Basic properties
| Modulus: | \(349\) | |
| Conductor: | \(349\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(87\) | 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 349.i
\(\chi_{349}(9,\cdot)\) \(\chi_{349}(12,\cdot)\) \(\chi_{349}(14,\cdot)\) \(\chi_{349}(15,\cdot)\) \(\chi_{349}(16,\cdot)\) \(\chi_{349}(19,\cdot)\) \(\chi_{349}(20,\cdot)\) \(\chi_{349}(23,\cdot)\) \(\chi_{349}(25,\cdot)\) \(\chi_{349}(26,\cdot)\) \(\chi_{349}(51,\cdot)\) \(\chi_{349}(68,\cdot)\) \(\chi_{349}(77,\cdot)\) \(\chi_{349}(81,\cdot)\) \(\chi_{349}(85,\cdot)\) \(\chi_{349}(87,\cdot)\) \(\chi_{349}(94,\cdot)\) \(\chi_{349}(106,\cdot)\) \(\chi_{349}(108,\cdot)\) \(\chi_{349}(111,\cdot)\) \(\chi_{349}(116,\cdot)\) \(\chi_{349}(135,\cdot)\) \(\chi_{349}(143,\cdot)\) \(\chi_{349}(144,\cdot)\) \(\chi_{349}(145,\cdot)\) \(\chi_{349}(147,\cdot)\) \(\chi_{349}(148,\cdot)\) \(\chi_{349}(151,\cdot)\) \(\chi_{349}(158,\cdot)\) \(\chi_{349}(180,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{87})$ |
| Fixed field: | Number field defined by a degree 87 polynomial |
Values on generators
\(2\) → \(e\left(\frac{11}{87}\right)\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 349 }(135, a) \) | \(1\) | \(1\) | \(e\left(\frac{11}{87}\right)\) | \(e\left(\frac{25}{87}\right)\) | \(e\left(\frac{22}{87}\right)\) | \(e\left(\frac{61}{87}\right)\) | \(e\left(\frac{12}{29}\right)\) | \(e\left(\frac{41}{87}\right)\) | \(e\left(\frac{11}{29}\right)\) | \(e\left(\frac{50}{87}\right)\) | \(e\left(\frac{24}{29}\right)\) | \(e\left(\frac{19}{29}\right)\) |