Basic properties
| Modulus: | \(547\) | |
| Conductor: | \(547\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(91\) | 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 547.m
\(\chi_{547}(10,\cdot)\) \(\chi_{547}(24,\cdot)\) \(\chi_{547}(29,\cdot)\) \(\chi_{547}(35,\cdot)\) \(\chi_{547}(44,\cdot)\) \(\chi_{547}(52,\cdot)\) \(\chi_{547}(64,\cdot)\) \(\chi_{547}(84,\cdot)\) \(\chi_{547}(85,\cdot)\) \(\chi_{547}(90,\cdot)\) \(\chi_{547}(93,\cdot)\) \(\chi_{547}(100,\cdot)\) \(\chi_{547}(114,\cdot)\) \(\chi_{547}(131,\cdot)\) \(\chi_{547}(149,\cdot)\) \(\chi_{547}(154,\cdot)\) \(\chi_{547}(161,\cdot)\) \(\chi_{547}(165,\cdot)\) \(\chi_{547}(167,\cdot)\) \(\chi_{547}(179,\cdot)\) \(\chi_{547}(185,\cdot)\) \(\chi_{547}(195,\cdot)\) \(\chi_{547}(204,\cdot)\) \(\chi_{547}(205,\cdot)\) \(\chi_{547}(209,\cdot)\) \(\chi_{547}(212,\cdot)\) \(\chi_{547}(215,\cdot)\) \(\chi_{547}(216,\cdot)\) \(\chi_{547}(218,\cdot)\) \(\chi_{547}(224,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{91})$ |
| Fixed field: | Number field defined by a degree 91 polynomial |
Values on generators
\(2\) → \(e\left(\frac{9}{91}\right)\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 547 }(468, a) \) | \(1\) | \(1\) | \(e\left(\frac{9}{91}\right)\) | \(e\left(\frac{3}{7}\right)\) | \(e\left(\frac{18}{91}\right)\) | \(e\left(\frac{64}{91}\right)\) | \(e\left(\frac{48}{91}\right)\) | \(e\left(\frac{17}{91}\right)\) | \(e\left(\frac{27}{91}\right)\) | \(e\left(\frac{6}{7}\right)\) | \(e\left(\frac{73}{91}\right)\) | \(e\left(\frac{12}{13}\right)\) |