Basic properties
Modulus: | \(2535\) | |
Conductor: | \(845\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(78\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
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Real: | no | |
Primitive: | no, induced from \(\chi_{845}(4,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 2535.cp
\(\chi_{2535}(4,\cdot)\) \(\chi_{2535}(49,\cdot)\) \(\chi_{2535}(199,\cdot)\) \(\chi_{2535}(244,\cdot)\) \(\chi_{2535}(394,\cdot)\) \(\chi_{2535}(439,\cdot)\) \(\chi_{2535}(589,\cdot)\) \(\chi_{2535}(634,\cdot)\) \(\chi_{2535}(784,\cdot)\) \(\chi_{2535}(829,\cdot)\) \(\chi_{2535}(979,\cdot)\) \(\chi_{2535}(1024,\cdot)\) \(\chi_{2535}(1174,\cdot)\) \(\chi_{2535}(1219,\cdot)\) \(\chi_{2535}(1369,\cdot)\) \(\chi_{2535}(1414,\cdot)\) \(\chi_{2535}(1564,\cdot)\) \(\chi_{2535}(1609,\cdot)\) \(\chi_{2535}(1759,\cdot)\) \(\chi_{2535}(1804,\cdot)\) \(\chi_{2535}(1954,\cdot)\) \(\chi_{2535}(1999,\cdot)\) \(\chi_{2535}(2149,\cdot)\) \(\chi_{2535}(2194,\cdot)\)
Related number fields
Field of values: | $\Q(\zeta_{39})$ |
Fixed field: | Number field defined by a degree 78 polynomial |
Values on generators
\((1691,1522,1861)\) → \((1,-1,e\left(\frac{1}{78}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(7\) | \(8\) | \(11\) | \(14\) | \(16\) | \(17\) | \(19\) | \(22\) |
\( \chi_{ 2535 }(4, a) \) | \(1\) | \(1\) | \(e\left(\frac{20}{39}\right)\) | \(e\left(\frac{1}{39}\right)\) | \(e\left(\frac{34}{39}\right)\) | \(e\left(\frac{7}{13}\right)\) | \(e\left(\frac{25}{78}\right)\) | \(e\left(\frac{5}{13}\right)\) | \(e\left(\frac{2}{39}\right)\) | \(e\left(\frac{29}{78}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{5}{6}\right)\) |