Basic properties
| Modulus: | \(575\) | |
| Conductor: | \(575\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(220\) | 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 575.x
\(\chi_{575}(2,\cdot)\) \(\chi_{575}(3,\cdot)\) \(\chi_{575}(8,\cdot)\) \(\chi_{575}(12,\cdot)\) \(\chi_{575}(13,\cdot)\) \(\chi_{575}(27,\cdot)\) \(\chi_{575}(48,\cdot)\) \(\chi_{575}(52,\cdot)\) \(\chi_{575}(58,\cdot)\) \(\chi_{575}(62,\cdot)\) \(\chi_{575}(72,\cdot)\) \(\chi_{575}(73,\cdot)\) \(\chi_{575}(77,\cdot)\) \(\chi_{575}(78,\cdot)\) \(\chi_{575}(87,\cdot)\) \(\chi_{575}(98,\cdot)\) \(\chi_{575}(108,\cdot)\) \(\chi_{575}(117,\cdot)\) \(\chi_{575}(123,\cdot)\) \(\chi_{575}(127,\cdot)\) \(\chi_{575}(128,\cdot)\) \(\chi_{575}(133,\cdot)\) \(\chi_{575}(142,\cdot)\) \(\chi_{575}(147,\cdot)\) \(\chi_{575}(163,\cdot)\) \(\chi_{575}(167,\cdot)\) \(\chi_{575}(173,\cdot)\) \(\chi_{575}(177,\cdot)\) \(\chi_{575}(187,\cdot)\) \(\chi_{575}(188,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{220})$ |
| Fixed field: | Number field defined by a degree 220 polynomial (not computed) |
Values on generators
\((277,51)\) → \((e\left(\frac{3}{20}\right),e\left(\frac{3}{11}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(7\) | \(8\) | \(9\) | \(11\) | \(12\) | \(13\) |
| \( \chi_{ 575 }(8, a) \) | \(-1\) | \(1\) | \(e\left(\frac{153}{220}\right)\) | \(e\left(\frac{91}{220}\right)\) | \(e\left(\frac{43}{110}\right)\) | \(e\left(\frac{6}{55}\right)\) | \(e\left(\frac{41}{44}\right)\) | \(e\left(\frac{19}{220}\right)\) | \(e\left(\frac{91}{110}\right)\) | \(e\left(\frac{47}{55}\right)\) | \(e\left(\frac{177}{220}\right)\) | \(e\left(\frac{147}{220}\right)\) |