Basic properties
| Modulus: | \(100014\) | |
| Conductor: | \(50007\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(910\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{50007}(89,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 100014.la
\(\chi_{100014}(89,\cdot)\) \(\chi_{100014}(719,\cdot)\) \(\chi_{100014}(1073,\cdot)\) \(\chi_{100014}(1601,\cdot)\) \(\chi_{100014}(1835,\cdot)\) \(\chi_{100014}(1985,\cdot)\) \(\chi_{100014}(1997,\cdot)\) \(\chi_{100014}(3089,\cdot)\) \(\chi_{100014}(4037,\cdot)\) \(\chi_{100014}(4355,\cdot)\) \(\chi_{100014}(4367,\cdot)\) \(\chi_{100014}(4871,\cdot)\) \(\chi_{100014}(4985,\cdot)\) \(\chi_{100014}(5039,\cdot)\) \(\chi_{100014}(5153,\cdot)\) \(\chi_{100014}(5303,\cdot)\) \(\chi_{100014}(5513,\cdot)\) \(\chi_{100014}(6251,\cdot)\) \(\chi_{100014}(6305,\cdot)\) \(\chi_{100014}(6779,\cdot)\) \(\chi_{100014}(6881,\cdot)\) \(\chi_{100014}(7049,\cdot)\) \(\chi_{100014}(7289,\cdot)\) \(\chi_{100014}(7685,\cdot)\) \(\chi_{100014}(8147,\cdot)\) \(\chi_{100014}(8237,\cdot)\) \(\chi_{100014}(8711,\cdot)\) \(\chi_{100014}(9419,\cdot)\) \(\chi_{100014}(9581,\cdot)\) \(\chi_{100014}(10019,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{455})$ |
| Fixed field: | Number field defined by a degree 910 polynomial (not computed) |
Values on generators
\((66677,1267,32707)\) → \((-1,e\left(\frac{11}{13}\right),e\left(\frac{33}{70}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(5\) | \(7\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) |
| \( \chi_{ 100014 }(89, a) \) | \(1\) | \(1\) | \(e\left(\frac{173}{910}\right)\) | \(e\left(\frac{341}{910}\right)\) | \(e\left(\frac{373}{910}\right)\) | \(e\left(\frac{298}{455}\right)\) | \(e\left(\frac{38}{455}\right)\) | \(e\left(\frac{44}{65}\right)\) | \(e\left(\frac{2}{5}\right)\) | \(e\left(\frac{173}{455}\right)\) | \(e\left(\frac{88}{455}\right)\) | \(e\left(\frac{109}{182}\right)\) |