Basic properties
| Modulus: | \(9450\) | |
| Conductor: | \(4725\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(180\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{4725}(67,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 9450.hc
\(\chi_{9450}(67,\cdot)\) \(\chi_{9450}(583,\cdot)\) \(\chi_{9450}(697,\cdot)\) \(\chi_{9450}(823,\cdot)\) \(\chi_{9450}(1087,\cdot)\) \(\chi_{9450}(1213,\cdot)\) \(\chi_{9450}(1327,\cdot)\) \(\chi_{9450}(1453,\cdot)\) \(\chi_{9450}(1717,\cdot)\) \(\chi_{9450}(2083,\cdot)\) \(\chi_{9450}(2347,\cdot)\) \(\chi_{9450}(2473,\cdot)\) \(\chi_{9450}(2587,\cdot)\) \(\chi_{9450}(2713,\cdot)\) \(\chi_{9450}(2977,\cdot)\) \(\chi_{9450}(3103,\cdot)\) \(\chi_{9450}(3217,\cdot)\) \(\chi_{9450}(3733,\cdot)\) \(\chi_{9450}(3847,\cdot)\) \(\chi_{9450}(3973,\cdot)\) \(\chi_{9450}(4237,\cdot)\) \(\chi_{9450}(4363,\cdot)\) \(\chi_{9450}(4477,\cdot)\) \(\chi_{9450}(4603,\cdot)\) \(\chi_{9450}(4867,\cdot)\) \(\chi_{9450}(5233,\cdot)\) \(\chi_{9450}(5497,\cdot)\) \(\chi_{9450}(5623,\cdot)\) \(\chi_{9450}(5737,\cdot)\) \(\chi_{9450}(5863,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{180})$ |
| Fixed field: | Number field defined by a degree 180 polynomial (not computed) |
Values on generators
\((9101,6427,6751)\) → \((e\left(\frac{4}{9}\right),e\left(\frac{13}{20}\right),e\left(\frac{2}{3}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(29\) | \(31\) | \(37\) | \(41\) | \(43\) |
| \( \chi_{ 9450 }(67, a) \) | \(-1\) | \(1\) | \(e\left(\frac{38}{45}\right)\) | \(e\left(\frac{163}{180}\right)\) | \(e\left(\frac{47}{60}\right)\) | \(e\left(\frac{11}{30}\right)\) | \(e\left(\frac{67}{180}\right)\) | \(e\left(\frac{67}{90}\right)\) | \(e\left(\frac{34}{45}\right)\) | \(e\left(\frac{17}{20}\right)\) | \(e\left(\frac{7}{45}\right)\) | \(e\left(\frac{19}{36}\right)\) |