Basic properties
Modulus: | \(675\) | |
Conductor: | \(675\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(90\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
Real: | no | |
Primitive: | yes | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 675.bh
\(\chi_{675}(14,\cdot)\) \(\chi_{675}(29,\cdot)\) \(\chi_{675}(59,\cdot)\) \(\chi_{675}(104,\cdot)\) \(\chi_{675}(119,\cdot)\) \(\chi_{675}(164,\cdot)\) \(\chi_{675}(194,\cdot)\) \(\chi_{675}(209,\cdot)\) \(\chi_{675}(239,\cdot)\) \(\chi_{675}(254,\cdot)\) \(\chi_{675}(284,\cdot)\) \(\chi_{675}(329,\cdot)\) \(\chi_{675}(344,\cdot)\) \(\chi_{675}(389,\cdot)\) \(\chi_{675}(419,\cdot)\) \(\chi_{675}(434,\cdot)\) \(\chi_{675}(464,\cdot)\) \(\chi_{675}(479,\cdot)\) \(\chi_{675}(509,\cdot)\) \(\chi_{675}(554,\cdot)\) \(\chi_{675}(569,\cdot)\) \(\chi_{675}(614,\cdot)\) \(\chi_{675}(644,\cdot)\) \(\chi_{675}(659,\cdot)\)
Related number fields
Field of values: | $\Q(\zeta_{45})$ |
Fixed field: | Number field defined by a degree 90 polynomial |
Values on generators
\((326,352)\) → \((e\left(\frac{7}{18}\right),e\left(\frac{1}{10}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(7\) | \(8\) | \(11\) | \(13\) | \(14\) | \(16\) | \(17\) | \(19\) |
\( \chi_{ 675 }(479, a) \) | \(-1\) | \(1\) | \(e\left(\frac{22}{45}\right)\) | \(e\left(\frac{44}{45}\right)\) | \(e\left(\frac{13}{18}\right)\) | \(e\left(\frac{7}{15}\right)\) | \(e\left(\frac{59}{90}\right)\) | \(e\left(\frac{1}{90}\right)\) | \(e\left(\frac{19}{90}\right)\) | \(e\left(\frac{43}{45}\right)\) | \(e\left(\frac{2}{15}\right)\) | \(e\left(\frac{7}{15}\right)\) |