Basic properties
Modulus: | \(415\) | |
Conductor: | \(415\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(164\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
Real: | no | |
Primitive: | yes | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 415.l
\(\chi_{415}(2,\cdot)\) \(\chi_{415}(8,\cdot)\) \(\chi_{415}(13,\cdot)\) \(\chi_{415}(18,\cdot)\) \(\chi_{415}(22,\cdot)\) \(\chi_{415}(32,\cdot)\) \(\chi_{415}(42,\cdot)\) \(\chi_{415}(43,\cdot)\) \(\chi_{415}(47,\cdot)\) \(\chi_{415}(52,\cdot)\) \(\chi_{415}(53,\cdot)\) \(\chi_{415}(57,\cdot)\) \(\chi_{415}(58,\cdot)\) \(\chi_{415}(62,\cdot)\) \(\chi_{415}(67,\cdot)\) \(\chi_{415}(72,\cdot)\) \(\chi_{415}(73,\cdot)\) \(\chi_{415}(88,\cdot)\) \(\chi_{415}(97,\cdot)\) \(\chi_{415}(98,\cdot)\) \(\chi_{415}(102,\cdot)\) \(\chi_{415}(103,\cdot)\) \(\chi_{415}(107,\cdot)\) \(\chi_{415}(117,\cdot)\) \(\chi_{415}(118,\cdot)\) \(\chi_{415}(122,\cdot)\) \(\chi_{415}(128,\cdot)\) \(\chi_{415}(133,\cdot)\) \(\chi_{415}(137,\cdot)\) \(\chi_{415}(138,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{164})$ |
Fixed field: | Number field defined by a degree 164 polynomial (not computed) |
Values on generators
\((167,251)\) → \((i,e\left(\frac{47}{82}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(7\) | \(8\) | \(9\) | \(11\) | \(12\) | \(13\) |
\( \chi_{ 415 }(102, a) \) | \(1\) | \(1\) | \(e\left(\frac{135}{164}\right)\) | \(e\left(\frac{3}{164}\right)\) | \(e\left(\frac{53}{82}\right)\) | \(e\left(\frac{69}{82}\right)\) | \(e\left(\frac{137}{164}\right)\) | \(e\left(\frac{77}{164}\right)\) | \(e\left(\frac{3}{82}\right)\) | \(e\left(\frac{31}{41}\right)\) | \(e\left(\frac{109}{164}\right)\) | \(e\left(\frac{145}{164}\right)\) |