Basic properties
| Modulus: | \(997\) | |
| Conductor: | \(997\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(166\) | 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 997.h
\(\chi_{997}(3,\cdot)\) \(\chi_{997}(4,\cdot)\) \(\chi_{997}(10,\cdot)\) \(\chi_{997}(25,\cdot)\) \(\chi_{997}(27,\cdot)\) \(\chi_{997}(31,\cdot)\) \(\chi_{997}(36,\cdot)\) \(\chi_{997}(48,\cdot)\) \(\chi_{997}(64,\cdot)\) \(\chi_{997}(83,\cdot)\) \(\chi_{997}(90,\cdot)\) \(\chi_{997}(97,\cdot)\) \(\chi_{997}(109,\cdot)\) \(\chi_{997}(120,\cdot)\) \(\chi_{997}(160,\cdot)\) \(\chi_{997}(167,\cdot)\) \(\chi_{997}(193,\cdot)\) \(\chi_{997}(199,\cdot)\) \(\chi_{997}(201,\cdot)\) \(\chi_{997}(222,\cdot)\) \(\chi_{997}(225,\cdot)\) \(\chi_{997}(243,\cdot)\) \(\chi_{997}(266,\cdot)\) \(\chi_{997}(268,\cdot)\) \(\chi_{997}(279,\cdot)\) \(\chi_{997}(296,\cdot)\) \(\chi_{997}(300,\cdot)\) \(\chi_{997}(311,\cdot)\) \(\chi_{997}(322,\cdot)\) \(\chi_{997}(324,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{83})$ |
| Fixed field: | Number field defined by a degree 166 polynomial (not computed) |
Values on generators
\(7\) → \(e\left(\frac{27}{166}\right)\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 997 }(329, a) \) | \(1\) | \(1\) | \(e\left(\frac{115}{166}\right)\) | \(e\left(\frac{81}{83}\right)\) | \(e\left(\frac{32}{83}\right)\) | \(e\left(\frac{105}{166}\right)\) | \(e\left(\frac{111}{166}\right)\) | \(e\left(\frac{27}{166}\right)\) | \(e\left(\frac{13}{166}\right)\) | \(e\left(\frac{79}{83}\right)\) | \(e\left(\frac{27}{83}\right)\) | \(e\left(\frac{147}{166}\right)\) |