Basic properties
Modulus: | \(2450\) | |
Conductor: | \(1225\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(210\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
Real: | no | |
Primitive: | no, induced from \(\chi_{1225}(61,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 2450.bs
\(\chi_{2450}(61,\cdot)\) \(\chi_{2450}(131,\cdot)\) \(\chi_{2450}(171,\cdot)\) \(\chi_{2450}(241,\cdot)\) \(\chi_{2450}(271,\cdot)\) \(\chi_{2450}(311,\cdot)\) \(\chi_{2450}(341,\cdot)\) \(\chi_{2450}(381,\cdot)\) \(\chi_{2450}(481,\cdot)\) \(\chi_{2450}(591,\cdot)\) \(\chi_{2450}(621,\cdot)\) \(\chi_{2450}(661,\cdot)\) \(\chi_{2450}(691,\cdot)\) \(\chi_{2450}(731,\cdot)\) \(\chi_{2450}(761,\cdot)\) \(\chi_{2450}(831,\cdot)\) \(\chi_{2450}(871,\cdot)\) \(\chi_{2450}(941,\cdot)\) \(\chi_{2450}(971,\cdot)\) \(\chi_{2450}(1041,\cdot)\) \(\chi_{2450}(1081,\cdot)\) \(\chi_{2450}(1111,\cdot)\) \(\chi_{2450}(1181,\cdot)\) \(\chi_{2450}(1221,\cdot)\) \(\chi_{2450}(1291,\cdot)\) \(\chi_{2450}(1321,\cdot)\) \(\chi_{2450}(1361,\cdot)\) \(\chi_{2450}(1431,\cdot)\) \(\chi_{2450}(1461,\cdot)\) \(\chi_{2450}(1531,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{105})$ |
Fixed field: | Number field defined by a degree 210 polynomial (not computed) |
Values on generators
\((1177,101)\) → \((e\left(\frac{4}{5}\right),e\left(\frac{11}{42}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(3\) | \(9\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(27\) | \(29\) | \(31\) |
\( \chi_{ 2450 }(61, a) \) | \(-1\) | \(1\) | \(e\left(\frac{181}{210}\right)\) | \(e\left(\frac{76}{105}\right)\) | \(e\left(\frac{29}{105}\right)\) | \(e\left(\frac{59}{70}\right)\) | \(e\left(\frac{199}{210}\right)\) | \(e\left(\frac{17}{30}\right)\) | \(e\left(\frac{79}{105}\right)\) | \(e\left(\frac{41}{70}\right)\) | \(e\left(\frac{11}{35}\right)\) | \(e\left(\frac{7}{30}\right)\) |