Properties

Label 1397.1.l.a.1015.1
Level $1397$
Weight $1$
Character 1397.1015
Analytic conductor $0.697$
Analytic rank $0$
Dimension $20$
Projective image $D_{25}$
CM discriminant -127
Inner twists $4$

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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 1015.1
Root \(0.187381 - 0.982287i\) of defining polynomial
Character \(\chi\) \(=\) 1397.1015
Dual form 1397.1.l.a.1269.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.41789 + 1.03016i) q^{2} +(0.640176 - 1.97026i) q^{4} +(0.580394 + 1.78627i) q^{8} +(-0.809017 + 0.587785i) q^{9} +O(q^{10})\) \(q+(-1.41789 + 1.03016i) q^{2} +(0.640176 - 1.97026i) q^{4} +(0.580394 + 1.78627i) q^{8} +(-0.809017 + 0.587785i) q^{9} +(-0.637424 - 0.770513i) q^{11} +(1.03137 - 0.749337i) q^{13} +(-0.987078 - 0.717154i) q^{16} +(-1.17950 - 0.856954i) q^{17} +(0.541587 - 1.66683i) q^{18} +(-0.263146 - 0.809880i) q^{19} +(1.69755 + 0.435857i) q^{22} +(0.309017 + 0.951057i) q^{25} +(-0.690441 + 2.12496i) q^{26} +(-1.41789 + 1.03016i) q^{31} +0.260160 q^{32} +2.55520 q^{34} +(0.640176 + 1.97026i) q^{36} +(0.450527 - 1.38658i) q^{37} +(1.20742 + 0.877242i) q^{38} +(-0.574633 - 1.76854i) q^{41} +(-1.92617 + 0.762627i) q^{44} +(-0.393950 - 1.21245i) q^{47} +(-0.809017 - 0.587785i) q^{49} +(-1.41789 - 1.03016i) q^{50} +(-0.816127 - 2.51178i) q^{52} +(0.303189 + 0.220280i) q^{61} +(0.949193 - 2.92132i) q^{62} +(0.618198 - 0.449147i) q^{64} +(-2.44351 + 1.77531i) q^{68} +(1.60528 + 1.16630i) q^{71} +(-1.51949 - 1.10397i) q^{72} +(0.598617 - 1.84235i) q^{73} +(0.789600 + 2.43014i) q^{74} -1.76413 q^{76} +(-0.866986 + 0.629902i) q^{79} +(0.309017 - 0.951057i) q^{81} +(2.63665 + 1.91564i) q^{82} +(1.00639 - 1.58581i) q^{88} +(1.80760 + 1.31330i) q^{94} +1.75261 q^{98} +(0.968583 + 0.248690i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 20 q - 5 q^{4} - 5 q^{9}+O(q^{10}) \) 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 \(\left(\mathbb{Z}/1397\mathbb{Z}\right)^\times\).

\(n\) \(255\) \(892\)
\(\chi(n)\) \(e\left(\frac{4}{5}\right)\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.41789 + 1.03016i −1.41789 + 1.03016i −0.425779 + 0.904827i \(0.640000\pi\)
−0.992115 + 0.125333i \(0.960000\pi\)
\(3\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(4\) 0.640176 1.97026i 0.640176 1.97026i
\(5\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(6\) 0 0
\(7\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(8\) 0.580394 + 1.78627i 0.580394 + 1.78627i
\(9\) −0.809017 + 0.587785i −0.809017 + 0.587785i
\(10\) 0 0
\(11\) −0.637424 0.770513i −0.637424 0.770513i
\(12\) 0 0
\(13\) 1.03137 0.749337i 1.03137 0.749337i 0.0627905 0.998027i \(-0.480000\pi\)
0.968583 + 0.248690i \(0.0800000\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) −0.987078 0.717154i −0.987078 0.717154i
\(17\) −1.17950 0.856954i −1.17950 0.856954i −0.187381 0.982287i \(-0.560000\pi\)
−0.992115 + 0.125333i \(0.960000\pi\)
\(18\) 0.541587 1.66683i 0.541587 1.66683i
\(19\) −0.263146 0.809880i −0.263146 0.809880i −0.992115 0.125333i \(-0.960000\pi\)
0.728969 0.684547i \(-0.240000\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 1.69755 + 0.435857i 1.69755 + 0.435857i
\(23\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(24\) 0 0
\(25\) 0.309017 + 0.951057i 0.309017 + 0.951057i
\(26\) −0.690441 + 2.12496i −0.690441 + 2.12496i
\(27\) 0 0
\(28\) 0 0
\(29\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(30\) 0 0
\(31\) −1.41789 + 1.03016i −1.41789 + 1.03016i −0.425779 + 0.904827i \(0.640000\pi\)
−0.992115 + 0.125333i \(0.960000\pi\)
\(32\) 0.260160 0.260160
\(33\) 0 0
\(34\) 2.55520 2.55520
\(35\) 0 0
\(36\) 0.640176 + 1.97026i 0.640176 + 1.97026i
\(37\) 0.450527 1.38658i 0.450527 1.38658i −0.425779 0.904827i \(-0.640000\pi\)
0.876307 0.481754i \(-0.160000\pi\)
\(38\) 1.20742 + 0.877242i 1.20742 + 0.877242i
\(39\) 0 0
\(40\) 0 0
\(41\) −0.574633 1.76854i −0.574633 1.76854i −0.637424 0.770513i \(-0.720000\pi\)
0.0627905 0.998027i \(-0.480000\pi\)
\(42\) 0 0
\(43\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(44\) −1.92617 + 0.762627i −1.92617 + 0.762627i
\(45\) 0 0
\(46\) 0 0
\(47\) −0.393950 1.21245i −0.393950 1.21245i −0.929776 0.368125i \(-0.880000\pi\)
0.535827 0.844328i \(-0.320000\pi\)
\(48\) 0 0
\(49\) −0.809017 0.587785i −0.809017 0.587785i
\(50\) −1.41789 1.03016i −1.41789 1.03016i
\(51\) 0 0
\(52\) −0.816127 2.51178i −0.816127 2.51178i
\(53\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(60\) 0 0
\(61\) 0.303189 + 0.220280i 0.303189 + 0.220280i 0.728969 0.684547i \(-0.240000\pi\)
−0.425779 + 0.904827i \(0.640000\pi\)
\(62\) 0.949193 2.92132i 0.949193 2.92132i
\(63\) 0 0
\(64\) 0.618198 0.449147i 0.618198 0.449147i
\(65\) 0 0
\(66\) 0 0
\(67\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(68\) −2.44351 + 1.77531i −2.44351 + 1.77531i
\(69\) 0 0
\(70\) 0 0
\(71\) 1.60528 + 1.16630i 1.60528 + 1.16630i 0.876307 + 0.481754i \(0.160000\pi\)
0.728969 + 0.684547i \(0.240000\pi\)
\(72\) −1.51949 1.10397i −1.51949 1.10397i
\(73\) 0.598617 1.84235i 0.598617 1.84235i 0.0627905 0.998027i \(-0.480000\pi\)
0.535827 0.844328i \(-0.320000\pi\)
\(74\) 0.789600 + 2.43014i 0.789600 + 2.43014i
\(75\) 0 0
\(76\) −1.76413 −1.76413
\(77\) 0 0
\(78\) 0 0
\(79\) −0.866986 + 0.629902i −0.866986 + 0.629902i −0.929776 0.368125i \(-0.880000\pi\)
0.0627905 + 0.998027i \(0.480000\pi\)
\(80\) 0 0
\(81\) 0.309017 0.951057i 0.309017 0.951057i
\(82\) 2.63665 + 1.91564i 2.63665 + 1.91564i
\(83\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 0 0
\(87\) 0 0
\(88\) 1.00639 1.58581i 1.00639 1.58581i
\(89\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 0 0
\(93\) 0 0
\(94\) 1.80760 + 1.31330i 1.80760 + 1.31330i
\(95\) 0 0
\(96\) 0 0
\(97\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(98\) 1.75261 1.75261
\(99\) 0.968583 + 0.248690i 0.968583 + 0.248690i
\(100\) 2.07165 2.07165
\(101\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(102\) 0 0
\(103\) 0.0388067 0.119435i 0.0388067 0.119435i −0.929776 0.368125i \(-0.880000\pi\)
0.968583 + 0.248690i \(0.0800000\pi\)
\(104\) 1.93712 + 1.40740i 1.93712 + 1.40740i
\(105\) 0 0
\(106\) 0 0
\(107\) −0.613161 1.88711i −0.613161 1.88711i −0.425779 0.904827i \(-0.640000\pi\)
−0.187381 0.982287i \(-0.560000\pi\)
\(108\) 0 0
\(109\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) 0.598617 + 1.84235i 0.598617 + 1.84235i 0.535827 + 0.844328i \(0.320000\pi\)
0.0627905 + 0.998027i \(0.480000\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 0 0
\(117\) −0.393950 + 1.21245i −0.393950 + 1.21245i
\(118\) 0 0
\(119\) 0 0
\(120\) 0 0
\(121\) −0.187381 + 0.982287i −0.187381 + 0.982287i
\(122\) −0.656814 −0.656814
\(123\) 0 0
\(124\) 1.12198 + 3.45310i 1.12198 + 3.45310i
\(125\) 0 0
\(126\) 0 0
\(127\) −0.809017 0.587785i −0.809017 0.587785i
\(128\) −0.494239 + 1.52111i −0.494239 + 1.52111i
\(129\) 0 0
\(130\) 0 0
\(131\) 0.618034 0.618034 0.309017 0.951057i \(-0.400000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 0 0
\(135\) 0 0
\(136\) 0.846178 2.60427i 0.846178 2.60427i
\(137\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(138\) 0 0
\(139\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) −3.47759 −3.47759
\(143\) −1.23480 0.317042i −1.23480 0.317042i
\(144\) 1.22010 1.22010
\(145\) 0 0
\(146\) 1.04914 + 3.22894i 1.04914 + 3.22894i
\(147\) 0 0
\(148\) −2.44351 1.77531i −2.44351 1.77531i
\(149\) 1.60528 + 1.16630i 1.60528 + 1.16630i 0.876307 + 0.481754i \(0.160000\pi\)
0.728969 + 0.684547i \(0.240000\pi\)
\(150\) 0 0
\(151\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(152\) 1.29394 0.940099i 1.29394 0.940099i
\(153\) 1.45794 1.45794
\(154\) 0 0
\(155\) 0 0
\(156\) 0 0
\(157\) −0.574633 1.76854i −0.574633 1.76854i −0.637424 0.770513i \(-0.720000\pi\)
0.0627905 0.998027i \(-0.480000\pi\)
\(158\) 0.580394 1.78627i 0.580394 1.78627i
\(159\) 0 0
\(160\) 0 0
\(161\) 0 0
\(162\) 0.541587 + 1.66683i 0.541587 + 1.66683i
\(163\) 1.30902 0.951057i 1.30902 0.951057i 0.309017 0.951057i \(-0.400000\pi\)
1.00000 \(0\)
\(164\) −3.85235 −3.85235
\(165\) 0 0
\(166\) 0 0
\(167\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(168\) 0 0
\(169\) 0.193209 0.594636i 0.193209 0.594636i
\(170\) 0 0
\(171\) 0.688925 + 0.500534i 0.688925 + 0.500534i
\(172\) 0 0
\(173\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0.0766104 + 1.21769i 0.0766104 + 1.21769i
\(177\) 0 0
\(178\) 0 0
\(179\) −0.115808 0.356420i −0.115808 0.356420i 0.876307 0.481754i \(-0.160000\pi\)
−0.992115 + 0.125333i \(0.960000\pi\)
\(180\) 0 0
\(181\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 0 0
\(186\) 0 0
\(187\) 0.0915446 + 1.45506i 0.0915446 + 1.45506i
\(188\) −2.64104 −2.64104
\(189\) 0 0
\(190\) 0 0
\(191\) 0.190983 0.587785i 0.190983 0.587785i −0.809017 0.587785i \(-0.800000\pi\)
1.00000 \(0\)
\(192\) 0 0
\(193\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) −1.67600 + 1.21769i −1.67600 + 1.21769i
\(197\) 1.07165 1.07165 0.535827 0.844328i \(-0.320000\pi\)
0.535827 + 0.844328i \(0.320000\pi\)
\(198\) −1.62954 + 0.645180i −1.62954 + 0.645180i
\(199\) −1.85955 −1.85955 −0.929776 0.368125i \(-0.880000\pi\)
−0.929776 + 0.368125i \(0.880000\pi\)
\(200\) −1.51949 + 1.10397i −1.51949 + 1.10397i
\(201\) 0 0
\(202\) 0 0
\(203\) 0 0
\(204\) 0 0
\(205\) 0 0
\(206\) 0.0680131 + 0.209323i 0.0680131 + 0.209323i
\(207\) 0 0
\(208\) −1.55544 −1.55544
\(209\) −0.456288 + 0.718995i −0.456288 + 0.718995i
\(210\) 0 0
\(211\) −1.56720 + 1.13864i −1.56720 + 1.13864i −0.637424 + 0.770513i \(0.720000\pi\)
−0.929776 + 0.368125i \(0.880000\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 2.81343 + 2.04407i 2.81343 + 2.04407i
\(215\) 0 0
\(216\) 0 0
\(217\) 0 0
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) −1.85865 −1.85865
\(222\) 0 0
\(223\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(224\) 0 0
\(225\) −0.809017 0.587785i −0.809017 0.587785i
\(226\) −2.74670 1.99559i −2.74670 1.99559i
\(227\) −0.500000 + 1.53884i −0.500000 + 1.53884i 0.309017 + 0.951057i \(0.400000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(228\) 0 0
\(229\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(234\) −0.690441 2.12496i −0.690441 2.12496i
\(235\) 0 0
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(240\) 0 0
\(241\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(242\) −0.746226 1.58581i −0.746226 1.58581i
\(243\) 0 0
\(244\) 0.628103 0.456344i 0.628103 0.456344i
\(245\) 0 0
\(246\) 0 0
\(247\) −0.878275 0.638104i −0.878275 0.638104i
\(248\) −2.66308 1.93484i −2.66308 1.93484i
\(249\) 0 0
\(250\) 0 0
\(251\) −1.56720 + 1.13864i −1.56720 + 1.13864i −0.637424 + 0.770513i \(0.720000\pi\)
−0.929776 + 0.368125i \(0.880000\pi\)
\(252\) 0 0
\(253\) 0 0
\(254\) 1.75261 1.75261
\(255\) 0 0
\(256\) −0.630080 1.93919i −0.630080 1.93919i
\(257\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 0 0
\(261\) 0 0
\(262\) −0.876307 + 0.636674i −0.876307 + 0.636674i
\(263\) −0.374763 −0.374763 −0.187381 0.982287i \(-0.560000\pi\)
−0.187381 + 0.982287i \(0.560000\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) 0.688925 + 0.500534i 0.688925 + 0.500534i 0.876307 0.481754i \(-0.160000\pi\)
−0.187381 + 0.982287i \(0.560000\pi\)
\(270\) 0 0
\(271\) −0.500000 + 1.53884i −0.500000 + 1.53884i 0.309017 + 0.951057i \(0.400000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(272\) 0.549686 + 1.69176i 0.549686 + 1.69176i
\(273\) 0 0
\(274\) 0 0
\(275\) 0.535827 0.844328i 0.535827 0.844328i
\(276\) 0 0
\(277\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(278\) 0 0
\(279\) 0.541587 1.66683i 0.541587 1.66683i
\(280\) 0 0
\(281\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(282\) 0 0
\(283\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(284\) 3.32557 2.41617i 3.32557 2.41617i
\(285\) 0 0
\(286\) 2.07741 0.822506i 2.07741 0.822506i
\(287\) 0 0
\(288\) −0.210474 + 0.152918i −0.210474 + 0.152918i
\(289\) 0.347824 + 1.07049i 0.347824 + 1.07049i
\(290\) 0 0
\(291\) 0 0
\(292\) −3.24670 2.35886i −3.24670 2.35886i
\(293\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 2.73829 2.73829
\(297\) 0 0
\(298\) −3.47759 −3.47759
\(299\) 0 0
\(300\) 0 0
\(301\) 0 0
\(302\) 0 0
\(303\) 0 0
\(304\) −0.321063 + 0.988131i −0.321063 + 0.988131i
\(305\) 0 0
\(306\) −2.06720 + 1.50191i −2.06720 + 1.50191i
\(307\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(312\) 0 0
\(313\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(314\) 2.63665 + 1.91564i 2.63665 + 1.91564i
\(315\) 0 0
\(316\) 0.686047 + 2.11144i 0.686047 + 2.11144i
\(317\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(318\) 0 0
\(319\) 0 0
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) −0.383650 + 1.18075i −0.383650 + 1.18075i
\(324\) −1.67600 1.21769i −1.67600 1.21769i
\(325\) 1.03137 + 0.749337i 1.03137 + 0.749337i
\(326\) −0.876307 + 2.69699i −0.876307 + 2.69699i
\(327\) 0 0
\(328\) 2.82557 2.05290i 2.82557 2.05290i
\(329\) 0 0
\(330\) 0 0
\(331\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(332\) 0 0
\(333\) 0.450527 + 1.38658i 0.450527 + 1.38658i
\(334\) 0 0
\(335\) 0 0
\(336\) 0 0
\(337\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(338\) 0.338621 + 1.04217i 0.338621 + 1.04217i
\(339\) 0 0
\(340\) 0 0
\(341\) 1.69755 + 0.435857i 1.69755 + 0.435857i
\(342\) −1.49245 −1.49245
\(343\) 0 0
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(348\) 0 0
\(349\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) −0.165832 0.200457i −0.165832 0.200457i
\(353\) −0.851559 −0.851559 −0.425779 0.904827i \(-0.640000\pi\)
−0.425779 + 0.904827i \(0.640000\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 0 0
\(357\) 0 0
\(358\) 0.531374 + 0.386066i 0.531374 + 0.386066i
\(359\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(360\) 0 0
\(361\) 0.222357 0.161552i 0.222357 0.161552i
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) 0 0
\(366\) 0 0
\(367\) −0.115808 + 0.356420i −0.115808 + 0.356420i −0.992115 0.125333i \(-0.960000\pi\)
0.876307 + 0.481754i \(0.160000\pi\)
\(368\) 0 0
\(369\) 1.50441 + 1.09302i 1.50441 + 1.09302i
\(370\) 0 0
\(371\) 0 0
\(372\) 0 0
\(373\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(374\) −1.62875 1.96882i −1.62875 1.96882i
\(375\) 0 0
\(376\) 1.93712 1.40740i 1.93712 1.40740i
\(377\) 0 0
\(378\) 0 0
\(379\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0.334719 + 1.03016i 0.334719 + 1.03016i
\(383\) 1.30902 0.951057i 1.30902 0.951057i 0.309017 0.951057i \(-0.400000\pi\)
1.00000 \(0\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) −0.393950 + 1.21245i −0.393950 + 1.21245i 0.535827 + 0.844328i \(0.320000\pi\)
−0.929776 + 0.368125i \(0.880000\pi\)
\(390\) 0 0
\(391\) 0 0
\(392\) 0.580394 1.78627i 0.580394 1.78627i
\(393\) 0 0
\(394\) −1.51949 + 1.10397i −1.51949 + 1.10397i
\(395\) 0 0
\(396\) 1.11005 1.74915i 1.11005 1.74915i
\(397\) −0.374763 −0.374763 −0.187381 0.982287i \(-0.560000\pi\)
−0.187381 + 0.982287i \(0.560000\pi\)
\(398\) 2.63665 1.91564i 2.63665 1.91564i
\(399\) 0 0
\(400\) 0.377030 1.16038i 0.377030 1.16038i
\(401\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(402\) 0 0
\(403\) −0.690441 + 2.12496i −0.690441 + 2.12496i
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) −1.35556 + 0.536702i −1.35556 + 0.536702i
\(408\) 0 0
\(409\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) −0.210474 0.152918i −0.210474 0.152918i
\(413\) 0 0
\(414\) 0 0
\(415\) 0 0
\(416\) 0.268323 0.194948i 0.268323 0.194948i
\(417\) 0 0
\(418\) −0.0937119 1.48951i −0.0937119 1.48951i
\(419\) −0.851559 −0.851559 −0.425779 0.904827i \(-0.640000\pi\)
−0.425779 + 0.904827i \(0.640000\pi\)
\(420\) 0 0
\(421\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(422\) 1.04914 3.22894i 1.04914 3.22894i
\(423\) 1.03137 + 0.749337i 1.03137 + 0.749337i
\(424\) 0 0
\(425\) 0.450527 1.38658i 0.450527 1.38658i
\(426\) 0 0
\(427\) 0 0
\(428\) −4.11064 −4.11064
\(429\) 0 0
\(430\) 0 0
\(431\) 1.50441 1.09302i 1.50441 1.09302i 0.535827 0.844328i \(-0.320000\pi\)
0.968583 0.248690i \(-0.0800000\pi\)
\(432\) 0 0
\(433\) −0.613161 + 1.88711i −0.613161 + 1.88711i −0.187381 + 0.982287i \(0.560000\pi\)
−0.425779 + 0.904827i \(0.640000\pi\)
\(434\) 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
\(442\) 2.63537 1.91471i 2.63537 1.91471i
\(443\) 0.450527 + 1.38658i 0.450527 + 1.38658i 0.876307 + 0.481754i \(0.160000\pi\)
−0.425779 + 0.904827i \(0.640000\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) 1.50441 1.09302i 1.50441 1.09302i 0.535827 0.844328i \(-0.320000\pi\)
0.968583 0.248690i \(-0.0800000\pi\)
\(450\) 1.75261 1.75261
\(451\) −0.996398 + 1.57007i −0.996398 + 1.57007i
\(452\) 4.01314 4.01314
\(453\) 0 0
\(454\) −0.876307 2.69699i −0.876307 2.69699i
\(455\) 0 0
\(456\) 0 0
\(457\) −0.866986 0.629902i −0.866986 0.629902i 0.0627905 0.998027i \(-0.480000\pi\)
−0.929776 + 0.368125i \(0.880000\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(462\) 0 0
\(463\) 1.45794 1.45794 0.728969 0.684547i \(-0.240000\pi\)
0.728969 + 0.684547i \(0.240000\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(468\) 2.13665 + 1.55237i 2.13665 + 1.55237i
\(469\) 0 0
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) 0 0
\(474\) 0 0
\(475\) 0.688925 0.500534i 0.688925 0.500534i
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) −1.56720 1.13864i −1.56720 1.13864i −0.929776 0.368125i \(-0.880000\pi\)
−0.637424 0.770513i \(-0.720000\pi\)
\(480\) 0 0
\(481\) −0.574354 1.76768i −0.574354 1.76768i
\(482\) 0 0
\(483\) 0 0
\(484\) 1.81540 + 0.998027i 1.81540 + 0.998027i
\(485\) 0 0
\(486\) 0 0
\(487\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(488\) −0.217510 + 0.669427i −0.217510 + 0.669427i
\(489\) 0 0
\(490\) 0 0
\(491\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(492\) 0 0
\(493\) 0 0
\(494\) 1.90265 1.90265
\(495\) 0 0
\(496\) 2.13835 2.13835
\(497\) 0 0
\(498\) 0 0
\(499\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 1.04914 3.22894i 1.04914 3.22894i
\(503\) 0.0388067 + 0.119435i 0.0388067 + 0.119435i 0.968583 0.248690i \(-0.0800000\pi\)
−0.929776 + 0.368125i \(0.880000\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) 0 0
\(508\) −1.67600 + 1.21769i −1.67600 + 1.21769i
\(509\) −0.500000 1.53884i −0.500000 1.53884i −0.809017 0.587785i \(-0.800000\pi\)
0.309017 0.951057i \(-0.400000\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 1.59713 + 1.16038i 1.59713 + 1.16038i
\(513\) 0 0
\(514\) 0 0
\(515\) 0 0
\(516\) 0 0
\(517\) −0.683098 + 1.07639i −0.683098 + 1.07639i
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 0.541587 1.66683i 0.541587 1.66683i −0.187381 0.982287i \(-0.560000\pi\)
0.728969 0.684547i \(-0.240000\pi\)
\(522\) 0 0
\(523\) −0.101597 0.0738147i −0.101597 0.0738147i 0.535827 0.844328i \(-0.320000\pi\)
−0.637424 + 0.770513i \(0.720000\pi\)
\(524\) 0.395651 1.21769i 0.395651 1.21769i
\(525\) 0 0
\(526\) 0.531374 0.386066i 0.531374 0.386066i
\(527\) 2.55520 2.55520
\(528\) 0 0
\(529\) 1.00000 1.00000
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) −1.91789 1.39343i −1.91789 1.39343i
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) 0 0
\(538\) −1.49245 −1.49245
\(539\) 0.0627905 + 0.998027i 0.0627905 + 0.998027i
\(540\) 0 0
\(541\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(542\) −0.876307 2.69699i −0.876307 2.69699i
\(543\) 0 0
\(544\) −0.306858 0.222946i −0.306858 0.222946i
\(545\) 0 0
\(546\) 0 0
\(547\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(548\) 0 0
\(549\) −0.374763 −0.374763
\(550\) 0.110048 + 1.74915i 0.110048 + 1.74915i
\(551\) 0 0
\(552\) 0 0
\(553\) 0 0
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 0.190983 0.587785i 0.190983 0.587785i −0.809017 0.587785i \(-0.800000\pi\)
1.00000 \(0\)
\(558\) 0.949193 + 2.92132i 0.949193 + 2.92132i
\(559\) 0 0
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 0 0
\(567\) 0 0
\(568\) −1.15163 + 3.54437i −1.15163 + 3.54437i
\(569\) 0.331159 + 1.01920i 0.331159 + 1.01920i 0.968583 + 0.248690i \(0.0800000\pi\)
−0.637424 + 0.770513i \(0.720000\pi\)
\(570\) 0 0
\(571\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(572\) −1.41514 + 2.22991i −1.41514 + 2.22991i
\(573\) 0 0
\(574\) 0 0
\(575\) 0 0
\(576\) −0.236131 + 0.726735i −0.236131 + 0.726735i
\(577\) 1.60528 + 1.16630i 1.60528 + 1.16630i 0.876307 + 0.481754i \(0.160000\pi\)
0.728969 + 0.684547i \(0.240000\pi\)
\(578\) −1.59595 1.15953i −1.59595 1.15953i
\(579\) 0 0
\(580\) 0 0
\(581\) 0 0
\(582\) 0 0
\(583\) 0 0
\(584\) 3.63837 3.63837
\(585\) 0 0
\(586\) 0 0
\(587\) −0.263146 + 0.809880i −0.263146 + 0.809880i 0.728969 + 0.684547i \(0.240000\pi\)
−0.992115 + 0.125333i \(0.960000\pi\)
\(588\) 0 0
\(589\) 1.20742 + 0.877242i 1.20742 + 0.877242i
\(590\) 0 0
\(591\) 0 0
\(592\) −1.43910 + 1.04557i −1.43910 + 1.04557i
\(593\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 3.32557 2.41617i 3.32557 2.41617i
\(597\) 0 0
\(598\) 0 0
\(599\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(600\) 0 0
\(601\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) 0 0
\(606\) 0 0
\(607\) 1.60528 1.16630i 1.60528 1.16630i 0.728969 0.684547i \(-0.240000\pi\)
0.876307 0.481754i \(-0.160000\pi\)
\(608\) −0.0684602 0.210699i −0.0684602 0.210699i
\(609\) 0 0
\(610\) 0 0
\(611\) −1.31484 0.955291i −1.31484 0.955291i
\(612\) 0.933337 2.87251i 0.933337 2.87251i
\(613\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(618\) 0 0
\(619\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 0 0
\(624\) 0 0
\(625\) −0.809017 + 0.587785i −0.809017 + 0.587785i
\(626\) 0 0
\(627\) 0 0
\(628\) −3.85235 −3.85235
\(629\) −1.71963 + 1.24939i −1.71963 + 1.24939i
\(630\) 0 0
\(631\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(632\) −1.62837 1.18308i −1.62837 1.18308i
\(633\) 0 0
\(634\) 0 0
\(635\) 0 0
\(636\) 0 0
\(637\) −1.27485 −1.27485
\(638\) 0 0
\(639\) −1.98423 −1.98423
\(640\) 0 0
\(641\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(642\) 0 0
\(643\) −0.101597 0.0738147i −0.101597 0.0738147i 0.535827 0.844328i \(-0.320000\pi\)
−0.637424 + 0.770513i \(0.720000\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) −0.672391 2.06941i −0.672391 2.06941i
\(647\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(648\) 1.87819 1.87819
\(649\) 0 0
\(650\) −2.23432 −2.23432
\(651\) 0 0
\(652\) −1.03583 3.18795i −1.03583 3.18795i
\(653\) 0.598617 1.84235i 0.598617 1.84235i 0.0627905 0.998027i \(-0.480000\pi\)
0.535827 0.844328i \(-0.320000\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) −0.701107 + 2.15779i −0.701107 + 2.15779i
\(657\) 0.598617 + 1.84235i 0.598617 + 1.84235i
\(658\) 0 0
\(659\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(660\) 0 0
\(661\) 1.93717 1.93717 0.968583 0.248690i \(-0.0800000\pi\)
0.968583 + 0.248690i \(0.0800000\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 0 0
\(666\) −2.06720 1.50191i −2.06720 1.50191i
\(667\) 0 0
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) −0.0235315 0.374023i −0.0235315 0.374023i
\(672\) 0 0
\(673\) 1.60528 1.16630i 1.60528 1.16630i 0.728969 0.684547i \(-0.240000\pi\)
0.876307 0.481754i \(-0.160000\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) −1.04790 0.761344i −1.04790 0.761344i
\(677\) 1.30902 + 0.951057i 1.30902 + 0.951057i 1.00000 \(0\)
0.309017 + 0.951057i \(0.400000\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 0 0
\(681\) 0 0
\(682\) −2.85595 + 1.13075i −2.85595 + 1.13075i
\(683\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(684\) 1.42721 1.03693i 1.42721 1.03693i
\(685\) 0 0
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) 0 0
\(690\) 0 0
\(691\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 0 0
\(696\) 0 0
\(697\) −0.837780 + 2.57842i −0.837780 + 2.57842i
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(702\) 0 0
\(703\) −1.24152 −1.24152
\(704\) −0.740128 0.190032i −0.740128 0.190032i
\(705\) 0 0
\(706\) 1.20742 0.877242i 1.20742 0.877242i
\(707\) 0 0
\(708\) 0 0
\(709\) 1.03137 + 0.749337i 1.03137 + 0.749337i 0.968583 0.248690i \(-0.0800000\pi\)
0.0627905 + 0.998027i \(0.480000\pi\)
\(710\) 0 0
\(711\) 0.331159 1.01920i 0.331159 1.01920i
\(712\) 0 0
\(713\) 0 0
\(714\) 0 0
\(715\) 0 0
\(716\) −0.776378 −0.776378
\(717\) 0 0
\(718\) 0 0
\(719\) 0.450527 1.38658i 0.450527 1.38658i −0.425779 0.904827i \(-0.640000\pi\)
0.876307 0.481754i \(-0.160000\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) −0.148854 + 0.458126i −0.148854 + 0.458126i
\(723\) 0 0
\(724\) 0 0
\(725\) 0 0
\(726\) 0 0
\(727\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(728\) 0 0
\(729\) 0.309017 + 0.951057i 0.309017 + 0.951057i
\(730\) 0 0
\(731\) 0 0
\(732\) 0 0
\(733\) 0.190983 0.587785i 0.190983 0.587785i −0.809017 0.587785i \(-0.800000\pi\)
1.00000 \(0\)
\(734\) −0.202967 0.624667i −0.202967 0.624667i
\(735\) 0 0
\(736\) 0 0
\(737\) 0 0
\(738\) −3.25908 −3.25908
\(739\) −0.101597 + 0.0738147i −0.101597 + 0.0738147i −0.637424 0.770513i \(-0.720000\pi\)
0.535827 + 0.844328i \(0.320000\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0 0
\(747\) 0 0
\(748\) 2.92545 + 0.751128i 2.92545 + 0.751128i
\(749\) 0 0
\(750\) 0 0
\(751\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(752\) −0.480656 + 1.47931i −0.480656 + 1.47931i
\(753\) 0 0
\(754\) 0 0
\(755\) 0 0
\(756\) 0 0
\(757\) −1.41789 + 1.03016i −1.41789 + 1.03016i −0.425779 + 0.904827i \(0.640000\pi\)
−0.992115 + 0.125333i \(0.960000\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) −1.03583 0.752572i −1.03583 0.752572i
\(765\) 0 0
\(766\) −0.876307 + 2.69699i −0.876307 + 2.69699i
\(767\) 0 0
\(768\) 0 0
\(769\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) −0.115808 0.356420i −0.115808 0.356420i 0.876307 0.481754i \(-0.160000\pi\)
−0.992115 + 0.125333i \(0.960000\pi\)
\(774\) 0 0
\(775\) −1.41789 1.03016i −1.41789 1.03016i
\(776\) 0 0
\(777\) 0 0
\(778\) −0.690441 2.12496i −0.690441 2.12496i
\(779\) −1.28109 + 0.930769i −1.28109 + 0.930769i
\(780\) 0 0
\(781\) −0.124591 1.98031i −0.124591 1.98031i
\(782\) 0 0
\(783\) 0 0
\(784\) 0.377030 + 1.16038i 0.377030 + 1.16038i
\(785\) 0 0
\(786\) 0 0
\(787\) 1.50441 + 1.09302i 1.50441 + 1.09302i 0.968583 + 0.248690i \(0.0800000\pi\)
0.535827 + 0.844328i \(0.320000\pi\)
\(788\) 0.686047 2.11144i 0.686047 2.11144i
\(789\) 0 0
\(790\) 0 0
\(791\) 0 0
\(792\) 0.117933 + 1.87449i 0.117933 + 1.87449i
\(793\) 0.477765 0.477765
\(794\) 0.531374 0.386066i 0.531374 0.386066i
\(795\) 0 0
\(796\) −1.19044 + 3.66380i −1.19044 + 3.66380i
\(797\) −0.500000 0.363271i −0.500000 0.363271i 0.309017 0.951057i \(-0.400000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(798\) 0 0
\(799\) −0.574354 + 1.76768i −0.574354 + 1.76768i
\(800\) 0.0803940 + 0.247427i 0.0803940 + 0.247427i
\(801\) 0 0
\(802\) 0 0
\(803\) −1.80113 + 0.713118i −1.80113 + 0.713118i
\(804\) 0 0
\(805\) 0 0
\(806\) −1.21008 3.72423i −1.21008 3.72423i
\(807\) 0 0
\(808\) 0 0
\(809\) 0.688925 + 0.500534i 0.688925 + 0.500534i 0.876307 0.481754i \(-0.160000\pi\)
−0.187381 + 0.982287i \(0.560000\pi\)
\(810\) 0 0
\(811\) 0.331159 + 1.01920i 0.331159 + 1.01920i 0.968583 + 0.248690i \(0.0800000\pi\)
−0.637424 + 0.770513i \(0.720000\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 1.36914 2.15743i 1.36914 2.15743i
\(815\) 0 0
\(816\) 0 0
\(817\) 0 0
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(822\) 0 0
\(823\) 0.303189 0.220280i 0.303189 0.220280i −0.425779 0.904827i \(-0.640000\pi\)
0.728969 + 0.684547i \(0.240000\pi\)
\(824\) 0.235866 0.235866
\(825\) 0 0
\(826\) 0 0
\(827\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(828\) 0 0
\(829\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0.301031 0.926477i 0.301031 0.926477i
\(833\) 0.450527 + 1.38658i 0.450527 + 1.38658i
\(834\) 0 0
\(835\) 0 0
\(836\) 1.12450 + 1.35929i 1.12450 + 1.35929i
\(837\) 0 0
\(838\) 1.20742 0.877242i 1.20742 0.877242i
\(839\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(840\) 0 0
\(841\) −0.809017 0.587785i −0.809017 0.587785i
\(842\) 0 0
\(843\) 0 0
\(844\) 1.24013 + 3.81672i 1.24013 + 3.81672i
\(845\) 0 0
\(846\) −2.23432 −2.23432
\(847\) 0 0
\(848\) 0 0
\(849\) 0 0
\(850\) 0.789600 + 2.43014i 0.789600 + 2.43014i
\(851\) 0 0
\(852\) 0 0
\(853\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 3.01502 2.19054i 3.01502 2.19054i
\(857\) 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
\(862\) −1.00711 + 3.09957i −1.00711 + 3.09957i
\(863\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(864\) 0 0
\(865\) 0 0
\(866\) −1.07463 3.30738i −1.07463 3.30738i
\(867\) 0 0
\(868\) 0 0
\(869\) 1.03799 + 0.266509i 1.03799 + 0.266509i
\(870\) 0 0
\(871\) 0 0
\(872\) 0 0
\(873\) 0 0
\(874\) 0 0
\(875\) 0 0
\(876\) 0 0
\(877\) −0.263146 0.809880i −0.263146 0.809880i −0.992115 0.125333i \(-0.960000\pi\)
0.728969 0.684547i \(-0.240000\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(882\) −1.41789 + 1.03016i −1.41789 + 1.03016i
\(883\) −0.613161 1.88711i −0.613161 1.88711i −0.425779 0.904827i \(-0.640000\pi\)
−0.187381 0.982287i \(-0.560000\pi\)
\(884\) −1.18986 + 3.66202i −1.18986 + 3.66202i
\(885\) 0 0
\(886\) −2.06720 1.50191i −2.06720 1.50191i
\(887\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(888\) 0 0
\(889\) 0 0
\(890\) 0 0
\(891\) −0.929776 + 0.368125i −0.929776 + 0.368125i
\(892\) 0 0
\(893\) −0.878275 + 0.638104i −0.878275 + 0.638104i
\(894\) 0 0
\(895\) 0 0
\(896\) 0 0
\(897\) 0 0
\(898\) −1.00711 + 3.09957i −1.00711 + 3.09957i
\(899\) 0 0
\(900\) −1.67600 + 1.21769i −1.67600 + 1.21769i
\(901\) 0 0
\(902\) −0.204639 3.25265i −0.204639 3.25265i
\(903\) 0 0
\(904\) −2.94351 + 2.13858i −2.94351 + 2.13858i
\(905\) 0 0
\(906\) 0 0
\(907\) 1.50441 + 1.09302i 1.50441 + 1.09302i 0.968583 + 0.248690i \(0.0800000\pi\)
0.535827 + 0.844328i \(0.320000\pi\)
\(908\) 2.71183 + 1.97026i 2.71183 + 1.97026i
\(909\) 0 0
\(910\) 0 0
\(911\) 1.30902 0.951057i 1.30902 0.951057i 0.309017 0.951057i \(-0.400000\pi\)
1.00000 \(0\)
\(912\) 0 0
\(913\) 0 0
\(914\) 1.87819 1.87819
\(915\) 0 0
\(916\) 0 0
\(917\) 0 0
\(918\) 0 0
\(919\) −1.17950 0.856954i −1.17950 0.856954i −0.187381 0.982287i \(-0.560000\pi\)
−0.992115 + 0.125333i \(0.960000\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 0 0
\(923\) 2.52959 2.52959
\(924\) 0 0
\(925\) 1.45794 1.45794
\(926\) −2.06720 + 1.50191i −2.06720 + 1.50191i
\(927\) 0.0388067 + 0.119435i 0.0388067 + 0.119435i
\(928\) 0 0
\(929\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(930\) 0 0
\(931\) −0.263146 + 0.809880i −0.263146 + 0.809880i
\(932\) 0 0
\(933\) 0 0
\(934\) 0 0
\(935\) 0 0
\(936\) −2.39441 −2.39441
\(937\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0 0
\(941\) −1.56720 1.13864i −1.56720 1.13864i −0.929776 0.368125i \(-0.880000\pi\)
−0.637424 0.770513i \(-0.720000\pi\)
\(942\) 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
\(949\) −0.763146 2.34872i −0.763146 2.34872i
\(950\) −0.461193 + 1.41941i −0.461193 + 1.41941i
\(951\) 0 0
\(952\) 0 0
\(953\) 0.0388067 0.119435i 0.0388067 0.119435i −0.929776 0.368125i \(-0.880000\pi\)
0.968583 + 0.248690i \(0.0800000\pi\)
\(954\) 0 0
\(955\) 0 0
\(956\) 0 0
\(957\) 0 0
\(958\) 3.39510 3.39510
\(959\) 0 0
\(960\) 0 0
\(961\) 0.640176 1.97026i 0.640176 1.97026i
\(962\) 2.63537 + 1.91471i 2.63537 + 1.91471i
\(963\) 1.60528 + 1.16630i 1.60528 + 1.16630i
\(964\) 0 0
\(965\) 0 0
\(966\) 0 0
\(967\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(968\) −1.86338 + 0.235400i −1.86338 + 0.235400i
\(969\) 0 0
\(970\) 0 0
\(971\) 0.331159 + 1.01920i 0.331159 + 1.01920i 0.968583 + 0.248690i \(0.0800000\pi\)
−0.637424 + 0.770513i \(0.720000\pi\)
\(972\) 0 0
\(973\) 0 0
\(974\) 0 0
\(975\) 0 0
\(976\) −0.141297 0.434867i −0.141297 0.434867i
\(977\) −0.101597 + 0.0738147i −0.101597 + 0.0738147i −0.637424 0.770513i \(-0.720000\pi\)
0.535827 + 0.844328i \(0.320000\pi\)
\(978\) 0 0
\(979\) 0 0
\(980\) 0 0
\(981\) 0 0
\(982\) 0 0
\(983\) 0.331159 1.01920i 0.331159 1.01920i −0.637424 0.770513i \(-0.720000\pi\)
0.968583 0.248690i \(-0.0800000\pi\)
\(984\) 0 0
\(985\) 0 0
\(986\) 0 0
\(987\) 0 0
\(988\) −1.81948 + 1.32193i −1.81948 + 1.32193i
\(989\) 0 0
\(990\) 0 0
\(991\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(992\) −0.368880 + 0.268007i −0.368880 + 0.268007i
\(993\) 0 0
\(994\) 0 0
\(995\) 0 0
\(996\) 0 0
\(997\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(998\) 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.1015.1 20
11.4 even 5 inner 1397.1.l.a.1269.1 yes 20
127.126 odd 2 CM 1397.1.l.a.1015.1 20
1397.1269 odd 10 inner 1397.1.l.a.1269.1 yes 20
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1397.1.l.a.1015.1 20 1.1 even 1 trivial
1397.1.l.a.1015.1 20 127.126 odd 2 CM
1397.1.l.a.1269.1 yes 20 11.4 even 5 inner
1397.1.l.a.1269.1 yes 20 1397.1269 odd 10 inner