Basic properties
Modulus: | \(4025\) | |
Conductor: | \(575\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(55\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
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Real: | no | |
Primitive: | no, induced from \(\chi_{575}(386,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 4025.cf
\(\chi_{4025}(36,\cdot)\) \(\chi_{4025}(71,\cdot)\) \(\chi_{4025}(141,\cdot)\) \(\chi_{4025}(211,\cdot)\) \(\chi_{4025}(246,\cdot)\) \(\chi_{4025}(386,\cdot)\) \(\chi_{4025}(491,\cdot)\) \(\chi_{4025}(561,\cdot)\) \(\chi_{4025}(771,\cdot)\) \(\chi_{4025}(841,\cdot)\) \(\chi_{4025}(946,\cdot)\) \(\chi_{4025}(1016,\cdot)\) \(\chi_{4025}(1156,\cdot)\) \(\chi_{4025}(1191,\cdot)\) \(\chi_{4025}(1296,\cdot)\) \(\chi_{4025}(1366,\cdot)\) \(\chi_{4025}(1646,\cdot)\) \(\chi_{4025}(1681,\cdot)\) \(\chi_{4025}(1821,\cdot)\) \(\chi_{4025}(1856,\cdot)\) \(\chi_{4025}(1961,\cdot)\) \(\chi_{4025}(1996,\cdot)\) \(\chi_{4025}(2171,\cdot)\) \(\chi_{4025}(2381,\cdot)\) \(\chi_{4025}(2486,\cdot)\) \(\chi_{4025}(2556,\cdot)\) \(\chi_{4025}(2661,\cdot)\) \(\chi_{4025}(2766,\cdot)\) \(\chi_{4025}(2906,\cdot)\) \(\chi_{4025}(3186,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{55})$ |
Fixed field: | Number field defined by a degree 55 polynomial |
Values on generators
\((2577,1151,3501)\) → \((e\left(\frac{4}{5}\right),1,e\left(\frac{6}{11}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(8\) | \(9\) | \(11\) | \(12\) | \(13\) | \(16\) |
\( \chi_{ 4025 }(386, a) \) | \(1\) | \(1\) | \(e\left(\frac{49}{55}\right)\) | \(e\left(\frac{18}{55}\right)\) | \(e\left(\frac{43}{55}\right)\) | \(e\left(\frac{12}{55}\right)\) | \(e\left(\frac{37}{55}\right)\) | \(e\left(\frac{36}{55}\right)\) | \(e\left(\frac{39}{55}\right)\) | \(e\left(\frac{6}{55}\right)\) | \(e\left(\frac{46}{55}\right)\) | \(e\left(\frac{31}{55}\right)\) |