Basic properties
| Modulus: | \(8712\) | |
| 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 \(\chi_{121}(47,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 8712.dd
\(\chi_{8712}(289,\cdot)\) \(\chi_{8712}(361,\cdot)\) \(\chi_{8712}(433,\cdot)\) \(\chi_{8712}(577,\cdot)\) \(\chi_{8712}(1081,\cdot)\) \(\chi_{8712}(1153,\cdot)\) \(\chi_{8712}(1225,\cdot)\) \(\chi_{8712}(1369,\cdot)\) \(\chi_{8712}(1873,\cdot)\) \(\chi_{8712}(2161,\cdot)\) \(\chi_{8712}(2737,\cdot)\) \(\chi_{8712}(2809,\cdot)\) \(\chi_{8712}(2953,\cdot)\) \(\chi_{8712}(3457,\cdot)\) \(\chi_{8712}(3529,\cdot)\) \(\chi_{8712}(3601,\cdot)\) \(\chi_{8712}(3745,\cdot)\) \(\chi_{8712}(4249,\cdot)\) \(\chi_{8712}(4321,\cdot)\) \(\chi_{8712}(4393,\cdot)\) \(\chi_{8712}(4537,\cdot)\) \(\chi_{8712}(5041,\cdot)\) \(\chi_{8712}(5113,\cdot)\) \(\chi_{8712}(5185,\cdot)\) \(\chi_{8712}(5329,\cdot)\) \(\chi_{8712}(5833,\cdot)\) \(\chi_{8712}(5905,\cdot)\) \(\chi_{8712}(5977,\cdot)\) \(\chi_{8712}(6121,\cdot)\) \(\chi_{8712}(6625,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{55})$ |
| Fixed field: | Number field defined by a degree 55 polynomial |
Values on generators
\((6535,4357,1937,5689)\) → \((1,1,1,e\left(\frac{49}{55}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(5\) | \(7\) | \(13\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) | \(35\) |
| \( \chi_{ 8712 }(289, a) \) | \(1\) | \(1\) | \(e\left(\frac{51}{55}\right)\) | \(e\left(\frac{13}{55}\right)\) | \(e\left(\frac{54}{55}\right)\) | \(e\left(\frac{36}{55}\right)\) | \(e\left(\frac{52}{55}\right)\) | \(e\left(\frac{4}{11}\right)\) | \(e\left(\frac{47}{55}\right)\) | \(e\left(\frac{8}{55}\right)\) | \(e\left(\frac{34}{55}\right)\) | \(e\left(\frac{9}{55}\right)\) |