Basic properties
| Modulus: | \(2028\) | |
| Conductor: | \(676\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(156\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{676}(7,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 2028.bs
\(\chi_{2028}(7,\cdot)\) \(\chi_{2028}(67,\cdot)\) \(\chi_{2028}(115,\cdot)\) \(\chi_{2028}(163,\cdot)\) \(\chi_{2028}(175,\cdot)\) \(\chi_{2028}(223,\cdot)\) \(\chi_{2028}(271,\cdot)\) \(\chi_{2028}(331,\cdot)\) \(\chi_{2028}(379,\cdot)\) \(\chi_{2028}(475,\cdot)\) \(\chi_{2028}(487,\cdot)\) \(\chi_{2028}(535,\cdot)\) \(\chi_{2028}(583,\cdot)\) \(\chi_{2028}(631,\cdot)\) \(\chi_{2028}(643,\cdot)\) \(\chi_{2028}(691,\cdot)\) \(\chi_{2028}(739,\cdot)\) \(\chi_{2028}(787,\cdot)\) \(\chi_{2028}(799,\cdot)\) \(\chi_{2028}(847,\cdot)\) \(\chi_{2028}(895,\cdot)\) \(\chi_{2028}(943,\cdot)\) \(\chi_{2028}(955,\cdot)\) \(\chi_{2028}(1003,\cdot)\) \(\chi_{2028}(1051,\cdot)\) \(\chi_{2028}(1099,\cdot)\) \(\chi_{2028}(1111,\cdot)\) \(\chi_{2028}(1159,\cdot)\) \(\chi_{2028}(1207,\cdot)\) \(\chi_{2028}(1255,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{156})$ |
| Fixed field: | Number field defined by a degree 156 polynomial (not computed) |
Values on generators
\((1015,677,1861)\) → \((-1,1,e\left(\frac{107}{156}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(5\) | \(7\) | \(11\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) | \(35\) |
| \( \chi_{ 2028 }(7, a) \) | \(1\) | \(1\) | \(e\left(\frac{9}{52}\right)\) | \(e\left(\frac{139}{156}\right)\) | \(e\left(\frac{23}{156}\right)\) | \(e\left(\frac{11}{78}\right)\) | \(e\left(\frac{1}{12}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{9}{26}\right)\) | \(e\left(\frac{17}{39}\right)\) | \(e\left(\frac{47}{52}\right)\) | \(e\left(\frac{5}{78}\right)\) |