Basic properties
| Modulus: | \(1150\) | |
| Conductor: | \(575\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(220\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{575}(17,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 1150.w
\(\chi_{1150}(17,\cdot)\) \(\chi_{1150}(33,\cdot)\) \(\chi_{1150}(37,\cdot)\) \(\chi_{1150}(53,\cdot)\) \(\chi_{1150}(63,\cdot)\) \(\chi_{1150}(67,\cdot)\) \(\chi_{1150}(83,\cdot)\) \(\chi_{1150}(97,\cdot)\) \(\chi_{1150}(103,\cdot)\) \(\chi_{1150}(113,\cdot)\) \(\chi_{1150}(153,\cdot)\) \(\chi_{1150}(203,\cdot)\) \(\chi_{1150}(217,\cdot)\) \(\chi_{1150}(227,\cdot)\) \(\chi_{1150}(237,\cdot)\) \(\chi_{1150}(247,\cdot)\) \(\chi_{1150}(263,\cdot)\) \(\chi_{1150}(267,\cdot)\) \(\chi_{1150}(273,\cdot)\) \(\chi_{1150}(283,\cdot)\) \(\chi_{1150}(287,\cdot)\) \(\chi_{1150}(297,\cdot)\) \(\chi_{1150}(313,\cdot)\) \(\chi_{1150}(327,\cdot)\) \(\chi_{1150}(333,\cdot)\) \(\chi_{1150}(337,\cdot)\) \(\chi_{1150}(373,\cdot)\) \(\chi_{1150}(383,\cdot)\) \(\chi_{1150}(387,\cdot)\) \(\chi_{1150}(433,\cdot)\) ...
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
| \(a\) | \(-1\) | \(1\) | \(3\) | \(7\) | \(9\) | \(11\) | \(13\) | \(17\) | \(19\) | \(21\) | \(27\) | \(29\) |
| \( \chi_{ 1150 }(17, a) \) | \(1\) | \(1\) | \(e\left(\frac{141}{220}\right)\) | \(e\left(\frac{13}{44}\right)\) | \(e\left(\frac{31}{110}\right)\) | \(e\left(\frac{29}{110}\right)\) | \(e\left(\frac{177}{220}\right)\) | \(e\left(\frac{149}{220}\right)\) | \(e\left(\frac{26}{55}\right)\) | \(e\left(\frac{103}{110}\right)\) | \(e\left(\frac{203}{220}\right)\) | \(e\left(\frac{3}{110}\right)\) |