Basic properties
| Modulus: | \(1900\) | |
| Conductor: | \(475\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(90\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{475}(29,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 1900.cp
\(\chi_{1900}(29,\cdot)\) \(\chi_{1900}(89,\cdot)\) \(\chi_{1900}(109,\cdot)\) \(\chi_{1900}(129,\cdot)\) \(\chi_{1900}(269,\cdot)\) \(\chi_{1900}(409,\cdot)\) \(\chi_{1900}(469,\cdot)\) \(\chi_{1900}(489,\cdot)\) \(\chi_{1900}(509,\cdot)\) \(\chi_{1900}(629,\cdot)\) \(\chi_{1900}(789,\cdot)\) \(\chi_{1900}(869,\cdot)\) \(\chi_{1900}(889,\cdot)\) \(\chi_{1900}(1009,\cdot)\) \(\chi_{1900}(1029,\cdot)\) \(\chi_{1900}(1169,\cdot)\) \(\chi_{1900}(1229,\cdot)\) \(\chi_{1900}(1269,\cdot)\) \(\chi_{1900}(1389,\cdot)\) \(\chi_{1900}(1409,\cdot)\) \(\chi_{1900}(1609,\cdot)\) \(\chi_{1900}(1629,\cdot)\) \(\chi_{1900}(1769,\cdot)\) \(\chi_{1900}(1789,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{45})$ |
| Fixed field: | Number field defined by a degree 90 polynomial |
Values on generators
\((951,77,401)\) → \((1,e\left(\frac{1}{10}\right),e\left(\frac{17}{18}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(7\) | \(9\) | \(11\) | \(13\) | \(17\) | \(21\) | \(23\) | \(27\) | \(29\) |
| \( \chi_{ 1900 }(29, a) \) | \(-1\) | \(1\) | \(e\left(\frac{44}{45}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{43}{45}\right)\) | \(e\left(\frac{14}{15}\right)\) | \(e\left(\frac{28}{45}\right)\) | \(e\left(\frac{67}{90}\right)\) | \(e\left(\frac{13}{90}\right)\) | \(e\left(\frac{89}{90}\right)\) | \(e\left(\frac{14}{15}\right)\) | \(e\left(\frac{23}{90}\right)\) |