Basic properties
Modulus: | \(731\) | |
Conductor: | \(731\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(112\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
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 731.bj
\(\chi_{731}(22,\cdot)\) \(\chi_{731}(27,\cdot)\) \(\chi_{731}(39,\cdot)\) \(\chi_{731}(45,\cdot)\) \(\chi_{731}(65,\cdot)\) \(\chi_{731}(75,\cdot)\) \(\chi_{731}(82,\cdot)\) \(\chi_{731}(88,\cdot)\) \(\chi_{731}(108,\cdot)\) \(\chi_{731}(113,\cdot)\) \(\chi_{731}(125,\cdot)\) \(\chi_{731}(131,\cdot)\) \(\chi_{731}(156,\cdot)\) \(\chi_{731}(180,\cdot)\) \(\chi_{731}(194,\cdot)\) \(\chi_{731}(199,\cdot)\) \(\chi_{731}(211,\cdot)\) \(\chi_{731}(260,\cdot)\) \(\chi_{731}(266,\cdot)\) \(\chi_{731}(303,\cdot)\) \(\chi_{731}(309,\cdot)\) \(\chi_{731}(328,\cdot)\) \(\chi_{731}(333,\cdot)\) \(\chi_{731}(346,\cdot)\) \(\chi_{731}(352,\cdot)\) \(\chi_{731}(371,\cdot)\) \(\chi_{731}(414,\cdot)\) \(\chi_{731}(419,\cdot)\) \(\chi_{731}(432,\cdot)\) \(\chi_{731}(452,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{112})$ |
Fixed field: | Number field defined by a degree 112 polynomial (not computed) |
Values on generators
\((173,562)\) → \((e\left(\frac{9}{16}\right),e\left(\frac{5}{14}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
\( \chi_{ 731 }(65, a) \) | \(1\) | \(1\) | \(e\left(\frac{29}{56}\right)\) | \(e\left(\frac{103}{112}\right)\) | \(e\left(\frac{1}{28}\right)\) | \(e\left(\frac{83}{112}\right)\) | \(e\left(\frac{7}{16}\right)\) | \(e\left(\frac{11}{16}\right)\) | \(e\left(\frac{31}{56}\right)\) | \(e\left(\frac{47}{56}\right)\) | \(e\left(\frac{29}{112}\right)\) | \(e\left(\frac{73}{112}\right)\) |