Basic properties
Modulus: | \(8112\) | |
Conductor: | \(1352\) | 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 \(\chi_{1352}(827,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | no | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 8112.ei
\(\chi_{8112}(151,\cdot)\) \(\chi_{8112}(343,\cdot)\) \(\chi_{8112}(967,\cdot)\) \(\chi_{8112}(1399,\cdot)\) \(\chi_{8112}(2023,\cdot)\) \(\chi_{8112}(2215,\cdot)\) \(\chi_{8112}(2647,\cdot)\) \(\chi_{8112}(2839,\cdot)\) \(\chi_{8112}(3271,\cdot)\) \(\chi_{8112}(3463,\cdot)\) \(\chi_{8112}(3895,\cdot)\) \(\chi_{8112}(4087,\cdot)\) \(\chi_{8112}(4519,\cdot)\) \(\chi_{8112}(4711,\cdot)\) \(\chi_{8112}(5143,\cdot)\) \(\chi_{8112}(5335,\cdot)\) \(\chi_{8112}(5767,\cdot)\) \(\chi_{8112}(5959,\cdot)\) \(\chi_{8112}(6391,\cdot)\) \(\chi_{8112}(6583,\cdot)\) \(\chi_{8112}(7015,\cdot)\) \(\chi_{8112}(7207,\cdot)\) \(\chi_{8112}(7639,\cdot)\) \(\chi_{8112}(7831,\cdot)\)
Related number fields
Field of values: | $\Q(\zeta_{52})$ |
Fixed field: | Number field defined by a degree 52 polynomial |
Values on generators
\((5071,6085,2705,3889)\) → \((-1,-1,1,e\left(\frac{5}{52}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(5\) | \(7\) | \(11\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) | \(35\) |
\( \chi_{ 8112 }(151, a) \) | \(1\) | \(1\) | \(e\left(\frac{19}{52}\right)\) | \(e\left(\frac{41}{52}\right)\) | \(e\left(\frac{47}{52}\right)\) | \(e\left(\frac{1}{26}\right)\) | \(i\) | \(1\) | \(e\left(\frac{19}{26}\right)\) | \(e\left(\frac{9}{26}\right)\) | \(e\left(\frac{27}{52}\right)\) | \(e\left(\frac{2}{13}\right)\) |