Basic properties
Modulus: | \(10009\) | |
Conductor: | \(10009\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(139\) | 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: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 10009.m
\(\chi_{10009}(26,\cdot)\) \(\chi_{10009}(51,\cdot)\) \(\chi_{10009}(82,\cdot)\) \(\chi_{10009}(193,\cdot)\) \(\chi_{10009}(195,\cdot)\) \(\chi_{10009}(346,\cdot)\) \(\chi_{10009}(351,\cdot)\) \(\chi_{10009}(385,\cdot)\) \(\chi_{10009}(485,\cdot)\) \(\chi_{10009}(615,\cdot)\) \(\chi_{10009}(676,\cdot)\) \(\chi_{10009}(693,\cdot)\) \(\chi_{10009}(873,\cdot)\) \(\chi_{10009}(1107,\cdot)\) \(\chi_{10009}(1326,\cdot)\) \(\chi_{10009}(1338,\cdot)\) \(\chi_{10009}(1445,\cdot)\) \(\chi_{10009}(1523,\cdot)\) \(\chi_{10009}(1543,\cdot)\) \(\chi_{10009}(1673,\cdot)\) \(\chi_{10009}(1703,\cdot)\) \(\chi_{10009}(1788,\cdot)\) \(\chi_{10009}(2132,\cdot)\) \(\chi_{10009}(2228,\cdot)\) \(\chi_{10009}(2534,\cdot)\) \(\chi_{10009}(2595,\cdot)\) \(\chi_{10009}(2601,\cdot)\) \(\chi_{10009}(2618,\cdot)\) \(\chi_{10009}(2645,\cdot)\) \(\chi_{10009}(2680,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{139})$ |
Fixed field: | Number field defined by a degree 139 polynomial (not computed) |
Values on generators
\(11\) → \(e\left(\frac{118}{139}\right)\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
\( \chi_{ 10009 }(26, a) \) | \(1\) | \(1\) | \(e\left(\frac{86}{139}\right)\) | \(e\left(\frac{90}{139}\right)\) | \(e\left(\frac{33}{139}\right)\) | \(e\left(\frac{98}{139}\right)\) | \(e\left(\frac{37}{139}\right)\) | \(e\left(\frac{2}{139}\right)\) | \(e\left(\frac{119}{139}\right)\) | \(e\left(\frac{41}{139}\right)\) | \(e\left(\frac{45}{139}\right)\) | \(e\left(\frac{118}{139}\right)\) |