Basic properties
Modulus: | \(8304\) | |
Conductor: | \(2076\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(86\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
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Real: | no | |
Primitive: | no, induced from \(\chi_{2076}(1967,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 8304.bq
\(\chi_{8304}(383,\cdot)\) \(\chi_{8304}(575,\cdot)\) \(\chi_{8304}(1151,\cdot)\) \(\chi_{8304}(1439,\cdot)\) \(\chi_{8304}(1535,\cdot)\) \(\chi_{8304}(1679,\cdot)\) \(\chi_{8304}(1967,\cdot)\) \(\chi_{8304}(2111,\cdot)\) \(\chi_{8304}(2303,\cdot)\) \(\chi_{8304}(2399,\cdot)\) \(\chi_{8304}(2447,\cdot)\) \(\chi_{8304}(2495,\cdot)\) \(\chi_{8304}(2543,\cdot)\) \(\chi_{8304}(2687,\cdot)\) \(\chi_{8304}(2783,\cdot)\) \(\chi_{8304}(2927,\cdot)\) \(\chi_{8304}(2975,\cdot)\) \(\chi_{8304}(3071,\cdot)\) \(\chi_{8304}(3311,\cdot)\) \(\chi_{8304}(3839,\cdot)\) \(\chi_{8304}(3983,\cdot)\) \(\chi_{8304}(4319,\cdot)\) \(\chi_{8304}(4415,\cdot)\) \(\chi_{8304}(4511,\cdot)\) \(\chi_{8304}(4655,\cdot)\) \(\chi_{8304}(5231,\cdot)\) \(\chi_{8304}(5279,\cdot)\) \(\chi_{8304}(5327,\cdot)\) \(\chi_{8304}(5567,\cdot)\) \(\chi_{8304}(5903,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{43})$ |
Fixed field: | Number field defined by a degree 86 polynomial |
Values on generators
\((1039,6229,5537,7441)\) → \((-1,1,-1,e\left(\frac{3}{86}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(5\) | \(7\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) |
\( \chi_{ 8304 }(1967, a) \) | \(1\) | \(1\) | \(e\left(\frac{37}{43}\right)\) | \(e\left(\frac{35}{43}\right)\) | \(e\left(\frac{69}{86}\right)\) | \(e\left(\frac{23}{43}\right)\) | \(e\left(\frac{2}{43}\right)\) | \(e\left(\frac{28}{43}\right)\) | \(e\left(\frac{30}{43}\right)\) | \(e\left(\frac{31}{43}\right)\) | \(e\left(\frac{45}{86}\right)\) | \(e\left(\frac{5}{86}\right)\) |