Basic properties
| Modulus: | \(2450\) | |
| Conductor: | \(1225\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(35\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{1225}(71,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 2450.bd
\(\chi_{2450}(71,\cdot)\) \(\chi_{2450}(141,\cdot)\) \(\chi_{2450}(211,\cdot)\) \(\chi_{2450}(281,\cdot)\) \(\chi_{2450}(421,\cdot)\) \(\chi_{2450}(561,\cdot)\) \(\chi_{2450}(631,\cdot)\) \(\chi_{2450}(771,\cdot)\) \(\chi_{2450}(841,\cdot)\) \(\chi_{2450}(911,\cdot)\) \(\chi_{2450}(1121,\cdot)\) \(\chi_{2450}(1191,\cdot)\) \(\chi_{2450}(1261,\cdot)\) \(\chi_{2450}(1331,\cdot)\) \(\chi_{2450}(1541,\cdot)\) \(\chi_{2450}(1611,\cdot)\) \(\chi_{2450}(1681,\cdot)\) \(\chi_{2450}(1821,\cdot)\) \(\chi_{2450}(1891,\cdot)\) \(\chi_{2450}(2031,\cdot)\) \(\chi_{2450}(2171,\cdot)\) \(\chi_{2450}(2241,\cdot)\) \(\chi_{2450}(2311,\cdot)\) \(\chi_{2450}(2381,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{35})$ |
| Fixed field: | Number field defined by a degree 35 polynomial |
Values on generators
\((1177,101)\) → \((e\left(\frac{3}{5}\right),e\left(\frac{4}{7}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(9\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(27\) | \(29\) | \(31\) |
| \( \chi_{ 2450 }(71, a) \) | \(1\) | \(1\) | \(e\left(\frac{27}{35}\right)\) | \(e\left(\frac{19}{35}\right)\) | \(e\left(\frac{16}{35}\right)\) | \(e\left(\frac{9}{35}\right)\) | \(e\left(\frac{3}{35}\right)\) | \(e\left(\frac{4}{5}\right)\) | \(e\left(\frac{11}{35}\right)\) | \(e\left(\frac{11}{35}\right)\) | \(e\left(\frac{17}{35}\right)\) | \(e\left(\frac{4}{5}\right)\) |