Basic properties
Modulus: | \(669\) | |
Conductor: | \(223\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(111\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
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Real: | no | |
Primitive: | no, induced from \(\chi_{223}(43,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 669.m
\(\chi_{669}(19,\cdot)\) \(\chi_{669}(25,\cdot)\) \(\chi_{669}(31,\cdot)\) \(\chi_{669}(37,\cdot)\) \(\chi_{669}(43,\cdot)\) \(\chi_{669}(55,\cdot)\) \(\chi_{669}(58,\cdot)\) \(\chi_{669}(73,\cdot)\) \(\chi_{669}(76,\cdot)\) \(\chi_{669}(94,\cdot)\) \(\chi_{669}(100,\cdot)\) \(\chi_{669}(106,\cdot)\) \(\chi_{669}(109,\cdot)\) \(\chi_{669}(121,\cdot)\) \(\chi_{669}(124,\cdot)\) \(\chi_{669}(127,\cdot)\) \(\chi_{669}(130,\cdot)\) \(\chi_{669}(133,\cdot)\) \(\chi_{669}(139,\cdot)\) \(\chi_{669}(148,\cdot)\) \(\chi_{669}(166,\cdot)\) \(\chi_{669}(172,\cdot)\) \(\chi_{669}(175,\cdot)\) \(\chi_{669}(178,\cdot)\) \(\chi_{669}(181,\cdot)\) \(\chi_{669}(199,\cdot)\) \(\chi_{669}(202,\cdot)\) \(\chi_{669}(211,\cdot)\) \(\chi_{669}(217,\cdot)\) \(\chi_{669}(220,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{111})$ |
Fixed field: | Number field defined by a degree 111 polynomial (not computed) |
Values on generators
\((224,226)\) → \((1,e\left(\frac{59}{111}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(11\) | \(13\) | \(14\) | \(16\) |
\( \chi_{ 669 }(43, a) \) | \(1\) | \(1\) | \(e\left(\frac{25}{37}\right)\) | \(e\left(\frac{13}{37}\right)\) | \(e\left(\frac{34}{111}\right)\) | \(e\left(\frac{23}{37}\right)\) | \(e\left(\frac{1}{37}\right)\) | \(e\left(\frac{109}{111}\right)\) | \(e\left(\frac{97}{111}\right)\) | \(e\left(\frac{5}{37}\right)\) | \(e\left(\frac{11}{37}\right)\) | \(e\left(\frac{26}{37}\right)\) |