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 \(\chi_{573}(428,\cdot)\) | 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
\((2675,2866,2311)\) → \((-1,1,e\left(\frac{89}{95}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(8\) | \(10\) | \(11\) | \(13\) | \(16\) | \(17\) | \(19\) |
\( \chi_{ 4011 }(428, a) \) | \(-1\) | \(1\) | \(e\left(\frac{137}{190}\right)\) | \(e\left(\frac{42}{95}\right)\) | \(e\left(\frac{13}{38}\right)\) | \(e\left(\frac{31}{190}\right)\) | \(e\left(\frac{6}{95}\right)\) | \(e\left(\frac{5}{38}\right)\) | \(e\left(\frac{88}{95}\right)\) | \(e\left(\frac{84}{95}\right)\) | \(e\left(\frac{59}{190}\right)\) | \(e\left(\frac{89}{95}\right)\) |