Basic properties
Modulus: | \(9464\) | |
Conductor: | \(4732\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(78\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
Real: | no | |
Primitive: | no, induced from \(\chi_{4732}(495,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | no | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 9464.hc
\(\chi_{9464}(495,\cdot)\) \(\chi_{9464}(703,\cdot)\) \(\chi_{9464}(1223,\cdot)\) \(\chi_{9464}(1431,\cdot)\) \(\chi_{9464}(1951,\cdot)\) \(\chi_{9464}(2159,\cdot)\) \(\chi_{9464}(2679,\cdot)\) \(\chi_{9464}(2887,\cdot)\) \(\chi_{9464}(3407,\cdot)\) \(\chi_{9464}(3615,\cdot)\) \(\chi_{9464}(4135,\cdot)\) \(\chi_{9464}(4343,\cdot)\) \(\chi_{9464}(4863,\cdot)\) \(\chi_{9464}(5591,\cdot)\) \(\chi_{9464}(5799,\cdot)\) \(\chi_{9464}(6319,\cdot)\) \(\chi_{9464}(6527,\cdot)\) \(\chi_{9464}(7047,\cdot)\) \(\chi_{9464}(7255,\cdot)\) \(\chi_{9464}(7983,\cdot)\) \(\chi_{9464}(8503,\cdot)\) \(\chi_{9464}(8711,\cdot)\) \(\chi_{9464}(9231,\cdot)\) \(\chi_{9464}(9439,\cdot)\)
Related number fields
Field of values: | $\Q(\zeta_{39})$ |
Fixed field: | Number field defined by a degree 78 polynomial |
Values on generators
\((2367,4733,2705,9297)\) → \((-1,1,e\left(\frac{5}{6}\right),e\left(\frac{4}{13}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(9\) | \(11\) | \(15\) | \(17\) | \(19\) | \(23\) | \(25\) | \(27\) |
\( \chi_{ 9464 }(495, a) \) | \(1\) | \(1\) | \(e\left(\frac{19}{39}\right)\) | \(e\left(\frac{73}{78}\right)\) | \(e\left(\frac{38}{39}\right)\) | \(e\left(\frac{41}{78}\right)\) | \(e\left(\frac{11}{26}\right)\) | \(e\left(\frac{59}{78}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{34}{39}\right)\) | \(e\left(\frac{6}{13}\right)\) |