Basic properties
| Modulus: | \(784\) | |
| Conductor: | \(784\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(84\) | 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 784.bt
\(\chi_{784}(37,\cdot)\) \(\chi_{784}(53,\cdot)\) \(\chi_{784}(93,\cdot)\) \(\chi_{784}(109,\cdot)\) \(\chi_{784}(149,\cdot)\) \(\chi_{784}(205,\cdot)\) \(\chi_{784}(221,\cdot)\) \(\chi_{784}(261,\cdot)\) \(\chi_{784}(277,\cdot)\) \(\chi_{784}(317,\cdot)\) \(\chi_{784}(333,\cdot)\) \(\chi_{784}(389,\cdot)\) \(\chi_{784}(429,\cdot)\) \(\chi_{784}(445,\cdot)\) \(\chi_{784}(485,\cdot)\) \(\chi_{784}(501,\cdot)\) \(\chi_{784}(541,\cdot)\) \(\chi_{784}(597,\cdot)\) \(\chi_{784}(613,\cdot)\) \(\chi_{784}(653,\cdot)\) \(\chi_{784}(669,\cdot)\) \(\chi_{784}(709,\cdot)\) \(\chi_{784}(725,\cdot)\) \(\chi_{784}(781,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{84})$ |
| Fixed field: | Number field defined by a degree 84 polynomial |
Values on generators
\((687,197,689)\) → \((1,-i,e\left(\frac{20}{21}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(23\) | \(25\) |
| \( \chi_{ 784 }(109, a) \) | \(1\) | \(1\) | \(e\left(\frac{17}{84}\right)\) | \(e\left(\frac{31}{84}\right)\) | \(e\left(\frac{17}{42}\right)\) | \(e\left(\frac{71}{84}\right)\) | \(e\left(\frac{19}{28}\right)\) | \(e\left(\frac{4}{7}\right)\) | \(e\left(\frac{17}{21}\right)\) | \(e\left(\frac{7}{12}\right)\) | \(e\left(\frac{29}{42}\right)\) | \(e\left(\frac{31}{42}\right)\) |