Basic properties
Modulus: | \(6018\) | |
Conductor: | \(3009\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(116\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
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Real: | no | |
Primitive: | no, induced from \(\chi_{3009}(2945,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 6018.bf
\(\chi_{6018}(47,\cdot)\) \(\chi_{6018}(89,\cdot)\) \(\chi_{6018}(149,\cdot)\) \(\chi_{6018}(191,\cdot)\) \(\chi_{6018}(455,\cdot)\) \(\chi_{6018}(659,\cdot)\) \(\chi_{6018}(701,\cdot)\) \(\chi_{6018}(863,\cdot)\) \(\chi_{6018}(1109,\cdot)\) \(\chi_{6018}(1211,\cdot)\) \(\chi_{6018}(1271,\cdot)\) \(\chi_{6018}(1517,\cdot)\) \(\chi_{6018}(1577,\cdot)\) \(\chi_{6018}(1721,\cdot)\) \(\chi_{6018}(1781,\cdot)\) \(\chi_{6018}(1883,\cdot)\) \(\chi_{6018}(1925,\cdot)\) \(\chi_{6018}(1985,\cdot)\) \(\chi_{6018}(2189,\cdot)\) \(\chi_{6018}(2333,\cdot)\) \(\chi_{6018}(2393,\cdot)\) \(\chi_{6018}(2639,\cdot)\) \(\chi_{6018}(2699,\cdot)\) \(\chi_{6018}(2843,\cdot)\) \(\chi_{6018}(2945,\cdot)\) \(\chi_{6018}(3005,\cdot)\) \(\chi_{6018}(3047,\cdot)\) \(\chi_{6018}(3107,\cdot)\) \(\chi_{6018}(3209,\cdot)\) \(\chi_{6018}(3251,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{116})$ |
Fixed field: | Number field defined by a degree 116 polynomial (not computed) |
Values on generators
\((4013,1771,1123)\) → \((-1,-i,e\left(\frac{35}{58}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(5\) | \(7\) | \(11\) | \(13\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) | \(35\) |
\( \chi_{ 6018 }(2945, a) \) | \(1\) | \(1\) | \(e\left(\frac{101}{116}\right)\) | \(e\left(\frac{13}{116}\right)\) | \(e\left(\frac{97}{116}\right)\) | \(e\left(\frac{9}{58}\right)\) | \(e\left(\frac{25}{58}\right)\) | \(e\left(\frac{93}{116}\right)\) | \(e\left(\frac{43}{58}\right)\) | \(e\left(\frac{17}{116}\right)\) | \(e\left(\frac{37}{116}\right)\) | \(e\left(\frac{57}{58}\right)\) |