Properties

Label 1008.2.r.g.673.2
Level $1008$
Weight $2$
Character 1008.673
Analytic conductor $8.049$
Analytic rank $0$
Dimension $6$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [1008,2,Mod(337,1008)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1008, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([0, 0, 2, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("1008.337");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1008 = 2^{4} \cdot 3^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1008.r (of order \(3\), 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: \(8.04892052375\)
Analytic rank: \(0\)
Dimension: \(6\)
Relative dimension: \(3\) over \(\Q(\zeta_{3})\)
Coefficient field: 6.0.309123.1
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{6} - 3x^{5} + 10x^{4} - 15x^{3} + 19x^{2} - 12x + 3 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 3 \)
Twist minimal: no (minimal twist has level 252)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 673.2
Root \(0.500000 - 2.05195i\) of defining polynomial
Character \(\chi\) \(=\) 1008.673
Dual form 1008.2.r.g.337.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.796790 + 1.53790i) q^{3} +(-1.02704 - 1.77889i) q^{5} +(0.500000 - 0.866025i) q^{7} +(-1.73025 - 2.45076i) q^{9} +O(q^{10})\) \(q+(-0.796790 + 1.53790i) q^{3} +(-1.02704 - 1.77889i) q^{5} +(0.500000 - 0.866025i) q^{7} +(-1.73025 - 2.45076i) q^{9} +(-2.52704 + 4.37697i) q^{11} +(0.500000 + 0.866025i) q^{13} +(3.55408 - 0.162084i) q^{15} +0.273346 q^{17} +5.38151 q^{19} +(0.933463 + 1.45899i) q^{21} +(-2.66372 - 4.61369i) q^{23} +(0.390369 - 0.676139i) q^{25} +(5.14766 - 0.708209i) q^{27} +(4.16372 - 7.21177i) q^{29} +(-5.08113 - 8.80077i) q^{31} +(-4.71780 - 7.37385i) q^{33} -2.05408 q^{35} +8.16225 q^{37} +(-1.73025 + 0.0789082i) q^{39} +(2.52704 + 4.37697i) q^{41} +(2.30039 - 3.98439i) q^{43} +(-2.58259 + 5.59496i) q^{45} +(0.690757 - 1.19643i) q^{47} +(-0.500000 - 0.866025i) q^{49} +(-0.217799 + 0.420378i) q^{51} +3.43560 q^{53} +10.3815 q^{55} +(-4.28794 + 8.27621i) q^{57} +(0.890369 + 1.54216i) q^{59} +(-0.390369 + 0.676139i) q^{61} +(-2.98755 + 0.273062i) q^{63} +(1.02704 - 1.77889i) q^{65} +(-4.19076 - 7.25860i) q^{67} +(9.21780 - 0.420378i) q^{69} +7.78074 q^{71} +9.38151 q^{73} +(0.728790 + 1.13909i) q^{75} +(2.52704 + 4.37697i) q^{77} +(6.47150 - 11.2090i) q^{79} +(-3.01245 + 8.48087i) q^{81} +(-2.86333 + 4.95943i) q^{83} +(-0.280738 - 0.486253i) q^{85} +(7.77335 + 12.1496i) q^{87} -13.8171 q^{89} +1.00000 q^{91} +(17.5833 - 0.801886i) q^{93} +(-5.52704 - 9.57312i) q^{95} +(1.10963 - 1.92194i) q^{97} +(15.0993 - 1.38008i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6 q - 2 q^{3} + 3 q^{5} + 3 q^{7} - 4 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 6 q - 2 q^{3} + 3 q^{5} + 3 q^{7} - 4 q^{9} - 6 q^{11} + 3 q^{13} + 3 q^{15} - 6 q^{19} + 2 q^{21} - 6 q^{23} - 6 q^{25} + 7 q^{27} + 15 q^{29} - 3 q^{31} + 6 q^{35} - 6 q^{37} - 4 q^{39} + 6 q^{41} + 3 q^{43} - 33 q^{45} - 15 q^{47} - 3 q^{49} + 27 q^{51} - 36 q^{53} + 24 q^{55} + 7 q^{57} - 3 q^{59} + 6 q^{61} + 4 q^{63} - 3 q^{65} - 6 q^{67} + 27 q^{69} + 30 q^{71} + 18 q^{73} - 47 q^{75} + 6 q^{77} + 3 q^{79} - 40 q^{81} - 18 q^{83} + 15 q^{85} + 45 q^{87} + 12 q^{89} + 6 q^{91} + 25 q^{93} - 24 q^{95} + 15 q^{97} + 24 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1008\mathbb{Z}\right)^\times\).

\(n\) \(127\) \(577\) \(757\) \(785\)
\(\chi(n)\) \(1\) \(1\) \(1\) \(e\left(\frac{2}{3}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) −0.796790 + 1.53790i −0.460027 + 0.887905i
\(4\) 0 0
\(5\) −1.02704 1.77889i −0.459307 0.795543i 0.539617 0.841910i \(-0.318569\pi\)
−0.998924 + 0.0463670i \(0.985236\pi\)
\(6\) 0 0
\(7\) 0.500000 0.866025i 0.188982 0.327327i
\(8\) 0 0
\(9\) −1.73025 2.45076i −0.576751 0.816920i
\(10\) 0 0
\(11\) −2.52704 + 4.37697i −0.761932 + 1.31970i 0.179922 + 0.983681i \(0.442416\pi\)
−0.941854 + 0.336024i \(0.890918\pi\)
\(12\) 0 0
\(13\) 0.500000 + 0.866025i 0.138675 + 0.240192i 0.926995 0.375073i \(-0.122382\pi\)
−0.788320 + 0.615265i \(0.789049\pi\)
\(14\) 0 0
\(15\) 3.55408 0.162084i 0.917661 0.0418500i
\(16\) 0 0
\(17\) 0.273346 0.0662962 0.0331481 0.999450i \(-0.489447\pi\)
0.0331481 + 0.999450i \(0.489447\pi\)
\(18\) 0 0
\(19\) 5.38151 1.23460 0.617302 0.786726i \(-0.288226\pi\)
0.617302 + 0.786726i \(0.288226\pi\)
\(20\) 0 0
\(21\) 0.933463 + 1.45899i 0.203698 + 0.318377i
\(22\) 0 0
\(23\) −2.66372 4.61369i −0.555423 0.962021i −0.997870 0.0652265i \(-0.979223\pi\)
0.442447 0.896794i \(-0.354110\pi\)
\(24\) 0 0
\(25\) 0.390369 0.676139i 0.0780738 0.135228i
\(26\) 0 0
\(27\) 5.14766 0.708209i 0.990668 0.136295i
\(28\) 0 0
\(29\) 4.16372 7.21177i 0.773183 1.33919i −0.162628 0.986687i \(-0.551997\pi\)
0.935810 0.352504i \(-0.114670\pi\)
\(30\) 0 0
\(31\) −5.08113 8.80077i −0.912597 1.58066i −0.810382 0.585903i \(-0.800740\pi\)
−0.102216 0.994762i \(-0.532593\pi\)
\(32\) 0 0
\(33\) −4.71780 7.37385i −0.821263 1.28362i
\(34\) 0 0
\(35\) −2.05408 −0.347204
\(36\) 0 0
\(37\) 8.16225 1.34187 0.670933 0.741518i \(-0.265894\pi\)
0.670933 + 0.741518i \(0.265894\pi\)
\(38\) 0 0
\(39\) −1.73025 + 0.0789082i −0.277062 + 0.0126354i
\(40\) 0 0
\(41\) 2.52704 + 4.37697i 0.394658 + 0.683567i 0.993057 0.117631i \(-0.0375299\pi\)
−0.598400 + 0.801198i \(0.704197\pi\)
\(42\) 0 0
\(43\) 2.30039 3.98439i 0.350806 0.607614i −0.635585 0.772031i \(-0.719241\pi\)
0.986391 + 0.164417i \(0.0525743\pi\)
\(44\) 0 0
\(45\) −2.58259 + 5.59496i −0.384990 + 0.834048i
\(46\) 0 0
\(47\) 0.690757 1.19643i 0.100757 0.174517i −0.811240 0.584714i \(-0.801207\pi\)
0.911997 + 0.410197i \(0.134540\pi\)
\(48\) 0 0
\(49\) −0.500000 0.866025i −0.0714286 0.123718i
\(50\) 0 0
\(51\) −0.217799 + 0.420378i −0.0304980 + 0.0588647i
\(52\) 0 0
\(53\) 3.43560 0.471916 0.235958 0.971763i \(-0.424177\pi\)
0.235958 + 0.971763i \(0.424177\pi\)
\(54\) 0 0
\(55\) 10.3815 1.39984
\(56\) 0 0
\(57\) −4.28794 + 8.27621i −0.567951 + 1.09621i
\(58\) 0 0
\(59\) 0.890369 + 1.54216i 0.115916 + 0.200773i 0.918146 0.396243i \(-0.129686\pi\)
−0.802229 + 0.597016i \(0.796353\pi\)
\(60\) 0 0
\(61\) −0.390369 + 0.676139i −0.0499816 + 0.0865707i −0.889934 0.456090i \(-0.849250\pi\)
0.839952 + 0.542660i \(0.182583\pi\)
\(62\) 0 0
\(63\) −2.98755 + 0.273062i −0.376396 + 0.0344026i
\(64\) 0 0
\(65\) 1.02704 1.77889i 0.127389 0.220644i
\(66\) 0 0
\(67\) −4.19076 7.25860i −0.511982 0.886780i −0.999904 0.0138919i \(-0.995578\pi\)
0.487921 0.872888i \(-0.337755\pi\)
\(68\) 0 0
\(69\) 9.21780 0.420378i 1.10969 0.0506076i
\(70\) 0 0
\(71\) 7.78074 0.923404 0.461702 0.887035i \(-0.347239\pi\)
0.461702 + 0.887035i \(0.347239\pi\)
\(72\) 0 0
\(73\) 9.38151 1.09802 0.549012 0.835815i \(-0.315004\pi\)
0.549012 + 0.835815i \(0.315004\pi\)
\(74\) 0 0
\(75\) 0.728790 + 1.13909i 0.0841534 + 0.131531i
\(76\) 0 0
\(77\) 2.52704 + 4.37697i 0.287983 + 0.498801i
\(78\) 0 0
\(79\) 6.47150 11.2090i 0.728100 1.26111i −0.229585 0.973289i \(-0.573737\pi\)
0.957685 0.287818i \(-0.0929298\pi\)
\(80\) 0 0
\(81\) −3.01245 + 8.48087i −0.334717 + 0.942319i
\(82\) 0 0
\(83\) −2.86333 + 4.95943i −0.314291 + 0.544368i −0.979287 0.202479i \(-0.935100\pi\)
0.664996 + 0.746847i \(0.268433\pi\)
\(84\) 0 0
\(85\) −0.280738 0.486253i −0.0304503 0.0527415i
\(86\) 0 0
\(87\) 7.77335 + 12.1496i 0.833390 + 1.30258i
\(88\) 0 0
\(89\) −13.8171 −1.46461 −0.732306 0.680976i \(-0.761556\pi\)
−0.732306 + 0.680976i \(0.761556\pi\)
\(90\) 0 0
\(91\) 1.00000 0.104828
\(92\) 0 0
\(93\) 17.5833 0.801886i 1.82330 0.0831517i
\(94\) 0 0
\(95\) −5.52704 9.57312i −0.567063 0.982181i
\(96\) 0 0
\(97\) 1.10963 1.92194i 0.112666 0.195143i −0.804178 0.594388i \(-0.797394\pi\)
0.916844 + 0.399245i \(0.130728\pi\)
\(98\) 0 0
\(99\) 15.0993 1.38008i 1.51754 0.138703i
\(100\) 0 0
\(101\) −1.36333 + 2.36135i −0.135656 + 0.234963i −0.925848 0.377896i \(-0.876648\pi\)
0.790192 + 0.612860i \(0.209981\pi\)
\(102\) 0 0
\(103\) 8.99115 + 15.5731i 0.885924 + 1.53447i 0.844651 + 0.535317i \(0.179808\pi\)
0.0412728 + 0.999148i \(0.486859\pi\)
\(104\) 0 0
\(105\) 1.63667 3.15897i 0.159723 0.308284i
\(106\) 0 0
\(107\) −1.10817 −0.107131 −0.0535653 0.998564i \(-0.517059\pi\)
−0.0535653 + 0.998564i \(0.517059\pi\)
\(108\) 0 0
\(109\) 3.38151 0.323890 0.161945 0.986800i \(-0.448223\pi\)
0.161945 + 0.986800i \(0.448223\pi\)
\(110\) 0 0
\(111\) −6.50360 + 12.5527i −0.617294 + 1.19145i
\(112\) 0 0
\(113\) −9.43560 16.3429i −0.887626 1.53741i −0.842673 0.538425i \(-0.819020\pi\)
−0.0449531 0.998989i \(-0.514314\pi\)
\(114\) 0 0
\(115\) −5.47150 + 9.47691i −0.510220 + 0.883726i
\(116\) 0 0
\(117\) 1.25729 2.72382i 0.116237 0.251818i
\(118\) 0 0
\(119\) 0.136673 0.236725i 0.0125288 0.0217005i
\(120\) 0 0
\(121\) −7.27188 12.5953i −0.661080 1.14502i
\(122\) 0 0
\(123\) −8.74484 + 0.398809i −0.788496 + 0.0359594i
\(124\) 0 0
\(125\) −11.8741 −1.06205
\(126\) 0 0
\(127\) −17.1623 −1.52290 −0.761452 0.648221i \(-0.775513\pi\)
−0.761452 + 0.648221i \(0.775513\pi\)
\(128\) 0 0
\(129\) 4.29465 + 6.71248i 0.378123 + 0.591001i
\(130\) 0 0
\(131\) −8.94445 15.4922i −0.781481 1.35356i −0.931079 0.364817i \(-0.881132\pi\)
0.149599 0.988747i \(-0.452202\pi\)
\(132\) 0 0
\(133\) 2.69076 4.66053i 0.233318 0.404119i
\(134\) 0 0
\(135\) −6.54669 8.42976i −0.563450 0.725518i
\(136\) 0 0
\(137\) 2.24630 3.89071i 0.191915 0.332406i −0.753970 0.656909i \(-0.771864\pi\)
0.945885 + 0.324503i \(0.105197\pi\)
\(138\) 0 0
\(139\) 9.07227 + 15.7136i 0.769500 + 1.33281i 0.937834 + 0.347083i \(0.112828\pi\)
−0.168334 + 0.985730i \(0.553839\pi\)
\(140\) 0 0
\(141\) 1.28959 + 2.01561i 0.108603 + 0.169745i
\(142\) 0 0
\(143\) −5.05408 −0.422644
\(144\) 0 0
\(145\) −17.1052 −1.42051
\(146\) 0 0
\(147\) 1.73025 0.0789082i 0.142709 0.00650824i
\(148\) 0 0
\(149\) 2.25370 + 3.90352i 0.184630 + 0.319788i 0.943452 0.331510i \(-0.107558\pi\)
−0.758822 + 0.651298i \(0.774225\pi\)
\(150\) 0 0
\(151\) −5.49115 + 9.51094i −0.446863 + 0.773990i −0.998180 0.0603064i \(-0.980792\pi\)
0.551317 + 0.834296i \(0.314126\pi\)
\(152\) 0 0
\(153\) −0.472958 0.669906i −0.0382364 0.0541587i
\(154\) 0 0
\(155\) −10.4371 + 18.0775i −0.838325 + 1.45202i
\(156\) 0 0
\(157\) −2.08998 3.61995i −0.166799 0.288904i 0.770494 0.637447i \(-0.220010\pi\)
−0.937293 + 0.348544i \(0.886676\pi\)
\(158\) 0 0
\(159\) −2.73745 + 5.28360i −0.217094 + 0.419016i
\(160\) 0 0
\(161\) −5.32743 −0.419860
\(162\) 0 0
\(163\) 5.61849 0.440074 0.220037 0.975492i \(-0.429382\pi\)
0.220037 + 0.975492i \(0.429382\pi\)
\(164\) 0 0
\(165\) −8.27188 + 15.9657i −0.643965 + 1.24293i
\(166\) 0 0
\(167\) −5.44592 9.43260i −0.421418 0.729917i 0.574661 0.818392i \(-0.305134\pi\)
−0.996078 + 0.0884750i \(0.971801\pi\)
\(168\) 0 0
\(169\) 6.00000 10.3923i 0.461538 0.799408i
\(170\) 0 0
\(171\) −9.31138 13.1888i −0.712059 1.00857i
\(172\) 0 0
\(173\) −7.30039 + 12.6446i −0.555038 + 0.961354i 0.442862 + 0.896590i \(0.353963\pi\)
−0.997901 + 0.0647648i \(0.979370\pi\)
\(174\) 0 0
\(175\) −0.390369 0.676139i −0.0295091 0.0511113i
\(176\) 0 0
\(177\) −3.08113 + 0.140515i −0.231592 + 0.0105617i
\(178\) 0 0
\(179\) 23.4897 1.75570 0.877851 0.478934i \(-0.158977\pi\)
0.877851 + 0.478934i \(0.158977\pi\)
\(180\) 0 0
\(181\) −1.39922 −0.104003 −0.0520017 0.998647i \(-0.516560\pi\)
−0.0520017 + 0.998647i \(0.516560\pi\)
\(182\) 0 0
\(183\) −0.728790 1.13909i −0.0538737 0.0842038i
\(184\) 0 0
\(185\) −8.38298 14.5197i −0.616329 1.06751i
\(186\) 0 0
\(187\) −0.690757 + 1.19643i −0.0505132 + 0.0874914i
\(188\) 0 0
\(189\) 1.96050 4.81211i 0.142606 0.350030i
\(190\) 0 0
\(191\) 11.6819 20.2336i 0.845273 1.46406i −0.0401112 0.999195i \(-0.512771\pi\)
0.885384 0.464860i \(-0.153895\pi\)
\(192\) 0 0
\(193\) 7.27188 + 12.5953i 0.523442 + 0.906628i 0.999628 + 0.0272830i \(0.00868552\pi\)
−0.476186 + 0.879345i \(0.657981\pi\)
\(194\) 0 0
\(195\) 1.91741 + 2.99689i 0.137309 + 0.214611i
\(196\) 0 0
\(197\) −17.3422 −1.23558 −0.617791 0.786343i \(-0.711972\pi\)
−0.617791 + 0.786343i \(0.711972\pi\)
\(198\) 0 0
\(199\) 11.5438 0.818316 0.409158 0.912464i \(-0.365822\pi\)
0.409158 + 0.912464i \(0.365822\pi\)
\(200\) 0 0
\(201\) 14.5021 0.661371i 1.02290 0.0466495i
\(202\) 0 0
\(203\) −4.16372 7.21177i −0.292236 0.506167i
\(204\) 0 0
\(205\) 5.19076 8.99066i 0.362538 0.627935i
\(206\) 0 0
\(207\) −6.69815 + 14.5110i −0.465554 + 1.00858i
\(208\) 0 0
\(209\) −13.5993 + 23.5547i −0.940684 + 1.62931i
\(210\) 0 0
\(211\) −12.2630 21.2402i −0.844222 1.46223i −0.886295 0.463120i \(-0.846730\pi\)
0.0420736 0.999115i \(-0.486604\pi\)
\(212\) 0 0
\(213\) −6.19961 + 11.9660i −0.424790 + 0.819895i
\(214\) 0 0
\(215\) −9.45038 −0.644511
\(216\) 0 0
\(217\) −10.1623 −0.689859
\(218\) 0 0
\(219\) −7.47509 + 14.4278i −0.505120 + 0.974940i
\(220\) 0 0
\(221\) 0.136673 + 0.236725i 0.00919363 + 0.0159238i
\(222\) 0 0
\(223\) 4.28074 7.41446i 0.286659 0.496509i −0.686351 0.727271i \(-0.740789\pi\)
0.973010 + 0.230762i \(0.0741219\pi\)
\(224\) 0 0
\(225\) −2.33249 + 0.213190i −0.155499 + 0.0142127i
\(226\) 0 0
\(227\) −10.5993 + 18.3586i −0.703501 + 1.21850i 0.263729 + 0.964597i \(0.415048\pi\)
−0.967230 + 0.253903i \(0.918286\pi\)
\(228\) 0 0
\(229\) 2.28074 + 3.95035i 0.150715 + 0.261047i 0.931491 0.363765i \(-0.118509\pi\)
−0.780775 + 0.624812i \(0.785176\pi\)
\(230\) 0 0
\(231\) −8.74484 + 0.398809i −0.575368 + 0.0262397i
\(232\) 0 0
\(233\) 13.5074 0.884899 0.442449 0.896794i \(-0.354110\pi\)
0.442449 + 0.896794i \(0.354110\pi\)
\(234\) 0 0
\(235\) −2.83775 −0.185114
\(236\) 0 0
\(237\) 12.0818 + 18.8837i 0.784797 + 1.22663i
\(238\) 0 0
\(239\) −6.82743 11.8255i −0.441630 0.764925i 0.556181 0.831061i \(-0.312266\pi\)
−0.997811 + 0.0661361i \(0.978933\pi\)
\(240\) 0 0
\(241\) −1.60963 + 2.78796i −0.103685 + 0.179588i −0.913200 0.407511i \(-0.866397\pi\)
0.809515 + 0.587099i \(0.199730\pi\)
\(242\) 0 0
\(243\) −10.6424 11.3903i −0.682711 0.730689i
\(244\) 0 0
\(245\) −1.02704 + 1.77889i −0.0656153 + 0.113649i
\(246\) 0 0
\(247\) 2.69076 + 4.66053i 0.171209 + 0.296542i
\(248\) 0 0
\(249\) −5.34562 8.35512i −0.338765 0.529484i
\(250\) 0 0
\(251\) −4.38151 −0.276559 −0.138279 0.990393i \(-0.544157\pi\)
−0.138279 + 0.990393i \(0.544157\pi\)
\(252\) 0 0
\(253\) 26.9253 1.69278
\(254\) 0 0
\(255\) 0.971495 0.0443051i 0.0608374 0.00277449i
\(256\) 0 0
\(257\) −5.72665 9.91886i −0.357219 0.618721i 0.630276 0.776371i \(-0.282942\pi\)
−0.987495 + 0.157650i \(0.949608\pi\)
\(258\) 0 0
\(259\) 4.08113 7.06872i 0.253589 0.439229i
\(260\) 0 0
\(261\) −24.8786 + 2.27391i −1.53995 + 0.140751i
\(262\) 0 0
\(263\) −3.41741 + 5.91913i −0.210727 + 0.364989i −0.951942 0.306278i \(-0.900916\pi\)
0.741216 + 0.671267i \(0.234250\pi\)
\(264\) 0 0
\(265\) −3.52850 6.11155i −0.216754 0.375429i
\(266\) 0 0
\(267\) 11.0093 21.2493i 0.673760 1.30044i
\(268\) 0 0
\(269\) 9.67257 0.589747 0.294873 0.955536i \(-0.404722\pi\)
0.294873 + 0.955536i \(0.404722\pi\)
\(270\) 0 0
\(271\) 12.8377 0.779838 0.389919 0.920849i \(-0.372503\pi\)
0.389919 + 0.920849i \(0.372503\pi\)
\(272\) 0 0
\(273\) −0.796790 + 1.53790i −0.0482239 + 0.0930777i
\(274\) 0 0
\(275\) 1.97296 + 3.41726i 0.118974 + 0.206069i
\(276\) 0 0
\(277\) −5.79153 + 10.0312i −0.347980 + 0.602718i −0.985890 0.167392i \(-0.946465\pi\)
0.637911 + 0.770110i \(0.279799\pi\)
\(278\) 0 0
\(279\) −12.7769 + 27.6802i −0.764936 + 1.65717i
\(280\) 0 0
\(281\) 2.46410 4.26795i 0.146996 0.254605i −0.783120 0.621871i \(-0.786373\pi\)
0.930116 + 0.367266i \(0.119706\pi\)
\(282\) 0 0
\(283\) −9.30039 16.1087i −0.552851 0.957565i −0.998067 0.0621426i \(-0.980207\pi\)
0.445217 0.895423i \(-0.353127\pi\)
\(284\) 0 0
\(285\) 19.1264 0.872258i 1.13295 0.0516681i
\(286\) 0 0
\(287\) 5.05408 0.298333
\(288\) 0 0
\(289\) −16.9253 −0.995605
\(290\) 0 0
\(291\) 2.07160 + 3.23788i 0.121439 + 0.189808i
\(292\) 0 0
\(293\) 12.3801 + 21.4429i 0.723250 + 1.25271i 0.959690 + 0.281060i \(0.0906861\pi\)
−0.236440 + 0.971646i \(0.575981\pi\)
\(294\) 0 0
\(295\) 1.82889 3.16774i 0.106482 0.184433i
\(296\) 0 0
\(297\) −9.90856 + 24.3208i −0.574953 + 1.41124i
\(298\) 0 0
\(299\) 2.66372 4.61369i 0.154047 0.266817i
\(300\) 0 0
\(301\) −2.30039 3.98439i −0.132592 0.229656i
\(302\) 0 0
\(303\) −2.54523 3.97816i −0.146220 0.228539i
\(304\) 0 0
\(305\) 1.60370 0.0918277
\(306\) 0 0
\(307\) −21.9430 −1.25235 −0.626176 0.779681i \(-0.715381\pi\)
−0.626176 + 0.779681i \(0.715381\pi\)
\(308\) 0 0
\(309\) −31.1139 + 1.41895i −1.77001 + 0.0807213i
\(310\) 0 0
\(311\) 13.5811 + 23.5232i 0.770115 + 1.33388i 0.937499 + 0.347987i \(0.113135\pi\)
−0.167384 + 0.985892i \(0.553532\pi\)
\(312\) 0 0
\(313\) 4.27188 7.39912i 0.241461 0.418223i −0.719670 0.694317i \(-0.755707\pi\)
0.961131 + 0.276094i \(0.0890400\pi\)
\(314\) 0 0
\(315\) 3.55408 + 5.03407i 0.200250 + 0.283638i
\(316\) 0 0
\(317\) −0.199612 + 0.345738i −0.0112113 + 0.0194186i −0.871577 0.490259i \(-0.836902\pi\)
0.860365 + 0.509678i \(0.170235\pi\)
\(318\) 0 0
\(319\) 21.0438 + 36.4489i 1.17822 + 2.04075i
\(320\) 0 0
\(321\) 0.882977 1.70425i 0.0492830 0.0951219i
\(322\) 0 0
\(323\) 1.47102 0.0818495
\(324\) 0 0
\(325\) 0.780738 0.0433076
\(326\) 0 0
\(327\) −2.69436 + 5.20042i −0.148998 + 0.287584i
\(328\) 0 0
\(329\) −0.690757 1.19643i −0.0380827 0.0659611i
\(330\) 0 0
\(331\) −2.80924 + 4.86575i −0.154410 + 0.267446i −0.932844 0.360281i \(-0.882681\pi\)
0.778434 + 0.627726i \(0.216014\pi\)
\(332\) 0 0
\(333\) −14.1228 20.0037i −0.773922 1.09620i
\(334\) 0 0
\(335\) −8.60817 + 14.9098i −0.470314 + 0.814609i
\(336\) 0 0
\(337\) 14.4911 + 25.0994i 0.789383 + 1.36725i 0.926345 + 0.376675i \(0.122933\pi\)
−0.136962 + 0.990576i \(0.543734\pi\)
\(338\) 0 0
\(339\) 32.6519 1.48909i 1.77341 0.0808764i
\(340\) 0 0
\(341\) 51.3609 2.78135
\(342\) 0 0
\(343\) −1.00000 −0.0539949
\(344\) 0 0
\(345\) −10.2149 15.9657i −0.549950 0.859564i
\(346\) 0 0
\(347\) 17.2345 + 29.8511i 0.925198 + 1.60249i 0.791243 + 0.611502i \(0.209434\pi\)
0.133955 + 0.990987i \(0.457232\pi\)
\(348\) 0 0
\(349\) −8.78074 + 15.2087i −0.470022 + 0.814102i −0.999412 0.0342762i \(-0.989087\pi\)
0.529390 + 0.848378i \(0.322421\pi\)
\(350\) 0 0
\(351\) 3.18716 + 4.10390i 0.170118 + 0.219050i
\(352\) 0 0
\(353\) −16.4445 + 28.4826i −0.875250 + 1.51598i −0.0187537 + 0.999824i \(0.505970\pi\)
−0.856496 + 0.516153i \(0.827364\pi\)
\(354\) 0 0
\(355\) −7.99115 13.8411i −0.424126 0.734608i
\(356\) 0 0
\(357\) 0.255158 + 0.398809i 0.0135044 + 0.0211072i
\(358\) 0 0
\(359\) −2.96362 −0.156414 −0.0782071 0.996937i \(-0.524920\pi\)
−0.0782071 + 0.996937i \(0.524920\pi\)
\(360\) 0 0
\(361\) 9.96070 0.524247
\(362\) 0 0
\(363\) 25.1644 1.14762i 1.32079 0.0602346i
\(364\) 0 0
\(365\) −9.63521 16.6887i −0.504330 0.873525i
\(366\) 0 0
\(367\) 6.68190 11.5734i 0.348792 0.604126i −0.637243 0.770663i \(-0.719925\pi\)
0.986035 + 0.166537i \(0.0532585\pi\)
\(368\) 0 0
\(369\) 6.35447 13.7664i 0.330801 0.716652i
\(370\) 0 0
\(371\) 1.71780 2.97532i 0.0891837 0.154471i
\(372\) 0 0
\(373\) −2.30039 3.98439i −0.119110 0.206304i 0.800305 0.599592i \(-0.204671\pi\)
−0.919415 + 0.393289i \(0.871337\pi\)
\(374\) 0 0
\(375\) 9.46118 18.2612i 0.488573 0.943003i
\(376\) 0 0
\(377\) 8.32743 0.428884
\(378\) 0 0
\(379\) 2.21926 0.113996 0.0569979 0.998374i \(-0.481847\pi\)
0.0569979 + 0.998374i \(0.481847\pi\)
\(380\) 0 0
\(381\) 13.6747 26.3938i 0.700576 1.35219i
\(382\) 0 0
\(383\) −15.5167 26.8758i −0.792868 1.37329i −0.924184 0.381947i \(-0.875254\pi\)
0.131317 0.991340i \(-0.458079\pi\)
\(384\) 0 0
\(385\) 5.19076 8.99066i 0.264545 0.458206i
\(386\) 0 0
\(387\) −13.7450 + 1.25630i −0.698699 + 0.0638613i
\(388\) 0 0
\(389\) 12.4174 21.5076i 0.629588 1.09048i −0.358047 0.933704i \(-0.616557\pi\)
0.987634 0.156774i \(-0.0501095\pi\)
\(390\) 0 0
\(391\) −0.728116 1.26113i −0.0368224 0.0637783i
\(392\) 0 0
\(393\) 30.9523 1.41158i 1.56134 0.0712049i
\(394\) 0 0
\(395\) −26.5860 −1.33769
\(396\) 0 0
\(397\) 17.7237 0.889528 0.444764 0.895648i \(-0.353287\pi\)
0.444764 + 0.895648i \(0.353287\pi\)
\(398\) 0 0
\(399\) 5.02344 + 7.85157i 0.251487 + 0.393070i
\(400\) 0 0
\(401\) −15.0885 26.1341i −0.753485 1.30507i −0.946124 0.323804i \(-0.895038\pi\)
0.192640 0.981270i \(-0.438295\pi\)
\(402\) 0 0
\(403\) 5.08113 8.80077i 0.253109 0.438398i
\(404\) 0 0
\(405\) 18.1804 3.35139i 0.903393 0.166532i
\(406\) 0 0
\(407\) −20.6264 + 35.7259i −1.02241 + 1.77087i
\(408\) 0 0
\(409\) −8.38151 14.5172i −0.414439 0.717830i 0.580930 0.813953i \(-0.302689\pi\)
−0.995369 + 0.0961236i \(0.969356\pi\)
\(410\) 0 0
\(411\) 4.19368 + 6.55466i 0.206859 + 0.323318i
\(412\) 0 0
\(413\) 1.78074 0.0876244
\(414\) 0 0
\(415\) 11.7630 0.577424
\(416\) 0 0
\(417\) −31.3946 + 1.43175i −1.53740 + 0.0701133i
\(418\) 0 0
\(419\) 1.44445 + 2.50187i 0.0705662 + 0.122224i 0.899150 0.437641i \(-0.144186\pi\)
−0.828583 + 0.559866i \(0.810853\pi\)
\(420\) 0 0
\(421\) 0.0899807 0.155851i 0.00438539 0.00759572i −0.863824 0.503793i \(-0.831937\pi\)
0.868210 + 0.496197i \(0.165271\pi\)
\(422\) 0 0
\(423\) −4.12734 + 0.377240i −0.200678 + 0.0183420i
\(424\) 0 0
\(425\) 0.106706 0.184820i 0.00517600 0.00896509i
\(426\) 0 0
\(427\) 0.390369 + 0.676139i 0.0188913 + 0.0327207i
\(428\) 0 0
\(429\) 4.02704 7.77266i 0.194427 0.375268i
\(430\) 0 0
\(431\) 4.76595 0.229568 0.114784 0.993390i \(-0.463382\pi\)
0.114784 + 0.993390i \(0.463382\pi\)
\(432\) 0 0
\(433\) −27.7630 −1.33421 −0.667103 0.744965i \(-0.732466\pi\)
−0.667103 + 0.744965i \(0.732466\pi\)
\(434\) 0 0
\(435\) 13.6293 26.3061i 0.653474 1.26128i
\(436\) 0 0
\(437\) −14.3348 24.8286i −0.685728 1.18771i
\(438\) 0 0
\(439\) −2.32889 + 4.03376i −0.111152 + 0.192521i −0.916235 0.400641i \(-0.868787\pi\)
0.805083 + 0.593162i \(0.202121\pi\)
\(440\) 0 0
\(441\) −1.25729 + 2.72382i −0.0598712 + 0.129706i
\(442\) 0 0
\(443\) −1.38151 + 2.39285i −0.0656377 + 0.113688i −0.896977 0.442078i \(-0.854242\pi\)
0.831339 + 0.555766i \(0.187575\pi\)
\(444\) 0 0
\(445\) 14.1908 + 24.5791i 0.672706 + 1.16516i
\(446\) 0 0
\(447\) −7.79893 + 0.355670i −0.368877 + 0.0168226i
\(448\) 0 0
\(449\) 19.9430 0.941168 0.470584 0.882355i \(-0.344043\pi\)
0.470584 + 0.882355i \(0.344043\pi\)
\(450\) 0 0
\(451\) −25.5438 −1.20281
\(452\) 0 0
\(453\) −10.2516 16.0230i −0.481660 0.752828i
\(454\) 0 0
\(455\) −1.02704 1.77889i −0.0481485 0.0833956i
\(456\) 0 0
\(457\) −13.6908 + 23.7131i −0.640427 + 1.10925i 0.344911 + 0.938635i \(0.387909\pi\)
−0.985338 + 0.170616i \(0.945424\pi\)
\(458\) 0 0
\(459\) 1.40709 0.193586i 0.0656775 0.00903583i
\(460\) 0 0
\(461\) 3.02558 5.24046i 0.140915 0.244072i −0.786926 0.617047i \(-0.788329\pi\)
0.927842 + 0.372975i \(0.121662\pi\)
\(462\) 0 0
\(463\) −8.77188 15.1933i −0.407664 0.706095i 0.586964 0.809613i \(-0.300323\pi\)
−0.994628 + 0.103519i \(0.966990\pi\)
\(464\) 0 0
\(465\) −19.4852 30.4551i −0.903605 1.41232i
\(466\) 0 0
\(467\) 23.6156 1.09280 0.546399 0.837525i \(-0.315998\pi\)
0.546399 + 0.837525i \(0.315998\pi\)
\(468\) 0 0
\(469\) −8.38151 −0.387022
\(470\) 0 0
\(471\) 7.23239 0.329833i 0.333251 0.0151979i
\(472\) 0 0
\(473\) 11.6264 + 20.1374i 0.534580 + 0.925920i
\(474\) 0 0
\(475\) 2.10078 3.63865i 0.0963902 0.166953i
\(476\) 0 0
\(477\) −5.94445 8.41983i −0.272178 0.385518i
\(478\) 0 0
\(479\) 19.1264 33.1278i 0.873906 1.51365i 0.0159814 0.999872i \(-0.494913\pi\)
0.857924 0.513776i \(-0.171754\pi\)
\(480\) 0 0
\(481\) 4.08113 + 7.06872i 0.186083 + 0.322306i
\(482\) 0 0
\(483\) 4.24484 8.19304i 0.193147 0.372796i
\(484\) 0 0
\(485\) −4.55855 −0.206993
\(486\) 0 0
\(487\) 6.57918 0.298131 0.149066 0.988827i \(-0.452373\pi\)
0.149066 + 0.988827i \(0.452373\pi\)
\(488\) 0 0
\(489\) −4.47675 + 8.64065i −0.202446 + 0.390744i
\(490\) 0 0
\(491\) −1.02704 1.77889i −0.0463498 0.0802801i 0.841920 0.539603i \(-0.181426\pi\)
−0.888270 + 0.459323i \(0.848092\pi\)
\(492\) 0 0
\(493\) 1.13814 1.97131i 0.0512591 0.0887833i
\(494\) 0 0
\(495\) −17.9626 25.4426i −0.807361 1.14356i
\(496\) 0 0
\(497\) 3.89037 6.73832i 0.174507 0.302255i
\(498\) 0 0
\(499\) −8.16225 14.1374i −0.365393 0.632879i 0.623446 0.781866i \(-0.285732\pi\)
−0.988839 + 0.148987i \(0.952399\pi\)
\(500\) 0 0
\(501\) 18.8456 0.859455i 0.841960 0.0383976i
\(502\) 0 0
\(503\) 5.60078 0.249726 0.124863 0.992174i \(-0.460151\pi\)
0.124863 + 0.992174i \(0.460151\pi\)
\(504\) 0 0
\(505\) 5.60078 0.249231
\(506\) 0 0
\(507\) 11.2016 + 17.5079i 0.497478 + 0.777551i
\(508\) 0 0
\(509\) −0.336285 0.582462i −0.0149056 0.0258172i 0.858476 0.512853i \(-0.171411\pi\)
−0.873382 + 0.487036i \(0.838078\pi\)
\(510\) 0 0
\(511\) 4.69076 8.12463i 0.207507 0.359412i
\(512\) 0 0
\(513\) 27.7022 3.81124i 1.22308 0.168270i
\(514\) 0 0
\(515\) 18.4686 31.9885i 0.813822 1.40958i
\(516\) 0 0
\(517\) 3.49115 + 6.04684i 0.153540 + 0.265940i
\(518\) 0 0
\(519\) −13.6293 21.3024i −0.598259 0.935070i
\(520\) 0 0
\(521\) 26.4533 1.15894 0.579470 0.814993i \(-0.303260\pi\)
0.579470 + 0.814993i \(0.303260\pi\)
\(522\) 0 0
\(523\) −27.3068 −1.19404 −0.597021 0.802225i \(-0.703649\pi\)
−0.597021 + 0.802225i \(0.703649\pi\)
\(524\) 0 0
\(525\) 1.35087 0.0616067i 0.0589570 0.00268874i
\(526\) 0 0
\(527\) −1.38891 2.40566i −0.0605017 0.104792i
\(528\) 0 0
\(529\) −2.69076 + 4.66053i −0.116989 + 0.202632i
\(530\) 0 0
\(531\) 2.23891 4.85041i 0.0971605 0.210490i
\(532\) 0 0
\(533\) −2.52704 + 4.37697i −0.109458 + 0.189587i
\(534\) 0 0
\(535\) 1.13814 + 1.97131i 0.0492059 + 0.0852271i
\(536\) 0 0
\(537\) −18.7163 + 36.1247i −0.807670 + 1.55890i
\(538\) 0 0
\(539\) 5.05408 0.217695
\(540\) 0 0
\(541\) −19.3245 −0.830825 −0.415413 0.909633i \(-0.636363\pi\)
−0.415413 + 0.909633i \(0.636363\pi\)
\(542\) 0 0
\(543\) 1.11489 2.15186i 0.0478444 0.0923452i
\(544\) 0 0
\(545\) −3.47296 6.01534i −0.148765 0.257669i
\(546\) 0 0
\(547\) −9.17111 + 15.8848i −0.392128 + 0.679186i −0.992730 0.120362i \(-0.961594\pi\)
0.600602 + 0.799548i \(0.294928\pi\)
\(548\) 0 0
\(549\) 2.33249 0.213190i 0.0995483 0.00909873i
\(550\) 0 0
\(551\) 22.4071 38.8102i 0.954574 1.65337i
\(552\) 0 0
\(553\) −6.47150 11.2090i −0.275196 0.476653i
\(554\) 0 0
\(555\) 29.0093 1.32297i 1.23138 0.0561570i
\(556\) 0 0
\(557\) 9.19863 0.389758 0.194879 0.980827i \(-0.437569\pi\)
0.194879 + 0.980827i \(0.437569\pi\)
\(558\) 0 0
\(559\) 4.60078 0.194592
\(560\) 0 0
\(561\) −1.28959 2.01561i −0.0544466 0.0850993i
\(562\) 0 0
\(563\) 16.5811 + 28.7194i 0.698811 + 1.21038i 0.968879 + 0.247535i \(0.0796206\pi\)
−0.270068 + 0.962841i \(0.587046\pi\)
\(564\) 0 0
\(565\) −19.3815 + 33.5698i −0.815386 + 1.41229i
\(566\) 0 0
\(567\) 5.83842 + 6.84929i 0.245191 + 0.287643i
\(568\) 0 0
\(569\) −13.1008 + 22.6912i −0.549213 + 0.951265i 0.449116 + 0.893474i \(0.351739\pi\)
−0.998329 + 0.0577914i \(0.981594\pi\)
\(570\) 0 0
\(571\) 4.89037 + 8.47037i 0.204656 + 0.354474i 0.950023 0.312180i \(-0.101059\pi\)
−0.745367 + 0.666654i \(0.767726\pi\)
\(572\) 0 0
\(573\) 21.8092 + 34.0875i 0.911094 + 1.42403i
\(574\) 0 0
\(575\) −4.15933 −0.173456
\(576\) 0 0
\(577\) 36.3068 1.51147 0.755736 0.654877i \(-0.227279\pi\)
0.755736 + 0.654877i \(0.227279\pi\)
\(578\) 0 0
\(579\) −25.1644 + 1.14762i −1.04580 + 0.0476936i
\(580\) 0 0
\(581\) 2.86333 + 4.95943i 0.118791 + 0.205752i
\(582\) 0 0
\(583\) −8.68190 + 15.0375i −0.359568 + 0.622789i
\(584\) 0 0
\(585\) −6.13667 + 0.560893i −0.253720 + 0.0231901i
\(586\) 0 0
\(587\) −12.0737 + 20.9123i −0.498336 + 0.863144i −0.999998 0.00191995i \(-0.999389\pi\)
0.501662 + 0.865064i \(0.332722\pi\)
\(588\) 0 0
\(589\) −27.3442 47.3615i −1.12670 1.95150i
\(590\) 0 0
\(591\) 13.8181 26.6705i 0.568401 1.09708i
\(592\) 0 0
\(593\) 41.4897 1.70378 0.851889 0.523723i \(-0.175457\pi\)
0.851889 + 0.523723i \(0.175457\pi\)
\(594\) 0 0
\(595\) −0.561476 −0.0230183
\(596\) 0 0
\(597\) −9.19795 + 17.7531i −0.376447 + 0.726587i
\(598\) 0 0
\(599\) −11.3422 19.6453i −0.463430 0.802685i 0.535699 0.844409i \(-0.320048\pi\)
−0.999129 + 0.0417243i \(0.986715\pi\)
\(600\) 0 0
\(601\) 20.1249 34.8573i 0.820912 1.42186i −0.0840927 0.996458i \(-0.526799\pi\)
0.905004 0.425403i \(-0.139867\pi\)
\(602\) 0 0
\(603\) −10.5380 + 22.8298i −0.429142 + 0.929700i
\(604\) 0 0
\(605\) −14.9371 + 25.8717i −0.607278 + 1.05184i
\(606\) 0 0
\(607\) 8.66225 + 15.0035i 0.351590 + 0.608972i 0.986528 0.163591i \(-0.0523078\pi\)
−0.634938 + 0.772563i \(0.718974\pi\)
\(608\) 0 0
\(609\) 14.4086 0.657103i 0.583864 0.0266272i
\(610\) 0 0
\(611\) 1.38151 0.0558901
\(612\) 0 0
\(613\) −32.9646 −1.33143 −0.665713 0.746207i \(-0.731873\pi\)
−0.665713 + 0.746207i \(0.731873\pi\)
\(614\) 0 0
\(615\) 9.69076 + 15.1465i 0.390769 + 0.610766i
\(616\) 0 0
\(617\) 13.4700 + 23.3308i 0.542283 + 0.939262i 0.998772 + 0.0495330i \(0.0157733\pi\)
−0.456489 + 0.889729i \(0.650893\pi\)
\(618\) 0 0
\(619\) −0.991146 + 1.71671i −0.0398375 + 0.0690006i −0.885257 0.465103i \(-0.846017\pi\)
0.845419 + 0.534103i \(0.179351\pi\)
\(620\) 0 0
\(621\) −16.9794 21.8633i −0.681358 0.877342i
\(622\) 0 0
\(623\) −6.90856 + 11.9660i −0.276785 + 0.479407i
\(624\) 0 0
\(625\) 10.2434 + 17.7421i 0.409735 + 0.709682i
\(626\) 0 0
\(627\) −25.3889 39.6825i −1.01394 1.58477i
\(628\) 0 0
\(629\) 2.23112 0.0889606
\(630\) 0 0
\(631\) 25.4868 1.01461 0.507306 0.861766i \(-0.330641\pi\)
0.507306 + 0.861766i \(0.330641\pi\)
\(632\) 0 0
\(633\) 42.4363 1.93531i 1.68669 0.0769216i
\(634\) 0 0
\(635\) 17.6264 + 30.5297i 0.699481 + 1.21154i
\(636\) 0 0
\(637\) 0.500000 0.866025i 0.0198107 0.0343132i
\(638\) 0 0
\(639\) −13.4626 19.0687i −0.532574 0.754347i
\(640\) 0 0
\(641\) 20.0423 34.7143i 0.791623 1.37113i −0.133338 0.991071i \(-0.542570\pi\)
0.924961 0.380061i \(-0.124097\pi\)
\(642\) 0 0
\(643\) 3.50885 + 6.07751i 0.138376 + 0.239674i 0.926882 0.375353i \(-0.122479\pi\)
−0.788506 + 0.615027i \(0.789145\pi\)
\(644\) 0 0
\(645\) 7.52997 14.5337i 0.296492 0.572264i
\(646\) 0 0
\(647\) 11.8142 0.464464 0.232232 0.972660i \(-0.425397\pi\)
0.232232 + 0.972660i \(0.425397\pi\)
\(648\) 0 0
\(649\) −9.00000 −0.353281
\(650\) 0 0
\(651\) 8.09718 15.6285i 0.317353 0.612529i
\(652\) 0 0
\(653\) −0.136673 0.236725i −0.00534843 0.00926375i 0.863339 0.504625i \(-0.168369\pi\)
−0.868687 + 0.495361i \(0.835036\pi\)
\(654\) 0 0
\(655\) −18.3727 + 31.8224i −0.717879 + 1.24340i
\(656\) 0 0
\(657\) −16.2324 22.9918i −0.633286 0.896997i
\(658\) 0 0
\(659\) 7.39970 12.8167i 0.288251 0.499266i −0.685141 0.728410i \(-0.740259\pi\)
0.973392 + 0.229144i \(0.0735928\pi\)
\(660\) 0 0
\(661\) 4.50885 + 7.80956i 0.175374 + 0.303757i 0.940291 0.340372i \(-0.110553\pi\)
−0.764917 + 0.644129i \(0.777220\pi\)
\(662\) 0 0
\(663\) −0.472958 + 0.0215693i −0.0183682 + 0.000837681i
\(664\) 0 0
\(665\) −11.0541 −0.428659
\(666\) 0 0
\(667\) −44.3638 −1.71777
\(668\) 0 0
\(669\) 7.99182 + 12.4911i 0.308982 + 0.482934i
\(670\) 0 0
\(671\) −1.97296 3.41726i −0.0761652 0.131922i
\(672\) 0 0
\(673\) −11.9803 + 20.7506i −0.461809 + 0.799876i −0.999051 0.0435519i \(-0.986133\pi\)
0.537243 + 0.843428i \(0.319466\pi\)
\(674\) 0 0
\(675\) 1.53064 3.75700i 0.0589144 0.144607i
\(676\) 0 0
\(677\) 3.32889 5.76581i 0.127940 0.221598i −0.794938 0.606690i \(-0.792497\pi\)
0.922878 + 0.385092i \(0.125830\pi\)
\(678\) 0 0
\(679\) −1.10963 1.92194i −0.0425837 0.0737572i
\(680\) 0 0
\(681\) −19.7881 30.9286i −0.758283 1.18518i
\(682\) 0 0
\(683\) 30.0728 1.15070 0.575351 0.817907i \(-0.304865\pi\)
0.575351 + 0.817907i \(0.304865\pi\)
\(684\) 0 0
\(685\) −9.22820 −0.352591
\(686\) 0 0
\(687\) −7.89251 + 0.359938i −0.301118 + 0.0137325i
\(688\) 0 0
\(689\) 1.71780 + 2.97532i 0.0654429 + 0.113351i
\(690\) 0 0
\(691\) −1.63814 + 2.83733i −0.0623176 + 0.107937i −0.895501 0.445060i \(-0.853183\pi\)
0.833183 + 0.552997i \(0.186516\pi\)
\(692\) 0 0
\(693\) 6.35447 13.7664i 0.241386 0.522943i
\(694\) 0 0
\(695\) 18.6352 32.2771i 0.706874 1.22434i
\(696\) 0 0
\(697\) 0.690757 + 1.19643i 0.0261643 + 0.0453179i
\(698\) 0 0
\(699\) −10.7626 + 20.7730i −0.407077 + 0.785706i
\(700\) 0 0
\(701\) −32.2891 −1.21954 −0.609771 0.792578i \(-0.708739\pi\)
−0.609771 + 0.792578i \(0.708739\pi\)
\(702\) 0 0
\(703\) 43.9253 1.65667
\(704\) 0 0
\(705\) 2.26109 4.36416i 0.0851575 0.164364i
\(706\) 0 0
\(707\) 1.36333 + 2.36135i 0.0512732 + 0.0888078i
\(708\) 0 0
\(709\) 24.5438 42.5111i 0.921761 1.59654i 0.125071 0.992148i \(-0.460084\pi\)
0.796690 0.604388i \(-0.206582\pi\)
\(710\) 0 0
\(711\) −38.6678 + 3.53424i −1.45016 + 0.132544i
\(712\) 0 0
\(713\) −27.0693 + 46.8855i −1.01376 + 1.75588i
\(714\) 0 0
\(715\) 5.19076 + 8.99066i 0.194123 + 0.336231i
\(716\) 0 0
\(717\) 23.6264 1.07748i 0.882342 0.0402393i
\(718\) 0 0
\(719\) 41.9617 1.56491 0.782453 0.622710i \(-0.213968\pi\)
0.782453 + 0.622710i \(0.213968\pi\)
\(720\) 0 0
\(721\) 17.9823 0.669696
\(722\) 0 0
\(723\) −3.00506 4.69687i −0.111759 0.174678i
\(724\) 0 0
\(725\) −3.25077 5.63050i −0.120731 0.209112i
\(726\) 0 0
\(727\) −14.2434 + 24.6703i −0.528258 + 0.914969i 0.471200 + 0.882027i \(0.343821\pi\)
−0.999457 + 0.0329425i \(0.989512\pi\)
\(728\) 0 0
\(729\) 25.9969 7.29124i 0.962847 0.270046i
\(730\) 0 0
\(731\) 0.628802 1.08912i 0.0232571 0.0402825i
\(732\) 0 0
\(733\) −14.2630 24.7043i −0.526817 0.912474i −0.999512 0.0312475i \(-0.990052\pi\)
0.472695 0.881226i \(-0.343281\pi\)
\(734\) 0 0
\(735\) −1.91741 2.99689i −0.0707248 0.110542i
\(736\) 0 0
\(737\) 42.3609 1.56038
\(738\) 0 0
\(739\) −7.85934 −0.289110 −0.144555 0.989497i \(-0.546175\pi\)
−0.144555 + 0.989497i \(0.546175\pi\)
\(740\) 0 0
\(741\) −9.31138 + 0.424646i −0.342062 + 0.0155998i
\(742\) 0 0
\(743\) −3.37364 5.84332i −0.123767 0.214371i 0.797483 0.603341i \(-0.206164\pi\)
−0.921250 + 0.388970i \(0.872831\pi\)
\(744\) 0 0
\(745\) 4.62928 8.01815i 0.169604 0.293762i
\(746\) 0 0
\(747\) 17.1086 1.56373i 0.625973 0.0572140i
\(748\) 0 0
\(749\) −0.554084 + 0.959702i −0.0202458 + 0.0350667i
\(750\) 0 0
\(751\) 11.0900 + 19.2084i 0.404679 + 0.700925i 0.994284 0.106767i \(-0.0340499\pi\)
−0.589605 + 0.807692i \(0.700717\pi\)
\(752\) 0 0
\(753\) 3.49115 6.73832i 0.127224 0.245558i
\(754\) 0 0
\(755\) 22.5586 0.820990
\(756\) 0 0
\(757\) −20.3815 −0.740779 −0.370389 0.928877i \(-0.620776\pi\)
−0.370389 + 0.928877i \(0.620776\pi\)
\(758\) 0 0
\(759\) −21.4538 + 41.4083i −0.778723 + 1.50303i
\(760\) 0 0
\(761\) −20.3274 35.2081i −0.736869 1.27629i −0.953899 0.300129i \(-0.902970\pi\)
0.217030 0.976165i \(-0.430363\pi\)
\(762\) 0 0
\(763\) 1.69076 2.92848i 0.0612095 0.106018i
\(764\) 0 0
\(765\) −0.705941 + 1.52936i −0.0255233 + 0.0552942i
\(766\) 0 0
\(767\) −0.890369 + 1.54216i −0.0321494 + 0.0556843i
\(768\) 0 0
\(769\) 16.9518 + 29.3615i 0.611299 + 1.05880i 0.991022 + 0.133701i \(0.0426861\pi\)
−0.379723 + 0.925100i \(0.623981\pi\)
\(770\) 0 0
\(771\) 19.8171 0.903760i 0.713696 0.0325481i
\(772\) 0 0
\(773\) −8.74825 −0.314653 −0.157326 0.987547i \(-0.550287\pi\)
−0.157326 + 0.987547i \(0.550287\pi\)
\(774\) 0 0
\(775\) −7.93406 −0.285000
\(776\) 0 0
\(777\) 7.61916 + 11.9086i 0.273336 + 0.427220i
\(778\) 0 0
\(779\) 13.5993 + 23.5547i 0.487246 + 0.843935i
\(780\) 0 0
\(781\) −19.6623 + 34.0560i −0.703571 + 1.21862i
\(782\) 0 0
\(783\) 16.3260 40.0725i 0.583442 1.43208i
\(784\) 0 0
\(785\) −4.29300 + 7.43569i −0.153224 + 0.265391i
\(786\) 0 0
\(787\) 4.64260 + 8.04122i 0.165491 + 0.286639i 0.936830 0.349786i \(-0.113746\pi\)
−0.771339 + 0.636425i \(0.780412\pi\)
\(788\) 0 0
\(789\) −6.38005 9.97193i −0.227136 0.355010i
\(790\) 0 0
\(791\) −18.8712 −0.670983
\(792\) 0 0
\(793\) −0.780738 −0.0277248
\(794\) 0 0
\(795\) 12.2104 0.556856i 0.433059 0.0197497i
\(796\) 0 0
\(797\) −11.2271 19.4460i −0.397685 0.688811i 0.595754 0.803167i \(-0.296853\pi\)
−0.993440 + 0.114355i \(0.963520\pi\)
\(798\) 0 0
\(799\) 0.188816 0.327039i 0.00667983 0.0115698i
\(800\) 0 0
\(801\) 23.9071 + 33.8624i 0.844716 + 1.19647i
\(802\) 0 0
\(803\) −23.7075 + 41.0626i −0.836619 + 1.44907i
\(804\) 0 0
\(805\) 5.47150 + 9.47691i 0.192845 + 0.334017i
\(806\) 0 0
\(807\) −7.70700 + 14.8754i −0.271299 + 0.523639i
\(808\) 0 0
\(809\) −5.40215 −0.189929 −0.0949647 0.995481i \(-0.530274\pi\)
−0.0949647 + 0.995481i \(0.530274\pi\)
\(810\) 0 0
\(811\) 0.0177088 0.000621841 0.000310920 1.00000i \(-0.499901\pi\)
0.000310920 1.00000i \(0.499901\pi\)
\(812\) 0 0
\(813\) −10.2290 + 19.7431i −0.358746 + 0.692422i
\(814\) 0 0
\(815\) −5.77042 9.99466i −0.202129 0.350098i
\(816\) 0 0
\(817\) 12.3796 21.4420i 0.433106 0.750162i
\(818\) 0 0
\(819\) −1.73025 2.45076i −0.0604599 0.0856365i
\(820\) 0 0
\(821\) 0.528505 0.915397i 0.0184449 0.0319476i −0.856656 0.515889i \(-0.827462\pi\)
0.875101 + 0.483941i \(0.160795\pi\)
\(822\) 0 0
\(823\) 6.76303 + 11.7139i 0.235744 + 0.408321i 0.959489 0.281747i \(-0.0909139\pi\)
−0.723744 + 0.690068i \(0.757581\pi\)
\(824\) 0 0
\(825\) −6.82743 + 0.311365i −0.237701 + 0.0108403i
\(826\) 0 0
\(827\) 49.3068 1.71457 0.857283 0.514846i \(-0.172151\pi\)
0.857283 + 0.514846i \(0.172151\pi\)
\(828\) 0 0
\(829\) −53.7060 −1.86529 −0.932644 0.360799i \(-0.882504\pi\)
−0.932644 + 0.360799i \(0.882504\pi\)
\(830\) 0 0
\(831\) −10.8124 16.8996i −0.375077 0.586239i
\(832\) 0 0
\(833\) −0.136673 0.236725i −0.00473544 0.00820203i
\(834\) 0 0
\(835\) −11.1864 + 19.3754i −0.387120 + 0.670512i
\(836\) 0 0
\(837\) −32.3887 41.7049i −1.11952 1.44153i
\(838\) 0 0
\(839\) −18.7163 + 32.4176i −0.646160 + 1.11918i 0.337873 + 0.941192i \(0.390293\pi\)
−0.984032 + 0.177990i \(0.943041\pi\)
\(840\) 0 0
\(841\) −20.1730 34.9407i −0.695622 1.20485i
\(842\) 0 0
\(843\) 4.60030 + 7.19020i 0.158443 + 0.247644i
\(844\) 0 0
\(845\) −24.6490 −0.847952
\(846\) 0 0
\(847\) −14.5438 −0.499730
\(848\) 0 0
\(849\) 32.1840 1.46775i 1.10455 0.0503732i
\(850\) 0 0
\(851\) −21.7419 37.6581i −0.745303 1.29090i
\(852\) 0 0
\(853\) 10.3092 17.8561i 0.352982 0.611382i −0.633789 0.773506i \(-0.718501\pi\)
0.986770 + 0.162124i \(0.0518344\pi\)
\(854\) 0 0
\(855\) −13.8982 + 30.1094i −0.475310 + 1.02972i
\(856\) 0 0
\(857\) −10.4445 + 18.0903i −0.356776 + 0.617954i −0.987420 0.158118i \(-0.949457\pi\)
0.630644 + 0.776072i \(0.282791\pi\)
\(858\) 0 0
\(859\) 13.4430 + 23.2839i 0.458669 + 0.794438i 0.998891 0.0470847i \(-0.0149931\pi\)
−0.540222 + 0.841523i \(0.681660\pi\)
\(860\) 0 0
\(861\) −4.02704 + 7.77266i −0.137241 + 0.264892i
\(862\) 0 0
\(863\) −26.8142 −0.912766 −0.456383 0.889784i \(-0.650855\pi\)
−0.456383 + 0.889784i \(0.650855\pi\)
\(864\) 0 0
\(865\) 29.9912 1.01973
\(866\) 0 0
\(867\) 13.4859 26.0293i 0.458005 0.884003i
\(868\) 0 0
\(869\) 32.7075 + 56.6510i 1.10953 + 1.92175i
\(870\) 0 0
\(871\) 4.19076 7.25860i 0.141998 0.245948i
\(872\) 0 0
\(873\) −6.63015 + 0.605997i −0.224397 + 0.0205099i
\(874\) 0 0
\(875\) −5.93706 + 10.2833i −0.200709 + 0.347639i
\(876\) 0 0
\(877\) 18.9538 + 32.8289i 0.640024 + 1.10855i 0.985427 + 0.170099i \(0.0544089\pi\)
−0.345403 + 0.938454i \(0.612258\pi\)
\(878\) 0 0
\(879\) −42.8412 + 1.95378i −1.44500 + 0.0658992i
\(880\) 0 0
\(881\) 7.47782 0.251934 0.125967 0.992034i \(-0.459797\pi\)
0.125967 + 0.992034i \(0.459797\pi\)
\(882\) 0 0
\(883\) −5.07472 −0.170778 −0.0853889 0.996348i \(-0.527213\pi\)
−0.0853889 + 0.996348i \(0.527213\pi\)
\(884\) 0 0
\(885\) 3.41441 + 5.33667i 0.114774 + 0.179390i
\(886\) 0 0
\(887\) 9.26157 + 16.0415i 0.310973 + 0.538621i 0.978573 0.205899i \(-0.0660118\pi\)
−0.667600 + 0.744520i \(0.732678\pi\)
\(888\) 0 0
\(889\) −8.58113 + 14.8629i −0.287802 + 0.498487i
\(890\) 0 0
\(891\) −29.5079 34.6169i −0.988551 1.15971i
\(892\) 0 0
\(893\) 3.71732 6.43859i 0.124395 0.215459i
\(894\) 0 0
\(895\) −24.1249 41.7855i −0.806406 1.39674i
\(896\) 0 0
\(897\) 4.97296 + 7.77266i 0.166042 + 0.259522i
\(898\) 0 0
\(899\) −84.6255 −2.82242
\(900\) 0 0
\(901\) 0.939108 0.0312862
\(902\) 0 0
\(903\) 7.96050 0.363039i 0.264909 0.0120812i
\(904\) 0 0
\(905\) 1.43706 + 2.48906i 0.0477695 + 0.0827393i
\(906\) 0 0
\(907\) −24.8245 + 42.9973i −0.824284 + 1.42770i 0.0781810 + 0.996939i \(0.475089\pi\)
−0.902465 + 0.430763i \(0.858245\pi\)
\(908\) 0 0
\(909\) 8.14601 0.744547i 0.270186 0.0246951i
\(910\) 0 0
\(911\) 11.9808 20.7514i 0.396943 0.687525i −0.596404 0.802684i \(-0.703405\pi\)
0.993347 + 0.115159i \(0.0367379\pi\)
\(912\) 0 0
\(913\) −14.4715 25.0654i −0.478937 0.829543i
\(914\) 0 0
\(915\) −1.27781 + 2.46633i −0.0422432 + 0.0815343i
\(916\) 0 0
\(917\) −17.8889 −0.590744
\(918\) 0 0
\(919\) 18.8377 0.621400 0.310700 0.950508i \(-0.399437\pi\)
0.310700 + 0.950508i \(0.399437\pi\)
\(920\) 0 0
\(921\) 17.4839 33.7461i 0.576116 1.11197i
\(922\) 0 0
\(923\) 3.89037 + 6.73832i 0.128053 + 0.221794i
\(924\) 0 0
\(925\) 3.18629 5.51882i 0.104765 0.181458i
\(926\) 0 0
\(927\) 22.6090 48.9806i 0.742578 1.60873i
\(928\) 0 0
\(929\) −7.45185 + 12.9070i −0.244487 + 0.423464i −0.961987 0.273094i \(-0.911953\pi\)
0.717500 + 0.696558i \(0.245286\pi\)
\(930\) 0 0
\(931\) −2.69076 4.66053i −0.0881860 0.152743i
\(932\) 0 0
\(933\) −46.9976 + 2.14333i −1.53863 + 0.0701693i
\(934\) 0 0
\(935\) 2.83775 0.0928043
\(936\) 0 0
\(937\) 3.94299 0.128812 0.0644059 0.997924i \(-0.479485\pi\)
0.0644059 + 0.997924i \(0.479485\pi\)
\(938\) 0 0
\(939\) 7.97529 + 12.4653i 0.260264 + 0.406788i
\(940\) 0 0
\(941\) 21.4056 + 37.0756i 0.697804 + 1.20863i 0.969226 + 0.246171i \(0.0791725\pi\)
−0.271423 + 0.962460i \(0.587494\pi\)
\(942\) 0 0
\(943\) 13.4626 23.3180i 0.438404 0.759338i
\(944\) 0 0
\(945\) −10.5737 + 1.45472i −0.343964 + 0.0473221i
\(946\) 0 0
\(947\) −13.5919 + 23.5419i −0.441678 + 0.765009i −0.997814 0.0660823i \(-0.978950\pi\)
0.556136 + 0.831091i \(0.312283\pi\)
\(948\) 0 0
\(949\) 4.69076 + 8.12463i 0.152268 + 0.263737i
\(950\) 0 0
\(951\) −0.372660 0.582462i −0.0120843 0.0188876i
\(952\) 0 0
\(953\) 1.12295 0.0363760 0.0181880 0.999835i \(-0.494210\pi\)
0.0181880 + 0.999835i \(0.494210\pi\)
\(954\) 0 0
\(955\) −47.9912 −1.55296
\(956\) 0 0
\(957\) −72.8221 + 3.32105i −2.35400 + 0.107354i
\(958\) 0 0
\(959\) −2.24630 3.89071i −0.0725369 0.125638i
\(960\) 0 0
\(961\) −36.1357 + 62.5889i −1.16567 + 2.01900i
\(962\) 0 0
\(963\) 1.91741 + 2.71586i 0.0617877 + 0.0875172i
\(964\) 0 0
\(965\) 14.9371 25.8717i 0.480841 0.832841i
\(966\) 0 0
\(967\) −4.75223 8.23111i −0.152822 0.264695i 0.779442 0.626474i \(-0.215503\pi\)
−0.932264 + 0.361780i \(0.882169\pi\)
\(968\) 0 0
\(969\) −1.17209 + 2.26227i −0.0376530 + 0.0726746i
\(970\) 0 0
\(971\) 24.5979 0.789383 0.394691 0.918814i \(-0.370852\pi\)
0.394691 + 0.918814i \(0.370852\pi\)
\(972\) 0 0
\(973\) 18.1445 0.581687
\(974\) 0 0
\(975\) −0.622084 + 1.20069i −0.0199226 + 0.0384530i
\(976\) 0 0
\(977\) 12.7016 + 21.9997i 0.406359 + 0.703834i 0.994479 0.104940i \(-0.0334650\pi\)
−0.588120 + 0.808774i \(0.700132\pi\)
\(978\) 0 0
\(979\) 34.9164 60.4770i 1.11593 1.93285i
\(980\) 0 0
\(981\) −5.85087 8.28728i −0.186804 0.264593i
\(982\) 0 0
\(983\) 11.4267 19.7917i 0.364457 0.631257i −0.624232 0.781239i \(-0.714588\pi\)
0.988689 + 0.149982i \(0.0479214\pi\)
\(984\) 0 0
\(985\) 17.8112 + 30.8499i 0.567512 + 0.982959i
\(986\) 0 0
\(987\) 2.39037 0.109013i 0.0760863 0.00346992i
\(988\) 0 0
\(989\) −24.5103 −0.779383
\(990\) 0 0
\(991\) −24.4690 −0.777285 −0.388642 0.921389i \(-0.627056\pi\)
−0.388642 + 0.921389i \(0.627056\pi\)
\(992\) 0 0
\(993\) −5.24465 8.19731i −0.166434 0.260134i
\(994\) 0 0
\(995\) −11.8559 20.5351i −0.375858 0.651006i
\(996\) 0 0
\(997\) −13.0000 + 22.5167i −0.411714 + 0.713110i −0.995077 0.0991016i \(-0.968403\pi\)
0.583363 + 0.812211i \(0.301736\pi\)
\(998\) 0 0
\(999\) 42.0165 5.78058i 1.32934 0.182889i
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 1008.2.r.g.673.2 6
3.2 odd 2 3024.2.r.i.2017.3 6
4.3 odd 2 252.2.j.b.169.2 yes 6
9.2 odd 6 9072.2.a.bz.1.1 3
9.4 even 3 inner 1008.2.r.g.337.2 6
9.5 odd 6 3024.2.r.i.1009.3 6
9.7 even 3 9072.2.a.bt.1.3 3
12.11 even 2 756.2.j.a.505.3 6
28.3 even 6 1764.2.l.g.961.3 6
28.11 odd 6 1764.2.l.d.961.1 6
28.19 even 6 1764.2.i.e.1537.2 6
28.23 odd 6 1764.2.i.f.1537.2 6
28.27 even 2 1764.2.j.d.1177.2 6
36.7 odd 6 2268.2.a.g.1.3 3
36.11 even 6 2268.2.a.j.1.1 3
36.23 even 6 756.2.j.a.253.3 6
36.31 odd 6 252.2.j.b.85.2 6
84.11 even 6 5292.2.l.g.3313.1 6
84.23 even 6 5292.2.i.d.2125.3 6
84.47 odd 6 5292.2.i.g.2125.1 6
84.59 odd 6 5292.2.l.d.3313.3 6
84.83 odd 2 5292.2.j.e.3529.1 6
252.23 even 6 5292.2.l.g.361.1 6
252.31 even 6 1764.2.i.e.373.2 6
252.59 odd 6 5292.2.i.g.1549.1 6
252.67 odd 6 1764.2.i.f.373.2 6
252.95 even 6 5292.2.i.d.1549.3 6
252.103 even 6 1764.2.l.g.949.3 6
252.131 odd 6 5292.2.l.d.361.3 6
252.139 even 6 1764.2.j.d.589.2 6
252.167 odd 6 5292.2.j.e.1765.1 6
252.247 odd 6 1764.2.l.d.949.1 6
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
252.2.j.b.85.2 6 36.31 odd 6
252.2.j.b.169.2 yes 6 4.3 odd 2
756.2.j.a.253.3 6 36.23 even 6
756.2.j.a.505.3 6 12.11 even 2
1008.2.r.g.337.2 6 9.4 even 3 inner
1008.2.r.g.673.2 6 1.1 even 1 trivial
1764.2.i.e.373.2 6 252.31 even 6
1764.2.i.e.1537.2 6 28.19 even 6
1764.2.i.f.373.2 6 252.67 odd 6
1764.2.i.f.1537.2 6 28.23 odd 6
1764.2.j.d.589.2 6 252.139 even 6
1764.2.j.d.1177.2 6 28.27 even 2
1764.2.l.d.949.1 6 252.247 odd 6
1764.2.l.d.961.1 6 28.11 odd 6
1764.2.l.g.949.3 6 252.103 even 6
1764.2.l.g.961.3 6 28.3 even 6
2268.2.a.g.1.3 3 36.7 odd 6
2268.2.a.j.1.1 3 36.11 even 6
3024.2.r.i.1009.3 6 9.5 odd 6
3024.2.r.i.2017.3 6 3.2 odd 2
5292.2.i.d.1549.3 6 252.95 even 6
5292.2.i.d.2125.3 6 84.23 even 6
5292.2.i.g.1549.1 6 252.59 odd 6
5292.2.i.g.2125.1 6 84.47 odd 6
5292.2.j.e.1765.1 6 252.167 odd 6
5292.2.j.e.3529.1 6 84.83 odd 2
5292.2.l.d.361.3 6 252.131 odd 6
5292.2.l.d.3313.3 6 84.59 odd 6
5292.2.l.g.361.1 6 252.23 even 6
5292.2.l.g.3313.1 6 84.11 even 6
9072.2.a.bt.1.3 3 9.7 even 3
9072.2.a.bz.1.1 3 9.2 odd 6