Basic properties
| Modulus: | \(1231\) | |
| Conductor: | \(1231\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(1230\) | 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 1231.p
\(\chi_{1231}(3,\cdot)\) \(\chi_{1231}(23,\cdot)\) \(\chi_{1231}(24,\cdot)\) \(\chi_{1231}(30,\cdot)\) \(\chi_{1231}(33,\cdot)\) \(\chi_{1231}(34,\cdot)\) \(\chi_{1231}(42,\cdot)\) \(\chi_{1231}(47,\cdot)\) \(\chi_{1231}(48,\cdot)\) \(\chi_{1231}(53,\cdot)\) \(\chi_{1231}(54,\cdot)\) \(\chi_{1231}(57,\cdot)\) \(\chi_{1231}(61,\cdot)\) \(\chi_{1231}(67,\cdot)\) \(\chi_{1231}(68,\cdot)\) \(\chi_{1231}(71,\cdot)\) \(\chi_{1231}(75,\cdot)\) \(\chi_{1231}(78,\cdot)\) \(\chi_{1231}(84,\cdot)\) \(\chi_{1231}(85,\cdot)\) \(\chi_{1231}(92,\cdot)\) \(\chi_{1231}(94,\cdot)\) \(\chi_{1231}(97,\cdot)\) \(\chi_{1231}(105,\cdot)\) \(\chi_{1231}(108,\cdot)\) \(\chi_{1231}(114,\cdot)\) \(\chi_{1231}(115,\cdot)\) \(\chi_{1231}(118,\cdot)\) \(\chi_{1231}(119,\cdot)\) \(\chi_{1231}(135,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{615})$ |
| Fixed field: | Number field defined by a degree 1230 polynomial (not computed) |
Values on generators
\(3\) → \(e\left(\frac{1069}{1230}\right)\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 1231 }(1229, a) \) | \(-1\) | \(1\) | \(e\left(\frac{353}{615}\right)\) | \(e\left(\frac{1069}{1230}\right)\) | \(e\left(\frac{91}{615}\right)\) | \(e\left(\frac{277}{615}\right)\) | \(e\left(\frac{109}{246}\right)\) | \(e\left(\frac{13}{615}\right)\) | \(e\left(\frac{148}{205}\right)\) | \(e\left(\frac{454}{615}\right)\) | \(e\left(\frac{1}{41}\right)\) | \(e\left(\frac{28}{41}\right)\) |