Basic properties
Modulus: | \(751\) | |
Conductor: | \(751\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(125\) | 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 751.l
\(\chi_{751}(8,\cdot)\) \(\chi_{751}(10,\cdot)\) \(\chi_{751}(26,\cdot)\) \(\chi_{751}(36,\cdot)\) \(\chi_{751}(38,\cdot)\) \(\chi_{751}(42,\cdot)\) \(\chi_{751}(43,\cdot)\) \(\chi_{751}(45,\cdot)\) \(\chi_{751}(46,\cdot)\) \(\chi_{751}(49,\cdot)\) \(\chi_{751}(64,\cdot)\) \(\chi_{751}(71,\cdot)\) \(\chi_{751}(93,\cdot)\) \(\chi_{751}(94,\cdot)\) \(\chi_{751}(100,\cdot)\) \(\chi_{751}(118,\cdot)\) \(\chi_{751}(125,\cdot)\) \(\chi_{751}(132,\cdot)\) \(\chi_{751}(148,\cdot)\) \(\chi_{751}(151,\cdot)\) \(\chi_{751}(154,\cdot)\) \(\chi_{751}(165,\cdot)\) \(\chi_{751}(185,\cdot)\) \(\chi_{751}(187,\cdot)\) \(\chi_{751}(189,\cdot)\) \(\chi_{751}(191,\cdot)\) \(\chi_{751}(207,\cdot)\) \(\chi_{751}(208,\cdot)\) \(\chi_{751}(237,\cdot)\) \(\chi_{751}(244,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{125})$ |
Fixed field: | Number field defined by a degree 125 polynomial (not computed) |
Values on generators
\(3\) → \(e\left(\frac{118}{125}\right)\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
\( \chi_{ 751 }(125, a) \) | \(1\) | \(1\) | \(e\left(\frac{88}{125}\right)\) | \(e\left(\frac{118}{125}\right)\) | \(e\left(\frac{51}{125}\right)\) | \(e\left(\frac{98}{125}\right)\) | \(e\left(\frac{81}{125}\right)\) | \(e\left(\frac{68}{125}\right)\) | \(e\left(\frac{14}{125}\right)\) | \(e\left(\frac{111}{125}\right)\) | \(e\left(\frac{61}{125}\right)\) | \(e\left(\frac{24}{25}\right)\) |