Basic properties
| Modulus: | \(3700\) | |
| Conductor: | \(925\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(180\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{925}(533,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 3700.ej
\(\chi_{3700}(17,\cdot)\) \(\chi_{3700}(113,\cdot)\) \(\chi_{3700}(353,\cdot)\) \(\chi_{3700}(513,\cdot)\) \(\chi_{3700}(533,\cdot)\) \(\chi_{3700}(537,\cdot)\) \(\chi_{3700}(573,\cdot)\) \(\chi_{3700}(577,\cdot)\) \(\chi_{3700}(597,\cdot)\) \(\chi_{3700}(653,\cdot)\) \(\chi_{3700}(853,\cdot)\) \(\chi_{3700}(997,\cdot)\) \(\chi_{3700}(1197,\cdot)\) \(\chi_{3700}(1253,\cdot)\) \(\chi_{3700}(1273,\cdot)\) \(\chi_{3700}(1277,\cdot)\) \(\chi_{3700}(1313,\cdot)\) \(\chi_{3700}(1317,\cdot)\) \(\chi_{3700}(1337,\cdot)\) \(\chi_{3700}(1497,\cdot)\) \(\chi_{3700}(1737,\cdot)\) \(\chi_{3700}(1833,\cdot)\) \(\chi_{3700}(1937,\cdot)\) \(\chi_{3700}(2013,\cdot)\) \(\chi_{3700}(2017,\cdot)\) \(\chi_{3700}(2053,\cdot)\) \(\chi_{3700}(2077,\cdot)\) \(\chi_{3700}(2133,\cdot)\) \(\chi_{3700}(2237,\cdot)\) \(\chi_{3700}(2333,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{180})$ |
| Fixed field: | Number field defined by a degree 180 polynomial (not computed) |
Values on generators
\((1851,1777,1001)\) → \((1,e\left(\frac{3}{20}\right),e\left(\frac{13}{36}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(7\) | \(9\) | \(11\) | \(13\) | \(17\) | \(19\) | \(21\) | \(23\) | \(27\) |
| \( \chi_{ 3700 }(533, a) \) | \(1\) | \(1\) | \(e\left(\frac{79}{180}\right)\) | \(e\left(\frac{11}{36}\right)\) | \(e\left(\frac{79}{90}\right)\) | \(e\left(\frac{7}{30}\right)\) | \(e\left(\frac{37}{45}\right)\) | \(e\left(\frac{43}{90}\right)\) | \(e\left(\frac{61}{180}\right)\) | \(e\left(\frac{67}{90}\right)\) | \(e\left(\frac{1}{15}\right)\) | \(e\left(\frac{19}{60}\right)\) |