Basic properties
| Modulus: | \(553\) | |
| Conductor: | \(553\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(39\) | 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 553.ba
\(\chi_{553}(18,\cdot)\) \(\chi_{553}(46,\cdot)\) \(\chi_{553}(65,\cdot)\) \(\chi_{553}(67,\cdot)\) \(\chi_{553}(100,\cdot)\) \(\chi_{553}(144,\cdot)\) \(\chi_{553}(179,\cdot)\) \(\chi_{553}(247,\cdot)\) \(\chi_{553}(275,\cdot)\) \(\chi_{553}(289,\cdot)\) \(\chi_{553}(324,\cdot)\) \(\chi_{553}(326,\cdot)\) \(\chi_{553}(338,\cdot)\) \(\chi_{553}(354,\cdot)\) \(\chi_{553}(368,\cdot)\) \(\chi_{553}(380,\cdot)\) \(\chi_{553}(403,\cdot)\) \(\chi_{553}(417,\cdot)\) \(\chi_{553}(457,\cdot)\) \(\chi_{553}(459,\cdot)\) \(\chi_{553}(492,\cdot)\) \(\chi_{553}(520,\cdot)\) \(\chi_{553}(536,\cdot)\) \(\chi_{553}(541,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{39})$ |
| Fixed field: | Number field defined by a degree 39 polynomial |
Values on generators
\((80,477)\) → \((e\left(\frac{2}{3}\right),e\left(\frac{6}{13}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(8\) | \(9\) | \(10\) | \(11\) | \(12\) |
| \( \chi_{ 553 }(354, a) \) | \(1\) | \(1\) | \(e\left(\frac{7}{39}\right)\) | \(e\left(\frac{5}{39}\right)\) | \(e\left(\frac{14}{39}\right)\) | \(e\left(\frac{37}{39}\right)\) | \(e\left(\frac{4}{13}\right)\) | \(e\left(\frac{7}{13}\right)\) | \(e\left(\frac{10}{39}\right)\) | \(e\left(\frac{5}{39}\right)\) | \(e\left(\frac{2}{39}\right)\) | \(e\left(\frac{19}{39}\right)\) |