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.bf
\(\chi_{675}(11,\cdot)\) \(\chi_{675}(41,\cdot)\) \(\chi_{675}(56,\cdot)\) \(\chi_{675}(86,\cdot)\) \(\chi_{675}(131,\cdot)\) \(\chi_{675}(146,\cdot)\) \(\chi_{675}(191,\cdot)\) \(\chi_{675}(221,\cdot)\) \(\chi_{675}(236,\cdot)\) \(\chi_{675}(266,\cdot)\) \(\chi_{675}(281,\cdot)\) \(\chi_{675}(311,\cdot)\) \(\chi_{675}(356,\cdot)\) \(\chi_{675}(371,\cdot)\) \(\chi_{675}(416,\cdot)\) \(\chi_{675}(446,\cdot)\) \(\chi_{675}(461,\cdot)\) \(\chi_{675}(491,\cdot)\) \(\chi_{675}(506,\cdot)\) \(\chi_{675}(536,\cdot)\) \(\chi_{675}(581,\cdot)\) \(\chi_{675}(596,\cdot)\) \(\chi_{675}(641,\cdot)\) \(\chi_{675}(671,\cdot)\)
Related number fields
Field of values: | $\Q(\zeta_{45})$ |
Fixed field: | Number field defined by a degree 90 polynomial |
Values on generators
\((326,352)\) → \((e\left(\frac{5}{18}\right),e\left(\frac{1}{5}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(7\) | \(8\) | \(11\) | \(13\) | \(14\) | \(16\) | \(17\) | \(19\) |
\( \chi_{ 675 }(491, a) \) | \(-1\) | \(1\) | \(e\left(\frac{43}{90}\right)\) | \(e\left(\frac{43}{45}\right)\) | \(e\left(\frac{4}{9}\right)\) | \(e\left(\frac{13}{30}\right)\) | \(e\left(\frac{73}{90}\right)\) | \(e\left(\frac{1}{45}\right)\) | \(e\left(\frac{83}{90}\right)\) | \(e\left(\frac{41}{45}\right)\) | \(e\left(\frac{23}{30}\right)\) | \(e\left(\frac{14}{15}\right)\) |