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 \(\chi_{473}(41,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 4730.cw
\(\chi_{4730}(41,\cdot)\) \(\chi_{4730}(391,\cdot)\) \(\chi_{4730}(821,\cdot)\) \(\chi_{4730}(871,\cdot)\) \(\chi_{4730}(981,\cdot)\) \(\chi_{4730}(1091,\cdot)\) \(\chi_{4730}(1251,\cdot)\) \(\chi_{4730}(1311,\cdot)\) \(\chi_{4730}(2191,\cdot)\) \(\chi_{4730}(2591,\cdot)\) \(\chi_{4730}(2701,\cdot)\) \(\chi_{4730}(2811,\cdot)\) \(\chi_{4730}(3021,\cdot)\) \(\chi_{4730}(3031,\cdot)\) \(\chi_{4730}(3131,\cdot)\) \(\chi_{4730}(3241,\cdot)\) \(\chi_{4730}(3401,\cdot)\) \(\chi_{4730}(3451,\cdot)\) \(\chi_{4730}(3461,\cdot)\) \(\chi_{4730}(3561,\cdot)\) \(\chi_{4730}(3671,\cdot)\) \(\chi_{4730}(3891,\cdot)\) \(\chi_{4730}(3911,\cdot)\) \(\chi_{4730}(4341,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{35})$ |
| Fixed field: | Number field defined by a degree 70 polynomial |
Values on generators
\((947,431,1981)\) → \((1,e\left(\frac{3}{10}\right),e\left(\frac{1}{7}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(7\) | \(9\) | \(13\) | \(17\) | \(19\) | \(21\) | \(23\) | \(27\) | \(29\) |
| \( \chi_{ 4730 }(41, a) \) | \(-1\) | \(1\) | \(e\left(\frac{19}{35}\right)\) | \(e\left(\frac{1}{10}\right)\) | \(e\left(\frac{3}{35}\right)\) | \(e\left(\frac{61}{70}\right)\) | \(e\left(\frac{9}{70}\right)\) | \(e\left(\frac{43}{70}\right)\) | \(e\left(\frac{9}{14}\right)\) | \(e\left(\frac{2}{7}\right)\) | \(e\left(\frac{22}{35}\right)\) | \(e\left(\frac{67}{70}\right)\) |