Properties

Label 1.95.4t1.a.b
Dimension $1$
Group $C_4$
Conductor $95$
Root number not computed
Indicator $0$

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Basic invariants

Dimension: $1$
Group: $C_4$
Conductor: \(95\)\(\medspace = 5 \cdot 19 \)
Artin field: Galois closure of 4.4.45125.1
Galois orbit size: $2$
Smallest permutation container: $C_4$
Parity: even
Dirichlet character: \(\chi_{95}(37,\cdot)\)
Projective image: $C_1$
Projective field: Galois closure of \(\Q\)

Defining polynomial

$f(x)$$=$ \( x^{4} - x^{3} - 24x^{2} + 24x + 101 \) Copy content Toggle raw display .

The roots of $f$ are computed in $\Q_{ 29 }$ to precision 5.

Roots:
$r_{ 1 }$ $=$ \( 9 + 8\cdot 29^{2} + 14\cdot 29^{3} + 15\cdot 29^{4} +O(29^{5})\) Copy content Toggle raw display
$r_{ 2 }$ $=$ \( 15 + 7\cdot 29 + 16\cdot 29^{2} + 15\cdot 29^{3} + 27\cdot 29^{4} +O(29^{5})\) Copy content Toggle raw display
$r_{ 3 }$ $=$ \( 17 + 16\cdot 29 + 24\cdot 29^{2} + 28\cdot 29^{3} + 21\cdot 29^{4} +O(29^{5})\) Copy content Toggle raw display
$r_{ 4 }$ $=$ \( 18 + 4\cdot 29 + 9\cdot 29^{2} + 28\cdot 29^{3} + 21\cdot 29^{4} +O(29^{5})\) Copy content Toggle raw display

Generators of the action on the roots $r_1, \ldots, r_{ 4 }$

Cycle notation
$(1,4,2,3)$
$(1,2)(3,4)$

Character values on conjugacy classes

SizeOrderAction on $r_1, \ldots, r_{ 4 }$ Character value
$1$$1$$()$$1$
$1$$2$$(1,2)(3,4)$$-1$
$1$$4$$(1,4,2,3)$$-\zeta_{4}$
$1$$4$$(1,3,2,4)$$\zeta_{4}$

The blue line marks the conjugacy class containing complex conjugation.