Basic properties
| Modulus: | \(76230\) | |
| Conductor: | \(7623\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(330\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{7623}(6268,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 76230.qr
\(\chi_{76230}(31,\cdot)\) \(\chi_{76230}(691,\cdot)\) \(\chi_{76230}(1951,\cdot)\) \(\chi_{76230}(3811,\cdot)\) \(\chi_{76230}(4471,\cdot)\) \(\chi_{76230}(5701,\cdot)\) \(\chi_{76230}(6361,\cdot)\) \(\chi_{76230}(6961,\cdot)\) \(\chi_{76230}(7621,\cdot)\) \(\chi_{76230}(8221,\cdot)\) \(\chi_{76230}(8881,\cdot)\) \(\chi_{76230}(10741,\cdot)\) \(\chi_{76230}(12631,\cdot)\) \(\chi_{76230}(13291,\cdot)\) \(\chi_{76230}(13891,\cdot)\) \(\chi_{76230}(14551,\cdot)\) \(\chi_{76230}(15151,\cdot)\) \(\chi_{76230}(17671,\cdot)\) \(\chi_{76230}(18331,\cdot)\) \(\chi_{76230}(19561,\cdot)\) \(\chi_{76230}(20221,\cdot)\) \(\chi_{76230}(21481,\cdot)\) \(\chi_{76230}(22081,\cdot)\) \(\chi_{76230}(22741,\cdot)\) \(\chi_{76230}(24601,\cdot)\) \(\chi_{76230}(25261,\cdot)\) \(\chi_{76230}(26491,\cdot)\) \(\chi_{76230}(27151,\cdot)\) \(\chi_{76230}(27751,\cdot)\) \(\chi_{76230}(28411,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{165})$ |
| Fixed field: | Number field defined by a degree 330 polynomial (not computed) |
Values on generators
\((8471,15247,65341,57961)\) → \((e\left(\frac{1}{3}\right),1,e\left(\frac{1}{6}\right),e\left(\frac{18}{55}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(13\) | \(17\) | \(19\) | \(23\) | \(29\) | \(31\) | \(37\) | \(41\) | \(43\) | \(47\) |
| \( \chi_{ 76230 }(13891, a) \) | \(-1\) | \(1\) | \(e\left(\frac{73}{330}\right)\) | \(e\left(\frac{67}{330}\right)\) | \(e\left(\frac{329}{330}\right)\) | \(e\left(\frac{10}{11}\right)\) | \(e\left(\frac{148}{165}\right)\) | \(e\left(\frac{323}{330}\right)\) | \(e\left(\frac{13}{165}\right)\) | \(e\left(\frac{229}{330}\right)\) | \(e\left(\frac{17}{33}\right)\) | \(e\left(\frac{79}{330}\right)\) |