Basic properties
Modulus: | \(4025\) | |
Conductor: | \(4025\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(110\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
Real: | no | |
Primitive: | yes | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 4025.cw
\(\chi_{4025}(6,\cdot)\) \(\chi_{4025}(41,\cdot)\) \(\chi_{4025}(146,\cdot)\) \(\chi_{4025}(216,\cdot)\) \(\chi_{4025}(496,\cdot)\) \(\chi_{4025}(531,\cdot)\) \(\chi_{4025}(671,\cdot)\) \(\chi_{4025}(706,\cdot)\) \(\chi_{4025}(811,\cdot)\) \(\chi_{4025}(846,\cdot)\) \(\chi_{4025}(1021,\cdot)\) \(\chi_{4025}(1231,\cdot)\) \(\chi_{4025}(1336,\cdot)\) \(\chi_{4025}(1406,\cdot)\) \(\chi_{4025}(1511,\cdot)\) \(\chi_{4025}(1616,\cdot)\) \(\chi_{4025}(1756,\cdot)\) \(\chi_{4025}(2036,\cdot)\) \(\chi_{4025}(2106,\cdot)\) \(\chi_{4025}(2141,\cdot)\) \(\chi_{4025}(2211,\cdot)\) \(\chi_{4025}(2281,\cdot)\) \(\chi_{4025}(2316,\cdot)\) \(\chi_{4025}(2421,\cdot)\) \(\chi_{4025}(2456,\cdot)\) \(\chi_{4025}(2561,\cdot)\) \(\chi_{4025}(2631,\cdot)\) \(\chi_{4025}(2841,\cdot)\) \(\chi_{4025}(2911,\cdot)\) \(\chi_{4025}(2946,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{55})$ |
Fixed field: | Number field defined by a degree 110 polynomial (not computed) |
Values on generators
\((2577,1151,3501)\) → \((e\left(\frac{1}{5}\right),-1,e\left(\frac{1}{11}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(8\) | \(9\) | \(11\) | \(12\) | \(13\) | \(16\) |
\( \chi_{ 4025 }(2141, a) \) | \(-1\) | \(1\) | \(e\left(\frac{21}{55}\right)\) | \(e\left(\frac{39}{110}\right)\) | \(e\left(\frac{42}{55}\right)\) | \(e\left(\frac{81}{110}\right)\) | \(e\left(\frac{8}{55}\right)\) | \(e\left(\frac{39}{55}\right)\) | \(e\left(\frac{1}{55}\right)\) | \(e\left(\frac{13}{110}\right)\) | \(e\left(\frac{63}{110}\right)\) | \(e\left(\frac{29}{55}\right)\) |