Basic properties
Modulus: | \(2009\) | |
Conductor: | \(2009\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(70\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
Real: | no | |
Primitive: | yes | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 2009.bt
\(\chi_{2009}(64,\cdot)\) \(\chi_{2009}(113,\cdot)\) \(\chi_{2009}(127,\cdot)\) \(\chi_{2009}(351,\cdot)\) \(\chi_{2009}(400,\cdot)\) \(\chi_{2009}(414,\cdot)\) \(\chi_{2009}(435,\cdot)\) \(\chi_{2009}(701,\cdot)\) \(\chi_{2009}(722,\cdot)\) \(\chi_{2009}(925,\cdot)\) \(\chi_{2009}(974,\cdot)\) \(\chi_{2009}(988,\cdot)\) \(\chi_{2009}(1009,\cdot)\) \(\chi_{2009}(1212,\cdot)\) \(\chi_{2009}(1261,\cdot)\) \(\chi_{2009}(1296,\cdot)\) \(\chi_{2009}(1499,\cdot)\) \(\chi_{2009}(1548,\cdot)\) \(\chi_{2009}(1562,\cdot)\) \(\chi_{2009}(1583,\cdot)\) \(\chi_{2009}(1786,\cdot)\) \(\chi_{2009}(1835,\cdot)\) \(\chi_{2009}(1849,\cdot)\) \(\chi_{2009}(1870,\cdot)\)
Related number fields
Field of values: | $\Q(\zeta_{35})$ |
Fixed field: | Number field defined by a degree 70 polynomial |
Values on generators
\((493,785)\) → \((e\left(\frac{4}{7}\right),e\left(\frac{7}{10}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(8\) | \(9\) | \(10\) | \(11\) | \(12\) |
\( \chi_{ 2009 }(1835, a) \) | \(1\) | \(1\) | \(e\left(\frac{2}{35}\right)\) | \(e\left(\frac{1}{14}\right)\) | \(e\left(\frac{4}{35}\right)\) | \(e\left(\frac{34}{35}\right)\) | \(e\left(\frac{9}{70}\right)\) | \(e\left(\frac{6}{35}\right)\) | \(e\left(\frac{1}{7}\right)\) | \(e\left(\frac{1}{35}\right)\) | \(e\left(\frac{67}{70}\right)\) | \(e\left(\frac{13}{70}\right)\) |