Basic properties
| Modulus: | \(8036\) | |
| Conductor: | \(2009\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(70\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{2009}(113,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 8036.dm
\(\chi_{8036}(113,\cdot)\) \(\chi_{8036}(701,\cdot)\) \(\chi_{8036}(925,\cdot)\) \(\chi_{8036}(1009,\cdot)\) \(\chi_{8036}(1261,\cdot)\) \(\chi_{8036}(1849,\cdot)\) \(\chi_{8036}(2073,\cdot)\) \(\chi_{8036}(2409,\cdot)\) \(\chi_{8036}(2997,\cdot)\) \(\chi_{8036}(3221,\cdot)\) \(\chi_{8036}(3305,\cdot)\) \(\chi_{8036}(3557,\cdot)\) \(\chi_{8036}(4145,\cdot)\) \(\chi_{8036}(4369,\cdot)\) \(\chi_{8036}(4453,\cdot)\) \(\chi_{8036}(5517,\cdot)\) \(\chi_{8036}(5601,\cdot)\) \(\chi_{8036}(5853,\cdot)\) \(\chi_{8036}(6441,\cdot)\) \(\chi_{8036}(6749,\cdot)\) \(\chi_{8036}(7001,\cdot)\) \(\chi_{8036}(7589,\cdot)\) \(\chi_{8036}(7813,\cdot)\) \(\chi_{8036}(7897,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{35})$ |
| Fixed field: | Number field defined by a degree 70 polynomial |
Values on generators
\((4019,493,785)\) → \((1,e\left(\frac{5}{7}\right),e\left(\frac{7}{10}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(23\) | \(25\) |
| \( \chi_{ 8036 }(113, a) \) | \(1\) | \(1\) | \(e\left(\frac{3}{14}\right)\) | \(e\left(\frac{4}{35}\right)\) | \(e\left(\frac{3}{7}\right)\) | \(e\left(\frac{47}{70}\right)\) | \(e\left(\frac{19}{70}\right)\) | \(e\left(\frac{23}{70}\right)\) | \(e\left(\frac{67}{70}\right)\) | \(e\left(\frac{3}{10}\right)\) | \(e\left(\frac{12}{35}\right)\) | \(e\left(\frac{8}{35}\right)\) |