Basic properties
Modulus: | \(8712\) | |
Conductor: | \(8712\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(330\) | 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 8712.en
\(\chi_{8712}(29,\cdot)\) \(\chi_{8712}(101,\cdot)\) \(\chi_{8712}(149,\cdot)\) \(\chi_{8712}(173,\cdot)\) \(\chi_{8712}(293,\cdot)\) \(\chi_{8712}(365,\cdot)\) \(\chi_{8712}(437,\cdot)\) \(\chi_{8712}(677,\cdot)\) \(\chi_{8712}(821,\cdot)\) \(\chi_{8712}(893,\cdot)\) \(\chi_{8712}(1085,\cdot)\) \(\chi_{8712}(1157,\cdot)\) \(\chi_{8712}(1229,\cdot)\) \(\chi_{8712}(1469,\cdot)\) \(\chi_{8712}(1733,\cdot)\) \(\chi_{8712}(1757,\cdot)\) \(\chi_{8712}(1877,\cdot)\) \(\chi_{8712}(1949,\cdot)\) \(\chi_{8712}(2021,\cdot)\) \(\chi_{8712}(2261,\cdot)\) \(\chi_{8712}(2405,\cdot)\) \(\chi_{8712}(2477,\cdot)\) \(\chi_{8712}(2525,\cdot)\) \(\chi_{8712}(2549,\cdot)\) \(\chi_{8712}(2669,\cdot)\) \(\chi_{8712}(2741,\cdot)\) \(\chi_{8712}(2813,\cdot)\) \(\chi_{8712}(3053,\cdot)\) \(\chi_{8712}(3197,\cdot)\) \(\chi_{8712}(3269,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{165})$ |
Fixed field: | Number field defined by a degree 330 polynomial (not computed) |
Values on generators
\((6535,4357,1937,5689)\) → \((1,-1,e\left(\frac{5}{6}\right),e\left(\frac{83}{110}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(5\) | \(7\) | \(13\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) | \(35\) |
\( \chi_{ 8712 }(1229, a) \) | \(1\) | \(1\) | \(e\left(\frac{83}{165}\right)\) | \(e\left(\frac{203}{330}\right)\) | \(e\left(\frac{62}{165}\right)\) | \(e\left(\frac{26}{55}\right)\) | \(e\left(\frac{7}{55}\right)\) | \(e\left(\frac{65}{66}\right)\) | \(e\left(\frac{1}{165}\right)\) | \(e\left(\frac{53}{330}\right)\) | \(e\left(\frac{92}{165}\right)\) | \(e\left(\frac{13}{110}\right)\) |