Basic properties
Modulus: | \(5625\) | |
Conductor: | \(5625\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(375\) | 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 5625.bo
\(\chi_{5625}(16,\cdot)\) \(\chi_{5625}(31,\cdot)\) \(\chi_{5625}(61,\cdot)\) \(\chi_{5625}(106,\cdot)\) \(\chi_{5625}(121,\cdot)\) \(\chi_{5625}(166,\cdot)\) \(\chi_{5625}(196,\cdot)\) \(\chi_{5625}(211,\cdot)\) \(\chi_{5625}(241,\cdot)\) \(\chi_{5625}(256,\cdot)\) \(\chi_{5625}(286,\cdot)\) \(\chi_{5625}(331,\cdot)\) \(\chi_{5625}(346,\cdot)\) \(\chi_{5625}(391,\cdot)\) \(\chi_{5625}(421,\cdot)\) \(\chi_{5625}(436,\cdot)\) \(\chi_{5625}(466,\cdot)\) \(\chi_{5625}(481,\cdot)\) \(\chi_{5625}(511,\cdot)\) \(\chi_{5625}(556,\cdot)\) \(\chi_{5625}(571,\cdot)\) \(\chi_{5625}(616,\cdot)\) \(\chi_{5625}(646,\cdot)\) \(\chi_{5625}(661,\cdot)\) \(\chi_{5625}(691,\cdot)\) \(\chi_{5625}(706,\cdot)\) \(\chi_{5625}(736,\cdot)\) \(\chi_{5625}(781,\cdot)\) \(\chi_{5625}(796,\cdot)\) \(\chi_{5625}(841,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{375})$ |
Fixed field: | Number field defined by a degree 375 polynomial (not computed) |
Values on generators
\((4376,1252)\) → \((e\left(\frac{2}{3}\right),e\left(\frac{1}{125}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(7\) | \(8\) | \(11\) | \(13\) | \(14\) | \(16\) | \(17\) | \(19\) |
\( \chi_{ 5625 }(16, a) \) | \(1\) | \(1\) | \(e\left(\frac{253}{375}\right)\) | \(e\left(\frac{131}{375}\right)\) | \(e\left(\frac{41}{75}\right)\) | \(e\left(\frac{3}{125}\right)\) | \(e\left(\frac{178}{375}\right)\) | \(e\left(\frac{167}{375}\right)\) | \(e\left(\frac{83}{375}\right)\) | \(e\left(\frac{262}{375}\right)\) | \(e\left(\frac{48}{125}\right)\) | \(e\left(\frac{43}{125}\right)\) |