Basic properties
sage: chi.conductor()
pari: znconreyconductor(g,chi)
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Conductor | = | 1000 |
sage: chi.multiplicative_order()
pari: charorder(g,chi)
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Order | = | 100 |
Real | = | No |
sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1 \\ if not primitive returns [cond,factorization]
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Primitive | = | No |
sage: chi.is_odd()
pari: zncharisodd(g,chi)
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Parity | = | Odd |
Orbit label | = | 4000.ct |
Orbit index | = | 72 |
Galois orbit
\(\chi_{4000}(17,\cdot)\) \(\chi_{4000}(113,\cdot)\) \(\chi_{4000}(177,\cdot)\) \(\chi_{4000}(273,\cdot)\) \(\chi_{4000}(337,\cdot)\) \(\chi_{4000}(433,\cdot)\) \(\chi_{4000}(497,\cdot)\) \(\chi_{4000}(753,\cdot)\) \(\chi_{4000}(817,\cdot)\) \(\chi_{4000}(913,\cdot)\) \(\chi_{4000}(977,\cdot)\) \(\chi_{4000}(1073,\cdot)\) \(\chi_{4000}(1137,\cdot)\) \(\chi_{4000}(1233,\cdot)\) \(\chi_{4000}(1297,\cdot)\) \(\chi_{4000}(1553,\cdot)\) \(\chi_{4000}(1617,\cdot)\) \(\chi_{4000}(1713,\cdot)\) \(\chi_{4000}(1777,\cdot)\) \(\chi_{4000}(1873,\cdot)\) \(\chi_{4000}(1937,\cdot)\) \(\chi_{4000}(2033,\cdot)\) \(\chi_{4000}(2097,\cdot)\) \(\chi_{4000}(2353,\cdot)\) \(\chi_{4000}(2417,\cdot)\) \(\chi_{4000}(2513,\cdot)\) \(\chi_{4000}(2577,\cdot)\) \(\chi_{4000}(2673,\cdot)\) \(\chi_{4000}(2737,\cdot)\) \(\chi_{4000}(2833,\cdot)\) ...
Inducing primitive character
Values on generators
\((2751,2501,1377)\) → \((1,-1,e\left(\frac{27}{100}\right))\)
Values
-1 | 1 | 3 | 7 | 9 | 11 | 13 | 17 | 19 | 21 | 23 | 27 |
\(-1\) | \(1\) | \(e\left(\frac{39}{100}\right)\) | \(e\left(\frac{19}{20}\right)\) | \(e\left(\frac{39}{50}\right)\) | \(e\left(\frac{1}{50}\right)\) | \(e\left(\frac{3}{100}\right)\) | \(e\left(\frac{71}{100}\right)\) | \(e\left(\frac{9}{25}\right)\) | \(e\left(\frac{17}{50}\right)\) | \(e\left(\frac{37}{100}\right)\) | \(e\left(\frac{17}{100}\right)\) |
Related number fields
Field of values | \(\Q(\zeta_{100})\) |