Basic properties
Modulus: | \(6042\) | |
Conductor: | \(3021\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(78\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
Real: | no | |
Primitive: | no, induced from \(\chi_{3021}(653,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 6042.cd
\(\chi_{6042}(11,\cdot)\) \(\chi_{6042}(197,\cdot)\) \(\chi_{6042}(467,\cdot)\) \(\chi_{6042}(539,\cdot)\) \(\chi_{6042}(653,\cdot)\) \(\chi_{6042}(695,\cdot)\) \(\chi_{6042}(767,\cdot)\) \(\chi_{6042}(1151,\cdot)\) \(\chi_{6042}(1223,\cdot)\) \(\chi_{6042}(1493,\cdot)\) \(\chi_{6042}(1607,\cdot)\) \(\chi_{6042}(1721,\cdot)\) \(\chi_{6042}(2021,\cdot)\) \(\chi_{6042}(2177,\cdot)\) \(\chi_{6042}(2975,\cdot)\) \(\chi_{6042}(3845,\cdot)\) \(\chi_{6042}(3959,\cdot)\) \(\chi_{6042}(4757,\cdot)\) \(\chi_{6042}(4799,\cdot)\) \(\chi_{6042}(4913,\cdot)\) \(\chi_{6042}(5099,\cdot)\) \(\chi_{6042}(5555,\cdot)\) \(\chi_{6042}(5711,\cdot)\) \(\chi_{6042}(5783,\cdot)\)
Related number fields
Field of values: | $\Q(\zeta_{39})$ |
Fixed field: | Number field defined by a degree 78 polynomial |
Values on generators
\((2015,4771,2281)\) → \((-1,e\left(\frac{1}{3}\right),e\left(\frac{5}{26}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(5\) | \(7\) | \(11\) | \(13\) | \(17\) | \(23\) | \(25\) | \(29\) | \(31\) | \(35\) |
\( \chi_{ 6042 }(653, a) \) | \(-1\) | \(1\) | \(e\left(\frac{34}{39}\right)\) | \(e\left(\frac{9}{13}\right)\) | \(e\left(\frac{17}{26}\right)\) | \(e\left(\frac{11}{39}\right)\) | \(e\left(\frac{59}{78}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{29}{39}\right)\) | \(e\left(\frac{1}{78}\right)\) | \(e\left(\frac{9}{26}\right)\) | \(e\left(\frac{22}{39}\right)\) |