Basic properties
| Modulus: | \(5390\) | |
| Conductor: | \(539\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(70\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{539}(41,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 5390.ct
\(\chi_{5390}(41,\cdot)\) \(\chi_{5390}(321,\cdot)\) \(\chi_{5390}(601,\cdot)\) \(\chi_{5390}(811,\cdot)\) \(\chi_{5390}(1091,\cdot)\) \(\chi_{5390}(1161,\cdot)\) \(\chi_{5390}(1581,\cdot)\) \(\chi_{5390}(1931,\cdot)\) \(\chi_{5390}(2141,\cdot)\) \(\chi_{5390}(2631,\cdot)\) \(\chi_{5390}(2701,\cdot)\) \(\chi_{5390}(2911,\cdot)\) \(\chi_{5390}(3121,\cdot)\) \(\chi_{5390}(3401,\cdot)\) \(\chi_{5390}(3471,\cdot)\) \(\chi_{5390}(3681,\cdot)\) \(\chi_{5390}(3891,\cdot)\) \(\chi_{5390}(4171,\cdot)\) \(\chi_{5390}(4241,\cdot)\) \(\chi_{5390}(4451,\cdot)\) \(\chi_{5390}(4661,\cdot)\) \(\chi_{5390}(4941,\cdot)\) \(\chi_{5390}(5011,\cdot)\) \(\chi_{5390}(5221,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{35})$ |
| Fixed field: | Number field defined by a degree 70 polynomial |
Values on generators
\((2157,4511,981)\) → \((1,e\left(\frac{5}{14}\right),e\left(\frac{3}{10}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(9\) | \(13\) | \(17\) | \(19\) | \(23\) | \(27\) | \(29\) | \(31\) | \(37\) |
| \( \chi_{ 5390 }(41, a) \) | \(1\) | \(1\) | \(e\left(\frac{53}{70}\right)\) | \(e\left(\frac{18}{35}\right)\) | \(e\left(\frac{3}{35}\right)\) | \(e\left(\frac{22}{35}\right)\) | \(e\left(\frac{2}{5}\right)\) | \(e\left(\frac{4}{7}\right)\) | \(e\left(\frac{19}{70}\right)\) | \(e\left(\frac{37}{70}\right)\) | \(e\left(\frac{3}{10}\right)\) | \(e\left(\frac{1}{35}\right)\) |