Basic properties
| Modulus: | \(35937\) | |
| Conductor: | \(11979\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(1815\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{11979}(8023,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | no | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 35937.cj
\(\chi_{35937}(37,\cdot)\) \(\chi_{35937}(64,\cdot)\) \(\chi_{35937}(91,\cdot)\) \(\chi_{35937}(181,\cdot)\) \(\chi_{35937}(235,\cdot)\) \(\chi_{35937}(262,\cdot)\) \(\chi_{35937}(280,\cdot)\) \(\chi_{35937}(289,\cdot)\) \(\chi_{35937}(334,\cdot)\) \(\chi_{35937}(361,\cdot)\) \(\chi_{35937}(388,\cdot)\) \(\chi_{35937}(478,\cdot)\) \(\chi_{35937}(532,\cdot)\) \(\chi_{35937}(559,\cdot)\) \(\chi_{35937}(577,\cdot)\) \(\chi_{35937}(586,\cdot)\) \(\chi_{35937}(631,\cdot)\) \(\chi_{35937}(658,\cdot)\) \(\chi_{35937}(685,\cdot)\) \(\chi_{35937}(775,\cdot)\) \(\chi_{35937}(829,\cdot)\) \(\chi_{35937}(883,\cdot)\) \(\chi_{35937}(955,\cdot)\) \(\chi_{35937}(982,\cdot)\) \(\chi_{35937}(1072,\cdot)\) \(\chi_{35937}(1126,\cdot)\) \(\chi_{35937}(1153,\cdot)\) \(\chi_{35937}(1171,\cdot)\) \(\chi_{35937}(1180,\cdot)\) \(\chi_{35937}(1225,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{1815})$ |
| Fixed field: | Number field defined by a degree 1815 polynomial (not computed) |
Values on generators
\((22628,13312)\) → \((e\left(\frac{1}{3}\right),e\left(\frac{571}{605}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(13\) | \(14\) | \(16\) | \(17\) |
| \( \chi_{ 35937 }(37, a) \) | \(1\) | \(1\) | \(e\left(\frac{503}{1815}\right)\) | \(e\left(\frac{1006}{1815}\right)\) | \(e\left(\frac{592}{1815}\right)\) | \(e\left(\frac{56}{1815}\right)\) | \(e\left(\frac{503}{605}\right)\) | \(e\left(\frac{73}{121}\right)\) | \(e\left(\frac{313}{1815}\right)\) | \(e\left(\frac{559}{1815}\right)\) | \(e\left(\frac{197}{1815}\right)\) | \(e\left(\frac{39}{605}\right)\) |