Basic properties
| Modulus: | \(38025\) | |
| Conductor: | \(7605\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(156\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{7605}(7,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 38025.kc
\(\chi_{38025}(7,\cdot)\) \(\chi_{38025}(1618,\cdot)\) \(\chi_{38025}(2182,\cdot)\) \(\chi_{38025}(2932,\cdot)\) \(\chi_{38025}(3343,\cdot)\) \(\chi_{38025}(4543,\cdot)\) \(\chi_{38025}(5107,\cdot)\) \(\chi_{38025}(5857,\cdot)\) \(\chi_{38025}(6268,\cdot)\) \(\chi_{38025}(7468,\cdot)\) \(\chi_{38025}(8782,\cdot)\) \(\chi_{38025}(9193,\cdot)\) \(\chi_{38025}(10393,\cdot)\) \(\chi_{38025}(10957,\cdot)\) \(\chi_{38025}(11707,\cdot)\) \(\chi_{38025}(12118,\cdot)\) \(\chi_{38025}(13318,\cdot)\) \(\chi_{38025}(13882,\cdot)\) \(\chi_{38025}(14632,\cdot)\) \(\chi_{38025}(15043,\cdot)\) \(\chi_{38025}(16807,\cdot)\) \(\chi_{38025}(17968,\cdot)\) \(\chi_{38025}(19168,\cdot)\) \(\chi_{38025}(19732,\cdot)\) \(\chi_{38025}(20482,\cdot)\) \(\chi_{38025}(20893,\cdot)\) \(\chi_{38025}(22093,\cdot)\) \(\chi_{38025}(22657,\cdot)\) \(\chi_{38025}(23407,\cdot)\) \(\chi_{38025}(23818,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{156})$ |
| Fixed field: | Number field defined by a degree 156 polynomial (not computed) |
Values on generators
\((29576,9127,37351)\) → \((e\left(\frac{2}{3}\right),i,e\left(\frac{107}{156}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(7\) | \(8\) | \(11\) | \(14\) | \(16\) | \(17\) | \(19\) | \(22\) |
| \( \chi_{ 38025 }(7, a) \) | \(1\) | \(1\) | \(e\left(\frac{47}{78}\right)\) | \(e\left(\frac{8}{39}\right)\) | \(e\left(\frac{4}{13}\right)\) | \(e\left(\frac{21}{26}\right)\) | \(e\left(\frac{49}{156}\right)\) | \(e\left(\frac{71}{78}\right)\) | \(e\left(\frac{16}{39}\right)\) | \(e\left(\frac{61}{156}\right)\) | \(e\left(\frac{1}{12}\right)\) | \(e\left(\frac{11}{12}\right)\) |