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.bk
\(\chi_{1225}(34,\cdot)\) \(\chi_{1225}(69,\cdot)\) \(\chi_{1225}(104,\cdot)\) \(\chi_{1225}(139,\cdot)\) \(\chi_{1225}(209,\cdot)\) \(\chi_{1225}(279,\cdot)\) \(\chi_{1225}(314,\cdot)\) \(\chi_{1225}(384,\cdot)\) \(\chi_{1225}(419,\cdot)\) \(\chi_{1225}(454,\cdot)\) \(\chi_{1225}(559,\cdot)\) \(\chi_{1225}(594,\cdot)\) \(\chi_{1225}(629,\cdot)\) \(\chi_{1225}(664,\cdot)\) \(\chi_{1225}(769,\cdot)\) \(\chi_{1225}(804,\cdot)\) \(\chi_{1225}(839,\cdot)\) \(\chi_{1225}(909,\cdot)\) \(\chi_{1225}(944,\cdot)\) \(\chi_{1225}(1014,\cdot)\) \(\chi_{1225}(1084,\cdot)\) \(\chi_{1225}(1119,\cdot)\) \(\chi_{1225}(1154,\cdot)\) \(\chi_{1225}(1189,\cdot)\)
Related number fields
Field of values: | $\Q(\zeta_{35})$ |
Fixed field: | Number field defined by a degree 70 polynomial |
Values on generators
\((1177,101)\) → \((e\left(\frac{9}{10}\right),e\left(\frac{5}{14}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(8\) | \(9\) | \(11\) | \(12\) | \(13\) | \(16\) |
\( \chi_{ 1225 }(1119, a) \) | \(-1\) | \(1\) | \(e\left(\frac{13}{70}\right)\) | \(e\left(\frac{23}{35}\right)\) | \(e\left(\frac{13}{35}\right)\) | \(e\left(\frac{59}{70}\right)\) | \(e\left(\frac{39}{70}\right)\) | \(e\left(\frac{11}{35}\right)\) | \(e\left(\frac{24}{35}\right)\) | \(e\left(\frac{1}{35}\right)\) | \(e\left(\frac{31}{35}\right)\) | \(e\left(\frac{26}{35}\right)\) |