Basic properties
Modulus: | \(4011\) | |
Conductor: | \(573\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(190\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
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Real: | no | |
Primitive: | no, induced from \(\chi_{573}(71,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 4011.bz
\(\chi_{4011}(29,\cdot)\) \(\chi_{4011}(71,\cdot)\) \(\chi_{4011}(113,\cdot)\) \(\chi_{4011}(176,\cdot)\) \(\chi_{4011}(302,\cdot)\) \(\chi_{4011}(323,\cdot)\) \(\chi_{4011}(365,\cdot)\) \(\chi_{4011}(470,\cdot)\) \(\chi_{4011}(533,\cdot)\) \(\chi_{4011}(617,\cdot)\) \(\chi_{4011}(785,\cdot)\) \(\chi_{4011}(806,\cdot)\) \(\chi_{4011}(827,\cdot)\) \(\chi_{4011}(869,\cdot)\) \(\chi_{4011}(890,\cdot)\) \(\chi_{4011}(932,\cdot)\) \(\chi_{4011}(953,\cdot)\) \(\chi_{4011}(974,\cdot)\) \(\chi_{4011}(1016,\cdot)\) \(\chi_{4011}(1079,\cdot)\) \(\chi_{4011}(1100,\cdot)\) \(\chi_{4011}(1142,\cdot)\) \(\chi_{4011}(1247,\cdot)\) \(\chi_{4011}(1289,\cdot)\) \(\chi_{4011}(1310,\cdot)\) \(\chi_{4011}(1394,\cdot)\) \(\chi_{4011}(1436,\cdot)\) \(\chi_{4011}(1478,\cdot)\) \(\chi_{4011}(1520,\cdot)\) \(\chi_{4011}(1604,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{95})$ |
Fixed field: | Number field defined by a degree 190 polynomial (not computed) |
Values on generators
\((2675,2866,2311)\) → \((-1,1,e\left(\frac{13}{190}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(8\) | \(10\) | \(11\) | \(13\) | \(16\) | \(17\) | \(19\) |
\( \chi_{ 4011 }(71, a) \) | \(1\) | \(1\) | \(e\left(\frac{97}{190}\right)\) | \(e\left(\frac{2}{95}\right)\) | \(e\left(\frac{35}{38}\right)\) | \(e\left(\frac{101}{190}\right)\) | \(e\left(\frac{41}{95}\right)\) | \(e\left(\frac{6}{19}\right)\) | \(e\left(\frac{63}{95}\right)\) | \(e\left(\frac{4}{95}\right)\) | \(e\left(\frac{39}{190}\right)\) | \(e\left(\frac{13}{190}\right)\) |