Basic properties
Modulus: | \(6018\) | |
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 \(\chi_{59}(36,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 6018.u
\(\chi_{6018}(205,\cdot)\) \(\chi_{6018}(307,\cdot)\) \(\chi_{6018}(715,\cdot)\) \(\chi_{6018}(1225,\cdot)\) \(\chi_{6018}(1327,\cdot)\) \(\chi_{6018}(1939,\cdot)\) \(\chi_{6018}(2041,\cdot)\) \(\chi_{6018}(2143,\cdot)\) \(\chi_{6018}(2245,\cdot)\) \(\chi_{6018}(2347,\cdot)\) \(\chi_{6018}(2653,\cdot)\) \(\chi_{6018}(2755,\cdot)\) \(\chi_{6018}(2857,\cdot)\) \(\chi_{6018}(2959,\cdot)\) \(\chi_{6018}(3163,\cdot)\) \(\chi_{6018}(3265,\cdot)\) \(\chi_{6018}(3367,\cdot)\) \(\chi_{6018}(3673,\cdot)\) \(\chi_{6018}(3979,\cdot)\) \(\chi_{6018}(4183,\cdot)\) \(\chi_{6018}(4387,\cdot)\) \(\chi_{6018}(4489,\cdot)\) \(\chi_{6018}(4591,\cdot)\) \(\chi_{6018}(4795,\cdot)\) \(\chi_{6018}(5101,\cdot)\) \(\chi_{6018}(5509,\cdot)\) \(\chi_{6018}(5713,\cdot)\) \(\chi_{6018}(5917,\cdot)\)
Related number fields
Field of values: | $\Q(\zeta_{29})$ |
Fixed field: | Number field defined by a degree 29 polynomial |
Values on generators
\((4013,1771,1123)\) → \((1,1,e\left(\frac{22}{29}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(5\) | \(7\) | \(11\) | \(13\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) | \(35\) |
\( \chi_{ 6018 }(3163, a) \) | \(1\) | \(1\) | \(e\left(\frac{16}{29}\right)\) | \(e\left(\frac{19}{29}\right)\) | \(e\left(\frac{28}{29}\right)\) | \(e\left(\frac{4}{29}\right)\) | \(e\left(\frac{24}{29}\right)\) | \(e\left(\frac{11}{29}\right)\) | \(e\left(\frac{3}{29}\right)\) | \(e\left(\frac{7}{29}\right)\) | \(e\left(\frac{5}{29}\right)\) | \(e\left(\frac{6}{29}\right)\) |