Basic properties
| Modulus: | \(7497\) | |
| Conductor: | \(7497\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(336\) | 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 7497.hp
\(\chi_{7497}(11,\cdot)\) \(\chi_{7497}(23,\cdot)\) \(\chi_{7497}(74,\cdot)\) \(\chi_{7497}(326,\cdot)\) \(\chi_{7497}(401,\cdot)\) \(\chi_{7497}(452,\cdot)\) \(\chi_{7497}(464,\cdot)\) \(\chi_{7497}(515,\cdot)\) \(\chi_{7497}(590,\cdot)\) \(\chi_{7497}(641,\cdot)\) \(\chi_{7497}(653,\cdot)\) \(\chi_{7497}(779,\cdot)\) \(\chi_{7497}(830,\cdot)\) \(\chi_{7497}(1031,\cdot)\) \(\chi_{7497}(1082,\cdot)\) \(\chi_{7497}(1094,\cdot)\) \(\chi_{7497}(1346,\cdot)\) \(\chi_{7497}(1397,\cdot)\) \(\chi_{7497}(1472,\cdot)\) \(\chi_{7497}(1523,\cdot)\) \(\chi_{7497}(1535,\cdot)\) \(\chi_{7497}(1661,\cdot)\) \(\chi_{7497}(1712,\cdot)\) \(\chi_{7497}(1724,\cdot)\) \(\chi_{7497}(1775,\cdot)\) \(\chi_{7497}(1850,\cdot)\) \(\chi_{7497}(1901,\cdot)\) \(\chi_{7497}(2102,\cdot)\) \(\chi_{7497}(2153,\cdot)\) \(\chi_{7497}(2165,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{336})$ |
| Fixed field: | Number field defined by a degree 336 polynomial (not computed) |
Values on generators
\((1667,5050,6616)\) → \((e\left(\frac{5}{6}\right),e\left(\frac{4}{21}\right),e\left(\frac{3}{16}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(8\) | \(10\) | \(11\) | \(13\) | \(16\) | \(19\) | \(20\) |
| \( \chi_{ 7497 }(2543, a) \) | \(1\) | \(1\) | \(e\left(\frac{23}{56}\right)\) | \(e\left(\frac{23}{28}\right)\) | \(e\left(\frac{211}{336}\right)\) | \(e\left(\frac{13}{56}\right)\) | \(e\left(\frac{13}{336}\right)\) | \(e\left(\frac{257}{336}\right)\) | \(e\left(\frac{59}{84}\right)\) | \(e\left(\frac{9}{14}\right)\) | \(e\left(\frac{7}{24}\right)\) | \(e\left(\frac{151}{336}\right)\) |