Basic properties
Modulus: | \(3025\) | |
Conductor: | \(605\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(220\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
Real: | no | |
Primitive: | no, induced from \(\chi_{605}(18,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | no | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 3025.cy
\(\chi_{3025}(7,\cdot)\) \(\chi_{3025}(18,\cdot)\) \(\chi_{3025}(57,\cdot)\) \(\chi_{3025}(68,\cdot)\) \(\chi_{3025}(107,\cdot)\) \(\chi_{3025}(182,\cdot)\) \(\chi_{3025}(193,\cdot)\) \(\chi_{3025}(293,\cdot)\) \(\chi_{3025}(332,\cdot)\) \(\chi_{3025}(343,\cdot)\) \(\chi_{3025}(382,\cdot)\) \(\chi_{3025}(393,\cdot)\) \(\chi_{3025}(468,\cdot)\) \(\chi_{3025}(557,\cdot)\) \(\chi_{3025}(568,\cdot)\) \(\chi_{3025}(607,\cdot)\) \(\chi_{3025}(618,\cdot)\) \(\chi_{3025}(657,\cdot)\) \(\chi_{3025}(668,\cdot)\) \(\chi_{3025}(732,\cdot)\) \(\chi_{3025}(743,\cdot)\) \(\chi_{3025}(832,\cdot)\) \(\chi_{3025}(843,\cdot)\) \(\chi_{3025}(882,\cdot)\) \(\chi_{3025}(893,\cdot)\) \(\chi_{3025}(932,\cdot)\) \(\chi_{3025}(943,\cdot)\) \(\chi_{3025}(1007,\cdot)\) \(\chi_{3025}(1018,\cdot)\) \(\chi_{3025}(1107,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{220})$ |
Fixed field: | Number field defined by a degree 220 polynomial (not computed) |
Values on generators
\((727,2301)\) → \((-i,e\left(\frac{67}{110}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(7\) | \(8\) | \(9\) | \(12\) | \(13\) | \(14\) |
\( \chi_{ 3025 }(18, a) \) | \(1\) | \(1\) | \(e\left(\frac{79}{220}\right)\) | \(e\left(\frac{17}{20}\right)\) | \(e\left(\frac{79}{110}\right)\) | \(e\left(\frac{23}{110}\right)\) | \(e\left(\frac{3}{220}\right)\) | \(e\left(\frac{17}{220}\right)\) | \(e\left(\frac{7}{10}\right)\) | \(e\left(\frac{25}{44}\right)\) | \(e\left(\frac{169}{220}\right)\) | \(e\left(\frac{41}{110}\right)\) |