Basic properties
| Modulus: | \(608\) | |
| Conductor: | \(608\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(72\) | 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 608.bt
\(\chi_{608}(3,\cdot)\) \(\chi_{608}(51,\cdot)\) \(\chi_{608}(59,\cdot)\) \(\chi_{608}(67,\cdot)\) \(\chi_{608}(91,\cdot)\) \(\chi_{608}(147,\cdot)\) \(\chi_{608}(155,\cdot)\) \(\chi_{608}(203,\cdot)\) \(\chi_{608}(211,\cdot)\) \(\chi_{608}(219,\cdot)\) \(\chi_{608}(243,\cdot)\) \(\chi_{608}(299,\cdot)\) \(\chi_{608}(307,\cdot)\) \(\chi_{608}(355,\cdot)\) \(\chi_{608}(363,\cdot)\) \(\chi_{608}(371,\cdot)\) \(\chi_{608}(395,\cdot)\) \(\chi_{608}(451,\cdot)\) \(\chi_{608}(459,\cdot)\) \(\chi_{608}(507,\cdot)\) \(\chi_{608}(515,\cdot)\) \(\chi_{608}(523,\cdot)\) \(\chi_{608}(547,\cdot)\) \(\chi_{608}(603,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{72})$ |
| Fixed field: | Number field defined by a degree 72 polynomial |
Values on generators
\((191,229,97)\) → \((-1,e\left(\frac{3}{8}\right),e\left(\frac{13}{18}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(21\) | \(23\) |
| \( \chi_{ 608 }(3, a) \) | \(1\) | \(1\) | \(e\left(\frac{1}{72}\right)\) | \(e\left(\frac{67}{72}\right)\) | \(e\left(\frac{7}{12}\right)\) | \(e\left(\frac{1}{36}\right)\) | \(e\left(\frac{1}{24}\right)\) | \(e\left(\frac{17}{72}\right)\) | \(e\left(\frac{17}{18}\right)\) | \(e\left(\frac{13}{18}\right)\) | \(e\left(\frac{43}{72}\right)\) | \(e\left(\frac{7}{36}\right)\) |