Basic properties
| Modulus: | \(2005\) | |
| Conductor: | \(2005\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(100\) | 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 2005.bt
\(\chi_{2005}(4,\cdot)\) \(\chi_{2005}(49,\cdot)\) \(\chi_{2005}(64,\cdot)\) \(\chi_{2005}(69,\cdot)\) \(\chi_{2005}(94,\cdot)\) \(\chi_{2005}(99,\cdot)\) \(\chi_{2005}(149,\cdot)\) \(\chi_{2005}(204,\cdot)\) \(\chi_{2005}(344,\cdot)\) \(\chi_{2005}(419,\cdot)\) \(\chi_{2005}(494,\cdot)\) \(\chi_{2005}(514,\cdot)\) \(\chi_{2005}(584,\cdot)\) \(\chi_{2005}(619,\cdot)\) \(\chi_{2005}(689,\cdot)\) \(\chi_{2005}(709,\cdot)\) \(\chi_{2005}(784,\cdot)\) \(\chi_{2005}(859,\cdot)\) \(\chi_{2005}(999,\cdot)\) \(\chi_{2005}(1054,\cdot)\) \(\chi_{2005}(1104,\cdot)\) \(\chi_{2005}(1109,\cdot)\) \(\chi_{2005}(1134,\cdot)\) \(\chi_{2005}(1139,\cdot)\) \(\chi_{2005}(1154,\cdot)\) \(\chi_{2005}(1199,\cdot)\) \(\chi_{2005}(1284,\cdot)\) \(\chi_{2005}(1319,\cdot)\) \(\chi_{2005}(1324,\cdot)\) \(\chi_{2005}(1359,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{100})$ |
| Fixed field: | Number field defined by a degree 100 polynomial |
Values on generators
\((402,1206)\) → \((-1,e\left(\frac{13}{100}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(7\) | \(8\) | \(9\) | \(11\) | \(12\) | \(13\) |
| \( \chi_{ 2005 }(4, a) \) | \(1\) | \(1\) | \(e\left(\frac{22}{25}\right)\) | \(e\left(\frac{63}{100}\right)\) | \(e\left(\frac{19}{25}\right)\) | \(e\left(\frac{51}{100}\right)\) | \(e\left(\frac{14}{25}\right)\) | \(e\left(\frac{16}{25}\right)\) | \(e\left(\frac{13}{50}\right)\) | \(e\left(\frac{11}{50}\right)\) | \(e\left(\frac{39}{100}\right)\) | \(e\left(\frac{97}{100}\right)\) |