Basic properties
| Modulus: | \(8100\) | |
| Conductor: | \(2700\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(90\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{2700}(779,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | no | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 8100.cv
\(\chi_{8100}(179,\cdot)\) \(\chi_{8100}(359,\cdot)\) \(\chi_{8100}(719,\cdot)\) \(\chi_{8100}(1259,\cdot)\) \(\chi_{8100}(1439,\cdot)\) \(\chi_{8100}(1979,\cdot)\) \(\chi_{8100}(2339,\cdot)\) \(\chi_{8100}(2519,\cdot)\) \(\chi_{8100}(2879,\cdot)\) \(\chi_{8100}(3059,\cdot)\) \(\chi_{8100}(3419,\cdot)\) \(\chi_{8100}(3959,\cdot)\) \(\chi_{8100}(4139,\cdot)\) \(\chi_{8100}(4679,\cdot)\) \(\chi_{8100}(5039,\cdot)\) \(\chi_{8100}(5219,\cdot)\) \(\chi_{8100}(5579,\cdot)\) \(\chi_{8100}(5759,\cdot)\) \(\chi_{8100}(6119,\cdot)\) \(\chi_{8100}(6659,\cdot)\) \(\chi_{8100}(6839,\cdot)\) \(\chi_{8100}(7379,\cdot)\) \(\chi_{8100}(7739,\cdot)\) \(\chi_{8100}(7919,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{45})$ |
| Fixed field: | Number field defined by a degree 90 polynomial |
Values on generators
\((4051,6401,7777)\) → \((-1,e\left(\frac{11}{18}\right),e\left(\frac{1}{10}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(7\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(29\) | \(31\) | \(37\) | \(41\) |
| \( \chi_{ 8100 }(179, a) \) | \(1\) | \(1\) | \(e\left(\frac{7}{9}\right)\) | \(e\left(\frac{2}{45}\right)\) | \(e\left(\frac{71}{90}\right)\) | \(e\left(\frac{7}{15}\right)\) | \(e\left(\frac{19}{30}\right)\) | \(e\left(\frac{29}{90}\right)\) | \(e\left(\frac{73}{90}\right)\) | \(e\left(\frac{47}{90}\right)\) | \(e\left(\frac{17}{30}\right)\) | \(e\left(\frac{71}{90}\right)\) |