Basic properties
Modulus: | \(6040\) | |
Conductor: | \(6040\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(100\) | 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
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Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 6040.ep
\(\chi_{6040}(123,\cdot)\) \(\chi_{6040}(427,\cdot)\) \(\chi_{6040}(547,\cdot)\) \(\chi_{6040}(563,\cdot)\) \(\chi_{6040}(827,\cdot)\) \(\chi_{6040}(987,\cdot)\) \(\chi_{6040}(1107,\cdot)\) \(\chi_{6040}(1403,\cdot)\) \(\chi_{6040}(1427,\cdot)\) \(\chi_{6040}(1443,\cdot)\) \(\chi_{6040}(1483,\cdot)\) \(\chi_{6040}(1507,\cdot)\) \(\chi_{6040}(1747,\cdot)\) \(\chi_{6040}(2123,\cdot)\) \(\chi_{6040}(2363,\cdot)\) \(\chi_{6040}(2507,\cdot)\) \(\chi_{6040}(2587,\cdot)\) \(\chi_{6040}(2747,\cdot)\) \(\chi_{6040}(2843,\cdot)\) \(\chi_{6040}(2947,\cdot)\) \(\chi_{6040}(2963,\cdot)\) \(\chi_{6040}(3147,\cdot)\) \(\chi_{6040}(3243,\cdot)\) \(\chi_{6040}(3403,\cdot)\) \(\chi_{6040}(3523,\cdot)\) \(\chi_{6040}(3747,\cdot)\) \(\chi_{6040}(3843,\cdot)\) \(\chi_{6040}(3923,\cdot)\) \(\chi_{6040}(4163,\cdot)\) \(\chi_{6040}(4187,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{100})$ |
Fixed field: | Number field defined by a degree 100 polynomial |
Values on generators
\((1511,3021,2417,761)\) → \((-1,-1,-i,e\left(\frac{22}{25}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(3\) | \(7\) | \(9\) | \(11\) | \(13\) | \(17\) | \(19\) | \(21\) | \(23\) | \(27\) |
\( \chi_{ 6040 }(123, a) \) | \(1\) | \(1\) | \(e\left(\frac{53}{100}\right)\) | \(e\left(\frac{21}{100}\right)\) | \(e\left(\frac{3}{50}\right)\) | \(e\left(\frac{18}{25}\right)\) | \(e\left(\frac{83}{100}\right)\) | \(e\left(\frac{79}{100}\right)\) | \(e\left(\frac{7}{10}\right)\) | \(e\left(\frac{37}{50}\right)\) | \(e\left(\frac{19}{20}\right)\) | \(e\left(\frac{59}{100}\right)\) |