Basic properties
| Modulus: | \(9025\) | |
| Conductor: | \(9025\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(3420\) | 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 9025.ct
\(\chi_{9025}(2,\cdot)\) \(\chi_{9025}(3,\cdot)\) \(\chi_{9025}(13,\cdot)\) \(\chi_{9025}(22,\cdot)\) \(\chi_{9025}(33,\cdot)\) \(\chi_{9025}(48,\cdot)\) \(\chi_{9025}(52,\cdot)\) \(\chi_{9025}(53,\cdot)\) \(\chi_{9025}(67,\cdot)\) \(\chi_{9025}(72,\cdot)\) \(\chi_{9025}(78,\cdot)\) \(\chi_{9025}(97,\cdot)\) \(\chi_{9025}(98,\cdot)\) \(\chi_{9025}(108,\cdot)\) \(\chi_{9025}(117,\cdot)\) \(\chi_{9025}(128,\cdot)\) \(\chi_{9025}(147,\cdot)\) \(\chi_{9025}(148,\cdot)\) \(\chi_{9025}(162,\cdot)\) \(\chi_{9025}(167,\cdot)\) \(\chi_{9025}(173,\cdot)\) \(\chi_{9025}(192,\cdot)\) \(\chi_{9025}(203,\cdot)\) \(\chi_{9025}(212,\cdot)\) \(\chi_{9025}(222,\cdot)\) \(\chi_{9025}(223,\cdot)\) \(\chi_{9025}(238,\cdot)\) \(\chi_{9025}(242,\cdot)\) \(\chi_{9025}(287,\cdot)\) \(\chi_{9025}(288,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{3420})$ |
| Fixed field: | Number field defined by a degree 3420 polynomial (not computed) |
Values on generators
\((5777,3251)\) → \((e\left(\frac{1}{20}\right),e\left(\frac{1}{342}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(7\) | \(8\) | \(9\) | \(11\) | \(12\) | \(13\) |
| \( \chi_{ 9025 }(2, a) \) | \(1\) | \(1\) | \(e\left(\frac{181}{3420}\right)\) | \(e\left(\frac{2587}{3420}\right)\) | \(e\left(\frac{181}{1710}\right)\) | \(e\left(\frac{692}{855}\right)\) | \(e\left(\frac{157}{228}\right)\) | \(e\left(\frac{181}{1140}\right)\) | \(e\left(\frac{877}{1710}\right)\) | \(e\left(\frac{28}{285}\right)\) | \(e\left(\frac{983}{1140}\right)\) | \(e\left(\frac{3119}{3420}\right)\) |