Basic properties
Modulus: | \(5625\) | |
Conductor: | \(625\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(125\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
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Real: | no | |
Primitive: | no, induced from \(\chi_{625}(46,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 5625.bf
\(\chi_{5625}(46,\cdot)\) \(\chi_{5625}(91,\cdot)\) \(\chi_{5625}(136,\cdot)\) \(\chi_{5625}(181,\cdot)\) \(\chi_{5625}(271,\cdot)\) \(\chi_{5625}(316,\cdot)\) \(\chi_{5625}(361,\cdot)\) \(\chi_{5625}(406,\cdot)\) \(\chi_{5625}(496,\cdot)\) \(\chi_{5625}(541,\cdot)\) \(\chi_{5625}(586,\cdot)\) \(\chi_{5625}(631,\cdot)\) \(\chi_{5625}(721,\cdot)\) \(\chi_{5625}(766,\cdot)\) \(\chi_{5625}(811,\cdot)\) \(\chi_{5625}(856,\cdot)\) \(\chi_{5625}(946,\cdot)\) \(\chi_{5625}(991,\cdot)\) \(\chi_{5625}(1036,\cdot)\) \(\chi_{5625}(1081,\cdot)\) \(\chi_{5625}(1171,\cdot)\) \(\chi_{5625}(1216,\cdot)\) \(\chi_{5625}(1261,\cdot)\) \(\chi_{5625}(1306,\cdot)\) \(\chi_{5625}(1396,\cdot)\) \(\chi_{5625}(1441,\cdot)\) \(\chi_{5625}(1486,\cdot)\) \(\chi_{5625}(1531,\cdot)\) \(\chi_{5625}(1621,\cdot)\) \(\chi_{5625}(1666,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{125})$ |
Fixed field: | Number field defined by a degree 125 polynomial (not computed) |
Values on generators
\((4376,1252)\) → \((1,e\left(\frac{108}{125}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(7\) | \(8\) | \(11\) | \(13\) | \(14\) | \(16\) | \(17\) | \(19\) |
\( \chi_{ 5625 }(46, a) \) | \(1\) | \(1\) | \(e\left(\frac{108}{125}\right)\) | \(e\left(\frac{91}{125}\right)\) | \(e\left(\frac{1}{25}\right)\) | \(e\left(\frac{74}{125}\right)\) | \(e\left(\frac{33}{125}\right)\) | \(e\left(\frac{12}{125}\right)\) | \(e\left(\frac{113}{125}\right)\) | \(e\left(\frac{57}{125}\right)\) | \(e\left(\frac{59}{125}\right)\) | \(e\left(\frac{19}{125}\right)\) |