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.ek
\(\chi_{2205}(47,\cdot)\) \(\chi_{2205}(122,\cdot)\) \(\chi_{2205}(173,\cdot)\) \(\chi_{2205}(248,\cdot)\) \(\chi_{2205}(437,\cdot)\) \(\chi_{2205}(488,\cdot)\) \(\chi_{2205}(563,\cdot)\) \(\chi_{2205}(677,\cdot)\) \(\chi_{2205}(752,\cdot)\) \(\chi_{2205}(878,\cdot)\) \(\chi_{2205}(992,\cdot)\) \(\chi_{2205}(1067,\cdot)\) \(\chi_{2205}(1118,\cdot)\) \(\chi_{2205}(1193,\cdot)\) \(\chi_{2205}(1307,\cdot)\) \(\chi_{2205}(1382,\cdot)\) \(\chi_{2205}(1433,\cdot)\) \(\chi_{2205}(1508,\cdot)\) \(\chi_{2205}(1622,\cdot)\) \(\chi_{2205}(1748,\cdot)\) \(\chi_{2205}(1823,\cdot)\) \(\chi_{2205}(1937,\cdot)\) \(\chi_{2205}(2012,\cdot)\) \(\chi_{2205}(2063,\cdot)\)
Related number fields
Field of values: | $\Q(\zeta_{84})$ |
Fixed field: | Number field defined by a degree 84 polynomial |
Values on generators
\((1226,442,1081)\) → \((e\left(\frac{5}{6}\right),-i,e\left(\frac{19}{42}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(8\) | \(11\) | \(13\) | \(16\) | \(17\) | \(19\) | \(22\) | \(23\) |
\( \chi_{ 2205 }(1508, a) \) | \(-1\) | \(1\) | \(e\left(\frac{29}{84}\right)\) | \(e\left(\frac{29}{42}\right)\) | \(e\left(\frac{1}{28}\right)\) | \(e\left(\frac{13}{14}\right)\) | \(e\left(\frac{71}{84}\right)\) | \(e\left(\frac{8}{21}\right)\) | \(e\left(\frac{47}{84}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{23}{84}\right)\) | \(e\left(\frac{17}{28}\right)\) |