Properties

Label 1397.1.l.a.126.3
Level $1397$
Weight $1$
Character 1397.126
Analytic conductor $0.697$
Analytic rank $0$
Dimension $20$
Projective image $D_{25}$
CM discriminant -127
Inner twists $4$

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [1397,1,Mod(126,1397)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1397, base_ring=CyclotomicField(10))
 
chi = DirichletCharacter(H, H._module([4, 5]))
 
N = Newforms(chi, 1, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("1397.126");
 
S:= CuspForms(chi, 1);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1397 = 11 \cdot 127 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 1397.l (of order \(10\), degree \(4\), 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: \(0.697193822648\)
Analytic rank: \(0\)
Dimension: \(20\)
Relative dimension: \(5\) over \(\Q(\zeta_{10})\)
Coefficient field: \(\Q(\zeta_{50})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{20} - x^{15} + x^{10} - x^{5} + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Projective image: \(D_{25}\)
Projective field: Galois closure of \(\mathbb{Q}[x]/(x^{25} - \cdots)\)

Embedding invariants

Embedding label 126.3
Root \(-0.535827 + 0.844328i\) of defining polynomial
Character \(\chi\) \(=\) 1397.126
Dual form 1397.1.l.a.1142.3

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.0388067 + 0.119435i) q^{2} +(0.796258 - 0.578516i) q^{4} +(0.201592 + 0.146465i) q^{8} +(0.309017 + 0.951057i) q^{9} +O(q^{10})\) \(q+(0.0388067 + 0.119435i) q^{2} +(0.796258 - 0.578516i) q^{4} +(0.201592 + 0.146465i) q^{8} +(0.309017 + 0.951057i) q^{9} +(0.876307 - 0.481754i) q^{11} +(0.541587 + 1.66683i) q^{13} +(0.294474 - 0.906297i) q^{16} +(-0.393950 + 1.21245i) q^{17} +(-0.101597 + 0.0738147i) q^{18} +(-1.56720 - 1.13864i) q^{19} +(0.0915446 + 0.0859661i) q^{22} +(-0.809017 - 0.587785i) q^{25} +(-0.178061 + 0.129369i) q^{26} +(0.0388067 + 0.119435i) q^{31} +0.368852 q^{32} -0.160097 q^{34} +(0.796258 + 0.578516i) q^{36} +(1.03137 - 0.749337i) q^{37} +(0.0751750 - 0.231365i) q^{38} +(0.688925 + 0.500534i) q^{41} +(0.419064 - 0.890557i) q^{44} +(-1.41789 - 1.03016i) q^{47} +(0.309017 - 0.951057i) q^{49} +(0.0388067 - 0.119435i) q^{50} +(1.39553 + 1.01391i) q^{52} +(0.331159 - 1.01920i) q^{61} +(-0.0127587 + 0.00926972i) q^{62} +(-0.280160 - 0.862243i) q^{64} +(0.387737 + 1.19333i) q^{68} +(-0.574633 + 1.76854i) q^{71} +(-0.0770013 + 0.236986i) q^{72} +(-1.17950 + 0.856954i) q^{73} +(0.129521 + 0.0941025i) q^{74} -1.90662 q^{76} +(-0.613161 - 1.88711i) q^{79} +(-0.809017 + 0.587785i) q^{81} +(-0.0330462 + 0.101706i) q^{82} +(0.247217 + 0.0312307i) q^{88} +(0.0680131 - 0.209323i) q^{94} +0.125581 q^{98} +(0.728969 + 0.684547i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 20 q - 5 q^{4} - 5 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 20 q - 5 q^{4} - 5 q^{9} - 5 q^{16} - 5 q^{25} - 10 q^{32} - 10 q^{34} - 5 q^{36} + 15 q^{38} - 5 q^{44} - 5 q^{49} + 15 q^{52} - 10 q^{62} - 5 q^{64} + 15 q^{74} - 5 q^{81} - 5 q^{88}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1397\mathbb{Z}\right)^\times\).

\(n\) \(255\) \(892\)
\(\chi(n)\) \(e\left(\frac{2}{5}\right)\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.0388067 + 0.119435i 0.0388067 + 0.119435i 0.968583 0.248690i \(-0.0800000\pi\)
−0.929776 + 0.368125i \(0.880000\pi\)
\(3\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(4\) 0.796258 0.578516i 0.796258 0.578516i
\(5\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(6\) 0 0
\(7\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(8\) 0.201592 + 0.146465i 0.201592 + 0.146465i
\(9\) 0.309017 + 0.951057i 0.309017 + 0.951057i
\(10\) 0 0
\(11\) 0.876307 0.481754i 0.876307 0.481754i
\(12\) 0 0
\(13\) 0.541587 + 1.66683i 0.541587 + 1.66683i 0.728969 + 0.684547i \(0.240000\pi\)
−0.187381 + 0.982287i \(0.560000\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0.294474 0.906297i 0.294474 0.906297i
\(17\) −0.393950 + 1.21245i −0.393950 + 1.21245i 0.535827 + 0.844328i \(0.320000\pi\)
−0.929776 + 0.368125i \(0.880000\pi\)
\(18\) −0.101597 + 0.0738147i −0.101597 + 0.0738147i
\(19\) −1.56720 1.13864i −1.56720 1.13864i −0.929776 0.368125i \(-0.880000\pi\)
−0.637424 0.770513i \(-0.720000\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0.0915446 + 0.0859661i 0.0915446 + 0.0859661i
\(23\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(24\) 0 0
\(25\) −0.809017 0.587785i −0.809017 0.587785i
\(26\) −0.178061 + 0.129369i −0.178061 + 0.129369i
\(27\) 0 0
\(28\) 0 0
\(29\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(30\) 0 0
\(31\) 0.0388067 + 0.119435i 0.0388067 + 0.119435i 0.968583 0.248690i \(-0.0800000\pi\)
−0.929776 + 0.368125i \(0.880000\pi\)
\(32\) 0.368852 0.368852
\(33\) 0 0
\(34\) −0.160097 −0.160097
\(35\) 0 0
\(36\) 0.796258 + 0.578516i 0.796258 + 0.578516i
\(37\) 1.03137 0.749337i 1.03137 0.749337i 0.0627905 0.998027i \(-0.480000\pi\)
0.968583 + 0.248690i \(0.0800000\pi\)
\(38\) 0.0751750 0.231365i 0.0751750 0.231365i
\(39\) 0 0
\(40\) 0 0
\(41\) 0.688925 + 0.500534i 0.688925 + 0.500534i 0.876307 0.481754i \(-0.160000\pi\)
−0.187381 + 0.982287i \(0.560000\pi\)
\(42\) 0 0
\(43\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(44\) 0.419064 0.890557i 0.419064 0.890557i
\(45\) 0 0
\(46\) 0 0
\(47\) −1.41789 1.03016i −1.41789 1.03016i −0.992115 0.125333i \(-0.960000\pi\)
−0.425779 0.904827i \(-0.640000\pi\)
\(48\) 0 0
\(49\) 0.309017 0.951057i 0.309017 0.951057i
\(50\) 0.0388067 0.119435i 0.0388067 0.119435i
\(51\) 0 0
\(52\) 1.39553 + 1.01391i 1.39553 + 1.01391i
\(53\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(60\) 0 0
\(61\) 0.331159 1.01920i 0.331159 1.01920i −0.637424 0.770513i \(-0.720000\pi\)
0.968583 0.248690i \(-0.0800000\pi\)
\(62\) −0.0127587 + 0.00926972i −0.0127587 + 0.00926972i
\(63\) 0 0
\(64\) −0.280160 0.862243i −0.280160 0.862243i
\(65\) 0 0
\(66\) 0 0
\(67\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(68\) 0.387737 + 1.19333i 0.387737 + 1.19333i
\(69\) 0 0
\(70\) 0 0
\(71\) −0.574633 + 1.76854i −0.574633 + 1.76854i 0.0627905 + 0.998027i \(0.480000\pi\)
−0.637424 + 0.770513i \(0.720000\pi\)
\(72\) −0.0770013 + 0.236986i −0.0770013 + 0.236986i
\(73\) −1.17950 + 0.856954i −1.17950 + 0.856954i −0.992115 0.125333i \(-0.960000\pi\)
−0.187381 + 0.982287i \(0.560000\pi\)
\(74\) 0.129521 + 0.0941025i 0.129521 + 0.0941025i
\(75\) 0 0
\(76\) −1.90662 −1.90662
\(77\) 0 0
\(78\) 0 0
\(79\) −0.613161 1.88711i −0.613161 1.88711i −0.425779 0.904827i \(-0.640000\pi\)
−0.187381 0.982287i \(-0.560000\pi\)
\(80\) 0 0
\(81\) −0.809017 + 0.587785i −0.809017 + 0.587785i
\(82\) −0.0330462 + 0.101706i −0.0330462 + 0.101706i
\(83\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 0 0
\(87\) 0 0
\(88\) 0.247217 + 0.0312307i 0.247217 + 0.0312307i
\(89\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 0 0
\(93\) 0 0
\(94\) 0.0680131 0.209323i 0.0680131 0.209323i
\(95\) 0 0
\(96\) 0 0
\(97\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(98\) 0.125581 0.125581
\(99\) 0.728969 + 0.684547i 0.728969 + 0.684547i
\(100\) −0.984229 −0.984229
\(101\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(102\) 0 0
\(103\) 0.303189 0.220280i 0.303189 0.220280i −0.425779 0.904827i \(-0.640000\pi\)
0.728969 + 0.684547i \(0.240000\pi\)
\(104\) −0.134954 + 0.415344i −0.134954 + 0.415344i
\(105\) 0 0
\(106\) 0 0
\(107\) 1.50441 + 1.09302i 1.50441 + 1.09302i 0.968583 + 0.248690i \(0.0800000\pi\)
0.535827 + 0.844328i \(0.320000\pi\)
\(108\) 0 0
\(109\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) −1.17950 0.856954i −1.17950 0.856954i −0.187381 0.982287i \(-0.560000\pi\)
−0.992115 + 0.125333i \(0.960000\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 0 0
\(117\) −1.41789 + 1.03016i −1.41789 + 1.03016i
\(118\) 0 0
\(119\) 0 0
\(120\) 0 0
\(121\) 0.535827 0.844328i 0.535827 0.844328i
\(122\) 0.134579 0.134579
\(123\) 0 0
\(124\) 0.0999949 + 0.0726506i 0.0999949 + 0.0726506i
\(125\) 0 0
\(126\) 0 0
\(127\) 0.309017 0.951057i 0.309017 0.951057i
\(128\) 0.390518 0.283728i 0.390518 0.283728i
\(129\) 0 0
\(130\) 0 0
\(131\) −1.61803 −1.61803 −0.809017 0.587785i \(-0.800000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 0 0
\(135\) 0 0
\(136\) −0.256999 + 0.186721i −0.256999 + 0.186721i
\(137\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(138\) 0 0
\(139\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) −0.233525 −0.233525
\(143\) 1.27760 + 1.19975i 1.27760 + 1.19975i
\(144\) 0.952937 0.952937
\(145\) 0 0
\(146\) −0.148122 0.107617i −0.148122 0.107617i
\(147\) 0 0
\(148\) 0.387737 1.19333i 0.387737 1.19333i
\(149\) −0.574633 + 1.76854i −0.574633 + 1.76854i 0.0627905 + 0.998027i \(0.480000\pi\)
−0.637424 + 0.770513i \(0.720000\pi\)
\(150\) 0 0
\(151\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(152\) −0.149164 0.459081i −0.149164 0.459081i
\(153\) −1.27485 −1.27485
\(154\) 0 0
\(155\) 0 0
\(156\) 0 0
\(157\) 0.688925 + 0.500534i 0.688925 + 0.500534i 0.876307 0.481754i \(-0.160000\pi\)
−0.187381 + 0.982287i \(0.560000\pi\)
\(158\) 0.201592 0.146465i 0.201592 0.146465i
\(159\) 0 0
\(160\) 0 0
\(161\) 0 0
\(162\) −0.101597 0.0738147i −0.101597 0.0738147i
\(163\) 0.190983 + 0.587785i 0.190983 + 0.587785i 1.00000 \(0\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(164\) 0.838129 0.838129
\(165\) 0 0
\(166\) 0 0
\(167\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(168\) 0 0
\(169\) −1.67600 + 1.21769i −1.67600 + 1.21769i
\(170\) 0 0
\(171\) 0.598617 1.84235i 0.598617 1.84235i
\(172\) 0 0
\(173\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) −0.178563 0.936058i −0.178563 0.936058i
\(177\) 0 0
\(178\) 0 0
\(179\) −0.866986 0.629902i −0.866986 0.629902i 0.0627905 0.998027i \(-0.480000\pi\)
−0.929776 + 0.368125i \(0.880000\pi\)
\(180\) 0 0
\(181\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 0 0
\(186\) 0 0
\(187\) 0.238883 + 1.25227i 0.238883 + 1.25227i
\(188\) −1.72497 −1.72497
\(189\) 0 0
\(190\) 0 0
\(191\) 1.30902 0.951057i 1.30902 0.951057i 0.309017 0.951057i \(-0.400000\pi\)
1.00000 \(0\)
\(192\) 0 0
\(193\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) −0.304144 0.936058i −0.304144 0.936058i
\(197\) −1.98423 −1.98423 −0.992115 0.125333i \(-0.960000\pi\)
−0.992115 + 0.125333i \(0.960000\pi\)
\(198\) −0.0534698 + 0.113629i −0.0534698 + 0.113629i
\(199\) −0.851559 −0.851559 −0.425779 0.904827i \(-0.640000\pi\)
−0.425779 + 0.904827i \(0.640000\pi\)
\(200\) −0.0770013 0.236986i −0.0770013 0.236986i
\(201\) 0 0
\(202\) 0 0
\(203\) 0 0
\(204\) 0 0
\(205\) 0 0
\(206\) 0.0380748 + 0.0276630i 0.0380748 + 0.0276630i
\(207\) 0 0
\(208\) 1.67013 1.67013
\(209\) −1.92189 0.242791i −1.92189 0.242791i
\(210\) 0 0
\(211\) 0.450527 + 1.38658i 0.450527 + 1.38658i 0.876307 + 0.481754i \(0.160000\pi\)
−0.425779 + 0.904827i \(0.640000\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) −0.0721631 + 0.222095i −0.0721631 + 0.222095i
\(215\) 0 0
\(216\) 0 0
\(217\) 0 0
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) −2.23432 −2.23432
\(222\) 0 0
\(223\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(224\) 0 0
\(225\) 0.309017 0.951057i 0.309017 0.951057i
\(226\) 0.0565777 0.174128i 0.0565777 0.174128i
\(227\) −0.500000 + 0.363271i −0.500000 + 0.363271i −0.809017 0.587785i \(-0.800000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(228\) 0 0
\(229\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(234\) −0.178061 0.129369i −0.178061 0.129369i
\(235\) 0 0
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(240\) 0 0
\(241\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(242\) 0.121636 + 0.0312307i 0.121636 + 0.0312307i
\(243\) 0 0
\(244\) −0.325937 1.00313i −0.325937 1.00313i
\(245\) 0 0
\(246\) 0 0
\(247\) 1.04914 3.22894i 1.04914 3.22894i
\(248\) −0.00966991 + 0.0297609i −0.00966991 + 0.0297609i
\(249\) 0 0
\(250\) 0 0
\(251\) 0.450527 + 1.38658i 0.450527 + 1.38658i 0.876307 + 0.481754i \(0.160000\pi\)
−0.425779 + 0.904827i \(0.640000\pi\)
\(252\) 0 0
\(253\) 0 0
\(254\) 0.125581 0.125581
\(255\) 0 0
\(256\) −0.684426 0.497265i −0.684426 0.497265i
\(257\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 0 0
\(261\) 0 0
\(262\) −0.0627905 0.193249i −0.0627905 0.193249i
\(263\) 1.07165 1.07165 0.535827 0.844328i \(-0.320000\pi\)
0.535827 + 0.844328i \(0.320000\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) 0.598617 1.84235i 0.598617 1.84235i 0.0627905 0.998027i \(-0.480000\pi\)
0.535827 0.844328i \(-0.320000\pi\)
\(270\) 0 0
\(271\) −0.500000 + 0.363271i −0.500000 + 0.363271i −0.809017 0.587785i \(-0.800000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(272\) 0.982834 + 0.714071i 0.982834 + 0.714071i
\(273\) 0 0
\(274\) 0 0
\(275\) −0.992115 0.125333i −0.992115 0.125333i
\(276\) 0 0
\(277\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(278\) 0 0
\(279\) −0.101597 + 0.0738147i −0.101597 + 0.0738147i
\(280\) 0 0
\(281\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(282\) 0 0
\(283\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(284\) 0.565571 + 1.74065i 0.565571 + 1.74065i
\(285\) 0 0
\(286\) −0.0937119 + 0.199148i −0.0937119 + 0.199148i
\(287\) 0 0
\(288\) 0.113982 + 0.350799i 0.113982 + 0.350799i
\(289\) −0.505828 0.367505i −0.505828 0.367505i
\(290\) 0 0
\(291\) 0 0
\(292\) −0.443422 + 1.36471i −0.443422 + 1.36471i
\(293\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 0.317669 0.317669
\(297\) 0 0
\(298\) −0.233525 −0.233525
\(299\) 0 0
\(300\) 0 0
\(301\) 0 0
\(302\) 0 0
\(303\) 0 0
\(304\) −1.49344 + 1.08505i −1.49344 + 1.08505i
\(305\) 0 0
\(306\) −0.0494726 0.152261i −0.0494726 0.152261i
\(307\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(312\) 0 0
\(313\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(314\) −0.0330462 + 0.101706i −0.0330462 + 0.101706i
\(315\) 0 0
\(316\) −1.57996 1.14791i −1.57996 1.14791i
\(317\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(318\) 0 0
\(319\) 0 0
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) 1.99794 1.45159i 1.99794 1.45159i
\(324\) −0.304144 + 0.936058i −0.304144 + 0.936058i
\(325\) 0.541587 1.66683i 0.541587 1.66683i
\(326\) −0.0627905 + 0.0456200i −0.0627905 + 0.0456200i
\(327\) 0 0
\(328\) 0.0655712 + 0.201807i 0.0655712 + 0.201807i
\(329\) 0 0
\(330\) 0 0
\(331\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(332\) 0 0
\(333\) 1.03137 + 0.749337i 1.03137 + 0.749337i
\(334\) 0 0
\(335\) 0 0
\(336\) 0 0
\(337\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(338\) −0.210474 0.152918i −0.210474 0.152918i
\(339\) 0 0
\(340\) 0 0
\(341\) 0.0915446 + 0.0859661i 0.0915446 + 0.0859661i
\(342\) 0.243271 0.243271
\(343\) 0 0
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(348\) 0 0
\(349\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0.323228 0.177696i 0.323228 0.177696i
\(353\) 1.93717 1.93717 0.968583 0.248690i \(-0.0800000\pi\)
0.968583 + 0.248690i \(0.0800000\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 0 0
\(357\) 0 0
\(358\) 0.0415873 0.127993i 0.0415873 0.127993i
\(359\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(360\) 0 0
\(361\) 0.850604 + 2.61789i 0.850604 + 2.61789i
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) 0 0
\(366\) 0 0
\(367\) −0.866986 + 0.629902i −0.866986 + 0.629902i −0.929776 0.368125i \(-0.880000\pi\)
0.0627905 + 0.998027i \(0.480000\pi\)
\(368\) 0 0
\(369\) −0.263146 + 0.809880i −0.263146 + 0.809880i
\(370\) 0 0
\(371\) 0 0
\(372\) 0 0
\(373\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(374\) −0.140294 + 0.0771272i −0.140294 + 0.0771272i
\(375\) 0 0
\(376\) −0.134954 0.415344i −0.134954 0.415344i
\(377\) 0 0
\(378\) 0 0
\(379\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0.164388 + 0.119435i 0.164388 + 0.119435i
\(383\) 0.190983 + 0.587785i 0.190983 + 0.587785i 1.00000 \(0\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) −1.41789 + 1.03016i −1.41789 + 1.03016i −0.425779 + 0.904827i \(0.640000\pi\)
−0.992115 + 0.125333i \(0.960000\pi\)
\(390\) 0 0
\(391\) 0 0
\(392\) 0.201592 0.146465i 0.201592 0.146465i
\(393\) 0 0
\(394\) −0.0770013 0.236986i −0.0770013 0.236986i
\(395\) 0 0
\(396\) 0.976468 + 0.123357i 0.976468 + 0.123357i
\(397\) 1.07165 1.07165 0.535827 0.844328i \(-0.320000\pi\)
0.535827 + 0.844328i \(0.320000\pi\)
\(398\) −0.0330462 0.101706i −0.0330462 0.101706i
\(399\) 0 0
\(400\) −0.770942 + 0.560122i −0.770942 + 0.560122i
\(401\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(402\) 0 0
\(403\) −0.178061 + 0.129369i −0.178061 + 0.129369i
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 0.542804 1.15352i 0.542804 1.15352i
\(408\) 0 0
\(409\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0.113982 0.350799i 0.113982 0.350799i
\(413\) 0 0
\(414\) 0 0
\(415\) 0 0
\(416\) 0.199766 + 0.614816i 0.199766 + 0.614816i
\(417\) 0 0
\(418\) −0.0455845 0.238962i −0.0455845 0.238962i
\(419\) 1.93717 1.93717 0.968583 0.248690i \(-0.0800000\pi\)
0.968583 + 0.248690i \(0.0800000\pi\)
\(420\) 0 0
\(421\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(422\) −0.148122 + 0.107617i −0.148122 + 0.107617i
\(423\) 0.541587 1.66683i 0.541587 1.66683i
\(424\) 0 0
\(425\) 1.03137 0.749337i 1.03137 0.749337i
\(426\) 0 0
\(427\) 0 0
\(428\) 1.83023 1.83023
\(429\) 0 0
\(430\) 0 0
\(431\) −0.263146 0.809880i −0.263146 0.809880i −0.992115 0.125333i \(-0.960000\pi\)
0.728969 0.684547i \(-0.240000\pi\)
\(432\) 0 0
\(433\) 1.50441 1.09302i 1.50441 1.09302i 0.535827 0.844328i \(-0.320000\pi\)
0.968583 0.248690i \(-0.0800000\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 0 0
\(438\) 0 0
\(439\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(440\) 0 0
\(441\) 1.00000 1.00000
\(442\) −0.0867064 0.266855i −0.0867064 0.266855i
\(443\) 1.03137 + 0.749337i 1.03137 + 0.749337i 0.968583 0.248690i \(-0.0800000\pi\)
0.0627905 + 0.998027i \(0.480000\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) −0.263146 0.809880i −0.263146 0.809880i −0.992115 0.125333i \(-0.960000\pi\)
0.728969 0.684547i \(-0.240000\pi\)
\(450\) 0.125581 0.125581
\(451\) 0.844844 + 0.106729i 0.844844 + 0.106729i
\(452\) −1.43494 −1.43494
\(453\) 0 0
\(454\) −0.0627905 0.0456200i −0.0627905 0.0456200i
\(455\) 0 0
\(456\) 0 0
\(457\) −0.613161 + 1.88711i −0.613161 + 1.88711i −0.187381 + 0.982287i \(0.560000\pi\)
−0.425779 + 0.904827i \(0.640000\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(462\) 0 0
\(463\) −1.27485 −1.27485 −0.637424 0.770513i \(-0.720000\pi\)
−0.637424 + 0.770513i \(0.720000\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(468\) −0.533046 + 1.64055i −0.533046 + 1.64055i
\(469\) 0 0
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) 0 0
\(474\) 0 0
\(475\) 0.598617 + 1.84235i 0.598617 + 1.84235i
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) 0.450527 1.38658i 0.450527 1.38658i −0.425779 0.904827i \(-0.640000\pi\)
0.876307 0.481754i \(-0.160000\pi\)
\(480\) 0 0
\(481\) 1.80760 + 1.31330i 1.80760 + 1.31330i
\(482\) 0 0
\(483\) 0 0
\(484\) −0.0618003 0.982287i −0.0618003 0.982287i
\(485\) 0 0
\(486\) 0 0
\(487\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(488\) 0.216037 0.156960i 0.216037 0.156960i
\(489\) 0 0
\(490\) 0 0
\(491\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(492\) 0 0
\(493\) 0 0
\(494\) 0.426361 0.426361
\(495\) 0 0
\(496\) 0.119671 0.119671
\(497\) 0 0
\(498\) 0 0
\(499\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) −0.148122 + 0.107617i −0.148122 + 0.107617i
\(503\) 0.303189 + 0.220280i 0.303189 + 0.220280i 0.728969 0.684547i \(-0.240000\pi\)
−0.425779 + 0.904827i \(0.640000\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) 0 0
\(508\) −0.304144 0.936058i −0.304144 0.936058i
\(509\) −0.500000 0.363271i −0.500000 0.363271i 0.309017 0.951057i \(-0.400000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 0.181995 0.560122i 0.181995 0.560122i
\(513\) 0 0
\(514\) 0 0
\(515\) 0 0
\(516\) 0 0
\(517\) −1.73879 0.219661i −1.73879 0.219661i
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) −0.101597 + 0.0738147i −0.101597 + 0.0738147i −0.637424 0.770513i \(-0.720000\pi\)
0.535827 + 0.844328i \(0.320000\pi\)
\(522\) 0 0
\(523\) −0.115808 + 0.356420i −0.115808 + 0.356420i −0.992115 0.125333i \(-0.960000\pi\)
0.876307 + 0.481754i \(0.160000\pi\)
\(524\) −1.28837 + 0.936058i −1.28837 + 0.936058i
\(525\) 0 0
\(526\) 0.0415873 + 0.127993i 0.0415873 + 0.127993i
\(527\) −0.160097 −0.160097
\(528\) 0 0
\(529\) 1.00000 1.00000
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) −0.461193 + 1.41941i −0.461193 + 1.41941i
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) 0 0
\(538\) 0.243271 0.243271
\(539\) −0.187381 0.982287i −0.187381 0.982287i
\(540\) 0 0
\(541\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(542\) −0.0627905 0.0456200i −0.0627905 0.0456200i
\(543\) 0 0
\(544\) −0.145309 + 0.447216i −0.145309 + 0.447216i
\(545\) 0 0
\(546\) 0 0
\(547\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(548\) 0 0
\(549\) 1.07165 1.07165
\(550\) −0.0235315 0.123357i −0.0235315 0.123357i
\(551\) 0 0
\(552\) 0 0
\(553\) 0 0
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 1.30902 0.951057i 1.30902 0.951057i 0.309017 0.951057i \(-0.400000\pi\)
1.00000 \(0\)
\(558\) −0.0127587 0.00926972i −0.0127587 0.00926972i
\(559\) 0 0
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 0 0
\(567\) 0 0
\(568\) −0.374871 + 0.272360i −0.374871 + 0.272360i
\(569\) 1.60528 + 1.16630i 1.60528 + 1.16630i 0.876307 + 0.481754i \(0.160000\pi\)
0.728969 + 0.684547i \(0.240000\pi\)
\(570\) 0 0
\(571\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(572\) 1.71137 + 0.216197i 1.71137 + 0.216197i
\(573\) 0 0
\(574\) 0 0
\(575\) 0 0
\(576\) 0.733468 0.532896i 0.733468 0.532896i
\(577\) −0.574633 + 1.76854i −0.574633 + 1.76854i 0.0627905 + 0.998027i \(0.480000\pi\)
−0.637424 + 0.770513i \(0.720000\pi\)
\(578\) 0.0242634 0.0746750i 0.0242634 0.0746750i
\(579\) 0 0
\(580\) 0 0
\(581\) 0 0
\(582\) 0 0
\(583\) 0 0
\(584\) −0.363291 −0.363291
\(585\) 0 0
\(586\) 0 0
\(587\) −1.56720 + 1.13864i −1.56720 + 1.13864i −0.637424 + 0.770513i \(0.720000\pi\)
−0.929776 + 0.368125i \(0.880000\pi\)
\(588\) 0 0
\(589\) 0.0751750 0.231365i 0.0751750 0.231365i
\(590\) 0 0
\(591\) 0 0
\(592\) −0.375409 1.15539i −0.375409 1.15539i
\(593\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0.565571 + 1.74065i 0.565571 + 1.74065i
\(597\) 0 0
\(598\) 0 0
\(599\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(600\) 0 0
\(601\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) 0 0
\(606\) 0 0
\(607\) −0.574633 1.76854i −0.574633 1.76854i −0.637424 0.770513i \(-0.720000\pi\)
0.0627905 0.998027i \(-0.480000\pi\)
\(608\) −0.578066 0.419989i −0.578066 0.419989i
\(609\) 0 0
\(610\) 0 0
\(611\) 0.949193 2.92132i 0.949193 2.92132i
\(612\) −1.01511 + 0.737519i −1.01511 + 0.737519i
\(613\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(618\) 0 0
\(619\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 0 0
\(624\) 0 0
\(625\) 0.309017 + 0.951057i 0.309017 + 0.951057i
\(626\) 0 0
\(627\) 0 0
\(628\) 0.838129 0.838129
\(629\) 0.502226 + 1.54569i 0.502226 + 1.54569i
\(630\) 0 0
\(631\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(632\) 0.152788 0.470234i 0.152788 0.470234i
\(633\) 0 0
\(634\) 0 0
\(635\) 0 0
\(636\) 0 0
\(637\) 1.75261 1.75261
\(638\) 0 0
\(639\) −1.85955 −1.85955
\(640\) 0 0
\(641\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(642\) 0 0
\(643\) −0.115808 + 0.356420i −0.115808 + 0.356420i −0.992115 0.125333i \(-0.960000\pi\)
0.876307 + 0.481754i \(0.160000\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0.250904 + 0.182292i 0.250904 + 0.182292i
\(647\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(648\) −0.249182 −0.249182
\(649\) 0 0
\(650\) 0.220095 0.220095
\(651\) 0 0
\(652\) 0.492115 + 0.357542i 0.492115 + 0.357542i
\(653\) −1.17950 + 0.856954i −1.17950 + 0.856954i −0.992115 0.125333i \(-0.960000\pi\)
−0.187381 + 0.982287i \(0.560000\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 0.656502 0.476977i 0.656502 0.476977i
\(657\) −1.17950 0.856954i −1.17950 0.856954i
\(658\) 0 0
\(659\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(660\) 0 0
\(661\) 1.45794 1.45794 0.728969 0.684547i \(-0.240000\pi\)
0.728969 + 0.684547i \(0.240000\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 0 0
\(666\) −0.0494726 + 0.152261i −0.0494726 + 0.152261i
\(667\) 0 0
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) −0.200808 1.05267i −0.200808 1.05267i
\(672\) 0 0
\(673\) −0.574633 1.76854i −0.574633 1.76854i −0.637424 0.770513i \(-0.720000\pi\)
0.0627905 0.998027i \(-0.480000\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) −0.630080 + 1.93919i −0.630080 + 1.93919i
\(677\) 0.190983 0.587785i 0.190983 0.587785i −0.809017 0.587785i \(-0.800000\pi\)
1.00000 \(0\)
\(678\) 0 0
\(679\) 0 0
\(680\) 0 0
\(681\) 0 0
\(682\) −0.00671479 + 0.0142697i −0.00671479 + 0.0142697i
\(683\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(684\) −0.589177 1.81330i −0.589177 1.81330i
\(685\) 0 0
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) 0 0
\(690\) 0 0
\(691\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 0 0
\(696\) 0 0
\(697\) −0.878275 + 0.638104i −0.878275 + 0.638104i
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(702\) 0 0
\(703\) −2.46959 −2.46959
\(704\) −0.660895 0.620621i −0.660895 0.620621i
\(705\) 0 0
\(706\) 0.0751750 + 0.231365i 0.0751750 + 0.231365i
\(707\) 0 0
\(708\) 0 0
\(709\) 0.541587 1.66683i 0.541587 1.66683i −0.187381 0.982287i \(-0.560000\pi\)
0.728969 0.684547i \(-0.240000\pi\)
\(710\) 0 0
\(711\) 1.60528 1.16630i 1.60528 1.16630i
\(712\) 0 0
\(713\) 0 0
\(714\) 0 0
\(715\) 0 0
\(716\) −1.05475 −1.05475
\(717\) 0 0
\(718\) 0 0
\(719\) 1.03137 0.749337i 1.03137 0.749337i 0.0627905 0.998027i \(-0.480000\pi\)
0.968583 + 0.248690i \(0.0800000\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) −0.279658 + 0.203183i −0.279658 + 0.203183i
\(723\) 0 0
\(724\) 0 0
\(725\) 0 0
\(726\) 0 0
\(727\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(728\) 0 0
\(729\) −0.809017 0.587785i −0.809017 0.587785i
\(730\) 0 0
\(731\) 0 0
\(732\) 0 0
\(733\) 1.30902 0.951057i 1.30902 0.951057i 0.309017 0.951057i \(-0.400000\pi\)
1.00000 \(0\)
\(734\) −0.108877 0.0791038i −0.108877 0.0791038i
\(735\) 0 0
\(736\) 0 0
\(737\) 0 0
\(738\) −0.106940 −0.106940
\(739\) −0.115808 0.356420i −0.115808 0.356420i 0.876307 0.481754i \(-0.160000\pi\)
−0.992115 + 0.125333i \(0.960000\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0 0
\(747\) 0 0
\(748\) 0.914668 + 0.858931i 0.914668 + 0.858931i
\(749\) 0 0
\(750\) 0 0
\(751\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(752\) −1.35116 + 0.981678i −1.35116 + 0.981678i
\(753\) 0 0
\(754\) 0 0
\(755\) 0 0
\(756\) 0 0
\(757\) 0.0388067 + 0.119435i 0.0388067 + 0.119435i 0.968583 0.248690i \(-0.0800000\pi\)
−0.929776 + 0.368125i \(0.880000\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 0.492115 1.51457i 0.492115 1.51457i
\(765\) 0 0
\(766\) −0.0627905 + 0.0456200i −0.0627905 + 0.0456200i
\(767\) 0 0
\(768\) 0 0
\(769\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) −0.866986 0.629902i −0.866986 0.629902i 0.0627905 0.998027i \(-0.480000\pi\)
−0.929776 + 0.368125i \(0.880000\pi\)
\(774\) 0 0
\(775\) 0.0388067 0.119435i 0.0388067 0.119435i
\(776\) 0 0
\(777\) 0 0
\(778\) −0.178061 0.129369i −0.178061 0.129369i
\(779\) −0.509758 1.56887i −0.509758 1.56887i
\(780\) 0 0
\(781\) 0.348445 + 1.82662i 0.348445 + 1.82662i
\(782\) 0 0
\(783\) 0 0
\(784\) −0.770942 0.560122i −0.770942 0.560122i
\(785\) 0 0
\(786\) 0 0
\(787\) −0.263146 + 0.809880i −0.263146 + 0.809880i 0.728969 + 0.684547i \(0.240000\pi\)
−0.992115 + 0.125333i \(0.960000\pi\)
\(788\) −1.57996 + 1.14791i −1.57996 + 1.14791i
\(789\) 0 0
\(790\) 0 0
\(791\) 0 0
\(792\) 0.0466920 + 0.244768i 0.0466920 + 0.244768i
\(793\) 1.87819 1.87819
\(794\) 0.0415873 + 0.127993i 0.0415873 + 0.127993i
\(795\) 0 0
\(796\) −0.678061 + 0.492640i −0.678061 + 0.492640i
\(797\) −0.500000 + 1.53884i −0.500000 + 1.53884i 0.309017 + 0.951057i \(0.400000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(798\) 0 0
\(799\) 1.80760 1.31330i 1.80760 1.31330i
\(800\) −0.298408 0.216806i −0.298408 0.216806i
\(801\) 0 0
\(802\) 0 0
\(803\) −0.620759 + 1.31918i −0.620759 + 1.31918i
\(804\) 0 0
\(805\) 0 0
\(806\) −0.0223610 0.0162462i −0.0223610 0.0162462i
\(807\) 0 0
\(808\) 0 0
\(809\) 0.598617 1.84235i 0.598617 1.84235i 0.0627905 0.998027i \(-0.480000\pi\)
0.535827 0.844328i \(-0.320000\pi\)
\(810\) 0 0
\(811\) 1.60528 + 1.16630i 1.60528 + 1.16630i 0.876307 + 0.481754i \(0.160000\pi\)
0.728969 + 0.684547i \(0.240000\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0.158834 + 0.0200654i 0.158834 + 0.0200654i
\(815\) 0 0
\(816\) 0 0
\(817\) 0 0
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(822\) 0 0
\(823\) 0.331159 + 1.01920i 0.331159 + 1.01920i 0.968583 + 0.248690i \(0.0800000\pi\)
−0.637424 + 0.770513i \(0.720000\pi\)
\(824\) 0.0933839 0.0933839
\(825\) 0 0
\(826\) 0 0
\(827\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(828\) 0 0
\(829\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 1.28549 0.933960i 1.28549 0.933960i
\(833\) 1.03137 + 0.749337i 1.03137 + 0.749337i
\(834\) 0 0
\(835\) 0 0
\(836\) −1.67078 + 0.918519i −1.67078 + 0.918519i
\(837\) 0 0
\(838\) 0.0751750 + 0.231365i 0.0751750 + 0.231365i
\(839\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(840\) 0 0
\(841\) 0.309017 0.951057i 0.309017 0.951057i
\(842\) 0 0
\(843\) 0 0
\(844\) 1.16089 + 0.843439i 1.16089 + 0.843439i
\(845\) 0 0
\(846\) 0.220095 0.220095
\(847\) 0 0
\(848\) 0 0
\(849\) 0 0
\(850\) 0.129521 + 0.0941025i 0.129521 + 0.0941025i
\(851\) 0 0
\(852\) 0 0
\(853\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0.143188 + 0.440688i 0.143188 + 0.440688i
\(857\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(858\) 0 0
\(859\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0.0865160 0.0628575i 0.0865160 0.0628575i
\(863\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(864\) 0 0
\(865\) 0 0
\(866\) 0.188925 + 0.137262i 0.188925 + 0.137262i
\(867\) 0 0
\(868\) 0 0
\(869\) −1.44644 1.35830i −1.44644 1.35830i
\(870\) 0 0
\(871\) 0 0
\(872\) 0 0
\(873\) 0 0
\(874\) 0 0
\(875\) 0 0
\(876\) 0 0
\(877\) −1.56720 1.13864i −1.56720 1.13864i −0.929776 0.368125i \(-0.880000\pi\)
−0.637424 0.770513i \(-0.720000\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(882\) 0.0388067 + 0.119435i 0.0388067 + 0.119435i
\(883\) 1.50441 + 1.09302i 1.50441 + 1.09302i 0.968583 + 0.248690i \(0.0800000\pi\)
0.535827 + 0.844328i \(0.320000\pi\)
\(884\) −1.77909 + 1.29259i −1.77909 + 1.29259i
\(885\) 0 0
\(886\) −0.0494726 + 0.152261i −0.0494726 + 0.152261i
\(887\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(888\) 0 0
\(889\) 0 0
\(890\) 0 0
\(891\) −0.425779 + 0.904827i −0.425779 + 0.904827i
\(892\) 0 0
\(893\) 1.04914 + 3.22894i 1.04914 + 3.22894i
\(894\) 0 0
\(895\) 0 0
\(896\) 0 0
\(897\) 0 0
\(898\) 0.0865160 0.0628575i 0.0865160 0.0628575i
\(899\) 0 0
\(900\) −0.304144 0.936058i −0.304144 0.936058i
\(901\) 0 0
\(902\) 0.0200385 + 0.105045i 0.0200385 + 0.105045i
\(903\) 0 0
\(904\) −0.112263 0.345510i −0.112263 0.345510i
\(905\) 0 0
\(906\) 0 0
\(907\) −0.263146 + 0.809880i −0.263146 + 0.809880i 0.728969 + 0.684547i \(0.240000\pi\)
−0.992115 + 0.125333i \(0.960000\pi\)
\(908\) −0.187971 + 0.578516i −0.187971 + 0.578516i
\(909\) 0 0
\(910\) 0 0
\(911\) 0.190983 + 0.587785i 0.190983 + 0.587785i 1.00000 \(0\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(912\) 0 0
\(913\) 0 0
\(914\) −0.249182 −0.249182
\(915\) 0 0
\(916\) 0 0
\(917\) 0 0
\(918\) 0 0
\(919\) −0.393950 + 1.21245i −0.393950 + 1.21245i 0.535827 + 0.844328i \(0.320000\pi\)
−0.929776 + 0.368125i \(0.880000\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 0 0
\(923\) −3.25908 −3.25908
\(924\) 0 0
\(925\) −1.27485 −1.27485
\(926\) −0.0494726 0.152261i −0.0494726 0.152261i
\(927\) 0.303189 + 0.220280i 0.303189 + 0.220280i
\(928\) 0 0
\(929\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(930\) 0 0
\(931\) −1.56720 + 1.13864i −1.56720 + 1.13864i
\(932\) 0 0
\(933\) 0 0
\(934\) 0 0
\(935\) 0 0
\(936\) −0.436719 −0.436719
\(937\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0 0
\(941\) 0.450527 1.38658i 0.450527 1.38658i −0.425779 0.904827i \(-0.640000\pi\)
0.876307 0.481754i \(-0.160000\pi\)
\(942\) 0 0
\(943\) 0 0
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(948\) 0 0
\(949\) −2.06720 1.50191i −2.06720 1.50191i
\(950\) −0.196811 + 0.142991i −0.196811 + 0.142991i
\(951\) 0 0
\(952\) 0 0
\(953\) 0.303189 0.220280i 0.303189 0.220280i −0.425779 0.904827i \(-0.640000\pi\)
0.728969 + 0.684547i \(0.240000\pi\)
\(954\) 0 0
\(955\) 0 0
\(956\) 0 0
\(957\) 0 0
\(958\) 0.183089 0.183089
\(959\) 0 0
\(960\) 0 0
\(961\) 0.796258 0.578516i 0.796258 0.578516i
\(962\) −0.0867064 + 0.266855i −0.0867064 + 0.266855i
\(963\) −0.574633 + 1.76854i −0.574633 + 1.76854i
\(964\) 0 0
\(965\) 0 0
\(966\) 0 0
\(967\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(968\) 0.231683 0.0917299i 0.231683 0.0917299i
\(969\) 0 0
\(970\) 0 0
\(971\) 1.60528 + 1.16630i 1.60528 + 1.16630i 0.876307 + 0.481754i \(0.160000\pi\)
0.728969 + 0.684547i \(0.240000\pi\)
\(972\) 0 0
\(973\) 0 0
\(974\) 0 0
\(975\) 0 0
\(976\) −0.826183 0.600257i −0.826183 0.600257i
\(977\) −0.115808 0.356420i −0.115808 0.356420i 0.876307 0.481754i \(-0.160000\pi\)
−0.992115 + 0.125333i \(0.960000\pi\)
\(978\) 0 0
\(979\) 0 0
\(980\) 0 0
\(981\) 0 0
\(982\) 0 0
\(983\) 1.60528 1.16630i 1.60528 1.16630i 0.728969 0.684547i \(-0.240000\pi\)
0.876307 0.481754i \(-0.160000\pi\)
\(984\) 0 0
\(985\) 0 0
\(986\) 0 0
\(987\) 0 0
\(988\) −1.03260 3.17801i −1.03260 3.17801i
\(989\) 0 0
\(990\) 0 0
\(991\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(992\) 0.0143139 + 0.0440538i 0.0143139 + 0.0440538i
\(993\) 0 0
\(994\) 0 0
\(995\) 0 0
\(996\) 0 0
\(997\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(998\) 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 1397.1.l.a.126.3 20
11.9 even 5 inner 1397.1.l.a.1142.3 yes 20
127.126 odd 2 CM 1397.1.l.a.126.3 20
1397.1142 odd 10 inner 1397.1.l.a.1142.3 yes 20
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1397.1.l.a.126.3 20 1.1 even 1 trivial
1397.1.l.a.126.3 20 127.126 odd 2 CM
1397.1.l.a.1142.3 yes 20 11.9 even 5 inner
1397.1.l.a.1142.3 yes 20 1397.1142 odd 10 inner