Basic properties
Modulus: | \(2205\) | |
Conductor: | \(2205\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(84\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
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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.ea
\(\chi_{2205}(157,\cdot)\) \(\chi_{2205}(187,\cdot)\) \(\chi_{2205}(283,\cdot)\) \(\chi_{2205}(502,\cdot)\) \(\chi_{2205}(598,\cdot)\) \(\chi_{2205}(628,\cdot)\) \(\chi_{2205}(787,\cdot)\) \(\chi_{2205}(817,\cdot)\) \(\chi_{2205}(943,\cdot)\) \(\chi_{2205}(1102,\cdot)\) \(\chi_{2205}(1132,\cdot)\) \(\chi_{2205}(1228,\cdot)\) \(\chi_{2205}(1258,\cdot)\) \(\chi_{2205}(1417,\cdot)\) \(\chi_{2205}(1447,\cdot)\) \(\chi_{2205}(1543,\cdot)\) \(\chi_{2205}(1573,\cdot)\) \(\chi_{2205}(1732,\cdot)\) \(\chi_{2205}(1762,\cdot)\) \(\chi_{2205}(1858,\cdot)\) \(\chi_{2205}(1888,\cdot)\) \(\chi_{2205}(2047,\cdot)\) \(\chi_{2205}(2173,\cdot)\) \(\chi_{2205}(2203,\cdot)\)
Related number fields
Field of values: | $\Q(\zeta_{84})$ |
Fixed field: | Number field defined by a degree 84 polynomial |
Values on generators
\((1226,442,1081)\) → \((e\left(\frac{1}{3}\right),i,e\left(\frac{31}{42}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(8\) | \(11\) | \(13\) | \(16\) | \(17\) | \(19\) | \(22\) | \(23\) |
\( \chi_{ 2205 }(1417, a) \) | \(1\) | \(1\) | \(e\left(\frac{65}{84}\right)\) | \(e\left(\frac{23}{42}\right)\) | \(e\left(\frac{9}{28}\right)\) | \(e\left(\frac{6}{7}\right)\) | \(e\left(\frac{65}{84}\right)\) | \(e\left(\frac{2}{21}\right)\) | \(e\left(\frac{59}{84}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{53}{84}\right)\) | \(e\left(\frac{13}{28}\right)\) |