Basic properties
| Modulus: | \(5700\) | |
| Conductor: | \(5700\) | 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: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 5700.fd
\(\chi_{5700}(131,\cdot)\) \(\chi_{5700}(491,\cdot)\) \(\chi_{5700}(671,\cdot)\) \(\chi_{5700}(731,\cdot)\) \(\chi_{5700}(1031,\cdot)\) \(\chi_{5700}(1271,\cdot)\) \(\chi_{5700}(1391,\cdot)\) \(\chi_{5700}(1631,\cdot)\) \(\chi_{5700}(1811,\cdot)\) \(\chi_{5700}(1871,\cdot)\) \(\chi_{5700}(2171,\cdot)\) \(\chi_{5700}(2411,\cdot)\) \(\chi_{5700}(2531,\cdot)\) \(\chi_{5700}(2771,\cdot)\) \(\chi_{5700}(3011,\cdot)\) \(\chi_{5700}(3311,\cdot)\) \(\chi_{5700}(3671,\cdot)\) \(\chi_{5700}(3911,\cdot)\) \(\chi_{5700}(4091,\cdot)\) \(\chi_{5700}(4691,\cdot)\) \(\chi_{5700}(4811,\cdot)\) \(\chi_{5700}(5231,\cdot)\) \(\chi_{5700}(5291,\cdot)\) \(\chi_{5700}(5591,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{45})$ |
| Fixed field: | Number field defined by a degree 90 polynomial |
Values on generators
\((2851,1901,3877,4201)\) → \((-1,-1,e\left(\frac{2}{5}\right),e\left(\frac{5}{9}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(7\) | \(11\) | \(13\) | \(17\) | \(23\) | \(29\) | \(31\) | \(37\) | \(41\) | \(43\) |
| \( \chi_{ 5700 }(131, a) \) | \(1\) | \(1\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{1}{15}\right)\) | \(e\left(\frac{17}{45}\right)\) | \(e\left(\frac{23}{90}\right)\) | \(e\left(\frac{23}{45}\right)\) | \(e\left(\frac{67}{90}\right)\) | \(e\left(\frac{1}{30}\right)\) | \(e\left(\frac{3}{5}\right)\) | \(e\left(\frac{29}{90}\right)\) | \(e\left(\frac{7}{18}\right)\) |