Basic properties
Modulus: | \(9408\) | |
Conductor: | \(3136\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(112\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
Real: | no | |
Primitive: | no, induced from \(\chi_{3136}(2661,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 9408.fh
\(\chi_{9408}(85,\cdot)\) \(\chi_{9408}(253,\cdot)\) \(\chi_{9408}(421,\cdot)\) \(\chi_{9408}(757,\cdot)\) \(\chi_{9408}(925,\cdot)\) \(\chi_{9408}(1093,\cdot)\) \(\chi_{9408}(1261,\cdot)\) \(\chi_{9408}(1429,\cdot)\) \(\chi_{9408}(1597,\cdot)\) \(\chi_{9408}(1933,\cdot)\) \(\chi_{9408}(2101,\cdot)\) \(\chi_{9408}(2269,\cdot)\) \(\chi_{9408}(2437,\cdot)\) \(\chi_{9408}(2605,\cdot)\) \(\chi_{9408}(2773,\cdot)\) \(\chi_{9408}(3109,\cdot)\) \(\chi_{9408}(3277,\cdot)\) \(\chi_{9408}(3445,\cdot)\) \(\chi_{9408}(3613,\cdot)\) \(\chi_{9408}(3781,\cdot)\) \(\chi_{9408}(3949,\cdot)\) \(\chi_{9408}(4285,\cdot)\) \(\chi_{9408}(4453,\cdot)\) \(\chi_{9408}(4621,\cdot)\) \(\chi_{9408}(4789,\cdot)\) \(\chi_{9408}(4957,\cdot)\) \(\chi_{9408}(5125,\cdot)\) \(\chi_{9408}(5461,\cdot)\) \(\chi_{9408}(5629,\cdot)\) \(\chi_{9408}(5797,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{112})$ |
Fixed field: | Number field defined by a degree 112 polynomial (not computed) |
Values on generators
\((1471,6469,3137,4609)\) → \((1,e\left(\frac{9}{16}\right),1,e\left(\frac{5}{7}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(5\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) | \(37\) |
\( \chi_{ 9408 }(5797, a) \) | \(1\) | \(1\) | \(e\left(\frac{31}{112}\right)\) | \(e\left(\frac{43}{112}\right)\) | \(e\left(\frac{1}{112}\right)\) | \(e\left(\frac{17}{28}\right)\) | \(e\left(\frac{15}{16}\right)\) | \(e\left(\frac{1}{56}\right)\) | \(e\left(\frac{31}{56}\right)\) | \(e\left(\frac{5}{112}\right)\) | \(-1\) | \(e\left(\frac{103}{112}\right)\) |