Basic properties
Modulus: | \(407\) | |
Conductor: | \(407\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(45\) | 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.bc
\(\chi_{407}(9,\cdot)\) \(\chi_{407}(16,\cdot)\) \(\chi_{407}(49,\cdot)\) \(\chi_{407}(53,\cdot)\) \(\chi_{407}(70,\cdot)\) \(\chi_{407}(71,\cdot)\) \(\chi_{407}(81,\cdot)\) \(\chi_{407}(86,\cdot)\) \(\chi_{407}(108,\cdot)\) \(\chi_{407}(157,\cdot)\) \(\chi_{407}(181,\cdot)\) \(\chi_{407}(192,\cdot)\) \(\chi_{407}(201,\cdot)\) \(\chi_{407}(218,\cdot)\) \(\chi_{407}(229,\cdot)\) \(\chi_{407}(234,\cdot)\) \(\chi_{407}(256,\cdot)\) \(\chi_{407}(268,\cdot)\) \(\chi_{407}(312,\cdot)\) \(\chi_{407}(345,\cdot)\) \(\chi_{407}(366,\cdot)\) \(\chi_{407}(367,\cdot)\) \(\chi_{407}(377,\cdot)\) \(\chi_{407}(379,\cdot)\)
Related number fields
Field of values: | $\Q(\zeta_{45})$ |
Fixed field: | Number field defined by a degree 45 polynomial |
Values on generators
\((112,298)\) → \((e\left(\frac{4}{5}\right),e\left(\frac{5}{9}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(12\) |
\( \chi_{ 407 }(366, a) \) | \(1\) | \(1\) | \(e\left(\frac{16}{45}\right)\) | \(e\left(\frac{38}{45}\right)\) | \(e\left(\frac{32}{45}\right)\) | \(e\left(\frac{44}{45}\right)\) | \(e\left(\frac{1}{5}\right)\) | \(e\left(\frac{17}{45}\right)\) | \(e\left(\frac{1}{15}\right)\) | \(e\left(\frac{31}{45}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{5}{9}\right)\) |