Basic properties
| Modulus: | \(7200\) | |
| Conductor: | \(7200\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(120\) | 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 7200.if
\(\chi_{7200}(11,\cdot)\) \(\chi_{7200}(131,\cdot)\) \(\chi_{7200}(371,\cdot)\) \(\chi_{7200}(491,\cdot)\) \(\chi_{7200}(731,\cdot)\) \(\chi_{7200}(1091,\cdot)\) \(\chi_{7200}(1211,\cdot)\) \(\chi_{7200}(1571,\cdot)\) \(\chi_{7200}(1811,\cdot)\) \(\chi_{7200}(1931,\cdot)\) \(\chi_{7200}(2171,\cdot)\) \(\chi_{7200}(2291,\cdot)\) \(\chi_{7200}(2531,\cdot)\) \(\chi_{7200}(2891,\cdot)\) \(\chi_{7200}(3011,\cdot)\) \(\chi_{7200}(3371,\cdot)\) \(\chi_{7200}(3611,\cdot)\) \(\chi_{7200}(3731,\cdot)\) \(\chi_{7200}(3971,\cdot)\) \(\chi_{7200}(4091,\cdot)\) \(\chi_{7200}(4331,\cdot)\) \(\chi_{7200}(4691,\cdot)\) \(\chi_{7200}(4811,\cdot)\) \(\chi_{7200}(5171,\cdot)\) \(\chi_{7200}(5411,\cdot)\) \(\chi_{7200}(5531,\cdot)\) \(\chi_{7200}(5771,\cdot)\) \(\chi_{7200}(5891,\cdot)\) \(\chi_{7200}(6131,\cdot)\) \(\chi_{7200}(6491,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{120})$ |
| Fixed field: | Number field defined by a degree 120 polynomial (not computed) |
Values on generators
\((6751,901,6401,577)\) → \((-1,e\left(\frac{5}{8}\right),e\left(\frac{1}{6}\right),e\left(\frac{4}{5}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(7\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(29\) | \(31\) | \(37\) | \(41\) |
| \( \chi_{ 7200 }(11, a) \) | \(1\) | \(1\) | \(e\left(\frac{5}{12}\right)\) | \(e\left(\frac{71}{120}\right)\) | \(e\left(\frac{109}{120}\right)\) | \(e\left(\frac{2}{5}\right)\) | \(e\left(\frac{11}{40}\right)\) | \(e\left(\frac{53}{60}\right)\) | \(e\left(\frac{77}{120}\right)\) | \(e\left(\frac{7}{30}\right)\) | \(e\left(\frac{33}{40}\right)\) | \(e\left(\frac{47}{60}\right)\) |