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 \(\chi_{1881}(344,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 3762.ed
\(\chi_{3762}(203,\cdot)\) \(\chi_{3762}(257,\cdot)\) \(\chi_{3762}(509,\cdot)\) \(\chi_{3762}(515,\cdot)\) \(\chi_{3762}(599,\cdot)\) \(\chi_{3762}(641,\cdot)\) \(\chi_{3762}(839,\cdot)\) \(\chi_{3762}(851,\cdot)\) \(\chi_{3762}(983,\cdot)\) \(\chi_{3762}(1181,\cdot)\) \(\chi_{3762}(1193,\cdot)\) \(\chi_{3762}(1325,\cdot)\) \(\chi_{3762}(1523,\cdot)\) \(\chi_{3762}(1571,\cdot)\) \(\chi_{3762}(1967,\cdot)\) \(\chi_{3762}(2225,\cdot)\) \(\chi_{3762}(2561,\cdot)\) \(\chi_{3762}(2567,\cdot)\) \(\chi_{3762}(2693,\cdot)\) \(\chi_{3762}(2891,\cdot)\) \(\chi_{3762}(2909,\cdot)\) \(\chi_{3762}(3281,\cdot)\) \(\chi_{3762}(3623,\cdot)\) \(\chi_{3762}(3677,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{45})$ |
| Fixed field: | Number field defined by a degree 90 polynomial |
Values on generators
\((2927,343,2377)\) → \((e\left(\frac{1}{6}\right),e\left(\frac{4}{5}\right),e\left(\frac{1}{18}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(5\) | \(7\) | \(13\) | \(17\) | \(23\) | \(25\) | \(29\) | \(31\) | \(35\) | \(37\) |
| \( \chi_{ 3762 }(2225, a) \) | \(1\) | \(1\) | \(e\left(\frac{83}{90}\right)\) | \(e\left(\frac{3}{5}\right)\) | \(e\left(\frac{37}{90}\right)\) | \(e\left(\frac{23}{90}\right)\) | \(e\left(\frac{17}{18}\right)\) | \(e\left(\frac{38}{45}\right)\) | \(e\left(\frac{32}{45}\right)\) | \(e\left(\frac{29}{30}\right)\) | \(e\left(\frac{47}{90}\right)\) | \(e\left(\frac{1}{10}\right)\) |