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.en
\(\chi_{2205}(23,\cdot)\) \(\chi_{2205}(137,\cdot)\) \(\chi_{2205}(212,\cdot)\) \(\chi_{2205}(338,\cdot)\) \(\chi_{2205}(452,\cdot)\) \(\chi_{2205}(527,\cdot)\) \(\chi_{2205}(578,\cdot)\) \(\chi_{2205}(653,\cdot)\) \(\chi_{2205}(767,\cdot)\) \(\chi_{2205}(842,\cdot)\) \(\chi_{2205}(893,\cdot)\) \(\chi_{2205}(968,\cdot)\) \(\chi_{2205}(1082,\cdot)\) \(\chi_{2205}(1208,\cdot)\) \(\chi_{2205}(1283,\cdot)\) \(\chi_{2205}(1397,\cdot)\) \(\chi_{2205}(1472,\cdot)\) \(\chi_{2205}(1523,\cdot)\) \(\chi_{2205}(1712,\cdot)\) \(\chi_{2205}(1787,\cdot)\) \(\chi_{2205}(1838,\cdot)\) \(\chi_{2205}(1913,\cdot)\) \(\chi_{2205}(2102,\cdot)\) \(\chi_{2205}(2153,\cdot)\)
Related number fields
Field of values: | $\Q(\zeta_{84})$ |
Fixed field: | Number field defined by a degree 84 polynomial |
Values on generators
\((1226,442,1081)\) → \((e\left(\frac{1}{6}\right),i,e\left(\frac{17}{21}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(8\) | \(11\) | \(13\) | \(16\) | \(17\) | \(19\) | \(22\) | \(23\) |
\( \chi_{ 2205 }(137, a) \) | \(1\) | \(1\) | \(e\left(\frac{13}{28}\right)\) | \(e\left(\frac{13}{14}\right)\) | \(e\left(\frac{11}{28}\right)\) | \(e\left(\frac{23}{42}\right)\) | \(e\left(\frac{67}{84}\right)\) | \(e\left(\frac{6}{7}\right)\) | \(e\left(\frac{83}{84}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{1}{84}\right)\) | \(e\left(\frac{29}{84}\right)\) |