Basic properties
Modulus: | \(10015\) | |
Conductor: | \(10015\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(4004\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
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Real: | no | |
Primitive: | yes | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 10015.bv
\(\chi_{10015}(3,\cdot)\) \(\chi_{10015}(12,\cdot)\) \(\chi_{10015}(13,\cdot)\) \(\chi_{10015}(27,\cdot)\) \(\chi_{10015}(47,\cdot)\) \(\chi_{10015}(52,\cdot)\) \(\chi_{10015}(58,\cdot)\) \(\chi_{10015}(62,\cdot)\) \(\chi_{10015}(73,\cdot)\) \(\chi_{10015}(77,\cdot)\) \(\chi_{10015}(82,\cdot)\) \(\chi_{10015}(107,\cdot)\) \(\chi_{10015}(108,\cdot)\) \(\chi_{10015}(117,\cdot)\) \(\chi_{10015}(122,\cdot)\) \(\chi_{10015}(138,\cdot)\) \(\chi_{10015}(147,\cdot)\) \(\chi_{10015}(167,\cdot)\) \(\chi_{10015}(173,\cdot)\) \(\chi_{10015}(177,\cdot)\) \(\chi_{10015}(187,\cdot)\) \(\chi_{10015}(188,\cdot)\) \(\chi_{10015}(192,\cdot)\) \(\chi_{10015}(197,\cdot)\) \(\chi_{10015}(198,\cdot)\) \(\chi_{10015}(203,\cdot)\) \(\chi_{10015}(212,\cdot)\) \(\chi_{10015}(217,\cdot)\) \(\chi_{10015}(218,\cdot)\) \(\chi_{10015}(222,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{4004})$ |
Fixed field: | Number field defined by a degree 4004 polynomial (not computed) |
Values on generators
\((4007,4011)\) → \((i,e\left(\frac{92}{1001}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(7\) | \(8\) | \(9\) | \(11\) | \(12\) | \(13\) |
\( \chi_{ 10015 }(117, a) \) | \(-1\) | \(1\) | \(e\left(\frac{75}{572}\right)\) | \(e\left(\frac{2203}{4004}\right)\) | \(e\left(\frac{75}{286}\right)\) | \(e\left(\frac{62}{91}\right)\) | \(e\left(\frac{2221}{4004}\right)\) | \(e\left(\frac{225}{572}\right)\) | \(e\left(\frac{201}{2002}\right)\) | \(e\left(\frac{72}{143}\right)\) | \(e\left(\frac{3253}{4004}\right)\) | \(e\left(\frac{243}{4004}\right)\) |