Basic properties
Modulus: | \(8820\) | |
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: | no, induced from \(\chi_{2205}(113,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 8820.if
\(\chi_{8820}(113,\cdot)\) \(\chi_{8820}(533,\cdot)\) \(\chi_{8820}(617,\cdot)\) \(\chi_{8820}(1037,\cdot)\) \(\chi_{8820}(1793,\cdot)\) \(\chi_{8820}(1877,\cdot)\) \(\chi_{8820}(2297,\cdot)\) \(\chi_{8820}(2633,\cdot)\) \(\chi_{8820}(3053,\cdot)\) \(\chi_{8820}(3557,\cdot)\) \(\chi_{8820}(3893,\cdot)\) \(\chi_{8820}(4397,\cdot)\) \(\chi_{8820}(4817,\cdot)\) \(\chi_{8820}(5153,\cdot)\) \(\chi_{8820}(5573,\cdot)\) \(\chi_{8820}(5657,\cdot)\) \(\chi_{8820}(6413,\cdot)\) \(\chi_{8820}(6833,\cdot)\) \(\chi_{8820}(6917,\cdot)\) \(\chi_{8820}(7337,\cdot)\) \(\chi_{8820}(7673,\cdot)\) \(\chi_{8820}(8093,\cdot)\) \(\chi_{8820}(8177,\cdot)\) \(\chi_{8820}(8597,\cdot)\)
Related number fields
Field of values: | $\Q(\zeta_{84})$ |
Fixed field: | Number field defined by a degree 84 polynomial |
Values on generators
\((4411,7841,7057,1081)\) → \((1,e\left(\frac{5}{6}\right),-i,e\left(\frac{5}{7}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(29\) | \(31\) | \(37\) | \(41\) | \(43\) |
\( \chi_{ 8820 }(113, a) \) | \(1\) | \(1\) | \(e\left(\frac{17}{42}\right)\) | \(e\left(\frac{41}{84}\right)\) | \(e\left(\frac{3}{28}\right)\) | \(-1\) | \(e\left(\frac{47}{84}\right)\) | \(e\left(\frac{4}{21}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{17}{28}\right)\) | \(e\left(\frac{37}{42}\right)\) | \(e\left(\frac{73}{84}\right)\) |