Basic properties
Modulus: | \(7350\) | |
Conductor: | \(735\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(84\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
Real: | no | |
Primitive: | no, induced from \(\chi_{735}(107,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 7350.cz
\(\chi_{7350}(107,\cdot)\) \(\chi_{7350}(443,\cdot)\) \(\chi_{7350}(893,\cdot)\) \(\chi_{7350}(1493,\cdot)\) \(\chi_{7350}(1607,\cdot)\) \(\chi_{7350}(1943,\cdot)\) \(\chi_{7350}(2207,\cdot)\) \(\chi_{7350}(2543,\cdot)\) \(\chi_{7350}(2657,\cdot)\) \(\chi_{7350}(2993,\cdot)\) \(\chi_{7350}(3257,\cdot)\) \(\chi_{7350}(3593,\cdot)\) \(\chi_{7350}(3707,\cdot)\) \(\chi_{7350}(4043,\cdot)\) \(\chi_{7350}(4307,\cdot)\) \(\chi_{7350}(4643,\cdot)\) \(\chi_{7350}(4757,\cdot)\) \(\chi_{7350}(5093,\cdot)\) \(\chi_{7350}(5357,\cdot)\) \(\chi_{7350}(5693,\cdot)\) \(\chi_{7350}(5807,\cdot)\) \(\chi_{7350}(6407,\cdot)\) \(\chi_{7350}(6857,\cdot)\) \(\chi_{7350}(7193,\cdot)\)
Related number fields
Field of values: | $\Q(\zeta_{84})$ |
Fixed field: | Number field defined by a degree 84 polynomial |
Values on generators
\((4901,1177,2551)\) → \((-1,i,e\left(\frac{1}{21}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(29\) | \(31\) | \(37\) | \(41\) | \(43\) |
\( \chi_{ 7350 }(107, a) \) | \(1\) | \(1\) | \(e\left(\frac{17}{42}\right)\) | \(e\left(\frac{9}{28}\right)\) | \(e\left(\frac{79}{84}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{5}{84}\right)\) | \(e\left(\frac{6}{7}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{65}{84}\right)\) | \(e\left(\frac{3}{14}\right)\) | \(e\left(\frac{1}{28}\right)\) |