Basic properties
Modulus: | \(1225\) | |
Conductor: | \(1225\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(70\) | 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 1225.bl
\(\chi_{1225}(6,\cdot)\) \(\chi_{1225}(41,\cdot)\) \(\chi_{1225}(111,\cdot)\) \(\chi_{1225}(181,\cdot)\) \(\chi_{1225}(216,\cdot)\) \(\chi_{1225}(286,\cdot)\) \(\chi_{1225}(321,\cdot)\) \(\chi_{1225}(356,\cdot)\) \(\chi_{1225}(461,\cdot)\) \(\chi_{1225}(496,\cdot)\) \(\chi_{1225}(531,\cdot)\) \(\chi_{1225}(566,\cdot)\) \(\chi_{1225}(671,\cdot)\) \(\chi_{1225}(706,\cdot)\) \(\chi_{1225}(741,\cdot)\) \(\chi_{1225}(811,\cdot)\) \(\chi_{1225}(846,\cdot)\) \(\chi_{1225}(916,\cdot)\) \(\chi_{1225}(986,\cdot)\) \(\chi_{1225}(1021,\cdot)\) \(\chi_{1225}(1056,\cdot)\) \(\chi_{1225}(1091,\cdot)\) \(\chi_{1225}(1161,\cdot)\) \(\chi_{1225}(1196,\cdot)\)
Related number fields
Field of values: | $\Q(\zeta_{35})$ |
Fixed field: | Number field defined by a degree 70 polynomial |
Values on generators
\((1177,101)\) → \((e\left(\frac{1}{5}\right),e\left(\frac{5}{14}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(8\) | \(9\) | \(11\) | \(12\) | \(13\) | \(16\) |
\( \chi_{ 1225 }(41, a) \) | \(-1\) | \(1\) | \(e\left(\frac{17}{35}\right)\) | \(e\left(\frac{53}{70}\right)\) | \(e\left(\frac{34}{35}\right)\) | \(e\left(\frac{17}{70}\right)\) | \(e\left(\frac{16}{35}\right)\) | \(e\left(\frac{18}{35}\right)\) | \(e\left(\frac{17}{35}\right)\) | \(e\left(\frac{51}{70}\right)\) | \(e\left(\frac{41}{70}\right)\) | \(e\left(\frac{33}{35}\right)\) |