Basic properties
| Modulus: | \(1900\) | |
| 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 \(\chi_{475}(73,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 1900.ct
\(\chi_{1900}(17,\cdot)\) \(\chi_{1900}(73,\cdot)\) \(\chi_{1900}(137,\cdot)\) \(\chi_{1900}(177,\cdot)\) \(\chi_{1900}(213,\cdot)\) \(\chi_{1900}(233,\cdot)\) \(\chi_{1900}(237,\cdot)\) \(\chi_{1900}(253,\cdot)\) \(\chi_{1900}(313,\cdot)\) \(\chi_{1900}(377,\cdot)\) \(\chi_{1900}(397,\cdot)\) \(\chi_{1900}(453,\cdot)\) \(\chi_{1900}(473,\cdot)\) \(\chi_{1900}(517,\cdot)\) \(\chi_{1900}(537,\cdot)\) \(\chi_{1900}(613,\cdot)\) \(\chi_{1900}(617,\cdot)\) \(\chi_{1900}(633,\cdot)\) \(\chi_{1900}(777,\cdot)\) \(\chi_{1900}(833,\cdot)\) \(\chi_{1900}(853,\cdot)\) \(\chi_{1900}(897,\cdot)\) \(\chi_{1900}(917,\cdot)\) \(\chi_{1900}(937,\cdot)\) \(\chi_{1900}(973,\cdot)\) \(\chi_{1900}(997,\cdot)\) \(\chi_{1900}(1013,\cdot)\) \(\chi_{1900}(1073,\cdot)\) \(\chi_{1900}(1137,\cdot)\) \(\chi_{1900}(1213,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{180})$ |
| Fixed field: | Number field defined by a degree 180 polynomial (not computed) |
Values on generators
\((951,77,401)\) → \((1,e\left(\frac{11}{20}\right),e\left(\frac{2}{9}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(7\) | \(9\) | \(11\) | \(13\) | \(17\) | \(21\) | \(23\) | \(27\) | \(29\) |
| \( \chi_{ 1900 }(73, a) \) | \(-1\) | \(1\) | \(e\left(\frac{133}{180}\right)\) | \(e\left(\frac{1}{12}\right)\) | \(e\left(\frac{43}{90}\right)\) | \(e\left(\frac{7}{15}\right)\) | \(e\left(\frac{101}{180}\right)\) | \(e\left(\frac{67}{180}\right)\) | \(e\left(\frac{37}{45}\right)\) | \(e\left(\frac{89}{180}\right)\) | \(e\left(\frac{13}{60}\right)\) | \(e\left(\frac{79}{90}\right)\) |