Basic properties
| Modulus: | \(5600\) | |
| Conductor: | \(5600\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(120\) | 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 5600.ie
\(\chi_{5600}(117,\cdot)\) \(\chi_{5600}(173,\cdot)\) \(\chi_{5600}(437,\cdot)\) \(\chi_{5600}(677,\cdot)\) \(\chi_{5600}(733,\cdot)\) \(\chi_{5600}(997,\cdot)\) \(\chi_{5600}(1053,\cdot)\) \(\chi_{5600}(1237,\cdot)\) \(\chi_{5600}(1613,\cdot)\) \(\chi_{5600}(1797,\cdot)\) \(\chi_{5600}(1853,\cdot)\) \(\chi_{5600}(2117,\cdot)\) \(\chi_{5600}(2173,\cdot)\) \(\chi_{5600}(2413,\cdot)\) \(\chi_{5600}(2677,\cdot)\) \(\chi_{5600}(2733,\cdot)\) \(\chi_{5600}(2917,\cdot)\) \(\chi_{5600}(2973,\cdot)\) \(\chi_{5600}(3237,\cdot)\) \(\chi_{5600}(3477,\cdot)\) \(\chi_{5600}(3533,\cdot)\) \(\chi_{5600}(3797,\cdot)\) \(\chi_{5600}(3853,\cdot)\) \(\chi_{5600}(4037,\cdot)\) \(\chi_{5600}(4413,\cdot)\) \(\chi_{5600}(4597,\cdot)\) \(\chi_{5600}(4653,\cdot)\) \(\chi_{5600}(4917,\cdot)\) \(\chi_{5600}(4973,\cdot)\) \(\chi_{5600}(5213,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{120})$ |
| Fixed field: | Number field defined by a degree 120 polynomial (not computed) |
Values on generators
\((351,4901,5377,801)\) → \((1,e\left(\frac{5}{8}\right),e\left(\frac{13}{20}\right),e\left(\frac{5}{6}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(9\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(27\) | \(29\) | \(31\) |
| \( \chi_{ 5600 }(117, a) \) | \(1\) | \(1\) | \(e\left(\frac{31}{120}\right)\) | \(e\left(\frac{31}{60}\right)\) | \(e\left(\frac{103}{120}\right)\) | \(e\left(\frac{9}{40}\right)\) | \(e\left(\frac{47}{60}\right)\) | \(e\left(\frac{29}{120}\right)\) | \(e\left(\frac{17}{30}\right)\) | \(e\left(\frac{31}{40}\right)\) | \(e\left(\frac{7}{40}\right)\) | \(e\left(\frac{1}{30}\right)\) |