Basic properties
| Modulus: | \(3762\) | |
| Conductor: | \(1881\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(90\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{1881}(713,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 3762.et
\(\chi_{3762}(59,\cdot)\) \(\chi_{3762}(185,\cdot)\) \(\chi_{3762}(317,\cdot)\) \(\chi_{3762}(383,\cdot)\) \(\chi_{3762}(401,\cdot)\) \(\chi_{3762}(713,\cdot)\) \(\chi_{3762}(1307,\cdot)\) \(\chi_{3762}(1769,\cdot)\) \(\chi_{3762}(1895,\cdot)\) \(\chi_{3762}(2027,\cdot)\) \(\chi_{3762}(2093,\cdot)\) \(\chi_{3762}(2237,\cdot)\) \(\chi_{3762}(2369,\cdot)\) \(\chi_{3762}(2423,\cdot)\) \(\chi_{3762}(2435,\cdot)\) \(\chi_{3762}(2579,\cdot)\) \(\chi_{3762}(2711,\cdot)\) \(\chi_{3762}(2765,\cdot)\) \(\chi_{3762}(2777,\cdot)\) \(\chi_{3762}(3017,\cdot)\) \(\chi_{3762}(3107,\cdot)\) \(\chi_{3762}(3359,\cdot)\) \(\chi_{3762}(3479,\cdot)\) \(\chi_{3762}(3701,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{45})$ |
| Fixed field: | Number field defined by a degree 90 polynomial |
Values on generators
\((2927,343,2377)\) → \((e\left(\frac{1}{6}\right),e\left(\frac{3}{5}\right),e\left(\frac{17}{18}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(5\) | \(7\) | \(13\) | \(17\) | \(23\) | \(25\) | \(29\) | \(31\) | \(35\) | \(37\) |
| \( \chi_{ 3762 }(713, a) \) | \(1\) | \(1\) | \(e\left(\frac{31}{90}\right)\) | \(e\left(\frac{8}{15}\right)\) | \(e\left(\frac{59}{90}\right)\) | \(e\left(\frac{31}{90}\right)\) | \(e\left(\frac{13}{18}\right)\) | \(e\left(\frac{31}{45}\right)\) | \(e\left(\frac{19}{45}\right)\) | \(e\left(\frac{1}{10}\right)\) | \(e\left(\frac{79}{90}\right)\) | \(e\left(\frac{7}{10}\right)\) |