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: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 2205.em
\(\chi_{2205}(38,\cdot)\) \(\chi_{2205}(257,\cdot)\) \(\chi_{2205}(353,\cdot)\) \(\chi_{2205}(383,\cdot)\) \(\chi_{2205}(542,\cdot)\) \(\chi_{2205}(572,\cdot)\) \(\chi_{2205}(698,\cdot)\) \(\chi_{2205}(857,\cdot)\) \(\chi_{2205}(887,\cdot)\) \(\chi_{2205}(983,\cdot)\) \(\chi_{2205}(1013,\cdot)\) \(\chi_{2205}(1172,\cdot)\) \(\chi_{2205}(1202,\cdot)\) \(\chi_{2205}(1298,\cdot)\) \(\chi_{2205}(1328,\cdot)\) \(\chi_{2205}(1487,\cdot)\) \(\chi_{2205}(1517,\cdot)\) \(\chi_{2205}(1613,\cdot)\) \(\chi_{2205}(1643,\cdot)\) \(\chi_{2205}(1802,\cdot)\) \(\chi_{2205}(1928,\cdot)\) \(\chi_{2205}(1958,\cdot)\) \(\chi_{2205}(2117,\cdot)\) \(\chi_{2205}(2147,\cdot)\)
Related number fields
Field of values: | $\Q(\zeta_{84})$ |
Fixed field: | Number field defined by a degree 84 polynomial |
Values on generators
\((1226,442,1081)\) → \((e\left(\frac{1}{6}\right),-i,e\left(\frac{25}{42}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(8\) | \(11\) | \(13\) | \(16\) | \(17\) | \(19\) | \(22\) | \(23\) |
\( \chi_{ 2205 }(1928, a) \) | \(-1\) | \(1\) | \(e\left(\frac{11}{28}\right)\) | \(e\left(\frac{11}{14}\right)\) | \(e\left(\frac{5}{28}\right)\) | \(e\left(\frac{41}{42}\right)\) | \(e\left(\frac{19}{84}\right)\) | \(e\left(\frac{4}{7}\right)\) | \(e\left(\frac{11}{84}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{31}{84}\right)\) | \(e\left(\frac{59}{84}\right)\) |