Basic properties
| Modulus: | \(2205\) | |
| 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 \(\chi_{245}(3,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 2205.eh
\(\chi_{2205}(73,\cdot)\) \(\chi_{2205}(82,\cdot)\) \(\chi_{2205}(208,\cdot)\) \(\chi_{2205}(262,\cdot)\) \(\chi_{2205}(388,\cdot)\) \(\chi_{2205}(397,\cdot)\) \(\chi_{2205}(523,\cdot)\) \(\chi_{2205}(577,\cdot)\) \(\chi_{2205}(703,\cdot)\) \(\chi_{2205}(712,\cdot)\) \(\chi_{2205}(838,\cdot)\) \(\chi_{2205}(892,\cdot)\) \(\chi_{2205}(1018,\cdot)\) \(\chi_{2205}(1027,\cdot)\) \(\chi_{2205}(1153,\cdot)\) \(\chi_{2205}(1333,\cdot)\) \(\chi_{2205}(1468,\cdot)\) \(\chi_{2205}(1522,\cdot)\) \(\chi_{2205}(1657,\cdot)\) \(\chi_{2205}(1837,\cdot)\) \(\chi_{2205}(1963,\cdot)\) \(\chi_{2205}(1972,\cdot)\) \(\chi_{2205}(2098,\cdot)\) \(\chi_{2205}(2152,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{84})$ |
| Fixed field: | Number field defined by a degree 84 polynomial |
Values on generators
\((1226,442,1081)\) → \((1,-i,e\left(\frac{1}{42}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(8\) | \(11\) | \(13\) | \(16\) | \(17\) | \(19\) | \(22\) | \(23\) |
| \( \chi_{ 2205 }(1963, a) \) | \(1\) | \(1\) | \(e\left(\frac{31}{84}\right)\) | \(e\left(\frac{31}{42}\right)\) | \(e\left(\frac{3}{28}\right)\) | \(e\left(\frac{20}{21}\right)\) | \(e\left(\frac{1}{28}\right)\) | \(e\left(\frac{10}{21}\right)\) | \(e\left(\frac{29}{84}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{9}{28}\right)\) | \(e\left(\frac{13}{84}\right)\) |