Basic properties
| Modulus: | \(35937\) | |
| Conductor: | \(3267\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(990\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{3267}(634,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | no | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 35937.cd
\(\chi_{35937}(40,\cdot)\) \(\chi_{35937}(94,\cdot)\) \(\chi_{35937}(112,\cdot)\) \(\chi_{35937}(403,\cdot)\) \(\chi_{35937}(457,\cdot)\) \(\chi_{35937}(475,\cdot)\) \(\chi_{35937}(481,\cdot)\) \(\chi_{35937}(844,\cdot)\) \(\chi_{35937}(1129,\cdot)\) \(\chi_{35937}(1183,\cdot)\) \(\chi_{35937}(1201,\cdot)\) \(\chi_{35937}(1546,\cdot)\) \(\chi_{35937}(1564,\cdot)\) \(\chi_{35937}(1570,\cdot)\) \(\chi_{35937}(1933,\cdot)\) \(\chi_{35937}(2218,\cdot)\) \(\chi_{35937}(2272,\cdot)\) \(\chi_{35937}(2290,\cdot)\) \(\chi_{35937}(2581,\cdot)\) \(\chi_{35937}(2635,\cdot)\) \(\chi_{35937}(2653,\cdot)\) \(\chi_{35937}(2659,\cdot)\) \(\chi_{35937}(3022,\cdot)\) \(\chi_{35937}(3307,\cdot)\) \(\chi_{35937}(3379,\cdot)\) \(\chi_{35937}(3670,\cdot)\) \(\chi_{35937}(3724,\cdot)\) \(\chi_{35937}(3742,\cdot)\) \(\chi_{35937}(3748,\cdot)\) \(\chi_{35937}(4111,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{495})$ |
| Fixed field: | Number field defined by a degree 990 polynomial (not computed) |
Values on generators
\((22628,13312)\) → \((e\left(\frac{4}{9}\right),e\left(\frac{17}{110}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(13\) | \(14\) | \(16\) | \(17\) |
| \( \chi_{ 35937 }(40, a) \) | \(-1\) | \(1\) | \(e\left(\frac{593}{990}\right)\) | \(e\left(\frac{98}{495}\right)\) | \(e\left(\frac{326}{495}\right)\) | \(e\left(\frac{191}{990}\right)\) | \(e\left(\frac{263}{330}\right)\) | \(e\left(\frac{17}{66}\right)\) | \(e\left(\frac{163}{990}\right)\) | \(e\left(\frac{392}{495}\right)\) | \(e\left(\frac{196}{495}\right)\) | \(e\left(\frac{79}{330}\right)\) |