Basic properties
| Modulus: | \(14994\) | |
| Conductor: | \(7497\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(336\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{7497}(4043,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 14994.hf
\(\chi_{14994}(11,\cdot)\) \(\chi_{14994}(23,\cdot)\) \(\chi_{14994}(401,\cdot)\) \(\chi_{14994}(515,\cdot)\) \(\chi_{14994}(641,\cdot)\) \(\chi_{14994}(653,\cdot)\) \(\chi_{14994}(779,\cdot)\) \(\chi_{14994}(1031,\cdot)\) \(\chi_{14994}(1397,\cdot)\) \(\chi_{14994}(1523,\cdot)\) \(\chi_{14994}(1535,\cdot)\) \(\chi_{14994}(1661,\cdot)\) \(\chi_{14994}(1775,\cdot)\) \(\chi_{14994}(1901,\cdot)\) \(\chi_{14994}(2153,\cdot)\) \(\chi_{14994}(2165,\cdot)\) \(\chi_{14994}(2417,\cdot)\) \(\chi_{14994}(2543,\cdot)\) \(\chi_{14994}(2657,\cdot)\) \(\chi_{14994}(2783,\cdot)\) \(\chi_{14994}(2795,\cdot)\) \(\chi_{14994}(3173,\cdot)\) \(\chi_{14994}(3287,\cdot)\) \(\chi_{14994}(3539,\cdot)\) \(\chi_{14994}(3665,\cdot)\) \(\chi_{14994}(3677,\cdot)\) \(\chi_{14994}(3917,\cdot)\) \(\chi_{14994}(4043,\cdot)\) \(\chi_{14994}(4295,\cdot)\) \(\chi_{14994}(4307,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{336})$ |
| Fixed field: | Number field defined by a degree 336 polynomial (not computed) |
Values on generators
\((1667,12547,14113)\) → \((e\left(\frac{1}{6}\right),e\left(\frac{8}{21}\right),e\left(\frac{9}{16}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(5\) | \(11\) | \(13\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) | \(37\) | \(41\) |
| \( \chi_{ 14994 }(4043, a) \) | \(1\) | \(1\) | \(e\left(\frac{233}{336}\right)\) | \(e\left(\frac{115}{336}\right)\) | \(e\left(\frac{13}{84}\right)\) | \(e\left(\frac{5}{24}\right)\) | \(e\left(\frac{251}{336}\right)\) | \(e\left(\frac{65}{168}\right)\) | \(e\left(\frac{113}{336}\right)\) | \(e\left(\frac{1}{16}\right)\) | \(e\left(\frac{253}{336}\right)\) | \(e\left(\frac{247}{336}\right)\) |