Basic properties
| Modulus: | \(1210\) | |
| Conductor: | \(121\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(55\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{121}(31,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 1210.s
\(\chi_{1210}(31,\cdot)\) \(\chi_{1210}(71,\cdot)\) \(\chi_{1210}(91,\cdot)\) \(\chi_{1210}(141,\cdot)\) \(\chi_{1210}(181,\cdot)\) \(\chi_{1210}(191,\cdot)\) \(\chi_{1210}(201,\cdot)\) \(\chi_{1210}(291,\cdot)\) \(\chi_{1210}(301,\cdot)\) \(\chi_{1210}(311,\cdot)\) \(\chi_{1210}(361,\cdot)\) \(\chi_{1210}(401,\cdot)\) \(\chi_{1210}(411,\cdot)\) \(\chi_{1210}(421,\cdot)\) \(\chi_{1210}(471,\cdot)\) \(\chi_{1210}(521,\cdot)\) \(\chi_{1210}(531,\cdot)\) \(\chi_{1210}(581,\cdot)\) \(\chi_{1210}(621,\cdot)\) \(\chi_{1210}(631,\cdot)\) \(\chi_{1210}(641,\cdot)\) \(\chi_{1210}(691,\cdot)\) \(\chi_{1210}(731,\cdot)\) \(\chi_{1210}(741,\cdot)\) \(\chi_{1210}(751,\cdot)\) \(\chi_{1210}(801,\cdot)\) \(\chi_{1210}(841,\cdot)\) \(\chi_{1210}(851,\cdot)\) \(\chi_{1210}(861,\cdot)\) \(\chi_{1210}(911,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{55})$ |
| Fixed field: | Number field defined by a degree 55 polynomial |
Values on generators
\((727,1091)\) → \((1,e\left(\frac{43}{55}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(7\) | \(9\) | \(13\) | \(17\) | \(19\) | \(21\) | \(23\) | \(27\) | \(29\) |
| \( \chi_{ 1210 }(31, a) \) | \(1\) | \(1\) | \(e\left(\frac{4}{5}\right)\) | \(e\left(\frac{26}{55}\right)\) | \(e\left(\frac{3}{5}\right)\) | \(e\left(\frac{53}{55}\right)\) | \(e\left(\frac{17}{55}\right)\) | \(e\left(\frac{49}{55}\right)\) | \(e\left(\frac{3}{11}\right)\) | \(e\left(\frac{8}{11}\right)\) | \(e\left(\frac{2}{5}\right)\) | \(e\left(\frac{16}{55}\right)\) |