Basic properties
Modulus: | \(4730\) | |
Conductor: | \(473\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(70\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
Real: | no | |
Primitive: | no, induced from \(\chi_{473}(156,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 4730.cr
\(\chi_{4730}(51,\cdot)\) \(\chi_{4730}(151,\cdot)\) \(\chi_{4730}(161,\cdot)\) \(\chi_{4730}(211,\cdot)\) \(\chi_{4730}(371,\cdot)\) \(\chi_{4730}(481,\cdot)\) \(\chi_{4730}(591,\cdot)\) \(\chi_{4730}(1421,\cdot)\) \(\chi_{4730}(1931,\cdot)\) \(\chi_{4730}(2301,\cdot)\) \(\chi_{4730}(2361,\cdot)\) \(\chi_{4730}(2521,\cdot)\) \(\chi_{4730}(2631,\cdot)\) \(\chi_{4730}(2741,\cdot)\) \(\chi_{4730}(2791,\cdot)\) \(\chi_{4730}(3141,\cdot)\) \(\chi_{4730}(3571,\cdot)\) \(\chi_{4730}(4001,\cdot)\) \(\chi_{4730}(4021,\cdot)\) \(\chi_{4730}(4241,\cdot)\) \(\chi_{4730}(4351,\cdot)\) \(\chi_{4730}(4451,\cdot)\) \(\chi_{4730}(4461,\cdot)\) \(\chi_{4730}(4671,\cdot)\)
Related number fields
Field of values: | $\Q(\zeta_{35})$ |
Fixed field: | Number field defined by a degree 70 polynomial |
Values on generators
\((947,431,1981)\) → \((1,e\left(\frac{1}{10}\right),e\left(\frac{1}{14}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(3\) | \(7\) | \(9\) | \(13\) | \(17\) | \(19\) | \(21\) | \(23\) | \(27\) | \(29\) |
\( \chi_{ 4730 }(2521, a) \) | \(1\) | \(1\) | \(e\left(\frac{61}{70}\right)\) | \(e\left(\frac{1}{5}\right)\) | \(e\left(\frac{26}{35}\right)\) | \(e\left(\frac{27}{70}\right)\) | \(e\left(\frac{43}{70}\right)\) | \(e\left(\frac{23}{35}\right)\) | \(e\left(\frac{1}{14}\right)\) | \(e\left(\frac{1}{7}\right)\) | \(e\left(\frac{43}{70}\right)\) | \(e\left(\frac{22}{35}\right)\) |