Basic properties
| Modulus: | \(9464\) | |
| Conductor: | \(1183\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(78\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{1183}(25,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 9464.hd
\(\chi_{9464}(25,\cdot)\) \(\chi_{9464}(233,\cdot)\) \(\chi_{9464}(753,\cdot)\) \(\chi_{9464}(961,\cdot)\) \(\chi_{9464}(1481,\cdot)\) \(\chi_{9464}(2209,\cdot)\) \(\chi_{9464}(2417,\cdot)\) \(\chi_{9464}(2937,\cdot)\) \(\chi_{9464}(3145,\cdot)\) \(\chi_{9464}(3665,\cdot)\) \(\chi_{9464}(3873,\cdot)\) \(\chi_{9464}(4601,\cdot)\) \(\chi_{9464}(5121,\cdot)\) \(\chi_{9464}(5329,\cdot)\) \(\chi_{9464}(5849,\cdot)\) \(\chi_{9464}(6057,\cdot)\) \(\chi_{9464}(6577,\cdot)\) \(\chi_{9464}(6785,\cdot)\) \(\chi_{9464}(7305,\cdot)\) \(\chi_{9464}(7513,\cdot)\) \(\chi_{9464}(8033,\cdot)\) \(\chi_{9464}(8241,\cdot)\) \(\chi_{9464}(8761,\cdot)\) \(\chi_{9464}(8969,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{39})$ |
| Fixed field: | Number field defined by a degree 78 polynomial |
Values on generators
\((2367,4733,2705,9297)\) → \((1,1,e\left(\frac{2}{3}\right),e\left(\frac{3}{26}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(9\) | \(11\) | \(15\) | \(17\) | \(19\) | \(23\) | \(25\) | \(27\) |
| \( \chi_{ 9464 }(25, a) \) | \(1\) | \(1\) | \(e\left(\frac{38}{39}\right)\) | \(e\left(\frac{29}{78}\right)\) | \(e\left(\frac{37}{39}\right)\) | \(e\left(\frac{43}{78}\right)\) | \(e\left(\frac{9}{26}\right)\) | \(e\left(\frac{20}{39}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{29}{39}\right)\) | \(e\left(\frac{12}{13}\right)\) |