Basic properties
| Modulus: | \(8030\) | |
| Conductor: | \(803\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(90\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{803}(41,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 8030.fj
\(\chi_{8030}(41,\cdot)\) \(\chi_{8030}(821,\cdot)\) \(\chi_{8030}(1091,\cdot)\) \(\chi_{8030}(1371,\cdot)\) \(\chi_{8030}(1531,\cdot)\) \(\chi_{8030}(1821,\cdot)\) \(\chi_{8030}(1861,\cdot)\) \(\chi_{8030}(2261,\cdot)\) \(\chi_{8030}(2591,\cdot)\) \(\chi_{8030}(2961,\cdot)\) \(\chi_{8030}(3011,\cdot)\) \(\chi_{8030}(3561,\cdot)\) \(\chi_{8030}(3691,\cdot)\) \(\chi_{8030}(4011,\cdot)\) \(\chi_{8030}(4451,\cdot)\) \(\chi_{8030}(4781,\cdot)\) \(\chi_{8030}(5881,\cdot)\) \(\chi_{8030}(5931,\cdot)\) \(\chi_{8030}(6201,\cdot)\) \(\chi_{8030}(6481,\cdot)\) \(\chi_{8030}(6641,\cdot)\) \(\chi_{8030}(6661,\cdot)\) \(\chi_{8030}(6971,\cdot)\) \(\chi_{8030}(7211,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{45})$ |
| Fixed field: | Number field defined by a degree 90 polynomial |
Values on generators
\((1607,2191,881)\) → \((1,e\left(\frac{3}{10}\right),e\left(\frac{1}{18}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(7\) | \(9\) | \(13\) | \(17\) | \(19\) | \(21\) | \(23\) | \(27\) | \(29\) |
| \( \chi_{ 8030 }(41, a) \) | \(-1\) | \(1\) | \(e\left(\frac{11}{15}\right)\) | \(e\left(\frac{14}{15}\right)\) | \(e\left(\frac{7}{15}\right)\) | \(e\left(\frac{26}{45}\right)\) | \(e\left(\frac{13}{15}\right)\) | \(e\left(\frac{31}{90}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{5}{9}\right)\) | \(e\left(\frac{1}{5}\right)\) | \(e\left(\frac{2}{45}\right)\) |