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
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Minimal: | yes | |
Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 2205.ep
\(\chi_{2205}(58,\cdot)\) \(\chi_{2205}(88,\cdot)\) \(\chi_{2205}(247,\cdot)\) \(\chi_{2205}(277,\cdot)\) \(\chi_{2205}(403,\cdot)\) \(\chi_{2205}(562,\cdot)\) \(\chi_{2205}(592,\cdot)\) \(\chi_{2205}(688,\cdot)\) \(\chi_{2205}(718,\cdot)\) \(\chi_{2205}(877,\cdot)\) \(\chi_{2205}(907,\cdot)\) \(\chi_{2205}(1003,\cdot)\) \(\chi_{2205}(1033,\cdot)\) \(\chi_{2205}(1192,\cdot)\) \(\chi_{2205}(1222,\cdot)\) \(\chi_{2205}(1318,\cdot)\) \(\chi_{2205}(1348,\cdot)\) \(\chi_{2205}(1507,\cdot)\) \(\chi_{2205}(1633,\cdot)\) \(\chi_{2205}(1663,\cdot)\) \(\chi_{2205}(1822,\cdot)\) \(\chi_{2205}(1852,\cdot)\) \(\chi_{2205}(1948,\cdot)\) \(\chi_{2205}(2167,\cdot)\)
Related number fields
Field of values: | $\Q(\zeta_{84})$ |
Fixed field: | Number field defined by a degree 84 polynomial |
Values on generators
\((1226,442,1081)\) → \((e\left(\frac{1}{3}\right),-i,e\left(\frac{4}{21}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(8\) | \(11\) | \(13\) | \(16\) | \(17\) | \(19\) | \(22\) | \(23\) |
\( \chi_{ 2205 }(1318, a) \) | \(-1\) | \(1\) | \(e\left(\frac{1}{28}\right)\) | \(e\left(\frac{1}{14}\right)\) | \(e\left(\frac{3}{28}\right)\) | \(e\left(\frac{20}{21}\right)\) | \(e\left(\frac{17}{84}\right)\) | \(e\left(\frac{1}{7}\right)\) | \(e\left(\frac{43}{84}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{83}{84}\right)\) | \(e\left(\frac{13}{84}\right)\) |