Basic properties
Modulus: | \(2450\) | |
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 \(\chi_{245}(93,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | no | |
Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 2450.bn
\(\chi_{2450}(93,\cdot)\) \(\chi_{2450}(107,\cdot)\) \(\chi_{2450}(193,\cdot)\) \(\chi_{2450}(207,\cdot)\) \(\chi_{2450}(443,\cdot)\) \(\chi_{2450}(457,\cdot)\) \(\chi_{2450}(543,\cdot)\) \(\chi_{2450}(793,\cdot)\) \(\chi_{2450}(807,\cdot)\) \(\chi_{2450}(893,\cdot)\) \(\chi_{2450}(907,\cdot)\) \(\chi_{2450}(1143,\cdot)\) \(\chi_{2450}(1257,\cdot)\) \(\chi_{2450}(1493,\cdot)\) \(\chi_{2450}(1507,\cdot)\) \(\chi_{2450}(1593,\cdot)\) \(\chi_{2450}(1607,\cdot)\) \(\chi_{2450}(1857,\cdot)\) \(\chi_{2450}(1943,\cdot)\) \(\chi_{2450}(1957,\cdot)\) \(\chi_{2450}(2193,\cdot)\) \(\chi_{2450}(2207,\cdot)\) \(\chi_{2450}(2293,\cdot)\) \(\chi_{2450}(2307,\cdot)\)
Related number fields
Field of values: | $\Q(\zeta_{84})$ |
Fixed field: | Number field defined by a degree 84 polynomial |
Values on generators
\((1177,101)\) → \((-i,e\left(\frac{4}{21}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(3\) | \(9\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(27\) | \(29\) | \(31\) |
\( \chi_{ 2450 }(93, a) \) | \(-1\) | \(1\) | \(e\left(\frac{37}{84}\right)\) | \(e\left(\frac{37}{42}\right)\) | \(e\left(\frac{13}{21}\right)\) | \(e\left(\frac{15}{28}\right)\) | \(e\left(\frac{43}{84}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{41}{84}\right)\) | \(e\left(\frac{9}{28}\right)\) | \(e\left(\frac{13}{14}\right)\) | \(e\left(\frac{1}{3}\right)\) |