Basic properties
| Modulus: | \(2513\) | |
| Conductor: | \(2513\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(358\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | yes | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 2513.l
\(\chi_{2513}(6,\cdot)\) \(\chi_{2513}(20,\cdot)\) \(\chi_{2513}(27,\cdot)\) \(\chi_{2513}(34,\cdot)\) \(\chi_{2513}(41,\cdot)\) \(\chi_{2513}(48,\cdot)\) \(\chi_{2513}(55,\cdot)\) \(\chi_{2513}(69,\cdot)\) \(\chi_{2513}(90,\cdot)\) \(\chi_{2513}(111,\cdot)\) \(\chi_{2513}(125,\cdot)\) \(\chi_{2513}(132,\cdot)\) \(\chi_{2513}(146,\cdot)\) \(\chi_{2513}(153,\cdot)\) \(\chi_{2513}(160,\cdot)\) \(\chi_{2513}(181,\cdot)\) \(\chi_{2513}(188,\cdot)\) \(\chi_{2513}(202,\cdot)\) \(\chi_{2513}(216,\cdot)\) \(\chi_{2513}(230,\cdot)\) \(\chi_{2513}(237,\cdot)\) \(\chi_{2513}(272,\cdot)\) \(\chi_{2513}(300,\cdot)\) \(\chi_{2513}(307,\cdot)\) \(\chi_{2513}(321,\cdot)\) \(\chi_{2513}(328,\cdot)\) \(\chi_{2513}(363,\cdot)\) \(\chi_{2513}(370,\cdot)\) \(\chi_{2513}(377,\cdot)\) \(\chi_{2513}(384,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{179})$ |
| Fixed field: | Number field defined by a degree 358 polynomial (not computed) |
Values on generators
\((360,1443)\) → \((-1,e\left(\frac{69}{179}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(8\) | \(9\) | \(10\) | \(11\) | \(12\) |
| \( \chi_{ 2513 }(391, a) \) | \(-1\) | \(1\) | \(e\left(\frac{7}{179}\right)\) | \(e\left(\frac{71}{358}\right)\) | \(e\left(\frac{14}{179}\right)\) | \(e\left(\frac{353}{358}\right)\) | \(e\left(\frac{85}{358}\right)\) | \(e\left(\frac{21}{179}\right)\) | \(e\left(\frac{71}{179}\right)\) | \(e\left(\frac{9}{358}\right)\) | \(e\left(\frac{34}{179}\right)\) | \(e\left(\frac{99}{358}\right)\) |