Basic properties
| Modulus: | \(10060\) | |
| Conductor: | \(2515\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(1004\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{2515}(2512,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 10060.u
\(\chi_{10060}(17,\cdot)\) \(\chi_{10060}(37,\cdot)\) \(\chi_{10060}(53,\cdot)\) \(\chi_{10060}(57,\cdot)\) \(\chi_{10060}(93,\cdot)\) \(\chi_{10060}(133,\cdot)\) \(\chi_{10060}(137,\cdot)\) \(\chi_{10060}(153,\cdot)\) \(\chi_{10060}(157,\cdot)\) \(\chi_{10060}(193,\cdot)\) \(\chi_{10060}(213,\cdot)\) \(\chi_{10060}(217,\cdot)\) \(\chi_{10060}(277,\cdot)\) \(\chi_{10060}(313,\cdot)\) \(\chi_{10060}(333,\cdot)\) \(\chi_{10060}(337,\cdot)\) \(\chi_{10060}(353,\cdot)\) \(\chi_{10060}(357,\cdot)\) \(\chi_{10060}(377,\cdot)\) \(\chi_{10060}(417,\cdot)\) \(\chi_{10060}(437,\cdot)\) \(\chi_{10060}(453,\cdot)\) \(\chi_{10060}(457,\cdot)\) \(\chi_{10060}(477,\cdot)\) \(\chi_{10060}(497,\cdot)\) \(\chi_{10060}(513,\cdot)\) \(\chi_{10060}(533,\cdot)\) \(\chi_{10060}(537,\cdot)\) \(\chi_{10060}(573,\cdot)\) \(\chi_{10060}(577,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{1004})$ |
| Fixed field: | Number field defined by a degree 1004 polynomial (not computed) |
Values on generators
\((5031,6037,6041)\) → \((1,i,e\left(\frac{407}{502}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(7\) | \(9\) | \(11\) | \(13\) | \(17\) | \(19\) | \(21\) | \(23\) | \(27\) |
| \( \chi_{ 10060 }(10057, a) \) | \(1\) | \(1\) | \(e\left(\frac{229}{1004}\right)\) | \(e\left(\frac{979}{1004}\right)\) | \(e\left(\frac{229}{502}\right)\) | \(e\left(\frac{13}{251}\right)\) | \(e\left(\frac{285}{1004}\right)\) | \(e\left(\frac{917}{1004}\right)\) | \(e\left(\frac{163}{251}\right)\) | \(e\left(\frac{51}{251}\right)\) | \(e\left(\frac{405}{1004}\right)\) | \(e\left(\frac{687}{1004}\right)\) |