Basic properties
Modulus: | \(2850\) | |
Conductor: | \(475\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(180\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
Real: | no | |
Primitive: | no, induced from \(\chi_{475}(298,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 2850.cs
\(\chi_{2850}(13,\cdot)\) \(\chi_{2850}(67,\cdot)\) \(\chi_{2850}(97,\cdot)\) \(\chi_{2850}(127,\cdot)\) \(\chi_{2850}(223,\cdot)\) \(\chi_{2850}(337,\cdot)\) \(\chi_{2850}(433,\cdot)\) \(\chi_{2850}(523,\cdot)\) \(\chi_{2850}(547,\cdot)\) \(\chi_{2850}(553,\cdot)\) \(\chi_{2850}(583,\cdot)\) \(\chi_{2850}(637,\cdot)\) \(\chi_{2850}(667,\cdot)\) \(\chi_{2850}(697,\cdot)\) \(\chi_{2850}(763,\cdot)\) \(\chi_{2850}(877,\cdot)\) \(\chi_{2850}(1003,\cdot)\) \(\chi_{2850}(1117,\cdot)\) \(\chi_{2850}(1123,\cdot)\) \(\chi_{2850}(1153,\cdot)\) \(\chi_{2850}(1237,\cdot)\) \(\chi_{2850}(1267,\cdot)\) \(\chi_{2850}(1333,\cdot)\) \(\chi_{2850}(1363,\cdot)\) \(\chi_{2850}(1447,\cdot)\) \(\chi_{2850}(1477,\cdot)\) \(\chi_{2850}(1573,\cdot)\) \(\chi_{2850}(1663,\cdot)\) \(\chi_{2850}(1687,\cdot)\) \(\chi_{2850}(1723,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{180})$ |
Fixed field: | Number field defined by a degree 180 polynomial (not computed) |
Values on generators
\((1901,1027,1351)\) → \((1,e\left(\frac{11}{20}\right),e\left(\frac{5}{18}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(7\) | \(11\) | \(13\) | \(17\) | \(23\) | \(29\) | \(31\) | \(37\) | \(41\) | \(43\) |
\( \chi_{ 2850 }(1723, a) \) | \(1\) | \(1\) | \(e\left(\frac{5}{12}\right)\) | \(e\left(\frac{2}{15}\right)\) | \(e\left(\frac{151}{180}\right)\) | \(e\left(\frac{167}{180}\right)\) | \(e\left(\frac{109}{180}\right)\) | \(e\left(\frac{37}{45}\right)\) | \(e\left(\frac{17}{30}\right)\) | \(e\left(\frac{9}{20}\right)\) | \(e\left(\frac{73}{90}\right)\) | \(e\left(\frac{25}{36}\right)\) |