Properties

Label 864.2.y.a.97.3
Level $864$
Weight $2$
Character 864.97
Analytic conductor $6.899$
Analytic rank $0$
Dimension $48$
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] = [864,2,Mod(97,864)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(864, base_ring=CyclotomicField(18))
 
chi = DirichletCharacter(H, H._module([0, 0, 4]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("864.97");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 864 = 2^{5} \cdot 3^{3} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 864.y (of order \(9\), degree \(6\), 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: \(6.89907473464\)
Analytic rank: \(0\)
Dimension: \(48\)
Relative dimension: \(8\) over \(\Q(\zeta_{9})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label 97.3
Character \(\chi\) \(=\) 864.97
Dual form 864.2.y.a.481.3

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.602286 - 1.62396i) q^{3} +(-2.89262 - 1.05283i) q^{5} +(-0.0578408 + 0.328031i) q^{7} +(-2.27450 + 1.95618i) q^{9} +O(q^{10})\) \(q+(-0.602286 - 1.62396i) q^{3} +(-2.89262 - 1.05283i) q^{5} +(-0.0578408 + 0.328031i) q^{7} +(-2.27450 + 1.95618i) q^{9} +(0.0918319 - 0.0334241i) q^{11} +(-0.709877 + 0.595658i) q^{13} +(0.0324330 + 5.33160i) q^{15} +(-1.04568 - 1.81118i) q^{17} +(-0.0352132 + 0.0609911i) q^{19} +(0.567547 - 0.103638i) q^{21} +(1.09484 + 6.20915i) q^{23} +(3.42857 + 2.87691i) q^{25} +(4.54666 + 2.51553i) q^{27} +(-5.42290 - 4.55035i) q^{29} +(1.69111 + 9.59077i) q^{31} +(-0.109589 - 0.129001i) q^{33} +(0.512672 - 0.887973i) q^{35} +(2.24591 + 3.89004i) q^{37} +(1.39487 + 0.794057i) q^{39} +(0.632082 - 0.530380i) q^{41} +(8.73217 - 3.17825i) q^{43} +(8.63879 - 3.26382i) q^{45} +(-0.949958 + 5.38748i) q^{47} +(6.47359 + 2.35619i) q^{49} +(-2.31148 + 2.78900i) q^{51} -8.63841 q^{53} -0.300825 q^{55} +(0.120256 + 0.0204508i) q^{57} +(13.0152 + 4.73715i) q^{59} +(-0.712093 + 4.03848i) q^{61} +(-0.510129 - 0.859255i) q^{63} +(2.68053 - 0.975633i) q^{65} +(-9.50406 + 7.97485i) q^{67} +(9.42401 - 5.51766i) q^{69} +(-2.92034 - 5.05819i) q^{71} +(-2.07395 + 3.59218i) q^{73} +(2.60702 - 7.30060i) q^{75} +(0.00565252 + 0.0320570i) q^{77} +(-4.81366 - 4.03914i) q^{79} +(1.34673 - 8.89867i) q^{81} +(-11.4212 - 9.58350i) q^{83} +(1.11791 + 6.33997i) q^{85} +(-4.12346 + 11.5472i) q^{87} +(1.08533 - 1.87984i) q^{89} +(-0.154335 - 0.267315i) q^{91} +(14.5565 - 8.52268i) q^{93} +(0.166072 - 0.139351i) q^{95} +(-2.94990 + 1.07368i) q^{97} +(-0.143489 + 0.255663i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 48 q - 12 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 48 q - 12 q^{9} - 12 q^{17} - 48 q^{21} + 24 q^{25} + 6 q^{29} - 6 q^{33} + 30 q^{37} - 12 q^{41} + 30 q^{45} - 6 q^{49} - 36 q^{53} - 6 q^{57} - 12 q^{61} - 60 q^{65} - 78 q^{69} + 48 q^{73} - 12 q^{77} - 36 q^{81} + 102 q^{85} - 66 q^{89} + 36 q^{93} + 6 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/864\mathbb{Z}\right)^\times\).

\(n\) \(325\) \(353\) \(703\)
\(\chi(n)\) \(1\) \(e\left(\frac{2}{9}\right)\) \(1\)

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
\(3\) −0.602286 1.62396i −0.347730 0.937595i
\(4\) 0 0
\(5\) −2.89262 1.05283i −1.29362 0.470839i −0.398705 0.917079i \(-0.630540\pi\)
−0.894913 + 0.446241i \(0.852763\pi\)
\(6\) 0 0
\(7\) −0.0578408 + 0.328031i −0.0218618 + 0.123984i −0.993786 0.111312i \(-0.964495\pi\)
0.971924 + 0.235296i \(0.0756059\pi\)
\(8\) 0 0
\(9\) −2.27450 + 1.95618i −0.758168 + 0.652060i
\(10\) 0 0
\(11\) 0.0918319 0.0334241i 0.0276884 0.0100777i −0.328139 0.944630i \(-0.606421\pi\)
0.355827 + 0.934552i \(0.384199\pi\)
\(12\) 0 0
\(13\) −0.709877 + 0.595658i −0.196885 + 0.165206i −0.735900 0.677090i \(-0.763241\pi\)
0.539016 + 0.842296i \(0.318796\pi\)
\(14\) 0 0
\(15\) 0.0324330 + 5.33160i 0.00837417 + 1.37661i
\(16\) 0 0
\(17\) −1.04568 1.81118i −0.253616 0.439275i 0.710903 0.703290i \(-0.248287\pi\)
−0.964519 + 0.264015i \(0.914953\pi\)
\(18\) 0 0
\(19\) −0.0352132 + 0.0609911i −0.00807847 + 0.0139923i −0.870036 0.492988i \(-0.835905\pi\)
0.861958 + 0.506980i \(0.169238\pi\)
\(20\) 0 0
\(21\) 0.567547 0.103638i 0.123849 0.0226156i
\(22\) 0 0
\(23\) 1.09484 + 6.20915i 0.228290 + 1.29470i 0.856295 + 0.516487i \(0.172761\pi\)
−0.628005 + 0.778209i \(0.716128\pi\)
\(24\) 0 0
\(25\) 3.42857 + 2.87691i 0.685715 + 0.575383i
\(26\) 0 0
\(27\) 4.54666 + 2.51553i 0.875005 + 0.484113i
\(28\) 0 0
\(29\) −5.42290 4.55035i −1.00701 0.844979i −0.0190669 0.999818i \(-0.506070\pi\)
−0.987940 + 0.154839i \(0.950514\pi\)
\(30\) 0 0
\(31\) 1.69111 + 9.59077i 0.303732 + 1.72255i 0.629412 + 0.777072i \(0.283296\pi\)
−0.325679 + 0.945480i \(0.605593\pi\)
\(32\) 0 0
\(33\) −0.109589 0.129001i −0.0190769 0.0224561i
\(34\) 0 0
\(35\) 0.512672 0.887973i 0.0866573 0.150095i
\(36\) 0 0
\(37\) 2.24591 + 3.89004i 0.369226 + 0.639518i 0.989445 0.144911i \(-0.0462895\pi\)
−0.620219 + 0.784429i \(0.712956\pi\)
\(38\) 0 0
\(39\) 1.39487 + 0.794057i 0.223359 + 0.127151i
\(40\) 0 0
\(41\) 0.632082 0.530380i 0.0987147 0.0828314i −0.592095 0.805868i \(-0.701699\pi\)
0.690809 + 0.723037i \(0.257254\pi\)
\(42\) 0 0
\(43\) 8.73217 3.17825i 1.33164 0.484679i 0.424473 0.905441i \(-0.360459\pi\)
0.907171 + 0.420762i \(0.138237\pi\)
\(44\) 0 0
\(45\) 8.63879 3.26382i 1.28779 0.486542i
\(46\) 0 0
\(47\) −0.949958 + 5.38748i −0.138566 + 0.785844i 0.833745 + 0.552150i \(0.186193\pi\)
−0.972310 + 0.233694i \(0.924919\pi\)
\(48\) 0 0
\(49\) 6.47359 + 2.35619i 0.924798 + 0.336599i
\(50\) 0 0
\(51\) −2.31148 + 2.78900i −0.323672 + 0.390538i
\(52\) 0 0
\(53\) −8.63841 −1.18658 −0.593288 0.804990i \(-0.702171\pi\)
−0.593288 + 0.804990i \(0.702171\pi\)
\(54\) 0 0
\(55\) −0.300825 −0.0405632
\(56\) 0 0
\(57\) 0.120256 + 0.0204508i 0.0159282 + 0.00270878i
\(58\) 0 0
\(59\) 13.0152 + 4.73715i 1.69444 + 0.616725i 0.995173 0.0981376i \(-0.0312885\pi\)
0.699265 + 0.714863i \(0.253511\pi\)
\(60\) 0 0
\(61\) −0.712093 + 4.03848i −0.0911741 + 0.517074i 0.904679 + 0.426095i \(0.140111\pi\)
−0.995853 + 0.0909796i \(0.971000\pi\)
\(62\) 0 0
\(63\) −0.510129 0.859255i −0.0642702 0.108256i
\(64\) 0 0
\(65\) 2.68053 0.975633i 0.332479 0.121012i
\(66\) 0 0
\(67\) −9.50406 + 7.97485i −1.16111 + 0.974283i −0.999920 0.0126410i \(-0.995976\pi\)
−0.161185 + 0.986924i \(0.551532\pi\)
\(68\) 0 0
\(69\) 9.42401 5.51766i 1.13452 0.664248i
\(70\) 0 0
\(71\) −2.92034 5.05819i −0.346581 0.600296i 0.639059 0.769158i \(-0.279324\pi\)
−0.985640 + 0.168862i \(0.945991\pi\)
\(72\) 0 0
\(73\) −2.07395 + 3.59218i −0.242737 + 0.420433i −0.961493 0.274829i \(-0.911379\pi\)
0.718756 + 0.695263i \(0.244712\pi\)
\(74\) 0 0
\(75\) 2.60702 7.30060i 0.301032 0.843000i
\(76\) 0 0
\(77\) 0.00565252 + 0.0320570i 0.000644164 + 0.00365324i
\(78\) 0 0
\(79\) −4.81366 4.03914i −0.541579 0.454438i 0.330499 0.943806i \(-0.392783\pi\)
−0.872077 + 0.489368i \(0.837227\pi\)
\(80\) 0 0
\(81\) 1.34673 8.89867i 0.149636 0.988741i
\(82\) 0 0
\(83\) −11.4212 9.58350i −1.25364 1.05193i −0.996330 0.0855956i \(-0.972721\pi\)
−0.257306 0.966330i \(-0.582835\pi\)
\(84\) 0 0
\(85\) 1.11791 + 6.33997i 0.121254 + 0.687667i
\(86\) 0 0
\(87\) −4.12346 + 11.5472i −0.442081 + 1.23799i
\(88\) 0 0
\(89\) 1.08533 1.87984i 0.115044 0.199263i −0.802753 0.596312i \(-0.796632\pi\)
0.917798 + 0.397049i \(0.129966\pi\)
\(90\) 0 0
\(91\) −0.154335 0.267315i −0.0161787 0.0280223i
\(92\) 0 0
\(93\) 14.5565 8.52268i 1.50944 0.883761i
\(94\) 0 0
\(95\) 0.166072 0.139351i 0.0170386 0.0142971i
\(96\) 0 0
\(97\) −2.94990 + 1.07368i −0.299517 + 0.109015i −0.487407 0.873175i \(-0.662057\pi\)
0.187890 + 0.982190i \(0.439835\pi\)
\(98\) 0 0
\(99\) −0.143489 + 0.255663i −0.0144211 + 0.0256951i
\(100\) 0 0
\(101\) −2.78788 + 15.8109i −0.277404 + 1.57324i 0.453815 + 0.891096i \(0.350063\pi\)
−0.731219 + 0.682142i \(0.761048\pi\)
\(102\) 0 0
\(103\) 4.48898 + 1.63386i 0.442313 + 0.160989i 0.553569 0.832803i \(-0.313265\pi\)
−0.111257 + 0.993792i \(0.535488\pi\)
\(104\) 0 0
\(105\) −1.75081 0.297745i −0.170862 0.0290569i
\(106\) 0 0
\(107\) −5.91001 −0.571342 −0.285671 0.958328i \(-0.592216\pi\)
−0.285671 + 0.958328i \(0.592216\pi\)
\(108\) 0 0
\(109\) −10.7056 −1.02541 −0.512706 0.858564i \(-0.671357\pi\)
−0.512706 + 0.858564i \(0.671357\pi\)
\(110\) 0 0
\(111\) 4.96459 5.99019i 0.471218 0.568564i
\(112\) 0 0
\(113\) −5.43312 1.97749i −0.511105 0.186027i 0.0735773 0.997290i \(-0.476558\pi\)
−0.584682 + 0.811263i \(0.698781\pi\)
\(114\) 0 0
\(115\) 3.37020 19.1134i 0.314273 1.78233i
\(116\) 0 0
\(117\) 0.449405 2.74347i 0.0415475 0.253634i
\(118\) 0 0
\(119\) 0.654607 0.238257i 0.0600077 0.0218410i
\(120\) 0 0
\(121\) −8.41917 + 7.06452i −0.765379 + 0.642230i
\(122\) 0 0
\(123\) −1.24201 0.707037i −0.111988 0.0637514i
\(124\) 0 0
\(125\) 0.806989 + 1.39775i 0.0721793 + 0.125018i
\(126\) 0 0
\(127\) 1.63144 2.82574i 0.144767 0.250744i −0.784519 0.620105i \(-0.787090\pi\)
0.929286 + 0.369361i \(0.120423\pi\)
\(128\) 0 0
\(129\) −10.4206 12.2665i −0.917485 1.08000i
\(130\) 0 0
\(131\) 2.51442 + 14.2600i 0.219686 + 1.24590i 0.872588 + 0.488457i \(0.162440\pi\)
−0.652902 + 0.757442i \(0.726449\pi\)
\(132\) 0 0
\(133\) −0.0179702 0.0150788i −0.00155822 0.00130750i
\(134\) 0 0
\(135\) −10.5033 12.0633i −0.903984 1.03824i
\(136\) 0 0
\(137\) −14.6111 12.2602i −1.24831 1.04746i −0.996827 0.0795971i \(-0.974637\pi\)
−0.251485 0.967861i \(-0.580919\pi\)
\(138\) 0 0
\(139\) 0.529619 + 3.00362i 0.0449217 + 0.254764i 0.998996 0.0448077i \(-0.0142675\pi\)
−0.954074 + 0.299571i \(0.903156\pi\)
\(140\) 0 0
\(141\) 9.32120 1.70211i 0.784987 0.143343i
\(142\) 0 0
\(143\) −0.0452801 + 0.0784274i −0.00378651 + 0.00655843i
\(144\) 0 0
\(145\) 10.8956 + 18.8718i 0.904833 + 1.56722i
\(146\) 0 0
\(147\) −0.0725841 11.9320i −0.00598664 0.984132i
\(148\) 0 0
\(149\) −12.7296 + 10.6814i −1.04285 + 0.875055i −0.992324 0.123667i \(-0.960534\pi\)
−0.0505265 + 0.998723i \(0.516090\pi\)
\(150\) 0 0
\(151\) −13.5710 + 4.93945i −1.10439 + 0.401966i −0.828934 0.559346i \(-0.811052\pi\)
−0.275460 + 0.961313i \(0.588830\pi\)
\(152\) 0 0
\(153\) 5.92140 + 2.07399i 0.478717 + 0.167672i
\(154\) 0 0
\(155\) 5.20568 29.5229i 0.418130 2.37133i
\(156\) 0 0
\(157\) −12.7462 4.63925i −1.01726 0.370253i −0.221044 0.975264i \(-0.570946\pi\)
−0.796217 + 0.605011i \(0.793169\pi\)
\(158\) 0 0
\(159\) 5.20279 + 14.0284i 0.412608 + 1.11253i
\(160\) 0 0
\(161\) −2.10012 −0.165513
\(162\) 0 0
\(163\) 9.43138 0.738722 0.369361 0.929286i \(-0.379577\pi\)
0.369361 + 0.929286i \(0.379577\pi\)
\(164\) 0 0
\(165\) 0.181182 + 0.488528i 0.0141050 + 0.0380318i
\(166\) 0 0
\(167\) 2.59637 + 0.945002i 0.200913 + 0.0731264i 0.440517 0.897744i \(-0.354795\pi\)
−0.239604 + 0.970871i \(0.577017\pi\)
\(168\) 0 0
\(169\) −2.10831 + 11.9568i −0.162178 + 0.919755i
\(170\) 0 0
\(171\) −0.0392169 0.207608i −0.00299899 0.0158762i
\(172\) 0 0
\(173\) 8.81604 3.20878i 0.670271 0.243959i 0.0156064 0.999878i \(-0.495032\pi\)
0.654665 + 0.755920i \(0.272810\pi\)
\(174\) 0 0
\(175\) −1.14203 + 0.958277i −0.0863293 + 0.0724389i
\(176\) 0 0
\(177\) −0.145931 23.9893i −0.0109689 1.80315i
\(178\) 0 0
\(179\) −2.89391 5.01240i −0.216301 0.374644i 0.737373 0.675486i \(-0.236066\pi\)
−0.953674 + 0.300841i \(0.902733\pi\)
\(180\) 0 0
\(181\) 6.75357 11.6975i 0.501989 0.869470i −0.498009 0.867172i \(-0.665935\pi\)
0.999997 0.00229800i \(-0.000731477\pi\)
\(182\) 0 0
\(183\) 6.98722 1.27591i 0.516510 0.0943178i
\(184\) 0 0
\(185\) −2.40104 13.6170i −0.176528 1.00114i
\(186\) 0 0
\(187\) −0.156564 0.131373i −0.0114491 0.00960694i
\(188\) 0 0
\(189\) −1.08815 + 1.34595i −0.0791516 + 0.0979033i
\(190\) 0 0
\(191\) 11.3363 + 9.51225i 0.820263 + 0.688282i 0.953034 0.302865i \(-0.0979430\pi\)
−0.132771 + 0.991147i \(0.542387\pi\)
\(192\) 0 0
\(193\) 1.85429 + 10.5162i 0.133475 + 0.756975i 0.975909 + 0.218176i \(0.0700106\pi\)
−0.842434 + 0.538799i \(0.818878\pi\)
\(194\) 0 0
\(195\) −3.19883 3.76547i −0.229073 0.269651i
\(196\) 0 0
\(197\) −6.17840 + 10.7013i −0.440193 + 0.762437i −0.997703 0.0677333i \(-0.978423\pi\)
0.557511 + 0.830170i \(0.311757\pi\)
\(198\) 0 0
\(199\) 2.77528 + 4.80693i 0.196734 + 0.340754i 0.947468 0.319851i \(-0.103633\pi\)
−0.750733 + 0.660605i \(0.770300\pi\)
\(200\) 0 0
\(201\) 18.6750 + 10.6311i 1.31723 + 0.749859i
\(202\) 0 0
\(203\) 1.80632 1.51568i 0.126779 0.106380i
\(204\) 0 0
\(205\) −2.38677 + 0.868714i −0.166699 + 0.0606736i
\(206\) 0 0
\(207\) −14.6364 11.9810i −1.01730 0.832738i
\(208\) 0 0
\(209\) −0.00119513 + 0.00677790i −8.26687e−5 + 0.000468837i
\(210\) 0 0
\(211\) −23.4853 8.54797i −1.61680 0.588466i −0.634029 0.773309i \(-0.718600\pi\)
−0.982768 + 0.184843i \(0.940822\pi\)
\(212\) 0 0
\(213\) −6.45542 + 7.78900i −0.442318 + 0.533694i
\(214\) 0 0
\(215\) −28.6050 −1.95084
\(216\) 0 0
\(217\) −3.24389 −0.220209
\(218\) 0 0
\(219\) 7.08268 + 1.20449i 0.478603 + 0.0813919i
\(220\) 0 0
\(221\) 1.82115 + 0.662844i 0.122504 + 0.0445877i
\(222\) 0 0
\(223\) 3.05241 17.3111i 0.204404 1.15923i −0.693970 0.720004i \(-0.744140\pi\)
0.898374 0.439230i \(-0.144749\pi\)
\(224\) 0 0
\(225\) −13.4261 + 0.163352i −0.895071 + 0.0108901i
\(226\) 0 0
\(227\) 2.65362 0.965838i 0.176127 0.0641049i −0.252452 0.967610i \(-0.581237\pi\)
0.428578 + 0.903505i \(0.359015\pi\)
\(228\) 0 0
\(229\) 18.0037 15.1069i 1.18972 0.998292i 0.189854 0.981812i \(-0.439199\pi\)
0.999864 0.0164797i \(-0.00524589\pi\)
\(230\) 0 0
\(231\) 0.0486550 0.0284870i 0.00320126 0.00187431i
\(232\) 0 0
\(233\) −8.78503 15.2161i −0.575527 0.996841i −0.995984 0.0895291i \(-0.971464\pi\)
0.420458 0.907312i \(-0.361870\pi\)
\(234\) 0 0
\(235\) 8.41995 14.5838i 0.549257 0.951340i
\(236\) 0 0
\(237\) −3.66021 + 10.2499i −0.237756 + 0.665803i
\(238\) 0 0
\(239\) −2.75271 15.6114i −0.178058 1.00982i −0.934555 0.355819i \(-0.884202\pi\)
0.756497 0.653997i \(-0.226909\pi\)
\(240\) 0 0
\(241\) 13.5895 + 11.4030i 0.875379 + 0.734531i 0.965224 0.261425i \(-0.0841925\pi\)
−0.0898443 + 0.995956i \(0.528637\pi\)
\(242\) 0 0
\(243\) −15.2622 + 3.17251i −0.979071 + 0.203517i
\(244\) 0 0
\(245\) −16.2450 13.6311i −1.03785 0.870861i
\(246\) 0 0
\(247\) −0.0113328 0.0642712i −0.000721086 0.00408948i
\(248\) 0 0
\(249\) −8.68442 + 24.3195i −0.550353 + 1.54119i
\(250\) 0 0
\(251\) −12.7955 + 22.1625i −0.807647 + 1.39889i 0.106842 + 0.994276i \(0.465926\pi\)
−0.914489 + 0.404610i \(0.867407\pi\)
\(252\) 0 0
\(253\) 0.308076 + 0.533604i 0.0193686 + 0.0335474i
\(254\) 0 0
\(255\) 9.62257 5.63392i 0.602589 0.352810i
\(256\) 0 0
\(257\) 8.12359 6.81650i 0.506735 0.425201i −0.353243 0.935531i \(-0.614921\pi\)
0.859979 + 0.510330i \(0.170477\pi\)
\(258\) 0 0
\(259\) −1.40596 + 0.511728i −0.0873621 + 0.0317972i
\(260\) 0 0
\(261\) 21.2357 0.258370i 1.31446 0.0159927i
\(262\) 0 0
\(263\) 4.02163 22.8078i 0.247984 1.40639i −0.565474 0.824766i \(-0.691307\pi\)
0.813459 0.581623i \(-0.197582\pi\)
\(264\) 0 0
\(265\) 24.9876 + 9.09475i 1.53498 + 0.558686i
\(266\) 0 0
\(267\) −3.70647 0.630327i −0.226832 0.0385754i
\(268\) 0 0
\(269\) 5.67441 0.345975 0.172987 0.984924i \(-0.444658\pi\)
0.172987 + 0.984924i \(0.444658\pi\)
\(270\) 0 0
\(271\) 32.2235 1.95744 0.978718 0.205207i \(-0.0657869\pi\)
0.978718 + 0.205207i \(0.0657869\pi\)
\(272\) 0 0
\(273\) −0.341156 + 0.411634i −0.0206477 + 0.0249132i
\(274\) 0 0
\(275\) 0.411011 + 0.149596i 0.0247849 + 0.00902096i
\(276\) 0 0
\(277\) 3.06996 17.4106i 0.184456 1.04610i −0.742197 0.670182i \(-0.766216\pi\)
0.926653 0.375919i \(-0.122673\pi\)
\(278\) 0 0
\(279\) −22.6077 18.5061i −1.35349 1.10793i
\(280\) 0 0
\(281\) 12.2941 4.47467i 0.733402 0.266936i 0.0517977 0.998658i \(-0.483505\pi\)
0.681604 + 0.731721i \(0.261283\pi\)
\(282\) 0 0
\(283\) −15.2400 + 12.7879i −0.905923 + 0.760160i −0.971339 0.237698i \(-0.923607\pi\)
0.0654159 + 0.997858i \(0.479163\pi\)
\(284\) 0 0
\(285\) −0.326322 0.185765i −0.0193297 0.0110038i
\(286\) 0 0
\(287\) 0.137421 + 0.238020i 0.00811171 + 0.0140499i
\(288\) 0 0
\(289\) 6.31309 10.9346i 0.371358 0.643211i
\(290\) 0 0
\(291\) 3.52029 + 4.14387i 0.206363 + 0.242918i
\(292\) 0 0
\(293\) 0.558677 + 3.16841i 0.0326382 + 0.185101i 0.996768 0.0803294i \(-0.0255972\pi\)
−0.964130 + 0.265430i \(0.914486\pi\)
\(294\) 0 0
\(295\) −32.6607 27.4056i −1.90158 1.59561i
\(296\) 0 0
\(297\) 0.501608 + 0.0790377i 0.0291062 + 0.00458623i
\(298\) 0 0
\(299\) −4.47573 3.75558i −0.258838 0.217191i
\(300\) 0 0
\(301\) 0.537490 + 3.04826i 0.0309804 + 0.175699i
\(302\) 0 0
\(303\) 27.3553 4.99525i 1.57152 0.286969i
\(304\) 0 0
\(305\) 6.31163 10.9321i 0.361403 0.625968i
\(306\) 0 0
\(307\) 10.3963 + 18.0069i 0.593348 + 1.02771i 0.993778 + 0.111381i \(0.0355275\pi\)
−0.400430 + 0.916327i \(0.631139\pi\)
\(308\) 0 0
\(309\) −0.0503320 8.27399i −0.00286329 0.470691i
\(310\) 0 0
\(311\) 6.80734 5.71204i 0.386009 0.323900i −0.429047 0.903282i \(-0.641151\pi\)
0.815056 + 0.579382i \(0.196706\pi\)
\(312\) 0 0
\(313\) 10.2159 3.71828i 0.577436 0.210169i −0.0367588 0.999324i \(-0.511703\pi\)
0.614194 + 0.789155i \(0.289481\pi\)
\(314\) 0 0
\(315\) 0.570961 + 3.02258i 0.0321700 + 0.170303i
\(316\) 0 0
\(317\) −4.65746 + 26.4138i −0.261589 + 1.48354i 0.516987 + 0.855993i \(0.327054\pi\)
−0.778576 + 0.627551i \(0.784057\pi\)
\(318\) 0 0
\(319\) −0.650086 0.236612i −0.0363979 0.0132477i
\(320\) 0 0
\(321\) 3.55952 + 9.59763i 0.198673 + 0.535687i
\(322\) 0 0
\(323\) 0.147288 0.00819531
\(324\) 0 0
\(325\) −4.14752 −0.230063
\(326\) 0 0
\(327\) 6.44784 + 17.3855i 0.356566 + 0.961421i
\(328\) 0 0
\(329\) −1.71232 0.623232i −0.0944030 0.0343599i
\(330\) 0 0
\(331\) −4.09405 + 23.2185i −0.225029 + 1.27621i 0.637599 + 0.770368i \(0.279928\pi\)
−0.862629 + 0.505837i \(0.831184\pi\)
\(332\) 0 0
\(333\) −12.7179 4.45449i −0.696939 0.244105i
\(334\) 0 0
\(335\) 35.8877 13.0621i 1.96076 0.713657i
\(336\) 0 0
\(337\) −11.1354 + 9.34371i −0.606584 + 0.508984i −0.893554 0.448955i \(-0.851796\pi\)
0.286970 + 0.957939i \(0.407352\pi\)
\(338\) 0 0
\(339\) 0.0609180 + 10.0142i 0.00330861 + 0.543896i
\(340\) 0 0
\(341\) 0.475861 + 0.824215i 0.0257693 + 0.0446337i
\(342\) 0 0
\(343\) −2.31316 + 4.00652i −0.124899 + 0.216332i
\(344\) 0 0
\(345\) −33.0692 + 6.03864i −1.78039 + 0.325109i
\(346\) 0 0
\(347\) 5.04724 + 28.6243i 0.270950 + 1.53663i 0.751540 + 0.659688i \(0.229312\pi\)
−0.480590 + 0.876946i \(0.659577\pi\)
\(348\) 0 0
\(349\) −18.5479 15.5636i −0.992849 0.833099i −0.00687094 0.999976i \(-0.502187\pi\)
−0.985978 + 0.166878i \(0.946632\pi\)
\(350\) 0 0
\(351\) −4.72596 + 0.922539i −0.252253 + 0.0492415i
\(352\) 0 0
\(353\) 8.25585 + 6.92748i 0.439414 + 0.368712i 0.835490 0.549505i \(-0.185184\pi\)
−0.396076 + 0.918218i \(0.629628\pi\)
\(354\) 0 0
\(355\) 3.12205 + 17.7060i 0.165701 + 0.939738i
\(356\) 0 0
\(357\) −0.781181 0.919557i −0.0413445 0.0486681i
\(358\) 0 0
\(359\) −15.9754 + 27.6703i −0.843152 + 1.46038i 0.0440654 + 0.999029i \(0.485969\pi\)
−0.887217 + 0.461353i \(0.847364\pi\)
\(360\) 0 0
\(361\) 9.49752 + 16.4502i 0.499869 + 0.865799i
\(362\) 0 0
\(363\) 16.5433 + 9.41755i 0.868296 + 0.494293i
\(364\) 0 0
\(365\) 9.78109 8.20730i 0.511965 0.429590i
\(366\) 0 0
\(367\) −4.89218 + 1.78061i −0.255370 + 0.0929470i −0.466533 0.884504i \(-0.654497\pi\)
0.211163 + 0.977451i \(0.432275\pi\)
\(368\) 0 0
\(369\) −0.400155 + 2.44282i −0.0208312 + 0.127168i
\(370\) 0 0
\(371\) 0.499652 2.83367i 0.0259407 0.147117i
\(372\) 0 0
\(373\) −23.3419 8.49577i −1.20860 0.439894i −0.342382 0.939561i \(-0.611234\pi\)
−0.866218 + 0.499667i \(0.833456\pi\)
\(374\) 0 0
\(375\) 1.78385 2.15236i 0.0921175 0.111147i
\(376\) 0 0
\(377\) 6.56004 0.337859
\(378\) 0 0
\(379\) 27.2176 1.39808 0.699038 0.715084i \(-0.253612\pi\)
0.699038 + 0.715084i \(0.253612\pi\)
\(380\) 0 0
\(381\) −5.57149 0.947495i −0.285436 0.0485417i
\(382\) 0 0
\(383\) 10.9645 + 3.99075i 0.560259 + 0.203918i 0.606599 0.795008i \(-0.292533\pi\)
−0.0463398 + 0.998926i \(0.514756\pi\)
\(384\) 0 0
\(385\) 0.0173999 0.0986799i 0.000886782 0.00502919i
\(386\) 0 0
\(387\) −13.6441 + 24.3106i −0.693570 + 1.23578i
\(388\) 0 0
\(389\) 7.81324 2.84379i 0.396147 0.144186i −0.136262 0.990673i \(-0.543509\pi\)
0.532409 + 0.846487i \(0.321287\pi\)
\(390\) 0 0
\(391\) 10.1010 8.47576i 0.510830 0.428638i
\(392\) 0 0
\(393\) 21.6432 12.6719i 1.09176 0.639213i
\(394\) 0 0
\(395\) 9.67156 + 16.7516i 0.486629 + 0.842866i
\(396\) 0 0
\(397\) 5.05659 8.75827i 0.253783 0.439565i −0.710781 0.703413i \(-0.751658\pi\)
0.964564 + 0.263848i \(0.0849918\pi\)
\(398\) 0 0
\(399\) −0.0136642 + 0.0382647i −0.000684066 + 0.00191563i
\(400\) 0 0
\(401\) 2.67186 + 15.1529i 0.133426 + 0.756699i 0.975943 + 0.218028i \(0.0699624\pi\)
−0.842516 + 0.538671i \(0.818927\pi\)
\(402\) 0 0
\(403\) −6.91330 5.80094i −0.344376 0.288966i
\(404\) 0 0
\(405\) −13.2643 + 24.3226i −0.659110 + 1.20860i
\(406\) 0 0
\(407\) 0.336268 + 0.282162i 0.0166682 + 0.0139863i
\(408\) 0 0
\(409\) −6.56680 37.2422i −0.324707 1.84151i −0.511724 0.859150i \(-0.670993\pi\)
0.187017 0.982357i \(-0.440118\pi\)
\(410\) 0 0
\(411\) −11.1100 + 31.1120i −0.548016 + 1.53464i
\(412\) 0 0
\(413\) −2.30675 + 3.99540i −0.113508 + 0.196601i
\(414\) 0 0
\(415\) 22.9473 + 39.7459i 1.12644 + 1.95105i
\(416\) 0 0
\(417\) 4.55878 2.66912i 0.223244 0.130707i
\(418\) 0 0
\(419\) −21.1838 + 17.7753i −1.03490 + 0.868380i −0.991425 0.130674i \(-0.958286\pi\)
−0.0434699 + 0.999055i \(0.513841\pi\)
\(420\) 0 0
\(421\) 5.14169 1.87142i 0.250591 0.0912075i −0.213671 0.976906i \(-0.568542\pi\)
0.464262 + 0.885698i \(0.346320\pi\)
\(422\) 0 0
\(423\) −8.37819 14.1121i −0.407361 0.686155i
\(424\) 0 0
\(425\) 1.62540 9.21810i 0.0788435 0.447144i
\(426\) 0 0
\(427\) −1.28356 0.467178i −0.0621158 0.0226083i
\(428\) 0 0
\(429\) 0.154635 + 0.0262974i 0.00746583 + 0.00126965i
\(430\) 0 0
\(431\) −22.4164 −1.07976 −0.539879 0.841743i \(-0.681530\pi\)
−0.539879 + 0.841743i \(0.681530\pi\)
\(432\) 0 0
\(433\) −38.6486 −1.85733 −0.928667 0.370914i \(-0.879044\pi\)
−0.928667 + 0.370914i \(0.879044\pi\)
\(434\) 0 0
\(435\) 24.0848 29.0603i 1.15478 1.39334i
\(436\) 0 0
\(437\) −0.417256 0.151869i −0.0199600 0.00726486i
\(438\) 0 0
\(439\) −0.129035 + 0.731792i −0.00615849 + 0.0349265i −0.987732 0.156158i \(-0.950089\pi\)
0.981574 + 0.191084i \(0.0612003\pi\)
\(440\) 0 0
\(441\) −19.3333 + 7.30433i −0.920635 + 0.347825i
\(442\) 0 0
\(443\) 17.9081 6.51802i 0.850840 0.309680i 0.120457 0.992719i \(-0.461564\pi\)
0.730383 + 0.683038i \(0.239342\pi\)
\(444\) 0 0
\(445\) −5.11858 + 4.29500i −0.242644 + 0.203603i
\(446\) 0 0
\(447\) 25.0131 + 14.2391i 1.18308 + 0.673488i
\(448\) 0 0
\(449\) 16.7956 + 29.0909i 0.792635 + 1.37288i 0.924330 + 0.381594i \(0.124625\pi\)
−0.131695 + 0.991290i \(0.542042\pi\)
\(450\) 0 0
\(451\) 0.0403179 0.0698326i 0.00189849 0.00328829i
\(452\) 0 0
\(453\) 16.1951 + 19.0639i 0.760912 + 0.895698i
\(454\) 0 0
\(455\) 0.164994 + 0.935729i 0.00773505 + 0.0438676i
\(456\) 0 0
\(457\) −20.9248 17.5580i −0.978822 0.821329i 0.00508919 0.999987i \(-0.498380\pi\)
−0.983911 + 0.178658i \(0.942824\pi\)
\(458\) 0 0
\(459\) −0.198305 10.8653i −0.00925609 0.507147i
\(460\) 0 0
\(461\) 6.47834 + 5.43597i 0.301726 + 0.253179i 0.781062 0.624453i \(-0.214678\pi\)
−0.479336 + 0.877631i \(0.659122\pi\)
\(462\) 0 0
\(463\) −3.61095 20.4787i −0.167815 0.951726i −0.946114 0.323833i \(-0.895028\pi\)
0.778299 0.627893i \(-0.216083\pi\)
\(464\) 0 0
\(465\) −51.0793 + 9.32739i −2.36875 + 0.432547i
\(466\) 0 0
\(467\) 6.73820 11.6709i 0.311807 0.540065i −0.666947 0.745105i \(-0.732399\pi\)
0.978754 + 0.205040i \(0.0657325\pi\)
\(468\) 0 0
\(469\) −2.06628 3.57890i −0.0954119 0.165258i
\(470\) 0 0
\(471\) 0.142915 + 23.4936i 0.00658519 + 1.08253i
\(472\) 0 0
\(473\) 0.695662 0.583730i 0.0319866 0.0268399i
\(474\) 0 0
\(475\) −0.296197 + 0.107807i −0.0135905 + 0.00494653i
\(476\) 0 0
\(477\) 19.6481 16.8983i 0.899624 0.773719i
\(478\) 0 0
\(479\) −1.31308 + 7.44684i −0.0599961 + 0.340255i −1.00000 0.000909967i \(-0.999710\pi\)
0.940003 + 0.341165i \(0.110821\pi\)
\(480\) 0 0
\(481\) −3.91145 1.42365i −0.178347 0.0649130i
\(482\) 0 0
\(483\) 1.26487 + 3.41052i 0.0575538 + 0.155184i
\(484\) 0 0
\(485\) 9.66334 0.438790
\(486\) 0 0
\(487\) 1.89534 0.0858860 0.0429430 0.999078i \(-0.486327\pi\)
0.0429430 + 0.999078i \(0.486327\pi\)
\(488\) 0 0
\(489\) −5.68039 15.3162i −0.256876 0.692622i
\(490\) 0 0
\(491\) 7.10930 + 2.58757i 0.320838 + 0.116776i 0.497419 0.867511i \(-0.334281\pi\)
−0.176580 + 0.984286i \(0.556504\pi\)
\(492\) 0 0
\(493\) −2.57086 + 14.5801i −0.115786 + 0.656653i
\(494\) 0 0
\(495\) 0.684226 0.588467i 0.0307537 0.0264496i
\(496\) 0 0
\(497\) 1.82816 0.665395i 0.0820041 0.0298471i
\(498\) 0 0
\(499\) −21.7824 + 18.2776i −0.975116 + 0.818220i −0.983345 0.181747i \(-0.941825\pi\)
0.00822925 + 0.999966i \(0.497381\pi\)
\(500\) 0 0
\(501\) −0.0291114 4.78557i −0.00130060 0.213803i
\(502\) 0 0
\(503\) −4.34878 7.53231i −0.193902 0.335849i 0.752638 0.658435i \(-0.228781\pi\)
−0.946540 + 0.322586i \(0.895448\pi\)
\(504\) 0 0
\(505\) 24.7104 42.7996i 1.09960 1.90456i
\(506\) 0 0
\(507\) 20.6872 3.77761i 0.918751 0.167770i
\(508\) 0 0
\(509\) 4.39133 + 24.9045i 0.194642 + 1.10387i 0.912927 + 0.408123i \(0.133817\pi\)
−0.718285 + 0.695749i \(0.755072\pi\)
\(510\) 0 0
\(511\) −1.05839 0.888095i −0.0468204 0.0392870i
\(512\) 0 0
\(513\) −0.313527 + 0.188726i −0.0138426 + 0.00833246i
\(514\) 0 0
\(515\) −11.2647 9.45225i −0.496384 0.416516i
\(516\) 0 0
\(517\) 0.0928351 + 0.526494i 0.00408288 + 0.0231552i
\(518\) 0 0
\(519\) −10.5207 12.3843i −0.461808 0.543611i
\(520\) 0 0
\(521\) −1.19117 + 2.06317i −0.0521863 + 0.0903892i −0.890938 0.454124i \(-0.849952\pi\)
0.838752 + 0.544513i \(0.183286\pi\)
\(522\) 0 0
\(523\) −15.7971 27.3615i −0.690761 1.19643i −0.971589 0.236675i \(-0.923942\pi\)
0.280828 0.959758i \(-0.409391\pi\)
\(524\) 0 0
\(525\) 2.24403 + 1.27746i 0.0979376 + 0.0557527i
\(526\) 0 0
\(527\) 15.6022 13.0918i 0.679643 0.570289i
\(528\) 0 0
\(529\) −15.7419 + 5.72958i −0.684430 + 0.249112i
\(530\) 0 0
\(531\) −38.8699 + 14.6854i −1.68681 + 0.637294i
\(532\) 0 0
\(533\) −0.132776 + 0.753009i −0.00575116 + 0.0326165i
\(534\) 0 0
\(535\) 17.0954 + 6.22222i 0.739099 + 0.269010i
\(536\) 0 0
\(537\) −6.39698 + 7.71850i −0.276050 + 0.333078i
\(538\) 0 0
\(539\) 0.673236 0.0289983
\(540\) 0 0
\(541\) −39.1910 −1.68495 −0.842477 0.538732i \(-0.818903\pi\)
−0.842477 + 0.538732i \(0.818903\pi\)
\(542\) 0 0
\(543\) −23.0639 3.92228i −0.989767 0.168321i
\(544\) 0 0
\(545\) 30.9673 + 11.2712i 1.32649 + 0.482803i
\(546\) 0 0
\(547\) 2.73073 15.4868i 0.116758 0.662166i −0.869107 0.494624i \(-0.835306\pi\)
0.985865 0.167542i \(-0.0535831\pi\)
\(548\) 0 0
\(549\) −6.28033 10.5785i −0.268038 0.451480i
\(550\) 0 0
\(551\) 0.468489 0.170516i 0.0199583 0.00726422i
\(552\) 0 0
\(553\) 1.60339 1.34540i 0.0681830 0.0572124i
\(554\) 0 0
\(555\) −20.6673 + 12.1005i −0.877278 + 0.513637i
\(556\) 0 0
\(557\) 5.08750 + 8.81182i 0.215564 + 0.373369i 0.953447 0.301561i \(-0.0975075\pi\)
−0.737883 + 0.674929i \(0.764174\pi\)
\(558\) 0 0
\(559\) −4.30562 + 7.45755i −0.182108 + 0.315421i
\(560\) 0 0
\(561\) −0.119048 + 0.333378i −0.00502622 + 0.0140752i
\(562\) 0 0
\(563\) 2.71490 + 15.3970i 0.114420 + 0.648906i 0.987036 + 0.160499i \(0.0513105\pi\)
−0.872616 + 0.488406i \(0.837578\pi\)
\(564\) 0 0
\(565\) 13.6340 + 11.4403i 0.573585 + 0.481295i
\(566\) 0 0
\(567\) 2.84115 + 0.956475i 0.119317 + 0.0401682i
\(568\) 0 0
\(569\) 33.2876 + 27.9316i 1.39549 + 1.17095i 0.963061 + 0.269284i \(0.0867871\pi\)
0.432427 + 0.901669i \(0.357657\pi\)
\(570\) 0 0
\(571\) 5.41229 + 30.6946i 0.226497 + 1.28453i 0.859802 + 0.510627i \(0.170587\pi\)
−0.633305 + 0.773902i \(0.718302\pi\)
\(572\) 0 0
\(573\) 8.61986 24.1387i 0.360100 1.00841i
\(574\) 0 0
\(575\) −14.1094 + 24.4383i −0.588405 + 1.01915i
\(576\) 0 0
\(577\) −0.920067 1.59360i −0.0383029 0.0663426i 0.846238 0.532804i \(-0.178862\pi\)
−0.884541 + 0.466462i \(0.845529\pi\)
\(578\) 0 0
\(579\) 15.9611 9.34508i 0.663322 0.388368i
\(580\) 0 0
\(581\) 3.80430 3.19218i 0.157829 0.132434i
\(582\) 0 0
\(583\) −0.793282 + 0.288731i −0.0328544 + 0.0119580i
\(584\) 0 0
\(585\) −4.18836 + 7.46267i −0.173167 + 0.308544i
\(586\) 0 0
\(587\) 1.10216 6.25069i 0.0454912 0.257994i −0.953577 0.301149i \(-0.902630\pi\)
0.999068 + 0.0431553i \(0.0137410\pi\)
\(588\) 0 0
\(589\) −0.644501 0.234579i −0.0265562 0.00966566i
\(590\) 0 0
\(591\) 21.0997 + 3.58824i 0.867925 + 0.147601i
\(592\) 0 0
\(593\) 19.5902 0.804472 0.402236 0.915536i \(-0.368233\pi\)
0.402236 + 0.915536i \(0.368233\pi\)
\(594\) 0 0
\(595\) −2.14437 −0.0879106
\(596\) 0 0
\(597\) 6.13475 7.40210i 0.251079 0.302948i
\(598\) 0 0
\(599\) 36.9383 + 13.4445i 1.50926 + 0.549325i 0.958439 0.285299i \(-0.0920927\pi\)
0.550820 + 0.834624i \(0.314315\pi\)
\(600\) 0 0
\(601\) 4.90024 27.7907i 0.199885 1.13360i −0.705403 0.708807i \(-0.749234\pi\)
0.905288 0.424798i \(-0.139655\pi\)
\(602\) 0 0
\(603\) 6.01677 36.7305i 0.245022 1.49578i
\(604\) 0 0
\(605\) 31.7912 11.5710i 1.29250 0.470430i
\(606\) 0 0
\(607\) −25.6678 + 21.5378i −1.04182 + 0.874194i −0.992210 0.124574i \(-0.960244\pi\)
−0.0496139 + 0.998768i \(0.515799\pi\)
\(608\) 0 0
\(609\) −3.54934 2.02052i −0.143826 0.0818757i
\(610\) 0 0
\(611\) −2.53474 4.39030i −0.102545 0.177612i
\(612\) 0 0
\(613\) 16.8676 29.2156i 0.681278 1.18001i −0.293313 0.956016i \(-0.594758\pi\)
0.974591 0.223992i \(-0.0719088\pi\)
\(614\) 0 0
\(615\) 2.84828 + 3.35281i 0.114854 + 0.135198i
\(616\) 0 0
\(617\) −0.464372 2.63359i −0.0186949 0.106024i 0.974032 0.226408i \(-0.0726984\pi\)
−0.992727 + 0.120384i \(0.961587\pi\)
\(618\) 0 0
\(619\) 22.4711 + 18.8555i 0.903191 + 0.757867i 0.970811 0.239844i \(-0.0770962\pi\)
−0.0676204 + 0.997711i \(0.521541\pi\)
\(620\) 0 0
\(621\) −10.6414 + 30.9850i −0.427025 + 1.24338i
\(622\) 0 0
\(623\) 0.553871 + 0.464753i 0.0221904 + 0.0186199i
\(624\) 0 0
\(625\) −4.74870 26.9312i −0.189948 1.07725i
\(626\) 0 0
\(627\) 0.0117269 0.00214140i 0.000468326 8.55191e-5i
\(628\) 0 0
\(629\) 4.69704 8.13550i 0.187283 0.324384i
\(630\) 0 0
\(631\) 6.64926 + 11.5168i 0.264703 + 0.458478i 0.967486 0.252926i \(-0.0813929\pi\)
−0.702783 + 0.711404i \(0.748060\pi\)
\(632\) 0 0
\(633\) 0.263326 + 43.2876i 0.0104663 + 1.72053i
\(634\) 0 0
\(635\) −7.69416 + 6.45616i −0.305333 + 0.256205i
\(636\) 0 0
\(637\) −5.99894 + 2.18344i −0.237687 + 0.0865109i
\(638\) 0 0
\(639\) 16.5370 + 5.79214i 0.654196 + 0.229134i
\(640\) 0 0
\(641\) 4.52695 25.6736i 0.178804 1.01405i −0.754857 0.655889i \(-0.772294\pi\)
0.933661 0.358158i \(-0.116595\pi\)
\(642\) 0 0
\(643\) 4.18214 + 1.52217i 0.164928 + 0.0600287i 0.423164 0.906053i \(-0.360919\pi\)
−0.258237 + 0.966082i \(0.583142\pi\)
\(644\) 0 0
\(645\) 17.2284 + 46.4534i 0.678367 + 1.82910i
\(646\) 0 0
\(647\) −25.3237 −0.995578 −0.497789 0.867298i \(-0.665855\pi\)
−0.497789 + 0.867298i \(0.665855\pi\)
\(648\) 0 0
\(649\) 1.35355 0.0531314
\(650\) 0 0
\(651\) 1.95375 + 5.26795i 0.0765734 + 0.206467i
\(652\) 0 0
\(653\) 12.8225 + 4.66701i 0.501784 + 0.182634i 0.580496 0.814263i \(-0.302859\pi\)
−0.0787124 + 0.996897i \(0.525081\pi\)
\(654\) 0 0
\(655\) 7.74003 43.8959i 0.302428 1.71515i
\(656\) 0 0
\(657\) −2.30975 12.2274i −0.0901120 0.477038i
\(658\) 0 0
\(659\) −25.2443 + 9.18818i −0.983379 + 0.357921i −0.783153 0.621829i \(-0.786390\pi\)
−0.200226 + 0.979750i \(0.564168\pi\)
\(660\) 0 0
\(661\) 27.2171 22.8378i 1.05862 0.888289i 0.0646483 0.997908i \(-0.479407\pi\)
0.993974 + 0.109619i \(0.0349630\pi\)
\(662\) 0 0
\(663\) −0.0204194 3.35670i −0.000793022 0.130363i
\(664\) 0 0
\(665\) 0.0361056 + 0.0625368i 0.00140012 + 0.00242507i
\(666\) 0 0
\(667\) 22.3166 38.6535i 0.864102 1.49667i
\(668\) 0 0
\(669\) −29.9509 + 5.46922i −1.15797 + 0.211452i
\(670\) 0 0
\(671\) 0.0695896 + 0.394662i 0.00268648 + 0.0152358i
\(672\) 0 0
\(673\) −5.75031 4.82508i −0.221658 0.185993i 0.525196 0.850981i \(-0.323992\pi\)
−0.746854 + 0.664988i \(0.768437\pi\)
\(674\) 0 0
\(675\) 8.35161 + 21.7050i 0.321453 + 0.835427i
\(676\) 0 0
\(677\) −8.47757 7.11352i −0.325819 0.273395i 0.465175 0.885219i \(-0.345992\pi\)
−0.790994 + 0.611824i \(0.790436\pi\)
\(678\) 0 0
\(679\) −0.181575 1.02976i −0.00696821 0.0395187i
\(680\) 0 0
\(681\) −3.16672 3.72766i −0.121349 0.142844i
\(682\) 0 0
\(683\) 16.9052 29.2807i 0.646861 1.12040i −0.337008 0.941502i \(-0.609415\pi\)
0.983868 0.178894i \(-0.0572519\pi\)
\(684\) 0 0
\(685\) 29.3565 + 50.8470i 1.12166 + 1.94276i
\(686\) 0 0
\(687\) −35.3764 20.1386i −1.34969 0.768337i
\(688\) 0 0
\(689\) 6.13221 5.14554i 0.233619 0.196029i
\(690\) 0 0
\(691\) 7.63368 2.77843i 0.290399 0.105697i −0.192713 0.981255i \(-0.561729\pi\)
0.483112 + 0.875559i \(0.339506\pi\)
\(692\) 0 0
\(693\) −0.0755660 0.0618565i −0.00287051 0.00234973i
\(694\) 0 0
\(695\) 1.63030 9.24592i 0.0618410 0.350718i
\(696\) 0 0
\(697\) −1.62157 0.590204i −0.0614214 0.0223556i
\(698\) 0 0
\(699\) −19.4193 + 23.4310i −0.734505 + 0.886242i
\(700\) 0 0
\(701\) 2.64774 0.100004 0.0500019 0.998749i \(-0.484077\pi\)
0.0500019 + 0.998749i \(0.484077\pi\)
\(702\) 0 0
\(703\) −0.316344 −0.0119311
\(704\) 0 0
\(705\) −28.7547 4.89007i −1.08296 0.184171i
\(706\) 0 0
\(707\) −5.02520 1.82902i −0.188992 0.0687875i
\(708\) 0 0
\(709\) 5.65574 32.0753i 0.212406 1.20461i −0.672946 0.739692i \(-0.734971\pi\)
0.885352 0.464922i \(-0.153918\pi\)
\(710\) 0 0
\(711\) 18.8499 0.229343i 0.706928 0.00860104i
\(712\) 0 0
\(713\) −57.6990 + 21.0007i −2.16084 + 0.786483i
\(714\) 0 0
\(715\) 0.213548 0.179188i 0.00798626 0.00670127i
\(716\) 0 0
\(717\) −23.6944 + 13.8728i −0.884882 + 0.518089i
\(718\) 0 0
\(719\) −6.00980 10.4093i −0.224128 0.388201i 0.731930 0.681380i \(-0.238620\pi\)
−0.956057 + 0.293179i \(0.905287\pi\)
\(720\) 0 0
\(721\) −0.795603 + 1.37802i −0.0296298 + 0.0513203i
\(722\) 0 0
\(723\) 10.3332 28.9368i 0.384296 1.07617i
\(724\) 0 0
\(725\) −5.50183 31.2024i −0.204333 1.15883i
\(726\) 0 0
\(727\) −11.3727 9.54283i −0.421790 0.353924i 0.407054 0.913404i \(-0.366556\pi\)
−0.828844 + 0.559480i \(0.811001\pi\)
\(728\) 0 0
\(729\) 14.3443 + 22.8745i 0.531269 + 0.847203i
\(730\) 0 0
\(731\) −14.8875 12.4921i −0.550633 0.462036i
\(732\) 0 0
\(733\) 2.45253 + 13.9090i 0.0905861 + 0.513740i 0.996011 + 0.0892326i \(0.0284414\pi\)
−0.905425 + 0.424507i \(0.860447\pi\)
\(734\) 0 0
\(735\) −12.3523 + 34.5910i −0.455623 + 1.27591i
\(736\) 0 0
\(737\) −0.606224 + 1.05001i −0.0223305 + 0.0386776i
\(738\) 0 0
\(739\) −18.6568 32.3145i −0.686300 1.18871i −0.973026 0.230694i \(-0.925900\pi\)
0.286726 0.958013i \(-0.407433\pi\)
\(740\) 0 0
\(741\) −0.0975485 + 0.0571136i −0.00358353 + 0.00209812i
\(742\) 0 0
\(743\) 26.2069 21.9902i 0.961437 0.806742i −0.0197490 0.999805i \(-0.506287\pi\)
0.981186 + 0.193063i \(0.0618423\pi\)
\(744\) 0 0
\(745\) 48.0676 17.4952i 1.76106 0.640973i
\(746\) 0 0
\(747\) 44.7245 0.544153i 1.63638 0.0199095i
\(748\) 0 0
\(749\) 0.341840 1.93867i 0.0124905 0.0708374i
\(750\) 0 0
\(751\) −27.3393 9.95070i −0.997626 0.363106i −0.208958 0.977925i \(-0.567007\pi\)
−0.788669 + 0.614818i \(0.789229\pi\)
\(752\) 0 0
\(753\) 43.6977 + 7.43129i 1.59243 + 0.270811i
\(754\) 0 0
\(755\) 44.4562 1.61793
\(756\) 0 0
\(757\) −22.3705 −0.813070 −0.406535 0.913635i \(-0.633263\pi\)
−0.406535 + 0.913635i \(0.633263\pi\)
\(758\) 0 0
\(759\) 0.681002 0.821686i 0.0247188 0.0298253i
\(760\) 0 0
\(761\) −3.32069 1.20863i −0.120375 0.0438129i 0.281130 0.959670i \(-0.409291\pi\)
−0.401505 + 0.915857i \(0.631513\pi\)
\(762\) 0 0
\(763\) 0.619221 3.51178i 0.0224173 0.127135i
\(764\) 0 0
\(765\) −14.9448 12.2335i −0.540331 0.442302i
\(766\) 0 0
\(767\) −12.0609 + 4.38982i −0.435495 + 0.158507i
\(768\) 0 0
\(769\) −13.8620 + 11.6316i −0.499876 + 0.419445i −0.857550 0.514401i \(-0.828014\pi\)
0.357674 + 0.933846i \(0.383570\pi\)
\(770\) 0 0
\(771\) −15.9625 9.08691i −0.574874 0.327257i
\(772\) 0 0
\(773\) −12.6595 21.9269i −0.455330 0.788654i 0.543377 0.839489i \(-0.317145\pi\)
−0.998707 + 0.0508344i \(0.983812\pi\)
\(774\) 0 0
\(775\) −21.7937 + 37.7478i −0.782854 + 1.35594i
\(776\) 0 0
\(777\) 1.67782 + 1.97502i 0.0601913 + 0.0708534i
\(778\) 0 0
\(779\) 0.0100908 + 0.0572278i 0.000361541 + 0.00205040i
\(780\) 0 0
\(781\) −0.437246 0.366893i −0.0156459 0.0131285i
\(782\) 0 0
\(783\) −13.2095 34.3303i −0.472071 1.22687i
\(784\) 0 0
\(785\) 31.9857 + 26.8392i 1.14162 + 0.957931i
\(786\) 0 0
\(787\) 2.54013 + 14.4058i 0.0905459 + 0.513511i 0.996022 + 0.0891131i \(0.0284032\pi\)
−0.905476 + 0.424398i \(0.860486\pi\)
\(788\) 0 0
\(789\) −39.4612 + 7.20584i −1.40485 + 0.256535i
\(790\) 0 0
\(791\) 0.962935 1.66785i 0.0342380 0.0593020i
\(792\) 0 0
\(793\) −1.90005 3.29099i −0.0674728 0.116866i
\(794\) 0 0
\(795\) −0.280170 46.0566i −0.00993660 1.63346i
\(796\) 0 0
\(797\) −5.74716 + 4.82244i −0.203575 + 0.170820i −0.738875 0.673842i \(-0.764643\pi\)
0.535300 + 0.844662i \(0.320198\pi\)
\(798\) 0 0
\(799\) 10.7510 3.91306i 0.380344 0.138434i
\(800\) 0 0
\(801\) 1.20873 + 6.39880i 0.0427083 + 0.226090i
\(802\) 0 0
\(803\) −0.0703892 + 0.399197i −0.00248398 + 0.0140874i
\(804\) 0 0
\(805\) 6.07485 + 2.21106i 0.214110 + 0.0779298i
\(806\) 0 0
\(807\) −3.41762 9.21503i −0.120306 0.324384i
\(808\) 0 0
\(809\) −29.1354 −1.02435 −0.512173 0.858882i \(-0.671159\pi\)
−0.512173 + 0.858882i \(0.671159\pi\)
\(810\) 0 0
\(811\) −37.0684 −1.30165 −0.650823 0.759229i \(-0.725576\pi\)
−0.650823 + 0.759229i \(0.725576\pi\)
\(812\) 0 0
\(813\) −19.4078 52.3297i −0.680660 1.83528i
\(814\) 0 0
\(815\) −27.2814 9.92961i −0.955625 0.347819i
\(816\) 0 0
\(817\) −0.113643 + 0.644501i −0.00397586 + 0.0225482i
\(818\) 0 0
\(819\) 0.873951 + 0.306103i 0.0305383 + 0.0106961i
\(820\) 0 0
\(821\) −9.72069 + 3.53804i −0.339254 + 0.123478i −0.506029 0.862517i \(-0.668887\pi\)
0.166774 + 0.985995i \(0.446665\pi\)
\(822\) 0 0
\(823\) 25.1697 21.1199i 0.877360 0.736192i −0.0882747 0.996096i \(-0.528135\pi\)
0.965634 + 0.259904i \(0.0836909\pi\)
\(824\) 0 0
\(825\) −0.00460839 0.757565i −0.000160444 0.0263750i
\(826\) 0 0
\(827\) −18.4009 31.8712i −0.639861 1.10827i −0.985463 0.169890i \(-0.945659\pi\)
0.345602 0.938381i \(-0.387675\pi\)
\(828\) 0 0
\(829\) 17.9054 31.0130i 0.621880 1.07713i −0.367255 0.930120i \(-0.619702\pi\)
0.989135 0.147008i \(-0.0469642\pi\)
\(830\) 0 0
\(831\) −30.1231 + 5.50066i −1.04496 + 0.190816i
\(832\) 0 0
\(833\) −2.50184 14.1887i −0.0866837 0.491608i
\(834\) 0 0
\(835\) −6.51539 5.46706i −0.225474 0.189195i
\(836\) 0 0
\(837\) −16.4369 + 47.8600i −0.568143 + 1.65428i
\(838\) 0 0
\(839\) −19.9870 16.7711i −0.690027 0.579001i 0.228890 0.973452i \(-0.426490\pi\)
−0.918917 + 0.394451i \(0.870935\pi\)
\(840\) 0 0
\(841\) 3.66632 + 20.7927i 0.126425 + 0.716991i
\(842\) 0 0
\(843\) −14.6712 17.2700i −0.505304 0.594812i
\(844\) 0 0
\(845\) 18.6870 32.3668i 0.642852 1.11345i
\(846\) 0 0
\(847\) −1.83041 3.17037i −0.0628938 0.108935i
\(848\) 0 0
\(849\) 29.9458 + 17.0472i 1.02774 + 0.585058i
\(850\) 0 0
\(851\) −21.6949 + 18.2042i −0.743692 + 0.624031i
\(852\) 0 0
\(853\) −20.0619 + 7.30193i −0.686906 + 0.250013i −0.661810 0.749672i \(-0.730211\pi\)
−0.0250961 + 0.999685i \(0.507989\pi\)
\(854\) 0 0
\(855\) −0.105136 + 0.641819i −0.00359556 + 0.0219497i
\(856\) 0 0
\(857\) 4.46145 25.3022i 0.152400 0.864306i −0.808724 0.588189i \(-0.799841\pi\)
0.961124 0.276117i \(-0.0890477\pi\)
\(858\) 0 0
\(859\) −6.92252 2.51959i −0.236193 0.0859673i 0.221212 0.975226i \(-0.428999\pi\)
−0.457405 + 0.889259i \(0.651221\pi\)
\(860\) 0 0
\(861\) 0.303769 0.366523i 0.0103524 0.0124911i
\(862\) 0 0
\(863\) −14.4586 −0.492176 −0.246088 0.969247i \(-0.579145\pi\)
−0.246088 + 0.969247i \(0.579145\pi\)
\(864\) 0 0
\(865\) −28.8797 −0.981940
\(866\) 0 0
\(867\) −21.5596 3.66646i −0.732204 0.124520i
\(868\) 0 0
\(869\) −0.577052 0.210030i −0.0195751 0.00712477i
\(870\) 0 0
\(871\) 1.99643 11.3223i 0.0676465 0.383643i
\(872\) 0 0
\(873\) 4.60926 8.21262i 0.156000 0.277955i
\(874\) 0 0
\(875\) −0.505181 + 0.183871i −0.0170782 + 0.00621597i
\(876\) 0 0
\(877\) 3.35388 2.81424i 0.113252 0.0950301i −0.584403 0.811464i \(-0.698671\pi\)
0.697655 + 0.716434i \(0.254227\pi\)
\(878\) 0 0
\(879\) 4.80890 2.81556i 0.162200 0.0949665i
\(880\) 0 0
\(881\) −2.66740 4.62007i −0.0898669 0.155654i 0.817588 0.575804i \(-0.195311\pi\)
−0.907455 + 0.420150i \(0.861977\pi\)
\(882\) 0 0
\(883\) 13.5393 23.4508i 0.455635 0.789184i −0.543089 0.839675i \(-0.682745\pi\)
0.998724 + 0.0504914i \(0.0160788\pi\)
\(884\) 0 0
\(885\) −24.8345 + 69.5457i −0.834803 + 2.33775i
\(886\) 0 0
\(887\) 5.99487 + 33.9986i 0.201288 + 1.14156i 0.903175 + 0.429273i \(0.141230\pi\)
−0.701887 + 0.712289i \(0.747659\pi\)
\(888\) 0 0
\(889\) 0.832568 + 0.698607i 0.0279234 + 0.0234305i
\(890\) 0 0
\(891\) −0.173757 0.862195i −0.00582109 0.0288846i
\(892\) 0 0
\(893\) −0.295137 0.247649i −0.00987639 0.00828727i
\(894\) 0 0
\(895\) 3.09379 + 17.5457i 0.103414 + 0.586490i
\(896\) 0 0
\(897\) −3.40325 + 9.53035i −0.113631 + 0.318209i
\(898\) 0 0
\(899\) 34.4706 59.7049i 1.14966 1.99127i
\(900\) 0 0
\(901\) 9.03305 + 15.6457i 0.300935 + 0.521234i
\(902\) 0 0
\(903\) 4.62653 2.70879i 0.153961 0.0901428i
\(904\) 0 0
\(905\) −31.8510 + 26.7261i −1.05876 + 0.888407i
\(906\) 0 0
\(907\) 13.9575 5.08010i 0.463450 0.168682i −0.0997331 0.995014i \(-0.531799\pi\)
0.563183 + 0.826332i \(0.309577\pi\)
\(908\) 0 0
\(909\) −24.5878 41.4154i −0.815526 1.37366i
\(910\) 0 0
\(911\) −2.28045 + 12.9331i −0.0755548 + 0.428492i 0.923443 + 0.383735i \(0.125363\pi\)
−0.998998 + 0.0447571i \(0.985749\pi\)
\(912\) 0 0
\(913\) −1.36915 0.498329i −0.0453122 0.0164923i
\(914\) 0 0
\(915\) −21.5547 3.66562i −0.712575 0.121182i
\(916\) 0 0
\(917\) −4.82315 −0.159275
\(918\) 0 0
\(919\) −27.3820 −0.903250 −0.451625 0.892208i \(-0.649156\pi\)
−0.451625 + 0.892208i \(0.649156\pi\)
\(920\) 0 0
\(921\) 22.9810 27.7285i 0.757250 0.913685i
\(922\) 0 0
\(923\) 5.08603 + 1.85116i 0.167409 + 0.0609318i
\(924\) 0 0
\(925\) −3.49103 + 19.7986i −0.114784 + 0.650974i
\(926\) 0 0
\(927\) −13.4063 + 5.06504i −0.440321 + 0.166358i
\(928\) 0 0
\(929\) −23.7384 + 8.64007i −0.778832 + 0.283472i −0.700685 0.713470i \(-0.747122\pi\)
−0.0781462 + 0.996942i \(0.524900\pi\)
\(930\) 0 0
\(931\) −0.371663 + 0.311862i −0.0121808 + 0.0102209i
\(932\) 0 0
\(933\) −13.3761 7.61458i −0.437914 0.249290i
\(934\) 0 0
\(935\) 0.314567 + 0.544847i 0.0102875 + 0.0178184i
\(936\) 0 0
\(937\) 16.0584 27.8140i 0.524605 0.908643i −0.474984 0.879994i \(-0.657546\pi\)
0.999590 0.0286488i \(-0.00912046\pi\)
\(938\) 0 0
\(939\) −12.1912 14.3507i −0.397845 0.468318i
\(940\) 0 0
\(941\) −0.719414 4.08000i −0.0234522 0.133004i 0.970834 0.239754i \(-0.0770668\pi\)
−0.994286 + 0.106750i \(0.965956\pi\)
\(942\) 0 0
\(943\) 3.98524 + 3.34401i 0.129777 + 0.108896i
\(944\) 0 0
\(945\) 4.56466 2.74767i 0.148489 0.0893819i
\(946\) 0 0
\(947\) 1.15127 + 0.966033i 0.0374113 + 0.0313918i 0.661302 0.750120i \(-0.270004\pi\)
−0.623890 + 0.781512i \(0.714449\pi\)
\(948\) 0 0
\(949\) −0.667463 3.78537i −0.0216668 0.122878i
\(950\) 0 0
\(951\) 45.7000 8.34510i 1.48193 0.270609i
\(952\) 0 0
\(953\) −13.8407 + 23.9729i −0.448346 + 0.776558i −0.998279 0.0586513i \(-0.981320\pi\)
0.549933 + 0.835209i \(0.314653\pi\)
\(954\) 0 0
\(955\) −22.7767 39.4504i −0.737037 1.27659i
\(956\) 0 0
\(957\) 0.00728899 + 1.19822i 0.000235620 + 0.0387331i
\(958\) 0 0
\(959\) 4.86684 4.08377i 0.157159 0.131872i
\(960\) 0 0
\(961\) −59.9925 + 21.8355i −1.93524 + 0.704370i
\(962\) 0 0
\(963\) 13.4423 11.5610i 0.433173 0.372549i
\(964\) 0 0
\(965\) 5.70800 32.3717i 0.183747 1.04208i
\(966\) 0 0
\(967\) 25.2872 + 9.20379i 0.813182 + 0.295974i 0.714937 0.699188i \(-0.246455\pi\)
0.0982442 + 0.995162i \(0.468677\pi\)
\(968\) 0 0
\(969\) −0.0887093 0.239190i −0.00284975 0.00768388i
\(970\) 0 0
\(971\) 0.449240 0.0144168 0.00720839 0.999974i \(-0.497705\pi\)
0.00720839 + 0.999974i \(0.497705\pi\)
\(972\) 0 0
\(973\) −1.01591 −0.0325687
\(974\) 0 0
\(975\) 2.49800 + 6.73542i 0.0799999 + 0.215706i
\(976\) 0 0
\(977\) −15.8034 5.75198i −0.505597 0.184022i 0.0766127 0.997061i \(-0.475590\pi\)
−0.582210 + 0.813039i \(0.697812\pi\)
\(978\) 0 0
\(979\) 0.0368357 0.208906i 0.00117727 0.00667665i
\(980\) 0 0
\(981\) 24.3500 20.9421i 0.777434 0.668630i
\(982\) 0 0
\(983\) −28.7692 + 10.4711i −0.917596 + 0.333978i −0.757282 0.653089i \(-0.773473\pi\)
−0.160314 + 0.987066i \(0.551251\pi\)
\(984\) 0 0
\(985\) 29.1384 24.4500i 0.928426 0.779042i
\(986\) 0 0
\(987\) 0.0191991 + 3.15610i 0.000611113 + 0.100460i
\(988\) 0 0
\(989\) 29.2946 + 50.7397i 0.931513 + 1.61343i
\(990\) 0 0
\(991\) −8.39924 + 14.5479i −0.266811 + 0.462129i −0.968036 0.250810i \(-0.919303\pi\)
0.701226 + 0.712939i \(0.252636\pi\)
\(992\) 0 0
\(993\) 40.1718 7.33561i 1.27481 0.232789i
\(994\) 0 0
\(995\) −2.96697 16.8265i −0.0940591 0.533436i
\(996\) 0 0
\(997\) 18.7023 + 15.6931i 0.592309 + 0.497006i 0.888963 0.457979i \(-0.151426\pi\)
−0.296654 + 0.954985i \(0.595871\pi\)
\(998\) 0 0
\(999\) 0.425918 + 23.3363i 0.0134755 + 0.738329i
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 864.2.y.a.97.3 48
4.3 odd 2 inner 864.2.y.a.97.6 yes 48
27.22 even 9 inner 864.2.y.a.481.3 yes 48
108.103 odd 18 inner 864.2.y.a.481.6 yes 48
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
864.2.y.a.97.3 48 1.1 even 1 trivial
864.2.y.a.97.6 yes 48 4.3 odd 2 inner
864.2.y.a.481.3 yes 48 27.22 even 9 inner
864.2.y.a.481.6 yes 48 108.103 odd 18 inner