Basic properties
Modulus: | \(2009\) | |
Conductor: | \(2009\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(168\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
Real: | no | |
Primitive: | yes | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 2009.cc
\(\chi_{2009}(44,\cdot)\) \(\chi_{2009}(109,\cdot)\) \(\chi_{2009}(137,\cdot)\) \(\chi_{2009}(191,\cdot)\) \(\chi_{2009}(219,\cdot)\) \(\chi_{2009}(249,\cdot)\) \(\chi_{2009}(284,\cdot)\) \(\chi_{2009}(331,\cdot)\) \(\chi_{2009}(366,\cdot)\) \(\chi_{2009}(396,\cdot)\) \(\chi_{2009}(424,\cdot)\) \(\chi_{2009}(478,\cdot)\) \(\chi_{2009}(506,\cdot)\) \(\chi_{2009}(536,\cdot)\) \(\chi_{2009}(571,\cdot)\) \(\chi_{2009}(653,\cdot)\) \(\chi_{2009}(683,\cdot)\) \(\chi_{2009}(711,\cdot)\) \(\chi_{2009}(793,\cdot)\) \(\chi_{2009}(823,\cdot)\) \(\chi_{2009}(858,\cdot)\) \(\chi_{2009}(905,\cdot)\) \(\chi_{2009}(940,\cdot)\) \(\chi_{2009}(970,\cdot)\) \(\chi_{2009}(1052,\cdot)\) \(\chi_{2009}(1080,\cdot)\) \(\chi_{2009}(1110,\cdot)\) \(\chi_{2009}(1192,\cdot)\) \(\chi_{2009}(1227,\cdot)\) \(\chi_{2009}(1257,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{168})$ |
Fixed field: | Number field defined by a degree 168 polynomial (not computed) |
Values on generators
\((493,785)\) → \((e\left(\frac{4}{21}\right),e\left(\frac{3}{8}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(8\) | \(9\) | \(10\) | \(11\) | \(12\) |
\( \chi_{ 2009 }(44, a) \) | \(-1\) | \(1\) | \(e\left(\frac{59}{84}\right)\) | \(e\left(\frac{137}{168}\right)\) | \(e\left(\frac{17}{42}\right)\) | \(e\left(\frac{65}{84}\right)\) | \(e\left(\frac{29}{56}\right)\) | \(e\left(\frac{3}{28}\right)\) | \(e\left(\frac{53}{84}\right)\) | \(e\left(\frac{10}{21}\right)\) | \(e\left(\frac{125}{168}\right)\) | \(e\left(\frac{37}{168}\right)\) |