Basic properties
Modulus: | \(2205\) | |
Conductor: | \(2205\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(84\) | 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 2205.ec
\(\chi_{2205}(92,\cdot)\) \(\chi_{2205}(113,\cdot)\) \(\chi_{2205}(218,\cdot)\) \(\chi_{2205}(302,\cdot)\) \(\chi_{2205}(407,\cdot)\) \(\chi_{2205}(428,\cdot)\) \(\chi_{2205}(533,\cdot)\) \(\chi_{2205}(617,\cdot)\) \(\chi_{2205}(722,\cdot)\) \(\chi_{2205}(743,\cdot)\) \(\chi_{2205}(848,\cdot)\) \(\chi_{2205}(1037,\cdot)\) \(\chi_{2205}(1058,\cdot)\) \(\chi_{2205}(1163,\cdot)\) \(\chi_{2205}(1247,\cdot)\) \(\chi_{2205}(1352,\cdot)\) \(\chi_{2205}(1478,\cdot)\) \(\chi_{2205}(1562,\cdot)\) \(\chi_{2205}(1688,\cdot)\) \(\chi_{2205}(1793,\cdot)\) \(\chi_{2205}(1877,\cdot)\) \(\chi_{2205}(1982,\cdot)\) \(\chi_{2205}(2003,\cdot)\) \(\chi_{2205}(2192,\cdot)\)
Related number fields
Field of values: | $\Q(\zeta_{84})$ |
Fixed field: | Number field defined by a degree 84 polynomial |
Values on generators
\((1226,442,1081)\) → \((e\left(\frac{5}{6}\right),i,e\left(\frac{2}{7}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(8\) | \(11\) | \(13\) | \(16\) | \(17\) | \(19\) | \(22\) | \(23\) |
\( \chi_{ 2205 }(2192, a) \) | \(1\) | \(1\) | \(e\left(\frac{43}{84}\right)\) | \(e\left(\frac{1}{42}\right)\) | \(e\left(\frac{15}{28}\right)\) | \(e\left(\frac{11}{42}\right)\) | \(e\left(\frac{71}{84}\right)\) | \(e\left(\frac{1}{21}\right)\) | \(e\left(\frac{25}{28}\right)\) | \(-1\) | \(e\left(\frac{65}{84}\right)\) | \(e\left(\frac{65}{84}\right)\) |