Basic properties
| Modulus: | \(18785\) | |
| Conductor: | \(18785\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(272\) | 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 18785.jb
\(\chi_{18785}(44,\cdot)\) \(\chi_{18785}(99,\cdot)\) \(\chi_{18785}(109,\cdot)\) \(\chi_{18785}(294,\cdot)\) \(\chi_{18785}(499,\cdot)\) \(\chi_{18785}(759,\cdot)\) \(\chi_{18785}(879,\cdot)\) \(\chi_{18785}(1074,\cdot)\) \(\chi_{18785}(1149,\cdot)\) \(\chi_{18785}(1204,\cdot)\) \(\chi_{18785}(1214,\cdot)\) \(\chi_{18785}(1399,\cdot)\) \(\chi_{18785}(1604,\cdot)\) \(\chi_{18785}(1864,\cdot)\) \(\chi_{18785}(1984,\cdot)\) \(\chi_{18785}(2179,\cdot)\) \(\chi_{18785}(2254,\cdot)\) \(\chi_{18785}(2309,\cdot)\) \(\chi_{18785}(2319,\cdot)\) \(\chi_{18785}(2504,\cdot)\) \(\chi_{18785}(2709,\cdot)\) \(\chi_{18785}(2969,\cdot)\) \(\chi_{18785}(3089,\cdot)\) \(\chi_{18785}(3284,\cdot)\) \(\chi_{18785}(3359,\cdot)\) \(\chi_{18785}(3414,\cdot)\) \(\chi_{18785}(3424,\cdot)\) \(\chi_{18785}(3609,\cdot)\) \(\chi_{18785}(3814,\cdot)\) \(\chi_{18785}(4074,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{272})$ |
| Fixed field: | Number field defined by a degree 272 polynomial (not computed) |
Values on generators
\((11272,10116,13586)\) → \((-1,-i,e\left(\frac{203}{272}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(7\) | \(8\) | \(9\) | \(11\) | \(12\) | \(14\) |
| \( \chi_{ 18785 }(109, a) \) | \(1\) | \(1\) | \(e\left(\frac{7}{136}\right)\) | \(e\left(\frac{67}{272}\right)\) | \(e\left(\frac{7}{68}\right)\) | \(e\left(\frac{81}{272}\right)\) | \(e\left(\frac{117}{272}\right)\) | \(e\left(\frac{21}{136}\right)\) | \(e\left(\frac{67}{136}\right)\) | \(e\left(\frac{113}{272}\right)\) | \(e\left(\frac{95}{272}\right)\) | \(e\left(\frac{131}{272}\right)\) |