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.eg
\(\chi_{2205}(22,\cdot)\) \(\chi_{2205}(43,\cdot)\) \(\chi_{2205}(232,\cdot)\) \(\chi_{2205}(337,\cdot)\) \(\chi_{2205}(358,\cdot)\) \(\chi_{2205}(463,\cdot)\) \(\chi_{2205}(547,\cdot)\) \(\chi_{2205}(652,\cdot)\) \(\chi_{2205}(673,\cdot)\) \(\chi_{2205}(778,\cdot)\) \(\chi_{2205}(862,\cdot)\) \(\chi_{2205}(967,\cdot)\) \(\chi_{2205}(988,\cdot)\) \(\chi_{2205}(1093,\cdot)\) \(\chi_{2205}(1282,\cdot)\) \(\chi_{2205}(1303,\cdot)\) \(\chi_{2205}(1408,\cdot)\) \(\chi_{2205}(1492,\cdot)\) \(\chi_{2205}(1597,\cdot)\) \(\chi_{2205}(1723,\cdot)\) \(\chi_{2205}(1807,\cdot)\) \(\chi_{2205}(1933,\cdot)\) \(\chi_{2205}(2038,\cdot)\) \(\chi_{2205}(2122,\cdot)\)
Related number fields
Field of values: | $\Q(\zeta_{84})$ |
Fixed field: | Number field defined by a degree 84 polynomial |
Values on generators
\((1226,442,1081)\) → \((e\left(\frac{1}{3}\right),-i,e\left(\frac{2}{7}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(8\) | \(11\) | \(13\) | \(16\) | \(17\) | \(19\) | \(22\) | \(23\) |
\( \chi_{ 2205 }(1408, a) \) | \(-1\) | \(1\) | \(e\left(\frac{43}{84}\right)\) | \(e\left(\frac{1}{42}\right)\) | \(e\left(\frac{15}{28}\right)\) | \(e\left(\frac{16}{21}\right)\) | \(e\left(\frac{29}{84}\right)\) | \(e\left(\frac{1}{21}\right)\) | \(e\left(\frac{25}{28}\right)\) | \(-1\) | \(e\left(\frac{23}{84}\right)\) | \(e\left(\frac{65}{84}\right)\) |