Basic properties
Modulus: | \(6018\) | |
Conductor: | \(3009\) | 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 \(\chi_{3009}(1835,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 6018.x
\(\chi_{6018}(101,\cdot)\) \(\chi_{6018}(305,\cdot)\) \(\chi_{6018}(509,\cdot)\) \(\chi_{6018}(917,\cdot)\) \(\chi_{6018}(1223,\cdot)\) \(\chi_{6018}(1427,\cdot)\) \(\chi_{6018}(1529,\cdot)\) \(\chi_{6018}(1631,\cdot)\) \(\chi_{6018}(1835,\cdot)\) \(\chi_{6018}(2039,\cdot)\) \(\chi_{6018}(2345,\cdot)\) \(\chi_{6018}(2651,\cdot)\) \(\chi_{6018}(2753,\cdot)\) \(\chi_{6018}(2855,\cdot)\) \(\chi_{6018}(3059,\cdot)\) \(\chi_{6018}(3161,\cdot)\) \(\chi_{6018}(3263,\cdot)\) \(\chi_{6018}(3365,\cdot)\) \(\chi_{6018}(3671,\cdot)\) \(\chi_{6018}(3773,\cdot)\) \(\chi_{6018}(3875,\cdot)\) \(\chi_{6018}(3977,\cdot)\) \(\chi_{6018}(4079,\cdot)\) \(\chi_{6018}(4691,\cdot)\) \(\chi_{6018}(4793,\cdot)\) \(\chi_{6018}(5303,\cdot)\) \(\chi_{6018}(5711,\cdot)\) \(\chi_{6018}(5813,\cdot)\)
Related number fields
Field of values: | $\Q(\zeta_{29})$ |
Fixed field: | Number field defined by a degree 58 polynomial |
Values on generators
\((4013,1771,1123)\) → \((-1,-1,e\left(\frac{51}{58}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(5\) | \(7\) | \(11\) | \(13\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) | \(35\) |
\( \chi_{ 6018 }(1835, a) \) | \(1\) | \(1\) | \(e\left(\frac{8}{29}\right)\) | \(e\left(\frac{19}{58}\right)\) | \(e\left(\frac{57}{58}\right)\) | \(e\left(\frac{33}{58}\right)\) | \(e\left(\frac{12}{29}\right)\) | \(e\left(\frac{11}{58}\right)\) | \(e\left(\frac{16}{29}\right)\) | \(e\left(\frac{18}{29}\right)\) | \(e\left(\frac{17}{29}\right)\) | \(e\left(\frac{35}{58}\right)\) |