Basic properties
| Modulus: | \(751\) | |
| Conductor: | \(751\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(75\) | 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.k
\(\chi_{751}(32,\cdot)\) \(\chi_{751}(52,\cdot)\) \(\chi_{751}(61,\cdot)\) \(\chi_{751}(86,\cdot)\) \(\chi_{751}(107,\cdot)\) \(\chi_{751}(119,\cdot)\) \(\chi_{751}(121,\cdot)\) \(\chi_{751}(130,\cdot)\) \(\chi_{751}(131,\cdot)\) \(\chi_{751}(163,\cdot)\) \(\chi_{751}(180,\cdot)\) \(\chi_{751}(184,\cdot)\) \(\chi_{751}(190,\cdot)\) \(\chi_{751}(194,\cdot)\) \(\chi_{751}(197,\cdot)\) \(\chi_{751}(200,\cdot)\) \(\chi_{751}(229,\cdot)\) \(\chi_{751}(273,\cdot)\) \(\chi_{751}(284,\cdot)\) \(\chi_{751}(296,\cdot)\) \(\chi_{751}(299,\cdot)\) \(\chi_{751}(307,\cdot)\) \(\chi_{751}(372,\cdot)\) \(\chi_{751}(374,\cdot)\) \(\chi_{751}(378,\cdot)\) \(\chi_{751}(399,\cdot)\) \(\chi_{751}(405,\cdot)\) \(\chi_{751}(451,\cdot)\) \(\chi_{751}(471,\cdot)\) \(\chi_{751}(500,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{75})$ |
| Fixed field: | Number field defined by a degree 75 polynomial |
Values on generators
\(3\) → \(e\left(\frac{52}{75}\right)\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 751 }(284, a) \) | \(1\) | \(1\) | \(e\left(\frac{32}{75}\right)\) | \(e\left(\frac{52}{75}\right)\) | \(e\left(\frac{64}{75}\right)\) | \(e\left(\frac{22}{75}\right)\) | \(e\left(\frac{3}{25}\right)\) | \(e\left(\frac{9}{25}\right)\) | \(e\left(\frac{7}{25}\right)\) | \(e\left(\frac{29}{75}\right)\) | \(e\left(\frac{18}{25}\right)\) | \(e\left(\frac{11}{15}\right)\) |