Basic properties
| Modulus: | \(9464\) | |
| Conductor: | \(9464\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(78\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | yes | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 9464.gt
\(\chi_{9464}(251,\cdot)\) \(\chi_{9464}(979,\cdot)\) \(\chi_{9464}(1427,\cdot)\) \(\chi_{9464}(1707,\cdot)\) \(\chi_{9464}(2155,\cdot)\) \(\chi_{9464}(2435,\cdot)\) \(\chi_{9464}(2883,\cdot)\) \(\chi_{9464}(3163,\cdot)\) \(\chi_{9464}(3611,\cdot)\) \(\chi_{9464}(3891,\cdot)\) \(\chi_{9464}(4339,\cdot)\) \(\chi_{9464}(4619,\cdot)\) \(\chi_{9464}(5067,\cdot)\) \(\chi_{9464}(5347,\cdot)\) \(\chi_{9464}(5795,\cdot)\) \(\chi_{9464}(6075,\cdot)\) \(\chi_{9464}(6523,\cdot)\) \(\chi_{9464}(6803,\cdot)\) \(\chi_{9464}(7251,\cdot)\) \(\chi_{9464}(7531,\cdot)\) \(\chi_{9464}(7979,\cdot)\) \(\chi_{9464}(8707,\cdot)\) \(\chi_{9464}(8987,\cdot)\) \(\chi_{9464}(9435,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{39})$ |
| Fixed field: | Number field defined by a degree 78 polynomial |
Values on generators
\((2367,4733,2705,9297)\) → \((-1,-1,-1,e\left(\frac{43}{78}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(9\) | \(11\) | \(15\) | \(17\) | \(19\) | \(23\) | \(25\) | \(27\) |
| \( \chi_{ 9464 }(251, a) \) | \(1\) | \(1\) | \(e\left(\frac{67}{78}\right)\) | \(e\left(\frac{25}{26}\right)\) | \(e\left(\frac{28}{39}\right)\) | \(e\left(\frac{61}{78}\right)\) | \(e\left(\frac{32}{39}\right)\) | \(e\left(\frac{77}{78}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{12}{13}\right)\) | \(e\left(\frac{15}{26}\right)\) |