Basic properties
Modulus: | \(931\) | |
Conductor: | \(931\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(126\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
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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.ch
\(\chi_{931}(13,\cdot)\) \(\chi_{931}(34,\cdot)\) \(\chi_{931}(41,\cdot)\) \(\chi_{931}(90,\cdot)\) \(\chi_{931}(167,\cdot)\) \(\chi_{931}(174,\cdot)\) \(\chi_{931}(181,\cdot)\) \(\chi_{931}(223,\cdot)\) \(\chi_{931}(230,\cdot)\) \(\chi_{931}(279,\cdot)\) \(\chi_{931}(300,\cdot)\) \(\chi_{931}(307,\cdot)\) \(\chi_{931}(314,\cdot)\) \(\chi_{931}(356,\cdot)\) \(\chi_{931}(363,\cdot)\) \(\chi_{931}(412,\cdot)\) \(\chi_{931}(433,\cdot)\) \(\chi_{931}(447,\cdot)\) \(\chi_{931}(496,\cdot)\) \(\chi_{931}(545,\cdot)\) \(\chi_{931}(566,\cdot)\) \(\chi_{931}(573,\cdot)\) \(\chi_{931}(580,\cdot)\) \(\chi_{931}(622,\cdot)\) \(\chi_{931}(629,\cdot)\) \(\chi_{931}(678,\cdot)\) \(\chi_{931}(699,\cdot)\) \(\chi_{931}(706,\cdot)\) \(\chi_{931}(713,\cdot)\) \(\chi_{931}(755,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{63})$ |
Fixed field: | Number field defined by a degree 126 polynomial (not computed) |
Values on generators
\((248,344)\) → \((e\left(\frac{1}{14}\right),e\left(\frac{17}{18}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(8\) | \(9\) | \(10\) | \(11\) | \(12\) |
\( \chi_{ 931 }(713, a) \) | \(1\) | \(1\) | \(e\left(\frac{101}{126}\right)\) | \(e\left(\frac{22}{63}\right)\) | \(e\left(\frac{38}{63}\right)\) | \(e\left(\frac{23}{126}\right)\) | \(e\left(\frac{19}{126}\right)\) | \(e\left(\frac{17}{42}\right)\) | \(e\left(\frac{44}{63}\right)\) | \(e\left(\frac{62}{63}\right)\) | \(e\left(\frac{4}{21}\right)\) | \(e\left(\frac{20}{21}\right)\) |