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: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 608.bv
\(\chi_{608}(13,\cdot)\) \(\chi_{608}(21,\cdot)\) \(\chi_{608}(29,\cdot)\) \(\chi_{608}(53,\cdot)\) \(\chi_{608}(109,\cdot)\) \(\chi_{608}(117,\cdot)\) \(\chi_{608}(165,\cdot)\) \(\chi_{608}(173,\cdot)\) \(\chi_{608}(181,\cdot)\) \(\chi_{608}(205,\cdot)\) \(\chi_{608}(261,\cdot)\) \(\chi_{608}(269,\cdot)\) \(\chi_{608}(317,\cdot)\) \(\chi_{608}(325,\cdot)\) \(\chi_{608}(333,\cdot)\) \(\chi_{608}(357,\cdot)\) \(\chi_{608}(413,\cdot)\) \(\chi_{608}(421,\cdot)\) \(\chi_{608}(469,\cdot)\) \(\chi_{608}(477,\cdot)\) \(\chi_{608}(485,\cdot)\) \(\chi_{608}(509,\cdot)\) \(\chi_{608}(565,\cdot)\) \(\chi_{608}(573,\cdot)\)
Related number fields
Field of values: | $\Q(\zeta_{72})$ |
Fixed field: | Number field defined by a degree 72 polynomial |
Values on generators
\((191,229,97)\) → \((1,e\left(\frac{7}{8}\right),e\left(\frac{5}{18}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(21\) | \(23\) |
\( \chi_{ 608 }(13, a) \) | \(-1\) | \(1\) | \(e\left(\frac{17}{72}\right)\) | \(e\left(\frac{23}{72}\right)\) | \(e\left(\frac{5}{12}\right)\) | \(e\left(\frac{17}{36}\right)\) | \(e\left(\frac{17}{24}\right)\) | \(e\left(\frac{37}{72}\right)\) | \(e\left(\frac{5}{9}\right)\) | \(e\left(\frac{5}{18}\right)\) | \(e\left(\frac{47}{72}\right)\) | \(e\left(\frac{29}{36}\right)\) |