Basic properties
| Modulus: | \(10060\) | |
| Conductor: | \(10060\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(1004\) | 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 10060.x
\(\chi_{10060}(87,\cdot)\) \(\chi_{10060}(103,\cdot)\) \(\chi_{10060}(107,\cdot)\) \(\chi_{10060}(123,\cdot)\) \(\chi_{10060}(127,\cdot)\) \(\chi_{10060}(163,\cdot)\) \(\chi_{10060}(167,\cdot)\) \(\chi_{10060}(187,\cdot)\) \(\chi_{10060}(203,\cdot)\) \(\chi_{10060}(227,\cdot)\) \(\chi_{10060}(247,\cdot)\) \(\chi_{10060}(267,\cdot)\) \(\chi_{10060}(287,\cdot)\) \(\chi_{10060}(303,\cdot)\) \(\chi_{10060}(307,\cdot)\) \(\chi_{10060}(327,\cdot)\) \(\chi_{10060}(347,\cdot)\) \(\chi_{10060}(403,\cdot)\) \(\chi_{10060}(407,\cdot)\) \(\chi_{10060}(447,\cdot)\) \(\chi_{10060}(467,\cdot)\) \(\chi_{10060}(487,\cdot)\) \(\chi_{10060}(523,\cdot)\) \(\chi_{10060}(543,\cdot)\) \(\chi_{10060}(563,\cdot)\) \(\chi_{10060}(583,\cdot)\) \(\chi_{10060}(623,\cdot)\) \(\chi_{10060}(627,\cdot)\) \(\chi_{10060}(643,\cdot)\) \(\chi_{10060}(663,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{1004})$ |
| Fixed field: | Number field defined by a degree 1004 polynomial (not computed) |
Values on generators
\((5031,6037,6041)\) → \((-1,i,e\left(\frac{361}{502}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(7\) | \(9\) | \(11\) | \(13\) | \(17\) | \(19\) | \(21\) | \(23\) | \(27\) |
| \( \chi_{ 10060 }(247, a) \) | \(-1\) | \(1\) | \(e\left(\frac{435}{1004}\right)\) | \(e\left(\frac{597}{1004}\right)\) | \(e\left(\frac{435}{502}\right)\) | \(e\left(\frac{353}{502}\right)\) | \(e\left(\frac{925}{1004}\right)\) | \(e\left(\frac{933}{1004}\right)\) | \(e\left(\frac{217}{502}\right)\) | \(e\left(\frac{7}{251}\right)\) | \(e\left(\frac{971}{1004}\right)\) | \(e\left(\frac{301}{1004}\right)\) |