Basic properties
| Modulus: | \(7605\) | |
| Conductor: | \(7605\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(156\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | yes | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 7605.fw
\(\chi_{7605}(292,\cdot)\) \(\chi_{7605}(457,\cdot)\) \(\chi_{7605}(553,\cdot)\) \(\chi_{7605}(583,\cdot)\) \(\chi_{7605}(877,\cdot)\) \(\chi_{7605}(1042,\cdot)\) \(\chi_{7605}(1138,\cdot)\) \(\chi_{7605}(1168,\cdot)\) \(\chi_{7605}(1462,\cdot)\) \(\chi_{7605}(1627,\cdot)\) \(\chi_{7605}(1723,\cdot)\) \(\chi_{7605}(1753,\cdot)\) \(\chi_{7605}(2212,\cdot)\) \(\chi_{7605}(2308,\cdot)\) \(\chi_{7605}(2338,\cdot)\) \(\chi_{7605}(2632,\cdot)\) \(\chi_{7605}(2797,\cdot)\) \(\chi_{7605}(2893,\cdot)\) \(\chi_{7605}(2923,\cdot)\) \(\chi_{7605}(3217,\cdot)\) \(\chi_{7605}(3382,\cdot)\) \(\chi_{7605}(3478,\cdot)\) \(\chi_{7605}(3508,\cdot)\) \(\chi_{7605}(3802,\cdot)\) \(\chi_{7605}(4063,\cdot)\) \(\chi_{7605}(4093,\cdot)\) \(\chi_{7605}(4387,\cdot)\) \(\chi_{7605}(4552,\cdot)\) \(\chi_{7605}(4648,\cdot)\) \(\chi_{7605}(4678,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{156})$ |
| Fixed field: | Number field defined by a degree 156 polynomial (not computed) |
Values on generators
\((6761,1522,6931)\) → \((e\left(\frac{1}{3}\right),i,e\left(\frac{53}{156}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(7\) | \(8\) | \(11\) | \(14\) | \(16\) | \(17\) | \(19\) | \(22\) |
| \( \chi_{ 7605 }(292, a) \) | \(1\) | \(1\) | \(e\left(\frac{12}{13}\right)\) | \(e\left(\frac{11}{13}\right)\) | \(e\left(\frac{73}{78}\right)\) | \(e\left(\frac{10}{13}\right)\) | \(e\left(\frac{17}{52}\right)\) | \(e\left(\frac{67}{78}\right)\) | \(e\left(\frac{9}{13}\right)\) | \(e\left(\frac{133}{156}\right)\) | \(e\left(\frac{7}{12}\right)\) | \(i\) |