Basic properties
Modulus: | \(7623\) | |
Conductor: | \(2541\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(110\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
Real: | no | |
Primitive: | no, induced from \(\chi_{2541}(377,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 7623.eu
\(\chi_{7623}(125,\cdot)\) \(\chi_{7623}(377,\cdot)\) \(\chi_{7623}(566,\cdot)\) \(\chi_{7623}(818,\cdot)\) \(\chi_{7623}(944,\cdot)\) \(\chi_{7623}(1070,\cdot)\) \(\chi_{7623}(1259,\cdot)\) \(\chi_{7623}(1511,\cdot)\) \(\chi_{7623}(1637,\cdot)\) \(\chi_{7623}(1763,\cdot)\) \(\chi_{7623}(1952,\cdot)\) \(\chi_{7623}(2204,\cdot)\) \(\chi_{7623}(2330,\cdot)\) \(\chi_{7623}(2456,\cdot)\) \(\chi_{7623}(2645,\cdot)\) \(\chi_{7623}(2897,\cdot)\) \(\chi_{7623}(3023,\cdot)\) \(\chi_{7623}(3338,\cdot)\) \(\chi_{7623}(3716,\cdot)\) \(\chi_{7623}(3842,\cdot)\) \(\chi_{7623}(4031,\cdot)\) \(\chi_{7623}(4283,\cdot)\) \(\chi_{7623}(4409,\cdot)\) \(\chi_{7623}(4535,\cdot)\) \(\chi_{7623}(4724,\cdot)\) \(\chi_{7623}(4976,\cdot)\) \(\chi_{7623}(5102,\cdot)\) \(\chi_{7623}(5228,\cdot)\) \(\chi_{7623}(5417,\cdot)\) \(\chi_{7623}(5669,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{55})$ |
Fixed field: | Number field defined by a degree 110 polynomial (not computed) |
Values on generators
\((848,4357,4600)\) → \((-1,-1,e\left(\frac{4}{55}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(8\) | \(10\) | \(13\) | \(16\) | \(17\) | \(19\) | \(20\) |
\( \chi_{ 7623 }(377, a) \) | \(1\) | \(1\) | \(e\left(\frac{63}{110}\right)\) | \(e\left(\frac{8}{55}\right)\) | \(e\left(\frac{21}{55}\right)\) | \(e\left(\frac{79}{110}\right)\) | \(e\left(\frac{21}{22}\right)\) | \(e\left(\frac{93}{110}\right)\) | \(e\left(\frac{16}{55}\right)\) | \(e\left(\frac{31}{55}\right)\) | \(e\left(\frac{59}{110}\right)\) | \(e\left(\frac{29}{55}\right)\) |