Basic properties
Modulus: | \(473\) | |
Conductor: | \(473\) | 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 473.v
\(\chi_{473}(4,\cdot)\) \(\chi_{473}(16,\cdot)\) \(\chi_{473}(47,\cdot)\) \(\chi_{473}(59,\cdot)\) \(\chi_{473}(64,\cdot)\) \(\chi_{473}(97,\cdot)\) \(\chi_{473}(102,\cdot)\) \(\chi_{473}(170,\cdot)\) \(\chi_{473}(207,\cdot)\) \(\chi_{473}(213,\cdot)\) \(\chi_{473}(236,\cdot)\) \(\chi_{473}(256,\cdot)\) \(\chi_{473}(262,\cdot)\) \(\chi_{473}(269,\cdot)\) \(\chi_{473}(279,\cdot)\) \(\chi_{473}(312,\cdot)\) \(\chi_{473}(317,\cdot)\) \(\chi_{473}(322,\cdot)\) \(\chi_{473}(355,\cdot)\) \(\chi_{473}(379,\cdot)\) \(\chi_{473}(422,\cdot)\) \(\chi_{473}(434,\cdot)\) \(\chi_{473}(465,\cdot)\) \(\chi_{473}(471,\cdot)\)
Related number fields
Field of values: | $\Q(\zeta_{35})$ |
Fixed field: | Number field defined by a degree 35 polynomial |
Values on generators
\((431,89)\) → \((e\left(\frac{4}{5}\right),e\left(\frac{1}{7}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(12\) |
\( \chi_{ 473 }(256, a) \) | \(1\) | \(1\) | \(e\left(\frac{23}{35}\right)\) | \(e\left(\frac{19}{35}\right)\) | \(e\left(\frac{11}{35}\right)\) | \(e\left(\frac{27}{35}\right)\) | \(e\left(\frac{1}{5}\right)\) | \(e\left(\frac{3}{5}\right)\) | \(e\left(\frac{34}{35}\right)\) | \(e\left(\frac{3}{35}\right)\) | \(e\left(\frac{3}{7}\right)\) | \(e\left(\frac{6}{7}\right)\) |