Basic properties
| Modulus: | \(35937\) | |
| Conductor: | \(11979\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(3630\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{11979}(4010,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | no | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 35937.co
\(\chi_{35937}(8,\cdot)\) \(\chi_{35937}(17,\cdot)\) \(\chi_{35937}(35,\cdot)\) \(\chi_{35937}(62,\cdot)\) \(\chi_{35937}(116,\cdot)\) \(\chi_{35937}(206,\cdot)\) \(\chi_{35937}(260,\cdot)\) \(\chi_{35937}(305,\cdot)\) \(\chi_{35937}(314,\cdot)\) \(\chi_{35937}(332,\cdot)\) \(\chi_{35937}(359,\cdot)\) \(\chi_{35937}(413,\cdot)\) \(\chi_{35937}(503,\cdot)\) \(\chi_{35937}(530,\cdot)\) \(\chi_{35937}(557,\cdot)\) \(\chi_{35937}(611,\cdot)\) \(\chi_{35937}(629,\cdot)\) \(\chi_{35937}(656,\cdot)\) \(\chi_{35937}(710,\cdot)\) \(\chi_{35937}(800,\cdot)\) \(\chi_{35937}(827,\cdot)\) \(\chi_{35937}(854,\cdot)\) \(\chi_{35937}(899,\cdot)\) \(\chi_{35937}(908,\cdot)\) \(\chi_{35937}(926,\cdot)\) \(\chi_{35937}(953,\cdot)\) \(\chi_{35937}(1007,\cdot)\) \(\chi_{35937}(1097,\cdot)\) \(\chi_{35937}(1124,\cdot)\) \(\chi_{35937}(1151,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{1815})$ |
| Fixed field: | Number field defined by a degree 3630 polynomial (not computed) |
Values on generators
\((22628,13312)\) → \((e\left(\frac{5}{6}\right),e\left(\frac{159}{1210}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(13\) | \(14\) | \(16\) | \(17\) |
| \( \chi_{ 35937 }(17, a) \) | \(1\) | \(1\) | \(e\left(\frac{1751}{1815}\right)\) | \(e\left(\frac{1687}{1815}\right)\) | \(e\left(\frac{1253}{3630}\right)\) | \(e\left(\frac{1909}{3630}\right)\) | \(e\left(\frac{541}{605}\right)\) | \(e\left(\frac{75}{242}\right)\) | \(e\left(\frac{1757}{3630}\right)\) | \(e\left(\frac{1781}{3630}\right)\) | \(e\left(\frac{1559}{1815}\right)\) | \(e\left(\frac{238}{605}\right)\) |