Basic properties
| Modulus: | \(3762\) | |
| Conductor: | \(209\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(90\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{209}(127,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 3762.ei
\(\chi_{3762}(127,\cdot)\) \(\chi_{3762}(325,\cdot)\) \(\chi_{3762}(469,\cdot)\) \(\chi_{3762}(523,\cdot)\) \(\chi_{3762}(667,\cdot)\) \(\chi_{3762}(811,\cdot)\) \(\chi_{3762}(865,\cdot)\) \(\chi_{3762}(1009,\cdot)\) \(\chi_{3762}(1117,\cdot)\) \(\chi_{3762}(1135,\cdot)\) \(\chi_{3762}(1207,\cdot)\) \(\chi_{3762}(1333,\cdot)\) \(\chi_{3762}(1459,\cdot)\) \(\chi_{3762}(1801,\cdot)\) \(\chi_{3762}(2503,\cdot)\) \(\chi_{3762}(2521,\cdot)\) \(\chi_{3762}(2701,\cdot)\) \(\chi_{3762}(2719,\cdot)\) \(\chi_{3762}(2845,\cdot)\) \(\chi_{3762}(2917,\cdot)\) \(\chi_{3762}(3043,\cdot)\) \(\chi_{3762}(3187,\cdot)\) \(\chi_{3762}(3385,\cdot)\) \(\chi_{3762}(3511,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{45})$ |
| Fixed field: | Number field defined by a degree 90 polynomial |
Values on generators
\((2927,343,2377)\) → \((1,e\left(\frac{9}{10}\right),e\left(\frac{5}{18}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(5\) | \(7\) | \(13\) | \(17\) | \(23\) | \(25\) | \(29\) | \(31\) | \(35\) | \(37\) |
| \( \chi_{ 3762 }(127, a) \) | \(1\) | \(1\) | \(e\left(\frac{2}{45}\right)\) | \(e\left(\frac{29}{30}\right)\) | \(e\left(\frac{13}{45}\right)\) | \(e\left(\frac{79}{90}\right)\) | \(e\left(\frac{5}{9}\right)\) | \(e\left(\frac{4}{45}\right)\) | \(e\left(\frac{1}{45}\right)\) | \(e\left(\frac{17}{30}\right)\) | \(e\left(\frac{1}{90}\right)\) | \(e\left(\frac{3}{10}\right)\) |