Basic properties
| Modulus: | \(2601\) | |
| Conductor: | \(2601\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(408\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | yes | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 2601.bl
\(\chi_{2601}(2,\cdot)\) \(\chi_{2601}(32,\cdot)\) \(\chi_{2601}(59,\cdot)\) \(\chi_{2601}(77,\cdot)\) \(\chi_{2601}(83,\cdot)\) \(\chi_{2601}(104,\cdot)\) \(\chi_{2601}(128,\cdot)\) \(\chi_{2601}(185,\cdot)\) \(\chi_{2601}(212,\cdot)\) \(\chi_{2601}(230,\cdot)\) \(\chi_{2601}(236,\cdot)\) \(\chi_{2601}(257,\cdot)\) \(\chi_{2601}(263,\cdot)\) \(\chi_{2601}(281,\cdot)\) \(\chi_{2601}(308,\cdot)\) \(\chi_{2601}(338,\cdot)\) \(\chi_{2601}(365,\cdot)\) \(\chi_{2601}(383,\cdot)\) \(\chi_{2601}(389,\cdot)\) \(\chi_{2601}(410,\cdot)\) \(\chi_{2601}(416,\cdot)\) \(\chi_{2601}(434,\cdot)\) \(\chi_{2601}(461,\cdot)\) \(\chi_{2601}(491,\cdot)\) \(\chi_{2601}(518,\cdot)\) \(\chi_{2601}(536,\cdot)\) \(\chi_{2601}(542,\cdot)\) \(\chi_{2601}(563,\cdot)\) \(\chi_{2601}(569,\cdot)\) \(\chi_{2601}(587,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{408})$ |
| Fixed field: | Number field defined by a degree 408 polynomial (not computed) |
Values on generators
\((290,2026)\) → \((e\left(\frac{5}{6}\right),e\left(\frac{67}{136}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(11\) | \(13\) | \(14\) | \(16\) |
| \( \chi_{ 2601 }(32, a) \) | \(-1\) | \(1\) | \(e\left(\frac{89}{204}\right)\) | \(e\left(\frac{89}{102}\right)\) | \(e\left(\frac{401}{408}\right)\) | \(e\left(\frac{283}{408}\right)\) | \(e\left(\frac{21}{68}\right)\) | \(e\left(\frac{57}{136}\right)\) | \(e\left(\frac{67}{408}\right)\) | \(e\left(\frac{23}{102}\right)\) | \(e\left(\frac{53}{408}\right)\) | \(e\left(\frac{38}{51}\right)\) |