Basic properties
Modulus: | \(8041\) | |
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: | no, induced from \(\chi_{731}(277,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 8041.fk
\(\chi_{8041}(12,\cdot)\) \(\chi_{8041}(177,\cdot)\) \(\chi_{8041}(243,\cdot)\) \(\chi_{8041}(320,\cdot)\) \(\chi_{8041}(364,\cdot)\) \(\chi_{8041}(507,\cdot)\) \(\chi_{8041}(760,\cdot)\) \(\chi_{8041}(793,\cdot)\) \(\chi_{8041}(804,\cdot)\) \(\chi_{8041}(958,\cdot)\) \(\chi_{8041}(980,\cdot)\) \(\chi_{8041}(1431,\cdot)\) \(\chi_{8041}(1508,\cdot)\) \(\chi_{8041}(1574,\cdot)\) \(\chi_{8041}(1695,\cdot)\) \(\chi_{8041}(1706,\cdot)\) \(\chi_{8041}(1739,\cdot)\) \(\chi_{8041}(1882,\cdot)\) \(\chi_{8041}(1926,\cdot)\) \(\chi_{8041}(2047,\cdot)\) \(\chi_{8041}(2069,\cdot)\) \(\chi_{8041}(2135,\cdot)\) \(\chi_{8041}(2179,\cdot)\) \(\chi_{8041}(2256,\cdot)\) \(\chi_{8041}(2377,\cdot)\) \(\chi_{8041}(2454,\cdot)\) \(\chi_{8041}(2608,\cdot)\) \(\chi_{8041}(2641,\cdot)\) \(\chi_{8041}(2696,\cdot)\) \(\chi_{8041}(2828,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{336})$ |
Fixed field: | Number field defined by a degree 336 polynomial (not computed) |
Values on generators
\((6580,2366,562)\) → \((1,e\left(\frac{5}{16}\right),e\left(\frac{19}{42}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(12\) |
\( \chi_{ 8041 }(1739, a) \) | \(1\) | \(1\) | \(e\left(\frac{33}{56}\right)\) | \(e\left(\frac{257}{336}\right)\) | \(e\left(\frac{5}{28}\right)\) | \(e\left(\frac{293}{336}\right)\) | \(e\left(\frac{17}{48}\right)\) | \(e\left(\frac{13}{48}\right)\) | \(e\left(\frac{43}{56}\right)\) | \(e\left(\frac{89}{168}\right)\) | \(e\left(\frac{155}{336}\right)\) | \(e\left(\frac{317}{336}\right)\) |