Properties

Label 952.1.e.d.237.3
Level $952$
Weight $1$
Character 952.237
Analytic conductor $0.475$
Analytic rank $0$
Dimension $4$
Projective image $D_{10}$
CM discriminant -119
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [952,1,Mod(237,952)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(952, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 1, 1, 1]))
 
N = Newforms(chi, 1, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("952.237");
 
S:= CuspForms(chi, 1);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 952 = 2^{3} \cdot 7 \cdot 17 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 952.e (of order \(2\), degree \(1\), 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: \(0.475109892027\)
Analytic rank: \(0\)
Dimension: \(4\)
Coefficient field: \(\Q(\zeta_{10})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{4} - x^{3} + x^{2} - x + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Projective image: \(D_{10}\)
Projective field: Galois closure of 10.2.6571095523328.1

Embedding invariants

Embedding label 237.3
Root \(0.809017 + 0.587785i\) of defining polynomial
Character \(\chi\) \(=\) 952.237
Dual form 952.1.e.d.237.4

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.809017 - 0.587785i) q^{2} +1.17557i q^{3} +(0.309017 - 0.951057i) q^{4} -1.90211i q^{5} +(0.690983 + 0.951057i) q^{6} -1.00000 q^{7} +(-0.309017 - 0.951057i) q^{8} -0.381966 q^{9} +O(q^{10})\) \(q+(0.809017 - 0.587785i) q^{2} +1.17557i q^{3} +(0.309017 - 0.951057i) q^{4} -1.90211i q^{5} +(0.690983 + 0.951057i) q^{6} -1.00000 q^{7} +(-0.309017 - 0.951057i) q^{8} -0.381966 q^{9} +(-1.11803 - 1.53884i) q^{10} +(1.11803 + 0.363271i) q^{12} +(-0.809017 + 0.587785i) q^{14} +2.23607 q^{15} +(-0.809017 - 0.587785i) q^{16} +1.00000 q^{17} +(-0.309017 + 0.224514i) q^{18} +(-1.80902 - 0.587785i) q^{20} -1.17557i q^{21} +(1.11803 - 0.363271i) q^{24} -2.61803 q^{25} +0.726543i q^{27} +(-0.309017 + 0.951057i) q^{28} +(1.80902 - 1.31433i) q^{30} +0.618034 q^{31} -1.00000 q^{32} +(0.809017 - 0.587785i) q^{34} +1.90211i q^{35} +(-0.118034 + 0.363271i) q^{36} +(-1.80902 + 0.587785i) q^{40} +1.61803 q^{41} +(-0.690983 - 0.951057i) q^{42} +1.17557i q^{43} +0.726543i q^{45} +(0.690983 - 0.951057i) q^{48} +1.00000 q^{49} +(-2.11803 + 1.53884i) q^{50} +1.17557i q^{51} +1.90211i q^{53} +(0.427051 + 0.587785i) q^{54} +(0.309017 + 0.951057i) q^{56} +(0.690983 - 2.12663i) q^{60} +1.17557i q^{61} +(0.500000 - 0.363271i) q^{62} +0.381966 q^{63} +(-0.809017 + 0.587785i) q^{64} -1.90211i q^{67} +(0.309017 - 0.951057i) q^{68} +(1.11803 + 1.53884i) q^{70} +(0.118034 + 0.363271i) q^{72} -1.61803 q^{73} -3.07768i q^{75} +(-1.11803 + 1.53884i) q^{80} -1.23607 q^{81} +(1.30902 - 0.951057i) q^{82} +(-1.11803 - 0.363271i) q^{84} -1.90211i q^{85} +(0.690983 + 0.951057i) q^{86} +(0.427051 + 0.587785i) q^{90} +0.726543i q^{93} -1.17557i q^{96} -0.618034 q^{97} +(0.809017 - 0.587785i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q + q^{2} - q^{4} + 5 q^{6} - 4 q^{7} + q^{8} - 6 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 4 q + q^{2} - q^{4} + 5 q^{6} - 4 q^{7} + q^{8} - 6 q^{9} - q^{14} - q^{16} + 4 q^{17} + q^{18} - 5 q^{20} - 6 q^{25} + q^{28} + 5 q^{30} - 2 q^{31} - 4 q^{32} + q^{34} + 4 q^{36} - 5 q^{40} + 2 q^{41} - 5 q^{42} + 5 q^{48} + 4 q^{49} - 4 q^{50} - 5 q^{54} - q^{56} + 5 q^{60} + 2 q^{62} + 6 q^{63} - q^{64} - q^{68} - 4 q^{72} - 2 q^{73} + 4 q^{81} + 3 q^{82} + 5 q^{86} - 5 q^{90} + 2 q^{97} + q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/952\mathbb{Z}\right)^\times\).

\(n\) \(239\) \(409\) \(477\) \(785\)
\(\chi(n)\) \(1\) \(-1\) \(-1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.809017 0.587785i 0.809017 0.587785i
\(3\) 1.17557i 1.17557i 0.809017 + 0.587785i \(0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(4\) 0.309017 0.951057i 0.309017 0.951057i
\(5\) 1.90211i 1.90211i −0.309017 0.951057i \(-0.600000\pi\)
0.309017 0.951057i \(-0.400000\pi\)
\(6\) 0.690983 + 0.951057i 0.690983 + 0.951057i
\(7\) −1.00000 −1.00000
\(8\) −0.309017 0.951057i −0.309017 0.951057i
\(9\) −0.381966 −0.381966
\(10\) −1.11803 1.53884i −1.11803 1.53884i
\(11\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(12\) 1.11803 + 0.363271i 1.11803 + 0.363271i
\(13\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(14\) −0.809017 + 0.587785i −0.809017 + 0.587785i
\(15\) 2.23607 2.23607
\(16\) −0.809017 0.587785i −0.809017 0.587785i
\(17\) 1.00000 1.00000
\(18\) −0.309017 + 0.224514i −0.309017 + 0.224514i
\(19\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(20\) −1.80902 0.587785i −1.80902 0.587785i
\(21\) 1.17557i 1.17557i
\(22\) 0 0
\(23\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(24\) 1.11803 0.363271i 1.11803 0.363271i
\(25\) −2.61803 −2.61803
\(26\) 0 0
\(27\) 0.726543i 0.726543i
\(28\) −0.309017 + 0.951057i −0.309017 + 0.951057i
\(29\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(30\) 1.80902 1.31433i 1.80902 1.31433i
\(31\) 0.618034 0.618034 0.309017 0.951057i \(-0.400000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(32\) −1.00000 −1.00000
\(33\) 0 0
\(34\) 0.809017 0.587785i 0.809017 0.587785i
\(35\) 1.90211i 1.90211i
\(36\) −0.118034 + 0.363271i −0.118034 + 0.363271i
\(37\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) −1.80902 + 0.587785i −1.80902 + 0.587785i
\(41\) 1.61803 1.61803 0.809017 0.587785i \(-0.200000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(42\) −0.690983 0.951057i −0.690983 0.951057i
\(43\) 1.17557i 1.17557i 0.809017 + 0.587785i \(0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(44\) 0 0
\(45\) 0.726543i 0.726543i
\(46\) 0 0
\(47\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(48\) 0.690983 0.951057i 0.690983 0.951057i
\(49\) 1.00000 1.00000
\(50\) −2.11803 + 1.53884i −2.11803 + 1.53884i
\(51\) 1.17557i 1.17557i
\(52\) 0 0
\(53\) 1.90211i 1.90211i 0.309017 + 0.951057i \(0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(54\) 0.427051 + 0.587785i 0.427051 + 0.587785i
\(55\) 0 0
\(56\) 0.309017 + 0.951057i 0.309017 + 0.951057i
\(57\) 0 0
\(58\) 0 0
\(59\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(60\) 0.690983 2.12663i 0.690983 2.12663i
\(61\) 1.17557i 1.17557i 0.809017 + 0.587785i \(0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(62\) 0.500000 0.363271i 0.500000 0.363271i
\(63\) 0.381966 0.381966
\(64\) −0.809017 + 0.587785i −0.809017 + 0.587785i
\(65\) 0 0
\(66\) 0 0
\(67\) 1.90211i 1.90211i −0.309017 0.951057i \(-0.600000\pi\)
0.309017 0.951057i \(-0.400000\pi\)
\(68\) 0.309017 0.951057i 0.309017 0.951057i
\(69\) 0 0
\(70\) 1.11803 + 1.53884i 1.11803 + 1.53884i
\(71\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(72\) 0.118034 + 0.363271i 0.118034 + 0.363271i
\(73\) −1.61803 −1.61803 −0.809017 0.587785i \(-0.800000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(74\) 0 0
\(75\) 3.07768i 3.07768i
\(76\) 0 0
\(77\) 0 0
\(78\) 0 0
\(79\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(80\) −1.11803 + 1.53884i −1.11803 + 1.53884i
\(81\) −1.23607 −1.23607
\(82\) 1.30902 0.951057i 1.30902 0.951057i
\(83\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(84\) −1.11803 0.363271i −1.11803 0.363271i
\(85\) 1.90211i 1.90211i
\(86\) 0.690983 + 0.951057i 0.690983 + 0.951057i
\(87\) 0 0
\(88\) 0 0
\(89\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(90\) 0.427051 + 0.587785i 0.427051 + 0.587785i
\(91\) 0 0
\(92\) 0 0
\(93\) 0.726543i 0.726543i
\(94\) 0 0
\(95\) 0 0
\(96\) 1.17557i 1.17557i
\(97\) −0.618034 −0.618034 −0.309017 0.951057i \(-0.600000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(98\) 0.809017 0.587785i 0.809017 0.587785i
\(99\) 0 0
\(100\) −0.809017 + 2.48990i −0.809017 + 2.48990i
\(101\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(102\) 0.690983 + 0.951057i 0.690983 + 0.951057i
\(103\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(104\) 0 0
\(105\) −2.23607 −2.23607
\(106\) 1.11803 + 1.53884i 1.11803 + 1.53884i
\(107\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(108\) 0.690983 + 0.224514i 0.690983 + 0.224514i
\(109\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0.809017 + 0.587785i 0.809017 + 0.587785i
\(113\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) −1.00000 −1.00000
\(120\) −0.690983 2.12663i −0.690983 2.12663i
\(121\) −1.00000 −1.00000
\(122\) 0.690983 + 0.951057i 0.690983 + 0.951057i
\(123\) 1.90211i 1.90211i
\(124\) 0.190983 0.587785i 0.190983 0.587785i
\(125\) 3.07768i 3.07768i
\(126\) 0.309017 0.224514i 0.309017 0.224514i
\(127\) −0.618034 −0.618034 −0.309017 0.951057i \(-0.600000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(128\) −0.309017 + 0.951057i −0.309017 + 0.951057i
\(129\) −1.38197 −1.38197
\(130\) 0 0
\(131\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) −1.11803 1.53884i −1.11803 1.53884i
\(135\) 1.38197 1.38197
\(136\) −0.309017 0.951057i −0.309017 0.951057i
\(137\) 1.61803 1.61803 0.809017 0.587785i \(-0.200000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(138\) 0 0
\(139\) 1.90211i 1.90211i −0.309017 0.951057i \(-0.600000\pi\)
0.309017 0.951057i \(-0.400000\pi\)
\(140\) 1.80902 + 0.587785i 1.80902 + 0.587785i
\(141\) 0 0
\(142\) 0 0
\(143\) 0 0
\(144\) 0.309017 + 0.224514i 0.309017 + 0.224514i
\(145\) 0 0
\(146\) −1.30902 + 0.951057i −1.30902 + 0.951057i
\(147\) 1.17557i 1.17557i
\(148\) 0 0
\(149\) 1.17557i 1.17557i 0.809017 + 0.587785i \(0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(150\) −1.80902 2.48990i −1.80902 2.48990i
\(151\) 1.61803 1.61803 0.809017 0.587785i \(-0.200000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(152\) 0 0
\(153\) −0.381966 −0.381966
\(154\) 0 0
\(155\) 1.17557i 1.17557i
\(156\) 0 0
\(157\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(158\) 0 0
\(159\) −2.23607 −2.23607
\(160\) 1.90211i 1.90211i
\(161\) 0 0
\(162\) −1.00000 + 0.726543i −1.00000 + 0.726543i
\(163\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(164\) 0.500000 1.53884i 0.500000 1.53884i
\(165\) 0 0
\(166\) 0 0
\(167\) −1.61803 −1.61803 −0.809017 0.587785i \(-0.800000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(168\) −1.11803 + 0.363271i −1.11803 + 0.363271i
\(169\) −1.00000 −1.00000
\(170\) −1.11803 1.53884i −1.11803 1.53884i
\(171\) 0 0
\(172\) 1.11803 + 0.363271i 1.11803 + 0.363271i
\(173\) 1.17557i 1.17557i −0.809017 0.587785i \(-0.800000\pi\)
0.809017 0.587785i \(-0.200000\pi\)
\(174\) 0 0
\(175\) 2.61803 2.61803
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) 1.17557i 1.17557i −0.809017 0.587785i \(-0.800000\pi\)
0.809017 0.587785i \(-0.200000\pi\)
\(180\) 0.690983 + 0.224514i 0.690983 + 0.224514i
\(181\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(182\) 0 0
\(183\) −1.38197 −1.38197
\(184\) 0 0
\(185\) 0 0
\(186\) 0.427051 + 0.587785i 0.427051 + 0.587785i
\(187\) 0 0
\(188\) 0 0
\(189\) 0.726543i 0.726543i
\(190\) 0 0
\(191\) −0.618034 −0.618034 −0.309017 0.951057i \(-0.600000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(192\) −0.690983 0.951057i −0.690983 0.951057i
\(193\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(194\) −0.500000 + 0.363271i −0.500000 + 0.363271i
\(195\) 0 0
\(196\) 0.309017 0.951057i 0.309017 0.951057i
\(197\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(198\) 0 0
\(199\) 1.61803 1.61803 0.809017 0.587785i \(-0.200000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(200\) 0.809017 + 2.48990i 0.809017 + 2.48990i
\(201\) 2.23607 2.23607
\(202\) 0 0
\(203\) 0 0
\(204\) 1.11803 + 0.363271i 1.11803 + 0.363271i
\(205\) 3.07768i 3.07768i
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) 0 0
\(210\) −1.80902 + 1.31433i −1.80902 + 1.31433i
\(211\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(212\) 1.80902 + 0.587785i 1.80902 + 0.587785i
\(213\) 0 0
\(214\) 0 0
\(215\) 2.23607 2.23607
\(216\) 0.690983 0.224514i 0.690983 0.224514i
\(217\) −0.618034 −0.618034
\(218\) 0 0
\(219\) 1.90211i 1.90211i
\(220\) 0 0
\(221\) 0 0
\(222\) 0 0
\(223\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(224\) 1.00000 1.00000
\(225\) 1.00000 1.00000
\(226\) 0 0
\(227\) 1.90211i 1.90211i 0.309017 + 0.951057i \(0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(228\) 0 0
\(229\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 0 0
\(237\) 0 0
\(238\) −0.809017 + 0.587785i −0.809017 + 0.587785i
\(239\) −1.61803 −1.61803 −0.809017 0.587785i \(-0.800000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(240\) −1.80902 1.31433i −1.80902 1.31433i
\(241\) 0.618034 0.618034 0.309017 0.951057i \(-0.400000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(242\) −0.809017 + 0.587785i −0.809017 + 0.587785i
\(243\) 0.726543i 0.726543i
\(244\) 1.11803 + 0.363271i 1.11803 + 0.363271i
\(245\) 1.90211i 1.90211i
\(246\) 1.11803 + 1.53884i 1.11803 + 1.53884i
\(247\) 0 0
\(248\) −0.190983 0.587785i −0.190983 0.587785i
\(249\) 0 0
\(250\) 1.80902 + 2.48990i 1.80902 + 2.48990i
\(251\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(252\) 0.118034 0.363271i 0.118034 0.363271i
\(253\) 0 0
\(254\) −0.500000 + 0.363271i −0.500000 + 0.363271i
\(255\) 2.23607 2.23607
\(256\) 0.309017 + 0.951057i 0.309017 + 0.951057i
\(257\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(258\) −1.11803 + 0.812299i −1.11803 + 0.812299i
\(259\) 0 0
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(264\) 0 0
\(265\) 3.61803 3.61803
\(266\) 0 0
\(267\) 0 0
\(268\) −1.80902 0.587785i −1.80902 0.587785i
\(269\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(270\) 1.11803 0.812299i 1.11803 0.812299i
\(271\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(272\) −0.809017 0.587785i −0.809017 0.587785i
\(273\) 0 0
\(274\) 1.30902 0.951057i 1.30902 0.951057i
\(275\) 0 0
\(276\) 0 0
\(277\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(278\) −1.11803 1.53884i −1.11803 1.53884i
\(279\) −0.236068 −0.236068
\(280\) 1.80902 0.587785i 1.80902 0.587785i
\(281\) −0.618034 −0.618034 −0.309017 0.951057i \(-0.600000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(282\) 0 0
\(283\) 1.90211i 1.90211i 0.309017 + 0.951057i \(0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) −1.61803 −1.61803
\(288\) 0.381966 0.381966
\(289\) 1.00000 1.00000
\(290\) 0 0
\(291\) 0.726543i 0.726543i
\(292\) −0.500000 + 1.53884i −0.500000 + 1.53884i
\(293\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(294\) 0.690983 + 0.951057i 0.690983 + 0.951057i
\(295\) 0 0
\(296\) 0 0
\(297\) 0 0
\(298\) 0.690983 + 0.951057i 0.690983 + 0.951057i
\(299\) 0 0
\(300\) −2.92705 0.951057i −2.92705 0.951057i
\(301\) 1.17557i 1.17557i
\(302\) 1.30902 0.951057i 1.30902 0.951057i
\(303\) 0 0
\(304\) 0 0
\(305\) 2.23607 2.23607
\(306\) −0.309017 + 0.224514i −0.309017 + 0.224514i
\(307\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) −0.690983 0.951057i −0.690983 0.951057i
\(311\) −0.618034 −0.618034 −0.309017 0.951057i \(-0.600000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(312\) 0 0
\(313\) −0.618034 −0.618034 −0.309017 0.951057i \(-0.600000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(314\) 0 0
\(315\) 0.726543i 0.726543i
\(316\) 0 0
\(317\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(318\) −1.80902 + 1.31433i −1.80902 + 1.31433i
\(319\) 0 0
\(320\) 1.11803 + 1.53884i 1.11803 + 1.53884i
\(321\) 0 0
\(322\) 0 0
\(323\) 0 0
\(324\) −0.381966 + 1.17557i −0.381966 + 1.17557i
\(325\) 0 0
\(326\) 0 0
\(327\) 0 0
\(328\) −0.500000 1.53884i −0.500000 1.53884i
\(329\) 0 0
\(330\) 0 0
\(331\) 1.90211i 1.90211i −0.309017 0.951057i \(-0.600000\pi\)
0.309017 0.951057i \(-0.400000\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) −1.30902 + 0.951057i −1.30902 + 0.951057i
\(335\) −3.61803 −3.61803
\(336\) −0.690983 + 0.951057i −0.690983 + 0.951057i
\(337\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(338\) −0.809017 + 0.587785i −0.809017 + 0.587785i
\(339\) 0 0
\(340\) −1.80902 0.587785i −1.80902 0.587785i
\(341\) 0 0
\(342\) 0 0
\(343\) −1.00000 −1.00000
\(344\) 1.11803 0.363271i 1.11803 0.363271i
\(345\) 0 0
\(346\) −0.690983 0.951057i −0.690983 0.951057i
\(347\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(348\) 0 0
\(349\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(350\) 2.11803 1.53884i 2.11803 1.53884i
\(351\) 0 0
\(352\) 0 0
\(353\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 0 0
\(357\) 1.17557i 1.17557i
\(358\) −0.690983 0.951057i −0.690983 0.951057i
\(359\) 0.618034 0.618034 0.309017 0.951057i \(-0.400000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(360\) 0.690983 0.224514i 0.690983 0.224514i
\(361\) −1.00000 −1.00000
\(362\) 0 0
\(363\) 1.17557i 1.17557i
\(364\) 0 0
\(365\) 3.07768i 3.07768i
\(366\) −1.11803 + 0.812299i −1.11803 + 0.812299i
\(367\) −1.61803 −1.61803 −0.809017 0.587785i \(-0.800000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(368\) 0 0
\(369\) −0.618034 −0.618034
\(370\) 0 0
\(371\) 1.90211i 1.90211i
\(372\) 0.690983 + 0.224514i 0.690983 + 0.224514i
\(373\) 1.17557i 1.17557i 0.809017 + 0.587785i \(0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(374\) 0 0
\(375\) −3.61803 −3.61803
\(376\) 0 0
\(377\) 0 0
\(378\) −0.427051 0.587785i −0.427051 0.587785i
\(379\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(380\) 0 0
\(381\) 0.726543i 0.726543i
\(382\) −0.500000 + 0.363271i −0.500000 + 0.363271i
\(383\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(384\) −1.11803 0.363271i −1.11803 0.363271i
\(385\) 0 0
\(386\) 0 0
\(387\) 0.449028i 0.449028i
\(388\) −0.190983 + 0.587785i −0.190983 + 0.587785i
\(389\) 1.90211i 1.90211i −0.309017 0.951057i \(-0.600000\pi\)
0.309017 0.951057i \(-0.400000\pi\)
\(390\) 0 0
\(391\) 0 0
\(392\) −0.309017 0.951057i −0.309017 0.951057i
\(393\) 0 0
\(394\) 0 0
\(395\) 0 0
\(396\) 0 0
\(397\) 1.90211i 1.90211i −0.309017 0.951057i \(-0.600000\pi\)
0.309017 0.951057i \(-0.400000\pi\)
\(398\) 1.30902 0.951057i 1.30902 0.951057i
\(399\) 0 0
\(400\) 2.11803 + 1.53884i 2.11803 + 1.53884i
\(401\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(402\) 1.80902 1.31433i 1.80902 1.31433i
\(403\) 0 0
\(404\) 0 0
\(405\) 2.35114i 2.35114i
\(406\) 0 0
\(407\) 0 0
\(408\) 1.11803 0.363271i 1.11803 0.363271i
\(409\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(410\) −1.80902 2.48990i −1.80902 2.48990i
\(411\) 1.90211i 1.90211i
\(412\) 0 0
\(413\) 0 0
\(414\) 0 0
\(415\) 0 0
\(416\) 0 0
\(417\) 2.23607 2.23607
\(418\) 0 0
\(419\) 1.90211i 1.90211i 0.309017 + 0.951057i \(0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(420\) −0.690983 + 2.12663i −0.690983 + 2.12663i
\(421\) 1.17557i 1.17557i −0.809017 0.587785i \(-0.800000\pi\)
0.809017 0.587785i \(-0.200000\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 1.80902 0.587785i 1.80902 0.587785i
\(425\) −2.61803 −2.61803
\(426\) 0 0
\(427\) 1.17557i 1.17557i
\(428\) 0 0
\(429\) 0 0
\(430\) 1.80902 1.31433i 1.80902 1.31433i
\(431\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(432\) 0.427051 0.587785i 0.427051 0.587785i
\(433\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(434\) −0.500000 + 0.363271i −0.500000 + 0.363271i
\(435\) 0 0
\(436\) 0 0
\(437\) 0 0
\(438\) −1.11803 1.53884i −1.11803 1.53884i
\(439\) −1.61803 −1.61803 −0.809017 0.587785i \(-0.800000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(440\) 0 0
\(441\) −0.381966 −0.381966
\(442\) 0 0
\(443\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 0 0
\(447\) −1.38197 −1.38197
\(448\) 0.809017 0.587785i 0.809017 0.587785i
\(449\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(450\) 0.809017 0.587785i 0.809017 0.587785i
\(451\) 0 0
\(452\) 0 0
\(453\) 1.90211i 1.90211i
\(454\) 1.11803 + 1.53884i 1.11803 + 1.53884i
\(455\) 0 0
\(456\) 0 0
\(457\) −0.618034 −0.618034 −0.309017 0.951057i \(-0.600000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(458\) 0 0
\(459\) 0.726543i 0.726543i
\(460\) 0 0
\(461\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(462\) 0 0
\(463\) −1.61803 −1.61803 −0.809017 0.587785i \(-0.800000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(464\) 0 0
\(465\) 1.38197 1.38197
\(466\) 0 0
\(467\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(468\) 0 0
\(469\) 1.90211i 1.90211i
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) 0 0
\(474\) 0 0
\(475\) 0 0
\(476\) −0.309017 + 0.951057i −0.309017 + 0.951057i
\(477\) 0.726543i 0.726543i
\(478\) −1.30902 + 0.951057i −1.30902 + 0.951057i
\(479\) 1.61803 1.61803 0.809017 0.587785i \(-0.200000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(480\) −2.23607 −2.23607
\(481\) 0 0
\(482\) 0.500000 0.363271i 0.500000 0.363271i
\(483\) 0 0
\(484\) −0.309017 + 0.951057i −0.309017 + 0.951057i
\(485\) 1.17557i 1.17557i
\(486\) −0.427051 0.587785i −0.427051 0.587785i
\(487\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(488\) 1.11803 0.363271i 1.11803 0.363271i
\(489\) 0 0
\(490\) −1.11803 1.53884i −1.11803 1.53884i
\(491\) 1.90211i 1.90211i 0.309017 + 0.951057i \(0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(492\) 1.80902 + 0.587785i 1.80902 + 0.587785i
\(493\) 0 0
\(494\) 0 0
\(495\) 0 0
\(496\) −0.500000 0.363271i −0.500000 0.363271i
\(497\) 0 0
\(498\) 0 0
\(499\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(500\) 2.92705 + 0.951057i 2.92705 + 0.951057i
\(501\) 1.90211i 1.90211i
\(502\) 0 0
\(503\) 0.618034 0.618034 0.309017 0.951057i \(-0.400000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(504\) −0.118034 0.363271i −0.118034 0.363271i
\(505\) 0 0
\(506\) 0 0
\(507\) 1.17557i 1.17557i
\(508\) −0.190983 + 0.587785i −0.190983 + 0.587785i
\(509\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(510\) 1.80902 1.31433i 1.80902 1.31433i
\(511\) 1.61803 1.61803
\(512\) 0.809017 + 0.587785i 0.809017 + 0.587785i
\(513\) 0 0
\(514\) 0 0
\(515\) 0 0
\(516\) −0.427051 + 1.31433i −0.427051 + 1.31433i
\(517\) 0 0
\(518\) 0 0
\(519\) 1.38197 1.38197
\(520\) 0 0
\(521\) −1.61803 −1.61803 −0.809017 0.587785i \(-0.800000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(522\) 0 0
\(523\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(524\) 0 0
\(525\) 3.07768i 3.07768i
\(526\) 1.61803 1.17557i 1.61803 1.17557i
\(527\) 0.618034 0.618034
\(528\) 0 0
\(529\) 1.00000 1.00000
\(530\) 2.92705 2.12663i 2.92705 2.12663i
\(531\) 0 0
\(532\) 0 0
\(533\) 0 0
\(534\) 0 0
\(535\) 0 0
\(536\) −1.80902 + 0.587785i −1.80902 + 0.587785i
\(537\) 1.38197 1.38197
\(538\) 0 0
\(539\) 0 0
\(540\) 0.427051 1.31433i 0.427051 1.31433i
\(541\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) −1.00000 −1.00000
\(545\) 0 0
\(546\) 0 0
\(547\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(548\) 0.500000 1.53884i 0.500000 1.53884i
\(549\) 0.449028i 0.449028i
\(550\) 0 0
\(551\) 0 0
\(552\) 0 0
\(553\) 0 0
\(554\) 0 0
\(555\) 0 0
\(556\) −1.80902 0.587785i −1.80902 0.587785i
\(557\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(558\) −0.190983 + 0.138757i −0.190983 + 0.138757i
\(559\) 0 0
\(560\) 1.11803 1.53884i 1.11803 1.53884i
\(561\) 0 0
\(562\) −0.500000 + 0.363271i −0.500000 + 0.363271i
\(563\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 1.11803 + 1.53884i 1.11803 + 1.53884i
\(567\) 1.23607 1.23607
\(568\) 0 0
\(569\) 1.61803 1.61803 0.809017 0.587785i \(-0.200000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(570\) 0 0
\(571\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(572\) 0 0
\(573\) 0.726543i 0.726543i
\(574\) −1.30902 + 0.951057i −1.30902 + 0.951057i
\(575\) 0 0
\(576\) 0.309017 0.224514i 0.309017 0.224514i
\(577\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(578\) 0.809017 0.587785i 0.809017 0.587785i
\(579\) 0 0
\(580\) 0 0
\(581\) 0 0
\(582\) −0.427051 0.587785i −0.427051 0.587785i
\(583\) 0 0
\(584\) 0.500000 + 1.53884i 0.500000 + 1.53884i
\(585\) 0 0
\(586\) 0 0
\(587\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(588\) 1.11803 + 0.363271i 1.11803 + 0.363271i
\(589\) 0 0
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(594\) 0 0
\(595\) 1.90211i 1.90211i
\(596\) 1.11803 + 0.363271i 1.11803 + 0.363271i
\(597\) 1.90211i 1.90211i
\(598\) 0 0
\(599\) −1.61803 −1.61803 −0.809017 0.587785i \(-0.800000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(600\) −2.92705 + 0.951057i −2.92705 + 0.951057i
\(601\) −2.00000 −2.00000 −1.00000 \(\pi\)
−1.00000 \(\pi\)
\(602\) −0.690983 0.951057i −0.690983 0.951057i
\(603\) 0.726543i 0.726543i
\(604\) 0.500000 1.53884i 0.500000 1.53884i
\(605\) 1.90211i 1.90211i
\(606\) 0 0
\(607\) −0.618034 −0.618034 −0.309017 0.951057i \(-0.600000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 1.80902 1.31433i 1.80902 1.31433i
\(611\) 0 0
\(612\) −0.118034 + 0.363271i −0.118034 + 0.363271i
\(613\) 1.90211i 1.90211i 0.309017 + 0.951057i \(0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(614\) 0 0
\(615\) 3.61803 3.61803
\(616\) 0 0
\(617\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(618\) 0 0
\(619\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(620\) −1.11803 0.363271i −1.11803 0.363271i
\(621\) 0 0
\(622\) −0.500000 + 0.363271i −0.500000 + 0.363271i
\(623\) 0 0
\(624\) 0 0
\(625\) 3.23607 3.23607
\(626\) −0.500000 + 0.363271i −0.500000 + 0.363271i
\(627\) 0 0
\(628\) 0 0
\(629\) 0 0
\(630\) −0.427051 0.587785i −0.427051 0.587785i
\(631\) −0.618034 −0.618034 −0.309017 0.951057i \(-0.600000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) 1.17557i 1.17557i
\(636\) −0.690983 + 2.12663i −0.690983 + 2.12663i
\(637\) 0 0
\(638\) 0 0
\(639\) 0 0
\(640\) 1.80902 + 0.587785i 1.80902 + 0.587785i
\(641\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(642\) 0 0
\(643\) 1.17557i 1.17557i −0.809017 0.587785i \(-0.800000\pi\)
0.809017 0.587785i \(-0.200000\pi\)
\(644\) 0 0
\(645\) 2.62866i 2.62866i
\(646\) 0 0
\(647\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(648\) 0.381966 + 1.17557i 0.381966 + 1.17557i
\(649\) 0 0
\(650\) 0 0
\(651\) 0.726543i 0.726543i
\(652\) 0 0
\(653\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) −1.30902 0.951057i −1.30902 0.951057i
\(657\) 0.618034 0.618034
\(658\) 0 0
\(659\) 1.90211i 1.90211i −0.309017 0.951057i \(-0.600000\pi\)
0.309017 0.951057i \(-0.400000\pi\)
\(660\) 0 0
\(661\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(662\) −1.11803 1.53884i −1.11803 1.53884i
\(663\) 0 0
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) 0 0
\(668\) −0.500000 + 1.53884i −0.500000 + 1.53884i
\(669\) 0 0
\(670\) −2.92705 + 2.12663i −2.92705 + 2.12663i
\(671\) 0 0
\(672\) 1.17557i 1.17557i
\(673\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(674\) 0 0
\(675\) 1.90211i 1.90211i
\(676\) −0.309017 + 0.951057i −0.309017 + 0.951057i
\(677\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(678\) 0 0
\(679\) 0.618034 0.618034
\(680\) −1.80902 + 0.587785i −1.80902 + 0.587785i
\(681\) −2.23607 −2.23607
\(682\) 0 0
\(683\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(684\) 0 0
\(685\) 3.07768i 3.07768i
\(686\) −0.809017 + 0.587785i −0.809017 + 0.587785i
\(687\) 0 0
\(688\) 0.690983 0.951057i 0.690983 0.951057i
\(689\) 0 0
\(690\) 0 0
\(691\) 1.17557i 1.17557i −0.809017 0.587785i \(-0.800000\pi\)
0.809017 0.587785i \(-0.200000\pi\)
\(692\) −1.11803 0.363271i −1.11803 0.363271i
\(693\) 0 0
\(694\) 0 0
\(695\) −3.61803 −3.61803
\(696\) 0 0
\(697\) 1.61803 1.61803
\(698\) 0 0
\(699\) 0 0
\(700\) 0.809017 2.48990i 0.809017 2.48990i
\(701\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(702\) 0 0
\(703\) 0 0
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 0 0
\(708\) 0 0
\(709\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) 0 0
\(714\) −0.690983 0.951057i −0.690983 0.951057i
\(715\) 0 0
\(716\) −1.11803 0.363271i −1.11803 0.363271i
\(717\) 1.90211i 1.90211i
\(718\) 0.500000 0.363271i 0.500000 0.363271i
\(719\) 1.61803 1.61803 0.809017 0.587785i \(-0.200000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(720\) 0.427051 0.587785i 0.427051 0.587785i
\(721\) 0 0
\(722\) −0.809017 + 0.587785i −0.809017 + 0.587785i
\(723\) 0.726543i 0.726543i
\(724\) 0 0
\(725\) 0 0
\(726\) −0.690983 0.951057i −0.690983 0.951057i
\(727\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(728\) 0 0
\(729\) −0.381966 −0.381966
\(730\) 1.80902 + 2.48990i 1.80902 + 2.48990i
\(731\) 1.17557i 1.17557i
\(732\) −0.427051 + 1.31433i −0.427051 + 1.31433i
\(733\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(734\) −1.30902 + 0.951057i −1.30902 + 0.951057i
\(735\) 2.23607 2.23607
\(736\) 0 0
\(737\) 0 0
\(738\) −0.500000 + 0.363271i −0.500000 + 0.363271i
\(739\) 1.17557i 1.17557i 0.809017 + 0.587785i \(0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) −1.11803 1.53884i −1.11803 1.53884i
\(743\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(744\) 0.690983 0.224514i 0.690983 0.224514i
\(745\) 2.23607 2.23607
\(746\) 0.690983 + 0.951057i 0.690983 + 0.951057i
\(747\) 0 0
\(748\) 0 0
\(749\) 0 0
\(750\) −2.92705 + 2.12663i −2.92705 + 2.12663i
\(751\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 3.07768i 3.07768i
\(756\) −0.690983 0.224514i −0.690983 0.224514i
\(757\) 1.17557i 1.17557i −0.809017 0.587785i \(-0.800000\pi\)
0.809017 0.587785i \(-0.200000\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(762\) −0.427051 0.587785i −0.427051 0.587785i
\(763\) 0 0
\(764\) −0.190983 + 0.587785i −0.190983 + 0.587785i
\(765\) 0.726543i 0.726543i
\(766\) 0 0
\(767\) 0 0
\(768\) −1.11803 + 0.363271i −1.11803 + 0.363271i
\(769\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(774\) −0.263932 0.363271i −0.263932 0.363271i
\(775\) −1.61803 −1.61803
\(776\) 0.190983 + 0.587785i 0.190983 + 0.587785i
\(777\) 0 0
\(778\) −1.11803 1.53884i −1.11803 1.53884i
\(779\) 0 0
\(780\) 0 0
\(781\) 0 0
\(782\) 0 0
\(783\) 0 0
\(784\) −0.809017 0.587785i −0.809017 0.587785i
\(785\) 0 0
\(786\) 0 0
\(787\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(788\) 0 0
\(789\) 2.35114i 2.35114i
\(790\) 0 0
\(791\) 0 0
\(792\) 0 0
\(793\) 0 0
\(794\) −1.11803 1.53884i −1.11803 1.53884i
\(795\) 4.25325i 4.25325i
\(796\) 0.500000 1.53884i 0.500000 1.53884i
\(797\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(798\) 0 0
\(799\) 0 0
\(800\) 2.61803 2.61803
\(801\) 0 0
\(802\) 0 0
\(803\) 0 0
\(804\) 0.690983 2.12663i 0.690983 2.12663i
\(805\) 0 0
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(810\) 1.38197 + 1.90211i 1.38197 + 1.90211i
\(811\) 1.17557i 1.17557i 0.809017 + 0.587785i \(0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) 0 0
\(816\) 0.690983 0.951057i 0.690983 0.951057i
\(817\) 0 0
\(818\) 0 0
\(819\) 0 0
\(820\) −2.92705 0.951057i −2.92705 0.951057i
\(821\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(822\) 1.11803 + 1.53884i 1.11803 + 1.53884i
\(823\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(828\) 0 0
\(829\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) 1.00000 1.00000
\(834\) 1.80902 1.31433i 1.80902 1.31433i
\(835\) 3.07768i 3.07768i
\(836\) 0 0
\(837\) 0.449028i 0.449028i
\(838\) 1.11803 + 1.53884i 1.11803 + 1.53884i
\(839\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(840\) 0.690983 + 2.12663i 0.690983 + 2.12663i
\(841\) −1.00000 −1.00000
\(842\) −0.690983 0.951057i −0.690983 0.951057i
\(843\) 0.726543i 0.726543i
\(844\) 0 0
\(845\) 1.90211i 1.90211i
\(846\) 0 0
\(847\) 1.00000 1.00000
\(848\) 1.11803 1.53884i 1.11803 1.53884i
\(849\) −2.23607 −2.23607
\(850\) −2.11803 + 1.53884i −2.11803 + 1.53884i
\(851\) 0 0
\(852\) 0 0
\(853\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(854\) −0.690983 0.951057i −0.690983 0.951057i
\(855\) 0 0
\(856\) 0 0
\(857\) −0.618034 −0.618034 −0.309017 0.951057i \(-0.600000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(858\) 0 0
\(859\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(860\) 0.690983 2.12663i 0.690983 2.12663i
\(861\) 1.90211i 1.90211i
\(862\) 0 0
\(863\) 0.618034 0.618034 0.309017 0.951057i \(-0.400000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(864\) 0.726543i 0.726543i
\(865\) −2.23607 −2.23607
\(866\) 0 0
\(867\) 1.17557i 1.17557i
\(868\) −0.190983 + 0.587785i −0.190983 + 0.587785i
\(869\) 0 0
\(870\) 0 0
\(871\) 0 0
\(872\) 0 0
\(873\) 0.236068 0.236068
\(874\) 0 0
\(875\) 3.07768i 3.07768i
\(876\) −1.80902 0.587785i −1.80902 0.587785i
\(877\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(878\) −1.30902 + 0.951057i −1.30902 + 0.951057i
\(879\) 0 0
\(880\) 0 0
\(881\) −0.618034 −0.618034 −0.309017 0.951057i \(-0.600000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(882\) −0.309017 + 0.224514i −0.309017 + 0.224514i
\(883\) 1.90211i 1.90211i 0.309017 + 0.951057i \(0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) −0.618034 −0.618034 −0.309017 0.951057i \(-0.600000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(888\) 0 0
\(889\) 0.618034 0.618034
\(890\) 0 0
\(891\) 0 0
\(892\) 0 0
\(893\) 0 0
\(894\) −1.11803 + 0.812299i −1.11803 + 0.812299i
\(895\) −2.23607 −2.23607
\(896\) 0.309017 0.951057i 0.309017 0.951057i
\(897\) 0 0
\(898\) 0 0
\(899\) 0 0
\(900\) 0.309017 0.951057i 0.309017 0.951057i
\(901\) 1.90211i 1.90211i
\(902\) 0 0
\(903\) 1.38197 1.38197
\(904\) 0 0
\(905\) 0 0
\(906\) 1.11803 + 1.53884i 1.11803 + 1.53884i
\(907\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(908\) 1.80902 + 0.587785i 1.80902 + 0.587785i
\(909\) 0 0
\(910\) 0 0
\(911\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(912\) 0 0
\(913\) 0 0
\(914\) −0.500000 + 0.363271i −0.500000 + 0.363271i
\(915\) 2.62866i 2.62866i
\(916\) 0 0
\(917\) 0 0
\(918\) 0.427051 + 0.587785i 0.427051 + 0.587785i
\(919\) 1.61803 1.61803 0.809017 0.587785i \(-0.200000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 0 0
\(923\) 0 0
\(924\) 0 0
\(925\) 0 0
\(926\) −1.30902 + 0.951057i −1.30902 + 0.951057i
\(927\) 0 0
\(928\) 0 0
\(929\) 0.618034 0.618034 0.309017 0.951057i \(-0.400000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(930\) 1.11803 0.812299i 1.11803 0.812299i
\(931\) 0 0
\(932\) 0 0
\(933\) 0.726543i 0.726543i
\(934\) 0 0
\(935\) 0 0
\(936\) 0 0
\(937\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(938\) 1.11803 + 1.53884i 1.11803 + 1.53884i
\(939\) 0.726543i 0.726543i
\(940\) 0 0
\(941\) 1.17557i 1.17557i −0.809017 0.587785i \(-0.800000\pi\)
0.809017 0.587785i \(-0.200000\pi\)
\(942\) 0 0
\(943\) 0 0
\(944\) 0 0
\(945\) −1.38197 −1.38197
\(946\) 0 0
\(947\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(948\) 0 0
\(949\) 0 0
\(950\) 0 0
\(951\) 0 0
\(952\) 0.309017 + 0.951057i 0.309017 + 0.951057i
\(953\) 0.618034 0.618034 0.309017 0.951057i \(-0.400000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(954\) −0.427051 0.587785i −0.427051 0.587785i
\(955\) 1.17557i 1.17557i
\(956\) −0.500000 + 1.53884i −0.500000 + 1.53884i
\(957\) 0 0
\(958\) 1.30902 0.951057i 1.30902 0.951057i
\(959\) −1.61803 −1.61803
\(960\) −1.80902 + 1.31433i −1.80902 + 1.31433i
\(961\) −0.618034 −0.618034
\(962\) 0 0
\(963\) 0 0
\(964\) 0.190983 0.587785i 0.190983 0.587785i
\(965\) 0 0
\(966\) 0 0
\(967\) −1.61803 −1.61803 −0.809017 0.587785i \(-0.800000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(968\) 0.309017 + 0.951057i 0.309017 + 0.951057i
\(969\) 0 0
\(970\) 0.690983 + 0.951057i 0.690983 + 0.951057i
\(971\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(972\) −0.690983 0.224514i −0.690983 0.224514i
\(973\) 1.90211i 1.90211i
\(974\) 0 0
\(975\) 0 0
\(976\) 0.690983 0.951057i 0.690983 0.951057i
\(977\) 0.618034 0.618034 0.309017 0.951057i \(-0.400000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(978\) 0 0
\(979\) 0 0
\(980\) −1.80902 0.587785i −1.80902 0.587785i
\(981\) 0 0
\(982\) 1.11803 + 1.53884i 1.11803 + 1.53884i
\(983\) −0.618034 −0.618034 −0.309017 0.951057i \(-0.600000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(984\) 1.80902 0.587785i 1.80902 0.587785i
\(985\) 0 0
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) 0 0
\(990\) 0 0
\(991\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(992\) −0.618034 −0.618034
\(993\) 2.23607 2.23607
\(994\) 0 0
\(995\) 3.07768i 3.07768i
\(996\) 0 0
\(997\) 1.17557i 1.17557i 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 952.1.e.d.237.3 yes 4
4.3 odd 2 3808.1.e.d.3569.2 4
7.6 odd 2 952.1.e.c.237.3 4
8.3 odd 2 3808.1.e.d.3569.3 4
8.5 even 2 inner 952.1.e.d.237.4 yes 4
17.16 even 2 952.1.e.c.237.3 4
28.27 even 2 3808.1.e.c.3569.3 4
56.13 odd 2 952.1.e.c.237.4 yes 4
56.27 even 2 3808.1.e.c.3569.2 4
68.67 odd 2 3808.1.e.c.3569.3 4
119.118 odd 2 CM 952.1.e.d.237.3 yes 4
136.67 odd 2 3808.1.e.c.3569.2 4
136.101 even 2 952.1.e.c.237.4 yes 4
476.475 even 2 3808.1.e.d.3569.2 4
952.237 odd 2 inner 952.1.e.d.237.4 yes 4
952.475 even 2 3808.1.e.d.3569.3 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
952.1.e.c.237.3 4 7.6 odd 2
952.1.e.c.237.3 4 17.16 even 2
952.1.e.c.237.4 yes 4 56.13 odd 2
952.1.e.c.237.4 yes 4 136.101 even 2
952.1.e.d.237.3 yes 4 1.1 even 1 trivial
952.1.e.d.237.3 yes 4 119.118 odd 2 CM
952.1.e.d.237.4 yes 4 8.5 even 2 inner
952.1.e.d.237.4 yes 4 952.237 odd 2 inner
3808.1.e.c.3569.2 4 56.27 even 2
3808.1.e.c.3569.2 4 136.67 odd 2
3808.1.e.c.3569.3 4 28.27 even 2
3808.1.e.c.3569.3 4 68.67 odd 2
3808.1.e.d.3569.2 4 4.3 odd 2
3808.1.e.d.3569.2 4 476.475 even 2
3808.1.e.d.3569.3 4 8.3 odd 2
3808.1.e.d.3569.3 4 952.475 even 2