Basic properties
| Modulus: | \(35937\) | |
| Conductor: | \(11979\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(726\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{11979}(7996,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | no | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 35937.ca
\(\chi_{35937}(10,\cdot)\) \(\chi_{35937}(208,\cdot)\) \(\chi_{35937}(307,\cdot)\) \(\chi_{35937}(505,\cdot)\) \(\chi_{35937}(802,\cdot)\) \(\chi_{35937}(901,\cdot)\) \(\chi_{35937}(1099,\cdot)\) \(\chi_{35937}(1198,\cdot)\) \(\chi_{35937}(1396,\cdot)\) \(\chi_{35937}(1495,\cdot)\) \(\chi_{35937}(1792,\cdot)\) \(\chi_{35937}(1990,\cdot)\) \(\chi_{35937}(2089,\cdot)\) \(\chi_{35937}(2287,\cdot)\) \(\chi_{35937}(2386,\cdot)\) \(\chi_{35937}(2584,\cdot)\) \(\chi_{35937}(2683,\cdot)\) \(\chi_{35937}(2881,\cdot)\) \(\chi_{35937}(2980,\cdot)\) \(\chi_{35937}(3178,\cdot)\) \(\chi_{35937}(3277,\cdot)\) \(\chi_{35937}(3475,\cdot)\) \(\chi_{35937}(3574,\cdot)\) \(\chi_{35937}(3772,\cdot)\) \(\chi_{35937}(4069,\cdot)\) \(\chi_{35937}(4168,\cdot)\) \(\chi_{35937}(4366,\cdot)\) \(\chi_{35937}(4465,\cdot)\) \(\chi_{35937}(4663,\cdot)\) \(\chi_{35937}(4762,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{363})$ |
| Fixed field: | Number field defined by a degree 726 polynomial (not computed) |
Values on generators
\((22628,13312)\) → \((e\left(\frac{1}{3}\right),e\left(\frac{37}{242}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(13\) | \(14\) | \(16\) | \(17\) |
| \( \chi_{ 35937 }(10, a) \) | \(-1\) | \(1\) | \(e\left(\frac{353}{726}\right)\) | \(e\left(\frac{353}{363}\right)\) | \(e\left(\frac{290}{363}\right)\) | \(e\left(\frac{359}{726}\right)\) | \(e\left(\frac{111}{242}\right)\) | \(e\left(\frac{69}{242}\right)\) | \(e\left(\frac{211}{726}\right)\) | \(e\left(\frac{356}{363}\right)\) | \(e\left(\frac{343}{363}\right)\) | \(e\left(\frac{75}{242}\right)\) |