Basic properties
| Modulus: | \(931\) | |
| Conductor: | \(931\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(63\) | 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 931.ca
\(\chi_{931}(4,\cdot)\) \(\chi_{931}(16,\cdot)\) \(\chi_{931}(25,\cdot)\) \(\chi_{931}(93,\cdot)\) \(\chi_{931}(100,\cdot)\) \(\chi_{931}(123,\cdot)\) \(\chi_{931}(137,\cdot)\) \(\chi_{931}(149,\cdot)\) \(\chi_{931}(158,\cdot)\) \(\chi_{931}(233,\cdot)\) \(\chi_{931}(256,\cdot)\) \(\chi_{931}(270,\cdot)\) \(\chi_{931}(282,\cdot)\) \(\chi_{931}(291,\cdot)\) \(\chi_{931}(359,\cdot)\) \(\chi_{931}(366,\cdot)\) \(\chi_{931}(389,\cdot)\) \(\chi_{931}(403,\cdot)\) \(\chi_{931}(415,\cdot)\) \(\chi_{931}(424,\cdot)\) \(\chi_{931}(492,\cdot)\) \(\chi_{931}(499,\cdot)\) \(\chi_{931}(522,\cdot)\) \(\chi_{931}(536,\cdot)\) \(\chi_{931}(548,\cdot)\) \(\chi_{931}(625,\cdot)\) \(\chi_{931}(632,\cdot)\) \(\chi_{931}(669,\cdot)\) \(\chi_{931}(681,\cdot)\) \(\chi_{931}(690,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{63})$ |
| Fixed field: | Number field defined by a degree 63 polynomial |
Values on generators
\((248,344)\) → \((e\left(\frac{5}{21}\right),e\left(\frac{1}{9}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(8\) | \(9\) | \(10\) | \(11\) | \(12\) |
| \( \chi_{ 931 }(4, a) \) | \(1\) | \(1\) | \(e\left(\frac{19}{63}\right)\) | \(e\left(\frac{43}{63}\right)\) | \(e\left(\frac{38}{63}\right)\) | \(e\left(\frac{43}{63}\right)\) | \(e\left(\frac{62}{63}\right)\) | \(e\left(\frac{19}{21}\right)\) | \(e\left(\frac{23}{63}\right)\) | \(e\left(\frac{62}{63}\right)\) | \(e\left(\frac{6}{7}\right)\) | \(e\left(\frac{2}{7}\right)\) |