Basic properties
| Modulus: | \(2151\) | |
| Conductor: | \(2151\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(102\) | 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 2151.v
\(\chi_{2151}(23,\cdot)\) \(\chi_{2151}(164,\cdot)\) \(\chi_{2151}(203,\cdot)\) \(\chi_{2151}(407,\cdot)\) \(\chi_{2151}(506,\cdot)\) \(\chi_{2151}(551,\cdot)\) \(\chi_{2151}(554,\cdot)\) \(\chi_{2151}(650,\cdot)\) \(\chi_{2151}(677,\cdot)\) \(\chi_{2151}(695,\cdot)\) \(\chi_{2151}(740,\cdot)\) \(\chi_{2151}(824,\cdot)\) \(\chi_{2151}(905,\cdot)\) \(\chi_{2151}(920,\cdot)\) \(\chi_{2151}(950,\cdot)\) \(\chi_{2151}(1067,\cdot)\) \(\chi_{2151}(1094,\cdot)\) \(\chi_{2151}(1247,\cdot)\) \(\chi_{2151}(1271,\cdot)\) \(\chi_{2151}(1541,\cdot)\) \(\chi_{2151}(1598,\cdot)\) \(\chi_{2151}(1622,\cdot)\) \(\chi_{2151}(1667,\cdot)\) \(\chi_{2151}(1784,\cdot)\) \(\chi_{2151}(1811,\cdot)\) \(\chi_{2151}(1841,\cdot)\) \(\chi_{2151}(1940,\cdot)\) \(\chi_{2151}(1964,\cdot)\) \(\chi_{2151}(1985,\cdot)\) \(\chi_{2151}(2084,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{51})$ |
| Fixed field: | Number field defined by a degree 102 polynomial (not computed) |
Values on generators
\((479,1441)\) → \((e\left(\frac{5}{6}\right),e\left(\frac{9}{34}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(11\) | \(13\) | \(14\) | \(16\) |
| \( \chi_{ 2151 }(23, a) \) | \(1\) | \(1\) | \(e\left(\frac{31}{102}\right)\) | \(e\left(\frac{31}{51}\right)\) | \(e\left(\frac{71}{102}\right)\) | \(e\left(\frac{61}{102}\right)\) | \(e\left(\frac{31}{34}\right)\) | \(1\) | \(e\left(\frac{91}{102}\right)\) | \(e\left(\frac{5}{102}\right)\) | \(e\left(\frac{46}{51}\right)\) | \(e\left(\frac{11}{51}\right)\) |