Basic properties
Modulus: | \(5700\) | |
Conductor: | \(475\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(45\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
Real: | no | |
Primitive: | no, induced from \(\chi_{475}(161,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 5700.ei
\(\chi_{5700}(61,\cdot)\) \(\chi_{5700}(481,\cdot)\) \(\chi_{5700}(541,\cdot)\) \(\chi_{5700}(841,\cdot)\) \(\chi_{5700}(1081,\cdot)\) \(\chi_{5700}(1441,\cdot)\) \(\chi_{5700}(1621,\cdot)\) \(\chi_{5700}(1681,\cdot)\) \(\chi_{5700}(1981,\cdot)\) \(\chi_{5700}(2221,\cdot)\) \(\chi_{5700}(2341,\cdot)\) \(\chi_{5700}(2581,\cdot)\) \(\chi_{5700}(2761,\cdot)\) \(\chi_{5700}(2821,\cdot)\) \(\chi_{5700}(3121,\cdot)\) \(\chi_{5700}(3361,\cdot)\) \(\chi_{5700}(3481,\cdot)\) \(\chi_{5700}(3721,\cdot)\) \(\chi_{5700}(3961,\cdot)\) \(\chi_{5700}(4261,\cdot)\) \(\chi_{5700}(4621,\cdot)\) \(\chi_{5700}(4861,\cdot)\) \(\chi_{5700}(5041,\cdot)\) \(\chi_{5700}(5641,\cdot)\)
Related number fields
Field of values: | $\Q(\zeta_{45})$ |
Fixed field: | Number field defined by a degree 45 polynomial |
Values on generators
\((2851,1901,3877,4201)\) → \((1,1,e\left(\frac{4}{5}\right),e\left(\frac{4}{9}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(7\) | \(11\) | \(13\) | \(17\) | \(23\) | \(29\) | \(31\) | \(37\) | \(41\) | \(43\) |
\( \chi_{ 5700 }(3961, a) \) | \(1\) | \(1\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{2}{15}\right)\) | \(e\left(\frac{19}{45}\right)\) | \(e\left(\frac{38}{45}\right)\) | \(e\left(\frac{31}{45}\right)\) | \(e\left(\frac{7}{45}\right)\) | \(e\left(\frac{1}{15}\right)\) | \(e\left(\frac{1}{5}\right)\) | \(e\left(\frac{44}{45}\right)\) | \(e\left(\frac{1}{9}\right)\) |