Basic properties
| Modulus: | \(3800\) | |
| Conductor: | \(1900\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(90\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{1900}(211,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | no | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 3800.fb
\(\chi_{3800}(71,\cdot)\) \(\chi_{3800}(231,\cdot)\) \(\chi_{3800}(431,\cdot)\) \(\chi_{3800}(471,\cdot)\) \(\chi_{3800}(591,\cdot)\) \(\chi_{3800}(831,\cdot)\) \(\chi_{3800}(991,\cdot)\) \(\chi_{3800}(1191,\cdot)\) \(\chi_{3800}(1231,\cdot)\) \(\chi_{3800}(1511,\cdot)\) \(\chi_{3800}(1591,\cdot)\) \(\chi_{3800}(1991,\cdot)\) \(\chi_{3800}(2111,\cdot)\) \(\chi_{3800}(2271,\cdot)\) \(\chi_{3800}(2511,\cdot)\) \(\chi_{3800}(2711,\cdot)\) \(\chi_{3800}(2871,\cdot)\) \(\chi_{3800}(3031,\cdot)\) \(\chi_{3800}(3111,\cdot)\) \(\chi_{3800}(3271,\cdot)\) \(\chi_{3800}(3471,\cdot)\) \(\chi_{3800}(3511,\cdot)\) \(\chi_{3800}(3631,\cdot)\) \(\chi_{3800}(3791,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{45})$ |
| Fixed field: | Number field defined by a degree 90 polynomial |
Values on generators
\((951,1901,1977,401)\) → \((-1,1,e\left(\frac{4}{5}\right),e\left(\frac{1}{18}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(7\) | \(9\) | \(11\) | \(13\) | \(17\) | \(21\) | \(23\) | \(27\) | \(29\) |
| \( \chi_{ 3800 }(2111, a) \) | \(1\) | \(1\) | \(e\left(\frac{37}{45}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{29}{45}\right)\) | \(e\left(\frac{29}{30}\right)\) | \(e\left(\frac{43}{90}\right)\) | \(e\left(\frac{43}{45}\right)\) | \(e\left(\frac{59}{90}\right)\) | \(e\left(\frac{37}{90}\right)\) | \(e\left(\frac{7}{15}\right)\) | \(e\left(\frac{49}{90}\right)\) |