Basic properties
Modulus: | \(574\) | |
Conductor: | \(287\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(120\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
Real: | no | |
Primitive: | no, induced from \(\chi_{287}(17,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 574.bf
\(\chi_{574}(17,\cdot)\) \(\chi_{574}(19,\cdot)\) \(\chi_{574}(47,\cdot)\) \(\chi_{574}(75,\cdot)\) \(\chi_{574}(89,\cdot)\) \(\chi_{574}(101,\cdot)\) \(\chi_{574}(117,\cdot)\) \(\chi_{574}(129,\cdot)\) \(\chi_{574}(145,\cdot)\) \(\chi_{574}(157,\cdot)\) \(\chi_{574}(171,\cdot)\) \(\chi_{574}(199,\cdot)\) \(\chi_{574}(227,\cdot)\) \(\chi_{574}(229,\cdot)\) \(\chi_{574}(257,\cdot)\) \(\chi_{574}(299,\cdot)\) \(\chi_{574}(311,\cdot)\) \(\chi_{574}(313,\cdot)\) \(\chi_{574}(339,\cdot)\) \(\chi_{574}(341,\cdot)\) \(\chi_{574}(381,\cdot)\) \(\chi_{574}(395,\cdot)\) \(\chi_{574}(397,\cdot)\) \(\chi_{574}(423,\cdot)\) \(\chi_{574}(425,\cdot)\) \(\chi_{574}(439,\cdot)\) \(\chi_{574}(479,\cdot)\) \(\chi_{574}(481,\cdot)\) \(\chi_{574}(507,\cdot)\) \(\chi_{574}(509,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{120})$ |
Fixed field: | Number field defined by a degree 120 polynomial (not computed) |
Values on generators
\((493,211)\) → \((e\left(\frac{1}{6}\right),e\left(\frac{33}{40}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(23\) | \(25\) |
\( \chi_{ 574 }(17, a) \) | \(1\) | \(1\) | \(e\left(\frac{13}{24}\right)\) | \(e\left(\frac{59}{60}\right)\) | \(e\left(\frac{1}{12}\right)\) | \(e\left(\frac{17}{120}\right)\) | \(e\left(\frac{3}{40}\right)\) | \(e\left(\frac{21}{40}\right)\) | \(e\left(\frac{47}{120}\right)\) | \(e\left(\frac{31}{120}\right)\) | \(e\left(\frac{1}{30}\right)\) | \(e\left(\frac{29}{30}\right)\) |