Basic properties
| Modulus: | \(2075\) | |
| Conductor: | \(415\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(164\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{415}(18,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 2075.r
\(\chi_{2075}(18,\cdot)\) \(\chi_{2075}(32,\cdot)\) \(\chi_{2075}(43,\cdot)\) \(\chi_{2075}(57,\cdot)\) \(\chi_{2075}(107,\cdot)\) \(\chi_{2075}(118,\cdot)\) \(\chi_{2075}(143,\cdot)\) \(\chi_{2075}(157,\cdot)\) \(\chi_{2075}(168,\cdot)\) \(\chi_{2075}(218,\cdot)\) \(\chi_{2075}(232,\cdot)\) \(\chi_{2075}(257,\cdot)\) \(\chi_{2075}(268,\cdot)\) \(\chi_{2075}(307,\cdot)\) \(\chi_{2075}(382,\cdot)\) \(\chi_{2075}(457,\cdot)\) \(\chi_{2075}(468,\cdot)\) \(\chi_{2075}(482,\cdot)\) \(\chi_{2075}(518,\cdot)\) \(\chi_{2075}(532,\cdot)\) \(\chi_{2075}(543,\cdot)\) \(\chi_{2075}(643,\cdot)\) \(\chi_{2075}(657,\cdot)\) \(\chi_{2075}(682,\cdot)\) \(\chi_{2075}(707,\cdot)\) \(\chi_{2075}(718,\cdot)\) \(\chi_{2075}(743,\cdot)\) \(\chi_{2075}(782,\cdot)\) \(\chi_{2075}(793,\cdot)\) \(\chi_{2075}(807,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{164})$ |
| Fixed field: | Number field defined by a degree 164 polynomial (not computed) |
Values on generators
\((1827,251)\) → \((-i,e\left(\frac{63}{82}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(7\) | \(8\) | \(9\) | \(11\) | \(12\) | \(13\) |
| \( \chi_{ 2075 }(18, a) \) | \(1\) | \(1\) | \(e\left(\frac{85}{164}\right)\) | \(e\left(\frac{93}{164}\right)\) | \(e\left(\frac{3}{82}\right)\) | \(e\left(\frac{7}{82}\right)\) | \(e\left(\frac{147}{164}\right)\) | \(e\left(\frac{91}{164}\right)\) | \(e\left(\frac{11}{82}\right)\) | \(e\left(\frac{18}{41}\right)\) | \(e\left(\frac{99}{164}\right)\) | \(e\left(\frac{67}{164}\right)\) |