Basic properties
| Modulus: | \(4050\) | |
| Conductor: | \(405\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(108\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{405}(257,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 4050.bm
\(\chi_{4050}(257,\cdot)\) \(\chi_{4050}(293,\cdot)\) \(\chi_{4050}(407,\cdot)\) \(\chi_{4050}(443,\cdot)\) \(\chi_{4050}(707,\cdot)\) \(\chi_{4050}(743,\cdot)\) \(\chi_{4050}(857,\cdot)\) \(\chi_{4050}(893,\cdot)\) \(\chi_{4050}(1157,\cdot)\) \(\chi_{4050}(1193,\cdot)\) \(\chi_{4050}(1307,\cdot)\) \(\chi_{4050}(1343,\cdot)\) \(\chi_{4050}(1607,\cdot)\) \(\chi_{4050}(1643,\cdot)\) \(\chi_{4050}(1757,\cdot)\) \(\chi_{4050}(1793,\cdot)\) \(\chi_{4050}(2057,\cdot)\) \(\chi_{4050}(2093,\cdot)\) \(\chi_{4050}(2207,\cdot)\) \(\chi_{4050}(2243,\cdot)\) \(\chi_{4050}(2507,\cdot)\) \(\chi_{4050}(2543,\cdot)\) \(\chi_{4050}(2657,\cdot)\) \(\chi_{4050}(2693,\cdot)\) \(\chi_{4050}(2957,\cdot)\) \(\chi_{4050}(2993,\cdot)\) \(\chi_{4050}(3107,\cdot)\) \(\chi_{4050}(3143,\cdot)\) \(\chi_{4050}(3407,\cdot)\) \(\chi_{4050}(3443,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{108})$ |
| Fixed field: | Number field defined by a degree 108 polynomial (not computed) |
Values on generators
\((2351,3727)\) → \((e\left(\frac{17}{54}\right),i)\)
First values
| \(a\) | \(-1\) | \(1\) | \(7\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(29\) | \(31\) | \(37\) | \(41\) |
| \( \chi_{ 4050 }(257, a) \) | \(1\) | \(1\) | \(e\left(\frac{31}{108}\right)\) | \(e\left(\frac{5}{54}\right)\) | \(e\left(\frac{29}{108}\right)\) | \(e\left(\frac{23}{36}\right)\) | \(e\left(\frac{11}{18}\right)\) | \(e\left(\frac{23}{108}\right)\) | \(e\left(\frac{4}{27}\right)\) | \(e\left(\frac{8}{27}\right)\) | \(e\left(\frac{17}{36}\right)\) | \(e\left(\frac{37}{54}\right)\) |