Basic properties
Modulus: | \(6069\) | |
Conductor: | \(2023\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(102\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
Real: | no | |
Primitive: | no, induced from \(\chi_{2023}(492,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 6069.cf
\(\chi_{6069}(16,\cdot)\) \(\chi_{6069}(67,\cdot)\) \(\chi_{6069}(373,\cdot)\) \(\chi_{6069}(424,\cdot)\) \(\chi_{6069}(730,\cdot)\) \(\chi_{6069}(781,\cdot)\) \(\chi_{6069}(1087,\cdot)\) \(\chi_{6069}(1138,\cdot)\) \(\chi_{6069}(1495,\cdot)\) \(\chi_{6069}(1801,\cdot)\) \(\chi_{6069}(1852,\cdot)\) \(\chi_{6069}(2158,\cdot)\) \(\chi_{6069}(2209,\cdot)\) \(\chi_{6069}(2515,\cdot)\) \(\chi_{6069}(2566,\cdot)\) \(\chi_{6069}(2872,\cdot)\) \(\chi_{6069}(2923,\cdot)\) \(\chi_{6069}(3229,\cdot)\) \(\chi_{6069}(3280,\cdot)\) \(\chi_{6069}(3586,\cdot)\) \(\chi_{6069}(3637,\cdot)\) \(\chi_{6069}(3943,\cdot)\) \(\chi_{6069}(3994,\cdot)\) \(\chi_{6069}(4300,\cdot)\) \(\chi_{6069}(4351,\cdot)\) \(\chi_{6069}(4657,\cdot)\) \(\chi_{6069}(4708,\cdot)\) \(\chi_{6069}(5014,\cdot)\) \(\chi_{6069}(5065,\cdot)\) \(\chi_{6069}(5371,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{51})$ |
Fixed field: | Number field defined by a degree 102 polynomial (not computed) |
Values on generators
\((2024,4336,3760)\) → \((1,e\left(\frac{1}{3}\right),e\left(\frac{1}{34}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(8\) | \(10\) | \(11\) | \(13\) | \(16\) | \(19\) | \(20\) |
\( \chi_{ 6069 }(2515, a) \) | \(1\) | \(1\) | \(e\left(\frac{13}{51}\right)\) | \(e\left(\frac{26}{51}\right)\) | \(e\left(\frac{41}{102}\right)\) | \(e\left(\frac{13}{17}\right)\) | \(e\left(\frac{67}{102}\right)\) | \(e\left(\frac{1}{102}\right)\) | \(e\left(\frac{13}{17}\right)\) | \(e\left(\frac{1}{51}\right)\) | \(e\left(\frac{4}{51}\right)\) | \(e\left(\frac{31}{34}\right)\) |