Basic properties
| Modulus: | \(9405\) | |
| Conductor: | \(9405\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(180\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | yes | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 9405.on
\(\chi_{9405}(13,\cdot)\) \(\chi_{9405}(52,\cdot)\) \(\chi_{9405}(238,\cdot)\) \(\chi_{9405}(832,\cdot)\) \(\chi_{9405}(952,\cdot)\) \(\chi_{9405}(1003,\cdot)\) \(\chi_{9405}(1447,\cdot)\) \(\chi_{9405}(1723,\cdot)\) \(\chi_{9405}(1762,\cdot)\) \(\chi_{9405}(1777,\cdot)\) \(\chi_{9405}(1933,\cdot)\) \(\chi_{9405}(2713,\cdot)\) \(\chi_{9405}(2833,\cdot)\) \(\chi_{9405}(3262,\cdot)\) \(\chi_{9405}(3328,\cdot)\) \(\chi_{9405}(3472,\cdot)\) \(\chi_{9405}(3517,\cdot)\) \(\chi_{9405}(3643,\cdot)\) \(\chi_{9405}(3658,\cdot)\) \(\chi_{9405}(4012,\cdot)\) \(\chi_{9405}(4252,\cdot)\) \(\chi_{9405}(4342,\cdot)\) \(\chi_{9405}(5143,\cdot)\) \(\chi_{9405}(5227,\cdot)\) \(\chi_{9405}(5353,\cdot)\) \(\chi_{9405}(5398,\cdot)\) \(\chi_{9405}(5722,\cdot)\) \(\chi_{9405}(5827,\cdot)\) \(\chi_{9405}(5893,\cdot)\) \(\chi_{9405}(6052,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{180})$ |
| Fixed field: | Number field defined by a degree 180 polynomial (not computed) |
Values on generators
\((1046,1882,5986,496)\) → \((e\left(\frac{1}{3}\right),-i,e\left(\frac{1}{10}\right),e\left(\frac{5}{18}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(7\) | \(8\) | \(13\) | \(14\) | \(16\) | \(17\) | \(23\) | \(26\) |
| \( \chi_{ 9405 }(13, a) \) | \(-1\) | \(1\) | \(e\left(\frac{83}{180}\right)\) | \(e\left(\frac{83}{90}\right)\) | \(e\left(\frac{9}{20}\right)\) | \(e\left(\frac{23}{60}\right)\) | \(e\left(\frac{73}{180}\right)\) | \(e\left(\frac{41}{45}\right)\) | \(e\left(\frac{38}{45}\right)\) | \(e\left(\frac{77}{180}\right)\) | \(e\left(\frac{17}{36}\right)\) | \(e\left(\frac{13}{15}\right)\) |