Properties

Label 2646.2.h.b.667.1
Level $2646$
Weight $2$
Character 2646.667
Analytic conductor $21.128$
Analytic rank $0$
Dimension $2$
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] = [2646,2,Mod(361,2646)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(2646, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([2, 4]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("2646.361");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 2646 = 2 \cdot 3^{3} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2646.h (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: \(21.1284163748\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\zeta_{6})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{2} - x + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 126)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 667.1
Root \(0.500000 - 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 2646.667
Dual form 2646.2.h.b.361.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} -2.00000 q^{5} +1.00000 q^{8} +O(q^{10})\) \(q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} -2.00000 q^{5} +1.00000 q^{8} +(1.00000 + 1.73205i) q^{10} -1.00000 q^{11} +(3.00000 + 5.19615i) q^{13} +(-0.500000 - 0.866025i) q^{16} +(-2.50000 - 4.33013i) q^{17} +(3.50000 - 6.06218i) q^{19} +(1.00000 - 1.73205i) q^{20} +(0.500000 + 0.866025i) q^{22} -4.00000 q^{23} -1.00000 q^{25} +(3.00000 - 5.19615i) q^{26} +(-2.00000 + 3.46410i) q^{29} +(3.00000 - 5.19615i) q^{31} +(-0.500000 + 0.866025i) q^{32} +(-2.50000 + 4.33013i) q^{34} +(-1.00000 + 1.73205i) q^{37} -7.00000 q^{38} -2.00000 q^{40} +(1.50000 + 2.59808i) q^{41} +(0.500000 - 0.866025i) q^{43} +(0.500000 - 0.866025i) q^{44} +(2.00000 + 3.46410i) q^{46} +(0.500000 + 0.866025i) q^{50} -6.00000 q^{52} +(6.00000 + 10.3923i) q^{53} +2.00000 q^{55} +4.00000 q^{58} +(-3.50000 + 6.06218i) q^{59} +(6.00000 + 10.3923i) q^{61} -6.00000 q^{62} +1.00000 q^{64} +(-6.00000 - 10.3923i) q^{65} +(-6.50000 + 11.2583i) q^{67} +5.00000 q^{68} +8.00000 q^{71} +(-0.500000 - 0.866025i) q^{73} +2.00000 q^{74} +(3.50000 + 6.06218i) q^{76} +(3.00000 + 5.19615i) q^{79} +(1.00000 + 1.73205i) q^{80} +(1.50000 - 2.59808i) q^{82} +(8.00000 - 13.8564i) q^{83} +(5.00000 + 8.66025i) q^{85} -1.00000 q^{86} -1.00000 q^{88} +(-3.00000 + 5.19615i) q^{89} +(2.00000 - 3.46410i) q^{92} +(-7.00000 + 12.1244i) q^{95} +(2.50000 - 4.33013i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q - q^{2} - q^{4} - 4 q^{5} + 2 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 2 q - q^{2} - q^{4} - 4 q^{5} + 2 q^{8} + 2 q^{10} - 2 q^{11} + 6 q^{13} - q^{16} - 5 q^{17} + 7 q^{19} + 2 q^{20} + q^{22} - 8 q^{23} - 2 q^{25} + 6 q^{26} - 4 q^{29} + 6 q^{31} - q^{32} - 5 q^{34} - 2 q^{37} - 14 q^{38} - 4 q^{40} + 3 q^{41} + q^{43} + q^{44} + 4 q^{46} + q^{50} - 12 q^{52} + 12 q^{53} + 4 q^{55} + 8 q^{58} - 7 q^{59} + 12 q^{61} - 12 q^{62} + 2 q^{64} - 12 q^{65} - 13 q^{67} + 10 q^{68} + 16 q^{71} - q^{73} + 4 q^{74} + 7 q^{76} + 6 q^{79} + 2 q^{80} + 3 q^{82} + 16 q^{83} + 10 q^{85} - 2 q^{86} - 2 q^{88} - 6 q^{89} + 4 q^{92} - 14 q^{95} + 5 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/2646\mathbb{Z}\right)^\times\).

\(n\) \(785\) \(1081\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{3}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.500000 0.866025i −0.353553 0.612372i
\(3\) 0 0
\(4\) −0.500000 + 0.866025i −0.250000 + 0.433013i
\(5\) −2.00000 −0.894427 −0.447214 0.894427i \(-0.647584\pi\)
−0.447214 + 0.894427i \(0.647584\pi\)
\(6\) 0 0
\(7\) 0 0
\(8\) 1.00000 0.353553
\(9\) 0 0
\(10\) 1.00000 + 1.73205i 0.316228 + 0.547723i
\(11\) −1.00000 −0.301511 −0.150756 0.988571i \(-0.548171\pi\)
−0.150756 + 0.988571i \(0.548171\pi\)
\(12\) 0 0
\(13\) 3.00000 + 5.19615i 0.832050 + 1.44115i 0.896410 + 0.443227i \(0.146166\pi\)
−0.0643593 + 0.997927i \(0.520500\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) −0.500000 0.866025i −0.125000 0.216506i
\(17\) −2.50000 4.33013i −0.606339 1.05021i −0.991838 0.127502i \(-0.959304\pi\)
0.385499 0.922708i \(-0.374029\pi\)
\(18\) 0 0
\(19\) 3.50000 6.06218i 0.802955 1.39076i −0.114708 0.993399i \(-0.536593\pi\)
0.917663 0.397360i \(-0.130073\pi\)
\(20\) 1.00000 1.73205i 0.223607 0.387298i
\(21\) 0 0
\(22\) 0.500000 + 0.866025i 0.106600 + 0.184637i
\(23\) −4.00000 −0.834058 −0.417029 0.908893i \(-0.636929\pi\)
−0.417029 + 0.908893i \(0.636929\pi\)
\(24\) 0 0
\(25\) −1.00000 −0.200000
\(26\) 3.00000 5.19615i 0.588348 1.01905i
\(27\) 0 0
\(28\) 0 0
\(29\) −2.00000 + 3.46410i −0.371391 + 0.643268i −0.989780 0.142605i \(-0.954452\pi\)
0.618389 + 0.785872i \(0.287786\pi\)
\(30\) 0 0
\(31\) 3.00000 5.19615i 0.538816 0.933257i −0.460152 0.887840i \(-0.652205\pi\)
0.998968 0.0454165i \(-0.0144615\pi\)
\(32\) −0.500000 + 0.866025i −0.0883883 + 0.153093i
\(33\) 0 0
\(34\) −2.50000 + 4.33013i −0.428746 + 0.742611i
\(35\) 0 0
\(36\) 0 0
\(37\) −1.00000 + 1.73205i −0.164399 + 0.284747i −0.936442 0.350823i \(-0.885902\pi\)
0.772043 + 0.635571i \(0.219235\pi\)
\(38\) −7.00000 −1.13555
\(39\) 0 0
\(40\) −2.00000 −0.316228
\(41\) 1.50000 + 2.59808i 0.234261 + 0.405751i 0.959058 0.283211i \(-0.0913998\pi\)
−0.724797 + 0.688963i \(0.758066\pi\)
\(42\) 0 0
\(43\) 0.500000 0.866025i 0.0762493 0.132068i −0.825380 0.564578i \(-0.809039\pi\)
0.901629 + 0.432511i \(0.142372\pi\)
\(44\) 0.500000 0.866025i 0.0753778 0.130558i
\(45\) 0 0
\(46\) 2.00000 + 3.46410i 0.294884 + 0.510754i
\(47\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(48\) 0 0
\(49\) 0 0
\(50\) 0.500000 + 0.866025i 0.0707107 + 0.122474i
\(51\) 0 0
\(52\) −6.00000 −0.832050
\(53\) 6.00000 + 10.3923i 0.824163 + 1.42749i 0.902557 + 0.430570i \(0.141688\pi\)
−0.0783936 + 0.996922i \(0.524979\pi\)
\(54\) 0 0
\(55\) 2.00000 0.269680
\(56\) 0 0
\(57\) 0 0
\(58\) 4.00000 0.525226
\(59\) −3.50000 + 6.06218i −0.455661 + 0.789228i −0.998726 0.0504625i \(-0.983930\pi\)
0.543065 + 0.839691i \(0.317264\pi\)
\(60\) 0 0
\(61\) 6.00000 + 10.3923i 0.768221 + 1.33060i 0.938527 + 0.345207i \(0.112191\pi\)
−0.170305 + 0.985391i \(0.554475\pi\)
\(62\) −6.00000 −0.762001
\(63\) 0 0
\(64\) 1.00000 0.125000
\(65\) −6.00000 10.3923i −0.744208 1.28901i
\(66\) 0 0
\(67\) −6.50000 + 11.2583i −0.794101 + 1.37542i 0.129307 + 0.991605i \(0.458725\pi\)
−0.923408 + 0.383819i \(0.874609\pi\)
\(68\) 5.00000 0.606339
\(69\) 0 0
\(70\) 0 0
\(71\) 8.00000 0.949425 0.474713 0.880141i \(-0.342552\pi\)
0.474713 + 0.880141i \(0.342552\pi\)
\(72\) 0 0
\(73\) −0.500000 0.866025i −0.0585206 0.101361i 0.835281 0.549823i \(-0.185305\pi\)
−0.893801 + 0.448463i \(0.851972\pi\)
\(74\) 2.00000 0.232495
\(75\) 0 0
\(76\) 3.50000 + 6.06218i 0.401478 + 0.695379i
\(77\) 0 0
\(78\) 0 0
\(79\) 3.00000 + 5.19615i 0.337526 + 0.584613i 0.983967 0.178352i \(-0.0570765\pi\)
−0.646440 + 0.762964i \(0.723743\pi\)
\(80\) 1.00000 + 1.73205i 0.111803 + 0.193649i
\(81\) 0 0
\(82\) 1.50000 2.59808i 0.165647 0.286910i
\(83\) 8.00000 13.8564i 0.878114 1.52094i 0.0247060 0.999695i \(-0.492135\pi\)
0.853408 0.521243i \(-0.174532\pi\)
\(84\) 0 0
\(85\) 5.00000 + 8.66025i 0.542326 + 0.939336i
\(86\) −1.00000 −0.107833
\(87\) 0 0
\(88\) −1.00000 −0.106600
\(89\) −3.00000 + 5.19615i −0.317999 + 0.550791i −0.980071 0.198650i \(-0.936344\pi\)
0.662071 + 0.749441i \(0.269678\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 2.00000 3.46410i 0.208514 0.361158i
\(93\) 0 0
\(94\) 0 0
\(95\) −7.00000 + 12.1244i −0.718185 + 1.24393i
\(96\) 0 0
\(97\) 2.50000 4.33013i 0.253837 0.439658i −0.710742 0.703452i \(-0.751641\pi\)
0.964579 + 0.263795i \(0.0849741\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0.500000 0.866025i 0.0500000 0.0866025i
\(101\) 4.00000 0.398015 0.199007 0.979998i \(-0.436228\pi\)
0.199007 + 0.979998i \(0.436228\pi\)
\(102\) 0 0
\(103\) 14.0000 1.37946 0.689730 0.724066i \(-0.257729\pi\)
0.689730 + 0.724066i \(0.257729\pi\)
\(104\) 3.00000 + 5.19615i 0.294174 + 0.509525i
\(105\) 0 0
\(106\) 6.00000 10.3923i 0.582772 1.00939i
\(107\) 1.50000 2.59808i 0.145010 0.251166i −0.784366 0.620298i \(-0.787012\pi\)
0.929377 + 0.369132i \(0.120345\pi\)
\(108\) 0 0
\(109\) 1.00000 + 1.73205i 0.0957826 + 0.165900i 0.909935 0.414751i \(-0.136131\pi\)
−0.814152 + 0.580651i \(0.802798\pi\)
\(110\) −1.00000 1.73205i −0.0953463 0.165145i
\(111\) 0 0
\(112\) 0 0
\(113\) −5.00000 8.66025i −0.470360 0.814688i 0.529065 0.848581i \(-0.322543\pi\)
−0.999425 + 0.0338931i \(0.989209\pi\)
\(114\) 0 0
\(115\) 8.00000 0.746004
\(116\) −2.00000 3.46410i −0.185695 0.321634i
\(117\) 0 0
\(118\) 7.00000 0.644402
\(119\) 0 0
\(120\) 0 0
\(121\) −10.0000 −0.909091
\(122\) 6.00000 10.3923i 0.543214 0.940875i
\(123\) 0 0
\(124\) 3.00000 + 5.19615i 0.269408 + 0.466628i
\(125\) 12.0000 1.07331
\(126\) 0 0
\(127\) −12.0000 −1.06483 −0.532414 0.846484i \(-0.678715\pi\)
−0.532414 + 0.846484i \(0.678715\pi\)
\(128\) −0.500000 0.866025i −0.0441942 0.0765466i
\(129\) 0 0
\(130\) −6.00000 + 10.3923i −0.526235 + 0.911465i
\(131\) 4.00000 0.349482 0.174741 0.984614i \(-0.444091\pi\)
0.174741 + 0.984614i \(0.444091\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 13.0000 1.12303
\(135\) 0 0
\(136\) −2.50000 4.33013i −0.214373 0.371305i
\(137\) 19.0000 1.62328 0.811640 0.584158i \(-0.198575\pi\)
0.811640 + 0.584158i \(0.198575\pi\)
\(138\) 0 0
\(139\) 2.50000 + 4.33013i 0.212047 + 0.367277i 0.952355 0.304991i \(-0.0986536\pi\)
−0.740308 + 0.672268i \(0.765320\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) −4.00000 6.92820i −0.335673 0.581402i
\(143\) −3.00000 5.19615i −0.250873 0.434524i
\(144\) 0 0
\(145\) 4.00000 6.92820i 0.332182 0.575356i
\(146\) −0.500000 + 0.866025i −0.0413803 + 0.0716728i
\(147\) 0 0
\(148\) −1.00000 1.73205i −0.0821995 0.142374i
\(149\) 24.0000 1.96616 0.983078 0.183186i \(-0.0586410\pi\)
0.983078 + 0.183186i \(0.0586410\pi\)
\(150\) 0 0
\(151\) 10.0000 0.813788 0.406894 0.913475i \(-0.366612\pi\)
0.406894 + 0.913475i \(0.366612\pi\)
\(152\) 3.50000 6.06218i 0.283887 0.491708i
\(153\) 0 0
\(154\) 0 0
\(155\) −6.00000 + 10.3923i −0.481932 + 0.834730i
\(156\) 0 0
\(157\) −1.00000 + 1.73205i −0.0798087 + 0.138233i −0.903167 0.429289i \(-0.858764\pi\)
0.823359 + 0.567521i \(0.192098\pi\)
\(158\) 3.00000 5.19615i 0.238667 0.413384i
\(159\) 0 0
\(160\) 1.00000 1.73205i 0.0790569 0.136931i
\(161\) 0 0
\(162\) 0 0
\(163\) 2.00000 3.46410i 0.156652 0.271329i −0.777007 0.629492i \(-0.783263\pi\)
0.933659 + 0.358162i \(0.116597\pi\)
\(164\) −3.00000 −0.234261
\(165\) 0 0
\(166\) −16.0000 −1.24184
\(167\) 10.0000 + 17.3205i 0.773823 + 1.34030i 0.935454 + 0.353450i \(0.114991\pi\)
−0.161630 + 0.986851i \(0.551675\pi\)
\(168\) 0 0
\(169\) −11.5000 + 19.9186i −0.884615 + 1.53220i
\(170\) 5.00000 8.66025i 0.383482 0.664211i
\(171\) 0 0
\(172\) 0.500000 + 0.866025i 0.0381246 + 0.0660338i
\(173\) 1.00000 + 1.73205i 0.0760286 + 0.131685i 0.901533 0.432710i \(-0.142443\pi\)
−0.825505 + 0.564396i \(0.809109\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0.500000 + 0.866025i 0.0376889 + 0.0652791i
\(177\) 0 0
\(178\) 6.00000 0.449719
\(179\) 12.0000 + 20.7846i 0.896922 + 1.55351i 0.831408 + 0.555663i \(0.187536\pi\)
0.0655145 + 0.997852i \(0.479131\pi\)
\(180\) 0 0
\(181\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) −4.00000 −0.294884
\(185\) 2.00000 3.46410i 0.147043 0.254686i
\(186\) 0 0
\(187\) 2.50000 + 4.33013i 0.182818 + 0.316650i
\(188\) 0 0
\(189\) 0 0
\(190\) 14.0000 1.01567
\(191\) 6.00000 + 10.3923i 0.434145 + 0.751961i 0.997225 0.0744412i \(-0.0237173\pi\)
−0.563081 + 0.826402i \(0.690384\pi\)
\(192\) 0 0
\(193\) −8.50000 + 14.7224i −0.611843 + 1.05974i 0.379086 + 0.925361i \(0.376238\pi\)
−0.990930 + 0.134382i \(0.957095\pi\)
\(194\) −5.00000 −0.358979
\(195\) 0 0
\(196\) 0 0
\(197\) −10.0000 −0.712470 −0.356235 0.934396i \(-0.615940\pi\)
−0.356235 + 0.934396i \(0.615940\pi\)
\(198\) 0 0
\(199\) −7.00000 12.1244i −0.496217 0.859473i 0.503774 0.863836i \(-0.331945\pi\)
−0.999990 + 0.00436292i \(0.998611\pi\)
\(200\) −1.00000 −0.0707107
\(201\) 0 0
\(202\) −2.00000 3.46410i −0.140720 0.243733i
\(203\) 0 0
\(204\) 0 0
\(205\) −3.00000 5.19615i −0.209529 0.362915i
\(206\) −7.00000 12.1244i −0.487713 0.844744i
\(207\) 0 0
\(208\) 3.00000 5.19615i 0.208013 0.360288i
\(209\) −3.50000 + 6.06218i −0.242100 + 0.419330i
\(210\) 0 0
\(211\) 8.00000 + 13.8564i 0.550743 + 0.953914i 0.998221 + 0.0596196i \(0.0189888\pi\)
−0.447478 + 0.894295i \(0.647678\pi\)
\(212\) −12.0000 −0.824163
\(213\) 0 0
\(214\) −3.00000 −0.205076
\(215\) −1.00000 + 1.73205i −0.0681994 + 0.118125i
\(216\) 0 0
\(217\) 0 0
\(218\) 1.00000 1.73205i 0.0677285 0.117309i
\(219\) 0 0
\(220\) −1.00000 + 1.73205i −0.0674200 + 0.116775i
\(221\) 15.0000 25.9808i 1.00901 1.74766i
\(222\) 0 0
\(223\) 2.00000 3.46410i 0.133930 0.231973i −0.791258 0.611482i \(-0.790574\pi\)
0.925188 + 0.379509i \(0.123907\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) −5.00000 + 8.66025i −0.332595 + 0.576072i
\(227\) −3.00000 −0.199117 −0.0995585 0.995032i \(-0.531743\pi\)
−0.0995585 + 0.995032i \(0.531743\pi\)
\(228\) 0 0
\(229\) −26.0000 −1.71813 −0.859064 0.511868i \(-0.828954\pi\)
−0.859064 + 0.511868i \(0.828954\pi\)
\(230\) −4.00000 6.92820i −0.263752 0.456832i
\(231\) 0 0
\(232\) −2.00000 + 3.46410i −0.131306 + 0.227429i
\(233\) −14.5000 + 25.1147i −0.949927 + 1.64532i −0.204354 + 0.978897i \(0.565509\pi\)
−0.745573 + 0.666424i \(0.767824\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) −3.50000 6.06218i −0.227831 0.394614i
\(237\) 0 0
\(238\) 0 0
\(239\) 3.00000 + 5.19615i 0.194054 + 0.336111i 0.946590 0.322440i \(-0.104503\pi\)
−0.752536 + 0.658551i \(0.771170\pi\)
\(240\) 0 0
\(241\) 23.0000 1.48156 0.740780 0.671748i \(-0.234456\pi\)
0.740780 + 0.671748i \(0.234456\pi\)
\(242\) 5.00000 + 8.66025i 0.321412 + 0.556702i
\(243\) 0 0
\(244\) −12.0000 −0.768221
\(245\) 0 0
\(246\) 0 0
\(247\) 42.0000 2.67240
\(248\) 3.00000 5.19615i 0.190500 0.329956i
\(249\) 0 0
\(250\) −6.00000 10.3923i −0.379473 0.657267i
\(251\) −3.00000 −0.189358 −0.0946792 0.995508i \(-0.530183\pi\)
−0.0946792 + 0.995508i \(0.530183\pi\)
\(252\) 0 0
\(253\) 4.00000 0.251478
\(254\) 6.00000 + 10.3923i 0.376473 + 0.652071i
\(255\) 0 0
\(256\) −0.500000 + 0.866025i −0.0312500 + 0.0541266i
\(257\) 15.0000 0.935674 0.467837 0.883815i \(-0.345033\pi\)
0.467837 + 0.883815i \(0.345033\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 12.0000 0.744208
\(261\) 0 0
\(262\) −2.00000 3.46410i −0.123560 0.214013i
\(263\) −18.0000 −1.10993 −0.554964 0.831875i \(-0.687268\pi\)
−0.554964 + 0.831875i \(0.687268\pi\)
\(264\) 0 0
\(265\) −12.0000 20.7846i −0.737154 1.27679i
\(266\) 0 0
\(267\) 0 0
\(268\) −6.50000 11.2583i −0.397051 0.687712i
\(269\) 10.0000 + 17.3205i 0.609711 + 1.05605i 0.991288 + 0.131713i \(0.0420477\pi\)
−0.381577 + 0.924337i \(0.624619\pi\)
\(270\) 0 0
\(271\) 3.00000 5.19615i 0.182237 0.315644i −0.760405 0.649449i \(-0.775000\pi\)
0.942642 + 0.333805i \(0.108333\pi\)
\(272\) −2.50000 + 4.33013i −0.151585 + 0.262553i
\(273\) 0 0
\(274\) −9.50000 16.4545i −0.573916 0.994052i
\(275\) 1.00000 0.0603023
\(276\) 0 0
\(277\) 2.00000 0.120168 0.0600842 0.998193i \(-0.480863\pi\)
0.0600842 + 0.998193i \(0.480863\pi\)
\(278\) 2.50000 4.33013i 0.149940 0.259704i
\(279\) 0 0
\(280\) 0 0
\(281\) 11.0000 19.0526i 0.656205 1.13658i −0.325385 0.945582i \(-0.605494\pi\)
0.981590 0.190999i \(-0.0611727\pi\)
\(282\) 0 0
\(283\) −2.00000 + 3.46410i −0.118888 + 0.205919i −0.919327 0.393494i \(-0.871266\pi\)
0.800439 + 0.599414i \(0.204600\pi\)
\(284\) −4.00000 + 6.92820i −0.237356 + 0.411113i
\(285\) 0 0
\(286\) −3.00000 + 5.19615i −0.177394 + 0.307255i
\(287\) 0 0
\(288\) 0 0
\(289\) −4.00000 + 6.92820i −0.235294 + 0.407541i
\(290\) −8.00000 −0.469776
\(291\) 0 0
\(292\) 1.00000 0.0585206
\(293\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(294\) 0 0
\(295\) 7.00000 12.1244i 0.407556 0.705907i
\(296\) −1.00000 + 1.73205i −0.0581238 + 0.100673i
\(297\) 0 0
\(298\) −12.0000 20.7846i −0.695141 1.20402i
\(299\) −12.0000 20.7846i −0.693978 1.20201i
\(300\) 0 0
\(301\) 0 0
\(302\) −5.00000 8.66025i −0.287718 0.498342i
\(303\) 0 0
\(304\) −7.00000 −0.401478
\(305\) −12.0000 20.7846i −0.687118 1.19012i
\(306\) 0 0
\(307\) 7.00000 0.399511 0.199756 0.979846i \(-0.435985\pi\)
0.199756 + 0.979846i \(0.435985\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 12.0000 0.681554
\(311\) 1.00000 1.73205i 0.0567048 0.0982156i −0.836280 0.548303i \(-0.815274\pi\)
0.892984 + 0.450088i \(0.148607\pi\)
\(312\) 0 0
\(313\) 8.50000 + 14.7224i 0.480448 + 0.832161i 0.999748 0.0224310i \(-0.00714060\pi\)
−0.519300 + 0.854592i \(0.673807\pi\)
\(314\) 2.00000 0.112867
\(315\) 0 0
\(316\) −6.00000 −0.337526
\(317\) −3.00000 5.19615i −0.168497 0.291845i 0.769395 0.638774i \(-0.220558\pi\)
−0.937892 + 0.346929i \(0.887225\pi\)
\(318\) 0 0
\(319\) 2.00000 3.46410i 0.111979 0.193952i
\(320\) −2.00000 −0.111803
\(321\) 0 0
\(322\) 0 0
\(323\) −35.0000 −1.94745
\(324\) 0 0
\(325\) −3.00000 5.19615i −0.166410 0.288231i
\(326\) −4.00000 −0.221540
\(327\) 0 0
\(328\) 1.50000 + 2.59808i 0.0828236 + 0.143455i
\(329\) 0 0
\(330\) 0 0
\(331\) −4.00000 6.92820i −0.219860 0.380808i 0.734905 0.678170i \(-0.237227\pi\)
−0.954765 + 0.297361i \(0.903893\pi\)
\(332\) 8.00000 + 13.8564i 0.439057 + 0.760469i
\(333\) 0 0
\(334\) 10.0000 17.3205i 0.547176 0.947736i
\(335\) 13.0000 22.5167i 0.710266 1.23022i
\(336\) 0 0
\(337\) 4.50000 + 7.79423i 0.245131 + 0.424579i 0.962168 0.272456i \(-0.0878358\pi\)
−0.717038 + 0.697034i \(0.754502\pi\)
\(338\) 23.0000 1.25104
\(339\) 0 0
\(340\) −10.0000 −0.542326
\(341\) −3.00000 + 5.19615i −0.162459 + 0.281387i
\(342\) 0 0
\(343\) 0 0
\(344\) 0.500000 0.866025i 0.0269582 0.0466930i
\(345\) 0 0
\(346\) 1.00000 1.73205i 0.0537603 0.0931156i
\(347\) −1.50000 + 2.59808i −0.0805242 + 0.139472i −0.903475 0.428640i \(-0.858993\pi\)
0.822951 + 0.568112i \(0.192326\pi\)
\(348\) 0 0
\(349\) 7.00000 12.1244i 0.374701 0.649002i −0.615581 0.788074i \(-0.711079\pi\)
0.990282 + 0.139072i \(0.0444119\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0.500000 0.866025i 0.0266501 0.0461593i
\(353\) 15.0000 0.798369 0.399185 0.916871i \(-0.369293\pi\)
0.399185 + 0.916871i \(0.369293\pi\)
\(354\) 0 0
\(355\) −16.0000 −0.849192
\(356\) −3.00000 5.19615i −0.159000 0.275396i
\(357\) 0 0
\(358\) 12.0000 20.7846i 0.634220 1.09850i
\(359\) 1.00000 1.73205i 0.0527780 0.0914141i −0.838429 0.545010i \(-0.816526\pi\)
0.891207 + 0.453596i \(0.149859\pi\)
\(360\) 0 0
\(361\) −15.0000 25.9808i −0.789474 1.36741i
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) 1.00000 + 1.73205i 0.0523424 + 0.0906597i
\(366\) 0 0
\(367\) −22.0000 −1.14839 −0.574195 0.818718i \(-0.694685\pi\)
−0.574195 + 0.818718i \(0.694685\pi\)
\(368\) 2.00000 + 3.46410i 0.104257 + 0.180579i
\(369\) 0 0
\(370\) −4.00000 −0.207950
\(371\) 0 0
\(372\) 0 0
\(373\) 22.0000 1.13912 0.569558 0.821951i \(-0.307114\pi\)
0.569558 + 0.821951i \(0.307114\pi\)
\(374\) 2.50000 4.33013i 0.129272 0.223906i
\(375\) 0 0
\(376\) 0 0
\(377\) −24.0000 −1.23606
\(378\) 0 0
\(379\) −17.0000 −0.873231 −0.436616 0.899648i \(-0.643823\pi\)
−0.436616 + 0.899648i \(0.643823\pi\)
\(380\) −7.00000 12.1244i −0.359092 0.621966i
\(381\) 0 0
\(382\) 6.00000 10.3923i 0.306987 0.531717i
\(383\) −4.00000 −0.204390 −0.102195 0.994764i \(-0.532587\pi\)
−0.102195 + 0.994764i \(0.532587\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 17.0000 0.865277
\(387\) 0 0
\(388\) 2.50000 + 4.33013i 0.126918 + 0.219829i
\(389\) −8.00000 −0.405616 −0.202808 0.979219i \(-0.565007\pi\)
−0.202808 + 0.979219i \(0.565007\pi\)
\(390\) 0 0
\(391\) 10.0000 + 17.3205i 0.505722 + 0.875936i
\(392\) 0 0
\(393\) 0 0
\(394\) 5.00000 + 8.66025i 0.251896 + 0.436297i
\(395\) −6.00000 10.3923i −0.301893 0.522894i
\(396\) 0 0
\(397\) −9.00000 + 15.5885i −0.451697 + 0.782362i −0.998492 0.0549046i \(-0.982515\pi\)
0.546795 + 0.837267i \(0.315848\pi\)
\(398\) −7.00000 + 12.1244i −0.350878 + 0.607739i
\(399\) 0 0
\(400\) 0.500000 + 0.866025i 0.0250000 + 0.0433013i
\(401\) −9.00000 −0.449439 −0.224719 0.974424i \(-0.572147\pi\)
−0.224719 + 0.974424i \(0.572147\pi\)
\(402\) 0 0
\(403\) 36.0000 1.79329
\(404\) −2.00000 + 3.46410i −0.0995037 + 0.172345i
\(405\) 0 0
\(406\) 0 0
\(407\) 1.00000 1.73205i 0.0495682 0.0858546i
\(408\) 0 0
\(409\) −5.50000 + 9.52628i −0.271957 + 0.471044i −0.969363 0.245633i \(-0.921004\pi\)
0.697406 + 0.716677i \(0.254338\pi\)
\(410\) −3.00000 + 5.19615i −0.148159 + 0.256620i
\(411\) 0 0
\(412\) −7.00000 + 12.1244i −0.344865 + 0.597324i
\(413\) 0 0
\(414\) 0 0
\(415\) −16.0000 + 27.7128i −0.785409 + 1.36037i
\(416\) −6.00000 −0.294174
\(417\) 0 0
\(418\) 7.00000 0.342381
\(419\) −6.00000 10.3923i −0.293119 0.507697i 0.681426 0.731887i \(-0.261360\pi\)
−0.974546 + 0.224189i \(0.928027\pi\)
\(420\) 0 0
\(421\) 6.00000 10.3923i 0.292422 0.506490i −0.681960 0.731390i \(-0.738872\pi\)
0.974382 + 0.224900i \(0.0722054\pi\)
\(422\) 8.00000 13.8564i 0.389434 0.674519i
\(423\) 0 0
\(424\) 6.00000 + 10.3923i 0.291386 + 0.504695i
\(425\) 2.50000 + 4.33013i 0.121268 + 0.210042i
\(426\) 0 0
\(427\) 0 0
\(428\) 1.50000 + 2.59808i 0.0725052 + 0.125583i
\(429\) 0 0
\(430\) 2.00000 0.0964486
\(431\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(432\) 0 0
\(433\) −25.0000 −1.20142 −0.600712 0.799466i \(-0.705116\pi\)
−0.600712 + 0.799466i \(0.705116\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) −2.00000 −0.0957826
\(437\) −14.0000 + 24.2487i −0.669711 + 1.15997i
\(438\) 0 0
\(439\) 12.0000 + 20.7846i 0.572729 + 0.991995i 0.996284 + 0.0861252i \(0.0274485\pi\)
−0.423556 + 0.905870i \(0.639218\pi\)
\(440\) 2.00000 0.0953463
\(441\) 0 0
\(442\) −30.0000 −1.42695
\(443\) 3.50000 + 6.06218i 0.166290 + 0.288023i 0.937113 0.349027i \(-0.113488\pi\)
−0.770823 + 0.637050i \(0.780155\pi\)
\(444\) 0 0
\(445\) 6.00000 10.3923i 0.284427 0.492642i
\(446\) −4.00000 −0.189405
\(447\) 0 0
\(448\) 0 0
\(449\) −17.0000 −0.802280 −0.401140 0.916017i \(-0.631386\pi\)
−0.401140 + 0.916017i \(0.631386\pi\)
\(450\) 0 0
\(451\) −1.50000 2.59808i −0.0706322 0.122339i
\(452\) 10.0000 0.470360
\(453\) 0 0
\(454\) 1.50000 + 2.59808i 0.0703985 + 0.121934i
\(455\) 0 0
\(456\) 0 0
\(457\) −0.500000 0.866025i −0.0233890 0.0405110i 0.854094 0.520119i \(-0.174112\pi\)
−0.877483 + 0.479608i \(0.840779\pi\)
\(458\) 13.0000 + 22.5167i 0.607450 + 1.05213i
\(459\) 0 0
\(460\) −4.00000 + 6.92820i −0.186501 + 0.323029i
\(461\) 7.00000 12.1244i 0.326023 0.564688i −0.655696 0.755025i \(-0.727625\pi\)
0.981719 + 0.190337i \(0.0609581\pi\)
\(462\) 0 0
\(463\) 4.00000 + 6.92820i 0.185896 + 0.321981i 0.943878 0.330294i \(-0.107148\pi\)
−0.757982 + 0.652275i \(0.773815\pi\)
\(464\) 4.00000 0.185695
\(465\) 0 0
\(466\) 29.0000 1.34340
\(467\) −6.50000 + 11.2583i −0.300784 + 0.520973i −0.976314 0.216359i \(-0.930582\pi\)
0.675530 + 0.737333i \(0.263915\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 0 0
\(471\) 0 0
\(472\) −3.50000 + 6.06218i −0.161101 + 0.279034i
\(473\) −0.500000 + 0.866025i −0.0229900 + 0.0398199i
\(474\) 0 0
\(475\) −3.50000 + 6.06218i −0.160591 + 0.278152i
\(476\) 0 0
\(477\) 0 0
\(478\) 3.00000 5.19615i 0.137217 0.237666i
\(479\) 20.0000 0.913823 0.456912 0.889512i \(-0.348956\pi\)
0.456912 + 0.889512i \(0.348956\pi\)
\(480\) 0 0
\(481\) −12.0000 −0.547153
\(482\) −11.5000 19.9186i −0.523811 0.907267i
\(483\) 0 0
\(484\) 5.00000 8.66025i 0.227273 0.393648i
\(485\) −5.00000 + 8.66025i −0.227038 + 0.393242i
\(486\) 0 0
\(487\) 5.00000 + 8.66025i 0.226572 + 0.392434i 0.956790 0.290780i \(-0.0939149\pi\)
−0.730218 + 0.683214i \(0.760582\pi\)
\(488\) 6.00000 + 10.3923i 0.271607 + 0.470438i
\(489\) 0 0
\(490\) 0 0
\(491\) 16.5000 + 28.5788i 0.744635 + 1.28974i 0.950365 + 0.311136i \(0.100710\pi\)
−0.205731 + 0.978609i \(0.565957\pi\)
\(492\) 0 0
\(493\) 20.0000 0.900755
\(494\) −21.0000 36.3731i −0.944835 1.63650i
\(495\) 0 0
\(496\) −6.00000 −0.269408
\(497\) 0 0
\(498\) 0 0
\(499\) −29.0000 −1.29822 −0.649109 0.760695i \(-0.724858\pi\)
−0.649109 + 0.760695i \(0.724858\pi\)
\(500\) −6.00000 + 10.3923i −0.268328 + 0.464758i
\(501\) 0 0
\(502\) 1.50000 + 2.59808i 0.0669483 + 0.115958i
\(503\) −6.00000 −0.267527 −0.133763 0.991013i \(-0.542706\pi\)
−0.133763 + 0.991013i \(0.542706\pi\)
\(504\) 0 0
\(505\) −8.00000 −0.355995
\(506\) −2.00000 3.46410i −0.0889108 0.153998i
\(507\) 0 0
\(508\) 6.00000 10.3923i 0.266207 0.461084i
\(509\) −30.0000 −1.32973 −0.664863 0.746965i \(-0.731510\pi\)
−0.664863 + 0.746965i \(0.731510\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 1.00000 0.0441942
\(513\) 0 0
\(514\) −7.50000 12.9904i −0.330811 0.572981i
\(515\) −28.0000 −1.23383
\(516\) 0 0
\(517\) 0 0
\(518\) 0 0
\(519\) 0 0
\(520\) −6.00000 10.3923i −0.263117 0.455733i
\(521\) −4.50000 7.79423i −0.197149 0.341471i 0.750454 0.660922i \(-0.229835\pi\)
−0.947603 + 0.319451i \(0.896501\pi\)
\(522\) 0 0
\(523\) 14.0000 24.2487i 0.612177 1.06032i −0.378695 0.925521i \(-0.623627\pi\)
0.990873 0.134801i \(-0.0430394\pi\)
\(524\) −2.00000 + 3.46410i −0.0873704 + 0.151330i
\(525\) 0 0
\(526\) 9.00000 + 15.5885i 0.392419 + 0.679689i
\(527\) −30.0000 −1.30682
\(528\) 0 0
\(529\) −7.00000 −0.304348
\(530\) −12.0000 + 20.7846i −0.521247 + 0.902826i
\(531\) 0 0
\(532\) 0 0
\(533\) −9.00000 + 15.5885i −0.389833 + 0.675211i
\(534\) 0 0
\(535\) −3.00000 + 5.19615i −0.129701 + 0.224649i
\(536\) −6.50000 + 11.2583i −0.280757 + 0.486286i
\(537\) 0 0
\(538\) 10.0000 17.3205i 0.431131 0.746740i
\(539\) 0 0
\(540\) 0 0
\(541\) 12.0000 20.7846i 0.515920 0.893600i −0.483909 0.875118i \(-0.660783\pi\)
0.999829 0.0184818i \(-0.00588327\pi\)
\(542\) −6.00000 −0.257722
\(543\) 0 0
\(544\) 5.00000 0.214373
\(545\) −2.00000 3.46410i −0.0856706 0.148386i
\(546\) 0 0
\(547\) 10.5000 18.1865i 0.448948 0.777600i −0.549370 0.835579i \(-0.685132\pi\)
0.998318 + 0.0579790i \(0.0184657\pi\)
\(548\) −9.50000 + 16.4545i −0.405820 + 0.702901i
\(549\) 0 0
\(550\) −0.500000 0.866025i −0.0213201 0.0369274i
\(551\) 14.0000 + 24.2487i 0.596420 + 1.03303i
\(552\) 0 0
\(553\) 0 0
\(554\) −1.00000 1.73205i −0.0424859 0.0735878i
\(555\) 0 0
\(556\) −5.00000 −0.212047
\(557\) −14.0000 24.2487i −0.593199 1.02745i −0.993798 0.111198i \(-0.964531\pi\)
0.400599 0.916253i \(-0.368802\pi\)
\(558\) 0 0
\(559\) 6.00000 0.253773
\(560\) 0 0
\(561\) 0 0
\(562\) −22.0000 −0.928014
\(563\) 15.5000 26.8468i 0.653247 1.13146i −0.329083 0.944301i \(-0.606740\pi\)
0.982330 0.187156i \(-0.0599271\pi\)
\(564\) 0 0
\(565\) 10.0000 + 17.3205i 0.420703 + 0.728679i
\(566\) 4.00000 0.168133
\(567\) 0 0
\(568\) 8.00000 0.335673
\(569\) −7.50000 12.9904i −0.314416 0.544585i 0.664897 0.746935i \(-0.268475\pi\)
−0.979313 + 0.202350i \(0.935142\pi\)
\(570\) 0 0
\(571\) 16.5000 28.5788i 0.690504 1.19599i −0.281170 0.959658i \(-0.590722\pi\)
0.971673 0.236329i \(-0.0759443\pi\)
\(572\) 6.00000 0.250873
\(573\) 0 0
\(574\) 0 0
\(575\) 4.00000 0.166812
\(576\) 0 0
\(577\) 17.5000 + 30.3109i 0.728535 + 1.26186i 0.957503 + 0.288425i \(0.0931316\pi\)
−0.228968 + 0.973434i \(0.573535\pi\)
\(578\) 8.00000 0.332756
\(579\) 0 0
\(580\) 4.00000 + 6.92820i 0.166091 + 0.287678i
\(581\) 0 0
\(582\) 0 0
\(583\) −6.00000 10.3923i −0.248495 0.430405i
\(584\) −0.500000 0.866025i −0.0206901 0.0358364i
\(585\) 0 0
\(586\) 0 0
\(587\) −23.5000 + 40.7032i −0.969949 + 1.68000i −0.274263 + 0.961655i \(0.588434\pi\)
−0.695686 + 0.718346i \(0.744900\pi\)
\(588\) 0 0
\(589\) −21.0000 36.3731i −0.865290 1.49873i
\(590\) −14.0000 −0.576371
\(591\) 0 0
\(592\) 2.00000 0.0821995
\(593\) −3.00000 + 5.19615i −0.123195 + 0.213380i −0.921026 0.389501i \(-0.872647\pi\)
0.797831 + 0.602881i \(0.205981\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) −12.0000 + 20.7846i −0.491539 + 0.851371i
\(597\) 0 0
\(598\) −12.0000 + 20.7846i −0.490716 + 0.849946i
\(599\) 12.0000 20.7846i 0.490307 0.849236i −0.509631 0.860393i \(-0.670218\pi\)
0.999938 + 0.0111569i \(0.00355143\pi\)
\(600\) 0 0
\(601\) 9.50000 16.4545i 0.387513 0.671192i −0.604601 0.796528i \(-0.706668\pi\)
0.992114 + 0.125336i \(0.0400009\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) −5.00000 + 8.66025i −0.203447 + 0.352381i
\(605\) 20.0000 0.813116
\(606\) 0 0
\(607\) −24.0000 −0.974130 −0.487065 0.873366i \(-0.661933\pi\)
−0.487065 + 0.873366i \(0.661933\pi\)
\(608\) 3.50000 + 6.06218i 0.141944 + 0.245854i
\(609\) 0 0
\(610\) −12.0000 + 20.7846i −0.485866 + 0.841544i
\(611\) 0 0
\(612\) 0 0
\(613\) −21.0000 36.3731i −0.848182 1.46909i −0.882829 0.469695i \(-0.844364\pi\)
0.0346469 0.999400i \(-0.488969\pi\)
\(614\) −3.50000 6.06218i −0.141249 0.244650i
\(615\) 0 0
\(616\) 0 0
\(617\) −8.50000 14.7224i −0.342197 0.592703i 0.642643 0.766165i \(-0.277838\pi\)
−0.984840 + 0.173463i \(0.944504\pi\)
\(618\) 0 0
\(619\) 37.0000 1.48716 0.743578 0.668649i \(-0.233127\pi\)
0.743578 + 0.668649i \(0.233127\pi\)
\(620\) −6.00000 10.3923i −0.240966 0.417365i
\(621\) 0 0
\(622\) −2.00000 −0.0801927
\(623\) 0 0
\(624\) 0 0
\(625\) −19.0000 −0.760000
\(626\) 8.50000 14.7224i 0.339728 0.588427i
\(627\) 0 0
\(628\) −1.00000 1.73205i −0.0399043 0.0691164i
\(629\) 10.0000 0.398726
\(630\) 0 0
\(631\) 8.00000 0.318475 0.159237 0.987240i \(-0.449096\pi\)
0.159237 + 0.987240i \(0.449096\pi\)
\(632\) 3.00000 + 5.19615i 0.119334 + 0.206692i
\(633\) 0 0
\(634\) −3.00000 + 5.19615i −0.119145 + 0.206366i
\(635\) 24.0000 0.952411
\(636\) 0 0
\(637\) 0 0
\(638\) −4.00000 −0.158362
\(639\) 0 0
\(640\) 1.00000 + 1.73205i 0.0395285 + 0.0684653i
\(641\) −1.00000 −0.0394976 −0.0197488 0.999805i \(-0.506287\pi\)
−0.0197488 + 0.999805i \(0.506287\pi\)
\(642\) 0 0
\(643\) 3.50000 + 6.06218i 0.138027 + 0.239069i 0.926750 0.375680i \(-0.122591\pi\)
−0.788723 + 0.614749i \(0.789257\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 17.5000 + 30.3109i 0.688528 + 1.19257i
\(647\) 6.00000 + 10.3923i 0.235884 + 0.408564i 0.959529 0.281609i \(-0.0908680\pi\)
−0.723645 + 0.690172i \(0.757535\pi\)
\(648\) 0 0
\(649\) 3.50000 6.06218i 0.137387 0.237961i
\(650\) −3.00000 + 5.19615i −0.117670 + 0.203810i
\(651\) 0 0
\(652\) 2.00000 + 3.46410i 0.0783260 + 0.135665i
\(653\) 6.00000 0.234798 0.117399 0.993085i \(-0.462544\pi\)
0.117399 + 0.993085i \(0.462544\pi\)
\(654\) 0 0
\(655\) −8.00000 −0.312586
\(656\) 1.50000 2.59808i 0.0585652 0.101438i
\(657\) 0 0
\(658\) 0 0
\(659\) 8.00000 13.8564i 0.311636 0.539769i −0.667081 0.744985i \(-0.732456\pi\)
0.978717 + 0.205216i \(0.0657898\pi\)
\(660\) 0 0
\(661\) −14.0000 + 24.2487i −0.544537 + 0.943166i 0.454099 + 0.890951i \(0.349961\pi\)
−0.998636 + 0.0522143i \(0.983372\pi\)
\(662\) −4.00000 + 6.92820i −0.155464 + 0.269272i
\(663\) 0 0
\(664\) 8.00000 13.8564i 0.310460 0.537733i
\(665\) 0 0
\(666\) 0 0
\(667\) 8.00000 13.8564i 0.309761 0.536522i
\(668\) −20.0000 −0.773823
\(669\) 0 0
\(670\) −26.0000 −1.00447
\(671\) −6.00000 10.3923i −0.231627 0.401190i
\(672\) 0 0
\(673\) −7.00000 + 12.1244i −0.269830 + 0.467360i −0.968818 0.247774i \(-0.920301\pi\)
0.698988 + 0.715134i \(0.253634\pi\)
\(674\) 4.50000 7.79423i 0.173334 0.300222i
\(675\) 0 0
\(676\) −11.5000 19.9186i −0.442308 0.766099i
\(677\) 15.0000 + 25.9808i 0.576497 + 0.998522i 0.995877 + 0.0907112i \(0.0289140\pi\)
−0.419380 + 0.907811i \(0.637753\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 5.00000 + 8.66025i 0.191741 + 0.332106i
\(681\) 0 0
\(682\) 6.00000 0.229752
\(683\) 19.5000 + 33.7750i 0.746147 + 1.29236i 0.949657 + 0.313291i \(0.101432\pi\)
−0.203510 + 0.979073i \(0.565235\pi\)
\(684\) 0 0
\(685\) −38.0000 −1.45191
\(686\) 0 0
\(687\) 0 0
\(688\) −1.00000 −0.0381246
\(689\) −36.0000 + 62.3538i −1.37149 + 2.37549i
\(690\) 0 0
\(691\) −16.0000 27.7128i −0.608669 1.05425i −0.991460 0.130410i \(-0.958371\pi\)
0.382791 0.923835i \(-0.374963\pi\)
\(692\) −2.00000 −0.0760286
\(693\) 0 0
\(694\) 3.00000 0.113878
\(695\) −5.00000 8.66025i −0.189661 0.328502i
\(696\) 0 0
\(697\) 7.50000 12.9904i 0.284083 0.492046i
\(698\) −14.0000 −0.529908
\(699\) 0 0
\(700\) 0 0
\(701\) −8.00000 −0.302156 −0.151078 0.988522i \(-0.548274\pi\)
−0.151078 + 0.988522i \(0.548274\pi\)
\(702\) 0 0
\(703\) 7.00000 + 12.1244i 0.264010 + 0.457279i
\(704\) −1.00000 −0.0376889
\(705\) 0 0
\(706\) −7.50000 12.9904i −0.282266 0.488899i
\(707\) 0 0
\(708\) 0 0
\(709\) 2.00000 + 3.46410i 0.0751116 + 0.130097i 0.901135 0.433539i \(-0.142735\pi\)
−0.826023 + 0.563636i \(0.809402\pi\)
\(710\) 8.00000 + 13.8564i 0.300235 + 0.520022i
\(711\) 0 0
\(712\) −3.00000 + 5.19615i −0.112430 + 0.194734i
\(713\) −12.0000 + 20.7846i −0.449404 + 0.778390i
\(714\) 0 0
\(715\) 6.00000 + 10.3923i 0.224387 + 0.388650i
\(716\) −24.0000 −0.896922
\(717\) 0 0
\(718\) −2.00000 −0.0746393
\(719\) 3.00000 5.19615i 0.111881 0.193784i −0.804648 0.593753i \(-0.797646\pi\)
0.916529 + 0.399969i \(0.130979\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) −15.0000 + 25.9808i −0.558242 + 0.966904i
\(723\) 0 0
\(724\) 0 0
\(725\) 2.00000 3.46410i 0.0742781 0.128654i
\(726\) 0 0
\(727\) 7.00000 12.1244i 0.259616 0.449667i −0.706523 0.707690i \(-0.749737\pi\)
0.966139 + 0.258022i \(0.0830708\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 1.00000 1.73205i 0.0370117 0.0641061i
\(731\) −5.00000 −0.184932
\(732\) 0 0
\(733\) −18.0000 −0.664845 −0.332423 0.943131i \(-0.607866\pi\)
−0.332423 + 0.943131i \(0.607866\pi\)
\(734\) 11.0000 + 19.0526i 0.406017 + 0.703243i
\(735\) 0 0
\(736\) 2.00000 3.46410i 0.0737210 0.127688i
\(737\) 6.50000 11.2583i 0.239431 0.414706i
\(738\) 0 0
\(739\) 16.5000 + 28.5788i 0.606962 + 1.05129i 0.991738 + 0.128279i \(0.0409454\pi\)
−0.384776 + 0.923010i \(0.625721\pi\)
\(740\) 2.00000 + 3.46410i 0.0735215 + 0.127343i
\(741\) 0 0
\(742\) 0 0
\(743\) −3.00000 5.19615i −0.110059 0.190628i 0.805735 0.592277i \(-0.201771\pi\)
−0.915794 + 0.401648i \(0.868437\pi\)
\(744\) 0 0
\(745\) −48.0000 −1.75858
\(746\) −11.0000 19.0526i −0.402739 0.697564i
\(747\) 0 0
\(748\) −5.00000 −0.182818
\(749\) 0 0
\(750\) 0 0
\(751\) −18.0000 −0.656829 −0.328415 0.944534i \(-0.606514\pi\)
−0.328415 + 0.944534i \(0.606514\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 12.0000 + 20.7846i 0.437014 + 0.756931i
\(755\) −20.0000 −0.727875
\(756\) 0 0
\(757\) −48.0000 −1.74459 −0.872295 0.488980i \(-0.837369\pi\)
−0.872295 + 0.488980i \(0.837369\pi\)
\(758\) 8.50000 + 14.7224i 0.308734 + 0.534743i
\(759\) 0 0
\(760\) −7.00000 + 12.1244i −0.253917 + 0.439797i
\(761\) −10.0000 −0.362500 −0.181250 0.983437i \(-0.558014\pi\)
−0.181250 + 0.983437i \(0.558014\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) −12.0000 −0.434145
\(765\) 0 0
\(766\) 2.00000 + 3.46410i 0.0722629 + 0.125163i
\(767\) −42.0000 −1.51653
\(768\) 0 0
\(769\) −11.0000 19.0526i −0.396670 0.687053i 0.596643 0.802507i \(-0.296501\pi\)
−0.993313 + 0.115454i \(0.963168\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) −8.50000 14.7224i −0.305922 0.529872i
\(773\) −26.0000 45.0333i −0.935155 1.61974i −0.774357 0.632749i \(-0.781927\pi\)
−0.160798 0.986987i \(-0.551407\pi\)
\(774\) 0 0
\(775\) −3.00000 + 5.19615i −0.107763 + 0.186651i
\(776\) 2.50000 4.33013i 0.0897448 0.155443i
\(777\) 0 0
\(778\) 4.00000 + 6.92820i 0.143407 + 0.248388i
\(779\) 21.0000 0.752403
\(780\) 0 0
\(781\) −8.00000 −0.286263
\(782\) 10.0000 17.3205i 0.357599 0.619380i
\(783\) 0 0
\(784\) 0 0
\(785\) 2.00000 3.46410i 0.0713831 0.123639i
\(786\) 0 0
\(787\) 6.00000 10.3923i 0.213877 0.370446i −0.739048 0.673653i \(-0.764724\pi\)
0.952925 + 0.303207i \(0.0980575\pi\)
\(788\) 5.00000 8.66025i 0.178118 0.308509i
\(789\) 0 0
\(790\) −6.00000 + 10.3923i −0.213470 + 0.369742i
\(791\) 0 0
\(792\) 0 0
\(793\) −36.0000 + 62.3538i −1.27840 + 2.21425i
\(794\) 18.0000 0.638796
\(795\) 0 0
\(796\) 14.0000 0.496217
\(797\) −6.00000 10.3923i −0.212531 0.368114i 0.739975 0.672634i \(-0.234837\pi\)
−0.952506 + 0.304520i \(0.901504\pi\)
\(798\) 0 0
\(799\) 0 0
\(800\) 0.500000 0.866025i 0.0176777 0.0306186i
\(801\) 0 0
\(802\) 4.50000 + 7.79423i 0.158901 + 0.275224i
\(803\) 0.500000 + 0.866025i 0.0176446 + 0.0305614i
\(804\) 0 0
\(805\) 0 0
\(806\) −18.0000 31.1769i −0.634023 1.09816i
\(807\) 0 0
\(808\) 4.00000 0.140720
\(809\) −21.5000 37.2391i −0.755900 1.30926i −0.944926 0.327285i \(-0.893866\pi\)
0.189026 0.981972i \(-0.439467\pi\)
\(810\) 0 0
\(811\) 31.0000 1.08856 0.544279 0.838905i \(-0.316803\pi\)
0.544279 + 0.838905i \(0.316803\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) −2.00000 −0.0701000
\(815\) −4.00000 + 6.92820i −0.140114 + 0.242684i
\(816\) 0 0
\(817\) −3.50000 6.06218i −0.122449 0.212089i
\(818\) 11.0000 0.384606
\(819\) 0 0
\(820\) 6.00000 0.209529
\(821\) 23.0000 + 39.8372i 0.802706 + 1.39033i 0.917829 + 0.396976i \(0.129940\pi\)
−0.115124 + 0.993351i \(0.536726\pi\)
\(822\) 0 0
\(823\) −17.0000 + 29.4449i −0.592583 + 1.02638i 0.401300 + 0.915947i \(0.368558\pi\)
−0.993883 + 0.110437i \(0.964775\pi\)
\(824\) 14.0000 0.487713
\(825\) 0 0
\(826\) 0 0
\(827\) −12.0000 −0.417281 −0.208640 0.977992i \(-0.566904\pi\)
−0.208640 + 0.977992i \(0.566904\pi\)
\(828\) 0 0
\(829\) −2.00000 3.46410i −0.0694629 0.120313i 0.829202 0.558949i \(-0.188795\pi\)
−0.898665 + 0.438636i \(0.855462\pi\)
\(830\) 32.0000 1.11074
\(831\) 0 0
\(832\) 3.00000 + 5.19615i 0.104006 + 0.180144i
\(833\) 0 0
\(834\) 0 0
\(835\) −20.0000 34.6410i −0.692129 1.19880i
\(836\) −3.50000 6.06218i −0.121050 0.209665i
\(837\) 0 0
\(838\) −6.00000 + 10.3923i −0.207267 + 0.358996i
\(839\) −10.0000 + 17.3205i −0.345238 + 0.597970i −0.985397 0.170272i \(-0.945535\pi\)
0.640159 + 0.768243i \(0.278869\pi\)
\(840\) 0 0
\(841\) 6.50000 + 11.2583i 0.224138 + 0.388218i
\(842\) −12.0000 −0.413547
\(843\) 0 0
\(844\) −16.0000 −0.550743
\(845\) 23.0000 39.8372i 0.791224 1.37044i
\(846\) 0 0
\(847\) 0 0
\(848\) 6.00000 10.3923i 0.206041 0.356873i
\(849\) 0 0
\(850\) 2.50000 4.33013i 0.0857493 0.148522i
\(851\) 4.00000 6.92820i 0.137118 0.237496i
\(852\) 0 0
\(853\) −22.0000 + 38.1051i −0.753266 + 1.30469i 0.192966 + 0.981205i \(0.438189\pi\)
−0.946232 + 0.323489i \(0.895144\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 1.50000 2.59808i 0.0512689 0.0888004i
\(857\) −30.0000 −1.02478 −0.512390 0.858753i \(-0.671240\pi\)
−0.512390 + 0.858753i \(0.671240\pi\)
\(858\) 0 0
\(859\) 29.0000 0.989467 0.494734 0.869045i \(-0.335266\pi\)
0.494734 + 0.869045i \(0.335266\pi\)
\(860\) −1.00000 1.73205i −0.0340997 0.0590624i
\(861\) 0 0
\(862\) 0 0
\(863\) 19.0000 32.9090i 0.646768 1.12023i −0.337123 0.941461i \(-0.609454\pi\)
0.983890 0.178774i \(-0.0572129\pi\)
\(864\) 0 0
\(865\) −2.00000 3.46410i −0.0680020 0.117783i
\(866\) 12.5000 + 21.6506i 0.424767 + 0.735719i
\(867\) 0 0
\(868\) 0 0
\(869\) −3.00000 5.19615i −0.101768 0.176267i
\(870\) 0 0
\(871\) −78.0000 −2.64293
\(872\) 1.00000 + 1.73205i 0.0338643 + 0.0586546i
\(873\) 0 0
\(874\) 28.0000 0.947114
\(875\) 0 0
\(876\) 0 0
\(877\) 16.0000 0.540282 0.270141 0.962821i \(-0.412930\pi\)
0.270141 + 0.962821i \(0.412930\pi\)
\(878\) 12.0000 20.7846i 0.404980 0.701447i
\(879\) 0 0
\(880\) −1.00000 1.73205i −0.0337100 0.0583874i
\(881\) −42.0000 −1.41502 −0.707508 0.706705i \(-0.750181\pi\)
−0.707508 + 0.706705i \(0.750181\pi\)
\(882\) 0 0
\(883\) 53.0000 1.78359 0.891796 0.452438i \(-0.149446\pi\)
0.891796 + 0.452438i \(0.149446\pi\)
\(884\) 15.0000 + 25.9808i 0.504505 + 0.873828i
\(885\) 0 0
\(886\) 3.50000 6.06218i 0.117585 0.203663i
\(887\) 6.00000 0.201460 0.100730 0.994914i \(-0.467882\pi\)
0.100730 + 0.994914i \(0.467882\pi\)
\(888\) 0 0
\(889\) 0 0
\(890\) −12.0000 −0.402241
\(891\) 0 0
\(892\) 2.00000 + 3.46410i 0.0669650 + 0.115987i
\(893\) 0 0
\(894\) 0 0
\(895\) −24.0000 41.5692i −0.802232 1.38951i
\(896\) 0 0
\(897\) 0 0
\(898\) 8.50000 + 14.7224i 0.283649 + 0.491294i
\(899\) 12.0000 + 20.7846i 0.400222 + 0.693206i
\(900\) 0 0
\(901\) 30.0000 51.9615i 0.999445 1.73109i
\(902\) −1.50000 + 2.59808i −0.0499445 + 0.0865065i
\(903\) 0 0
\(904\) −5.00000 8.66025i −0.166298 0.288036i
\(905\) 0 0
\(906\) 0 0
\(907\) −27.0000 −0.896520 −0.448260 0.893903i \(-0.647956\pi\)
−0.448260 + 0.893903i \(0.647956\pi\)
\(908\) 1.50000 2.59808i 0.0497792 0.0862202i
\(909\) 0 0
\(910\) 0 0
\(911\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(912\) 0 0
\(913\) −8.00000 + 13.8564i −0.264761 + 0.458580i
\(914\) −0.500000 + 0.866025i −0.0165385 + 0.0286456i
\(915\) 0 0
\(916\) 13.0000 22.5167i 0.429532 0.743971i
\(917\) 0 0
\(918\) 0 0
\(919\) −8.00000 + 13.8564i −0.263896 + 0.457081i −0.967274 0.253735i \(-0.918341\pi\)
0.703378 + 0.710816i \(0.251674\pi\)
\(920\) 8.00000 0.263752
\(921\) 0 0
\(922\) −14.0000 −0.461065
\(923\) 24.0000 + 41.5692i 0.789970 + 1.36827i
\(924\) 0 0
\(925\) 1.00000 1.73205i 0.0328798 0.0569495i
\(926\) 4.00000 6.92820i 0.131448 0.227675i
\(927\) 0 0
\(928\) −2.00000 3.46410i −0.0656532 0.113715i
\(929\) −9.00000 15.5885i −0.295280 0.511441i 0.679770 0.733426i \(-0.262080\pi\)
−0.975050 + 0.221985i \(0.928746\pi\)
\(930\) 0 0
\(931\) 0 0
\(932\) −14.5000 25.1147i −0.474963 0.822661i
\(933\) 0 0
\(934\) 13.0000 0.425373
\(935\) −5.00000 8.66025i −0.163517 0.283221i
\(936\) 0 0
\(937\) 2.00000 0.0653372 0.0326686 0.999466i \(-0.489599\pi\)
0.0326686 + 0.999466i \(0.489599\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0 0
\(941\) 10.0000 17.3205i 0.325991 0.564632i −0.655722 0.755003i \(-0.727636\pi\)
0.981712 + 0.190370i \(0.0609689\pi\)
\(942\) 0 0
\(943\) −6.00000 10.3923i −0.195387 0.338420i
\(944\) 7.00000 0.227831
\(945\) 0 0
\(946\) 1.00000 0.0325128
\(947\) −18.5000 32.0429i −0.601169 1.04126i −0.992644 0.121067i \(-0.961368\pi\)
0.391475 0.920189i \(-0.371965\pi\)
\(948\) 0 0
\(949\) 3.00000 5.19615i 0.0973841 0.168674i
\(950\) 7.00000 0.227110
\(951\) 0 0
\(952\) 0 0
\(953\) 35.0000 1.13376 0.566881 0.823800i \(-0.308150\pi\)
0.566881 + 0.823800i \(0.308150\pi\)
\(954\) 0 0
\(955\) −12.0000 20.7846i −0.388311 0.672574i
\(956\) −6.00000 −0.194054
\(957\) 0 0
\(958\) −10.0000 17.3205i −0.323085 0.559600i
\(959\) 0 0
\(960\) 0 0
\(961\) −2.50000 4.33013i −0.0806452 0.139682i
\(962\) 6.00000 + 10.3923i 0.193448 + 0.335061i
\(963\) 0 0
\(964\) −11.5000 + 19.9186i −0.370390 + 0.641534i
\(965\) 17.0000 29.4449i 0.547249 0.947864i
\(966\) 0 0
\(967\) −7.00000 12.1244i −0.225105 0.389893i 0.731246 0.682114i \(-0.238939\pi\)
−0.956351 + 0.292221i \(0.905606\pi\)
\(968\) −10.0000 −0.321412
\(969\) 0 0
\(970\) 10.0000 0.321081
\(971\) −6.00000 + 10.3923i −0.192549 + 0.333505i −0.946094 0.323891i \(-0.895009\pi\)
0.753545 + 0.657396i \(0.228342\pi\)
\(972\) 0 0
\(973\) 0 0
\(974\) 5.00000 8.66025i 0.160210 0.277492i
\(975\) 0 0
\(976\) 6.00000 10.3923i 0.192055 0.332650i
\(977\) −7.50000 + 12.9904i −0.239946 + 0.415599i −0.960699 0.277594i \(-0.910463\pi\)
0.720752 + 0.693193i \(0.243796\pi\)
\(978\) 0 0
\(979\) 3.00000 5.19615i 0.0958804 0.166070i
\(980\) 0 0
\(981\) 0 0
\(982\) 16.5000 28.5788i 0.526536 0.911987i
\(983\) 60.0000 1.91370 0.956851 0.290578i \(-0.0938475\pi\)
0.956851 + 0.290578i \(0.0938475\pi\)
\(984\) 0 0
\(985\) 20.0000 0.637253
\(986\) −10.0000 17.3205i −0.318465 0.551597i
\(987\) 0 0
\(988\) −21.0000 + 36.3731i −0.668099 + 1.15718i
\(989\) −2.00000 + 3.46410i −0.0635963 + 0.110152i
\(990\) 0 0
\(991\) 14.0000 + 24.2487i 0.444725 + 0.770286i 0.998033 0.0626908i \(-0.0199682\pi\)
−0.553308 + 0.832977i \(0.686635\pi\)
\(992\) 3.00000 + 5.19615i 0.0952501 + 0.164978i
\(993\) 0 0
\(994\) 0 0
\(995\) 14.0000 + 24.2487i 0.443830 + 0.768736i
\(996\) 0 0
\(997\) 2.00000 0.0633406 0.0316703 0.999498i \(-0.489917\pi\)
0.0316703 + 0.999498i \(0.489917\pi\)
\(998\) 14.5000 + 25.1147i 0.458989 + 0.794993i
\(999\) 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 2646.2.h.b.667.1 2
3.2 odd 2 882.2.h.h.79.1 2
7.2 even 3 378.2.f.b.127.1 2
7.3 odd 6 2646.2.e.h.2125.1 2
7.4 even 3 2646.2.e.i.2125.1 2
7.5 odd 6 2646.2.f.b.883.1 2
7.6 odd 2 2646.2.h.c.667.1 2
9.4 even 3 2646.2.e.i.1549.1 2
9.5 odd 6 882.2.e.a.373.1 2
21.2 odd 6 126.2.f.b.43.1 2
21.5 even 6 882.2.f.f.295.1 2
21.11 odd 6 882.2.e.a.655.1 2
21.17 even 6 882.2.e.e.655.1 2
21.20 even 2 882.2.h.g.79.1 2
28.23 odd 6 3024.2.r.c.2017.1 2
63.2 odd 6 1134.2.a.c.1.1 1
63.4 even 3 inner 2646.2.h.b.361.1 2
63.5 even 6 882.2.f.f.589.1 2
63.13 odd 6 2646.2.e.h.1549.1 2
63.16 even 3 1134.2.a.f.1.1 1
63.23 odd 6 126.2.f.b.85.1 yes 2
63.31 odd 6 2646.2.h.c.361.1 2
63.32 odd 6 882.2.h.h.67.1 2
63.40 odd 6 2646.2.f.b.1765.1 2
63.41 even 6 882.2.e.e.373.1 2
63.47 even 6 7938.2.a.e.1.1 1
63.58 even 3 378.2.f.b.253.1 2
63.59 even 6 882.2.h.g.67.1 2
63.61 odd 6 7938.2.a.bb.1.1 1
84.23 even 6 1008.2.r.a.673.1 2
252.23 even 6 1008.2.r.a.337.1 2
252.79 odd 6 9072.2.a.f.1.1 1
252.191 even 6 9072.2.a.t.1.1 1
252.247 odd 6 3024.2.r.c.1009.1 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
126.2.f.b.43.1 2 21.2 odd 6
126.2.f.b.85.1 yes 2 63.23 odd 6
378.2.f.b.127.1 2 7.2 even 3
378.2.f.b.253.1 2 63.58 even 3
882.2.e.a.373.1 2 9.5 odd 6
882.2.e.a.655.1 2 21.11 odd 6
882.2.e.e.373.1 2 63.41 even 6
882.2.e.e.655.1 2 21.17 even 6
882.2.f.f.295.1 2 21.5 even 6
882.2.f.f.589.1 2 63.5 even 6
882.2.h.g.67.1 2 63.59 even 6
882.2.h.g.79.1 2 21.20 even 2
882.2.h.h.67.1 2 63.32 odd 6
882.2.h.h.79.1 2 3.2 odd 2
1008.2.r.a.337.1 2 252.23 even 6
1008.2.r.a.673.1 2 84.23 even 6
1134.2.a.c.1.1 1 63.2 odd 6
1134.2.a.f.1.1 1 63.16 even 3
2646.2.e.h.1549.1 2 63.13 odd 6
2646.2.e.h.2125.1 2 7.3 odd 6
2646.2.e.i.1549.1 2 9.4 even 3
2646.2.e.i.2125.1 2 7.4 even 3
2646.2.f.b.883.1 2 7.5 odd 6
2646.2.f.b.1765.1 2 63.40 odd 6
2646.2.h.b.361.1 2 63.4 even 3 inner
2646.2.h.b.667.1 2 1.1 even 1 trivial
2646.2.h.c.361.1 2 63.31 odd 6
2646.2.h.c.667.1 2 7.6 odd 2
3024.2.r.c.1009.1 2 252.247 odd 6
3024.2.r.c.2017.1 2 28.23 odd 6
7938.2.a.e.1.1 1 63.47 even 6
7938.2.a.bb.1.1 1 63.61 odd 6
9072.2.a.f.1.1 1 252.79 odd 6
9072.2.a.t.1.1 1 252.191 even 6