Properties

Label 964.1.bh.a.159.1
Level $964$
Weight $1$
Character 964.159
Analytic conductor $0.481$
Analytic rank $0$
Dimension $16$
Projective image $D_{60}$
CM discriminant -4
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [964,1,Mod(83,964)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(964, base_ring=CyclotomicField(60))
 
chi = DirichletCharacter(H, H._module([30, 37]))
 
N = Newforms(chi, 1, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("964.83");
 
S:= CuspForms(chi, 1);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 964 = 2^{2} \cdot 241 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 964.bh (of order \(60\), degree \(16\), 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: \(0.481098672178\)
Analytic rank: \(0\)
Dimension: \(16\)
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: \(\Z[a_1, \ldots, a_{9}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Projective image: \(D_{60}\)
Projective field: Galois closure of \(\mathbb{Q}[x]/(x^{60} - \cdots)\)

Embedding invariants

Embedding label 159.1
Root \(0.207912 + 0.978148i\) of defining polynomial
Character \(\chi\) \(=\) 964.159
Dual form 964.1.bh.a.867.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.866025 - 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{4} +(0.786610 - 1.08268i) q^{5} -1.00000i q^{8} +(-0.669131 - 0.743145i) q^{9} +O(q^{10})\) \(q+(-0.866025 - 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{4} +(0.786610 - 1.08268i) q^{5} -1.00000i q^{8} +(-0.669131 - 0.743145i) q^{9} +(-1.22256 + 0.544320i) q^{10} +(1.01693 - 0.390362i) q^{13} +(-0.500000 + 0.866025i) q^{16} +(-1.49452 - 0.761497i) q^{17} +(0.207912 + 0.978148i) q^{18} +(1.33093 + 0.139886i) q^{20} +(-0.244415 - 0.752232i) q^{25} +(-1.07587 - 0.170401i) q^{26} +(-0.873619 + 0.786610i) q^{29} +(0.866025 - 0.500000i) q^{32} +(0.913545 + 1.40674i) q^{34} +(0.309017 - 0.951057i) q^{36} +(1.32028 + 0.506809i) q^{37} +(-1.08268 - 0.786610i) q^{40} +(1.64728 - 0.535233i) q^{41} +(-1.33093 + 0.139886i) q^{45} +(-0.406737 + 0.913545i) q^{49} +(-0.164446 + 0.773659i) q^{50} +(0.846528 + 0.685505i) q^{52} +(-0.309017 - 1.45381i) q^{53} +(1.14988 - 0.244415i) q^{58} +(-0.363271 - 0.500000i) q^{61} -1.00000 q^{64} +(0.377291 - 1.40807i) q^{65} +(-0.0877853 - 1.67504i) q^{68} +(-0.743145 + 0.669131i) q^{72} +(-0.142040 - 0.896802i) q^{73} +(-0.889993 - 1.09905i) q^{74} +(0.544320 + 1.22256i) q^{80} +(-0.104528 + 0.994522i) q^{81} +(-1.69420 - 0.360114i) q^{82} +(-2.00006 + 1.01908i) q^{85} +(0.185505 + 0.692314i) q^{89} +(1.22256 + 0.544320i) q^{90} +(0.978148 - 0.207912i) q^{97} +(0.809017 - 0.587785i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16 q + 8 q^{4} - 2 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 16 q + 8 q^{4} - 2 q^{9} + 2 q^{10} + 4 q^{13} - 8 q^{16} - 8 q^{17} - 2 q^{26} + 2 q^{34} - 4 q^{36} + 2 q^{37} + 4 q^{40} + 2 q^{52} + 4 q^{53} - 16 q^{64} - 18 q^{65} + 8 q^{68} + 4 q^{73} - 2 q^{74} + 2 q^{81} - 2 q^{85} - 4 q^{89} - 2 q^{90} - 2 q^{97} + 4 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/964\mathbb{Z}\right)^\times\).

\(n\) \(483\) \(489\)
\(\chi(n)\) \(-1\) \(e\left(\frac{19}{60}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.866025 0.500000i −0.866025 0.500000i
\(3\) 0 0 0.406737 0.913545i \(-0.366667\pi\)
−0.406737 + 0.913545i \(0.633333\pi\)
\(4\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(5\) 0.786610 1.08268i 0.786610 1.08268i −0.207912 0.978148i \(-0.566667\pi\)
0.994522 0.104528i \(-0.0333333\pi\)
\(6\) 0 0
\(7\) 0 0 −0.544639 0.838671i \(-0.683333\pi\)
0.544639 + 0.838671i \(0.316667\pi\)
\(8\) 1.00000i 1.00000i
\(9\) −0.669131 0.743145i −0.669131 0.743145i
\(10\) −1.22256 + 0.544320i −1.22256 + 0.544320i
\(11\) 0 0 0.965926 0.258819i \(-0.0833333\pi\)
−0.965926 + 0.258819i \(0.916667\pi\)
\(12\) 0 0
\(13\) 1.01693 0.390362i 1.01693 0.390362i 0.207912 0.978148i \(-0.433333\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(17\) −1.49452 0.761497i −1.49452 0.761497i −0.500000 0.866025i \(-0.666667\pi\)
−0.994522 + 0.104528i \(0.966667\pi\)
\(18\) 0.207912 + 0.978148i 0.207912 + 0.978148i
\(19\) 0 0 0.965926 0.258819i \(-0.0833333\pi\)
−0.965926 + 0.258819i \(0.916667\pi\)
\(20\) 1.33093 + 0.139886i 1.33093 + 0.139886i
\(21\) 0 0
\(22\) 0 0
\(23\) 0 0 −0.987688 0.156434i \(-0.950000\pi\)
0.987688 + 0.156434i \(0.0500000\pi\)
\(24\) 0 0
\(25\) −0.244415 0.752232i −0.244415 0.752232i
\(26\) −1.07587 0.170401i −1.07587 0.170401i
\(27\) 0 0
\(28\) 0 0
\(29\) −0.873619 + 0.786610i −0.873619 + 0.786610i −0.978148 0.207912i \(-0.933333\pi\)
0.104528 + 0.994522i \(0.466667\pi\)
\(30\) 0 0
\(31\) 0 0 0.838671 0.544639i \(-0.183333\pi\)
−0.838671 + 0.544639i \(0.816667\pi\)
\(32\) 0.866025 0.500000i 0.866025 0.500000i
\(33\) 0 0
\(34\) 0.913545 + 1.40674i 0.913545 + 1.40674i
\(35\) 0 0
\(36\) 0.309017 0.951057i 0.309017 0.951057i
\(37\) 1.32028 + 0.506809i 1.32028 + 0.506809i 0.913545 0.406737i \(-0.133333\pi\)
0.406737 + 0.913545i \(0.366667\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) −1.08268 0.786610i −1.08268 0.786610i
\(41\) 1.64728 0.535233i 1.64728 0.535233i 0.669131 0.743145i \(-0.266667\pi\)
0.978148 + 0.207912i \(0.0666667\pi\)
\(42\) 0 0
\(43\) 0 0 −0.453990 0.891007i \(-0.650000\pi\)
0.453990 + 0.891007i \(0.350000\pi\)
\(44\) 0 0
\(45\) −1.33093 + 0.139886i −1.33093 + 0.139886i
\(46\) 0 0
\(47\) 0 0 −0.951057 0.309017i \(-0.900000\pi\)
0.951057 + 0.309017i \(0.100000\pi\)
\(48\) 0 0
\(49\) −0.406737 + 0.913545i −0.406737 + 0.913545i
\(50\) −0.164446 + 0.773659i −0.164446 + 0.773659i
\(51\) 0 0
\(52\) 0.846528 + 0.685505i 0.846528 + 0.685505i
\(53\) −0.309017 1.45381i −0.309017 1.45381i −0.809017 0.587785i \(-0.800000\pi\)
0.500000 0.866025i \(-0.333333\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 0 0
\(57\) 0 0
\(58\) 1.14988 0.244415i 1.14988 0.244415i
\(59\) 0 0 −0.406737 0.913545i \(-0.633333\pi\)
0.406737 + 0.913545i \(0.366667\pi\)
\(60\) 0 0
\(61\) −0.363271 0.500000i −0.363271 0.500000i 0.587785 0.809017i \(-0.300000\pi\)
−0.951057 + 0.309017i \(0.900000\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) −1.00000 −1.00000
\(65\) 0.377291 1.40807i 0.377291 1.40807i
\(66\) 0 0
\(67\) 0 0 0.207912 0.978148i \(-0.433333\pi\)
−0.207912 + 0.978148i \(0.566667\pi\)
\(68\) −0.0877853 1.67504i −0.0877853 1.67504i
\(69\) 0 0
\(70\) 0 0
\(71\) 0 0 −0.998630 0.0523360i \(-0.983333\pi\)
0.998630 + 0.0523360i \(0.0166667\pi\)
\(72\) −0.743145 + 0.669131i −0.743145 + 0.669131i
\(73\) −0.142040 0.896802i −0.142040 0.896802i −0.951057 0.309017i \(-0.900000\pi\)
0.809017 0.587785i \(-0.200000\pi\)
\(74\) −0.889993 1.09905i −0.889993 1.09905i
\(75\) 0 0
\(76\) 0 0
\(77\) 0 0
\(78\) 0 0
\(79\) 0 0 0.587785 0.809017i \(-0.300000\pi\)
−0.587785 + 0.809017i \(0.700000\pi\)
\(80\) 0.544320 + 1.22256i 0.544320 + 1.22256i
\(81\) −0.104528 + 0.994522i −0.104528 + 0.994522i
\(82\) −1.69420 0.360114i −1.69420 0.360114i
\(83\) 0 0 0.913545 0.406737i \(-0.133333\pi\)
−0.913545 + 0.406737i \(0.866667\pi\)
\(84\) 0 0
\(85\) −2.00006 + 1.01908i −2.00006 + 1.01908i
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 0.185505 + 0.692314i 0.185505 + 0.692314i 0.994522 + 0.104528i \(0.0333333\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(90\) 1.22256 + 0.544320i 1.22256 + 0.544320i
\(91\) 0 0
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 0 0
\(96\) 0 0
\(97\) 0.978148 0.207912i 0.978148 0.207912i 0.309017 0.951057i \(-0.400000\pi\)
0.669131 + 0.743145i \(0.266667\pi\)
\(98\) 0.809017 0.587785i 0.809017 0.587785i
\(99\) 0 0
\(100\) 0.529244 0.587785i 0.529244 0.587785i
\(101\) 0.705634 + 1.38488i 0.705634 + 1.38488i 0.913545 + 0.406737i \(0.133333\pi\)
−0.207912 + 0.978148i \(0.566667\pi\)
\(102\) 0 0
\(103\) 0 0 0.891007 0.453990i \(-0.150000\pi\)
−0.891007 + 0.453990i \(0.850000\pi\)
\(104\) −0.390362 1.01693i −0.390362 1.01693i
\(105\) 0 0
\(106\) −0.459289 + 1.41355i −0.459289 + 1.41355i
\(107\) 0 0 0.669131 0.743145i \(-0.266667\pi\)
−0.669131 + 0.743145i \(0.733333\pi\)
\(108\) 0 0
\(109\) −1.66365 + 0.638616i −1.66365 + 0.638616i −0.994522 0.104528i \(-0.966667\pi\)
−0.669131 + 0.743145i \(0.733333\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) 1.69420 + 0.978148i 1.69420 + 0.978148i 0.951057 + 0.309017i \(0.100000\pi\)
0.743145 + 0.669131i \(0.233333\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) −1.11803 0.363271i −1.11803 0.363271i
\(117\) −0.970554 0.494522i −0.970554 0.494522i
\(118\) 0 0
\(119\) 0 0
\(120\) 0 0
\(121\) 0.866025 0.500000i 0.866025 0.500000i
\(122\) 0.0646021 + 0.614648i 0.0646021 + 0.614648i
\(123\) 0 0
\(124\) 0 0
\(125\) 0.266080 + 0.0864545i 0.266080 + 0.0864545i
\(126\) 0 0
\(127\) 0 0 0.629320 0.777146i \(-0.283333\pi\)
−0.629320 + 0.777146i \(0.716667\pi\)
\(128\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(129\) 0 0
\(130\) −1.03078 + 1.03078i −1.03078 + 1.03078i
\(131\) 0 0 0.777146 0.629320i \(-0.216667\pi\)
−0.777146 + 0.629320i \(0.783333\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 0 0
\(135\) 0 0
\(136\) −0.761497 + 1.49452i −0.761497 + 1.49452i
\(137\) 0.451057 + 1.17504i 0.451057 + 1.17504i 0.951057 + 0.309017i \(0.100000\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(138\) 0 0
\(139\) 0 0 0.987688 0.156434i \(-0.0500000\pi\)
−0.987688 + 0.156434i \(0.950000\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 0 0
\(144\) 0.978148 0.207912i 0.978148 0.207912i
\(145\) 0.164446 + 1.56460i 0.164446 + 1.56460i
\(146\) −0.325391 + 0.847673i −0.325391 + 0.847673i
\(147\) 0 0
\(148\) 0.221232 + 1.39680i 0.221232 + 1.39680i
\(149\) 0.669131 + 1.74314i 0.669131 + 1.74314i 0.669131 + 0.743145i \(0.266667\pi\)
1.00000i \(0.5\pi\)
\(150\) 0 0
\(151\) 0 0 −0.913545 0.406737i \(-0.866667\pi\)
0.913545 + 0.406737i \(0.133333\pi\)
\(152\) 0 0
\(153\) 0.434128 + 1.62019i 0.434128 + 1.62019i
\(154\) 0 0
\(155\) 0 0
\(156\) 0 0
\(157\) −0.0658722 0.0813454i −0.0658722 0.0813454i 0.743145 0.669131i \(-0.233333\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0.139886 1.33093i 0.139886 1.33093i
\(161\) 0 0
\(162\) 0.587785 0.809017i 0.587785 0.809017i
\(163\) 0 0 0.544639 0.838671i \(-0.316667\pi\)
−0.544639 + 0.838671i \(0.683333\pi\)
\(164\) 1.28716 + 1.15897i 1.28716 + 1.15897i
\(165\) 0 0
\(166\) 0 0
\(167\) 0 0 −0.629320 0.777146i \(-0.716667\pi\)
0.629320 + 0.777146i \(0.283333\pi\)
\(168\) 0 0
\(169\) 0.138616 0.124811i 0.138616 0.124811i
\(170\) 2.24164 + 0.117480i 2.24164 + 0.117480i
\(171\) 0 0
\(172\) 0 0
\(173\) −0.104528 1.99452i −0.104528 1.99452i −0.104528 0.994522i \(-0.533333\pi\)
1.00000i \(-0.5\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) 0 0
\(178\) 0.185505 0.692314i 0.185505 0.692314i
\(179\) 0 0 0.998630 0.0523360i \(-0.0166667\pi\)
−0.998630 + 0.0523360i \(0.983333\pi\)
\(180\) −0.786610 1.08268i −0.786610 1.08268i
\(181\) −0.951057 + 1.64728i −0.951057 + 1.64728i −0.207912 + 0.978148i \(0.566667\pi\)
−0.743145 + 0.669131i \(0.766667\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 1.58726 1.03078i 1.58726 1.03078i
\(186\) 0 0
\(187\) 0 0
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 0 0 0.207912 0.978148i \(-0.433333\pi\)
−0.207912 + 0.978148i \(0.566667\pi\)
\(192\) 0 0
\(193\) 1.07394 + 1.47815i 1.07394 + 1.47815i 0.866025 + 0.500000i \(0.166667\pi\)
0.207912 + 0.978148i \(0.433333\pi\)
\(194\) −0.951057 0.309017i −0.951057 0.309017i
\(195\) 0 0
\(196\) −0.994522 + 0.104528i −0.994522 + 0.104528i
\(197\) −1.32028 1.32028i −1.32028 1.32028i −0.913545 0.406737i \(-0.866667\pi\)
−0.406737 0.913545i \(-0.633333\pi\)
\(198\) 0 0
\(199\) 0 0 −0.933580 0.358368i \(-0.883333\pi\)
0.933580 + 0.358368i \(0.116667\pi\)
\(200\) −0.752232 + 0.244415i −0.752232 + 0.244415i
\(201\) 0 0
\(202\) 0.0813454 1.55216i 0.0813454 1.55216i
\(203\) 0 0
\(204\) 0 0
\(205\) 0.716282 2.20449i 0.716282 2.20449i
\(206\) 0 0
\(207\) 0 0
\(208\) −0.170401 + 1.07587i −0.170401 + 1.07587i
\(209\) 0 0
\(210\) 0 0
\(211\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(212\) 1.10453 0.994522i 1.10453 0.994522i
\(213\) 0 0
\(214\) 0 0
\(215\) 0 0
\(216\) 0 0
\(217\) 0 0
\(218\) 1.76007 + 0.278768i 1.76007 + 0.278768i
\(219\) 0 0
\(220\) 0 0
\(221\) −1.81708 0.190983i −1.81708 0.190983i
\(222\) 0 0
\(223\) 0 0 −0.207912 0.978148i \(-0.566667\pi\)
0.207912 + 0.978148i \(0.433333\pi\)
\(224\) 0 0
\(225\) −0.395472 + 0.684977i −0.395472 + 0.684977i
\(226\) −0.978148 1.69420i −0.978148 1.69420i
\(227\) 0 0 −0.0523360 0.998630i \(-0.516667\pi\)
0.0523360 + 0.998630i \(0.483333\pi\)
\(228\) 0 0
\(229\) 0.809017 0.0850311i 0.809017 0.0850311i 0.309017 0.951057i \(-0.400000\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0.786610 + 0.873619i 0.786610 + 0.873619i
\(233\) 1.61803i 1.61803i 0.587785 + 0.809017i \(0.300000\pi\)
−0.587785 + 0.809017i \(0.700000\pi\)
\(234\) 0.593263 + 0.913545i 0.593263 + 0.913545i
\(235\) 0 0
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(240\) 0 0
\(241\) −1.00000 −1.00000
\(242\) −1.00000 −1.00000
\(243\) 0 0
\(244\) 0.251377 0.564602i 0.251377 0.564602i
\(245\) 0.669131 + 1.15897i 0.669131 + 1.15897i
\(246\) 0 0
\(247\) 0 0
\(248\) 0 0
\(249\) 0 0
\(250\) −0.187205 0.207912i −0.187205 0.207912i
\(251\) 0 0 0.913545 0.406737i \(-0.133333\pi\)
−0.913545 + 0.406737i \(0.866667\pi\)
\(252\) 0 0
\(253\) 0 0
\(254\) 0 0
\(255\) 0 0
\(256\) −0.500000 0.866025i −0.500000 0.866025i
\(257\) −0.978148 + 1.69420i −0.978148 + 1.69420i −0.309017 + 0.951057i \(0.600000\pi\)
−0.669131 + 0.743145i \(0.733333\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 1.40807 0.377291i 1.40807 0.377291i
\(261\) 1.16913 + 0.122881i 1.16913 + 0.122881i
\(262\) 0 0
\(263\) 0 0 −0.965926 0.258819i \(-0.916667\pi\)
0.965926 + 0.258819i \(0.0833333\pi\)
\(264\) 0 0
\(265\) −1.81708 0.809017i −1.81708 0.809017i
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) −0.571411 + 1.12146i −0.571411 + 1.12146i 0.406737 + 0.913545i \(0.366667\pi\)
−0.978148 + 0.207912i \(0.933333\pi\)
\(270\) 0 0
\(271\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(272\) 1.40674 0.913545i 1.40674 0.913545i
\(273\) 0 0
\(274\) 0.196895 1.24314i 0.196895 1.24314i
\(275\) 0 0
\(276\) 0 0
\(277\) −0.564602 + 1.73767i −0.564602 + 1.73767i 0.104528 + 0.994522i \(0.466667\pi\)
−0.669131 + 0.743145i \(0.733333\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) −1.60917 1.16913i −1.60917 1.16913i −0.866025 0.500000i \(-0.833333\pi\)
−0.743145 0.669131i \(-0.766667\pi\)
\(282\) 0 0
\(283\) 0 0 −0.933580 0.358368i \(-0.883333\pi\)
0.933580 + 0.358368i \(0.116667\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 0 0
\(288\) −0.951057 0.309017i −0.951057 0.309017i
\(289\) 1.06593 + 1.46713i 1.06593 + 1.46713i
\(290\) 0.639886 1.43721i 0.639886 1.43721i
\(291\) 0 0
\(292\) 0.705634 0.571411i 0.705634 0.571411i
\(293\) −0.978148 0.792088i −0.978148 0.792088i 1.00000i \(-0.5\pi\)
−0.978148 + 0.207912i \(0.933333\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 0.506809 1.32028i 0.506809 1.32028i
\(297\) 0 0
\(298\) 0.292088 1.84417i 0.292088 1.84417i
\(299\) 0 0
\(300\) 0 0
\(301\) 0 0
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) −0.827091 −0.827091
\(306\) 0.434128 1.62019i 0.434128 1.62019i
\(307\) 0 0 0.629320 0.777146i \(-0.283333\pi\)
−0.629320 + 0.777146i \(0.716667\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 0 0 −0.838671 0.544639i \(-0.816667\pi\)
0.838671 + 0.544639i \(0.183333\pi\)
\(312\) 0 0
\(313\) 1.41355 1.27276i 1.41355 1.27276i 0.500000 0.866025i \(-0.333333\pi\)
0.913545 0.406737i \(-0.133333\pi\)
\(314\) 0.0163743 + 0.103383i 0.0163743 + 0.103383i
\(315\) 0 0
\(316\) 0 0
\(317\) −1.26007 1.26007i −1.26007 1.26007i −0.951057 0.309017i \(-0.900000\pi\)
−0.309017 0.951057i \(-0.600000\pi\)
\(318\) 0 0
\(319\) 0 0
\(320\) −0.786610 + 1.08268i −0.786610 + 1.08268i
\(321\) 0 0
\(322\) 0 0
\(323\) 0 0
\(324\) −0.913545 + 0.406737i −0.913545 + 0.406737i
\(325\) −0.542195 0.669556i −0.542195 0.669556i
\(326\) 0 0
\(327\) 0 0
\(328\) −0.535233 1.64728i −0.535233 1.64728i
\(329\) 0 0
\(330\) 0 0
\(331\) 0 0 −0.913545 0.406737i \(-0.866667\pi\)
0.913545 + 0.406737i \(0.133333\pi\)
\(332\) 0 0
\(333\) −0.506809 1.32028i −0.506809 1.32028i
\(334\) 0 0
\(335\) 0 0
\(336\) 0 0
\(337\) −0.198825 1.89169i −0.198825 1.89169i −0.406737 0.913545i \(-0.633333\pi\)
0.207912 0.978148i \(-0.433333\pi\)
\(338\) −0.182451 + 0.0387811i −0.182451 + 0.0387811i
\(339\) 0 0
\(340\) −1.88258 1.22256i −1.88258 1.22256i
\(341\) 0 0
\(342\) 0 0
\(343\) 0 0
\(344\) 0 0
\(345\) 0 0
\(346\) −0.906737 + 1.77957i −0.906737 + 1.77957i
\(347\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(348\) 0 0
\(349\) 0.604528 + 0.544320i 0.604528 + 0.544320i 0.913545 0.406737i \(-0.133333\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) 1.55216 0.0813454i 1.55216 0.0813454i 0.743145 0.669131i \(-0.233333\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) −0.506809 + 0.506809i −0.506809 + 0.506809i
\(357\) 0 0
\(358\) 0 0
\(359\) 0 0 0.104528 0.994522i \(-0.466667\pi\)
−0.104528 + 0.994522i \(0.533333\pi\)
\(360\) 0.139886 + 1.33093i 0.139886 + 1.33093i
\(361\) 0.866025 0.500000i 0.866025 0.500000i
\(362\) 1.64728 0.951057i 1.64728 0.951057i
\(363\) 0 0
\(364\) 0 0
\(365\) −1.08268 0.551651i −1.08268 0.551651i
\(366\) 0 0
\(367\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(368\) 0 0
\(369\) −1.50000 0.866025i −1.50000 0.866025i
\(370\) −1.88999 + 0.0990504i −1.88999 + 0.0990504i
\(371\) 0 0
\(372\) 0 0
\(373\) −0.292088 + 0.112122i −0.292088 + 0.112122i −0.500000 0.866025i \(-0.666667\pi\)
0.207912 + 0.978148i \(0.433333\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) −0.581345 + 1.14095i −0.581345 + 1.14095i
\(378\) 0 0
\(379\) 0 0 0.891007 0.453990i \(-0.150000\pi\)
−0.891007 + 0.453990i \(0.850000\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 0 0 −0.838671 0.544639i \(-0.816667\pi\)
0.838671 + 0.544639i \(0.183333\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) −0.190983 1.81708i −0.190983 1.81708i
\(387\) 0 0
\(388\) 0.669131 + 0.743145i 0.669131 + 0.743145i
\(389\) −0.312440 1.97267i −0.312440 1.97267i −0.207912 0.978148i \(-0.566667\pi\)
−0.104528 0.994522i \(-0.533333\pi\)
\(390\) 0 0
\(391\) 0 0
\(392\) 0.913545 + 0.406737i 0.913545 + 0.406737i
\(393\) 0 0
\(394\) 0.483257 + 1.80354i 0.483257 + 1.80354i
\(395\) 0 0
\(396\) 0 0
\(397\) 0.278768 0.142040i 0.278768 0.142040i −0.309017 0.951057i \(-0.600000\pi\)
0.587785 + 0.809017i \(0.300000\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0.773659 + 0.164446i 0.773659 + 0.164446i
\(401\) −0.207912 + 1.97815i −0.207912 + 1.97815i 1.00000i \(0.5\pi\)
−0.207912 + 0.978148i \(0.566667\pi\)
\(402\) 0 0
\(403\) 0 0
\(404\) −0.846528 + 1.30354i −0.846528 + 1.30354i
\(405\) 0.994522 + 0.895472i 0.994522 + 0.895472i
\(406\) 0 0
\(407\) 0 0
\(408\) 0 0
\(409\) −0.302208 1.90807i −0.302208 1.90807i −0.406737 0.913545i \(-0.633333\pi\)
0.104528 0.994522i \(-0.466667\pi\)
\(410\) −1.72256 + 1.55100i −1.72256 + 1.55100i
\(411\) 0 0
\(412\) 0 0
\(413\) 0 0
\(414\) 0 0
\(415\) 0 0
\(416\) 0.685505 0.846528i 0.685505 0.846528i
\(417\) 0 0
\(418\) 0 0
\(419\) 0 0 0.258819 0.965926i \(-0.416667\pi\)
−0.258819 + 0.965926i \(0.583333\pi\)
\(420\) 0 0
\(421\) −0.244415 0.336408i −0.244415 0.336408i 0.669131 0.743145i \(-0.266667\pi\)
−0.913545 + 0.406737i \(0.866667\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) −1.45381 + 0.309017i −1.45381 + 0.309017i
\(425\) −0.207539 + 1.31035i −0.207539 + 1.31035i
\(426\) 0 0
\(427\) 0 0
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 0 0 0.777146 0.629320i \(-0.216667\pi\)
−0.777146 + 0.629320i \(0.783333\pi\)
\(432\) 0 0
\(433\) 0.406737 0.913545i 0.406737 0.913545i −0.587785 0.809017i \(-0.700000\pi\)
0.994522 0.104528i \(-0.0333333\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) −1.38488 1.12146i −1.38488 1.12146i
\(437\) 0 0
\(438\) 0 0
\(439\) 0 0 −0.453990 0.891007i \(-0.650000\pi\)
0.453990 + 0.891007i \(0.350000\pi\)
\(440\) 0 0
\(441\) 0.951057 0.309017i 0.951057 0.309017i
\(442\) 1.47815 + 1.07394i 1.47815 + 1.07394i
\(443\) 0 0 0.0523360 0.998630i \(-0.483333\pi\)
−0.0523360 + 0.998630i \(0.516667\pi\)
\(444\) 0 0
\(445\) 0.895472 + 0.343739i 0.895472 + 0.343739i
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) −0.0809764 + 0.511265i −0.0809764 + 0.511265i 0.913545 + 0.406737i \(0.133333\pi\)
−0.994522 + 0.104528i \(0.966667\pi\)
\(450\) 0.684977 0.395472i 0.684977 0.395472i
\(451\) 0 0
\(452\) 1.95630i 1.95630i
\(453\) 0 0
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) −0.500000 1.53884i −0.500000 1.53884i −0.809017 0.587785i \(-0.800000\pi\)
0.309017 0.951057i \(-0.400000\pi\)
\(458\) −0.743145 0.330869i −0.743145 0.330869i
\(459\) 0 0
\(460\) 0 0
\(461\) 1.95106 0.309017i 1.95106 0.309017i 0.951057 0.309017i \(-0.100000\pi\)
1.00000 \(0\)
\(462\) 0 0
\(463\) 0 0 0.965926 0.258819i \(-0.0833333\pi\)
−0.965926 + 0.258819i \(0.916667\pi\)
\(464\) −0.244415 1.14988i −0.244415 1.14988i
\(465\) 0 0
\(466\) 0.809017 1.40126i 0.809017 1.40126i
\(467\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(468\) −0.0570084 1.08779i −0.0570084 1.08779i
\(469\) 0 0
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) 0 0
\(474\) 0 0
\(475\) 0 0
\(476\) 0 0
\(477\) −0.873619 + 1.20243i −0.873619 + 1.20243i
\(478\) 0 0
\(479\) 0 0 0.406737 0.913545i \(-0.366667\pi\)
−0.406737 + 0.913545i \(0.633333\pi\)
\(480\) 0 0
\(481\) 1.54047 1.54047
\(482\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(483\) 0 0
\(484\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(485\) 0.544320 1.22256i 0.544320 1.22256i
\(486\) 0 0
\(487\) 0 0 0.587785 0.809017i \(-0.300000\pi\)
−0.587785 + 0.809017i \(0.700000\pi\)
\(488\) −0.500000 + 0.363271i −0.500000 + 0.363271i
\(489\) 0 0
\(490\) 1.33826i 1.33826i
\(491\) 0 0 −0.669131 0.743145i \(-0.733333\pi\)
0.669131 + 0.743145i \(0.266667\pi\)
\(492\) 0 0
\(493\) 1.90464 0.510348i 1.90464 0.510348i
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 0 0
\(498\) 0 0
\(499\) 0 0 −0.891007 0.453990i \(-0.850000\pi\)
0.891007 + 0.453990i \(0.150000\pi\)
\(500\) 0.0581680 + 0.273659i 0.0581680 + 0.273659i
\(501\) 0 0
\(502\) 0 0
\(503\) 0 0 0.987688 0.156434i \(-0.0500000\pi\)
−0.987688 + 0.156434i \(0.950000\pi\)
\(504\) 0 0
\(505\) 2.05444 + 0.325391i 2.05444 + 0.325391i
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) −1.53884 + 0.500000i −1.53884 + 0.500000i −0.951057 0.309017i \(-0.900000\pi\)
−0.587785 + 0.809017i \(0.700000\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 1.00000i 1.00000i
\(513\) 0 0
\(514\) 1.69420 0.978148i 1.69420 0.978148i
\(515\) 0 0
\(516\) 0 0
\(517\) 0 0
\(518\) 0 0
\(519\) 0 0
\(520\) −1.40807 0.377291i −1.40807 0.377291i
\(521\) 0.00547810 0.104528i 0.00547810 0.104528i −0.994522 0.104528i \(-0.966667\pi\)
1.00000 \(0\)
\(522\) −0.951057 0.690983i −0.951057 0.690983i
\(523\) 0 0 0.951057 0.309017i \(-0.100000\pi\)
−0.951057 + 0.309017i \(0.900000\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 0 0
\(528\) 0 0
\(529\) 0.951057 + 0.309017i 0.951057 + 0.309017i
\(530\) 1.16913 + 1.60917i 1.16913 + 1.60917i
\(531\) 0 0
\(532\) 0 0
\(533\) 1.46623 1.18733i 1.46623 1.18733i
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) 0 0
\(538\) 1.05558 0.685505i 1.05558 0.685505i
\(539\) 0 0
\(540\) 0 0
\(541\) 0.251377 + 0.564602i 0.251377 + 0.564602i 0.994522 0.104528i \(-0.0333333\pi\)
−0.743145 + 0.669131i \(0.766667\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) −1.67504 + 0.0877853i −1.67504 + 0.0877853i
\(545\) −0.617231 + 2.30354i −0.617231 + 2.30354i
\(546\) 0 0
\(547\) 0 0 0.258819 0.965926i \(-0.416667\pi\)
−0.258819 + 0.965926i \(0.583333\pi\)
\(548\) −0.792088 + 0.978148i −0.792088 + 0.978148i
\(549\) −0.128496 + 0.604528i −0.128496 + 0.604528i
\(550\) 0 0
\(551\) 0 0
\(552\) 0 0
\(553\) 0 0
\(554\) 1.35779 1.22256i 1.35779 1.22256i
\(555\) 0 0
\(556\) 0 0
\(557\) −1.47815 0.155360i −1.47815 0.155360i −0.669131 0.743145i \(-0.733333\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(558\) 0 0
\(559\) 0 0
\(560\) 0 0
\(561\) 0 0
\(562\) 0.809017 + 1.81708i 0.809017 + 1.81708i
\(563\) 0 0 0.104528 0.994522i \(-0.466667\pi\)
−0.104528 + 0.994522i \(0.533333\pi\)
\(564\) 0 0
\(565\) 2.39169 1.06485i 2.39169 1.06485i
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 0.128496 + 0.395472i 0.128496 + 0.395472i 0.994522 0.104528i \(-0.0333333\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(570\) 0 0
\(571\) 0 0 −0.258819 0.965926i \(-0.583333\pi\)
0.258819 + 0.965926i \(0.416667\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 0 0
\(576\) 0.669131 + 0.743145i 0.669131 + 0.743145i
\(577\) −0.557008 + 1.45106i −0.557008 + 1.45106i 0.309017 + 0.951057i \(0.400000\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(578\) −0.189560 1.80354i −0.189560 1.80354i
\(579\) 0 0
\(580\) −1.27276 + 0.924716i −1.27276 + 0.924716i
\(581\) 0 0
\(582\) 0 0
\(583\) 0 0
\(584\) −0.896802 + 0.142040i −0.896802 + 0.142040i
\(585\) −1.29885 + 0.661799i −1.29885 + 0.661799i
\(586\) 0.451057 + 1.17504i 0.451057 + 1.17504i
\(587\) 0 0 0.453990 0.891007i \(-0.350000\pi\)
−0.453990 + 0.891007i \(0.650000\pi\)
\(588\) 0 0
\(589\) 0 0
\(590\) 0 0
\(591\) 0 0
\(592\) −1.09905 + 0.889993i −1.09905 + 0.889993i
\(593\) −1.32028 + 1.32028i −1.32028 + 1.32028i −0.406737 + 0.913545i \(0.633333\pi\)
−0.913545 + 0.406737i \(0.866667\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) −1.17504 + 1.45106i −1.17504 + 1.45106i
\(597\) 0 0
\(598\) 0 0
\(599\) 0 0 −0.891007 0.453990i \(-0.850000\pi\)
0.891007 + 0.453990i \(0.150000\pi\)
\(600\) 0 0
\(601\) −0.155360 1.47815i −0.155360 1.47815i −0.743145 0.669131i \(-0.766667\pi\)
0.587785 0.809017i \(-0.300000\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) 0.139886 1.33093i 0.139886 1.33093i
\(606\) 0 0
\(607\) 0 0 −0.951057 0.309017i \(-0.900000\pi\)
0.951057 + 0.309017i \(0.100000\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0.716282 + 0.413545i 0.716282 + 0.413545i
\(611\) 0 0
\(612\) −1.18606 + 1.18606i −1.18606 + 1.18606i
\(613\) −0.402280 + 0.325760i −0.402280 + 0.325760i −0.809017 0.587785i \(-0.800000\pi\)
0.406737 + 0.913545i \(0.366667\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 0.500000 1.53884i 0.500000 1.53884i −0.309017 0.951057i \(-0.600000\pi\)
0.809017 0.587785i \(-0.200000\pi\)
\(618\) 0 0
\(619\) 0 0 −0.358368 0.933580i \(-0.616667\pi\)
0.358368 + 0.933580i \(0.383333\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 0 0
\(624\) 0 0
\(625\) 0.942790 0.684977i 0.942790 0.684977i
\(626\) −1.86055 + 0.395472i −1.86055 + 0.395472i
\(627\) 0 0
\(628\) 0.0375111 0.0977196i 0.0375111 0.0977196i
\(629\) −1.58726 1.76283i −1.58726 1.76283i
\(630\) 0 0
\(631\) 0 0 −0.358368 0.933580i \(-0.616667\pi\)
0.358368 + 0.933580i \(0.383333\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0.461219 + 1.72129i 0.461219 + 1.72129i
\(635\) 0 0
\(636\) 0 0
\(637\) −0.0570084 + 1.08779i −0.0570084 + 1.08779i
\(638\) 0 0
\(639\) 0 0
\(640\) 1.22256 0.544320i 1.22256 0.544320i
\(641\) 0.978148 + 0.207912i 0.978148 + 0.207912i 0.669131 0.743145i \(-0.266667\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(642\) 0 0
\(643\) 0 0 −0.406737 0.913545i \(-0.633333\pi\)
0.406737 + 0.913545i \(0.366667\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(648\) 0.994522 + 0.104528i 0.994522 + 0.104528i
\(649\) 0 0
\(650\) 0.134777 + 0.850950i 0.134777 + 0.850950i
\(651\) 0 0
\(652\) 0 0
\(653\) −0.601105 0.390362i −0.601105 0.390362i 0.207912 0.978148i \(-0.433333\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) −0.360114 + 1.69420i −0.360114 + 1.69420i
\(657\) −0.571411 + 0.705634i −0.571411 + 0.705634i
\(658\) 0 0
\(659\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(660\) 0 0
\(661\) −1.92920 + 0.101105i −1.92920 + 0.101105i −0.978148 0.207912i \(-0.933333\pi\)
−0.951057 + 0.309017i \(0.900000\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 0 0
\(666\) −0.221232 + 1.39680i −0.221232 + 1.39680i
\(667\) 0 0
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 0 0
\(672\) 0 0
\(673\) −0.128496 + 0.604528i −0.128496 + 0.604528i 0.866025 + 0.500000i \(0.166667\pi\)
−0.994522 + 0.104528i \(0.966667\pi\)
\(674\) −0.773659 + 1.73767i −0.773659 + 1.73767i
\(675\) 0 0
\(676\) 0.177397 + 0.0576399i 0.177397 + 0.0576399i
\(677\) 1.53516 + 1.24314i 1.53516 + 1.24314i 0.866025 + 0.500000i \(0.166667\pi\)
0.669131 + 0.743145i \(0.266667\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 1.01908 + 2.00006i 1.01908 + 2.00006i
\(681\) 0 0
\(682\) 0 0
\(683\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(684\) 0 0
\(685\) 1.62700 + 0.435952i 1.62700 + 0.435952i
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) −0.881761 1.35779i −0.881761 1.35779i
\(690\) 0 0
\(691\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(692\) 1.67504 1.08779i 1.67504 1.08779i
\(693\) 0 0
\(694\) 0 0
\(695\) 0 0
\(696\) 0 0
\(697\) −2.86947 0.454480i −2.86947 0.454480i
\(698\) −0.251377 0.773659i −0.251377 0.773659i
\(699\) 0 0
\(700\) 0 0
\(701\) −1.50133 0.402280i −1.50133 0.402280i −0.587785 0.809017i \(-0.700000\pi\)
−0.913545 + 0.406737i \(0.866667\pi\)
\(702\) 0 0
\(703\) 0 0
\(704\) 0 0
\(705\) 0 0
\(706\) −1.38488 0.705634i −1.38488 0.705634i
\(707\) 0 0
\(708\) 0 0
\(709\) 0.0375111 + 0.715754i 0.0375111 + 0.715754i 0.951057 + 0.309017i \(0.100000\pi\)
−0.913545 + 0.406737i \(0.866667\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0.692314 0.185505i 0.692314 0.185505i
\(713\) 0 0
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(720\) 0.544320 1.22256i 0.544320 1.22256i
\(721\) 0 0
\(722\) −1.00000 −1.00000
\(723\) 0 0
\(724\) −1.90211 −1.90211
\(725\) 0.805239 + 0.464905i 0.805239 + 0.464905i
\(726\) 0 0
\(727\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(728\) 0 0
\(729\) 0.809017 0.587785i 0.809017 0.587785i
\(730\) 0.661799 + 1.01908i 0.661799 + 1.01908i
\(731\) 0 0
\(732\) 0 0
\(733\) −1.58231 + 0.704489i −1.58231 + 0.704489i −0.994522 0.104528i \(-0.966667\pi\)
−0.587785 + 0.809017i \(0.700000\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 0 0
\(738\) 0.866025 + 1.50000i 0.866025 + 1.50000i
\(739\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(740\) 1.68631 + 0.859217i 1.68631 + 0.859217i
\(741\) 0 0
\(742\) 0 0
\(743\) 0 0 −0.994522 0.104528i \(-0.966667\pi\)
0.994522 + 0.104528i \(0.0333333\pi\)
\(744\) 0 0
\(745\) 2.41361 + 0.646724i 2.41361 + 0.646724i
\(746\) 0.309017 + 0.0489435i 0.309017 + 0.0489435i
\(747\) 0 0
\(748\) 0 0
\(749\) 0 0
\(750\) 0 0
\(751\) 0 0 0.453990 0.891007i \(-0.350000\pi\)
−0.453990 + 0.891007i \(0.650000\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 1.07394 0.697423i 1.07394 0.697423i
\(755\) 0 0
\(756\) 0 0
\(757\) −0.494522 0.761497i −0.494522 0.761497i 0.500000 0.866025i \(-0.333333\pi\)
−0.994522 + 0.104528i \(0.966667\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 0.302208 + 0.0809764i 0.302208 + 0.0809764i 0.406737 0.913545i \(-0.366667\pi\)
−0.104528 + 0.994522i \(0.533333\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 0 0
\(765\) 2.09563 + 0.804436i 2.09563 + 0.804436i
\(766\) 0 0
\(767\) 0 0
\(768\) 0 0
\(769\) 1.38488 + 1.12146i 1.38488 + 1.12146i 0.978148 + 0.207912i \(0.0666667\pi\)
0.406737 + 0.913545i \(0.366667\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) −0.743145 + 1.66913i −0.743145 + 1.66913i
\(773\) 0.207912 0.978148i 0.207912 0.978148i −0.743145 0.669131i \(-0.766667\pi\)
0.951057 0.309017i \(-0.100000\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) −0.207912 0.978148i −0.207912 0.978148i
\(777\) 0 0
\(778\) −0.715754 + 1.86460i −0.715754 + 1.86460i
\(779\) 0 0
\(780\) 0 0
\(781\) 0 0
\(782\) 0 0
\(783\) 0 0
\(784\) −0.587785 0.809017i −0.587785 0.809017i
\(785\) −0.139886 + 0.00733113i −0.139886 + 0.00733113i
\(786\) 0 0
\(787\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(788\) 0.483257 1.80354i 0.483257 1.80354i
\(789\) 0 0
\(790\) 0 0
\(791\) 0 0
\(792\) 0 0
\(793\) −0.564602 0.366657i −0.564602 0.366657i
\(794\) −0.312440 0.0163743i −0.312440 0.0163743i
\(795\) 0 0
\(796\) 0 0
\(797\) 0.571411 + 0.705634i 0.571411 + 0.705634i 0.978148 0.207912i \(-0.0666667\pi\)
−0.406737 + 0.913545i \(0.633333\pi\)
\(798\) 0 0
\(799\) 0 0
\(800\) −0.587785 0.529244i −0.587785 0.529244i
\(801\) 0.390362 0.601105i 0.390362 0.601105i
\(802\) 1.16913 1.60917i 1.16913 1.60917i
\(803\) 0 0
\(804\) 0 0
\(805\) 0 0
\(806\) 0 0
\(807\) 0 0
\(808\) 1.38488 0.705634i 1.38488 0.705634i
\(809\) 0.103383 1.97267i 0.103383 1.97267i −0.104528 0.994522i \(-0.533333\pi\)
0.207912 0.978148i \(-0.433333\pi\)
\(810\) −0.413545 1.27276i −0.413545 1.27276i
\(811\) 0 0 −0.258819 0.965926i \(-0.583333\pi\)
0.258819 + 0.965926i \(0.416667\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) 0 0
\(816\) 0 0
\(817\) 0 0
\(818\) −0.692314 + 1.80354i −0.692314 + 1.80354i
\(819\) 0 0
\(820\) 2.26728 0.481926i 2.26728 0.481926i
\(821\) −1.53884 + 1.11803i −1.53884 + 1.11803i −0.587785 + 0.809017i \(0.700000\pi\)
−0.951057 + 0.309017i \(0.900000\pi\)
\(822\) 0 0
\(823\) 0 0 0.669131 0.743145i \(-0.266667\pi\)
−0.669131 + 0.743145i \(0.733333\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) 0 0 −0.358368 0.933580i \(-0.616667\pi\)
0.358368 + 0.933580i \(0.383333\pi\)
\(828\) 0 0
\(829\) 0.614648 1.89169i 0.614648 1.89169i 0.207912 0.978148i \(-0.433333\pi\)
0.406737 0.913545i \(-0.366667\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) −1.01693 + 0.390362i −1.01693 + 0.390362i
\(833\) 1.30354 1.05558i 1.30354 1.05558i
\(834\) 0 0
\(835\) 0 0
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) 0 0 −0.951057 0.309017i \(-0.900000\pi\)
0.951057 + 0.309017i \(0.100000\pi\)
\(840\) 0 0
\(841\) 0.0399263 0.379874i 0.0399263 0.379874i
\(842\) 0.0434654 + 0.413545i 0.0434654 + 0.413545i
\(843\) 0 0
\(844\) 0 0
\(845\) −0.0260925 0.248254i −0.0260925 0.248254i
\(846\) 0 0
\(847\) 0 0
\(848\) 1.41355 + 0.459289i 1.41355 + 0.459289i
\(849\) 0 0
\(850\) 0.834908 1.03103i 0.834908 1.03103i
\(851\) 0 0
\(852\) 0 0
\(853\) −1.00000 + 1.00000i −1.00000 + 1.00000i 1.00000i \(0.5\pi\)
−1.00000 \(\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) −0.994522 + 1.10453i −0.994522 + 1.10453i 1.00000i \(0.5\pi\)
−0.994522 + 0.104528i \(0.966667\pi\)
\(858\) 0 0
\(859\) 0 0 0.453990 0.891007i \(-0.350000\pi\)
−0.453990 + 0.891007i \(0.650000\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) 0 0 −0.453990 0.891007i \(-0.650000\pi\)
0.453990 + 0.891007i \(0.350000\pi\)
\(864\) 0 0
\(865\) −2.24164 1.45574i −2.24164 1.45574i
\(866\) −0.809017 + 0.587785i −0.809017 + 0.587785i
\(867\) 0 0
\(868\) 0 0
\(869\) 0 0
\(870\) 0 0
\(871\) 0 0
\(872\) 0.638616 + 1.66365i 0.638616 + 1.66365i
\(873\) −0.809017 0.587785i −0.809017 0.587785i
\(874\) 0 0
\(875\) 0 0
\(876\) 0 0
\(877\) −0.614648 1.89169i −0.614648 1.89169i −0.406737 0.913545i \(-0.633333\pi\)
−0.207912 0.978148i \(-0.566667\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) 1.58231 0.704489i 1.58231 0.704489i 0.587785 0.809017i \(-0.300000\pi\)
0.994522 + 0.104528i \(0.0333333\pi\)
\(882\) −0.978148 0.207912i −0.978148 0.207912i
\(883\) 0 0 0.104528 0.994522i \(-0.466667\pi\)
−0.104528 + 0.994522i \(0.533333\pi\)
\(884\) −0.743145 1.66913i −0.743145 1.66913i
\(885\) 0 0
\(886\) 0 0
\(887\) 0 0 −0.743145 0.669131i \(-0.766667\pi\)
0.743145 + 0.669131i \(0.233333\pi\)
\(888\) 0 0
\(889\) 0 0
\(890\) −0.603631 0.745423i −0.603631 0.745423i
\(891\) 0 0
\(892\) 0 0
\(893\) 0 0
\(894\) 0 0
\(895\) 0 0
\(896\) 0 0
\(897\) 0 0
\(898\) 0.325760 0.402280i 0.325760 0.402280i
\(899\) 0 0
\(900\) −0.790943 −0.790943
\(901\) −0.645240 + 2.40807i −0.645240 + 2.40807i
\(902\) 0 0
\(903\) 0 0
\(904\) 0.978148 1.69420i 0.978148 1.69420i
\(905\) 1.03536 + 2.32545i 1.03536 + 2.32545i
\(906\) 0 0
\(907\) 0 0 0.156434 0.987688i \(-0.450000\pi\)
−0.156434 + 0.987688i \(0.550000\pi\)
\(908\) 0 0
\(909\) 0.557008 1.45106i 0.557008 1.45106i
\(910\) 0 0
\(911\) 0 0 −0.207912 0.978148i \(-0.566667\pi\)
0.207912 + 0.978148i \(0.433333\pi\)
\(912\) 0 0
\(913\) 0 0
\(914\) −0.336408 + 1.58268i −0.336408 + 1.58268i
\(915\) 0 0
\(916\) 0.478148 + 0.658114i 0.478148 + 0.658114i
\(917\) 0 0
\(918\) 0 0
\(919\) 0 0 0.994522 0.104528i \(-0.0333333\pi\)
−0.994522 + 0.104528i \(0.966667\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) −1.84417 0.707912i −1.84417 0.707912i
\(923\) 0 0
\(924\) 0 0
\(925\) 0.0585410 1.11703i 0.0585410 1.11703i
\(926\) 0 0
\(927\) 0 0
\(928\) −0.363271 + 1.11803i −0.363271 + 1.11803i
\(929\) 0.516929 + 0.0270911i 0.516929 + 0.0270911i 0.309017 0.951057i \(-0.400000\pi\)
0.207912 + 0.978148i \(0.433333\pi\)
\(930\) 0 0
\(931\) 0 0
\(932\) −1.40126 + 0.809017i −1.40126 + 0.809017i
\(933\) 0 0
\(934\) 0 0
\(935\) 0 0
\(936\) −0.494522 + 0.970554i −0.494522 + 0.970554i
\(937\) 1.73767 0.564602i 1.73767 0.564602i 0.743145 0.669131i \(-0.233333\pi\)
0.994522 + 0.104528i \(0.0333333\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0 0
\(941\) 1.90807 + 0.302208i 1.90807 + 0.302208i 0.994522 0.104528i \(-0.0333333\pi\)
0.913545 + 0.406737i \(0.133333\pi\)
\(942\) 0 0
\(943\) 0 0
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) 0 0 −0.891007 0.453990i \(-0.850000\pi\)
0.891007 + 0.453990i \(0.150000\pi\)
\(948\) 0 0
\(949\) −0.494522 0.856537i −0.494522 0.856537i
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) −1.72129 + 0.461219i −1.72129 + 0.461219i −0.978148 0.207912i \(-0.933333\pi\)
−0.743145 + 0.669131i \(0.766667\pi\)
\(954\) 1.35779 0.604528i 1.35779 0.604528i
\(955\) 0 0
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) 0 0
\(960\) 0 0
\(961\) 0.406737 0.913545i 0.406737 0.913545i
\(962\) −1.33409 0.770236i −1.33409 0.770236i
\(963\) 0 0
\(964\) −0.500000 0.866025i −0.500000 0.866025i
\(965\) 2.44512 2.44512
\(966\) 0 0
\(967\) 0 0 0.406737 0.913545i \(-0.366667\pi\)
−0.406737 + 0.913545i \(0.633333\pi\)
\(968\) −0.500000 0.866025i −0.500000 0.866025i
\(969\) 0 0
\(970\) −1.08268 + 0.786610i −1.08268 + 0.786610i
\(971\) 0 0 −0.544639 0.838671i \(-0.683333\pi\)
0.544639 + 0.838671i \(0.316667\pi\)
\(972\) 0 0
\(973\) 0 0
\(974\) 0 0
\(975\) 0 0
\(976\) 0.614648 0.0646021i 0.614648 0.0646021i
\(977\) −0.292088 + 0.112122i −0.292088 + 0.112122i −0.500000 0.866025i \(-0.666667\pi\)
0.207912 + 0.978148i \(0.433333\pi\)
\(978\) 0 0
\(979\) 0 0
\(980\) −0.669131 + 1.15897i −0.669131 + 1.15897i
\(981\) 1.58779 + 0.809017i 1.58779 + 0.809017i
\(982\) 0 0
\(983\) 0 0 0.965926 0.258819i \(-0.0833333\pi\)
−0.965926 + 0.258819i \(0.916667\pi\)
\(984\) 0 0
\(985\) −2.46799 + 0.390890i −2.46799 + 0.390890i
\(986\) −1.90464 0.510348i −1.90464 0.510348i
\(987\) 0 0
\(988\) 0 0
\(989\) 0 0
\(990\) 0 0
\(991\) 0 0 0.951057 0.309017i \(-0.100000\pi\)
−0.951057 + 0.309017i \(0.900000\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0 0
\(995\) 0 0
\(996\) 0 0
\(997\) 0.0809764 0.511265i 0.0809764 0.511265i −0.913545 0.406737i \(-0.866667\pi\)
0.994522 0.104528i \(-0.0333333\pi\)
\(998\) 0 0
\(999\) 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 964.1.bh.a.159.1 16
4.3 odd 2 CM 964.1.bh.a.159.1 16
241.144 even 60 inner 964.1.bh.a.867.1 yes 16
964.867 odd 60 inner 964.1.bh.a.867.1 yes 16
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
964.1.bh.a.159.1 16 1.1 even 1 trivial
964.1.bh.a.159.1 16 4.3 odd 2 CM
964.1.bh.a.867.1 yes 16 241.144 even 60 inner
964.1.bh.a.867.1 yes 16 964.867 odd 60 inner