Basic properties
Modulus: | \(1521\) | |
Conductor: | \(169\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(78\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
Real: | no | |
Primitive: | no, induced from \(\chi_{169}(10,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 1521.bt
\(\chi_{1521}(10,\cdot)\) \(\chi_{1521}(82,\cdot)\) \(\chi_{1521}(127,\cdot)\) \(\chi_{1521}(199,\cdot)\) \(\chi_{1521}(244,\cdot)\) \(\chi_{1521}(433,\cdot)\) \(\chi_{1521}(478,\cdot)\) \(\chi_{1521}(550,\cdot)\) \(\chi_{1521}(595,\cdot)\) \(\chi_{1521}(667,\cdot)\) \(\chi_{1521}(712,\cdot)\) \(\chi_{1521}(784,\cdot)\) \(\chi_{1521}(829,\cdot)\) \(\chi_{1521}(901,\cdot)\) \(\chi_{1521}(946,\cdot)\) \(\chi_{1521}(1018,\cdot)\) \(\chi_{1521}(1063,\cdot)\) \(\chi_{1521}(1135,\cdot)\) \(\chi_{1521}(1180,\cdot)\) \(\chi_{1521}(1252,\cdot)\) \(\chi_{1521}(1297,\cdot)\) \(\chi_{1521}(1369,\cdot)\) \(\chi_{1521}(1414,\cdot)\) \(\chi_{1521}(1486,\cdot)\)
Related number fields
Field of values: | $\Q(\zeta_{39})$ |
Fixed field: | Number field defined by a degree 78 polynomial |
Values on generators
\((677,847)\) → \((1,e\left(\frac{5}{78}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(11\) | \(14\) | \(16\) | \(17\) |
\( \chi_{ 1521 }(10, a) \) | \(1\) | \(1\) | \(e\left(\frac{5}{78}\right)\) | \(e\left(\frac{5}{39}\right)\) | \(e\left(\frac{15}{26}\right)\) | \(e\left(\frac{67}{78}\right)\) | \(e\left(\frac{5}{26}\right)\) | \(e\left(\frac{25}{39}\right)\) | \(e\left(\frac{47}{78}\right)\) | \(e\left(\frac{12}{13}\right)\) | \(e\left(\frac{10}{39}\right)\) | \(e\left(\frac{14}{39}\right)\) |