Basic properties
Modulus: | \(5054\) | |
Conductor: | \(2527\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(171\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
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Real: | no | |
Primitive: | no, induced from \(\chi_{2527}(9,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 5054.cb
\(\chi_{5054}(9,\cdot)\) \(\chi_{5054}(23,\cdot)\) \(\chi_{5054}(81,\cdot)\) \(\chi_{5054}(177,\cdot)\) \(\chi_{5054}(207,\cdot)\) \(\chi_{5054}(263,\cdot)\) \(\chi_{5054}(275,\cdot)\) \(\chi_{5054}(289,\cdot)\) \(\chi_{5054}(347,\cdot)\) \(\chi_{5054}(443,\cdot)\) \(\chi_{5054}(473,\cdot)\) \(\chi_{5054}(529,\cdot)\) \(\chi_{5054}(541,\cdot)\) \(\chi_{5054}(555,\cdot)\) \(\chi_{5054}(613,\cdot)\) \(\chi_{5054}(709,\cdot)\) \(\chi_{5054}(739,\cdot)\) \(\chi_{5054}(795,\cdot)\) \(\chi_{5054}(807,\cdot)\) \(\chi_{5054}(879,\cdot)\) \(\chi_{5054}(975,\cdot)\) \(\chi_{5054}(1005,\cdot)\) \(\chi_{5054}(1061,\cdot)\) \(\chi_{5054}(1073,\cdot)\) \(\chi_{5054}(1087,\cdot)\) \(\chi_{5054}(1241,\cdot)\) \(\chi_{5054}(1271,\cdot)\) \(\chi_{5054}(1327,\cdot)\) \(\chi_{5054}(1339,\cdot)\) \(\chi_{5054}(1353,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{171})$ |
Fixed field: | Number field defined by a degree 171 polynomial (not computed) |
Values on generators
\((1445,1807)\) → \((e\left(\frac{1}{3}\right),e\left(\frac{139}{171}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(23\) | \(25\) | \(27\) |
\( \chi_{ 5054 }(9, a) \) | \(1\) | \(1\) | \(e\left(\frac{55}{171}\right)\) | \(e\left(\frac{43}{171}\right)\) | \(e\left(\frac{110}{171}\right)\) | \(e\left(\frac{14}{57}\right)\) | \(e\left(\frac{74}{171}\right)\) | \(e\left(\frac{98}{171}\right)\) | \(e\left(\frac{7}{171}\right)\) | \(e\left(\frac{59}{171}\right)\) | \(e\left(\frac{86}{171}\right)\) | \(e\left(\frac{55}{57}\right)\) |