Basic properties
Modulus: | \(8033\) | |
Conductor: | \(8033\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(92\) | 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 8033.bt
\(\chi_{8033}(104,\cdot)\) \(\chi_{8033}(128,\cdot)\) \(\chi_{8033}(244,\cdot)\) \(\chi_{8033}(539,\cdot)\) \(\chi_{8033}(713,\cdot)\) \(\chi_{8033}(940,\cdot)\) \(\chi_{8033}(1699,\cdot)\) \(\chi_{8033}(1810,\cdot)\) \(\chi_{8033}(1931,\cdot)\) \(\chi_{8033}(2071,\cdot)\) \(\chi_{8033}(2134,\cdot)\) \(\chi_{8033}(2535,\cdot)\) \(\chi_{8033}(2709,\cdot)\) \(\chi_{8033}(2738,\cdot)\) \(\chi_{8033}(2772,\cdot)\) \(\chi_{8033}(2796,\cdot)\) \(\chi_{8033}(3120,\cdot)\) \(\chi_{8033}(3463,\cdot)\) \(\chi_{8033}(3550,\cdot)\) \(\chi_{8033}(3753,\cdot)\) \(\chi_{8033}(3840,\cdot)\) \(\chi_{8033}(3932,\cdot)\) \(\chi_{8033}(4101,\cdot)\) \(\chi_{8033}(4193,\cdot)\) \(\chi_{8033}(4280,\cdot)\) \(\chi_{8033}(4483,\cdot)\) \(\chi_{8033}(4570,\cdot)\) \(\chi_{8033}(4913,\cdot)\) \(\chi_{8033}(5237,\cdot)\) \(\chi_{8033}(5261,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{92})$ |
Fixed field: | Number field defined by a degree 92 polynomial |
Values on generators
\((5541,1944)\) → \((-i,e\left(\frac{29}{92}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
\( \chi_{ 8033 }(1699, a) \) | \(1\) | \(1\) | \(e\left(\frac{2}{23}\right)\) | \(e\left(\frac{1}{92}\right)\) | \(e\left(\frac{4}{23}\right)\) | \(e\left(\frac{75}{92}\right)\) | \(e\left(\frac{9}{92}\right)\) | \(e\left(\frac{43}{46}\right)\) | \(e\left(\frac{6}{23}\right)\) | \(e\left(\frac{1}{46}\right)\) | \(e\left(\frac{83}{92}\right)\) | \(e\left(\frac{22}{23}\right)\) |