Properties

Label 1397.1.l.a.126.1
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 $4$

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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 126.1
Root \(-0.968583 - 0.248690i\) of defining polynomial
Character \(\chi\) \(=\) 1397.126
Dual form 1397.1.l.a.1142.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.574633 - 1.76854i) q^{2} +(-1.98851 + 1.44474i) q^{4} +(2.19334 + 1.59355i) q^{8} +(0.309017 + 0.951057i) q^{9} +O(q^{10})\) \(q+(-0.574633 - 1.76854i) q^{2} +(-1.98851 + 1.44474i) q^{4} +(2.19334 + 1.59355i) q^{8} +(0.309017 + 0.951057i) q^{9} +(-0.992115 - 0.125333i) q^{11} +(-0.613161 - 1.88711i) q^{13} +(0.798351 - 2.45707i) q^{16} +(0.331159 - 1.01920i) q^{17} +(1.50441 - 1.09302i) q^{18} +(-0.101597 - 0.0738147i) q^{19} +(0.348445 + 1.82662i) q^{22} +(-0.809017 - 0.587785i) q^{25} +(-2.98509 + 2.16880i) q^{26} +(-0.574633 - 1.76854i) q^{31} -2.09308 q^{32} -1.99280 q^{34} +(-1.98851 - 1.44474i) q^{36} +(-0.866986 + 0.629902i) q^{37} +(-0.0721631 + 0.222095i) q^{38} +(-1.41789 - 1.03016i) q^{41} +(2.15391 - 1.18412i) q^{44} +(1.60528 + 1.16630i) q^{47} +(0.309017 - 0.951057i) q^{49} +(-0.574633 + 1.76854i) q^{50} +(3.94567 + 2.86669i) q^{52} +(0.598617 - 1.84235i) q^{61} +(-2.79753 + 2.03252i) q^{62} +(0.404401 + 1.24462i) q^{64} +(0.813968 + 2.50514i) q^{68} +(-0.393950 + 1.21245i) q^{71} +(-0.837780 + 2.57842i) q^{72} +(0.303189 - 0.220280i) q^{73} +(1.61221 + 1.17134i) q^{74} +0.308670 q^{76} +(0.450527 + 1.38658i) q^{79} +(-0.809017 + 0.587785i) q^{81} +(-1.00711 + 3.09957i) q^{82} +(-1.97632 - 1.85588i) q^{88} +(1.14020 - 3.50919i) q^{94} -1.85955 q^{98} +(-0.187381 - 0.982287i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 20 q - 5 q^{4} - 5 q^{9}+O(q^{10}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.574633 1.76854i −0.574633 1.76854i −0.637424 0.770513i \(-0.720000\pi\)
0.0627905 0.998027i \(-0.480000\pi\)
\(3\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(4\) −1.98851 + 1.44474i −1.98851 + 1.44474i
\(5\) 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 \(0.800000\pi\)
\(8\) 2.19334 + 1.59355i 2.19334 + 1.59355i
\(9\) 0.309017 + 0.951057i 0.309017 + 0.951057i
\(10\) 0 0
\(11\) −0.992115 0.125333i −0.992115 0.125333i
\(12\) 0 0
\(13\) −0.613161 1.88711i −0.613161 1.88711i −0.425779 0.904827i \(-0.640000\pi\)
−0.187381 0.982287i \(-0.560000\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0.798351 2.45707i 0.798351 2.45707i
\(17\) 0.331159 1.01920i 0.331159 1.01920i −0.637424 0.770513i \(-0.720000\pi\)
0.968583 0.248690i \(-0.0800000\pi\)
\(18\) 1.50441 1.09302i 1.50441 1.09302i
\(19\) −0.101597 0.0738147i −0.101597 0.0738147i 0.535827 0.844328i \(-0.320000\pi\)
−0.637424 + 0.770513i \(0.720000\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0.348445 + 1.82662i 0.348445 + 1.82662i
\(23\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(24\) 0 0
\(25\) −0.809017 0.587785i −0.809017 0.587785i
\(26\) −2.98509 + 2.16880i −2.98509 + 2.16880i
\(27\) 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
\(31\) −0.574633 1.76854i −0.574633 1.76854i −0.637424 0.770513i \(-0.720000\pi\)
0.0627905 0.998027i \(-0.480000\pi\)
\(32\) −2.09308 −2.09308
\(33\) 0 0
\(34\) −1.99280 −1.99280
\(35\) 0 0
\(36\) −1.98851 1.44474i −1.98851 1.44474i
\(37\) −0.866986 + 0.629902i −0.866986 + 0.629902i −0.929776 0.368125i \(-0.880000\pi\)
0.0627905 + 0.998027i \(0.480000\pi\)
\(38\) −0.0721631 + 0.222095i −0.0721631 + 0.222095i
\(39\) 0 0
\(40\) 0 0
\(41\) −1.41789 1.03016i −1.41789 1.03016i −0.992115 0.125333i \(-0.960000\pi\)
−0.425779 0.904827i \(-0.640000\pi\)
\(42\) 0 0
\(43\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(44\) 2.15391 1.18412i 2.15391 1.18412i
\(45\) 0 0
\(46\) 0 0
\(47\) 1.60528 + 1.16630i 1.60528 + 1.16630i 0.876307 + 0.481754i \(0.160000\pi\)
0.728969 + 0.684547i \(0.240000\pi\)
\(48\) 0 0
\(49\) 0.309017 0.951057i 0.309017 0.951057i
\(50\) −0.574633 + 1.76854i −0.574633 + 1.76854i
\(51\) 0 0
\(52\) 3.94567 + 2.86669i 3.94567 + 2.86669i
\(53\) 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
\(61\) 0.598617 1.84235i 0.598617 1.84235i 0.0627905 0.998027i \(-0.480000\pi\)
0.535827 0.844328i \(-0.320000\pi\)
\(62\) −2.79753 + 2.03252i −2.79753 + 2.03252i
\(63\) 0 0
\(64\) 0.404401 + 1.24462i 0.404401 + 1.24462i
\(65\) 0 0
\(66\) 0 0
\(67\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(68\) 0.813968 + 2.50514i 0.813968 + 2.50514i
\(69\) 0 0
\(70\) 0 0
\(71\) −0.393950 + 1.21245i −0.393950 + 1.21245i 0.535827 + 0.844328i \(0.320000\pi\)
−0.929776 + 0.368125i \(0.880000\pi\)
\(72\) −0.837780 + 2.57842i −0.837780 + 2.57842i
\(73\) 0.303189 0.220280i 0.303189 0.220280i −0.425779 0.904827i \(-0.640000\pi\)
0.728969 + 0.684547i \(0.240000\pi\)
\(74\) 1.61221 + 1.17134i 1.61221 + 1.17134i
\(75\) 0 0
\(76\) 0.308670 0.308670
\(77\) 0 0
\(78\) 0 0
\(79\) 0.450527 + 1.38658i 0.450527 + 1.38658i 0.876307 + 0.481754i \(0.160000\pi\)
−0.425779 + 0.904827i \(0.640000\pi\)
\(80\) 0 0
\(81\) −0.809017 + 0.587785i −0.809017 + 0.587785i
\(82\) −1.00711 + 3.09957i −1.00711 + 3.09957i
\(83\) 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
\(88\) −1.97632 1.85588i −1.97632 1.85588i
\(89\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 0 0
\(93\) 0 0
\(94\) 1.14020 3.50919i 1.14020 3.50919i
\(95\) 0 0
\(96\) 0 0
\(97\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(98\) −1.85955 −1.85955
\(99\) −0.187381 0.982287i −0.187381 0.982287i
\(100\) 2.45794 2.45794
\(101\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(102\) 0 0
\(103\) 0.688925 0.500534i 0.688925 0.500534i −0.187381 0.982287i \(-0.560000\pi\)
0.876307 + 0.481754i \(0.160000\pi\)
\(104\) 1.66235 5.11618i 1.66235 5.11618i
\(105\) 0 0
\(106\) 0 0
\(107\) 1.03137 + 0.749337i 1.03137 + 0.749337i 0.968583 0.248690i \(-0.0800000\pi\)
0.0627905 + 0.998027i \(0.480000\pi\)
\(108\) 0 0
\(109\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) 0.303189 + 0.220280i 0.303189 + 0.220280i 0.728969 0.684547i \(-0.240000\pi\)
−0.425779 + 0.904827i \(0.640000\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 0 0
\(117\) 1.60528 1.16630i 1.60528 1.16630i
\(118\) 0 0
\(119\) 0 0
\(120\) 0 0
\(121\) 0.968583 + 0.248690i 0.968583 + 0.248690i
\(122\) −3.60226 −3.60226
\(123\) 0 0
\(124\) 3.69775 + 2.68657i 3.69775 + 2.68657i
\(125\) 0 0
\(126\) 0 0
\(127\) 0.309017 0.951057i 0.309017 0.951057i
\(128\) 0.275441 0.200120i 0.275441 0.200120i
\(129\) 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
\(136\) 2.35050 1.70774i 2.35050 1.70774i
\(137\) 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
\(142\) 2.37065 2.37065
\(143\) 0.371808 + 1.94908i 0.371808 + 1.94908i
\(144\) 2.58352 2.58352
\(145\) 0 0
\(146\) −0.563797 0.409622i −0.563797 0.409622i
\(147\) 0 0
\(148\) 0.813968 2.50514i 0.813968 2.50514i
\(149\) −0.393950 + 1.21245i −0.393950 + 1.21245i 0.535827 + 0.844328i \(0.320000\pi\)
−0.929776 + 0.368125i \(0.880000\pi\)
\(150\) 0 0
\(151\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(152\) −0.105209 0.323801i −0.105209 0.323801i
\(153\) 1.07165 1.07165
\(154\) 0 0
\(155\) 0 0
\(156\) 0 0
\(157\) −1.41789 1.03016i −1.41789 1.03016i −0.992115 0.125333i \(-0.960000\pi\)
−0.425779 0.904827i \(-0.640000\pi\)
\(158\) 2.19334 1.59355i 2.19334 1.59355i
\(159\) 0 0
\(160\) 0 0
\(161\) 0 0
\(162\) 1.50441 + 1.09302i 1.50441 + 1.09302i
\(163\) 0.190983 + 0.587785i 0.190983 + 0.587785i 1.00000 \(0\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(164\) 4.30781 4.30781
\(165\) 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
\(169\) −2.37622 + 1.72642i −2.37622 + 1.72642i
\(170\) 0 0
\(171\) 0.0388067 0.119435i 0.0388067 0.119435i
\(172\) 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
\(176\) −1.10001 + 2.33764i −1.10001 + 2.33764i
\(177\) 0 0
\(178\) 0 0
\(179\) −1.56720 1.13864i −1.56720 1.13864i −0.929776 0.368125i \(-0.880000\pi\)
−0.637424 0.770513i \(-0.720000\pi\)
\(180\) 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
\(187\) −0.456288 + 0.969661i −0.456288 + 0.969661i
\(188\) −4.87711 −4.87711
\(189\) 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
\(196\) 0.759544 + 2.33764i 0.759544 + 2.33764i
\(197\) 1.45794 1.45794 0.728969 0.684547i \(-0.240000\pi\)
0.728969 + 0.684547i \(0.240000\pi\)
\(198\) −1.62954 + 0.895846i −1.62954 + 0.895846i
\(199\) 1.75261 1.75261 0.876307 0.481754i \(-0.160000\pi\)
0.876307 + 0.481754i \(0.160000\pi\)
\(200\) −0.837780 2.57842i −0.837780 2.57842i
\(201\) 0 0
\(202\) 0 0
\(203\) 0 0
\(204\) 0 0
\(205\) 0 0
\(206\) −1.28109 0.930769i −1.28109 0.930769i
\(207\) 0 0
\(208\) −5.12629 −5.12629
\(209\) 0.0915446 + 0.0859661i 0.0915446 + 0.0859661i
\(210\) 0 0
\(211\) −0.115808 0.356420i −0.115808 0.356420i 0.876307 0.481754i \(-0.160000\pi\)
−0.992115 + 0.125333i \(0.960000\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0.732570 2.25462i 0.732570 2.25462i
\(215\) 0 0
\(216\) 0 0
\(217\) 0 0
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) −2.12641 −2.12641
\(222\) 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
\(226\) 0.215351 0.662783i 0.215351 0.662783i
\(227\) −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 \(0.400000\pi\)
\(234\) −2.98509 2.16880i −2.98509 2.16880i
\(235\) 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 \(\pi\)
\(242\) −0.116762 1.85588i −0.116762 1.85588i
\(243\) 0 0
\(244\) 1.47136 + 4.52839i 1.47136 + 4.52839i
\(245\) 0 0
\(246\) 0 0
\(247\) −0.0770013 + 0.236986i −0.0770013 + 0.236986i
\(248\) 1.55790 4.79471i 1.55790 4.79471i
\(249\) 0 0
\(250\) 0 0
\(251\) −0.115808 0.356420i −0.115808 0.356420i 0.876307 0.481754i \(-0.160000\pi\)
−0.992115 + 0.125333i \(0.960000\pi\)
\(252\) 0 0
\(253\) 0 0
\(254\) −1.85955 −1.85955
\(255\) 0 0
\(256\) 0.546539 + 0.397084i 0.546539 + 0.397084i
\(257\) 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
\(262\) 0.929776 + 2.86156i 0.929776 + 2.86156i
\(263\) 1.93717 1.93717 0.968583 0.248690i \(-0.0800000\pi\)
0.968583 + 0.248690i \(0.0800000\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) 0.0388067 0.119435i 0.0388067 0.119435i −0.929776 0.368125i \(-0.880000\pi\)
0.968583 + 0.248690i \(0.0800000\pi\)
\(270\) 0 0
\(271\) −0.500000 + 0.363271i −0.500000 + 0.363271i −0.809017 0.587785i \(-0.800000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(272\) −2.23987 1.62736i −2.23987 1.62736i
\(273\) 0 0
\(274\) 0 0
\(275\) 0.728969 + 0.684547i 0.728969 + 0.684547i
\(276\) 0 0
\(277\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(278\) 0 0
\(279\) 1.50441 1.09302i 1.50441 1.09302i
\(280\) 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 \(0.200000\pi\)
\(284\) −0.968304 2.98013i −0.968304 2.98013i
\(285\) 0 0
\(286\) 3.23338 1.77756i 3.23338 1.77756i
\(287\) 0 0
\(288\) −0.646797 1.99064i −0.646797 1.99064i
\(289\) −0.120092 0.0872517i −0.120092 0.0872517i
\(290\) 0 0
\(291\) 0 0
\(292\) −0.284649 + 0.876059i −0.284649 + 0.876059i
\(293\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) −2.90537 −2.90537
\(297\) 0 0
\(298\) 2.37065 2.37065
\(299\) 0 0
\(300\) 0 0
\(301\) 0 0
\(302\) 0 0
\(303\) 0 0
\(304\) −0.262478 + 0.190702i −0.262478 + 0.190702i
\(305\) 0 0
\(306\) −0.615808 1.89526i −0.615808 1.89526i
\(307\) 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 \(0.600000\pi\)
\(314\) −1.00711 + 3.09957i −1.00711 + 3.09957i
\(315\) 0 0
\(316\) −2.89913 2.10634i −2.89913 2.10634i
\(317\) 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
\(323\) −0.108877 + 0.0791038i −0.108877 + 0.0791038i
\(324\) 0.759544 2.33764i 0.759544 2.33764i
\(325\) −0.613161 + 1.88711i −0.613161 + 1.88711i
\(326\) 0.929776 0.675522i 0.929776 0.675522i
\(327\) 0 0
\(328\) −1.46830 4.51897i −1.46830 4.51897i
\(329\) 0 0
\(330\) 0 0
\(331\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(332\) 0 0
\(333\) −0.866986 0.629902i −0.866986 0.629902i
\(334\) 0 0
\(335\) 0 0
\(336\) 0 0
\(337\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(338\) 4.41870 + 3.21038i 4.41870 + 3.21038i
\(339\) 0 0
\(340\) 0 0
\(341\) 0.348445 + 1.82662i 0.348445 + 1.82662i
\(342\) −0.233525 −0.233525
\(343\) 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
\(352\) 2.07657 + 0.262332i 2.07657 + 0.262332i
\(353\) 0.125581 0.125581 0.0627905 0.998027i \(-0.480000\pi\)
0.0627905 + 0.998027i \(0.480000\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 0 0
\(357\) 0 0
\(358\) −1.11316 + 3.42596i −1.11316 + 3.42596i
\(359\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(360\) 0 0
\(361\) −0.304144 0.936058i −0.304144 0.936058i
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) 0 0
\(366\) 0 0
\(367\) −1.56720 + 1.13864i −1.56720 + 1.13864i −0.637424 + 0.770513i \(0.720000\pi\)
−0.929776 + 0.368125i \(0.880000\pi\)
\(368\) 0 0
\(369\) 0.541587 1.66683i 0.541587 1.66683i
\(370\) 0 0
\(371\) 0 0
\(372\) 0 0
\(373\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(374\) 1.97708 + 0.249764i 1.97708 + 0.249764i
\(375\) 0 0
\(376\) 1.66235 + 5.11618i 1.66235 + 5.11618i
\(377\) 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
\(382\) −2.43419 1.76854i −2.43419 1.76854i
\(383\) 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
\(389\) 1.60528 1.16630i 1.60528 1.16630i 0.728969 0.684547i \(-0.240000\pi\)
0.876307 0.481754i \(-0.160000\pi\)
\(390\) 0 0
\(391\) 0 0
\(392\) 2.19334 1.59355i 2.19334 1.59355i
\(393\) 0 0
\(394\) −0.837780 2.57842i −0.837780 2.57842i
\(395\) 0 0
\(396\) 1.79176 + 1.68257i 1.79176 + 1.68257i
\(397\) 1.93717 1.93717 0.968583 0.248690i \(-0.0800000\pi\)
0.968583 + 0.248690i \(0.0800000\pi\)
\(398\) −1.00711 3.09957i −1.00711 3.09957i
\(399\) 0 0
\(400\) −2.09011 + 1.51855i −2.09011 + 1.51855i
\(401\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(402\) 0 0
\(403\) −2.98509 + 2.16880i −2.98509 + 2.16880i
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 0.939097 0.516273i 0.939097 0.516273i
\(408\) 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
\(412\) −0.646797 + 1.99064i −0.646797 + 1.99064i
\(413\) 0 0
\(414\) 0 0
\(415\) 0 0
\(416\) 1.28339 + 3.94988i 1.28339 + 3.94988i
\(417\) 0 0
\(418\) 0.0994299 0.211299i 0.0994299 0.211299i
\(419\) 0.125581 0.125581 0.0627905 0.998027i \(-0.480000\pi\)
0.0627905 + 0.998027i \(0.480000\pi\)
\(420\) 0 0
\(421\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(422\) −0.563797 + 0.409622i −0.563797 + 0.409622i
\(423\) −0.613161 + 1.88711i −0.613161 + 1.88711i
\(424\) 0 0
\(425\) −0.866986 + 0.629902i −0.866986 + 0.629902i
\(426\) 0 0
\(427\) 0 0
\(428\) −3.13350 −3.13350
\(429\) 0 0
\(430\) 0 0
\(431\) 0.541587 + 1.66683i 0.541587 + 1.66683i 0.728969 + 0.684547i \(0.240000\pi\)
−0.187381 + 0.982287i \(0.560000\pi\)
\(432\) 0 0
\(433\) 1.03137 0.749337i 1.03137 0.749337i 0.0627905 0.998027i \(-0.480000\pi\)
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
\(442\) 1.22190 + 3.76064i 1.22190 + 3.76064i
\(443\) −0.866986 0.629902i −0.866986 0.629902i 0.0627905 0.998027i \(-0.480000\pi\)
−0.929776 + 0.368125i \(0.880000\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) 0.541587 + 1.66683i 0.541587 + 1.66683i 0.728969 + 0.684547i \(0.240000\pi\)
−0.187381 + 0.982287i \(0.560000\pi\)
\(450\) −1.85955 −1.85955
\(451\) 1.27760 + 1.19975i 1.27760 + 1.19975i
\(452\) −0.921143 −0.921143
\(453\) 0 0
\(454\) 0.929776 + 0.675522i 0.929776 + 0.675522i
\(455\) 0 0
\(456\) 0 0
\(457\) 0.450527 1.38658i 0.450527 1.38658i −0.425779 0.904827i \(-0.640000\pi\)
0.876307 0.481754i \(-0.160000\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(462\) 0 0
\(463\) 1.07165 1.07165 0.535827 0.844328i \(-0.320000\pi\)
0.535827 + 0.844328i \(0.320000\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(468\) −1.50711 + 4.63841i −1.50711 + 4.63841i
\(469\) 0 0
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) 0 0
\(474\) 0 0
\(475\) 0.0388067 + 0.119435i 0.0388067 + 0.119435i
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) −0.115808 + 0.356420i −0.115808 + 0.356420i −0.992115 0.125333i \(-0.960000\pi\)
0.876307 + 0.481754i \(0.160000\pi\)
\(480\) 0 0
\(481\) 1.72030 + 1.24987i 1.72030 + 1.24987i
\(482\) 0 0
\(483\) 0 0
\(484\) −2.28533 + 0.904827i −2.28533 + 0.904827i
\(485\) 0 0
\(486\) 0 0
\(487\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(488\) 4.24886 3.08697i 4.24886 3.08697i
\(489\) 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
\(494\) 0.463366 0.463366
\(495\) 0 0
\(496\) −4.80419 −4.80419
\(497\) 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
\(502\) −0.563797 + 0.409622i −0.563797 + 0.409622i
\(503\) 0.688925 + 0.500534i 0.688925 + 0.500534i 0.876307 0.481754i \(-0.160000\pi\)
−0.187381 + 0.982287i \(0.560000\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) 0 0
\(508\) 0.759544 + 2.33764i 0.759544 + 2.33764i
\(509\) −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
\(512\) 0.493408 1.51855i 0.493408 1.51855i
\(513\) 0 0
\(514\) 0 0
\(515\) 0 0
\(516\) 0 0
\(517\) −1.44644 1.35830i −1.44644 1.35830i
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 1.50441 1.09302i 1.50441 1.09302i 0.535827 0.844328i \(-0.320000\pi\)
0.968583 0.248690i \(-0.0800000\pi\)
\(522\) 0 0
\(523\) −0.263146 + 0.809880i −0.263146 + 0.809880i 0.728969 + 0.684547i \(0.240000\pi\)
−0.992115 + 0.125333i \(0.960000\pi\)
\(524\) 3.21748 2.33764i 3.21748 2.33764i
\(525\) 0 0
\(526\) −1.11316 3.42596i −1.11316 3.42596i
\(527\) −1.99280 −1.99280
\(528\) 0 0
\(529\) 1.00000 1.00000
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) −1.07463 + 3.30738i −1.07463 + 3.30738i
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) 0 0
\(538\) −0.233525 −0.233525
\(539\) −0.425779 + 0.904827i −0.425779 + 0.904827i
\(540\) 0 0
\(541\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(542\) 0.929776 + 0.675522i 0.929776 + 0.675522i
\(543\) 0 0
\(544\) −0.693142 + 2.13327i −0.693142 + 2.13327i
\(545\) 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
\(549\) 1.93717 1.93717
\(550\) 0.791759 1.68257i 0.791759 1.68257i
\(551\) 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 \(0\)
\(558\) −2.79753 2.03252i −2.79753 2.03252i
\(559\) 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
\(568\) −2.79617 + 2.03154i −2.79617 + 2.03154i
\(569\) −1.17950 0.856954i −1.17950 0.856954i −0.187381 0.982287i \(-0.560000\pi\)
−0.992115 + 0.125333i \(0.960000\pi\)
\(570\) 0 0
\(571\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(572\) −3.55526 3.33861i −3.55526 3.33861i
\(573\) 0 0
\(574\) 0 0
\(575\) 0 0
\(576\) −1.05874 + 0.769217i −1.05874 + 0.769217i
\(577\) −0.393950 + 1.21245i −0.393950 + 1.21245i 0.535827 + 0.844328i \(0.320000\pi\)
−0.929776 + 0.368125i \(0.880000\pi\)
\(578\) −0.0852994 + 0.262525i −0.0852994 + 0.262525i
\(579\) 0 0
\(580\) 0 0
\(581\) 0 0
\(582\) 0 0
\(583\) 0 0
\(584\) 1.01602 1.01602
\(585\) 0 0
\(586\) 0 0
\(587\) −0.101597 + 0.0738147i −0.101597 + 0.0738147i −0.637424 0.770513i \(-0.720000\pi\)
0.535827 + 0.844328i \(0.320000\pi\)
\(588\) 0 0
\(589\) −0.0721631 + 0.222095i −0.0721631 + 0.222095i
\(590\) 0 0
\(591\) 0 0
\(592\) 0.855556 + 2.63313i 0.855556 + 2.63313i
\(593\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) −0.968304 2.98013i −0.968304 2.98013i
\(597\) 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
\(607\) −0.393950 1.21245i −0.393950 1.21245i −0.929776 0.368125i \(-0.880000\pi\)
0.535827 0.844328i \(-0.320000\pi\)
\(608\) 0.212651 + 0.154500i 0.212651 + 0.154500i
\(609\) 0 0
\(610\) 0 0
\(611\) 1.21665 3.74447i 1.21665 3.74447i
\(612\) −2.13100 + 1.54826i −2.13100 + 1.54826i
\(613\) 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
\(628\) 4.30781 4.30781
\(629\) 0.354888 + 1.09223i 0.354888 + 1.09223i
\(630\) 0 0
\(631\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(632\) −1.22143 + 3.75918i −1.22143 + 3.75918i
\(633\) 0 0
\(634\) 0 0
\(635\) 0 0
\(636\) 0 0
\(637\) −1.98423 −1.98423
\(638\) 0 0
\(639\) −1.27485 −1.27485
\(640\) 0 0
\(641\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(642\) 0 0
\(643\) −0.263146 + 0.809880i −0.263146 + 0.809880i 0.728969 + 0.684547i \(0.240000\pi\)
−0.992115 + 0.125333i \(0.960000\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0.202463 + 0.147098i 0.202463 + 0.147098i
\(647\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(648\) −2.71111 −2.71111
\(649\) 0 0
\(650\) 3.68978 3.68978
\(651\) 0 0
\(652\) −1.22897 0.892898i −1.22897 0.892898i
\(653\) 0.303189 0.220280i 0.303189 0.220280i −0.425779 0.904827i \(-0.640000\pi\)
0.728969 + 0.684547i \(0.240000\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) −3.66316 + 2.66144i −3.66316 + 2.66144i
\(657\) 0.303189 + 0.220280i 0.303189 + 0.220280i
\(658\) 0 0
\(659\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(660\) 0 0
\(661\) −0.374763 −0.374763 −0.187381 0.982287i \(-0.560000\pi\)
−0.187381 + 0.982287i \(0.560000\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 0 0
\(666\) −0.615808 + 1.89526i −0.615808 + 1.89526i
\(667\) 0 0
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) −0.824805 + 1.75280i −0.824805 + 1.75280i
\(672\) 0 0
\(673\) −0.393950 1.21245i −0.393950 1.21245i −0.929776 0.368125i \(-0.880000\pi\)
0.535827 0.844328i \(-0.320000\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 2.23091 6.86603i 2.23091 6.86603i
\(677\) 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
\(682\) 3.03021 1.66587i 3.03021 1.66587i
\(683\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(684\) 0.0953844 + 0.293563i 0.0953844 + 0.293563i
\(685\) 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
\(697\) −1.51949 + 1.10397i −1.51949 + 1.10397i
\(698\) 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
\(703\) 0.134579 0.134579
\(704\) −0.245220 1.28549i −0.245220 1.28549i
\(705\) 0 0
\(706\) −0.0721631 0.222095i −0.0721631 0.222095i
\(707\) 0 0
\(708\) 0 0
\(709\) −0.613161 + 1.88711i −0.613161 + 1.88711i −0.187381 + 0.982287i \(0.560000\pi\)
−0.425779 + 0.904827i \(0.640000\pi\)
\(710\) 0 0
\(711\) −1.17950 + 0.856954i −1.17950 + 0.856954i
\(712\) 0 0
\(713\) 0 0
\(714\) 0 0
\(715\) 0 0
\(716\) 4.76143 4.76143
\(717\) 0 0
\(718\) 0 0
\(719\) −0.866986 + 0.629902i −0.866986 + 0.629902i −0.929776 0.368125i \(-0.880000\pi\)
0.0627905 + 0.998027i \(0.480000\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) −1.48068 + 1.07578i −1.48068 + 1.07578i
\(723\) 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 \(0\)
\(734\) 2.91429 + 2.11736i 2.91429 + 2.11736i
\(735\) 0 0
\(736\) 0 0
\(737\) 0 0
\(738\) −3.25908 −3.25908
\(739\) −0.263146 0.809880i −0.263146 0.809880i −0.992115 0.125333i \(-0.960000\pi\)
0.728969 0.684547i \(-0.240000\pi\)
\(740\) 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
\(748\) −0.493573 2.58740i −0.493573 2.58740i
\(749\) 0 0
\(750\) 0 0
\(751\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(752\) 4.14726 3.01316i 4.14726 3.01316i
\(753\) 0 0
\(754\) 0 0
\(755\) 0 0
\(756\) 0 0
\(757\) −0.574633 1.76854i −0.574633 1.76854i −0.637424 0.770513i \(-0.720000\pi\)
0.0627905 0.998027i \(-0.480000\pi\)
\(758\) 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
\(764\) −1.22897 + 3.78238i −1.22897 + 3.78238i
\(765\) 0 0
\(766\) 0.929776 0.675522i 0.929776 0.675522i
\(767\) 0 0
\(768\) 0 0
\(769\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) −1.56720 1.13864i −1.56720 1.13864i −0.929776 0.368125i \(-0.880000\pi\)
−0.637424 0.770513i \(-0.720000\pi\)
\(774\) 0 0
\(775\) −0.574633 + 1.76854i −0.574633 + 1.76854i
\(776\) 0 0
\(777\) 0 0
\(778\) −2.98509 2.16880i −2.98509 2.16880i
\(779\) 0.0680131 + 0.209323i 0.0680131 + 0.209323i
\(780\) 0 0
\(781\) 0.542804 1.15352i 0.542804 1.15352i
\(782\) 0 0
\(783\) 0 0
\(784\) −2.09011 1.51855i −2.09011 1.51855i
\(785\) 0 0
\(786\) 0 0
\(787\) 0.541587 1.66683i 0.541587 1.66683i −0.187381 0.982287i \(-0.560000\pi\)
0.728969 0.684547i \(-0.240000\pi\)
\(788\) −2.89913 + 2.10634i −2.89913 + 2.10634i
\(789\) 0 0
\(790\) 0 0
\(791\) 0 0
\(792\) 1.15434 2.45309i 1.15434 2.45309i
\(793\) −3.84378 −3.84378
\(794\) −1.11316 3.42596i −1.11316 3.42596i
\(795\) 0 0
\(796\) −3.48509 + 2.53207i −3.48509 + 2.53207i
\(797\) −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
\(799\) 1.72030 1.24987i 1.72030 1.24987i
\(800\) 1.69334 + 1.23028i 1.69334 + 1.23028i
\(801\) 0 0
\(802\) 0 0
\(803\) −0.328407 + 0.180543i −0.328407 + 0.180543i
\(804\) 0 0
\(805\) 0 0
\(806\) 5.55094 + 4.03299i 5.55094 + 4.03299i
\(807\) 0 0
\(808\) 0 0
\(809\) 0.0388067 0.119435i 0.0388067 0.119435i −0.929776 0.368125i \(-0.880000\pi\)
0.968583 + 0.248690i \(0.0800000\pi\)
\(810\) 0 0
\(811\) −1.17950 0.856954i −1.17950 0.856954i −0.187381 0.982287i \(-0.560000\pi\)
−0.992115 + 0.125333i \(0.960000\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) −1.45269 1.36416i −1.45269 1.36416i
\(815\) 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
\(823\) 0.598617 + 1.84235i 0.598617 + 1.84235i 0.535827 + 0.844328i \(0.320000\pi\)
0.0627905 + 0.998027i \(0.480000\pi\)
\(824\) 2.30867 2.30867
\(825\) 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
\(832\) 2.10078 1.52630i 2.10078 1.52630i
\(833\) −0.866986 0.629902i −0.866986 0.629902i
\(834\) 0 0
\(835\) 0 0
\(836\) −0.306236 0.0386866i −0.306236 0.0386866i
\(837\) 0 0
\(838\) −0.0721631 0.222095i −0.0721631 0.222095i
\(839\) 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
\(844\) 0.745220 + 0.541434i 0.745220 + 0.541434i
\(845\) 0 0
\(846\) 3.68978 3.68978
\(847\) 0 0
\(848\) 0 0
\(849\) 0 0
\(850\) 1.61221 + 1.17134i 1.61221 + 1.17134i
\(851\) 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
\(856\) 1.06804 + 3.28709i 1.06804 + 3.28709i
\(857\) 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
\(862\) 2.63665 1.91564i 2.63665 1.91564i
\(863\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(864\) 0 0
\(865\) 0 0
\(866\) −1.91789 1.39343i −1.91789 1.39343i
\(867\) 0 0
\(868\) 0 0
\(869\) −0.273190 1.43211i −0.273190 1.43211i
\(870\) 0 0
\(871\) 0 0
\(872\) 0 0
\(873\) 0 0
\(874\) 0 0
\(875\) 0 0
\(876\) 0 0
\(877\) −0.101597 0.0738147i −0.101597 0.0738147i 0.535827 0.844328i \(-0.320000\pi\)
−0.637424 + 0.770513i \(0.720000\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(882\) −0.574633 1.76854i −0.574633 1.76854i
\(883\) 1.03137 + 0.749337i 1.03137 + 0.749337i 0.968583 0.248690i \(-0.0800000\pi\)
0.0627905 + 0.998027i \(0.480000\pi\)
\(884\) 4.22839 3.07210i 4.22839 3.07210i
\(885\) 0 0
\(886\) −0.615808 + 1.89526i −0.615808 + 1.89526i
\(887\) 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
\(891\) 0.876307 0.481754i 0.876307 0.481754i
\(892\) 0 0
\(893\) −0.0770013 0.236986i −0.0770013 0.236986i
\(894\) 0 0
\(895\) 0 0
\(896\) 0 0
\(897\) 0 0
\(898\) 2.63665 1.91564i 2.63665 1.91564i
\(899\) 0 0
\(900\) 0.759544 + 2.33764i 0.759544 + 2.33764i
\(901\) 0 0
\(902\) 1.38765 2.94890i 1.38765 2.94890i
\(903\) 0 0
\(904\) 0.313968 + 0.966296i 0.313968 + 0.966296i
\(905\) 0 0
\(906\) 0 0
\(907\) 0.541587 1.66683i 0.541587 1.66683i −0.187381 0.982287i \(-0.560000\pi\)
0.728969 0.684547i \(-0.240000\pi\)
\(908\) 0.469424 1.44474i 0.469424 1.44474i
\(909\) 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
\(914\) −2.71111 −2.71111
\(915\) 0 0
\(916\) 0 0
\(917\) 0 0
\(918\) 0 0
\(919\) 0.331159 1.01920i 0.331159 1.01920i −0.637424 0.770513i \(-0.720000\pi\)
0.968583 0.248690i \(-0.0800000\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 0 0
\(923\) 2.52959 2.52959
\(924\) 0 0
\(925\) 1.07165 1.07165
\(926\) −0.615808 1.89526i −0.615808 1.89526i
\(927\) 0.688925 + 0.500534i 0.688925 + 0.500534i
\(928\) 0 0
\(929\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(930\) 0 0
\(931\) −0.101597 + 0.0738147i −0.101597 + 0.0738147i
\(932\) 0 0
\(933\) 0 0
\(934\) 0 0
\(935\) 0 0
\(936\) 5.37947 5.37947
\(937\) 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
\(941\) −0.115808 + 0.356420i −0.115808 + 0.356420i −0.992115 0.125333i \(-0.960000\pi\)
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
\(949\) −0.601597 0.437086i −0.601597 0.437086i
\(950\) 0.188925 0.137262i 0.188925 0.137262i
\(951\) 0 0
\(952\) 0 0
\(953\) 0.688925 0.500534i 0.688925 0.500534i −0.187381 0.982287i \(-0.560000\pi\)
0.876307 + 0.481754i \(0.160000\pi\)
\(954\) 0 0
\(955\) 0 0
\(956\) 0 0
\(957\) 0 0
\(958\) 0.696891 0.696891
\(959\) 0 0
\(960\) 0 0
\(961\) −1.98851 + 1.44474i −1.98851 + 1.44474i
\(962\) 1.22190 3.76064i 1.22190 3.76064i
\(963\) −0.393950 + 1.21245i −0.393950 + 1.21245i
\(964\) 0 0
\(965\) 0 0
\(966\) 0 0
\(967\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(968\) 1.72813 + 2.08895i 1.72813 + 2.08895i
\(969\) 0 0
\(970\) 0 0
\(971\) −1.17950 0.856954i −1.17950 0.856954i −0.187381 0.982287i \(-0.560000\pi\)
−0.992115 + 0.125333i \(0.960000\pi\)
\(972\) 0 0
\(973\) 0 0
\(974\) 0 0
\(975\) 0 0
\(976\) −4.04889 2.94169i −4.04889 2.94169i
\(977\) −0.263146 0.809880i −0.263146 0.809880i −0.992115 0.125333i \(-0.960000\pi\)
0.728969 0.684547i \(-0.240000\pi\)
\(978\) 0 0
\(979\) 0 0
\(980\) 0 0
\(981\) 0 0
\(982\) 0 0
\(983\) −1.17950 + 0.856954i −1.17950 + 0.856954i −0.992115 0.125333i \(-0.960000\pi\)
−0.187381 + 0.982287i \(0.560000\pi\)
\(984\) 0 0
\(985\) 0 0
\(986\) 0 0
\(987\) 0 0
\(988\) −0.189264 0.582496i −0.189264 0.582496i
\(989\) 0 0
\(990\) 0 0
\(991\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(992\) 1.20275 + 3.70169i 1.20275 + 3.70169i
\(993\) 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.126.1 20
11.9 even 5 inner 1397.1.l.a.1142.1 yes 20
127.126 odd 2 CM 1397.1.l.a.126.1 20
1397.1142 odd 10 inner 1397.1.l.a.1142.1 yes 20
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1397.1.l.a.126.1 20 1.1 even 1 trivial
1397.1.l.a.126.1 20 127.126 odd 2 CM
1397.1.l.a.1142.1 yes 20 11.9 even 5 inner
1397.1.l.a.1142.1 yes 20 1397.1142 odd 10 inner