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.gc
\(\chi_{7623}(74,\cdot)\) \(\chi_{7623}(149,\cdot)\) \(\chi_{7623}(200,\cdot)\) \(\chi_{7623}(326,\cdot)\) \(\chi_{7623}(338,\cdot)\) \(\chi_{7623}(464,\cdot)\) \(\chi_{7623}(590,\cdot)\) \(\chi_{7623}(767,\cdot)\) \(\chi_{7623}(842,\cdot)\) \(\chi_{7623}(893,\cdot)\) \(\chi_{7623}(1019,\cdot)\) \(\chi_{7623}(1031,\cdot)\) \(\chi_{7623}(1157,\cdot)\) \(\chi_{7623}(1271,\cdot)\) \(\chi_{7623}(1283,\cdot)\) \(\chi_{7623}(1460,\cdot)\) \(\chi_{7623}(1535,\cdot)\) \(\chi_{7623}(1586,\cdot)\) \(\chi_{7623}(1712,\cdot)\) \(\chi_{7623}(1724,\cdot)\) \(\chi_{7623}(1850,\cdot)\) \(\chi_{7623}(1964,\cdot)\) \(\chi_{7623}(2153,\cdot)\) \(\chi_{7623}(2228,\cdot)\) \(\chi_{7623}(2279,\cdot)\) \(\chi_{7623}(2405,\cdot)\) \(\chi_{7623}(2543,\cdot)\) \(\chi_{7623}(2657,\cdot)\) \(\chi_{7623}(2669,\cdot)\) \(\chi_{7623}(2846,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{165})$ |
Fixed field: | Number field defined by a degree 330 polynomial (not computed) |
Values on generators
\((848,4357,4600)\) → \((e\left(\frac{1}{6}\right),e\left(\frac{2}{3}\right),e\left(\frac{109}{110}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(8\) | \(10\) | \(13\) | \(16\) | \(17\) | \(19\) | \(20\) |
\( \chi_{ 7623 }(1271, a) \) | \(1\) | \(1\) | \(e\left(\frac{27}{55}\right)\) | \(e\left(\frac{54}{55}\right)\) | \(e\left(\frac{163}{330}\right)\) | \(e\left(\frac{26}{55}\right)\) | \(e\left(\frac{65}{66}\right)\) | \(e\left(\frac{137}{330}\right)\) | \(e\left(\frac{53}{55}\right)\) | \(e\left(\frac{119}{165}\right)\) | \(e\left(\frac{191}{330}\right)\) | \(e\left(\frac{157}{330}\right)\) |