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: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 1225.bj
\(\chi_{1225}(29,\cdot)\) \(\chi_{1225}(64,\cdot)\) \(\chi_{1225}(134,\cdot)\) \(\chi_{1225}(169,\cdot)\) \(\chi_{1225}(204,\cdot)\) \(\chi_{1225}(239,\cdot)\) \(\chi_{1225}(309,\cdot)\) \(\chi_{1225}(379,\cdot)\) \(\chi_{1225}(414,\cdot)\) \(\chi_{1225}(484,\cdot)\) \(\chi_{1225}(519,\cdot)\) \(\chi_{1225}(554,\cdot)\) \(\chi_{1225}(659,\cdot)\) \(\chi_{1225}(694,\cdot)\) \(\chi_{1225}(729,\cdot)\) \(\chi_{1225}(764,\cdot)\) \(\chi_{1225}(869,\cdot)\) \(\chi_{1225}(904,\cdot)\) \(\chi_{1225}(939,\cdot)\) \(\chi_{1225}(1009,\cdot)\) \(\chi_{1225}(1044,\cdot)\) \(\chi_{1225}(1114,\cdot)\) \(\chi_{1225}(1184,\cdot)\) \(\chi_{1225}(1219,\cdot)\)
Related number fields
Field of values: | $\Q(\zeta_{35})$ |
Fixed field: | Number field defined by a degree 70 polynomial |
Values on generators
\((1177,101)\) → \((e\left(\frac{3}{10}\right),e\left(\frac{5}{7}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(8\) | \(9\) | \(11\) | \(12\) | \(13\) | \(16\) |
\( \chi_{ 1225 }(64, a) \) | \(1\) | \(1\) | \(e\left(\frac{61}{70}\right)\) | \(e\left(\frac{57}{70}\right)\) | \(e\left(\frac{26}{35}\right)\) | \(e\left(\frac{24}{35}\right)\) | \(e\left(\frac{43}{70}\right)\) | \(e\left(\frac{22}{35}\right)\) | \(e\left(\frac{13}{35}\right)\) | \(e\left(\frac{39}{70}\right)\) | \(e\left(\frac{19}{70}\right)\) | \(e\left(\frac{17}{35}\right)\) |