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.fc
\(\chi_{7623}(5,\cdot)\) \(\chi_{7623}(38,\cdot)\) \(\chi_{7623}(257,\cdot)\) \(\chi_{7623}(290,\cdot)\) \(\chi_{7623}(383,\cdot)\) \(\chi_{7623}(416,\cdot)\) \(\chi_{7623}(509,\cdot)\) \(\chi_{7623}(542,\cdot)\) \(\chi_{7623}(698,\cdot)\) \(\chi_{7623}(731,\cdot)\) \(\chi_{7623}(950,\cdot)\) \(\chi_{7623}(983,\cdot)\) \(\chi_{7623}(1076,\cdot)\) \(\chi_{7623}(1109,\cdot)\) \(\chi_{7623}(1202,\cdot)\) \(\chi_{7623}(1235,\cdot)\) \(\chi_{7623}(1391,\cdot)\) \(\chi_{7623}(1424,\cdot)\) \(\chi_{7623}(1643,\cdot)\) \(\chi_{7623}(1676,\cdot)\) \(\chi_{7623}(1769,\cdot)\) \(\chi_{7623}(1802,\cdot)\) \(\chi_{7623}(1895,\cdot)\) \(\chi_{7623}(1928,\cdot)\) \(\chi_{7623}(2117,\cdot)\) \(\chi_{7623}(2336,\cdot)\) \(\chi_{7623}(2369,\cdot)\) \(\chi_{7623}(2462,\cdot)\) \(\chi_{7623}(2495,\cdot)\) \(\chi_{7623}(2588,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{165})$ |
Fixed field: | Number field defined by a degree 330 polynomial (not computed) |
Values on generators
\((848,4357,4600)\) → \((e\left(\frac{5}{6}\right),e\left(\frac{5}{6}\right),e\left(\frac{41}{55}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(8\) | \(10\) | \(13\) | \(16\) | \(17\) | \(19\) | \(20\) |
\( \chi_{ 7623 }(1643, a) \) | \(1\) | \(1\) | \(e\left(\frac{27}{110}\right)\) | \(e\left(\frac{27}{55}\right)\) | \(e\left(\frac{82}{165}\right)\) | \(e\left(\frac{81}{110}\right)\) | \(e\left(\frac{49}{66}\right)\) | \(e\left(\frac{151}{330}\right)\) | \(e\left(\frac{54}{55}\right)\) | \(e\left(\frac{142}{165}\right)\) | \(e\left(\frac{13}{330}\right)\) | \(e\left(\frac{163}{165}\right)\) |