Basic properties
| Modulus: | \(7605\) | |
| Conductor: | \(1521\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(156\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{1521}(11,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 7605.hf
\(\chi_{7605}(11,\cdot)\) \(\chi_{7605}(176,\cdot)\) \(\chi_{7605}(236,\cdot)\) \(\chi_{7605}(266,\cdot)\) \(\chi_{7605}(761,\cdot)\) \(\chi_{7605}(821,\cdot)\) \(\chi_{7605}(851,\cdot)\) \(\chi_{7605}(1181,\cdot)\) \(\chi_{7605}(1346,\cdot)\) \(\chi_{7605}(1406,\cdot)\) \(\chi_{7605}(1436,\cdot)\) \(\chi_{7605}(1766,\cdot)\) \(\chi_{7605}(1931,\cdot)\) \(\chi_{7605}(1991,\cdot)\) \(\chi_{7605}(2021,\cdot)\) \(\chi_{7605}(2351,\cdot)\) \(\chi_{7605}(2576,\cdot)\) \(\chi_{7605}(2606,\cdot)\) \(\chi_{7605}(2936,\cdot)\) \(\chi_{7605}(3101,\cdot)\) \(\chi_{7605}(3161,\cdot)\) \(\chi_{7605}(3191,\cdot)\) \(\chi_{7605}(3521,\cdot)\) \(\chi_{7605}(3686,\cdot)\) \(\chi_{7605}(3746,\cdot)\) \(\chi_{7605}(3776,\cdot)\) \(\chi_{7605}(4106,\cdot)\) \(\chi_{7605}(4271,\cdot)\) \(\chi_{7605}(4331,\cdot)\) \(\chi_{7605}(4361,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{156})$ |
| Fixed field: | Number field defined by a degree 156 polynomial (not computed) |
Values on generators
\((6761,1522,6931)\) → \((e\left(\frac{1}{6}\right),1,e\left(\frac{103}{156}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(7\) | \(8\) | \(11\) | \(14\) | \(16\) | \(17\) | \(19\) | \(22\) |
| \( \chi_{ 7605 }(11, a) \) | \(1\) | \(1\) | \(e\left(\frac{43}{52}\right)\) | \(e\left(\frac{17}{26}\right)\) | \(e\left(\frac{49}{156}\right)\) | \(e\left(\frac{25}{52}\right)\) | \(e\left(\frac{9}{52}\right)\) | \(e\left(\frac{11}{78}\right)\) | \(e\left(\frac{4}{13}\right)\) | \(e\left(\frac{35}{39}\right)\) | \(e\left(\frac{11}{12}\right)\) | \(1\) |