Basic properties
| Modulus: | \(7605\) | |
| Conductor: | \(2535\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(156\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{2535}(107,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 7605.ge
\(\chi_{7605}(107,\cdot)\) \(\chi_{7605}(152,\cdot)\) \(\chi_{7605}(458,\cdot)\) \(\chi_{7605}(503,\cdot)\) \(\chi_{7605}(692,\cdot)\) \(\chi_{7605}(737,\cdot)\) \(\chi_{7605}(1043,\cdot)\) \(\chi_{7605}(1088,\cdot)\) \(\chi_{7605}(1277,\cdot)\) \(\chi_{7605}(1322,\cdot)\) \(\chi_{7605}(1628,\cdot)\) \(\chi_{7605}(1673,\cdot)\) \(\chi_{7605}(1862,\cdot)\) \(\chi_{7605}(1907,\cdot)\) \(\chi_{7605}(2213,\cdot)\) \(\chi_{7605}(2258,\cdot)\) \(\chi_{7605}(2447,\cdot)\) \(\chi_{7605}(2492,\cdot)\) \(\chi_{7605}(2798,\cdot)\) \(\chi_{7605}(2843,\cdot)\) \(\chi_{7605}(3032,\cdot)\) \(\chi_{7605}(3077,\cdot)\) \(\chi_{7605}(3383,\cdot)\) \(\chi_{7605}(3428,\cdot)\) \(\chi_{7605}(3617,\cdot)\) \(\chi_{7605}(3662,\cdot)\) \(\chi_{7605}(3968,\cdot)\) \(\chi_{7605}(4013,\cdot)\) \(\chi_{7605}(4553,\cdot)\) \(\chi_{7605}(4598,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{156})$ |
| Fixed field: | Number field defined by a degree 156 polynomial (not computed) |
Values on generators
\((6761,1522,6931)\) → \((-1,i,e\left(\frac{25}{39}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(7\) | \(8\) | \(11\) | \(14\) | \(16\) | \(17\) | \(19\) | \(22\) |
| \( \chi_{ 7605 }(107, a) \) | \(1\) | \(1\) | \(e\left(\frac{61}{156}\right)\) | \(e\left(\frac{61}{78}\right)\) | \(e\left(\frac{131}{156}\right)\) | \(e\left(\frac{9}{52}\right)\) | \(e\left(\frac{41}{78}\right)\) | \(e\left(\frac{3}{13}\right)\) | \(e\left(\frac{22}{39}\right)\) | \(e\left(\frac{53}{156}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{11}{12}\right)\) |