Basic properties
Modulus: | \(4012\) | |
Conductor: | \(59\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(29\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
Real: | no | |
Primitive: | no, induced from \(\chi_{59}(51,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 4012.u
\(\chi_{4012}(137,\cdot)\) \(\chi_{4012}(205,\cdot)\) \(\chi_{4012}(341,\cdot)\) \(\chi_{4012}(477,\cdot)\) \(\chi_{4012}(749,\cdot)\) \(\chi_{4012}(953,\cdot)\) \(\chi_{4012}(1089,\cdot)\) \(\chi_{4012}(1157,\cdot)\) \(\chi_{4012}(1225,\cdot)\) \(\chi_{4012}(1361,\cdot)\) \(\chi_{4012}(1497,\cdot)\) \(\chi_{4012}(1701,\cdot)\) \(\chi_{4012}(1905,\cdot)\) \(\chi_{4012}(1973,\cdot)\) \(\chi_{4012}(2041,\cdot)\) \(\chi_{4012}(2177,\cdot)\) \(\chi_{4012}(2245,\cdot)\) \(\chi_{4012}(2313,\cdot)\) \(\chi_{4012}(2381,\cdot)\) \(\chi_{4012}(2585,\cdot)\) \(\chi_{4012}(2653,\cdot)\) \(\chi_{4012}(2721,\cdot)\) \(\chi_{4012}(2789,\cdot)\) \(\chi_{4012}(2857,\cdot)\) \(\chi_{4012}(3265,\cdot)\) \(\chi_{4012}(3333,\cdot)\) \(\chi_{4012}(3673,\cdot)\) \(\chi_{4012}(3945,\cdot)\)
Related number fields
Field of values: | $\Q(\zeta_{29})$ |
Fixed field: | Number field defined by a degree 29 polynomial |
Values on generators
\((2007,3777,3129)\) → \((1,1,e\left(\frac{16}{29}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(19\) | \(21\) | \(23\) |
\( \chi_{ 4012 }(3945, a) \) | \(1\) | \(1\) | \(e\left(\frac{17}{29}\right)\) | \(e\left(\frac{9}{29}\right)\) | \(e\left(\frac{27}{29}\right)\) | \(e\left(\frac{5}{29}\right)\) | \(e\left(\frac{23}{29}\right)\) | \(e\left(\frac{24}{29}\right)\) | \(e\left(\frac{26}{29}\right)\) | \(e\left(\frac{28}{29}\right)\) | \(e\left(\frac{15}{29}\right)\) | \(e\left(\frac{8}{29}\right)\) |