Basic properties
| Modulus: | \(7605\) | |
| Conductor: | \(845\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(78\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{845}(199,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 7605.fo
\(\chi_{7605}(199,\cdot)\) \(\chi_{7605}(244,\cdot)\) \(\chi_{7605}(784,\cdot)\) \(\chi_{7605}(829,\cdot)\) \(\chi_{7605}(1369,\cdot)\) \(\chi_{7605}(1414,\cdot)\) \(\chi_{7605}(1954,\cdot)\) \(\chi_{7605}(1999,\cdot)\) \(\chi_{7605}(2539,\cdot)\) \(\chi_{7605}(2584,\cdot)\) \(\chi_{7605}(3124,\cdot)\) \(\chi_{7605}(3169,\cdot)\) \(\chi_{7605}(3709,\cdot)\) \(\chi_{7605}(3754,\cdot)\) \(\chi_{7605}(4294,\cdot)\) \(\chi_{7605}(4339,\cdot)\) \(\chi_{7605}(5464,\cdot)\) \(\chi_{7605}(5509,\cdot)\) \(\chi_{7605}(6049,\cdot)\) \(\chi_{7605}(6094,\cdot)\) \(\chi_{7605}(6634,\cdot)\) \(\chi_{7605}(6679,\cdot)\) \(\chi_{7605}(7219,\cdot)\) \(\chi_{7605}(7264,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{39})$ |
| Fixed field: | Number field defined by a degree 78 polynomial |
Values on generators
\((6761,1522,6931)\) → \((1,-1,e\left(\frac{67}{78}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(7\) | \(8\) | \(11\) | \(14\) | \(16\) | \(17\) | \(19\) | \(22\) |
| \( \chi_{ 7605 }(199, a) \) | \(1\) | \(1\) | \(e\left(\frac{14}{39}\right)\) | \(e\left(\frac{28}{39}\right)\) | \(e\left(\frac{16}{39}\right)\) | \(e\left(\frac{1}{13}\right)\) | \(e\left(\frac{37}{78}\right)\) | \(e\left(\frac{10}{13}\right)\) | \(e\left(\frac{17}{39}\right)\) | \(e\left(\frac{71}{78}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{5}{6}\right)\) |