Basic properties
| Modulus: | \(243675\) | |
| Conductor: | \(81225\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(1140\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{81225}(28138,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | no | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 243675.zz
\(\chi_{243675}(37,\cdot)\) \(\chi_{243675}(208,\cdot)\) \(\chi_{243675}(1063,\cdot)\) \(\chi_{243675}(1747,\cdot)\) \(\chi_{243675}(2602,\cdot)\) \(\chi_{243675}(2773,\cdot)\) \(\chi_{243675}(3628,\cdot)\) \(\chi_{243675}(4312,\cdot)\) \(\chi_{243675}(5167,\cdot)\) \(\chi_{243675}(5338,\cdot)\) \(\chi_{243675}(6877,\cdot)\) \(\chi_{243675}(7903,\cdot)\) \(\chi_{243675}(8758,\cdot)\) \(\chi_{243675}(9442,\cdot)\) \(\chi_{243675}(10297,\cdot)\) \(\chi_{243675}(11323,\cdot)\) \(\chi_{243675}(12862,\cdot)\) \(\chi_{243675}(13033,\cdot)\) \(\chi_{243675}(13888,\cdot)\) \(\chi_{243675}(14572,\cdot)\) \(\chi_{243675}(15427,\cdot)\) \(\chi_{243675}(15598,\cdot)\) \(\chi_{243675}(16453,\cdot)\) \(\chi_{243675}(17137,\cdot)\) \(\chi_{243675}(17992,\cdot)\) \(\chi_{243675}(18163,\cdot)\) \(\chi_{243675}(19702,\cdot)\) \(\chi_{243675}(20728,\cdot)\) \(\chi_{243675}(21583,\cdot)\) \(\chi_{243675}(22267,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{1140})$ |
| Fixed field: | Number field defined by a degree 1140 polynomial (not computed) |
Values on generators
\((36101,77977,129601)\) → \((e\left(\frac{1}{3}\right),e\left(\frac{19}{20}\right),e\left(\frac{7}{38}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(7\) | \(8\) | \(11\) | \(13\) | \(14\) | \(16\) | \(17\) | \(22\) |
| \( \chi_{ 243675 }(1063, a) \) | \(1\) | \(1\) | \(e\left(\frac{533}{1140}\right)\) | \(e\left(\frac{533}{570}\right)\) | \(e\left(\frac{163}{228}\right)\) | \(e\left(\frac{153}{380}\right)\) | \(e\left(\frac{92}{285}\right)\) | \(e\left(\frac{367}{1140}\right)\) | \(e\left(\frac{52}{285}\right)\) | \(e\left(\frac{248}{285}\right)\) | \(e\left(\frac{373}{380}\right)\) | \(e\left(\frac{901}{1140}\right)\) |