Basic properties
Modulus: | \(9464\) | |
Conductor: | \(676\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(52\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
Real: | no | |
Primitive: | no, induced from \(\chi_{676}(463,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | no | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 9464.fr
\(\chi_{9464}(463,\cdot)\) \(\chi_{9464}(967,\cdot)\) \(\chi_{9464}(1191,\cdot)\) \(\chi_{9464}(1695,\cdot)\) \(\chi_{9464}(1919,\cdot)\) \(\chi_{9464}(2423,\cdot)\) \(\chi_{9464}(2647,\cdot)\) \(\chi_{9464}(3151,\cdot)\) \(\chi_{9464}(3375,\cdot)\) \(\chi_{9464}(3879,\cdot)\) \(\chi_{9464}(4103,\cdot)\) \(\chi_{9464}(4607,\cdot)\) \(\chi_{9464}(5335,\cdot)\) \(\chi_{9464}(5559,\cdot)\) \(\chi_{9464}(6063,\cdot)\) \(\chi_{9464}(6287,\cdot)\) \(\chi_{9464}(6791,\cdot)\) \(\chi_{9464}(7015,\cdot)\) \(\chi_{9464}(7519,\cdot)\) \(\chi_{9464}(7743,\cdot)\) \(\chi_{9464}(8247,\cdot)\) \(\chi_{9464}(8471,\cdot)\) \(\chi_{9464}(8975,\cdot)\) \(\chi_{9464}(9199,\cdot)\)
Related number fields
Field of values: | $\Q(\zeta_{52})$ |
Fixed field: | Number field defined by a degree 52 polynomial |
Values on generators
\((2367,4733,2705,9297)\) → \((-1,1,1,e\left(\frac{9}{52}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(9\) | \(11\) | \(15\) | \(17\) | \(19\) | \(23\) | \(25\) | \(27\) |
\( \chi_{ 9464 }(463, a) \) | \(1\) | \(1\) | \(e\left(\frac{25}{26}\right)\) | \(e\left(\frac{29}{52}\right)\) | \(e\left(\frac{12}{13}\right)\) | \(e\left(\frac{17}{52}\right)\) | \(e\left(\frac{27}{52}\right)\) | \(e\left(\frac{7}{26}\right)\) | \(-i\) | \(1\) | \(e\left(\frac{3}{26}\right)\) | \(e\left(\frac{23}{26}\right)\) |