Basic properties
| Modulus: | \(5950\) | |
| Conductor: | \(2975\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(240\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{2975}(487,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 5950.fn
\(\chi_{5950}(177,\cdot)\) \(\chi_{5950}(233,\cdot)\) \(\chi_{5950}(303,\cdot)\) \(\chi_{5950}(317,\cdot)\) \(\chi_{5950}(347,\cdot)\) \(\chi_{5950}(403,\cdot)\) \(\chi_{5950}(473,\cdot)\) \(\chi_{5950}(487,\cdot)\) \(\chi_{5950}(513,\cdot)\) \(\chi_{5950}(583,\cdot)\) \(\chi_{5950}(683,\cdot)\) \(\chi_{5950}(737,\cdot)\) \(\chi_{5950}(753,\cdot)\) \(\chi_{5950}(877,\cdot)\) \(\chi_{5950}(1047,\cdot)\) \(\chi_{5950}(1367,\cdot)\) \(\chi_{5950}(1423,\cdot)\) \(\chi_{5950}(1537,\cdot)\) \(\chi_{5950}(1663,\cdot)\) \(\chi_{5950}(1677,\cdot)\) \(\chi_{5950}(1703,\cdot)\) \(\chi_{5950}(1773,\cdot)\) \(\chi_{5950}(1873,\cdot)\) \(\chi_{5950}(1927,\cdot)\) \(\chi_{5950}(2067,\cdot)\) \(\chi_{5950}(2097,\cdot)\) \(\chi_{5950}(2237,\cdot)\) \(\chi_{5950}(2613,\cdot)\) \(\chi_{5950}(2683,\cdot)\) \(\chi_{5950}(2697,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{240})$ |
| Fixed field: | Number field defined by a degree 240 polynomial (not computed) |
Values on generators
\((477,2551,2451)\) → \((e\left(\frac{9}{20}\right),e\left(\frac{2}{3}\right),e\left(\frac{7}{16}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(9\) | \(11\) | \(13\) | \(19\) | \(23\) | \(27\) | \(29\) | \(31\) | \(33\) |
| \( \chi_{ 5950 }(487, a) \) | \(1\) | \(1\) | \(e\left(\frac{61}{240}\right)\) | \(e\left(\frac{61}{120}\right)\) | \(e\left(\frac{223}{240}\right)\) | \(e\left(\frac{3}{10}\right)\) | \(e\left(\frac{67}{120}\right)\) | \(e\left(\frac{203}{240}\right)\) | \(e\left(\frac{61}{80}\right)\) | \(e\left(\frac{47}{80}\right)\) | \(e\left(\frac{49}{240}\right)\) | \(e\left(\frac{11}{60}\right)\) |