Basic properties
| Modulus: | \(4011\) | |
| Conductor: | \(573\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(190\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{573}(80,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 4011.ca
\(\chi_{4011}(8,\cdot)\) \(\chi_{4011}(50,\cdot)\) \(\chi_{4011}(92,\cdot)\) \(\chi_{4011}(134,\cdot)\) \(\chi_{4011}(218,\cdot)\) \(\chi_{4011}(239,\cdot)\) \(\chi_{4011}(281,\cdot)\) \(\chi_{4011}(386,\cdot)\) \(\chi_{4011}(428,\cdot)\) \(\chi_{4011}(449,\cdot)\) \(\chi_{4011}(512,\cdot)\) \(\chi_{4011}(554,\cdot)\) \(\chi_{4011}(575,\cdot)\) \(\chi_{4011}(596,\cdot)\) \(\chi_{4011}(638,\cdot)\) \(\chi_{4011}(659,\cdot)\) \(\chi_{4011}(701,\cdot)\) \(\chi_{4011}(722,\cdot)\) \(\chi_{4011}(743,\cdot)\) \(\chi_{4011}(911,\cdot)\) \(\chi_{4011}(995,\cdot)\) \(\chi_{4011}(1058,\cdot)\) \(\chi_{4011}(1163,\cdot)\) \(\chi_{4011}(1205,\cdot)\) \(\chi_{4011}(1226,\cdot)\) \(\chi_{4011}(1352,\cdot)\) \(\chi_{4011}(1415,\cdot)\) \(\chi_{4011}(1457,\cdot)\) \(\chi_{4011}(1499,\cdot)\) \(\chi_{4011}(1541,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{95})$ |
| Fixed field: | Number field defined by a degree 190 polynomial (not computed) |
Values on generators
\((2675,2866,2311)\) → \((-1,1,e\left(\frac{18}{95}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(8\) | \(10\) | \(11\) | \(13\) | \(16\) | \(17\) | \(19\) |
| \( \chi_{ 4011 }(1226, a) \) | \(-1\) | \(1\) | \(e\left(\frac{159}{190}\right)\) | \(e\left(\frac{64}{95}\right)\) | \(e\left(\frac{37}{38}\right)\) | \(e\left(\frac{97}{190}\right)\) | \(e\left(\frac{77}{95}\right)\) | \(e\left(\frac{23}{38}\right)\) | \(e\left(\frac{21}{95}\right)\) | \(e\left(\frac{33}{95}\right)\) | \(e\left(\frac{13}{190}\right)\) | \(e\left(\frac{18}{95}\right)\) |