Properties

Label 3332.1.cc.c.135.2
Level $3332$
Weight $1$
Character 3332.135
Analytic conductor $1.663$
Analytic rank $0$
Dimension $24$
Projective image $D_{42}$
CM discriminant -68
Inner twists $8$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [3332,1,Mod(135,3332)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(3332, base_ring=CyclotomicField(42))
 
chi = DirichletCharacter(H, H._module([21, 32, 21]))
 
N = Newforms(chi, 1, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("3332.135");
 
S:= CuspForms(chi, 1);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 3332 = 2^{2} \cdot 7^{2} \cdot 17 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 3332.cc (of order \(42\), degree \(12\), 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: \(1.66288462209\)
Analytic rank: \(0\)
Dimension: \(24\)
Relative dimension: \(2\) over \(\Q(\zeta_{42})\)
Coefficient field: \(\Q(\zeta_{84})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{24} + x^{22} - x^{18} - x^{16} + x^{12} - x^{8} - x^{6} + x^{2} + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Projective image: \(D_{42}\)
Projective field: Galois closure of \(\mathbb{Q}[x]/(x^{42} - \cdots)\)

Embedding invariants

Embedding label 135.2
Root \(0.294755 - 0.955573i\) of defining polynomial
Character \(\chi\) \(=\) 3332.135
Dual form 3332.1.cc.c.543.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.826239 + 0.563320i) q^{2} +(0.997204 - 0.925270i) q^{3} +(0.365341 - 0.930874i) q^{4} +(-0.302705 + 1.32624i) q^{6} +(-0.974928 + 0.222521i) q^{7} +(0.222521 + 0.974928i) q^{8} +(0.0635609 - 0.848162i) q^{9} +O(q^{10})\) \(q+(-0.826239 + 0.563320i) q^{2} +(0.997204 - 0.925270i) q^{3} +(0.365341 - 0.930874i) q^{4} +(-0.302705 + 1.32624i) q^{6} +(-0.974928 + 0.222521i) q^{7} +(0.222521 + 0.974928i) q^{8} +(0.0635609 - 0.848162i) q^{9} +(0.0841939 + 1.12349i) q^{11} +(-0.496990 - 1.26631i) q^{12} +(1.48883 + 0.716983i) q^{13} +(0.680173 - 0.733052i) q^{14} +(-0.733052 - 0.680173i) q^{16} +(-0.988831 - 0.149042i) q^{17} +(0.425270 + 0.736589i) q^{18} +(-0.766310 + 1.12397i) q^{21} +(-0.702449 - 0.880843i) q^{22} +(-0.858075 + 0.129334i) q^{23} +(1.12397 + 0.766310i) q^{24} +(0.826239 + 0.563320i) q^{25} +(-1.63402 + 0.246289i) q^{26} +(0.126766 + 0.158960i) q^{27} +(-0.149042 + 0.988831i) q^{28} +(0.974928 + 1.68862i) q^{31} +(0.988831 + 0.149042i) q^{32} +(1.12349 + 1.04245i) q^{33} +(0.900969 - 0.433884i) q^{34} +(-0.766310 - 0.369035i) q^{36} +(2.14807 - 0.662592i) q^{39} -1.36035i q^{42} +(1.07659 + 0.332083i) q^{44} +(0.636119 - 0.590232i) q^{46} -1.36035 q^{48} +(0.900969 - 0.433884i) q^{49} -1.00000 q^{50} +(-1.12397 + 0.766310i) q^{51} +(1.21135 - 1.12397i) q^{52} +(0.698220 - 1.77904i) q^{53} +(-0.194285 - 0.0599289i) q^{54} +(-0.433884 - 0.900969i) q^{56} +(-1.75676 - 0.846011i) q^{62} +(0.126766 + 0.841040i) q^{63} +(-0.900969 + 0.433884i) q^{64} +(-1.51550 - 0.228425i) q^{66} +(-0.500000 + 0.866025i) q^{68} +(-0.736007 + 0.922924i) q^{69} +(0.367554 + 0.460898i) q^{71} +(0.841040 - 0.126766i) q^{72} +(1.34515 - 0.202749i) q^{75} +(-0.332083 - 1.07659i) q^{77} +(-1.40157 + 1.75751i) q^{78} +(-0.997204 + 1.72721i) q^{79} +(1.11453 + 0.167989i) q^{81} +(0.766310 + 1.12397i) q^{84} +(-1.07659 + 0.332083i) q^{88} +(0.109562 - 1.46200i) q^{89} +(-1.61105 - 0.367711i) q^{91} +(-0.193096 + 0.846011i) q^{92} +(2.53464 + 0.781831i) q^{93} +(1.12397 - 0.766310i) q^{96} +(-0.500000 + 0.866025i) q^{98} +0.958252 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 24 q - 2 q^{2} + 2 q^{4} + 4 q^{8} - 24 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 24 q - 2 q^{2} + 2 q^{4} + 4 q^{8} - 24 q^{9} + 10 q^{13} + 2 q^{16} + 2 q^{17} + 10 q^{18} + 6 q^{21} + 2 q^{25} - 2 q^{26} - 2 q^{32} + 8 q^{33} + 4 q^{34} + 6 q^{36} + 4 q^{49} - 24 q^{50} + 2 q^{52} - 2 q^{53} - 4 q^{64} - 22 q^{66} - 12 q^{68} - 14 q^{69} - 4 q^{72} - 6 q^{77} + 30 q^{81} - 6 q^{84} + 2 q^{89} - 12 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/3332\mathbb{Z}\right)^\times\).

\(n\) \(785\) \(885\) \(1667\)
\(\chi(n)\) \(-1\) \(e\left(\frac{16}{21}\right)\) \(-1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.826239 + 0.563320i −0.826239 + 0.563320i
\(3\) 0.997204 0.925270i 0.997204 0.925270i 1.00000i \(-0.5\pi\)
0.997204 + 0.0747301i \(0.0238095\pi\)
\(4\) 0.365341 0.930874i 0.365341 0.930874i
\(5\) 0 0 −0.955573 0.294755i \(-0.904762\pi\)
0.955573 + 0.294755i \(0.0952381\pi\)
\(6\) −0.302705 + 1.32624i −0.302705 + 1.32624i
\(7\) −0.974928 + 0.222521i −0.974928 + 0.222521i
\(8\) 0.222521 + 0.974928i 0.222521 + 0.974928i
\(9\) 0.0635609 0.848162i 0.0635609 0.848162i
\(10\) 0 0
\(11\) 0.0841939 + 1.12349i 0.0841939 + 1.12349i 0.866025 + 0.500000i \(0.166667\pi\)
−0.781831 + 0.623490i \(0.785714\pi\)
\(12\) −0.496990 1.26631i −0.496990 1.26631i
\(13\) 1.48883 + 0.716983i 1.48883 + 0.716983i 0.988831 0.149042i \(-0.0476190\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(14\) 0.680173 0.733052i 0.680173 0.733052i
\(15\) 0 0
\(16\) −0.733052 0.680173i −0.733052 0.680173i
\(17\) −0.988831 0.149042i −0.988831 0.149042i
\(18\) 0.425270 + 0.736589i 0.425270 + 0.736589i
\(19\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(20\) 0 0
\(21\) −0.766310 + 1.12397i −0.766310 + 1.12397i
\(22\) −0.702449 0.880843i −0.702449 0.880843i
\(23\) −0.858075 + 0.129334i −0.858075 + 0.129334i −0.563320 0.826239i \(-0.690476\pi\)
−0.294755 + 0.955573i \(0.595238\pi\)
\(24\) 1.12397 + 0.766310i 1.12397 + 0.766310i
\(25\) 0.826239 + 0.563320i 0.826239 + 0.563320i
\(26\) −1.63402 + 0.246289i −1.63402 + 0.246289i
\(27\) 0.126766 + 0.158960i 0.126766 + 0.158960i
\(28\) −0.149042 + 0.988831i −0.149042 + 0.988831i
\(29\) 0 0 0.623490 0.781831i \(-0.285714\pi\)
−0.623490 + 0.781831i \(0.714286\pi\)
\(30\) 0 0
\(31\) 0.974928 + 1.68862i 0.974928 + 1.68862i 0.680173 + 0.733052i \(0.261905\pi\)
0.294755 + 0.955573i \(0.404762\pi\)
\(32\) 0.988831 + 0.149042i 0.988831 + 0.149042i
\(33\) 1.12349 + 1.04245i 1.12349 + 1.04245i
\(34\) 0.900969 0.433884i 0.900969 0.433884i
\(35\) 0 0
\(36\) −0.766310 0.369035i −0.766310 0.369035i
\(37\) 0 0 −0.365341 0.930874i \(-0.619048\pi\)
0.365341 + 0.930874i \(0.380952\pi\)
\(38\) 0 0
\(39\) 2.14807 0.662592i 2.14807 0.662592i
\(40\) 0 0
\(41\) 0 0 −0.222521 0.974928i \(-0.571429\pi\)
0.222521 + 0.974928i \(0.428571\pi\)
\(42\) 1.36035i 1.36035i
\(43\) 0 0 0.222521 0.974928i \(-0.428571\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(44\) 1.07659 + 0.332083i 1.07659 + 0.332083i
\(45\) 0 0
\(46\) 0.636119 0.590232i 0.636119 0.590232i
\(47\) 0 0 0.826239 0.563320i \(-0.190476\pi\)
−0.826239 + 0.563320i \(0.809524\pi\)
\(48\) −1.36035 −1.36035
\(49\) 0.900969 0.433884i 0.900969 0.433884i
\(50\) −1.00000 −1.00000
\(51\) −1.12397 + 0.766310i −1.12397 + 0.766310i
\(52\) 1.21135 1.12397i 1.21135 1.12397i
\(53\) 0.698220 1.77904i 0.698220 1.77904i 0.0747301 0.997204i \(-0.476190\pi\)
0.623490 0.781831i \(-0.285714\pi\)
\(54\) −0.194285 0.0599289i −0.194285 0.0599289i
\(55\) 0 0
\(56\) −0.433884 0.900969i −0.433884 0.900969i
\(57\) 0 0
\(58\) 0 0
\(59\) 0 0 0.955573 0.294755i \(-0.0952381\pi\)
−0.955573 + 0.294755i \(0.904762\pi\)
\(60\) 0 0
\(61\) 0 0 −0.365341 0.930874i \(-0.619048\pi\)
0.365341 + 0.930874i \(0.380952\pi\)
\(62\) −1.75676 0.846011i −1.75676 0.846011i
\(63\) 0.126766 + 0.841040i 0.126766 + 0.841040i
\(64\) −0.900969 + 0.433884i −0.900969 + 0.433884i
\(65\) 0 0
\(66\) −1.51550 0.228425i −1.51550 0.228425i
\(67\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(68\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(69\) −0.736007 + 0.922924i −0.736007 + 0.922924i
\(70\) 0 0
\(71\) 0.367554 + 0.460898i 0.367554 + 0.460898i 0.930874 0.365341i \(-0.119048\pi\)
−0.563320 + 0.826239i \(0.690476\pi\)
\(72\) 0.841040 0.126766i 0.841040 0.126766i
\(73\) 0 0 −0.826239 0.563320i \(-0.809524\pi\)
0.826239 + 0.563320i \(0.190476\pi\)
\(74\) 0 0
\(75\) 1.34515 0.202749i 1.34515 0.202749i
\(76\) 0 0
\(77\) −0.332083 1.07659i −0.332083 1.07659i
\(78\) −1.40157 + 1.75751i −1.40157 + 1.75751i
\(79\) −0.997204 + 1.72721i −0.997204 + 1.72721i −0.433884 + 0.900969i \(0.642857\pi\)
−0.563320 + 0.826239i \(0.690476\pi\)
\(80\) 0 0
\(81\) 1.11453 + 0.167989i 1.11453 + 0.167989i
\(82\) 0 0
\(83\) 0 0 0.900969 0.433884i \(-0.142857\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(84\) 0.766310 + 1.12397i 0.766310 + 1.12397i
\(85\) 0 0
\(86\) 0 0
\(87\) 0 0
\(88\) −1.07659 + 0.332083i −1.07659 + 0.332083i
\(89\) 0.109562 1.46200i 0.109562 1.46200i −0.623490 0.781831i \(-0.714286\pi\)
0.733052 0.680173i \(-0.238095\pi\)
\(90\) 0 0
\(91\) −1.61105 0.367711i −1.61105 0.367711i
\(92\) −0.193096 + 0.846011i −0.193096 + 0.846011i
\(93\) 2.53464 + 0.781831i 2.53464 + 0.781831i
\(94\) 0 0
\(95\) 0 0
\(96\) 1.12397 0.766310i 1.12397 0.766310i
\(97\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(98\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(99\) 0.958252 0.958252
\(100\) 0.826239 0.563320i 0.826239 0.563320i
\(101\) −1.32091 + 1.22563i −1.32091 + 1.22563i −0.365341 + 0.930874i \(0.619048\pi\)
−0.955573 + 0.294755i \(0.904762\pi\)
\(102\) 0.496990 1.26631i 0.496990 1.26631i
\(103\) 0 0 −0.955573 0.294755i \(-0.904762\pi\)
0.955573 + 0.294755i \(0.0952381\pi\)
\(104\) −0.367711 + 1.61105i −0.367711 + 1.61105i
\(105\) 0 0
\(106\) 0.425270 + 1.86323i 0.425270 + 1.86323i
\(107\) 0.139129 1.85654i 0.139129 1.85654i −0.294755 0.955573i \(-0.595238\pi\)
0.433884 0.900969i \(-0.357143\pi\)
\(108\) 0.194285 0.0599289i 0.194285 0.0599289i
\(109\) 0 0 −0.0747301 0.997204i \(-0.523810\pi\)
0.0747301 + 0.997204i \(0.476190\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(113\) 0 0 0.900969 0.433884i \(-0.142857\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 0 0
\(117\) 0.702749 1.21720i 0.702749 1.21720i
\(118\) 0 0
\(119\) 0.997204 0.0747301i 0.997204 0.0747301i
\(120\) 0 0
\(121\) −0.266310 + 0.0401398i −0.266310 + 0.0401398i
\(122\) 0 0
\(123\) 0 0
\(124\) 1.92808 0.290611i 1.92808 0.290611i
\(125\) 0 0
\(126\) −0.578514 0.623490i −0.578514 0.623490i
\(127\) 0 0 0.623490 0.781831i \(-0.285714\pi\)
−0.623490 + 0.781831i \(0.714286\pi\)
\(128\) 0.500000 0.866025i 0.500000 0.866025i
\(129\) 0 0
\(130\) 0 0
\(131\) −0.636119 0.590232i −0.636119 0.590232i 0.294755 0.955573i \(-0.404762\pi\)
−0.930874 + 0.365341i \(0.880952\pi\)
\(132\) 1.38084 0.664979i 1.38084 0.664979i
\(133\) 0 0
\(134\) 0 0
\(135\) 0 0
\(136\) −0.0747301 0.997204i −0.0747301 0.997204i
\(137\) 1.40097 0.432142i 1.40097 0.432142i 0.500000 0.866025i \(-0.333333\pi\)
0.900969 + 0.433884i \(0.142857\pi\)
\(138\) 0.0882162 1.17716i 0.0882162 1.17716i
\(139\) −0.443797 1.94440i −0.443797 1.94440i −0.294755 0.955573i \(-0.595238\pi\)
−0.149042 0.988831i \(-0.547619\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) −0.563320 0.173761i −0.563320 0.173761i
\(143\) −0.680173 + 1.73305i −0.680173 + 1.73305i
\(144\) −0.623490 + 0.578514i −0.623490 + 0.578514i
\(145\) 0 0
\(146\) 0 0
\(147\) 0.496990 1.26631i 0.496990 1.26631i
\(148\) 0 0
\(149\) −1.21135 + 0.825886i −1.21135 + 0.825886i −0.988831 0.149042i \(-0.952381\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(150\) −0.997204 + 0.925270i −0.997204 + 0.925270i
\(151\) 0 0 0.365341 0.930874i \(-0.380952\pi\)
−0.365341 + 0.930874i \(0.619048\pi\)
\(152\) 0 0
\(153\) −0.189263 + 0.829215i −0.189263 + 0.829215i
\(154\) 0.880843 + 0.702449i 0.880843 + 0.702449i
\(155\) 0 0
\(156\) 0.167989 2.24165i 0.167989 2.24165i
\(157\) 0.142820 0.0440542i 0.142820 0.0440542i −0.222521 0.974928i \(-0.571429\pi\)
0.365341 + 0.930874i \(0.380952\pi\)
\(158\) −0.149042 1.98883i −0.149042 1.98883i
\(159\) −0.949820 2.42010i −0.949820 2.42010i
\(160\) 0 0
\(161\) 0.807782 0.317031i 0.807782 0.317031i
\(162\) −1.01550 + 0.489040i −1.01550 + 0.489040i
\(163\) 0 0 0.680173 0.733052i \(-0.261905\pi\)
−0.680173 + 0.733052i \(0.738095\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) −0.185853 + 0.233052i −0.185853 + 0.233052i −0.866025 0.500000i \(-0.833333\pi\)
0.680173 + 0.733052i \(0.261905\pi\)
\(168\) −1.26631 0.496990i −1.26631 0.496990i
\(169\) 1.07906 + 1.35310i 1.07906 + 1.35310i
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) 0 0 0.988831 0.149042i \(-0.0476190\pi\)
−0.988831 + 0.149042i \(0.952381\pi\)
\(174\) 0 0
\(175\) −0.930874 0.365341i −0.930874 0.365341i
\(176\) 0.702449 0.880843i 0.702449 0.880843i
\(177\) 0 0
\(178\) 0.733052 + 1.26968i 0.733052 + 1.26968i
\(179\) 0 0 −0.988831 0.149042i \(-0.952381\pi\)
0.988831 + 0.149042i \(0.0476190\pi\)
\(180\) 0 0
\(181\) 0 0 0.900969 0.433884i \(-0.142857\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(182\) 1.53825 0.603718i 1.53825 0.603718i
\(183\) 0 0
\(184\) −0.317031 0.807782i −0.317031 0.807782i
\(185\) 0 0
\(186\) −2.53464 + 0.781831i −2.53464 + 0.781831i
\(187\) 0.0841939 1.12349i 0.0841939 1.12349i
\(188\) 0 0
\(189\) −0.158960 0.126766i −0.158960 0.126766i
\(190\) 0 0
\(191\) 0 0 −0.955573 0.294755i \(-0.904762\pi\)
0.955573 + 0.294755i \(0.0952381\pi\)
\(192\) −0.496990 + 1.26631i −0.496990 + 1.26631i
\(193\) 0 0 0.733052 0.680173i \(-0.238095\pi\)
−0.733052 + 0.680173i \(0.761905\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) −0.0747301 0.997204i −0.0747301 0.997204i
\(197\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(198\) −0.791745 + 0.539803i −0.791745 + 0.539803i
\(199\) 0.432142 0.400969i 0.432142 0.400969i −0.433884 0.900969i \(-0.642857\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(200\) −0.365341 + 0.930874i −0.365341 + 0.930874i
\(201\) 0 0
\(202\) 0.400969 1.75676i 0.400969 1.75676i
\(203\) 0 0
\(204\) 0.302705 + 1.32624i 0.302705 + 1.32624i
\(205\) 0 0
\(206\) 0 0
\(207\) 0.0551561 + 0.736007i 0.0551561 + 0.736007i
\(208\) −0.603718 1.53825i −0.603718 1.53825i
\(209\) 0 0
\(210\) 0 0
\(211\) 1.40881 0.678448i 1.40881 0.678448i 0.433884 0.900969i \(-0.357143\pi\)
0.974928 + 0.222521i \(0.0714286\pi\)
\(212\) −1.40097 1.29991i −1.40097 1.29991i
\(213\) 0.792981 + 0.119523i 0.792981 + 0.119523i
\(214\) 0.930874 + 1.61232i 0.930874 + 1.61232i
\(215\) 0 0
\(216\) −0.126766 + 0.158960i −0.126766 + 0.158960i
\(217\) −1.32624 1.42935i −1.32624 1.42935i
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) −1.36534 0.930874i −1.36534 0.930874i
\(222\) 0 0
\(223\) 0 0 −0.623490 0.781831i \(-0.714286\pi\)
0.623490 + 0.781831i \(0.285714\pi\)
\(224\) −0.997204 + 0.0747301i −0.997204 + 0.0747301i
\(225\) 0.530303 0.664979i 0.530303 0.664979i
\(226\) 0 0
\(227\) 0.294755 + 0.510531i 0.294755 + 0.510531i 0.974928 0.222521i \(-0.0714286\pi\)
−0.680173 + 0.733052i \(0.738095\pi\)
\(228\) 0 0
\(229\) 0.914101 + 0.848162i 0.914101 + 0.848162i 0.988831 0.149042i \(-0.0476190\pi\)
−0.0747301 + 0.997204i \(0.523810\pi\)
\(230\) 0 0
\(231\) −1.32729 0.766310i −1.32729 0.766310i
\(232\) 0 0
\(233\) 0 0 −0.365341 0.930874i \(-0.619048\pi\)
0.365341 + 0.930874i \(0.380952\pi\)
\(234\) 0.105033 + 1.40157i 0.105033 + 1.40157i
\(235\) 0 0
\(236\) 0 0
\(237\) 0.603718 + 2.64506i 0.603718 + 2.64506i
\(238\) −0.781831 + 0.623490i −0.781831 + 0.623490i
\(239\) 0 0 0.222521 0.974928i \(-0.428571\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(240\) 0 0
\(241\) 0 0 0.365341 0.930874i \(-0.380952\pi\)
−0.365341 + 0.930874i \(0.619048\pi\)
\(242\) 0.197424 0.183183i 0.197424 0.183183i
\(243\) 1.09886 0.749192i 1.09886 0.749192i
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) 0 0
\(248\) −1.42935 + 1.32624i −1.42935 + 1.32624i
\(249\) 0 0
\(250\) 0 0
\(251\) 0 0 0.222521 0.974928i \(-0.428571\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(252\) 0.829215 + 0.189263i 0.829215 + 0.189263i
\(253\) −0.217550 0.953150i −0.217550 0.953150i
\(254\) 0 0
\(255\) 0 0
\(256\) 0.0747301 + 0.997204i 0.0747301 + 0.997204i
\(257\) 0.365341 + 0.930874i 0.365341 + 0.930874i 0.988831 + 0.149042i \(0.0476190\pi\)
−0.623490 + 0.781831i \(0.714286\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 0 0
\(261\) 0 0
\(262\) 0.858075 + 0.129334i 0.858075 + 0.129334i
\(263\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(264\) −0.766310 + 1.32729i −0.766310 + 1.32729i
\(265\) 0 0
\(266\) 0 0
\(267\) −1.24349 1.55929i −1.24349 1.55929i
\(268\) 0 0
\(269\) 0 0 −0.826239 0.563320i \(-0.809524\pi\)
0.826239 + 0.563320i \(0.190476\pi\)
\(270\) 0 0
\(271\) 0 0 0.988831 0.149042i \(-0.0476190\pi\)
−0.988831 + 0.149042i \(0.952381\pi\)
\(272\) 0.623490 + 0.781831i 0.623490 + 0.781831i
\(273\) −1.94677 + 1.12397i −1.94677 + 1.12397i
\(274\) −0.914101 + 1.14625i −0.914101 + 1.14625i
\(275\) −0.563320 + 0.975699i −0.563320 + 0.975699i
\(276\) 0.590232 + 1.02231i 0.590232 + 1.02231i
\(277\) 0 0 −0.988831 0.149042i \(-0.952381\pi\)
0.988831 + 0.149042i \(0.0476190\pi\)
\(278\) 1.46200 + 1.35654i 1.46200 + 1.35654i
\(279\) 1.49419 0.719566i 1.49419 0.719566i
\(280\) 0 0
\(281\) 0.900969 + 0.433884i 0.900969 + 0.433884i 0.826239 0.563320i \(-0.190476\pi\)
0.0747301 + 0.997204i \(0.476190\pi\)
\(282\) 0 0
\(283\) −0.0841939 1.12349i −0.0841939 1.12349i −0.866025 0.500000i \(-0.833333\pi\)
0.781831 0.623490i \(-0.214286\pi\)
\(284\) 0.563320 0.173761i 0.563320 0.173761i
\(285\) 0 0
\(286\) −0.414278 1.81507i −0.414278 1.81507i
\(287\) 0 0
\(288\) 0.189263 0.829215i 0.189263 0.829215i
\(289\) 0.955573 + 0.294755i 0.955573 + 0.294755i
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) 0.149460 0.149460 0.0747301 0.997204i \(-0.476190\pi\)
0.0747301 + 0.997204i \(0.476190\pi\)
\(294\) 0.302705 + 1.32624i 0.302705 + 1.32624i
\(295\) 0 0
\(296\) 0 0
\(297\) −0.167917 + 0.155804i −0.167917 + 0.155804i
\(298\) 0.535628 1.36476i 0.535628 1.36476i
\(299\) −1.37026 0.422669i −1.37026 0.422669i
\(300\) 0.302705 1.32624i 0.302705 1.32624i
\(301\) 0 0
\(302\) 0 0
\(303\) −0.183183 + 2.44440i −0.183183 + 2.44440i
\(304\) 0 0
\(305\) 0 0
\(306\) −0.310737 0.791745i −0.310737 0.791745i
\(307\) 0 0 −0.900969 0.433884i \(-0.857143\pi\)
0.900969 + 0.433884i \(0.142857\pi\)
\(308\) −1.12349 0.0841939i −1.12349 0.0841939i
\(309\) 0 0
\(310\) 0 0
\(311\) −1.71271 0.258149i −1.71271 0.258149i −0.781831 0.623490i \(-0.785714\pi\)
−0.930874 + 0.365341i \(0.880952\pi\)
\(312\) 1.12397 + 1.94677i 1.12397 + 1.94677i
\(313\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(314\) −0.0931869 + 0.116853i −0.0931869 + 0.116853i
\(315\) 0 0
\(316\) 1.24349 + 1.55929i 1.24349 + 1.55929i
\(317\) 0 0 0.988831 0.149042i \(-0.0476190\pi\)
−0.988831 + 0.149042i \(0.952381\pi\)
\(318\) 2.14807 + 1.46453i 2.14807 + 1.46453i
\(319\) 0 0
\(320\) 0 0
\(321\) −1.57906 1.98008i −1.57906 1.98008i
\(322\) −0.488831 + 0.716983i −0.488831 + 0.716983i
\(323\) 0 0
\(324\) 0.563561 0.976116i 0.563561 0.976116i
\(325\) 0.826239 + 1.43109i 0.826239 + 1.43109i
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) 0 0
\(330\) 0 0
\(331\) 0 0 −0.365341 0.930874i \(-0.619048\pi\)
0.365341 + 0.930874i \(0.380952\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0.0222759 0.297251i 0.0222759 0.297251i
\(335\) 0 0
\(336\) 1.32624 0.302705i 1.32624 0.302705i
\(337\) 0 0 0.222521 0.974928i \(-0.428571\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(338\) −1.65379 0.510127i −1.65379 0.510127i
\(339\) 0 0
\(340\) 0 0
\(341\) −1.81507 + 1.23749i −1.81507 + 1.23749i
\(342\) 0 0
\(343\) −0.781831 + 0.623490i −0.781831 + 0.623490i
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) −0.571270 + 1.45557i −0.571270 + 1.45557i 0.294755 + 0.955573i \(0.404762\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(348\) 0 0
\(349\) −0.277479 + 1.21572i −0.277479 + 1.21572i 0.623490 + 0.781831i \(0.285714\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(350\) 0.974928 0.222521i 0.974928 0.222521i
\(351\) 0.0747620 + 0.327554i 0.0747620 + 0.327554i
\(352\) −0.0841939 + 1.12349i −0.0841939 + 1.12349i
\(353\) −0.955573 + 0.294755i −0.955573 + 0.294755i −0.733052 0.680173i \(-0.761905\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) −1.32091 0.636119i −1.32091 0.636119i
\(357\) 0.925270 0.997204i 0.925270 0.997204i
\(358\) 0 0
\(359\) 0 0 −0.733052 0.680173i \(-0.761905\pi\)
0.733052 + 0.680173i \(0.238095\pi\)
\(360\) 0 0
\(361\) −0.500000 0.866025i −0.500000 0.866025i
\(362\) 0 0
\(363\) −0.228425 + 0.286436i −0.228425 + 0.286436i
\(364\) −0.930874 + 1.36534i −0.930874 + 1.36534i
\(365\) 0 0
\(366\) 0 0
\(367\) −1.53825 1.04876i −1.53825 1.04876i −0.974928 0.222521i \(-0.928571\pi\)
−0.563320 0.826239i \(-0.690476\pi\)
\(368\) 0.716983 + 0.488831i 0.716983 + 0.488831i
\(369\) 0 0
\(370\) 0 0
\(371\) −0.284841 + 1.88980i −0.284841 + 1.88980i
\(372\) 1.65379 2.07379i 1.65379 2.07379i
\(373\) 0.826239 1.43109i 0.826239 1.43109i −0.0747301 0.997204i \(-0.523810\pi\)
0.900969 0.433884i \(-0.142857\pi\)
\(374\) 0.563320 + 0.975699i 0.563320 + 0.975699i
\(375\) 0 0
\(376\) 0 0
\(377\) 0 0
\(378\) 0.202749 + 0.0151939i 0.202749 + 0.0151939i
\(379\) −1.56052 0.751509i −1.56052 0.751509i −0.563320 0.826239i \(-0.690476\pi\)
−0.997204 + 0.0747301i \(0.976190\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 0 0 0.0747301 0.997204i \(-0.476190\pi\)
−0.0747301 + 0.997204i \(0.523810\pi\)
\(384\) −0.302705 1.32624i −0.302705 1.32624i
\(385\) 0 0
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) −1.44973 + 1.34515i −1.44973 + 1.34515i −0.623490 + 0.781831i \(0.714286\pi\)
−0.826239 + 0.563320i \(0.809524\pi\)
\(390\) 0 0
\(391\) 0.867767 0.867767
\(392\) 0.623490 + 0.781831i 0.623490 + 0.781831i
\(393\) −1.18046 −1.18046
\(394\) 0 0
\(395\) 0 0
\(396\) 0.350089 0.892012i 0.350089 0.892012i
\(397\) 0 0 −0.955573 0.294755i \(-0.904762\pi\)
0.955573 + 0.294755i \(0.0952381\pi\)
\(398\) −0.131178 + 0.574730i −0.131178 + 0.574730i
\(399\) 0 0
\(400\) −0.222521 0.974928i −0.222521 0.974928i
\(401\) 0 0 0.0747301 0.997204i \(-0.476190\pi\)
−0.0747301 + 0.997204i \(0.523810\pi\)
\(402\) 0 0
\(403\) 0.240787 + 3.21308i 0.240787 + 3.21308i
\(404\) 0.658322 + 1.67738i 0.658322 + 1.67738i
\(405\) 0 0
\(406\) 0 0
\(407\) 0 0
\(408\) −0.997204 0.925270i −0.997204 0.925270i
\(409\) −1.88980 0.284841i −1.88980 0.284841i −0.900969 0.433884i \(-0.857143\pi\)
−0.988831 + 0.149042i \(0.952381\pi\)
\(410\) 0 0
\(411\) 0.997204 1.72721i 0.997204 1.72721i
\(412\) 0 0
\(413\) 0 0
\(414\) −0.460180 0.577047i −0.460180 0.577047i
\(415\) 0 0
\(416\) 1.36534 + 0.930874i 1.36534 + 0.930874i
\(417\) −2.24165 1.52833i −2.24165 1.52833i
\(418\) 0 0
\(419\) 1.24349 + 1.55929i 1.24349 + 1.55929i 0.680173 + 0.733052i \(0.261905\pi\)
0.563320 + 0.826239i \(0.309524\pi\)
\(420\) 0 0
\(421\) 0.277479 0.347948i 0.277479 0.347948i −0.623490 0.781831i \(-0.714286\pi\)
0.900969 + 0.433884i \(0.142857\pi\)
\(422\) −0.781831 + 1.35417i −0.781831 + 1.35417i
\(423\) 0 0
\(424\) 1.88980 + 0.284841i 1.88980 + 0.284841i
\(425\) −0.733052 0.680173i −0.733052 0.680173i
\(426\) −0.722521 + 0.347948i −0.722521 + 0.347948i
\(427\) 0 0
\(428\) −1.67738 0.807782i −1.67738 0.807782i
\(429\) 0.925270 + 2.35755i 0.925270 + 2.35755i
\(430\) 0 0
\(431\) 1.65510 0.510531i 1.65510 0.510531i 0.680173 0.733052i \(-0.261905\pi\)
0.974928 + 0.222521i \(0.0714286\pi\)
\(432\) 0.0151939 0.202749i 0.0151939 0.202749i
\(433\) −0.400969 1.75676i −0.400969 1.75676i −0.623490 0.781831i \(-0.714286\pi\)
0.222521 0.974928i \(-0.428571\pi\)
\(434\) 1.90097 + 0.433884i 1.90097 + 0.433884i
\(435\) 0 0
\(436\) 0 0
\(437\) 0 0
\(438\) 0 0
\(439\) −1.64786 + 1.12349i −1.64786 + 1.12349i −0.781831 + 0.623490i \(0.785714\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(440\) 0 0
\(441\) −0.310737 0.791745i −0.310737 0.791745i
\(442\) 1.65248 1.65248
\(443\) 0 0 0.826239 0.563320i \(-0.190476\pi\)
−0.826239 + 0.563320i \(0.809524\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 0 0
\(447\) −0.443797 + 1.94440i −0.443797 + 1.94440i
\(448\) 0.781831 0.623490i 0.781831 0.623490i
\(449\) 0 0 −0.222521 0.974928i \(-0.571429\pi\)
0.222521 + 0.974928i \(0.428571\pi\)
\(450\) −0.0635609 + 0.848162i −0.0635609 + 0.848162i
\(451\) 0 0
\(452\) 0 0
\(453\) 0 0
\(454\) −0.531130 0.255779i −0.531130 0.255779i
\(455\) 0 0
\(456\) 0 0
\(457\) −1.32091 1.22563i −1.32091 1.22563i −0.955573 0.294755i \(-0.904762\pi\)
−0.365341 0.930874i \(-0.619048\pi\)
\(458\) −1.23305 0.185853i −1.23305 0.185853i
\(459\) −0.101659 0.176078i −0.101659 0.176078i
\(460\) 0 0
\(461\) 1.19158 1.49419i 1.19158 1.49419i 0.365341 0.930874i \(-0.380952\pi\)
0.826239 0.563320i \(-0.190476\pi\)
\(462\) 1.52833 0.114533i 1.52833 0.114533i
\(463\) 0 0 −0.623490 0.781831i \(-0.714286\pi\)
0.623490 + 0.781831i \(0.285714\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 0 0 0.988831 0.149042i \(-0.0476190\pi\)
−0.988831 + 0.149042i \(0.952381\pi\)
\(468\) −0.876314 1.09886i −0.876314 1.09886i
\(469\) 0 0
\(470\) 0 0
\(471\) 0.101659 0.176078i 0.101659 0.176078i
\(472\) 0 0
\(473\) 0 0
\(474\) −1.98883 1.84537i −1.98883 1.84537i
\(475\) 0 0
\(476\) 0.294755 0.955573i 0.294755 0.955573i
\(477\) −1.46453 0.705280i −1.46453 0.705280i
\(478\) 0 0
\(479\) −0.0648483 0.865341i −0.0648483 0.865341i −0.930874 0.365341i \(-0.880952\pi\)
0.866025 0.500000i \(-0.166667\pi\)
\(480\) 0 0
\(481\) 0 0
\(482\) 0 0
\(483\) 0.512184 1.06356i 0.512184 1.06356i
\(484\) −0.0599289 + 0.262566i −0.0599289 + 0.262566i
\(485\) 0 0
\(486\) −0.485888 + 1.23802i −0.485888 + 1.23802i
\(487\) 1.26968 1.17809i 1.26968 1.17809i 0.294755 0.955573i \(-0.404762\pi\)
0.974928 0.222521i \(-0.0714286\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(492\) 0 0
\(493\) 0 0
\(494\) 0 0
\(495\) 0 0
\(496\) 0.433884 1.90097i 0.433884 1.90097i
\(497\) −0.460898 0.367554i −0.460898 0.367554i
\(498\) 0 0
\(499\) −0.149042 + 1.98883i −0.149042 + 1.98883i 1.00000i \(0.5\pi\)
−0.149042 + 0.988831i \(0.547619\pi\)
\(500\) 0 0
\(501\) 0.0303029 + 0.404364i 0.0303029 + 0.404364i
\(502\) 0 0
\(503\) −1.67738 0.807782i −1.67738 0.807782i −0.997204 0.0747301i \(-0.976190\pi\)
−0.680173 0.733052i \(-0.738095\pi\)
\(504\) −0.791745 + 0.310737i −0.791745 + 0.310737i
\(505\) 0 0
\(506\) 0.716677 + 0.664979i 0.716677 + 0.664979i
\(507\) 2.32803 + 0.350894i 2.32803 + 0.350894i
\(508\) 0 0
\(509\) 0.900969 1.56052i 0.900969 1.56052i 0.0747301 0.997204i \(-0.476190\pi\)
0.826239 0.563320i \(-0.190476\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) −0.623490 0.781831i −0.623490 0.781831i
\(513\) 0 0
\(514\) −0.826239 0.563320i −0.826239 0.563320i
\(515\) 0 0
\(516\) 0 0
\(517\) 0 0
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(522\) 0 0
\(523\) 0 0 −0.733052 0.680173i \(-0.761905\pi\)
0.733052 + 0.680173i \(0.238095\pi\)
\(524\) −0.781831 + 0.376510i −0.781831 + 0.376510i
\(525\) −1.26631 + 0.496990i −1.26631 + 0.496990i
\(526\) 0 0
\(527\) −0.712362 1.81507i −0.712362 1.81507i
\(528\) −0.114533 1.52833i −0.114533 1.52833i
\(529\) −0.236007 + 0.0727985i −0.236007 + 0.0727985i
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) 0 0
\(534\) 1.90580 + 0.587862i 1.90580 + 0.587862i
\(535\) 0 0
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) 0.563320 + 0.975699i 0.563320 + 0.975699i
\(540\) 0 0
\(541\) 0 0 0.826239 0.563320i \(-0.190476\pi\)
−0.826239 + 0.563320i \(0.809524\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) −0.955573 0.294755i −0.955573 0.294755i
\(545\) 0 0
\(546\) 0.975345 2.02532i 0.975345 2.02532i
\(547\) 0.0663300 + 0.290611i 0.0663300 + 0.290611i 0.997204 0.0747301i \(-0.0238095\pi\)
−0.930874 + 0.365341i \(0.880952\pi\)
\(548\) 0.109562 1.46200i 0.109562 1.46200i
\(549\) 0 0
\(550\) −0.0841939 1.12349i −0.0841939 1.12349i
\(551\) 0 0
\(552\) −1.06356 0.512184i −1.06356 0.512184i
\(553\) 0.587862 1.90580i 0.587862 1.90580i
\(554\) 0 0
\(555\) 0 0
\(556\) −1.97213 0.297251i −1.97213 0.297251i
\(557\) 0.955573 + 1.65510i 0.955573 + 1.65510i 0.733052 + 0.680173i \(0.238095\pi\)
0.222521 + 0.974928i \(0.428571\pi\)
\(558\) −0.829215 + 1.43624i −0.829215 + 1.43624i
\(559\) 0 0
\(560\) 0 0
\(561\) −0.955573 1.19825i −0.955573 1.19825i
\(562\) −0.988831 + 0.149042i −0.988831 + 0.149042i
\(563\) 0 0 −0.826239 0.563320i \(-0.809524\pi\)
0.826239 + 0.563320i \(0.190476\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 0.702449 + 0.880843i 0.702449 + 0.880843i
\(567\) −1.12397 + 0.0842299i −1.12397 + 0.0842299i
\(568\) −0.367554 + 0.460898i −0.367554 + 0.460898i
\(569\) −0.826239 + 1.43109i −0.826239 + 1.43109i 0.0747301 + 0.997204i \(0.476190\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(570\) 0 0
\(571\) 1.92808 + 0.290611i 1.92808 + 0.290611i 0.997204 0.0747301i \(-0.0238095\pi\)
0.930874 + 0.365341i \(0.119048\pi\)
\(572\) 1.36476 + 1.26631i 1.36476 + 1.26631i
\(573\) 0 0
\(574\) 0 0
\(575\) −0.781831 0.376510i −0.781831 0.376510i
\(576\) 0.310737 + 0.791745i 0.310737 + 0.791745i
\(577\) −0.0546039 0.728639i −0.0546039 0.728639i −0.955573 0.294755i \(-0.904762\pi\)
0.900969 0.433884i \(-0.142857\pi\)
\(578\) −0.955573 + 0.294755i −0.955573 + 0.294755i
\(579\) 0 0
\(580\) 0 0
\(581\) 0 0
\(582\) 0 0
\(583\) 2.05751 + 0.634659i 2.05751 + 0.634659i
\(584\) 0 0
\(585\) 0 0
\(586\) −0.123490 + 0.0841939i −0.123490 + 0.0841939i
\(587\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(588\) −0.997204 0.925270i −0.997204 0.925270i
\(589\) 0 0
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) 0.698220 + 0.215372i 0.698220 + 0.215372i 0.623490 0.781831i \(-0.285714\pi\)
0.0747301 + 0.997204i \(0.476190\pi\)
\(594\) 0.0509719 0.223322i 0.0509719 0.223322i
\(595\) 0 0
\(596\) 0.326239 + 1.42935i 0.326239 + 1.42935i
\(597\) 0.0599289 0.799695i 0.0599289 0.799695i
\(598\) 1.37026 0.422669i 1.37026 0.422669i
\(599\) 0 0 −0.0747301 0.997204i \(-0.523810\pi\)
0.0747301 + 0.997204i \(0.476190\pi\)
\(600\) 0.496990 + 1.26631i 0.496990 + 1.26631i
\(601\) 0 0 −0.900969 0.433884i \(-0.857143\pi\)
0.900969 + 0.433884i \(0.142857\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) 0 0
\(606\) −1.22563 2.12285i −1.22563 2.12285i
\(607\) 0.866025 1.50000i 0.866025 1.50000i 1.00000i \(-0.5\pi\)
0.866025 0.500000i \(-0.166667\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 0 0
\(612\) 0.702749 + 0.479126i 0.702749 + 0.479126i
\(613\) −1.63402 1.11406i −1.63402 1.11406i −0.900969 0.433884i \(-0.857143\pi\)
−0.733052 0.680173i \(-0.761905\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0.975699 0.563320i 0.975699 0.563320i
\(617\) 0 0 0.623490 0.781831i \(-0.285714\pi\)
−0.623490 + 0.781831i \(0.714286\pi\)
\(618\) 0 0
\(619\) −0.866025 1.50000i −0.866025 1.50000i −0.866025 0.500000i \(-0.833333\pi\)
1.00000i \(-0.5\pi\)
\(620\) 0 0
\(621\) −0.129334 0.120004i −0.129334 0.120004i
\(622\) 1.56052 0.751509i 1.56052 0.751509i
\(623\) 0.218511 + 1.44973i 0.218511 + 1.44973i
\(624\) −2.02532 0.975345i −2.02532 0.975345i
\(625\) 0.365341 + 0.930874i 0.365341 + 0.930874i
\(626\) 0 0
\(627\) 0 0
\(628\) 0.0111692 0.149042i 0.0111692 0.149042i
\(629\) 0 0
\(630\) 0 0
\(631\) 0 0 0.222521 0.974928i \(-0.428571\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(632\) −1.90580 0.587862i −1.90580 0.587862i
\(633\) 0.777125 1.98008i 0.777125 1.98008i
\(634\) 0 0
\(635\) 0 0
\(636\) −2.59982 −2.59982
\(637\) 1.65248 1.65248
\(638\) 0 0
\(639\) 0.414278 0.282450i 0.414278 0.282450i
\(640\) 0 0
\(641\) 0 0 0.365341 0.930874i \(-0.380952\pi\)
−0.365341 + 0.930874i \(0.619048\pi\)
\(642\) 2.42010 + 0.746503i 2.42010 + 0.746503i
\(643\) 0.0663300 0.290611i 0.0663300 0.290611i −0.930874 0.365341i \(-0.880952\pi\)
0.997204 + 0.0747301i \(0.0238095\pi\)
\(644\) 0.867767i 0.867767i
\(645\) 0 0
\(646\) 0 0
\(647\) 0 0 0.955573 0.294755i \(-0.0952381\pi\)
−0.955573 + 0.294755i \(0.904762\pi\)
\(648\) 0.0842299 + 1.12397i 0.0842299 + 1.12397i
\(649\) 0 0
\(650\) −1.48883 0.716983i −1.48883 0.716983i
\(651\) −2.64506 0.198220i −2.64506 0.198220i
\(652\) 0 0
\(653\) 0 0 −0.733052 0.680173i \(-0.761905\pi\)
0.733052 + 0.680173i \(0.238095\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) 0 0 −0.623490 0.781831i \(-0.714286\pi\)
0.623490 + 0.781831i \(0.285714\pi\)
\(660\) 0 0
\(661\) −0.367711 0.250701i −0.367711 0.250701i 0.365341 0.930874i \(-0.380952\pi\)
−0.733052 + 0.680173i \(0.761905\pi\)
\(662\) 0 0
\(663\) −2.22283 + 0.335038i −2.22283 + 0.335038i
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) 0 0
\(668\) 0.149042 + 0.258149i 0.149042 + 0.258149i
\(669\) 0 0
\(670\) 0 0
\(671\) 0 0
\(672\) −0.925270 + 0.997204i −0.925270 + 0.997204i
\(673\) 0 0 −0.900969 0.433884i \(-0.857143\pi\)
0.900969 + 0.433884i \(0.142857\pi\)
\(674\) 0 0
\(675\) 0.0151939 + 0.202749i 0.0151939 + 0.202749i
\(676\) 1.65379 0.510127i 1.65379 0.510127i
\(677\) 0 0 0.0747301 0.997204i \(-0.476190\pi\)
−0.0747301 + 0.997204i \(0.523810\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 0 0
\(681\) 0.766310 + 0.236375i 0.766310 + 0.236375i
\(682\) 0.802576 2.04493i 0.802576 2.04493i
\(683\) 0.432142 0.400969i 0.432142 0.400969i −0.433884 0.900969i \(-0.642857\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 0.294755 0.955573i 0.294755 0.955573i
\(687\) 1.69632 1.69632
\(688\) 0 0
\(689\) 2.31507 2.14807i 2.31507 2.14807i
\(690\) 0 0
\(691\) 1.86323 + 0.574730i 1.86323 + 0.574730i 0.997204 + 0.0747301i \(0.0238095\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(692\) 0 0
\(693\) −0.934227 + 0.213231i −0.934227 + 0.213231i
\(694\) −0.347948 1.52446i −0.347948 1.52446i
\(695\) 0 0
\(696\) 0 0
\(697\) 0 0
\(698\) −0.455573 1.16078i −0.455573 1.16078i
\(699\) 0 0
\(700\) −0.680173 + 0.733052i −0.680173 + 0.733052i
\(701\) 1.72188 0.829215i 1.72188 0.829215i 0.733052 0.680173i \(-0.238095\pi\)
0.988831 0.149042i \(-0.0476190\pi\)
\(702\) −0.246289 0.228523i −0.246289 0.228523i
\(703\) 0 0
\(704\) −0.563320 0.975699i −0.563320 0.975699i
\(705\) 0 0
\(706\) 0.623490 0.781831i 0.623490 0.781831i
\(707\) 1.01507 1.48883i 1.01507 1.48883i
\(708\) 0 0
\(709\) 0 0 0.988831 0.149042i \(-0.0476190\pi\)
−0.988831 + 0.149042i \(0.952381\pi\)
\(710\) 0 0
\(711\) 1.40157 + 0.955573i 1.40157 + 0.955573i
\(712\) 1.44973 0.218511i 1.44973 0.218511i
\(713\) −1.05496 1.32288i −1.05496 1.32288i
\(714\) −0.202749 + 1.34515i −0.202749 + 1.34515i
\(715\) 0 0
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) −0.825886 0.766310i −0.825886 0.766310i 0.149042 0.988831i \(-0.452381\pi\)
−0.974928 + 0.222521i \(0.928571\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) 0.900969 + 0.433884i 0.900969 + 0.433884i
\(723\) 0 0
\(724\) 0 0
\(725\) 0 0
\(726\) 0.0273785 0.365341i 0.0273785 0.365341i
\(727\) 0 0 −0.222521 0.974928i \(-0.571429\pi\)
0.222521 + 0.974928i \(0.428571\pi\)
\(728\) 1.65248i 1.65248i
\(729\) 0.151777 0.664979i 0.151777 0.664979i
\(730\) 0 0
\(731\) 0 0
\(732\) 0 0
\(733\) −0.826239 + 0.563320i −0.826239 + 0.563320i −0.900969 0.433884i \(-0.857143\pi\)
0.0747301 + 0.997204i \(0.476190\pi\)
\(734\) 1.86175 1.86175
\(735\) 0 0
\(736\) −0.867767 −0.867767
\(737\) 0 0
\(738\) 0 0
\(739\) 0 0 0.365341 0.930874i \(-0.380952\pi\)
−0.365341 + 0.930874i \(0.619048\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) −0.829215 1.72188i −0.829215 1.72188i
\(743\) −0.302705 1.32624i −0.302705 1.32624i −0.866025 0.500000i \(-0.833333\pi\)
0.563320 0.826239i \(-0.309524\pi\)
\(744\) −0.198220 + 2.64506i −0.198220 + 2.64506i
\(745\) 0 0
\(746\) 0.123490 + 1.64786i 0.123490 + 1.64786i
\(747\) 0 0
\(748\) −1.01507 0.488831i −1.01507 0.488831i
\(749\) 0.277479 + 1.84095i 0.277479 + 1.84095i
\(750\) 0 0
\(751\) 1.46200 + 1.35654i 1.46200 + 1.35654i 0.781831 + 0.623490i \(0.214286\pi\)
0.680173 + 0.733052i \(0.261905\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 0 0
\(756\) −0.176078 + 0.101659i −0.176078 + 0.101659i
\(757\) 0.623490 + 0.781831i 0.623490 + 0.781831i 0.988831 0.149042i \(-0.0476190\pi\)
−0.365341 + 0.930874i \(0.619048\pi\)
\(758\) 1.71271 0.258149i 1.71271 0.258149i
\(759\) −1.09886 0.749192i −1.09886 0.749192i
\(760\) 0 0
\(761\) −1.95557 + 0.294755i −1.95557 + 0.294755i −0.955573 + 0.294755i \(0.904762\pi\)
−1.00000 \(1.00000\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 0 0
\(768\) 0.997204 + 0.925270i 0.997204 + 0.925270i
\(769\) −0.900969 + 0.433884i −0.900969 + 0.433884i −0.826239 0.563320i \(-0.809524\pi\)
−0.0747301 + 0.997204i \(0.523810\pi\)
\(770\) 0 0
\(771\) 1.22563 + 0.590232i 1.22563 + 0.590232i
\(772\) 0 0
\(773\) 0.147791 + 1.97213i 0.147791 + 1.97213i 0.222521 + 0.974928i \(0.428571\pi\)
−0.0747301 + 0.997204i \(0.523810\pi\)
\(774\) 0 0
\(775\) −0.145713 + 1.94440i −0.145713 + 1.94440i
\(776\) 0 0
\(777\) 0 0
\(778\) 0.440071 1.92808i 0.440071 1.92808i
\(779\) 0 0
\(780\) 0 0
\(781\) −0.486868 + 0.451748i −0.486868 + 0.451748i
\(782\) −0.716983 + 0.488831i −0.716983 + 0.488831i
\(783\) 0 0
\(784\) −0.955573 0.294755i −0.955573 0.294755i
\(785\) 0 0
\(786\) 0.975345 0.664979i 0.975345 0.664979i
\(787\) 1.14625 1.06356i 1.14625 1.06356i 0.149042 0.988831i \(-0.452381\pi\)
0.997204 0.0747301i \(-0.0238095\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 0 0
\(792\) 0.213231 + 0.934227i 0.213231 + 0.934227i
\(793\) 0 0
\(794\) 0 0
\(795\) 0 0
\(796\) −0.215372 0.548760i −0.215372 0.548760i
\(797\) −1.72188 0.829215i −1.72188 0.829215i −0.988831 0.149042i \(-0.952381\pi\)
−0.733052 0.680173i \(-0.761905\pi\)
\(798\) 0 0
\(799\) 0 0
\(800\) 0.733052 + 0.680173i 0.733052 + 0.680173i
\(801\) −1.23305 0.185853i −1.23305 0.185853i
\(802\) 0 0
\(803\) 0 0
\(804\) 0 0
\(805\) 0 0
\(806\) −2.00894 2.51913i −2.00894 2.51913i
\(807\) 0 0
\(808\) −1.48883 1.01507i −1.48883 1.01507i
\(809\) 0 0 −0.826239 0.563320i \(-0.809524\pi\)
0.826239 + 0.563320i \(0.190476\pi\)
\(810\) 0 0
\(811\) 0.367554 + 0.460898i 0.367554 + 0.460898i 0.930874 0.365341i \(-0.119048\pi\)
−0.563320 + 0.826239i \(0.690476\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) 0 0
\(816\) 1.34515 + 0.202749i 1.34515 + 0.202749i
\(817\) 0 0
\(818\) 1.72188 0.829215i 1.72188 0.829215i
\(819\) −0.414278 + 1.34306i −0.414278 + 1.34306i
\(820\) 0 0
\(821\) 0 0 −0.365341 0.930874i \(-0.619048\pi\)
0.365341 + 0.930874i \(0.380952\pi\)
\(822\) 0.149042 + 1.98883i 0.149042 + 1.98883i
\(823\) −1.29991 + 0.400969i −1.29991 + 0.400969i −0.866025 0.500000i \(-0.833333\pi\)
−0.433884 + 0.900969i \(0.642857\pi\)
\(824\) 0 0
\(825\) 0.341040 + 1.49419i 0.341040 + 1.49419i
\(826\) 0 0
\(827\) 0.414278 1.81507i 0.414278 1.81507i −0.149042 0.988831i \(-0.547619\pi\)
0.563320 0.826239i \(-0.309524\pi\)
\(828\) 0.705280 + 0.217550i 0.705280 + 0.217550i
\(829\) 0.266948 0.680173i 0.266948 0.680173i −0.733052 0.680173i \(-0.761905\pi\)
1.00000 \(0\)
\(830\) 0 0
\(831\) 0 0
\(832\) −1.65248 −1.65248
\(833\) −0.955573 + 0.294755i −0.955573 + 0.294755i
\(834\) 2.71308 2.71308
\(835\) 0 0
\(836\) 0 0
\(837\) −0.144836 + 0.369035i −0.144836 + 0.369035i
\(838\) −1.90580 0.587862i −1.90580 0.587862i
\(839\) 0.347948 1.52446i 0.347948 1.52446i −0.433884 0.900969i \(-0.642857\pi\)
0.781831 0.623490i \(-0.214286\pi\)
\(840\) 0 0
\(841\) −0.222521 0.974928i −0.222521 0.974928i
\(842\) −0.0332580 + 0.443797i −0.0332580 + 0.443797i
\(843\) 1.29991 0.400969i 1.29991 0.400969i
\(844\) −0.116853 1.55929i −0.116853 1.55929i
\(845\) 0 0
\(846\) 0 0
\(847\) 0.250701 0.0983929i 0.250701 0.0983929i
\(848\) −1.72188 + 0.829215i −1.72188 + 0.829215i
\(849\) −1.12349 1.04245i −1.12349 1.04245i
\(850\) 0.988831 + 0.149042i 0.988831 + 0.149042i
\(851\) 0 0
\(852\) 0.400969 0.694498i 0.400969 0.694498i
\(853\) 0 0 0.623490 0.781831i \(-0.285714\pi\)
−0.623490 + 0.781831i \(0.714286\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 1.84095 0.277479i 1.84095 0.277479i
\(857\) 0 0 −0.826239 0.563320i \(-0.809524\pi\)
0.826239 + 0.563320i \(0.190476\pi\)
\(858\) −2.09255 1.42668i −2.09255 1.42668i
\(859\) 0 0 0.988831 0.149042i \(-0.0476190\pi\)
−0.988831 + 0.149042i \(0.952381\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) −1.07992 + 1.35417i −1.07992 + 1.35417i
\(863\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(864\) 0.101659 + 0.176078i 0.101659 + 0.176078i
\(865\) 0 0
\(866\) 1.32091 + 1.22563i 1.32091 + 1.22563i
\(867\) 1.22563 0.590232i 1.22563 0.590232i
\(868\) −1.81507 + 0.712362i −1.81507 + 0.712362i
\(869\) −2.02446 0.974928i −2.02446 0.974928i
\(870\) 0 0
\(871\) 0 0
\(872\) 0 0
\(873\) 0 0
\(874\) 0 0
\(875\) 0 0
\(876\) 0 0
\(877\) 0 0 −0.955573 0.294755i \(-0.904762\pi\)
0.955573 + 0.294755i \(0.0952381\pi\)
\(878\) 0.728639 1.85654i 0.728639 1.85654i
\(879\) 0.149042 0.138291i 0.149042 0.138291i
\(880\) 0 0
\(881\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(882\) 0.702749 + 0.479126i 0.702749 + 0.479126i
\(883\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(884\) −1.36534 + 0.930874i −1.36534 + 0.930874i
\(885\) 0 0
\(886\) 0 0
\(887\) 1.07659 + 0.332083i 1.07659 + 0.332083i 0.781831 0.623490i \(-0.214286\pi\)
0.294755 + 0.955573i \(0.404762\pi\)
\(888\) 0 0
\(889\) 0 0
\(890\) 0 0
\(891\) −0.0948968 + 1.26631i −0.0948968 + 1.26631i
\(892\) 0 0
\(893\) 0 0
\(894\) −0.728639 1.85654i −0.728639 1.85654i
\(895\) 0 0
\(896\) −0.294755 + 0.955573i −0.294755 + 0.955573i
\(897\) −1.75751 + 0.846372i −1.75751 + 0.846372i
\(898\) 0 0
\(899\) 0 0
\(900\) −0.425270 0.736589i −0.425270 0.736589i
\(901\) −0.955573 + 1.65510i −0.955573 + 1.65510i
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) 0 0
\(906\) 0 0
\(907\) −1.61105 1.09839i −1.61105 1.09839i −0.930874 0.365341i \(-0.880952\pi\)
−0.680173 0.733052i \(-0.738095\pi\)
\(908\) 0.582926 0.0878620i 0.582926 0.0878620i
\(909\) 0.955573 + 1.19825i 0.955573 + 1.19825i
\(910\) 0 0
\(911\) −0.541044 + 0.678448i −0.541044 + 0.678448i −0.974928 0.222521i \(-0.928571\pi\)
0.433884 + 0.900969i \(0.357143\pi\)
\(912\) 0 0
\(913\) 0 0
\(914\) 1.78181 + 0.268565i 1.78181 + 0.268565i
\(915\) 0 0
\(916\) 1.12349 0.541044i 1.12349 0.541044i
\(917\) 0.751509 + 0.433884i 0.751509 + 0.433884i
\(918\) 0.183183 + 0.0882162i 0.183183 + 0.0882162i
\(919\) 0 0 −0.365341 0.930874i \(-0.619048\pi\)
0.365341 + 0.930874i \(0.380952\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) −0.142820 + 1.90580i −0.142820 + 1.90580i
\(923\) 0.216769 + 0.949729i 0.216769 + 0.949729i
\(924\) −1.19825 + 0.955573i −1.19825 + 0.955573i
\(925\) 0 0
\(926\) 0 0
\(927\) 0 0
\(928\) 0 0
\(929\) 0 0 0.826239 0.563320i \(-0.190476\pi\)
−0.826239 + 0.563320i \(0.809524\pi\)
\(930\) 0 0
\(931\) 0 0
\(932\) 0 0
\(933\) −1.94677 + 1.32729i −1.94677 + 1.32729i
\(934\) 0 0
\(935\) 0 0
\(936\) 1.34306 + 0.414278i 1.34306 + 0.414278i
\(937\) 0.0990311 0.433884i 0.0990311 0.433884i −0.900969 0.433884i \(-0.857143\pi\)
1.00000 \(0\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0 0
\(941\) 0 0 0.955573 0.294755i \(-0.0952381\pi\)
−0.955573 + 0.294755i \(0.904762\pi\)
\(942\) 0.0151939 + 0.202749i 0.0151939 + 0.202749i
\(943\) 0 0
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) −1.26968 1.17809i −1.26968 1.17809i −0.974928 0.222521i \(-0.928571\pi\)
−0.294755 0.955573i \(-0.595238\pi\)
\(948\) 2.68278 + 0.404364i 2.68278 + 0.404364i
\(949\) 0 0
\(950\) 0 0
\(951\) 0 0
\(952\) 0.294755 + 0.955573i 0.294755 + 0.955573i
\(953\) 1.23305 + 1.54620i 1.23305 + 1.54620i 0.733052 + 0.680173i \(0.238095\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(954\) 1.60735 0.242269i 1.60735 0.242269i
\(955\) 0 0
\(956\) 0 0
\(957\) 0 0
\(958\) 0.541044 + 0.678448i 0.541044 + 0.678448i
\(959\) −1.26968 + 0.733052i −1.26968 + 0.733052i
\(960\) 0 0
\(961\) −1.40097 + 2.42655i −1.40097 + 2.42655i
\(962\) 0 0
\(963\) −1.56580 0.236007i −1.56580 0.236007i
\(964\) 0 0
\(965\) 0 0
\(966\) 0.175939 + 1.16728i 0.175939 + 1.16728i
\(967\) 0 0 −0.900969 0.433884i \(-0.857143\pi\)
0.900969 + 0.433884i \(0.142857\pi\)
\(968\) −0.0983929 0.250701i −0.0983929 0.250701i
\(969\) 0 0
\(970\) 0 0
\(971\) 0 0 0.0747301 0.997204i \(-0.476190\pi\)
−0.0747301 + 0.997204i \(0.523810\pi\)
\(972\) −0.295943 1.29661i −0.295943 1.29661i
\(973\) 0.865341 + 1.79690i 0.865341 + 1.79690i
\(974\) −0.385418 + 1.68862i −0.385418 + 1.68862i
\(975\) 2.14807 + 0.662592i 2.14807 + 0.662592i
\(976\) 0 0
\(977\) 1.32091 1.22563i 1.32091 1.22563i 0.365341 0.930874i \(-0.380952\pi\)
0.955573 0.294755i \(-0.0952381\pi\)
\(978\) 0 0
\(979\) 1.65177 1.65177
\(980\) 0 0
\(981\) 0 0
\(982\) 0 0
\(983\) 0.825886 0.766310i 0.825886 0.766310i −0.149042 0.988831i \(-0.547619\pi\)
0.974928 + 0.222521i \(0.0714286\pi\)
\(984\) 0 0
\(985\) 0 0
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) 0 0
\(990\) 0 0
\(991\) −0.0222759 0.297251i −0.0222759 0.297251i −0.997204 0.0747301i \(-0.976190\pi\)
0.974928 0.222521i \(-0.0714286\pi\)
\(992\) 0.712362 + 1.81507i 0.712362 + 1.81507i
\(993\) 0 0
\(994\) 0.587862 + 0.0440542i 0.587862 + 0.0440542i
\(995\) 0 0
\(996\) 0 0
\(997\) 0 0 −0.988831 0.149042i \(-0.952381\pi\)
0.988831 + 0.149042i \(0.0476190\pi\)
\(998\) −0.997204 1.72721i −0.997204 1.72721i
\(999\) 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 3332.1.cc.c.135.2 yes 24
4.3 odd 2 inner 3332.1.cc.c.135.1 24
17.16 even 2 inner 3332.1.cc.c.135.1 24
49.4 even 21 inner 3332.1.cc.c.543.2 yes 24
68.67 odd 2 CM 3332.1.cc.c.135.2 yes 24
196.151 odd 42 inner 3332.1.cc.c.543.1 yes 24
833.543 even 42 inner 3332.1.cc.c.543.1 yes 24
3332.543 odd 42 inner 3332.1.cc.c.543.2 yes 24
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
3332.1.cc.c.135.1 24 4.3 odd 2 inner
3332.1.cc.c.135.1 24 17.16 even 2 inner
3332.1.cc.c.135.2 yes 24 1.1 even 1 trivial
3332.1.cc.c.135.2 yes 24 68.67 odd 2 CM
3332.1.cc.c.543.1 yes 24 196.151 odd 42 inner
3332.1.cc.c.543.1 yes 24 833.543 even 42 inner
3332.1.cc.c.543.2 yes 24 49.4 even 21 inner
3332.1.cc.c.543.2 yes 24 3332.543 odd 42 inner