Basic properties
| Modulus: | \(4730\) | |
| Conductor: | \(2365\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(70\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{2365}(59,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 4730.ct
\(\chi_{4730}(59,\cdot)\) \(\chi_{4730}(269,\cdot)\) \(\chi_{4730}(279,\cdot)\) \(\chi_{4730}(379,\cdot)\) \(\chi_{4730}(489,\cdot)\) \(\chi_{4730}(709,\cdot)\) \(\chi_{4730}(729,\cdot)\) \(\chi_{4730}(1159,\cdot)\) \(\chi_{4730}(1589,\cdot)\) \(\chi_{4730}(1939,\cdot)\) \(\chi_{4730}(1989,\cdot)\) \(\chi_{4730}(2099,\cdot)\) \(\chi_{4730}(2209,\cdot)\) \(\chi_{4730}(2369,\cdot)\) \(\chi_{4730}(2429,\cdot)\) \(\chi_{4730}(2799,\cdot)\) \(\chi_{4730}(3309,\cdot)\) \(\chi_{4730}(4139,\cdot)\) \(\chi_{4730}(4249,\cdot)\) \(\chi_{4730}(4359,\cdot)\) \(\chi_{4730}(4519,\cdot)\) \(\chi_{4730}(4569,\cdot)\) \(\chi_{4730}(4579,\cdot)\) \(\chi_{4730}(4679,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{35})$ |
| Fixed field: | Number field defined by a degree 70 polynomial |
Values on generators
\((947,431,1981)\) → \((-1,e\left(\frac{1}{5}\right),e\left(\frac{4}{7}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(7\) | \(9\) | \(13\) | \(17\) | \(19\) | \(21\) | \(23\) | \(27\) | \(29\) |
| \( \chi_{ 4730 }(59, a) \) | \(1\) | \(1\) | \(e\left(\frac{47}{70}\right)\) | \(e\left(\frac{9}{10}\right)\) | \(e\left(\frac{12}{35}\right)\) | \(e\left(\frac{69}{70}\right)\) | \(e\left(\frac{1}{70}\right)\) | \(e\left(\frac{16}{35}\right)\) | \(e\left(\frac{4}{7}\right)\) | \(e\left(\frac{9}{14}\right)\) | \(e\left(\frac{1}{70}\right)\) | \(e\left(\frac{29}{35}\right)\) |