Basic properties
| Modulus: | \(4011\) | |
| Conductor: | \(191\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(190\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{191}(58,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 4011.cb
\(\chi_{4011}(22,\cdot)\) \(\chi_{4011}(106,\cdot)\) \(\chi_{4011}(127,\cdot)\) \(\chi_{4011}(148,\cdot)\) \(\chi_{4011}(253,\cdot)\) \(\chi_{4011}(274,\cdot)\) \(\chi_{4011}(337,\cdot)\) \(\chi_{4011}(358,\cdot)\) \(\chi_{4011}(379,\cdot)\) \(\chi_{4011}(505,\cdot)\) \(\chi_{4011}(547,\cdot)\) \(\chi_{4011}(631,\cdot)\) \(\chi_{4011}(799,\cdot)\) \(\chi_{4011}(820,\cdot)\) \(\chi_{4011}(883,\cdot)\) \(\chi_{4011}(904,\cdot)\) \(\chi_{4011}(946,\cdot)\) \(\chi_{4011}(988,\cdot)\) \(\chi_{4011}(1219,\cdot)\) \(\chi_{4011}(1240,\cdot)\) \(\chi_{4011}(1303,\cdot)\) \(\chi_{4011}(1324,\cdot)\) \(\chi_{4011}(1366,\cdot)\) \(\chi_{4011}(1408,\cdot)\) \(\chi_{4011}(1450,\cdot)\) \(\chi_{4011}(1513,\cdot)\) \(\chi_{4011}(1639,\cdot)\) \(\chi_{4011}(1660,\cdot)\) \(\chi_{4011}(1702,\cdot)\) \(\chi_{4011}(1807,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{95})$ |
| Fixed field: | Number field defined by a degree 190 polynomial (not computed) |
Values on generators
\((2675,2866,2311)\) → \((1,1,e\left(\frac{77}{190}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(8\) | \(10\) | \(11\) | \(13\) | \(16\) | \(17\) | \(19\) |
| \( \chi_{ 4011 }(631, a) \) | \(-1\) | \(1\) | \(e\left(\frac{79}{95}\right)\) | \(e\left(\frac{63}{95}\right)\) | \(e\left(\frac{5}{19}\right)\) | \(e\left(\frac{47}{95}\right)\) | \(e\left(\frac{9}{95}\right)\) | \(e\left(\frac{17}{38}\right)\) | \(e\left(\frac{37}{95}\right)\) | \(e\left(\frac{31}{95}\right)\) | \(e\left(\frac{68}{95}\right)\) | \(e\left(\frac{77}{190}\right)\) |