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 \(\chi_{1183}(73,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 9464.im
\(\chi_{9464}(73,\cdot)\) \(\chi_{9464}(369,\cdot)\) \(\chi_{9464}(593,\cdot)\) \(\chi_{9464}(801,\cdot)\) \(\chi_{9464}(1097,\cdot)\) \(\chi_{9464}(1305,\cdot)\) \(\chi_{9464}(1321,\cdot)\) \(\chi_{9464}(1529,\cdot)\) \(\chi_{9464}(1825,\cdot)\) \(\chi_{9464}(2033,\cdot)\) \(\chi_{9464}(2049,\cdot)\) \(\chi_{9464}(2257,\cdot)\) \(\chi_{9464}(2553,\cdot)\) \(\chi_{9464}(2761,\cdot)\) \(\chi_{9464}(2777,\cdot)\) \(\chi_{9464}(2985,\cdot)\) \(\chi_{9464}(3489,\cdot)\) \(\chi_{9464}(3505,\cdot)\) \(\chi_{9464}(3713,\cdot)\) \(\chi_{9464}(4009,\cdot)\) \(\chi_{9464}(4217,\cdot)\) \(\chi_{9464}(4233,\cdot)\) \(\chi_{9464}(4441,\cdot)\) \(\chi_{9464}(4737,\cdot)\) \(\chi_{9464}(4945,\cdot)\) \(\chi_{9464}(4961,\cdot)\) \(\chi_{9464}(5465,\cdot)\) \(\chi_{9464}(5673,\cdot)\) \(\chi_{9464}(5689,\cdot)\) \(\chi_{9464}(5897,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{156})$ |
Fixed field: | Number field defined by a degree 156 polynomial (not computed) |
Values on generators
\((2367,4733,2705,9297)\) → \((1,1,e\left(\frac{1}{6}\right),e\left(\frac{17}{52}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(9\) | \(11\) | \(15\) | \(17\) | \(19\) | \(23\) | \(25\) | \(27\) |
\( \chi_{ 9464 }(73, a) \) | \(1\) | \(1\) | \(e\left(\frac{55}{78}\right)\) | \(e\left(\frac{121}{156}\right)\) | \(e\left(\frac{16}{39}\right)\) | \(e\left(\frac{53}{156}\right)\) | \(e\left(\frac{25}{52}\right)\) | \(e\left(\frac{35}{39}\right)\) | \(e\left(\frac{1}{12}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{43}{78}\right)\) | \(e\left(\frac{3}{26}\right)\) |