Basic properties
Modulus: | \(491\) | |
Conductor: | \(491\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(35\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
Real: | no | |
Primitive: | yes | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 491.g
\(\chi_{491}(12,\cdot)\) \(\chi_{491}(20,\cdot)\) \(\chi_{491}(41,\cdot)\) \(\chi_{491}(56,\cdot)\) \(\chi_{491}(114,\cdot)\) \(\chi_{491}(144,\cdot)\) \(\chi_{491}(181,\cdot)\) \(\chi_{491}(190,\cdot)\) \(\chi_{491}(197,\cdot)\) \(\chi_{491}(208,\cdot)\) \(\chi_{491}(213,\cdot)\) \(\chi_{491}(221,\cdot)\) \(\chi_{491}(226,\cdot)\) \(\chi_{491}(230,\cdot)\) \(\chi_{491}(232,\cdot)\) \(\chi_{491}(255,\cdot)\) \(\chi_{491}(257,\cdot)\) \(\chi_{491}(305,\cdot)\) \(\chi_{491}(329,\cdot)\) \(\chi_{491}(355,\cdot)\) \(\chi_{491}(363,\cdot)\) \(\chi_{491}(400,\cdot)\) \(\chi_{491}(425,\cdot)\) \(\chi_{491}(428,\cdot)\)
Related number fields
Field of values: | $\Q(\zeta_{35})$ |
Fixed field: | Number field defined by a degree 35 polynomial |
Values on generators
\(2\) → \(e\left(\frac{8}{35}\right)\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
\( \chi_{ 491 }(221, a) \) | \(1\) | \(1\) | \(e\left(\frac{8}{35}\right)\) | \(e\left(\frac{1}{7}\right)\) | \(e\left(\frac{16}{35}\right)\) | \(e\left(\frac{33}{35}\right)\) | \(e\left(\frac{13}{35}\right)\) | \(e\left(\frac{32}{35}\right)\) | \(e\left(\frac{24}{35}\right)\) | \(e\left(\frac{2}{7}\right)\) | \(e\left(\frac{6}{35}\right)\) | \(e\left(\frac{8}{35}\right)\) |