Basic properties
| Modulus: | \(786\) | |
| Conductor: | \(393\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(130\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{393}(17,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 786.o
\(\chi_{786}(17,\cdot)\) \(\chi_{786}(23,\cdot)\) \(\chi_{786}(29,\cdot)\) \(\chi_{786}(83,\cdot)\) \(\chi_{786}(95,\cdot)\) \(\chi_{786}(119,\cdot)\) \(\chi_{786}(137,\cdot)\) \(\chi_{786}(161,\cdot)\) \(\chi_{786}(185,\cdot)\) \(\chi_{786}(197,\cdot)\) \(\chi_{786}(203,\cdot)\) \(\chi_{786}(221,\cdot)\) \(\chi_{786}(227,\cdot)\) \(\chi_{786}(251,\cdot)\) \(\chi_{786}(257,\cdot)\) \(\chi_{786}(293,\cdot)\) \(\chi_{786}(299,\cdot)\) \(\chi_{786}(329,\cdot)\) \(\chi_{786}(347,\cdot)\) \(\chi_{786}(359,\cdot)\) \(\chi_{786}(365,\cdot)\) \(\chi_{786}(377,\cdot)\) \(\chi_{786}(389,\cdot)\) \(\chi_{786}(395,\cdot)\) \(\chi_{786}(401,\cdot)\) \(\chi_{786}(407,\cdot)\) \(\chi_{786}(419,\cdot)\) \(\chi_{786}(443,\cdot)\) \(\chi_{786}(449,\cdot)\) \(\chi_{786}(491,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{65})$ |
| Fixed field: | Number field defined by a degree 130 polynomial (not computed) |
Values on generators
\((263,133)\) → \((-1,e\left(\frac{43}{130}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(5\) | \(7\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) |
| \( \chi_{ 786 }(17, a) \) | \(1\) | \(1\) | \(e\left(\frac{93}{130}\right)\) | \(e\left(\frac{49}{65}\right)\) | \(e\left(\frac{3}{130}\right)\) | \(e\left(\frac{62}{65}\right)\) | \(e\left(\frac{47}{65}\right)\) | \(e\left(\frac{15}{26}\right)\) | \(e\left(\frac{7}{65}\right)\) | \(e\left(\frac{28}{65}\right)\) | \(e\left(\frac{24}{65}\right)\) | \(e\left(\frac{77}{130}\right)\) |