Basic properties
| Modulus: | \(8041\) | |
| Conductor: | \(8041\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(240\) | 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 8041.fd
\(\chi_{8041}(6,\cdot)\) \(\chi_{8041}(79,\cdot)\) \(\chi_{8041}(294,\cdot)\) \(\chi_{8041}(337,\cdot)\) \(\chi_{8041}(380,\cdot)\) \(\chi_{8041}(436,\cdot)\) \(\chi_{8041}(479,\cdot)\) \(\chi_{8041}(651,\cdot)\) \(\chi_{8041}(810,\cdot)\) \(\chi_{8041}(853,\cdot)\) \(\chi_{8041}(1025,\cdot)\) \(\chi_{8041}(1382,\cdot)\) \(\chi_{8041}(1425,\cdot)\) \(\chi_{8041}(1756,\cdot)\) \(\chi_{8041}(1799,\cdot)\) \(\chi_{8041}(1812,\cdot)\) \(\chi_{8041}(1898,\cdot)\) \(\chi_{8041}(2186,\cdot)\) \(\chi_{8041}(2272,\cdot)\) \(\chi_{8041}(2285,\cdot)\) \(\chi_{8041}(2543,\cdot)\) \(\chi_{8041}(2659,\cdot)\) \(\chi_{8041}(2844,\cdot)\) \(\chi_{8041}(2917,\cdot)\) \(\chi_{8041}(3016,\cdot)\) \(\chi_{8041}(3218,\cdot)\) \(\chi_{8041}(3274,\cdot)\) \(\chi_{8041}(3390,\cdot)\) \(\chi_{8041}(3648,\cdot)\) \(\chi_{8041}(3747,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{240})$ |
| Fixed field: | Number field defined by a degree 240 polynomial (not computed) |
Values on generators
\((6580,2366,562)\) → \((e\left(\frac{1}{10}\right),e\left(\frac{11}{16}\right),e\left(\frac{2}{3}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(12\) |
| \( \chi_{ 8041 }(3016, a) \) | \(1\) | \(1\) | \(e\left(\frac{29}{40}\right)\) | \(e\left(\frac{37}{240}\right)\) | \(e\left(\frac{9}{20}\right)\) | \(e\left(\frac{121}{240}\right)\) | \(e\left(\frac{211}{240}\right)\) | \(e\left(\frac{143}{240}\right)\) | \(e\left(\frac{7}{40}\right)\) | \(e\left(\frac{37}{120}\right)\) | \(e\left(\frac{11}{48}\right)\) | \(e\left(\frac{29}{48}\right)\) |