Basic properties
| Modulus: | \(9464\) | |
| Conductor: | \(1352\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(156\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{1352}(267,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 9464.it
\(\chi_{9464}(267,\cdot)\) \(\chi_{9464}(323,\cdot)\) \(\chi_{9464}(379,\cdot)\) \(\chi_{9464}(435,\cdot)\) \(\chi_{9464}(1051,\cdot)\) \(\chi_{9464}(1107,\cdot)\) \(\chi_{9464}(1163,\cdot)\) \(\chi_{9464}(1723,\cdot)\) \(\chi_{9464}(1835,\cdot)\) \(\chi_{9464}(1891,\cdot)\) \(\chi_{9464}(2451,\cdot)\) \(\chi_{9464}(2507,\cdot)\) \(\chi_{9464}(2563,\cdot)\) \(\chi_{9464}(2619,\cdot)\) \(\chi_{9464}(3179,\cdot)\) \(\chi_{9464}(3235,\cdot)\) \(\chi_{9464}(3347,\cdot)\) \(\chi_{9464}(3907,\cdot)\) \(\chi_{9464}(3963,\cdot)\) \(\chi_{9464}(4019,\cdot)\) \(\chi_{9464}(4635,\cdot)\) \(\chi_{9464}(4691,\cdot)\) \(\chi_{9464}(4747,\cdot)\) \(\chi_{9464}(4803,\cdot)\) \(\chi_{9464}(5363,\cdot)\) \(\chi_{9464}(5419,\cdot)\) \(\chi_{9464}(5475,\cdot)\) \(\chi_{9464}(5531,\cdot)\) \(\chi_{9464}(6091,\cdot)\) \(\chi_{9464}(6147,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{156})$ |
| Fixed field: | Number field defined by a degree 156 polynomial (not computed) |
Values on generators
\((2367,4733,2705,9297)\) → \((-1,-1,1,e\left(\frac{59}{156}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(9\) | \(11\) | \(15\) | \(17\) | \(19\) | \(23\) | \(25\) | \(27\) |
| \( \chi_{ 9464 }(267, a) \) | \(1\) | \(1\) | \(e\left(\frac{35}{39}\right)\) | \(e\left(\frac{47}{52}\right)\) | \(e\left(\frac{31}{39}\right)\) | \(e\left(\frac{149}{156}\right)\) | \(e\left(\frac{125}{156}\right)\) | \(e\left(\frac{17}{78}\right)\) | \(e\left(\frac{7}{12}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{21}{26}\right)\) | \(e\left(\frac{9}{13}\right)\) |