Basic properties
Modulus: | \(3549\) | |
Conductor: | \(1183\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(52\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
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Real: | no | |
Primitive: | no, induced from \(\chi_{1183}(1175,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 3549.cu
\(\chi_{3549}(34,\cdot)\) \(\chi_{3549}(265,\cdot)\) \(\chi_{3549}(307,\cdot)\) \(\chi_{3549}(538,\cdot)\) \(\chi_{3549}(580,\cdot)\) \(\chi_{3549}(811,\cdot)\) \(\chi_{3549}(853,\cdot)\) \(\chi_{3549}(1126,\cdot)\) \(\chi_{3549}(1357,\cdot)\) \(\chi_{3549}(1399,\cdot)\) \(\chi_{3549}(1630,\cdot)\) \(\chi_{3549}(1672,\cdot)\) \(\chi_{3549}(1903,\cdot)\) \(\chi_{3549}(1945,\cdot)\) \(\chi_{3549}(2176,\cdot)\) \(\chi_{3549}(2218,\cdot)\) \(\chi_{3549}(2449,\cdot)\) \(\chi_{3549}(2491,\cdot)\) \(\chi_{3549}(2722,\cdot)\) \(\chi_{3549}(2764,\cdot)\) \(\chi_{3549}(2995,\cdot)\) \(\chi_{3549}(3037,\cdot)\) \(\chi_{3549}(3268,\cdot)\) \(\chi_{3549}(3541,\cdot)\)
Related number fields
Field of values: | $\Q(\zeta_{52})$ |
Fixed field: | Number field defined by a degree 52 polynomial |
Values on generators
\((1184,1522,3382)\) → \((1,-1,e\left(\frac{27}{52}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(8\) | \(10\) | \(11\) | \(16\) | \(17\) | \(19\) | \(20\) |
\( \chi_{ 3549 }(3541, a) \) | \(1\) | \(1\) | \(e\left(\frac{27}{52}\right)\) | \(e\left(\frac{1}{26}\right)\) | \(e\left(\frac{9}{52}\right)\) | \(e\left(\frac{29}{52}\right)\) | \(e\left(\frac{9}{13}\right)\) | \(e\left(\frac{25}{52}\right)\) | \(e\left(\frac{1}{13}\right)\) | \(e\left(\frac{4}{13}\right)\) | \(i\) | \(e\left(\frac{11}{52}\right)\) |