Basic properties
| Modulus: | \(9025\) | |
| Conductor: | \(1805\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(114\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{1805}(49,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | no | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 9025.br
\(\chi_{9025}(49,\cdot)\) \(\chi_{9025}(349,\cdot)\) \(\chi_{9025}(524,\cdot)\) \(\chi_{9025}(824,\cdot)\) \(\chi_{9025}(999,\cdot)\) \(\chi_{9025}(1299,\cdot)\) \(\chi_{9025}(1474,\cdot)\) \(\chi_{9025}(1774,\cdot)\) \(\chi_{9025}(1949,\cdot)\) \(\chi_{9025}(2249,\cdot)\) \(\chi_{9025}(2424,\cdot)\) \(\chi_{9025}(2724,\cdot)\) \(\chi_{9025}(2899,\cdot)\) \(\chi_{9025}(3199,\cdot)\) \(\chi_{9025}(3374,\cdot)\) \(\chi_{9025}(3674,\cdot)\) \(\chi_{9025}(3849,\cdot)\) \(\chi_{9025}(4149,\cdot)\) \(\chi_{9025}(4324,\cdot)\) \(\chi_{9025}(4799,\cdot)\) \(\chi_{9025}(5099,\cdot)\) \(\chi_{9025}(5274,\cdot)\) \(\chi_{9025}(5574,\cdot)\) \(\chi_{9025}(5749,\cdot)\) \(\chi_{9025}(6049,\cdot)\) \(\chi_{9025}(6224,\cdot)\) \(\chi_{9025}(6524,\cdot)\) \(\chi_{9025}(6699,\cdot)\) \(\chi_{9025}(6999,\cdot)\) \(\chi_{9025}(7174,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{57})$ |
| Fixed field: | Number field defined by a degree 114 polynomial (not computed) |
Values on generators
\((5777,3251)\) → \((-1,e\left(\frac{50}{57}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(7\) | \(8\) | \(9\) | \(11\) | \(12\) | \(13\) |
| \( \chi_{ 9025 }(49, a) \) | \(1\) | \(1\) | \(e\left(\frac{43}{114}\right)\) | \(e\left(\frac{49}{114}\right)\) | \(e\left(\frac{43}{57}\right)\) | \(e\left(\frac{46}{57}\right)\) | \(e\left(\frac{3}{38}\right)\) | \(e\left(\frac{5}{38}\right)\) | \(e\left(\frac{49}{57}\right)\) | \(e\left(\frac{9}{19}\right)\) | \(e\left(\frac{7}{38}\right)\) | \(e\left(\frac{11}{114}\right)\) |