Basic properties
Modulus: | \(2365\) | |
Conductor: | \(215\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(84\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
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Real: | no | |
Primitive: | no, induced from \(\chi_{215}(12,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 2365.cz
\(\chi_{2365}(12,\cdot)\) \(\chi_{2365}(177,\cdot)\) \(\chi_{2365}(243,\cdot)\) \(\chi_{2365}(287,\cdot)\) \(\chi_{2365}(463,\cdot)\) \(\chi_{2365}(507,\cdot)\) \(\chi_{2365}(562,\cdot)\) \(\chi_{2365}(628,\cdot)\) \(\chi_{2365}(793,\cdot)\) \(\chi_{2365}(837,\cdot)\) \(\chi_{2365}(958,\cdot)\) \(\chi_{2365}(1123,\cdot)\) \(\chi_{2365}(1222,\cdot)\) \(\chi_{2365}(1233,\cdot)\) \(\chi_{2365}(1277,\cdot)\) \(\chi_{2365}(1453,\cdot)\) \(\chi_{2365}(1508,\cdot)\) \(\chi_{2365}(1662,\cdot)\) \(\chi_{2365}(1783,\cdot)\) \(\chi_{2365}(1882,\cdot)\) \(\chi_{2365}(2047,\cdot)\) \(\chi_{2365}(2168,\cdot)\) \(\chi_{2365}(2212,\cdot)\) \(\chi_{2365}(2223,\cdot)\)
Related number fields
Field of values: | $\Q(\zeta_{84})$ |
Fixed field: | Number field defined by a degree 84 polynomial |
Values on generators
\((947,431,1981)\) → \((i,1,e\left(\frac{13}{42}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(7\) | \(8\) | \(9\) | \(12\) | \(13\) | \(14\) |
\( \chi_{ 2365 }(12, a) \) | \(1\) | \(1\) | \(e\left(\frac{17}{28}\right)\) | \(e\left(\frac{5}{84}\right)\) | \(e\left(\frac{3}{14}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{1}{12}\right)\) | \(e\left(\frac{23}{28}\right)\) | \(e\left(\frac{5}{42}\right)\) | \(e\left(\frac{23}{84}\right)\) | \(e\left(\frac{55}{84}\right)\) | \(e\left(\frac{29}{42}\right)\) |