Basic properties
| Modulus: | \(9072\) | |
| Conductor: | \(1296\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(108\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{1296}(155,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 9072.jn
\(\chi_{9072}(155,\cdot)\) \(\chi_{9072}(491,\cdot)\) \(\chi_{9072}(659,\cdot)\) \(\chi_{9072}(995,\cdot)\) \(\chi_{9072}(1163,\cdot)\) \(\chi_{9072}(1499,\cdot)\) \(\chi_{9072}(1667,\cdot)\) \(\chi_{9072}(2003,\cdot)\) \(\chi_{9072}(2171,\cdot)\) \(\chi_{9072}(2507,\cdot)\) \(\chi_{9072}(2675,\cdot)\) \(\chi_{9072}(3011,\cdot)\) \(\chi_{9072}(3179,\cdot)\) \(\chi_{9072}(3515,\cdot)\) \(\chi_{9072}(3683,\cdot)\) \(\chi_{9072}(4019,\cdot)\) \(\chi_{9072}(4187,\cdot)\) \(\chi_{9072}(4523,\cdot)\) \(\chi_{9072}(4691,\cdot)\) \(\chi_{9072}(5027,\cdot)\) \(\chi_{9072}(5195,\cdot)\) \(\chi_{9072}(5531,\cdot)\) \(\chi_{9072}(5699,\cdot)\) \(\chi_{9072}(6035,\cdot)\) \(\chi_{9072}(6203,\cdot)\) \(\chi_{9072}(6539,\cdot)\) \(\chi_{9072}(6707,\cdot)\) \(\chi_{9072}(7043,\cdot)\) \(\chi_{9072}(7211,\cdot)\) \(\chi_{9072}(7547,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{108})$ |
| Fixed field: | Number field defined by a degree 108 polynomial (not computed) |
Values on generators
\((1135,6805,3809,2593)\) → \((-1,i,e\left(\frac{43}{54}\right),1)\)
First values
| \(a\) | \(-1\) | \(1\) | \(5\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) | \(37\) |
| \( \chi_{ 9072 }(155, a) \) | \(1\) | \(1\) | \(e\left(\frac{61}{108}\right)\) | \(e\left(\frac{11}{108}\right)\) | \(e\left(\frac{13}{108}\right)\) | \(e\left(\frac{5}{18}\right)\) | \(e\left(\frac{17}{36}\right)\) | \(e\left(\frac{41}{54}\right)\) | \(e\left(\frac{7}{54}\right)\) | \(e\left(\frac{23}{108}\right)\) | \(e\left(\frac{23}{54}\right)\) | \(e\left(\frac{25}{36}\right)\) |