Basic properties
Modulus: | \(407\) | |
Conductor: | \(407\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(180\) | 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 407.bj
\(\chi_{407}(2,\cdot)\) \(\chi_{407}(13,\cdot)\) \(\chi_{407}(17,\cdot)\) \(\chi_{407}(18,\cdot)\) \(\chi_{407}(19,\cdot)\) \(\chi_{407}(24,\cdot)\) \(\chi_{407}(35,\cdot)\) \(\chi_{407}(39,\cdot)\) \(\chi_{407}(50,\cdot)\) \(\chi_{407}(52,\cdot)\) \(\chi_{407}(57,\cdot)\) \(\chi_{407}(61,\cdot)\) \(\chi_{407}(72,\cdot)\) \(\chi_{407}(79,\cdot)\) \(\chi_{407}(94,\cdot)\) \(\chi_{407}(96,\cdot)\) \(\chi_{407}(106,\cdot)\) \(\chi_{407}(116,\cdot)\) \(\chi_{407}(128,\cdot)\) \(\chi_{407}(129,\cdot)\) \(\chi_{407}(150,\cdot)\) \(\chi_{407}(161,\cdot)\) \(\chi_{407}(167,\cdot)\) \(\chi_{407}(172,\cdot)\) \(\chi_{407}(183,\cdot)\) \(\chi_{407}(200,\cdot)\) \(\chi_{407}(204,\cdot)\) \(\chi_{407}(205,\cdot)\) \(\chi_{407}(217,\cdot)\) \(\chi_{407}(227,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{180})$ |
Fixed field: | Number field defined by a degree 180 polynomial (not computed) |
Values on generators
\((112,298)\) → \((e\left(\frac{3}{10}\right),e\left(\frac{23}{36}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(12\) |
\( \chi_{ 407 }(338, a) \) | \(1\) | \(1\) | \(e\left(\frac{169}{180}\right)\) | \(e\left(\frac{1}{90}\right)\) | \(e\left(\frac{79}{90}\right)\) | \(e\left(\frac{161}{180}\right)\) | \(e\left(\frac{19}{20}\right)\) | \(e\left(\frac{49}{90}\right)\) | \(e\left(\frac{49}{60}\right)\) | \(e\left(\frac{1}{45}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{8}{9}\right)\) |