Basic properties
| Modulus: | \(751\) | |
| Conductor: | \(751\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(375\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | yes | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 751.o
\(\chi_{751}(2,\cdot)\) \(\chi_{751}(4,\cdot)\) \(\chi_{751}(5,\cdot)\) \(\chi_{751}(9,\cdot)\) \(\chi_{751}(13,\cdot)\) \(\chi_{751}(16,\cdot)\) \(\chi_{751}(18,\cdot)\) \(\chi_{751}(19,\cdot)\) \(\chi_{751}(20,\cdot)\) \(\chi_{751}(21,\cdot)\) \(\chi_{751}(23,\cdot)\) \(\chi_{751}(25,\cdot)\) \(\chi_{751}(33,\cdot)\) \(\chi_{751}(37,\cdot)\) \(\chi_{751}(40,\cdot)\) \(\chi_{751}(47,\cdot)\) \(\chi_{751}(50,\cdot)\) \(\chi_{751}(59,\cdot)\) \(\chi_{751}(65,\cdot)\) \(\chi_{751}(66,\cdot)\) \(\chi_{751}(74,\cdot)\) \(\chi_{751}(77,\cdot)\) \(\chi_{751}(81,\cdot)\) \(\chi_{751}(84,\cdot)\) \(\chi_{751}(87,\cdot)\) \(\chi_{751}(89,\cdot)\) \(\chi_{751}(90,\cdot)\) \(\chi_{751}(92,\cdot)\) \(\chi_{751}(95,\cdot)\) \(\chi_{751}(97,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{375})$ |
| Fixed field: | Number field defined by a degree 375 polynomial (not computed) |
Values on generators
\(3\) → \(e\left(\frac{208}{375}\right)\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 751 }(2, a) \) | \(1\) | \(1\) | \(e\left(\frac{278}{375}\right)\) | \(e\left(\frac{208}{375}\right)\) | \(e\left(\frac{181}{375}\right)\) | \(e\left(\frac{88}{375}\right)\) | \(e\left(\frac{37}{125}\right)\) | \(e\left(\frac{11}{125}\right)\) | \(e\left(\frac{28}{125}\right)\) | \(e\left(\frac{41}{375}\right)\) | \(e\left(\frac{122}{125}\right)\) | \(e\left(\frac{44}{75}\right)\) |