Basic properties
Modulus: | \(7220\) | |
Conductor: | \(361\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(171\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
Real: | no | |
Primitive: | no, induced from \(\chi_{361}(61,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 7220.ce
\(\chi_{7220}(61,\cdot)\) \(\chi_{7220}(81,\cdot)\) \(\chi_{7220}(101,\cdot)\) \(\chi_{7220}(161,\cdot)\) \(\chi_{7220}(301,\cdot)\) \(\chi_{7220}(321,\cdot)\) \(\chi_{7220}(441,\cdot)\) \(\chi_{7220}(461,\cdot)\) \(\chi_{7220}(481,\cdot)\) \(\chi_{7220}(541,\cdot)\) \(\chi_{7220}(681,\cdot)\) \(\chi_{7220}(701,\cdot)\) \(\chi_{7220}(841,\cdot)\) \(\chi_{7220}(861,\cdot)\) \(\chi_{7220}(921,\cdot)\) \(\chi_{7220}(1061,\cdot)\) \(\chi_{7220}(1081,\cdot)\) \(\chi_{7220}(1201,\cdot)\) \(\chi_{7220}(1221,\cdot)\) \(\chi_{7220}(1241,\cdot)\) \(\chi_{7220}(1301,\cdot)\) \(\chi_{7220}(1441,\cdot)\) \(\chi_{7220}(1461,\cdot)\) \(\chi_{7220}(1581,\cdot)\) \(\chi_{7220}(1601,\cdot)\) \(\chi_{7220}(1621,\cdot)\) \(\chi_{7220}(1681,\cdot)\) \(\chi_{7220}(1821,\cdot)\) \(\chi_{7220}(1841,\cdot)\) \(\chi_{7220}(1961,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{171})$ |
Fixed field: | Number field defined by a degree 171 polynomial (not computed) |
Values on generators
\((3611,5777,6861)\) → \((1,1,e\left(\frac{46}{171}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(3\) | \(7\) | \(9\) | \(11\) | \(13\) | \(17\) | \(21\) | \(23\) | \(27\) | \(29\) |
\( \chi_{ 7220 }(61, a) \) | \(1\) | \(1\) | \(e\left(\frac{67}{171}\right)\) | \(e\left(\frac{20}{57}\right)\) | \(e\left(\frac{134}{171}\right)\) | \(e\left(\frac{25}{57}\right)\) | \(e\left(\frac{86}{171}\right)\) | \(e\left(\frac{136}{171}\right)\) | \(e\left(\frac{127}{171}\right)\) | \(e\left(\frac{47}{171}\right)\) | \(e\left(\frac{10}{57}\right)\) | \(e\left(\frac{98}{171}\right)\) |