Basic properties
Modulus: | \(4009\) | |
Conductor: | \(4009\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(630\) | 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 4009.eu
\(\chi_{4009}(60,\cdot)\) \(\chi_{4009}(86,\cdot)\) \(\chi_{4009}(89,\cdot)\) \(\chi_{4009}(90,\cdot)\) \(\chi_{4009}(97,\cdot)\) \(\chi_{4009}(98,\cdot)\) \(\chi_{4009}(124,\cdot)\) \(\chi_{4009}(129,\cdot)\) \(\chi_{4009}(135,\cdot)\) \(\chi_{4009}(146,\cdot)\) \(\chi_{4009}(147,\cdot)\) \(\chi_{4009}(186,\cdot)\) \(\chi_{4009}(200,\cdot)\) \(\chi_{4009}(219,\cdot)\) \(\chi_{4009}(238,\cdot)\) \(\chi_{4009}(279,\cdot)\) \(\chi_{4009}(300,\cdot)\) \(\chi_{4009}(326,\cdot)\) \(\chi_{4009}(357,\cdot)\) \(\chi_{4009}(409,\cdot)\) \(\chi_{4009}(440,\cdot)\) \(\chi_{4009}(450,\cdot)\) \(\chi_{4009}(490,\cdot)\) \(\chi_{4009}(508,\cdot)\) \(\chi_{4009}(546,\cdot)\) \(\chi_{4009}(554,\cdot)\) \(\chi_{4009}(622,\cdot)\) \(\chi_{4009}(641,\cdot)\) \(\chi_{4009}(660,\cdot)\) \(\chi_{4009}(661,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{315})$ |
Fixed field: | Number field defined by a degree 630 polynomial (not computed) |
Values on generators
\((2111,1901)\) → \((e\left(\frac{13}{18}\right),e\left(\frac{59}{70}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
\( \chi_{ 4009 }(60, a) \) | \(1\) | \(1\) | \(e\left(\frac{178}{315}\right)\) | \(e\left(\frac{199}{315}\right)\) | \(e\left(\frac{41}{315}\right)\) | \(e\left(\frac{256}{315}\right)\) | \(e\left(\frac{62}{315}\right)\) | \(e\left(\frac{103}{210}\right)\) | \(e\left(\frac{73}{105}\right)\) | \(e\left(\frac{83}{315}\right)\) | \(e\left(\frac{17}{45}\right)\) | \(e\left(\frac{22}{105}\right)\) |