Basic properties
Modulus: | \(953\) | |
Conductor: | \(953\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(476\) | 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 953.o
\(\chi_{953}(9,\cdot)\) \(\chi_{953}(13,\cdot)\) \(\chi_{953}(14,\cdot)\) \(\chi_{953}(17,\cdot)\) \(\chi_{953}(25,\cdot)\) \(\chi_{953}(30,\cdot)\) \(\chi_{953}(36,\cdot)\) \(\chi_{953}(37,\cdot)\) \(\chi_{953}(41,\cdot)\) \(\chi_{953}(52,\cdot)\) \(\chi_{953}(55,\cdot)\) \(\chi_{953}(56,\cdot)\) \(\chi_{953}(57,\cdot)\) \(\chi_{953}(58,\cdot)\) \(\chi_{953}(59,\cdot)\) \(\chi_{953}(63,\cdot)\) \(\chi_{953}(66,\cdot)\) \(\chi_{953}(68,\cdot)\) \(\chi_{953}(73,\cdot)\) \(\chi_{953}(79,\cdot)\) \(\chi_{953}(83,\cdot)\) \(\chi_{953}(91,\cdot)\) \(\chi_{953}(93,\cdot)\) \(\chi_{953}(100,\cdot)\) \(\chi_{953}(103,\cdot)\) \(\chi_{953}(106,\cdot)\) \(\chi_{953}(113,\cdot)\) \(\chi_{953}(115,\cdot)\) \(\chi_{953}(120,\cdot)\) \(\chi_{953}(121,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{476})$ |
Fixed field: | Number field defined by a degree 476 polynomial (not computed) |
Values on generators
\(3\) → \(e\left(\frac{47}{476}\right)\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
\( \chi_{ 953 }(25, a) \) | \(1\) | \(1\) | \(e\left(\frac{15}{34}\right)\) | \(e\left(\frac{47}{476}\right)\) | \(e\left(\frac{15}{17}\right)\) | \(e\left(\frac{305}{476}\right)\) | \(e\left(\frac{257}{476}\right)\) | \(e\left(\frac{46}{119}\right)\) | \(e\left(\frac{11}{34}\right)\) | \(e\left(\frac{47}{238}\right)\) | \(e\left(\frac{39}{476}\right)\) | \(e\left(\frac{337}{476}\right)\) |