Basic properties
Modulus: | \(9072\) | |
Conductor: | \(9072\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(108\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
Real: | no | |
Primitive: | yes | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 9072.jz
\(\chi_{9072}(139,\cdot)\) \(\chi_{9072}(475,\cdot)\) \(\chi_{9072}(643,\cdot)\) \(\chi_{9072}(979,\cdot)\) \(\chi_{9072}(1147,\cdot)\) \(\chi_{9072}(1483,\cdot)\) \(\chi_{9072}(1651,\cdot)\) \(\chi_{9072}(1987,\cdot)\) \(\chi_{9072}(2155,\cdot)\) \(\chi_{9072}(2491,\cdot)\) \(\chi_{9072}(2659,\cdot)\) \(\chi_{9072}(2995,\cdot)\) \(\chi_{9072}(3163,\cdot)\) \(\chi_{9072}(3499,\cdot)\) \(\chi_{9072}(3667,\cdot)\) \(\chi_{9072}(4003,\cdot)\) \(\chi_{9072}(4171,\cdot)\) \(\chi_{9072}(4507,\cdot)\) \(\chi_{9072}(4675,\cdot)\) \(\chi_{9072}(5011,\cdot)\) \(\chi_{9072}(5179,\cdot)\) \(\chi_{9072}(5515,\cdot)\) \(\chi_{9072}(5683,\cdot)\) \(\chi_{9072}(6019,\cdot)\) \(\chi_{9072}(6187,\cdot)\) \(\chi_{9072}(6523,\cdot)\) \(\chi_{9072}(6691,\cdot)\) \(\chi_{9072}(7027,\cdot)\) \(\chi_{9072}(7195,\cdot)\) \(\chi_{9072}(7531,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{108})$ |
Fixed field: | Number field defined by a degree 108 polynomial (not computed) |
Values on generators
\((1135,6805,3809,2593)\) → \((-1,i,e\left(\frac{19}{27}\right),-1)\)
First values
\(a\) | \(-1\) | \(1\) | \(5\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) | \(37\) |
\( \chi_{ 9072 }(139, a) \) | \(1\) | \(1\) | \(e\left(\frac{101}{108}\right)\) | \(e\left(\frac{97}{108}\right)\) | \(e\left(\frac{95}{108}\right)\) | \(e\left(\frac{13}{18}\right)\) | \(e\left(\frac{19}{36}\right)\) | \(e\left(\frac{20}{27}\right)\) | \(e\left(\frac{47}{54}\right)\) | \(e\left(\frac{85}{108}\right)\) | \(e\left(\frac{2}{27}\right)\) | \(e\left(\frac{29}{36}\right)\) |