Basic properties
Modulus: | \(4730\) | |
Conductor: | \(2365\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(70\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
Real: | no | |
Primitive: | no, induced from \(\chi_{2365}(954,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 4730.cx
\(\chi_{4730}(39,\cdot)\) \(\chi_{4730}(409,\cdot)\) \(\chi_{4730}(469,\cdot)\) \(\chi_{4730}(629,\cdot)\) \(\chi_{4730}(739,\cdot)\) \(\chi_{4730}(849,\cdot)\) \(\chi_{4730}(899,\cdot)\) \(\chi_{4730}(1249,\cdot)\) \(\chi_{4730}(1679,\cdot)\) \(\chi_{4730}(2109,\cdot)\) \(\chi_{4730}(2129,\cdot)\) \(\chi_{4730}(2349,\cdot)\) \(\chi_{4730}(2459,\cdot)\) \(\chi_{4730}(2559,\cdot)\) \(\chi_{4730}(2569,\cdot)\) \(\chi_{4730}(2779,\cdot)\) \(\chi_{4730}(2889,\cdot)\) \(\chi_{4730}(2989,\cdot)\) \(\chi_{4730}(2999,\cdot)\) \(\chi_{4730}(3049,\cdot)\) \(\chi_{4730}(3209,\cdot)\) \(\chi_{4730}(3319,\cdot)\) \(\chi_{4730}(3429,\cdot)\) \(\chi_{4730}(4259,\cdot)\)
Related number fields
Field of values: | $\Q(\zeta_{35})$ |
Fixed field: | Number field defined by a degree 70 polynomial |
Values on generators
\((947,431,1981)\) → \((-1,e\left(\frac{3}{10}\right),e\left(\frac{13}{14}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(3\) | \(7\) | \(9\) | \(13\) | \(17\) | \(19\) | \(21\) | \(23\) | \(27\) | \(29\) |
\( \chi_{ 4730 }(3319, a) \) | \(1\) | \(1\) | \(e\left(\frac{29}{35}\right)\) | \(e\left(\frac{1}{10}\right)\) | \(e\left(\frac{23}{35}\right)\) | \(e\left(\frac{18}{35}\right)\) | \(e\left(\frac{17}{35}\right)\) | \(e\left(\frac{19}{35}\right)\) | \(e\left(\frac{13}{14}\right)\) | \(e\left(\frac{5}{14}\right)\) | \(e\left(\frac{17}{35}\right)\) | \(e\left(\frac{6}{35}\right)\) |