Basic properties
| Modulus: | \(7350\) | |
| Conductor: | \(3675\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(420\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{3675}(23,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 7350.dq
\(\chi_{7350}(23,\cdot)\) \(\chi_{7350}(53,\cdot)\) \(\chi_{7350}(137,\cdot)\) \(\chi_{7350}(233,\cdot)\) \(\chi_{7350}(317,\cdot)\) \(\chi_{7350}(347,\cdot)\) \(\chi_{7350}(473,\cdot)\) \(\chi_{7350}(527,\cdot)\) \(\chi_{7350}(653,\cdot)\) \(\chi_{7350}(683,\cdot)\) \(\chi_{7350}(737,\cdot)\) \(\chi_{7350}(767,\cdot)\) \(\chi_{7350}(947,\cdot)\) \(\chi_{7350}(977,\cdot)\) \(\chi_{7350}(1073,\cdot)\) \(\chi_{7350}(1103,\cdot)\) \(\chi_{7350}(1187,\cdot)\) \(\chi_{7350}(1283,\cdot)\) \(\chi_{7350}(1313,\cdot)\) \(\chi_{7350}(1367,\cdot)\) \(\chi_{7350}(1397,\cdot)\) \(\chi_{7350}(1523,\cdot)\) \(\chi_{7350}(1577,\cdot)\) \(\chi_{7350}(1703,\cdot)\) \(\chi_{7350}(1787,\cdot)\) \(\chi_{7350}(1817,\cdot)\) \(\chi_{7350}(1913,\cdot)\) \(\chi_{7350}(1997,\cdot)\) \(\chi_{7350}(2123,\cdot)\) \(\chi_{7350}(2153,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{420})$ |
| Fixed field: | Number field defined by a degree 420 polynomial (not computed) |
Values on generators
\((4901,1177,2551)\) → \((-1,e\left(\frac{11}{20}\right),e\left(\frac{19}{21}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(29\) | \(31\) | \(37\) | \(41\) | \(43\) |
| \( \chi_{ 7350 }(23, a) \) | \(1\) | \(1\) | \(e\left(\frac{103}{210}\right)\) | \(e\left(\frac{43}{140}\right)\) | \(e\left(\frac{113}{420}\right)\) | \(e\left(\frac{17}{30}\right)\) | \(e\left(\frac{391}{420}\right)\) | \(e\left(\frac{31}{35}\right)\) | \(e\left(\frac{11}{15}\right)\) | \(e\left(\frac{379}{420}\right)\) | \(e\left(\frac{19}{70}\right)\) | \(e\left(\frac{19}{28}\right)\) |