Basic properties
| Modulus: | \(8030\) | |
| Conductor: | \(803\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(180\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{803}(61,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 8030.ft
\(\chi_{8030}(61,\cdot)\) \(\chi_{8030}(171,\cdot)\) \(\chi_{8030}(371,\cdot)\) \(\chi_{8030}(651,\cdot)\) \(\chi_{8030}(711,\cdot)\) \(\chi_{8030}(1041,\cdot)\) \(\chi_{8030}(1381,\cdot)\) \(\chi_{8030}(1581,\cdot)\) \(\chi_{8030}(1641,\cdot)\) \(\chi_{8030}(1691,\cdot)\) \(\chi_{8030}(1921,\cdot)\) \(\chi_{8030}(2021,\cdot)\) \(\chi_{8030}(2251,\cdot)\) \(\chi_{8030}(2301,\cdot)\) \(\chi_{8030}(2361,\cdot)\) \(\chi_{8030}(2371,\cdot)\) \(\chi_{8030}(2901,\cdot)\) \(\chi_{8030}(3031,\cdot)\) \(\chi_{8030}(3231,\cdot)\) \(\chi_{8030}(3291,\cdot)\) \(\chi_{8030}(3571,\cdot)\) \(\chi_{8030}(4021,\cdot)\) \(\chi_{8030}(4111,\cdot)\) \(\chi_{8030}(4441,\cdot)\) \(\chi_{8030}(4501,\cdot)\) \(\chi_{8030}(4551,\cdot)\) \(\chi_{8030}(4561,\cdot)\) \(\chi_{8030}(4611,\cdot)\) \(\chi_{8030}(4941,\cdot)\) \(\chi_{8030}(5221,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{180})$ |
| Fixed field: | Number field defined by a degree 180 polynomial (not computed) |
Values on generators
\((1607,2191,881)\) → \((1,e\left(\frac{9}{10}\right),e\left(\frac{29}{36}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(7\) | \(9\) | \(13\) | \(17\) | \(19\) | \(21\) | \(23\) | \(27\) | \(29\) |
| \( \chi_{ 8030 }(61, a) \) | \(-1\) | \(1\) | \(e\left(\frac{1}{30}\right)\) | \(e\left(\frac{53}{60}\right)\) | \(e\left(\frac{1}{15}\right)\) | \(e\left(\frac{77}{180}\right)\) | \(e\left(\frac{1}{60}\right)\) | \(e\left(\frac{29}{45}\right)\) | \(e\left(\frac{11}{12}\right)\) | \(e\left(\frac{1}{18}\right)\) | \(e\left(\frac{1}{10}\right)\) | \(e\left(\frac{89}{180}\right)\) |