Basic properties
Modulus: | \(38025\) | |
Conductor: | \(38025\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(195\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
Real: | no | |
Primitive: | yes | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 38025.lw
\(\chi_{38025}(61,\cdot)\) \(\chi_{38025}(211,\cdot)\) \(\chi_{38025}(646,\cdot)\) \(\chi_{38025}(796,\cdot)\) \(\chi_{38025}(1231,\cdot)\) \(\chi_{38025}(1381,\cdot)\) \(\chi_{38025}(1816,\cdot)\) \(\chi_{38025}(1966,\cdot)\) \(\chi_{38025}(2986,\cdot)\) \(\chi_{38025}(3136,\cdot)\) \(\chi_{38025}(3721,\cdot)\) \(\chi_{38025}(4156,\cdot)\) \(\chi_{38025}(4306,\cdot)\) \(\chi_{38025}(4741,\cdot)\) \(\chi_{38025}(4891,\cdot)\) \(\chi_{38025}(5911,\cdot)\) \(\chi_{38025}(6496,\cdot)\) \(\chi_{38025}(6646,\cdot)\) \(\chi_{38025}(7081,\cdot)\) \(\chi_{38025}(7231,\cdot)\) \(\chi_{38025}(7666,\cdot)\) \(\chi_{38025}(7816,\cdot)\) \(\chi_{38025}(8836,\cdot)\) \(\chi_{38025}(8986,\cdot)\) \(\chi_{38025}(9421,\cdot)\) \(\chi_{38025}(9571,\cdot)\) \(\chi_{38025}(10006,\cdot)\) \(\chi_{38025}(10156,\cdot)\) \(\chi_{38025}(10591,\cdot)\) \(\chi_{38025}(10741,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{195})$ |
Fixed field: | Number field defined by a degree 195 polynomial (not computed) |
Values on generators
\((29576,9127,37351)\) → \((e\left(\frac{2}{3}\right),e\left(\frac{4}{5}\right),e\left(\frac{35}{39}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(7\) | \(8\) | \(11\) | \(14\) | \(16\) | \(17\) | \(19\) | \(22\) |
\( \chi_{ 38025 }(61, a) \) | \(1\) | \(1\) | \(e\left(\frac{71}{195}\right)\) | \(e\left(\frac{142}{195}\right)\) | \(e\left(\frac{9}{13}\right)\) | \(e\left(\frac{6}{65}\right)\) | \(e\left(\frac{176}{195}\right)\) | \(e\left(\frac{11}{195}\right)\) | \(e\left(\frac{89}{195}\right)\) | \(e\left(\frac{83}{195}\right)\) | \(e\left(\frac{11}{15}\right)\) | \(e\left(\frac{4}{15}\right)\) |