Basic properties
| Modulus: | \(7350\) | |
| 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 \(\chi_{1225}(211,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 7350.cf
\(\chi_{7350}(211,\cdot)\) \(\chi_{7350}(421,\cdot)\) \(\chi_{7350}(631,\cdot)\) \(\chi_{7350}(841,\cdot)\) \(\chi_{7350}(1261,\cdot)\) \(\chi_{7350}(1681,\cdot)\) \(\chi_{7350}(1891,\cdot)\) \(\chi_{7350}(2311,\cdot)\) \(\chi_{7350}(2521,\cdot)\) \(\chi_{7350}(2731,\cdot)\) \(\chi_{7350}(3361,\cdot)\) \(\chi_{7350}(3571,\cdot)\) \(\chi_{7350}(3781,\cdot)\) \(\chi_{7350}(3991,\cdot)\) \(\chi_{7350}(4621,\cdot)\) \(\chi_{7350}(4831,\cdot)\) \(\chi_{7350}(5041,\cdot)\) \(\chi_{7350}(5461,\cdot)\) \(\chi_{7350}(5671,\cdot)\) \(\chi_{7350}(6091,\cdot)\) \(\chi_{7350}(6511,\cdot)\) \(\chi_{7350}(6721,\cdot)\) \(\chi_{7350}(6931,\cdot)\) \(\chi_{7350}(7141,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{35})$ |
| Fixed field: | Number field defined by a degree 35 polynomial |
Values on generators
\((4901,1177,2551)\) → \((1,e\left(\frac{4}{5}\right),e\left(\frac{5}{7}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(29\) | \(31\) | \(37\) | \(41\) | \(43\) |
| \( \chi_{ 7350 }(211, a) \) | \(1\) | \(1\) | \(e\left(\frac{13}{35}\right)\) | \(e\left(\frac{27}{35}\right)\) | \(e\left(\frac{9}{35}\right)\) | \(e\left(\frac{2}{5}\right)\) | \(e\left(\frac{33}{35}\right)\) | \(e\left(\frac{16}{35}\right)\) | \(e\left(\frac{2}{5}\right)\) | \(e\left(\frac{2}{35}\right)\) | \(e\left(\frac{32}{35}\right)\) | \(e\left(\frac{2}{7}\right)\) |