Basic properties
Modulus: | \(899\) | |
Conductor: | \(899\) | 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 899.bd
\(\chi_{899}(16,\cdot)\) \(\chi_{899}(78,\cdot)\) \(\chi_{899}(132,\cdot)\) \(\chi_{899}(140,\cdot)\) \(\chi_{899}(190,\cdot)\) \(\chi_{899}(194,\cdot)\) \(\chi_{899}(219,\cdot)\) \(\chi_{899}(252,\cdot)\) \(\chi_{899}(256,\cdot)\) \(\chi_{899}(281,\cdot)\) \(\chi_{899}(314,\cdot)\) \(\chi_{899}(326,\cdot)\) \(\chi_{899}(343,\cdot)\) \(\chi_{899}(442,\cdot)\) \(\chi_{899}(500,\cdot)\) \(\chi_{899}(529,\cdot)\) \(\chi_{899}(574,\cdot)\) \(\chi_{899}(605,\cdot)\) \(\chi_{899}(690,\cdot)\) \(\chi_{899}(721,\cdot)\) \(\chi_{899}(748,\cdot)\) \(\chi_{899}(777,\cdot)\) \(\chi_{899}(779,\cdot)\) \(\chi_{899}(808,\cdot)\)
Related number fields
Field of values: | $\Q(\zeta_{35})$ |
Fixed field: | Number field defined by a degree 35 polynomial |
Values on generators
\((466,871)\) → \((e\left(\frac{1}{7}\right),e\left(\frac{4}{5}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
\( \chi_{ 899 }(219, a) \) | \(1\) | \(1\) | \(e\left(\frac{12}{35}\right)\) | \(e\left(\frac{18}{35}\right)\) | \(e\left(\frac{24}{35}\right)\) | \(e\left(\frac{1}{7}\right)\) | \(e\left(\frac{6}{7}\right)\) | \(e\left(\frac{4}{35}\right)\) | \(e\left(\frac{1}{35}\right)\) | \(e\left(\frac{1}{35}\right)\) | \(e\left(\frac{17}{35}\right)\) | \(e\left(\frac{34}{35}\right)\) |