Basic properties
Modulus: | \(4015\) | |
Conductor: | \(4015\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(90\) | 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 4015.ff
\(\chi_{4015}(69,\cdot)\) \(\chi_{4015}(114,\cdot)\) \(\chi_{4015}(434,\cdot)\) \(\chi_{4015}(509,\cdot)\) \(\chi_{4015}(839,\cdot)\) \(\chi_{4015}(874,\cdot)\) \(\chi_{4015}(894,\cdot)\) \(\chi_{4015}(1164,\cdot)\) \(\chi_{4015}(1204,\cdot)\) \(\chi_{4015}(1259,\cdot)\) \(\chi_{4015}(1444,\cdot)\) \(\chi_{4015}(1604,\cdot)\) \(\chi_{4015}(1809,\cdot)\) \(\chi_{4015}(1934,\cdot)\) \(\chi_{4015}(1939,\cdot)\) \(\chi_{4015}(1989,\cdot)\) \(\chi_{4015}(2259,\cdot)\) \(\chi_{4015}(2304,\cdot)\) \(\chi_{4015}(2539,\cdot)\) \(\chi_{4015}(2699,\cdot)\) \(\chi_{4015}(3029,\cdot)\) \(\chi_{4015}(3034,\cdot)\) \(\chi_{4015}(3084,\cdot)\) \(\chi_{4015}(3634,\cdot)\)
Related number fields
Field of values: | $\Q(\zeta_{45})$ |
Fixed field: | Number field defined by a degree 90 polynomial |
Values on generators
\((1607,2191,881)\) → \((-1,e\left(\frac{4}{5}\right),e\left(\frac{13}{18}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(7\) | \(8\) | \(9\) | \(12\) | \(13\) | \(14\) |
\( \chi_{ 4015 }(69, a) \) | \(1\) | \(1\) | \(e\left(\frac{7}{90}\right)\) | \(e\left(\frac{7}{30}\right)\) | \(e\left(\frac{7}{45}\right)\) | \(e\left(\frac{14}{45}\right)\) | \(e\left(\frac{14}{15}\right)\) | \(e\left(\frac{7}{30}\right)\) | \(e\left(\frac{7}{15}\right)\) | \(e\left(\frac{7}{18}\right)\) | \(e\left(\frac{41}{45}\right)\) | \(e\left(\frac{1}{90}\right)\) |