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: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 2205.el
\(\chi_{2205}(2,\cdot)\) \(\chi_{2205}(32,\cdot)\) \(\chi_{2205}(158,\cdot)\) \(\chi_{2205}(317,\cdot)\) \(\chi_{2205}(347,\cdot)\) \(\chi_{2205}(443,\cdot)\) \(\chi_{2205}(473,\cdot)\) \(\chi_{2205}(632,\cdot)\) \(\chi_{2205}(662,\cdot)\) \(\chi_{2205}(758,\cdot)\) \(\chi_{2205}(788,\cdot)\) \(\chi_{2205}(947,\cdot)\) \(\chi_{2205}(977,\cdot)\) \(\chi_{2205}(1073,\cdot)\) \(\chi_{2205}(1103,\cdot)\) \(\chi_{2205}(1262,\cdot)\) \(\chi_{2205}(1388,\cdot)\) \(\chi_{2205}(1418,\cdot)\) \(\chi_{2205}(1577,\cdot)\) \(\chi_{2205}(1607,\cdot)\) \(\chi_{2205}(1703,\cdot)\) \(\chi_{2205}(1922,\cdot)\) \(\chi_{2205}(2018,\cdot)\) \(\chi_{2205}(2048,\cdot)\)
Related number fields
Field of values: | $\Q(\zeta_{84})$ |
Fixed field: | Number field defined by a degree 84 polynomial |
Values on generators
\((1226,442,1081)\) → \((e\left(\frac{1}{6}\right),i,e\left(\frac{4}{21}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(8\) | \(11\) | \(13\) | \(16\) | \(17\) | \(19\) | \(22\) | \(23\) |
\( \chi_{ 2205 }(632, a) \) | \(1\) | \(1\) | \(e\left(\frac{31}{84}\right)\) | \(e\left(\frac{31}{42}\right)\) | \(e\left(\frac{3}{28}\right)\) | \(e\left(\frac{11}{14}\right)\) | \(e\left(\frac{31}{84}\right)\) | \(e\left(\frac{10}{21}\right)\) | \(e\left(\frac{43}{84}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{13}{84}\right)\) | \(e\left(\frac{23}{28}\right)\) |