Basic properties
Modulus: | \(4730\) | |
Conductor: | \(473\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(105\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
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Real: | no | |
Primitive: | no, induced from \(\chi_{473}(225,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 4730.dc
\(\chi_{4730}(31,\cdot)\) \(\chi_{4730}(81,\cdot)\) \(\chi_{4730}(181,\cdot)\) \(\chi_{4730}(311,\cdot)\) \(\chi_{4730}(361,\cdot)\) \(\chi_{4730}(401,\cdot)\) \(\chi_{4730}(411,\cdot)\) \(\chi_{4730}(511,\cdot)\) \(\chi_{4730}(531,\cdot)\) \(\chi_{4730}(741,\cdot)\) \(\chi_{4730}(841,\cdot)\) \(\chi_{4730}(961,\cdot)\) \(\chi_{4730}(971,\cdot)\) \(\chi_{4730}(1131,\cdot)\) \(\chi_{4730}(1171,\cdot)\) \(\chi_{4730}(1391,\cdot)\) \(\chi_{4730}(1401,\cdot)\) \(\chi_{4730}(1571,\cdot)\) \(\chi_{4730}(1631,\cdot)\) \(\chi_{4730}(1831,\cdot)\) \(\chi_{4730}(1901,\cdot)\) \(\chi_{4730}(2061,\cdot)\) \(\chi_{4730}(2121,\cdot)\) \(\chi_{4730}(2181,\cdot)\) \(\chi_{4730}(2231,\cdot)\) \(\chi_{4730}(2491,\cdot)\) \(\chi_{4730}(2511,\cdot)\) \(\chi_{4730}(2561,\cdot)\) \(\chi_{4730}(2611,\cdot)\) \(\chi_{4730}(2891,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{105})$ |
Fixed field: | Number field defined by a degree 105 polynomial (not computed) |
Values on generators
\((947,431,1981)\) → \((1,e\left(\frac{2}{5}\right),e\left(\frac{5}{21}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(3\) | \(7\) | \(9\) | \(13\) | \(17\) | \(19\) | \(21\) | \(23\) | \(27\) | \(29\) |
\( \chi_{ 4730 }(1171, a) \) | \(1\) | \(1\) | \(e\left(\frac{46}{105}\right)\) | \(e\left(\frac{2}{15}\right)\) | \(e\left(\frac{92}{105}\right)\) | \(e\left(\frac{2}{105}\right)\) | \(e\left(\frac{68}{105}\right)\) | \(e\left(\frac{76}{105}\right)\) | \(e\left(\frac{4}{7}\right)\) | \(e\left(\frac{17}{21}\right)\) | \(e\left(\frac{11}{35}\right)\) | \(e\left(\frac{59}{105}\right)\) |