Basic properties
| Modulus: | \(9802\) | |
| Conductor: | \(4901\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(1092\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{4901}(735,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 9802.cy
\(\chi_{9802}(37,\cdot)\) \(\chi_{9802}(85,\cdot)\) \(\chi_{9802}(119,\cdot)\) \(\chi_{9802}(163,\cdot)\) \(\chi_{9802}(189,\cdot)\) \(\chi_{9802}(253,\cdot)\) \(\chi_{9802}(271,\cdot)\) \(\chi_{9802}(275,\cdot)\) \(\chi_{9802}(301,\cdot)\) \(\chi_{9802}(345,\cdot)\) \(\chi_{9802}(375,\cdot)\) \(\chi_{9802}(379,\cdot)\) \(\chi_{9802}(409,\cdot)\) \(\chi_{9802}(453,\cdot)\) \(\chi_{9802}(479,\cdot)\) \(\chi_{9802}(483,\cdot)\) \(\chi_{9802}(501,\cdot)\) \(\chi_{9802}(565,\cdot)\) \(\chi_{9802}(591,\cdot)\) \(\chi_{9802}(635,\cdot)\) \(\chi_{9802}(669,\cdot)\) \(\chi_{9802}(717,\cdot)\) \(\chi_{9802}(735,\cdot)\) \(\chi_{9802}(773,\cdot)\) \(\chi_{9802}(791,\cdot)\) \(\chi_{9802}(839,\cdot)\) \(\chi_{9802}(873,\cdot)\) \(\chi_{9802}(917,\cdot)\) \(\chi_{9802}(943,\cdot)\) \(\chi_{9802}(1007,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{1092})$ |
| Fixed field: | Number field defined by a degree 1092 polynomial (not computed) |
Values on generators
\((5917,8789)\) → \((e\left(\frac{35}{156}\right),e\left(\frac{23}{28}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(15\) | \(17\) | \(19\) | \(21\) | \(23\) |
| \( \chi_{ 9802 }(735, a) \) | \(1\) | \(1\) | \(e\left(\frac{1013}{1092}\right)\) | \(e\left(\frac{33}{364}\right)\) | \(e\left(\frac{943}{1092}\right)\) | \(e\left(\frac{467}{546}\right)\) | \(e\left(\frac{176}{273}\right)\) | \(e\left(\frac{5}{273}\right)\) | \(e\left(\frac{1}{156}\right)\) | \(e\left(\frac{41}{42}\right)\) | \(e\left(\frac{72}{91}\right)\) | \(e\left(\frac{25}{42}\right)\) |