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 \(\chi_{605}(7,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| 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
\((727,2301)\) → \((i,e\left(\frac{7}{110}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(7\) | \(8\) | \(9\) | \(12\) | \(13\) | \(14\) |
| \( \chi_{ 3025 }(7, a) \) | \(1\) | \(1\) | \(e\left(\frac{69}{220}\right)\) | \(e\left(\frac{7}{20}\right)\) | \(e\left(\frac{69}{110}\right)\) | \(e\left(\frac{73}{110}\right)\) | \(e\left(\frac{153}{220}\right)\) | \(e\left(\frac{207}{220}\right)\) | \(e\left(\frac{7}{10}\right)\) | \(e\left(\frac{43}{44}\right)\) | \(e\left(\frac{39}{220}\right)\) | \(e\left(\frac{1}{110}\right)\) |