Basic properties
Modulus: | \(9408\) | |
Conductor: | \(1568\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(56\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
Real: | no | |
Primitive: | no, induced from \(\chi_{1568}(1261,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | no | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 9408.ex
\(\chi_{9408}(169,\cdot)\) \(\chi_{9408}(505,\cdot)\) \(\chi_{9408}(841,\cdot)\) \(\chi_{9408}(1513,\cdot)\) \(\chi_{9408}(1849,\cdot)\) \(\chi_{9408}(2185,\cdot)\) \(\chi_{9408}(2521,\cdot)\) \(\chi_{9408}(2857,\cdot)\) \(\chi_{9408}(3193,\cdot)\) \(\chi_{9408}(3865,\cdot)\) \(\chi_{9408}(4201,\cdot)\) \(\chi_{9408}(4537,\cdot)\) \(\chi_{9408}(4873,\cdot)\) \(\chi_{9408}(5209,\cdot)\) \(\chi_{9408}(5545,\cdot)\) \(\chi_{9408}(6217,\cdot)\) \(\chi_{9408}(6553,\cdot)\) \(\chi_{9408}(6889,\cdot)\) \(\chi_{9408}(7225,\cdot)\) \(\chi_{9408}(7561,\cdot)\) \(\chi_{9408}(7897,\cdot)\) \(\chi_{9408}(8569,\cdot)\) \(\chi_{9408}(8905,\cdot)\) \(\chi_{9408}(9241,\cdot)\)
Related number fields
Field of values: | $\Q(\zeta_{56})$ |
Fixed field: | Number field defined by a degree 56 polynomial |
Values on generators
\((1471,6469,3137,4609)\) → \((1,e\left(\frac{7}{8}\right),1,e\left(\frac{2}{7}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(5\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) | \(37\) |
\( \chi_{ 9408 }(4201, a) \) | \(1\) | \(1\) | \(e\left(\frac{9}{56}\right)\) | \(e\left(\frac{45}{56}\right)\) | \(e\left(\frac{31}{56}\right)\) | \(e\left(\frac{9}{14}\right)\) | \(e\left(\frac{1}{8}\right)\) | \(e\left(\frac{3}{28}\right)\) | \(e\left(\frac{9}{28}\right)\) | \(e\left(\frac{43}{56}\right)\) | \(1\) | \(e\left(\frac{1}{56}\right)\) |