Properties

Label 882.3.n.d.19.2
Level $882$
Weight $3$
Character 882.19
Analytic conductor $24.033$
Analytic rank $0$
Dimension $4$
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] = [882,3,Mod(19,882)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(882, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([0, 5]))
 
N = Newforms(chi, 3, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("882.19");
 
S:= CuspForms(chi, 3);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 882 = 2 \cdot 3^{2} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 882.n (of order \(6\), degree \(2\), 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: \(24.0327593166\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\Q(\sqrt{2}, \sqrt{-3})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{4} + 2x^{2} + 4 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{25}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 42)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 19.2
Root \(0.707107 - 1.22474i\) of defining polynomial
Character \(\chi\) \(=\) 882.19
Dual form 882.3.n.d.325.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.707107 - 1.22474i) q^{2} +(-1.00000 - 1.73205i) q^{4} +(0.878680 + 0.507306i) q^{5} -2.82843 q^{8} +O(q^{10})\) \(q+(0.707107 - 1.22474i) q^{2} +(-1.00000 - 1.73205i) q^{4} +(0.878680 + 0.507306i) q^{5} -2.82843 q^{8} +(1.24264 - 0.717439i) q^{10} +(-5.12132 - 8.87039i) q^{11} -8.95743i q^{13} +(-2.00000 + 3.46410i) q^{16} +(-26.3345 + 15.2042i) q^{17} +(13.9706 + 8.06591i) q^{19} -2.02922i q^{20} -14.4853 q^{22} +(-3.36396 + 5.82655i) q^{23} +(-11.9853 - 20.7591i) q^{25} +(-10.9706 - 6.33386i) q^{26} -30.0000 q^{29} +(43.4558 - 25.0892i) q^{31} +(2.82843 + 4.89898i) q^{32} +43.0041i q^{34} +(-15.4558 + 26.7703i) q^{37} +(19.7574 - 11.4069i) q^{38} +(-2.48528 - 1.43488i) q^{40} +7.10228i q^{41} -74.4264 q^{43} +(-10.2426 + 17.7408i) q^{44} +(4.75736 + 8.23999i) q^{46} +(-50.4853 - 29.1477i) q^{47} -33.8995 q^{50} +(-15.5147 + 8.95743i) q^{52} +(-35.4853 - 61.4623i) q^{53} -10.3923i q^{55} +(-21.2132 + 36.7423i) q^{58} +(0.426407 - 0.246186i) q^{59} +(-2.48528 - 1.43488i) q^{61} -70.9631i q^{62} +8.00000 q^{64} +(4.54416 - 7.87071i) q^{65} +(-13.5147 - 23.4082i) q^{67} +(52.6690 + 30.4085i) q^{68} -50.6102 q^{71} +(-61.1543 + 35.3075i) q^{73} +(21.8579 + 37.8589i) q^{74} -32.2636i q^{76} +(-66.9117 + 115.894i) q^{79} +(-3.51472 + 2.02922i) q^{80} +(8.69848 + 5.02207i) q^{82} +104.415i q^{83} -30.8528 q^{85} +(-52.6274 + 91.1534i) q^{86} +(14.4853 + 25.0892i) q^{88} +(125.548 + 72.4850i) q^{89} +13.4558 q^{92} +(-71.3970 + 41.2211i) q^{94} +(8.18377 + 14.1747i) q^{95} -100.705i q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q - 4 q^{4} + 12 q^{5}+O(q^{10}) \) Copy content Toggle raw display \( 4 q - 4 q^{4} + 12 q^{5} - 12 q^{10} - 12 q^{11} - 8 q^{16} - 12 q^{17} - 12 q^{19} - 24 q^{22} + 12 q^{23} - 14 q^{25} + 24 q^{26} - 120 q^{29} + 72 q^{31} + 40 q^{37} + 96 q^{38} + 24 q^{40} - 128 q^{43} - 24 q^{44} + 36 q^{46} - 168 q^{47} - 96 q^{50} - 96 q^{52} - 108 q^{53} - 168 q^{59} + 24 q^{61} + 32 q^{64} + 120 q^{65} - 88 q^{67} + 24 q^{68} + 120 q^{71} - 24 q^{73} + 144 q^{74} - 64 q^{79} - 48 q^{80} - 84 q^{82} + 216 q^{85} - 120 q^{86} + 24 q^{88} + 324 q^{89} - 48 q^{92} - 48 q^{94} - 120 q^{95}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/882\mathbb{Z}\right)^\times\).

\(n\) \(199\) \(785\)
\(\chi(n)\) \(e\left(\frac{5}{6}\right)\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.707107 1.22474i 0.353553 0.612372i
\(3\) 0 0
\(4\) −1.00000 1.73205i −0.250000 0.433013i
\(5\) 0.878680 + 0.507306i 0.175736 + 0.101461i 0.585288 0.810826i \(-0.300982\pi\)
−0.409552 + 0.912287i \(0.634315\pi\)
\(6\) 0 0
\(7\) 0 0
\(8\) −2.82843 −0.353553
\(9\) 0 0
\(10\) 1.24264 0.717439i 0.124264 0.0717439i
\(11\) −5.12132 8.87039i −0.465575 0.806399i 0.533653 0.845704i \(-0.320819\pi\)
−0.999227 + 0.0393049i \(0.987486\pi\)
\(12\) 0 0
\(13\) 8.95743i 0.689033i −0.938780 0.344516i \(-0.888043\pi\)
0.938780 0.344516i \(-0.111957\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) −2.00000 + 3.46410i −0.125000 + 0.216506i
\(17\) −26.3345 + 15.2042i −1.54909 + 0.894367i −0.550878 + 0.834586i \(0.685707\pi\)
−0.998211 + 0.0597816i \(0.980960\pi\)
\(18\) 0 0
\(19\) 13.9706 + 8.06591i 0.735293 + 0.424521i 0.820355 0.571854i \(-0.193776\pi\)
−0.0850625 + 0.996376i \(0.527109\pi\)
\(20\) 2.02922i 0.101461i
\(21\) 0 0
\(22\) −14.4853 −0.658422
\(23\) −3.36396 + 5.82655i −0.146259 + 0.253328i −0.929842 0.367959i \(-0.880057\pi\)
0.783583 + 0.621287i \(0.213390\pi\)
\(24\) 0 0
\(25\) −11.9853 20.7591i −0.479411 0.830365i
\(26\) −10.9706 6.33386i −0.421945 0.243610i
\(27\) 0 0
\(28\) 0 0
\(29\) −30.0000 −1.03448 −0.517241 0.855840i \(-0.673041\pi\)
−0.517241 + 0.855840i \(0.673041\pi\)
\(30\) 0 0
\(31\) 43.4558 25.0892i 1.40180 0.809330i 0.407224 0.913328i \(-0.366497\pi\)
0.994578 + 0.103998i \(0.0331635\pi\)
\(32\) 2.82843 + 4.89898i 0.0883883 + 0.153093i
\(33\) 0 0
\(34\) 43.0041i 1.26483i
\(35\) 0 0
\(36\) 0 0
\(37\) −15.4558 + 26.7703i −0.417726 + 0.723522i −0.995710 0.0925257i \(-0.970506\pi\)
0.577985 + 0.816048i \(0.303839\pi\)
\(38\) 19.7574 11.4069i 0.519931 0.300182i
\(39\) 0 0
\(40\) −2.48528 1.43488i −0.0621320 0.0358719i
\(41\) 7.10228i 0.173226i 0.996242 + 0.0866132i \(0.0276044\pi\)
−0.996242 + 0.0866132i \(0.972396\pi\)
\(42\) 0 0
\(43\) −74.4264 −1.73085 −0.865423 0.501041i \(-0.832950\pi\)
−0.865423 + 0.501041i \(0.832950\pi\)
\(44\) −10.2426 + 17.7408i −0.232787 + 0.403199i
\(45\) 0 0
\(46\) 4.75736 + 8.23999i 0.103421 + 0.179130i
\(47\) −50.4853 29.1477i −1.07415 0.620164i −0.144841 0.989455i \(-0.546267\pi\)
−0.929314 + 0.369291i \(0.879600\pi\)
\(48\) 0 0
\(49\) 0 0
\(50\) −33.8995 −0.677990
\(51\) 0 0
\(52\) −15.5147 + 8.95743i −0.298360 + 0.172258i
\(53\) −35.4853 61.4623i −0.669534 1.15967i −0.978035 0.208442i \(-0.933161\pi\)
0.308501 0.951224i \(-0.400173\pi\)
\(54\) 0 0
\(55\) 10.3923i 0.188951i
\(56\) 0 0
\(57\) 0 0
\(58\) −21.2132 + 36.7423i −0.365745 + 0.633489i
\(59\) 0.426407 0.246186i 0.00722724 0.00417265i −0.496382 0.868104i \(-0.665338\pi\)
0.503609 + 0.863932i \(0.332005\pi\)
\(60\) 0 0
\(61\) −2.48528 1.43488i −0.0407423 0.0235226i 0.479490 0.877547i \(-0.340821\pi\)
−0.520233 + 0.854024i \(0.674155\pi\)
\(62\) 70.9631i 1.14457i
\(63\) 0 0
\(64\) 8.00000 0.125000
\(65\) 4.54416 7.87071i 0.0699101 0.121088i
\(66\) 0 0
\(67\) −13.5147 23.4082i −0.201712 0.349376i 0.747368 0.664410i \(-0.231317\pi\)
−0.949080 + 0.315035i \(0.897984\pi\)
\(68\) 52.6690 + 30.4085i 0.774545 + 0.447184i
\(69\) 0 0
\(70\) 0 0
\(71\) −50.6102 −0.712819 −0.356410 0.934330i \(-0.615999\pi\)
−0.356410 + 0.934330i \(0.615999\pi\)
\(72\) 0 0
\(73\) −61.1543 + 35.3075i −0.837731 + 0.483664i −0.856492 0.516160i \(-0.827361\pi\)
0.0187616 + 0.999824i \(0.494028\pi\)
\(74\) 21.8579 + 37.8589i 0.295377 + 0.511607i
\(75\) 0 0
\(76\) 32.2636i 0.424521i
\(77\) 0 0
\(78\) 0 0
\(79\) −66.9117 + 115.894i −0.846983 + 1.46702i 0.0369042 + 0.999319i \(0.488250\pi\)
−0.883888 + 0.467699i \(0.845083\pi\)
\(80\) −3.51472 + 2.02922i −0.0439340 + 0.0253653i
\(81\) 0 0
\(82\) 8.69848 + 5.02207i 0.106079 + 0.0612448i
\(83\) 104.415i 1.25802i 0.777398 + 0.629009i \(0.216539\pi\)
−0.777398 + 0.629009i \(0.783461\pi\)
\(84\) 0 0
\(85\) −30.8528 −0.362974
\(86\) −52.6274 + 91.1534i −0.611947 + 1.05992i
\(87\) 0 0
\(88\) 14.4853 + 25.0892i 0.164605 + 0.285105i
\(89\) 125.548 + 72.4850i 1.41065 + 0.814438i 0.995449 0.0952921i \(-0.0303785\pi\)
0.415199 + 0.909730i \(0.363712\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 13.4558 0.146259
\(93\) 0 0
\(94\) −71.3970 + 41.2211i −0.759542 + 0.438522i
\(95\) 8.18377 + 14.1747i 0.0861449 + 0.149207i
\(96\) 0 0
\(97\) 100.705i 1.03820i −0.854714 0.519099i \(-0.826268\pi\)
0.854714 0.519099i \(-0.173732\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) −23.9706 + 41.5182i −0.239706 + 0.415182i
\(101\) 120.276 69.4412i 1.19085 0.687536i 0.232349 0.972632i \(-0.425359\pi\)
0.958499 + 0.285096i \(0.0920255\pi\)
\(102\) 0 0
\(103\) −68.3087 39.4380i −0.663191 0.382893i 0.130301 0.991475i \(-0.458406\pi\)
−0.793492 + 0.608581i \(0.791739\pi\)
\(104\) 25.3354i 0.243610i
\(105\) 0 0
\(106\) −100.368 −0.946864
\(107\) −18.8787 + 32.6988i −0.176436 + 0.305597i −0.940657 0.339358i \(-0.889790\pi\)
0.764221 + 0.644954i \(0.223124\pi\)
\(108\) 0 0
\(109\) −15.9706 27.6618i −0.146519 0.253778i 0.783420 0.621493i \(-0.213474\pi\)
−0.929939 + 0.367715i \(0.880140\pi\)
\(110\) −12.7279 7.34847i −0.115708 0.0668043i
\(111\) 0 0
\(112\) 0 0
\(113\) 106.971 0.946642 0.473321 0.880890i \(-0.343055\pi\)
0.473321 + 0.880890i \(0.343055\pi\)
\(114\) 0 0
\(115\) −5.91169 + 3.41311i −0.0514060 + 0.0296793i
\(116\) 30.0000 + 51.9615i 0.258621 + 0.447944i
\(117\) 0 0
\(118\) 0.696320i 0.00590101i
\(119\) 0 0
\(120\) 0 0
\(121\) 8.04416 13.9329i 0.0664806 0.115148i
\(122\) −3.51472 + 2.02922i −0.0288092 + 0.0166330i
\(123\) 0 0
\(124\) −86.9117 50.1785i −0.700901 0.404665i
\(125\) 49.6861i 0.397489i
\(126\) 0 0
\(127\) 22.0589 0.173692 0.0868460 0.996222i \(-0.472321\pi\)
0.0868460 + 0.996222i \(0.472321\pi\)
\(128\) 5.65685 9.79796i 0.0441942 0.0765466i
\(129\) 0 0
\(130\) −6.42641 11.1309i −0.0494339 0.0856220i
\(131\) −61.4558 35.4815i −0.469129 0.270852i 0.246746 0.969080i \(-0.420639\pi\)
−0.715875 + 0.698229i \(0.753972\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) −38.2254 −0.285264
\(135\) 0 0
\(136\) 74.4853 43.0041i 0.547686 0.316207i
\(137\) −52.8823 91.5947i −0.386002 0.668575i 0.605906 0.795536i \(-0.292811\pi\)
−0.991908 + 0.126962i \(0.959477\pi\)
\(138\) 0 0
\(139\) 181.322i 1.30447i 0.758015 + 0.652237i \(0.226169\pi\)
−0.758015 + 0.652237i \(0.773831\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) −35.7868 + 61.9845i −0.252020 + 0.436511i
\(143\) −79.4558 + 45.8739i −0.555635 + 0.320796i
\(144\) 0 0
\(145\) −26.3604 15.2192i −0.181796 0.104960i
\(146\) 99.8646i 0.684004i
\(147\) 0 0
\(148\) 61.8234 0.417726
\(149\) 20.5736 35.6345i 0.138078 0.239158i −0.788691 0.614790i \(-0.789241\pi\)
0.926769 + 0.375632i \(0.122574\pi\)
\(150\) 0 0
\(151\) −40.1838 69.6003i −0.266118 0.460929i 0.701738 0.712435i \(-0.252408\pi\)
−0.967856 + 0.251506i \(0.919074\pi\)
\(152\) −39.5147 22.8138i −0.259965 0.150091i
\(153\) 0 0
\(154\) 0 0
\(155\) 50.9117 0.328463
\(156\) 0 0
\(157\) −49.6325 + 28.6553i −0.316130 + 0.182518i −0.649666 0.760219i \(-0.725091\pi\)
0.333536 + 0.942737i \(0.391758\pi\)
\(158\) 94.6274 + 163.899i 0.598908 + 1.03734i
\(159\) 0 0
\(160\) 5.73951i 0.0358719i
\(161\) 0 0
\(162\) 0 0
\(163\) 87.4558 151.478i 0.536539 0.929313i −0.462548 0.886594i \(-0.653065\pi\)
0.999087 0.0427185i \(-0.0136019\pi\)
\(164\) 12.3015 7.10228i 0.0750092 0.0433066i
\(165\) 0 0
\(166\) 127.882 + 73.8329i 0.770375 + 0.444776i
\(167\) 196.163i 1.17463i −0.809359 0.587315i \(-0.800185\pi\)
0.809359 0.587315i \(-0.199815\pi\)
\(168\) 0 0
\(169\) 88.7645 0.525234
\(170\) −21.8162 + 37.7868i −0.128331 + 0.222275i
\(171\) 0 0
\(172\) 74.4264 + 128.910i 0.432712 + 0.749479i
\(173\) −33.3640 19.2627i −0.192855 0.111345i 0.400463 0.916313i \(-0.368849\pi\)
−0.593319 + 0.804968i \(0.702183\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 40.9706 0.232787
\(177\) 0 0
\(178\) 177.551 102.509i 0.997479 0.575895i
\(179\) −95.5477 165.494i −0.533786 0.924545i −0.999221 0.0394627i \(-0.987435\pi\)
0.465435 0.885082i \(-0.345898\pi\)
\(180\) 0 0
\(181\) 120.793i 0.667367i 0.942685 + 0.333683i \(0.108292\pi\)
−0.942685 + 0.333683i \(0.891708\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 9.51472 16.4800i 0.0517104 0.0895651i
\(185\) −27.1615 + 15.6817i −0.146819 + 0.0847659i
\(186\) 0 0
\(187\) 269.735 + 155.732i 1.44243 + 0.832789i
\(188\) 116.591i 0.620164i
\(189\) 0 0
\(190\) 23.1472 0.121827
\(191\) 56.0330 97.0520i 0.293367 0.508126i −0.681237 0.732063i \(-0.738558\pi\)
0.974604 + 0.223937i \(0.0718910\pi\)
\(192\) 0 0
\(193\) 11.4558 + 19.8421i 0.0593567 + 0.102809i 0.894177 0.447714i \(-0.147762\pi\)
−0.834820 + 0.550523i \(0.814428\pi\)
\(194\) −123.338 71.2093i −0.635763 0.367058i
\(195\) 0 0
\(196\) 0 0
\(197\) 116.059 0.589131 0.294566 0.955631i \(-0.404825\pi\)
0.294566 + 0.955631i \(0.404825\pi\)
\(198\) 0 0
\(199\) 141.250 81.5506i 0.709798 0.409802i −0.101188 0.994867i \(-0.532264\pi\)
0.810986 + 0.585065i \(0.198931\pi\)
\(200\) 33.8995 + 58.7156i 0.169497 + 0.293578i
\(201\) 0 0
\(202\) 196.409i 0.972323i
\(203\) 0 0
\(204\) 0 0
\(205\) −3.60303 + 6.24063i −0.0175758 + 0.0304421i
\(206\) −96.6030 + 55.7738i −0.468947 + 0.270747i
\(207\) 0 0
\(208\) 31.0294 + 17.9149i 0.149180 + 0.0861291i
\(209\) 165.232i 0.790586i
\(210\) 0 0
\(211\) 106.426 0.504391 0.252195 0.967676i \(-0.418847\pi\)
0.252195 + 0.967676i \(0.418847\pi\)
\(212\) −70.9706 + 122.925i −0.334767 + 0.579833i
\(213\) 0 0
\(214\) 26.6985 + 46.2431i 0.124759 + 0.216089i
\(215\) −65.3970 37.7570i −0.304172 0.175614i
\(216\) 0 0
\(217\) 0 0
\(218\) −45.1716 −0.207209
\(219\) 0 0
\(220\) −18.0000 + 10.3923i −0.0818182 + 0.0472377i
\(221\) 136.191 + 235.890i 0.616248 + 1.06737i
\(222\) 0 0
\(223\) 57.0047i 0.255627i −0.991798 0.127813i \(-0.959204\pi\)
0.991798 0.127813i \(-0.0407958\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 75.6396 131.012i 0.334689 0.579698i
\(227\) −248.912 + 143.709i −1.09653 + 0.633080i −0.935307 0.353838i \(-0.884876\pi\)
−0.161221 + 0.986918i \(0.551543\pi\)
\(228\) 0 0
\(229\) −120.728 69.7023i −0.527196 0.304377i 0.212678 0.977122i \(-0.431782\pi\)
−0.739874 + 0.672746i \(0.765115\pi\)
\(230\) 9.65375i 0.0419728i
\(231\) 0 0
\(232\) 84.8528 0.365745
\(233\) 181.368 314.138i 0.778401 1.34823i −0.154461 0.987999i \(-0.549364\pi\)
0.932863 0.360232i \(-0.117302\pi\)
\(234\) 0 0
\(235\) −29.5736 51.2230i −0.125845 0.217970i
\(236\) −0.852814 0.492372i −0.00361362 0.00208632i
\(237\) 0 0
\(238\) 0 0
\(239\) −18.4781 −0.0773144 −0.0386572 0.999253i \(-0.512308\pi\)
−0.0386572 + 0.999253i \(0.512308\pi\)
\(240\) 0 0
\(241\) −154.243 + 89.0520i −0.640011 + 0.369510i −0.784619 0.619979i \(-0.787141\pi\)
0.144608 + 0.989489i \(0.453808\pi\)
\(242\) −11.3762 19.7041i −0.0470089 0.0814218i
\(243\) 0 0
\(244\) 5.73951i 0.0235226i
\(245\) 0 0
\(246\) 0 0
\(247\) 72.2498 125.140i 0.292509 0.506641i
\(248\) −122.912 + 70.9631i −0.495612 + 0.286142i
\(249\) 0 0
\(250\) −60.8528 35.1334i −0.243411 0.140534i
\(251\) 50.6709i 0.201876i −0.994893 0.100938i \(-0.967816\pi\)
0.994893 0.100938i \(-0.0321844\pi\)
\(252\) 0 0
\(253\) 68.9117 0.272378
\(254\) 15.5980 27.0165i 0.0614094 0.106364i
\(255\) 0 0
\(256\) −8.00000 13.8564i −0.0312500 0.0541266i
\(257\) 162.452 + 93.7919i 0.632110 + 0.364949i 0.781569 0.623819i \(-0.214420\pi\)
−0.149459 + 0.988768i \(0.547753\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) −18.1766 −0.0699101
\(261\) 0 0
\(262\) −86.9117 + 50.1785i −0.331724 + 0.191521i
\(263\) −201.489 348.989i −0.766117 1.32695i −0.939654 0.342127i \(-0.888853\pi\)
0.173537 0.984827i \(-0.444481\pi\)
\(264\) 0 0
\(265\) 72.0076i 0.271727i
\(266\) 0 0
\(267\) 0 0
\(268\) −27.0294 + 46.8164i −0.100856 + 0.174688i
\(269\) 416.158 240.269i 1.54706 0.893193i 0.548691 0.836025i \(-0.315126\pi\)
0.998365 0.0571675i \(-0.0182069\pi\)
\(270\) 0 0
\(271\) 32.3087 + 18.6534i 0.119220 + 0.0688318i 0.558424 0.829556i \(-0.311406\pi\)
−0.439204 + 0.898387i \(0.644739\pi\)
\(272\) 121.634i 0.447184i
\(273\) 0 0
\(274\) −149.574 −0.545889
\(275\) −122.761 + 212.628i −0.446403 + 0.773193i
\(276\) 0 0
\(277\) 41.3381 + 71.5997i 0.149235 + 0.258483i 0.930945 0.365160i \(-0.118986\pi\)
−0.781710 + 0.623642i \(0.785652\pi\)
\(278\) 222.073 + 128.214i 0.798824 + 0.461201i
\(279\) 0 0
\(280\) 0 0
\(281\) 150.853 0.536843 0.268421 0.963302i \(-0.413498\pi\)
0.268421 + 0.963302i \(0.413498\pi\)
\(282\) 0 0
\(283\) 246.088 142.079i 0.869570 0.502046i 0.00236468 0.999997i \(-0.499247\pi\)
0.867205 + 0.497951i \(0.165914\pi\)
\(284\) 50.6102 + 87.6594i 0.178205 + 0.308660i
\(285\) 0 0
\(286\) 129.751i 0.453674i
\(287\) 0 0
\(288\) 0 0
\(289\) 317.838 550.512i 1.09979 1.90488i
\(290\) −37.2792 + 21.5232i −0.128549 + 0.0742178i
\(291\) 0 0
\(292\) 122.309 + 70.6149i 0.418865 + 0.241832i
\(293\) 537.237i 1.83357i 0.399379 + 0.916786i \(0.369226\pi\)
−0.399379 + 0.916786i \(0.630774\pi\)
\(294\) 0 0
\(295\) 0.499567 0.00169345
\(296\) 43.7157 75.7179i 0.147688 0.255804i
\(297\) 0 0
\(298\) −29.0955 50.3948i −0.0976358 0.169110i
\(299\) 52.1909 + 30.1324i 0.174552 + 0.100777i
\(300\) 0 0
\(301\) 0 0
\(302\) −113.657 −0.376347
\(303\) 0 0
\(304\) −55.8823 + 32.2636i −0.183823 + 0.106130i
\(305\) −1.45584 2.52160i −0.00477326 0.00826753i
\(306\) 0 0
\(307\) 34.7430i 0.113169i −0.998398 0.0565847i \(-0.981979\pi\)
0.998398 0.0565847i \(-0.0180211\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 36.0000 62.3538i 0.116129 0.201141i
\(311\) 77.2203 44.5832i 0.248297 0.143354i −0.370687 0.928758i \(-0.620878\pi\)
0.618984 + 0.785403i \(0.287544\pi\)
\(312\) 0 0
\(313\) −450.073 259.850i −1.43793 0.830191i −0.440227 0.897886i \(-0.645102\pi\)
−0.997706 + 0.0676951i \(0.978435\pi\)
\(314\) 81.0495i 0.258119i
\(315\) 0 0
\(316\) 267.647 0.846983
\(317\) 271.014 469.411i 0.854935 1.48079i −0.0217710 0.999763i \(-0.506930\pi\)
0.876706 0.481027i \(-0.159736\pi\)
\(318\) 0 0
\(319\) 153.640 + 266.112i 0.481629 + 0.834206i
\(320\) 7.02944 + 4.05845i 0.0219670 + 0.0126826i
\(321\) 0 0
\(322\) 0 0
\(323\) −490.544 −1.51871
\(324\) 0 0
\(325\) −185.948 + 107.357i −0.572149 + 0.330330i
\(326\) −123.681 214.222i −0.379390 0.657123i
\(327\) 0 0
\(328\) 20.0883i 0.0612448i
\(329\) 0 0
\(330\) 0 0
\(331\) −89.8162 + 155.566i −0.271348 + 0.469989i −0.969207 0.246246i \(-0.920803\pi\)
0.697859 + 0.716235i \(0.254136\pi\)
\(332\) 180.853 104.415i 0.544737 0.314504i
\(333\) 0 0
\(334\) −240.250 138.708i −0.719311 0.415294i
\(335\) 27.4244i 0.0818638i
\(336\) 0 0
\(337\) 291.823 0.865945 0.432972 0.901407i \(-0.357465\pi\)
0.432972 + 0.901407i \(0.357465\pi\)
\(338\) 62.7660 108.714i 0.185698 0.321639i
\(339\) 0 0
\(340\) 30.8528 + 53.4386i 0.0907436 + 0.157172i
\(341\) −445.103 256.980i −1.30529 0.753607i
\(342\) 0 0
\(343\) 0 0
\(344\) 210.510 0.611947
\(345\) 0 0
\(346\) −47.1838 + 27.2416i −0.136369 + 0.0787328i
\(347\) 226.040 + 391.513i 0.651413 + 1.12828i 0.982780 + 0.184778i \(0.0591566\pi\)
−0.331368 + 0.943502i \(0.607510\pi\)
\(348\) 0 0
\(349\) 235.067i 0.673543i 0.941586 + 0.336772i \(0.109335\pi\)
−0.941586 + 0.336772i \(0.890665\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 28.9706 50.1785i 0.0823027 0.142553i
\(353\) 21.8635 12.6229i 0.0619363 0.0357590i −0.468712 0.883351i \(-0.655282\pi\)
0.530648 + 0.847592i \(0.321948\pi\)
\(354\) 0 0
\(355\) −44.4701 25.6748i −0.125268 0.0723235i
\(356\) 289.940i 0.814438i
\(357\) 0 0
\(358\) −270.250 −0.754888
\(359\) −53.1213 + 92.0088i −0.147970 + 0.256292i −0.930477 0.366350i \(-0.880607\pi\)
0.782507 + 0.622642i \(0.213941\pi\)
\(360\) 0 0
\(361\) −50.3823 87.2646i −0.139563 0.241730i
\(362\) 147.941 + 85.4138i 0.408677 + 0.235950i
\(363\) 0 0
\(364\) 0 0
\(365\) −71.6468 −0.196292
\(366\) 0 0
\(367\) −248.044 + 143.208i −0.675868 + 0.390213i −0.798297 0.602265i \(-0.794265\pi\)
0.122428 + 0.992477i \(0.460932\pi\)
\(368\) −13.4558 23.3062i −0.0365648 0.0633321i
\(369\) 0 0
\(370\) 44.3545i 0.119877i
\(371\) 0 0
\(372\) 0 0
\(373\) 211.735 366.736i 0.567654 0.983206i −0.429143 0.903237i \(-0.641184\pi\)
0.996797 0.0799696i \(-0.0254823\pi\)
\(374\) 381.463 220.238i 1.01995 0.588871i
\(375\) 0 0
\(376\) 142.794 + 82.4421i 0.379771 + 0.219261i
\(377\) 268.723i 0.712793i
\(378\) 0 0
\(379\) 101.103 0.266761 0.133381 0.991065i \(-0.457417\pi\)
0.133381 + 0.991065i \(0.457417\pi\)
\(380\) 16.3675 28.3494i 0.0430725 0.0746037i
\(381\) 0 0
\(382\) −79.2426 137.252i −0.207441 0.359299i
\(383\) 190.867 + 110.197i 0.498348 + 0.287721i 0.728031 0.685544i \(-0.240436\pi\)
−0.229683 + 0.973265i \(0.573769\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 32.4020 0.0839431
\(387\) 0 0
\(388\) −174.426 + 100.705i −0.449553 + 0.259549i
\(389\) −191.735 332.095i −0.492892 0.853714i 0.507074 0.861902i \(-0.330727\pi\)
−0.999966 + 0.00818803i \(0.997394\pi\)
\(390\) 0 0
\(391\) 204.586i 0.523238i
\(392\) 0 0
\(393\) 0 0
\(394\) 82.0660 142.143i 0.208289 0.360768i
\(395\) −117.588 + 67.8894i −0.297691 + 0.171872i
\(396\) 0 0
\(397\) 420.177 + 242.589i 1.05838 + 0.611056i 0.924984 0.380007i \(-0.124078\pi\)
0.133396 + 0.991063i \(0.457412\pi\)
\(398\) 230.660i 0.579548i
\(399\) 0 0
\(400\) 95.8823 0.239706
\(401\) −126.588 + 219.257i −0.315680 + 0.546775i −0.979582 0.201045i \(-0.935566\pi\)
0.663901 + 0.747820i \(0.268899\pi\)
\(402\) 0 0
\(403\) −224.735 389.253i −0.557655 0.965887i
\(404\) −240.551 138.882i −0.595424 0.343768i
\(405\) 0 0
\(406\) 0 0
\(407\) 316.617 0.777930
\(408\) 0 0
\(409\) 4.66905 2.69568i 0.0114158 0.00659089i −0.494281 0.869302i \(-0.664569\pi\)
0.505697 + 0.862711i \(0.331235\pi\)
\(410\) 5.09545 + 8.82559i 0.0124279 + 0.0215258i
\(411\) 0 0
\(412\) 157.752i 0.382893i
\(413\) 0 0
\(414\) 0 0
\(415\) −52.9706 + 91.7477i −0.127640 + 0.221079i
\(416\) 43.8823 25.3354i 0.105486 0.0609025i
\(417\) 0 0
\(418\) −202.368 116.837i −0.484133 0.279514i
\(419\) 294.431i 0.702700i −0.936244 0.351350i \(-0.885723\pi\)
0.936244 0.351350i \(-0.114277\pi\)
\(420\) 0 0
\(421\) −290.441 −0.689883 −0.344941 0.938624i \(-0.612101\pi\)
−0.344941 + 0.938624i \(0.612101\pi\)
\(422\) 75.2548 130.345i 0.178329 0.308875i
\(423\) 0 0
\(424\) 100.368 + 173.842i 0.236716 + 0.410004i
\(425\) 631.253 + 364.454i 1.48530 + 0.857540i
\(426\) 0 0
\(427\) 0 0
\(428\) 75.5147 0.176436
\(429\) 0 0
\(430\) −92.4853 + 53.3964i −0.215082 + 0.124178i
\(431\) 25.3568 + 43.9193i 0.0588325 + 0.101901i 0.893942 0.448183i \(-0.147929\pi\)
−0.835109 + 0.550084i \(0.814596\pi\)
\(432\) 0 0
\(433\) 724.761i 1.67381i −0.547347 0.836906i \(-0.684362\pi\)
0.547347 0.836906i \(-0.315638\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) −31.9411 + 55.3237i −0.0732595 + 0.126889i
\(437\) −93.9929 + 54.2668i −0.215087 + 0.124180i
\(438\) 0 0
\(439\) 321.926 + 185.864i 0.733317 + 0.423381i 0.819634 0.572887i \(-0.194177\pi\)
−0.0863177 + 0.996268i \(0.527510\pi\)
\(440\) 29.3939i 0.0668043i
\(441\) 0 0
\(442\) 385.206 0.871507
\(443\) −114.629 + 198.543i −0.258756 + 0.448178i −0.965909 0.258882i \(-0.916646\pi\)
0.707153 + 0.707061i \(0.249979\pi\)
\(444\) 0 0
\(445\) 73.5442 + 127.382i 0.165268 + 0.286252i
\(446\) −69.8162 40.3084i −0.156539 0.0903776i
\(447\) 0 0
\(448\) 0 0
\(449\) 600.323 1.33702 0.668511 0.743702i \(-0.266932\pi\)
0.668511 + 0.743702i \(0.266932\pi\)
\(450\) 0 0
\(451\) 63.0000 36.3731i 0.139690 0.0806498i
\(452\) −106.971 185.278i −0.236661 0.409908i
\(453\) 0 0
\(454\) 406.471i 0.895311i
\(455\) 0 0
\(456\) 0 0
\(457\) −241.912 + 419.003i −0.529347 + 0.916856i 0.470067 + 0.882631i \(0.344230\pi\)
−0.999414 + 0.0342255i \(0.989104\pi\)
\(458\) −170.735 + 98.5739i −0.372784 + 0.215227i
\(459\) 0 0
\(460\) 11.8234 + 6.82623i 0.0257030 + 0.0148396i
\(461\) 274.661i 0.595794i −0.954598 0.297897i \(-0.903715\pi\)
0.954598 0.297897i \(-0.0962852\pi\)
\(462\) 0 0
\(463\) −153.470 −0.331469 −0.165734 0.986170i \(-0.552999\pi\)
−0.165734 + 0.986170i \(0.552999\pi\)
\(464\) 60.0000 103.923i 0.129310 0.223972i
\(465\) 0 0
\(466\) −256.492 444.258i −0.550413 0.953343i
\(467\) −53.4701 30.8710i −0.114497 0.0661049i 0.441658 0.897184i \(-0.354391\pi\)
−0.556155 + 0.831079i \(0.687724\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) −83.6468 −0.177972
\(471\) 0 0
\(472\) −1.20606 + 0.696320i −0.00255521 + 0.00147525i
\(473\) 381.161 + 660.191i 0.805838 + 1.39575i
\(474\) 0 0
\(475\) 386.689i 0.814082i
\(476\) 0 0
\(477\) 0 0
\(478\) −13.0660 + 22.6310i −0.0273348 + 0.0473452i
\(479\) −481.955 + 278.257i −1.00617 + 0.580912i −0.910068 0.414459i \(-0.863971\pi\)
−0.0961020 + 0.995371i \(0.530637\pi\)
\(480\) 0 0
\(481\) 239.793 + 138.445i 0.498530 + 0.287827i
\(482\) 251.877i 0.522567i
\(483\) 0 0
\(484\) −32.1766 −0.0664806
\(485\) 51.0883 88.4876i 0.105337 0.182449i
\(486\) 0 0
\(487\) 162.610 + 281.649i 0.333902 + 0.578335i 0.983273 0.182136i \(-0.0583013\pi\)
−0.649371 + 0.760471i \(0.724968\pi\)
\(488\) 7.02944 + 4.05845i 0.0144046 + 0.00831649i
\(489\) 0 0
\(490\) 0 0
\(491\) −643.477 −1.31054 −0.655272 0.755393i \(-0.727446\pi\)
−0.655272 + 0.755393i \(0.727446\pi\)
\(492\) 0 0
\(493\) 790.036 456.127i 1.60251 0.925208i
\(494\) −102.177 176.975i −0.206835 0.358249i
\(495\) 0 0
\(496\) 200.714i 0.404665i
\(497\) 0 0
\(498\) 0 0
\(499\) −377.713 + 654.218i −0.756939 + 1.31106i 0.187465 + 0.982271i \(0.439973\pi\)
−0.944404 + 0.328786i \(0.893360\pi\)
\(500\) −86.0589 + 49.6861i −0.172118 + 0.0993722i
\(501\) 0 0
\(502\) −62.0589 35.8297i −0.123623 0.0713739i
\(503\) 509.409i 1.01274i 0.862316 + 0.506371i \(0.169013\pi\)
−0.862316 + 0.506371i \(0.830987\pi\)
\(504\) 0 0
\(505\) 140.912 0.279033
\(506\) 48.7279 84.3992i 0.0963002 0.166797i
\(507\) 0 0
\(508\) −22.0589 38.2071i −0.0434230 0.0752108i
\(509\) −666.349 384.717i −1.30913 0.755828i −0.327182 0.944961i \(-0.606099\pi\)
−0.981951 + 0.189133i \(0.939432\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) −22.6274 −0.0441942
\(513\) 0 0
\(514\) 229.742 132.642i 0.446969 0.258058i
\(515\) −40.0143 69.3068i −0.0776976 0.134576i
\(516\) 0 0
\(517\) 597.099i 1.15493i
\(518\) 0 0
\(519\) 0 0
\(520\) −12.8528 + 22.2617i −0.0247169 + 0.0428110i
\(521\) −463.503 + 267.604i −0.889641 + 0.513635i −0.873825 0.486240i \(-0.838368\pi\)
−0.0158162 + 0.999875i \(0.505035\pi\)
\(522\) 0 0
\(523\) −726.999 419.733i −1.39006 0.802549i −0.396735 0.917933i \(-0.629857\pi\)
−0.993321 + 0.115384i \(0.963190\pi\)
\(524\) 141.926i 0.270852i
\(525\) 0 0
\(526\) −569.897 −1.08345
\(527\) −762.926 + 1321.43i −1.44768 + 2.50745i
\(528\) 0 0
\(529\) 241.868 + 418.927i 0.457217 + 0.791922i
\(530\) −88.1909 50.9170i −0.166398 0.0960699i
\(531\) 0 0
\(532\) 0 0
\(533\) 63.6182 0.119359
\(534\) 0 0
\(535\) −33.1766 + 19.1545i −0.0620124 + 0.0358029i
\(536\) 38.2254 + 66.2083i 0.0713160 + 0.123523i
\(537\) 0 0
\(538\) 679.583i 1.26317i
\(539\) 0 0
\(540\) 0 0
\(541\) −142.926 + 247.555i −0.264188 + 0.457588i −0.967351 0.253442i \(-0.918437\pi\)
0.703162 + 0.711029i \(0.251771\pi\)
\(542\) 45.6913 26.3799i 0.0843014 0.0486714i
\(543\) 0 0
\(544\) −148.971 86.0082i −0.273843 0.158103i
\(545\) 32.4078i 0.0594639i
\(546\) 0 0
\(547\) −741.470 −1.35552 −0.677761 0.735283i \(-0.737049\pi\)
−0.677761 + 0.735283i \(0.737049\pi\)
\(548\) −105.765 + 183.189i −0.193001 + 0.334287i
\(549\) 0 0
\(550\) 173.610 + 300.702i 0.315655 + 0.546730i
\(551\) −419.117 241.977i −0.760648 0.439160i
\(552\) 0 0
\(553\) 0 0
\(554\) 116.922 0.211050
\(555\) 0 0
\(556\) 314.059 181.322i 0.564854 0.326119i
\(557\) 417.426 + 723.004i 0.749419 + 1.29803i 0.948101 + 0.317968i \(0.103000\pi\)
−0.198682 + 0.980064i \(0.563666\pi\)
\(558\) 0 0
\(559\) 666.669i 1.19261i
\(560\) 0 0
\(561\) 0 0
\(562\) 106.669 184.756i 0.189803 0.328748i
\(563\) 361.809 208.891i 0.642645 0.371031i −0.142988 0.989724i \(-0.545671\pi\)
0.785633 + 0.618693i \(0.212338\pi\)
\(564\) 0 0
\(565\) 93.9929 + 54.2668i 0.166359 + 0.0960474i
\(566\) 401.861i 0.710001i
\(567\) 0 0
\(568\) 143.147 0.252020
\(569\) 336.515 582.861i 0.591414 1.02436i −0.402628 0.915364i \(-0.631903\pi\)
0.994042 0.108996i \(-0.0347635\pi\)
\(570\) 0 0
\(571\) 132.544 + 229.573i 0.232126 + 0.402055i 0.958434 0.285315i \(-0.0920984\pi\)
−0.726307 + 0.687370i \(0.758765\pi\)
\(572\) 158.912 + 91.7477i 0.277818 + 0.160398i
\(573\) 0 0
\(574\) 0 0
\(575\) 161.272 0.280473
\(576\) 0 0
\(577\) 405.941 234.370i 0.703537 0.406188i −0.105126 0.994459i \(-0.533525\pi\)
0.808664 + 0.588271i \(0.200191\pi\)
\(578\) −449.491 778.541i −0.777666 1.34696i
\(579\) 0 0
\(580\) 60.8767i 0.104960i
\(581\) 0 0
\(582\) 0 0
\(583\) −363.463 + 629.536i −0.623436 + 1.07982i
\(584\) 172.971 99.8646i 0.296182 0.171001i
\(585\) 0 0
\(586\) 657.978 + 379.884i 1.12283 + 0.648266i
\(587\) 120.530i 0.205332i 0.994716 + 0.102666i \(0.0327372\pi\)
−0.994716 + 0.102666i \(0.967263\pi\)
\(588\) 0 0
\(589\) 809.470 1.37431
\(590\) 0.353247 0.611842i 0.000598724 0.00103702i
\(591\) 0 0
\(592\) −61.8234 107.081i −0.104431 0.180880i
\(593\) 486.245 + 280.734i 0.819975 + 0.473413i 0.850408 0.526124i \(-0.176355\pi\)
−0.0304327 + 0.999537i \(0.509689\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) −82.2944 −0.138078
\(597\) 0 0
\(598\) 73.8091 42.6137i 0.123427 0.0712604i
\(599\) 470.054 + 814.158i 0.784732 + 1.35920i 0.929159 + 0.369680i \(0.120533\pi\)
−0.144427 + 0.989515i \(0.546134\pi\)
\(600\) 0 0
\(601\) 563.527i 0.937649i 0.883291 + 0.468824i \(0.155322\pi\)
−0.883291 + 0.468824i \(0.844678\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) −80.3675 + 139.201i −0.133059 + 0.230465i
\(605\) 14.1365 8.16170i 0.0233661 0.0134904i
\(606\) 0 0
\(607\) 265.514 + 153.294i 0.437420 + 0.252544i 0.702503 0.711681i \(-0.252066\pi\)
−0.265083 + 0.964226i \(0.585399\pi\)
\(608\) 91.2553i 0.150091i
\(609\) 0 0
\(610\) −4.11775 −0.00675041
\(611\) −261.088 + 452.218i −0.427313 + 0.740128i
\(612\) 0 0
\(613\) −137.794 238.666i −0.224786 0.389341i 0.731469 0.681875i \(-0.238835\pi\)
−0.956255 + 0.292533i \(0.905502\pi\)
\(614\) −42.5513 24.5670i −0.0693018 0.0400114i
\(615\) 0 0
\(616\) 0 0
\(617\) −461.294 −0.747639 −0.373820 0.927501i \(-0.621952\pi\)
−0.373820 + 0.927501i \(0.621952\pi\)
\(618\) 0 0
\(619\) −324.676 + 187.452i −0.524517 + 0.302830i −0.738781 0.673946i \(-0.764598\pi\)
0.214264 + 0.976776i \(0.431265\pi\)
\(620\) −50.9117 88.1816i −0.0821156 0.142228i
\(621\) 0 0
\(622\) 126.100i 0.202734i
\(623\) 0 0
\(624\) 0 0
\(625\) −274.426 + 475.320i −0.439082 + 0.760512i
\(626\) −636.500 + 367.483i −1.01677 + 0.587034i
\(627\) 0 0
\(628\) 99.2649 + 57.3106i 0.158065 + 0.0912590i
\(629\) 939.978i 1.49440i
\(630\) 0 0
\(631\) −1127.32 −1.78656 −0.893282 0.449496i \(-0.851603\pi\)
−0.893282 + 0.449496i \(0.851603\pi\)
\(632\) 189.255 327.799i 0.299454 0.518669i
\(633\) 0 0
\(634\) −383.272 663.847i −0.604530 1.04708i
\(635\) 19.3827 + 11.1906i 0.0305239 + 0.0176230i
\(636\) 0 0
\(637\) 0 0
\(638\) 434.558 0.681126
\(639\) 0 0
\(640\) 9.94113 5.73951i 0.0155330 0.00896799i
\(641\) −442.176 765.871i −0.689822 1.19481i −0.971895 0.235414i \(-0.924356\pi\)
0.282074 0.959393i \(-0.408978\pi\)
\(642\) 0 0
\(643\) 300.765i 0.467753i −0.972266 0.233876i \(-0.924859\pi\)
0.972266 0.233876i \(-0.0751411\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) −346.867 + 600.791i −0.536946 + 0.930018i
\(647\) 814.587 470.302i 1.25902 0.726896i 0.286137 0.958189i \(-0.407629\pi\)
0.972884 + 0.231292i \(0.0742953\pi\)
\(648\) 0 0
\(649\) −4.36753 2.52160i −0.00672963 0.00388536i
\(650\) 303.652i 0.467157i
\(651\) 0 0
\(652\) −349.823 −0.536539
\(653\) −227.985 + 394.881i −0.349135 + 0.604719i −0.986096 0.166177i \(-0.946858\pi\)
0.636961 + 0.770896i \(0.280191\pi\)
\(654\) 0 0
\(655\) −36.0000 62.3538i −0.0549618 0.0951967i
\(656\) −24.6030 14.2046i −0.0375046 0.0216533i
\(657\) 0 0
\(658\) 0 0
\(659\) −403.684 −0.612571 −0.306285 0.951940i \(-0.599086\pi\)
−0.306285 + 0.951940i \(0.599086\pi\)
\(660\) 0 0
\(661\) −998.881 + 576.704i −1.51117 + 0.872473i −0.511252 + 0.859431i \(0.670818\pi\)
−0.999915 + 0.0130418i \(0.995849\pi\)
\(662\) 127.019 + 220.004i 0.191872 + 0.332332i
\(663\) 0 0
\(664\) 295.331i 0.444776i
\(665\) 0 0
\(666\) 0 0
\(667\) 100.919 174.797i 0.151303 0.262064i
\(668\) −339.765 + 196.163i −0.508629 + 0.293657i
\(669\) 0 0
\(670\) −33.5879 19.3920i −0.0501312 0.0289432i
\(671\) 29.3939i 0.0438061i
\(672\) 0 0
\(673\) −607.440 −0.902585 −0.451293 0.892376i \(-0.649037\pi\)
−0.451293 + 0.892376i \(0.649037\pi\)
\(674\) 206.350 357.409i 0.306158 0.530281i
\(675\) 0 0
\(676\) −88.7645 153.745i −0.131308 0.227433i
\(677\) −985.180 568.794i −1.45521 0.840168i −0.456444 0.889752i \(-0.650877\pi\)
−0.998770 + 0.0495834i \(0.984211\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 87.2649 0.128331
\(681\) 0 0
\(682\) −629.470 + 363.425i −0.922977 + 0.532881i
\(683\) −409.055 708.505i −0.598910 1.03734i −0.992982 0.118263i \(-0.962268\pi\)
0.394073 0.919079i \(-0.371066\pi\)
\(684\) 0 0
\(685\) 107.310i 0.156657i
\(686\) 0 0
\(687\) 0 0
\(688\) 148.853 257.821i 0.216356 0.374739i
\(689\) −550.544 + 317.857i −0.799048 + 0.461331i
\(690\) 0 0
\(691\) −176.912 102.140i −0.256023 0.147815i 0.366496 0.930420i \(-0.380557\pi\)
−0.622519 + 0.782605i \(0.713891\pi\)
\(692\) 77.0508i 0.111345i
\(693\) 0 0
\(694\) 639.338 0.921236
\(695\) −91.9857 + 159.324i −0.132354 + 0.229243i
\(696\) 0 0
\(697\) −107.985 187.035i −0.154928 0.268343i
\(698\) 287.897 + 166.217i 0.412459 + 0.238133i
\(699\) 0 0
\(700\) 0 0
\(701\) 318.853 0.454854 0.227427 0.973795i \(-0.426969\pi\)
0.227427 + 0.973795i \(0.426969\pi\)
\(702\) 0 0
\(703\) −431.854 + 249.331i −0.614301 + 0.354667i
\(704\) −40.9706 70.9631i −0.0581968 0.100800i
\(705\) 0 0
\(706\) 35.7030i 0.0505708i
\(707\) 0 0
\(708\) 0 0
\(709\) 108.823 188.488i 0.153489 0.265850i −0.779019 0.627000i \(-0.784283\pi\)
0.932508 + 0.361150i \(0.117616\pi\)
\(710\) −62.8903 + 36.3097i −0.0885778 + 0.0511404i
\(711\) 0 0
\(712\) −355.103 205.019i −0.498740 0.287947i
\(713\) 337.597i 0.473488i
\(714\) 0 0
\(715\) −93.0883 −0.130193
\(716\) −191.095 + 330.987i −0.266893 + 0.462272i
\(717\) 0 0
\(718\) 75.1249 + 130.120i 0.104631 + 0.181226i
\(719\) 1045.60 + 603.679i 1.45425 + 0.839609i 0.998718 0.0506134i \(-0.0161176\pi\)
0.455527 + 0.890222i \(0.349451\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) −142.503 −0.197372
\(723\) 0 0
\(724\) 209.220 120.793i 0.288978 0.166842i
\(725\) 359.558 + 622.773i 0.495943 + 0.858998i
\(726\) 0 0
\(727\) 123.231i 0.169506i 0.996402 + 0.0847528i \(0.0270100\pi\)
−0.996402 + 0.0847528i \(0.972990\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) −50.6619 + 87.7490i −0.0693999 + 0.120204i
\(731\) 1959.98 1131.60i 2.68124 1.54801i
\(732\) 0 0
\(733\) 325.434 + 187.890i 0.443976 + 0.256330i 0.705283 0.708926i \(-0.250820\pi\)
−0.261307 + 0.965256i \(0.584153\pi\)
\(734\) 405.054i 0.551844i
\(735\) 0 0
\(736\) −38.0589 −0.0517104
\(737\) −138.426 + 239.762i −0.187824 + 0.325321i
\(738\) 0 0
\(739\) −361.265 625.729i −0.488856 0.846724i 0.511061 0.859544i \(-0.329252\pi\)
−0.999918 + 0.0128200i \(0.995919\pi\)
\(740\) 54.3229 + 31.3634i 0.0734094 + 0.0423829i
\(741\) 0 0
\(742\) 0 0
\(743\) −1268.48 −1.70724 −0.853618 0.520899i \(-0.825597\pi\)
−0.853618 + 0.520899i \(0.825597\pi\)
\(744\) 0 0
\(745\) 36.1552 20.8742i 0.0485305 0.0280191i
\(746\) −299.439 518.643i −0.401392 0.695232i
\(747\) 0 0
\(748\) 622.926i 0.832789i
\(749\) 0 0
\(750\) 0 0
\(751\) −219.581 + 380.325i −0.292384 + 0.506425i −0.974373 0.224938i \(-0.927782\pi\)
0.681989 + 0.731363i \(0.261115\pi\)
\(752\) 201.941 116.591i 0.268539 0.155041i
\(753\) 0 0
\(754\) 329.117 + 190.016i 0.436495 + 0.252010i
\(755\) 81.5419i 0.108002i
\(756\) 0 0
\(757\) −668.530 −0.883131 −0.441565 0.897229i \(-0.645577\pi\)
−0.441565 + 0.897229i \(0.645577\pi\)
\(758\) 71.4903 123.825i 0.0943144 0.163357i
\(759\) 0 0
\(760\) −23.1472 40.0921i −0.0304568 0.0527528i
\(761\) 762.202 + 440.058i 1.00158 + 0.578263i 0.908715 0.417416i \(-0.137064\pi\)
0.0928647 + 0.995679i \(0.470398\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) −224.132 −0.293367
\(765\) 0 0
\(766\) 269.927 155.842i 0.352385 0.203450i
\(767\) −2.20519 3.81951i −0.00287509 0.00497980i
\(768\) 0 0
\(769\) 1163.41i 1.51289i −0.654059 0.756444i \(-0.726935\pi\)
0.654059 0.756444i \(-0.273065\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 22.9117 39.6842i 0.0296784 0.0514044i
\(773\) −464.511 + 268.186i −0.600920 + 0.346941i −0.769403 0.638763i \(-0.779446\pi\)
0.168483 + 0.985704i \(0.446113\pi\)
\(774\) 0 0
\(775\) −1041.66 601.403i −1.34408 0.776004i
\(776\) 284.837i 0.367058i
\(777\) 0 0
\(778\) −542.309 −0.697055
\(779\) −57.2864 + 99.2229i −0.0735383 + 0.127372i
\(780\) 0 0
\(781\) 259.191 + 448.932i 0.331871 + 0.574817i
\(782\) −250.566 144.664i −0.320416 0.184992i
\(783\) 0 0
\(784\) 0 0
\(785\) −58.1481 −0.0740740
\(786\) 0 0
\(787\) −72.6762 + 41.9596i −0.0923459 + 0.0533159i −0.545462 0.838136i \(-0.683646\pi\)
0.453116 + 0.891452i \(0.350312\pi\)
\(788\) −116.059 201.020i −0.147283 0.255101i
\(789\) 0 0
\(790\) 192.020i 0.243064i
\(791\) 0 0
\(792\) 0 0
\(793\) −12.8528 + 22.2617i −0.0162078 + 0.0280728i
\(794\) 594.219 343.073i 0.748387 0.432082i
\(795\) 0 0
\(796\) −282.500 163.101i −0.354899 0.204901i
\(797\) 1005.57i 1.26169i −0.775908 0.630846i \(-0.782708\pi\)
0.775908 0.630846i \(-0.217292\pi\)
\(798\) 0 0
\(799\) 1772.67 2.21862
\(800\) 67.7990 117.431i 0.0847487 0.146789i
\(801\) 0 0
\(802\) 179.022 + 310.076i 0.223220 + 0.386628i
\(803\) 626.382 + 361.642i 0.780052 + 0.450363i
\(804\) 0 0
\(805\) 0 0
\(806\) −635.647 −0.788644
\(807\) 0 0
\(808\) −340.191 + 196.409i −0.421028 + 0.243081i
\(809\) −141.426 244.958i −0.174816 0.302791i 0.765281 0.643696i \(-0.222600\pi\)
−0.940098 + 0.340905i \(0.889266\pi\)
\(810\) 0 0
\(811\) 923.997i 1.13933i 0.821877 + 0.569665i \(0.192927\pi\)
−0.821877 + 0.569665i \(0.807073\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 223.882 387.775i 0.275040 0.476383i
\(815\) 153.691 88.7337i 0.188578 0.108876i
\(816\) 0 0
\(817\) −1039.78 600.317i −1.27268 0.734782i
\(818\) 7.62452i 0.00932093i
\(819\) 0 0
\(820\) 14.4121 0.0175758
\(821\) 636.161 1101.86i 0.774862 1.34210i −0.160010 0.987115i \(-0.551153\pi\)
0.934872 0.354985i \(-0.115514\pi\)
\(822\) 0 0
\(823\) −190.926 330.693i −0.231988 0.401815i 0.726405 0.687267i \(-0.241190\pi\)
−0.958393 + 0.285452i \(0.907856\pi\)
\(824\) 193.206 + 111.548i 0.234473 + 0.135373i
\(825\) 0 0
\(826\) 0 0
\(827\) −653.022 −0.789628 −0.394814 0.918761i \(-0.629191\pi\)
−0.394814 + 0.918761i \(0.629191\pi\)
\(828\) 0 0
\(829\) −186.698 + 107.790i −0.225208 + 0.130024i −0.608360 0.793662i \(-0.708172\pi\)
0.383151 + 0.923686i \(0.374839\pi\)
\(830\) 74.9117 + 129.751i 0.0902550 + 0.156326i
\(831\) 0 0
\(832\) 71.6594i 0.0861291i
\(833\) 0 0
\(834\) 0 0
\(835\) 99.5147 172.365i 0.119179 0.206425i
\(836\) −286.191 + 165.232i −0.342334 + 0.197646i
\(837\) 0 0
\(838\) −360.603 208.194i −0.430314 0.248442i
\(839\) 632.267i 0.753596i 0.926295 + 0.376798i \(0.122975\pi\)
−0.926295 + 0.376798i \(0.877025\pi\)
\(840\) 0 0
\(841\) 59.0000 0.0701546
\(842\) −205.373 + 355.716i −0.243910 + 0.422465i
\(843\) 0 0
\(844\) −106.426 184.336i −0.126098 0.218408i
\(845\) 77.9956 + 45.0308i 0.0923024 + 0.0532908i
\(846\) 0 0
\(847\) 0 0
\(848\) 283.882 0.334767
\(849\) 0 0
\(850\) 892.727 515.416i 1.05027 0.606372i
\(851\) −103.986 180.109i −0.122192 0.211643i
\(852\) 0 0
\(853\) 919.650i 1.07814i 0.842262 + 0.539068i \(0.181224\pi\)
−0.842262 + 0.539068i \(0.818776\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 53.3970 92.4863i 0.0623796 0.108045i
\(857\) −456.525 + 263.575i −0.532702 + 0.307556i −0.742116 0.670272i \(-0.766178\pi\)
0.209414 + 0.977827i \(0.432844\pi\)
\(858\) 0 0
\(859\) 207.676 + 119.902i 0.241765 + 0.139583i 0.615988 0.787756i \(-0.288757\pi\)
−0.374223 + 0.927339i \(0.622090\pi\)
\(860\) 151.028i 0.175614i
\(861\) 0 0
\(862\) 71.7199 0.0832018
\(863\) 181.253 313.940i 0.210027 0.363778i −0.741696 0.670737i \(-0.765978\pi\)
0.951723 + 0.306959i \(0.0993115\pi\)
\(864\) 0 0
\(865\) −19.5442 33.8515i −0.0225944 0.0391346i
\(866\) −887.647 512.483i −1.02500 0.591782i
\(867\) 0 0
\(868\) 0 0
\(869\) 1370.70 1.57734
\(870\) 0 0
\(871\) −209.677 + 121.057i −0.240731 + 0.138986i
\(872\) 45.1716 + 78.2395i 0.0518023 + 0.0897242i
\(873\) 0 0
\(874\) 153.490i 0.175617i
\(875\) 0 0
\(876\) 0 0
\(877\) 430.823 746.208i 0.491247 0.850864i −0.508702 0.860942i \(-0.669875\pi\)
0.999949 + 0.0100781i \(0.00320801\pi\)
\(878\) 455.272 262.851i 0.518533 0.299375i
\(879\) 0 0
\(880\) 36.0000 + 20.7846i 0.0409091 + 0.0236189i
\(881\) 334.553i 0.379742i 0.981809 + 0.189871i \(0.0608071\pi\)
−0.981809 + 0.189871i \(0.939193\pi\)
\(882\) 0 0
\(883\) −1488.01 −1.68518 −0.842590 0.538555i \(-0.818970\pi\)
−0.842590 + 0.538555i \(0.818970\pi\)
\(884\) 272.382 471.779i 0.308124 0.533687i
\(885\) 0 0
\(886\) 162.110 + 280.782i 0.182968 + 0.316910i
\(887\) −694.118 400.749i −0.782545 0.451803i 0.0547862 0.998498i \(-0.482552\pi\)
−0.837332 + 0.546695i \(0.815886\pi\)
\(888\) 0 0
\(889\) 0 0
\(890\) 208.014 0.233724
\(891\) 0 0
\(892\) −98.7351 + 57.0047i −0.110690 + 0.0639066i
\(893\) −470.205 814.419i −0.526546 0.912004i
\(894\) 0 0
\(895\) 193.888i 0.216634i
\(896\) 0 0
\(897\) 0 0
\(898\) 424.492 735.242i 0.472709 0.818756i
\(899\) −1303.68 + 752.677i −1.45014 + 0.837238i
\(900\) 0 0
\(901\) 1868.98 + 1079.05i 2.07434 + 1.19762i
\(902\) 102.879i 0.114056i
\(903\) 0 0
\(904\) −302.558 −0.334689
\(905\) −61.2792 + 106.139i −0.0677118 + 0.117280i
\(906\) 0 0
\(907\) 403.640 + 699.124i 0.445027 + 0.770810i 0.998054 0.0623537i \(-0.0198607\pi\)
−0.553027 + 0.833163i \(0.686527\pi\)
\(908\) 497.823 + 287.418i 0.548264 + 0.316540i
\(909\) 0 0
\(910\) 0 0
\(911\) 442.742 0.485996 0.242998 0.970027i \(-0.421869\pi\)
0.242998 + 0.970027i \(0.421869\pi\)
\(912\) 0 0
\(913\) 926.205 534.745i 1.01446 0.585701i
\(914\) 342.115 + 592.560i 0.374305 + 0.648315i
\(915\) 0 0
\(916\) 278.809i 0.304377i
\(917\) 0 0
\(918\) 0 0
\(919\) 59.2275 102.585i 0.0644478 0.111627i −0.832001 0.554774i \(-0.812805\pi\)
0.896449 + 0.443147i \(0.146138\pi\)
\(920\) 16.7208 9.65375i 0.0181748 0.0104932i
\(921\) 0 0
\(922\) −336.390 194.215i −0.364848 0.210645i
\(923\) 453.337i 0.491156i
\(924\) 0 0
\(925\) 740.971 0.801049
\(926\) −108.520 + 187.962i −0.117192 + 0.202982i
\(927\) 0 0
\(928\) −84.8528 146.969i −0.0914362 0.158372i
\(929\) −544.988 314.649i −0.586639 0.338696i 0.177128 0.984188i \(-0.443319\pi\)
−0.763767 + 0.645492i \(0.776653\pi\)
\(930\) 0 0
\(931\) 0 0
\(932\) −725.470 −0.778401
\(933\) 0 0
\(934\) −75.6182 + 43.6582i −0.0809617 + 0.0467432i
\(935\) 158.007 + 273.676i 0.168992 + 0.292702i
\(936\) 0 0
\(937\) 210.631i 0.224793i −0.993663 0.112397i \(-0.964147\pi\)
0.993663 0.112397i \(-0.0358527\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) −59.1472 + 102.446i −0.0629225 + 0.108985i
\(941\) 154.518 89.2112i 0.164206 0.0948047i −0.415645 0.909527i \(-0.636444\pi\)
0.579851 + 0.814722i \(0.303111\pi\)
\(942\) 0 0
\(943\) −41.3818 23.8918i −0.0438832 0.0253360i
\(944\) 1.96949i 0.00208632i
\(945\) 0 0
\(946\) 1078.09 1.13963
\(947\) 211.731 366.730i 0.223581 0.387254i −0.732312 0.680970i \(-0.761559\pi\)
0.955893 + 0.293716i \(0.0948918\pi\)
\(948\) 0 0
\(949\) 316.264 + 547.785i 0.333260 + 0.577224i
\(950\) −473.595 273.430i −0.498521 0.287821i
\(951\) 0 0
\(952\) 0 0
\(953\) 546.706 0.573669 0.286834 0.957980i \(-0.407397\pi\)
0.286834 + 0.957980i \(0.407397\pi\)
\(954\) 0 0
\(955\) 98.4701 56.8518i 0.103110 0.0595306i
\(956\) 18.4781 + 32.0051i 0.0193286 + 0.0334781i
\(957\) 0 0
\(958\) 787.030i 0.821534i
\(959\) 0 0
\(960\) 0 0
\(961\) 778.440 1348.30i 0.810031 1.40302i
\(962\) 339.119 195.790i 0.352514 0.203524i
\(963\) 0 0
\(964\) 308.485 + 178.104i 0.320005 + 0.184755i
\(965\) 23.2465i 0.0240896i
\(966\) 0 0
\(967\) 1262.32 1.30540 0.652701 0.757616i \(-0.273636\pi\)
0.652701 + 0.757616i \(0.273636\pi\)
\(968\) −22.7523 + 39.4082i −0.0235045 + 0.0407109i
\(969\) 0 0
\(970\) −72.2498 125.140i −0.0744843 0.129011i
\(971\) −936.116 540.467i −0.964074 0.556608i −0.0666496 0.997776i \(-0.521231\pi\)
−0.897425 + 0.441168i \(0.854564\pi\)
\(972\) 0 0
\(973\) 0 0
\(974\) 459.931 0.472208
\(975\) 0 0
\(976\) 9.94113 5.73951i 0.0101856 0.00588065i
\(977\) 900.131 + 1559.07i 0.921322 + 1.59578i 0.797373 + 0.603487i \(0.206223\pi\)
0.123949 + 0.992289i \(0.460444\pi\)
\(978\) 0 0
\(979\) 1484.88i 1.51673i
\(980\) 0 0
\(981\) 0 0
\(982\) −455.007 + 788.095i −0.463347 + 0.802541i
\(983\) −863.263 + 498.405i −0.878192 + 0.507025i −0.870062 0.492942i \(-0.835921\pi\)
−0.00813046 + 0.999967i \(0.502588\pi\)
\(984\) 0 0
\(985\) 101.979 + 58.8774i 0.103532 + 0.0597740i
\(986\) 1290.12i 1.30844i
\(987\) 0 0
\(988\) −288.999 −0.292509
\(989\) 250.368 433.649i 0.253152 0.438472i
\(990\) 0 0
\(991\) −394.360 683.052i −0.397942 0.689256i 0.595530 0.803333i \(-0.296942\pi\)
−0.993472 + 0.114078i \(0.963609\pi\)
\(992\) 245.823 + 141.926i 0.247806 + 0.143071i
\(993\) 0 0
\(994\) 0 0
\(995\) 165.484 0.166316
\(996\) 0 0
\(997\) 1682.42 971.348i 1.68749 0.974271i 0.731054 0.682320i \(-0.239029\pi\)
0.956433 0.291952i \(-0.0943046\pi\)
\(998\) 534.167 + 925.204i 0.535237 + 0.927058i
\(999\) 0 0
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 882.3.n.d.19.2 4
3.2 odd 2 294.3.g.c.19.1 4
7.2 even 3 126.3.c.b.55.1 4
7.3 odd 6 inner 882.3.n.d.325.2 4
7.4 even 3 882.3.n.a.325.2 4
7.5 odd 6 126.3.c.b.55.2 4
7.6 odd 2 882.3.n.a.19.2 4
21.2 odd 6 42.3.c.a.13.4 yes 4
21.5 even 6 42.3.c.a.13.3 4
21.11 odd 6 294.3.g.b.31.1 4
21.17 even 6 294.3.g.c.31.1 4
21.20 even 2 294.3.g.b.19.1 4
28.19 even 6 1008.3.f.g.433.3 4
28.23 odd 6 1008.3.f.g.433.2 4
84.23 even 6 336.3.f.c.97.1 4
84.47 odd 6 336.3.f.c.97.4 4
105.2 even 12 1050.3.h.a.349.8 8
105.23 even 12 1050.3.h.a.349.1 8
105.44 odd 6 1050.3.f.a.601.1 4
105.47 odd 12 1050.3.h.a.349.5 8
105.68 odd 12 1050.3.h.a.349.4 8
105.89 even 6 1050.3.f.a.601.2 4
168.5 even 6 1344.3.f.f.769.3 4
168.107 even 6 1344.3.f.e.769.4 4
168.131 odd 6 1344.3.f.e.769.1 4
168.149 odd 6 1344.3.f.f.769.2 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
42.3.c.a.13.3 4 21.5 even 6
42.3.c.a.13.4 yes 4 21.2 odd 6
126.3.c.b.55.1 4 7.2 even 3
126.3.c.b.55.2 4 7.5 odd 6
294.3.g.b.19.1 4 21.20 even 2
294.3.g.b.31.1 4 21.11 odd 6
294.3.g.c.19.1 4 3.2 odd 2
294.3.g.c.31.1 4 21.17 even 6
336.3.f.c.97.1 4 84.23 even 6
336.3.f.c.97.4 4 84.47 odd 6
882.3.n.a.19.2 4 7.6 odd 2
882.3.n.a.325.2 4 7.4 even 3
882.3.n.d.19.2 4 1.1 even 1 trivial
882.3.n.d.325.2 4 7.3 odd 6 inner
1008.3.f.g.433.2 4 28.23 odd 6
1008.3.f.g.433.3 4 28.19 even 6
1050.3.f.a.601.1 4 105.44 odd 6
1050.3.f.a.601.2 4 105.89 even 6
1050.3.h.a.349.1 8 105.23 even 12
1050.3.h.a.349.4 8 105.68 odd 12
1050.3.h.a.349.5 8 105.47 odd 12
1050.3.h.a.349.8 8 105.2 even 12
1344.3.f.e.769.1 4 168.131 odd 6
1344.3.f.e.769.4 4 168.107 even 6
1344.3.f.f.769.2 4 168.149 odd 6
1344.3.f.f.769.3 4 168.5 even 6