Basic properties
Modulus: | \(7623\) | |
Conductor: | \(7623\) | 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 7623.fz
\(\chi_{7623}(47,\cdot)\) \(\chi_{7623}(59,\cdot)\) \(\chi_{7623}(185,\cdot)\) \(\chi_{7623}(236,\cdot)\) \(\chi_{7623}(311,\cdot)\) \(\chi_{7623}(488,\cdot)\) \(\chi_{7623}(500,\cdot)\) \(\chi_{7623}(740,\cdot)\) \(\chi_{7623}(752,\cdot)\) \(\chi_{7623}(878,\cdot)\) \(\chi_{7623}(929,\cdot)\) \(\chi_{7623}(1004,\cdot)\) \(\chi_{7623}(1181,\cdot)\) \(\chi_{7623}(1193,\cdot)\) \(\chi_{7623}(1307,\cdot)\) \(\chi_{7623}(1433,\cdot)\) \(\chi_{7623}(1445,\cdot)\) \(\chi_{7623}(1571,\cdot)\) \(\chi_{7623}(1622,\cdot)\) \(\chi_{7623}(1874,\cdot)\) \(\chi_{7623}(1886,\cdot)\) \(\chi_{7623}(2000,\cdot)\) \(\chi_{7623}(2126,\cdot)\) \(\chi_{7623}(2264,\cdot)\) \(\chi_{7623}(2315,\cdot)\) \(\chi_{7623}(2390,\cdot)\) \(\chi_{7623}(2567,\cdot)\) \(\chi_{7623}(2579,\cdot)\) \(\chi_{7623}(2693,\cdot)\) \(\chi_{7623}(2819,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{165})$ |
Fixed field: | Number field defined by a degree 330 polynomial (not computed) |
Values on generators
\((848,4357,4600)\) → \((e\left(\frac{1}{6}\right),e\left(\frac{5}{6}\right),e\left(\frac{4}{55}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(8\) | \(10\) | \(13\) | \(16\) | \(17\) | \(19\) | \(20\) |
\( \chi_{ 7623 }(740, a) \) | \(1\) | \(1\) | \(e\left(\frac{299}{330}\right)\) | \(e\left(\frac{134}{165}\right)\) | \(e\left(\frac{21}{55}\right)\) | \(e\left(\frac{79}{110}\right)\) | \(e\left(\frac{19}{66}\right)\) | \(e\left(\frac{59}{330}\right)\) | \(e\left(\frac{103}{165}\right)\) | \(e\left(\frac{148}{165}\right)\) | \(e\left(\frac{67}{330}\right)\) | \(e\left(\frac{32}{165}\right)\) |