Basic properties
Modulus: | \(7623\) | |
Conductor: | \(1089\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(330\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
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Real: | no | |
Primitive: | no, induced from \(\chi_{1089}(1058,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 7623.fn
\(\chi_{7623}(29,\cdot)\) \(\chi_{7623}(50,\cdot)\) \(\chi_{7623}(281,\cdot)\) \(\chi_{7623}(365,\cdot)\) \(\chi_{7623}(470,\cdot)\) \(\chi_{7623}(491,\cdot)\) \(\chi_{7623}(722,\cdot)\) \(\chi_{7623}(743,\cdot)\) \(\chi_{7623}(932,\cdot)\) \(\chi_{7623}(974,\cdot)\) \(\chi_{7623}(1058,\cdot)\) \(\chi_{7623}(1163,\cdot)\) \(\chi_{7623}(1184,\cdot)\) \(\chi_{7623}(1289,\cdot)\) \(\chi_{7623}(1415,\cdot)\) \(\chi_{7623}(1436,\cdot)\) \(\chi_{7623}(1625,\cdot)\) \(\chi_{7623}(1751,\cdot)\) \(\chi_{7623}(1856,\cdot)\) \(\chi_{7623}(1877,\cdot)\) \(\chi_{7623}(1982,\cdot)\) \(\chi_{7623}(2108,\cdot)\) \(\chi_{7623}(2129,\cdot)\) \(\chi_{7623}(2318,\cdot)\) \(\chi_{7623}(2360,\cdot)\) \(\chi_{7623}(2444,\cdot)\) \(\chi_{7623}(2549,\cdot)\) \(\chi_{7623}(2570,\cdot)\) \(\chi_{7623}(2675,\cdot)\) \(\chi_{7623}(2801,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{165})$ |
Fixed field: | Number field defined by a degree 330 polynomial (not computed) |
Values on generators
\((848,4357,4600)\) → \((e\left(\frac{5}{6}\right),1,e\left(\frac{31}{110}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(8\) | \(10\) | \(13\) | \(16\) | \(17\) | \(19\) | \(20\) |
\( \chi_{ 7623 }(1058, a) \) | \(1\) | \(1\) | \(e\left(\frac{19}{165}\right)\) | \(e\left(\frac{38}{165}\right)\) | \(e\left(\frac{7}{330}\right)\) | \(e\left(\frac{19}{55}\right)\) | \(e\left(\frac{3}{22}\right)\) | \(e\left(\frac{43}{330}\right)\) | \(e\left(\frac{76}{165}\right)\) | \(e\left(\frac{17}{55}\right)\) | \(e\left(\frac{43}{110}\right)\) | \(e\left(\frac{83}{330}\right)\) |