Basic properties
| Modulus: | \(259200\) | |
| Conductor: | \(43200\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(720\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{43200}(14173,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | no | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 259200.xx
\(\chi_{259200}(73,\cdot)\) \(\chi_{259200}(2953,\cdot)\) \(\chi_{259200}(3097,\cdot)\) \(\chi_{259200}(5977,\cdot)\) \(\chi_{259200}(7273,\cdot)\) \(\chi_{259200}(7417,\cdot)\) \(\chi_{259200}(8713,\cdot)\) \(\chi_{259200}(10297,\cdot)\) \(\chi_{259200}(11737,\cdot)\) \(\chi_{259200}(13033,\cdot)\) \(\chi_{259200}(14617,\cdot)\) \(\chi_{259200}(15913,\cdot)\) \(\chi_{259200}(17353,\cdot)\) \(\chi_{259200}(18937,\cdot)\) \(\chi_{259200}(20233,\cdot)\) \(\chi_{259200}(20377,\cdot)\) \(\chi_{259200}(21673,\cdot)\) \(\chi_{259200}(24553,\cdot)\) \(\chi_{259200}(24697,\cdot)\) \(\chi_{259200}(27577,\cdot)\) \(\chi_{259200}(28873,\cdot)\) \(\chi_{259200}(29017,\cdot)\) \(\chi_{259200}(30313,\cdot)\) \(\chi_{259200}(31897,\cdot)\) \(\chi_{259200}(33337,\cdot)\) \(\chi_{259200}(34633,\cdot)\) \(\chi_{259200}(36217,\cdot)\) \(\chi_{259200}(37513,\cdot)\) \(\chi_{259200}(38953,\cdot)\) \(\chi_{259200}(40537,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{720})$ |
| Fixed field: | Number field defined by a degree 720 polynomial (not computed) |
Values on generators
\((157951,202501,6401,72577)\) → \((1,e\left(\frac{11}{16}\right),e\left(\frac{5}{9}\right),e\left(\frac{11}{20}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(7\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(29\) | \(31\) | \(37\) | \(41\) |
| \( \chi_{ 259200 }(73, a) \) | \(-1\) | \(1\) | \(e\left(\frac{37}{72}\right)\) | \(e\left(\frac{331}{720}\right)\) | \(e\left(\frac{149}{720}\right)\) | \(e\left(\frac{11}{15}\right)\) | \(e\left(\frac{91}{240}\right)\) | \(e\left(\frac{283}{360}\right)\) | \(e\left(\frac{157}{720}\right)\) | \(e\left(\frac{1}{90}\right)\) | \(e\left(\frac{113}{240}\right)\) | \(e\left(\frac{97}{360}\right)\) |