Basic properties
Modulus: | \(2535\) | |
Conductor: | \(2535\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(52\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
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Real: | no | |
Primitive: | yes | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 2535.bz
\(\chi_{2535}(38,\cdot)\) \(\chi_{2535}(77,\cdot)\) \(\chi_{2535}(233,\cdot)\) \(\chi_{2535}(272,\cdot)\) \(\chi_{2535}(428,\cdot)\) \(\chi_{2535}(467,\cdot)\) \(\chi_{2535}(623,\cdot)\) \(\chi_{2535}(662,\cdot)\) \(\chi_{2535}(818,\cdot)\) \(\chi_{2535}(857,\cdot)\) \(\chi_{2535}(1052,\cdot)\) \(\chi_{2535}(1208,\cdot)\) \(\chi_{2535}(1247,\cdot)\) \(\chi_{2535}(1403,\cdot)\) \(\chi_{2535}(1442,\cdot)\) \(\chi_{2535}(1598,\cdot)\) \(\chi_{2535}(1637,\cdot)\) \(\chi_{2535}(1793,\cdot)\) \(\chi_{2535}(1832,\cdot)\) \(\chi_{2535}(1988,\cdot)\) \(\chi_{2535}(2183,\cdot)\) \(\chi_{2535}(2222,\cdot)\) \(\chi_{2535}(2378,\cdot)\) \(\chi_{2535}(2417,\cdot)\)
Related number fields
Field of values: | $\Q(\zeta_{52})$ |
Fixed field: | Number field defined by a degree 52 polynomial |
Values on generators
\((1691,1522,1861)\) → \((-1,-i,e\left(\frac{11}{26}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(7\) | \(8\) | \(11\) | \(14\) | \(16\) | \(17\) | \(19\) | \(22\) |
\( \chi_{ 2535 }(38, a) \) | \(1\) | \(1\) | \(e\left(\frac{35}{52}\right)\) | \(e\left(\frac{9}{26}\right)\) | \(e\left(\frac{1}{52}\right)\) | \(e\left(\frac{1}{52}\right)\) | \(e\left(\frac{1}{13}\right)\) | \(e\left(\frac{9}{13}\right)\) | \(e\left(\frac{9}{13}\right)\) | \(e\left(\frac{1}{52}\right)\) | \(1\) | \(-i\) |