Basic properties
| Modulus: | \(316\) | |
| Conductor: | \(316\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(78\) | 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 316.p
\(\chi_{316}(3,\cdot)\) \(\chi_{316}(7,\cdot)\) \(\chi_{316}(35,\cdot)\) \(\chi_{316}(39,\cdot)\) \(\chi_{316}(43,\cdot)\) \(\chi_{316}(47,\cdot)\) \(\chi_{316}(59,\cdot)\) \(\chi_{316}(63,\cdot)\) \(\chi_{316}(75,\cdot)\) \(\chi_{316}(107,\cdot)\) \(\chi_{316}(127,\cdot)\) \(\chi_{316}(139,\cdot)\) \(\chi_{316}(147,\cdot)\) \(\chi_{316}(187,\cdot)\) \(\chi_{316}(195,\cdot)\) \(\chi_{316}(211,\cdot)\) \(\chi_{316}(235,\cdot)\) \(\chi_{316}(243,\cdot)\) \(\chi_{316}(267,\cdot)\) \(\chi_{316}(271,\cdot)\) \(\chi_{316}(291,\cdot)\) \(\chi_{316}(303,\cdot)\) \(\chi_{316}(307,\cdot)\) \(\chi_{316}(311,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{39})$ |
| Fixed field: | Number field defined by a degree 78 polynomial |
Values on generators
\((159,161)\) → \((-1,e\left(\frac{59}{78}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(21\) |
| \( \chi_{ 316 }(47, a) \) | \(1\) | \(1\) | \(e\left(\frac{10}{39}\right)\) | \(e\left(\frac{35}{39}\right)\) | \(e\left(\frac{23}{39}\right)\) | \(e\left(\frac{20}{39}\right)\) | \(e\left(\frac{73}{78}\right)\) | \(e\left(\frac{28}{39}\right)\) | \(e\left(\frac{2}{13}\right)\) | \(e\left(\frac{23}{26}\right)\) | \(e\left(\frac{55}{78}\right)\) | \(e\left(\frac{11}{13}\right)\) |