Basic properties
| Modulus: | \(3025\) | |
| Conductor: | \(3025\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(220\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | yes | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 3025.cw
\(\chi_{3025}(87,\cdot)\) \(\chi_{3025}(98,\cdot)\) \(\chi_{3025}(142,\cdot)\) \(\chi_{3025}(153,\cdot)\) \(\chi_{3025}(197,\cdot)\) \(\chi_{3025}(208,\cdot)\) \(\chi_{3025}(252,\cdot)\) \(\chi_{3025}(263,\cdot)\) \(\chi_{3025}(373,\cdot)\) \(\chi_{3025}(417,\cdot)\) \(\chi_{3025}(428,\cdot)\) \(\chi_{3025}(472,\cdot)\) \(\chi_{3025}(527,\cdot)\) \(\chi_{3025}(538,\cdot)\) \(\chi_{3025}(637,\cdot)\) \(\chi_{3025}(648,\cdot)\) \(\chi_{3025}(692,\cdot)\) \(\chi_{3025}(703,\cdot)\) \(\chi_{3025}(747,\cdot)\) \(\chi_{3025}(758,\cdot)\) \(\chi_{3025}(802,\cdot)\) \(\chi_{3025}(813,\cdot)\) \(\chi_{3025}(912,\cdot)\) \(\chi_{3025}(923,\cdot)\) \(\chi_{3025}(978,\cdot)\) \(\chi_{3025}(1022,\cdot)\) \(\chi_{3025}(1033,\cdot)\) \(\chi_{3025}(1077,\cdot)\) \(\chi_{3025}(1187,\cdot)\) \(\chi_{3025}(1198,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{220})$ |
| Fixed field: | Number field defined by a degree 220 polynomial (not computed) |
Values on generators
\((727,2301)\) → \((e\left(\frac{9}{20}\right),e\left(\frac{21}{22}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(7\) | \(8\) | \(9\) | \(12\) | \(13\) | \(14\) |
| \( \chi_{ 3025 }(87, a) \) | \(1\) | \(1\) | \(e\left(\frac{89}{220}\right)\) | \(e\left(\frac{3}{20}\right)\) | \(e\left(\frac{89}{110}\right)\) | \(e\left(\frac{61}{110}\right)\) | \(e\left(\frac{41}{44}\right)\) | \(e\left(\frac{47}{220}\right)\) | \(e\left(\frac{3}{10}\right)\) | \(e\left(\frac{211}{220}\right)\) | \(e\left(\frac{211}{220}\right)\) | \(e\left(\frac{37}{110}\right)\) |