Basic properties
| Modulus: | \(1225\) | |
| Conductor: | \(245\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(84\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{245}(82,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 1225.bn
\(\chi_{1225}(82,\cdot)\) \(\chi_{1225}(143,\cdot)\) \(\chi_{1225}(157,\cdot)\) \(\chi_{1225}(243,\cdot)\) \(\chi_{1225}(257,\cdot)\) \(\chi_{1225}(318,\cdot)\) \(\chi_{1225}(332,\cdot)\) \(\chi_{1225}(418,\cdot)\) \(\chi_{1225}(432,\cdot)\) \(\chi_{1225}(493,\cdot)\) \(\chi_{1225}(507,\cdot)\) \(\chi_{1225}(593,\cdot)\) \(\chi_{1225}(682,\cdot)\) \(\chi_{1225}(768,\cdot)\) \(\chi_{1225}(782,\cdot)\) \(\chi_{1225}(843,\cdot)\) \(\chi_{1225}(857,\cdot)\) \(\chi_{1225}(943,\cdot)\) \(\chi_{1225}(957,\cdot)\) \(\chi_{1225}(1018,\cdot)\) \(\chi_{1225}(1032,\cdot)\) \(\chi_{1225}(1118,\cdot)\) \(\chi_{1225}(1132,\cdot)\) \(\chi_{1225}(1193,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{84})$ |
| Fixed field: | Number field defined by a degree 84 polynomial |
Values on generators
\((1177,101)\) → \((i,e\left(\frac{41}{42}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(8\) | \(9\) | \(11\) | \(12\) | \(13\) | \(16\) |
| \( \chi_{ 1225 }(82, a) \) | \(1\) | \(1\) | \(e\left(\frac{53}{84}\right)\) | \(e\left(\frac{61}{84}\right)\) | \(e\left(\frac{11}{42}\right)\) | \(e\left(\frac{5}{14}\right)\) | \(e\left(\frac{25}{28}\right)\) | \(e\left(\frac{19}{42}\right)\) | \(e\left(\frac{1}{21}\right)\) | \(e\left(\frac{83}{84}\right)\) | \(e\left(\frac{27}{28}\right)\) | \(e\left(\frac{11}{21}\right)\) |