Basic properties
Modulus: | \(9464\) | |
Conductor: | \(1183\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(156\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
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Real: | no | |
Primitive: | no, induced from \(\chi_{1183}(41,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 9464.in
\(\chi_{9464}(41,\cdot)\) \(\chi_{9464}(97,\cdot)\) \(\chi_{9464}(713,\cdot)\) \(\chi_{9464}(769,\cdot)\) \(\chi_{9464}(825,\cdot)\) \(\chi_{9464}(1385,\cdot)\) \(\chi_{9464}(1497,\cdot)\) \(\chi_{9464}(1553,\cdot)\) \(\chi_{9464}(2113,\cdot)\) \(\chi_{9464}(2169,\cdot)\) \(\chi_{9464}(2225,\cdot)\) \(\chi_{9464}(2281,\cdot)\) \(\chi_{9464}(2841,\cdot)\) \(\chi_{9464}(2897,\cdot)\) \(\chi_{9464}(3009,\cdot)\) \(\chi_{9464}(3569,\cdot)\) \(\chi_{9464}(3625,\cdot)\) \(\chi_{9464}(3681,\cdot)\) \(\chi_{9464}(4297,\cdot)\) \(\chi_{9464}(4353,\cdot)\) \(\chi_{9464}(4409,\cdot)\) \(\chi_{9464}(4465,\cdot)\) \(\chi_{9464}(5025,\cdot)\) \(\chi_{9464}(5081,\cdot)\) \(\chi_{9464}(5137,\cdot)\) \(\chi_{9464}(5193,\cdot)\) \(\chi_{9464}(5753,\cdot)\) \(\chi_{9464}(5809,\cdot)\) \(\chi_{9464}(5865,\cdot)\) \(\chi_{9464}(5921,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{156})$ |
Fixed field: | Number field defined by a degree 156 polynomial (not computed) |
Values on generators
\((2367,4733,2705,9297)\) → \((1,1,-1,e\left(\frac{85}{156}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(9\) | \(11\) | \(15\) | \(17\) | \(19\) | \(23\) | \(25\) | \(27\) |
\( \chi_{ 9464 }(41, a) \) | \(1\) | \(1\) | \(e\left(\frac{5}{78}\right)\) | \(e\left(\frac{21}{52}\right)\) | \(e\left(\frac{5}{39}\right)\) | \(e\left(\frac{19}{156}\right)\) | \(e\left(\frac{73}{156}\right)\) | \(e\left(\frac{2}{39}\right)\) | \(e\left(\frac{11}{12}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{21}{26}\right)\) | \(e\left(\frac{5}{26}\right)\) |