Basic properties
Modulus: | \(1216\) | |
Conductor: | \(608\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(72\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
Real: | no | |
Primitive: | no, induced from \(\chi_{608}(299,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | no | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 1216.cb
\(\chi_{1216}(71,\cdot)\) \(\chi_{1216}(135,\cdot)\) \(\chi_{1216}(167,\cdot)\) \(\chi_{1216}(231,\cdot)\) \(\chi_{1216}(279,\cdot)\) \(\chi_{1216}(295,\cdot)\) \(\chi_{1216}(375,\cdot)\) \(\chi_{1216}(439,\cdot)\) \(\chi_{1216}(471,\cdot)\) \(\chi_{1216}(535,\cdot)\) \(\chi_{1216}(583,\cdot)\) \(\chi_{1216}(599,\cdot)\) \(\chi_{1216}(679,\cdot)\) \(\chi_{1216}(743,\cdot)\) \(\chi_{1216}(775,\cdot)\) \(\chi_{1216}(839,\cdot)\) \(\chi_{1216}(887,\cdot)\) \(\chi_{1216}(903,\cdot)\) \(\chi_{1216}(983,\cdot)\) \(\chi_{1216}(1047,\cdot)\) \(\chi_{1216}(1079,\cdot)\) \(\chi_{1216}(1143,\cdot)\) \(\chi_{1216}(1191,\cdot)\) \(\chi_{1216}(1207,\cdot)\)
Related number fields
Field of values: | $\Q(\zeta_{72})$ |
Fixed field: | Number field defined by a degree 72 polynomial |
Values on generators
\((191,837,705)\) → \((-1,e\left(\frac{5}{8}\right),e\left(\frac{7}{18}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(21\) | \(23\) |
\( \chi_{ 1216 }(71, a) \) | \(1\) | \(1\) | \(e\left(\frac{31}{72}\right)\) | \(e\left(\frac{61}{72}\right)\) | \(e\left(\frac{1}{12}\right)\) | \(e\left(\frac{31}{36}\right)\) | \(e\left(\frac{7}{24}\right)\) | \(e\left(\frac{23}{72}\right)\) | \(e\left(\frac{5}{18}\right)\) | \(e\left(\frac{7}{18}\right)\) | \(e\left(\frac{37}{72}\right)\) | \(e\left(\frac{1}{36}\right)\) |