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: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 575.w
\(\chi_{575}(17,\cdot)\) \(\chi_{575}(28,\cdot)\) \(\chi_{575}(33,\cdot)\) \(\chi_{575}(37,\cdot)\) \(\chi_{575}(38,\cdot)\) \(\chi_{575}(42,\cdot)\) \(\chi_{575}(53,\cdot)\) \(\chi_{575}(63,\cdot)\) \(\chi_{575}(67,\cdot)\) \(\chi_{575}(83,\cdot)\) \(\chi_{575}(88,\cdot)\) \(\chi_{575}(97,\cdot)\) \(\chi_{575}(102,\cdot)\) \(\chi_{575}(103,\cdot)\) \(\chi_{575}(112,\cdot)\) \(\chi_{575}(113,\cdot)\) \(\chi_{575}(122,\cdot)\) \(\chi_{575}(148,\cdot)\) \(\chi_{575}(152,\cdot)\) \(\chi_{575}(153,\cdot)\) \(\chi_{575}(158,\cdot)\) \(\chi_{575}(172,\cdot)\) \(\chi_{575}(178,\cdot)\) \(\chi_{575}(198,\cdot)\) \(\chi_{575}(203,\cdot)\) \(\chi_{575}(212,\cdot)\) \(\chi_{575}(217,\cdot)\) \(\chi_{575}(222,\cdot)\) \(\chi_{575}(227,\cdot)\) \(\chi_{575}(228,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{220})$ |
| Fixed field: | Number field defined by a degree 220 polynomial (not computed) |
Values on generators
\((277,51)\) → \((e\left(\frac{13}{20}\right),e\left(\frac{7}{22}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(7\) | \(8\) | \(9\) | \(11\) | \(12\) | \(13\) |
| \( \chi_{ 575 }(17, a) \) | \(1\) | \(1\) | \(e\left(\frac{63}{220}\right)\) | \(e\left(\frac{141}{220}\right)\) | \(e\left(\frac{63}{110}\right)\) | \(e\left(\frac{51}{55}\right)\) | \(e\left(\frac{13}{44}\right)\) | \(e\left(\frac{189}{220}\right)\) | \(e\left(\frac{31}{110}\right)\) | \(e\left(\frac{29}{110}\right)\) | \(e\left(\frac{47}{220}\right)\) | \(e\left(\frac{177}{220}\right)\) |