Basic properties
| Modulus: | \(9464\) | |
| Conductor: | \(1183\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(39\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{1183}(417,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 9464.fi
\(\chi_{9464}(417,\cdot)\) \(\chi_{9464}(625,\cdot)\) \(\chi_{9464}(1145,\cdot)\) \(\chi_{9464}(1873,\cdot)\) \(\chi_{9464}(2081,\cdot)\) \(\chi_{9464}(2601,\cdot)\) \(\chi_{9464}(2809,\cdot)\) \(\chi_{9464}(3329,\cdot)\) \(\chi_{9464}(3537,\cdot)\) \(\chi_{9464}(4265,\cdot)\) \(\chi_{9464}(4785,\cdot)\) \(\chi_{9464}(4993,\cdot)\) \(\chi_{9464}(5513,\cdot)\) \(\chi_{9464}(5721,\cdot)\) \(\chi_{9464}(6241,\cdot)\) \(\chi_{9464}(6449,\cdot)\) \(\chi_{9464}(6969,\cdot)\) \(\chi_{9464}(7177,\cdot)\) \(\chi_{9464}(7697,\cdot)\) \(\chi_{9464}(7905,\cdot)\) \(\chi_{9464}(8425,\cdot)\) \(\chi_{9464}(8633,\cdot)\) \(\chi_{9464}(9153,\cdot)\) \(\chi_{9464}(9361,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{39})$ |
| Fixed field: | Number field defined by a degree 39 polynomial |
Values on generators
\((2367,4733,2705,9297)\) → \((1,1,e\left(\frac{2}{3}\right),e\left(\frac{2}{13}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(9\) | \(11\) | \(15\) | \(17\) | \(19\) | \(23\) | \(25\) | \(27\) |
| \( \chi_{ 9464 }(417, a) \) | \(1\) | \(1\) | \(e\left(\frac{29}{39}\right)\) | \(e\left(\frac{28}{39}\right)\) | \(e\left(\frac{19}{39}\right)\) | \(e\left(\frac{20}{39}\right)\) | \(e\left(\frac{6}{13}\right)\) | \(e\left(\frac{5}{39}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{17}{39}\right)\) | \(e\left(\frac{3}{13}\right)\) |