Basic properties
| Modulus: | \(10060\) | |
| Conductor: | \(10060\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(502\) | 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 10060.o
\(\chi_{10060}(19,\cdot)\) \(\chi_{10060}(119,\cdot)\) \(\chi_{10060}(139,\cdot)\) \(\chi_{10060}(159,\cdot)\) \(\chi_{10060}(179,\cdot)\) \(\chi_{10060}(239,\cdot)\) \(\chi_{10060}(259,\cdot)\) \(\chi_{10060}(279,\cdot)\) \(\chi_{10060}(319,\cdot)\) \(\chi_{10060}(359,\cdot)\) \(\chi_{10060}(399,\cdot)\) \(\chi_{10060}(419,\cdot)\) \(\chi_{10060}(439,\cdot)\) \(\chi_{10060}(459,\cdot)\) \(\chi_{10060}(479,\cdot)\) \(\chi_{10060}(499,\cdot)\) \(\chi_{10060}(579,\cdot)\) \(\chi_{10060}(619,\cdot)\) \(\chi_{10060}(639,\cdot)\) \(\chi_{10060}(799,\cdot)\) \(\chi_{10060}(859,\cdot)\) \(\chi_{10060}(939,\cdot)\) \(\chi_{10060}(959,\cdot)\) \(\chi_{10060}(979,\cdot)\) \(\chi_{10060}(999,\cdot)\) \(\chi_{10060}(1059,\cdot)\) \(\chi_{10060}(1099,\cdot)\) \(\chi_{10060}(1139,\cdot)\) \(\chi_{10060}(1159,\cdot)\) \(\chi_{10060}(1199,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{251})$ |
| Fixed field: | Number field defined by a degree 502 polynomial (not computed) |
Values on generators
\((5031,6037,6041)\) → \((-1,-1,e\left(\frac{493}{502}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(7\) | \(9\) | \(11\) | \(13\) | \(17\) | \(19\) | \(21\) | \(23\) | \(27\) |
| \( \chi_{ 10060 }(10039, a) \) | \(1\) | \(1\) | \(e\left(\frac{51}{251}\right)\) | \(e\left(\frac{115}{251}\right)\) | \(e\left(\frac{102}{251}\right)\) | \(e\left(\frac{375}{502}\right)\) | \(e\left(\frac{139}{502}\right)\) | \(e\left(\frac{99}{251}\right)\) | \(e\left(\frac{63}{251}\right)\) | \(e\left(\frac{166}{251}\right)\) | \(e\left(\frac{145}{251}\right)\) | \(e\left(\frac{153}{251}\right)\) |