Basic properties
Modulus: | \(7623\) | |
Conductor: | \(363\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(110\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
Real: | no | |
Primitive: | no, induced from \(\chi_{363}(314,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | no | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 7623.ew
\(\chi_{7623}(8,\cdot)\) \(\chi_{7623}(134,\cdot)\) \(\chi_{7623}(260,\cdot)\) \(\chi_{7623}(512,\cdot)\) \(\chi_{7623}(701,\cdot)\) \(\chi_{7623}(827,\cdot)\) \(\chi_{7623}(953,\cdot)\) \(\chi_{7623}(1205,\cdot)\) \(\chi_{7623}(1394,\cdot)\) \(\chi_{7623}(1520,\cdot)\) \(\chi_{7623}(1646,\cdot)\) \(\chi_{7623}(1898,\cdot)\) \(\chi_{7623}(2087,\cdot)\) \(\chi_{7623}(2213,\cdot)\) \(\chi_{7623}(2591,\cdot)\) \(\chi_{7623}(2906,\cdot)\) \(\chi_{7623}(3032,\cdot)\) \(\chi_{7623}(3284,\cdot)\) \(\chi_{7623}(3473,\cdot)\) \(\chi_{7623}(3599,\cdot)\) \(\chi_{7623}(3725,\cdot)\) \(\chi_{7623}(3977,\cdot)\) \(\chi_{7623}(4166,\cdot)\) \(\chi_{7623}(4292,\cdot)\) \(\chi_{7623}(4418,\cdot)\) \(\chi_{7623}(4670,\cdot)\) \(\chi_{7623}(4859,\cdot)\) \(\chi_{7623}(4985,\cdot)\) \(\chi_{7623}(5111,\cdot)\) \(\chi_{7623}(5363,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{55})$ |
Fixed field: | Number field defined by a degree 110 polynomial (not computed) |
Values on generators
\((848,4357,4600)\) → \((-1,1,e\left(\frac{69}{110}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(8\) | \(10\) | \(13\) | \(16\) | \(17\) | \(19\) | \(20\) |
\( \chi_{ 7623 }(4670, a) \) | \(1\) | \(1\) | \(e\left(\frac{7}{55}\right)\) | \(e\left(\frac{14}{55}\right)\) | \(e\left(\frac{101}{110}\right)\) | \(e\left(\frac{21}{55}\right)\) | \(e\left(\frac{1}{22}\right)\) | \(e\left(\frac{39}{110}\right)\) | \(e\left(\frac{28}{55}\right)\) | \(e\left(\frac{13}{55}\right)\) | \(e\left(\frac{7}{110}\right)\) | \(e\left(\frac{19}{110}\right)\) |