Basic properties
| Modulus: | \(9464\) | |
| Conductor: | \(1183\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(156\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{1183}(145,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 9464.ie
\(\chi_{9464}(145,\cdot)\) \(\chi_{9464}(241,\cdot)\) \(\chi_{9464}(409,\cdot)\) \(\chi_{9464}(817,\cdot)\) \(\chi_{9464}(873,\cdot)\) \(\chi_{9464}(969,\cdot)\) \(\chi_{9464}(1137,\cdot)\) \(\chi_{9464}(1545,\cdot)\) \(\chi_{9464}(1697,\cdot)\) \(\chi_{9464}(1865,\cdot)\) \(\chi_{9464}(2273,\cdot)\) \(\chi_{9464}(2329,\cdot)\) \(\chi_{9464}(2425,\cdot)\) \(\chi_{9464}(2593,\cdot)\) \(\chi_{9464}(3001,\cdot)\) \(\chi_{9464}(3057,\cdot)\) \(\chi_{9464}(3153,\cdot)\) \(\chi_{9464}(3321,\cdot)\) \(\chi_{9464}(3729,\cdot)\) \(\chi_{9464}(3785,\cdot)\) \(\chi_{9464}(3881,\cdot)\) \(\chi_{9464}(4049,\cdot)\) \(\chi_{9464}(4457,\cdot)\) \(\chi_{9464}(4513,\cdot)\) \(\chi_{9464}(4609,\cdot)\) \(\chi_{9464}(4777,\cdot)\) \(\chi_{9464}(5185,\cdot)\) \(\chi_{9464}(5241,\cdot)\) \(\chi_{9464}(5337,\cdot)\) \(\chi_{9464}(5505,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{156})$ |
| Fixed field: | Number field defined by a degree 156 polynomial (not computed) |
Values on generators
\((2367,4733,2705,9297)\) → \((1,1,e\left(\frac{5}{6}\right),e\left(\frac{49}{156}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(9\) | \(11\) | \(15\) | \(17\) | \(19\) | \(23\) | \(25\) | \(27\) |
| \( \chi_{ 9464 }(145, a) \) | \(1\) | \(1\) | \(e\left(\frac{61}{78}\right)\) | \(e\left(\frac{155}{156}\right)\) | \(e\left(\frac{22}{39}\right)\) | \(e\left(\frac{107}{156}\right)\) | \(e\left(\frac{121}{156}\right)\) | \(e\left(\frac{9}{13}\right)\) | \(e\left(\frac{7}{12}\right)\) | \(-1\) | \(e\left(\frac{77}{78}\right)\) | \(e\left(\frac{9}{26}\right)\) |