Basic properties
Modulus: | \(2500\) | |
Conductor: | \(2500\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(250\) | 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 2500.t
\(\chi_{2500}(11,\cdot)\) \(\chi_{2500}(31,\cdot)\) \(\chi_{2500}(71,\cdot)\) \(\chi_{2500}(91,\cdot)\) \(\chi_{2500}(111,\cdot)\) \(\chi_{2500}(131,\cdot)\) \(\chi_{2500}(171,\cdot)\) \(\chi_{2500}(191,\cdot)\) \(\chi_{2500}(211,\cdot)\) \(\chi_{2500}(231,\cdot)\) \(\chi_{2500}(271,\cdot)\) \(\chi_{2500}(291,\cdot)\) \(\chi_{2500}(311,\cdot)\) \(\chi_{2500}(331,\cdot)\) \(\chi_{2500}(371,\cdot)\) \(\chi_{2500}(391,\cdot)\) \(\chi_{2500}(411,\cdot)\) \(\chi_{2500}(431,\cdot)\) \(\chi_{2500}(471,\cdot)\) \(\chi_{2500}(491,\cdot)\) \(\chi_{2500}(511,\cdot)\) \(\chi_{2500}(531,\cdot)\) \(\chi_{2500}(571,\cdot)\) \(\chi_{2500}(591,\cdot)\) \(\chi_{2500}(611,\cdot)\) \(\chi_{2500}(631,\cdot)\) \(\chi_{2500}(671,\cdot)\) \(\chi_{2500}(691,\cdot)\) \(\chi_{2500}(711,\cdot)\) \(\chi_{2500}(731,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{125})$ |
Fixed field: | Number field defined by a degree 250 polynomial (not computed) |
Values on generators
\((1251,1877)\) → \((-1,e\left(\frac{79}{125}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(3\) | \(7\) | \(9\) | \(11\) | \(13\) | \(17\) | \(19\) | \(21\) | \(23\) | \(27\) |
\( \chi_{ 2500 }(411, a) \) | \(-1\) | \(1\) | \(e\left(\frac{31}{250}\right)\) | \(e\left(\frac{1}{50}\right)\) | \(e\left(\frac{31}{125}\right)\) | \(e\left(\frac{83}{250}\right)\) | \(e\left(\frac{106}{125}\right)\) | \(e\left(\frac{42}{125}\right)\) | \(e\left(\frac{169}{250}\right)\) | \(e\left(\frac{18}{125}\right)\) | \(e\left(\frac{223}{250}\right)\) | \(e\left(\frac{93}{250}\right)\) |