Basic properties
Modulus: | \(407\) | |
Conductor: | \(407\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(90\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
Real: | no | |
Primitive: | yes | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 407.bh
\(\chi_{407}(7,\cdot)\) \(\chi_{407}(46,\cdot)\) \(\chi_{407}(83,\cdot)\) \(\chi_{407}(90,\cdot)\) \(\chi_{407}(107,\cdot)\) \(\chi_{407}(118,\cdot)\) \(\chi_{407}(123,\cdot)\) \(\chi_{407}(127,\cdot)\) \(\chi_{407}(145,\cdot)\) \(\chi_{407}(160,\cdot)\) \(\chi_{407}(182,\cdot)\) \(\chi_{407}(194,\cdot)\) \(\chi_{407}(238,\cdot)\) \(\chi_{407}(255,\cdot)\) \(\chi_{407}(266,\cdot)\) \(\chi_{407}(271,\cdot)\) \(\chi_{407}(292,\cdot)\) \(\chi_{407}(293,\cdot)\) \(\chi_{407}(303,\cdot)\) \(\chi_{407}(305,\cdot)\) \(\chi_{407}(349,\cdot)\) \(\chi_{407}(382,\cdot)\) \(\chi_{407}(403,\cdot)\) \(\chi_{407}(404,\cdot)\)
Related number fields
Field of values: | $\Q(\zeta_{45})$ |
Fixed field: | Number field defined by a degree 90 polynomial |
Values on generators
\((112,298)\) → \((e\left(\frac{7}{10}\right),e\left(\frac{8}{9}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(12\) |
\( \chi_{ 407 }(7, a) \) | \(-1\) | \(1\) | \(e\left(\frac{53}{90}\right)\) | \(e\left(\frac{32}{45}\right)\) | \(e\left(\frac{8}{45}\right)\) | \(e\left(\frac{11}{45}\right)\) | \(e\left(\frac{3}{10}\right)\) | \(e\left(\frac{31}{90}\right)\) | \(e\left(\frac{23}{30}\right)\) | \(e\left(\frac{19}{45}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{8}{9}\right)\) |