.13897i
\(540\) 0 0
\(541\) 6.29385 + 35.6942i 0.270594 + 1.53461i 0.752619 + 0.658456i \(0.228790\pi\)
−0.482025 + 0.876157i \(0.660099\pi\)
\(542\) 0 0
\(543\) 9.45723 16.3804i 0.405849 0.702951i
\(544\) 0 0
\(545\) −30.3050 + 25.4289i −1.29812 + 1.08925i
\(546\) 0 0
\(547\) −16.1604 5.88192i −0.690971 0.251493i −0.0274199 0.999624i \(-0.508729\pi\)
−0.663551 + 0.748131i \(0.730951\pi\)
\(548\) 0 0
\(549\) 1.19846 6.79682i 0.0511492 0.290081i
\(550\) 0 0
\(551\) −11.5621 + 11.6978i −0.492563 + 0.498342i
\(552\) 0 0
\(553\) −0.252212 + 1.43036i −0.0107251 + 0.0608253i
\(554\) 0 0
\(555\) 21.6668 + 7.88609i 0.919706 + 0.334746i
\(556\) 0 0
\(557\) −12.6932 + 10.6509i −0.537830 + 0.451293i −0.870795 0.491646i \(-0.836395\pi\)
0.332965 + 0.942939i \(0.391951\pi\)
\(558\) 0 0
\(559\) 5.66503 9.81212i 0.239605 0.415008i
\(560\) 0 0
\(561\) −0.701867 3.98048i −0.0296328 0.168056i
\(562\) 0 0
\(563\) −15.3486 26.5846i −0.646868 1.12041i −0.983867 0.178903i \(-0.942745\pi\)
0.336999 0.941505i \(-0.390588\pi\)
\(564\) 0 0
\(565\) −6.22193 + 2.26460i −0.261759 + 0.0952724i
\(566\) 0 0
\(567\) 3.73783 + 3.13641i 0.156974 + 0.131717i
\(568\) 0 0
\(569\) 13.4534 0.563994 0.281997 0.959415i \(-0.409003\pi\)
0.281997 + 0.959415i \(0.409003\pi\)
\(570\) 0 0
\(571\) 9.47565 0.396544 0.198272 0.980147i \(-0.436467\pi\)
0.198272 + 0.980147i \(0.436467\pi\)
\(572\) 0 0
\(573\) −7.73055 6.48670i −0.322948 0.270986i
\(574\) 0 0
\(575\) −21.2802 + 7.74535i −0.887445 + 0.323004i
\(576\) 0 0
\(577\) 9.38191 + 16.2499i 0.390574 + 0.676494i 0.992525 0.122039i \(-0.0389432\pi\)
−0.601951 + 0.798533i \(0.705610\pi\)
\(578\) 0 0
\(579\) −0.438348 2.48600i −0.0182171 0.103315i
\(580\) 0 0
\(581\) 38.0690 65.9374i 1.57937 2.73554i
\(582\) 0 0
\(583\) 1.64749 1.38241i 0.0682320 0.0572535i
\(584\) 0 0
\(585\) −8.70961 3.17004i −0.360098 0.131065i
\(586\) 0 0
\(587\) 3.15611 17.8992i 0.130266 0.738778i −0.847773 0.530359i \(-0.822057\pi\)
0.978040 0.208419i \(-0.0668317\pi\)
\(588\) 0 0
\(589\) −12.0348 + 26.2066i −0.495884 + 1.07983i
\(590\) 0 0
\(591\) −2.57991 + 14.6314i −0.106123 + 0.601855i
\(592\) 0 0
\(593\) 30.7221 + 11.1819i 1.26161 + 0.459187i 0.884307 0.466905i \(-0.154631\pi\)
0.377298 + 0.926092i \(0.376853\pi\)
\(594\) 0 0
\(595\) 15.1079 12.6770i 0.619363 0.519707i
\(596\) 0 0
\(597\) −4.03462 + 6.98816i −0.165126 + 0.286006i
\(598\) 0 0
\(599\) −1.53343 8.69653i −0.0626544 0.355331i −0.999976 0.00686632i \(-0.997814\pi\)
0.937322 0.348464i \(-0.113297\pi\)
\(600\) 0 0
\(601\) −16.5262 28.6241i −0.674116 1.16760i −0.976726 0.214489i \(-0.931191\pi\)
0.302610 0.953114i \(-0.402142\pi\)
\(602\) 0 0
\(603\) 0.666374 0.242540i 0.0271369 0.00987701i
\(604\) 0 0
\(605\) 1.66772 + 1.39938i 0.0678024 + 0.0568930i
\(606\) 0 0
\(607\) −5.16250 −0.209540 −0.104770 0.994497i \(-0.533411\pi\)
−0.104770 + 0.994497i \(0.533411\pi\)
\(608\) 0 0
\(609\) −18.4115 −0.746071
\(610\) 0 0
\(611\) −5.94634 4.98957i −0.240563 0.201856i
\(612\) 0 0
\(613\) 44.2486 16.1052i 1.78718 0.650481i 0.787779 0.615959i \(-0.211231\pi\)
0.999404 0.0345227i \(-0.0109911\pi\)
\(614\) 0 0
\(615\) 11.1800 + 19.3644i 0.450823 + 0.780848i
\(616\) 0 0
\(617\) −7.36009 41.7411i −0.296306 1.68044i −0.661846 0.749640i \(-0.730227\pi\)
0.365540 0.930796i \(-0.380884\pi\)
\(618\) 0 0
\(619\) −0.928081 + 1.60748i −0.0373027 + 0.0646102i −0.884074 0.467347i \(-0.845210\pi\)
0.846771 + 0.531957i \(0.178543\pi\)
\(620\) 0 0
\(621\) −2.61334 + 2.19285i −0.104870 + 0.0879962i
\(622\) 0 0
\(623\) −31.0565 11.3036i −1.24425 0.452871i
\(624\) 0 0
\(625\) −2.45290 + 13.9111i −0.0981159 + 0.556443i
\(626\) 0 0
\(627\) 12.2306 + 8.45805i 0.488441 + 0.337782i
\(628\) 0 0
\(629\) 1.39053 7.88609i 0.0554440 0.314439i
\(630\) 0 0
\(631\) 23.1618 + 8.43020i 0.922056 + 0.335601i 0.759056 0.651025i \(-0.225661\pi\)
0.163000 + 0.986626i \(0.447883\pi\)
\(632\) 0 0
\(633\) 6.08512 5.10602i 0.241862 0.202946i
\(634\) 0 0
\(635\) −10.3773 + 17.9741i −0.411812 + 0.713279i
\(636\) 0 0
\(637\) 7.92989 + 44.9727i 0.314194 + 1.78188i
\(638\) 0 0
\(639\) 3.97906 + 6.89193i 0.157409 + 0.272640i
\(640\) 0 0
\(641\) −16.5744 + 6.03260i −0.654651 + 0.238274i −0.647925 0.761704i \(-0.724363\pi\)
−0.00672584 + 0.999977i \(0.502141\pi\)
\(642\) 0 0
\(643\) −22.8653 19.1863i −0.901720 0.756633i 0.0688062 0.997630i \(-0.478081\pi\)
−0.970526 + 0.240997i \(0.922525\pi\)
\(644\) 0 0
\(645\) 14.2267 0.560175
\(646\) 0 0
\(647\) −23.9391 −0.941144 −0.470572 0.882362i \(-0.655952\pi\)
−0.470572 + 0.882362i \(0.655952\pi\)
\(648\) 0 0
\(649\) −30.4145 25.5208i −1.19387 1.00178i
\(650\) 0 0
\(651\) −30.3346 + 11.0409i −1.18891 + 0.432726i
\(652\) 0 0
\(653\) 13.2430 + 22.9376i 0.518240 + 0.897618i 0.999775 + 0.0211916i \(0.00674602\pi\)
−0.481535 + 0.876427i \(0.659921\pi\)
\(654\) 0 0
\(655\) 11.0209 + 62.5029i 0.430624 + 2.44219i
\(656\) 0 0
\(657\) 6.37211 11.0368i 0.248600 0.430587i
\(658\) 0 0
\(659\) 4.05509 3.40263i 0.157964 0.132548i −0.560380 0.828236i \(-0.689345\pi\)
0.718344 + 0.695688i \(0.244900\pi\)
\(660\) 0 0
\(661\) −43.3264 15.7695i −1.68520 0.613363i −0.691194 0.722669i \(-0.742915\pi\)
−0.994008 + 0.109306i \(0.965137\pi\)
\(662\) 0 0
\(663\) −0.558963 + 3.17004i −0.0217083 + 0.123114i
\(664\) 0 0
\(665\) −5.90214 + 72.3173i −0.228875 + 2.80435i
\(666\) 0 0
\(667\) 2.23530 12.6770i 0.0865512 0.490856i
\(668\) 0 0
\(669\) −11.2464 4.09337i −0.434813 0.158259i
\(670\) 0 0
\(671\) 18.0364 15.1344i 0.696289 0.584255i
\(672\) 0 0
\(673\) −1.19072 + 2.06239i −0.0458990 + 0.0794994i −0.888062 0.459723i \(-0.847949\pi\)
0.842163 + 0.539223i \(0.181282\pi\)
\(674\) 0 0
\(675\) −1.15270 6.53731i −0.0443676 0.251621i
\(676\) 0 0
\(677\) −7.97431 13.8119i −0.306478 0.530835i 0.671112 0.741356i \(-0.265817\pi\)
−0.977589 + 0.210522i \(0.932484\pi\)
\(678\) 0 0
\(679\) 32.6721 11.8917i 1.25384 0.456360i
\(680\) 0 0
\(681\) 20.3726 + 17.0946i 0.780679 + 0.655067i
\(682\) 0 0
\(683\) 1.26083 0.0482443 0.0241222 0.999709i \(-0.492321\pi\)
0.0241222 + 0.999709i \(0.492321\pi\)
\(684\) 0 0
\(685\) 15.5107 0.592635
\(686\) 0 0
\(687\) 15.2463 + 12.7931i 0.581682 + 0.488089i
\(688\) 0 0
\(689\) −1.60947 + 0.585799i −0.0613159 + 0.0223172i
\(690\) 0 0
\(691\) −4.05438 7.02239i −0.154236 0.267144i 0.778545 0.627589i \(-0.215958\pi\)
−0.932780 + 0.360445i \(0.882625\pi\)
\(692\) 0 0
\(693\) 2.89053 + 16.3930i 0.109802 + 0.622719i
\(694\) 0 0
\(695\) −5.14203 + 8.90625i −0.195048 + 0.337833i
\(696\) 0 0
\(697\) 5.94878 4.99162i 0.225326 0.189071i
\(698\) 0 0
\(699\) −4.05051 1.47426i −0.153204 0.0557618i
\(700\) 0 0
\(701\) 1.77615 10.0730i 0.0670842 0.380454i −0.932719 0.360605i \(-0.882570\pi\)
0.999803 0.0198489i \(-0.00631853\pi\)
\(702\) 0 0
\(703\) 17.0385 + 24.0339i 0.642619 + 0.906456i
\(704\) 0 0
\(705\) 1.69253 9.59883i 0.0637445 0.361513i
\(706\) 0 0
\(707\) 21.3020 + 7.75330i 0.801144 + 0.291593i
\(708\) 0 0
\(709\) 0.156574 0.131381i 0.00588026 0.00493413i −0.639843 0.768506i \(-0.721001\pi\)
0.645723 + 0.763572i \(0.276556\pi\)
\(710\) 0 0
\(711\) 0.148833 0.257787i 0.00558168 0.00966776i
\(712\) 0 0
\(713\) −3.91921 22.2270i −0.146776 0.832407i
\(714\) 0 0
\(715\) −15.8097 27.3833i −0.591251 1.02408i
\(716\) 0 0
\(717\) −0.268571 + 0.0977517i −0.0100300 + 0.00365061i
\(718\) 0 0
\(719\) −12.2103 10.2457i −0.455368 0.382099i 0.386055 0.922476i \(-0.373837\pi\)
−0.841423 + 0.540376i \(0.818282\pi\)
\(720\) 0 0
\(721\) 60.4184 2.25010
\(722\) 0 0
\(723\) −9.56624 −0.355772
\(724\) 0 0
\(725\) 19.1878 + 16.1005i 0.712616 + 0.597956i
\(726\) 0 0
\(727\) −29.0959 + 10.5900i −1.07911 + 0.392762i −0.819575 0.572972i \(-0.805790\pi\)
−0.259531 + 0.965735i \(0.583568\pi\)
\(728\) 0 0
\(729\) −0.500000 0.866025i −0.0185185 0.0320750i
\(730\) 0 0
\(731\) −0.857974 4.86581i −0.0317333 0.179969i
\(732\) 0 0
\(733\) −1.97906 + 3.42782i −0.0730981 + 0.126610i −0.900258 0.435358i \(-0.856622\pi\)
0.827160 + 0.561967i \(0.189955\pi\)
\(734\) 0 0
\(735\) −43.9261 + 36.8584i −1.62024 + 1.35954i
\(736\) 0 0
\(737\) 2.27332 + 0.827420i 0.0837388 + 0.0304784i
\(738\) 0 0
\(739\) 4.48070 25.4113i 0.164825 0.934771i −0.784419 0.620231i \(-0.787039\pi\)
0.949244 0.314540i \(-0.101850\pi\)
\(740\) 0 0
\(741\) −6.84911 9.66112i −0.251608 0.354910i
\(742\) 0 0
\(743\) −5.54189 + 31.4296i −0.203312 + 1.15304i 0.696761 + 0.717303i \(0.254624\pi\)
−0.900074 + 0.435738i \(0.856487\pi\)
\(744\) 0 0
\(745\) −3.79813 1.38241i −0.139153 0.0506475i
\(746\) 0 0
\(747\) −11.9534 + 10.0301i −0.437351 + 0.366981i
\(748\) 0 0
\(749\) 9.51233 16.4758i 0.347573 0.602014i
\(750\) 0 0
\(751\) 0.0882212 + 0.500327i 0.00321924 + 0.0182572i 0.986375 0.164512i \(-0.0526050\pi\)
−0.983156 + 0.182769i \(0.941494\pi\)
\(752\) 0 0
\(753\) −14.8439 25.7104i −0.540942 0.936938i
\(754\) 0 0
\(755\) −11.6630 + 4.24497i −0.424459 + 0.154490i
\(756\) 0 0
\(757\) −36.8999 30.9627i −1.34115 1.12536i −0.981329 0.192338i \(-0.938393\pi\)
−0.359822 0.933021i \(-0.617162\pi\)
\(758\) 0 0
\(759\) −11.6382 −0.422438
\(760\) 0 0
\(761\) 5.15064 0.186711 0.0933554 0.995633i \(-0.470241\pi\)
0.0933554 + 0.995633i \(0.470241\pi\)
\(762\) 0 0
\(763\) −43.3448 36.3706i −1.56919 1.31671i
\(764\) 0 0
\(765\) −3.79813 + 1.38241i −0.137322 + 0.0499810i
\(766\) 0 0
\(767\) 15.8097 + 27.3833i 0.570857 + 0.988753i
\(768\) 0 0
\(769\) 3.39874 + 19.2752i 0.122562 + 0.695081i 0.982726 + 0.185065i \(0.0592496\pi\)
−0.860165 + 0.510016i \(0.829639\pi\)
\(770\) 0 0
\(771\) 7.89827 13.6802i 0.284449 0.492681i
\(772\) 0 0
\(773\) 17.1552 14.3949i 0.617031 0.517750i −0.279838 0.960047i \(-0.590281\pi\)
0.896869 + 0.442297i \(0.145836\pi\)
\(774\) 0 0
\(775\) 41.2686 + 15.0206i 1.48241 + 0.539554i
\(776\) 0 0
\(777\) −5.72668 + 32.4776i −0.205444 + 1.16513i
\(778\) 0 0
\(779\) −2.32399 + 28.4752i −0.0832655 + 1.02023i
\(780\) 0 0
\(781\) −4.71436 + 26.7364i −0.168693 + 0.956705i
\(782\) 0 0
\(783\) 3.54576 + 1.29055i 0.126715 + 0.0461205i
\(784\) 0 0
\(785\) 16.3889 13.7520i 0.584946 0.490828i
\(786\) 0 0
\(787\) 16.8444 29.1753i 0.600437 1.03999i −0.392318 0.919830i \(-0.628327\pi\)
0.992755 0.120157i \(-0.0383398\pi\)
\(788\) 0 0
\(789\) 1.88666 + 10.6998i 0.0671668 + 0.380922i
\(790\) 0 0
\(791\) −4.73514 8.20150i −0.168362 0.291612i
\(792\) 0 0
\(793\) −17.6202 + 6.41323i −0.625712 + 0.227740i
\(794\) 0 0
\(795\) −1.64749 1.38241i −0.0584304 0.0490289i
\(796\) 0 0
\(797\) −47.8631 −1.69540 −0.847699 0.530478i \(-0.822012\pi\)
−0.847699 + 0.530478i \(0.822012\pi\)
\(798\) 0 0
\(799\) −3.38507 −0.119755
\(800\) 0 0
\(801\) 5.18866 + 4.35381i 0.183332 + 0.153834i
\(802\) 0 0
\(803\) 40.8546 14.8699i 1.44173 0.524746i
\(804\) 0 0
\(805\) −28.3935 49.1790i −1.00074 1.73333i
\(806\) 0 0
\(807\) 3.00299 + 17.0308i 0.105710 + 0.599513i
\(808\) 0 0
\(809\) 1.83703 3.18183i 0.0645865 0.111867i −0.831924 0.554890i \(-0.812760\pi\)
0.896510 + 0.443022i \(0.146094\pi\)
\(810\) 0 0
\(811\) 14.3289 12.0234i 0.503155 0.422197i −0.355558 0.934654i \(-0.615709\pi\)
0.858713 + 0.512457i \(0.171265\pi\)
\(812\) 0 0
\(813\) −1.35844 0.494432i −0.0476426 0.0173405i
\(814\) 0 0
\(815\) 11.4324 64.8365i 0.400460 2.27112i
\(816\) 0 0
\(817\) 14.9508 + 10.3393i 0.523064 + 0.361725i
\(818\) 0 0
\(819\) 2.30200 13.0553i 0.0804385 0.456190i
\(820\) 0 0
\(821\) 20.9706 + 7.63267i 0.731879 + 0.266382i 0.680960 0.732321i \(-0.261563\pi\)
0.0509190 + 0.998703i \(0.483785\pi\)
\(822\) 0 0
\(823\) 20.2264 16.9720i 0.705049 0.591606i −0.218156 0.975914i \(-0.570004\pi\)
0.923205 + 0.384307i \(0.125560\pi\)
\(824\) 0 0
\(825\) 11.3229 19.6119i 0.394214 0.682799i
\(826\) 0 0
\(827\) −5.15224 29.2198i −0.179161 1.01607i −0.933231 0.359277i \(-0.883023\pi\)
0.754070 0.656794i \(-0.228088\pi\)
\(828\) 0 0
\(829\) −0.884133 1.53136i −0.0307072 0.0531864i 0.850263 0.526357i \(-0.176443\pi\)
−0.880971 + 0.473171i \(0.843109\pi\)
\(830\) 0 0
\(831\) 19.9128 7.24767i 0.690768 0.251419i
\(832\) 0 0
\(833\) 15.2554 + 12.8008i 0.528567 + 0.443520i
\(834\) 0 0
\(835\) 26.3432 0.911643
\(836\) 0 0
\(837\) 6.61587 0.228678
\(838\) 0 0
\(839\) −20.4643 17.1716i −0.706505 0.592828i 0.217111 0.976147i \(-0.430337\pi\)
−0.923616 + 0.383319i \(0.874781\pi\)
\(840\) 0 0
\(841\) 13.8718 5.04892i 0.478338 0.174101i
\(842\) 0 0
\(843\) −12.1839 21.1032i −0.419636 0.726831i
\(844\) 0 0
\(845\) −3.32841 18.8764i −0.114501 0.649366i
\(846\) 0 0
\(847\) −1.55690 + 2.69664i −0.0534958 + 0.0926575i
\(848\) 0 0
\(849\) −3.16044 + 2.65193i −0.108466 + 0.0910139i
\(850\) 0 0
\(851\) −21.6668 7.88609i −0.742730 0.270332i
\(852\) 0 0
\(853\) 2.41828 13.7148i 0.0828004 0.469584i −0.915009 0.403433i \(-0.867817\pi\)
0.997810 0.0661513i \(-0.0210720\pi\)
\(854\) 0 0
\(855\) 6.20574 13.5135i 0.212232 0.462151i
\(856\) 0 0
\(857\) −3.41551 + 19.3703i −0.116671 + 0.661677i 0.869238 + 0.494395i \(0.164610\pi\)
−0.985909 + 0.167282i \(0.946501\pi\)
\(858\) 0 0
\(859\) −40.7806 14.8429i −1.39142 0.506435i −0.465799 0.884891i \(-0.654233\pi\)
−0.925619 + 0.378456i \(0.876455\pi\)
\(860\) 0 0
\(861\) −24.4991 + 20.5572i −0.834928 + 0.700588i
\(862\) 0 0
\(863\) −14.7096 + 25.4778i −0.500721 + 0.867274i 0.499279 + 0.866441i \(0.333598\pi\)
−1.00000 0.000832579i \(0.999735\pi\)
\(864\) 0 0
\(865\) −8.58693 48.6989i −0.291964 1.65581i
\(866\) 0 0
\(867\) −7.79813 13.5068i −0.264838 0.458714i
\(868\) 0 0
\(869\) 0.954241 0.347315i 0.0323704 0.0117819i
\(870\) 0 0
\(871\) −1.47590 1.23843i −0.0500090 0.0419625i
\(872\) 0 0
\(873\) −7.12567 −0.241167
\(874\) 0 0
\(875\) 27.2686 0.921846
\(876\) 0 0
\(877\) −20.0437 16.8187i −0.676828 0.567926i 0.238250 0.971204i \(-0.423426\pi\)
−0.915077 + 0.403278i \(0.867871\pi\)
\(878\) 0 0
\(879\) 2.61334 0.951178i 0.0881458 0.0320824i
\(880\) 0 0
\(881\) −11.3143 19.5970i −0.381189 0.660240i 0.610043 0.792368i \(-0.291152\pi\)
−0.991233 + 0.132129i \(0.957819\pi\)
\(882\) 0 0
\(883\) 1.43810 + 8.15587i 0.0483959 + 0.274467i 0.999397 0.0347205i \(-0.0110541\pi\)
−0.951001 + 0.309187i \(0.899943\pi\)
\(884\) 0 0
\(885\) −19.8516 + 34.3840i −0.667305 + 1.15581i
\(886\) 0 0
\(887\) −30.9152 + 25.9409i −1.03803 + 0.871011i −0.991785 0.127919i \(-0.959170\pi\)
−0.0462457 + 0.998930i \(0.514726\pi\)
\(888\) 0 0
\(889\) −27.8949 10.1529i −0.935564 0.340517i
\(890\) 0 0
\(891\) 0.592396 3.35965i 0.0198460 0.112552i
\(892\) 0 0
\(893\) 8.75465 8.85737i 0.292963 0.296401i
\(894\) 0 0
\(895\) 5.81908 33.0016i 0.194510 1.10312i
\(896\) 0 0
\(897\) 8.70961 + 3.17004i 0.290805 + 0.105844i
\(898\) 0 0
\(899\) −19.1234 + 16.0464i −0.637800 + 0.535178i
\(900\) 0 0
\(901\) −0.373455 + 0.646844i −0.0124416 + 0.0215495i
\(902\) 0 0
\(903\) 3.53343 + 20.0391i 0.117585 + 0.666859i
\(904\) 0 0
\(905\) −32.2631 55.8813i −1.07246 1.85756i
\(906\) 0 0
\(907\) −18.0903 + 6.58434i −0.600680 + 0.218630i −0.624420 0.781089i \(-0.714665\pi\)
0.0237404 + 0.999718i \(0.492442\pi\)
\(908\) 0 0
\(909\) −3.55896 2.98632i −0.118043 0.0990501i
\(910\) 0 0
\(911\) 58.7684 1.94708 0.973542 0.228510i \(-0.0733853\pi\)
0.973542 + 0.228510i \(0.0733853\pi\)
\(912\) 0 0
\(913\) −53.2327 −1.76174
\(914\) 0 0
\(915\) −18.0364 15.1344i −0.596266 0.500326i
\(916\) 0 0
\(917\) −85.3016 + 31.0473i −2.81691 + 1.02527i
\(918\) 0 0
\(919\) −26.8714 46.5426i −0.886406 1.53530i −0.844094 0.536195i \(-0.819861\pi\)
−0.0423114 0.999104i \(-0.513472\pi\)
\(920\) 0 0
\(921\) −4.34524 24.6431i −0.143180 0.812017i
\(922\) 0 0
\(923\) 10.8106 18.7245i 0.355836 0.616326i
\(924\) 0 0
\(925\) 34.3692 28.8392i 1.13005 0.948226i
\(926\) 0 0
\(927\) −11.6356 4.23502i −0.382164 0.139096i
\(928\) 0 0
\(929\) −5.38981 + 30.5672i −0.176834 + 1.00288i 0.759171 + 0.650891i \(0.225604\pi\)
−0.936006 + 0.351985i \(0.885507\pi\)
\(930\) 0 0
\(931\) −72.9488 + 6.81115i −2.39080 + 0.223226i
\(932\) 0 0
\(933\) 4.16297 23.6094i 0.136290 0.772936i
\(934\) 0 0
\(935\) −12.9572 4.71605i −0.423747 0.154231i
\(936\) 0 0
\(937\) −15.8899 + 13.3332i −0.519100 + 0.435577i −0.864318 0.502946i \(-0.832250\pi\)
0.345218 + 0.938523i \(0.387805\pi\)
\(938\) 0 0
\(939\) −6.31908 + 10.9450i −0.206215 + 0.357175i
\(940\) 0 0
\(941\) −2.58095 14.6373i −0.0841365 0.477162i −0.997540 0.0701055i \(-0.977666\pi\)
0.913403 0.407056i \(-0.133445\pi\)
\(942\) 0 0
\(943\) −11.1800 19.3644i −0.364072 0.630592i
\(944\) 0 0
\(945\) 15.6420 5.69323i 0.508835 0.185201i
\(946\) 0 0
\(947\) 19.3043 + 16.1982i 0.627305 + 0.526371i 0.900090 0.435704i \(-0.143500\pi\)
−0.272785 + 0.962075i \(0.587945\pi\)
\(948\) 0 0
\(949\) −34.6245 −1.12396
\(950\) 0 0
\(951\) 14.1334 0.458307
\(952\) 0 0
\(953\) −9.48751 7.96097i −0.307331 0.257881i 0.476057 0.879414i \(-0.342066\pi\)
−0.783388 + 0.621533i \(0.786510\pi\)
\(954\) 0 0
\(955\) −32.3508 + 11.7747i −1.04685 + 0.381021i
\(956\) 0 0
\(957\) 6.43629 + 11.1480i 0.208056 + 0.360363i
\(958\) 0 0
\(959\) 3.85235 + 21.8478i 0.124399 + 0.705501i
\(960\) 0 0
\(961\) −6.38485 + 11.0589i −0.205963 + 0.356738i
\(962\) 0 0
\(963\) −2.98680 + 2.50622i −0.0962482 + 0.0807618i
\(964\) 0 0
\(965\) −8.09240 2.94539i −0.260503 0.0948155i
\(966\) 0 0
\(967\) 0.591929 3.35700i 0.0190352 0.107954i −0.973810 0.227364i \(-0.926989\pi\)
0.992845 + 0.119410i \(0.0381004\pi\)
\(968\) 0 0
\(969\) −4.99613 1.30753i −0.160499 0.0420038i
\(970\) 0 0
\(971\) 2.41323 13.6861i 0.0774442 0.439208i −0.921289 0.388880i \(-0.872862\pi\)
0.998733 0.0503282i \(-0.0160267\pi\)
\(972\) 0 0
\(973\) −13.8221 5.03082i −0.443115 0.161281i
\(974\) 0 0
\(975\) −13.8157 + 11.5927i −0.442456 + 0.371264i
\(976\) 0 0
\(977\) −6.42009 + 11.1199i −0.205397 + 0.355758i −0.950259 0.311460i \(-0.899182\pi\)
0.744862 + 0.667218i \(0.232515\pi\)
\(978\) 0 0
\(979\) 4.01249 + 22.7560i 0.128240 + 0.727283i
\(980\) 0 0
\(981\) 5.79813 + 10.0427i 0.185120 + 0.320638i
\(982\) 0 0
\(983\) −0.814330 + 0.296392i −0.0259731 + 0.00945343i −0.354974 0.934876i \(-0.615510\pi\)
0.329001 + 0.944330i \(0.393288\pi\)
\(984\) 0 0
\(985\) 38.8267 + 32.5794i 1.23712 + 1.03807i
\(986\) 0 0
\(987\) 13.9409 0.443743
\(988\) 0 0
\(989\) −14.2267 −0.452382
\(990\) 0 0
\(991\) 16.0646 + 13.4798i 0.510310 + 0.428201i 0.861238 0.508201i \(-0.169689\pi\)
−0.350928 + 0.936402i \(0.614134\pi\)
\(992\) 0 0
\(993\) −27.7190 + 10.0889i −0.879636 + 0.320161i
\(994\) 0 0
\(995\) 13.7640 + 23.8399i 0.436348 + 0.755776i
\(996\) 0 0
\(997\) 6.90208 + 39.1437i 0.218591 + 1.23969i 0.874565 + 0.484909i \(0.161147\pi\)
−0.655974 + 0.754784i \(0.727742\pi\)
\(998\) 0 0
\(999\) 3.37939 5.85327i 0.106919 0.185189i
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 912.2.bo.a.625.1 6
4.3 odd 2 114.2.i.a.55.1 6
12.11 even 2 342.2.u.e.55.1 6
19.9 even 9 inner 912.2.bo.a.769.1 6
76.3 even 18 2166.2.a.s.1.3 3
76.35 odd 18 2166.2.a.q.1.3 3
76.47 odd 18 114.2.i.a.85.1 yes 6
228.35 even 18 6498.2.a.br.1.1 3
228.47 even 18 342.2.u.e.199.1 6
228.155 odd 18 6498.2.a.bm.1.1 3
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
114.2.i.a.55.1 6 4.3 odd 2
114.2.i.a.85.1 yes 6 76.47 odd 18
342.2.u.e.55.1 6 12.11 even 2
342.2.u.e.199.1 6 228.47 even 18
912.2.bo.a.625.1 6 1.1 even 1 trivial
912.2.bo.a.769.1 6 19.9 even 9 inner
2166.2.a.q.1.3 3 76.35 odd 18
2166.2.a.s.1.3 3 76.3 even 18
6498.2.a.bm.1.1 3 228.155 odd 18
6498.2.a.br.1.1 3 228.35 even 18