Basic properties
| Modulus: | \(7220\) | |
| Conductor: | \(1805\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(342\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{1805}(9,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 7220.cl
\(\chi_{7220}(9,\cdot)\) \(\chi_{7220}(149,\cdot)\) \(\chi_{7220}(169,\cdot)\) \(\chi_{7220}(289,\cdot)\) \(\chi_{7220}(309,\cdot)\) \(\chi_{7220}(329,\cdot)\) \(\chi_{7220}(529,\cdot)\) \(\chi_{7220}(549,\cdot)\) \(\chi_{7220}(669,\cdot)\) \(\chi_{7220}(689,\cdot)\) \(\chi_{7220}(709,\cdot)\) \(\chi_{7220}(769,\cdot)\) \(\chi_{7220}(909,\cdot)\) \(\chi_{7220}(929,\cdot)\) \(\chi_{7220}(1049,\cdot)\) \(\chi_{7220}(1069,\cdot)\) \(\chi_{7220}(1089,\cdot)\) \(\chi_{7220}(1149,\cdot)\) \(\chi_{7220}(1289,\cdot)\) \(\chi_{7220}(1309,\cdot)\) \(\chi_{7220}(1429,\cdot)\) \(\chi_{7220}(1449,\cdot)\) \(\chi_{7220}(1469,\cdot)\) \(\chi_{7220}(1529,\cdot)\) \(\chi_{7220}(1669,\cdot)\) \(\chi_{7220}(1809,\cdot)\) \(\chi_{7220}(1829,\cdot)\) \(\chi_{7220}(1849,\cdot)\) \(\chi_{7220}(1909,\cdot)\) \(\chi_{7220}(2049,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{171})$ |
| Fixed field: | Number field defined by a degree 342 polynomial (not computed) |
Values on generators
\((3611,5777,6861)\) → \((1,-1,e\left(\frac{139}{171}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(7\) | \(9\) | \(11\) | \(13\) | \(17\) | \(21\) | \(23\) | \(27\) | \(29\) |
| \( \chi_{ 7220 }(9, a) \) | \(1\) | \(1\) | \(e\left(\frac{167}{342}\right)\) | \(e\left(\frac{49}{114}\right)\) | \(e\left(\frac{167}{171}\right)\) | \(e\left(\frac{52}{57}\right)\) | \(e\left(\frac{319}{342}\right)\) | \(e\left(\frac{71}{342}\right)\) | \(e\left(\frac{157}{171}\right)\) | \(e\left(\frac{61}{342}\right)\) | \(e\left(\frac{53}{114}\right)\) | \(e\left(\frac{140}{171}\right)\) |