Basic properties
| Modulus: | \(751\) | |
| Conductor: | \(751\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(750\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | yes | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 751.p
\(\chi_{751}(3,\cdot)\) \(\chi_{751}(12,\cdot)\) \(\chi_{751}(14,\cdot)\) \(\chi_{751}(15,\cdot)\) \(\chi_{751}(17,\cdot)\) \(\chi_{751}(24,\cdot)\) \(\chi_{751}(28,\cdot)\) \(\chi_{751}(29,\cdot)\) \(\chi_{751}(30,\cdot)\) \(\chi_{751}(31,\cdot)\) \(\chi_{751}(35,\cdot)\) \(\chi_{751}(39,\cdot)\) \(\chi_{751}(44,\cdot)\) \(\chi_{751}(54,\cdot)\) \(\chi_{751}(55,\cdot)\) \(\chi_{751}(57,\cdot)\) \(\chi_{751}(62,\cdot)\) \(\chi_{751}(63,\cdot)\) \(\chi_{751}(67,\cdot)\) \(\chi_{751}(69,\cdot)\) \(\chi_{751}(79,\cdot)\) \(\chi_{751}(82,\cdot)\) \(\chi_{751}(88,\cdot)\) \(\chi_{751}(91,\cdot)\) \(\chi_{751}(96,\cdot)\) \(\chi_{751}(101,\cdot)\) \(\chi_{751}(103,\cdot)\) \(\chi_{751}(110,\cdot)\) \(\chi_{751}(113,\cdot)\) \(\chi_{751}(116,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{375})$ |
| Fixed field: | Number field defined by a degree 750 polynomial (not computed) |
Values on generators
\(3\) → \(e\left(\frac{329}{750}\right)\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 751 }(17, a) \) | \(-1\) | \(1\) | \(e\left(\frac{182}{375}\right)\) | \(e\left(\frac{329}{750}\right)\) | \(e\left(\frac{364}{375}\right)\) | \(e\left(\frac{322}{375}\right)\) | \(e\left(\frac{231}{250}\right)\) | \(e\left(\frac{143}{250}\right)\) | \(e\left(\frac{57}{125}\right)\) | \(e\left(\frac{329}{375}\right)\) | \(e\left(\frac{43}{125}\right)\) | \(e\left(\frac{97}{150}\right)\) |