Basic properties
| Modulus: | \(4598\) | |
| Conductor: | \(2299\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(99\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{2299}(23,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 4598.bh
\(\chi_{4598}(23,\cdot)\) \(\chi_{4598}(111,\cdot)\) \(\chi_{4598}(177,\cdot)\) \(\chi_{4598}(199,\cdot)\) \(\chi_{4598}(309,\cdot)\) \(\chi_{4598}(397,\cdot)\) \(\chi_{4598}(441,\cdot)\) \(\chi_{4598}(529,\cdot)\) \(\chi_{4598}(595,\cdot)\) \(\chi_{4598}(617,\cdot)\) \(\chi_{4598}(815,\cdot)\) \(\chi_{4598}(859,\cdot)\) \(\chi_{4598}(947,\cdot)\) \(\chi_{4598}(1013,\cdot)\) \(\chi_{4598}(1035,\cdot)\) \(\chi_{4598}(1145,\cdot)\) \(\chi_{4598}(1233,\cdot)\) \(\chi_{4598}(1277,\cdot)\) \(\chi_{4598}(1365,\cdot)\) \(\chi_{4598}(1431,\cdot)\) \(\chi_{4598}(1563,\cdot)\) \(\chi_{4598}(1651,\cdot)\) \(\chi_{4598}(1783,\cdot)\) \(\chi_{4598}(1849,\cdot)\) \(\chi_{4598}(1871,\cdot)\) \(\chi_{4598}(1981,\cdot)\) \(\chi_{4598}(2069,\cdot)\) \(\chi_{4598}(2113,\cdot)\) \(\chi_{4598}(2201,\cdot)\) \(\chi_{4598}(2267,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{99})$ |
| Fixed field: | Number field defined by a degree 99 polynomial |
Values on generators
\((3269,3631)\) → \((e\left(\frac{7}{11}\right),e\left(\frac{1}{9}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(13\) | \(15\) | \(17\) | \(21\) | \(23\) | \(25\) |
| \( \chi_{ 4598 }(23, a) \) | \(1\) | \(1\) | \(e\left(\frac{4}{9}\right)\) | \(e\left(\frac{86}{99}\right)\) | \(e\left(\frac{4}{33}\right)\) | \(e\left(\frac{8}{9}\right)\) | \(e\left(\frac{82}{99}\right)\) | \(e\left(\frac{31}{99}\right)\) | \(e\left(\frac{29}{99}\right)\) | \(e\left(\frac{56}{99}\right)\) | \(e\left(\frac{76}{99}\right)\) | \(e\left(\frac{73}{99}\right)\) |