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 \(\chi_{4732}(335,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | no | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 9464.gz
\(\chi_{9464}(335,\cdot)\) \(\chi_{9464}(615,\cdot)\) \(\chi_{9464}(1063,\cdot)\) \(\chi_{9464}(1343,\cdot)\) \(\chi_{9464}(1791,\cdot)\) \(\chi_{9464}(2071,\cdot)\) \(\chi_{9464}(2519,\cdot)\) \(\chi_{9464}(2799,\cdot)\) \(\chi_{9464}(3247,\cdot)\) \(\chi_{9464}(3975,\cdot)\) \(\chi_{9464}(4255,\cdot)\) \(\chi_{9464}(4703,\cdot)\) \(\chi_{9464}(4983,\cdot)\) \(\chi_{9464}(5711,\cdot)\) \(\chi_{9464}(6159,\cdot)\) \(\chi_{9464}(6439,\cdot)\) \(\chi_{9464}(6887,\cdot)\) \(\chi_{9464}(7167,\cdot)\) \(\chi_{9464}(7615,\cdot)\) \(\chi_{9464}(7895,\cdot)\) \(\chi_{9464}(8343,\cdot)\) \(\chi_{9464}(8623,\cdot)\) \(\chi_{9464}(9071,\cdot)\) \(\chi_{9464}(9351,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{39})$ |
| Fixed field: | Number field defined by a degree 78 polynomial |
Values on generators
\((2367,4733,2705,9297)\) → \((-1,1,-1,e\left(\frac{23}{78}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(9\) | \(11\) | \(15\) | \(17\) | \(19\) | \(23\) | \(25\) | \(27\) |
| \( \chi_{ 9464 }(335, a) \) | \(1\) | \(1\) | \(e\left(\frac{22}{39}\right)\) | \(e\left(\frac{2}{13}\right)\) | \(e\left(\frac{5}{39}\right)\) | \(e\left(\frac{34}{39}\right)\) | \(e\left(\frac{28}{39}\right)\) | \(e\left(\frac{43}{78}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{4}{13}\right)\) | \(e\left(\frac{9}{13}\right)\) |