Basic properties
| Modulus: | \(9464\) | |
| Conductor: | \(4732\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(156\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{4732}(135,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | no | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 9464.ig
\(\chi_{9464}(135,\cdot)\) \(\chi_{9464}(151,\cdot)\) \(\chi_{9464}(359,\cdot)\) \(\chi_{9464}(655,\cdot)\) \(\chi_{9464}(863,\cdot)\) \(\chi_{9464}(879,\cdot)\) \(\chi_{9464}(1087,\cdot)\) \(\chi_{9464}(1383,\cdot)\) \(\chi_{9464}(1607,\cdot)\) \(\chi_{9464}(1815,\cdot)\) \(\chi_{9464}(2111,\cdot)\) \(\chi_{9464}(2319,\cdot)\) \(\chi_{9464}(2335,\cdot)\) \(\chi_{9464}(2543,\cdot)\) \(\chi_{9464}(2839,\cdot)\) \(\chi_{9464}(3047,\cdot)\) \(\chi_{9464}(3063,\cdot)\) \(\chi_{9464}(3271,\cdot)\) \(\chi_{9464}(3567,\cdot)\) \(\chi_{9464}(3775,\cdot)\) \(\chi_{9464}(3791,\cdot)\) \(\chi_{9464}(3999,\cdot)\) \(\chi_{9464}(4503,\cdot)\) \(\chi_{9464}(4519,\cdot)\) \(\chi_{9464}(4727,\cdot)\) \(\chi_{9464}(5023,\cdot)\) \(\chi_{9464}(5231,\cdot)\) \(\chi_{9464}(5247,\cdot)\) \(\chi_{9464}(5455,\cdot)\) \(\chi_{9464}(5751,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{156})$ |
| Fixed field: | Number field defined by a degree 156 polynomial (not computed) |
Values on generators
\((2367,4733,2705,9297)\) → \((-1,1,e\left(\frac{1}{3}\right),e\left(\frac{23}{52}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(9\) | \(11\) | \(15\) | \(17\) | \(19\) | \(23\) | \(25\) | \(27\) |
| \( \chi_{ 9464 }(135, a) \) | \(1\) | \(1\) | \(e\left(\frac{53}{78}\right)\) | \(e\left(\frac{101}{156}\right)\) | \(e\left(\frac{14}{39}\right)\) | \(e\left(\frac{61}{156}\right)\) | \(e\left(\frac{17}{52}\right)\) | \(e\left(\frac{71}{78}\right)\) | \(e\left(\frac{11}{12}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{23}{78}\right)\) | \(e\left(\frac{1}{26}\right)\) |