Basic properties
| Modulus: | \(9310\) | |
| Conductor: | \(4655\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(252\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{4655}(663,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 9310.hb
\(\chi_{9310}(187,\cdot)\) \(\chi_{9310}(213,\cdot)\) \(\chi_{9310}(367,\cdot)\) \(\chi_{9310}(397,\cdot)\) \(\chi_{9310}(453,\cdot)\) \(\chi_{9310}(537,\cdot)\) \(\chi_{9310}(633,\cdot)\) \(\chi_{9310}(663,\cdot)\) \(\chi_{9310}(997,\cdot)\) \(\chi_{9310}(1263,\cdot)\) \(\chi_{9310}(1277,\cdot)\) \(\chi_{9310}(1517,\cdot)\) \(\chi_{9310}(1543,\cdot)\) \(\chi_{9310}(1727,\cdot)\) \(\chi_{9310}(1867,\cdot)\) \(\chi_{9310}(1963,\cdot)\) \(\chi_{9310}(1993,\cdot)\) \(\chi_{9310}(2133,\cdot)\) \(\chi_{9310}(2327,\cdot)\) \(\chi_{9310}(2593,\cdot)\) \(\chi_{9310}(2607,\cdot)\) \(\chi_{9310}(2847,\cdot)\) \(\chi_{9310}(3027,\cdot)\) \(\chi_{9310}(3113,\cdot)\) \(\chi_{9310}(3197,\cdot)\) \(\chi_{9310}(3293,\cdot)\) \(\chi_{9310}(3323,\cdot)\) \(\chi_{9310}(3463,\cdot)\) \(\chi_{9310}(3923,\cdot)\) \(\chi_{9310}(3937,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{252})$ |
| Fixed field: | Number field defined by a degree 252 polynomial (not computed) |
Values on generators
\((5587,3041,6861)\) → \((-i,e\left(\frac{17}{42}\right),e\left(\frac{5}{9}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(9\) | \(11\) | \(13\) | \(17\) | \(23\) | \(27\) | \(29\) | \(31\) | \(33\) |
| \( \chi_{ 9310 }(663, a) \) | \(1\) | \(1\) | \(e\left(\frac{221}{252}\right)\) | \(e\left(\frac{95}{126}\right)\) | \(e\left(\frac{6}{7}\right)\) | \(e\left(\frac{97}{252}\right)\) | \(e\left(\frac{107}{252}\right)\) | \(e\left(\frac{187}{252}\right)\) | \(e\left(\frac{53}{84}\right)\) | \(e\left(\frac{29}{126}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{185}{252}\right)\) |