Properties

Label 2025.1.y.a.1646.1
Level $2025$
Weight $1$
Character 2025.1646
Analytic conductor $1.011$
Analytic rank $0$
Dimension $16$
Projective image $A_{5}$
CM/RM no
Inner twists $8$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [2025,1,Mod(296,2025)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(2025, base_ring=CyclotomicField(30))
 
chi = DirichletCharacter(H, H._module([25, 18]))
 
N = Newforms(chi, 1, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("2025.296");
 
S:= CuspForms(chi, 1);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 2025 = 3^{4} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 2025.y (of order \(30\), degree \(8\), 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: \(1.01060665058\)
Analytic rank: \(0\)
Dimension: \(16\)
Relative dimension: \(2\) over \(\Q(\zeta_{30})\)
Coefficient field: \(\Q(\zeta_{60})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{16} + x^{14} - x^{10} - x^{8} - x^{6} + x^{2} + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{4}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 675)
Projective image: \(A_{5}\)
Projective field: Galois closure of 5.1.31640625.2

Embedding invariants

Embedding label 1646.1
Root \(0.743145 + 0.669131i\) of defining polynomial
Character \(\chi\) \(=\) 2025.1646
Dual form 2025.1.y.a.1106.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.459289 + 0.413545i) q^{2} +(-0.0646021 + 0.614648i) q^{4} +(-0.743145 - 0.669131i) q^{5} +(-0.309017 + 0.535233i) q^{7} +(-0.587785 - 0.809017i) q^{8} +O(q^{10})\) \(q+(-0.459289 + 0.413545i) q^{2} +(-0.0646021 + 0.614648i) q^{4} +(-0.743145 - 0.669131i) q^{5} +(-0.309017 + 0.535233i) q^{7} +(-0.587785 - 0.809017i) q^{8} +0.618034 q^{10} +(0.743145 - 0.669131i) q^{11} +(-0.0794152 - 0.373619i) q^{14} +(0.587785 + 0.809017i) q^{17} +(0.809017 - 0.587785i) q^{19} +(0.459289 - 0.413545i) q^{20} +(-0.0646021 + 0.614648i) q^{22} +(0.207912 + 0.978148i) q^{23} +(0.104528 + 0.994522i) q^{25} +(-0.309017 - 0.224514i) q^{28} +(-0.658114 - 1.47815i) q^{29} +(0.866025 - 0.500000i) q^{32} +(-0.604528 - 0.128496i) q^{34} +(0.587785 - 0.190983i) q^{35} +(0.500000 + 1.53884i) q^{37} +(-0.128496 + 0.604528i) q^{38} +(-0.104528 + 0.994522i) q^{40} +(0.743145 + 0.669131i) q^{41} +(0.363271 + 0.500000i) q^{44} +(-0.500000 - 0.363271i) q^{46} +(0.658114 + 1.47815i) q^{47} +(0.309017 + 0.535233i) q^{49} +(-0.459289 - 0.413545i) q^{50} +(0.363271 - 0.500000i) q^{53} -1.00000 q^{55} +(0.614648 - 0.0646021i) q^{56} +(0.913545 + 0.406737i) q^{58} +(-0.669131 - 0.743145i) q^{61} +(-0.190983 + 0.587785i) q^{64} +(0.564602 + 0.251377i) q^{67} +(-0.535233 + 0.309017i) q^{68} +(-0.190983 + 0.330792i) q^{70} +(-0.951057 + 1.30902i) q^{71} +(-0.866025 - 0.500000i) q^{74} +(0.309017 + 0.535233i) q^{76} +(0.128496 + 0.604528i) q^{77} +(1.47815 - 0.658114i) q^{79} -0.618034 q^{82} +(-0.614648 + 0.0646021i) q^{83} +(0.104528 - 0.994522i) q^{85} +(-0.978148 - 0.207912i) q^{88} +(-0.951057 - 0.309017i) q^{89} +(-0.614648 + 0.0646021i) q^{92} +(-0.913545 - 0.406737i) q^{94} +(-0.994522 - 0.104528i) q^{95} +(0.913545 - 0.406737i) q^{97} +(-0.363271 - 0.118034i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16 q + 4 q^{4} + 4 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 16 q + 4 q^{4} + 4 q^{7} - 8 q^{10} + 4 q^{19} + 4 q^{22} - 2 q^{25} + 4 q^{28} - 6 q^{34} + 8 q^{37} + 2 q^{40} - 8 q^{46} - 4 q^{49} - 16 q^{55} + 2 q^{58} - 2 q^{61} - 12 q^{64} + 4 q^{67} - 12 q^{70} - 4 q^{76} + 6 q^{79} + 8 q^{82} - 2 q^{85} + 2 q^{88} - 2 q^{94} + 2 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/2025\mathbb{Z}\right)^\times\).

\(n\) \(326\) \(1702\)
\(\chi(n)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{3}{5}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.459289 + 0.413545i −0.459289 + 0.413545i −0.866025 0.500000i \(-0.833333\pi\)
0.406737 + 0.913545i \(0.366667\pi\)
\(3\) 0 0
\(4\) −0.0646021 + 0.614648i −0.0646021 + 0.614648i
\(5\) −0.743145 0.669131i −0.743145 0.669131i
\(6\) 0 0
\(7\) −0.309017 + 0.535233i −0.309017 + 0.535233i −0.978148 0.207912i \(-0.933333\pi\)
0.669131 + 0.743145i \(0.266667\pi\)
\(8\) −0.587785 0.809017i −0.587785 0.809017i
\(9\) 0 0
\(10\) 0.618034 0.618034
\(11\) 0.743145 0.669131i 0.743145 0.669131i −0.207912 0.978148i \(-0.566667\pi\)
0.951057 + 0.309017i \(0.100000\pi\)
\(12\) 0 0
\(13\) 0 0 −0.743145 0.669131i \(-0.766667\pi\)
0.743145 + 0.669131i \(0.233333\pi\)
\(14\) −0.0794152 0.373619i −0.0794152 0.373619i
\(15\) 0 0
\(16\) 0 0
\(17\) 0.587785 + 0.809017i 0.587785 + 0.809017i 0.994522 0.104528i \(-0.0333333\pi\)
−0.406737 + 0.913545i \(0.633333\pi\)
\(18\) 0 0
\(19\) 0.809017 0.587785i 0.809017 0.587785i −0.104528 0.994522i \(-0.533333\pi\)
0.913545 + 0.406737i \(0.133333\pi\)
\(20\) 0.459289 0.413545i 0.459289 0.413545i
\(21\) 0 0
\(22\) −0.0646021 + 0.614648i −0.0646021 + 0.614648i
\(23\) 0.207912 + 0.978148i 0.207912 + 0.978148i 0.951057 + 0.309017i \(0.100000\pi\)
−0.743145 + 0.669131i \(0.766667\pi\)
\(24\) 0 0
\(25\) 0.104528 + 0.994522i 0.104528 + 0.994522i
\(26\) 0 0
\(27\) 0 0
\(28\) −0.309017 0.224514i −0.309017 0.224514i
\(29\) −0.658114 1.47815i −0.658114 1.47815i −0.866025 0.500000i \(-0.833333\pi\)
0.207912 0.978148i \(-0.433333\pi\)
\(30\) 0 0
\(31\) 0 0 0.406737 0.913545i \(-0.366667\pi\)
−0.406737 + 0.913545i \(0.633333\pi\)
\(32\) 0.866025 0.500000i 0.866025 0.500000i
\(33\) 0 0
\(34\) −0.604528 0.128496i −0.604528 0.128496i
\(35\) 0.587785 0.190983i 0.587785 0.190983i
\(36\) 0 0
\(37\) 0.500000 + 1.53884i 0.500000 + 1.53884i 0.809017 + 0.587785i \(0.200000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(38\) −0.128496 + 0.604528i −0.128496 + 0.604528i
\(39\) 0 0
\(40\) −0.104528 + 0.994522i −0.104528 + 0.994522i
\(41\) 0.743145 + 0.669131i 0.743145 + 0.669131i 0.951057 0.309017i \(-0.100000\pi\)
−0.207912 + 0.978148i \(0.566667\pi\)
\(42\) 0 0
\(43\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(44\) 0.363271 + 0.500000i 0.363271 + 0.500000i
\(45\) 0 0
\(46\) −0.500000 0.363271i −0.500000 0.363271i
\(47\) 0.658114 + 1.47815i 0.658114 + 1.47815i 0.866025 + 0.500000i \(0.166667\pi\)
−0.207912 + 0.978148i \(0.566667\pi\)
\(48\) 0 0
\(49\) 0.309017 + 0.535233i 0.309017 + 0.535233i
\(50\) −0.459289 0.413545i −0.459289 0.413545i
\(51\) 0 0
\(52\) 0 0
\(53\) 0.363271 0.500000i 0.363271 0.500000i −0.587785 0.809017i \(-0.700000\pi\)
0.951057 + 0.309017i \(0.100000\pi\)
\(54\) 0 0
\(55\) −1.00000 −1.00000
\(56\) 0.614648 0.0646021i 0.614648 0.0646021i
\(57\) 0 0
\(58\) 0.913545 + 0.406737i 0.913545 + 0.406737i
\(59\) 0 0 0.669131 0.743145i \(-0.266667\pi\)
−0.669131 + 0.743145i \(0.733333\pi\)
\(60\) 0 0
\(61\) −0.669131 0.743145i −0.669131 0.743145i 0.309017 0.951057i \(-0.400000\pi\)
−0.978148 + 0.207912i \(0.933333\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) −0.190983 + 0.587785i −0.190983 + 0.587785i
\(65\) 0 0
\(66\) 0 0
\(67\) 0.564602 + 0.251377i 0.564602 + 0.251377i 0.669131 0.743145i \(-0.266667\pi\)
−0.104528 + 0.994522i \(0.533333\pi\)
\(68\) −0.535233 + 0.309017i −0.535233 + 0.309017i
\(69\) 0 0
\(70\) −0.190983 + 0.330792i −0.190983 + 0.330792i
\(71\) −0.951057 + 1.30902i −0.951057 + 1.30902i 1.00000i \(0.5\pi\)
−0.951057 + 0.309017i \(0.900000\pi\)
\(72\) 0 0
\(73\) 0 0 −0.951057 0.309017i \(-0.900000\pi\)
0.951057 + 0.309017i \(0.100000\pi\)
\(74\) −0.866025 0.500000i −0.866025 0.500000i
\(75\) 0 0
\(76\) 0.309017 + 0.535233i 0.309017 + 0.535233i
\(77\) 0.128496 + 0.604528i 0.128496 + 0.604528i
\(78\) 0 0
\(79\) 1.47815 0.658114i 1.47815 0.658114i 0.500000 0.866025i \(-0.333333\pi\)
0.978148 + 0.207912i \(0.0666667\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) −0.618034 −0.618034
\(83\) −0.614648 + 0.0646021i −0.614648 + 0.0646021i −0.406737 0.913545i \(-0.633333\pi\)
−0.207912 + 0.978148i \(0.566667\pi\)
\(84\) 0 0
\(85\) 0.104528 0.994522i 0.104528 0.994522i
\(86\) 0 0
\(87\) 0 0
\(88\) −0.978148 0.207912i −0.978148 0.207912i
\(89\) −0.951057 0.309017i −0.951057 0.309017i −0.207912 0.978148i \(-0.566667\pi\)
−0.743145 + 0.669131i \(0.766667\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) −0.614648 + 0.0646021i −0.614648 + 0.0646021i
\(93\) 0 0
\(94\) −0.913545 0.406737i −0.913545 0.406737i
\(95\) −0.994522 0.104528i −0.994522 0.104528i
\(96\) 0 0
\(97\) 0.913545 0.406737i 0.913545 0.406737i 0.104528 0.994522i \(-0.466667\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(98\) −0.363271 0.118034i −0.363271 0.118034i
\(99\) 0 0
\(100\) −0.618034 −0.618034
\(101\) 0.866025 + 0.500000i 0.866025 + 0.500000i 0.866025 0.500000i \(-0.166667\pi\)
1.00000i \(0.5\pi\)
\(102\) 0 0
\(103\) 0 0 −0.994522 0.104528i \(-0.966667\pi\)
0.994522 + 0.104528i \(0.0333333\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0.0399263 + 0.379874i 0.0399263 + 0.379874i
\(107\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(108\) 0 0
\(109\) 0.309017 + 0.951057i 0.309017 + 0.951057i 0.978148 + 0.207912i \(0.0666667\pi\)
−0.669131 + 0.743145i \(0.733333\pi\)
\(110\) 0.459289 0.413545i 0.459289 0.413545i
\(111\) 0 0
\(112\) 0 0
\(113\) 0 0 0.669131 0.743145i \(-0.266667\pi\)
−0.669131 + 0.743145i \(0.733333\pi\)
\(114\) 0 0
\(115\) 0.500000 0.866025i 0.500000 0.866025i
\(116\) 0.951057 0.309017i 0.951057 0.309017i
\(117\) 0 0
\(118\) 0 0
\(119\) −0.614648 + 0.0646021i −0.614648 + 0.0646021i
\(120\) 0 0
\(121\) 0 0
\(122\) 0.614648 + 0.0646021i 0.614648 + 0.0646021i
\(123\) 0 0
\(124\) 0 0
\(125\) 0.587785 0.809017i 0.587785 0.809017i
\(126\) 0 0
\(127\) 0.500000 1.53884i 0.500000 1.53884i −0.309017 0.951057i \(-0.600000\pi\)
0.809017 0.587785i \(-0.200000\pi\)
\(128\) 0.251377 + 0.564602i 0.251377 + 0.564602i
\(129\) 0 0
\(130\) 0 0
\(131\) 0.658114 1.47815i 0.658114 1.47815i −0.207912 0.978148i \(-0.566667\pi\)
0.866025 0.500000i \(-0.166667\pi\)
\(132\) 0 0
\(133\) 0.0646021 + 0.614648i 0.0646021 + 0.614648i
\(134\) −0.363271 + 0.118034i −0.363271 + 0.118034i
\(135\) 0 0
\(136\) 0.309017 0.951057i 0.309017 0.951057i
\(137\) −0.207912 + 0.978148i −0.207912 + 0.978148i 0.743145 + 0.669131i \(0.233333\pi\)
−0.951057 + 0.309017i \(0.900000\pi\)
\(138\) 0 0
\(139\) 0.978148 0.207912i 0.978148 0.207912i 0.309017 0.951057i \(-0.400000\pi\)
0.669131 + 0.743145i \(0.266667\pi\)
\(140\) 0.0794152 + 0.373619i 0.0794152 + 0.373619i
\(141\) 0 0
\(142\) −0.104528 0.994522i −0.104528 0.994522i
\(143\) 0 0
\(144\) 0 0
\(145\) −0.500000 + 1.53884i −0.500000 + 1.53884i
\(146\) 0 0
\(147\) 0 0
\(148\) −0.978148 + 0.207912i −0.978148 + 0.207912i
\(149\) −0.535233 + 0.309017i −0.535233 + 0.309017i −0.743145 0.669131i \(-0.766667\pi\)
0.207912 + 0.978148i \(0.433333\pi\)
\(150\) 0 0
\(151\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(152\) −0.951057 0.309017i −0.951057 0.309017i
\(153\) 0 0
\(154\) −0.309017 0.224514i −0.309017 0.224514i
\(155\) 0 0
\(156\) 0 0
\(157\) −0.809017 1.40126i −0.809017 1.40126i −0.913545 0.406737i \(-0.866667\pi\)
0.104528 0.994522i \(-0.466667\pi\)
\(158\) −0.406737 + 0.913545i −0.406737 + 0.913545i
\(159\) 0 0
\(160\) −0.978148 0.207912i −0.978148 0.207912i
\(161\) −0.587785 0.190983i −0.587785 0.190983i
\(162\) 0 0
\(163\) −0.309017 0.951057i −0.309017 0.951057i −0.978148 0.207912i \(-0.933333\pi\)
0.669131 0.743145i \(-0.266667\pi\)
\(164\) −0.459289 + 0.413545i −0.459289 + 0.413545i
\(165\) 0 0
\(166\) 0.255585 0.283856i 0.255585 0.283856i
\(167\) 0 0 −0.913545 0.406737i \(-0.866667\pi\)
0.913545 + 0.406737i \(0.133333\pi\)
\(168\) 0 0
\(169\) 0.104528 + 0.994522i 0.104528 + 0.994522i
\(170\) 0.363271 + 0.500000i 0.363271 + 0.500000i
\(171\) 0 0
\(172\) 0 0
\(173\) −1.20243 + 1.08268i −1.20243 + 1.08268i −0.207912 + 0.978148i \(0.566667\pi\)
−0.994522 + 0.104528i \(0.966667\pi\)
\(174\) 0 0
\(175\) −0.564602 0.251377i −0.564602 0.251377i
\(176\) 0 0
\(177\) 0 0
\(178\) 0.564602 0.251377i 0.564602 0.251377i
\(179\) 0.951057 1.30902i 0.951057 1.30902i 1.00000i \(-0.5\pi\)
0.951057 0.309017i \(-0.100000\pi\)
\(180\) 0 0
\(181\) −0.809017 + 0.587785i −0.809017 + 0.587785i −0.913545 0.406737i \(-0.866667\pi\)
0.104528 + 0.994522i \(0.466667\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0.669131 0.743145i 0.669131 0.743145i
\(185\) 0.658114 1.47815i 0.658114 1.47815i
\(186\) 0 0
\(187\) 0.978148 + 0.207912i 0.978148 + 0.207912i
\(188\) −0.951057 + 0.309017i −0.951057 + 0.309017i
\(189\) 0 0
\(190\) 0.500000 0.363271i 0.500000 0.363271i
\(191\) −0.128496 + 0.604528i −0.128496 + 0.604528i 0.866025 + 0.500000i \(0.166667\pi\)
−0.994522 + 0.104528i \(0.966667\pi\)
\(192\) 0 0
\(193\) −0.500000 0.866025i −0.500000 0.866025i 0.500000 0.866025i \(-0.333333\pi\)
−1.00000 \(\pi\)
\(194\) −0.251377 + 0.564602i −0.251377 + 0.564602i
\(195\) 0 0
\(196\) −0.348943 + 0.155360i −0.348943 + 0.155360i
\(197\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(198\) 0 0
\(199\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(200\) 0.743145 0.669131i 0.743145 0.669131i
\(201\) 0 0
\(202\) −0.604528 + 0.128496i −0.604528 + 0.128496i
\(203\) 0.994522 + 0.104528i 0.994522 + 0.104528i
\(204\) 0 0
\(205\) −0.104528 0.994522i −0.104528 0.994522i
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) 0.207912 0.978148i 0.207912 0.978148i
\(210\) 0 0
\(211\) 0.604528 0.128496i 0.604528 0.128496i 0.104528 0.994522i \(-0.466667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(212\) 0.283856 + 0.255585i 0.283856 + 0.255585i
\(213\) 0 0
\(214\) 0 0
\(215\) 0 0
\(216\) 0 0
\(217\) 0 0
\(218\) −0.535233 0.309017i −0.535233 0.309017i
\(219\) 0 0
\(220\) 0.0646021 0.614648i 0.0646021 0.614648i
\(221\) 0 0
\(222\) 0 0
\(223\) −0.413545 0.459289i −0.413545 0.459289i 0.500000 0.866025i \(-0.333333\pi\)
−0.913545 + 0.406737i \(0.866667\pi\)
\(224\) 0.618034i 0.618034i
\(225\) 0 0
\(226\) 0 0
\(227\) 0.459289 0.413545i 0.459289 0.413545i −0.406737 0.913545i \(-0.633333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(228\) 0 0
\(229\) 0 0 −0.994522 0.104528i \(-0.966667\pi\)
0.994522 + 0.104528i \(0.0333333\pi\)
\(230\) 0.128496 + 0.604528i 0.128496 + 0.604528i
\(231\) 0 0
\(232\) −0.809017 + 1.40126i −0.809017 + 1.40126i
\(233\) 0.587785 + 0.809017i 0.587785 + 0.809017i 0.994522 0.104528i \(-0.0333333\pi\)
−0.406737 + 0.913545i \(0.633333\pi\)
\(234\) 0 0
\(235\) 0.500000 1.53884i 0.500000 1.53884i
\(236\) 0 0
\(237\) 0 0
\(238\) 0.255585 0.283856i 0.255585 0.283856i
\(239\) 0.128496 + 0.604528i 0.128496 + 0.604528i 0.994522 + 0.104528i \(0.0333333\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(240\) 0 0
\(241\) 1.58268 + 0.336408i 1.58268 + 0.336408i 0.913545 0.406737i \(-0.133333\pi\)
0.669131 + 0.743145i \(0.266667\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0.500000 0.363271i 0.500000 0.363271i
\(245\) 0.128496 0.604528i 0.128496 0.604528i
\(246\) 0 0
\(247\) 0 0
\(248\) 0 0
\(249\) 0 0
\(250\) 0.0646021 + 0.614648i 0.0646021 + 0.614648i
\(251\) 1.00000i 1.00000i 0.866025 + 0.500000i \(0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(252\) 0 0
\(253\) 0.809017 + 0.587785i 0.809017 + 0.587785i
\(254\) 0.406737 + 0.913545i 0.406737 + 0.913545i
\(255\) 0 0
\(256\) −0.913545 0.406737i −0.913545 0.406737i
\(257\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(258\) 0 0
\(259\) −0.978148 0.207912i −0.978148 0.207912i
\(260\) 0 0
\(261\) 0 0
\(262\) 0.309017 + 0.951057i 0.309017 + 0.951057i
\(263\) 0.207912 0.978148i 0.207912 0.978148i −0.743145 0.669131i \(-0.766667\pi\)
0.951057 0.309017i \(-0.100000\pi\)
\(264\) 0 0
\(265\) −0.604528 + 0.128496i −0.604528 + 0.128496i
\(266\) −0.283856 0.255585i −0.283856 0.255585i
\(267\) 0 0
\(268\) −0.190983 + 0.330792i −0.190983 + 0.330792i
\(269\) −0.587785 0.809017i −0.587785 0.809017i 0.406737 0.913545i \(-0.366667\pi\)
−0.994522 + 0.104528i \(0.966667\pi\)
\(270\) 0 0
\(271\) −0.809017 0.587785i −0.809017 0.587785i 0.104528 0.994522i \(-0.466667\pi\)
−0.913545 + 0.406737i \(0.866667\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) −0.309017 0.535233i −0.309017 0.535233i
\(275\) 0.743145 + 0.669131i 0.743145 + 0.669131i
\(276\) 0 0
\(277\) 0 0 0.743145 0.669131i \(-0.233333\pi\)
−0.743145 + 0.669131i \(0.766667\pi\)
\(278\) −0.363271 + 0.500000i −0.363271 + 0.500000i
\(279\) 0 0
\(280\) −0.500000 0.363271i −0.500000 0.363271i
\(281\) 0.994522 0.104528i 0.994522 0.104528i 0.406737 0.913545i \(-0.366667\pi\)
0.587785 + 0.809017i \(0.300000\pi\)
\(282\) 0 0
\(283\) −0.913545 0.406737i −0.913545 0.406737i −0.104528 0.994522i \(-0.533333\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(284\) −0.743145 0.669131i −0.743145 0.669131i
\(285\) 0 0
\(286\) 0 0
\(287\) −0.587785 + 0.190983i −0.587785 + 0.190983i
\(288\) 0 0
\(289\) 0 0
\(290\) −0.406737 0.913545i −0.406737 0.913545i
\(291\) 0 0
\(292\) 0 0
\(293\) −0.866025 + 0.500000i −0.866025 + 0.500000i −0.866025 0.500000i \(-0.833333\pi\)
1.00000i \(0.5\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 0.951057 1.30902i 0.951057 1.30902i
\(297\) 0 0
\(298\) 0.118034 0.363271i 0.118034 0.363271i
\(299\) 0 0
\(300\) 0 0
\(301\) 0 0
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) 1.00000i 1.00000i
\(306\) 0 0
\(307\) −1.61803 −1.61803 −0.809017 0.587785i \(-0.800000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(308\) −0.379874 + 0.0399263i −0.379874 + 0.0399263i
\(309\) 0 0
\(310\) 0 0
\(311\) −0.207912 0.978148i −0.207912 0.978148i −0.951057 0.309017i \(-0.900000\pi\)
0.743145 0.669131i \(-0.233333\pi\)
\(312\) 0 0
\(313\) 0.604528 + 0.128496i 0.604528 + 0.128496i 0.500000 0.866025i \(-0.333333\pi\)
0.104528 + 0.994522i \(0.466667\pi\)
\(314\) 0.951057 + 0.309017i 0.951057 + 0.309017i
\(315\) 0 0
\(316\) 0.309017 + 0.951057i 0.309017 + 0.951057i
\(317\) 0.614648 0.0646021i 0.614648 0.0646021i 0.207912 0.978148i \(-0.433333\pi\)
0.406737 + 0.913545i \(0.366667\pi\)
\(318\) 0 0
\(319\) −1.47815 0.658114i −1.47815 0.658114i
\(320\) 0.535233 0.309017i 0.535233 0.309017i
\(321\) 0 0
\(322\) 0.348943 0.155360i 0.348943 0.155360i
\(323\) 0.951057 + 0.309017i 0.951057 + 0.309017i
\(324\) 0 0
\(325\) 0 0
\(326\) 0.535233 + 0.309017i 0.535233 + 0.309017i
\(327\) 0 0
\(328\) 0.104528 0.994522i 0.104528 0.994522i
\(329\) −0.994522 0.104528i −0.994522 0.104528i
\(330\) 0 0
\(331\) 0 0 0.994522 0.104528i \(-0.0333333\pi\)
−0.994522 + 0.104528i \(0.966667\pi\)
\(332\) 0.381966i 0.381966i
\(333\) 0 0
\(334\) 0 0
\(335\) −0.251377 0.564602i −0.251377 0.564602i
\(336\) 0 0
\(337\) 0 0 −0.743145 0.669131i \(-0.766667\pi\)
0.743145 + 0.669131i \(0.233333\pi\)
\(338\) −0.459289 0.413545i −0.459289 0.413545i
\(339\) 0 0
\(340\) 0.604528 + 0.128496i 0.604528 + 0.128496i
\(341\) 0 0
\(342\) 0 0
\(343\) −1.00000 −1.00000
\(344\) 0 0
\(345\) 0 0
\(346\) 0.104528 0.994522i 0.104528 0.994522i
\(347\) −0.994522 0.104528i −0.994522 0.104528i −0.406737 0.913545i \(-0.633333\pi\)
−0.587785 + 0.809017i \(0.700000\pi\)
\(348\) 0 0
\(349\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(350\) 0.363271 0.118034i 0.363271 0.118034i
\(351\) 0 0
\(352\) 0.309017 0.951057i 0.309017 0.951057i
\(353\) −0.251377 0.564602i −0.251377 0.564602i 0.743145 0.669131i \(-0.233333\pi\)
−0.994522 + 0.104528i \(0.966667\pi\)
\(354\) 0 0
\(355\) 1.58268 0.336408i 1.58268 0.336408i
\(356\) 0.251377 0.564602i 0.251377 0.564602i
\(357\) 0 0
\(358\) 0.104528 + 0.994522i 0.104528 + 0.994522i
\(359\) 0.951057 0.309017i 0.951057 0.309017i 0.207912 0.978148i \(-0.433333\pi\)
0.743145 + 0.669131i \(0.233333\pi\)
\(360\) 0 0
\(361\) 0 0
\(362\) 0.128496 0.604528i 0.128496 0.604528i
\(363\) 0 0
\(364\) 0 0
\(365\) 0 0
\(366\) 0 0
\(367\) −0.104528 0.994522i −0.104528 0.994522i −0.913545 0.406737i \(-0.866667\pi\)
0.809017 0.587785i \(-0.200000\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0.309017 + 0.951057i 0.309017 + 0.951057i
\(371\) 0.155360 + 0.348943i 0.155360 + 0.348943i
\(372\) 0 0
\(373\) 0.978148 0.207912i 0.978148 0.207912i 0.309017 0.951057i \(-0.400000\pi\)
0.669131 + 0.743145i \(0.266667\pi\)
\(374\) −0.535233 + 0.309017i −0.535233 + 0.309017i
\(375\) 0 0
\(376\) 0.809017 1.40126i 0.809017 1.40126i
\(377\) 0 0
\(378\) 0 0
\(379\) −1.30902 0.951057i −1.30902 0.951057i −0.309017 0.951057i \(-0.600000\pi\)
−1.00000 \(\pi\)
\(380\) 0.128496 0.604528i 0.128496 0.604528i
\(381\) 0 0
\(382\) −0.190983 0.330792i −0.190983 0.330792i
\(383\) 0.658114 1.47815i 0.658114 1.47815i −0.207912 0.978148i \(-0.566667\pi\)
0.866025 0.500000i \(-0.166667\pi\)
\(384\) 0 0
\(385\) 0.309017 0.535233i 0.309017 0.535233i
\(386\) 0.587785 + 0.190983i 0.587785 + 0.190983i
\(387\) 0 0
\(388\) 0.190983 + 0.587785i 0.190983 + 0.587785i
\(389\) 0 0 −0.669131 0.743145i \(-0.733333\pi\)
0.669131 + 0.743145i \(0.266667\pi\)
\(390\) 0 0
\(391\) −0.669131 + 0.743145i −0.669131 + 0.743145i
\(392\) 0.251377 0.564602i 0.251377 0.564602i
\(393\) 0 0
\(394\) 0 0
\(395\) −1.53884 0.500000i −1.53884 0.500000i
\(396\) 0 0
\(397\) −0.500000 0.363271i −0.500000 0.363271i 0.309017 0.951057i \(-0.400000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) −0.535233 + 0.309017i −0.535233 + 0.309017i −0.743145 0.669131i \(-0.766667\pi\)
0.207912 + 0.978148i \(0.433333\pi\)
\(402\) 0 0
\(403\) 0 0
\(404\) −0.363271 + 0.500000i −0.363271 + 0.500000i
\(405\) 0 0
\(406\) −0.500000 + 0.363271i −0.500000 + 0.363271i
\(407\) 1.40126 + 0.809017i 1.40126 + 0.809017i
\(408\) 0 0
\(409\) 0 0 −0.743145 0.669131i \(-0.766667\pi\)
0.743145 + 0.669131i \(0.233333\pi\)
\(410\) 0.459289 + 0.413545i 0.459289 + 0.413545i
\(411\) 0 0
\(412\) 0 0
\(413\) 0 0
\(414\) 0 0
\(415\) 0.500000 + 0.363271i 0.500000 + 0.363271i
\(416\) 0 0
\(417\) 0 0
\(418\) 0.309017 + 0.535233i 0.309017 + 0.535233i
\(419\) −0.251377 + 0.564602i −0.251377 + 0.564602i −0.994522 0.104528i \(-0.966667\pi\)
0.743145 + 0.669131i \(0.233333\pi\)
\(420\) 0 0
\(421\) −0.913545 + 0.406737i −0.913545 + 0.406737i −0.809017 0.587785i \(-0.800000\pi\)
−0.104528 + 0.994522i \(0.533333\pi\)
\(422\) −0.224514 + 0.309017i −0.224514 + 0.309017i
\(423\) 0 0
\(424\) −0.618034 −0.618034
\(425\) −0.743145 + 0.669131i −0.743145 + 0.669131i
\(426\) 0 0
\(427\) 0.604528 0.128496i 0.604528 0.128496i
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(432\) 0 0
\(433\) −0.809017 + 0.587785i −0.809017 + 0.587785i −0.913545 0.406737i \(-0.866667\pi\)
0.104528 + 0.994522i \(0.466667\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) −0.604528 + 0.128496i −0.604528 + 0.128496i
\(437\) 0.743145 + 0.669131i 0.743145 + 0.669131i
\(438\) 0 0
\(439\) −0.669131 0.743145i −0.669131 0.743145i 0.309017 0.951057i \(-0.400000\pi\)
−0.978148 + 0.207912i \(0.933333\pi\)
\(440\) 0.587785 + 0.809017i 0.587785 + 0.809017i
\(441\) 0 0
\(442\) 0 0
\(443\) −0.866025 0.500000i −0.866025 0.500000i 1.00000i \(-0.5\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(444\) 0 0
\(445\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(446\) 0.379874 + 0.0399263i 0.379874 + 0.0399263i
\(447\) 0 0
\(448\) −0.255585 0.283856i −0.255585 0.283856i
\(449\) 1.61803i 1.61803i −0.587785 0.809017i \(-0.700000\pi\)
0.587785 0.809017i \(-0.300000\pi\)
\(450\) 0 0
\(451\) 1.00000 1.00000
\(452\) 0 0
\(453\) 0 0
\(454\) −0.0399263 + 0.379874i −0.0399263 + 0.379874i
\(455\) 0 0
\(456\) 0 0
\(457\) −0.500000 + 0.866025i −0.500000 + 0.866025i 0.500000 + 0.866025i \(0.333333\pi\)
−1.00000 \(\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0.500000 + 0.363271i 0.500000 + 0.363271i
\(461\) −0.743145 + 0.669131i −0.743145 + 0.669131i −0.951057 0.309017i \(-0.900000\pi\)
0.207912 + 0.978148i \(0.433333\pi\)
\(462\) 0 0
\(463\) −0.669131 + 0.743145i −0.669131 + 0.743145i −0.978148 0.207912i \(-0.933333\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) −0.604528 0.128496i −0.604528 0.128496i
\(467\) −0.951057 1.30902i −0.951057 1.30902i −0.951057 0.309017i \(-0.900000\pi\)
1.00000i \(-0.5\pi\)
\(468\) 0 0
\(469\) −0.309017 + 0.224514i −0.309017 + 0.224514i
\(470\) 0.406737 + 0.913545i 0.406737 + 0.913545i
\(471\) 0 0
\(472\) 0 0
\(473\) 0 0
\(474\) 0 0
\(475\) 0.669131 + 0.743145i 0.669131 + 0.743145i
\(476\) 0.381966i 0.381966i
\(477\) 0 0
\(478\) −0.309017 0.224514i −0.309017 0.224514i
\(479\) 0 0 0.913545 0.406737i \(-0.133333\pi\)
−0.913545 + 0.406737i \(0.866667\pi\)
\(480\) 0 0
\(481\) 0 0
\(482\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(483\) 0 0
\(484\) 0 0
\(485\) −0.951057 0.309017i −0.951057 0.309017i
\(486\) 0 0
\(487\) 0.309017 + 0.951057i 0.309017 + 0.951057i 0.978148 + 0.207912i \(0.0666667\pi\)
−0.669131 + 0.743145i \(0.733333\pi\)
\(488\) −0.207912 + 0.978148i −0.207912 + 0.978148i
\(489\) 0 0
\(490\) 0.190983 + 0.330792i 0.190983 + 0.330792i
\(491\) 0 0 0.669131 0.743145i \(-0.266667\pi\)
−0.669131 + 0.743145i \(0.733333\pi\)
\(492\) 0 0
\(493\) 0.809017 1.40126i 0.809017 1.40126i
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) −0.406737 0.913545i −0.406737 0.913545i
\(498\) 0 0
\(499\) 0.500000 + 0.866025i 0.500000 + 0.866025i 1.00000 \(0\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(500\) 0.459289 + 0.413545i 0.459289 + 0.413545i
\(501\) 0 0
\(502\) −0.413545 0.459289i −0.413545 0.459289i
\(503\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(504\) 0 0
\(505\) −0.309017 0.951057i −0.309017 0.951057i
\(506\) −0.614648 + 0.0646021i −0.614648 + 0.0646021i
\(507\) 0 0
\(508\) 0.913545 + 0.406737i 0.913545 + 0.406737i
\(509\) 0.459289 + 0.413545i 0.459289 + 0.413545i 0.866025 0.500000i \(-0.166667\pi\)
−0.406737 + 0.913545i \(0.633333\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) 0 0
\(516\) 0 0
\(517\) 1.47815 + 0.658114i 1.47815 + 0.658114i
\(518\) 0.535233 0.309017i 0.535233 0.309017i
\(519\) 0 0
\(520\) 0 0
\(521\) 0.363271 0.500000i 0.363271 0.500000i −0.587785 0.809017i \(-0.700000\pi\)
0.951057 + 0.309017i \(0.100000\pi\)
\(522\) 0 0
\(523\) 0 0 −0.951057 0.309017i \(-0.900000\pi\)
0.951057 + 0.309017i \(0.100000\pi\)
\(524\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(525\) 0 0
\(526\) 0.309017 + 0.535233i 0.309017 + 0.535233i
\(527\) 0 0
\(528\) 0 0
\(529\) 0 0
\(530\) 0.224514 0.309017i 0.224514 0.309017i
\(531\) 0 0
\(532\) −0.381966 −0.381966
\(533\) 0 0
\(534\) 0 0
\(535\) 0 0
\(536\) −0.128496 0.604528i −0.128496 0.604528i
\(537\) 0 0
\(538\) 0.604528 + 0.128496i 0.604528 + 0.128496i
\(539\) 0.587785 + 0.190983i 0.587785 + 0.190983i
\(540\) 0 0
\(541\) 0.309017 + 0.951057i 0.309017 + 0.951057i 0.978148 + 0.207912i \(0.0666667\pi\)
−0.669131 + 0.743145i \(0.733333\pi\)
\(542\) 0.614648 0.0646021i 0.614648 0.0646021i
\(543\) 0 0
\(544\) 0.913545 + 0.406737i 0.913545 + 0.406737i
\(545\) 0.406737 0.913545i 0.406737 0.913545i
\(546\) 0 0
\(547\) −0.913545 + 0.406737i −0.913545 + 0.406737i −0.809017 0.587785i \(-0.800000\pi\)
−0.104528 + 0.994522i \(0.533333\pi\)
\(548\) −0.587785 0.190983i −0.587785 0.190983i
\(549\) 0 0
\(550\) −0.618034 −0.618034
\(551\) −1.40126 0.809017i −1.40126 0.809017i
\(552\) 0 0
\(553\) −0.104528 + 0.994522i −0.104528 + 0.994522i
\(554\) 0 0
\(555\) 0 0
\(556\) 0.0646021 + 0.614648i 0.0646021 + 0.614648i
\(557\) 1.61803i 1.61803i 0.587785 + 0.809017i \(0.300000\pi\)
−0.587785 + 0.809017i \(0.700000\pi\)
\(558\) 0 0
\(559\) 0 0
\(560\) 0 0
\(561\) 0 0
\(562\) −0.413545 + 0.459289i −0.413545 + 0.459289i
\(563\) 0.459289 + 0.413545i 0.459289 + 0.413545i 0.866025 0.500000i \(-0.166667\pi\)
−0.406737 + 0.913545i \(0.633333\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 0.587785 0.190983i 0.587785 0.190983i
\(567\) 0 0
\(568\) 1.61803 1.61803
\(569\) 0.614648 0.0646021i 0.614648 0.0646021i 0.207912 0.978148i \(-0.433333\pi\)
0.406737 + 0.913545i \(0.366667\pi\)
\(570\) 0 0
\(571\) 0 0 −0.994522 0.104528i \(-0.966667\pi\)
0.994522 + 0.104528i \(0.0333333\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0.190983 0.330792i 0.190983 0.330792i
\(575\) −0.951057 + 0.309017i −0.951057 + 0.309017i
\(576\) 0 0
\(577\) 0.500000 1.53884i 0.500000 1.53884i −0.309017 0.951057i \(-0.600000\pi\)
0.809017 0.587785i \(-0.200000\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) −0.913545 0.406737i −0.913545 0.406737i
\(581\) 0.155360 0.348943i 0.155360 0.348943i
\(582\) 0 0
\(583\) −0.0646021 0.614648i −0.0646021 0.614648i
\(584\) 0 0
\(585\) 0 0
\(586\) 0.190983 0.587785i 0.190983 0.587785i
\(587\) 0 0 −0.978148 0.207912i \(-0.933333\pi\)
0.978148 + 0.207912i \(0.0666667\pi\)
\(588\) 0 0
\(589\) 0 0
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) 1.00000i 1.00000i 0.866025 + 0.500000i \(0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(594\) 0 0
\(595\) 0.500000 + 0.363271i 0.500000 + 0.363271i
\(596\) −0.155360 0.348943i −0.155360 0.348943i
\(597\) 0 0
\(598\) 0 0
\(599\) 0.535233 0.309017i 0.535233 0.309017i −0.207912 0.978148i \(-0.566667\pi\)
0.743145 + 0.669131i \(0.233333\pi\)
\(600\) 0 0
\(601\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) 0 0
\(606\) 0 0
\(607\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(608\) 0.406737 0.913545i 0.406737 0.913545i
\(609\) 0 0
\(610\) −0.413545 0.459289i −0.413545 0.459289i
\(611\) 0 0
\(612\) 0 0
\(613\) 0.309017 + 0.951057i 0.309017 + 0.951057i 0.978148 + 0.207912i \(0.0666667\pi\)
−0.669131 + 0.743145i \(0.733333\pi\)
\(614\) 0.743145 0.669131i 0.743145 0.669131i
\(615\) 0 0
\(616\) 0.413545 0.459289i 0.413545 0.459289i
\(617\) −0.406737 + 0.913545i −0.406737 + 0.913545i 0.587785 + 0.809017i \(0.300000\pi\)
−0.994522 + 0.104528i \(0.966667\pi\)
\(618\) 0 0
\(619\) 0.0646021 + 0.614648i 0.0646021 + 0.614648i 0.978148 + 0.207912i \(0.0666667\pi\)
−0.913545 + 0.406737i \(0.866667\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0.500000 + 0.363271i 0.500000 + 0.363271i
\(623\) 0.459289 0.413545i 0.459289 0.413545i
\(624\) 0 0
\(625\) −0.978148 + 0.207912i −0.978148 + 0.207912i
\(626\) −0.330792 + 0.190983i −0.330792 + 0.190983i
\(627\) 0 0
\(628\) 0.913545 0.406737i 0.913545 0.406737i
\(629\) −0.951057 + 1.30902i −0.951057 + 1.30902i
\(630\) 0 0
\(631\) −0.500000 + 0.363271i −0.500000 + 0.363271i −0.809017 0.587785i \(-0.800000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(632\) −1.40126 0.809017i −1.40126 0.809017i
\(633\) 0 0
\(634\) −0.255585 + 0.283856i −0.255585 + 0.283856i
\(635\) −1.40126 + 0.809017i −1.40126 + 0.809017i
\(636\) 0 0
\(637\) 0 0
\(638\) 0.951057 0.309017i 0.951057 0.309017i
\(639\) 0 0
\(640\) 0.190983 0.587785i 0.190983 0.587785i
\(641\) −0.207912 + 0.978148i −0.207912 + 0.978148i 0.743145 + 0.669131i \(0.233333\pi\)
−0.951057 + 0.309017i \(0.900000\pi\)
\(642\) 0 0
\(643\) 0.500000 + 0.866025i 0.500000 + 0.866025i 1.00000 \(0\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(644\) 0.155360 0.348943i 0.155360 0.348943i
\(645\) 0 0
\(646\) −0.564602 + 0.251377i −0.564602 + 0.251377i
\(647\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(648\) 0 0
\(649\) 0 0
\(650\) 0 0
\(651\) 0 0
\(652\) 0.604528 0.128496i 0.604528 0.128496i
\(653\) −0.994522 0.104528i −0.994522 0.104528i −0.406737 0.913545i \(-0.633333\pi\)
−0.587785 + 0.809017i \(0.700000\pi\)
\(654\) 0 0
\(655\) −1.47815 + 0.658114i −1.47815 + 0.658114i
\(656\) 0 0
\(657\) 0 0
\(658\) 0.500000 0.363271i 0.500000 0.363271i
\(659\) −0.336408 + 1.58268i −0.336408 + 1.58268i 0.406737 + 0.913545i \(0.366667\pi\)
−0.743145 + 0.669131i \(0.766667\pi\)
\(660\) 0 0
\(661\) 0 0 −0.207912 0.978148i \(-0.566667\pi\)
0.207912 + 0.978148i \(0.433333\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0.413545 + 0.459289i 0.413545 + 0.459289i
\(665\) 0.363271 0.500000i 0.363271 0.500000i
\(666\) 0 0
\(667\) 1.30902 0.951057i 1.30902 0.951057i
\(668\) 0 0
\(669\) 0 0
\(670\) 0.348943 + 0.155360i 0.348943 + 0.155360i
\(671\) −0.994522 0.104528i −0.994522 0.104528i
\(672\) 0 0
\(673\) 0.413545 + 0.459289i 0.413545 + 0.459289i 0.913545 0.406737i \(-0.133333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) −0.618034 −0.618034
\(677\) 0.459289 0.413545i 0.459289 0.413545i −0.406737 0.913545i \(-0.633333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(678\) 0 0
\(679\) −0.0646021 + 0.614648i −0.0646021 + 0.614648i
\(680\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(681\) 0 0
\(682\) 0 0
\(683\) −0.587785 0.809017i −0.587785 0.809017i 0.406737 0.913545i \(-0.366667\pi\)
−0.994522 + 0.104528i \(0.966667\pi\)
\(684\) 0 0
\(685\) 0.809017 0.587785i 0.809017 0.587785i
\(686\) 0.459289 0.413545i 0.459289 0.413545i
\(687\) 0 0
\(688\) 0 0
\(689\) 0 0
\(690\) 0 0
\(691\) 0 0 0.207912 0.978148i \(-0.433333\pi\)
−0.207912 + 0.978148i \(0.566667\pi\)
\(692\) −0.587785 0.809017i −0.587785 0.809017i
\(693\) 0 0
\(694\) 0.500000 0.363271i 0.500000 0.363271i
\(695\) −0.866025 0.500000i −0.866025 0.500000i
\(696\) 0 0
\(697\) −0.104528 + 0.994522i −0.104528 + 0.994522i
\(698\) 0 0
\(699\) 0 0
\(700\) 0.190983 0.330792i 0.190983 0.330792i
\(701\) 1.00000i 1.00000i 0.866025 + 0.500000i \(0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(702\) 0 0
\(703\) 1.30902 + 0.951057i 1.30902 + 0.951057i
\(704\) 0.251377 + 0.564602i 0.251377 + 0.564602i
\(705\) 0 0
\(706\) 0.348943 + 0.155360i 0.348943 + 0.155360i
\(707\) −0.535233 + 0.309017i −0.535233 + 0.309017i
\(708\) 0 0
\(709\) 0 0 0.207912 0.978148i \(-0.433333\pi\)
−0.207912 + 0.978148i \(0.566667\pi\)
\(710\) −0.587785 + 0.809017i −0.587785 + 0.809017i
\(711\) 0 0
\(712\) 0.309017 + 0.951057i 0.309017 + 0.951057i
\(713\) 0 0
\(714\) 0 0
\(715\) 0 0
\(716\) 0.743145 + 0.669131i 0.743145 + 0.669131i
\(717\) 0 0
\(718\) −0.309017 + 0.535233i −0.309017 + 0.535233i
\(719\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) 0 0
\(723\) 0 0
\(724\) −0.309017 0.535233i −0.309017 0.535233i
\(725\) 1.40126 0.809017i 1.40126 0.809017i
\(726\) 0 0
\(727\) −1.33826 1.48629i −1.33826 1.48629i −0.669131 0.743145i \(-0.733333\pi\)
−0.669131 0.743145i \(-0.733333\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) 0 0
\(732\) 0 0
\(733\) −0.913545 0.406737i −0.913545 0.406737i −0.104528 0.994522i \(-0.533333\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(734\) 0.459289 + 0.413545i 0.459289 + 0.413545i
\(735\) 0 0
\(736\) 0.669131 + 0.743145i 0.669131 + 0.743145i
\(737\) 0.587785 0.190983i 0.587785 0.190983i
\(738\) 0 0
\(739\) 0 0 −0.951057 0.309017i \(-0.900000\pi\)
0.951057 + 0.309017i \(0.100000\pi\)
\(740\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(741\) 0 0
\(742\) −0.215659 0.0960175i −0.215659 0.0960175i
\(743\) 0.866025 0.500000i 0.866025 0.500000i 1.00000i \(-0.5\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(744\) 0 0
\(745\) 0.604528 + 0.128496i 0.604528 + 0.128496i
\(746\) −0.363271 + 0.500000i −0.363271 + 0.500000i
\(747\) 0 0
\(748\) −0.190983 + 0.587785i −0.190983 + 0.587785i
\(749\) 0 0
\(750\) 0 0
\(751\) −0.309017 0.535233i −0.309017 0.535233i 0.669131 0.743145i \(-0.266667\pi\)
−0.978148 + 0.207912i \(0.933333\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 0 0
\(756\) 0 0
\(757\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(758\) 0.994522 0.104528i 0.994522 0.104528i
\(759\) 0 0
\(760\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(761\) 0.336408 + 1.58268i 0.336408 + 1.58268i 0.743145 + 0.669131i \(0.233333\pi\)
−0.406737 + 0.913545i \(0.633333\pi\)
\(762\) 0 0
\(763\) −0.604528 0.128496i −0.604528 0.128496i
\(764\) −0.363271 0.118034i −0.363271 0.118034i
\(765\) 0 0
\(766\) 0.309017 + 0.951057i 0.309017 + 0.951057i
\(767\) 0 0
\(768\) 0 0
\(769\) 0 0 0.406737 0.913545i \(-0.366667\pi\)
−0.406737 + 0.913545i \(0.633333\pi\)
\(770\) 0.0794152 + 0.373619i 0.0794152 + 0.373619i
\(771\) 0 0
\(772\) 0.564602 0.251377i 0.564602 0.251377i
\(773\) 0.951057 + 0.309017i 0.951057 + 0.309017i 0.743145 0.669131i \(-0.233333\pi\)
0.207912 + 0.978148i \(0.433333\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) −0.866025 0.500000i −0.866025 0.500000i
\(777\) 0 0
\(778\) 0 0
\(779\) 0.994522 + 0.104528i 0.994522 + 0.104528i
\(780\) 0 0
\(781\) 0.169131 + 1.60917i 0.169131 + 1.60917i
\(782\) 0.618034i 0.618034i
\(783\) 0 0
\(784\) 0 0
\(785\) −0.336408 + 1.58268i −0.336408 + 1.58268i
\(786\) 0 0
\(787\) 0.413545 0.459289i 0.413545 0.459289i −0.500000 0.866025i \(-0.666667\pi\)
0.913545 + 0.406737i \(0.133333\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0.913545 0.406737i 0.913545 0.406737i
\(791\) 0 0
\(792\) 0 0
\(793\) 0 0
\(794\) 0.379874 0.0399263i 0.379874 0.0399263i
\(795\) 0 0
\(796\) 0 0
\(797\) 0.994522 + 0.104528i 0.994522 + 0.104528i 0.587785 0.809017i \(-0.300000\pi\)
0.406737 + 0.913545i \(0.366667\pi\)
\(798\) 0 0
\(799\) −0.809017 + 1.40126i −0.809017 + 1.40126i
\(800\) 0.587785 + 0.809017i 0.587785 + 0.809017i
\(801\) 0 0
\(802\) 0.118034 0.363271i 0.118034 0.363271i
\(803\) 0 0
\(804\) 0 0
\(805\) 0.309017 + 0.535233i 0.309017 + 0.535233i
\(806\) 0 0
\(807\) 0 0
\(808\) −0.104528 0.994522i −0.104528 0.994522i
\(809\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(810\) 0 0
\(811\) 0.309017 0.951057i 0.309017 0.951057i −0.669131 0.743145i \(-0.733333\pi\)
0.978148 0.207912i \(-0.0666667\pi\)
\(812\) −0.128496 + 0.604528i −0.128496 + 0.604528i
\(813\) 0 0
\(814\) −0.978148 + 0.207912i −0.978148 + 0.207912i
\(815\) −0.406737 + 0.913545i −0.406737 + 0.913545i
\(816\) 0 0
\(817\) 0 0
\(818\) 0 0
\(819\) 0 0
\(820\) 0.618034 0.618034
\(821\) 0 0 0.913545 0.406737i \(-0.133333\pi\)
−0.913545 + 0.406737i \(0.866667\pi\)
\(822\) 0 0
\(823\) 0.978148 0.207912i 0.978148 0.207912i 0.309017 0.951057i \(-0.400000\pi\)
0.669131 + 0.743145i \(0.266667\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) 1.53884 + 0.500000i 1.53884 + 0.500000i 0.951057 0.309017i \(-0.100000\pi\)
0.587785 + 0.809017i \(0.300000\pi\)
\(828\) 0 0
\(829\) 0.809017 + 0.587785i 0.809017 + 0.587785i 0.913545 0.406737i \(-0.133333\pi\)
−0.104528 + 0.994522i \(0.533333\pi\)
\(830\) −0.379874 + 0.0399263i −0.379874 + 0.0399263i
\(831\) 0 0
\(832\) 0 0
\(833\) −0.251377 + 0.564602i −0.251377 + 0.564602i
\(834\) 0 0
\(835\) 0 0
\(836\) 0.587785 + 0.190983i 0.587785 + 0.190983i
\(837\) 0 0
\(838\) −0.118034 0.363271i −0.118034 0.363271i
\(839\) 0 0 −0.669131 0.743145i \(-0.733333\pi\)
0.669131 + 0.743145i \(0.266667\pi\)
\(840\) 0 0
\(841\) −1.08268 + 1.20243i −1.08268 + 1.20243i
\(842\) 0.251377 0.564602i 0.251377 0.564602i
\(843\) 0 0
\(844\) 0.0399263 + 0.379874i 0.0399263 + 0.379874i
\(845\) 0.587785 0.809017i 0.587785 0.809017i
\(846\) 0 0
\(847\) 0 0
\(848\) 0 0
\(849\) 0 0
\(850\) 0.0646021 0.614648i 0.0646021 0.614648i
\(851\) −1.40126 + 0.809017i −1.40126 + 0.809017i
\(852\) 0 0
\(853\) −1.47815 + 0.658114i −1.47815 + 0.658114i −0.978148 0.207912i \(-0.933333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(854\) −0.224514 + 0.309017i −0.224514 + 0.309017i
\(855\) 0 0
\(856\) 0 0
\(857\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(858\) 0 0
\(859\) 0 0 −0.743145 0.669131i \(-0.766667\pi\)
0.743145 + 0.669131i \(0.233333\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(864\) 0 0
\(865\) 1.61803 1.61803
\(866\) 0.128496 0.604528i 0.128496 0.604528i
\(867\) 0 0
\(868\) 0 0
\(869\) 0.658114 1.47815i 0.658114 1.47815i
\(870\) 0 0
\(871\) 0 0
\(872\) 0.587785 0.809017i 0.587785 0.809017i
\(873\) 0 0
\(874\) −0.618034 −0.618034
\(875\) 0.251377 + 0.564602i 0.251377 + 0.564602i
\(876\) 0 0
\(877\) 0 0 −0.207912 0.978148i \(-0.566667\pi\)
0.207912 + 0.978148i \(0.433333\pi\)
\(878\) 0.614648 + 0.0646021i 0.614648 + 0.0646021i
\(879\) 0 0
\(880\) 0 0
\(881\) −1.17557 1.61803i −1.17557 1.61803i −0.587785 0.809017i \(-0.700000\pi\)
−0.587785 0.809017i \(-0.700000\pi\)
\(882\) 0 0
\(883\) 0.809017 0.587785i 0.809017 0.587785i −0.104528 0.994522i \(-0.533333\pi\)
0.913545 + 0.406737i \(0.133333\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0.604528 0.128496i 0.604528 0.128496i
\(887\) −0.743145 0.669131i −0.743145 0.669131i 0.207912 0.978148i \(-0.433333\pi\)
−0.951057 + 0.309017i \(0.900000\pi\)
\(888\) 0 0
\(889\) 0.669131 + 0.743145i 0.669131 + 0.743145i
\(890\) −0.587785 0.190983i −0.587785 0.190983i
\(891\) 0 0
\(892\) 0.309017 0.224514i 0.309017 0.224514i
\(893\) 1.40126 + 0.809017i 1.40126 + 0.809017i
\(894\) 0 0
\(895\) −1.58268 + 0.336408i −1.58268 + 0.336408i
\(896\) −0.379874 0.0399263i −0.379874 0.0399263i
\(897\) 0 0
\(898\) 0.669131 + 0.743145i 0.669131 + 0.743145i
\(899\) 0 0
\(900\) 0 0
\(901\) 0.618034 0.618034
\(902\) −0.459289 + 0.413545i −0.459289 + 0.413545i
\(903\) 0 0
\(904\) 0 0
\(905\) 0.994522 + 0.104528i 0.994522 + 0.104528i
\(906\) 0 0
\(907\) −0.500000 + 0.866025i −0.500000 + 0.866025i 0.500000 + 0.866025i \(0.333333\pi\)
−1.00000 \(\pi\)
\(908\) 0.224514 + 0.309017i 0.224514 + 0.309017i
\(909\) 0 0
\(910\) 0 0
\(911\) −1.20243 + 1.08268i −1.20243 + 1.08268i −0.207912 + 0.978148i \(0.566667\pi\)
−0.994522 + 0.104528i \(0.966667\pi\)
\(912\) 0 0
\(913\) −0.413545 + 0.459289i −0.413545 + 0.459289i
\(914\) −0.128496 0.604528i −0.128496 0.604528i
\(915\) 0 0
\(916\) 0 0
\(917\) 0.587785 + 0.809017i 0.587785 + 0.809017i
\(918\) 0 0
\(919\) −0.500000 + 0.363271i −0.500000 + 0.363271i −0.809017 0.587785i \(-0.800000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(920\) −0.994522 + 0.104528i −0.994522 + 0.104528i
\(921\) 0 0
\(922\) 0.0646021 0.614648i 0.0646021 0.614648i
\(923\) 0 0
\(924\) 0 0
\(925\) −1.47815 + 0.658114i −1.47815 + 0.658114i
\(926\) 0.618034i 0.618034i
\(927\) 0 0
\(928\) −1.30902 0.951057i −1.30902 0.951057i
\(929\) 0.251377 + 0.564602i 0.251377 + 0.564602i 0.994522 0.104528i \(-0.0333333\pi\)
−0.743145 + 0.669131i \(0.766667\pi\)
\(930\) 0 0
\(931\) 0.564602 + 0.251377i 0.564602 + 0.251377i
\(932\) −0.535233 + 0.309017i −0.535233 + 0.309017i
\(933\) 0 0
\(934\) 0.978148 + 0.207912i 0.978148 + 0.207912i
\(935\) −0.587785 0.809017i −0.587785 0.809017i
\(936\) 0 0
\(937\) 0 0 0.951057 0.309017i \(-0.100000\pi\)
−0.951057 + 0.309017i \(0.900000\pi\)
\(938\) 0.0490813 0.230909i 0.0490813 0.230909i
\(939\) 0 0
\(940\) 0.913545 + 0.406737i 0.913545 + 0.406737i
\(941\) 0 0 0.669131 0.743145i \(-0.266667\pi\)
−0.669131 + 0.743145i \(0.733333\pi\)
\(942\) 0 0
\(943\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) −0.658114 1.47815i −0.658114 1.47815i −0.866025 0.500000i \(-0.833333\pi\)
0.207912 0.978148i \(-0.433333\pi\)
\(948\) 0 0
\(949\) 0 0
\(950\) −0.614648 0.0646021i −0.614648 0.0646021i
\(951\) 0 0
\(952\) 0.413545 + 0.459289i 0.413545 + 0.459289i
\(953\) 0.587785 0.809017i 0.587785 0.809017i −0.406737 0.913545i \(-0.633333\pi\)
0.994522 + 0.104528i \(0.0333333\pi\)
\(954\) 0 0
\(955\) 0.500000 0.363271i 0.500000 0.363271i
\(956\) −0.379874 + 0.0399263i −0.379874 + 0.0399263i
\(957\) 0 0
\(958\) 0 0
\(959\) −0.459289 0.413545i −0.459289 0.413545i
\(960\) 0 0
\(961\) −0.669131 0.743145i −0.669131 0.743145i
\(962\) 0 0
\(963\) 0 0
\(964\) −0.309017 + 0.951057i −0.309017 + 0.951057i
\(965\) −0.207912 + 0.978148i −0.207912 + 0.978148i
\(966\) 0 0
\(967\) −1.47815 0.658114i −1.47815 0.658114i −0.500000 0.866025i \(-0.666667\pi\)
−0.978148 + 0.207912i \(0.933333\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0.564602 0.251377i 0.564602 0.251377i
\(971\) −0.587785 + 0.809017i −0.587785 + 0.809017i −0.994522 0.104528i \(-0.966667\pi\)
0.406737 + 0.913545i \(0.366667\pi\)
\(972\) 0 0
\(973\) −0.190983 + 0.587785i −0.190983 + 0.587785i
\(974\) −0.535233 0.309017i −0.535233 0.309017i
\(975\) 0 0
\(976\) 0 0
\(977\) −0.207912 0.978148i −0.207912 0.978148i −0.951057 0.309017i \(-0.900000\pi\)
0.743145 0.669131i \(-0.233333\pi\)
\(978\) 0 0
\(979\) −0.913545 + 0.406737i −0.913545 + 0.406737i
\(980\) 0.363271 + 0.118034i 0.363271 + 0.118034i
\(981\) 0 0
\(982\) 0 0
\(983\) 1.60917 0.169131i 1.60917 0.169131i 0.743145 0.669131i \(-0.233333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(984\) 0 0
\(985\) 0 0
\(986\) 0.207912 + 0.978148i 0.207912 + 0.978148i
\(987\) 0 0
\(988\) 0 0
\(989\) 0 0
\(990\) 0 0
\(991\) 0.190983 + 0.587785i 0.190983 + 0.587785i 1.00000 \(0\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0.564602 + 0.251377i 0.564602 + 0.251377i
\(995\) 0 0
\(996\) 0 0
\(997\) 0.564602 0.251377i 0.564602 0.251377i −0.104528 0.994522i \(-0.533333\pi\)
0.669131 + 0.743145i \(0.266667\pi\)
\(998\) −0.587785 0.190983i −0.587785 0.190983i
\(999\) 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 2025.1.y.a.1646.1 16
3.2 odd 2 inner 2025.1.y.a.1646.2 16
9.2 odd 6 675.1.o.a.296.1 8
9.4 even 3 inner 2025.1.y.a.296.1 16
9.5 odd 6 inner 2025.1.y.a.296.2 16
9.7 even 3 675.1.o.a.296.2 yes 8
25.6 even 5 inner 2025.1.y.a.431.2 16
45.2 even 12 3375.1.m.b.2024.2 8
45.7 odd 12 3375.1.m.a.2024.2 8
45.29 odd 6 3375.1.o.a.2726.2 8
45.34 even 6 3375.1.o.a.2726.1 8
45.38 even 12 3375.1.m.a.2024.1 8
45.43 odd 12 3375.1.m.b.2024.1 8
75.56 odd 10 inner 2025.1.y.a.431.1 16
225.31 even 15 inner 2025.1.y.a.1106.2 16
225.56 odd 30 675.1.o.a.431.2 yes 8
225.83 even 60 3375.1.m.a.1349.1 8
225.92 even 60 3375.1.m.b.1349.2 8
225.106 even 15 675.1.o.a.431.1 yes 8
225.119 odd 30 3375.1.o.a.26.1 8
225.131 odd 30 inner 2025.1.y.a.1106.1 16
225.133 odd 60 3375.1.m.b.1349.1 8
225.142 odd 60 3375.1.m.a.1349.2 8
225.169 even 30 3375.1.o.a.26.2 8
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
675.1.o.a.296.1 8 9.2 odd 6
675.1.o.a.296.2 yes 8 9.7 even 3
675.1.o.a.431.1 yes 8 225.106 even 15
675.1.o.a.431.2 yes 8 225.56 odd 30
2025.1.y.a.296.1 16 9.4 even 3 inner
2025.1.y.a.296.2 16 9.5 odd 6 inner
2025.1.y.a.431.1 16 75.56 odd 10 inner
2025.1.y.a.431.2 16 25.6 even 5 inner
2025.1.y.a.1106.1 16 225.131 odd 30 inner
2025.1.y.a.1106.2 16 225.31 even 15 inner
2025.1.y.a.1646.1 16 1.1 even 1 trivial
2025.1.y.a.1646.2 16 3.2 odd 2 inner
3375.1.m.a.1349.1 8 225.83 even 60
3375.1.m.a.1349.2 8 225.142 odd 60
3375.1.m.a.2024.1 8 45.38 even 12
3375.1.m.a.2024.2 8 45.7 odd 12
3375.1.m.b.1349.1 8 225.133 odd 60
3375.1.m.b.1349.2 8 225.92 even 60
3375.1.m.b.2024.1 8 45.43 odd 12
3375.1.m.b.2024.2 8 45.2 even 12
3375.1.o.a.26.1 8 225.119 odd 30
3375.1.o.a.26.2 8 225.169 even 30
3375.1.o.a.2726.1 8 45.34 even 6
3375.1.o.a.2726.2 8 45.29 odd 6