Basic properties
| Modulus: | \(847\) | |
| 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 \(\chi_{121}(15,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 847.v
\(\chi_{847}(15,\cdot)\) \(\chi_{847}(36,\cdot)\) \(\chi_{847}(64,\cdot)\) \(\chi_{847}(71,\cdot)\) \(\chi_{847}(92,\cdot)\) \(\chi_{847}(113,\cdot)\) \(\chi_{847}(141,\cdot)\) \(\chi_{847}(169,\cdot)\) \(\chi_{847}(190,\cdot)\) \(\chi_{847}(218,\cdot)\) \(\chi_{847}(225,\cdot)\) \(\chi_{847}(246,\cdot)\) \(\chi_{847}(267,\cdot)\) \(\chi_{847}(295,\cdot)\) \(\chi_{847}(302,\cdot)\) \(\chi_{847}(344,\cdot)\) \(\chi_{847}(379,\cdot)\) \(\chi_{847}(400,\cdot)\) \(\chi_{847}(421,\cdot)\) \(\chi_{847}(449,\cdot)\) \(\chi_{847}(456,\cdot)\) \(\chi_{847}(477,\cdot)\) \(\chi_{847}(498,\cdot)\) \(\chi_{847}(526,\cdot)\) \(\chi_{847}(533,\cdot)\) \(\chi_{847}(554,\cdot)\) \(\chi_{847}(575,\cdot)\) \(\chi_{847}(603,\cdot)\) \(\chi_{847}(610,\cdot)\) \(\chi_{847}(631,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{55})$ |
| Fixed field: | Number field defined by a degree 55 polynomial |
Values on generators
\((122,365)\) → \((1,e\left(\frac{26}{55}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(8\) | \(9\) | \(10\) | \(12\) | \(13\) |
| \( \chi_{ 847 }(15, a) \) | \(1\) | \(1\) | \(e\left(\frac{26}{55}\right)\) | \(e\left(\frac{3}{5}\right)\) | \(e\left(\frac{52}{55}\right)\) | \(e\left(\frac{54}{55}\right)\) | \(e\left(\frac{4}{55}\right)\) | \(e\left(\frac{23}{55}\right)\) | \(e\left(\frac{1}{5}\right)\) | \(e\left(\frac{5}{11}\right)\) | \(e\left(\frac{6}{11}\right)\) | \(e\left(\frac{41}{55}\right)\) |