Basic properties
| Modulus: | \(1573\) | |
| Conductor: | \(1573\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(660\) | 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 1573.bv
\(\chi_{1573}(2,\cdot)\) \(\chi_{1573}(6,\cdot)\) \(\chi_{1573}(7,\cdot)\) \(\chi_{1573}(19,\cdot)\) \(\chi_{1573}(24,\cdot)\) \(\chi_{1573}(28,\cdot)\) \(\chi_{1573}(41,\cdot)\) \(\chi_{1573}(46,\cdot)\) \(\chi_{1573}(50,\cdot)\) \(\chi_{1573}(63,\cdot)\) \(\chi_{1573}(72,\cdot)\) \(\chi_{1573}(84,\cdot)\) \(\chi_{1573}(85,\cdot)\) \(\chi_{1573}(106,\cdot)\) \(\chi_{1573}(123,\cdot)\) \(\chi_{1573}(128,\cdot)\) \(\chi_{1573}(145,\cdot)\) \(\chi_{1573}(149,\cdot)\) \(\chi_{1573}(150,\cdot)\) \(\chi_{1573}(162,\cdot)\) \(\chi_{1573}(167,\cdot)\) \(\chi_{1573}(171,\cdot)\) \(\chi_{1573}(184,\cdot)\) \(\chi_{1573}(189,\cdot)\) \(\chi_{1573}(193,\cdot)\) \(\chi_{1573}(206,\cdot)\) \(\chi_{1573}(227,\cdot)\) \(\chi_{1573}(228,\cdot)\) \(\chi_{1573}(249,\cdot)\) \(\chi_{1573}(266,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{660})$ |
| Fixed field: | Number field defined by a degree 660 polynomial (not computed) |
Values on generators
\((365,1211)\) → \((e\left(\frac{7}{110}\right),e\left(\frac{11}{12}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(12\) |
| \( \chi_{ 1573 }(7, a) \) | \(1\) | \(1\) | \(e\left(\frac{647}{660}\right)\) | \(e\left(\frac{4}{15}\right)\) | \(e\left(\frac{317}{330}\right)\) | \(e\left(\frac{211}{220}\right)\) | \(e\left(\frac{163}{660}\right)\) | \(e\left(\frac{349}{660}\right)\) | \(e\left(\frac{207}{220}\right)\) | \(e\left(\frac{8}{15}\right)\) | \(e\left(\frac{31}{33}\right)\) | \(e\left(\frac{5}{22}\right)\) |