Properties

Label 490.2.c.e.99.3
Level $490$
Weight $2$
Character 490.99
Analytic conductor $3.913$
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] = [490,2,Mod(99,490)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(490, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([1, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("490.99");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 490 = 2 \cdot 5 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 490.c (of order \(2\), degree \(1\), 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: \(3.91266969904\)
Analytic rank: \(0\)
Dimension: \(4\)
Coefficient field: \(\Q(i, \sqrt{6})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{4} + 9 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 70)
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 99.3
Root \(-1.22474 - 1.22474i\) of defining polynomial
Character \(\chi\) \(=\) 490.99
Dual form 490.2.c.e.99.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+1.00000i q^{2} -2.44949i q^{3} -1.00000 q^{4} +(0.224745 + 2.22474i) q^{5} +2.44949 q^{6} -1.00000i q^{8} -3.00000 q^{9} +O(q^{10})\) \(q+1.00000i q^{2} -2.44949i q^{3} -1.00000 q^{4} +(0.224745 + 2.22474i) q^{5} +2.44949 q^{6} -1.00000i q^{8} -3.00000 q^{9} +(-2.22474 + 0.224745i) q^{10} +4.89898 q^{11} +2.44949i q^{12} +0.449490i q^{13} +(5.44949 - 0.550510i) q^{15} +1.00000 q^{16} +2.00000i q^{17} -3.00000i q^{18} +6.44949 q^{19} +(-0.224745 - 2.22474i) q^{20} +4.89898i q^{22} -6.89898i q^{23} -2.44949 q^{24} +(-4.89898 + 1.00000i) q^{25} -0.449490 q^{26} +2.89898 q^{29} +(0.550510 + 5.44949i) q^{30} +0.898979 q^{31} +1.00000i q^{32} -12.0000i q^{33} -2.00000 q^{34} +3.00000 q^{36} -2.00000i q^{37} +6.44949i q^{38} +1.10102 q^{39} +(2.22474 - 0.224745i) q^{40} +10.8990 q^{41} +8.89898i q^{43} -4.89898 q^{44} +(-0.674235 - 6.67423i) q^{45} +6.89898 q^{46} -0.898979i q^{47} -2.44949i q^{48} +(-1.00000 - 4.89898i) q^{50} +4.89898 q^{51} -0.449490i q^{52} -1.10102i q^{53} +(1.10102 + 10.8990i) q^{55} -15.7980i q^{57} +2.89898i q^{58} -6.44949 q^{59} +(-5.44949 + 0.550510i) q^{60} -8.44949 q^{61} +0.898979i q^{62} -1.00000 q^{64} +(-1.00000 + 0.101021i) q^{65} +12.0000 q^{66} +8.00000i q^{67} -2.00000i q^{68} -16.8990 q^{69} -10.8990 q^{71} +3.00000i q^{72} +6.89898i q^{73} +2.00000 q^{74} +(2.44949 + 12.0000i) q^{75} -6.44949 q^{76} +1.10102i q^{78} +2.89898 q^{79} +(0.224745 + 2.22474i) q^{80} -9.00000 q^{81} +10.8990i q^{82} -2.44949i q^{83} +(-4.44949 + 0.449490i) q^{85} -8.89898 q^{86} -7.10102i q^{87} -4.89898i q^{88} -10.0000 q^{89} +(6.67423 - 0.674235i) q^{90} +6.89898i q^{92} -2.20204i q^{93} +0.898979 q^{94} +(1.44949 + 14.3485i) q^{95} +2.44949 q^{96} -3.79796i q^{97} -14.6969 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q - 4 q^{4} - 4 q^{5} - 12 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 4 q - 4 q^{4} - 4 q^{5} - 12 q^{9} - 4 q^{10} + 12 q^{15} + 4 q^{16} + 16 q^{19} + 4 q^{20} + 8 q^{26} - 8 q^{29} + 12 q^{30} - 16 q^{31} - 8 q^{34} + 12 q^{36} + 24 q^{39} + 4 q^{40} + 24 q^{41} + 12 q^{45} + 8 q^{46} - 4 q^{50} + 24 q^{55} - 16 q^{59} - 12 q^{60} - 24 q^{61} - 4 q^{64} - 4 q^{65} + 48 q^{66} - 48 q^{69} - 24 q^{71} + 8 q^{74} - 16 q^{76} - 8 q^{79} - 4 q^{80} - 36 q^{81} - 8 q^{85} - 16 q^{86} - 40 q^{89} + 12 q^{90} - 16 q^{94} - 4 q^{95}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/490\mathbb{Z}\right)^\times\).

\(n\) \(101\) \(197\)
\(\chi(n)\) \(1\) \(-1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000i 0.707107i
\(3\) 2.44949i 1.41421i −0.707107 0.707107i \(-0.750000\pi\)
0.707107 0.707107i \(-0.250000\pi\)
\(4\) −1.00000 −0.500000
\(5\) 0.224745 + 2.22474i 0.100509 + 0.994936i
\(6\) 2.44949 1.00000
\(7\) 0 0
\(8\) 1.00000i 0.353553i
\(9\) −3.00000 −1.00000
\(10\) −2.22474 + 0.224745i −0.703526 + 0.0710706i
\(11\) 4.89898 1.47710 0.738549 0.674200i \(-0.235511\pi\)
0.738549 + 0.674200i \(0.235511\pi\)
\(12\) 2.44949i 0.707107i
\(13\) 0.449490i 0.124666i 0.998055 + 0.0623330i \(0.0198541\pi\)
−0.998055 + 0.0623330i \(0.980146\pi\)
\(14\) 0 0
\(15\) 5.44949 0.550510i 1.40705 0.142141i
\(16\) 1.00000 0.250000
\(17\) 2.00000i 0.485071i 0.970143 + 0.242536i \(0.0779791\pi\)
−0.970143 + 0.242536i \(0.922021\pi\)
\(18\) 3.00000i 0.707107i
\(19\) 6.44949 1.47961 0.739807 0.672819i \(-0.234917\pi\)
0.739807 + 0.672819i \(0.234917\pi\)
\(20\) −0.224745 2.22474i −0.0502545 0.497468i
\(21\) 0 0
\(22\) 4.89898i 1.04447i
\(23\) 6.89898i 1.43854i −0.694732 0.719268i \(-0.744477\pi\)
0.694732 0.719268i \(-0.255523\pi\)
\(24\) −2.44949 −0.500000
\(25\) −4.89898 + 1.00000i −0.979796 + 0.200000i
\(26\) −0.449490 −0.0881522
\(27\) 0 0
\(28\) 0 0
\(29\) 2.89898 0.538327 0.269163 0.963095i \(-0.413253\pi\)
0.269163 + 0.963095i \(0.413253\pi\)
\(30\) 0.550510 + 5.44949i 0.100509 + 0.994936i
\(31\) 0.898979 0.161461 0.0807307 0.996736i \(-0.474275\pi\)
0.0807307 + 0.996736i \(0.474275\pi\)
\(32\) 1.00000i 0.176777i
\(33\) 12.0000i 2.08893i
\(34\) −2.00000 −0.342997
\(35\) 0 0
\(36\) 3.00000 0.500000
\(37\) 2.00000i 0.328798i −0.986394 0.164399i \(-0.947432\pi\)
0.986394 0.164399i \(-0.0525685\pi\)
\(38\) 6.44949i 1.04625i
\(39\) 1.10102 0.176304
\(40\) 2.22474 0.224745i 0.351763 0.0355353i
\(41\) 10.8990 1.70213 0.851067 0.525057i \(-0.175956\pi\)
0.851067 + 0.525057i \(0.175956\pi\)
\(42\) 0 0
\(43\) 8.89898i 1.35708i 0.734563 + 0.678541i \(0.237387\pi\)
−0.734563 + 0.678541i \(0.762613\pi\)
\(44\) −4.89898 −0.738549
\(45\) −0.674235 6.67423i −0.100509 0.994936i
\(46\) 6.89898 1.01720
\(47\) 0.898979i 0.131130i −0.997848 0.0655648i \(-0.979115\pi\)
0.997848 0.0655648i \(-0.0208849\pi\)
\(48\) 2.44949i 0.353553i
\(49\) 0 0
\(50\) −1.00000 4.89898i −0.141421 0.692820i
\(51\) 4.89898 0.685994
\(52\) 0.449490i 0.0623330i
\(53\) 1.10102i 0.151237i −0.997137 0.0756184i \(-0.975907\pi\)
0.997137 0.0756184i \(-0.0240931\pi\)
\(54\) 0 0
\(55\) 1.10102 + 10.8990i 0.148462 + 1.46962i
\(56\) 0 0
\(57\) 15.7980i 2.09249i
\(58\) 2.89898i 0.380655i
\(59\) −6.44949 −0.839652 −0.419826 0.907605i \(-0.637909\pi\)
−0.419826 + 0.907605i \(0.637909\pi\)
\(60\) −5.44949 + 0.550510i −0.703526 + 0.0710706i
\(61\) −8.44949 −1.08185 −0.540923 0.841072i \(-0.681925\pi\)
−0.540923 + 0.841072i \(0.681925\pi\)
\(62\) 0.898979i 0.114171i
\(63\) 0 0
\(64\) −1.00000 −0.125000
\(65\) −1.00000 + 0.101021i −0.124035 + 0.0125301i
\(66\) 12.0000 1.47710
\(67\) 8.00000i 0.977356i 0.872464 + 0.488678i \(0.162521\pi\)
−0.872464 + 0.488678i \(0.837479\pi\)
\(68\) 2.00000i 0.242536i
\(69\) −16.8990 −2.03440
\(70\) 0 0
\(71\) −10.8990 −1.29347 −0.646735 0.762714i \(-0.723866\pi\)
−0.646735 + 0.762714i \(0.723866\pi\)
\(72\) 3.00000i 0.353553i
\(73\) 6.89898i 0.807464i 0.914877 + 0.403732i \(0.132287\pi\)
−0.914877 + 0.403732i \(0.867713\pi\)
\(74\) 2.00000 0.232495
\(75\) 2.44949 + 12.0000i 0.282843 + 1.38564i
\(76\) −6.44949 −0.739807
\(77\) 0 0
\(78\) 1.10102i 0.124666i
\(79\) 2.89898 0.326161 0.163080 0.986613i \(-0.447857\pi\)
0.163080 + 0.986613i \(0.447857\pi\)
\(80\) 0.224745 + 2.22474i 0.0251272 + 0.248734i
\(81\) −9.00000 −1.00000
\(82\) 10.8990i 1.20359i
\(83\) 2.44949i 0.268866i −0.990923 0.134433i \(-0.957079\pi\)
0.990923 0.134433i \(-0.0429214\pi\)
\(84\) 0 0
\(85\) −4.44949 + 0.449490i −0.482615 + 0.0487540i
\(86\) −8.89898 −0.959602
\(87\) 7.10102i 0.761309i
\(88\) 4.89898i 0.522233i
\(89\) −10.0000 −1.06000 −0.529999 0.847998i \(-0.677808\pi\)
−0.529999 + 0.847998i \(0.677808\pi\)
\(90\) 6.67423 0.674235i 0.703526 0.0710706i
\(91\) 0 0
\(92\) 6.89898i 0.719268i
\(93\) 2.20204i 0.228341i
\(94\) 0.898979 0.0927227
\(95\) 1.44949 + 14.3485i 0.148715 + 1.47212i
\(96\) 2.44949 0.250000
\(97\) 3.79796i 0.385624i −0.981236 0.192812i \(-0.938239\pi\)
0.981236 0.192812i \(-0.0617608\pi\)
\(98\) 0 0
\(99\) −14.6969 −1.47710
\(100\) 4.89898 1.00000i 0.489898 0.100000i
\(101\) −8.44949 −0.840756 −0.420378 0.907349i \(-0.638102\pi\)
−0.420378 + 0.907349i \(0.638102\pi\)
\(102\) 4.89898i 0.485071i
\(103\) 3.10102i 0.305553i −0.988261 0.152776i \(-0.951179\pi\)
0.988261 0.152776i \(-0.0488214\pi\)
\(104\) 0.449490 0.0440761
\(105\) 0 0
\(106\) 1.10102 0.106941
\(107\) 8.00000i 0.773389i 0.922208 + 0.386695i \(0.126383\pi\)
−0.922208 + 0.386695i \(0.873617\pi\)
\(108\) 0 0
\(109\) 2.89898 0.277672 0.138836 0.990315i \(-0.455664\pi\)
0.138836 + 0.990315i \(0.455664\pi\)
\(110\) −10.8990 + 1.10102i −1.03918 + 0.104978i
\(111\) −4.89898 −0.464991
\(112\) 0 0
\(113\) 0.202041i 0.0190064i 0.999955 + 0.00950321i \(0.00302501\pi\)
−0.999955 + 0.00950321i \(0.996975\pi\)
\(114\) 15.7980 1.47961
\(115\) 15.3485 1.55051i 1.43125 0.144586i
\(116\) −2.89898 −0.269163
\(117\) 1.34847i 0.124666i
\(118\) 6.44949i 0.593724i
\(119\) 0 0
\(120\) −0.550510 5.44949i −0.0502545 0.497468i
\(121\) 13.0000 1.18182
\(122\) 8.44949i 0.764981i
\(123\) 26.6969i 2.40718i
\(124\) −0.898979 −0.0807307
\(125\) −3.32577 10.6742i −0.297465 0.954733i
\(126\) 0 0
\(127\) 5.10102i 0.452642i 0.974053 + 0.226321i \(0.0726699\pi\)
−0.974053 + 0.226321i \(0.927330\pi\)
\(128\) 1.00000i 0.0883883i
\(129\) 21.7980 1.91920
\(130\) −0.101021 1.00000i −0.00886009 0.0877058i
\(131\) 1.55051 0.135469 0.0677344 0.997703i \(-0.478423\pi\)
0.0677344 + 0.997703i \(0.478423\pi\)
\(132\) 12.0000i 1.04447i
\(133\) 0 0
\(134\) −8.00000 −0.691095
\(135\) 0 0
\(136\) 2.00000 0.171499
\(137\) 17.7980i 1.52058i −0.649582 0.760291i \(-0.725056\pi\)
0.649582 0.760291i \(-0.274944\pi\)
\(138\) 16.8990i 1.43854i
\(139\) 6.44949 0.547039 0.273519 0.961867i \(-0.411812\pi\)
0.273519 + 0.961867i \(0.411812\pi\)
\(140\) 0 0
\(141\) −2.20204 −0.185445
\(142\) 10.8990i 0.914622i
\(143\) 2.20204i 0.184144i
\(144\) −3.00000 −0.250000
\(145\) 0.651531 + 6.44949i 0.0541067 + 0.535601i
\(146\) −6.89898 −0.570964
\(147\) 0 0
\(148\) 2.00000i 0.164399i
\(149\) −15.7980 −1.29422 −0.647110 0.762397i \(-0.724022\pi\)
−0.647110 + 0.762397i \(0.724022\pi\)
\(150\) −12.0000 + 2.44949i −0.979796 + 0.200000i
\(151\) −19.5959 −1.59469 −0.797347 0.603522i \(-0.793764\pi\)
−0.797347 + 0.603522i \(0.793764\pi\)
\(152\) 6.44949i 0.523123i
\(153\) 6.00000i 0.485071i
\(154\) 0 0
\(155\) 0.202041 + 2.00000i 0.0162283 + 0.160644i
\(156\) −1.10102 −0.0881522
\(157\) 8.44949i 0.674343i 0.941443 + 0.337171i \(0.109470\pi\)
−0.941443 + 0.337171i \(0.890530\pi\)
\(158\) 2.89898i 0.230630i
\(159\) −2.69694 −0.213881
\(160\) −2.22474 + 0.224745i −0.175882 + 0.0177676i
\(161\) 0 0
\(162\) 9.00000i 0.707107i
\(163\) 16.8990i 1.32363i −0.749667 0.661815i \(-0.769786\pi\)
0.749667 0.661815i \(-0.230214\pi\)
\(164\) −10.8990 −0.851067
\(165\) 26.6969 2.69694i 2.07835 0.209956i
\(166\) 2.44949 0.190117
\(167\) 4.89898i 0.379094i 0.981872 + 0.189547i \(0.0607020\pi\)
−0.981872 + 0.189547i \(0.939298\pi\)
\(168\) 0 0
\(169\) 12.7980 0.984458
\(170\) −0.449490 4.44949i −0.0344743 0.341260i
\(171\) −19.3485 −1.47961
\(172\) 8.89898i 0.678541i
\(173\) 18.2474i 1.38733i −0.720299 0.693664i \(-0.755995\pi\)
0.720299 0.693664i \(-0.244005\pi\)
\(174\) 7.10102 0.538327
\(175\) 0 0
\(176\) 4.89898 0.369274
\(177\) 15.7980i 1.18745i
\(178\) 10.0000i 0.749532i
\(179\) 5.79796 0.433360 0.216680 0.976243i \(-0.430477\pi\)
0.216680 + 0.976243i \(0.430477\pi\)
\(180\) 0.674235 + 6.67423i 0.0502545 + 0.497468i
\(181\) −14.2474 −1.05900 −0.529502 0.848309i \(-0.677621\pi\)
−0.529502 + 0.848309i \(0.677621\pi\)
\(182\) 0 0
\(183\) 20.6969i 1.52996i
\(184\) −6.89898 −0.508600
\(185\) 4.44949 0.449490i 0.327133 0.0330471i
\(186\) 2.20204 0.161461
\(187\) 9.79796i 0.716498i
\(188\) 0.898979i 0.0655648i
\(189\) 0 0
\(190\) −14.3485 + 1.44949i −1.04095 + 0.105157i
\(191\) −16.6969 −1.20815 −0.604074 0.796928i \(-0.706457\pi\)
−0.604074 + 0.796928i \(0.706457\pi\)
\(192\) 2.44949i 0.176777i
\(193\) 17.5959i 1.26658i 0.773914 + 0.633291i \(0.218296\pi\)
−0.773914 + 0.633291i \(0.781704\pi\)
\(194\) 3.79796 0.272678
\(195\) 0.247449 + 2.44949i 0.0177202 + 0.175412i
\(196\) 0 0
\(197\) 9.10102i 0.648421i −0.945985 0.324210i \(-0.894901\pi\)
0.945985 0.324210i \(-0.105099\pi\)
\(198\) 14.6969i 1.04447i
\(199\) 7.10102 0.503378 0.251689 0.967808i \(-0.419014\pi\)
0.251689 + 0.967808i \(0.419014\pi\)
\(200\) 1.00000 + 4.89898i 0.0707107 + 0.346410i
\(201\) 19.5959 1.38219
\(202\) 8.44949i 0.594504i
\(203\) 0 0
\(204\) −4.89898 −0.342997
\(205\) 2.44949 + 24.2474i 0.171080 + 1.69352i
\(206\) 3.10102 0.216058
\(207\) 20.6969i 1.43854i
\(208\) 0.449490i 0.0311665i
\(209\) 31.5959 2.18554
\(210\) 0 0
\(211\) 12.0000 0.826114 0.413057 0.910705i \(-0.364461\pi\)
0.413057 + 0.910705i \(0.364461\pi\)
\(212\) 1.10102i 0.0756184i
\(213\) 26.6969i 1.82924i
\(214\) −8.00000 −0.546869
\(215\) −19.7980 + 2.00000i −1.35021 + 0.136399i
\(216\) 0 0
\(217\) 0 0
\(218\) 2.89898i 0.196344i
\(219\) 16.8990 1.14193
\(220\) −1.10102 10.8990i −0.0742308 0.734809i
\(221\) −0.898979 −0.0604719
\(222\) 4.89898i 0.328798i
\(223\) 4.00000i 0.267860i 0.990991 + 0.133930i \(0.0427597\pi\)
−0.990991 + 0.133930i \(0.957240\pi\)
\(224\) 0 0
\(225\) 14.6969 3.00000i 0.979796 0.200000i
\(226\) −0.202041 −0.0134396
\(227\) 7.34847i 0.487735i −0.969809 0.243868i \(-0.921584\pi\)
0.969809 0.243868i \(-0.0784162\pi\)
\(228\) 15.7980i 1.04625i
\(229\) 15.1464 1.00090 0.500452 0.865764i \(-0.333167\pi\)
0.500452 + 0.865764i \(0.333167\pi\)
\(230\) 1.55051 + 15.3485i 0.102238 + 1.01205i
\(231\) 0 0
\(232\) 2.89898i 0.190327i
\(233\) 10.2020i 0.668358i 0.942510 + 0.334179i \(0.108459\pi\)
−0.942510 + 0.334179i \(0.891541\pi\)
\(234\) 1.34847 0.0881522
\(235\) 2.00000 0.202041i 0.130466 0.0131797i
\(236\) 6.44949 0.419826
\(237\) 7.10102i 0.461261i
\(238\) 0 0
\(239\) 25.7980 1.66873 0.834366 0.551211i \(-0.185834\pi\)
0.834366 + 0.551211i \(0.185834\pi\)
\(240\) 5.44949 0.550510i 0.351763 0.0355353i
\(241\) −20.6969 −1.33321 −0.666604 0.745412i \(-0.732253\pi\)
−0.666604 + 0.745412i \(0.732253\pi\)
\(242\) 13.0000i 0.835672i
\(243\) 22.0454i 1.41421i
\(244\) 8.44949 0.540923
\(245\) 0 0
\(246\) 26.6969 1.70213
\(247\) 2.89898i 0.184458i
\(248\) 0.898979i 0.0570853i
\(249\) −6.00000 −0.380235
\(250\) 10.6742 3.32577i 0.675098 0.210340i
\(251\) 1.55051 0.0978673 0.0489337 0.998802i \(-0.484418\pi\)
0.0489337 + 0.998802i \(0.484418\pi\)
\(252\) 0 0
\(253\) 33.7980i 2.12486i
\(254\) −5.10102 −0.320066
\(255\) 1.10102 + 10.8990i 0.0689486 + 0.682521i
\(256\) 1.00000 0.0625000
\(257\) 20.6969i 1.29104i 0.763744 + 0.645520i \(0.223359\pi\)
−0.763744 + 0.645520i \(0.776641\pi\)
\(258\) 21.7980i 1.35708i
\(259\) 0 0
\(260\) 1.00000 0.101021i 0.0620174 0.00626503i
\(261\) −8.69694 −0.538327
\(262\) 1.55051i 0.0957908i
\(263\) 9.79796i 0.604168i −0.953281 0.302084i \(-0.902318\pi\)
0.953281 0.302084i \(-0.0976823\pi\)
\(264\) −12.0000 −0.738549
\(265\) 2.44949 0.247449i 0.150471 0.0152007i
\(266\) 0 0
\(267\) 24.4949i 1.49906i
\(268\) 8.00000i 0.488678i
\(269\) −15.1464 −0.923494 −0.461747 0.887012i \(-0.652777\pi\)
−0.461747 + 0.887012i \(0.652777\pi\)
\(270\) 0 0
\(271\) −12.0000 −0.728948 −0.364474 0.931214i \(-0.618751\pi\)
−0.364474 + 0.931214i \(0.618751\pi\)
\(272\) 2.00000i 0.121268i
\(273\) 0 0
\(274\) 17.7980 1.07521
\(275\) −24.0000 + 4.89898i −1.44725 + 0.295420i
\(276\) 16.8990 1.01720
\(277\) 5.10102i 0.306491i 0.988188 + 0.153245i \(0.0489725\pi\)
−0.988188 + 0.153245i \(0.951028\pi\)
\(278\) 6.44949i 0.386815i
\(279\) −2.69694 −0.161461
\(280\) 0 0
\(281\) −18.0000 −1.07379 −0.536895 0.843649i \(-0.680403\pi\)
−0.536895 + 0.843649i \(0.680403\pi\)
\(282\) 2.20204i 0.131130i
\(283\) 28.2474i 1.67914i −0.543254 0.839568i \(-0.682808\pi\)
0.543254 0.839568i \(-0.317192\pi\)
\(284\) 10.8990 0.646735
\(285\) 35.1464 3.55051i 2.08189 0.210314i
\(286\) −2.20204 −0.130209
\(287\) 0 0
\(288\) 3.00000i 0.176777i
\(289\) 13.0000 0.764706
\(290\) −6.44949 + 0.651531i −0.378727 + 0.0382592i
\(291\) −9.30306 −0.545355
\(292\) 6.89898i 0.403732i
\(293\) 6.24745i 0.364980i 0.983208 + 0.182490i \(0.0584157\pi\)
−0.983208 + 0.182490i \(0.941584\pi\)
\(294\) 0 0
\(295\) −1.44949 14.3485i −0.0843926 0.835400i
\(296\) −2.00000 −0.116248
\(297\) 0 0
\(298\) 15.7980i 0.915151i
\(299\) 3.10102 0.179337
\(300\) −2.44949 12.0000i −0.141421 0.692820i
\(301\) 0 0
\(302\) 19.5959i 1.12762i
\(303\) 20.6969i 1.18901i
\(304\) 6.44949 0.369904
\(305\) −1.89898 18.7980i −0.108735 1.07637i
\(306\) 6.00000 0.342997
\(307\) 4.24745i 0.242415i 0.992627 + 0.121207i \(0.0386766\pi\)
−0.992627 + 0.121207i \(0.961323\pi\)
\(308\) 0 0
\(309\) −7.59592 −0.432117
\(310\) −2.00000 + 0.202041i −0.113592 + 0.0114752i
\(311\) −12.0000 −0.680458 −0.340229 0.940343i \(-0.610505\pi\)
−0.340229 + 0.940343i \(0.610505\pi\)
\(312\) 1.10102i 0.0623330i
\(313\) 17.5959i 0.994580i −0.867584 0.497290i \(-0.834328\pi\)
0.867584 0.497290i \(-0.165672\pi\)
\(314\) −8.44949 −0.476832
\(315\) 0 0
\(316\) −2.89898 −0.163080
\(317\) 26.4949i 1.48810i −0.668123 0.744051i \(-0.732902\pi\)
0.668123 0.744051i \(-0.267098\pi\)
\(318\) 2.69694i 0.151237i
\(319\) 14.2020 0.795162
\(320\) −0.224745 2.22474i −0.0125636 0.124367i
\(321\) 19.5959 1.09374
\(322\) 0 0
\(323\) 12.8990i 0.717718i
\(324\) 9.00000 0.500000
\(325\) −0.449490 2.20204i −0.0249332 0.122147i
\(326\) 16.8990 0.935948
\(327\) 7.10102i 0.392687i
\(328\) 10.8990i 0.601795i
\(329\) 0 0
\(330\) 2.69694 + 26.6969i 0.148462 + 1.46962i
\(331\) 10.6969 0.587957 0.293978 0.955812i \(-0.405021\pi\)
0.293978 + 0.955812i \(0.405021\pi\)
\(332\) 2.44949i 0.134433i
\(333\) 6.00000i 0.328798i
\(334\) −4.89898 −0.268060
\(335\) −17.7980 + 1.79796i −0.972406 + 0.0982330i
\(336\) 0 0
\(337\) 29.5959i 1.61219i 0.591785 + 0.806096i \(0.298424\pi\)
−0.591785 + 0.806096i \(0.701576\pi\)
\(338\) 12.7980i 0.696117i
\(339\) 0.494897 0.0268791
\(340\) 4.44949 0.449490i 0.241307 0.0243770i
\(341\) 4.40408 0.238494
\(342\) 19.3485i 1.04625i
\(343\) 0 0
\(344\) 8.89898 0.479801
\(345\) −3.79796 37.5959i −0.204475 2.02410i
\(346\) 18.2474 0.980989
\(347\) 19.1010i 1.02540i −0.858569 0.512698i \(-0.828646\pi\)
0.858569 0.512698i \(-0.171354\pi\)
\(348\) 7.10102i 0.380655i
\(349\) −3.55051 −0.190054 −0.0950272 0.995475i \(-0.530294\pi\)
−0.0950272 + 0.995475i \(0.530294\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 4.89898i 0.261116i
\(353\) 13.1010i 0.697297i −0.937254 0.348648i \(-0.886641\pi\)
0.937254 0.348648i \(-0.113359\pi\)
\(354\) −15.7980 −0.839652
\(355\) −2.44949 24.2474i −0.130005 1.28692i
\(356\) 10.0000 0.529999
\(357\) 0 0
\(358\) 5.79796i 0.306432i
\(359\) −11.5959 −0.612009 −0.306005 0.952030i \(-0.598992\pi\)
−0.306005 + 0.952030i \(0.598992\pi\)
\(360\) −6.67423 + 0.674235i −0.351763 + 0.0355353i
\(361\) 22.5959 1.18926
\(362\) 14.2474i 0.748829i
\(363\) 31.8434i 1.67134i
\(364\) 0 0
\(365\) −15.3485 + 1.55051i −0.803376 + 0.0811574i
\(366\) −20.6969 −1.08185
\(367\) 32.0000i 1.67039i 0.549957 + 0.835193i \(0.314644\pi\)
−0.549957 + 0.835193i \(0.685356\pi\)
\(368\) 6.89898i 0.359634i
\(369\) −32.6969 −1.70213
\(370\) 0.449490 + 4.44949i 0.0233679 + 0.231318i
\(371\) 0 0
\(372\) 2.20204i 0.114171i
\(373\) 24.6969i 1.27876i 0.768891 + 0.639380i \(0.220809\pi\)
−0.768891 + 0.639380i \(0.779191\pi\)
\(374\) −9.79796 −0.506640
\(375\) −26.1464 + 8.14643i −1.35020 + 0.420680i
\(376\) −0.898979 −0.0463613
\(377\) 1.30306i 0.0671111i
\(378\) 0 0
\(379\) −1.30306 −0.0669338 −0.0334669 0.999440i \(-0.510655\pi\)
−0.0334669 + 0.999440i \(0.510655\pi\)
\(380\) −1.44949 14.3485i −0.0743573 0.736061i
\(381\) 12.4949 0.640133
\(382\) 16.6969i 0.854290i
\(383\) 16.8990i 0.863498i 0.901994 + 0.431749i \(0.142103\pi\)
−0.901994 + 0.431749i \(0.857897\pi\)
\(384\) −2.44949 −0.125000
\(385\) 0 0
\(386\) −17.5959 −0.895609
\(387\) 26.6969i 1.35708i
\(388\) 3.79796i 0.192812i
\(389\) −22.8990 −1.16102 −0.580512 0.814252i \(-0.697148\pi\)
−0.580512 + 0.814252i \(0.697148\pi\)
\(390\) −2.44949 + 0.247449i −0.124035 + 0.0125301i
\(391\) 13.7980 0.697793
\(392\) 0 0
\(393\) 3.79796i 0.191582i
\(394\) 9.10102 0.458503
\(395\) 0.651531 + 6.44949i 0.0327821 + 0.324509i
\(396\) 14.6969 0.738549
\(397\) 17.3485i 0.870695i −0.900263 0.435347i \(-0.856626\pi\)
0.900263 0.435347i \(-0.143374\pi\)
\(398\) 7.10102i 0.355942i
\(399\) 0 0
\(400\) −4.89898 + 1.00000i −0.244949 + 0.0500000i
\(401\) 29.3939 1.46786 0.733930 0.679225i \(-0.237684\pi\)
0.733930 + 0.679225i \(0.237684\pi\)
\(402\) 19.5959i 0.977356i
\(403\) 0.404082i 0.0201288i
\(404\) 8.44949 0.420378
\(405\) −2.02270 20.0227i −0.100509 0.994936i
\(406\) 0 0
\(407\) 9.79796i 0.485667i
\(408\) 4.89898i 0.242536i
\(409\) −14.4949 −0.716727 −0.358363 0.933582i \(-0.616665\pi\)
−0.358363 + 0.933582i \(0.616665\pi\)
\(410\) −24.2474 + 2.44949i −1.19750 + 0.120972i
\(411\) −43.5959 −2.15043
\(412\) 3.10102i 0.152776i
\(413\) 0 0
\(414\) −20.6969 −1.01720
\(415\) 5.44949 0.550510i 0.267505 0.0270235i
\(416\) −0.449490 −0.0220380
\(417\) 15.7980i 0.773629i
\(418\) 31.5959i 1.54541i
\(419\) −6.44949 −0.315078 −0.157539 0.987513i \(-0.550356\pi\)
−0.157539 + 0.987513i \(0.550356\pi\)
\(420\) 0 0
\(421\) −23.7980 −1.15984 −0.579921 0.814673i \(-0.696917\pi\)
−0.579921 + 0.814673i \(0.696917\pi\)
\(422\) 12.0000i 0.584151i
\(423\) 2.69694i 0.131130i
\(424\) −1.10102 −0.0534703
\(425\) −2.00000 9.79796i −0.0970143 0.475271i
\(426\) −26.6969 −1.29347
\(427\) 0 0
\(428\) 8.00000i 0.386695i
\(429\) 5.39388 0.260419
\(430\) −2.00000 19.7980i −0.0964486 0.954742i
\(431\) 17.7980 0.857298 0.428649 0.903471i \(-0.358990\pi\)
0.428649 + 0.903471i \(0.358990\pi\)
\(432\) 0 0
\(433\) 19.7980i 0.951429i 0.879600 + 0.475715i \(0.157810\pi\)
−0.879600 + 0.475715i \(0.842190\pi\)
\(434\) 0 0
\(435\) 15.7980 1.59592i 0.757454 0.0765184i
\(436\) −2.89898 −0.138836
\(437\) 44.4949i 2.12848i
\(438\) 16.8990i 0.807464i
\(439\) 37.3939 1.78471 0.892356 0.451332i \(-0.149051\pi\)
0.892356 + 0.451332i \(0.149051\pi\)
\(440\) 10.8990 1.10102i 0.519588 0.0524891i
\(441\) 0 0
\(442\) 0.898979i 0.0427601i
\(443\) 9.79796i 0.465515i −0.972535 0.232758i \(-0.925225\pi\)
0.972535 0.232758i \(-0.0747749\pi\)
\(444\) 4.89898 0.232495
\(445\) −2.24745 22.2474i −0.106539 1.05463i
\(446\) −4.00000 −0.189405
\(447\) 38.6969i 1.83030i
\(448\) 0 0
\(449\) 10.0000 0.471929 0.235965 0.971762i \(-0.424175\pi\)
0.235965 + 0.971762i \(0.424175\pi\)
\(450\) 3.00000 + 14.6969i 0.141421 + 0.692820i
\(451\) 53.3939 2.51422
\(452\) 0.202041i 0.00950321i
\(453\) 48.0000i 2.25524i
\(454\) 7.34847 0.344881
\(455\) 0 0
\(456\) −15.7980 −0.739807
\(457\) 9.59592i 0.448878i 0.974488 + 0.224439i \(0.0720550\pi\)
−0.974488 + 0.224439i \(0.927945\pi\)
\(458\) 15.1464i 0.707746i
\(459\) 0 0
\(460\) −15.3485 + 1.55051i −0.715626 + 0.0722929i
\(461\) −2.65153 −0.123494 −0.0617470 0.998092i \(-0.519667\pi\)
−0.0617470 + 0.998092i \(0.519667\pi\)
\(462\) 0 0
\(463\) 35.5959i 1.65428i −0.561994 0.827141i \(-0.689966\pi\)
0.561994 0.827141i \(-0.310034\pi\)
\(464\) 2.89898 0.134582
\(465\) 4.89898 0.494897i 0.227185 0.0229503i
\(466\) −10.2020 −0.472600
\(467\) 5.55051i 0.256847i 0.991719 + 0.128423i \(0.0409917\pi\)
−0.991719 + 0.128423i \(0.959008\pi\)
\(468\) 1.34847i 0.0623330i
\(469\) 0 0
\(470\) 0.202041 + 2.00000i 0.00931946 + 0.0922531i
\(471\) 20.6969 0.953665
\(472\) 6.44949i 0.296862i
\(473\) 43.5959i 2.00454i
\(474\) 7.10102 0.326161
\(475\) −31.5959 + 6.44949i −1.44972 + 0.295923i
\(476\) 0 0
\(477\) 3.30306i 0.151237i
\(478\) 25.7980i 1.17997i
\(479\) 38.6969 1.76811 0.884054 0.467385i \(-0.154804\pi\)
0.884054 + 0.467385i \(0.154804\pi\)
\(480\) 0.550510 + 5.44949i 0.0251272 + 0.248734i
\(481\) 0.898979 0.0409899
\(482\) 20.6969i 0.942720i
\(483\) 0 0
\(484\) −13.0000 −0.590909
\(485\) 8.44949 0.853572i 0.383672 0.0387587i
\(486\) −22.0454 −1.00000
\(487\) 36.6969i 1.66290i 0.555602 + 0.831449i \(0.312488\pi\)
−0.555602 + 0.831449i \(0.687512\pi\)
\(488\) 8.44949i 0.382490i
\(489\) −41.3939 −1.87190
\(490\) 0 0
\(491\) −19.5959 −0.884351 −0.442176 0.896928i \(-0.645793\pi\)
−0.442176 + 0.896928i \(0.645793\pi\)
\(492\) 26.6969i 1.20359i
\(493\) 5.79796i 0.261127i
\(494\) −2.89898 −0.130431
\(495\) −3.30306 32.6969i −0.148462 1.46962i
\(496\) 0.898979 0.0403654
\(497\) 0 0
\(498\) 6.00000i 0.268866i
\(499\) −25.7980 −1.15488 −0.577438 0.816435i \(-0.695947\pi\)
−0.577438 + 0.816435i \(0.695947\pi\)
\(500\) 3.32577 + 10.6742i 0.148733 + 0.477366i
\(501\) 12.0000 0.536120
\(502\) 1.55051i 0.0692027i
\(503\) 4.00000i 0.178351i 0.996016 + 0.0891756i \(0.0284232\pi\)
−0.996016 + 0.0891756i \(0.971577\pi\)
\(504\) 0 0
\(505\) −1.89898 18.7980i −0.0845035 0.836498i
\(506\) 33.7980 1.50250
\(507\) 31.3485i 1.39223i
\(508\) 5.10102i 0.226321i
\(509\) −36.4495 −1.61560 −0.807798 0.589460i \(-0.799341\pi\)
−0.807798 + 0.589460i \(0.799341\pi\)
\(510\) −10.8990 + 1.10102i −0.482615 + 0.0487540i
\(511\) 0 0
\(512\) 1.00000i 0.0441942i
\(513\) 0 0
\(514\) −20.6969 −0.912903
\(515\) 6.89898 0.696938i 0.304005 0.0307108i
\(516\) −21.7980 −0.959602
\(517\) 4.40408i 0.193691i
\(518\) 0 0
\(519\) −44.6969 −1.96198
\(520\) 0.101021 + 1.00000i 0.00443004 + 0.0438529i
\(521\) −3.30306 −0.144710 −0.0723549 0.997379i \(-0.523051\pi\)
−0.0723549 + 0.997379i \(0.523051\pi\)
\(522\) 8.69694i 0.380655i
\(523\) 1.14643i 0.0501298i −0.999686 0.0250649i \(-0.992021\pi\)
0.999686 0.0250649i \(-0.00797924\pi\)
\(524\) −1.55051 −0.0677344
\(525\) 0 0
\(526\) 9.79796 0.427211
\(527\) 1.79796i 0.0783203i
\(528\) 12.0000i 0.522233i
\(529\) −24.5959 −1.06939
\(530\) 0.247449 + 2.44949i 0.0107485 + 0.106399i
\(531\) 19.3485 0.839652
\(532\) 0 0
\(533\) 4.89898i 0.212198i
\(534\) −24.4949 −1.06000
\(535\) −17.7980 + 1.79796i −0.769473 + 0.0777325i
\(536\) 8.00000 0.345547
\(537\) 14.2020i 0.612863i
\(538\) 15.1464i 0.653009i
\(539\) 0 0
\(540\) 0 0
\(541\) −29.5959 −1.27243 −0.636214 0.771513i \(-0.719500\pi\)
−0.636214 + 0.771513i \(0.719500\pi\)
\(542\) 12.0000i 0.515444i
\(543\) 34.8990i 1.49766i
\(544\) −2.00000 −0.0857493
\(545\) 0.651531 + 6.44949i 0.0279085 + 0.276266i
\(546\) 0 0
\(547\) 10.6969i 0.457368i −0.973501 0.228684i \(-0.926558\pi\)
0.973501 0.228684i \(-0.0734423\pi\)
\(548\) 17.7980i 0.760291i
\(549\) 25.3485 1.08185
\(550\) −4.89898 24.0000i −0.208893 1.02336i
\(551\) 18.6969 0.796516
\(552\) 16.8990i 0.719268i
\(553\) 0 0
\(554\) −5.10102 −0.216722
\(555\) −1.10102 10.8990i −0.0467357 0.462636i
\(556\) −6.44949 −0.273519
\(557\) 16.6969i 0.707472i 0.935345 + 0.353736i \(0.115089\pi\)
−0.935345 + 0.353736i \(0.884911\pi\)
\(558\) 2.69694i 0.114171i
\(559\) −4.00000 −0.169182
\(560\) 0 0
\(561\) 24.0000 1.01328
\(562\) 18.0000i 0.759284i
\(563\) 14.0454i 0.591943i −0.955197 0.295972i \(-0.904357\pi\)
0.955197 0.295972i \(-0.0956434\pi\)
\(564\) 2.20204 0.0927227
\(565\) −0.449490 + 0.0454077i −0.0189102 + 0.00191032i
\(566\) 28.2474 1.18733
\(567\) 0 0
\(568\) 10.8990i 0.457311i
\(569\) −14.2020 −0.595381 −0.297690 0.954663i \(-0.596216\pi\)
−0.297690 + 0.954663i \(0.596216\pi\)
\(570\) 3.55051 + 35.1464i 0.148715 + 1.47212i
\(571\) −20.8990 −0.874595 −0.437298 0.899317i \(-0.644064\pi\)
−0.437298 + 0.899317i \(0.644064\pi\)
\(572\) 2.20204i 0.0920720i
\(573\) 40.8990i 1.70858i
\(574\) 0 0
\(575\) 6.89898 + 33.7980i 0.287707 + 1.40947i
\(576\) 3.00000 0.125000
\(577\) 46.4949i 1.93561i 0.251705 + 0.967804i \(0.419009\pi\)
−0.251705 + 0.967804i \(0.580991\pi\)
\(578\) 13.0000i 0.540729i
\(579\) 43.1010 1.79122
\(580\) −0.651531 6.44949i −0.0270533 0.267800i
\(581\) 0 0
\(582\) 9.30306i 0.385624i
\(583\) 5.39388i 0.223392i
\(584\) 6.89898 0.285482
\(585\) 3.00000 0.303062i 0.124035 0.0125301i
\(586\) −6.24745 −0.258080
\(587\) 33.1464i 1.36810i −0.729435 0.684050i \(-0.760217\pi\)
0.729435 0.684050i \(-0.239783\pi\)
\(588\) 0 0
\(589\) 5.79796 0.238901
\(590\) 14.3485 1.44949i 0.590717 0.0596745i
\(591\) −22.2929 −0.917006
\(592\) 2.00000i 0.0821995i
\(593\) 1.10102i 0.0452135i 0.999744 + 0.0226067i \(0.00719656\pi\)
−0.999744 + 0.0226067i \(0.992803\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 15.7980 0.647110
\(597\) 17.3939i 0.711884i
\(598\) 3.10102i 0.126810i
\(599\) 22.8990 0.935627 0.467813 0.883827i \(-0.345042\pi\)
0.467813 + 0.883827i \(0.345042\pi\)
\(600\) 12.0000 2.44949i 0.489898 0.100000i
\(601\) −19.3939 −0.791093 −0.395546 0.918446i \(-0.629445\pi\)
−0.395546 + 0.918446i \(0.629445\pi\)
\(602\) 0 0
\(603\) 24.0000i 0.977356i
\(604\) 19.5959 0.797347
\(605\) 2.92168 + 28.9217i 0.118783 + 1.17583i
\(606\) −20.6969 −0.840756
\(607\) 25.3939i 1.03071i −0.856978 0.515353i \(-0.827661\pi\)
0.856978 0.515353i \(-0.172339\pi\)
\(608\) 6.44949i 0.261561i
\(609\) 0 0
\(610\) 18.7980 1.89898i 0.761107 0.0768874i
\(611\) 0.404082 0.0163474
\(612\) 6.00000i 0.242536i
\(613\) 8.20204i 0.331277i −0.986187 0.165639i \(-0.947031\pi\)
0.986187 0.165639i \(-0.0529685\pi\)
\(614\) −4.24745 −0.171413
\(615\) 59.3939 6.00000i 2.39499 0.241943i
\(616\) 0 0
\(617\) 9.59592i 0.386317i 0.981168 + 0.193159i \(0.0618732\pi\)
−0.981168 + 0.193159i \(0.938127\pi\)
\(618\) 7.59592i 0.305553i
\(619\) −46.4495 −1.86696 −0.933481 0.358626i \(-0.883245\pi\)
−0.933481 + 0.358626i \(0.883245\pi\)
\(620\) −0.202041 2.00000i −0.00811416 0.0803219i
\(621\) 0 0
\(622\) 12.0000i 0.481156i
\(623\) 0 0
\(624\) 1.10102 0.0440761
\(625\) 23.0000 9.79796i 0.920000 0.391918i
\(626\) 17.5959 0.703274
\(627\) 77.3939i 3.09081i
\(628\) 8.44949i 0.337171i
\(629\) 4.00000 0.159490
\(630\) 0 0
\(631\) 6.49490 0.258558 0.129279 0.991608i \(-0.458734\pi\)
0.129279 + 0.991608i \(0.458734\pi\)
\(632\) 2.89898i 0.115315i
\(633\) 29.3939i 1.16830i
\(634\) 26.4949 1.05225
\(635\) −11.3485 + 1.14643i −0.450350 + 0.0454946i
\(636\) 2.69694 0.106941
\(637\) 0 0
\(638\) 14.2020i 0.562264i
\(639\) 32.6969 1.29347
\(640\) 2.22474 0.224745i 0.0879408 0.00888382i
\(641\) 6.20204 0.244966 0.122483 0.992471i \(-0.460914\pi\)
0.122483 + 0.992471i \(0.460914\pi\)
\(642\) 19.5959i 0.773389i
\(643\) 9.14643i 0.360700i 0.983603 + 0.180350i \(0.0577230\pi\)
−0.983603 + 0.180350i \(0.942277\pi\)
\(644\) 0 0
\(645\) 4.89898 + 48.4949i 0.192897 + 1.90948i
\(646\) −12.8990 −0.507504
\(647\) 22.2929i 0.876423i 0.898872 + 0.438211i \(0.144388\pi\)
−0.898872 + 0.438211i \(0.855612\pi\)
\(648\) 9.00000i 0.353553i
\(649\) −31.5959 −1.24025
\(650\) 2.20204 0.449490i 0.0863712 0.0176304i
\(651\) 0 0
\(652\) 16.8990i 0.661815i
\(653\) 39.7980i 1.55741i −0.627387 0.778707i \(-0.715876\pi\)
0.627387 0.778707i \(-0.284124\pi\)
\(654\) 7.10102 0.277672
\(655\) 0.348469 + 3.44949i 0.0136158 + 0.134783i
\(656\) 10.8990 0.425534
\(657\) 20.6969i 0.807464i
\(658\) 0 0
\(659\) −7.10102 −0.276616 −0.138308 0.990389i \(-0.544166\pi\)
−0.138308 + 0.990389i \(0.544166\pi\)
\(660\) −26.6969 + 2.69694i −1.03918 + 0.104978i
\(661\) −12.9444 −0.503478 −0.251739 0.967795i \(-0.581003\pi\)
−0.251739 + 0.967795i \(0.581003\pi\)
\(662\) 10.6969i 0.415748i
\(663\) 2.20204i 0.0855202i
\(664\) −2.44949 −0.0950586
\(665\) 0 0
\(666\) −6.00000 −0.232495
\(667\) 20.0000i 0.774403i
\(668\) 4.89898i 0.189547i
\(669\) 9.79796 0.378811
\(670\) −1.79796 17.7980i −0.0694612 0.687595i
\(671\) −41.3939 −1.59799
\(672\) 0 0
\(673\) 1.79796i 0.0693062i 0.999399 + 0.0346531i \(0.0110326\pi\)
−0.999399 + 0.0346531i \(0.988967\pi\)
\(674\) −29.5959 −1.13999
\(675\) 0 0
\(676\) −12.7980 −0.492229
\(677\) 31.5505i 1.21258i −0.795242 0.606292i \(-0.792656\pi\)
0.795242 0.606292i \(-0.207344\pi\)
\(678\) 0.494897i 0.0190064i
\(679\) 0 0
\(680\) 0.449490 + 4.44949i 0.0172371 + 0.170630i
\(681\) −18.0000 −0.689761
\(682\) 4.40408i 0.168641i
\(683\) 35.5959i 1.36204i −0.732265 0.681020i \(-0.761537\pi\)
0.732265 0.681020i \(-0.238463\pi\)
\(684\) 19.3485 0.739807
\(685\) 39.5959 4.00000i 1.51288 0.152832i
\(686\) 0 0
\(687\) 37.1010i 1.41549i
\(688\) 8.89898i 0.339270i
\(689\) 0.494897 0.0188541
\(690\) 37.5959 3.79796i 1.43125 0.144586i
\(691\) 13.1464 0.500114 0.250057 0.968231i \(-0.419551\pi\)
0.250057 + 0.968231i \(0.419551\pi\)
\(692\) 18.2474i 0.693664i
\(693\) 0 0
\(694\) 19.1010 0.725065
\(695\) 1.44949 + 14.3485i 0.0549823 + 0.544268i
\(696\) −7.10102 −0.269163
\(697\) 21.7980i 0.825657i
\(698\) 3.55051i 0.134389i
\(699\) 24.9898 0.945201
\(700\) 0 0
\(701\) 40.6969 1.53710 0.768551 0.639788i \(-0.220978\pi\)
0.768551 + 0.639788i \(0.220978\pi\)
\(702\) 0 0
\(703\) 12.8990i 0.486494i
\(704\) −4.89898 −0.184637
\(705\) −0.494897 4.89898i −0.0186389 0.184506i
\(706\) 13.1010 0.493063
\(707\) 0 0
\(708\) 15.7980i 0.593724i
\(709\) −40.2929 −1.51323 −0.756615 0.653861i \(-0.773148\pi\)
−0.756615 + 0.653861i \(0.773148\pi\)
\(710\) 24.2474 2.44949i 0.909991 0.0919277i
\(711\) −8.69694 −0.326161
\(712\) 10.0000i 0.374766i
\(713\) 6.20204i 0.232268i
\(714\) 0 0
\(715\) −4.89898 + 0.494897i −0.183211 + 0.0185081i
\(716\) −5.79796 −0.216680
\(717\) 63.1918i 2.35994i
\(718\) 11.5959i 0.432756i
\(719\) 44.4949 1.65938 0.829690 0.558225i \(-0.188517\pi\)
0.829690 + 0.558225i \(0.188517\pi\)
\(720\) −0.674235 6.67423i −0.0251272 0.248734i
\(721\) 0 0
\(722\) 22.5959i 0.840933i
\(723\) 50.6969i 1.88544i
\(724\) 14.2474 0.529502
\(725\) −14.2020 + 2.89898i −0.527451 + 0.107665i
\(726\) 31.8434 1.18182
\(727\) 6.69694i 0.248376i −0.992259 0.124188i \(-0.960367\pi\)
0.992259 0.124188i \(-0.0396325\pi\)
\(728\) 0 0
\(729\) 27.0000 1.00000
\(730\) −1.55051 15.3485i −0.0573870 0.568072i
\(731\) −17.7980 −0.658281
\(732\) 20.6969i 0.764981i
\(733\) 43.6413i 1.61193i 0.591964 + 0.805965i \(0.298353\pi\)
−0.591964 + 0.805965i \(0.701647\pi\)
\(734\) −32.0000 −1.18114
\(735\) 0 0
\(736\) 6.89898 0.254300
\(737\) 39.1918i 1.44365i
\(738\) 32.6969i 1.20359i
\(739\) 44.4949 1.63677 0.818386 0.574669i \(-0.194869\pi\)
0.818386 + 0.574669i \(0.194869\pi\)
\(740\) −4.44949 + 0.449490i −0.163566 + 0.0165236i
\(741\) 7.10102 0.260863
\(742\) 0 0
\(743\) 15.3031i 0.561415i −0.959793 0.280707i \(-0.909431\pi\)
0.959793 0.280707i \(-0.0905691\pi\)
\(744\) −2.20204 −0.0807307
\(745\) −3.55051 35.1464i −0.130081 1.28767i
\(746\) −24.6969 −0.904219
\(747\) 7.34847i 0.268866i
\(748\) 9.79796i 0.358249i
\(749\) 0 0
\(750\) −8.14643 26.1464i −0.297465 0.954733i
\(751\) −22.2020 −0.810164 −0.405082 0.914280i \(-0.632757\pi\)
−0.405082 + 0.914280i \(0.632757\pi\)
\(752\) 0.898979i 0.0327824i
\(753\) 3.79796i 0.138405i
\(754\) −1.30306 −0.0474547
\(755\) −4.40408 43.5959i −0.160281 1.58662i
\(756\) 0 0
\(757\) 32.2020i 1.17040i 0.810888 + 0.585202i \(0.198985\pi\)
−0.810888 + 0.585202i \(0.801015\pi\)
\(758\) 1.30306i 0.0473293i
\(759\) −82.7878 −3.00501
\(760\) 14.3485 1.44949i 0.520474 0.0525785i
\(761\) 30.8990 1.12009 0.560044 0.828463i \(-0.310784\pi\)
0.560044 + 0.828463i \(0.310784\pi\)
\(762\) 12.4949i 0.452642i
\(763\) 0 0
\(764\) 16.6969 0.604074
\(765\) 13.3485 1.34847i 0.482615 0.0487540i
\(766\) −16.8990 −0.610585
\(767\) 2.89898i 0.104676i
\(768\) 2.44949i 0.0883883i
\(769\) −11.3031 −0.407599 −0.203799 0.979013i \(-0.565329\pi\)
−0.203799 + 0.979013i \(0.565329\pi\)
\(770\) 0 0
\(771\) 50.6969 1.82581
\(772\) 17.5959i 0.633291i
\(773\) 13.3485i 0.480111i 0.970759 + 0.240056i \(0.0771657\pi\)
−0.970759 + 0.240056i \(0.922834\pi\)
\(774\) 26.6969 0.959602
\(775\) −4.40408 + 0.898979i −0.158199 + 0.0322923i
\(776\) −3.79796 −0.136339
\(777\) 0 0
\(778\) 22.8990i 0.820968i
\(779\) 70.2929 2.51850
\(780\) −0.247449 2.44949i −0.00886009 0.0877058i
\(781\) −53.3939 −1.91058
\(782\) 13.7980i 0.493414i
\(783\) 0 0
\(784\) 0 0
\(785\) −18.7980 + 1.89898i −0.670928 + 0.0677775i
\(786\) 3.79796 0.135469
\(787\) 45.5505i 1.62370i 0.583866 + 0.811850i \(0.301539\pi\)
−0.583866 + 0.811850i \(0.698461\pi\)
\(788\) 9.10102i 0.324210i
\(789\) −24.0000 −0.854423
\(790\) −6.44949 + 0.651531i −0.229463 + 0.0231804i
\(791\) 0 0
\(792\) 14.6969i 0.522233i
\(793\) 3.79796i 0.134869i
\(794\) 17.3485 0.615674
\(795\) −0.606123 6.00000i −0.0214970 0.212798i
\(796\) −7.10102 −0.251689
\(797\) 52.9444i 1.87539i 0.347464 + 0.937693i \(0.387043\pi\)
−0.347464 + 0.937693i \(0.612957\pi\)
\(798\) 0 0
\(799\) 1.79796 0.0636072
\(800\) −1.00000 4.89898i −0.0353553 0.173205i
\(801\) 30.0000 1.06000
\(802\) 29.3939i 1.03793i
\(803\) 33.7980i 1.19270i
\(804\) −19.5959 −0.691095
\(805\) 0 0
\(806\) −0.404082 −0.0142332
\(807\) 37.1010i 1.30602i
\(808\) 8.44949i 0.297252i
\(809\) −8.40408 −0.295472 −0.147736 0.989027i \(-0.547199\pi\)
−0.147736 + 0.989027i \(0.547199\pi\)
\(810\) 20.0227 2.02270i 0.703526 0.0710706i
\(811\) 38.9444 1.36752 0.683761 0.729706i \(-0.260343\pi\)
0.683761 + 0.729706i \(0.260343\pi\)
\(812\) 0 0
\(813\) 29.3939i 1.03089i
\(814\) 9.79796 0.343418
\(815\) 37.5959 3.79796i 1.31693 0.133037i
\(816\) 4.89898 0.171499
\(817\) 57.3939i 2.00796i
\(818\) 14.4949i 0.506802i
\(819\) 0 0
\(820\) −2.44949 24.2474i −0.0855399 0.846758i
\(821\) 27.7980 0.970155 0.485078 0.874471i \(-0.338791\pi\)
0.485078 + 0.874471i \(0.338791\pi\)
\(822\) 43.5959i 1.52058i
\(823\) 39.1918i 1.36614i 0.730352 + 0.683071i \(0.239356\pi\)
−0.730352 + 0.683071i \(0.760644\pi\)
\(824\) −3.10102 −0.108029
\(825\) 12.0000 + 58.7878i 0.417786 + 2.04673i
\(826\) 0 0
\(827\) 23.5959i 0.820510i −0.911971 0.410255i \(-0.865440\pi\)
0.911971 0.410255i \(-0.134560\pi\)
\(828\) 20.6969i 0.719268i
\(829\) 39.6413 1.37680 0.688400 0.725331i \(-0.258313\pi\)
0.688400 + 0.725331i \(0.258313\pi\)
\(830\) 0.550510 + 5.44949i 0.0191085 + 0.189155i
\(831\) 12.4949 0.433443
\(832\) 0.449490i 0.0155833i
\(833\) 0 0
\(834\) 15.7980 0.547039
\(835\) −10.8990 + 1.10102i −0.377175 + 0.0381024i
\(836\) −31.5959 −1.09277
\(837\) 0 0
\(838\) 6.44949i 0.222794i
\(839\) 27.1010 0.935631 0.467816 0.883826i \(-0.345041\pi\)
0.467816 + 0.883826i \(0.345041\pi\)
\(840\) 0 0
\(841\) −20.5959 −0.710204
\(842\) 23.7980i 0.820132i
\(843\) 44.0908i 1.51857i
\(844\) −12.0000 −0.413057
\(845\) 2.87628 + 28.4722i 0.0989469 + 0.979473i
\(846\) −2.69694 −0.0927227
\(847\) 0 0
\(848\) 1.10102i 0.0378092i
\(849\) −69.1918 −2.37466
\(850\) 9.79796 2.00000i 0.336067 0.0685994i
\(851\) −13.7980 −0.472988
\(852\) 26.6969i 0.914622i
\(853\) 29.8434i 1.02182i −0.859635 0.510909i \(-0.829309\pi\)
0.859635 0.510909i \(-0.170691\pi\)
\(854\) 0 0
\(855\) −4.34847 43.0454i −0.148715 1.47212i
\(856\) 8.00000 0.273434
\(857\) 25.1918i 0.860537i 0.902701 + 0.430268i \(0.141581\pi\)
−0.902701 + 0.430268i \(0.858419\pi\)
\(858\) 5.39388i 0.184144i
\(859\) −29.6413 −1.01135 −0.505674 0.862724i \(-0.668756\pi\)
−0.505674 + 0.862724i \(0.668756\pi\)
\(860\) 19.7980 2.00000i 0.675105 0.0681994i
\(861\) 0 0
\(862\) 17.7980i 0.606201i
\(863\) 13.3939i 0.455933i 0.973669 + 0.227966i \(0.0732076\pi\)
−0.973669 + 0.227966i \(0.926792\pi\)
\(864\) 0 0
\(865\) 40.5959 4.10102i 1.38030 0.139439i
\(866\) −19.7980 −0.672762
\(867\) 31.8434i 1.08146i
\(868\) 0 0
\(869\) 14.2020 0.481771
\(870\) 1.59592 + 15.7980i 0.0541067 + 0.535601i
\(871\) −3.59592 −0.121843
\(872\) 2.89898i 0.0981718i
\(873\) 11.3939i 0.385624i
\(874\) 44.4949 1.50506
\(875\) 0 0
\(876\) −16.8990 −0.570964
\(877\) 19.3939i 0.654885i −0.944871 0.327442i \(-0.893813\pi\)
0.944871 0.327442i \(-0.106187\pi\)
\(878\) 37.3939i 1.26198i
\(879\) 15.3031 0.516159
\(880\) 1.10102 + 10.8990i 0.0371154 + 0.367405i
\(881\) −27.7980 −0.936537 −0.468269 0.883586i \(-0.655122\pi\)
−0.468269 + 0.883586i \(0.655122\pi\)
\(882\) 0 0
\(883\) 41.7980i 1.40661i 0.710887 + 0.703307i \(0.248294\pi\)
−0.710887 + 0.703307i \(0.751706\pi\)
\(884\) 0.898979 0.0302360
\(885\) −35.1464 + 3.55051i −1.18143 + 0.119349i
\(886\) 9.79796 0.329169
\(887\) 26.6969i 0.896395i −0.893934 0.448198i \(-0.852066\pi\)
0.893934 0.448198i \(-0.147934\pi\)
\(888\) 4.89898i 0.164399i
\(889\) 0 0
\(890\) 22.2474 2.24745i 0.745736 0.0753347i
\(891\) −44.0908 −1.47710
\(892\) 4.00000i 0.133930i
\(893\) 5.79796i 0.194021i
\(894\) −38.6969 −1.29422
\(895\) 1.30306 + 12.8990i 0.0435565 + 0.431165i
\(896\) 0 0
\(897\) 7.59592i 0.253620i
\(898\) 10.0000i 0.333704i
\(899\) 2.60612 0.0869191
\(900\) −14.6969 + 3.00000i −0.489898 + 0.100000i
\(901\) 2.20204 0.0733606
\(902\) 53.3939i 1.77782i
\(903\) 0 0
\(904\) 0.202041 0.00671978
\(905\) −3.20204 31.6969i −0.106439 1.05364i
\(906\) −48.0000 −1.59469
\(907\) 22.2020i 0.737207i 0.929587 + 0.368603i \(0.120164\pi\)
−0.929587 + 0.368603i \(0.879836\pi\)
\(908\) 7.34847i 0.243868i
\(909\) 25.3485 0.840756
\(910\) 0 0
\(911\) 3.59592 0.119138 0.0595690 0.998224i \(-0.481027\pi\)
0.0595690 + 0.998224i \(0.481027\pi\)
\(912\) 15.7980i 0.523123i
\(913\) 12.0000i 0.397142i
\(914\) −9.59592 −0.317405
\(915\) −46.0454 + 4.65153i −1.52221 + 0.153775i
\(916\) −15.1464 −0.500452
\(917\) 0 0
\(918\) 0 0
\(919\) 17.1010 0.564111 0.282055 0.959398i \(-0.408984\pi\)
0.282055 + 0.959398i \(0.408984\pi\)
\(920\) −1.55051 15.3485i −0.0511188 0.506024i
\(921\) 10.4041 0.342826
\(922\) 2.65153i 0.0873235i
\(923\) 4.89898i 0.161252i
\(924\) 0 0
\(925\) 2.00000 + 9.79796i 0.0657596 + 0.322155i
\(926\) 35.5959 1.16975
\(927\) 9.30306i 0.305553i
\(928\) 2.89898i 0.0951637i
\(929\) 40.2929 1.32197 0.660983 0.750401i \(-0.270140\pi\)
0.660983 + 0.750401i \(0.270140\pi\)
\(930\) 0.494897 + 4.89898i 0.0162283 + 0.160644i
\(931\) 0 0
\(932\) 10.2020i 0.334179i
\(933\) 29.3939i 0.962312i
\(934\) −5.55051 −0.181618
\(935\) −21.7980 + 2.20204i −0.712869 + 0.0720144i
\(936\) −1.34847 −0.0440761
\(937\) 50.8990i 1.66280i −0.555677 0.831399i \(-0.687541\pi\)
0.555677 0.831399i \(-0.312459\pi\)
\(938\) 0 0
\(939\) −43.1010 −1.40655
\(940\) −2.00000 + 0.202041i −0.0652328 + 0.00658985i
\(941\) 24.4495 0.797031 0.398515 0.917162i \(-0.369526\pi\)
0.398515 + 0.917162i \(0.369526\pi\)
\(942\) 20.6969i 0.674343i
\(943\) 75.1918i 2.44858i
\(944\) −6.44949 −0.209913
\(945\) 0 0
\(946\) −43.5959 −1.41743
\(947\) 44.0908i 1.43276i 0.697711 + 0.716379i \(0.254202\pi\)
−0.697711 + 0.716379i \(0.745798\pi\)
\(948\) 7.10102i 0.230630i
\(949\) −3.10102 −0.100663
\(950\) −6.44949 31.5959i −0.209249 1.02511i
\(951\) −64.8990 −2.10449
\(952\) 0 0
\(953\) 21.7980i 0.706105i 0.935603 + 0.353053i \(0.114856\pi\)
−0.935603 + 0.353053i \(0.885144\pi\)
\(954\) −3.30306 −0.106941
\(955\) −3.75255 37.1464i −0.121430 1.20203i
\(956\) −25.7980 −0.834366
\(957\) 34.7878i 1.12453i
\(958\) 38.6969i 1.25024i
\(959\) 0 0
\(960\) −5.44949 + 0.550510i −0.175882 + 0.0177676i
\(961\) −30.1918 −0.973930
\(962\) 0.898979i 0.0289843i
\(963\) 24.0000i 0.773389i
\(964\) 20.6969 0.666604
\(965\) −39.1464 + 3.95459i −1.26017 + 0.127303i
\(966\) 0 0
\(967\) 32.2929i 1.03847i −0.854632 0.519234i \(-0.826217\pi\)
0.854632 0.519234i \(-0.173783\pi\)
\(968\) 13.0000i 0.417836i
\(969\) 31.5959 1.01501
\(970\) 0.853572 + 8.44949i 0.0274065 + 0.271297i
\(971\) 14.4495 0.463706 0.231853 0.972751i \(-0.425521\pi\)
0.231853 + 0.972751i \(0.425521\pi\)
\(972\) 22.0454i 0.707107i
\(973\) 0 0
\(974\) −36.6969 −1.17585
\(975\) −5.39388 + 1.10102i −0.172742 + 0.0352609i
\(976\) −8.44949 −0.270462
\(977\) 29.3939i 0.940393i −0.882562 0.470197i \(-0.844183\pi\)
0.882562 0.470197i \(-0.155817\pi\)
\(978\) 41.3939i 1.32363i
\(979\) −48.9898 −1.56572
\(980\) 0 0
\(981\) −8.69694 −0.277672
\(982\) 19.5959i 0.625331i
\(983\) 42.6969i 1.36182i 0.732367 + 0.680910i \(0.238416\pi\)
−0.732367 + 0.680910i \(0.761584\pi\)
\(984\) −26.6969 −0.851067
\(985\) 20.2474 2.04541i 0.645137 0.0651721i
\(986\) −5.79796 −0.184645
\(987\) 0 0
\(988\) 2.89898i 0.0922288i
\(989\) 61.3939 1.95221
\(990\) 32.6969 3.30306i 1.03918 0.104978i
\(991\) 60.6969 1.92810 0.964051 0.265718i \(-0.0856089\pi\)
0.964051 + 0.265718i \(0.0856089\pi\)
\(992\) 0.898979i 0.0285426i
\(993\) 26.2020i 0.831497i
\(994\) 0 0
\(995\) 1.59592 + 15.7980i 0.0505940 + 0.500829i
\(996\) 6.00000 0.190117
\(997\) 42.6515i 1.35079i 0.737457 + 0.675394i \(0.236026\pi\)
−0.737457 + 0.675394i \(0.763974\pi\)
\(998\) 25.7980i 0.816620i
\(999\) 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 490.2.c.e.99.3 4
5.2 odd 4 2450.2.a.bl.1.1 2
5.3 odd 4 2450.2.a.bq.1.2 2
5.4 even 2 inner 490.2.c.e.99.2 4
7.2 even 3 490.2.i.f.459.4 8
7.3 odd 6 490.2.i.c.79.2 8
7.4 even 3 490.2.i.f.79.1 8
7.5 odd 6 490.2.i.c.459.3 8
7.6 odd 2 70.2.c.a.29.4 yes 4
21.20 even 2 630.2.g.g.379.2 4
28.27 even 2 560.2.g.e.449.1 4
35.4 even 6 490.2.i.f.79.4 8
35.9 even 6 490.2.i.f.459.1 8
35.13 even 4 350.2.a.h.1.1 2
35.19 odd 6 490.2.i.c.459.2 8
35.24 odd 6 490.2.i.c.79.3 8
35.27 even 4 350.2.a.g.1.2 2
35.34 odd 2 70.2.c.a.29.1 4
56.13 odd 2 2240.2.g.j.449.2 4
56.27 even 2 2240.2.g.i.449.4 4
84.83 odd 2 5040.2.t.t.1009.4 4
105.62 odd 4 3150.2.a.bt.1.1 2
105.83 odd 4 3150.2.a.bs.1.1 2
105.104 even 2 630.2.g.g.379.4 4
140.27 odd 4 2800.2.a.bm.1.1 2
140.83 odd 4 2800.2.a.bl.1.2 2
140.139 even 2 560.2.g.e.449.3 4
280.69 odd 2 2240.2.g.j.449.4 4
280.139 even 2 2240.2.g.i.449.2 4
420.419 odd 2 5040.2.t.t.1009.3 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
70.2.c.a.29.1 4 35.34 odd 2
70.2.c.a.29.4 yes 4 7.6 odd 2
350.2.a.g.1.2 2 35.27 even 4
350.2.a.h.1.1 2 35.13 even 4
490.2.c.e.99.2 4 5.4 even 2 inner
490.2.c.e.99.3 4 1.1 even 1 trivial
490.2.i.c.79.2 8 7.3 odd 6
490.2.i.c.79.3 8 35.24 odd 6
490.2.i.c.459.2 8 35.19 odd 6
490.2.i.c.459.3 8 7.5 odd 6
490.2.i.f.79.1 8 7.4 even 3
490.2.i.f.79.4 8 35.4 even 6
490.2.i.f.459.1 8 35.9 even 6
490.2.i.f.459.4 8 7.2 even 3
560.2.g.e.449.1 4 28.27 even 2
560.2.g.e.449.3 4 140.139 even 2
630.2.g.g.379.2 4 21.20 even 2
630.2.g.g.379.4 4 105.104 even 2
2240.2.g.i.449.2 4 280.139 even 2
2240.2.g.i.449.4 4 56.27 even 2
2240.2.g.j.449.2 4 56.13 odd 2
2240.2.g.j.449.4 4 280.69 odd 2
2450.2.a.bl.1.1 2 5.2 odd 4
2450.2.a.bq.1.2 2 5.3 odd 4
2800.2.a.bl.1.2 2 140.83 odd 4
2800.2.a.bm.1.1 2 140.27 odd 4
3150.2.a.bs.1.1 2 105.83 odd 4
3150.2.a.bt.1.1 2 105.62 odd 4
5040.2.t.t.1009.3 4 420.419 odd 2
5040.2.t.t.1009.4 4 84.83 odd 2