Basic properties
Modulus: | \(731\) | |
Conductor: | \(731\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(336\) | 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 731.bm
\(\chi_{731}(3,\cdot)\) \(\chi_{731}(5,\cdot)\) \(\chi_{731}(12,\cdot)\) \(\chi_{731}(20,\cdot)\) \(\chi_{731}(28,\cdot)\) \(\chi_{731}(29,\cdot)\) \(\chi_{731}(46,\cdot)\) \(\chi_{731}(48,\cdot)\) \(\chi_{731}(61,\cdot)\) \(\chi_{731}(62,\cdot)\) \(\chi_{731}(63,\cdot)\) \(\chi_{731}(71,\cdot)\) \(\chi_{731}(73,\cdot)\) \(\chi_{731}(91,\cdot)\) \(\chi_{731}(105,\cdot)\) \(\chi_{731}(112,\cdot)\) \(\chi_{731}(114,\cdot)\) \(\chi_{731}(116,\cdot)\) \(\chi_{731}(141,\cdot)\) \(\chi_{731}(147,\cdot)\) \(\chi_{731}(148,\cdot)\) \(\chi_{731}(158,\cdot)\) \(\chi_{731}(159,\cdot)\) \(\chi_{731}(163,\cdot)\) \(\chi_{731}(175,\cdot)\) \(\chi_{731}(177,\cdot)\) \(\chi_{731}(184,\cdot)\) \(\chi_{731}(190,\cdot)\) \(\chi_{731}(192,\cdot)\) \(\chi_{731}(198,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{336})$ |
Fixed field: | Number field defined by a degree 336 polynomial (not computed) |
Values on generators
\((173,562)\) → \((e\left(\frac{1}{16}\right),e\left(\frac{13}{42}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
\( \chi_{ 731 }(700, a) \) | \(1\) | \(1\) | \(e\left(\frac{13}{56}\right)\) | \(e\left(\frac{125}{336}\right)\) | \(e\left(\frac{13}{28}\right)\) | \(e\left(\frac{17}{336}\right)\) | \(e\left(\frac{29}{48}\right)\) | \(e\left(\frac{25}{48}\right)\) | \(e\left(\frac{39}{56}\right)\) | \(e\left(\frac{125}{168}\right)\) | \(e\left(\frac{95}{336}\right)\) | \(e\left(\frac{81}{112}\right)\) |