Basic properties
Modulus: | \(4730\) | |
Conductor: | \(473\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(35\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
Real: | no | |
Primitive: | no, induced from \(\chi_{473}(422,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 4730.cf
\(\chi_{4730}(471,\cdot)\) \(\chi_{4730}(1301,\cdot)\) \(\chi_{4730}(1411,\cdot)\) \(\chi_{4730}(1521,\cdot)\) \(\chi_{4730}(1681,\cdot)\) \(\chi_{4730}(1731,\cdot)\) \(\chi_{4730}(1741,\cdot)\) \(\chi_{4730}(1841,\cdot)\) \(\chi_{4730}(1951,\cdot)\) \(\chi_{4730}(2161,\cdot)\) \(\chi_{4730}(2171,\cdot)\) \(\chi_{4730}(2271,\cdot)\) \(\chi_{4730}(2381,\cdot)\) \(\chi_{4730}(2601,\cdot)\) \(\chi_{4730}(2621,\cdot)\) \(\chi_{4730}(3051,\cdot)\) \(\chi_{4730}(3481,\cdot)\) \(\chi_{4730}(3831,\cdot)\) \(\chi_{4730}(3881,\cdot)\) \(\chi_{4730}(3991,\cdot)\) \(\chi_{4730}(4101,\cdot)\) \(\chi_{4730}(4261,\cdot)\) \(\chi_{4730}(4321,\cdot)\) \(\chi_{4730}(4691,\cdot)\)
Related number fields
Field of values: | $\Q(\zeta_{35})$ |
Fixed field: | Number field defined by a degree 35 polynomial |
Values on generators
\((947,431,1981)\) → \((1,e\left(\frac{1}{5}\right),e\left(\frac{3}{7}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(3\) | \(7\) | \(9\) | \(13\) | \(17\) | \(19\) | \(21\) | \(23\) | \(27\) | \(29\) |
\( \chi_{ 4730 }(1841, a) \) | \(1\) | \(1\) | \(e\left(\frac{1}{35}\right)\) | \(e\left(\frac{2}{5}\right)\) | \(e\left(\frac{2}{35}\right)\) | \(e\left(\frac{32}{35}\right)\) | \(e\left(\frac{3}{35}\right)\) | \(e\left(\frac{26}{35}\right)\) | \(e\left(\frac{3}{7}\right)\) | \(e\left(\frac{6}{7}\right)\) | \(e\left(\frac{3}{35}\right)\) | \(e\left(\frac{34}{35}\right)\) |