Basic properties
| Modulus: | \(3009\) | |
| Conductor: | \(3009\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(58\) | 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 3009.v
\(\chi_{3009}(50,\cdot)\) \(\chi_{3009}(101,\cdot)\) \(\chi_{3009}(152,\cdot)\) \(\chi_{3009}(254,\cdot)\) \(\chi_{3009}(305,\cdot)\) \(\chi_{3009}(356,\cdot)\) \(\chi_{3009}(509,\cdot)\) \(\chi_{3009}(662,\cdot)\) \(\chi_{3009}(764,\cdot)\) \(\chi_{3009}(866,\cdot)\) \(\chi_{3009}(917,\cdot)\) \(\chi_{3009}(968,\cdot)\) \(\chi_{3009}(1070,\cdot)\) \(\chi_{3009}(1223,\cdot)\) \(\chi_{3009}(1427,\cdot)\) \(\chi_{3009}(1529,\cdot)\) \(\chi_{3009}(1631,\cdot)\) \(\chi_{3009}(1682,\cdot)\) \(\chi_{3009}(1784,\cdot)\) \(\chi_{3009}(1835,\cdot)\) \(\chi_{3009}(2039,\cdot)\) \(\chi_{3009}(2294,\cdot)\) \(\chi_{3009}(2345,\cdot)\) \(\chi_{3009}(2651,\cdot)\) \(\chi_{3009}(2702,\cdot)\) \(\chi_{3009}(2753,\cdot)\) \(\chi_{3009}(2804,\cdot)\) \(\chi_{3009}(2855,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{29})$ |
| Fixed field: | Number field defined by a degree 58 polynomial |
Values on generators
\((1004,1771,1123)\) → \((-1,-1,e\left(\frac{5}{58}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(11\) | \(13\) | \(14\) | \(16\) |
| \( \chi_{ 3009 }(917, a) \) | \(1\) | \(1\) | \(e\left(\frac{17}{29}\right)\) | \(e\left(\frac{5}{29}\right)\) | \(e\left(\frac{15}{29}\right)\) | \(e\left(\frac{3}{58}\right)\) | \(e\left(\frac{22}{29}\right)\) | \(e\left(\frac{3}{29}\right)\) | \(e\left(\frac{9}{58}\right)\) | \(e\left(\frac{51}{58}\right)\) | \(e\left(\frac{37}{58}\right)\) | \(e\left(\frac{10}{29}\right)\) |