Basic properties
| Modulus: | \(9025\) | |
| Conductor: | \(9025\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(855\) | 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.cm
\(\chi_{9025}(6,\cdot)\) \(\chi_{9025}(16,\cdot)\) \(\chi_{9025}(36,\cdot)\) \(\chi_{9025}(61,\cdot)\) \(\chi_{9025}(66,\cdot)\) \(\chi_{9025}(81,\cdot)\) \(\chi_{9025}(111,\cdot)\) \(\chi_{9025}(131,\cdot)\) \(\chi_{9025}(156,\cdot)\) \(\chi_{9025}(161,\cdot)\) \(\chi_{9025}(196,\cdot)\) \(\chi_{9025}(206,\cdot)\) \(\chi_{9025}(256,\cdot)\) \(\chi_{9025}(271,\cdot)\) \(\chi_{9025}(291,\cdot)\) \(\chi_{9025}(321,\cdot)\) \(\chi_{9025}(346,\cdot)\) \(\chi_{9025}(366,\cdot)\) \(\chi_{9025}(386,\cdot)\) \(\chi_{9025}(396,\cdot)\) \(\chi_{9025}(416,\cdot)\) \(\chi_{9025}(441,\cdot)\) \(\chi_{9025}(446,\cdot)\) \(\chi_{9025}(461,\cdot)\) \(\chi_{9025}(481,\cdot)\) \(\chi_{9025}(491,\cdot)\) \(\chi_{9025}(511,\cdot)\) \(\chi_{9025}(536,\cdot)\) \(\chi_{9025}(541,\cdot)\) \(\chi_{9025}(556,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{855})$ |
| Fixed field: | Number field defined by a degree 855 polynomial (not computed) |
Values on generators
\((5777,3251)\) → \((e\left(\frac{2}{5}\right),e\left(\frac{70}{171}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(7\) | \(8\) | \(9\) | \(11\) | \(12\) | \(13\) |
| \( \chi_{ 9025 }(6, a) \) | \(1\) | \(1\) | \(e\left(\frac{692}{855}\right)\) | \(e\left(\frac{599}{855}\right)\) | \(e\left(\frac{529}{855}\right)\) | \(e\left(\frac{436}{855}\right)\) | \(e\left(\frac{23}{57}\right)\) | \(e\left(\frac{122}{285}\right)\) | \(e\left(\frac{343}{855}\right)\) | \(e\left(\frac{44}{285}\right)\) | \(e\left(\frac{91}{285}\right)\) | \(e\left(\frac{238}{855}\right)\) |