Basic properties
Modulus: | \(6018\) | |
Conductor: | \(1003\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(58\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
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Real: | no | |
Primitive: | no, induced from \(\chi_{1003}(611,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 6018.bb
\(\chi_{6018}(169,\cdot)\) \(\chi_{6018}(271,\cdot)\) \(\chi_{6018}(373,\cdot)\) \(\chi_{6018}(475,\cdot)\) \(\chi_{6018}(577,\cdot)\) \(\chi_{6018}(883,\cdot)\) \(\chi_{6018}(985,\cdot)\) \(\chi_{6018}(1087,\cdot)\) \(\chi_{6018}(1189,\cdot)\) \(\chi_{6018}(1393,\cdot)\) \(\chi_{6018}(1495,\cdot)\) \(\chi_{6018}(1597,\cdot)\) \(\chi_{6018}(1903,\cdot)\) \(\chi_{6018}(2209,\cdot)\) \(\chi_{6018}(2413,\cdot)\) \(\chi_{6018}(2617,\cdot)\) \(\chi_{6018}(2719,\cdot)\) \(\chi_{6018}(2821,\cdot)\) \(\chi_{6018}(3025,\cdot)\) \(\chi_{6018}(3331,\cdot)\) \(\chi_{6018}(3739,\cdot)\) \(\chi_{6018}(3943,\cdot)\) \(\chi_{6018}(4147,\cdot)\) \(\chi_{6018}(4453,\cdot)\) \(\chi_{6018}(4555,\cdot)\) \(\chi_{6018}(4963,\cdot)\) \(\chi_{6018}(5473,\cdot)\) \(\chi_{6018}(5575,\cdot)\)
Related number fields
Field of values: | $\Q(\zeta_{29})$ |
Fixed field: | Number field defined by a degree 58 polynomial |
Values on generators
\((4013,1771,1123)\) → \((1,-1,e\left(\frac{5}{29}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(5\) | \(7\) | \(11\) | \(13\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) | \(35\) |
\( \chi_{ 6018 }(2617, a) \) | \(1\) | \(1\) | \(e\left(\frac{31}{58}\right)\) | \(e\left(\frac{35}{58}\right)\) | \(e\left(\frac{47}{58}\right)\) | \(e\left(\frac{22}{29}\right)\) | \(e\left(\frac{16}{29}\right)\) | \(e\left(\frac{5}{58}\right)\) | \(e\left(\frac{2}{29}\right)\) | \(e\left(\frac{19}{58}\right)\) | \(e\left(\frac{55}{58}\right)\) | \(e\left(\frac{4}{29}\right)\) |