Basic properties
| Modulus: | \(4018\) | |
| 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 4018.bt
\(\chi_{4018}(113,\cdot)\) \(\chi_{4018}(127,\cdot)\) \(\chi_{4018}(351,\cdot)\) \(\chi_{4018}(435,\cdot)\) \(\chi_{4018}(701,\cdot)\) \(\chi_{4018}(925,\cdot)\) \(\chi_{4018}(1009,\cdot)\) \(\chi_{4018}(1261,\cdot)\) \(\chi_{4018}(1499,\cdot)\) \(\chi_{4018}(1583,\cdot)\) \(\chi_{4018}(1835,\cdot)\) \(\chi_{4018}(1849,\cdot)\) \(\chi_{4018}(2073,\cdot)\) \(\chi_{4018}(2409,\cdot)\) \(\chi_{4018}(2423,\cdot)\) \(\chi_{4018}(2731,\cdot)\) \(\chi_{4018}(2983,\cdot)\) \(\chi_{4018}(2997,\cdot)\) \(\chi_{4018}(3221,\cdot)\) \(\chi_{4018}(3305,\cdot)\) \(\chi_{4018}(3557,\cdot)\) \(\chi_{4018}(3571,\cdot)\) \(\chi_{4018}(3795,\cdot)\) \(\chi_{4018}(3879,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{35})$ |
| Fixed field: | Number field defined by a degree 70 polynomial |
Values on generators
\((493,785)\) → \((e\left(\frac{5}{7}\right),e\left(\frac{7}{10}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(23\) | \(25\) |
| \( \chi_{ 4018 }(113, a) \) | \(1\) | \(1\) | \(e\left(\frac{3}{14}\right)\) | \(e\left(\frac{4}{35}\right)\) | \(e\left(\frac{3}{7}\right)\) | \(e\left(\frac{47}{70}\right)\) | \(e\left(\frac{19}{70}\right)\) | \(e\left(\frac{23}{70}\right)\) | \(e\left(\frac{67}{70}\right)\) | \(e\left(\frac{3}{10}\right)\) | \(e\left(\frac{12}{35}\right)\) | \(e\left(\frac{8}{35}\right)\) |