Properties

Label 1911.1.ds.a.1271.1
Level $1911$
Weight $1$
Character 1911.1271
Analytic conductor $0.954$
Analytic rank $0$
Dimension $12$
Projective image $D_{42}$
CM discriminant -3
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [1911,1,Mod(179,1911)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1911, base_ring=CyclotomicField(42))
 
chi = DirichletCharacter(H, H._module([21, 4, 35]))
 
N = Newforms(chi, 1, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("1911.179");
 
S:= CuspForms(chi, 1);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1911 = 3 \cdot 7^{2} \cdot 13 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 1911.ds (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: \(0.953713239142\)
Analytic rank: \(0\)
Dimension: \(12\)
Coefficient field: \(\Q(\zeta_{21})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{12} - x^{11} + x^{9} - x^{8} + x^{6} - x^{4} + x^{3} - x + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{4}]\)
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 1271.1
Root \(0.0747301 + 0.997204i\) of defining polynomial
Character \(\chi\) \(=\) 1911.1271
Dual form 1911.1.ds.a.212.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.900969 - 0.433884i) q^{3} +(-0.955573 + 0.294755i) q^{4} +(-0.988831 + 0.149042i) q^{7} +(0.623490 - 0.781831i) q^{9} +O(q^{10})\) \(q+(0.900969 - 0.433884i) q^{3} +(-0.955573 + 0.294755i) q^{4} +(-0.988831 + 0.149042i) q^{7} +(0.623490 - 0.781831i) q^{9} +(-0.733052 + 0.680173i) q^{12} +(-0.0747301 - 0.997204i) q^{13} +(0.826239 - 0.563320i) q^{16} -1.86175i q^{19} +(-0.826239 + 0.563320i) q^{21} +(-0.365341 - 0.930874i) q^{25} +(0.222521 - 0.974928i) q^{27} +(0.900969 - 0.433884i) q^{28} +(1.68862 + 0.974928i) q^{31} +(-0.365341 + 0.930874i) q^{36} +(-0.173761 + 0.563320i) q^{37} +(-0.500000 - 0.866025i) q^{39} +(0.603718 - 0.411608i) q^{43} +(0.500000 - 0.866025i) q^{48} +(0.955573 - 0.294755i) q^{49} +(0.365341 + 0.930874i) q^{52} +(-0.807782 - 1.67738i) q^{57} +(-0.326239 - 1.42935i) q^{61} +(-0.500000 + 0.866025i) q^{63} +(-0.623490 + 0.781831i) q^{64} +0.867767i q^{67} +(-1.26631 + 0.496990i) q^{73} +(-0.733052 - 0.680173i) q^{75} +(0.548760 + 1.77904i) q^{76} +(-0.222521 - 0.385418i) q^{79} +(-0.222521 - 0.974928i) q^{81} +(0.623490 - 0.781831i) q^{84} +(0.222521 + 0.974928i) q^{91} +(1.94440 + 0.145713i) q^{93} +(-1.61232 - 0.930874i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12 q + 2 q^{3} - q^{4} + q^{7} - 2 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 12 q + 2 q^{3} - q^{4} + q^{7} - 2 q^{9} + q^{12} - q^{13} + q^{16} - q^{21} - q^{25} + 2 q^{27} + 2 q^{28} - q^{36} - 11 q^{37} - 6 q^{39} - q^{43} + 6 q^{48} + q^{49} + q^{52} + 5 q^{61} - 6 q^{63} + 2 q^{64} - 3 q^{73} + q^{75} - 3 q^{76} - 2 q^{79} - 2 q^{81} - 2 q^{84} + 2 q^{91} + 3 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1911\mathbb{Z}\right)^\times\).

\(n\) \(638\) \(1471\) \(1522\)
\(\chi(n)\) \(-1\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{11}{21}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0 −0.149042 0.988831i \(-0.547619\pi\)
0.149042 + 0.988831i \(0.452381\pi\)
\(3\) 0.900969 0.433884i 0.900969 0.433884i
\(4\) −0.955573 + 0.294755i −0.955573 + 0.294755i
\(5\) 0 0 0.563320 0.826239i \(-0.309524\pi\)
−0.563320 + 0.826239i \(0.690476\pi\)
\(6\) 0 0
\(7\) −0.988831 + 0.149042i −0.988831 + 0.149042i
\(8\) 0 0
\(9\) 0.623490 0.781831i 0.623490 0.781831i
\(10\) 0 0
\(11\) 0 0 0.781831 0.623490i \(-0.214286\pi\)
−0.781831 + 0.623490i \(0.785714\pi\)
\(12\) −0.733052 + 0.680173i −0.733052 + 0.680173i
\(13\) −0.0747301 0.997204i −0.0747301 0.997204i
\(14\) 0 0
\(15\) 0 0
\(16\) 0.826239 0.563320i 0.826239 0.563320i
\(17\) 0 0 0.733052 0.680173i \(-0.238095\pi\)
−0.733052 + 0.680173i \(0.761905\pi\)
\(18\) 0 0
\(19\) 1.86175i 1.86175i −0.365341 0.930874i \(-0.619048\pi\)
0.365341 0.930874i \(-0.380952\pi\)
\(20\) 0 0
\(21\) −0.826239 + 0.563320i −0.826239 + 0.563320i
\(22\) 0 0
\(23\) 0 0 −0.733052 0.680173i \(-0.761905\pi\)
0.733052 + 0.680173i \(0.238095\pi\)
\(24\) 0 0
\(25\) −0.365341 0.930874i −0.365341 0.930874i
\(26\) 0 0
\(27\) 0.222521 0.974928i 0.222521 0.974928i
\(28\) 0.900969 0.433884i 0.900969 0.433884i
\(29\) 0 0 0.733052 0.680173i \(-0.238095\pi\)
−0.733052 + 0.680173i \(0.761905\pi\)
\(30\) 0 0
\(31\) 1.68862 + 0.974928i 1.68862 + 0.974928i 0.955573 + 0.294755i \(0.0952381\pi\)
0.733052 + 0.680173i \(0.238095\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) 0 0
\(36\) −0.365341 + 0.930874i −0.365341 + 0.930874i
\(37\) −0.173761 + 0.563320i −0.173761 + 0.563320i 0.826239 + 0.563320i \(0.190476\pi\)
−1.00000 \(\pi\)
\(38\) 0 0
\(39\) −0.500000 0.866025i −0.500000 0.866025i
\(40\) 0 0
\(41\) 0 0 0.563320 0.826239i \(-0.309524\pi\)
−0.563320 + 0.826239i \(0.690476\pi\)
\(42\) 0 0
\(43\) 0.603718 0.411608i 0.603718 0.411608i −0.222521 0.974928i \(-0.571429\pi\)
0.826239 + 0.563320i \(0.190476\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 0 0 −0.930874 0.365341i \(-0.880952\pi\)
0.930874 + 0.365341i \(0.119048\pi\)
\(48\) 0.500000 0.866025i 0.500000 0.866025i
\(49\) 0.955573 0.294755i 0.955573 0.294755i
\(50\) 0 0
\(51\) 0 0
\(52\) 0.365341 + 0.930874i 0.365341 + 0.930874i
\(53\) 0 0 −0.733052 0.680173i \(-0.761905\pi\)
0.733052 + 0.680173i \(0.238095\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 0 0
\(57\) −0.807782 1.67738i −0.807782 1.67738i
\(58\) 0 0
\(59\) 0 0 0.997204 0.0747301i \(-0.0238095\pi\)
−0.997204 + 0.0747301i \(0.976190\pi\)
\(60\) 0 0
\(61\) −0.326239 1.42935i −0.326239 1.42935i −0.826239 0.563320i \(-0.809524\pi\)
0.500000 0.866025i \(-0.333333\pi\)
\(62\) 0 0
\(63\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(64\) −0.623490 + 0.781831i −0.623490 + 0.781831i
\(65\) 0 0
\(66\) 0 0
\(67\) 0.867767i 0.867767i 0.900969 + 0.433884i \(0.142857\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 0 0 0.680173 0.733052i \(-0.261905\pi\)
−0.680173 + 0.733052i \(0.738095\pi\)
\(72\) 0 0
\(73\) −1.26631 + 0.496990i −1.26631 + 0.496990i −0.900969 0.433884i \(-0.857143\pi\)
−0.365341 + 0.930874i \(0.619048\pi\)
\(74\) 0 0
\(75\) −0.733052 0.680173i −0.733052 0.680173i
\(76\) 0.548760 + 1.77904i 0.548760 + 1.77904i
\(77\) 0 0
\(78\) 0 0
\(79\) −0.222521 0.385418i −0.222521 0.385418i 0.733052 0.680173i \(-0.238095\pi\)
−0.955573 + 0.294755i \(0.904762\pi\)
\(80\) 0 0
\(81\) −0.222521 0.974928i −0.222521 0.974928i
\(82\) 0 0
\(83\) 0 0 −0.781831 0.623490i \(-0.785714\pi\)
0.781831 + 0.623490i \(0.214286\pi\)
\(84\) 0.623490 0.781831i 0.623490 0.781831i
\(85\) 0 0
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 0 0 0.930874 0.365341i \(-0.119048\pi\)
−0.930874 + 0.365341i \(0.880952\pi\)
\(90\) 0 0
\(91\) 0.222521 + 0.974928i 0.222521 + 0.974928i
\(92\) 0 0
\(93\) 1.94440 + 0.145713i 1.94440 + 0.145713i
\(94\) 0 0
\(95\) 0 0
\(96\) 0 0
\(97\) −1.61232 0.930874i −1.61232 0.930874i −0.988831 0.149042i \(-0.952381\pi\)
−0.623490 0.781831i \(-0.714286\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0.623490 + 0.781831i 0.623490 + 0.781831i
\(101\) 0 0 0.900969 0.433884i \(-0.142857\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(102\) 0 0
\(103\) 0.603718 + 0.411608i 0.603718 + 0.411608i 0.826239 0.563320i \(-0.190476\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 0 0 −0.365341 0.930874i \(-0.619048\pi\)
0.365341 + 0.930874i \(0.380952\pi\)
\(108\) 0.0747301 + 0.997204i 0.0747301 + 0.997204i
\(109\) 0.297251 + 1.97213i 0.297251 + 1.97213i 0.222521 + 0.974928i \(0.428571\pi\)
0.0747301 + 0.997204i \(0.476190\pi\)
\(110\) 0 0
\(111\) 0.0878620 + 0.582926i 0.0878620 + 0.582926i
\(112\) −0.733052 + 0.680173i −0.733052 + 0.680173i
\(113\) 0 0 −0.365341 0.930874i \(-0.619048\pi\)
0.365341 + 0.930874i \(0.380952\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 0 0
\(117\) −0.826239 0.563320i −0.826239 0.563320i
\(118\) 0 0
\(119\) 0 0
\(120\) 0 0
\(121\) 0.222521 0.974928i 0.222521 0.974928i
\(122\) 0 0
\(123\) 0 0
\(124\) −1.90097 0.433884i −1.90097 0.433884i
\(125\) 0 0
\(126\) 0 0
\(127\) −1.44973 + 1.34515i −1.44973 + 1.34515i −0.623490 + 0.781831i \(0.714286\pi\)
−0.826239 + 0.563320i \(0.809524\pi\)
\(128\) 0 0
\(129\) 0.365341 0.632789i 0.365341 0.632789i
\(130\) 0 0
\(131\) 0 0 −0.0747301 0.997204i \(-0.523810\pi\)
0.0747301 + 0.997204i \(0.476190\pi\)
\(132\) 0 0
\(133\) 0.277479 + 1.84095i 0.277479 + 1.84095i
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 0 0 0.997204 0.0747301i \(-0.0238095\pi\)
−0.997204 + 0.0747301i \(0.976190\pi\)
\(138\) 0 0
\(139\) −0.134659 + 1.79690i −0.134659 + 1.79690i 0.365341 + 0.930874i \(0.380952\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 0 0
\(144\) 0.0747301 0.997204i 0.0747301 0.997204i
\(145\) 0 0
\(146\) 0 0
\(147\) 0.733052 0.680173i 0.733052 0.680173i
\(148\) 0.589510i 0.589510i
\(149\) 0 0 0.781831 0.623490i \(-0.214286\pi\)
−0.781831 + 0.623490i \(0.785714\pi\)
\(150\) 0 0
\(151\) −1.06356 + 1.14625i −1.06356 + 1.14625i −0.0747301 + 0.997204i \(0.523810\pi\)
−0.988831 + 0.149042i \(0.952381\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 0 0
\(156\) 0.733052 + 0.680173i 0.733052 + 0.680173i
\(157\) 1.36534 0.930874i 1.36534 0.930874i 0.365341 0.930874i \(-0.380952\pi\)
1.00000 \(0\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 0 0
\(162\) 0 0
\(163\) 0.488831 1.01507i 0.488831 1.01507i −0.500000 0.866025i \(-0.666667\pi\)
0.988831 0.149042i \(-0.0476190\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 0 0 −0.680173 0.733052i \(-0.738095\pi\)
0.680173 + 0.733052i \(0.261905\pi\)
\(168\) 0 0
\(169\) −0.988831 + 0.149042i −0.988831 + 0.149042i
\(170\) 0 0
\(171\) −1.45557 1.16078i −1.45557 1.16078i
\(172\) −0.455573 + 0.571270i −0.455573 + 0.571270i
\(173\) 0 0 0.222521 0.974928i \(-0.428571\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(174\) 0 0
\(175\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) 0 0 −0.222521 0.974928i \(-0.571429\pi\)
0.222521 + 0.974928i \(0.428571\pi\)
\(180\) 0 0
\(181\) 1.03030 1.29196i 1.03030 1.29196i 0.0747301 0.997204i \(-0.476190\pi\)
0.955573 0.294755i \(-0.0952381\pi\)
\(182\) 0 0
\(183\) −0.914101 1.14625i −0.914101 1.14625i
\(184\) 0 0
\(185\) 0 0
\(186\) 0 0
\(187\) 0 0
\(188\) 0 0
\(189\) −0.0747301 + 0.997204i −0.0747301 + 0.997204i
\(190\) 0 0
\(191\) 0 0 0.900969 0.433884i \(-0.142857\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(192\) −0.222521 + 0.974928i −0.222521 + 0.974928i
\(193\) 0.488831 + 1.01507i 0.488831 + 1.01507i 0.988831 + 0.149042i \(0.0476190\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) −0.826239 + 0.563320i −0.826239 + 0.563320i
\(197\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(198\) 0 0
\(199\) 1.63402 + 1.11406i 1.63402 + 1.11406i 0.900969 + 0.433884i \(0.142857\pi\)
0.733052 + 0.680173i \(0.238095\pi\)
\(200\) 0 0
\(201\) 0.376510 + 0.781831i 0.376510 + 0.781831i
\(202\) 0 0
\(203\) 0 0
\(204\) 0 0
\(205\) 0 0
\(206\) 0 0
\(207\) 0 0
\(208\) −0.623490 0.781831i −0.623490 0.781831i
\(209\) 0 0
\(210\) 0 0
\(211\) 1.88980 + 0.284841i 1.88980 + 0.284841i 0.988831 0.149042i \(-0.0476190\pi\)
0.900969 + 0.433884i \(0.142857\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) 0 0
\(216\) 0 0
\(217\) −1.81507 0.712362i −1.81507 0.712362i
\(218\) 0 0
\(219\) −0.925270 + 0.997204i −0.925270 + 0.997204i
\(220\) 0 0
\(221\) 0 0
\(222\) 0 0
\(223\) 0.574730 + 1.86323i 0.574730 + 1.86323i 0.500000 + 0.866025i \(0.333333\pi\)
0.0747301 + 0.997204i \(0.476190\pi\)
\(224\) 0 0
\(225\) −0.955573 0.294755i −0.955573 0.294755i
\(226\) 0 0
\(227\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(228\) 1.26631 + 1.36476i 1.26631 + 1.36476i
\(229\) 0.297251 0.0222759i 0.297251 0.0222759i 0.0747301 0.997204i \(-0.476190\pi\)
0.222521 + 0.974928i \(0.428571\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 0 0 0.733052 0.680173i \(-0.238095\pi\)
−0.733052 + 0.680173i \(0.761905\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 0 0
\(237\) −0.367711 0.250701i −0.367711 0.250701i
\(238\) 0 0
\(239\) 0 0 0.433884 0.900969i \(-0.357143\pi\)
−0.433884 + 0.900969i \(0.642857\pi\)
\(240\) 0 0
\(241\) −0.255779 0.829215i −0.255779 0.829215i −0.988831 0.149042i \(-0.952381\pi\)
0.733052 0.680173i \(-0.238095\pi\)
\(242\) 0 0
\(243\) −0.623490 0.781831i −0.623490 0.781831i
\(244\) 0.733052 + 1.26968i 0.733052 + 1.26968i
\(245\) 0 0
\(246\) 0 0
\(247\) −1.85654 + 0.139129i −1.85654 + 0.139129i
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 0 0 0.826239 0.563320i \(-0.190476\pi\)
−0.826239 + 0.563320i \(0.809524\pi\)
\(252\) 0.222521 0.974928i 0.222521 0.974928i
\(253\) 0 0
\(254\) 0 0
\(255\) 0 0
\(256\) 0.365341 0.930874i 0.365341 0.930874i
\(257\) 0 0 −0.955573 0.294755i \(-0.904762\pi\)
0.955573 + 0.294755i \(0.0952381\pi\)
\(258\) 0 0
\(259\) 0.0878620 0.582926i 0.0878620 0.582926i
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) 0 0
\(268\) −0.255779 0.829215i −0.255779 0.829215i
\(269\) 0 0 −0.988831 0.149042i \(-0.952381\pi\)
0.988831 + 0.149042i \(0.0476190\pi\)
\(270\) 0 0
\(271\) 1.35654 1.46200i 1.35654 1.46200i 0.623490 0.781831i \(-0.285714\pi\)
0.733052 0.680173i \(-0.238095\pi\)
\(272\) 0 0
\(273\) 0.623490 + 0.781831i 0.623490 + 0.781831i
\(274\) 0 0
\(275\) 0 0
\(276\) 0 0
\(277\) −0.109562 + 0.101659i −0.109562 + 0.101659i −0.733052 0.680173i \(-0.761905\pi\)
0.623490 + 0.781831i \(0.285714\pi\)
\(278\) 0 0
\(279\) 1.81507 0.712362i 1.81507 0.712362i
\(280\) 0 0
\(281\) 0 0 0.781831 0.623490i \(-0.214286\pi\)
−0.781831 + 0.623490i \(0.785714\pi\)
\(282\) 0 0
\(283\) 0.914101 + 1.14625i 0.914101 + 1.14625i 0.988831 + 0.149042i \(0.0476190\pi\)
−0.0747301 + 0.997204i \(0.523810\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 0 0
\(288\) 0 0
\(289\) 0.0747301 0.997204i 0.0747301 0.997204i
\(290\) 0 0
\(291\) −1.85654 0.139129i −1.85654 0.139129i
\(292\) 1.06356 0.848162i 1.06356 0.848162i
\(293\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 0 0
\(300\) 0.900969 + 0.433884i 0.900969 + 0.433884i
\(301\) −0.535628 + 0.496990i −0.535628 + 0.496990i
\(302\) 0 0
\(303\) 0 0
\(304\) −1.04876 1.53825i −1.04876 1.53825i
\(305\) 0 0
\(306\) 0 0
\(307\) 1.22252 0.974928i 1.22252 0.974928i 0.222521 0.974928i \(-0.428571\pi\)
1.00000 \(0\)
\(308\) 0 0
\(309\) 0.722521 + 0.108903i 0.722521 + 0.108903i
\(310\) 0 0
\(311\) 0 0 −0.955573 0.294755i \(-0.904762\pi\)
0.955573 + 0.294755i \(0.0952381\pi\)
\(312\) 0 0
\(313\) 0.955573 + 1.65510i 0.955573 + 1.65510i 0.733052 + 0.680173i \(0.238095\pi\)
0.222521 + 0.974928i \(0.428571\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0.326239 + 0.302705i 0.326239 + 0.302705i
\(317\) 0 0 −0.294755 0.955573i \(-0.595238\pi\)
0.294755 + 0.955573i \(0.404762\pi\)
\(318\) 0 0
\(319\) 0 0
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) 0 0
\(324\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(325\) −0.900969 + 0.433884i −0.900969 + 0.433884i
\(326\) 0 0
\(327\) 1.12349 + 1.64786i 1.12349 + 1.64786i
\(328\) 0 0
\(329\) 0 0
\(330\) 0 0
\(331\) 0.290611 0.0663300i 0.290611 0.0663300i −0.0747301 0.997204i \(-0.523810\pi\)
0.365341 + 0.930874i \(0.380952\pi\)
\(332\) 0 0
\(333\) 0.332083 + 0.487076i 0.332083 + 0.487076i
\(334\) 0 0
\(335\) 0 0
\(336\) −0.365341 + 0.930874i −0.365341 + 0.930874i
\(337\) 0.134659 + 0.0648483i 0.134659 + 0.0648483i 0.500000 0.866025i \(-0.333333\pi\)
−0.365341 + 0.930874i \(0.619048\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) 0 0
\(342\) 0 0
\(343\) −0.900969 + 0.433884i −0.900969 + 0.433884i
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 0 0 0.955573 0.294755i \(-0.0952381\pi\)
−0.955573 + 0.294755i \(0.904762\pi\)
\(348\) 0 0
\(349\) −0.297251 + 0.0222759i −0.297251 + 0.0222759i −0.222521 0.974928i \(-0.571429\pi\)
−0.0747301 + 0.997204i \(0.523810\pi\)
\(350\) 0 0
\(351\) −0.988831 0.149042i −0.988831 0.149042i
\(352\) 0 0
\(353\) 0 0 0.433884 0.900969i \(-0.357143\pi\)
−0.433884 + 0.900969i \(0.642857\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 0 0 0.997204 0.0747301i \(-0.0238095\pi\)
−0.997204 + 0.0747301i \(0.976190\pi\)
\(360\) 0 0
\(361\) −2.46610 −2.46610
\(362\) 0 0
\(363\) −0.222521 0.974928i −0.222521 0.974928i
\(364\) −0.500000 0.866025i −0.500000 0.866025i
\(365\) 0 0
\(366\) 0 0
\(367\) 0.0931869 0.116853i 0.0931869 0.116853i −0.733052 0.680173i \(-0.761905\pi\)
0.826239 + 0.563320i \(0.190476\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) 0 0
\(372\) −1.90097 + 0.433884i −1.90097 + 0.433884i
\(373\) −1.24698 −1.24698 −0.623490 0.781831i \(-0.714286\pi\)
−0.623490 + 0.781831i \(0.714286\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 0 0
\(378\) 0 0
\(379\) −1.45557 0.571270i −1.45557 0.571270i −0.500000 0.866025i \(-0.666667\pi\)
−0.955573 + 0.294755i \(0.904762\pi\)
\(380\) 0 0
\(381\) −0.722521 + 1.84095i −0.722521 + 1.84095i
\(382\) 0 0
\(383\) 0 0 −0.781831 0.623490i \(-0.785714\pi\)
0.781831 + 0.623490i \(0.214286\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) 0.0546039 0.728639i 0.0546039 0.728639i
\(388\) 1.81507 + 0.414278i 1.81507 + 0.414278i
\(389\) 0 0 0.0747301 0.997204i \(-0.476190\pi\)
−0.0747301 + 0.997204i \(0.523810\pi\)
\(390\) 0 0
\(391\) 0 0
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) 0 0
\(396\) 0 0
\(397\) 0.590232 + 1.22563i 0.590232 + 1.22563i 0.955573 + 0.294755i \(0.0952381\pi\)
−0.365341 + 0.930874i \(0.619048\pi\)
\(398\) 0 0
\(399\) 1.04876 + 1.53825i 1.04876 + 1.53825i
\(400\) −0.826239 0.563320i −0.826239 0.563320i
\(401\) 0 0 0.930874 0.365341i \(-0.119048\pi\)
−0.930874 + 0.365341i \(0.880952\pi\)
\(402\) 0 0
\(403\) 0.846011 1.75676i 0.846011 1.75676i
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 0 0
\(408\) 0 0
\(409\) 0.400969 + 0.432142i 0.400969 + 0.432142i 0.900969 0.433884i \(-0.142857\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) −0.698220 0.215372i −0.698220 0.215372i
\(413\) 0 0
\(414\) 0 0
\(415\) 0 0
\(416\) 0 0
\(417\) 0.658322 + 1.67738i 0.658322 + 1.67738i
\(418\) 0 0
\(419\) 0 0 0.955573 0.294755i \(-0.0952381\pi\)
−0.955573 + 0.294755i \(0.904762\pi\)
\(420\) 0 0
\(421\) −0.846011 + 0.193096i −0.846011 + 0.193096i −0.623490 0.781831i \(-0.714286\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) 0 0
\(426\) 0 0
\(427\) 0.535628 + 1.36476i 0.535628 + 1.36476i
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 0 0 0.433884 0.900969i \(-0.357143\pi\)
−0.433884 + 0.900969i \(0.642857\pi\)
\(432\) −0.365341 0.930874i −0.365341 0.930874i
\(433\) −0.0931869 + 1.24349i −0.0931869 + 1.24349i 0.733052 + 0.680173i \(0.238095\pi\)
−0.826239 + 0.563320i \(0.809524\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) −0.865341 1.79690i −0.865341 1.79690i
\(437\) 0 0
\(438\) 0 0
\(439\) −0.147791 + 0.0222759i −0.147791 + 0.0222759i −0.222521 0.974928i \(-0.571429\pi\)
0.0747301 + 0.997204i \(0.476190\pi\)
\(440\) 0 0
\(441\) 0.365341 0.930874i 0.365341 0.930874i
\(442\) 0 0
\(443\) 0 0 0.365341 0.930874i \(-0.380952\pi\)
−0.365341 + 0.930874i \(0.619048\pi\)
\(444\) −0.255779 0.531130i −0.255779 0.531130i
\(445\) 0 0
\(446\) 0 0
\(447\) 0 0
\(448\) 0.500000 0.866025i 0.500000 0.866025i
\(449\) 0 0 −0.997204 0.0747301i \(-0.976190\pi\)
0.997204 + 0.0747301i \(0.0238095\pi\)
\(450\) 0 0
\(451\) 0 0
\(452\) 0 0
\(453\) −0.460898 + 1.49419i −0.460898 + 1.49419i
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) −1.09839 1.61105i −1.09839 1.61105i −0.733052 0.680173i \(-0.761905\pi\)
−0.365341 0.930874i \(-0.619048\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 0 0 0.294755 0.955573i \(-0.404762\pi\)
−0.294755 + 0.955573i \(0.595238\pi\)
\(462\) 0 0
\(463\) 1.94440 + 0.443797i 1.94440 + 0.443797i 0.988831 + 0.149042i \(0.0476190\pi\)
0.955573 + 0.294755i \(0.0952381\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 0 0 0.955573 0.294755i \(-0.0952381\pi\)
−0.955573 + 0.294755i \(0.904762\pi\)
\(468\) 0.955573 + 0.294755i 0.955573 + 0.294755i
\(469\) −0.129334 0.858075i −0.129334 0.858075i
\(470\) 0 0
\(471\) 0.826239 1.43109i 0.826239 1.43109i
\(472\) 0 0
\(473\) 0 0
\(474\) 0 0
\(475\) −1.73305 + 0.680173i −1.73305 + 0.680173i
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) 0 0 0.781831 0.623490i \(-0.214286\pi\)
−0.781831 + 0.623490i \(0.785714\pi\)
\(480\) 0 0
\(481\) 0.574730 + 0.131178i 0.574730 + 0.131178i
\(482\) 0 0
\(483\) 0 0
\(484\) 0.0747301 + 0.997204i 0.0747301 + 0.997204i
\(485\) 0 0
\(486\) 0 0
\(487\) −0.332083 + 0.487076i −0.332083 + 0.487076i −0.955573 0.294755i \(-0.904762\pi\)
0.623490 + 0.781831i \(0.285714\pi\)
\(488\) 0 0
\(489\) 1.12664i 1.12664i
\(490\) 0 0
\(491\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(492\) 0 0
\(493\) 0 0
\(494\) 0 0
\(495\) 0 0
\(496\) 1.94440 0.145713i 1.94440 0.145713i
\(497\) 0 0
\(498\) 0 0
\(499\) −0.202749 + 1.34515i −0.202749 + 1.34515i 0.623490 + 0.781831i \(0.285714\pi\)
−0.826239 + 0.563320i \(0.809524\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) 0 0 0.988831 0.149042i \(-0.0476190\pi\)
−0.988831 + 0.149042i \(0.952381\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) −0.826239 + 0.563320i −0.826239 + 0.563320i
\(508\) 0.988831 1.71271i 0.988831 1.71271i
\(509\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(510\) 0 0
\(511\) 1.17809 0.680173i 1.17809 0.680173i
\(512\) 0 0
\(513\) −1.81507 0.414278i −1.81507 0.414278i
\(514\) 0 0
\(515\) 0 0
\(516\) −0.162592 + 0.712362i −0.162592 + 0.712362i
\(517\) 0 0
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(522\) 0 0
\(523\) 1.57906 1.07659i 1.57906 1.07659i 0.623490 0.781831i \(-0.285714\pi\)
0.955573 0.294755i \(-0.0952381\pi\)
\(524\) 0 0
\(525\) 0.826239 + 0.563320i 0.826239 + 0.563320i
\(526\) 0 0
\(527\) 0 0
\(528\) 0 0
\(529\) 0.0747301 + 0.997204i 0.0747301 + 0.997204i
\(530\) 0 0
\(531\) 0 0
\(532\) −0.807782 1.67738i −0.807782 1.67738i
\(533\) 0 0
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) 0 0
\(540\) 0 0
\(541\) 0.277479 + 0.108903i 0.277479 + 0.108903i 0.500000 0.866025i \(-0.333333\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(542\) 0 0
\(543\) 0.367711 1.61105i 0.367711 1.61105i
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) −1.72188 + 0.829215i −1.72188 + 0.829215i −0.733052 + 0.680173i \(0.761905\pi\)
−0.988831 + 0.149042i \(0.952381\pi\)
\(548\) 0 0
\(549\) −1.32091 0.636119i −1.32091 0.636119i
\(550\) 0 0
\(551\) 0 0
\(552\) 0 0
\(553\) 0.277479 + 0.347948i 0.277479 + 0.347948i
\(554\) 0 0
\(555\) 0 0
\(556\) −0.400969 1.75676i −0.400969 1.75676i
\(557\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(558\) 0 0
\(559\) −0.455573 0.571270i −0.455573 0.571270i
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) 0 0 −0.988831 0.149042i \(-0.952381\pi\)
0.988831 + 0.149042i \(0.0476190\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 0 0
\(567\) 0.365341 + 0.930874i 0.365341 + 0.930874i
\(568\) 0 0
\(569\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(570\) 0 0
\(571\) −1.82624 0.563320i −1.82624 0.563320i −0.826239 0.563320i \(-0.809524\pi\)
−1.00000 \(\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 0 0
\(576\) 0.222521 + 0.974928i 0.222521 + 0.974928i
\(577\) 0.167917 + 1.11406i 0.167917 + 1.11406i 0.900969 + 0.433884i \(0.142857\pi\)
−0.733052 + 0.680173i \(0.761905\pi\)
\(578\) 0 0
\(579\) 0.880843 + 0.702449i 0.880843 + 0.702449i
\(580\) 0 0
\(581\) 0 0
\(582\) 0 0
\(583\) 0 0
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(588\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(589\) 1.81507 3.14379i 1.81507 3.14379i
\(590\) 0 0
\(591\) 0 0
\(592\) 0.173761 + 0.563320i 0.173761 + 0.563320i
\(593\) 0 0 0.563320 0.826239i \(-0.309524\pi\)
−0.563320 + 0.826239i \(0.690476\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) 1.95557 + 0.294755i 1.95557 + 0.294755i
\(598\) 0 0
\(599\) 0 0 0.988831 0.149042i \(-0.0476190\pi\)
−0.988831 + 0.149042i \(0.952381\pi\)
\(600\) 0 0
\(601\) 0.365341 0.930874i 0.365341 0.930874i −0.623490 0.781831i \(-0.714286\pi\)
0.988831 0.149042i \(-0.0476190\pi\)
\(602\) 0 0
\(603\) 0.678448 + 0.541044i 0.678448 + 0.541044i
\(604\) 0.678448 1.40881i 0.678448 1.40881i
\(605\) 0 0
\(606\) 0 0
\(607\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 0 0
\(612\) 0 0
\(613\) −1.06356 0.848162i −1.06356 0.848162i −0.0747301 0.997204i \(-0.523810\pi\)
−0.988831 + 0.149042i \(0.952381\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 0 0 0.294755 0.955573i \(-0.404762\pi\)
−0.294755 + 0.955573i \(0.595238\pi\)
\(618\) 0 0
\(619\) −1.50000 0.866025i −1.50000 0.866025i −0.500000 0.866025i \(-0.666667\pi\)
−1.00000 \(\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 0 0
\(624\) −0.900969 0.433884i −0.900969 0.433884i
\(625\) −0.733052 + 0.680173i −0.733052 + 0.680173i
\(626\) 0 0
\(627\) 0 0
\(628\) −1.03030 + 1.29196i −1.03030 + 1.29196i
\(629\) 0 0
\(630\) 0 0
\(631\) −0.332083 0.487076i −0.332083 0.487076i 0.623490 0.781831i \(-0.285714\pi\)
−0.955573 + 0.294755i \(0.904762\pi\)
\(632\) 0 0
\(633\) 1.82624 0.563320i 1.82624 0.563320i
\(634\) 0 0
\(635\) 0 0
\(636\) 0 0
\(637\) −0.365341 0.930874i −0.365341 0.930874i
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) 0 0 0.955573 0.294755i \(-0.0952381\pi\)
−0.955573 + 0.294755i \(0.904762\pi\)
\(642\) 0 0
\(643\) 0.634659 + 0.930874i 0.634659 + 0.930874i 1.00000 \(0\)
−0.365341 + 0.930874i \(0.619048\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 0 0 −0.900969 0.433884i \(-0.857143\pi\)
0.900969 + 0.433884i \(0.142857\pi\)
\(648\) 0 0
\(649\) 0 0
\(650\) 0 0
\(651\) −1.94440 + 0.145713i −1.94440 + 0.145713i
\(652\) −0.167917 + 1.11406i −0.167917 + 1.11406i
\(653\) 0 0 0.826239 0.563320i \(-0.190476\pi\)
−0.826239 + 0.563320i \(0.809524\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 0 0
\(657\) −0.400969 + 1.29991i −0.400969 + 1.29991i
\(658\) 0 0
\(659\) 0 0 −0.733052 0.680173i \(-0.761905\pi\)
0.733052 + 0.680173i \(0.238095\pi\)
\(660\) 0 0
\(661\) 0 0 0.623490 0.781831i \(-0.285714\pi\)
−0.623490 + 0.781831i \(0.714286\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) 0 0
\(668\) 0 0
\(669\) 1.32624 + 1.42935i 1.32624 + 1.42935i
\(670\) 0 0
\(671\) 0 0
\(672\) 0 0
\(673\) 0.603718 1.53825i 0.603718 1.53825i −0.222521 0.974928i \(-0.571429\pi\)
0.826239 0.563320i \(-0.190476\pi\)
\(674\) 0 0
\(675\) −0.988831 + 0.149042i −0.988831 + 0.149042i
\(676\) 0.900969 0.433884i 0.900969 0.433884i
\(677\) 0 0 −0.988831 0.149042i \(-0.952381\pi\)
0.988831 + 0.149042i \(0.0476190\pi\)
\(678\) 0 0
\(679\) 1.73305 + 0.680173i 1.73305 + 0.680173i
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 0 0 0.563320 0.826239i \(-0.309524\pi\)
−0.563320 + 0.826239i \(0.690476\pi\)
\(684\) 1.73305 + 0.680173i 1.73305 + 0.680173i
\(685\) 0 0
\(686\) 0 0
\(687\) 0.258149 0.149042i 0.258149 0.149042i
\(688\) 0.266948 0.680173i 0.266948 0.680173i
\(689\) 0 0
\(690\) 0 0
\(691\) 1.72721 + 0.129436i 1.72721 + 0.129436i 0.900969 0.433884i \(-0.142857\pi\)
0.826239 + 0.563320i \(0.190476\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 0 0
\(696\) 0 0
\(697\) 0 0
\(698\) 0 0
\(699\) 0 0
\(700\) −0.733052 0.680173i −0.733052 0.680173i
\(701\) 0 0 0.623490 0.781831i \(-0.285714\pi\)
−0.623490 + 0.781831i \(0.714286\pi\)
\(702\) 0 0
\(703\) 1.04876 + 0.323500i 1.04876 + 0.323500i
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 0 0
\(708\) 0 0
\(709\) −0.290611 0.0663300i −0.290611 0.0663300i 0.0747301 0.997204i \(-0.476190\pi\)
−0.365341 + 0.930874i \(0.619048\pi\)
\(710\) 0 0
\(711\) −0.440071 0.0663300i −0.440071 0.0663300i
\(712\) 0 0
\(713\) 0 0
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) 0 0 −0.900969 0.433884i \(-0.857143\pi\)
0.900969 + 0.433884i \(0.142857\pi\)
\(720\) 0 0
\(721\) −0.658322 0.317031i −0.658322 0.317031i
\(722\) 0 0
\(723\) −0.590232 0.636119i −0.590232 0.636119i
\(724\) −0.603718 + 1.53825i −0.603718 + 1.53825i
\(725\) 0 0
\(726\) 0 0
\(727\) 1.80194 0.867767i 1.80194 0.867767i 0.900969 0.433884i \(-0.142857\pi\)
0.900969 0.433884i \(-0.142857\pi\)
\(728\) 0 0
\(729\) −0.900969 0.433884i −0.900969 0.433884i
\(730\) 0 0
\(731\) 0 0
\(732\) 1.21135 + 0.825886i 1.21135 + 0.825886i
\(733\) −1.45557 0.571270i −1.45557 0.571270i −0.500000 0.866025i \(-0.666667\pi\)
−0.955573 + 0.294755i \(0.904762\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 0 0
\(738\) 0 0
\(739\) 1.94440 + 0.443797i 1.94440 + 0.443797i 0.988831 + 0.149042i \(0.0476190\pi\)
0.955573 + 0.294755i \(0.0952381\pi\)
\(740\) 0 0
\(741\) −1.61232 + 0.930874i −1.61232 + 0.930874i
\(742\) 0 0
\(743\) 0 0 0.563320 0.826239i \(-0.309524\pi\)
−0.563320 + 0.826239i \(0.690476\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) 0 0
\(750\) 0 0
\(751\) −1.63402 + 1.11406i −1.63402 + 1.11406i −0.733052 + 0.680173i \(0.761905\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 0 0
\(756\) −0.222521 0.974928i −0.222521 0.974928i
\(757\) 1.72188 0.531130i 1.72188 0.531130i 0.733052 0.680173i \(-0.238095\pi\)
0.988831 + 0.149042i \(0.0476190\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 0 0 −0.974928 0.222521i \(-0.928571\pi\)
0.974928 + 0.222521i \(0.0714286\pi\)
\(762\) 0 0
\(763\) −0.587862 1.90580i −0.587862 1.90580i
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 0 0
\(768\) −0.0747301 0.997204i −0.0747301 0.997204i
\(769\) 0.258149 1.71271i 0.258149 1.71271i −0.365341 0.930874i \(-0.619048\pi\)
0.623490 0.781831i \(-0.285714\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) −0.766310 0.825886i −0.766310 0.825886i
\(773\) 0 0 −0.930874 0.365341i \(-0.880952\pi\)
0.930874 + 0.365341i \(0.119048\pi\)
\(774\) 0 0
\(775\) 0.290611 1.92808i 0.290611 1.92808i
\(776\) 0 0
\(777\) −0.173761 0.563320i −0.173761 0.563320i
\(778\) 0 0
\(779\) 0 0
\(780\) 0 0
\(781\) 0 0
\(782\) 0 0
\(783\) 0 0
\(784\) 0.623490 0.781831i 0.623490 0.781831i
\(785\) 0 0
\(786\) 0 0
\(787\) −0.332083 + 0.487076i −0.332083 + 0.487076i −0.955573 0.294755i \(-0.904762\pi\)
0.623490 + 0.781831i \(0.285714\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 0 0
\(792\) 0 0
\(793\) −1.40097 + 0.432142i −1.40097 + 0.432142i
\(794\) 0 0
\(795\) 0 0
\(796\) −1.88980 0.582926i −1.88980 0.582926i
\(797\) 0 0 0.988831 0.149042i \(-0.0476190\pi\)
−0.988831 + 0.149042i \(0.952381\pi\)
\(798\) 0 0
\(799\) 0 0
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) 0 0
\(804\) −0.590232 0.636119i −0.590232 0.636119i
\(805\) 0 0
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) 0 0 0.623490 0.781831i \(-0.285714\pi\)
−0.623490 + 0.781831i \(0.714286\pi\)
\(810\) 0 0
\(811\) 1.09839 + 0.250701i 1.09839 + 0.250701i 0.733052 0.680173i \(-0.238095\pi\)
0.365341 + 0.930874i \(0.380952\pi\)
\(812\) 0 0
\(813\) 0.587862 1.90580i 0.587862 1.90580i
\(814\) 0 0
\(815\) 0 0
\(816\) 0 0
\(817\) −0.766310 1.12397i −0.766310 1.12397i
\(818\) 0 0
\(819\) 0.900969 + 0.433884i 0.900969 + 0.433884i
\(820\) 0 0
\(821\) 0 0 0.294755 0.955573i \(-0.404762\pi\)
−0.294755 + 0.955573i \(0.595238\pi\)
\(822\) 0 0
\(823\) 0.0931869 + 1.24349i 0.0931869 + 1.24349i 0.826239 + 0.563320i \(0.190476\pi\)
−0.733052 + 0.680173i \(0.761905\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) 0 0 0.433884 0.900969i \(-0.357143\pi\)
−0.433884 + 0.900969i \(0.642857\pi\)
\(828\) 0 0
\(829\) 0.425270 1.86323i 0.425270 1.86323i −0.0747301 0.997204i \(-0.523810\pi\)
0.500000 0.866025i \(-0.333333\pi\)
\(830\) 0 0
\(831\) −0.0546039 + 0.139129i −0.0546039 + 0.139129i
\(832\) 0.826239 + 0.563320i 0.826239 + 0.563320i
\(833\) 0 0
\(834\) 0 0
\(835\) 0 0
\(836\) 0 0
\(837\) 1.32624 1.42935i 1.32624 1.42935i
\(838\) 0 0
\(839\) 0 0 −0.563320 0.826239i \(-0.690476\pi\)
0.563320 + 0.826239i \(0.309524\pi\)
\(840\) 0 0
\(841\) 0.0747301 0.997204i 0.0747301 0.997204i
\(842\) 0 0
\(843\) 0 0
\(844\) −1.88980 + 0.284841i −1.88980 + 0.284841i
\(845\) 0 0
\(846\) 0 0
\(847\) −0.0747301 + 0.997204i −0.0747301 + 0.997204i
\(848\) 0 0
\(849\) 1.32091 + 0.636119i 1.32091 + 0.636119i
\(850\) 0 0
\(851\) 0 0
\(852\) 0 0
\(853\) 1.52446 0.347948i 1.52446 0.347948i 0.623490 0.781831i \(-0.285714\pi\)
0.900969 + 0.433884i \(0.142857\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) 0 0 −0.365341 0.930874i \(-0.619048\pi\)
0.365341 + 0.930874i \(0.380952\pi\)
\(858\) 0 0
\(859\) 1.88980 0.582926i 1.88980 0.582926i 0.900969 0.433884i \(-0.142857\pi\)
0.988831 0.149042i \(-0.0476190\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(864\) 0 0
\(865\) 0 0
\(866\) 0 0
\(867\) −0.365341 0.930874i −0.365341 0.930874i
\(868\) 1.94440 + 0.145713i 1.94440 + 0.145713i
\(869\) 0 0
\(870\) 0 0
\(871\) 0.865341 0.0648483i 0.865341 0.0648483i
\(872\) 0 0
\(873\) −1.73305 + 0.680173i −1.73305 + 0.680173i
\(874\) 0 0
\(875\) 0 0
\(876\) 0.590232 1.22563i 0.590232 1.22563i
\(877\) 0.678448 + 1.40881i 0.678448 + 1.40881i 0.900969 + 0.433884i \(0.142857\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(882\) 0 0
\(883\) −1.65248 −1.65248 −0.826239 0.563320i \(-0.809524\pi\)
−0.826239 + 0.563320i \(0.809524\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) 0 0 0.0747301 0.997204i \(-0.476190\pi\)
−0.0747301 + 0.997204i \(0.523810\pi\)
\(888\) 0 0
\(889\) 1.23305 1.54620i 1.23305 1.54620i
\(890\) 0 0
\(891\) 0 0
\(892\) −1.09839 1.61105i −1.09839 1.61105i
\(893\) 0 0
\(894\) 0 0
\(895\) 0 0
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) 0 0
\(900\) 1.00000 1.00000
\(901\) 0 0
\(902\) 0 0
\(903\) −0.266948 + 0.680173i −0.266948 + 0.680173i
\(904\) 0 0
\(905\) 0 0
\(906\) 0 0
\(907\) −0.0931869 + 0.116853i −0.0931869 + 0.116853i −0.826239 0.563320i \(-0.809524\pi\)
0.733052 + 0.680173i \(0.238095\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) 0 0 −0.222521 0.974928i \(-0.571429\pi\)
0.222521 + 0.974928i \(0.428571\pi\)
\(912\) −1.61232 0.930874i −1.61232 0.930874i
\(913\) 0 0
\(914\) 0 0
\(915\) 0 0
\(916\) −0.277479 + 0.108903i −0.277479 + 0.108903i
\(917\) 0 0
\(918\) 0 0
\(919\) 0.367711 + 1.61105i 0.367711 + 1.61105i 0.733052 + 0.680173i \(0.238095\pi\)
−0.365341 + 0.930874i \(0.619048\pi\)
\(920\) 0 0
\(921\) 0.678448 1.40881i 0.678448 1.40881i
\(922\) 0 0
\(923\) 0 0
\(924\) 0 0
\(925\) 0.587862 0.0440542i 0.587862 0.0440542i
\(926\) 0 0
\(927\) 0.698220 0.215372i 0.698220 0.215372i
\(928\) 0 0
\(929\) 0 0 0.781831 0.623490i \(-0.214286\pi\)
−0.781831 + 0.623490i \(0.785714\pi\)
\(930\) 0 0
\(931\) −0.548760 1.77904i −0.548760 1.77904i
\(932\) 0 0
\(933\) 0 0
\(934\) 0 0
\(935\) 0 0
\(936\) 0 0
\(937\) −1.78181 0.858075i −1.78181 0.858075i −0.955573 0.294755i \(-0.904762\pi\)
−0.826239 0.563320i \(-0.809524\pi\)
\(938\) 0 0
\(939\) 1.57906 + 1.07659i 1.57906 + 1.07659i
\(940\) 0 0
\(941\) 0 0 −0.563320 0.826239i \(-0.690476\pi\)
0.563320 + 0.826239i \(0.309524\pi\)
\(942\) 0 0
\(943\) 0 0
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) 0 0 −0.563320 0.826239i \(-0.690476\pi\)
0.563320 + 0.826239i \(0.309524\pi\)
\(948\) 0.425270 + 0.131178i 0.425270 + 0.131178i
\(949\) 0.590232 + 1.22563i 0.590232 + 1.22563i
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) 0 0 −0.733052 0.680173i \(-0.761905\pi\)
0.733052 + 0.680173i \(0.238095\pi\)
\(954\) 0 0
\(955\) 0 0
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) 0 0
\(960\) 0 0
\(961\) 1.40097 + 2.42655i 1.40097 + 2.42655i
\(962\) 0 0
\(963\) 0 0
\(964\) 0.488831 + 0.716983i 0.488831 + 0.716983i
\(965\) 0 0
\(966\) 0 0
\(967\) −0.233052 + 0.185853i −0.233052 + 0.185853i −0.733052 0.680173i \(-0.761905\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) 0 0 0.623490 0.781831i \(-0.285714\pi\)
−0.623490 + 0.781831i \(0.714286\pi\)
\(972\) 0.826239 + 0.563320i 0.826239 + 0.563320i
\(973\) −0.134659 1.79690i −0.134659 1.79690i
\(974\) 0 0
\(975\) −0.623490 + 0.781831i −0.623490 + 0.781831i
\(976\) −1.07473 0.997204i −1.07473 0.997204i
\(977\) 0 0 −0.433884 0.900969i \(-0.642857\pi\)
0.433884 + 0.900969i \(0.357143\pi\)
\(978\) 0 0
\(979\) 0 0
\(980\) 0 0
\(981\) 1.72721 + 0.997204i 1.72721 + 0.997204i
\(982\) 0 0
\(983\) 0 0 −0.997204 0.0747301i \(-0.976190\pi\)
0.997204 + 0.0747301i \(0.0238095\pi\)
\(984\) 0 0
\(985\) 0 0
\(986\) 0 0
\(987\) 0 0
\(988\) 1.73305 0.680173i 1.73305 0.680173i
\(989\) 0 0
\(990\) 0 0
\(991\) 0.455573 + 0.571270i 0.455573 + 0.571270i 0.955573 0.294755i \(-0.0952381\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(992\) 0 0
\(993\) 0.233052 0.185853i 0.233052 0.185853i
\(994\) 0 0
\(995\) 0 0
\(996\) 0 0
\(997\) 0.733052 0.680173i 0.733052 0.680173i −0.222521 0.974928i \(-0.571429\pi\)
0.955573 + 0.294755i \(0.0952381\pi\)
\(998\) 0 0
\(999\) 0.510531 + 0.294755i 0.510531 + 0.294755i
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 1911.1.ds.a.1271.1 yes 12
3.2 odd 2 CM 1911.1.ds.a.1271.1 yes 12
13.4 even 6 1911.1.da.a.95.1 12
39.17 odd 6 1911.1.da.a.95.1 12
49.16 even 21 1911.1.da.a.1388.1 yes 12
147.65 odd 42 1911.1.da.a.1388.1 yes 12
637.212 even 42 inner 1911.1.ds.a.212.1 yes 12
1911.212 odd 42 inner 1911.1.ds.a.212.1 yes 12
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1911.1.da.a.95.1 12 13.4 even 6
1911.1.da.a.95.1 12 39.17 odd 6
1911.1.da.a.1388.1 yes 12 49.16 even 21
1911.1.da.a.1388.1 yes 12 147.65 odd 42
1911.1.ds.a.212.1 yes 12 637.212 even 42 inner
1911.1.ds.a.212.1 yes 12 1911.212 odd 42 inner
1911.1.ds.a.1271.1 yes 12 1.1 even 1 trivial
1911.1.ds.a.1271.1 yes 12 3.2 odd 2 CM