Basic properties
| Modulus: | \(6069\) | |
| Conductor: | \(6069\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(102\) | 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 6069.cc
\(\chi_{6069}(101,\cdot)\) \(\chi_{6069}(152,\cdot)\) \(\chi_{6069}(458,\cdot)\) \(\chi_{6069}(509,\cdot)\) \(\chi_{6069}(815,\cdot)\) \(\chi_{6069}(1172,\cdot)\) \(\chi_{6069}(1223,\cdot)\) \(\chi_{6069}(1529,\cdot)\) \(\chi_{6069}(1580,\cdot)\) \(\chi_{6069}(1886,\cdot)\) \(\chi_{6069}(1937,\cdot)\) \(\chi_{6069}(2243,\cdot)\) \(\chi_{6069}(2294,\cdot)\) \(\chi_{6069}(2651,\cdot)\) \(\chi_{6069}(2957,\cdot)\) \(\chi_{6069}(3008,\cdot)\) \(\chi_{6069}(3314,\cdot)\) \(\chi_{6069}(3365,\cdot)\) \(\chi_{6069}(3671,\cdot)\) \(\chi_{6069}(3722,\cdot)\) \(\chi_{6069}(4028,\cdot)\) \(\chi_{6069}(4079,\cdot)\) \(\chi_{6069}(4385,\cdot)\) \(\chi_{6069}(4436,\cdot)\) \(\chi_{6069}(4742,\cdot)\) \(\chi_{6069}(4793,\cdot)\) \(\chi_{6069}(5099,\cdot)\) \(\chi_{6069}(5150,\cdot)\) \(\chi_{6069}(5456,\cdot)\) \(\chi_{6069}(5507,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{51})$ |
| Fixed field: | Number field defined by a degree 102 polynomial (not computed) |
Values on generators
\((2024,4336,3760)\) → \((-1,e\left(\frac{1}{6}\right),e\left(\frac{9}{34}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(8\) | \(10\) | \(11\) | \(13\) | \(16\) | \(19\) | \(20\) |
| \( \chi_{ 6069 }(101, a) \) | \(1\) | \(1\) | \(e\left(\frac{13}{102}\right)\) | \(e\left(\frac{13}{51}\right)\) | \(e\left(\frac{97}{102}\right)\) | \(e\left(\frac{13}{34}\right)\) | \(e\left(\frac{4}{51}\right)\) | \(e\left(\frac{13}{51}\right)\) | \(e\left(\frac{13}{34}\right)\) | \(e\left(\frac{26}{51}\right)\) | \(e\left(\frac{55}{102}\right)\) | \(e\left(\frac{7}{34}\right)\) |