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: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 407.bg
\(\chi_{407}(3,\cdot)\) \(\chi_{407}(4,\cdot)\) \(\chi_{407}(25,\cdot)\) \(\chi_{407}(58,\cdot)\) \(\chi_{407}(102,\cdot)\) \(\chi_{407}(104,\cdot)\) \(\chi_{407}(114,\cdot)\) \(\chi_{407}(115,\cdot)\) \(\chi_{407}(136,\cdot)\) \(\chi_{407}(141,\cdot)\) \(\chi_{407}(152,\cdot)\) \(\chi_{407}(169,\cdot)\) \(\chi_{407}(213,\cdot)\) \(\chi_{407}(225,\cdot)\) \(\chi_{407}(247,\cdot)\) \(\chi_{407}(262,\cdot)\) \(\chi_{407}(280,\cdot)\) \(\chi_{407}(284,\cdot)\) \(\chi_{407}(289,\cdot)\) \(\chi_{407}(300,\cdot)\) \(\chi_{407}(317,\cdot)\) \(\chi_{407}(324,\cdot)\) \(\chi_{407}(361,\cdot)\) \(\chi_{407}(400,\cdot)\)
Related number fields
Field of values: | $\Q(\zeta_{45})$ |
Fixed field: | Number field defined by a degree 90 polynomial |
Values on generators
\((112,298)\) → \((e\left(\frac{3}{5}\right),e\left(\frac{11}{18}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(12\) |
\( \chi_{ 407 }(317, a) \) | \(1\) | \(1\) | \(e\left(\frac{19}{90}\right)\) | \(e\left(\frac{31}{45}\right)\) | \(e\left(\frac{19}{45}\right)\) | \(e\left(\frac{41}{90}\right)\) | \(e\left(\frac{9}{10}\right)\) | \(e\left(\frac{34}{45}\right)\) | \(e\left(\frac{19}{30}\right)\) | \(e\left(\frac{17}{45}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{1}{9}\right)\) |