Basic properties
Modulus: | \(8470\) | |
Conductor: | \(4235\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(132\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
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Real: | no | |
Primitive: | no, induced from \(\chi_{4235}(912,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 8470.da
\(\chi_{8470}(263,\cdot)\) \(\chi_{8470}(373,\cdot)\) \(\chi_{8470}(417,\cdot)\) \(\chi_{8470}(527,\cdot)\) \(\chi_{8470}(1033,\cdot)\) \(\chi_{8470}(1143,\cdot)\) \(\chi_{8470}(1187,\cdot)\) \(\chi_{8470}(1297,\cdot)\) \(\chi_{8470}(1803,\cdot)\) \(\chi_{8470}(1913,\cdot)\) \(\chi_{8470}(1957,\cdot)\) \(\chi_{8470}(2067,\cdot)\) \(\chi_{8470}(2573,\cdot)\) \(\chi_{8470}(2683,\cdot)\) \(\chi_{8470}(2727,\cdot)\) \(\chi_{8470}(2837,\cdot)\) \(\chi_{8470}(3343,\cdot)\) \(\chi_{8470}(3453,\cdot)\) \(\chi_{8470}(3497,\cdot)\) \(\chi_{8470}(3607,\cdot)\) \(\chi_{8470}(4223,\cdot)\) \(\chi_{8470}(4267,\cdot)\) \(\chi_{8470}(4377,\cdot)\) \(\chi_{8470}(4883,\cdot)\) \(\chi_{8470}(4993,\cdot)\) \(\chi_{8470}(5037,\cdot)\) \(\chi_{8470}(5147,\cdot)\) \(\chi_{8470}(5653,\cdot)\) \(\chi_{8470}(5763,\cdot)\) \(\chi_{8470}(5917,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{132})$ |
Fixed field: | Number field defined by a degree 132 polynomial (not computed) |
Values on generators
\((6777,6051,7141)\) → \((i,e\left(\frac{1}{3}\right),e\left(\frac{13}{22}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(3\) | \(9\) | \(13\) | \(17\) | \(19\) | \(23\) | \(27\) | \(29\) | \(31\) | \(37\) |
\( \chi_{ 8470 }(5147, a) \) | \(1\) | \(1\) | \(e\left(\frac{1}{12}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{19}{44}\right)\) | \(e\left(\frac{71}{132}\right)\) | \(e\left(\frac{7}{33}\right)\) | \(e\left(\frac{103}{132}\right)\) | \(i\) | \(e\left(\frac{6}{11}\right)\) | \(e\left(\frac{5}{33}\right)\) | \(e\left(\frac{97}{132}\right)\) |