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.fw
\(\chi_{7623}(13,\cdot)\) \(\chi_{7623}(139,\cdot)\) \(\chi_{7623}(160,\cdot)\) \(\chi_{7623}(349,\cdot)\) \(\chi_{7623}(391,\cdot)\) \(\chi_{7623}(580,\cdot)\) \(\chi_{7623}(601,\cdot)\) \(\chi_{7623}(706,\cdot)\) \(\chi_{7623}(832,\cdot)\) \(\chi_{7623}(853,\cdot)\) \(\chi_{7623}(1042,\cdot)\) \(\chi_{7623}(1084,\cdot)\) \(\chi_{7623}(1168,\cdot)\) \(\chi_{7623}(1273,\cdot)\) \(\chi_{7623}(1294,\cdot)\) \(\chi_{7623}(1399,\cdot)\) \(\chi_{7623}(1525,\cdot)\) \(\chi_{7623}(1735,\cdot)\) \(\chi_{7623}(1777,\cdot)\) \(\chi_{7623}(1861,\cdot)\) \(\chi_{7623}(1966,\cdot)\) \(\chi_{7623}(1987,\cdot)\) \(\chi_{7623}(2092,\cdot)\) \(\chi_{7623}(2239,\cdot)\) \(\chi_{7623}(2428,\cdot)\) \(\chi_{7623}(2470,\cdot)\) \(\chi_{7623}(2554,\cdot)\) \(\chi_{7623}(2680,\cdot)\) \(\chi_{7623}(2785,\cdot)\) \(\chi_{7623}(2911,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{165})$ |
Fixed field: | Number field defined by a degree 330 polynomial (not computed) |
Values on generators
\((848,4357,4600)\) → \((e\left(\frac{1}{3}\right),-1,e\left(\frac{101}{110}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(8\) | \(10\) | \(13\) | \(16\) | \(17\) | \(19\) | \(20\) |
\( \chi_{ 7623 }(13, a) \) | \(1\) | \(1\) | \(e\left(\frac{83}{330}\right)\) | \(e\left(\frac{83}{165}\right)\) | \(e\left(\frac{37}{330}\right)\) | \(e\left(\frac{83}{110}\right)\) | \(e\left(\frac{4}{11}\right)\) | \(e\left(\frac{149}{165}\right)\) | \(e\left(\frac{1}{165}\right)\) | \(e\left(\frac{27}{55}\right)\) | \(e\left(\frac{39}{55}\right)\) | \(e\left(\frac{203}{330}\right)\) |