Basic properties
| Modulus: | \(3675\) | |
| Conductor: | \(1225\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(140\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{1225}(13,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 3675.df
\(\chi_{3675}(13,\cdot)\) \(\chi_{3675}(202,\cdot)\) \(\chi_{3675}(223,\cdot)\) \(\chi_{3675}(328,\cdot)\) \(\chi_{3675}(412,\cdot)\) \(\chi_{3675}(433,\cdot)\) \(\chi_{3675}(517,\cdot)\) \(\chi_{3675}(622,\cdot)\) \(\chi_{3675}(727,\cdot)\) \(\chi_{3675}(748,\cdot)\) \(\chi_{3675}(853,\cdot)\) \(\chi_{3675}(937,\cdot)\) \(\chi_{3675}(958,\cdot)\) \(\chi_{3675}(1042,\cdot)\) \(\chi_{3675}(1063,\cdot)\) \(\chi_{3675}(1147,\cdot)\) \(\chi_{3675}(1252,\cdot)\) \(\chi_{3675}(1378,\cdot)\) \(\chi_{3675}(1462,\cdot)\) \(\chi_{3675}(1483,\cdot)\) \(\chi_{3675}(1588,\cdot)\) \(\chi_{3675}(1672,\cdot)\) \(\chi_{3675}(1777,\cdot)\) \(\chi_{3675}(1798,\cdot)\) \(\chi_{3675}(1903,\cdot)\) \(\chi_{3675}(1987,\cdot)\) \(\chi_{3675}(2092,\cdot)\) \(\chi_{3675}(2113,\cdot)\) \(\chi_{3675}(2197,\cdot)\) \(\chi_{3675}(2323,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{140})$ |
| Fixed field: | Number field defined by a degree 140 polynomial (not computed) |
Values on generators
\((1226,1177,2551)\) → \((1,e\left(\frac{19}{20}\right),e\left(\frac{11}{14}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(8\) | \(11\) | \(13\) | \(16\) | \(17\) | \(19\) | \(22\) | \(23\) |
| \( \chi_{ 3675 }(13, a) \) | \(1\) | \(1\) | \(e\left(\frac{53}{140}\right)\) | \(e\left(\frac{53}{70}\right)\) | \(e\left(\frac{19}{140}\right)\) | \(e\left(\frac{22}{35}\right)\) | \(e\left(\frac{137}{140}\right)\) | \(e\left(\frac{18}{35}\right)\) | \(e\left(\frac{139}{140}\right)\) | \(e\left(\frac{3}{5}\right)\) | \(e\left(\frac{1}{140}\right)\) | \(e\left(\frac{43}{140}\right)\) |